LMFDB - Embedded newform 693.2.m.k.379.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			379.3
Character	$\chi$	$=$	693.379
Dual form			693.2.m.k.64.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.405703 - 1.24862i) q^{2} +(0.223566 - 0.162430i) q^{4} +(-1.06900 + 3.29005i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(-2.41780 - 1.75664i) q^{8} +O(q^{10})$	\(q+(-0.405703 - 1.24862i) q^{2} +(0.223566 - 0.162430i) q^{4} +(-1.06900 + 3.29005i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(-2.41780 - 1.75664i) q^{8} +4.54174 q^{10} +(-0.955473 + 3.17602i) q^{11} +(-1.71137 - 5.26705i) q^{13} +(1.06214 + 0.771692i) q^{14} +(-1.04168 + 3.20596i) q^{16} +(1.53461 - 4.72305i) q^{17} +(-6.65796 - 4.83729i) q^{19} +(0.295411 + 0.909181i) q^{20} +(4.35329 - 0.0954909i) q^{22} -7.56119 q^{23} +(-5.63660 - 4.09523i) q^{25} +(-5.88226 + 4.27371i) q^{26} +(-0.0853944 + 0.262817i) q^{28} +(1.18934 - 0.864109i) q^{29} +(0.745166 + 2.29339i) q^{31} -1.55148 q^{32} -6.51991 q^{34} +(-1.06900 - 3.29005i) q^{35} +(2.29469 - 1.66719i) q^{37} +(-3.33881 + 10.2758i) q^{38} +(8.36407 - 6.07685i) q^{40} +(-5.60900 - 4.07518i) q^{41} +5.62936 q^{43} +(0.302269 + 0.865245i) q^{44} +(3.06760 + 9.44109i) q^{46} +(0.0337463 + 0.0245181i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-2.82662 + 8.69945i) q^{50} +(-1.23813 - 0.899554i) q^{52} +(-1.38175 - 4.25260i) q^{53} +(-9.42786 - 6.53873i) q^{55} +2.98857 q^{56} +(-1.56147 - 1.13447i) q^{58} +(2.42289 - 1.76034i) q^{59} +(-3.60574 + 11.0973i) q^{61} +(2.56126 - 1.86087i) q^{62} +(2.71280 + 8.34914i) q^{64} +19.1583 q^{65} +9.95852 q^{67} +(-0.424078 - 1.30518i) q^{68} +(-3.67434 + 2.66957i) q^{70} +(-2.16099 + 6.65086i) q^{71} +(-5.97313 + 4.33973i) q^{73} +(-3.01266 - 2.18882i) q^{74} -2.27421 q^{76} +(-1.09382 - 3.13106i) q^{77} +(5.02941 + 15.4789i) q^{79} +(-9.43424 - 6.85437i) q^{80} +(-2.81278 + 8.65684i) q^{82} +(-2.98009 + 9.17177i) q^{83} +(13.8986 + 10.0979i) q^{85} +(-2.28385 - 7.02896i) q^{86} +(7.88925 - 6.00056i) q^{88} -7.94906 q^{89} +(4.48042 + 3.25522i) q^{91} +(-1.69042 + 1.22816i) q^{92} +(0.0169230 - 0.0520835i) q^{94} +(23.0323 - 16.7340i) q^{95} +(-0.726752 - 2.23671i) q^{97} -1.31288 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{4} - 8 q^{7}+O(q^{10}) $ 32 * q - 10 * q^4 - 8 * q^7	$ 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52} - 12 q^{55} - 104 q^{58} + 34 q^{61} - 52 q^{64} + 104 q^{67} + 18 q^{70} + 2 q^{73} - 28 q^{76} - 42 q^{79} - 172 q^{82} - 30 q^{85} - 16 q^{88} - 10 q^{91} + 150 q^{94} - 74 q^{97}+O(q^{100}) $ 32 * q - 10 * q^4 - 8 * q^7 - 12 * q^10 + 10 * q^13 - 26 * q^16 - 10 * q^19 - 6 * q^22 - 52 * q^25 - 10 * q^28 - 20 * q^31 + 24 * q^34 - 4 * q^37 + 124 * q^40 + 32 * q^43 + 30 * q^46 - 8 * q^49 + 24 * q^52 - 12 * q^55 - 104 * q^58 + 34 * q^61 - 52 * q^64 + 104 * q^67 + 18 * q^70 + 2 * q^73 - 28 * q^76 - 42 * q^79 - 172 * q^82 - 30 * q^85 - 16 * q^88 - 10 * q^91 + 150 * q^94 - 74 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.405703	−	1.24862i	−0.286875	−	0.882911i	−0.985830	−	0.167745i	$-0.946351\pi$
$2$	−0.405703	−	1.24862i	−0.286875	−	0.882911i	0.698955	−	0.715165i	$-0.253649\pi$
$3$		0			0
$3$		0			0
$4$	0.223566	−	0.162430i	0.111783	−	0.0812149i
$5$	−1.06900	+	3.29005i	−0.478073	+	1.47136i	0.363695	+	0.931518i	$0.381515\pi$
$5$	−1.06900	+	3.29005i	−0.478073	+	1.47136i	−0.841768	+	0.539839i	$0.818485\pi$
$6$		0			0
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$	−2.41780	−	1.75664i	−0.854822	−	0.621065i
$9$		0			0
$10$	4.54174			1.43622
$11$	−0.955473	+	3.17602i	−0.288086	+	0.957605i
$11$	−0.955473	+	3.17602i	−0.288086	+	0.957605i
$12$		0			0
$13$	−1.71137	−	5.26705i	−0.474648	−	1.46082i	−0.846432	−	0.532497i	$-0.821254\pi$
$13$	−1.71137	−	5.26705i	−0.474648	−	1.46082i	0.371783	−	0.928319i	$-0.378746\pi$
$14$	1.06214	+	0.771692i	0.283870	+	0.206243i
$15$		0			0
$16$	−1.04168	+	3.20596i	−0.260420	+	0.801491i
$17$	1.53461	−	4.72305i	0.372198	−	1.14551i	−0.573152	−	0.819449i	$-0.694280\pi$
$17$	1.53461	−	4.72305i	0.372198	−	1.14551i	0.945350	−	0.326058i	$-0.105720\pi$
$18$		0			0
$19$	−6.65796	−	4.83729i	−1.52744	−	1.10975i	−0.957641	−	0.287966i	$-0.907021\pi$
$19$	−6.65796	−	4.83729i	−1.52744	−	1.10975i	−0.569799	−	0.821784i	$-0.692979\pi$
$20$	0.295411	+	0.909181i	0.0660558	+	0.203299i
$21$		0			0
$22$	4.35329	−	0.0954909i	0.928124	−	0.0203587i
$23$	−7.56119			−1.57662			−0.788309	−	0.615280i	$-0.789043\pi$
$23$	−7.56119			−1.57662			−0.788309	+	0.615280i	$0.789043\pi$
$24$		0			0
$25$	−5.63660	−	4.09523i	−1.12732	−	0.819046i
$26$	−5.88226	+	4.27371i	−1.15361	+	0.838144i
$27$		0			0
$28$	−0.0853944	+	0.262817i	−0.0161380	+	0.0496678i
$29$	1.18934	−	0.864109i	0.220856	−	0.160461i	−0.471856	−	0.881676i	$-0.656416\pi$
$29$	1.18934	−	0.864109i	0.220856	−	0.160461i	0.692712	+	0.721215i	$0.256416\pi$
$30$		0			0
$31$	0.745166	+	2.29339i	0.133836	+	0.411904i	0.995407	−	0.0957322i	$-0.0305193\pi$
$31$	0.745166	+	2.29339i	0.133836	+	0.411904i	−0.861571	+	0.507637i	$0.830519\pi$
$32$	−1.55148			−0.274265
$33$		0			0
$34$	−6.51991			−1.11815
$35$	−1.06900	−	3.29005i	−0.180695	−	0.556121i
$36$		0			0
$37$	2.29469	−	1.66719i	0.377245	−	0.274084i	−0.382964	−	0.923763i	$-0.625097\pi$
$37$	2.29469	−	1.66719i	0.377245	−	0.274084i	0.760209	+	0.649679i	$0.225097\pi$
$38$	−3.33881	+	10.2758i	−0.541626	+	1.66695i
$39$		0			0
$40$	8.36407	−	6.07685i	1.32247	−	0.960834i
$41$	−5.60900	−	4.07518i	−0.875979	−	0.636436i	0.0562060	−	0.998419i	$-0.482100\pi$
$41$	−5.60900	−	4.07518i	−0.875979	−	0.636436i	−0.932184	+	0.361984i	$0.882100\pi$
$42$		0			0
$43$	5.62936			0.858470			0.429235	−	0.903193i	$-0.358783\pi$
$43$	5.62936			0.858470			0.429235	+	0.903193i	$0.358783\pi$
$44$	0.302269	+	0.865245i	0.0455687	+	0.130441i
$45$		0			0
$46$	3.06760	+	9.44109i	0.452292	+	1.39201i
$47$	0.0337463	+	0.0245181i	0.00492241	+	0.00357634i	0.590244	−	0.807225i	$-0.299032\pi$
$47$	0.0337463	+	0.0245181i	0.00492241	+	0.00357634i	−0.585321	+	0.810801i	$0.699032\pi$
$48$		0			0
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−2.82662	+	8.69945i	−0.399745	+	1.23029i
$51$		0			0
$52$	−1.23813	−	0.899554i	−0.171698	−	0.124746i
$53$	−1.38175	−	4.25260i	−0.189799	−	0.584140i	0.810199	−	0.586154i	$-0.199359\pi$
$53$	−1.38175	−	4.25260i	−0.189799	−	0.584140i	−0.999998	+	0.00201437i	$0.999359\pi$
$54$		0			0
$55$	−9.42786	−	6.53873i	−1.27125	−	0.881682i
$56$	2.98857			0.399364
$57$		0			0
$58$	−1.56147	−	1.13447i	−0.205031	−	0.148964i
$59$	2.42289	−	1.76034i	0.315434	−	0.229176i	−0.418791	−	0.908083i	$-0.637546\pi$
$59$	2.42289	−	1.76034i	0.315434	−	0.229176i	0.734225	+	0.678907i	$0.237546\pi$
$60$		0			0
$61$	−3.60574	+	11.0973i	−0.461668	+	1.42087i	0.401456	+	0.915878i	$0.368504\pi$
$61$	−3.60574	+	11.0973i	−0.461668	+	1.42087i	−0.863125	+	0.504991i	$0.831496\pi$
$62$	2.56126	−	1.86087i	0.325281	−	0.236330i
$63$		0			0
$64$	2.71280	+	8.34914i	0.339100	+	1.04364i
$65$	19.1583			2.37630
$66$		0			0
$67$	9.95852			1.21663			0.608314	−	0.793697i	$-0.291846\pi$
$67$	9.95852			1.21663			0.608314	+	0.793697i	$0.291846\pi$
$68$	−0.424078	−	1.30518i	−0.0514270	−	0.158276i
$69$		0			0
$70$	−3.67434	+	2.66957i	−0.439168	+	0.319074i
$71$	−2.16099	+	6.65086i	−0.256463	+	0.789311i	0.737075	+	0.675811i	$0.236206\pi$
$71$	−2.16099	+	6.65086i	−0.256463	+	0.789311i	−0.993538	+	0.113501i	$0.963794\pi$
$72$		0			0
$73$	−5.97313	+	4.33973i	−0.699102	+	0.507927i	−0.879640	−	0.475641i	$-0.842216\pi$
$73$	−5.97313	+	4.33973i	−0.699102	+	0.507927i	0.180538	+	0.983568i	$0.442216\pi$
$74$	−3.01266	−	2.18882i	−0.350214	−	0.254445i
$75$		0			0
$76$	−2.27421			−0.260870
$77$	−1.09382	−	3.13106i	−0.124652	−	0.356818i
$78$		0			0
$79$	5.02941	+	15.4789i	0.565853	+	1.74152i	0.665403	+	0.746485i	$0.268260\pi$
$79$	5.02941	+	15.4789i	0.565853	+	1.74152i	−0.0995496	+	0.995033i	$0.531740\pi$
$80$	−9.43424	−	6.85437i	−1.05478	−	0.766342i
$81$		0			0
$82$	−2.81278	+	8.65684i	−0.310619	+	0.955988i
$83$	−2.98009	+	9.17177i	−0.327107	+	1.00673i	0.643373	+	0.765553i	$0.277534\pi$
$83$	−2.98009	+	9.17177i	−0.327107	+	1.00673i	−0.970480	+	0.241180i	$0.922466\pi$
$84$		0			0
$85$	13.8986	+	10.0979i	1.50751	+	1.09527i
$86$	−2.28385	−	7.02896i	−0.246274	−	0.757952i
$87$		0			0
$88$	7.88925	−	6.00056i	0.840997	−	0.639662i
$89$	−7.94906			−0.842599			−0.421300	−	0.906922i	$-0.638426\pi$
$89$	−7.94906			−0.842599			−0.421300	+	0.906922i	$0.638426\pi$
$90$		0			0
$91$	4.48042	+	3.25522i	0.469676	+	0.341239i
$92$	−1.69042	+	1.22816i	−0.176239	+	0.128045i
$93$		0			0
$94$	0.0169230	−	0.0520835i	0.00174547	−	0.00537201i
$95$	23.0323	−	16.7340i	2.36307	−	1.71687i
$96$		0			0
$97$	−0.726752	−	2.23671i	−0.0737905	−	0.227104i	0.907358	−	0.420358i	$-0.138096\pi$
$97$	−0.726752	−	2.23671i	−0.0737905	−	0.227104i	−0.981149	+	0.193255i	$0.938096\pi$
$98$	−1.31288			−0.132621
$99$		0			0
$100$	−1.92534			−0.192534
$101$	−4.27994	−	13.1723i	−0.425870	−	1.31069i	−0.902159	−	0.431404i	$-0.858018\pi$
$101$	−4.27994	−	13.1723i	−0.425870	−	1.31069i	0.476289	−	0.879289i	$-0.341982\pi$
$102$		0			0
$103$	−3.07210	+	2.23201i	−0.302703	+	0.219926i	−0.728759	−	0.684770i	$-0.759903\pi$
$103$	−3.07210	+	2.23201i	−0.302703	+	0.219926i	0.426056	+	0.904697i	$0.359903\pi$
$104$	−5.11454	+	15.7409i	−0.501522	+	1.54353i
$105$		0			0
$106$	−4.74932	+	3.45059i	−0.461295	+	0.335150i
$107$	1.08542	+	0.788603i	0.104931	+	0.0762372i	0.639014	−	0.769195i	$-0.279343\pi$
$107$	1.08542	+	0.788603i	0.104931	+	0.0762372i	−0.534082	+	0.845433i	$0.679343\pi$
$108$		0			0
$109$	−17.5860			−1.68443			−0.842216	−	0.539140i	$-0.818749\pi$
$109$	−17.5860			−1.68443			−0.842216	+	0.539140i	$0.818749\pi$
$110$	−4.33951	+	14.4246i	−0.413756	+	1.37533i
$111$		0			0
$112$	−1.04168	−	3.20596i	−0.0984296	−	0.302935i
$113$	10.3264	+	7.50257i	0.971426	+	0.705782i	0.955776	−	0.294095i	$-0.0950184\pi$
$113$	10.3264	+	7.50257i	0.971426	+	0.705782i	0.0156497	+	0.999878i	$0.495018\pi$
$114$		0			0
$115$	8.08294	−	24.8767i	0.753738	−	2.31977i
$116$	0.125539	−	0.386370i	0.0116560	−	0.0358736i
$117$		0			0
$118$	−3.18097	−	2.31111i	−0.292832	−	0.212755i
$119$	1.53461	+	4.72305i	0.140678	+	0.432961i
$120$		0			0
$121$	−9.17414	−	6.06919i	−0.834013	−	0.551745i
$122$	15.3193			1.38694
$123$		0			0
$124$	0.539108	+	0.391685i	0.0484133	+	0.0351743i
$125$	5.50564	−	4.00008i	0.492440	−	0.357778i
$126$		0			0
$127$	1.23226	−	3.79250i	0.109345	−	0.336530i	−0.881381	−	0.472407i	$-0.843385\pi$
$127$	1.23226	−	3.79250i	0.109345	−	0.336530i	0.990726	+	0.135877i	$0.0433853\pi$
$128$	6.81401	−	4.95067i	0.602279	−	0.437581i
$129$		0			0
$130$	−7.77259	−	23.9216i	−0.681701	−	2.09806i
$131$	−2.02685			−0.177087			−0.0885433	−	0.996072i	$-0.528221\pi$
$131$	−2.02685			−0.177087			−0.0885433	+	0.996072i	$0.528221\pi$
$132$		0			0
$133$	8.22969			0.713604
$134$	−4.04020	−	12.4345i	−0.349020	−	1.07417i
$135$		0			0
$136$	−12.0071	+	8.72364i	−1.02960	+	0.748046i
$137$	4.72561	−	14.5439i	0.403736	−	1.24257i	−0.518210	−	0.855253i	$-0.673401\pi$
$137$	4.72561	−	14.5439i	0.403736	−	1.24257i	0.921946	−	0.387318i	$-0.126599\pi$
$138$		0			0
$139$	17.4123	−	12.6508i	1.47690	−	1.07303i	0.498355	−	0.866973i	$-0.333938\pi$
$139$	17.4123	−	12.6508i	1.47690	−	1.07303i	0.978541	−	0.206054i	$-0.0660624\pi$
$140$	−0.773395	−	0.561905i	−0.0653638	−	0.0474896i
$141$		0			0
$142$	9.18114			0.770464
$143$	18.3634	−	0.402807i	1.53562	−	0.0336844i
$144$		0			0
$145$	1.57155	+	4.83674i	0.130510	+	0.401670i
$146$	7.84201	+	5.69756i	0.649010	+	0.471533i
$147$		0			0
$148$	0.242212	−	0.745452i	0.0199097	−	0.0612758i
$149$	0.374352	−	1.15214i	0.0306681	−	0.0943867i	−0.934551	−	0.355830i	$-0.884198\pi$
$149$	0.374352	−	1.15214i	0.0306681	−	0.0943867i	0.965219	+	0.261443i	$0.0841983\pi$
$150$		0			0
$151$	−7.86153	−	5.71174i	−0.639763	−	0.464815i	0.220006	−	0.975499i	$-0.429392\pi$
$151$	−7.86153	−	5.71174i	−0.639763	−	0.464815i	−0.859769	+	0.510684i	$0.829392\pi$
$152$	7.60026	+	23.3912i	0.616463	+	1.89728i
$153$		0			0
$154$	−3.46576	+	2.63605i	−0.279279	+	0.212419i
$155$	−8.34195			−0.670042
$156$		0			0
$157$	−13.3799	−	9.72108i	−1.06783	−	0.775827i	−0.0923120	−	0.995730i	$-0.529426\pi$
$157$	−13.3799	−	9.72108i	−1.06783	−	0.775827i	−0.975522	+	0.219904i	$0.929426\pi$
$158$	17.2869	−	12.5597i	1.37528	−	0.999196i
$159$		0			0
$160$	1.65853	−	5.10444i	0.131119	−	0.403542i
$161$	6.11713	−	4.44436i	0.482098	−	0.350264i
$162$		0			0
$163$	−2.34860	−	7.22824i	−0.183956	−	0.566159i	0.815973	−	0.578091i	$-0.196202\pi$
$163$	−2.34860	−	7.22824i	−0.183956	−	0.566159i	−0.999929	+	0.0119314i	$0.996202\pi$
$164$	−1.91591			−0.149607
$165$		0			0
$166$	12.6611			0.982694
$167$	−1.26252	−	3.88564i	−0.0976969	−	0.300680i	0.890250	−	0.455472i	$-0.150529\pi$
$167$	−1.26252	−	3.88564i	−0.0976969	−	0.300680i	−0.987947	+	0.154792i	$0.950529\pi$
$168$		0			0
$169$	−14.2958	+	10.3865i	−1.09968	+	0.798963i
$170$	6.96980	−	21.4508i	0.534559	−	1.64520i
$171$		0			0
$172$	1.25853	−	0.914376i	0.0959621	−	0.0697206i
$173$	−2.59920	−	1.88843i	−0.197614	−	0.143575i	0.484578	−	0.874748i	$-0.338973\pi$
$173$	−2.59920	−	1.88843i	−0.197614	−	0.143575i	−0.682192	+	0.731173i	$0.738973\pi$
$174$		0			0
$175$	6.96722			0.526673
$176$	−9.18689	−	6.37161i	−0.692488	−	0.480278i
$177$		0			0
$178$	3.22496	+	9.92540i	0.241721	+	0.743940i
$179$	−0.168133	−	0.122156i	−0.0125669	−	0.00913035i	0.581484	−	0.813558i	$-0.302472\pi$
$179$	−0.168133	−	0.122156i	−0.0125669	−	0.00913035i	−0.594051	+	0.804427i	$0.702472\pi$
$180$		0			0
$181$	−1.62394	+	4.99798i	−0.120707	+	0.371497i	−0.993094	−	0.117318i	$-0.962570\pi$
$181$	−1.62394	+	4.99798i	−0.120707	+	0.371497i	0.872388	+	0.488814i	$0.162570\pi$
$182$	2.24682	−	6.91501i	0.166546	−	0.512575i
$183$		0			0
$184$	18.2815	+	13.2823i	1.34773	+	0.979181i
$185$	3.03211	+	9.33188i	0.222925	+	0.686094i
$186$		0			0
$187$	13.5342	+	9.38669i	0.989718	+	0.686423i
$188$	0.0115270			0.000840692
$189$		0			0
$190$	−30.2387	−	21.9697i	−2.19375	−	1.59385i
$191$	−2.19062	+	1.59158i	−0.158508	+	0.115162i	−0.664212	−	0.747544i	$-0.731233\pi$
$191$	−2.19062	+	1.59158i	−0.158508	+	0.115162i	0.505704	+	0.862707i	$0.331233\pi$
$192$		0			0
$193$	−5.09565	+	15.6828i	−0.366793	+	1.12887i	0.582057	+	0.813148i	$0.302248\pi$
$193$	−5.09565	+	15.6828i	−0.366793	+	1.12887i	−0.948851	+	0.315726i	$0.897752\pi$
$194$	−2.49797	+	1.81488i	−0.179344	+	0.130301i
$195$		0			0
$196$	−0.0853944	−	0.262817i	−0.00609960	−	0.0187726i
$197$	−3.21597			−0.229128			−0.114564	−	0.993416i	$-0.536547\pi$
$197$	−3.21597			−0.229128			−0.114564	+	0.993416i	$0.536547\pi$
$198$		0			0
$199$	8.63547			0.612152			0.306076	−	0.952007i	$-0.400984\pi$
$199$	8.63547			0.612152			0.306076	+	0.952007i	$0.400984\pi$
$200$	6.43436	+	19.8029i	0.454978	+	1.40028i
$201$		0			0
$202$	−14.7109	+	10.6881i	−1.03505	+	0.752011i
$203$	−0.454289	+	1.39816i	−0.0318848	+	0.0981315i
$204$		0			0
$205$	19.4036	−	14.0975i	1.35521	−	0.984614i
$206$	4.03330	+	2.93036i	0.281013	+	0.204168i
$207$		0			0
$208$	18.6687			1.29444
$209$	21.7248	−	16.5239i	1.50274	−	1.14298i
$210$		0			0
$211$	1.51867	+	4.67398i	0.104549	+	0.321770i	0.989624	−	0.143678i	$-0.0458930\pi$
$211$	1.51867	+	4.67398i	0.104549	+	0.321770i	−0.885075	+	0.465448i	$0.845893\pi$
$212$	−0.999663	−	0.726297i	−0.0686571	−	0.0498823i
$213$		0			0
$214$	0.544312	−	1.67522i	0.0372084	−	0.114516i
$215$	−6.01781	+	18.5209i	−0.410411	+	1.26312i
$216$		0			0
$217$	−1.95087	−	1.41739i	−0.132434	−	0.0962188i
$218$	7.13468	+	21.9583i	0.483222	+	1.48720i
$219$		0			0
$220$	−3.16983	+	0.0695313i	−0.213710	+	0.00468780i
$221$	−27.5028			−1.85004
$222$		0			0
$223$	0.935085	+	0.679379i	0.0626180	+	0.0454946i	0.618654	−	0.785664i	$-0.287678\pi$
$223$	0.935085	+	0.679379i	0.0626180	+	0.0454946i	−0.556036	+	0.831158i	$0.687678\pi$
$224$	1.25517	−	0.911935i	0.0838646	−	0.0609312i
$225$		0			0
$226$	5.17844	−	15.9376i	0.344465	−	1.06015i
$227$	−2.12294	+	1.54241i	−0.140905	+	0.102373i	−0.656005	−	0.754757i	$-0.727755\pi$
$227$	−2.12294	+	1.54241i	−0.140905	+	0.102373i	0.515100	+	0.857130i	$0.327755\pi$
$228$		0			0
$229$	−3.34613	−	10.2983i	−0.221119	−	0.680533i	−0.998662	−	0.0517042i	$-0.983535\pi$
$229$	−3.34613	−	10.2983i	−0.221119	−	0.680533i	0.777544	−	0.628829i	$-0.216465\pi$
$230$	−34.3410			−2.26438
$231$		0			0
$232$	−4.39352			−0.288449
$233$	−5.18859	−	15.9688i	−0.339916	−	1.04615i	−0.964250	−	0.264995i	$-0.914630\pi$
$233$	−5.18859	−	15.9688i	−0.339916	−	1.04615i	0.624334	−	0.781157i	$-0.285370\pi$
$234$		0			0
$235$	−0.116741	+	0.0848172i	−0.00761534	+	0.00553287i
$236$	0.255745	−	0.787101i	0.0166475	−	0.0512359i
$237$		0			0
$238$	5.27472	−	3.83231i	0.341909	−	0.248411i
$239$	10.4011	+	7.55682i	0.672789	+	0.488810i	0.870958	−	0.491358i	$-0.163499\pi$
$239$	10.4011	+	7.55682i	0.672789	+	0.488810i	−0.198169	+	0.980168i	$0.563499\pi$
$240$		0			0
$241$	1.12325			0.0723548			0.0361774	−	0.999345i	$-0.488482\pi$
$241$	1.12325			0.0723548			0.0361774	+	0.999345i	$0.488482\pi$
$242$	−3.85617	+	13.9173i	−0.247884	+	0.894641i
$243$		0			0
$244$	0.996419	+	3.06666i	0.0637892	+	0.196323i
$245$	2.79869	+	2.03337i	0.178802	+	0.129907i
$246$		0			0
$247$	−14.0840	+	43.3462i	−0.896145	+	2.75805i
$248$	2.22698	−	6.85394i	0.141413	−	0.435226i
$249$		0			0
$250$	−7.22825	−	5.25163i	−0.457155	−	0.332143i
$251$	−7.68456	−	23.6506i	−0.485045	−	1.49282i	−0.831916	−	0.554902i	$-0.812756\pi$
$251$	−7.68456	−	23.6506i	−0.485045	−	1.49282i	0.346871	−	0.937913i	$-0.387244\pi$
$252$		0			0
$253$	7.22451	−	24.0145i	0.454201	−	1.50978i
$254$	−5.23533			−0.328494
$255$		0			0
$256$	5.25842	+	3.82047i	0.328651	+	0.238779i
$257$	−10.5144	+	7.63916i	−0.655870	+	0.476518i	−0.865266	−	0.501313i	$-0.832850\pi$
$257$	−10.5144	+	7.63916i	−0.655870	+	0.476518i	0.209395	+	0.977831i	$0.432850\pi$
$258$		0			0
$259$	−0.876494	+	2.69757i	−0.0544627	+	0.167619i
$260$	4.28314	−	3.11189i	0.265629	−	0.192991i
$261$		0			0
$262$	0.822298	+	2.53077i	0.0508017	+	0.156352i
$263$	28.0645			1.73053			0.865266	−	0.501313i	$-0.167149\pi$
$263$	28.0645			1.73053			0.865266	+	0.501313i	$0.167149\pi$
$264$		0			0
$265$	15.4684			0.950216
$266$	−3.33881	−	10.2758i	−0.204715	−	0.630049i
$267$		0			0
$268$	2.22638	−	1.61756i	0.135998	−	0.0988083i
$269$	9.42144	−	28.9962i	0.574435	−	1.76793i	−0.0636587	−	0.997972i	$-0.520277\pi$
$269$	9.42144	−	28.9962i	0.574435	−	1.76793i	0.638094	−	0.769958i	$-0.279723\pi$
$270$		0			0
$271$	0.0968832	−	0.0703897i	0.00588523	−	0.00427587i	−0.584839	−	0.811150i	$-0.698842\pi$
$271$	0.0968832	−	0.0703897i	0.00588523	−	0.00427587i	0.590724	+	0.806874i	$0.298842\pi$
$272$	13.5433	+	9.83982i	0.821186	+	0.596626i
$273$		0			0
$274$	−20.0771			−1.21290
$275$	18.3921	−	13.9890i	1.10909	−	0.843571i
$276$		0			0
$277$	−1.74126	−	5.35904i	−0.104622	−	0.321994i	0.885019	−	0.465554i	$-0.154145\pi$
$277$	−1.74126	−	5.35904i	−0.104622	−	0.321994i	−0.989642	+	0.143560i	$0.954145\pi$
$278$	−22.8603	−	16.6090i	−1.37107	−	0.996142i
$279$		0			0
$280$	−3.19479	+	9.83255i	−0.190925	+	0.587607i
$281$	−1.28738	+	3.96215i	−0.0767987	+	0.236362i	−0.982085	−	0.188441i	$-0.939657\pi$
$281$	−1.28738	+	3.96215i	−0.0767987	+	0.236362i	0.905286	+	0.424803i	$0.139657\pi$
$282$		0			0
$283$	−11.0630	−	8.03774i	−0.657627	−	0.477794i	0.208234	−	0.978079i	$-0.433229\pi$
$283$	−11.0630	−	8.03774i	−0.657627	−	0.477794i	−0.865861	+	0.500285i	$0.833229\pi$
$284$	0.597174	+	1.83791i	0.0354358	+	0.109060i
$285$		0			0
$286$	−7.95303	−	22.7656i	−0.470273	−	1.34616i
$287$	6.93310			0.409248
$288$		0			0
$289$	−6.19885	−	4.50373i	−0.364638	−	0.264925i
$290$	5.40169	−	3.92456i	0.317198	−	0.230458i
$291$		0			0
$292$	−0.630484	+	1.94043i	−0.0368963	+	0.113555i
$293$	−2.49991	+	1.81629i	−0.146046	+	0.106109i	−0.658409	−	0.752660i	$-0.728770\pi$
$293$	−2.49991	+	1.81629i	−0.146046	+	0.106109i	0.512363	+	0.858769i	$0.328770\pi$
$294$		0			0
$295$	3.20152	+	9.85326i	0.186400	+	0.573679i
$296$	−8.47675			−0.492701
$297$		0			0
$298$	−1.59046			−0.0921329
$299$	12.9400	+	39.8252i	0.748339	+	2.30315i
$300$		0			0
$301$	−4.55425	+	3.30886i	−0.262503	+	0.190719i
$302$	−3.94237	+	12.1334i	−0.226858	+	0.698197i
$303$		0			0
$304$	22.4436	−	16.3063i	1.28723	−	0.935228i
$305$	−32.6563	−	23.7262i	−1.86989	−	1.35856i
$306$		0			0
$307$	5.33016			0.304208			0.152104	−	0.988364i	$-0.451395\pi$
$307$	5.33016			0.304208			0.152104	+	0.988364i	$0.451395\pi$
$308$	−0.753119	−	0.522329i	−0.0429129	−	0.0297624i
$309$		0			0
$310$	3.38435	+	10.4160i	0.192218	+	0.591587i
$311$	−6.11017	−	4.43930i	−0.346476	−	0.251730i	0.400913	−	0.916116i	$-0.368693\pi$
$311$	−6.11017	−	4.43930i	−0.346476	−	0.251730i	−0.747389	+	0.664386i	$0.768693\pi$
$312$		0			0
$313$	1.49793	−	4.61015i	0.0846679	−	0.260581i	−0.899756	−	0.436394i	$-0.856255\pi$
$313$	1.49793	−	4.61015i	0.0846679	−	0.260581i	0.984424	+	0.175813i	$0.0562554\pi$
$314$	−6.70971	+	20.6504i	−0.378651	+	1.16537i
$315$		0			0
$316$	3.63865	+	2.64363i	0.204690	+	0.148716i
$317$	9.60864	+	29.5724i	0.539675	+	1.66095i	0.733325	+	0.679878i	$0.237967\pi$
$317$	9.60864	+	29.5724i	0.539675	+	1.66095i	−0.193650	+	0.981071i	$0.562033\pi$
$318$		0			0
$319$	1.60804	+	4.60301i	0.0900328	+	0.257719i
$320$	−30.3691			−1.69769
$321$		0			0
$322$	−8.03107	−	5.83491i	−0.447554	−	0.325167i
$323$	−33.0641	+	24.0225i	−1.83974	+	1.33665i
$324$		0			0
$325$	−11.9235	+	36.6967i	−0.661396	+	2.03557i
$326$	−8.07252	+	5.86503i	−0.447096	+	0.324834i
$327$		0			0
$328$	6.40285	+	19.7059i	0.353538	+	1.08808i
$329$	−0.0417127			−0.00229970
$330$		0			0
$331$	−27.0887			−1.48893			−0.744465	−	0.667661i	$-0.767295\pi$
$331$	−27.0887			−1.48893			−0.744465	+	0.667661i	$0.767295\pi$
$332$	0.823524	+	2.53455i	0.0451968	+	0.139101i
$333$		0			0
$334$	−4.33950	+	3.15283i	−0.237447	+	0.172515i
$335$	−10.6457	+	32.7641i	−0.581637	+	1.79009i
$336$		0			0
$337$	−5.05145	+	3.67010i	−0.275170	+	0.199923i	−0.716808	−	0.697271i	$-0.754398\pi$
$337$	−5.05145	+	3.67010i	−0.275170	+	0.199923i	0.441638	+	0.897193i	$0.354398\pi$
$338$	18.7687	+	13.6363i	1.02088	+	0.741715i
$339$		0			0
$340$	4.74744			0.257466
$341$	−7.99582	+	0.175391i	−0.432998	+	0.00949795i
$342$		0			0
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	−13.6107	−	9.88874i	−0.733839	−	0.533165i
$345$		0			0
$346$	−1.30344	+	4.01157i	−0.0700732	+	0.215663i
$347$	0.479695	−	1.47635i	0.0257514	−	0.0792546i	−0.937355	−	0.348376i	$-0.886733\pi$
$347$	0.479695	−	1.47635i	0.0257514	−	0.0792546i	0.963106	+	0.269121i	$0.0867333\pi$
$348$		0			0
$349$	4.61727	+	3.35464i	0.247157	+	0.179570i	0.704466	−	0.709738i	$-0.251187\pi$
$349$	4.61727	+	3.35464i	0.247157	+	0.179570i	−0.457309	+	0.889308i	$0.651187\pi$
$350$	−2.82662	−	8.69945i	−0.151089	−	0.465005i
$351$		0			0
$352$	1.48239	−	4.92751i	0.0790119	−	0.262637i
$353$	−17.0387			−0.906877			−0.453438	−	0.891288i	$-0.649803\pi$
$353$	−17.0387			−0.906877			−0.453438	+	0.891288i	$0.649803\pi$
$354$		0			0
$355$	−19.5716	−	14.2196i	−1.03875	−	0.754697i
$356$	−1.77714	+	1.29117i	−0.0941881	+	0.0684316i
$357$		0			0
$358$	−0.0843147	+	0.259494i	−0.00445617	+	0.0137147i
$359$	−13.4051	+	9.73939i	−0.707495	+	0.514025i	−0.882365	−	0.470566i	$-0.844050\pi$
$359$	−13.4051	+	9.73939i	−0.707495	+	0.514025i	0.174870	+	0.984592i	$0.444050\pi$
$360$		0			0
$361$	15.0577	+	46.3428i	0.792510	+	2.43910i
$362$	6.89944			0.362626
$363$		0			0
$364$	1.53041			0.0802154
$365$	−7.89266	−	24.2911i	−0.413121	−	1.27145i
$366$		0			0
$367$	−16.4734	+	11.9686i	−0.859905	+	0.624757i	−0.927859	−	0.372931i	$-0.878353\pi$
$367$	−16.4734	+	11.9686i	−0.859905	+	0.624757i	0.0679542	+	0.997688i	$0.478353\pi$
$368$	7.87635	−	24.2409i	0.410583	−	1.26364i
$369$		0			0
$370$	10.4219	−	7.57194i	0.541808	−	0.393646i
$371$	3.61748	+	2.62825i	0.187810	+	0.136452i
$372$		0			0
$373$	13.5841			0.703356			0.351678	−	0.936121i	$-0.385611\pi$
$373$	13.5841			0.703356			0.351678	+	0.936121i	$0.385611\pi$
$374$	6.22960	−	20.7073i	0.322125	−	1.07075i
$375$		0			0
$376$	−0.0385225	−	0.118560i	−0.00198664	−	0.00611426i
$377$	−6.58671	−	4.78553i	−0.339233	−	0.246467i
$378$		0			0
$379$	3.94189	−	12.1319i	0.202481	−	0.623174i	−0.797326	−	0.603549i	$-0.793753\pi$
$379$	3.94189	−	12.1319i	0.202481	−	0.623174i	0.999807	−	0.0196248i	$-0.00624718\pi$
$380$	2.43114	−	7.48227i	0.124715	−	0.383832i
$381$		0			0
$382$	2.87602	+	2.08955i	0.147150	+	0.106911i
$383$	3.63020	+	11.1726i	0.185494	+	0.570893i	0.999957	−	0.00932355i	$-0.00296782\pi$
$383$	3.63020	+	11.1726i	0.185494	+	0.570893i	−0.814462	+	0.580217i	$0.802968\pi$
$384$		0			0
$385$	11.4707	−	0.251613i	0.584599	−	0.0128234i
$386$	21.6493			1.10192
$387$		0			0
$388$	−0.525785	−	0.382006i	−0.0266927	−	0.0193934i
$389$	25.6381	−	18.6272i	1.29990	−	0.944436i	0.299950	−	0.953955i	$-0.403030\pi$
$389$	25.6381	−	18.6272i	1.29990	−	0.944436i	0.999955	+	0.00951928i	$0.00303013\pi$
$390$		0			0
$391$	−11.6035	+	35.7119i	−0.586814	+	1.80603i
$392$	−2.41780	+	1.75664i	−0.122117	+	0.0887235i
$393$		0			0
$394$	1.30473	+	4.01554i	0.0657313	+	0.202300i
$395$	−56.3030			−2.83291
$396$		0			0
$397$	24.2723			1.21819			0.609097	−	0.793096i	$-0.291532\pi$
$397$	24.2723			1.21819			0.609097	+	0.793096i	$0.291532\pi$
$398$	−3.50343	−	10.7825i	−0.175611	−	0.540476i
$399$		0			0
$400$	19.0007	−	13.8048i	0.950035	−	0.690241i
$401$	2.45393	−	7.55243i	0.122544	−	0.377150i	−0.870902	−	0.491457i	$-0.836465\pi$
$401$	2.45393	−	7.55243i	0.122544	−	0.377150i	0.993446	+	0.114307i	$0.0364646\pi$
$402$		0			0
$403$	10.8041	−	7.84966i	0.538192	−	0.391019i
$404$	−3.09642	−	2.24968i	−0.154053	−	0.111926i
$405$		0			0
$406$	1.93008			0.0957883
$407$	3.10251	+	8.88092i	0.153785	+	0.440211i
$408$		0			0
$409$	−0.489307	−	1.50593i	−0.0241947	−	0.0744635i	0.938230	−	0.346012i	$-0.112464\pi$
$409$	−0.489307	−	1.50593i	−0.0241947	−	0.0744635i	−0.962425	+	0.271548i	$0.912464\pi$
$410$	−25.4746	−	18.5084i	−1.25810	−	0.914064i
$411$		0			0
$412$	−0.324270	+	0.998000i	−0.0159756	+	0.0491679i
$413$	−0.925463	+	2.84828i	−0.0455391	+	0.140155i
$414$		0			0
$415$	−26.9899	−	19.6093i	−1.32488	−	0.962583i
$416$	2.65515	+	8.17170i	0.130179	+	0.400651i
$417$		0			0
$418$	−29.4459	−	20.4223i	−1.44025	−	0.998889i
$419$	18.0433			0.881472			0.440736	−	0.897637i	$-0.354718\pi$
$419$	18.0433			0.881472			0.440736	+	0.897637i	$0.354718\pi$
$420$		0			0
$421$	5.63461	+	4.09379i	0.274614	+	0.199519i	0.716565	−	0.697520i	$-0.245713\pi$
$421$	5.63461	+	4.09379i	0.274614	+	0.199519i	−0.441951	+	0.897039i	$0.645713\pi$
$422$	5.21992	−	3.79249i	0.254102	−	0.184616i
$423$		0			0
$424$	−4.12947	+	12.7092i	−0.200545	+	0.617213i
$425$	−27.9920	+	20.3373i	−1.35781	+	0.986506i
$426$		0			0
$427$	−3.60574	−	11.0973i	−0.174494	−	0.537038i
$428$	0.370755			0.0179211
$429$		0			0
$430$	25.5671			1.23295
$431$	7.44055	+	22.8997i	0.358399	+	1.10304i	0.954013	+	0.299767i	$0.0969088\pi$
$431$	7.44055	+	22.8997i	0.358399	+	1.10304i	−0.595614	+	0.803271i	$0.703091\pi$
$432$		0			0
$433$	19.6338	−	14.2648i	0.943542	−	0.685523i	−0.00572899	−	0.999984i	$-0.501824\pi$
$433$	19.6338	−	14.2648i	0.943542	−	0.685523i	0.949271	+	0.314461i	$0.101824\pi$
$434$	−0.978315	+	3.01094i	−0.0469606	+	0.144530i
$435$		0			0
$436$	−3.93162	+	2.85649i	−0.188290	+	0.136801i
$437$	50.3421	+	36.5757i	2.40819	+	1.74965i
$438$		0			0
$439$	−8.71332			−0.415864			−0.207932	−	0.978143i	$-0.566673\pi$
$439$	−8.71332			−0.415864			−0.207932	+	0.978143i	$0.566673\pi$
$440$	11.3085	+	32.3707i	0.539113	+	1.54321i
$441$		0			0
$442$	11.1580	+	34.3407i	0.530730	+	1.63342i
$443$	−20.4847	−	14.8830i	−0.973258	−	0.707114i	−0.0170665	−	0.999854i	$-0.505433\pi$
$443$	−20.4847	−	14.8830i	−0.973258	−	0.707114i	−0.956192	+	0.292741i	$0.905433\pi$
$444$		0			0
$445$	8.49758	−	26.1529i	0.402824	−	1.23976i
$446$	0.468923	−	1.44320i	0.0222041	−	0.0683373i
$447$		0			0
$448$	−7.10220	−	5.16005i	−0.335548	−	0.243790i
$449$	−6.66910	−	20.5254i	−0.314734	−	0.968652i	−0.975864	−	0.218380i	$-0.929923\pi$
$449$	−6.66910	−	20.5254i	−0.314734	−	0.968652i	0.661130	−	0.750272i	$-0.270077\pi$
$450$		0			0
$451$	18.3021	−	13.9205i	0.861811	−	0.655493i
$452$	3.52727			0.165909
$453$		0			0
$454$	2.78717	+	2.02500i	0.130809	+	0.0950380i
$455$	−15.4994	+	11.2610i	−0.726624	+	0.527923i
$456$		0			0
$457$	9.14375	−	28.1416i	0.427727	−	1.31641i	−0.472632	−	0.881260i	$-0.656696\pi$
$457$	9.14375	−	28.1416i	0.427727	−	1.31641i	0.900359	−	0.435148i	$-0.143304\pi$
$458$	−11.5012	+	8.35612i	−0.537416	+	0.390456i
$459$		0			0
$460$	−2.23366	−	6.87449i	−0.104145	−	0.320525i
$461$	−18.2856			−0.851643			−0.425821	−	0.904807i	$-0.640015\pi$
$461$	−18.2856			−0.851643			−0.425821	+	0.904807i	$0.640015\pi$
$462$		0			0
$463$	21.5147			0.999875			0.499937	−	0.866062i	$-0.333356\pi$
$463$	21.5147			0.999875			0.499937	+	0.866062i	$0.333356\pi$
$464$	1.53139	+	4.71312i	0.0710928	+	0.218801i
$465$		0			0
$466$	−17.8340	+	12.9572i	−0.826146	+	0.600230i
$467$	10.2144	−	31.4367i	0.472666	−	1.45472i	−0.376413	−	0.926452i	$-0.622843\pi$
$467$	10.2144	−	31.4367i	0.472666	−	1.45472i	0.849080	−	0.528265i	$-0.177157\pi$
$468$		0			0
$469$	−8.05662	+	5.85347i	−0.372020	+	0.270288i
$470$	0.153267	+	0.111355i	0.00706968	+	0.00513642i
$471$		0			0
$472$	−8.95035			−0.411973
$473$	−5.37870	+	17.8789i	−0.247313	+	0.822074i
$474$		0			0
$475$	17.7184	+	54.5317i	0.812978	+	2.50209i
$476$	1.11025	+	0.806644i	0.0508882	+	0.0369725i
$477$		0			0
$478$	5.21588	−	16.0528i	0.238569	−	0.734240i
$479$	−2.54237	+	7.82463i	−0.116164	+	0.357516i	−0.992188	−	0.124751i	$-0.960187\pi$
$479$	−2.54237	+	7.82463i	−0.116164	+	0.357516i	0.876024	+	0.482268i	$0.160187\pi$
$480$		0			0
$481$	−12.7082	−	9.23307i	−0.579445	−	0.420992i
$482$	−0.455705	−	1.40252i	−0.0207568	−	0.0638828i
$483$		0			0
$484$	−3.03684	+	0.133292i	−0.138038	+	0.00605875i
$485$	8.13580			0.369428
$486$		0			0
$487$	−13.5666	−	9.85668i	−0.614759	−	0.446649i	0.236328	−	0.971673i	$-0.424056\pi$
$487$	−13.5666	−	9.85668i	−0.614759	−	0.446649i	−0.851087	+	0.525025i	$0.824056\pi$
$488$	28.2120	−	20.4972i	1.27710	−	0.927864i
$489$		0			0
$490$	1.40347	−	4.31945i	0.0634025	−	0.195133i
$491$	−17.6075	+	12.7926i	−0.794616	+	0.577322i	−0.909330	−	0.416076i	$-0.863405\pi$
$491$	−17.6075	+	12.7926i	−0.794616	+	0.577322i	0.114714	+	0.993399i	$0.463405\pi$
$492$		0			0
$493$	−2.25605	−	6.94340i	−0.101607	−	0.312715i
$494$	59.8370			2.69219
$495$		0			0
$496$	−8.12874			−0.364991
$497$	−2.16099	−	6.65086i	−0.0969338	−	0.298332i
$498$		0			0
$499$	−22.2207	+	16.1443i	−0.994737	+	0.722719i	−0.960953	−	0.276710i	$-0.910756\pi$
$499$	−22.2207	+	16.1443i	−0.994737	+	0.722719i	−0.0337838	+	0.999429i	$0.510756\pi$
$500$	0.581139	−	1.78856i	0.0259893	−	0.0799869i
$501$		0			0
$502$	−26.4131	+	19.1903i	−1.17888	+	0.856503i
$503$	−12.4720	−	9.06143i	−0.556098	−	0.404029i	0.273931	−	0.961749i	$-0.411676\pi$
$503$	−12.4720	−	9.06143i	−0.556098	−	0.404029i	−0.830029	+	0.557720i	$0.811676\pi$
$504$		0			0
$505$	47.9129			2.13209
$506$	−32.9160	+	0.722025i	−1.46330	+	0.0320979i
$507$		0			0
$508$	−0.340525	−	1.04803i	−0.0151083	−	0.0464987i
$509$	19.8705	+	14.4367i	0.880742	+	0.639897i	0.933448	−	0.358713i	$-0.116784\pi$
$509$	19.8705	+	14.4367i	0.880742	+	0.639897i	−0.0527054	+	0.998610i	$0.516784\pi$
$510$		0			0
$511$	2.28153	−	7.02184i	0.100929	−	0.310628i
$512$	7.84241	−	24.1365i	0.346589	−	1.06669i
$513$		0			0
$514$	13.8042	+	10.0293i	0.608876	+	0.442374i
$515$	−4.05935	−	12.4934i	−0.178876	−	0.550524i
$516$		0			0
$517$	−0.110114	+	0.0837524i	−0.00484279	+	0.00368343i
$518$	3.72385			0.163616
$519$		0			0
$520$	−46.3211	−	33.6542i	−2.03131	−	1.47584i
$521$	−9.85691	+	7.16146i	−0.431839	+	0.313749i	−0.782384	−	0.622797i	$-0.785996\pi$
$521$	−9.85691	+	7.16146i	−0.431839	+	0.313749i	0.350545	+	0.936546i	$0.385996\pi$
$522$		0			0
$523$	9.22433	−	28.3896i	0.403352	−	1.24139i	−0.518912	−	0.854828i	$-0.673663\pi$
$523$	9.22433	−	28.3896i	0.403352	−	1.24139i	0.922264	−	0.386562i	$-0.126337\pi$
$524$	−0.453133	+	0.329221i	−0.0197952	+	0.0143821i
$525$		0			0
$526$	−11.3858	−	35.0420i	−0.496447	−	1.52791i
$527$	11.9753			0.521653
$528$		0			0
$529$	34.1716			1.48572
$530$	−6.27557	−	19.3142i	−0.272593	−	0.838956i
$531$		0			0
$532$	1.83987	−	1.33675i	0.0797687	−	0.0579553i
$533$	−11.8651	+	36.5170i	−0.513934	+	1.58173i
$534$		0			0
$535$	−3.75486	+	2.72807i	−0.162337	+	0.117945i
$536$	−24.0777	−	17.4935i	−1.04000	−	0.755604i
$537$		0			0
$538$	−40.0277			−1.72572
$539$	2.72531	+	1.89015i	0.117388	+	0.0814146i
$540$		0			0
$541$	−10.3766	−	31.9357i	−0.446123	−	1.37303i	−0.881248	−	0.472655i	$-0.843296\pi$
$541$	−10.3766	−	31.9357i	−0.446123	−	1.37303i	0.435125	−	0.900370i	$-0.356704\pi$
$542$	−0.127196	−	0.0924134i	−0.00546354	−	0.00396949i
$543$		0			0
$544$	−2.38091	+	7.32770i	−0.102081	+	0.314172i
$545$	18.7995	−	57.8588i	0.805281	−	2.47840i
$546$		0			0
$547$	−20.7161	−	15.0511i	−0.885757	−	0.643540i	0.0490113	−	0.998798i	$-0.484393\pi$
$547$	−20.7161	−	15.0511i	−0.885757	−	0.643540i	−0.934768	+	0.355258i	$0.884393\pi$
$548$	−1.30589	−	4.01910i	−0.0557846	−	0.171687i
$549$		0			0
$550$	−24.9288	−	17.2895i	−1.06297	−	0.737226i
$551$	−12.0985			−0.515415
$552$		0			0
$553$	−13.1672	−	9.56651i	−0.559925	−	0.406810i
$554$	−5.98500	+	4.34836i	−0.254278	+	0.184744i
$555$		0			0
$556$	1.83793	−	5.65657i	0.0779456	−	0.239892i
$557$	4.73952	−	3.44347i	0.200820	−	0.145904i	−0.482830	−	0.875714i	$-0.660391\pi$
$557$	4.73952	−	3.44347i	0.200820	−	0.145904i	0.683651	+	0.729810i	$0.260391\pi$
$558$		0			0
$559$	−9.63391	−	29.6501i	−0.407471	−	1.25407i
$560$	11.6614			0.492782
$561$		0			0
$562$	5.46953			0.230718
$563$	1.90737	+	5.87028i	0.0803861	+	0.247403i	0.983170	−	0.182690i	$-0.0584806\pi$
$563$	1.90737	+	5.87028i	0.0803861	+	0.247403i	−0.902784	+	0.430093i	$0.858481\pi$
$564$		0			0
$565$	−35.7228	+	25.9541i	−1.50287	+	1.09190i
$566$	−5.54783	+	17.0745i	−0.233193	+	0.717694i
$567$		0			0
$568$	16.9080	−	12.2844i	0.709443	−	0.515441i
$569$	−21.8556	−	15.8790i	−0.916235	−	0.665684i	0.0263490	−	0.999653i	$-0.491612\pi$
$569$	−21.8556	−	15.8790i	−0.916235	−	0.665684i	−0.942584	+	0.333969i	$0.891612\pi$
$570$		0			0
$571$	30.7018			1.28483			0.642416	−	0.766356i	$-0.277932\pi$
$571$	30.7018			1.28483			0.642416	+	0.766356i	$0.277932\pi$
$572$	4.03999	−	3.07282i	0.168921	−	0.128481i
$573$		0			0
$574$	−2.81278	−	8.65684i	−0.117403	−	0.361330i
$575$	42.6194	+	30.9648i	1.77735	+	1.29132i
$576$		0			0
$577$	−2.80159	+	8.62241i	−0.116632	+	0.358955i	−0.992284	−	0.123987i	$-0.960432\pi$
$577$	−2.80159	+	8.62241i	−0.116632	+	0.358955i	0.875652	+	0.482942i	$0.160432\pi$
$578$	−3.10858	+	9.56721i	−0.129300	+	0.397943i
$579$		0			0
$580$	1.13698	+	0.826062i	0.0472104	+	0.0343004i
$581$	−2.98009	−	9.17177i	−0.123635	−	0.380509i
$582$		0			0
$583$	14.8266	−	0.325226i	0.614053	−	0.0134695i
$584$	22.0652			0.913064
$585$		0			0
$586$	3.28208	+	2.38457i	0.135581	+	0.0985057i
$587$	−5.48448	+	3.98471i	−0.226369	+	0.164466i	−0.695189	−	0.718827i	$-0.744679\pi$
$587$	−5.48448	+	3.98471i	−0.226369	+	0.164466i	0.468820	+	0.883294i	$0.344679\pi$
$588$		0			0
$589$	6.13249	−	18.8739i	0.252685	−	0.777683i
$590$	11.0042	−	7.99498i	0.453034	−	0.329148i
$591$		0			0
$592$	2.95462	+	9.09337i	0.121434	+	0.373735i
$593$	32.2361			1.32378			0.661890	−	0.749601i	$-0.269755\pi$
$593$	32.2361			1.32378			0.661890	+	0.749601i	$0.269755\pi$
$594$		0			0
$595$	−17.1796			−0.704294
$596$	−0.103449	−	0.318384i	−0.00423744	−	0.0130415i
$597$		0			0
$598$	44.4769	−	32.3144i	1.81880	−	1.32143i
$599$	−8.24933	+	25.3888i	−0.337059	+	1.03736i	0.628640	+	0.777696i	$0.283612\pi$
$599$	−8.24933	+	25.3888i	−0.337059	+	1.03736i	−0.965699	+	0.259664i	$0.916388\pi$
$600$		0			0
$601$	−3.44843	+	2.50543i	−0.140664	+	0.102199i	−0.655892	−	0.754855i	$-0.727707\pi$
$601$	−3.44843	+	2.50543i	−0.140664	+	0.102199i	0.515228	+	0.857053i	$0.327707\pi$
$602$	5.97919	+	4.34414i	0.243694	+	0.177054i
$603$		0			0
$604$	−2.68532			−0.109264
$605$	29.7752	−	23.6954i	1.21053	−	0.963357i
$606$		0			0
$607$	2.15648	+	6.63696i	0.0875288	+	0.269386i	0.985235	−	0.171209i	$-0.0547674\pi$
$607$	2.15648	+	6.63696i	0.0875288	+	0.269386i	−0.897706	+	0.440595i	$0.854767\pi$
$608$	10.3297	+	7.50494i	0.418923	+	0.304365i
$609$		0			0
$610$	−16.3764	+	50.4012i	−0.663059	+	2.04069i
$611$	0.0713859	−	0.219703i	0.00288796	−	0.00888824i
$612$		0			0
$613$	20.5382	+	14.9219i	0.829529	+	0.602688i	0.919426	−	0.393263i	$-0.128654\pi$
$613$	20.5382	+	14.9219i	0.829529	+	0.602688i	−0.0898971	+	0.995951i	$0.528654\pi$
$614$	−2.16246	−	6.65537i	−0.0872698	−	0.268589i
$615$		0			0
$616$	−2.85550	+	9.49174i	−0.115051	+	0.382433i
$617$	8.20576			0.330351			0.165176	−	0.986264i	$-0.447181\pi$
$617$	8.20576			0.330351			0.165176	+	0.986264i	$0.447181\pi$
$618$		0			0
$619$	3.43228	+	2.49370i	0.137955	+	0.100230i	0.654622	−	0.755956i	$-0.272828\pi$
$619$	3.43228	+	2.49370i	0.137955	+	0.100230i	−0.516667	+	0.856186i	$0.672828\pi$
$620$	−1.86497	+	1.35498i	−0.0748991	+	0.0544174i
$621$		0			0
$622$	−3.06411	+	9.43035i	−0.122859	+	0.378122i
$623$	6.43093	−	4.67234i	0.257650	−	0.187193i
$624$		0			0
$625$	−3.49001	−	10.7412i	−0.139601	−	0.429646i
$626$	−6.36406			−0.254359
$627$		0			0
$628$	−4.57028			−0.182374
$629$	−4.35276	−	13.3964i	−0.173556	−	0.534150i
$630$		0			0
$631$	−29.0110	+	21.0777i	−1.15491	+	0.839090i	−0.989126	−	0.147072i	$-0.953015\pi$
$631$	−29.0110	+	21.0777i	−1.15491	+	0.839090i	−0.165783	+	0.986162i	$0.553015\pi$
$632$	15.0307	−	46.2599i	0.597891	−	1.84012i
$633$		0			0
$634$	33.0265	−	23.9952i	1.31165	−	0.952970i
$635$	11.1602	+	8.10838i	0.442880	+	0.321771i
$636$		0			0
$637$	−5.53810			−0.219428
$638$	5.09504	−	3.87529i	0.201715	−	0.153424i
$639$		0			0
$640$	9.00376	+	27.7107i	0.355905	+	1.09536i
$641$	24.9876	+	18.1546i	0.986953	+	0.717063i	0.959252	−	0.282553i	$-0.0911814\pi$
$641$	24.9876	+	18.1546i	0.986953	+	0.717063i	0.0277010	+	0.999616i	$0.491181\pi$
$642$		0			0
$643$	3.44185	−	10.5929i	0.135733	−	0.417745i	−0.859970	−	0.510345i	$-0.829518\pi$
$643$	3.44185	−	10.5929i	0.135733	−	0.417745i	0.995703	+	0.0926001i	$0.0295178\pi$
$644$	0.645684	−	1.98721i	0.0254435	−	0.0783071i
$645$		0			0
$646$	43.4093	+	31.5387i	1.70791	+	1.24087i
$647$	−5.92400	−	18.2322i	−0.232897	−	0.716782i	−0.997393	−	0.0721546i	$-0.977012\pi$
$647$	−5.92400	−	18.2322i	−0.232897	−	0.716782i	0.764497	−	0.644627i	$-0.222988\pi$
$648$		0			0
$649$	3.27584	+	9.37710i	0.128588	+	0.368083i
$650$	50.6578			1.98696
$651$		0			0
$652$	−1.69915	−	1.23450i	−0.0665437	−	0.0483469i
$653$	5.12386	−	3.72270i	0.200512	−	0.145681i	−0.482998	−	0.875621i	$-0.660452\pi$
$653$	5.12386	−	3.72270i	0.200512	−	0.145681i	0.683511	+	0.729941i	$0.260452\pi$
$654$		0			0
$655$	2.16671	−	6.66844i	0.0846602	−	0.260557i
$656$	18.9077	−	13.7372i	0.738220	−	0.536348i
$657$		0			0
$658$	0.0169230	+	0.0520835i	0.000659726	+	0.00203043i
$659$	33.0256			1.28650			0.643248	−	0.765658i	$-0.277586\pi$
$659$	33.0256			1.28650			0.643248	+	0.765658i	$0.277586\pi$
$660$		0			0
$661$	−20.1870			−0.785181			−0.392591	−	0.919713i	$-0.628421\pi$
$661$	−20.1870			−0.785181			−0.392591	+	0.919713i	$0.628421\pi$
$662$	10.9900	+	33.8236i	0.427137	+	1.31459i
$663$		0			0
$664$	23.3167	−	16.9406i	0.904864	−	0.657422i
$665$	−8.79756	+	27.0761i	−0.341155	+	1.04997i
$666$		0			0
$667$	−8.99286	+	6.53370i	−0.348205	+	0.252986i
$668$	−0.913401	−	0.663624i	−0.0353405	−	0.0256764i
$669$		0			0
$670$	45.2290			1.74735
$671$	−31.8001	−	22.0551i	−1.22763	−	0.851428i
$672$		0			0
$673$	−7.19412	−	22.1412i	−0.277313	−	0.853481i	−0.988598	−	0.150578i	$-0.951887\pi$
$673$	−7.19412	−	22.1412i	−0.277313	−	0.853481i	0.711285	−	0.702903i	$-0.248113\pi$
$674$	6.63196	+	4.81840i	0.255453	+	0.185598i
$675$		0			0
$676$	−1.50897	+	4.64414i	−0.0580373	+	0.178621i
$677$	3.61932	−	11.1391i	0.139102	−	0.428112i	−0.857104	−	0.515144i	$-0.827738\pi$
$677$	3.61932	−	11.1391i	0.139102	−	0.428112i	0.996205	+	0.0870325i	$0.0277384\pi$
$678$		0			0
$679$	1.90266	+	1.38236i	0.0730174	+	0.0530503i
$680$	−15.8657	−	48.8295i	−0.608420	−	1.87252i
$681$		0			0
$682$	3.46292	+	9.91262i	0.132602	+	0.379574i
$683$	−20.9286			−0.800811			−0.400405	−	0.916338i	$-0.631131\pi$
$683$	−20.9286			−0.800811			−0.400405	+	0.916338i	$0.631131\pi$
$684$		0			0
$685$	42.7986	+	31.0950i	1.63525	+	1.18808i
$686$	1.06214	−	0.771692i	0.0405528	−	0.0294634i
$687$		0			0
$688$	−5.86400	+	18.0475i	−0.223563	+	0.688056i
$689$	−20.0340	+	14.5555i	−0.763234	+	0.554522i
$690$		0			0
$691$	1.56528	+	4.81743i	0.0595459	+	0.183264i	0.976405	−	0.215948i	$-0.0692840\pi$
$691$	1.56528	+	4.81743i	0.0595459	+	0.183264i	−0.916859	+	0.399211i	$0.869284\pi$
$692$	−0.887829			−0.0337502
$693$		0			0
$694$	−2.03802			−0.0773622
$695$	23.0080	+	70.8113i	0.872743	+	2.68603i
$696$		0			0
$697$	−27.8549	+	20.2378i	−1.05508	+	0.766560i
$698$	2.31545	−	7.12623i	0.0876411	−	0.269732i
$699$		0			0
$700$	1.55763	−	1.13169i	0.0588729	−	0.0427737i
$701$	−26.3167	−	19.1202i	−0.993970	−	0.722161i	−0.0331829	−	0.999449i	$-0.510564\pi$
$701$	−26.3167	−	19.1202i	−0.993970	−	0.722161i	−0.960787	+	0.277288i	$0.910564\pi$
$702$		0			0
$703$	−23.3426			−0.880384
$704$	−29.1090	+	0.638516i	−1.09709	+	0.0240650i
$705$		0			0
$706$	6.91263	+	21.2749i	0.260160	+	0.800691i
$707$	11.2050	+	8.14093i	0.421409	+	0.306171i
$708$		0			0
$709$	4.23859	−	13.0450i	0.159184	−	0.489917i	−0.839377	−	0.543549i	$-0.817080\pi$
$709$	4.23859	−	13.0450i	0.159184	−	0.489917i	0.998561	+	0.0536328i	$0.0170801\pi$
$710$	−9.81467	+	30.2065i	−0.368338	+	1.13363i
$711$		0			0
$712$	19.2193	+	13.9636i	0.720272	+	0.523308i
$713$	−5.63435	−	17.3407i	−0.211008	−	0.649416i
$714$		0			0
$715$	−18.3053	+	60.8472i	−0.684578	+	2.27556i
$716$	−0.0574305			−0.00214628
$717$		0			0
$718$	17.5993	+	12.7867i	0.656801	+	0.477194i
$719$	−35.0969	+	25.4994i	−1.30889	+	0.950967i	−1.00000		0.000129629i	$-0.999959\pi$
$719$	−35.0969	+	25.4994i	−1.30889	+	0.950967i	−0.308894	+	0.951097i	$0.599959\pi$
$720$		0			0
$721$	1.17344	−	3.61147i	0.0437011	−	0.134498i
$722$	51.7558	−	37.6028i	1.92615	−	1.39943i
$723$		0			0
$724$	0.448764	+	1.38115i	0.0166782	+	0.0513301i
$725$	−10.2426			−0.380400
$726$		0			0
$727$	−2.79407			−0.103626			−0.0518132	−	0.998657i	$-0.516500\pi$
$727$	−2.79407			−0.103626			−0.0518132	+	0.998657i	$0.516500\pi$
$728$	−5.11454	−	15.7409i	−0.189557	−	0.583398i
$729$		0			0
$730$	−27.1284	+	19.7099i	−1.00407	+	0.729498i
$731$	8.63888	−	26.5877i	0.319520	−	0.983383i
$732$		0			0
$733$	10.9931	−	7.98698i	0.406040	−	0.295006i	−0.365956	−	0.930632i	$-0.619258\pi$
$733$	10.9931	−	7.98698i	0.406040	−	0.295006i	0.771997	+	0.635626i	$0.219258\pi$
$734$	21.6276	+	15.7134i	0.798290	+	0.579992i
$735$		0			0
$736$	11.7310			0.432411
$737$	−9.51510	+	31.6284i	−0.350493	+	1.16505i
$738$		0			0
$739$	7.20209	+	22.1658i	0.264933	+	0.815381i	0.991709	+	0.128506i	$0.0410180\pi$
$739$	7.20209	+	22.1658i	0.264933	+	0.815381i	−0.726776	+	0.686875i	$0.758982\pi$
$740$	2.19365	+	1.59378i	0.0806403	+	0.0585886i
$741$		0			0
$742$	1.81408	−	5.58316i	0.0665970	−	0.204964i
$743$	6.59020	−	20.2825i	0.241771	−	0.744094i	−0.754380	−	0.656438i	$-0.772062\pi$
$743$	6.59020	−	20.2825i	0.241771	−	0.744094i	0.996151	−	0.0876561i	$-0.0279377\pi$
$744$		0			0
$745$	3.39041	+	2.46328i	0.124215	+	0.0902474i
$746$	−5.51109	−	16.9614i	−0.201775	−	0.621001i
$747$		0			0
$748$	4.55046	−	0.0998158i	0.166381	−	0.00364963i
$749$	−1.34165			−0.0490229
$750$		0			0
$751$	−6.93984	−	5.04209i	−0.253239	−	0.183989i	0.453922	−	0.891041i	$-0.350024\pi$
$751$	−6.93984	−	5.04209i	−0.253239	−	0.183989i	−0.707161	+	0.707053i	$0.750024\pi$
$752$	−0.113757	+	0.0826494i	−0.00414830	+	0.00301391i
$753$		0			0
$754$	−3.30308	+	10.1658i	−0.120291	+	0.370218i
$755$	27.1959	−	19.7590i	0.989761	−	0.719104i
$756$		0			0
$757$	−15.5359	−	47.8144i	−0.564660	−	1.73785i	−0.668959	−	0.743299i	$-0.733260\pi$
$757$	−15.5359	−	47.8144i	−0.564660	−	1.73785i	0.104299	−	0.994546i	$-0.466740\pi$
$758$	−16.7474			−0.608294
$759$		0			0
$760$	−85.0830			−3.08629
$761$	3.25429	+	10.0157i	0.117968	+	0.363068i	0.992555	−	0.121801i	$-0.0388670\pi$
$761$	3.25429	+	10.0157i	0.117968	+	0.363068i	−0.874586	+	0.484870i	$0.838867\pi$
$762$		0			0
$763$	14.2274	−	10.3368i	0.515065	−	0.374217i
$764$	−0.231227	+	0.711643i	−0.00836550	+	0.0257464i
$765$		0			0
$766$	12.4776	−	9.06551i	0.450834	−	0.327550i
$767$	−13.4182	−	9.74892i	−0.484505	−	0.352013i
$768$		0			0
$769$	−49.1715			−1.77317			−0.886584	−	0.462567i	$-0.846929\pi$
$769$	−49.1715			−1.77317			−0.886584	+	0.462567i	$0.846929\pi$
$770$	−4.96785	−	14.2205i	−0.179029	−	0.512470i
$771$		0			0
$772$	1.40814	+	4.33382i	0.0506802	+	0.155978i
$773$	12.4676	+	9.05826i	0.448429	+	0.325803i	0.788975	−	0.614425i	$-0.210612\pi$
$773$	12.4676	+	9.05826i	0.448429	+	0.325803i	−0.340546	+	0.940228i	$0.610612\pi$
$774$		0			0
$775$	5.19174	−	15.9785i	0.186493	−	0.573966i
$776$	−2.17195	+	6.68456i	−0.0779683	+	0.239962i
$777$		0			0
$778$	−33.6598	−	24.4553i	−1.20676	−	0.876764i
$779$	17.6317	+	54.2647i	0.631720	+	1.94423i
$780$		0			0
$781$	−19.0584	−	13.2181i	−0.681965	−	0.472980i
$782$	49.2983			1.76290
$783$		0			0
$784$	2.72716	+	1.98140i	0.0973984	+	0.0707641i
$785$	46.2860	−	33.6288i	1.65202	−	1.20026i
$786$		0			0
$787$	3.59043	−	11.0502i	0.127985	−	0.393898i	−0.866448	−	0.499267i	$-0.833603\pi$
$787$	3.59043	−	11.0502i	0.127985	−	0.393898i	0.994433	+	0.105370i	$0.0336025\pi$
$788$	−0.718980	+	0.522370i	−0.0256126	+	0.0186087i
$789$		0			0
$790$	22.8423	+	70.3013i	0.812692	+	2.50121i
$791$	−12.7641			−0.453840
$792$		0			0
$793$	64.6210			2.29476
$794$	−9.84735	−	30.3070i	−0.349469	−	1.07556i
$795$		0			0
$796$	1.93059	−	1.40266i	0.0684281	−	0.0497159i
$797$	−2.67876	+	8.24439i	−0.0948867	+	0.292031i	−0.987224	−	0.159338i	$-0.949064\pi$
$797$	−2.67876	+	8.24439i	−0.0948867	+	0.292031i	0.892337	+	0.451369i	$0.149064\pi$
$798$		0			0
$799$	0.167588	−	0.121760i	0.00592883	−	0.00430755i
$800$	8.74506	+	6.35365i	0.309184	+	0.224636i
$801$		0			0
$802$	−10.4257			−0.368145
$803$	−8.07589	−	23.1173i	−0.284992	−	0.815790i
$804$		0			0
$805$	8.08294	+	24.8767i	0.284886	+	0.876789i
$806$	−14.1845	−	10.3057i	−0.499629	−	0.363002i
$807$		0			0
$808$	−12.7909	+	39.3663i	−0.449982	+	1.38490i
$809$	4.99988	−	15.3881i	0.175787	−	0.541015i	−0.823882	−	0.566761i	$-0.808196\pi$
$809$	4.99988	−	15.3881i	0.175787	−	0.541015i	0.999669	+	0.0257461i	$0.00819615\pi$
$810$		0			0
$811$	−3.70872	−	2.69455i	−0.130231	−	0.0946183i	0.520763	−	0.853701i	$-0.325648\pi$
$811$	−3.70872	−	2.69455i	−0.130231	−	0.0946183i	−0.650994	+	0.759083i	$0.725648\pi$
$812$	0.125539	+	0.386370i	0.00440556	+	0.0135589i
$813$		0			0
$814$	9.83024	−	7.47688i	0.344550	−	0.262064i
$815$	26.2920			0.920967
$816$		0			0
$817$	−37.4800	−	27.2308i	−1.31126	−	0.952687i
$818$	−1.68183	+	1.22192i	−0.0588038	+	0.0427235i
$819$		0			0
$820$	2.04811	−	6.30345i	0.0715232	−	0.220126i
$821$	−37.9257	+	27.5546i	−1.32362	+	0.961663i	−0.323736	+	0.946147i	$0.604939\pi$
$821$	−37.9257	+	27.5546i	−1.32362	+	0.961663i	−0.999880	+	0.0155159i	$0.995061\pi$
$822$		0			0
$823$	−0.251597	−	0.774335i	−0.00877010	−	0.0269916i	0.946576	−	0.322482i	$-0.104517\pi$
$823$	−0.251597	−	0.774335i	−0.00877010	−	0.0269916i	−0.955346	+	0.295490i	$0.904517\pi$
$824$	11.3485			0.395345
$825$		0			0
$826$	3.93190			0.136808
$827$	8.18806	+	25.2003i	0.284727	+	0.876299i	0.986480	+	0.163879i	$0.0524007\pi$
$827$	8.18806	+	25.2003i	0.284727	+	0.876299i	−0.701754	+	0.712420i	$0.747599\pi$
$828$		0			0
$829$	−26.6403	+	19.3553i	−0.925256	+	0.672238i	−0.944827	−	0.327571i	$-0.893770\pi$
$829$	−26.6403	+	19.3553i	−0.925256	+	0.672238i	0.0195709	+	0.999808i	$0.493770\pi$
$830$	−13.5348	+	41.6558i	−0.469799	+	1.44589i
$831$		0			0
$832$	39.3327	−	28.5769i	1.36362	−	0.990726i
$833$	−4.01766	−	2.91900i	−0.139204	−	0.101137i
$834$		0			0
$835$	14.1336			0.489114
$836$	2.17295	−	7.22292i	0.0751529	−	0.249810i
$837$		0			0
$838$	−7.32021	−	22.5293i	−0.252872	−	0.778261i
$839$	25.4353	+	18.4799i	0.878126	+	0.637996i	0.932755	−	0.360511i	$-0.117398\pi$
$839$	25.4353	+	18.4799i	0.878126	+	0.637996i	−0.0546294	+	0.998507i	$0.517398\pi$
$840$		0			0
$841$	−8.29364	+	25.5252i	−0.285988	+	0.880179i
$842$	2.82562	−	8.69638i	0.0973775	−	0.299697i
$843$		0			0
$844$	1.09872	+	0.798264i	0.0378194	+	0.0274774i
$845$	−18.8899	−	58.1372i	−0.649833	−	1.99998i
$846$		0			0
$847$	10.9894	−	0.482345i	0.377601	−	0.0165736i
$848$	15.0730			0.517610
$849$		0			0
$850$	36.7501	+	26.7005i	1.26052	+	0.915821i
$851$	−17.3506	+	12.6059i	−0.594771	+	0.432126i
$852$		0			0
$853$	−16.4077	+	50.4978i	−0.561790	+	1.72901i	0.115512	+	0.993306i	$0.463149\pi$
$853$	−16.4077	+	50.4978i	−0.561790	+	1.72901i	−0.677302	+	0.735705i	$0.736851\pi$
$854$	−12.3936	+	9.00444i	−0.424099	+	0.308126i
$855$		0			0
$856$	−1.23904	−	3.81337i	−0.0423495	−	0.130338i
$857$	−38.6964			−1.32185			−0.660923	−	0.750454i	$-0.729835\pi$
$857$	−38.6964			−1.32185			−0.660923	+	0.750454i	$0.729835\pi$
$858$		0			0
$859$	−4.54428			−0.155049			−0.0775245	−	0.996990i	$-0.524702\pi$
$859$	−4.54428			−0.155049			−0.0775245	+	0.996990i	$0.524702\pi$
$860$	1.66297	+	5.11811i	0.0567069	+	0.174526i
$861$		0			0
$862$	25.5744	−	18.5809i	0.871068	−	0.632868i
$863$	−4.59850	+	14.1527i	−0.156535	+	0.481764i	−0.998313	−	0.0580590i	$-0.981509\pi$
$863$	−4.59850	+	14.1527i	−0.156535	+	0.481764i	0.841779	+	0.539823i	$0.181509\pi$
$864$		0			0
$865$	8.99159	−	6.53277i	0.305723	−	0.222121i
$866$	−25.7769	−	18.7280i	−0.875934	−	0.636404i
$867$		0			0
$868$	−0.666374			−0.0226182
$869$	−53.9668	+	1.18378i	−1.83070	+	0.0401570i
$870$		0			0
$871$	−17.0427	−	52.4520i	−0.577470	−	1.77727i
$872$	42.5194	+	30.8922i	1.43989	+	1.04614i
$873$		0			0
$874$	25.2454	−	77.6972i	0.853937	−	2.62815i
$875$	−2.10297	+	6.47227i	−0.0710933	+	0.218803i
$876$		0			0
$877$	−33.2855	−	24.1833i	−1.12397	−	0.816612i	−0.139164	−	0.990269i	$-0.544441\pi$
$877$	−33.2855	−	24.1833i	−1.12397	−	0.816612i	−0.984806	+	0.173657i	$0.944441\pi$
$878$	3.53502	+	10.8797i	0.119301	+	0.367171i
$879$		0			0
$880$	30.7838	−	23.4141i	1.03772	−	0.789289i
$881$	9.03118			0.304268			0.152134	−	0.988360i	$-0.451385\pi$
$881$	9.03118			0.304268			0.152134	+	0.988360i	$0.451385\pi$
$882$		0			0
$883$	−24.7492	−	17.9813i	−0.832876	−	0.605120i	0.0874959	−	0.996165i	$-0.472114\pi$
$883$	−24.7492	−	17.9813i	−0.832876	−	0.605120i	−0.920371	+	0.391045i	$0.872114\pi$
$884$	−6.14868	+	4.46728i	−0.206802	+	0.150251i
$885$		0			0
$886$	−10.2726	+	31.6158i	−0.345115	+	1.06215i
$887$	24.0665	−	17.4853i	0.808073	−	0.587099i	−0.105198	−	0.994451i	$-0.533548\pi$
$887$	24.0665	−	17.4853i	0.808073	−	0.587099i	0.913271	+	0.407352i	$0.133548\pi$
$888$		0			0
$889$	1.23226	+	3.79250i	0.0413286	+	0.127196i
$890$	−36.1026			−1.21016
$891$		0			0
$892$	0.319404			0.0106945
$893$	−0.106080	−	0.326481i	−0.00354984	−	0.0109253i
$894$		0			0
$895$	0.581634	−	0.422582i	0.0194419	−	0.0141254i
$896$	−2.60272	+	8.01035i	−0.0869508	+	0.267607i
$897$		0			0
$898$	−22.9228	+	16.6544i	−0.764944	+	0.555764i
$899$	2.86800	+	2.08372i	0.0956530	+	0.0694960i
$900$		0			0
$901$	−22.2057			−0.739779
$902$	−24.8067	−	17.2048i	−0.825974	−	0.572857i
$903$		0			0
$904$	−11.7879	−	36.2794i	−0.392060	−	1.20664i
$905$	−14.7076	−	10.6857i	−0.488898	−	0.355205i
$906$		0			0
$907$	12.0976	−	37.2325i	0.401693	−	1.23628i	−0.521933	−	0.852987i	$-0.674789\pi$
$907$	12.0976	−	37.2325i	0.401693	−	1.23628i	0.923625	−	0.383296i	$-0.125211\pi$
$908$	−0.224084	+	0.689659i	−0.00743648	+	0.0228871i
$909$		0			0
$910$	20.3489	+	14.7843i	0.674560	+	0.490096i
$911$	8.65035	+	26.6231i	0.286599	+	0.882061i	0.985915	+	0.167248i	$0.0534881\pi$
$911$	8.65035	+	26.6231i	0.286599	+	0.882061i	−0.699316	+	0.714813i	$0.746512\pi$
$912$		0			0
$913$	−26.2823	−	18.2282i	−0.869817	−	0.603265i
$914$	−38.8479			−1.28497
$915$		0			0
$916$	−2.42084	−	1.75884i	−0.0799867	−	0.0581137i
$917$	1.63975	−	1.19135i	0.0541495	−	0.0393419i
$918$		0			0
$919$	−11.8924	+	36.6009i	−0.392293	+	1.20735i	0.538757	+	0.842461i	$0.318894\pi$
$919$	−11.8924	+	36.6009i	−0.392293	+	1.20735i	−0.931050	+	0.364892i	$0.881106\pi$
$920$	−63.2423	+	45.9482i	−2.08504	+	1.51487i
$921$		0			0
$922$	7.41850	+	22.8318i	0.244315	+	0.751925i
$923$	38.7287			1.27477
$924$		0			0
$925$	−19.7618			−0.649763
$926$	−8.72859	−	26.8638i	−0.286839	−	0.882800i
$927$		0			0
$928$	−1.84524	+	1.34065i	−0.0605730	+	0.0440088i
$929$	14.5969	−	44.9247i	0.478910	−	1.47393i	−0.361702	−	0.932294i	$-0.617804\pi$
$929$	14.5969	−	44.9247i	0.478910	−	1.47393i	0.840612	−	0.541638i	$-0.182196\pi$
$930$		0			0
$931$	−6.65796	+	4.83729i	−0.218206	+	0.158536i
$932$	−3.75380	−	2.72730i	−0.122960	−	0.0893356i
$933$		0			0
$934$	−43.3966			−1.41998
$935$	−45.3508	+	34.4938i	−1.48313	+	1.12807i
$936$		0			0
$937$	−13.4677	−	41.4494i	−0.439971	−	1.35409i	−0.887906	−	0.460026i	$-0.847840\pi$
$937$	−13.4677	−	41.4494i	−0.439971	−	1.35409i	0.447934	−	0.894066i	$-0.352160\pi$
$938$	10.5774	+	7.68492i	0.345364	+	0.250921i
$939$		0			0
$940$	−0.0123224	+	0.0379244i	−0.000401912	+	0.00123696i
$941$	10.4499	−	32.1614i	0.340656	−	1.04843i	−0.623213	−	0.782052i	$-0.714173\pi$
$941$	10.4499	−	32.1614i	0.340656	−	1.04843i	0.963869	−	0.266378i	$-0.0858270\pi$
$942$		0			0
$943$	42.4107	+	30.8132i	1.38108	+	1.00342i
$944$	3.11969	+	9.60142i	0.101537	+	0.312500i
$945$		0			0
$946$	24.5062	−	0.537553i	0.796766	−	0.0174773i
$947$	−3.79141			−0.123204			−0.0616021	−	0.998101i	$-0.519621\pi$
$947$	−3.79141			−0.123204			−0.0616021	+	0.998101i	$0.519621\pi$
$948$		0			0
$949$	33.0798	+	24.0339i	1.07382	+	0.780173i
$950$	60.9012	−	44.2473i	1.97590	−	1.43557i
$951$		0			0
$952$	4.58629	−	14.1151i	0.148642	−	0.457474i
$953$	−2.56452	+	1.86323i	−0.0830729	+	0.0603560i	−0.628547	−	0.777772i	$-0.716350\pi$
$953$	−2.56452	+	1.86323i	−0.0830729	+	0.0603560i	0.545474	+	0.838128i	$0.316350\pi$
$954$		0			0
$955$	−2.89460	−	8.90865i	−0.0936669	−	0.288277i
$956$	3.55277			0.114905
$957$		0			0
$958$	10.8015			0.348980
$959$	4.72561	+	14.5439i	0.152598	+	0.469648i
$960$		0			0
$961$	20.3752	−	14.8034i	0.657264	−	0.477530i
$962$	−6.37287	+	19.6137i	−0.205470	+	0.632371i
$963$		0			0
$964$	0.251120	−	0.182449i	0.00808802	−	0.00587629i
$965$	−46.1500	−	33.5300i	−1.48562	−	1.07937i
$966$		0			0
$967$	24.6865			0.793865			0.396932	−	0.917848i	$-0.370075\pi$
$967$	24.6865			0.793865			0.396932	+	0.917848i	$0.370075\pi$
$968$	11.5199	+	30.7897i	0.370264	+	0.989620i
$969$		0			0
$970$	−3.30072	−	10.1586i	−0.105980	−	0.326172i
$971$	−16.3478	−	11.8774i	−0.524626	−	0.381163i	0.293718	−	0.955892i	$-0.405107\pi$
$971$	−16.3478	−	11.8774i	−0.524626	−	0.381163i	−0.818344	+	0.574729i	$0.805107\pi$
$972$		0			0
$973$	−6.65092	+	20.4694i	−0.213219	+	0.656220i
$974$	−6.80330	+	20.9384i	−0.217992	+	0.670910i
$975$		0			0
$976$	−31.8216	−	23.1198i	−1.01859	−	0.740046i
$977$	−10.6023	−	32.6306i	−0.339198	−	1.04394i	−0.964617	−	0.263656i	$-0.915072\pi$
$977$	−10.6023	−	32.6306i	−0.339198	−	1.04394i	0.625419	−	0.780289i	$-0.284928\pi$
$978$		0			0
$979$	7.59512	−	25.2463i	0.242741	−	0.806877i
$980$	0.955969			0.0305373
$981$		0			0
$982$	23.1166	+	16.7952i	0.737680	+	0.535956i
$983$	−26.7408	+	19.4283i	−0.852898	+	0.619667i	−0.925944	−	0.377662i	$-0.876728\pi$
$983$	−26.7408	+	19.4283i	−0.852898	+	0.619667i	0.0730454	+	0.997329i	$0.476728\pi$
$984$		0			0
$985$	3.43788	−	10.5807i	0.109540	−	0.337130i
$986$	−7.75441	+	5.63391i	−0.246951	+	0.179420i
$987$		0			0
$988$	3.89201	+	11.9784i	0.123821	+	0.381083i
$989$	−42.5647			−1.35348
$990$		0			0
$991$	39.3191			1.24901			0.624506	−	0.781020i	$-0.285300\pi$
$991$	39.3191			1.24901			0.624506	+	0.781020i	$0.285300\pi$
$992$	−1.15611	−	3.55814i	−0.0367065	−	0.112971i
$993$		0			0
$994$	−7.42770	+	5.39654i	−0.235592	+	0.171168i
$995$	−9.23135	+	28.4112i	−0.292653	+	0.900695i
$996$		0			0
$997$	1.95384	−	1.41955i	0.0618789	−	0.0449576i	−0.556416	−	0.830904i	$-0.687824\pi$
$997$	1.95384	−	1.41955i	0.0618789	−	0.0449576i	0.618295	+	0.785946i	$0.287824\pi$
$998$	29.1732	+	21.1956i	0.923462	+	0.670934i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.k.379.3	yes	32
3.2	odd	2	inner	693.2.m.k.379.6	yes	32
11.3	even	5		7623.2.a.dc.1.5		16
11.8	odd	10		7623.2.a.db.1.12		16
11.9	even	5	inner	693.2.m.k.64.3	✓	32
33.8	even	10		7623.2.a.db.1.5		16
33.14	odd	10		7623.2.a.dc.1.12		16
33.20	odd	10	inner	693.2.m.k.64.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.m.k.64.3	✓	32	11.9	even	5	inner
693.2.m.k.64.6	yes	32	33.20	odd	10	inner
693.2.m.k.379.3	yes	32	1.1	even	1	trivial
693.2.m.k.379.6	yes	32	3.2	odd	2	inner
7623.2.a.db.1.5		16	33.8	even	10
7623.2.a.db.1.12		16	11.8	odd	10
7623.2.a.dc.1.5		16	11.3	even	5
7623.2.a.dc.1.12		16	33.14	odd	10

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.405703 - 1.24862i) q^{2} +(0.223566 - 0.162430i) q^{4} +(-1.06900 + 3.29005i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(-2.41780 - 1.75664i) q^{8} +O(q^{10})\)	\(q+(-0.405703 - 1.24862i) q^{2} +(0.223566 - 0.162430i) q^{4} +(-1.06900 + 3.29005i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(-2.41780 - 1.75664i) q^{8} +4.54174 q^{10} +(-0.955473 + 3.17602i) q^{11} +(-1.71137 - 5.26705i) q^{13} +(1.06214 + 0.771692i) q^{14} +(-1.04168 + 3.20596i) q^{16} +(1.53461 - 4.72305i) q^{17} +(-6.65796 - 4.83729i) q^{19} +(0.295411 + 0.909181i) q^{20} +(4.35329 - 0.0954909i) q^{22} -7.56119 q^{23} +(-5.63660 - 4.09523i) q^{25} +(-5.88226 + 4.27371i) q^{26} +(-0.0853944 + 0.262817i) q^{28} +(1.18934 - 0.864109i) q^{29} +(0.745166 + 2.29339i) q^{31} -1.55148 q^{32} -6.51991 q^{34} +(-1.06900 - 3.29005i) q^{35} +(2.29469 - 1.66719i) q^{37} +(-3.33881 + 10.2758i) q^{38} +(8.36407 - 6.07685i) q^{40} +(-5.60900 - 4.07518i) q^{41} +5.62936 q^{43} +(0.302269 + 0.865245i) q^{44} +(3.06760 + 9.44109i) q^{46} +(0.0337463 + 0.0245181i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-2.82662 + 8.69945i) q^{50} +(-1.23813 - 0.899554i) q^{52} +(-1.38175 - 4.25260i) q^{53} +(-9.42786 - 6.53873i) q^{55} +2.98857 q^{56} +(-1.56147 - 1.13447i) q^{58} +(2.42289 - 1.76034i) q^{59} +(-3.60574 + 11.0973i) q^{61} +(2.56126 - 1.86087i) q^{62} +(2.71280 + 8.34914i) q^{64} +19.1583 q^{65} +9.95852 q^{67} +(-0.424078 - 1.30518i) q^{68} +(-3.67434 + 2.66957i) q^{70} +(-2.16099 + 6.65086i) q^{71} +(-5.97313 + 4.33973i) q^{73} +(-3.01266 - 2.18882i) q^{74} -2.27421 q^{76} +(-1.09382 - 3.13106i) q^{77} +(5.02941 + 15.4789i) q^{79} +(-9.43424 - 6.85437i) q^{80} +(-2.81278 + 8.65684i) q^{82} +(-2.98009 + 9.17177i) q^{83} +(13.8986 + 10.0979i) q^{85} +(-2.28385 - 7.02896i) q^{86} +(7.88925 - 6.00056i) q^{88} -7.94906 q^{89} +(4.48042 + 3.25522i) q^{91} +(-1.69042 + 1.22816i) q^{92} +(0.0169230 - 0.0520835i) q^{94} +(23.0323 - 16.7340i) q^{95} +(-0.726752 - 2.23671i) q^{97} -1.31288 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{4} - 8 q^{7}+O(q^{10}) \) 32 * q - 10 * q^4 - 8 * q^7	\( 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52} - 12 q^{55} - 104 q^{58} + 34 q^{61} - 52 q^{64} + 104 q^{67} + 18 q^{70} + 2 q^{73} - 28 q^{76} - 42 q^{79} - 172 q^{82} - 30 q^{85} - 16 q^{88} - 10 q^{91} + 150 q^{94} - 74 q^{97}+O(q^{100}) \) 32 * q - 10 * q^4 - 8 * q^7 - 12 * q^10 + 10 * q^13 - 26 * q^16 - 10 * q^19 - 6 * q^22 - 52 * q^25 - 10 * q^28 - 20 * q^31 + 24 * q^34 - 4 * q^37 + 124 * q^40 + 32 * q^43 + 30 * q^46 - 8 * q^49 + 24 * q^52 - 12 * q^55 - 104 * q^58 + 34 * q^61 - 52 * q^64 + 104 * q^67 + 18 * q^70 + 2 * q^73 - 28 * q^76 - 42 * q^79 - 172 * q^82 - 30 * q^85 - 16 * q^88 - 10 * q^91 + 150 * q^94 - 74 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more