LMFDB - Embedded newform 675.3.j.e.476.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,3,Mod(251,675)] 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("675.251"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	675.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,18,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$18.3924178443$
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:	$ 2^{2}\cdot 3^{12} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			476.10
Root			$0.961330 + 1.44078i$ of defining polynomial
Character	$\chi$	$=$	675.476
Dual form			675.3.j.e.251.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	3.19328	−	1.84364i	1.59664	−	0.921819i	0.604509	−	0.796599i	$-0.293369\pi$
$2$	3.19328	−	1.84364i	1.59664	−	0.921819i	0.992129	−	0.125221i	$-0.0399639\pi$
$3$		0			0
$3$		0			0
$4$	4.79800	−	8.31039i	1.19950	−	2.07760i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.28370	+	2.22343i	0.183385	+	0.317633i	0.943031	−	0.332704i	$-0.107961\pi$
$7$	1.28370	+	2.22343i	0.183385	+	0.317633i	−0.759646	+	0.650337i	$0.774628\pi$
$8$		−	20.6340i		−	2.57925i
$9$		0			0
$10$		0			0
$11$	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
$13$	6.03166	−	10.4471i	0.463974	−	0.803626i	−0.535181	−	0.844738i	$-0.679757\pi$
$13$	6.03166	−	10.4471i	0.463974	−	0.803626i	0.999155	+	0.0411114i	$0.0130898\pi$
$14$	8.19840	+	4.73335i	0.585600	+	0.338096i
$15$		0			0
$16$	−18.8497	−	32.6486i	−1.17810	−	2.04054i
$17$		−	4.28451i		−	0.252030i	−0.992028	−	0.126015i	$-0.959781\pi$
$17$		−	4.28451i		−	0.252030i	0.992028	−	0.126015i	$-0.0402188\pi$
$18$		0			0
$19$	−7.16698			−0.377210			−0.188605	−	0.982053i	$-0.560397\pi$
$19$	−7.16698			−0.377210			−0.188605	+	0.982053i	$0.560397\pi$
$20$		0			0
$21$		0			0
$22$	18.1231	−	31.3902i	0.823779	−	1.42683i
$23$	−0.442140	−	0.255270i	−0.0192235	−	0.0110987i	0.490357	−	0.871521i	$-0.336866\pi$
$23$	−0.442140	−	0.255270i	−0.0192235	−	0.0110987i	−0.509581	+	0.860423i	$0.670200\pi$
$24$		0			0
$25$		0			0
$26$		−	44.4808i		−	1.71080i
$27$		0			0
$28$	24.6367			0.879884
$29$	−26.4589	+	15.2761i	−0.912376	+	0.526760i	−0.881195	−	0.472753i	$-0.843260\pi$
$29$	−26.4589	+	15.2761i	−0.912376	+	0.526760i	−0.0311810	+	0.999514i	$0.509927\pi$
$30$		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	$0.0662986\pi$
$32$	−48.9060	−	28.2359i	−1.52831	−	0.882372i
$33$		0			0
$34$	−7.89910	−	13.6816i	−0.232326	−	0.402401i
$35$		0			0
$36$		0			0
$37$	1.31851			0.0356355			0.0178177	−	0.999841i	$-0.494328\pi$
$37$	1.31851			0.0356355			0.0178177	+	0.999841i	$0.494328\pi$
$38$	−22.8862	+	13.2133i	−0.602267	+	0.347719i
$39$		0			0
$40$		0			0
$41$	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
$43$	−25.9734	−	44.9872i	−0.604032	−	1.04621i	−0.992204	−	0.124627i	$-0.960227\pi$
$43$	−25.9734	−	44.9872i	−0.604032	−	1.04621i	0.388172	−	0.921587i	$-0.373107\pi$
$44$		−	94.3297i		−	2.14386i
$45$		0			0
$46$	−1.88250			−0.0409239
$47$	−44.1078	+	25.4656i	−0.938463	+	0.541822i	−0.889478	−	0.456977i	$-0.848932\pi$
$47$	−44.1078	+	25.4656i	−0.938463	+	0.541822i	−0.0489851	+	0.998800i	$0.515599\pi$
$48$		0			0
$49$	21.2042	−	36.7268i	0.432740	−	0.749527i
$50$		0			0
$51$		0			0
$52$	−57.8799	−	100.251i	−1.11307	−	1.92790i
$53$			86.6349i			1.63462i	0.576197	+	0.817311i	$0.304536\pi$
$53$			86.6349i			1.63462i	−0.576197	+	0.817311i	$0.695464\pi$
$54$		0			0
$55$		0			0
$56$	45.8783	−	26.4879i	0.819255	−	0.472997i
$57$		0			0
$58$	−56.3270	+	97.5613i	−0.971156	+	1.68209i
$59$	91.7656	+	52.9809i	1.55535	+	0.897982i	0.997691	+	0.0679111i	$0.0216334\pi$
$59$	91.7656	+	52.9809i	1.55535	+	0.897982i	0.557658	+	0.830071i	$0.311700\pi$
$60$		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	$0.915976\pi$
$62$		−	70.8961i		−	1.14348i
$63$		0			0
$64$	−57.4297			−0.897339
$65$		0			0
$66$		0			0
$67$	−39.0271	+	67.5968i	−0.582493	+	1.00891i	0.412689	+	0.910872i	$0.364589\pi$
$67$	−39.0271	+	67.5968i	−0.582493	+	1.00891i	−0.995183	+	0.0980363i	$0.968744\pi$
$68$	−35.6060	−	20.5571i	−0.523617	−	0.302311i
$69$		0			0
$70$		0			0
$71$			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
$73$	30.3097			0.415201			0.207601	−	0.978214i	$-0.433435\pi$
$73$	30.3097			0.415201			0.207601	+	0.978214i	$0.433435\pi$
$74$	4.21037	−	2.43086i	0.0568969	−	0.0328494i
$75$		0			0
$76$	−34.3872	+	59.5604i	−0.452463	+	0.783690i
$77$	21.8565	+	12.6189i	0.283851	+	0.163881i
$78$		0			0
$79$	57.6398	+	99.8350i	0.729617	+	1.26373i	0.957045	+	0.289940i	$0.0936352\pi$
$79$	57.6398	+	99.8350i	0.729617	+	1.26373i	−0.227428	+	0.973795i	$0.573031\pi$
$80$		0			0
$81$		0			0
$82$	127.618			1.55632
$83$	51.9734	−	30.0069i	0.626186	−	0.361529i	−0.153087	−	0.988213i	$-0.548922\pi$
$83$	51.9734	−	30.0069i	0.626186	−	0.361529i	0.779274	+	0.626684i	$0.215588\pi$
$84$		0			0
$85$		0			0
$86$	−165.880	−	95.7710i	−1.92884	−	1.11362i
$87$		0			0
$88$	−101.417	−	175.660i	−1.15247	−	1.99613i
$89$			71.2992i			0.801115i	0.916272	+	0.400558i	$0.131184\pi$
$89$			71.2992i			0.801115i	−0.916272	+	0.400558i	$0.868816\pi$
$90$		0			0
$91$	30.9713			0.340344
$92$	−4.24278	+	2.44957i	−0.0461171	+	0.0266257i
$93$		0			0
$94$	−93.8989	+	162.638i	−0.998924	+	1.73019i
$95$		0			0
$96$		0			0
$97$	−63.9819	−	110.820i	−0.659607	−	1.14247i	−0.980717	−	0.195431i	$-0.937389\pi$
$97$	−63.9819	−	110.820i	−0.659607	−	1.14247i	0.321111	−	0.947042i	$-0.395944\pi$
$98$		−	156.372i		−	1.59563i
$99$		0			0
$100$		0			0
$101$	−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
$103$	−20.4416	+	35.4060i	−0.198463	+	0.343747i	−0.948030	−	0.318181i	$-0.896928\pi$
$103$	−20.4416	+	35.4060i	−0.198463	+	0.343747i	0.749568	+	0.661928i	$0.230261\pi$
$104$	−215.567	−	124.457i	−2.07276	−	1.19671i
$105$		0			0
$106$	159.723	+	276.649i	1.50683	+	2.60990i
$107$		−	1.66026i		−	0.0155165i	−0.999970	−	0.00775823i	$-0.997530\pi$
$107$		−	1.66026i		−	0.0155165i	0.999970	−	0.00775823i	$-0.00246955\pi$
$108$		0			0
$109$	148.641			1.36368			0.681839	−	0.731502i	$-0.261180\pi$
$109$	148.641			1.36368			0.681839	+	0.731502i	$0.261180\pi$
$110$		0			0
$111$		0			0
$112$	48.3946	−	83.8218i	0.432094	−	0.748409i
$113$	−113.845	−	65.7284i	−1.00748	−	0.581667i	−0.0970249	−	0.995282i	$-0.530933\pi$
$113$	−113.845	−	65.7284i	−1.00748	−	0.581667i	−0.910452	+	0.413615i	$0.864266\pi$
$114$		0			0
$115$		0			0
$116$			293.178i			2.52740i
$117$		0			0
$118$	390.711			3.31111
$119$	9.52631	−	5.50002i	0.0800531	−	0.0462187i
$120$		0			0
$121$	−12.1846	+	21.1044i	−0.100699	+	0.174416i
$122$	−100.013	−	57.7428i	−0.819782	−	0.473301i
$123$		0			0
$124$	−92.2523	−	159.786i	−0.743970	−	1.28859i
$125$		0			0
$126$		0			0
$127$	101.150			0.796460			0.398230	−	0.917286i	$-0.369625\pi$
$127$	101.150			0.796460			0.398230	+	0.917286i	$0.369625\pi$
$128$	12.2351	−	7.06394i	0.0955867	−	0.0551870i
$129$		0			0
$130$		0			0
$131$	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
$133$	−9.20024	−	15.9353i	−0.0691747	−	0.119814i
$134$			287.807i			2.14781i
$135$		0			0
$136$	−88.4068			−0.650050
$137$	60.3847	−	34.8631i	0.440764	−	0.254475i	−0.263158	−	0.964753i	$-0.584764\pi$
$137$	60.3847	−	34.8631i	0.440764	−	0.254475i	0.703922	+	0.710278i	$0.251431\pi$
$138$		0			0
$139$	69.4587	−	120.306i	0.499703	−	0.865511i	−0.500297	−	0.865854i	$-0.666776\pi$
$139$	69.4587	−	120.306i	0.499703	−	0.865511i	1.00000		0.000342926i	$0.000109157\pi$
$140$		0			0
$141$		0			0
$142$	133.989	+	232.075i	0.943582	+	1.63433i
$143$		−	118.584i		−	0.829256i
$144$		0			0
$145$		0			0
$146$	96.7872	−	55.8801i	0.662926	−	0.382740i
$147$		0			0
$148$	6.32622	−	10.9573i	0.0427448	−	0.0740361i
$149$	41.3586	+	23.8784i	0.277574	+	0.160258i	0.632325	−	0.774703i	$-0.282101\pi$
$149$	41.3586	+	23.8784i	0.277574	+	0.160258i	−0.354750	+	0.934961i	$0.615434\pi$
$150$		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	$0.892156\pi$
$152$			147.884i			0.972920i
$153$		0			0
$154$	93.0585			0.604276
$155$		0			0
$156$		0			0
$157$	−5.53607	+	9.58875i	−0.0352616	+	0.0610749i	−0.883118	−	0.469152i	$-0.844560\pi$
$157$	−5.53607	+	9.58875i	−0.0352616	+	0.0610749i	0.847856	+	0.530226i	$0.177893\pi$
$158$	368.119	+	212.534i	2.32987	+	1.34515i
$159$		0			0
$160$		0			0
$161$		−	1.31076i		−	0.00814134i
$162$		0			0
$163$	−216.230			−1.32656			−0.663282	−	0.748370i	$-0.730837\pi$
$163$	−216.230			−1.32656			−0.663282	+	0.748370i	$0.730837\pi$
$164$	287.626	−	166.061i	1.75382	−	1.01257i
$165$		0			0
$166$	110.644	−	191.640i	0.666528	−	1.15446i
$167$	−53.6475	−	30.9734i	−0.321242	−	0.185469i	0.330704	−	0.943735i	$-0.392714\pi$
$167$	−53.6475	−	30.9734i	−0.321242	−	0.185469i	−0.651946	+	0.758265i	$0.726047\pi$
$168$		0			0
$169$	11.7382	+	20.3311i	0.0694567	+	0.120302i
$170$		0			0
$171$		0			0
$172$	−498.481			−2.89815
$173$	−288.794	+	166.735i	−1.66933	+	0.963788i	−0.701330	+	0.712837i	$0.747410\pi$
$173$	−288.794	+	166.735i	−1.66933	+	0.963788i	−0.968000	+	0.250951i	$0.919257\pi$
$174$		0			0
$175$		0			0
$176$	−320.939	−	185.294i	−1.82352	−	1.05281i
$177$		0			0
$178$	131.450	+	227.678i	0.738483	+	1.27909i
$179$			193.521i			1.08112i	0.841304	+	0.540562i	$0.181788\pi$
$179$			193.521i			1.08112i	−0.841304	+	0.540562i	$0.818212\pi$
$180$		0			0
$181$	243.865			1.34732			0.673661	−	0.739041i	$-0.264721\pi$
$181$	243.865			1.34732			0.673661	+	0.739041i	$0.264721\pi$
$182$	98.8999	−	57.0999i	0.543406	−	0.313736i
$183$		0			0
$184$	−5.26724	+	9.12313i	−0.0286263	+	0.0495822i
$185$		0			0
$186$		0			0
$187$	−21.0586	−	36.4746i	−0.112613	−	0.195051i
$188$			488.737i			2.59966i
$189$		0			0
$190$		0			0
$191$	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
$193$	−110.711	+	191.757i	−0.573633	+	0.993561i	0.422556	+	0.906337i	$0.361133\pi$
$193$	−110.711	+	191.757i	−0.573633	+	0.993561i	−0.996189	+	0.0872244i	$0.972200\pi$
$194$	−408.623	−	235.919i	−2.10631	−	1.21608i
$195$		0			0
$196$	−203.476	−	352.431i	−1.03814	−	1.79812i
$197$			28.4424i			0.144378i	0.997391	+	0.0721889i	$0.0229984\pi$
$197$			28.4424i			0.144378i	−0.997391	+	0.0721889i	$0.977002\pi$
$198$		0			0
$199$	−153.875			−0.773244			−0.386622	−	0.922238i	$-0.626358\pi$
$199$	−153.875			−0.773244			−0.386622	+	0.922238i	$0.626358\pi$
$200$		0			0
$201$		0			0
$202$	−158.694	+	274.866i	−0.785615	+	1.36072i
$203$	−67.9304	−	39.2197i	−0.334633	−	0.193200i
$204$		0			0
$205$		0			0
$206$			150.748i			0.731786i
$207$		0			0
$208$	−454.779			−2.18644
$209$	−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	$0.307083\pi$
$212$	719.970	+	415.675i	3.39608	+	1.96073i
$213$		0			0
$214$	−3.06092	−	5.30167i	−0.0143034	−	0.0247742i
$215$		0			0
$216$		0			0
$217$	49.3638			0.227483
$218$	474.651	−	274.040i	2.17730	−	1.25706i
$219$		0			0
$220$		0			0
$221$	−44.7609	−	25.8427i	−0.202538	−	0.116935i
$222$		0			0
$223$	−107.701	−	186.544i	−0.482966	−	0.836521i	0.516843	−	0.856080i	$-0.327107\pi$
$223$	−107.701	−	186.544i	−0.482966	−	0.836521i	−0.999809	+	0.0195592i	$0.993774\pi$
$224$		−	144.985i		−	0.647256i
$225$		0			0
$226$	−484.717			−2.14477
$227$	−43.6615	+	25.2080i	−0.192341	+	0.111048i	−0.593078	−	0.805145i	$-0.702088\pi$
$227$	−43.6615	+	25.2080i	−0.192341	+	0.111048i	0.400737	+	0.916193i	$0.368754\pi$
$228$		0			0
$229$	−3.08352	+	5.34081i	−0.0134652	+	0.0233223i	−0.872679	−	0.488294i	$-0.837620\pi$
$229$	−3.08352	+	5.34081i	−0.0134652	+	0.0233223i	0.859214	+	0.511616i	$0.170953\pi$
$230$		0			0
$231$		0			0
$232$	315.207	+	545.954i	1.35865	+	2.35325i
$233$			52.5336i			0.225466i	0.993625	+	0.112733i	$0.0359605\pi$
$233$			52.5336i			0.225466i	−0.993625	+	0.112733i	$0.964040\pi$
$234$		0			0
$235$		0			0
$236$	880.584	−	508.405i	3.73129	−	2.15426i
$237$		0			0
$238$	20.2801	−	35.1262i	0.0852105	−	0.147589i
$239$	84.5102	+	48.7920i	0.353599	+	0.204151i	0.666269	−	0.745711i	$-0.267890\pi$
$239$	84.5102	+	48.7920i	0.353599	+	0.204151i	−0.312670	+	0.949862i	$0.601223\pi$
$240$		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	$0.737641\pi$
$242$			89.8560i			0.371306i
$243$		0			0
$244$	−300.547			−1.23175
$245$		0			0
$246$		0			0
$247$	−43.2288	+	74.8745i	−0.175015	+	0.303136i
$248$	−343.583	−	198.367i	−1.38541	−	0.799869i
$249$		0			0
$250$		0			0
$251$		−	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
$253$	−5.01865			−0.0198366
$254$	323.001	−	186.485i	1.27166	−	0.734192i
$255$		0			0
$256$	140.906	−	244.057i	0.550415	−	0.953346i
$257$	−123.613	−	71.3682i	−0.480986	−	0.277697i	0.239841	−	0.970812i	$-0.422905\pi$
$257$	−123.613	−	71.3682i	−0.480986	−	0.277697i	−0.720827	+	0.693115i	$0.756238\pi$
$258$		0			0
$259$	1.69257	+	2.93162i	0.00653502	+	0.0113190i
$260$		0			0
$261$		0			0
$262$	316.357			1.20747
$263$	−218.644	+	126.234i	−0.831347	+	0.479979i	−0.854314	−	0.519758i	$-0.826022\pi$
$263$	−218.644	+	126.234i	−0.831347	+	0.479979i	0.0229665	+	0.999736i	$0.492689\pi$
$264$		0			0
$265$		0			0
$266$	−58.7578	−	33.9238i	−0.220894	−	0.127533i
$267$		0			0
$268$	374.504	+	648.660i	1.39740	+	2.42037i
$269$		−	388.672i		−	1.44488i	−0.691435	−	0.722439i	$-0.743021\pi$
$269$		−	388.672i		−	1.44488i	0.691435	−	0.722439i	$-0.256979\pi$
$270$		0			0
$271$	−163.253			−0.602410			−0.301205	−	0.953559i	$-0.597389\pi$
$271$	−163.253			−0.602410			−0.301205	+	0.953559i	$0.597389\pi$
$272$	−139.883	+	80.7617i	−0.514277	+	0.296918i
$273$		0			0
$274$	128.550	−	222.655i	0.469160	−	0.812610i
$275$		0			0
$276$		0			0
$277$	−241.912	−	419.003i	−0.873328	−	1.51265i	−0.858534	−	0.512757i	$-0.828624\pi$
$277$	−241.912	−	419.003i	−0.873328	−	1.51265i	−0.0147939	−	0.999891i	$-0.504709\pi$
$278$		−	512.227i		−	1.84254i
$279$		0			0
$280$		0			0
$281$	−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
$283$	245.898	−	425.908i	0.868898	−	1.50498i	0.00577475	−	0.999983i	$-0.498162\pi$
$283$	245.898	−	425.908i	0.868898	−	1.50498i	0.863124	−	0.504993i	$-0.168505\pi$
$284$	603.967	+	348.701i	2.12664	+	1.22782i
$285$		0			0
$286$	−218.625	−	378.670i	−0.764424	−	1.32402i
$287$			88.8586i			0.309612i
$288$		0			0
$289$	270.643			0.936481
$290$		0			0
$291$		0			0
$292$	145.426	−	251.885i	0.498034	−	0.862621i
$293$	278.986	+	161.073i	0.952172	+	0.549737i	0.893755	−	0.448555i	$-0.148061\pi$
$293$	278.986	+	161.073i	0.952172	+	0.549737i	0.0584171	+	0.998292i	$0.481395\pi$
$294$		0			0
$295$		0			0
$296$		−	27.2062i		−	0.0919129i
$297$		0			0
$298$	176.092			0.590914
$299$	−5.33367	+	3.07940i	−0.0178384	+	0.0102990i
$300$		0			0
$301$	66.6839	−	115.500i	0.221541	−	0.383720i
$302$	−177.199	−	102.306i	−0.586752	−	0.338762i
$303$		0			0
$304$	135.095	+	233.992i	0.444392	+	0.769710i
$305$		0			0
$306$		0			0
$307$	426.031			1.38772			0.693861	−	0.720109i	$-0.255908\pi$
$307$	426.031			1.38772			0.693861	+	0.720109i	$0.255908\pi$
$308$	209.735	−	121.091i	0.680959	−	0.393152i
$309$		0			0
$310$		0			0
$311$	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
$313$	−130.475	−	225.989i	−0.416852	−	0.722009i	0.578769	−	0.815492i	$-0.303533\pi$
$313$	−130.475	−	225.989i	−0.416852	−	0.722009i	−0.995621	+	0.0934824i	$0.970200\pi$
$314$			40.8260i			0.130019i
$315$		0			0
$316$	1106.22			3.50071
$317$	−113.480	+	65.5178i	−0.357981	+	0.206681i	−0.668195	−	0.743986i	$-0.732933\pi$
$317$	−113.480	+	65.5178i	−0.357981	+	0.206681i	0.310213	+	0.950667i	$0.399599\pi$
$318$		0			0
$319$	−150.165	+	260.094i	−0.470737	+	0.815340i
$320$		0			0
$321$		0			0
$322$	−2.41656	−	4.18560i	−0.00750484	−	0.0129988i
$323$			30.7071i			0.0950683i
$324$		0			0
$325$		0			0
$326$	−690.482	+	398.650i	−2.11804	+	1.22285i
$327$		0			0
$328$	357.076	−	618.474i	1.08865	−	1.88559i
$329$	−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	$0.927745\pi$
$332$		−	575.893i		−	1.73462i
$333$		0			0
$334$	−228.415			−0.683877
$335$		0			0
$336$		0			0
$337$	−231.798	+	401.485i	−0.687827	+	1.19135i	0.284712	+	0.958613i	$0.408102\pi$
$337$	−231.798	+	401.485i	−0.687827	+	1.19135i	−0.972539	+	0.232738i	$0.925231\pi$
$338$	74.9664	+	43.2819i	0.221794	+	0.128053i
$339$		0			0
$340$		0			0
$341$		−	189.005i		−	0.554268i
$342$		0			0
$343$	234.682			0.684203
$344$	−928.267	+	535.935i	−2.69845	+	1.55795i
$345$		0			0
$346$	−614.799	+	1064.86i	−1.77688	+	3.07764i
$347$	−8.41662	−	4.85934i	−0.0242554	−	0.0140039i	0.487823	−	0.872942i	$-0.337791\pi$
$347$	−8.41662	−	4.85934i	−0.0242554	−	0.0140039i	−0.512079	+	0.858939i	$0.671124\pi$
$348$		0			0
$349$	−24.6679	−	42.7260i	−0.0706816	−	0.122424i	0.828519	−	0.559962i	$-0.189184\pi$
$349$	−24.6679	−	42.7260i	−0.0706816	−	0.122424i	−0.899200	+	0.437537i	$0.855851\pi$
$350$		0			0
$351$		0			0
$352$	−555.123			−1.57705
$353$	−82.5859	+	47.6810i	−0.233954	+	0.135074i	−0.612395	−	0.790552i	$-0.709794\pi$
$353$	−82.5859	+	47.6810i	−0.233954	+	0.135074i	0.378441	+	0.925626i	$0.376460\pi$
$354$		0			0
$355$		0			0
$356$	592.524	+	342.094i	1.66439	+	0.960938i
$357$		0			0
$358$	356.783	+	617.966i	0.996600	+	1.72616i
$359$		−	539.284i		−	1.50219i	−0.660197	−	0.751093i	$-0.729527\pi$
$359$		−	539.284i		−	1.50219i	0.660197	−	0.751093i	$-0.270473\pi$
$360$		0			0
$361$	−309.634			−0.857713
$362$	778.729	−	449.599i	2.15118	−	1.24199i
$363$		0			0
$364$	148.600	−	257.383i	0.408243	−	0.707098i
$365$		0			0
$366$		0			0
$367$	−151.544	−	262.482i	−0.412927	−	0.715211i	0.582281	−	0.812987i	$-0.302160\pi$
$367$	−151.544	−	262.482i	−0.412927	−	0.715211i	−0.995208	+	0.0977766i	$0.968827\pi$
$368$			19.2470i			0.0523016i
$369$		0			0
$370$		0			0
$371$	−192.627	+	111.213i	−0.519209	+	0.299766i
$372$		0			0
$373$	−65.3325	+	113.159i	−0.175154	+	0.303376i	−0.940215	−	0.340582i	$-0.889376\pi$
$373$	−65.3325	+	113.159i	−0.175154	+	0.303376i	0.765060	+	0.643959i	$0.222709\pi$
$374$	−134.492	−	77.6489i	−0.359604	−	0.207617i
$375$		0			0
$376$	525.459	+	910.121i	1.39750	+	2.42054i
$377$			368.560i			0.977612i
$378$		0			0
$379$	−545.141			−1.43837			−0.719183	−	0.694821i	$-0.755484\pi$
$379$	−545.141			−1.43837			−0.719183	+	0.694821i	$0.755484\pi$
$380$		0			0
$381$		0			0
$382$	260.995	−	452.056i	0.683232	−	1.18339i
$383$	−1.07950	−	0.623248i	−0.00281853	−	0.00162728i	0.498590	−	0.866838i	$-0.333851\pi$
$383$	−1.07950	−	0.623248i	−0.00281853	−	0.00162728i	−0.501409	+	0.865211i	$0.667185\pi$
$384$		0			0
$385$		0			0
$386$			816.445i			2.11514i
$387$		0			0
$388$	−1227.94			−3.16480
$389$	−345.001	+	199.187i	−0.886893	+	0.512048i	−0.872925	−	0.487855i	$-0.837780\pi$
$389$	−345.001	+	199.187i	−0.886893	+	0.512048i	−0.0139679	+	0.999902i	$0.504446\pi$
$390$		0			0
$391$	−1.09371	+	1.89435i	−0.00279720	+	0.00484490i
$392$	−757.822	−	437.529i	−1.93322	−	1.11615i
$393$		0			0
$394$	52.4376	+	90.8245i	0.133090	+	0.230519i
$395$		0			0
$396$		0			0
$397$	−685.998			−1.72795			−0.863977	−	0.503531i	$-0.832034\pi$
$397$	−685.998			−1.72795			−0.863977	+	0.503531i	$0.832034\pi$
$398$	−491.367	+	283.691i	−1.23459	+	0.712791i
$399$		0			0
$400$		0			0
$401$	−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
$403$	−115.972	−	200.869i	−0.287772	−	0.498435i
$404$			825.992i			2.04453i
$405$		0			0
$406$	−289.227			−0.712383
$407$	11.2246	−	6.48055i	0.0275790	−	0.0159227i
$408$		0			0
$409$	−135.648	+	234.950i	−0.331658	+	0.574449i	−0.982837	−	0.184475i	$-0.940941\pi$
$409$	−135.648	+	234.950i	−0.331658	+	0.574449i	0.651179	+	0.758924i	$0.274275\pi$
$410$		0			0
$411$		0			0
$412$	196.158	+	339.756i	0.476112	+	0.824650i
$413$			272.046i			0.658707i
$414$		0			0
$415$		0			0
$416$	−589.969	+	340.619i	−1.41819	+	0.818795i
$417$		0			0
$418$	−129.888	+	224.973i	−0.310738	+	0.538213i
$419$	23.9467	+	13.8256i	0.0571520	+	0.0329967i	0.528304	−	0.849055i	$-0.322828\pi$
$419$	23.9467	+	13.8256i	0.0571520	+	0.0329967i	−0.471152	+	0.882052i	$0.656162\pi$
$420$		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	$0.659537\pi$
$422$			664.367i			1.57433i
$423$		0			0
$424$	1787.63			4.21610
$425$		0			0
$426$		0			0
$427$	40.2054	−	69.6378i	0.0941579	−	0.163086i
$428$	−13.7974	−	7.96594i	−0.0322369	−	0.0186120i
$429$		0			0
$430$		0			0
$431$		−	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
$433$	−526.426			−1.21576			−0.607882	−	0.794028i	$-0.707981\pi$
$433$	−526.426			−1.21576			−0.607882	+	0.794028i	$0.707981\pi$
$434$	157.632	−	91.0091i	0.363208	−	0.209698i
$435$		0			0
$436$	713.180	−	1235.26i	1.63573	−	2.83317i
$437$	3.16881	+	1.82951i	0.00725128	+	0.00418653i
$438$		0			0
$439$	−208.124	−	360.481i	−0.474087	−	0.821142i	0.525473	−	0.850810i	$-0.323888\pi$
$439$	−208.124	−	360.481i	−0.474087	−	0.821142i	−0.999560	+	0.0296681i	$0.990555\pi$
$440$		0			0
$441$		0			0
$442$	−190.579			−0.431173
$443$	369.935	−	213.582i	0.835069	−	0.482127i	−0.0205163	−	0.999790i	$-0.506531\pi$
$443$	369.935	−	213.582i	0.835069	−	0.482127i	0.855585	+	0.517662i	$0.173198\pi$
$444$		0			0
$445$		0			0
$446$	−687.840	−	397.125i	−1.54224	−	0.890414i
$447$		0			0
$448$	−73.7224	−	127.691i	−0.164559	−	0.285024i
$449$		−	236.730i		−	0.527239i	−0.964627	−	0.263620i	$-0.915084\pi$
$449$		−	236.730i		−	0.527239i	0.964627	−	0.263620i	$-0.0849164\pi$
$450$		0			0
$451$	340.224			0.754376
$452$	−1092.46	+	630.730i	−2.41694	+	1.39542i
$453$		0			0
$454$	−92.9488	+	160.992i	−0.204733	+	0.354608i
$455$		0			0
$456$		0			0
$457$	348.891	+	604.296i	0.763437	+	1.32231i	0.941069	+	0.338214i	$0.109823\pi$
$457$	348.891	+	604.296i	0.763437	+	1.32231i	−0.177633	+	0.984097i	$0.556844\pi$
$458$			22.7396i			0.0496497i
$459$		0			0
$460$		0			0
$461$	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
$463$	−135.056	+	233.924i	−0.291698	+	0.505235i	−0.974211	−	0.225638i	$-0.927553\pi$
$463$	−135.056	+	233.924i	−0.291698	+	0.505235i	0.682514	+	0.730873i	$0.260887\pi$
$464$	997.483	+	575.897i	2.14975	+	1.24116i
$465$		0			0
$466$	96.8529	+	167.754i	0.207839	+	0.359987i
$467$		−	777.952i		−	1.66585i	−0.553385	−	0.832926i	$-0.686664\pi$
$467$		−	777.952i		−	1.66585i	0.553385	−	0.832926i	$-0.313336\pi$
$468$		0			0
$469$	−200.396			−0.427283
$470$		0			0
$471$		0			0
$472$	1093.21	−	1893.50i	2.31612	−	4.01164i
$473$	−442.228	−	255.321i	−0.934943	−	0.539790i
$474$		0			0
$475$		0			0
$476$		−	105.556i		−	0.221757i
$477$		0			0
$478$	359.819			0.752760
$479$	62.8429	−	36.2824i	0.131196	−	0.0757460i	−0.432966	−	0.901410i	$-0.642533\pi$
$479$	62.8429	−	36.2824i	0.131196	−	0.0757460i	0.564162	+	0.825664i	$0.309200\pi$
$480$		0			0
$481$	7.95281	−	13.7747i	0.0165339	−	0.0286376i
$482$	455.774	+	263.141i	0.945590	+	0.545936i
$483$		0			0
$484$	116.924	+	202.518i	0.241578	+	0.418425i
$485$		0			0
$486$		0			0
$487$	729.487			1.49792			0.748959	−	0.662616i	$-0.230554\pi$
$487$	729.487			1.49792			0.748959	+	0.662616i	$0.230554\pi$
$488$	−559.676	+	323.129i	−1.14688	+	0.662150i
$489$		0			0
$490$		0			0
$491$	−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
$493$	65.4505	+	113.364i	0.132760	+	0.229946i
$494$			318.793i			0.645330i
$495$		0			0
$496$	−724.853			−1.46140
$497$	−161.590	+	93.2942i	−0.325131	+	0.187715i
$498$		0			0
$499$	102.651	−	177.797i	0.205714	−	0.356307i	−0.744646	−	0.667460i	$-0.767382\pi$
$499$	102.651	−	177.797i	0.205714	−	0.356307i	0.950360	+	0.311152i	$0.100715\pi$
$500$		0			0
$501$		0			0
$502$	−469.448	−	813.107i	−0.935155	−	1.61974i
$503$			224.016i			0.445360i	0.974892	+	0.222680i	$0.0714806\pi$
$503$			224.016i			0.445360i	−0.974892	+	0.222680i	$0.928519\pi$
$504$		0			0
$505$		0			0
$506$	−16.0259	+	9.25257i	−0.0316718	+	0.0182857i
$507$		0			0
$508$	485.320	−	840.599i	0.955354	−	1.65472i
$509$	−399.073	−	230.405i	−0.784033	−	0.452662i	0.0538245	−	0.998550i	$-0.482859\pi$
$509$	−399.073	−	230.405i	−0.784033	−	0.452662i	−0.837858	+	0.545889i	$0.816192\pi$
$510$		0			0
$511$	38.9085	+	67.3915i	0.0761418	+	0.131882i
$512$		−	982.608i		−	1.91916i
$513$		0			0
$514$	−526.309			−1.02395
$515$		0			0
$516$		0			0
$517$	−250.330	+	433.584i	−0.484197	+	0.838653i
$518$	10.8097	+	6.24097i	0.0208681	+	0.0120482i
$519$		0			0
$520$		0			0
$521$		−	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
$523$	431.339			0.824741			0.412370	−	0.911016i	$-0.364701\pi$
$523$	431.339			0.824741			0.412370	+	0.911016i	$0.364701\pi$
$524$	713.006	−	411.654i	1.36070	−	0.785599i
$525$		0			0
$526$	−465.461	+	806.202i	−0.884907	+	1.53270i
$527$	−71.3426	−	41.1896i	−0.135375	−	0.0781587i
$528$		0			0
$529$	−264.370	−	457.902i	−0.499754	−	0.865599i
$530$		0			0
$531$		0			0
$532$	−176.571			−0.331901
$533$	361.580	−	208.758i	0.678386	−	0.391666i
$534$		0			0
$535$		0			0
$536$	1394.80	+	805.285i	2.60223	+	1.50240i
$537$		0			0
$538$	−716.571	−	1241.14i	−1.33192	−	2.30695i
$539$		−	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	$0.705099\pi$
$542$	−521.312	+	300.980i	−0.961830	+	0.555313i
$543$		0			0
$544$	−120.977	+	209.539i	−0.222384	+	0.385181i
$545$		0			0
$546$		0			0
$547$	−212.658	−	368.334i	−0.388771	−	0.673371i	0.603513	−	0.797353i	$-0.293767\pi$
$547$	−212.658	−	368.334i	−0.388771	−	0.673371i	−0.992285	+	0.123982i	$0.960434\pi$
$548$		−	669.094i		−	1.22097i
$549$		0			0
$550$		0			0
$551$	189.631	−	109.483i	0.344157	−	0.198699i
$552$		0			0
$553$	−147.984	+	256.316i	−0.267602	+	0.463501i
$554$	−1544.98	−	891.995i	−2.78878	−	1.61010i
$555$		0			0
$556$	−666.526	−	1154.46i	−1.19879	−	2.07636i
$557$			325.885i			0.585073i	0.956254	+	0.292536i	$0.0944992\pi$
$557$			325.885i			0.585073i	−0.956254	+	0.292536i	$0.905501\pi$
$558$		0			0
$559$	−626.650			−1.12102
$560$		0			0
$561$		0			0
$562$	−493.464	+	854.705i	−0.878050	+	1.52083i
$563$	−612.075	−	353.382i	−1.08717	−	0.627676i	−0.154346	−	0.988017i	$-0.549327\pi$
$563$	−612.075	−	353.382i	−1.08717	−	0.627676i	−0.932821	+	0.360341i	$0.882660\pi$
$564$		0			0
$565$		0			0
$566$		−	1813.39i		−	3.20387i
$567$		0			0
$568$	1499.60			2.64015
$569$	−485.178	+	280.118i	−0.852686	+	0.492299i	−0.861556	−	0.507662i	$-0.830510\pi$
$569$	−485.178	+	280.118i	−0.852686	+	0.492299i	0.00887015	+	0.999961i	$0.497177\pi$
$570$		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	$0.107602\pi$
$572$	−985.475	−	568.965i	−1.72286	−	0.994693i
$573$		0			0
$574$	163.823	+	283.750i	0.285406	+	0.494338i
$575$		0			0
$576$		0			0
$577$	502.258			0.870464			0.435232	−	0.900318i	$-0.356666\pi$
$577$	502.258			0.870464			0.435232	+	0.900318i	$0.356666\pi$
$578$	864.237	−	498.968i	1.49522	−	0.863266i
$579$		0			0
$580$		0			0
$581$	133.436	+	77.0395i	0.229667	+	0.132598i
$582$		0			0
$583$	425.815	+	737.533i	0.730386	+	1.26507i
$584$		−	625.411i		−	1.07091i
$585$		0			0
$586$	1187.84			2.02703
$587$	354.873	−	204.886i	0.604554	−	0.349040i	−0.166277	−	0.986079i	$-0.553175\pi$
$587$	354.873	−	204.886i	0.604554	−	0.349040i	0.770831	+	0.637040i	$0.219841\pi$
$588$		0			0
$589$	−68.9006	+	119.339i	−0.116979	+	0.202613i
$590$		0			0
$591$		0			0
$592$	−24.8535	−	43.0476i	−0.0419823	−	0.0727155i
$593$		−	944.139i		−	1.59214i	−0.605204	−	0.796070i	$-0.706908\pi$
$593$		−	944.139i		−	1.59214i	0.605204	−	0.796070i	$-0.293092\pi$
$594$		0			0
$595$		0			0
$596$	396.877	−	229.137i	0.665902	−	0.384458i
$597$		0			0
$598$	−11.3546	+	19.6667i	−0.0189876	+	0.0328875i
$599$	461.021	+	266.171i	0.769652	+	0.444359i	0.832750	−	0.553649i	$-0.186765\pi$
$599$	461.021	+	266.171i	0.769652	+	0.444359i	−0.0630986	+	0.998007i	$0.520098\pi$
$600$		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	$0.974440\pi$
$602$		−	491.764i		−	0.816883i
$603$		0			0
$604$	−532.496			−0.881615
$605$		0			0
$606$		0			0
$607$	85.5764	−	148.223i	0.140983	−	0.244189i	−0.786884	−	0.617101i	$-0.788307\pi$
$607$	85.5764	−	148.223i	0.140983	−	0.244189i	0.927867	+	0.372912i	$0.121640\pi$
$608$	350.509	+	202.366i	0.576494	+	0.332839i
$609$		0			0
$610$		0			0
$611$			614.400i			1.00557i
$612$		0			0
$613$	875.826			1.42875			0.714377	−	0.699761i	$-0.246710\pi$
$613$	875.826			1.42875			0.714377	+	0.699761i	$0.246710\pi$
$614$	1360.43	−	785.447i	2.21569	−	1.27923i
$615$		0			0
$616$	260.378	−	450.988i	0.422692	−	0.732124i
$617$	980.122	+	565.874i	1.58853	+	0.917137i	0.993550	+	0.113396i	$0.0361728\pi$
$617$	980.122	+	565.874i	1.58853	+	0.917137i	0.594978	+	0.803742i	$0.297161\pi$
$618$		0			0
$619$	260.187	+	450.658i	0.420335	+	0.728042i	0.995972	−	0.0896637i	$-0.0285792\pi$
$619$	260.187	+	450.658i	0.420335	+	0.728042i	−0.575637	+	0.817705i	$0.695246\pi$
$620$		0			0
$621$		0			0
$622$	4.30664			0.00692386
$623$	−158.529	+	91.5266i	−0.254460	+	0.146913i
$624$		0			0
$625$		0			0
$626$	−833.284	−	481.097i	−1.33112	−	0.768525i
$627$		0			0
$628$	53.1242	+	92.0138i	0.0845926	+	0.146519i
$629$		−	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	$0.659857\pi$
$632$	2060.00	−	1189.34i	3.25949	−	1.88187i
$633$		0			0
$634$	−241.582	+	418.433i	−0.381044	+	0.659988i
$635$		0			0
$636$		0			0
$637$	−255.794	−	443.047i	−0.401560	−	0.695522i
$638$			1107.40i			1.73574i
$639$		0			0
$640$		0			0
$641$	−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
$643$	−398.761	+	690.674i	−0.620157	+	1.07414i	0.369299	+	0.929311i	$0.379598\pi$
$643$	−398.761	+	690.674i	−0.620157	+	1.07414i	−0.989456	+	0.144833i	$0.953736\pi$
$644$	−10.8929	−	6.28901i	−0.0169144	−	0.00976554i
$645$		0			0
$646$	56.6127	+	98.0561i	0.0876357	+	0.151790i
$647$		−	849.489i		−	1.31297i	−0.754341	−	0.656483i	$-0.772043\pi$
$647$		−	849.489i		−	1.31297i	0.754341	−	0.656483i	$-0.227957\pi$
$648$		0			0
$649$	1041.61			1.60495
$650$		0			0
$651$		0			0
$652$	−1037.47	+	1796.95i	−1.59122	+	2.75607i
$653$	901.696	+	520.594i	1.38085	+	0.797235i	0.992260	−	0.124175i	$-0.0396285\pi$
$653$	901.696	+	520.594i	1.38085	+	0.797235i	0.388591	+	0.921410i	$0.372962\pi$
$654$		0			0
$655$		0			0
$656$		−	1304.79i		−	1.98901i
$657$		0			0
$658$	−482.151			−0.732752
$659$	556.318	−	321.190i	0.844185	−	0.487390i	−0.0144997	−	0.999895i	$-0.504616\pi$
$659$	556.318	−	321.190i	0.844185	−	0.487390i	0.858685	+	0.512505i	$0.171282\pi$
$660$		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	$-0.0370591\pi$
$662$	−617.847	−	356.714i	−0.933304	−	0.538843i
$663$		0			0
$664$	−619.163	−	1072.42i	−0.932474	−	1.61509i
$665$		0			0
$666$		0			0
$667$	15.5980			0.0233854
$668$	−514.802	+	297.221i	−0.770661	+	0.444941i
$669$		0			0
$670$		0			0
$671$	−266.631	−	153.939i	−0.397363	−	0.229418i
$672$		0			0
$673$	−507.967	−	879.824i	−0.754780	−	1.30732i	−0.945484	−	0.325669i	$-0.894410\pi$
$673$	−507.967	−	879.824i	−0.754780	−	1.30732i	0.190704	−	0.981648i	$-0.438923\pi$
$674$			1709.40i			2.53621i
$675$		0			0
$676$	225.279			0.333253
$677$	−643.996	+	371.811i	−0.951249	+	0.549204i	−0.893469	−	0.449126i	$-0.851736\pi$
$677$	−643.996	+	371.811i	−0.951249	+	0.549204i	−0.0577802	+	0.998329i	$0.518402\pi$
$678$		0			0
$679$	164.267	−	284.518i	0.241924	−	0.419025i
$680$		0			0
$681$		0			0
$682$	−348.458	−	603.546i	−0.510935	−	0.884965i
$683$			152.482i			0.223254i	0.993750	+	0.111627i	$0.0356061\pi$
$683$			152.482i			0.223254i	−0.993750	+	0.111627i	$0.964394\pi$
$684$		0			0
$685$		0			0
$686$	749.403	−	432.668i	1.09242	−	0.630711i
$687$		0			0
$688$	−979.179	+	1695.99i	−1.42322	+	2.46510i
$689$	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	$-0.356770\pi$
$692$			3199.99i			4.62426i
$693$		0			0
$694$	−35.8355			−0.0516361
$695$		0			0
$696$		0			0
$697$	74.1444	−	128.422i	0.106376	−	0.184249i
$698$	−157.543	−	90.9573i	−0.225706	−	0.130311i
$699$		0			0
$700$		0			0
$701$			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
$703$	−9.44975			−0.0134420
$704$	−488.906	+	282.270i	−0.694468	+	0.400952i
$705$		0			0
$706$	−175.813	+	304.517i	−0.249027	+	0.431327i
$707$	−191.385	−	110.496i	−0.270701	−	0.156289i
$708$		0			0
$709$	−179.227	−	310.431i	−0.252789	−	0.437843i	0.711504	−	0.702682i	$-0.248014\pi$
$709$	−179.227	−	310.431i	−0.252789	−	0.437843i	−0.964293	+	0.264839i	$0.914681\pi$
$710$		0			0
$711$		0			0
$712$	1471.19			2.06628
$713$	−8.50112	+	4.90812i	−0.0119230	+	0.00688376i
$714$		0			0
$715$		0			0
$716$	1608.24	+	928.515i	2.24614	+	1.29681i
$717$		0			0
$718$	−994.245	−	1722.08i	−1.38474	−	2.39845i
$719$			283.414i			0.394178i	0.980386	+	0.197089i	$0.0631488\pi$
$719$			283.414i			0.394178i	−0.980386	+	0.197089i	$0.936851\pi$
$720$		0			0
$721$	−104.964			−0.145580
$722$	−988.748	+	570.854i	−1.36946	+	0.790656i
$723$		0			0
$724$	1170.07	−	2026.61i	1.61611	−	2.79919i
$725$		0			0
$726$		0			0
$727$	77.6796	+	134.545i	0.106850	+	0.185069i	0.914492	−	0.404603i	$-0.132590\pi$
$727$	77.6796	+	134.545i	0.106850	+	0.185069i	−0.807643	+	0.589672i	$0.799257\pi$
$728$		−	639.063i		−	0.877833i
$729$		0			0
$730$		0			0
$731$	−192.748	+	111.283i	−0.263677	+	0.152234i
$732$		0			0
$733$	52.4658	−	90.8735i	0.0715768	−	0.123975i	−0.828016	−	0.560705i	$-0.810530\pi$
$733$	52.4658	−	90.8735i	0.0715768	−	0.123975i	0.899593	+	0.436730i	$0.143864\pi$
$734$	−967.845	−	558.786i	−1.31859	−	0.761288i
$735$		0			0
$736$	14.4155	+	24.9684i	0.0195863	+	0.0339245i
$737$			767.279i			1.04108i
$738$		0			0
$739$	627.375			0.848951			0.424476	−	0.905439i	$-0.360458\pi$
$739$	627.375			0.848951			0.424476	+	0.905439i	$0.360458\pi$
$740$		0			0
$741$		0			0
$742$	−410.073	+	710.268i	−0.552659	+	0.957234i
$743$	334.797	+	193.295i	0.450602	+	0.260155i	0.708084	−	0.706128i	$-0.249560\pi$
$743$	334.797	+	193.295i	0.450602	+	0.260155i	−0.257483	+	0.966283i	$0.582893\pi$
$744$		0			0
$745$		0			0
$746$			481.798i			0.645842i
$747$		0			0
$748$	−404.157			−0.540317
$749$	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	$0.960772\pi$
$752$	1662.83	+	960.038i	2.21122	+	1.27665i
$753$		0			0
$754$	679.491	+	1176.91i	0.901182	+	1.56089i
$755$		0			0
$756$		0			0
$757$	−332.222			−0.438867			−0.219433	−	0.975627i	$-0.570421\pi$
$757$	−332.222			−0.438867			−0.219433	+	0.975627i	$0.570421\pi$
$758$	−1740.78	+	1005.04i	−2.29655	+	1.32591i
$759$		0			0
$760$		0			0
$761$	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
$763$	190.810	+	330.492i	0.250079	+	0.433149i
$764$		−	1358.46i		−	1.77809i
$765$		0			0
$766$	−4.59618			−0.00600023
$767$	1107.00	−	639.126i	1.44328	−	0.833280i
$768$		0			0
$769$	−458.196	+	793.618i	−0.595833	+	1.03201i	0.397595	+	0.917561i	$0.369845\pi$
$769$	−458.196	+	793.618i	−0.595833	+	1.03201i	−0.993429	+	0.114453i	$0.963489\pi$
$770$		0			0
$771$		0			0
$772$	1062.39	+	1840.11i	1.37615	+	2.38356i
$773$			1186.06i			1.53436i	0.641434	+	0.767178i	$0.278340\pi$
$773$			1186.06i			1.53436i	−0.641434	+	0.767178i	$0.721660\pi$
$774$		0			0
$775$		0			0
$776$	−2286.66	+	1320.20i	−2.94673	+	1.70129i
$777$		0			0
$778$	−734.456	+	1272.12i	−0.944031	+	1.63511i
$779$	−214.820	−	124.026i	−0.275763	−	0.159212i
$780$		0			0
$781$	357.207	+	618.701i	0.457371	+	0.792190i
$782$			8.06559i			0.0103141i
$783$		0			0
$784$	−1598.77			−2.03925
$785$		0			0
$786$		0			0
$787$	441.240	−	764.249i	0.560660	−	0.971092i	−0.436779	−	0.899569i	$-0.643881\pi$
$787$	441.240	−	764.249i	0.560660	−	0.971092i	0.997439	−	0.0715229i	$-0.0227859\pi$
$788$	236.368	+	136.467i	0.299959	+	0.173181i
$789$		0			0
$790$		0			0
$791$		−	337.501i		−	0.426677i
$792$		0			0
$793$	−377.823			−0.476448
$794$	−2190.58	+	1264.73i	−2.75892	+	1.59286i
$795$		0			0
$796$	−738.295	+	1278.76i	−0.927507	+	1.60649i
$797$	−124.537	−	71.9016i	−0.156258	−	0.0902153i	0.419832	−	0.907602i	$-0.362089\pi$
$797$	−124.537	−	71.9016i	−0.156258	−	0.0902153i	−0.576090	+	0.817386i	$0.695422\pi$
$798$		0			0
$799$	109.108	+	188.980i	0.136556	+	0.236521i
$800$		0			0
$801$		0			0
$802$	−191.261			−0.238480
$803$	258.030	−	148.974i	0.321332	−	0.185521i
$804$		0			0
$805$		0			0
$806$	−740.661	−	427.621i	−0.918934	−	0.530547i
$807$		0			0
$808$	888.054	+	1538.15i	1.09908	+	1.90366i
$809$			52.3078i			0.0646574i	0.999477	+	0.0323287i	$0.0102923\pi$
$809$			52.3078i			0.0646574i	−0.999477	+	0.0323287i	$0.989708\pi$
$810$		0			0
$811$	1518.65			1.87256			0.936281	−	0.351253i	$-0.114244\pi$
$811$	1518.65			1.87256			0.936281	+	0.351253i	$0.114244\pi$
$812$	−651.861	+	376.352i	−0.802785	+	0.463488i
$813$		0			0
$814$	23.8956	−	41.3883i	0.0293557	−	0.0508456i
$815$		0			0
$816$		0			0
$817$	186.151	+	322.422i	0.227847	+	0.394642i
$818$			1000.35i			1.22292i
$819$		0			0
$820$		0			0
$821$	−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
$823$	478.550	−	828.873i	0.581470	−	1.00714i	−0.413835	−	0.910352i	$-0.635811\pi$
$823$	478.550	−	828.873i	0.581470	−	1.00714i	0.995305	−	0.0967841i	$-0.0308556\pi$
$824$	730.568	+	421.793i	0.886611	+	0.511885i
$825$		0			0
$826$	501.554	+	868.717i	0.607208	+	1.05172i
$827$			171.626i			0.207529i	0.994602	+	0.103764i	$0.0330888\pi$
$827$			171.626i			0.207529i	−0.994602	+	0.103764i	$0.966911\pi$
$828$		0			0
$829$	−203.896			−0.245954			−0.122977	−	0.992410i	$-0.539244\pi$
$829$	−203.896			−0.245954			−0.122977	+	0.992410i	$0.539244\pi$
$830$		0			0
$831$		0			0
$832$	−346.397	+	599.976i	−0.416342	+	0.721126i
$833$	−157.357	−	90.8499i	−0.188904	−	0.109063i
$834$		0			0
$835$		0			0
$836$			676.059i			0.808683i
$837$		0			0
$838$	101.958			0.121668
$839$	−1348.10	+	778.323i	−1.60679	+	0.927680i	−0.616705	+	0.787194i	$0.711533\pi$
$839$	−1348.10	+	778.323i	−1.60679	+	0.927680i	−0.990083	+	0.140486i	$0.955134\pi$
$840$		0			0
$841$	46.2156	−	80.0477i	0.0549531	−	0.0951816i
$842$	1396.18	+	806.087i	1.65817	+	0.957347i
$843$		0			0
$844$	864.495	+	1497.35i	1.02428	+	1.77411i
$845$		0			0
$846$		0			0
$847$	−62.5654			−0.0738670
$848$	2828.51	−	1633.04i	3.33551	−	1.92576i
$849$		0			0
$850$		0			0
$851$	−0.582966	−	0.336576i	−0.000685037	−	0.000395506i
$852$		0			0
$853$	281.964	+	488.377i	0.330556	+	0.572540i	0.982621	−	0.185623i	$-0.0594304\pi$
$853$	281.964	+	488.377i	0.330556	+	0.572540i	−0.652065	+	0.758163i	$0.726097\pi$
$854$		−	296.497i		−	0.347186i
$855$		0			0
$856$	−34.2579			−0.0400209
$857$	−826.107	+	476.953i	−0.963952	+	0.556538i	−0.897387	−	0.441244i	$-0.854537\pi$
$857$	−826.107	+	476.953i	−0.963952	+	0.556538i	−0.0665649	+	0.997782i	$0.521204\pi$
$858$		0			0
$859$	422.728	−	732.186i	0.492116	−	0.852371i	−0.507842	−	0.861450i	$-0.669557\pi$
$859$	422.728	−	732.186i	0.492116	−	0.852371i	0.999959	+	0.00907936i	$0.00289009\pi$
$860$		0			0
$861$		0			0
$862$	−100.221	−	173.587i	−0.116265	−	0.201377i
$863$		−	1109.42i		−	1.28554i	−0.766061	−	0.642768i	$-0.777786\pi$
$863$		−	1109.42i		−	1.28554i	0.766061	−	0.642768i	$-0.222214\pi$
$864$		0			0
$865$		0			0
$866$	−1681.02	+	970.538i	−1.94113	+	1.12071i
$867$		0			0
$868$	236.848	−	410.233i	0.272866	−	0.472618i
$869$	981.388	+	566.605i	1.12933	+	0.652019i
$870$		0			0
$871$	470.796	+	815.442i	0.540523	+	0.936214i
$872$		−	3067.06i		−	3.51727i
$873$		0			0
$874$	13.4918			0.0154369
$875$		0			0
$876$		0			0
$877$	−507.331	+	878.724i	−0.578485	+	1.00197i	0.417168	+	0.908829i	$0.363023\pi$
$877$	−507.331	+	878.724i	−0.578485	+	1.00197i	−0.995653	+	0.0931364i	$0.970311\pi$
$878$	−1329.19	−	767.411i	−1.51389	−	0.874044i
$879$		0			0
$880$		0			0
$881$		−	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
$883$	659.407			0.746780			0.373390	−	0.927674i	$-0.378195\pi$
$883$	659.407			0.746780			0.373390	+	0.927674i	$0.378195\pi$
$884$	−429.526	+	247.987i	−0.485889	+	0.280528i
$885$		0			0
$886$	787.537	−	1364.05i	0.888868	−	1.53956i
$887$	−668.543	−	385.984i	−0.753713	−	0.435156i	0.0733209	−	0.997308i	$-0.476640\pi$
$887$	−668.543	−	385.984i	−0.753713	−	0.435156i	−0.827034	+	0.562152i	$0.809974\pi$
$888$		0			0
$889$	129.846	+	224.901i	0.146059	+	0.252982i
$890$		0			0
$891$		0			0
$892$	−2067.01			−2.31727
$893$	316.120	−	182.512i	0.353998	−	0.204381i
$894$		0			0
$895$		0			0
$896$	31.4123	+	18.1359i	0.0350584	+	0.0202410i
$897$		0			0
$898$	−436.445	−	755.945i	−0.486019	−	0.841810i
$899$			587.432i			0.653428i
$900$		0			0
$901$	371.189			0.411974
$902$	1086.43	−	627.249i	1.20447	−	0.695398i
$903$		0			0
$904$	−1356.24	+	2349.08i	−1.50027	+	2.59854i
$905$		0			0
$906$		0			0
$907$	60.7354	+	105.197i	0.0669629	+	0.115983i	0.897563	−	0.440886i	$-0.145336\pi$
$907$	60.7354	+	105.197i	0.0669629	+	0.115983i	−0.830600	+	0.556869i	$0.812002\pi$
$908$			483.792i			0.532810i
$909$		0			0
$910$		0			0
$911$	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
$913$	294.971	−	510.904i	0.323078	−	0.559588i
$914$	2228.21	+	1286.46i	2.43786	+	1.40750i
$915$		0			0
$916$	29.5895	+	51.2505i	0.0323029	+	0.0559503i
$917$			220.275i			0.240212i
$918$		0			0
$919$	994.576			1.08224			0.541119	−	0.840946i	$-0.318001\pi$
$919$	994.576			1.08224			0.541119	+	0.840946i	$0.318001\pi$
$920$		0			0
$921$		0			0
$922$	707.501	−	1225.43i	0.767354	−	1.32910i
$923$	759.258	+	438.358i	0.822598	+	0.474927i
$924$		0			0
$925$		0			0
$926$			995.977i			1.07557i
$927$		0			0
$928$	1725.33			1.85919
$929$	140.236	−	80.9655i	0.150954	−	0.0871534i	−0.422620	−	0.906307i	$-0.638890\pi$
$929$	140.236	−	80.9655i	0.150954	−	0.0871534i	0.573575	+	0.819153i	$0.305556\pi$
$930$		0			0
$931$	−151.970	+	263.221i	−0.163234	+	0.282729i
$932$	436.574	+	252.056i	0.468427	+	0.270447i
$933$		0			0
$934$	−1434.26	−	2484.22i	−1.53561	−	2.65976i
$935$		0			0
$936$		0			0
$937$	−660.489			−0.704898			−0.352449	−	0.935831i	$-0.614651\pi$
$937$	−660.489			−0.704898			−0.352449	+	0.935831i	$0.614651\pi$
$938$	−639.919	+	369.457i	−0.682216	+	0.393878i
$939$		0			0
$940$		0			0
$941$	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
$943$	−8.83498	−	15.3026i	−0.00936902	−	0.0162276i
$944$		−	3994.69i		−	4.23167i
$945$		0			0
$946$	−1882.88			−1.99035
$947$	1353.91	−	781.678i	1.42968	−	0.825426i	0.432584	−	0.901594i	$-0.357602\pi$
$947$	1353.91	−	781.678i	1.42968	−	0.825426i	0.997095	+	0.0761680i	$0.0242685\pi$
$948$		0			0
$949$	182.818	−	316.650i	0.192643	−	0.333667i
$950$		0			0
$951$		0			0
$952$	−113.488	−	196.566i	−0.119210	−	0.206477i
$953$		−	996.612i		−	1.04576i	−0.852405	−	0.522881i	$-0.824857\pi$
$953$		−	996.612i		−	1.04576i	0.852405	−	0.522881i	$-0.175143\pi$
$954$		0			0
$955$		0			0
$956$	810.961	−	468.209i	0.848285	−	0.489758i
$957$		0			0
$958$	133.783	−	231.719i	0.139648	−	0.241878i
$959$	155.031	+	89.5074i	0.161659	+	0.0933341i
$960$		0			0
$961$	295.657	+	512.093i	0.307656	+	0.532875i
$962$		−	58.6484i		−	0.0609651i
$963$		0			0
$964$	1369.63			1.42078
$965$		0			0
$966$		0			0
$967$	325.000	−	562.916i	0.336091	−	0.582126i	−0.647603	−	0.761978i	$-0.724229\pi$
$967$	325.000	−	562.916i	0.336091	−	0.582126i	0.983694	+	0.179852i	$0.0575618\pi$
$968$	435.468	+	251.418i	0.449864	+	0.259729i
$969$		0			0
$970$		0			0
$971$			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
$973$	356.656			0.366553
$974$	2329.45	−	1344.91i	2.39163	−	1.38081i
$975$		0			0
$976$	−590.372	+	1022.55i	−0.604889	+	1.04770i
$977$	−244.324	−	141.061i	−0.250076	−	0.144381i	0.369723	−	0.929142i	$-0.379453\pi$
$977$	−244.324	−	141.061i	−0.250076	−	0.144381i	−0.619799	+	0.784761i	$0.712786\pi$
$978$		0			0
$979$	350.439	+	606.979i	0.357956	+	0.619998i
$980$		0			0
$981$		0			0
$982$	−14.0695			−0.0143274
$983$	333.017	−	192.267i	0.338776	−	0.195592i	−0.320955	−	0.947095i	$-0.604004\pi$
$983$	333.017	−	192.267i	0.338776	−	0.195592i	0.659731	+	0.751502i	$0.270670\pi$
$984$		0			0
$985$		0			0
$986$	418.003	+	241.334i	0.423938	+	0.244761i
$987$		0			0
$988$	414.824	+	718.496i	0.419862	+	0.727223i
$989$			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	$0.435439\pi$
$992$	−940.326	+	542.898i	−0.947910	+	0.547276i
$993$		0			0
$994$	−344.002	+	595.828i	−0.346078	+	0.599425i
$995$		0			0
$996$		0			0
$997$	726.087	+	1257.62i	0.728272	+	1.26140i	0.957613	+	0.288058i	$0.0930095\pi$
$997$	726.087	+	1257.62i	0.728272	+	1.26140i	−0.229341	+	0.973346i	$0.573657\pi$
$998$		−	757.008i		−	0.758525i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.h.a.14.1	✓	20	15.2	even	4
45.3.h.a.14.10	yes	20	15.8	even	4
45.3.h.a.29.1	yes	20	45.43	odd	12
45.3.h.a.29.10	yes	20	45.7	odd	12
135.3.h.a.44.1		20	5.3	odd	4
135.3.h.a.44.10		20	5.2	odd	4
135.3.h.a.89.1		20	45.2	even	12
135.3.h.a.89.10		20	45.38	even	12
225.3.j.e.101.1		20	9.7	even	3
225.3.j.e.101.10		20	45.34	even	6
225.3.j.e.176.1		20	3.2	odd	2
225.3.j.e.176.10		20	15.14	odd	2
405.3.d.a.404.1		20	45.22	odd	12
405.3.d.a.404.2		20	45.23	even	12
405.3.d.a.404.19		20	45.13	odd	12
405.3.d.a.404.20		20	45.32	even	12
675.3.j.e.251.1		20	45.29	odd	6	inner
675.3.j.e.251.10		20	9.2	odd	6	inner
675.3.j.e.476.1		20	5.4	even	2	inner
675.3.j.e.476.10		20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	675.j (of order \(6\), degree \(2\), not minimal)

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

Introduction

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