LMFDB - Embedded newform 475.2.u.b.99.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(24,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("475.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.u (of order $18$, degree $6$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			99.2
Character	$\chi$	$=$	475.99
Dual form			475.2.u.b.24.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.429906 + 1.18116i) q^{2} +(-2.96649 + 0.523072i) q^{3} +(0.321776 + 0.270002i) q^{4} +(0.657481 - 3.72876i) q^{6} +(3.22501 + 1.86196i) q^{7} +(-2.63437 + 1.52095i) q^{8} +(5.70738 - 2.07732i) q^{9} +O(q^{10})$	\(q+(-0.429906 + 1.18116i) q^{2} +(-2.96649 + 0.523072i) q^{3} +(0.321776 + 0.270002i) q^{4} +(0.657481 - 3.72876i) q^{6} +(3.22501 + 1.86196i) q^{7} +(-2.63437 + 1.52095i) q^{8} +(5.70738 - 2.07732i) q^{9} +(1.67794 + 2.90627i) q^{11} +(-1.09578 - 0.632646i) q^{12} +(4.76776 + 0.840684i) q^{13} +(-3.58572 + 3.00877i) q^{14} +(-0.518073 - 2.93814i) q^{16} +(0.914991 - 2.51392i) q^{17} +7.63436i q^{18} +(-0.961823 + 4.25146i) q^{19} +(-10.5409 - 3.83657i) q^{21} +(-4.15412 + 0.732484i) q^{22} +(-1.20653 + 1.43789i) q^{23} +(7.01926 - 5.88986i) q^{24} +(-3.04267 + 5.27006i) q^{26} +(-8.01823 + 4.62933i) q^{27} +(0.534997 + 1.46989i) q^{28} +(-4.93461 + 1.79605i) q^{29} +(1.55945 - 2.70105i) q^{31} +(-2.29826 - 0.405246i) q^{32} +(-6.49778 - 7.74375i) q^{33} +(2.57597 + 2.16150i) q^{34} +(2.39738 + 0.872573i) q^{36} -0.992927i q^{37} +(-4.60815 - 2.96379i) q^{38} -14.5832 q^{39} +(0.0723041 + 0.410057i) q^{41} +(9.06319 - 10.8011i) q^{42} +(-4.64013 - 5.52990i) q^{43} +(-0.244780 + 1.38822i) q^{44} +(-1.17968 - 2.04326i) q^{46} +(0.766421 + 2.10572i) q^{47} +(3.07372 + 8.44496i) q^{48} +(3.43378 + 5.94749i) q^{49} +(-1.39935 + 7.93612i) q^{51} +(1.30716 + 1.55782i) q^{52} +(-0.167287 + 0.199365i) q^{53} +(-2.02088 - 11.4610i) q^{54} -11.3278 q^{56} +(0.629417 - 13.1150i) q^{57} -6.60069i q^{58} +(-4.87590 - 1.77468i) q^{59} +(0.589041 + 0.494264i) q^{61} +(2.51995 + 3.00316i) q^{62} +(22.2742 + 3.92754i) q^{63} +(4.45016 - 7.70790i) q^{64} +(11.9400 - 4.34581i) q^{66} +(3.68611 + 10.1275i) q^{67} +(0.973185 - 0.561868i) q^{68} +(2.82704 - 4.89658i) q^{69} +(1.53320 - 1.28651i) q^{71} +(-11.8758 + 14.1531i) q^{72} +(-4.49331 + 0.792291i) q^{73} +(1.17280 + 0.426865i) q^{74} +(-1.45739 + 1.10832i) q^{76} +12.4970i q^{77} +(6.26942 - 17.2251i) q^{78} +(2.09282 + 11.8690i) q^{79} +(7.40643 - 6.21473i) q^{81} +(-0.515426 - 0.0908835i) q^{82} +(11.7529 + 6.78553i) q^{83} +(-2.35592 - 4.08058i) q^{84} +(8.52650 - 3.10339i) q^{86} +(13.6990 - 7.90913i) q^{87} +(-8.84062 - 5.10413i) q^{88} +(1.33178 - 7.55289i) q^{89} +(13.8107 + 11.5886i) q^{91} +(-0.776465 + 0.136912i) q^{92} +(-3.21326 + 8.82836i) q^{93} -2.81668 q^{94} +7.02975 q^{96} +(2.47244 - 6.79298i) q^{97} +(-8.50112 + 1.49898i) q^{98} +(15.6139 + 13.1016i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{4} - 12 q^{6} - 6 q^{9}+O(q^{10}) $ 36 * q + 6 * q^4 - 12 * q^6 - 6 * q^9	$ 36 q + 6 q^{4} - 12 q^{6} - 6 q^{9} + 24 q^{14} - 6 q^{16} - 42 q^{21} + 30 q^{24} + 6 q^{26} - 30 q^{29} - 36 q^{31} + 24 q^{34} + 150 q^{36} - 72 q^{39} - 60 q^{41} - 84 q^{44} + 18 q^{46} - 18 q^{49} - 90 q^{51} + 132 q^{54} - 36 q^{59} - 60 q^{61} - 72 q^{64} + 78 q^{66} - 30 q^{69} - 24 q^{71} + 30 q^{74} - 66 q^{76} + 102 q^{79} + 54 q^{81} - 96 q^{84} + 126 q^{86} + 108 q^{89} + 60 q^{91} - 60 q^{94} - 132 q^{96} + 186 q^{99}+O(q^{100}) $ 36 * q + 6 * q^4 - 12 * q^6 - 6 * q^9 + 24 * q^14 - 6 * q^16 - 42 * q^21 + 30 * q^24 + 6 * q^26 - 30 * q^29 - 36 * q^31 + 24 * q^34 + 150 * q^36 - 72 * q^39 - 60 * q^41 - 84 * q^44 + 18 * q^46 - 18 * q^49 - 90 * q^51 + 132 * q^54 - 36 * q^59 - 60 * q^61 - 72 * q^64 + 78 * q^66 - 30 * q^69 - 24 * q^71 + 30 * q^74 - 66 * q^76 + 102 * q^79 + 54 * q^81 - 96 * q^84 + 126 * q^86 + 108 * q^89 + 60 * q^91 - 60 * q^94 - 132 * q^96 + 186 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.429906	+	1.18116i	−0.303989	+	0.835204i	0.689807	+	0.723993i	$0.257695\pi$
$2$	−0.429906	+	1.18116i	−0.303989	+	0.835204i	−0.993797	+	0.111211i	$0.964527\pi$
$3$	−2.96649	+	0.523072i	−1.71270	+	0.301996i	−0.942103	−	0.335323i	$-0.891155\pi$
$3$	−2.96649	+	0.523072i	−1.71270	+	0.301996i	−0.770600	+	0.637319i	$0.780043\pi$
$4$	0.321776	+	0.270002i	0.160888	+	0.135001i
$5$		0			0
$5$		0			0
$6$	0.657481	−	3.72876i	0.268416	−	1.52226i
$7$	3.22501	+	1.86196i	1.21894	+	0.703754i	0.964691	−	0.263385i	$-0.0848389\pi$
$7$	3.22501	+	1.86196i	1.21894	+	0.703754i	0.254247	+	0.967139i	$0.418172\pi$
$8$	−2.63437	+	1.52095i	−0.931390	+	0.537738i
$9$	5.70738	−	2.07732i	1.90246	−	0.692439i
$10$		0			0
$11$	1.67794	+	2.90627i	0.505917	+	0.876275i	0.999977	+	0.00684646i	$0.00217931\pi$
$11$	1.67794	+	2.90627i	0.505917	+	0.876275i	−0.494059	+	0.869428i	$0.664487\pi$
$12$	−1.09578	−	0.632646i	−0.316323	−	0.182629i
$13$	4.76776	+	0.840684i	1.32234	+	0.233164i	0.789864	−	0.613282i	$-0.210151\pi$
$13$	4.76776	+	0.840684i	1.32234	+	0.233164i	0.532474	+	0.846446i	$0.321262\pi$
$14$	−3.58572	+	3.00877i	−0.958323	+	0.804129i
$15$		0			0
$16$	−0.518073	−	2.93814i	−0.129518	−	0.734534i
$17$	0.914991	−	2.51392i	0.221918	−	0.609715i	−0.777908	−	0.628378i	$-0.783719\pi$
$17$	0.914991	−	2.51392i	0.221918	−	0.609715i	0.999826	+	0.0186637i	$0.00594120\pi$
$18$			7.63436i			1.79944i
$19$	−0.961823	+	4.25146i	−0.220657	+	0.975351i
$19$	−0.961823	+	4.25146i	−0.220657	+	0.975351i
$20$		0			0
$21$	−10.5409	−	3.83657i	−2.30021	−	0.837208i
$22$	−4.15412	+	0.732484i	−0.885662	+	0.156166i
$23$	−1.20653	+	1.43789i	−0.251579	+	0.299820i	−0.877023	−	0.480449i	$-0.840474\pi$
$23$	−1.20653	+	1.43789i	−0.251579	+	0.299820i	0.625443	+	0.780270i	$0.284918\pi$
$24$	7.01926	−	5.88986i	1.43280	−	1.20226i
$25$		0			0
$26$	−3.04267	+	5.27006i	−0.596716	+	1.03354i
$27$	−8.01823	+	4.62933i	−1.54311	+	0.890914i
$28$	0.534997	+	1.46989i	0.101105	+	0.277783i
$29$	−4.93461	+	1.79605i	−0.916335	+	0.333519i	−0.756779	−	0.653670i	$-0.773228\pi$
$29$	−4.93461	+	1.79605i	−0.916335	+	0.333519i	−0.159555	+	0.987189i	$0.551006\pi$
$30$		0			0
$31$	1.55945	−	2.70105i	0.280086	−	0.485124i	−0.691319	−	0.722549i	$-0.742970\pi$
$31$	1.55945	−	2.70105i	0.280086	−	0.485124i	0.971406	+	0.237426i	$0.0763036\pi$
$32$	−2.29826	−	0.405246i	−0.406279	−	0.0716380i
$33$	−6.49778	−	7.74375i	−1.13112	−	1.34801i
$34$	2.57597	+	2.16150i	0.441776	+	0.370694i
$35$		0			0
$36$	2.39738	+	0.872573i	0.399563	+	0.145429i
$37$		−	0.992927i		−	0.163236i	−0.996664	−	0.0816181i	$-0.973991\pi$
$37$		−	0.992927i		−	0.163236i	0.996664	−	0.0816181i	$-0.0260088\pi$
$38$	−4.60815	−	2.96379i	−0.747540	−	0.480790i
$39$	−14.5832			−2.33519
$40$		0			0
$41$	0.0723041	+	0.410057i	0.0112920	+	0.0640401i	0.989933	−	0.141536i	$-0.0452042\pi$
$41$	0.0723041	+	0.410057i	0.0112920	+	0.0640401i	−0.978641	+	0.205576i	$0.934093\pi$
$42$	9.06319	−	10.8011i	1.39848	−	1.66664i
$43$	−4.64013	−	5.52990i	−0.707614	−	0.843301i	0.285751	−	0.958304i	$-0.407757\pi$
$43$	−4.64013	−	5.52990i	−0.707614	−	0.843301i	−0.993365	+	0.115003i	$0.963312\pi$
$44$	−0.244780	+	1.38822i	−0.0369020	+	0.209281i
$45$		0			0
$46$	−1.17968	−	2.04326i	−0.173934	−	0.301262i
$47$	0.766421	+	2.10572i	0.111794	+	0.307151i	0.982955	−	0.183846i	$-0.0588547\pi$
$47$	0.766421	+	2.10572i	0.111794	+	0.307151i	−0.871161	+	0.490997i	$0.836633\pi$
$48$	3.07372	+	8.44496i	0.443653	+	1.21893i
$49$	3.43378	+	5.94749i	0.490540	+	0.849641i
$50$		0			0
$51$	−1.39935	+	7.93612i	−0.195948	+	1.11128i
$52$	1.30716	+	1.55782i	0.181271	+	0.216030i
$53$	−0.167287	+	0.199365i	−0.0229786	+	0.0273848i	−0.777411	−	0.628993i	$-0.783468\pi$
$53$	−0.167287	+	0.199365i	−0.0229786	+	0.0273848i	0.754433	+	0.656377i	$0.227912\pi$
$54$	−2.02088	−	11.4610i	−0.275007	−	1.55964i
$55$		0			0
$56$	−11.3278			−1.51374
$57$	0.629417	−	13.1150i	0.0833683	−	1.73713i
$58$		−	6.60069i		−	0.866713i
$59$	−4.87590	−	1.77468i	−0.634789	−	0.231044i	0.00452556	−	0.999990i	$-0.498559\pi$
$59$	−4.87590	−	1.77468i	−0.634789	−	0.231044i	−0.639314	+	0.768946i	$0.720782\pi$
$60$		0			0
$61$	0.589041	+	0.494264i	0.0754189	+	0.0632840i	0.679718	−	0.733474i	$-0.262102\pi$
$61$	0.589041	+	0.494264i	0.0754189	+	0.0632840i	−0.604299	+	0.796758i	$0.706547\pi$
$62$	2.51995	+	3.00316i	0.320034	+	0.381402i
$63$	22.2742	+	3.92754i	2.80629	+	0.494824i
$64$	4.45016	−	7.70790i	0.556270	−	0.963488i
$65$		0			0
$66$	11.9400	−	4.34581i	1.46971	−	0.534933i
$67$	3.68611	+	10.1275i	0.450330	+	1.23727i	0.932492	+	0.361190i	$0.117629\pi$
$67$	3.68611	+	10.1275i	0.450330	+	1.23727i	−0.482162	+	0.876082i	$0.660148\pi$
$68$	0.973185	−	0.561868i	0.118016	−	0.0681366i
$69$	2.82704	−	4.89658i	0.340336	−	0.589479i
$70$		0			0
$71$	1.53320	−	1.28651i	0.181958	−	0.152681i	−0.547259	−	0.836963i	$-0.684329\pi$
$71$	1.53320	−	1.28651i	0.181958	−	0.152681i	0.729217	+	0.684282i	$0.239884\pi$
$72$	−11.8758	+	14.1531i	−1.39958	+	1.66796i
$73$	−4.49331	+	0.792291i	−0.525902	+	0.0927307i	−0.430295	−	0.902688i	$-0.641590\pi$
$73$	−4.49331	+	0.792291i	−0.525902	+	0.0927307i	−0.0956071	+	0.995419i	$0.530479\pi$
$74$	1.17280	+	0.426865i	0.136336	+	0.0496221i
$75$		0			0
$76$	−1.45739	+	1.10832i	−0.167174	+	0.127133i
$77$			12.4970i			1.42417i
$78$	6.26942	−	17.2251i	0.709872	−	1.95036i
$79$	2.09282	+	11.8690i	0.235460	+	1.33536i	0.841642	+	0.540036i	$0.181589\pi$
$79$	2.09282	+	11.8690i	0.235460	+	1.33536i	−0.606181	+	0.795326i	$0.707299\pi$
$80$		0			0
$81$	7.40643	−	6.21473i	0.822937	−	0.690526i
$82$	−0.515426	−	0.0908835i	−0.0569192	−	0.0100364i
$83$	11.7529	+	6.78553i	1.29005	+	0.744809i	0.978662	−	0.205475i	$-0.0658741\pi$
$83$	11.7529	+	6.78553i	1.29005	+	0.744809i	0.311384	+	0.950284i	$0.399207\pi$
$84$	−2.35592	−	4.08058i	−0.257052	−	0.445227i
$85$		0			0
$86$	8.52650	−	3.10339i	0.919436	−	0.334647i
$87$	13.6990	−	7.90913i	1.46869	−	0.847948i
$88$	−8.84062	−	5.10413i	−0.942413	−	0.544102i
$89$	1.33178	−	7.55289i	0.141168	−	0.800605i	−0.829196	−	0.558958i	$-0.811201\pi$
$89$	1.33178	−	7.55289i	0.141168	−	0.800605i	0.970364	−	0.241647i	$-0.0776876\pi$
$90$		0			0
$91$	13.8107	+	11.5886i	1.44776	+	1.21481i
$92$	−0.776465	+	0.136912i	−0.0809521	+	0.0142740i
$93$	−3.21326	+	8.82836i	−0.333199	+	0.915458i
$94$	−2.81668			−0.290518
$95$		0			0
$96$	7.02975			0.717471
$97$	2.47244	−	6.79298i	0.251039	−	0.689723i	−0.748605	−	0.663017i	$-0.769276\pi$
$97$	2.47244	−	6.79298i	0.251039	−	0.689723i	0.999643	−	0.0267064i	$-0.00850192\pi$
$98$	−8.50112	+	1.49898i	−0.858743	+	0.151420i
$99$	15.6139	+	13.1016i	1.56925	+	1.31676i
$100$		0			0
$101$	0.779999	−	4.42360i	0.0776128	−	0.440164i	−0.921095	−	0.389339i	$-0.872704\pi$
$101$	0.779999	−	4.42360i	0.0776128	−	0.440164i	0.998708	−	0.0508257i	$-0.0161853\pi$
$102$	−8.77221	−	5.06464i	−0.868578	−	0.501474i
$103$	9.30504	−	5.37227i	0.916853	−	0.529345i	0.0342231	−	0.999414i	$-0.489104\pi$
$103$	9.30504	−	5.37227i	0.916853	−	0.529345i	0.882630	+	0.470069i	$0.155771\pi$
$104$	−13.8387	+	5.03686i	−1.35699	+	0.493905i
$105$		0			0
$106$	−0.163563	−	0.283300i	−0.0158867	−	0.0275165i
$107$	1.19393	+	0.689315i	0.115421	+	0.0666386i	0.556599	−	0.830781i	$-0.312106\pi$
$107$	1.19393	+	0.689315i	0.115421	+	0.0666386i	−0.441178	+	0.897420i	$0.645439\pi$
$108$	−3.83000	−	0.675332i	−0.368542	−	0.0649839i
$109$	−7.27648	+	6.10570i	−0.696961	+	0.584820i	−0.920907	−	0.389782i	$-0.872550\pi$
$109$	−7.27648	+	6.10570i	−0.696961	+	0.584820i	0.223946	+	0.974601i	$0.428106\pi$
$110$		0			0
$111$	0.519372	+	2.94551i	0.0492966	+	0.279575i
$112$	3.79990	−	10.4401i	0.359057	−	0.986501i
$113$		−	17.0436i		−	1.60333i	−0.597772	−	0.801666i	$-0.703947\pi$
$113$		−	17.0436i		−	1.60333i	0.597772	−	0.801666i	$-0.296053\pi$
$114$	15.2203	+	6.38166i	1.42551	+	0.597697i
$115$		0			0
$116$	−2.07278	−	0.754429i	−0.192453	−	0.0700470i
$117$	28.9578	−	5.10603i	2.67715	−	0.472053i
$118$	4.19236	−	4.99626i	0.385938	−	0.459943i
$119$	7.63167	−	6.40373i	0.699594	−	0.587029i
$120$		0			0
$121$	−0.130955	+	0.226821i	−0.0119050	+	0.0206201i
$122$	−0.837035	+	0.483263i	−0.0757816	+	0.0437525i
$123$	−0.428979	−	1.17861i	−0.0386797	−	0.106272i
$124$	1.23108	−	0.448078i	0.110555	−	0.0402386i
$125$		0			0
$126$	−14.2149	+	24.6209i	−1.26636	+	2.19340i
$127$	−19.5581	−	3.44862i	−1.73550	−	0.306016i	−0.785640	−	0.618685i	$-0.787666\pi$
$127$	−19.5581	−	3.44862i	−1.73550	−	0.306016i	−0.949862	+	0.312669i	$0.898777\pi$
$128$	4.19092	+	4.99455i	0.370429	+	0.441460i
$129$	16.6574	+	13.9773i	1.46661	+	1.23063i
$130$		0			0
$131$	−5.09611	−	1.85483i	−0.445249	−	0.162057i	0.109659	−	0.993969i	$-0.465024\pi$
$131$	−5.09611	−	1.85483i	−0.445249	−	0.162057i	−0.554908	+	0.831912i	$0.687246\pi$
$132$		−	4.24616i		−	0.369581i
$133$	−11.0179	+	11.9201i	−0.955375	+	1.03360i
$134$	−13.5469			−1.17027
$135$		0			0
$136$	1.41313	+	8.01425i	0.121175	+	0.687216i
$137$	−11.9311	+	14.2189i	−1.01934	+	1.21480i	−0.0428860	+	0.999080i	$0.513655\pi$
$137$	−11.9311	+	14.2189i	−1.01934	+	1.21480i	−0.976455	+	0.215723i	$0.930789\pi$
$138$	4.56827	+	5.44425i	0.388877	+	0.463446i
$139$	1.82551	−	10.3530i	0.154838	−	0.878128i	−0.804096	−	0.594499i	$-0.797350\pi$
$139$	1.82551	−	10.3530i	0.154838	−	0.878128i	0.958934	−	0.283629i	$-0.0915385\pi$
$140$		0			0
$141$	−3.37502	−	5.84571i	−0.284228	−	0.492298i
$142$	0.860438	+	2.36404i	0.0722064	+	0.198385i
$143$	5.55674	+	15.2670i	0.464678	+	1.27669i
$144$	−9.06027	−	15.6929i	−0.755023	−	1.30774i
$145$		0			0
$146$	0.995879	−	5.64791i	0.0824196	−	0.467425i
$147$	−13.2972	−	15.8470i	−1.09674	−	1.30704i
$148$	0.268092	−	0.319500i	0.0220370	−	0.0262627i
$149$	−2.62919	−	14.9109i	−0.215392	−	1.22155i	−0.880225	−	0.474556i	$-0.842609\pi$
$149$	−2.62919	−	14.9109i	−0.215392	−	1.22155i	0.664834	−	0.746992i	$-0.268502\pi$
$150$		0			0
$151$	11.3432			0.923095			0.461548	−	0.887115i	$-0.347294\pi$
$151$	11.3432			0.923095			0.461548	+	0.887115i	$0.347294\pi$
$152$	−3.93248	−	12.6628i	−0.318966	−	1.02709i
$153$		−	16.2486i		−	1.31362i
$154$	−14.7609	−	5.37254i	−1.18947	−	0.432932i
$155$		0			0
$156$	−4.69253	−	3.93750i	−0.375703	−	0.315253i
$157$	2.70953	+	3.22909i	0.216244	+	0.257710i	0.863252	−	0.504774i	$-0.168424\pi$
$157$	2.70953	+	3.22909i	0.216244	+	0.257710i	−0.647007	+	0.762484i	$0.723980\pi$
$158$	−14.9188	−	2.63059i	−1.18688	−	0.209279i
$159$	0.391972	−	0.678916i	0.0310854	−	0.0538415i
$160$		0			0
$161$	−6.56836	+	2.39069i	−0.517659	+	0.188413i
$162$	4.15651	+	11.4199i	0.326566	+	0.897233i
$163$	−12.0426	+	6.95280i	−0.943249	+	0.544585i	−0.890977	−	0.454048i	$-0.849980\pi$
$163$	−12.0426	+	6.95280i	−0.943249	+	0.544585i	−0.0522718	+	0.998633i	$0.516646\pi$
$164$	−0.0874505	+	0.151469i	−0.00682873	+	0.0118277i
$165$		0			0
$166$	−13.0674	+	10.9649i	−1.01423	+	0.851038i
$167$	11.3273	−	13.4994i	0.876537	−	1.04462i	−0.122105	−	0.992517i	$-0.538965\pi$
$167$	11.3273	−	13.4994i	0.876537	−	1.04462i	0.998642	−	0.0520984i	$-0.0165910\pi$
$168$	33.6038	−	5.92526i	2.59259	−	0.457144i
$169$	9.80875	+	3.57009i	0.754519	+	0.274623i
$170$		0			0
$171$	3.34214	+	26.2627i	0.255580	+	2.00836i
$172$		−	3.03223i		−	0.231206i
$173$	−4.55510	+	12.5150i	−0.346317	+	0.951499i	0.637202	+	0.770697i	$0.280092\pi$
$173$	−4.55510	+	12.5150i	−0.346317	+	0.951499i	−0.983519	+	0.180803i	$0.942131\pi$
$174$	3.45264	+	19.5809i	0.261744	+	1.48442i
$175$		0			0
$176$	7.66974	−	6.43567i	0.578128	−	0.485107i
$177$	15.3926	+	2.71413i	1.15698	+	0.204007i
$178$	8.34861	+	4.82007i	0.625755	+	0.361280i
$179$	7.31322	+	12.6669i	0.546616	+	0.946767i	0.998503	+	0.0546916i	$0.0174176\pi$
$179$	7.31322	+	12.6669i	0.546616	+	0.946767i	−0.451887	+	0.892075i	$0.649249\pi$
$180$		0			0
$181$	8.25497	−	3.00456i	0.613587	−	0.223328i	−0.0164849	−	0.999864i	$-0.505248\pi$
$181$	8.25497	−	3.00456i	0.613587	−	0.223328i	0.630072	+	0.776537i	$0.283025\pi$
$182$	−19.6253	+	11.3306i	−1.45472	+	0.839883i
$183$	−2.00592	−	1.15812i	−0.148282	−	0.0856105i
$184$	0.991488	−	5.62301i	0.0730934	−	0.414533i
$185$		0			0
$186$	−9.04628	−	7.59073i	−0.663305	−	0.556579i
$187$	8.84144	−	1.55898i	0.646550	−	0.114004i
$188$	−0.321934	+	0.884506i	−0.0234794	+	0.0645092i
$189$	−34.4785			−2.50794
$190$		0			0
$191$	−9.70737			−0.702401			−0.351200	−	0.936300i	$-0.614226\pi$
$191$	−9.70737			−0.702401			−0.351200	+	0.936300i	$0.614226\pi$
$192$	−9.16956	+	25.1932i	−0.661756	+	1.81816i
$193$	19.9469	−	3.51718i	1.43581	−	0.253172i	0.599038	−	0.800721i	$-0.295550\pi$
$193$	19.9469	−	3.51718i	1.43581	−	0.253172i	0.836774	+	0.547549i	$0.184439\pi$
$194$	6.96066	+	5.84069i	0.499747	+	0.419337i
$195$		0			0
$196$	−0.500925	+	2.84089i	−0.0357803	+	0.202920i
$197$	−8.02097	−	4.63091i	−0.571470	−	0.329939i	0.186266	−	0.982499i	$-0.440361\pi$
$197$	−8.02097	−	4.63091i	−0.571470	−	0.329939i	−0.757736	+	0.652561i	$0.773695\pi$
$198$	−22.1875	+	12.8100i	−1.57680	+	0.910366i
$199$	17.0574	−	6.20837i	1.20916	−	0.440100i	0.342750	−	0.939427i	$-0.388642\pi$
$199$	17.0574	−	6.20837i	1.20916	−	0.440100i	0.866414	+	0.499327i	$0.166419\pi$
$200$		0			0
$201$	−16.2322	−	28.1150i	−1.14493	−	1.98308i
$202$	4.88964	+	2.82303i	0.344034	+	0.198628i
$203$	−19.2583	−	3.39577i	−1.35167	−	0.238336i
$204$	−2.59304	+	2.17582i	−0.181549	+	0.152338i
$205$		0			0
$206$	2.34520	+	13.3003i	0.163398	+	0.926675i
$207$	−3.89918	+	10.7129i	−0.271012	+	0.744599i
$208$		−	14.4439i		−	1.00150i
$209$	−13.9698	+	4.33836i	−0.966310	+	0.300091i
$210$		0			0
$211$	−16.3337	−	5.94498i	−1.12446	−	0.409269i	−0.288181	−	0.957576i	$-0.593050\pi$
$211$	−16.3337	−	5.94498i	−1.12446	−	0.409269i	−0.836277	+	0.548307i	$0.815273\pi$
$212$	−0.107658	+	0.0189829i	−0.00739396	+	0.00130375i
$213$	−3.87530	+	4.61840i	−0.265531	+	0.316448i
$214$	−1.32747	+	1.11388i	−0.0907438	+	0.0761431i
$215$		0			0
$216$	14.0820	−	24.3907i	0.958157	−	1.65958i
$217$	10.0585	−	5.80728i	0.682816	−	0.394224i
$218$	−4.08358	−	11.2195i	−0.276575	−	0.759884i
$219$	12.9149	−	4.70065i	0.872710	−	0.317640i
$220$		0			0
$221$	6.47587	−	11.2165i	0.435614	−	0.754505i
$222$	−3.70239	−	0.652831i	−0.248488	−	0.0438151i
$223$	−5.60941	−	6.68504i	−0.375634	−	0.447663i	0.544797	−	0.838568i	$-0.316607\pi$
$223$	−5.60941	−	6.68504i	−0.375634	−	0.447663i	−0.920431	+	0.390905i	$0.872162\pi$
$224$	−6.65737	−	5.58619i	−0.444814	−	0.373243i
$225$		0			0
$226$	20.1312	+	7.32717i	1.33911	+	0.487396i
$227$			20.1154i			1.33510i	0.744563	+	0.667552i	$0.232658\pi$
$227$			20.1154i			1.33510i	−0.744563	+	0.667552i	$0.767342\pi$
$228$	3.74361	−	4.05015i	0.247927	−	0.268228i
$229$	20.8410			1.37721			0.688607	−	0.725135i	$-0.258222\pi$
$229$	20.8410			1.37721			0.688607	+	0.725135i	$0.258222\pi$
$230$		0			0
$231$	−6.53684	−	37.0723i	−0.430092	−	2.43918i
$232$	10.2679	−	12.2368i	0.674119	−	0.803384i
$233$	0.349709	+	0.416767i	0.0229102	+	0.0273033i	0.777378	−	0.629034i	$-0.216549\pi$
$233$	0.349709	+	0.416767i	0.0229102	+	0.0273033i	−0.754468	+	0.656337i	$0.772105\pi$
$234$	−6.41809	+	36.3988i	−0.419563	+	2.37946i
$235$		0			0
$236$	−1.08978	−	1.88755i	−0.0709386	−	0.122869i
$237$	−12.4166	−	34.1145i	−0.806548	−	2.21597i
$238$	4.28291	+	11.7672i	0.277620	+	0.762754i
$239$	−11.1117	−	19.2461i	−0.718758	−	1.24493i	−0.961492	−	0.274833i	$-0.911377\pi$
$239$	−11.1117	−	19.2461i	−0.718758	−	1.24493i	0.242733	−	0.970093i	$-0.421956\pi$
$240$		0			0
$241$	3.77399	−	21.4034i	0.243104	−	1.37871i	−0.581750	−	0.813368i	$-0.697632\pi$
$241$	3.77399	−	21.4034i	0.243104	−	1.37871i	0.824854	−	0.565345i	$-0.191257\pi$
$242$	−0.211613	−	0.252190i	−0.0136030	−	0.0162114i
$243$	−0.866300	+	1.03242i	−0.0555732	+	0.0662295i
$244$	0.0560868	+	0.318084i	0.00359059	+	0.0203633i
$245$		0			0
$246$	1.57654			0.100517
$247$	−8.15987	+	19.4613i	−0.519200	+	1.23829i
$248$			9.48743i			0.602452i
$249$	−38.4141	−	13.9816i	−2.43440	−	0.886048i
$250$		0			0
$251$	13.6539	+	11.4570i	0.861828	+	0.723160i	0.962361	−	0.271774i	$-0.0876104\pi$
$251$	13.6539	+	11.4570i	0.861828	+	0.723160i	−0.100533	+	0.994934i	$0.532055\pi$
$252$	6.10686	+	7.27787i	0.384696	+	0.458463i
$253$	−6.20338	−	1.09382i	−0.390003	−	0.0687681i
$254$	12.4815	−	21.6186i	0.783160	−	1.35647i
$255$		0			0
$256$	9.02608	−	3.28522i	0.564130	−	0.205326i
$257$	5.37788	+	14.7756i	0.335463	+	0.921678i	0.986664	+	0.162772i	$0.0520434\pi$
$257$	5.37788	+	14.7756i	0.335463	+	0.921678i	−0.651201	+	0.758906i	$0.725734\pi$
$258$	−23.6705	+	13.6662i	−1.47366	+	0.850817i
$259$	1.84879	−	3.20220i	0.114878	−	0.198975i
$260$		0			0
$261$	−24.4327	+	20.5015i	−1.51235	+	1.26901i
$262$	4.38170	−	5.22190i	0.270702	−	0.322610i
$263$	29.9878	−	5.28766i	1.84913	−	0.326051i	0.864761	−	0.502184i	$-0.167470\pi$
$263$	29.9878	−	5.28766i	1.84913	−	0.326051i	0.984366	+	0.176133i	$0.0563589\pi$
$264$	28.8954	+	10.5171i	1.77839	+	0.647281i
$265$		0			0
$266$	−9.34285	−	18.1384i	−0.572847	−	1.11214i
$267$			23.1022i			1.41383i
$268$	−1.54835	+	4.25404i	−0.0945802	+	0.259857i
$269$	−0.453555	−	2.57224i	−0.0276537	−	0.156832i	0.967854	−	0.251513i	$-0.0809281\pi$
$269$	−0.453555	−	2.57224i	−0.0276537	−	0.156832i	−0.995508	+	0.0946808i	$0.969817\pi$
$270$		0			0
$271$	−7.36033	+	6.17605i	−0.447108	+	0.375168i	−0.838361	−	0.545115i	$-0.816486\pi$
$271$	−7.36033	+	6.17605i	−0.447108	+	0.375168i	0.391253	+	0.920283i	$0.372042\pi$
$272$	−7.86027	−	1.38598i	−0.476599	−	0.0840372i
$273$	−47.0311	−	27.1534i	−2.84645	−	1.64340i
$274$	−11.6655	−	20.2053i	−0.704740	−	1.22064i
$275$		0			0
$276$	2.23176	−	0.812295i	0.134336	−	0.0488944i
$277$	−17.3787	+	10.0336i	−1.04418	+	0.602860i	−0.921015	−	0.389526i	$-0.872639\pi$
$277$	−17.3787	+	10.0336i	−1.04418	+	0.602860i	−0.123168	+	0.992386i	$0.539305\pi$
$278$	11.4437	+	6.60702i	0.686348	+	0.396263i
$279$	3.28945	−	18.6554i	0.196934	−	1.11687i
$280$		0			0
$281$	20.3428	+	17.0696i	1.21355	+	1.01829i	0.999137	+	0.0415429i	$0.0132273\pi$
$281$	20.3428	+	17.0696i	1.21355	+	1.01829i	0.214410	+	0.976744i	$0.431217\pi$
$282$	8.35565	−	1.47333i	0.497572	−	0.0877353i
$283$	−5.73869	+	15.7669i	−0.341130	+	0.937247i	0.643938	+	0.765078i	$0.277300\pi$
$283$	−5.73869	+	15.7669i	−0.341130	+	0.937247i	−0.985067	+	0.172169i	$0.944923\pi$
$284$	0.840709			0.0498869
$285$		0			0
$286$	−20.4216			−1.20756
$287$	−0.530328	+	1.45706i	−0.0313043	+	0.0860078i
$288$	−13.9589	+	2.46133i	−0.822535	+	0.145035i
$289$	7.54018	+	6.32696i	0.443540	+	0.372174i
$290$		0			0
$291$	−3.78126	+	21.4446i	−0.221661	+	1.25710i
$292$	−1.65976	−	0.958262i	−0.0971300	−	0.0560780i
$293$	11.5864	−	6.68939i	0.676883	−	0.390799i	−0.121797	−	0.992555i	$-0.538866\pi$
$293$	11.5864	−	6.68939i	0.676883	−	0.390799i	0.798680	+	0.601757i	$0.205532\pi$
$294$	24.4344	−	8.89340i	1.42504	−	0.518674i
$295$		0			0
$296$	1.51020	+	2.61574i	0.0877783	+	0.152037i
$297$	−26.9082	−	15.5355i	−1.56137	−	0.901458i
$298$	18.7424	+	3.30479i	1.08572	+	0.191441i
$299$	−6.96126	+	5.84119i	−0.402580	+	0.337805i
$300$		0			0
$301$	−4.66803	−	26.4737i	−0.269061	−	1.52592i
$302$	−4.87650	+	13.3981i	−0.280611	+	0.770973i
$303$			13.5305i			0.777310i
$304$	12.9897	+	0.623401i	0.745008	+	0.0357545i
$305$		0			0
$306$	19.1922	+	6.98537i	1.09714	+	0.399327i
$307$	27.5473	−	4.85734i	1.57221	−	0.277223i	0.681508	−	0.731811i	$-0.261325\pi$
$307$	27.5473	−	4.85734i	1.57221	−	0.277223i	0.890702	+	0.454588i	$0.150213\pi$
$308$	−3.37422	+	4.02124i	−0.192264	+	0.229131i
$309$	−24.7932	+	20.8040i	−1.41044	+	1.18350i
$310$		0			0
$311$	−12.4175	+	21.5078i	−0.704132	+	1.21959i	0.262871	+	0.964831i	$0.415331\pi$
$311$	−12.4175	+	21.5078i	−0.704132	+	1.21959i	−0.967004	+	0.254762i	$0.918003\pi$
$312$	38.4176	−	22.1804i	2.17497	−	1.25572i
$313$	7.61769	+	20.9294i	0.430577	+	1.18300i	0.945459	+	0.325741i	$0.105614\pi$
$313$	7.61769	+	20.9294i	0.430577	+	1.18300i	−0.514882	+	0.857261i	$0.672164\pi$
$314$	−4.97891	+	1.81218i	−0.280976	+	0.102267i
$315$		0			0
$316$	−2.53122	+	4.38421i	−0.142393	+	0.246631i
$317$	13.8618	+	2.44421i	0.778557	+	0.137281i	0.548785	−	0.835964i	$-0.315091\pi$
$317$	13.8618	+	2.44421i	0.778557	+	0.137281i	0.229772	+	0.973244i	$0.426202\pi$
$318$	0.633395	+	0.754851i	0.0355190	+	0.0423299i
$319$	−13.4998	−	11.3277i	−0.755844	−	0.634228i
$320$		0			0
$321$	−3.90234	−	1.42034i	−0.217807	−	0.0792754i
$322$		−	8.78604i		−	0.489627i
$323$	9.80776	+	6.30799i	0.545718	+	0.350986i
$324$	4.06120			0.225622
$325$		0			0
$326$	−3.03516	−	17.2133i	−0.168102	−	0.953354i
$327$	18.3919	−	21.9186i	1.01707	−	1.21210i
$328$	−0.814153	−	0.970270i	−0.0449541	−	0.0535742i
$329$	−1.44906	+	8.21802i	−0.0798892	+	0.453074i
$330$		0			0
$331$	2.64274	+	4.57737i	0.145258	+	0.251595i	0.929469	−	0.368899i	$-0.120265\pi$
$331$	2.64274	+	4.57737i	0.145258	+	0.251595i	−0.784211	+	0.620494i	$0.786932\pi$
$332$	1.94969	+	5.35672i	0.107003	+	0.293988i
$333$	−2.06262	−	5.66701i	−0.113031	−	0.310550i
$334$	11.0752	+	19.1829i	0.606009	+	1.04964i
$335$		0			0
$336$	−5.81142	+	32.9582i	−0.317039	+	1.79802i
$337$	−15.3550	−	18.2993i	−0.836438	−	0.996828i	−0.999947	−	0.0102861i	$-0.996726\pi$
$337$	−15.3550	−	18.2993i	−0.836438	−	0.996828i	0.163509	−	0.986542i	$-0.447719\pi$
$338$	−8.43368	+	10.0509i	−0.458732	+	0.546695i
$339$	8.91506	+	50.5598i	0.484200	+	2.74603i
$340$		0			0
$341$	10.4667			0.566802
$342$	−32.4572	−	7.34290i	−1.75508	−	0.397059i
$343$		−	0.493173i		−	0.0266288i
$344$	20.6345	+	7.51036i	1.11254	+	0.404931i
$345$		0			0
$346$	−12.8239	−	10.7606i	−0.689419	−	0.578492i
$347$	5.63534	+	6.71594i	0.302521	+	0.360531i	0.895793	−	0.444472i	$-0.146609\pi$
$347$	5.63534	+	6.71594i	0.302521	+	0.360531i	−0.593272	+	0.805002i	$0.702164\pi$
$348$	6.54349	+	1.15379i	0.350768	+	0.0618499i
$349$	1.02005	−	1.76679i	0.0546023	−	0.0945739i	−0.837432	−	0.546541i	$-0.815944\pi$
$349$	1.02005	−	1.76679i	0.0546023	−	0.0945739i	0.892035	+	0.451967i	$0.149278\pi$
$350$		0			0
$351$	−42.1208	+	15.3307i	−2.24824	+	0.818293i
$352$	−2.67859	−	7.35936i	−0.142769	−	0.392255i
$353$	7.85009	−	4.53225i	0.417818	−	0.241227i	−0.276325	−	0.961064i	$-0.589117\pi$
$353$	7.85009	−	4.53225i	0.417818	−	0.241227i	0.694143	+	0.719837i	$0.255783\pi$
$354$	−9.82319	+	17.0143i	−0.522097	+	0.904298i
$355$		0			0
$356$	2.46783	−	2.07076i	0.130795	−	0.109750i
$357$	−19.2896	+	22.9885i	−1.02092	+	1.21668i
$358$	−18.1056	+	3.19250i	−0.956909	+	0.168729i
$359$	−22.1964	−	8.07884i	−1.17148	−	0.426385i	−0.318297	−	0.947991i	$-0.603111\pi$
$359$	−22.1964	−	8.07884i	−1.17148	−	0.426385i	−0.853186	+	0.521606i	$0.825333\pi$
$360$		0			0
$361$	−17.1498	−	8.17830i	−0.902621	−	0.430437i
$362$			11.0421i			0.580360i
$363$	0.269833	−	0.741361i	0.0141626	−	0.0389113i
$364$	1.31502	+	7.45785i	0.0689258	+	0.390898i
$365$		0			0
$366$	2.23028	−	1.87142i	0.116578	−	0.0978208i
$367$	−10.2628	−	1.80960i	−0.535713	−	0.0944606i	−0.100755	−	0.994911i	$-0.532126\pi$
$367$	−10.2628	−	1.80960i	−0.535713	−	0.0944606i	−0.434958	+	0.900451i	$0.643237\pi$
$368$	4.84978	+	2.80002i	0.252812	+	0.145961i
$369$	1.26448	+	2.19015i	0.0658264	+	0.114015i
$370$		0			0
$371$	−0.910709	+	0.331471i	−0.0472817	+	0.0172091i
$372$	−3.41762	+	1.97317i	−0.177195	+	0.102304i
$373$	−7.97137	−	4.60227i	−0.412742	−	0.238297i	0.279225	−	0.960226i	$-0.409922\pi$
$373$	−7.97137	−	4.60227i	−0.412742	−	0.238297i	−0.691967	+	0.721929i	$0.743256\pi$
$374$	−1.95958	+	11.1133i	−0.101328	+	0.574657i
$375$		0			0
$376$	−5.22174	−	4.38156i	−0.269291	−	0.225962i
$377$	−25.0370	+	4.41469i	−1.28947	+	0.227368i
$378$	14.8225	−	40.7245i	0.762387	−	2.09464i
$379$	−12.6143			−0.647954			−0.323977	−	0.946065i	$-0.605020\pi$
$379$	−12.6143			−0.647954			−0.323977	+	0.946065i	$0.605020\pi$
$380$		0			0
$381$	59.8228			3.06482
$382$	4.17326	−	11.4659i	0.213522	−	0.586648i
$383$	−0.521688	+	0.0919877i	−0.0266570	+	0.00470035i	−0.186961	−	0.982367i	$-0.559864\pi$
$383$	−0.521688	+	0.0919877i	−0.0266570	+	0.00470035i	0.160304	+	0.987068i	$0.448753\pi$
$384$	−15.0448	−	12.6241i	−0.767754	−	0.644222i
$385$		0			0
$386$	−4.42096	+	25.0725i	−0.225021	+	1.27616i
$387$	−37.9703	−	21.9222i	−1.93014	−	1.11437i
$388$	2.62969	−	1.51825i	0.133502	−	0.0770776i
$389$	28.5541	−	10.3928i	1.44775	−	0.526938i	0.505788	−	0.862658i	$-0.331202\pi$
$389$	28.5541	−	10.3928i	1.44775	−	0.526938i	0.941962	+	0.335720i	$0.108980\pi$
$390$		0			0
$391$	2.51077	+	4.34878i	0.126975	+	0.219927i
$392$	−18.0917	−	10.4452i	−0.913769	−	0.527565i
$393$	16.0878	+	2.83671i	0.811521	+	0.143093i
$394$	8.91809	−	7.48317i	0.449287	−	0.376997i
$395$		0			0
$396$	1.48671	+	8.43156i	0.0747100	+	0.423702i
$397$	4.14727	−	11.3945i	0.208146	−	0.571875i	−0.791060	−	0.611739i	$-0.790470\pi$
$397$	4.14727	−	11.3945i	0.208146	−	0.571875i	0.999205	+	0.0398640i	$0.0126925\pi$
$398$			22.8164i			1.14368i
$399$	26.4495	−	41.1241i	1.32413	−	2.05878i
$400$		0			0
$401$	10.8916	+	3.96422i	0.543900	+	0.197963i	0.599334	−	0.800499i	$-0.295432\pi$
$401$	10.8916	+	3.96422i	0.543900	+	0.197963i	−0.0554341	+	0.998462i	$0.517654\pi$
$402$	40.1866	−	7.08598i	2.00433	−	0.353417i
$403$	9.70583	−	11.5670i	0.483482	−	0.576191i
$404$	1.44536	−	1.21280i	0.0719096	−	0.0603393i
$405$		0			0
$406$	12.2902	−	21.2873i	0.609953	−	1.05647i
$407$	2.88572	−	1.66607i	0.143040	−	0.0825840i
$408$	−8.38406	−	23.0350i	−0.415073	−	1.14040i
$409$	4.54489	−	1.65420i	0.224730	−	0.0817952i	−0.227201	−	0.973848i	$-0.572957\pi$
$409$	4.54489	−	1.65420i	0.224730	−	0.0817952i	0.451931	+	0.892053i	$0.350735\pi$
$410$		0			0
$411$	27.9559	−	48.4210i	1.37896	−	2.38843i
$412$	4.44466	+	0.783713i	0.218973	+	0.0386108i
$413$	−12.4204	−	14.8021i	−0.611170	−	0.728364i
$414$	−10.9774	−	9.21110i	−0.539508	−	0.452701i
$415$		0			0
$416$	−10.6169	−	3.86423i	−0.520535	−	0.189459i
$417$			31.6669i			1.55073i
$418$	0.881404	−	18.3656i	0.0431109	−	0.898291i
$419$	−12.4329			−0.607385			−0.303693	−	0.952770i	$-0.598220\pi$
$419$	−12.4329			−0.607385			−0.303693	+	0.952770i	$0.598220\pi$
$420$		0			0
$421$	4.79547	+	27.1965i	0.233717	+	1.32547i	0.845299	+	0.534294i	$0.179422\pi$
$421$	4.79547	+	27.1965i	0.233717	+	1.32547i	−0.611582	+	0.791181i	$0.709467\pi$
$422$	14.0439	−	16.7369i	0.683647	−	0.814738i
$423$	8.74850	+	10.4261i	0.425367	+	0.506932i
$424$	0.137471	−	0.779635i	0.00667617	−	0.0378624i
$425$		0			0
$426$	−3.78904	−	6.56281i	−0.183580	−	0.317969i
$427$	0.979362	+	2.69077i	0.0473946	+	0.130216i
$428$	0.198061	+	0.544168i	0.00957364	+	0.0263034i
$429$	−24.4698	−	42.3829i	−1.18141	−	2.04627i
$430$		0			0
$431$	1.23145	−	6.98391i	0.0593170	−	0.336403i	−0.940679	−	0.339298i	$-0.889810\pi$
$431$	1.23145	−	6.98391i	0.0593170	−	0.336403i	0.999996	+	0.00289506i	$0.000921529\pi$
$432$	17.7556	+	21.1603i	0.854268	+	1.01808i
$433$	4.23203	−	5.04353i	0.203378	−	0.242377i	−0.654709	−	0.755881i	$-0.727209\pi$
$433$	4.23203	−	5.04353i	0.203378	−	0.242377i	0.858087	+	0.513505i	$0.171653\pi$
$434$	2.53510	+	14.3773i	0.121689	+	0.690131i
$435$		0			0
$436$	−3.98995			−0.191084
$437$	−4.95265	−	6.51251i	−0.236917	−	0.311536i
$438$			17.2754i			0.825450i
$439$	4.16119	+	1.51455i	0.198603	+	0.0722855i	0.439407	−	0.898288i	$-0.355189\pi$
$439$	4.16119	+	1.51455i	0.198603	+	0.0722855i	−0.240804	+	0.970574i	$0.577411\pi$
$440$		0			0
$441$	31.9527	+	26.8115i	1.52156	+	1.27674i
$442$	10.4645	+	12.4711i	0.497744	+	0.593188i
$443$	−2.73002	−	0.481376i	−0.129707	−	0.0228709i	0.108418	−	0.994105i	$-0.465422\pi$
$443$	−2.73002	−	0.481376i	−0.129707	−	0.0228709i	−0.238125	+	0.971235i	$0.576533\pi$
$444$	−0.628171	+	1.08802i	−0.0298117	+	0.0516353i
$445$		0			0
$446$	10.3076	−	3.75166i	0.488079	−	0.177646i
$447$	15.5989	+	42.8577i	0.737805	+	2.02710i
$448$	28.7036	−	16.5720i	1.35612	−	0.782955i
$449$	13.1785	−	22.8258i	0.621930	−	1.07721i	−0.367196	−	0.930144i	$-0.619682\pi$
$449$	13.1785	−	22.8258i	0.621930	−	1.07721i	0.989126	−	0.147071i	$-0.0469845\pi$
$450$		0			0
$451$	−1.07042	+	0.898186i	−0.0504039	+	0.0422939i
$452$	4.60182	−	5.48423i	0.216451	−	0.257957i
$453$	−33.6494	+	5.93330i	−1.58099	+	0.278771i
$454$	−23.7594	−	8.64772i	−1.11508	−	0.405857i
$455$		0			0
$456$	18.2892	+	35.5071i	0.856470	+	1.66277i
$457$		−	33.5784i		−	1.57073i	−0.619032	−	0.785366i	$-0.712475\pi$
$457$		−	33.5784i		−	1.57073i	0.619032	−	0.785366i	$-0.287525\pi$
$458$	−8.95969	+	24.6165i	−0.418659	+	1.15026i
$459$	4.30114	+	24.3930i	0.200760	+	1.13857i
$460$		0			0
$461$	23.3279	−	19.5745i	1.08649	−	0.911674i	0.0900469	−	0.995938i	$-0.471298\pi$
$461$	23.3279	−	19.5745i	1.08649	−	0.911674i	0.996443	+	0.0842639i	$0.0268539\pi$
$462$	46.5984	+	8.21655i	2.16795	+	0.382269i
$463$	24.7477	+	14.2881i	1.15013	+	0.664025i	0.948918	−	0.315523i	$-0.102180\pi$
$463$	24.7477	+	14.2881i	1.15013	+	0.664025i	0.201208	+	0.979549i	$0.435513\pi$
$464$	7.83354	+	13.5681i	0.363663	+	0.629883i
$465$		0			0
$466$	−0.642610	+	0.233891i	−0.0297683	+	0.0108348i
$467$	9.71443	−	5.60863i	0.449530	−	0.259536i	−0.258101	−	0.966118i	$-0.583097\pi$
$467$	9.71443	−	5.60863i	0.449530	−	0.259536i	0.707632	+	0.706581i	$0.249764\pi$
$468$	10.6965	+	6.17565i	0.494448	+	0.285470i
$469$	−6.96927	+	39.5247i	−0.321811	+	1.82508i
$470$		0			0
$471$	−9.72684	−	8.16179i	−0.448189	−	0.376075i
$472$	15.5441	−	2.74085i	0.715477	−	0.126158i
$473$	8.28554	−	22.7643i	0.380969	−	1.04670i
$474$	45.6325			2.09597
$475$		0			0
$476$	4.18470			0.191806
$477$	−0.540625	+	1.48536i	−0.0247535	+	0.0680098i
$478$	27.5097	−	4.85070i	1.25826	−	0.221866i
$479$	13.3219	+	11.1784i	0.608695	+	0.510755i	0.894227	−	0.447614i	$-0.147726\pi$
$479$	13.3219	+	11.1784i	0.608695	+	0.510755i	−0.285532	+	0.958369i	$0.592170\pi$
$480$		0			0
$481$	0.834738	−	4.73403i	0.0380608	−	0.215853i
$482$	23.6583	+	13.6591i	1.07761	+	0.622156i
$483$	18.2345	−	10.5277i	0.829697	−	0.479026i
$484$	−0.103380	+	0.0376273i	−0.00469910	+	0.00171033i
$485$		0			0
$486$	−0.847018	−	1.46708i	−0.0384215	−	0.0665480i
$487$	13.2911	+	7.67364i	0.602278	+	0.347726i	0.769937	−	0.638119i	$-0.220287\pi$
$487$	13.2911	+	7.67364i	0.602278	+	0.347726i	−0.167659	+	0.985845i	$0.553621\pi$
$488$	−2.30350	−	0.406170i	−0.104275	−	0.0183864i
$489$	32.0874	−	26.9246i	1.45104	−	1.21757i
$490$		0			0
$491$	1.45066	+	8.22710i	0.0654673	+	0.371284i	0.999886	+	0.0151068i	$0.00480884\pi$
$491$	1.45066	+	8.22710i	0.0654673	+	0.371284i	−0.934419	+	0.356177i	$0.884080\pi$
$492$	0.180192	−	0.495073i	0.00812368	−	0.0223196i
$493$			14.0486i			0.632717i
$494$	−19.4789	−	18.0046i	−0.876398	−	0.810067i
$495$		0			0
$496$	−8.74398	−	3.18255i	−0.392616	−	0.142901i
$497$	7.34003	−	1.29425i	0.329245	−	0.0580548i
$498$	33.0289	−	39.3623i	1.48006	−	1.76387i
$499$	−0.207470	+	0.174088i	−0.00928764	+	0.00779325i	−0.647420	−	0.762134i	$-0.724152\pi$
$499$	−0.207470	+	0.174088i	−0.00928764	+	0.00779325i	0.638132	+	0.769927i	$0.279707\pi$
$500$		0			0
$501$	−26.5413	+	45.9709i	−1.18578	+	2.05383i
$502$	−19.4024	+	11.2020i	−0.865973	+	0.499970i
$503$	−14.2279	−	39.0907i	−0.634389	−	1.74297i	−0.668672	−	0.743558i	$-0.733137\pi$
$503$	−14.2279	−	39.0907i	−0.634389	−	1.74297i	0.0342827	−	0.999412i	$-0.489085\pi$
$504$	−64.6521	+	23.5314i	−2.87983	+	1.04817i
$505$		0			0
$506$	3.95885	−	6.85693i	0.175992	−	0.304828i
$507$	−30.9650	−	5.45996i	−1.37520	−	0.242485i
$508$	−5.36219	−	6.39041i	−0.237909	−	0.283529i
$509$	−1.24694	−	1.04631i	−0.0552696	−	0.0463767i	0.614734	−	0.788734i	$-0.289263\pi$
$509$	−1.24694	−	1.04631i	−0.0552696	−	0.0463767i	−0.670004	+	0.742357i	$0.733708\pi$
$510$		0			0
$511$	−15.9662	−	5.81121i	−0.706301	−	0.257073i
$512$			25.1134i			1.10987i
$513$	−11.9693	−	38.5418i	−0.528456	−	1.70166i
$514$	−19.7643			−0.871766
$515$		0			0
$516$	1.58608	+	8.99508i	0.0698231	+	0.395987i
$517$	−4.83380	+	5.76070i	−0.212590	+	0.253355i
$518$	2.98749	+	3.56035i	0.131263	+	0.156433i
$519$	6.96638	−	39.5083i	0.305790	−	1.73422i
$520$		0			0
$521$	4.57062	+	7.91655i	0.200243	+	0.346830i	0.948607	−	0.316458i	$-0.102494\pi$
$521$	4.57062	+	7.91655i	0.200243	+	0.346830i	−0.748364	+	0.663288i	$0.769160\pi$
$522$	−13.7117	−	37.6726i	−0.600145	−	1.64889i
$523$	−12.7572	−	35.0501i	−0.557833	−	1.53263i	−0.822774	−	0.568368i	$-0.807575\pi$
$523$	−12.7572	−	35.0501i	−0.557833	−	1.53263i	0.264942	−	0.964264i	$-0.414647\pi$
$524$	−1.13900	−	1.97280i	−0.0497573	−	0.0861822i
$525$		0			0
$526$	−6.64638	+	37.6935i	−0.289796	+	1.64351i
$527$	−5.36334	−	6.39178i	−0.233631	−	0.278430i
$528$	−19.3859	+	23.1032i	−0.843662	+	1.00544i
$529$	3.38210	+	19.1809i	0.147048	+	0.833951i
$530$		0			0
$531$	−31.5152			−1.36764
$532$	−6.76376	+	0.860742i	−0.293246	+	0.0373179i
$533$			2.01584i			0.0873156i
$534$	−27.2873	−	9.93177i	−1.18084	−	0.429790i
$535$		0			0
$536$	−25.1140	−	21.0732i	−1.08476	−	0.910223i
$537$	−28.3203	−	33.7508i	−1.22211	−	1.45645i
$538$	3.23320	+	0.570101i	0.139393	+	0.0245788i
$539$	−11.5234	+	19.9590i	−0.496346	+	0.859696i
$540$		0			0
$541$	34.0583	−	12.3962i	1.46428	−	0.532955i	0.517741	−	0.855538i	$-0.326773\pi$
$541$	34.0583	−	12.3962i	1.46428	−	0.532955i	0.946541	+	0.322582i	$0.104551\pi$
$542$	−4.13063	−	11.3488i	−0.177426	−	0.487474i
$543$	−22.9167	+	13.2310i	−0.983449	+	0.567795i
$544$	−3.12165	+	5.40685i	−0.133839	+	0.231817i
$545$		0			0
$546$	52.2914	−	43.8777i	2.23786	−	1.87779i
$547$	−9.70823	+	11.5698i	−0.415094	+	0.494690i	−0.932561	−	0.361014i	$-0.882431\pi$
$547$	−9.70823	+	11.5698i	−0.415094	+	0.494690i	0.517466	+	0.855704i	$0.326875\pi$
$548$	−7.67826	+	1.35388i	−0.327999	+	0.0578351i
$549$	4.38862	+	1.59733i	0.187302	+	0.0681722i
$550$		0			0
$551$	−2.88962	−	22.7068i	−0.123102	−	0.967342i
$552$			17.1992i			0.732047i
$553$	−15.3502	+	42.1742i	−0.652755	+	1.79343i
$554$	−4.38004	−	24.8404i	−0.186090	−	1.05537i
$555$		0			0
$556$	3.38273	−	2.83845i	0.143460	−	0.120377i
$557$	9.22051	+	1.62582i	0.390685	+	0.0688884i	0.365541	−	0.930795i	$-0.380884\pi$
$557$	9.22051	+	1.62582i	0.390685	+	0.0688884i	0.0251450	+	0.999684i	$0.491995\pi$
$558$	20.6208	+	11.9054i	0.872949	+	0.503997i
$559$	−17.4741	−	30.2661i	−0.739077	−	1.28012i
$560$		0			0
$561$	−25.4126	+	9.24942i	−1.07292	+	0.390511i
$562$	−28.9073	+	16.6897i	−1.21938	+	0.704011i
$563$	12.5101	+	7.22271i	0.527238	+	0.304401i	0.739891	−	0.672727i	$-0.234877\pi$
$563$	12.5101	+	7.22271i	0.527238	+	0.304401i	−0.212653	+	0.977128i	$0.568210\pi$
$564$	0.492353	−	2.79227i	0.0207318	−	0.117576i
$565$		0			0
$566$	−16.1561	−	13.5566i	−0.679092	−	0.569826i
$567$	35.4574	−	6.25209i	1.48907	−	0.262563i
$568$	−2.08230	+	5.72108i	−0.0873715	+	0.240051i
$569$	37.8642			1.58735			0.793675	−	0.608342i	$-0.208165\pi$
$569$	37.8642			1.58735			0.793675	+	0.608342i	$0.208165\pi$
$570$		0			0
$571$	−18.5203			−0.775048			−0.387524	−	0.921860i	$-0.626670\pi$
$571$	−18.5203			−0.775048			−0.387524	+	0.921860i	$0.626670\pi$
$572$	−2.33410	+	6.41289i	−0.0975937	+	0.268136i
$573$	28.7968	−	5.07766i	1.20300	−	0.212122i
$574$	−1.49303	−	1.25280i	−0.0623179	−	0.0522909i
$575$		0			0
$576$	9.38699	−	53.2363i	0.391125	−	2.21818i
$577$	−7.86434	−	4.54048i	−0.327397	−	0.189022i	0.327288	−	0.944925i	$-0.393865\pi$
$577$	−7.86434	−	4.54048i	−0.327397	−	0.189022i	−0.654685	+	0.755902i	$0.727199\pi$
$578$	−10.7147	+	6.18614i	−0.445673	+	0.257309i
$579$	−57.3326	+	20.8674i	−2.38266	+	0.867218i
$580$		0			0
$581$	25.2688	+	43.7668i	1.04832	+	1.81575i
$582$	−23.7038	−	13.6854i	−0.982556	−	0.567279i
$583$	−0.860105	−	0.151660i	−0.0356219	−	0.00628110i
$584$	10.6320	−	8.92130i	0.439955	−	0.369166i
$585$		0			0
$586$	2.92017	+	16.5611i	0.120631	+	0.684134i
$587$	7.87923	−	21.6480i	0.325211	−	0.893509i	−0.664094	−	0.747649i	$-0.731183\pi$
$587$	7.87923	−	21.6480i	0.325211	−	0.893509i	0.989305	−	0.145860i	$-0.0465950\pi$
$588$		−	8.68948i		−	0.358348i
$589$	9.98350	+	9.22789i	0.411363	+	0.380229i
$590$		0			0
$591$	26.2164	+	9.54200i	1.07840	+	0.392505i
$592$	−2.91735	+	0.514408i	−0.119903	+	0.0211421i
$593$	−25.8678	+	30.8280i	−1.06226	+	1.26596i	−0.0996654	+	0.995021i	$0.531777\pi$
$593$	−25.8678	+	30.8280i	−1.06226	+	1.26596i	−0.962598	+	0.270935i	$0.912667\pi$
$594$	29.9178	−	25.1040i	1.22754	−	1.03003i
$595$		0			0
$596$	3.17996	−	5.50785i	0.130256	−	0.225610i
$597$	−47.3530	+	27.3393i	−1.93803	+	1.11892i
$598$	−3.90668	−	10.7335i	−0.159756	−	0.438926i
$599$	−35.4913	+	12.9178i	−1.45014	+	0.527807i	−0.942629	−	0.333841i	$-0.891655\pi$
$599$	−35.4913	+	12.9178i	−1.45014	+	0.527807i	−0.507507	+	0.861647i	$0.669433\pi$
$600$		0			0
$601$	−21.9195	+	37.9656i	−0.894113	+	1.54865i	−0.0592147	+	0.998245i	$0.518860\pi$
$601$	−21.9195	+	37.9656i	−0.894113	+	1.54865i	−0.834898	+	0.550404i	$0.814474\pi$
$602$	33.2764	+	5.86753i	1.35625	+	0.239143i
$603$	42.0760	+	50.1443i	1.71347	+	2.04203i
$604$	3.64996	+	3.06268i	0.148515	+	0.124619i
$605$		0			0
$606$	−15.9817	−	5.81686i	−0.649212	−	0.236294i
$607$			7.80810i			0.316921i	0.987365	+	0.158461i	$0.0506531\pi$
$607$			7.80810i			0.316921i	−0.987365	+	0.158461i	$0.949347\pi$
$608$	3.93341	−	9.38120i	0.159521	−	0.380458i
$609$	58.9059			2.38699
$610$		0			0
$611$	1.88386	+	10.6839i	0.0762128	+	0.432224i
$612$	4.38715	−	5.22841i	0.177340	−	0.211346i
$613$	−25.0017	−	29.7958i	−1.00981	−	1.20344i	−0.978988	−	0.203918i	$-0.934633\pi$
$613$	−25.0017	−	29.7958i	−1.00981	−	1.20344i	−0.0308202	−	0.999525i	$-0.509812\pi$
$614$	−6.10549	+	34.6259i	−0.246397	+	1.39739i
$615$		0			0
$616$	−19.0074	−	32.9217i	−0.765829	−	1.32645i
$617$	4.26208	+	11.7100i	0.171585	+	0.471426i	0.995442	−	0.0953722i	$-0.0304041\pi$
$617$	4.26208	+	11.7100i	0.171585	+	0.471426i	−0.823857	+	0.566798i	$0.808182\pi$
$618$	−13.9140	−	38.2284i	−0.559704	−	1.53777i
$619$	−1.37870	−	2.38799i	−0.0554148	−	0.0959813i	0.836987	−	0.547222i	$-0.184315\pi$
$619$	−1.37870	−	2.38799i	−0.0554148	−	0.0959813i	−0.892402	+	0.451241i	$0.850981\pi$
$620$		0			0
$621$	3.01779	−	17.1147i	0.121100	−	0.686791i
$622$	−20.0657	−	23.9133i	−0.804561	−	0.958838i
$623$	18.3582	−	21.8784i	0.735505	−	0.876540i
$624$	7.55518	+	42.8476i	0.302449	+	1.71527i
$625$		0			0
$626$	−27.9958			−1.11894
$627$	39.1719	−	20.1769i	1.56438	−	0.805789i
$628$			1.77062i			0.0706555i
$629$	−2.49614	−	0.908519i	−0.0995275	−	0.0362250i
$630$		0			0
$631$	−30.5821	−	25.6614i	−1.21745	−	1.02156i	−0.998954	−	0.0457265i	$-0.985440\pi$
$631$	−30.5821	−	25.6614i	−1.21745	−	1.02156i	−0.218498	−	0.975837i	$-0.570116\pi$
$632$	−23.5654	−	28.0841i	−0.937381	−	1.11713i
$633$	51.5634	+	9.09201i	2.04946	+	0.361375i
$634$	−8.84628	+	15.3222i	−0.351331	+	0.608522i
$635$		0			0
$636$	0.309436	−	0.112625i	0.0122699	−	0.00446589i
$637$	11.3715	+	31.2429i	0.450555	+	1.23789i
$638$	19.1834	−	11.0755i	0.759479	−	0.438485i
$639$	6.07809	−	10.5276i	0.240445	−	0.416464i
$640$		0			0
$641$	−3.83994	+	3.22209i	−0.151668	+	0.127265i	−0.715464	−	0.698649i	$-0.753785\pi$
$641$	−3.83994	+	3.22209i	−0.151668	+	0.127265i	0.563796	+	0.825914i	$0.309340\pi$
$642$	3.35528	−	3.99866i	0.132422	−	0.157815i
$643$	−49.2161	+	8.67812i	−1.94089	+	0.342232i	−0.940899	+	0.338688i	$0.890017\pi$
$643$	−49.2161	+	8.67812i	−1.94089	+	0.342232i	−0.999994	+	0.00354380i	$0.998872\pi$
$644$	−2.75903	−	1.00420i	−0.108721	−	0.0395712i
$645$		0			0
$646$	−11.6671	+	8.87266i	−0.459038	+	0.349090i
$647$		−	32.7681i		−	1.28825i	−0.764922	−	0.644123i	$-0.777223\pi$
$647$		−	32.7681i		−	1.28825i	0.764922	−	0.644123i	$-0.222777\pi$
$648$	−10.0589	+	27.6367i	−0.395153	+	1.08567i
$649$	−3.02375	−	17.1485i	−0.118693	−	0.673139i
$650$		0			0
$651$	−26.8008	+	22.4886i	−1.05041	+	0.881396i
$652$	−5.75229	−	1.01428i	−0.225277	−	0.0397224i
$653$	−13.6828	−	7.89978i	−0.535450	−	0.309142i	0.207783	−	0.978175i	$-0.433375\pi$
$653$	−13.6828	−	7.89978i	−0.535450	−	0.309142i	−0.743233	+	0.669033i	$0.766709\pi$
$654$	17.9825	+	31.1467i	0.703173	+	1.21793i
$655$		0			0
$656$	1.16734	−	0.424879i	0.0455772	−	0.0165887i
$657$	−23.9992	+	13.8559i	−0.936296	+	0.540571i
$658$	−9.08381	−	5.24454i	−0.354124	−	0.204453i
$659$	2.35267	−	13.3426i	0.0916468	−	0.519755i	−0.904077	−	0.427370i	$-0.859440\pi$
$659$	2.35267	−	13.3426i	0.0916468	−	0.519755i	0.995723	−	0.0923845i	$-0.0294489\pi$
$660$		0			0
$661$	2.80202	+	2.35117i	0.108986	+	0.0914501i	0.695652	−	0.718379i	$-0.255115\pi$
$661$	2.80202	+	2.35117i	0.108986	+	0.0914501i	−0.586666	+	0.809829i	$0.699560\pi$
$662$	−6.54272	+	1.15366i	−0.254290	+	0.0448382i
$663$	−13.3435	+	36.6611i	−0.518220	+	1.42380i
$664$	−41.2819			−1.60205
$665$		0			0
$666$	7.58036			0.293733
$667$	3.37124	−	9.26242i	0.130535	−	0.358642i
$668$	7.28973	−	1.28538i	0.282048	−	0.0497327i
$669$	20.1370	+	16.8970i	0.778542	+	0.653275i
$670$		0			0
$671$	−0.448092	+	2.54126i	−0.0172984	+	0.0981042i
$672$	22.6710	+	13.0891i	0.874552	+	0.504923i
$673$	−23.3223	+	13.4651i	−0.899009	+	0.519043i	−0.876878	−	0.480712i	$-0.840378\pi$
$673$	−23.3223	+	13.4651i	−0.899009	+	0.519043i	−0.0221303	+	0.999755i	$0.507045\pi$
$674$	28.2156	−	10.2696i	1.08682	−	0.395571i
$675$		0			0
$676$	2.19229	+	3.79715i	0.0843187	+	0.146044i
$677$	17.9209	+	10.3467i	0.688757	+	0.397654i	0.803146	−	0.595782i	$-0.203158\pi$
$677$	17.9209	+	10.3467i	0.688757	+	0.397654i	−0.114389	+	0.993436i	$0.536491\pi$
$678$	−63.5517	−	11.2059i	−2.44069	−	0.430359i
$679$	20.6219	−	17.3038i	0.791396	−	0.664060i
$680$		0			0
$681$	−10.5218	−	59.6720i	−0.403196	−	2.28664i
$682$	−4.49969	+	12.3628i	−0.172302	+	0.473396i
$683$			26.9573i			1.03149i	0.856742	+	0.515745i	$0.172485\pi$
$683$			26.9573i			1.03149i	−0.856742	+	0.515745i	$0.827515\pi$
$684$	−6.01556	+	9.35308i	−0.230011	+	0.357624i
$685$		0			0
$686$	0.582515	+	0.212018i	0.0222405	+	0.00809489i
$687$	−61.8247	+	10.9014i	−2.35876	+	0.415913i
$688$	−13.8437	+	16.4982i	−0.527785	+	0.628989i
$689$	−0.965185	+	0.809886i	−0.0367706	+	0.0308542i
$690$		0			0
$691$	−4.35021	+	7.53479i	−0.165490	+	0.286637i	−0.936829	−	0.349787i	$-0.886254\pi$
$691$	−4.35021	+	7.53479i	−0.165490	+	0.286637i	0.771339	+	0.636424i	$0.219587\pi$
$692$	−4.84480	+	2.79715i	−0.184172	+	0.106332i
$693$	25.9602	+	71.3252i	0.986148	+	2.70942i
$694$	−10.3553	+	3.76900i	−0.393080	+	0.143069i
$695$		0			0
$696$	−24.0588	+	41.6711i	−0.911948	+	1.57954i
$697$	1.09701	+	0.193432i	0.0415521	+	0.00732676i
$698$	1.64832	+	1.96440i	0.0623900	+	0.0743535i
$699$	−1.25541	−	1.05341i	−0.0474839	−	0.0398437i
$700$		0			0
$701$	0.378762	+	0.137858i	0.0143056	+	0.00520683i	0.349163	−	0.937062i	$-0.386466\pi$
$701$	0.378762	+	0.137858i	0.0143056	+	0.00520683i	−0.334857	+	0.942269i	$0.608688\pi$
$702$		−	56.3420i		−	2.12649i
$703$	4.22139	+	0.955019i	0.159213	+	0.0360192i
$704$	29.8684			1.12571
$705$		0			0
$706$	1.97850	+	11.2206i	0.0744618	+	0.422294i
$707$	10.7521	−	12.8138i	0.404373	−	0.481913i
$708$	4.22015	+	5.02938i	0.158603	+	0.189016i
$709$	−6.95535	+	39.4457i	−0.261214	+	1.48142i	0.518391	+	0.855144i	$0.326531\pi$
$709$	−6.95535	+	39.4457i	−0.261214	+	1.48142i	−0.779604	+	0.626272i	$0.784580\pi$
$710$		0			0
$711$	36.6001	+	63.3932i	1.37261	+	2.37743i
$712$	7.97920	+	21.9227i	0.299033	+	0.821587i
$713$	2.00228	+	5.50123i	0.0749861	+	0.206023i
$714$	−18.8603	−	32.6670i	−0.705829	−	1.22253i
$715$		0			0
$716$	−1.06686	+	6.05048i	−0.0398705	+	0.226117i
$717$	43.0299	+	51.2811i	1.60698	+	1.91513i
$718$	19.0848	−	22.7443i	0.712237	−	0.848811i
$719$	−3.13880	−	17.8010i	−0.117058	−	0.663867i	−0.985711	−	0.168446i	$-0.946125\pi$
$719$	−3.13880	−	17.8010i	−0.117058	−	0.663867i	0.868653	−	0.495421i	$-0.164986\pi$
$720$		0			0
$721$	40.0118			1.49012
$722$	17.0327	−	16.7407i	0.633890	−	0.623024i
$723$			65.4670i			2.43474i
$724$	3.46749	+	1.26206i	0.128868	+	0.0469042i
$725$		0			0
$726$	0.759660	+	0.637431i	0.0281936	+	0.0236573i
$727$	−16.9448	−	20.1940i	−0.628446	−	0.748953i	0.354052	−	0.935226i	$-0.384804\pi$
$727$	−16.9448	−	20.1940i	−0.628446	−	0.748953i	−0.982498	+	0.186273i	$0.940359\pi$
$728$	−54.0083	−	9.52311i	−2.00168	−	0.352950i
$729$	−12.4728	+	21.6035i	−0.461954	+	0.800129i
$730$		0			0
$731$	−18.1474	+	6.60511i	−0.671205	+	0.244299i
$732$	−0.332762	−	0.914256i	−0.0122992	−	0.0337919i
$733$	−2.86584	+	1.65460i	−0.105852	+	0.0611139i	−0.551992	−	0.833850i	$-0.686132\pi$
$733$	−2.86584	+	1.65460i	−0.105852	+	0.0611139i	0.446139	+	0.894964i	$0.352799\pi$
$734$	6.54946	−	11.3440i	0.241745	−	0.418714i
$735$		0			0
$736$	3.35562	−	2.81570i	0.123690	−	0.103788i
$737$	−23.2482	+	27.7062i	−0.856360	+	1.02057i
$738$	−3.13052	+	0.551996i	−0.115236	+	0.0203192i
$739$	16.6272	+	6.05179i	0.611640	+	0.222619i	0.629221	−	0.777227i	$-0.283374\pi$
$739$	16.6272	+	6.05179i	0.611640	+	0.222619i	−0.0175807	+	0.999845i	$0.505596\pi$
$740$		0			0
$741$	14.0265	−	62.0000i	0.515276	−	2.27763i
$742$		−	1.21819i		−	0.0447212i
$743$	12.7413	−	35.0065i	0.467434	−	1.28427i	−0.452350	−	0.891841i	$-0.649414\pi$
$743$	12.7413	−	35.0065i	0.467434	−	1.28427i	0.919784	−	0.392425i	$-0.128364\pi$
$744$	−4.96261	−	28.1444i	−0.181938	−	1.03182i
$745$		0			0
$746$	8.86295	−	7.43689i	0.324496	−	0.272284i
$747$	81.1738	+	14.3131i	2.96999	+	0.523690i
$748$	3.26589	+	1.88556i	0.119413	+	0.0689430i
$749$	2.56695	+	4.44609i	0.0937944	+	0.162457i
$750$		0			0
$751$	12.7466	−	4.63939i	0.465131	−	0.169294i	−0.0988146	−	0.995106i	$-0.531505\pi$
$751$	12.7466	−	4.63939i	0.465131	−	0.169294i	0.563945	+	0.825812i	$0.309283\pi$
$752$	5.78984	−	3.34277i	0.211134	−	0.121898i
$753$	−46.4971	−	26.8451i	−1.69445	−	0.978289i
$754$	5.54909	−	31.4705i	0.202086	−	1.14609i
$755$		0			0
$756$	−11.0943	−	9.30925i	−0.403497	−	0.338574i
$757$	12.3465	−	2.17703i	0.448743	−	0.0791255i	0.0552901	−	0.998470i	$-0.482392\pi$
$757$	12.3465	−	2.17703i	0.448743	−	0.0791255i	0.393453	+	0.919345i	$0.371281\pi$
$758$	5.42297	−	14.8995i	0.196971	−	0.541174i
$759$	18.9744			0.688728
$760$		0			0
$761$	−27.2282			−0.987022			−0.493511	−	0.869740i	$-0.664287\pi$
$761$	−27.2282			−0.987022			−0.493511	+	0.869740i	$0.664287\pi$
$762$	−25.7182	+	70.6601i	−0.931672	+	2.55975i
$763$	−34.8353	+	6.14240i	−1.26112	+	0.222370i
$764$	−3.12360	−	2.62101i	−0.113008	−	0.0948248i
$765$		0			0
$766$	0.115625	−	0.655742i	0.00417770	−	0.0236929i
$767$	−21.7552	−	12.5604i	−0.785534	−	0.453528i
$768$	−25.0574	+	14.4669i	−0.904179	+	0.522028i
$769$	−0.864690	+	0.314721i	−0.0311815	+	0.0113491i	−0.357564	−	0.933889i	$-0.616393\pi$
$769$	−0.864690	+	0.314721i	−0.0311815	+	0.0113491i	0.326382	+	0.945238i	$0.394170\pi$
$770$		0			0
$771$	−23.6821	−	41.0187i	−0.852892	−	1.47725i
$772$	7.36809	+	4.25397i	0.265183	+	0.153104i
$773$	−1.80207	−	0.317753i	−0.0648158	−	0.0114288i	0.141146	−	0.989989i	$-0.454921\pi$
$773$	−1.80207	−	0.317753i	−0.0648158	−	0.0114288i	−0.205962	+	0.978560i	$0.566032\pi$
$774$	42.2172	−	35.4245i	1.51747	−	1.27331i
$775$		0			0
$776$	3.81848	+	21.6557i	0.137076	+	0.777394i
$777$	−3.80943	+	10.4663i	−0.136663	+	0.375478i
$778$			38.1948i			1.36935i
$779$	−1.81288	−	0.0870041i	−0.0649533	−	0.00311725i
$780$		0			0
$781$	6.31158	+	2.29723i	0.225846	+	0.0822013i
$782$	−6.21598	+	1.09605i	−0.222283	+	0.0391945i
$783$	31.2524	−	37.2451i	1.11687	−	1.33103i
$784$	15.6956	−	13.1702i	0.560556	−	0.470363i
$785$		0			0
$786$	−10.2668	+	17.7827i	−0.366206	+	0.634287i
$787$	2.51571	−	1.45244i	0.0896752	−	0.0517740i	−0.454492	−	0.890751i	$-0.650179\pi$
$787$	2.51571	−	1.45244i	0.0896752	−	0.0517740i	0.544167	+	0.838977i	$0.316846\pi$
$788$	−1.33060	−	3.65579i	−0.0474006	−	0.130232i
$789$	−86.1927	+	31.3716i	−3.06854	+	1.11686i
$790$		0			0
$791$	31.7346	−	54.9659i	1.12835	−	1.95436i
$792$	−61.0596	−	10.7665i	−2.16966	−	0.382570i
$793$	2.39288	+	2.85173i	0.0849737	+	0.101268i
$794$	11.6758	+	9.79716i	0.414358	+	0.347688i
$795$		0			0
$796$	7.16491	+	2.60782i	0.253954	+	0.0924316i
$797$		−	19.9042i		−	0.705044i	−0.935804	−	0.352522i	$-0.885324\pi$
$797$		−	19.9042i		−	0.705044i	0.935804	−	0.352522i	$-0.114676\pi$
$798$	37.2032	+	48.9205i	1.31698	+	1.73177i
$799$	5.99488			0.212084
$800$		0			0
$801$	−8.08878	−	45.8737i	−0.285803	−	1.62087i
$802$	−9.36472	+	11.1604i	−0.330680	+	0.394089i
$803$	−9.84211	−	11.7294i	−0.347320	−	0.413920i
$804$	2.36798	−	13.4295i	0.0835121	−	0.473621i
$805$		0			0
$806$	9.48980	+	16.4368i	0.334264	+	0.578962i
$807$	2.69093	+	7.39327i	0.0947252	+	0.260255i
$808$	4.67328	+	12.8397i	0.164405	+	0.451700i
$809$	22.2093	+	38.4677i	0.780838	+	1.35245i	0.931454	+	0.363859i	$0.118541\pi$
$809$	22.2093	+	38.4677i	0.780838	+	1.35245i	−0.150616	+	0.988592i	$0.548126\pi$
$810$		0			0
$811$	5.91262	−	33.5322i	0.207620	−	1.17747i	−0.685642	−	0.727939i	$-0.740479\pi$
$811$	5.91262	−	33.5322i	0.207620	−	1.17747i	0.893263	−	0.449535i	$-0.148410\pi$
$812$	−5.28001	−	6.29247i	−0.185292	−	0.220822i
$813$	18.6038	−	22.1712i	0.652464	−	0.777577i
$814$	0.727303	+	4.12474i	0.0254920	+	0.144572i
$815$		0			0
$816$	24.0424			0.841651
$817$	27.9731	−	14.4086i	0.978655	−	0.504092i
$818$			6.07938i			0.212561i
$819$	102.896	+	37.4512i	3.59548	+	1.30865i
$820$		0			0
$821$	−20.5350	−	17.2309i	−0.716675	−	0.601362i	0.209788	−	0.977747i	$-0.432723\pi$
$821$	−20.5350	−	17.2309i	−0.716675	−	0.601362i	−0.926463	+	0.376385i	$0.877167\pi$
$822$	45.1744	+	53.8368i	1.57564	+	1.87777i
$823$	10.8729	+	1.91719i	0.379006	+	0.0668290i	0.359906	−	0.932989i	$-0.382809\pi$
$823$	10.8729	+	1.91719i	0.379006	+	0.0668290i	0.0191001	+	0.999818i	$0.493920\pi$
$824$	−16.3419	+	28.3051i	−0.569298	+	0.986054i
$825$		0			0
$826$	22.8232	−	8.30698i	0.794122	−	0.289037i
$827$	4.06958	+	11.1811i	0.141513	+	0.388804i	0.990121	−	0.140219i	$-0.0447807\pi$
$827$	4.06958	+	11.1811i	0.141513	+	0.388804i	−0.848607	+	0.529023i	$0.822558\pi$
$828$	−4.14717	+	2.39437i	−0.144124	+	0.0832101i
$829$	5.60968	−	9.71626i	0.194832	−	0.337460i	−0.752013	−	0.659148i	$-0.770917\pi$
$829$	5.60968	−	9.71626i	0.194832	−	0.337460i	0.946846	+	0.321689i	$0.104250\pi$
$830$		0			0
$831$	46.3054	−	38.8548i	1.60632	−	1.34786i
$832$	27.6972	−	33.0082i	0.960227	−	1.14435i
$833$	18.0934	−	3.19035i	0.626898	−	0.110539i
$834$	−37.4036	−	13.6138i	−1.29518	−	0.471407i
$835$		0			0
$836$	−5.66651	−	2.37589i	−0.195980	−	0.0821718i
$837$			28.8769i			0.998132i
$838$	5.34496	−	14.6852i	0.184639	−	0.507291i
$839$	6.22171	+	35.2851i	0.214797	+	1.21818i	0.881258	+	0.472636i	$0.156697\pi$
$839$	6.22171	+	35.2851i	0.214797	+	1.21818i	−0.666460	+	0.745540i	$0.732191\pi$
$840$		0			0
$841$	−1.09068	+	0.915188i	−0.0376096	+	0.0315582i
$842$	−34.1849	−	6.02772i	−1.17809	−	0.207729i
$843$	−69.2752	−	39.9960i	−2.38596	−	1.37754i
$844$	−3.65063	−	6.32308i	−0.125660	−	0.217649i
$845$		0			0
$846$	−16.0759	+	5.85113i	−0.552699	+	0.201166i
$847$	−0.844662	+	0.487666i	−0.0290229	+	0.0167564i
$848$	0.672427	+	0.388226i	0.0230912	+	0.0133317i
$849$	8.77653	−	49.7742i	0.301210	−	1.70825i
$850$		0			0
$851$	1.42772	+	1.19800i	0.0489415	+	0.0410668i
$852$	−2.49395	+	0.439751i	−0.0854415	+	0.0150656i
$853$	4.46788	−	12.2754i	0.152977	−	0.420302i	−0.839404	−	0.543509i	$-0.817096\pi$
$853$	4.46788	−	12.2754i	0.152977	−	0.420302i	0.992381	+	0.123207i	$0.0393178\pi$
$854$	−3.59926			−0.123164
$855$		0			0
$856$	−4.19366			−0.143337
$857$	8.27355	−	22.7314i	0.282619	−	0.776489i	−0.714429	−	0.699708i	$-0.753313\pi$
$857$	8.27355	−	22.7314i	0.282619	−	0.776489i	0.997048	−	0.0767813i	$-0.0244643\pi$
$858$	60.5806	−	10.6820i	2.06819	−	0.364677i
$859$	−41.4832	−	34.8086i	−1.41539	−	1.18765i	−0.953756	−	0.300581i	$-0.902819\pi$
$859$	−41.4832	−	34.8086i	−1.41539	−	1.18765i	−0.461633	−	0.887071i	$-0.652736\pi$
$860$		0			0
$861$	0.811063	−	4.59977i	0.0276409	−	0.156760i
$862$	7.71969	+	4.45696i	0.262934	+	0.151805i
$863$	43.0287	−	24.8426i	1.46471	−	0.845653i	0.465490	−	0.885053i	$-0.345878\pi$
$863$	43.0287	−	24.8426i	1.46471	−	0.845653i	0.999224	+	0.0394004i	$0.0125448\pi$
$864$	20.3040	−	7.39006i	0.690757	−	0.251415i
$865$		0			0
$866$	4.13783	+	7.16693i	0.140609	+	0.243542i
$867$	−25.6773	−	14.8248i	−0.872048	−	0.503477i
$868$	4.80456	+	0.847174i	0.163077	+	0.0287549i
$869$	−30.9828	+	25.9977i	−1.05102	+	0.881911i
$870$		0			0
$871$	9.06045	+	51.3843i	0.307001	+	1.74109i
$872$	9.88246	−	27.1518i	0.334662	−	0.919478i
$873$		−	43.9062i		−	1.48600i
$874$	9.82147	−	3.05009i	0.332216	−	0.103171i
$875$		0			0
$876$	5.42489	+	1.97450i	0.183290	+	0.0667122i
$877$	−8.14572	+	1.43631i	−0.275061	+	0.0485007i	−0.309477	−	0.950907i	$-0.600154\pi$
$877$	−8.14572	+	1.43631i	−0.275061	+	0.0485007i	0.0344159	+	0.999408i	$0.489043\pi$
$878$	−3.57784	+	4.26391i	−0.120746	+	0.143900i
$879$	−30.8718	+	25.9045i	−1.04128	+	0.873738i
$880$		0			0
$881$	12.2596	−	21.2343i	0.413037	−	0.715402i	−0.582183	−	0.813058i	$-0.697801\pi$
$881$	12.2596	−	21.2343i	0.413037	−	0.715402i	0.995220	+	0.0976562i	$0.0311346\pi$
$882$	−45.4053	+	26.2147i	−1.52887	+	0.882696i
$883$	−16.8217	−	46.2172i	−0.566095	−	1.55533i	−0.810549	−	0.585671i	$-0.800831\pi$
$883$	−16.8217	−	46.2172i	−0.566095	−	1.55533i	0.244454	−	0.969661i	$-0.421391\pi$
$884$	5.11226	−	1.86071i	0.171944	−	0.0625825i
$885$		0			0
$886$	1.74223	−	3.01764i	0.0585315	−	0.101380i
$887$	−21.3177	−	3.75889i	−0.715779	−	0.126211i	−0.196114	−	0.980581i	$-0.562832\pi$
$887$	−21.3177	−	3.75889i	−0.715779	−	0.126211i	−0.519665	+	0.854370i	$0.673943\pi$
$888$	−5.84820	−	6.96961i	−0.196253	−	0.233885i
$889$	−56.6539	−	47.5382i	−1.90011	−	1.59438i
$890$		0			0
$891$	30.4893	+	11.0972i	1.02143	+	0.371770i
$892$		−	3.66564i		−	0.122735i
$893$	−9.68955	+	1.23307i	−0.324249	+	0.0412632i
$894$	−57.3278			−1.91733
$895$		0			0
$896$	4.21612	+	23.9108i	0.140851	+	0.798803i
$897$	17.5951	−	20.9691i	0.587484	−	0.700137i
$898$	21.2953	+	25.3788i	0.710634	+	0.846900i
$899$	−2.84407	+	16.1295i	−0.0948550	+	0.537950i
$900$		0			0
$901$	0.348120	+	0.602962i	0.0115976	+	0.0200876i
$902$	−0.600720	−	1.65047i	−0.0200018	−	0.0549545i
$903$	27.6953	+	76.0922i	0.921642	+	2.53219i
$904$	25.9226	+	44.8993i	0.862173	+	1.49333i
$905$		0			0
$906$	7.45793	−	42.2960i	0.247773	−	1.40519i
$907$	−8.67336	−	10.3365i	−0.287994	−	0.343218i	0.602578	−	0.798060i	$-0.294140\pi$
$907$	−8.67336	−	10.3365i	−0.287994	−	0.343218i	−0.890572	+	0.454842i	$0.849696\pi$
$908$	−5.43119	+	6.47264i	−0.180240	+	0.214802i
$909$	−4.73745	−	26.8674i	−0.157131	−	0.891137i
$910$		0			0
$911$	16.2069			0.536958			0.268479	−	0.963286i	$-0.413479\pi$
$911$	16.2069			0.536958			0.268479	+	0.963286i	$0.413479\pi$
$912$	−38.8598	+	4.94522i	−1.28678	+	0.163752i
$913$			45.5428i			1.50725i
$914$	39.6614	+	14.4356i	1.31188	+	0.477486i
$915$		0			0
$916$	6.70614	+	5.62712i	0.221577	+	0.185925i
$917$	−12.9814	−	15.4706i	−0.428683	−	0.510884i
$918$	−30.6610	−	5.40636i	−1.01196	−	0.178437i
$919$	9.86867	−	17.0930i	0.325537	−	0.563847i	−0.656084	−	0.754688i	$-0.727788\pi$
$919$	9.86867	−	17.0930i	0.325537	−	0.563847i	0.981621	+	0.190841i	$0.0611215\pi$
$920$		0			0
$921$	−79.1782	+	28.8185i	−2.60901	+	0.949602i
$922$	13.0917	+	35.9691i	0.431152	+	1.18458i
$923$	8.39150	−	4.84483i	0.276210	−	0.159470i
$924$	7.90618	−	13.6939i	0.260094	−	0.450497i
$925$		0			0
$926$	−27.5157	+	23.0884i	−0.904223	+	0.758733i
$927$	41.9475	−	49.9911i	1.37774	−	1.64192i
$928$	12.0689	−	2.12807i	0.396181	−	0.0698573i
$929$	6.09658	+	2.21897i	0.200022	+	0.0728022i	0.440089	−	0.897954i	$-0.354947\pi$
$929$	6.09658	+	2.21897i	0.200022	+	0.0728022i	−0.240066	+	0.970756i	$0.577169\pi$
$930$		0			0
$931$	−28.5882	+	8.87816i	−0.936940	+	0.290970i
$932$			0.228528i			0.00748568i
$933$	25.5863	−	70.2978i	0.837658	−	2.30145i
$934$	2.44838	+	13.8855i	0.0801135	+	0.454346i
$935$		0			0
$936$	−68.5194	+	57.4946i	−2.23963	+	1.87927i
$937$	7.28885	+	1.28522i	0.238116	+	0.0419863i	0.291433	−	0.956591i	$-0.405868\pi$
$937$	7.28885	+	1.28522i	0.238116	+	0.0419863i	−0.0533164	+	0.998578i	$0.516979\pi$
$938$	−43.6887	−	25.2237i	−1.42649	−	0.823583i
$939$	−33.5454	−	58.1024i	−1.09471	−	1.89610i
$940$		0			0
$941$	−49.8981	+	18.1614i	−1.62663	+	0.592046i	−0.984629	−	0.174657i	$-0.944118\pi$
$941$	−49.8981	+	18.1614i	−1.62663	+	0.592046i	−0.642002	+	0.766703i	$0.721896\pi$
$942$	13.8220	−	7.98013i	0.450345	−	0.260007i
$943$	−0.676853	−	0.390781i	−0.0220414	−	0.0127256i
$944$	−2.68819	+	15.2455i	−0.0874932	+	0.496198i
$945$		0			0
$946$	23.3262	+	19.5730i	0.758402	+	0.636375i
$947$	15.0450	−	2.65283i	0.488896	−	0.0862055i	0.0762341	−	0.997090i	$-0.475710\pi$
$947$	15.0450	−	2.65283i	0.488896	−	0.0862055i	0.412661	+	0.910884i	$0.364599\pi$
$948$	5.21559	−	14.3297i	0.169395	−	0.465408i
$949$	−22.0891			−0.717041
$950$		0			0
$951$	−42.3994			−1.37490
$952$	−10.3649	+	28.4772i	−0.335927	+	0.922951i
$953$	16.6552	−	2.93675i	0.539514	−	0.0951308i	0.102750	−	0.994707i	$-0.467236\pi$
$953$	16.6552	−	2.93675i	0.539514	−	0.0951308i	0.436763	+	0.899576i	$0.356125\pi$
$954$	−1.52202	−	1.27713i	−0.0492772	−	0.0413485i
$955$		0			0
$956$	1.62099	−	9.19312i	0.0524267	−	0.297327i
$957$	45.9722	+	26.5421i	1.48607	+	0.857983i
$958$	−18.9307	+	10.9296i	−0.611622	+	0.353120i
$959$	−64.9528	+	23.6409i	−2.09744	+	0.763404i
$960$		0			0
$961$	10.6362	+	18.4224i	0.343103	+	0.594272i
$962$	5.23278	+	3.02115i	0.168712	+	0.0974057i
$963$	8.24613	+	1.45401i	0.265728	+	0.0468550i
$964$	6.99333	−	5.86810i	0.225240	−	0.188999i
$965$		0			0
$966$	4.59573	+	26.0637i	0.147865	+	0.838585i
$967$	−4.96803	+	13.6496i	−0.159761	+	0.438940i	−0.993585	−	0.113091i	$-0.963925\pi$
$967$	−4.96803	+	13.6496i	−0.159761	+	0.438940i	0.833823	+	0.552031i	$0.186147\pi$
$968$		−	0.796706i		−	0.0256071i
$969$	−32.3941	−	13.5824i	−1.04065	−	0.436330i
$970$		0			0
$971$	−28.7590	−	10.4674i	−0.922920	−	0.335915i	−0.163520	−	0.986540i	$-0.552285\pi$
$971$	−28.7590	−	10.4674i	−0.922920	−	0.335915i	−0.759400	+	0.650625i	$0.774507\pi$
$972$	−0.557509	+	0.0983038i	−0.0178821	+	0.00315310i
$973$	25.1641	−	29.9894i	0.806724	−	0.961417i
$974$	−14.7777	+	12.4000i	−0.473508	+	0.397321i
$975$		0			0
$976$	1.14705	−	1.98675i	0.0367161	−	0.0635942i
$977$	38.1064	−	22.0007i	1.21913	−	0.703865i	0.254399	−	0.967099i	$-0.418122\pi$
$977$	38.1064	−	22.0007i	1.21913	−	0.703865i	0.964732	+	0.263234i	$0.0847892\pi$
$978$	18.0075	+	49.4753i	0.575818	+	1.58205i
$979$	24.1854	−	8.80277i	0.772970	−	0.281338i
$980$		0			0
$981$	−28.8462	+	49.9631i	−0.920988	+	1.59520i
$982$	−10.3411	−	1.82342i	−0.329999	−	0.0581878i
$983$	22.7302	+	27.0888i	0.724982	+	0.864000i	0.995105	−	0.0988259i	$-0.0315087\pi$
$983$	22.7302	+	27.0888i	0.724982	+	0.864000i	−0.270123	+	0.962826i	$0.587064\pi$
$984$	2.92270	+	2.45244i	0.0931722	+	0.0781808i
$985$		0			0
$986$	−16.5936	−	6.03957i	−0.528448	−	0.192339i
$987$		−	25.1366i		−	0.800108i
$988$	−7.88025	+	4.05900i	−0.250704	+	0.129134i
$989$	13.5498			0.430860
$990$		0			0
$991$	5.58302	+	31.6629i	0.177350	+	1.00580i	0.935396	+	0.353602i	$0.115043\pi$
$991$	5.58302	+	31.6629i	0.177350	+	1.00580i	−0.758045	+	0.652202i	$0.773845\pi$
$992$	−4.67863	+	5.57577i	−0.148547	+	0.177031i
$993$	−10.2340	−	12.1964i	−0.324765	−	0.387040i
$994$	−1.62682	+	9.22613i	−0.0515995	+	0.292635i
$995$		0			0
$996$	−8.58568	−	14.8708i	−0.272048	−	0.471200i
$997$	−2.84338	−	7.81213i	−0.0900509	−	0.247413i	0.886489	−	0.462750i	$-0.153137\pi$
$997$	−2.84338	−	7.81213i	−0.0900509	−	0.247413i	−0.976540	+	0.215337i	$0.930915\pi$
$998$	−0.116433	−	0.319896i	−0.00368561	−	0.0101261i
$999$	4.59658	+	7.96151i	0.145429	+	0.251891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.u.b.99.2		36
5.2	odd	4		95.2.k.a.61.2	✓	18
5.3	odd	4		475.2.l.c.251.2		18
5.4	even	2	inner	475.2.u.b.99.5		36
15.2	even	4		855.2.bs.c.631.2		18
19.5	even	9	inner	475.2.u.b.24.5		36
95.24	even	18	inner	475.2.u.b.24.2		36
95.28	odd	36		9025.2.a.cc.1.4		9
95.43	odd	36		475.2.l.c.176.2		18
95.47	odd	36		1805.2.a.v.1.6		9
95.48	even	36		9025.2.a.cf.1.6		9
95.62	odd	36		95.2.k.a.81.2	yes	18
95.67	even	36		1805.2.a.s.1.4		9
285.62	even	36		855.2.bs.c.271.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.61.2	✓	18	5.2	odd	4
95.2.k.a.81.2	yes	18	95.62	odd	36
475.2.l.c.176.2		18	95.43	odd	36
475.2.l.c.251.2		18	5.3	odd	4
475.2.u.b.24.2		36	95.24	even	18	inner
475.2.u.b.24.5		36	19.5	even	9	inner
475.2.u.b.99.2		36	1.1	even	1	trivial
475.2.u.b.99.5		36	5.4	even	2	inner
855.2.bs.c.271.2		18	285.62	even	36
855.2.bs.c.631.2		18	15.2	even	4
1805.2.a.s.1.4		9	95.67	even	36
1805.2.a.v.1.6		9	95.47	odd	36
9025.2.a.cc.1.4		9	95.28	odd	36
9025.2.a.cf.1.6		9	95.48	even	36

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.429906 + 1.18116i) q^{2} +(-2.96649 + 0.523072i) q^{3} +(0.321776 + 0.270002i) q^{4} +(0.657481 - 3.72876i) q^{6} +(3.22501 + 1.86196i) q^{7} +(-2.63437 + 1.52095i) q^{8} +(5.70738 - 2.07732i) q^{9} +O(q^{10})\)	\(q+(-0.429906 + 1.18116i) q^{2} +(-2.96649 + 0.523072i) q^{3} +(0.321776 + 0.270002i) q^{4} +(0.657481 - 3.72876i) q^{6} +(3.22501 + 1.86196i) q^{7} +(-2.63437 + 1.52095i) q^{8} +(5.70738 - 2.07732i) q^{9} +(1.67794 + 2.90627i) q^{11} +(-1.09578 - 0.632646i) q^{12} +(4.76776 + 0.840684i) q^{13} +(-3.58572 + 3.00877i) q^{14} +(-0.518073 - 2.93814i) q^{16} +(0.914991 - 2.51392i) q^{17} +7.63436i q^{18} +(-0.961823 + 4.25146i) q^{19} +(-10.5409 - 3.83657i) q^{21} +(-4.15412 + 0.732484i) q^{22} +(-1.20653 + 1.43789i) q^{23} +(7.01926 - 5.88986i) q^{24} +(-3.04267 + 5.27006i) q^{26} +(-8.01823 + 4.62933i) q^{27} +(0.534997 + 1.46989i) q^{28} +(-4.93461 + 1.79605i) q^{29} +(1.55945 - 2.70105i) q^{31} +(-2.29826 - 0.405246i) q^{32} +(-6.49778 - 7.74375i) q^{33} +(2.57597 + 2.16150i) q^{34} +(2.39738 + 0.872573i) q^{36} -0.992927i q^{37} +(-4.60815 - 2.96379i) q^{38} -14.5832 q^{39} +(0.0723041 + 0.410057i) q^{41} +(9.06319 - 10.8011i) q^{42} +(-4.64013 - 5.52990i) q^{43} +(-0.244780 + 1.38822i) q^{44} +(-1.17968 - 2.04326i) q^{46} +(0.766421 + 2.10572i) q^{47} +(3.07372 + 8.44496i) q^{48} +(3.43378 + 5.94749i) q^{49} +(-1.39935 + 7.93612i) q^{51} +(1.30716 + 1.55782i) q^{52} +(-0.167287 + 0.199365i) q^{53} +(-2.02088 - 11.4610i) q^{54} -11.3278 q^{56} +(0.629417 - 13.1150i) q^{57} -6.60069i q^{58} +(-4.87590 - 1.77468i) q^{59} +(0.589041 + 0.494264i) q^{61} +(2.51995 + 3.00316i) q^{62} +(22.2742 + 3.92754i) q^{63} +(4.45016 - 7.70790i) q^{64} +(11.9400 - 4.34581i) q^{66} +(3.68611 + 10.1275i) q^{67} +(0.973185 - 0.561868i) q^{68} +(2.82704 - 4.89658i) q^{69} +(1.53320 - 1.28651i) q^{71} +(-11.8758 + 14.1531i) q^{72} +(-4.49331 + 0.792291i) q^{73} +(1.17280 + 0.426865i) q^{74} +(-1.45739 + 1.10832i) q^{76} +12.4970i q^{77} +(6.26942 - 17.2251i) q^{78} +(2.09282 + 11.8690i) q^{79} +(7.40643 - 6.21473i) q^{81} +(-0.515426 - 0.0908835i) q^{82} +(11.7529 + 6.78553i) q^{83} +(-2.35592 - 4.08058i) q^{84} +(8.52650 - 3.10339i) q^{86} +(13.6990 - 7.90913i) q^{87} +(-8.84062 - 5.10413i) q^{88} +(1.33178 - 7.55289i) q^{89} +(13.8107 + 11.5886i) q^{91} +(-0.776465 + 0.136912i) q^{92} +(-3.21326 + 8.82836i) q^{93} -2.81668 q^{94} +7.02975 q^{96} +(2.47244 - 6.79298i) q^{97} +(-8.50112 + 1.49898i) q^{98} +(15.6139 + 13.1016i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{4} - 12 q^{6} - 6 q^{9}+O(q^{10}) \) 36 * q + 6 * q^4 - 12 * q^6 - 6 * q^9	\( 36 q + 6 q^{4} - 12 q^{6} - 6 q^{9} + 24 q^{14} - 6 q^{16} - 42 q^{21} + 30 q^{24} + 6 q^{26} - 30 q^{29} - 36 q^{31} + 24 q^{34} + 150 q^{36} - 72 q^{39} - 60 q^{41} - 84 q^{44} + 18 q^{46} - 18 q^{49} - 90 q^{51} + 132 q^{54} - 36 q^{59} - 60 q^{61} - 72 q^{64} + 78 q^{66} - 30 q^{69} - 24 q^{71} + 30 q^{74} - 66 q^{76} + 102 q^{79} + 54 q^{81} - 96 q^{84} + 126 q^{86} + 108 q^{89} + 60 q^{91} - 60 q^{94} - 132 q^{96} + 186 q^{99}+O(q^{100}) \) 36 * q + 6 * q^4 - 12 * q^6 - 6 * q^9 + 24 * q^14 - 6 * q^16 - 42 * q^21 + 30 * q^24 + 6 * q^26 - 30 * q^29 - 36 * q^31 + 24 * q^34 + 150 * q^36 - 72 * q^39 - 60 * q^41 - 84 * q^44 + 18 * q^46 - 18 * q^49 - 90 * q^51 + 132 * q^54 - 36 * q^59 - 60 * q^61 - 72 * q^64 + 78 * q^66 - 30 * q^69 - 24 * q^71 + 30 * q^74 - 66 * q^76 + 102 * q^79 + 54 * q^81 - 96 * q^84 + 126 * q^86 + 108 * q^89 + 60 * q^91 - 60 * q^94 - 132 * q^96 + 186 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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