LMFDB - Embedded newform 750.2.h.d.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(49,750)]

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, 7]))

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

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

chi := DirichletCharacter("750.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.h (of order $10$, 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 $\Q(\zeta_{10})$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			199.1
Root			$-1.16141 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	750.199
Dual form			750.2.h.d.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} -0.533559i q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} -0.533559i q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(1.16034 - 0.843033i) q^{11} +(0.587785 - 0.809017i) q^{12} +(-3.86406 + 5.31842i) q^{13} +(-0.431658 + 0.313618i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(0.911505 - 0.296166i) q^{17} -1.00000i q^{18} +(-0.0657863 - 0.202470i) q^{19} +(-0.164879 + 0.507445i) q^{21} +(-1.36406 - 0.443209i) q^{22} +(2.21243 + 3.04515i) q^{23} -1.00000 q^{24} +6.57392 q^{26} +(-0.587785 - 0.809017i) q^{27} +(0.507445 + 0.164879i) q^{28} +(-1.91420 + 5.89130i) q^{29} +(-0.722398 - 2.22331i) q^{31} +1.00000i q^{32} +(-1.36406 + 0.443209i) q^{33} +(-0.775373 - 0.563341i) q^{34} +(-0.809017 + 0.587785i) q^{36} +(2.38812 - 3.28696i) q^{37} +(-0.125133 + 0.172231i) q^{38} +(5.31842 - 3.86406i) q^{39} +(6.42486 + 4.66793i) q^{41} +(0.507445 - 0.164879i) q^{42} +11.3607i q^{43} +(0.443209 + 1.36406i) q^{44} +(1.16314 - 3.57979i) q^{46} +(9.65219 + 3.13619i) q^{47} +(0.587785 + 0.809017i) q^{48} +6.71531 q^{49} -0.958413 q^{51} +(-3.86406 - 5.31842i) q^{52} +(3.07528 + 0.999220i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-0.164879 - 0.507445i) q^{56} +0.212889i q^{57} +(5.89130 - 1.91420i) q^{58} +(6.08749 + 4.42282i) q^{59} +(-10.1710 + 7.38968i) q^{61} +(-1.37408 + 1.89126i) q^{62} +(0.313618 - 0.431658i) q^{63} +(0.809017 - 0.587785i) q^{64} +(1.16034 + 0.843033i) q^{66} +(6.57451 - 2.13619i) q^{67} +0.958413i q^{68} +(-1.16314 - 3.57979i) q^{69} +(3.12869 - 9.62913i) q^{71} +(0.951057 + 0.309017i) q^{72} +(-8.21552 - 11.3077i) q^{73} -4.06291 q^{74} +0.212889 q^{76} +(-0.449808 - 0.619107i) q^{77} +(-6.25217 - 2.03145i) q^{78} +(-4.79840 + 14.7679i) q^{79} +(0.309017 + 0.951057i) q^{81} -7.94156i q^{82} +(15.5315 - 5.04650i) q^{83} +(-0.431658 - 0.313618i) q^{84} +(9.19103 - 6.67767i) q^{86} +(3.64102 - 5.01144i) q^{87} +(0.843033 - 1.16034i) q^{88} +(4.54845 - 3.30464i) q^{89} +(2.83769 + 2.06170i) q^{91} +(-3.57979 + 1.16314i) q^{92} +2.33773i q^{93} +(-3.13619 - 9.65219i) q^{94} +(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^{6} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 - 4 * q^6 + 4 * q^9	$ 16 q + 4 q^{4} - 4 q^{6} + 4 q^{9} + 2 q^{11} - 20 q^{13} + 2 q^{14} - 4 q^{16} + 30 q^{17} - 2 q^{21} + 20 q^{22} + 10 q^{23} - 16 q^{24} + 4 q^{26} - 10 q^{29} - 18 q^{31} + 20 q^{33} + 12 q^{34} - 4 q^{36} - 20 q^{37} - 10 q^{38} - 4 q^{39} + 22 q^{41} + 8 q^{44} - 6 q^{46} + 50 q^{47} - 52 q^{49} + 28 q^{51} - 20 q^{52} - 30 q^{53} + 4 q^{54} - 2 q^{56} + 30 q^{58} + 20 q^{59} + 12 q^{61} - 50 q^{62} - 10 q^{63} + 4 q^{64} + 2 q^{66} + 50 q^{67} + 6 q^{69} - 28 q^{71} - 20 q^{73} + 12 q^{74} + 20 q^{76} - 100 q^{77} - 20 q^{79} - 4 q^{81} + 30 q^{83} + 2 q^{84} - 6 q^{86} - 10 q^{87} + 70 q^{89} + 12 q^{91} + 30 q^{92} + 2 q^{94} - 4 q^{96} + 10 q^{97} - 60 q^{98} - 12 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 4 * q^6 + 4 * q^9 + 2 * q^11 - 20 * q^13 + 2 * q^14 - 4 * q^16 + 30 * q^17 - 2 * q^21 + 20 * q^22 + 10 * q^23 - 16 * q^24 + 4 * q^26 - 10 * q^29 - 18 * q^31 + 20 * q^33 + 12 * q^34 - 4 * q^36 - 20 * q^37 - 10 * q^38 - 4 * q^39 + 22 * q^41 + 8 * q^44 - 6 * q^46 + 50 * q^47 - 52 * q^49 + 28 * q^51 - 20 * q^52 - 30 * q^53 + 4 * q^54 - 2 * q^56 + 30 * q^58 + 20 * q^59 + 12 * q^61 - 50 * q^62 - 10 * q^63 + 4 * q^64 + 2 * q^66 + 50 * q^67 + 6 * q^69 - 28 * q^71 - 20 * q^73 + 12 * q^74 + 20 * q^76 - 100 * q^77 - 20 * q^79 - 4 * q^81 + 30 * q^83 + 2 * q^84 - 6 * q^86 - 10 * q^87 + 70 * q^89 + 12 * q^91 + 30 * q^92 + 2 * q^94 - 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 $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	−0.587785	−	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
$5$		0			0
$5$		0			0
$6$	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
$10$		0			0
$11$	1.16034	−	0.843033i	0.349854	−	0.254184i	−0.398954	−	0.916971i	$-0.630627\pi$
$11$	1.16034	−	0.843033i	0.349854	−	0.254184i	0.748808	+	0.662787i	$0.230627\pi$
$12$	0.587785	−	0.809017i	0.169679	−	0.233543i
$13$	−3.86406	+	5.31842i	−1.07170	+	1.47506i	−0.203349	+	0.979106i	$0.565183\pi$
$13$	−3.86406	+	5.31842i	−1.07170	+	1.47506i	−0.868347	+	0.495957i	$0.834817\pi$
$14$	−0.431658	+	0.313618i	−0.115366	+	0.0838180i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.911505	−	0.296166i	0.221072	−	0.0718308i	−0.196387	−	0.980527i	$-0.562921\pi$
$17$	0.911505	−	0.296166i	0.221072	−	0.0718308i	0.417459	+	0.908696i	$0.362921\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−0.0657863	−	0.202470i	−0.0150924	−	0.0464497i	0.943227	−	0.332150i	$-0.107774\pi$
$19$	−0.0657863	−	0.202470i	−0.0150924	−	0.0464497i	−0.958319	+	0.285700i	$0.907774\pi$
$20$		0			0
$21$	−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	$-0.0716362\pi$
$23$	2.21243	+	3.04515i	0.461324	+	0.634957i	−0.513459	+	0.858114i	$0.671636\pi$
$24$	−1.00000			−0.204124
$25$		0			0
$26$	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	0.600285	+	0.799786i	$0.295054\pi$
$29$	−1.91420	+	5.89130i	−0.355458	+	1.09399i	−0.955743	+	0.294201i	$0.904946\pi$
$30$		0			0
$31$	−0.722398	−	2.22331i	−0.129747	−	0.399319i	0.864989	−	0.501790i	$-0.167325\pi$
$31$	−0.722398	−	2.22331i	−0.129747	−	0.399319i	−0.994736	+	0.102471i	$0.967325\pi$
$32$			1.00000i			0.176777i
$33$	−1.36406	+	0.443209i	−0.237452	+	0.0771527i
$34$	−0.775373	−	0.563341i	−0.132975	−	0.0966122i
$35$		0			0
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	2.38812	−	3.28696i	0.392604	−	0.540373i	−0.566264	−	0.824224i	$-0.691612\pi$
$37$	2.38812	−	3.28696i	0.392604	−	0.540373i	0.958869	+	0.283850i	$0.0916119\pi$
$38$	−0.125133	+	0.172231i	−0.0202993	+	0.0279395i
$39$	5.31842	−	3.86406i	0.851628	−	0.618744i
$40$		0			0
$41$	6.42486	+	4.66793i	1.00339	+	0.729009i	0.962813	−	0.270167i	$-0.0870790\pi$
$41$	6.42486	+	4.66793i	1.00339	+	0.729009i	0.0405813	+	0.999176i	$0.487079\pi$
$42$	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
$45$		0			0
$46$	1.16314	−	3.57979i	0.171496	−	0.527811i
$47$	9.65219	+	3.13619i	1.40792	+	0.457460i	0.911742	−	0.410763i	$-0.134737\pi$
$47$	9.65219	+	3.13619i	1.40792	+	0.457460i	0.496175	+	0.868223i	$0.334737\pi$
$48$	0.587785	+	0.809017i	0.0848395	+	0.116772i
$49$	6.71531			0.959331
$50$		0			0
$51$	−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	$-0.328715\pi$
$53$	3.07528	+	0.999220i	0.422423	+	0.137253i	−0.0900889	+	0.995934i	$0.528715\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$		0			0
$56$	−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	0.908711	−	0.417425i	$-0.137067\pi$
$59$	6.08749	+	4.42282i	0.792524	+	0.575802i	−0.116188	+	0.993227i	$0.537067\pi$
$60$		0			0
$61$	−10.1710	+	7.38968i	−1.30227	+	0.946151i	−0.999975	−	0.00706498i	$-0.997751\pi$
$61$	−10.1710	+	7.38968i	−1.30227	+	0.946151i	−0.302290	+	0.953216i	$0.597751\pi$
$62$	−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
$65$		0			0
$66$	1.16034	+	0.843033i	0.142827	+	0.103770i
$67$	6.57451	−	2.13619i	0.803204	−	0.260977i	0.121487	−	0.992593i	$-0.461234\pi$
$67$	6.57451	−	2.13619i	0.803204	−	0.260977i	0.681717	+	0.731616i	$0.261234\pi$
$68$			0.958413i			0.116225i
$69$	−1.16314	−	3.57979i	−0.140026	−	0.430956i
$70$		0			0
$71$	3.12869	−	9.62913i	0.371308	−	1.14277i	−0.574628	−	0.818415i	$-0.694853\pi$
$71$	3.12869	−	9.62913i	0.371308	−	1.14277i	0.945936	−	0.324353i	$-0.105147\pi$
$72$	0.951057	+	0.309017i	0.112083	+	0.0364180i
$73$	−8.21552	−	11.3077i	−0.961554	−	1.32347i	−0.946199	−	0.323584i	$-0.895112\pi$
$73$	−8.21552	−	11.3077i	−0.961554	−	1.32347i	−0.0153549	−	0.999882i	$-0.504888\pi$
$74$	−4.06291			−0.472304
$75$		0			0
$76$	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	0.193041	+	0.981191i	$0.438165\pi$
$79$	−4.79840	+	14.7679i	−0.539862	+	1.66152i	−0.732903	+	0.680333i	$0.761835\pi$
$80$		0			0
$81$	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	$-0.246266\pi$
$83$	15.5315	−	5.04650i	1.70481	−	0.553926i	0.989455	+	0.144838i	$0.0462662\pi$
$84$	−0.431658	−	0.313618i	−0.0470978	−	0.0342185i
$85$		0			0
$86$	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	−0.320017	−	0.947412i	$-0.603689\pi$
$89$	4.54845	−	3.30464i	0.482135	−	0.350291i	0.802152	+	0.597120i	$0.203689\pi$
$90$		0			0
$91$	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			0
$96$	0.309017	−	0.951057i	0.0315389	−	0.0970668i
$97$	−5.29318	−	1.71986i	−0.537441	−	0.174625i	0.0277049	−	0.999616i	$-0.491180\pi$
$97$	−5.29318	−	1.71986i	−0.537441	−	0.174625i	−0.565146	+	0.824991i	$0.691180\pi$
$98$	−3.94716	−	5.43280i	−0.398724	−	0.548796i
$99$	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	$0.655391\pi$
$102$	0.563341	+	0.775373i	0.0557791	+	0.0767733i
$103$	−7.60723	−	2.47174i	−0.749562	−	0.243548i	−0.0907695	−	0.995872i	$-0.528933\pi$
$103$	−7.60723	−	2.47174i	−0.749562	−	0.243548i	−0.658793	+	0.752324i	$0.728933\pi$
$104$	−2.03145	+	6.25217i	−0.199200	+	0.613076i
$105$		0			0
$106$	−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	0.480137	−	0.877194i	$-0.340587\pi$
$109$	−2.14813	−	1.56071i	−0.205754	−	0.149489i	−0.685891	+	0.727705i	$0.740587\pi$
$110$		0			0
$111$	−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	$-0.846017\pi$
$113$	−1.80029	+	2.47788i	−0.169357	+	0.233099i	0.715899	+	0.698203i	$0.246017\pi$
$114$	0.172231	−	0.125133i	0.0161309	−	0.0117198i
$115$		0			0
$116$	−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
$120$		0			0
$121$	−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
$125$		0			0
$126$	−0.533559			−0.0475332
$127$	3.81036	+	5.24451i	0.338115	+	0.465375i	0.943890	−	0.330261i	$-0.107137\pi$
$127$	3.81036	+	5.24451i	0.338115	+	0.465375i	−0.605775	+	0.795636i	$0.707137\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	3.51066	−	10.8047i	0.309096	−	0.951301i
$130$		0			0
$131$	−2.92266	−	8.99503i	−0.255354	−	0.785900i	−0.993760	−	0.111543i	$-0.964421\pi$
$131$	−2.92266	−	8.99503i	−0.255354	−	0.785900i	0.738405	−	0.674357i	$-0.235579\pi$
$132$		−	1.43425i		−	0.124836i
$133$	−0.108029	+	0.0351009i	−0.00936734	+	0.00304363i
$134$	−5.59261	−	4.06327i	−0.483128	−	0.351013i
$135$		0			0
$136$	0.775373	−	0.563341i	0.0664877	−	0.0483061i
$137$	−7.25096	+	9.98010i	−0.619492	+	0.852657i	−0.997316	−	0.0732202i	$-0.976672\pi$
$137$	−7.25096	+	9.98010i	−0.619492	+	0.852657i	0.377824	+	0.925877i	$0.376672\pi$
$138$	−2.21243	+	3.04515i	−0.188335	+	0.259220i
$139$	3.67227	−	2.66806i	0.311478	−	0.226302i	−0.421052	−	0.907036i	$-0.638339\pi$
$139$	3.67227	−	2.66806i	0.311478	−	0.226302i	0.732530	+	0.680734i	$0.238339\pi$
$140$		0			0
$141$	−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
$145$		0			0
$146$	−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	$0.649879\pi$
$150$		0			0
$151$	−1.63387			−0.132962			−0.0664812	−	0.997788i	$-0.521177\pi$
$151$	−1.63387			−0.132962			−0.0664812	+	0.997788i	$0.521177\pi$
$152$	−0.125133	−	0.172231i	−0.0101496	−	0.0139698i
$153$	0.911505	+	0.296166i	0.0736908	+	0.0239436i
$154$	−0.236478	+	0.727804i	−0.0190559	+	0.0586481i
$155$		0			0
$156$	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
$160$		0			0
$161$	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	$-0.670373\pi$
$163$	5.94451	−	8.18191i	0.465610	−	0.640857i	0.975660	+	0.219288i	$0.0703733\pi$
$164$	−6.42486	+	4.66793i	−0.501697	+	0.364504i
$165$		0			0
$166$	−13.2119	−	9.59902i	−1.02544	−	0.745028i
$167$	−12.1625	+	3.95185i	−0.941166	+	0.305803i	−0.739121	−	0.673573i	$-0.764759\pi$
$167$	−12.1625	+	3.95185i	−0.941166	+	0.305803i	−0.202045	+	0.979376i	$0.564759\pi$
$168$			0.533559i			0.0411650i
$169$	−9.33741	−	28.7376i	−0.718262	−	2.21058i
$170$		0			0
$171$	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	$-0.373763\pi$
$173$	−8.02770	−	11.0492i	−0.610335	−	0.840054i	−0.996605	+	0.0823317i	$0.973763\pi$
$174$	−6.19448			−0.469602
$175$		0			0
$176$	−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	−0.979641	−	0.200757i	$-0.935660\pi$
$179$	−0.924399	+	2.84501i	−0.0690928	+	0.212646i	0.910548	+	0.413403i	$0.135660\pi$
$180$		0			0
$181$	2.35559	+	7.24976i	0.175090	+	0.538871i	0.999638	−	0.0269215i	$-0.00857041\pi$
$181$	2.35559	+	7.24976i	0.175090	+	0.538871i	−0.824548	+	0.565792i	$0.808570\pi$
$182$		−	3.50758i		−	0.259999i
$183$	11.9567	−	3.88498i	0.883868	−	0.287186i
$184$	3.04515	+	2.21243i	0.224491	+	0.163102i
$185$		0			0
$186$	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			0
$191$	6.79610	+	4.93766i	0.491749	+	0.357276i	0.805856	−	0.592111i	$-0.201705\pi$
$191$	6.79610	+	4.93766i	0.491749	+	0.357276i	−0.314108	+	0.949387i	$0.601705\pi$
$192$	−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			0
$196$	−2.07515	+	6.38664i	−0.148225	+	0.456189i
$197$	−9.70843	−	3.15446i	−0.691697	−	0.224746i	−0.0579878	−	0.998317i	$-0.518468\pi$
$197$	−9.70843	−	3.15446i	−0.691697	−	0.224746i	−0.633709	+	0.773571i	$0.718468\pi$
$198$	−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	$0.543495\pi$
$200$		0			0
$201$	−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
$205$		0			0
$206$	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			0
$211$	−4.24669	+	3.08540i	−0.292354	+	0.212408i	−0.724288	−	0.689498i	$-0.757831\pi$
$211$	−4.24669	+	3.08540i	−0.292354	+	0.212408i	0.431934	+	0.901905i	$0.357831\pi$
$212$	−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
$215$		0			0
$216$	−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
$220$		0			0
$221$	−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	−0.997312	−	0.0732716i	$-0.976656\pi$
$223$	−11.3315	−	15.5964i	−0.758811	−	1.04441i	0.238501	−	0.971142i	$-0.423344\pi$
$224$	0.533559			0.0356499
$225$		0			0
$226$	3.06283			0.203736
$227$	−4.96066	−	6.82776i	−0.329250	−	0.453174i	0.612013	−	0.790848i	$-0.290360\pi$
$227$	−4.96066	−	6.82776i	−0.329250	−	0.453174i	−0.941263	+	0.337673i	$0.890360\pi$
$228$	−0.202470	−	0.0657863i	−0.0134089	−	0.00435681i
$229$	−1.84041	+	5.66419i	−0.121618	+	0.374300i	−0.993270	−	0.115825i	$-0.963049\pi$
$229$	−1.84041	+	5.66419i	−0.121618	+	0.374300i	0.871652	+	0.490125i	$0.163049\pi$
$230$		0			0
$231$	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	$-0.621839\pi$
$233$	−1.99049	+	0.646750i	−0.130401	+	0.0423700i	0.243089	+	0.970004i	$0.421839\pi$
$234$	5.31842	+	3.86406i	0.347676	+	0.252601i
$235$		0			0
$236$	−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	−0.297855	−	0.954611i	$-0.596271\pi$
$239$	8.00797	−	5.81813i	0.517993	−	0.376344i	0.815847	+	0.578268i	$0.196271\pi$
$240$		0			0
$241$	17.3588	+	12.6119i	1.11818	+	0.812406i	0.983932	−	0.178542i	$-0.0571379\pi$
$241$	17.3588	+	12.6119i	1.11818	+	0.812406i	0.134249	+	0.990948i	$0.457138\pi$
$242$	8.50522	−	2.76351i	0.546736	−	0.177645i
$243$		−	1.00000i		−	0.0641500i
$244$	−3.88498	−	11.9567i	−0.248711	−	0.765452i
$245$		0			0
$246$	−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
$250$		0			0
$251$	−4.10753			−0.259265			−0.129632	−	0.991562i	$-0.541380\pi$
$251$	−4.10753			−0.259265			−0.129632	+	0.991562i	$0.541380\pi$
$252$	0.313618	+	0.431658i	0.0197561	+	0.0271919i
$253$	5.13432	+	1.66824i	0.322792	+	0.104881i
$254$	2.00323	−	6.16529i	0.125694	−	0.386845i
$255$		0			0
$256$	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
$260$		0			0
$261$	−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	0.122183	−	0.992508i	$-0.461011\pi$
$263$	16.6771	−	22.9541i	1.02836	−	1.41541i	0.906174	−	0.422904i	$-0.138989\pi$
$264$	−1.16034	+	0.843033i	−0.0714137	+	0.0518851i
$265$		0			0
$266$	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	−0.999855	−	0.0170443i	$-0.994574\pi$
$269$	−3.29621	−	10.1447i	−0.200974	−	0.618533i	0.798881	−	0.601489i	$-0.205426\pi$
$270$		0			0
$271$	7.05917	−	21.7259i	0.428814	−	1.31975i	−0.470481	−	0.882410i	$-0.655920\pi$
$271$	7.05917	−	21.7259i	0.428814	−	1.31975i	0.899295	−	0.437343i	$-0.144080\pi$
$272$	−0.911505	−	0.296166i	−0.0552681	−	0.0179577i
$273$	−2.06170	−	2.83769i	−0.124780	−	0.171745i
$274$	12.3361			0.745250
$275$		0			0
$276$	3.76401			0.226567
$277$	18.4912	+	25.4510i	1.11103	+	1.52920i	0.819889	+	0.572522i	$0.194035\pi$
$277$	18.4912	+	25.4510i	1.11103	+	1.52920i	0.291141	+	0.956680i	$0.405965\pi$
$278$	−4.31701	−	1.40268i	−0.258917	−	0.0841273i
$279$	0.722398	−	2.22331i	0.0432488	−	0.133106i
$280$		0			0
$281$	−3.33074	−	10.2510i	−0.198695	−	0.611522i	−0.999914	−	0.0131494i	$-0.995814\pi$
$281$	−3.33074	−	10.2510i	−0.198695	−	0.611522i	0.801218	−	0.598372i	$-0.204186\pi$
$282$			10.1489i			0.604359i
$283$	−3.96046	+	1.28683i	−0.235425	+	0.0764943i	−0.424354	−	0.905497i	$-0.639499\pi$
$283$	−3.96046	+	1.28683i	−0.235425	+	0.0764943i	0.188928	+	0.981991i	$0.439499\pi$
$284$	8.19103	+	5.95113i	0.486048	+	0.353135i
$285$		0			0
$286$	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
$290$		0			0
$291$	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
$295$		0			0
$296$	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
$300$		0			0
$301$	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			0
$306$	−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
$310$		0			0
$311$	15.7375	−	11.4339i	0.892390	−	0.648359i	−0.0441099	−	0.999027i	$-0.514045\pi$
$311$	15.7375	−	11.4339i	0.892390	−	0.648359i	0.936500	+	0.350667i	$0.114045\pi$
$312$	3.86406	−	5.31842i	0.218759	−	0.301096i
$313$	−3.45800	+	4.75953i	−0.195458	+	0.269024i	−0.895485	−	0.445092i	$-0.853171\pi$
$313$	−3.45800	+	4.75953i	−0.195458	+	0.269024i	0.700027	+	0.714116i	$0.253171\pi$
$314$	5.37627	−	3.90609i	0.303401	−	0.220433i
$315$		0			0
$316$	−12.5624	−	9.12709i	−0.706688	−	0.513439i
$317$	10.2344	−	3.32534i	0.574818	−	0.186770i	−0.00715959	−	0.999974i	$-0.502279\pi$
$317$	10.2344	−	3.32534i	0.574818	−	0.186770i	0.581978	+	0.813205i	$0.302279\pi$
$318$			3.23354i			0.181328i
$319$	2.74545	+	8.44962i	0.153716	+	0.473088i
$320$		0			0
$321$	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
$325$		0			0
$326$	−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
$330$		0			0
$331$	−0.190692	−	0.586889i	−0.0104814	−	0.0322584i	0.945679	−	0.325102i	$-0.105399\pi$
$331$	−0.190692	−	0.586889i	−0.0104814	−	0.0322584i	−0.956160	+	0.292843i	$0.905399\pi$
$332$			16.3308i			0.896270i
$333$	3.86406	−	1.25551i	0.211749	−	0.0688014i
$334$	10.3461	+	7.51686i	0.566112	+	0.411304i
$335$		0			0
$336$	0.431658	−	0.313618i	0.0235489	−	0.0171093i
$337$	−9.05814	+	12.4675i	−0.493429	+	0.679146i	−0.981016	−	0.193928i	$-0.937877\pi$
$337$	−9.05814	+	12.4675i	−0.493429	+	0.679146i	0.487587	+	0.873074i	$0.337877\pi$
$338$	−17.7608	+	24.4456i	−0.966060	+	1.32967i
$339$	2.47788	−	1.80029i	0.134580	−	0.0977781i
$340$		0			0
$341$	−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
$345$		0			0
$346$	−4.22041	+	12.9891i	−0.226891	+	0.698298i
$347$	21.5477	+	7.00126i	1.15674	+	0.375847i	0.823678	−	0.567058i	$-0.191919\pi$
$347$	21.5477	+	7.00126i	1.15674	+	0.375847i	0.333061	+	0.942905i	$0.391919\pi$
$348$	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	$0.350078\pi$
$350$		0			0
$351$	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	$-0.451581\pi$
$353$	−5.76583	−	1.87343i	−0.306884	−	0.0997127i	−0.458411	+	0.888740i	$0.651581\pi$
$354$	−2.32521	+	7.15627i	−0.123584	+	0.380352i
$355$		0			0
$356$	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	0.912943	−	0.408088i	$-0.133804\pi$
$359$	15.2894	+	11.1084i	0.806943	+	0.586279i	−0.105999	+	0.994366i	$0.533804\pi$
$360$		0			0
$361$	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
$365$		0			0
$366$	−10.1710	−	7.38968i	−0.531648	−	0.386265i
$367$	23.8224	−	7.74036i	1.24352	−	0.404044i	0.387924	−	0.921691i	$-0.373192\pi$
$367$	23.8224	−	7.74036i	1.24352	−	0.404044i	0.855594	+	0.517648i	$0.173192\pi$
$368$		−	3.76401i		−	0.196213i
$369$	2.45408	+	7.55288i	0.127754	+	0.393187i
$370$		0			0
$371$	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	$-0.299647\pi$
$373$	−6.99196	−	9.62360i	−0.362030	−	0.498291i	−0.950713	+	0.310073i	$0.899647\pi$
$374$	−1.37461			−0.0710792
$375$		0			0
$376$	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	0.454423	+	0.890786i	$0.349845\pi$
$379$	−8.50366	+	26.1716i	−0.436804	+	1.34434i	−0.891227	+	0.453558i	$0.850155\pi$
$380$		0			0
$381$	−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	$-0.790305\pi$
$383$	−20.9531	+	6.80809i	−1.07066	+	0.347877i	−0.279912	+	0.960026i	$0.590305\pi$
$384$	0.809017	+	0.587785i	0.0412850	+	0.0299953i
$385$		0			0
$386$	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	−0.168162	−	0.985759i	$-0.553783\pi$
$389$	14.1491	−	10.2799i	0.717386	−	0.521212i	0.885548	+	0.464548i	$0.153783\pi$
$390$		0			0
$391$	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
$395$		0			0
$396$	−0.443209	+	1.36406i	−0.0222721	+	0.0685464i
$397$	−23.3000	−	7.57062i	−1.16939	−	0.379959i	−0.340976	−	0.940072i	$-0.610758\pi$
$397$	−23.3000	−	7.57062i	−1.16939	−	0.379959i	−0.828416	+	0.560113i	$0.810758\pi$
$398$	2.25896	+	3.10920i	0.113232	+	0.155850i
$399$	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	$0.491725\pi$
$402$	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
$405$		0			0
$406$	−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	0.935968	−	0.352085i	$-0.114527\pi$
$409$	18.0061	+	13.0822i	0.890345	+	0.646873i	−0.0456231	+	0.998959i	$0.514527\pi$
$410$		0			0
$411$	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
$415$		0			0
$416$	−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	0.959312	+	0.282347i	$0.0911129\pi$
$419$	7.14737	+	21.9973i	0.349172	+	1.07464i	−0.610141	+	0.792293i	$0.708887\pi$
$420$		0			0
$421$	3.01643	−	9.28363i	0.147012	−	0.452457i	−0.850252	−	0.526376i	$-0.823551\pi$
$421$	3.01643	−	9.28363i	0.147012	−	0.452457i	0.997264	+	0.0739190i	$0.0235506\pi$
$422$	4.99228	+	1.62209i	0.243021	+	0.0789622i
$423$	5.96538	+	8.21065i	0.290047	+	0.399215i
$424$	3.23354			0.157035
$425$		0			0
$426$	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			0
$431$	2.62448	+	8.07731i	0.126417	+	0.389070i	0.994157	−	0.107948i	$-0.0344281\pi$
$431$	2.62448	+	8.07731i	0.126417	+	0.389070i	−0.867740	+	0.497019i	$0.834428\pi$
$432$			1.00000i			0.0481125i
$433$	20.9272	−	6.79967i	1.00570	−	0.326771i	0.240558	−	0.970635i	$-0.422670\pi$
$433$	20.9272	−	6.79967i	1.00570	−	0.326771i	0.765140	+	0.643864i	$0.222670\pi$
$434$	1.00910	+	0.733154i	0.0484384	+	0.0351925i
$435$		0			0
$436$	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	−0.503898	+	0.863763i	$0.668101\pi$
$439$	−31.0325	+	22.5464i	−1.48110	+	1.07608i	−0.977201	+	0.212318i	$0.931899\pi$
$440$		0			0
$441$	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			0
$446$	−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	$0.639930\pi$
$450$		0			0
$451$	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
$455$		0			0
$456$	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
$460$		0			0
$461$	−25.8954	+	18.8141i	−1.20607	+	0.876260i	−0.994868	−	0.101183i	$-0.967737\pi$
$461$	−25.8954	+	18.8141i	−1.20607	+	0.876260i	−0.211200	+	0.977443i	$0.567737\pi$
$462$	0.449808	−	0.619107i	0.0209270	−	0.0288035i
$463$	−16.9150	+	23.2815i	−0.786108	+	1.08198i	0.208474	+	0.978028i	$0.433150\pi$
$463$	−16.9150	+	23.2815i	−0.786108	+	1.08198i	−0.994582	+	0.103957i	$0.966850\pi$
$464$	5.01144	−	3.64102i	0.232650	−	0.169030i
$465$		0			0
$466$	1.69321	+	1.23019i	0.0784366	+	0.0569875i
$467$	−4.94859	+	1.60789i	−0.228993	+	0.0744045i	−0.421266	−	0.906937i	$-0.638414\pi$
$467$	−4.94859	+	1.60789i	−0.228993	+	0.0744045i	0.192273	+	0.981342i	$0.438414\pi$
$468$		−	6.57392i		−	0.303880i
$469$	−1.13978	−	3.50789i	−0.0526303	−	0.161979i
$470$		0			0
$471$	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			0
$476$	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	−0.123609	−	0.992331i	$-0.539447\pi$
$479$	12.2490	−	37.6985i	0.559670	−	1.72249i	0.683279	−	0.730157i	$-0.260553\pi$
$480$		0			0
$481$	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
$485$		0			0
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	−3.19936	+	4.40354i	−0.144977	+	0.199544i	−0.875330	−	0.483527i	$-0.839356\pi$
$487$	−3.19936	+	4.40354i	−0.144977	+	0.199544i	0.730353	+	0.683070i	$0.239356\pi$
$488$	−7.38968	+	10.1710i	−0.334515	+	0.460420i
$489$	−8.18191	+	5.94451i	−0.369999	+	0.268820i
$490$		0			0
$491$	−0.707053	−	0.513704i	−0.0319088	−	0.0231831i	0.571717	−	0.820451i	$-0.306278\pi$
$491$	−0.707053	−	0.513704i	−0.0319088	−	0.0231831i	−0.603625	+	0.797268i	$0.706278\pi$
$492$	7.55288	−	2.45408i	0.340510	−	0.110638i
$493$			5.93687i			0.267383i
$494$	−0.432474	−	1.33102i	−0.0194579	−	0.0598854i
$495$		0			0
$496$	−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	$0.213933\pi$
$500$		0			0
$501$	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	$-0.397731\pi$
$503$	0.304076	+	0.0988002i	0.0135581	+	0.00440528i	−0.302230	+	0.953235i	$0.597731\pi$
$504$	0.164879	−	0.507445i	0.00734429	−	0.0226034i
$505$		0			0
$506$	−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	0.892593	−	0.450863i	$-0.148884\pi$
$509$	16.6867	+	12.1236i	0.739624	+	0.537368i	−0.152969	+	0.988231i	$0.548884\pi$
$510$		0			0
$511$	−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
$515$		0			0
$516$	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
$520$		0			0
$521$	−1.30417	+	4.01383i	−0.0571368	+	0.175849i	−0.975552	−	0.219769i	$-0.929470\pi$
$521$	−1.30417	+	4.01383i	−0.0571368	+	0.175849i	0.918415	+	0.395618i	$0.129470\pi$
$522$	5.89130	+	1.91420i	0.257855	+	0.0837823i
$523$	12.6714	+	17.4407i	0.554081	+	0.762627i	0.990559	−	0.137088i	$-0.0437742\pi$
$523$	12.6714	+	17.4407i	0.554081	+	0.762627i	−0.436478	+	0.899715i	$0.643774\pi$
$524$	9.45794			0.413172
$525$		0			0
$526$	−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
$530$		0			0
$531$	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
$535$		0			0
$536$	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			0
$541$	7.22987	+	5.25281i	0.310837	+	0.225836i	0.732255	−	0.681030i	$-0.238468\pi$
$541$	7.22987	+	5.25281i	0.310837	+	0.225836i	−0.421419	+	0.906866i	$0.638468\pi$
$542$	−21.7259	+	7.05917i	−0.933206	+	0.303217i
$543$		−	7.62285i		−	0.327128i
$544$	0.296166	+	0.911505i	0.0126980	+	0.0390805i
$545$		0			0
$546$	−1.08390	+	3.33590i	−0.0463867	+	0.142764i
$547$	−11.4874	−	3.73249i	−0.491167	−	0.159590i	0.0529536	−	0.998597i	$-0.483136\pi$
$547$	−11.4874	−	3.73249i	−0.491167	−	0.159590i	−0.544120	+	0.839007i	$0.683136\pi$
$548$	−7.25096	−	9.98010i	−0.309746	−	0.426329i
$549$	−12.5721			−0.536563
$550$		0			0
$551$	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			0
$556$	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			0
$561$	−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	$-0.700202\pi$
$563$	8.60271	−	11.8406i	0.362561	−	0.499022i	0.950860	+	0.309621i	$0.100202\pi$
$564$	8.21065	−	5.96538i	0.345731	−	0.251188i
$565$		0			0
$566$	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	−0.921065	−	0.389408i	$-0.872679\pi$
$569$	−9.65590	−	29.7178i	−0.404796	−	1.24583i	0.516269	−	0.856427i	$-0.327321\pi$
$570$		0			0
$571$	8.10430	−	24.9425i	0.339154	−	1.04381i	−0.625485	−	0.780236i	$-0.715099\pi$
$571$	8.10430	−	24.9425i	0.339154	−	1.04381i	0.964639	−	0.263574i	$-0.0849012\pi$
$572$	−8.96720	−	2.91362i	−0.374937	−	0.121825i
$573$	−4.93766	−	6.79610i	−0.206274	−	0.283911i
$574$	−4.23729			−0.176861
$575$		0			0
$576$	1.00000			0.0416667
$577$	−5.25092	−	7.22727i	−0.218599	−	0.300875i	0.685608	−	0.727971i	$-0.259537\pi$
$577$	−5.25092	−	7.22727i	−0.218599	−	0.300875i	−0.904206	+	0.427096i	$0.859537\pi$
$578$	15.2944	+	4.96944i	0.636162	+	0.206701i
$579$	3.25290	−	10.0114i	0.135186	−	0.416060i
$580$		0			0
$581$	−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
$585$		0			0
$586$	14.5302	−	10.5568i	0.600237	−	0.436098i
$587$	2.34738	−	3.23089i	0.0968867	−	0.133353i	−0.757821	−	0.652462i	$-0.773736\pi$
$587$	2.34738	−	3.23089i	0.0968867	−	0.133353i	0.854708	+	0.519109i	$0.173736\pi$
$588$	3.94716	−	5.43280i	0.162778	−	0.224045i
$589$	−0.402629	+	0.292527i	−0.0165900	+	0.0120534i
$590$		0			0
$591$	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
$595$		0			0
$596$	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	$0.456637\pi$
$600$		0			0
$601$	−10.7465			−0.438359			−0.219179	−	0.975685i	$-0.570338\pi$
$601$	−10.7465			−0.438359			−0.219179	+	0.975685i	$0.570338\pi$
$602$	−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
$605$		0			0
$606$	−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
$610$		0			0
$611$	−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	$-0.635350\pi$
$613$	14.3929	−	19.8101i	0.581324	−	0.800123i	0.993840	+	0.110827i	$0.0353500\pi$
$614$	−16.8416	+	12.2362i	−0.679673	+	0.493812i
$615$		0			0
$616$	−0.619107	−	0.449808i	−0.0249445	−	0.0181233i
$617$	17.9899	−	5.84526i	0.724244	−	0.235321i	0.0763819	−	0.997079i	$-0.475663\pi$
$617$	17.9899	−	5.84526i	0.724244	−	0.235321i	0.647862	+	0.761757i	$0.275663\pi$
$618$		−	7.99871i		−	0.321755i
$619$	−0.788010	−	2.42524i	−0.0316728	−	0.0974788i	0.933970	−	0.357350i	$-0.116320\pi$
$619$	−0.788010	−	2.42524i	−0.0316728	−	0.0974788i	−0.965643	+	0.259872i	$0.916320\pi$
$620$		0			0
$621$	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
$625$		0			0
$626$	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			0
$631$	−11.2646	−	34.6688i	−0.448436	−	1.38014i	−0.878671	−	0.477428i	$-0.841569\pi$
$631$	−11.2646	−	34.6688i	−0.448436	−	1.38014i	0.430235	−	0.902717i	$-0.358431\pi$
$632$			15.5279i			0.617668i
$633$	4.99228	−	1.62209i	0.198425	−	0.0644723i
$634$	−8.70586	−	6.32518i	−0.345754	−	0.251205i
$635$		0			0
$636$	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
$640$		0			0
$641$	16.4772	+	11.9714i	0.650809	+	0.472840i	0.863546	−	0.504269i	$-0.168238\pi$
$641$	16.4772	+	11.9714i	0.650809	+	0.472840i	−0.212738	+	0.977109i	$0.568238\pi$
$642$	−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
$645$		0			0
$646$	−0.0630505	+	0.194049i	−0.00248069	+	0.00763477i
$647$	5.60379	+	1.82078i	0.220308	+	0.0715823i	0.417091	−	0.908865i	$-0.363050\pi$
$647$	5.60379	+	1.82078i	0.220308	+	0.0715823i	−0.196783	+	0.980447i	$0.563050\pi$
$648$	0.587785	+	0.809017i	0.0230904	+	0.0317812i
$649$	10.7921			0.423627
$650$		0			0
$651$	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	$-0.508639\pi$
$653$	−16.2691	−	5.28614i	−0.636658	−	0.206863i	−0.609522	+	0.792769i	$0.708639\pi$
$654$	0.820514	−	2.52528i	0.0320847	−	0.0987464i
$655$		0			0
$656$	−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	0.0110052	−	0.999939i	$-0.496497\pi$
$659$	−24.0433	−	17.4685i	−0.936593	−	0.680475i	−0.947598	+	0.319465i	$0.896497\pi$
$660$		0			0
$661$	−37.4604	+	27.2166i	−1.45704	+	1.05860i	−0.472920	+	0.881105i	$0.656800\pi$
$661$	−37.4604	+	27.2166i	−1.45704	+	1.05860i	−0.984121	+	0.177497i	$0.943200\pi$
$662$	−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			0
$666$	−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
$670$		0			0
$671$	−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	$-0.0759775\pi$
$673$	11.5841	+	15.9441i	0.446534	+	0.614601i	−0.525114	+	0.851032i	$0.675977\pi$
$674$	15.4106			0.593595
$675$		0			0
$676$	30.2165			1.16217
$677$	14.5638	+	20.0453i	0.559732	+	0.770405i	0.991292	−	0.131679i	$-0.0420368\pi$
$677$	14.5638	+	20.0453i	0.559732	+	0.770405i	−0.431560	+	0.902084i	$0.642037\pi$
$678$	−2.91292	−	0.946466i	−0.111870	−	0.0363488i
$679$	−0.917646	+	2.82422i	−0.0352160	+	0.108384i
$680$		0			0
$681$	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	$-0.702793\pi$
$683$	−15.7755	+	5.12579i	−0.603635	+	0.196133i	−0.00877377	+	0.999962i	$0.502793\pi$
$684$	0.172231	+	0.125133i	0.00658541	+	0.00478458i
$685$		0			0
$686$	−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
$690$		0			0
$691$	−34.2128	−	24.8570i	−1.30152	−	0.945606i	−0.301546	−	0.953452i	$-0.597503\pi$
$691$	−34.2128	−	24.8570i	−1.30152	−	0.945606i	−0.999969	+	0.00784530i	$0.997503\pi$
$692$	12.9891	−	4.22041i	0.493771	−	0.160436i
$693$		−	0.765259i		−	0.0290698i
$694$	−7.00126	−	21.5477i	−0.265764	−	0.817938i
$695$		0			0
$696$	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			0
$701$	−22.7240			−0.858273			−0.429137	−	0.903240i	$-0.641182\pi$
$701$	−22.7240			−0.858273			−0.429137	+	0.903240i	$0.641182\pi$
$702$	−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
$705$		0			0
$706$	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	0.993300	+	0.115565i	$0.0368678\pi$
$709$	37.5483	+	27.2804i	1.41016	+	1.02454i	0.416855	+	0.908973i	$0.363132\pi$
$710$		0			0
$711$	−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
$715$		0			0
$716$	−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	0.971412	+	0.237400i	$0.0762952\pi$
$719$	8.71631	+	26.8260i	0.325063	+	1.00044i	−0.646349	+	0.763042i	$0.723705\pi$
$720$		0			0
$721$	−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
$725$		0			0
$726$	−8.94292			−0.331903
$727$	0.500553	+	0.688953i	0.0185645	+	0.0255518i	0.818198	−	0.574936i	$-0.194973\pi$
$727$	0.500553	+	0.688953i	0.0185645	+	0.0255518i	−0.799634	+	0.600488i	$0.794973\pi$
$728$	3.33590	+	1.08390i	0.123637	+	0.0401720i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$		0			0
$731$	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	$-0.792096\pi$
$733$	−29.2259	+	9.49607i	−1.07948	+	0.350745i	−0.285309	+	0.958436i	$0.592096\pi$
$734$	−20.2645	−	14.7230i	−0.747978	−	0.543437i
$735$		0			0
$736$	−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	−0.556636	−	0.830756i	$-0.687908\pi$
$739$	1.67050	−	1.21369i	0.0614502	−	0.0446462i	0.618086	+	0.786110i	$0.287908\pi$
$740$		0			0
$741$	−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
$745$		0			0
$746$	−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			0
$751$	−40.6331			−1.48272			−0.741361	−	0.671106i	$-0.765819\pi$
$751$	−40.6331			−1.48272			−0.741361	+	0.671106i	$0.765819\pi$
$752$	−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
$755$		0			0
$756$	−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			0
$761$	24.4172	−	17.7401i	0.885121	−	0.643078i	−0.0494802	−	0.998775i	$-0.515756\pi$
$761$	24.4172	−	17.7401i	0.885121	−	0.643078i	0.934601	+	0.355697i	$0.115756\pi$
$762$	−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
$765$		0			0
$766$	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	−0.997035	−	0.0769513i	$-0.975481\pi$
$769$	−6.53471	−	20.1118i	−0.235648	−	0.725249i	0.761387	−	0.648297i	$-0.224519\pi$
$770$		0			0
$771$	−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	$-0.0223543\pi$
$773$	17.3085	+	23.8231i	0.622544	+	0.856858i	−0.374991	+	0.927028i	$0.622354\pi$
$774$	11.3607			0.408353
$775$		0			0
$776$	−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
$780$		0			0
$781$	−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
$785$		0			0
$786$	7.65163	−	5.55924i	0.272925	−	0.198291i
$787$	3.03811	−	4.18161i	0.108297	−	0.149058i	−0.751428	−	0.659815i	$-0.770635\pi$
$787$	3.03811	−	4.18161i	0.108297	−	0.149058i	0.859725	+	0.510757i	$0.170635\pi$
$788$	6.00014	−	8.25848i	0.213746	−	0.294196i
$789$	−22.9541	+	16.6771i	−0.817189	+	0.593722i
$790$		0			0
$791$	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
$795$		0			0
$796$	1.18761	−	3.65508i	0.0420937	−	0.129551i
$797$	3.57413	+	1.16131i	0.126602	+	0.0411356i	0.371633	−	0.928380i	$-0.378798\pi$
$797$	3.57413	+	1.16131i	0.126602	+	0.0411356i	−0.245031	+	0.969515i	$0.578798\pi$
$798$	−0.0667659	−	0.0918954i	−0.00236349	−	0.00325306i
$799$	9.72686			0.344111
$800$		0			0
$801$	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			0
$806$	−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	0.249722	−	0.968317i	$-0.419661\pi$
$809$	−16.8961	−	12.2757i	−0.594034	−	0.431591i	−0.843756	+	0.536727i	$0.819661\pi$
$810$		0			0
$811$	29.5317	−	21.4560i	1.03700	−	0.753423i	0.0673004	−	0.997733i	$-0.478561\pi$
$811$	29.5317	−	21.4560i	1.03700	−	0.753423i	0.969697	+	0.244310i	$0.0785614\pi$
$812$	−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
$815$		0			0
$816$	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			0
$821$	10.2662	−	31.5961i	0.358293	−	1.10271i	−0.595783	−	0.803146i	$-0.703158\pi$
$821$	10.2662	−	31.5961i	0.358293	−	1.10271i	0.954076	−	0.299566i	$-0.0968419\pi$
$822$	−11.7323	−	3.81206i	−0.409211	−	0.132961i
$823$	19.2733	+	26.5275i	0.671827	+	0.924690i	0.999800	−	0.0199969i	$-0.00636565\pi$
$823$	19.2733	+	26.5275i	0.671827	+	0.924690i	−0.327973	+	0.944687i	$0.606366\pi$
$824$	−7.99871			−0.278648
$825$		0			0
$826$	−4.01479			−0.139692
$827$	3.05011	+	4.19811i	0.106063	+	0.145983i	0.858749	−	0.512397i	$-0.171242\pi$
$827$	3.05011	+	4.19811i	0.106063	+	0.145983i	−0.752686	+	0.658379i	$0.771242\pi$
$828$	−3.57979	−	1.16314i	−0.124406	−	0.0404220i
$829$	1.71758	−	5.28616i	0.0596539	−	0.183596i	−0.916789	−	0.399372i	$-0.869228\pi$
$829$	1.71758	−	5.28616i	0.0596539	−	0.183596i	0.976443	+	0.215776i	$0.0692282\pi$
$830$		0			0
$831$	−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
$835$		0			0
$836$	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	0.217725	−	0.976010i	$-0.430136\pi$
$839$	35.1423	−	25.5324i	1.21325	−	0.881475i	0.995522	+	0.0945346i	$0.0301363\pi$
$840$		0			0
$841$	−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
$845$		0			0
$846$	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
$850$		0			0
$851$	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	$-0.381771\pi$
$853$	3.17978	+	1.03317i	0.108874	+	0.0353752i	−0.254074	+	0.967185i	$0.581771\pi$
$854$	2.07287	−	6.37963i	0.0709321	−	0.218306i
$855$		0			0
$856$	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	0.207739	−	0.978184i	$-0.433390\pi$
$859$	−19.2961	−	14.0195i	−0.658375	−	0.478338i	−0.866114	+	0.499847i	$0.833390\pi$
$860$		0			0
$861$	−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	$-0.768904\pi$
$863$	3.36837	−	4.63616i	0.114661	−	0.157817i	0.862490	+	0.506074i	$0.168904\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$		0			0
$866$	−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
$870$		0			0
$871$	−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
$875$		0			0
$876$	−13.9771			−0.472242
$877$	29.3000	+	40.3280i	0.989392	+	1.36178i	0.931613	+	0.363452i	$0.118402\pi$
$877$	29.3000	+	40.3280i	0.989392	+	1.36178i	0.0577792	+	0.998329i	$0.481598\pi$
$878$	36.4808	+	11.8533i	1.23117	+	0.400031i
$879$	5.55004	−	17.0813i	0.187198	−	0.576137i
$880$		0			0
$881$	−2.36586	−	7.28138i	−0.0797079	−	0.245316i	0.903260	−	0.429094i	$-0.141167\pi$
$881$	−2.36586	−	7.28138i	−0.0797079	−	0.245316i	−0.982968	+	0.183778i	$0.941167\pi$
$882$		−	6.71531i		−	0.226116i
$883$	−37.0873	+	12.0504i	−1.24809	+	0.405528i	−0.857235	−	0.514925i	$-0.827820\pi$
$883$	−37.0873	+	12.0504i	−1.24809	+	0.405528i	−0.390852	+	0.920453i	$0.627820\pi$
$884$	−5.09724	−	3.70336i	−0.171439	−	0.124558i
$885$		0			0
$886$	−10.3132	+	7.49296i	−0.346478	+	0.251731i
$887$	19.1229	−	26.3204i	0.642083	−	0.883752i	−0.356641	−	0.934241i	$-0.616078\pi$
$887$	19.1229	−	26.3204i	0.642083	−	0.883752i	0.998725	+	0.0504894i	$0.0160781\pi$
$888$	−2.38812	+	3.28696i	−0.0801400	+	0.110303i
$889$	2.79826	−	2.03305i	0.0938505	−	0.0681864i
$890$		0			0
$891$	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
$895$		0			0
$896$	−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
$900$		0			0
$901$	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
$905$		0			0
$906$	−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
$910$		0			0
$911$	23.1152	−	16.7942i	0.765842	−	0.556417i	−0.134855	−	0.990865i	$-0.543057\pi$
$911$	23.1152	−	16.7942i	0.765842	−	0.556417i	0.900697	+	0.434449i	$0.143057\pi$
$912$	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
$915$		0			0
$916$	−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	0.952989	−	0.303005i	$-0.0979900\pi$
$919$	0.118310	+	0.364122i	0.00390270	+	0.0120113i	−0.949086	+	0.315016i	$0.897990\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$	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	−0.914314	−	0.405006i	$-0.867270\pi$
$929$	1.93355	−	5.95087i	0.0634378	−	0.195242i	0.977752	+	0.209764i	$0.0672696\pi$
$930$		0			0
$931$	−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			0
$936$	−5.31842	+	3.86406i	−0.173838	+	0.126301i
$937$	2.89904	−	3.99019i	0.0947075	−	0.130354i	−0.759034	−	0.651052i	$-0.774328\pi$
$937$	2.89904	−	3.99019i	0.0947075	−	0.130354i	0.853741	+	0.520698i	$0.174328\pi$
$938$	−2.16800	+	2.98399i	−0.0707876	+	0.0974307i
$939$	4.75953	−	3.45800i	0.155321	−	0.112847i
$940$		0			0
$941$	−24.1174	−	17.5223i	−0.786204	−	0.571210i	0.120631	−	0.992697i	$-0.461508\pi$
$941$	−24.1174	−	17.5223i	−0.786204	−	0.571210i	−0.906834	+	0.421487i	$0.861508\pi$
$942$	−6.32019	+	2.05355i	−0.205923	+	0.0669084i
$943$			29.8921i			0.973422i
$944$	−2.32521	−	7.15627i	−0.0756793	−	0.232917i
$945$		0			0
$946$	5.03518	−	15.4967i	0.163708	−	0.503840i
$947$	25.5953	+	8.31642i	0.831736	+	0.270247i	0.693777	−	0.720190i	$-0.255946\pi$
$947$	25.5953	+	8.31642i	0.831736	+	0.270247i	0.137960	+	0.990438i	$0.455946\pi$
$948$	9.12709	+	12.5624i	0.296434	+	0.408007i
$949$	91.8843			2.98269
$950$		0			0
$951$	−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	$-0.193949\pi$
$953$	35.4113	+	11.5058i	1.14709	+	0.372711i	0.327041	+	0.945010i	$0.393949\pi$
$954$	0.999220	−	3.07528i	0.0323510	−	0.0995660i
$955$		0			0
$956$	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			0
$961$	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
$965$		0			0
$966$	1.62477	+	1.18046i	0.0522760	+	0.0379807i
$967$	15.2973	−	4.97039i	0.491928	−	0.159837i	−0.0525399	−	0.998619i	$-0.516732\pi$
$967$	15.2973	−	4.97039i	0.491928	−	0.159837i	0.544468	+	0.838782i	$0.316732\pi$
$968$			8.94292i			0.287436i
$969$	0.0630505	+	0.194049i	0.00202547	+	0.00623377i
$970$		0			0
$971$	3.78758	−	11.6570i	0.121549	−	0.374090i	−0.871707	−	0.490027i	$-0.836987\pi$
$971$	3.78758	−	11.6570i	0.121549	−	0.374090i	0.993257	+	0.115937i	$0.0369870\pi$
$972$	0.951057	+	0.309017i	0.0305052	+	0.00991172i
$973$	−1.42357	−	1.95937i	−0.0456375	−	0.0628146i
$974$	5.44308			0.174407
$975$		0			0
$976$	12.5721			0.402422
$977$	10.5930	+	14.5800i	0.338899	+	0.466454i	0.944119	−	0.329604i	$-0.106915\pi$
$977$	10.5930	+	14.5800i	0.338899	+	0.466454i	−0.605221	+	0.796058i	$0.706915\pi$
$978$	9.61841	+	3.12521i	0.307563	+	0.0999333i
$979$	2.49180	−	7.66899i	0.0796384	−	0.245102i
$980$		0			0
$981$	−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	$-0.888808\pi$
$983$	−46.9850	+	15.2663i	−1.49859	+	0.486921i	−0.558982	+	0.829180i	$0.688808\pi$
$984$	−6.42486	−	4.66793i	−0.204817	−	0.148808i
$985$		0			0
$986$	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
$990$		0			0
$991$	24.7287	+	17.9665i	0.785533	+	0.570723i	0.906635	−	0.421917i	$-0.138643\pi$
$991$	24.7287	+	17.9665i	0.785533	+	0.570723i	−0.121101	+	0.992640i	$0.538643\pi$
$992$	2.22331	−	0.722398i	0.0705902	−	0.0229362i
$993$			0.617092i			0.0195828i
$994$	1.66934	+	5.13771i	0.0529484	+	0.162958i
$995$		0			0
$996$	5.04650	−	15.5315i	0.159905	−	0.492136i
$997$	−6.47717	−	2.10456i	−0.205134	−	0.0666521i	0.204648	−	0.978836i	$-0.434395\pi$
$997$	−6.47717	−	2.10456i	−0.205134	−	0.0666521i	−0.409782	+	0.912184i	$0.634395\pi$
$998$	−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	750.2.h.d.199.1		16
5.2	odd	4		750.2.g.g.301.3		16
5.3	odd	4		750.2.g.f.301.2		16
5.4	even	2		150.2.h.b.139.3	yes	16
15.14	odd	2		450.2.l.c.289.2		16
25.3	odd	20		3750.2.a.v.1.3		8
25.4	even	10		3750.2.c.k.1249.6		16
25.9	even	10	inner	750.2.h.d.49.2		16
25.12	odd	20		750.2.g.g.451.3		16
25.13	odd	20		750.2.g.f.451.2		16
25.16	even	5		150.2.h.b.109.3	✓	16
25.21	even	5		3750.2.c.k.1249.11		16
25.22	odd	20		3750.2.a.u.1.6		8
75.41	odd	10		450.2.l.c.109.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.109.3	✓	16	25.16	even	5
150.2.h.b.139.3	yes	16	5.4	even	2
450.2.l.c.109.2		16	75.41	odd	10
450.2.l.c.289.2		16	15.14	odd	2
750.2.g.f.301.2		16	5.3	odd	4
750.2.g.f.451.2		16	25.13	odd	20
750.2.g.g.301.3		16	5.2	odd	4
750.2.g.g.451.3		16	25.12	odd	20
750.2.h.d.49.2		16	25.9	even	10	inner
750.2.h.d.199.1		16	1.1	even	1	trivial
3750.2.a.u.1.6		8	25.22	odd	20
3750.2.a.v.1.3		8	25.3	odd	20
3750.2.c.k.1249.6		16	25.4	even	10
3750.2.c.k.1249.11		16	25.21	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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} -0.533559i q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} -0.533559i q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(1.16034 - 0.843033i) q^{11} +(0.587785 - 0.809017i) q^{12} +(-3.86406 + 5.31842i) q^{13} +(-0.431658 + 0.313618i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(0.911505 - 0.296166i) q^{17} -1.00000i q^{18} +(-0.0657863 - 0.202470i) q^{19} +(-0.164879 + 0.507445i) q^{21} +(-1.36406 - 0.443209i) q^{22} +(2.21243 + 3.04515i) q^{23} -1.00000 q^{24} +6.57392 q^{26} +(-0.587785 - 0.809017i) q^{27} +(0.507445 + 0.164879i) q^{28} +(-1.91420 + 5.89130i) q^{29} +(-0.722398 - 2.22331i) q^{31} +1.00000i q^{32} +(-1.36406 + 0.443209i) q^{33} +(-0.775373 - 0.563341i) q^{34} +(-0.809017 + 0.587785i) q^{36} +(2.38812 - 3.28696i) q^{37} +(-0.125133 + 0.172231i) q^{38} +(5.31842 - 3.86406i) q^{39} +(6.42486 + 4.66793i) q^{41} +(0.507445 - 0.164879i) q^{42} +11.3607i q^{43} +(0.443209 + 1.36406i) q^{44} +(1.16314 - 3.57979i) q^{46} +(9.65219 + 3.13619i) q^{47} +(0.587785 + 0.809017i) q^{48} +6.71531 q^{49} -0.958413 q^{51} +(-3.86406 - 5.31842i) q^{52} +(3.07528 + 0.999220i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-0.164879 - 0.507445i) q^{56} +0.212889i q^{57} +(5.89130 - 1.91420i) q^{58} +(6.08749 + 4.42282i) q^{59} +(-10.1710 + 7.38968i) q^{61} +(-1.37408 + 1.89126i) q^{62} +(0.313618 - 0.431658i) q^{63} +(0.809017 - 0.587785i) q^{64} +(1.16034 + 0.843033i) q^{66} +(6.57451 - 2.13619i) q^{67} +0.958413i q^{68} +(-1.16314 - 3.57979i) q^{69} +(3.12869 - 9.62913i) q^{71} +(0.951057 + 0.309017i) q^{72} +(-8.21552 - 11.3077i) q^{73} -4.06291 q^{74} +0.212889 q^{76} +(-0.449808 - 0.619107i) q^{77} +(-6.25217 - 2.03145i) q^{78} +(-4.79840 + 14.7679i) q^{79} +(0.309017 + 0.951057i) q^{81} -7.94156i q^{82} +(15.5315 - 5.04650i) q^{83} +(-0.431658 - 0.313618i) q^{84} +(9.19103 - 6.67767i) q^{86} +(3.64102 - 5.01144i) q^{87} +(0.843033 - 1.16034i) q^{88} +(4.54845 - 3.30464i) q^{89} +(2.83769 + 2.06170i) q^{91} +(-3.57979 + 1.16314i) q^{92} +2.33773i q^{93} +(-3.13619 - 9.65219i) q^{94} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 4 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 - 4 * q^6 + 4 * q^9	\( 16 q + 4 q^{4} - 4 q^{6} + 4 q^{9} + 2 q^{11} - 20 q^{13} + 2 q^{14} - 4 q^{16} + 30 q^{17} - 2 q^{21} + 20 q^{22} + 10 q^{23} - 16 q^{24} + 4 q^{26} - 10 q^{29} - 18 q^{31} + 20 q^{33} + 12 q^{34} - 4 q^{36} - 20 q^{37} - 10 q^{38} - 4 q^{39} + 22 q^{41} + 8 q^{44} - 6 q^{46} + 50 q^{47} - 52 q^{49} + 28 q^{51} - 20 q^{52} - 30 q^{53} + 4 q^{54} - 2 q^{56} + 30 q^{58} + 20 q^{59} + 12 q^{61} - 50 q^{62} - 10 q^{63} + 4 q^{64} + 2 q^{66} + 50 q^{67} + 6 q^{69} - 28 q^{71} - 20 q^{73} + 12 q^{74} + 20 q^{76} - 100 q^{77} - 20 q^{79} - 4 q^{81} + 30 q^{83} + 2 q^{84} - 6 q^{86} - 10 q^{87} + 70 q^{89} + 12 q^{91} + 30 q^{92} + 2 q^{94} - 4 q^{96} + 10 q^{97} - 60 q^{98} - 12 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 4 * q^6 + 4 * q^9 + 2 * q^11 - 20 * q^13 + 2 * q^14 - 4 * q^16 + 30 * q^17 - 2 * q^21 + 20 * q^22 + 10 * q^23 - 16 * q^24 + 4 * q^26 - 10 * q^29 - 18 * q^31 + 20 * q^33 + 12 * q^34 - 4 * q^36 - 20 * q^37 - 10 * q^38 - 4 * q^39 + 22 * q^41 + 8 * q^44 - 6 * q^46 + 50 * q^47 - 52 * q^49 + 28 * q^51 - 20 * q^52 - 30 * q^53 + 4 * q^54 - 2 * q^56 + 30 * q^58 + 20 * q^59 + 12 * q^61 - 50 * q^62 - 10 * q^63 + 4 * q^64 + 2 * q^66 + 50 * q^67 + 6 * q^69 - 28 * q^71 - 20 * q^73 + 12 * q^74 + 20 * q^76 - 100 * q^77 - 20 * q^79 - 4 * q^81 + 30 * q^83 + 2 * q^84 - 6 * q^86 - 10 * q^87 + 70 * q^89 + 12 * q^91 + 30 * q^92 + 2 * q^94 - 4 * q^96 + 10 * q^97 - 60 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

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Database

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