LMFDB - Embedded newform 150.2.h.b.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(19,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("150.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.h (of order $10$, 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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.3
Root			$0.543374 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	150.109
Dual form			150.2.h.b.139.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.36682 - 1.76969i) q^{5} +(0.309017 - 0.951057i) q^{6} -0.533559i q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.36682 - 1.76969i) q^{5} +(0.309017 - 0.951057i) q^{6} -0.533559i q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-2.23511 + 0.0655797i) q^{10} +(1.16034 + 0.843033i) q^{11} +(-0.587785 - 0.809017i) q^{12} +(3.86406 + 5.31842i) q^{13} +(-0.431658 - 0.313618i) q^{14} +(-1.84679 - 1.26071i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.911505 - 0.296166i) q^{17} -1.00000i q^{18} +(-0.0657863 + 0.202470i) q^{19} +(-1.26071 + 1.84679i) q^{20} +(-0.164879 - 0.507445i) q^{21} +(1.36406 - 0.443209i) q^{22} +(-2.21243 + 3.04515i) q^{23} -1.00000 q^{24} +(-1.26362 + 4.83769i) q^{25} +6.57392 q^{26} +(0.587785 - 0.809017i) q^{27} +(-0.507445 + 0.164879i) q^{28} +(-1.91420 - 5.89130i) q^{29} +(-2.10545 + 0.753056i) q^{30} +(-0.722398 + 2.22331i) q^{31} +1.00000i q^{32} +(1.36406 + 0.443209i) q^{33} +(-0.775373 + 0.563341i) q^{34} +(-0.944235 + 0.729278i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(-2.38812 - 3.28696i) q^{37} +(0.125133 + 0.172231i) q^{38} +(5.31842 + 3.86406i) q^{39} +(0.753056 + 2.10545i) q^{40} +(6.42486 - 4.66793i) q^{41} +(-0.507445 - 0.164879i) q^{42} +11.3607i q^{43} +(0.443209 - 1.36406i) q^{44} +(-2.14598 - 0.628316i) q^{45} +(1.16314 + 3.57979i) q^{46} +(-9.65219 + 3.13619i) q^{47} +(-0.587785 + 0.809017i) q^{48} +6.71531 q^{49} +(3.17104 + 3.86581i) q^{50} -0.958413 q^{51} +(3.86406 - 5.31842i) q^{52} +(-3.07528 + 0.999220i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-0.0940579 - 3.20571i) q^{55} +(-0.164879 + 0.507445i) q^{56} +0.212889i q^{57} +(-5.89130 - 1.91420i) q^{58} +(6.08749 - 4.42282i) q^{59} +(-0.628316 + 2.14598i) q^{60} +(-10.1710 - 7.38968i) q^{61} +(1.37408 + 1.89126i) q^{62} +(-0.313618 - 0.431658i) q^{63} +(0.809017 + 0.587785i) q^{64} +(4.13050 - 14.1075i) q^{65} +(1.16034 - 0.843033i) q^{66} +(-6.57451 - 2.13619i) q^{67} +0.958413i q^{68} +(-1.16314 + 3.57979i) q^{69} +(0.0349907 + 1.19256i) q^{70} +(3.12869 + 9.62913i) q^{71} +(-0.951057 + 0.309017i) q^{72} +(8.21552 - 11.3077i) q^{73} -4.06291 q^{74} +(0.293155 + 4.99140i) q^{75} +0.212889 q^{76} +(0.449808 - 0.619107i) q^{77} +(6.25217 - 2.03145i) q^{78} +(-4.79840 - 14.7679i) q^{79} +(2.14598 + 0.628316i) q^{80} +(0.309017 - 0.951057i) q^{81} -7.94156i q^{82} +(-15.5315 - 5.04650i) q^{83} +(-0.431658 + 0.313618i) q^{84} +(0.721739 + 2.01789i) q^{85} +(9.19103 + 6.67767i) q^{86} +(-3.64102 - 5.01144i) q^{87} +(-0.843033 - 1.16034i) q^{88} +(4.54845 + 3.30464i) q^{89} +(-1.76969 + 1.36682i) q^{90} +(2.83769 - 2.06170i) q^{91} +(3.57979 + 1.16314i) q^{92} +2.33773i q^{93} +(-3.13619 + 9.65219i) q^{94} +(0.448227 - 0.160317i) q^{95} +(0.309017 + 0.951057i) q^{96} +(5.29318 - 1.71986i) q^{97} +(3.94716 - 5.43280i) q^{98} +1.43425 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^9	$ 16 q + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{9} + 2 q^{10} + 2 q^{11} + 20 q^{13} + 2 q^{14} - 2 q^{15} - 4 q^{16} - 30 q^{17} - 4 q^{20} - 2 q^{21} - 20 q^{22} - 10 q^{23} - 16 q^{24} + 24 q^{25} + 4 q^{26} - 10 q^{29} - 6 q^{30} - 18 q^{31} - 20 q^{33} + 12 q^{34} - 34 q^{35} - 4 q^{36} + 20 q^{37} + 10 q^{38} - 4 q^{39} - 2 q^{40} + 22 q^{41} + 8 q^{44} - 4 q^{45} - 6 q^{46} - 50 q^{47} - 52 q^{49} + 12 q^{50} + 28 q^{51} + 20 q^{52} + 30 q^{53} + 4 q^{54} + 18 q^{55} - 2 q^{56} - 30 q^{58} + 20 q^{59} + 2 q^{60} + 12 q^{61} + 50 q^{62} + 10 q^{63} + 4 q^{64} - 8 q^{65} + 2 q^{66} - 50 q^{67} + 6 q^{69} - 12 q^{70} - 28 q^{71} + 20 q^{73} + 12 q^{74} + 28 q^{75} + 20 q^{76} + 100 q^{77} - 20 q^{79} + 4 q^{80} - 4 q^{81} - 30 q^{83} + 2 q^{84} - 4 q^{85} - 6 q^{86} + 10 q^{87} + 70 q^{89} + 8 q^{90} + 12 q^{91} - 30 q^{92} + 2 q^{94} - 30 q^{95} - 4 q^{96} - 10 q^{97} + 60 q^{98} - 12 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^9 + 2 * q^10 + 2 * q^11 + 20 * q^13 + 2 * q^14 - 2 * q^15 - 4 * q^16 - 30 * q^17 - 4 * q^20 - 2 * q^21 - 20 * q^22 - 10 * q^23 - 16 * q^24 + 24 * q^25 + 4 * q^26 - 10 * q^29 - 6 * q^30 - 18 * q^31 - 20 * q^33 + 12 * q^34 - 34 * q^35 - 4 * q^36 + 20 * q^37 + 10 * q^38 - 4 * q^39 - 2 * q^40 + 22 * q^41 + 8 * q^44 - 4 * q^45 - 6 * q^46 - 50 * q^47 - 52 * q^49 + 12 * q^50 + 28 * q^51 + 20 * q^52 + 30 * q^53 + 4 * q^54 + 18 * q^55 - 2 * q^56 - 30 * q^58 + 20 * q^59 + 2 * q^60 + 12 * q^61 + 50 * q^62 + 10 * q^63 + 4 * q^64 - 8 * q^65 + 2 * q^66 - 50 * q^67 + 6 * q^69 - 12 * q^70 - 28 * q^71 + 20 * q^73 + 12 * q^74 + 28 * q^75 + 20 * q^76 + 100 * q^77 - 20 * q^79 + 4 * q^80 - 4 * q^81 - 30 * q^83 + 2 * q^84 - 4 * q^85 - 6 * q^86 + 10 * q^87 + 70 * q^89 + 8 * q^90 + 12 * q^91 - 30 * q^92 + 2 * q^94 - 30 * q^95 - 4 * q^96 - 10 * q^97 + 60 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−1.36682	−	1.76969i	−0.611259	−	0.791430i
$5$	−1.36682	−	1.76969i	−0.611259	−	0.791430i
$6$	0.309017	−	0.951057i	0.126156	−	0.388267i
$7$		−	0.533559i		−	0.201666i	−0.994903	−	0.100833i	$-0.967849\pi$
$7$		−	0.533559i		−	0.201666i	0.994903	−	0.100833i	$-0.0321508\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	−2.23511	+	0.0655797i	−0.706803	+	0.0207381i
$11$	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	$0.630627\pi$
$12$	−0.587785	−	0.809017i	−0.169679	−	0.233543i
$13$	3.86406	+	5.31842i	1.07170	+	1.47506i	0.868347	+	0.495957i	$0.165183\pi$
$13$	3.86406	+	5.31842i	1.07170	+	1.47506i	0.203349	+	0.979106i	$0.434817\pi$
$14$	−0.431658	−	0.313618i	−0.115366	−	0.0838180i
$15$	−1.84679	−	1.26071i	−0.476838	−	0.325513i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.911505	−	0.296166i	−0.221072	−	0.0718308i	0.196387	−	0.980527i	$-0.437079\pi$
$17$	−0.911505	−	0.296166i	−0.221072	−	0.0718308i	−0.417459	+	0.908696i	$0.637079\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−0.0657863	+	0.202470i	−0.0150924	+	0.0464497i	−0.958319	−	0.285700i	$-0.907774\pi$
$19$	−0.0657863	+	0.202470i	−0.0150924	+	0.0464497i	0.943227	+	0.332150i	$0.107774\pi$
$20$	−1.26071	+	1.84679i	−0.281903	+	0.412954i
$21$	−0.164879	−	0.507445i	−0.0359795	−	0.110734i
$22$	1.36406	−	0.443209i	0.290818	−	0.0944924i
$23$	−2.21243	+	3.04515i	−0.461324	+	0.634957i	−0.974783	−	0.223157i	$-0.928364\pi$
$23$	−2.21243	+	3.04515i	−0.461324	+	0.634957i	0.513459	+	0.858114i	$0.328364\pi$
$24$	−1.00000			−0.204124
$25$	−1.26362	+	4.83769i	−0.252724	+	0.967538i
$26$	6.57392			1.28925
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$	−0.507445	+	0.164879i	−0.0958981	+	0.0311592i
$29$	−1.91420	−	5.89130i	−0.355458	−	1.09399i	−0.955743	−	0.294201i	$-0.904946\pi$
$29$	−1.91420	−	5.89130i	−0.355458	−	1.09399i	0.600285	−	0.799786i	$-0.295054\pi$
$30$	−2.10545	+	0.753056i	−0.384400	+	0.137489i
$31$	−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	$0.167325\pi$
$32$			1.00000i			0.176777i
$33$	1.36406	+	0.443209i	0.237452	+	0.0771527i
$34$	−0.775373	+	0.563341i	−0.132975	+	0.0966122i
$35$	−0.944235	+	0.729278i	−0.159605	+	0.123270i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	−2.38812	−	3.28696i	−0.392604	−	0.540373i	0.566264	−	0.824224i	$-0.308388\pi$
$37$	−2.38812	−	3.28696i	−0.392604	−	0.540373i	−0.958869	+	0.283850i	$0.908388\pi$
$38$	0.125133	+	0.172231i	0.0202993	+	0.0279395i
$39$	5.31842	+	3.86406i	0.851628	+	0.618744i
$40$	0.753056	+	2.10545i	0.119069	+	0.332900i
$41$	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	$0.0870790\pi$
$42$	−0.507445	−	0.164879i	−0.0783004	−	0.0254414i
$43$			11.3607i			1.73250i	0.499614	+	0.866248i	$0.333475\pi$
$43$			11.3607i			1.73250i	−0.499614	+	0.866248i	$0.666525\pi$
$44$	0.443209	−	1.36406i	0.0668162	−	0.205639i
$45$	−2.14598	−	0.628316i	−0.319903	−	0.0936638i
$46$	1.16314	+	3.57979i	0.171496	+	0.527811i
$47$	−9.65219	+	3.13619i	−1.40792	+	0.457460i	−0.911742	−	0.410763i	$-0.865263\pi$
$47$	−9.65219	+	3.13619i	−1.40792	+	0.457460i	−0.496175	+	0.868223i	$0.665263\pi$
$48$	−0.587785	+	0.809017i	−0.0848395	+	0.116772i
$49$	6.71531			0.959331
$50$	3.17104	+	3.86581i	0.448453	+	0.546709i
$51$	−0.958413			−0.134205
$52$	3.86406	−	5.31842i	0.535848	−	0.737532i
$53$	−3.07528	+	0.999220i	−0.422423	+	0.137253i	−0.512512	−	0.858680i	$-0.671285\pi$
$53$	−3.07528	+	0.999220i	−0.422423	+	0.137253i	0.0900889	+	0.995934i	$0.471285\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	−0.0940579	−	3.20571i	−0.0126828	−	0.432258i
$56$	−0.164879	+	0.507445i	−0.0220329	+	0.0678102i
$57$			0.212889i			0.0281978i
$58$	−5.89130	−	1.91420i	−0.773566	−	0.251347i
$59$	6.08749	−	4.42282i	0.792524	−	0.575802i	−0.116188	−	0.993227i	$-0.537067\pi$
$59$	6.08749	−	4.42282i	0.792524	−	0.575802i	0.908711	+	0.417425i	$0.137067\pi$
$60$	−0.628316	+	2.14598i	−0.0811152	+	0.277045i
$61$	−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	$0.997751\pi$
$62$	1.37408	+	1.89126i	0.174509	+	0.240191i
$63$	−0.313618	−	0.431658i	−0.0395122	−	0.0543838i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	4.13050	−	14.1075i	0.512325	−	1.74982i
$66$	1.16034	−	0.843033i	0.142827	−	0.103770i
$67$	−6.57451	−	2.13619i	−0.803204	−	0.260977i	−0.121487	−	0.992593i	$-0.538766\pi$
$67$	−6.57451	−	2.13619i	−0.803204	−	0.260977i	−0.681717	+	0.731616i	$0.738766\pi$
$68$			0.958413i			0.116225i
$69$	−1.16314	+	3.57979i	−0.140026	+	0.430956i
$70$	0.0349907	+	1.19256i	0.00418218	+	0.142538i
$71$	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	$0.694853\pi$
$72$	−0.951057	+	0.309017i	−0.112083	+	0.0364180i
$73$	8.21552	−	11.3077i	0.961554	−	1.32347i	0.0153549	−	0.999882i	$-0.495112\pi$
$73$	8.21552	−	11.3077i	0.961554	−	1.32347i	0.946199	−	0.323584i	$-0.104888\pi$
$74$	−4.06291			−0.472304
$75$	0.293155	+	4.99140i	0.0338507	+	0.576357i
$76$	0.212889			0.0244201
$77$	0.449808	−	0.619107i	0.0512604	−	0.0705538i
$78$	6.25217	−	2.03145i	0.707919	−	0.230017i
$79$	−4.79840	−	14.7679i	−0.539862	−	1.66152i	−0.732903	−	0.680333i	$-0.761835\pi$
$79$	−4.79840	−	14.7679i	−0.539862	−	1.66152i	0.193041	−	0.981191i	$-0.438165\pi$
$80$	2.14598	+	0.628316i	0.239928	+	0.0702478i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		−	7.94156i		−	0.876999i
$83$	−15.5315	−	5.04650i	−1.70481	−	0.553926i	−0.715352	−	0.698764i	$-0.753734\pi$
$83$	−15.5315	−	5.04650i	−1.70481	−	0.553926i	−0.989455	+	0.144838i	$0.953734\pi$
$84$	−0.431658	+	0.313618i	−0.0470978	+	0.0342185i
$85$	0.721739	+	2.01789i	0.0782835	+	0.218871i
$86$	9.19103	+	6.67767i	0.991094	+	0.720072i
$87$	−3.64102	−	5.01144i	−0.390359	−	0.537283i
$88$	−0.843033	−	1.16034i	−0.0898676	−	0.123692i
$89$	4.54845	+	3.30464i	0.482135	+	0.350291i	0.802152	−	0.597120i	$-0.203689\pi$
$89$	4.54845	+	3.30464i	0.482135	+	0.350291i	−0.320017	+	0.947412i	$0.603689\pi$
$90$	−1.76969	+	1.36682i	−0.186542	+	0.144075i
$91$	2.83769	−	2.06170i	0.297471	−	0.216125i
$92$	3.57979	+	1.16314i	0.373219	+	0.121266i
$93$			2.33773i			0.242411i
$94$	−3.13619	+	9.65219i	−0.323473	+	0.995548i
$95$	0.448227	−	0.160317i	0.0459871	−	0.0164482i
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	5.29318	−	1.71986i	0.537441	−	0.174625i	−0.0277049	−	0.999616i	$-0.508820\pi$
$97$	5.29318	−	1.71986i	0.537441	−	0.174625i	0.565146	+	0.824991i	$0.308820\pi$
$98$	3.94716	−	5.43280i	0.398724	−	0.548796i
$99$	1.43425			0.144148
$100$	4.99140	−	0.293155i	0.499140	−	0.0293155i
$101$	−9.42708			−0.938029			−0.469015	−	0.883190i	$-0.655391\pi$
$101$	−9.42708			−0.938029			−0.469015	+	0.883190i	$0.655391\pi$
$102$	−0.563341	+	0.775373i	−0.0557791	+	0.0767733i
$103$	7.60723	−	2.47174i	0.749562	−	0.243548i	0.0907695	−	0.995872i	$-0.471067\pi$
$103$	7.60723	−	2.47174i	0.749562	−	0.243548i	0.658793	+	0.752324i	$0.271067\pi$
$104$	−2.03145	−	6.25217i	−0.199200	−	0.613076i
$105$	−0.672662	+	0.985369i	−0.0656451	+	0.0961622i
$106$	−0.999220	+	3.07528i	−0.0970529	+	0.298698i
$107$			18.9260i			1.82964i	0.403857	+	0.914822i	$0.367669\pi$
$107$			18.9260i			1.82964i	−0.403857	+	0.914822i	$0.632331\pi$
$108$	−0.951057	−	0.309017i	−0.0915155	−	0.0297352i
$109$	−2.14813	+	1.56071i	−0.205754	+	0.149489i	−0.685891	−	0.727705i	$-0.740587\pi$
$109$	−2.14813	+	1.56071i	−0.205754	+	0.149489i	0.480137	+	0.877194i	$0.340587\pi$
$110$	−2.64876	−	1.80817i	−0.252549	−	0.172403i
$111$	−3.28696	−	2.38812i	−0.311985	−	0.226670i
$112$	0.313618	+	0.431658i	0.0296341	+	0.0407879i
$113$	1.80029	+	2.47788i	0.169357	+	0.233099i	0.885256	−	0.465104i	$-0.153983\pi$
$113$	1.80029	+	2.47788i	0.169357	+	0.233099i	−0.715899	+	0.698203i	$0.753983\pi$
$114$	0.172231	+	0.125133i	0.0161309	+	0.0117198i
$115$	8.41296	−	0.246843i	0.784513	−	0.0230182i
$116$	−5.01144	+	3.64102i	−0.465301	+	0.338061i
$117$	6.25217	+	2.03145i	0.578014	+	0.187808i
$118$		−	7.52455i		−	0.692691i
$119$	−0.158022	+	0.486342i	−0.0144859	+	0.0445829i
$120$	1.36682	+	1.76969i	0.124773	+	0.161550i
$121$	−2.76351	−	8.50522i	−0.251229	−	0.773202i
$122$	−11.9567	+	3.88498i	−1.08251	+	0.351730i
$123$	4.66793	−	6.42486i	0.420893	−	0.579310i
$124$	2.33773			0.209934
$125$	10.2884	−	4.37602i	0.920219	−	0.391404i
$126$	−0.533559			−0.0475332
$127$	−3.81036	+	5.24451i	−0.338115	+	0.465375i	−0.943890	−	0.330261i	$-0.892863\pi$
$127$	−3.81036	+	5.24451i	−0.338115	+	0.465375i	0.605775	+	0.795636i	$0.292863\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	3.51066	+	10.8047i	0.309096	+	0.951301i
$130$	−8.98535	−	11.6338i	−0.788068	−	1.02035i
$131$	−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	$0.964421\pi$
$132$		−	1.43425i		−	0.124836i
$133$	0.108029	+	0.0351009i	0.00936734	+	0.00304363i
$134$	−5.59261	+	4.06327i	−0.483128	+	0.351013i
$135$	−2.23511	+	0.0655797i	−0.192367	+	0.00564420i
$136$	0.775373	+	0.563341i	0.0664877	+	0.0483061i
$137$	7.25096	+	9.98010i	0.619492	+	0.852657i	0.997316	−	0.0732202i	$-0.0233276\pi$
$137$	7.25096	+	9.98010i	0.619492	+	0.852657i	−0.377824	+	0.925877i	$0.623328\pi$
$138$	2.21243	+	3.04515i	0.188335	+	0.259220i
$139$	3.67227	+	2.66806i	0.311478	+	0.226302i	0.732530	−	0.680734i	$-0.238339\pi$
$139$	3.67227	+	2.66806i	0.311478	+	0.226302i	−0.421052	+	0.907036i	$0.638339\pi$
$140$	0.985369	+	0.672662i	0.0832789	+	0.0568503i
$141$	−8.21065	+	5.96538i	−0.691461	+	0.502376i
$142$	9.62913	+	3.12869i	0.808059	+	0.262554i
$143$			9.42867i			0.788465i
$144$	−0.309017	+	0.951057i	−0.0257514	+	0.0792547i
$145$	−7.80943	+	11.4399i	−0.648538	+	0.950030i
$146$	−4.31916	−	13.2930i	−0.357456	−	1.10014i
$147$	6.38664	−	2.07515i	0.526761	−	0.171155i
$148$	−2.38812	+	3.28696i	−0.196302	+	0.270187i
$149$	−11.0750			−0.907303			−0.453651	−	0.891179i	$-0.649879\pi$
$149$	−11.0750			−0.907303			−0.453651	+	0.891179i	$0.649879\pi$
$150$	4.21044	+	2.69670i	0.343781	+	0.220185i
$151$	−1.63387			−0.132962			−0.0664812	−	0.997788i	$-0.521177\pi$
$151$	−1.63387			−0.132962			−0.0664812	+	0.997788i	$0.521177\pi$
$152$	0.125133	−	0.172231i	0.0101496	−	0.0139698i
$153$	−0.911505	+	0.296166i	−0.0736908	+	0.0239436i
$154$	−0.236478	−	0.727804i	−0.0190559	−	0.0586481i
$155$	4.92196	−	1.76044i	0.395342	−	0.141402i
$156$	2.03145	−	6.25217i	0.162647	−	0.500574i
$157$			6.64544i			0.530364i	0.964198	+	0.265182i	$0.0854320\pi$
$157$			6.64544i			0.530364i	−0.964198	+	0.265182i	$0.914568\pi$
$158$	−14.7679	−	4.79840i	−1.17487	−	0.381740i
$159$	−2.61599	+	1.90063i	−0.207462	+	0.150730i
$160$	1.76969	−	1.36682i	0.139906	−	0.108056i
$161$	1.62477	+	1.18046i	0.128050	+	0.0930335i
$162$	−0.587785	−	0.809017i	−0.0461808	−	0.0635624i
$163$	−5.94451	−	8.18191i	−0.465610	−	0.640857i	0.510051	−	0.860144i	$-0.329627\pi$
$163$	−5.94451	−	8.18191i	−0.465610	−	0.640857i	−0.975660	+	0.219288i	$0.929627\pi$
$164$	−6.42486	−	4.66793i	−0.501697	−	0.364504i
$165$	−1.08007	−	3.01974i	−0.0840835	−	0.235087i
$166$	−13.2119	+	9.59902i	−1.02544	+	0.745028i
$167$	12.1625	+	3.95185i	0.941166	+	0.305803i	0.739121	−	0.673573i	$-0.235241\pi$
$167$	12.1625	+	3.95185i	0.941166	+	0.305803i	0.202045	+	0.979376i	$0.435241\pi$
$168$			0.533559i			0.0411650i
$169$	−9.33741	+	28.7376i	−0.718262	+	2.21058i
$170$	2.05673	+	0.602186i	0.157744	+	0.0461856i
$171$	0.0657863	+	0.202470i	0.00503081	+	0.0154832i
$172$	10.8047	−	3.51066i	0.823851	−	0.267685i
$173$	8.02770	−	11.0492i	0.610335	−	0.840054i	−0.386270	−	0.922386i	$-0.626237\pi$
$173$	8.02770	−	11.0492i	0.610335	−	0.840054i	0.996605	+	0.0823317i	$0.0262367\pi$
$174$	−6.19448			−0.469602
$175$	2.58119	+	0.674216i	0.195120	+	0.0509659i
$176$	−1.43425			−0.108111
$177$	4.42282	−	6.08749i	0.332439	−	0.457564i
$178$	5.34703	−	1.73735i	0.400776	−	0.130220i
$179$	−0.924399	−	2.84501i	−0.0690928	−	0.212646i	0.910548	−	0.413403i	$-0.135660\pi$
$179$	−0.924399	−	2.84501i	−0.0690928	−	0.212646i	−0.979641	+	0.200757i	$0.935660\pi$
$180$	0.0655797	+	2.23511i	0.00488802	+	0.166595i
$181$	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	$0.00857041\pi$
$182$		−	3.50758i		−	0.259999i
$183$	−11.9567	−	3.88498i	−0.883868	−	0.287186i
$184$	3.04515	−	2.21243i	0.224491	−	0.163102i
$185$	−2.55279	+	8.71891i	−0.187685	+	0.641027i
$186$	1.89126	+	1.37408i	0.138674	+	0.100753i
$187$	−0.807974	−	1.11208i	−0.0590849	−	0.0813234i
$188$	5.96538	+	8.21065i	0.435070	+	0.598823i
$189$	−0.431658	−	0.313618i	−0.0313985	−	0.0228124i
$190$	0.133762	−	0.456855i	0.00970408	−	0.0331438i
$191$	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	$0.201705\pi$
$192$	0.951057	+	0.309017i	0.0686366	+	0.0223014i
$193$			10.5266i			0.757723i	0.925453	+	0.378861i	$0.123684\pi$
$193$			10.5266i			0.757723i	−0.925453	+	0.378861i	$0.876316\pi$
$194$	1.71986	−	5.29318i	0.123479	−	0.380028i
$195$	−0.431116	−	14.6934i	−0.0308729	−	1.05222i
$196$	−2.07515	−	6.38664i	−0.148225	−	0.456189i
$197$	9.70843	−	3.15446i	0.691697	−	0.224746i	0.0579878	−	0.998317i	$-0.481532\pi$
$197$	9.70843	−	3.15446i	0.691697	−	0.224746i	0.633709	+	0.773571i	$0.281532\pi$
$198$	0.843033	−	1.16034i	0.0599117	−	0.0824614i
$199$	−3.84318			−0.272436			−0.136218	−	0.990679i	$-0.543495\pi$
$199$	−3.84318			−0.272436			−0.136218	+	0.990679i	$0.543495\pi$
$200$	2.69670	−	4.21044i	0.190686	−	0.297723i
$201$	−6.91285			−0.487595
$202$	−5.54110	+	7.62667i	−0.389870	+	0.536610i
$203$	−3.14336	+	1.02134i	−0.220620	+	0.0716839i
$204$	0.296166	+	0.911505i	0.0207358	+	0.0638181i
$205$	−17.0424	−	4.98981i	−1.19029	−	0.348503i
$206$	2.47174	−	7.60723i	0.172214	−	0.530021i
$207$			3.76401i			0.261617i
$208$	−6.25217	−	2.03145i	−0.433510	−	0.140856i
$209$	−0.247023	+	0.179472i	−0.0170869	+	0.0124144i
$210$	0.401800	+	1.12338i	0.0277268	+	0.0775206i
$211$	−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	$0.757831\pi$
$212$	1.90063	+	2.61599i	0.130536	+	0.179667i
$213$	5.95113	+	8.19103i	0.407765	+	0.561240i
$214$	15.3114	+	11.1244i	1.04667	+	0.760450i
$215$	20.1050	−	15.5281i	1.37115	−	1.05900i
$216$	−0.809017	+	0.587785i	−0.0550466	+	0.0399937i
$217$	1.18627	+	0.385442i	0.0805292	+	0.0261655i
$218$			2.65524i			0.179836i
$219$	4.31916	−	13.2930i	0.291862	−	0.898258i
$220$	−3.01974	+	1.08007i	−0.203591	+	0.0728185i
$221$	−1.94697	−	5.99217i	−0.130968	−	0.403077i
$222$	−3.86406	+	1.25551i	−0.259338	+	0.0842642i
$223$	11.3315	−	15.5964i	0.758811	−	1.04441i	−0.238501	−	0.971142i	$-0.576656\pi$
$223$	11.3315	−	15.5964i	0.758811	−	1.04441i	0.997312	−	0.0732716i	$-0.0233440\pi$
$224$	0.533559			0.0356499
$225$	1.82123	+	4.65651i	0.121416	+	0.310434i
$226$	3.06283			0.203736
$227$	4.96066	−	6.82776i	0.329250	−	0.453174i	−0.612013	−	0.790848i	$-0.709640\pi$
$227$	4.96066	−	6.82776i	0.329250	−	0.453174i	0.941263	+	0.337673i	$0.109640\pi$
$228$	0.202470	−	0.0657863i	0.0134089	−	0.00435681i
$229$	−1.84041	−	5.66419i	−0.121618	−	0.374300i	0.871652	−	0.490125i	$-0.163049\pi$
$229$	−1.84041	−	5.66419i	−0.121618	−	0.374300i	−0.993270	+	0.115825i	$0.963049\pi$
$230$	4.74532	−	6.95132i	0.312897	−	0.458357i
$231$	0.236478	−	0.727804i	0.0155591	−	0.0478860i
$232$			6.19448i			0.406688i
$233$	1.99049	+	0.646750i	0.130401	+	0.0423700i	0.373491	−	0.927634i	$-0.378161\pi$
$233$	1.99049	+	0.646750i	0.130401	+	0.0423700i	−0.243089	+	0.970004i	$0.578161\pi$
$234$	5.31842	−	3.86406i	0.347676	−	0.252601i
$235$	18.7429	+	12.7948i	1.22265	+	0.834642i
$236$	−6.08749	−	4.42282i	−0.396262	−	0.287901i
$237$	−9.12709	−	12.5624i	−0.592868	−	0.816013i
$238$	0.300576	+	0.413707i	0.0194834	+	0.0268167i
$239$	8.00797	+	5.81813i	0.517993	+	0.376344i	0.815847	−	0.578268i	$-0.196271\pi$
$239$	8.00797	+	5.81813i	0.517993	+	0.376344i	−0.297855	+	0.954611i	$0.596271\pi$
$240$	2.23511	−	0.0655797i	0.144275	−	0.00423315i
$241$	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	$0.0571379\pi$
$242$	−8.50522	−	2.76351i	−0.546736	−	0.177645i
$243$		−	1.00000i		−	0.0641500i
$244$	−3.88498	+	11.9567i	−0.248711	+	0.765452i
$245$	−9.17861	−	11.8840i	−0.586400	−	0.759243i
$246$	−2.45408	−	7.55288i	−0.156466	−	0.481554i
$247$	−1.33102	+	0.432474i	−0.0846907	+	0.0275177i
$248$	1.37408	−	1.89126i	0.0872543	−	0.120095i
$249$	−16.3308			−1.03492
$250$	2.50707	−	10.8956i	0.158561	−	0.689100i
$251$	−4.10753			−0.259265			−0.129632	−	0.991562i	$-0.541380\pi$
$251$	−4.10753			−0.259265			−0.129632	+	0.991562i	$0.541380\pi$
$252$	−0.313618	+	0.431658i	−0.0197561	+	0.0271919i
$253$	−5.13432	+	1.66824i	−0.322792	+	0.104881i
$254$	2.00323	+	6.16529i	0.125694	+	0.386845i
$255$	1.30998	+	1.69610i	0.0820339	+	0.106214i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$		−	30.7748i		−	1.91968i	−0.280552	−	0.959839i	$-0.590518\pi$
$257$		−	30.7748i		−	1.91968i	0.280552	−	0.959839i	$-0.409482\pi$
$258$	10.8047	+	3.51066i	0.672671	+	0.218564i
$259$	−1.75379	+	1.27420i	−0.108975	+	0.0791751i
$260$	−14.6934	+	0.431116i	−0.911247	+	0.0267367i
$261$	−5.01144	−	3.64102i	−0.310200	−	0.225374i
$262$	5.55924	+	7.65163i	0.343451	+	0.472719i
$263$	−16.6771	−	22.9541i	−1.02836	−	1.41541i	−0.906174	−	0.422904i	$-0.861011\pi$
$263$	−16.6771	−	22.9541i	−1.02836	−	1.41541i	−0.122183	−	0.992508i	$-0.538989\pi$
$264$	−1.16034	−	0.843033i	−0.0714137	−	0.0518851i
$265$	5.97166	+	4.07655i	0.366836	+	0.250421i
$266$	0.0918954	−	0.0667659i	0.00563447	−	0.00409368i
$267$	5.34703	+	1.73735i	0.327233	+	0.106324i
$268$			6.91285i			0.422269i
$269$	−3.29621	+	10.1447i	−0.200974	+	0.618533i	0.798881	+	0.601489i	$0.205426\pi$
$269$	−3.29621	+	10.1447i	−0.200974	+	0.618533i	−0.999855	+	0.0170443i	$0.994574\pi$
$270$	−1.26071	+	1.84679i	−0.0767242	+	0.112392i
$271$	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	$0.655920\pi$
$272$	0.911505	−	0.296166i	0.0552681	−	0.0179577i
$273$	2.06170	−	2.83769i	0.124780	−	0.171745i
$274$	12.3361			0.745250
$275$	−5.54456	+	4.54807i	−0.334349	+	0.274259i
$276$	3.76401			0.226567
$277$	−18.4912	+	25.4510i	−1.11103	+	1.52920i	−0.291141	+	0.956680i	$0.594035\pi$
$277$	−18.4912	+	25.4510i	−1.11103	+	1.52920i	−0.819889	+	0.572522i	$0.805965\pi$
$278$	4.31701	−	1.40268i	0.258917	−	0.0841273i
$279$	0.722398	+	2.22331i	0.0432488	+	0.133106i
$280$	1.12338	−	0.401800i	0.0671348	−	0.0240121i
$281$	−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	$0.995814\pi$
$282$			10.1489i			0.604359i
$283$	3.96046	+	1.28683i	0.235425	+	0.0764943i	0.424354	−	0.905497i	$-0.360501\pi$
$283$	3.96046	+	1.28683i	0.235425	+	0.0764943i	−0.188928	+	0.981991i	$0.560501\pi$
$284$	8.19103	−	5.95113i	0.486048	−	0.353135i
$285$	0.376748	−	0.290981i	0.0223166	−	0.0172362i
$286$	7.62795	+	5.54203i	0.451050	+	0.327707i
$287$	−2.49062	−	3.42804i	−0.147017	−	0.202351i
$288$	0.587785	+	0.809017i	0.0346356	+	0.0476718i
$289$	−13.0102	−	9.45244i	−0.765304	−	0.556026i
$290$	4.66479	+	13.0422i	0.273926	+	0.765862i
$291$	4.50265	−	3.27137i	0.263950	−	0.191771i
$292$	−13.2930	−	4.31916i	−0.777914	−	0.252760i
$293$			17.9603i			1.04925i	0.851333	+	0.524626i	$0.175795\pi$
$293$			17.9603i			1.04925i	−0.851333	+	0.524626i	$0.824205\pi$
$294$	2.07515	−	6.38664i	0.121025	−	0.372477i
$295$	−16.1475	−	4.72779i	−0.940145	−	0.275263i
$296$	1.25551	+	3.86406i	0.0729749	+	0.224594i
$297$	1.36406	−	0.443209i	0.0791505	−	0.0257176i
$298$	−6.50975	+	8.95990i	−0.377099	+	0.519033i
$299$	−24.7443			−1.43100
$300$	4.65651	−	1.82123i	0.268844	−	0.105149i
$301$	6.06163			0.349386
$302$	−0.960365	+	1.32183i	−0.0552628	+	0.0760627i
$303$	−8.96568	+	2.91313i	−0.515065	+	0.167355i
$304$	−0.0657863	−	0.202470i	−0.00377311	−	0.0116124i
$305$	0.824473	+	28.0999i	0.0472092	+	1.60900i
$306$	−0.296166	+	0.911505i	−0.0169307	+	0.0521073i
$307$		−	20.8174i		−	1.18811i	−0.804423	−	0.594056i	$-0.797526\pi$
$307$		−	20.8174i		−	1.18811i	0.804423	−	0.594056i	$-0.202474\pi$
$308$	−0.727804	−	0.236478i	−0.0414705	−	0.0134746i
$309$	6.47109	−	4.70153i	0.368128	−	0.267460i
$310$	1.46883	−	5.01671i	0.0834240	−	0.284930i
$311$	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	$0.514045\pi$
$312$	−3.86406	−	5.31842i	−0.218759	−	0.301096i
$313$	3.45800	+	4.75953i	0.195458	+	0.269024i	0.895485	−	0.445092i	$-0.146829\pi$
$313$	3.45800	+	4.75953i	0.195458	+	0.269024i	−0.700027	+	0.714116i	$0.746829\pi$
$314$	5.37627	+	3.90609i	0.303401	+	0.220433i
$315$	−0.335244	+	1.14501i	−0.0188888	+	0.0645138i
$316$	−12.5624	+	9.12709i	−0.706688	+	0.513439i
$317$	−10.2344	−	3.32534i	−0.574818	−	0.186770i	0.00715959	−	0.999974i	$-0.497721\pi$
$317$	−10.2344	−	3.32534i	−0.574818	−	0.186770i	−0.581978	+	0.813205i	$0.697721\pi$
$318$			3.23354i			0.181328i
$319$	2.74545	−	8.44962i	0.153716	−	0.473088i
$320$	−0.0655797	−	2.23511i	−0.00366602	−	0.124946i
$321$	5.84845	+	17.9997i	0.326429	+	1.00464i
$322$	1.91003	−	0.620606i	0.106442	−	0.0345850i
$323$	0.119929	−	0.165068i	0.00667304	−	0.00918465i
$324$	−1.00000			−0.0555556
$325$	−30.6116	+	11.9727i	−1.69802	+	0.664123i
$326$	−10.1134			−0.560129
$327$	−1.56071	+	2.14813i	−0.0863075	+	0.118792i
$328$	−7.55288	+	2.45408i	−0.417038	+	0.135504i
$329$	1.67334	+	5.15002i	0.0922543	+	0.283930i
$330$	−3.07787	−	0.901164i	−0.169431	−	0.0496074i
$331$	−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	$0.105399\pi$
$332$			16.3308i			0.896270i
$333$	−3.86406	−	1.25551i	−0.211749	−	0.0688014i
$334$	10.3461	−	7.51686i	0.566112	−	0.411304i
$335$	5.20576	+	14.5546i	0.284421	+	0.795205i
$336$	0.431658	+	0.313618i	0.0235489	+	0.0171093i
$337$	9.05814	+	12.4675i	0.493429	+	0.679146i	0.981016	−	0.193928i	$-0.0621229\pi$
$337$	9.05814	+	12.4675i	0.493429	+	0.679146i	−0.487587	+	0.873074i	$0.662123\pi$
$338$	17.7608	+	24.4456i	0.966060	+	1.32967i
$339$	2.47788	+	1.80029i	0.134580	+	0.0977781i
$340$	1.69610	−	1.30998i	0.0919837	−	0.0710434i
$341$	−2.71255	+	1.97078i	−0.146893	+	0.106724i
$342$	0.202470	+	0.0657863i	0.0109483	+	0.00355732i
$343$		−	7.31793i		−	0.395131i
$344$	3.51066	−	10.8047i	0.189282	−	0.582551i
$345$	7.92492	−	2.83451i	0.426664	−	0.152605i
$346$	−4.22041	−	12.9891i	−0.226891	−	0.698298i
$347$	−21.5477	+	7.00126i	−1.15674	+	0.375847i	−0.823678	−	0.567058i	$-0.808081\pi$
$347$	−21.5477	+	7.00126i	−1.15674	+	0.375847i	−0.333061	+	0.942905i	$0.608081\pi$
$348$	−3.64102	+	5.01144i	−0.195179	+	0.268641i
$349$	16.9543			0.907544			0.453772	−	0.891118i	$-0.350078\pi$
$349$	16.9543			0.907544			0.453772	+	0.891118i	$0.350078\pi$
$350$	2.06264	−	1.69194i	0.110253	−	0.0904378i
$351$	6.57392			0.350890
$352$	−0.843033	+	1.16034i	−0.0449338	+	0.0618461i
$353$	5.76583	−	1.87343i	0.306884	−	0.0997127i	−0.151526	−	0.988453i	$-0.548419\pi$
$353$	5.76583	−	1.87343i	0.306884	−	0.0997127i	0.458411	+	0.888740i	$0.348419\pi$
$354$	−2.32521	−	7.15627i	−0.123584	−	0.380352i
$355$	12.7642	−	18.6981i	0.677456	−	0.992392i
$356$	1.73735	−	5.34703i	0.0920796	−	0.283392i
$357$			0.511370i			0.0270646i
$358$	−2.84501	−	0.924399i	−0.150363	−	0.0488560i
$359$	15.2894	−	11.1084i	0.806943	−	0.586279i	−0.105999	−	0.994366i	$-0.533804\pi$
$359$	15.2894	−	11.1084i	0.806943	−	0.586279i	0.912943	+	0.408088i	$0.133804\pi$
$360$	1.84679	+	1.26071i	0.0973341	+	0.0664451i
$361$	15.3347	+	11.1413i	0.807087	+	0.586383i
$362$	−4.48060	−	6.16702i	−0.235495	−	0.324131i
$363$	−5.25652	−	7.23497i	−0.275896	−	0.379738i
$364$	−2.83769	−	2.06170i	−0.148735	−	0.108063i
$365$	−31.2403	+	0.916613i	−1.63519	+	0.0479777i
$366$	−10.1710	+	7.38968i	−0.531648	+	0.386265i
$367$	−23.8224	−	7.74036i	−1.24352	−	0.404044i	−0.387924	−	0.921691i	$-0.626808\pi$
$367$	−23.8224	−	7.74036i	−1.24352	−	0.404044i	−0.855594	+	0.517648i	$0.826808\pi$
$368$		−	3.76401i		−	0.196213i
$369$	2.45408	−	7.55288i	0.127754	−	0.393187i
$370$	5.55325	+	7.19010i	0.288700	+	0.373795i
$371$	0.533143	+	1.64085i	0.0276794	+	0.0851885i
$372$	2.22331	−	0.722398i	0.115273	−	0.0374546i
$373$	6.99196	−	9.62360i	0.362030	−	0.498291i	−0.588683	−	0.808364i	$-0.700353\pi$
$373$	6.99196	−	9.62360i	0.362030	−	0.498291i	0.950713	+	0.310073i	$0.100353\pi$
$374$	−1.37461			−0.0710792
$375$	8.43255	−	7.34113i	0.435455	−	0.379094i
$376$	10.1489			0.523390
$377$	23.9358	−	32.9448i	1.23276	−	1.69675i
$378$	−0.507445	+	0.164879i	−0.0261001	+	0.00848045i
$379$	−8.50366	−	26.1716i	−0.436804	−	1.34434i	−0.891227	−	0.453558i	$-0.850155\pi$
$379$	−8.50366	−	26.1716i	−0.436804	−	1.34434i	0.454423	−	0.890786i	$-0.349845\pi$
$380$	−0.290981	−	0.376748i	−0.0149270	−	0.0193268i
$381$	−2.00323	+	6.16529i	−0.102628	+	0.315858i
$382$		−	8.40045i		−	0.429804i
$383$	20.9531	+	6.80809i	1.07066	+	0.347877i	0.790743	−	0.612149i	$-0.209695\pi$
$383$	20.9531	+	6.80809i	1.07066	+	0.347877i	0.279912	+	0.960026i	$0.409695\pi$
$384$	0.809017	−	0.587785i	0.0412850	−	0.0299953i
$385$	−1.71043	+	0.0501855i	−0.0871718	+	0.00255769i
$386$	8.51621	+	6.18739i	0.433464	+	0.314930i
$387$	6.67767	+	9.19103i	0.339445	+	0.467206i
$388$	−3.27137	−	4.50265i	−0.166078	−	0.228587i
$389$	14.1491	+	10.2799i	0.717386	+	0.521212i	0.885548	−	0.464548i	$-0.153783\pi$
$389$	14.1491	+	10.2799i	0.717386	+	0.521212i	−0.168162	+	0.985759i	$0.553783\pi$
$390$	−12.1406	−	8.28779i	−0.614765	−	0.419669i
$391$	2.91851	−	2.12042i	0.147595	−	0.107234i
$392$	−6.38664	−	2.07515i	−0.322574	−	0.104811i
$393$			9.45794i			0.477090i
$394$	3.15446	−	9.70843i	0.158919	−	0.489104i
$395$	−19.5762	+	28.6768i	−0.984985	+	1.44288i
$396$	−0.443209	−	1.36406i	−0.0222721	−	0.0685464i
$397$	23.3000	−	7.57062i	1.16939	−	0.379959i	0.340976	−	0.940072i	$-0.389242\pi$
$397$	23.3000	−	7.57062i	1.16939	−	0.379959i	0.828416	+	0.560113i	$0.189242\pi$
$398$	−2.25896	+	3.10920i	−0.113232	+	0.155850i
$399$	0.113589			0.00568656
$400$	−1.82123	−	4.65651i	−0.0910617	−	0.232826i
$401$	1.04105			0.0519875			0.0259937	−	0.999662i	$-0.491725\pi$
$401$	1.04105			0.0519875			0.0259937	+	0.999662i	$0.491725\pi$
$402$	−4.06327	+	5.59261i	−0.202658	+	0.278934i
$403$	−14.6159	+	4.74899i	−0.728069	+	0.236564i
$404$	2.91313	+	8.96568i	0.144934	+	0.446059i
$405$	−2.10545	+	0.753056i	−0.104621	+	0.0374196i
$406$	−1.02134	+	3.14336i	−0.0506882	+	0.156002i
$407$		−	5.82724i		−	0.288845i
$408$	0.911505	+	0.296166i	0.0451262	+	0.0146624i
$409$	18.0061	−	13.0822i	0.890345	−	0.646873i	−0.0456231	−	0.998959i	$-0.514527\pi$
$409$	18.0061	−	13.0822i	0.890345	−	0.646873i	0.935968	+	0.352085i	$0.114527\pi$
$410$	−14.0541	+	10.8547i	−0.694084	+	0.536074i
$411$	9.98010	+	7.25096i	0.492282	+	0.357664i
$412$	−4.70153	−	6.47109i	−0.231628	−	0.318808i
$413$	−2.35984	−	3.24804i	−0.116120	−	0.159825i
$414$	3.04515	+	2.21243i	0.149661	+	0.108735i
$415$	12.2980	+	34.3837i	0.603686	+	1.68783i
$416$	−5.31842	+	3.86406i	−0.260757	+	0.189451i
$417$	4.31701	+	1.40268i	0.211405	+	0.0686897i
$418$			0.305337i			0.0149345i
$419$	7.14737	−	21.9973i	0.349172	−	1.07464i	−0.610141	−	0.792293i	$-0.708887\pi$
$419$	7.14737	−	21.9973i	0.349172	−	1.07464i	0.959312	−	0.282347i	$-0.0911129\pi$
$420$	1.14501	+	0.335244i	0.0558706	+	0.0163582i
$421$	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	$0.823551\pi$
$422$	−4.99228	+	1.62209i	−0.243021	+	0.0789622i
$423$	−5.96538	+	8.21065i	−0.290047	+	0.399215i
$424$	3.23354			0.157035
$425$	2.58456	−	4.03534i	0.125369	−	0.195743i
$426$	10.1247			0.490542
$427$	−3.94283	+	5.42684i	−0.190807	+	0.262623i
$428$	17.9997	−	5.84845i	0.870048	−	0.282696i
$429$	2.91362	+	8.96720i	0.140671	+	0.432940i
$430$	−0.745034	−	25.3925i	−0.0359287	−	1.22453i
$431$	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	$0.0344281\pi$
$432$			1.00000i			0.0481125i
$433$	−20.9272	−	6.79967i	−1.00570	−	0.326771i	−0.240558	−	0.970635i	$-0.577330\pi$
$433$	−20.9272	−	6.79967i	−1.00570	−	0.326771i	−0.765140	+	0.643864i	$0.777330\pi$
$434$	1.00910	−	0.733154i	0.0484384	−	0.0351925i
$435$	−3.89209	+	13.2932i	−0.186611	+	0.637361i
$436$	2.14813	+	1.56071i	0.102877	+	0.0747445i
$437$	−0.471002	−	0.648279i	−0.0225311	−	0.0310114i
$438$	−8.21552	−	11.3077i	−0.392553	−	0.540303i
$439$	−31.0325	−	22.5464i	−1.48110	−	1.07608i	−0.977201	−	0.212318i	$-0.931899\pi$
$439$	−31.0325	−	22.5464i	−1.48110	−	1.07608i	−0.503898	−	0.863763i	$-0.668101\pi$
$440$	−0.901164	+	3.07787i	−0.0429613	+	0.146732i
$441$	5.43280	−	3.94716i	0.258705	−	0.187960i
$442$	−5.99217	−	1.94697i	−0.285018	−	0.0926080i
$443$		−	12.7478i		−	0.605666i	−0.953044	−	0.302833i	$-0.902068\pi$
$443$		−	12.7478i		−	0.605666i	0.953044	−	0.302833i	$-0.0979324\pi$
$444$	−1.25551	+	3.86406i	−0.0595838	+	0.183380i
$445$	−0.368702	−	12.5662i	−0.0174782	−	0.595695i
$446$	−5.95730	−	18.3347i	−0.282087	−	0.868173i
$447$	−10.5330	+	3.42238i	−0.498193	+	0.161873i
$448$	0.313618	−	0.431658i	0.0148171	−	0.0203939i
$449$	−18.0358			−0.851161			−0.425580	−	0.904921i	$-0.639930\pi$
$449$	−18.0358			−0.851161			−0.425580	+	0.904921i	$0.639930\pi$
$450$	4.83769	+	1.26362i	0.228051	+	0.0595676i
$451$	11.3902			0.536344
$452$	1.80029	−	2.47788i	0.0846783	−	0.116550i
$453$	−1.55390	+	0.504894i	−0.0730087	+	0.0237220i
$454$	−2.60797	−	8.02651i	−0.122398	−	0.376703i
$455$	−7.52718	−	2.20387i	−0.352880	−	0.103319i
$456$	0.0657863	−	0.202470i	0.00308073	−	0.00948150i
$457$		−	21.1495i		−	0.989334i	−0.869083	−	0.494667i	$-0.835290\pi$
$457$		−	21.1495i		−	0.989334i	0.869083	−	0.494667i	$-0.164710\pi$
$458$	−5.66419	−	1.84041i	−0.264670	−	0.0859966i
$459$	−0.775373	+	0.563341i	−0.0361913	+	0.0262945i
$460$	−2.83451	−	7.92492i	−0.132160	−	0.369502i
$461$	−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	$0.967737\pi$
$462$	−0.449808	−	0.619107i	−0.0209270	−	0.0288035i
$463$	16.9150	+	23.2815i	0.786108	+	1.08198i	0.994582	+	0.103957i	$0.0331503\pi$
$463$	16.9150	+	23.2815i	0.786108	+	1.08198i	−0.208474	+	0.978028i	$0.566850\pi$
$464$	5.01144	+	3.64102i	0.232650	+	0.169030i
$465$	4.13706	−	3.19525i	0.191852	−	0.148176i
$466$	1.69321	−	1.23019i	0.0784366	−	0.0569875i
$467$	4.94859	+	1.60789i	0.228993	+	0.0744045i	0.421266	−	0.906937i	$-0.361586\pi$
$467$	4.94859	+	1.60789i	0.228993	+	0.0744045i	−0.192273	+	0.981342i	$0.561586\pi$
$468$		−	6.57392i		−	0.303880i
$469$	−1.13978	+	3.50789i	−0.0526303	+	0.161979i
$470$	21.3680	−	7.64270i	0.985633	−	0.352532i
$471$	2.05355	+	6.32019i	0.0946227	+	0.291219i
$472$	−7.15627	+	2.32521i	−0.329394	+	0.107027i
$473$	−9.57747	+	13.1823i	−0.440373	+	0.606121i
$474$	−15.5279			−0.713222
$475$	−0.896356	−	0.574099i	−0.0411276	−	0.0263414i
$476$	0.511370			0.0234386
$477$	−1.90063	+	2.61599i	−0.0870239	+	0.119778i
$478$	9.41393	−	3.05877i	0.430583	−	0.139905i
$479$	12.2490	+	37.6985i	0.559670	+	1.72249i	0.683279	+	0.730157i	$0.260553\pi$
$479$	12.2490	+	37.6985i	0.559670	+	1.72249i	−0.123609	+	0.992331i	$0.539447\pi$
$480$	1.26071	−	1.84679i	0.0575432	−	0.0842938i
$481$	8.25361	−	25.4020i	0.376332	−	1.15823i
$482$		−	21.4567i		−	0.977326i
$483$	1.91003	+	0.620606i	0.0869093	+	0.0282385i
$484$	−7.23497	+	5.25652i	−0.328862	+	0.238933i
$485$	−10.2784	−	7.01657i	−0.466719	−	0.318606i
$486$	−0.809017	−	0.587785i	−0.0366978	−	0.0266625i
$487$	3.19936	+	4.40354i	0.144977	+	0.199544i	0.875330	−	0.483527i	$-0.160644\pi$
$487$	3.19936	+	4.40354i	0.144977	+	0.199544i	−0.730353	+	0.683070i	$0.760644\pi$
$488$	7.38968	+	10.1710i	0.334515	+	0.460420i
$489$	−8.18191	−	5.94451i	−0.369999	−	0.268820i
$490$	−15.0094	+	0.440388i	−0.678057	+	0.0198947i
$491$	−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	$0.306278\pi$
$492$	−7.55288	−	2.45408i	−0.340510	−	0.110638i
$493$			5.93687i			0.267383i
$494$	−0.432474	+	1.33102i	−0.0194579	+	0.0598854i
$495$	−1.96036	−	2.53819i	−0.0881117	−	0.114083i
$496$	−0.722398	−	2.22331i	−0.0324366	−	0.0998297i
$497$	5.13771	−	1.66934i	0.230458	−	0.0748803i
$498$	−9.59902	+	13.2119i	−0.430142	+	0.592040i
$499$	34.9604			1.56504			0.782522	−	0.622623i	$-0.213933\pi$
$499$	34.9604			1.56504			0.782522	+	0.622623i	$0.213933\pi$
$500$	−7.34113	−	8.43255i	−0.328305	−	0.377115i
$501$	12.7885			0.571346
$502$	−2.41434	+	3.32306i	−0.107757	+	0.148315i
$503$	−0.304076	+	0.0988002i	−0.0135581	+	0.00440528i	−0.315788	−	0.948830i	$-0.602269\pi$
$503$	−0.304076	+	0.0988002i	−0.0135581	+	0.00440528i	0.302230	+	0.953235i	$0.402269\pi$
$504$	0.164879	+	0.507445i	0.00734429	+	0.0226034i
$505$	12.8851	+	16.6830i	0.573379	+	0.742385i
$506$	−1.66824	+	5.13432i	−0.0741624	+	0.228248i
$507$			30.2165i			1.34196i
$508$	6.16529	+	2.00323i	0.273541	+	0.0888788i
$509$	16.6867	−	12.1236i	0.739624	−	0.537368i	−0.152969	−	0.988231i	$-0.548884\pi$
$509$	16.6867	−	12.1236i	0.739624	−	0.537368i	0.892593	+	0.450863i	$0.148884\pi$
$510$	2.14216	−	0.0628525i	0.0948562	−	0.00278315i
$511$	−6.03333	−	4.38347i	−0.266899	−	0.193913i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	0.125133	+	0.172231i	0.00552476	+	0.00760418i
$514$	−24.8973	−	18.0890i	−1.09817	−	0.797870i
$515$	−14.7719	−	10.0840i	−0.650928	−	0.444356i
$516$	9.19103	−	6.67767i	0.404613	−	0.293968i
$517$	−13.8437	−	4.49809i	−0.608845	−	0.197826i
$518$			2.16780i			0.0952477i
$519$	4.22041	−	12.9891i	0.185256	−	0.570158i
$520$	−8.28779	+	12.1406i	−0.363444	+	0.532402i
$521$	−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	$0.929470\pi$
$522$	−5.89130	+	1.91420i	−0.257855	+	0.0837823i
$523$	−12.6714	+	17.4407i	−0.554081	+	0.762627i	−0.990559	−	0.137088i	$-0.956226\pi$
$523$	−12.6714	+	17.4407i	−0.554081	+	0.762627i	0.436478	+	0.899715i	$0.356226\pi$
$524$	9.45794			0.413172
$525$	2.66321	−	0.156416i	0.116232	−	0.00682654i
$526$	−28.3729			−1.23712
$527$	1.31694	−	1.81261i	0.0573668	−	0.0789586i
$528$	−1.36406	+	0.443209i	−0.0593629	+	0.0192882i
$529$	2.72931	+	8.39994i	0.118666	+	0.365215i
$530$	6.80806	−	2.43504i	0.295723	−	0.105771i
$531$	2.32521	−	7.15627i	0.100906	−	0.310556i
$532$		−	0.113589i		−	0.00492470i
$533$	49.6520	+	16.1329i	2.15067	+	0.698795i
$534$	4.54845	−	3.30464i	0.196831	−	0.143006i
$535$	33.4932	−	25.8684i	1.44804	−	1.11839i
$536$	5.59261	+	4.06327i	0.241564	+	0.175507i
$537$	−1.75831	−	2.42011i	−0.0758767	−	0.104435i
$538$	6.26977	+	8.62960i	0.270309	+	0.372048i
$539$	7.79201	+	5.66123i	0.335626	+	0.243846i
$540$	0.753056	+	2.10545i	0.0324064	+	0.0906040i
$541$	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	$0.238468\pi$
$542$	21.7259	+	7.05917i	0.933206	+	0.303217i
$543$		−	7.62285i		−	0.327128i
$544$	0.296166	−	0.911505i	0.0126980	−	0.0390805i
$545$	5.69809	+	1.66833i	0.244079	+	0.0714634i
$546$	−1.08390	−	3.33590i	−0.0463867	−	0.142764i
$547$	11.4874	−	3.73249i	0.491167	−	0.159590i	−0.0529536	−	0.998597i	$-0.516864\pi$
$547$	11.4874	−	3.73249i	0.491167	−	0.159590i	0.544120	+	0.839007i	$0.316864\pi$
$548$	7.25096	−	9.98010i	0.309746	−	0.426329i
$549$	−12.5721			−0.536563
$550$	0.420459	+	7.15893i	0.0179284	+	0.305258i
$551$	1.31874			0.0561801
$552$	2.21243	−	3.04515i	0.0941673	−	0.129610i
$553$	−7.87957	+	2.56023i	−0.335073	+	0.108872i
$554$	9.72142	+	29.9194i	0.413023	+	1.27116i
$555$	0.266444	+	9.08103i	0.0113099	+	0.385468i
$556$	1.40268	−	4.31701i	0.0594870	−	0.183082i
$557$			8.23596i			0.348969i	0.984660	+	0.174484i	$0.0558259\pi$
$557$			8.23596i			0.348969i	−0.984660	+	0.174484i	$0.944174\pi$
$558$	2.22331	+	0.722398i	0.0941203	+	0.0305815i
$559$	−60.4211	+	43.8985i	−2.55554	+	1.85671i
$560$	0.335244	−	1.14501i	0.0141666	−	0.0483853i
$561$	−1.11208	−	0.807974i	−0.0469521	−	0.0341127i
$562$	6.33545	+	8.72000i	0.267245	+	0.367831i
$563$	−8.60271	−	11.8406i	−0.362561	−	0.499022i	0.588299	−	0.808643i	$-0.299798\pi$
$563$	−8.60271	−	11.8406i	−0.362561	−	0.499022i	−0.950860	+	0.309621i	$0.899798\pi$
$564$	8.21065	+	5.96538i	0.345731	+	0.251188i
$565$	1.92442	−	6.57276i	0.0809611	−	0.276518i
$566$	3.36897	−	2.44770i	0.141608	−	0.102885i
$567$	−0.507445	−	0.164879i	−0.0213107	−	0.00692426i
$568$		−	10.1247i		−	0.424822i
$569$	−9.65590	+	29.7178i	−0.404796	+	1.24583i	0.516269	+	0.856427i	$0.327321\pi$
$569$	−9.65590	+	29.7178i	−0.404796	+	1.24583i	−0.921065	+	0.389408i	$0.872679\pi$
$570$	−0.0139612	−	0.475830i	−0.000584771	−	0.0199303i
$571$	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	$0.715099\pi$
$572$	8.96720	−	2.91362i	0.374937	−	0.121825i
$573$	4.93766	−	6.79610i	0.206274	−	0.283911i
$574$	−4.23729			−0.176861
$575$	−11.9358	−	14.5510i	−0.497758	−	0.606817i
$576$	1.00000			0.0416667
$577$	5.25092	−	7.22727i	0.218599	−	0.300875i	−0.685608	−	0.727971i	$-0.740463\pi$
$577$	5.25092	−	7.22727i	0.218599	−	0.300875i	0.904206	+	0.427096i	$0.140463\pi$
$578$	−15.2944	+	4.96944i	−0.636162	+	0.206701i
$579$	3.25290	+	10.0114i	0.135186	+	0.416060i
$580$	13.2932	+	3.89209i	0.551971	+	0.161610i
$581$	−2.69261	+	8.28699i	−0.111708	+	0.343802i
$582$		−	5.56558i		−	0.230701i
$583$	−4.41074	−	1.43313i	−0.182674	−	0.0593544i
$584$	−11.3077	+	8.21552i	−0.467916	+	0.339961i
$585$	−4.95053	−	13.8410i	−0.204679	−	0.572257i
$586$	14.5302	+	10.5568i	0.600237	+	0.436098i
$587$	−2.34738	−	3.23089i	−0.0968867	−	0.133353i	0.757821	−	0.652462i	$-0.226264\pi$
$587$	−2.34738	−	3.23089i	−0.0968867	−	0.133353i	−0.854708	+	0.519109i	$0.826264\pi$
$588$	−3.94716	−	5.43280i	−0.162778	−	0.224045i
$589$	−0.402629	−	0.292527i	−0.0165900	−	0.0120534i
$590$	−13.3161	+	10.2847i	−0.548217	+	0.423414i
$591$	8.25848	−	6.00014i	0.339709	−	0.246813i
$592$	3.86406	+	1.25551i	0.158812	+	0.0516011i
$593$		−	11.2114i		−	0.460396i	−0.973144	−	0.230198i	$-0.926063\pi$
$593$		−	11.2114i		−	0.460396i	0.973144	−	0.230198i	$-0.0739374\pi$
$594$	0.443209	−	1.36406i	0.0181851	−	0.0559679i
$595$	1.07666	−	0.385090i	0.0441389	−	0.0157872i
$596$	3.42238	+	10.5330i	0.140186	+	0.431448i
$597$	−3.65508	+	1.18761i	−0.149593	+	0.0486056i
$598$	−14.5443	+	20.0186i	−0.594763	+	0.818620i
$599$	6.64762			0.271614			0.135807	−	0.990735i	$-0.456637\pi$
$599$	6.64762			0.271614			0.135807	+	0.990735i	$0.456637\pi$
$600$	1.26362	−	4.83769i	0.0515871	−	0.197498i
$601$	−10.7465			−0.438359			−0.219179	−	0.975685i	$-0.570338\pi$
$601$	−10.7465			−0.438359			−0.219179	+	0.975685i	$0.570338\pi$
$602$	3.56293	−	4.90396i	0.145214	−	0.199870i
$603$	−6.57451	+	2.13619i	−0.267735	+	0.0869923i
$604$	0.504894	+	1.55390i	0.0205438	+	0.0632274i
$605$	−11.2744	+	16.5157i	−0.458370	+	0.671457i
$606$	−2.91313	+	8.96568i	−0.118338	+	0.364206i
$607$			15.4591i			0.627466i	0.949511	+	0.313733i	$0.101580\pi$
$607$			15.4591i			0.627466i	−0.949511	+	0.313733i	$0.898420\pi$
$608$	−0.202470	−	0.0657863i	−0.00821122	−	0.00266799i
$609$	−2.67390	+	1.94270i	−0.108352	+	0.0787223i
$610$	23.2179	+	15.8497i	0.940066	+	0.641735i
$611$	−53.9762	−	39.2160i	−2.18364	−	1.58651i
$612$	0.563341	+	0.775373i	0.0227717	+	0.0313426i
$613$	−14.3929	−	19.8101i	−0.581324	−	0.800123i	0.412516	−	0.910950i	$-0.364650\pi$
$613$	−14.3929	−	19.8101i	−0.581324	−	0.800123i	−0.993840	+	0.110827i	$0.964650\pi$
$614$	−16.8416	−	12.2362i	−0.679673	−	0.493812i
$615$	−17.7502	+	0.520806i	−0.715759	+	0.0210009i
$616$	−0.619107	+	0.449808i	−0.0249445	+	0.0181233i
$617$	−17.9899	−	5.84526i	−0.724244	−	0.235321i	−0.0763819	−	0.997079i	$-0.524337\pi$
$617$	−17.9899	−	5.84526i	−0.724244	−	0.235321i	−0.647862	+	0.761757i	$0.724337\pi$
$618$		−	7.99871i		−	0.321755i
$619$	−0.788010	+	2.42524i	−0.0316728	+	0.0974788i	−0.965643	−	0.259872i	$-0.916320\pi$
$619$	−0.788010	+	2.42524i	−0.0316728	+	0.0974788i	0.933970	+	0.357350i	$0.116320\pi$
$620$	−3.19525	−	4.13706i	−0.128324	−	0.166148i
$621$	1.16314	+	3.57979i	0.0466753	+	0.143652i
$622$	18.5005	−	6.01118i	0.741803	−	0.241026i
$623$	1.76322	−	2.42687i	0.0706420	−	0.0972304i
$624$	−6.57392			−0.263168
$625$	−21.8065	−	12.2260i	−0.872261	−	0.489040i
$626$	5.88310			0.235136
$627$	−0.179472	+	0.247023i	−0.00716744	+	0.00986513i
$628$	6.32019	−	2.05355i	0.252203	−	0.0819457i
$629$	1.20330	+	3.70336i	0.0479785	+	0.147663i
$630$	0.729278	+	0.944235i	0.0290551	+	0.0376192i
$631$	−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	$0.841569\pi$
$632$			15.5279i			0.617668i
$633$	−4.99228	−	1.62209i	−0.198425	−	0.0644723i
$634$	−8.70586	+	6.32518i	−0.345754	+	0.251205i
$635$	14.4892	−	0.425125i	0.574988	−	0.0168706i
$636$	2.61599	+	1.90063i	0.103731	+	0.0753649i
$637$	25.9483	+	35.7148i	1.02811	+	1.41507i
$638$	−5.22215	−	7.18767i	−0.206747	−	0.284563i
$639$	8.19103	+	5.95113i	0.324032	+	0.235423i
$640$	−1.84679	−	1.26071i	−0.0730006	−	0.0498338i
$641$	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	$0.168238\pi$
$642$	17.9997	+	5.84845i	0.710391	+	0.230820i
$643$			11.4218i			0.450433i	0.974309	+	0.225217i	$0.0723090\pi$
$643$			11.4218i			0.450433i	−0.974309	+	0.225217i	$0.927691\pi$
$644$	0.620606	−	1.91003i	0.0244553	−	0.0752656i
$645$	14.3226	−	20.9808i	0.563950	−	0.826120i
$646$	−0.0630505	−	0.194049i	−0.00248069	−	0.00763477i
$647$	−5.60379	+	1.82078i	−0.220308	+	0.0715823i	−0.417091	−	0.908865i	$-0.636950\pi$
$647$	−5.60379	+	1.82078i	−0.220308	+	0.0715823i	0.196783	+	0.980447i	$0.436950\pi$
$648$	−0.587785	+	0.809017i	−0.0230904	+	0.0317812i
$649$	10.7921			0.423627
$650$	−8.30694	+	31.8026i	−0.325825	+	1.24740i
$651$	1.24732			0.0488862
$652$	−5.94451	+	8.18191i	−0.232805	+	0.320428i
$653$	16.2691	−	5.28614i	0.636658	−	0.206863i	0.0271359	−	0.999632i	$-0.491361\pi$
$653$	16.2691	−	5.28614i	0.636658	−	0.206863i	0.609522	+	0.792769i	$0.291361\pi$
$654$	0.820514	+	2.52528i	0.0320847	+	0.0987464i
$655$	19.9132	−	7.12235i	0.778073	−	0.278293i
$656$	−2.45408	+	7.55288i	−0.0958157	+	0.294890i
$657$		−	13.9771i		−	0.545298i
$658$	5.15002	+	1.67334i	0.200769	+	0.0652337i
$659$	−24.0433	+	17.4685i	−0.936593	+	0.680475i	−0.947598	−	0.319465i	$-0.896497\pi$
$659$	−24.0433	+	17.4685i	−0.936593	+	0.680475i	0.0110052	+	0.999939i	$0.496497\pi$
$660$	−2.53819	+	1.96036i	−0.0987988	+	0.0763070i
$661$	−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	$-0.656800\pi$
$662$	0.362718	+	0.499238i	0.0140974	+	0.0194034i
$663$	−3.70336	−	5.09724i	−0.143827	−	0.197960i
$664$	13.2119	+	9.59902i	0.512722	+	0.372514i
$665$	−0.0855388	−	0.239155i	−0.00331705	−	0.00927405i
$666$	−3.28696	+	2.38812i	−0.127367	+	0.0925377i
$667$	22.1749	+	7.20507i	0.858616	+	0.278981i
$668$		−	12.7885i		−	0.494800i
$669$	5.95730	−	18.3347i	0.230323	−	0.708860i
$670$	14.8348	+	4.34345i	0.573119	+	0.167802i
$671$	−5.57205	−	17.1490i	−0.215107	−	0.662030i
$672$	0.507445	−	0.164879i	0.0195751	−	0.00636034i
$673$	−11.5841	+	15.9441i	−0.446534	+	0.614601i	−0.971648	−	0.236430i	$-0.924023\pi$
$673$	−11.5841	+	15.9441i	−0.446534	+	0.614601i	0.525114	+	0.851032i	$0.324023\pi$
$674$	15.4106			0.593595
$675$	3.17104	+	3.86581i	0.122053	+	0.148795i
$676$	30.2165			1.16217
$677$	−14.5638	+	20.0453i	−0.559732	+	0.770405i	−0.991292	−	0.131679i	$-0.957963\pi$
$677$	−14.5638	+	20.0453i	−0.559732	+	0.770405i	0.431560	+	0.902084i	$0.357963\pi$
$678$	2.91292	−	0.946466i	0.111870	−	0.0363488i
$679$	−0.917646	−	2.82422i	−0.0352160	−	0.108384i
$680$	−0.0628525	−	2.14216i	−0.00241028	−	0.0821479i
$681$	2.60797	−	8.02651i	0.0999377	−	0.307577i
$682$			3.35289i			0.128389i
$683$	15.7755	+	5.12579i	0.603635	+	0.196133i	0.594861	−	0.803829i	$-0.297207\pi$
$683$	15.7755	+	5.12579i	0.603635	+	0.196133i	0.00877377	+	0.999962i	$0.497207\pi$
$684$	0.172231	−	0.125133i	0.00658541	−	0.00478458i
$685$	7.75095	−	26.4729i	0.296149	−	1.01148i
$686$	−5.92033	−	4.30137i	−0.226039	−	0.164227i
$687$	−3.50066	−	4.81825i	−0.133559	−	0.183828i
$688$	−6.67767	−	9.19103i	−0.254584	−	0.350405i
$689$	−17.1973	−	12.4946i	−0.655166	−	0.476006i
$690$	2.36499	−	8.07748i	0.0900335	−	0.307504i
$691$	−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	$0.597503\pi$
$692$	−12.9891	−	4.22041i	−0.493771	−	0.160436i
$693$		−	0.765259i		−	0.0290698i
$694$	−7.00126	+	21.5477i	−0.265764	+	0.817938i
$695$	−0.297678	−	10.1455i	−0.0112916	−	0.384842i
$696$	1.91420	+	5.89130i	0.0725576	+	0.223309i
$697$	−7.23878	+	2.35202i	−0.274188	+	0.0890892i
$698$	9.96550	−	13.7163i	0.377200	−	0.519171i
$699$	2.09293			0.0791617
$700$	−0.156416	−	2.66321i	−0.00591196	−	0.100660i
$701$	−22.7240			−0.858273			−0.429137	−	0.903240i	$-0.641182\pi$
$701$	−22.7240			−0.858273			−0.429137	+	0.903240i	$0.641182\pi$
$702$	3.86406	−	5.31842i	0.145839	−	0.200731i
$703$	0.822615	−	0.267284i	0.0310255	−	0.0100808i
$704$	0.443209	+	1.36406i	0.0167041	+	0.0514098i
$705$	21.7793	+	6.37672i	0.820258	+	0.240161i
$706$	1.87343	−	5.76583i	0.0705076	−	0.217000i
$707$			5.02990i			0.189169i
$708$	−7.15627	−	2.32521i	−0.268949	−	0.0873869i
$709$	37.5483	−	27.2804i	1.41016	−	1.02454i	0.416855	−	0.908973i	$-0.363132\pi$
$709$	37.5483	−	27.2804i	1.41016	−	1.02454i	0.993300	−	0.115565i	$-0.0368678\pi$
$710$	−7.62444	−	21.3170i	−0.286140	−	0.800011i
$711$	−12.5624	−	9.12709i	−0.471125	−	0.342293i
$712$	−3.30464	−	4.54845i	−0.123847	−	0.170460i
$713$	−5.17206	−	7.11873i	−0.193695	−	0.266599i
$714$	0.413707	+	0.300576i	0.0154826	+	0.0112488i
$715$	16.6858	−	12.8873i	0.624015	−	0.481957i
$716$	−2.42011	+	1.75831i	−0.0904437	+	0.0657112i
$717$	9.41393	+	3.05877i	0.351570	+	0.114232i
$718$		−	18.8987i		−	0.705294i
$719$	8.71631	−	26.8260i	0.325063	−	1.00044i	−0.646349	−	0.763042i	$-0.723705\pi$
$719$	8.71631	−	26.8260i	0.325063	−	1.00044i	0.971412	−	0.237400i	$-0.0762952\pi$
$720$	2.10545	−	0.753056i	0.0784654	−	0.0280647i
$721$	−1.31882	−	4.05891i	−0.0491154	−	0.151162i
$722$	18.0270	−	5.85732i	0.670894	−	0.217987i
$723$	12.6119	−	17.3588i	0.469043	−	0.645582i
$724$	−7.62285			−0.283301
$725$	30.9191	−	1.81594i	1.14831	−	0.0674425i
$726$	−8.94292			−0.331903
$727$	−0.500553	+	0.688953i	−0.0185645	+	0.0255518i	−0.818198	−	0.574936i	$-0.805027\pi$
$727$	−0.500553	+	0.688953i	−0.0185645	+	0.0255518i	0.799634	+	0.600488i	$0.205027\pi$
$728$	−3.33590	+	1.08390i	−0.123637	+	0.0401720i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	−17.6210	+	25.8127i	−0.652183	+	0.955370i
$731$	3.36466	−	10.3554i	0.124447	−	0.383007i
$732$			12.5721i			0.464677i
$733$	29.2259	+	9.49607i	1.07948	+	0.350745i	0.794174	−	0.607690i	$-0.207904\pi$
$733$	29.2259	+	9.49607i	1.07948	+	0.350745i	0.285309	+	0.958436i	$0.407904\pi$
$734$	−20.2645	+	14.7230i	−0.747978	+	0.543437i
$735$	−12.4017	−	8.46605i	−0.457445	−	0.312275i
$736$	−3.04515	−	2.21243i	−0.112246	−	0.0815512i
$737$	−5.82776	−	8.02122i	−0.214668	−	0.295465i
$738$	−4.66793	−	6.42486i	−0.171829	−	0.236502i
$739$	1.67050	+	1.21369i	0.0614502	+	0.0446462i	0.618086	−	0.786110i	$-0.287908\pi$
$739$	1.67050	+	1.21369i	0.0614502	+	0.0446462i	−0.556636	+	0.830756i	$0.687908\pi$
$740$	9.08103	−	0.266444i	0.333825	−	0.00979469i
$741$	−1.13223	+	0.822615i	−0.0415936	+	0.0302195i
$742$	1.64085	+	0.533143i	0.0602373	+	0.0195723i
$743$		−	37.8972i		−	1.39031i	−0.718858	−	0.695157i	$-0.755335\pi$
$743$		−	37.8972i		−	1.39031i	0.718858	−	0.695157i	$-0.244665\pi$
$744$	0.722398	−	2.22331i	0.0264844	−	0.0815106i
$745$	15.1376	+	19.5994i	0.554597	+	0.718067i
$746$	−3.67589	−	11.3132i	−0.134584	−	0.414207i
$747$	−15.5315	+	5.04650i	−0.568269	+	0.184642i
$748$	−0.807974	+	1.11208i	−0.0295424	+	0.0406617i
$749$	10.0981			0.368978
$750$	−0.982568	−	11.1371i	−0.0358783	−	0.406669i
$751$	−40.6331			−1.48272			−0.741361	−	0.671106i	$-0.765819\pi$
$751$	−40.6331			−1.48272			−0.741361	+	0.671106i	$0.765819\pi$
$752$	5.96538	−	8.21065i	0.217535	−	0.299411i
$753$	−3.90649	+	1.26930i	−0.142360	+	0.0462557i
$754$	−12.5838	−	38.7290i	−0.458275	−	1.41043i
$755$	2.23320	+	2.89145i	0.0812746	+	0.105231i
$756$	−0.164879	+	0.507445i	−0.00599659	+	0.0184556i
$757$		−	10.0032i		−	0.363572i	−0.983338	−	0.181786i	$-0.941812\pi$
$757$		−	10.0032i		−	0.363572i	0.983338	−	0.181786i	$-0.0581877\pi$
$758$	−26.1716	−	8.50366i	−0.950594	−	0.308867i
$759$	−4.36751	+	3.17318i	−0.158531	+	0.115179i
$760$	−0.475830	+	0.0139612i	−0.0172602	+	0.000506426i
$761$	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	$0.515756\pi$
$762$	3.81036	+	5.24451i	0.138035	+	0.189989i
$763$	0.832732	+	1.14616i	0.0301469	+	0.0414937i
$764$	−6.79610	−	4.93766i	−0.245874	−	0.178638i
$765$	1.76998	+	1.20828i	0.0639939	+	0.0436854i
$766$	17.8238	−	12.9497i	0.644000	−	0.467893i
$767$	47.0448	+	15.2858i	1.69869	+	0.551938i
$768$		−	1.00000i		−	0.0360844i
$769$	−6.53471	+	20.1118i	−0.235648	+	0.725249i	0.761387	+	0.648297i	$0.224519\pi$
$769$	−6.53471	+	20.1118i	−0.235648	+	0.725249i	−0.997035	+	0.0769513i	$0.975481\pi$
$770$	−0.964767	+	1.41327i	−0.0347678	+	0.0509307i
$771$	−9.50993	−	29.2685i	−0.342492	−	1.05408i
$772$	10.0114	−	3.25290i	0.360319	−	0.117075i
$773$	−17.3085	+	23.8231i	−0.622544	+	0.856858i	−0.997535	−	0.0701705i	$-0.977646\pi$
$773$	−17.3085	+	23.8231i	−0.622544	+	0.856858i	0.374991	+	0.927028i	$0.377646\pi$
$774$	11.3607			0.408353
$775$	−9.84286	−	6.30416i	−0.353566	−	0.226452i
$776$	−5.56558			−0.199793
$777$	−1.27420	+	1.75379i	−0.0457117	+	0.0629168i
$778$	16.6332	−	5.40446i	0.596330	−	0.193759i
$779$	0.522446	+	1.60792i	0.0187186	+	0.0576099i
$780$	−13.8410	+	4.95053i	−0.495589	+	0.177257i
$781$	−4.48734	+	13.8106i	−0.160570	+	0.494183i
$782$		−	3.60748i		−	0.129003i
$783$	−5.89130	−	1.91420i	−0.210538	−	0.0684079i
$784$	−5.43280	+	3.94716i	−0.194029	+	0.140970i
$785$	11.7604	−	9.08310i	0.419746	−	0.324190i
$786$	7.65163	+	5.55924i	0.272925	+	0.198291i
$787$	−3.03811	−	4.18161i	−0.108297	−	0.149058i	0.751428	−	0.659815i	$-0.229365\pi$
$787$	−3.03811	−	4.18161i	−0.108297	−	0.149058i	−0.859725	+	0.510757i	$0.829365\pi$
$788$	−6.00014	−	8.25848i	−0.213746	−	0.294196i
$789$	−22.9541	−	16.6771i	−0.817189	−	0.593722i
$790$	11.6934	+	32.6932i	0.416033	+	1.16317i
$791$	1.32210	−	0.960559i	0.0470083	−	0.0341536i
$792$	−1.36406	−	0.443209i	−0.0484696	−	0.0157487i
$793$		−	82.6478i		−	2.93491i
$794$	7.57062	−	23.3000i	0.268671	−	0.826885i
$795$	6.93911	+	2.03169i	0.246105	+	0.0720565i
$796$	1.18761	+	3.65508i	0.0420937	+	0.129551i
$797$	−3.57413	+	1.16131i	−0.126602	+	0.0411356i	−0.371633	−	0.928380i	$-0.621202\pi$
$797$	−3.57413	+	1.16131i	−0.126602	+	0.0411356i	0.245031	+	0.969515i	$0.421202\pi$
$798$	0.0667659	−	0.0918954i	0.00236349	−	0.00325306i
$799$	9.72686			0.344111
$800$	−4.83769	−	1.26362i	−0.171038	−	0.0446757i
$801$	5.62220			0.198650
$802$	0.611913	−	0.842226i	0.0216074	−	0.0297400i
$803$	19.0655	−	6.19476i	0.672808	−	0.218608i
$804$	2.13619	+	6.57451i	0.0753375	+	0.231865i
$805$	−0.131705	−	4.48881i	−0.00464200	−	0.158210i
$806$	−4.74899	+	14.6159i	−0.167276	+	0.514823i
$807$			10.6668i			0.375488i
$808$	8.96568	+	2.91313i	0.315412	+	0.102483i
$809$	−16.8961	+	12.2757i	−0.594034	+	0.431591i	−0.843756	−	0.536727i	$-0.819661\pi$
$809$	−16.8961	+	12.2757i	−0.594034	+	0.431591i	0.249722	+	0.968317i	$0.419661\pi$
$810$	−0.628316	+	2.14598i	−0.0220768	+	0.0754020i
$811$	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	$0.478561\pi$
$812$	1.94270	+	2.67390i	0.0681755	+	0.0938355i
$813$	13.4273	+	18.4811i	0.470917	+	0.648162i
$814$	−4.71434	−	3.42516i	−0.165237	−	0.120052i
$815$	−6.35441	+	21.7031i	−0.222585	+	0.760227i
$816$	0.775373	−	0.563341i	0.0271435	−	0.0197209i
$817$	−2.30020	−	0.747381i	−0.0804739	−	0.0261476i
$818$		−	22.2568i		−	0.778190i
$819$	1.08390	−	3.33590i	0.0378746	−	0.116566i
$820$	0.520806	+	17.7502i	0.0181873	+	0.619865i
$821$	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	$0.703158\pi$
$822$	11.7323	−	3.81206i	0.409211	−	0.132961i
$823$	−19.2733	+	26.5275i	−0.671827	+	0.924690i	−0.999800	−	0.0199969i	$-0.993634\pi$
$823$	−19.2733	+	26.5275i	−0.671827	+	0.924690i	0.327973	+	0.944687i	$0.393634\pi$
$824$	−7.99871			−0.278648
$825$	−3.86775	+	6.03883i	−0.134658	+	0.210245i
$826$	−4.01479			−0.139692
$827$	−3.05011	+	4.19811i	−0.106063	+	0.145983i	−0.858749	−	0.512397i	$-0.828758\pi$
$827$	−3.05011	+	4.19811i	−0.106063	+	0.145983i	0.752686	+	0.658379i	$0.228758\pi$
$828$	3.57979	−	1.16314i	0.124406	−	0.0404220i
$829$	1.71758	+	5.28616i	0.0596539	+	0.183596i	0.976443	−	0.215776i	$-0.0692282\pi$
$829$	1.71758	+	5.28616i	0.0596539	+	0.183596i	−0.916789	+	0.399372i	$0.869228\pi$
$830$	35.0456	+	10.2609i	1.21645	+	0.356162i
$831$	−9.72142	+	29.9194i	−0.337232	+	1.03789i
$832$			6.57392i			0.227910i
$833$	−6.12104	−	1.98885i	−0.212082	−	0.0689095i
$834$	3.67227	−	2.66806i	0.127160	−	0.0923874i
$835$	−9.63042	−	26.9254i	−0.333274	−	0.931792i
$836$	0.247023	+	0.179472i	0.00854346	+	0.00620718i
$837$	1.37408	+	1.89126i	0.0474952	+	0.0653716i
$838$	−13.5951	−	18.7121i	−0.469635	−	0.646397i
$839$	35.1423	+	25.5324i	1.21325	+	0.881475i	0.995522	−	0.0945346i	$-0.0301363\pi$
$839$	35.1423	+	25.5324i	1.21325	+	0.881475i	0.217725	+	0.976010i	$0.430136\pi$
$840$	0.944235	−	0.729278i	0.0325792	−	0.0251625i
$841$	−7.58178	+	5.50849i	−0.261441	+	0.189948i
$842$	9.28363	+	3.01643i	0.319935	+	0.103953i
$843$			10.7785i			0.371232i
$844$	−1.62209	+	4.99228i	−0.0558347	+	0.171841i
$845$	63.6192	−	22.7547i	2.18857	−	0.782785i
$846$	3.13619	+	9.65219i	0.107824	+	0.331849i
$847$	−4.53804	+	1.47450i	−0.155929	+	0.0506644i
$848$	1.90063	−	2.61599i	0.0652679	−	0.0898336i
$849$	4.16428			0.142918
$850$	−1.74549	−	4.46286i	−0.0598700	−	0.153075i
$851$	15.2928			0.524231
$852$	5.95113	−	8.19103i	0.203882	−	0.280620i
$853$	−3.17978	+	1.03317i	−0.108874	+	0.0353752i	−0.362947	−	0.931810i	$-0.618229\pi$
$853$	−3.17978	+	1.03317i	−0.108874	+	0.0353752i	0.254074	+	0.967185i	$0.418229\pi$
$854$	2.07287	+	6.37963i	0.0709321	+	0.218306i
$855$	0.268391	−	0.393160i	0.00917877	−	0.0134458i
$856$	5.84845	−	17.9997i	0.199896	−	0.615217i
$857$			34.5415i			1.17991i	0.807434	+	0.589957i	$0.200855\pi$
$857$			34.5415i			1.17991i	−0.807434	+	0.589957i	$0.799145\pi$
$858$	8.96720	+	2.91362i	0.306135	+	0.0994693i
$859$	−19.2961	+	14.0195i	−0.658375	+	0.478338i	−0.866114	−	0.499847i	$-0.833390\pi$
$859$	−19.2961	+	14.0195i	−0.658375	+	0.478338i	0.207739	+	0.978184i	$0.433390\pi$
$860$	−20.9808	−	14.3226i	−0.715441	−	0.488395i
$861$	−3.42804	−	2.49062i	−0.116827	−	0.0848801i
$862$	−4.99205	−	6.87097i	−0.170030	−	0.234026i
$863$	−3.36837	−	4.63616i	−0.114661	−	0.157817i	0.747829	−	0.663891i	$-0.231096\pi$
$863$	−3.36837	−	4.63616i	−0.114661	−	0.157817i	−0.862490	+	0.506074i	$0.831096\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	−30.5261	+	0.895658i	−1.03792	+	0.0304533i
$866$	−17.8018	+	12.9337i	−0.604928	+	0.439506i
$867$	−15.2944	−	4.96944i	−0.519424	−	0.168771i
$868$		−	1.24732i		−	0.0423367i
$869$	6.88211	−	21.1810i	0.233460	−	0.718515i
$870$	8.46673	+	10.9623i	0.287049	+	0.371658i
$871$	−14.0431	−	43.2203i	−0.475834	−	1.46447i
$872$	2.52528	−	0.820514i	0.0855169	−	0.0277861i
$873$	3.27137	−	4.50265i	0.110719	−	0.152392i
$874$	−0.801317			−0.0271049
$875$	−2.33487	−	5.48945i	−0.0789329	−	0.185577i
$876$	−13.9771			−0.472242
$877$	−29.3000	+	40.3280i	−0.989392	+	1.36178i	−0.0577792	+	0.998329i	$0.518402\pi$
$877$	−29.3000	+	40.3280i	−0.989392	+	1.36178i	−0.931613	+	0.363452i	$0.881598\pi$
$878$	−36.4808	+	11.8533i	−1.23117	+	0.400031i
$879$	5.55004	+	17.0813i	0.187198	+	0.576137i
$880$	1.96036	+	2.53819i	0.0660838	+	0.0855622i
$881$	−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	$0.141167\pi$
$882$		−	6.71531i		−	0.226116i
$883$	37.0873	+	12.0504i	1.24809	+	0.405528i	0.857235	−	0.514925i	$-0.172180\pi$
$883$	37.0873	+	12.0504i	1.24809	+	0.405528i	0.390852	+	0.920453i	$0.372180\pi$
$884$	−5.09724	+	3.70336i	−0.171439	+	0.124558i
$885$	−16.8182	+	0.493458i	−0.565337	+	0.0165874i
$886$	−10.3132	−	7.49296i	−0.346478	−	0.251731i
$887$	−19.1229	−	26.3204i	−0.642083	−	0.883752i	0.356641	−	0.934241i	$-0.383922\pi$
$887$	−19.1229	−	26.3204i	−0.642083	−	0.883752i	−0.998725	+	0.0504894i	$0.983922\pi$
$888$	2.38812	+	3.28696i	0.0801400	+	0.110303i
$889$	2.79826	+	2.03305i	0.0938505	+	0.0681864i
$890$	−10.3830	−	7.08794i	−0.348039	−	0.237588i
$891$	1.16034	−	0.843033i	0.0388727	−	0.0282427i
$892$	−18.3347	−	5.95730i	−0.613891	−	0.199465i
$893$		−	2.16059i		−	0.0723015i
$894$	−3.42238	+	10.5330i	−0.114461	+	0.352276i
$895$	−3.77130	+	5.52451i	−0.126061	+	0.184664i
$896$	−0.164879	−	0.507445i	−0.00550822	−	0.0169525i
$897$	−23.5332	+	7.64642i	−0.785752	+	0.255306i
$898$	−10.6012	+	14.5912i	−0.353765	+	0.486916i
$899$	14.4810			0.482969
$900$	3.86581	−	3.17104i	0.128860	−	0.105701i
$901$	3.09907			0.103245
$902$	6.69500	−	9.21488i	0.222919	−	0.306822i
$903$	5.76495	−	1.87315i	0.191845	−	0.0623344i
$904$	−0.946466	−	2.91292i	−0.0314790	−	0.0968824i
$905$	−16.0495	+	5.74043i	−0.533504	+	0.190818i
$906$	−0.504894	+	1.55390i	−0.0167740	+	0.0516250i
$907$		−	16.5820i		−	0.550595i	−0.961359	−	0.275297i	$-0.911224\pi$
$907$		−	16.5820i		−	0.550595i	0.961359	−	0.275297i	$-0.0887763\pi$
$908$	−8.02651	−	2.60797i	−0.266369	−	0.0865486i
$909$	−7.62667	+	5.54110i	−0.252961	+	0.183787i
$910$	−6.20733	+	4.79422i	−0.205771	+	0.158927i
$911$	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	$0.543057\pi$
$912$	−0.125133	−	0.172231i	−0.00414357	−	0.00570313i
$913$	−13.7674	−	18.9492i	−0.455635	−	0.627128i
$914$	−17.1103	−	12.4314i	−0.565960	−	0.411194i
$915$	9.46747	+	26.4698i	0.312985	+	0.875065i
$916$	−4.81825	+	3.50066i	−0.159199	+	0.115665i
$917$	4.79938	+	1.55941i	0.158490	+	0.0514964i
$918$			0.958413i			0.0316324i
$919$	0.118310	−	0.364122i	0.00390270	−	0.0120113i	−0.949086	−	0.315016i	$-0.897990\pi$
$919$	0.118310	−	0.364122i	0.00390270	−	0.0120113i	0.952989	+	0.303005i	$0.0979900\pi$
$920$	−8.07748	−	2.36499i	−0.266307	−	0.0779713i
$921$	−6.43293	−	19.7985i	−0.211972	−	0.652384i
$922$	−30.4419	+	9.89116i	−1.00255	+	0.325748i
$923$	−39.1223	+	53.8472i	−1.28773	+	1.77240i
$924$	−0.765259			−0.0251752
$925$	18.9190	−	7.39951i	0.622052	−	0.243294i
$926$	28.7776			0.945689
$927$	4.70153	−	6.47109i	0.154418	−	0.212539i
$928$	5.89130	−	1.91420i	0.193391	−	0.0628367i
$929$	1.93355	+	5.95087i	0.0634378	+	0.195242i	0.977752	−	0.209764i	$-0.0672696\pi$
$929$	1.93355	+	5.95087i	0.0634378	+	0.195242i	−0.914314	+	0.405006i	$0.867270\pi$
$930$	−0.153308	−	5.22507i	−0.00502715	−	0.171337i
$931$	−0.441776	+	1.35965i	−0.0144786	+	0.0445606i
$932$		−	2.09293i		−	0.0685561i
$933$	18.5005	+	6.01118i	0.605679	+	0.196797i
$934$	4.20952	−	3.05840i	0.137740	−	0.100074i
$935$	−0.863687	+	2.94988i	−0.0282456	+	0.0964713i
$936$	−5.31842	−	3.86406i	−0.173838	−	0.126301i
$937$	−2.89904	−	3.99019i	−0.0947075	−	0.130354i	0.759034	−	0.651052i	$-0.225672\pi$
$937$	−2.89904	−	3.99019i	−0.0947075	−	0.130354i	−0.853741	+	0.520698i	$0.825672\pi$
$938$	2.16800	+	2.98399i	0.0707876	+	0.0974307i
$939$	4.75953	+	3.45800i	0.155321	+	0.112847i
$940$	6.37672	−	21.7793i	0.207986	−	0.710364i
$941$	−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	$0.461508\pi$
$942$	6.32019	+	2.05355i	0.205923	+	0.0669084i
$943$			29.8921i			0.973422i
$944$	−2.32521	+	7.15627i	−0.0756793	+	0.232917i
$945$	0.0349907	+	1.19256i	0.00113825	+	0.0387940i
$946$	5.03518	+	15.4967i	0.163708	+	0.503840i
$947$	−25.5953	+	8.31642i	−0.831736	+	0.270247i	−0.693777	−	0.720190i	$-0.744054\pi$
$947$	−25.5953	+	8.31642i	−0.831736	+	0.270247i	−0.137960	+	0.990438i	$0.544054\pi$
$948$	−9.12709	+	12.5624i	−0.296434	+	0.408007i
$949$	91.8843			2.98269
$950$	−0.991321	+	0.387721i	−0.0321627	+	0.0125793i
$951$	−10.7610			−0.348950
$952$	0.300576	−	0.413707i	0.00974172	−	0.0134083i
$953$	−35.4113	+	11.5058i	−1.14709	+	0.372711i	−0.820045	−	0.572300i	$-0.806051\pi$
$953$	−35.4113	+	11.5058i	−1.14709	+	0.372711i	−0.327041	+	0.945010i	$0.606051\pi$
$954$	0.999220	+	3.07528i	0.0323510	+	0.0995660i
$955$	−18.0272	−	5.27813i	−0.583345	−	0.170796i
$956$	3.05877	−	9.41393i	0.0989278	−	0.304468i
$957$		−	8.88445i		−	0.287194i
$958$	37.6985	+	12.2490i	1.21798	+	0.395747i
$959$	5.32497	−	3.86882i	0.171952	−	0.124931i
$960$	−0.753056	−	2.10545i	−0.0243048	−	0.0679530i
$961$	20.6583	+	15.0091i	0.666396	+	0.484165i
$962$	−15.6993	−	21.6082i	−0.506166	−	0.696678i
$963$	11.1244	+	15.3114i	0.358479	+	0.493405i
$964$	−17.3588	−	12.6119i	−0.559091	−	0.406203i
$965$	18.6289	−	14.3880i	0.599685	−	0.463165i
$966$	1.62477	−	1.18046i	0.0522760	−	0.0379807i
$967$	−15.2973	−	4.97039i	−0.491928	−	0.159837i	0.0525399	−	0.998619i	$-0.483268\pi$
$967$	−15.2973	−	4.97039i	−0.491928	−	0.159837i	−0.544468	+	0.838782i	$0.683268\pi$
$968$			8.94292i			0.287436i
$969$	0.0630505	−	0.194049i	0.00202547	−	0.00623377i
$970$	−11.7180	+	4.19119i	−0.376243	+	0.134571i
$971$	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	$0.836987\pi$
$972$	−0.951057	+	0.309017i	−0.0305052	+	0.00991172i
$973$	1.42357	−	1.95937i	0.0456375	−	0.0628146i
$974$	5.44308			0.174407
$975$	−25.4136	+	20.8462i	−0.813886	+	0.667612i
$976$	12.5721			0.402422
$977$	−10.5930	+	14.5800i	−0.338899	+	0.466454i	−0.944119	−	0.329604i	$-0.893085\pi$
$977$	−10.5930	+	14.5800i	−0.338899	+	0.466454i	0.605221	+	0.796058i	$0.293085\pi$
$978$	−9.61841	+	3.12521i	−0.307563	+	0.0999333i
$979$	2.49180	+	7.66899i	0.0796384	+	0.245102i
$980$	−8.46605	+	12.4017i	−0.270438	+	0.396159i
$981$	−0.820514	+	2.52528i	−0.0261970	+	0.0806261i
$982$			0.873965i			0.0278893i
$983$	46.9850	+	15.2663i	1.49859	+	0.486921i	0.939606	−	0.342259i	$-0.111192\pi$
$983$	46.9850	+	15.2663i	1.49859	+	0.486921i	0.558982	+	0.829180i	$0.311192\pi$
$984$	−6.42486	+	4.66793i	−0.204817	+	0.148808i
$985$	−18.8521	−	12.8694i	−0.600677	−	0.410052i
$986$	4.80303	+	3.48961i	0.152960	+	0.111132i
$987$	3.18289	+	4.38087i	0.101312	+	0.139444i
$988$	0.822615	+	1.13223i	0.0261709	+	0.0360211i
$989$	−34.5951	−	25.1348i	−1.10006	−	0.799241i
$990$	−3.20571	+	0.0940579i	−0.101884	+	0.00298936i
$991$	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	$0.138643\pi$
$992$	−2.22331	−	0.722398i	−0.0705902	−	0.0229362i
$993$			0.617092i			0.0195828i
$994$	1.66934	−	5.13771i	0.0529484	−	0.162958i
$995$	5.25293	+	6.80125i	0.166529	+	0.215614i
$996$	5.04650	+	15.5315i	0.159905	+	0.492136i
$997$	6.47717	−	2.10456i	0.205134	−	0.0666521i	−0.204648	−	0.978836i	$-0.565605\pi$
$997$	6.47717	−	2.10456i	0.205134	−	0.0666521i	0.409782	+	0.912184i	$0.365605\pi$
$998$	20.5492	−	28.2836i	0.650474	−	0.895301i
$999$	−4.06291			−0.128545

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.109.3	✓	16	1.1	even	1	trivial
150.2.h.b.139.3	yes	16	25.14	even	10	inner
450.2.l.c.109.2		16	3.2	odd	2
450.2.l.c.289.2		16	75.14	odd	10
750.2.g.f.301.2		16	25.23	odd	20
750.2.g.f.451.2		16	5.3	odd	4
750.2.g.g.301.3		16	25.2	odd	20
750.2.g.g.451.3		16	5.2	odd	4
750.2.h.d.49.2		16	5.4	even	2
750.2.h.d.199.1		16	25.11	even	5
3750.2.a.u.1.6		8	25.17	odd	20
3750.2.a.v.1.3		8	25.8	odd	20
3750.2.c.k.1249.6		16	25.19	even	10
3750.2.c.k.1249.11		16	25.6	even	5

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.36682 - 1.76969i) q^{5} +(0.309017 - 0.951057i) q^{6} -0.533559i q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.36682 - 1.76969i) q^{5} +(0.309017 - 0.951057i) q^{6} -0.533559i q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-2.23511 + 0.0655797i) q^{10} +(1.16034 + 0.843033i) q^{11} +(-0.587785 - 0.809017i) q^{12} +(3.86406 + 5.31842i) q^{13} +(-0.431658 - 0.313618i) q^{14} +(-1.84679 - 1.26071i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.911505 - 0.296166i) q^{17} -1.00000i q^{18} +(-0.0657863 + 0.202470i) q^{19} +(-1.26071 + 1.84679i) q^{20} +(-0.164879 - 0.507445i) q^{21} +(1.36406 - 0.443209i) q^{22} +(-2.21243 + 3.04515i) q^{23} -1.00000 q^{24} +(-1.26362 + 4.83769i) q^{25} +6.57392 q^{26} +(0.587785 - 0.809017i) q^{27} +(-0.507445 + 0.164879i) q^{28} +(-1.91420 - 5.89130i) q^{29} +(-2.10545 + 0.753056i) q^{30} +(-0.722398 + 2.22331i) q^{31} +1.00000i q^{32} +(1.36406 + 0.443209i) q^{33} +(-0.775373 + 0.563341i) q^{34} +(-0.944235 + 0.729278i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(-2.38812 - 3.28696i) q^{37} +(0.125133 + 0.172231i) q^{38} +(5.31842 + 3.86406i) q^{39} +(0.753056 + 2.10545i) q^{40} +(6.42486 - 4.66793i) q^{41} +(-0.507445 - 0.164879i) q^{42} +11.3607i q^{43} +(0.443209 - 1.36406i) q^{44} +(-2.14598 - 0.628316i) q^{45} +(1.16314 + 3.57979i) q^{46} +(-9.65219 + 3.13619i) q^{47} +(-0.587785 + 0.809017i) q^{48} +6.71531 q^{49} +(3.17104 + 3.86581i) q^{50} -0.958413 q^{51} +(3.86406 - 5.31842i) q^{52} +(-3.07528 + 0.999220i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-0.0940579 - 3.20571i) q^{55} +(-0.164879 + 0.507445i) q^{56} +0.212889i q^{57} +(-5.89130 - 1.91420i) q^{58} +(6.08749 - 4.42282i) q^{59} +(-0.628316 + 2.14598i) q^{60} +(-10.1710 - 7.38968i) q^{61} +(1.37408 + 1.89126i) q^{62} +(-0.313618 - 0.431658i) q^{63} +(0.809017 + 0.587785i) q^{64} +(4.13050 - 14.1075i) q^{65} +(1.16034 - 0.843033i) q^{66} +(-6.57451 - 2.13619i) q^{67} +0.958413i q^{68} +(-1.16314 + 3.57979i) q^{69} +(0.0349907 + 1.19256i) q^{70} +(3.12869 + 9.62913i) q^{71} +(-0.951057 + 0.309017i) q^{72} +(8.21552 - 11.3077i) q^{73} -4.06291 q^{74} +(0.293155 + 4.99140i) q^{75} +0.212889 q^{76} +(0.449808 - 0.619107i) q^{77} +(6.25217 - 2.03145i) q^{78} +(-4.79840 - 14.7679i) q^{79} +(2.14598 + 0.628316i) q^{80} +(0.309017 - 0.951057i) q^{81} -7.94156i q^{82} +(-15.5315 - 5.04650i) q^{83} +(-0.431658 + 0.313618i) q^{84} +(0.721739 + 2.01789i) q^{85} +(9.19103 + 6.67767i) q^{86} +(-3.64102 - 5.01144i) q^{87} +(-0.843033 - 1.16034i) q^{88} +(4.54845 + 3.30464i) q^{89} +(-1.76969 + 1.36682i) q^{90} +(2.83769 - 2.06170i) q^{91} +(3.57979 + 1.16314i) q^{92} +2.33773i q^{93} +(-3.13619 + 9.65219i) q^{94} +(0.448227 - 0.160317i) q^{95} +(0.309017 + 0.951057i) q^{96} +(5.29318 - 1.71986i) q^{97} +(3.94716 - 5.43280i) q^{98} +1.43425 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^9	\( 16 q + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{9} + 2 q^{10} + 2 q^{11} + 20 q^{13} + 2 q^{14} - 2 q^{15} - 4 q^{16} - 30 q^{17} - 4 q^{20} - 2 q^{21} - 20 q^{22} - 10 q^{23} - 16 q^{24} + 24 q^{25} + 4 q^{26} - 10 q^{29} - 6 q^{30} - 18 q^{31} - 20 q^{33} + 12 q^{34} - 34 q^{35} - 4 q^{36} + 20 q^{37} + 10 q^{38} - 4 q^{39} - 2 q^{40} + 22 q^{41} + 8 q^{44} - 4 q^{45} - 6 q^{46} - 50 q^{47} - 52 q^{49} + 12 q^{50} + 28 q^{51} + 20 q^{52} + 30 q^{53} + 4 q^{54} + 18 q^{55} - 2 q^{56} - 30 q^{58} + 20 q^{59} + 2 q^{60} + 12 q^{61} + 50 q^{62} + 10 q^{63} + 4 q^{64} - 8 q^{65} + 2 q^{66} - 50 q^{67} + 6 q^{69} - 12 q^{70} - 28 q^{71} + 20 q^{73} + 12 q^{74} + 28 q^{75} + 20 q^{76} + 100 q^{77} - 20 q^{79} + 4 q^{80} - 4 q^{81} - 30 q^{83} + 2 q^{84} - 4 q^{85} - 6 q^{86} + 10 q^{87} + 70 q^{89} + 8 q^{90} + 12 q^{91} - 30 q^{92} + 2 q^{94} - 30 q^{95} - 4 q^{96} - 10 q^{97} + 60 q^{98} - 12 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^9 + 2 * q^10 + 2 * q^11 + 20 * q^13 + 2 * q^14 - 2 * q^15 - 4 * q^16 - 30 * q^17 - 4 * q^20 - 2 * q^21 - 20 * q^22 - 10 * q^23 - 16 * q^24 + 24 * q^25 + 4 * q^26 - 10 * q^29 - 6 * q^30 - 18 * q^31 - 20 * q^33 + 12 * q^34 - 34 * q^35 - 4 * q^36 + 20 * q^37 + 10 * q^38 - 4 * q^39 - 2 * q^40 + 22 * q^41 + 8 * q^44 - 4 * q^45 - 6 * q^46 - 50 * q^47 - 52 * q^49 + 12 * q^50 + 28 * q^51 + 20 * q^52 + 30 * q^53 + 4 * q^54 + 18 * q^55 - 2 * q^56 - 30 * q^58 + 20 * q^59 + 2 * q^60 + 12 * q^61 + 50 * q^62 + 10 * q^63 + 4 * q^64 - 8 * q^65 + 2 * q^66 - 50 * q^67 + 6 * q^69 - 12 * q^70 - 28 * q^71 + 20 * q^73 + 12 * q^74 + 28 * q^75 + 20 * q^76 + 100 * q^77 - 20 * q^79 + 4 * q^80 - 4 * q^81 - 30 * q^83 + 2 * q^84 - 4 * q^85 - 6 * q^86 + 10 * q^87 + 70 * q^89 + 8 * q^90 + 12 * q^91 - 30 * q^92 + 2 * q^94 - 30 * q^95 - 4 * q^96 - 10 * q^97 + 60 * q^98 - 12 * q^99

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