LMFDB - Embedded newform 85.2.l.a.66.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(26,85)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("85.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.l (of order $8$, 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:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			66.6
Character	$\chi$	$=$	85.66
Dual form			85.2.l.a.76.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.86672 + 1.86672i) q^{2} +(-0.811501 - 1.95914i) q^{3} +4.96928i q^{4} +(0.923880 - 0.382683i) q^{5} +(2.14231 - 5.17200i) q^{6} +(-3.75274 - 1.55444i) q^{7} +(-5.54282 + 5.54282i) q^{8} +(-1.05836 + 1.05836i) q^{9} +(2.43899 + 1.01026i) q^{10} +(-0.669316 + 1.61587i) q^{11} +(9.73550 - 4.03258i) q^{12} -1.67715i q^{13} +(-4.10362 - 9.90701i) q^{14} +(-1.49946 - 1.49946i) q^{15} -10.7552 q^{16} +(4.08018 + 0.593395i) q^{17} -3.95133 q^{18} +(-0.176096 - 0.176096i) q^{19} +(1.90166 + 4.59102i) q^{20} +8.61356i q^{21} +(-4.26580 + 1.76695i) q^{22} +(-0.198886 + 0.480154i) q^{23} +(15.3571 + 6.36113i) q^{24} +(0.707107 - 0.707107i) q^{25} +(3.13077 - 3.13077i) q^{26} +(-2.94507 - 1.21989i) q^{27} +(7.72443 - 18.6484i) q^{28} +(0.449816 - 0.186320i) q^{29} -5.59814i q^{30} +(3.64713 + 8.80495i) q^{31} +(-8.99131 - 8.99131i) q^{32} +3.70886 q^{33} +(6.50885 + 8.72426i) q^{34} -4.06194 q^{35} +(-5.25930 - 5.25930i) q^{36} +(1.63395 + 3.94470i) q^{37} -0.657443i q^{38} +(-3.28577 + 1.36101i) q^{39} +(-2.99975 + 7.24204i) q^{40} +(-4.88624 - 2.02395i) q^{41} +(-16.0791 + 16.0791i) q^{42} +(-2.24825 + 2.24825i) q^{43} +(-8.02972 - 3.32602i) q^{44} +(-0.572782 + 1.38282i) q^{45} +(-1.26758 + 0.525048i) q^{46} -6.26212i q^{47} +(8.72786 + 21.0709i) q^{48} +(6.71704 + 6.71704i) q^{49} +2.63994 q^{50} +(-2.14853 - 8.47517i) q^{51} +8.33425 q^{52} +(-7.24333 - 7.24333i) q^{53} +(-3.22043 - 7.77481i) q^{54} +1.74901i q^{55} +(29.4167 - 12.1848i) q^{56} +(-0.202094 + 0.487898i) q^{57} +(1.18749 + 0.491874i) q^{58} +(8.20143 - 8.20143i) q^{59} +(7.45123 - 7.45123i) q^{60} +(-4.02196 - 1.66595i) q^{61} +(-9.62820 + 23.2445i) q^{62} +(5.61692 - 2.32660i) q^{63} -12.0581i q^{64} +(-0.641819 - 1.54949i) q^{65} +(6.92340 + 6.92340i) q^{66} +9.73489 q^{67} +(-2.94875 + 20.2756i) q^{68} +1.10208 q^{69} +(-7.58250 - 7.58250i) q^{70} +(-0.384985 - 0.929437i) q^{71} -11.7326i q^{72} +(2.69318 - 1.11555i) q^{73} +(-4.31353 + 10.4138i) q^{74} +(-1.95914 - 0.811501i) q^{75} +(0.875070 - 0.875070i) q^{76} +(5.02354 - 5.02354i) q^{77} +(-8.67424 - 3.59299i) q^{78} +(2.60922 - 6.29920i) q^{79} +(-9.93651 + 4.11584i) q^{80} +11.2500i q^{81} +(-5.34310 - 12.8994i) q^{82} +(-2.26046 - 2.26046i) q^{83} -42.8032 q^{84} +(3.99668 - 1.01319i) q^{85} -8.39371 q^{86} +(-0.730053 - 0.730053i) q^{87} +(-5.24658 - 12.6664i) q^{88} +3.30525i q^{89} +(-3.65055 + 1.51211i) q^{90} +(-2.60703 + 6.29392i) q^{91} +(-2.38602 - 0.988323i) q^{92} +(14.2904 - 14.2904i) q^{93} +(11.6896 - 11.6896i) q^{94} +(-0.230080 - 0.0953024i) q^{95} +(-10.3188 + 24.9117i) q^{96} +(1.57147 - 0.650923i) q^{97} +25.0777i q^{98} +(-1.00180 - 2.41856i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35}+ \cdots - 8 q^{99}+O(q^{100}) $ 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 + 24 * q^12 - 8 * q^15 - 24 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 32 * q^22 - 16 * q^23 - 8 * q^24 + 16 * q^26 + 24 * q^27 + 48 * q^28 - 8 * q^29 + 16 * q^34 - 32 * q^35 - 24 * q^36 + 24 * q^37 + 8 * q^39 + 16 * q^40 + 16 * q^41 - 24 * q^42 + 8 * q^43 + 16 * q^44 + 16 * q^45 + 8 * q^46 + 80 * q^48 + 8 * q^50 - 56 * q^51 - 48 * q^52 + 24 * q^53 - 32 * q^54 + 64 * q^56 + 32 * q^57 - 64 * q^58 + 32 * q^59 + 24 * q^60 + 32 * q^61 - 32 * q^62 - 56 * q^63 + 8 * q^65 + 96 * q^66 + 16 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^75 - 8 * q^76 + 24 * q^77 - 112 * q^78 - 32 * q^80 - 80 * q^82 - 96 * q^83 - 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 + 80 * q^92 + 64 * q^93 + 56 * q^94 - 16 * q^95 - 168 * q^96 - 40 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	1.86672	+	1.86672i	1.31997	+	1.31997i	0.913796	+	0.406174i	$0.133137\pi$
$2$	1.86672	+	1.86672i	1.31997	+	1.31997i	0.406174	+	0.913796i	$0.366863\pi$
$3$	−0.811501	−	1.95914i	−0.468520	−	1.13111i	−0.964809	−	0.262951i	$-0.915304\pi$
$3$	−0.811501	−	1.95914i	−0.468520	−	1.13111i	0.496289	−	0.868157i	$-0.334696\pi$
$4$			4.96928i			2.48464i
$5$	0.923880	−	0.382683i	0.413171	−	0.171141i
$5$	0.923880	−	0.382683i	0.413171	−	0.171141i
$6$	2.14231	−	5.17200i	0.874596	−	2.11146i
$7$	−3.75274	−	1.55444i	−1.41840	−	0.587522i	−0.463944	−	0.885865i	$-0.653566\pi$
$7$	−3.75274	−	1.55444i	−1.41840	−	0.587522i	−0.954459	+	0.298343i	$0.903566\pi$
$8$	−5.54282	+	5.54282i	−1.95968	+	1.95968i
$9$	−1.05836	+	1.05836i	−0.352787	+	0.352787i
$10$	2.43899	+	1.01026i	0.771275	+	0.319473i
$11$	−0.669316	+	1.61587i	−0.201806	+	0.487203i	−0.992089	−	0.125539i	$-0.959934\pi$
$11$	−0.669316	+	1.61587i	−0.201806	+	0.487203i	0.790282	+	0.612743i	$0.209934\pi$
$12$	9.73550	−	4.03258i	2.81040	−	1.16410i
$13$		−	1.67715i		−	0.465159i	−0.972577	−	0.232579i	$-0.925283\pi$
$13$		−	1.67715i		−	0.465159i	0.972577	−	0.232579i	$-0.0747165\pi$
$14$	−4.10362	−	9.90701i	−1.09674	−	2.64776i
$15$	−1.49946	−	1.49946i	−0.387158	−	0.387158i
$16$	−10.7552			−2.68880
$17$	4.08018	+	0.593395i	0.989589	+	0.143920i
$17$	4.08018	+	0.593395i	0.989589	+	0.143920i
$18$	−3.95133			−0.931338
$19$	−0.176096	−	0.176096i	−0.0403992	−	0.0403992i	0.686619	−	0.727018i	$-0.259094\pi$
$19$	−0.176096	−	0.176096i	−0.0403992	−	0.0403992i	−0.727018	+	0.686619i	$0.759094\pi$
$20$	1.90166	+	4.59102i	0.425225	+	1.02658i
$21$			8.61356i			1.87963i
$22$	−4.26580	+	1.76695i	−0.909472	+	0.376716i
$23$	−0.198886	+	0.480154i	−0.0414707	+	0.100119i	−0.943258	−	0.332062i	$-0.892256\pi$
$23$	−0.198886	+	0.480154i	−0.0414707	+	0.100119i	0.901787	+	0.432181i	$0.142256\pi$
$24$	15.3571	+	6.36113i	3.13476	+	1.29846i
$25$	0.707107	−	0.707107i	0.141421	−	0.141421i
$26$	3.13077	−	3.13077i	0.613995	−	0.613995i
$27$	−2.94507	−	1.21989i	−0.566779	−	0.234768i
$28$	7.72443	−	18.6484i	1.45978	−	3.52422i
$29$	0.449816	−	0.186320i	0.0835288	−	0.0345988i	−0.340528	−	0.940234i	$-0.610606\pi$
$29$	0.449816	−	0.186320i	0.0835288	−	0.0345988i	0.424057	+	0.905636i	$0.360606\pi$
$30$		−	5.59814i		−	1.02208i
$31$	3.64713	+	8.80495i	0.655043	+	1.58141i	0.805366	+	0.592778i	$0.201969\pi$
$31$	3.64713	+	8.80495i	0.655043	+	1.58141i	−0.150323	+	0.988637i	$0.548031\pi$
$32$	−8.99131	−	8.99131i	−1.58945	−	1.58945i
$33$	3.70886			0.645630
$34$	6.50885	+	8.72426i	1.11626	+	1.49620i
$35$	−4.06194			−0.686593
$36$	−5.25930	−	5.25930i	−0.876550	−	0.876550i
$37$	1.63395	+	3.94470i	0.268620	+	0.648505i	0.999419	−	0.0340875i	$-0.0108525\pi$
$37$	1.63395	+	3.94470i	0.268620	+	0.648505i	−0.730799	+	0.682592i	$0.760852\pi$
$38$		−	0.657443i		−	0.106651i
$39$	−3.28577	+	1.36101i	−0.526145	+	0.217936i
$40$	−2.99975	+	7.24204i	−0.474302	+	1.14507i
$41$	−4.88624	−	2.02395i	−0.763103	−	0.316087i	−0.0330276	−	0.999454i	$-0.510515\pi$
$41$	−4.88624	−	2.02395i	−0.763103	−	0.316087i	−0.730075	+	0.683367i	$0.760515\pi$
$42$	−16.0791	+	16.0791i	−2.48106	+	2.48106i
$43$	−2.24825	+	2.24825i	−0.342855	+	0.342855i	−0.857440	−	0.514584i	$-0.827946\pi$
$43$	−2.24825	+	2.24825i	−0.342855	+	0.342855i	0.514584	+	0.857440i	$0.327946\pi$
$44$	−8.02972	−	3.32602i	−1.21053	−	0.501416i
$45$	−0.572782	+	1.38282i	−0.0853852	+	0.206138i
$46$	−1.26758	+	0.525048i	−0.186894	+	0.0774141i
$47$		−	6.26212i		−	0.913423i	−0.889615	−	0.456712i	$-0.849027\pi$
$47$		−	6.26212i		−	0.913423i	0.889615	−	0.456712i	$-0.150973\pi$
$48$	8.72786	+	21.0709i	1.25976	+	3.04132i
$49$	6.71704	+	6.71704i	0.959578	+	0.959578i
$50$	2.63994			0.373344
$51$	−2.14853	−	8.47517i	−0.300854	−	1.18676i
$52$	8.33425			1.15575
$53$	−7.24333	−	7.24333i	−0.994948	−	0.994948i	0.00503923	−	0.999987i	$-0.498396\pi$
$53$	−7.24333	−	7.24333i	−0.994948	−	0.994948i	−0.999987	+	0.00503923i	$0.998396\pi$
$54$	−3.22043	−	7.77481i	−0.438245	−	1.05802i
$55$			1.74901i			0.235836i
$56$	29.4167	−	12.1848i	3.93097	−	1.62826i
$57$	−0.202094	+	0.487898i	−0.0267680	+	0.0646236i
$58$	1.18749	+	0.491874i	0.155925	+	0.0645862i
$59$	8.20143	−	8.20143i	1.06773	−	1.06773i	0.0702021	−	0.997533i	$-0.477636\pi$
$59$	8.20143	−	8.20143i	1.06773	−	1.06773i	0.997533	−	0.0702021i	$-0.0223644\pi$
$60$	7.45123	−	7.45123i	0.961950	−	0.961950i
$61$	−4.02196	−	1.66595i	−0.514959	−	0.213303i	0.110042	−	0.993927i	$-0.464901\pi$
$61$	−4.02196	−	1.66595i	−0.514959	−	0.213303i	−0.625001	+	0.780624i	$0.714901\pi$
$62$	−9.62820	+	23.2445i	−1.22278	+	2.95206i
$63$	5.61692	−	2.32660i	0.707665	−	0.293124i
$64$		−	12.0581i		−	1.50726i
$65$	−0.641819	−	1.54949i	−0.0796078	−	0.192190i
$66$	6.92340	+	6.92340i	0.852212	+	0.852212i
$67$	9.73489			1.18931			0.594653	−	0.803982i	$-0.297289\pi$
$67$	9.73489			1.18931			0.594653	+	0.803982i	$0.297289\pi$
$68$	−2.94875	+	20.2756i	−0.357588	+	2.45877i
$69$	1.10208			0.132675
$70$	−7.58250	−	7.58250i	−0.906282	−	0.906282i
$71$	−0.384985	−	0.929437i	−0.0456894	−	0.110304i	0.899387	−	0.437153i	$-0.144013\pi$
$71$	−0.384985	−	0.929437i	−0.0456894	−	0.110304i	−0.945077	+	0.326849i	$0.894013\pi$
$72$		−	11.7326i		−	1.38270i
$73$	2.69318	−	1.11555i	0.315213	−	0.130565i	−0.219467	−	0.975620i	$-0.570432\pi$
$73$	2.69318	−	1.11555i	0.315213	−	0.130565i	0.534680	+	0.845054i	$0.320432\pi$
$74$	−4.31353	+	10.4138i	−0.501437	+	1.21058i
$75$	−1.95914	−	0.811501i	−0.226222	−	0.0937041i
$76$	0.875070	−	0.875070i	0.100377	−	0.100377i
$77$	5.02354	−	5.02354i	0.572485	−	0.572485i
$78$	−8.67424	−	3.59299i	−0.982164	−	0.406826i
$79$	2.60922	−	6.29920i	0.293560	−	0.708716i	−0.706440	−	0.707773i	$-0.749700\pi$
$79$	2.60922	−	6.29920i	0.293560	−	0.708716i	1.00000		0.000942651i	$-0.000300055\pi$
$80$	−9.93651	+	4.11584i	−1.11094	+	0.460165i
$81$			11.2500i			1.25000i
$82$	−5.34310	−	12.8994i	−0.590047	−	1.42450i
$83$	−2.26046	−	2.26046i	−0.248118	−	0.248118i	0.572080	−	0.820198i	$-0.306137\pi$
$83$	−2.26046	−	2.26046i	−0.248118	−	0.248118i	−0.820198	+	0.572080i	$0.806137\pi$
$84$	−42.8032			−4.67021
$85$	3.99668	−	1.01319i	0.433501	−	0.109896i
$86$	−8.39371			−0.905118
$87$	−0.730053	−	0.730053i	−0.0782699	−	0.0782699i
$88$	−5.24658	−	12.6664i	−0.559288	−	1.35024i
$89$			3.30525i			0.350356i	0.984537	+	0.175178i	$0.0560501\pi$
$89$			3.30525i			0.350356i	−0.984537	+	0.175178i	$0.943950\pi$
$90$	−3.65055	+	1.51211i	−0.384802	+	0.159390i
$91$	−2.60703	+	6.29392i	−0.273291	+	0.659782i
$92$	−2.38602	−	0.988323i	−0.248760	−	0.103040i
$93$	14.2904	−	14.2904i	1.48185	−	1.48185i
$94$	11.6896	−	11.6896i	1.20569	−	1.20569i
$95$	−0.230080	−	0.0953024i	−0.0236057	−	0.00977782i
$96$	−10.3188	+	24.9117i	−1.05315	+	2.54254i
$97$	1.57147	−	0.650923i	0.159558	−	0.0660912i	−0.301475	−	0.953474i	$-0.597479\pi$
$97$	1.57147	−	0.650923i	0.159558	−	0.0660912i	0.461033	+	0.887383i	$0.347479\pi$
$98$			25.0777i			2.53323i
$99$	−1.00180	−	2.41856i	−0.100685	−	0.243074i
$100$	3.51381	+	3.51381i	0.351381	+	0.351381i
$101$	−9.86464			−0.981569			−0.490784	−	0.871281i	$-0.663290\pi$
$101$	−9.86464			−0.981569			−0.490784	+	0.871281i	$0.663290\pi$
$102$	11.8101	−	19.8315i	1.16937	−	1.96361i
$103$	−14.0029			−1.37975			−0.689875	−	0.723928i	$-0.742335\pi$
$103$	−14.0029			−1.37975			−0.689875	+	0.723928i	$0.742335\pi$
$104$	9.29615	+	9.29615i	0.911563	+	0.911563i
$105$	3.29627	+	7.95789i	0.321683	+	0.776611i
$106$		−	27.0425i		−	2.62660i
$107$	12.4975	−	5.17664i	1.20818	−	0.500445i	0.314547	−	0.949242i	$-0.398147\pi$
$107$	12.4975	−	5.17664i	1.20818	−	0.500445i	0.893634	+	0.448797i	$0.148147\pi$
$108$	6.06197	−	14.6349i	0.583313	−	1.40824i
$109$	−5.88507	−	2.43767i	−0.563687	−	0.233487i	0.0825979	−	0.996583i	$-0.473678\pi$
$109$	−5.88507	−	2.43767i	−0.563687	−	0.233487i	−0.646285	+	0.763096i	$0.723678\pi$
$110$	−3.26490	+	3.26490i	−0.311296	+	0.311296i
$111$	6.40226	−	6.40226i	0.607675	−	0.607675i
$112$	40.3615	+	16.7183i	3.81380	+	1.57973i
$113$	−4.99721	+	12.0643i	−0.470098	+	1.13492i	0.494022	+	0.869450i	$0.335526\pi$
$113$	−4.99721	+	12.0643i	−0.470098	+	1.13492i	−0.964120	+	0.265468i	$0.914474\pi$
$114$	−1.28802	+	0.533516i	−0.120634	+	0.0499683i
$115$			0.519715i			0.0484637i
$116$	0.925877	+	2.23527i	0.0859655	+	0.207539i
$117$	1.77504	+	1.77504i	0.164102	+	0.164102i
$118$	30.6195			2.81876
$119$	−14.3895	−	8.56924i	−1.31908	−	0.785541i
$120$	16.6224			1.51741
$121$	5.61512	+	5.61512i	0.510465	+	0.510465i
$122$	−4.39801	−	10.6177i	−0.398177	−	0.961284i
$123$			11.2152i			1.01124i
$124$	−43.7543	+	18.1236i	−3.92925	+	1.62755i
$125$	0.382683	−	0.923880i	0.0342282	−	0.0826343i
$126$	14.8283	+	6.14209i	1.32101	+	0.547181i
$127$	−11.4130	+	11.4130i	−1.01274	+	1.01274i	−0.0128204	+	0.999918i	$0.504081\pi$
$127$	−11.4130	+	11.4130i	−1.01274	+	1.01274i	−0.999918	+	0.0128204i	$0.995919\pi$
$128$	4.52648	−	4.52648i	0.400088	−	0.400088i
$129$	6.22909	+	2.58018i	0.548441	+	0.227172i
$130$	1.69436	−	4.09055i	0.148605	−	0.358765i
$131$	14.5463	−	6.02526i	1.27091	−	0.526429i	0.357671	−	0.933848i	$-0.383571\pi$
$131$	14.5463	−	6.02526i	1.27091	−	0.526429i	0.913242	+	0.407418i	$0.133571\pi$
$132$			18.4304i			1.60416i
$133$	0.387112	+	0.934572i	0.0335669	+	0.0810376i
$134$	18.1723	+	18.1723i	1.56985	+	1.56985i
$135$	−3.18772			−0.274355
$136$	−25.9048	+	19.3266i	−2.22132	+	1.65724i
$137$	−15.5752			−1.33068			−0.665339	−	0.746541i	$-0.731713\pi$
$137$	−15.5752			−1.33068			−0.665339	+	0.746541i	$0.731713\pi$
$138$	2.05728	+	2.05728i	0.175127	+	0.175127i
$139$	−4.02615	−	9.71998i	−0.341493	−	0.824438i	−0.997565	−	0.0697396i	$-0.977783\pi$
$139$	−4.02615	−	9.71998i	−0.341493	−	0.824438i	0.656072	−	0.754698i	$-0.272217\pi$
$140$		−	20.1849i		−	1.70594i
$141$	−12.2683	+	5.08171i	−1.03318	+	0.427957i
$142$	1.01634	−	2.45366i	0.0852892	−	0.205906i
$143$	2.71006	+	1.12254i	0.226627	+	0.0938719i
$144$	11.3829	−	11.3829i	0.948575	−	0.948575i
$145$	0.344275	−	0.344275i	0.0285904	−	0.0285904i
$146$	7.10983	+	2.94499i	0.588414	+	0.243729i
$147$	7.70872	−	18.6105i	0.635804	−	1.53497i
$148$	−19.6023	+	8.11955i	−1.61130	+	0.667423i
$149$		−	7.79902i		−	0.638920i	−0.947600	−	0.319460i	$-0.896498\pi$
$149$		−	7.79902i		−	0.638920i	0.947600	−	0.319460i	$-0.103502\pi$
$150$	−2.14231	−	5.17200i	−0.174919	−	0.422292i
$151$	−2.66025	−	2.66025i	−0.216488	−	0.216488i	0.590529	−	0.807017i	$-0.298919\pi$
$151$	−2.66025	−	2.66025i	−0.216488	−	0.216488i	−0.807017	+	0.590529i	$0.798919\pi$
$152$	1.95213			0.158339
$153$	−4.94634	+	3.69028i	−0.399888	+	0.298342i
$154$	18.7551			1.51133
$155$	6.73901	+	6.73901i	0.541291	+	0.541291i
$156$	−6.76325	−	16.3279i	−0.541493	−	1.30728i
$157$			17.5226i			1.39846i	0.714898	+	0.699229i	$0.246473\pi$
$157$			17.5226i			1.39846i	−0.714898	+	0.699229i	$0.753527\pi$
$158$	16.6295	−	6.88817i	1.32297	−	0.547993i
$159$	−8.31271	+	20.0686i	−0.659240	+	1.59155i
$160$	−11.7477	−	4.86606i	−0.928739	−	0.384696i
$161$	1.49274	−	1.49274i	0.117644	−	0.117644i
$162$	−21.0006	+	21.0006i	−1.64996	+	1.64996i
$163$	14.9365	+	6.18688i	1.16991	+	0.484594i	0.881164	−	0.472811i	$-0.156761\pi$
$163$	14.9365	+	6.18688i	1.16991	+	0.484594i	0.288749	+	0.957405i	$0.406761\pi$
$164$	10.0576	−	24.2811i	0.785364	−	1.89604i
$165$	3.42654	−	1.41932i	0.266756	−	0.110494i
$166$		−	8.43930i		−	0.655017i
$167$	5.49382	+	13.2632i	0.425124	+	1.02634i	0.980813	+	0.194951i	$0.0624546\pi$
$167$	5.49382	+	13.2632i	0.425124	+	1.02634i	−0.555689	+	0.831390i	$0.687545\pi$
$168$	−47.7434	−	47.7434i	−3.68348	−	3.68348i
$169$	10.1872			0.783628
$170$	9.35202	+	5.56933i	0.717267	+	0.427148i
$171$	0.372746			0.0285046
$172$	−11.1722	−	11.1722i	−0.851873	−	0.851873i
$173$	−6.91876	−	16.7034i	−0.526024	−	1.26993i	−0.934109	−	0.356989i	$-0.883803\pi$
$173$	−6.91876	−	16.7034i	−0.526024	−	1.26993i	0.408085	−	0.912944i	$-0.366197\pi$
$174$		−	2.72561i		−	0.206628i
$175$	−3.75274	+	1.55444i	−0.283681	+	0.117504i
$176$	7.19863	−	17.3790i	0.542617	−	1.30999i
$177$	−22.7232	−	9.41225i	−1.70798	−	0.707468i
$178$	−6.16998	+	6.16998i	−0.462460	+	0.462460i
$179$	−5.31584	+	5.31584i	−0.397325	+	0.397325i	−0.877288	−	0.479964i	$-0.840650\pi$
$179$	−5.31584	+	5.31584i	−0.397325	+	0.397325i	0.479964	+	0.877288i	$0.340650\pi$
$180$	−6.87161	−	2.84631i	−0.512179	−	0.212152i
$181$	1.68148	−	4.05945i	0.124983	−	0.301737i	−0.848986	−	0.528415i	$-0.822787\pi$
$181$	1.68148	−	4.05945i	0.124983	−	0.301737i	0.973970	+	0.226678i	$0.0727866\pi$
$182$	−16.6156	+	6.88239i	−1.23163	+	0.510157i
$183$			9.23149i			0.682411i
$184$	−1.55902	−	3.76380i	−0.114932	−	0.277471i
$185$	3.01914	+	3.01914i	0.221972	+	0.221972i
$186$	53.3525			3.91199
$187$	−3.68978	+	6.19588i	−0.269823	+	0.453087i
$188$	31.1182			2.26953
$189$	9.15585	+	9.15585i	0.665990	+	0.665990i
$190$	−0.251593	−	0.607398i	−0.0182524	−	0.0440653i
$191$		−	5.03076i		−	0.364013i	−0.983297	−	0.182007i	$-0.941741\pi$
$191$		−	5.03076i		−	0.364013i	0.983297	−	0.182007i	$-0.0582592\pi$
$192$	−23.6235	+	9.78517i	−1.70488	+	0.706184i
$193$	−10.2895	+	24.8411i	−0.740656	+	1.78810i	−0.137461	+	0.990507i	$0.543894\pi$
$193$	−10.2895	+	24.8411i	−0.740656	+	1.78810i	−0.603194	+	0.797594i	$0.706106\pi$
$194$	4.14858	+	1.71840i	0.297850	+	0.123374i
$195$	−2.51482	+	2.51482i	−0.180090	+	0.180090i
$196$	−33.3789	+	33.3789i	−2.38421	+	2.38421i
$197$	7.86573	+	3.25809i	0.560410	+	0.232129i	0.644863	−	0.764298i	$-0.276914\pi$
$197$	7.86573	+	3.25809i	0.560410	+	0.232129i	−0.0844532	+	0.996427i	$0.526914\pi$
$198$	2.64469	−	6.38484i	0.187950	−	0.453751i
$199$	−15.4917	+	6.41688i	−1.09818	+	0.454881i	−0.856852	−	0.515563i	$-0.827583\pi$
$199$	−15.4917	+	6.41688i	−1.09818	+	0.454881i	−0.241328	+	0.970444i	$0.577583\pi$
$200$			7.83873i			0.554282i
$201$	−7.89987	−	19.0720i	−0.557214	−	1.34523i
$202$	−18.4145	−	18.4145i	−1.29564	−	1.29564i
$203$	−1.97767			−0.138805
$204$	42.1155	−	10.6766i	2.94868	−	0.747515i
$205$	−5.28883			−0.369388
$206$	−26.1396	−	26.1396i	−1.82123	−	1.82123i
$207$	−0.297683	−	0.718671i	−0.0206904	−	0.0499511i
$208$			18.0381i			1.25072i
$209$	0.402412	−	0.166684i	0.0278354	−	0.0115298i
$210$	−8.70194	+	21.0084i	−0.600491	+	1.44971i
$211$	4.39135	+	1.81896i	0.302313	+	0.125222i	0.528683	−	0.848819i	$-0.322686\pi$
$211$	4.39135	+	1.81896i	0.302313	+	0.125222i	−0.226370	+	0.974041i	$0.572686\pi$
$212$	35.9942	−	35.9942i	2.47209	−	2.47209i
$213$	−1.50848	+	1.50848i	−0.103359	+	0.103359i
$214$	32.9927	+	13.6660i	2.25534	+	0.934190i
$215$	−1.21675	+	2.93748i	−0.0829814	+	0.200335i
$216$	23.0856	−	9.56237i	1.57078	−	0.650637i
$217$		−	38.7119i		−	2.62794i
$218$	−6.43531	−	15.5362i	−0.435854	−	1.05225i
$219$	−4.37104	−	4.37104i	−0.295367	−	0.295367i
$220$	−8.69131			−0.585968
$221$	0.995215	−	6.84309i	0.0669454	−	0.460316i
$222$	23.9024			1.60423
$223$	15.3689	+	15.3689i	1.02918	+	1.02918i	0.999561	+	0.0296162i	$0.00942852\pi$
$223$	15.3689	+	15.3689i	1.02918	+	1.02918i	0.0296162	+	0.999561i	$0.490571\pi$
$224$	19.7656	+	47.7185i	1.32065	+	3.18833i
$225$			1.49675i			0.0997834i
$226$	−31.8491	+	13.1923i	−2.11857	+	0.877541i
$227$	1.07881	−	2.60448i	0.0716031	−	0.172865i	−0.884026	−	0.467438i	$-0.845177\pi$
$227$	1.07881	−	2.60448i	0.0716031	−	0.172865i	0.955629	+	0.294572i	$0.0951772\pi$
$228$	−2.42450	−	1.00426i	−0.160567	−	0.0665088i
$229$	16.4117	−	16.4117i	1.08451	−	1.08451i	0.0884319	−	0.996082i	$-0.471814\pi$
$229$	16.4117	−	16.4117i	1.08451	−	1.08451i	0.996082	−	0.0884319i	$-0.0281856\pi$
$230$	−0.970163	+	0.970163i	−0.0639706	+	0.0639706i
$231$	−13.9184	−	5.76519i	−0.915763	−	0.379322i
$232$	−1.46051	+	3.52599i	−0.0958873	+	0.231492i
$233$	8.95925	−	3.71104i	0.586940	−	0.243118i	−0.0693936	−	0.997589i	$-0.522106\pi$
$233$	8.95925	−	3.71104i	0.586940	−	0.243118i	0.656333	+	0.754471i	$0.272106\pi$
$234$			6.62699i			0.433220i
$235$	−2.39641	−	5.78544i	−0.156324	−	0.377401i
$236$	40.7552	+	40.7552i	2.65294	+	2.65294i
$237$	−14.4584			−0.939173
$238$	−10.8647	−	42.8575i	−0.704256	−	2.77804i
$239$	6.98497			0.451820			0.225910	−	0.974148i	$-0.427464\pi$
$239$	6.98497			0.451820			0.225910	+	0.974148i	$0.427464\pi$
$240$	16.1270	+	16.1270i	1.04099	+	1.04099i
$241$	−1.46650	−	3.54044i	−0.0944655	−	0.228060i	0.869583	−	0.493787i	$-0.164388\pi$
$241$	−1.46650	−	3.54044i	−0.0944655	−	0.228060i	−0.964048	+	0.265727i	$0.914388\pi$
$242$			20.9637i			1.34760i
$243$	13.2051	−	5.46971i	0.847105	−	0.350882i
$244$	8.27857	−	19.9862i	0.529981	−	1.27949i
$245$	8.77624	+	3.63524i	0.560693	+	0.232247i
$246$	−20.9357	+	20.9357i	−1.33481	+	1.33481i
$247$	−0.295340	+	0.295340i	−0.0187920	+	0.0187920i
$248$	−69.0196	−	28.5888i	−4.38275	−	1.81539i
$249$	−2.59419	+	6.26292i	−0.164400	+	0.396897i
$250$	2.43899	−	1.01026i	0.154255	−	0.0638945i
$251$			12.5111i			0.789693i	0.918747	+	0.394846i	$0.129202\pi$
$251$			12.5111i			0.789693i	−0.918747	+	0.394846i	$0.870798\pi$
$252$	11.5615	+	27.9120i	0.728309	+	1.75829i
$253$	−0.642750	−	0.642750i	−0.0404093	−	0.0404093i
$254$	−42.6097			−2.67357
$255$	−5.22829	−	7.00783i	−0.327408	−	0.438848i
$256$	−7.21688			−0.451055
$257$	9.81977	+	9.81977i	0.612541	+	0.612541i	0.943607	−	0.331067i	$-0.107409\pi$
$257$	9.81977	+	9.81977i	0.612541	+	0.612541i	−0.331067	+	0.943607i	$0.607409\pi$
$258$	6.81151	+	16.4444i	0.424066	+	1.02379i
$259$		−	17.3433i		−	1.07766i
$260$	7.69984	−	3.18938i	0.477524	−	0.197797i
$261$	−0.278875	+	0.673263i	−0.0172619	+	0.0416739i
$262$	38.4013	+	15.9063i	2.37244	+	0.982696i
$263$	−21.2162	+	21.2162i	−1.30825	+	1.30825i	−0.385565	+	0.922681i	$0.625993\pi$
$263$	−21.2162	+	21.2162i	−1.30825	+	1.30825i	−0.922681	+	0.385565i	$0.874007\pi$
$264$	−20.5575	+	20.5575i	−1.26523	+	1.26523i
$265$	−9.46387	−	3.92006i	−0.581361	−	0.240808i
$266$	−1.02195	+	2.46721i	−0.0626600	+	0.151275i
$267$	6.47545	−	2.68222i	0.396291	−	0.164149i
$268$			48.3754i			2.95500i
$269$	−2.78440	−	6.72213i	−0.169768	−	0.409856i	0.815981	−	0.578078i	$-0.196197\pi$
$269$	−2.78440	−	6.72213i	−0.169768	−	0.409856i	−0.985749	+	0.168223i	$0.946197\pi$
$270$	−5.95058	−	5.95058i	−0.362141	−	0.362141i
$271$	6.39386			0.388399			0.194200	−	0.980962i	$-0.437789\pi$
$271$	6.39386			0.388399			0.194200	+	0.980962i	$0.437789\pi$
$272$	−43.8832	−	6.38209i	−2.66081	−	0.386971i
$273$	14.4463			0.874327
$274$	−29.0745	−	29.0745i	−1.75646	−	1.75646i
$275$	0.669316	+	1.61587i	0.0403613	+	0.0974407i
$276$			5.47657i			0.329651i
$277$	7.19598	−	2.98067i	0.432365	−	0.179091i	−0.155877	−	0.987776i	$-0.549820\pi$
$277$	7.19598	−	2.98067i	0.432365	−	0.179091i	0.588242	+	0.808685i	$0.299820\pi$
$278$	10.6288	−	25.6602i	0.637472	−	1.53899i
$279$	−13.1788	−	5.45884i	−0.788994	−	0.326812i
$280$	22.5146	−	22.5146i	1.34550	−	1.34550i
$281$	15.1363	−	15.1363i	0.902954	−	0.902954i	−0.0927365	−	0.995691i	$-0.529561\pi$
$281$	15.1363	−	15.1363i	0.902954	−	0.902954i	0.995691	+	0.0927365i	$0.0295614\pi$
$282$	−32.3877	−	13.4154i	−1.92866	−	0.798876i
$283$	1.69298	−	4.08722i	0.100637	−	0.242960i	−0.865539	−	0.500841i	$-0.833024\pi$
$283$	1.69298	−	4.08722i	0.100637	−	0.242960i	0.966177	+	0.257881i	$0.0830242\pi$
$284$	4.61864	−	1.91310i	0.274066	−	0.113522i
$285$			0.528097i			0.0312817i
$286$	2.96345	+	7.15440i	0.175232	+	0.423049i
$287$	15.1907	+	15.1907i	0.896679	+	0.896679i
$288$	19.0321			1.12148
$289$	16.2958	+	4.84232i	0.958574	+	0.284842i
$290$	1.28533			0.0754771
$291$	−2.55049	−	2.55049i	−0.149513	−	0.149513i
$292$	5.54349	+	13.3832i	0.324408	+	0.783191i
$293$		−	19.6200i		−	1.14621i	−0.819481	−	0.573107i	$-0.805738\pi$
$293$		−	19.6200i		−	1.14621i	0.819481	−	0.573107i	$-0.194262\pi$
$294$	49.1306	−	20.3506i	2.86535	−	1.18687i
$295$	4.43858	−	10.7157i	0.258424	−	0.623891i
$296$	−30.9214	−	12.8081i	−1.79727	−	0.744454i
$297$	3.94236	−	3.94236i	0.228759	−	0.228759i
$298$	14.5586	−	14.5586i	0.843356	−	0.843356i
$299$	0.805292	+	0.333563i	0.0465712	+	0.0192904i
$300$	4.03258	−	9.73550i	0.232821	−	0.562080i
$301$	11.9319	−	4.94234i	0.687742	−	0.284872i
$302$		−	9.93189i		−	0.571516i
$303$	8.00517	+	19.3262i	0.459885	+	1.11026i
$304$	1.89395	+	1.89395i	0.108625	+	0.108625i
$305$	−4.35334			−0.249271
$306$	−16.1221	−	2.34470i	−0.921642	−	0.134038i
$307$	−13.3437			−0.761567			−0.380784	−	0.924664i	$-0.624346\pi$
$307$	−13.3437			−0.761567			−0.380784	+	0.924664i	$0.624346\pi$
$308$	24.9634	+	24.9634i	1.42242	+	1.42242i
$309$	11.3634	+	27.4337i	0.646441	+	1.56065i
$310$			25.1597i			1.42897i
$311$	4.94363	−	2.04772i	0.280328	−	0.116116i	−0.238090	−	0.971243i	$-0.576521\pi$
$311$	4.94363	−	2.04772i	0.280328	−	0.116116i	0.518418	+	0.855128i	$0.326521\pi$
$312$	10.6686	−	25.7563i	0.603990	−	1.45816i
$313$	−14.7039	−	6.09054i	−0.831112	−	0.344258i	−0.0737690	−	0.997275i	$-0.523503\pi$
$313$	−14.7039	−	6.09054i	−0.831112	−	0.344258i	−0.757343	+	0.653018i	$0.773503\pi$
$314$	−32.7098	+	32.7098i	−1.84592	+	1.84592i
$315$	4.29900	−	4.29900i	0.242221	−	0.242221i
$316$	31.3025	+	12.9659i	1.76090	+	0.729390i
$317$	−0.908669	+	2.19372i	−0.0510359	+	0.123212i	−0.947341	−	0.320226i	$-0.896241\pi$
$317$	−0.908669	+	2.19372i	−0.0510359	+	0.123212i	0.896305	+	0.443438i	$0.146241\pi$
$318$	−52.9800	+	21.9450i	−2.97097	+	1.23062i
$319$			0.851552i			0.0476778i
$320$	−4.61444	−	11.1402i	−0.257955	−	0.622758i
$321$	−20.2835	−	20.2835i	−1.13211	−	1.13211i
$322$	5.57305			0.310574
$323$	−0.614009	−	0.822997i	−0.0341643	−	0.0457928i
$324$	−55.9044			−3.10580
$325$	−1.18593	−	1.18593i	−0.0657833	−	0.0657833i
$326$	16.3330	+	39.4313i	0.904601	+	2.18390i
$327$			13.5078i			0.746985i
$328$	38.3019	−	15.8652i	2.11487	−	0.876008i
$329$	−9.73406	+	23.5001i	−0.536656	+	1.29560i
$330$	9.04586	+	3.74692i	0.497958	+	0.206261i
$331$	1.94947	−	1.94947i	0.107153	−	0.107153i	−0.651498	−	0.758650i	$-0.725859\pi$
$331$	1.94947	−	1.94947i	0.107153	−	0.107153i	0.758650	+	0.651498i	$0.225859\pi$
$332$	11.2329	−	11.2329i	0.616484	−	0.616484i
$333$	−5.90423	−	2.44561i	−0.323550	−	0.134019i
$334$	−14.5033	+	35.0142i	−0.793588	+	1.91589i
$335$	8.99387	−	3.72538i	0.491387	−	0.203539i
$336$		−	92.6406i		−	5.05396i
$337$	−9.65599	−	23.3116i	−0.525995	−	1.26986i	−0.934127	−	0.356941i	$-0.883820\pi$
$337$	−9.65599	−	23.3116i	−0.525995	−	1.26986i	0.408132	−	0.912923i	$-0.366180\pi$
$338$	19.0166	+	19.0166i	1.03436	+	1.03436i
$339$	27.6909			1.50396
$340$	5.03484	+	19.8606i	0.273052	+	1.07709i
$341$	−16.6687			−0.902663
$342$	0.695813	+	0.695813i	0.0376253	+	0.0376253i
$343$	−3.88505	−	9.37935i	−0.209773	−	0.506437i
$344$		−	24.9233i		−	1.34377i
$345$	1.01819	−	0.421749i	0.0548177	−	0.0227062i
$346$	18.2651	−	44.0959i	0.981938	−	2.37061i
$347$	8.88626	+	3.68081i	0.477039	+	0.197596i	0.608230	−	0.793761i	$-0.291880\pi$
$347$	8.88626	+	3.68081i	0.477039	+	0.197596i	−0.131190	+	0.991357i	$0.541880\pi$
$348$	3.62784	−	3.62784i	0.194473	−	0.194473i
$349$	−16.3752	+	16.3752i	−0.876547	+	0.876547i	−0.993176	−	0.116629i	$-0.962791\pi$
$349$	−16.3752	+	16.3752i	−0.876547	+	0.876547i	0.116629	+	0.993176i	$0.462791\pi$
$350$	−9.90701	−	4.10362i	−0.529552	−	0.219348i
$351$	−2.04594	+	4.93934i	−0.109204	+	0.263642i
$352$	20.5468	−	8.51077i	1.09515	−	0.453626i
$353$		−	15.4317i		−	0.821349i	−0.911782	−	0.410674i	$-0.865293\pi$
$353$		−	15.4317i		−	0.821349i	0.911782	−	0.410674i	$-0.134707\pi$
$354$	−24.8478	−	59.9878i	−1.32064	−	3.18832i
$355$	−0.711360	−	0.711360i	−0.0377551	−	0.0377551i
$356$	−16.4247			−0.870510
$357$	−5.11125	+	35.1449i	−0.270516	+	1.86006i
$358$	−19.8464			−1.04891
$359$	−5.67430	−	5.67430i	−0.299478	−	0.299478i	0.541331	−	0.840809i	$-0.317920\pi$
$359$	−5.67430	−	5.67430i	−0.299478	−	0.299478i	−0.840809	+	0.541331i	$0.817920\pi$
$360$	−4.48988	−	10.8395i	−0.236637	−	0.571293i
$361$		−	18.9380i		−	0.996736i
$362$	10.7167	−	4.43901i	0.563258	−	0.233309i
$363$	6.44411	−	15.5575i	0.338228	−	0.816555i
$364$	−31.2763	−	12.9551i	−1.63932	−	0.679029i
$365$	2.06127	−	2.06127i	0.107892	−	0.107892i
$366$	−17.2326	+	17.2326i	−0.900762	+	0.900762i
$367$	−19.1975	−	7.95185i	−1.00210	−	0.415083i	−0.179533	−	0.983752i	$-0.557459\pi$
$367$	−19.1975	−	7.95185i	−1.00210	−	0.415083i	−0.822567	+	0.568669i	$0.807459\pi$
$368$	2.13906	−	5.16416i	0.111506	−	0.269200i
$369$	7.31348	−	3.02934i	0.380725	−	0.157701i
$370$			11.2718i			0.585992i
$371$	15.9230	+	38.4416i	0.826683	+	1.99579i
$372$	71.0133	+	71.0133i	3.68187	+	3.68187i
$373$	−12.6951			−0.657330			−0.328665	−	0.944447i	$-0.606599\pi$
$373$	−12.6951			−0.657330			−0.328665	+	0.944447i	$0.606599\pi$
$374$	−18.4537	+	4.67818i	−0.954221	+	0.241903i
$375$	−2.12055			−0.109505
$376$	34.7098	+	34.7098i	1.79002	+	1.79002i
$377$	−0.312487	−	0.754411i	−0.0160939	−	0.0388541i
$378$			34.1828i			1.75817i
$379$	−16.2697	+	6.73914i	−0.835720	+	0.346167i	−0.759164	−	0.650899i	$-0.774392\pi$
$379$	−16.2697	+	6.73914i	−0.835720	+	0.346167i	−0.0765554	+	0.997065i	$0.524392\pi$
$380$	0.473584	−	1.14333i	0.0242944	−	0.0586518i
$381$	31.6212	+	13.0979i	1.62000	+	0.671028i
$382$	9.39102	−	9.39102i	0.480486	−	0.480486i
$383$	26.0027	−	26.0027i	1.32868	−	1.32868i	0.422150	−	0.906526i	$-0.361275\pi$
$383$	26.0027	−	26.0027i	1.32868	−	1.32868i	0.906526	−	0.422150i	$-0.138725\pi$
$384$	−12.5412	−	5.19475i	−0.639992	−	0.265093i
$385$	2.71872	−	6.56357i	0.138559	−	0.334510i
$386$	−65.5790	+	27.1637i	−3.33788	+	1.38260i
$387$		−	4.75893i		−	0.241910i
$388$	3.23462	+	7.80906i	0.164213	+	0.396445i
$389$	−6.60727	−	6.60727i	−0.335002	−	0.335002i	0.519480	−	0.854482i	$-0.326126\pi$
$389$	−6.60727	−	6.60727i	−0.335002	−	0.335002i	−0.854482	+	0.519480i	$0.826126\pi$
$390$	−9.38893			−0.475427
$391$	−1.09641	+	1.84110i	−0.0554480	+	0.0931083i
$392$	−74.4627			−3.76093
$393$	−23.6086	−	23.6086i	−1.19090	−	1.19090i
$394$	8.60117	+	20.7651i	0.433321	+	1.04613i
$395$		−	6.81821i		−	0.343061i
$396$	12.0185	−	4.97822i	0.603952	−	0.250165i
$397$	−1.53063	+	3.69526i	−0.0768200	+	0.185460i	−0.957624	−	0.288021i	$-0.907003\pi$
$397$	−1.53063	+	3.69526i	−0.0768200	+	0.185460i	0.880804	+	0.473481i	$0.157003\pi$
$398$	−40.8972	−	16.9402i	−2.04999	−	0.849135i
$399$	1.51681	−	1.51681i	0.0759356	−	0.0759356i
$400$	−7.60508	+	7.60508i	−0.380254	+	0.380254i
$401$	19.8522	+	8.22305i	0.991371	+	0.410639i	0.818626	−	0.574327i	$-0.194736\pi$
$401$	19.8522	+	8.22305i	0.991371	+	0.410639i	0.172745	+	0.984967i	$0.444736\pi$
$402$	20.8552	−	50.3489i	1.04016	−	2.51117i
$403$	14.7672	−	6.11679i	0.735609	−	0.304699i
$404$		−	49.0202i		−	2.43885i
$405$	4.30518	+	10.3936i	0.213926	+	0.516464i
$406$	−3.69175	−	3.69175i	−0.183218	−	0.183218i
$407$	−7.46776			−0.370163
$408$	58.8852	+	35.0674i	2.91525	+	1.73610i
$409$	18.4461			0.912103			0.456051	−	0.889954i	$-0.349263\pi$
$409$	18.4461			0.912103			0.456051	+	0.889954i	$0.349263\pi$
$410$	−9.87276	−	9.87276i	−0.487581	−	0.487581i
$411$	12.6393	+	30.5139i	0.623450	+	1.50514i
$412$		−	69.5846i		−	3.42819i
$413$	−43.5264	+	18.0292i	−2.14180	+	0.887161i
$414$	0.785866	−	1.89725i	0.0386232	−	0.0932447i
$415$	−2.95344	−	1.22335i	−0.144979	−	0.0600521i
$416$	−15.0798	+	15.0798i	−0.739348	+	0.739348i
$417$	−15.7755	+	15.7755i	−0.772532	+	0.772532i
$418$	1.06234	+	0.440037i	0.0519609	+	0.0215229i
$419$	−6.37490	+	15.3904i	−0.311434	+	0.751869i	0.688218	+	0.725504i	$0.258393\pi$
$419$	−6.37490	+	15.3904i	−0.311434	+	0.751869i	−0.999652	+	0.0263648i	$0.991607\pi$
$420$	−39.5450	+	16.3801i	−1.92960	+	0.799266i
$421$			34.9909i			1.70535i	0.522440	+	0.852676i	$0.325022\pi$
$421$			34.9909i			1.70535i	−0.522440	+	0.852676i	$0.674978\pi$
$422$	4.80193	+	11.5929i	0.233755	+	0.564333i
$423$	6.62759	+	6.62759i	0.322244	+	0.322244i
$424$	80.2969			3.89956
$425$	3.30472	−	2.46553i	0.160302	−	0.119596i
$426$	−5.63181			−0.272862
$427$	12.5038	+	12.5038i	0.605099	+	0.605099i
$428$	25.7242	+	62.1037i	1.24343	+	3.00190i
$429$		−	6.22033i		−	0.300320i
$430$	−7.75478	+	3.21214i	−0.373969	+	0.154903i
$431$	1.60471	−	3.87411i	0.0772962	−	0.186610i	−0.880508	−	0.474032i	$-0.842798\pi$
$431$	1.60471	−	3.87411i	0.0772962	−	0.186610i	0.957804	+	0.287422i	$0.0927982\pi$
$432$	31.6748	+	13.1202i	1.52396	+	0.631244i
$433$	−2.59223	+	2.59223i	−0.124575	+	0.124575i	−0.766645	−	0.642071i	$-0.778076\pi$
$433$	−2.59223	+	2.59223i	−0.124575	+	0.124575i	0.642071	+	0.766645i	$0.278076\pi$
$434$	72.2643	−	72.2643i	3.46880	−	3.46880i
$435$	−0.953860	−	0.395102i	−0.0457341	−	0.0189437i
$436$	12.1135	−	29.2446i	0.580131	−	1.40056i
$437$	0.119576	−	0.0495301i	0.00572011	−	0.00236935i
$438$		−	16.3190i		−	0.779752i
$439$	9.64359	+	23.2817i	0.460263	+	1.11117i	0.968289	+	0.249832i	$0.0803754\pi$
$439$	9.64359	+	23.2817i	0.460263	+	1.11117i	−0.508026	+	0.861342i	$0.669625\pi$
$440$	−9.69442	−	9.69442i	−0.462163	−	0.462163i
$441$	−14.2181			−0.677054
$442$	14.6319	−	10.9163i	0.695969	−	0.519237i
$443$	35.8208			1.70190			0.850949	−	0.525248i	$-0.176027\pi$
$443$	35.8208			1.70190			0.850949	+	0.525248i	$0.176027\pi$
$444$	31.8146	+	31.8146i	1.50986	+	1.50986i
$445$	1.26487	+	3.05366i	0.0599604	+	0.144757i
$446$			57.3788i			2.71697i
$447$	−15.2793	+	6.32891i	−0.722688	+	0.299347i
$448$	−18.7436	+	45.2510i	−0.885550	+	2.13791i
$449$	4.48941	+	1.85957i	0.211868	+	0.0877587i	0.486094	−	0.873907i	$-0.338421\pi$
$449$	4.48941	+	1.85957i	0.211868	+	0.0877587i	−0.274225	+	0.961665i	$0.588421\pi$
$450$	−2.79401	+	2.79401i	−0.131711	+	0.131711i
$451$	6.54087	−	6.54087i	0.307998	−	0.307998i
$452$	−59.9511	−	24.8326i	−2.81986	−	1.16802i
$453$	−3.05300	+	7.37059i	−0.143442	+	0.346301i
$454$	6.87566	−	2.84799i	0.322691	−	0.133663i
$455$			6.81249i			0.319374i
$456$	−1.58416	−	3.82450i	−0.0741850	−	0.179098i
$457$	−5.77124	−	5.77124i	−0.269967	−	0.269967i	0.559120	−	0.829087i	$-0.311139\pi$
$457$	−5.77124	−	5.77124i	−0.269967	−	0.269967i	−0.829087	+	0.559120i	$0.811139\pi$
$458$	61.2720			2.86305
$459$	−11.2926	−	6.72496i	−0.527091	−	0.313894i
$460$	−2.58261			−0.120415
$461$	−18.3007	−	18.3007i	−0.852349	−	0.852349i	0.138073	−	0.990422i	$-0.455909\pi$
$461$	−18.3007	−	18.3007i	−0.852349	−	0.852349i	−0.990422	+	0.138073i	$0.955909\pi$
$462$	−15.2198	−	36.7437i	−0.708087	−	1.70947i
$463$		−	2.13987i		−	0.0994481i	−0.998763	−	0.0497240i	$-0.984166\pi$
$463$		−	2.13987i		−	0.0994481i	0.998763	−	0.0497240i	$-0.0158342\pi$
$464$	−4.83787	+	2.00391i	−0.224592	+	0.0930292i
$465$	7.73393	−	18.6714i	0.358653	−	0.865864i
$466$	23.6519	+	9.79693i	1.09565	+	0.453834i
$467$	−9.34534	+	9.34534i	−0.432451	+	0.432451i	−0.889461	−	0.457010i	$-0.848920\pi$
$467$	−9.34534	+	9.34534i	−0.432451	+	0.432451i	0.457010	+	0.889461i	$0.348920\pi$
$468$	−8.82065	+	8.82065i	−0.407735	+	0.407735i
$469$	−36.5325	−	15.1323i	−1.68691	−	0.698743i
$470$	6.32637	−	15.2732i	0.291814	−	0.704501i
$471$	34.3292	−	14.2196i	1.58181	−	0.655206i
$472$			90.9180i			4.18484i
$473$	−2.12810	−	5.13768i	−0.0978499	−	0.236231i
$474$	−26.9897	−	26.9897i	−1.23968	−	1.23968i
$475$	−0.249037			−0.0114266
$476$	42.5830	−	71.5053i	1.95179	−	3.27744i
$477$	15.3321			0.702010
$478$	13.0390	+	13.0390i	0.596389	+	0.596389i
$479$	−9.02613	−	21.7910i	−0.412414	−	0.995656i	−0.984488	−	0.175454i	$-0.943861\pi$
$479$	−9.02613	−	21.7910i	−0.412414	−	0.995656i	0.572073	−	0.820202i	$-0.306139\pi$
$480$			26.9642i			1.23074i
$481$	6.61587	−	2.74038i	0.301658	−	0.124951i
$482$	3.87147	−	9.34656i	0.176341	−	0.425724i
$483$	−4.13584	−	1.71312i	−0.188187	−	0.0779496i
$484$	−27.9031	+	27.9031i	−1.26832	+	1.26832i
$485$	1.20275	−	1.20275i	0.0546140	−	0.0546140i
$486$	34.8605	+	14.4397i	1.58131	+	0.654999i
$487$	−11.0851	+	26.7618i	−0.502313	+	1.21269i	0.445907	+	0.895079i	$0.352881\pi$
$487$	−11.0851	+	26.7618i	−0.502313	+	1.21269i	−0.948221	+	0.317612i	$0.897119\pi$
$488$	31.5270	−	13.0589i	1.42716	−	0.591150i
$489$		−	34.2832i		−	1.55034i
$490$	9.59681	+	23.1687i	0.433540	+	1.04666i
$491$	−25.1208	−	25.1208i	−1.13369	−	1.13369i	−0.989559	−	0.144129i	$-0.953962\pi$
$491$	−25.1208	−	25.1208i	−1.13369	−	1.13369i	−0.144129	−	0.989559i	$-0.546038\pi$
$492$	−55.7317			−2.51258
$493$	1.94589	−	0.493301i	0.0876387	−	0.0222171i
$494$	−1.10263			−0.0496098
$495$	−1.85108	−	1.85108i	−0.0832000	−	0.0832000i
$496$	−39.2256	−	94.6990i	−1.76128	−	4.25211i
$497$			4.08637i			0.183299i
$498$	−16.5337	+	6.84850i	−0.740895	+	0.306889i
$499$	12.9940	−	31.3704i	0.581693	−	1.40433i	−0.309584	−	0.950872i	$-0.600190\pi$
$499$	12.9940	−	31.3704i	0.581693	−	1.40433i	0.891277	−	0.453460i	$-0.149810\pi$
$500$	4.59102	+	1.90166i	0.205317	+	0.0850449i
$501$	21.5263	−	21.5263i	0.961723	−	0.961723i
$502$	−23.3547	+	23.3547i	−1.04237	+	1.04237i
$503$	−18.1158	−	7.50380i	−0.807743	−	0.334578i	−0.0596898	−	0.998217i	$-0.519011\pi$
$503$	−18.1158	−	7.50380i	−0.807743	−	0.334578i	−0.748053	+	0.663639i	$0.769011\pi$
$504$	−18.2376	+	44.0295i	−0.812367	+	1.96123i
$505$	−9.11374	+	3.77504i	−0.405556	+	0.167987i
$506$		−	2.39967i		−	0.106678i
$507$	−8.26689	−	19.9580i	−0.367145	−	0.886367i
$508$	−56.7143	−	56.7143i	−2.51629	−	2.51629i
$509$	1.06322			0.0471265			0.0235632	−	0.999722i	$-0.492499\pi$
$509$	1.06322			0.0471265			0.0235632	+	0.999722i	$0.492499\pi$
$510$	3.32191	−	22.8414i	0.147097	−	1.01143i
$511$	−11.8409			−0.523809
$512$	−22.5249	−	22.5249i	−0.995467	−	0.995467i
$513$	0.303798	+	0.733432i	0.0134130	+	0.0323818i
$514$			36.6615i			1.61707i
$515$	−12.9370	+	5.35869i	−0.570074	+	0.236132i
$516$	−12.8216	+	30.9541i	−0.564440	+	1.36268i
$517$	10.1188	+	4.19133i	0.445023	+	0.184335i
$518$	32.3751	−	32.3751i	1.42248	−	1.42248i
$519$	−27.1096	+	27.1096i	−1.18998	+	1.18998i
$520$	12.1460	+	5.03104i	0.532638	+	0.220626i
$521$	−7.76891	+	18.7558i	−0.340362	+	0.821707i	0.657317	+	0.753614i	$0.271691\pi$
$521$	−7.76891	+	18.7558i	−0.340362	+	0.821707i	−0.997679	+	0.0680927i	$0.978309\pi$
$522$	−1.77737	+	0.736212i	−0.0777935	+	0.0322231i
$523$		−	27.3245i		−	1.19482i	−0.801937	−	0.597408i	$-0.796197\pi$
$523$		−	27.3245i		−	1.19482i	0.801937	−	0.597408i	$-0.203803\pi$
$524$	29.9412	+	72.2845i	1.30799	+	3.15776i
$525$	6.09071	+	6.09071i	0.265820	+	0.265820i
$526$	−79.2093			−3.45369
$527$	9.65613	+	38.0900i	0.420628	+	1.65922i
$528$	−39.8896			−1.73597
$529$	16.0725	+	16.0725i	0.698803	+	0.698803i
$530$	−10.3487	−	24.9840i	−0.449520	−	1.08524i
$531$			17.3602i			0.753367i
$532$	−4.64415	+	1.92367i	−0.201349	+	0.0834017i
$533$	−3.39447	+	8.19497i	−0.147031	+	0.354964i
$534$	17.0948	+	7.08089i	0.739764	+	0.306420i
$535$	9.56519	−	9.56519i	0.413539	−	0.413539i
$536$	−53.9587	+	53.9587i	−2.33066	+	2.33066i
$537$	14.7283	+	6.10065i	0.635572	+	0.263262i
$538$	7.35065	−	17.7460i	0.316909	−	0.765086i
$539$	−15.3497	+	6.35805i	−0.661158	+	0.273861i
$540$		−	15.8407i		−	0.681675i
$541$	−9.90457	−	23.9118i	−0.425831	−	1.02805i	−0.980596	−	0.196040i	$-0.937192\pi$
$541$	−9.90457	−	23.9118i	−0.425831	−	1.02805i	0.554765	−	0.832007i	$-0.312808\pi$
$542$	11.9355	+	11.9355i	0.512675	+	0.512675i
$543$	−9.31754			−0.399854
$544$	−31.3508	−	42.0216i	−1.34415	−	1.80166i
$545$	−6.36995			−0.272859
$546$	26.9671	+	26.9671i	1.15409	+	1.15409i
$547$	−13.6138	−	32.8667i	−0.582085	−	1.40528i	−0.890919	−	0.454162i	$-0.849939\pi$
$547$	−13.6138	−	32.8667i	−0.582085	−	1.40528i	0.308834	−	0.951116i	$-0.400061\pi$
$548$		−	77.3975i		−	3.30626i
$549$	6.01987	−	2.49351i	0.256922	−	0.106420i
$550$	−1.76695	+	4.26580i	−0.0753431	+	0.181894i
$551$	−0.112021	−	0.0464006i	−0.00477225	−	0.00197673i
$552$	−6.10865	+	6.10865i	−0.260002	+	0.260002i
$553$	−19.5834	+	19.5834i	−0.832772	+	0.832772i
$554$	18.9970	+	7.86880i	0.807103	+	0.334313i
$555$	3.46488	−	8.36495i	0.147076	−	0.355072i
$556$	48.3013	−	20.0071i	2.04843	−	0.848489i
$557$			13.1772i			0.558337i	0.960242	+	0.279168i	$0.0900588\pi$
$557$			13.1772i			0.558337i	−0.960242	+	0.279168i	$0.909941\pi$
$558$	−14.4110	−	34.7913i	−0.610067	−	1.47283i
$559$	3.77066	+	3.77066i	0.159482	+	0.159482i
$560$	43.6870			1.84611
$561$	15.1328	+	2.20082i	0.638909	+	0.0929188i
$562$	56.5103			2.38374
$563$	3.07738	+	3.07738i	0.129696	+	0.129696i	0.768975	−	0.639279i	$-0.220767\pi$
$563$	3.07738	+	3.07738i	0.129696	+	0.129696i	−0.639279	+	0.768975i	$0.720767\pi$
$564$	−25.2525	−	60.9648i	−1.06332	−	2.56708i
$565$			13.0583i			0.549369i
$566$	10.7900	−	4.46937i	0.453538	−	0.187862i
$567$	17.4874	−	42.2183i	0.734401	−	1.77300i
$568$	7.28560	+	3.01780i	0.305697	+	0.126624i
$569$	−13.7629	+	13.7629i	−0.576971	+	0.576971i	−0.934067	−	0.357097i	$-0.883767\pi$
$569$	−13.7629	+	13.7629i	−0.576971	+	0.576971i	0.357097	+	0.934067i	$0.383767\pi$
$570$	−0.985808	+	0.985808i	−0.0412910	+	0.0412910i
$571$	−16.9783	−	7.03263i	−0.710519	−	0.294307i	−0.00199965	−	0.999998i	$-0.500637\pi$
$571$	−16.9783	−	7.03263i	−0.710519	−	0.294307i	−0.708519	+	0.705691i	$0.750637\pi$
$572$	−5.57824	+	13.4671i	−0.233238	+	0.563086i
$573$	−9.85595	+	4.08247i	−0.411738	+	0.170547i
$574$			56.7135i			2.36718i
$575$	0.198886	+	0.480154i	0.00829414	+	0.0200238i
$576$	12.7618	+	12.7618i	0.531744	+	0.531744i
$577$	23.8985			0.994906			0.497453	−	0.867491i	$-0.334269\pi$
$577$	23.8985			0.994906			0.497453	+	0.867491i	$0.334269\pi$
$578$	21.3804	+	39.4589i	0.889306	+	1.64127i
$579$	57.0171			2.36955
$580$	1.71080	+	1.71080i	0.0710370	+	0.0710370i
$581$	4.96919	+	11.9967i	0.206157	+	0.497706i
$582$		−	9.52211i		−	0.394704i
$583$	16.5524	−	6.85621i	0.685529	−	0.283955i
$584$	−8.74451	+	21.1111i	−0.361850	+	0.873584i
$585$	2.31920	+	0.960642i	0.0958869	+	0.0397177i
$586$	36.6251	−	36.6251i	1.51297	−	1.51297i
$587$	0.529847	−	0.529847i	0.0218691	−	0.0218691i	−0.696088	−	0.717957i	$-0.745078\pi$
$587$	0.529847	−	0.529847i	0.0218691	−	0.0218691i	0.717957	+	0.696088i	$0.245078\pi$
$588$	92.4808	+	38.3068i	3.81384	+	1.57975i
$589$	0.908270	−	2.19276i	0.0374246	−	0.0903510i
$590$	28.2888	−	11.7176i	1.16463	−	0.482405i
$591$		−	18.0540i		−	0.742642i
$592$	−17.5735	−	42.4261i	−0.722264	−	1.74370i
$593$	−14.1641	−	14.1641i	−0.581651	−	0.581651i	0.353706	−	0.935357i	$-0.384921\pi$
$593$	−14.1641	−	14.1641i	−0.581651	−	0.581651i	−0.935357	+	0.353706i	$0.884921\pi$
$594$	14.7186			0.603911
$595$	−16.5734	−	2.41033i	−0.679445	−	0.0988141i
$596$	38.7555			1.58749
$597$	25.1431	+	25.1431i	1.02904	+	1.02904i
$598$	0.880586	+	2.12592i	0.0360098	+	0.0869354i
$599$		−	12.9934i		−	0.530897i	−0.964125	−	0.265449i	$-0.914480\pi$
$599$		−	12.9934i		−	0.530897i	0.964125	−	0.265449i	$-0.0855200\pi$
$600$	15.3571	−	6.36113i	0.626953	−	0.259692i
$601$	−2.91712	+	7.04254i	−0.118992	+	0.287271i	−0.972142	−	0.234395i	$-0.924689\pi$
$601$	−2.91712	+	7.04254i	−0.118992	+	0.287271i	0.853150	+	0.521666i	$0.174689\pi$
$602$	31.4994	+	13.0475i	1.28382	+	0.531776i
$603$	−10.3030	+	10.3030i	−0.419572	+	0.419572i
$604$	13.2195	−	13.2195i	0.537895	−	0.537895i
$605$	7.33651	+	3.03888i	0.298271	+	0.123548i
$606$	−21.1332	+	51.0200i	−0.858476	+	2.07254i
$607$	−44.8967	+	18.5968i	−1.82230	+	0.754822i	−0.847845	+	0.530244i	$0.822100\pi$
$607$	−44.8967	+	18.5968i	−1.82230	+	0.754822i	−0.974456	+	0.224577i	$0.927900\pi$
$608$			3.16667i			0.128425i
$609$	1.60488	+	3.87452i	0.0650330	+	0.157003i
$610$	−8.12646	−	8.12646i	−0.329031	−	0.329031i
$611$	−10.5025			−0.424887
$612$	−18.3381	−	24.5798i	−0.741272	−	0.993578i
$613$	5.92605			0.239351			0.119675	−	0.992813i	$-0.461815\pi$
$613$	5.92605			0.239351			0.119675	+	0.992813i	$0.461815\pi$
$614$	−24.9090	−	24.9090i	−1.00525	−	1.00525i
$615$	4.29189	+	10.3615i	0.173066	+	0.417818i
$616$			55.6891i			2.24378i
$617$	36.5708	−	15.1481i	1.47229	−	0.609841i	0.504907	−	0.863174i	$-0.331527\pi$
$617$	36.5708	−	15.1481i	1.47229	−	0.609841i	0.967379	+	0.253332i	$0.0815266\pi$
$618$	−29.9987	+	72.4232i	−1.20672	+	2.91329i
$619$	−40.7525	−	16.8802i	−1.63798	−	0.678475i	−0.641890	−	0.766796i	$-0.721850\pi$
$619$	−40.7525	−	16.8802i	−1.63798	−	0.678475i	−0.996092	+	0.0883219i	$0.971850\pi$
$620$	−33.4881	+	33.4881i	−1.34491	+	1.34491i
$621$	1.17147	−	1.17147i	0.0470094	−	0.0470094i
$622$	13.0509	+	5.40586i	0.523293	+	0.216755i
$623$	5.13781	−	12.4038i	0.205842	−	0.496946i
$624$	35.3391	−	14.6380i	1.41470	−	0.585987i
$625$		−	1.00000i		−	0.0400000i
$626$	−16.0787	−	38.8173i	−0.642633	−	1.55145i
$627$	−0.653115	−	0.653115i	−0.0260829	−	0.0260829i
$628$	−87.0749			−3.47467
$629$	4.32604	+	17.0647i	0.172491	+	0.680413i
$630$	16.0501			0.639450
$631$	−1.59788	−	1.59788i	−0.0636106	−	0.0636106i	0.674586	−	0.738196i	$-0.264322\pi$
$631$	−1.59788	−	1.59788i	−0.0636106	−	0.0636106i	−0.738196	+	0.674586i	$0.764322\pi$
$632$	20.4529	+	49.3777i	0.813574	+	1.96414i
$633$		−	10.0793i		−	0.400618i
$634$	−5.79129	+	2.39883i	−0.230002	+	0.0952698i
$635$	−6.17666	+	14.9118i	−0.245113	+	0.591756i
$636$	−99.7268	−	41.3082i	−3.95442	−	1.63798i
$637$	11.2655	−	11.2655i	0.446356	−	0.446356i
$638$	−1.58961	+	1.58961i	−0.0629332	+	0.0629332i
$639$	1.39114	+	0.576227i	0.0550325	+	0.0227952i
$640$	2.44971	−	5.91413i	0.0968334	−	0.233777i
$641$	−33.9893	+	14.0788i	−1.34250	+	0.556080i	−0.934193	−	0.356767i	$-0.883879\pi$
$641$	−33.9893	+	14.0788i	−1.34250	+	0.556080i	−0.408302	+	0.912847i	$0.633879\pi$
$642$		−	75.7272i		−	2.98872i
$643$	9.40393	+	22.7031i	0.370855	+	0.895322i	0.993606	+	0.112903i	$0.0360148\pi$
$643$	9.40393	+	22.7031i	0.370855	+	0.895322i	−0.622751	+	0.782420i	$0.713985\pi$
$644$	7.41784	+	7.41784i	0.292304	+	0.292304i
$645$	6.74232			0.265479
$646$	0.390124	−	2.68249i	0.0153492	−	0.105541i
$647$	39.0064			1.53350			0.766750	−	0.641946i	$-0.221873\pi$
$647$	39.0064			1.53350			0.766750	+	0.641946i	$0.221873\pi$
$648$	−62.3566	−	62.3566i	−2.44960	−	2.44960i
$649$	7.76310	+	18.7418i	0.304728	+	0.735680i
$650$		−	4.42758i		−	0.173664i
$651$	−75.8419	+	31.4147i	−2.97248	+	1.23124i
$652$	−30.7444	+	74.2235i	−1.20404	+	2.90681i
$653$	25.7997	+	10.6866i	1.00962	+	0.418199i	0.825317	−	0.564670i	$-0.190997\pi$
$653$	25.7997	+	10.6866i	1.00962	+	0.418199i	0.184305	+	0.982869i	$0.440997\pi$
$654$	−25.2153	+	25.2153i	−0.985997	+	0.985997i
$655$	11.1332	−	11.1332i	0.435011	−	0.435011i
$656$	52.5525	+	21.7680i	2.05183	+	0.849896i
$657$	−1.66970	+	4.03102i	−0.0651413	+	0.157265i
$658$	−62.0388	+	25.6973i	−2.41853	+	1.00179i
$659$			19.5830i			0.762847i	0.924400	+	0.381423i	$0.124566\pi$
$659$			19.5830i			0.762847i	−0.924400	+	0.381423i	$0.875434\pi$
$660$	7.05300	+	17.0275i	0.274538	+	0.662793i
$661$	19.1171	+	19.1171i	0.743568	+	0.743568i	0.973263	−	0.229695i	$-0.0737729\pi$
$661$	19.1171	+	19.1171i	0.743568	+	0.743568i	−0.229695	+	0.973263i	$0.573773\pi$
$662$	7.27823			0.282876
$663$	−14.2142	+	3.60341i	−0.552032	+	0.139945i
$664$	25.0587			0.972465
$665$	0.715290	+	0.715290i	0.0277378	+	0.0277378i
$666$	−6.45627	−	15.5868i	−0.250175	−	0.603977i
$667$			0.253038i			0.00979766i
$668$	−65.9088	+	27.3003i	−2.55009	+	1.05628i
$669$	17.6379	−	42.5817i	0.681920	−	1.64630i
$670$	23.7433	+	9.83478i	0.917282	+	0.379951i
$671$	5.38392	−	5.38392i	0.207844	−	0.207844i
$672$	77.4472	−	77.4472i	2.98759	−	2.98759i
$673$	46.3058	+	19.1805i	1.78496	+	0.739353i	0.991402	+	0.130854i	$0.0417720\pi$
$673$	46.3058	+	19.1805i	1.78496	+	0.739353i	0.793555	+	0.608499i	$0.208228\pi$
$674$	25.4912	−	61.5413i	0.981885	−	2.37048i
$675$	−2.94507	+	1.21989i	−0.113356	+	0.0469535i
$676$			50.6229i			1.94703i
$677$	−0.821918	−	1.98429i	−0.0315889	−	0.0762623i	0.907298	−	0.420489i	$-0.138141\pi$
$677$	−0.821918	−	1.98429i	−0.0315889	−	0.0762623i	−0.938887	+	0.344226i	$0.888141\pi$
$678$	51.6912	+	51.6912i	1.98519	+	1.98519i
$679$	−6.90912			−0.265148
$680$	−16.5369	+	27.7688i	−0.634162	+	1.06488i
$681$	−5.97798			−0.229077
$682$	−31.1158	−	31.1158i	−1.19149	−	1.19149i
$683$	−1.30316	−	3.14612i	−0.0498642	−	0.120383i	0.896985	−	0.442062i	$-0.145753\pi$
$683$	−1.30316	−	3.14612i	−0.0498642	−	0.120383i	−0.946849	+	0.321679i	$0.895753\pi$
$684$			1.85228i			0.0708238i
$685$	−14.3896	+	5.96037i	−0.549798	+	0.227734i
$686$	10.2563	−	24.7609i	0.391588	−	0.945376i
$687$	−45.4708	−	18.8346i	−1.73482	−	0.718586i
$688$	24.1804	−	24.1804i	0.921870	−	0.921870i
$689$	−12.1482	+	12.1482i	−0.462809	+	0.462809i
$690$	2.68797	+	1.11339i	0.102329	+	0.0423862i
$691$	−0.579345	+	1.39866i	−0.0220393	+	0.0532077i	−0.934516	−	0.355921i	$-0.884167\pi$
$691$	−0.579345	+	1.39866i	−0.0220393	+	0.0532077i	0.912477	+	0.409129i	$0.134167\pi$
$692$	83.0037	−	34.3813i	3.15533	−	1.30698i
$693$			10.6334i			0.403931i
$694$	9.71711	+	23.4592i	0.368857	+	0.890499i
$695$	−7.43935	−	7.43935i	−0.282191	−	0.282191i
$696$	8.09310			0.306768
$697$	−18.7357	−	11.1575i	−0.709667	−	0.422622i
$698$	−61.1360			−2.31403
$699$	−14.5409	−	14.5409i	−0.549987	−	0.549987i
$700$	−7.72443	−	18.6484i	−0.291956	−	0.704844i
$701$		−	46.4213i		−	1.75331i	−0.481121	−	0.876654i	$-0.659770\pi$
$701$		−	46.4213i		−	1.75331i	0.481121	−	0.876654i	$-0.340230\pi$
$702$	−13.0395	+	5.40116i	−0.492146	+	0.203854i
$703$	0.406914	−	0.982377i	0.0153470	−	0.0370511i
$704$	19.4843	+	8.07068i	0.734344	+	0.304175i
$705$	−9.38978	+	9.38978i	−0.353640	+	0.353640i
$706$	28.8067	−	28.8067i	1.08416	−	1.08416i
$707$	37.0195	+	15.3340i	1.39226	+	0.576693i
$708$	46.7721	−	112.918i	1.75780	−	4.24372i
$709$	12.4538	−	5.15853i	0.467712	−	0.193733i	−0.136365	−	0.990659i	$-0.543542\pi$
$709$	12.4538	−	5.15853i	0.467712	−	0.193733i	0.604077	+	0.796926i	$0.293542\pi$
$710$		−	2.65582i		−	0.0996712i
$711$	3.90534	+	9.42833i	0.146462	+	0.353590i
$712$	−18.3204	−	18.3204i	−0.686587	−	0.686587i
$713$	−4.95310			−0.185495
$714$	−75.1469	+	56.0644i	−2.81230	+	2.09816i
$715$	2.93335			0.109701
$716$	−26.4159	−	26.4159i	−0.987209	−	0.987209i
$717$	−5.66831	−	13.6845i	−0.211687	−	0.511057i
$718$		−	21.1846i		−	0.790604i
$719$	32.3747	−	13.4100i	1.20737	−	0.500110i	0.313999	−	0.949423i	$-0.398331\pi$
$719$	32.3747	−	13.4100i	1.20737	−	0.500110i	0.893374	+	0.449313i	$0.148331\pi$
$720$	6.16038	−	14.8725i	0.229584	−	0.554265i
$721$	52.5494	+	21.7667i	1.95704	+	0.810633i
$722$	35.3519	−	35.3519i	1.31566	−	1.31566i
$723$	−5.74615	+	5.74615i	−0.213701	+	0.213701i
$724$	20.1726	+	8.35575i	0.749707	+	0.310539i
$725$	0.186320	−	0.449816i	0.00691975	−	0.0167058i
$726$	41.0708	−	17.0121i	1.52428	−	0.631377i
$727$			15.6299i			0.579682i	0.957075	+	0.289841i	$0.0936024\pi$
$727$			15.6299i			0.579682i	−0.957075	+	0.289841i	$0.906398\pi$
$728$	−20.4358	−	49.3363i	−0.757400	−	1.82853i
$729$	2.43301	+	2.43301i	0.0901113	+	0.0901113i
$730$	7.69563			0.284828
$731$	−10.5074	+	7.83918i	−0.388630	+	0.289942i
$732$	−45.8739			−1.69555
$733$	6.81328	+	6.81328i	0.251654	+	0.251654i	0.821649	−	0.569994i	$-0.193055\pi$
$733$	6.81328	+	6.81328i	0.251654	+	0.251654i	−0.569994	+	0.821649i	$0.693055\pi$
$734$	−20.9924	−	50.6801i	−0.774844	−	1.87064i
$735$		−	20.1439i		−	0.743017i
$736$	6.10547	−	2.52897i	0.225051	−	0.0932190i
$737$	−6.51571	+	15.7303i	−0.240009	+	0.579434i
$738$	19.3072	+	7.99729i	0.710706	+	0.294384i
$739$	−0.0749710	+	0.0749710i	−0.00275785	+	0.00275785i	−0.708484	−	0.705727i	$-0.750621\pi$
$739$	−0.0749710	+	0.0749710i	−0.00275785	+	0.00275785i	0.705727	+	0.708484i	$0.250621\pi$
$740$	−15.0030	+	15.0030i	−0.551520	+	0.551520i
$741$	0.818279	+	0.338942i	0.0300602	+	0.0124514i
$742$	−42.0359	+	101.484i	−1.54319	+	3.72558i
$743$	−3.32309	+	1.37647i	−0.121913	+	0.0504978i	−0.442806	−	0.896618i	$-0.646017\pi$
$743$	−3.32309	+	1.37647i	−0.121913	+	0.0504978i	0.320893	+	0.947115i	$0.396017\pi$
$744$			158.419i			5.80791i
$745$	−2.98455	−	7.20535i	−0.109346	−	0.263984i
$746$	−23.6983	−	23.6983i	−0.867656	−	0.867656i
$747$	4.78478			0.175066
$748$	−30.7891	−	18.3356i	−1.12576	−	0.670414i
$749$	−54.9467			−2.00771
$750$	−3.95848	−	3.95848i	−0.144543	−	0.144543i
$751$	6.52082	+	15.7426i	0.237948	+	0.574457i	0.997070	−	0.0764908i	$-0.0243716\pi$
$751$	6.52082	+	15.7426i	0.237948	+	0.574457i	−0.759122	+	0.650948i	$0.774372\pi$
$752$			67.3503i			2.45601i
$753$	24.5109	−	10.1528i	0.893228	−	0.369987i
$754$	0.824948	−	1.99160i	0.0300428	−	0.0725298i
$755$	−3.47579	−	1.43972i	−0.126497	−	0.0523967i
$756$	−45.4980	+	45.4980i	−1.65475	+	1.65475i
$757$	32.1745	−	32.1745i	1.16940	−	1.16940i	0.187051	−	0.982350i	$-0.440107\pi$
$757$	32.1745	−	32.1745i	1.16940	−	1.16940i	0.982350	−	0.187051i	$-0.0598928\pi$
$758$	−42.9511	−	17.7909i	−1.56005	−	0.646196i
$759$	−0.737642	+	1.78083i	−0.0267747	+	0.0646399i
$760$	1.80354	−	0.747049i	0.0654212	−	0.0270983i
$761$			11.3019i			0.409693i	0.978794	+	0.204846i	$0.0656695\pi$
$761$			11.3019i			0.409693i	−0.978794	+	0.204846i	$0.934330\pi$
$762$	34.5778	+	83.4781i	1.25262	+	3.02409i
$763$	18.2959	+	18.2959i	0.662357	+	0.662357i
$764$	24.9993			0.904442
$765$	−3.15761	+	5.30226i	−0.114164	+	0.191704i
$766$	97.0795			3.50763
$767$	−13.7550	−	13.7550i	−0.496666	−	0.496666i
$768$	5.85651	+	14.1389i	0.211329	+	0.510192i
$769$			9.75206i			0.351668i	0.984420	+	0.175834i	$0.0562622\pi$
$769$			9.75206i			0.351668i	−0.984420	+	0.175834i	$0.943738\pi$
$770$	17.3274	−	7.17725i	0.624437	−	0.258650i
$771$	11.2695	−	27.2070i	0.405862	−	0.979837i
$772$	−123.442	−	51.1315i	−4.44279	−	1.84026i
$773$	−1.60247	+	1.60247i	−0.0576370	+	0.0576370i	−0.735338	−	0.677701i	$-0.762976\pi$
$773$	−1.60247	+	1.60247i	−0.0576370	+	0.0576370i	0.677701	+	0.735338i	$0.262976\pi$
$774$	8.88359	−	8.88359i	0.319314	−	0.319314i
$775$	8.80495	+	3.64713i	0.316283	+	0.131009i
$776$	−5.10241	+	12.3183i	−0.183166	+	0.442201i
$777$	−33.9779	+	14.0741i	−1.21895	+	0.504906i
$778$		−	24.6679i		−	0.884385i
$779$	0.504038	+	1.21686i	0.0180590	+	0.0435984i
$780$	−12.4969	−	12.4969i	−0.447459	−	0.447459i
$781$	1.75953			0.0629608
$782$	−5.48351	+	1.39012i	−0.196090	+	0.0497105i
$783$	−1.55203			−0.0554651
$784$	−72.2432	−	72.2432i	−2.58011	−	2.58011i
$785$	6.70562	+	16.1888i	0.239334	+	0.577803i
$786$		−	88.1413i		−	3.14390i
$787$	18.1799	−	7.53036i	0.648043	−	0.268428i	−0.0343542	−	0.999410i	$-0.510937\pi$
$787$	18.1799	−	7.53036i	0.648043	−	0.268428i	0.682397	+	0.730982i	$0.260937\pi$
$788$	−16.1904	+	39.0870i	−0.576758	+	1.39242i
$789$	58.7823	+	24.3484i	2.09271	+	0.866827i
$790$	12.7277	−	12.7277i	0.452831	−	0.452831i
$791$	37.5065	−	37.5065i	1.33358	−	1.33358i
$792$	18.9584	+	7.85282i	0.673657	+	0.279038i
$793$	−2.79405	+	6.74544i	−0.0992197	+	0.239538i
$794$	−9.75528	+	4.04077i	−0.346202	+	0.143401i
$795$			21.7221i			0.770405i
$796$	−31.8873	−	76.9828i	−1.13022	−	2.72858i
$797$	−33.0747	−	33.0747i	−1.17156	−	1.17156i	−0.981837	−	0.189728i	$-0.939239\pi$
$797$	−33.0747	−	33.0747i	−1.17156	−	1.17156i	−0.189728	−	0.981837i	$-0.560761\pi$
$798$	5.66292			0.200465
$799$	3.71591	−	25.5506i	0.131459	−	0.903914i
$800$	−12.7156			−0.449566
$801$	−3.49816	−	3.49816i	−0.123601	−	0.123601i
$802$	21.7083	+	52.4086i	0.766548	+	1.85061i
$803$			5.09849i			0.179922i
$804$	94.7741	−	39.2567i	3.34242	−	1.38448i
$805$	0.807864	−	1.95036i	0.0284735	−	0.0687410i
$806$	38.9846	+	16.1480i	1.37317	+	0.568788i
$807$	−10.9100	+	10.9100i	−0.384052	+	0.384052i
$808$	54.6779	−	54.6779i	1.92356	−	1.92356i
$809$	−6.35514	−	2.63238i	−0.223435	−	0.0925497i	0.268158	−	0.963375i	$-0.413585\pi$
$809$	−6.35514	−	2.63238i	−0.223435	−	0.0925497i	−0.491593	+	0.870825i	$0.663585\pi$
$810$	−11.3654	+	27.4386i	−0.399340	+	0.964093i
$811$	9.13598	−	3.78425i	0.320808	−	0.132883i	−0.216468	−	0.976290i	$-0.569454\pi$
$811$	9.13598	−	3.78425i	0.320808	−	0.132883i	0.537275	+	0.843407i	$0.319454\pi$
$812$		−	9.82759i		−	0.344881i
$813$	−5.18862	−	12.5264i	−0.181973	−	0.439322i
$814$	−13.9402	−	13.9402i	−0.488604	−	0.488604i
$815$	16.1671			0.566309
$816$	23.1079	+	91.1522i	0.808937	+	3.19097i
$817$	0.791816			0.0277021
$818$	34.4338	+	34.4338i	1.20395	+	1.20395i
$819$	−3.90207	−	9.42043i	−0.136349	−	0.329176i
$820$		−	26.2817i		−	0.917796i
$821$	3.68695	−	1.52718i	0.128675	−	0.0532991i	−0.317417	−	0.948286i	$-0.602815\pi$
$821$	3.68695	−	1.52718i	0.128675	−	0.0532991i	0.446092	+	0.894987i	$0.352815\pi$
$822$	−33.3669	+	80.5549i	−1.16381	+	2.80968i
$823$	31.8186	+	13.1797i	1.10913	+	0.459415i	0.860637	−	0.509220i	$-0.170066\pi$
$823$	31.8186	+	13.1797i	1.10913	+	0.459415i	0.248489	+	0.968635i	$0.420066\pi$
$824$	77.6157	−	77.6157i	2.70387	−	2.70387i
$825$	2.62256	−	2.62256i	0.0913059	−	0.0913059i
$826$	−114.907	−	47.5961i	−3.99813	−	1.65608i
$827$	16.4079	−	39.6123i	0.570560	−	1.37745i	−0.330519	−	0.943799i	$-0.607224\pi$
$827$	16.4079	−	39.6123i	0.570560	−	1.37745i	0.901079	−	0.433654i	$-0.142776\pi$
$828$	3.57128	−	1.47927i	0.124111	−	0.0514083i
$829$		−	26.1065i		−	0.906716i	−0.891328	−	0.453358i	$-0.850226\pi$
$829$		−	26.1065i		−	0.906716i	0.891328	−	0.453358i	$-0.149774\pi$
$830$	−3.22958	−	7.79690i	−0.112100	−	0.270634i
$831$	−11.6791	−	11.6791i	−0.405143	−	0.405143i
$832$	−20.2233			−0.701117
$833$	23.4209	+	31.3926i	0.811486	+	1.08769i
$834$	−58.8970			−2.03944
$835$	10.1513	+	10.1513i	0.351299	+	0.351299i
$836$	0.828302	+	1.99970i	0.0286474	+	0.0691610i
$837$		−	30.3803i		−	1.05010i
$838$	−40.6296	+	16.8293i	−1.40353	+	0.581360i
$839$	4.27345	−	10.3170i	0.147536	−	0.356183i	−0.832784	−	0.553598i	$-0.813254\pi$
$839$	4.27345	−	10.3170i	0.147536	−	0.356183i	0.980320	+	0.197415i	$0.0632545\pi$
$840$	−62.3797	−	25.8385i	−2.15231	−	0.891514i
$841$	−20.3385	+	20.3385i	−0.701327	+	0.701327i
$842$	−65.3182	+	65.3182i	−2.25101	+	2.25101i
$843$	−41.9371	−	17.3709i	−1.44439	−	0.598286i
$844$	−9.03891	+	21.8219i	−0.311132	+	0.751139i
$845$	9.41171	−	3.89846i	0.323773	−	0.134111i
$846$			24.7437i			0.850706i
$847$	−12.3437	−	29.8004i	−0.424136	−	1.02395i
$848$	77.9035	+	77.9035i	2.67522	+	2.67522i
$849$	−9.38128			−0.321965
$850$	10.7714	+	1.56653i	0.369457	+	0.0537315i
$851$	−2.21904			−0.0760676
$852$	−7.49605	−	7.49605i	−0.256811	−	0.256811i
$853$	8.08038	+	19.5078i	0.276667	+	0.667933i	0.999739	−	0.0228394i	$-0.00727064\pi$
$853$	8.08038	+	19.5078i	0.276667	+	0.667933i	−0.723072	+	0.690772i	$0.757271\pi$
$854$			46.6820i			1.59743i
$855$	0.344373	−	0.142644i	0.0117773	−	0.00487832i
$856$	−40.5783	+	97.9647i	−1.38694	+	3.34836i
$857$	−51.3596	−	21.2739i	−1.75441	−	0.726701i	−0.997302	−	0.0734132i	$-0.976611\pi$
$857$	−51.3596	−	21.2739i	−1.75441	−	0.726701i	−0.757110	−	0.653288i	$-0.773389\pi$
$858$	11.6116	−	11.6116i	0.396414	−	0.396414i
$859$	−1.30531	+	1.30531i	−0.0445366	+	0.0445366i	−0.729024	−	0.684488i	$-0.760026\pi$
$859$	−1.30531	+	1.30531i	−0.0445366	+	0.0445366i	0.684488	+	0.729024i	$0.260026\pi$
$860$	−14.5972	−	6.04635i	−0.497760	−	0.206179i
$861$	17.4334	−	42.0879i	0.594128	−	1.43435i
$862$	10.2274	−	4.23634i	0.348348	−	0.144290i
$863$		−	13.2346i		−	0.450512i	−0.974300	−	0.225256i	$-0.927678\pi$
$863$		−	13.2346i		−	0.450512i	0.974300	−	0.225256i	$-0.0723219\pi$
$864$	15.5117	+	37.4485i	0.527717	+	1.27402i
$865$	−12.7842	−	12.7842i	−0.434676	−	0.434676i
$866$	−9.67794			−0.328870
$867$	−3.73726	−	35.8552i	−0.126924	−	1.21771i
$868$	192.370			6.52948
$869$	8.43231	+	8.43231i	0.286047	+	0.286047i
$870$	−1.04305	−	2.51813i	−0.0353625	−	0.0853727i
$871$		−	16.3269i		−	0.553216i
$872$	46.1314	−	19.1083i	1.56221	−	0.647088i
$873$	−0.974269	+	2.35209i	−0.0329740	+	0.0796063i
$874$	0.315674	+	0.130756i	0.0106778	+	0.00442290i
$875$	−2.87222	+	2.87222i	−0.0970989	+	0.0970989i
$876$	21.7209	−	21.7209i	0.733882	−	0.733882i
$877$	33.7252	+	13.9695i	1.13882	+	0.471715i	0.870770	−	0.491690i	$-0.163621\pi$
$877$	33.7252	+	13.9695i	1.13882	+	0.471715i	0.268050	+	0.963405i	$0.413621\pi$
$878$	−25.4585	+	61.4622i	−0.859182	+	2.07425i
$879$	−38.4383	+	15.9217i	−1.29649	+	0.537024i
$880$		−	18.8109i		−	0.634116i
$881$	9.19237	+	22.1923i	0.309699	+	0.747679i	0.999715	+	0.0238847i	$0.00760345\pi$
$881$	9.19237	+	22.1923i	0.309699	+	0.747679i	−0.690016	+	0.723794i	$0.742397\pi$
$882$	−26.5413	−	26.5413i	−0.893691	−	0.893691i
$883$	−42.2659			−1.42236			−0.711181	−	0.703009i	$-0.751839\pi$
$883$	−42.2659			−1.42236			−0.711181	+	0.703009i	$0.751839\pi$
$884$	34.0052	+	4.94550i	1.14372	+	0.166335i
$885$	−24.5954			−0.826765
$886$	66.8674	+	66.8674i	2.24645	+	2.24645i
$887$	−2.83594	−	6.84656i	−0.0952214	−	0.229885i	0.869091	−	0.494653i	$-0.164705\pi$
$887$	−2.83594	−	6.84656i	−0.0952214	−	0.229885i	−0.964312	+	0.264768i	$0.914705\pi$
$888$			70.9731i			2.38170i
$889$	60.5707	−	25.0892i	2.03148	−	0.841465i
$890$	−3.33917	+	8.06147i	−0.111929	+	0.270221i
$891$	−18.1785	−	7.52979i	−0.609004	−	0.252258i
$892$	−76.3724	+	76.3724i	−2.55714	+	2.55714i
$893$	−1.10273	+	1.10273i	−0.0369015	+	0.0369015i
$894$	−40.3365	−	16.7079i	−1.34906	−	0.558797i
$895$	−2.87691	+	6.94548i	−0.0961646	+	0.232162i
$896$	−24.0228	+	9.95058i	−0.802546	+	0.332426i
$897$		−	1.84836i		−	0.0617151i
$898$	4.90916	+	11.8518i	0.163821	+	0.395499i
$899$	3.28108	+	3.28108i	0.109430	+	0.109430i
$900$	−7.43778			−0.247926
$901$	−25.2559	−	33.8523i	−0.841398	−	1.12778i
$902$	24.4200			0.813096
$903$	−19.3655	−	19.3655i	−0.644442	−	0.644442i
$904$	−39.1718	−	94.5690i	−1.30283	−	3.14532i
$905$		−	4.39392i		−	0.146059i
$906$	−19.4579	+	8.05973i	−0.646446	+	0.267767i
$907$	4.07329	−	9.83379i	0.135251	−	0.326526i	−0.841714	−	0.539924i	$-0.818453\pi$
$907$	4.07329	−	9.83379i	0.135251	−	0.326526i	0.976965	+	0.213398i	$0.0684531\pi$
$908$	12.9424	+	5.36091i	0.429508	+	0.177908i
$909$	10.4404	−	10.4404i	0.346285	−	0.346285i
$910$	−12.7170	+	12.7170i	−0.421565	+	0.421565i
$911$	6.00286	+	2.48647i	0.198884	+	0.0823803i	0.479902	−	0.877322i	$-0.340672\pi$
$911$	6.00286	+	2.48647i	0.198884	+	0.0823803i	−0.281018	+	0.959702i	$0.590672\pi$
$912$	2.17356	−	5.24744i	0.0719738	−	0.173760i
$913$	5.16558	−	2.13965i	0.170956	−	0.0708122i
$914$		−	21.5466i		−	0.712697i
$915$	3.53274	+	8.52878i	0.116789	+	0.281953i
$916$	81.5543	+	81.5543i	2.69463	+	2.69463i
$917$	−63.9542			−2.11195
$918$	−8.52641	−	33.6336i	−0.281414	−	1.11008i
$919$	−9.77664			−0.322502			−0.161251	−	0.986913i	$-0.551553\pi$
$919$	−9.77664			−0.322502			−0.161251	+	0.986913i	$0.551553\pi$
$920$	−2.88069	−	2.88069i	−0.0949734	−	0.0949734i
$921$	10.8285	+	26.1422i	0.356810	+	0.861415i
$922$		−	68.3246i		−	2.25015i
$923$	−1.55881	+	0.645679i	−0.0513088	+	0.0212528i
$924$	28.6489	−	69.1644i	0.942478	−	2.27534i
$925$	3.94470	+	1.63395i	0.129701	+	0.0537239i
$926$	3.99453	−	3.99453i	0.131268	−	0.131268i
$927$	14.8202	−	14.8202i	0.486759	−	0.486759i
$928$	−5.71970	−	2.36918i	−0.187758	−	0.0777721i
$929$	−8.67635	+	20.9466i	−0.284662	+	0.687234i	−0.999933	−	0.0116131i	$-0.996303\pi$
$929$	−8.67635	+	20.9466i	−0.284662	+	0.687234i	0.715271	+	0.698847i	$0.246303\pi$
$930$	49.2913	−	20.4171i	1.61632	−	0.669504i
$931$		−	2.36569i		−	0.0775322i
$932$	18.4412	+	44.5210i	0.604062	+	1.45834i
$933$	−8.02353	−	8.02353i	−0.262678	−	0.262678i
$934$	−34.8903			−1.14164
$935$	−1.03785	+	7.13626i	−0.0339414	+	0.233381i
$936$	−19.6774			−0.643176
$937$	16.0606	+	16.0606i	0.524678	+	0.524678i	0.918981	−	0.394303i	$-0.129014\pi$
$937$	16.0606	+	16.0606i	0.524678	+	0.524678i	−0.394303	+	0.918981i	$0.629014\pi$
$938$	−39.9483	−	96.4437i	−1.30436	−	3.14900i
$939$			33.7494i			1.10137i
$940$	28.7495	−	11.9084i	0.937705	−	0.388410i
$941$	−14.3382	+	34.6155i	−0.467412	+	1.12843i	0.497877	+	0.867248i	$0.334113\pi$
$941$	−14.3382	+	34.6155i	−0.467412	+	1.12843i	−0.965289	+	0.261185i	$0.915887\pi$
$942$	90.6271	+	37.5390i	2.95279	+	1.22309i
$943$	1.94361	−	1.94361i	0.0632928	−	0.0632928i
$944$	−88.2080	+	88.2080i	−2.87093	+	2.87093i
$945$	11.9627	+	4.95511i	0.389147	+	0.161190i
$946$	5.61804	−	13.5632i	0.182658	−	0.440976i
$947$	−25.0912	+	10.3931i	−0.815354	+	0.337731i	−0.751088	−	0.660202i	$-0.770471\pi$
$947$	−25.0912	+	10.3931i	−0.815354	+	0.337731i	−0.0642663	+	0.997933i	$0.520471\pi$
$948$		−	71.8478i		−	2.33351i
$949$	−1.87095	−	4.51688i	−0.0607336	−	0.146624i
$950$	−0.464882	−	0.464882i	−0.0150828	−	0.0150828i
$951$	5.03519			0.163277
$952$	127.256	−	32.2605i	4.12439	−	1.04557i
$953$	−0.783845			−0.0253912			−0.0126956	−	0.999919i	$-0.504041\pi$
$953$	−0.783845			−0.0253912			−0.0126956	+	0.999919i	$0.504041\pi$
$954$	28.6208	+	28.6208i	0.926633	+	0.926633i
$955$	−1.92519	−	4.64782i	−0.0622976	−	0.150400i
$956$			34.7103i			1.12261i
$957$	1.66831	−	0.691035i	0.0539287	−	0.0223380i
$958$	23.8284	−	57.5269i	0.769862	−	1.85861i
$959$	58.4496	+	24.2106i	1.88744	+	0.781802i
$960$	−18.0806	+	18.0806i	−0.583550	+	0.583550i
$961$	−42.3052	+	42.3052i	−1.36468	+	1.36468i
$962$	17.4655	+	7.23444i	0.563110	+	0.233248i
$963$	−7.74814	+	18.7057i	−0.249680	+	0.602782i
$964$	17.5935	−	7.28745i	0.566647	−	0.234713i
$965$			26.8878i			0.865549i
$966$	−4.52253	−	10.9184i	−0.145510	−	0.351292i
$967$	37.4547	+	37.4547i	1.20446	+	1.20446i	0.972795	+	0.231668i	$0.0744184\pi$
$967$	37.4547	+	37.4547i	1.20446	+	1.20446i	0.231668	+	0.972795i	$0.425582\pi$
$968$	−62.2472			−2.00070
$969$	−1.11410	+	1.87079i	−0.0357899	+	0.0600984i
$970$	4.49039			0.144178
$971$	5.09957	+	5.09957i	0.163653	+	0.163653i	0.784183	−	0.620530i	$-0.213082\pi$
$971$	5.09957	+	5.09957i	0.163653	+	0.163653i	−0.620530	+	0.784183i	$0.713082\pi$
$972$	27.1805	+	65.6196i	0.871816	+	2.10475i
$973$			42.7350i			1.37002i
$974$	−70.6495	+	29.2640i	−2.26375	+	0.937678i
$975$	−1.36101	+	3.28577i	−0.0435872	+	0.105229i
$976$	43.2570	+	17.9176i	1.38462	+	0.573529i
$977$	7.08744	−	7.08744i	0.226747	−	0.226747i	−0.584585	−	0.811332i	$-0.698743\pi$
$977$	7.08744	−	7.08744i	0.226747	−	0.226747i	0.811332	+	0.584585i	$0.198743\pi$
$978$	63.9971	−	63.9971i	2.04640	−	2.04640i
$979$	−5.34087	−	2.21226i	−0.170695	−	0.0707041i
$980$	−18.0645	+	43.6116i	−0.577050	+	1.39312i
$981$	8.80848	−	3.64859i	0.281233	−	0.116491i
$982$		−	93.7871i		−	2.99287i
$983$	−1.01522	−	2.45095i	−0.0323804	−	0.0781733i	0.906862	−	0.421427i	$-0.138471\pi$
$983$	−1.01522	−	2.45095i	−0.0323804	−	0.0781733i	−0.939243	+	0.343254i	$0.888471\pi$
$984$	−62.1641	−	62.1641i	−1.98172	−	1.98172i
$985$	8.51380			0.271272
$986$	4.55329	+	2.71158i	0.145006	+	0.0863544i
$987$	53.9391			1.71690
$988$	−1.46763	−	1.46763i	−0.0466914	−	0.0466914i
$989$	−0.632361	−	1.52666i	−0.0201079	−	0.0485448i
$990$		−	6.91090i		−	0.219643i
$991$	−25.8108	+	10.6912i	−0.819907	+	0.339616i	−0.752899	−	0.658136i	$-0.771345\pi$
$991$	−25.8108	+	10.6912i	−0.819907	+	0.339616i	−0.0670076	+	0.997752i	$0.521345\pi$
$992$	46.3756	−	111.960i	1.47243	−	3.55475i
$993$	−5.40128	−	2.23728i	−0.171404	−	0.0709980i
$994$	−7.62811	+	7.62811i	−0.241949	+	0.241949i
$995$	−11.8569	+	11.8569i	−0.375888	+	0.375888i
$996$	−31.1222	−	12.8913i	−0.986146	−	0.408475i
$997$	−9.94558	+	24.0108i	−0.314980	+	0.760428i	0.684526	+	0.728989i	$0.260009\pi$
$997$	−9.94558	+	24.0108i	−0.314980	+	0.760428i	−0.999506	+	0.0314398i	$0.989991\pi$
$998$	82.8160	−	34.3035i	2.62149	−	1.08586i
$999$		−	13.6107i		−	0.430622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.l.a.66.6	✓	24
3.2	odd	2		765.2.be.b.406.1		24
5.2	odd	4		425.2.n.c.49.1		24
5.3	odd	4		425.2.n.f.49.6		24
5.4	even	2		425.2.m.b.151.1		24
17.3	odd	16		1445.2.d.j.866.21		24
17.5	odd	16		1445.2.a.q.1.2		12
17.8	even	8	inner	85.2.l.a.76.6	yes	24
17.12	odd	16		1445.2.a.p.1.2		12
17.14	odd	16		1445.2.d.j.866.22		24
51.8	odd	8		765.2.be.b.586.1		24
85.8	odd	8		425.2.n.c.399.1		24
85.29	odd	16		7225.2.a.bs.1.11		12
85.39	odd	16		7225.2.a.bq.1.11		12
85.42	odd	8		425.2.n.f.399.6		24
85.59	even	8		425.2.m.b.76.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.6	✓	24	1.1	even	1	trivial
85.2.l.a.76.6	yes	24	17.8	even	8	inner
425.2.m.b.76.1		24	85.59	even	8
425.2.m.b.151.1		24	5.4	even	2
425.2.n.c.49.1		24	5.2	odd	4
425.2.n.c.399.1		24	85.8	odd	8
425.2.n.f.49.6		24	5.3	odd	4
425.2.n.f.399.6		24	85.42	odd	8
765.2.be.b.406.1		24	3.2	odd	2
765.2.be.b.586.1		24	51.8	odd	8
1445.2.a.p.1.2		12	17.12	odd	16
1445.2.a.q.1.2		12	17.5	odd	16
1445.2.d.j.866.21		24	17.3	odd	16
1445.2.d.j.866.22		24	17.14	odd	16
7225.2.a.bq.1.11		12	85.39	odd	16
7225.2.a.bs.1.11		12	85.29	odd	16

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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.86672 + 1.86672i) q^{2} +(-0.811501 - 1.95914i) q^{3} +4.96928i q^{4} +(0.923880 - 0.382683i) q^{5} +(2.14231 - 5.17200i) q^{6} +(-3.75274 - 1.55444i) q^{7} +(-5.54282 + 5.54282i) q^{8} +(-1.05836 + 1.05836i) q^{9} +(2.43899 + 1.01026i) q^{10} +(-0.669316 + 1.61587i) q^{11} +(9.73550 - 4.03258i) q^{12} -1.67715i q^{13} +(-4.10362 - 9.90701i) q^{14} +(-1.49946 - 1.49946i) q^{15} -10.7552 q^{16} +(4.08018 + 0.593395i) q^{17} -3.95133 q^{18} +(-0.176096 - 0.176096i) q^{19} +(1.90166 + 4.59102i) q^{20} +8.61356i q^{21} +(-4.26580 + 1.76695i) q^{22} +(-0.198886 + 0.480154i) q^{23} +(15.3571 + 6.36113i) q^{24} +(0.707107 - 0.707107i) q^{25} +(3.13077 - 3.13077i) q^{26} +(-2.94507 - 1.21989i) q^{27} +(7.72443 - 18.6484i) q^{28} +(0.449816 - 0.186320i) q^{29} -5.59814i q^{30} +(3.64713 + 8.80495i) q^{31} +(-8.99131 - 8.99131i) q^{32} +3.70886 q^{33} +(6.50885 + 8.72426i) q^{34} -4.06194 q^{35} +(-5.25930 - 5.25930i) q^{36} +(1.63395 + 3.94470i) q^{37} -0.657443i q^{38} +(-3.28577 + 1.36101i) q^{39} +(-2.99975 + 7.24204i) q^{40} +(-4.88624 - 2.02395i) q^{41} +(-16.0791 + 16.0791i) q^{42} +(-2.24825 + 2.24825i) q^{43} +(-8.02972 - 3.32602i) q^{44} +(-0.572782 + 1.38282i) q^{45} +(-1.26758 + 0.525048i) q^{46} -6.26212i q^{47} +(8.72786 + 21.0709i) q^{48} +(6.71704 + 6.71704i) q^{49} +2.63994 q^{50} +(-2.14853 - 8.47517i) q^{51} +8.33425 q^{52} +(-7.24333 - 7.24333i) q^{53} +(-3.22043 - 7.77481i) q^{54} +1.74901i q^{55} +(29.4167 - 12.1848i) q^{56} +(-0.202094 + 0.487898i) q^{57} +(1.18749 + 0.491874i) q^{58} +(8.20143 - 8.20143i) q^{59} +(7.45123 - 7.45123i) q^{60} +(-4.02196 - 1.66595i) q^{61} +(-9.62820 + 23.2445i) q^{62} +(5.61692 - 2.32660i) q^{63} -12.0581i q^{64} +(-0.641819 - 1.54949i) q^{65} +(6.92340 + 6.92340i) q^{66} +9.73489 q^{67} +(-2.94875 + 20.2756i) q^{68} +1.10208 q^{69} +(-7.58250 - 7.58250i) q^{70} +(-0.384985 - 0.929437i) q^{71} -11.7326i q^{72} +(2.69318 - 1.11555i) q^{73} +(-4.31353 + 10.4138i) q^{74} +(-1.95914 - 0.811501i) q^{75} +(0.875070 - 0.875070i) q^{76} +(5.02354 - 5.02354i) q^{77} +(-8.67424 - 3.59299i) q^{78} +(2.60922 - 6.29920i) q^{79} +(-9.93651 + 4.11584i) q^{80} +11.2500i q^{81} +(-5.34310 - 12.8994i) q^{82} +(-2.26046 - 2.26046i) q^{83} -42.8032 q^{84} +(3.99668 - 1.01319i) q^{85} -8.39371 q^{86} +(-0.730053 - 0.730053i) q^{87} +(-5.24658 - 12.6664i) q^{88} +3.30525i q^{89} +(-3.65055 + 1.51211i) q^{90} +(-2.60703 + 6.29392i) q^{91} +(-2.38602 - 0.988323i) q^{92} +(14.2904 - 14.2904i) q^{93} +(11.6896 - 11.6896i) q^{94} +(-0.230080 - 0.0953024i) q^{95} +(-10.3188 + 24.9117i) q^{96} +(1.57147 - 0.650923i) q^{97} +25.0777i q^{98} +(-1.00180 - 2.41856i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35}+ \cdots - 8 q^{99}+O(q^{100}) \) 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 + 24 * q^12 - 8 * q^15 - 24 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 32 * q^22 - 16 * q^23 - 8 * q^24 + 16 * q^26 + 24 * q^27 + 48 * q^28 - 8 * q^29 + 16 * q^34 - 32 * q^35 - 24 * q^36 + 24 * q^37 + 8 * q^39 + 16 * q^40 + 16 * q^41 - 24 * q^42 + 8 * q^43 + 16 * q^44 + 16 * q^45 + 8 * q^46 + 80 * q^48 + 8 * q^50 - 56 * q^51 - 48 * q^52 + 24 * q^53 - 32 * q^54 + 64 * q^56 + 32 * q^57 - 64 * q^58 + 32 * q^59 + 24 * q^60 + 32 * q^61 - 32 * q^62 - 56 * q^63 + 8 * q^65 + 96 * q^66 + 16 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^75 - 8 * q^76 + 24 * q^77 - 112 * q^78 - 32 * q^80 - 80 * q^82 - 96 * q^83 - 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 + 80 * q^92 + 64 * q^93 + 56 * q^94 - 16 * q^95 - 168 * q^96 - 40 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more