LMFDB - Embedded newform 693.2.m.k.64.6

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			64.6
Character	$\chi$	$=$	693.64
Dual form			693.2.m.k.379.6

$q$-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 $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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	−0.698955	−	0.715165i	$-0.746351\pi$
$2$	0.405703	−	1.24862i	0.286875	−	0.882911i	0.985830	−	0.167745i	$-0.0536487\pi$
$3$		0			0
$3$		0			0
$4$	0.223566	+	0.162430i	0.111783	+	0.0812149i
$5$	1.06900	+	3.29005i	0.478073	+	1.47136i	0.841768	+	0.539839i	$0.181515\pi$
$5$	1.06900	+	3.29005i	0.478073	+	1.47136i	−0.363695	+	0.931518i	$0.618485\pi$
$6$		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	0.371783	+	0.928319i	$0.378746\pi$
$13$	−1.71137	+	5.26705i	−0.474648	+	1.46082i	−0.846432	+	0.532497i	$0.821254\pi$
$14$	−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	−0.945350	−	0.326058i	$-0.894280\pi$
$17$	−1.53461	−	4.72305i	−0.372198	−	1.14551i	0.573152	−	0.819449i	$-0.305720\pi$
$18$		0			0
$19$	−6.65796	+	4.83729i	−1.52744	+	1.10975i	−0.569799	+	0.821784i	$0.692979\pi$
$19$	−6.65796	+	4.83729i	−1.52744	+	1.10975i	−0.957641	+	0.287966i	$0.907021\pi$
$20$	−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	$-0.210957\pi$
$23$	7.56119			1.57662			0.788309	+	0.615280i	$0.210957\pi$
$24$		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	$-0.343584\pi$
$29$	−1.18934	−	0.864109i	−0.220856	−	0.160461i	−0.692712	+	0.721215i	$0.743584\pi$
$30$		0			0
$31$	0.745166	−	2.29339i	0.133836	−	0.411904i	−0.861571	−	0.507637i	$-0.830519\pi$
$31$	0.745166	−	2.29339i	0.133836	−	0.411904i	0.995407	+	0.0957322i	$0.0305193\pi$
$32$	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	0.760209	−	0.649679i	$-0.225097\pi$
$37$	2.29469	+	1.66719i	0.377245	+	0.274084i	−0.382964	+	0.923763i	$0.625097\pi$
$38$	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	$-0.517900\pi$
$41$	5.60900	−	4.07518i	0.875979	−	0.636436i	0.932184	+	0.361984i	$0.117900\pi$
$42$		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	$-0.700968\pi$
$47$	−0.0337463	+	0.0245181i	−0.00492241	+	0.00357634i	0.585321	+	0.810801i	$0.300968\pi$
$48$		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	$-0.800641\pi$
$53$	1.38175	−	4.25260i	0.189799	−	0.584140i	0.999998	+	0.00201437i	$0.000641193\pi$
$54$		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	$-0.362454\pi$
$59$	−2.42289	−	1.76034i	−0.315434	−	0.229176i	−0.734225	+	0.678907i	$0.762454\pi$
$60$		0			0
$61$	−3.60574	−	11.0973i	−0.461668	−	1.42087i	−0.863125	−	0.504991i	$-0.831496\pi$
$61$	−3.60574	−	11.0973i	−0.461668	−	1.42087i	0.401456	−	0.915878i	$-0.368504\pi$
$62$	−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	0.993538	+	0.113501i	$0.0362064\pi$
$71$	2.16099	+	6.65086i	0.256463	+	0.789311i	−0.737075	+	0.675811i	$0.763794\pi$
$72$		0			0
$73$	−5.97313	−	4.33973i	−0.699102	−	0.507927i	0.180538	−	0.983568i	$-0.442216\pi$
$73$	−5.97313	−	4.33973i	−0.699102	−	0.507927i	−0.879640	+	0.475641i	$0.842216\pi$
$74$	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	−0.0995496	−	0.995033i	$-0.531740\pi$
$79$	5.02941	−	15.4789i	0.565853	−	1.74152i	0.665403	−	0.746485i	$-0.268260\pi$
$80$	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	0.970480	+	0.241180i	$0.0775343\pi$
$83$	2.98009	+	9.17177i	0.327107	+	1.00673i	−0.643373	+	0.765553i	$0.722466\pi$
$84$		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	$-0.361574\pi$
$89$	7.94906			0.842599			0.421300	+	0.906922i	$0.361574\pi$
$90$		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	−0.981149	−	0.193255i	$-0.938096\pi$
$97$	−0.726752	+	2.23671i	−0.0737905	+	0.227104i	0.907358	+	0.420358i	$0.138096\pi$
$98$	1.31288			0.132621
$99$		0			0
$100$	−1.92534			−0.192534
$101$	4.27994	−	13.1723i	0.425870	−	1.31069i	−0.476289	−	0.879289i	$-0.658018\pi$
$101$	4.27994	−	13.1723i	0.425870	−	1.31069i	0.902159	−	0.431404i	$-0.141982\pi$
$102$		0			0
$103$	−3.07210	−	2.23201i	−0.302703	−	0.219926i	0.426056	−	0.904697i	$-0.359903\pi$
$103$	−3.07210	−	2.23201i	−0.302703	−	0.219926i	−0.728759	+	0.684770i	$0.759903\pi$
$104$	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	$-0.720657\pi$
$107$	−1.08542	+	0.788603i	−0.104931	+	0.0762372i	0.534082	+	0.845433i	$0.320657\pi$
$108$		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	$-0.904982\pi$
$113$	−10.3264	+	7.50257i	−0.971426	+	0.705782i	−0.0156497	+	0.999878i	$0.504982\pi$
$114$		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	0.990726	−	0.135877i	$-0.0433853\pi$
$127$	1.23226	+	3.79250i	0.109345	+	0.336530i	−0.881381	+	0.472407i	$0.843385\pi$
$128$	−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	$-0.471779\pi$
$131$	2.02685			0.177087			0.0885433	+	0.996072i	$0.471779\pi$
$132$		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	−0.921946	−	0.387318i	$-0.873401\pi$
$137$	−4.72561	−	14.5439i	−0.403736	−	1.24257i	0.518210	−	0.855253i	$-0.326599\pi$
$138$		0			0
$139$	17.4123	+	12.6508i	1.47690	+	1.07303i	0.978541	+	0.206054i	$0.0660624\pi$
$139$	17.4123	+	12.6508i	1.47690	+	1.07303i	0.498355	+	0.866973i	$0.333938\pi$
$140$	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	$-0.115802\pi$
$149$	−0.374352	−	1.15214i	−0.0306681	−	0.0943867i	−0.965219	+	0.261443i	$0.915802\pi$
$150$		0			0
$151$	−7.86153	+	5.71174i	−0.639763	+	0.464815i	−0.859769	−	0.510684i	$-0.829392\pi$
$151$	−7.86153	+	5.71174i	−0.639763	+	0.464815i	0.220006	+	0.975499i	$0.429392\pi$
$152$	−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	−0.975522	−	0.219904i	$-0.929426\pi$
$157$	−13.3799	+	9.72108i	−1.06783	+	0.775827i	−0.0923120	+	0.995730i	$0.529426\pi$
$158$	−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	−0.999929	−	0.0119314i	$-0.996202\pi$
$163$	−2.34860	+	7.22824i	−0.183956	+	0.566159i	0.815973	+	0.578091i	$0.196202\pi$
$164$	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	$-0.849471\pi$
$167$	1.26252	−	3.88564i	0.0976969	−	0.300680i	0.987947	+	0.154792i	$0.0494706\pi$
$168$		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	$-0.661027\pi$
$173$	2.59920	−	1.88843i	0.197614	−	0.143575i	0.682192	+	0.731173i	$0.261027\pi$
$174$		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	$-0.697528\pi$
$179$	0.168133	−	0.122156i	0.0125669	−	0.00913035i	0.594051	+	0.804427i	$0.297528\pi$
$180$		0			0
$181$	−1.62394	−	4.99798i	−0.120707	−	0.371497i	0.872388	−	0.488814i	$-0.162570\pi$
$181$	−1.62394	−	4.99798i	−0.120707	−	0.371497i	−0.993094	+	0.117318i	$0.962570\pi$
$182$	−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	$-0.268767\pi$
$191$	2.19062	+	1.59158i	0.158508	+	0.115162i	−0.505704	+	0.862707i	$0.668767\pi$
$192$		0			0
$193$	−5.09565	−	15.6828i	−0.366793	−	1.12887i	−0.948851	−	0.315726i	$-0.897752\pi$
$193$	−5.09565	−	15.6828i	−0.366793	−	1.12887i	0.582057	−	0.813148i	$-0.302248\pi$
$194$	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	$-0.463453\pi$
$197$	3.21597			0.229128			0.114564	+	0.993416i	$0.463453\pi$
$198$		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	−0.885075	−	0.465448i	$-0.845893\pi$
$211$	1.51867	−	4.67398i	0.104549	−	0.321770i	0.989624	+	0.143678i	$0.0458930\pi$
$212$	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	−0.556036	−	0.831158i	$-0.687678\pi$
$223$	0.935085	−	0.679379i	0.0626180	−	0.0454946i	0.618654	+	0.785664i	$0.287678\pi$
$224$	−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	$-0.272245\pi$
$227$	2.12294	+	1.54241i	0.140905	+	0.102373i	−0.515100	+	0.857130i	$0.672245\pi$
$228$		0			0
$229$	−3.34613	+	10.2983i	−0.221119	+	0.680533i	0.777544	+	0.628829i	$0.216465\pi$
$229$	−3.34613	+	10.2983i	−0.221119	+	0.680533i	−0.998662	+	0.0517042i	$0.983535\pi$
$230$	34.3410			2.26438
$231$		0			0
$232$	−4.39352			−0.288449
$233$	5.18859	−	15.9688i	0.339916	−	1.04615i	−0.624334	−	0.781157i	$-0.714630\pi$
$233$	5.18859	−	15.9688i	0.339916	−	1.04615i	0.964250	−	0.264995i	$-0.0853704\pi$
$234$		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	$-0.836501\pi$
$239$	−10.4011	+	7.55682i	−0.672789	+	0.488810i	0.198169	+	0.980168i	$0.436501\pi$
$240$		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	−0.346871	−	0.937913i	$-0.612756\pi$
$251$	7.68456	−	23.6506i	0.485045	−	1.49282i	0.831916	−	0.554902i	$-0.187244\pi$
$252$		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	$-0.167150\pi$
$257$	10.5144	+	7.63916i	0.655870	+	0.476518i	−0.209395	+	0.977831i	$0.567150\pi$
$258$		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	$-0.832851\pi$
$263$	−28.0645			−1.73053			−0.865266	+	0.501313i	$0.832851\pi$
$264$		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	−0.638094	−	0.769958i	$-0.720277\pi$
$269$	−9.42144	−	28.9962i	−0.574435	−	1.76793i	0.0636587	−	0.997972i	$-0.479723\pi$
$270$		0			0
$271$	0.0968832	+	0.0703897i	0.00588523	+	0.00427587i	0.590724	−	0.806874i	$-0.298842\pi$
$271$	0.0968832	+	0.0703897i	0.00588523	+	0.00427587i	−0.584839	+	0.811150i	$0.698842\pi$
$272$	−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	−0.989642	−	0.143560i	$-0.954145\pi$
$277$	−1.74126	+	5.35904i	−0.104622	+	0.321994i	0.885019	+	0.465554i	$0.154145\pi$
$278$	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	$-0.0603434\pi$
$281$	1.28738	+	3.96215i	0.0767987	+	0.236362i	−0.905286	+	0.424803i	$0.860343\pi$
$282$		0			0
$283$	−11.0630	+	8.03774i	−0.657627	+	0.477794i	−0.865861	−	0.500285i	$-0.833229\pi$
$283$	−11.0630	+	8.03774i	−0.657627	+	0.477794i	0.208234	+	0.978079i	$0.433229\pi$
$284$	−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	$-0.271230\pi$
$293$	2.49991	+	1.81629i	0.146046	+	0.106109i	−0.512363	+	0.858769i	$0.671230\pi$
$294$		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	$-0.631307\pi$
$311$	6.11017	−	4.43930i	0.346476	−	0.251730i	0.747389	+	0.664386i	$0.231307\pi$
$312$		0			0
$313$	1.49793	+	4.61015i	0.0846679	+	0.260581i	0.984424	−	0.175813i	$-0.0562554\pi$
$313$	1.49793	+	4.61015i	0.0846679	+	0.260581i	−0.899756	+	0.436394i	$0.856255\pi$
$314$	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	0.193650	+	0.981071i	$0.437967\pi$
$317$	−9.60864	+	29.5724i	−0.539675	+	1.66095i	−0.733325	+	0.679878i	$0.762033\pi$
$318$		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	0.441638	−	0.897193i	$-0.354398\pi$
$337$	−5.05145	−	3.67010i	−0.275170	−	0.199923i	−0.716808	+	0.697271i	$0.754398\pi$
$338$	−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	$-0.113267\pi$
$347$	−0.479695	−	1.47635i	−0.0257514	−	0.0792546i	−0.963106	+	0.269121i	$0.913267\pi$
$348$		0			0
$349$	4.61727	−	3.35464i	0.247157	−	0.179570i	−0.457309	−	0.889308i	$-0.651187\pi$
$349$	4.61727	−	3.35464i	0.247157	−	0.179570i	0.704466	+	0.709738i	$0.251187\pi$
$350$	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	$-0.350197\pi$
$353$	17.0387			0.906877			0.453438	+	0.891288i	$0.350197\pi$
$354$		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	$-0.155950\pi$
$359$	13.4051	+	9.73939i	0.707495	+	0.514025i	−0.174870	+	0.984592i	$0.555950\pi$
$360$		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	0.0679542	−	0.997688i	$-0.478353\pi$
$367$	−16.4734	−	11.9686i	−0.859905	−	0.624757i	−0.927859	+	0.372931i	$0.878353\pi$
$368$	−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	0.999807	+	0.0196248i	$0.00624718\pi$
$379$	3.94189	+	12.1319i	0.202481	+	0.623174i	−0.797326	+	0.603549i	$0.793753\pi$
$380$	−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	$-0.997032\pi$
$383$	−3.63020	+	11.1726i	−0.185494	+	0.570893i	0.814462	+	0.580217i	$0.197032\pi$
$384$		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	$-0.596970\pi$
$389$	−25.6381	−	18.6272i	−1.29990	−	0.944436i	−0.999955	+	0.00951928i	$0.996970\pi$
$390$		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	$-0.163535\pi$
$401$	−2.45393	−	7.55243i	−0.122544	−	0.377150i	−0.993446	+	0.114307i	$0.963535\pi$
$402$		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	−0.962425	−	0.271548i	$-0.912464\pi$
$409$	−0.489307	+	1.50593i	−0.0241947	+	0.0744635i	0.938230	+	0.346012i	$0.112464\pi$
$410$	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	$-0.645282\pi$
$419$	−18.0433			−0.881472			−0.440736	+	0.897637i	$0.645282\pi$
$420$		0			0
$421$	5.63461	−	4.09379i	0.274614	−	0.199519i	−0.441951	−	0.897039i	$-0.645713\pi$
$421$	5.63461	−	4.09379i	0.274614	−	0.199519i	0.716565	+	0.697520i	$0.245713\pi$
$422$	−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	0.595614	+	0.803271i	$0.296909\pi$
$431$	−7.44055	+	22.8997i	−0.358399	+	1.10304i	−0.954013	+	0.299767i	$0.903091\pi$
$432$		0			0
$433$	19.6338	+	14.2648i	0.943542	+	0.685523i	0.949271	−	0.314461i	$-0.101824\pi$
$433$	19.6338	+	14.2648i	0.943542	+	0.685523i	−0.00572899	+	0.999984i	$0.501824\pi$
$434$	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	$-0.494567\pi$
$443$	20.4847	−	14.8830i	0.973258	−	0.707114i	0.956192	+	0.292741i	$0.0945673\pi$
$444$		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	−0.661130	−	0.750272i	$-0.729923\pi$
$449$	6.66910	−	20.5254i	0.314734	−	0.968652i	0.975864	−	0.218380i	$-0.0700773\pi$
$450$		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	0.900359	+	0.435148i	$0.143304\pi$
$457$	9.14375	+	28.1416i	0.427727	+	1.31641i	−0.472632	+	0.881260i	$0.656696\pi$
$458$	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	$-0.359985\pi$
$461$	18.2856			0.851643			0.425821	+	0.904807i	$0.359985\pi$
$462$		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	−0.849080	−	0.528265i	$-0.822843\pi$
$467$	−10.2144	−	31.4367i	−0.472666	−	1.45472i	0.376413	−	0.926452i	$-0.377157\pi$
$468$		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	$-0.0398133\pi$
$479$	2.54237	+	7.82463i	0.116164	+	0.357516i	−0.876024	+	0.482268i	$0.839813\pi$
$480$		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	−0.851087	−	0.525025i	$-0.824056\pi$
$487$	−13.5666	+	9.85668i	−0.614759	+	0.446649i	0.236328	+	0.971673i	$0.424056\pi$
$488$	−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	$-0.136595\pi$
$491$	17.6075	+	12.7926i	0.794616	+	0.577322i	−0.114714	+	0.993399i	$0.536595\pi$
$492$		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	−0.0337838	−	0.999429i	$-0.510756\pi$
$499$	−22.2207	−	16.1443i	−0.994737	−	0.722719i	−0.960953	+	0.276710i	$0.910756\pi$
$500$	−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	$-0.588324\pi$
$503$	12.4720	−	9.06143i	0.556098	−	0.404029i	0.830029	+	0.557720i	$0.188324\pi$
$504$		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	$-0.883216\pi$
$509$	−19.8705	+	14.4367i	−0.880742	+	0.639897i	0.0527054	+	0.998610i	$0.483216\pi$
$510$		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	$-0.214004\pi$
$521$	9.85691	+	7.16146i	0.431839	+	0.313749i	−0.350545	+	0.936546i	$0.614004\pi$
$522$		0			0
$523$	9.22433	+	28.3896i	0.403352	+	1.24139i	0.922264	+	0.386562i	$0.126337\pi$
$523$	9.22433	+	28.3896i	0.403352	+	1.24139i	−0.518912	+	0.854828i	$0.673663\pi$
$524$	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	0.435125	+	0.900370i	$0.356704\pi$
$541$	−10.3766	+	31.9357i	−0.446123	+	1.37303i	−0.881248	+	0.472655i	$0.843296\pi$
$542$	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	−0.934768	−	0.355258i	$-0.884393\pi$
$547$	−20.7161	+	15.0511i	−0.885757	+	0.643540i	0.0490113	+	0.998798i	$0.484393\pi$
$548$	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	$-0.339609\pi$
$557$	−4.73952	−	3.44347i	−0.200820	−	0.145904i	−0.683651	+	0.729810i	$0.739609\pi$
$558$		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	$-0.941519\pi$
$563$	−1.90737	+	5.87028i	−0.0803861	+	0.247403i	0.902784	+	0.430093i	$0.141519\pi$
$564$		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	$-0.508388\pi$
$569$	21.8556	−	15.8790i	0.916235	−	0.665684i	0.942584	+	0.333969i	$0.108388\pi$
$570$		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	0.875652	−	0.482942i	$-0.160432\pi$
$577$	−2.80159	−	8.62241i	−0.116632	−	0.358955i	−0.992284	+	0.123987i	$0.960432\pi$
$578$	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	$-0.255321\pi$
$587$	5.48448	+	3.98471i	0.226369	+	0.164466i	−0.468820	+	0.883294i	$0.655321\pi$
$588$		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	$-0.730245\pi$
$593$	−32.2361			−1.32378			−0.661890	+	0.749601i	$0.730245\pi$
$594$		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	0.965699	+	0.259664i	$0.0836117\pi$
$599$	8.24933	+	25.3888i	0.337059	+	1.03736i	−0.628640	+	0.777696i	$0.716388\pi$
$600$		0			0
$601$	−3.44843	−	2.50543i	−0.140664	−	0.102199i	0.515228	−	0.857053i	$-0.327707\pi$
$601$	−3.44843	−	2.50543i	−0.140664	−	0.102199i	−0.655892	+	0.754855i	$0.727707\pi$
$602$	−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	−0.897706	−	0.440595i	$-0.854767\pi$
$607$	2.15648	−	6.63696i	0.0875288	−	0.269386i	0.985235	+	0.171209i	$0.0547674\pi$
$608$	−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	−0.0898971	−	0.995951i	$-0.528654\pi$
$613$	20.5382	−	14.9219i	0.829529	−	0.602688i	0.919426	+	0.393263i	$0.128654\pi$
$614$	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	$-0.552819\pi$
$617$	−8.20576			−0.330351			−0.165176	+	0.986264i	$0.552819\pi$
$618$		0			0
$619$	3.43228	−	2.49370i	0.137955	−	0.100230i	−0.516667	−	0.856186i	$-0.672828\pi$
$619$	3.43228	−	2.49370i	0.137955	−	0.100230i	0.654622	+	0.755956i	$0.272828\pi$
$620$	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	−0.165783	−	0.986162i	$-0.553015\pi$
$631$	−29.0110	−	21.0777i	−1.15491	−	0.839090i	−0.989126	+	0.147072i	$0.953015\pi$
$632$	−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	$-0.908819\pi$
$641$	−24.9876	+	18.1546i	−0.986953	+	0.717063i	−0.0277010	+	0.999616i	$0.508819\pi$
$642$		0			0
$643$	3.44185	+	10.5929i	0.135733	+	0.417745i	0.995703	−	0.0926001i	$-0.0295178\pi$
$643$	3.44185	+	10.5929i	0.135733	+	0.417745i	−0.859970	+	0.510345i	$0.829518\pi$
$644$	−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	−0.764497	−	0.644627i	$-0.777012\pi$
$647$	5.92400	−	18.2322i	0.232897	−	0.716782i	0.997393	−	0.0721546i	$-0.0229875\pi$
$648$		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	$-0.339548\pi$
$653$	−5.12386	−	3.72270i	−0.200512	−	0.145681i	−0.683511	+	0.729941i	$0.739548\pi$
$654$		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	$-0.722414\pi$
$659$	−33.0256			−1.28650			−0.643248	+	0.765658i	$0.722414\pi$
$660$		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	0.711285	+	0.702903i	$0.248113\pi$
$673$	−7.19412	+	22.1412i	−0.277313	+	0.853481i	−0.988598	+	0.150578i	$0.951887\pi$
$674$	−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	$-0.172262\pi$
$677$	−3.61932	−	11.1391i	−0.139102	−	0.428112i	−0.996205	+	0.0870325i	$0.972262\pi$
$678$		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	$-0.368869\pi$
$683$	20.9286			0.800811			0.400405	+	0.916338i	$0.368869\pi$
$684$		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	−0.916859	−	0.399211i	$-0.869284\pi$
$691$	1.56528	−	4.81743i	0.0595459	−	0.183264i	0.976405	+	0.215948i	$0.0692840\pi$
$692$	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	$-0.489436\pi$
$701$	26.3167	−	19.1202i	0.993970	−	0.722161i	0.960787	+	0.277288i	$0.0894356\pi$
$702$		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	0.998561	−	0.0536328i	$-0.0170801\pi$
$709$	4.23859	+	13.0450i	0.159184	+	0.489917i	−0.839377	+	0.543549i	$0.817080\pi$
$710$	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	$-4.12621e-5\pi$
$719$	35.0969	+	25.4994i	1.30889	+	0.950967i	0.308894	+	0.951097i	$0.400041\pi$
$720$		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	0.771997	−	0.635626i	$-0.219258\pi$
$733$	10.9931	+	7.98698i	0.406040	+	0.295006i	−0.365956	+	0.930632i	$0.619258\pi$
$734$	−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	−0.726776	−	0.686875i	$-0.758982\pi$
$739$	7.20209	−	22.1658i	0.264933	−	0.815381i	0.991709	−	0.128506i	$-0.0410180\pi$
$740$	−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	−0.996151	−	0.0876561i	$-0.972062\pi$
$743$	−6.59020	−	20.2825i	−0.241771	−	0.744094i	0.754380	−	0.656438i	$-0.227938\pi$
$744$		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	−0.707161	−	0.707053i	$-0.750024\pi$
$751$	−6.93984	+	5.04209i	−0.253239	+	0.183989i	0.453922	+	0.891041i	$0.350024\pi$
$752$	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	0.104299	+	0.994546i	$0.466740\pi$
$757$	−15.5359	+	47.8144i	−0.564660	+	1.73785i	−0.668959	+	0.743299i	$0.733260\pi$
$758$	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	$-0.961133\pi$
$761$	−3.25429	+	10.0157i	−0.117968	+	0.363068i	0.874586	+	0.484870i	$0.161133\pi$
$762$		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	$-0.789388\pi$
$773$	−12.4676	+	9.05826i	−0.448429	+	0.325803i	0.340546	+	0.940228i	$0.389388\pi$
$774$		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	0.994433	−	0.105370i	$-0.0336025\pi$
$787$	3.59043	+	11.0502i	0.127985	+	0.393898i	−0.866448	+	0.499267i	$0.833603\pi$
$788$	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	$-0.0509359\pi$
$797$	2.67876	+	8.24439i	0.0948867	+	0.292031i	−0.892337	+	0.451369i	$0.850936\pi$
$798$		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	$-0.191804\pi$
$809$	−4.99988	−	15.3881i	−0.175787	−	0.541015i	−0.999669	+	0.0257461i	$0.991804\pi$
$810$		0			0
$811$	−3.70872	+	2.69455i	−0.130231	+	0.0946183i	−0.650994	−	0.759083i	$-0.725648\pi$
$811$	−3.70872	+	2.69455i	−0.130231	+	0.0946183i	0.520763	+	0.853701i	$0.325648\pi$
$812$	−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	0.999880	+	0.0155159i	$0.00493907\pi$
$821$	37.9257	+	27.5546i	1.32362	+	0.961663i	0.323736	+	0.946147i	$0.395061\pi$
$822$		0			0
$823$	−0.251597	+	0.774335i	−0.00877010	+	0.0269916i	−0.955346	−	0.295490i	$-0.904517\pi$
$823$	−0.251597	+	0.774335i	−0.00877010	+	0.0269916i	0.946576	+	0.322482i	$0.104517\pi$
$824$	−11.3485			−0.395345
$825$		0			0
$826$	3.93190			0.136808
$827$	−8.18806	+	25.2003i	−0.284727	+	0.876299i	0.701754	+	0.712420i	$0.252401\pi$
$827$	−8.18806	+	25.2003i	−0.284727	+	0.876299i	−0.986480	+	0.163879i	$0.947599\pi$
$828$		0			0
$829$	−26.6403	−	19.3553i	−0.925256	−	0.672238i	0.0195709	−	0.999808i	$-0.493770\pi$
$829$	−26.6403	−	19.3553i	−0.925256	−	0.672238i	−0.944827	+	0.327571i	$0.893770\pi$
$830$	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	$-0.882602\pi$
$839$	−25.4353	+	18.4799i	−0.878126	+	0.637996i	0.0546294	+	0.998507i	$0.482602\pi$
$840$		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	−0.677302	−	0.735705i	$-0.736851\pi$
$853$	−16.4077	−	50.4978i	−0.561790	−	1.72901i	0.115512	−	0.993306i	$-0.463149\pi$
$854$	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	$-0.270165\pi$
$857$	38.6964			1.32185			0.660923	+	0.750454i	$0.270165\pi$
$858$		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	$-0.0184911\pi$
$863$	4.59850	+	14.1527i	0.156535	+	0.481764i	−0.841779	+	0.539823i	$0.818491\pi$
$864$		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	−0.984806	−	0.173657i	$-0.944441\pi$
$877$	−33.2855	+	24.1833i	−1.12397	+	0.816612i	−0.139164	+	0.990269i	$0.544441\pi$
$878$	−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	$-0.548615\pi$
$881$	−9.03118			−0.304268			−0.152134	+	0.988360i	$0.548615\pi$
$882$		0			0
$883$	−24.7492	+	17.9813i	−0.832876	+	0.605120i	−0.920371	−	0.391045i	$-0.872114\pi$
$883$	−24.7492	+	17.9813i	−0.832876	+	0.605120i	0.0874959	+	0.996165i	$0.472114\pi$
$884$	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	$-0.466452\pi$
$887$	−24.0665	−	17.4853i	−0.808073	−	0.587099i	−0.913271	+	0.407352i	$0.866452\pi$
$888$		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	0.923625	+	0.383296i	$0.125211\pi$
$907$	12.0976	+	37.2325i	0.401693	+	1.23628i	−0.521933	+	0.852987i	$0.674789\pi$
$908$	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	0.699316	+	0.714813i	$0.253488\pi$
$911$	−8.65035	+	26.6231i	−0.286599	+	0.882061i	−0.985915	+	0.167248i	$0.946512\pi$
$912$		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	−0.931050	−	0.364892i	$-0.881106\pi$
$919$	−11.8924	−	36.6009i	−0.392293	−	1.20735i	0.538757	−	0.842461i	$-0.318894\pi$
$920$	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	−0.840612	−	0.541638i	$-0.817804\pi$
$929$	−14.5969	−	44.9247i	−0.478910	−	1.47393i	0.361702	−	0.932294i	$-0.382196\pi$
$930$		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	0.447934	+	0.894066i	$0.352160\pi$
$937$	−13.4677	+	41.4494i	−0.439971	+	1.35409i	−0.887906	+	0.460026i	$0.847840\pi$
$938$	−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	−0.963869	−	0.266378i	$-0.914173\pi$
$941$	−10.4499	−	32.1614i	−0.340656	−	1.04843i	0.623213	−	0.782052i	$-0.285827\pi$
$942$		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	$-0.480379\pi$
$947$	3.79141			0.123204			0.0616021	+	0.998101i	$0.480379\pi$
$948$		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	$-0.283650\pi$
$953$	2.56452	+	1.86323i	0.0830729	+	0.0603560i	−0.545474	+	0.838128i	$0.683650\pi$
$954$		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	$-0.594893\pi$
$971$	16.3478	−	11.8774i	0.524626	−	0.381163i	0.818344	+	0.574729i	$0.194893\pi$
$972$		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	−0.625419	−	0.780289i	$-0.715072\pi$
$977$	10.6023	−	32.6306i	0.339198	−	1.04394i	0.964617	−	0.263656i	$-0.0849282\pi$
$978$		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	$-0.123272\pi$
$983$	26.7408	+	19.4283i	0.852898	+	0.619667i	−0.0730454	+	0.997329i	$0.523272\pi$
$984$		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	0.618295	−	0.785946i	$-0.287824\pi$
$997$	1.95384	+	1.41955i	0.0618789	+	0.0449576i	−0.556416	+	0.830904i	$0.687824\pi$
$998$	−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.64.6	yes	32
3.2	odd	2	inner	693.2.m.k.64.3	✓	32
11.4	even	5		7623.2.a.dc.1.12		16
11.5	even	5	inner	693.2.m.k.379.6	yes	32
11.7	odd	10		7623.2.a.db.1.5		16
33.5	odd	10	inner	693.2.m.k.379.3	yes	32
33.26	odd	10		7623.2.a.dc.1.5		16
33.29	even	10		7623.2.a.db.1.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.m.k.64.3	✓	32	3.2	odd	2	inner
693.2.m.k.64.6	yes	32	1.1	even	1	trivial
693.2.m.k.379.3	yes	32	33.5	odd	10	inner
693.2.m.k.379.6	yes	32	11.5	even	5	inner
7623.2.a.db.1.5		16	11.7	odd	10
7623.2.a.db.1.12		16	33.29	even	10
7623.2.a.dc.1.5		16	33.26	odd	10
7623.2.a.dc.1.12		16	11.4	even	5

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

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