LMFDB - Embedded newform 475.2.n.a.39.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(39,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("475.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.n (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.15
Character	$\chi$	$=$	475.39
Dual form			475.2.n.a.134.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.636441 + 0.875986i) q^{2} +(0.575766 + 0.187078i) q^{3} +(0.255740 - 0.787086i) q^{4} +(-2.22529 - 0.219241i) q^{5} +(0.202564 + 0.623427i) q^{6} -2.44664i q^{7} +(2.91181 - 0.946103i) q^{8} +(-2.13054 - 1.54793i) q^{9} +O(q^{10})$	\(q+(0.636441 + 0.875986i) q^{2} +(0.575766 + 0.187078i) q^{3} +(0.255740 - 0.787086i) q^{4} +(-2.22529 - 0.219241i) q^{5} +(0.202564 + 0.623427i) q^{6} -2.44664i q^{7} +(2.91181 - 0.946103i) q^{8} +(-2.13054 - 1.54793i) q^{9} +(-1.22422 - 2.08886i) q^{10} +(0.599428 - 0.435510i) q^{11} +(0.294493 - 0.405334i) q^{12} +(2.27650 - 3.13334i) q^{13} +(2.14322 - 1.55714i) q^{14} +(-1.24023 - 0.542534i) q^{15} +(1.34289 + 0.975670i) q^{16} +(-0.0270256 + 0.00878114i) q^{17} -2.85149i q^{18} +(-0.309017 - 0.951057i) q^{19} +(-0.741658 + 1.69543i) q^{20} +(0.457712 - 1.40869i) q^{21} +(0.763002 + 0.247914i) q^{22} +(3.08220 + 4.24229i) q^{23} +1.85351 q^{24} +(4.90387 + 0.975751i) q^{25} +4.19362 q^{26} +(-2.00464 - 2.75915i) q^{27} +(-1.92572 - 0.625704i) q^{28} +(-0.933881 + 2.87419i) q^{29} +(-0.314083 - 1.43172i) q^{30} +(-1.10742 - 3.40830i) q^{31} -4.32600i q^{32} +(0.426605 - 0.138612i) q^{33} +(-0.0248923 - 0.0180853i) q^{34} +(-0.536404 + 5.44450i) q^{35} +(-1.76322 + 1.28105i) q^{36} +(-0.842856 + 1.16009i) q^{37} +(0.636441 - 0.875986i) q^{38} +(1.89691 - 1.37819i) q^{39} +(-6.68705 + 1.46697i) q^{40} +(4.01328 + 2.91582i) q^{41} +(1.52530 - 0.495600i) q^{42} +4.48656i q^{43} +(-0.189486 - 0.583179i) q^{44} +(4.40171 + 3.91170i) q^{45} +(-1.75455 + 5.39993i) q^{46} +(-6.45725 - 2.09809i) q^{47} +(0.590667 + 0.812983i) q^{48} +1.01395 q^{49} +(2.26628 + 4.91673i) q^{50} -0.0172031 q^{51} +(-1.88402 - 2.59312i) q^{52} +(-4.67017 - 1.51743i) q^{53} +(1.14114 - 3.51207i) q^{54} +(-1.42939 + 0.837719i) q^{55} +(-2.31477 - 7.12414i) q^{56} -0.605396i q^{57} +(-3.11211 + 1.01119i) q^{58} +(9.65317 + 7.01344i) q^{59} +(-0.744198 + 0.837423i) q^{60} +(5.70845 - 4.14743i) q^{61} +(2.28081 - 3.13927i) q^{62} +(-3.78723 + 5.21267i) q^{63} +(6.47530 - 4.70458i) q^{64} +(-5.75285 + 6.47350i) q^{65} +(0.392931 + 0.285481i) q^{66} +(-10.3479 + 3.36224i) q^{67} +0.0235171i q^{68} +(0.980990 + 3.01918i) q^{69} +(-5.11069 + 2.99522i) q^{70} +(-3.23523 + 9.95702i) q^{71} +(-7.66823 - 2.49156i) q^{72} +(1.29041 + 1.77609i) q^{73} -1.55265 q^{74} +(2.64094 + 1.47921i) q^{75} -0.827592 q^{76} +(-1.06554 - 1.46659i) q^{77} +(2.41454 + 0.784533i) q^{78} +(1.54438 - 4.75312i) q^{79} +(-2.77443 - 2.46557i) q^{80} +(1.80336 + 5.55016i) q^{81} +5.37132i q^{82} +(15.7298 - 5.11092i) q^{83} +(-0.991708 - 0.720518i) q^{84} +(0.0620650 - 0.0136155i) q^{85} +(-3.93016 + 2.85543i) q^{86} +(-1.07539 + 1.48015i) q^{87} +(1.33338 - 1.83524i) q^{88} +(1.61408 - 1.17270i) q^{89} +(-0.625164 + 6.34541i) q^{90} +(-7.66615 - 5.56979i) q^{91} +(4.12729 - 1.34104i) q^{92} -2.16956i q^{93} +(-2.27176 - 6.99177i) q^{94} +(0.479143 + 2.18413i) q^{95} +(0.809297 - 2.49076i) q^{96} +(-7.93458 - 2.57810i) q^{97} +(0.645318 + 0.888203i) q^{98} -1.95125 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9}+O(q^{10}) $ 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9	$ 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9} - 36 q^{10} + 20 q^{11} + 45 q^{12} - 10 q^{14} - 20 q^{16} - 15 q^{17} + 20 q^{19} + 12 q^{20} + 16 q^{21} + 15 q^{23} + 72 q^{24} + 41 q^{25} - 84 q^{26} + 15 q^{27} + 30 q^{28} - 24 q^{29} - 40 q^{30} + 8 q^{31} - 75 q^{33} - 24 q^{34} - 33 q^{35} - 32 q^{36} - 15 q^{37} - 30 q^{39} - 28 q^{40} + 13 q^{41} - 130 q^{42} - 24 q^{44} + 6 q^{45} + 30 q^{46} + 145 q^{48} - 28 q^{49} + 77 q^{50} - 36 q^{51} - 5 q^{52} - 10 q^{53} + 15 q^{54} - 8 q^{55} + 48 q^{56} - 60 q^{58} - 19 q^{59} - 110 q^{60} + 8 q^{61} + 110 q^{62} + 55 q^{63} + 16 q^{64} - 43 q^{65} - 17 q^{66} - 65 q^{67} - 42 q^{69} + 4 q^{70} + 18 q^{71} + 100 q^{73} + 22 q^{74} + 115 q^{75} + 64 q^{76} - 145 q^{78} - 16 q^{79} - 97 q^{80} + q^{81} - 70 q^{83} - 46 q^{84} - 16 q^{85} + 64 q^{86} + 10 q^{87} + 30 q^{88} + 4 q^{89} - 8 q^{90} + 16 q^{91} - 135 q^{92} + 38 q^{94} - 2 q^{95} + 50 q^{96} + 150 q^{97} + 130 q^{98} + 178 q^{99}+O(q^{100}) $ 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9 - 36 * q^10 + 20 * q^11 + 45 * q^12 - 10 * q^14 - 20 * q^16 - 15 * q^17 + 20 * q^19 + 12 * q^20 + 16 * q^21 + 15 * q^23 + 72 * q^24 + 41 * q^25 - 84 * q^26 + 15 * q^27 + 30 * q^28 - 24 * q^29 - 40 * q^30 + 8 * q^31 - 75 * q^33 - 24 * q^34 - 33 * q^35 - 32 * q^36 - 15 * q^37 - 30 * q^39 - 28 * q^40 + 13 * q^41 - 130 * q^42 - 24 * q^44 + 6 * q^45 + 30 * q^46 + 145 * q^48 - 28 * q^49 + 77 * q^50 - 36 * q^51 - 5 * q^52 - 10 * q^53 + 15 * q^54 - 8 * q^55 + 48 * q^56 - 60 * q^58 - 19 * q^59 - 110 * q^60 + 8 * q^61 + 110 * q^62 + 55 * q^63 + 16 * q^64 - 43 * q^65 - 17 * q^66 - 65 * q^67 - 42 * q^69 + 4 * q^70 + 18 * q^71 + 100 * q^73 + 22 * q^74 + 115 * q^75 + 64 * q^76 - 145 * q^78 - 16 * q^79 - 97 * q^80 + q^81 - 70 * q^83 - 46 * q^84 - 16 * q^85 + 64 * q^86 + 10 * q^87 + 30 * q^88 + 4 * q^89 - 8 * q^90 + 16 * q^91 - 135 * q^92 + 38 * q^94 - 2 * q^95 + 50 * q^96 + 150 * q^97 + 130 * q^98 + 178 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	0.636441	+	0.875986i	0.450032	+	0.619416i	0.972404	−	0.233302i	$-0.0749530\pi$
$2$	0.636441	+	0.875986i	0.450032	+	0.619416i	−0.522373	+	0.852717i	$0.674953\pi$
$3$	0.575766	+	0.187078i	0.332419	+	0.108009i	0.470471	−	0.882416i	$-0.344084\pi$
$3$	0.575766	+	0.187078i	0.332419	+	0.108009i	−0.138052	+	0.990425i	$0.544084\pi$
$4$	0.255740	−	0.787086i	0.127870	−	0.393543i
$5$	−2.22529	−	0.219241i	−0.995182	−	0.0980475i
$5$	−2.22529	−	0.219241i	−0.995182	−	0.0980475i
$6$	0.202564	+	0.623427i	0.0826962	+	0.254513i
$7$		−	2.44664i		−	0.924743i	−0.886686	−	0.462372i	$-0.846999\pi$
$7$		−	2.44664i		−	0.924743i	0.886686	−	0.462372i	$-0.153001\pi$
$8$	2.91181	−	0.946103i	1.02948	−	0.334498i
$9$	−2.13054	−	1.54793i	−0.710181	−	0.515977i
$10$	−1.22422	−	2.08886i	−0.387131	−	0.660556i
$11$	0.599428	−	0.435510i	0.180734	−	0.131311i	−0.493740	−	0.869610i	$-0.664370\pi$
$11$	0.599428	−	0.435510i	0.180734	−	0.131311i	0.674474	+	0.738298i	$0.264370\pi$
$12$	0.294493	−	0.405334i	0.0850127	−	0.117010i
$13$	2.27650	−	3.13334i	0.631389	−	0.869032i	−0.366731	−	0.930327i	$-0.619523\pi$
$13$	2.27650	−	3.13334i	0.631389	−	0.869032i	0.998120	+	0.0612952i	$0.0195231\pi$
$14$	2.14322	−	1.55714i	0.572800	−	0.416164i
$15$	−1.24023	−	0.542534i	−0.320227	−	0.140082i
$16$	1.34289	+	0.975670i	0.335724	+	0.243917i
$17$	−0.0270256	+	0.00878114i	−0.00655466	+	0.00212974i	−0.312292	−	0.949986i	$-0.601097\pi$
$17$	−0.0270256	+	0.00878114i	−0.00655466	+	0.00212974i	0.305738	+	0.952116i	$0.401097\pi$
$18$		−	2.85149i		−	0.672103i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	−0.741658	+	1.69543i	−0.165840	+	0.379110i
$21$	0.457712	−	1.40869i	0.0998809	−	0.307402i
$22$	0.763002	+	0.247914i	0.162673	+	0.0528555i
$23$	3.08220	+	4.24229i	0.642684	+	0.884579i	0.998755	−	0.0498801i	$-0.0158839\pi$
$23$	3.08220	+	4.24229i	0.642684	+	0.884579i	−0.356071	+	0.934459i	$0.615884\pi$
$24$	1.85351			0.378347
$25$	4.90387	+	0.975751i	0.980773	+	0.195150i
$26$	4.19362			0.822437
$27$	−2.00464	−	2.75915i	−0.385793	−	0.530998i
$28$	−1.92572	−	0.625704i	−0.363927	−	0.118247i
$29$	−0.933881	+	2.87419i	−0.173417	+	0.533724i	−0.999558	−	0.0297407i	$-0.990532\pi$
$29$	−0.933881	+	2.87419i	−0.173417	+	0.533724i	0.826140	+	0.563464i	$0.190532\pi$
$30$	−0.314083	−	1.43172i	−0.0573434	−	0.261395i
$31$	−1.10742	−	3.40830i	−0.198899	−	0.612148i	−0.999909	−	0.0134972i	$-0.995704\pi$
$31$	−1.10742	−	3.40830i	−0.198899	−	0.612148i	0.801010	−	0.598651i	$-0.204296\pi$
$32$		−	4.32600i		−	0.764735i
$33$	0.426605	−	0.138612i	0.0742623	−	0.0241293i
$34$	−0.0248923	−	0.0180853i	−0.00426900	−	0.00310161i
$35$	−0.536404	+	5.44450i	−0.0906688	+	0.920288i
$36$	−1.76322	+	1.28105i	−0.293870	+	0.213509i
$37$	−0.842856	+	1.16009i	−0.138565	+	0.190718i	−0.872660	−	0.488329i	$-0.837607\pi$
$37$	−0.842856	+	1.16009i	−0.138565	+	0.190718i	0.734095	+	0.679047i	$0.237607\pi$
$38$	0.636441	−	0.875986i	0.103244	−	0.142104i
$39$	1.89691	−	1.37819i	0.303749	−	0.220686i
$40$	−6.68705	+	1.46697i	−1.05732	+	0.231948i
$41$	4.01328	+	2.91582i	0.626769	+	0.455374i	0.855279	−	0.518167i	$-0.173386\pi$
$41$	4.01328	+	2.91582i	0.626769	+	0.455374i	−0.228511	+	0.973541i	$0.573386\pi$
$42$	1.52530	−	0.495600i	0.235359	−	0.0764728i
$43$			4.48656i			0.684193i	0.939665	+	0.342097i	$0.111137\pi$
$43$			4.48656i			0.684193i	−0.939665	+	0.342097i	$0.888863\pi$
$44$	−0.189486	−	0.583179i	−0.0285662	−	0.0879176i
$45$	4.40171	+	3.91170i	0.656169	+	0.583122i
$46$	−1.75455	+	5.39993i	−0.258694	+	0.796177i
$47$	−6.45725	−	2.09809i	−0.941887	−	0.306038i	−0.202472	−	0.979288i	$-0.564898\pi$
$47$	−6.45725	−	2.09809i	−0.941887	−	0.306038i	−0.739415	+	0.673250i	$0.764898\pi$
$48$	0.590667	+	0.812983i	0.0852554	+	0.117344i
$49$	1.01395			0.144850
$50$	2.26628	+	4.91673i	0.320500	+	0.695330i
$51$	−0.0172031			−0.00240892
$52$	−1.88402	−	2.59312i	−0.261266	−	0.359602i
$53$	−4.67017	−	1.51743i	−0.641497	−	0.208435i	−0.0298360	−	0.999555i	$-0.509499\pi$
$53$	−4.67017	−	1.51743i	−0.641497	−	0.208435i	−0.611661	+	0.791120i	$0.709499\pi$
$54$	1.14114	−	3.51207i	0.155290	−	0.477932i
$55$	−1.42939	+	0.837719i	−0.192738	+	0.112958i
$56$	−2.31477	−	7.12414i	−0.309325	−	0.952004i
$57$		−	0.605396i		−	0.0801867i
$58$	−3.11211	+	1.01119i	−0.408640	+	0.132775i
$59$	9.65317	+	7.01344i	1.25674	+	0.913072i	0.998593	−	0.0530348i	$-0.0168894\pi$
$59$	9.65317	+	7.01344i	1.25674	+	0.913072i	0.258143	+	0.966107i	$0.416889\pi$
$60$	−0.744198	+	0.837423i	−0.0960756	+	0.108111i
$61$	5.70845	−	4.14743i	0.730892	−	0.531024i	−0.158954	−	0.987286i	$-0.550812\pi$
$61$	5.70845	−	4.14743i	0.730892	−	0.531024i	0.889845	+	0.456262i	$0.150812\pi$
$62$	2.28081	−	3.13927i	0.289663	−	0.398687i
$63$	−3.78723	+	5.21267i	−0.477146	+	0.656735i
$64$	6.47530	−	4.70458i	0.809412	−	0.588073i
$65$	−5.75285	+	6.47350i	−0.713553	+	0.802938i
$66$	0.392931	+	0.285481i	0.0483665	+	0.0351403i
$67$	−10.3479	+	3.36224i	−1.26420	+	0.410763i	−0.862988	−	0.505224i	$-0.831410\pi$
$67$	−10.3479	+	3.36224i	−1.26420	+	0.410763i	−0.401209	+	0.915986i	$0.631410\pi$
$68$			0.0235171i			0.00285187i
$69$	0.980990	+	3.01918i	0.118097	+	0.363466i
$70$	−5.11069	+	2.99522i	−0.610844	+	0.357997i
$71$	−3.23523	+	9.95702i	−0.383951	+	1.18168i	0.553287	+	0.832991i	$0.313373\pi$
$71$	−3.23523	+	9.95702i	−0.383951	+	1.18168i	−0.937238	+	0.348690i	$0.886627\pi$
$72$	−7.66823	−	2.49156i	−0.903709	−	0.293633i
$73$	1.29041	+	1.77609i	0.151031	+	0.207876i	0.877828	−	0.478976i	$-0.158992\pi$
$73$	1.29041	+	1.77609i	0.151031	+	0.207876i	−0.726797	+	0.686852i	$0.758992\pi$
$74$	−1.55265			−0.180492
$75$	2.64094	+	1.47921i	0.304949	+	0.170804i
$76$	−0.827592			−0.0949313
$77$	−1.06554	−	1.46659i	−0.121429	−	0.167133i
$78$	2.41454	+	0.784533i	0.273393	+	0.0888308i
$79$	1.54438	−	4.75312i	0.173757	−	0.534768i	−0.825818	−	0.563937i	$-0.809286\pi$
$79$	1.54438	−	4.75312i	0.173757	−	0.534768i	0.999574	+	0.0291692i	$0.00928615\pi$
$80$	−2.77443	−	2.46557i	−0.310190	−	0.275659i
$81$	1.80336	+	5.55016i	0.200373	+	0.616685i
$82$			5.37132i			0.593163i
$83$	15.7298	−	5.11092i	1.72657	−	0.560996i	0.733622	−	0.679558i	$-0.237828\pi$
$83$	15.7298	−	5.11092i	1.72657	−	0.560996i	0.992947	+	0.118562i	$0.0378284\pi$
$84$	−0.991708	−	0.720518i	−0.108204	−	0.0786149i
$85$	0.0620650	−	0.0136155i	0.00673189	−	0.00147681i
$86$	−3.93016	+	2.85543i	−0.423800	+	0.307909i
$87$	−1.07539	+	1.48015i	−0.115294	+	0.158689i
$88$	1.33338	−	1.83524i	0.142139	−	0.195638i
$89$	1.61408	−	1.17270i	0.171092	−	0.124306i	−0.498944	−	0.866634i	$-0.666279\pi$
$89$	1.61408	−	1.17270i	0.171092	−	0.124306i	0.670036	+	0.742328i	$0.266279\pi$
$90$	−0.625164	+	6.34541i	−0.0658980	+	0.668865i
$91$	−7.66615	−	5.56979i	−0.803631	−	0.583872i
$92$	4.12729	−	1.34104i	0.430300	−	0.139813i
$93$		−	2.16956i		−	0.224972i
$94$	−2.27176	−	6.99177i	−0.234315	−	0.721146i
$95$	0.479143	+	2.18413i	0.0491591	+	0.224087i
$96$	0.809297	−	2.49076i	0.0825985	−	0.254212i
$97$	−7.93458	−	2.57810i	−0.805635	−	0.261767i	−0.122887	−	0.992421i	$-0.539215\pi$
$97$	−7.93458	−	2.57810i	−0.805635	−	0.261767i	−0.682748	+	0.730654i	$0.739215\pi$
$98$	0.645318	+	0.888203i	0.0651869	+	0.0897221i
$99$	−1.95125			−0.196108
$100$	2.02211	−	3.61023i	0.202211	−	0.361023i
$101$	13.8024			1.37339			0.686694	−	0.726947i	$-0.259061\pi$
$101$	13.8024			1.37339			0.686694	+	0.726947i	$0.259061\pi$
$102$	−0.0109488	−	0.0150697i	−0.00108409	−	0.00149212i
$103$	−2.20183	−	0.715419i	−0.216953	−	0.0704923i	0.198524	−	0.980096i	$-0.436385\pi$
$103$	−2.20183	−	0.715419i	−0.216953	−	0.0704923i	−0.415477	+	0.909604i	$0.636385\pi$
$104$	3.66428	−	11.2775i	0.359312	−	1.10585i
$105$	−1.32739	+	3.03441i	−0.129540	+	0.296128i
$106$	−1.64304	−	5.05676i	−0.159586	−	0.491156i
$107$		−	9.62493i		−	0.930478i	−0.885185	−	0.465239i	$-0.845968\pi$
$107$		−	9.62493i		−	0.930478i	0.885185	−	0.465239i	$-0.154032\pi$
$108$	−2.68436	+	0.872200i	−0.258302	+	0.0839275i
$109$	6.85821	+	4.98278i	0.656897	+	0.477264i	0.865614	−	0.500713i	$-0.166929\pi$
$109$	6.85821	+	4.98278i	0.656897	+	0.477264i	−0.208717	+	0.977976i	$0.566929\pi$
$110$	−1.64355	−	0.718963i	−0.156706	−	0.0685505i
$111$	−0.702315	+	0.510261i	−0.0666608	+	0.0484319i
$112$	2.38711	−	3.28558i	0.225561	−	0.310458i
$113$	−9.69686	+	13.3466i	−0.912203	+	1.25554i	0.0542052	+	0.998530i	$0.482737\pi$
$113$	−9.69686	+	13.3466i	−0.912203	+	1.25554i	−0.966409	+	0.257010i	$0.917263\pi$
$114$	0.530318	−	0.385299i	0.0496689	−	0.0360865i
$115$	−5.92873	−	10.1161i	−0.552857	−	0.943330i
$116$	2.02341	+	1.47009i	0.187869	+	0.136494i
$117$	−9.70038	+	3.15184i	−0.896800	+	0.291388i
$118$			12.9197i			1.18935i
$119$	0.0214843	+	0.0661218i	0.00196946	+	0.00606138i
$120$	−4.12461	−	0.406366i	−0.376524	−	0.0370960i
$121$	−3.22954	+	9.93951i	−0.293595	+	0.903592i
$122$	7.26618	+	2.36092i	0.657849	+	0.213748i
$123$	1.76522	+	2.42962i	0.159165	+	0.219072i
$124$	−2.96584			−0.266340
$125$	−10.6986	−	3.24646i	−0.956914	−	0.290372i
$126$	−6.97658			−0.621523
$127$	−1.71192	−	2.35625i	−0.151908	−	0.209084i	0.726280	−	0.687399i	$-0.241248\pi$
$127$	−1.71192	−	2.35625i	−0.151908	−	0.209084i	−0.878188	+	0.478315i	$0.841248\pi$
$128$	0.0137585	+	0.00447041i	0.00121609	+	0.000395132i
$129$	−0.839334	+	2.58321i	−0.0738993	+	0.227439i
$130$	−9.33204	−	0.919413i	−0.818474	−	0.0806379i
$131$	1.33126	+	4.09719i	0.116313	+	0.357973i	0.992219	−	0.124509i	$-0.0397354\pi$
$131$	1.33126	+	4.09719i	0.116313	+	0.357973i	−0.875906	+	0.482482i	$0.839735\pi$
$132$		−	0.371223i		−	0.0323109i
$133$	−2.32689	+	0.756054i	−0.201767	+	0.0655582i
$134$	−9.53110	−	6.92475i	−0.823362	−	0.598207i
$135$	3.85599	+	6.57942i	0.331871	+	0.566266i
$136$	−0.0703853	+	0.0511379i	−0.00603549	+	0.00438504i
$137$	7.78579	−	10.7162i	0.665185	−	0.915548i	−0.334454	−	0.942412i	$-0.608552\pi$
$137$	7.78579	−	10.7162i	0.665185	−	0.915548i	0.999639	+	0.0268636i	$0.00855199\pi$
$138$	−2.02041	+	2.78086i	−0.171989	+	0.236723i
$139$	−4.06254	+	2.95161i	−0.344580	+	0.250352i	−0.746592	−	0.665283i	$-0.768311\pi$
$139$	−4.06254	+	2.95161i	−0.344580	+	0.250352i	0.402012	+	0.915635i	$0.368311\pi$
$140$	4.14811	+	1.81457i	0.350579	+	0.153359i
$141$	−3.32536	−	2.41602i	−0.280046	−	0.203465i
$142$	−10.7812	+	3.50304i	−0.904742	+	0.293968i
$143$		−	2.86965i		−	0.239972i
$144$	−1.35083	−	4.15741i	−0.112569	−	0.346451i
$145$	2.70830	−	6.19117i	0.224912	−	0.514149i
$146$	−0.734564	+	2.26076i	−0.0607929	+	0.187101i
$147$	0.583796	+	0.189687i	0.0481507	+	0.0156451i
$148$	0.697540	+	0.960082i	0.0573375	+	0.0789182i
$149$	−22.5422			−1.84673			−0.923364	−	0.383926i	$-0.874572\pi$
$149$	−22.5422			−1.84673			−0.923364	+	0.383926i	$0.874572\pi$
$150$	0.385036	+	3.25485i	0.0314380	+	0.265758i
$151$	13.1289			1.06841			0.534207	−	0.845354i	$-0.320610\pi$
$151$	13.1289			1.06841			0.534207	+	0.845354i	$0.320610\pi$
$152$	−1.79960	−	2.47693i	−0.145966	−	0.200906i
$153$	0.0711717	+	0.0231251i	0.00575389	+	0.00186955i
$154$	0.606557	−	1.86679i	0.0488778	−	0.150430i
$155$	1.71710	+	7.82726i	0.137921	+	0.628700i
$156$	−0.599636	−	1.84549i	−0.0480093	−	0.147757i
$157$		−	1.12235i		−	0.0895736i	−0.998997	−	0.0447868i	$-0.985739\pi$
$157$		−	1.12235i		−	0.0895736i	0.998997	−	0.0447868i	$-0.0142608\pi$
$158$	5.14657	−	1.67222i	0.409439	−	0.133035i
$159$	−2.40505	−	1.74737i	−0.190733	−	0.138575i
$160$	−0.948435	+	9.62661i	−0.0749804	+	0.761051i
$161$	10.3794	−	7.54105i	0.818008	−	0.594318i
$162$	−3.71413	+	5.11207i	−0.291810	+	0.401642i
$163$	−7.44166	+	10.2426i	−0.582876	+	0.802260i	−0.994007	−	0.109316i	$-0.965134\pi$
$163$	−7.44166	+	10.2426i	−0.582876	+	0.802260i	0.411131	+	0.911576i	$0.365134\pi$
$164$	3.32135	−	2.41311i	0.259354	−	0.188432i
$165$	−0.979710	+	0.214924i	−0.0762703	+	0.0167318i
$166$	14.4882	+	10.5263i	1.12450	+	0.816997i
$167$	−3.79052	+	1.23161i	−0.293319	+	0.0953052i	−0.451980	−	0.892028i	$-0.649282\pi$
$167$	−3.79052	+	1.23161i	−0.293319	+	0.0953052i	0.158661	+	0.987333i	$0.449282\pi$
$168$		−	4.53488i		−	0.349874i
$169$	−0.618120	−	1.90238i	−0.0475477	−	0.146337i
$170$	0.0514277	+	0.0457026i	0.00394432	+	0.00350523i
$171$	−0.813795	+	2.50460i	−0.0622325	+	0.191532i
$172$	3.53131	+	1.14739i	0.269260	+	0.0874878i
$173$	12.4541	+	17.1415i	0.946864	+	1.30325i	0.952906	+	0.303265i	$0.0980768\pi$
$173$	12.4541	+	17.1415i	0.946864	+	1.30325i	−0.00604195	+	0.999982i	$0.501923\pi$
$174$	−1.98102			−0.150181
$175$	2.38731	−	11.9980i	0.180464	−	0.906964i
$176$	1.22988			0.0927059
$177$	4.24591	+	5.84399i	0.319142	+	0.439261i
$178$	2.05454	+	0.667559i	0.153994	+	0.0500357i
$179$	1.11994	−	3.44681i	0.0837079	−	0.257626i	−0.900439	−	0.434983i	$-0.856754\pi$
$179$	1.11994	−	3.44681i	0.0837079	−	0.257626i	0.984147	+	0.177356i	$0.0567545\pi$
$180$	4.20454	−	2.46415i	0.313388	−	0.183667i
$181$	−5.97833	−	18.3994i	−0.444366	−	1.36762i	−0.883178	−	0.469038i	$-0.844601\pi$
$181$	−5.97833	−	18.3994i	−0.444366	−	1.36762i	0.438812	−	0.898579i	$-0.355399\pi$
$182$		−	10.2603i		−	0.760543i
$183$	4.06262	−	1.32002i	0.300317	−	0.0975791i
$184$	12.9884	+	9.43664i	0.957519	+	0.695679i
$185$	2.12994	−	2.39676i	0.156596	−	0.176213i
$186$	1.90050	−	1.38079i	0.139351	−	0.101245i
$187$	−0.0123756	+	0.0170336i	−0.000904994	+	0.00124562i
$188$	−3.30275	+	4.54585i	−0.240878	+	0.331540i
$189$	−6.75065	+	4.90463i	−0.491037	+	0.356760i
$190$	−1.60832	+	1.80979i	−0.116680	+	0.131296i
$191$	11.3872	+	8.27329i	0.823949	+	0.598634i	0.917841	−	0.396948i	$-0.129931\pi$
$191$	11.3872	+	8.27329i	0.823949	+	0.598634i	−0.0938917	+	0.995582i	$0.529931\pi$
$192$	4.60838	−	1.49735i	0.332581	−	0.108062i
$193$		−	13.9813i		−	1.00640i	−0.864171	−	0.503198i	$-0.832157\pi$
$193$		−	13.9813i		−	1.00640i	0.864171	−	0.503198i	$-0.167843\pi$
$194$	−2.79151	−	8.59139i	−0.200419	−	0.616826i
$195$	−4.52334	+	2.65099i	−0.323923	+	0.189841i
$196$	0.259307	−	0.798064i	0.0185219	−	0.0570046i
$197$	13.2495	+	4.30501i	0.943986	+	0.306720i	0.740269	−	0.672310i	$-0.234698\pi$
$197$	13.2495	+	4.30501i	0.943986	+	0.306720i	0.203716	+	0.979030i	$0.434698\pi$
$198$	−1.24185	−	1.70927i	−0.0882547	−	0.121472i
$199$	23.8392			1.68992			0.844958	−	0.534832i	$-0.179625\pi$
$199$	23.8392			1.68992			0.844958	+	0.534832i	$0.179625\pi$
$200$	15.2023	−	1.79837i	1.07496	−	0.127164i
$201$	−6.58697			−0.464609
$202$	8.78440	+	12.0907i	0.618068	+	0.850698i
$203$	7.03211	+	2.28487i	0.493558	+	0.160367i
$204$	−0.00439953	+	0.0135404i	−0.000308029	+	0.000948015i
$205$	−8.29145	−	7.36842i	−0.579100	−	0.514633i
$206$	−0.774640	−	2.38410i	−0.0539717	−	0.166108i
$207$		−	13.8094i		−	0.959821i
$208$	6.11421	−	1.98663i	0.423944	−	0.137748i
$209$	−0.599428	−	0.435510i	−0.0414633	−	0.0301249i
$210$	−3.50290	+	0.768448i	−0.241723	+	0.0530280i
$211$	16.9850	−	12.3403i	1.16930	−	0.849543i	0.178371	−	0.983963i	$-0.442917\pi$
$211$	16.9850	−	12.3403i	1.16930	−	0.849543i	0.990924	+	0.134420i	$0.0429171\pi$
$212$	−2.38870	+	3.28776i	−0.164056	+	0.225804i
$213$	−3.72547	+	5.12767i	−0.255265	+	0.351342i
$214$	8.43131	−	6.12570i	0.576352	−	0.418744i
$215$	0.983637	−	9.98391i	0.0670835	−	0.680897i
$216$	−8.44756	−	6.13751i	−0.574784	−	0.417605i
$217$	−8.33888	+	2.70947i	−0.566080	+	0.183931i
$218$			9.17894i			0.621676i
$219$	0.410705	+	1.26402i	0.0277529	+	0.0854145i
$220$	0.293806	+	1.33929i	0.0198084	+	0.0902948i
$221$	−0.0340095	+	0.104670i	−0.00228773	+	0.00704090i
$222$	−0.893964	−	0.290466i	−0.0599989	−	0.0194948i
$223$	2.03444	+	2.80016i	0.136236	+	0.187513i	0.871684	−	0.490068i	$-0.163028\pi$
$223$	2.03444	+	2.80016i	0.136236	+	0.187513i	−0.735448	+	0.677581i	$0.763028\pi$
$224$	−10.5842			−0.707184
$225$	−8.93750	−	9.66972i	−0.595834	−	0.644648i
$226$	−17.8629			−1.18822
$227$	10.8937	+	14.9939i	0.723041	+	0.995180i	0.999417	+	0.0341308i	$0.0108663\pi$
$227$	10.8937	+	14.9939i	0.723041	+	0.995180i	−0.276377	+	0.961049i	$0.589134\pi$
$228$	−0.476499	−	0.154824i	−0.0315569	−	0.0102535i
$229$	0.549985	−	1.69268i	0.0363440	−	0.111855i	−0.931239	−	0.364410i	$-0.881271\pi$
$229$	0.549985	−	1.69268i	0.0363440	−	0.111855i	0.967583	+	0.252555i	$0.0812707\pi$
$230$	5.08827	−	11.6318i	0.335510	−	0.766976i
$231$	−0.339134	−	1.04375i	−0.0223134	−	0.0686736i
$232$			9.25263i			0.607465i
$233$	−14.4555	+	4.69688i	−0.947013	+	0.307703i	−0.741501	−	0.670952i	$-0.765886\pi$
$233$	−14.4555	+	4.69688i	−0.947013	+	0.307703i	−0.205512	+	0.978655i	$0.565886\pi$
$234$	−8.93469	−	6.49143i	−0.584079	−	0.424358i
$235$	13.9093	+	6.08456i	0.907343	+	0.396913i
$236$	7.98888	−	5.80426i	0.520032	−	0.377825i
$237$	1.77840	−	2.44776i	0.115520	−	0.158999i
$238$	−0.0442483	+	0.0609026i	−0.00286819	+	0.00394773i
$239$	−10.3554	+	7.52362i	−0.669833	+	0.486662i	−0.869969	−	0.493106i	$-0.835862\pi$
$239$	−10.3554	+	7.52362i	−0.669833	+	0.486662i	0.200136	+	0.979768i	$0.435862\pi$
$240$	−1.13617	−	1.93862i	−0.0733393	−	0.125138i
$241$	4.01138	+	2.91444i	0.258396	+	0.187735i	0.709439	−	0.704766i	$-0.248948\pi$
$241$	4.01138	+	2.91444i	0.258396	+	0.187735i	−0.451044	+	0.892502i	$0.648948\pi$
$242$	−10.7623	+	3.49688i	−0.691826	+	0.224788i
$243$			13.7644i			0.882990i
$244$	−1.80451	−	5.55370i	−0.115522	−	0.355539i
$245$	−2.25633	−	0.222299i	−0.144152	−	0.0142021i
$246$	−1.00485	+	3.09262i	−0.0640671	+	0.197178i
$247$	−3.68346	−	1.19683i	−0.234373	−	0.0761524i
$248$	−6.44920	−	8.87657i	−0.409525	−	0.563663i
$249$	10.0128			0.634536
$250$	−3.96519	−	11.4380i	−0.250780	−	0.723404i
$251$	26.4464			1.66928			0.834640	−	0.550795i	$-0.185676\pi$
$251$	26.4464			1.66928			0.834640	+	0.550795i	$0.185676\pi$
$252$	3.13428	+	4.31397i	0.197441	+	0.271754i
$253$	3.69512	+	1.20062i	0.232310	+	0.0754822i
$254$	0.974510	−	2.99923i	0.0611462	−	0.188189i
$255$	0.0382821	+	0.00377163i	0.00239732	+	0.000236189i
$256$	−4.94185	−	15.2094i	−0.308866	−	0.950590i
$257$			11.1144i			0.693299i	0.937995	+	0.346649i	$0.112681\pi$
$257$			11.1144i			0.693299i	−0.937995	+	0.346649i	$0.887319\pi$
$258$	−2.79704	+	0.908813i	−0.174136	+	0.0565802i
$259$	2.83833	+	2.06217i	0.176365	+	0.128137i
$260$	3.62397	+	6.18352i	0.224749	+	0.383486i
$261$	6.43872	−	4.67800i	0.398547	−	0.289561i
$262$	−2.74182	+	3.77379i	−0.169390	+	0.233145i
$263$	9.57085	−	13.1731i	0.590164	−	0.812291i	−0.404600	−	0.914494i	$-0.632589\pi$
$263$	9.57085	−	13.1731i	0.590164	−	0.812291i	0.994764	+	0.102203i	$0.0325892\pi$
$264$	1.11105	−	0.807224i	0.0683803	−	0.0496812i
$265$	10.0598	+	4.40062i	0.617970	+	0.270328i
$266$	−2.14322	−	1.55714i	−0.131409	−	0.0954745i
$267$	1.14872	−	0.373242i	0.0703005	−	0.0228420i
$268$			9.00455i			0.550041i
$269$	−5.20295	−	16.0130i	−0.317229	−	0.976331i	−0.974827	−	0.222962i	$-0.928427\pi$
$269$	−5.20295	−	16.0130i	−0.317229	−	0.976331i	0.657598	−	0.753369i	$-0.271573\pi$
$270$	−3.30936	+	7.56521i	−0.201401	+	0.460404i
$271$	−1.31773	+	4.05555i	−0.0800462	+	0.246357i	−0.983069	−	0.183236i	$-0.941343\pi$
$271$	−1.31773	+	4.05555i	−0.0800462	+	0.246357i	0.903023	+	0.429593i	$0.141343\pi$
$272$	−0.0448599	−	0.0145759i	−0.00272003	−	0.000883793i
$273$	−3.37193	−	4.64106i	−0.204078	−	0.280890i
$274$	14.3425			0.866459
$275$	3.36447	−	1.55079i	0.202885	−	0.0935163i
$276$	2.62723			0.158141
$277$	−3.59380	−	4.94644i	−0.215930	−	0.297203i	0.687287	−	0.726386i	$-0.258801\pi$
$277$	−3.59380	−	4.94644i	−0.215930	−	0.297203i	−0.903217	+	0.429183i	$0.858801\pi$
$278$	−5.17113	−	1.68020i	−0.310144	−	0.100772i
$279$	−2.91639	+	8.97574i	−0.174600	+	0.537363i
$280$	3.58915	+	16.3608i	0.214493	+	0.977745i
$281$	−1.82596	−	5.61972i	−0.108927	−	0.335244i	0.881705	−	0.471802i	$-0.156396\pi$
$281$	−1.82596	−	5.61972i	−0.108927	−	0.335244i	−0.990632	+	0.136557i	$0.956396\pi$
$282$		−	4.45062i		−	0.265031i
$283$	−2.99296	+	0.972471i	−0.177913	+	0.0578074i	−0.396619	−	0.917983i	$-0.629816\pi$
$283$	−2.99296	+	0.972471i	−0.177913	+	0.0578074i	0.218706	+	0.975791i	$0.429816\pi$
$284$	7.00966	+	5.09281i	0.415947	+	0.302203i
$285$	−0.132728	+	1.34718i	−0.00786210	+	0.0798003i
$286$	2.51378	−	1.82636i	0.148643	−	0.107995i
$287$	7.13396	−	9.81905i	0.421104	−	0.579600i
$288$	−6.69634	+	9.21672i	−0.394586	+	0.543100i
$289$	−13.7526	+	9.99187i	−0.808979	+	0.587757i
$290$	7.14705	−	1.56788i	0.419689	−	0.0920693i
$291$	−4.08616	−	2.96877i	−0.239535	−	0.174032i
$292$	1.72795	−	0.561444i	0.101120	−	0.0328560i
$293$		−	29.8258i		−	1.74244i	−0.490891	−	0.871221i	$-0.663329\pi$
$293$		−	29.8258i		−	1.74244i	0.490891	−	0.871221i	$-0.336671\pi$
$294$	0.205389	+	0.632122i	0.0119785	+	0.0368661i
$295$	−19.9435	−	17.7233i	−1.16116	−	1.03189i
$296$	−1.35667	+	4.17539i	−0.0788546	+	0.242690i
$297$	−2.40328	−	0.780872i	−0.139452	−	0.0453108i
$298$	−14.3468	−	19.7466i	−0.831086	−	1.14389i
$299$	20.3092			1.17451
$300$	1.83966	−	1.70035i	0.106213	−	0.0981700i
$301$	10.9770			0.632703
$302$	8.35576	+	11.5007i	0.480820	+	0.661792i
$303$	7.94694	+	2.58212i	0.456540	+	0.148339i
$304$	0.512940	−	1.57867i	0.0294191	−	0.0905428i
$305$	−13.6123	+	7.97772i	−0.779436	+	0.456803i
$306$	0.0250393	+	0.0770631i	0.00143140	+	0.00440541i
$307$		−	20.0271i		−	1.14301i	−0.820600	−	0.571503i	$-0.806361\pi$
$307$		−	20.0271i		−	1.14301i	0.820600	−	0.571503i	$-0.193639\pi$
$308$	−1.42683	+	0.463605i	−0.0813012	+	0.0264164i
$309$	−1.13390	−	0.823828i	−0.0645054	−	0.0468659i
$310$	−5.76373	+	6.48575i	−0.327358	+	0.368366i
$311$	−1.75308	+	1.27369i	−0.0994079	+	0.0722241i	−0.636379	−	0.771377i	$-0.719568\pi$
$311$	−1.75308	+	1.27369i	−0.0994079	+	0.0722241i	0.536971	+	0.843601i	$0.319568\pi$
$312$	4.21953	−	5.80768i	0.238884	−	0.328795i
$313$	−3.68843	+	5.07669i	−0.208482	+	0.286951i	−0.900434	−	0.434992i	$-0.856751\pi$
$313$	−3.68843	+	5.07669i	−0.208482	+	0.286951i	0.691952	+	0.721944i	$0.256751\pi$
$314$	0.983166	−	0.714312i	0.0554833	−	0.0403109i
$315$	9.57053	−	10.7694i	0.539238	−	0.606788i
$316$	−3.34616	−	2.43112i	−0.188236	−	0.136761i
$317$	−18.0875	+	5.87700i	−1.01590	+	0.330085i	−0.769201	−	0.639007i	$-0.779345\pi$
$317$	−18.0875	+	5.87700i	−1.01590	+	0.330085i	−0.246697	+	0.969093i	$0.579345\pi$
$318$		−	3.21889i		−	0.180506i
$319$	0.691945	+	2.12959i	0.0387415	+	0.119234i
$320$	−15.4409	+	9.04942i	−0.863172	+	0.505878i
$321$	1.80061	−	5.54171i	0.100500	−	0.309308i
$322$	13.2117	+	4.29274i	0.736259	+	0.239225i
$323$	0.0167027	+	0.0229893i	0.000929364	+	0.00127916i
$324$	4.82965			0.268314
$325$	14.2210	−	13.1442i	0.788841	−	0.729108i
$326$	−13.7085			−0.759245
$327$	3.01655	+	4.15193i	0.166816	+	0.229602i
$328$	14.4445	+	4.69332i	0.797567	+	0.259145i
$329$	−5.13327	+	15.7986i	−0.283006	+	0.871004i
$330$	−0.811798	−	0.721426i	−0.0446880	−	0.0397132i
$331$	9.16260	+	28.1996i	0.503622	+	1.54999i	0.803075	+	0.595878i	$0.203196\pi$
$331$	9.16260	+	28.1996i	0.503622	+	1.54999i	−0.299453	+	0.954111i	$0.596804\pi$
$332$		−	13.6878i		−	0.751214i
$333$	3.59148	−	1.16694i	0.196812	−	0.0639481i
$334$	−3.49132	−	2.53659i	−0.191036	−	0.138796i
$335$	23.7643	−	5.21328i	1.29838	−	0.284832i
$336$	1.98908	−	1.44515i	0.108513	−	0.0788393i
$337$	−13.0548	+	17.9684i	−0.711141	+	0.978802i	0.288631	+	0.957440i	$0.406800\pi$
$337$	−13.0548	+	17.9684i	−0.711141	+	0.978802i	−0.999772	+	0.0213612i	$0.993200\pi$
$338$	1.27306	−	1.75222i	0.0692453	−	0.0953080i
$339$	−8.07996	+	5.87044i	−0.438843	+	0.318838i
$340$	0.00515592	−	0.0523325i	0.000279619	−	0.00283813i
$341$	−2.14817	−	1.56074i	−0.116330	−	0.0845186i
$342$	−2.71193	+	0.881159i	−0.146644	+	0.0476476i
$343$		−	19.6073i		−	1.05869i
$344$	4.24475	+	13.0640i	0.228861	+	0.704363i
$345$	−1.52106	−	6.93363i	−0.0818914	−	0.373294i
$346$	−7.08947	+	21.8192i	−0.381132	+	1.17300i
$347$	24.0496	+	7.81420i	1.29105	+	0.419488i	0.872459	−	0.488686i	$-0.162524\pi$
$347$	24.0496	+	7.81420i	1.29105	+	0.419488i	0.418592	+	0.908174i	$0.362524\pi$
$348$	0.889987	+	1.22496i	0.0477083	+	0.0656648i
$349$	−0.341531			−0.0182817			−0.00914086	−	0.999958i	$-0.502910\pi$
$349$	−0.341531			−0.0182817			−0.00914086	+	0.999958i	$0.502910\pi$
$350$	12.0295	−	5.54477i	0.643002	−	0.296380i
$351$	−13.2089			−0.705040
$352$	−1.88402	−	2.59313i	−0.100418	−	0.138214i
$353$	−13.4918	−	4.38375i	−0.718096	−	0.233323i	−0.0728984	−	0.997339i	$-0.523225\pi$
$353$	−13.4918	−	4.38375i	−0.718096	−	0.233323i	−0.645197	+	0.764016i	$0.723225\pi$
$354$	−2.41698	+	7.43871i	−0.128461	+	0.395363i
$355$	9.38233	−	21.4480i	0.497962	−	1.13834i
$356$	−0.510231	−	1.57033i	−0.0270422	−	0.0832273i
$357$			0.0420899i			0.00222763i
$358$	3.73213	−	1.21264i	0.197249	−	0.0640901i
$359$	−15.9267	−	11.5714i	−0.840580	−	0.610717i	0.0819528	−	0.996636i	$-0.473884\pi$
$359$	−15.9267	−	11.5714i	−0.840580	−	0.610717i	−0.922533	+	0.385919i	$0.873884\pi$
$360$	16.5178	+	7.22564i	0.870565	+	0.380825i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	12.3128	−	16.9471i	0.647144	−	0.890718i
$363$	−3.71892	+	5.11865i	−0.195193	+	0.268660i
$364$	−6.34445	+	4.60951i	−0.332539	+	0.241604i
$365$	−2.48214	−	4.23524i	−0.129921	−	0.221682i
$366$	3.74194	+	2.71868i	0.195594	+	0.142108i
$367$	−13.5329	+	4.39712i	−0.706414	+	0.229528i	−0.640123	−	0.768273i	$-0.721117\pi$
$367$	−13.5329	+	4.39712i	−0.706414	+	0.229528i	−0.0662909	+	0.997800i	$0.521117\pi$
$368$			8.70416i			0.453736i
$369$	−4.03698	−	12.4245i	−0.210157	−	0.646796i
$370$	3.45511	+	0.340405i	0.179622	+	0.0176968i
$371$	−3.71261	+	11.4262i	−0.192749	+	0.593220i
$372$	−1.70763	−	0.554842i	−0.0885364	−	0.0287672i
$373$	−16.0600	−	22.1046i	−0.831553	−	1.14453i	−0.987632	−	0.156790i	$-0.949885\pi$
$373$	−16.0600	−	22.1046i	−0.831553	−	1.14453i	0.156079	−	0.987745i	$-0.450115\pi$
$374$	−0.0227975			−0.00117883
$375$	−5.55256	−	3.87067i	−0.286733	−	0.199881i
$376$	−20.7873			−1.07202
$377$	6.87983	+	9.46927i	0.354329	+	0.487692i
$378$	−8.59278	−	2.79196i	−0.441965	−	0.143603i
$379$	−5.97035	+	18.3748i	−0.306676	+	0.943853i	0.672370	+	0.740215i	$0.265276\pi$
$379$	−5.97035	+	18.3748i	−0.306676	+	0.943853i	−0.979046	+	0.203637i	$0.934724\pi$
$380$	1.84163	+	0.181442i	0.0944739	+	0.00930778i
$381$	−0.544862	−	1.67691i	−0.0279141	−	0.0859108i
$382$			15.2405i			0.779771i
$383$	18.7767	−	6.10091i	0.959442	−	0.311742i	0.212896	−	0.977075i	$-0.431711\pi$
$383$	18.7767	−	6.10091i	0.959442	−	0.311742i	0.746547	+	0.665333i	$0.231711\pi$
$384$	0.00708536	+	0.00514782i	0.000361573	+	0.000262698i
$385$	2.04960	+	3.49720i	0.104457	+	0.178234i
$386$	12.2474	−	8.89827i	0.623377	−	0.452910i
$387$	6.94487	−	9.55880i	0.353028	−	0.485901i
$388$	−4.05838	+	5.58588i	−0.206033	+	0.283580i
$389$	−11.9884	+	8.71008i	−0.607836	+	0.441618i	−0.848651	−	0.528952i	$-0.822585\pi$
$389$	−11.9884	+	8.71008i	−0.607836	+	0.441618i	0.240816	+	0.970571i	$0.422585\pi$
$390$	−5.20107	−	2.27518i	−0.263366	−	0.115208i
$391$	−0.120550	−	0.0875850i	−0.00609650	−	0.00442936i
$392$	2.95242	−	0.959299i	0.149120	−	0.0484519i
$393$			2.60807i			0.131560i
$394$	4.66137	+	14.3462i	0.234837	+	0.722753i
$395$	−4.47878	+	10.2385i	−0.225352	+	0.515155i
$396$	−0.499012	+	1.53580i	−0.0250763	+	0.0771769i
$397$	−8.87846	−	2.88479i	−0.445597	−	0.144783i	0.0776193	−	0.996983i	$-0.475268\pi$
$397$	−8.87846	−	2.88479i	−0.445597	−	0.144783i	−0.523217	+	0.852200i	$0.675268\pi$
$398$	15.1723	+	20.8828i	0.760516	+	1.04676i
$399$	−1.48119			−0.0741521
$400$	5.63336	+	6.09488i	0.281668	+	0.304744i
$401$	−16.9956			−0.848721			−0.424361	−	0.905493i	$-0.639501\pi$
$401$	−16.9956			−0.848721			−0.424361	+	0.905493i	$0.639501\pi$
$402$	−4.19222	−	5.77009i	−0.209089	−	0.287786i
$403$	−13.2004	−	4.28907i	−0.657559	−	0.213654i
$404$	3.52982	−	10.8637i	0.175615	−	0.540488i
$405$	−2.79618	−	12.7461i	−0.138943	−	0.633359i
$406$	2.47401	+	7.61422i	0.122783	+	0.377887i
$407$			1.06246i			0.0526644i
$408$	−0.0500922	+	0.0162760i	−0.00247993	+	0.000805780i
$409$	−1.98318	−	1.44087i	−0.0980622	−	0.0712463i	0.537674	−	0.843153i	$-0.319303\pi$
$409$	−1.98318	−	1.44087i	−0.0980622	−	0.0712463i	−0.635736	+	0.771907i	$0.719303\pi$
$410$	1.17761	−	11.9528i	0.0581581	−	0.590305i
$411$	6.48756	−	4.71349i	0.320008	−	0.232499i
$412$	−1.12619	+	1.55007i	−0.0554836	+	0.0763666i
$413$	17.1594	−	23.6178i	0.844357	−	1.16216i
$414$	12.0969	−	8.78888i	0.594528	−	0.431950i
$415$	−36.1239	+	7.92468i	−1.77325	+	0.389007i
$416$	−13.5548	−	9.84815i	−0.664579	−	0.482845i
$417$	−2.89125	+	0.939424i	−0.141585	+	0.0460038i
$418$		−	0.802267i		−	0.0392402i
$419$	−1.52668	−	4.69864i	−0.0745832	−	0.229544i	0.906814	−	0.421530i	$-0.138507\pi$
$419$	−1.52668	−	4.69864i	−0.0745832	−	0.229544i	−0.981397	+	0.191987i	$0.938507\pi$
$420$	2.04887	+	1.82079i	0.0999748	+	0.0888453i
$421$	−5.11698	+	15.7484i	−0.249386	+	0.767532i	0.745498	+	0.666508i	$0.232212\pi$
$421$	−5.11698	+	15.7484i	−0.249386	+	0.767532i	−0.994884	+	0.101024i	$0.967788\pi$
$422$	21.6199	+	7.02473i	1.05244	+	0.341959i
$423$	10.5098	+	14.4654i	0.511002	+	0.703334i
$424$	−15.0343			−0.730129
$425$	−0.141098	+	0.0166913i	−0.00684425	+	0.000809647i
$426$	−6.86281			−0.332504
$427$	−10.1473	−	13.9665i	−0.491061	−	0.675887i
$428$	−7.57566	−	2.46148i	−0.366183	−	0.118980i
$429$	0.536848	−	1.65225i	0.0259193	−	0.0797713i
$430$	9.37179	−	5.49252i	0.451948	−	0.264873i
$431$	0.0235211	+	0.0723905i	0.00113297	+	0.00348693i	0.951621	−	0.307273i	$-0.0994165\pi$
$431$	0.0235211	+	0.0723905i	0.00113297	+	0.00348693i	−0.950488	+	0.310760i	$0.899416\pi$
$432$		−	5.66111i		−	0.272370i
$433$	−23.6931	+	7.69834i	−1.13862	+	0.369959i	−0.816844	−	0.576859i	$-0.804278\pi$
$433$	−23.6931	+	7.69834i	−1.13862	+	0.369959i	−0.321771	+	0.946817i	$0.604278\pi$
$434$	−7.68066	−	5.58033i	−0.368683	−	0.267864i
$435$	2.71758	−	3.05800i	0.130298	−	0.146620i
$436$	5.67579	−	4.12371i	0.271821	−	0.197490i
$437$	3.08220	−	4.24229i	0.147442	−	0.202936i
$438$	−0.845874	+	1.16425i	−0.0404174	+	0.0556298i
$439$	−5.86729	+	4.26284i	−0.280031	+	0.203454i	−0.718931	−	0.695082i	$-0.755368\pi$
$439$	−5.86729	+	4.26284i	−0.280031	+	0.203454i	0.438900	+	0.898536i	$0.355368\pi$
$440$	−3.36953	+	3.79162i	−0.160636	+	0.180759i
$441$	−2.16026	−	1.56952i	−0.102869	−	0.0747390i
$442$	−0.113335	+	0.0368247i	−0.00539079	+	0.00175157i
$443$		−	14.3117i		−	0.679970i	−0.940431	−	0.339985i	$-0.889578\pi$
$443$		−	14.3117i		−	0.679970i	0.940431	−	0.339985i	$-0.110422\pi$
$444$	0.222010	+	0.683277i	0.0105361	+	0.0324269i
$445$	−3.84891	+	2.25573i	−0.182456	+	0.106932i
$446$	−1.15810	+	3.56428i	−0.0548378	+	0.168773i
$447$	−12.9790	−	4.21714i	−0.613887	−	0.199464i
$448$	−11.5104	−	15.8427i	−0.543816	−	0.748499i
$449$	−21.9487			−1.03582			−0.517912	−	0.855434i	$-0.673291\pi$
$449$	−21.9487			−1.03582			−0.517912	+	0.855434i	$0.673291\pi$
$450$	2.78235	−	13.9833i	0.131161	−	0.659181i
$451$	3.67554			0.173074
$452$	8.02504	+	11.0455i	0.377466	+	0.519537i
$453$	7.55916	+	2.45612i	0.355160	+	0.115399i
$454$	−6.20124	+	19.0855i	−0.291039	+	0.895725i
$455$	15.8383	+	14.0751i	0.742512	+	0.659853i
$456$	−0.572767	−	1.76280i	−0.0268223	−	0.0825505i
$457$			20.1014i			0.940304i	0.882585	+	0.470152i	$0.155801\pi$
$457$			20.1014i			0.940304i	−0.882585	+	0.470152i	$0.844199\pi$
$458$	1.83280	−	0.595511i	0.0856409	−	0.0278264i
$459$	0.0784049	+	0.0569645i	0.00365963	+	0.00265888i
$460$	−9.47845	+	2.07933i	−0.441935	+	0.0969494i
$461$	−20.8226	+	15.1285i	−0.969804	+	0.704603i	−0.955407	−	0.295293i	$-0.904583\pi$
$461$	−20.8226	+	15.1285i	−0.969804	+	0.704603i	−0.0143967	+	0.999896i	$0.504583\pi$
$462$	0.698470	−	0.961361i	0.0324958	−	0.0447266i
$463$	7.44153	−	10.2424i	0.345837	−	0.476004i	−0.600298	−	0.799777i	$-0.704951\pi$
$463$	7.44153	−	10.2424i	0.345837	−	0.476004i	0.946135	+	0.323772i	$0.104951\pi$
$464$	−4.05836	+	2.94857i	−0.188405	+	0.136884i
$465$	−0.475655	+	4.82790i	−0.0220580	+	0.223888i
$466$	−13.3145	−	9.67354i	−0.616782	−	0.448118i
$467$	−25.8697	+	8.40557i	−1.19711	+	0.388963i	−0.838696	−	0.544601i	$-0.816681\pi$
$467$	−25.8697	+	8.40557i	−1.19711	+	0.388963i	−0.358411	+	0.933564i	$0.616681\pi$
$468$			8.44109i			0.390189i
$469$	8.22619	+	25.3176i	0.379850	+	1.16906i
$470$	3.52246	+	16.0568i	0.162479	+	0.740645i
$471$	0.209967	−	0.646213i	0.00967478	−	0.0297759i
$472$	34.7436	+	11.2889i	1.59920	+	0.519613i
$473$	1.95394	+	2.68937i	0.0898423	+	0.123657i
$474$	3.27606			0.150474
$475$	−0.587384	−	4.96538i	−0.0269510	−	0.227827i
$476$	0.0575380			0.00263725
$477$	7.60112	+	10.4620i	0.348032	+	0.479024i
$478$	−13.1812	−	4.28282i	−0.602892	−	0.195892i
$479$	3.88127	−	11.9453i	0.177340	−	0.545796i	−0.822393	−	0.568920i	$-0.807361\pi$
$479$	3.88127	−	11.9453i	0.177340	−	0.545796i	0.999733	+	0.0231241i	$0.00736128\pi$
$480$	−2.34700	+	5.36524i	−0.107125	+	0.244889i
$481$	1.71619	+	5.28190i	0.0782517	+	0.240834i
$482$			5.36878i			0.244541i
$483$	7.38684	−	2.40013i	0.336113	−	0.109210i
$484$	6.99733	+	5.08386i	0.318060	+	0.231084i
$485$	17.0916	+	7.47662i	0.776088	+	0.339496i
$486$	−12.0575	+	8.76026i	−0.546938	+	0.397373i
$487$	−8.56783	+	11.7926i	−0.388245	+	0.534374i	−0.957745	−	0.287617i	$-0.907137\pi$
$487$	−8.56783	+	11.7926i	−0.388245	+	0.534374i	0.569500	+	0.821991i	$0.307137\pi$
$488$	12.6980	−	17.4773i	0.574811	−	0.791160i
$489$	−6.20081	+	4.50515i	−0.280410	+	0.203730i
$490$	−1.24129	−	2.11799i	−0.0560758	−	0.0956812i
$491$	12.1261	+	8.81012i	0.547243	+	0.397595i	0.826768	−	0.562543i	$-0.190177\pi$
$491$	12.1261	+	8.81012i	0.547243	+	0.397595i	−0.279525	+	0.960138i	$0.590177\pi$
$492$	2.36376	−	0.768032i	0.106567	−	0.0346256i
$493$		−	0.0858771i		−	0.00386771i
$494$	−1.29590	−	3.98837i	−0.0583053	−	0.179445i
$495$	4.34210	+	0.427793i	0.195163	+	0.0192279i
$496$	1.83822	−	5.65746i	0.0825386	−	0.254028i
$497$	24.3613	+	7.91545i	1.09275	+	0.355056i
$498$	6.37256	+	8.77108i	0.285561	+	0.393042i
$499$	2.84375			0.127304			0.0636519	−	0.997972i	$-0.479725\pi$
$499$	2.84375			0.127304			0.0636519	+	0.997972i	$0.479725\pi$
$500$	−5.29131	+	7.59049i	−0.236635	+	0.339457i
$501$	−2.41286			−0.107799
$502$	16.8316	+	23.1667i	0.751229	+	1.03398i
$503$	−17.7140	−	5.75563i	−0.789828	−	0.256631i	−0.113797	−	0.993504i	$-0.536301\pi$
$503$	−17.7140	−	5.75563i	−0.789828	−	0.256631i	−0.676031	+	0.736873i	$0.736301\pi$
$504$	−6.09595	+	18.7614i	−0.271535	+	0.835699i
$505$	−30.7143	−	3.02605i	−1.36677	−	0.134657i
$506$	1.30000	+	4.00100i	0.0577922	+	0.177866i
$507$		−	1.21096i		−	0.0537807i
$508$	−2.29238	+	0.744840i	−0.101708	+	0.0330469i
$509$	−14.9272	−	10.8452i	−0.661634	−	0.480705i	0.205580	−	0.978640i	$-0.434092\pi$
$509$	−14.9272	−	10.8452i	−0.661634	−	0.480705i	−0.867214	+	0.497935i	$0.834092\pi$
$510$	0.0210604	+	0.0359350i	0.000932569	+	0.00159123i
$511$	4.34546	−	3.15716i	0.192232	−	0.139665i
$512$	10.1951	−	14.0323i	0.450563	−	0.620146i
$513$	−2.00464	+	2.75915i	−0.0885070	+	0.121819i
$514$	−9.73608	+	7.07367i	−0.429440	+	0.312006i
$515$	4.74288	+	2.07475i	0.208996	+	0.0914244i
$516$	1.81856	+	1.32126i	0.0800574	+	0.0581651i
$517$	−4.78440	+	1.55455i	−0.210418	+	0.0683688i
$518$			3.79878i			0.166909i
$519$	3.96382	+	12.1994i	0.173992	+	0.535494i
$520$	−10.6266	+	24.2924i	−0.466006	+	1.06529i
$521$	−11.3605	+	34.9639i	−0.497711	+	1.53180i	0.314979	+	0.949099i	$0.398003\pi$
$521$	−11.3605	+	34.9639i	−0.497711	+	1.53180i	−0.812689	+	0.582697i	$0.801997\pi$
$522$	8.19573	+	2.66295i	0.358717	+	0.116554i
$523$	−15.2680	−	21.0146i	−0.667622	−	0.918903i	0.332082	−	0.943251i	$-0.392249\pi$
$523$	−15.2680	−	21.0146i	−0.667622	−	0.918903i	−0.999704	+	0.0243481i	$0.992249\pi$
$524$	3.56530			0.155751
$525$	3.61909	−	6.46143i	0.157950	−	0.282000i
$526$	17.6308			0.768738
$527$	0.0598574	+	0.0823867i	0.00260743	+	0.00358882i
$528$	0.708125	+	0.230084i	0.0308172	+	0.0100131i
$529$	−1.38965	+	4.27691i	−0.0604197	+	0.185953i
$530$	2.54760	+	11.6130i	0.110661	+	0.504436i
$531$	−9.71018	−	29.8849i	−0.421386	−	1.29689i
$532$			2.02482i			0.0877871i
$533$	18.2725	−	5.93709i	0.791469	−	0.257164i
$534$	1.05805	+	0.768716i	0.0457862	+	0.0332656i
$535$	−2.11018	+	21.4183i	−0.0912310	+	0.925994i
$536$	−26.9501	+	19.5804i	−1.16407	+	0.845743i
$537$	1.28964	−	1.77504i	0.0556521	−	0.0765986i
$538$	10.7158	−	14.7490i	0.461991	−	0.635877i
$539$	0.607789	−	0.441584i	0.0261793	−	0.0190204i
$540$	6.16470	−	1.35238i	0.265287	−	0.0581972i
$541$	−28.5347	−	20.7317i	−1.22680	−	0.891324i	−0.230156	−	0.973154i	$-0.573924\pi$
$541$	−28.5347	−	20.7317i	−1.22680	−	0.891324i	−0.996646	+	0.0818300i	$0.973924\pi$
$542$	−4.39126	+	1.42681i	−0.188621	+	0.0612866i
$543$		−	11.7122i		−	0.502617i
$544$	0.0379872	+	0.116912i	0.00162869	+	0.00501258i
$545$	−14.1691	−	12.5917i	−0.606937	−	0.539371i
$546$	1.91947	−	5.90752i	0.0821457	−	0.252819i
$547$	−4.18761	−	1.36064i	−0.179049	−	0.0581766i	0.218120	−	0.975922i	$-0.430008\pi$
$547$	−4.18761	−	1.36064i	−0.179049	−	0.0581766i	−0.397170	+	0.917745i	$0.630008\pi$
$548$	−6.44345	−	8.86865i	−0.275251	−	0.378850i
$549$	−18.5820			−0.793061
$550$	3.49976	+	1.96024i	0.149230	+	0.0835848i
$551$	3.02210			0.128746
$552$	5.71291	+	7.86314i	0.243157	+	0.334678i
$553$	−11.6292	−	3.77855i	−0.494523	−	0.160680i
$554$	2.04577	−	6.29623i	0.0869164	−	0.267501i
$555$	1.67473	−	0.981506i	0.0710882	−	0.0416626i
$556$	1.28422	+	3.95241i	0.0544629	+	0.167620i
$557$		−	27.2898i		−	1.15630i	−0.815929	−	0.578152i	$-0.803774\pi$
$557$		−	27.2898i		−	1.15630i	0.815929	−	0.578152i	$-0.196226\pi$
$558$	−9.71873	+	3.15781i	−0.411427	+	0.133681i
$559$	14.0579	+	10.2137i	0.594586	+	0.431992i
$560$	−6.03236	+	6.78803i	−0.254914	+	0.286847i
$561$	−0.0103121	+	0.00749215i	−0.000435375	+	0.000316319i
$562$	3.76068	−	5.17613i	0.158635	−	0.218342i
$563$	−15.5466	+	21.3980i	−0.655210	+	0.901819i	−0.999311	−	0.0371136i	$-0.988184\pi$
$563$	−15.5466	+	21.3980i	−0.655210	+	0.901819i	0.344101	+	0.938933i	$0.388184\pi$
$564$	−2.75204	+	1.99947i	−0.115882	+	0.0841931i
$565$	24.5045	−	27.5741i	1.03091	−	1.16005i
$566$	−2.75671	−	2.00287i	−0.115873	−	0.0841868i
$567$	13.5793	−	4.41217i	0.570275	−	0.185294i
$568$			32.0538i			1.34495i
$569$	11.6483	+	35.8498i	0.488323	+	1.50290i	0.827110	+	0.562040i	$0.189983\pi$
$569$	11.6483	+	35.8498i	0.488323	+	1.50290i	−0.338787	+	0.940863i	$0.610017\pi$
$570$	−1.26459	+	0.741136i	−0.0529677	+	0.0310428i
$571$	0.760876	−	2.34174i	0.0318417	−	0.0979986i	−0.933873	−	0.357606i	$-0.883593\pi$
$571$	0.760876	−	2.34174i	0.0318417	−	0.0979986i	0.965714	+	0.259607i	$0.0835931\pi$
$572$	−2.25867	−	0.733885i	−0.0944395	−	0.0306853i
$573$	5.00862	+	6.89377i	0.209238	+	0.287991i
$574$	13.1417			0.548523
$575$	10.9753	+	23.8111i	0.457702	+	0.992991i
$576$	−21.0783			−0.878261
$577$	18.5210	+	25.4919i	0.771038	+	1.06124i	0.996215	+	0.0869254i	$0.0277042\pi$
$577$	18.5210	+	25.4919i	0.771038	+	1.06124i	−0.225176	+	0.974318i	$0.572296\pi$
$578$	−17.5055	−	5.68788i	−0.728132	−	0.236584i
$579$	2.61559	−	8.04995i	0.108700	−	0.334544i
$580$	−4.18037	−	3.71500i	−0.173580	−	0.154257i
$581$	−12.5046	−	38.4851i	−0.518777	−	1.59663i
$582$		−	5.46886i		−	0.226692i
$583$	−3.46029	+	1.12432i	−0.143311	+	0.0465644i
$584$	5.43778	+	3.95078i	0.225017	+	0.163484i
$585$	22.2772	−	4.88706i	0.921049	−	0.202055i
$586$	26.1270	−	18.9824i	1.07930	−	0.784154i
$587$	18.9777	−	26.1206i	0.783295	−	1.07811i	−0.211616	−	0.977353i	$-0.567872\pi$
$587$	18.9777	−	26.1206i	0.783295	−	1.07811i	0.994911	−	0.100760i	$-0.0321275\pi$
$588$	0.298600	−	0.410988i	0.0123141	−	0.0169488i
$589$	−2.89927	+	2.10644i	−0.119462	+	0.0867945i
$590$	2.83252	−	28.7501i	0.116613	−	1.18362i
$591$	6.82322	+	4.95736i	0.280670	+	0.203919i
$592$	−2.26373	+	0.735531i	−0.0930388	+	0.0302301i
$593$		−	26.0643i		−	1.07033i	−0.844747	−	0.535167i	$-0.820249\pi$
$593$		−	26.0643i		−	1.07033i	0.844747	−	0.535167i	$-0.179751\pi$
$594$	−0.845511	−	2.60221i	−0.0346917	−	0.106770i
$595$	−0.0333122	−	0.151851i	−0.00136567	−	0.00622527i
$596$	−5.76494	+	17.7426i	−0.236141	+	0.726767i
$597$	13.7258	+	4.45978i	0.561760	+	0.182527i
$598$	12.9256	+	17.7906i	0.528567	+	0.727510i
$599$	22.1927			0.906770			0.453385	−	0.891315i	$-0.350216\pi$
$599$	22.1927			0.906770			0.453385	+	0.891315i	$0.350216\pi$
$600$	9.08938	+	1.80857i	0.371072	+	0.0738345i
$601$	−46.5664			−1.89948			−0.949742	−	0.313033i	$-0.898655\pi$
$601$	−46.5664			−1.89948			−0.949742	+	0.313033i	$0.898655\pi$
$602$	6.98621	+	9.61569i	0.284737	+	0.391906i
$603$	27.2512	+	8.85444i	1.10975	+	0.360581i
$604$	3.35758	−	10.3336i	0.136618	−	0.420467i
$605$	9.36583	−	21.4103i	0.380775	−	0.870452i
$606$	2.79586	+	8.60477i	0.113574	+	0.349545i
$607$		−	17.4767i		−	0.709359i	−0.934988	−	0.354679i	$-0.884590\pi$
$607$		−	17.4767i		−	0.709359i	0.934988	−	0.354679i	$-0.115410\pi$
$608$	−4.11427	+	1.33681i	−0.166856	+	0.0542147i
$609$	3.62140	+	2.63110i	0.146747	+	0.106618i
$610$	−15.6518	−	6.84679i	−0.633722	−	0.277219i
$611$	−21.2740	+	15.4565i	−0.860653	+	0.625301i
$612$	0.0364029	−	0.0501043i	0.00147150	−	0.00202534i
$613$	24.3899	−	33.5698i	0.985097	−	1.35587i	0.0510589	−	0.998696i	$-0.483740\pi$
$613$	24.3899	−	33.5698i	0.985097	−	1.35587i	0.934038	−	0.357174i	$-0.116260\pi$
$614$	17.5434	−	12.7461i	0.707996	−	0.514389i
$615$	−3.39547	−	5.79363i	−0.136919	−	0.233622i
$616$	−4.49018	−	3.26231i	−0.180915	−	0.131442i
$617$	−39.4003	+	12.8019i	−1.58620	+	0.515387i	−0.963644	−	0.267190i	$-0.913905\pi$
$617$	−39.4003	+	12.8019i	−1.58620	+	0.515387i	−0.622554	+	0.782577i	$0.713905\pi$
$618$		−	1.51760i		−	0.0610468i
$619$	1.35341	+	4.16537i	0.0543981	+	0.167420i	0.974564	−	0.224108i	$-0.0719467\pi$
$619$	1.35341	+	4.16537i	0.0543981	+	0.167420i	−0.920166	+	0.391528i	$0.871947\pi$
$620$	6.59986	+	0.650233i	0.265057	+	0.0261140i
$621$	5.52640	−	17.0085i	0.221767	−	0.682529i
$622$	−2.23146	−	0.725045i	−0.0894734	−	0.0290717i
$623$	−2.86918	−	3.94908i	−0.114951	−	0.158217i
$624$	3.89200			0.155805
$625$	23.0958	+	9.56991i	0.923833	+	0.382796i
$626$	−6.79458			−0.271566
$627$	−0.263656	−	0.362892i	−0.0105294	−	0.0144925i
$628$	−0.883389	−	0.287031i	−0.0352511	−	0.0114538i
$629$	0.0125917	−	0.0387533i	0.000502065	−	0.00154520i
$630$	15.5249	+	1.52955i	0.618528	+	0.0609388i
$631$	−13.4424	−	41.3714i	−0.535132	−	1.64697i	−0.743363	−	0.668888i	$-0.766770\pi$
$631$	−13.4424	−	41.3714i	−0.535132	−	1.64697i	0.208231	−	0.978080i	$-0.433230\pi$
$632$		−	15.3013i		−	0.608653i
$633$	12.0880	−	3.92762i	0.480454	−	0.156109i
$634$	−16.6598	−	12.1041i	−0.661646	−	0.480714i
$635$	3.29293	+	5.61868i	0.130676	+	0.222970i
$636$	−1.99040	+	1.44611i	−0.0789244	+	0.0573419i
$637$	2.30825	−	3.17704i	0.0914564	−	0.125879i
$638$	−1.42511	+	1.96149i	−0.0564205	+	0.0776561i
$639$	22.3056	−	16.2059i	0.882395	−	0.641097i
$640$	−0.0296366	−	0.0129644i	−0.00117149	−	0.000512463i
$641$	26.6714	+	19.3779i	1.05346	+	0.765383i	0.972867	−	0.231364i	$-0.0743190\pi$
$641$	26.6714	+	19.3779i	1.05346	+	0.765383i	0.0805918	+	0.996747i	$0.474319\pi$
$642$	6.00044	−	1.94966i	0.236818	−	0.0769470i
$643$		−	23.4501i		−	0.924783i	−0.886676	−	0.462391i	$-0.846992\pi$
$643$		−	23.4501i		−	0.924783i	0.886676	−	0.462391i	$-0.153008\pi$
$644$	−3.28104	−	10.0980i	−0.129291	−	0.397917i
$645$	2.43411	−	5.56438i	0.0958430	−	0.219097i
$646$	−0.00950802	+	0.0292627i	−0.000374088	+	0.00115132i
$647$	−46.2079	−	15.0139i	−1.81662	−	0.590255i	−0.999913	−	0.0132021i	$-0.995798\pi$
$647$	−46.2079	−	15.0139i	−1.81662	−	0.590255i	−0.816707	−	0.577053i	$-0.804202\pi$
$648$	10.5021	+	14.4548i	0.412560	+	0.567840i
$649$	8.84081			0.347032
$650$	20.5650	+	4.09193i	0.806624	+	0.160499i
$651$	−5.30812			−0.208042
$652$	6.15866	+	8.47667i	0.241192	+	0.331972i
$653$	23.6779	+	7.69342i	0.926588	+	0.301067i	0.733167	−	0.680049i	$-0.238042\pi$
$653$	23.6779	+	7.69342i	0.926588	+	0.301067i	0.193421	+	0.981116i	$0.438042\pi$
$654$	−1.71717	+	5.28492i	−0.0671468	+	0.206657i
$655$	−2.06417	−	9.40933i	−0.0806538	−	0.367653i
$656$	2.54453	+	7.83127i	0.0993473	+	0.305760i
$657$		−	5.78150i		−	0.225558i
$658$	−17.1064	+	5.55819i	−0.666875	+	0.216681i
$659$	9.85826	+	7.16244i	0.384023	+	0.279009i	0.763002	−	0.646396i	$-0.223725\pi$
$659$	9.85826	+	7.16244i	0.384023	+	0.279009i	−0.378979	+	0.925405i	$0.623725\pi$
$660$	−0.0813874	+	0.826081i	−0.00316800	+	0.0321552i
$661$	15.7428	−	11.4378i	0.612326	−	0.444881i	−0.237907	−	0.971288i	$-0.576461\pi$
$661$	15.7428	−	11.4378i	0.612326	−	0.444881i	0.850233	+	0.526407i	$0.176461\pi$
$662$	−18.8710	+	25.9737i	−0.733442	+	1.00950i
$663$	−0.0391630	+	0.0539033i	−0.00152097	+	0.00209343i
$664$	40.9666	−	29.7640i	1.58981	−	1.15507i
$665$	5.34378	−	1.17229i	0.207223	−	0.0454595i
$666$	3.30799	+	2.40340i	0.128182	+	0.0931297i
$667$	−15.0716	+	4.89705i	−0.583573	+	0.189614i
$668$			3.29844i			0.127620i
$669$	0.647512	+	1.99284i	0.0250343	+	0.0770475i
$670$	19.6913	+	17.4992i	0.760742	+	0.676054i
$671$	1.61556	−	4.97217i	0.0623679	−	0.191949i
$672$	−6.09400	−	1.98006i	−0.235081	−	0.0763825i
$673$	1.07875	+	1.48477i	0.0415828	+	0.0572338i	0.829302	−	0.558801i	$-0.188738\pi$
$673$	1.07875	+	1.48477i	0.0415828	+	0.0572338i	−0.787719	+	0.616034i	$0.788738\pi$
$674$	−24.0487			−0.926321
$675$	−7.13824	−	15.4865i	−0.274751	−	0.596077i
$676$	−1.65541			−0.0636698
$677$	−8.57273	−	11.7993i	−0.329477	−	0.453486i	0.611854	−	0.790970i	$-0.290424\pi$
$677$	−8.57273	−	11.7993i	−0.329477	−	0.453486i	−0.941331	+	0.337485i	$0.890424\pi$
$678$	−10.2848	−	3.34175i	−0.394987	−	0.128339i
$679$	−6.30769	+	19.4131i	−0.242067	+	0.745006i
$680$	0.167840	−	0.0983656i	0.00643635	−	0.00377215i
$681$	3.46720	+	10.6709i	0.132863	+	0.408911i
$682$		−	2.87508i		−	0.110093i
$683$	−28.3701	+	9.21802i	−1.08555	+	0.352718i	−0.796527	−	0.604603i	$-0.793332\pi$
$683$	−28.3701	+	9.21802i	−1.08555	+	0.352718i	−0.289027	+	0.957321i	$0.593332\pi$
$684$	1.76322	+	1.28105i	0.0674184	+	0.0489823i
$685$	−19.6751	+	22.1398i	−0.751747	+	0.845917i
$686$	17.1757	−	12.4789i	0.655770	−	0.476445i
$687$	0.633325	−	0.871697i	0.0241628	−	0.0332573i
$688$	−4.37740	+	6.02497i	−0.166887	+	0.229700i
$689$	−15.3863	+	11.1788i	−0.586171	+	0.425878i
$690$	5.10569	−	5.74528i	0.194370	−	0.218719i
$691$	−11.2840	−	8.19830i	−0.429263	−	0.311878i	0.352091	−	0.935966i	$-0.385471\pi$
$691$	−11.2840	−	8.19830i	−0.429263	−	0.311878i	−0.781354	+	0.624088i	$0.785471\pi$
$692$	16.6769	−	5.41864i	0.633959	−	0.205986i
$693$			4.77400i			0.181349i
$694$	8.46104	+	26.0404i	0.321177	+	0.988480i
$695$	9.68745	−	5.67752i	0.367466	−	0.215361i
$696$	−1.73096	+	5.32735i	−0.0656119	+	0.201933i
$697$	−0.134065	−	0.0435604i	−0.00507808	−	0.00164997i
$698$	−0.217364	−	0.299176i	−0.00822735	−	0.0113240i
$699$	−9.20168			−0.348039
$700$	−8.83293	−	4.94739i	−0.333854	−	0.186994i
$701$	−38.2789			−1.44577			−0.722886	−	0.690967i	$-0.757185\pi$
$701$	−38.2789			−1.44577			−0.722886	+	0.690967i	$0.757185\pi$
$702$	−8.40670	−	11.5708i	−0.317290	−	0.436713i
$703$	1.36377	+	0.443115i	0.0514355	+	0.0167124i
$704$	1.83259	−	5.64012i	0.0690682	−	0.212570i
$705$	6.87021	+	6.10540i	0.258747	+	0.229943i
$706$	−4.74663	−	14.6086i	−0.178642	−	0.549803i
$707$		−	33.7695i		−	1.27003i
$708$	5.68557	−	1.84735i	0.213677	−	0.0694279i
$709$	32.6763	+	23.7407i	1.22718	+	0.891602i	0.996676	−	0.0814688i	$-0.0259611\pi$
$709$	32.6763	+	23.7407i	1.22718	+	0.891602i	0.230508	+	0.973070i	$0.425961\pi$
$710$	24.7594	−	5.43160i	0.929205	−	0.203844i
$711$	−10.6479	+	7.73613i	−0.399326	+	0.290127i
$712$	3.59040	−	4.94176i	0.134556	−	0.185200i
$713$	11.0457	−	15.2031i	0.413664	−	0.569360i
$714$	−0.0368702	+	0.0267878i	−0.00137983	+	0.00100251i
$715$	−0.629145	+	6.38582i	−0.0235287	+	0.238816i
$716$	−2.42652	−	1.76297i	−0.0906834	−	0.0658853i
$717$	−7.36977	+	2.39458i	−0.275229	+	0.0894274i
$718$		−	21.3161i		−	0.795510i
$719$	2.70664	+	8.33020i	0.100941	+	0.310664i	0.988756	−	0.149536i	$-0.0477779\pi$
$719$	2.70664	+	8.33020i	0.100941	+	0.310664i	−0.887816	+	0.460200i	$0.847778\pi$
$720$	2.09451	+	9.54762i	0.0780577	+	0.355819i
$721$	−1.75037	+	5.38710i	−0.0651873	+	0.200626i
$722$	−1.02978	−	0.334597i	−0.0383246	−	0.0124524i
$723$	1.76439	+	2.42847i	0.0656183	+	0.0903159i
$724$	−16.0108			−0.595037
$725$	−7.38412	+	13.1834i	−0.274239	+	0.489620i
$726$	−6.85074			−0.254255
$727$	28.4720	+	39.1883i	1.05597	+	1.45341i	0.883518	+	0.468397i	$0.155168\pi$
$727$	28.4720	+	39.1883i	1.05597	+	1.45341i	0.172449	+	0.985018i	$0.444832\pi$
$728$	−27.5920	−	8.96517i	−1.02263	−	0.332271i
$729$	2.83505	−	8.72539i	0.105002	−	0.323163i
$730$	2.13027	−	4.86980i	0.0788449	−	0.180239i
$731$	−0.0393971	−	0.121252i	−0.00145715	−	0.00448466i
$732$		−	3.53522i		−	0.130665i
$733$	17.7833	−	5.77815i	0.656842	−	0.213421i	0.0384134	−	0.999262i	$-0.487770\pi$
$733$	17.7833	−	5.77815i	0.656842	−	0.213421i	0.618429	+	0.785841i	$0.287770\pi$
$734$	−12.4647	−	9.05616i	−0.460082	−	0.334269i
$735$	−1.25753	−	0.550101i	−0.0463847	−	0.0202908i
$736$	18.3521	−	13.3336i	0.676469	−	0.491483i
$737$	−4.73854	+	6.52204i	−0.174546	+	0.240242i
$738$	8.31442	−	11.4438i	0.306058	−	0.421253i
$739$	13.3125	−	9.67209i	0.489708	−	0.355794i	−0.315364	−	0.948971i	$-0.602127\pi$
$739$	13.3125	−	9.67209i	0.489708	−	0.355794i	0.805072	+	0.593177i	$0.202127\pi$
$740$	−1.34174	−	2.28939i	−0.0493235	−	0.0841598i
$741$	−1.89691	−	1.37819i	−0.0696848	−	0.0506289i
$742$	−12.3721	+	4.01993i	−0.454193	+	0.147576i
$743$			6.92915i			0.254206i	0.991890	+	0.127103i	$0.0405678\pi$
$743$			6.92915i			0.254206i	−0.991890	+	0.127103i	$0.959432\pi$
$744$	−2.05262	−	6.31733i	−0.0752528	−	0.231604i
$745$	50.1630	+	4.94217i	1.83783	+	0.181067i
$746$	9.14213	−	28.1366i	0.334717	−	1.03015i
$747$	−41.4243	−	13.4596i	−1.51564	−	0.492460i
$748$	0.0102420	+	0.0140968i	0.000374483	+	0.000515432i
$749$	−23.5488			−0.860453
$750$	−0.143221	−	7.32742i	−0.00522969	−	0.267560i
$751$	44.1884			1.61246			0.806229	−	0.591604i	$-0.201505\pi$
$751$	44.1884			1.61246			0.806229	+	0.591604i	$0.201505\pi$
$752$	−6.62437	−	9.11766i	−0.241566	−	0.332487i
$753$	15.2269	+	4.94753i	0.554900	+	0.180298i
$754$	−3.91634	+	12.0533i	−0.142625	+	0.438954i
$755$	−29.2156	−	2.87839i	−1.06327	−	0.104755i
$756$	2.13396	+	6.56765i	0.0776114	+	0.238863i
$757$		−	20.0944i		−	0.730342i	−0.930940	−	0.365171i	$-0.881011\pi$
$757$		−	20.0944i		−	0.730342i	0.930940	−	0.365171i	$-0.118989\pi$
$758$	−19.8959	+	6.46456i	−0.722651	+	0.234804i
$759$	1.90292	+	1.38255i	0.0690715	+	0.0501834i
$760$	3.46158	+	5.90644i	0.125565	+	0.214249i
$761$	−36.0080	+	26.1613i	−1.30529	+	0.948348i	−0.999992	−	0.00390991i	$-0.998755\pi$
$761$	−36.0080	+	26.1613i	−1.30529	+	0.948348i	−0.305296	+	0.952257i	$0.598755\pi$
$762$	1.12218	−	1.54455i	0.0406522	−	0.0559530i
$763$	12.1911	−	16.7796i	0.441346	−	0.607461i
$764$	9.42396	−	6.84691i	0.340947	−	0.247712i
$765$	−0.153308	−	0.0670638i	−0.00554286	−	0.00242470i
$766$	17.2945	+	12.5652i	0.624877	+	0.454000i
$767$	43.9510	−	14.2805i	1.58698	−	0.515640i
$768$		−	9.68159i		−	0.349354i
$769$	1.54459	+	4.75375i	0.0556992	+	0.171424i	0.975036	−	0.222047i	$-0.0712739\pi$
$769$	1.54459	+	4.75375i	0.0556992	+	0.171424i	−0.919337	+	0.393472i	$0.871274\pi$
$770$	−1.75905	+	4.02118i	−0.0633916	+	0.144913i
$771$	−2.07926	+	6.39931i	−0.0748827	+	0.230465i
$772$	−11.0045	−	3.57557i	−0.396060	−	0.128688i
$773$	−12.6651	−	17.4320i	−0.455530	−	0.626984i	0.518044	−	0.855354i	$-0.326660\pi$
$773$	−12.6651	−	17.4320i	−0.455530	−	0.626984i	−0.973574	+	0.228370i	$0.926660\pi$
$774$	12.7934			0.459848
$775$	−2.10501	−	17.7944i	−0.0756140	−	0.639194i
$776$	−25.5431			−0.916945
$777$	1.24843	+	1.71831i	0.0447871	+	0.0616441i
$778$	−15.2598	−	4.95821i	−0.547091	−	0.177760i
$779$	1.53294	−	4.71789i	0.0549231	−	0.169036i
$780$	0.929760	+	4.23822i	0.0332907	+	0.151753i
$781$	2.39709	+	7.37750i	0.0857748	+	0.263988i
$782$		−	0.161343i		−	0.00576962i
$783$	9.80241	−	3.18500i	0.350310	−	0.113823i
$784$	1.36162	+	0.989278i	0.0486294	+	0.0353313i
$785$	−0.246066	+	2.49757i	−0.00878246	+	0.0891420i
$786$	−2.28463	+	1.65988i	−0.0814902	+	0.0592061i
$787$	12.4198	−	17.0944i	0.442719	−	0.609350i	−0.528095	−	0.849186i	$-0.677093\pi$
$787$	12.4198	−	17.0944i	0.442719	−	0.609350i	0.970814	+	0.239835i	$0.0770934\pi$
$788$	6.77684	−	9.32751i	0.241415	−	0.332279i
$789$	7.97497	−	5.79415i	0.283916	−	0.206277i
$790$	−11.8193	+	2.59285i	−0.420510	+	0.0922494i
$791$	32.6543	+	23.7247i	1.16105	+	0.843554i
$792$	−5.68165	+	1.84608i	−0.201889	+	0.0655976i
$793$		−	27.3281i		−	0.970450i
$794$	−3.12358	−	9.61341i	−0.110852	−	0.341167i
$795$	4.96884	+	4.41570i	0.176227	+	0.156609i
$796$	6.09664	−	18.7635i	0.216090	−	0.665055i
$797$	−20.1508	−	6.54740i	−0.713779	−	0.231921i	−0.0704551	−	0.997515i	$-0.522445\pi$
$797$	−20.1508	−	6.54740i	−0.713779	−	0.231921i	−0.643324	+	0.765594i	$0.722445\pi$
$798$	−0.942688	−	1.29750i	−0.0333708	−	0.0459310i
$799$	0.192934			0.00682553
$800$	4.22109	−	21.2141i	0.149238	−	0.750032i
$801$	−5.25413			−0.185646
$802$	−10.8167	−	14.8879i	−0.381951	−	0.525711i
$803$	1.54701	+	0.502655i	0.0545929	+	0.0177383i
$804$	−1.68455	+	5.18451i	−0.0594095	+	0.182844i
$805$	−24.7504	+	14.5055i	−0.872338	+	0.511251i
$806$	−4.64411	−	14.2931i	−0.163582	−	0.503453i
$807$		−	10.1931i		−	0.358814i
$808$	40.1898	−	13.0585i	1.41387	−	0.459395i
$809$	11.8685	+	8.62298i	0.417275	+	0.303168i	0.776540	−	0.630068i	$-0.216973\pi$
$809$	11.8685	+	8.62298i	0.417275	+	0.303168i	−0.359266	+	0.933235i	$0.616973\pi$
$810$	9.38581	−	10.5616i	0.329784	−	0.371095i
$811$	28.9283	−	21.0177i	1.01581	−	0.738030i	0.0503910	−	0.998730i	$-0.483953\pi$
$811$	28.9283	−	21.0177i	1.01581	−	0.738030i	0.965420	+	0.260700i	$0.0839532\pi$
$812$	3.59678	−	4.95055i	0.126222	−	0.173730i
$813$	−1.51740	+	2.08853i	−0.0532177	+	0.0732479i
$814$	−0.930703	+	0.676196i	−0.0326211	+	0.0237006i
$815$	18.8055	−	21.1612i	0.658727	−	0.741245i
$816$	−0.0231020	−	0.0167846i	−0.000808732	−	0.000587578i
$817$	4.26697	−	1.38642i	0.149282	−	0.0485048i
$818$		−	2.65427i		−	0.0928043i
$819$	7.71143	+	23.7333i	0.269459	+	0.829310i
$820$	−7.92004	+	4.64169i	−0.276580	+	0.162095i
$821$	−7.44249	+	22.9056i	−0.259745	+	0.799412i	0.733113	+	0.680107i	$0.238067\pi$
$821$	−7.44249	+	22.9056i	−0.259745	+	0.799412i	−0.992858	+	0.119305i	$0.961933\pi$
$822$	8.25789	+	2.68315i	0.288027	+	0.0935857i
$823$	10.3250	+	14.2111i	0.359907	+	0.495370i	0.950123	−	0.311876i	$-0.100957\pi$
$823$	10.3250	+	14.2111i	0.359907	+	0.495370i	−0.590216	+	0.807246i	$0.700957\pi$
$824$	−7.08817			−0.246928
$825$	2.22726	−	0.263476i	0.0775434	−	0.00917306i
$826$	31.6098			1.09985
$827$	13.3019	+	18.3085i	0.462554	+	0.636650i	0.975036	−	0.222047i	$-0.0712740\pi$
$827$	13.3019	+	18.3085i	0.462554	+	0.636650i	−0.512482	+	0.858698i	$0.671274\pi$
$828$	−10.8692	−	3.53162i	−0.377731	−	0.122732i
$829$	4.82570	−	14.8520i	0.167603	−	0.515830i	−0.831615	−	0.555352i	$-0.812584\pi$
$829$	4.82570	−	14.8520i	0.167603	−	0.515830i	0.999219	+	0.0395220i	$0.0125835\pi$
$830$	−29.9327	−	26.6005i	−1.03898	−	0.923315i
$831$	−1.14382	−	3.52031i	−0.0396786	−	0.122118i
$832$		−	30.9993i		−	1.07471i
$833$	−0.0274025	+	0.00890361i	−0.000949440	+	0.000308492i
$834$	−2.66303	−	1.93481i	−0.0922133	−	0.0669969i
$835$	8.70504	−	1.90967i	0.301250	−	0.0660867i
$836$	−0.496082	+	0.360425i	−0.0171574	+	0.0124655i
$837$	−7.18402	+	9.88795i	−0.248316	+	0.341778i
$838$	3.14430	−	4.32776i	0.108618	−	0.149500i
$839$	0.331697	−	0.240992i	0.0114515	−	0.00831998i	−0.582045	−	0.813157i	$-0.697747\pi$
$839$	0.331697	−	0.240992i	0.0114515	−	0.00831998i	0.593496	+	0.804837i	$0.297747\pi$
$840$	−0.994232	+	10.0914i	−0.0343042	+	0.348188i
$841$	16.0727	+	11.6775i	0.554230	+	0.402671i
$842$	−17.0521	+	5.54055i	−0.587653	+	0.190940i
$843$		−	3.57724i		−	0.123207i
$844$	−5.36916	−	16.5246i	−0.184814	−	0.568800i
$845$	0.958420	+	4.36887i	0.0329706	+	0.150294i
$846$	−5.98268	+	18.4128i	−0.205689	+	0.633045i
$847$	24.3184	+	7.90153i	0.835590	+	0.271500i
$848$	−4.79103	−	6.59429i	−0.164525	−	0.226449i
$849$	−1.90517			−0.0653853
$850$	−0.104422	−	0.112977i	−0.00358164	−	0.00387507i
$851$	−7.51930			−0.257758
$852$	3.08317	+	4.24362i	0.105628	+	0.145384i
$853$	40.8041	+	13.2580i	1.39710	+	0.453947i	0.908253	−	0.418421i	$-0.137416\pi$
$853$	40.8041	+	13.2580i	1.39710	+	0.453947i	0.488851	+	0.872367i	$0.337416\pi$
$854$	5.77633	−	17.7777i	0.197662	−	0.608341i
$855$	2.36004	−	5.39506i	0.0807118	−	0.184507i
$856$	−9.10618	−	28.0259i	−0.311243	−	0.957907i
$857$			8.90525i			0.304198i	0.988365	+	0.152099i	$0.0486032\pi$
$857$			8.90525i			0.304198i	−0.988365	+	0.152099i	$0.951397\pi$
$858$	1.78902	−	0.581287i	0.0610761	−	0.0198448i
$859$	42.9658	+	31.2165i	1.46598	+	1.06509i	0.981756	+	0.190147i	$0.0608965\pi$
$859$	42.9658	+	31.2165i	1.46598	+	1.06509i	0.484220	+	0.874946i	$0.339104\pi$
$860$	−7.60664	−	3.32749i	−0.259384	−	0.113466i
$861$	5.94441	−	4.31887i	0.202585	−	0.147187i
$862$	−0.0484433	+	0.0666765i	−0.00164999	+	0.00227101i
$863$	−16.2066	+	22.3065i	−0.551679	+	0.759321i	−0.990239	−	0.139381i	$-0.955489\pi$
$863$	−16.2066	+	22.3065i	−0.551679	+	0.759321i	0.438560	+	0.898702i	$0.355489\pi$
$864$	−11.9361	+	8.67206i	−0.406073	+	0.295030i
$865$	−23.9558	−	40.8754i	−0.814522	−	1.38981i
$866$	−21.8229	−	15.8552i	−0.741571	−	0.538783i
$867$	−9.78755	+	3.18017i	−0.332403	+	0.108004i
$868$			7.25634i			0.246296i
$869$	−1.14429	−	3.52175i	−0.0388172	−	0.119467i
$870$	4.40835	+	0.434320i	0.149457	+	0.0147248i
$871$	−13.0220	+	40.0776i	−0.441234	+	1.35798i
$872$	24.6840	+	8.02031i	0.835905	+	0.271602i
$873$	12.9142	+	17.7749i	0.437081	+	0.601590i
$874$	5.67783			0.192055
$875$	−7.94292	+	26.1757i	−0.268520	+	0.884900i
$876$	1.09993			0.0371631
$877$	22.2193	+	30.5822i	0.750291	+	1.03269i	0.997960	+	0.0638424i	$0.0203355\pi$
$877$	22.2193	+	30.5822i	0.750291	+	1.03269i	−0.247669	+	0.968845i	$0.579665\pi$
$878$	−7.46837	−	2.42662i	−0.252045	−	0.0818945i
$879$	5.57974	−	17.1727i	0.188200	−	0.579220i
$880$	−2.73685	−	0.269641i	−0.0922593	−	0.00908959i
$881$	8.83191	+	27.1818i	0.297555	+	0.915779i	0.982351	+	0.187045i	$0.0598910\pi$
$881$	8.83191	+	27.1818i	0.297555	+	0.915779i	−0.684797	+	0.728734i	$0.740109\pi$
$882$		−	2.89126i		−	0.0973538i
$883$	−37.4790	+	12.1777i	−1.26127	+	0.409811i	−0.861947	−	0.506999i	$-0.830755\pi$
$883$	−37.4790	+	12.1777i	−1.26127	+	0.409811i	−0.399323	+	0.916810i	$0.630755\pi$
$884$	0.0736871	+	0.0535368i	0.00247837	+	0.00180064i
$885$	−8.16715	−	13.9355i	−0.274536	−	0.468436i
$886$	12.5369	−	9.10856i	0.421184	−	0.306008i
$887$	−20.4762	+	28.1830i	−0.687522	+	0.946293i	−0.999993	−	0.00363408i	$-0.998843\pi$
$887$	−20.4762	+	28.1830i	−0.687522	+	0.946293i	0.312471	+	0.949927i	$0.398843\pi$
$888$	−1.56224	+	2.15024i	−0.0524255	+	0.0721575i
$889$	−5.76491	+	4.18845i	−0.193349	+	0.140476i
$890$	−4.42559	−	1.93595i	−0.148346	−	0.0648933i
$891$	3.49814	+	2.54155i	0.117192	+	0.0851450i
$892$	2.72426	−	0.885165i	0.0912149	−	0.0296375i
$893$			6.78956i			0.227204i
$894$	−4.56623	−	14.0534i	−0.152717	−	0.470016i
$895$	−3.24787	+	7.42462i	−0.108564	+	0.248178i
$896$	0.0109375	−	0.0336621i	0.000365396	−	0.00112457i
$897$	11.6933	+	3.79939i	0.390429	+	0.126858i
$898$	−13.9691	−	19.2268i	−0.466154	−	0.641606i
$899$	10.8303			0.361211
$900$	−9.89658	+	4.56166i	−0.329886	+	0.152055i
$901$	0.139539			0.00464871
$902$	2.33926	+	3.21972i	0.0778890	+	0.107205i
$903$	6.32018	+	2.05355i	0.210322	+	0.0683379i
$904$	−15.6081	+	48.0369i	−0.519119	+	1.59768i
$905$	9.26964	+	42.2548i	0.308133	+	1.40460i
$906$	2.65943	+	8.18489i	0.0883537	+	0.271925i
$907$			47.3329i			1.57166i	0.618440	+	0.785832i	$0.287765\pi$
$907$			47.3329i			1.57166i	−0.618440	+	0.785832i	$0.712235\pi$
$908$	14.5875	−	4.73975i	0.484102	−	0.157294i
$909$	−29.4066	−	21.3651i	−0.975354	−	0.708636i
$910$	−2.24947	+	22.8321i	−0.0745693	+	0.756878i
$911$	−26.1253	+	18.9812i	−0.865571	+	0.628874i	−0.929395	−	0.369087i	$-0.879670\pi$
$911$	−26.1253	+	18.9812i	−0.865571	+	0.628874i	0.0638237	+	0.997961i	$0.479670\pi$
$912$	0.590667	−	0.812983i	0.0195589	−	0.0269206i
$913$	7.20303	−	9.91411i	0.238385	−	0.328109i
$914$	−17.6085	+	12.7934i	−0.582439	+	0.423167i
$915$	−9.32993	+	2.04675i	−0.308438	+	0.0676635i
$916$	−1.19163	−	0.865771i	−0.0393726	−	0.0286059i
$917$	10.0244	−	3.25711i	0.331034	−	0.107559i
$918$			0.104936i			0.00346341i
$919$	−14.9258	−	45.9370i	−0.492358	−	1.51532i	−0.821034	−	0.570879i	$-0.806603\pi$
$919$	−14.9258	−	45.9370i	−0.492358	−	1.51532i	0.328677	−	0.944442i	$-0.393397\pi$
$920$	−26.8342	−	23.8469i	−0.884696	−	0.786209i
$921$	3.74662	−	11.5309i	0.123455	−	0.379956i
$922$	−26.5047	−	8.61189i	−0.872885	−	0.283617i
$923$	23.8337	+	32.8043i	0.784496	+	1.07977i
$924$	−0.908251			−0.0298793
$925$	−5.26521	+	4.86652i	−0.173119	+	0.160010i
$926$	13.7083			0.450482
$927$	3.58368	+	4.93252i	0.117704	+	0.162005i
$928$	12.4337	+	4.03997i	0.408157	+	0.132618i
$929$	13.0119	−	40.0466i	0.426908	−	1.31389i	−0.474248	−	0.880391i	$-0.657280\pi$
$929$	13.0119	−	40.0466i	0.426908	−	1.31389i	0.901156	−	0.433495i	$-0.142720\pi$
$930$	−4.53190	+	2.65601i	−0.148607	+	0.0870938i
$931$	−0.313327	−	0.964321i	−0.0102689	−	0.0316043i
$932$			12.5789i			0.412037i
$933$	−1.24764	+	0.405383i	−0.0408459	+	0.0132716i
$934$	−23.8277	−	17.3118i	−0.779666	−	0.566460i
$935$	0.0312738	−	0.0351915i	0.00102276	−	0.00115088i
$936$	−25.2636	+	18.3551i	−0.825768	+	0.599956i
$937$	−29.8374	+	41.0677i	−0.974746	+	1.34162i	−0.0351329	+	0.999383i	$0.511185\pi$
$937$	−29.8374	+	41.0677i	−0.974746	+	1.34162i	−0.939613	+	0.342240i	$0.888815\pi$
$938$	−16.9424	+	23.3192i	−0.553188	+	0.761398i
$939$	−3.07341	+	2.23296i	−0.100297	+	0.0728699i
$940$	8.34624	−	9.39176i	0.272224	−	0.306325i
$941$	38.5299	+	27.9936i	1.25604	+	0.912566i	0.998556	−	0.0537166i	$-0.0171068\pi$
$941$	38.5299	+	27.9936i	1.25604	+	0.912566i	0.257483	+	0.966283i	$0.417107\pi$
$942$	0.699705	−	0.227348i	0.0227976	−	0.00740740i
$943$			26.0126i			0.847088i
$944$	6.12039	+	18.8366i	0.199202	+	0.613079i
$945$	16.0975	−	9.43423i	0.523651	−	0.306896i
$946$	−1.11228	+	3.42325i	−0.0361634	+	0.111299i
$947$	−23.8806	−	7.75928i	−0.776015	−	0.252143i	−0.105877	−	0.994379i	$-0.533765\pi$
$947$	−23.8806	−	7.75928i	−0.776015	−	0.252143i	−0.670138	+	0.742237i	$0.733765\pi$
$948$	−1.47179	−	2.02575i	−0.0478016	−	0.0657933i
$949$	8.50271			0.276010
$950$	3.97577	−	3.67471i	0.128991	−	0.119223i
$951$	−11.5136			−0.373356
$952$	0.125116	+	0.172208i	0.00405504	+	0.00558128i
$953$	−12.6526	−	4.11107i	−0.409857	−	0.133171i	0.0968293	−	0.995301i	$-0.469130\pi$
$953$	−12.6526	−	4.11107i	−0.409857	−	0.133171i	−0.506687	+	0.862130i	$0.669130\pi$
$954$	−4.32694	+	13.3170i	−0.140090	+	0.431152i
$955$	−23.5260	−	20.9070i	−0.761285	−	0.676536i
$956$	3.27346	+	10.0747i	0.105871	+	0.325838i
$957$			1.35559i			0.0438200i
$958$	12.9341	−	4.20256i	0.417883	−	0.135778i
$959$	−26.2187	−	19.0490i	−0.846647	−	0.615125i
$960$	−10.5833	+	2.32171i	−0.341574	+	0.0749327i
$961$	14.6894	−	10.6725i	0.473852	−	0.344274i
$962$	−3.53462	+	4.86498i	−0.113961	+	0.156853i
$963$	−14.8987	+	20.5063i	−0.480105	+	0.660807i
$964$	3.31978	−	2.41196i	0.106923	−	0.0776841i
$965$	−3.06527	+	31.1125i	−0.0986746	+	1.00155i
$966$	6.80377	+	4.94323i	0.218908	+	0.159046i
$967$	30.6761	−	9.96728i	0.986478	−	0.320526i	0.229028	−	0.973420i	$-0.426445\pi$
$967$	30.6761	−	9.96728i	0.986478	−	0.320526i	0.757450	+	0.652894i	$0.226445\pi$
$968$			31.9974i			1.02844i
$969$	0.00531606	+	0.0163612i	0.000170777	+	0.000525596i
$970$	4.32835	+	19.7304i	0.138975	+	0.633505i
$971$	0.785894	−	2.41873i	0.0252205	−	0.0776208i	−0.937654	−	0.347570i	$-0.887007\pi$
$971$	0.785894	−	2.41873i	0.0252205	−	0.0776208i	0.962875	+	0.269949i	$0.0870069\pi$
$972$	10.8338	+	3.52012i	0.347495	+	0.112908i
$973$	7.22152	+	9.93957i	0.231511	+	0.318648i
$974$	−15.7831			−0.505722
$975$	10.6470	−	4.90753i	0.340976	−	0.157167i
$976$	11.7124			0.374903
$977$	−0.174485	−	0.240159i	−0.00558228	−	0.00768335i	0.806217	−	0.591620i	$-0.201512\pi$
$977$	−0.174485	−	0.240159i	−0.00558228	−	0.00768335i	−0.811799	+	0.583937i	$0.801512\pi$
$978$	−7.89290	−	2.56456i	−0.252387	−	0.0820056i
$979$	0.456804	−	1.40590i	0.0145995	−	0.0449327i
$980$	−0.752002	+	1.71908i	−0.0240218	+	0.0549139i
$981$	−6.89871	−	21.2320i	−0.220259	−	0.677887i
$982$			16.2294i			0.517901i
$983$	−11.6409	+	3.78237i	−0.371288	+	0.120639i	−0.488717	−	0.872442i	$-0.662535\pi$
$983$	−11.6409	+	3.78237i	−0.371288	+	0.120639i	0.117429	+	0.993081i	$0.462535\pi$
$984$	7.43866	+	5.40450i	0.237136	+	0.172289i
$985$	−28.5401	−	12.4847i	−0.909364	−	0.397797i
$986$	0.0752271	−	0.0546557i	0.00239572	−	0.00174059i
$987$	−5.91112	+	8.13596i	−0.188153	+	0.258971i
$988$	−1.88402	+	2.59312i	−0.0599385	+	0.0824983i
$989$	−19.0333	+	13.8285i	−0.605223	+	0.439720i
$990$	2.38875	+	4.07588i	0.0759194	+	0.129540i
$991$	31.0617	+	22.5676i	0.986706	+	0.716884i	0.959197	−	0.282738i	$-0.0912426\pi$
$991$	31.0617	+	22.5676i	0.986706	+	0.716884i	0.0275087	+	0.999622i	$0.491243\pi$
$992$	−14.7443	+	4.79071i	−0.468131	+	0.152105i
$993$			17.9505i			0.569641i
$994$	8.57068	+	26.3778i	0.271845	+	0.836654i
$995$	−53.0493	−	5.22653i	−1.68177	−	0.165692i
$996$	2.56068	−	7.88095i	0.0811381	−	0.249717i
$997$	3.40010	+	1.10476i	0.107682	+	0.0349881i	0.362363	−	0.932037i	$-0.381970\pi$
$997$	3.40010	+	1.10476i	0.107682	+	0.0349881i	−0.254680	+	0.967025i	$0.581970\pi$
$998$	1.80988	+	2.49108i	0.0572907	+	0.0788539i
$999$	4.89049			0.154728

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.n.a.39.15	✓	80
25.9	even	10	inner	475.2.n.a.134.15	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.n.a.39.15	✓	80	1.1	even	1	trivial
475.2.n.a.134.15	yes	80	25.9	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.636441 + 0.875986i) q^{2} +(0.575766 + 0.187078i) q^{3} +(0.255740 - 0.787086i) q^{4} +(-2.22529 - 0.219241i) q^{5} +(0.202564 + 0.623427i) q^{6} -2.44664i q^{7} +(2.91181 - 0.946103i) q^{8} +(-2.13054 - 1.54793i) q^{9} +O(q^{10})\)	\(q+(0.636441 + 0.875986i) q^{2} +(0.575766 + 0.187078i) q^{3} +(0.255740 - 0.787086i) q^{4} +(-2.22529 - 0.219241i) q^{5} +(0.202564 + 0.623427i) q^{6} -2.44664i q^{7} +(2.91181 - 0.946103i) q^{8} +(-2.13054 - 1.54793i) q^{9} +(-1.22422 - 2.08886i) q^{10} +(0.599428 - 0.435510i) q^{11} +(0.294493 - 0.405334i) q^{12} +(2.27650 - 3.13334i) q^{13} +(2.14322 - 1.55714i) q^{14} +(-1.24023 - 0.542534i) q^{15} +(1.34289 + 0.975670i) q^{16} +(-0.0270256 + 0.00878114i) q^{17} -2.85149i q^{18} +(-0.309017 - 0.951057i) q^{19} +(-0.741658 + 1.69543i) q^{20} +(0.457712 - 1.40869i) q^{21} +(0.763002 + 0.247914i) q^{22} +(3.08220 + 4.24229i) q^{23} +1.85351 q^{24} +(4.90387 + 0.975751i) q^{25} +4.19362 q^{26} +(-2.00464 - 2.75915i) q^{27} +(-1.92572 - 0.625704i) q^{28} +(-0.933881 + 2.87419i) q^{29} +(-0.314083 - 1.43172i) q^{30} +(-1.10742 - 3.40830i) q^{31} -4.32600i q^{32} +(0.426605 - 0.138612i) q^{33} +(-0.0248923 - 0.0180853i) q^{34} +(-0.536404 + 5.44450i) q^{35} +(-1.76322 + 1.28105i) q^{36} +(-0.842856 + 1.16009i) q^{37} +(0.636441 - 0.875986i) q^{38} +(1.89691 - 1.37819i) q^{39} +(-6.68705 + 1.46697i) q^{40} +(4.01328 + 2.91582i) q^{41} +(1.52530 - 0.495600i) q^{42} +4.48656i q^{43} +(-0.189486 - 0.583179i) q^{44} +(4.40171 + 3.91170i) q^{45} +(-1.75455 + 5.39993i) q^{46} +(-6.45725 - 2.09809i) q^{47} +(0.590667 + 0.812983i) q^{48} +1.01395 q^{49} +(2.26628 + 4.91673i) q^{50} -0.0172031 q^{51} +(-1.88402 - 2.59312i) q^{52} +(-4.67017 - 1.51743i) q^{53} +(1.14114 - 3.51207i) q^{54} +(-1.42939 + 0.837719i) q^{55} +(-2.31477 - 7.12414i) q^{56} -0.605396i q^{57} +(-3.11211 + 1.01119i) q^{58} +(9.65317 + 7.01344i) q^{59} +(-0.744198 + 0.837423i) q^{60} +(5.70845 - 4.14743i) q^{61} +(2.28081 - 3.13927i) q^{62} +(-3.78723 + 5.21267i) q^{63} +(6.47530 - 4.70458i) q^{64} +(-5.75285 + 6.47350i) q^{65} +(0.392931 + 0.285481i) q^{66} +(-10.3479 + 3.36224i) q^{67} +0.0235171i q^{68} +(0.980990 + 3.01918i) q^{69} +(-5.11069 + 2.99522i) q^{70} +(-3.23523 + 9.95702i) q^{71} +(-7.66823 - 2.49156i) q^{72} +(1.29041 + 1.77609i) q^{73} -1.55265 q^{74} +(2.64094 + 1.47921i) q^{75} -0.827592 q^{76} +(-1.06554 - 1.46659i) q^{77} +(2.41454 + 0.784533i) q^{78} +(1.54438 - 4.75312i) q^{79} +(-2.77443 - 2.46557i) q^{80} +(1.80336 + 5.55016i) q^{81} +5.37132i q^{82} +(15.7298 - 5.11092i) q^{83} +(-0.991708 - 0.720518i) q^{84} +(0.0620650 - 0.0136155i) q^{85} +(-3.93016 + 2.85543i) q^{86} +(-1.07539 + 1.48015i) q^{87} +(1.33338 - 1.83524i) q^{88} +(1.61408 - 1.17270i) q^{89} +(-0.625164 + 6.34541i) q^{90} +(-7.66615 - 5.56979i) q^{91} +(4.12729 - 1.34104i) q^{92} -2.16956i q^{93} +(-2.27176 - 6.99177i) q^{94} +(0.479143 + 2.18413i) q^{95} +(0.809297 - 2.49076i) q^{96} +(-7.93458 - 2.57810i) q^{97} +(0.645318 + 0.888203i) q^{98} -1.95125 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9}+O(q^{10}) \) 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9	\( 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9} - 36 q^{10} + 20 q^{11} + 45 q^{12} - 10 q^{14} - 20 q^{16} - 15 q^{17} + 20 q^{19} + 12 q^{20} + 16 q^{21} + 15 q^{23} + 72 q^{24} + 41 q^{25} - 84 q^{26} + 15 q^{27} + 30 q^{28} - 24 q^{29} - 40 q^{30} + 8 q^{31} - 75 q^{33} - 24 q^{34} - 33 q^{35} - 32 q^{36} - 15 q^{37} - 30 q^{39} - 28 q^{40} + 13 q^{41} - 130 q^{42} - 24 q^{44} + 6 q^{45} + 30 q^{46} + 145 q^{48} - 28 q^{49} + 77 q^{50} - 36 q^{51} - 5 q^{52} - 10 q^{53} + 15 q^{54} - 8 q^{55} + 48 q^{56} - 60 q^{58} - 19 q^{59} - 110 q^{60} + 8 q^{61} + 110 q^{62} + 55 q^{63} + 16 q^{64} - 43 q^{65} - 17 q^{66} - 65 q^{67} - 42 q^{69} + 4 q^{70} + 18 q^{71} + 100 q^{73} + 22 q^{74} + 115 q^{75} + 64 q^{76} - 145 q^{78} - 16 q^{79} - 97 q^{80} + q^{81} - 70 q^{83} - 46 q^{84} - 16 q^{85} + 64 q^{86} + 10 q^{87} + 30 q^{88} + 4 q^{89} - 8 q^{90} + 16 q^{91} - 135 q^{92} + 38 q^{94} - 2 q^{95} + 50 q^{96} + 150 q^{97} + 130 q^{98} + 178 q^{99}+O(q^{100}) \) 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9 - 36 * q^10 + 20 * q^11 + 45 * q^12 - 10 * q^14 - 20 * q^16 - 15 * q^17 + 20 * q^19 + 12 * q^20 + 16 * q^21 + 15 * q^23 + 72 * q^24 + 41 * q^25 - 84 * q^26 + 15 * q^27 + 30 * q^28 - 24 * q^29 - 40 * q^30 + 8 * q^31 - 75 * q^33 - 24 * q^34 - 33 * q^35 - 32 * q^36 - 15 * q^37 - 30 * q^39 - 28 * q^40 + 13 * q^41 - 130 * q^42 - 24 * q^44 + 6 * q^45 + 30 * q^46 + 145 * q^48 - 28 * q^49 + 77 * q^50 - 36 * q^51 - 5 * q^52 - 10 * q^53 + 15 * q^54 - 8 * q^55 + 48 * q^56 - 60 * q^58 - 19 * q^59 - 110 * q^60 + 8 * q^61 + 110 * q^62 + 55 * q^63 + 16 * q^64 - 43 * q^65 - 17 * q^66 - 65 * q^67 - 42 * q^69 + 4 * q^70 + 18 * q^71 + 100 * q^73 + 22 * q^74 + 115 * q^75 + 64 * q^76 - 145 * q^78 - 16 * q^79 - 97 * q^80 + q^81 - 70 * q^83 - 46 * q^84 - 16 * q^85 + 64 * q^86 + 10 * q^87 + 30 * q^88 + 4 * q^89 - 8 * q^90 + 16 * q^91 - 135 * q^92 + 38 * q^94 - 2 * q^95 + 50 * q^96 + 150 * q^97 + 130 * q^98 + 178 * q^99

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