LMFDB - Embedded newform 864.2.v.b.109.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(109,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("864.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.v (of order $8$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.6
Character	$\chi$	$=$	864.109
Dual form			864.2.v.b.325.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14607 - 0.828563i) q^{2} +(0.626968 + 1.89919i) q^{4} +(-2.89399 + 1.19873i) q^{5} +(-3.03933 + 3.03933i) q^{7} +(0.855044 - 2.69609i) q^{8} +O(q^{10})$	\(q+(-1.14607 - 0.828563i) q^{2} +(0.626968 + 1.89919i) q^{4} +(-2.89399 + 1.19873i) q^{5} +(-3.03933 + 3.03933i) q^{7} +(0.855044 - 2.69609i) q^{8} +(4.30995 + 1.02402i) q^{10} +(-2.07833 - 5.01753i) q^{11} +(0.154565 + 0.0640231i) q^{13} +(6.00158 - 0.965021i) q^{14} +(-3.21382 + 2.38146i) q^{16} +4.77723i q^{17} +(-3.30151 - 1.36753i) q^{19} +(-4.09106 - 4.74467i) q^{20} +(-1.77542 + 7.47248i) q^{22} +(1.87996 + 1.87996i) q^{23} +(3.40271 - 3.40271i) q^{25} +(-0.124096 - 0.201442i) q^{26} +(-7.67783 - 3.86670i) q^{28} +(1.81073 - 4.37148i) q^{29} +9.71647 q^{31} +(5.65646 - 0.0664742i) q^{32} +(3.95824 - 5.47506i) q^{34} +(5.15247 - 12.4392i) q^{35} +(8.56912 - 3.54945i) q^{37} +(2.65069 + 4.30280i) q^{38} +(0.757396 + 8.82744i) q^{40} +(-3.98159 - 3.98159i) q^{41} +(-0.172185 - 0.415692i) q^{43} +(8.22618 - 7.09296i) q^{44} +(-0.596908 - 3.71224i) q^{46} -6.11328i q^{47} -11.4751i q^{49} +(-6.71911 + 1.08040i) q^{50} +(-0.0246842 + 0.333689i) q^{52} +(2.21266 + 5.34183i) q^{53} +(12.0293 + 12.0293i) q^{55} +(5.59555 + 10.7931i) q^{56} +(-5.69727 + 3.50974i) q^{58} +(2.09529 - 0.867896i) q^{59} +(-3.46853 + 8.37378i) q^{61} +(-11.1358 - 8.05070i) q^{62} +(-6.53780 - 4.61055i) q^{64} -0.524058 q^{65} +(4.88800 - 11.8007i) q^{67} +(-9.07286 + 2.99517i) q^{68} +(-16.2117 + 9.98705i) q^{70} +(-8.20687 + 8.20687i) q^{71} +(-1.88142 - 1.88142i) q^{73} +(-12.7618 - 3.03213i) q^{74} +(0.527254 - 7.12759i) q^{76} +(21.5667 + 8.93321i) q^{77} -15.0641i q^{79} +(6.44605 - 10.7444i) q^{80} +(1.26420 + 7.86220i) q^{82} +(1.42473 + 0.590143i) q^{83} +(-5.72662 - 13.8253i) q^{85} +(-0.147090 + 0.619080i) q^{86} +(-15.3048 + 1.31315i) q^{88} +(-1.32189 + 1.32189i) q^{89} +(-0.664364 + 0.275188i) q^{91} +(-2.39172 + 4.74908i) q^{92} +(-5.06523 + 7.00626i) q^{94} +11.1939 q^{95} -1.06320 q^{97} +(-9.50784 + 13.1513i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) $ 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.14607	−	0.828563i	−0.810396	−	0.585882i
$2$	−1.14607	−	0.828563i	−0.810396	−	0.585882i
$3$		0			0
$3$		0			0
$4$	0.626968	+	1.89919i	0.313484	+	0.949593i
$5$	−2.89399	+	1.19873i	−1.29423	+	0.536089i	−0.920244	−	0.391344i	$-0.872010\pi$
$5$	−2.89399	+	1.19873i	−1.29423	+	0.536089i	−0.373989	+	0.927433i	$0.622010\pi$
$6$		0			0
$7$	−3.03933	+	3.03933i	−1.14876	+	1.14876i	−0.161964	+	0.986797i	$0.551783\pi$
$7$	−3.03933	+	3.03933i	−1.14876	+	1.14876i	−0.986797	+	0.161964i	$0.948217\pi$
$8$	0.855044	−	2.69609i	0.302304	−	0.953212i
$9$		0			0
$10$	4.30995	+	1.02402i	1.36293	+	0.323824i
$11$	−2.07833	−	5.01753i	−0.626639	−	1.51284i	−0.843774	−	0.536699i	$-0.819671\pi$
$11$	−2.07833	−	5.01753i	−0.626639	−	1.51284i	0.217134	−	0.976142i	$-0.430329\pi$
$12$		0			0
$13$	0.154565	+	0.0640231i	0.0428687	+	0.0177568i	0.404015	−	0.914752i	$-0.367614\pi$
$13$	0.154565	+	0.0640231i	0.0428687	+	0.0177568i	−0.361146	+	0.932509i	$0.617614\pi$
$14$	6.00158	−	0.965021i	1.60399	−	0.257913i
$15$		0			0
$16$	−3.21382	+	2.38146i	−0.803456	+	0.595365i
$17$			4.77723i			1.15865i	0.815097	+	0.579325i	$0.196684\pi$
$17$			4.77723i			1.15865i	−0.815097	+	0.579325i	$0.803316\pi$
$18$		0			0
$19$	−3.30151	−	1.36753i	−0.757419	−	0.313733i	−0.0296543	−	0.999560i	$-0.509441\pi$
$19$	−3.30151	−	1.36753i	−0.757419	−	0.313733i	−0.727765	+	0.685827i	$0.759441\pi$
$20$	−4.09106	−	4.74467i	−0.914788	−	1.06094i
$21$		0			0
$22$	−1.77542	+	7.47248i	−0.378521	+	1.59314i
$23$	1.87996	+	1.87996i	0.391999	+	0.391999i	0.875399	−	0.483400i	$-0.160598\pi$
$23$	1.87996	+	1.87996i	0.391999	+	0.391999i	−0.483400	+	0.875399i	$0.660598\pi$
$24$		0			0
$25$	3.40271	−	3.40271i	0.680542	−	0.680542i
$26$	−0.124096	−	0.201442i	−0.0243373	−	0.0395061i
$27$		0			0
$28$	−7.67783	−	3.86670i	−1.45097	−	0.730737i
$29$	1.81073	−	4.37148i	0.336243	−	0.811763i	−0.661826	−	0.749657i	$-0.730218\pi$
$29$	1.81073	−	4.37148i	0.336243	−	0.811763i	0.998070	−	0.0621060i	$-0.0197817\pi$
$30$		0			0
$31$	9.71647			1.74513			0.872565	−	0.488499i	$-0.162455\pi$
$31$	9.71647			1.74513			0.872565	+	0.488499i	$0.162455\pi$
$32$	5.65646	−	0.0664742i	0.999931	−	0.0117511i
$33$		0			0
$34$	3.95824	−	5.47506i	0.678832	−	0.938965i
$35$	5.15247	−	12.4392i	0.870926	−	2.10260i
$36$		0			0
$37$	8.56912	−	3.54945i	1.40876	−	0.583526i	0.456747	−	0.889597i	$-0.349015\pi$
$37$	8.56912	−	3.54945i	1.40876	−	0.583526i	0.952009	+	0.306071i	$0.0990146\pi$
$38$	2.65069	+	4.30280i	0.429999	+	0.698006i
$39$		0			0
$40$	0.757396	+	8.82744i	0.119755	+	1.39574i
$41$	−3.98159	−	3.98159i	−0.621821	−	0.621821i	0.324176	−	0.945997i	$-0.394913\pi$
$41$	−3.98159	−	3.98159i	−0.621821	−	0.621821i	−0.945997	+	0.324176i	$0.894913\pi$
$42$		0			0
$43$	−0.172185	−	0.415692i	−0.0262580	−	0.0633924i	0.910207	−	0.414154i	$-0.135923\pi$
$43$	−0.172185	−	0.415692i	−0.0262580	−	0.0633924i	−0.936465	+	0.350762i	$0.885923\pi$
$44$	8.22618	−	7.09296i	1.24014	−	1.06930i
$45$		0			0
$46$	−0.596908	−	3.71224i	−0.0880093	−	0.547340i
$47$		−	6.11328i		−	0.891713i	−0.895104	−	0.445856i	$-0.852899\pi$
$47$		−	6.11328i		−	0.891713i	0.895104	−	0.445856i	$-0.147101\pi$
$48$		0			0
$49$		−	11.4751i		−	1.63930i
$50$	−6.71911	+	1.08040i	−0.950226	+	0.152791i
$51$		0			0
$52$	−0.0246842	+	0.333689i	−0.00342309	+	0.0462743i
$53$	2.21266	+	5.34183i	0.303932	+	0.733757i	0.999877	+	0.0156620i	$0.00498558\pi$
$53$	2.21266	+	5.34183i	0.303932	+	0.733757i	−0.695945	+	0.718095i	$0.745014\pi$
$54$		0			0
$55$	12.0293	+	12.0293i	1.62204	+	1.62204i
$56$	5.59555	+	10.7931i	0.747737	+	1.44229i
$57$		0			0
$58$	−5.69727	+	3.50974i	−0.748088	+	0.460851i
$59$	2.09529	−	0.867896i	0.272783	−	0.112990i	−0.242099	−	0.970252i	$-0.577836\pi$
$59$	2.09529	−	0.867896i	0.272783	−	0.112990i	0.514882	+	0.857261i	$0.327836\pi$
$60$		0			0
$61$	−3.46853	+	8.37378i	−0.444100	+	1.07215i	0.530396	+	0.847750i	$0.322043\pi$
$61$	−3.46853	+	8.37378i	−0.444100	+	1.07215i	−0.974496	+	0.224403i	$0.927957\pi$
$62$	−11.1358	−	8.05070i	−1.41425	−	1.02244i
$63$		0			0
$64$	−6.53780	−	4.61055i	−0.817225	−	0.576319i
$65$	−0.524058			−0.0650014
$66$		0			0
$67$	4.88800	−	11.8007i	0.597164	−	1.44168i	−0.279296	−	0.960205i	$-0.590101\pi$
$67$	4.88800	−	11.8007i	0.597164	−	1.44168i	0.876459	−	0.481476i	$-0.159899\pi$
$68$	−9.07286	+	2.99517i	−1.10025	+	0.363218i
$69$		0			0
$70$	−16.2117	+	9.98705i	−1.93767	+	1.19368i
$71$	−8.20687	+	8.20687i	−0.973976	+	0.973976i	−0.999670	−	0.0256934i	$-0.991821\pi$
$71$	−8.20687	+	8.20687i	−0.973976	+	0.973976i	0.0256934	+	0.999670i	$0.491821\pi$
$72$		0			0
$73$	−1.88142	−	1.88142i	−0.220204	−	0.220204i	0.588380	−	0.808584i	$-0.299766\pi$
$73$	−1.88142	−	1.88142i	−0.220204	−	0.220204i	−0.808584	+	0.588380i	$0.799766\pi$
$74$	−12.7618	−	3.03213i	−1.48353	−	0.352478i
$75$		0			0
$76$	0.527254	−	7.12759i	0.0604802	−	0.817590i
$77$	21.5667	+	8.93321i	2.45775	+	1.01803i
$78$		0			0
$79$		−	15.0641i		−	1.69485i	−0.530917	−	0.847424i	$-0.678152\pi$
$79$		−	15.0641i		−	1.69485i	0.530917	−	0.847424i	$-0.321848\pi$
$80$	6.44605	−	10.7444i	0.720690	−	1.20126i
$81$		0			0
$82$	1.26420	+	7.86220i	0.139607	+	0.868235i
$83$	1.42473	+	0.590143i	0.156385	+	0.0647766i	0.459503	−	0.888176i	$-0.348028\pi$
$83$	1.42473	+	0.590143i	0.156385	+	0.0647766i	−0.303118	+	0.952953i	$0.598028\pi$
$84$		0			0
$85$	−5.72662	−	13.8253i	−0.621139	−	1.49956i
$86$	−0.147090	+	0.619080i	−0.0158611	+	0.0667571i
$87$		0			0
$88$	−15.3048	+	1.31315i	−1.63149	+	0.139983i
$89$	−1.32189	+	1.32189i	−0.140120	+	0.140120i	−0.773687	−	0.633568i	$-0.781590\pi$
$89$	−1.32189	+	1.32189i	−0.140120	+	0.140120i	0.633568	+	0.773687i	$0.281590\pi$
$90$		0			0
$91$	−0.664364	+	0.275188i	−0.0696442	+	0.0288476i
$92$	−2.39172	+	4.74908i	−0.249354	+	0.495125i
$93$		0			0
$94$	−5.06523	+	7.00626i	−0.522439	+	0.722641i
$95$	11.1939			1.14847
$96$		0			0
$97$	−1.06320			−0.107952			−0.0539759	−	0.998542i	$-0.517189\pi$
$97$	−1.06320			−0.107952			−0.0539759	+	0.998542i	$0.517189\pi$
$98$	−9.50784	+	13.1513i	−0.960437	+	1.32848i
$99$		0			0
$100$	8.59577	+	4.32899i	0.859577	+	0.432899i
$101$	−5.27745	+	2.18599i	−0.525125	+	0.217514i	−0.629467	−	0.777027i	$-0.716727\pi$
$101$	−5.27745	+	2.18599i	−0.525125	+	0.217514i	0.104341	+	0.994542i	$0.466727\pi$
$102$		0			0
$103$	−4.14160	+	4.14160i	−0.408084	+	0.408084i	−0.881070	−	0.472986i	$-0.843176\pi$
$103$	−4.14160	+	4.14160i	−0.408084	+	0.408084i	0.472986	+	0.881070i	$0.343176\pi$
$104$	0.304772	−	0.361980i	0.0298854	−	0.0354950i
$105$		0			0
$106$	1.89017	−	7.95545i	0.183590	−	0.772702i
$107$	−4.42929	−	10.6932i	−0.428195	−	1.03376i	−0.979859	−	0.199689i	$-0.936007\pi$
$107$	−4.42929	−	10.6932i	−0.428195	−	1.03376i	0.551664	−	0.834066i	$-0.313993\pi$
$108$		0			0
$109$	12.2310	+	5.06625i	1.17152	+	0.485259i	0.881694	−	0.471821i	$-0.156403\pi$
$109$	12.2310	+	5.06625i	1.17152	+	0.485259i	0.289824	+	0.957080i	$0.406403\pi$
$110$	−3.81944	−	23.7536i	−0.364170	−	2.26481i
$111$		0			0
$112$	2.52983	−	17.0059i	0.239046	−	1.60691i
$113$		−	2.93674i		−	0.276265i	−0.990414	−	0.138133i	$-0.955890\pi$
$113$		−	2.93674i		−	0.276265i	0.990414	−	0.138133i	$-0.0441100\pi$
$114$		0			0
$115$	−7.69417	−	3.18703i	−0.717485	−	0.297192i
$116$	9.43752	+	0.698129i	0.876252	+	0.0648197i
$117$		0			0
$118$	−3.12046	−	0.741403i	−0.287261	−	0.0682517i
$119$	−14.5196	−	14.5196i	−1.33101	−	1.33101i
$120$		0			0
$121$	−13.0779	+	13.0779i	−1.18890	+	1.18890i
$122$	10.9134	−	6.72307i	0.988052	−	0.608678i
$123$		0			0
$124$	6.09192	+	18.4534i	0.547070	+	1.65716i
$125$	0.225172	−	0.543613i	0.0201400	−	0.0486222i
$126$		0			0
$127$	−1.29466			−0.114882			−0.0574412	−	0.998349i	$-0.518294\pi$
$127$	−1.29466			−0.114882			−0.0574412	+	0.998349i	$0.518294\pi$
$128$	3.67267	+	10.7010i	0.324621	+	0.945844i
$129$		0			0
$130$	0.600609	+	0.434215i	0.0526769	+	0.0380832i
$131$	−0.734568	+	1.77340i	−0.0641795	+	0.154943i	−0.952715	−	0.303864i	$-0.901723\pi$
$131$	−0.734568	+	1.77340i	−0.0641795	+	0.154943i	0.888536	+	0.458807i	$0.151723\pi$
$132$		0			0
$133$	14.1908	−	5.87801i	1.23050	−	0.509688i
$134$	−15.3796	+	9.47442i	−1.32859	+	0.818465i
$135$		0			0
$136$	12.8799	+	4.08474i	1.10444	+	0.350264i
$137$	7.45884	+	7.45884i	0.637252	+	0.637252i	0.949877	−	0.312625i	$-0.101208\pi$
$137$	7.45884	+	7.45884i	0.637252	+	0.637252i	−0.312625	+	0.949877i	$0.601208\pi$
$138$		0			0
$139$	−4.48857	−	10.8364i	−0.380716	−	0.919129i	−0.991828	−	0.127585i	$-0.959278\pi$
$139$	−4.48857	−	10.8364i	−0.380716	−	0.919129i	0.611112	−	0.791544i	$-0.290722\pi$
$140$	26.8547	+	1.98654i	2.26964	+	0.167894i
$141$		0			0
$142$	16.2056	−	2.60577i	1.35994	−	0.218671i
$143$		−	0.908597i		−	0.0759807i
$144$		0			0
$145$			14.8216i			1.23087i
$146$	0.597372	+	3.71513i	0.0494389	+	0.307466i
$147$		0			0
$148$	12.1136	+	14.0490i	0.995734	+	1.15482i
$149$	1.02055	+	2.46383i	0.0836068	+	0.201845i	0.960154	−	0.279471i	$-0.0901591\pi$
$149$	1.02055	+	2.46383i	0.0836068	+	0.201845i	−0.876547	+	0.481316i	$0.840159\pi$
$150$		0			0
$151$	−10.4711	−	10.4711i	−0.852128	−	0.852128i	0.138267	−	0.990395i	$-0.455847\pi$
$151$	−10.4711	−	10.4711i	−0.852128	−	0.852128i	−0.990395	+	0.138267i	$0.955847\pi$
$152$	−6.50992	+	7.73187i	−0.528025	+	0.627138i
$153$		0			0
$154$	−17.3153	−	28.1074i	−1.39530	−	2.26496i
$155$	−28.1194	+	11.6474i	−2.25860	+	0.935545i
$156$		0			0
$157$	3.37313	−	8.14346i	0.269205	−	0.649919i	−0.730241	−	0.683189i	$-0.760592\pi$
$157$	3.37313	−	8.14346i	0.269205	−	0.649919i	0.999446	+	0.0332707i	$0.0105923\pi$
$158$	−12.4816	+	17.2646i	−0.992981	+	1.37350i
$159$		0			0
$160$	−16.2901	+	6.97296i	−1.28784	+	0.551261i
$161$	−11.4277			−0.900626
$162$		0			0
$163$	8.77772	−	21.1913i	0.687524	−	1.65983i	−0.0621857	−	0.998065i	$-0.519807\pi$
$163$	8.77772	−	21.1913i	0.687524	−	1.65983i	0.749710	−	0.661766i	$-0.230193\pi$
$164$	5.06546	−	10.0581i	0.395546	−	0.785408i
$165$		0			0
$166$	−1.14388	−	1.85683i	−0.0887820	−	0.144118i
$167$	1.59009	−	1.59009i	0.123045	−	0.123045i	−0.642903	−	0.765948i	$-0.722270\pi$
$167$	1.59009	−	1.59009i	0.123045	−	0.123045i	0.765948	+	0.642903i	$0.222270\pi$
$168$		0			0
$169$	−9.17260	−	9.17260i	−0.705584	−	0.705584i
$170$	−4.89199	+	20.5897i	−0.375198	+	1.57915i
$171$		0			0
$172$	0.681522	−	0.587637i	0.0519656	−	0.0448069i
$173$	4.55540	+	1.88691i	0.346341	+	0.143459i	0.549071	−	0.835776i	$-0.314982\pi$
$173$	4.55540	+	1.88691i	0.346341	+	0.143459i	−0.202731	+	0.979235i	$0.564982\pi$
$174$		0			0
$175$			20.6839i			1.56356i
$176$	18.6284	+	11.1760i	1.40417	+	0.842421i
$177$		0			0
$178$	2.61025	−	0.419714i	0.195646	−	0.0314589i
$179$	13.9431	+	5.77541i	1.04215	+	0.431674i	0.837085	−	0.547073i	$-0.184258\pi$
$179$	13.9431	+	5.77541i	1.04215	+	0.431674i	0.205069	+	0.978747i	$0.434258\pi$
$180$		0			0
$181$	3.42297	+	8.26378i	0.254427	+	0.614242i	0.998552	−	0.0537992i	$-0.0171331\pi$
$181$	3.42297	+	8.26378i	0.254427	+	0.614242i	−0.744125	+	0.668041i	$0.767133\pi$
$182$	0.989420	+	0.235081i	0.0733407	+	0.0174253i
$183$		0			0
$184$	6.67600	−	3.46110i	0.492161	−	0.255155i
$185$	−20.5442	+	20.5442i	−1.51044	+	1.51044i
$186$		0			0
$187$	23.9699	−	9.92866i	1.75285	−	0.726055i
$188$	11.6103	−	3.83283i	0.846765	−	0.279538i
$189$		0			0
$190$	−12.8290	−	9.27481i	−0.930712	−	0.672866i
$191$	−0.522075			−0.0377760			−0.0188880	−	0.999822i	$-0.506013\pi$
$191$	−0.522075			−0.0377760			−0.0188880	+	0.999822i	$0.506013\pi$
$192$		0			0
$193$	10.9570			0.788705			0.394353	−	0.918959i	$-0.370969\pi$
$193$	10.9570			0.788705			0.394353	+	0.918959i	$0.370969\pi$
$194$	1.21851	+	0.880930i	0.0874838	+	0.0632471i
$195$		0			0
$196$	21.7934	−	7.19453i	1.55667	−	0.513895i
$197$	−20.1650	+	8.35262i	−1.43670	+	0.595100i	−0.958995	−	0.283422i	$-0.908530\pi$
$197$	−20.1650	+	8.35262i	−1.43670	+	0.595100i	−0.477702	+	0.878522i	$0.658530\pi$
$198$		0			0
$199$	−4.19008	+	4.19008i	−0.297027	+	0.297027i	−0.839848	−	0.542821i	$-0.817356\pi$
$199$	−4.19008	+	4.19008i	−0.297027	+	0.297027i	0.542821	+	0.839848i	$0.317356\pi$
$200$	−6.26454	−	12.0835i	−0.442970	−	0.854431i
$201$		0			0
$202$	7.85957	+	1.86739i	0.552997	+	0.131389i
$203$	7.78299	+	18.7898i	0.546259	+	1.31878i
$204$		0			0
$205$	16.2956	+	6.74985i	1.13813	+	0.471430i
$206$	8.17815	−	1.31500i	0.569798	−	0.0916205i
$207$		0			0
$208$	−0.649214	+	0.162332i	−0.0450149	+	0.0112557i
$209$			19.4076i			1.34245i
$210$		0			0
$211$	−5.32672	−	2.20640i	−0.366707	−	0.151895i	0.191718	−	0.981450i	$-0.438594\pi$
$211$	−5.32672	−	2.20640i	−0.366707	−	0.151895i	−0.558425	+	0.829555i	$0.688594\pi$
$212$	−8.75787	+	7.55141i	−0.601493	+	0.518633i
$213$		0			0
$214$	−3.78373	+	15.9252i	−0.258651	+	1.08862i
$215$	0.996606	+	0.996606i	0.0679680	+	0.0679680i
$216$		0			0
$217$	−29.5316	+	29.5316i	−2.00474	+	2.00474i
$218$	−9.81993	−	15.9405i	−0.665090	−	1.07962i
$219$		0			0
$220$	−15.3039	+	30.3880i	−1.03179	+	2.04876i
$221$	−0.305853	+	0.738395i	−0.0205739	+	0.0496698i
$222$		0			0
$223$	15.9884			1.07066			0.535332	−	0.844642i	$-0.320187\pi$
$223$	15.9884			1.07066			0.535332	+	0.844642i	$0.320187\pi$
$224$	−16.9898	+	17.3939i	−1.13518	+	1.16218i
$225$		0			0
$226$	−2.43327	+	3.36572i	−0.161859	+	0.223884i
$227$	7.20470	−	17.3937i	0.478192	−	1.15446i	−0.482263	−	0.876026i	$-0.660185\pi$
$227$	7.20470	−	17.3937i	0.478192	−	1.15446i	0.960456	−	0.278432i	$-0.0898148\pi$
$228$		0			0
$229$	−0.156196	+	0.0646985i	−0.0103217	+	0.00427540i	−0.387838	−	0.921727i	$-0.626778\pi$
$229$	−0.156196	+	0.0646985i	−0.0103217	+	0.00427540i	0.377517	+	0.926003i	$0.376778\pi$
$230$	6.17743	+	10.0277i	0.407328	+	0.661205i
$231$		0			0
$232$	−10.2377	−	8.61969i	−0.672135	−	0.565910i
$233$	20.4708	+	20.4708i	1.34108	+	1.34108i	0.894982	+	0.446102i	$0.147188\pi$
$233$	20.4708	+	20.4708i	1.34108	+	1.34108i	0.446102	+	0.894982i	$0.352812\pi$
$234$		0			0
$235$	7.32818	+	17.6918i	0.478038	+	1.15408i
$236$	2.96197	+	3.43520i	0.192808	+	0.223612i
$237$		0			0
$238$	4.61013	+	28.6709i	0.298830	+	1.85846i
$239$		−	29.7686i		−	1.92557i	−0.270270	−	0.962785i	$-0.587113\pi$
$239$		−	29.7686i		−	1.92557i	0.270270	−	0.962785i	$-0.412887\pi$
$240$		0			0
$241$			18.8662i			1.21528i	0.794212	+	0.607640i	$0.207884\pi$
$241$			18.8662i			1.21528i	−0.794212	+	0.607640i	$0.792116\pi$
$242$	25.8242	−	4.15239i	1.66004	−	0.266926i
$243$		0			0
$244$	−18.0780	−	1.33730i	−1.15733	−	0.0856119i
$245$	13.7556	+	33.2089i	0.878811	+	2.12164i
$246$		0			0
$247$	−0.422746	−	0.422746i	−0.0268987	−	0.0268987i
$248$	8.30801	−	26.1965i	0.527559	−	1.66348i
$249$		0			0
$250$	−0.708481	+	0.436451i	−0.0448083	+	0.0276036i
$251$	7.20956	−	2.98630i	0.455063	−	0.188493i	−0.143365	−	0.989670i	$-0.545792\pi$
$251$	7.20956	−	2.98630i	0.455063	−	0.188493i	0.598428	+	0.801177i	$0.295792\pi$
$252$		0			0
$253$	5.52558	−	13.3399i	0.347390	−	0.838675i
$254$	1.48377	+	1.07271i	0.0931003	+	0.0673076i
$255$		0			0
$256$	4.65730	−	15.3072i	0.291081	−	0.956698i
$257$	17.7208			1.10539			0.552696	−	0.833383i	$-0.313599\pi$
$257$	17.7208			1.10539			0.552696	+	0.833383i	$0.313599\pi$
$258$		0			0
$259$	−15.2565	+	36.8324i	−0.947991	+	2.28865i
$260$	−0.328568	−	0.995284i	−0.0203769	−	0.0617249i
$261$		0			0
$262$	2.31125	−	1.42382i	0.142789	−	0.0879636i
$263$	6.87392	−	6.87392i	0.423864	−	0.423864i	−0.462668	−	0.886532i	$-0.653108\pi$
$263$	6.87392	−	6.87392i	0.423864	−	0.423864i	0.886532	+	0.462668i	$0.153108\pi$
$264$		0			0
$265$	−12.8068	−	12.8068i	−0.786718	−	0.786718i
$266$	−21.1340	−	5.02132i	−1.29581	−	0.307877i
$267$		0			0
$268$	25.4763	+	1.88458i	1.55621	+	0.115119i
$269$	−23.8231	−	9.86787i	−1.45252	−	0.601655i	−0.489725	−	0.871877i	$-0.662903\pi$
$269$	−23.8231	−	9.86787i	−1.45252	−	0.601655i	−0.962798	+	0.270223i	$0.912903\pi$
$270$		0			0
$271$			18.6652i			1.13383i	0.823775	+	0.566916i	$0.191864\pi$
$271$			18.6652i			1.13383i	−0.823775	+	0.566916i	$0.808136\pi$
$272$	−11.3768	−	15.3532i	−0.689819	−	0.930923i
$273$		0			0
$274$	−2.36826	−	14.7285i	−0.143072	−	0.889781i
$275$	−24.1451	−	10.0012i	−1.45601	−	0.603097i
$276$		0			0
$277$	−5.19701	−	12.5467i	−0.312258	−	0.753858i	−0.999621	−	0.0275432i	$-0.991232\pi$
$277$	−5.19701	−	12.5467i	−0.312258	−	0.753858i	0.687363	−	0.726314i	$-0.258768\pi$
$278$	−3.83438	+	16.1383i	−0.229971	+	0.967913i
$279$		0			0
$280$	−29.1315	−	24.5275i	−1.74094	−	1.46580i
$281$	16.4615	−	16.4615i	0.982008	−	0.982008i	−0.0178325	−	0.999841i	$-0.505677\pi$
$281$	16.4615	−	16.4615i	0.982008	−	0.982008i	0.999841	+	0.0178325i	$0.00567656\pi$
$282$		0			0
$283$	−1.69249	+	0.701052i	−0.100608	+	0.0416732i	−0.432420	−	0.901672i	$-0.642340\pi$
$283$	−1.69249	+	0.701052i	−0.100608	+	0.0416732i	0.331812	+	0.943346i	$0.392340\pi$
$284$	−20.7318	−	10.4409i	−1.23021	−	0.619556i
$285$		0			0
$286$	−0.752829	+	1.04132i	−0.0445157	+	0.0615745i
$287$	24.2028			1.42865
$288$		0			0
$289$	−5.82196			−0.342468
$290$	12.2806	−	16.9867i	0.721144	−	0.997491i
$291$		0			0
$292$	2.39358	−	4.75277i	0.140074	−	0.278135i
$293$	−27.7774	+	11.5058i	−1.62277	+	0.672174i	−0.994394	−	0.105735i	$-0.966281\pi$
$293$	−27.7774	+	11.5058i	−1.62277	+	0.672174i	−0.628377	+	0.777909i	$0.716281\pi$
$294$		0			0
$295$	−5.02337	+	5.02337i	−0.292472	+	0.292472i
$296$	−2.24265	−	26.1381i	−0.130352	−	1.51924i
$297$		0			0
$298$	0.871809	−	3.66932i	0.0505026	−	0.212558i
$299$	0.170216	+	0.410938i	0.00984386	+	0.0237652i
$300$		0			0
$301$	1.78676	+	0.740098i	0.102987	+	0.0426586i
$302$	3.32469	+	20.6767i	0.191315	+	1.18981i
$303$		0			0
$304$	13.8672	−	3.46741i	0.795338	−	0.198870i
$305$		−	28.3915i		−	1.62569i
$306$		0			0
$307$	−17.1668	−	7.11073i	−0.979763	−	0.405831i	−0.165425	−	0.986222i	$-0.552900\pi$
$307$	−17.1668	−	7.11073i	−0.979763	−	0.405831i	−0.814338	+	0.580391i	$0.802900\pi$
$308$	−3.44422	+	46.5600i	−0.196252	+	2.65300i
$309$		0			0
$310$	41.8775	+	9.94987i	2.37848	+	0.565114i
$311$	−13.7172	−	13.7172i	−0.777832	−	0.777832i	0.201630	−	0.979462i	$-0.435376\pi$
$311$	−13.7172	−	13.7172i	−0.777832	−	0.777832i	−0.979462	+	0.201630i	$0.935376\pi$
$312$		0			0
$313$	8.67327	−	8.67327i	0.490242	−	0.490242i	−0.418140	−	0.908382i	$-0.637318\pi$
$313$	8.67327	−	8.67327i	0.490242	−	0.490242i	0.908382	+	0.418140i	$0.137318\pi$
$314$	−10.6132	+	6.53815i	−0.598939	+	0.368969i
$315$		0			0
$316$	28.6096	−	9.44473i	1.60942	−	0.531308i
$317$	−0.485904	+	1.17307i	−0.0272911	+	0.0658864i	−0.936938	−	0.349497i	$-0.886353\pi$
$317$	−0.485904	+	1.17307i	−0.0272911	+	0.0658864i	0.909646	+	0.415383i	$0.136353\pi$
$318$		0			0
$319$	−25.6973			−1.43877
$320$	24.4472	+	5.50584i	1.36664	+	0.307786i
$321$		0			0
$322$	13.0969	+	9.46854i	0.729864	+	0.527661i
$323$	6.53302	−	15.7721i	0.363507	−	0.877583i
$324$		0			0
$325$	0.743793	−	0.308089i	0.0412582	−	0.0170897i
$326$	−27.6182	+	17.0139i	−1.52963	+	0.942312i
$327$		0			0
$328$	−14.1392	+	7.33030i	−0.780705	+	0.404748i
$329$	18.5803	+	18.5803i	1.02436	+	1.02436i
$330$		0			0
$331$	−3.36914	−	8.13382i	−0.185185	−	0.447075i	0.803836	−	0.594850i	$-0.202789\pi$
$331$	−3.36914	−	8.13382i	−0.185185	−	0.447075i	−0.989021	+	0.147775i	$0.952789\pi$
$332$	−0.227531	+	3.07583i	−0.0124874	+	0.168808i
$333$		0			0
$334$	−3.13985	+	0.504871i	−0.171805	+	0.0276253i
$335$			40.0105i			2.18600i
$336$		0			0
$337$			6.76122i			0.368307i	0.982897	+	0.184154i	$0.0589544\pi$
$337$			6.76122i			0.368307i	−0.982897	+	0.184154i	$0.941046\pi$
$338$	2.91240	+	18.1125i	0.158414	+	0.985192i
$339$		0			0
$340$	22.6664	−	19.5439i	1.22926	−	1.05992i
$341$	−20.1940	−	48.7526i	−1.09357	−	2.64010i
$342$		0			0
$343$	13.6013	+	13.6013i	0.734403	+	0.734403i
$344$	−1.26797	+	0.108792i	−0.0683643	+	0.00586567i
$345$		0			0
$346$	−3.65740	−	5.93697i	−0.196623	−	0.319174i
$347$	17.8881	−	7.40950i	0.960285	−	0.397763i	0.153198	−	0.988196i	$-0.451043\pi$
$347$	17.8881	−	7.40950i	0.960285	−	0.397763i	0.807087	+	0.590432i	$0.201043\pi$
$348$		0			0
$349$	3.93563	−	9.50144i	0.210669	−	0.508601i	−0.782857	−	0.622201i	$-0.786239\pi$
$349$	3.93563	−	9.50144i	0.210669	−	0.508601i	0.993526	+	0.113601i	$0.0362385\pi$
$350$	17.1379	−	23.7053i	0.916062	−	1.26710i
$351$		0			0
$352$	−12.0895	−	28.2433i	−0.644374	−	1.50537i
$353$	−3.64417			−0.193960			−0.0969798	−	0.995286i	$-0.530918\pi$
$353$	−3.64417			−0.193960			−0.0969798	+	0.995286i	$0.530918\pi$
$354$		0			0
$355$	13.9128	−	33.5885i	0.738415	−	1.78269i
$356$	−3.33929	−	1.68173i	−0.176982	−	0.0891316i
$357$		0			0
$358$	−11.1945	−	18.1717i	−0.591647	−	0.960407i
$359$	8.66290	−	8.66290i	0.457210	−	0.457210i	−0.440528	−	0.897739i	$-0.645209\pi$
$359$	8.66290	−	8.66290i	0.457210	−	0.457210i	0.897739	+	0.440528i	$0.145209\pi$
$360$		0			0
$361$	−4.40519	−	4.40519i	−0.231852	−	0.231852i
$362$	2.92408	−	12.3070i	0.153686	−	0.646844i
$363$		0			0
$364$	−0.939169	−	1.08922i	−0.0492258	−	0.0570904i
$365$	7.70015	+	3.18951i	0.403044	+	0.166946i
$366$		0			0
$367$			31.3403i			1.63595i	0.575252	+	0.817976i	$0.304904\pi$
$367$			31.3403i			1.63595i	−0.575252	+	0.817976i	$0.695096\pi$
$368$	−10.5189	−	1.56481i	−0.548337	−	0.0815714i
$369$		0			0
$370$	40.5672	−	6.52299i	2.10899	−	0.339114i
$371$	−22.9606	−	9.51060i	−1.19206	−	0.493766i
$372$		0			0
$373$	2.39894	+	5.79155i	0.124212	+	0.299875i	0.973738	−	0.227672i	$-0.0731116\pi$
$373$	2.39894	+	5.79155i	0.124212	+	0.299875i	−0.849525	+	0.527548i	$0.823112\pi$
$374$	−35.6978	−	8.48159i	−1.84589	−	0.438573i
$375$		0			0
$376$	−16.4819	−	5.22712i	−0.849991	−	0.269568i
$377$	0.559751	−	0.559751i	0.0288287	−	0.0288287i
$378$		0			0
$379$	−20.9093	+	8.66092i	−1.07404	+	0.444881i	−0.848414	−	0.529333i	$-0.822442\pi$
$379$	−20.9093	+	8.66092i	−1.07404	+	0.444881i	−0.225624	+	0.974214i	$0.572442\pi$
$380$	7.01819	+	21.2592i	0.360026	+	1.09058i
$381$		0			0
$382$	0.598336	+	0.432572i	0.0306135	+	0.0221323i
$383$	−0.320505			−0.0163771			−0.00818853	−	0.999966i	$-0.502607\pi$
$383$	−0.320505			−0.0163771			−0.00818853	+	0.999966i	$0.502607\pi$
$384$		0			0
$385$	−73.1223			−3.72666
$386$	−12.5576	−	9.07860i	−0.639164	−	0.462088i
$387$		0			0
$388$	−0.666594	−	2.01922i	−0.0338412	−	0.102510i
$389$	21.6672	−	8.97486i	1.09857	−	0.455043i	0.241584	−	0.970380i	$-0.422333\pi$
$389$	21.6672	−	8.97486i	1.09857	−	0.455043i	0.856988	+	0.515337i	$0.172333\pi$
$390$		0			0
$391$	−8.98102	+	8.98102i	−0.454190	+	0.454190i
$392$	−30.9379	−	9.81172i	−1.56260	−	0.495567i
$393$		0			0
$394$	30.0312	+	7.13526i	1.51295	+	0.359469i
$395$	18.0579	+	43.5955i	0.908589	+	2.19353i
$396$		0			0
$397$	−14.0703	−	5.82810i	−0.706167	−	0.292504i	0.000550210	−	1.00000i	$-0.499825\pi$
$397$	−14.0703	−	5.82810i	−0.706167	−	0.292504i	−0.706718	+	0.707496i	$0.749825\pi$
$398$	8.27389	−	1.33040i	0.414732	−	0.0666867i
$399$		0			0
$400$	−2.83229	+	19.0391i	−0.141614	+	0.951956i
$401$		−	35.8868i		−	1.79210i	−0.443952	−	0.896051i	$-0.646424\pi$
$401$		−	35.8868i		−	1.79210i	0.443952	−	0.896051i	$-0.353576\pi$
$402$		0			0
$403$	1.50183	+	0.622078i	0.0748115	+	0.0309879i
$404$	−7.46039	−	8.65231i	−0.371168	−	0.430469i
$405$		0			0
$406$	6.64864	−	27.9832i	0.329967	−	1.38878i
$407$	−35.6189	−	35.6189i	−1.76556	−	1.76556i
$408$		0			0
$409$	14.6781	−	14.6781i	0.725787	−	0.725787i	−0.243990	−	0.969778i	$-0.578457\pi$
$409$	14.6781	−	14.6781i	0.725787	−	0.725787i	0.969778	+	0.243990i	$0.0784566\pi$
$410$	−13.0833	−	21.2377i	−0.646136	−	1.04886i
$411$		0			0
$412$	−10.4623	−	5.26902i	−0.515441	−	0.259586i
$413$	−3.73045	+	9.00610i	−0.183563	+	0.443161i
$414$		0			0
$415$	−4.83059			−0.237124
$416$	0.878550	+	0.351870i	0.0430744	+	0.0172518i
$417$		0			0
$418$	16.0804	−	22.2425i	0.786519	−	1.08792i
$419$	−1.01746	+	2.45637i	−0.0497063	+	0.120002i	−0.946782	−	0.321875i	$-0.895687\pi$
$419$	−1.01746	+	2.45637i	−0.0497063	+	0.120002i	0.897076	+	0.441876i	$0.145687\pi$
$420$		0			0
$421$	6.99423	−	2.89711i	0.340878	−	0.141196i	−0.205676	−	0.978620i	$-0.565939\pi$
$421$	6.99423	−	2.89711i	0.340878	−	0.141196i	0.546554	+	0.837424i	$0.315939\pi$
$422$	4.27667	+	6.94222i	0.208185	+	0.337942i
$423$		0			0
$424$	16.2940	−	1.39803i	0.791305	−	0.0678942i
$425$	16.2555	+	16.2555i	0.788510	+	0.788510i
$426$		0			0
$427$	−14.9087	−	35.9927i	−0.721482	−	1.74181i
$428$	17.5314	−	15.1164i	0.847415	−	0.730677i
$429$		0			0
$430$	−0.316433	−	1.96793i	−0.0152598	−	0.0949022i
$431$			15.5614i			0.749567i	0.927112	+	0.374783i	$0.122283\pi$
$431$			15.5614i			0.749567i	−0.927112	+	0.374783i	$0.877717\pi$
$432$		0			0
$433$		−	17.1441i		−	0.823891i	−0.911208	−	0.411946i	$-0.864849\pi$
$433$		−	17.1441i		−	0.823891i	0.911208	−	0.411946i	$-0.135151\pi$
$434$	58.3141	−	9.37660i	2.79917	−	0.450091i
$435$		0			0
$436$	−1.95330	+	26.4054i	−0.0935463	+	1.26459i
$437$	−3.63581	−	8.77763i	−0.173924	−	0.419891i
$438$		0			0
$439$	8.64120	+	8.64120i	0.412422	+	0.412422i	0.882582	−	0.470159i	$-0.155804\pi$
$439$	8.64120	+	8.64120i	0.412422	+	0.412422i	−0.470159	+	0.882582i	$0.655804\pi$
$440$	42.7178	−	22.1466i	2.03649	−	1.05580i
$441$		0			0
$442$	0.962337	−	0.592836i	0.0457737	−	0.0281984i
$443$	2.60225	−	1.07789i	0.123637	−	0.0512120i	−0.320007	−	0.947415i	$-0.603685\pi$
$443$	2.60225	−	1.07789i	0.123637	−	0.0512120i	0.443644	+	0.896203i	$0.353685\pi$
$444$		0			0
$445$	2.24095	−	5.41012i	0.106231	−	0.256465i
$446$	−18.3239	−	13.2474i	−0.867662	−	0.627283i
$447$		0			0
$448$	33.8836	−	5.85756i	1.60085	−	0.276744i
$449$	−11.6595			−0.550248			−0.275124	−	0.961409i	$-0.588719\pi$
$449$	−11.6595			−0.550248			−0.275124	+	0.961409i	$0.588719\pi$
$450$		0			0
$451$	−11.7027	+	28.2528i	−0.551059	+	1.33037i
$452$	5.57742	−	1.84124i	0.262340	−	0.0866047i
$453$		0			0
$454$	−22.6689	+	13.9649i	−1.06390	+	0.655404i
$455$	1.59279	−	1.59279i	0.0746710	−	0.0746710i
$456$		0			0
$457$	0.916734	+	0.916734i	0.0428830	+	0.0428830i	0.728223	−	0.685340i	$-0.240346\pi$
$457$	0.916734	+	0.916734i	0.0428830	+	0.0428830i	−0.685340	+	0.728223i	$0.740346\pi$
$458$	0.232619	+	0.0552689i	0.0108696	+	0.00258255i
$459$		0			0
$460$	1.22877	−	16.6108i	0.0572915	−	0.774484i
$461$	19.2249	+	7.96323i	0.895395	+	0.370885i	0.782448	−	0.622716i	$-0.213971\pi$
$461$	19.2249	+	7.96323i	0.895395	+	0.370885i	0.112947	+	0.993601i	$0.463971\pi$
$462$		0			0
$463$			2.04111i			0.0948585i	0.998875	+	0.0474292i	$0.0151029\pi$
$463$			2.04111i			0.0948585i	−0.998875	+	0.0474292i	$0.984897\pi$
$464$	4.59115	+	18.3613i	0.213139	+	0.852403i
$465$		0			0
$466$	−6.49969	−	40.4223i	−0.301092	−	1.87253i
$467$	20.2562	+	8.39040i	0.937346	+	0.388261i	0.798460	−	0.602047i	$-0.205648\pi$
$467$	20.2562	+	8.39040i	0.937346	+	0.388261i	0.138885	+	0.990308i	$0.455648\pi$
$468$		0			0
$469$	21.0099	+	50.7224i	0.970148	+	2.34214i
$470$	6.26012	−	26.3479i	0.288758	−	1.21534i
$471$		0			0
$472$	−0.548364	−	6.39117i	−0.0252405	−	0.294177i
$473$	−1.72789	+	1.72789i	−0.0794484	+	0.0794484i
$474$		0			0
$475$	−15.8874	+	6.58078i	−0.728964	+	0.301947i
$476$	18.4721	−	36.6788i	0.846668	−	1.68117i
$477$		0			0
$478$	−24.6651	+	34.1170i	−1.12816	+	1.56047i
$479$	−0.106626			−0.00487185			−0.00243592	−	0.999997i	$-0.500775\pi$
$479$	−0.106626			−0.00487185			−0.00243592	+	0.999997i	$0.500775\pi$
$480$		0			0
$481$	1.55174			0.0707531
$482$	15.6319	−	21.6221i	0.712011	−	0.984859i
$483$		0			0
$484$	−33.0369	−	16.6380i	−1.50168	−	0.756273i
$485$	3.07690	−	1.27449i	0.139715	−	0.0578718i
$486$		0			0
$487$	−1.49752	+	1.49752i	−0.0678589	+	0.0678589i	−0.740222	−	0.672363i	$-0.765279\pi$
$487$	−1.49752	+	1.49752i	−0.0678589	+	0.0678589i	0.672363	+	0.740222i	$0.265279\pi$
$488$	19.6107	+	16.5114i	0.887735	+	0.747437i
$489$		0			0
$490$	11.7507	−	49.4572i	0.530845	−	2.23425i
$491$	4.50143	+	10.8674i	0.203147	+	0.490440i	0.992315	−	0.123737i	$-0.0394881\pi$
$491$	4.50143	+	10.8674i	0.203147	+	0.490440i	−0.789168	+	0.614177i	$0.789488\pi$
$492$		0			0
$493$	20.8836	+	8.65026i	0.940549	+	0.389588i
$494$	0.134226	+	0.834769i	0.00603913	+	0.0375581i
$495$		0			0
$496$	−31.2270	+	23.1394i	−1.40213	+	1.03899i
$497$		−	49.8869i		−	2.23773i
$498$		0			0
$499$	−35.1359	−	14.5538i	−1.57290	−	0.651516i	−0.585629	−	0.810579i	$-0.699153\pi$
$499$	−35.1359	−	14.5538i	−1.57290	−	0.651516i	−0.987268	+	0.159063i	$0.949153\pi$
$500$	1.17360	+	0.0868155i	0.0524849	+	0.00388251i
$501$		0			0
$502$	−10.7370	−	2.55105i	−0.479216	−	0.113859i
$503$	7.22205	+	7.22205i	0.322015	+	0.322015i	0.849540	−	0.527525i	$-0.176880\pi$
$503$	7.22205	+	7.22205i	0.322015	+	0.322015i	−0.527525	+	0.849540i	$0.676880\pi$
$504$		0			0
$505$	12.6525	−	12.6525i	0.563028	−	0.563028i
$506$	−17.3857	+	10.7103i	−0.772889	+	0.476129i
$507$		0			0
$508$	−0.811710	−	2.45880i	−0.0360138	−	0.109092i
$509$	13.6482	−	32.9496i	0.604945	−	1.46047i	−0.263490	−	0.964662i	$-0.584874\pi$
$509$	13.6482	−	32.9496i	0.604945	−	1.46047i	0.868435	−	0.495803i	$-0.165126\pi$
$510$		0			0
$511$	11.4366			0.505923
$512$	−18.0206	+	13.6843i	−0.796404	+	0.604765i
$513$		0			0
$514$	−20.3093	−	14.6828i	−0.895806	−	0.647630i
$515$	7.02109	−	16.9504i	0.309386	−	0.746925i
$516$		0			0
$517$	−30.6735	+	12.7054i	−1.34902	+	0.558782i
$518$	48.0030	−	29.5717i	2.10913	−	1.29930i
$519$		0			0
$520$	−0.448092	+	1.41291i	−0.0196502	+	0.0619601i
$521$	11.0804	+	11.0804i	0.485441	+	0.485441i	0.906864	−	0.421423i	$-0.138469\pi$
$521$	11.0804	+	11.0804i	0.485441	+	0.485441i	−0.421423	+	0.906864i	$0.638469\pi$
$522$		0			0
$523$	−5.54859	−	13.3955i	−0.242623	−	0.585743i	0.754919	−	0.655818i	$-0.227676\pi$
$523$	−5.54859	−	13.3955i	−0.242623	−	0.585743i	−0.997542	+	0.0700750i	$0.977676\pi$
$524$	−3.82858	−	0.283214i	−0.167252	−	0.0123723i
$525$		0			0
$526$	−13.5735	+	2.18254i	−0.591832	+	0.0951634i
$527$			46.4178i			2.02199i
$528$		0			0
$529$		−	15.9315i		−	0.692673i
$530$	4.06631	+	25.2888i	0.176629	+	1.09848i
$531$		0			0
$532$	20.0606	+	23.2656i	0.869738	+	1.00869i
$533$	−0.360503	−	0.870331i	−0.0156151	−	0.0376982i
$534$		0			0
$535$	25.6367	+	25.6367i	1.10837	+	1.10837i
$536$	−27.6362	−	23.2686i	−1.19370	−	1.00505i
$537$		0			0
$538$	19.1269	+	31.0483i	0.824620	+	1.33859i
$539$	−57.5766	+	23.8490i	−2.48000	+	1.02725i
$540$		0			0
$541$	0.609513	−	1.47149i	0.0262050	−	0.0632644i	−0.910235	−	0.414091i	$-0.864099\pi$
$541$	0.609513	−	1.47149i	0.0262050	−	0.0632644i	0.936440	+	0.350827i	$0.114099\pi$
$542$	15.4653	−	21.3917i	0.664293	−	0.918854i
$543$		0			0
$544$	0.317563	+	27.0222i	0.0136154	+	1.15857i
$545$	−41.4696			−1.77636
$546$		0			0
$547$	4.75146	−	11.4711i	0.203158	−	0.490467i	−0.789159	−	0.614189i	$-0.789483\pi$
$547$	4.75146	−	11.4711i	0.203158	−	0.490467i	0.992317	+	0.123722i	$0.0394832\pi$
$548$	−9.48927	+	18.8422i	−0.405362	+	0.804898i
$549$		0			0
$550$	19.3854	+	31.4679i	0.826598	+	1.34180i
$551$	−11.9563	+	11.9563i	−0.509354	+	0.509354i
$552$		0			0
$553$	45.7850	+	45.7850i	1.94697	+	1.94697i
$554$	−4.43956	+	18.6855i	−0.188619	+	0.793870i
$555$		0			0
$556$	17.7661	−	15.3187i	0.753450	−	0.649657i
$557$	−1.89110	−	0.783320i	−0.0801286	−	0.0331903i	0.342259	−	0.939606i	$-0.388808\pi$
$557$	−1.89110	−	0.783320i	−0.0801286	−	0.0331903i	−0.422388	+	0.906415i	$0.638808\pi$
$558$		0			0
$559$		−	0.0752754i		−	0.00318381i
$560$	13.0642	+	52.2476i	0.552065	+	2.20787i
$561$		0			0
$562$	−32.5054	+	5.22669i	−1.37116	+	0.220475i
$563$	−31.3299	−	12.9773i	−1.32040	−	0.546927i	−0.392497	−	0.919753i	$-0.628389\pi$
$563$	−31.3299	−	12.9773i	−1.32040	−	0.546927i	−0.927901	+	0.372827i	$0.878389\pi$
$564$		0			0
$565$	3.52036	+	8.49890i	0.148103	+	0.357552i
$566$	2.52058	+	0.598876i	0.105948	+	0.0251727i
$567$		0			0
$568$	15.1092	+	29.1437i	0.633969	+	1.22284i
$569$	−8.76894	+	8.76894i	−0.367613	+	0.367613i	−0.866606	−	0.498993i	$-0.833703\pi$
$569$	−8.76894	+	8.76894i	−0.367613	+	0.367613i	0.498993	+	0.866606i	$0.333703\pi$
$570$		0			0
$571$	−3.18862	+	1.32077i	−0.133440	+	0.0552725i	−0.448404	−	0.893831i	$-0.648007\pi$
$571$	−3.18862	+	1.32077i	−0.133440	+	0.0552725i	0.314964	+	0.949103i	$0.398007\pi$
$572$	1.72560	−	0.569661i	0.0721508	−	0.0238187i
$573$		0			0
$574$	−27.7382	−	20.0535i	−1.15777	−	0.837018i
$575$	12.7939			0.533544
$576$		0			0
$577$	25.0765			1.04395			0.521974	−	0.852961i	$-0.325196\pi$
$577$	25.0765			1.04395			0.521974	+	0.852961i	$0.325196\pi$
$578$	6.67240	+	4.82386i	0.277535	+	0.200646i
$579$		0			0
$580$	−28.1490	+	9.29268i	−1.16882	+	0.385857i
$581$	−6.12388	+	2.53659i	−0.254061	+	0.105236i
$582$		0			0
$583$	22.2041	−	22.2041i	0.919602	−	0.919602i
$584$	−6.68119	+	3.46379i	−0.276470	+	0.143333i
$585$		0			0
$586$	41.3682	+	9.82884i	1.70890	+	0.406026i
$587$	7.42363	+	17.9222i	0.306406	+	0.739729i	0.999816	+	0.0191861i	$0.00610750\pi$
$587$	7.42363	+	17.9222i	0.306406	+	0.739729i	−0.693410	+	0.720543i	$0.743892\pi$
$588$		0			0
$589$	−32.0790	−	13.2876i	−1.32179	−	0.547505i
$590$	9.91933	−	1.59497i	0.408372	−	0.0656641i
$591$		0			0
$592$	−19.0868	+	31.8143i	−0.784462	+	1.30756i
$593$		−	29.1981i		−	1.19902i	−0.800367	−	0.599510i	$-0.795362\pi$
$593$		−	29.1981i		−	1.19902i	0.800367	−	0.599510i	$-0.204638\pi$
$594$		0			0
$595$	59.4248	+	24.6146i	2.43618	+	1.00910i
$596$	−4.03942	+	3.48296i	−0.165461	+	0.142668i
$597$		0			0
$598$	0.145408	−	0.612000i	0.00594617	−	0.0250265i
$599$	−12.1085	−	12.1085i	−0.494741	−	0.494741i	0.415055	−	0.909796i	$-0.363762\pi$
$599$	−12.1085	−	12.1085i	−0.494741	−	0.494741i	−0.909796	+	0.415055i	$0.863762\pi$
$600$		0			0
$601$	−29.2254	+	29.2254i	−1.19213	+	1.19213i	−0.215663	+	0.976468i	$0.569191\pi$
$601$	−29.2254	+	29.2254i	−1.19213	+	1.19213i	−0.976468	+	0.215663i	$0.930809\pi$
$602$	−1.43453	−	2.32865i	−0.0584673	−	0.0949085i
$603$		0			0
$604$	13.3216	−	26.4517i	0.542047	−	1.07630i
$605$	22.1706	−	53.5245i	0.901361	−	2.17608i
$606$		0			0
$607$	9.78275			0.397070			0.198535	−	0.980094i	$-0.436382\pi$
$607$	9.78275			0.397070			0.198535	+	0.980094i	$0.436382\pi$
$608$	−18.7658	−	7.51592i	−0.761053	−	0.304811i
$609$		0			0
$610$	−23.5241	+	32.5387i	−0.952465	+	1.31746i
$611$	0.391391	−	0.944901i	0.0158340	−	0.0382266i
$612$		0			0
$613$	15.8338	−	6.55859i	0.639522	−	0.264899i	−0.0392705	−	0.999229i	$-0.512503\pi$
$613$	15.8338	−	6.55859i	0.639522	−	0.264899i	0.678793	+	0.734330i	$0.262503\pi$
$614$	13.7828	+	22.3732i	0.556227	+	0.902910i
$615$		0			0
$616$	42.5252	−	50.5074i	1.71339	−	2.03500i
$617$	−29.1705	−	29.1705i	−1.17436	−	1.17436i	−0.981159	−	0.193200i	$-0.938113\pi$
$617$	−29.1705	−	29.1705i	−1.17436	−	1.17436i	−0.193200	−	0.981159i	$-0.561887\pi$
$618$		0			0
$619$	−13.8703	−	33.4858i	−0.557494	−	1.34591i	−0.911744	−	0.410759i	$-0.865264\pi$
$619$	−13.8703	−	33.4858i	−0.557494	−	1.34591i	0.354250	−	0.935151i	$-0.384736\pi$
$620$	−39.7506	−	46.1014i	−1.59642	−	1.85148i
$621$		0			0
$622$	4.35536	+	27.0865i	0.174634	+	1.08607i
$623$		−	8.03532i		−	0.321928i
$624$		0			0
$625$			25.9039i			1.03616i
$626$	−17.1265	+	2.75385i	−0.684514	+	0.110066i
$627$		0			0
$628$	17.5808	+	1.30052i	0.701550	+	0.0518963i
$629$	16.9565	+	40.9367i	0.676101	+	1.63225i
$630$		0			0
$631$	−6.70079	−	6.70079i	−0.266754	−	0.266754i	0.561037	−	0.827791i	$-0.310403\pi$
$631$	−6.70079	−	6.70079i	−0.266754	−	0.266754i	−0.827791	+	0.561037i	$0.810403\pi$
$632$	−40.6143	−	12.8805i	−1.61555	−	0.512359i
$633$		0			0
$634$	1.52885	−	0.941828i	0.0607183	−	0.0374048i
$635$	3.74674	−	1.55195i	0.148685	−	0.0615872i
$636$		0			0
$637$	0.734672	−	1.77365i	0.0291088	−	0.0702748i
$638$	29.4510	+	21.2918i	1.16598	+	0.842951i
$639$		0			0
$640$	−23.4563	−	26.5661i	−0.927192	−	1.05012i
$641$	8.08573			0.319367			0.159684	−	0.987168i	$-0.448953\pi$
$641$	8.08573			0.319367			0.159684	+	0.987168i	$0.448953\pi$
$642$		0			0
$643$	5.26286	−	12.7057i	0.207547	−	0.501062i	−0.785489	−	0.618876i	$-0.787588\pi$
$643$	5.26286	−	12.7057i	0.207547	−	0.501062i	0.993036	+	0.117813i	$0.0375885\pi$
$644$	−7.16478	−	21.7033i	−0.282332	−	0.855229i
$645$		0			0
$646$	−20.5555	+	12.6630i	−0.808745	+	0.498218i
$647$	−1.82520	+	1.82520i	−0.0717562	+	0.0717562i	−0.742074	−	0.670318i	$-0.766158\pi$
$647$	−1.82520	+	1.82520i	−0.0717562	+	0.0717562i	0.670318	+	0.742074i	$0.266158\pi$
$648$		0			0
$649$	−8.70938	−	8.70938i	−0.341873	−	0.341873i
$650$	−1.10771	−	0.263186i	−0.0434481	−	0.0103230i
$651$		0			0
$652$	45.7496	+	3.38427i	1.79169	+	0.132538i
$653$	−6.14025	−	2.54338i	−0.240287	−	0.0995300i	0.259290	−	0.965799i	$-0.416511\pi$
$653$	−6.14025	−	2.54338i	−0.240287	−	0.0995300i	−0.499577	+	0.866269i	$0.666511\pi$
$654$		0			0
$655$		−	6.01277i		−	0.234938i
$656$	22.2781	+	3.31413i	0.869815	+	0.129395i
$657$		0			0
$658$	−5.89944	−	36.6893i	−0.229984	−	1.43030i
$659$	19.1064	+	7.91412i	0.744278	+	0.308290i	0.722405	−	0.691471i	$-0.243037\pi$
$659$	19.1064	+	7.91412i	0.744278	+	0.308290i	0.0218737	+	0.999761i	$0.493037\pi$
$660$		0			0
$661$	3.64083	+	8.78973i	0.141612	+	0.341881i	0.978734	−	0.205135i	$-0.0657635\pi$
$661$	3.64083	+	8.78973i	0.141612	+	0.341881i	−0.837122	+	0.547016i	$0.815763\pi$
$662$	−2.87810	+	12.1135i	−0.111860	+	0.470804i
$663$		0			0
$664$	2.80929	−	3.33661i	0.109021	−	0.129485i
$665$	−34.0219	+	34.0219i	−1.31931	+	1.31931i
$666$		0			0
$667$	11.6223	−	4.81412i	0.450018	−	0.186403i
$668$	4.01682	+	2.02294i	0.155415	+	0.0782701i
$669$		0			0
$670$	33.1512	−	45.8549i	1.28074	−	1.77153i
$671$	49.2244			1.90029
$672$		0			0
$673$	−40.0366			−1.54330			−0.771648	−	0.636050i	$-0.780567\pi$
$673$	−40.0366			−1.54330			−0.771648	+	0.636050i	$0.780567\pi$
$674$	5.60209	−	7.74885i	0.215785	−	0.298475i
$675$		0			0
$676$	11.6696	−	23.1714i	0.448829	−	0.891208i
$677$	−19.7757	+	8.19136i	−0.760041	+	0.314819i	−0.728831	−	0.684693i	$-0.759936\pi$
$677$	−19.7757	+	8.19136i	−0.760041	+	0.314819i	−0.0312100	+	0.999513i	$0.509936\pi$
$678$		0			0
$679$	3.23143	−	3.23143i	0.124011	−	0.124011i
$680$	−42.1707	+	3.61826i	−1.61717	+	0.138754i
$681$		0			0
$682$	−17.2508	+	72.6061i	−0.660567	+	2.78023i
$683$	−2.17719	−	5.25621i	−0.0833080	−	0.201123i	0.876736	−	0.480971i	$-0.159716\pi$
$683$	−2.17719	−	5.25621i	−0.0833080	−	0.201123i	−0.960044	+	0.279848i	$0.909716\pi$
$684$		0			0
$685$	−30.5270	−	12.6447i	−1.16638	−	0.483129i
$686$	−4.31857	−	26.8577i	−0.164884	−	1.02543i
$687$		0			0
$688$	1.54333	+	0.925908i	0.0588388	+	0.0352999i
$689$			0.967323i			0.0368521i
$690$		0			0
$691$	22.9683	+	9.51376i	0.873754	+	0.361921i	0.774071	−	0.633099i	$-0.218217\pi$
$691$	22.9683	+	9.51376i	0.873754	+	0.361921i	0.0996825	+	0.995019i	$0.468217\pi$
$692$	−0.727502	+	9.83459i	−0.0276555	+	0.373855i
$693$		0			0
$694$	−26.6403	−	6.32960i	−1.01125	−	0.240268i
$695$	25.9798	+	25.9798i	0.985470	+	0.985470i
$696$		0			0
$697$	19.0210	−	19.0210i	0.720472	−	0.720472i
$698$	−12.3831	+	7.62844i	−0.468706	+	0.288741i
$699$		0			0
$700$	−39.2827	+	12.9682i	−1.48475	+	0.490151i
$701$	−3.00103	+	7.24514i	−0.113348	+	0.273645i	−0.970366	−	0.241641i	$-0.922314\pi$
$701$	−3.00103	+	7.24514i	−0.113348	+	0.273645i	0.857018	+	0.515286i	$0.172314\pi$
$702$		0			0
$703$	−33.1450			−1.25009
$704$	−9.54587	+	42.3858i	−0.359773	+	1.59748i
$705$		0			0
$706$	4.17649	+	3.01942i	0.157184	+	0.113638i
$707$	9.39597	−	22.6839i	0.353372	−	0.853115i
$708$		0			0
$709$	15.4583	−	6.40306i	0.580550	−	0.240472i	−0.0730290	−	0.997330i	$-0.523267\pi$
$709$	15.4583	−	6.40306i	0.580550	−	0.240472i	0.653579	+	0.756858i	$0.273267\pi$
$710$	−43.7752	+	26.9672i	−1.64286	+	1.01206i
$711$		0			0
$712$	2.43366	+	4.69420i	0.0912051	+	0.175923i
$713$	18.2666	+	18.2666i	0.684089	+	0.684089i
$714$		0			0
$715$	1.08916	+	2.62947i	0.0407324	+	0.0983368i
$716$	−2.22672	+	30.1015i	−0.0832165	+	1.12495i
$717$		0			0
$718$	−17.1061	+	2.75056i	−0.638393	+	0.102650i
$719$		−	34.6573i		−	1.29250i	−0.763125	−	0.646250i	$-0.776336\pi$
$719$		−	34.6573i		−	1.29250i	0.763125	−	0.646250i	$-0.223664\pi$
$720$		0			0
$721$		−	25.1754i		−	0.937581i
$722$	1.39869	+	8.69864i	0.0520540	+	0.323730i
$723$		0			0
$724$	−13.5484	+	11.6820i	−0.503521	+	0.434157i
$725$	−8.71350	−	21.0363i	−0.323611	−	0.781267i
$726$		0			0
$727$	−15.5200	−	15.5200i	−0.575605	−	0.575605i	0.358084	−	0.933689i	$-0.383430\pi$
$727$	−15.5200	−	15.5200i	−0.575605	−	0.575605i	−0.933689	+	0.358084i	$0.883430\pi$
$728$	0.173873	+	2.02648i	0.00644415	+	0.0751064i
$729$		0			0
$730$	−6.18223	−	10.0355i	−0.228815	−	0.371429i
$731$	1.98586	−	0.822569i	0.0734496	−	0.0304238i
$732$		0			0
$733$	−13.9034	+	33.5658i	−0.513534	+	1.23978i	0.428279	+	0.903646i	$0.359120\pi$
$733$	−13.9034	+	33.5658i	−0.513534	+	1.23978i	−0.941814	+	0.336135i	$0.890880\pi$
$734$	25.9674	−	35.9183i	0.958475	−	1.32577i
$735$		0			0
$736$	10.7589	+	10.5090i	0.396579	+	0.387366i
$737$	−69.3690			−2.55524
$738$		0			0
$739$	12.0261	−	29.0335i	0.442386	−	1.06801i	−0.532724	−	0.846289i	$-0.678832\pi$
$739$	12.0261	−	29.0335i	0.442386	−	1.06801i	0.975109	−	0.221724i	$-0.0711685\pi$
$740$	−51.8977	−	26.1367i	−1.90780	−	0.960803i
$741$		0			0
$742$	18.4344	+	29.9242i	0.676749	+	1.09855i
$743$	−25.4316	+	25.4316i	−0.932995	+	0.932995i	−0.997892	−	0.0648970i	$-0.979328\pi$
$743$	−25.4316	+	25.4316i	−0.932995	+	0.932995i	0.0648970	+	0.997892i	$0.479328\pi$
$744$		0			0
$745$	−5.90693	−	5.90693i	−0.216413	−	0.216413i
$746$	2.04930	−	8.62522i	0.0750303	−	0.315792i
$747$		0			0
$748$	33.8847	+	39.2984i	1.23895	+	1.43689i
$749$	45.9624	+	19.0383i	1.67943	+	0.695643i
$750$		0			0
$751$			36.6217i			1.33634i	0.744007	+	0.668172i	$0.232923\pi$
$751$			36.6217i			1.33634i	−0.744007	+	0.668172i	$0.767077\pi$
$752$	14.5585	+	19.6470i	0.530895	+	0.716452i
$753$		0			0
$754$	−1.10530	+	0.177727i	−0.0402528	+	0.00647244i
$755$	42.8554	+	17.7513i	1.55967	+	0.646036i
$756$		0			0
$757$	−8.01093	−	19.3401i	−0.291162	−	0.702928i	0.708835	−	0.705375i	$-0.249221\pi$
$757$	−8.01093	−	19.3401i	−0.291162	−	0.702928i	−0.999997	+	0.00244664i	$0.999221\pi$
$758$	31.1397	+	7.39862i	1.13104	+	0.268730i
$759$		0			0
$760$	9.57124	−	30.1796i	0.347185	−	1.09473i
$761$	16.1825	−	16.1825i	0.586617	−	0.586617i	−0.350097	−	0.936714i	$-0.613851\pi$
$761$	16.1825	−	16.1825i	0.586617	−	0.586617i	0.936714	+	0.350097i	$0.113851\pi$
$762$		0			0
$763$	−52.5722	+	21.7761i	−1.90324	+	0.788348i
$764$	−0.327324	−	0.991517i	−0.0118422	−	0.0358718i
$765$		0			0
$766$	0.367323	+	0.265559i	0.0132719	+	0.00959503i
$767$	0.379424			0.0137002
$768$		0			0
$769$	−10.8742			−0.392133			−0.196066	−	0.980591i	$-0.562817\pi$
$769$	−10.8742			−0.392133			−0.196066	+	0.980591i	$0.562817\pi$
$770$	83.8036	+	60.5864i	3.02007	+	2.18338i
$771$		0			0
$772$	6.86972	+	20.8095i	0.247247	+	0.748949i
$773$	39.3921	−	16.3167i	1.41683	−	0.586872i	0.462772	−	0.886478i	$-0.346855\pi$
$773$	39.3921	−	16.3167i	1.41683	−	0.586872i	0.954063	+	0.299605i	$0.0968550\pi$
$774$		0			0
$775$	33.0623	−	33.0623i	1.18763	−	1.18763i
$776$	−0.909085	+	2.86649i	−0.0326342	+	0.102901i
$777$		0			0
$778$	−32.2685	−	7.66681i	−1.15688	−	0.274868i
$779$	7.70033	+	18.5902i	0.275893	+	0.666064i
$780$		0			0
$781$	58.2348	+	24.1216i	2.08380	+	0.863140i
$782$	17.7342	−	2.85157i	0.634175	−	0.101972i
$783$		0			0
$784$	27.3275	+	36.8789i	0.975982	+	1.31711i
$785$			27.6106i			0.985464i
$786$		0			0
$787$	43.8276	+	18.1540i	1.56228	+	0.647119i	0.985484	−	0.169767i	$-0.0543014\pi$
$787$	43.8276	+	18.1540i	1.56228	+	0.647119i	0.576799	+	0.816886i	$0.304301\pi$
$788$	−28.5060	−	33.0603i	−1.01548	−	1.17772i
$789$		0			0
$790$	15.4260	−	64.9257i	0.548832	−	2.30995i
$791$	8.92573	+	8.92573i	0.317362	+	0.317362i
$792$		0			0
$793$	−1.07223	+	1.07223i	−0.0380760	+	0.0380760i
$794$	11.2966	+	18.3375i	0.400902	+	0.650775i
$795$		0			0
$796$	−10.5848	−	5.33070i	−0.375168	−	0.188942i
$797$	5.42445	−	13.0958i	0.192144	−	0.463876i	−0.798220	−	0.602366i	$-0.794225\pi$
$797$	5.42445	−	13.0958i	0.192144	−	0.463876i	0.990364	+	0.138490i	$0.0442248\pi$
$798$		0			0
$799$	29.2046			1.03318
$800$	19.0211	−	19.4735i	0.672498	−	0.688492i
$801$		0			0
$802$	−29.7345	+	41.1289i	−1.04996	+	1.45231i
$803$	−5.52988	+	13.3503i	−0.195145	+	0.471122i
$804$		0			0
$805$	33.0716	−	13.6987i	1.16562	−	0.482816i
$806$	−1.20578	−	1.95731i	−0.0424717	−	0.0689432i
$807$		0			0
$808$	1.38118	+	16.0976i	0.0485896	+	0.566311i
$809$	−7.81837	−	7.81837i	−0.274879	−	0.274879i	0.556182	−	0.831061i	$-0.312266\pi$
$809$	−7.81837	−	7.81837i	−0.274879	−	0.274879i	−0.831061	+	0.556182i	$0.812266\pi$
$810$		0			0
$811$	−4.97807	−	12.0181i	−0.174804	−	0.422014i	0.812059	−	0.583576i	$-0.198347\pi$
$811$	−4.97807	−	12.0181i	−0.174804	−	0.422014i	−0.986863	+	0.161562i	$0.948347\pi$
$812$	−30.8056	+	26.5619i	−1.08107	+	0.932141i
$813$		0			0
$814$	11.3094	+	70.3343i	0.396394	+	2.46522i
$815$			71.8496i			2.51678i
$816$		0			0
$817$			1.60788i			0.0562526i
$818$	−28.9840	+	4.66047i	−1.01340	+	0.162949i
$819$		0			0
$820$	−2.60242	+	35.1803i	−0.0908804	+	1.22855i
$821$	−8.07956	−	19.5058i	−0.281979	−	0.680757i	0.717903	−	0.696143i	$-0.245102\pi$
$821$	−8.07956	−	19.5058i	−0.281979	−	0.680757i	−0.999882	+	0.0153865i	$0.995102\pi$
$822$		0			0
$823$	13.5114	+	13.5114i	0.470978	+	0.470978i	0.902231	−	0.431253i	$-0.141928\pi$
$823$	13.5114	+	13.5114i	0.470978	+	0.470978i	−0.431253	+	0.902231i	$0.641928\pi$
$824$	7.62487	+	14.7074i	0.265625	+	0.512355i
$825$		0			0
$826$	11.7375	−	7.23074i	0.408399	−	0.251590i
$827$	0.535900	−	0.221977i	0.0186351	−	0.00771889i	−0.373346	−	0.927692i	$-0.621790\pi$
$827$	0.535900	−	0.221977i	0.0186351	−	0.00771889i	0.391981	+	0.919973i	$0.371790\pi$
$828$		0			0
$829$	−0.662385	+	1.59914i	−0.0230056	+	0.0555404i	−0.934965	−	0.354740i	$-0.884569\pi$
$829$	−0.662385	+	1.59914i	−0.0230056	+	0.0555404i	0.911959	+	0.410281i	$0.134569\pi$
$830$	5.53621	+	4.00244i	0.192165	+	0.138927i
$831$		0			0
$832$	−0.715336	−	1.13120i	−0.0247998	−	0.0392174i
$833$	54.8193			1.89937
$834$		0			0
$835$	−2.69562	+	6.50781i	−0.0932858	+	0.225212i
$836$	−36.8587	+	12.1679i	−1.27478	+	0.420837i
$837$		0			0
$838$	3.20135	−	1.97215i	0.110589	−	0.0681269i
$839$	−37.2491	+	37.2491i	−1.28598	+	1.28598i	−0.348776	+	0.937206i	$0.613403\pi$
$839$	−37.2491	+	37.2491i	−1.28598	+	1.28598i	−0.937206	+	0.348776i	$0.886597\pi$
$840$		0			0
$841$	4.67499	+	4.67499i	0.161207	+	0.161207i
$842$	−10.4163	−	2.47486i	−0.358971	−	0.0852894i
$843$		0			0
$844$	0.850682	−	11.4998i	0.0292817	−	0.395839i
$845$	37.5409	+	15.5500i	1.29145	+	0.534935i
$846$		0			0
$847$		−	79.4965i		−	2.73153i
$848$	−19.8324	−	11.8983i	−0.681049	−	0.408590i
$849$		0			0
$850$	−5.16131	−	32.0988i	−0.177031	−	1.10098i
$851$	22.7825	+	9.43680i	0.780973	+	0.323489i
$852$		0			0
$853$	−16.8084	−	40.5790i	−0.575508	−	1.38940i	−0.896807	−	0.442422i	$-0.854119\pi$
$853$	−16.8084	−	40.5790i	−0.575508	−	1.38940i	0.321299	−	0.946978i	$-0.395881\pi$
$854$	−12.7358	+	53.6031i	−0.435810	+	1.83426i
$855$		0			0
$856$	−32.6172	+	2.79856i	−1.11483	+	0.0956529i
$857$	−7.85318	+	7.85318i	−0.268260	+	0.268260i	−0.828399	−	0.560139i	$-0.810748\pi$
$857$	−7.85318	+	7.85318i	−0.268260	+	0.268260i	0.560139	+	0.828399i	$0.310748\pi$
$858$		0			0
$859$	39.7901	−	16.4816i	1.35762	−	0.562344i	0.419216	−	0.907887i	$-0.362305\pi$
$859$	39.7901	−	16.4816i	1.35762	−	0.562344i	0.938403	+	0.345542i	$0.112305\pi$
$860$	−1.26790	+	2.51758i	−0.0432351	+	0.0858488i
$861$		0			0
$862$	12.8936	−	17.8345i	0.439158	−	0.607446i
$863$	38.0040			1.29367			0.646836	−	0.762629i	$-0.276092\pi$
$863$	38.0040			1.29367			0.646836	+	0.762629i	$0.276092\pi$
$864$		0			0
$865$	−15.4452			−0.525153
$866$	−14.2049	+	19.6484i	−0.482703	+	0.667679i
$867$		0			0
$868$	−74.6014	−	37.5707i	−2.53214	−	1.27523i
$869$	−75.5847	+	31.3082i	−2.56404	+	1.06206i
$870$		0			0
$871$	1.51103	−	1.51103i	0.0511993	−	0.0511993i
$872$	24.1171	−	28.6440i	0.816709	−	0.970010i
$873$		0			0
$874$	−3.10591	+	13.0723i	−0.105059	+	0.442177i
$875$	0.967849	+	2.33659i	0.0327193	+	0.0789913i
$876$		0			0
$877$	−20.5623	−	8.51717i	−0.694339	−	0.287604i	0.00746783	−	0.999972i	$-0.497623\pi$
$877$	−20.5623	−	8.51717i	−0.694339	−	0.287604i	−0.701807	+	0.712368i	$0.747623\pi$
$878$	−2.74368	−	17.0632i	−0.0925946	−	0.575856i
$879$		0			0
$880$	−67.3075	−	10.0128i	−2.26894	−	0.337530i
$881$		−	54.2712i		−	1.82844i	−0.405215	−	0.914222i	$-0.632803\pi$
$881$		−	54.2712i		−	1.82844i	0.405215	−	0.914222i	$-0.367197\pi$
$882$		0			0
$883$	−11.7438	−	4.86446i	−0.395212	−	0.163702i	0.176222	−	0.984350i	$-0.443612\pi$
$883$	−11.7438	−	4.86446i	−0.395212	−	0.163702i	−0.571433	+	0.820648i	$0.693612\pi$
$884$	−1.59411	−	0.117922i	−0.0536157	−	0.00396616i
$885$		0			0
$886$	−3.87547	−	0.920789i	−0.130199	−	0.0309345i
$887$	−5.49834	−	5.49834i	−0.184616	−	0.184616i	0.608748	−	0.793364i	$-0.291672\pi$
$887$	−5.49834	−	5.49834i	−0.184616	−	0.184616i	−0.793364	+	0.608748i	$0.791672\pi$
$888$		0			0
$889$	3.93490	−	3.93490i	0.131972	−	0.131972i
$890$	−7.05092	+	4.34363i	−0.236347	+	0.145599i
$891$		0			0
$892$	10.0242	+	30.3650i	0.335636	+	1.01670i
$893$	−8.36009	+	20.1831i	−0.279760	+	0.675400i
$894$		0			0
$895$	−47.2743			−1.58021
$896$	−43.6864	−	21.3615i	−1.45946	−	0.713636i
$897$		0			0
$898$	13.3627	+	9.66066i	0.445919	+	0.322380i
$899$	17.5939	−	42.4753i	0.586788	−	1.41663i
$900$		0			0
$901$	−25.5192	+	10.5704i	−0.850167	+	0.352151i
$902$	36.8214	−	22.6834i	1.22602	−	0.755274i
$903$		0			0
$904$	−7.91771	−	2.51104i	−0.263339	−	0.0835159i
$905$	−19.8121	−	19.8121i	−0.658577	−	0.658577i
$906$		0			0
$907$	14.6149	+	35.2835i	0.485281	+	1.17157i	0.957069	+	0.289859i	$0.0936085\pi$
$907$	14.6149	+	35.2835i	0.485281	+	1.17157i	−0.471789	+	0.881712i	$0.656391\pi$
$908$	37.5510	+	2.77778i	1.24617	+	0.0921840i
$909$		0			0
$910$	−3.14517	+	0.505727i	−0.104262	+	0.0167647i
$911$			17.3918i			0.576217i	0.957598	+	0.288109i	$0.0930264\pi$
$911$			17.3918i			0.576217i	−0.957598	+	0.288109i	$0.906974\pi$
$912$		0			0
$913$		−	8.37514i		−	0.277177i
$914$	−0.291073	−	1.81022i	−0.00962783	−	0.0598766i
$915$		0			0
$916$	−0.220804	−	0.256082i	−0.00729559	−	0.00846117i
$917$	−3.15737	−	7.62257i	−0.104266	−	0.251719i
$918$		0			0
$919$	−24.1543	−	24.1543i	−0.796777	−	0.796777i	0.185809	−	0.982586i	$-0.440509\pi$
$919$	−24.1543	−	24.1543i	−0.796777	−	0.796777i	−0.982586	+	0.185809i	$0.940509\pi$
$920$	−15.1714	+	18.0191i	−0.500185	+	0.594073i
$921$		0			0
$922$	−15.4352	−	25.0555i	−0.508330	−	0.825160i
$923$	−1.79393	+	0.743069i	−0.0590479	+	0.0244584i
$924$		0			0
$925$	17.0805	−	41.2360i	0.561603	−	1.35583i
$926$	1.69119	−	2.33926i	0.0555759	−	0.0768730i
$927$		0			0
$928$	9.95172	−	24.8475i	0.326681	−	0.815659i
$929$	25.7477			0.844756			0.422378	−	0.906420i	$-0.361195\pi$
$929$	25.7477			0.844756			0.422378	+	0.906420i	$0.361195\pi$
$930$		0			0
$931$	−15.6926	+	37.8852i	−0.514303	+	1.24164i
$932$	−26.0433	+	51.7123i	−0.853076	+	1.69389i
$933$		0			0
$934$	−16.2631	−	26.3995i	−0.532146	−	0.863820i
$935$	−57.4669	+	57.4669i	−1.87937	+	1.87937i
$936$		0			0
$937$	27.5785	+	27.5785i	0.900952	+	0.900952i	0.995519	−	0.0945669i	$-0.0301466\pi$
$937$	27.5785	+	27.5785i	0.900952	+	0.900952i	−0.0945669	+	0.995519i	$0.530147\pi$
$938$	17.9478	−	75.5396i	0.586016	−	2.46646i
$939$		0			0
$940$	−29.0055	+	25.0098i	−0.946054	+	0.815729i
$941$	−28.8141	−	11.9352i	−0.939313	−	0.389076i	−0.140109	−	0.990136i	$-0.544745\pi$
$941$	−28.8141	−	11.9352i	−0.939313	−	0.389076i	−0.799204	+	0.601060i	$0.794745\pi$
$942$		0			0
$943$		−	14.9705i		−	0.487506i
$944$	−4.66702	+	7.77910i	−0.151899	+	0.253188i
$945$		0			0
$946$	3.41195	−	0.548623i	0.110932	−	0.0178373i
$947$	−38.5836	−	15.9818i	−1.25380	−	0.519340i	−0.345797	−	0.938309i	$-0.612392\pi$
$947$	−38.5836	−	15.9818i	−1.25380	−	0.519340i	−0.908000	+	0.418969i	$0.862392\pi$
$948$		0			0
$949$	−0.170349	−	0.411258i	−0.00552975	−	0.0133500i
$950$	23.6607	+	5.62165i	0.767655	+	0.182390i
$951$		0			0
$952$	−51.5611	+	26.7313i	−1.67110	+	0.866365i
$953$	33.3209	−	33.3209i	1.07937	−	1.07937i	0.0828040	−	0.996566i	$-0.473612\pi$
$953$	33.3209	−	33.3209i	1.07937	−	1.07937i	0.996566	−	0.0828040i	$-0.0263875\pi$
$954$		0			0
$955$	1.51088	−	0.625827i	0.0488910	−	0.0202513i
$956$	56.5361	−	18.6639i	1.82851	−	0.603635i
$957$		0			0
$958$	0.122201	+	0.0883460i	0.00394813	+	0.00285433i
$959$	−45.3398			−1.46410
$960$		0			0
$961$	63.4098			2.04548
$962$	−1.77840	−	1.28571i	−0.0573380	−	0.0414530i
$963$		0			0
$964$	−35.8305	+	11.8285i	−1.15402	+	0.380971i
$965$	−31.7096	+	13.1346i	−1.02077	+	0.422816i
$966$		0			0
$967$	−27.1005	+	27.1005i	−0.871493	+	0.871493i	−0.992635	−	0.121142i	$-0.961344\pi$
$967$	−27.1005	+	27.1005i	−0.871493	+	0.871493i	0.121142	+	0.992635i	$0.461344\pi$
$968$	24.0771	+	46.4415i	0.773868	+	1.49269i
$969$		0			0
$970$	−4.58235	−	1.08874i	−0.147131	−	0.0349574i
$971$	−7.76310	−	18.7418i	−0.249130	−	0.601452i	0.749001	−	0.662569i	$-0.230534\pi$
$971$	−7.76310	−	18.7418i	−0.249130	−	0.601452i	−0.998131	+	0.0611168i	$0.980534\pi$
$972$		0			0
$973$	46.5776	+	19.2931i	1.49321	+	0.618508i
$974$	2.95705	−	0.475477i	0.0947499	−	0.0152353i
$975$		0			0
$976$	−8.79457	−	35.1720i	−0.281507	−	1.12583i
$977$			54.6327i			1.74785i	0.486058	+	0.873927i	$0.338434\pi$
$977$			54.6327i			1.74785i	−0.486058	+	0.873927i	$0.661566\pi$
$978$		0			0
$979$	9.37992	+	3.88529i	0.299784	+	0.124174i
$980$	−54.4456	+	46.9453i	−1.73920	+	1.49961i
$981$		0			0
$982$	3.84536	−	16.1846i	0.122710	−	0.516470i
$983$	3.97460	+	3.97460i	0.126770	+	0.126770i	0.767645	−	0.640875i	$-0.221428\pi$
$983$	3.97460	+	3.97460i	0.126770	+	0.126770i	−0.640875	+	0.767645i	$0.721428\pi$
$984$		0			0
$985$	48.3449	−	48.3449i	1.54040	−	1.54040i
$986$	−16.7668	−	27.2172i	−0.533965	−	0.866772i
$987$		0			0
$988$	0.537825	−	1.06792i	0.0171105	−	0.0339751i
$989$	0.457783	−	1.10519i	0.0145567	−	0.0351429i
$990$		0			0
$991$	19.2183			0.610489			0.305245	−	0.952274i	$-0.401262\pi$
$991$	19.2183			0.610489			0.305245	+	0.952274i	$0.401262\pi$
$992$	54.9609	−	0.645895i	1.74501	−	0.0205072i
$993$		0			0
$994$	−41.3344	+	57.1740i	−1.31105	+	1.81345i
$995$	7.10329	−	17.1489i	0.225189	−	0.543655i
$996$		0			0
$997$	30.6773	−	12.7070i	0.971561	−	0.402434i	0.160268	−	0.987073i	$-0.448764\pi$
$997$	30.6773	−	12.7070i	0.971561	−	0.402434i	0.811293	+	0.584640i	$0.198764\pi$
$998$	28.2096	+	45.7919i	0.892959	+	1.44952i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.b.109.6	✓	128
3.2	odd	2	inner	864.2.v.b.109.27	yes	128
32.5	even	8	inner	864.2.v.b.325.6	yes	128
96.5	odd	8	inner	864.2.v.b.325.27	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.b.109.6	✓	128	1.1	even	1	trivial
864.2.v.b.109.27	yes	128	3.2	odd	2	inner
864.2.v.b.325.6	yes	128	32.5	even	8	inner
864.2.v.b.325.27	yes	128	96.5	odd	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14607 - 0.828563i) q^{2} +(0.626968 + 1.89919i) q^{4} +(-2.89399 + 1.19873i) q^{5} +(-3.03933 + 3.03933i) q^{7} +(0.855044 - 2.69609i) q^{8} +O(q^{10})\)	\(q+(-1.14607 - 0.828563i) q^{2} +(0.626968 + 1.89919i) q^{4} +(-2.89399 + 1.19873i) q^{5} +(-3.03933 + 3.03933i) q^{7} +(0.855044 - 2.69609i) q^{8} +(4.30995 + 1.02402i) q^{10} +(-2.07833 - 5.01753i) q^{11} +(0.154565 + 0.0640231i) q^{13} +(6.00158 - 0.965021i) q^{14} +(-3.21382 + 2.38146i) q^{16} +4.77723i q^{17} +(-3.30151 - 1.36753i) q^{19} +(-4.09106 - 4.74467i) q^{20} +(-1.77542 + 7.47248i) q^{22} +(1.87996 + 1.87996i) q^{23} +(3.40271 - 3.40271i) q^{25} +(-0.124096 - 0.201442i) q^{26} +(-7.67783 - 3.86670i) q^{28} +(1.81073 - 4.37148i) q^{29} +9.71647 q^{31} +(5.65646 - 0.0664742i) q^{32} +(3.95824 - 5.47506i) q^{34} +(5.15247 - 12.4392i) q^{35} +(8.56912 - 3.54945i) q^{37} +(2.65069 + 4.30280i) q^{38} +(0.757396 + 8.82744i) q^{40} +(-3.98159 - 3.98159i) q^{41} +(-0.172185 - 0.415692i) q^{43} +(8.22618 - 7.09296i) q^{44} +(-0.596908 - 3.71224i) q^{46} -6.11328i q^{47} -11.4751i q^{49} +(-6.71911 + 1.08040i) q^{50} +(-0.0246842 + 0.333689i) q^{52} +(2.21266 + 5.34183i) q^{53} +(12.0293 + 12.0293i) q^{55} +(5.59555 + 10.7931i) q^{56} +(-5.69727 + 3.50974i) q^{58} +(2.09529 - 0.867896i) q^{59} +(-3.46853 + 8.37378i) q^{61} +(-11.1358 - 8.05070i) q^{62} +(-6.53780 - 4.61055i) q^{64} -0.524058 q^{65} +(4.88800 - 11.8007i) q^{67} +(-9.07286 + 2.99517i) q^{68} +(-16.2117 + 9.98705i) q^{70} +(-8.20687 + 8.20687i) q^{71} +(-1.88142 - 1.88142i) q^{73} +(-12.7618 - 3.03213i) q^{74} +(0.527254 - 7.12759i) q^{76} +(21.5667 + 8.93321i) q^{77} -15.0641i q^{79} +(6.44605 - 10.7444i) q^{80} +(1.26420 + 7.86220i) q^{82} +(1.42473 + 0.590143i) q^{83} +(-5.72662 - 13.8253i) q^{85} +(-0.147090 + 0.619080i) q^{86} +(-15.3048 + 1.31315i) q^{88} +(-1.32189 + 1.32189i) q^{89} +(-0.664364 + 0.275188i) q^{91} +(-2.39172 + 4.74908i) q^{92} +(-5.06523 + 7.00626i) q^{94} +11.1939 q^{95} -1.06320 q^{97} +(-9.50784 + 13.1513i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) \) 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * q^94

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