LMFDB - Embedded newform 930.2.n.g.841.2

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			841.2
Root			$-2.02450 - 1.47089i$ of defining polynomial
Character	$\chi$	$=$	930.841
Dual form			930.2.n.g.721.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-2.02450 + 1.47089i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-2.02450 + 1.47089i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.309017 + 0.951057i) q^{10} +(-3.70403 + 2.69113i) q^{11} +(0.309017 + 0.951057i) q^{12} +(-1.05155 + 3.23634i) q^{13} +(-2.02450 - 1.47089i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.73107 - 1.98424i) q^{17} +(0.309017 - 0.951057i) q^{18} +(-0.469241 - 1.44418i) q^{19} +(-0.809017 + 0.587785i) q^{20} +(0.773291 + 2.37995i) q^{21} +(-3.70403 - 2.69113i) q^{22} +(-1.23733 - 0.898973i) q^{23} +(-0.809017 + 0.587785i) q^{24} +1.00000 q^{25} -3.40289 q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.773291 - 2.37995i) q^{28} +(0.491628 + 1.51308i) q^{29} +1.00000 q^{30} +(-5.47106 + 1.03318i) q^{31} +1.00000 q^{32} +(1.41481 + 4.35435i) q^{33} +(1.04318 - 3.21057i) q^{34} +(-2.02450 + 1.47089i) q^{35} +1.00000 q^{36} -6.10827 q^{37} +(1.22849 - 0.892550i) q^{38} +(2.75299 + 2.00017i) q^{39} +(-0.809017 - 0.587785i) q^{40} +(3.10641 + 9.56056i) q^{41} +(-2.02450 + 1.47089i) q^{42} +(1.09614 + 3.37358i) q^{43} +(1.41481 - 4.35435i) q^{44} +(-0.809017 - 0.587785i) q^{45} +(0.472618 - 1.45457i) q^{46} +(-0.297476 + 0.915536i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(-0.228017 + 0.701763i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-2.73107 + 1.98424i) q^{51} +(-1.05155 - 3.23634i) q^{52} +(2.97499 + 2.16146i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(-3.70403 + 2.69113i) q^{55} +2.50242 q^{56} -1.51850 q^{57} +(-1.28710 + 0.935132i) q^{58} +(1.84736 - 5.68558i) q^{59} +(0.309017 + 0.951057i) q^{60} +7.03799 q^{61} +(-2.67327 - 4.88402i) q^{62} +2.50242 q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.05155 + 3.23634i) q^{65} +(-3.70403 + 2.69113i) q^{66} -4.22873 q^{67} +3.37579 q^{68} +(-1.23733 + 0.898973i) q^{69} +(-2.02450 - 1.47089i) q^{70} +(-3.66396 - 2.66202i) q^{71} +(0.309017 + 0.951057i) q^{72} +(-3.97678 + 2.88930i) q^{73} +(-1.88756 - 5.80931i) q^{74} +(0.309017 - 0.951057i) q^{75} +(1.22849 + 0.892550i) q^{76} +(3.54046 - 10.8964i) q^{77} +(-1.05155 + 3.23634i) q^{78} +(-0.930429 - 0.675996i) q^{79} +(0.309017 - 0.951057i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-8.13270 + 5.90875i) q^{82} +(-1.37778 - 4.24037i) q^{83} +(-2.02450 - 1.47089i) q^{84} +(-2.73107 - 1.98424i) q^{85} +(-2.86974 + 2.08499i) q^{86} +1.59094 q^{87} +4.57843 q^{88} +(7.53417 - 5.47390i) q^{89} +(0.309017 - 0.951057i) q^{90} +(-2.63142 - 8.09868i) q^{91} +1.52942 q^{92} +(-0.708034 + 5.52256i) q^{93} -0.962651 q^{94} +(-0.469241 - 1.44418i) q^{95} +(0.309017 - 0.951057i) q^{96} +(-0.190722 + 0.138568i) q^{97} -0.737877 q^{98} +4.57843 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.00000			0.408248
$7$	−2.02450	+	1.47089i	−0.765190	+	0.555943i	−0.900498	−	0.434860i	$-0.856798\pi$
$7$	−2.02450	+	1.47089i	−0.765190	+	0.555943i	0.135308	+	0.990804i	$0.456798\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	0.309017	+	0.951057i	0.0977198	+	0.300750i
$11$	−3.70403	+	2.69113i	−1.11681	+	0.811407i	−0.983722	−	0.179697i	$-0.942488\pi$
$11$	−3.70403	+	2.69113i	−1.11681	+	0.811407i	−0.133084	+	0.991105i	$0.542488\pi$
$12$	0.309017	+	0.951057i	0.0892055	+	0.274546i
$13$	−1.05155	+	3.23634i	−0.291647	+	0.897598i	0.692680	+	0.721245i	$0.256430\pi$
$13$	−1.05155	+	3.23634i	−0.291647	+	0.897598i	−0.984327	+	0.176353i	$0.943570\pi$
$14$	−2.02450	−	1.47089i	−0.541071	−	0.393111i
$15$	0.309017	−	0.951057i	0.0797878	−	0.245562i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.73107	−	1.98424i	−0.662383	−	0.481249i	0.205084	−	0.978744i	$-0.434253\pi$
$17$	−2.73107	−	1.98424i	−0.662383	−	0.481249i	−0.867467	+	0.497495i	$0.834253\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$	−0.469241	−	1.44418i	−0.107651	−	0.331317i	0.882692	−	0.469951i	$-0.155729\pi$
$19$	−0.469241	−	1.44418i	−0.107651	−	0.331317i	−0.990344	+	0.138635i	$0.955729\pi$
$20$	−0.809017	+	0.587785i	−0.180902	+	0.131433i
$21$	0.773291	+	2.37995i	0.168746	+	0.519347i
$22$	−3.70403	−	2.69113i	−0.789701	−	0.573752i
$23$	−1.23733	−	0.898973i	−0.258001	−	0.187449i	0.451264	−	0.892390i	$-0.350973\pi$
$23$	−1.23733	−	0.898973i	−0.258001	−	0.187449i	−0.709265	+	0.704942i	$0.750973\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	1.00000			0.200000
$26$	−3.40289			−0.667361
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	0.773291	−	2.37995i	0.146138	−	0.449768i
$29$	0.491628	+	1.51308i	0.0912930	+	0.280971i	0.986270	−	0.165142i	$-0.0528081\pi$
$29$	0.491628	+	1.51308i	0.0912930	+	0.280971i	−0.894977	+	0.446113i	$0.852808\pi$
$30$	1.00000			0.182574
$31$	−5.47106	+	1.03318i	−0.982632	+	0.185565i
$31$	−5.47106	+	1.03318i	−0.982632	+	0.185565i
$32$	1.00000			0.176777
$33$	1.41481	+	4.35435i	0.246287	+	0.757994i
$34$	1.04318	−	3.21057i	0.178903	−	0.550608i
$35$	−2.02450	+	1.47089i	−0.342203	+	0.248625i
$36$	1.00000			0.166667
$37$	−6.10827			−1.00419			−0.502097	−	0.864812i	$-0.667438\pi$
$37$	−6.10827			−1.00419			−0.502097	+	0.864812i	$0.667438\pi$
$38$	1.22849	−	0.892550i	0.199287	−	0.144791i
$39$	2.75299	+	2.00017i	0.440832	+	0.320283i
$40$	−0.809017	−	0.587785i	−0.127917	−	0.0929370i
$41$	3.10641	+	9.56056i	0.485140	+	1.49311i	0.831777	+	0.555109i	$0.187324\pi$
$41$	3.10641	+	9.56056i	0.485140	+	1.49311i	−0.346637	+	0.937999i	$0.612676\pi$
$42$	−2.02450	+	1.47089i	−0.312388	+	0.226963i
$43$	1.09614	+	3.37358i	0.167160	+	0.514467i	0.999189	−	0.0402659i	$-0.0128205\pi$
$43$	1.09614	+	3.37358i	0.167160	+	0.514467i	−0.832029	+	0.554733i	$0.812821\pi$
$44$	1.41481	−	4.35435i	0.213291	−	0.656442i
$45$	−0.809017	−	0.587785i	−0.120601	−	0.0876219i
$46$	0.472618	−	1.45457i	0.0696837	−	0.214464i
$47$	−0.297476	+	0.915536i	−0.0433913	+	0.133545i	−0.970405	−	0.241482i	$-0.922366\pi$
$47$	−0.297476	+	0.915536i	−0.0433913	+	0.133545i	0.927014	+	0.375027i	$0.122366\pi$
$48$	−0.809017	−	0.587785i	−0.116772	−	0.0848395i
$49$	−0.228017	+	0.701763i	−0.0325738	+	0.100252i
$50$	0.309017	+	0.951057i	0.0437016	+	0.134500i
$51$	−2.73107	+	1.98424i	−0.382427	+	0.277849i
$52$	−1.05155	−	3.23634i	−0.145824	−	0.448799i
$53$	2.97499	+	2.16146i	0.408647	+	0.296899i	0.773054	−	0.634340i	$-0.218728\pi$
$53$	2.97499	+	2.16146i	0.408647	+	0.296899i	−0.364407	+	0.931240i	$0.618728\pi$
$54$	−0.809017	−	0.587785i	−0.110093	−	0.0799874i
$55$	−3.70403	+	2.69113i	−0.499451	+	0.362872i
$56$	2.50242			0.334400
$57$	−1.51850			−0.201130
$58$	−1.28710	+	0.935132i	−0.169004	+	0.122789i
$59$	1.84736	−	5.68558i	0.240505	−	0.740199i	−0.755838	−	0.654759i	$-0.772770\pi$
$59$	1.84736	−	5.68558i	0.240505	−	0.740199i	0.996343	−	0.0854404i	$-0.0272297\pi$
$60$	0.309017	+	0.951057i	0.0398939	+	0.122781i
$61$	7.03799			0.901122			0.450561	−	0.892746i	$-0.351224\pi$
$61$	7.03799			0.901122			0.450561	+	0.892746i	$0.351224\pi$
$62$	−2.67327	−	4.88402i	−0.339505	−	0.620271i
$63$	2.50242			0.315276
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−1.05155	+	3.23634i	−0.130429	+	0.401418i
$66$	−3.70403	+	2.69113i	−0.455934	+	0.331256i
$67$	−4.22873			−0.516621			−0.258311	−	0.966062i	$-0.583166\pi$
$67$	−4.22873			−0.516621			−0.258311	+	0.966062i	$0.583166\pi$
$68$	3.37579			0.409375
$69$	−1.23733	+	0.898973i	−0.148957	+	0.108224i
$70$	−2.02450	−	1.47089i	−0.241974	−	0.175805i
$71$	−3.66396	−	2.66202i	−0.434832	−	0.315924i	0.348746	−	0.937217i	$-0.386608\pi$
$71$	−3.66396	−	2.66202i	−0.434832	−	0.315924i	−0.783578	+	0.621293i	$0.786608\pi$
$72$	0.309017	+	0.951057i	0.0364180	+	0.112083i
$73$	−3.97678	+	2.88930i	−0.465446	+	0.338167i	−0.795664	−	0.605738i	$-0.792878\pi$
$73$	−3.97678	+	2.88930i	−0.465446	+	0.338167i	0.330218	+	0.943905i	$0.392878\pi$
$74$	−1.88756	−	5.80931i	−0.219424	−	0.675318i
$75$	0.309017	−	0.951057i	0.0356822	−	0.109819i
$76$	1.22849	+	0.892550i	0.140917	+	0.102382i
$77$	3.54046	−	10.8964i	0.403473	−	1.24176i
$78$	−1.05155	+	3.23634i	−0.119065	+	0.366443i
$79$	−0.930429	−	0.675996i	−0.104681	−	0.0760555i	0.534213	−	0.845350i	$-0.320608\pi$
$79$	−0.930429	−	0.675996i	−0.104681	−	0.0760555i	−0.638895	+	0.769294i	$0.720608\pi$
$80$	0.309017	−	0.951057i	0.0345492	−	0.106331i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−8.13270	+	5.90875i	−0.898106	+	0.652512i
$83$	−1.37778	−	4.24037i	−0.151231	−	0.465441i	0.846529	−	0.532343i	$-0.178688\pi$
$83$	−1.37778	−	4.24037i	−0.151231	−	0.465441i	−0.997760	+	0.0669024i	$0.978688\pi$
$84$	−2.02450	−	1.47089i	−0.220891	−	0.160487i
$85$	−2.73107	−	1.98424i	−0.296227	−	0.215221i
$86$	−2.86974	+	2.08499i	−0.309452	+	0.224830i
$87$	1.59094			0.170567
$88$	4.57843			0.488062
$89$	7.53417	−	5.47390i	0.798621	−	0.580232i	−0.111888	−	0.993721i	$-0.535690\pi$
$89$	7.53417	−	5.47390i	0.798621	−	0.580232i	0.910509	+	0.413489i	$0.135690\pi$
$90$	0.309017	−	0.951057i	0.0325733	−	0.100250i
$91$	−2.63142	−	8.09868i	−0.275848	−	0.848973i
$92$	1.52942			0.159453
$93$	−0.708034	+	5.52256i	−0.0734197	+	0.572663i
$94$	−0.962651			−0.0992899
$95$	−0.469241	−	1.44418i	−0.0481431	−	0.148169i
$96$	0.309017	−	0.951057i	0.0315389	−	0.0970668i
$97$	−0.190722	+	0.138568i	−0.0193649	+	0.0140694i	−0.597426	−	0.801924i	$-0.703810\pi$
$97$	−0.190722	+	0.138568i	−0.0193649	+	0.0140694i	0.578061	+	0.815994i	$0.303810\pi$
$98$	−0.737877			−0.0745369
$99$	4.57843			0.460149
$100$	−0.809017	+	0.587785i	−0.0809017	+	0.0587785i
$101$	3.33412	+	2.42238i	0.331757	+	0.241036i	0.741176	−	0.671311i	$-0.234268\pi$
$101$	3.33412	+	2.42238i	0.331757	+	0.241036i	−0.409419	+	0.912347i	$0.634268\pi$
$102$	−2.73107	−	1.98424i	−0.270417	−	0.196469i
$103$	3.27937	+	10.0929i	0.323126	+	0.994480i	0.972279	+	0.233823i	$0.0751235\pi$
$103$	3.27937	+	10.0929i	0.323126	+	0.994480i	−0.649153	+	0.760658i	$0.724877\pi$
$104$	2.75299	−	2.00017i	0.269953	−	0.196132i
$105$	0.773291	+	2.37995i	0.0754655	+	0.232259i
$106$	−1.13635	+	3.49732i	−0.110372	+	0.339689i
$107$	−11.8036	−	8.57584i	−1.14110	−	0.829058i	−0.153828	−	0.988098i	$-0.549160\pi$
$107$	−11.8036	−	8.57584i	−1.14110	−	0.829058i	−0.987272	+	0.159040i	$0.949160\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	−2.84393	+	8.75273i	−0.272399	+	0.838359i	0.717496	+	0.696562i	$0.245288\pi$
$109$	−2.84393	+	8.75273i	−0.272399	+	0.838359i	−0.989896	+	0.141797i	$0.954712\pi$
$110$	−3.70403	−	2.69113i	−0.353165	−	0.256590i
$111$	−1.88756	+	5.80931i	−0.179159	+	0.551395i
$112$	0.773291	+	2.37995i	0.0730692	+	0.224884i
$113$	6.04043	−	4.38863i	0.568236	−	0.412847i	−0.266228	−	0.963910i	$-0.585777\pi$
$113$	6.04043	−	4.38863i	0.568236	−	0.412847i	0.834464	+	0.551063i	$0.185777\pi$
$114$	−0.469241	−	1.44418i	−0.0439485	−	0.135259i
$115$	−1.23733	−	0.898973i	−0.115382	−	0.0838296i
$116$	−1.28710	−	0.935132i	−0.119504	−	0.0868248i
$117$	2.75299	−	2.00017i	0.254514	−	0.184915i
$118$	5.97817			0.550335
$119$	8.44766			0.774396
$120$	−0.809017	+	0.587785i	−0.0738528	+	0.0536572i
$121$	3.07843	−	9.47444i	0.279858	−	0.861313i
$122$	2.17486	+	6.69352i	0.196902	+	0.606003i
$123$	10.0526			0.906409
$124$	3.81889	−	4.05167i	0.342947	−	0.363851i
$125$	1.00000			0.0894427
$126$	0.773291	+	2.37995i	0.0688903	+	0.212022i
$127$	−6.20902	+	19.1094i	−0.550962	+	1.69569i	0.155415	+	0.987849i	$0.450329\pi$
$127$	−6.20902	+	19.1094i	−0.550962	+	1.69569i	−0.706376	+	0.707836i	$0.749671\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	3.54720			0.312313
$130$	−3.40289			−0.298453
$131$	8.09861	−	5.88398i	0.707579	−	0.514086i	−0.174813	−	0.984602i	$-0.555932\pi$
$131$	8.09861	−	5.88398i	0.707579	−	0.514086i	0.882392	+	0.470516i	$0.155932\pi$
$132$	−3.70403	−	2.69113i	−0.322394	−	0.234233i
$133$	3.07420	+	2.23354i	0.266567	+	0.193672i
$134$	−1.30675	−	4.02176i	−0.112886	−	0.347427i
$135$	−0.809017	+	0.587785i	−0.0696291	+	0.0505885i
$136$	1.04318	+	3.21057i	0.0894517	+	0.275304i
$137$	3.45955	−	10.6474i	0.295570	−	0.909670i	−0.687460	−	0.726222i	$-0.741274\pi$
$137$	3.45955	−	10.6474i	0.295570	−	0.909670i	0.983030	−	0.183448i	$-0.0587257\pi$
$138$	−1.23733	−	0.898973i	−0.105328	−	0.0765256i
$139$	−1.40221	+	4.31554i	−0.118934	+	0.366040i	−0.992747	−	0.120221i	$-0.961640\pi$
$139$	−1.40221	+	4.31554i	−0.118934	+	0.366040i	0.873814	+	0.486261i	$0.161640\pi$
$140$	0.773291	−	2.37995i	0.0653550	−	0.201142i
$141$	0.778801	+	0.565832i	0.0655869	+	0.0476517i
$142$	1.39951	−	4.30724i	0.117444	−	0.361456i
$143$	−4.81445	−	14.8173i	−0.402604	−	1.23909i
$144$	−0.809017	+	0.587785i	−0.0674181	+	0.0489821i
$145$	0.491628	+	1.51308i	0.0408275	+	0.125654i
$146$	−3.97678	−	2.88930i	−0.329120	−	0.239120i
$147$	0.596955	+	0.433713i	0.0492360	+	0.0357721i
$148$	4.94169	−	3.59035i	0.406205	−	0.295125i
$149$	19.9787			1.63672			0.818361	−	0.574705i	$-0.194883\pi$
$149$	19.9787			1.63672			0.818361	+	0.574705i	$0.194883\pi$
$150$	1.00000			0.0816497
$151$	−0.677121	+	0.491957i	−0.0551033	+	0.0400349i	−0.614996	−	0.788530i	$-0.710842\pi$
$151$	−0.677121	+	0.491957i	−0.0551033	+	0.0400349i	0.559893	+	0.828565i	$0.310842\pi$
$152$	−0.469241	+	1.44418i	−0.0380605	+	0.117138i
$153$	1.04318	+	3.21057i	0.0843359	+	0.259559i
$154$	11.4572			0.923245
$155$	−5.47106	+	1.03318i	−0.439446	+	0.0829874i
$156$	−3.40289			−0.272449
$157$	−1.75863	−	5.41251i	−0.140354	−	0.431965i	0.856030	−	0.516925i	$-0.172924\pi$
$157$	−1.75863	−	5.41251i	−0.140354	−	0.431965i	−0.996384	+	0.0849605i	$0.972924\pi$
$158$	0.355392	−	1.09378i	0.0282735	−	0.0870168i
$159$	2.97499	−	2.16146i	0.235932	−	0.171415i
$160$	1.00000			0.0790569
$161$	3.82727			0.301631
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	−13.6449	−	9.91359i	−1.06875	−	0.776493i	−0.0930632	−	0.995660i	$-0.529666\pi$
$163$	−13.6449	−	9.91359i	−1.06875	−	0.776493i	−0.975687	+	0.219168i	$0.929666\pi$
$164$	−8.13270	−	5.90875i	−0.635057	−	0.461396i
$165$	1.41481	+	4.35435i	0.110143	+	0.338985i
$166$	3.60707	−	2.62069i	0.279963	−	0.203405i
$167$	1.96038	+	6.03343i	0.151699	+	0.466880i	0.997811	−	0.0661234i	$-0.0210631\pi$
$167$	1.96038	+	6.03343i	0.151699	+	0.466880i	−0.846113	+	0.533004i	$0.821063\pi$
$168$	0.773291	−	2.37995i	0.0596607	−	0.183617i
$169$	1.14910	+	0.834872i	0.0883925	+	0.0642209i
$170$	1.04318	−	3.21057i	0.0800081	−	0.246239i
$171$	−0.469241	+	1.44418i	−0.0358838	+	0.110439i
$172$	−2.86974	−	2.08499i	−0.218816	−	0.158979i
$173$	3.78881	−	11.6608i	0.288058	−	0.886552i	−0.697407	−	0.716675i	$-0.745663\pi$
$173$	3.78881	−	11.6608i	0.288058	−	0.886552i	0.985465	−	0.169877i	$-0.0543369\pi$
$174$	0.491628	+	1.51308i	0.0372702	+	0.114706i
$175$	−2.02450	+	1.47089i	−0.153038	+	0.111189i
$176$	1.41481	+	4.35435i	0.106646	+	0.328221i
$177$	−4.83644	−	3.51388i	−0.363529	−	0.264119i
$178$	7.53417	+	5.47390i	0.564710	+	0.410286i
$179$	6.42759	−	4.66992i	0.480421	−	0.349046i	−0.321068	−	0.947056i	$-0.604042\pi$
$179$	6.42759	−	4.66992i	0.480421	−	0.349046i	0.801489	+	0.598010i	$0.204042\pi$
$180$	1.00000			0.0745356
$181$	−2.95414			−0.219579			−0.109790	−	0.993955i	$-0.535018\pi$
$181$	−2.95414			−0.219579			−0.109790	+	0.993955i	$0.535018\pi$
$182$	6.88915	−	5.00526i	0.510658	−	0.371015i
$183$	2.17486	−	6.69352i	0.160770	−	0.494799i
$184$	0.472618	+	1.45457i	0.0348419	+	0.107232i
$185$	−6.10827			−0.449089
$186$	−5.47106	+	1.03318i	−0.401158	+	0.0757568i
$187$	15.4558			1.13024
$188$	−0.297476	−	0.915536i	−0.0216956	−	0.0667723i
$189$	0.773291	−	2.37995i	0.0562487	−	0.173116i
$190$	1.22849	−	0.892550i	0.0891240	−	0.0647524i
$191$	16.7424			1.21144			0.605718	−	0.795680i	$-0.292886\pi$
$191$	16.7424			1.21144			0.605718	+	0.795680i	$0.292886\pi$
$192$	1.00000			0.0721688
$193$	16.4651	−	11.9626i	1.18519	−	0.861087i	0.192438	−	0.981309i	$-0.438361\pi$
$193$	16.4651	−	11.9626i	1.18519	−	0.861087i	0.992747	+	0.120222i	$0.0383605\pi$
$194$	−0.190722	−	0.138568i	−0.0136931	−	0.00994859i
$195$	2.75299	+	2.00017i	0.197146	+	0.143235i
$196$	−0.228017	−	0.701763i	−0.0162869	−	0.0501259i
$197$	−2.94092	+	2.13670i	−0.209532	+	0.152234i	−0.687602	−	0.726088i	$-0.741337\pi$
$197$	−2.94092	+	2.13670i	−0.209532	+	0.152234i	0.478070	+	0.878322i	$0.341337\pi$
$198$	1.41481	+	4.35435i	0.100546	+	0.309450i
$199$	−5.35557	+	16.4828i	−0.379646	+	1.16843i	0.560644	+	0.828057i	$0.310554\pi$
$199$	−5.35557	+	16.4828i	−0.379646	+	1.16843i	−0.940290	+	0.340374i	$0.889446\pi$
$200$	−0.809017	−	0.587785i	−0.0572061	−	0.0415627i
$201$	−1.30675	+	4.02176i	−0.0921709	+	0.283673i
$202$	−1.27352	+	3.91949i	−0.0896046	+	0.275774i
$203$	−3.22087	−	2.34010i	−0.226060	−	0.164243i
$204$	1.04318	−	3.21057i	0.0730370	−	0.224785i
$205$	3.10641	+	9.56056i	0.216961	+	0.667738i
$206$	−8.58551	+	6.23774i	−0.598181	+	0.434604i
$207$	0.472618	+	1.45457i	0.0328492	+	0.101099i
$208$	2.75299	+	2.00017i	0.190886	+	0.138687i
$209$	5.62455	+	4.08648i	0.389058	+	0.282667i
$210$	−2.02450	+	1.47089i	−0.139704	+	0.101501i
$211$	−1.79724			−0.123727			−0.0618637	−	0.998085i	$-0.519704\pi$
$211$	−1.79724			−0.123727			−0.0618637	+	0.998085i	$0.519704\pi$
$212$	−3.67730			−0.252558
$213$	−3.66396	+	2.66202i	−0.251050	+	0.182399i
$214$	4.50858	−	13.8760i	0.308201	−	0.948544i
$215$	1.09614	+	3.37358i	0.0747564	+	0.230077i
$216$	1.00000			0.0680414
$217$	9.55648	−	10.1390i	0.648736	−	0.688280i
$218$	−9.20316			−0.623317
$219$	1.51899	+	4.67498i	0.102644	+	0.315906i
$220$	1.41481	−	4.35435i	0.0953866	−	0.293570i
$221$	9.29353	−	6.75215i	0.625151	−	0.454198i
$222$	−6.10827			−0.409960
$223$	−17.3442			−1.16145			−0.580727	−	0.814098i	$-0.697232\pi$
$223$	−17.3442			−1.16145			−0.580727	+	0.814098i	$0.697232\pi$
$224$	−2.02450	+	1.47089i	−0.135268	+	0.0982778i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	6.04043	+	4.38863i	0.401803	+	0.291927i
$227$	8.58932	+	26.4352i	0.570093	+	1.75457i	0.652311	+	0.757951i	$0.273800\pi$
$227$	8.58932	+	26.4352i	0.570093	+	1.75457i	−0.0822180	+	0.996614i	$0.526200\pi$
$228$	1.22849	−	0.892550i	0.0813587	−	0.0591105i
$229$	5.76557	+	17.7446i	0.381000	+	1.17260i	0.939341	+	0.342985i	$0.111438\pi$
$229$	5.76557	+	17.7446i	0.381000	+	1.17260i	−0.558341	+	0.829612i	$0.688562\pi$
$230$	0.472618	−	1.45457i	0.0311635	−	0.0959114i
$231$	−9.26904	−	6.73436i	−0.609858	−	0.443088i
$232$	0.491628	−	1.51308i	0.0322770	−	0.0993382i
$233$	−3.00333	+	9.24329i	−0.196754	+	0.605548i	0.803197	+	0.595713i	$0.203131\pi$
$233$	−3.00333	+	9.24329i	−0.196754	+	0.605548i	−0.999952	+	0.00983465i	$0.996869\pi$
$234$	2.75299	+	2.00017i	0.179969	+	0.130755i
$235$	−0.297476	+	0.915536i	−0.0194052	+	0.0597230i
$236$	1.84736	+	5.68558i	0.120253	+	0.370100i
$237$	−0.930429	+	0.675996i	−0.0604379	+	0.0439107i
$238$	2.61047	+	8.03420i	0.169212	+	0.520780i
$239$	10.9281	+	7.93972i	0.706879	+	0.513578i	0.882165	−	0.470940i	$-0.156085\pi$
$239$	10.9281	+	7.93972i	0.706879	+	0.513578i	−0.175286	+	0.984517i	$0.556085\pi$
$240$	−0.809017	−	0.587785i	−0.0522218	−	0.0379414i
$241$	0.490877	−	0.356643i	0.0316202	−	0.0229734i	−0.571863	−	0.820349i	$-0.693779\pi$
$241$	0.490877	−	0.356643i	0.0316202	−	0.0229734i	0.603483	+	0.797376i	$0.293779\pi$
$242$	9.96202			0.640383
$243$	1.00000			0.0641500
$244$	−5.69385	+	4.13682i	−0.364511	+	0.264833i
$245$	−0.228017	+	0.701763i	−0.0145674	+	0.0448340i
$246$	3.10641	+	9.56056i	0.198058	+	0.609559i
$247$	5.16727			0.328785
$248$	5.03347	+	2.37995i	0.319626	+	0.151127i
$249$	−4.45859			−0.282551
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−5.10157	+	15.7010i	−0.322008	+	0.991039i	0.650765	+	0.759279i	$0.274448\pi$
$251$	−5.10157	+	15.7010i	−0.322008	+	0.991039i	−0.972773	+	0.231760i	$0.925552\pi$
$252$	−2.02450	+	1.47089i	−0.127532	+	0.0926572i
$253$	7.00236			0.440234
$254$	−20.0928			−1.26074
$255$	−2.73107	+	1.98424i	−0.171026	+	0.124258i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−16.7249	−	12.1514i	−1.04327	−	0.757980i	−0.0723493	−	0.997379i	$-0.523050\pi$
$257$	−16.7249	−	12.1514i	−1.04327	−	0.757980i	−0.970921	+	0.239399i	$0.923050\pi$
$258$	1.09614	+	3.37358i	0.0682430	+	0.210030i
$259$	12.3662	−	8.98458i	0.768399	−	0.558274i
$260$	−1.05155	−	3.23634i	−0.0652143	−	0.200709i
$261$	0.491628	−	1.51308i	0.0304310	−	0.0936570i
$262$	8.09861	+	5.88398i	0.500334	+	0.363514i
$263$	3.48685	−	10.7314i	0.215008	−	0.661728i	−0.784145	−	0.620578i	$-0.786898\pi$
$263$	3.48685	−	10.7314i	0.215008	−	0.661728i	0.999153	−	0.0411495i	$-0.0131020\pi$
$264$	1.41481	−	4.35435i	0.0870757	−	0.267991i
$265$	2.97499	+	2.16146i	0.182752	+	0.132777i
$266$	−1.17424	+	3.61394i	−0.0719973	+	0.221585i
$267$	−2.87780	−	8.85695i	−0.176118	−	0.542037i
$268$	3.42111	−	2.48558i	0.208978	−	0.151831i
$269$	−2.79471	−	8.60123i	−0.170396	−	0.524426i	0.828997	−	0.559253i	$-0.188912\pi$
$269$	−2.79471	−	8.60123i	−0.170396	−	0.524426i	−0.999393	+	0.0348269i	$0.988912\pi$
$270$	−0.809017	−	0.587785i	−0.0492352	−	0.0357715i
$271$	−14.9774	−	10.8817i	−0.909814	−	0.661018i	0.0311540	−	0.999515i	$-0.490082\pi$
$271$	−14.9774	−	10.8817i	−0.909814	−	0.661018i	−0.940968	+	0.338496i	$0.890082\pi$
$272$	−2.73107	+	1.98424i	−0.165596	+	0.120312i
$273$	−8.51546			−0.515379
$274$	11.1954			0.676336
$275$	−3.70403	+	2.69113i	−0.223361	+	0.162281i
$276$	0.472618	−	1.45457i	0.0284483	−	0.0875547i
$277$	2.79718	+	8.60883i	0.168066	+	0.517255i	0.999249	−	0.0387444i	$-0.0123358\pi$
$277$	2.79718	+	8.60883i	0.168066	+	0.517255i	−0.831183	+	0.555999i	$0.812336\pi$
$278$	−4.53763			−0.272149
$279$	5.03347	+	2.37995i	0.301346	+	0.142484i
$280$	2.50242			0.149548
$281$	4.87646	+	15.0082i	0.290905	+	0.895314i	0.984566	+	0.175012i	$0.0559965\pi$
$281$	4.87646	+	15.0082i	0.290905	+	0.895314i	−0.693661	+	0.720301i	$0.744003\pi$
$282$	−0.297476	+	0.915536i	−0.0177144	+	0.0545194i
$283$	−3.40084	+	2.47085i	−0.202159	+	0.146877i	−0.684259	−	0.729239i	$-0.739874\pi$
$283$	−3.40084	+	2.47085i	−0.202159	+	0.146877i	0.482100	+	0.876116i	$0.339874\pi$
$284$	4.52890			0.268741
$285$	−1.51850			−0.0899480
$286$	12.6044	−	9.15762i	0.745313	−	0.541501i
$287$	−20.3515	−	14.7862i	−1.20131	−	0.872802i
$288$	−0.809017	−	0.587785i	−0.0476718	−	0.0346356i
$289$	−1.73174	−	5.32974i	−0.101867	−	0.313514i
$290$	−1.28710	+	0.935132i	−0.0755810	+	0.0549128i
$291$	0.0728494	+	0.224207i	0.00427051	+	0.0131433i
$292$	1.51899	−	4.67498i	0.0888923	−	0.273583i
$293$	−18.8962	−	13.7289i	−1.10393	−	0.802050i	−0.122230	−	0.992502i	$-0.539005\pi$
$293$	−18.8962	−	13.7289i	−1.10393	−	0.802050i	−0.981697	+	0.190452i	$0.939005\pi$
$294$	−0.228017	+	0.701763i	−0.0132982	+	0.0409276i
$295$	1.84736	−	5.68558i	0.107557	−	0.331027i
$296$	4.94169	+	3.59035i	0.287230	+	0.208685i
$297$	1.41481	−	4.35435i	0.0820958	−	0.252665i
$298$	6.17377	+	19.0009i	0.357637	+	1.10069i
$299$	4.21049	−	3.05910i	0.243499	−	0.176912i
$300$	0.309017	+	0.951057i	0.0178411	+	0.0549093i
$301$	−7.18131	−	5.21753i	−0.413924	−	0.300733i
$302$	−0.677121	−	0.491957i	−0.0389639	−	0.0283090i
$303$	3.33412	−	2.42238i	0.191540	−	0.139162i
$304$	−1.51850			−0.0870917
$305$	7.03799			0.402994
$306$	−2.73107	+	1.98424i	−0.156125	+	0.113432i
$307$	−9.94291	+	30.6011i	−0.567472	+	1.74650i	0.0930189	+	0.995664i	$0.470348\pi$
$307$	−9.94291	+	30.6011i	−0.567472	+	1.74650i	−0.660491	+	0.750834i	$0.729652\pi$
$308$	3.54046	+	10.8964i	0.201736	+	0.620881i
$309$	10.6123			0.603711
$310$	−2.67327	−	4.88402i	−0.151831	−	0.277394i
$311$	27.3706			1.55204			0.776022	−	0.630705i	$-0.217234\pi$
$311$	27.3706			1.55204			0.776022	+	0.630705i	$0.217234\pi$
$312$	−1.05155	−	3.23634i	−0.0595323	−	0.183221i
$313$	1.27362	−	3.91979i	0.0719890	−	0.221559i	−0.908588	−	0.417693i	$-0.862839\pi$
$313$	1.27362	−	3.91979i	0.0719890	−	0.221559i	0.980577	+	0.196134i	$0.0628387\pi$
$314$	4.60415	−	3.34511i	0.259827	−	0.188776i
$315$	2.50242			0.140996
$316$	1.15007			0.0646967
$317$	−21.2127	+	15.4120i	−1.19143	+	0.865622i	−0.993414	−	0.114578i	$-0.963448\pi$
$317$	−21.2127	+	15.4120i	−1.19143	+	0.865622i	−0.198012	+	0.980200i	$0.563448\pi$
$318$	2.97499	+	2.16146i	0.166829	+	0.121209i
$319$	−5.89289	−	4.28144i	−0.329938	−	0.239714i
$320$	0.309017	+	0.951057i	0.0172746	+	0.0531657i
$321$	−11.8036	+	8.57584i	−0.658814	+	0.478657i
$322$	1.18269	+	3.63995i	0.0659087	+	0.202846i
$323$	−1.58406	+	4.87524i	−0.0881395	+	0.271266i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	−1.05155	+	3.23634i	−0.0583295	+	0.179520i
$326$	5.21188	−	16.0405i	0.288660	−	0.888403i
$327$	7.44551	+	5.40948i	0.411738	+	0.299145i
$328$	3.10641	−	9.56056i	0.171523	−	0.527894i
$329$	−0.744410	−	2.29106i	−0.0410407	−	0.126310i
$330$	−3.70403	+	2.69113i	−0.203900	+	0.148142i
$331$	−4.50534	−	13.8660i	−0.247636	−	0.762146i	−0.995192	−	0.0979464i	$-0.968773\pi$
$331$	−4.50534	−	13.8660i	−0.247636	−	0.762146i	0.747556	−	0.664199i	$-0.231227\pi$
$332$	3.60707	+	2.62069i	0.197964	+	0.143829i
$333$	4.94169	+	3.59035i	0.270803	+	0.196750i
$334$	−5.13234	+	3.72886i	−0.280829	+	0.204034i
$335$	−4.22873			−0.231040
$336$	2.50242			0.136518
$337$	−11.8104	+	8.58077i	−0.643354	+	0.467424i	−0.861001	−	0.508603i	$-0.830162\pi$
$337$	−11.8104	+	8.58077i	−0.643354	+	0.467424i	0.217647	+	0.976028i	$0.430162\pi$
$338$	−0.438918	+	1.35085i	−0.0238740	+	0.0734766i
$339$	−2.30724	−	7.10095i	−0.125312	−	0.385671i
$340$	3.37579			0.183078
$341$	17.4845	−	18.5503i	0.946840	−	1.00456i
$342$	−1.51850			−0.0821109
$343$	−5.98363	−	18.4157i	−0.323086	−	0.994356i
$344$	1.09614	−	3.37358i	0.0591001	−	0.181891i
$345$	−1.23733	+	0.898973i	−0.0666156	+	0.0483991i
$346$	12.2609			0.659148
$347$	−32.8114			−1.76141			−0.880705	−	0.473665i	$-0.842931\pi$
$347$	−32.8114			−1.76141			−0.880705	+	0.473665i	$0.842931\pi$
$348$	−1.28710	+	0.935132i	−0.0689957	+	0.0501283i
$349$	28.4884	+	20.6980i	1.52495	+	1.10794i	0.958966	+	0.283520i	$0.0915021\pi$
$349$	28.4884	+	20.6980i	1.52495	+	1.10794i	0.565980	+	0.824419i	$0.308498\pi$
$350$	−2.02450	−	1.47089i	−0.108214	−	0.0786222i
$351$	−1.05155	−	3.23634i	−0.0561276	−	0.172743i
$352$	−3.70403	+	2.69113i	−0.197425	+	0.143438i
$353$	3.02486	+	9.30955i	0.160997	+	0.495497i	0.998719	−	0.0505993i	$-0.0161131\pi$
$353$	3.02486	+	9.30955i	0.160997	+	0.495497i	−0.837722	+	0.546097i	$0.816113\pi$
$354$	1.84736	−	5.68558i	0.0981859	−	0.302185i
$355$	−3.66396	−	2.66202i	−0.194463	−	0.141285i
$356$	−2.87780	+	8.85695i	−0.152523	+	0.469417i
$357$	2.61047	−	8.03420i	0.138161	−	0.425215i
$358$	6.42759	+	4.66992i	0.339709	+	0.246813i
$359$	1.39262	−	4.28604i	0.0734997	−	0.226209i	−0.907557	−	0.419928i	$-0.862055\pi$
$359$	1.39262	−	4.28604i	0.0734997	−	0.226209i	0.981057	+	0.193720i	$0.0620552\pi$
$360$	0.309017	+	0.951057i	0.0162866	+	0.0501251i
$361$	13.5059	−	9.81259i	0.710835	−	0.516452i
$362$	−0.912879	−	2.80955i	−0.0479798	−	0.147667i
$363$	−8.05944	−	5.85553i	−0.423011	−	0.307335i
$364$	6.88915	+	5.00526i	0.361090	+	0.262347i
$365$	−3.97678	+	2.88930i	−0.208154	+	0.151233i
$366$	7.03799			0.367881
$367$	−26.4386			−1.38008			−0.690042	−	0.723770i	$-0.742408\pi$
$367$	−26.4386			−1.38008			−0.690042	+	0.723770i	$0.742408\pi$
$368$	−1.23733	+	0.898973i	−0.0645003	+	0.0468622i
$369$	3.10641	−	9.56056i	0.161713	−	0.497703i
$370$	−1.88756	−	5.80931i	−0.0981295	−	0.302012i
$371$	−9.20215			−0.477752
$372$	−2.67327	−	4.88402i	−0.138603	−	0.253225i
$373$	21.4662			1.11148			0.555740	−	0.831356i	$-0.312435\pi$
$373$	21.4662			1.11148			0.555740	+	0.831356i	$0.312435\pi$
$374$	4.77611	+	14.6994i	0.246967	+	0.760086i
$375$	0.309017	−	0.951057i	0.0159576	−	0.0491123i
$376$	0.778801	−	0.565832i	0.0401636	−	0.0291806i
$377$	−5.41379			−0.278824
$378$	2.50242			0.128711
$379$	0.311303	−	0.226175i	0.0159906	−	0.0116178i	−0.579761	−	0.814786i	$-0.696854\pi$
$379$	0.311303	−	0.226175i	0.0159906	−	0.0116178i	0.595752	+	0.803169i	$0.296854\pi$
$380$	1.22849	+	0.892550i	0.0630202	+	0.0457868i
$381$	16.2554	+	11.8103i	0.832791	+	0.605058i
$382$	5.17368	+	15.9229i	0.264708	+	0.814689i
$383$	−3.83972	+	2.78972i	−0.196200	+	0.142548i	−0.681548	−	0.731773i	$-0.738693\pi$
$383$	−3.83972	+	2.78972i	−0.196200	+	0.142548i	0.485348	+	0.874321i	$0.338693\pi$
$384$	0.309017	+	0.951057i	0.0157695	+	0.0485334i
$385$	3.54046	−	10.8964i	0.180439	−	0.555333i
$386$	16.4651	+	11.9626i	0.838053	+	0.608881i
$387$	1.09614	−	3.37358i	0.0557201	−	0.171489i
$388$	0.0728494	−	0.224207i	0.00369837	−	0.0113824i
$389$	25.9787	+	18.8746i	1.31717	+	0.956981i	0.999963	+	0.00862535i	$0.00274557\pi$
$389$	25.9787	+	18.8746i	1.31717	+	0.956981i	0.317209	+	0.948356i	$0.397254\pi$
$390$	−1.05155	+	3.23634i	−0.0532473	+	0.163878i
$391$	1.59546	+	4.91032i	0.0806859	+	0.248326i
$392$	0.596955	−	0.433713i	0.0301508	−	0.0219058i
$393$	−3.09339	−	9.52049i	−0.156041	−	0.480245i
$394$	−2.94092	−	2.13670i	−0.148161	−	0.107646i
$395$	−0.930429	−	0.675996i	−0.0468150	−	0.0340131i
$396$	−3.70403	+	2.69113i	−0.186134	+	0.135235i
$397$	−33.5558			−1.68412			−0.842059	−	0.539385i	$-0.818657\pi$
$397$	−33.5558			−1.68412			−0.842059	+	0.539385i	$0.818657\pi$
$398$	−17.3310			−0.868724
$399$	3.07420	−	2.23354i	0.153903	−	0.111817i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	0.0256432	+	0.0789217i	0.00128056	+	0.00394116i	0.951695	−	0.307046i	$-0.0993405\pi$
$401$	0.0256432	+	0.0789217i	0.00128056	+	0.00394116i	−0.950414	+	0.310987i	$0.899340\pi$
$402$	−4.22873			−0.210910
$403$	2.40936	−	18.7926i	0.120019	−	0.936128i
$404$	−4.12120			−0.205037
$405$	0.309017	+	0.951057i	0.0153552	+	0.0472584i
$406$	1.23026	−	3.78635i	0.0610568	−	0.187914i
$407$	22.6252	−	16.4382i	1.12149	−	0.814810i
$408$	3.37579			0.167127
$409$	−33.8563			−1.67409			−0.837043	−	0.547136i	$-0.815718\pi$
$409$	−33.8563			−1.67409			−0.837043	+	0.547136i	$0.815718\pi$
$410$	−8.13270	+	5.90875i	−0.401645	+	0.291812i
$411$	−9.05723	−	6.58046i	−0.446760	−	0.324590i
$412$	−8.58551	−	6.23774i	−0.422978	−	0.307311i
$413$	4.62287	+	14.2277i	0.227476	+	0.700100i
$414$	−1.23733	+	0.898973i	−0.0608114	+	0.0441821i
$415$	−1.37778	−	4.24037i	−0.0676325	−	0.208151i
$416$	−1.05155	+	3.23634i	−0.0515565	+	0.158674i
$417$	3.67102	+	2.66715i	0.179771	+	0.130611i
$418$	−2.14839	+	6.61206i	−0.105081	+	0.323406i
$419$	−3.15702	+	9.71630i	−0.154230	+	0.474672i	−0.998082	−	0.0619042i	$-0.980283\pi$
$419$	−3.15702	+	9.71630i	−0.154230	+	0.474672i	0.843852	+	0.536576i	$0.180283\pi$
$420$	−2.02450	−	1.47089i	−0.0987856	−	0.0717720i
$421$	0.280813	−	0.864254i	0.0136860	−	0.0421211i	−0.943980	−	0.330002i	$-0.892951\pi$
$421$	0.280813	−	0.864254i	0.0136860	−	0.0421211i	0.957666	+	0.287881i	$0.0929506\pi$
$422$	−0.555379	−	1.70928i	−0.0270354	−	0.0832065i
$423$	0.778801	−	0.565832i	0.0378666	−	0.0275117i
$424$	−1.13635	−	3.49732i	−0.0551859	−	0.169845i
$425$	−2.73107	−	1.98424i	−0.132477	−	0.0962498i
$426$	−3.66396	−	2.66202i	−0.177519	−	0.128975i
$427$	−14.2484	+	10.3521i	−0.689530	+	0.500973i
$428$	14.5901			0.705238
$429$	−15.5799			−0.752203
$430$	−2.86974	+	2.08499i	−0.138391	+	0.100547i
$431$	8.67319	−	26.6933i	0.417773	−	1.28577i	−0.491974	−	0.870610i	$-0.663725\pi$
$431$	8.67319	−	26.6933i	0.417773	−	1.28577i	0.909747	−	0.415163i	$-0.136275\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	22.4017			1.07656			0.538278	−	0.842767i	$-0.319075\pi$
$433$	22.4017			1.07656			0.538278	+	0.842767i	$0.319075\pi$
$434$	12.5959	+	5.95563i	0.604622	+	0.285880i
$435$	1.59094			0.0762798
$436$	−2.84393	−	8.75273i	−0.136200	−	0.419180i
$437$	−0.717668	+	2.20876i	−0.0343307	+	0.105659i
$438$	−3.97678	+	2.88930i	−0.190018	+	0.138056i
$439$	30.8234			1.47112			0.735561	−	0.677458i	$-0.236919\pi$
$439$	30.8234			1.47112			0.735561	+	0.677458i	$0.236919\pi$
$440$	4.57843			0.218268
$441$	0.596955	−	0.433713i	0.0284264	−	0.0206530i
$442$	9.29353	+	6.75215i	0.442048	+	0.321167i
$443$	−20.3191	−	14.7627i	−0.965389	−	0.701396i	−0.0109931	−	0.999940i	$-0.503499\pi$
$443$	−20.3191	−	14.7627i	−0.965389	−	0.701396i	−0.954396	+	0.298543i	$0.903499\pi$
$444$	−1.88756	−	5.80931i	−0.0895796	−	0.275698i
$445$	7.53417	−	5.47390i	0.357154	−	0.259488i
$446$	−5.35966	−	16.4953i	−0.253787	−	0.781076i
$447$	6.17377	−	19.0009i	0.292009	−	0.898712i
$448$	−2.02450	−	1.47089i	−0.0956488	−	0.0694929i
$449$	−2.38125	+	7.32873i	−0.112378	+	0.345864i	−0.991391	−	0.130934i	$-0.958203\pi$
$449$	−2.38125	+	7.32873i	−0.112378	+	0.345864i	0.879013	+	0.476798i	$0.158203\pi$
$450$	0.309017	−	0.951057i	0.0145672	−	0.0448332i
$451$	−37.2350	−	27.0528i	−1.75333	−	1.27387i
$452$	−2.30724	+	7.10095i	−0.108523	+	0.334001i
$453$	0.258637	+	0.796004i	0.0121518	+	0.0373995i
$454$	−22.4871	+	16.3379i	−1.05537	+	0.766773i
$455$	−2.63142	−	8.09868i	−0.123363	−	0.379672i
$456$	1.22849	+	0.892550i	0.0575293	+	0.0417975i
$457$	−0.210324	−	0.152809i	−0.00983852	−	0.00714811i	0.582855	−	0.812576i	$-0.301936\pi$
$457$	−0.210324	−	0.152809i	−0.00983852	−	0.00714811i	−0.592694	+	0.805428i	$0.701936\pi$
$458$	−15.0945	+	10.9668i	−0.705318	+	0.512444i
$459$	3.37579			0.157569
$460$	1.52942			0.0713097
$461$	−21.5908	+	15.6867i	−1.00558	+	0.730600i	−0.963278	−	0.268505i	$-0.913471\pi$
$461$	−21.5908	+	15.6867i	−1.00558	+	0.730600i	−0.0423064	+	0.999105i	$0.513471\pi$
$462$	3.54046	−	10.8964i	0.164717	−	0.506947i
$463$	−2.96033	−	9.11096i	−0.137578	−	0.423422i	0.858404	−	0.512974i	$-0.171456\pi$
$463$	−2.96033	−	9.11096i	−0.137578	−	0.423422i	−0.995982	+	0.0895521i	$0.971456\pi$
$464$	1.59094			0.0738576
$465$	−0.708034	+	5.52256i	−0.0328343	+	0.256103i
$466$	−9.71897			−0.450222
$467$	−3.21622	−	9.89851i	−0.148829	−	0.458048i	0.848655	−	0.528947i	$-0.177413\pi$
$467$	−3.21622	−	9.89851i	−0.148829	−	0.458048i	−0.997483	+	0.0708991i	$0.977413\pi$
$468$	−1.05155	+	3.23634i	−0.0486079	+	0.149600i
$469$	8.56107	−	6.21998i	0.395313	−	0.287212i
$470$	−0.962651			−0.0444038
$471$	−5.69104			−0.262229
$472$	−4.83644	+	3.51388i	−0.222615	+	0.161739i
$473$	−13.1389	−	9.54598i	−0.604128	−	0.438925i
$474$	−0.930429	−	0.675996i	−0.0427360	−	0.0310495i
$475$	−0.469241	−	1.44418i	−0.0215303	−	0.0662633i
$476$	−6.83430	+	4.96541i	−0.313250	+	0.227589i
$477$	−1.13635	−	3.49732i	−0.0520298	−	0.160131i
$478$	−4.17416	+	12.8467i	−0.190921	+	0.587596i
$479$	−31.1683	−	22.6451i	−1.42411	−	1.03468i	−0.991075	−	0.133305i	$-0.957441\pi$
$479$	−31.1683	−	22.6451i	−1.42411	−	1.03468i	−0.433040	−	0.901375i	$-0.642559\pi$
$480$	0.309017	−	0.951057i	0.0141046	−	0.0434096i
$481$	6.42315	−	19.7684i	0.292870	−	0.901362i
$482$	0.490877	+	0.356643i	0.0223588	+	0.0162446i
$483$	1.18269	−	3.63995i	0.0538143	−	0.165623i
$484$	3.07843	+	9.47444i	0.139929	+	0.430656i
$485$	−0.190722	+	0.138568i	−0.00866025	+	0.00629204i
$486$	0.309017	+	0.951057i	0.0140173	+	0.0431408i
$487$	−12.4145	−	9.01963i	−0.562553	−	0.408719i	0.269840	−	0.962905i	$-0.413029\pi$
$487$	−12.4145	−	9.01963i	−0.562553	−	0.408719i	−0.832392	+	0.554187i	$0.813029\pi$
$488$	−5.69385	−	4.13682i	−0.257748	−	0.187265i
$489$	−13.6449	+	9.91359i	−0.617043	+	0.448308i
$490$	−0.737877			−0.0333339
$491$	−30.5035			−1.37660			−0.688302	−	0.725424i	$-0.741644\pi$
$491$	−30.5035			−1.37660			−0.688302	+	0.725424i	$0.741644\pi$
$492$	−8.13270	+	5.90875i	−0.366650	+	0.266387i
$493$	1.65963	−	5.10783i	0.0747462	−	0.230045i
$494$	1.59677	+	4.91436i	0.0718423	+	0.221108i
$495$	4.57843			0.205785
$496$	−0.708034	+	5.52256i	−0.0317917	+	0.247970i
$497$	11.3332			0.508365
$498$	−1.37778	−	4.24037i	−0.0617398	−	0.190015i
$499$	−10.9393	+	33.6678i	−0.489712	+	1.50718i	0.335327	+	0.942102i	$0.391153\pi$
$499$	−10.9393	+	33.6678i	−0.489712	+	1.50718i	−0.825039	+	0.565076i	$0.808847\pi$
$500$	−0.809017	+	0.587785i	−0.0361803	+	0.0262866i
$501$	6.34392			0.283425
$502$	−16.5090			−0.736834
$503$	20.5893	−	14.9590i	0.918033	−	0.666990i	−0.0250005	−	0.999687i	$-0.507959\pi$
$503$	20.5893	−	14.9590i	0.918033	−	0.666990i	0.943034	+	0.332697i	$0.107959\pi$
$504$	−2.02450	−	1.47089i	−0.0901785	−	0.0655185i
$505$	3.33412	+	2.42238i	0.148366	+	0.107794i
$506$	2.16385	+	6.65964i	0.0961948	+	0.296057i
$507$	1.14910	−	0.834872i	0.0510335	−	0.0370780i
$508$	−6.20902	−	19.1094i	−0.275481	−	0.847843i
$509$	−4.70825	+	14.4905i	−0.208689	+	0.642280i	0.790852	+	0.612007i	$0.209638\pi$
$509$	−4.70825	+	14.4905i	−0.208689	+	0.642280i	−0.999542	+	0.0302730i	$0.990362\pi$
$510$	−2.73107	−	1.98424i	−0.120934	−	0.0878637i
$511$	3.80116	−	11.6988i	0.168154	−	0.517524i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	1.22849	+	0.892550i	0.0542391	+	0.0394070i
$514$	6.38834	−	19.6613i	0.281778	−	0.867223i
$515$	3.27937	+	10.0929i	0.144506	+	0.444745i
$516$	−2.86974	+	2.08499i	−0.126333	+	0.0917866i
$517$	−1.36197	−	4.19172i	−0.0598994	−	0.184351i
$518$	12.3662	+	8.98458i	0.543340	+	0.394760i
$519$	−9.91924	−	7.20675i	−0.435406	−	0.316341i
$520$	2.75299	−	2.00017i	0.120727	−	0.0877131i
$521$	−43.5660			−1.90866			−0.954331	−	0.298750i	$-0.903430\pi$
$521$	−43.5660			−1.90866			−0.954331	+	0.298750i	$0.903430\pi$
$522$	1.59094			0.0696336
$523$	−36.2040	+	26.3038i	−1.58309	+	1.15018i	−0.670052	+	0.742314i	$0.733728\pi$
$523$	−36.2040	+	26.3038i	−1.58309	+	1.15018i	−0.913040	+	0.407870i	$0.866272\pi$
$524$	−3.09339	+	9.52049i	−0.135136	+	0.415904i
$525$	0.773291	+	2.37995i	0.0337492	+	0.103869i
$526$	11.2837			0.491992
$527$	16.9920	+	8.03420i	0.740182	+	0.349975i
$528$	4.57843			0.199251
$529$	−6.38456	−	19.6496i	−0.277589	−	0.854333i
$530$	−1.13635	+	3.49732i	−0.0493598	+	0.151914i
$531$	−4.83644	+	3.51388i	−0.209884	+	0.152489i
$532$	−3.79992			−0.164747
$533$	−34.2077			−1.48170
$534$	7.53417	−	5.47390i	0.326036	−	0.236879i
$535$	−11.8036	−	8.57584i	−0.510315	−	0.370766i
$536$	3.42111	+	2.48558i	0.147769	+	0.107361i
$537$	−2.45512	−	7.55609i	−0.105946	−	0.326069i
$538$	7.31664	−	5.31585i	0.315443	−	0.229183i
$539$	−1.04396	−	3.21297i	−0.0449665	−	0.138393i
$540$	0.309017	−	0.951057i	0.0132980	−	0.0409270i
$541$	5.96505	+	4.33386i	0.256458	+	0.186327i	0.708584	−	0.705627i	$-0.249334\pi$
$541$	5.96505	+	4.33386i	0.256458	+	0.186327i	−0.452126	+	0.891954i	$0.649334\pi$
$542$	5.72087	−	17.6070i	0.245732	−	0.756286i
$543$	−0.912879	+	2.80955i	−0.0391754	+	0.120569i
$544$	−2.73107	−	1.98424i	−0.117094	−	0.0850736i
$545$	−2.84393	+	8.75273i	−0.121821	+	0.374926i
$546$	−2.63142	−	8.09868i	−0.112614	−	0.346592i
$547$	25.4238	−	18.4715i	1.08704	−	0.789784i	0.108147	−	0.994135i	$-0.465508\pi$
$547$	25.4238	−	18.4715i	1.08704	−	0.789784i	0.978898	+	0.204351i	$0.0655084\pi$
$548$	3.45955	+	10.6474i	0.147785	+	0.454835i
$549$	−5.69385	−	4.13682i	−0.243008	−	0.176555i
$550$	−3.70403	−	2.69113i	−0.157940	−	0.114750i
$551$	1.95445	−	1.41999i	0.0832625	−	0.0604938i
$552$	1.52942			0.0650966
$553$	2.87797			0.122384
$554$	−7.32311	+	5.32055i	−0.311129	+	0.226049i
$555$	−1.88756	+	5.80931i	−0.0801224	+	0.246591i
$556$	−1.40221	−	4.31554i	−0.0594668	−	0.183020i
$557$	−9.26274			−0.392475			−0.196237	−	0.980556i	$-0.562872\pi$
$557$	−9.26274			−0.392475			−0.196237	+	0.980556i	$0.562872\pi$
$558$	−0.708034	+	5.52256i	−0.0299735	+	0.233789i
$559$	−12.0707			−0.510536
$560$	0.773291	+	2.37995i	0.0326775	+	0.100571i
$561$	4.77611	−	14.6994i	0.201648	−	0.620608i
$562$	−12.7667	+	9.27557i	−0.538532	+	0.391266i
$563$	13.5890			0.572707			0.286354	−	0.958124i	$-0.407557\pi$
$563$	13.5890			0.572707			0.286354	+	0.958124i	$0.407557\pi$
$564$	−0.962651			−0.0405349
$565$	6.04043	−	4.38863i	0.254123	−	0.184631i
$566$	−3.40084	−	2.47085i	−0.142948	−	0.103858i
$567$	−2.02450	−	1.47089i	−0.0850211	−	0.0617715i
$568$	1.39951	+	4.30724i	0.0587220	+	0.180728i
$569$	−11.0842	+	8.05314i	−0.464674	+	0.337605i	−0.795362	−	0.606135i	$-0.792719\pi$
$569$	−11.0842	+	8.05314i	−0.464674	+	0.337605i	0.330688	+	0.943740i	$0.392719\pi$
$570$	−0.469241	−	1.44418i	−0.0196543	−	0.0604899i
$571$	−2.05758	+	6.33257i	−0.0861069	+	0.265010i	−0.984834	−	0.173498i	$-0.944493\pi$
$571$	−2.05758	+	6.33257i	−0.0861069	+	0.265010i	0.898727	+	0.438508i	$0.144493\pi$
$572$	12.6044	+	9.15762i	0.527016	+	0.382899i
$573$	5.17368	−	15.9229i	0.216134	−	0.665191i
$574$	7.77356	−	23.9246i	0.324462	−	0.998592i
$575$	−1.23733	−	0.898973i	−0.0516002	−	0.0374897i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	14.3148	+	44.0565i	0.595934	+	1.83410i	0.550023	+	0.835150i	$0.314619\pi$
$577$	14.3148	+	44.0565i	0.595934	+	1.83410i	0.0459109	+	0.998946i	$0.485381\pi$
$578$	4.53375	−	3.29396i	0.188579	−	0.137011i
$579$	−6.28912	−	19.3559i	−0.261367	−	0.804404i
$580$	−1.28710	−	0.935132i	−0.0534439	−	0.0388292i
$581$	9.02642	+	6.55808i	0.374479	+	0.272075i
$582$	−0.190722	+	0.138568i	−0.00790569	+	0.00574382i
$583$	−16.8362			−0.697286
$584$	4.91556			0.203408
$585$	2.75299	−	2.00017i	0.113822	−	0.0826967i
$586$	7.21770	−	22.2138i	0.298160	−	0.917643i
$587$	3.89514	+	11.9880i	0.160770	+	0.494798i	0.998700	−	0.0509794i	$-0.0162343\pi$
$587$	3.89514	+	11.9880i	0.160770	+	0.494798i	−0.837930	+	0.545778i	$0.816234\pi$
$588$	−0.737877			−0.0304295
$589$	4.05935	+	7.41636i	0.167263	+	0.305586i
$590$	5.97817			0.246117
$591$	1.12333	+	3.45726i	0.0462077	+	0.142213i
$592$	−1.88756	+	5.80931i	−0.0775782	+	0.238761i
$593$	−1.15898	+	0.842048i	−0.0475936	+	0.0345788i	−0.611328	−	0.791378i	$-0.709364\pi$
$593$	−1.15898	+	0.842048i	−0.0475936	+	0.0345788i	0.563734	+	0.825956i	$0.309364\pi$
$594$	4.57843			0.187855
$595$	8.44766			0.346320
$596$	−16.1631	+	11.7432i	−0.662068	+	0.481020i
$597$	14.0211	+	10.1869i	0.573844	+	0.416922i
$598$	4.21049	+	3.05910i	0.172180	+	0.125096i
$599$	5.80251	+	17.8583i	0.237084	+	0.729670i	0.996838	+	0.0794596i	$0.0253195\pi$
$599$	5.80251	+	17.8583i	0.237084	+	0.729670i	−0.759754	+	0.650211i	$0.774681\pi$
$600$	−0.809017	+	0.587785i	−0.0330280	+	0.0239962i
$601$	−14.2681	−	43.9126i	−0.582007	−	1.79123i	−0.610973	−	0.791652i	$-0.709221\pi$
$601$	−14.2681	−	43.9126i	−0.582007	−	1.79123i	0.0289659	−	0.999580i	$-0.490779\pi$
$602$	2.74302	−	8.44214i	0.111797	−	0.344076i
$603$	3.42111	+	2.48558i	0.139318	+	0.101221i
$604$	0.258637	−	0.796004i	0.0105238	−	0.0323889i
$605$	3.07843	−	9.47444i	0.125156	−	0.385191i
$606$	3.33412	+	2.42238i	0.135439	+	0.0984024i
$607$	−9.80860	+	30.1878i	−0.398119	+	1.22528i	0.528387	+	0.849004i	$0.322797\pi$
$607$	−9.80860	+	30.1878i	−0.398119	+	1.22528i	−0.926506	+	0.376280i	$0.877203\pi$
$608$	−0.469241	−	1.44418i	−0.0190302	−	0.0585691i
$609$	−3.22087	+	2.34010i	−0.130516	+	0.0948255i
$610$	2.17486	+	6.69352i	0.0880574	+	0.271013i
$611$	−2.65017	−	1.92546i	−0.107214	−	0.0778959i
$612$	−2.73107	−	1.98424i	−0.110397	−	0.0802082i
$613$	10.8988	−	7.91845i	0.440199	−	0.319823i	−0.345515	−	0.938413i	$-0.612296\pi$
$613$	10.8988	−	7.91845i	0.440199	−	0.319823i	0.785714	+	0.618590i	$0.212296\pi$
$614$	−32.1759			−1.29851
$615$	10.0526			0.405359
$616$	−9.26904	+	6.73436i	−0.373460	+	0.271335i
$617$	−14.0601	+	43.2725i	−0.566038	+	1.74208i	0.0988104	+	0.995106i	$0.468496\pi$
$617$	−14.0601	+	43.2725i	−0.566038	+	1.74208i	−0.664848	+	0.746979i	$0.731504\pi$
$618$	3.27937	+	10.0929i	0.131916	+	0.405995i
$619$	25.5456			1.02676			0.513382	−	0.858160i	$-0.328392\pi$
$619$	25.5456			1.02676			0.513382	+	0.858160i	$0.328392\pi$
$620$	3.81889	−	4.05167i	0.153370	−	0.162719i
$621$	1.52942			0.0613737
$622$	8.45798	+	26.0310i	0.339134	+	1.04375i
$623$	−7.20147	+	22.1638i	−0.288521	+	0.887976i
$624$	2.75299	−	2.00017i	0.110208	−	0.0800707i
$625$	1.00000			0.0400000
$626$	4.12151			0.164729
$627$	5.62455	−	4.08648i	0.224623	−	0.163198i
$628$	4.60415	+	3.34511i	0.183726	+	0.133485i
$629$	16.6821	+	12.1203i	0.665160	+	0.483267i
$630$	0.773291	+	2.37995i	0.0308087	+	0.0948193i
$631$	7.92169	−	5.75545i	0.315358	−	0.229121i	−0.418834	−	0.908063i	$-0.637561\pi$
$631$	7.92169	−	5.75545i	0.315358	−	0.229121i	0.734192	+	0.678942i	$0.237561\pi$
$632$	0.355392	+	1.09378i	0.0141367	+	0.0435084i
$633$	−0.555379	+	1.70928i	−0.0220743	+	0.0679378i
$634$	−21.2127	−	15.4120i	−0.842466	−	0.612087i
$635$	−6.20902	+	19.1094i	−0.246398	+	0.758334i
$636$	−1.13635	+	3.49732i	−0.0450591	+	0.138678i
$637$	−2.03137	−	1.47588i	−0.0804858	−	0.0584764i
$638$	2.25088	−	6.92751i	0.0891133	−	0.274263i
$639$	1.39951	+	4.30724i	0.0553637	+	0.170392i
$640$	−0.809017	+	0.587785i	−0.0319792	+	0.0232343i
$641$	10.9642	+	33.7445i	0.433062	+	1.33283i	0.895060	+	0.445946i	$0.147133\pi$
$641$	10.9642	+	33.7445i	0.433062	+	1.33283i	−0.461998	+	0.886881i	$0.652867\pi$
$642$	−11.8036	−	8.57584i	−0.465852	−	0.338461i
$643$	15.5980	+	11.3326i	0.615125	+	0.446915i	0.851215	−	0.524816i	$-0.175866\pi$
$643$	15.5980	+	11.3326i	0.615125	+	0.446915i	−0.236090	+	0.971731i	$0.575866\pi$
$644$	−3.09632	+	2.24961i	−0.122012	+	0.0886471i
$645$	3.54720			0.139671
$646$	−5.12613			−0.201685
$647$	28.5901	−	20.7719i	1.12399	−	0.816627i	0.139182	−	0.990267i	$-0.455553\pi$
$647$	28.5901	−	20.7719i	1.12399	−	0.816627i	0.984809	+	0.173640i	$0.0555528\pi$
$648$	0.309017	−	0.951057i	0.0121393	−	0.0373610i
$649$	8.45799	+	26.0310i	0.332005	+	1.02181i
$650$	−3.40289			−0.133472
$651$	−6.68965	−	12.2219i	−0.262188	−	0.479013i
$652$	16.8660			0.660524
$653$	5.22422	+	16.0785i	0.204440	+	0.629200i	0.999736	+	0.0229795i	$0.00731525\pi$
$653$	5.22422	+	16.0785i	0.204440	+	0.629200i	−0.795296	+	0.606221i	$0.792685\pi$
$654$	−2.84393	+	8.75273i	−0.111207	+	0.342259i
$655$	8.09861	−	5.88398i	0.316439	−	0.229906i
$656$	10.0526			0.392487
$657$	4.91556			0.191774
$658$	1.94889	−	1.41595i	0.0759757	−	0.0551996i
$659$	13.7342	+	9.97848i	0.535008	+	0.388706i	0.822228	−	0.569158i	$-0.192731\pi$
$659$	13.7342	+	9.97848i	0.535008	+	0.388706i	−0.287219	+	0.957865i	$0.592731\pi$
$660$	−3.70403	−	2.69113i	−0.144179	−	0.104752i
$661$	−0.0383211	−	0.117940i	−0.00149052	−	0.00458735i	0.950308	−	0.311310i	$-0.100768\pi$
$661$	−0.0383211	−	0.117940i	−0.00149052	−	0.00458735i	−0.951799	+	0.306722i	$0.900768\pi$
$662$	11.7951	−	8.56967i	0.458431	−	0.333070i
$663$	−3.54981	−	10.9252i	−0.137863	−	0.424300i
$664$	−1.37778	+	4.24037i	−0.0534682	+	0.164558i
$665$	3.07420	+	2.23354i	0.119212	+	0.0866129i
$666$	−1.88756	+	5.80931i	−0.0731414	+	0.225106i
$667$	0.751907	−	2.31413i	0.0291140	−	0.0896036i
$668$	−5.13234	−	3.72886i	−0.198576	−	0.144274i
$669$	−5.35966	+	16.4953i	−0.207216	+	0.637746i
$670$	−1.30675	−	4.02176i	−0.0504841	−	0.155374i
$671$	−26.0689	+	18.9402i	−1.00638	+	0.731177i
$672$	0.773291	+	2.37995i	0.0298304	+	0.0918084i
$673$	−15.9087	−	11.5583i	−0.613234	−	0.445541i	0.237318	−	0.971432i	$-0.423732\pi$
$673$	−15.9087	−	11.5583i	−0.613234	−	0.445541i	−0.850552	+	0.525891i	$0.823732\pi$
$674$	−11.8104	−	8.58077i	−0.454920	−	0.330519i
$675$	−0.809017	+	0.587785i	−0.0311391	+	0.0226239i
$676$	−1.42037			−0.0546296
$677$	47.6673			1.83200			0.916002	−	0.401174i	$-0.131398\pi$
$677$	47.6673			1.83200			0.916002	+	0.401174i	$0.131398\pi$
$678$	6.04043	−	4.38863i	0.231981	−	0.168544i
$679$	0.182300	−	0.561062i	0.00699603	−	0.0215316i
$680$	1.04318	+	3.21057i	0.0400040	+	0.123120i
$681$	27.7956			1.06513
$682$	23.0454	+	10.8964i	0.882454	+	0.417245i
$683$	2.02046			0.0773107			0.0386554	−	0.999253i	$-0.487693\pi$
$683$	2.02046			0.0773107			0.0386554	+	0.999253i	$0.487693\pi$
$684$	−0.469241	−	1.44418i	−0.0179419	−	0.0552194i
$685$	3.45955	−	10.6474i	0.132183	−	0.406817i
$686$	15.6654	−	11.3815i	0.598106	−	0.434549i
$687$	18.6578			0.711839
$688$	3.54720			0.135236
$689$	−10.1236	+	7.35520i	−0.385677	+	0.280211i
$690$	−1.23733	−	0.898973i	−0.0471043	−	0.0342233i
$691$	−6.15848	−	4.47439i	−0.234279	−	0.170214i	0.464451	−	0.885599i	$-0.346252\pi$
$691$	−6.15848	−	4.47439i	−0.234279	−	0.170214i	−0.698731	+	0.715385i	$0.746252\pi$
$692$	3.78881	+	11.6608i	0.144029	+	0.443276i
$693$	−9.26904	+	6.73436i	−0.352102	+	0.255817i
$694$	−10.1393	−	31.2055i	−0.384882	−	1.18455i
$695$	−1.40221	+	4.31554i	−0.0531887	+	0.163698i
$696$	−1.28710	−	0.935132i	−0.0487873	−	0.0354461i
$697$	10.4866	−	32.2745i	0.397209	−	1.22248i
$698$	−10.8816	+	33.4901i	−0.411874	+	1.26762i
$699$	7.86281	+	5.71267i	0.297399	+	0.216073i
$700$	0.773291	−	2.37995i	0.0292277	−	0.0899535i
$701$	7.34138	+	22.5944i	0.277280	+	0.853380i	0.988607	+	0.150519i	$0.0480944\pi$
$701$	7.34138	+	22.5944i	0.277280	+	0.853380i	−0.711327	+	0.702861i	$0.751906\pi$
$702$	2.75299	−	2.00017i	0.103905	−	0.0754914i
$703$	2.86625	+	8.82141i	0.108103	+	0.332706i
$704$	−3.70403	−	2.69113i	−0.139601	−	0.101426i
$705$	0.778801	+	0.565832i	0.0293314	+	0.0213105i
$706$	−7.91918	+	5.75362i	−0.298042	+	0.216540i
$707$	−10.3130			−0.387860
$708$	5.97817			0.224673
$709$	−26.9678	+	19.5933i	−1.01280	+	0.735841i	−0.964794	−	0.263006i	$-0.915286\pi$
$709$	−26.9678	+	19.5933i	−1.01280	+	0.735841i	−0.0480044	+	0.998847i	$0.515286\pi$
$710$	1.39951	−	4.30724i	0.0525226	−	0.161648i
$711$	0.355392	+	1.09378i	0.0133282	+	0.0410201i
$712$	−9.31275			−0.349010
$713$	7.69831	+	3.63995i	0.288304	+	0.136317i
$714$	8.44766			0.316146
$715$	−4.81445	−	14.8173i	−0.180050	−	0.554137i
$716$	−2.45512	+	7.55609i	−0.0917522	+	0.282384i
$717$	10.9281	−	7.93972i	0.408117	−	0.296514i
$718$	4.50661			0.168185
$719$	−29.1835			−1.08836			−0.544181	−	0.838968i	$-0.683160\pi$
$719$	−29.1835			−1.08836			−0.544181	+	0.838968i	$0.683160\pi$
$720$	−0.809017	+	0.587785i	−0.0301503	+	0.0219055i
$721$	−21.4846	−	15.6095i	−0.800128	−	0.581327i
$722$	13.5059	+	9.81259i	0.502636	+	0.365187i
$723$	−0.187498	−	0.577060i	−0.00697314	−	0.0214611i
$724$	2.38995	−	1.73640i	0.0888217	−	0.0645327i
$725$	0.491628	+	1.51308i	0.0182586	+	0.0561942i
$726$	3.07843	−	9.47444i	0.114251	−	0.351630i
$727$	43.0122	+	31.2502i	1.59523	+	1.15900i	0.895945	+	0.444165i	$0.146499\pi$
$727$	43.0122	+	31.2502i	1.59523	+	1.15900i	0.699288	+	0.714840i	$0.253501\pi$
$728$	−2.63142	+	8.09868i	−0.0975270	+	0.300157i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−3.97678	−	2.88930i	−0.147187	−	0.106938i
$731$	3.70036	−	11.3885i	0.136863	−	0.421220i
$732$	2.17486	+	6.69352i	0.0803850	+	0.247400i
$733$	−19.2063	+	13.9542i	−0.709401	+	0.515410i	−0.882980	−	0.469410i	$-0.844467\pi$
$733$	−19.2063	+	13.9542i	−0.709401	+	0.515410i	0.173580	+	0.984820i	$0.444467\pi$
$734$	−8.16998	−	25.1446i	−0.301559	−	0.928104i
$735$	0.596955	+	0.433713i	0.0220190	+	0.0159978i
$736$	−1.23733	−	0.898973i	−0.0456086	−	0.0331366i
$737$	15.6633	−	11.3801i	0.576966	−	0.419190i
$738$	10.0526			0.370040
$739$	−39.4918			−1.45273			−0.726364	−	0.687310i	$-0.758791\pi$
$739$	−39.4918			−1.45273			−0.726364	+	0.687310i	$0.758791\pi$
$740$	4.94169	−	3.59035i	0.181660	−	0.131984i
$741$	1.59677	−	4.91436i	0.0586590	−	0.180534i
$742$	−2.84362	−	8.75177i	−0.104393	−	0.321287i
$743$	48.5945			1.78276			0.891379	−	0.453258i	$-0.149738\pi$
$743$	48.5945			1.78276			0.891379	+	0.453258i	$0.149738\pi$
$744$	3.81889	−	4.05167i	0.140007	−	0.148542i
$745$	19.9787			0.731964
$746$	6.63343	+	20.4156i	0.242867	+	0.747468i
$747$	−1.37778	+	4.24037i	−0.0504103	+	0.155147i
$748$	−12.5040	+	9.08471i	−0.457193	+	0.332170i
$749$	36.5106			1.33407
$750$	1.00000			0.0365148
$751$	−4.69598	+	3.41183i	−0.171359	+	0.124499i	−0.670159	−	0.742217i	$-0.733774\pi$
$751$	−4.69598	+	3.41183i	−0.171359	+	0.124499i	0.498800	+	0.866717i	$0.333774\pi$
$752$	0.778801	+	0.565832i	0.0284000	+	0.0206338i
$753$	13.3561	+	9.70376i	0.486723	+	0.353625i
$754$	−1.67295	−	5.14882i	−0.0609254	−	0.187509i
$755$	−0.677121	+	0.491957i	−0.0246430	+	0.0179042i
$756$	0.773291	+	2.37995i	0.0281243	+	0.0865578i
$757$	2.44905	−	7.53739i	0.0890122	−	0.273951i	−0.896635	−	0.442771i	$-0.853996\pi$
$757$	2.44905	−	7.53739i	0.0890122	−	0.273951i	0.985647	+	0.168820i	$0.0539955\pi$
$758$	0.311303	+	0.226175i	0.0113070	+	0.00821504i
$759$	2.16385	−	6.65964i	0.0785427	−	0.241730i
$760$	−0.469241	+	1.44418i	−0.0170212	+	0.0523858i
$761$	9.45409	+	6.86880i	0.342711	+	0.248994i	0.745805	−	0.666165i	$-0.232065\pi$
$761$	9.45409	+	6.86880i	0.342711	+	0.248994i	−0.403094	+	0.915159i	$0.632065\pi$
$762$	−6.20902	+	19.1094i	−0.224929	+	0.692261i
$763$	−7.11673	−	21.9030i	−0.257643	−	0.792943i
$764$	−13.5449	+	9.84092i	−0.490036	+	0.356032i
$765$	1.04318	+	3.21057i	0.0377162	+	0.116078i
$766$	−3.83972	−	2.78972i	−0.138735	−	0.100797i
$767$	16.4579	+	11.9573i	0.594259	+	0.431754i
$768$	−0.809017	+	0.587785i	−0.0291929	+	0.0212099i
$769$	−30.1917			−1.08874			−0.544371	−	0.838845i	$-0.683232\pi$
$769$	−30.1917			−1.08874			−0.544371	+	0.838845i	$0.683232\pi$
$770$	11.4572			0.412888
$771$	−16.7249	+	12.1514i	−0.602333	+	0.437620i
$772$	−6.28912	+	19.3559i	−0.226350	+	0.696634i
$773$	−0.0998166	−	0.307204i	−0.00359016	−	0.0110494i	0.949245	−	0.314536i	$-0.101849\pi$
$773$	−0.0998166	−	0.307204i	−0.00359016	−	0.0110494i	−0.952836	+	0.303487i	$0.901849\pi$
$774$	3.54720			0.127501
$775$	−5.47106	+	1.03318i	−0.196526	+	0.0371131i
$776$	0.235746			0.00846277
$777$	−4.72347	−	14.5373i	−0.169454	−	0.521524i
$778$	−9.92297	+	30.5398i	−0.355756	+	1.09490i
$779$	12.3495	−	8.97242i	0.442466	−	0.321470i
$780$	−3.40289			−0.121843
$781$	20.7353			0.741966
$782$	−4.17697	+	3.03475i	−0.149368	+	0.108522i
$783$	−1.28710	−	0.935132i	−0.0459971	−	0.0334189i
$784$	0.596955	+	0.433713i	0.0213198	+	0.0154898i
$785$	−1.75863	−	5.41251i	−0.0627682	−	0.193181i
$786$	8.09861	−	5.88398i	0.288868	−	0.209875i
$787$	−10.5057	−	32.3333i	−0.374489	−	1.15256i	−0.943823	−	0.330452i	$-0.892799\pi$
$787$	−10.5057	−	32.3333i	−0.374489	−	1.15256i	0.569334	−	0.822106i	$-0.307201\pi$
$788$	1.12333	−	3.45726i	0.0400170	−	0.123160i
$789$	−9.12869	−	6.63238i	−0.324990	−	0.236119i
$790$	0.355392	−	1.09378i	0.0126443	−	0.0389151i
$791$	−5.77369	+	17.7696i	−0.205289	+	0.631814i
$792$	−3.70403	−	2.69113i	−0.131617	−	0.0956253i
$793$	−7.40079	+	22.7773i	−0.262810	+	0.808845i
$794$	−10.3693	−	31.9135i	−0.367993	−	1.13257i
$795$	2.97499	−	2.16146i	0.105512	−	0.0766591i
$796$	−5.35557	−	16.4828i	−0.189823	−	0.584216i
$797$	−21.3723	−	15.5279i	−0.757047	−	0.550027i	0.140956	−	0.990016i	$-0.454982\pi$
$797$	−21.3723	−	15.5279i	−0.757047	−	0.550027i	−0.898003	+	0.439989i	$0.854982\pi$
$798$	3.07420	+	2.23354i	0.108826	+	0.0790664i
$799$	2.62907	−	1.91013i	0.0930099	−	0.0675756i
$800$	1.00000			0.0353553
$801$	−9.31275			−0.329050
$802$	−0.0671348	+	0.0487763i	−0.00237061	+	0.00172235i
$803$	6.95460	−	21.4041i	0.245423	−	0.755333i
$804$	−1.30675	−	4.02176i	−0.0460854	−	0.141836i
$805$	3.82727			0.134893
$806$	18.6174	−	3.51581i	0.655770	−	0.123839i
$807$	−9.04387			−0.318359
$808$	−1.27352	−	3.91949i	−0.0448023	−	0.137887i
$809$	7.84650	−	24.1491i	0.275868	−	0.849036i	−0.713120	−	0.701042i	$-0.752718\pi$
$809$	7.84650	−	24.1491i	0.275868	−	0.849036i	0.988988	−	0.147994i	$-0.0472815\pi$
$810$	−0.809017	+	0.587785i	−0.0284260	+	0.0206527i
$811$	25.8217			0.906723			0.453362	−	0.891327i	$-0.350225\pi$
$811$	25.8217			0.906723			0.453362	+	0.891327i	$0.350225\pi$
$812$	3.98121			0.139713
$813$	−14.9774	+	10.8817i	−0.525281	+	0.381639i
$814$	22.6252	+	16.4382i	0.793013	+	0.576157i
$815$	−13.6449	−	9.91359i	−0.477960	−	0.347258i
$816$	1.04318	+	3.21057i	0.0365185	+	0.112392i
$817$	4.35769	−	3.16605i	0.152456	−	0.110766i
$818$	−10.4622	−	32.1993i	−0.365801	−	1.12582i
$819$	−2.63142	+	8.09868i	−0.0919493	+	0.282991i
$820$	−8.13270	−	5.90875i	−0.284006	−	0.206343i
$821$	−2.22264	+	6.84058i	−0.0775706	+	0.238738i	−0.982321	−	0.187204i	$-0.940057\pi$
$821$	−2.22264	+	6.84058i	−0.0775706	+	0.238738i	0.904750	+	0.425942i	$0.140057\pi$
$822$	3.45955	−	10.6474i	0.120666	−	0.371371i
$823$	9.52466	+	6.92007i	0.332009	+	0.241218i	0.741283	−	0.671193i	$-0.234218\pi$
$823$	9.52466	+	6.92007i	0.332009	+	0.241218i	−0.409274	+	0.912412i	$0.634218\pi$
$824$	3.27937	−	10.0929i	0.114242	−	0.351602i
$825$	1.41481	+	4.35435i	0.0492575	+	0.151599i
$826$	−12.1028	+	8.79321i	−0.421111	+	0.305955i
$827$	2.69177	+	8.28442i	0.0936020	+	0.288077i	0.986887	−	0.161414i	$-0.0516054\pi$
$827$	2.69177	+	8.28442i	0.0936020	+	0.288077i	−0.893285	+	0.449491i	$0.851605\pi$
$828$	−1.23733	−	0.898973i	−0.0430002	−	0.0312415i
$829$	13.3763	+	9.71846i	0.464579	+	0.337536i	0.795325	−	0.606184i	$-0.207300\pi$
$829$	13.3763	+	9.71846i	0.464579	+	0.337536i	−0.330746	+	0.943720i	$0.607300\pi$
$830$	3.60707	−	2.62069i	0.125203	−	0.0909655i
$831$	9.05186			0.314006
$832$	−3.40289			−0.117974
$833$	2.01520	−	1.46413i	0.0698224	−	0.0507290i
$834$	−1.40221	+	4.31554i	−0.0485544	+	0.149435i
$835$	1.96038	+	6.03343i	0.0678417	+	0.208795i
$836$	−6.95233			−0.240451
$837$	3.81889	−	4.05167i	0.132000	−	0.140046i
$838$	−10.2163			−0.352917
$839$	1.57870	+	4.85875i	0.0545029	+	0.167743i	0.974603	−	0.223942i	$-0.0718925\pi$
$839$	1.57870	+	4.85875i	0.0545029	+	0.167743i	−0.920100	+	0.391684i	$0.871893\pi$
$840$	0.773291	−	2.37995i	0.0266811	−	0.0821159i
$841$	21.4138	−	15.5580i	0.738407	−	0.536484i
$842$	0.908730			0.0313169
$843$	15.7805			0.543511
$844$	1.45400	−	1.05639i	0.0500488	−	0.0363626i
$845$	1.14910	+	0.834872i	0.0395303	+	0.0287205i
$846$	0.778801	+	0.565832i	0.0267757	+	0.0194537i
$847$	7.70354	+	23.7091i	0.264697	+	0.814653i
$848$	2.97499	−	2.16146i	0.102162	−	0.0742249i
$849$	1.29900	+	3.99792i	0.0445817	+	0.137208i
$850$	1.04318	−	3.21057i	0.0357807	−	0.110122i
$851$	7.55794	+	5.49117i	0.259083	+	0.188235i
$852$	1.39951	−	4.30724i	0.0479463	−	0.147564i
$853$	5.95605	−	18.3309i	0.203931	−	0.627636i	−0.795824	−	0.605528i	$-0.792962\pi$
$853$	5.95605	−	18.3309i	0.203931	−	0.627636i	0.999756	−	0.0221086i	$-0.00703795\pi$
$854$	−14.2484	−	10.3521i	−0.487571	−	0.354241i
$855$	−0.469241	+	1.44418i	−0.0160477	+	0.0493898i
$856$	4.50858	+	13.8760i	0.154100	+	0.474272i
$857$	24.0041	−	17.4400i	0.819964	−	0.595739i	−0.0967384	−	0.995310i	$-0.530841\pi$
$857$	24.0041	−	17.4400i	0.819964	−	0.595739i	0.916702	+	0.399571i	$0.130841\pi$
$858$	−4.81445	−	14.8173i	−0.164362	−	0.505856i
$859$	−10.1272	−	7.35785i	−0.345536	−	0.251047i	0.401458	−	0.915877i	$-0.368504\pi$
$859$	−10.1272	−	7.35785i	−0.345536	−	0.251047i	−0.746994	+	0.664831i	$0.768504\pi$
$860$	−2.86974	−	2.08499i	−0.0978574	−	0.0710976i
$861$	−20.3515	+	14.7862i	−0.693576	+	0.503912i
$862$	28.0670			0.955967
$863$	−7.84330			−0.266989			−0.133495	−	0.991050i	$-0.542620\pi$
$863$	−7.84330			−0.266989			−0.133495	+	0.991050i	$0.542620\pi$
$864$	−0.809017	+	0.587785i	−0.0275233	+	0.0199969i
$865$	3.78881	−	11.6608i	0.128823	−	0.396478i
$866$	6.92250	+	21.3053i	0.235236	+	0.723983i
$867$	−5.60402			−0.190323
$868$	−1.77180	+	13.8198i	−0.0601389	+	0.469074i
$869$	5.26553			0.178621
$870$	0.491628	+	1.51308i	0.0166677	+	0.0512980i
$871$	4.44671	−	13.6856i	0.150671	−	0.463718i
$872$	7.44551	−	5.40948i	0.252137	−	0.183188i
$873$	0.235746			0.00797878
$874$	−2.32242			−0.0785572
$875$	−2.02450	+	1.47089i	−0.0684407	+	0.0497251i
$876$	−3.97678	−	2.88930i	−0.134363	−	0.0976203i
$877$	−22.6878	−	16.4836i	−0.766112	−	0.556613i	0.134667	−	0.990891i	$-0.457003\pi$
$877$	−22.6878	−	16.4836i	−0.766112	−	0.556613i	−0.900779	+	0.434278i	$0.857003\pi$
$878$	9.52497	+	29.3148i	0.321452	+	0.989328i
$879$	−18.8962	+	13.7289i	−0.637352	+	0.463064i
$880$	1.41481	+	4.35435i	0.0476933	+	0.146785i
$881$	1.94020	−	5.97131i	0.0653669	−	0.201179i	−0.913039	−	0.407873i	$-0.866271\pi$
$881$	1.94020	−	5.97131i	0.0653669	−	0.201179i	0.978406	+	0.206694i	$0.0662706\pi$
$882$	0.596955	+	0.433713i	0.0201005	+	0.0146039i
$883$	−11.0669	+	34.0605i	−0.372432	+	1.14623i	0.572763	+	0.819721i	$0.305872\pi$
$883$	−11.0669	+	34.0605i	−0.372432	+	1.14623i	−0.945195	+	0.326507i	$0.894128\pi$
$884$	−3.54981	+	10.9252i	−0.119393	+	0.367454i
$885$	−4.83644	−	3.51388i	−0.162575	−	0.118118i
$886$	7.76120	−	23.8865i	0.260743	−	0.802483i
$887$	−8.62099	−	26.5327i	−0.289465	−	0.890881i	−0.985025	−	0.172413i	$-0.944844\pi$
$887$	−8.62099	−	26.5327i	−0.289465	−	0.890881i	0.695560	−	0.718468i	$-0.255156\pi$
$888$	4.94169	−	3.59035i	0.165832	−	0.120484i
$889$	−15.5376	−	47.8198i	−0.521115	−	1.60383i
$890$	7.53417	+	5.47390i	0.252546	+	0.183485i
$891$	−3.70403	−	2.69113i	−0.124090	−	0.0901564i
$892$	14.0318	−	10.1947i	0.469818	−	0.341343i
$893$	1.46178			0.0489167
$894$	19.9787			0.668189
$895$	6.42759	−	4.66992i	0.214851	−	0.156098i
$896$	0.773291	−	2.37995i	0.0258339	−	0.0795084i
$897$	−1.60826	−	4.94973i	−0.0536984	−	0.165267i
$898$	−7.70588			−0.257149
$899$	−4.25301	−	7.77019i	−0.141846	−	0.259150i
$900$	1.00000			0.0333333
$901$	−3.83607	−	11.8062i	−0.127798	−	0.393322i
$902$	14.2225	−	43.7723i	0.473557	−	1.45746i
$903$	−7.18131	+	5.21753i	−0.238979	+	0.173628i
$904$	−7.46638			−0.248328
$905$	−2.95414			−0.0981989
$906$	−0.677121	+	0.491957i	−0.0224958	+	0.0163442i
$907$	−1.93798	−	1.40802i	−0.0643494	−	0.0467526i	0.555146	−	0.831753i	$-0.312663\pi$
$907$	−1.93798	−	1.40802i	−0.0643494	−	0.0467526i	−0.619495	+	0.785001i	$0.712663\pi$
$908$	−22.4871	−	16.3379i	−0.746261	−	0.542191i
$909$	−1.27352	−	3.91949i	−0.0422400	−	0.130001i
$910$	6.88915	−	5.00526i	0.228373	−	0.165923i
$911$	6.60532	+	20.3291i	0.218844	+	0.673533i	0.998858	+	0.0477709i	$0.0152117\pi$
$911$	6.60532	+	20.3291i	0.218844	+	0.673533i	−0.780014	+	0.625762i	$0.784788\pi$
$912$	−0.469241	+	1.44418i	−0.0155381	+	0.0478214i
$913$	16.5147	+	11.9987i	0.546558	+	0.397097i
$914$	0.0803365	−	0.247250i	0.00265729	−	0.00817831i
$915$	2.17486	−	6.69352i	0.0718986	−	0.221281i
$916$	−15.0945	−	10.9668i	−0.498735	−	0.362352i
$917$	−7.74098	+	23.8243i	−0.255630	+	0.786747i
$918$	1.04318	+	3.21057i	0.0344300	+	0.105965i
$919$	8.56327	−	6.22158i	0.282476	−	0.205231i	−0.437521	−	0.899208i	$-0.644143\pi$
$919$	8.56327	−	6.22158i	0.282476	−	0.205231i	0.719997	+	0.693977i	$0.244143\pi$
$920$	0.472618	+	1.45457i	0.0155817	+	0.0479557i
$921$	26.0309	+	18.9125i	0.857746	+	0.623189i
$922$	−21.5908	−	15.6867i	−0.711056	−	0.516612i
$923$	12.4680	−	9.05856i	0.410390	−	0.298166i
$924$	11.4572			0.376913
$925$	−6.10827			−0.200839
$926$	7.75025	−	5.63088i	0.254689	−	0.185042i
$927$	3.27937	−	10.0929i	0.107709	−	0.331493i
$928$	0.491628	+	1.51308i	0.0161385	+	0.0496691i
$929$	−7.96913			−0.261459			−0.130729	−	0.991418i	$-0.541732\pi$
$929$	−7.96913			−0.261459			−0.130729	+	0.991418i	$0.541732\pi$
$930$	−5.47106	+	1.03318i	−0.179403	+	0.0338795i
$931$	1.12046			0.0367217
$932$	−3.00333	−	9.24329i	−0.0983772	−	0.302774i
$933$	8.45798	−	26.0310i	0.276902	−	0.852216i
$934$	8.42017	−	6.11761i	0.275517	−	0.200174i
$935$	15.4558			0.505460
$936$	−3.40289			−0.111227
$937$	10.7068	−	7.77895i	0.349776	−	0.254127i	−0.398999	−	0.916951i	$-0.630642\pi$
$937$	10.7068	−	7.77895i	0.349776	−	0.254127i	0.748775	+	0.662824i	$0.230642\pi$
$938$	8.56107	+	6.21998i	0.279529	+	0.203090i
$939$	−3.33437	−	2.42256i	−0.108813	−	0.0790573i
$940$	−0.297476	−	0.915536i	−0.00970259	−	0.0298615i
$941$	−19.1313	+	13.8997i	−0.623662	+	0.453117i	−0.854199	−	0.519946i	$-0.825952\pi$
$941$	−19.1313	+	13.8997i	−0.623662	+	0.453117i	0.230536	+	0.973064i	$0.425952\pi$
$942$	−1.75863	−	5.41251i	−0.0572992	−	0.176349i
$943$	4.75102	−	14.6221i	0.154715	−	0.476163i
$944$	−4.83644	−	3.51388i	−0.157413	−	0.114367i
$945$	0.773291	−	2.37995i	0.0251552	−	0.0774197i
$946$	5.01862	−	15.4457i	0.163169	−	0.502184i
$947$	−14.5803	−	10.5932i	−0.473795	−	0.344232i	0.325124	−	0.945672i	$-0.394594\pi$
$947$	−14.5803	−	10.5932i	−0.473795	−	0.344232i	−0.798918	+	0.601439i	$0.794594\pi$
$948$	0.355392	−	1.09378i	0.0115426	−	0.0355245i
$949$	−5.16896	−	15.9084i	−0.167792	−	0.516409i
$950$	1.22849	−	0.892550i	0.0398575	−	0.0289581i
$951$	8.10255	+	24.9371i	0.262743	+	0.808640i
$952$	−6.83430	−	4.96541i	−0.221501	−	0.160930i
$953$	40.5879	+	29.4889i	1.31477	+	0.955238i	0.999982	+	0.00607713i	$0.00193442\pi$
$953$	40.5879	+	29.4889i	1.31477	+	0.955238i	0.314791	+	0.949161i	$0.398066\pi$
$954$	2.97499	−	2.16146i	0.0963190	−	0.0699799i
$955$	16.7424			0.541771
$956$	−13.5079			−0.436875
$957$	−5.89289	+	4.28144i	−0.190490	+	0.138399i
$958$	11.9052	−	36.6405i	0.384640	−	1.18380i
$959$	8.65727	+	26.6443i	0.279558	+	0.860390i
$960$	1.00000			0.0322749
$961$	28.8651	−	11.3052i	0.931131	−	0.364685i
$962$	20.7857			0.670159
$963$	4.50858	+	13.8760i	0.145287	+	0.447148i
$964$	−0.187498	+	0.577060i	−0.00603891	+	0.0185859i
$965$	16.4651	−	11.9626i	0.530031	−	0.385090i
$966$	3.82727			0.123140
$967$	58.5632			1.88327			0.941633	−	0.336642i	$-0.109291\pi$
$967$	58.5632			1.88327			0.941633	+	0.336642i	$0.109291\pi$
$968$	−8.05944	+	5.85553i	−0.259040	+	0.188204i
$969$	4.14713	+	3.01306i	0.133225	+	0.0967935i
$970$	−0.190722	−	0.138568i	−0.00612372	−	0.00444914i
$971$	−6.74437	−	20.7570i	−0.216437	−	0.666125i	−0.999048	−	0.0436144i	$-0.986113\pi$
$971$	−6.74437	−	20.7570i	−0.216437	−	0.666125i	0.782611	−	0.622511i	$-0.213887\pi$
$972$	−0.809017	+	0.587785i	−0.0259492	+	0.0188532i
$973$	−3.50891	−	10.7993i	−0.112491	−	0.346210i
$974$	4.74190	−	14.5941i	0.151940	−	0.467624i
$975$	2.75299	+	2.00017i	0.0881663	+	0.0640566i
$976$	2.17486	−	6.69352i	0.0696155	−	0.214254i
$977$	−9.81928	+	30.2206i	−0.314146	+	0.966843i	0.661958	+	0.749541i	$0.269726\pi$
$977$	−9.81928	+	30.2206i	−0.314146	+	0.966843i	−0.976104	+	0.217302i	$0.930274\pi$
$978$	−13.6449	−	9.91359i	−0.436316	−	0.317002i
$979$	−13.1758	+	40.5509i	−0.421100	+	1.29601i
$980$	−0.228017	−	0.701763i	−0.00728372	−	0.0224170i
$981$	7.44551	−	5.40948i	0.237717	−	0.172712i
$982$	−9.42611	−	29.0106i	−0.300799	−	0.925765i
$983$	24.0160	+	17.4486i	0.765991	+	0.556525i	0.900742	−	0.434354i	$-0.143023\pi$
$983$	24.0160	+	17.4486i	0.765991	+	0.556525i	−0.134751	+	0.990880i	$0.543023\pi$
$984$	−8.13270	−	5.90875i	−0.259261	−	0.188364i
$985$	−2.94092	+	2.13670i	−0.0937055	+	0.0680811i
$986$	5.37069			0.171038
$987$	−2.40896			−0.0766781
$988$	−4.18041	+	3.03724i	−0.132997	+	0.0966276i
$989$	1.67647	−	5.15964i	0.0533086	−	0.164067i
$990$	1.41481	+	4.35435i	0.0449657	+	0.138390i
$991$	16.5009			0.524167			0.262084	−	0.965045i	$-0.415590\pi$
$991$	16.5009			0.524167			0.262084	+	0.965045i	$0.415590\pi$
$992$	−5.47106	+	1.03318i	−0.173706	+	0.0328036i
$993$	−14.5796			−0.462670
$994$	3.50216	+	10.7785i	0.111082	+	0.341875i
$995$	−5.35557	+	16.4828i	−0.169783	+	0.522538i
$996$	3.60707	−	2.62069i	0.114294	−	0.0830398i
$997$	10.7588			0.340735			0.170367	−	0.985381i	$-0.445505\pi$
$997$	10.7588			0.340735			0.170367	+	0.985381i	$0.445505\pi$
$998$	−35.4004			−1.12058
$999$	4.94169	−	3.59035i	0.156348	−	0.113594i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.g.841.2	yes	16
31.8	even	5	inner	930.2.n.g.721.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.g.721.2	✓	16	31.8	even	5	inner
930.2.n.g.841.2	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)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-2.02450 + 1.47089i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-2.02450 + 1.47089i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.309017 + 0.951057i) q^{10} +(-3.70403 + 2.69113i) q^{11} +(0.309017 + 0.951057i) q^{12} +(-1.05155 + 3.23634i) q^{13} +(-2.02450 - 1.47089i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.73107 - 1.98424i) q^{17} +(0.309017 - 0.951057i) q^{18} +(-0.469241 - 1.44418i) q^{19} +(-0.809017 + 0.587785i) q^{20} +(0.773291 + 2.37995i) q^{21} +(-3.70403 - 2.69113i) q^{22} +(-1.23733 - 0.898973i) q^{23} +(-0.809017 + 0.587785i) q^{24} +1.00000 q^{25} -3.40289 q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.773291 - 2.37995i) q^{28} +(0.491628 + 1.51308i) q^{29} +1.00000 q^{30} +(-5.47106 + 1.03318i) q^{31} +1.00000 q^{32} +(1.41481 + 4.35435i) q^{33} +(1.04318 - 3.21057i) q^{34} +(-2.02450 + 1.47089i) q^{35} +1.00000 q^{36} -6.10827 q^{37} +(1.22849 - 0.892550i) q^{38} +(2.75299 + 2.00017i) q^{39} +(-0.809017 - 0.587785i) q^{40} +(3.10641 + 9.56056i) q^{41} +(-2.02450 + 1.47089i) q^{42} +(1.09614 + 3.37358i) q^{43} +(1.41481 - 4.35435i) q^{44} +(-0.809017 - 0.587785i) q^{45} +(0.472618 - 1.45457i) q^{46} +(-0.297476 + 0.915536i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(-0.228017 + 0.701763i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-2.73107 + 1.98424i) q^{51} +(-1.05155 - 3.23634i) q^{52} +(2.97499 + 2.16146i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(-3.70403 + 2.69113i) q^{55} +2.50242 q^{56} -1.51850 q^{57} +(-1.28710 + 0.935132i) q^{58} +(1.84736 - 5.68558i) q^{59} +(0.309017 + 0.951057i) q^{60} +7.03799 q^{61} +(-2.67327 - 4.88402i) q^{62} +2.50242 q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.05155 + 3.23634i) q^{65} +(-3.70403 + 2.69113i) q^{66} -4.22873 q^{67} +3.37579 q^{68} +(-1.23733 + 0.898973i) q^{69} +(-2.02450 - 1.47089i) q^{70} +(-3.66396 - 2.66202i) q^{71} +(0.309017 + 0.951057i) q^{72} +(-3.97678 + 2.88930i) q^{73} +(-1.88756 - 5.80931i) q^{74} +(0.309017 - 0.951057i) q^{75} +(1.22849 + 0.892550i) q^{76} +(3.54046 - 10.8964i) q^{77} +(-1.05155 + 3.23634i) q^{78} +(-0.930429 - 0.675996i) q^{79} +(0.309017 - 0.951057i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-8.13270 + 5.90875i) q^{82} +(-1.37778 - 4.24037i) q^{83} +(-2.02450 - 1.47089i) q^{84} +(-2.73107 - 1.98424i) q^{85} +(-2.86974 + 2.08499i) q^{86} +1.59094 q^{87} +4.57843 q^{88} +(7.53417 - 5.47390i) q^{89} +(0.309017 - 0.951057i) q^{90} +(-2.63142 - 8.09868i) q^{91} +1.52942 q^{92} +(-0.708034 + 5.52256i) q^{93} -0.962651 q^{94} +(-0.469241 - 1.44418i) q^{95} +(0.309017 - 0.951057i) q^{96} +(-0.190722 + 0.138568i) q^{97} -0.737877 q^{98} +4.57843 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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