LMFDB - Embedded newform 135.3.h.a.44.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,3,Mod(44,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.44"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{18} - 19 x^{16} + 66 x^{14} + 109 x^{12} - 813 x^{10} + 981 x^{8} + 5346 x^{6} + \cdots + 59049 $ x^20 - 3x^18 - 19x^16 + 66x^14 + 109x^12 - 813x^10 + 981x^8 + 5346x^6 - 13851x^4 - 19683*x^2 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{12} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			44.10
Root			$-1.44078 - 0.961330i$ of defining polynomial
Character	$\chi$	$=$	135.44
Dual form			135.3.h.a.89.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.84364 + 3.19328i) q^{2} +(-4.79800 + 8.31039i) q^{4} +(4.90060 + 0.992036i) q^{5} +(-2.22343 + 1.28370i) q^{7} -20.6340 q^{8} +(5.86709 + 17.4779i) q^{10} +(8.51311 - 4.91505i) q^{11} +(-10.4471 - 6.03166i) q^{13} +(-8.19840 - 4.73335i) q^{14} +(-18.8497 - 32.6486i) q^{16} +4.28451 q^{17} +7.16698 q^{19} +(-31.7573 + 35.9661i) q^{20} +(31.3902 + 18.1231i) q^{22} +(-0.255270 + 0.442140i) q^{23} +(23.0317 + 9.72314i) q^{25} -44.4808i q^{26} -24.6367i q^{28} +(26.4589 - 15.2761i) q^{29} +(9.61361 - 16.6513i) q^{31} +(28.2359 - 48.9060i) q^{32} +(7.89910 + 13.6816i) q^{34} +(-12.1696 + 4.08516i) q^{35} +1.31851i q^{37} +(13.2133 + 22.8862i) q^{38} +(-101.119 - 20.4697i) q^{40} +(29.9735 + 17.3052i) q^{41} +(-44.9872 + 25.9734i) q^{43} +94.3297i q^{44} -1.88250 q^{46} +(-25.4656 - 44.1078i) q^{47} +(-21.2042 + 36.7268i) q^{49} +(11.4135 + 91.4726i) q^{50} +(100.251 - 57.8799i) q^{52} +86.6349 q^{53} +(46.5953 - 15.6414i) q^{55} +(45.8783 - 26.4879i) q^{56} +(97.5613 + 56.3270i) q^{58} +(-91.7656 - 52.9809i) q^{59} +(-15.6600 - 27.1239i) q^{61} +70.8961 q^{62} +57.4297 q^{64} +(-45.2136 - 39.9227i) q^{65} +(-67.5968 - 39.0271i) q^{67} +(-20.5571 + 35.6060i) q^{68} +(-35.4814 - 31.3293i) q^{70} +72.6762i q^{71} -30.3097i q^{73} +(-4.21037 + 2.43086i) q^{74} +(-34.3872 + 59.5604i) q^{76} +(-12.6189 + 21.8565i) q^{77} +(-57.6398 - 99.8350i) q^{79} +(-59.9861 - 178.697i) q^{80} +127.618i q^{82} +(-30.0069 - 51.9734i) q^{83} +(20.9967 + 4.25039i) q^{85} +(-165.880 - 95.7710i) q^{86} +(-175.660 + 101.417i) q^{88} -71.2992i q^{89} +30.9713 q^{91} +(-2.44957 - 4.24278i) q^{92} +(93.8989 - 162.638i) q^{94} +(35.1225 + 7.10991i) q^{95} +(110.820 - 63.9819i) q^{97} -156.372 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 18 q^{4} + 12 q^{5} + 4 q^{10} + 24 q^{11} - 30 q^{14} - 26 q^{16} - 8 q^{19} - 144 q^{20} + 2 q^{25} + 114 q^{29} + 28 q^{31} - 4 q^{34} - 34 q^{40} - 102 q^{41} + 116 q^{46} - 40 q^{49} + 408 q^{50}+ \cdots + 762 q^{95}+O(q^{100}) $ 20 * q - 18 * q^4 + 12 * q^5 + 4 * q^10 + 24 * q^11 - 30 * q^14 - 26 * q^16 - 8 * q^19 - 144 * q^20 + 2 * q^25 + 114 * q^29 + 28 * q^31 - 4 * q^34 - 34 * q^40 - 102 * q^41 + 116 * q^46 - 40 * q^49 + 408 * q^50 + 36 * q^55 + 618 * q^56 - 120 * q^59 - 50 * q^61 + 140 * q^64 - 492 * q^65 - 54 * q^70 - 504 * q^74 - 96 * q^76 - 128 * q^79 - 74 * q^85 - 1488 * q^86 - 288 * q^91 + 218 * q^94 + 762 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.84364	+	3.19328i	0.921819	+	1.59664i	0.796599	+	0.604509i	$0.206631\pi$
$2$	1.84364	+	3.19328i	0.921819	+	1.59664i	0.125221	+	0.992129i	$0.460036\pi$
$3$		0			0
$3$		0			0
$4$	−4.79800	+	8.31039i	−1.19950	+	2.07760i
$5$	4.90060	+	0.992036i	0.980120	+	0.198407i
$5$	4.90060	+	0.992036i	0.980120	+	0.198407i
$6$		0			0
$7$	−2.22343	+	1.28370i	−0.317633	+	0.183385i	−0.650337	−	0.759646i	$-0.725372\pi$
$7$	−2.22343	+	1.28370i	−0.317633	+	0.183385i	0.332704	+	0.943031i	$0.392039\pi$
$8$	−20.6340			−2.57925
$9$		0			0
$10$	5.86709	+	17.4779i	0.586709	+	1.74779i
$11$	8.51311	−	4.91505i	0.773919	−	0.446823i	−0.0603516	−	0.998177i	$-0.519222\pi$
$11$	8.51311	−	4.91505i	0.773919	−	0.446823i	0.834271	+	0.551355i	$0.185889\pi$
$12$		0			0
$13$	−10.4471	−	6.03166i	−0.803626	−	0.463974i	0.0411114	−	0.999155i	$-0.486910\pi$
$13$	−10.4471	−	6.03166i	−0.803626	−	0.463974i	−0.844738	+	0.535181i	$0.820243\pi$
$14$	−8.19840	−	4.73335i	−0.585600	−	0.338096i
$15$		0			0
$16$	−18.8497	−	32.6486i	−1.17810	−	2.04054i
$17$	4.28451			0.252030			0.126015	−	0.992028i	$-0.459781\pi$
$17$	4.28451			0.252030			0.126015	+	0.992028i	$0.459781\pi$
$18$		0			0
$19$	7.16698			0.377210			0.188605	−	0.982053i	$-0.439603\pi$
$19$	7.16698			0.377210			0.188605	+	0.982053i	$0.439603\pi$
$20$	−31.7573	+	35.9661i	−1.58786	+	1.79830i
$21$		0			0
$22$	31.3902	+	18.1231i	1.42683	+	0.823779i
$23$	−0.255270	+	0.442140i	−0.0110987	+	0.0192235i	−0.871521	−	0.490357i	$-0.836866\pi$
$23$	−0.255270	+	0.442140i	−0.0110987	+	0.0192235i	0.860423	+	0.509581i	$0.170200\pi$
$24$		0			0
$25$	23.0317	+	9.72314i	0.921269	+	0.388926i
$26$		−	44.4808i		−	1.71080i
$27$		0			0
$28$		−	24.6367i		−	0.879884i
$29$	26.4589	−	15.2761i	0.912376	−	0.526760i	0.0311810	−	0.999514i	$-0.490073\pi$
$29$	26.4589	−	15.2761i	0.912376	−	0.526760i	0.881195	+	0.472753i	$0.156740\pi$
$30$		0			0
$31$	9.61361	−	16.6513i	0.310116	−	0.537137i	−0.668271	−	0.743918i	$-0.732965\pi$
$31$	9.61361	−	16.6513i	0.310116	−	0.537137i	0.978387	+	0.206781i	$0.0662986\pi$
$32$	28.2359	−	48.9060i	0.882372	−	1.52831i
$33$		0			0
$34$	7.89910	+	13.6816i	0.232326	+	0.402401i
$35$	−12.1696	+	4.08516i	−0.347703	+	0.116719i
$36$		0			0
$37$			1.31851i			0.0356355i	0.999841	+	0.0178177i	$0.00567186\pi$
$37$			1.31851i			0.0356355i	−0.999841	+	0.0178177i	$0.994328\pi$
$38$	13.2133	+	22.8862i	0.347719	+	0.602267i
$39$		0			0
$40$	−101.119	−	20.4697i	−2.52798	−	0.511743i
$41$	29.9735	+	17.3052i	0.731061	+	0.422078i	0.818810	−	0.574064i	$-0.194634\pi$
$41$	29.9735	+	17.3052i	0.731061	+	0.422078i	−0.0877493	+	0.996143i	$0.527967\pi$
$42$		0			0
$43$	−44.9872	+	25.9734i	−1.04621	+	0.604032i	−0.921587	−	0.388172i	$-0.873107\pi$
$43$	−44.9872	+	25.9734i	−1.04621	+	0.604032i	−0.124627	+	0.992204i	$0.539773\pi$
$44$			94.3297i			2.14386i
$45$		0			0
$46$	−1.88250			−0.0409239
$47$	−25.4656	−	44.1078i	−0.541822	−	0.938463i	−0.998800	−	0.0489851i	$-0.984401\pi$
$47$	−25.4656	−	44.1078i	−0.541822	−	0.938463i	0.456977	−	0.889478i	$-0.348932\pi$
$48$		0			0
$49$	−21.2042	+	36.7268i	−0.432740	+	0.749527i
$50$	11.4135	+	91.4726i	0.228270	+	1.82945i
$51$		0			0
$52$	100.251	−	57.8799i	1.92790	−	1.11307i
$53$	86.6349			1.63462			0.817311	−	0.576197i	$-0.195464\pi$
$53$	86.6349			1.63462			0.817311	+	0.576197i	$0.195464\pi$
$54$		0			0
$55$	46.5953	−	15.6414i	0.847186	−	0.284388i
$56$	45.8783	−	26.4879i	0.819255	−	0.472997i
$57$		0			0
$58$	97.5613	+	56.3270i	1.68209	+	0.971156i
$59$	−91.7656	−	52.9809i	−1.55535	−	0.897982i	−0.997691	−	0.0679111i	$-0.978367\pi$
$59$	−91.7656	−	52.9809i	−1.55535	−	0.897982i	−0.557658	−	0.830071i	$-0.688300\pi$
$60$		0			0
$61$	−15.6600	−	27.1239i	−0.256721	−	0.444655i	0.708640	−	0.705570i	$-0.249309\pi$
$61$	−15.6600	−	27.1239i	−0.256721	−	0.444655i	−0.965362	+	0.260915i	$0.915976\pi$
$62$	70.8961			1.14348
$63$		0			0
$64$	57.4297			0.897339
$65$	−45.2136	−	39.9227i	−0.695594	−	0.614195i
$66$		0			0
$67$	−67.5968	−	39.0271i	−1.00891	−	0.582493i	−0.0980363	−	0.995183i	$-0.531256\pi$
$67$	−67.5968	−	39.0271i	−1.00891	−	0.582493i	−0.910872	+	0.412689i	$0.864589\pi$
$68$	−20.5571	+	35.6060i	−0.302311	+	0.523617i
$69$		0			0
$70$	−35.4814	−	31.3293i	−0.506877	−	0.447562i
$71$			72.6762i			1.02361i	0.859102	+	0.511804i	$0.171023\pi$
$71$			72.6762i			1.02361i	−0.859102	+	0.511804i	$0.828977\pi$
$72$		0			0
$73$		−	30.3097i		−	0.415201i	−0.978214	−	0.207601i	$-0.933435\pi$
$73$		−	30.3097i		−	0.415201i	0.978214	−	0.207601i	$-0.0665654\pi$
$74$	−4.21037	+	2.43086i	−0.0568969	+	0.0328494i
$75$		0			0
$76$	−34.3872	+	59.5604i	−0.452463	+	0.783690i
$77$	−12.6189	+	21.8565i	−0.163881	+	0.283851i
$78$		0			0
$79$	−57.6398	−	99.8350i	−0.729617	−	1.26373i	−0.957045	−	0.289940i	$-0.906365\pi$
$79$	−57.6398	−	99.8350i	−0.729617	−	1.26373i	0.227428	−	0.973795i	$-0.426969\pi$
$80$	−59.9861	−	178.697i	−0.749826	−	2.23371i
$81$		0			0
$82$			127.618i			1.55632i
$83$	−30.0069	−	51.9734i	−0.361529	−	0.626186i	0.626684	−	0.779274i	$-0.284412\pi$
$83$	−30.0069	−	51.9734i	−0.361529	−	0.626186i	−0.988213	+	0.153087i	$0.951078\pi$
$84$		0			0
$85$	20.9967	+	4.25039i	0.247020	+	0.0500046i
$86$	−165.880	−	95.7710i	−1.92884	−	1.11362i
$87$		0			0
$88$	−175.660	+	101.417i	−1.99613	+	1.15247i
$89$		−	71.2992i		−	0.801115i	−0.916272	−	0.400558i	$-0.868816\pi$
$89$		−	71.2992i		−	0.801115i	0.916272	−	0.400558i	$-0.131184\pi$
$90$		0			0
$91$	30.9713			0.340344
$92$	−2.44957	−	4.24278i	−0.0266257	−	0.0461171i
$93$		0			0
$94$	93.8989	−	162.638i	0.998924	−	1.73019i
$95$	35.1225	+	7.10991i	0.369711	+	0.0748412i
$96$		0			0
$97$	110.820	−	63.9819i	1.14247	−	0.659607i	0.195431	−	0.980717i	$-0.437389\pi$
$97$	110.820	−	63.9819i	1.14247	−	0.659607i	0.947042	+	0.321111i	$0.104056\pi$
$98$	−156.372			−1.59563
$99$		0			0
$100$	−191.309	+	144.751i	−1.91309	+	1.44751i
$101$	−74.5445	+	43.0383i	−0.738065	+	0.426122i	−0.821365	−	0.570403i	$-0.806787\pi$
$101$	−74.5445	+	43.0383i	−0.738065	+	0.426122i	0.0833005	+	0.996524i	$0.473454\pi$
$102$		0			0
$103$	35.4060	+	20.4416i	0.343747	+	0.198463i	0.661928	−	0.749568i	$-0.269739\pi$
$103$	35.4060	+	20.4416i	0.343747	+	0.198463i	−0.318181	+	0.948030i	$0.603072\pi$
$104$	215.567	+	124.457i	2.07276	+	1.19671i
$105$		0			0
$106$	159.723	+	276.649i	1.50683	+	2.60990i
$107$	1.66026			0.0155165			0.00775823	−	0.999970i	$-0.497530\pi$
$107$	1.66026			0.0155165			0.00775823	+	0.999970i	$0.497530\pi$
$108$		0			0
$109$	−148.641			−1.36368			−0.681839	−	0.731502i	$-0.738820\pi$
$109$	−148.641			−1.36368			−0.681839	+	0.731502i	$0.738820\pi$
$110$	135.852	+	119.954i	1.23502	+	1.09050i
$111$		0			0
$112$	83.8218	+	48.3946i	0.748409	+	0.432094i
$113$	−65.7284	+	113.845i	−0.581667	+	1.00748i	0.413615	+	0.910452i	$0.364266\pi$
$113$	−65.7284	+	113.845i	−0.581667	+	1.00748i	−0.995282	+	0.0970249i	$0.969067\pi$
$114$		0			0
$115$	−1.68959	+	1.91351i	−0.0146921	+	0.0166392i
$116$			293.178i			2.52740i
$117$		0			0
$118$		−	390.711i		−	3.31111i
$119$	−9.52631	+	5.50002i	−0.0800531	+	0.0462187i
$120$		0			0
$121$	−12.1846	+	21.1044i	−0.100699	+	0.174416i
$122$	57.7428	−	100.013i	0.473301	−	0.819782i
$123$		0			0
$124$	92.2523	+	159.786i	0.743970	+	1.28859i
$125$	103.224	+	70.4975i	0.825788	+	0.563980i
$126$		0			0
$127$			101.150i			0.796460i	0.917286	+	0.398230i	$0.130375\pi$
$127$			101.150i			0.796460i	−0.917286	+	0.398230i	$0.869625\pi$
$128$	−7.06394	−	12.2351i	−0.0551870	−	0.0955867i
$129$		0			0
$130$	44.1266	−	217.982i	0.339435	−	1.67679i
$131$	74.3023	+	42.8985i	0.567193	+	0.327469i	0.756028	−	0.654540i	$-0.227138\pi$
$131$	74.3023	+	42.8985i	0.567193	+	0.327469i	−0.188834	+	0.982009i	$0.560471\pi$
$132$		0			0
$133$	−15.9353	+	9.20024i	−0.119814	+	0.0691747i
$134$		−	287.807i		−	2.14781i
$135$		0			0
$136$	−88.4068			−0.650050
$137$	34.8631	+	60.3847i	0.254475	+	0.440764i	0.964753	−	0.263158i	$-0.0847639\pi$
$137$	34.8631	+	60.3847i	0.254475	+	0.440764i	−0.710278	+	0.703922i	$0.751431\pi$
$138$		0			0
$139$	−69.4587	+	120.306i	−0.499703	+	0.865511i	−1.00000		0.000342926i	$-0.999891\pi$
$139$	−69.4587	+	120.306i	−0.499703	+	0.865511i	0.500297	+	0.865854i	$0.333224\pi$
$140$	24.4405	−	120.735i	0.174575	−	0.862391i
$141$		0			0
$142$	−232.075	+	133.989i	−1.63433	+	0.943582i
$143$	−118.584			−0.829256
$144$		0			0
$145$	144.819	−	48.6136i	0.998751	−	0.335266i
$146$	96.7872	−	55.8801i	0.662926	−	0.382740i
$147$		0			0
$148$	−10.9573	−	6.32622i	−0.0740361	−	0.0427448i
$149$	−41.3586	−	23.8784i	−0.277574	−	0.160258i	0.354750	−	0.934961i	$-0.384566\pi$
$149$	−41.3586	−	23.8784i	−0.277574	−	0.160258i	−0.632325	+	0.774703i	$0.717899\pi$
$150$		0			0
$151$	−27.7457	−	48.0569i	−0.183746	−	0.318258i	0.759407	−	0.650616i	$-0.225489\pi$
$151$	−27.7457	−	48.0569i	−0.183746	−	0.318258i	−0.943153	+	0.332358i	$0.892156\pi$
$152$	−147.884			−0.972920
$153$		0			0
$154$	−93.0585			−0.604276
$155$	63.6311	−	72.0641i	0.410523	−	0.464929i
$156$		0			0
$157$	−9.58875	−	5.53607i	−0.0610749	−	0.0352616i	0.469152	−	0.883118i	$-0.344560\pi$
$157$	−9.58875	−	5.53607i	−0.0610749	−	0.0352616i	−0.530226	+	0.847856i	$0.677893\pi$
$158$	212.534	−	368.119i	1.34515	−	2.32987i
$159$		0			0
$160$	186.889	−	211.658i	1.16806	−	1.32286i
$161$		−	1.31076i		−	0.00814134i
$162$		0			0
$163$			216.230i			1.32656i	0.748370	+	0.663282i	$0.230837\pi$
$163$			216.230i			1.32656i	−0.748370	+	0.663282i	$0.769163\pi$
$164$	−287.626	+	166.061i	−1.75382	+	1.01257i
$165$		0			0
$166$	110.644	−	191.640i	0.666528	−	1.15446i
$167$	30.9734	−	53.6475i	0.185469	−	0.321242i	−0.758265	−	0.651946i	$-0.773953\pi$
$167$	30.9734	−	53.6475i	0.185469	−	0.321242i	0.943735	+	0.330704i	$0.107286\pi$
$168$		0			0
$169$	−11.7382	−	20.3311i	−0.0694567	−	0.120302i
$170$	25.1376	+	74.8844i	0.147868	+	0.440496i
$171$		0			0
$172$		−	498.481i		−	2.89815i
$173$	166.735	+	288.794i	0.963788	+	1.66933i	0.712837	+	0.701330i	$0.247410\pi$
$173$	166.735	+	288.794i	0.963788	+	1.66933i	0.250951	+	0.968000i	$0.419257\pi$
$174$		0			0
$175$	−63.6910	+	7.94705i	−0.363948	+	0.0454117i
$176$	−320.939	−	185.294i	−1.82352	−	1.05281i
$177$		0			0
$178$	227.678	−	131.450i	1.27909	−	0.738483i
$179$		−	193.521i		−	1.08112i	−0.841304	−	0.540562i	$-0.818212\pi$
$179$		−	193.521i		−	1.08112i	0.841304	−	0.540562i	$-0.181788\pi$
$180$		0			0
$181$	243.865			1.34732			0.673661	−	0.739041i	$-0.264721\pi$
$181$	243.865			1.34732			0.673661	+	0.739041i	$0.264721\pi$
$182$	57.0999	+	98.8999i	0.313736	+	0.543406i
$183$		0			0
$184$	5.26724	−	9.12313i	0.0286263	−	0.0495822i
$185$	−1.30801	+	6.46150i	−0.00707033	+	0.0349270i
$186$		0			0
$187$	36.4746	−	21.0586i	0.195051	−	0.112613i
$188$	488.737			2.59966
$189$		0			0
$190$	42.0493	+	125.264i	0.221312	+	0.659284i
$191$	122.599	−	70.7825i	0.641879	−	0.370589i	−0.143459	−	0.989656i	$-0.545823\pi$
$191$	122.599	−	70.7825i	0.641879	−	0.370589i	0.785338	+	0.619067i	$0.212489\pi$
$192$		0			0
$193$	191.757	+	110.711i	0.993561	+	0.573633i	0.906337	−	0.422556i	$-0.138867\pi$
$193$	191.757	+	110.711i	0.993561	+	0.573633i	0.0872244	+	0.996189i	$0.472200\pi$
$194$	408.623	+	235.919i	2.10631	+	1.21608i
$195$		0			0
$196$	−203.476	−	352.431i	−1.03814	−	1.79812i
$197$	−28.4424			−0.144378			−0.0721889	−	0.997391i	$-0.522998\pi$
$197$	−28.4424			−0.144378			−0.0721889	+	0.997391i	$0.522998\pi$
$198$		0			0
$199$	153.875			0.773244			0.386622	−	0.922238i	$-0.373642\pi$
$199$	153.875			0.773244			0.386622	+	0.922238i	$0.373642\pi$
$200$	−475.237	−	200.628i	−2.37619	−	1.00314i
$201$		0			0
$202$	−274.866	−	158.694i	−1.36072	−	0.785615i
$203$	−39.2197	+	67.9304i	−0.193200	+	0.334633i
$204$		0			0
$205$	129.721	+	114.541i	0.632784	+	0.558735i
$206$			150.748i			0.731786i
$207$		0			0
$208$			454.779i			2.18644i
$209$	61.0133	−	35.2261i	0.291930	−	0.168546i
$210$		0			0
$211$	−90.0891	+	156.039i	−0.426962	+	0.739521i	−0.996601	−	0.0823744i	$-0.973750\pi$
$211$	−90.0891	+	156.039i	−0.426962	+	0.739521i	0.569639	+	0.821895i	$0.307083\pi$
$212$	−415.675	+	719.970i	−1.96073	+	3.39608i
$213$		0			0
$214$	3.06092	+	5.30167i	0.0143034	+	0.0247742i
$215$	−246.231	+	82.6561i	−1.14526	+	0.384447i
$216$		0			0
$217$			49.3638i			0.227483i
$218$	−274.040	−	474.651i	−1.25706	−	2.17730i
$219$		0			0
$220$	−93.5785	+	462.272i	−0.425357	+	2.10124i
$221$	−44.7609	−	25.8427i	−0.202538	−	0.116935i
$222$		0			0
$223$	−186.544	+	107.701i	−0.836521	+	0.482966i	−0.856080	−	0.516843i	$-0.827107\pi$
$223$	−186.544	+	107.701i	−0.836521	+	0.482966i	0.0195592	+	0.999809i	$0.493774\pi$
$224$			144.985i			0.647256i
$225$		0			0
$226$	−484.717			−2.14477
$227$	−25.2080	−	43.6615i	−0.111048	−	0.192341i	0.805145	−	0.593078i	$-0.202088\pi$
$227$	−25.2080	−	43.6615i	−0.111048	−	0.192341i	−0.916193	+	0.400737i	$0.868754\pi$
$228$		0			0
$229$	3.08352	−	5.34081i	0.0134652	−	0.0233223i	−0.859214	−	0.511616i	$-0.829047\pi$
$229$	3.08352	−	5.34081i	0.0134652	−	0.0233223i	0.872679	+	0.488294i	$0.162380\pi$
$230$	−9.22537	−	1.86751i	−0.0401103	−	0.00811960i
$231$		0			0
$232$	−545.954	+	315.207i	−2.35325	+	1.35865i
$233$	52.5336			0.225466			0.112733	−	0.993625i	$-0.464040\pi$
$233$	52.5336			0.225466			0.112733	+	0.993625i	$0.464040\pi$
$234$		0			0
$235$	−81.0403	−	241.417i	−0.344853	−	1.02731i
$236$	880.584	−	508.405i	3.73129	−	2.15426i
$237$		0			0
$238$	−35.1262	−	20.2801i	−0.147589	−	0.0852105i
$239$	−84.5102	−	48.7920i	−0.353599	−	0.204151i	0.312670	−	0.949862i	$-0.398777\pi$
$239$	−84.5102	−	48.7920i	−0.353599	−	0.204151i	−0.666269	+	0.745711i	$0.732110\pi$
$240$		0			0
$241$	71.3647	+	123.607i	0.296119	+	0.512893i	0.975245	−	0.221129i	$-0.0709742\pi$
$241$	71.3647	+	123.607i	0.296119	+	0.512893i	−0.679126	+	0.734022i	$0.737641\pi$
$242$	−89.8560			−0.371306
$243$		0			0
$244$	300.547			1.23175
$245$	−140.348	+	158.948i	−0.572848	+	0.648767i
$246$		0			0
$247$	−74.8745	−	43.2288i	−0.303136	−	0.175015i
$248$	−198.367	+	343.583i	−0.799869	+	1.38541i
$249$		0			0
$250$	−34.8112	+	459.593i	−0.139245	+	1.83837i
$251$		−	254.631i		−	1.01447i	−0.861809	−	0.507233i	$-0.830668\pi$
$251$		−	254.631i		−	1.01447i	0.861809	−	0.507233i	$-0.169332\pi$
$252$		0			0
$253$			5.01865i			0.0198366i
$254$	−323.001	+	186.485i	−1.27166	+	0.734192i
$255$		0			0
$256$	140.906	−	244.057i	0.550415	−	0.953346i
$257$	71.3682	−	123.613i	0.277697	−	0.480986i	−0.693115	−	0.720827i	$-0.743762\pi$
$257$	71.3682	−	123.613i	0.277697	−	0.480986i	0.970812	+	0.239841i	$0.0770955\pi$
$258$		0			0
$259$	−1.69257	−	2.93162i	−0.00653502	−	0.0113190i
$260$	548.708	−	184.193i	2.11042	−	0.708436i
$261$		0			0
$262$			316.357i			1.20747i
$263$	126.234	+	218.644i	0.479979	+	0.831347i	0.999736	−	0.0229665i	$-0.00731110\pi$
$263$	126.234	+	218.644i	0.479979	+	0.831347i	−0.519758	+	0.854314i	$0.673978\pi$
$264$		0			0
$265$	424.563	+	85.9450i	1.60212	+	0.324321i
$266$	−58.7578	−	33.9238i	−0.220894	−	0.127533i
$267$		0			0
$268$	648.660	−	374.504i	2.42037	−	1.39740i
$269$			388.672i			1.44488i	0.691435	+	0.722439i	$0.256979\pi$
$269$			388.672i			1.44488i	−0.691435	+	0.722439i	$0.743021\pi$
$270$		0			0
$271$	−163.253			−0.602410			−0.301205	−	0.953559i	$-0.597389\pi$
$271$	−163.253			−0.602410			−0.301205	+	0.953559i	$0.597389\pi$
$272$	−80.7617	−	139.883i	−0.296918	−	0.514277i
$273$		0			0
$274$	−128.550	+	222.655i	−0.469160	+	0.812610i
$275$	243.861	−	30.4278i	0.886769	−	0.110647i
$276$		0			0
$277$	419.003	−	241.912i	1.51265	−	0.873328i	0.512757	−	0.858534i	$-0.328624\pi$
$277$	419.003	−	241.912i	1.51265	−	0.873328i	0.999891	−	0.0147939i	$-0.00470921\pi$
$278$	−512.227			−1.84254
$279$		0			0
$280$	251.108	−	84.2934i	0.896814	−	0.301048i
$281$	−231.798	+	133.829i	−0.824906	+	0.476260i	−0.852105	−	0.523371i	$-0.824674\pi$
$281$	−231.798	+	133.829i	−0.824906	+	0.476260i	0.0271995	+	0.999630i	$0.491341\pi$
$282$		0			0
$283$	−425.908	−	245.898i	−1.50498	−	0.868898i	−0.999983	−	0.00577475i	$-0.998162\pi$
$283$	−425.908	−	245.898i	−1.50498	−	0.868898i	−0.504993	−	0.863124i	$-0.668505\pi$
$284$	−603.967	−	348.701i	−2.12664	−	1.22782i
$285$		0			0
$286$	−218.625	−	378.670i	−0.764424	−	1.32402i
$287$	−88.8586			−0.309612
$288$		0			0
$289$	−270.643			−0.936481
$290$	422.230	+	372.820i	1.45597	+	1.28559i
$291$		0			0
$292$	251.885	+	145.426i	0.862621	+	0.498034i
$293$	161.073	−	278.986i	0.549737	−	0.952172i	−0.448555	−	0.893755i	$-0.648061\pi$
$293$	161.073	−	278.986i	0.549737	−	0.952172i	0.998292	−	0.0584171i	$-0.0186053\pi$
$294$		0			0
$295$	−397.148	−	350.673i	−1.34626	−	1.18872i
$296$		−	27.2062i		−	0.0919129i
$297$		0			0
$298$		−	176.092i		−	0.590914i
$299$	5.33367	−	3.07940i	0.0178384	−	0.0102990i
$300$		0			0
$301$	66.6839	−	115.500i	0.221541	−	0.383720i
$302$	102.306	−	177.199i	0.338762	−	0.586752i
$303$		0			0
$304$	−135.095	−	233.992i	−0.444392	−	0.769710i
$305$	−49.8355	−	148.459i	−0.163395	−	0.486750i
$306$		0			0
$307$			426.031i			1.38772i	0.720109	+	0.693861i	$0.244092\pi$
$307$			426.031i			1.38772i	−0.720109	+	0.693861i	$0.755908\pi$
$308$	−121.091	−	209.735i	−0.393152	−	0.680959i
$309$		0			0
$310$	347.433	+	70.3315i	1.12075	+	0.226876i
$311$	1.01150	+	0.583987i	0.00325240	+	0.00187777i	0.501625	−	0.865085i	$-0.332736\pi$
$311$	1.01150	+	0.583987i	0.00325240	+	0.00187777i	−0.498373	+	0.866963i	$0.666069\pi$
$312$		0			0
$313$	−225.989	+	130.475i	−0.722009	+	0.416852i	−0.815492	−	0.578769i	$-0.803533\pi$
$313$	−225.989	+	130.475i	−0.722009	+	0.416852i	0.0934824	+	0.995621i	$0.470200\pi$
$314$		−	40.8260i		−	0.130019i
$315$		0			0
$316$	1106.22			3.50071
$317$	−65.5178	−	113.480i	−0.206681	−	0.357981i	0.743986	−	0.668195i	$-0.232933\pi$
$317$	−65.5178	−	113.480i	−0.206681	−	0.357981i	−0.950667	+	0.310213i	$0.899599\pi$
$318$		0			0
$319$	150.165	−	260.094i	0.470737	−	0.815340i
$320$	281.440	+	56.9724i	0.879500	+	0.178039i
$321$		0			0
$322$	4.18560	−	2.41656i	0.0129988	−	0.00750484i
$323$	30.7071			0.0950683
$324$		0			0
$325$	−181.969	−	240.499i	−0.559905	−	0.739996i
$326$	−690.482	+	398.650i	−2.11804	+	1.22285i
$327$		0			0
$328$	−618.474	−	357.076i	−1.88559	−	1.08865i
$329$	113.242	+	65.3803i	0.344201	+	0.198724i
$330$		0			0
$331$	−96.7419	−	167.562i	−0.292272	−	0.506229i	0.682075	−	0.731282i	$-0.261078\pi$
$331$	−96.7419	−	167.562i	−0.292272	−	0.506229i	−0.974347	+	0.225053i	$0.927745\pi$
$332$	575.893			1.73462
$333$		0			0
$334$	228.415			0.683877
$335$	−292.549	−	258.314i	−0.873280	−	0.771088i
$336$		0			0
$337$	−401.485	−	231.798i	−1.19135	−	0.687827i	−0.232738	−	0.972539i	$-0.574769\pi$
$337$	−401.485	−	231.798i	−1.19135	−	0.687827i	−0.958613	+	0.284712i	$0.908102\pi$
$338$	43.2819	−	74.9664i	0.128053	−	0.221794i
$339$		0			0
$340$	−136.065	+	154.097i	−0.400190	+	0.453227i
$341$		−	189.005i		−	0.554268i
$342$		0			0
$343$		−	234.682i		−	0.684203i
$344$	928.267	−	535.935i	2.69845	−	1.55795i
$345$		0			0
$346$	−614.799	+	1064.86i	−1.77688	+	3.07764i
$347$	4.85934	−	8.41662i	0.0140039	−	0.0242554i	−0.858939	−	0.512079i	$-0.828876\pi$
$347$	4.85934	−	8.41662i	0.0140039	−	0.0242554i	0.872942	+	0.487823i	$0.162209\pi$
$348$		0			0
$349$	24.6679	+	42.7260i	0.0706816	+	0.122424i	0.899200	−	0.437537i	$-0.144149\pi$
$349$	24.6679	+	42.7260i	0.0706816	+	0.122424i	−0.828519	+	0.559962i	$0.810816\pi$
$350$	−142.800	−	188.731i	−0.408001	−	0.539232i
$351$		0			0
$352$		−	555.123i		−	1.57705i
$353$	47.6810	+	82.5859i	0.135074	+	0.233954i	0.925626	−	0.378441i	$-0.123540\pi$
$353$	47.6810	+	82.5859i	0.135074	+	0.233954i	−0.790552	+	0.612395i	$0.790206\pi$
$354$		0			0
$355$	−72.0974	+	356.157i	−0.203091	+	1.00326i
$356$	592.524	+	342.094i	1.66439	+	0.960938i
$357$		0			0
$358$	617.966	−	356.783i	1.72616	−	0.996600i
$359$			539.284i			1.50219i	0.660197	+	0.751093i	$0.270473\pi$
$359$			539.284i			1.50219i	−0.660197	+	0.751093i	$0.729527\pi$
$360$		0			0
$361$	−309.634			−0.857713
$362$	449.599	+	778.729i	1.24199	+	2.15118i
$363$		0			0
$364$	−148.600	+	257.383i	−0.408243	+	0.707098i
$365$	30.0683	−	148.536i	0.0823790	−	0.406947i
$366$		0			0
$367$	262.482	−	151.544i	0.715211	−	0.412927i	−0.0977766	−	0.995208i	$-0.531173\pi$
$367$	262.482	−	151.544i	0.715211	−	0.412927i	0.812987	+	0.582281i	$0.197840\pi$
$368$	19.2470			0.0523016
$369$		0			0
$370$	−23.0448	+	7.73582i	−0.0622833	+	0.0209076i
$371$	−192.627	+	111.213i	−0.519209	+	0.299766i
$372$		0			0
$373$	113.159	+	65.3325i	0.303376	+	0.175154i	0.643959	−	0.765060i	$-0.277291\pi$
$373$	113.159	+	65.3325i	0.303376	+	0.175154i	−0.340582	+	0.940215i	$0.610624\pi$
$374$	134.492	+	77.6489i	0.359604	+	0.207617i
$375$		0			0
$376$	525.459	+	910.121i	1.39750	+	2.42054i
$377$	−368.560			−0.977612
$378$		0			0
$379$	545.141			1.43837			0.719183	−	0.694821i	$-0.244516\pi$
$379$	545.141			1.43837			0.719183	+	0.694821i	$0.244516\pi$
$380$	−227.604	+	257.768i	−0.598958	+	0.678338i
$381$		0			0
$382$	452.056	+	260.995i	1.18339	+	0.683232i
$383$	−0.623248	+	1.07950i	−0.00162728	+	0.00281853i	−0.866838	−	0.498590i	$-0.833851\pi$
$383$	−0.623248	+	1.07950i	−0.00162728	+	0.00281853i	0.865211	+	0.501409i	$0.167185\pi$
$384$		0			0
$385$	−83.5225	+	94.5917i	−0.216941	+	0.245693i
$386$			816.445i			2.11514i
$387$		0			0
$388$			1227.94i			3.16480i
$389$	345.001	−	199.187i	0.886893	−	0.512048i	0.0139679	−	0.999902i	$-0.495554\pi$
$389$	345.001	−	199.187i	0.886893	−	0.512048i	0.872925	+	0.487855i	$0.162220\pi$
$390$		0			0
$391$	−1.09371	+	1.89435i	−0.00279720	+	0.00484490i
$392$	437.529	−	757.822i	1.11615	−	1.93322i
$393$		0			0
$394$	−52.4376	−	90.8245i	−0.133090	−	0.230519i
$395$	−183.429	−	546.432i	−0.464378	−	1.38337i
$396$		0			0
$397$		−	685.998i		−	1.72795i	−0.503531	−	0.863977i	$-0.667966\pi$
$397$		−	685.998i		−	1.72795i	0.503531	−	0.863977i	$-0.332034\pi$
$398$	283.691	+	491.367i	0.712791	+	1.23459i
$399$		0			0
$400$	−116.694	−	935.232i	−0.291734	−	2.33808i
$401$	−44.9212	−	25.9353i	−0.112023	−	0.0646764i	0.442942	−	0.896550i	$-0.353935\pi$
$401$	−44.9212	−	25.9353i	−0.112023	−	0.0646764i	−0.554965	+	0.831874i	$0.687268\pi$
$402$		0			0
$403$	−200.869	+	115.972i	−0.498435	+	0.287772i
$404$		−	825.992i		−	2.04453i
$405$		0			0
$406$	−289.227			−0.712383
$407$	6.48055	+	11.2246i	0.0159227	+	0.0275790i
$408$		0			0
$409$	135.648	−	234.950i	0.331658	−	0.574449i	−0.651179	−	0.758924i	$-0.725725\pi$
$409$	135.648	−	234.950i	0.331658	−	0.574449i	0.982837	+	0.184475i	$0.0590586\pi$
$410$	−126.602	+	625.405i	−0.308785	+	1.52538i
$411$		0			0
$412$	−339.756	+	196.158i	−0.824650	+	0.476112i
$413$	272.046			0.658707
$414$		0			0
$415$	−95.4921	−	284.469i	−0.230101	−	0.685467i
$416$	−589.969	+	340.619i	−1.41819	+	0.818795i
$417$		0			0
$418$	224.973	+	129.888i	0.538213	+	0.310738i
$419$	−23.9467	−	13.8256i	−0.0571520	−	0.0329967i	0.471152	−	0.882052i	$-0.343838\pi$
$419$	−23.9467	−	13.8256i	−0.0571520	−	0.0329967i	−0.528304	+	0.849055i	$0.677172\pi$
$420$		0			0
$421$	218.613	+	378.649i	0.519271	+	0.899403i	0.999749	+	0.0223967i	$0.00712970\pi$
$421$	218.613	+	378.649i	0.519271	+	0.899403i	−0.480478	+	0.877007i	$0.659537\pi$
$422$	−664.367			−1.57433
$423$		0			0
$424$	−1787.63			−4.21610
$425$	98.6798	+	41.6590i	0.232188	+	0.0980211i
$426$		0			0
$427$	69.6378	+	40.2054i	0.163086	+	0.0941579i
$428$	−7.96594	+	13.7974i	−0.0186120	+	0.0322369i
$429$		0			0
$430$	−717.904	−	633.894i	−1.66954	−	1.47417i
$431$		−	54.3602i		−	0.126126i	−0.998010	−	0.0630629i	$-0.979913\pi$
$431$		−	54.3602i		−	0.126126i	0.998010	−	0.0630629i	$-0.0200869\pi$
$432$		0			0
$433$			526.426i			1.21576i	0.794028	+	0.607882i	$0.207981\pi$
$433$			526.426i			1.21576i	−0.794028	+	0.607882i	$0.792019\pi$
$434$	−157.632	+	91.0091i	−0.363208	+	0.209698i
$435$		0			0
$436$	713.180	−	1235.26i	1.63573	−	2.83317i
$437$	−1.82951	+	3.16881i	−0.00418653	+	0.00725128i
$438$		0			0
$439$	208.124	+	360.481i	0.474087	+	0.821142i	0.999560	−	0.0296681i	$-0.00944503\pi$
$439$	208.124	+	360.481i	0.474087	+	0.821142i	−0.525473	+	0.850810i	$0.676112\pi$
$440$	−961.448	+	322.744i	−2.18511	+	0.733510i
$441$		0			0
$442$		−	190.579i		−	0.431173i
$443$	−213.582	−	369.935i	−0.482127	−	0.835069i	0.517662	−	0.855585i	$-0.326802\pi$
$443$	−213.582	−	369.935i	−0.482127	−	0.835069i	−0.999790	+	0.0205163i	$0.993469\pi$
$444$		0			0
$445$	70.7314	−	349.409i	0.158947	−	0.785189i
$446$	−687.840	−	397.125i	−1.54224	−	0.890414i
$447$		0			0
$448$	−127.691	+	73.7224i	−0.285024	+	0.164559i
$449$			236.730i			0.527239i	0.964627	+	0.263620i	$0.0849164\pi$
$449$			236.730i			0.527239i	−0.964627	+	0.263620i	$0.915084\pi$
$450$		0			0
$451$	340.224			0.754376
$452$	−630.730	−	1092.46i	−1.39542	−	2.41694i
$453$		0			0
$454$	92.9488	−	160.992i	0.204733	−	0.354608i
$455$	151.778	+	30.7247i	0.333578	+	0.0675267i
$456$		0			0
$457$	−604.296	+	348.891i	−1.32231	+	0.763437i	−0.984097	−	0.177633i	$-0.943156\pi$
$457$	−604.296	+	348.891i	−1.32231	+	0.763437i	−0.338214	+	0.941069i	$0.609823\pi$
$458$	22.7396			0.0496497
$459$		0			0
$460$	−7.79536	−	23.2222i	−0.0169464	−	0.0504831i
$461$	332.339	−	191.876i	0.720910	−	0.416217i	−0.0941777	−	0.995555i	$-0.530022\pi$
$461$	332.339	−	191.876i	0.720910	−	0.416217i	0.815087	+	0.579338i	$0.196689\pi$
$462$		0			0
$463$	233.924	+	135.056i	0.505235	+	0.291698i	0.730873	−	0.682514i	$-0.239113\pi$
$463$	233.924	+	135.056i	0.505235	+	0.291698i	−0.225638	+	0.974211i	$0.572447\pi$
$464$	−997.483	−	575.897i	−2.14975	−	1.24116i
$465$		0			0
$466$	96.8529	+	167.754i	0.207839	+	0.359987i
$467$	777.952			1.66585			0.832926	−	0.553385i	$-0.186664\pi$
$467$	777.952			1.66585			0.832926	+	0.553385i	$0.186664\pi$
$468$		0			0
$469$	200.396			0.427283
$470$	621.503	−	703.870i	1.32235	−	1.49760i
$471$		0			0
$472$	1893.50	+	1093.21i	4.01164	+	2.31612i
$473$	−255.321	+	442.228i	−0.539790	+	0.934943i
$474$		0			0
$475$	165.068	+	69.6856i	0.347512	+	0.146707i
$476$		−	105.556i		−	0.221757i
$477$		0			0
$478$		−	359.819i		−	0.752760i
$479$	−62.8429	+	36.2824i	−0.131196	+	0.0757460i	−0.564162	−	0.825664i	$-0.690800\pi$
$479$	−62.8429	+	36.2824i	−0.131196	+	0.0757460i	0.432966	+	0.901410i	$0.357467\pi$
$480$		0			0
$481$	7.95281	−	13.7747i	0.0165339	−	0.0286376i
$482$	−263.141	+	455.774i	−0.545936	+	0.945590i
$483$		0			0
$484$	−116.924	−	202.518i	−0.241578	−	0.418425i
$485$	606.556	−	203.612i	1.25063	−	0.419819i
$486$		0			0
$487$			729.487i			1.49792i	0.662616	+	0.748959i	$0.269446\pi$
$487$			729.487i			1.49792i	−0.662616	+	0.748959i	$0.730554\pi$
$488$	323.129	+	559.676i	0.662150	+	1.14688i
$489$		0			0
$490$	−766.315	−	155.127i	−1.56391	−	0.316585i
$491$	−3.30449	−	1.90785i	−0.00673012	−	0.00388564i	0.496631	−	0.867962i	$-0.334570\pi$
$491$	−3.30449	−	1.90785i	−0.00673012	−	0.00388564i	−0.503361	+	0.864076i	$0.667904\pi$
$492$		0			0
$493$	113.364	−	65.4505i	0.229946	−	0.132760i
$494$		−	318.793i		−	0.645330i
$495$		0			0
$496$	−724.853			−1.46140
$497$	−93.2942	−	161.590i	−0.187715	−	0.325131i
$498$		0			0
$499$	−102.651	+	177.797i	−0.205714	+	0.356307i	−0.950360	−	0.311152i	$-0.899285\pi$
$499$	−102.651	+	177.797i	−0.205714	+	0.356307i	0.744646	+	0.667460i	$0.232618\pi$
$500$	−1081.13	+	519.580i	−2.16226	+	1.03916i
$501$		0			0
$502$	813.107	−	469.448i	1.61974	−	0.935155i
$503$	224.016			0.445360			0.222680	−	0.974892i	$-0.428519\pi$
$503$	224.016			0.445360			0.222680	+	0.974892i	$0.428519\pi$
$504$		0			0
$505$	−408.008	+	136.963i	−0.807937	+	0.271213i
$506$	−16.0259	+	9.25257i	−0.0316718	+	0.0182857i
$507$		0			0
$508$	−840.599	−	485.320i	−1.65472	−	0.955354i
$509$	399.073	+	230.405i	0.784033	+	0.452662i	0.837858	−	0.545889i	$-0.183808\pi$
$509$	399.073	+	230.405i	0.784033	+	0.452662i	−0.0538245	+	0.998550i	$0.517141\pi$
$510$		0			0
$511$	38.9085	+	67.3915i	0.0761418	+	0.131882i
$512$	982.608			1.91916
$513$		0			0
$514$	526.309			1.02395
$515$	153.232	+	135.300i	0.297537	+	0.262719i
$516$		0			0
$517$	−433.584	−	250.330i	−0.838653	−	0.484197i
$518$	6.24097	−	10.8097i	0.0120482	−	0.0208681i
$519$		0			0
$520$	932.939	+	823.766i	1.79411	+	1.58417i
$521$		−	182.438i		−	0.350168i	−0.984554	−	0.175084i	$-0.943980\pi$
$521$		−	182.438i		−	0.350168i	0.984554	−	0.175084i	$-0.0560197\pi$
$522$		0			0
$523$		−	431.339i		−	0.824741i	−0.911016	−	0.412370i	$-0.864701\pi$
$523$		−	431.339i		−	0.824741i	0.911016	−	0.412370i	$-0.135299\pi$
$524$	−713.006	+	411.654i	−1.36070	+	0.785599i
$525$		0			0
$526$	−465.461	+	806.202i	−0.884907	+	1.53270i
$527$	41.1896	−	71.3426i	0.0781587	−	0.135375i
$528$		0			0
$529$	264.370	+	457.902i	0.499754	+	0.865599i
$530$	508.295	+	1514.20i	0.959046	+	2.85698i
$531$		0			0
$532$		−	176.571i		−	0.331901i
$533$	−208.758	−	361.580i	−0.391666	−	0.678386i
$534$		0			0
$535$	8.13627	+	1.64704i	0.0152080	+	0.00307858i
$536$	1394.80	+	805.285i	2.60223	+	1.50240i
$537$		0			0
$538$	−1241.14	+	716.571i	−2.30695	+	1.33192i
$539$			416.879i			0.773431i
$540$		0			0
$541$	−649.924			−1.20134			−0.600669	−	0.799498i	$-0.705099\pi$
$541$	−649.924			−1.20134			−0.600669	+	0.799498i	$0.705099\pi$
$542$	−300.980	−	521.312i	−0.555313	−	0.961830i
$543$		0			0
$544$	120.977	−	209.539i	0.222384	−	0.385181i
$545$	−728.429	−	147.457i	−1.33657	−	0.270564i
$546$		0			0
$547$	368.334	−	212.658i	0.673371	−	0.388771i	−0.123982	−	0.992285i	$-0.539566\pi$
$547$	368.334	−	212.658i	0.673371	−	0.388771i	0.797353	+	0.603513i	$0.206233\pi$
$548$	−669.094			−1.22097
$549$		0			0
$550$	546.757	+	722.619i	0.994103	+	1.31385i
$551$	189.631	−	109.483i	0.344157	−	0.198699i
$552$		0			0
$553$	256.316	+	147.984i	0.463501	+	0.267602i
$554$	1544.98	+	891.995i	2.78878	+	1.61010i
$555$		0			0
$556$	−666.526	−	1154.46i	−1.19879	−	2.07636i
$557$	−325.885			−0.585073			−0.292536	−	0.956254i	$-0.594499\pi$
$557$	−325.885			−0.585073			−0.292536	+	0.956254i	$0.594499\pi$
$558$		0			0
$559$	626.650			1.12102
$560$	362.768	+	320.317i	0.647800	+	0.571994i
$561$		0			0
$562$	−854.705	−	493.464i	−1.52083	−	0.878050i
$563$	−353.382	+	612.075i	−0.627676	+	1.08717i	0.360341	+	0.932821i	$0.382660\pi$
$563$	−353.382	+	612.075i	−0.627676	+	1.08717i	−0.988017	+	0.154346i	$0.950673\pi$
$564$		0			0
$565$	−435.047	+	492.703i	−0.769994	+	0.872041i
$566$		−	1813.39i		−	3.20387i
$567$		0			0
$568$		−	1499.60i		−	2.64015i
$569$	485.178	−	280.118i	0.852686	−	0.492299i	−0.00887015	−	0.999961i	$-0.502823\pi$
$569$	485.178	−	280.118i	0.852686	−	0.492299i	0.861556	+	0.507662i	$0.169490\pi$
$570$		0			0
$571$	105.346	−	182.465i	0.184494	−	0.319553i	−0.758912	−	0.651193i	$-0.774269\pi$
$571$	105.346	−	182.465i	0.184494	−	0.319553i	0.943406	+	0.331640i	$0.107602\pi$
$572$	568.965	−	985.475i	0.994693	−	1.72286i
$573$		0			0
$574$	−163.823	−	283.750i	−0.285406	−	0.494338i
$575$	−10.1783	+	7.70122i	−0.0177014	+	0.0133934i
$576$		0			0
$577$			502.258i			0.870464i	0.900318	+	0.435232i	$0.143334\pi$
$577$			502.258i			0.870464i	−0.900318	+	0.435232i	$0.856666\pi$
$578$	−498.968	−	864.237i	−0.863266	−	1.49522i
$579$		0			0
$580$	−290.844	+	1436.75i	−0.501454	+	2.47715i
$581$	133.436	+	77.0395i	0.229667	+	0.132598i
$582$		0			0
$583$	737.533	−	425.815i	1.26507	−	0.730386i
$584$			625.411i			1.07091i
$585$		0			0
$586$	1187.84			2.02703
$587$	204.886	+	354.873i	0.349040	+	0.604554i	0.986079	−	0.166277i	$-0.0531746\pi$
$587$	204.886	+	354.873i	0.349040	+	0.604554i	−0.637040	+	0.770831i	$0.719841\pi$
$588$		0			0
$589$	68.9006	−	119.339i	0.116979	−	0.202613i
$590$	387.599	−	1914.72i	0.656948	−	3.24528i
$591$		0			0
$592$	43.0476	−	24.8535i	0.0727155	−	0.0419823i
$593$	−944.139			−1.59214			−0.796070	−	0.605204i	$-0.793092\pi$
$593$	−944.139			−1.59214			−0.796070	+	0.605204i	$0.793092\pi$
$594$		0			0
$595$	−52.1409	+	17.5029i	−0.0876317	+	0.0294167i
$596$	396.877	−	229.137i	0.665902	−	0.384458i
$597$		0			0
$598$	19.6667	+	11.3546i	0.0328875	+	0.0189876i
$599$	−461.021	−	266.171i	−0.769652	−	0.444359i	0.0630986	−	0.998007i	$-0.479902\pi$
$599$	−461.021	−	266.171i	−0.769652	−	0.444359i	−0.832750	+	0.553649i	$0.813235\pi$
$600$		0			0
$601$	−257.783	−	446.493i	−0.428923	−	0.742917i	0.567855	−	0.823129i	$-0.307774\pi$
$601$	−257.783	−	446.493i	−0.428923	−	0.742917i	−0.996778	+	0.0802121i	$0.974440\pi$
$602$	491.764			0.816883
$603$		0			0
$604$	532.496			0.881615
$605$	−80.6481	+	91.3364i	−0.133303	+	0.150969i
$606$		0			0
$607$	148.223	+	85.5764i	0.244189	+	0.140983i	0.617101	−	0.786884i	$-0.288307\pi$
$607$	148.223	+	85.5764i	0.244189	+	0.140983i	−0.372912	+	0.927867i	$0.621640\pi$
$608$	202.366	−	350.509i	0.332839	−	0.576494i
$609$		0			0
$610$	382.191	−	432.843i	0.626543	−	0.709578i
$611$			614.400i			1.00557i
$612$		0			0
$613$		−	875.826i		−	1.42875i	−0.699761	−	0.714377i	$-0.746710\pi$
$613$		−	875.826i		−	1.42875i	0.699761	−	0.714377i	$-0.253290\pi$
$614$	−1360.43	+	785.447i	−2.21569	+	1.27923i
$615$		0			0
$616$	260.378	−	450.988i	0.422692	−	0.732124i
$617$	−565.874	+	980.122i	−0.917137	+	1.58853i	−0.113396	+	0.993550i	$0.536173\pi$
$617$	−565.874	+	980.122i	−0.917137	+	1.58853i	−0.803742	+	0.594978i	$0.797161\pi$
$618$		0			0
$619$	−260.187	−	450.658i	−0.420335	−	0.728042i	0.575637	−	0.817705i	$-0.304754\pi$
$619$	−260.187	−	450.658i	−0.420335	−	0.728042i	−0.995972	+	0.0896637i	$0.971421\pi$
$620$	293.578	+	874.563i	0.473513	+	1.41058i
$621$		0			0
$622$			4.30664i			0.00692386i
$623$	91.5266	+	158.529i	0.146913	+	0.254460i
$624$		0			0
$625$	435.921	+	447.882i	0.697474	+	0.716611i
$626$	−833.284	−	481.097i	−1.33112	−	0.768525i
$627$		0			0
$628$	92.0138	−	53.1242i	0.146519	−	0.0845926i
$629$			5.64918i			0.00898121i
$630$		0			0
$631$	−607.475			−0.962718			−0.481359	−	0.876523i	$-0.659857\pi$
$631$	−607.475			−0.962718			−0.481359	+	0.876523i	$0.659857\pi$
$632$	1189.34	+	2060.00i	1.88187	+	3.25949i
$633$		0			0
$634$	241.582	−	418.433i	0.381044	−	0.659988i
$635$	−100.345	+	495.697i	−0.158023	+	0.780626i
$636$		0			0
$637$	443.047	−	255.794i	0.695522	−	0.401560i
$638$	1107.40			1.73574
$639$		0			0
$640$	−22.4799	−	66.9670i	−0.0351248	−	0.104636i
$641$	−161.252	+	93.0990i	−0.251564	+	0.145240i	−0.620480	−	0.784222i	$-0.713062\pi$
$641$	−161.252	+	93.0990i	−0.251564	+	0.145240i	0.368916	+	0.929463i	$0.379729\pi$
$642$		0			0
$643$	690.674	+	398.761i	1.07414	+	0.620157i	0.929311	−	0.369299i	$-0.120402\pi$
$643$	690.674	+	398.761i	1.07414	+	0.620157i	0.144833	+	0.989456i	$0.453736\pi$
$644$	10.8929	+	6.28901i	0.0169144	+	0.00976554i
$645$		0			0
$646$	56.6127	+	98.0561i	0.0876357	+	0.151790i
$647$	849.489			1.31297			0.656483	−	0.754341i	$-0.272043\pi$
$647$	849.489			1.31297			0.656483	+	0.754341i	$0.272043\pi$
$648$		0			0
$649$	−1041.61			−1.60495
$650$	432.493	−	1024.47i	0.665374	−	1.57611i
$651$		0			0
$652$	−1796.95	−	1037.47i	−2.75607	−	1.59122i
$653$	520.594	−	901.696i	0.797235	−	1.38085i	−0.124175	−	0.992260i	$-0.539629\pi$
$653$	520.594	−	901.696i	0.797235	−	1.38085i	0.921410	−	0.388591i	$-0.127038\pi$
$654$		0			0
$655$	321.569	+	283.939i	0.490945	+	0.433494i
$656$		−	1304.79i		−	1.98901i
$657$		0			0
$658$			482.151i			0.732752i
$659$	−556.318	+	321.190i	−0.844185	+	0.487390i	−0.858685	−	0.512505i	$-0.828718\pi$
$659$	−556.318	+	321.190i	−0.844185	+	0.487390i	0.0144997	+	0.999895i	$0.495384\pi$
$660$		0			0
$661$	394.759	−	683.742i	0.597214	−	1.03441i	−0.396016	−	0.918244i	$-0.629608\pi$
$661$	394.759	−	683.742i	0.597214	−	1.03441i	0.993230	−	0.116162i	$-0.0370591\pi$
$662$	356.714	−	617.847i	0.538843	−	0.933304i
$663$		0			0
$664$	619.163	+	1072.42i	0.932474	+	1.61509i
$665$	−87.2194	+	29.2783i	−0.131157	+	0.0440275i
$666$		0			0
$667$			15.5980i			0.0233854i
$668$	297.221	+	514.802i	0.444941	+	0.770661i
$669$		0			0
$670$	285.515	−	1410.43i	0.426142	−	2.10511i
$671$	−266.631	−	153.939i	−0.397363	−	0.229418i
$672$		0			0
$673$	−879.824	+	507.967i	−1.30732	+	0.754780i	−0.981648	−	0.190704i	$-0.938923\pi$
$673$	−879.824	+	507.967i	−1.30732	+	0.754780i	−0.325669	+	0.945484i	$0.605590\pi$
$674$		−	1709.40i		−	2.53621i
$675$		0			0
$676$	225.279			0.333253
$677$	−371.811	−	643.996i	−0.549204	−	0.951249i	−0.998329	−	0.0577802i	$-0.981598\pi$
$677$	−371.811	−	643.996i	−0.549204	−	0.951249i	0.449126	−	0.893469i	$-0.351736\pi$
$678$		0			0
$679$	−164.267	+	284.518i	−0.241924	+	0.419025i
$680$	−433.246	−	87.7028i	−0.637127	−	0.128975i
$681$		0			0
$682$	603.546	−	348.458i	0.884965	−	0.510935i
$683$	152.482			0.223254			0.111627	−	0.993750i	$-0.464394\pi$
$683$	152.482			0.223254			0.111627	+	0.993750i	$0.464394\pi$
$684$		0			0
$685$	110.946	+	330.507i	0.161965	+	0.482491i
$686$	749.403	−	432.668i	1.09242	−	0.630711i
$687$		0			0
$688$	1695.99	+	979.179i	2.46510	+	1.42322i
$689$	−905.087	−	522.552i	−1.31362	−	0.758422i
$690$		0			0
$691$	−388.586	−	673.050i	−0.562353	−	0.974023i	−0.997291	−	0.0735628i	$-0.976563\pi$
$691$	−388.586	−	673.050i	−0.562353	−	0.974023i	0.434938	−	0.900460i	$-0.356770\pi$
$692$	−3199.99			−4.62426
$693$		0			0
$694$	35.8355			0.0516361
$695$	−459.737	+	520.666i	−0.661492	+	0.749160i
$696$		0			0
$697$	128.422	+	74.1444i	0.184249	+	0.106376i
$698$	−90.9573	+	157.543i	−0.130311	+	0.225706i
$699$		0			0
$700$	239.547	−	567.427i	0.342209	−	0.810610i
$701$			461.657i			0.658569i	0.944231	+	0.329284i	$0.106808\pi$
$701$			461.657i			0.658569i	−0.944231	+	0.329284i	$0.893192\pi$
$702$		0			0
$703$			9.44975i			0.0134420i
$704$	488.906	−	282.270i	0.694468	−	0.400952i
$705$		0			0
$706$	−175.813	+	304.517i	−0.249027	+	0.431327i
$707$	110.496	−	191.385i	0.156289	−	0.270701i
$708$		0			0
$709$	179.227	+	310.431i	0.252789	+	0.437843i	0.964293	−	0.264839i	$-0.0853189\pi$
$709$	179.227	+	310.431i	0.252789	+	0.437843i	−0.711504	+	0.702682i	$0.751986\pi$
$710$	−1270.23	+	426.397i	−1.78905	+	0.600560i
$711$		0			0
$712$			1471.19i			2.06628i
$713$	4.90812	+	8.50112i	0.00688376	+	0.0119230i
$714$		0			0
$715$	−581.130	−	117.639i	−0.812770	−	0.164530i
$716$	1608.24	+	928.515i	2.24614	+	1.29681i
$717$		0			0
$718$	−1722.08	+	994.245i	−2.39845	+	1.38474i
$719$		−	283.414i		−	0.394178i	−0.980386	−	0.197089i	$-0.936851\pi$
$719$		−	283.414i		−	0.394178i	0.980386	−	0.197089i	$-0.0631488\pi$
$720$		0			0
$721$	−104.964			−0.145580
$722$	−570.854	−	988.748i	−0.790656	−	1.36946i
$723$		0			0
$724$	−1170.07	+	2026.61i	−1.61611	+	2.79919i
$725$	757.925	−	94.5702i	1.04541	−	0.130442i
$726$		0			0
$727$	−134.545	+	77.6796i	−0.185069	+	0.106850i	−0.589672	−	0.807643i	$-0.700743\pi$
$727$	−134.545	+	77.6796i	−0.185069	+	0.106850i	0.404603	+	0.914492i	$0.367410\pi$
$728$	−639.063			−0.877833
$729$		0			0
$730$	529.750	−	177.830i	0.725685	−	0.243602i
$731$	−192.748	+	111.283i	−0.263677	+	0.152234i
$732$		0			0
$733$	−90.8735	−	52.4658i	−0.123975	−	0.0715768i	0.436730	−	0.899593i	$-0.356136\pi$
$733$	−90.8735	−	52.4658i	−0.123975	−	0.0715768i	−0.560705	+	0.828016i	$0.689470\pi$
$734$	967.845	+	558.786i	1.31859	+	0.761288i
$735$		0			0
$736$	14.4155	+	24.9684i	0.0195863	+	0.0339245i
$737$	−767.279			−1.04108
$738$		0			0
$739$	−627.375			−0.848951			−0.424476	−	0.905439i	$-0.639542\pi$
$739$	−627.375			−0.848951			−0.424476	+	0.905439i	$0.639542\pi$
$740$	−47.4217	−	41.8724i	−0.0640834	−	0.0565843i
$741$		0			0
$742$	−710.268	−	410.073i	−0.957234	−	0.552659i
$743$	193.295	−	334.797i	0.260155	−	0.450602i	−0.706128	−	0.708084i	$-0.749560\pi$
$743$	193.295	−	334.797i	0.260155	−	0.450602i	0.966283	+	0.257483i	$0.0828930\pi$
$744$		0			0
$745$	−178.994	−	158.048i	−0.240260	−	0.212144i
$746$			481.798i			0.645842i
$747$		0			0
$748$			404.157i			0.540317i
$749$	−3.69147	+	2.13127i	−0.00492853	+	0.00284549i
$750$		0			0
$751$	−452.601	+	783.928i	−0.602665	+	1.04385i	0.389751	+	0.920920i	$0.372561\pi$
$751$	−452.601	+	783.928i	−0.602665	+	1.04385i	−0.992416	+	0.122926i	$0.960772\pi$
$752$	−960.038	+	1662.83i	−1.27665	+	2.21122i
$753$		0			0
$754$	−679.491	−	1176.91i	−0.901182	−	1.56089i
$755$	−88.2962	−	263.032i	−0.116949	−	0.348387i
$756$		0			0
$757$		−	332.222i		−	0.438867i	−0.975627	−	0.219433i	$-0.929579\pi$
$757$		−	332.222i		−	0.438867i	0.975627	−	0.219433i	$-0.0704209\pi$
$758$	1005.04	+	1740.78i	1.32591	+	2.29655i
$759$		0			0
$760$	−724.719	−	146.706i	−0.953578	−	0.193034i
$761$	396.726	+	229.050i	0.521322	+	0.300986i	0.737475	−	0.675374i	$-0.236018\pi$
$761$	396.726	+	229.050i	0.521322	+	0.300986i	−0.216153	+	0.976359i	$0.569351\pi$
$762$		0			0
$763$	330.492	−	190.810i	0.433149	−	0.250079i
$764$			1358.46i			1.77809i
$765$		0			0
$766$	−4.59618			−0.00600023
$767$	639.126	+	1107.00i	0.833280	+	1.44328i
$768$		0			0
$769$	458.196	−	793.618i	0.595833	−	1.03201i	−0.397595	−	0.917561i	$-0.630155\pi$
$769$	458.196	−	793.618i	0.595833	−	1.03201i	0.993429	−	0.114453i	$-0.0365115\pi$
$770$	−456.042	−	92.3174i	−0.592263	−	0.119893i
$771$		0			0
$772$	−1840.11	+	1062.39i	−2.38356	+	1.37615i
$773$	1186.06			1.53436			0.767178	−	0.641434i	$-0.221660\pi$
$773$	1186.06			1.53436			0.767178	+	0.641434i	$0.221660\pi$
$774$		0			0
$775$	383.321	−	290.033i	0.494607	−	0.374236i
$776$	−2286.66	+	1320.20i	−2.94673	+	1.70129i
$777$		0			0
$778$	1272.12	+	734.456i	1.63511	+	0.944031i
$779$	214.820	+	124.026i	0.275763	+	0.159212i
$780$		0			0
$781$	357.207	+	618.701i	0.457371	+	0.792190i
$782$	−8.06559			−0.0103141
$783$		0			0
$784$	1598.77			2.03925
$785$	−41.4986	−	36.6424i	−0.0528645	−	0.0466783i
$786$		0			0
$787$	764.249	+	441.240i	0.971092	+	0.560660i	0.899569	−	0.436779i	$-0.143881\pi$
$787$	764.249	+	441.240i	0.971092	+	0.560660i	0.0715229	+	0.997439i	$0.477214\pi$
$788$	136.467	−	236.368i	0.173181	−	0.299959i
$789$		0			0
$790$	1406.73	−	1593.16i	1.78067	−	2.01666i
$791$		−	337.501i		−	0.426677i
$792$		0			0
$793$			377.823i			0.476448i
$794$	2190.58	−	1264.73i	2.75892	−	1.59286i
$795$		0			0
$796$	−738.295	+	1278.76i	−0.927507	+	1.60649i
$797$	71.9016	−	124.537i	0.0902153	−	0.156258i	−0.817386	−	0.576090i	$-0.804578\pi$
$797$	71.9016	−	124.537i	0.0902153	−	0.156258i	0.907602	+	0.419832i	$0.137911\pi$
$798$		0			0
$799$	−109.108	−	188.980i	−0.136556	−	0.236521i
$800$	1125.84	−	851.848i	1.40730	−	1.06481i
$801$		0			0
$802$		−	191.261i		−	0.238480i
$803$	−148.974	−	258.030i	−0.185521	−	0.321332i
$804$		0			0
$805$	1.30032	−	6.42348i	0.00161530	−	0.00797948i
$806$	−740.661	−	427.621i	−0.918934	−	0.530547i
$807$		0			0
$808$	1538.15	−	888.054i	1.90366	−	1.09908i
$809$		−	52.3078i		−	0.0646574i	−0.999477	−	0.0323287i	$-0.989708\pi$
$809$		−	52.3078i		−	0.0646574i	0.999477	−	0.0323287i	$-0.0102923\pi$
$810$		0			0
$811$	1518.65			1.87256			0.936281	−	0.351253i	$-0.114244\pi$
$811$	1518.65			1.87256			0.936281	+	0.351253i	$0.114244\pi$
$812$	−376.352	−	651.861i	−0.463488	−	0.802785i
$813$		0			0
$814$	−23.8956	+	41.3883i	−0.0293557	+	0.0508456i
$815$	−214.508	+	1059.66i	−0.263200	+	1.30019i
$816$		0			0
$817$	−322.422	+	186.151i	−0.394642	+	0.227847i
$818$	1000.35			1.22292
$819$		0			0
$820$	−1574.28	+	528.462i	−1.91985	+	0.644466i
$821$	−950.059	+	548.517i	−1.15720	+	0.668108i	−0.950631	−	0.310324i	$-0.899562\pi$
$821$	−950.059	+	548.517i	−1.15720	+	0.668108i	−0.206567	+	0.978432i	$0.566229\pi$
$822$		0			0
$823$	−828.873	−	478.550i	−1.00714	−	0.581470i	−0.0967841	−	0.995305i	$-0.530856\pi$
$823$	−828.873	−	478.550i	−1.00714	−	0.581470i	−0.910352	+	0.413835i	$0.864189\pi$
$824$	−730.568	−	421.793i	−0.886611	−	0.511885i
$825$		0			0
$826$	501.554	+	868.717i	0.607208	+	1.05172i
$827$	−171.626			−0.207529			−0.103764	−	0.994602i	$-0.533089\pi$
$827$	−171.626			−0.207529			−0.103764	+	0.994602i	$0.533089\pi$
$828$		0			0
$829$	203.896			0.245954			0.122977	−	0.992410i	$-0.460756\pi$
$829$	203.896			0.245954			0.122977	+	0.992410i	$0.460756\pi$
$830$	732.334	−	829.390i	0.882331	−	0.999265i
$831$		0			0
$832$	−599.976	−	346.397i	−0.721126	−	0.416342i
$833$	−90.8499	+	157.357i	−0.109063	+	0.188904i
$834$		0			0
$835$	205.008	−	232.178i	0.245519	−	0.278057i
$836$			676.059i			0.808683i
$837$		0			0
$838$		−	101.958i		−	0.121668i
$839$	1348.10	−	778.323i	1.60679	−	0.927680i	0.616705	−	0.787194i	$-0.288467\pi$
$839$	1348.10	−	778.323i	1.60679	−	0.927680i	0.990083	−	0.140486i	$-0.0448664\pi$
$840$		0			0
$841$	46.2156	−	80.0477i	0.0549531	−	0.0951816i
$842$	−806.087	+	1396.18i	−0.957347	+	1.65817i
$843$		0			0
$844$	−864.495	−	1497.35i	−1.02428	−	1.77411i
$845$	−37.3549	−	111.279i	−0.0442069	−	0.131692i
$846$		0			0
$847$		−	62.5654i		−	0.0738670i
$848$	−1633.04	−	2828.51i	−1.92576	−	3.33551i
$849$		0			0
$850$	48.9013	+	391.916i	0.0575310	+	0.461077i
$851$	−0.582966	−	0.336576i	−0.000685037	−	0.000395506i
$852$		0			0
$853$	488.377	−	281.964i	0.572540	−	0.330556i	−0.185623	−	0.982621i	$-0.559430\pi$
$853$	488.377	−	281.964i	0.572540	−	0.330556i	0.758163	+	0.652065i	$0.226097\pi$
$854$			296.497i			0.347186i
$855$		0			0
$856$	−34.2579			−0.0400209
$857$	−476.953	−	826.107i	−0.556538	−	0.963952i	−0.997782	−	0.0665649i	$-0.978796\pi$
$857$	−476.953	−	826.107i	−0.556538	−	0.963952i	0.441244	−	0.897387i	$-0.354537\pi$
$858$		0			0
$859$	−422.728	+	732.186i	−0.492116	+	0.852371i	−0.999959	−	0.00907936i	$-0.997110\pi$
$859$	−422.728	+	732.186i	−0.492116	+	0.852371i	0.507842	+	0.861450i	$0.330443\pi$
$860$	494.511	−	2442.86i	0.575013	−	2.84053i
$861$		0			0
$862$	173.587	−	100.221i	0.201377	−	0.116265i
$863$	−1109.42			−1.28554			−0.642768	−	0.766061i	$-0.722214\pi$
$863$	−1109.42			−1.28554			−0.642768	+	0.766061i	$0.722214\pi$
$864$		0			0
$865$	530.609	+	1580.67i	0.613420	+	1.82737i
$866$	−1681.02	+	970.538i	−1.94113	+	1.12071i
$867$		0			0
$868$	−410.233	−	236.848i	−0.472618	−	0.272866i
$869$	−981.388	−	566.605i	−1.12933	−	0.652019i
$870$		0			0
$871$	470.796	+	815.442i	0.540523	+	0.936214i
$872$	3067.06			3.51727
$873$		0			0
$874$	−13.4918			−0.0154369
$875$	−320.008	−	24.2385i	−0.365723	−	0.0277011i
$876$		0			0
$877$	−878.724	−	507.331i	−1.00197	−	0.578485i	−0.0931364	−	0.995653i	$-0.529689\pi$
$877$	−878.724	−	507.331i	−1.00197	−	0.578485i	−0.908829	+	0.417168i	$0.863023\pi$
$878$	−767.411	+	1329.19i	−0.874044	+	1.51389i
$879$		0			0
$880$	−1388.97	−	1226.43i	−1.57838	−	1.39368i
$881$		−	1226.86i		−	1.39257i	−0.717764	−	0.696287i	$-0.754834\pi$
$881$		−	1226.86i		−	1.39257i	0.717764	−	0.696287i	$-0.245166\pi$
$882$		0			0
$883$		−	659.407i		−	0.746780i	−0.927674	−	0.373390i	$-0.878195\pi$
$883$		−	659.407i		−	0.746780i	0.927674	−	0.373390i	$-0.121805\pi$
$884$	429.526	−	247.987i	0.485889	−	0.280528i
$885$		0			0
$886$	787.537	−	1364.05i	0.888868	−	1.53956i
$887$	385.984	−	668.543i	0.435156	−	0.753713i	−0.562152	−	0.827034i	$-0.690026\pi$
$887$	385.984	−	668.543i	0.435156	−	0.753713i	0.997308	+	0.0733209i	$0.0233597\pi$
$888$		0			0
$889$	−129.846	−	224.901i	−0.146059	−	0.252982i
$890$	1246.16	−	418.319i	1.40018	−	0.470021i
$891$		0			0
$892$		−	2067.01i		−	2.31727i
$893$	−182.512	−	316.120i	−0.204381	−	0.353998i
$894$		0			0
$895$	191.980	−	948.369i	0.214503	−	1.05963i
$896$	31.4123	+	18.1359i	0.0350584	+	0.0202410i
$897$		0			0
$898$	−755.945	+	436.445i	−0.841810	+	0.486019i
$899$		−	587.432i		−	0.653428i
$900$		0			0
$901$	371.189			0.411974
$902$	627.249	+	1086.43i	0.695398	+	1.20447i
$903$		0			0
$904$	1356.24	−	2349.08i	1.50027	−	2.59854i
$905$	1195.09	+	241.923i	1.32054	+	0.267318i
$906$		0			0
$907$	−105.197	+	60.7354i	−0.115983	+	0.0669629i	−0.556869	−	0.830600i	$-0.687998\pi$
$907$	−105.197	+	60.7354i	−0.115983	+	0.0669629i	0.440886	+	0.897563i	$0.354664\pi$
$908$	483.792			0.532810
$909$		0			0
$910$	181.711	+	541.314i	0.199683	+	0.594850i
$911$	1000.46	−	577.616i	1.09820	−	0.634046i	0.162453	−	0.986716i	$-0.448060\pi$
$911$	1000.46	−	577.616i	1.09820	−	0.634046i	0.935748	+	0.352670i	$0.114726\pi$
$912$		0			0
$913$	−510.904	−	294.971i	−0.559588	−	0.323078i
$914$	−2228.21	−	1286.46i	−2.43786	−	1.40750i
$915$		0			0
$916$	29.5895	+	51.2505i	0.0323029	+	0.0559503i
$917$	−220.275			−0.240212
$918$		0			0
$919$	−994.576			−1.08224			−0.541119	−	0.840946i	$-0.681999\pi$
$919$	−994.576			−1.08224			−0.541119	+	0.840946i	$0.681999\pi$
$920$	34.8631	−	39.4835i	0.0378947	−	0.0429168i
$921$		0			0
$922$	1225.43	+	707.501i	1.32910	+	0.767354i
$923$	438.358	−	759.258i	0.474927	−	0.822598i
$924$		0			0
$925$	−12.8201	+	30.3676i	−0.0138595	+	0.0328298i
$926$			995.977i			1.07557i
$927$		0			0
$928$		−	1725.33i		−	1.85919i
$929$	−140.236	+	80.9655i	−0.150954	+	0.0871534i	−0.573575	−	0.819153i	$-0.694444\pi$
$929$	−140.236	+	80.9655i	−0.150954	+	0.0871534i	0.422620	+	0.906307i	$0.361110\pi$
$930$		0			0
$931$	−151.970	+	263.221i	−0.163234	+	0.282729i
$932$	−252.056	+	436.574i	−0.270447	+	0.468427i
$933$		0			0
$934$	1434.26	+	2484.22i	1.53561	+	2.65976i
$935$	199.638	−	67.0156i	0.213517	−	0.0716745i
$936$		0			0
$937$		−	660.489i		−	0.704898i	−0.935831	−	0.352449i	$-0.885349\pi$
$937$		−	660.489i		−	0.704898i	0.935831	−	0.352449i	$-0.114651\pi$
$938$	369.457	+	639.919i	0.393878	+	0.682216i
$939$		0			0
$940$	2395.10	+	484.845i	2.54798	+	0.515792i
$941$	1378.06	+	795.624i	1.46446	+	0.845509i	0.999213	−	0.0396696i	$-0.0126305\pi$
$941$	1378.06	+	795.624i	1.46446	+	0.845509i	0.465252	+	0.885179i	$0.345964\pi$
$942$		0			0
$943$	−15.3026	+	8.83498i	−0.0162276	+	0.00936902i
$944$			3994.69i			4.23167i
$945$		0			0
$946$	−1882.88			−1.99035
$947$	781.678	+	1353.91i	0.825426	+	1.42968i	0.901594	+	0.432584i	$0.142398\pi$
$947$	781.678	+	1353.91i	0.825426	+	1.42968i	−0.0761680	+	0.997095i	$0.524269\pi$
$948$		0			0
$949$	−182.818	+	316.650i	−0.192643	+	0.333667i
$950$	81.8004	+	655.583i	0.0861057	+	0.690087i
$951$		0			0
$952$	196.566	−	113.488i	0.206477	−	0.119210i
$953$	−996.612			−1.04576			−0.522881	−	0.852405i	$-0.675143\pi$
$953$	−996.612			−1.04576			−0.522881	+	0.852405i	$0.675143\pi$
$954$		0			0
$955$	671.027	−	225.254i	0.702646	−	0.235868i
$956$	810.961	−	468.209i	0.848285	−	0.489758i
$957$		0			0
$958$	−231.719	−	133.783i	−0.241878	−	0.139648i
$959$	−155.031	−	89.5074i	−0.161659	−	0.0933341i
$960$		0			0
$961$	295.657	+	512.093i	0.307656	+	0.532875i
$962$	58.6484			0.0609651
$963$		0			0
$964$	−1369.63			−1.42078
$965$	829.896	+	732.781i	0.859996	+	0.759359i
$966$		0			0
$967$	562.916	+	325.000i	0.582126	+	0.336091i	0.761978	−	0.647603i	$-0.224229\pi$
$967$	562.916	+	325.000i	0.582126	+	0.336091i	−0.179852	+	0.983694i	$0.557562\pi$
$968$	251.418	−	435.468i	0.259729	−	0.449864i
$969$		0			0
$970$	1768.46	+	1561.51i	1.82315	+	1.60981i
$971$			1717.75i			1.76905i	0.466495	+	0.884524i	$0.345517\pi$
$971$			1717.75i			1.76905i	−0.466495	+	0.884524i	$0.654483\pi$
$972$		0			0
$973$		−	356.656i		−	0.366553i
$974$	−2329.45	+	1344.91i	−2.39163	+	1.38081i
$975$		0			0
$976$	−590.372	+	1022.55i	−0.604889	+	1.04770i
$977$	141.061	−	244.324i	0.144381	−	0.250076i	−0.784761	−	0.619799i	$-0.787214\pi$
$977$	141.061	−	244.324i	0.144381	−	0.250076i	0.929142	+	0.369723i	$0.120547\pi$
$978$		0			0
$979$	−350.439	−	606.979i	−0.357956	−	0.619998i
$980$	−647.530	−	1928.98i	−0.660745	−	1.96834i
$981$		0			0
$982$		−	14.0695i		−	0.0143274i
$983$	−192.267	−	333.017i	−0.195592	−	0.338776i	0.751502	−	0.659731i	$-0.229330\pi$
$983$	−192.267	−	333.017i	−0.195592	−	0.338776i	−0.947095	+	0.320955i	$0.895996\pi$
$984$		0			0
$985$	−139.385	−	28.2159i	−0.141508	−	0.0286456i
$986$	418.003	+	241.334i	0.423938	+	0.244761i
$987$		0			0
$988$	718.496	−	414.824i	0.727223	−	0.419862i
$989$		−	26.5208i		−	0.0268158i
$990$		0			0
$991$	399.250			0.402876			0.201438	−	0.979501i	$-0.435439\pi$
$991$	399.250			0.402876			0.201438	+	0.979501i	$0.435439\pi$
$992$	−542.898	−	940.326i	−0.547276	−	0.947910i
$993$		0			0
$994$	344.002	−	595.828i	0.346078	−	0.599425i
$995$	754.082	+	152.650i	0.757871	+	0.153417i
$996$		0			0
$997$	−1257.62	+	726.087i	−1.26140	+	0.728272i	−0.973346	−	0.229341i	$-0.926343\pi$
$997$	−1257.62	+	726.087i	−1.26140	+	0.728272i	−0.288058	+	0.957613i	$0.593009\pi$
$998$	−757.008			−0.758525
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.h.a.44.10		20
3.2	odd	2		45.3.h.a.14.1	✓	20
5.2	odd	4		675.3.j.e.476.1		20
5.3	odd	4		675.3.j.e.476.10		20
5.4	even	2	inner	135.3.h.a.44.1		20
9.2	odd	6	inner	135.3.h.a.89.1		20
9.4	even	3		405.3.d.a.404.1		20
9.5	odd	6		405.3.d.a.404.20		20
9.7	even	3		45.3.h.a.29.10	yes	20
15.2	even	4		225.3.j.e.176.10		20
15.8	even	4		225.3.j.e.176.1		20
15.14	odd	2		45.3.h.a.14.10	yes	20
45.2	even	12		675.3.j.e.251.1		20
45.4	even	6		405.3.d.a.404.19		20
45.7	odd	12		225.3.j.e.101.10		20
45.14	odd	6		405.3.d.a.404.2		20
45.29	odd	6	inner	135.3.h.a.89.10		20
45.34	even	6		45.3.h.a.29.1	yes	20
45.38	even	12		675.3.j.e.251.10		20
45.43	odd	12		225.3.j.e.101.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.h.a.14.1	✓	20	3.2	odd	2
45.3.h.a.14.10	yes	20	15.14	odd	2
45.3.h.a.29.1	yes	20	45.34	even	6
45.3.h.a.29.10	yes	20	9.7	even	3
135.3.h.a.44.1		20	5.4	even	2	inner
135.3.h.a.44.10		20	1.1	even	1	trivial
135.3.h.a.89.1		20	9.2	odd	6	inner
135.3.h.a.89.10		20	45.29	odd	6	inner
225.3.j.e.101.1		20	45.43	odd	12
225.3.j.e.101.10		20	45.7	odd	12
225.3.j.e.176.1		20	15.8	even	4
225.3.j.e.176.10		20	15.2	even	4
405.3.d.a.404.1		20	9.4	even	3
405.3.d.a.404.2		20	45.14	odd	6
405.3.d.a.404.19		20	45.4	even	6
405.3.d.a.404.20		20	9.5	odd	6
675.3.j.e.251.1		20	45.2	even	12
675.3.j.e.251.10		20	45.38	even	12
675.3.j.e.476.1		20	5.2	odd	4
675.3.j.e.476.10		20	5.3	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.84364 + 3.19328i) q^{2} +(-4.79800 + 8.31039i) q^{4} +(4.90060 + 0.992036i) q^{5} +(-2.22343 + 1.28370i) q^{7} -20.6340 q^{8} +(5.86709 + 17.4779i) q^{10} +(8.51311 - 4.91505i) q^{11} +(-10.4471 - 6.03166i) q^{13} +(-8.19840 - 4.73335i) q^{14} +(-18.8497 - 32.6486i) q^{16} +4.28451 q^{17} +7.16698 q^{19} +(-31.7573 + 35.9661i) q^{20} +(31.3902 + 18.1231i) q^{22} +(-0.255270 + 0.442140i) q^{23} +(23.0317 + 9.72314i) q^{25} -44.4808i q^{26} -24.6367i q^{28} +(26.4589 - 15.2761i) q^{29} +(9.61361 - 16.6513i) q^{31} +(28.2359 - 48.9060i) q^{32} +(7.89910 + 13.6816i) q^{34} +(-12.1696 + 4.08516i) q^{35} +1.31851i q^{37} +(13.2133 + 22.8862i) q^{38} +(-101.119 - 20.4697i) q^{40} +(29.9735 + 17.3052i) q^{41} +(-44.9872 + 25.9734i) q^{43} +94.3297i q^{44} -1.88250 q^{46} +(-25.4656 - 44.1078i) q^{47} +(-21.2042 + 36.7268i) q^{49} +(11.4135 + 91.4726i) q^{50} +(100.251 - 57.8799i) q^{52} +86.6349 q^{53} +(46.5953 - 15.6414i) q^{55} +(45.8783 - 26.4879i) q^{56} +(97.5613 + 56.3270i) q^{58} +(-91.7656 - 52.9809i) q^{59} +(-15.6600 - 27.1239i) q^{61} +70.8961 q^{62} +57.4297 q^{64} +(-45.2136 - 39.9227i) q^{65} +(-67.5968 - 39.0271i) q^{67} +(-20.5571 + 35.6060i) q^{68} +(-35.4814 - 31.3293i) q^{70} +72.6762i q^{71} -30.3097i q^{73} +(-4.21037 + 2.43086i) q^{74} +(-34.3872 + 59.5604i) q^{76} +(-12.6189 + 21.8565i) q^{77} +(-57.6398 - 99.8350i) q^{79} +(-59.9861 - 178.697i) q^{80} +127.618i q^{82} +(-30.0069 - 51.9734i) q^{83} +(20.9967 + 4.25039i) q^{85} +(-165.880 - 95.7710i) q^{86} +(-175.660 + 101.417i) q^{88} -71.2992i q^{89} +30.9713 q^{91} +(-2.44957 - 4.24278i) q^{92} +(93.8989 - 162.638i) q^{94} +(35.1225 + 7.10991i) q^{95} +(110.820 - 63.9819i) q^{97} -156.372 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 18 q^{4} + 12 q^{5} + 4 q^{10} + 24 q^{11} - 30 q^{14} - 26 q^{16} - 8 q^{19} - 144 q^{20} + 2 q^{25} + 114 q^{29} + 28 q^{31} - 4 q^{34} - 34 q^{40} - 102 q^{41} + 116 q^{46} - 40 q^{49} + 408 q^{50}+ \cdots + 762 q^{95}+O(q^{100}) \) 20 * q - 18 * q^4 + 12 * q^5 + 4 * q^10 + 24 * q^11 - 30 * q^14 - 26 * q^16 - 8 * q^19 - 144 * q^20 + 2 * q^25 + 114 * q^29 + 28 * q^31 - 4 * q^34 - 34 * q^40 - 102 * q^41 + 116 * q^46 - 40 * q^49 + 408 * q^50 + 36 * q^55 + 618 * q^56 - 120 * q^59 - 50 * q^61 + 140 * q^64 - 492 * q^65 - 54 * q^70 - 504 * q^74 - 96 * q^76 - 128 * q^79 - 74 * q^85 - 1488 * q^86 - 288 * q^91 + 218 * q^94 + 762 * q^95

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