LMFDB - Embedded newform 363.2.f.h.215.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(161,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

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

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

chi := DirichletCharacter("363.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.f (of order $10$, degree $4$, not 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:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.26873856000000000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 2x^{14} - 8x^{10} - 16x^{8} - 32x^{6} + 128x^{2} + 256 $ x^16 + 2x^14 - 8x^10 - 16x^8 - 32x^6 + 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			215.1
Root			$1.40647 + 0.147826i$ of defining polynomial
Character	$\chi$	$=$	363.215
Dual form			363.2.f.h.233.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.756934 - 2.32960i) q^{2} +(0.704489 + 1.58231i) q^{3} +(-3.23607 + 2.35114i) q^{4} +(-1.64728 - 0.535233i) q^{5} +(3.15290 - 2.83888i) q^{6} +(-0.831254 - 1.14412i) q^{7} +(3.96336 + 2.87955i) q^{8} +(-2.00739 + 2.22943i) q^{9} +O(q^{10})$	\(q+(-0.756934 - 2.32960i) q^{2} +(0.704489 + 1.58231i) q^{3} +(-3.23607 + 2.35114i) q^{4} +(-1.64728 - 0.535233i) q^{5} +(3.15290 - 2.83888i) q^{6} +(-0.831254 - 1.14412i) q^{7} +(3.96336 + 2.87955i) q^{8} +(-2.00739 + 2.22943i) q^{9} +4.24264i q^{10} +(-6.00000 - 3.46410i) q^{12} +(-2.68999 + 0.874032i) q^{13} +(-2.03615 + 2.80252i) q^{14} +(-0.313585 - 2.98357i) q^{15} +(1.23607 - 3.80423i) q^{16} +(-0.756934 + 2.32960i) q^{17} +(6.71316 + 2.98889i) q^{18} +(-1.66251 + 2.28825i) q^{19} +(6.58911 - 2.14093i) q^{20} +(1.22474 - 2.12132i) q^{21} +8.66025i q^{23} +(-1.76419 + 8.29986i) q^{24} +(-1.61803 - 1.17557i) q^{25} +(4.07230 + 5.60503i) q^{26} +(-4.94183 - 1.60570i) q^{27} +(5.37999 + 1.74806i) q^{28} +(-3.96336 + 2.87955i) q^{29} +(-6.71316 + 2.98889i) q^{30} +(0.927051 + 2.85317i) q^{31} +6.00000 q^{34} +(0.756934 + 2.32960i) q^{35} +(1.25434 - 11.9343i) q^{36} +(-2.42705 + 1.76336i) q^{37} +(6.58911 + 2.14093i) q^{38} +(-3.27806 - 3.64065i) q^{39} +(-4.98752 - 6.86474i) q^{40} +(-7.92672 - 5.75910i) q^{41} +(-5.86889 - 1.24747i) q^{42} -9.89949i q^{43} +(4.50000 - 2.59808i) q^{45} +(20.1750 - 6.55524i) q^{46} +(4.07230 - 5.60503i) q^{47} +(6.89025 - 0.724194i) q^{48} +(1.54508 - 4.75528i) q^{49} +(-1.51387 + 4.65921i) q^{50} +(-4.21940 + 0.443477i) q^{51} +(6.65003 - 9.15298i) q^{52} +(3.29456 - 1.07047i) q^{53} +12.7279i q^{54} -6.92820i q^{56} +(-4.79193 - 1.01856i) q^{57} +(9.70820 + 7.05342i) q^{58} +(1.01807 + 1.40126i) q^{59} +(8.02957 + 8.91774i) q^{60} +(2.68999 + 0.874032i) q^{61} +(5.94504 - 4.31932i) q^{62} +(4.21940 + 0.443477i) q^{63} +(-2.47214 - 7.60845i) q^{64} +4.89898 q^{65} -3.00000 q^{67} +(-3.02774 - 9.31841i) q^{68} +(-13.7032 + 6.10105i) q^{69} +(4.85410 - 3.52671i) q^{70} +(-1.64728 - 0.535233i) q^{71} +(-14.3758 + 3.05567i) q^{72} +(3.32502 + 4.57649i) q^{73} +(5.94504 + 4.31932i) q^{74} +(0.720227 - 3.38840i) q^{75} -11.3137i q^{76} +(-6.00000 + 10.3923i) q^{78} +(-9.41498 + 3.05911i) q^{79} +(-4.07230 + 5.60503i) q^{80} +(-0.940756 - 8.95070i) q^{81} +(-7.41641 + 22.8254i) q^{82} +(0.756934 - 2.32960i) q^{83} +(1.02417 + 9.74428i) q^{84} +(2.49376 - 3.43237i) q^{85} +(-23.0619 + 7.49326i) q^{86} +(-7.34847 - 4.24264i) q^{87} -8.66025i q^{89} +(-9.45869 - 8.51664i) q^{90} +(3.23607 + 2.35114i) q^{91} +(-20.3615 - 28.0252i) q^{92} +(-3.86149 + 3.47690i) q^{93} +(-16.1400 - 5.24419i) q^{94} +(3.96336 - 2.87955i) q^{95} +(4.01722 + 12.3637i) q^{97} -12.2474 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{3} - 16 q^{4} - 6 q^{9}+O(q^{10}) $ 16 * q + 6 * q^3 - 16 * q^4 - 6 * q^9	$ 16 q + 6 q^{3} - 16 q^{4} - 6 q^{9} - 96 q^{12} + 6 q^{15} - 16 q^{16} - 8 q^{25} - 12 q^{31} + 96 q^{34} - 24 q^{36} - 12 q^{37} + 12 q^{42} + 72 q^{45} + 24 q^{48} - 20 q^{49} + 48 q^{58} + 24 q^{60} + 32 q^{64} - 48 q^{67} - 30 q^{69} + 24 q^{70} + 12 q^{75} - 96 q^{78} + 18 q^{81} + 96 q^{82} + 16 q^{91} + 18 q^{93} - 52 q^{97}+O(q^{100}) $ 16 * q + 6 * q^3 - 16 * q^4 - 6 * q^9 - 96 * q^12 + 6 * q^15 - 16 * q^16 - 8 * q^25 - 12 * q^31 + 96 * q^34 - 24 * q^36 - 12 * q^37 + 12 * q^42 + 72 * q^45 + 24 * q^48 - 20 * q^49 + 48 * q^58 + 24 * q^60 + 32 * q^64 - 48 * q^67 - 30 * q^69 + 24 * q^70 + 12 * q^75 - 96 * q^78 + 18 * q^81 + 96 * q^82 + 16 * q^91 + 18 * q^93 - 52 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.756934	−	2.32960i	−0.535233	−	1.64728i	−0.743145	−	0.669131i	$-0.766667\pi$
$2$	−0.756934	−	2.32960i	−0.535233	−	1.64728i	0.207912	−	0.978148i	$-0.433333\pi$
$3$	0.704489	+	1.58231i	0.406737	+	0.913545i
$3$	0.704489	+	1.58231i	0.406737	+	0.913545i
$4$	−3.23607	+	2.35114i	−1.61803	+	1.17557i
$5$	−1.64728	−	0.535233i	−0.736685	−	0.239364i	−0.0834430	−	0.996513i	$-0.526592\pi$
$5$	−1.64728	−	0.535233i	−0.736685	−	0.239364i	−0.653242	+	0.757149i	$0.726592\pi$
$6$	3.15290	−	2.83888i	1.28716	−	1.15897i
$7$	−0.831254	−	1.14412i	−0.314184	−	0.432438i	0.622496	−	0.782623i	$-0.286119\pi$
$7$	−0.831254	−	1.14412i	−0.314184	−	0.432438i	−0.936680	+	0.350185i	$0.886119\pi$
$8$	3.96336	+	2.87955i	1.40126	+	1.01807i
$9$	−2.00739	+	2.22943i	−0.669131	+	0.743145i
$10$			4.24264i			1.34164i
$11$		0			0
$11$		0			0
$12$	−6.00000	−	3.46410i	−1.73205	−	1.00000i
$13$	−2.68999	+	0.874032i	−0.746070	+	0.242413i	−0.657289	−	0.753638i	$-0.728297\pi$
$13$	−2.68999	+	0.874032i	−0.746070	+	0.242413i	−0.0887808	+	0.996051i	$0.528297\pi$
$14$	−2.03615	+	2.80252i	−0.544183	+	0.749004i
$15$	−0.313585	−	2.98357i	−0.0809674	−	0.770353i
$16$	1.23607	−	3.80423i	0.309017	−	0.951057i
$17$	−0.756934	+	2.32960i	−0.183583	+	0.565012i	−0.999921	−	0.0125632i	$-0.996001\pi$
$17$	−0.756934	+	2.32960i	−0.183583	+	0.565012i	0.816338	+	0.577575i	$0.196001\pi$
$18$	6.71316	+	2.98889i	1.58231	+	0.704489i
$19$	−1.66251	+	2.28825i	−0.381405	+	0.524960i	−0.955956	−	0.293509i	$-0.905177\pi$
$19$	−1.66251	+	2.28825i	−0.381405	+	0.524960i	0.574551	+	0.818469i	$0.305177\pi$
$20$	6.58911	−	2.14093i	1.47337	−	0.478727i
$21$	1.22474	−	2.12132i	0.267261	−	0.462910i
$22$		0			0
$23$			8.66025i			1.80579i	0.429863	+	0.902894i	$0.358562\pi$
$23$			8.66025i			1.80579i	−0.429863	+	0.902894i	$0.641438\pi$
$24$	−1.76419	+	8.29986i	−0.360114	+	1.69420i
$25$	−1.61803	−	1.17557i	−0.323607	−	0.235114i
$26$	4.07230	+	5.60503i	0.798643	+	1.09924i
$27$	−4.94183	−	1.60570i	−0.951057	−	0.309017i
$28$	5.37999	+	1.74806i	1.01672	+	0.330353i
$29$	−3.96336	+	2.87955i	−0.735977	+	0.534719i	−0.891449	−	0.453122i	$-0.850310\pi$
$29$	−3.96336	+	2.87955i	−0.735977	+	0.534719i	0.155472	+	0.987840i	$0.450310\pi$
$30$	−6.71316	+	2.98889i	−1.22565	+	0.545694i
$31$	0.927051	+	2.85317i	0.166503	+	0.512444i	0.999144	−	0.0413693i	$-0.0131720\pi$
$31$	0.927051	+	2.85317i	0.166503	+	0.512444i	−0.832641	+	0.553814i	$0.813172\pi$
$32$		0			0
$33$		0			0
$34$	6.00000			1.02899
$35$	0.756934	+	2.32960i	0.127945	+	0.393775i
$36$	1.25434	−	11.9343i	0.209057	−	1.98904i
$37$	−2.42705	+	1.76336i	−0.399005	+	0.289894i	−0.769135	−	0.639086i	$-0.779313\pi$
$37$	−2.42705	+	1.76336i	−0.399005	+	0.289894i	0.370131	+	0.928980i	$0.379313\pi$
$38$	6.58911	+	2.14093i	1.06890	+	0.347305i
$39$	−3.27806	−	3.64065i	−0.524909	−	0.582971i
$40$	−4.98752	−	6.86474i	−0.788597	−	1.08541i
$41$	−7.92672	−	5.75910i	−1.23794	−	0.899420i	−0.240485	−	0.970653i	$-0.577307\pi$
$41$	−7.92672	−	5.75910i	−1.23794	−	0.899420i	−0.997460	+	0.0712331i	$0.977307\pi$
$42$	−5.86889	−	1.24747i	−0.905589	−	0.192489i
$43$		−	9.89949i		−	1.50966i	−0.655921	−	0.754829i	$-0.727720\pi$
$43$		−	9.89949i		−	1.50966i	0.655921	−	0.754829i	$-0.272280\pi$
$44$		0			0
$45$	4.50000	−	2.59808i	0.670820	−	0.387298i
$46$	20.1750	−	6.55524i	2.97463	−	0.966517i
$47$	4.07230	−	5.60503i	0.594005	−	0.817578i	−0.401138	−	0.916018i	$-0.631385\pi$
$47$	4.07230	−	5.60503i	0.594005	−	0.817578i	0.995143	+	0.0984395i	$0.0313851\pi$
$48$	6.89025	−	0.724194i	0.994522	−	0.104528i
$49$	1.54508	−	4.75528i	0.220726	−	0.679326i
$50$	−1.51387	+	4.65921i	−0.214093	+	0.658911i
$51$	−4.21940	+	0.443477i	−0.590834	+	0.0620992i
$52$	6.65003	−	9.15298i	0.922193	−	1.26929i
$53$	3.29456	−	1.07047i	0.452542	−	0.147040i	−0.0738728	−	0.997268i	$-0.523536\pi$
$53$	3.29456	−	1.07047i	0.452542	−	0.147040i	0.526415	+	0.850228i	$0.323536\pi$
$54$			12.7279i			1.73205i
$55$		0			0
$56$		−	6.92820i		−	0.925820i
$57$	−4.79193	−	1.01856i	−0.634706	−	0.134911i
$58$	9.70820	+	7.05342i	1.27475	+	0.926160i
$59$	1.01807	+	1.40126i	0.132542	+	0.182428i	0.870129	−	0.492823i	$-0.164035\pi$
$59$	1.01807	+	1.40126i	0.132542	+	0.182428i	−0.737588	+	0.675252i	$0.764035\pi$
$60$	8.02957	+	8.91774i	1.03661	+	1.15128i
$61$	2.68999	+	0.874032i	0.344418	+	0.111908i	0.476118	−	0.879381i	$-0.342043\pi$
$61$	2.68999	+	0.874032i	0.344418	+	0.111908i	−0.131700	+	0.991290i	$0.542043\pi$
$62$	5.94504	−	4.31932i	0.755020	−	0.548554i
$63$	4.21940	+	0.443477i	0.531594	+	0.0558728i
$64$	−2.47214	−	7.60845i	−0.309017	−	0.951057i
$65$	4.89898			0.607644
$66$		0			0
$67$	−3.00000			−0.366508			−0.183254	−	0.983066i	$-0.558663\pi$
$67$	−3.00000			−0.366508			−0.183254	+	0.983066i	$0.558663\pi$
$68$	−3.02774	−	9.31841i	−0.367167	−	1.13002i
$69$	−13.7032	+	6.10105i	−1.64967	+	0.734480i
$70$	4.85410	−	3.52671i	0.580176	−	0.421523i
$71$	−1.64728	−	0.535233i	−0.195496	−	0.0635205i	0.209633	−	0.977780i	$-0.432773\pi$
$71$	−1.64728	−	0.535233i	−0.195496	−	0.0635205i	−0.405129	+	0.914260i	$0.632773\pi$
$72$	−14.3758	+	3.05567i	−1.69420	+	0.360114i
$73$	3.32502	+	4.57649i	0.389164	+	0.535638i	0.957983	−	0.286825i	$-0.0925997\pi$
$73$	3.32502	+	4.57649i	0.389164	+	0.535638i	−0.568819	+	0.822462i	$0.692600\pi$
$74$	5.94504	+	4.31932i	0.691096	+	0.502111i
$75$	0.720227	−	3.38840i	0.0831647	−	0.391259i
$76$		−	11.3137i		−	1.29777i
$77$		0			0
$78$	−6.00000	+	10.3923i	−0.679366	+	1.17670i
$79$	−9.41498	+	3.05911i	−1.05927	+	0.344177i	−0.786299	−	0.617846i	$-0.788006\pi$
$79$	−9.41498	+	3.05911i	−1.05927	+	0.344177i	−0.272969	+	0.962023i	$0.588006\pi$
$80$	−4.07230	+	5.60503i	−0.455296	+	0.626662i
$81$	−0.940756	−	8.95070i	−0.104528	−	0.994522i
$82$	−7.41641	+	22.8254i	−0.819005	+	2.52064i
$83$	0.756934	−	2.32960i	0.0830843	−	0.255707i	−0.900881	−	0.434066i	$-0.857079\pi$
$83$	0.756934	−	2.32960i	0.0830843	−	0.255707i	0.983966	+	0.178358i	$0.0570786\pi$
$84$	1.02417	+	9.74428i	0.111746	+	1.06319i
$85$	2.49376	−	3.43237i	0.270486	−	0.372293i
$86$	−23.0619	+	7.49326i	−2.48683	+	0.808019i
$87$	−7.34847	−	4.24264i	−0.787839	−	0.454859i
$88$		0			0
$89$		−	8.66025i		−	0.917985i	−0.888440	−	0.458993i	$-0.848210\pi$
$89$		−	8.66025i		−	0.917985i	0.888440	−	0.458993i	$-0.151790\pi$
$90$	−9.45869	−	8.51664i	−0.997033	−	0.897733i
$91$	3.23607	+	2.35114i	0.339232	+	0.246467i
$92$	−20.3615	−	28.0252i	−2.12283	−	2.92183i
$93$	−3.86149	+	3.47690i	−0.400418	+	0.360538i
$94$	−16.1400	−	5.24419i	−1.66471	−	0.540897i
$95$	3.96336	−	2.87955i	0.406632	−	0.295435i
$96$		0			0
$97$	4.01722	+	12.3637i	0.407887	+	1.25535i	0.918460	+	0.395513i	$0.129433\pi$
$97$	4.01722	+	12.3637i	0.407887	+	1.25535i	−0.510573	+	0.859834i	$0.670567\pi$
$98$	−12.2474			−1.23718
$99$		0			0
$100$	8.00000			0.800000
$101$	3.78467	+	11.6480i	0.376589	+	1.15902i	0.942401	+	0.334486i	$0.108563\pi$
$101$	3.78467	+	11.6480i	0.376589	+	1.15902i	−0.565812	+	0.824534i	$0.691437\pi$
$102$	4.22693	+	9.49384i	0.418529	+	0.940031i
$103$	1.61803	−	1.17557i	0.159430	−	0.115832i	−0.505210	−	0.862996i	$-0.668585\pi$
$103$	1.61803	−	1.17557i	0.159430	−	0.115832i	0.664640	+	0.747164i	$0.268585\pi$
$104$	−13.1782	−	4.28187i	−1.29223	−	0.419871i
$105$	−3.15290	+	2.83888i	−0.307691	+	0.277046i
$106$	−4.98752	−	6.86474i	−0.484431	−	0.666762i
$107$	−1.98168	−	1.43977i	−0.191576	−	0.139188i	0.487863	−	0.872920i	$-0.337777\pi$
$107$	−1.98168	−	1.43977i	−0.191576	−	0.139188i	−0.679439	+	0.733732i	$0.737777\pi$
$108$	19.7673	−	6.42280i	1.90211	−	0.618034i
$109$			18.3848i			1.76094i	0.474100	+	0.880471i	$0.342774\pi$
$109$			18.3848i			1.76094i	−0.474100	+	0.880471i	$0.657226\pi$
$110$		0			0
$111$	−4.50000	−	2.59808i	−0.427121	−	0.246598i
$112$	−5.37999	+	1.74806i	−0.508361	+	0.165177i
$113$	−1.01807	+	1.40126i	−0.0957723	+	0.131819i	−0.854214	−	0.519922i	$-0.825961\pi$
$113$	−1.01807	+	1.40126i	−0.0957723	+	0.131819i	0.758442	+	0.651741i	$0.225961\pi$
$114$	1.25434	+	11.9343i	0.117480	+	1.11775i
$115$	4.63525	−	14.2658i	0.432240	−	1.33030i
$116$	6.05547	−	18.6368i	0.562236	−	1.73039i
$117$	3.45127	−	7.75169i	0.319070	−	0.716644i
$118$	2.49376	−	3.43237i	0.229569	−	0.315975i
$119$	3.29456	−	1.07047i	0.302011	−	0.0981295i
$120$	7.34847	−	12.7279i	0.670820	−	1.16190i
$121$		0			0
$122$		−	6.92820i		−	0.627250i
$123$	3.52838	−	16.5997i	0.318143	−	1.49675i
$124$	−9.70820	−	7.05342i	−0.871822	−	0.633416i
$125$	7.12652	+	9.80881i	0.637415	+	0.877327i
$126$	−2.16068	−	10.1652i	−0.192489	−	0.905589i
$127$	2.68999	+	0.874032i	0.238698	+	0.0775578i	0.425923	−	0.904759i	$-0.359949\pi$
$127$	2.68999	+	0.874032i	0.238698	+	0.0775578i	−0.187225	+	0.982317i	$0.559949\pi$
$128$	−15.8534	+	11.5182i	−1.40126	+	1.01807i
$129$	15.6640	−	6.97408i	1.37914	−	0.614034i
$130$	−3.70820	−	11.4127i	−0.325231	−	1.00096i
$131$	−12.2474			−1.07006			−0.535032	−	0.844832i	$-0.679701\pi$
$131$	−12.2474			−1.07006			−0.535032	+	0.844832i	$0.679701\pi$
$132$		0			0
$133$	4.00000			0.346844
$134$	2.27080	+	6.98881i	0.196167	+	0.603741i
$135$	7.28115	+	5.29007i	0.626662	+	0.455296i
$136$	−9.70820	+	7.05342i	−0.832472	+	0.604826i
$137$	14.8255	+	4.81710i	1.26663	+	0.411552i	0.863852	−	0.503746i	$-0.168045\pi$
$137$	14.8255	+	4.81710i	1.26663	+	0.411552i	0.402776	+	0.915298i	$0.368045\pi$
$138$	24.5854	+	27.3049i	2.09285	+	2.32435i
$139$	−9.14379	−	12.5854i	−0.775566	−	1.06748i	−0.995757	−	0.0920187i	$-0.970668\pi$
$139$	−9.14379	−	12.5854i	−0.775566	−	1.06748i	0.220191	−	0.975457i	$-0.429332\pi$
$140$	−7.92672	−	5.75910i	−0.669930	−	0.486732i
$141$	11.7378	+	2.49494i	0.988499	+	0.210112i
$142$			4.24264i			0.356034i
$143$		0			0
$144$	6.00000	+	10.3923i	0.500000	+	0.866025i
$145$	8.06998	−	2.62210i	0.670176	−	0.217753i
$146$	8.14459	−	11.2101i	0.674051	−	0.927752i
$147$	8.61281	−	0.905243i	0.710373	−	0.0746632i
$148$	3.70820	−	11.4127i	0.304812	−	0.938116i
$149$	−0.756934	+	2.32960i	−0.0620104	+	0.190849i	−0.977262	−	0.212033i	$-0.931991\pi$
$149$	−0.756934	+	2.32960i	−0.0620104	+	0.190849i	0.915252	+	0.402882i	$0.131991\pi$
$150$	−8.43880	+	0.886953i	−0.689025	+	0.0724194i
$151$	−5.81878	+	8.00886i	−0.473525	+	0.651752i	−0.977245	−	0.212116i	$-0.931965\pi$
$151$	−5.81878	+	8.00886i	−0.473525	+	0.651752i	0.503719	+	0.863867i	$0.331965\pi$
$152$	−13.1782	+	4.28187i	−1.06890	+	0.347305i
$153$	−3.67423	−	6.36396i	−0.297044	−	0.514496i
$154$		0			0
$155$		−	5.19615i		−	0.417365i
$156$	19.1677	+	4.07422i	1.53464	+	0.326199i
$157$	−12.1353	−	8.81678i	−0.968499	−	0.703656i	−0.0133898	−	0.999910i	$-0.504262\pi$
$157$	−12.1353	−	8.81678i	−0.968499	−	0.703656i	−0.955109	+	0.296255i	$0.904262\pi$
$158$	14.2530	+	19.6176i	1.13391	+	1.56069i
$159$	4.01478	+	4.45887i	0.318393	+	0.353611i
$160$		0			0
$161$	9.90839	−	7.19887i	0.780891	−	0.567350i
$162$	−20.1395	+	8.96668i	−1.58231	+	0.704489i
$163$	−3.09017	−	9.51057i	−0.242041	−	0.744925i	−0.996109	−	0.0881289i	$-0.971911\pi$
$163$	−3.09017	−	9.51057i	−0.242041	−	0.744925i	0.754068	−	0.656796i	$-0.228089\pi$
$164$	39.1918			3.06037
$165$		0			0
$166$	−6.00000			−0.465690
$167$	6.05547	+	18.6368i	0.468586	+	1.44216i	0.854415	+	0.519591i	$0.173915\pi$
$167$	6.05547	+	18.6368i	0.468586	+	1.44216i	−0.385829	+	0.922570i	$0.626085\pi$
$168$	10.9625	−	4.88084i	0.845779	−	0.376565i
$169$	−4.04508	+	2.93893i	−0.311160	+	0.226071i
$170$	−9.88367	−	3.21140i	−0.758043	−	0.246303i
$171$	−1.76419	−	8.29986i	−0.134911	−	0.634706i
$172$	23.2751	+	32.0354i	1.77471	+	2.44268i
$173$	1.98168	+	1.43977i	0.150664	+	0.109464i	0.660564	−	0.750770i	$-0.270317\pi$
$173$	1.98168	+	1.43977i	0.150664	+	0.109464i	−0.509899	+	0.860234i	$0.670317\pi$
$174$	−4.32136	+	20.3304i	−0.327602	+	1.54124i
$175$			2.82843i			0.213809i
$176$		0			0
$177$	−1.50000	+	2.59808i	−0.112747	+	0.195283i
$178$	−20.1750	+	6.55524i	−1.51218	+	0.491336i
$179$	9.16267	−	12.6113i	0.684850	−	0.942615i	−0.315130	−	0.949049i	$-0.602048\pi$
$179$	9.16267	−	12.6113i	0.684850	−	0.942615i	0.999979	+	0.00643384i	$0.00204797\pi$
$180$	−8.45386	+	18.9877i	−0.630114	+	1.41526i
$181$	−1.54508	+	4.75528i	−0.114845	+	0.353457i	−0.991915	−	0.126906i	$-0.959495\pi$
$181$	−1.54508	+	4.75528i	−0.114845	+	0.353457i	0.877069	+	0.480364i	$0.159495\pi$
$182$	3.02774	−	9.31841i	0.224431	−	0.690727i
$183$	0.512083	+	4.87214i	0.0378542	+	0.360159i
$184$	−24.9376	+	34.3237i	−1.83843	+	2.53038i
$185$	4.94183	−	1.60570i	0.363331	−	0.118053i
$186$	11.0227	+	6.36396i	0.808224	+	0.466628i
$187$		0			0
$188$			27.7128i			2.02116i
$189$	2.27080	+	6.98881i	0.165177	+	0.508361i
$190$	−9.70820	−	7.05342i	−0.704307	−	0.511709i
$191$	−3.05422	−	4.20378i	−0.220996	−	0.304175i	0.684095	−	0.729393i	$-0.260197\pi$
$191$	−3.05422	−	4.20378i	−0.220996	−	0.304175i	−0.905091	+	0.425218i	$0.860197\pi$
$192$	10.2973	−	9.27175i	0.743145	−	0.669131i
$193$	13.4500	+	4.37016i	0.968150	+	0.314571i	0.750069	−	0.661360i	$-0.230020\pi$
$193$	13.4500	+	4.37016i	0.968150	+	0.314571i	0.218081	+	0.975931i	$0.430020\pi$
$194$	25.7618	−	18.7171i	1.84959	−	1.34381i
$195$	3.45127	+	7.75169i	0.247151	+	0.555110i
$196$	6.18034	+	19.0211i	0.441453	+	1.35865i
$197$	7.34847			0.523557			0.261778	−	0.965128i	$-0.415691\pi$
$197$	7.34847			0.523557			0.261778	+	0.965128i	$0.415691\pi$
$198$		0			0
$199$	−18.0000			−1.27599			−0.637993	−	0.770042i	$-0.720235\pi$
$199$	−18.0000			−1.27599			−0.637993	+	0.770042i	$0.720235\pi$
$200$	−3.02774	−	9.31841i	−0.214093	−	0.658911i
$201$	−2.11347	−	4.74692i	−0.149072	−	0.334822i
$202$	24.2705	−	17.6336i	1.70767	−	1.24069i
$203$	6.58911	+	2.14093i	0.462465	+	0.150264i
$204$	12.6116	−	11.3555i	0.882988	−	0.795046i
$205$	9.97505	+	13.7295i	0.696687	+	0.958908i
$206$	−3.96336	−	2.87955i	−0.276140	−	0.200628i
$207$	−19.3075	−	17.3845i	−1.34196	−	1.20831i
$208$			11.3137i			0.784465i
$209$		0			0
$210$	9.00000	+	5.19615i	0.621059	+	0.358569i
$211$	−5.37999	+	1.74806i	−0.370374	+	0.120342i	−0.488289	−	0.872682i	$-0.662379\pi$
$211$	−5.37999	+	1.74806i	−0.370374	+	0.120342i	0.117915	+	0.993024i	$0.462379\pi$
$212$	−8.14459	+	11.2101i	−0.559373	+	0.769911i
$213$	−0.313585	−	2.98357i	−0.0214865	−	0.204431i
$214$	−1.85410	+	5.70634i	−0.126744	+	0.390077i
$215$	−5.29854	+	16.3072i	−0.361357	+	1.11214i
$216$	−14.9626	−	20.5942i	−1.01807	−	1.40126i
$217$	2.49376	−	3.43237i	0.169288	−	0.233004i
$218$	42.8292	−	13.9161i	2.90076	−	0.942515i
$219$	−4.89898	+	8.48528i	−0.331042	+	0.573382i
$220$		0			0
$221$		−	6.92820i		−	0.466041i
$222$	−2.64628	+	12.4498i	−0.177607	+	0.835575i
$223$	8.89919	+	6.46564i	0.595934	+	0.432971i	0.844433	−	0.535661i	$-0.179937\pi$
$223$	8.89919	+	6.46564i	0.595934	+	0.432971i	−0.248500	+	0.968632i	$0.579937\pi$
$224$		0			0
$225$	5.86889	−	1.24747i	0.391259	−	0.0831647i
$226$	4.03499	+	1.31105i	0.268404	+	0.0872096i
$227$	−17.8351	+	12.9580i	−1.18376	+	0.860050i	−0.992591	−	0.121507i	$-0.961227\pi$
$227$	−17.8351	+	12.9580i	−1.18376	+	0.860050i	−0.191167	+	0.981557i	$0.561227\pi$
$228$	17.9018	−	7.97038i	1.18557	−	0.527851i
$229$	−2.78115	−	8.55951i	−0.183784	−	0.565628i	0.816142	−	0.577852i	$-0.196109\pi$
$229$	−2.78115	−	8.55951i	−0.183784	−	0.565628i	−0.999925	+	0.0122238i	$0.996109\pi$
$230$	−36.7423			−2.42272
$231$		0			0
$232$	−24.0000			−1.57568
$233$	−7.56934	−	23.2960i	−0.495884	−	1.52617i	−0.815575	−	0.578652i	$-0.803579\pi$
$233$	−7.56934	−	23.2960i	−0.495884	−	1.52617i	0.319691	−	0.947522i	$-0.396421\pi$
$234$	−20.6707	−	2.17258i	−1.35129	−	0.142026i
$235$	−9.70820	+	7.05342i	−0.633293	+	0.460115i
$236$	−6.58911	−	2.14093i	−0.428915	−	0.139363i
$237$	−11.4732	−	12.7423i	−0.745264	−	0.827700i
$238$	−4.98752	−	6.86474i	−0.323293	−	0.444975i
$239$	17.8351	+	12.9580i	1.15366	+	0.838181i	0.988963	−	0.148164i	$-0.0473362\pi$
$239$	17.8351	+	12.9580i	1.15366	+	0.838181i	0.164694	+	0.986345i	$0.447336\pi$
$240$	−11.7378	−	2.49494i	−0.757670	−	0.161048i
$241$		−	2.82843i		−	0.182195i	−0.995842	−	0.0910975i	$-0.970963\pi$
$241$		−	2.82843i		−	0.182195i	0.995842	−	0.0910975i	$-0.0290375\pi$
$242$		0			0
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	−10.7600	+	3.49613i	−0.688837	+	0.223817i
$245$	−5.09037	+	7.00629i	−0.325212	+	0.447616i
$246$	−41.3415	+	4.34517i	−2.63584	+	0.277038i
$247$	2.47214	−	7.60845i	0.157298	−	0.484114i
$248$	−4.54160	+	13.9776i	−0.288392	+	0.887580i
$249$	4.21940	−	0.443477i	0.267394	−	0.0281042i
$250$	17.4563	−	24.0266i	1.10404	−	1.51957i
$251$	−14.8255	+	4.81710i	−0.935778	+	0.304053i	−0.736923	−	0.675977i	$-0.763722\pi$
$251$	−14.8255	+	4.81710i	−0.935778	+	0.304053i	−0.198854	+	0.980029i	$0.563722\pi$
$252$	−14.6969	+	8.48528i	−0.925820	+	0.534522i
$253$		0			0
$254$		−	6.92820i		−	0.434714i
$255$	7.18789	+	1.52783i	0.450123	+	0.0956766i
$256$	25.8885	+	18.8091i	1.61803	+	1.17557i
$257$	6.10844	+	8.40755i	0.381034	+	0.524449i	0.955858	−	0.293828i	$-0.0949295\pi$
$257$	6.10844	+	8.40755i	0.381034	+	0.524449i	−0.574824	+	0.818277i	$0.694929\pi$
$258$	−28.1035	−	31.2121i	−1.74965	−	1.94318i
$259$	4.03499	+	1.31105i	0.250722	+	0.0814646i
$260$	−15.8534	+	11.5182i	−0.983188	+	0.714328i
$261$	1.53625	−	14.6164i	0.0950914	−	0.904734i
$262$	9.27051	+	28.5317i	0.572734	+	1.76269i
$263$	12.2474			0.755210			0.377605	−	0.925967i	$-0.376748\pi$
$263$	12.2474			0.755210			0.377605	+	0.925967i	$0.376748\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$	−3.02774	−	9.31841i	−0.185642	−	0.571349i
$267$	13.7032	−	6.10105i	0.838621	−	0.373378i
$268$	9.70820	−	7.05342i	0.593023	−	0.430856i
$269$	−16.4728	−	5.35233i	−1.00436	−	0.326337i	−0.239755	−	0.970833i	$-0.577067\pi$
$269$	−16.4728	−	5.35233i	−1.00436	−	0.326337i	−0.764608	+	0.644496i	$0.777067\pi$
$270$	6.81241	−	20.9664i	0.414590	−	1.27598i
$271$	−3.32502	−	4.57649i	−0.201980	−	0.278002i	0.695996	−	0.718045i	$-0.254963\pi$
$271$	−3.32502	−	4.57649i	−0.201980	−	0.278002i	−0.897976	+	0.440043i	$0.854963\pi$
$272$	7.92672	+	5.75910i	0.480628	+	0.349196i
$273$	−1.44045	+	6.77681i	−0.0871803	+	0.410151i
$274$		−	38.1838i		−	2.30677i
$275$		0			0
$276$	30.0000	−	51.9615i	1.80579	−	3.12772i
$277$	17.4850	−	5.68121i	1.05057	−	0.341351i	0.267678	−	0.963509i	$-0.413744\pi$
$277$	17.4850	−	5.68121i	1.05057	−	0.341351i	0.782892	+	0.622158i	$0.213744\pi$
$278$	−22.3976	+	30.8277i	−1.34332	+	1.84892i
$279$	−8.22191	−	3.66063i	−0.492233	−	0.219156i
$280$	−3.70820	+	11.4127i	−0.221608	+	0.682038i
$281$	6.81241	−	20.9664i	0.406394	−	1.25075i	−0.513332	−	0.858190i	$-0.671589\pi$
$281$	6.81241	−	20.9664i	0.406394	−	1.25075i	0.919726	−	0.392562i	$-0.128411\pi$
$282$	−3.07250	−	29.2329i	−0.182965	−	1.74079i
$283$	−11.6376	+	16.0177i	−0.691781	+	0.952155i	0.308219	+	0.951315i	$0.400267\pi$
$283$	−11.6376	+	16.0177i	−0.691781	+	0.952155i	−1.00000		0.000839101i	$0.999733\pi$
$284$	6.58911	−	2.14093i	0.390992	−	0.127041i
$285$	7.34847	+	4.24264i	0.435286	+	0.251312i
$286$		0			0
$287$			13.8564i			0.817918i
$288$		0			0
$289$	8.89919	+	6.46564i	0.523482	+	0.380332i
$290$	−12.2169	−	16.8151i	−0.717400	−	0.987417i
$291$	−16.7331	+	15.0666i	−0.980914	+	0.883219i
$292$	−21.5200	−	6.99226i	−1.25936	−	0.409191i
$293$	−3.96336	+	2.87955i	−0.231542	+	0.168225i	−0.697507	−	0.716578i	$-0.745707\pi$
$293$	−3.96336	+	2.87955i	−0.231542	+	0.168225i	0.465965	+	0.884803i	$0.345707\pi$
$294$	−8.62819	−	19.3792i	−0.503206	−	1.13022i
$295$	−0.927051	−	2.85317i	−0.0539750	−	0.166118i
$296$	−14.6969			−0.854242
$297$		0			0
$298$	6.00000			0.347571
$299$	−7.56934	−	23.2960i	−0.437746	−	1.34724i
$300$	5.63591	+	12.6585i	0.325389	+	0.730836i
$301$	−11.3262	+	8.22899i	−0.652834	+	0.474311i
$302$	23.0619	+	7.49326i	1.32706	+	0.431189i
$303$	−15.7645	+	14.1944i	−0.905646	+	0.815447i
$304$	6.65003	+	9.15298i	0.381405	+	0.524960i
$305$	−3.96336	−	2.87955i	−0.226941	−	0.164882i
$306$	−12.0444	+	13.3766i	−0.688530	+	0.764690i
$307$		−	2.82843i		−	0.161427i	−0.996737	−	0.0807134i	$-0.974280\pi$
$307$		−	2.82843i		−	0.161427i	0.996737	−	0.0807134i	$-0.0257199\pi$
$308$		0			0
$309$	3.00000	+	1.73205i	0.170664	+	0.0985329i
$310$	−12.1050	+	3.93314i	−0.687516	+	0.223388i
$311$	−10.1807	+	14.0126i	−0.577297	+	0.794581i	−0.993396	−	0.114739i	$-0.963397\pi$
$311$	−10.1807	+	14.0126i	−0.577297	+	0.794581i	0.416099	+	0.909319i	$0.363397\pi$
$312$	−2.50868	−	23.8685i	−0.142026	−	1.35129i
$313$	−10.1976	+	31.3849i	−0.576400	+	1.77398i	0.0549609	+	0.998489i	$0.482497\pi$
$313$	−10.1976	+	31.3849i	−0.576400	+	1.77398i	−0.631361	+	0.775489i	$0.717503\pi$
$314$	−11.3540	+	34.9440i	−0.640744	+	1.97201i
$315$	−6.71316	−	2.98889i	−0.378244	−	0.168405i
$316$	23.2751	−	32.0354i	1.30933	−	1.80213i
$317$	1.64728	−	0.535233i	0.0925204	−	0.0300617i	−0.262391	−	0.964962i	$-0.584511\pi$
$317$	1.64728	−	0.535233i	0.0925204	−	0.0300617i	0.354911	+	0.934900i	$0.384511\pi$
$318$	7.34847	−	12.7279i	0.412082	−	0.713746i
$319$		0			0
$320$			13.8564i			0.774597i
$321$	0.882095	−	4.14993i	0.0492337	−	0.231626i
$322$	−24.2705	−	17.6336i	−1.35254	−	0.982680i
$323$	−4.07230	−	5.60503i	−0.226589	−	0.311872i
$324$	24.0887	+	26.7532i	1.33826	+	1.48629i
$325$	5.37999	+	1.74806i	0.298428	+	0.0969651i
$326$	−19.8168	+	14.3977i	−1.09755	+	0.797417i
$327$	−29.0904	+	12.9519i	−1.60870	+	0.716240i
$328$	−14.8328	−	45.6507i	−0.819005	−	2.52064i
$329$	−9.79796			−0.540179
$330$		0			0
$331$	5.00000			0.274825			0.137412	−	0.990514i	$-0.456121\pi$
$331$	5.00000			0.274825			0.137412	+	0.990514i	$0.456121\pi$
$332$	3.02774	+	9.31841i	0.166169	+	0.511414i
$333$	0.940756	−	8.95070i	0.0515531	−	0.490495i
$334$	38.8328	−	28.2137i	2.12484	−	1.54378i
$335$	4.94183	+	1.60570i	0.270001	+	0.0877287i
$336$	−6.55611	−	7.28130i	−0.357665	−	0.397228i
$337$	14.1313	+	19.4501i	0.769782	+	1.05951i	0.996337	+	0.0855154i	$0.0272537\pi$
$337$	14.1313	+	19.4501i	0.769782	+	1.05951i	−0.226555	+	0.973998i	$0.572746\pi$
$338$	9.90839	+	7.19887i	0.538946	+	0.391567i
$339$	−2.93444	−	0.623735i	−0.159377	−	0.0338766i
$340$			16.9706i			0.920358i
$341$		0			0
$342$	−18.0000	+	10.3923i	−0.973329	+	0.561951i
$343$	−16.1400	+	5.24419i	−0.871476	+	0.283160i
$344$	28.5061	−	39.2352i	1.53694	−	2.11542i
$345$	25.8384	−	2.71573i	1.39109	−	0.146210i
$346$	1.85410	−	5.70634i	0.0996771	−	0.306775i
$347$	−3.02774	+	9.31841i	−0.162537	+	0.500239i	−0.998846	−	0.0480198i	$-0.984709\pi$
$347$	−3.02774	+	9.31841i	−0.162537	+	0.500239i	0.836309	+	0.548258i	$0.184709\pi$
$348$	33.7552	−	3.54781i	1.80947	−	0.190183i
$349$	−5.81878	+	8.00886i	−0.311472	+	0.428704i	−0.935840	−	0.352426i	$-0.885357\pi$
$349$	−5.81878	+	8.00886i	−0.311472	+	0.428704i	0.624368	+	0.781131i	$0.285357\pi$
$350$	6.58911	−	2.14093i	0.352203	−	0.114438i
$351$	14.6969			0.784465
$352$		0			0
$353$			25.9808i			1.38282i	0.722464	+	0.691408i	$0.243009\pi$
$353$			25.9808i			1.38282i	−0.722464	+	0.691408i	$0.756991\pi$
$354$	7.18789	+	1.52783i	0.382032	+	0.0812034i
$355$	2.42705	+	1.76336i	0.128814	+	0.0935892i
$356$	20.3615	+	28.0252i	1.07916	+	1.48533i
$357$	4.01478	+	4.45887i	0.212485	+	0.235988i
$358$	−36.3149	−	11.7994i	−1.91930	−	0.623619i
$359$	19.8168	−	14.3977i	1.04589	−	0.759884i	0.0744635	−	0.997224i	$-0.476276\pi$
$359$	19.8168	−	14.3977i	1.04589	−	0.759884i	0.971427	+	0.237340i	$0.0762756\pi$
$360$	25.3164	+	2.66086i	1.33429	+	0.140240i
$361$	3.39919	+	10.4616i	0.178905	+	0.550612i
$362$	12.2474			0.643712
$363$		0			0
$364$	−16.0000			−0.838628
$365$	−3.02774	−	9.31841i	−0.158479	−	0.487748i
$366$	10.9625	−	4.88084i	0.573021	−	0.255126i
$367$	5.66312	−	4.11450i	0.295612	−	0.214775i	−0.430086	−	0.902788i	$-0.641517\pi$
$367$	5.66312	−	4.11450i	0.295612	−	0.214775i	0.725698	+	0.688013i	$0.241517\pi$
$368$	32.9456	+	10.7047i	1.71741	+	0.558019i
$369$	28.7516	−	6.11133i	1.49675	−	0.318143i
$370$	−7.48128	−	10.2971i	−0.388933	−	0.535321i
$371$	−3.96336	−	2.87955i	−0.205767	−	0.149499i
$372$	4.32136	−	20.3304i	0.224052	−	1.05408i
$373$			32.5269i			1.68418i	0.539337	+	0.842090i	$0.318675\pi$
$373$			32.5269i			1.68418i	−0.539337	+	0.842090i	$0.681325\pi$
$374$		0			0
$375$	−10.5000	+	18.1865i	−0.542218	+	0.939149i
$376$	32.2799	−	10.4884i	1.66471	−	0.540897i
$377$	8.14459	−	11.2101i	0.419468	−	0.577348i
$378$	14.5623	−	10.5801i	0.749004	−	0.544183i
$379$	5.25329	−	16.1680i	0.269843	−	0.830492i	−0.720695	−	0.693253i	$-0.756177\pi$
$379$	5.25329	−	16.1680i	0.269843	−	0.830492i	0.990538	−	0.137240i	$-0.0438230\pi$
$380$	−6.05547	+	18.6368i	−0.310639	+	0.956049i
$381$	0.512083	+	4.87214i	0.0262348	+	0.249607i
$382$	−7.48128	+	10.2971i	−0.382776	+	0.526846i
$383$	−21.4146	+	6.95803i	−1.09424	+	0.355539i	−0.799882	−	0.600158i	$-0.795104\pi$
$383$	−21.4146	+	6.95803i	−1.09424	+	0.355539i	−0.294354	+	0.955696i	$0.595104\pi$
$384$	−29.3939	−	16.9706i	−1.50000	−	0.866025i
$385$		0			0
$386$		−	34.6410i		−	1.76318i
$387$	22.0703	+	19.8722i	1.12190	+	1.01016i
$388$	−42.0689	−	30.5648i	−2.13572	−	1.55169i
$389$	−13.2350	−	18.2164i	−0.671039	−	0.923606i	0.328744	−	0.944419i	$-0.393375\pi$
$389$	−13.2350	−	18.2164i	−0.671039	−	0.923606i	−0.999783	+	0.0208128i	$0.993375\pi$
$390$	15.4460	−	13.9076i	0.782137	−	0.704240i
$391$	−20.1750	−	6.55524i	−1.02029	−	0.331513i
$392$	19.8168	−	14.3977i	1.00090	−	0.727196i
$393$	−8.62819	−	19.3792i	−0.435234	−	0.977553i
$394$	−5.56231	−	17.1190i	−0.280225	−	0.862444i
$395$	17.1464			0.862730
$396$		0			0
$397$	32.0000			1.60603			0.803017	−	0.595956i	$-0.203227\pi$
$397$	32.0000			1.60603			0.803017	+	0.595956i	$0.203227\pi$
$398$	13.6248	+	41.9329i	0.682950	+	2.10190i
$399$	2.81795	+	6.32923i	0.141074	+	0.316858i
$400$	−6.47214	+	4.70228i	−0.323607	+	0.235114i
$401$	−9.88367	−	3.21140i	−0.493567	−	0.160370i	0.0516490	−	0.998665i	$-0.483552\pi$
$401$	−9.88367	−	3.21140i	−0.493567	−	0.160370i	−0.545216	+	0.838296i	$0.683552\pi$
$402$	−9.45869	+	8.51664i	−0.471757	+	0.424772i
$403$	−4.98752	−	6.86474i	−0.248446	−	0.341957i
$404$	−39.6336	−	28.7955i	−1.97184	−	1.43263i
$405$	−3.24102	+	15.2478i	−0.161048	+	0.757670i
$406$		−	16.9706i		−	0.842235i
$407$		0			0
$408$	−18.0000	−	10.3923i	−0.891133	−	0.514496i
$409$	17.4850	−	5.68121i	0.864576	−	0.280918i	0.157037	−	0.987593i	$-0.449806\pi$
$409$	17.4850	−	5.68121i	0.864576	−	0.280918i	0.707538	+	0.706675i	$0.249806\pi$
$410$	24.4338	−	33.6302i	1.20670	−	1.66088i
$411$	2.82227	+	26.8521i	0.139212	+	1.32452i
$412$	−2.47214	+	7.60845i	−0.121793	+	0.374842i
$413$	0.756934	−	2.32960i	0.0372463	−	0.114632i
$414$	−25.8846	+	58.1377i	−1.27216	+	2.85731i
$415$	−2.49376	+	3.43237i	−0.122414	+	0.168488i
$416$		0			0
$417$	13.4722	−	23.3345i	0.659736	−	1.14270i
$418$		0			0
$419$		−	6.92820i		−	0.338465i	−0.985576	−	0.169232i	$-0.945871\pi$
$419$		−	6.92820i		−	0.338465i	0.985576	−	0.169232i	$-0.0541289\pi$
$420$	3.52838	−	16.5997i	0.172167	−	0.809983i
$421$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$421$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$422$	8.14459	+	11.2101i	0.396473	+	0.545698i
$423$	4.32136	+	20.3304i	0.210112	+	0.988499i
$424$	16.1400	+	5.24419i	0.783826	+	0.254680i
$425$	3.96336	−	2.87955i	0.192251	−	0.139679i
$426$	−6.71316	+	2.98889i	−0.325254	+	0.144812i
$427$	−1.23607	−	3.80423i	−0.0598175	−	0.184099i
$428$	9.79796			0.473602
$429$		0			0
$430$	42.0000			2.02542
$431$	−2.27080	−	6.98881i	−0.109381	−	0.336639i	0.881353	−	0.472458i	$-0.156633\pi$
$431$	−2.27080	−	6.98881i	−0.109381	−	0.336639i	−0.990734	+	0.135819i	$0.956633\pi$
$432$	−12.2169	+	16.8151i	−0.587785	+	0.809017i
$433$	−4.04508	+	2.93893i	−0.194394	+	0.141236i	−0.680725	−	0.732539i	$-0.738335\pi$
$433$	−4.04508	+	2.93893i	−0.194394	+	0.141236i	0.486331	+	0.873775i	$0.338335\pi$
$434$	−9.88367	−	3.21140i	−0.474431	−	0.154152i
$435$	9.83417	+	10.9220i	0.471512	+	0.523668i
$436$	−43.2252	−	59.4944i	−2.07011	−	2.84926i
$437$	−19.8168	−	14.3977i	−0.947966	−	0.688737i
$438$	23.4755	+	4.98988i	1.12170	+	0.238426i
$439$		−	5.65685i		−	0.269987i	−0.990846	−	0.134993i	$-0.956899\pi$
$439$		−	5.65685i		−	0.269987i	0.990846	−	0.134993i	$-0.0431013\pi$
$440$		0			0
$441$	7.50000	+	12.9904i	0.357143	+	0.618590i
$442$	−16.1400	+	5.24419i	−0.767700	+	0.249441i
$443$	−15.2711	+	21.0189i	−0.725552	+	0.998637i	0.273769	+	0.961796i	$0.411730\pi$
$443$	−15.2711	+	21.0189i	−0.725552	+	0.998637i	−0.999321	+	0.0368415i	$0.988270\pi$
$444$	20.6707	−	2.17258i	0.980990	−	0.103106i
$445$	−4.63525	+	14.2658i	−0.219732	+	0.676266i
$446$	8.32627	−	25.6256i	0.394260	−	1.21341i
$447$	−4.21940	+	0.443477i	−0.199571	+	0.0209757i
$448$	−6.65003	+	9.15298i	−0.314184	+	0.432438i
$449$	11.5309	−	3.74663i	0.544179	−	0.176814i	−0.0240112	−	0.999712i	$-0.507644\pi$
$449$	11.5309	−	3.74663i	0.544179	−	0.176814i	0.568190	+	0.822897i	$0.307644\pi$
$450$	−7.34847	−	12.7279i	−0.346410	−	0.600000i
$451$		0			0
$452$		−	6.92820i		−	0.325875i
$453$	−16.7717	−	3.56494i	−0.788005	−	0.167496i
$454$	43.6869	+	31.7404i	2.05033	+	1.48965i
$455$	−4.07230	−	5.60503i	−0.190912	−	0.262768i
$456$	−16.0591	−	17.8355i	−0.752038	−	0.835223i
$457$	29.5899	+	9.61435i	1.38416	+	0.449740i	0.904034	−	0.427460i	$-0.140591\pi$
$457$	29.5899	+	9.61435i	1.38416	+	0.449740i	0.480124	+	0.877200i	$0.340591\pi$
$458$	−17.8351	+	12.9580i	−0.833380	+	0.605486i
$459$	7.48128	−	10.2971i	0.349196	−	0.480628i
$460$	18.5410	+	57.0634i	0.864479	+	2.66059i
$461$	−4.89898			−0.228168			−0.114084	−	0.993471i	$-0.536393\pi$
$461$	−4.89898			−0.228168			−0.114084	+	0.993471i	$0.536393\pi$
$462$		0			0
$463$	19.0000			0.883005			0.441502	−	0.897260i	$-0.354446\pi$
$463$	19.0000			0.883005			0.441502	+	0.897260i	$0.354446\pi$
$464$	6.05547	+	18.6368i	0.281118	+	0.865193i
$465$	8.22191	−	3.66063i	0.381282	−	0.169758i
$466$	−48.5410	+	35.2671i	−2.24862	+	1.63372i
$467$	−24.7092	−	8.02850i	−1.14340	−	0.371515i	−0.324749	−	0.945800i	$-0.605280\pi$
$467$	−24.7092	−	8.02850i	−1.14340	−	0.371515i	−0.818655	+	0.574286i	$0.805280\pi$
$468$	7.05676	+	33.1994i	0.326199	+	1.53464i
$469$	2.49376	+	3.43237i	0.115151	+	0.158492i
$470$	23.7801	+	17.2773i	1.09690	+	0.796942i
$471$	5.40170	−	25.4130i	0.248897	−	1.17097i
$472$			8.48528i			0.390567i
$473$		0			0
$474$	−21.0000	+	36.3731i	−0.964562	+	1.67067i
$475$	5.37999	−	1.74806i	0.246851	−	0.0802067i
$476$	−8.14459	+	11.2101i	−0.373307	+	0.513813i
$477$	−4.22693	+	9.49384i	−0.193538	+	0.434693i
$478$	16.6869	−	51.3571i	0.763242	−	2.34902i
$479$	9.08321	−	27.9552i	0.415022	−	1.27731i	−0.497209	−	0.867631i	$-0.665642\pi$
$479$	9.08321	−	27.9552i	0.415022	−	1.27731i	0.912231	−	0.409676i	$-0.134358\pi$
$480$		0			0
$481$	4.98752	−	6.86474i	0.227411	−	0.313005i
$482$	−6.58911	+	2.14093i	−0.300126	+	0.0975168i
$483$	18.3712	+	10.6066i	0.835917	+	0.482617i
$484$		0			0
$485$		−	22.5167i		−	1.02243i
$486$	−28.3761	−	25.5499i	−1.28716	−	1.15897i
$487$	−21.8435	−	15.8702i	−0.989822	−	0.719147i	−0.0299396	−	0.999552i	$-0.509531\pi$
$487$	−21.8435	−	15.8702i	−0.989822	−	0.719147i	−0.959882	+	0.280404i	$0.909531\pi$
$488$	8.14459	+	11.2101i	0.368688	+	0.507456i
$489$	12.8716	−	11.5897i	0.582076	−	0.524104i
$490$	20.1750	+	6.55524i	0.911412	+	0.296136i
$491$	−19.8168	+	14.3977i	−0.894319	+	0.649761i	−0.937001	−	0.349328i	$-0.886410\pi$
$491$	−19.8168	+	14.3977i	−0.894319	+	0.649761i	0.0426814	+	0.999089i	$0.486410\pi$
$492$	27.6102	+	62.0135i	1.24476	+	2.79579i
$493$	−3.70820	−	11.4127i	−0.167009	−	0.514001i
$494$	−19.5959			−0.881662
$495$		0			0
$496$	12.0000			0.538816
$497$	0.756934	+	2.32960i	0.0339531	+	0.104497i
$498$	−4.22693	−	9.49384i	−0.189413	−	0.425429i
$499$	−4.85410	+	3.52671i	−0.217299	+	0.157877i	−0.691110	−	0.722749i	$-0.742878\pi$
$499$	−4.85410	+	3.52671i	−0.217299	+	0.157877i	0.473811	+	0.880627i	$0.342878\pi$
$500$	−46.1238	−	14.9865i	−2.06272	−	0.670218i
$501$	−25.2232	+	22.7110i	−1.12689	+	1.01465i
$502$	22.4439	+	30.8913i	1.00172	+	1.37875i
$503$	17.8351	+	12.9580i	0.795228	+	0.577767i	0.909510	−	0.415681i	$-0.136457\pi$
$503$	17.8351	+	12.9580i	0.795228	+	0.577767i	−0.114282	+	0.993448i	$0.536457\pi$
$504$	15.4460	+	13.9076i	0.688018	+	0.619495i
$505$		−	21.2132i		−	0.943975i
$506$		0			0
$507$	−7.50000	−	4.33013i	−0.333087	−	0.192308i
$508$	−10.7600	+	3.49613i	−0.477397	+	0.155116i
$509$	−17.3073	+	23.8214i	−0.767131	+	1.05586i	0.229457	+	0.973319i	$0.426305\pi$
$509$	−17.3073	+	23.8214i	−0.767131	+	1.05586i	−0.996587	+	0.0825459i	$0.973695\pi$
$510$	−1.88151	−	17.9014i	−0.0833148	−	0.792687i
$511$	2.47214	−	7.60845i	0.109361	−	0.336578i
$512$	12.1109	−	37.2737i	0.535233	−	1.64728i
$513$	11.8901	−	8.63864i	0.524960	−	0.381405i
$514$	14.9626	−	20.5942i	0.659971	−	0.908372i
$515$	−3.29456	+	1.07047i	−0.145176	+	0.0471704i
$516$	−34.2929	+	59.3970i	−1.50966	+	2.61481i
$517$		0			0
$518$		−	10.3923i		−	0.456612i
$519$	−0.882095	+	4.14993i	−0.0387197	+	0.182162i
$520$	19.4164	+	14.1068i	0.851466	+	0.618626i
$521$	−23.4157	−	32.2289i	−1.02586	−	1.41198i	−0.908012	−	0.418944i	$-0.862400\pi$
$521$	−23.4157	−	32.2289i	−1.02586	−	1.41198i	−0.117848	−	0.993032i	$-0.537600\pi$
$522$	−35.2133	+	7.48482i	−1.54124	+	0.327602i
$523$	−26.8999	−	8.74032i	−1.17625	−	0.382188i	−0.345279	−	0.938500i	$-0.612216\pi$
$523$	−26.8999	−	8.74032i	−1.17625	−	0.382188i	−0.830973	+	0.556313i	$0.812216\pi$
$524$	39.6336	−	28.7955i	1.73140	−	1.25794i
$525$	−4.47544	+	1.99259i	−0.195324	+	0.0869640i
$526$	−9.27051	−	28.5317i	−0.404213	−	1.24404i
$527$	−7.34847			−0.320104
$528$		0			0
$529$	−52.0000			−2.26087
$530$	4.54160	+	13.9776i	0.197275	+	0.607149i
$531$	−5.16769	−	0.543146i	−0.224259	−	0.0235705i
$532$	−12.9443	+	9.40456i	−0.561205	+	0.407740i
$533$	26.3565	+	8.56373i	1.14162	+	0.370936i
$534$	−24.5854	−	27.3049i	−1.06392	−	1.18160i
$535$	2.49376	+	3.43237i	0.107815	+	0.148394i
$536$	−11.8901	−	8.63864i	−0.513573	−	0.373133i
$537$	26.4100	+	5.61362i	1.13967	+	0.242245i
$538$			42.4264i			1.82913i
$539$		0			0
$540$	−36.0000			−1.54919
$541$	−13.4500	+	4.37016i	−0.578259	+	0.187888i	−0.583521	−	0.812098i	$-0.698325\pi$
$541$	−13.4500	+	4.37016i	−0.578259	+	0.187888i	0.00526127	+	0.999986i	$0.498325\pi$
$542$	−8.14459	+	11.2101i	−0.349840	+	0.481514i
$543$	−8.61281	+	0.905243i	−0.369611	+	0.0388477i
$544$		0			0
$545$	9.84014	−	30.2848i	0.421505	−	1.29726i
$546$	16.8776	−	1.77391i	0.722294	−	0.0759162i
$547$	8.31254	−	11.4412i	0.355418	−	0.489192i	−0.593447	−	0.804873i	$-0.702233\pi$
$547$	8.31254	−	11.4412i	0.355418	−	0.489192i	0.948865	+	0.315682i	$0.102233\pi$
$548$	−59.3020	+	19.2684i	−2.53326	+	0.823105i
$549$	−7.34847	+	4.24264i	−0.313625	+	0.181071i
$550$		0			0
$551$		−	13.8564i		−	0.590303i
$552$	−71.8789	−	15.2783i	−3.05937	−	0.650289i
$553$	11.3262	+	8.22899i	0.481641	+	0.349932i
$554$	−26.4699	−	36.4327i	−1.12460	−	1.54788i
$555$	6.02218	+	6.68830i	0.255627	+	0.283903i
$556$	59.1799	+	19.2287i	2.50979	+	0.815479i
$557$	25.7618	−	18.7171i	1.09156	−	0.793067i	0.111901	−	0.993719i	$-0.464306\pi$
$557$	25.7618	−	18.7171i	1.09156	−	0.793067i	0.979663	+	0.200652i	$0.0643061\pi$
$558$	−2.30437	+	21.9246i	−0.0975519	+	0.928144i
$559$	8.65248	+	26.6296i	0.365961	+	1.12631i
$560$	9.79796			0.414039
$561$		0			0
$562$	−54.0000			−2.27785
$563$	−1.51387	−	4.65921i	−0.0638019	−	0.196362i	0.914074	−	0.405547i	$-0.132919\pi$
$563$	−1.51387	−	4.65921i	−0.0638019	−	0.196362i	−0.977876	+	0.209185i	$0.932919\pi$
$564$	−43.8502	+	19.5234i	−1.84643	+	0.822082i
$565$	2.42705	−	1.76336i	0.102107	−	0.0741849i
$566$	46.1238	+	14.9865i	1.93873	+	0.629931i
$567$	−9.45869	+	8.51664i	−0.397228	+	0.357665i
$568$	−4.98752	−	6.86474i	−0.209272	−	0.288038i
$569$	23.7801	+	17.2773i	0.996916	+	0.724302i	0.961425	−	0.275068i	$-0.0887005\pi$
$569$	23.7801	+	17.2773i	0.996916	+	0.724302i	0.0354909	+	0.999370i	$0.488701\pi$
$570$	4.32136	−	20.3304i	0.181002	−	0.851547i
$571$		−	19.7990i		−	0.828562i	−0.910149	−	0.414281i	$-0.864033\pi$
$571$		−	19.7990i		−	0.828562i	0.910149	−	0.414281i	$-0.135967\pi$
$572$		0			0
$573$	4.50000	−	7.79423i	0.187990	−	0.325609i
$574$	32.2799	−	10.4884i	1.34734	−	0.437777i
$575$	10.1807	−	14.0126i	0.424566	−	0.584365i
$576$	21.9251	+	9.76168i	0.913545	+	0.406737i
$577$	0.927051	−	2.85317i	0.0385936	−	0.118779i	−0.929904	−	0.367803i	$-0.880110\pi$
$577$	0.927051	−	2.85317i	0.0385936	−	0.118779i	0.968497	+	0.249024i	$0.0801099\pi$
$578$	8.32627	−	25.6256i	0.346327	−	1.06589i
$579$	2.56041	+	24.3607i	0.106407	+	1.01240i
$580$	−19.9501	+	27.4589i	−0.828383	+	1.14017i
$581$	−3.29456	+	1.07047i	−0.136681	+	0.0444104i
$582$	47.7650	+	27.5772i	1.97993	+	1.14311i
$583$		0			0
$584$			27.7128i			1.14676i
$585$	−9.83417	+	10.9220i	−0.406593	+	0.451567i
$586$	9.70820	+	7.05342i	0.401042	+	0.291374i
$587$	16.2892	+	22.4201i	0.672327	+	0.925378i	0.999810	−	0.0194787i	$-0.00620067\pi$
$587$	16.2892	+	22.4201i	0.672327	+	0.925378i	−0.327484	+	0.944857i	$0.606201\pi$
$588$	−25.7433	+	23.1794i	−1.06164	+	0.955901i
$589$	−8.06998	−	2.62210i	−0.332518	−	0.108042i
$590$	−5.94504	+	4.31932i	−0.244753	+	0.177824i
$591$	5.17691	+	11.6275i	0.212950	+	0.478293i
$592$	3.70820	+	11.4127i	0.152406	+	0.469058i
$593$	−19.5959			−0.804708			−0.402354	−	0.915484i	$-0.631808\pi$
$593$	−19.5959			−0.804708			−0.402354	+	0.915484i	$0.631808\pi$
$594$		0			0
$595$	−6.00000			−0.245976
$596$	−3.02774	−	9.31841i	−0.124021	−	0.381697i
$597$	−12.6808	−	28.4815i	−0.518990	−	1.16567i
$598$	−48.5410	+	35.2671i	−1.98499	+	1.44218i
$599$	−19.7673	−	6.42280i	−0.807672	−	0.262428i	−0.124060	−	0.992275i	$-0.539592\pi$
$599$	−19.7673	−	6.42280i	−0.807672	−	0.262428i	−0.683611	+	0.729846i	$0.739592\pi$
$600$	12.6116	−	11.3555i	0.514866	−	0.463587i
$601$	0.831254	+	1.14412i	0.0339076	+	0.0466697i	0.825634	−	0.564206i	$-0.190818\pi$
$601$	0.831254	+	1.14412i	0.0339076	+	0.0466697i	−0.791727	+	0.610876i	$0.790818\pi$
$602$	27.7435	+	20.1568i	1.13074	+	0.821531i
$603$	6.02218	−	6.68830i	0.245242	−	0.272369i
$604$		−	39.5980i		−	1.61122i
$605$		0			0
$606$	45.0000	+	25.9808i	1.82800	+	1.05540i
$607$	−9.41498	+	3.05911i	−0.382142	+	0.124166i	−0.493788	−	0.869583i	$-0.664388\pi$
$607$	−9.41498	+	3.05911i	−0.382142	+	0.124166i	0.111645	+	0.993748i	$0.464388\pi$
$608$		0			0
$609$	1.25434	+	11.9343i	0.0508285	+	0.483601i
$610$	−3.70820	+	11.4127i	−0.150141	+	0.462086i
$611$	−6.05547	+	18.6368i	−0.244978	+	0.753965i
$612$	26.8526	+	11.9556i	1.08545	+	0.483275i
$613$	6.65003	−	9.15298i	0.268592	−	0.369685i	−0.653322	−	0.757081i	$-0.726625\pi$
$613$	6.65003	−	9.15298i	0.268592	−	0.369685i	0.921914	+	0.387395i	$0.126625\pi$
$614$	−6.58911	+	2.14093i	−0.265915	+	0.0864010i
$615$	−14.6969	+	25.4558i	−0.592638	+	1.02648i
$616$		0			0
$617$			10.3923i			0.418378i	0.977875	+	0.209189i	$0.0670825\pi$
$617$			10.3923i			0.418378i	−0.977875	+	0.209189i	$0.932918\pi$
$618$	1.76419	−	8.29986i	0.0709661	−	0.333869i
$619$	20.2254	+	14.6946i	0.812928	+	0.590627i	0.914678	−	0.404183i	$-0.132444\pi$
$619$	20.2254	+	14.6946i	0.812928	+	0.590627i	−0.101750	+	0.994810i	$0.532444\pi$
$620$	12.2169	+	16.8151i	0.490642	+	0.675311i
$621$	13.9058	−	42.7975i	0.558019	−	1.71741i
$622$	40.3499	+	13.1105i	1.61788	+	0.525682i
$623$	−9.90839	+	7.19887i	−0.396971	+	0.288417i
$624$	−17.9018	+	7.97038i	−0.716644	+	0.319070i
$625$	−3.39919	−	10.4616i	−0.135967	−	0.418465i
$626$	80.8332			3.23074
$627$		0			0
$628$	60.0000			2.39426
$629$	−2.27080	−	6.98881i	−0.0905428	−	0.278662i
$630$	−1.88151	+	17.9014i	−0.0749612	+	0.713209i
$631$	31.5517	−	22.9236i	1.25605	−	0.912575i	0.257495	−	0.966280i	$-0.417103\pi$
$631$	31.5517	−	22.9236i	1.25605	−	0.912575i	0.998557	+	0.0537045i	$0.0171029\pi$
$632$	−46.1238	−	14.9865i	−1.83471	−	0.596132i
$633$	−6.55611	−	7.28130i	−0.260582	−	0.289406i
$634$	−2.49376	−	3.43237i	−0.0990399	−	0.136317i
$635$	−3.96336	−	2.87955i	−0.157281	−	0.114271i
$636$	−23.4755	−	4.98988i	−0.930866	−	0.197862i
$637$			14.1421i			0.560332i
$638$		0			0
$639$	4.50000	−	2.59808i	0.178017	−	0.102778i
$640$	32.2799	−	10.4884i	1.27598	−	0.414590i
$641$	5.09037	−	7.00629i	0.201058	−	0.276732i	−0.696568	−	0.717491i	$-0.745291\pi$
$641$	5.09037	−	7.00629i	0.201058	−	0.276732i	0.897626	+	0.440759i	$0.145291\pi$
$642$	−10.3354	+	1.08629i	−0.407905	+	0.0428725i
$643$	2.16312	−	6.65740i	0.0853051	−	0.262542i	−0.899301	−	0.437330i	$-0.855924\pi$
$643$	2.16312	−	6.65740i	0.0853051	−	0.262542i	0.984606	+	0.174788i	$0.0559241\pi$
$644$	−15.1387	+	46.5921i	−0.596548	+	1.83598i
$645$	−29.5358	+	3.10434i	−1.16297	+	0.122233i
$646$	−9.97505	+	13.7295i	−0.392463	+	0.540179i
$647$	28.0037	−	9.09896i	1.10094	−	0.357717i	0.298476	−	0.954417i	$-0.403522\pi$
$647$	28.0037	−	9.09896i	1.10094	−	0.357717i	0.802464	+	0.596700i	$0.203522\pi$
$648$	22.0454	−	38.1838i	0.866025	−	1.50000i
$649$		0			0
$650$		−	13.8564i		−	0.543493i
$651$	7.18789	+	1.52783i	0.281716	+	0.0598805i
$652$	32.3607	+	23.5114i	1.26734	+	0.920778i
$653$	1.01807	+	1.40126i	0.0398403	+	0.0548355i	0.828472	−	0.560030i	$-0.189210\pi$
$653$	1.01807	+	1.40126i	0.0398403	+	0.0548355i	−0.788632	+	0.614865i	$0.789210\pi$
$654$	52.1922	+	57.9653i	2.04088	+	2.26662i
$655$	20.1750	+	6.55524i	0.788301	+	0.256134i
$656$	−31.7069	+	23.0364i	−1.23794	+	0.899420i
$657$	−16.8776	−	1.77391i	−0.658458	−	0.0692067i
$658$	7.41641	+	22.8254i	0.289122	+	0.889825i
$659$	−36.7423			−1.43128			−0.715639	−	0.698470i	$-0.753865\pi$
$659$	−36.7423			−1.43128			−0.715639	+	0.698470i	$0.753865\pi$
$660$		0			0
$661$	15.0000			0.583432			0.291716	−	0.956505i	$-0.405774\pi$
$661$	15.0000			0.583432			0.291716	+	0.956505i	$0.405774\pi$
$662$	−3.78467	−	11.6480i	−0.147095	−	0.452713i
$663$	10.9625	−	4.88084i	0.425750	−	0.189556i
$664$	9.70820	−	7.05342i	0.376751	−	0.273726i
$665$	−6.58911	−	2.14093i	−0.255515	−	0.0830218i
$666$	−21.5637	+	4.58350i	−0.835575	+	0.177607i
$667$	−24.9376	−	34.3237i	−0.965588	−	1.32902i
$668$	−63.4137	−	46.0728i	−2.45355	−	1.78261i
$669$	−3.96125	+	18.6362i	−0.153151	+	0.720518i
$670$		−	12.7279i		−	0.491723i
$671$		0			0
$672$		0			0
$673$	30.9349	−	10.0514i	1.19245	−	0.387452i	0.355474	−	0.934686i	$-0.384319\pi$
$673$	30.9349	−	10.0514i	1.19245	−	0.387452i	0.836980	+	0.547234i	$0.184319\pi$
$674$	34.6145	−	47.6428i	1.33330	−	1.83513i
$675$	6.10844	+	8.40755i	0.235114	+	0.323607i
$676$	6.18034	−	19.0211i	0.237705	−	0.731582i
$677$	−12.8679	+	39.6033i	−0.494553	+	1.52208i	0.323100	+	0.946365i	$0.395275\pi$
$677$	−12.8679	+	39.6033i	−0.494553	+	1.52208i	−0.817653	+	0.575712i	$0.804725\pi$
$678$	0.768124	+	7.30821i	0.0294996	+	0.280670i
$679$	10.8063	−	14.8736i	0.414708	−	0.570796i
$680$	19.7673	−	6.42280i	0.758043	−	0.246303i
$681$	−33.0681	−	19.0919i	−1.26717	−	0.731603i
$682$		0			0
$683$		−	45.0333i		−	1.72315i	−0.507628	−	0.861576i	$-0.669478\pi$
$683$		−	45.0333i		−	1.72315i	0.507628	−	0.861576i	$-0.330522\pi$
$684$	25.2232	+	22.7110i	0.964432	+	0.868379i
$685$	−21.8435	−	15.8702i	−0.834596	−	0.606369i
$686$	24.4338	+	33.6302i	0.932886	+	1.28401i
$687$	11.5845	−	10.4307i	0.441976	−	0.397957i
$688$	−37.6599	−	12.2364i	−1.43577	−	0.466510i
$689$	−7.92672	+	5.75910i	−0.301984	+	0.219404i
$690$	−25.8846	−	58.1377i	−0.985408	−	2.21326i
$691$	1.54508	+	4.75528i	0.0587778	+	0.180899i	0.976135	−	0.217167i	$-0.0696815\pi$
$691$	1.54508	+	4.75528i	0.0587778	+	0.180899i	−0.917357	+	0.398066i	$0.869681\pi$
$692$	−9.79796			−0.372463
$693$		0			0
$694$	24.0000			0.911028
$695$	8.32627	+	25.6256i	0.315834	+	0.972036i
$696$	−16.9077	−	37.9754i	−0.640886	−	1.43945i
$697$	19.4164	−	14.1068i	0.735449	−	0.534335i
$698$	23.0619	+	7.49326i	0.872906	+	0.283624i
$699$	31.5290	−	28.3888i	1.19253	−	1.07376i
$700$	−6.65003	−	9.15298i	−0.251348	−	0.345950i
$701$	21.7985	+	15.8375i	0.823317	+	0.598175i	0.917661	−	0.397365i	$-0.130075\pi$
$701$	21.7985	+	15.8375i	0.823317	+	0.598175i	−0.0943439	+	0.995540i	$0.530075\pi$
$702$	−11.1246	−	34.2380i	−0.419871	−	1.29223i
$703$		−	8.48528i		−	0.320028i
$704$		0			0
$705$	−18.0000	−	10.3923i	−0.677919	−	0.391397i
$706$	60.5249	−	19.6657i	2.27788	−	0.740129i
$707$	10.1807	−	14.0126i	0.382886	−	0.526998i
$708$	−1.25434	−	11.9343i	−0.0471410	−	0.448517i
$709$	0.927051	−	2.85317i	0.0348161	−	0.107153i	−0.932138	−	0.362103i	$-0.882059\pi$
$709$	0.927051	−	2.85317i	0.0348161	−	0.107153i	0.966954	+	0.254950i	$0.0820589\pi$
$710$	2.27080	−	6.98881i	0.0852217	−	0.262285i
$711$	12.0795	−	27.1309i	0.453015	−	1.01749i
$712$	24.9376	−	34.3237i	0.934577	−	1.28633i
$713$	−24.7092	+	8.02850i	−0.925366	+	0.300670i
$714$	7.34847	−	12.7279i	0.275010	−	0.476331i
$715$		0			0
$716$			62.3538i			2.33027i
$717$	−7.93885	+	37.3494i	−0.296482	+	1.39484i
$718$	−48.5410	−	35.2671i	−1.81153	−	1.31616i
$719$	7.12652	+	9.80881i	0.265774	+	0.365807i	0.920957	−	0.389663i	$-0.127409\pi$
$719$	7.12652	+	9.80881i	0.265774	+	0.365807i	−0.655183	+	0.755470i	$0.727409\pi$
$720$	−4.32136	−	20.3304i	−0.161048	−	0.757670i
$721$	−2.68999	−	0.874032i	−0.100181	−	0.0325507i
$722$	21.7985	−	15.8375i	0.811255	−	0.589411i
$723$	4.47544	−	1.99259i	0.166443	−	0.0741054i
$724$	−6.18034	−	19.0211i	−0.229691	−	0.706915i
$725$	9.79796			0.363887
$726$		0			0
$727$	−3.00000			−0.111264			−0.0556319	−	0.998451i	$-0.517717\pi$
$727$	−3.00000			−0.111264			−0.0556319	+	0.998451i	$0.517717\pi$
$728$	6.05547	+	18.6368i	0.224431	+	0.690727i
$729$	21.8435	+	15.8702i	0.809017	+	0.587785i
$730$	−19.4164	+	14.1068i	−0.718633	+	0.522118i
$731$	23.0619	+	7.49326i	0.852975	+	0.277148i
$732$	−13.1122	−	14.5626i	−0.484642	−	0.538249i
$733$	−21.6126	−	29.7472i	−0.798280	−	1.09874i	−0.993027	−	0.117884i	$-0.962389\pi$
$733$	−21.6126	−	29.7472i	−0.798280	−	1.09874i	0.194748	−	0.980853i	$-0.437611\pi$
$734$	−13.8718	−	10.0784i	−0.512016	−	0.372001i
$735$	−14.6722	−	3.11868i	−0.541193	−	0.115034i
$736$		0			0
$737$		0			0
$738$	−36.0000	−	62.3538i	−1.32518	−	2.29528i
$739$	−49.7649	+	16.1696i	−1.83063	+	0.594808i	−0.831397	+	0.555679i	$0.812458\pi$
$739$	−49.7649	+	16.1696i	−1.83063	+	0.594808i	−0.999234	+	0.0391291i	$0.987542\pi$
$740$	−12.2169	+	16.8151i	−0.449102	+	0.618135i
$741$	13.7805	−	1.44839i	0.506239	−	0.0532079i
$742$	−3.70820	+	11.4127i	−0.136132	+	0.418973i
$743$	4.54160	−	13.9776i	0.166615	−	0.512789i	−0.832536	−	0.553970i	$-0.813112\pi$
$743$	4.54160	−	13.9776i	0.166615	−	0.512789i	0.999152	+	0.0411812i	$0.0131121\pi$
$744$	−25.3164	+	2.66086i	−0.928144	+	0.0975519i
$745$	2.49376	−	3.43237i	0.0913644	−	0.125752i
$746$	75.7748	−	24.6207i	2.77431	−	0.901429i
$747$	3.67423	+	6.36396i	0.134433	+	0.232845i
$748$		0			0
$749$			3.46410i			0.126576i
$750$	50.3152	+	10.6948i	1.83725	+	0.390520i
$751$	−21.8435	−	15.8702i	−0.797079	−	0.579112i	0.112977	−	0.993598i	$-0.463961\pi$
$751$	−21.8435	−	15.8702i	−0.797079	−	0.579112i	−0.910056	+	0.414486i	$0.863961\pi$
$752$	−16.2892	−	22.4201i	−0.594005	−	0.817578i
$753$	−18.0665	−	20.0649i	−0.658381	−	0.731206i
$754$	−32.2799	−	10.4884i	−1.17557	−	0.381964i
$755$	13.8718	−	10.0784i	0.504845	−	0.366791i
$756$	−23.7801	−	17.2773i	−0.864876	−	0.628369i
$757$	−9.27051	−	28.5317i	−0.336942	−	1.03700i	−0.965757	−	0.259447i	$-0.916460\pi$
$757$	−9.27051	−	28.5317i	−0.336942	−	1.03700i	0.628815	−	0.777555i	$-0.283540\pi$
$758$	−41.6413			−1.51248
$759$		0			0
$760$	24.0000			0.870572
$761$	7.56934	+	23.2960i	0.274388	+	0.844480i	0.989381	+	0.145348i	$0.0464302\pi$
$761$	7.56934	+	23.2960i	0.274388	+	0.844480i	−0.714992	+	0.699132i	$0.753570\pi$
$762$	10.9625	−	4.88084i	0.397131	−	0.176814i
$763$	21.0344	−	15.2824i	0.761498	−	0.553261i
$764$	19.7673	+	6.42280i	0.715157	+	0.232369i
$765$	2.64628	+	12.4498i	0.0956766	+	0.450123i
$766$	32.4189	+	44.6208i	1.17134	+	1.61221i
$767$	−3.96336	−	2.87955i	−0.143109	−	0.103974i
$768$	−11.5236	+	54.2144i	−0.415823	+	1.95630i
$769$			14.1421i			0.509978i	0.966944	+	0.254989i	$0.0820719\pi$
$769$			14.1421i			0.509978i	−0.966944	+	0.254989i	$0.917928\pi$
$770$		0			0
$771$	−9.00000	+	15.5885i	−0.324127	+	0.561405i
$772$	−53.7999	+	17.4806i	−1.93630	+	0.629142i
$773$	−2.03615	+	2.80252i	−0.0732351	+	0.100800i	−0.844063	−	0.536244i	$-0.819843\pi$
$773$	−2.03615	+	2.80252i	−0.0732351	+	0.100800i	0.770828	+	0.637043i	$0.219843\pi$
$774$	29.5885	−	66.4569i	1.06354	−	2.38874i
$775$	1.85410	−	5.70634i	0.0666013	−	0.204978i
$776$	−19.6803	+	60.5697i	−0.706481	+	2.17432i
$777$	0.768124	+	7.30821i	0.0275563	+	0.262181i
$778$	−32.4189	+	44.6208i	−1.16227	+	1.59973i
$779$	26.3565	−	8.56373i	0.944318	−	0.306827i
$780$	−29.3939	−	16.9706i	−1.05247	−	0.607644i
$781$		0			0
$782$			51.9615i			1.85814i
$783$	24.2099	−	7.86629i	0.865193	−	0.281118i
$784$	−16.1803	−	11.7557i	−0.577869	−	0.419847i
$785$	15.2711	+	21.0189i	0.545049	+	0.750196i
$786$	−38.6149	+	34.7690i	−1.37735	+	1.24017i
$787$	−26.8999	−	8.74032i	−0.958879	−	0.311559i	−0.212561	−	0.977148i	$-0.568180\pi$
$787$	−26.8999	−	8.74032i	−0.958879	−	0.311559i	−0.746318	+	0.665589i	$0.768180\pi$
$788$	−23.7801	+	17.2773i	−0.847133	+	0.615478i
$789$	8.62819	+	19.3792i	0.307172	+	0.689919i
$790$	−12.9787	−	39.9444i	−0.461762	−	1.42116i
$791$	2.44949			0.0870938
$792$		0			0
$793$	−8.00000			−0.284088
$794$	−24.2219	−	74.5473i	−0.859603	−	2.64558i
$795$	−4.22693	−	9.49384i	−0.149914	−	0.336712i
$796$	58.2492	−	42.3205i	2.06459	−	1.50001i
$797$	31.2983	+	10.1694i	1.10864	+	0.360220i	0.805423	−	0.592701i	$-0.201938\pi$
$797$	31.2983	+	10.1694i	1.10864	+	0.360220i	0.303220	+	0.952921i	$0.401938\pi$
$798$	12.6116	−	11.3555i	0.446445	−	0.401981i
$799$	9.97505	+	13.7295i	0.352892	+	0.485714i
$800$		0			0
$801$	19.3075	+	17.3845i	0.682196	+	0.614252i
$802$			25.4558i			0.898877i
$803$		0			0
$804$	18.0000	+	10.3923i	0.634811	+	0.366508i
$805$	−20.1750	+	6.55524i	−0.711074	+	0.231042i
$806$	−12.2169	+	16.8151i	−0.430321	+	0.592287i
$807$	−3.13585	−	29.8357i	−0.110387	−	1.05026i
$808$	−18.5410	+	57.0634i	−0.652271	+	2.00748i
$809$	−15.1387	+	46.5921i	−0.532248	+	1.63809i	0.217275	+	0.976111i	$0.430283\pi$
$809$	−15.1387	+	46.5921i	−0.532248	+	1.63809i	−0.749522	+	0.661979i	$0.769717\pi$
$810$	37.9746	−	3.99129i	1.33429	−	0.140240i
$811$	9.14379	−	12.5854i	0.321082	−	0.441931i	−0.617715	−	0.786402i	$-0.711942\pi$
$811$	9.14379	−	12.5854i	0.321082	−	0.441931i	0.938797	+	0.344470i	$0.111942\pi$
$812$	−26.3565	+	8.56373i	−0.924930	+	0.300528i
$813$	4.89898	−	8.48528i	0.171815	−	0.297592i
$814$		0			0
$815$			17.3205i			0.606711i
$816$	−3.52838	+	16.5997i	−0.123518	+	0.581106i
$817$	22.6525	+	16.4580i	0.792510	+	0.575792i
$818$	−26.4699	−	36.4327i	−0.925499	−	1.27384i
$819$	−11.7378	+	2.49494i	−0.410151	+	0.0871803i
$820$	−64.5599	−	20.9768i	−2.25453	−	0.732541i
$821$	−25.7618	+	18.7171i	−0.899094	+	0.653230i	−0.938233	−	0.346004i	$-0.887538\pi$
$821$	−25.7618	+	18.7171i	−0.899094	+	0.653230i	0.0391392	+	0.999234i	$0.487538\pi$
$822$	60.4184	−	26.9000i	2.10734	−	0.938246i
$823$	9.57953	+	29.4828i	0.333921	+	1.02770i	0.967251	+	0.253822i	$0.0816877\pi$
$823$	9.57953	+	29.4828i	0.333921	+	1.02770i	−0.633330	+	0.773882i	$0.718312\pi$
$824$	9.79796			0.341328
$825$		0			0
$826$	−6.00000			−0.208767
$827$	−1.51387	−	4.65921i	−0.0526423	−	0.162016i	0.921279	−	0.388902i	$-0.127146\pi$
$827$	−1.51387	−	4.65921i	−0.0526423	−	0.162016i	−0.973921	+	0.226886i	$0.927146\pi$
$828$	103.354	+	10.8629i	3.59179	+	0.377512i
$829$	−25.0795	+	18.2213i	−0.871048	+	0.632853i	−0.930868	−	0.365356i	$-0.880947\pi$
$829$	−25.0795	+	18.2213i	−0.871048	+	0.632853i	0.0598200	+	0.998209i	$0.480947\pi$
$830$	9.88367	+	3.21140i	0.343067	+	0.111469i
$831$	21.3074	+	23.6642i	0.739145	+	0.820903i
$832$	13.3001	+	18.3060i	0.461097	+	0.634645i
$833$	9.90839	+	7.19887i	0.343306	+	0.249426i
$834$	−64.5577	−	13.7222i	−2.23545	−	0.475160i
$835$		−	33.9411i		−	1.17458i
$836$		0			0
$837$		−	15.5885i		−	0.538816i
$838$	−16.1400	+	5.24419i	−0.557546	+	0.181158i
$839$	−27.4880	+	37.8340i	−0.948991	+	1.30617i	0.00298311	+	0.999996i	$0.499050\pi$
$839$	−27.4880	+	37.8340i	−0.948991	+	1.30617i	−0.951974	+	0.306179i	$0.900950\pi$
$840$	−20.6707	+	2.17258i	−0.713209	+	0.0749612i
$841$	−1.54508	+	4.75528i	−0.0532788	+	0.163975i
$842$		0			0
$843$	37.9746	−	3.99129i	1.30791	−	0.137467i
$844$	13.3001	−	18.3060i	0.457807	−	0.630117i
$845$	8.23639	−	2.67617i	0.283340	−	0.0920629i
$846$	44.0908	−	25.4558i	1.51587	−	0.875190i
$847$		0			0
$848$		−	13.8564i		−	0.475831i
$849$	−33.5435	−	7.12989i	−1.15121	−	0.244697i
$850$	−9.70820	−	7.05342i	−0.332989	−	0.241930i
$851$	−15.2711	−	21.0189i	−0.523487	−	0.720518i
$852$	8.02957	+	8.91774i	0.275088	+	0.305517i
$853$	−55.1449	−	17.9177i	−1.88812	−	0.613489i	−0.981470	−	0.191615i	$-0.938628\pi$
$853$	−55.1449	−	17.9177i	−1.88812	−	0.613489i	−0.906654	−	0.421874i	$-0.861372\pi$
$854$	−7.92672	+	5.75910i	−0.271247	+	0.197072i
$855$	−1.53625	+	14.6164i	−0.0525386	+	0.499871i
$856$	−3.70820	−	11.4127i	−0.126744	−	0.390077i
$857$	−19.5959			−0.669384			−0.334692	−	0.942328i	$-0.608632\pi$
$857$	−19.5959			−0.669384			−0.334692	+	0.942328i	$0.608632\pi$
$858$		0			0
$859$	25.0000			0.852989			0.426494	−	0.904490i	$-0.359748\pi$
$859$	25.0000			0.852989			0.426494	+	0.904490i	$0.359748\pi$
$860$	−21.1942	−	65.2289i	−0.722715	−	2.22429i
$861$	−21.9251	+	9.76168i	−0.747205	+	0.332677i
$862$	−14.5623	+	10.5801i	−0.495994	+	0.360361i
$863$	−19.7673	−	6.42280i	−0.672888	−	0.218635i	−0.0474090	−	0.998876i	$-0.515096\pi$
$863$	−19.7673	−	6.42280i	−0.672888	−	0.218635i	−0.625479	+	0.780241i	$0.715096\pi$
$864$		0			0
$865$	−2.49376	−	3.43237i	−0.0847904	−	0.116704i
$866$	9.90839	+	7.19887i	0.336701	+	0.244628i
$867$	−3.96125	+	18.6362i	−0.134531	+	0.632919i
$868$			16.9706i			0.576018i
$869$		0			0
$870$	18.0000	−	31.1769i	0.610257	−	1.05700i
$871$	8.06998	−	2.62210i	0.273441	−	0.0888463i
$872$	−52.9398	+	72.8654i	−1.79277	+	2.46754i
$873$	−35.6283	−	15.8627i	−1.20583	−	0.536872i
$874$	−18.5410	+	57.0634i	−0.627159	+	1.93020i
$875$	5.29854	−	16.3072i	0.179123	−	0.551285i
$876$	−4.09666	−	38.9771i	−0.138413	−	1.31692i
$877$	−16.6251	+	22.8825i	−0.561389	+	0.772686i	−0.991502	−	0.130089i	$-0.958474\pi$
$877$	−16.6251	+	22.8825i	−0.561389	+	0.772686i	0.430113	+	0.902775i	$0.358474\pi$
$878$	−13.1782	+	4.28187i	−0.444744	+	0.144506i
$879$	−7.34847	−	4.24264i	−0.247858	−	0.143101i
$880$		0			0
$881$			1.73205i			0.0583543i	0.999574	+	0.0291771i	$0.00928869\pi$
$881$			1.73205i			0.0583543i	−0.999574	+	0.0291771i	$0.990711\pi$
$882$	24.5854	−	27.3049i	0.827834	−	0.919403i
$883$	−4.85410	−	3.52671i	−0.163354	−	0.118683i	0.503105	−	0.864225i	$-0.332191\pi$
$883$	−4.85410	−	3.52671i	−0.163354	−	0.118683i	−0.666459	+	0.745542i	$0.732191\pi$
$884$	16.2892	+	22.4201i	0.547865	+	0.754071i
$885$	3.86149	−	3.47690i	0.129803	−	0.116875i
$886$	60.5249	+	19.6657i	2.03337	+	0.660683i
$887$	−17.8351	+	12.9580i	−0.598844	+	0.435086i	−0.845468	−	0.534025i	$-0.820679\pi$
$887$	−17.8351	+	12.9580i	−0.598844	+	0.435086i	0.246624	+	0.969111i	$0.420679\pi$
$888$	−10.3538	−	23.2551i	−0.347452	−	0.780389i
$889$	−1.23607	−	3.80423i	−0.0414564	−	0.127590i
$890$	36.7423			1.23161
$891$		0			0
$892$	−44.0000			−1.47323
$893$	6.05547	+	18.6368i	0.202639	+	0.623658i
$894$	4.22693	+	9.49384i	0.141370	+	0.317522i
$895$	−21.8435	+	15.8702i	−0.730146	+	0.530482i
$896$	26.3565	+	8.56373i	0.880507	+	0.286094i
$897$	31.5290	−	28.3888i	1.05272	−	0.947875i
$898$	−17.4563	−	24.0266i	−0.582525	−	0.801777i
$899$	−11.8901	−	8.63864i	−0.396556	−	0.288115i
$900$	−16.0591	+	17.8355i	−0.535304	+	0.594516i
$901$			8.48528i			0.282686i
$902$		0			0
$903$	−21.0000	−	12.1244i	−0.698836	−	0.403473i
$904$	−8.06998	+	2.62210i	−0.268404	+	0.0872096i
$905$	5.09037	−	7.00629i	0.169210	−	0.232897i
$906$	4.39020	+	41.7699i	0.145854	+	1.38771i
$907$	6.79837	−	20.9232i	0.225736	−	0.694745i	−0.772480	−	0.635039i	$-0.780984\pi$
$907$	6.79837	−	20.9232i	0.225736	−	0.694745i	0.998216	−	0.0597055i	$-0.0190162\pi$
$908$	27.2496	−	83.8657i	0.904310	−	2.78318i
$909$	−33.5658	−	14.9445i	−1.11331	−	0.495676i
$910$	−9.97505	+	13.7295i	−0.330670	+	0.455128i
$911$	−3.29456	+	1.07047i	−0.109154	+	0.0354661i	−0.363085	−	0.931756i	$-0.618276\pi$
$911$	−3.29456	+	1.07047i	−0.109154	+	0.0354661i	0.253931	+	0.967222i	$0.418276\pi$
$912$	−9.79796	+	16.9706i	−0.324443	+	0.561951i
$913$		0			0
$914$		−	76.2102i		−	2.52081i
$915$	1.76419	−	8.29986i	0.0583223	−	0.274385i
$916$	29.1246	+	21.1603i	0.962304	+	0.699155i
$917$	10.1807	+	14.0126i	0.336198	+	0.462736i
$918$	−29.6510	−	9.63420i	−0.978629	−	0.317976i
$919$	6.72499	+	2.18508i	0.221837	+	0.0720791i	0.417827	−	0.908527i	$-0.362792\pi$
$919$	6.72499	+	2.18508i	0.221837	+	0.0720791i	−0.195990	+	0.980606i	$0.562792\pi$
$920$	59.4504	−	43.1932i	1.96002	−	1.42404i
$921$	4.47544	−	1.99259i	0.147471	−	0.0656582i
$922$	3.70820	+	11.4127i	0.122123	+	0.375857i
$923$	4.89898			0.161252
$924$		0			0
$925$	6.00000			0.197279
$926$	−14.3817	−	44.2625i	−0.472613	−	1.45455i
$927$	−0.627171	+	5.96713i	−0.0205990	+	0.195986i
$928$		0			0
$929$	−42.8292	−	13.9161i	−1.40518	−	0.456571i	−0.494319	−	0.869281i	$-0.664582\pi$
$929$	−42.8292	−	13.9161i	−1.40518	−	0.456571i	−0.910863	+	0.412709i	$0.864582\pi$
$930$	−14.7513	−	16.3829i	−0.483713	−	0.537217i
$931$	8.31254	+	11.4412i	0.272432	+	0.374971i
$932$	79.2672	+	57.5910i	2.59648	+	1.88645i
$933$	−29.3444	−	6.23735i	−0.960693	−	0.204202i
$934$			63.6396i			2.08235i
$935$		0			0
$936$	36.0000	−	20.7846i	1.17670	−	0.679366i
$937$	53.7999	−	17.4806i	1.75757	−	0.571068i	0.760622	−	0.649195i	$-0.224894\pi$
$937$	53.7999	−	17.4806i	1.75757	−	0.571068i	0.996943	+	0.0781272i	$0.0248940\pi$
$938$	6.10844	−	8.40755i	0.199448	−	0.274516i
$939$	−56.8446	+	5.97460i	−1.85505	+	0.194974i
$940$	14.8328	−	45.6507i	0.483793	−	1.48896i
$941$	2.27080	−	6.98881i	0.0740260	−	0.227829i	−0.907197	−	0.420707i	$-0.861782\pi$
$941$	2.27080	−	6.98881i	0.0740260	−	0.227829i	0.981223	+	0.192878i	$0.0617822\pi$
$942$	−63.2910	+	6.65215i	−2.06213	+	0.216739i
$943$	49.8752	−	68.6474i	1.62416	−	2.23547i
$944$	6.58911	−	2.14093i	0.214457	−	0.0696814i
$945$		−	12.7279i		−	0.414039i
$946$		0			0
$947$			50.2295i			1.63224i	0.577883	+	0.816119i	$0.303879\pi$
$947$			50.2295i			1.63224i	−0.577883	+	0.816119i	$0.696121\pi$
$948$	67.0870	+	14.2598i	2.17888	+	0.463136i
$949$	−12.9443	−	9.40456i	−0.420189	−	0.305285i
$950$	−8.14459	−	11.2101i	−0.264245	−	0.363703i
$951$	2.00739	+	2.22943i	0.0650941	+	0.0722944i
$952$	16.1400	+	5.24419i	0.523099	+	0.169965i
$953$	5.94504	−	4.31932i	0.192579	−	0.139917i	−0.487318	−	0.873225i	$-0.662025\pi$
$953$	5.94504	−	4.31932i	0.192579	−	0.139917i	0.679896	+	0.733308i	$0.262025\pi$
$954$	25.3164	+	2.66086i	0.819649	+	0.0861485i
$955$	2.78115	+	8.55951i	0.0899960	+	0.276979i
$956$	−88.1816			−2.85200
$957$		0			0
$958$	−72.0000			−2.32621
$959$	−6.81241	−	20.9664i	−0.219984	−	0.677041i
$960$	−21.9251	+	9.76168i	−0.707629	+	0.315057i
$961$	17.7984	−	12.9313i	0.574141	−	0.417138i
$962$	−19.7673	−	6.42280i	−0.637325	−	0.207079i
$963$	7.18789	−	1.52783i	0.231626	−	0.0492337i
$964$	6.65003	+	9.15298i	0.214183	+	0.294798i
$965$	−19.8168	−	14.3977i	−0.637925	−	0.463480i
$966$	10.8034	−	50.8260i	0.347594	−	1.63530i
$967$		−	31.1127i		−	1.00052i	−0.865876	−	0.500258i	$-0.833238\pi$
$967$		−	31.1127i		−	1.00052i	0.865876	−	0.500258i	$-0.166762\pi$
$968$		0			0
$969$	6.00000	−	10.3923i	0.192748	−	0.333849i
$970$	−52.4549	+	17.0436i	−1.68422	+	0.547238i
$971$	23.4157	−	32.2289i	0.751446	−	1.03428i	−0.246432	−	0.969160i	$-0.579258\pi$
$971$	23.4157	−	32.2289i	0.751446	−	1.03428i	0.997878	−	0.0651161i	$-0.0207418\pi$
$972$	−25.3616	+	56.9631i	−0.813473	+	1.82709i
$973$	−6.79837	+	20.9232i	−0.217946	+	0.670768i
$974$	−20.4372	+	62.8993i	−0.654851	+	2.01542i
$975$	1.02417	+	9.74428i	0.0327995	+	0.312067i
$976$	6.65003	−	9.15298i	0.212862	−	0.292980i
$977$	34.5928	−	11.2399i	1.10672	−	0.359596i	0.302037	−	0.953296i	$-0.402333\pi$
$977$	34.5928	−	11.2399i	1.10672	−	0.359596i	0.804686	+	0.593700i	$0.202333\pi$
$978$	−36.7423	−	21.2132i	−1.17489	−	0.678323i
$979$		0			0
$980$		−	34.6410i		−	1.10657i
$981$	−40.9877	−	36.9054i	−1.30864	−	1.17830i
$982$	48.5410	+	35.2671i	1.54901	+	1.12542i
$983$	1.01807	+	1.40126i	0.0324715	+	0.0446932i	0.824944	−	0.565214i	$-0.191207\pi$
$983$	1.01807	+	1.40126i	0.0324715	+	0.0446932i	−0.792473	+	0.609908i	$0.791207\pi$
$984$	61.7839	−	55.6305i	1.96960	−	1.77343i
$985$	−12.1050	−	3.93314i	−0.385697	−	0.125320i
$986$	−23.7801	+	17.2773i	−0.757314	+	0.550221i
$987$	−6.90255	−	15.5034i	−0.219711	−	0.493478i
$988$	9.88854	+	30.4338i	0.314596	+	0.968228i
$989$	85.7321			2.72612
$990$		0			0
$991$	18.0000			0.571789			0.285894	−	0.958261i	$-0.407709\pi$
$991$	18.0000			0.571789			0.285894	+	0.958261i	$0.407709\pi$
$992$		0			0
$993$	3.52244	+	7.91154i	0.111781	+	0.251065i
$994$	4.85410	−	3.52671i	0.153963	−	0.111860i
$995$	29.6510	+	9.63420i	0.940000	+	0.305425i
$996$	−12.6116	+	11.3555i	−0.399613	+	0.359814i
$997$	0.831254	+	1.14412i	0.0263261	+	0.0362347i	0.821977	−	0.569520i	$-0.192871\pi$
$997$	0.831254	+	1.14412i	0.0263261	+	0.0362347i	−0.795651	+	0.605755i	$0.792871\pi$
$998$	11.8901	+	8.63864i	0.376374	+	0.273451i
$999$	14.8255	−	4.81710i	0.469058	−	0.152406i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.f.h.215.1		16
3.2	odd	2	inner	363.2.f.h.215.4		16
11.2	odd	10	inner	363.2.f.h.233.4		16
11.3	even	5		363.2.d.c.362.1	✓	4
11.4	even	5	inner	363.2.f.h.239.4		16
11.5	even	5	inner	363.2.f.h.161.3		16
11.6	odd	10	inner	363.2.f.h.161.1		16
11.7	odd	10	inner	363.2.f.h.239.2		16
11.8	odd	10		363.2.d.c.362.3	yes	4
11.9	even	5	inner	363.2.f.h.233.2		16
11.10	odd	2	inner	363.2.f.h.215.3		16
33.2	even	10	inner	363.2.f.h.233.1		16
33.5	odd	10	inner	363.2.f.h.161.2		16
33.8	even	10		363.2.d.c.362.2	yes	4
33.14	odd	10		363.2.d.c.362.4	yes	4
33.17	even	10	inner	363.2.f.h.161.4		16
33.20	odd	10	inner	363.2.f.h.233.3		16
33.26	odd	10	inner	363.2.f.h.239.1		16
33.29	even	10	inner	363.2.f.h.239.3		16
33.32	even	2	inner	363.2.f.h.215.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.2.d.c.362.1	✓	4	11.3	even	5
363.2.d.c.362.2	yes	4	33.8	even	10
363.2.d.c.362.3	yes	4	11.8	odd	10
363.2.d.c.362.4	yes	4	33.14	odd	10
363.2.f.h.161.1		16	11.6	odd	10	inner
363.2.f.h.161.2		16	33.5	odd	10	inner
363.2.f.h.161.3		16	11.5	even	5	inner
363.2.f.h.161.4		16	33.17	even	10	inner
363.2.f.h.215.1		16	1.1	even	1	trivial
363.2.f.h.215.2		16	33.32	even	2	inner
363.2.f.h.215.3		16	11.10	odd	2	inner
363.2.f.h.215.4		16	3.2	odd	2	inner
363.2.f.h.233.1		16	33.2	even	10	inner
363.2.f.h.233.2		16	11.9	even	5	inner
363.2.f.h.233.3		16	33.20	odd	10	inner
363.2.f.h.233.4		16	11.2	odd	10	inner
363.2.f.h.239.1		16	33.26	odd	10	inner
363.2.f.h.239.2		16	11.7	odd	10	inner
363.2.f.h.239.3		16	33.29	even	10	inner
363.2.f.h.239.4		16	11.4	even	5	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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.f (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.756934 - 2.32960i) q^{2} +(0.704489 + 1.58231i) q^{3} +(-3.23607 + 2.35114i) q^{4} +(-1.64728 - 0.535233i) q^{5} +(3.15290 - 2.83888i) q^{6} +(-0.831254 - 1.14412i) q^{7} +(3.96336 + 2.87955i) q^{8} +(-2.00739 + 2.22943i) q^{9} +O(q^{10})\)	\(q+(-0.756934 - 2.32960i) q^{2} +(0.704489 + 1.58231i) q^{3} +(-3.23607 + 2.35114i) q^{4} +(-1.64728 - 0.535233i) q^{5} +(3.15290 - 2.83888i) q^{6} +(-0.831254 - 1.14412i) q^{7} +(3.96336 + 2.87955i) q^{8} +(-2.00739 + 2.22943i) q^{9} +4.24264i q^{10} +(-6.00000 - 3.46410i) q^{12} +(-2.68999 + 0.874032i) q^{13} +(-2.03615 + 2.80252i) q^{14} +(-0.313585 - 2.98357i) q^{15} +(1.23607 - 3.80423i) q^{16} +(-0.756934 + 2.32960i) q^{17} +(6.71316 + 2.98889i) q^{18} +(-1.66251 + 2.28825i) q^{19} +(6.58911 - 2.14093i) q^{20} +(1.22474 - 2.12132i) q^{21} +8.66025i q^{23} +(-1.76419 + 8.29986i) q^{24} +(-1.61803 - 1.17557i) q^{25} +(4.07230 + 5.60503i) q^{26} +(-4.94183 - 1.60570i) q^{27} +(5.37999 + 1.74806i) q^{28} +(-3.96336 + 2.87955i) q^{29} +(-6.71316 + 2.98889i) q^{30} +(0.927051 + 2.85317i) q^{31} +6.00000 q^{34} +(0.756934 + 2.32960i) q^{35} +(1.25434 - 11.9343i) q^{36} +(-2.42705 + 1.76336i) q^{37} +(6.58911 + 2.14093i) q^{38} +(-3.27806 - 3.64065i) q^{39} +(-4.98752 - 6.86474i) q^{40} +(-7.92672 - 5.75910i) q^{41} +(-5.86889 - 1.24747i) q^{42} -9.89949i q^{43} +(4.50000 - 2.59808i) q^{45} +(20.1750 - 6.55524i) q^{46} +(4.07230 - 5.60503i) q^{47} +(6.89025 - 0.724194i) q^{48} +(1.54508 - 4.75528i) q^{49} +(-1.51387 + 4.65921i) q^{50} +(-4.21940 + 0.443477i) q^{51} +(6.65003 - 9.15298i) q^{52} +(3.29456 - 1.07047i) q^{53} +12.7279i q^{54} -6.92820i q^{56} +(-4.79193 - 1.01856i) q^{57} +(9.70820 + 7.05342i) q^{58} +(1.01807 + 1.40126i) q^{59} +(8.02957 + 8.91774i) q^{60} +(2.68999 + 0.874032i) q^{61} +(5.94504 - 4.31932i) q^{62} +(4.21940 + 0.443477i) q^{63} +(-2.47214 - 7.60845i) q^{64} +4.89898 q^{65} -3.00000 q^{67} +(-3.02774 - 9.31841i) q^{68} +(-13.7032 + 6.10105i) q^{69} +(4.85410 - 3.52671i) q^{70} +(-1.64728 - 0.535233i) q^{71} +(-14.3758 + 3.05567i) q^{72} +(3.32502 + 4.57649i) q^{73} +(5.94504 + 4.31932i) q^{74} +(0.720227 - 3.38840i) q^{75} -11.3137i q^{76} +(-6.00000 + 10.3923i) q^{78} +(-9.41498 + 3.05911i) q^{79} +(-4.07230 + 5.60503i) q^{80} +(-0.940756 - 8.95070i) q^{81} +(-7.41641 + 22.8254i) q^{82} +(0.756934 - 2.32960i) q^{83} +(1.02417 + 9.74428i) q^{84} +(2.49376 - 3.43237i) q^{85} +(-23.0619 + 7.49326i) q^{86} +(-7.34847 - 4.24264i) q^{87} -8.66025i q^{89} +(-9.45869 - 8.51664i) q^{90} +(3.23607 + 2.35114i) q^{91} +(-20.3615 - 28.0252i) q^{92} +(-3.86149 + 3.47690i) q^{93} +(-16.1400 - 5.24419i) q^{94} +(3.96336 - 2.87955i) q^{95} +(4.01722 + 12.3637i) q^{97} -12.2474 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{3} - 16 q^{4} - 6 q^{9}+O(q^{10}) \) 16 * q + 6 * q^3 - 16 * q^4 - 6 * q^9	\( 16 q + 6 q^{3} - 16 q^{4} - 6 q^{9} - 96 q^{12} + 6 q^{15} - 16 q^{16} - 8 q^{25} - 12 q^{31} + 96 q^{34} - 24 q^{36} - 12 q^{37} + 12 q^{42} + 72 q^{45} + 24 q^{48} - 20 q^{49} + 48 q^{58} + 24 q^{60} + 32 q^{64} - 48 q^{67} - 30 q^{69} + 24 q^{70} + 12 q^{75} - 96 q^{78} + 18 q^{81} + 96 q^{82} + 16 q^{91} + 18 q^{93} - 52 q^{97}+O(q^{100}) \) 16 * q + 6 * q^3 - 16 * q^4 - 6 * q^9 - 96 * q^12 + 6 * q^15 - 16 * q^16 - 8 * q^25 - 12 * q^31 + 96 * q^34 - 24 * q^36 - 12 * q^37 + 12 * q^42 + 72 * q^45 + 24 * q^48 - 20 * q^49 + 48 * q^58 + 24 * q^60 + 32 * q^64 - 48 * q^67 - 30 * q^69 + 24 * q^70 + 12 * q^75 - 96 * q^78 + 18 * q^81 + 96 * q^82 + 16 * q^91 + 18 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more