LMFDB - Embedded newform 930.2.n.g.901.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 31 x^{14} + 20 x^{13} + 474 x^{12} + 463 x^{11} + 6637 x^{10} + 13567 x^{9} + \cdots + 22848400 $ x^16 - x^15 + 31x^14 + 20x^13 + 474x^12 + 463x^11 + 6637x^10 + 13567x^9 + 108596x^8 + 172826x^7 + 917001x^6 + 1583565x^5 + 3229491x^4 - 1732290x^3 + 4672960x^2 - 5544800x + 22848400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			901.2
Root			$-0.530826 + 1.63371i$ of defining polynomial
Character	$\chi$	$=$	930.901
Dual form			930.2.n.g.481.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-0.530826 - 1.63371i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-0.530826 - 1.63371i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(0.890814 + 2.74164i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(0.180762 - 0.131331i) q^{13} +(-0.530826 + 1.63371i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.60240 - 4.93169i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(0.261465 + 0.189965i) q^{19} +(0.309017 + 0.951057i) q^{20} +(1.38972 + 1.00969i) q^{21} +(0.890814 - 2.74164i) q^{22} +(0.871763 - 2.68301i) q^{23} +(0.309017 + 0.951057i) q^{24} +1.00000 q^{25} -0.223434 q^{26} +(0.309017 + 0.951057i) q^{27} +(1.38972 - 1.00969i) q^{28} +(-3.51438 - 2.55335i) q^{29} +1.00000 q^{30} +(0.731733 + 5.51947i) q^{31} +1.00000 q^{32} +(-2.33218 - 1.69443i) q^{33} +(-4.19514 + 3.04795i) q^{34} +(-0.530826 - 1.63371i) q^{35} +1.00000 q^{36} +2.36659 q^{37} +(-0.0998708 - 0.307371i) q^{38} +(-0.0690450 + 0.212499i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-4.56395 - 3.31590i) q^{41} +(-0.530826 - 1.63371i) q^{42} +(5.84403 + 4.24594i) q^{43} +(-2.33218 + 1.69443i) q^{44} +(0.309017 - 0.951057i) q^{45} +(-2.28230 + 1.65819i) q^{46} +(6.83776 - 4.96792i) q^{47} +(0.309017 - 0.951057i) q^{48} +(3.27587 - 2.38006i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(1.60240 + 4.93169i) q^{51} +(0.180762 + 0.131331i) q^{52} +(1.25037 - 3.84823i) q^{53} +(0.309017 - 0.951057i) q^{54} +(0.890814 + 2.74164i) q^{55} -1.71779 q^{56} -0.323189 q^{57} +(1.34237 + 4.13140i) q^{58} +(4.48514 - 3.25864i) q^{59} +(-0.809017 - 0.587785i) q^{60} +12.0647 q^{61} +(2.65228 - 4.89545i) q^{62} -1.71779 q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.180762 - 0.131331i) q^{65} +(0.890814 + 2.74164i) q^{66} +10.7024 q^{67} +5.18548 q^{68} +(0.871763 + 2.68301i) q^{69} +(-0.530826 + 1.63371i) q^{70} +(2.26300 - 6.96480i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-1.54022 - 4.74030i) q^{73} +(-1.91461 - 1.39104i) q^{74} +(-0.809017 + 0.587785i) q^{75} +(-0.0998708 + 0.307371i) q^{76} +(4.00619 - 2.91067i) q^{77} +(0.180762 - 0.131331i) q^{78} +(-1.72100 + 5.29668i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(1.74327 + 5.36524i) q^{82} +(-2.25271 - 1.63669i) q^{83} +(-0.530826 + 1.63371i) q^{84} +(1.60240 - 4.93169i) q^{85} +(-2.23222 - 6.87007i) q^{86} +4.34401 q^{87} +2.88274 q^{88} +(-1.46075 - 4.49572i) q^{89} +(-0.809017 + 0.587785i) q^{90} +(-0.310511 - 0.225599i) q^{91} +2.82108 q^{92} +(-3.83625 - 4.03524i) q^{93} -8.45194 q^{94} +(0.261465 + 0.189965i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(-2.06009 - 6.34030i) q^{97} -4.04920 q^{98} +2.88274 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{12} + 4 q^{13} + q^{14} - 4 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 12 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{23} - 4 q^{24} + 16 q^{25} + 4 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 16 q^{30} + 17 q^{31} + 16 q^{32} + 5 q^{33} + 3 q^{34} + q^{35} + 16 q^{36} + 4 q^{37} + 3 q^{38} - 6 q^{39} - 4 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} + 5 q^{44} - 4 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 33 q^{49} - 4 q^{50} + 3 q^{51} + 4 q^{52} + 9 q^{53} - 4 q^{54} + 6 q^{56} + 18 q^{57} - 15 q^{58} - 7 q^{59} - 4 q^{60} + 30 q^{61} + 12 q^{62} + 6 q^{63} - 4 q^{64} + 4 q^{65} + 86 q^{67} - 12 q^{68} - 2 q^{69} + q^{70} - 3 q^{71} - 4 q^{72} + 8 q^{73} - q^{74} - 4 q^{75} + 3 q^{76} + 2 q^{77} + 4 q^{78} + 30 q^{79} - 4 q^{80} - 4 q^{81} - 7 q^{82} + 16 q^{83} + q^{84} + 3 q^{85} - 12 q^{86} - 10 q^{88} - 29 q^{89} - 4 q^{90} + 30 q^{91} + 8 q^{92} - 8 q^{93} + 24 q^{94} - 12 q^{95} - 4 q^{96} - 5 q^{97} + 62 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^12 + 4 * q^13 + q^14 - 4 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 12 * q^19 - 4 * q^20 - 4 * q^21 - 2 * q^23 - 4 * q^24 + 16 * q^25 + 4 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 16 * q^30 + 17 * q^31 + 16 * q^32 + 5 * q^33 + 3 * q^34 + q^35 + 16 * q^36 + 4 * q^37 + 3 * q^38 - 6 * q^39 - 4 * q^40 - 7 * q^41 + q^42 - 2 * q^43 + 5 * q^44 - 4 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 33 * q^49 - 4 * q^50 + 3 * q^51 + 4 * q^52 + 9 * q^53 - 4 * q^54 + 6 * q^56 + 18 * q^57 - 15 * q^58 - 7 * q^59 - 4 * q^60 + 30 * q^61 + 12 * q^62 + 6 * q^63 - 4 * q^64 + 4 * q^65 + 86 * q^67 - 12 * q^68 - 2 * q^69 + q^70 - 3 * q^71 - 4 * q^72 + 8 * q^73 - q^74 - 4 * q^75 + 3 * q^76 + 2 * q^77 + 4 * q^78 + 30 * q^79 - 4 * q^80 - 4 * q^81 - 7 * q^82 + 16 * q^83 + q^84 + 3 * q^85 - 12 * q^86 - 10 * q^88 - 29 * q^89 - 4 * q^90 + 30 * q^91 + 8 * q^92 - 8 * q^93 + 24 * q^94 - 12 * q^95 - 4 * q^96 - 5 * q^97 + 62 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.00000			0.408248
$7$	−0.530826	−	1.63371i	−0.200633	−	0.617486i	−0.999864	−	0.0164621i	$-0.994760\pi$
$7$	−0.530826	−	1.63371i	−0.200633	−	0.617486i	0.799231	−	0.601024i	$-0.205240\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−0.809017	−	0.587785i	−0.255834	−	0.185874i
$11$	0.890814	+	2.74164i	0.268591	+	0.826637i	0.990844	+	0.135009i	$0.0431062\pi$
$11$	0.890814	+	2.74164i	0.268591	+	0.826637i	−0.722254	+	0.691628i	$0.756894\pi$
$12$	−0.809017	−	0.587785i	−0.233543	−	0.169679i
$13$	0.180762	−	0.131331i	0.0501344	−	0.0364248i	−0.562436	−	0.826841i	$-0.690136\pi$
$13$	0.180762	−	0.131331i	0.0501344	−	0.0364248i	0.612570	+	0.790416i	$0.290136\pi$
$14$	−0.530826	+	1.63371i	−0.141869	+	0.436628i
$15$	−0.809017	+	0.587785i	−0.208887	+	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.60240	−	4.93169i	0.388640	−	1.19611i	−0.545166	−	0.838328i	$-0.683533\pi$
$17$	1.60240	−	4.93169i	0.388640	−	1.19611i	0.933805	−	0.357781i	$-0.116467\pi$
$18$	−0.809017	+	0.587785i	−0.190687	+	0.138542i
$19$	0.261465	+	0.189965i	0.0599842	+	0.0435811i	0.617373	−	0.786670i	$-0.288197\pi$
$19$	0.261465	+	0.189965i	0.0599842	+	0.0435811i	−0.557389	+	0.830251i	$0.688197\pi$
$20$	0.309017	+	0.951057i	0.0690983	+	0.212663i
$21$	1.38972	+	1.00969i	0.303262	+	0.220333i
$22$	0.890814	−	2.74164i	0.189922	−	0.584520i
$23$	0.871763	−	2.68301i	0.181775	−	0.559446i	−0.818103	−	0.575072i	$-0.804974\pi$
$23$	0.871763	−	2.68301i	0.181775	−	0.559446i	0.999878	+	0.0156258i	$0.00497404\pi$
$24$	0.309017	+	0.951057i	0.0630778	+	0.194134i
$25$	1.00000			0.200000
$26$	−0.223434			−0.0438191
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	1.38972	−	1.00969i	0.262632	−	0.190814i
$29$	−3.51438	−	2.55335i	−0.652604	−	0.474145i	0.211553	−	0.977366i	$-0.432148\pi$
$29$	−3.51438	−	2.55335i	−0.652604	−	0.474145i	−0.864157	+	0.503222i	$0.832148\pi$
$30$	1.00000			0.182574
$31$	0.731733	+	5.51947i	0.131423	+	0.991326i
$31$	0.731733	+	5.51947i	0.131423	+	0.991326i
$32$	1.00000			0.176777
$33$	−2.33218	−	1.69443i	−0.405981	−	0.294962i
$34$	−4.19514	+	3.04795i	−0.719461	+	0.522719i
$35$	−0.530826	−	1.63371i	−0.0897259	−	0.276148i
$36$	1.00000			0.166667
$37$	2.36659			0.389064			0.194532	−	0.980896i	$-0.437681\pi$
$37$	2.36659			0.389064			0.194532	+	0.980896i	$0.437681\pi$
$38$	−0.0998708	−	0.307371i	−0.0162012	−	0.0498621i
$39$	−0.0690450	+	0.212499i	−0.0110560	+	0.0340270i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	−4.56395	−	3.31590i	−0.712769	−	0.517857i	0.171297	−	0.985219i	$-0.445204\pi$
$41$	−4.56395	−	3.31590i	−0.712769	−	0.517857i	−0.884066	+	0.467363i	$0.845204\pi$
$42$	−0.530826	−	1.63371i	−0.0819082	−	0.252088i
$43$	5.84403	+	4.24594i	0.891206	+	0.647499i	0.936192	−	0.351488i	$-0.114324\pi$
$43$	5.84403	+	4.24594i	0.891206	+	0.647499i	−0.0449859	+	0.998988i	$0.514324\pi$
$44$	−2.33218	+	1.69443i	−0.351590	+	0.255445i
$45$	0.309017	−	0.951057i	0.0460655	−	0.141775i
$46$	−2.28230	+	1.65819i	−0.336507	+	0.244487i
$47$	6.83776	−	4.96792i	0.997390	−	0.724646i	0.0358630	−	0.999357i	$-0.488582\pi$
$47$	6.83776	−	4.96792i	0.997390	−	0.724646i	0.961527	+	0.274711i	$0.0885820\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	3.27587	−	2.38006i	0.467982	−	0.340009i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$	1.60240	+	4.93169i	0.224381	+	0.690574i
$52$	0.180762	+	0.131331i	0.0250672	+	0.0182124i
$53$	1.25037	−	3.84823i	0.171751	−	0.528596i	−0.827719	−	0.561143i	$-0.810362\pi$
$53$	1.25037	−	3.84823i	0.171751	−	0.528596i	0.999470	+	0.0325471i	$0.0103619\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	0.890814	+	2.74164i	0.120117	+	0.369683i
$56$	−1.71779			−0.229549
$57$	−0.323189			−0.0428074
$58$	1.34237	+	4.13140i	0.176262	+	0.542480i
$59$	4.48514	−	3.25864i	0.583915	−	0.424239i	−0.256218	−	0.966619i	$-0.582477\pi$
$59$	4.48514	−	3.25864i	0.583915	−	0.424239i	0.840133	+	0.542380i	$0.182477\pi$
$60$	−0.809017	−	0.587785i	−0.104444	−	0.0758827i
$61$	12.0647			1.54472			0.772362	−	0.635183i	$-0.219075\pi$
$61$	12.0647			1.54472			0.772362	+	0.635183i	$0.219075\pi$
$62$	2.65228	−	4.89545i	0.336840	−	0.621723i
$63$	−1.71779			−0.216421
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.180762	−	0.131331i	0.0224208	−	0.0162897i
$66$	0.890814	+	2.74164i	0.109652	+	0.337473i
$67$	10.7024			1.30751			0.653754	−	0.756707i	$-0.273193\pi$
$67$	10.7024			1.30751			0.653754	+	0.756707i	$0.273193\pi$
$68$	5.18548			0.628832
$69$	0.871763	+	2.68301i	0.104948	+	0.322996i
$70$	−0.530826	+	1.63371i	−0.0634458	+	0.195266i
$71$	2.26300	−	6.96480i	0.268569	−	0.826570i	−0.722281	−	0.691600i	$-0.756906\pi$
$71$	2.26300	−	6.96480i	0.268569	−	0.826570i	0.990850	−	0.134970i	$-0.0430938\pi$
$72$	−0.809017	−	0.587785i	−0.0953436	−	0.0692712i
$73$	−1.54022	−	4.74030i	−0.180269	−	0.554810i	0.819566	−	0.572985i	$-0.194215\pi$
$73$	−1.54022	−	4.74030i	−0.180269	−	0.554810i	−0.999835	+	0.0181747i	$0.994215\pi$
$74$	−1.91461	−	1.39104i	−0.222569	−	0.161706i
$75$	−0.809017	+	0.587785i	−0.0934172	+	0.0678716i
$76$	−0.0998708	+	0.307371i	−0.0114560	+	0.0352578i
$77$	4.00619	−	2.91067i	0.456548	−	0.331702i
$78$	0.180762	−	0.131331i	0.0204673	−	0.0148703i
$79$	−1.72100	+	5.29668i	−0.193627	+	0.595923i	0.806363	+	0.591421i	$0.201433\pi$
$79$	−1.72100	+	5.29668i	−0.193627	+	0.595923i	−0.999990	+	0.00450179i	$0.998567\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	1.74327	+	5.36524i	0.192512	+	0.592492i
$83$	−2.25271	−	1.63669i	−0.247267	−	0.179650i	0.457248	−	0.889339i	$-0.348835\pi$
$83$	−2.25271	−	1.63669i	−0.247267	−	0.179650i	−0.704515	+	0.709689i	$0.748835\pi$
$84$	−0.530826	+	1.63371i	−0.0579178	+	0.178253i
$85$	1.60240	−	4.93169i	0.173805	−	0.534916i
$86$	−2.23222	−	6.87007i	−0.240707	−	0.740819i
$87$	4.34401			0.465727
$88$	2.88274			0.307301
$89$	−1.46075	−	4.49572i	−0.154839	−	0.476545i	0.843306	−	0.537434i	$-0.180606\pi$
$89$	−1.46075	−	4.49572i	−0.154839	−	0.476545i	−0.998145	+	0.0608891i	$0.980606\pi$
$90$	−0.809017	+	0.587785i	−0.0852779	+	0.0619580i
$91$	−0.310511	−	0.225599i	−0.0325504	−	0.0236493i
$92$	2.82108			0.294118
$93$	−3.83625	−	4.03524i	−0.397800	−	0.418435i
$94$	−8.45194			−0.871751
$95$	0.261465	+	0.189965i	0.0268257	+	0.0194900i
$96$	−0.809017	+	0.587785i	−0.0825700	+	0.0599906i
$97$	−2.06009	−	6.34030i	−0.209170	−	0.643760i	−0.999516	−	0.0310990i	$-0.990099\pi$
$97$	−2.06009	−	6.34030i	−0.209170	−	0.643760i	0.790346	−	0.612661i	$-0.209901\pi$
$98$	−4.04920			−0.409031
$99$	2.88274			0.289726
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	−1.34795	+	4.14856i	−0.134126	+	0.412798i	−0.995453	−	0.0952534i	$-0.969634\pi$
$101$	−1.34795	+	4.14856i	−0.134126	+	0.412798i	0.861327	+	0.508051i	$0.169634\pi$
$102$	1.60240	−	4.93169i	0.158661	−	0.488310i
$103$	0.0978841	+	0.0711170i	0.00964481	+	0.00700736i	0.592597	−	0.805499i	$-0.298103\pi$
$103$	0.0978841	+	0.0711170i	0.00964481	+	0.00700736i	−0.582952	+	0.812506i	$0.698103\pi$
$104$	−0.0690450	−	0.212499i	−0.00677042	−	0.0208372i
$105$	1.38972	+	1.00969i	0.135623	+	0.0985357i
$106$	−3.27350	+	2.37834i	−0.317951	+	0.231005i
$107$	5.37576	−	16.5449i	0.519694	−	1.59945i	−0.254881	−	0.966973i	$-0.582036\pi$
$107$	5.37576	−	16.5449i	0.519694	−	1.59945i	0.774575	−	0.632482i	$-0.217964\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	−2.77497	+	2.01613i	−0.265794	+	0.193110i	−0.712697	−	0.701472i	$-0.752527\pi$
$109$	−2.77497	+	2.01613i	−0.265794	+	0.193110i	0.446904	+	0.894582i	$0.352527\pi$
$110$	0.890814	−	2.74164i	0.0849358	−	0.261405i
$111$	−1.91461	+	1.39104i	−0.181727	+	0.132032i
$112$	1.38972	+	1.00969i	0.131316	+	0.0954068i
$113$	−0.730108	−	2.24704i	−0.0686828	−	0.211384i	0.910824	−	0.412795i	$-0.135447\pi$
$113$	−0.730108	−	2.24704i	−0.0686828	−	0.211384i	−0.979507	+	0.201411i	$0.935447\pi$
$114$	0.261465	+	0.189965i	0.0244884	+	0.0177919i
$115$	0.871763	−	2.68301i	0.0812923	−	0.250192i
$116$	1.34237	−	4.13140i	0.124636	−	0.383591i
$117$	−0.0690450	−	0.212499i	−0.00638321	−	0.0196455i
$118$	−5.54393			−0.510361
$119$	−8.90756			−0.816555
$120$	0.309017	+	0.951057i	0.0282093	+	0.0868192i
$121$	2.17613	−	1.58105i	0.197830	−	0.143732i
$122$	−9.76053	−	7.09144i	−0.883677	−	0.642029i
$123$	5.64135			0.508663
$124$	−5.02321	+	2.40153i	−0.451098	+	0.215664i
$125$	1.00000			0.0894427
$126$	1.38972	+	1.00969i	0.123806	+	0.0899504i
$127$	−7.64441	+	5.55399i	−0.678331	+	0.492837i	−0.872804	−	0.488071i	$-0.837701\pi$
$127$	−7.64441	+	5.55399i	−0.678331	+	0.492837i	0.194472	+	0.980908i	$0.437701\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−7.22362			−0.636004
$130$	−0.223434			−0.0195965
$131$	3.86613	+	11.8987i	0.337785	+	1.03960i	0.965334	+	0.261018i	$0.0840582\pi$
$131$	3.86613	+	11.8987i	0.337785	+	1.03960i	−0.627549	+	0.778577i	$0.715942\pi$
$132$	0.890814	−	2.74164i	0.0775354	−	0.238629i
$133$	0.171557	−	0.527998i	0.0148759	−	0.0457832i
$134$	−8.65843	−	6.29072i	−0.747974	−	0.543435i
$135$	0.309017	+	0.951057i	0.0265959	+	0.0818539i
$136$	−4.19514	−	3.04795i	−0.359731	−	0.261360i
$137$	4.64471	−	3.37458i	0.396824	−	0.288310i	−0.371422	−	0.928464i	$-0.621130\pi$
$137$	4.64471	−	3.37458i	0.396824	−	0.288310i	0.768246	+	0.640154i	$0.221130\pi$
$138$	0.871763	−	2.68301i	0.0742094	−	0.228393i
$139$	−0.0826333	+	0.0600366i	−0.00700887	+	0.00509224i	−0.591284	−	0.806463i	$-0.701379\pi$
$139$	−0.0826333	+	0.0600366i	−0.00700887	+	0.00509224i	0.584275	+	0.811556i	$0.301379\pi$
$140$	1.38972	−	1.00969i	0.117453	−	0.0853344i
$141$	−2.61179	+	8.03827i	−0.219953	+	0.676944i
$142$	−5.92461	+	4.30448i	−0.497182	+	0.361224i
$143$	0.521089	+	0.378594i	0.0435757	+	0.0316596i
$144$	0.309017	+	0.951057i	0.0257514	+	0.0792547i
$145$	−3.51438	−	2.55335i	−0.291853	−	0.212044i
$146$	−1.54022	+	4.74030i	−0.127469	+	0.392310i
$147$	−1.25127	+	3.85102i	−0.103203	+	0.317627i
$148$	0.731316	+	2.25076i	0.0601138	+	0.185011i
$149$	6.70517			0.549309			0.274655	−	0.961543i	$-0.411437\pi$
$149$	6.70517			0.549309			0.274655	+	0.961543i	$0.411437\pi$
$150$	1.00000			0.0816497
$151$	1.17488	+	3.61590i	0.0956100	+	0.294257i	0.987412	−	0.158168i	$-0.0505588\pi$
$151$	1.17488	+	3.61590i	0.0956100	+	0.294257i	−0.891802	+	0.452426i	$0.850559\pi$
$152$	0.261465	−	0.189965i	0.0212076	−	0.0154082i
$153$	−4.19514	−	3.04795i	−0.339157	−	0.246412i
$154$	−4.95193			−0.399038
$155$	0.731733	+	5.51947i	0.0587742	+	0.443335i
$156$	−0.223434			−0.0178891
$157$	−6.20238	−	4.50629i	−0.495004	−	0.359641i	0.312102	−	0.950049i	$-0.398967\pi$
$157$	−6.20238	−	4.50629i	−0.495004	−	0.359641i	−0.807105	+	0.590408i	$0.798967\pi$
$158$	4.50563	−	3.27353i	0.358448	−	0.260428i
$159$	1.25037	+	3.84823i	0.0991605	+	0.305185i
$160$	1.00000			0.0790569
$161$	−4.84602			−0.381920
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	−5.59974	+	17.2342i	−0.438605	+	1.34989i	0.450742	+	0.892654i	$0.351160\pi$
$163$	−5.59974	+	17.2342i	−0.438605	+	1.34989i	−0.889347	+	0.457233i	$0.848840\pi$
$164$	1.74327	−	5.36524i	0.136127	−	0.418955i
$165$	−2.33218	−	1.69443i	−0.181560	−	0.131911i
$166$	0.860459	+	2.64822i	0.0667845	+	0.205542i
$167$	8.79403	+	6.38924i	0.680503	+	0.494414i	0.873524	−	0.486780i	$-0.161829\pi$
$167$	8.79403	+	6.38924i	0.680503	+	0.494414i	−0.193022	+	0.981194i	$0.561829\pi$
$168$	1.38972	−	1.00969i	0.107219	−	0.0778993i
$169$	−4.00179	+	12.3163i	−0.307830	+	0.947404i
$170$	−4.19514	+	3.04795i	−0.321753	+	0.233767i
$171$	0.261465	−	0.189965i	0.0199947	−	0.0145270i
$172$	−2.23222	+	6.87007i	−0.170205	+	0.523838i
$173$	−13.8128	+	10.0356i	−1.05016	+	0.762989i	−0.972244	−	0.233970i	$-0.924828\pi$
$173$	−13.8128	+	10.0356i	−1.05016	+	0.762989i	−0.0779210	+	0.996960i	$0.524828\pi$
$174$	−3.51438	−	2.55335i	−0.266425	−	0.193569i
$175$	−0.530826	−	1.63371i	−0.0401267	−	0.123497i
$176$	−2.33218	−	1.69443i	−0.175795	−	0.127722i
$177$	−1.71317	+	5.27259i	−0.128770	+	0.396312i
$178$	−1.46075	+	4.49572i	−0.109488	+	0.336968i
$179$	4.37829	+	13.4750i	0.327248	+	1.00717i	0.970415	+	0.241441i	$0.0776201\pi$
$179$	4.37829	+	13.4750i	0.327248	+	1.00717i	−0.643167	+	0.765726i	$0.722380\pi$
$180$	1.00000			0.0745356
$181$	−0.250680			−0.0186329			−0.00931643	−	0.999957i	$-0.502966\pi$
$181$	−0.250680			−0.0186329			−0.00931643	+	0.999957i	$0.502966\pi$
$182$	0.118605	+	0.365028i	0.00879156	+	0.0270576i
$183$	−9.76053	+	7.09144i	−0.721519	+	0.524214i
$184$	−2.28230	−	1.65819i	−0.168254	−	0.122243i
$185$	2.36659			0.173995
$186$	0.731733	+	5.51947i	0.0536533	+	0.404707i
$187$	14.9484			1.09313
$188$	6.83776	+	4.96792i	0.498695	+	0.362323i
$189$	1.38972	−	1.00969i	0.101087	−	0.0734442i
$190$	−0.0998708	−	0.307371i	−0.00724539	−	0.0222990i
$191$	9.05636			0.655295			0.327647	−	0.944800i	$-0.393744\pi$
$191$	9.05636			0.655295			0.327647	+	0.944800i	$0.393744\pi$
$192$	1.00000			0.0721688
$193$	−0.983094	−	3.02565i	−0.0707646	−	0.217791i	0.909419	−	0.415880i	$-0.136526\pi$
$193$	−0.983094	−	3.02565i	−0.0707646	−	0.217791i	−0.980184	+	0.198089i	$0.936526\pi$
$194$	−2.06009	+	6.34030i	−0.147906	+	0.455207i
$195$	−0.0690450	+	0.212499i	−0.00494441	+	0.0152173i
$196$	3.27587	+	2.38006i	0.233991	+	0.170004i
$197$	−2.85989	−	8.80184i	−0.203759	−	0.627105i	−0.999762	−	0.0218126i	$-0.993056\pi$
$197$	−2.85989	−	8.80184i	−0.203759	−	0.627105i	0.796003	−	0.605292i	$-0.206944\pi$
$198$	−2.33218	−	1.69443i	−0.165741	−	0.120418i
$199$	−4.42762	+	3.21685i	−0.313866	+	0.228037i	−0.733553	−	0.679632i	$-0.762140\pi$
$199$	−4.42762	+	3.21685i	−0.313866	+	0.228037i	0.419688	+	0.907669i	$0.362140\pi$
$200$	0.309017	−	0.951057i	0.0218508	−	0.0672499i
$201$	−8.65843	+	6.29072i	−0.610719	+	0.443713i
$202$	3.52898	−	2.56395i	0.248298	−	0.180399i
$203$	−2.30591	+	7.09687i	−0.161843	+	0.498103i
$204$	−4.19514	+	3.04795i	−0.293719	+	0.213399i
$205$	−4.56395	−	3.31590i	−0.318760	−	0.231593i
$206$	−0.0373884	−	0.115070i	−0.00260497	−	0.00801728i
$207$	−2.28230	−	1.65819i	−0.158631	−	0.115252i
$208$	−0.0690450	+	0.212499i	−0.00478741	+	0.0147341i
$209$	−0.287901	+	0.886068i	−0.0199145	+	0.0612906i
$210$	−0.530826	−	1.63371i	−0.0366305	−	0.112737i
$211$	−19.6781			−1.35470			−0.677348	−	0.735663i	$-0.736871\pi$
$211$	−19.6781			−1.35470			−0.677348	+	0.735663i	$0.736871\pi$
$212$	4.04627			0.277899
$213$	2.26300	+	6.96480i	0.155058	+	0.477220i
$214$	−14.0739	+	10.2253i	−0.962073	+	0.698987i
$215$	5.84403	+	4.24594i	0.398560	+	0.289571i
$216$	1.00000			0.0680414
$217$	8.62881	−	4.12532i	0.585762	−	0.280045i
$218$	3.43005			0.232312
$219$	4.03234	+	2.92967i	0.272480	+	0.197968i
$220$	−2.33218	+	1.69443i	−0.157236	+	0.114238i
$221$	−0.358032	−	1.10191i	−0.0240838	−	0.0741223i
$222$	2.36659			0.158835
$223$	1.96582			0.131641			0.0658206	−	0.997831i	$-0.479033\pi$
$223$	1.96582			0.131641			0.0658206	+	0.997831i	$0.479033\pi$
$224$	−0.530826	−	1.63371i	−0.0354673	−	0.109157i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	−0.730108	+	2.24704i	−0.0485661	+	0.149471i
$227$	−16.7349	−	12.1586i	−1.11074	−	0.806996i	−0.127956	−	0.991780i	$-0.540842\pi$
$227$	−16.7349	−	12.1586i	−1.11074	−	0.806996i	−0.982779	+	0.184783i	$0.940842\pi$
$228$	−0.0998708	−	0.307371i	−0.00661410	−	0.0203561i
$229$	17.2964	+	12.5666i	1.14298	+	0.830424i	0.987532	−	0.157421i	$-0.0503178\pi$
$229$	17.2964	+	12.5666i	1.14298	+	0.830424i	0.155448	+	0.987844i	$0.450318\pi$
$230$	−2.28230	+	1.65819i	−0.150491	+	0.109338i
$231$	−1.53023	+	4.70956i	−0.100682	+	0.309867i
$232$	−3.51438	+	2.55335i	−0.230730	+	0.167635i
$233$	−20.0389	+	14.5591i	−1.31279	+	0.953798i	−0.312799	+	0.949819i	$0.601266\pi$
$233$	−20.0389	+	14.5591i	−1.31279	+	0.953798i	−0.999992	+	0.00397881i	$0.998734\pi$
$234$	−0.0690450	+	0.212499i	−0.00451361	+	0.0138915i
$235$	6.83776	−	4.96792i	0.446046	−	0.324072i
$236$	4.48514	+	3.25864i	0.291958	+	0.212120i
$237$	−1.72100	−	5.29668i	−0.111791	−	0.344056i
$238$	7.20637	+	5.23573i	0.467119	+	0.339382i
$239$	−2.69159	+	8.28387i	−0.174105	+	0.535839i	−0.999591	−	0.0285824i	$-0.990901\pi$
$239$	−2.69159	+	8.28387i	−0.174105	+	0.535839i	0.825487	+	0.564421i	$0.190901\pi$
$240$	0.309017	−	0.951057i	0.0199470	−	0.0613904i
$241$	−9.25619	−	28.4876i	−0.596244	−	1.83505i	−0.548436	−	0.836193i	$-0.684777\pi$
$241$	−9.25619	−	28.4876i	−0.596244	−	1.83505i	−0.0478078	−	0.998857i	$-0.515223\pi$
$242$	−2.68984			−0.172909
$243$	1.00000			0.0641500
$244$	3.72819	+	11.4742i	0.238673	+	0.734560i
$245$	3.27587	−	2.38006i	0.209288	−	0.152057i
$246$	−4.56395	−	3.31590i	−0.290987	−	0.211414i
$247$	0.0722114			0.00459470
$248$	5.47545	+	1.00969i	0.347691	+	0.0641154i
$249$	2.78450			0.176461
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	−14.2036	+	10.3195i	−0.896523	+	0.651362i	−0.937570	−	0.347795i	$-0.886930\pi$
$251$	−14.2036	+	10.3195i	−0.896523	+	0.651362i	0.0410478	+	0.999157i	$0.486930\pi$
$252$	−0.530826	−	1.63371i	−0.0334389	−	0.102914i
$253$	8.13244			0.511282
$254$	9.44901			0.592883
$255$	1.60240	+	4.93169i	0.100346	+	0.308834i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	6.09771	−	18.7668i	0.380365	−	1.17064i	−0.559422	−	0.828883i	$-0.688977\pi$
$257$	6.09771	−	18.7668i	0.380365	−	1.17064i	0.939787	−	0.341760i	$-0.111023\pi$
$258$	5.84403	+	4.24594i	0.363833	+	0.264341i
$259$	−1.25625	−	3.86633i	−0.0780593	−	0.240242i
$260$	0.180762	+	0.131331i	0.0112104	+	0.00814483i
$261$	−3.51438	+	2.55335i	−0.217535	+	0.158048i
$262$	3.86613	−	11.8987i	0.238850	−	0.735105i
$263$	−12.1942	+	8.85958i	−0.751924	+	0.546305i	−0.896423	−	0.443200i	$-0.853843\pi$
$263$	−12.1942	+	8.85958i	−0.751924	+	0.546305i	0.144499	+	0.989505i	$0.453843\pi$
$264$	−2.33218	+	1.69443i	−0.143536	+	0.104285i
$265$	1.25037	−	3.84823i	0.0768094	−	0.236395i
$266$	−0.449142	+	0.326320i	−0.0275386	+	0.0200080i
$267$	3.82429	+	2.77851i	0.234042	+	0.170042i
$268$	3.30723	+	10.1786i	0.202021	+	0.621757i
$269$	5.74835	+	4.17642i	0.350483	+	0.254641i	0.749072	−	0.662489i	$-0.230500\pi$
$269$	5.74835	+	4.17642i	0.350483	+	0.254641i	−0.398589	+	0.917130i	$0.630500\pi$
$270$	0.309017	−	0.951057i	0.0188062	−	0.0578795i
$271$	−0.863951	+	2.65897i	−0.0524813	+	0.161521i	−0.973862	−	0.227140i	$-0.927062\pi$
$271$	−0.863951	+	2.65897i	−0.0524813	+	0.161521i	0.921381	+	0.388661i	$0.127062\pi$
$272$	1.60240	+	4.93169i	0.0971599	+	0.299027i
$273$	0.383813			0.0232294
$274$	−5.74118			−0.346837
$275$	0.890814	+	2.74164i	0.0537181	+	0.165327i
$276$	−2.28230	+	1.65819i	−0.137379	+	0.0998114i
$277$	19.3237	+	14.0395i	1.16105	+	0.843552i	0.989910	−	0.141695i	$-0.0452553\pi$
$277$	19.3237	+	14.0395i	1.16105	+	0.843552i	0.171139	+	0.985247i	$0.445255\pi$
$278$	0.102140			0.00612597
$279$	5.47545	+	1.00969i	0.327806	+	0.0604486i
$280$	−1.71779			−0.102657
$281$	−12.3433	−	8.96795i	−0.736341	−	0.534983i	0.155222	−	0.987880i	$-0.450391\pi$
$281$	−12.3433	−	8.96795i	−0.736341	−	0.534983i	−0.891563	+	0.452897i	$0.850391\pi$
$282$	6.83776	−	4.96792i	0.407183	−	0.295836i
$283$	−5.98758	−	18.4279i	−0.355925	−	1.09542i	−0.955471	−	0.295084i	$-0.904652\pi$
$283$	−5.98758	−	18.4279i	−0.355925	−	1.09542i	0.599547	−	0.800340i	$-0.295348\pi$
$284$	7.32322			0.434553
$285$	−0.323189			−0.0191440
$286$	−0.199038	−	0.612577i	−0.0117694	−	0.0362224i
$287$	−2.99457	+	9.21635i	−0.176764	+	0.544024i
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	−8.00055	−	5.81274i	−0.470621	−	0.341926i
$290$	1.34237	+	4.13140i	0.0788269	+	0.242604i
$291$	5.39338	+	3.91852i	0.316165	+	0.229708i
$292$	4.03234	−	2.92967i	0.235975	−	0.171446i
$293$	−3.03319	+	9.33519i	−0.177201	+	0.545368i	−0.999727	−	0.0233591i	$-0.992564\pi$
$293$	−3.03319	+	9.33519i	−0.177201	+	0.545368i	0.822526	+	0.568727i	$0.192564\pi$
$294$	3.27587	−	2.38006i	0.191053	−	0.138808i
$295$	4.48514	−	3.25864i	0.261135	−	0.189726i
$296$	0.731316	−	2.25076i	0.0425069	−	0.130823i
$297$	−2.33218	+	1.69443i	−0.135327	+	0.0983208i
$298$	−5.42460	−	3.94120i	−0.314238	−	0.228308i
$299$	−0.194782	−	0.599476i	−0.0112645	−	0.0346686i
$300$	−0.809017	−	0.587785i	−0.0467086	−	0.0339358i
$301$	3.83448	−	11.8013i	0.221016	−	0.680217i
$302$	1.17488	−	3.61590i	0.0676065	−	0.208071i
$303$	−1.34795	−	4.14856i	−0.0774377	−	0.238329i
$304$	−0.323189			−0.0185361
$305$	12.0647			0.690821
$306$	1.60240	+	4.93169i	0.0916032	+	0.281926i
$307$	−26.2594	+	19.0786i	−1.49870	+	1.08887i	−0.527809	+	0.849363i	$0.676986\pi$
$307$	−26.2594	+	19.0786i	−1.49870	+	1.08887i	−0.970894	+	0.239509i	$0.923014\pi$
$308$	4.00619	+	2.91067i	0.228274	+	0.165851i
$309$	−0.120991			−0.00688296
$310$	2.65228	−	4.89545i	0.150639	−	0.278043i
$311$	−2.01199			−0.114089			−0.0570447	−	0.998372i	$-0.518168\pi$
$311$	−2.01199			−0.114089			−0.0570447	+	0.998372i	$0.518168\pi$
$312$	0.180762	+	0.131331i	0.0102336	+	0.00743517i
$313$	−10.4051	+	7.55973i	−0.588130	+	0.427301i	−0.841646	−	0.540030i	$-0.818413\pi$
$313$	−10.4051	+	7.55973i	−0.588130	+	0.427301i	0.253516	+	0.967331i	$0.418413\pi$
$314$	2.36910	+	7.29133i	0.133696	+	0.411474i
$315$	−1.71779			−0.0967864
$316$	−5.56926			−0.313295
$317$	−8.20440	−	25.2505i	−0.460805	−	1.41821i	−0.864183	−	0.503178i	$-0.832164\pi$
$317$	−8.20440	−	25.2505i	−0.460805	−	1.41821i	0.403378	−	0.915033i	$-0.367836\pi$
$318$	1.25037	−	3.84823i	0.0701171	−	0.215798i
$319$	3.86971	−	11.9097i	0.216662	−	0.666817i
$320$	−0.809017	−	0.587785i	−0.0452254	−	0.0328582i
$321$	5.37576	+	16.5449i	0.300046	+	0.923446i
$322$	3.92052	+	2.84842i	0.218482	+	0.158736i
$323$	1.35582	−	0.985063i	0.0754400	−	0.0548103i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	0.180762	−	0.131331i	0.0100269	−	0.00728495i
$326$	14.6603	−	10.6513i	0.811959	−	0.589923i
$327$	1.05994	−	3.26217i	0.0586150	−	0.180398i
$328$	−4.56395	+	3.31590i	−0.252002	+	0.183090i
$329$	−11.7458	−	8.53384i	−0.647568	−	0.470486i
$330$	0.890814	+	2.74164i	0.0490377	+	0.150923i
$331$	10.2079	+	7.41647i	0.561077	+	0.407646i	0.831853	−	0.554996i	$-0.187280\pi$
$331$	10.2079	+	7.41647i	0.561077	+	0.407646i	−0.270776	+	0.962642i	$0.587280\pi$
$332$	0.860459	−	2.64822i	0.0472238	−	0.145340i
$333$	0.731316	−	2.25076i	0.0400758	−	0.123341i
$334$	−3.35902	−	10.3380i	−0.183797	−	0.565670i
$335$	10.7024			0.584735
$336$	−1.71779			−0.0937130
$337$	1.98791	+	6.11815i	0.108288	+	0.333277i	0.990488	−	0.137598i	$-0.0439383\pi$
$337$	1.98791	+	6.11815i	0.108288	+	0.333277i	−0.882200	+	0.470875i	$0.843938\pi$
$338$	10.4768	−	7.61186i	0.569865	−	0.414031i
$339$	1.91145	+	1.38875i	0.103816	+	0.0754264i
$340$	5.18548			0.281222
$341$	−14.4806	+	6.92298i	−0.784168	+	0.374900i
$342$	−0.323189			−0.0174760
$343$	−15.3553	−	11.1563i	−0.829108	−	0.602382i
$344$	5.84403	−	4.24594i	0.315089	−	0.228926i
$345$	0.871763	+	2.68301i	0.0469341	+	0.144448i
$346$	17.0735			0.917878
$347$	6.15717			0.330534			0.165267	−	0.986249i	$-0.447151\pi$
$347$	6.15717			0.330534			0.165267	+	0.986249i	$0.447151\pi$
$348$	1.34237	+	4.13140i	0.0719588	+	0.221466i
$349$	−5.24895	+	16.1546i	−0.280970	+	0.864737i	0.706608	+	0.707606i	$0.250225\pi$
$349$	−5.24895	+	16.1546i	−0.280970	+	0.864737i	−0.987578	+	0.157131i	$0.949775\pi$
$350$	−0.530826	+	1.63371i	−0.0283738	+	0.0873257i
$351$	0.180762	+	0.131331i	0.00964837	+	0.00700995i
$352$	0.890814	+	2.74164i	0.0474806	+	0.146130i
$353$	11.1730	+	8.11768i	0.594680	+	0.432061i	0.843987	−	0.536364i	$-0.180203\pi$
$353$	11.1730	+	8.11768i	0.594680	+	0.432061i	−0.249306	+	0.968425i	$0.580203\pi$
$354$	4.48514	−	3.25864i	0.238382	−	0.173195i
$355$	2.26300	−	6.96480i	0.120108	−	0.369653i
$356$	3.82429	−	2.77851i	0.202687	−	0.147261i
$357$	7.20637	−	5.23573i	0.381401	−	0.277104i
$358$	4.37829	−	13.4750i	0.231400	−	0.712175i
$359$	−14.0906	+	10.2374i	−0.743672	+	0.540309i	−0.893859	−	0.448348i	$-0.852012\pi$
$359$	−14.0906	+	10.2374i	−0.743672	+	0.540309i	0.150187	+	0.988658i	$0.452012\pi$
$360$	−0.809017	−	0.587785i	−0.0426389	−	0.0309790i
$361$	−5.83905	−	17.9707i	−0.307318	−	0.945828i
$362$	0.202804	+	0.147346i	0.0106591	+	0.00774432i
$363$	−0.831206	+	2.55819i	−0.0436270	+	0.134270i
$364$	0.118605	−	0.365028i	0.00621657	−	0.0191326i
$365$	−1.54022	−	4.74030i	−0.0806186	−	0.248119i
$366$	12.0647			0.630631
$367$	6.65365			0.347318			0.173659	−	0.984806i	$-0.444441\pi$
$367$	6.65365			0.347318			0.173659	+	0.984806i	$0.444441\pi$
$368$	0.871763	+	2.68301i	0.0454438	+	0.139862i
$369$	−4.56395	+	3.31590i	−0.237590	+	0.172619i
$370$	−1.91461	−	1.39104i	−0.0995358	−	0.0723170i
$371$	−6.95064			−0.360859
$372$	2.65228	−	4.89545i	0.137514	−	0.253817i
$373$	−24.2905			−1.25771			−0.628856	−	0.777521i	$-0.716477\pi$
$373$	−24.2905			−1.25771			−0.628856	+	0.777521i	$0.716477\pi$
$374$	−12.0935	−	8.78643i	−0.625339	−	0.454336i
$375$	−0.809017	+	0.587785i	−0.0417775	+	0.0303531i
$376$	−2.61179	−	8.03827i	−0.134693	−	0.414542i
$377$	−0.970601			−0.0499885
$378$	−1.71779			−0.0883535
$379$	−3.44040	−	10.5884i	−0.176721	−	0.543892i	0.822987	−	0.568061i	$-0.192306\pi$
$379$	−3.44040	−	10.5884i	−0.176721	−	0.543892i	−0.999708	+	0.0241686i	$0.992306\pi$
$380$	−0.0998708	+	0.307371i	−0.00512326	+	0.0157678i
$381$	2.91990	−	8.98654i	0.149591	−	0.460394i
$382$	−7.32675	−	5.32319i	−0.374869	−	0.272358i
$383$	5.12924	+	15.7862i	0.262092	+	0.806637i	0.992349	+	0.123464i	$0.0394004\pi$
$383$	5.12924	+	15.7862i	0.262092	+	0.806637i	−0.730257	+	0.683173i	$0.760600\pi$
$384$	−0.809017	−	0.587785i	−0.0412850	−	0.0299953i
$385$	4.00619	−	2.91067i	0.204175	−	0.148342i
$386$	−0.983094	+	3.02565i	−0.0500382	+	0.154002i
$387$	5.84403	−	4.24594i	0.297069	−	0.215833i
$388$	5.39338	−	3.91852i	0.273807	−	0.198933i
$389$	−0.257381	+	0.792137i	−0.0130497	+	0.0401629i	−0.957369	−	0.288867i	$-0.906722\pi$
$389$	−0.257381	+	0.792137i	−0.0130497	+	0.0401629i	0.944320	+	0.329030i	$0.106722\pi$
$390$	0.180762	−	0.131331i	0.00915325	−	0.00665022i
$391$	−11.8348	−	8.59852i	−0.598514	−	0.434846i
$392$	−1.25127	−	3.85102i	−0.0631988	−	0.194506i
$393$	−10.1216	−	7.35381i	−0.510570	−	0.370951i
$394$	−2.85989	+	8.80184i	−0.144079	+	0.443430i
$395$	−1.72100	+	5.29668i	−0.0865927	+	0.266505i
$396$	0.890814	+	2.74164i	0.0447651	+	0.137773i
$397$	2.61800			0.131393			0.0656967	−	0.997840i	$-0.479073\pi$
$397$	2.61800			0.131393			0.0656967	+	0.997840i	$0.479073\pi$
$398$	5.47284			0.274329
$399$	0.171557	+	0.527998i	0.00858858	+	0.0264329i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	14.2264	+	10.3361i	0.710434	+	0.516160i	0.883314	−	0.468783i	$-0.155307\pi$
$401$	14.2264	+	10.3361i	0.710434	+	0.516160i	−0.172880	+	0.984943i	$0.555307\pi$
$402$	10.7024			0.533788
$403$	0.857149	+	0.901612i	0.0426977	+	0.0449125i
$404$	−4.36206			−0.217021
$405$	−0.809017	−	0.587785i	−0.0402004	−	0.0292073i
$406$	6.03696	−	4.38611i	0.299609	−	0.217679i
$407$	2.10819	+	6.48834i	0.104499	+	0.321615i
$408$	5.18548			0.256720
$409$	12.7199			0.628959			0.314479	−	0.949264i	$-0.398170\pi$
$409$	12.7199			0.628959			0.314479	+	0.949264i	$0.398170\pi$
$410$	1.74327	+	5.36524i	0.0860941	+	0.264970i
$411$	−1.77412	+	5.46019i	−0.0875110	+	0.269331i
$412$	−0.0373884	+	0.115070i	−0.00184199	+	0.00566908i
$413$	−7.70452	−	5.59766i	−0.379114	−	0.275443i
$414$	0.871763	+	2.68301i	0.0428448	+	0.131863i
$415$	−2.25271	−	1.63669i	−0.110581	−	0.0803419i
$416$	0.180762	−	0.131331i	0.00886259	−	0.00643905i
$417$	0.0315631	−	0.0971413i	0.00154565	−	0.00475703i
$418$	0.753734	−	0.547620i	0.0368664	−	0.0267850i
$419$	8.81298	−	6.40301i	0.430542	−	0.312807i	−0.351323	−	0.936254i	$-0.614268\pi$
$419$	8.81298	−	6.40301i	0.430542	−	0.312807i	0.781866	+	0.623447i	$0.214268\pi$
$420$	−0.530826	+	1.63371i	−0.0259016	+	0.0797171i
$421$	30.7604	−	22.3487i	1.49917	−	1.08921i	0.528458	−	0.848960i	$-0.322770\pi$
$421$	30.7604	−	22.3487i	1.49917	−	1.08921i	0.970711	−	0.240250i	$-0.0772295\pi$
$422$	15.9199	+	11.5665i	0.774969	+	0.563048i
$423$	−2.61179	−	8.03827i	−0.126990	−	0.390834i
$424$	−3.27350	−	2.37834i	−0.158975	−	0.115502i
$425$	1.60240	−	4.93169i	0.0777279	−	0.239222i
$426$	2.26300	−	6.96480i	0.109643	−	0.337446i
$427$	−6.40424	−	19.7102i	−0.309923	−	0.953845i
$428$	17.3963			0.840883
$429$	−0.644102			−0.0310975
$430$	−2.23222	−	6.87007i	−0.107647	−	0.331304i
$431$	−25.7012	+	18.6730i	−1.23798	+	0.899448i	−0.997462	−	0.0711964i	$-0.977318\pi$
$431$	−25.7012	+	18.6730i	−1.23798	+	0.899448i	−0.240521	+	0.970644i	$0.577318\pi$
$432$	−0.809017	−	0.587785i	−0.0389238	−	0.0282798i
$433$	−11.1758			−0.537074			−0.268537	−	0.963269i	$-0.586540\pi$
$433$	−11.1758			−0.537074			−0.268537	+	0.963269i	$0.586540\pi$
$434$	−9.40566	−	1.73443i	−0.451486	−	0.0832555i
$435$	4.34401			0.208280
$436$	−2.77497	−	2.01613i	−0.132897	−	0.0965552i
$437$	0.737615	−	0.535908i	0.0352849	−	0.0256360i
$438$	−1.54022	−	4.74030i	−0.0735944	−	0.226500i
$439$	27.2132			1.29882			0.649408	−	0.760440i	$-0.275017\pi$
$439$	27.2132			1.29882			0.649408	+	0.760440i	$0.275017\pi$
$440$	2.88274			0.137429
$441$	−1.25127	−	3.85102i	−0.0595844	−	0.183382i
$442$	−0.358032	+	1.10191i	−0.0170298	+	0.0524124i
$443$	6.30304	−	19.3988i	0.299466	−	0.921663i	−0.682218	−	0.731149i	$-0.738985\pi$
$443$	6.30304	−	19.3988i	0.299466	−	0.921663i	0.981684	−	0.190514i	$-0.0610154\pi$
$444$	−1.91461	−	1.39104i	−0.0908633	−	0.0660161i
$445$	−1.46075	−	4.49572i	−0.0692461	−	0.213117i
$446$	−1.59038	−	1.15548i	−0.0753069	−	0.0547137i
$447$	−5.42460	+	3.94120i	−0.256575	+	0.186412i
$448$	−0.530826	+	1.63371i	−0.0250792	+	0.0771857i
$449$	−13.2127	+	9.59957i	−0.623545	+	0.453032i	−0.854158	−	0.520014i	$-0.825927\pi$
$449$	−13.2127	+	9.59957i	−0.623545	+	0.453032i	0.230613	+	0.973045i	$0.425927\pi$
$450$	−0.809017	+	0.587785i	−0.0381374	+	0.0277085i
$451$	5.02539	−	15.4666i	0.236637	−	0.728292i
$452$	1.91145	−	1.38875i	0.0899069	−	0.0653212i
$453$	−3.07586	−	2.23475i	−0.144517	−	0.104998i
$454$	6.39217	+	19.6731i	0.299999	+	0.923303i
$455$	−0.310511	−	0.225599i	−0.0145570	−	0.0105763i
$456$	−0.0998708	+	0.307371i	−0.00467688	+	0.0143939i
$457$	−3.06118	+	9.42133i	−0.143196	+	0.440711i	−0.996775	−	0.0802526i	$-0.974427\pi$
$457$	−3.06118	+	9.42133i	−0.143196	+	0.440711i	0.853579	+	0.520964i	$0.174427\pi$
$458$	−6.60665	−	20.3332i	−0.308708	−	0.950106i
$459$	5.18548			0.242038
$460$	2.82108			0.131534
$461$	−5.25816	−	16.1830i	−0.244897	−	0.753715i	−0.995653	−	0.0931362i	$-0.970311\pi$
$461$	−5.25816	−	16.1830i	−0.244897	−	0.753715i	0.750756	−	0.660579i	$-0.229689\pi$
$462$	4.00619	−	2.91067i	0.186385	−	0.135417i
$463$	4.56597	+	3.31737i	0.212199	+	0.154171i	0.688808	−	0.724944i	$-0.258134\pi$
$463$	4.56597	+	3.31737i	0.212199	+	0.154171i	−0.476609	+	0.879115i	$0.658134\pi$
$464$	4.34401			0.201666
$465$	−3.83625	−	4.03524i	−0.177902	−	0.187130i
$466$	24.7694			1.14742
$467$	−28.0908	−	20.4092i	−1.29989	−	0.944424i	−0.299934	−	0.953960i	$-0.596965\pi$
$467$	−28.0908	−	20.4092i	−1.29989	−	0.944424i	−0.999955	+	0.00953589i	$0.996965\pi$
$468$	0.180762	−	0.131331i	0.00835573	−	0.00607079i
$469$	−5.68111	−	17.4847i	−0.262329	−	0.807367i
$470$	−8.45194			−0.389859
$471$	7.66656			0.353256
$472$	−1.71317	−	5.27259i	−0.0788550	−	0.242691i
$473$	−6.43490	+	19.8046i	−0.295877	+	0.910616i
$474$	−1.72100	+	5.29668i	−0.0790480	+	0.243285i
$475$	0.261465	+	0.189965i	0.0119968	+	0.00871621i
$476$	−2.75259	−	8.47159i	−0.126165	−	0.388295i
$477$	−3.27350	−	2.37834i	−0.149883	−	0.108897i
$478$	7.04668	−	5.11971i	0.322308	−	0.234170i
$479$	3.41731	−	10.5174i	0.156141	−	0.480553i	−0.842134	−	0.539269i	$-0.818701\pi$
$479$	3.41731	−	10.5174i	0.156141	−	0.480553i	0.998275	+	0.0587161i	$0.0187007\pi$
$480$	−0.809017	+	0.587785i	−0.0369264	+	0.0268286i
$481$	0.427789	−	0.310807i	0.0195055	−	0.0141716i
$482$	−9.25619	+	28.4876i	−0.421608	+	1.29758i
$483$	3.92052	−	2.84842i	0.178390	−	0.129608i
$484$	2.17613	+	1.58105i	0.0989148	+	0.0718658i
$485$	−2.06009	−	6.34030i	−0.0935437	−	0.287898i
$486$	−0.809017	−	0.587785i	−0.0366978	−	0.0266625i
$487$	0.974386	−	2.99885i	0.0441536	−	0.135891i	−0.926550	−	0.376173i	$-0.877240\pi$
$487$	0.974386	−	2.99885i	0.0441536	−	0.135891i	0.970703	+	0.240282i	$0.0772399\pi$
$488$	3.72819	−	11.4742i	0.168767	−	0.519412i
$489$	−5.59974	−	17.2342i	−0.253229	−	0.779358i
$490$	−4.04920			−0.182924
$491$	21.5318			0.971715			0.485858	−	0.874038i	$-0.338507\pi$
$491$	21.5318			0.971715			0.485858	+	0.874038i	$0.338507\pi$
$492$	1.74327	+	5.36524i	0.0785928	+	0.241884i
$493$	−18.2238	+	13.2403i	−0.820757	+	0.596315i
$494$	−0.0584203	−	0.0424448i	−0.00262845	−	0.00190968i
$495$	2.88274			0.129569
$496$	−3.83625	−	4.03524i	−0.172253	−	0.181188i
$497$	−12.5797			−0.564279
$498$	−2.25271	−	1.63669i	−0.100946	−	0.0733418i
$499$	15.3351	−	11.1416i	0.686495	−	0.498768i	−0.189011	−	0.981975i	$-0.560528\pi$
$499$	15.3351	−	11.1416i	0.686495	−	0.498768i	0.875506	+	0.483207i	$0.160528\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$	−10.8700			−0.485637
$502$	17.5566			0.783590
$503$	6.84683	+	21.0724i	0.305285	+	0.939570i	0.979571	+	0.201100i	$0.0644515\pi$
$503$	6.84683	+	21.0724i	0.305285	+	0.939570i	−0.674286	+	0.738470i	$0.735548\pi$
$504$	−0.530826	+	1.63371i	−0.0236449	+	0.0727714i
$505$	−1.34795	+	4.14856i	−0.0599830	+	0.184609i
$506$	−6.57928	−	4.78013i	−0.292485	−	0.212503i
$507$	−4.00179	−	12.3163i	−0.177726	−	0.546984i
$508$	−7.64441	−	5.55399i	−0.339166	−	0.246418i
$509$	18.5646	−	13.4880i	0.822863	−	0.597845i	−0.0946682	−	0.995509i	$-0.530179\pi$
$509$	18.5646	−	13.4880i	0.822863	−	0.597845i	0.917531	+	0.397664i	$0.130179\pi$
$510$	1.60240	−	4.93169i	0.0709556	−	0.218379i
$511$	−6.92670	+	5.03254i	−0.306419	+	0.222627i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−0.0998708	+	0.307371i	−0.00440940	+	0.0135707i
$514$	−15.9640	+	11.5985i	−0.704143	+	0.511590i
$515$	0.0978841	+	0.0711170i	0.00431329	+	0.00313379i
$516$	−2.23222	−	6.87007i	−0.0982681	−	0.302438i
$517$	19.7115	+	14.3212i	0.866909	+	0.629846i
$518$	−1.25625	+	3.86633i	−0.0551962	+	0.169877i
$519$	5.27601	−	16.2379i	0.231591	−	0.712764i
$520$	−0.0690450	−	0.212499i	−0.00302782	−	0.00931868i
$521$	4.64824			0.203643			0.101822	−	0.994803i	$-0.467533\pi$
$521$	4.64824			0.203643			0.101822	+	0.994803i	$0.467533\pi$
$522$	4.34401			0.190132
$523$	−6.72491	−	20.6971i	−0.294060	−	0.905023i	−0.983536	−	0.180714i	$-0.942159\pi$
$523$	−6.72491	−	20.6971i	−0.294060	−	0.905023i	0.689476	−	0.724309i	$-0.257841\pi$
$524$	−10.1216	+	7.35381i	−0.442166	+	0.321253i
$525$	1.38972	+	1.00969i	0.0606523	+	0.0440665i
$526$	15.0728			0.657206
$527$	28.3928	+	5.23573i	1.23681	+	0.228072i
$528$	2.88274			0.125455
$529$	12.1688	+	8.84116i	0.529079	+	0.384398i
$530$	−3.27350	+	2.37834i	−0.142192	+	0.103308i
$531$	−1.71317	−	5.27259i	−0.0743452	−	0.228811i
$532$	0.555170			0.0240697
$533$	−1.26047			−0.0545971
$534$	−1.46075	−	4.49572i	−0.0632127	−	0.194549i
$535$	5.37576	−	16.5449i	0.232414	−	0.715298i
$536$	3.30723	−	10.1786i	0.142850	−	0.439648i
$537$	−11.4625	−	8.32799i	−0.494643	−	0.359379i
$538$	−2.19567	−	6.75759i	−0.0946622	−	0.291340i
$539$	9.44348	+	6.86109i	0.406759	+	0.295528i
$540$	−0.809017	+	0.587785i	−0.0348145	+	0.0252942i
$541$	1.51691	−	4.66856i	0.0652169	−	0.200717i	−0.913138	−	0.407650i	$-0.866348\pi$
$541$	1.51691	−	4.66856i	0.0652169	−	0.200717i	0.978355	+	0.206933i	$0.0663483\pi$
$542$	2.26185	−	1.64333i	0.0971549	−	0.0705872i
$543$	0.202804	−	0.147346i	0.00870316	−	0.00632321i
$544$	1.60240	−	4.93169i	0.0687024	−	0.211444i
$545$	−2.77497	+	2.01613i	−0.118867	+	0.0863616i
$546$	−0.310511	−	0.225599i	−0.0132886	−	0.00965477i
$547$	9.50176	+	29.2434i	0.406266	+	1.25036i	0.919833	+	0.392309i	$0.128324\pi$
$547$	9.50176	+	29.2434i	0.406266	+	1.25036i	−0.513567	+	0.858049i	$0.671676\pi$
$548$	4.64471	+	3.37458i	0.198412	+	0.144155i
$549$	3.72819	−	11.4742i	0.159115	−	0.489706i
$550$	0.890814	−	2.74164i	0.0379844	−	0.116904i
$551$	−0.433840	−	1.33522i	−0.0184822	−	0.0568824i
$552$	2.82108			0.120073
$553$	9.56681			0.406822
$554$	−7.38100	−	22.7164i	−0.313589	−	0.965127i
$555$	−1.91461	+	1.39104i	−0.0812706	+	0.0590466i
$556$	−0.0826333	−	0.0600366i	−0.00350443	−	0.00254612i
$557$	−1.22781			−0.0520240			−0.0260120	−	0.999662i	$-0.508281\pi$
$557$	−1.22781			−0.0520240			−0.0260120	+	0.999662i	$0.508281\pi$
$558$	−3.83625	−	4.03524i	−0.162401	−	0.170826i
$559$	1.61400			0.0682651
$560$	1.38972	+	1.00969i	0.0587264	+	0.0426672i
$561$	−12.0935	+	8.78643i	−0.510587	+	0.370963i
$562$	4.71473	+	14.5104i	0.198879	+	0.612086i
$563$	45.9900			1.93825			0.969124	−	0.246573i	$-0.0793045\pi$
$563$	45.9900			1.93825			0.969124	+	0.246573i	$0.0793045\pi$
$564$	−8.45194			−0.355891
$565$	−0.730108	−	2.24704i	−0.0307159	−	0.0945337i
$566$	−5.98758	+	18.4279i	−0.251677	+	0.774581i
$567$	−0.530826	+	1.63371i	−0.0222926	+	0.0686095i
$568$	−5.92461	−	4.30448i	−0.248591	−	0.180612i
$569$	12.0958	+	37.2269i	0.507080	+	1.56063i	0.797245	+	0.603656i	$0.206290\pi$
$569$	12.0958	+	37.2269i	0.507080	+	1.56063i	−0.290165	+	0.956977i	$0.593710\pi$
$570$	0.261465	+	0.189965i	0.0109516	+	0.00795678i
$571$	14.5027	−	10.5369i	0.606921	−	0.440954i	−0.241408	−	0.970424i	$-0.577609\pi$
$571$	14.5027	−	10.5369i	0.606921	−	0.440954i	0.848329	+	0.529470i	$0.177609\pi$
$572$	−0.199038	+	0.612577i	−0.00832221	+	0.0256131i
$573$	−7.32675	+	5.32319i	−0.306079	+	0.222380i
$574$	7.83990	−	5.69602i	0.327231	−	0.237747i
$575$	0.871763	−	2.68301i	0.0363550	−	0.111889i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	20.5739	+	14.9478i	0.856501	+	0.622284i	0.926931	−	0.375232i	$-0.122437\pi$
$577$	20.5739	+	14.9478i	0.856501	+	0.622284i	−0.0704298	+	0.997517i	$0.522437\pi$
$578$	3.05594	+	9.40521i	0.127110	+	0.391205i
$579$	2.57377	+	1.86996i	0.106962	+	0.0777127i
$580$	1.34237	−	4.13140i	0.0557390	−	0.171547i
$581$	−1.47809	+	4.54908i	−0.0613213	+	0.188728i
$582$	−2.06009	−	6.34030i	−0.0853934	−	0.262814i
$583$	11.6643			0.483087
$584$	−4.98424			−0.206249
$585$	−0.0690450	−	0.212499i	−0.00285466	−	0.00878574i
$586$	7.94099	−	5.76947i	0.328039	−	0.238334i
$587$	23.8910	+	17.3579i	0.986089	+	0.716435i	0.959061	−	0.283199i	$-0.0913958\pi$
$587$	23.8910	+	17.3579i	0.986089	+	0.716435i	0.0270277	+	0.999635i	$0.491396\pi$
$588$	−4.04920			−0.166986
$589$	−0.857186	+	1.58215i	−0.0353197	+	0.0651915i
$590$	−5.54393			−0.228240
$591$	7.48729	+	5.43983i	0.307986	+	0.223765i
$592$	−1.91461	+	1.39104i	−0.0786899	+	0.0571716i
$593$	−2.53419	−	7.79943i	−0.104067	−	0.320284i	0.885444	−	0.464747i	$-0.153855\pi$
$593$	−2.53419	−	7.79943i	−0.104067	−	0.320284i	−0.989510	+	0.144463i	$0.953855\pi$
$594$	2.88274			0.118280
$595$	−8.90756			−0.365174
$596$	2.07201	+	6.37700i	0.0848729	+	0.261212i
$597$	1.69120	−	5.20498i	0.0692162	−	0.213026i
$598$	−0.194782	+	0.599476i	−0.00796521	+	0.0245144i
$599$	−4.72997	−	3.43653i	−0.193261	−	0.140413i	0.486947	−	0.873432i	$-0.338111\pi$
$599$	−4.72997	−	3.43653i	−0.193261	−	0.140413i	−0.680208	+	0.733019i	$0.738111\pi$
$600$	0.309017	+	0.951057i	0.0126156	+	0.0388267i
$601$	−16.9820	−	12.3381i	−0.692709	−	0.503283i	0.184840	−	0.982769i	$-0.440823\pi$
$601$	−16.9820	−	12.3381i	−0.692709	−	0.503283i	−0.877550	+	0.479486i	$0.840823\pi$
$602$	−10.0388	+	7.29362i	−0.409151	+	0.297266i
$603$	3.30723	−	10.1786i	0.134681	−	0.414504i
$604$	−3.07586	+	2.23475i	−0.125155	+	0.0909305i
$605$	2.17613	−	1.58105i	0.0884721	−	0.0642787i
$606$	−1.34795	+	4.14856i	−0.0547567	+	0.168524i
$607$	−27.1705	+	19.7405i	−1.10282	+	0.801242i	−0.981517	−	0.191374i	$-0.938706\pi$
$607$	−27.1705	+	19.7405i	−1.10282	+	0.801242i	−0.121298	+	0.992616i	$0.538706\pi$
$608$	0.261465	+	0.189965i	0.0106038	+	0.00770412i
$609$	−2.30591	−	7.09687i	−0.0934404	−	0.287580i
$610$	−9.76053	−	7.09144i	−0.395192	−	0.287124i
$611$	0.583564	−	1.79603i	0.0236085	−	0.0726594i
$612$	1.60240	−	4.93169i	0.0647733	−	0.199352i
$613$	−6.62349	−	20.3850i	−0.267520	−	0.823343i	−0.991102	−	0.133104i	$-0.957506\pi$
$613$	−6.62349	−	20.3850i	−0.267520	−	0.823343i	0.723582	−	0.690239i	$-0.242494\pi$
$614$	32.4584			1.30991
$615$	5.64135			0.227481
$616$	−1.53023	−	4.70956i	−0.0616547	−	0.189754i
$617$	−14.8926	+	10.8201i	−0.599552	+	0.435600i	−0.845720	−	0.533627i	$-0.820829\pi$
$617$	−14.8926	+	10.8201i	−0.599552	+	0.435600i	0.246168	+	0.969227i	$0.420829\pi$
$618$	0.0978841	+	0.0711170i	0.00393748	+	0.00286074i
$619$	−5.35806			−0.215359			−0.107679	−	0.994186i	$-0.534342\pi$
$619$	−5.35806			−0.215359			−0.107679	+	0.994186i	$0.534342\pi$
$620$	−5.02321	+	2.40153i	−0.201737	+	0.0964478i
$621$	2.82108			0.113206
$622$	1.62773	+	1.18262i	0.0652662	+	0.0474187i
$623$	−6.56931	+	4.77289i	−0.263194	+	0.191222i
$624$	−0.0690450	−	0.212499i	−0.00276401	−	0.00850675i
$625$	1.00000			0.0400000
$626$	12.8614			0.514044
$627$	−0.287901	−	0.886068i	−0.0114977	−	0.0353861i
$628$	2.36910	−	7.29133i	0.0945373	−	0.290956i
$629$	3.79222	−	11.6713i	0.151206	−	0.465364i
$630$	1.38972	+	1.00969i	0.0553678	+	0.0402270i
$631$	1.16992	+	3.60064i	0.0465737	+	0.143339i	0.971639	−	0.236469i	$-0.0759901\pi$
$631$	1.16992	+	3.60064i	0.0465737	+	0.143339i	−0.925065	+	0.379808i	$0.875990\pi$
$632$	4.50563	+	3.27353i	0.179224	+	0.130214i
$633$	15.9199	−	11.5665i	0.632760	−	0.459727i
$634$	−8.20440	+	25.2505i	−0.325838	+	1.00283i
$635$	−7.64441	+	5.55399i	−0.303359	+	0.220403i
$636$	−3.27350	+	2.37834i	−0.129803	+	0.0943073i
$637$	0.279577	−	0.860450i	0.0110773	−	0.0340923i
$638$	−10.1310	+	7.36062i	−0.401091	+	0.291410i
$639$	−5.92461	−	4.30448i	−0.234374	−	0.170283i
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	−29.8685	−	21.7007i	−1.17973	−	0.857127i	−0.187593	−	0.982247i	$-0.560068\pi$
$641$	−29.8685	−	21.7007i	−1.17973	−	0.857127i	−0.992142	+	0.125120i	$0.960068\pi$
$642$	5.37576	−	16.5449i	0.212164	−	0.652975i
$643$	0.522563	−	1.60828i	0.0206079	−	0.0634245i	−0.940224	−	0.340557i	$-0.889384\pi$
$643$	0.522563	−	1.60828i	0.0206079	−	0.0634245i	0.960832	+	0.277133i	$0.0893842\pi$
$644$	−1.49750	−	4.60884i	−0.0590099	−	0.181614i
$645$	−7.22362			−0.284430
$646$	−1.67589			−0.0659369
$647$	−3.47861	−	10.7061i	−0.136758	−	0.420898i	0.859101	−	0.511806i	$-0.171023\pi$
$647$	−3.47861	−	10.7061i	−0.136758	−	0.420898i	−0.995859	+	0.0909074i	$0.971023\pi$
$648$	−0.809017	+	0.587785i	−0.0317812	+	0.0230904i
$649$	12.9295	+	9.39380i	0.507526	+	0.368739i
$650$	−0.223434			−0.00876381
$651$	−4.55605	+	8.40934i	−0.178566	+	0.329588i
$652$	−18.1211			−0.709678
$653$	4.40137	+	3.19778i	0.172239	+	0.125139i	0.670565	−	0.741851i	$-0.266052\pi$
$653$	4.40137	+	3.19778i	0.172239	+	0.125139i	−0.498326	+	0.866990i	$0.666052\pi$
$654$	−2.77497	+	2.01613i	−0.108510	+	0.0788370i
$655$	3.86613	+	11.8987i	0.151062	+	0.464921i
$656$	5.64135			0.220258
$657$	−4.98424			−0.194454
$658$	4.48651	+	13.8080i	0.174902	+	0.538294i
$659$	−13.1938	+	40.6063i	−0.513957	+	1.58180i	0.271214	+	0.962519i	$0.412575\pi$
$659$	−13.1938	+	40.6063i	−0.513957	+	1.58180i	−0.785172	+	0.619278i	$0.787425\pi$
$660$	0.890814	−	2.74164i	0.0346749	−	0.106718i
$661$	−17.5400	−	12.7436i	−0.682228	−	0.495668i	0.191868	−	0.981421i	$-0.438545\pi$
$661$	−17.5400	−	12.7436i	−0.682228	−	0.495668i	−0.874096	+	0.485753i	$0.838545\pi$
$662$	−3.89907	−	12.0001i	−0.151542	−	0.466397i
$663$	0.937339	+	0.681016i	0.0364032	+	0.0264485i
$664$	−2.25271	+	1.63669i	−0.0874221	+	0.0635159i
$665$	0.171557	−	0.527998i	0.00665269	−	0.0204749i
$666$	−1.91461	+	1.39104i	−0.0741896	+	0.0539019i
$667$	−9.91436	+	7.20321i	−0.383886	+	0.278909i
$668$	−3.35902	+	10.3380i	−0.129964	+	0.399989i
$669$	−1.59038	+	1.15548i	−0.0614878	+	0.0446735i
$670$	−8.65843	−	6.29072i	−0.334504	−	0.243032i
$671$	10.7474	+	33.0770i	0.414898	+	1.27693i
$672$	1.38972	+	1.00969i	0.0536096	+	0.0389497i
$673$	8.99547	−	27.6852i	0.346750	−	1.06719i	−0.613891	−	0.789391i	$-0.710396\pi$
$673$	8.99547	−	27.6852i	0.346750	−	1.06719i	0.960640	−	0.277795i	$-0.0896036\pi$
$674$	1.98791	−	6.11815i	0.0765713	−	0.235662i
$675$	0.309017	+	0.951057i	0.0118941	+	0.0366062i
$676$	−12.9501			−0.498080
$677$	16.4637			0.632753			0.316376	−	0.948634i	$-0.397534\pi$
$677$	16.4637			0.632753			0.316376	+	0.948634i	$0.397534\pi$
$678$	−0.730108	−	2.24704i	−0.0280396	−	0.0862971i
$679$	−9.26468	+	6.73119i	−0.355546	+	0.258319i
$680$	−4.19514	−	3.04795i	−0.160876	−	0.116884i
$681$	20.6855			0.792670
$682$	15.7843	+	2.91067i	0.604411	+	0.111455i
$683$	−26.7204			−1.02243			−0.511214	−	0.859453i	$-0.670804\pi$
$683$	−26.7204			−1.02243			−0.511214	+	0.859453i	$0.670804\pi$
$684$	0.261465	+	0.189965i	0.00999737	+	0.00726351i
$685$	4.64471	−	3.37458i	0.177465	−	0.128936i
$686$	5.86520	+	18.0512i	0.223934	+	0.689199i
$687$	−21.3796			−0.815681
$688$	−7.22362			−0.275398
$689$	−0.279375	−	0.859827i	−0.0106433	−	0.0327568i
$690$	0.871763	−	2.68301i	0.0331874	−	0.102140i
$691$	9.93480	−	30.5762i	0.377937	−	1.16317i	−0.563538	−	0.826090i	$-0.690560\pi$
$691$	9.93480	−	30.5762i	0.377937	−	1.16317i	0.941475	−	0.337082i	$-0.109440\pi$
$692$	−13.8128	−	10.0356i	−0.525082	−	0.381495i
$693$	−1.53023	−	4.70956i	−0.0581286	−	0.178902i
$694$	−4.98126	−	3.61910i	−0.189086	−	0.137379i
$695$	−0.0826333	+	0.0600366i	−0.00313446	+	0.00227732i
$696$	1.34237	−	4.13140i	0.0508826	−	0.156600i
$697$	−23.6663	+	17.1946i	−0.896424	+	0.651290i
$698$	13.7419	−	9.98410i	0.520140	−	0.377904i
$699$	7.65417	−	23.5571i	0.289507	−	0.891012i
$700$	1.38972	−	1.00969i	0.0525265	−	0.0381627i
$701$	−17.5419	−	12.7450i	−0.662549	−	0.481370i	0.204974	−	0.978768i	$-0.434289\pi$
$701$	−17.5419	−	12.7450i	−0.662549	−	0.481370i	−0.867523	+	0.497397i	$0.834289\pi$
$702$	−0.0690450	−	0.212499i	−0.00260594	−	0.00802024i
$703$	0.618780	+	0.449570i	0.0233377	+	0.0169558i
$704$	0.890814	−	2.74164i	0.0335738	−	0.103330i
$705$	−2.61179	+	8.03827i	−0.0983658	+	0.302739i
$706$	−4.26772	−	13.1347i	−0.160618	−	0.494330i
$707$	7.49309			0.281807
$708$	−5.54393			−0.208354
$709$	14.7129	+	45.2817i	0.552555	+	1.70059i	0.702314	+	0.711868i	$0.252150\pi$
$709$	14.7129	+	45.2817i	0.552555	+	1.70059i	−0.149758	+	0.988723i	$0.547850\pi$
$710$	−5.92461	+	4.30448i	−0.222347	+	0.161544i
$711$	4.50563	+	3.27353i	0.168974	+	0.122767i
$712$	−4.72708			−0.177155
$713$	15.4467	+	2.84842i	0.578483	+	0.106674i
$714$	−8.90756			−0.333357
$715$	0.521089	+	0.378594i	0.0194876	+	0.0141586i
$716$	−11.4625	+	8.32799i	−0.428374	+	0.311232i
$717$	−2.69159	−	8.28387i	−0.100519	−	0.309367i
$718$	17.4169			0.649993
$719$	41.9163			1.56321			0.781606	−	0.623772i	$-0.214401\pi$
$719$	41.9163			1.56321			0.781606	+	0.623772i	$0.214401\pi$
$720$	0.309017	+	0.951057i	0.0115164	+	0.0354438i
$721$	0.0642254	−	0.197665i	0.00239188	−	0.00736144i
$722$	−5.83905	+	17.9707i	−0.217307	+	0.668802i
$723$	24.2330	+	17.6063i	0.901236	+	0.654786i
$724$	−0.0774643	−	0.238410i	−0.00287894	−	0.00886046i
$725$	−3.51438	−	2.55335i	−0.130521	−	0.0948289i
$726$	2.17613	−	1.58105i	0.0807636	−	0.0586782i
$727$	−13.0808	+	40.2585i	−0.485139	+	1.49311i	0.346640	+	0.937998i	$0.387323\pi$
$727$	−13.0808	+	40.2585i	−0.485139	+	1.49311i	−0.831779	+	0.555107i	$0.812677\pi$
$728$	−0.310511	+	0.225599i	−0.0115083	+	0.00836127i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−1.54022	+	4.74030i	−0.0570060	+	0.175446i
$731$	30.3041	−	22.0172i	1.12084	−	0.814337i
$732$	−9.76053	−	7.09144i	−0.360759	−	0.262107i
$733$	11.4307	+	35.1800i	0.422202	+	1.29940i	0.905648	+	0.424029i	$0.139385\pi$
$733$	11.4307	+	35.1800i	0.422202	+	1.29940i	−0.483447	+	0.875374i	$0.660615\pi$
$734$	−5.38292	−	3.91092i	−0.198687	−	0.144355i
$735$	−1.25127	+	3.85102i	−0.0461539	+	0.142047i
$736$	0.871763	−	2.68301i	0.0321336	−	0.0988971i
$737$	9.53386	+	29.3422i	0.351184	+	1.08083i
$738$	5.64135			0.207661
$739$	−14.2737			−0.525068			−0.262534	−	0.964923i	$-0.584558\pi$
$739$	−14.2737			−0.525068			−0.262534	+	0.964923i	$0.584558\pi$
$740$	0.731316	+	2.25076i	0.0268837	+	0.0827395i
$741$	−0.0584203	+	0.0424448i	−0.00214612	+	0.00155925i
$742$	5.62319	+	4.08548i	0.206434	+	0.149983i
$743$	−32.8920			−1.20669			−0.603346	−	0.797480i	$-0.706166\pi$
$743$	−32.8920			−1.20669			−0.603346	+	0.797480i	$0.706166\pi$
$744$	−5.02321	+	2.40153i	−0.184160	+	0.0880444i
$745$	6.70517			0.245658
$746$	19.6514	+	14.2776i	0.719489	+	0.522739i
$747$	−2.25271	+	1.63669i	−0.0824223	+	0.0598833i
$748$	4.61930	+	14.2167i	0.168898	+	0.519816i
$749$	−29.8832			−1.09191
$750$	1.00000			0.0365148
$751$	3.27727	+	10.0864i	0.119589	+	0.368057i	0.992877	−	0.119148i	$-0.0380163\pi$
$751$	3.27727	+	10.0864i	0.119589	+	0.368057i	−0.873287	+	0.487205i	$0.838016\pi$
$752$	−2.61179	+	8.03827i	−0.0952423	+	0.293126i
$753$	5.42529	−	16.6973i	0.197709	−	0.608484i
$754$	0.785233	+	0.570505i	0.0285965	+	0.0207766i
$755$	1.17488	+	3.61590i	0.0427581	+	0.131596i
$756$	1.38972	+	1.00969i	0.0505436	+	0.0367221i
$757$	−29.6083	+	21.5117i	−1.07613	+	0.781855i	−0.977004	−	0.213220i	$-0.931605\pi$
$757$	−29.6083	+	21.5117i	−1.07613	+	0.781855i	−0.0991269	+	0.995075i	$0.531605\pi$
$758$	−3.44040	+	10.5884i	−0.124961	+	0.384590i
$759$	−6.57928	+	4.78013i	−0.238813	+	0.173508i
$760$	0.261465	−	0.189965i	0.00948433	−	0.00689077i
$761$	−5.04217	+	15.5182i	−0.182778	+	0.562534i	−0.999903	−	0.0139269i	$-0.995567\pi$
$761$	−5.04217	+	15.5182i	−0.182778	+	0.562534i	0.817125	+	0.576461i	$0.195567\pi$
$762$	−7.64441	+	5.55399i	−0.276928	+	0.201200i
$763$	4.76681	+	3.46329i	0.172570	+	0.125379i
$764$	2.79857	+	8.61311i	0.101249	+	0.311611i
$765$	−4.19514	−	3.04795i	−0.151676	−	0.110199i
$766$	5.12924	−	15.7862i	0.185327	−	0.570378i
$767$	0.382781	−	1.17808i	0.0138214	−	0.0425379i
$768$	0.309017	+	0.951057i	0.0111507	+	0.0343183i
$769$	24.8089			0.894633			0.447316	−	0.894376i	$-0.352380\pi$
$769$	24.8089			0.894633			0.447316	+	0.894376i	$0.352380\pi$
$770$	−4.95193			−0.178455
$771$	6.09771	+	18.7668i	0.219604	+	0.675871i
$772$	2.57377	−	1.86996i	0.0926321	−	0.0673012i
$773$	31.0428	+	22.5539i	1.11653	+	0.811209i	0.983680	−	0.179927i	$-0.0575862\pi$
$773$	31.0428	+	22.5539i	1.11653	+	0.811209i	0.132853	+	0.991136i	$0.457586\pi$
$774$	−7.22362			−0.259648
$775$	0.731733	+	5.51947i	0.0262846	+	0.198265i
$776$	−6.66658			−0.239316
$777$	3.28889	+	2.38952i	0.117988	+	0.0857236i
$778$	0.673832	−	0.489568i	0.0241580	−	0.0175519i
$779$	−0.563406	−	1.73399i	−0.0201861	−	0.0621265i
$780$	−0.223434			−0.00800023
$781$	21.1109			0.755408
$782$	4.52051	+	13.9127i	0.161653	+	0.497517i
$783$	1.34237	−	4.13140i	0.0479725	−	0.147644i
$784$	−1.25127	+	3.85102i	−0.0446883	+	0.137536i
$785$	−6.20238	−	4.50629i	−0.221372	−	0.160836i
$786$	3.86613	+	11.8987i	0.137900	+	0.424413i
$787$	−37.0670	−	26.9307i	−1.32129	−	0.959977i	−0.999915	−	0.0130266i	$-0.995853\pi$
$787$	−37.0670	−	26.9307i	−1.32129	−	0.959977i	−0.321380	−	0.946950i	$-0.604147\pi$
$788$	7.48729	−	5.43983i	0.266724	−	0.193786i
$789$	4.65775	−	14.3351i	0.165820	−	0.510343i
$790$	4.50563	−	3.27353i	0.160303	−	0.116467i
$791$	−3.28346	+	2.38557i	−0.116746	+	0.0848213i
$792$	0.890814	−	2.74164i	0.0316537	−	0.0974201i
$793$	2.18084	−	1.58447i	0.0774438	−	0.0562662i
$794$	−2.11800	−	1.53882i	−0.0751651	−	0.0546106i
$795$	1.25037	+	3.84823i	0.0443459	+	0.136483i
$796$	−4.42762	−	3.21685i	−0.156933	−	0.114018i
$797$	−0.576362	+	1.77386i	−0.0204158	+	0.0628333i	−0.960745	−	0.277432i	$-0.910517\pi$
$797$	−0.576362	+	1.77386i	−0.0204158	+	0.0628333i	0.940330	+	0.340265i	$0.110517\pi$
$798$	0.171557	−	0.527998i	0.00607305	−	0.0186909i
$799$	−13.5434	−	41.6823i	−0.479131	−	1.47461i
$800$	1.00000			0.0353553
$801$	−4.72708			−0.167023
$802$	−5.43401	−	16.7242i	−0.191882	−	0.590551i
$803$	11.6242	−	8.44545i	0.410208	−	0.298033i
$804$	−8.65843	−	6.29072i	−0.305359	−	0.221857i
$805$	−4.84602			−0.170800
$806$	−0.163494	−	1.23324i	−0.00575884	−	0.0434390i
$807$	−7.10535			−0.250120
$808$	3.52898	+	2.56395i	0.124149	+	0.0901996i
$809$	9.94669	−	7.22669i	0.349707	−	0.254077i	−0.399039	−	0.916934i	$-0.630656\pi$
$809$	9.94669	−	7.22669i	0.349707	−	0.254077i	0.748746	+	0.662857i	$0.230656\pi$
$810$	0.309017	+	0.951057i	0.0108578	+	0.0334167i
$811$	6.27472			0.220335			0.110168	−	0.993913i	$-0.464861\pi$
$811$	6.27472			0.220335			0.110168	+	0.993913i	$0.464861\pi$
$812$	−7.46210			−0.261868
$813$	−0.863951	−	2.65897i	−0.0303001	−	0.0932541i
$814$	2.10819	−	6.48834i	0.0738920	−	0.227416i
$815$	−5.59974	+	17.2342i	−0.196150	+	0.603688i
$816$	−4.19514	−	3.04795i	−0.146859	−	0.106700i
$817$	0.721428	+	2.22033i	0.0252396	+	0.0776795i
$818$	−10.2906	−	7.47657i	−0.359803	−	0.261412i
$819$	−0.310511	+	0.225599i	−0.0108501	+	0.00788308i
$820$	1.74327	−	5.36524i	0.0608777	−	0.187362i
$821$	−18.3403	+	13.3250i	−0.640080	+	0.465045i	−0.859878	−	0.510500i	$-0.829460\pi$
$821$	−18.3403	+	13.3250i	−0.640080	+	0.465045i	0.219798	+	0.975545i	$0.429460\pi$
$822$	4.64471	−	3.37458i	0.162003	−	0.117702i
$823$	−7.84493	+	24.1442i	−0.273457	+	0.841614i	0.716166	+	0.697930i	$0.245895\pi$
$823$	−7.84493	+	24.1442i	−0.273457	+	0.841614i	−0.989624	+	0.143685i	$0.954105\pi$
$824$	0.0978841	−	0.0711170i	0.00340995	−	0.00247748i
$825$	−2.33218	−	1.69443i	−0.0811961	−	0.0589925i
$826$	2.94286	+	9.05720i	0.102395	+	0.315140i
$827$	−4.72503	−	3.43293i	−0.164305	−	0.119375i	0.502594	−	0.864522i	$-0.332379\pi$
$827$	−4.72503	−	3.43293i	−0.164305	−	0.119375i	−0.666900	+	0.745148i	$0.732379\pi$
$828$	0.871763	−	2.68301i	0.0302958	−	0.0932410i
$829$	10.0578	−	30.9546i	0.349321	−	1.07510i	−0.609909	−	0.792471i	$-0.708794\pi$
$829$	10.0578	−	30.9546i	0.349321	−	1.07510i	0.959230	−	0.282627i	$-0.0912060\pi$
$830$	0.860459	+	2.64822i	0.0298670	+	0.0919210i
$831$	−23.8854			−0.828576
$832$	−0.223434			−0.00774619
$833$	−6.48845	−	19.9694i	−0.224812	−	0.691899i
$834$	−0.0826333	+	0.0600366i	−0.00286136	+	0.00207890i
$835$	8.79403	+	6.38924i	0.304330	+	0.221109i
$836$	−0.931667			−0.0322224
$837$	−5.02321	+	2.40153i	−0.173628	+	0.0830090i
$838$	−10.8934			−0.376308
$839$	−37.4837	−	27.2335i	−1.29408	−	0.940206i	−0.294203	−	0.955743i	$-0.595054\pi$
$839$	−37.4837	−	27.2335i	−1.29408	−	0.940206i	−0.999879	+	0.0155373i	$0.995054\pi$
$840$	1.38972	−	1.00969i	0.0479499	−	0.0348376i
$841$	−3.13020	−	9.63377i	−0.107938	−	0.332199i
$842$	−38.0219			−1.31032
$843$	15.2572			0.525485
$844$	−6.08087	−	18.7150i	−0.209312	−	0.644196i
$845$	−4.00179	+	12.3163i	−0.137666	+	0.423692i
$846$	−2.61179	+	8.03827i	−0.0897953	+	0.276361i
$847$	−3.73812	−	2.71590i	−0.128443	−	0.0933196i
$848$	1.25037	+	3.84823i	0.0429378	+	0.132149i
$849$	15.6757	+	11.3891i	0.537988	+	0.390871i
$850$	−4.19514	+	3.04795i	−0.143892	+	0.104544i
$851$	2.06310	−	6.34958i	0.0707222	−	0.217661i
$852$	−5.92461	+	4.30448i	−0.202974	+	0.147469i
$853$	24.7517	−	17.9831i	0.847481	−	0.615731i	−0.0769696	−	0.997033i	$-0.524524\pi$
$853$	24.7517	−	17.9831i	0.847481	−	0.615731i	0.924450	+	0.381303i	$0.124524\pi$
$854$	−6.40424	+	19.7102i	−0.219149	+	0.674470i
$855$	0.261465	−	0.189965i	0.00894192	−	0.00649668i
$856$	−14.0739	−	10.2253i	−0.481037	−	0.349494i
$857$	11.0430	+	33.9868i	0.377221	+	1.16097i	0.941968	+	0.335702i	$0.108974\pi$
$857$	11.0430	+	33.9868i	0.377221	+	1.16097i	−0.564748	+	0.825264i	$0.691026\pi$
$858$	0.521089	+	0.378594i	0.0177897	+	0.0129250i
$859$	4.64621	−	14.2996i	0.158527	−	0.487895i	−0.839974	−	0.542626i	$-0.817430\pi$
$859$	4.64621	−	14.2996i	0.158527	−	0.487895i	0.998501	+	0.0547311i	$0.0174301\pi$
$860$	−2.23222	+	6.87007i	−0.0761181	+	0.234267i
$861$	−2.99457	−	9.21635i	−0.102055	−	0.314092i
$862$	31.7684			1.08204
$863$	−54.7870			−1.86497			−0.932486	−	0.361207i	$-0.882365\pi$
$863$	−54.7870			−1.86497			−0.932486	+	0.361207i	$0.882365\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	−13.8128	+	10.0356i	−0.469648	+	0.341219i
$866$	9.04140	+	6.56896i	0.307239	+	0.223222i
$867$	9.88922			0.335856
$868$	6.58986	+	6.93170i	0.223675	+	0.235277i
$869$	−16.0547			−0.544618
$870$	−3.51438	−	2.55335i	−0.119149	−	0.0865666i
$871$	1.93459	−	1.40556i	0.0655511	−	0.0476257i
$872$	1.05994	+	3.26217i	0.0358942	+	0.110471i
$873$	−6.66658			−0.225630
$874$	−0.911742			−0.0308401
$875$	−0.530826	−	1.63371i	−0.0179452	−	0.0552296i
$876$	−1.54022	+	4.74030i	−0.0520391	+	0.160160i
$877$	−17.2967	+	53.2338i	−0.584068	+	1.79758i	0.0189133	+	0.999821i	$0.493979\pi$
$877$	−17.2967	+	53.2338i	−0.584068	+	1.79758i	−0.602981	+	0.797755i	$0.706021\pi$
$878$	−22.0159	−	15.9955i	−0.743002	−	0.539823i
$879$	−3.03319	−	9.33519i	−0.102307	−	0.314868i
$880$	−2.33218	−	1.69443i	−0.0786178	−	0.0571192i
$881$	−40.6404	+	29.5269i	−1.36921	+	0.994788i	−0.371410	+	0.928469i	$0.621125\pi$
$881$	−40.6404	+	29.5269i	−1.36921	+	0.994788i	−0.997798	+	0.0663189i	$0.978875\pi$
$882$	−1.25127	+	3.85102i	−0.0421325	+	0.129671i
$883$	9.53684	−	6.92892i	0.320940	−	0.233177i	−0.415636	−	0.909531i	$-0.636441\pi$
$883$	9.53684	−	6.92892i	0.320940	−	0.233177i	0.736577	+	0.676354i	$0.236441\pi$
$884$	0.937339	−	0.681016i	0.0315261	−	0.0229051i
$885$	−1.71317	+	5.27259i	−0.0575876	+	0.177236i
$886$	−16.5016	+	11.9891i	−0.554381	+	0.402781i
$887$	7.20354	+	5.23368i	0.241871	+	0.175730i	0.702117	−	0.712062i	$-0.252239\pi$
$887$	7.20354	+	5.23368i	0.241871	+	0.175730i	−0.460245	+	0.887792i	$0.652239\pi$
$888$	0.731316	+	2.25076i	0.0245413	+	0.0755305i
$889$	13.1315	+	9.54057i	0.440415	+	0.319981i
$890$	−1.46075	+	4.49572i	−0.0489644	+	0.150697i
$891$	0.890814	−	2.74164i	0.0298434	−	0.0918485i
$892$	0.607473	+	1.86961i	0.0203397	+	0.0625991i
$893$	2.73157			0.0914085
$894$	6.70517			0.224254
$895$	4.37829	+	13.4750i	0.146350	+	0.450419i
$896$	1.38972	−	1.00969i	0.0464273	−	0.0337314i
$897$	0.509945	+	0.370497i	0.0170266	+	0.0123705i
$898$	16.3318			0.544998
$899$	11.5215	−	21.2659i	0.384265	−	0.709257i
$900$	1.00000			0.0333333
$901$	−16.9747	−	12.3328i	−0.565509	−	0.410866i
$902$	−13.1567	+	9.55887i	−0.438069	+	0.318275i
$903$	3.83448	+	11.8013i	0.127604	+	0.392724i
$904$	−2.36268			−0.0785815
$905$	−0.250680			−0.00833287
$906$	1.17488	+	3.61590i	0.0390326	+	0.120130i
$907$	−6.79583	+	20.9154i	−0.225652	+	0.694485i	0.772573	+	0.634926i	$0.218969\pi$
$907$	−6.79583	+	20.9154i	−0.225652	+	0.694485i	−0.998225	+	0.0595589i	$0.981031\pi$
$908$	6.39217	−	19.6731i	0.212132	−	0.652874i
$909$	3.52898	+	2.56395i	0.117049	+	0.0850410i
$910$	0.118605	+	0.365028i	0.00393171	+	0.0121005i
$911$	40.1443	+	29.1666i	1.33004	+	0.966331i	0.999748	+	0.0224527i	$0.00714750\pi$
$911$	40.1443	+	29.1666i	1.33004	+	0.966331i	0.330293	+	0.943879i	$0.392852\pi$
$912$	0.261465	−	0.189965i	0.00865797	−	0.00629039i
$913$	2.48047	−	7.63411i	0.0820917	−	0.252652i
$914$	8.01426	−	5.82270i	0.265088	−	0.192598i
$915$	−9.76053	+	7.09144i	−0.322673	+	0.234436i
$916$	−6.60665	+	20.3332i	−0.218290	+	0.671827i
$917$	17.3868	−	12.6323i	0.574164	−	0.417155i
$918$	−4.19514	−	3.04795i	−0.138460	−	0.100597i
$919$	−1.53895	−	4.73639i	−0.0507652	−	0.156239i	0.922460	−	0.386092i	$-0.126175\pi$
$919$	−1.53895	−	4.73639i	−0.0507652	−	0.156239i	−0.973225	+	0.229853i	$0.926175\pi$
$920$	−2.28230	−	1.65819i	−0.0752454	−	0.0546689i
$921$	10.0302	−	30.8698i	0.330506	−	1.01719i
$922$	−5.25816	+	16.1830i	−0.173168	+	0.532957i
$923$	−0.505632	−	1.55617i	−0.0166431	−	0.0512221i
$924$	−4.95193			−0.162906
$925$	2.36659			0.0778129
$926$	−1.74405	−	5.36762i	−0.0573129	−	0.176391i
$927$	0.0978841	−	0.0711170i	0.00321494	−	0.00233579i
$928$	−3.51438	−	2.55335i	−0.115365	−	0.0838177i
$929$	−26.9209			−0.883244			−0.441622	−	0.897201i	$-0.645597\pi$
$929$	−26.9209			−0.883244			−0.441622	+	0.897201i	$0.645597\pi$
$930$	0.731733	+	5.51947i	0.0239945	+	0.180991i
$931$	1.30866			0.0428895
$932$	−20.0389	−	14.5591i	−0.656395	−	0.476899i
$933$	1.62773	−	1.18262i	0.0532896	−	0.0387172i
$934$	10.7297	+	33.0227i	0.351088	+	1.08054i
$935$	14.9484			0.488864
$936$	−0.223434			−0.00730318
$937$	−3.36425	−	10.3541i	−0.109905	−	0.338254i	0.880945	−	0.473218i	$-0.156908\pi$
$937$	−3.36425	−	10.3541i	−0.109905	−	0.338254i	−0.990850	+	0.134965i	$0.956908\pi$
$938$	−5.68111	+	17.4847i	−0.185495	+	0.570895i
$939$	3.97438	−	12.2319i	0.129699	−	0.399173i
$940$	6.83776	+	4.96792i	0.223023	+	0.162036i
$941$	−12.9130	−	39.7421i	−0.420952	−	1.29556i	−0.906818	−	0.421523i	$-0.861496\pi$
$941$	−12.9130	−	39.7421i	−0.420952	−	1.29556i	0.485866	−	0.874034i	$-0.338504\pi$
$942$	−6.20238	−	4.50629i	−0.202084	−	0.146823i
$943$	−12.8753	+	9.35444i	−0.419277	+	0.304622i
$944$	−1.71317	+	5.27259i	−0.0557589	+	0.171608i
$945$	1.38972	−	1.00969i	0.0452076	−	0.0328452i
$946$	16.8468	−	12.2399i	0.547737	−	0.397954i
$947$	2.66896	−	8.21421i	0.0867295	−	0.266926i	−0.898281	−	0.439422i	$-0.855183\pi$
$947$	2.66896	−	8.21421i	0.0867295	−	0.266926i	0.985010	+	0.172496i	$0.0551833\pi$
$948$	4.50563	−	3.27353i	0.146336	−	0.106319i
$949$	−0.900962	−	0.654588i	−0.0292465	−	0.0212488i
$950$	−0.0998708	−	0.307371i	−0.00324024	−	0.00997242i
$951$	21.4794	+	15.6057i	0.696517	+	0.506049i
$952$	−2.75259	+	8.47159i	−0.0892119	+	0.274566i
$953$	3.71846	−	11.4442i	0.120453	−	0.370715i	−0.872592	−	0.488449i	$-0.837563\pi$
$953$	3.71846	−	11.4442i	0.120453	−	0.370715i	0.993045	+	0.117734i	$0.0375629\pi$
$954$	1.25037	+	3.84823i	0.0404821	+	0.124591i
$955$	9.05636			0.293057
$956$	−8.71018			−0.281707
$957$	3.86971	+	11.9097i	0.125090	+	0.384987i
$958$	−8.94664	+	6.50012i	−0.289053	+	0.210009i
$959$	−7.97863	−	5.79681i	−0.257643	−	0.187189i
$960$	1.00000			0.0322749
$961$	−29.9291	+	8.07756i	−0.965456	+	0.260567i
$962$	−0.528777			−0.0170484
$963$	−14.0739	−	10.2253i	−0.453526	−	0.329506i
$964$	24.2330	−	17.6063i	0.780493	−	0.567061i
$965$	−0.983094	−	3.02565i	−0.0316469	−	0.0973992i
$966$	−4.84602			−0.155918
$967$	−46.4710			−1.49441			−0.747203	−	0.664596i	$-0.768604\pi$
$967$	−46.4710			−1.49441			−0.747203	+	0.664596i	$0.768604\pi$
$968$	−0.831206	−	2.55819i	−0.0267160	−	0.0822233i
$969$	−0.517878	+	1.59386i	−0.0166366	+	0.0512023i
$970$	−2.06009	+	6.34030i	−0.0661454	+	0.203575i
$971$	24.6465	+	17.9067i	0.790943	+	0.574654i	0.908243	−	0.418443i	$-0.137424\pi$
$971$	24.6465	+	17.9067i	0.790943	+	0.574654i	−0.117300	+	0.993097i	$0.537424\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	0.141947	+	0.103130i	0.00455060	+	0.00330620i
$974$	−2.55097	+	1.85339i	−0.0817385	+	0.0593865i
$975$	−0.0690450	+	0.212499i	−0.00221121	+	0.00680540i
$976$	−9.76053	+	7.09144i	−0.312427	+	0.226991i
$977$	−27.3604	+	19.8785i	−0.875338	+	0.635970i	−0.932014	−	0.362423i	$-0.881950\pi$
$977$	−27.3604	+	19.8785i	−0.875338	+	0.635970i	0.0566763	+	0.998393i	$0.481950\pi$
$978$	−5.59974	+	17.2342i	−0.179060	+	0.551089i
$979$	11.0244	−	8.00970i	0.352341	−	0.255991i
$980$	3.27587	+	2.38006i	0.104644	+	0.0760283i
$981$	1.05994	+	3.26217i	0.0338414	+	0.104153i
$982$	−17.4196	−	12.6561i	−0.555881	−	0.403871i
$983$	11.0708	−	34.0725i	0.353105	−	1.08675i	−0.603995	−	0.796988i	$-0.706425\pi$
$983$	11.0708	−	34.0725i	0.353105	−	1.08675i	0.957100	−	0.289757i	$-0.0935746\pi$
$984$	1.74327	−	5.36524i	0.0555735	−	0.171038i
$985$	−2.85989	−	8.80184i	−0.0911237	−	0.280450i
$986$	22.5258			0.717368
$987$	14.5186			0.462133
$988$	0.0223146	+	0.0686771i	0.000709920	+	0.00218491i
$989$	16.4865	−	11.9781i	0.524240	−	0.380883i
$990$	−2.33218	−	1.69443i	−0.0741216	−	0.0538525i
$991$	5.35746			0.170185			0.0850927	−	0.996373i	$-0.472881\pi$
$991$	5.35746			0.170185			0.0850927	+	0.996373i	$0.472881\pi$
$992$	0.731733	+	5.51947i	0.0232326	+	0.175243i
$993$	−12.6177			−0.400409
$994$	10.1772	+	7.39419i	0.322802	+	0.234529i
$995$	−4.42762	+	3.21685i	−0.140365	+	0.101981i
$996$	0.860459	+	2.64822i	0.0272647	+	0.0839120i
$997$	27.8556			0.882195			0.441097	−	0.897459i	$-0.354589\pi$
$997$	27.8556			0.882195			0.441097	+	0.897459i	$0.354589\pi$
$998$	−18.9553			−0.600019
$999$	0.731316	+	2.25076i	0.0231378	+	0.0712108i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.g.901.2	yes	16
31.16	even	5	inner	930.2.n.g.481.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.g.481.2	✓	16	31.16	even	5	inner
930.2.n.g.901.2	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-0.530826 - 1.63371i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-0.530826 - 1.63371i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(0.890814 + 2.74164i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(0.180762 - 0.131331i) q^{13} +(-0.530826 + 1.63371i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.60240 - 4.93169i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(0.261465 + 0.189965i) q^{19} +(0.309017 + 0.951057i) q^{20} +(1.38972 + 1.00969i) q^{21} +(0.890814 - 2.74164i) q^{22} +(0.871763 - 2.68301i) q^{23} +(0.309017 + 0.951057i) q^{24} +1.00000 q^{25} -0.223434 q^{26} +(0.309017 + 0.951057i) q^{27} +(1.38972 - 1.00969i) q^{28} +(-3.51438 - 2.55335i) q^{29} +1.00000 q^{30} +(0.731733 + 5.51947i) q^{31} +1.00000 q^{32} +(-2.33218 - 1.69443i) q^{33} +(-4.19514 + 3.04795i) q^{34} +(-0.530826 - 1.63371i) q^{35} +1.00000 q^{36} +2.36659 q^{37} +(-0.0998708 - 0.307371i) q^{38} +(-0.0690450 + 0.212499i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-4.56395 - 3.31590i) q^{41} +(-0.530826 - 1.63371i) q^{42} +(5.84403 + 4.24594i) q^{43} +(-2.33218 + 1.69443i) q^{44} +(0.309017 - 0.951057i) q^{45} +(-2.28230 + 1.65819i) q^{46} +(6.83776 - 4.96792i) q^{47} +(0.309017 - 0.951057i) q^{48} +(3.27587 - 2.38006i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(1.60240 + 4.93169i) q^{51} +(0.180762 + 0.131331i) q^{52} +(1.25037 - 3.84823i) q^{53} +(0.309017 - 0.951057i) q^{54} +(0.890814 + 2.74164i) q^{55} -1.71779 q^{56} -0.323189 q^{57} +(1.34237 + 4.13140i) q^{58} +(4.48514 - 3.25864i) q^{59} +(-0.809017 - 0.587785i) q^{60} +12.0647 q^{61} +(2.65228 - 4.89545i) q^{62} -1.71779 q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.180762 - 0.131331i) q^{65} +(0.890814 + 2.74164i) q^{66} +10.7024 q^{67} +5.18548 q^{68} +(0.871763 + 2.68301i) q^{69} +(-0.530826 + 1.63371i) q^{70} +(2.26300 - 6.96480i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-1.54022 - 4.74030i) q^{73} +(-1.91461 - 1.39104i) q^{74} +(-0.809017 + 0.587785i) q^{75} +(-0.0998708 + 0.307371i) q^{76} +(4.00619 - 2.91067i) q^{77} +(0.180762 - 0.131331i) q^{78} +(-1.72100 + 5.29668i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(1.74327 + 5.36524i) q^{82} +(-2.25271 - 1.63669i) q^{83} +(-0.530826 + 1.63371i) q^{84} +(1.60240 - 4.93169i) q^{85} +(-2.23222 - 6.87007i) q^{86} +4.34401 q^{87} +2.88274 q^{88} +(-1.46075 - 4.49572i) q^{89} +(-0.809017 + 0.587785i) q^{90} +(-0.310511 - 0.225599i) q^{91} +2.82108 q^{92} +(-3.83625 - 4.03524i) q^{93} -8.45194 q^{94} +(0.261465 + 0.189965i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(-2.06009 - 6.34030i) q^{97} -4.04920 q^{98} +2.88274 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{12} + 4 q^{13} + q^{14} - 4 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 12 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{23} - 4 q^{24} + 16 q^{25} + 4 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 16 q^{30} + 17 q^{31} + 16 q^{32} + 5 q^{33} + 3 q^{34} + q^{35} + 16 q^{36} + 4 q^{37} + 3 q^{38} - 6 q^{39} - 4 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} + 5 q^{44} - 4 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 33 q^{49} - 4 q^{50} + 3 q^{51} + 4 q^{52} + 9 q^{53} - 4 q^{54} + 6 q^{56} + 18 q^{57} - 15 q^{58} - 7 q^{59} - 4 q^{60} + 30 q^{61} + 12 q^{62} + 6 q^{63} - 4 q^{64} + 4 q^{65} + 86 q^{67} - 12 q^{68} - 2 q^{69} + q^{70} - 3 q^{71} - 4 q^{72} + 8 q^{73} - q^{74} - 4 q^{75} + 3 q^{76} + 2 q^{77} + 4 q^{78} + 30 q^{79} - 4 q^{80} - 4 q^{81} - 7 q^{82} + 16 q^{83} + q^{84} + 3 q^{85} - 12 q^{86} - 10 q^{88} - 29 q^{89} - 4 q^{90} + 30 q^{91} + 8 q^{92} - 8 q^{93} + 24 q^{94} - 12 q^{95} - 4 q^{96} - 5 q^{97} + 62 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^12 + 4 * q^13 + q^14 - 4 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 12 * q^19 - 4 * q^20 - 4 * q^21 - 2 * q^23 - 4 * q^24 + 16 * q^25 + 4 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 16 * q^30 + 17 * q^31 + 16 * q^32 + 5 * q^33 + 3 * q^34 + q^35 + 16 * q^36 + 4 * q^37 + 3 * q^38 - 6 * q^39 - 4 * q^40 - 7 * q^41 + q^42 - 2 * q^43 + 5 * q^44 - 4 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 33 * q^49 - 4 * q^50 + 3 * q^51 + 4 * q^52 + 9 * q^53 - 4 * q^54 + 6 * q^56 + 18 * q^57 - 15 * q^58 - 7 * q^59 - 4 * q^60 + 30 * q^61 + 12 * q^62 + 6 * q^63 - 4 * q^64 + 4 * q^65 + 86 * q^67 - 12 * q^68 - 2 * q^69 + q^70 - 3 * q^71 - 4 * q^72 + 8 * q^73 - q^74 - 4 * q^75 + 3 * q^76 + 2 * q^77 + 4 * q^78 + 30 * q^79 - 4 * q^80 - 4 * q^81 - 7 * q^82 + 16 * q^83 + q^84 + 3 * q^85 - 12 * q^86 - 10 * q^88 - 29 * q^89 - 4 * q^90 + 30 * q^91 + 8 * q^92 - 8 * q^93 + 24 * q^94 - 12 * q^95 - 4 * q^96 - 5 * q^97 + 62 * q^98 - 10 * q^99

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