LMFDB - Embedded newform 322.2.e.b.277.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(93,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("322.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.e (of order $3$, degree $2$, 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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1767277521.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 $ x^8 - 2x^7 + x^6 - 10x^5 + 38x^4 - 40x^3 + 64x^2 - 38x + 7
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.4
Root			$-1.54162 - 1.88572i$ of defining polynomial
Character	$\chi$	$=$	322.277
Dual form			322.2.e.b.93.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.60400 - 2.77821i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.79990 + 3.11751i) q^{5} -3.20800 q^{6} +(1.82854 + 1.91218i) q^{7} +1.00000 q^{8} +(-3.64562 - 6.31440i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.60400 - 2.77821i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.79990 + 3.11751i) q^{5} -3.20800 q^{6} +(1.82854 + 1.91218i) q^{7} +1.00000 q^{8} +(-3.64562 - 6.31440i) q^{9} +(1.79990 - 3.11751i) q^{10} +(2.04162 - 3.53619i) q^{11} +(1.60400 + 2.77821i) q^{12} +0.932540 q^{13} +(0.741726 - 2.53965i) q^{14} +11.5481 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.17514 + 5.49951i) q^{17} +(-3.64562 + 6.31440i) q^{18} +(-2.00789 - 3.47777i) q^{19} -3.59979 q^{20} +(8.24541 - 2.01293i) q^{21} -4.08324 q^{22} +(-0.500000 - 0.866025i) q^{23} +(1.60400 - 2.77821i) q^{24} +(-3.97924 + 6.89225i) q^{25} +(-0.466270 - 0.807603i) q^{26} -13.7663 q^{27} +(-2.57027 + 0.627473i) q^{28} -5.14054 q^{29} +(-5.77406 - 10.0010i) q^{30} +(-0.766165 + 1.32704i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-6.54951 - 11.3441i) q^{33} +6.35028 q^{34} +(-2.67006 + 9.14222i) q^{35} +7.29124 q^{36} +(-0.528647 - 0.915643i) q^{37} +(-2.00789 + 3.47777i) q^{38} +(1.49579 - 2.59079i) q^{39} +(1.79990 + 3.11751i) q^{40} -2.51655 q^{41} +(-5.86595 - 6.13427i) q^{42} +0.532330 q^{43} +(2.04162 + 3.53619i) q^{44} +(13.1235 - 22.7305i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(3.63352 + 6.29344i) q^{47} -3.20800 q^{48} +(-0.312869 + 6.99300i) q^{49} +7.95849 q^{50} +(10.1858 + 17.6424i) q^{51} +(-0.466270 + 0.807603i) q^{52} +(-0.212204 + 0.367548i) q^{53} +(6.88314 + 11.9219i) q^{54} +14.6988 q^{55} +(1.82854 + 1.91218i) q^{56} -12.8826 q^{57} +(2.57027 + 4.45183i) q^{58} +(0.384537 - 0.666038i) q^{59} +(-5.77406 + 10.0010i) q^{60} +(-5.86659 - 10.1612i) q^{61} +1.53233 q^{62} +(5.40810 - 18.5172i) q^{63} +1.00000 q^{64} +(1.67847 + 2.90720i) q^{65} +(-6.54951 + 11.3441i) q^{66} +(2.37945 - 4.12134i) q^{67} +(-3.17514 - 5.49951i) q^{68} -3.20800 q^{69} +(9.25242 - 2.25877i) q^{70} -5.83072 q^{71} +(-3.64562 - 6.31440i) q^{72} +(5.69870 - 9.87045i) q^{73} +(-0.528647 + 0.915643i) q^{74} +(12.7654 + 22.1103i) q^{75} +4.01578 q^{76} +(10.4950 - 2.56213i) q^{77} -2.99158 q^{78} +(1.78335 + 3.08885i) q^{79} +(1.79990 - 3.11751i) q^{80} +(-11.1442 + 19.3024i) q^{81} +(1.25827 + 2.17939i) q^{82} -12.4547 q^{83} +(-2.37945 + 8.14720i) q^{84} -22.8597 q^{85} +(-0.266165 - 0.461011i) q^{86} +(-8.24541 + 14.2815i) q^{87} +(2.04162 - 3.53619i) q^{88} +(5.49134 + 9.51129i) q^{89} -26.2469 q^{90} +(1.70519 + 1.78318i) q^{91} +1.00000 q^{92} +(2.45785 + 4.25713i) q^{93} +(3.63352 - 6.29344i) q^{94} +(7.22799 - 12.5192i) q^{95} +(1.60400 + 2.77821i) q^{96} +16.4419 q^{97} +(6.21255 - 3.22555i) q^{98} -29.7719 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 5 q^{3} - 4 q^{4} + 5 q^{5} - 10 q^{6} + q^{7} + 8 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 + 5 * q^5 - 10 * q^6 + q^7 + 8 * q^8 - 7 * q^9	\( 8 q - 4 q^{2} + 5 q^{3} - 4 q^{4} + 5 q^{5} - 10 q^{6} + q^{7} + 8 q^{8} - 7 q^{9} + 5 q^{10} + 2 q^{11} + 5 q^{12} - 14 q^{13} + q^{14} + 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{18} + 9 q^{19} - 10 q^{20} + 25 q^{21} - 4 q^{22} - 4 q^{23} + 5 q^{24} - 11 q^{25} + 7 q^{26} - 34 q^{27} - 2 q^{28} - 4 q^{29} - q^{30} + 14 q^{31} - 4 q^{32} - 13 q^{33} + 6 q^{34} + 16 q^{35} + 14 q^{36} + 9 q^{38} + q^{39} + 5 q^{40} - 30 q^{41} - 8 q^{42} - 36 q^{43} + 2 q^{44} + 11 q^{45} - 4 q^{46} + 21 q^{47} - 10 q^{48} + 17 q^{49} + 22 q^{50} - 6 q^{51} + 7 q^{52} + 3 q^{53} + 17 q^{54} + 20 q^{55} + q^{56} - 18 q^{57} + 2 q^{58} + 16 q^{59} - q^{60} + q^{61} - 28 q^{62} + 37 q^{63} + 8 q^{64} - 2 q^{65} - 13 q^{66} + 17 q^{67} - 3 q^{68} - 10 q^{69} + 4 q^{70} - 2 q^{71} - 7 q^{72} + 4 q^{73} + 22 q^{75} - 18 q^{76} + 13 q^{77} - 2 q^{78} - 5 q^{79} + 5 q^{80} - 16 q^{81} + 15 q^{82} - 8 q^{83} - 17 q^{84} - 108 q^{85} + 18 q^{86} - 25 q^{87} + 2 q^{88} + 9 q^{89} - 22 q^{90} + 38 q^{91} + 8 q^{92} - 13 q^{93} + 21 q^{94} + 3 q^{95} + 5 q^{96} + 80 q^{97} + 2 q^{98} - 82 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 + 5 * q^5 - 10 * q^6 + q^7 + 8 * q^8 - 7 * q^9 + 5 * q^10 + 2 * q^11 + 5 * q^12 - 14 * q^13 + q^14 + 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^18 + 9 * q^19 - 10 * q^20 + 25 * q^21 - 4 * q^22 - 4 * q^23 + 5 * q^24 - 11 * q^25 + 7 * q^26 - 34 * q^27 - 2 * q^28 - 4 * q^29 - q^30 + 14 * q^31 - 4 * q^32 - 13 * q^33 + 6 * q^34 + 16 * q^35 + 14 * q^36 + 9 * q^38 + q^39 + 5 * q^40 - 30 * q^41 - 8 * q^42 - 36 * q^43 + 2 * q^44 + 11 * q^45 - 4 * q^46 + 21 * q^47 - 10 * q^48 + 17 * q^49 + 22 * q^50 - 6 * q^51 + 7 * q^52 + 3 * q^53 + 17 * q^54 + 20 * q^55 + q^56 - 18 * q^57 + 2 * q^58 + 16 * q^59 - q^60 + q^61 - 28 * q^62 + 37 * q^63 + 8 * q^64 - 2 * q^65 - 13 * q^66 + 17 * q^67 - 3 * q^68 - 10 * q^69 + 4 * q^70 - 2 * q^71 - 7 * q^72 + 4 * q^73 + 22 * q^75 - 18 * q^76 + 13 * q^77 - 2 * q^78 - 5 * q^79 + 5 * q^80 - 16 * q^81 + 15 * q^82 - 8 * q^83 - 17 * q^84 - 108 * q^85 + 18 * q^86 - 25 * q^87 + 2 * q^88 + 9 * q^89 - 22 * q^90 + 38 * q^91 + 8 * q^92 - 13 * q^93 + 21 * q^94 + 3 * q^95 + 5 * q^96 + 80 * q^97 + 2 * q^98 - 82 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.60400	−	2.77821i	0.926069	−	1.60400i	0.136235	−	0.990677i	$-0.456500\pi$
$3$	1.60400	−	2.77821i	0.926069	−	1.60400i	0.789833	−	0.613321i	$-0.210167\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.79990	+	3.11751i	0.804938	+	1.39419i	0.916333	+	0.400417i	$0.131135\pi$
$5$	1.79990	+	3.11751i	0.804938	+	1.39419i	−0.111396	+	0.993776i	$0.535532\pi$
$6$	−3.20800			−1.30966
$7$	1.82854	+	1.91218i	0.691124	+	0.722736i
$7$	1.82854	+	1.91218i	0.691124	+	0.722736i
$8$	1.00000			0.353553
$9$	−3.64562	−	6.31440i	−1.21521	−	2.10480i
$10$	1.79990	−	3.11751i	0.569177	−	0.985843i
$11$	2.04162	−	3.53619i	0.615572	−	1.06620i	−0.374712	−	0.927141i	$-0.622258\pi$
$11$	2.04162	−	3.53619i	0.615572	−	1.06620i	0.990284	−	0.139061i	$-0.0444083\pi$
$12$	1.60400	+	2.77821i	0.463034	+	0.801999i
$13$	0.932540			0.258640			0.129320	−	0.991603i	$-0.458721\pi$
$13$	0.932540			0.258640			0.129320	+	0.991603i	$0.458721\pi$
$14$	0.741726	−	2.53965i	0.198235	−	0.678751i
$15$	11.5481			2.98171
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.17514	+	5.49951i	−0.770085	+	1.33383i	0.167431	+	0.985884i	$0.446453\pi$
$17$	−3.17514	+	5.49951i	−0.770085	+	1.33383i	−0.937516	+	0.347942i	$0.886881\pi$
$18$	−3.64562	+	6.31440i	−0.859281	+	1.48832i
$19$	−2.00789	−	3.47777i	−0.460642	−	0.797855i	0.538351	−	0.842721i	$-0.319047\pi$
$19$	−2.00789	−	3.47777i	−0.460642	−	0.797855i	−0.998993	+	0.0448656i	$0.985714\pi$
$20$	−3.59979			−0.804938
$21$	8.24541	−	2.01293i	1.79930	−	0.439258i
$22$	−4.08324			−0.870550
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	1.60400	−	2.77821i	0.327415	−	0.567099i
$25$	−3.97924	+	6.89225i	−0.795849	+	1.37845i
$26$	−0.466270	−	0.807603i	−0.0914431	−	0.158384i
$27$	−13.7663			−2.64932
$28$	−2.57027	+	0.627473i	−0.485735	+	0.118581i
$29$	−5.14054			−0.954574			−0.477287	−	0.878748i	$-0.658380\pi$
$29$	−5.14054			−0.954574			−0.477287	+	0.878748i	$0.658380\pi$
$30$	−5.77406	−	10.0010i	−1.05419	−	1.82592i
$31$	−0.766165	+	1.32704i	−0.137607	+	0.238343i	−0.926590	−	0.376072i	$-0.877275\pi$
$31$	−0.766165	+	1.32704i	−0.137607	+	0.238343i	0.788983	+	0.614415i	$0.210608\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−6.54951	−	11.3441i	−1.14012	−	1.97475i
$34$	6.35028			1.08906
$35$	−2.67006	+	9.14222i	−0.451322	+	1.54532i
$36$	7.29124			1.21521
$37$	−0.528647	−	0.915643i	−0.0869090	−	0.150531i	0.819294	−	0.573374i	$-0.194366\pi$
$37$	−0.528647	−	0.915643i	−0.0869090	−	0.150531i	−0.906203	+	0.422843i	$0.861032\pi$
$38$	−2.00789	+	3.47777i	−0.325723	+	0.564169i
$39$	1.49579	−	2.59079i	0.239518	−	0.414858i
$40$	1.79990	+	3.11751i	0.284588	+	0.492922i
$41$	−2.51655			−0.393019			−0.196509	−	0.980502i	$-0.562961\pi$
$41$	−2.51655			−0.393019			−0.196509	+	0.980502i	$0.562961\pi$
$42$	−5.86595	−	6.13427i	−0.905137	−	0.946538i
$43$	0.532330			0.0811795			0.0405898	−	0.999176i	$-0.487076\pi$
$43$	0.532330			0.0811795			0.0405898	+	0.999176i	$0.487076\pi$
$44$	2.04162	+	3.53619i	0.307786	+	0.533101i
$45$	13.1235	−	22.7305i	1.95633	−	3.38846i
$46$	−0.500000	+	0.866025i	−0.0737210	+	0.127688i
$47$	3.63352	+	6.29344i	0.530003	+	0.917993i	0.999387	+	0.0349986i	$0.0111427\pi$
$47$	3.63352	+	6.29344i	0.530003	+	0.917993i	−0.469384	+	0.882994i	$0.655524\pi$
$48$	−3.20800			−0.463034
$49$	−0.312869	+	6.99300i	−0.0446956	+	0.999001i
$50$	7.95849			1.12550
$51$	10.1858	+	17.6424i	1.42630	+	2.47043i
$52$	−0.466270	+	0.807603i	−0.0646600	+	0.111994i
$53$	−0.212204	+	0.367548i	−0.0291484	+	0.0504866i	−0.880232	−	0.474544i	$-0.842613\pi$
$53$	−0.212204	+	0.367548i	−0.0291484	+	0.0504866i	0.851083	+	0.525031i	$0.175946\pi$
$54$	6.88314	+	11.9219i	0.936676	+	1.62237i
$55$	14.6988			1.98199
$56$	1.82854	+	1.91218i	0.244349	+	0.255526i
$57$	−12.8826			−1.70634
$58$	2.57027	+	4.45183i	0.337493	+	0.584555i
$59$	0.384537	−	0.666038i	0.0500625	−	0.0867108i	−0.839908	−	0.542728i	$-0.817391\pi$
$59$	0.384537	−	0.666038i	0.0500625	−	0.0867108i	0.889971	+	0.456018i	$0.150725\pi$
$60$	−5.77406	+	10.0010i	−0.745427	+	1.29112i
$61$	−5.86659	−	10.1612i	−0.751140	−	1.30101i	−0.947271	−	0.320435i	$-0.896171\pi$
$61$	−5.86659	−	10.1612i	−0.751140	−	1.30101i	0.196131	−	0.980578i	$-0.437162\pi$
$62$	1.53233			0.194606
$63$	5.40810	−	18.5172i	0.681357	−	2.33295i
$64$	1.00000			0.125000
$65$	1.67847	+	2.90720i	0.208189	+	0.360594i
$66$	−6.54951	+	11.3441i	−0.806189	+	1.39636i
$67$	2.37945	−	4.12134i	0.290697	−	0.503501i	−0.683278	−	0.730158i	$-0.739446\pi$
$67$	2.37945	−	4.12134i	0.290697	−	0.503501i	0.973975	+	0.226657i	$0.0727796\pi$
$68$	−3.17514	−	5.49951i	−0.385042	−	0.666913i
$69$	−3.20800			−0.386197
$70$	9.25242	−	2.25877i	1.10588	−	0.269975i
$71$	−5.83072			−0.691979			−0.345989	−	0.938238i	$-0.612457\pi$
$71$	−5.83072			−0.691979			−0.345989	+	0.938238i	$0.612457\pi$
$72$	−3.64562	−	6.31440i	−0.429640	−	0.744159i
$73$	5.69870	−	9.87045i	0.666983	−	1.15525i	−0.311761	−	0.950161i	$-0.600919\pi$
$73$	5.69870	−	9.87045i	0.666983	−	1.15525i	0.978744	−	0.205088i	$-0.0657480\pi$
$74$	−0.528647	+	0.915643i	−0.0614540	+	0.106441i
$75$	12.7654	+	22.1103i	1.47402	+	2.55308i
$76$	4.01578			0.460642
$77$	10.4950	−	2.56213i	1.19602	−	0.291981i
$78$	−2.99158			−0.338730
$79$	1.78335	+	3.08885i	0.200642	+	0.347523i	0.948736	−	0.316071i	$-0.102364\pi$
$79$	1.78335	+	3.08885i	0.200642	+	0.347523i	−0.748093	+	0.663594i	$0.769030\pi$
$80$	1.79990	−	3.11751i	0.201234	−	0.348548i
$81$	−11.1442	+	19.3024i	−1.23825	+	2.14471i
$82$	1.25827	+	2.17939i	0.138953	+	0.240674i
$83$	−12.4547			−1.36708			−0.683541	−	0.729912i	$-0.739561\pi$
$83$	−12.4547			−1.36708			−0.683541	+	0.729912i	$0.739561\pi$
$84$	−2.37945	+	8.14720i	−0.259620	+	0.888932i
$85$	−22.8597			−2.47948
$86$	−0.266165	−	0.461011i	−0.0287013	−	0.0497121i
$87$	−8.24541	+	14.2815i	−0.884001	+	1.53113i
$88$	2.04162	−	3.53619i	0.217638	−	0.376959i
$89$	5.49134	+	9.51129i	0.582081	+	1.00819i	0.995232	+	0.0975318i	$0.0310948\pi$
$89$	5.49134	+	9.51129i	0.582081	+	1.00819i	−0.413151	+	0.910662i	$0.635572\pi$
$90$	−26.2469			−2.76667
$91$	1.70519	+	1.78318i	0.178752	+	0.186929i
$92$	1.00000			0.104257
$93$	2.45785	+	4.25713i	0.254868	+	0.441444i
$94$	3.63352	−	6.29344i	0.374769	−	0.649119i
$95$	7.22799	−	12.5192i	0.741576	−	1.28445i
$96$	1.60400	+	2.77821i	0.163707	+	0.283549i
$97$	16.4419			1.66943			0.834713	−	0.550685i	$-0.185633\pi$
$97$	16.4419			1.66943			0.834713	+	0.550685i	$0.185633\pi$
$98$	6.21255	−	3.22555i	0.627563	−	0.325830i
$99$	−29.7719			−2.99219
$100$	−3.97924	−	6.89225i	−0.397924	−	0.689225i
$101$	−8.55232	+	14.8131i	−0.850988	+	1.47395i	0.0293304	+	0.999570i	$0.490663\pi$
$101$	−8.55232	+	14.8131i	−0.850988	+	1.47395i	−0.880318	+	0.474384i	$0.842671\pi$
$102$	10.1858	−	17.6424i	1.00855	−	1.74686i
$103$	6.74962	+	11.6907i	0.665060	+	1.15192i	0.979269	+	0.202563i	$0.0649272\pi$
$103$	6.74962	+	11.6907i	0.665060	+	1.15192i	−0.314210	+	0.949354i	$0.601739\pi$
$104$	0.932540			0.0914431
$105$	21.1162	+	22.0821i	2.06073	+	2.15499i
$106$	0.424408			0.0412221
$107$	−3.51297	−	6.08465i	−0.339612	−	0.588225i	0.644748	−	0.764395i	$-0.276962\pi$
$107$	−3.51297	−	6.08465i	−0.339612	−	0.588225i	−0.984360	+	0.176170i	$0.943629\pi$
$108$	6.88314	−	11.9219i	0.662330	−	1.14719i
$109$	6.36508	−	11.0246i	0.609664	−	1.05597i	−0.381632	−	0.924315i	$-0.624638\pi$
$109$	6.36508	−	11.0246i	0.609664	−	1.05597i	0.991296	−	0.131655i	$-0.0420290\pi$
$110$	−7.34941	−	12.7295i	−0.700738	−	1.21371i
$111$	−3.39179			−0.321935
$112$	0.741726	−	2.53965i	0.0700865	−	0.239975i
$113$	−6.27371			−0.590181			−0.295090	−	0.955469i	$-0.595350\pi$
$113$	−6.27371			−0.590181			−0.295090	+	0.955469i	$0.595350\pi$
$114$	6.44131	+	11.1567i	0.603284	+	1.04492i
$115$	1.79990	−	3.11751i	0.167841	−	0.290709i
$116$	2.57027	−	4.45183i	0.238643	−	0.413342i
$117$	−3.39969	−	5.88843i	−0.314301	−	0.544385i
$118$	−0.769075			−0.0707990
$119$	−16.3219	+	3.98463i	−1.49623	+	0.365271i
$120$	11.5481			1.05419
$121$	−2.83643	−	4.91285i	−0.257858	−	0.446622i
$122$	−5.86659	+	10.1612i	−0.531136	+	0.919955i
$123$	−4.03654	+	6.99149i	−0.363962	+	0.630401i
$124$	−0.766165	−	1.32704i	−0.0688036	−	0.119171i
$125$	−10.6499			−0.952559
$126$	−18.7404	+	4.57506i	−1.66953	+	0.407579i
$127$	6.97602			0.619022			0.309511	−	0.950896i	$-0.399835\pi$
$127$	6.97602			0.619022			0.309511	+	0.950896i	$0.399835\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	0.853856	−	1.47892i	0.0751778	−	0.130212i
$130$	1.67847	−	2.90720i	0.147212	−	0.254978i
$131$	4.21220	+	7.29575i	0.368022	+	0.637433i	0.989256	−	0.146192i	$-0.0467018\pi$
$131$	4.21220	+	7.29575i	0.368022	+	0.637433i	−0.621234	+	0.783625i	$0.713368\pi$
$132$	13.0990			1.14012
$133$	2.97861	−	10.1987i	0.258278	−	0.884339i
$134$	−4.75891			−0.411107
$135$	−24.7778	−	42.9165i	−2.13254	−	3.69366i
$136$	−3.17514	+	5.49951i	−0.272266	+	0.471579i
$137$	−5.39611	+	9.34634i	−0.461021	+	0.798512i	−0.999012	−	0.0444388i	$-0.985850\pi$
$137$	−5.39611	+	9.34634i	−0.461021	+	0.798512i	0.537991	+	0.842950i	$0.319183\pi$
$138$	1.60400	+	2.77821i	0.136541	+	0.236497i
$139$	−7.85793			−0.666501			−0.333251	−	0.942838i	$-0.608145\pi$
$139$	−7.85793			−0.666501			−0.333251	+	0.942838i	$0.608145\pi$
$140$	−6.58237	−	6.88345i	−0.556312	−	0.581758i
$141$	23.3126			1.96328
$142$	2.91536	+	5.04955i	0.244651	+	0.423749i
$143$	1.90389	−	3.29764i	0.159212	−	0.275762i
$144$	−3.64562	+	6.31440i	−0.303802	+	0.526200i
$145$	−9.25242	−	16.0257i	−0.768372	−	1.33086i
$146$	−11.3974			−0.943256
$147$	18.9262	+	12.0860i	1.56100	+	0.996835i
$148$	1.05729			0.0869090
$149$	5.23394	+	9.06546i	0.428781	+	0.742671i	0.996765	−	0.0803685i	$-0.0256097\pi$
$149$	5.23394	+	9.06546i	0.428781	+	0.742671i	−0.567984	+	0.823040i	$0.692276\pi$
$150$	12.7654	−	22.1103i	1.04229	−	1.80530i
$151$	−2.61634	+	4.53163i	−0.212915	+	0.368779i	−0.952625	−	0.304146i	$-0.901629\pi$
$151$	−2.61634	+	4.53163i	−0.212915	+	0.368779i	0.739711	+	0.672925i	$0.234962\pi$
$152$	−2.00789	−	3.47777i	−0.162861	−	0.282084i
$153$	46.3014			3.74325
$154$	−7.46638	−	7.80790i	−0.601658	−	0.629178i
$155$	−5.51607			−0.443061
$156$	1.49579	+	2.59079i	0.119759	+	0.207429i
$157$	9.84432	−	17.0509i	0.785663	−	1.36081i	−0.142940	−	0.989731i	$-0.545656\pi$
$157$	9.84432	−	17.0509i	0.785663	−	1.36081i	0.928602	−	0.371076i	$-0.121011\pi$
$158$	1.78335	−	3.08885i	0.141875	−	0.245736i
$159$	0.680749	+	1.17909i	0.0539869	+	0.0935081i
$160$	−3.59979			−0.284588
$161$	0.741726	−	2.53965i	0.0584562	−	0.200153i
$162$	22.2884			1.75115
$163$	−7.48650	−	12.9670i	−0.586388	−	1.01565i	−0.994701	−	0.102812i	$-0.967216\pi$
$163$	−7.48650	−	12.9670i	−0.586388	−	1.01565i	0.408313	−	0.912842i	$-0.366117\pi$
$164$	1.25827	−	2.17939i	0.0982547	−	0.170182i
$165$	23.5769	−	40.8363i	1.83546	−	3.17910i
$166$	6.22735	+	10.7861i	0.483336	+	0.837163i
$167$	5.08149			0.393218			0.196609	−	0.980482i	$-0.437007\pi$
$167$	5.08149			0.393218			0.196609	+	0.980482i	$0.437007\pi$
$168$	8.24541	−	2.01293i	0.636147	−	0.155301i
$169$	−12.1304			−0.933105
$170$	11.4298	+	19.7971i	0.876629	+	1.51837i
$171$	−14.6400	+	25.3572i	−1.11955	+	1.93912i
$172$	−0.266165	+	0.461011i	−0.0202949	+	0.0351518i
$173$	6.01245	+	10.4139i	0.457118	+	0.791752i	0.998807	−	0.0488272i	$-0.0155484\pi$
$173$	6.01245	+	10.4139i	0.457118	+	0.791752i	−0.541689	+	0.840579i	$0.682215\pi$
$174$	16.4908			1.25017
$175$	−20.4554	+	4.99374i	−1.54629	+	0.377491i
$176$	−4.08324			−0.307786
$177$	−1.23359	−	2.13665i	−0.0927226	−	0.160600i
$178$	5.49134	−	9.51129i	0.411594	−	0.712901i
$179$	3.99492	−	6.91940i	0.298594	−	0.517180i	−0.677220	−	0.735780i	$-0.736816\pi$
$179$	3.99492	−	6.91940i	0.298594	−	0.517180i	0.975815	+	0.218600i	$0.0701490\pi$
$180$	13.1235	+	22.7305i	0.978165	+	1.69423i
$181$	0.525446			0.0390561			0.0195280	−	0.999809i	$-0.493784\pi$
$181$	0.525446			0.0390561			0.0195280	+	0.999809i	$0.493784\pi$
$182$	0.691689	−	2.36833i	0.0512714	−	0.175552i
$183$	−37.6400			−2.78243
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$	1.90302	−	3.29612i	0.139913	−	0.242336i
$186$	2.45785	−	4.25713i	0.180219	−	0.312148i
$187$	12.9649	+	22.4558i	0.948085	+	1.64213i
$188$	−7.26704			−0.530003
$189$	−25.1722	−	26.3236i	−1.83101	−	1.91476i
$190$	−14.4560			−1.04875
$191$	2.46778	+	4.27432i	0.178562	+	0.309279i	0.941388	−	0.337325i	$-0.109522\pi$
$191$	2.46778	+	4.27432i	0.178562	+	0.309279i	−0.762826	+	0.646604i	$0.776189\pi$
$192$	1.60400	−	2.77821i	0.115759	−	0.200500i
$193$	4.36238	−	7.55587i	0.314011	−	0.543883i	−0.665216	−	0.746651i	$-0.731660\pi$
$193$	4.36238	−	7.55587i	0.314011	−	0.543883i	0.979227	+	0.202768i	$0.0649938\pi$
$194$	−8.22097	−	14.2391i	−0.590231	−	1.02231i
$195$	10.7691			0.771189
$196$	−5.89969	−	3.76745i	−0.421406	−	0.269104i
$197$	−14.2413			−1.01465			−0.507326	−	0.861754i	$-0.669366\pi$
$197$	−14.2413			−1.01465			−0.507326	+	0.861754i	$0.669366\pi$
$198$	14.8859	+	25.7832i	1.05790	+	1.83233i
$199$	6.86000	−	11.8819i	0.486292	−	0.842283i	−0.513584	−	0.858040i	$-0.671682\pi$
$199$	6.86000	−	11.8819i	0.486292	−	0.842283i	0.999876	+	0.0157567i	$0.00501571\pi$
$200$	−3.97924	+	6.89225i	−0.281375	+	0.487356i
$201$	−7.63328	−	13.2212i	−0.538410	−	0.932553i
$202$	17.1046			1.20348
$203$	−9.39969	−	9.82963i	−0.659729	−	0.689905i
$204$	−20.3717			−1.42630
$205$	−4.52952	−	7.84536i	−0.316356	−	0.547944i
$206$	6.74962	−	11.6907i	0.470268	−	0.814528i
$207$	−3.64562	+	6.31440i	−0.253388	+	0.438881i
$208$	−0.466270	−	0.807603i	−0.0323300	−	0.0559972i
$209$	−16.3974			−1.13423
$210$	8.56553	−	29.3282i	0.591078	−	2.02384i
$211$	1.96410			0.135214			0.0676072	−	0.997712i	$-0.478464\pi$
$211$	1.96410			0.135214			0.0676072	+	0.997712i	$0.478464\pi$
$212$	−0.212204	−	0.367548i	−0.0145742	−	0.0252433i
$213$	−9.35246	+	16.1989i	−0.640820	+	1.10993i
$214$	−3.51297	+	6.08465i	−0.240142	+	0.415938i
$215$	0.958138	+	1.65954i	0.0653445	+	0.113180i
$216$	−13.7663			−0.936676
$217$	−3.93850	+	0.961496i	−0.267363	+	0.0652706i
$218$	−12.7302			−0.862195
$219$	−18.2814	−	31.6644i	−1.23534	−	2.13968i
$220$	−7.34941	+	12.7295i	−0.495497	+	0.858226i
$221$	−2.96095	+	5.12851i	−0.199175	+	0.344981i
$222$	1.69590	+	2.93738i	0.113821	+	0.197144i
$223$	7.00667			0.469201			0.234601	−	0.972092i	$-0.424622\pi$
$223$	7.00667			0.469201			0.234601	+	0.972092i	$0.424622\pi$
$224$	−2.57027	+	0.627473i	−0.171733	+	0.0419248i
$225$	58.0272			3.86848
$226$	3.13685	+	5.43319i	0.208660	+	0.361410i
$227$	12.5699	−	21.7716i	0.834290	−	1.44503i	−0.0603165	−	0.998179i	$-0.519211\pi$
$227$	12.5699	−	21.7716i	0.834290	−	1.44503i	0.894607	−	0.446854i	$-0.147456\pi$
$228$	6.44131	−	11.1567i	0.426586	−	0.738868i
$229$	7.92118	+	13.7199i	0.523447	+	0.906636i	0.999628	+	0.0272888i	$0.00868737\pi$
$229$	7.92118	+	13.7199i	0.523447	+	0.906636i	−0.476181	+	0.879347i	$0.657979\pi$
$230$	−3.59979			−0.237363
$231$	9.71589	−	33.2670i	0.639258	−	2.18881i
$232$	−5.14054			−0.337493
$233$	−2.56249	−	4.43836i	−0.167874	−	0.290766i	0.769798	−	0.638287i	$-0.220357\pi$
$233$	−2.56249	−	4.43836i	−0.167874	−	0.290766i	−0.937672	+	0.347521i	$0.887024\pi$
$234$	−3.39969	+	5.88843i	−0.222244	+	0.384939i
$235$	−13.0799	+	22.6551i	−0.853239	+	1.47785i
$236$	0.384537	+	0.666038i	0.0250312	+	0.0433554i
$237$	11.4419			0.743234
$238$	11.6118	+	12.1429i	0.752678	+	0.787106i
$239$	−13.2069			−0.854286			−0.427143	−	0.904184i	$-0.640480\pi$
$239$	−13.2069			−0.854286			−0.427143	+	0.904184i	$0.640480\pi$
$240$	−5.77406	−	10.0010i	−0.372714	−	0.645559i
$241$	−13.8311	+	23.9562i	−0.890940	+	1.54315i	−0.0521897	+	0.998637i	$0.516620\pi$
$241$	−13.8311	+	23.9562i	−0.890940	+	1.54315i	−0.838750	+	0.544516i	$0.816713\pi$
$242$	−2.83643	+	4.91285i	−0.182333	+	0.315810i
$243$	15.1012	+	26.1560i	0.968742	+	1.67791i
$244$	11.7332			0.751140
$245$	−22.3639	+	11.6113i	−1.42878	+	0.741819i
$246$	8.07308			0.514721
$247$	−1.87244	−	3.24316i	−0.119140	−	0.206357i
$248$	−0.766165	+	1.32704i	−0.0486515	+	0.0842669i
$249$	−19.9773	+	34.6017i	−1.26601	+	2.19280i
$250$	5.32497	+	9.22312i	0.336781	+	0.583321i
$251$	13.8333			0.873147			0.436574	−	0.899669i	$-0.356192\pi$
$251$	13.8333			0.873147			0.436574	+	0.899669i	$0.356192\pi$
$252$	13.3323	+	13.9422i	0.839858	+	0.878274i
$253$	−4.08324			−0.256711
$254$	−3.48801	−	6.04141i	−0.218857	−	0.379072i
$255$	−36.6669	+	63.5089i	−2.29617	+	3.97708i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.0746	−	20.9138i	−0.753192	−	1.30457i	−0.946268	−	0.323383i	$-0.895180\pi$
$257$	−12.0746	−	20.9138i	−0.753192	−	1.30457i	0.193076	−	0.981184i	$-0.438154\pi$
$258$	−1.70771			−0.106318
$259$	0.784222	−	2.68516i	0.0487292	−	0.166848i
$260$	−3.35695			−0.208189
$261$	18.7404	+	32.4594i	1.16000	+	2.00919i
$262$	4.21220	−	7.29575i	0.260231	−	0.450733i
$263$	−14.1521	+	24.5122i	−0.872656	+	1.51149i	−0.0134181	+	0.999910i	$0.504271\pi$
$263$	−14.1521	+	24.5122i	−0.872656	+	1.51149i	−0.859238	+	0.511575i	$0.829062\pi$
$264$	−6.54951	−	11.3441i	−0.403095	−	0.698180i
$265$	−1.52778			−0.0938507
$266$	−10.3216	+	2.51980i	−0.632860	+	0.154499i
$267$	35.2324			2.15619
$268$	2.37945	+	4.12134i	0.145348	+	0.251751i
$269$	15.1139	−	26.1781i	0.921513	−	1.59611i	0.124437	−	0.992228i	$-0.460288\pi$
$269$	15.1139	−	26.1781i	0.921513	−	1.59611i	0.797076	−	0.603879i	$-0.206379\pi$
$270$	−24.7778	+	42.9165i	−1.50793	+	2.61181i
$271$	4.57665	+	7.92699i	0.278012	+	0.481530i	0.970891	−	0.239524i	$-0.0769913\pi$
$271$	4.57665	+	7.92699i	0.278012	+	0.481530i	−0.692879	+	0.721054i	$0.743658\pi$
$272$	6.35028			0.385042
$273$	7.68917	−	1.87714i	0.465370	−	0.113610i
$274$	10.7922			0.651982
$275$	16.2482	+	28.1427i	0.979804	+	1.69707i
$276$	1.60400	−	2.77821i	0.0965493	−	0.167228i
$277$	−9.42722	+	16.3284i	−0.566426	+	0.981079i	0.430489	+	0.902596i	$0.358341\pi$
$277$	−9.42722	+	16.3284i	−0.566426	+	0.981079i	−0.996915	+	0.0784836i	$0.974992\pi$
$278$	3.92897	+	6.80517i	0.235644	+	0.408147i
$279$	11.1726			0.668885
$280$	−2.67006	+	9.14222i	−0.159566	+	0.546352i
$281$	12.1176			0.722876			0.361438	−	0.932396i	$-0.382286\pi$
$281$	12.1176			0.722876			0.361438	+	0.932396i	$0.382286\pi$
$282$	−11.6563	−	20.1893i	−0.694124	−	1.20226i
$283$	6.60463	−	11.4396i	0.392605	−	0.680011i	−0.600188	−	0.799859i	$-0.704907\pi$
$283$	6.60463	−	11.4396i	0.392605	−	0.680011i	0.992792	+	0.119848i	$0.0382408\pi$
$284$	2.91536	−	5.04955i	0.172995	−	0.299636i
$285$	−23.1873	−	40.1617i	−1.37350	−	2.37897i
$286$	−3.80779			−0.225159
$287$	−4.60161	−	4.81209i	−0.271625	−	0.284049i
$288$	7.29124			0.429640
$289$	−11.6630	−	20.2010i	−0.686061	−	1.18829i
$290$	−9.25242	+	16.0257i	−0.543321	+	0.941060i
$291$	26.3728	−	45.6791i	1.54600	−	2.67776i
$292$	5.69870	+	9.87045i	0.333491	+	0.577624i
$293$	14.8724			0.868858			0.434429	−	0.900706i	$-0.356950\pi$
$293$	14.8724			0.868858			0.434429	+	0.900706i	$0.356950\pi$
$294$	1.00368	−	22.4335i	0.0585360	−	1.30835i
$295$	2.76851			0.161189
$296$	−0.528647	−	0.915643i	−0.0307270	−	0.0532207i
$297$	−28.1055	+	48.6802i	−1.63085	+	2.82471i
$298$	5.23394	−	9.06546i	0.303194	−	0.525148i
$299$	−0.466270	−	0.807603i	−0.0269651	−	0.0467049i
$300$	−25.5308			−1.47402
$301$	0.973387	+	1.01791i	0.0561051	+	0.0586714i
$302$	5.23268			0.301107
$303$	27.4358	+	47.5202i	1.57615	+	2.72996i
$304$	−2.00789	+	3.47777i	−0.115160	+	0.199464i
$305$	21.1185	−	36.5783i	1.20924	−	2.09447i
$306$	−23.1507	−	40.0982i	−1.32344	−	2.29226i
$307$	−10.6673			−0.608812			−0.304406	−	0.952542i	$-0.598458\pi$
$307$	−10.6673			−0.608812			−0.304406	+	0.952542i	$0.598458\pi$
$308$	−3.02865	+	10.3700i	−0.172573	+	0.590887i
$309$	43.3055			2.46356
$310$	2.75803	+	4.77705i	0.156646	+	0.271318i
$311$	8.45610	−	14.6464i	0.479502	−	0.830521i	−0.520222	−	0.854031i	$-0.674151\pi$
$311$	8.45610	−	14.6464i	0.479502	−	0.830521i	0.999724	+	0.0235099i	$0.00748412\pi$
$312$	1.49579	−	2.59079i	0.0846825	−	0.146674i
$313$	−13.2189	−	22.8959i	−0.747178	−	1.29415i	−0.949170	−	0.314764i	$-0.898075\pi$
$313$	−13.2189	−	22.8959i	−0.747178	−	1.29415i	0.201992	−	0.979387i	$-0.435259\pi$
$314$	−19.6886			−1.11109
$315$	67.4616	−	16.4692i	3.80103	−	0.927937i
$316$	−3.56669			−0.200642
$317$	−10.6283	−	18.4088i	−0.596945	−	1.03394i	−0.993269	−	0.115829i	$-0.963048\pi$
$317$	−10.6283	−	18.4088i	−0.596945	−	1.03394i	0.396324	−	0.918111i	$-0.370286\pi$
$318$	0.680749	−	1.17909i	0.0381745	−	0.0661202i
$319$	−10.4950	+	18.1779i	−0.587609	+	1.01777i
$320$	1.79990	+	3.11751i	0.100617	+	0.174274i
$321$	−22.5392			−1.25802
$322$	−2.57027	+	0.627473i	−0.143235	+	0.0349677i
$323$	25.5013			1.41893
$324$	−11.1442	−	19.3024i	−0.619123	−	1.07235i
$325$	−3.71080	+	6.42730i	−0.205838	+	0.356522i
$326$	−7.48650	+	12.9670i	−0.414639	+	0.718176i
$327$	−20.4191	−	35.3670i	−1.12918	−	1.95580i
$328$	−2.51655			−0.138953
$329$	−5.39015	+	18.4558i	−0.297169	+	1.01750i
$330$	−47.1537			−2.59573
$331$	12.0724	+	20.9101i	0.663561	+	1.14932i	0.979673	+	0.200600i	$0.0642892\pi$
$331$	12.0724	+	20.9101i	0.663561	+	1.14932i	−0.316112	+	0.948722i	$0.602377\pi$
$332$	6.22735	−	10.7861i	0.341770	−	0.591964i
$333$	−3.85449	+	6.67617i	−0.211225	+	0.365852i
$334$	−2.54075	−	4.40070i	−0.139023	−	0.240796i
$335$	17.1311			0.935970
$336$	−5.86595	−	6.13427i	−0.320014	−	0.334652i
$337$	−7.45947			−0.406343			−0.203172	−	0.979143i	$-0.565125\pi$
$337$	−7.45947			−0.406343			−0.203172	+	0.979143i	$0.565125\pi$
$338$	6.06518	+	10.5052i	0.329903	+	0.571408i
$339$	−10.0630	+	17.4296i	−0.546548	+	0.946648i
$340$	11.4298	−	19.7971i	0.619870	−	1.07365i
$341$	3.12844	+	5.41861i	0.169414	+	0.293434i
$342$	29.2800			1.58328
$343$	−13.9440	+	12.1887i	−0.752904	+	0.658130i
$344$	0.532330			0.0287013
$345$	−5.77406	−	10.0010i	−0.310865	−	0.538433i
$346$	6.01245	−	10.4139i	0.323231	−	0.559853i
$347$	8.23903	−	14.2704i	0.442294	−	0.766076i	−0.555565	−	0.831473i	$-0.687498\pi$
$347$	8.23903	−	14.2704i	0.442294	−	0.766076i	0.997859	+	0.0653970i	$0.0208314\pi$
$348$	−8.24541	−	14.2815i	−0.442000	−	0.765567i
$349$	−20.1896			−1.08073			−0.540363	−	0.841432i	$-0.681713\pi$
$349$	−20.1896			−1.08073			−0.540363	+	0.841432i	$0.681713\pi$
$350$	14.5524	+	15.2181i	0.777860	+	0.813440i
$351$	−12.8376			−0.685220
$352$	2.04162	+	3.53619i	0.108819	+	0.188480i
$353$	11.6707	−	20.2142i	0.621168	−	1.07589i	−0.368100	−	0.929786i	$-0.619992\pi$
$353$	11.6707	−	20.2142i	0.621168	−	1.07589i	0.989269	−	0.146109i	$-0.0466750\pi$
$354$	−1.23359	+	2.13665i	−0.0655648	+	0.113562i
$355$	−10.4947	−	18.1773i	−0.557000	−	0.964752i
$356$	−10.9827			−0.582081
$357$	−15.1102	+	51.7370i	−0.799717	+	2.73821i
$358$	−7.98983			−0.422276
$359$	−1.68117	−	2.91188i	−0.0887289	−	0.153683i	0.818245	−	0.574869i	$-0.194947\pi$
$359$	−1.68117	−	2.91188i	−0.0887289	−	0.153683i	−0.906974	+	0.421186i	$0.861614\pi$
$360$	13.1235	−	22.7305i	0.691667	−	1.19800i
$361$	1.43675	−	2.48852i	0.0756183	−	0.130975i
$362$	−0.262723	−	0.455050i	−0.0138084	−	0.0239169i
$363$	−18.1985			−0.955175
$364$	−2.39688	+	0.585144i	−0.125631	+	0.0306699i
$365$	41.0283			2.14752
$366$	18.8200	+	32.5972i	0.983737	+	1.70388i
$367$	1.32918	−	2.30220i	0.0693824	−	0.120174i	−0.829247	−	0.558882i	$-0.811230\pi$
$367$	1.32918	−	2.30220i	0.0693824	−	0.120174i	0.898630	+	0.438708i	$0.144564\pi$
$368$	−0.500000	+	0.866025i	−0.0260643	+	0.0451447i
$369$	9.17438	+	15.8905i	0.477599	+	0.827226i
$370$	−3.80604			−0.197866
$371$	−1.09084	+	0.266305i	−0.0566337	+	0.0138258i
$372$	−4.91571			−0.254868
$373$	−12.4062	−	21.4881i	−0.642367	−	1.11261i	−0.984903	−	0.173108i	$-0.944619\pi$
$373$	−12.4062	−	21.4881i	−0.642367	−	1.11261i	0.342535	−	0.939505i	$-0.388714\pi$
$374$	12.9649	−	22.4558i	0.670397	−	1.16116i
$375$	−17.0825	+	29.5877i	−0.882135	+	1.52790i
$376$	3.63352	+	6.29344i	0.187384	+	0.324559i
$377$	−4.79375			−0.246891
$378$	−10.2108	+	34.9616i	−0.525187	+	1.79823i
$379$	8.02490			0.412211			0.206106	−	0.978530i	$-0.433921\pi$
$379$	8.02490			0.412211			0.206106	+	0.978530i	$0.433921\pi$
$380$	7.22799	+	12.5192i	0.370788	+	0.642223i
$381$	11.1895	−	19.3808i	0.573257	−	0.992910i
$382$	2.46778	−	4.27432i	0.126263	−	0.218693i
$383$	−1.60796	−	2.78508i	−0.0821632	−	0.142311i	0.822016	−	0.569465i	$-0.192850\pi$
$383$	−1.60796	−	2.78508i	−0.0821632	−	0.142311i	−0.904179	+	0.427154i	$0.859516\pi$
$384$	−3.20800			−0.163707
$385$	26.8774	+	28.1068i	1.36980	+	1.43245i
$386$	−8.72476			−0.444079
$387$	−1.94067	−	3.36134i	−0.0986499	−	0.170867i
$388$	−8.22097	+	14.2391i	−0.417357	+	0.722883i
$389$	−1.79036	+	3.10100i	−0.0907750	+	0.157227i	−0.907837	−	0.419322i	$-0.862268\pi$
$389$	−1.79036	+	3.10100i	−0.0907750	+	0.157227i	0.817062	+	0.576549i	$0.195601\pi$
$390$	−5.38454	−	9.32629i	−0.272657	−	0.472255i
$391$	6.35028			0.321148
$392$	−0.312869	+	6.99300i	−0.0158023	+	0.353200i
$393$	27.0255			1.36325
$394$	7.12066	+	12.3333i	0.358733	+	0.621345i
$395$	−6.41967	+	11.1192i	−0.323009	+	0.559468i
$396$	14.8859	−	25.7832i	0.748047	−	1.29566i
$397$	1.41750	+	2.45518i	0.0711424	+	0.123222i	0.899402	−	0.437122i	$-0.144002\pi$
$397$	1.41750	+	2.45518i	0.0711424	+	0.123222i	−0.828260	+	0.560344i	$0.810669\pi$
$398$	−13.7200			−0.687721
$399$	−23.5564	−	24.6339i	−1.17929	−	1.23324i
$400$	7.95849			0.397924
$401$	13.3428	+	23.1104i	0.666308	+	1.15408i	0.978929	+	0.204202i	$0.0654599\pi$
$401$	13.3428	+	23.1104i	0.666308	+	1.15408i	−0.312620	+	0.949878i	$0.601207\pi$
$402$	−7.63328	+	13.2212i	−0.380713	+	0.659415i
$403$	−0.714479	+	1.23751i	−0.0355908	+	0.0616450i
$404$	−8.55232	−	14.8131i	−0.425494	−	0.736977i
$405$	−80.2337			−3.98684
$406$	−3.81287	+	13.0552i	−0.189230	+	0.647918i
$407$	−4.31719			−0.213995
$408$	10.1858	+	17.6424i	0.504274	+	0.873429i
$409$	−9.01234	+	15.6098i	−0.445632	+	0.771856i	−0.998096	−	0.0616800i	$-0.980354\pi$
$409$	−9.01234	+	15.6098i	−0.445632	+	0.771856i	0.552464	+	0.833536i	$0.313688\pi$
$410$	−4.52952	+	7.84536i	−0.223697	+	0.387455i
$411$	17.3107	+	29.9830i	0.853874	+	1.47895i
$412$	−13.4992			−0.665060
$413$	1.97673	−	0.482574i	0.0972684	−	0.0237459i
$414$	7.29124			0.358345
$415$	−22.4172	−	38.8277i	−1.10042	−	1.90597i
$416$	−0.466270	+	0.807603i	−0.0228608	+	0.0395960i
$417$	−12.6041	+	21.8310i	−0.617226	+	1.06907i
$418$	8.19870	+	14.2006i	0.401012	+	0.694573i
$419$	0.704693			0.0344265			0.0172133	−	0.999852i	$-0.494521\pi$
$419$	0.704693			0.0344265			0.0172133	+	0.999852i	$0.494521\pi$
$420$	−29.6817	+	7.24613i	−1.44832	+	0.353575i
$421$	10.2408			0.499107			0.249554	−	0.968361i	$-0.419716\pi$
$421$	10.2408			0.499107			0.249554	+	0.968361i	$0.419716\pi$
$422$	−0.982052	−	1.70096i	−0.0478055	−	0.0828016i
$423$	26.4929	−	45.8870i	1.28813	−	2.23110i
$424$	−0.212204	+	0.367548i	−0.0103055	+	0.0178497i
$425$	−25.2693	−	43.7678i	−1.22574	−	2.12305i
$426$	18.7049			0.906256
$427$	8.70280	−	29.7982i	0.421158	−	1.44204i
$428$	7.02595			0.339612
$429$	−6.10768	−	10.5788i	−0.294882	−	0.510750i
$430$	0.958138	−	1.65954i	0.0462055	−	0.0800303i
$431$	16.4745	−	28.5347i	0.793549	−	1.37447i	−0.130207	−	0.991487i	$-0.541564\pi$
$431$	16.4745	−	28.5347i	0.793549	−	1.37447i	0.923756	−	0.382981i	$-0.125102\pi$
$432$	6.88314	+	11.9219i	0.331165	+	0.573595i
$433$	24.7235			1.18814			0.594068	−	0.804415i	$-0.297521\pi$
$433$	24.7235			1.18814			0.594068	+	0.804415i	$0.297521\pi$
$434$	2.80193	+	2.93009i	0.134497	+	0.140649i
$435$	−59.3635			−2.84626
$436$	6.36508	+	11.0246i	0.304832	+	0.527985i
$437$	−2.00789	+	3.47777i	−0.0960505	+	0.166364i
$438$	−18.2814	+	31.6644i	−0.873520	+	1.51298i
$439$	7.30561	+	12.6537i	0.348678	+	0.603928i	0.986015	−	0.166657i	$-0.0532974\pi$
$439$	7.30561	+	12.6537i	0.348678	+	0.603928i	−0.637337	+	0.770585i	$0.719964\pi$
$440$	14.6988			0.700738
$441$	45.2972	−	23.5183i	2.15701	−	1.11992i
$442$	5.92189			0.281676
$443$	10.6276	+	18.4075i	0.504931	+	0.874566i	0.999984	+	0.00570286i	$0.00181529\pi$
$443$	10.6276	+	18.4075i	0.504931	+	0.874566i	−0.495053	+	0.868863i	$0.664851\pi$
$444$	1.69590	−	2.93738i	0.0804837	−	0.139402i
$445$	−19.7677	+	34.2386i	−0.937078	+	1.62307i
$446$	−3.50333	−	6.06795i	−0.165888	−	0.287326i
$447$	33.5809			1.58832
$448$	1.82854	+	1.91218i	0.0863905	+	0.0903420i
$449$	−30.0560			−1.41843			−0.709215	−	0.704993i	$-0.750950\pi$
$449$	−30.0560			−1.41843			−0.709215	+	0.704993i	$0.750950\pi$
$450$	−29.0136	−	50.2531i	−1.36771	−	2.36895i
$451$	−5.13784	+	8.89900i	−0.241931	+	0.419037i
$452$	3.13685	−	5.43319i	0.147545	−	0.255556i
$453$	8.39320	+	14.5375i	0.394347	+	0.683029i
$454$	−25.1397			−1.17986
$455$	−2.48994	+	8.52549i	−0.116730	+	0.399681i
$456$	−12.8826			−0.603284
$457$	−1.48247	−	2.56771i	−0.0693469	−	0.120112i	0.829267	−	0.558852i	$-0.188758\pi$
$457$	−1.48247	−	2.56771i	−0.0693469	−	0.120112i	−0.898614	+	0.438740i	$0.855425\pi$
$458$	7.92118	−	13.7199i	0.370133	−	0.641089i
$459$	43.7099	−	75.7077i	2.04020	−	3.53373i
$460$	1.79990	+	3.11751i	0.0839205	+	0.145355i
$461$	−16.1609			−0.752687			−0.376343	−	0.926480i	$-0.622819\pi$
$461$	−16.1609			−0.752687			−0.376343	+	0.926480i	$0.622819\pi$
$462$	−33.6680	+	8.21929i	−1.56638	+	0.382396i
$463$	−32.1830			−1.49567			−0.747835	−	0.663885i	$-0.768906\pi$
$463$	−32.1830			−1.49567			−0.747835	+	0.663885i	$0.768906\pi$
$464$	2.57027	+	4.45183i	0.119322	+	0.206671i
$465$	−8.84776	+	15.3248i	−0.410305	+	0.710669i
$466$	−2.56249	+	4.43836i	−0.118705	+	0.205603i
$467$	1.84930	+	3.20308i	0.0855753	+	0.148221i	0.905636	−	0.424055i	$-0.139394\pi$
$467$	1.84930	+	3.20308i	0.0855753	+	0.148221i	−0.820061	+	0.572276i	$0.806061\pi$
$468$	6.79937			0.314301
$469$	12.2317	−	2.98609i	0.564806	−	0.137885i
$470$	26.1598			1.20666
$471$	−31.5806	−	54.6991i	−1.45515	−	2.52040i
$472$	0.384537	−	0.666038i	0.0176998	−	0.0306569i
$473$	1.08682	−	1.88242i	0.0499718	−	0.0865538i
$474$	−5.72097	−	9.90901i	−0.262773	−	0.455136i
$475$	31.9596			1.46640
$476$	4.71017	−	16.1275i	0.215890	−	0.739204i
$477$	3.09446			0.141686
$478$	6.60347	+	11.4376i	0.302036	+	0.523141i
$479$	18.7783	−	32.5249i	0.858001	−	1.48610i	−0.0158322	−	0.999875i	$-0.505040\pi$
$479$	18.7783	−	32.5249i	0.858001	−	1.48610i	0.873833	−	0.486226i	$-0.161627\pi$
$480$	−5.77406	+	10.0010i	−0.263548	+	0.456479i
$481$	−0.492984	−	0.853874i	−0.0224781	−	0.0389333i
$482$	27.6622			1.25998
$483$	−5.86595	−	6.13427i	−0.266910	−	0.279119i
$484$	5.67287			0.257858
$485$	29.5938	+	51.2579i	1.34378	+	2.32750i
$486$	15.1012	−	26.1560i	0.685004	−	1.18646i
$487$	8.87829	−	15.3777i	0.402314	−	0.696828i	−0.591691	−	0.806165i	$-0.701539\pi$
$487$	8.87829	−	15.3777i	0.402314	−	0.696828i	0.994005	+	0.109337i	$0.0348727\pi$
$488$	−5.86659	−	10.1612i	−0.265568	−	0.459977i
$489$	−48.0333			−2.17214
$490$	21.2376	+	13.5620i	0.959418	+	0.612671i
$491$	6.93794			0.313105			0.156552	−	0.987670i	$-0.449962\pi$
$491$	6.93794			0.313105			0.156552	+	0.987670i	$0.449962\pi$
$492$	−4.03654	−	6.99149i	−0.181981	−	0.315201i
$493$	16.3219	−	28.2704i	0.735103	−	1.27324i
$494$	−1.87244	+	3.24316i	−0.0842450	+	0.145917i
$495$	−53.5863	−	92.8142i	−2.40852	−	4.17169i
$496$	1.53233			0.0688036
$497$	−10.6617	−	11.1494i	−0.478243	−	0.500118i
$498$	39.9546			1.79041
$499$	2.79593	+	4.84269i	0.125163	+	0.216789i	0.921797	−	0.387674i	$-0.126721\pi$
$499$	2.79593	+	4.84269i	0.125163	+	0.216789i	−0.796634	+	0.604462i	$0.793388\pi$
$500$	5.32497	−	9.22312i	0.238140	−	0.412470i
$501$	8.15070	−	14.1174i	0.364147	−	0.630720i
$502$	−6.91663	−	11.9799i	−0.308704	−	0.534691i
$503$	−10.1204			−0.451247			−0.225624	−	0.974215i	$-0.572442\pi$
$503$	−10.1204			−0.451247			−0.225624	+	0.974215i	$0.572442\pi$
$504$	5.40810	−	18.5172i	0.240896	−	0.824823i
$505$	−61.5731			−2.73997
$506$	2.04162	+	3.53619i	0.0907611	+	0.157203i
$507$	−19.4571	+	33.7007i	−0.864120	+	1.49670i
$508$	−3.48801	+	6.04141i	−0.154755	+	0.268044i
$509$	12.7225	+	22.0360i	0.563915	+	0.976730i	0.997150	+	0.0754487i	$0.0240389\pi$
$509$	12.7225	+	22.0360i	0.563915	+	0.976730i	−0.433234	+	0.901281i	$0.642628\pi$
$510$	73.3338			3.24727
$511$	29.2944	−	7.15157i	1.29591	−	0.316367i
$512$	1.00000			0.0441942
$513$	27.6412	+	47.8759i	1.22039	+	2.11377i
$514$	−12.0746	+	20.9138i	−0.532587	+	0.922468i
$515$	−24.2972	+	42.0840i	−1.07066	+	1.85444i
$516$	0.853856	+	1.47892i	0.0375889	+	0.0651059i
$517$	29.6731			1.30502
$518$	−2.71753	+	0.663424i	−0.119401	+	0.0291492i
$519$	38.5758			1.69329
$520$	1.67847	+	2.90720i	0.0736059	+	0.127489i
$521$	−1.88864	+	3.27123i	−0.0827430	+	0.143315i	−0.904427	−	0.426628i	$-0.859701\pi$
$521$	−1.88864	+	3.27123i	−0.0827430	+	0.143315i	0.821684	+	0.569943i	$0.193035\pi$
$522$	18.7404	−	32.4594i	0.820247	−	1.42071i
$523$	3.60681	+	6.24717i	0.157715	+	0.273170i	0.934044	−	0.357158i	$-0.116254\pi$
$523$	3.60681	+	6.24717i	0.157715	+	0.273170i	−0.776330	+	0.630327i	$0.782921\pi$
$524$	−8.42441			−0.368022
$525$	−18.9369	+	64.8394i	−0.826472	+	2.82982i
$526$	28.3042			1.23412
$527$	−4.86536	−	8.42706i	−0.211939	−	0.367088i
$528$	−6.54951	+	11.3441i	−0.285031	+	0.493688i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	0.763890	+	1.32310i	0.0331812	+	0.0574716i
$531$	−5.60751			−0.243345
$532$	7.34303	+	7.67890i	0.318361	+	0.332923i
$533$	−2.34678			−0.101650
$534$	−17.6162	−	30.5122i	−0.762328	−	1.32039i
$535$	12.6460	−	21.9035i	0.546733	−	0.946969i
$536$	2.37945	−	4.12134i	0.102777	−	0.178015i
$537$	−12.8157	−	22.1974i	−0.553037	−	0.957889i
$538$	−30.2279			−1.30322
$539$	24.0898	+	15.3834i	1.03762	+	0.662611i
$540$	49.5557			2.13254
$541$	5.19997	+	9.00662i	0.223564	+	0.387225i	0.955888	−	0.293732i	$-0.0948974\pi$
$541$	5.19997	+	9.00662i	0.223564	+	0.387225i	−0.732323	+	0.680957i	$0.761564\pi$
$542$	4.57665	−	7.92699i	0.196584	−	0.340493i
$543$	0.842814	−	1.45980i	0.0361686	−	0.0626459i
$544$	−3.17514	−	5.49951i	−0.136133	−	0.235789i
$545$	45.8259			1.96297
$546$	−5.47024	−	5.72045i	−0.234105	−	0.244813i
$547$	24.3221			1.03994			0.519969	−	0.854185i	$-0.325943\pi$
$547$	24.3221			1.03994			0.519969	+	0.854185i	$0.325943\pi$
$548$	−5.39611	−	9.34634i	−0.230510	−	0.399256i
$549$	−42.7747	+	74.0879i	−1.82558	+	3.16200i
$550$	16.2482	−	28.1427i	0.692826	−	1.20001i
$551$	10.3216	+	17.8776i	0.439716	+	0.761611i
$552$	−3.20800			−0.136541
$553$	−2.64551	+	9.05817i	−0.112499	+	0.385193i
$554$	18.8544			0.801048
$555$	−6.10487	−	10.5740i	−0.259137	−	0.448839i
$556$	3.92897	−	6.80517i	0.166625	−	0.288603i
$557$	2.24618	−	3.89049i	0.0951735	−	0.164845i	−0.814508	−	0.580153i	$-0.802993\pi$
$557$	2.24618	−	3.89049i	0.0951735	−	0.164845i	0.909681	+	0.415308i	$0.136326\pi$
$558$	−5.58629	−	9.67574i	−0.236487	−	0.409607i
$559$	0.496419			0.0209963
$560$	9.25242	−	2.25877i	0.390986	−	0.0954506i
$561$	83.1825			3.51197
$562$	−6.05880	−	10.4942i	−0.255575	−	0.442669i
$563$	−19.5361	+	33.8376i	−0.823349	+	1.42608i	0.0798249	+	0.996809i	$0.474564\pi$
$563$	−19.5361	+	33.8376i	−0.823349	+	1.42608i	−0.903174	+	0.429274i	$0.858769\pi$
$564$	−11.6563	+	20.1893i	−0.490820	+	0.850124i
$565$	−11.2920	−	19.5583i	−0.475058	−	0.822825i
$566$	−13.2093			−0.555227
$567$	−57.2873	+	13.9854i	−2.40584	+	0.587332i
$568$	−5.83072			−0.244651
$569$	−4.66357	−	8.07755i	−0.195507	−	0.338628i	0.751559	−	0.659665i	$-0.229302\pi$
$569$	−4.66357	−	8.07755i	−0.195507	−	0.338628i	−0.947067	+	0.321037i	$0.895969\pi$
$570$	−23.1873	+	40.1617i	−0.971211	+	1.68219i
$571$	14.5593	−	25.2175i	0.609289	−	1.05532i	−0.382069	−	0.924134i	$-0.624788\pi$
$571$	14.5593	−	25.2175i	0.609289	−	1.05532i	0.991358	−	0.131186i	$-0.0418785\pi$
$572$	1.90389	+	3.29764i	0.0796058	+	0.137881i
$573$	15.8333			0.661444
$574$	−1.86659	+	6.39116i	−0.0779099	+	0.266762i
$575$	7.95849			0.331892
$576$	−3.64562	−	6.31440i	−0.151901	−	0.263100i
$577$	4.97364	−	8.61459i	0.207055	−	0.358630i	−0.743730	−	0.668480i	$-0.766945\pi$
$577$	4.97364	−	8.61459i	0.207055	−	0.358630i	0.950786	+	0.309850i	$0.100279\pi$
$578$	−11.6630	+	20.2010i	−0.485119	+	0.840250i
$579$	−13.9945	−	24.2392i	−0.581592	−	1.00735i
$580$	18.5048			0.768372
$581$	−22.7739	−	23.8156i	−0.944823	−	0.988039i
$582$	−52.7457			−2.18638
$583$	0.866480	+	1.50079i	0.0358859	+	0.0621563i
$584$	5.69870	−	9.87045i	0.235814	−	0.408442i
$585$	12.2382	−	21.1971i	0.505985	−	0.876392i
$586$	−7.43622	−	12.8799i	−0.307188	−	0.532064i
$587$	28.5555			1.17861			0.589305	−	0.807910i	$-0.299402\pi$
$587$	28.5555			1.17861			0.589305	+	0.807910i	$0.299402\pi$
$588$	−19.9298	+	10.3476i	−0.821893	+	0.426726i
$589$	6.15350			0.253551
$590$	−1.38425	−	2.39760i	−0.0569888	−	0.0987075i
$591$	−22.8430	+	39.5653i	−0.939637	+	1.62750i
$592$	−0.528647	+	0.915643i	−0.0217273	+	0.0376327i
$593$	13.1399	+	22.7589i	0.539590	+	0.934598i	0.998926	+	0.0463349i	$0.0147541\pi$
$593$	13.1399	+	22.7589i	0.539590	+	0.934598i	−0.459336	+	0.888263i	$0.651913\pi$
$594$	56.2110			2.30637
$595$	−41.7999	−	43.7118i	−1.71363	−	1.79201i
$596$	−10.4679			−0.428781
$597$	−22.0068	−	38.1170i	−0.900680	−	1.56002i
$598$	−0.466270	+	0.807603i	−0.0190672	+	0.0330254i
$599$	14.4809	−	25.0816i	0.591673	−	1.02481i	−0.402334	−	0.915493i	$-0.631801\pi$
$599$	14.4809	−	25.0816i	0.591673	−	1.02481i	0.994007	−	0.109315i	$-0.0348658\pi$
$600$	12.7654	+	22.1103i	0.521145	+	0.902650i
$601$	2.92666			0.119381			0.0596905	−	0.998217i	$-0.480989\pi$
$601$	2.92666			0.119381			0.0596905	+	0.998217i	$0.480989\pi$
$602$	0.394843	−	1.35193i	0.0160926	−	0.0551007i
$603$	−34.6983			−1.41303
$604$	−2.61634	−	4.53163i	−0.106457	−	0.184389i
$605$	10.2106	−	17.6852i	0.415118	−	0.719006i
$606$	27.4358	−	47.5202i	1.11450	−	1.93038i
$607$	11.7275	+	20.3126i	0.476003	+	0.824461i	0.999622	−	0.0274912i	$-0.00875182\pi$
$607$	11.7275	+	20.3126i	0.476003	+	0.824461i	−0.523619	+	0.851952i	$0.675418\pi$
$608$	4.01578			0.162861
$609$	−42.3858	+	10.3476i	−1.71756	+	0.419304i
$610$	−42.2370			−1.71013
$611$	3.38840	+	5.86888i	0.137080	+	0.237430i
$612$	−23.1507	+	40.0982i	−0.935812	+	1.62087i
$613$	−2.64054	+	4.57354i	−0.106650	+	0.184724i	−0.914411	−	0.404786i	$-0.867346\pi$
$613$	−2.64054	+	4.57354i	−0.106650	+	0.184724i	0.807761	+	0.589510i	$0.200679\pi$
$614$	5.33363	+	9.23811i	0.215248	+	0.372820i
$615$	−29.0614			−1.17187
$616$	10.4950	−	2.56213i	0.422857	−	0.103231i
$617$	7.69908			0.309953			0.154977	−	0.987918i	$-0.450470\pi$
$617$	7.69908			0.309953			0.154977	+	0.987918i	$0.450470\pi$
$618$	−21.6527	−	37.5037i	−0.871001	−	1.50862i
$619$	7.09751	−	12.2933i	0.285273	−	0.494108i	−0.687402	−	0.726277i	$-0.741249\pi$
$619$	7.09751	−	12.2933i	0.285273	−	0.494108i	0.972675	+	0.232169i	$0.0745823\pi$
$620$	2.75803	−	4.77705i	0.110765	−	0.191851i
$621$	6.88314	+	11.9219i	0.276211	+	0.478411i
$622$	−16.9122			−0.678118
$623$	−8.14614	+	27.8922i	−0.326368	+	1.11748i
$624$	−2.99158			−0.119759
$625$	0.727453	+	1.25999i	0.0290981	+	0.0503995i
$626$	−13.2189	+	22.8959i	−0.528335	+	0.915103i
$627$	−26.3014	+	45.5554i	−1.05038	+	1.81931i
$628$	9.84432	+	17.0509i	0.392831	+	0.680404i
$629$	6.71411			0.267709
$630$	−47.9936	−	50.1889i	−1.91211	−	1.99957i
$631$	−7.60667			−0.302817			−0.151408	−	0.988471i	$-0.548381\pi$
$631$	−7.60667			−0.302817			−0.151408	+	0.988471i	$0.548381\pi$
$632$	1.78335	+	3.08885i	0.0709377	+	0.122868i
$633$	3.15042	−	5.45668i	0.125218	−	0.216884i
$634$	−10.6283	+	18.4088i	−0.422104	+	0.731105i
$635$	12.5561	+	21.7478i	0.498274	+	0.863036i
$636$	−1.36150			−0.0539869
$637$	−0.291763	+	6.52126i	−0.0115601	+	0.258382i
$638$	20.9901			0.831004
$639$	21.2566	+	36.8175i	0.840897	+	1.45648i
$640$	1.79990	−	3.11751i	0.0711471	−	0.123230i
$641$	−4.24057	+	7.34488i	−0.167492	+	0.290105i	−0.937538	−	0.347884i	$-0.886900\pi$
$641$	−4.24057	+	7.34488i	−0.167492	+	0.290105i	0.770045	+	0.637989i	$0.220234\pi$
$642$	11.2696	+	19.5195i	0.444776	+	0.770374i
$643$	18.9051			0.745543			0.372771	−	0.927923i	$-0.378408\pi$
$643$	18.9051			0.745543			0.372771	+	0.927923i	$0.378408\pi$
$644$	1.82854	+	1.91218i	0.0720546	+	0.0753505i
$645$	6.14740			0.242054
$646$	−12.7507	−	22.0848i	−0.501669	−	0.868915i
$647$	5.53730	−	9.59089i	0.217694	−	0.377057i	−0.736409	−	0.676537i	$-0.763480\pi$
$647$	5.53730	−	9.59089i	0.217694	−	0.377057i	0.954103	+	0.299480i	$0.0968132\pi$
$648$	−11.1442	+	19.3024i	−0.437786	+	0.758268i
$649$	−1.57016	−	2.71959i	−0.0616341	−	0.106753i
$650$	7.42161			0.291099
$651$	−3.64611	+	12.4842i	−0.142902	+	0.489294i
$652$	14.9730			0.586388
$653$	11.8858	+	20.5869i	0.465129	+	0.805627i	0.999207	−	0.0398083i	$-0.0126747\pi$
$653$	11.8858	+	20.5869i	0.465129	+	0.805627i	−0.534079	+	0.845435i	$0.679341\pi$
$654$	−20.4191	+	35.3670i	−0.798452	+	1.38296i
$655$	−15.1630	+	26.2632i	−0.592469	+	1.02619i
$656$	1.25827	+	2.17939i	0.0491273	+	0.0850911i
$657$	−83.1012			−3.24209
$658$	18.6782	−	4.55987i	0.728154	−	0.177762i
$659$	7.07118			0.275454			0.137727	−	0.990470i	$-0.456020\pi$
$659$	7.07118			0.275454			0.137727	+	0.990470i	$0.456020\pi$
$660$	23.5769	+	40.8363i	0.917728	+	1.58955i
$661$	−4.53948	+	7.86261i	−0.176565	+	0.305820i	−0.940702	−	0.339235i	$-0.889832\pi$
$661$	−4.53948	+	7.86261i	−0.176565	+	0.305820i	0.764137	+	0.645054i	$0.223165\pi$
$662$	12.0724	−	20.9101i	0.469209	−	0.812693i
$663$	9.49870	+	16.4522i	0.368899	+	0.638952i
$664$	−12.4547			−0.483336
$665$	37.1557	−	9.07074i	1.44084	−	0.351748i
$666$	7.70898			0.298717
$667$	2.57027	+	4.45183i	0.0995212	+	0.172376i
$668$	−2.54075	+	4.40070i	−0.0983044	+	0.170268i
$669$	11.2387	−	19.4660i	0.434512	−	0.752597i
$670$	−8.56553	−	14.8359i	−0.330915	−	0.573162i
$671$	−47.9094			−1.84952
$672$	−2.37945	+	8.14720i	−0.0917894	+	0.314285i
$673$	−49.4544			−1.90633			−0.953164	−	0.302453i	$-0.902194\pi$
$673$	−49.4544			−1.90633			−0.953164	+	0.302453i	$0.902194\pi$
$674$	3.72974	+	6.46009i	0.143664	+	0.248833i
$675$	54.7794	−	94.8806i	2.10846	−	3.65196i
$676$	6.06518	−	10.5052i	0.233276	−	0.404046i
$677$	−16.2963	−	28.2261i	−0.626319	−	1.08482i	−0.988284	−	0.152624i	$-0.951228\pi$
$677$	−16.2963	−	28.2261i	−0.626319	−	1.08482i	0.361966	−	0.932191i	$-0.382106\pi$
$678$	20.1260			0.772935
$679$	30.0648	+	31.4400i	1.15378	+	1.20655i
$680$	−22.8597			−0.876629
$681$	−40.3240	−	69.8433i	−1.54522	−	2.67640i
$682$	3.12844	−	5.41861i	0.119794	−	0.207489i
$683$	−16.4157	+	28.4328i	−0.628130	+	1.08795i	0.359797	+	0.933031i	$0.382846\pi$
$683$	−16.4157	+	28.4328i	−0.628130	+	1.08795i	−0.987927	+	0.154922i	$0.950487\pi$
$684$	−14.6400	−	25.3572i	−0.559775	−	0.969558i
$685$	−38.8497			−1.48437
$686$	17.5277	+	5.98147i	0.669213	+	0.228374i
$687$	50.8223			1.93899
$688$	−0.266165	−	0.461011i	−0.0101474	−	0.0175759i
$689$	−0.197889	+	0.342753i	−0.00753896	+	0.0130579i
$690$	−5.77406	+	10.0010i	−0.219815	+	0.380730i
$691$	−19.1784	−	33.2180i	−0.729581	−	1.26367i	−0.957060	−	0.289889i	$-0.906382\pi$
$691$	−19.1784	−	33.2180i	−0.729581	−	1.26367i	0.227479	−	0.973783i	$-0.426952\pi$
$692$	−12.0249			−0.457118
$693$	−54.4391	−	56.9292i	−2.06797	−	2.16256i
$694$	−16.4781			−0.625498
$695$	−14.1435	−	24.4972i	−0.536492	−	0.929231i
$696$	−8.24541	+	14.2815i	−0.312541	+	0.541338i
$697$	7.99039	−	13.8398i	0.302658	−	0.524219i
$698$	10.0948	+	17.4847i	0.382094	+	0.661807i
$699$	−16.4409			−0.621852
$700$	5.90302	−	20.2118i	0.223113	−	0.763934i
$701$	−42.6512			−1.61091			−0.805457	−	0.592654i	$-0.798080\pi$
$701$	−42.6512			−1.61091			−0.805457	+	0.592654i	$0.798080\pi$
$702$	6.41880	+	11.1177i	0.242262	+	0.419610i
$703$	−2.12293	+	3.67702i	−0.0800678	+	0.138682i
$704$	2.04162	−	3.53619i	0.0769465	−	0.133275i
$705$	41.9603	+	72.6774i	1.58032	+	2.73719i
$706$	−23.3414			−0.878465
$707$	−43.9635	+	10.7327i	−1.65342	+	0.403645i
$708$	2.46719			0.0927226
$709$	−6.36151	−	11.0185i	−0.238911	−	0.413807i	0.721491	−	0.692424i	$-0.243457\pi$
$709$	−6.36151	−	11.0185i	−0.238911	−	0.413807i	−0.960402	+	0.278617i	$0.910124\pi$
$710$	−10.4947	+	18.1773i	−0.393858	+	0.682182i
$711$	13.0028	−	22.5215i	0.487643	−	0.844623i
$712$	5.49134	+	9.51129i	0.205797	+	0.356450i
$713$	1.53233			0.0573862
$714$	52.3607	−	12.7827i	1.95955	−	0.478380i
$715$	13.7072			0.512621
$716$	3.99492	+	6.91940i	0.149297	+	0.258590i
$717$	−21.1839	+	36.6916i	−0.791128	+	1.37027i
$718$	−1.68117	+	2.91188i	−0.0627408	+	0.108670i
$719$	−1.22475	−	2.12134i	−0.0456757	−	0.0791125i	0.842284	−	0.539034i	$-0.181211\pi$
$719$	−1.22475	−	2.12134i	−0.0456757	−	0.0791125i	−0.887959	+	0.459922i	$0.847877\pi$
$720$	−26.2469			−0.978165
$721$	−10.0127	+	34.2834i	−0.372894	+	1.27678i
$722$	−2.87350			−0.106940
$723$	44.3701	+	76.8513i	1.65014	+	2.85813i
$724$	−0.262723	+	0.455050i	−0.00976402	+	0.0169118i
$725$	20.4554	−	35.4299i	0.759696	−	1.31583i
$726$	9.09927	+	15.7604i	0.337705	+	0.584923i
$727$	22.6449			0.839853			0.419926	−	0.907558i	$-0.362056\pi$
$727$	22.6449			0.839853			0.419926	+	0.907558i	$0.362056\pi$
$728$	1.70519	+	1.78318i	0.0631985	+	0.0660892i
$729$	30.0238			1.11199
$730$	−20.5141	−	35.5315i	−0.759262	−	1.31508i
$731$	−1.69022	+	2.92755i	−0.0625151	+	0.108279i
$732$	18.8200	−	32.5972i	0.695607	−	1.20483i
$733$	−2.21880	−	3.84307i	−0.0819531	−	0.141947i	0.822136	−	0.569292i	$-0.192782\pi$
$733$	−2.21880	−	3.84307i	−0.0819531	−	0.141947i	−0.904089	+	0.427345i	$0.859449\pi$
$734$	−2.65835			−0.0981216
$735$	−3.61305	+	80.7560i	−0.133269	+	2.97873i
$736$	1.00000			0.0368605
$737$	−9.71589	−	16.8284i	−0.357889	−	0.619882i
$738$	9.17438	−	15.8905i	0.337713	−	0.584937i
$739$	18.3038	−	31.7031i	0.673316	−	1.16622i	−0.303642	−	0.952786i	$-0.598203\pi$
$739$	18.3038	−	31.7031i	0.673316	−	1.16622i	0.976958	−	0.213431i	$-0.0684640\pi$
$740$	1.90302	+	3.29612i	0.0699563	+	0.121168i
$741$	−12.0135			−0.441329
$742$	0.776047	+	0.811544i	0.0284896	+	0.0297927i
$743$	−14.2954			−0.524446			−0.262223	−	0.965007i	$-0.584456\pi$
$743$	−14.2954			−0.524446			−0.262223	+	0.965007i	$0.584456\pi$
$744$	2.45785	+	4.25713i	0.0901093	+	0.156074i
$745$	−18.8411	+	32.6337i	−0.690285	+	1.19561i
$746$	−12.4062	+	21.4881i	−0.454222	+	0.786736i
$747$	45.4051	+	78.6439i	1.66129	+	2.87743i
$748$	−25.9297			−0.948085
$749$	5.21133	−	17.8435i	0.190418	−	0.651986i
$750$	34.1650			1.24753
$751$	18.9503	+	32.8228i	0.691505	+	1.19772i	0.971345	+	0.237675i	$0.0763852\pi$
$751$	18.9503	+	32.8228i	0.691505	+	1.19772i	−0.279840	+	0.960047i	$0.590282\pi$
$752$	3.63352	−	6.29344i	0.132501	−	0.229498i
$753$	22.1885	−	38.4316i	0.808594	−	1.40053i
$754$	2.39688	+	4.15151i	0.0872891	+	0.151189i
$755$	−18.8365			−0.685532
$756$	35.3830	−	8.63797i	1.28687	−	0.314160i
$757$	17.8790			0.649822			0.324911	−	0.945745i	$-0.394666\pi$
$757$	17.8790			0.649822			0.324911	+	0.945745i	$0.394666\pi$
$758$	−4.01245	−	6.94977i	−0.145739	−	0.252427i
$759$	−6.54951	+	11.3441i	−0.237732	+	0.411764i
$760$	7.22799	−	12.5192i	0.262187	−	0.454121i
$761$	6.00551	+	10.4018i	0.217699	+	0.377066i	0.954104	−	0.299475i	$-0.0968114\pi$
$761$	6.00551	+	10.4018i	0.217699	+	0.377066i	−0.736405	+	0.676541i	$0.763478\pi$
$762$	−22.3790			−0.810707
$763$	32.7199	−	7.98784i	1.18454	−	0.289179i
$764$	−4.93556			−0.178562
$765$	83.3377	+	144.345i	3.01308	+	5.21881i
$766$	−1.60796	+	2.78508i	−0.0580981	+	0.100629i
$767$	0.358596	−	0.621107i	0.0129482	−	0.0224269i
$768$	1.60400	+	2.77821i	0.0578793	+	0.100250i
$769$	2.51353			0.0906402			0.0453201	−	0.998973i	$-0.485569\pi$
$769$	2.51353			0.0906402			0.0453201	+	0.998973i	$0.485569\pi$
$770$	10.9025	−	37.3299i	0.392899	−	1.34528i
$771$	−77.4704			−2.79003
$772$	4.36238	+	7.55587i	0.157006	+	0.271942i
$773$	−14.6047	+	25.2962i	−0.525296	+	0.909840i	0.474270	+	0.880380i	$0.342712\pi$
$773$	−14.6047	+	25.2962i	−0.525296	+	0.909840i	−0.999566	+	0.0294602i	$0.990621\pi$
$774$	−1.94067	+	3.36134i	−0.0697560	+	0.120821i
$775$	−6.09751	−	10.5612i	−0.219029	−	0.379370i
$776$	16.4419			0.590231
$777$	−6.20204	−	6.48572i	−0.222497	−	0.232674i
$778$	3.58073			0.128375
$779$	5.05295	+	8.75197i	0.181041	+	0.313572i
$780$	−5.38454	+	9.32629i	−0.192797	+	0.333935i
$781$	−11.9041	+	20.6185i	−0.425963	+	0.737789i
$782$	−3.17514	−	5.49951i	−0.113543	−	0.196662i
$783$	70.7660			2.52897
$784$	6.21255	−	3.22555i	0.221877	−	0.115198i
$785$	70.8750			2.52964
$786$	−13.5127	−	23.4047i	−0.481983	−	0.834819i
$787$	−10.7537	+	18.6260i	−0.383329	+	0.663945i	−0.991536	−	0.129833i	$-0.958556\pi$
$787$	−10.7537	+	18.6260i	−0.383329	+	0.663945i	0.608207	+	0.793778i	$0.291889\pi$
$788$	7.12066	−	12.3333i	0.253663	−	0.439357i
$789$	45.3999	+	78.6350i	1.61628	+	2.79948i
$790$	12.8393			0.456804
$791$	−11.4717	−	11.9965i	−0.407888	−	0.426545i
$792$	−29.7719			−1.05790
$793$	−5.47083	−	9.47575i	−0.194275	−	0.336494i
$794$	1.41750	−	2.45518i	0.0503052	−	0.0871312i
$795$	−2.45055	+	4.24448i	−0.0869122	+	0.150536i
$796$	6.86000	+	11.8819i	0.243146	+	0.421141i
$797$	16.0971			0.570190			0.285095	−	0.958499i	$-0.407975\pi$
$797$	16.0971			0.570190			0.285095	+	0.958499i	$0.407975\pi$
$798$	−9.55537	+	32.7174i	−0.338256	+	1.15818i
$799$	−46.1478			−1.63259
$800$	−3.97924	−	6.89225i	−0.140688	−	0.243678i
$801$	40.0387	−	69.3490i	1.41470	−	2.45033i
$802$	13.3428	−	23.1104i	0.471151	−	0.816058i
$803$	−23.2692	−	40.3034i	−0.821152	−	1.42228i
$804$	15.2666			0.538410
$805$	9.25242	−	2.25877i	0.326105	−	0.0796113i
$806$	1.42896			0.0503329
$807$	−48.4854	−	83.9792i	−1.70677	−	2.95621i
$808$	−8.55232	+	14.8131i	−0.300870	+	0.521121i
$809$	−19.6424	+	34.0216i	−0.690590	+	1.19614i	0.281055	+	0.959692i	$0.409316\pi$
$809$	−19.6424	+	34.0216i	−0.690590	+	1.19614i	−0.971645	+	0.236445i	$0.924018\pi$
$810$	40.1168	+	69.4844i	1.40956	+	2.44143i
$811$	−35.6464			−1.25172			−0.625858	−	0.779937i	$-0.715251\pi$
$811$	−35.6464			−1.25172			−0.625858	+	0.779937i	$0.715251\pi$
$812$	13.2126	−	3.22555i	0.463670	−	0.113195i
$813$	29.3637			1.02983
$814$	2.15859	+	3.73879i	0.0756587	+	0.131045i
$815$	26.9498	−	46.6785i	0.944011	−	1.63508i
$816$	10.1858	−	17.6424i	0.356576	−	0.617607i
$817$	−1.06886	−	1.85132i	−0.0373947	−	0.0647695i
$818$	18.0247			0.630218
$819$	5.04327	−	17.2680i	0.176226	−	0.603394i
$820$	9.05904			0.316356
$821$	−11.6972	−	20.2602i	−0.408236	−	0.707086i	0.586456	−	0.809981i	$-0.300523\pi$
$821$	−11.6972	−	20.2602i	−0.408236	−	0.707086i	−0.994692	+	0.102895i	$0.967189\pi$
$822$	17.3107	−	29.9830i	0.603780	−	1.04578i
$823$	22.9229	−	39.7037i	0.799044	−	1.38398i	−0.121196	−	0.992629i	$-0.538673\pi$
$823$	22.9229	−	39.7037i	0.799044	−	1.38398i	0.920240	−	0.391355i	$-0.127994\pi$
$824$	6.74962	+	11.6907i	0.235134	+	0.407264i
$825$	104.248			3.62946
$826$	−1.40628	−	1.47061i	−0.0489309	−	0.0511690i
$827$	40.7537			1.41715			0.708573	−	0.705638i	$-0.249339\pi$
$827$	40.7537			1.41715			0.708573	+	0.705638i	$0.249339\pi$
$828$	−3.64562	−	6.31440i	−0.126694	−	0.219440i
$829$	−13.2097	+	22.8798i	−0.458791	+	0.794650i	−0.998897	−	0.0469470i	$-0.985051\pi$
$829$	−13.2097	+	22.8798i	−0.458791	+	0.794650i	0.540106	+	0.841597i	$0.318384\pi$
$830$	−22.4172	+	38.8277i	−0.778111	+	1.34773i
$831$	30.2425	+	52.3815i	1.04910	+	1.81709i
$832$	0.932540			0.0323300
$833$	−37.4647	−	23.9244i	−1.29807	−	0.828931i
$834$	25.2082			0.872889
$835$	9.14615	+	15.8416i	0.316516	+	0.548221i
$836$	8.19870	−	14.2006i	0.283558	−	0.491137i
$837$	10.5472	−	18.2683i	0.364566	−	0.631447i
$838$	−0.352347	−	0.610282i	−0.0121716	−	0.0210819i
$839$	9.35546			0.322986			0.161493	−	0.986874i	$-0.448369\pi$
$839$	9.35546			0.322986			0.161493	+	0.986874i	$0.448369\pi$
$840$	21.1162	+	22.0821i	0.728578	+	0.761904i
$841$	−2.57489			−0.0887894
$842$	−5.12041	−	8.86882i	−0.176461	−	0.305640i
$843$	19.4366	−	33.6652i	0.669433	−	1.15949i
$844$	−0.982052	+	1.70096i	−0.0338036	+	0.0585496i
$845$	−21.8334	−	37.8165i	−0.751091	−	1.30093i
$846$	−52.9857			−1.82169
$847$	4.20771	−	14.4071i	0.144579	−	0.495034i
$848$	0.424408			0.0145742
$849$	−21.1876	−	36.6981i	−0.727158	−	1.25947i
$850$	−25.2693	+	43.7678i	−0.866731	+	1.50122i
$851$	−0.528647	+	0.915643i	−0.0181218	+	0.0313878i
$852$	−9.35246	−	16.1989i	−0.320410	−	0.554966i
$853$	−31.8348			−1.09000			−0.545001	−	0.838435i	$-0.683471\pi$
$853$	−31.8348			−1.09000			−0.545001	+	0.838435i	$0.683471\pi$
$854$	−30.1574	+	7.36226i	−1.03197	+	0.251931i
$855$	−105.402			−3.60467
$856$	−3.51297	−	6.08465i	−0.120071	−	0.207969i
$857$	10.7230	−	18.5728i	0.366292	−	0.634436i	−0.622691	−	0.782468i	$-0.713961\pi$
$857$	10.7230	−	18.5728i	0.366292	−	0.634436i	0.988983	+	0.148032i	$0.0472938\pi$
$858$	−6.10768	+	10.5788i	−0.208513	+	0.361155i
$859$	−13.3164	−	23.0647i	−0.454350	−	0.786958i	0.544300	−	0.838891i	$-0.316795\pi$
$859$	−13.3164	−	23.0647i	−0.454350	−	0.786958i	−0.998651	+	0.0519325i	$0.983462\pi$
$860$	−1.91628			−0.0653445
$861$	−20.7500	+	5.06564i	−0.707157	+	0.172637i
$862$	−32.9490			−1.12225
$863$	−20.2714	−	35.1110i	−0.690045	−	1.19519i	−0.971823	−	0.235714i	$-0.924257\pi$
$863$	−20.2714	−	35.1110i	−0.690045	−	1.19519i	0.281777	−	0.959480i	$-0.409076\pi$
$864$	6.88314	−	11.9219i	0.234169	−	0.405593i
$865$	−21.6436	+	37.4877i	−0.735903	+	1.27462i
$866$	−12.3617	−	21.4112i	−0.420069	−	0.727581i
$867$	−74.8300			−2.54136
$868$	1.13657	−	3.89159i	0.0385777	−	0.132089i
$869$	14.5637			0.494039
$870$	29.6817	+	51.4103i	1.00631	+	1.74297i
$871$	2.21894	−	3.84331i	0.0751858	−	0.130226i
$872$	6.36508	−	11.0246i	0.215549	−	0.373341i
$873$	−59.9410	−	103.821i	−2.02870	−	3.51381i
$874$	4.01578			0.135836
$875$	−19.4739	−	20.3646i	−0.658336	−	0.688449i
$876$	36.5628			1.23534
$877$	11.0378	+	19.1180i	0.372719	+	0.645568i	0.989983	−	0.141188i	$-0.0450923\pi$
$877$	11.0378	+	19.1180i	0.372719	+	0.645568i	−0.617264	+	0.786756i	$0.711759\pi$
$878$	7.30561	−	12.6537i	0.246552	−	0.427041i
$879$	23.8554	−	41.3187i	0.804622	−	1.39365i
$880$	−7.34941	−	12.7295i	−0.247748	−	0.429113i
$881$	−55.1259			−1.85724			−0.928619	−	0.371034i	$-0.879003\pi$
$881$	−55.1259			−1.85724			−0.928619	+	0.371034i	$0.879003\pi$
$882$	−43.0160	−	27.4694i	−1.44842	−	0.924943i
$883$	−1.32125			−0.0444638			−0.0222319	−	0.999753i	$-0.507077\pi$
$883$	−1.32125			−0.0444638			−0.0222319	+	0.999753i	$0.507077\pi$
$884$	−2.96095	−	5.12851i	−0.0995874	−	0.172490i
$885$	4.44068	−	7.69148i	0.149272	−	0.258546i
$886$	10.6276	−	18.4075i	0.357040	−	0.618411i
$887$	11.3116	+	19.5923i	0.379806	+	0.657844i	0.991034	−	0.133611i	$-0.0426573\pi$
$887$	11.3116	+	19.5923i	0.379806	+	0.657844i	−0.611227	+	0.791455i	$0.709324\pi$
$888$	−3.39179			−0.113821
$889$	12.7559	+	13.3394i	0.427821	+	0.447389i
$890$	39.5354			1.32523
$891$	45.5045	+	78.8162i	1.52446	+	2.64044i
$892$	−3.50333	+	6.06795i	−0.117300	+	0.203170i
$893$	14.5914	−	25.2731i	0.488283	−	0.845732i
$894$	−16.7905	−	29.0820i	−0.561557	−	0.972646i
$895$	28.7617			0.961398
$896$	0.741726	−	2.53965i	0.0247793	−	0.0848439i
$897$	−2.99158			−0.0998861
$898$	15.0280	+	26.0292i	0.501491	+	0.868607i
$899$	3.93850	−	6.82168i	0.131356	−	0.227516i
$900$	−29.0136	+	50.2531i	−0.967121	+	1.67510i
$901$	−1.34755	−	2.33403i	−0.0448936	−	0.0777579i
$902$	10.2757			0.342143
$903$	4.38928	−	1.07154i	0.146066	−	0.0356588i
$904$	−6.27371			−0.208660
$905$	0.945748	+	1.63808i	0.0314377	+	0.0544517i
$906$	8.39320	−	14.5375i	0.278845	−	0.482974i
$907$	−5.84787	+	10.1288i	−0.194175	+	0.336321i	−0.946630	−	0.322323i	$-0.895536\pi$
$907$	−5.84787	+	10.1288i	−0.194175	+	0.336321i	0.752455	+	0.658644i	$0.228870\pi$
$908$	12.5699	+	21.7716i	0.417145	+	0.722517i
$909$	124.714			4.13650
$910$	8.62825	−	2.10640i	0.286024	−	0.0698263i
$911$	−24.2629			−0.803867			−0.401933	−	0.915669i	$-0.631662\pi$
$911$	−24.2629			−0.803867			−0.401933	+	0.915669i	$0.631662\pi$
$912$	6.44131	+	11.1567i	0.213293	+	0.369434i
$913$	−25.4278	+	44.0422i	−0.841537	+	1.45758i
$914$	−1.48247	+	2.56771i	−0.0490357	+	0.0849323i
$915$	−67.7480	−	117.343i	−2.23968	−	3.87924i
$916$	−15.8424			−0.523447
$917$	−6.24860	+	21.3951i	−0.206347	+	0.706528i
$918$	−87.4197			−2.88528
$919$	10.6854	+	18.5077i	0.352479	+	0.610512i	0.986683	−	0.162654i	$-0.0520053\pi$
$919$	10.6854	+	18.5077i	0.352479	+	0.610512i	−0.634204	+	0.773166i	$0.718672\pi$
$920$	1.79990	−	3.11751i	0.0593408	−	0.102781i
$921$	−17.1102	+	29.6358i	−0.563802	+	0.976533i
$922$	8.08043	+	13.9957i	0.266115	+	0.460925i
$923$	−5.43737			−0.178973
$924$	23.9521	+	25.0477i	0.787967	+	0.824009i
$925$	8.41446			0.276666
$926$	16.0915	+	27.8713i	0.528799	+	0.915907i
$927$	49.2131	−	85.2395i	1.61637	−	2.79963i
$928$	2.57027	−	4.45183i	0.0843732	−	0.146139i
$929$	−3.27342	−	5.66973i	−0.107397	−	0.186018i	0.807318	−	0.590117i	$-0.200918\pi$
$929$	−3.27342	−	5.66973i	−0.107397	−	0.186018i	−0.914715	+	0.404099i	$0.867585\pi$
$930$	17.6955			0.580259
$931$	24.9483	−	12.9531i	0.817646	−	0.424521i
$932$	5.12497			0.167874
$933$	−27.1271	−	46.9856i	−0.888103	−	1.53824i
$934$	1.84930	−	3.20308i	0.0605109	−	0.104808i
$935$	−46.6708	+	80.8362i	−1.52630	+	2.64363i
$936$	−3.39969	−	5.88843i	−0.111122	−	0.192469i
$937$	42.1077			1.37560			0.687799	−	0.725902i	$-0.258577\pi$
$937$	42.1077			1.37560			0.687799	+	0.725902i	$0.258577\pi$
$938$	−8.70186	−	9.09989i	−0.284126	−	0.297122i
$939$	−84.8126			−2.76775
$940$	−13.0799	−	22.6551i	−0.426620	−	0.738927i
$941$	6.43587	−	11.1473i	0.209803	−	0.363390i	−0.741849	−	0.670567i	$-0.766051\pi$
$941$	6.43587	−	11.1473i	0.209803	−	0.363390i	0.951653	+	0.307177i	$0.0993843\pi$
$942$	−31.5806	+	54.6991i	−1.02895	+	1.78219i
$943$	1.25827	+	2.17939i	0.0409750	+	0.0709708i
$944$	−0.769075			−0.0250312
$945$	36.7567	−	125.854i	1.19570	−	4.09404i
$946$	−2.17363			−0.0706709
$947$	12.1418	+	21.0302i	0.394556	+	0.683390i	0.993044	−	0.117741i	$-0.0375652\pi$
$947$	12.1418	+	21.0302i	0.394556	+	0.683390i	−0.598489	+	0.801131i	$0.704232\pi$
$948$	−5.72097	+	9.90901i	−0.185808	+	0.321830i
$949$	5.31427	−	9.20458i	0.172508	−	0.298793i
$950$	−15.9798	−	27.6778i	−0.518452	−	0.897986i
$951$	−68.1911			−2.21125
$952$	−16.3219	+	3.98463i	−0.528997	+	0.129143i
$953$	6.91655			0.224049			0.112025	−	0.993705i	$-0.464266\pi$
$953$	6.91655			0.224049			0.112025	+	0.993705i	$0.464266\pi$
$954$	−1.54723	−	2.67988i	−0.0500934	−	0.0867643i
$955$	−8.88349	+	15.3867i	−0.287463	+	0.497900i
$956$	6.60347	−	11.4376i	0.213572	−	0.369917i
$957$	33.6680	+	58.3147i	1.08833	+	1.88505i
$958$	−37.5565			−1.21340
$959$	−27.7389	+	6.77183i	−0.895736	+	0.218674i
$960$	11.5481			0.372714
$961$	14.3260	+	24.8133i	0.462128	+	0.800430i
$962$	−0.492984	+	0.853874i	−0.0158945	+	0.0275300i
$963$	−25.6139	+	44.3646i	−0.825397	+	1.42963i
$964$	−13.8311	−	23.9562i	−0.445470	−	0.771577i
$965$	31.4073			1.01104
$966$	−2.37945	+	8.14720i	−0.0765577	+	0.262132i
$967$	18.2218			0.585972			0.292986	−	0.956117i	$-0.405351\pi$
$967$	18.2218			0.585972			0.292986	+	0.956117i	$0.405351\pi$
$968$	−2.83643	−	4.91285i	−0.0911664	−	0.157905i
$969$	40.9041	−	70.8480i	1.31403	−	2.27597i
$970$	29.5938	−	51.2579i	0.950199	−	1.64579i
$971$	24.2880	+	42.0681i	0.779439	+	1.35003i	0.932265	+	0.361776i	$0.117829\pi$
$971$	24.2880	+	42.0681i	0.779439	+	1.35003i	−0.152826	+	0.988253i	$0.548837\pi$
$972$	−30.2024			−0.968742
$973$	−14.3686	−	15.0258i	−0.460635	−	0.481705i
$974$	−17.7566			−0.568958
$975$	11.9042	+	20.6188i	0.381241	+	0.660329i
$976$	−5.86659	+	10.1612i	−0.187785	+	0.325253i
$977$	13.8576	−	24.0022i	0.443345	−	0.767897i	−0.554590	−	0.832124i	$-0.687125\pi$
$977$	13.8576	−	24.0022i	0.443345	−	0.767897i	0.997935	+	0.0642270i	$0.0204582\pi$
$978$	24.0167	+	41.5981i	0.767968	+	1.33016i
$979$	44.8450			1.43325
$980$	1.12626	−	25.1733i	0.0359772	−	0.804133i
$981$	−92.8186			−2.96347
$982$	−3.46897	−	6.00843i	−0.110699	−	0.191737i
$983$	7.51872	−	13.0228i	0.239810	−	0.415363i	−0.720850	−	0.693091i	$-0.756248\pi$
$983$	7.51872	−	13.0228i	0.239810	−	0.415363i	0.960660	+	0.277728i	$0.0895815\pi$
$984$	−4.03654	+	6.99149i	−0.128680	+	0.222881i
$985$	−25.6329	−	44.3974i	−0.816731	−	1.41462i
$986$	−32.6439			−1.03959
$987$	42.6281	+	44.5780i	1.35687	+	1.41893i
$988$	3.74488			0.119140
$989$	−0.266165	−	0.461011i	−0.00846355	−	0.0146593i
$990$	−53.5863	+	92.8142i	−1.70308	+	2.94983i
$991$	−23.4463	+	40.6101i	−0.744795	+	1.29002i	0.205496	+	0.978658i	$0.434119\pi$
$991$	−23.4463	+	40.6101i	−0.744795	+	1.29002i	−0.950291	+	0.311365i	$0.899214\pi$
$992$	−0.766165	−	1.32704i	−0.0243258	−	0.0421335i
$993$	77.4567			2.45801
$994$	−4.32479	+	14.8080i	−0.137174	+	0.469681i
$995$	49.3891			1.56574
$996$	−19.9773	−	34.6017i	−0.633006	−	1.09640i
$997$	−10.5901	+	18.3426i	−0.335391	+	0.580915i	−0.983560	−	0.180582i	$-0.942202\pi$
$997$	−10.5901	+	18.3426i	−0.335391	+	0.580915i	0.648169	+	0.761497i	$0.275535\pi$
$998$	2.79593	−	4.84269i	0.0885036	−	0.153293i
$999$	7.27750	+	12.6050i	0.230250	+	0.398804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.e.b.277.4	yes	8
7.2	even	3	inner	322.2.e.b.93.4	✓	8
7.3	odd	6		2254.2.a.ba.1.4		4
7.4	even	3		2254.2.a.w.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.e.b.93.4	✓	8	7.2	even	3	inner
322.2.e.b.277.4	yes	8	1.1	even	1	trivial
2254.2.a.w.1.1		4	7.4	even	3
2254.2.a.ba.1.4		4	7.3	odd	6

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.60400 - 2.77821i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.79990 + 3.11751i) q^{5} -3.20800 q^{6} +(1.82854 + 1.91218i) q^{7} +1.00000 q^{8} +(-3.64562 - 6.31440i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.60400 - 2.77821i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.79990 + 3.11751i) q^{5} -3.20800 q^{6} +(1.82854 + 1.91218i) q^{7} +1.00000 q^{8} +(-3.64562 - 6.31440i) q^{9} +(1.79990 - 3.11751i) q^{10} +(2.04162 - 3.53619i) q^{11} +(1.60400 + 2.77821i) q^{12} +0.932540 q^{13} +(0.741726 - 2.53965i) q^{14} +11.5481 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.17514 + 5.49951i) q^{17} +(-3.64562 + 6.31440i) q^{18} +(-2.00789 - 3.47777i) q^{19} -3.59979 q^{20} +(8.24541 - 2.01293i) q^{21} -4.08324 q^{22} +(-0.500000 - 0.866025i) q^{23} +(1.60400 - 2.77821i) q^{24} +(-3.97924 + 6.89225i) q^{25} +(-0.466270 - 0.807603i) q^{26} -13.7663 q^{27} +(-2.57027 + 0.627473i) q^{28} -5.14054 q^{29} +(-5.77406 - 10.0010i) q^{30} +(-0.766165 + 1.32704i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-6.54951 - 11.3441i) q^{33} +6.35028 q^{34} +(-2.67006 + 9.14222i) q^{35} +7.29124 q^{36} +(-0.528647 - 0.915643i) q^{37} +(-2.00789 + 3.47777i) q^{38} +(1.49579 - 2.59079i) q^{39} +(1.79990 + 3.11751i) q^{40} -2.51655 q^{41} +(-5.86595 - 6.13427i) q^{42} +0.532330 q^{43} +(2.04162 + 3.53619i) q^{44} +(13.1235 - 22.7305i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(3.63352 + 6.29344i) q^{47} -3.20800 q^{48} +(-0.312869 + 6.99300i) q^{49} +7.95849 q^{50} +(10.1858 + 17.6424i) q^{51} +(-0.466270 + 0.807603i) q^{52} +(-0.212204 + 0.367548i) q^{53} +(6.88314 + 11.9219i) q^{54} +14.6988 q^{55} +(1.82854 + 1.91218i) q^{56} -12.8826 q^{57} +(2.57027 + 4.45183i) q^{58} +(0.384537 - 0.666038i) q^{59} +(-5.77406 + 10.0010i) q^{60} +(-5.86659 - 10.1612i) q^{61} +1.53233 q^{62} +(5.40810 - 18.5172i) q^{63} +1.00000 q^{64} +(1.67847 + 2.90720i) q^{65} +(-6.54951 + 11.3441i) q^{66} +(2.37945 - 4.12134i) q^{67} +(-3.17514 - 5.49951i) q^{68} -3.20800 q^{69} +(9.25242 - 2.25877i) q^{70} -5.83072 q^{71} +(-3.64562 - 6.31440i) q^{72} +(5.69870 - 9.87045i) q^{73} +(-0.528647 + 0.915643i) q^{74} +(12.7654 + 22.1103i) q^{75} +4.01578 q^{76} +(10.4950 - 2.56213i) q^{77} -2.99158 q^{78} +(1.78335 + 3.08885i) q^{79} +(1.79990 - 3.11751i) q^{80} +(-11.1442 + 19.3024i) q^{81} +(1.25827 + 2.17939i) q^{82} -12.4547 q^{83} +(-2.37945 + 8.14720i) q^{84} -22.8597 q^{85} +(-0.266165 - 0.461011i) q^{86} +(-8.24541 + 14.2815i) q^{87} +(2.04162 - 3.53619i) q^{88} +(5.49134 + 9.51129i) q^{89} -26.2469 q^{90} +(1.70519 + 1.78318i) q^{91} +1.00000 q^{92} +(2.45785 + 4.25713i) q^{93} +(3.63352 - 6.29344i) q^{94} +(7.22799 - 12.5192i) q^{95} +(1.60400 + 2.77821i) q^{96} +16.4419 q^{97} +(6.21255 - 3.22555i) q^{98} -29.7719 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 5 q^{3} - 4 q^{4} + 5 q^{5} - 10 q^{6} + q^{7} + 8 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 + 5 * q^5 - 10 * q^6 + q^7 + 8 * q^8 - 7 * q^9	\( 8 q - 4 q^{2} + 5 q^{3} - 4 q^{4} + 5 q^{5} - 10 q^{6} + q^{7} + 8 q^{8} - 7 q^{9} + 5 q^{10} + 2 q^{11} + 5 q^{12} - 14 q^{13} + q^{14} + 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{18} + 9 q^{19} - 10 q^{20} + 25 q^{21} - 4 q^{22} - 4 q^{23} + 5 q^{24} - 11 q^{25} + 7 q^{26} - 34 q^{27} - 2 q^{28} - 4 q^{29} - q^{30} + 14 q^{31} - 4 q^{32} - 13 q^{33} + 6 q^{34} + 16 q^{35} + 14 q^{36} + 9 q^{38} + q^{39} + 5 q^{40} - 30 q^{41} - 8 q^{42} - 36 q^{43} + 2 q^{44} + 11 q^{45} - 4 q^{46} + 21 q^{47} - 10 q^{48} + 17 q^{49} + 22 q^{50} - 6 q^{51} + 7 q^{52} + 3 q^{53} + 17 q^{54} + 20 q^{55} + q^{56} - 18 q^{57} + 2 q^{58} + 16 q^{59} - q^{60} + q^{61} - 28 q^{62} + 37 q^{63} + 8 q^{64} - 2 q^{65} - 13 q^{66} + 17 q^{67} - 3 q^{68} - 10 q^{69} + 4 q^{70} - 2 q^{71} - 7 q^{72} + 4 q^{73} + 22 q^{75} - 18 q^{76} + 13 q^{77} - 2 q^{78} - 5 q^{79} + 5 q^{80} - 16 q^{81} + 15 q^{82} - 8 q^{83} - 17 q^{84} - 108 q^{85} + 18 q^{86} - 25 q^{87} + 2 q^{88} + 9 q^{89} - 22 q^{90} + 38 q^{91} + 8 q^{92} - 13 q^{93} + 21 q^{94} + 3 q^{95} + 5 q^{96} + 80 q^{97} + 2 q^{98} - 82 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 + 5 * q^5 - 10 * q^6 + q^7 + 8 * q^8 - 7 * q^9 + 5 * q^10 + 2 * q^11 + 5 * q^12 - 14 * q^13 + q^14 + 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^18 + 9 * q^19 - 10 * q^20 + 25 * q^21 - 4 * q^22 - 4 * q^23 + 5 * q^24 - 11 * q^25 + 7 * q^26 - 34 * q^27 - 2 * q^28 - 4 * q^29 - q^30 + 14 * q^31 - 4 * q^32 - 13 * q^33 + 6 * q^34 + 16 * q^35 + 14 * q^36 + 9 * q^38 + q^39 + 5 * q^40 - 30 * q^41 - 8 * q^42 - 36 * q^43 + 2 * q^44 + 11 * q^45 - 4 * q^46 + 21 * q^47 - 10 * q^48 + 17 * q^49 + 22 * q^50 - 6 * q^51 + 7 * q^52 + 3 * q^53 + 17 * q^54 + 20 * q^55 + q^56 - 18 * q^57 + 2 * q^58 + 16 * q^59 - q^60 + q^61 - 28 * q^62 + 37 * q^63 + 8 * q^64 - 2 * q^65 - 13 * q^66 + 17 * q^67 - 3 * q^68 - 10 * q^69 + 4 * q^70 - 2 * q^71 - 7 * q^72 + 4 * q^73 + 22 * q^75 - 18 * q^76 + 13 * q^77 - 2 * q^78 - 5 * q^79 + 5 * q^80 - 16 * q^81 + 15 * q^82 - 8 * q^83 - 17 * q^84 - 108 * q^85 + 18 * q^86 - 25 * q^87 + 2 * q^88 + 9 * q^89 - 22 * q^90 + 38 * q^91 + 8 * q^92 - 13 * q^93 + 21 * q^94 + 3 * q^95 + 5 * q^96 + 80 * q^97 + 2 * q^98 - 82 * q^99

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