LMFDB - Embedded newform 750.2.g.f.451.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(151,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("750.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.g (of order $5$, degree $4$, not 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:	$5.98878015160$
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} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 $ x^16 - 4x^15 - 24x^14 + 94x^13 + 262x^12 - 936x^11 - 1584x^10 + 4642x^9 + 6259x^8 - 11958x^7 - 15752x^6 + 14670x^5 + 18271x^4 - 10440x^3 + 1135x^2 + 21080*x + 11105
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 5^{6} $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			451.2
Root			$0.543374 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	750.451
Dual form			750.2.g.f.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.309017 - 0.951057i) q^{6} -0.533559 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.309017 - 0.951057i) q^{6} -0.533559 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(1.16034 + 0.843033i) q^{11} +(-0.809017 + 0.587785i) q^{12} +(-5.31842 + 3.86406i) q^{13} +(0.431658 + 0.313618i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-0.296166 + 0.911505i) q^{17} +1.00000 q^{18} +(0.0657863 - 0.202470i) q^{19} +(-0.164879 - 0.507445i) q^{21} +(-0.443209 - 1.36406i) q^{22} +(-3.04515 - 2.21243i) q^{23} +1.00000 q^{24} +6.57392 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.164879 - 0.507445i) q^{28} +(1.91420 + 5.89130i) q^{29} +(-0.722398 + 2.22331i) q^{31} +1.00000 q^{32} +(-0.443209 + 1.36406i) q^{33} +(0.775373 - 0.563341i) q^{34} +(-0.809017 - 0.587785i) q^{36} +(-3.28696 + 2.38812i) q^{37} +(-0.172231 + 0.125133i) q^{38} +(-5.31842 - 3.86406i) q^{39} +(6.42486 - 4.66793i) q^{41} +(-0.164879 + 0.507445i) q^{42} -11.3607 q^{43} +(-0.443209 + 1.36406i) q^{44} +(1.16314 + 3.57979i) q^{46} +(3.13619 + 9.65219i) q^{47} +(-0.809017 - 0.587785i) q^{48} -6.71531 q^{49} -0.958413 q^{51} +(-5.31842 - 3.86406i) q^{52} +(-0.999220 - 3.07528i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-0.164879 + 0.507445i) q^{56} +0.212889 q^{57} +(1.91420 - 5.89130i) q^{58} +(-6.08749 + 4.42282i) q^{59} +(-10.1710 - 7.38968i) q^{61} +(1.89126 - 1.37408i) q^{62} +(0.431658 - 0.313618i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.16034 - 0.843033i) q^{66} +(-2.13619 + 6.57451i) q^{67} -0.958413 q^{68} +(1.16314 - 3.57979i) q^{69} +(3.12869 + 9.62913i) q^{71} +(0.309017 + 0.951057i) q^{72} +(11.3077 + 8.21552i) q^{73} +4.06291 q^{74} +0.212889 q^{76} +(-0.619107 - 0.449808i) q^{77} +(2.03145 + 6.25217i) q^{78} +(4.79840 + 14.7679i) q^{79} +(0.309017 - 0.951057i) q^{81} -7.94156 q^{82} +(5.04650 - 15.5315i) q^{83} +(0.431658 - 0.313618i) q^{84} +(9.19103 + 6.67767i) q^{86} +(-5.01144 + 3.64102i) q^{87} +(1.16034 - 0.843033i) q^{88} +(-4.54845 - 3.30464i) q^{89} +(2.83769 - 2.06170i) q^{91} +(1.16314 - 3.57979i) q^{92} -2.33773 q^{93} +(3.13619 - 9.65219i) q^{94} +(0.309017 + 0.951057i) q^{96} +(-1.71986 - 5.29318i) q^{97} +(5.43280 + 3.94716i) q^{98} -1.43425 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9	$ 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9} + 2 q^{11} - 4 q^{12} + 4 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{17} + 16 q^{18} - 2 q^{21} - 8 q^{22} - 6 q^{23} + 16 q^{24} + 4 q^{26} - 4 q^{27} - 2 q^{28} + 10 q^{29} - 18 q^{31} + 16 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 2 q^{37} - 10 q^{38} + 4 q^{39} + 22 q^{41} - 2 q^{42} + 4 q^{43} - 8 q^{44} - 6 q^{46} - 2 q^{47} - 4 q^{48} + 52 q^{49} + 28 q^{51} + 4 q^{52} - 16 q^{53} - 4 q^{54} - 2 q^{56} + 20 q^{57} + 10 q^{58} - 20 q^{59} + 12 q^{61} + 2 q^{62} - 2 q^{63} - 4 q^{64} + 2 q^{66} + 18 q^{67} + 28 q^{68} - 6 q^{69} - 28 q^{71} - 4 q^{72} + 24 q^{73} - 12 q^{74} + 20 q^{76} - 14 q^{77} - 6 q^{78} + 20 q^{79} - 4 q^{81} + 12 q^{82} - 36 q^{83} - 2 q^{84} - 6 q^{86} - 20 q^{87} + 2 q^{88} - 70 q^{89} + 12 q^{91} - 6 q^{92} + 32 q^{93} - 2 q^{94} - 4 q^{96} + 28 q^{97} - 38 q^{98} + 12 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9 + 2 * q^11 - 4 * q^12 + 4 * q^13 - 2 * q^14 - 4 * q^16 - 2 * q^17 + 16 * q^18 - 2 * q^21 - 8 * q^22 - 6 * q^23 + 16 * q^24 + 4 * q^26 - 4 * q^27 - 2 * q^28 + 10 * q^29 - 18 * q^31 + 16 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 2 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 - 2 * q^42 + 4 * q^43 - 8 * q^44 - 6 * q^46 - 2 * q^47 - 4 * q^48 + 52 * q^49 + 28 * q^51 + 4 * q^52 - 16 * q^53 - 4 * q^54 - 2 * q^56 + 20 * q^57 + 10 * q^58 - 20 * q^59 + 12 * q^61 + 2 * q^62 - 2 * q^63 - 4 * q^64 + 2 * q^66 + 18 * q^67 + 28 * q^68 - 6 * q^69 - 28 * q^71 - 4 * q^72 + 24 * q^73 - 12 * q^74 + 20 * q^76 - 14 * q^77 - 6 * q^78 + 20 * q^79 - 4 * q^81 + 12 * q^82 - 36 * q^83 - 2 * q^84 - 6 * q^86 - 20 * q^87 + 2 * q^88 - 70 * q^89 + 12 * q^91 - 6 * q^92 + 32 * q^93 - 2 * q^94 - 4 * q^96 + 28 * q^97 - 38 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	0.309017	−	0.951057i	0.126156	−	0.388267i
$7$	−0.533559			−0.201666			−0.100833	−	0.994903i	$-0.532151\pi$
$7$	−0.533559			−0.201666			−0.100833	+	0.994903i	$0.532151\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	1.16034	+	0.843033i	0.349854	+	0.254184i	0.748808	−	0.662787i	$-0.230627\pi$
$11$	1.16034	+	0.843033i	0.349854	+	0.254184i	−0.398954	+	0.916971i	$0.630627\pi$
$12$	−0.809017	+	0.587785i	−0.233543	+	0.169679i
$13$	−5.31842	+	3.86406i	−1.47506	+	1.07170i	−0.495957	+	0.868347i	$0.665183\pi$
$13$	−5.31842	+	3.86406i	−1.47506	+	1.07170i	−0.979106	+	0.203349i	$0.934817\pi$
$14$	0.431658	+	0.313618i	0.115366	+	0.0838180i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.296166	+	0.911505i	−0.0718308	+	0.221072i	−0.980527	−	0.196387i	$-0.937079\pi$
$17$	−0.296166	+	0.911505i	−0.0718308	+	0.221072i	0.908696	+	0.417459i	$0.137079\pi$
$18$	1.00000			0.235702
$19$	0.0657863	−	0.202470i	0.0150924	−	0.0464497i	−0.943227	−	0.332150i	$-0.892226\pi$
$19$	0.0657863	−	0.202470i	0.0150924	−	0.0464497i	0.958319	+	0.285700i	$0.0922261\pi$
$20$		0			0
$21$	−0.164879	−	0.507445i	−0.0359795	−	0.110734i
$22$	−0.443209	−	1.36406i	−0.0944924	−	0.290818i
$23$	−3.04515	−	2.21243i	−0.634957	−	0.461324i	0.223157	−	0.974783i	$-0.428364\pi$
$23$	−3.04515	−	2.21243i	−0.634957	−	0.461324i	−0.858114	+	0.513459i	$0.828364\pi$
$24$	1.00000			0.204124
$25$		0			0
$26$	6.57392			1.28925
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−0.164879	−	0.507445i	−0.0311592	−	0.0958981i
$29$	1.91420	+	5.89130i	0.355458	+	1.09399i	0.955743	+	0.294201i	$0.0950537\pi$
$29$	1.91420	+	5.89130i	0.355458	+	1.09399i	−0.600285	+	0.799786i	$0.704946\pi$
$30$		0			0
$31$	−0.722398	+	2.22331i	−0.129747	+	0.399319i	−0.994736	−	0.102471i	$-0.967325\pi$
$31$	−0.722398	+	2.22331i	−0.129747	+	0.399319i	0.864989	+	0.501790i	$0.167325\pi$
$32$	1.00000			0.176777
$33$	−0.443209	+	1.36406i	−0.0771527	+	0.237452i
$34$	0.775373	−	0.563341i	0.132975	−	0.0966122i
$35$		0			0
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	−3.28696	+	2.38812i	−0.540373	+	0.392604i	−0.824224	−	0.566264i	$-0.808388\pi$
$37$	−3.28696	+	2.38812i	−0.540373	+	0.392604i	0.283850	+	0.958869i	$0.408388\pi$
$38$	−0.172231	+	0.125133i	−0.0279395	+	0.0202993i
$39$	−5.31842	−	3.86406i	−0.851628	−	0.618744i
$40$		0			0
$41$	6.42486	−	4.66793i	1.00339	−	0.729009i	0.0405813	−	0.999176i	$-0.487079\pi$
$41$	6.42486	−	4.66793i	1.00339	−	0.729009i	0.962813	+	0.270167i	$0.0870790\pi$
$42$	−0.164879	+	0.507445i	−0.0254414	+	0.0783004i
$43$	−11.3607			−1.73250			−0.866248	−	0.499614i	$-0.833475\pi$
$43$	−11.3607			−1.73250			−0.866248	+	0.499614i	$0.833475\pi$
$44$	−0.443209	+	1.36406i	−0.0668162	+	0.205639i
$45$		0			0
$46$	1.16314	+	3.57979i	0.171496	+	0.527811i
$47$	3.13619	+	9.65219i	0.457460	+	1.40792i	0.868223	+	0.496175i	$0.165263\pi$
$47$	3.13619	+	9.65219i	0.457460	+	1.40792i	−0.410763	+	0.911742i	$0.634737\pi$
$48$	−0.809017	−	0.587785i	−0.116772	−	0.0848395i
$49$	−6.71531			−0.959331
$50$		0			0
$51$	−0.958413			−0.134205
$52$	−5.31842	−	3.86406i	−0.737532	−	0.535848i
$53$	−0.999220	−	3.07528i	−0.137253	−	0.422423i	0.858680	−	0.512512i	$-0.171285\pi$
$53$	−0.999220	−	3.07528i	−0.137253	−	0.422423i	−0.995934	+	0.0900889i	$0.971285\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$		0			0
$56$	−0.164879	+	0.507445i	−0.0220329	+	0.0678102i
$57$	0.212889			0.0281978
$58$	1.91420	−	5.89130i	0.251347	−	0.773566i
$59$	−6.08749	+	4.42282i	−0.792524	+	0.575802i	−0.908711	−	0.417425i	$-0.862933\pi$
$59$	−6.08749	+	4.42282i	−0.792524	+	0.575802i	0.116188	+	0.993227i	$0.462933\pi$
$60$		0			0
$61$	−10.1710	−	7.38968i	−1.30227	−	0.946151i	−0.302290	−	0.953216i	$-0.597751\pi$
$61$	−10.1710	−	7.38968i	−1.30227	−	0.946151i	−0.999975	+	0.00706498i	$0.997751\pi$
$62$	1.89126	−	1.37408i	0.240191	−	0.174509i
$63$	0.431658	−	0.313618i	0.0543838	−	0.0395122i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$		0			0
$66$	1.16034	−	0.843033i	0.142827	−	0.103770i
$67$	−2.13619	+	6.57451i	−0.260977	+	0.803204i	0.731616	+	0.681717i	$0.238766\pi$
$67$	−2.13619	+	6.57451i	−0.260977	+	0.803204i	−0.992593	+	0.121487i	$0.961234\pi$
$68$	−0.958413			−0.116225
$69$	1.16314	−	3.57979i	0.140026	−	0.430956i
$70$		0			0
$71$	3.12869	+	9.62913i	0.371308	+	1.14277i	0.945936	+	0.324353i	$0.105147\pi$
$71$	3.12869	+	9.62913i	0.371308	+	1.14277i	−0.574628	+	0.818415i	$0.694853\pi$
$72$	0.309017	+	0.951057i	0.0364180	+	0.112083i
$73$	11.3077	+	8.21552i	1.32347	+	0.961554i	0.999882	+	0.0153549i	$0.00488781\pi$
$73$	11.3077	+	8.21552i	1.32347	+	0.961554i	0.323584	+	0.946199i	$0.395112\pi$
$74$	4.06291			0.472304
$75$		0			0
$76$	0.212889			0.0244201
$77$	−0.619107	−	0.449808i	−0.0705538	−	0.0512604i
$78$	2.03145	+	6.25217i	0.230017	+	0.707919i
$79$	4.79840	+	14.7679i	0.539862	+	1.66152i	0.732903	+	0.680333i	$0.238165\pi$
$79$	4.79840	+	14.7679i	0.539862	+	1.66152i	−0.193041	+	0.981191i	$0.561835\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−7.94156			−0.876999
$83$	5.04650	−	15.5315i	0.553926	−	1.70481i	−0.144838	−	0.989455i	$-0.546266\pi$
$83$	5.04650	−	15.5315i	0.553926	−	1.70481i	0.698764	−	0.715352i	$-0.253734\pi$
$84$	0.431658	−	0.313618i	0.0470978	−	0.0342185i
$85$		0			0
$86$	9.19103	+	6.67767i	0.991094	+	0.720072i
$87$	−5.01144	+	3.64102i	−0.537283	+	0.390359i
$88$	1.16034	−	0.843033i	0.123692	−	0.0898676i
$89$	−4.54845	−	3.30464i	−0.482135	−	0.350291i	0.320017	−	0.947412i	$-0.396311\pi$
$89$	−4.54845	−	3.30464i	−0.482135	−	0.350291i	−0.802152	+	0.597120i	$0.796311\pi$
$90$		0			0
$91$	2.83769	−	2.06170i	0.297471	−	0.216125i
$92$	1.16314	−	3.57979i	0.121266	−	0.373219i
$93$	−2.33773			−0.242411
$94$	3.13619	−	9.65219i	0.323473	−	0.995548i
$95$		0			0
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	−1.71986	−	5.29318i	−0.174625	−	0.537441i	0.824991	−	0.565146i	$-0.191180\pi$
$97$	−1.71986	−	5.29318i	−0.174625	−	0.537441i	−0.999616	+	0.0277049i	$0.991180\pi$
$98$	5.43280	+	3.94716i	0.548796	+	0.398724i
$99$	−1.43425			−0.144148
$100$		0			0
$101$	−9.42708			−0.938029			−0.469015	−	0.883190i	$-0.655391\pi$
$101$	−9.42708			−0.938029			−0.469015	+	0.883190i	$0.655391\pi$
$102$	0.775373	+	0.563341i	0.0767733	+	0.0557791i
$103$	2.47174	+	7.60723i	0.243548	+	0.749562i	0.995872	+	0.0907695i	$0.0289327\pi$
$103$	2.47174	+	7.60723i	0.243548	+	0.749562i	−0.752324	+	0.658793i	$0.771067\pi$
$104$	2.03145	+	6.25217i	0.199200	+	0.613076i
$105$		0			0
$106$	−0.999220	+	3.07528i	−0.0970529	+	0.298698i
$107$	18.9260			1.82964			0.914822	−	0.403857i	$-0.132331\pi$
$107$	18.9260			1.82964			0.914822	+	0.403857i	$0.132331\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	2.14813	−	1.56071i	0.205754	−	0.149489i	−0.480137	−	0.877194i	$-0.659413\pi$
$109$	2.14813	−	1.56071i	0.205754	−	0.149489i	0.685891	+	0.727705i	$0.259413\pi$
$110$		0			0
$111$	−3.28696	−	2.38812i	−0.311985	−	0.226670i
$112$	0.431658	−	0.313618i	0.0407879	−	0.0296341i
$113$	−2.47788	+	1.80029i	−0.233099	+	0.169357i	−0.698203	−	0.715899i	$-0.746017\pi$
$113$	−2.47788	+	1.80029i	−0.233099	+	0.169357i	0.465104	+	0.885256i	$0.346017\pi$
$114$	−0.172231	−	0.125133i	−0.0161309	−	0.0117198i
$115$		0			0
$116$	−5.01144	+	3.64102i	−0.465301	+	0.338061i
$117$	2.03145	−	6.25217i	0.187808	−	0.578014i
$118$	7.52455			0.692691
$119$	0.158022	−	0.486342i	0.0144859	−	0.0445829i
$120$		0			0
$121$	−2.76351	−	8.50522i	−0.251229	−	0.773202i
$122$	3.88498	+	11.9567i	0.351730	+	1.08251i
$123$	6.42486	+	4.66793i	0.579310	+	0.420893i
$124$	−2.33773			−0.209934
$125$		0			0
$126$	−0.533559			−0.0475332
$127$	5.24451	+	3.81036i	0.465375	+	0.338115i	0.795636	−	0.605775i	$-0.207137\pi$
$127$	5.24451	+	3.81036i	0.465375	+	0.338115i	−0.330261	+	0.943890i	$0.607137\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−3.51066	−	10.8047i	−0.309096	−	0.951301i
$130$		0			0
$131$	−2.92266	+	8.99503i	−0.255354	+	0.785900i	0.738405	+	0.674357i	$0.235579\pi$
$131$	−2.92266	+	8.99503i	−0.255354	+	0.785900i	−0.993760	+	0.111543i	$0.964421\pi$
$132$	−1.43425			−0.124836
$133$	−0.0351009	+	0.108029i	−0.00304363	+	0.00936734i
$134$	5.59261	−	4.06327i	0.483128	−	0.351013i
$135$		0			0
$136$	0.775373	+	0.563341i	0.0664877	+	0.0483061i
$137$	9.98010	−	7.25096i	0.852657	−	0.619492i	−0.0732202	−	0.997316i	$-0.523328\pi$
$137$	9.98010	−	7.25096i	0.852657	−	0.619492i	0.925877	+	0.377824i	$0.123328\pi$
$138$	−3.04515	+	2.21243i	−0.259220	+	0.188335i
$139$	−3.67227	−	2.66806i	−0.311478	−	0.226302i	0.421052	−	0.907036i	$-0.361661\pi$
$139$	−3.67227	−	2.66806i	−0.311478	−	0.226302i	−0.732530	+	0.680734i	$0.761661\pi$
$140$		0			0
$141$	−8.21065	+	5.96538i	−0.691461	+	0.502376i
$142$	3.12869	−	9.62913i	0.262554	−	0.808059i
$143$	−9.42867			−0.788465
$144$	0.309017	−	0.951057i	0.0257514	−	0.0792547i
$145$		0			0
$146$	−4.31916	−	13.2930i	−0.357456	−	1.10014i
$147$	−2.07515	−	6.38664i	−0.171155	−	0.526761i
$148$	−3.28696	−	2.38812i	−0.270187	−	0.196302i
$149$	11.0750			0.907303			0.453651	−	0.891179i	$-0.350121\pi$
$149$	11.0750			0.907303			0.453651	+	0.891179i	$0.350121\pi$
$150$		0			0
$151$	−1.63387			−0.132962			−0.0664812	−	0.997788i	$-0.521177\pi$
$151$	−1.63387			−0.132962			−0.0664812	+	0.997788i	$0.521177\pi$
$152$	−0.172231	−	0.125133i	−0.0139698	−	0.0101496i
$153$	−0.296166	−	0.911505i	−0.0239436	−	0.0736908i
$154$	0.236478	+	0.727804i	0.0190559	+	0.0586481i
$155$		0			0
$156$	2.03145	−	6.25217i	0.162647	−	0.500574i
$157$	6.64544			0.530364			0.265182	−	0.964198i	$-0.414568\pi$
$157$	6.64544			0.530364			0.265182	+	0.964198i	$0.414568\pi$
$158$	4.79840	−	14.7679i	0.381740	−	1.17487i
$159$	2.61599	−	1.90063i	0.207462	−	0.150730i
$160$		0			0
$161$	1.62477	+	1.18046i	0.128050	+	0.0930335i
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	8.18191	−	5.94451i	0.640857	−	0.465610i	−0.219288	−	0.975660i	$-0.570373\pi$
$163$	8.18191	−	5.94451i	0.640857	−	0.465610i	0.860144	+	0.510051i	$0.170373\pi$
$164$	6.42486	+	4.66793i	0.501697	+	0.364504i
$165$		0			0
$166$	−13.2119	+	9.59902i	−1.02544	+	0.745028i
$167$	3.95185	−	12.1625i	0.305803	−	0.941166i	−0.673573	−	0.739121i	$-0.735241\pi$
$167$	3.95185	−	12.1625i	0.305803	−	0.941166i	0.979376	−	0.202045i	$-0.0647587\pi$
$168$	−0.533559			−0.0411650
$169$	9.33741	−	28.7376i	0.718262	−	2.21058i
$170$		0			0
$171$	0.0657863	+	0.202470i	0.00503081	+	0.0154832i
$172$	−3.51066	−	10.8047i	−0.267685	−	0.823851i
$173$	11.0492	+	8.02770i	0.840054	+	0.610335i	0.922386	−	0.386270i	$-0.126237\pi$
$173$	11.0492	+	8.02770i	0.840054	+	0.610335i	−0.0823317	+	0.996605i	$0.526237\pi$
$174$	6.19448			0.469602
$175$		0			0
$176$	−1.43425			−0.108111
$177$	−6.08749	−	4.42282i	−0.457564	−	0.332439i
$178$	1.73735	+	5.34703i	0.130220	+	0.400776i
$179$	0.924399	+	2.84501i	0.0690928	+	0.212646i	0.979641	−	0.200757i	$-0.0643401\pi$
$179$	0.924399	+	2.84501i	0.0690928	+	0.212646i	−0.910548	+	0.413403i	$0.864340\pi$
$180$		0			0
$181$	2.35559	−	7.24976i	0.175090	−	0.538871i	−0.824548	−	0.565792i	$-0.808570\pi$
$181$	2.35559	−	7.24976i	0.175090	−	0.538871i	0.999638	+	0.0269215i	$0.00857041\pi$
$182$	−3.50758			−0.259999
$183$	3.88498	−	11.9567i	0.287186	−	0.883868i
$184$	−3.04515	+	2.21243i	−0.224491	+	0.163102i
$185$		0			0
$186$	1.89126	+	1.37408i	0.138674	+	0.100753i
$187$	−1.11208	+	0.807974i	−0.0813234	+	0.0590849i
$188$	−8.21065	+	5.96538i	−0.598823	+	0.435070i
$189$	0.431658	+	0.313618i	0.0313985	+	0.0228124i
$190$		0			0
$191$	6.79610	−	4.93766i	0.491749	−	0.357276i	−0.314108	−	0.949387i	$-0.601705\pi$
$191$	6.79610	−	4.93766i	0.491749	−	0.357276i	0.805856	+	0.592111i	$0.201705\pi$
$192$	0.309017	−	0.951057i	0.0223014	−	0.0686366i
$193$	−10.5266			−0.757723			−0.378861	−	0.925453i	$-0.623684\pi$
$193$	−10.5266			−0.757723			−0.378861	+	0.925453i	$0.623684\pi$
$194$	−1.71986	+	5.29318i	−0.123479	+	0.380028i
$195$		0			0
$196$	−2.07515	−	6.38664i	−0.148225	−	0.456189i
$197$	−3.15446	−	9.70843i	−0.224746	−	0.691697i	−0.998317	−	0.0579878i	$-0.981532\pi$
$197$	−3.15446	−	9.70843i	−0.224746	−	0.691697i	0.773571	−	0.633709i	$-0.218468\pi$
$198$	1.16034	+	0.843033i	0.0824614	+	0.0599117i
$199$	3.84318			0.272436			0.136218	−	0.990679i	$-0.456505\pi$
$199$	3.84318			0.272436			0.136218	+	0.990679i	$0.456505\pi$
$200$		0			0
$201$	−6.91285			−0.487595
$202$	7.62667	+	5.54110i	0.536610	+	0.389870i
$203$	−1.02134	−	3.14336i	−0.0716839	−	0.220620i
$204$	−0.296166	−	0.911505i	−0.0207358	−	0.0638181i
$205$		0			0
$206$	2.47174	−	7.60723i	0.172214	−	0.530021i
$207$	3.76401			0.261617
$208$	2.03145	−	6.25217i	0.140856	−	0.433510i
$209$	0.247023	−	0.179472i	0.0170869	−	0.0124144i
$210$		0			0
$211$	−4.24669	−	3.08540i	−0.292354	−	0.212408i	0.431934	−	0.901905i	$-0.357831\pi$
$211$	−4.24669	−	3.08540i	−0.292354	−	0.212408i	−0.724288	+	0.689498i	$0.757831\pi$
$212$	2.61599	−	1.90063i	0.179667	−	0.130536i
$213$	−8.19103	+	5.95113i	−0.561240	+	0.407765i
$214$	−15.3114	−	11.1244i	−1.04667	−	0.760450i
$215$		0			0
$216$	−0.809017	+	0.587785i	−0.0550466	+	0.0399937i
$217$	0.385442	−	1.18627i	0.0261655	−	0.0805292i
$218$	−2.65524			−0.179836
$219$	−4.31916	+	13.2930i	−0.291862	+	0.898258i
$220$		0			0
$221$	−1.94697	−	5.99217i	−0.130968	−	0.403077i
$222$	1.25551	+	3.86406i	0.0842642	+	0.259338i
$223$	15.5964	+	11.3315i	1.04441	+	0.758811i	0.971142	−	0.238501i	$-0.0766560\pi$
$223$	15.5964	+	11.3315i	1.04441	+	0.758811i	0.0732716	+	0.997312i	$0.476656\pi$
$224$	−0.533559			−0.0356499
$225$		0			0
$226$	3.06283			0.203736
$227$	−6.82776	−	4.96066i	−0.453174	−	0.329250i	0.337673	−	0.941263i	$-0.390360\pi$
$227$	−6.82776	−	4.96066i	−0.453174	−	0.329250i	−0.790848	+	0.612013i	$0.790360\pi$
$228$	0.0657863	+	0.202470i	0.00435681	+	0.0134089i
$229$	1.84041	+	5.66419i	0.121618	+	0.374300i	0.993270	−	0.115825i	$-0.0369511\pi$
$229$	1.84041	+	5.66419i	0.121618	+	0.374300i	−0.871652	+	0.490125i	$0.836951\pi$
$230$		0			0
$231$	0.236478	−	0.727804i	0.0155591	−	0.0478860i
$232$	6.19448			0.406688
$233$	−0.646750	+	1.99049i	−0.0423700	+	0.130401i	−0.970004	−	0.243089i	$-0.921839\pi$
$233$	−0.646750	+	1.99049i	−0.0423700	+	0.130401i	0.927634	+	0.373491i	$0.121839\pi$
$234$	−5.31842	+	3.86406i	−0.347676	+	0.252601i
$235$		0			0
$236$	−6.08749	−	4.42282i	−0.396262	−	0.287901i
$237$	−12.5624	+	9.12709i	−0.816013	+	0.592868i
$238$	−0.413707	+	0.300576i	−0.0268167	+	0.0194834i
$239$	−8.00797	−	5.81813i	−0.517993	−	0.376344i	0.297855	−	0.954611i	$-0.403729\pi$
$239$	−8.00797	−	5.81813i	−0.517993	−	0.376344i	−0.815847	+	0.578268i	$0.803729\pi$
$240$		0			0
$241$	17.3588	−	12.6119i	1.11818	−	0.812406i	0.134249	−	0.990948i	$-0.457138\pi$
$241$	17.3588	−	12.6119i	1.11818	−	0.812406i	0.983932	+	0.178542i	$0.0571379\pi$
$242$	−2.76351	+	8.50522i	−0.177645	+	0.546736i
$243$	1.00000			0.0641500
$244$	3.88498	−	11.9567i	0.248711	−	0.765452i
$245$		0			0
$246$	−2.45408	−	7.55288i	−0.156466	−	0.481554i
$247$	0.432474	+	1.33102i	0.0275177	+	0.0846907i
$248$	1.89126	+	1.37408i	0.120095	+	0.0872543i
$249$	16.3308			1.03492
$250$		0			0
$251$	−4.10753			−0.259265			−0.129632	−	0.991562i	$-0.541380\pi$
$251$	−4.10753			−0.259265			−0.129632	+	0.991562i	$0.541380\pi$
$252$	0.431658	+	0.313618i	0.0271919	+	0.0197561i
$253$	−1.66824	−	5.13432i	−0.104881	−	0.322792i
$254$	−2.00323	−	6.16529i	−0.125694	−	0.386845i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−30.7748			−1.91968			−0.959839	−	0.280552i	$-0.909482\pi$
$257$	−30.7748			−1.91968			−0.959839	+	0.280552i	$0.909482\pi$
$258$	−3.51066	+	10.8047i	−0.218564	+	0.672671i
$259$	1.75379	−	1.27420i	0.108975	−	0.0791751i
$260$		0			0
$261$	−5.01144	−	3.64102i	−0.310200	−	0.225374i
$262$	7.65163	−	5.55924i	0.472719	−	0.343451i
$263$	22.9541	−	16.6771i	1.41541	−	1.02836i	0.422904	−	0.906174i	$-0.361011\pi$
$263$	22.9541	−	16.6771i	1.41541	−	1.02836i	0.992508	−	0.122183i	$-0.0389894\pi$
$264$	1.16034	+	0.843033i	0.0714137	+	0.0518851i
$265$		0			0
$266$	0.0918954	−	0.0667659i	0.00563447	−	0.00409368i
$267$	1.73735	−	5.34703i	0.106324	−	0.327233i
$268$	−6.91285			−0.422269
$269$	3.29621	−	10.1447i	0.200974	−	0.618533i	−0.798881	−	0.601489i	$-0.794574\pi$
$269$	3.29621	−	10.1447i	0.200974	−	0.618533i	0.999855	−	0.0170443i	$-0.00542564\pi$
$270$		0			0
$271$	7.05917	+	21.7259i	0.428814	+	1.31975i	0.899295	+	0.437343i	$0.144080\pi$
$271$	7.05917	+	21.7259i	0.428814	+	1.31975i	−0.470481	+	0.882410i	$0.655920\pi$
$272$	−0.296166	−	0.911505i	−0.0179577	−	0.0552681i
$273$	2.83769	+	2.06170i	0.171745	+	0.124780i
$274$	−12.3361			−0.745250
$275$		0			0
$276$	3.76401			0.226567
$277$	25.4510	+	18.4912i	1.52920	+	1.11103i	0.956680	+	0.291141i	$0.0940350\pi$
$277$	25.4510	+	18.4912i	1.52920	+	1.11103i	0.572522	+	0.819889i	$0.305965\pi$
$278$	1.40268	+	4.31701i	0.0841273	+	0.258917i
$279$	−0.722398	−	2.22331i	−0.0432488	−	0.133106i
$280$		0			0
$281$	−3.33074	+	10.2510i	−0.198695	+	0.611522i	0.801218	+	0.598372i	$0.204186\pi$
$281$	−3.33074	+	10.2510i	−0.198695	+	0.611522i	−0.999914	+	0.0131494i	$0.995814\pi$
$282$	10.1489			0.604359
$283$	−1.28683	+	3.96046i	−0.0764943	+	0.235425i	−0.981991	−	0.188928i	$-0.939499\pi$
$283$	−1.28683	+	3.96046i	−0.0764943	+	0.235425i	0.905497	+	0.424354i	$0.139499\pi$
$284$	−8.19103	+	5.95113i	−0.486048	+	0.353135i
$285$		0			0
$286$	7.62795	+	5.54203i	0.451050	+	0.327707i
$287$	−3.42804	+	2.49062i	−0.202351	+	0.147017i
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	13.0102	+	9.45244i	0.765304	+	0.556026i
$290$		0			0
$291$	4.50265	−	3.27137i	0.263950	−	0.191771i
$292$	−4.31916	+	13.2930i	−0.252760	+	0.777914i
$293$	−17.9603			−1.04925			−0.524626	−	0.851333i	$-0.675795\pi$
$293$	−17.9603			−1.04925			−0.524626	+	0.851333i	$0.675795\pi$
$294$	−2.07515	+	6.38664i	−0.121025	+	0.372477i
$295$		0			0
$296$	1.25551	+	3.86406i	0.0729749	+	0.224594i
$297$	−0.443209	−	1.36406i	−0.0257176	−	0.0791505i
$298$	−8.95990	−	6.50975i	−0.519033	−	0.377099i
$299$	24.7443			1.43100
$300$		0			0
$301$	6.06163			0.349386
$302$	1.32183	+	0.960365i	0.0760627	+	0.0552628i
$303$	−2.91313	−	8.96568i	−0.167355	−	0.515065i
$304$	0.0657863	+	0.202470i	0.00377311	+	0.0116124i
$305$		0			0
$306$	−0.296166	+	0.911505i	−0.0169307	+	0.0521073i
$307$	−20.8174			−1.18811			−0.594056	−	0.804423i	$-0.702474\pi$
$307$	−20.8174			−1.18811			−0.594056	+	0.804423i	$0.702474\pi$
$308$	0.236478	−	0.727804i	0.0134746	−	0.0414705i
$309$	−6.47109	+	4.70153i	−0.368128	+	0.267460i
$310$		0			0
$311$	15.7375	+	11.4339i	0.892390	+	0.648359i	0.936500	−	0.350667i	$-0.114045\pi$
$311$	15.7375	+	11.4339i	0.892390	+	0.648359i	−0.0441099	+	0.999027i	$0.514045\pi$
$312$	−5.31842	+	3.86406i	−0.301096	+	0.218759i
$313$	−4.75953	+	3.45800i	−0.269024	+	0.195458i	−0.714116	−	0.700027i	$-0.753171\pi$
$313$	−4.75953	+	3.45800i	−0.269024	+	0.195458i	0.445092	+	0.895485i	$0.353171\pi$
$314$	−5.37627	−	3.90609i	−0.303401	−	0.220433i
$315$		0			0
$316$	−12.5624	+	9.12709i	−0.706688	+	0.513439i
$317$	−3.32534	+	10.2344i	−0.186770	+	0.574818i	−0.999974	−	0.00715959i	$-0.997721\pi$
$317$	−3.32534	+	10.2344i	−0.186770	+	0.574818i	0.813205	+	0.581978i	$0.197721\pi$
$318$	−3.23354			−0.181328
$319$	−2.74545	+	8.44962i	−0.153716	+	0.473088i
$320$		0			0
$321$	5.84845	+	17.9997i	0.326429	+	1.00464i
$322$	−0.620606	−	1.91003i	−0.0345850	−	0.106442i
$323$	0.165068	+	0.119929i	0.00918465	+	0.00667304i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−10.1134			−0.560129
$327$	2.14813	+	1.56071i	0.118792	+	0.0863075i
$328$	−2.45408	−	7.55288i	−0.135504	−	0.417038i
$329$	−1.67334	−	5.15002i	−0.0922543	−	0.283930i
$330$		0			0
$331$	−0.190692	+	0.586889i	−0.0104814	+	0.0322584i	−0.956160	−	0.292843i	$-0.905399\pi$
$331$	−0.190692	+	0.586889i	−0.0104814	+	0.0322584i	0.945679	+	0.325102i	$0.105399\pi$
$332$	16.3308			0.896270
$333$	1.25551	−	3.86406i	0.0688014	−	0.211749i
$334$	−10.3461	+	7.51686i	−0.566112	+	0.411304i
$335$		0			0
$336$	0.431658	+	0.313618i	0.0235489	+	0.0171093i
$337$	12.4675	−	9.05814i	0.679146	−	0.493429i	−0.193928	−	0.981016i	$-0.562123\pi$
$337$	12.4675	−	9.05814i	0.679146	−	0.493429i	0.873074	+	0.487587i	$0.162123\pi$
$338$	−24.4456	+	17.7608i	−1.32967	+	0.966060i
$339$	−2.47788	−	1.80029i	−0.134580	−	0.0977781i
$340$		0			0
$341$	−2.71255	+	1.97078i	−0.146893	+	0.106724i
$342$	0.0657863	−	0.202470i	0.00355732	−	0.0109483i
$343$	7.31793			0.395131
$344$	−3.51066	+	10.8047i	−0.189282	+	0.582551i
$345$		0			0
$346$	−4.22041	−	12.9891i	−0.226891	−	0.698298i
$347$	7.00126	+	21.5477i	0.375847	+	1.15674i	0.942905	+	0.333061i	$0.108081\pi$
$347$	7.00126	+	21.5477i	0.375847	+	1.15674i	−0.567058	+	0.823678i	$0.691919\pi$
$348$	−5.01144	−	3.64102i	−0.268641	−	0.195179i
$349$	−16.9543			−0.907544			−0.453772	−	0.891118i	$-0.649922\pi$
$349$	−16.9543			−0.907544			−0.453772	+	0.891118i	$0.649922\pi$
$350$		0			0
$351$	6.57392			0.350890
$352$	1.16034	+	0.843033i	0.0618461	+	0.0449338i
$353$	1.87343	+	5.76583i	0.0997127	+	0.306884i	0.988453	−	0.151526i	$-0.0484189\pi$
$353$	1.87343	+	5.76583i	0.0997127	+	0.306884i	−0.888740	+	0.458411i	$0.848419\pi$
$354$	2.32521	+	7.15627i	0.123584	+	0.380352i
$355$		0			0
$356$	1.73735	−	5.34703i	0.0920796	−	0.283392i
$357$	0.511370			0.0270646
$358$	0.924399	−	2.84501i	0.0488560	−	0.150363i
$359$	−15.2894	+	11.1084i	−0.806943	+	0.586279i	−0.912943	−	0.408088i	$-0.866196\pi$
$359$	−15.2894	+	11.1084i	−0.806943	+	0.586279i	0.105999	+	0.994366i	$0.466196\pi$
$360$		0			0
$361$	15.3347	+	11.1413i	0.807087	+	0.586383i
$362$	−6.16702	+	4.48060i	−0.324131	+	0.235495i
$363$	7.23497	−	5.25652i	0.379738	−	0.275896i
$364$	2.83769	+	2.06170i	0.148735	+	0.108063i
$365$		0			0
$366$	−10.1710	+	7.38968i	−0.531648	+	0.386265i
$367$	−7.74036	+	23.8224i	−0.404044	+	1.24352i	0.517648	+	0.855594i	$0.326808\pi$
$367$	−7.74036	+	23.8224i	−0.404044	+	1.24352i	−0.921691	+	0.387924i	$0.873192\pi$
$368$	3.76401			0.196213
$369$	−2.45408	+	7.55288i	−0.127754	+	0.393187i
$370$		0			0
$371$	0.533143	+	1.64085i	0.0276794	+	0.0851885i
$372$	−0.722398	−	2.22331i	−0.0374546	−	0.115273i
$373$	9.62360	+	6.99196i	0.498291	+	0.362030i	0.808364	−	0.588683i	$-0.200353\pi$
$373$	9.62360	+	6.99196i	0.498291	+	0.362030i	−0.310073	+	0.950713i	$0.600353\pi$
$374$	1.37461			0.0710792
$375$		0			0
$376$	10.1489			0.523390
$377$	−32.9448	−	23.9358i	−1.69675	−	1.23276i
$378$	−0.164879	−	0.507445i	−0.00848045	−	0.0261001i
$379$	8.50366	+	26.1716i	0.436804	+	1.34434i	0.891227	+	0.453558i	$0.149845\pi$
$379$	8.50366	+	26.1716i	0.436804	+	1.34434i	−0.454423	+	0.890786i	$0.650155\pi$
$380$		0			0
$381$	−2.00323	+	6.16529i	−0.102628	+	0.315858i
$382$	−8.40045			−0.429804
$383$	−6.80809	+	20.9531i	−0.347877	+	1.07066i	0.612149	+	0.790743i	$0.290305\pi$
$383$	−6.80809	+	20.9531i	−0.347877	+	1.07066i	−0.960026	+	0.279912i	$0.909695\pi$
$384$	−0.809017	+	0.587785i	−0.0412850	+	0.0299953i
$385$		0			0
$386$	8.51621	+	6.18739i	0.433464	+	0.314930i
$387$	9.19103	−	6.67767i	0.467206	−	0.339445i
$388$	4.50265	−	3.27137i	0.228587	−	0.166078i
$389$	−14.1491	−	10.2799i	−0.717386	−	0.521212i	0.168162	−	0.985759i	$-0.446217\pi$
$389$	−14.1491	−	10.2799i	−0.717386	−	0.521212i	−0.885548	+	0.464548i	$0.846217\pi$
$390$		0			0
$391$	2.91851	−	2.12042i	0.147595	−	0.107234i
$392$	−2.07515	+	6.38664i	−0.104811	+	0.322574i
$393$	−9.45794			−0.477090
$394$	−3.15446	+	9.70843i	−0.158919	+	0.489104i
$395$		0			0
$396$	−0.443209	−	1.36406i	−0.0222721	−	0.0685464i
$397$	−7.57062	−	23.3000i	−0.379959	−	1.16939i	−0.940072	−	0.340976i	$-0.889242\pi$
$397$	−7.57062	−	23.3000i	−0.379959	−	1.16939i	0.560113	−	0.828416i	$-0.310758\pi$
$398$	−3.10920	−	2.25896i	−0.155850	−	0.113232i
$399$	−0.113589			−0.00568656
$400$		0			0
$401$	1.04105			0.0519875			0.0259937	−	0.999662i	$-0.491725\pi$
$401$	1.04105			0.0519875			0.0259937	+	0.999662i	$0.491725\pi$
$402$	5.59261	+	4.06327i	0.278934	+	0.202658i
$403$	−4.74899	−	14.6159i	−0.236564	−	0.728069i
$404$	−2.91313	−	8.96568i	−0.144934	−	0.446059i
$405$		0			0
$406$	−1.02134	+	3.14336i	−0.0506882	+	0.156002i
$407$	−5.82724			−0.288845
$408$	−0.296166	+	0.911505i	−0.0146624	+	0.0451262i
$409$	−18.0061	+	13.0822i	−0.890345	+	0.646873i	−0.935968	−	0.352085i	$-0.885473\pi$
$409$	−18.0061	+	13.0822i	−0.890345	+	0.646873i	0.0456231	+	0.998959i	$0.485473\pi$
$410$		0			0
$411$	9.98010	+	7.25096i	0.492282	+	0.357664i
$412$	−6.47109	+	4.70153i	−0.318808	+	0.231628i
$413$	3.24804	−	2.35984i	0.159825	−	0.116120i
$414$	−3.04515	−	2.21243i	−0.149661	−	0.108735i
$415$		0			0
$416$	−5.31842	+	3.86406i	−0.260757	+	0.189451i
$417$	1.40268	−	4.31701i	0.0686897	−	0.211405i
$418$	−0.305337			−0.0149345
$419$	−7.14737	+	21.9973i	−0.349172	+	1.07464i	0.610141	+	0.792293i	$0.291113\pi$
$419$	−7.14737	+	21.9973i	−0.349172	+	1.07464i	−0.959312	+	0.282347i	$0.908887\pi$
$420$		0			0
$421$	3.01643	+	9.28363i	0.147012	+	0.452457i	0.997264	−	0.0739190i	$-0.0235506\pi$
$421$	3.01643	+	9.28363i	0.147012	+	0.452457i	−0.850252	+	0.526376i	$0.823551\pi$
$422$	1.62209	+	4.99228i	0.0789622	+	0.243021i
$423$	−8.21065	−	5.96538i	−0.399215	−	0.290047i
$424$	−3.23354			−0.157035
$425$		0			0
$426$	10.1247			0.490542
$427$	5.42684	+	3.94283i	0.262623	+	0.190807i
$428$	5.84845	+	17.9997i	0.282696	+	0.870048i
$429$	−2.91362	−	8.96720i	−0.140671	−	0.432940i
$430$		0			0
$431$	2.62448	−	8.07731i	0.126417	−	0.389070i	−0.867740	−	0.497019i	$-0.834428\pi$
$431$	2.62448	−	8.07731i	0.126417	−	0.389070i	0.994157	+	0.107948i	$0.0344281\pi$
$432$	1.00000			0.0481125
$433$	6.79967	−	20.9272i	0.326771	−	1.00570i	−0.643864	−	0.765140i	$-0.722670\pi$
$433$	6.79967	−	20.9272i	0.326771	−	1.00570i	0.970635	−	0.240558i	$-0.0773304\pi$
$434$	−1.00910	+	0.733154i	−0.0484384	+	0.0351925i
$435$		0			0
$436$	2.14813	+	1.56071i	0.102877	+	0.0747445i
$437$	−0.648279	+	0.471002i	−0.0310114	+	0.0225311i
$438$	11.3077	−	8.21552i	0.540303	−	0.392553i
$439$	31.0325	+	22.5464i	1.48110	+	1.07608i	0.977201	+	0.212318i	$0.0681013\pi$
$439$	31.0325	+	22.5464i	1.48110	+	1.07608i	0.503898	+	0.863763i	$0.331899\pi$
$440$		0			0
$441$	5.43280	−	3.94716i	0.258705	−	0.187960i
$442$	−1.94697	+	5.99217i	−0.0926080	+	0.285018i
$443$	12.7478			0.605666			0.302833	−	0.953044i	$-0.402068\pi$
$443$	12.7478			0.605666			0.302833	+	0.953044i	$0.402068\pi$
$444$	1.25551	−	3.86406i	0.0595838	−	0.183380i
$445$		0			0
$446$	−5.95730	−	18.3347i	−0.282087	−	0.868173i
$447$	3.42238	+	10.5330i	0.161873	+	0.498193i
$448$	0.431658	+	0.313618i	0.0203939	+	0.0148171i
$449$	18.0358			0.851161			0.425580	−	0.904921i	$-0.360070\pi$
$449$	18.0358			0.851161			0.425580	+	0.904921i	$0.360070\pi$
$450$		0			0
$451$	11.3902			0.536344
$452$	−2.47788	−	1.80029i	−0.116550	−	0.0846783i
$453$	−0.504894	−	1.55390i	−0.0237220	−	0.0730087i
$454$	2.60797	+	8.02651i	0.122398	+	0.376703i
$455$		0			0
$456$	0.0657863	−	0.202470i	0.00308073	−	0.00948150i
$457$	−21.1495			−0.989334			−0.494667	−	0.869083i	$-0.664710\pi$
$457$	−21.1495			−0.989334			−0.494667	+	0.869083i	$0.664710\pi$
$458$	1.84041	−	5.66419i	0.0859966	−	0.264670i
$459$	0.775373	−	0.563341i	0.0361913	−	0.0262945i
$460$		0			0
$461$	−25.8954	−	18.8141i	−1.20607	−	0.876260i	−0.211200	−	0.977443i	$-0.567737\pi$
$461$	−25.8954	−	18.8141i	−1.20607	−	0.876260i	−0.994868	+	0.101183i	$0.967737\pi$
$462$	−0.619107	+	0.449808i	−0.0288035	+	0.0209270i
$463$	−23.2815	+	16.9150i	−1.08198	+	0.786108i	−0.978028	−	0.208474i	$-0.933150\pi$
$463$	−23.2815	+	16.9150i	−1.08198	+	0.786108i	−0.103957	+	0.994582i	$0.533150\pi$
$464$	−5.01144	−	3.64102i	−0.232650	−	0.169030i
$465$		0			0
$466$	1.69321	−	1.23019i	0.0784366	−	0.0569875i
$467$	1.60789	−	4.94859i	0.0744045	−	0.228993i	−0.906937	−	0.421266i	$-0.861586\pi$
$467$	1.60789	−	4.94859i	0.0744045	−	0.228993i	0.981342	+	0.192273i	$0.0615858\pi$
$468$	6.57392			0.303880
$469$	1.13978	−	3.50789i	0.0526303	−	0.161979i
$470$		0			0
$471$	2.05355	+	6.32019i	0.0946227	+	0.291219i
$472$	2.32521	+	7.15627i	0.107027	+	0.329394i
$473$	−13.1823	−	9.57747i	−0.606121	−	0.440373i
$474$	15.5279			0.713222
$475$		0			0
$476$	0.511370			0.0234386
$477$	2.61599	+	1.90063i	0.119778	+	0.0870239i
$478$	3.05877	+	9.41393i	0.139905	+	0.430583i
$479$	−12.2490	−	37.6985i	−0.559670	−	1.72249i	−0.683279	−	0.730157i	$-0.739447\pi$
$479$	−12.2490	−	37.6985i	−0.559670	−	1.72249i	0.123609	−	0.992331i	$-0.460553\pi$
$480$		0			0
$481$	8.25361	−	25.4020i	0.376332	−	1.15823i
$482$	−21.4567			−0.977326
$483$	−0.620606	+	1.91003i	−0.0282385	+	0.0869093i
$484$	7.23497	−	5.25652i	0.328862	−	0.238933i
$485$		0			0
$486$	−0.809017	−	0.587785i	−0.0366978	−	0.0266625i
$487$	4.40354	−	3.19936i	0.199544	−	0.144977i	−0.483527	−	0.875330i	$-0.660644\pi$
$487$	4.40354	−	3.19936i	0.199544	−	0.144977i	0.683070	+	0.730353i	$0.260644\pi$
$488$	−10.1710	+	7.38968i	−0.460420	+	0.334515i
$489$	8.18191	+	5.94451i	0.369999	+	0.268820i
$490$		0			0
$491$	−0.707053	+	0.513704i	−0.0319088	+	0.0231831i	−0.603625	−	0.797268i	$-0.706278\pi$
$491$	−0.707053	+	0.513704i	−0.0319088	+	0.0231831i	0.571717	+	0.820451i	$0.306278\pi$
$492$	−2.45408	+	7.55288i	−0.110638	+	0.340510i
$493$	−5.93687			−0.267383
$494$	0.432474	−	1.33102i	0.0194579	−	0.0598854i
$495$		0			0
$496$	−0.722398	−	2.22331i	−0.0324366	−	0.0998297i
$497$	−1.66934	−	5.13771i	−0.0748803	−	0.230458i
$498$	−13.2119	−	9.59902i	−0.592040	−	0.430142i
$499$	−34.9604			−1.56504			−0.782522	−	0.622623i	$-0.786067\pi$
$499$	−34.9604			−1.56504			−0.782522	+	0.622623i	$0.786067\pi$
$500$		0			0
$501$	12.7885			0.571346
$502$	3.32306	+	2.41434i	0.148315	+	0.107757i
$503$	−0.0988002	−	0.304076i	−0.00440528	−	0.0135581i	0.948830	−	0.315788i	$-0.102269\pi$
$503$	−0.0988002	−	0.304076i	−0.00440528	−	0.0135581i	−0.953235	+	0.302230i	$0.902269\pi$
$504$	−0.164879	−	0.507445i	−0.00734429	−	0.0226034i
$505$		0			0
$506$	−1.66824	+	5.13432i	−0.0741624	+	0.228248i
$507$	30.2165			1.34196
$508$	−2.00323	+	6.16529i	−0.0888788	+	0.273541i
$509$	−16.6867	+	12.1236i	−0.739624	+	0.537368i	−0.892593	−	0.450863i	$-0.851116\pi$
$509$	−16.6867	+	12.1236i	−0.739624	+	0.537368i	0.152969	+	0.988231i	$0.451116\pi$
$510$		0			0
$511$	−6.03333	−	4.38347i	−0.266899	−	0.193913i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−0.172231	+	0.125133i	−0.00760418	+	0.00552476i
$514$	24.8973	+	18.0890i	1.09817	+	0.797870i
$515$		0			0
$516$	9.19103	−	6.67767i	0.404613	−	0.293968i
$517$	−4.49809	+	13.8437i	−0.197826	+	0.608845i
$518$	−2.16780			−0.0952477
$519$	−4.22041	+	12.9891i	−0.185256	+	0.570158i
$520$		0			0
$521$	−1.30417	−	4.01383i	−0.0571368	−	0.175849i	0.918415	−	0.395618i	$-0.129470\pi$
$521$	−1.30417	−	4.01383i	−0.0571368	−	0.175849i	−0.975552	+	0.219769i	$0.929470\pi$
$522$	1.91420	+	5.89130i	0.0837823	+	0.257855i
$523$	−17.4407	−	12.6714i	−0.762627	−	0.554081i	0.137088	−	0.990559i	$-0.456226\pi$
$523$	−17.4407	−	12.6714i	−0.762627	−	0.554081i	−0.899715	+	0.436478i	$0.856226\pi$
$524$	−9.45794			−0.413172
$525$		0			0
$526$	−28.3729			−1.23712
$527$	−1.81261	−	1.31694i	−0.0789586	−	0.0573668i
$528$	−0.443209	−	1.36406i	−0.0192882	−	0.0593629i
$529$	−2.72931	−	8.39994i	−0.118666	−	0.365215i
$530$		0			0
$531$	2.32521	−	7.15627i	0.100906	−	0.310556i
$532$	−0.113589			−0.00492470
$533$	−16.1329	+	49.6520i	−0.698795	+	2.15067i
$534$	−4.54845	+	3.30464i	−0.196831	+	0.143006i
$535$		0			0
$536$	5.59261	+	4.06327i	0.241564	+	0.175507i
$537$	−2.42011	+	1.75831i	−0.104435	+	0.0758767i
$538$	−8.62960	+	6.26977i	−0.372048	+	0.270309i
$539$	−7.79201	−	5.66123i	−0.335626	−	0.243846i
$540$		0			0
$541$	7.22987	−	5.25281i	0.310837	−	0.225836i	−0.421419	−	0.906866i	$-0.638468\pi$
$541$	7.22987	−	5.25281i	0.310837	−	0.225836i	0.732255	+	0.681030i	$0.238468\pi$
$542$	7.05917	−	21.7259i	0.303217	−	0.933206i
$543$	7.62285			0.327128
$544$	−0.296166	+	0.911505i	−0.0126980	+	0.0390805i
$545$		0			0
$546$	−1.08390	−	3.33590i	−0.0463867	−	0.142764i
$547$	−3.73249	−	11.4874i	−0.159590	−	0.491167i	0.839007	−	0.544120i	$-0.183136\pi$
$547$	−3.73249	−	11.4874i	−0.159590	−	0.491167i	−0.998597	+	0.0529536i	$0.983136\pi$
$548$	9.98010	+	7.25096i	0.426329	+	0.309746i
$549$	12.5721			0.536563
$550$		0			0
$551$	1.31874			0.0561801
$552$	−3.04515	−	2.21243i	−0.129610	−	0.0941673i
$553$	−2.56023	−	7.87957i	−0.108872	−	0.335073i
$554$	−9.72142	−	29.9194i	−0.413023	−	1.27116i
$555$		0			0
$556$	1.40268	−	4.31701i	0.0594870	−	0.183082i
$557$	8.23596			0.348969			0.174484	−	0.984660i	$-0.444174\pi$
$557$	8.23596			0.348969			0.174484	+	0.984660i	$0.444174\pi$
$558$	−0.722398	+	2.22331i	−0.0305815	+	0.0941203i
$559$	60.4211	−	43.8985i	2.55554	−	1.85671i
$560$		0			0
$561$	−1.11208	−	0.807974i	−0.0469521	−	0.0341127i
$562$	8.72000	−	6.33545i	0.367831	−	0.267245i
$563$	11.8406	−	8.60271i	0.499022	−	0.362561i	−0.309621	−	0.950860i	$-0.600202\pi$
$563$	11.8406	−	8.60271i	0.499022	−	0.362561i	0.808643	+	0.588299i	$0.200202\pi$
$564$	−8.21065	−	5.96538i	−0.345731	−	0.251188i
$565$		0			0
$566$	3.36897	−	2.44770i	0.141608	−	0.102885i
$567$	−0.164879	+	0.507445i	−0.00692426	+	0.0213107i
$568$	10.1247			0.424822
$569$	9.65590	−	29.7178i	0.404796	−	1.24583i	−0.516269	−	0.856427i	$-0.672679\pi$
$569$	9.65590	−	29.7178i	0.404796	−	1.24583i	0.921065	−	0.389408i	$-0.127321\pi$
$570$		0			0
$571$	8.10430	+	24.9425i	0.339154	+	1.04381i	0.964639	+	0.263574i	$0.0849012\pi$
$571$	8.10430	+	24.9425i	0.339154	+	1.04381i	−0.625485	+	0.780236i	$0.715099\pi$
$572$	−2.91362	−	8.96720i	−0.121825	−	0.374937i
$573$	6.79610	+	4.93766i	0.283911	+	0.206274i
$574$	4.23729			0.176861
$575$		0			0
$576$	1.00000			0.0416667
$577$	−7.22727	−	5.25092i	−0.300875	−	0.218599i	0.427096	−	0.904206i	$-0.359537\pi$
$577$	−7.22727	−	5.25092i	−0.300875	−	0.218599i	−0.727971	+	0.685608i	$0.759537\pi$
$578$	−4.96944	−	15.2944i	−0.206701	−	0.636162i
$579$	−3.25290	−	10.0114i	−0.135186	−	0.416060i
$580$		0			0
$581$	−2.69261	+	8.28699i	−0.111708	+	0.343802i
$582$	−5.56558			−0.230701
$583$	1.43313	−	4.41074i	0.0593544	−	0.182674i
$584$	11.3077	−	8.21552i	0.467916	−	0.339961i
$585$		0			0
$586$	14.5302	+	10.5568i	0.600237	+	0.436098i
$587$	−3.23089	+	2.34738i	−0.133353	+	0.0968867i	−0.652462	−	0.757821i	$-0.726264\pi$
$587$	−3.23089	+	2.34738i	−0.133353	+	0.0968867i	0.519109	+	0.854708i	$0.326264\pi$
$588$	5.43280	−	3.94716i	0.224045	−	0.162778i
$589$	0.402629	+	0.292527i	0.0165900	+	0.0120534i
$590$		0			0
$591$	8.25848	−	6.00014i	0.339709	−	0.246813i
$592$	1.25551	−	3.86406i	0.0516011	−	0.158812i
$593$	11.2114			0.460396			0.230198	−	0.973144i	$-0.426063\pi$
$593$	11.2114			0.460396			0.230198	+	0.973144i	$0.426063\pi$
$594$	−0.443209	+	1.36406i	−0.0181851	+	0.0559679i
$595$		0			0
$596$	3.42238	+	10.5330i	0.140186	+	0.431448i
$597$	1.18761	+	3.65508i	0.0486056	+	0.149593i
$598$	−20.0186	−	14.5443i	−0.818620	−	0.594763i
$599$	−6.64762			−0.271614			−0.135807	−	0.990735i	$-0.543363\pi$
$599$	−6.64762			−0.271614			−0.135807	+	0.990735i	$0.543363\pi$
$600$		0			0
$601$	−10.7465			−0.438359			−0.219179	−	0.975685i	$-0.570338\pi$
$601$	−10.7465			−0.438359			−0.219179	+	0.975685i	$0.570338\pi$
$602$	−4.90396	−	3.56293i	−0.199870	−	0.145214i
$603$	−2.13619	−	6.57451i	−0.0869923	−	0.267735i
$604$	−0.504894	−	1.55390i	−0.0205438	−	0.0632274i
$605$		0			0
$606$	−2.91313	+	8.96568i	−0.118338	+	0.364206i
$607$	15.4591			0.627466			0.313733	−	0.949511i	$-0.398420\pi$
$607$	15.4591			0.627466			0.313733	+	0.949511i	$0.398420\pi$
$608$	0.0657863	−	0.202470i	0.00266799	−	0.00821122i
$609$	2.67390	−	1.94270i	0.108352	−	0.0787223i
$610$		0			0
$611$	−53.9762	−	39.2160i	−2.18364	−	1.58651i
$612$	0.775373	−	0.563341i	0.0313426	−	0.0227717i
$613$	19.8101	−	14.3929i	0.800123	−	0.581324i	−0.110827	−	0.993840i	$-0.535350\pi$
$613$	19.8101	−	14.3929i	0.800123	−	0.581324i	0.910950	+	0.412516i	$0.135350\pi$
$614$	16.8416	+	12.2362i	0.679673	+	0.493812i
$615$		0			0
$616$	−0.619107	+	0.449808i	−0.0249445	+	0.0181233i
$617$	−5.84526	+	17.9899i	−0.235321	+	0.724244i	0.761757	+	0.647862i	$0.224337\pi$
$617$	−5.84526	+	17.9899i	−0.235321	+	0.724244i	−0.997079	+	0.0763819i	$0.975663\pi$
$618$	7.99871			0.321755
$619$	0.788010	−	2.42524i	0.0316728	−	0.0974788i	−0.933970	−	0.357350i	$-0.883680\pi$
$619$	0.788010	−	2.42524i	0.0316728	−	0.0974788i	0.965643	+	0.259872i	$0.0836802\pi$
$620$		0			0
$621$	1.16314	+	3.57979i	0.0466753	+	0.143652i
$622$	−6.01118	−	18.5005i	−0.241026	−	0.741803i
$623$	2.42687	+	1.76322i	0.0972304	+	0.0706420i
$624$	6.57392			0.263168
$625$		0			0
$626$	5.88310			0.235136
$627$	0.247023	+	0.179472i	0.00986513	+	0.00716744i
$628$	2.05355	+	6.32019i	0.0819457	+	0.252203i
$629$	−1.20330	−	3.70336i	−0.0479785	−	0.147663i
$630$		0			0
$631$	−11.2646	+	34.6688i	−0.448436	+	1.38014i	0.430235	+	0.902717i	$0.358431\pi$
$631$	−11.2646	+	34.6688i	−0.448436	+	1.38014i	−0.878671	+	0.477428i	$0.841569\pi$
$632$	15.5279			0.617668
$633$	1.62209	−	4.99228i	0.0644723	−	0.198425i
$634$	8.70586	−	6.32518i	0.345754	−	0.251205i
$635$		0			0
$636$	2.61599	+	1.90063i	0.103731	+	0.0753649i
$637$	35.7148	−	25.9483i	1.41507	−	1.02811i
$638$	7.18767	−	5.22215i	0.284563	−	0.206747i
$639$	−8.19103	−	5.95113i	−0.324032	−	0.235423i
$640$		0			0
$641$	16.4772	−	11.9714i	0.650809	−	0.472840i	−0.212738	−	0.977109i	$-0.568238\pi$
$641$	16.4772	−	11.9714i	0.650809	−	0.472840i	0.863546	+	0.504269i	$0.168238\pi$
$642$	5.84845	−	17.9997i	0.230820	−	0.710391i
$643$	−11.4218			−0.450433			−0.225217	−	0.974309i	$-0.572309\pi$
$643$	−11.4218			−0.450433			−0.225217	+	0.974309i	$0.572309\pi$
$644$	−0.620606	+	1.91003i	−0.0244553	+	0.0752656i
$645$		0			0
$646$	−0.0630505	−	0.194049i	−0.00248069	−	0.00763477i
$647$	1.82078	+	5.60379i	0.0715823	+	0.220308i	0.980447	−	0.196783i	$-0.0630496\pi$
$647$	1.82078	+	5.60379i	0.0715823	+	0.220308i	−0.908865	+	0.417091i	$0.863050\pi$
$648$	−0.809017	−	0.587785i	−0.0317812	−	0.0230904i
$649$	−10.7921			−0.423627
$650$		0			0
$651$	1.24732			0.0488862
$652$	8.18191	+	5.94451i	0.320428	+	0.232805i
$653$	5.28614	+	16.2691i	0.206863	+	0.636658i	0.999632	+	0.0271359i	$0.00863868\pi$
$653$	5.28614	+	16.2691i	0.206863	+	0.636658i	−0.792769	+	0.609522i	$0.791361\pi$
$654$	−0.820514	−	2.52528i	−0.0320847	−	0.0987464i
$655$		0			0
$656$	−2.45408	+	7.55288i	−0.0958157	+	0.294890i
$657$	−13.9771			−0.545298
$658$	−1.67334	+	5.15002i	−0.0652337	+	0.200769i
$659$	24.0433	−	17.4685i	0.936593	−	0.680475i	−0.0110052	−	0.999939i	$-0.503503\pi$
$659$	24.0433	−	17.4685i	0.936593	−	0.680475i	0.947598	+	0.319465i	$0.103503\pi$
$660$		0			0
$661$	−37.4604	−	27.2166i	−1.45704	−	1.05860i	−0.984121	−	0.177497i	$-0.943200\pi$
$661$	−37.4604	−	27.2166i	−1.45704	−	1.05860i	−0.472920	−	0.881105i	$-0.656800\pi$
$662$	0.499238	−	0.362718i	0.0194034	−	0.0140974i
$663$	5.09724	−	3.70336i	0.197960	−	0.143827i
$664$	−13.2119	−	9.59902i	−0.512722	−	0.372514i
$665$		0			0
$666$	−3.28696	+	2.38812i	−0.127367	+	0.0925377i
$667$	7.20507	−	22.1749i	0.278981	−	0.858616i
$668$	12.7885			0.494800
$669$	−5.95730	+	18.3347i	−0.230323	+	0.708860i
$670$		0			0
$671$	−5.57205	−	17.1490i	−0.215107	−	0.662030i
$672$	−0.164879	−	0.507445i	−0.00636034	−	0.0195751i
$673$	−15.9441	−	11.5841i	−0.614601	−	0.446534i	0.236430	−	0.971648i	$-0.424023\pi$
$673$	−15.9441	−	11.5841i	−0.614601	−	0.446534i	−0.851032	+	0.525114i	$0.824023\pi$
$674$	−15.4106			−0.593595
$675$		0			0
$676$	30.2165			1.16217
$677$	20.0453	+	14.5638i	0.770405	+	0.559732i	0.902084	−	0.431560i	$-0.142037\pi$
$677$	20.0453	+	14.5638i	0.770405	+	0.559732i	−0.131679	+	0.991292i	$0.542037\pi$
$678$	0.946466	+	2.91292i	0.0363488	+	0.111870i
$679$	0.917646	+	2.82422i	0.0352160	+	0.108384i
$680$		0			0
$681$	2.60797	−	8.02651i	0.0999377	−	0.307577i
$682$	3.35289			0.128389
$683$	−5.12579	+	15.7755i	−0.196133	+	0.603635i	0.803829	+	0.594861i	$0.202793\pi$
$683$	−5.12579	+	15.7755i	−0.196133	+	0.603635i	−0.999962	+	0.00877377i	$0.997207\pi$
$684$	−0.172231	+	0.125133i	−0.00658541	+	0.00478458i
$685$		0			0
$686$	−5.92033	−	4.30137i	−0.226039	−	0.164227i
$687$	−4.81825	+	3.50066i	−0.183828	+	0.133559i
$688$	9.19103	−	6.67767i	0.350405	−	0.254584i
$689$	17.1973	+	12.4946i	0.655166	+	0.476006i
$690$		0			0
$691$	−34.2128	+	24.8570i	−1.30152	+	0.945606i	−0.999969	−	0.00784530i	$-0.997503\pi$
$691$	−34.2128	+	24.8570i	−1.30152	+	0.945606i	−0.301546	+	0.953452i	$0.597503\pi$
$692$	−4.22041	+	12.9891i	−0.160436	+	0.493771i
$693$	0.765259			0.0290698
$694$	7.00126	−	21.5477i	0.265764	−	0.817938i
$695$		0			0
$696$	1.91420	+	5.89130i	0.0725576	+	0.223309i
$697$	2.35202	+	7.23878i	0.0890892	+	0.274188i
$698$	13.7163	+	9.96550i	0.519171	+	0.377200i
$699$	−2.09293			−0.0791617
$700$		0			0
$701$	−22.7240			−0.858273			−0.429137	−	0.903240i	$-0.641182\pi$
$701$	−22.7240			−0.858273			−0.429137	+	0.903240i	$0.641182\pi$
$702$	−5.31842	−	3.86406i	−0.200731	−	0.145839i
$703$	0.267284	+	0.822615i	0.0100808	+	0.0310255i
$704$	−0.443209	−	1.36406i	−0.0167041	−	0.0514098i
$705$		0			0
$706$	1.87343	−	5.76583i	0.0705076	−	0.217000i
$707$	5.02990			0.189169
$708$	2.32521	−	7.15627i	0.0873869	−	0.268949i
$709$	−37.5483	+	27.2804i	−1.41016	+	1.02454i	−0.416855	+	0.908973i	$0.636868\pi$
$709$	−37.5483	+	27.2804i	−1.41016	+	1.02454i	−0.993300	+	0.115565i	$0.963132\pi$
$710$		0			0
$711$	−12.5624	−	9.12709i	−0.471125	−	0.342293i
$712$	−4.54845	+	3.30464i	−0.170460	+	0.123847i
$713$	7.11873	−	5.17206i	0.266599	−	0.193695i
$714$	−0.413707	−	0.300576i	−0.0154826	−	0.0112488i
$715$		0			0
$716$	−2.42011	+	1.75831i	−0.0904437	+	0.0657112i
$717$	3.05877	−	9.41393i	0.114232	−	0.351570i
$718$	18.8987			0.705294
$719$	−8.71631	+	26.8260i	−0.325063	+	1.00044i	0.646349	+	0.763042i	$0.276295\pi$
$719$	−8.71631	+	26.8260i	−0.325063	+	1.00044i	−0.971412	+	0.237400i	$0.923705\pi$
$720$		0			0
$721$	−1.31882	−	4.05891i	−0.0491154	−	0.151162i
$722$	−5.85732	−	18.0270i	−0.217987	−	0.670894i
$723$	17.3588	+	12.6119i	0.645582	+	0.469043i
$724$	7.62285			0.283301
$725$		0			0
$726$	−8.94292			−0.331903
$727$	0.688953	+	0.500553i	0.0255518	+	0.0185645i	0.600488	−	0.799634i	$-0.294973\pi$
$727$	0.688953	+	0.500553i	0.0255518	+	0.0185645i	−0.574936	+	0.818198i	$0.694973\pi$
$728$	−1.08390	−	3.33590i	−0.0401720	−	0.123637i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	3.36466	−	10.3554i	0.124447	−	0.383007i
$732$	12.5721			0.464677
$733$	−9.49607	+	29.2259i	−0.350745	+	1.07948i	0.607690	+	0.794174i	$0.292096\pi$
$733$	−9.49607	+	29.2259i	−0.350745	+	1.07948i	−0.958436	+	0.285309i	$0.907904\pi$
$734$	20.2645	−	14.7230i	0.747978	−	0.543437i
$735$		0			0
$736$	−3.04515	−	2.21243i	−0.112246	−	0.0815512i
$737$	−8.02122	+	5.82776i	−0.295465	+	0.214668i
$738$	6.42486	−	4.66793i	0.236502	−	0.171829i
$739$	−1.67050	−	1.21369i	−0.0614502	−	0.0446462i	0.556636	−	0.830756i	$-0.312092\pi$
$739$	−1.67050	−	1.21369i	−0.0614502	−	0.0446462i	−0.618086	+	0.786110i	$0.712092\pi$
$740$		0			0
$741$	−1.13223	+	0.822615i	−0.0415936	+	0.0302195i
$742$	0.533143	−	1.64085i	0.0195723	−	0.0602373i
$743$	37.8972			1.39031			0.695157	−	0.718858i	$-0.255335\pi$
$743$	37.8972			1.39031			0.695157	+	0.718858i	$0.255335\pi$
$744$	−0.722398	+	2.22331i	−0.0264844	+	0.0815106i
$745$		0			0
$746$	−3.67589	−	11.3132i	−0.134584	−	0.414207i
$747$	5.04650	+	15.5315i	0.184642	+	0.568269i
$748$	−1.11208	−	0.807974i	−0.0406617	−	0.0295424i
$749$	−10.0981			−0.368978
$750$		0			0
$751$	−40.6331			−1.48272			−0.741361	−	0.671106i	$-0.765819\pi$
$751$	−40.6331			−1.48272			−0.741361	+	0.671106i	$0.765819\pi$
$752$	−8.21065	−	5.96538i	−0.299411	−	0.217535i
$753$	−1.26930	−	3.90649i	−0.0462557	−	0.142360i
$754$	12.5838	+	38.7290i	0.458275	+	1.41043i
$755$		0			0
$756$	−0.164879	+	0.507445i	−0.00599659	+	0.0184556i
$757$	−10.0032			−0.363572			−0.181786	−	0.983338i	$-0.558188\pi$
$757$	−10.0032			−0.363572			−0.181786	+	0.983338i	$0.558188\pi$
$758$	8.50366	−	26.1716i	0.308867	−	0.950594i
$759$	4.36751	−	3.17318i	0.158531	−	0.115179i
$760$		0			0
$761$	24.4172	+	17.7401i	0.885121	+	0.643078i	0.934601	−	0.355697i	$-0.115756\pi$
$761$	24.4172	+	17.7401i	0.885121	+	0.643078i	−0.0494802	+	0.998775i	$0.515756\pi$
$762$	5.24451	−	3.81036i	0.189989	−	0.138035i
$763$	−1.14616	+	0.832732i	−0.0414937	+	0.0301469i
$764$	6.79610	+	4.93766i	0.245874	+	0.178638i
$765$		0			0
$766$	17.8238	−	12.9497i	0.644000	−	0.467893i
$767$	15.2858	−	47.0448i	0.551938	−	1.69869i
$768$	1.00000			0.0360844
$769$	6.53471	−	20.1118i	0.235648	−	0.725249i	−0.761387	−	0.648297i	$-0.775481\pi$
$769$	6.53471	−	20.1118i	0.235648	−	0.725249i	0.997035	−	0.0769513i	$-0.0245186\pi$
$770$		0			0
$771$	−9.50993	−	29.2685i	−0.342492	−	1.05408i
$772$	−3.25290	−	10.0114i	−0.117075	−	0.360319i
$773$	−23.8231	−	17.3085i	−0.856858	−	0.622544i	0.0701705	−	0.997535i	$-0.477646\pi$
$773$	−23.8231	−	17.3085i	−0.856858	−	0.622544i	−0.927028	+	0.374991i	$0.877646\pi$
$774$	−11.3607			−0.408353
$775$		0			0
$776$	−5.56558			−0.199793
$777$	1.75379	+	1.27420i	0.0629168	+	0.0457117i
$778$	5.40446	+	16.6332i	0.193759	+	0.596330i
$779$	−0.522446	−	1.60792i	−0.0187186	−	0.0576099i
$780$		0			0
$781$	−4.48734	+	13.8106i	−0.160570	+	0.494183i
$782$	−3.60748			−0.129003
$783$	1.91420	−	5.89130i	0.0684079	−	0.210538i
$784$	5.43280	−	3.94716i	0.194029	−	0.140970i
$785$		0			0
$786$	7.65163	+	5.55924i	0.272925	+	0.198291i
$787$	−4.18161	+	3.03811i	−0.149058	+	0.108297i	−0.659815	−	0.751428i	$-0.729365\pi$
$787$	−4.18161	+	3.03811i	−0.149058	+	0.108297i	0.510757	+	0.859725i	$0.329365\pi$
$788$	8.25848	−	6.00014i	0.294196	−	0.213746i
$789$	22.9541	+	16.6771i	0.817189	+	0.593722i
$790$		0			0
$791$	1.32210	−	0.960559i	0.0470083	−	0.0341536i
$792$	−0.443209	+	1.36406i	−0.0157487	+	0.0484696i
$793$	82.6478			2.93491
$794$	−7.57062	+	23.3000i	−0.268671	+	0.826885i
$795$		0			0
$796$	1.18761	+	3.65508i	0.0420937	+	0.129551i
$797$	1.16131	+	3.57413i	0.0411356	+	0.126602i	0.969515	−	0.245031i	$-0.0787980\pi$
$797$	1.16131	+	3.57413i	0.0411356	+	0.126602i	−0.928380	+	0.371633i	$0.878798\pi$
$798$	0.0918954	+	0.0667659i	0.00325306	+	0.00236349i
$799$	−9.72686			−0.344111
$800$		0			0
$801$	5.62220			0.198650
$802$	−0.842226	−	0.611913i	−0.0297400	−	0.0216074i
$803$	6.19476	+	19.0655i	0.218608	+	0.672808i
$804$	−2.13619	−	6.57451i	−0.0753375	−	0.231865i
$805$		0			0
$806$	−4.74899	+	14.6159i	−0.167276	+	0.514823i
$807$	10.6668			0.375488
$808$	−2.91313	+	8.96568i	−0.102483	+	0.315412i
$809$	16.8961	−	12.2757i	0.594034	−	0.431591i	−0.249722	−	0.968317i	$-0.580339\pi$
$809$	16.8961	−	12.2757i	0.594034	−	0.431591i	0.843756	+	0.536727i	$0.180339\pi$
$810$		0			0
$811$	29.5317	+	21.4560i	1.03700	+	0.753423i	0.969697	−	0.244310i	$-0.0785614\pi$
$811$	29.5317	+	21.4560i	1.03700	+	0.753423i	0.0673004	+	0.997733i	$0.478561\pi$
$812$	2.67390	−	1.94270i	0.0938355	−	0.0681755i
$813$	−18.4811	+	13.4273i	−0.648162	+	0.470917i
$814$	4.71434	+	3.42516i	0.165237	+	0.120052i
$815$		0			0
$816$	0.775373	−	0.563341i	0.0271435	−	0.0197209i
$817$	−0.747381	+	2.30020i	−0.0261476	+	0.0804739i
$818$	22.2568			0.778190
$819$	−1.08390	+	3.33590i	−0.0378746	+	0.116566i
$820$		0			0
$821$	10.2662	+	31.5961i	0.358293	+	1.10271i	0.954076	+	0.299566i	$0.0968419\pi$
$821$	10.2662	+	31.5961i	0.358293	+	1.10271i	−0.595783	+	0.803146i	$0.703158\pi$
$822$	−3.81206	−	11.7323i	−0.132961	−	0.409211i
$823$	−26.5275	−	19.2733i	−0.924690	−	0.671827i	0.0199969	−	0.999800i	$-0.493634\pi$
$823$	−26.5275	−	19.2733i	−0.924690	−	0.671827i	−0.944687	+	0.327973i	$0.893634\pi$
$824$	7.99871			0.278648
$825$		0			0
$826$	−4.01479			−0.139692
$827$	4.19811	+	3.05011i	0.145983	+	0.106063i	0.658379	−	0.752686i	$-0.271242\pi$
$827$	4.19811	+	3.05011i	0.145983	+	0.106063i	−0.512397	+	0.858749i	$0.671242\pi$
$828$	1.16314	+	3.57979i	0.0404220	+	0.124406i
$829$	−1.71758	−	5.28616i	−0.0596539	−	0.183596i	0.916789	−	0.399372i	$-0.130772\pi$
$829$	−1.71758	−	5.28616i	−0.0596539	−	0.183596i	−0.976443	+	0.215776i	$0.930772\pi$
$830$		0			0
$831$	−9.72142	+	29.9194i	−0.337232	+	1.03789i
$832$	6.57392			0.227910
$833$	1.98885	−	6.12104i	0.0689095	−	0.212082i
$834$	−3.67227	+	2.66806i	−0.127160	+	0.0923874i
$835$		0			0
$836$	0.247023	+	0.179472i	0.00854346	+	0.00620718i
$837$	1.89126	−	1.37408i	0.0653716	−	0.0474952i
$838$	18.7121	−	13.5951i	0.646397	−	0.469635i
$839$	−35.1423	−	25.5324i	−1.21325	−	0.881475i	−0.217725	−	0.976010i	$-0.569864\pi$
$839$	−35.1423	−	25.5324i	−1.21325	−	0.881475i	−0.995522	+	0.0945346i	$0.969864\pi$
$840$		0			0
$841$	−7.58178	+	5.50849i	−0.261441	+	0.189948i
$842$	3.01643	−	9.28363i	0.103953	−	0.319935i
$843$	−10.7785			−0.371232
$844$	1.62209	−	4.99228i	0.0558347	−	0.171841i
$845$		0			0
$846$	3.13619	+	9.65219i	0.107824	+	0.331849i
$847$	1.47450	+	4.53804i	0.0506644	+	0.155929i
$848$	2.61599	+	1.90063i	0.0898336	+	0.0652679i
$849$	−4.16428			−0.142918
$850$		0			0
$851$	15.2928			0.524231
$852$	−8.19103	−	5.95113i	−0.280620	−	0.203882i
$853$	−1.03317	−	3.17978i	−0.0353752	−	0.108874i	0.931810	−	0.362947i	$-0.118229\pi$
$853$	−1.03317	−	3.17978i	−0.0353752	−	0.108874i	−0.967185	+	0.254074i	$0.918229\pi$
$854$	−2.07287	−	6.37963i	−0.0709321	−	0.218306i
$855$		0			0
$856$	5.84845	−	17.9997i	0.199896	−	0.615217i
$857$	34.5415			1.17991			0.589957	−	0.807434i	$-0.299145\pi$
$857$	34.5415			1.17991			0.589957	+	0.807434i	$0.299145\pi$
$858$	−2.91362	+	8.96720i	−0.0994693	+	0.306135i
$859$	19.2961	−	14.0195i	0.658375	−	0.478338i	−0.207739	−	0.978184i	$-0.566610\pi$
$859$	19.2961	−	14.0195i	0.658375	−	0.478338i	0.866114	+	0.499847i	$0.166610\pi$
$860$		0			0
$861$	−3.42804	−	2.49062i	−0.116827	−	0.0848801i
$862$	−6.87097	+	4.99205i	−0.234026	+	0.170030i
$863$	4.63616	−	3.36837i	0.157817	−	0.114661i	−0.506074	−	0.862490i	$-0.668904\pi$
$863$	4.63616	−	3.36837i	0.157817	−	0.114661i	0.663891	+	0.747829i	$0.268904\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$		0			0
$866$	−17.8018	+	12.9337i	−0.604928	+	0.439506i
$867$	−4.96944	+	15.2944i	−0.168771	+	0.519424i
$868$	1.24732			0.0423367
$869$	−6.88211	+	21.1810i	−0.233460	+	0.718515i
$870$		0			0
$871$	−14.0431	−	43.2203i	−0.475834	−	1.46447i
$872$	−0.820514	−	2.52528i	−0.0277861	−	0.0855169i
$873$	4.50265	+	3.27137i	0.152392	+	0.110719i
$874$	0.801317			0.0271049
$875$		0			0
$876$	−13.9771			−0.472242
$877$	40.3280	+	29.3000i	1.36178	+	0.989392i	0.998329	+	0.0577792i	$0.0184019\pi$
$877$	40.3280	+	29.3000i	1.36178	+	0.989392i	0.363452	+	0.931613i	$0.381598\pi$
$878$	−11.8533	−	36.4808i	−0.400031	−	1.23117i
$879$	−5.55004	−	17.0813i	−0.187198	−	0.576137i
$880$		0			0
$881$	−2.36586	+	7.28138i	−0.0797079	+	0.245316i	−0.982968	−	0.183778i	$-0.941167\pi$
$881$	−2.36586	+	7.28138i	−0.0797079	+	0.245316i	0.903260	+	0.429094i	$0.141167\pi$
$882$	−6.71531			−0.226116
$883$	−12.0504	+	37.0873i	−0.405528	+	1.24809i	0.514925	+	0.857235i	$0.327820\pi$
$883$	−12.0504	+	37.0873i	−0.405528	+	1.24809i	−0.920453	+	0.390852i	$0.872180\pi$
$884$	5.09724	−	3.70336i	0.171439	−	0.124558i
$885$		0			0
$886$	−10.3132	−	7.49296i	−0.346478	−	0.251731i
$887$	−26.3204	+	19.1229i	−0.883752	+	0.642083i	−0.934241	−	0.356641i	$-0.883922\pi$
$887$	−26.3204	+	19.1229i	−0.883752	+	0.642083i	0.0504894	+	0.998725i	$0.483922\pi$
$888$	−3.28696	+	2.38812i	−0.110303	+	0.0801400i
$889$	−2.79826	−	2.03305i	−0.0938505	−	0.0681864i
$890$		0			0
$891$	1.16034	−	0.843033i	0.0388727	−	0.0282427i
$892$	−5.95730	+	18.3347i	−0.199465	+	0.613891i
$893$	2.16059			0.0723015
$894$	3.42238	−	10.5330i	0.114461	−	0.352276i
$895$		0			0
$896$	−0.164879	−	0.507445i	−0.00550822	−	0.0169525i
$897$	7.64642	+	23.5332i	0.255306	+	0.785752i
$898$	−14.5912	−	10.6012i	−0.486916	−	0.353765i
$899$	−14.4810			−0.482969
$900$		0			0
$901$	3.09907			0.103245
$902$	−9.21488	−	6.69500i	−0.306822	−	0.222919i
$903$	1.87315	+	5.76495i	0.0623344	+	0.191845i
$904$	0.946466	+	2.91292i	0.0314790	+	0.0968824i
$905$		0			0
$906$	−0.504894	+	1.55390i	−0.0167740	+	0.0516250i
$907$	−16.5820			−0.550595			−0.275297	−	0.961359i	$-0.588776\pi$
$907$	−16.5820			−0.550595			−0.275297	+	0.961359i	$0.588776\pi$
$908$	2.60797	−	8.02651i	0.0865486	−	0.266369i
$909$	7.62667	−	5.54110i	0.252961	−	0.183787i
$910$		0			0
$911$	23.1152	+	16.7942i	0.765842	+	0.556417i	0.900697	−	0.434449i	$-0.143057\pi$
$911$	23.1152	+	16.7942i	0.765842	+	0.556417i	−0.134855	+	0.990865i	$0.543057\pi$
$912$	−0.172231	+	0.125133i	−0.00570313	+	0.00414357i
$913$	18.9492	−	13.7674i	0.627128	−	0.455635i
$914$	17.1103	+	12.4314i	0.565960	+	0.411194i
$915$		0			0
$916$	−4.81825	+	3.50066i	−0.159199	+	0.115665i
$917$	1.55941	−	4.79938i	0.0514964	−	0.158490i
$918$	−0.958413			−0.0316324
$919$	−0.118310	+	0.364122i	−0.00390270	+	0.0120113i	−0.952989	−	0.303005i	$-0.902010\pi$
$919$	−0.118310	+	0.364122i	−0.00390270	+	0.0120113i	0.949086	+	0.315016i	$0.102010\pi$
$920$		0			0
$921$	−6.43293	−	19.7985i	−0.211972	−	0.652384i
$922$	9.89116	+	30.4419i	0.325748	+	1.00255i
$923$	−53.8472	−	39.1223i	−1.77240	−	1.28773i
$924$	0.765259			0.0251752
$925$		0			0
$926$	28.7776			0.945689
$927$	−6.47109	−	4.70153i	−0.212539	−	0.154418i
$928$	1.91420	+	5.89130i	0.0628367	+	0.193391i
$929$	−1.93355	−	5.95087i	−0.0634378	−	0.195242i	0.914314	−	0.405006i	$-0.132730\pi$
$929$	−1.93355	−	5.95087i	−0.0634378	−	0.195242i	−0.977752	+	0.209764i	$0.932730\pi$
$930$		0			0
$931$	−0.441776	+	1.35965i	−0.0144786	+	0.0445606i
$932$	−2.09293			−0.0685561
$933$	−6.01118	+	18.5005i	−0.196797	+	0.605679i
$934$	−4.20952	+	3.05840i	−0.137740	+	0.100074i
$935$		0			0
$936$	−5.31842	−	3.86406i	−0.173838	−	0.126301i
$937$	−3.99019	+	2.89904i	−0.130354	+	0.0947075i	−0.651052	−	0.759034i	$-0.725672\pi$
$937$	−3.99019	+	2.89904i	−0.130354	+	0.0947075i	0.520698	+	0.853741i	$0.325672\pi$
$938$	−2.98399	+	2.16800i	−0.0974307	+	0.0707876i
$939$	−4.75953	−	3.45800i	−0.155321	−	0.112847i
$940$		0			0
$941$	−24.1174	+	17.5223i	−0.786204	+	0.571210i	−0.906834	−	0.421487i	$-0.861508\pi$
$941$	−24.1174	+	17.5223i	−0.786204	+	0.571210i	0.120631	+	0.992697i	$0.461508\pi$
$942$	2.05355	−	6.32019i	0.0669084	−	0.205923i
$943$	−29.8921			−0.973422
$944$	2.32521	−	7.15627i	0.0756793	−	0.232917i
$945$		0			0
$946$	5.03518	+	15.4967i	0.163708	+	0.503840i
$947$	8.31642	+	25.5953i	0.270247	+	0.831736i	0.990438	+	0.137960i	$0.0440545\pi$
$947$	8.31642	+	25.5953i	0.270247	+	0.831736i	−0.720190	+	0.693777i	$0.755946\pi$
$948$	−12.5624	−	9.12709i	−0.408007	−	0.296434i
$949$	−91.8843			−2.98269
$950$		0			0
$951$	−10.7610			−0.348950
$952$	−0.413707	−	0.300576i	−0.0134083	−	0.00974172i
$953$	−11.5058	−	35.4113i	−0.372711	−	1.14709i	−0.945010	−	0.327041i	$-0.893949\pi$
$953$	−11.5058	−	35.4113i	−0.372711	−	1.14709i	0.572300	−	0.820045i	$-0.306051\pi$
$954$	−0.999220	−	3.07528i	−0.0323510	−	0.0995660i
$955$		0			0
$956$	3.05877	−	9.41393i	0.0989278	−	0.304468i
$957$	−8.88445			−0.287194
$958$	−12.2490	+	37.6985i	−0.395747	+	1.21798i
$959$	−5.32497	+	3.86882i	−0.171952	+	0.124931i
$960$		0			0
$961$	20.6583	+	15.0091i	0.666396	+	0.484165i
$962$	−21.6082	+	15.6993i	−0.696678	+	0.506166i
$963$	−15.3114	+	11.1244i	−0.493405	+	0.358479i
$964$	17.3588	+	12.6119i	0.559091	+	0.406203i
$965$		0			0
$966$	1.62477	−	1.18046i	0.0522760	−	0.0379807i
$967$	−4.97039	+	15.2973i	−0.159837	+	0.491928i	−0.998619	−	0.0525399i	$-0.983268\pi$
$967$	−4.97039	+	15.2973i	−0.159837	+	0.491928i	0.838782	+	0.544468i	$0.183268\pi$
$968$	−8.94292			−0.287436
$969$	−0.0630505	+	0.194049i	−0.00202547	+	0.00623377i
$970$		0			0
$971$	3.78758	+	11.6570i	0.121549	+	0.374090i	0.993257	−	0.115937i	$-0.0369870\pi$
$971$	3.78758	+	11.6570i	0.121549	+	0.374090i	−0.871707	+	0.490027i	$0.836987\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	1.95937	+	1.42357i	0.0628146	+	0.0456375i
$974$	−5.44308			−0.174407
$975$		0			0
$976$	12.5721			0.402422
$977$	14.5800	+	10.5930i	0.466454	+	0.338899i	0.796058	−	0.605221i	$-0.206915\pi$
$977$	14.5800	+	10.5930i	0.466454	+	0.338899i	−0.329604	+	0.944119i	$0.606915\pi$
$978$	−3.12521	−	9.61841i	−0.0999333	−	0.307563i
$979$	−2.49180	−	7.66899i	−0.0796384	−	0.245102i
$980$		0			0
$981$	−0.820514	+	2.52528i	−0.0261970	+	0.0806261i
$982$	0.873965			0.0278893
$983$	−15.2663	+	46.9850i	−0.486921	+	1.49859i	0.342259	+	0.939606i	$0.388808\pi$
$983$	−15.2663	+	46.9850i	−0.486921	+	1.49859i	−0.829180	+	0.558982i	$0.811192\pi$
$984$	6.42486	−	4.66793i	0.204817	−	0.148808i
$985$		0			0
$986$	4.80303	+	3.48961i	0.152960	+	0.111132i
$987$	4.38087	−	3.18289i	0.139444	−	0.101312i
$988$	−1.13223	+	0.822615i	−0.0360211	+	0.0261709i
$989$	34.5951	+	25.1348i	1.10006	+	0.799241i
$990$		0			0
$991$	24.7287	−	17.9665i	0.785533	−	0.570723i	−0.121101	−	0.992640i	$-0.538643\pi$
$991$	24.7287	−	17.9665i	0.785533	−	0.570723i	0.906635	+	0.421917i	$0.138643\pi$
$992$	−0.722398	+	2.22331i	−0.0229362	+	0.0705902i
$993$	−0.617092			−0.0195828
$994$	−1.66934	+	5.13771i	−0.0529484	+	0.162958i
$995$		0			0
$996$	5.04650	+	15.5315i	0.159905	+	0.492136i
$997$	−2.10456	−	6.47717i	−0.0666521	−	0.205134i	0.912184	−	0.409782i	$-0.134395\pi$
$997$	−2.10456	−	6.47717i	−0.0666521	−	0.205134i	−0.978836	+	0.204648i	$0.934395\pi$
$998$	28.2836	+	20.5492i	0.895301	+	0.650474i
$999$	4.06291			0.128545

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.g.f.451.2		16
5.2	odd	4		150.2.h.b.109.3	✓	16
5.3	odd	4		750.2.h.d.49.2		16
5.4	even	2		750.2.g.g.451.3		16
15.2	even	4		450.2.l.c.109.2		16
25.2	odd	20		750.2.h.d.199.1		16
25.6	even	5		3750.2.a.v.1.3		8
25.8	odd	20		3750.2.c.k.1249.6		16
25.11	even	5	inner	750.2.g.f.301.2		16
25.14	even	10		750.2.g.g.301.3		16
25.17	odd	20		3750.2.c.k.1249.11		16
25.19	even	10		3750.2.a.u.1.6		8
25.23	odd	20		150.2.h.b.139.3	yes	16
75.23	even	20		450.2.l.c.289.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.109.3	✓	16	5.2	odd	4
150.2.h.b.139.3	yes	16	25.23	odd	20
450.2.l.c.109.2		16	15.2	even	4
450.2.l.c.289.2		16	75.23	even	20
750.2.g.f.301.2		16	25.11	even	5	inner
750.2.g.f.451.2		16	1.1	even	1	trivial
750.2.g.g.301.3		16	25.14	even	10
750.2.g.g.451.3		16	5.4	even	2
750.2.h.d.49.2		16	5.3	odd	4
750.2.h.d.199.1		16	25.2	odd	20
3750.2.a.u.1.6		8	25.19	even	10
3750.2.a.v.1.3		8	25.6	even	5
3750.2.c.k.1249.6		16	25.8	odd	20
3750.2.c.k.1249.11		16	25.17	odd	20

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.309017 - 0.951057i) q^{6} -0.533559 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.309017 - 0.951057i) q^{6} -0.533559 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(1.16034 + 0.843033i) q^{11} +(-0.809017 + 0.587785i) q^{12} +(-5.31842 + 3.86406i) q^{13} +(0.431658 + 0.313618i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-0.296166 + 0.911505i) q^{17} +1.00000 q^{18} +(0.0657863 - 0.202470i) q^{19} +(-0.164879 - 0.507445i) q^{21} +(-0.443209 - 1.36406i) q^{22} +(-3.04515 - 2.21243i) q^{23} +1.00000 q^{24} +6.57392 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.164879 - 0.507445i) q^{28} +(1.91420 + 5.89130i) q^{29} +(-0.722398 + 2.22331i) q^{31} +1.00000 q^{32} +(-0.443209 + 1.36406i) q^{33} +(0.775373 - 0.563341i) q^{34} +(-0.809017 - 0.587785i) q^{36} +(-3.28696 + 2.38812i) q^{37} +(-0.172231 + 0.125133i) q^{38} +(-5.31842 - 3.86406i) q^{39} +(6.42486 - 4.66793i) q^{41} +(-0.164879 + 0.507445i) q^{42} -11.3607 q^{43} +(-0.443209 + 1.36406i) q^{44} +(1.16314 + 3.57979i) q^{46} +(3.13619 + 9.65219i) q^{47} +(-0.809017 - 0.587785i) q^{48} -6.71531 q^{49} -0.958413 q^{51} +(-5.31842 - 3.86406i) q^{52} +(-0.999220 - 3.07528i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-0.164879 + 0.507445i) q^{56} +0.212889 q^{57} +(1.91420 - 5.89130i) q^{58} +(-6.08749 + 4.42282i) q^{59} +(-10.1710 - 7.38968i) q^{61} +(1.89126 - 1.37408i) q^{62} +(0.431658 - 0.313618i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.16034 - 0.843033i) q^{66} +(-2.13619 + 6.57451i) q^{67} -0.958413 q^{68} +(1.16314 - 3.57979i) q^{69} +(3.12869 + 9.62913i) q^{71} +(0.309017 + 0.951057i) q^{72} +(11.3077 + 8.21552i) q^{73} +4.06291 q^{74} +0.212889 q^{76} +(-0.619107 - 0.449808i) q^{77} +(2.03145 + 6.25217i) q^{78} +(4.79840 + 14.7679i) q^{79} +(0.309017 - 0.951057i) q^{81} -7.94156 q^{82} +(5.04650 - 15.5315i) q^{83} +(0.431658 - 0.313618i) q^{84} +(9.19103 + 6.67767i) q^{86} +(-5.01144 + 3.64102i) q^{87} +(1.16034 - 0.843033i) q^{88} +(-4.54845 - 3.30464i) q^{89} +(2.83769 - 2.06170i) q^{91} +(1.16314 - 3.57979i) q^{92} -2.33773 q^{93} +(3.13619 - 9.65219i) q^{94} +(0.309017 + 0.951057i) q^{96} +(-1.71986 - 5.29318i) q^{97} +(5.43280 + 3.94716i) q^{98} -1.43425 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9} + 2 q^{11} - 4 q^{12} + 4 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{17} + 16 q^{18} - 2 q^{21} - 8 q^{22} - 6 q^{23} + 16 q^{24} + 4 q^{26} - 4 q^{27} - 2 q^{28} + 10 q^{29} - 18 q^{31} + 16 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 2 q^{37} - 10 q^{38} + 4 q^{39} + 22 q^{41} - 2 q^{42} + 4 q^{43} - 8 q^{44} - 6 q^{46} - 2 q^{47} - 4 q^{48} + 52 q^{49} + 28 q^{51} + 4 q^{52} - 16 q^{53} - 4 q^{54} - 2 q^{56} + 20 q^{57} + 10 q^{58} - 20 q^{59} + 12 q^{61} + 2 q^{62} - 2 q^{63} - 4 q^{64} + 2 q^{66} + 18 q^{67} + 28 q^{68} - 6 q^{69} - 28 q^{71} - 4 q^{72} + 24 q^{73} - 12 q^{74} + 20 q^{76} - 14 q^{77} - 6 q^{78} + 20 q^{79} - 4 q^{81} + 12 q^{82} - 36 q^{83} - 2 q^{84} - 6 q^{86} - 20 q^{87} + 2 q^{88} - 70 q^{89} + 12 q^{91} - 6 q^{92} + 32 q^{93} - 2 q^{94} - 4 q^{96} + 28 q^{97} - 38 q^{98} + 12 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9 + 2 * q^11 - 4 * q^12 + 4 * q^13 - 2 * q^14 - 4 * q^16 - 2 * q^17 + 16 * q^18 - 2 * q^21 - 8 * q^22 - 6 * q^23 + 16 * q^24 + 4 * q^26 - 4 * q^27 - 2 * q^28 + 10 * q^29 - 18 * q^31 + 16 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 2 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 - 2 * q^42 + 4 * q^43 - 8 * q^44 - 6 * q^46 - 2 * q^47 - 4 * q^48 + 52 * q^49 + 28 * q^51 + 4 * q^52 - 16 * q^53 - 4 * q^54 - 2 * q^56 + 20 * q^57 + 10 * q^58 - 20 * q^59 + 12 * q^61 + 2 * q^62 - 2 * q^63 - 4 * q^64 + 2 * q^66 + 18 * q^67 + 28 * q^68 - 6 * q^69 - 28 * q^71 - 4 * q^72 + 24 * q^73 - 12 * q^74 + 20 * q^76 - 14 * q^77 - 6 * q^78 + 20 * q^79 - 4 * q^81 + 12 * q^82 - 36 * q^83 - 2 * q^84 - 6 * q^86 - 20 * q^87 + 2 * q^88 - 70 * q^89 + 12 * q^91 - 6 * q^92 + 32 * q^93 - 2 * q^94 - 4 * q^96 + 28 * q^97 - 38 * q^98 + 12 * q^99

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