LMFDB - Embedded newform 25.4.d.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,4,Mod(6,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("25.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	25.d (of order $5$, 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:	$1.47504775014$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	25.11
Dual form			25.4.d.a.16.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.51671 + 1.10196i) q^{2} +(-0.496278 + 1.52739i) q^{3} +(-1.38603 + 4.26575i) q^{4} +(2.00572 + 10.9990i) q^{5} +(-0.930402 - 2.86348i) q^{6} -5.91678 q^{7} +(-7.23313 - 22.2613i) q^{8} +(19.7568 + 14.3542i) q^{9} +O(q^{10})$	\(q+(-1.51671 + 1.10196i) q^{2} +(-0.496278 + 1.52739i) q^{3} +(-1.38603 + 4.26575i) q^{4} +(2.00572 + 10.9990i) q^{5} +(-0.930402 - 2.86348i) q^{6} -5.91678 q^{7} +(-7.23313 - 22.2613i) q^{8} +(19.7568 + 14.3542i) q^{9} +(-15.1625 - 14.4720i) q^{10} +(46.2426 - 33.5972i) q^{11} +(-5.82760 - 4.23400i) q^{12} +(-23.8943 - 17.3602i) q^{13} +(8.97406 - 6.52004i) q^{14} +(-17.7951 - 2.39503i) q^{15} +(6.47220 + 4.70233i) q^{16} +(16.1964 + 49.8475i) q^{17} -45.7831 q^{18} +(28.8671 + 88.8439i) q^{19} +(-49.6988 - 6.68896i) q^{20} +(2.93637 - 9.03722i) q^{21} +(-33.1141 + 101.915i) q^{22} +(101.186 - 73.5160i) q^{23} +37.5912 q^{24} +(-116.954 + 44.1216i) q^{25} +55.3710 q^{26} +(-66.8097 + 48.5401i) q^{27} +(8.20082 - 25.2395i) q^{28} +(42.2327 - 129.979i) q^{29} +(29.6292 - 15.9768i) q^{30} +(-22.0658 - 67.9115i) q^{31} +172.257 q^{32} +(28.3668 + 87.3040i) q^{33} +(-79.4951 - 57.7566i) q^{34} +(-11.8674 - 65.0785i) q^{35} +(-88.6149 + 64.3825i) q^{36} +(-149.002 - 108.256i) q^{37} +(-141.685 - 102.940i) q^{38} +(38.3741 - 27.8804i) q^{39} +(230.343 - 124.207i) q^{40} +(-28.3279 - 20.5814i) q^{41} +(5.50499 + 16.9426i) q^{42} +185.374 q^{43} +(79.2239 + 243.826i) q^{44} +(-118.254 + 246.095i) q^{45} +(-72.4588 + 223.005i) q^{46} +(130.295 - 401.007i) q^{47} +(-10.3943 + 7.55189i) q^{48} -307.992 q^{49} +(128.766 - 195.798i) q^{50} -84.1744 q^{51} +(107.173 - 77.8655i) q^{52} +(-214.260 + 659.426i) q^{53} +(47.8420 - 147.243i) q^{54} +(462.284 + 441.234i) q^{55} +(42.7968 + 131.715i) q^{56} -150.025 q^{57} +(79.1762 + 243.679i) q^{58} +(-466.375 - 338.841i) q^{59} +(34.8811 - 72.5897i) q^{60} +(29.5121 - 21.4418i) q^{61} +(108.303 + 78.6867i) q^{62} +(-116.897 - 84.9306i) q^{63} +(-313.042 + 227.438i) q^{64} +(143.019 - 297.633i) q^{65} +(-139.229 - 101.156i) q^{66} +(-48.1248 - 148.113i) q^{67} -235.086 q^{68} +(62.0710 + 191.035i) q^{69} +(89.7130 + 85.6279i) q^{70} +(120.884 - 372.044i) q^{71} +(176.639 - 543.638i) q^{72} +(946.113 - 687.392i) q^{73} +345.287 q^{74} +(-9.34899 - 200.531i) q^{75} -418.997 q^{76} +(-273.608 + 198.788i) q^{77} +(-27.4794 + 84.5730i) q^{78} +(323.388 - 995.287i) q^{79} +(-38.7393 + 80.6190i) q^{80} +(162.771 + 500.956i) q^{81} +65.6451 q^{82} +(289.936 + 892.333i) q^{83} +(34.4806 + 25.0517i) q^{84} +(-515.785 + 278.124i) q^{85} +(-281.159 + 204.274i) q^{86} +(177.569 + 129.011i) q^{87} +(-1082.40 - 786.407i) q^{88} +(-378.143 + 274.737i) q^{89} +(-91.8280 - 503.567i) q^{90} +(141.378 + 102.717i) q^{91} +(173.354 + 533.530i) q^{92} +114.678 q^{93} +(244.272 + 751.791i) q^{94} +(-919.291 + 495.704i) q^{95} +(-85.4873 + 263.103i) q^{96} +(-529.272 + 1628.93i) q^{97} +(467.135 - 339.393i) q^{98} +1395.87 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9}+O(q^{10}) $ 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9} - 25 q^{10} - 89 q^{11} + 139 q^{12} + 33 q^{13} - 17 q^{14} + 225 q^{15} - 207 q^{16} - 191 q^{17} - 552 q^{18} - 115 q^{19} - 225 q^{20} - 144 q^{21} + 808 q^{22} + 433 q^{23} + 780 q^{24} + 90 q^{25} + 586 q^{26} + 35 q^{27} - 13 q^{28} - 5 q^{29} + 675 q^{30} - 639 q^{31} - 1386 q^{32} + 251 q^{33} - 777 q^{34} - 1030 q^{35} + 673 q^{36} + 699 q^{37} - 2355 q^{38} - 1133 q^{39} + 410 q^{40} + 341 q^{41} - 2407 q^{42} - 172 q^{43} + 548 q^{44} + 470 q^{45} - 1239 q^{46} + 2319 q^{47} + 4738 q^{48} + 1344 q^{49} + 2335 q^{50} + 2006 q^{51} + 2344 q^{52} - 927 q^{53} + 1615 q^{54} + 1225 q^{55} - 2910 q^{56} - 770 q^{57} + 2410 q^{58} - 1905 q^{59} - 12030 q^{60} + 1391 q^{61} - 3832 q^{62} - 6142 q^{63} - 3596 q^{64} + 1215 q^{65} + 3632 q^{66} - 3611 q^{67} + 3622 q^{68} + 2687 q^{69} + 560 q^{70} - 3719 q^{71} + 9025 q^{72} + 4593 q^{73} + 4848 q^{74} + 3815 q^{75} + 3520 q^{76} + 1368 q^{77} - 3679 q^{78} + 775 q^{79} + 9500 q^{80} - 3712 q^{81} - 6762 q^{82} - 2447 q^{83} - 7612 q^{84} - 8185 q^{85} + 3891 q^{86} - 85 q^{87} - 10960 q^{88} - 5075 q^{89} + 685 q^{90} + 376 q^{91} - 8456 q^{92} + 4366 q^{93} + 3573 q^{94} + 3265 q^{95} - 7754 q^{96} + 7439 q^{97} + 7082 q^{98} + 6572 q^{99}+O(q^{100}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9 - 25 * q^10 - 89 * q^11 + 139 * q^12 + 33 * q^13 - 17 * q^14 + 225 * q^15 - 207 * q^16 - 191 * q^17 - 552 * q^18 - 115 * q^19 - 225 * q^20 - 144 * q^21 + 808 * q^22 + 433 * q^23 + 780 * q^24 + 90 * q^25 + 586 * q^26 + 35 * q^27 - 13 * q^28 - 5 * q^29 + 675 * q^30 - 639 * q^31 - 1386 * q^32 + 251 * q^33 - 777 * q^34 - 1030 * q^35 + 673 * q^36 + 699 * q^37 - 2355 * q^38 - 1133 * q^39 + 410 * q^40 + 341 * q^41 - 2407 * q^42 - 172 * q^43 + 548 * q^44 + 470 * q^45 - 1239 * q^46 + 2319 * q^47 + 4738 * q^48 + 1344 * q^49 + 2335 * q^50 + 2006 * q^51 + 2344 * q^52 - 927 * q^53 + 1615 * q^54 + 1225 * q^55 - 2910 * q^56 - 770 * q^57 + 2410 * q^58 - 1905 * q^59 - 12030 * q^60 + 1391 * q^61 - 3832 * q^62 - 6142 * q^63 - 3596 * q^64 + 1215 * q^65 + 3632 * q^66 - 3611 * q^67 + 3622 * q^68 + 2687 * q^69 + 560 * q^70 - 3719 * q^71 + 9025 * q^72 + 4593 * q^73 + 4848 * q^74 + 3815 * q^75 + 3520 * q^76 + 1368 * q^77 - 3679 * q^78 + 775 * q^79 + 9500 * q^80 - 3712 * q^81 - 6762 * q^82 - 2447 * q^83 - 7612 * q^84 - 8185 * q^85 + 3891 * q^86 - 85 * q^87 - 10960 * q^88 - 5075 * q^89 + 685 * q^90 + 376 * q^91 - 8456 * q^92 + 4366 * q^93 + 3573 * q^94 + 3265 * q^95 - 7754 * q^96 + 7439 * q^97 + 7082 * q^98 + 6572 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−1.51671	+	1.10196i	−0.536239	+	0.389600i	−0.822686	−	0.568496i	$-0.807526\pi$
$2$	−1.51671	+	1.10196i	−0.536239	+	0.389600i	0.286447	+	0.958096i	$0.407526\pi$
$3$	−0.496278	+	1.52739i	−0.0955088	+	0.293946i	−0.987386	−	0.158332i	$-0.949388\pi$
$3$	−0.496278	+	1.52739i	−0.0955088	+	0.293946i	0.891877	+	0.452278i	$0.149388\pi$
$4$	−1.38603	+	4.26575i	−0.173253	+	0.533219i
$5$	2.00572	+	10.9990i	0.179397	+	0.983777i
$5$	2.00572	+	10.9990i	0.179397	+	0.983777i
$6$	−0.930402	−	2.86348i	−0.0633059	−	0.194835i
$7$	−5.91678			−0.319476			−0.159738	−	0.987159i	$-0.551065\pi$
$7$	−5.91678			−0.319476			−0.159738	+	0.987159i	$0.551065\pi$
$8$	−7.23313	−	22.2613i	−0.319662	−	0.983819i
$9$	19.7568	+	14.3542i	0.731735	+	0.531636i
$10$	−15.1625	−	14.4720i	−0.479479	−	0.457646i
$11$	46.2426	−	33.5972i	1.26752	−	0.920904i	0.268415	−	0.963303i	$-0.413500\pi$
$11$	46.2426	−	33.5972i	1.26752	−	0.920904i	0.999101	+	0.0423993i	$0.0135002\pi$
$12$	−5.82760	−	4.23400i	−0.140190	−	0.101854i
$13$	−23.8943	−	17.3602i	−0.509777	−	0.370374i	0.302962	−	0.953003i	$-0.402024\pi$
$13$	−23.8943	−	17.3602i	−0.509777	−	0.370374i	−0.812739	+	0.582628i	$0.802024\pi$
$14$	8.97406	−	6.52004i	0.171316	−	0.124468i
$15$	−17.7951	−	2.39503i	−0.306311	−	0.0412264i
$16$	6.47220	+	4.70233i	0.101128	+	0.0734739i
$17$	16.1964	+	49.8475i	0.231071	+	0.711165i	0.997618	+	0.0689764i	$0.0219733\pi$
$17$	16.1964	+	49.8475i	0.231071	+	0.711165i	−0.766547	+	0.642188i	$0.778027\pi$
$18$	−45.7831			−0.599510
$19$	28.8671	+	88.8439i	0.348557	+	1.07275i	0.959652	+	0.281190i	$0.0907291\pi$
$19$	28.8671	+	88.8439i	0.348557	+	1.07275i	−0.611096	+	0.791557i	$0.709271\pi$
$20$	−49.6988	−	6.68896i	−0.555650	−	0.0747848i
$21$	2.93637	−	9.03722i	0.0305128	−	0.0939087i
$22$	−33.1141	+	101.915i	−0.320907	+	0.987649i
$23$	101.186	−	73.5160i	0.917338	−	0.666485i	−0.0255223	−	0.999674i	$-0.508125\pi$
$23$	101.186	−	73.5160i	0.917338	−	0.666485i	0.942860	+	0.333189i	$0.108125\pi$
$24$	37.5912			0.319720
$25$	−116.954	+	44.1216i	−0.935634	+	0.352973i
$26$	55.3710			0.417660
$27$	−66.8097	+	48.5401i	−0.476205	+	0.345983i
$28$	8.20082	−	25.2395i	0.0553503	−	0.170351i
$29$	42.2327	−	129.979i	0.270428	−	0.832293i	−0.719965	−	0.694011i	$-0.755842\pi$
$29$	42.2327	−	129.979i	0.270428	−	0.832293i	0.990393	−	0.138282i	$-0.0441580\pi$
$30$	29.6292	−	15.9768i	0.180318	−	0.0972317i
$31$	−22.0658	−	67.9115i	−0.127843	−	0.393460i	0.866565	−	0.499064i	$-0.166323\pi$
$31$	−22.0658	−	67.9115i	−0.127843	−	0.393460i	−0.994408	+	0.105603i	$0.966323\pi$
$32$	172.257			0.951594
$33$	28.3668	+	87.3040i	0.149637	+	0.460535i
$34$	−79.4951	−	57.7566i	−0.400979	−	0.291329i
$35$	−11.8674	−	65.0785i	−0.0573131	−	0.314293i
$36$	−88.6149	+	64.3825i	−0.410254	+	0.298067i
$37$	−149.002	−	108.256i	−0.662048	−	0.481006i	0.205306	−	0.978698i	$-0.434181\pi$
$37$	−149.002	−	108.256i	−0.662048	−	0.481006i	−0.867354	+	0.497692i	$0.834181\pi$
$38$	−141.685	−	102.940i	−0.604852	−	0.439451i
$39$	38.3741	−	27.8804i	0.157558	−	0.114473i
$40$	230.343	−	124.207i	0.910512	−	0.490970i
$41$	−28.3279	−	20.5814i	−0.107904	−	0.0783971i	0.532525	−	0.846415i	$-0.321243\pi$
$41$	−28.3279	−	20.5814i	−0.107904	−	0.0783971i	−0.640429	+	0.768017i	$0.721243\pi$
$42$	5.50499	+	16.9426i	0.0202247	+	0.0622453i
$43$	185.374			0.657425			0.328712	−	0.944430i	$-0.393385\pi$
$43$	185.374			0.657425			0.328712	+	0.944430i	$0.393385\pi$
$44$	79.2239	+	243.826i	0.271442	+	0.835413i
$45$	−118.254	+	246.095i	−0.391741	+	0.815238i
$46$	−72.4588	+	223.005i	−0.232249	+	0.714790i
$47$	130.295	−	401.007i	0.404372	−	1.24453i	−0.517047	−	0.855957i	$-0.672969\pi$
$47$	130.295	−	401.007i	0.404372	−	1.24453i	0.921419	−	0.388571i	$-0.127031\pi$
$48$	−10.3943	+	7.55189i	−0.0312560	+	0.0227088i
$49$	−307.992			−0.897935
$50$	128.766	−	195.798i	0.364205	−	0.553801i
$51$	−84.1744			−0.231113
$52$	107.173	−	77.8655i	0.285811	−	0.207654i
$53$	−214.260	+	659.426i	−0.555301	+	1.70904i	0.139847	+	0.990173i	$0.455339\pi$
$53$	−214.260	+	659.426i	−0.555301	+	1.70904i	−0.695148	+	0.718867i	$0.744661\pi$
$54$	47.8420	−	147.243i	0.120564	−	0.371059i
$55$	462.284	+	441.234i	1.13335	+	1.08175i
$56$	42.7968	+	131.715i	0.102124	+	0.314307i
$57$	−150.025			−0.348620
$58$	79.1762	+	243.679i	0.179247	+	0.551667i
$59$	−466.375	−	338.841i	−1.02910	−	0.747684i	−0.0609711	−	0.998140i	$-0.519420\pi$
$59$	−466.375	−	338.841i	−1.02910	−	0.747684i	−0.968128	+	0.250455i	$0.919420\pi$
$60$	34.8811	−	72.5897i	0.0750521	−	0.156188i
$61$	29.5121	−	21.4418i	0.0619448	−	0.0450056i	−0.556382	−	0.830927i	$-0.687811\pi$
$61$	29.5121	−	21.4418i	0.0619448	−	0.0450056i	0.618327	+	0.785921i	$0.287811\pi$
$62$	108.303	+	78.6867i	0.221847	+	0.161181i
$63$	−116.897	−	84.9306i	−0.233772	−	0.169845i
$64$	−313.042	+	227.438i	−0.611410	+	0.444215i
$65$	143.019	−	297.633i	0.272913	−	0.567950i
$66$	−139.229	−	101.156i	−0.259666	−	0.188658i
$67$	−48.1248	−	148.113i	−0.0877519	−	0.270073i	0.897545	−	0.440923i	$-0.145349\pi$
$67$	−48.1248	−	148.113i	−0.0877519	−	0.270073i	−0.985297	+	0.170850i	$0.945349\pi$
$68$	−235.086			−0.419240
$69$	62.0710	+	191.035i	0.108297	+	0.333303i
$70$	89.7130	+	85.6279i	0.153182	+	0.146207i
$71$	120.884	−	372.044i	0.202061	−	0.621880i	−0.797760	−	0.602975i	$-0.793982\pi$
$71$	120.884	−	372.044i	0.202061	−	0.621880i	0.999821	−	0.0189054i	$-0.00601814\pi$
$72$	176.639	−	543.638i	0.289126	−	0.889838i
$73$	946.113	−	687.392i	1.51691	−	1.10210i	0.553913	−	0.832575i	$-0.313134\pi$
$73$	946.113	−	687.392i	1.51691	−	1.10210i	0.962994	−	0.269523i	$-0.0868659\pi$
$74$	345.287			0.542416
$75$	−9.34899	−	200.531i	−0.0143937	−	0.308738i
$76$	−418.997			−0.632397
$77$	−273.608	+	198.788i	−0.404941	+	0.294207i
$78$	−27.4794	+	84.5730i	−0.0398902	+	0.122769i
$79$	323.388	−	995.287i	0.460557	−	1.41745i	−0.403927	−	0.914791i	$-0.632355\pi$
$79$	323.388	−	995.287i	0.460557	−	1.41745i	0.864485	−	0.502659i	$-0.167645\pi$
$80$	−38.7393	+	80.6190i	−0.0541398	+	0.112668i
$81$	162.771	+	500.956i	0.223279	+	0.687183i
$82$	65.6451			0.0884060
$83$	289.936	+	892.333i	0.383430	+	1.18007i	0.937613	+	0.347680i	$0.113031\pi$
$83$	289.936	+	892.333i	0.383430	+	1.18007i	−0.554184	+	0.832395i	$0.686969\pi$
$84$	34.4806	+	25.0517i	0.0447875	+	0.0325400i
$85$	−515.785	+	278.124i	−0.658174	+	0.354903i
$86$	−281.159	+	204.274i	−0.352537	+	0.256133i
$87$	177.569	+	129.011i	0.218821	+	0.158983i
$88$	−1082.40	−	786.407i	−1.31118	−	0.952628i
$89$	−378.143	+	274.737i	−0.450371	+	0.327214i	−0.789742	−	0.613439i	$-0.789786\pi$
$89$	−378.143	+	274.737i	−0.450371	+	0.327214i	0.339371	+	0.940653i	$0.389786\pi$
$90$	−91.8280	−	503.567i	−0.107550	−	0.589784i
$91$	141.378	+	102.717i	0.162862	+	0.118326i
$92$	173.354	+	533.530i	0.196451	+	0.604613i
$93$	114.678			0.127866
$94$	244.272	+	751.791i	0.268029	+	0.824908i
$95$	−919.291	+	495.704i	−0.992813	+	0.535349i
$96$	−85.4873	+	263.103i	−0.0908856	+	0.279717i
$97$	−529.272	+	1628.93i	−0.554014	+	1.70508i	0.144518	+	0.989502i	$0.453837\pi$
$97$	−529.272	+	1628.93i	−0.554014	+	1.70508i	−0.698532	+	0.715579i	$0.746163\pi$
$98$	467.135	−	339.393i	0.481508	−	0.349836i
$99$	1395.87			1.41707
$100$	−26.1103	−	560.051i	−0.0261103	−	0.560051i
$101$	1054.59			1.03896			0.519482	−	0.854482i	$-0.326125\pi$
$101$	1054.59			1.03896			0.519482	+	0.854482i	$0.326125\pi$
$102$	127.668	−	92.7565i	0.123932	−	0.0900418i
$103$	28.4548	−	87.5749i	0.0272207	−	0.0837768i	−0.936523	−	0.350606i	$-0.885976\pi$
$103$	28.4548	−	87.5749i	0.0272207	−	0.0837768i	0.963744	+	0.266829i	$0.0859758\pi$
$104$	−213.631	+	657.487i	−0.201425	+	0.619922i
$105$	105.290	+	14.1709i	0.0978591	+	0.0131708i
$106$	−401.687	−	1236.26i	−0.368069	−	1.13280i
$107$	−66.9507			−0.0604894			−0.0302447	−	0.999543i	$-0.509629\pi$
$107$	−66.9507			−0.0604894			−0.0302447	+	0.999543i	$0.509629\pi$
$108$	−114.460	−	352.271i	−0.101981	−	0.313864i
$109$	−160.237	−	116.419i	−0.140806	−	0.102302i	0.515152	−	0.857099i	$-0.327735\pi$
$109$	−160.237	−	116.419i	−0.140806	−	0.102302i	−0.655958	+	0.754797i	$0.727735\pi$
$110$	−1187.37	−	159.808i	−1.02920	−	0.138519i
$111$	239.296	−	173.858i	0.204621	−	0.148666i
$112$	−38.2946	−	27.8227i	−0.0323080	−	0.0234732i
$113$	−1326.05	−	963.435i	−1.10394	−	0.802056i	−0.122237	−	0.992501i	$-0.539007\pi$
$113$	−1326.05	−	963.435i	−1.10394	−	0.802056i	−0.981698	+	0.190445i	$0.939007\pi$
$114$	227.545	−	165.321i	0.186943	−	0.135822i
$115$	1011.55	+	965.490i	0.820240	+	0.782890i
$116$	495.922	+	360.309i	0.396942	+	0.288395i
$117$	−222.884	−	685.967i	−0.176117	−	0.542032i
$118$	1080.74			0.843141
$119$	−95.8308	−	294.937i	−0.0738218	−	0.227200i
$120$	75.3974	+	413.464i	0.0573568	+	0.314533i
$121$	598.304	−	1841.39i	0.449515	−	1.38346i
$122$	−21.1334	+	65.0420i	−0.0156830	+	0.0482675i
$123$	45.4944	−	33.0536i	0.0333503	−	0.0242304i
$124$	320.277			0.231950
$125$	−719.869	−	1197.88i	−0.515096	−	0.857132i
$126$	270.889			0.191529
$127$	−404.153	+	293.635i	−0.282384	+	0.205164i	−0.719957	−	0.694019i	$-0.755838\pi$
$127$	−404.153	+	293.635i	−0.282384	+	0.205164i	0.437572	+	0.899183i	$0.355838\pi$
$128$	−201.675	+	620.692i	−0.139263	+	0.428609i
$129$	−91.9971	+	283.138i	−0.0627898	+	0.193247i
$130$	111.059	+	609.024i	0.0749269	+	0.410884i
$131$	80.0952	+	246.508i	0.0534195	+	0.164408i	0.974207	−	0.225656i	$-0.0724527\pi$
$131$	80.0952	+	246.508i	0.0534195	+	0.164408i	−0.920787	+	0.390065i	$0.872453\pi$
$132$	−411.734			−0.271491
$133$	−170.801	−	525.670i	−0.111356	−	0.342717i
$134$	236.205	+	171.613i	0.152276	+	0.110635i
$135$	−667.891	−	637.479i	−0.425800	−	0.406411i
$136$	992.519	−	721.107i	0.625792	−	0.454665i
$137$	123.196	+	89.5073i	0.0768275	+	0.0558184i	0.625536	−	0.780195i	$-0.284880\pi$
$137$	123.196	+	89.5073i	0.0768275	+	0.0558184i	−0.548709	+	0.836014i	$0.684880\pi$
$138$	−304.656	−	221.345i	−0.187928	−	0.136537i
$139$	−1835.62	+	1333.66i	−1.12011	+	0.813809i	−0.984226	−	0.176916i	$-0.943388\pi$
$139$	−1835.62	+	1333.66i	−1.12011	+	0.813809i	−0.135885	+	0.990725i	$0.543388\pi$
$140$	294.057	+	39.5771i	0.177517	+	0.0238920i
$141$	547.830	+	398.022i	0.327203	+	0.237727i
$142$	226.629	+	697.493i	0.133932	+	0.412200i
$143$	−1688.19			−0.987229
$144$	60.3721	+	185.806i	0.0349376	+	0.107527i
$145$	1514.34	+	203.815i	0.867304	+	0.116730i
$146$	−677.506	+	2085.15i	−0.384047	+	1.18197i
$147$	152.850	−	470.423i	0.0857607	−	0.263944i
$148$	668.315	−	485.559i	0.371184	−	0.269681i
$149$	1563.68			0.859744			0.429872	−	0.902890i	$-0.358559\pi$
$149$	1563.68			0.859744			0.429872	+	0.902890i	$0.358559\pi$
$150$	235.156	+	293.846i	0.128003	+	0.159949i
$151$	−2328.94			−1.25514			−0.627571	−	0.778559i	$-0.715951\pi$
$151$	−2328.94			−1.25514			−0.627571	+	0.778559i	$0.715951\pi$
$152$	1768.98	−	1285.24i	0.943968	−	0.685833i
$153$	−395.530	+	1217.32i	−0.208998	+	0.643230i
$154$	195.929	−	603.007i	0.102522	−	0.315530i
$155$	702.698	−	378.912i	0.364142	−	0.196354i
$156$	65.7433	+	202.337i	0.0337415	+	0.103846i
$157$	−290.519			−0.147681			−0.0738406	−	0.997270i	$-0.523526\pi$
$157$	−290.519			−0.147681			−0.0738406	+	0.997270i	$0.523526\pi$
$158$	606.275	+	1865.92i	0.305270	+	0.939525i
$159$	−900.866	−	654.517i	−0.449329	−	0.326457i
$160$	345.499	+	1894.65i	0.170713	+	0.936156i
$161$	−598.696	+	434.978i	−0.293068	+	0.212926i
$162$	−798.908	−	580.441i	−0.387458	−	0.281505i
$163$	1590.13	+	1155.30i	0.764102	+	0.555153i	0.900166	−	0.435547i	$-0.143445\pi$
$163$	1590.13	+	1155.30i	0.764102	+	0.555153i	−0.136064	+	0.990700i	$0.543445\pi$
$164$	127.059	−	92.3135i	0.0604976	−	0.0439541i
$165$	−903.357	+	487.112i	−0.426220	+	0.229828i
$166$	−1423.06	−	1033.91i	−0.665367	−	0.483418i
$167$	−634.745	−	1953.54i	−0.294120	−	0.905208i	−0.983516	−	0.180823i	$-0.942124\pi$
$167$	−634.745	−	1953.54i	−0.294120	−	0.905208i	0.689396	−	0.724385i	$-0.257876\pi$
$168$	−222.419			−0.102143
$169$	−409.350	−	1259.85i	−0.186322	−	0.573440i
$170$	475.817	−	990.207i	0.214668	−	0.446738i
$171$	−704.958	+	2169.64i	−0.315260	+	0.970271i
$172$	−256.933	+	790.759i	−0.113901	+	0.350551i
$173$	1034.32	−	751.479i	0.454555	−	0.330254i	−0.336836	−	0.941563i	$-0.609357\pi$
$173$	1034.32	−	751.479i	0.454555	−	0.330254i	0.791392	+	0.611310i	$0.209357\pi$
$174$	−411.486			−0.179280
$175$	691.993	−	261.058i	0.298913	−	0.112767i
$176$	457.276			0.195844
$177$	748.994	−	544.176i	0.318067	−	0.231089i
$178$	270.786	−	833.393i	0.114024	−	0.350930i
$179$	144.118	−	443.549i	0.0601781	−	0.185209i	−0.916448	−	0.400153i	$-0.868957\pi$
$179$	144.118	−	443.549i	0.0601781	−	0.185209i	0.976626	+	0.214944i	$0.0689569\pi$
$180$	−885.877	−	845.538i	−0.366830	−	0.350126i
$181$	360.349	+	1109.04i	0.147981	+	0.455439i	0.997382	−	0.0723088i	$-0.0230367\pi$
$181$	360.349	+	1109.04i	0.147981	+	0.455439i	−0.849401	+	0.527748i	$0.823037\pi$
$182$	−327.619			−0.133432
$183$	18.1037	+	55.7175i	0.00731292	+	0.0225069i
$184$	−2368.45	−	1720.78i	−0.948938	−	0.689444i
$185$	891.850	−	1856.00i	0.354433	−	0.737598i
$186$	−173.933	+	126.370i	−0.0685667	+	0.0498167i
$187$	2423.70	+	1760.92i	0.947801	+	0.688618i
$188$	1530.00	+	1111.61i	0.593547	+	0.431237i
$189$	395.298	−	287.201i	0.152136	−	0.110533i
$190$	848.056	−	1764.86i	0.323813	−	0.673875i
$191$	−1809.34	−	1314.56i	−0.685440	−	0.498001i	0.189718	−	0.981839i	$-0.439243\pi$
$191$	−1809.34	−	1314.56i	−0.685440	−	0.498001i	−0.875158	+	0.483837i	$0.839243\pi$
$192$	−192.030	−	591.009i	−0.0721802	−	0.222148i
$193$	1902.42			0.709530			0.354765	−	0.934956i	$-0.384561\pi$
$193$	1902.42			0.709530			0.354765	+	0.934956i	$0.384561\pi$
$194$	−992.257	−	3053.85i	−0.367216	−	1.13017i
$195$	383.623	+	366.154i	0.140881	+	0.134466i
$196$	426.885	−	1313.82i	0.155570	−	0.478796i
$197$	559.983	−	1723.45i	0.202524	−	0.623304i	−0.797282	−	0.603607i	$-0.793730\pi$
$197$	559.983	−	1723.45i	0.202524	−	0.623304i	0.999806	−	0.0196971i	$-0.00627019\pi$
$198$	−2117.13	+	1538.19i	−0.759889	+	0.552091i
$199$	−3011.24			−1.07267			−0.536335	−	0.844005i	$-0.680192\pi$
$199$	−3011.24			−1.07267			−0.536335	+	0.844005i	$0.680192\pi$
$200$	1828.15	+	2284.41i	0.646348	+	0.807662i
$201$	250.109			0.0877678
$202$	−1599.50	+	1162.11i	−0.557132	+	0.404780i
$203$	−249.882	+	769.058i	−0.0863954	+	0.265898i
$204$	116.668	−	359.067i	0.0400411	−	0.123234i
$205$	169.557	−	352.858i	0.0577675	−	0.120218i
$206$	53.3459	+	164.182i	0.0180427	+	0.0555296i
$207$	3054.38			1.02558
$208$	−73.0153	−	224.718i	−0.0243399	−	0.0749105i
$209$	4319.80	+	3138.52i	1.42970	+	1.03874i
$210$	−175.310	+	94.5313i	−0.0576072	+	0.0310632i
$211$	−3153.40	+	2291.08i	−1.02886	+	0.747509i	−0.968080	−	0.250642i	$-0.919358\pi$
$211$	−3153.40	+	2291.08i	−1.02886	+	0.747509i	−0.0607784	+	0.998151i	$0.519358\pi$
$212$	−2515.98	−	1827.96i	−0.815085	−	0.592194i
$213$	508.263	+	369.275i	0.163501	+	0.118790i
$214$	101.545	−	73.7767i	0.0324368	−	0.0235667i
$215$	371.808	+	2038.92i	0.117940	+	0.646759i
$216$	1563.81	+	1136.17i	0.492609	+	0.357901i
$217$	130.558	+	401.818i	0.0408428	+	0.125701i
$218$	371.321			0.115362
$219$	580.378	+	1786.22i	0.179079	+	0.551148i
$220$	−2522.93	+	1360.43i	−0.773164	+	0.416909i
$221$	478.362	−	1472.25i	0.145602	−	0.448118i
$222$	−171.358	+	527.387i	−0.0518055	+	0.159441i
$223$	−2941.83	+	2137.36i	−0.883406	+	0.641832i	−0.934150	−	0.356880i	$-0.883841\pi$
$223$	−2941.83	+	2137.36i	−0.883406	+	0.641832i	0.0507445	+	0.998712i	$0.483841\pi$
$224$	−1019.21			−0.304012
$225$	−2943.98	−	807.078i	−0.872289	−	0.239134i
$226$	3072.90			0.904454
$227$	−562.815	+	408.909i	−0.164561	+	0.119561i	−0.667018	−	0.745042i	$-0.732430\pi$
$227$	−562.815	+	408.909i	−0.164561	+	0.119561i	0.502457	+	0.864602i	$0.332430\pi$
$228$	207.939	−	639.970i	0.0603995	−	0.185891i
$229$	−1706.92	+	5253.37i	−0.492562	+	1.51595i	0.328160	+	0.944622i	$0.393572\pi$
$229$	−1706.92	+	5253.37i	−0.492562	+	1.51595i	−0.820722	+	0.571328i	$0.806428\pi$
$230$	−2598.16	−	349.686i	−0.744859	−	0.100250i
$231$	−167.840	−	516.559i	−0.0478055	−	0.147130i
$232$	−3198.97			−0.905271
$233$	−1653.81	−	5089.90i	−0.464998	−	1.43112i	−0.858985	−	0.512001i	$-0.828904\pi$
$233$	−1653.81	−	5089.90i	−0.464998	−	1.43112i	0.393986	−	0.919116i	$-0.371096\pi$
$234$	1093.96	+	794.806i	0.305616	+	0.222043i
$235$	4671.99	+	628.802i	1.29688	+	0.174547i
$236$	2091.82	−	1519.80i	0.576974	−	0.419196i
$237$	1359.70	+	987.879i	0.372666	+	0.270758i
$238$	470.355	+	341.733i	0.128103	+	0.0930726i
$239$	4030.36	−	2928.23i	1.09081	−	0.792517i	0.111271	−	0.993790i	$-0.464508\pi$
$239$	4030.36	−	2928.23i	1.09081	−	0.792517i	0.979535	+	0.201273i	$0.0645079\pi$
$240$	−103.911	−	99.1793i	−0.0279476	−	0.0266750i
$241$	1105.03	+	802.852i	0.295358	+	0.214590i	0.725588	−	0.688129i	$-0.241568\pi$
$241$	1105.03	+	802.852i	0.295358	+	0.214590i	−0.430230	+	0.902719i	$0.641568\pi$
$242$	1121.68	+	3452.17i	0.297951	+	0.916998i
$243$	−3075.63			−0.811941
$244$	50.5608	+	155.610i	0.0132657	+	0.0408275i
$245$	−617.745	−	3387.59i	−0.161087	−	0.883368i
$246$	−32.5783	+	100.266i	−0.00844355	+	0.0259866i
$247$	852.591	−	2624.01i	0.219632	−	0.675957i
$248$	−1352.19	+	982.425i	−0.346227	+	0.251549i
$249$	−1506.83			−0.383499
$250$	2411.84	+	1023.57i	0.610154	+	0.258946i
$251$	−56.3223			−0.0141635			−0.00708174	−	0.999975i	$-0.502254\pi$
$251$	−56.3223			−0.0141635			−0.00708174	+	0.999975i	$0.502254\pi$
$252$	524.315	−	380.937i	0.131066	−	0.0952254i
$253$	2209.18	−	6799.15i	0.548971	−	1.68956i
$254$	289.412	−	890.719i	0.0714934	−	0.220034i
$255$	−168.830	−	925.831i	−0.0414610	−	0.227364i
$256$	−1334.66	−	4107.67i	−0.325845	−	1.00285i
$257$	−587.079			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$257$	−587.079			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$258$	−172.472	−	530.815i	−0.0416188	−	0.128090i
$259$	881.612	+	640.529i	0.211509	+	0.153670i
$260$	1071.40	+	1022.61i	0.255559	+	0.243922i
$261$	2700.13	−	1961.76i	0.640359	−	0.465248i
$262$	−393.122	−	285.620i	−0.0926991	−	0.0673498i
$263$	388.238	+	282.072i	0.0910258	+	0.0661341i	0.632367	−	0.774669i	$-0.282083\pi$
$263$	388.238	+	282.072i	0.0910258	+	0.0661341i	−0.541341	+	0.840803i	$0.682083\pi$
$264$	1738.32	−	1262.96i	0.405250	−	0.294431i
$265$	−7682.74	−	1034.02i	−1.78093	−	0.239696i
$266$	838.321	+	609.076i	0.193236	+	0.140394i
$267$	−231.966	−	713.916i	−0.0531688	−	0.163637i
$268$	698.515			0.159211
$269$	1495.78	+	4603.53i	0.339030	+	1.04343i	0.964703	+	0.263342i	$0.0848246\pi$
$269$	1495.78	+	4603.53i	0.339030	+	1.04343i	−0.625673	+	0.780086i	$0.715175\pi$
$270$	1715.47	+	230.885i	0.386668	+	0.0520416i
$271$	1441.77	−	4437.32i	0.323179	−	0.994643i	−0.649077	−	0.760723i	$-0.724845\pi$
$271$	1441.77	−	4437.32i	0.323179	−	0.994643i	0.972256	−	0.233920i	$-0.0751553\pi$
$272$	−129.573	+	398.784i	−0.0288842	+	0.0888964i
$273$	−227.051	+	164.962i	−0.0503361	+	0.0365713i
$274$	−285.486			−0.0629448
$275$	−3925.90	+	5969.64i	−0.860876	+	1.30903i
$276$	−900.939			−0.196486
$277$	−6762.05	+	4912.91i	−1.46676	+	1.06566i	−0.485221	+	0.874392i	$0.661261\pi$
$277$	−6762.05	+	4912.91i	−1.46676	+	1.06566i	−0.981537	+	0.191271i	$0.938739\pi$
$278$	1314.48	−	4045.55i	0.283587	−	0.872791i
$279$	538.864	−	1658.45i	0.115631	−	0.355874i
$280$	−1362.89	+	734.904i	−0.290887	+	0.156853i
$281$	1708.18	+	5257.23i	0.362638	+	1.11609i	0.951447	+	0.307813i	$0.0995970\pi$
$281$	1708.18	+	5257.23i	0.362638	+	1.11609i	−0.588809	+	0.808272i	$0.700403\pi$
$282$	−1269.50			−0.268077
$283$	−161.101	−	495.817i	−0.0338390	−	0.104146i	0.932710	−	0.360626i	$-0.117437\pi$
$283$	−161.101	−	495.817i	−0.0338390	−	0.104146i	−0.966549	+	0.256481i	$0.917437\pi$
$284$	1419.50	+	1031.33i	0.296591	+	0.215486i
$285$	−300.908	−	1650.12i	−0.0625413	−	0.342964i
$286$	2560.50	−	1860.31i	0.529390	−	0.384625i
$287$	167.610	+	121.776i	0.0344729	+	0.0250460i
$288$	3403.25	+	2472.61i	0.696314	+	0.505902i
$289$	1752.25	−	1273.08i	0.356656	−	0.259126i
$290$	−2521.41	+	1359.61i	−0.510560	+	0.275307i
$291$	−2225.34	−	1616.81i	−0.448288	−	0.325700i
$292$	1620.90	+	4988.63i	0.324850	+	0.999786i
$293$	−2209.70			−0.440587			−0.220294	−	0.975434i	$-0.570702\pi$
$293$	−2209.70			−0.440587			−0.220294	+	0.975434i	$0.570702\pi$
$294$	286.556	+	881.929i	0.0568445	+	0.174949i
$295$	2791.48	−	5809.26i	0.550937	−	1.14654i
$296$	−1332.17	+	4100.01i	−0.261591	+	0.805094i
$297$	−1458.64	+	4489.24i	−0.284980	+	0.877078i
$298$	−2371.66	+	1723.11i	−0.461028	+	0.334957i
$299$	−3694.03			−0.714486
$300$	868.373	+	238.061i	0.167118	+	0.0458148i
$301$	−1096.82			−0.210032
$302$	3532.33	−	2566.39i	0.673056	−	0.489004i
$303$	−523.368	+	1610.76i	−0.0992301	+	0.305399i
$304$	−230.939	+	710.758i	−0.0435700	+	0.134095i
$305$	295.030	+	281.596i	0.0553881	+	0.0528660i
$306$	−741.524	−	2282.18i	−0.138530	−	0.426351i
$307$	10095.6			1.87683			0.938413	−	0.345516i	$-0.112296\pi$
$307$	10095.6			1.87683			0.938413	+	0.345516i	$0.112296\pi$
$308$	−468.751	−	1442.67i	−0.0867193	−	0.266895i
$309$	119.639	+	86.9230i	0.0220260	+	0.0160028i
$310$	−648.246	+	1349.04i	−0.118767	+	0.247163i
$311$	−4497.20	+	3267.41i	−0.819977	+	0.595748i	−0.916706	−	0.399563i	$-0.869162\pi$
$311$	−4497.20	+	3267.41i	−0.819977	+	0.595748i	0.0967289	+	0.995311i	$0.469162\pi$
$312$	−898.217	−	652.593i	−0.162986	−	0.118416i
$313$	4746.67	+	3448.66i	0.857180	+	0.622778i	0.927116	−	0.374773i	$-0.122279\pi$
$313$	4746.67	+	3448.66i	0.857180	+	0.622778i	−0.0699360	+	0.997551i	$0.522279\pi$
$314$	440.634	−	320.139i	0.0791923	−	0.0575366i
$315$	699.686	−	1456.09i	0.125152	−	0.260449i
$316$	3797.42	+	2758.99i	0.676018	+	0.491156i
$317$	−98.5888	−	303.425i	−0.0174678	−	0.0537604i	0.941943	−	0.335774i	$-0.108998\pi$
$317$	−98.5888	−	303.425i	−0.0174678	−	0.0537604i	−0.959410	+	0.282013i	$0.908998\pi$
$318$	2087.60			0.368135
$319$	−2413.98	−	7429.47i	−0.423690	−	1.30398i
$320$	−3129.46	−	2986.96i	−0.546694	−	0.521800i
$321$	33.2262	−	102.260i	0.00577727	−	0.0177806i
$322$	428.723	−	1319.47i	0.0741982	−	0.228358i
$323$	−3961.10	+	2877.91i	−0.682358	+	0.495762i
$324$	−2362.56			−0.405103
$325$	3560.50	+	976.097i	0.607696	+	0.166597i
$326$	−3684.86			−0.626029
$327$	257.338	−	186.967i	0.0435194	−	0.0316187i
$328$	−253.270	+	779.484i	−0.0426356	+	0.131219i
$329$	−770.927	+	2372.67i	−0.129187	+	0.397597i
$330$	833.356	−	1734.27i	0.139014	−	0.289298i
$331$	904.957	+	2785.17i	0.150275	+	0.462498i	0.997652	−	0.0684939i	$-0.0218194\pi$
$331$	904.957	+	2785.17i	0.150275	+	0.462498i	−0.847377	+	0.530992i	$0.821819\pi$
$332$	−4208.33			−0.695669
$333$	−1389.88	−	4277.60i	−0.228723	−	0.703938i
$334$	3115.44	+	2263.50i	0.510388	+	0.370818i
$335$	1532.56	−	826.395i	0.249949	−	0.134779i
$336$	61.5007	−	44.6829i	0.00998554	−	0.00725492i
$337$	−4174.94	−	3033.27i	−0.674848	−	0.490306i	0.196797	−	0.980444i	$-0.436946\pi$
$337$	−4174.94	−	3033.27i	−0.674848	−	0.490306i	−0.871644	+	0.490139i	$0.836946\pi$
$338$	2009.16	+	1459.74i	0.323326	+	0.234910i
$339$	2129.63	−	1547.27i	0.341196	−	0.247894i
$340$	−471.516	−	2585.70i	−0.0752104	−	0.412439i
$341$	−3302.02	−	2399.06i	−0.524382	−	0.380986i
$342$	−1321.63	−	4067.55i	−0.208963	−	0.643123i
$343$	3851.78			0.606345
$344$	−1340.83	−	4126.66i	−0.210154	−	0.646787i
$345$	−1976.69	+	1065.88i	−0.308467	+	0.166333i
$346$	−740.672	+	2279.55i	−0.115083	+	0.354190i
$347$	540.620	−	1663.86i	0.0836369	−	0.257408i	−0.900489	−	0.434878i	$-0.856791\pi$
$347$	540.620	−	1663.86i	0.0836369	−	0.257408i	0.984126	+	0.177470i	$0.0567914\pi$
$348$	−796.446	+	578.652i	−0.122684	+	0.0891351i
$349$	−1775.11			−0.272262			−0.136131	−	0.990691i	$-0.543467\pi$
$349$	−1775.11			−0.272262			−0.136131	+	0.990691i	$0.543467\pi$
$350$	−761.879	+	1158.50i	−0.116355	+	0.176926i
$351$	2439.04			0.370901
$352$	7965.61	−	5787.35i	1.20616	−	0.876327i
$353$	101.976	−	313.851i	0.0153758	−	0.0473218i	−0.943074	−	0.332582i	$-0.892080\pi$
$353$	101.976	−	313.851i	0.0153758	−	0.0473218i	0.958450	+	0.285260i	$0.0920801\pi$
$354$	−536.350	+	1650.72i	−0.0805274	+	0.247838i
$355$	4334.56	+	583.388i	0.648041	+	0.0872197i
$356$	−647.843	−	1993.86i	−0.0964484	−	0.296838i
$357$	498.042			0.0738352
$358$	270.186	+	831.548i	0.0398877	+	0.122762i
$359$	−3398.46	−	2469.12i	−0.499620	−	0.362995i	0.309252	−	0.950980i	$-0.399921\pi$
$359$	−3398.46	−	2469.12i	−0.499620	−	0.362995i	−0.808872	+	0.587985i	$0.799921\pi$
$360$	6333.74	+	852.457i	0.927271	+	0.124801i
$361$	−1510.88	+	1097.72i	−0.220277	+	0.160040i
$362$	−1768.66	−	1285.01i	−0.256792	−	0.186570i
$363$	2515.59	+	1827.68i	0.363731	+	0.264266i
$364$	−634.118	+	460.713i	−0.0913099	+	0.0663405i
$365$	9458.23	+	9027.55i	1.35635	+	1.29458i
$366$	−88.8563	−	64.5579i	−0.0126901	−	0.00921993i
$367$	−3499.21	−	10769.5i	−0.497704	−	1.53177i	−0.812700	−	0.582682i	$-0.802003\pi$
$367$	−3499.21	−	10769.5i	−0.497704	−	1.53177i	0.314997	−	0.949093i	$-0.397997\pi$
$368$	1000.59			0.141738
$369$	−264.240	−	813.248i	−0.0372786	−	0.114732i
$370$	692.548	+	3797.79i	0.0973077	+	0.533616i
$371$	1267.73	−	3901.68i	0.177405	−	0.545998i
$372$	−158.947	+	489.188i	−0.0221532	+	0.0681806i
$373$	−6524.79	+	4740.54i	−0.905740	+	0.658059i	−0.939934	−	0.341357i	$-0.889114\pi$
$373$	−6524.79	+	4740.54i	−0.905740	+	0.658059i	0.0341938	+	0.999415i	$0.489114\pi$
$374$	−5616.52			−0.776533
$375$	2186.88	−	505.038i	0.301147	−	0.0695468i
$376$	−9869.36			−1.35365
$377$	−3265.59	+	2372.59i	−0.446118	+	0.324124i
$378$	−283.071	+	871.203i	−0.0385175	+	0.118545i
$379$	804.469	−	2475.90i	0.109031	−	0.335563i	−0.881624	−	0.471952i	$-0.843550\pi$
$379$	804.469	−	2475.90i	0.109031	−	0.335563i	0.990655	+	0.136389i	$0.0435496\pi$
$380$	−840.389	−	4608.53i	−0.113450	−	0.622138i
$381$	−247.921	−	763.023i	−0.0333370	−	0.102601i
$382$	4192.83			0.561581
$383$	2941.06	+	9051.66i	0.392380	+	1.20762i	0.930984	+	0.365061i	$0.118952\pi$
$383$	2941.06	+	9051.66i	0.392380	+	1.20762i	−0.538604	+	0.842559i	$0.681048\pi$
$384$	−847.950	−	616.072i	−0.112687	−	0.0818718i
$385$	−2735.24	−	2610.69i	−0.362079	−	0.345592i
$386$	−2885.42	+	2096.38i	−0.380477	+	0.276433i
$387$	3662.40	+	2660.89i	0.481061	+	0.349511i
$388$	−6215.03	−	4515.48i	−0.813197	−	0.590822i
$389$	−3945.71	+	2866.72i	−0.514281	+	0.373647i	−0.814445	−	0.580241i	$-0.802959\pi$
$389$	−3945.71	+	2866.72i	−0.514281	+	0.373647i	0.300164	+	0.953888i	$0.402959\pi$
$390$	−985.331	−	132.616i	−0.127934	−	0.0172186i
$391$	5303.45	+	3853.18i	0.685951	+	0.498373i
$392$	2227.74	+	6856.29i	0.287036	+	0.883405i
$393$	−416.262			−0.0534291
$394$	1049.83	+	3231.06i	0.134238	+	0.413143i
$395$	11595.7	+	1560.67i	1.47708	+	0.198800i
$396$	−1934.71	+	5954.43i	−0.245512	+	0.755609i
$397$	230.334	−	708.897i	0.0291188	−	0.0896184i	−0.935441	−	0.353483i	$-0.884997\pi$
$397$	230.334	−	708.897i	0.0291188	−	0.0896184i	0.964560	+	0.263865i	$0.0849972\pi$
$398$	4567.19	−	3318.26i	0.575207	−	0.417912i
$399$	887.666			0.111376
$400$	−964.425	−	264.393i	−0.120553	−	0.0330491i
$401$	14597.9			1.81792			0.908960	−	0.416883i	$-0.136878\pi$
$401$	14597.9			1.81792			0.908960	+	0.416883i	$0.136878\pi$
$402$	−379.343	+	275.609i	−0.0470645	+	0.0341944i
$403$	−651.713	+	2005.77i	−0.0805562	+	0.247926i
$404$	−1461.69	+	4498.60i	−0.180004	+	0.553995i
$405$	−5183.53	+	2795.08i	−0.635979	+	0.342936i
$406$	−468.469	−	1441.80i	−0.0572653	−	0.176244i
$407$	−10527.4			−1.28212
$408$	608.844	+	1873.83i	0.0738781	+	0.227374i
$409$	−1138.26	−	826.991i	−0.137612	−	0.0999807i	0.516850	−	0.856076i	$-0.327105\pi$
$409$	−1138.26	−	826.991i	−0.137612	−	0.0999807i	−0.654461	+	0.756095i	$0.727105\pi$
$410$	131.666	+	722.028i	0.0158598	+	0.0869718i
$411$	−197.852	+	143.748i	−0.0237453	+	0.0172520i
$412$	334.134	+	242.762i	0.0399553	+	0.0290292i
$413$	2759.44	+	2004.85i	0.328773	+	0.238867i
$414$	−4632.62	+	3365.79i	−0.549953	+	0.399564i
$415$	−9233.20	+	4978.77i	−1.09214	+	0.588911i
$416$	−4115.96	−	2990.42i	−0.485100	−	0.352446i
$417$	−1126.03	−	3465.57i	−0.132235	−	0.406978i
$418$	−10010.4			−1.17135
$419$	−1471.61	−	4529.15i	−0.171582	−	0.528075i	0.827879	−	0.560907i	$-0.189547\pi$
$419$	−1471.61	−	4529.15i	−0.171582	−	0.528075i	−0.999461	+	0.0328318i	$0.989547\pi$
$420$	−206.384	+	429.498i	−0.0239774	+	0.0498984i
$421$	−1185.64	+	3649.02i	−0.137255	+	0.422429i	−0.995934	−	0.0900856i	$-0.971286\pi$
$421$	−1185.64	+	3649.02i	−0.137255	+	0.422429i	0.858679	+	0.512515i	$0.171286\pi$
$422$	2258.13	−	6949.82i	0.260484	−	0.801687i
$423$	8330.34	−	6052.34i	0.957529	−	0.695686i
$424$	16229.4			1.85889
$425$	−4093.60	−	5115.26i	−0.467220	−	0.583828i
$426$	−1177.81			−0.133956
$427$	−174.617	+	126.866i	−0.0197899	+	0.0143782i
$428$	92.7955	−	285.595i	0.0104800	−	0.0322541i
$429$	837.813	−	2578.52i	0.0942890	−	0.290192i
$430$	−2810.73	−	2682.74i	−0.315222	−	0.300868i
$431$	−901.448	−	2774.37i	−0.100745	−	0.310062i	0.887963	−	0.459915i	$-0.152120\pi$
$431$	−901.448	−	2774.37i	−0.100745	−	0.310062i	−0.988708	+	0.149853i	$0.952120\pi$
$432$	−660.657			−0.0735784
$433$	648.396	+	1995.56i	0.0719629	+	0.221479i	0.980569	−	0.196175i	$-0.0628522\pi$
$433$	648.396	+	1995.56i	0.0719629	+	0.221479i	−0.908606	+	0.417655i	$0.862852\pi$
$434$	−640.805	−	465.572i	−0.0708747	−	0.0514935i
$435$	−1062.84	+	2211.84i	−0.117148	+	0.243792i
$436$	718.705	−	522.170i	0.0789443	−	0.0573564i
$437$	9452.40	+	6867.57i	1.03471	+	0.751763i
$438$	−2848.60	−	2069.63i	−0.310757	−	0.225778i
$439$	92.6878	−	67.3416i	0.0100769	−	0.00732127i	−0.582735	−	0.812662i	$-0.698018\pi$
$439$	92.6878	−	67.3416i	0.0100769	−	0.00732127i	0.592812	+	0.805341i	$0.298018\pi$
$440$	6478.67	−	13482.5i	0.701951	−	1.46081i
$441$	−6084.94	−	4420.97i	−0.657050	−	0.477375i
$442$	896.814	+	2760.11i	0.0965093	+	0.297025i
$443$	251.202			0.0269413			0.0134706	−	0.999909i	$-0.495712\pi$
$443$	251.202			0.0269413			0.0134706	+	0.999909i	$0.495712\pi$
$444$	409.967	+	1261.75i	0.0438202	+	0.134865i
$445$	−3780.27	−	3608.13i	−0.402701	−	0.384364i
$446$	2106.63	−	6483.53i	0.223659	−	0.688350i
$447$	−776.022	+	2388.35i	−0.0821131	+	0.252718i
$448$	1852.20	−	1345.70i	0.195331	−	0.141916i
$449$	9890.92			1.03960			0.519801	−	0.854287i	$-0.326006\pi$
$449$	9890.92			1.03960			0.519801	+	0.854287i	$0.326006\pi$
$450$	5354.53	−	2020.03i	0.560922	−	0.211611i
$451$	−2001.44			−0.208967
$452$	5947.72	−	4321.27i	0.618932	−	0.449680i
$453$	1155.80	−	3557.19i	0.119877	−	0.368944i
$454$	403.029	−	1240.39i	0.0416632	−	0.128226i
$455$	−846.215	+	1761.03i	−0.0871893	+	0.181447i
$456$	1085.15	+	3339.75i	0.111440	+	0.342978i
$457$	−3340.55			−0.341935			−0.170967	−	0.985277i	$-0.554689\pi$
$457$	−3340.55			−0.341935			−0.170967	+	0.985277i	$0.554689\pi$
$458$	−3200.07	−	9848.81i	−0.326484	−	1.00481i
$459$	−3501.68	−	2544.12i	−0.356088	−	0.258713i
$460$	−5520.58	+	2976.83i	−0.559561	+	0.301729i
$461$	9858.66	−	7162.73i	0.996016	−	0.723648i	0.0347857	−	0.999395i	$-0.488925\pi$
$461$	9858.66	−	7162.73i	0.996016	−	0.723648i	0.961230	+	0.275747i	$0.0889251\pi$
$462$	823.790	+	598.518i	0.0829571	+	0.0602719i
$463$	−8431.33	−	6125.72i	−0.846301	−	0.614873i	0.0778229	−	0.996967i	$-0.475203\pi$
$463$	−8431.33	−	6125.72i	−0.846301	−	0.614873i	−0.924124	+	0.382094i	$0.875203\pi$
$464$	884.542	−	642.658i	0.0884997	−	0.0642988i
$465$	230.012	+	1261.34i	0.0229388	+	0.125792i
$466$	8117.20	+	5897.49i	0.806914	+	0.586257i
$467$	4094.04	+	12600.2i	0.405673	+	1.24853i	0.920332	+	0.391139i	$0.127919\pi$
$467$	4094.04	+	12600.2i	0.405673	+	1.24853i	−0.514658	+	0.857395i	$0.672081\pi$
$468$	3235.09			0.319534
$469$	284.744	+	876.352i	0.0280347	+	0.0862818i
$470$	−7778.98	+	4194.61i	−0.763441	+	0.411666i
$471$	144.178	−	443.735i	0.0141048	−	0.0434102i
$472$	−4169.69	+	12833.0i	−0.406622	+	1.25145i
$473$	8572.18	−	6228.05i	0.833296	−	0.605425i
$474$	−3150.87			−0.305325
$475$	−7296.07	−	9117.00i	−0.704772	−	0.880667i
$476$	1390.95			0.133937
$477$	−13698.6	+	9952.64i	−1.31492	+	0.955346i
$478$	−2886.12	+	8882.57i	−0.276168	+	0.849957i
$479$	232.883	−	716.739i	0.0222144	−	0.0683688i	−0.939335	−	0.343002i	$-0.888556\pi$
$479$	232.883	−	716.739i	0.0222144	−	0.0683688i	0.961549	+	0.274633i	$0.0885563\pi$
$480$	−3065.32	−	412.561i	−0.291484	−	0.0392308i
$481$	1680.95	+	5173.42i	0.159344	+	0.490411i
$482$	−2560.72			−0.241987
$483$	−367.260	−	1130.31i	−0.0345982	−	0.106482i
$484$	7025.65	+	5104.43i	0.659810	+	0.479380i
$485$	−18978.1	−	2554.26i	−1.77681	−	0.239140i
$486$	4664.84	−	3389.21i	0.435394	−	0.316332i
$487$	−1593.20	−	1157.53i	−0.148244	−	0.107705i	0.511191	−	0.859467i	$-0.329204\pi$
$487$	−1593.20	−	1157.53i	−0.148244	−	0.107705i	−0.659435	+	0.751762i	$0.729204\pi$
$488$	−690.786	−	501.886i	−0.0640787	−	0.0465559i
$489$	−2553.73	+	1855.40i	−0.236163	+	0.171583i
$490$	4669.91	+	4457.27i	0.430541	+	0.410936i
$491$	−12244.4	−	8896.07i	−1.12542	−	0.817666i	−0.140398	−	0.990095i	$-0.544838\pi$
$491$	−12244.4	−	8896.07i	−1.12542	−	0.817666i	−0.985022	+	0.172429i	$0.944838\pi$
$492$	77.9420	+	239.881i	0.00714207	+	0.0219810i
$493$	7163.15			0.654386
$494$	1598.40	+	4919.38i	0.145578	+	0.448043i
$495$	2799.72	+	15353.1i	0.254218	+	1.39408i
$496$	176.528	−	543.297i	0.0159805	−	0.0491830i
$497$	−715.247	+	2201.30i	−0.0645538	+	0.198676i
$498$	2285.42	−	1660.46i	0.205647	−	0.149411i
$499$	12081.3			1.08384			0.541918	−	0.840431i	$-0.317698\pi$
$499$	12081.3			1.08384			0.541918	+	0.840431i	$0.317698\pi$
$500$	6107.61	−	1410.49i	0.546281	−	0.126158i
$501$	3298.83			0.294173
$502$	85.4248	−	62.0647i	0.00759501	−	0.00551810i
$503$	−1951.30	+	6005.48i	−0.172970	+	0.532348i	−0.999535	−	0.0304937i	$-0.990292\pi$
$503$	−1951.30	+	6005.48i	−0.172970	+	0.532348i	0.826565	+	0.562842i	$0.190292\pi$
$504$	−1045.13	+	3216.59i	−0.0923689	+	0.284282i
$505$	2115.20	+	11599.4i	0.186387	+	1.02211i
$506$	4141.67	+	12746.8i	0.363873	+	1.11989i
$507$	2127.43			0.186356
$508$	−692.405	−	2131.00i	−0.0604734	−	0.186118i
$509$	−1730.89	−	1257.57i	−0.150728	−	0.109510i	0.509865	−	0.860254i	$-0.329695\pi$
$509$	−1730.89	−	1257.57i	−0.150728	−	0.109510i	−0.660593	+	0.750744i	$0.729695\pi$
$510$	1276.29	+	1218.18i	0.110814	+	0.105768i
$511$	−5597.95	+	4067.15i	−0.484616	+	0.352094i
$512$	2326.83	+	1690.54i	0.200845	+	0.145922i
$513$	−6241.09	−	4534.42i	−0.537136	−	0.390252i
$514$	890.430	−	646.935i	0.0764108	−	0.0555157i
$515$	1020.30	+	137.323i	0.0873010	+	0.0117498i
$516$	−1080.29	−	784.873i	−0.0921646	−	0.0669615i
$517$	−7447.53	−	22921.1i	−0.633544	−	1.94985i
$518$	−2042.99			−0.173289
$519$	634.488	+	1952.75i	0.0536627	+	0.165157i
$520$	−7660.16	−	1030.98i	−0.646000	−	0.0869451i
$521$	3873.88	−	11922.6i	0.325754	−	1.00257i	−0.645345	−	0.763891i	$-0.723286\pi$
$521$	3873.88	−	11922.6i	0.325754	−	1.00257i	0.971099	−	0.238677i	$-0.0767137\pi$
$522$	−1933.55	+	5950.84i	−0.162125	+	0.498968i
$523$	4612.96	−	3351.51i	0.385680	−	0.280213i	−0.378003	−	0.925804i	$-0.623389\pi$
$523$	4612.96	−	3351.51i	0.385680	−	0.280213i	0.763683	+	0.645591i	$0.223389\pi$
$524$	−1162.56			−0.0969207
$525$	55.3160	+	1186.50i	0.00459845	+	0.0986343i
$526$	−899.676			−0.0745774
$527$	3027.83	−	2199.85i	0.250274	−	0.181835i
$528$	−226.936	+	698.438i	−0.0187048	+	0.0575675i
$529$	1074.22	−	3306.10i	0.0882893	−	0.271727i
$530$	12792.0	−	6897.74i	1.04839	−	0.565318i
$531$	−4350.31	−	13388.9i	−0.355531	−	1.09421i
$532$	2479.11			0.202036
$533$	319.578	+	983.559i	0.0259708	+	0.0799300i
$534$	1138.53	+	827.190i	0.0922640	+	0.0670337i
$535$	−134.284	−	736.388i	−0.0108516	−	0.0595081i
$536$	−2949.09	+	2142.64i	−0.237652	+	0.172664i
$537$	605.949	+	440.248i	0.0486939	+	0.0353782i
$538$	−7341.55	−	5333.95i	−0.588321	−	0.427440i
$539$	−14242.3	+	10347.7i	−1.13815	+	0.826912i
$540$	3645.04	−	1965.50i	0.290477	−	0.156632i
$541$	13794.1	+	10022.0i	1.09622	+	0.796448i	0.980438	−	0.196827i	$-0.0630638\pi$
$541$	13794.1	+	10022.0i	1.09622	+	0.796448i	0.115778	+	0.993275i	$0.463064\pi$
$542$	2702.98	+	8318.91i	0.214212	+	0.659276i
$543$	−1872.77			−0.148008
$544$	2789.95	+	8586.58i	0.219886	+	0.676740i
$545$	959.094	−	1995.94i	0.0753818	−	0.156874i
$546$	162.590	−	500.400i	0.0127440	−	0.0392219i
$547$	2044.23	−	6291.50i	0.159790	−	0.491783i	−0.838825	−	0.544401i	$-0.816757\pi$
$547$	2044.23	−	6291.50i	0.159790	−	0.491783i	0.998615	+	0.0526188i	$0.0167568\pi$
$548$	−552.569	+	401.465i	−0.0430741	+	0.0312951i
$549$	890.845			0.0692538
$550$	−623.810	−	13380.4i	−0.0483624	−	1.03735i
$551$	12767.0			0.987099
$552$	3803.71	−	2763.56i	0.293291	−	0.213088i
$553$	−1913.42	+	5888.90i	−0.147137	+	0.452842i
$554$	4842.26	−	14903.0i	0.371350	−	1.14290i
$555$	2392.22	+	2283.29i	0.182962	+	0.174631i
$556$	−3144.83	−	9678.80i	−0.239875	−	0.738260i
$557$	567.016			0.0431333			0.0215667	−	0.999767i	$-0.493135\pi$
$557$	567.016			0.0431333			0.0215667	+	0.999767i	$0.493135\pi$
$558$	1010.24	+	3109.20i	0.0766432	+	0.235883i
$559$	−4429.39	−	3218.14i	−0.335140	−	0.243493i
$560$	229.212	−	477.005i	0.0172964	−	0.0359949i
$561$	−3892.45	+	2828.03i	−0.292940	+	0.212833i
$562$	−8384.05	−	6091.37i	−0.629288	−	0.457204i
$563$	−13555.5	−	9848.62i	−1.01473	−	0.737247i	−0.0495366	−	0.998772i	$-0.515774\pi$
$563$	−13555.5	−	9848.62i	−1.01473	−	0.737247i	−0.965197	+	0.261526i	$0.915774\pi$
$564$	−2457.17	+	1785.24i	−0.183449	+	0.133284i
$565$	7937.09	−	16517.6i	0.591001	−	1.22991i
$566$	790.712	+	574.486i	0.0587210	+	0.0426633i
$567$	−963.079	−	2964.05i	−0.0713324	−	0.219539i
$568$	−9156.55			−0.676409
$569$	1889.04	+	5813.88i	0.139179	+	0.428349i	0.996217	−	0.0869048i	$-0.0276976\pi$
$569$	1889.04	+	5813.88i	0.139179	+	0.428349i	−0.857038	+	0.515254i	$0.827698\pi$
$570$	2274.75	+	2171.17i	0.167156	+	0.159544i
$571$	−3930.14	+	12095.7i	−0.288041	+	0.886499i	0.697430	+	0.716653i	$0.254327\pi$
$571$	−3930.14	+	12095.7i	−0.288041	+	0.886499i	−0.985471	+	0.169846i	$0.945673\pi$
$572$	2339.88	−	7201.41i	0.171041	−	0.526409i
$573$	2905.78	−	2111.17i	0.211851	−	0.153919i
$574$	−388.408			−0.0282436
$575$	−8590.49	+	13062.5i	−0.623041	+	0.947381i
$576$	−9449.40			−0.683551
$577$	8937.40	−	6493.40i	0.644833	−	0.468499i	−0.216674	−	0.976244i	$-0.569521\pi$
$577$	8937.40	−	6493.40i	0.644833	−	0.468499i	0.861507	+	0.507745i	$0.169521\pi$
$578$	−1254.78	+	3861.80i	−0.0902972	+	0.277906i
$579$	−944.130	+	2905.73i	−0.0677663	+	0.208563i
$580$	−2968.34	+	6177.31i	−0.212506	+	0.442239i
$581$	−1715.49	−	5279.74i	−0.122497	−	0.377006i
$582$	5156.85			0.367282
$583$	12246.9	+	37692.1i	0.870009	+	2.67761i
$584$	−22145.6	−	16089.7i	−1.56916	−	1.14006i
$585$	7097.88	−	3827.35i	0.501643	−	0.270498i
$586$	3351.48	−	2434.99i	0.236260	−	0.171653i
$587$	−6410.81	−	4657.73i	−0.450771	−	0.327504i	0.339129	−	0.940740i	$-0.389868\pi$
$587$	−6410.81	−	4657.73i	−0.450771	−	0.327504i	−0.789900	+	0.613236i	$0.789868\pi$
$588$	1794.85	+	1304.04i	0.125882	+	0.0914584i
$589$	5396.55	−	3920.82i	0.377523	−	0.274286i
$590$	2167.67	+	11887.1i	0.151257	+	0.829463i
$591$	2354.47	+	1710.62i	0.163875	+	0.119062i
$592$	−455.314	−	1401.31i	−0.0316103	−	0.0972864i
$593$	14752.2			1.02158			0.510792	−	0.859704i	$-0.329352\pi$
$593$	14752.2			1.02158			0.510792	+	0.859704i	$0.329352\pi$
$594$	−2734.60	−	8416.24i	−0.188892	−	0.581351i
$595$	3051.79	−	1645.60i	0.210271	−	0.113383i
$596$	−2167.31	+	6670.28i	−0.148954	+	0.458432i
$597$	1494.41	−	4599.33i	0.102449	−	0.315307i
$598$	5602.78	−	4070.66i	0.383135	−	0.278364i
$599$	−610.057			−0.0416131			−0.0208065	−	0.999784i	$-0.506623\pi$
$599$	−610.057			−0.0416131			−0.0208065	+	0.999784i	$0.506623\pi$
$600$	−4396.45	+	1658.59i	−0.299141	+	0.112853i
$601$	−16775.8			−1.13860			−0.569300	−	0.822130i	$-0.692786\pi$
$601$	−16775.8			−1.13860			−0.569300	+	0.822130i	$0.692786\pi$
$602$	1663.56	−	1208.64i	0.112627	−	0.0818284i
$603$	1175.25	−	3617.04i	0.0793693	−	0.244274i
$604$	3227.97	−	9934.68i	0.217458	−	0.669266i
$605$	21453.4	+	2887.41i	1.44166	+	0.194033i
$606$	−981.190	−	3019.79i	−0.0657725	−	0.202427i
$607$	10205.9			0.682445			0.341222	−	0.939983i	$-0.389159\pi$
$607$	10205.9			0.682445			0.341222	+	0.939983i	$0.389159\pi$
$608$	4972.56	+	15304.0i	0.331684	+	1.02082i
$609$	−1050.64	−	763.333i	−0.0699080	−	0.0507912i
$610$	−757.782	−	101.990i	−0.0502979	−	0.00676959i
$611$	−10074.9	+	7319.83i	−0.667080	+	0.484662i
$612$	−4644.55	−	3374.47i	−0.306773	−	0.222883i
$613$	−7211.16	−	5239.22i	−0.475132	−	0.345204i	0.324306	−	0.945952i	$-0.394869\pi$
$613$	−7211.16	−	5239.22i	−0.475132	−	0.345204i	−0.799438	+	0.600749i	$0.794869\pi$
$614$	−15312.1	+	11124.9i	−1.00643	+	0.731212i
$615$	454.804	+	434.094i	0.0298203	+	0.0284624i
$616$	6404.30	+	4653.00i	0.418891	+	0.304342i
$617$	5702.91	+	17551.7i	0.372108	+	1.14523i	0.945409	+	0.325885i	$0.105662\pi$
$617$	5702.91	+	17551.7i	0.372108	+	1.14523i	−0.573302	+	0.819344i	$0.694338\pi$
$618$	−277.244			−0.0180459
$619$	5256.38	+	16177.5i	0.341312	+	1.05045i	0.963529	+	0.267605i	$0.0862321\pi$
$619$	5256.38	+	16177.5i	0.341312	+	1.05045i	−0.622217	+	0.782845i	$0.713768\pi$
$620$	642.386	+	3522.72i	0.0416110	+	0.228187i
$621$	−3191.74	+	9823.16i	−0.206248	+	0.634766i
$622$	3220.42	−	9911.43i	0.207600	−	0.638927i
$623$	2237.39	−	1625.56i	0.143883	−	0.104537i
$624$	379.467			0.0243443
$625$	11731.6	−	10320.4i	0.750820	−	0.660507i
$626$	−10999.6			−0.702288
$627$	−6937.56	+	5040.43i	−0.441881	+	0.321045i
$628$	402.667	−	1239.28i	0.0255862	−	0.0787464i
$629$	2983.01	−	9180.75i	0.189094	−	0.581972i
$630$	543.327	+	2979.49i	0.0343598	+	0.188422i
$631$	6272.07	+	19303.5i	0.395701	+	1.21784i	0.928414	+	0.371547i	$0.121172\pi$
$631$	6272.07	+	19303.5i	0.395701	+	1.21784i	−0.532713	+	0.846296i	$0.678828\pi$
$632$	−24495.5			−1.54174
$633$	−1934.40	−	5953.48i	−0.121462	−	0.373822i
$634$	483.892	+	351.568i	0.0303120	+	0.0220230i
$635$	−4040.29	−	3856.32i	−0.252495	−	0.240997i
$636$	4040.63	−	2935.69i	0.251921	−	0.183031i
$637$	7359.25	+	5346.81i	0.457746	+	0.332572i
$638$	11848.3	+	8608.27i	0.735231	+	0.534177i
$639$	7728.68	−	5615.22i	0.478470	−	0.347628i
$640$	−7231.47	−	973.282i	−0.446639	−	0.0601131i
$641$	−13946.6	−	10132.8i	−0.859371	−	0.624370i	0.0683428	−	0.997662i	$-0.478229\pi$
$641$	−13946.6	−	10132.8i	−0.859371	−	0.624370i	−0.927714	+	0.373292i	$0.878229\pi$
$642$	62.2911	+	191.712i	0.00382934	+	0.0117855i
$643$	1616.35			0.0991331			0.0495666	−	0.998771i	$-0.484216\pi$
$643$	1616.35			0.0991331			0.0495666	+	0.998771i	$0.484216\pi$
$644$	−1025.70	−	3156.78i	−0.0627613	−	0.193159i
$645$	−3298.74	−	443.977i	−0.201376	−	0.0271032i
$646$	2836.52	−	8729.92i	0.172758	−	0.531694i
$647$	−1752.03	+	5392.20i	−0.106460	+	0.327649i	−0.990070	−	0.140573i	$-0.955105\pi$
$647$	−1752.03	+	5392.20i	−0.106460	+	0.327649i	0.883611	+	0.468223i	$0.155105\pi$
$648$	9974.59	−	7246.96i	0.604690	−	0.439333i
$649$	−32950.5			−1.99295
$650$	−6475.88	+	2443.06i	−0.390777	+	0.147423i
$651$	−678.524			−0.0408502
$652$	−7132.18	+	5181.83i	−0.428401	+	0.311252i
$653$	−7617.70	+	23444.9i	−0.456514	+	1.40501i	0.412835	+	0.910806i	$0.364539\pi$
$653$	−7617.70	+	23444.9i	−0.456514	+	1.40501i	−0.869349	+	0.494199i	$0.835461\pi$
$654$	−184.278	+	567.151i	−0.0110181	+	0.0339103i
$655$	−2550.68	+	1375.39i	−0.152158	+	0.0820472i
$656$	−86.5632	−	266.414i	−0.00515202	−	0.0158563i
$657$	28559.2			1.69589
$658$	−1445.30	−	4448.18i	−0.0856288	−	0.263538i
$659$	1095.83	+	796.169i	0.0647763	+	0.0470627i	0.619702	−	0.784837i	$-0.287253\pi$
$659$	1095.83	+	796.169i	0.0647763	+	0.0470627i	−0.554926	+	0.831900i	$0.687253\pi$
$660$	−825.823	−	4528.65i	−0.0487047	−	0.267087i
$661$	−7325.16	+	5322.04i	−0.431037	+	0.313167i	−0.782064	−	0.623199i	$-0.785833\pi$
$661$	−7325.16	+	5322.04i	−0.431037	+	0.313167i	0.351026	+	0.936366i	$0.385833\pi$
$662$	−4441.70	−	3227.08i	−0.260773	−	0.189462i
$663$	2011.29	+	1461.29i	0.117816	+	0.0855984i
$664$	17767.3	−	12908.7i	1.03841	−	0.754450i
$665$	5439.25	−	2932.97i	0.317180	−	0.171031i
$666$	6821.77	+	4956.31i	0.396905	+	0.288368i
$667$	−5282.17	−	16256.9i	−0.306636	−	0.943730i
$668$	9213.10			0.533631
$669$	−1804.62	−	5554.04i	−0.104291	−	0.320974i
$670$	−1413.81	+	2942.22i	−0.0815225	+	0.169654i
$671$	644.331	−	1983.05i	0.0370703	−	0.114091i
$672$	505.810	−	1556.72i	0.0290358	−	0.0893630i
$673$	−6967.78	+	5062.39i	−0.399091	+	0.289956i	−0.769171	−	0.639044i	$-0.779330\pi$
$673$	−6967.78	+	5062.39i	−0.399091	+	0.289956i	0.370080	+	0.929000i	$0.379330\pi$
$674$	9674.72			0.552903
$675$	5672.00	−	8624.71i	0.323430	−	0.491801i
$676$	5941.57			0.338050
$677$	6541.98	−	4753.03i	0.371387	−	0.269828i	−0.386399	−	0.922332i	$-0.626281\pi$
$677$	6541.98	−	4753.03i	0.371387	−	0.269828i	0.757786	+	0.652503i	$0.226281\pi$
$678$	−1525.02	+	4693.52i	−0.0863833	+	0.265860i
$679$	3131.59	−	9638.03i	0.176994	−	0.544733i
$680$	9922.14	+	9470.33i	0.559554	+	0.534075i
$681$	−345.250	−	1062.57i	−0.0194273	−	0.0597911i
$682$	7651.86			0.429626
$683$	−10597.5	−	32615.7i	−0.593706	−	1.82724i	−0.561064	−	0.827773i	$-0.689608\pi$
$683$	−10597.5	−	32615.7i	−0.593706	−	1.82724i	−0.0326425	−	0.999467i	$-0.510392\pi$
$684$	−8278.05	−	6014.35i	−0.462747	−	0.336206i
$685$	−737.390	+	1534.56i	−0.0411303	+	0.0855948i
$686$	−5842.04	+	4244.49i	−0.325146	+	0.236232i
$687$	−7176.82	−	5214.27i	−0.398563	−	0.289573i
$688$	1199.78	+	871.689i	0.0664841	+	0.0483035i
$689$	16567.4	−	12036.9i	0.916064	−	0.665559i
$690$	1823.51	−	3794.85i	0.100609	−	0.209373i
$691$	−8077.57	−	5868.70i	−0.444697	−	0.323091i	0.342802	−	0.939408i	$-0.388624\pi$
$691$	−8077.57	−	5868.70i	−0.444697	−	0.323091i	−0.787498	+	0.616317i	$0.788624\pi$
$692$	1772.02	+	5453.73i	0.0973443	+	0.299595i
$693$	−8259.05			−0.452721
$694$	1013.53	+	3119.33i	0.0554368	+	0.170617i
$695$	−18350.6	−	17515.0i	−1.00155	−	0.955945i
$696$	1587.58	−	4886.07i	0.0864613	−	0.266101i
$697$	567.122	−	1745.42i	0.0308196	−	0.0948531i
$698$	2692.33	−	1956.09i	0.145997	−	0.106073i
$699$	8595.00			0.465082
$700$	154.489	+	3313.70i	0.00834161	+	0.178923i
$701$	2668.87			0.143797			0.0718987	−	0.997412i	$-0.477094\pi$
$701$	2668.87			0.143797			0.0718987	+	0.997412i	$0.477094\pi$
$702$	−3699.32	+	2687.71i	−0.198892	+	0.144503i
$703$	5316.65	−	16363.0i	0.285236	−	0.877867i
$704$	−6834.58	+	21034.7i	−0.365892	+	1.12610i
$705$	−3279.03	+	6823.88i	−0.175171	+	0.364542i
$706$	191.181	+	588.395i	0.0101915	+	0.0313662i
$707$	−6239.76			−0.331924
$708$	1283.19	+	3949.26i	0.0681149	+	0.209636i
$709$	11300.0	+	8209.94i	0.598563	+	0.434881i	0.845368	−	0.534184i	$-0.179381\pi$
$709$	11300.0	+	8209.94i	0.598563	+	0.434881i	−0.246806	+	0.969065i	$0.579381\pi$
$710$	−7217.14	+	3891.66i	−0.381485	+	0.205706i
$711$	20675.7	−	15021.8i	1.09057	−	0.792348i
$712$	8851.15	+	6430.74i	0.465886	+	0.338486i
$713$	−7225.33	−	5249.51i	−0.379510	−	0.275730i
$714$	−755.386	+	548.820i	−0.0395933	+	0.0287662i
$715$	−3386.04	−	18568.4i	−0.177106	−	0.971213i
$716$	1692.32	+	1229.54i	0.0883310	+	0.0641762i
$717$	2472.36	+	7609.14i	0.128775	+	0.396330i
$718$	7875.35			0.409339
$719$	8185.68	+	25192.9i	0.424582	+	1.30673i	0.903394	+	0.428811i	$0.141067\pi$
$719$	8185.68	+	25192.9i	0.424582	+	1.30673i	−0.478812	+	0.877917i	$0.658933\pi$
$720$	−1922.59	+	1036.71i	−0.0995146	+	0.0536607i
$721$	−168.361	+	518.162i	−0.00869638	+	0.0267647i
$722$	1081.93	−	3329.84i	0.0557691	−	0.171640i
$723$	−1774.67	+	1289.37i	−0.0912872	+	0.0663240i
$724$	−5230.35			−0.268487
$725$	795.589	+	17065.0i	0.0407551	+	0.874175i
$726$	−5829.46			−0.298005
$727$	−13903.6	+	10101.6i	−0.709295	+	0.515333i	−0.882946	−	0.469474i	$-0.844444\pi$
$727$	−13903.6	+	10101.6i	−0.709295	+	0.515333i	0.173651	+	0.984807i	$0.444444\pi$
$728$	1264.01	−	3890.21i	0.0643505	−	0.198050i
$729$	−2868.44	+	8828.15i	−0.145732	+	0.448516i
$730$	−24293.4	−	3269.64i	−1.23170	−	0.165774i
$731$	3002.40	+	9240.43i	0.151912	+	0.467537i
$732$	−262.769			−0.0132681
$733$	−3541.75	−	10900.4i	−0.178469	−	0.549270i	0.821306	−	0.570488i	$-0.193246\pi$
$733$	−3541.75	−	10900.4i	−0.178469	−	0.549270i	−0.999775	+	0.0212175i	$0.993246\pi$
$734$	17174.8	+	12478.2i	0.863668	+	0.627491i
$735$	5480.73	+	737.651i	0.275047	+	0.0370186i
$736$	17430.0	−	12663.6i	0.872933	−	0.634223i
$737$	−7201.60	−	5232.27i	−0.359938	−	0.261510i
$738$	1296.94	+	942.282i	0.0646898	+	0.0469999i
$739$	−30512.3	+	22168.5i	−1.51883	+	1.10349i	−0.556760	+	0.830673i	$0.687956\pi$
$739$	−30512.3	+	22168.5i	−1.51883	+	1.10349i	−0.962066	+	0.272818i	$0.912044\pi$
$740$	6681.10	+	6376.87i	0.331895	+	0.316782i
$741$	3584.75	+	2604.47i	0.177718	+	0.129120i
$742$	2376.69	+	7314.71i	0.117589	+	0.361902i
$743$	−31924.8			−1.57632			−0.788160	−	0.615470i	$-0.788966\pi$
$743$	−31924.8			−1.57632			−0.788160	+	0.615470i	$0.788966\pi$
$744$	−829.480	−	2552.88i	−0.0408739	−	0.125797i
$745$	3136.31	+	17198.9i	0.154235	+	0.845796i
$746$	4672.37	−	14380.1i	0.229313	−	0.705753i
$747$	−7080.48	+	21791.5i	−0.346802	+	1.06735i
$748$	−10871.0	+	7898.23i	−0.531394	+	0.386080i
$749$	396.133			0.0193249
$750$	−2760.34	+	3175.84i	−0.134391	+	0.154620i
$751$	26464.6			1.28589			0.642946	−	0.765911i	$-0.277712\pi$
$751$	26464.6			1.28589			0.642946	+	0.765911i	$0.277712\pi$
$752$	2728.96	−	1982.70i	0.132334	−	0.0961460i
$753$	27.9516	−	86.0260i	0.00135274	−	0.00416330i
$754$	2338.47	−	7197.07i	0.112947	−	0.347615i
$755$	−4671.20	−	25615.9i	−0.225169	−	1.23478i
$756$	677.234	+	2084.31i	0.0325804	+	0.100272i
$757$	−10652.8			−0.511470			−0.255735	−	0.966747i	$-0.582317\pi$
$757$	−10652.8			−0.511470			−0.255735	+	0.966747i	$0.582317\pi$
$758$	1508.19	+	4641.72i	0.0722688	+	0.222421i
$759$	9288.56	+	6748.54i	0.444207	+	0.322736i
$760$	17684.4	+	16879.1i	0.844051	+	0.805617i
$761$	−9424.61	+	6847.38i	−0.448938	+	0.326173i	−0.789176	−	0.614167i	$-0.789492\pi$
$761$	−9424.61	+	6847.38i	−0.448938	+	0.326173i	0.340238	+	0.940339i	$0.389492\pi$
$762$	1216.84	+	884.088i	0.0578498	+	0.0420304i
$763$	948.085	+	688.824i	0.0449842	+	0.0326830i
$764$	8115.38	−	5896.17i	0.384299	−	0.279209i
$765$	−14182.5	−	1908.83i	−0.670288	−	0.0902140i
$766$	−14435.3	−	10487.8i	−0.680898	−	0.494701i
$767$	5261.35	+	16192.8i	0.247688	+	0.762304i
$768$	6936.37			0.325904
$769$	−3694.13	−	11369.4i	−0.173230	−	0.533147i	0.826318	−	0.563203i	$-0.190431\pi$
$769$	−3694.13	−	11369.4i	−0.173230	−	0.533147i	−0.999548	+	0.0300565i	$0.990431\pi$
$770$	7025.43	+	945.551i	0.328804	+	0.0442536i
$771$	291.354	−	896.697i	0.0136094	−	0.0418855i
$772$	−2636.81	+	8115.25i	−0.122928	+	0.378335i
$773$	−16241.6	+	11800.2i	−0.755717	+	0.549061i	−0.897594	−	0.440824i	$-0.854686\pi$
$773$	−16241.6	+	11800.2i	−0.755717	+	0.549061i	0.141877	+	0.989884i	$0.454686\pi$
$774$	−8487.00			−0.394133
$775$	5577.05	+	6968.96i	0.258495	+	0.323009i
$776$	40090.4			1.85459
$777$	−1415.86	+	1028.68i	−0.0653716	+	0.0474952i
$778$	2825.50	−	8695.99i	0.130204	−	0.400728i
$779$	1010.79	−	3110.89i	0.0464895	−	0.143080i
$780$	−2093.64	+	1128.94i	−0.0961079	+	0.0518237i
$781$	−6909.64	−	21265.7i	−0.316576	−	0.974322i
$782$	−12289.8			−0.562000
$783$	3487.63	+	10733.8i	0.159180	+	0.489905i
$784$	−1993.38	−	1448.28i	−0.0908064	−	0.0659747i
$785$	−582.699	−	3195.41i	−0.0264935	−	0.145285i
$786$	631.350	−	458.703i	0.0286508	−	0.0208160i
$787$	22616.7	+	16432.0i	1.02439	+	0.744266i	0.967179	−	0.254096i	$-0.0817780\pi$
$787$	22616.7	+	16432.0i	1.02439	+	0.744266i	0.0572147	+	0.998362i	$0.481778\pi$
$788$	6575.66	+	4777.50i	0.297269	+	0.215979i
$789$	−623.507	+	453.004i	−0.0281336	+	0.0204403i
$790$	−19307.2	+	10410.9i	−0.869518	+	0.468866i
$791$	7845.98	+	5700.43i	0.352681	+	0.256238i
$792$	−10096.5	−	31073.8i	−0.452984	−	1.39414i
$793$	−1077.41			−0.0482469
$794$	431.822	+	1329.01i	0.0193007	+	0.0594015i
$795$	5392.13	−	11221.4i	0.240552	−	0.500605i
$796$	4173.66	−	12845.2i	0.185844	−	0.571968i
$797$	9441.64	−	29058.4i	0.419624	−	1.29147i	−0.488426	−	0.872605i	$-0.662429\pi$
$797$	9441.64	−	29058.4i	0.419624	−	1.29147i	0.908049	−	0.418863i	$-0.137571\pi$
$798$	−1346.33	+	978.169i	−0.0597240	+	0.0433920i
$799$	22099.5			0.978503
$800$	−20146.2	+	7600.25i	−0.890343	+	0.335887i
$801$	−11414.5			−0.503511
$802$	−22140.9	+	16086.3i	−0.974839	+	0.708262i
$803$	20656.3	−	63573.6i	0.907777	−	2.79385i
$804$	−346.658	+	1066.90i	−0.0152061	+	0.0467995i
$805$	−5985.13	−	5712.59i	−0.262047	−	0.250115i
$806$	−1221.81	−	3760.33i	−0.0533949	−	0.164332i
$807$	−7773.69			−0.339091
$808$	−7627.96	−	23476.4i	−0.332117	−	1.02215i
$809$	2550.54	+	1853.08i	0.110843	+	0.0805324i	0.641826	−	0.766850i	$-0.278177\pi$
$809$	2550.54	+	1853.08i	0.110843	+	0.0805324i	−0.530983	+	0.847383i	$0.678177\pi$
$810$	4781.86	−	9951.36i	0.207429	−	0.431673i
$811$	−292.128	+	212.243i	−0.0126486	+	0.00918973i	−0.594092	−	0.804397i	$-0.702488\pi$
$811$	−292.128	+	212.243i	−0.0126486	+	0.00918973i	0.581443	+	0.813587i	$0.302488\pi$
$812$	−2934.27	−	2131.87i	−0.126813	−	0.0921354i
$813$	6061.99	+	4404.29i	0.261505	+	0.189994i
$814$	15967.0	−	11600.7i	0.687521	−	0.499513i
$815$	−9517.72	+	19807.0i	−0.409069	+	0.851299i
$816$	−544.793	−	395.816i	−0.0233720	−	0.0169808i
$817$	5351.21	+	16469.3i	0.229150	+	0.705250i
$818$	2637.71			0.112745
$819$	1318.76	+	4058.72i	0.0562651	+	0.173166i
$820$	1270.20	+	1212.36i	0.0540941	+	0.0516309i
$821$	−5224.35	+	16078.9i	−0.222084	+	0.683505i	0.776490	+	0.630129i	$0.216998\pi$
$821$	−5224.35	+	16078.9i	−0.222084	+	0.683505i	−0.998574	+	0.0533758i	$0.983002\pi$
$822$	141.681	−	436.048i	0.00601178	−	0.0185023i
$823$	10939.7	−	7948.18i	0.463348	−	0.336642i	−0.331495	−	0.943457i	$-0.607553\pi$
$823$	10939.7	−	7948.18i	0.463348	−	0.336642i	0.794843	+	0.606815i	$0.207553\pi$
$824$	−2155.35			−0.0911226
$825$	−7169.61	−	8958.97i	−0.302562	−	0.378075i
$826$	−6394.53			−0.269364
$827$	26154.0	−	19002.0i	1.09971	−	0.798988i	0.118700	−	0.992930i	$-0.462127\pi$
$827$	26154.0	−	19002.0i	1.09971	−	0.798988i	0.981013	+	0.193942i	$0.0621273\pi$
$828$	−4233.45	+	13029.2i	−0.177684	+	0.546856i
$829$	−8942.80	+	27523.1i	−0.374664	+	1.15310i	0.569042	+	0.822309i	$0.307314\pi$
$829$	−8942.80	+	27523.1i	−0.374664	+	1.15310i	−0.943705	+	0.330787i	$0.892686\pi$
$830$	8517.72	−	17725.9i	0.356210	−	0.741297i
$831$	−4148.07	−	12766.4i	−0.173159	−	0.532928i
$832$	11428.3			0.476208
$833$	−4988.37	−	15352.6i	−0.207487	−	0.638580i
$834$	5526.77	+	4015.44i	0.229468	+	0.166718i
$835$	20213.8	−	10899.8i	0.837758	−	0.451740i
$836$	−19375.5	+	14077.1i	−0.801574	+	0.582377i
$837$	4770.64	+	3466.07i	0.197010	+	0.143136i
$838$	7222.93	+	5247.77i	0.297747	+	0.216326i
$839$	16807.4	−	12211.3i	0.691603	−	0.502479i	−0.185584	−	0.982628i	$-0.559418\pi$
$839$	16807.4	−	12211.3i	0.691603	−	0.502479i	0.877187	+	0.480150i	$0.159418\pi$
$840$	−446.110	−	2446.38i	−0.0183241	−	0.100486i
$841$	4620.18	+	3356.76i	0.189437	+	0.137634i
$842$	−2222.79	−	6841.04i	−0.0909767	−	0.279998i
$843$	−8877.55			−0.362704
$844$	−5402.48	−	16627.1i	−0.220333	−	0.678115i
$845$	13036.0	−	7029.32i	0.530712	−	0.286173i
$846$	−5965.31	+	18359.3i	−0.242425	+	0.746107i
$847$	−3540.04	+	10895.1i	−0.143609	+	0.441984i
$848$	−4487.57	+	3260.41i	−0.181726	+	0.132032i
$849$	837.255			0.0338451
$850$	11845.6	+	3247.42i	0.478001	+	0.131042i
$851$	−23035.5			−0.927905
$852$	−2279.70	+	1656.30i	−0.0916681	+	0.0666008i
$853$	−10310.8	+	31733.5i	−0.413877	+	1.27378i	0.499375	+	0.866386i	$0.333563\pi$
$853$	−10310.8	+	31733.5i	−0.413877	+	1.27378i	−0.913252	+	0.407395i	$0.866437\pi$
$854$	125.042	−	384.840i	0.00501036	−	0.0154203i
$855$	−25277.7	−	3402.12i	−1.01109	−	0.136082i
$856$	484.263	+	1490.41i	0.0193362	+	0.0595106i
$857$	−25175.7			−1.00348			−0.501742	−	0.865017i	$-0.667307\pi$
$857$	−25175.7			−1.00348			−0.501742	+	0.865017i	$0.667307\pi$
$858$	1570.70	+	4834.11i	0.0624974	+	0.192347i
$859$	−5184.10	−	3766.47i	−0.205913	−	0.149604i	0.480050	−	0.877241i	$-0.340619\pi$
$859$	−5184.10	−	3766.47i	−0.205913	−	0.149604i	−0.685963	+	0.727637i	$0.740619\pi$
$860$	−9212.87	−	1239.96i	−0.365298	−	0.0491654i
$861$	−269.180	+	195.571i	−0.0106546	+	0.00774104i
$862$	4424.47	+	3214.57i	0.174824	+	0.127017i
$863$	39146.1	+	28441.3i	1.54409	+	1.12185i	0.947704	+	0.319149i	$0.103397\pi$
$863$	39146.1	+	28441.3i	1.54409	+	1.12185i	0.596386	+	0.802698i	$0.296603\pi$
$864$	−11508.4	+	8361.36i	−0.453153	+	0.329235i
$865$	10340.0	+	9869.21i	0.406442	+	0.387934i
$866$	−3182.45	−	2312.18i	−0.124878	−	0.0907289i
$867$	1074.89	+	3308.17i	0.0421051	+	0.129586i
$868$	−1895.01			−0.0741024
$869$	−18484.6	−	56889.6i	−0.721572	−	2.22077i
$870$	−825.325	−	4525.92i	−0.0321622	−	0.176371i
$871$	−1421.37	+	4374.52i	−0.0552941	+	0.170178i
$872$	−1432.62	+	4409.14i	−0.0556359	+	0.171230i
$873$	−33838.7	+	24585.3i	−1.31187	+	0.953133i
$874$	−21904.3			−0.847741
$875$	4259.31	+	7087.59i	0.164561	+	0.273833i
$876$	−8423.99			−0.324909
$877$	21739.2	−	15794.5i	0.837036	−	0.608142i	−0.0845052	−	0.996423i	$-0.526931\pi$
$877$	21739.2	−	15794.5i	0.837036	−	0.608142i	0.921541	+	0.388281i	$0.126931\pi$
$878$	−66.3732	+	204.276i	−0.00255124	+	0.00785190i
$879$	1096.63	−	3375.07i	0.0420800	−	0.129509i
$880$	917.168	+	5029.57i	0.0351338	+	0.192667i
$881$	11453.8	+	35251.1i	0.438011	+	1.34806i	0.889970	+	0.456020i	$0.150725\pi$
$881$	11453.8	+	35251.1i	0.438011	+	1.34806i	−0.451959	+	0.892039i	$0.649275\pi$
$882$	14100.8			0.538321
$883$	−656.803	−	2021.43i	−0.0250319	−	0.0770403i	0.937760	−	0.347284i	$-0.112896\pi$
$883$	−656.803	−	2021.43i	−0.0250319	−	0.0770403i	−0.962792	+	0.270243i	$0.912896\pi$
$884$	5617.22	+	4081.15i	0.213719	+	0.155276i
$885$	7487.64	+	7146.69i	0.284400	+	0.271450i
$886$	−381.001	+	276.814i	−0.0144469	+	0.0104963i
$887$	1712.00	+	1243.84i	0.0648065	+	0.0470847i	0.619717	−	0.784825i	$-0.287247\pi$
$887$	1712.00	+	1243.84i	0.0648065	+	0.0470847i	−0.554910	+	0.831910i	$0.687247\pi$
$888$	−5601.17	−	4069.49i	−0.211670	−	0.153787i
$889$	2391.29	−	1737.37i	0.0902151	−	0.0655451i
$890$	9709.58	+	1306.81i	0.365692	+	0.0492184i
$891$	24357.7	+	17696.9i	0.915840	+	0.665397i
$892$	−5040.01	−	15511.6i	−0.189184	−	0.582248i
$893$	39388.2			1.47601
$894$	−1454.85	−	4477.58i	−0.0544268	−	0.167509i
$895$	5167.64	+	695.512i	0.193000	+	0.0259759i
$896$	1193.27	−	3672.50i	0.0444914	−	0.136930i
$897$	1833.27	−	5642.22i	0.0682397	−	0.210020i
$898$	−15001.7	+	10899.4i	−0.557475	+	0.405029i
$899$	−9758.97			−0.362046
$900$	7523.22	−	11439.6i	0.278638	−	0.423690i
$901$	−36341.0			−1.34372
$902$	3035.60	−	2205.49i	0.112056	−	0.0814135i
$903$	544.327	−	1675.27i	0.0200599	−	0.0617379i
$904$	−11855.8	+	36488.3i	−0.436191	+	1.34246i
$905$	−11475.5	+	6187.89i	−0.421503	+	0.227285i
$906$	2166.85	+	6668.88i	0.0794579	+	0.244546i
$907$	−4188.50			−0.153337			−0.0766687	−	0.997057i	$-0.524428\pi$
$907$	−4188.50			−0.153337			−0.0766687	+	0.997057i	$0.524428\pi$
$908$	−964.228	−	2967.59i	−0.0352412	−	0.108461i
$909$	20835.3	+	15137.7i	0.760246	+	0.552351i
$910$	−657.110	−	3603.46i	−0.0239374	−	0.131268i
$911$	11515.9	−	8366.82i	0.418815	−	0.304287i	−0.358346	−	0.933589i	$-0.616659\pi$
$911$	11515.9	−	8366.82i	0.418815	−	0.304287i	0.777161	+	0.629302i	$0.216659\pi$
$912$	−970.992	−	705.467i	−0.0352552	−	0.0256144i
$913$	43387.3	+	31522.7i	1.57274	+	1.14266i
$914$	5066.65	−	3681.14i	0.183359	−	0.133218i
$915$	−576.523	+	310.875i	−0.0208298	+	0.0112319i
$916$	−20043.7	−	14562.6i	−0.722995	−	0.525287i
$917$	−473.906	−	1458.53i	−0.0170663	−	0.0525245i
$918$	8114.55			0.291743
$919$	−9951.33	−	30627.0i	−0.357197	−	1.09934i	−0.954725	−	0.297491i	$-0.903850\pi$
$919$	−9951.33	−	30627.0i	−0.357197	−	1.09934i	0.597528	−	0.801848i	$-0.296150\pi$
$920$	14176.4	−	29501.9i	0.508022	−	1.05723i
$921$	−5010.22	+	15419.9i	−0.179253	+	0.551685i
$922$	−7059.73	+	21727.6i	−0.252169	+	0.776096i
$923$	−9347.23	+	6791.16i	−0.333335	+	0.242182i
$924$	2436.14			0.0867350
$925$	22202.8	+	6086.81i	0.789216	+	0.216360i
$926$	19538.2			0.693374
$927$	1819.24	−	1321.76i	0.0644572	−	0.0468309i
$928$	7274.88	−	22389.8i	0.257338	−	0.792005i
$929$	−4869.12	+	14985.6i	−0.171960	+	0.529238i	−0.999482	−	0.0321958i	$-0.989750\pi$
$929$	−4869.12	+	14985.6i	−0.171960	+	0.529238i	0.827522	+	0.561434i	$0.189750\pi$
$930$	−1738.80	−	1659.62i	−0.0613091	−	0.0585174i
$931$	−8890.84	−	27363.2i	−0.312981	−	0.963257i
$932$	24004.5			0.843662
$933$	−2758.73	−	8490.51i	−0.0968027	−	0.297928i
$934$	−20094.3	−	14599.4i	−0.703967	−	0.511462i
$935$	−14507.1	+	30190.1i	−0.507414	+	1.05596i
$936$	−13658.4	+	9923.38i	−0.476963	+	0.346534i
$937$	−31461.7	−	22858.3i	−1.09692	−	0.796956i	−0.116362	−	0.993207i	$-0.537123\pi$
$937$	−31461.7	−	22858.3i	−1.09692	−	0.796956i	−0.980554	+	0.196251i	$0.937123\pi$
$938$	−1397.58	−	1015.40i	−0.0486487	−	0.0353454i
$939$	−7623.10	+	5538.51i	−0.264931	+	0.192484i
$940$	−9157.82	+	19058.0i	−0.317761	+	0.661281i
$941$	−32883.6	−	23891.4i	−1.13919	−	0.827669i	−0.152182	−	0.988352i	$-0.548630\pi$
$941$	−32883.6	−	23891.4i	−1.13919	−	0.827669i	−0.987006	+	0.160684i	$0.948630\pi$
$942$	270.299	+	831.896i	0.00934908	+	0.0287735i
$943$	−4379.46			−0.151235
$944$	−1425.13	−	4386.10i	−0.0491356	−	0.151224i
$945$	3951.77	+	3771.83i	0.136033	+	0.129839i
$946$	−6138.49	+	18892.3i	−0.210972	+	0.649305i
$947$	6376.19	−	19623.9i	0.218794	−	0.673380i	−0.780068	−	0.625695i	$-0.784816\pi$
$947$	6376.19	−	19623.9i	0.218794	−	0.673380i	0.998862	−	0.0476852i	$-0.0151844\pi$
$948$	−6098.62	+	4430.91i	−0.208939	+	0.151803i
$949$	−34540.0			−1.18147
$950$	21112.6	+	5787.92i	0.721034	+	0.197668i
$951$	512.375			0.0174710
$952$	−5872.52	+	4266.63i	−0.199926	+	0.145255i
$953$	−6682.98	+	20568.1i	−0.227160	+	0.699125i	0.770906	+	0.636949i	$0.219804\pi$
$953$	−6682.98	+	20568.1i	−0.227160	+	0.699125i	−0.998065	+	0.0621759i	$0.980196\pi$
$954$	9809.51	−	30190.6i	0.332908	−	1.02459i
$955$	10829.8	−	22537.5i	0.366956	−	0.763660i
$956$	6904.91	+	21251.1i	0.233599	+	0.718945i
$957$	12545.7			0.423766
$958$	436.599	+	1343.71i	0.0147243	+	0.0453167i
$959$	−728.926	−	529.595i	−0.0245446	−	0.0178327i
$960$	6115.32	−	3297.53i	0.205595	−	0.110862i
$961$	19976.4	−	14513.7i	0.670550	−	0.487183i
$962$	−8250.40	−	5994.26i	−0.276511	−	0.200897i
$963$	−1322.73	−	961.023i	−0.0442622	−	0.0321584i
$964$	−4956.37	+	3601.01i	−0.165595	+	0.120312i
$965$	3815.72	+	20924.6i	0.127287	+	0.698019i
$966$	1802.58	+	1309.65i	0.0600384	+	0.0436205i
$967$	−9371.85	−	28843.6i	−0.311663	−	0.959201i	−0.977106	−	0.212752i	$-0.931757\pi$
$967$	−9371.85	−	28843.6i	−0.311663	−	0.959201i	0.665443	−	0.746449i	$-0.268243\pi$
$968$	−45319.3			−1.50477
$969$	−2429.87	−	7478.38i	−0.0805560	−	0.247926i
$970$	31599.0	−	17039.0i	1.04596	−	0.564008i
$971$	10840.7	−	33364.3i	0.358285	−	1.10269i	−0.595795	−	0.803137i	$-0.703163\pi$
$971$	10840.7	−	33364.3i	0.358285	−	1.10269i	0.954080	−	0.299552i	$-0.0968372\pi$
$972$	4262.90	−	13119.9i	0.140672	−	0.432942i
$973$	10861.0	−	7890.97i	0.357849	−	0.259993i
$974$	3691.96			0.121456
$975$	−3257.88	+	4953.85i	−0.107011	+	0.162718i
$976$	291.834			0.00957110
$977$	36271.9	−	26353.1i	1.18776	−	0.862958i	0.194733	−	0.980856i	$-0.437616\pi$
$977$	36271.9	−	26353.1i	1.18776	−	0.862958i	0.993026	+	0.117899i	$0.0376158\pi$
$978$	1828.71	−	5628.21i	0.0597913	−	0.184019i
$979$	−8255.92	+	25409.1i	−0.269520	+	0.829498i
$980$	15306.8	+	2060.14i	0.498937	+	0.0671519i
$981$	−1494.67	−	4600.13i	−0.0486455	−	0.149715i
$982$	28374.3			0.922057
$983$	6943.28	+	21369.2i	0.225286	+	0.693359i	0.998262	+	0.0589243i	$0.0187671\pi$
$983$	6943.28	+	21369.2i	0.225286	+	0.693359i	−0.772976	+	0.634435i	$0.781233\pi$
$984$	−1064.88	−	773.682i	−0.0344992	−	0.0250651i
$985$	20079.3	+	2702.47i	0.649524	+	0.0874193i
$986$	−10864.4	+	7893.48i	−0.350907	+	0.254949i
$987$	−3241.39	−	2355.01i	−0.104534	−	0.0759481i
$988$	10011.6	+	7273.88i	0.322381	+	0.234224i
$989$	18757.3	−	13628.0i	0.603081	−	0.438164i
$990$	−21164.8	−	20201.1i	−0.679456	−	0.648517i
$991$	27174.0	+	19743.1i	0.871049	+	0.632854i	0.930868	−	0.365355i	$-0.119052\pi$
$991$	27174.0	+	19743.1i	0.871049	+	0.632854i	−0.0598190	+	0.998209i	$0.519052\pi$
$992$	−3800.98	−	11698.2i	−0.121655	−	0.374414i
$993$	−4703.15			−0.150302
$994$	−1340.92	−	4126.92i	−0.0427880	−	0.131688i
$995$	−6039.70	−	33120.5i	−0.192434	−	1.05527i
$996$	2088.50	−	6427.75i	0.0664425	−	0.204489i
$997$	−16212.5	+	49896.8i	−0.514999	+	1.58500i	0.268285	+	0.963339i	$0.413543\pi$
$997$	−16212.5	+	49896.8i	−0.514999	+	1.58500i	−0.783284	+	0.621664i	$0.786457\pi$
$998$	−18323.9	+	13313.1i	−0.581195	+	0.422263i
$999$	15209.5			0.481690

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.4.d.a.11.3	✓	28
3.2	odd	2		225.4.h.b.136.5		28
5.2	odd	4		125.4.e.b.74.6		56
5.3	odd	4		125.4.e.b.74.9		56
5.4	even	2		125.4.d.a.51.5		28
25.4	even	10		625.4.a.d.1.6		14
25.9	even	10		125.4.d.a.76.5		28
25.12	odd	20		125.4.e.b.49.9		56
25.13	odd	20		125.4.e.b.49.6		56
25.16	even	5	inner	25.4.d.a.16.3	yes	28
25.21	even	5		625.4.a.c.1.9		14
75.41	odd	10		225.4.h.b.91.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.11.3	✓	28	1.1	even	1	trivial
25.4.d.a.16.3	yes	28	25.16	even	5	inner
125.4.d.a.51.5		28	5.4	even	2
125.4.d.a.76.5		28	25.9	even	10
125.4.e.b.49.6		56	25.13	odd	20
125.4.e.b.49.9		56	25.12	odd	20
125.4.e.b.74.6		56	5.2	odd	4
125.4.e.b.74.9		56	5.3	odd	4
225.4.h.b.91.5		28	75.41	odd	10
225.4.h.b.136.5		28	3.2	odd	2
625.4.a.c.1.9		14	25.21	even	5
625.4.a.d.1.6		14	25.4	even	10

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	25.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.51671 + 1.10196i) q^{2} +(-0.496278 + 1.52739i) q^{3} +(-1.38603 + 4.26575i) q^{4} +(2.00572 + 10.9990i) q^{5} +(-0.930402 - 2.86348i) q^{6} -5.91678 q^{7} +(-7.23313 - 22.2613i) q^{8} +(19.7568 + 14.3542i) q^{9} +O(q^{10})\)	\(q+(-1.51671 + 1.10196i) q^{2} +(-0.496278 + 1.52739i) q^{3} +(-1.38603 + 4.26575i) q^{4} +(2.00572 + 10.9990i) q^{5} +(-0.930402 - 2.86348i) q^{6} -5.91678 q^{7} +(-7.23313 - 22.2613i) q^{8} +(19.7568 + 14.3542i) q^{9} +(-15.1625 - 14.4720i) q^{10} +(46.2426 - 33.5972i) q^{11} +(-5.82760 - 4.23400i) q^{12} +(-23.8943 - 17.3602i) q^{13} +(8.97406 - 6.52004i) q^{14} +(-17.7951 - 2.39503i) q^{15} +(6.47220 + 4.70233i) q^{16} +(16.1964 + 49.8475i) q^{17} -45.7831 q^{18} +(28.8671 + 88.8439i) q^{19} +(-49.6988 - 6.68896i) q^{20} +(2.93637 - 9.03722i) q^{21} +(-33.1141 + 101.915i) q^{22} +(101.186 - 73.5160i) q^{23} +37.5912 q^{24} +(-116.954 + 44.1216i) q^{25} +55.3710 q^{26} +(-66.8097 + 48.5401i) q^{27} +(8.20082 - 25.2395i) q^{28} +(42.2327 - 129.979i) q^{29} +(29.6292 - 15.9768i) q^{30} +(-22.0658 - 67.9115i) q^{31} +172.257 q^{32} +(28.3668 + 87.3040i) q^{33} +(-79.4951 - 57.7566i) q^{34} +(-11.8674 - 65.0785i) q^{35} +(-88.6149 + 64.3825i) q^{36} +(-149.002 - 108.256i) q^{37} +(-141.685 - 102.940i) q^{38} +(38.3741 - 27.8804i) q^{39} +(230.343 - 124.207i) q^{40} +(-28.3279 - 20.5814i) q^{41} +(5.50499 + 16.9426i) q^{42} +185.374 q^{43} +(79.2239 + 243.826i) q^{44} +(-118.254 + 246.095i) q^{45} +(-72.4588 + 223.005i) q^{46} +(130.295 - 401.007i) q^{47} +(-10.3943 + 7.55189i) q^{48} -307.992 q^{49} +(128.766 - 195.798i) q^{50} -84.1744 q^{51} +(107.173 - 77.8655i) q^{52} +(-214.260 + 659.426i) q^{53} +(47.8420 - 147.243i) q^{54} +(462.284 + 441.234i) q^{55} +(42.7968 + 131.715i) q^{56} -150.025 q^{57} +(79.1762 + 243.679i) q^{58} +(-466.375 - 338.841i) q^{59} +(34.8811 - 72.5897i) q^{60} +(29.5121 - 21.4418i) q^{61} +(108.303 + 78.6867i) q^{62} +(-116.897 - 84.9306i) q^{63} +(-313.042 + 227.438i) q^{64} +(143.019 - 297.633i) q^{65} +(-139.229 - 101.156i) q^{66} +(-48.1248 - 148.113i) q^{67} -235.086 q^{68} +(62.0710 + 191.035i) q^{69} +(89.7130 + 85.6279i) q^{70} +(120.884 - 372.044i) q^{71} +(176.639 - 543.638i) q^{72} +(946.113 - 687.392i) q^{73} +345.287 q^{74} +(-9.34899 - 200.531i) q^{75} -418.997 q^{76} +(-273.608 + 198.788i) q^{77} +(-27.4794 + 84.5730i) q^{78} +(323.388 - 995.287i) q^{79} +(-38.7393 + 80.6190i) q^{80} +(162.771 + 500.956i) q^{81} +65.6451 q^{82} +(289.936 + 892.333i) q^{83} +(34.4806 + 25.0517i) q^{84} +(-515.785 + 278.124i) q^{85} +(-281.159 + 204.274i) q^{86} +(177.569 + 129.011i) q^{87} +(-1082.40 - 786.407i) q^{88} +(-378.143 + 274.737i) q^{89} +(-91.8280 - 503.567i) q^{90} +(141.378 + 102.717i) q^{91} +(173.354 + 533.530i) q^{92} +114.678 q^{93} +(244.272 + 751.791i) q^{94} +(-919.291 + 495.704i) q^{95} +(-85.4873 + 263.103i) q^{96} +(-529.272 + 1628.93i) q^{97} +(467.135 - 339.393i) q^{98} +1395.87 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9}+O(q^{10}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9} - 25 q^{10} - 89 q^{11} + 139 q^{12} + 33 q^{13} - 17 q^{14} + 225 q^{15} - 207 q^{16} - 191 q^{17} - 552 q^{18} - 115 q^{19} - 225 q^{20} - 144 q^{21} + 808 q^{22} + 433 q^{23} + 780 q^{24} + 90 q^{25} + 586 q^{26} + 35 q^{27} - 13 q^{28} - 5 q^{29} + 675 q^{30} - 639 q^{31} - 1386 q^{32} + 251 q^{33} - 777 q^{34} - 1030 q^{35} + 673 q^{36} + 699 q^{37} - 2355 q^{38} - 1133 q^{39} + 410 q^{40} + 341 q^{41} - 2407 q^{42} - 172 q^{43} + 548 q^{44} + 470 q^{45} - 1239 q^{46} + 2319 q^{47} + 4738 q^{48} + 1344 q^{49} + 2335 q^{50} + 2006 q^{51} + 2344 q^{52} - 927 q^{53} + 1615 q^{54} + 1225 q^{55} - 2910 q^{56} - 770 q^{57} + 2410 q^{58} - 1905 q^{59} - 12030 q^{60} + 1391 q^{61} - 3832 q^{62} - 6142 q^{63} - 3596 q^{64} + 1215 q^{65} + 3632 q^{66} - 3611 q^{67} + 3622 q^{68} + 2687 q^{69} + 560 q^{70} - 3719 q^{71} + 9025 q^{72} + 4593 q^{73} + 4848 q^{74} + 3815 q^{75} + 3520 q^{76} + 1368 q^{77} - 3679 q^{78} + 775 q^{79} + 9500 q^{80} - 3712 q^{81} - 6762 q^{82} - 2447 q^{83} - 7612 q^{84} - 8185 q^{85} + 3891 q^{86} - 85 q^{87} - 10960 q^{88} - 5075 q^{89} + 685 q^{90} + 376 q^{91} - 8456 q^{92} + 4366 q^{93} + 3573 q^{94} + 3265 q^{95} - 7754 q^{96} + 7439 q^{97} + 7082 q^{98} + 6572 q^{99}+O(q^{100}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9 - 25 * q^10 - 89 * q^11 + 139 * q^12 + 33 * q^13 - 17 * q^14 + 225 * q^15 - 207 * q^16 - 191 * q^17 - 552 * q^18 - 115 * q^19 - 225 * q^20 - 144 * q^21 + 808 * q^22 + 433 * q^23 + 780 * q^24 + 90 * q^25 + 586 * q^26 + 35 * q^27 - 13 * q^28 - 5 * q^29 + 675 * q^30 - 639 * q^31 - 1386 * q^32 + 251 * q^33 - 777 * q^34 - 1030 * q^35 + 673 * q^36 + 699 * q^37 - 2355 * q^38 - 1133 * q^39 + 410 * q^40 + 341 * q^41 - 2407 * q^42 - 172 * q^43 + 548 * q^44 + 470 * q^45 - 1239 * q^46 + 2319 * q^47 + 4738 * q^48 + 1344 * q^49 + 2335 * q^50 + 2006 * q^51 + 2344 * q^52 - 927 * q^53 + 1615 * q^54 + 1225 * q^55 - 2910 * q^56 - 770 * q^57 + 2410 * q^58 - 1905 * q^59 - 12030 * q^60 + 1391 * q^61 - 3832 * q^62 - 6142 * q^63 - 3596 * q^64 + 1215 * q^65 + 3632 * q^66 - 3611 * q^67 + 3622 * q^68 + 2687 * q^69 + 560 * q^70 - 3719 * q^71 + 9025 * q^72 + 4593 * q^73 + 4848 * q^74 + 3815 * q^75 + 3520 * q^76 + 1368 * q^77 - 3679 * q^78 + 775 * q^79 + 9500 * q^80 - 3712 * q^81 - 6762 * q^82 - 2447 * q^83 - 7612 * q^84 - 8185 * q^85 + 3891 * q^86 - 85 * q^87 - 10960 * q^88 - 5075 * q^89 + 685 * q^90 + 376 * q^91 - 8456 * q^92 + 4366 * q^93 + 3573 * q^94 + 3265 * q^95 - 7754 * q^96 + 7439 * q^97 + 7082 * q^98 + 6572 * q^99

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