LMFDB - Embedded newform 525.2.bb.a.41.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(41,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 2, 5]))

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

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

chi := DirichletCharacter("525.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bb (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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.19
Character	$\chi$	$=$	525.41
Dual form			525.2.bb.a.461.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.990929 + 1.36390i) q^{2} +(-1.48109 + 0.897991i) q^{3} +(-0.260241 - 0.800939i) q^{4} +(-1.04257 + 1.97814i) q^{5} +(0.242884 - 2.90989i) q^{6} +(-0.769360 + 2.53142i) q^{7} +(-1.85644 - 0.603193i) q^{8} +(1.38723 - 2.66000i) q^{9} +O(q^{10})$	\(q+(-0.990929 + 1.36390i) q^{2} +(-1.48109 + 0.897991i) q^{3} +(-0.260241 - 0.800939i) q^{4} +(-1.04257 + 1.97814i) q^{5} +(0.242884 - 2.90989i) q^{6} +(-0.769360 + 2.53142i) q^{7} +(-1.85644 - 0.603193i) q^{8} +(1.38723 - 2.66000i) q^{9} +(-1.66486 - 3.38216i) q^{10} +(-2.06540 + 2.84279i) q^{11} +(1.10467 + 0.952565i) q^{12} +(-0.245541 - 0.337958i) q^{13} +(-2.69021 - 3.55779i) q^{14} +(-0.232211 - 3.86602i) q^{15} +(4.02493 - 2.92428i) q^{16} +(-1.70453 + 5.24599i) q^{17} +(2.25333 + 4.52791i) q^{18} +(-1.12360 - 0.365079i) q^{19} +(1.85569 + 0.320245i) q^{20} +(-1.13370 - 4.44013i) q^{21} +(-1.83060 - 5.63400i) q^{22} +(0.0709236 - 0.0976180i) q^{23} +(3.29120 - 0.773682i) q^{24} +(-2.82608 - 4.12472i) q^{25} +0.704253 q^{26} +(0.334056 + 5.18540i) q^{27} +(2.22773 - 0.0425682i) q^{28} +(4.12563 - 1.34050i) q^{29} +(5.50295 + 3.51424i) q^{30} +(5.87405 + 1.90859i) q^{31} +4.48340i q^{32} +(0.506245 - 6.06512i) q^{33} +(-5.46593 - 7.52321i) q^{34} +(-4.20539 - 4.16109i) q^{35} +(-2.49151 - 0.418842i) q^{36} +(2.02615 - 1.47208i) q^{37} +(1.61134 - 1.17070i) q^{38} +(0.667149 + 0.280051i) q^{39} +(3.12867 - 3.04342i) q^{40} +(-2.10494 + 1.52933i) q^{41} +(7.17930 + 2.85360i) q^{42} +2.72678 q^{43} +(2.81440 + 0.914454i) q^{44} +(3.81557 + 5.51738i) q^{45} +(0.0628606 + 0.193465i) q^{46} +(-1.23977 - 3.81561i) q^{47} +(-3.33528 + 7.94546i) q^{48} +(-5.81617 - 3.89515i) q^{49} +(8.42613 + 0.232821i) q^{50} +(-2.18630 - 9.30041i) q^{51} +(-0.206784 + 0.284614i) q^{52} +(10.3120 - 3.35057i) q^{53} +(-7.40338 - 4.68275i) q^{54} +(-3.47009 - 7.04948i) q^{55} +(2.95520 - 4.23535i) q^{56} +(1.99198 - 0.468267i) q^{57} +(-2.25991 + 6.95527i) q^{58} +(-6.37221 + 4.62968i) q^{59} +(-3.03601 + 1.19208i) q^{60} +(8.51535 - 11.7204i) q^{61} +(-8.42390 + 6.12032i) q^{62} +(5.66630 + 5.55815i) q^{63} +(1.93496 + 1.40583i) q^{64} +(0.924522 - 0.133368i) q^{65} +(7.77055 + 6.70057i) q^{66} +(-3.14330 + 9.67410i) q^{67} +4.64531 q^{68} +(-0.0173839 + 0.208269i) q^{69} +(9.84255 - 1.61237i) q^{70} +(-3.22622 + 1.04826i) q^{71} +(-4.17979 + 4.10136i) q^{72} +(-6.05823 + 8.33844i) q^{73} +4.22218i q^{74} +(7.88962 + 3.57126i) q^{75} +0.994942i q^{76} +(-5.60724 - 7.41553i) q^{77} +(-1.04306 + 0.632413i) q^{78} +(3.56443 + 10.9702i) q^{79} +(1.58835 + 11.0107i) q^{80} +(-5.15121 - 7.38004i) q^{81} -4.38638i q^{82} +(3.68232 - 11.3330i) q^{83} +(-3.26123 + 2.06353i) q^{84} +(-8.60022 - 8.84113i) q^{85} +(-2.70205 + 3.71905i) q^{86} +(-4.90665 + 5.69017i) q^{87} +(5.54904 - 4.03161i) q^{88} +(-13.3111 - 9.67105i) q^{89} +(-11.3061 - 0.263284i) q^{90} +(1.04442 - 0.361555i) q^{91} +(-0.0966433 - 0.0314013i) q^{92} +(-10.4139 + 2.44805i) q^{93} +(6.43262 + 2.09008i) q^{94} +(1.89361 - 1.84201i) q^{95} +(-4.02605 - 6.64030i) q^{96} +(-2.83435 + 0.920938i) q^{97} +(11.0760 - 4.07284i) q^{98} +(4.69663 + 9.43756i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9}+O(q^{10}) $ 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9	$ 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9} + 8 q^{15} - 92 q^{16} - 16 q^{18} + 12 q^{21} - 48 q^{22} - 32 q^{25} - 36 q^{28} - 14 q^{30} - 8 q^{36} - 4 q^{37} - 26 q^{39} - 11 q^{42} - 20 q^{49} + 20 q^{51} - 168 q^{57} + 32 q^{58} + 76 q^{60} + 29 q^{63} + 68 q^{64} - 44 q^{67} + 30 q^{70} - 114 q^{72} - 124 q^{78} - 68 q^{79} - 2 q^{81} + 102 q^{84} + 72 q^{85} - 156 q^{88} + 70 q^{91} - 32 q^{93} - 36 q^{99}+O(q^{100}) $ 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9 + 8 * q^15 - 92 * q^16 - 16 * q^18 + 12 * q^21 - 48 * q^22 - 32 * q^25 - 36 * q^28 - 14 * q^30 - 8 * q^36 - 4 * q^37 - 26 * q^39 - 11 * q^42 - 20 * q^49 + 20 * q^51 - 168 * q^57 + 32 * q^58 + 76 * q^60 + 29 * q^63 + 68 * q^64 - 44 * q^67 + 30 * q^70 - 114 * q^72 - 124 * q^78 - 68 * q^79 - 2 * q^81 + 102 * q^84 + 72 * q^85 - 156 * q^88 + 70 * q^91 - 32 * q^93 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$	$-1$

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 $

$2$	−0.990929	+	1.36390i	−0.700693	+	0.964421i	0.299255	+	0.954173i	$0.403262\pi$
$2$	−0.990929	+	1.36390i	−0.700693	+	0.964421i	−0.999947	+	0.0102478i	$0.996738\pi$
$3$	−1.48109	+	0.897991i	−0.855105	+	0.518455i
$3$	−1.48109	+	0.897991i	−0.855105	+	0.518455i
$4$	−0.260241	−	0.800939i	−0.130120	−	0.400470i
$5$	−1.04257	+	1.97814i	−0.466253	+	0.884651i
$5$	−1.04257	+	1.97814i	−0.466253	+	0.884651i
$6$	0.242884	−	2.90989i	0.0991569	−	1.18796i
$7$	−0.769360	+	2.53142i	−0.290791	+	0.956787i
$7$	−0.769360	+	2.53142i	−0.290791	+	0.956787i
$8$	−1.85644	−	0.603193i	−0.656349	−	0.213261i
$9$	1.38723	−	2.66000i	0.462409	−	0.886667i
$10$	−1.66486	−	3.38216i	−0.526476	−	1.06953i
$11$	−2.06540	+	2.84279i	−0.622743	+	0.857132i	−0.997549	−	0.0699711i	$-0.977709\pi$
$11$	−2.06540	+	2.84279i	−0.622743	+	0.857132i	0.374806	+	0.927103i	$0.377709\pi$
$12$	1.10467	+	0.952565i	0.318892	+	0.274982i
$13$	−0.245541	−	0.337958i	−0.0681007	−	0.0937326i	0.773608	−	0.633664i	$-0.218450\pi$
$13$	−0.245541	−	0.337958i	−0.0681007	−	0.0937326i	−0.841709	+	0.539932i	$0.818450\pi$
$14$	−2.69021	−	3.55779i	−0.718990	−	0.950858i
$15$	−0.232211	−	3.86602i	−0.0599565	−	0.998201i
$16$	4.02493	−	2.92428i	1.00623	−	0.731070i
$17$	−1.70453	+	5.24599i	−0.413408	+	1.27234i	0.500258	+	0.865876i	$0.333238\pi$
$17$	−1.70453	+	5.24599i	−0.413408	+	1.27234i	−0.913667	+	0.406464i	$0.866762\pi$
$18$	2.25333	+	4.52791i	0.531114	+	1.06724i
$19$	−1.12360	−	0.365079i	−0.257771	−	0.0837549i	0.177281	−	0.984160i	$-0.443270\pi$
$19$	−1.12360	−	0.365079i	−0.257771	−	0.0837549i	−0.435052	+	0.900405i	$0.643270\pi$
$20$	1.85569	+	0.320245i	0.414945	+	0.0716090i
$21$	−1.13370	−	4.44013i	−0.247394	−	0.968915i
$22$	−1.83060	−	5.63400i	−0.390285	−	1.20117i
$23$	0.0709236	−	0.0976180i	0.0147886	−	0.0203548i	−0.801559	−	0.597916i	$-0.795996\pi$
$23$	0.0709236	−	0.0976180i	0.0147886	−	0.0203548i	0.816347	+	0.577561i	$0.195996\pi$
$24$	3.29120	−	0.773682i	0.671814	−	0.157927i
$25$	−2.82608	−	4.12472i	−0.565216	−	0.824943i
$26$	0.704253			0.138115
$27$	0.334056	+	5.18540i	0.0642892	+	0.997931i
$28$	2.22773	−	0.0425682i	0.421002	−	0.00804464i
$29$	4.12563	−	1.34050i	0.766110	−	0.248924i	0.100211	−	0.994966i	$-0.468048\pi$
$29$	4.12563	−	1.34050i	0.766110	−	0.248924i	0.665899	+	0.746042i	$0.268048\pi$
$30$	5.50295	+	3.51424i	1.00470	+	0.641609i
$31$	5.87405	+	1.90859i	1.05501	+	0.342794i	0.784633	−	0.619961i	$-0.212851\pi$
$31$	5.87405	+	1.90859i	1.05501	+	0.342794i	0.270378	+	0.962754i	$0.412851\pi$
$32$			4.48340i			0.792561i
$33$	0.506245	−	6.06512i	0.0881260	−	1.05580i
$34$	−5.46593	−	7.52321i	−0.937399	−	1.29022i
$35$	−4.20539	−	4.16109i	−0.710840	−	0.703353i
$36$	−2.49151	−	0.418842i	−0.415252	−	0.0698071i
$37$	2.02615	−	1.47208i	0.333096	−	0.242009i	−0.408647	−	0.912693i	$-0.633999\pi$
$37$	2.02615	−	1.47208i	0.333096	−	0.242009i	0.741743	+	0.670684i	$0.233999\pi$
$38$	1.61134	−	1.17070i	0.261393	−	0.189913i
$39$	0.667149	+	0.280051i	0.106829	+	0.0448440i
$40$	3.12867	−	3.04342i	0.494686	−	0.481207i
$41$	−2.10494	+	1.52933i	−0.328737	+	0.238841i	−0.739894	−	0.672723i	$-0.765125\pi$
$41$	−2.10494	+	1.52933i	−0.328737	+	0.238841i	0.411158	+	0.911564i	$0.365125\pi$
$42$	7.17930	+	2.85360i	1.10779	+	0.440320i
$43$	2.72678			0.415830			0.207915	−	0.978147i	$-0.433332\pi$
$43$	2.72678			0.415830			0.207915	+	0.978147i	$0.433332\pi$
$44$	2.81440	+	0.914454i	0.424287	+	0.137859i
$45$	3.81557	+	5.51738i	0.568792	+	0.822482i
$46$	0.0628606	+	0.193465i	0.00926829	+	0.0285249i
$47$	−1.23977	−	3.81561i	−0.180838	−	0.556563i	0.819013	−	0.573774i	$-0.194521\pi$
$47$	−1.23977	−	3.81561i	−0.180838	−	0.556563i	−0.999852	+	0.0172109i	$0.994521\pi$
$48$	−3.33528	+	7.94546i	−0.481407	+	1.14683i
$49$	−5.81617	−	3.89515i	−0.830881	−	0.556450i
$50$	8.42613	+	0.232821i	1.19164	+	0.0329258i
$51$	−2.18630	−	9.30041i	−0.306144	−	1.30232i
$52$	−0.206784	+	0.284614i	−0.0286758	+	0.0394688i
$53$	10.3120	−	3.35057i	1.41646	−	0.460237i	0.501987	−	0.864875i	$-0.332603\pi$
$53$	10.3120	−	3.35057i	1.41646	−	0.460237i	0.914477	+	0.404639i	$0.132603\pi$
$54$	−7.40338	−	4.68275i	−1.00747	−	0.637242i
$55$	−3.47009	−	7.04948i	−0.467907	−	0.950551i
$56$	2.95520	−	4.23535i	0.394905	−	0.565972i
$57$	1.99198	−	0.468267i	0.263844	−	0.0620235i
$58$	−2.25991	+	6.95527i	−0.296740	+	0.913272i
$59$	−6.37221	+	4.62968i	−0.829591	+	0.602733i	−0.919444	−	0.393222i	$-0.871360\pi$
$59$	−6.37221	+	4.62968i	−0.829591	+	0.602733i	0.0898526	+	0.995955i	$0.471360\pi$
$60$	−3.03601	+	1.19208i	−0.391948	+	0.153897i
$61$	8.51535	−	11.7204i	1.09028	−	1.50064i	0.242603	−	0.970126i	$-0.421999\pi$
$61$	8.51535	−	11.7204i	1.09028	−	1.50064i	0.847676	−	0.530515i	$-0.178001\pi$
$62$	−8.42390	+	6.12032i	−1.06984	+	0.777281i
$63$	5.66630	+	5.55815i	0.713887	+	0.700261i
$64$	1.93496	+	1.40583i	0.241870	+	0.175728i
$65$	0.924522	−	0.133368i	0.114673	−	0.0165423i
$66$	7.77055	+	6.70057i	0.956489	+	0.824784i
$67$	−3.14330	+	9.67410i	−0.384016	+	1.18188i	0.553176	+	0.833064i	$0.313416\pi$
$67$	−3.14330	+	9.67410i	−0.384016	+	1.18188i	−0.937192	+	0.348815i	$0.886584\pi$
$68$	4.64531			0.563326
$69$	−0.0173839	+	0.208269i	−0.00209277	+	0.0250727i
$70$	9.84255	−	1.61237i	1.17641	−	0.192715i
$71$	−3.22622	+	1.04826i	−0.382882	+	0.124406i	−0.494133	−	0.869387i	$-0.664514\pi$
$71$	−3.22622	+	1.04826i	−0.382882	+	0.124406i	0.111251	+	0.993792i	$0.464514\pi$
$72$	−4.17979	+	4.10136i	−0.492593	+	0.483350i
$73$	−6.05823	+	8.33844i	−0.709062	+	0.975940i	0.290755	+	0.956798i	$0.406094\pi$
$73$	−6.05823	+	8.33844i	−0.709062	+	0.975940i	−0.999817	+	0.0191426i	$0.993906\pi$
$74$			4.22218i			0.490819i
$75$	7.88962	+	3.57126i	0.911015	+	0.412374i
$76$			0.994942i			0.114128i
$77$	−5.60724	−	7.41553i	−0.639005	−	0.845078i
$78$	−1.04306	+	0.632413i	−0.118103	+	0.0716066i
$79$	3.56443	+	10.9702i	0.401029	+	1.23424i	0.924166	+	0.381992i	$0.124762\pi$
$79$	3.56443	+	10.9702i	0.401029	+	1.23424i	−0.523136	+	0.852249i	$0.675238\pi$
$80$	1.58835	+	11.0107i	0.177583	+	1.23103i
$81$	−5.15121	−	7.38004i	−0.572357	−	0.820005i
$82$		−	4.38638i		−	0.484395i
$83$	3.68232	−	11.3330i	0.404187	−	1.24396i	−0.517385	−	0.855753i	$-0.673094\pi$
$83$	3.68232	−	11.3330i	0.404187	−	1.24396i	0.921572	−	0.388207i	$-0.126906\pi$
$84$	−3.26123	+	2.06353i	−0.355830	+	0.225150i
$85$	−8.60022	−	8.84113i	−0.932824	−	0.958955i
$86$	−2.70205	+	3.71905i	−0.291369	+	0.401036i
$87$	−4.90665	+	5.69017i	−0.526048	+	0.610050i
$88$	5.54904	−	4.03161i	0.591530	−	0.429771i
$89$	−13.3111	−	9.67105i	−1.41097	−	1.02513i	−0.993181	−	0.116585i	$-0.962805\pi$
$89$	−13.3111	−	9.67105i	−1.41097	−	1.02513i	−0.417789	−	0.908544i	$-0.637195\pi$
$90$	−11.3061	−	0.263284i	−1.19177	−	0.0277526i
$91$	1.04442	−	0.361555i	0.109485	−	0.0379013i
$92$	−0.0966433	−	0.0314013i	−0.0100758	−	0.00327381i
$93$	−10.4139	+	2.44805i	−1.07987	+	0.253851i
$94$	6.43262	+	2.09008i	0.663474	+	0.215576i
$95$	1.89361	−	1.84201i	0.194280	−	0.188986i
$96$	−4.02605	−	6.64030i	−0.410907	−	0.677723i
$97$	−2.83435	+	0.920938i	−0.287785	+	0.0935071i	−0.449352	−	0.893355i	$-0.648345\pi$
$97$	−2.83435	+	0.920938i	−0.287785	+	0.0935071i	0.161567	+	0.986862i	$0.448345\pi$
$98$	11.0760	−	4.07284i	1.11884	−	0.411419i
$99$	4.69663	+	9.43756i	0.472029	+	0.948511i
$100$	−2.56819	+	3.33694i	−0.256819	+	0.333694i
$101$	4.74732			0.472376			0.236188	−	0.971707i	$-0.424102\pi$
$101$	4.74732			0.472376			0.236188	+	0.971707i	$0.424102\pi$
$102$	14.8513	+	6.23416i	1.47050	+	0.617274i
$103$	−16.2399	+	5.27665i	−1.60016	+	0.519924i	−0.967147	−	0.254217i	$-0.918182\pi$
$103$	−16.2399	+	5.27665i	−1.60016	+	0.519924i	−0.633013	+	0.774141i	$0.718182\pi$
$104$	0.251977	+	0.775505i	0.0247084	+	0.0760445i
$105$	9.96516	+	2.38654i	0.972500	+	0.232902i
$106$	−5.64863	+	17.3847i	−0.548644	+	1.68855i
$107$			9.61229i			0.929255i	0.885506	+	0.464627i	$0.153812\pi$
$107$			9.61229i			0.929255i	−0.885506	+	0.464627i	$0.846188\pi$
$108$	4.06626	−	1.61701i	0.391276	−	0.155597i
$109$	−15.2767	+	11.0992i	−1.46324	+	1.06311i	−0.480742	+	0.876862i	$0.659633\pi$
$109$	−15.2767	+	11.0992i	−1.46324	+	1.06311i	−0.982503	+	0.186248i	$0.940367\pi$
$110$	13.0534	+	2.25268i	1.24459	+	0.214785i
$111$	−1.67898	+	3.99974i	−0.159362	+	0.379638i
$112$	4.30596	+	12.4386i	0.406875	+	1.17534i
$113$	−6.25809	−	8.61352i	−0.588711	−	0.810291i	0.405905	−	0.913915i	$-0.366956\pi$
$113$	−6.25809	−	8.61352i	−0.588711	−	0.810291i	−0.994617	+	0.103624i	$0.966956\pi$
$114$	−1.33524	+	3.18088i	−0.125057	+	0.297916i
$115$	0.119159	+	0.242071i	0.0111116	+	0.0225732i
$116$	−2.14731	−	2.95553i	−0.199373	−	0.274414i
$117$	−1.23959	+	0.184315i	−0.114600	+	0.0170399i
$118$		−	13.2787i		−	1.22241i
$119$	−11.9684	−	8.35093i	−1.09714	−	0.765528i
$120$	−1.90087	+	7.31708i	−0.173525	+	0.667955i
$121$	−0.416347	−	1.28139i	−0.0378498	−	0.116490i
$122$	7.54728	+	23.2281i	0.683298	+	2.10298i
$123$	1.74427	−	4.15529i	0.157276	−	0.374669i
$124$		−	5.20145i		−	0.467104i
$125$	11.1057	−	1.29006i	0.993321	−	0.115386i
$126$	−13.1957	+	2.22052i	−1.17556	+	0.197820i
$127$	−11.5910	−	8.42133i	−1.02853	−	0.747272i	−0.0605179	−	0.998167i	$-0.519275\pi$
$127$	−11.5910	−	8.42133i	−1.02853	−	0.747272i	−0.968014	+	0.250895i	$0.919275\pi$
$128$	−12.3627	+	4.01690i	−1.09272	+	0.355047i
$129$	−4.03860	+	2.44862i	−0.355578	+	0.215589i
$130$	−0.734236	+	1.39311i	−0.0643968	+	0.122184i
$131$	−0.394222	+	1.21329i	−0.0344433	+	0.106006i	−0.966800	−	0.255534i	$-0.917749\pi$
$131$	−0.394222	+	1.21329i	−0.0344433	+	0.106006i	0.932357	+	0.361540i	$0.117749\pi$
$132$	−4.98954	+	1.17292i	−0.434284	+	0.102090i
$133$	1.78862	−	2.56342i	0.155093	−	0.222277i
$134$	−10.0797	−	13.8735i	−0.870752	−	1.19849i
$135$	−10.6057	−	4.74536i	−0.912796	−	0.408415i
$136$	6.32869	−	8.71069i	0.542681	−	0.746936i
$137$	−8.56796	−	11.7928i	−0.732010	−	1.00753i	−0.999039	−	0.0438367i	$-0.986042\pi$
$137$	−8.56796	−	11.7928i	−0.732010	−	1.00753i	0.267029	−	0.963689i	$-0.413958\pi$
$138$	−0.266832	−	0.230090i	−0.0227142	−	0.0195866i
$139$	−3.09895	+	4.26534i	−0.262850	+	0.361781i	−0.919960	−	0.392013i	$-0.871779\pi$
$139$	−3.09895	+	4.26534i	−0.262850	+	0.361781i	0.657110	+	0.753795i	$0.271779\pi$
$140$	−2.23837	+	4.45115i	−0.189177	+	0.376191i
$141$	5.26258	+	4.53794i	0.443189	+	0.382163i
$142$	1.76723	−	5.43898i	0.148303	−	0.456429i
$143$	1.46788			0.122750
$144$	−2.19511	−	14.7630i	−0.182926	−	1.23025i
$145$	−1.64958	+	9.55864i	−0.136990	+	0.793802i
$146$	−5.36950	−	16.5256i	−0.444383	−	1.36767i
$147$	12.1120	+	0.546178i	0.998985	+	0.0450480i
$148$	−1.70633	−	1.23972i	−0.140260	−	0.101905i
$149$			19.5778i			1.60388i	0.597406	+	0.801939i	$0.296198\pi$
$149$			19.5778i			1.60388i	−0.597406	+	0.801939i	$0.703802\pi$
$150$	−12.6889	+	7.22176i	−1.03604	+	0.589654i
$151$	−12.6389			−1.02854			−0.514271	−	0.857628i	$-0.671937\pi$
$151$	−12.6389			−1.02854			−0.514271	+	0.857628i	$0.671937\pi$
$152$	1.86567	+	1.35549i	0.151326	+	0.109945i
$153$	11.5898	+	11.8114i	0.936978	+	0.954897i
$154$	15.6704	−	0.299435i	1.26276	−	0.0241292i
$155$	−9.89960	+	9.62984i	−0.795155	+	0.773488i
$156$	0.0506842	−	0.607227i	0.00405798	−	0.0486171i
$157$		−	0.908476i		−	0.0725043i	−0.999343	−	0.0362521i	$-0.988458\pi$
$157$		−	0.908476i		−	0.0725043i	0.999343	−	0.0362521i	$-0.0115419\pi$
$158$	−18.4943	−	6.00916i	−1.47133	−	0.478063i
$159$	−12.2642	+	14.2226i	−0.972612	+	1.12792i
$160$	−8.86880	−	4.67428i	−0.701140	−	0.369534i
$161$	0.192546	+	0.254641i	0.0151748	+	0.0200685i
$162$	15.1701	+	0.287382i	1.19188	+	0.0225788i
$163$	9.76970	−	7.09810i	0.765222	−	0.555966i	−0.135286	−	0.990807i	$-0.543195\pi$
$163$	9.76970	−	7.09810i	0.765222	−	0.555966i	0.900507	+	0.434840i	$0.143195\pi$
$164$	1.77269	+	1.28794i	0.138424	+	0.100571i
$165$	11.4699	+	7.32476i	0.892928	+	0.570232i
$166$	11.8081	+	16.2525i	0.916490	+	1.26144i
$167$	2.80773	−	8.64131i	0.217269	−	0.668685i	−0.781716	−	0.623635i	$-0.785655\pi$
$167$	2.80773	−	8.64131i	0.217269	−	0.668685i	0.998985	−	0.0450500i	$-0.0143447\pi$
$168$	−0.573604	+	8.92665i	−0.0442545	+	0.688706i
$169$	3.96330	−	12.1978i	0.304869	−	0.938290i
$170$	20.5806	−	2.96888i	1.57846	−	0.227702i
$171$	−2.52979	+	2.48232i	−0.193458	+	0.189828i
$172$	−0.709620	−	2.18399i	−0.0541080	−	0.166527i
$173$	5.41044	+	3.93092i	0.411348	+	0.298862i	0.774147	−	0.633005i	$-0.218179\pi$
$173$	5.41044	+	3.93092i	0.411348	+	0.298862i	−0.362799	+	0.931867i	$0.618179\pi$
$174$	−2.89866	−	12.3307i	−0.219747	−	0.934790i
$175$	12.6157	−	3.98060i	0.953654	−	0.300905i
$176$			17.4818i			1.31774i
$177$	5.28037	−	12.5791i	0.396897	−	0.945506i
$178$	26.3806	−	8.57159i	1.97731	−	0.642468i
$179$	18.9269	−	6.14973i	1.41466	−	0.459652i	0.500762	−	0.865585i	$-0.333053\pi$
$179$	18.9269	−	6.14973i	1.41466	−	0.459652i	0.913903	+	0.405933i	$0.133053\pi$
$180$	3.42611	−	4.49189i	0.255368	−	0.334805i
$181$	−16.6040	−	5.39497i	−1.23417	−	0.401005i	−0.381945	−	0.924185i	$-0.624745\pi$
$181$	−16.6040	−	5.39497i	−1.23417	−	0.401005i	−0.852222	+	0.523180i	$0.824745\pi$
$182$	−0.541824	+	1.78276i	−0.0401627	+	0.132147i
$183$	−2.08717	+	25.0056i	−0.154288	+	1.84847i
$184$	−0.190548	+	0.138441i	−0.0140474	+	0.0102060i
$185$	0.799576	+	5.54276i	0.0587860	+	0.407511i
$186$	6.98052	−	16.6293i	0.511836	−	1.21932i
$187$	−11.3927	−	15.6807i	−0.833117	−	1.14669i
$188$	−2.73343	+	1.98595i	−0.199356	+	0.144841i
$189$	−13.3834	−	3.14381i	−0.973502	−	0.228678i
$190$	0.635880	+	4.40799i	0.0461316	+	0.319790i
$191$	3.36427	+	4.63052i	0.243430	+	0.335053i	0.913197	−	0.407519i	$-0.133606\pi$
$191$	3.36427	+	4.63052i	0.243430	+	0.335053i	−0.669767	+	0.742572i	$0.733606\pi$
$192$	−4.12825	−	0.344578i	−0.297931	−	0.0248678i
$193$	13.4801			0.970317			0.485159	−	0.874426i	$-0.338762\pi$
$193$	13.4801			0.970317			0.485159	+	0.874426i	$0.338762\pi$
$194$	1.55258	−	4.77835i	0.111469	−	0.343066i
$195$	−1.24953	+	1.02774i	−0.0894809	+	0.0735981i
$196$	−1.60617	+	5.67207i	−0.114726	+	0.405148i
$197$	−0.249300	+	0.0810025i	−0.0177619	+	0.00577119i	−0.317884	−	0.948129i	$-0.602972\pi$
$197$	−0.249300	+	0.0810025i	−0.0177619	+	0.00577119i	0.300123	+	0.953901i	$0.402972\pi$
$198$	−17.5259	−	2.94624i	−1.24551	−	0.209380i
$199$			18.4445i			1.30749i	0.756714	+	0.653746i	$0.226804\pi$
$199$			18.4445i			1.30749i	−0.756714	+	0.653746i	$0.773196\pi$
$200$	2.75844	+	9.36194i	0.195051	+	0.661989i
$201$	−4.03175	−	17.1508i	−0.284377	−	1.20973i
$202$	−4.70426	+	6.47486i	−0.330990	+	0.455569i
$203$	0.219268	+	11.4750i	0.0153896	+	0.805389i
$204$	−6.88010	+	4.17144i	−0.481703	+	0.292059i
$205$	−0.830671	−	5.75831i	−0.0580166	−	0.402178i
$206$	8.89574	−	27.3783i	0.619796	−	1.90754i
$207$	−0.161277	−	0.324075i	−0.0112095	−	0.0225248i
$208$	−1.97657	−	0.642226i	−0.137050	−	0.0445303i
$209$	3.35852	−	2.44011i	0.232314	−	0.168786i
$210$	−13.1298	+	11.2266i	−0.906040	+	0.774707i
$211$	18.1439	+	13.1823i	1.24908	+	0.907510i	0.998168	−	0.0605000i	$-0.0192695\pi$
$211$	18.1439	+	13.1823i	1.24908	+	0.907510i	0.250912	+	0.968010i	$0.419270\pi$
$212$	−5.36721	−	7.38733i	−0.368622	−	0.507364i
$213$	3.83697	−	4.44968i	0.262905	−	0.304887i
$214$	−13.1102	−	9.52510i	−0.896193	−	0.651122i
$215$	−2.84287	+	5.39396i	−0.193882	+	0.367865i
$216$	2.50764	−	9.82787i	0.170623	−	0.668702i
$217$	−9.35071	+	13.4013i	−0.634768	+	0.909739i
$218$		−	31.8344i		−	2.15610i
$219$	1.48491	−	17.7902i	0.100341	−	1.20215i
$220$	−4.74314	+	4.61389i	−0.319783	+	0.311069i
$221$	2.19145	−	0.712047i	0.147413	−	0.0478974i
$222$	−3.79148	−	6.25341i	−0.254468	−	0.419702i
$223$	0.0715397	−	0.0984660i	0.00479065	−	0.00659377i	−0.806615	−	0.591077i	$-0.798703\pi$
$223$	0.0715397	−	0.0984660i	0.00479065	−	0.00659377i	0.811406	+	0.584483i	$0.198703\pi$
$224$	−11.3494	−	3.44935i	−0.758312	−	0.230470i
$225$	−14.8922	+	1.79546i	−0.992810	+	0.119697i
$226$	17.9493			1.19397
$227$	−5.78934	−	4.20620i	−0.384252	−	0.279175i	0.378844	−	0.925460i	$-0.376322\pi$
$227$	−5.78934	−	4.20620i	−0.384252	−	0.279175i	−0.763096	+	0.646285i	$0.776322\pi$
$228$	−0.893448	−	1.47359i	−0.0591701	−	0.0975911i
$229$	5.91669	−	1.92245i	0.390986	−	0.127039i	−0.106925	−	0.994267i	$-0.534101\pi$
$229$	5.91669	−	1.92245i	0.390986	−	0.127039i	0.497911	+	0.867228i	$0.334101\pi$
$230$	−0.448238	−	0.0773546i	−0.0295559	−	0.00510061i
$231$	14.9639	+	5.94778i	0.984551	+	0.391335i
$232$	−8.46754			−0.555921
$233$	5.11628	+	1.66238i	0.335179	+	0.108906i	0.471771	−	0.881721i	$-0.343615\pi$
$233$	5.11628	+	1.66238i	0.335179	+	0.108906i	−0.136592	+	0.990627i	$0.543615\pi$
$234$	0.976958	−	1.87331i	0.0638657	−	0.122462i
$235$	8.84035	+	1.52562i	0.576681	+	0.0995206i
$236$	5.36640	+	3.89892i	0.349323	+	0.253798i
$237$	−15.1303	−	13.0469i	−0.982821	−	0.847490i
$238$	23.2497	−	8.04851i	1.50705	−	0.521707i
$239$	2.50838	−	3.45249i	0.162253	−	0.223323i	−0.720147	−	0.693821i	$-0.755926\pi$
$239$	2.50838	−	3.45249i	0.162253	−	0.223323i	0.882401	+	0.470498i	$0.155926\pi$
$240$	−12.2400	−	14.8814i	−0.790085	−	0.960590i
$241$	−1.26275	−	1.73802i	−0.0813406	−	0.111956i	0.766408	−	0.642354i	$-0.222042\pi$
$241$	−1.26275	−	1.73802i	−0.0813406	−	0.111956i	−0.847748	+	0.530399i	$0.822042\pi$
$242$	2.16025	+	0.701907i	0.138866	+	0.0451203i
$243$	14.2566	+	6.30473i	0.914561	+	0.404449i
$244$	−11.6034	−	3.77016i	−0.742828	−	0.241360i
$245$	13.7689	−	7.44422i	0.879665	−	0.475594i
$246$	3.93893	+	6.49661i	0.251137	+	0.414208i
$247$	0.152508	+	0.469370i	0.00970383	+	0.0298653i
$248$	−9.75355	−	7.08637i	−0.619351	−	0.449985i
$249$	4.72311	+	20.0918i	0.299315	+	1.27327i
$250$	−9.24542	+	16.4253i	−0.584732	+	1.03883i
$251$	15.4282			0.973821			0.486911	−	0.873452i	$-0.338124\pi$
$251$	15.4282			0.973821			0.486911	+	0.873452i	$0.338124\pi$
$252$	2.97714	−	5.98482i	0.187542	−	0.377008i
$253$	0.131021	+	0.403241i	0.00823722	+	0.0253516i
$254$	22.9717	−	7.46395i	1.44137	−	0.468330i
$255$	20.6769	+	5.37155i	1.29484	+	0.336380i
$256$	5.29380	−	16.2926i	0.330862	−	1.01829i
$257$	−3.95846			−0.246922			−0.123461	−	0.992349i	$-0.539399\pi$
$257$	−3.95846			−0.246922			−0.123461	+	0.992349i	$0.539399\pi$
$258$	0.662291	−	7.93464i	0.0412324	−	0.493989i
$259$	2.16762	+	6.26159i	0.134689	+	0.389076i
$260$	−0.347418	−	0.705778i	−0.0215460	−	0.0437705i
$261$	2.15745	−	12.8337i	0.133543	−	0.794389i
$262$	−1.26416	−	1.73996i	−0.0781000	−	0.107495i
$263$	4.01938	+	5.53221i	0.247846	+	0.341131i	0.914755	−	0.404008i	$-0.132383\pi$
$263$	4.01938	+	5.53221i	0.247846	+	0.341131i	−0.666910	+	0.745139i	$0.732383\pi$
$264$	−4.59825	+	10.9541i	−0.283003	+	0.674181i
$265$	−4.12312	+	23.8918i	−0.253282	+	1.46766i
$266$	1.72385	+	4.97966i	0.105696	+	0.305323i
$267$	28.3993	+	2.37044i	1.73801	+	0.145069i
$268$	8.56638			0.523275
$269$	0.0403815	−	0.124282i	0.00246211	−	0.00757758i	−0.949818	−	0.312803i	$-0.898732\pi$
$269$	0.0403815	−	0.124282i	0.00246211	−	0.00757758i	0.952280	+	0.305226i	$0.0987319\pi$
$270$	16.9817	−	9.76282i	1.03347	−	0.594146i
$271$	−18.8781	+	6.13387i	−1.14676	+	0.372606i	−0.819923	−	0.572474i	$-0.805984\pi$
$271$	−18.8781	+	6.13387i	−1.14676	+	0.372606i	−0.326840	+	0.945080i	$0.605984\pi$
$272$	8.48017	+	26.0993i	0.514186	+	1.58250i
$273$	−1.22220	+	1.47338i	−0.0739712	+	0.0891727i
$274$	24.5744			1.48459
$275$	17.5627	+	0.485271i	1.05907	+	0.0292629i
$276$	0.171335	−	0.0402768i	0.0103132	−	0.00242438i
$277$	−5.72034	−	4.15607i	−0.343702	−	0.249714i	0.402520	−	0.915411i	$-0.368134\pi$
$277$	−5.72034	−	4.15607i	−0.343702	−	0.249714i	−0.746222	+	0.665697i	$0.768134\pi$
$278$	−2.74664	−	8.45330i	−0.164733	−	0.506995i
$279$	13.2255	−	12.9773i	0.791790	−	0.776932i
$280$	5.29709	+	10.2615i	0.316562	+	0.613240i
$281$	−7.87623	−	2.55914i	−0.469857	−	0.152666i	0.0645125	−	0.997917i	$-0.479451\pi$
$281$	−7.87623	−	2.55914i	−0.469857	−	0.152666i	−0.534369	+	0.845251i	$0.679451\pi$
$282$	−11.4041	+	2.68084i	−0.679106	+	0.159642i
$283$	11.3268	+	3.68031i	0.673309	+	0.218771i	0.625664	−	0.780093i	$-0.284828\pi$
$283$	11.3268	+	3.68031i	0.673309	+	0.218771i	0.0476455	+	0.998864i	$0.484828\pi$
$284$	1.67919	+	2.31120i	0.0996414	+	0.137145i
$285$	−1.15049	+	4.42862i	−0.0681491	+	0.262329i
$286$	−1.45457	+	2.00204i	−0.0860104	+	0.118383i
$287$	−2.25192	−	6.50510i	−0.132926	−	0.383984i
$288$	11.9259	+	6.21949i	0.702738	+	0.366487i
$289$	−10.8617	−	7.89152i	−0.638926	−	0.464207i
$290$	−11.4024	−	11.7218i	−0.669571	−	0.688328i
$291$	3.37093	−	3.90921i	0.197607	−	0.229162i
$292$	8.25518	+	2.68227i	0.483098	+	0.156968i
$293$	2.99032			0.174696			0.0873481	−	0.996178i	$-0.472161\pi$
$293$	2.99032			0.174696			0.0873481	+	0.996178i	$0.472161\pi$
$294$	−12.7471	+	15.9784i	−0.743427	+	0.931877i
$295$	−2.51466	−	17.4319i	−0.146409	−	1.01493i
$296$	−4.64936	+	1.51067i	−0.270238	+	0.0878058i
$297$	−15.4310	−	9.76031i	−0.895395	−	0.566350i
$298$	−26.7022	−	19.4002i	−1.54681	−	1.12383i
$299$	−0.0504054			−0.00291502
$300$	0.807162	−	7.24849i	0.0466015	−	0.418492i
$301$	−2.09788	+	6.90263i	−0.120920	+	0.397861i
$302$	12.5243	−	17.2382i	0.720692	−	0.991947i
$303$	−7.03118	+	4.26305i	−0.403931	+	0.244906i
$304$	−5.58999	+	1.81630i	−0.320608	+	0.104172i
$305$	14.3067	+	29.0639i	0.819197	+	1.66420i
$306$	−27.5942	+	4.10299i	−1.57746	+	0.234552i
$307$		−	16.7356i		−	0.955150i	−0.878591	−	0.477575i	$-0.841516\pi$
$307$		−	16.7356i		−	0.955150i	0.878591	−	0.477575i	$-0.158484\pi$
$308$	−4.48016	+	6.42089i	−0.255281	+	0.365864i
$309$	19.3142	−	22.3984i	1.09875	−	1.27420i
$310$	−3.32431	−	23.0445i	−0.188808	−	1.30884i
$311$	−5.94572	−	4.31982i	−0.337151	−	0.244954i	0.406308	−	0.913736i	$-0.366816\pi$
$311$	−5.94572	−	4.31982i	−0.337151	−	0.244954i	−0.743459	+	0.668782i	$0.766816\pi$
$312$	−1.06960	−	0.922316i	−0.0605539	−	0.0522159i
$313$	−7.87508	−	10.8391i	−0.445126	−	0.612663i	0.526216	−	0.850351i	$-0.323610\pi$
$313$	−7.87508	−	10.8391i	−0.445126	−	0.612663i	−0.971342	+	0.237688i	$0.923610\pi$
$314$	1.23907	+	0.900236i	0.0699247	+	0.0508032i
$315$	−16.9023	+	5.41396i	−0.952339	+	0.305042i
$316$	7.85883	−	5.70978i	0.442094	−	0.321200i
$317$	−9.91633	−	3.22201i	−0.556957	−	0.180966i	0.0169948	−	0.999856i	$-0.494590\pi$
$317$	−9.91633	−	3.22201i	−0.556957	−	0.180966i	−0.573951	+	0.818889i	$0.694590\pi$
$318$	−7.24519	−	30.8206i	−0.406290	−	1.72834i
$319$	−4.71034	+	14.4969i	−0.263729	+	0.811673i
$320$	−4.79826	+	2.36194i	−0.268231	+	0.132036i
$321$	−8.63174	−	14.2366i	−0.481777	−	0.794610i
$322$	−0.538104	+	0.0102823i	−0.0299874	+	0.000573008i
$323$	3.83040	−	5.27210i	0.213129	−	0.293347i
$324$	−4.57041	+	6.04639i	−0.253912	+	0.335911i
$325$	−0.700062	+	1.96788i	−0.0388325	+	0.109158i
$326$			20.3586i			1.12756i
$327$	12.6592	−	30.1572i	0.700053	−	1.66770i
$328$	4.83017	−	1.56942i	0.266702	−	0.0866566i
$329$	10.6127	−	0.202791i	0.585099	−	0.0111803i
$330$	−21.3561	+	8.38539i	−1.17561	+	0.461601i
$331$	−6.88795	+	21.1989i	−0.378596	+	1.16520i	0.562424	+	0.826849i	$0.309869\pi$
$331$	−6.88795	+	21.1989i	−0.378596	+	1.16520i	−0.941020	+	0.338350i	$0.890131\pi$
$332$	−10.0353			−0.550761
$333$	−1.10502	−	7.43166i	−0.0605545	−	0.407252i
$334$	9.00360	+	12.3924i	0.492655	+	0.678081i
$335$	−15.8596	−	16.3039i	−0.866502	−	0.890775i
$336$	−17.5473	−	14.5559i	−0.957281	−	0.794091i
$337$	21.8132	−	15.8482i	1.18824	−	0.863309i	0.195165	−	0.980770i	$-0.437476\pi$
$337$	21.8132	−	15.8482i	1.18824	−	0.863309i	0.993077	+	0.117462i	$0.0374757\pi$
$338$	12.7092	+	17.4927i	0.691287	+	0.951475i
$339$	17.0036	+	7.13765i	0.923510	+	0.387664i
$340$	−4.84308	+	9.18907i	−0.262653	+	0.498347i
$341$	−17.5580	+	12.7566i	−0.950820	+	0.690811i
$342$	−0.878787	−	5.91019i	−0.0475194	−	0.319586i
$343$	14.3350	−	11.7264i	0.774016	−	0.633166i
$344$	−5.06210	−	1.64477i	−0.272930	−	0.0886803i
$345$	−0.393862	−	0.251524i	−0.0212048	−	0.0135416i
$346$	−10.7227	+	3.48403i	−0.576458	+	0.187303i
$347$	−31.8515	+	10.3492i	−1.70988	+	0.555574i	−0.990313	−	0.138850i	$-0.955659\pi$
$347$	−31.8515	+	10.3492i	−1.70988	+	0.555574i	−0.719566	+	0.694424i	$0.755659\pi$
$348$	5.83439	+	2.44912i	0.312756	+	0.131286i
$349$			24.7683i			1.32582i	0.748700	+	0.662909i	$0.230678\pi$
$349$			24.7683i			1.32582i	−0.748700	+	0.662909i	$0.769322\pi$
$350$	−7.07210	+	21.1510i	−0.378020	+	1.13057i
$351$	1.67042	−	1.38612i	0.0891606	−	0.0739858i
$352$	−12.7454	−	9.26004i	−0.679330	−	0.493562i
$353$	−6.75157	−	20.7792i	−0.359350	−	1.10597i	−0.953444	−	0.301570i	$-0.902489\pi$
$353$	−6.75157	−	20.7792i	−0.359350	−	1.10597i	0.594094	−	0.804396i	$-0.297511\pi$
$354$	11.9242	+	19.6669i	0.633763	+	1.04529i
$355$	1.28996	−	7.47480i	0.0684641	−	0.396721i
$356$	−4.28184	+	13.1782i	−0.226937	+	0.698441i
$357$	25.2253	+	1.62091i	1.33506	+	0.0857878i
$358$	−10.3676	+	31.9083i	−0.547947	+	1.68641i
$359$	4.91420	+	6.76381i	0.259361	+	0.356980i	0.918762	−	0.394811i	$-0.129190\pi$
$359$	4.91420	+	6.76381i	0.259361	+	0.356980i	−0.659401	+	0.751792i	$0.729190\pi$
$360$	−3.75532	−	12.5442i	−0.197923	−	0.661136i
$361$	−14.2421	−	10.3475i	−0.749586	−	0.544606i
$362$	23.8116	−	17.3001i	1.25151	−	0.909275i
$363$	1.76732	+	1.52396i	0.0927601	+	0.0799874i
$364$	−0.561385	−	0.742427i	−0.0294246	−	0.0389137i
$365$	−10.1784	−	20.6775i	−0.532764	−	1.08231i
$366$	−32.0368	−	27.6255i	−1.67459	−	1.44401i
$367$	−1.37677	−	0.447339i	−0.0718667	−	0.0233509i	0.272863	−	0.962053i	$-0.412029\pi$
$367$	−1.37677	−	0.447339i	−0.0718667	−	0.0233509i	−0.344730	+	0.938702i	$0.612029\pi$
$368$		−	0.600306i		−	0.0312931i
$369$	1.14799	+	7.72067i	0.0597619	+	0.401922i
$370$	−8.35207	−	4.40194i	−0.434204	−	0.228846i
$371$	0.548061	+	28.6818i	0.0284539	+	1.48909i
$372$	4.67085	+	7.70379i	0.242172	+	0.399423i
$373$	−10.3809	−	7.54220i	−0.537505	−	0.390520i	0.285653	−	0.958333i	$-0.407790\pi$
$373$	−10.3809	−	7.54220i	−0.537505	−	0.390520i	−0.823158	+	0.567813i	$0.807790\pi$
$374$	32.6762			1.68965
$375$	−15.2900	+	11.8835i	−0.789571	+	0.613660i
$376$			7.83125i			0.403866i
$377$	−1.46604	−	1.06514i	−0.0755050	−	0.0548576i
$378$	17.5499	−	15.1383i	0.902668	−	0.778633i
$379$	3.59456	+	11.0629i	0.184640	+	0.568264i	0.999942	−	0.0107722i	$-0.00342896\pi$
$379$	3.59456	+	11.0629i	0.184640	+	0.568264i	−0.815302	+	0.579036i	$0.803429\pi$
$380$	−1.96813	−	1.03730i	−0.100963	−	0.0532124i
$381$	24.7295	+	2.06413i	1.26693	+	0.105748i
$382$	−9.64931			−0.493702
$383$	−10.7557	+	33.1027i	−0.549591	+	1.69147i	0.160224	+	0.987081i	$0.448778\pi$
$383$	−10.7557	+	33.1027i	−0.549591	+	1.69147i	−0.709816	+	0.704387i	$0.751222\pi$
$384$	14.7031	−	17.0510i	0.750317	−	0.870130i
$385$	20.5149	−	3.36067i	1.04554	−	0.171276i
$386$	−13.3578	+	18.3854i	−0.679895	+	0.935795i
$387$	3.78266	−	7.25324i	0.192284	−	0.368703i
$388$	1.47523	+	2.03048i	0.0748935	+	0.103082i
$389$	6.96219	−	9.58263i	0.352997	−	0.485859i	−0.595184	−	0.803589i	$-0.702921\pi$
$389$	6.96219	−	9.58263i	0.352997	−	0.485859i	0.948181	+	0.317731i	$0.102921\pi$
$390$	−0.163535	−	2.72265i	−0.00828092	−	0.137867i
$391$	0.391212	+	0.538457i	0.0197845	+	0.0272310i
$392$	8.44782	+	10.7394i	0.426679	+	0.542420i
$393$	−0.505647	−	2.15099i	−0.0255065	−	0.108503i
$394$	0.136560	−	0.420287i	0.00687978	−	0.0211738i
$395$	−25.4167	−	4.38628i	−1.27885	−	0.220698i
$396$	6.33666	−	6.21776i	0.318429	−	0.312454i
$397$	−3.16957	+	1.02986i	−0.159076	+	0.0516871i	−0.387473	−	0.921881i	$-0.626652\pi$
$397$	−3.16957	+	1.02986i	−0.159076	+	0.0516871i	0.228396	+	0.973568i	$0.426652\pi$
$398$	−25.1563	−	18.2772i	−1.26097	−	0.916151i
$399$	−0.347171	+	5.40281i	−0.0173803	+	0.270479i
$400$	−23.4366	−	8.33744i	−1.17183	−	0.416872i
$401$		−	37.8101i		−	1.88814i	−0.329739	−	0.944072i	$-0.606961\pi$
$401$		−	37.8101i		−	1.88814i	0.329739	−	0.944072i	$-0.393039\pi$
$402$	27.3871	+	11.4964i	1.36595	+	0.573386i
$403$	−0.797294	−	2.45382i	−0.0397160	−	0.122233i
$404$	−1.23545	−	3.80231i	−0.0614658	−	0.189172i
$405$	19.9693	−	2.49557i	0.992281	−	0.124006i
$406$	−15.8680	−	11.0719i	−0.787517	−	0.549488i
$407$			8.80034i			0.436217i
$408$	−1.55121	+	18.5844i	−0.0767961	+	0.920064i
$409$	17.9549	+	24.7128i	0.887814	+	1.22197i	0.974195	+	0.225709i	$0.0724699\pi$
$409$	17.9549	+	24.7128i	0.887814	+	1.22197i	−0.0863806	+	0.996262i	$0.527530\pi$
$410$	8.67688	+	4.57313i	0.428521	+	0.225851i
$411$	23.2797	+	9.77217i	1.14830	+	0.482025i
$412$	8.45255	+	11.6339i	0.416427	+	0.573163i
$413$	−6.81714	−	19.6926i	−0.335450	−	0.969011i
$414$	0.601819	+	0.101170i	0.0295778	+	0.00497226i
$415$	18.5792	+	19.0997i	0.912017	+	0.937565i
$416$	1.51520	−	1.10086i	0.0742888	−	0.0539740i
$417$	0.759575	−	9.10016i	0.0371965	−	0.445637i
$418$			6.99866i			0.342316i
$419$	−8.41371	+	25.8947i	−0.411037	+	1.26504i	0.504712	+	0.863288i	$0.331599\pi$
$419$	−8.41371	+	25.8947i	−0.411037	+	1.26504i	−0.915748	+	0.401753i	$0.868401\pi$
$420$	−0.681873	−	8.60256i	−0.0332720	−	0.419762i
$421$	4.08817	+	12.5821i	0.199245	+	0.613213i	0.999901	+	0.0140886i	$0.00448470\pi$
$421$	4.08817	+	12.5821i	0.199245	+	0.613213i	−0.800656	+	0.599125i	$0.795515\pi$
$422$	−35.9587	+	11.6837i	−1.75044	+	0.568754i
$423$	−11.8694	−	1.99533i	−0.577108	−	0.0970163i
$424$	−21.1646			−1.02784
$425$	26.4554	−	7.79490i	1.28327	−	0.378108i
$426$	2.26673	+	9.64255i	0.109824	+	0.467183i
$427$	23.1178	+	30.5731i	1.11875	+	1.47954i
$428$	7.69886	−	2.50151i	0.372138	−	0.120915i
$429$	−2.17406	+	1.31814i	−0.104965	+	0.0636406i
$430$	−4.53972	−	9.22242i	−0.218925	−	0.444744i
$431$	−25.2039	−	8.18923i	−1.21403	−	0.394461i	−0.369124	−	0.929380i	$-0.620342\pi$
$431$	−25.2039	−	8.18923i	−1.21403	−	0.394461i	−0.844904	+	0.534919i	$0.820342\pi$
$432$	16.5081	+	19.8940i	0.794248	+	0.957151i
$433$	−4.39790	−	1.42896i	−0.211349	−	0.0686716i	0.201429	−	0.979503i	$-0.435442\pi$
$433$	−4.39790	−	1.42896i	−0.211349	−	0.0686716i	−0.412778	+	0.910832i	$0.635442\pi$
$434$	−9.01208	−	26.0331i	−0.432594	−	1.24963i
$435$	−6.14040	−	15.6385i	−0.294410	−	0.749807i
$436$	12.8654	+	9.34727i	0.616141	+	0.447653i
$437$	−0.115328	+	0.0837906i	−0.00551688	+	0.00400825i
$438$	22.7925	+	19.6541i	1.08907	+	0.939108i
$439$	19.4051	−	26.7089i	0.926156	−	1.27474i	−0.0351845	−	0.999381i	$-0.511202\pi$
$439$	19.4051	−	26.7089i	0.926156	−	1.27474i	0.961340	−	0.275363i	$-0.0887981\pi$
$440$	2.18981	+	15.1800i	0.104395	+	0.723680i
$441$	−18.4294	+	10.0676i	−0.877592	+	0.479408i
$442$	−1.20042	+	3.69451i	−0.0570981	+	0.175730i
$443$			23.7650i			1.12911i	0.825397	+	0.564553i	$0.190952\pi$
$443$			23.7650i			1.12911i	−0.825397	+	0.564553i	$0.809048\pi$
$444$	3.64049	+	0.303865i	0.172770	+	0.0144208i
$445$	33.0085	−	16.2484i	1.56475	−	0.770246i
$446$	0.0634067	+	0.195146i	0.00300239	+	0.00924042i
$447$	−17.5807	−	28.9964i	−0.831539	−	1.37148i
$448$	−5.04742	+	3.81660i	−0.238468	+	0.180317i
$449$			25.8691i			1.22084i	0.792078	+	0.610420i	$0.208999\pi$
$449$			25.8691i			1.22084i	−0.792078	+	0.610420i	$0.791001\pi$
$450$	12.3083	−	22.0905i	0.580217	−	1.04136i
$451$		−	9.14258i		−	0.430507i
$452$	−5.27029	+	7.25394i	−0.247894	+	0.341196i
$453$	18.7193	−	11.3496i	0.879511	−	0.533253i
$454$	11.4736	−	3.72801i	0.538485	−	0.174964i
$455$	−0.373680	+	2.44296i	−0.0175184	+	0.114528i
$456$	−3.98044	−	0.332240i	−0.186401	−	0.0155586i
$457$	21.3387			0.998181			0.499090	−	0.866550i	$-0.333668\pi$
$457$	21.3387			0.998181			0.499090	+	0.866550i	$0.333668\pi$
$458$	−3.24100	+	9.97477i	−0.151442	+	0.466090i
$459$	−27.7720	−	7.08620i	−1.29629	−	0.330755i
$460$	0.162874	−	0.158436i	0.00759404	−	0.00738711i
$461$	−3.61608	−	2.62724i	−0.168418	−	0.122363i	0.500384	−	0.865804i	$-0.333192\pi$
$461$	−3.61608	−	2.62724i	−0.168418	−	0.122363i	−0.668801	+	0.743441i	$0.733192\pi$
$462$	−22.9403	+	14.5154i	−1.06728	+	0.675316i
$463$	−30.3911	+	22.0804i	−1.41240	+	1.02617i	−0.419427	+	0.907789i	$0.637769\pi$
$463$	−30.3911	+	22.0804i	−1.41240	+	1.02617i	−0.992969	+	0.118376i	$0.962231\pi$
$464$	12.6854	−	17.4599i	0.588903	−	0.810556i
$465$	6.01464	−	23.1524i	0.278922	−	1.07367i
$466$	−7.33720	+	5.33078i	−0.339889	+	0.246944i
$467$	−2.78187	+	8.56170i	−0.128729	+	0.396188i	−0.994562	−	0.104145i	$-0.966789\pi$
$467$	−2.78187	+	8.56170i	−0.128729	+	0.396188i	0.865833	+	0.500334i	$0.166789\pi$
$468$	0.470216	+	0.944868i	0.0217358	+	0.0436766i
$469$	−22.0709	−	15.3999i	−1.01914	−	0.711101i
$470$	−10.8410	+	10.5456i	−0.500056	+	0.486430i
$471$	0.815803	+	1.34553i	0.0375902	+	0.0619988i
$472$	14.6222	−	4.75104i	0.673041	−	0.218684i
$473$	−5.63191	+	7.75166i	−0.258955	+	0.356422i
$474$	32.7878	−	7.70762i	1.50599	−	0.354023i
$475$	1.66953	+	5.66626i	0.0766032	+	0.259986i
$476$	−3.57392	+	11.7592i	−0.163810	+	0.538983i
$477$	5.39255	−	32.0780i	0.246908	−	1.46875i
$478$	2.22321	+	6.84234i	0.101687	+	0.312961i
$479$	−9.45055	−	29.0858i	−0.431807	−	1.32896i	−0.896324	−	0.443400i	$-0.853772\pi$
$479$	−9.45055	−	29.0858i	−0.431807	−	1.32896i	0.464517	−	0.885564i	$-0.346228\pi$
$480$	17.3329	−	1.04109i	0.791135	−	0.0475192i
$481$	−0.995002	−	0.323296i	−0.0453682	−	0.0147410i
$482$	3.62177			0.164967
$483$	−0.513843	−	0.204240i	−0.0233806	−	0.00929324i
$484$	−0.917961	+	0.666938i	−0.0417255	+	0.0303154i
$485$	1.13328	−	6.56690i	0.0514596	−	0.298187i
$486$	−22.7263	+	13.1970i	−1.03089	+	0.598627i
$487$	−33.1371	+	24.0755i	−1.50158	+	1.09097i	−0.531840	+	0.846845i	$0.678499\pi$
$487$	−33.1371	+	24.0755i	−1.50158	+	1.09097i	−0.969745	+	0.244120i	$0.921501\pi$
$488$	−22.8778	+	16.6217i	−1.03563	+	0.752430i
$489$	−8.09572	+	19.2860i	−0.366101	+	0.872142i
$490$	−3.49089	+	26.1561i	−0.157702	+	1.18161i
$491$	14.1181	+	19.4319i	0.637141	+	0.876949i	0.998459	−	0.0554933i	$-0.0176732\pi$
$491$	14.1181	+	19.4319i	0.637141	+	0.876949i	−0.361318	+	0.932443i	$0.617673\pi$
$492$	−3.78206	−	0.315682i	−0.170509	−	0.0142321i
$493$			23.9279i			1.07766i
$494$	−0.791297	−	0.257108i	−0.0356021	−	0.0115678i
$495$	−23.5654	−	0.548766i	−1.05919	−	0.0246652i
$496$	29.2239	−	9.49542i	1.31219	−	0.426357i
$497$	−0.171467	−	8.97340i	−0.00769133	−	0.402512i
$498$	−32.0835	−	13.4678i	−1.43770	−	0.603505i
$499$	34.9100			1.56278			0.781392	−	0.624040i	$-0.214510\pi$
$499$	34.9100			1.56278			0.781392	+	0.624040i	$0.214510\pi$
$500$	−3.92341	−	8.55923i	−0.175460	−	0.382781i
$501$	3.60133	+	15.3198i	0.160895	+	0.684440i
$502$	−15.2883	+	21.0425i	−0.682350	+	0.939174i
$503$	4.47932	+	13.7859i	0.199723	+	0.614684i	0.999889	+	0.0149056i	$0.00474478\pi$
$503$	4.47932	+	13.7859i	0.199723	+	0.614684i	−0.800166	+	0.599779i	$0.795255\pi$
$504$	−7.16649	−	13.7362i	−0.319221	−	0.611860i
$505$	−4.94943	+	9.39086i	−0.220247	+	0.417888i
$506$	−0.679813	−	0.220884i	−0.0302214	−	0.00981951i
$507$	5.08350	+	21.6249i	0.225766	+	0.960397i
$508$	−3.72853	+	11.4752i	−0.165427	+	0.509131i
$509$	−21.7234	+	15.7830i	−0.962873	+	0.699568i	−0.953816	−	0.300391i	$-0.902883\pi$
$509$	−21.7234	+	15.7830i	−0.962873	+	0.699568i	−0.00905705	+	0.999959i	$0.502883\pi$
$510$	−27.8156	+	22.8783i	−1.23170	+	1.01307i
$511$	−16.4471	−	21.7512i	−0.727578	−	0.962216i
$512$	1.69450	+	2.33228i	0.0748870	+	0.103073i
$513$	1.51774	−	5.94826i	0.0670097	−	0.262622i
$514$	3.92255	−	5.39893i	0.173016	−	0.238137i
$515$	6.49330	−	37.6260i	0.286129	−	1.65800i
$516$	3.01221	+	2.59744i	0.132605	+	0.114346i
$517$	13.4076	+	4.35638i	0.589664	+	0.191594i
$518$	−10.6881	−	3.24838i	−0.469609	−	0.142726i
$519$	−11.5433	−	0.963495i	−0.506693	−	0.0422928i
$520$	−1.79676	−	0.310076i	−0.0787932	−	0.0135977i
$521$	9.85126	+	30.3191i	0.431591	+	1.32830i	0.896539	+	0.442964i	$0.146073\pi$
$521$	9.85126	+	30.3191i	0.431591	+	1.32830i	−0.464948	+	0.885338i	$0.653927\pi$
$522$	15.3660	+	15.6599i	0.672553	+	0.685414i
$523$	4.32310	−	5.95023i	0.189036	−	0.260186i	−0.703971	−	0.710229i	$-0.748591\pi$
$523$	4.32310	−	5.95023i	0.189036	−	0.260186i	0.893007	+	0.450043i	$0.148591\pi$
$524$	1.07437			0.0469339
$525$	−15.1103	+	17.2243i	−0.659469	+	0.751732i
$526$	−11.5283			−0.502657
$527$	−20.0249	+	27.5620i	−0.872300	+	1.20062i
$528$	−15.6985	−	25.8921i	−0.683191	−	1.12681i
$529$	7.10289	+	21.8605i	0.308821	+	0.950454i
$530$	−28.5003	−	29.2986i	−1.23797	−	1.27265i
$531$	3.47526	+	23.3725i	0.150814	+	1.01428i
$532$	−2.51861	−	0.765469i	−0.109196	−	0.0331873i
$533$	1.03370	+	0.335869i	0.0447744	+	0.0145481i
$534$	−31.3748	+	36.3848i	−1.35772	+	1.57452i
$535$	−19.0145	−	10.0215i	−0.822067	−	0.433268i
$536$	11.6707	−	16.0633i	0.504097	−	0.693830i
$537$	−22.5100	+	26.1045i	−0.971378	+	1.12649i
$538$	0.129492	+	0.178231i	0.00558280	+	0.00768407i
$539$	23.0858	−	8.48907i	0.994376	−	0.365650i
$540$	−1.04070	+	9.72948i	−0.0447844	+	0.418690i
$541$	11.9353	−	8.67152i	0.513140	−	0.372818i	−0.300874	−	0.953664i	$-0.597278\pi$
$541$	11.9353	−	8.67152i	0.513140	−	0.372818i	0.814013	+	0.580846i	$0.197278\pi$
$542$	10.3409	−	31.8260i	0.444180	−	1.36704i
$543$	29.4366	−	6.91984i	1.26325	−	0.296959i
$544$	−23.5199	−	7.64208i	−1.00841	−	0.327651i
$545$	−6.02864	−	41.7912i	−0.258239	−	1.79014i
$546$	−0.798414	−	3.12697i	−0.0341690	−	0.133822i
$547$	−2.92546	−	9.00365i	−0.125084	−	0.384968i	0.868833	−	0.495106i	$-0.164871\pi$
$547$	−2.92546	−	9.00365i	−0.125084	−	0.384968i	−0.993916	+	0.110138i	$0.964871\pi$
$548$	−7.21557	+	9.93138i	−0.308234	+	0.424247i
$549$	−19.3635	−	38.9096i	−0.826414	−	1.66062i
$550$	−18.0652	+	23.4728i	−0.770304	+	1.00088i
$551$	−5.12493			−0.218329
$552$	0.157899	−	0.376153i	0.00672061	−	0.0160101i
$553$	−30.5124	+	0.583041i	−1.29752	+	0.0247934i
$554$	11.3369	−	3.68358i	0.481659	−	0.156500i
$555$	−6.16158	−	7.49128i	−0.261545	−	0.317987i
$556$	4.22275	+	1.37206i	0.179085	+	0.0581881i
$557$			5.38207i			0.228045i	0.993478	+	0.114023i	$0.0363737\pi$
$557$			5.38207i			0.228045i	−0.993478	+	0.114023i	$0.963626\pi$
$558$	4.59421	+	30.8978i	0.194488	+	1.30801i
$559$	−0.669536	−	0.921537i	−0.0283183	−	0.0389769i
$560$	−29.0946	−	4.45037i	−1.22947	−	0.188062i
$561$	30.9547	+	12.9939i	1.30691	+	0.548604i
$562$	11.2952	−	8.20644i	0.476459	−	0.346168i
$563$	−10.4999	+	7.62861i	−0.442517	+	0.321508i	−0.786634	−	0.617419i	$-0.788178\pi$
$563$	−10.4999	+	7.62861i	−0.442517	+	0.321508i	0.344117	+	0.938927i	$0.388178\pi$
$564$	2.26508	−	5.39596i	0.0953769	−	0.227211i
$565$	23.5633	−	3.39914i	0.991314	−	0.143003i
$566$	−16.2436	+	11.8017i	−0.682771	+	0.496062i
$567$	22.6451	−	7.36196i	0.951006	−	0.309173i
$568$	6.62157			0.277835
$569$	36.4760	+	11.8518i	1.52915	+	0.496852i	0.948359	−	0.317199i	$-0.102742\pi$
$569$	36.4760	+	11.8518i	1.52915	+	0.496852i	0.580793	+	0.814051i	$0.302742\pi$
$570$	−4.90013	−	5.95760i	−0.205244	−	0.249536i
$571$	−2.33626	−	7.19026i	−0.0977693	−	0.300903i	0.890196	−	0.455577i	$-0.150567\pi$
$571$	−2.33626	−	7.19026i	−0.0977693	−	0.300903i	−0.987966	+	0.154674i	$0.950567\pi$
$572$	−0.382003	−	1.17568i	−0.0159723	−	0.0491578i
$573$	−9.14094	−	3.83711i	−0.381868	−	0.160298i
$574$	11.1038	+	3.37471i	0.463463	+	0.140858i
$575$	−0.603082	−	0.0166636i	−0.0251503	−	0.000694922i
$576$	6.42372	−	3.19678i	0.267655	−	0.133199i
$577$	−2.01333	+	2.77111i	−0.0838160	+	0.115363i	−0.848866	−	0.528608i	$-0.822714\pi$
$577$	−2.01333	+	2.77111i	−0.0838160	+	0.115363i	0.765050	+	0.643971i	$0.222714\pi$
$578$	21.5264	−	6.99437i	0.895382	−	0.290927i
$579$	−19.9651	+	12.1050i	−0.829723	+	0.503066i
$580$	8.08518	−	1.16634i	0.335719	−	0.0484295i
$581$	25.8556	+	18.0407i	1.07267	+	0.748453i
$582$	1.99141	+	8.47135i	0.0825467	+	0.351149i
$583$	−11.7735	+	36.2351i	−0.487609	+	1.50071i
$584$	16.2764	−	11.8255i	0.673522	−	0.489342i
$585$	0.927762	−	2.64424i	0.0383582	−	0.109326i
$586$	−2.96319	+	4.07849i	−0.122408	+	0.168481i
$587$	34.9078	−	25.3620i	1.44080	−	1.04680i	0.452923	−	0.891550i	$-0.350381\pi$
$587$	34.9078	−	25.3620i	1.44080	−	1.04680i	0.987875	−	0.155252i	$-0.0496188\pi$
$588$	−2.71459	−	9.84315i	−0.111948	−	0.405925i
$589$	−5.90328	−	4.28898i	−0.243240	−	0.176724i
$590$	26.2672	+	13.8441i	1.08140	+	0.569951i
$591$	0.296495	−	0.343841i	0.0121962	−	0.0141437i
$592$	3.85031	−	11.8500i	0.158247	−	0.487034i
$593$	33.6080			1.38012			0.690058	−	0.723754i	$-0.257585\pi$
$593$	33.6080			1.38012			0.690058	+	0.723754i	$0.257585\pi$
$594$	28.6030	−	11.3745i	1.17360	−	0.466700i
$595$	28.9973	−	14.9687i	1.18877	−	0.613659i
$596$	15.6807	−	5.09495i	0.642305	−	0.208697i
$597$	−16.5629	−	27.3178i	−0.677876	−	1.11804i
$598$	0.0499482	−	0.0687478i	0.00204253	−	0.00281131i
$599$		−	31.2268i		−	1.27589i	−0.770080	−	0.637947i	$-0.779784\pi$
$599$		−	31.2268i		−	1.27589i	0.770080	−	0.637947i	$-0.220216\pi$
$600$	−12.4924	−	11.3888i	−0.510001	−	0.464945i
$601$		−	2.83146i		−	0.115498i	−0.998331	−	0.0577488i	$-0.981608\pi$
$601$		−	2.83146i		−	0.115498i	0.998331	−	0.0577488i	$-0.0183922\pi$
$602$	−7.33563	−	9.70131i	−0.298978	−	0.395396i
$603$	21.3726	+	21.7814i	0.870361	+	0.887005i
$604$	3.28917	+	10.1230i	0.133834	+	0.411900i
$605$	2.96883	+	0.512346i	0.120700	+	0.0208298i
$606$	1.15305	−	13.8142i	0.0468393	−	0.561163i
$607$			27.6370i			1.12175i	0.827900	+	0.560876i	$0.189536\pi$
$607$			27.6370i			1.12175i	−0.827900	+	0.560876i	$0.810464\pi$
$608$	1.63680	−	5.03754i	0.0663808	−	0.204299i
$609$	−10.6292	−	16.7986i	−0.430718	−	0.680713i
$610$	−53.8171	−	9.28747i	−2.17899	−	0.376039i
$611$	−0.985101	+	1.35587i	−0.0398529	+	0.0548528i
$612$	6.44409	−	12.3565i	0.260487	−	0.499483i
$613$	36.3180	−	26.3865i	1.46687	−	1.06574i	0.485362	−	0.874313i	$-0.338688\pi$
$613$	36.3180	−	26.3865i	1.46687	−	1.06574i	0.981506	−	0.191429i	$-0.0613123\pi$
$614$	22.8256	+	16.5838i	0.921167	+	0.669267i
$615$	6.40120	+	7.78261i	0.258121	+	0.313825i
$616$	5.93649	+	17.1487i	0.239188	+	0.690941i
$617$	−1.37579	−	0.447020i	−0.0553870	−	0.0179963i	0.281192	−	0.959651i	$-0.409270\pi$
$617$	−1.37579	−	0.447020i	−0.0553870	−	0.0179963i	−0.336579	+	0.941655i	$0.609270\pi$
$618$	11.4101	+	48.5379i	0.458981	+	1.95248i
$619$	−46.2066	−	15.0134i	−1.85720	−	0.603441i	−0.995355	−	0.0962678i	$-0.969309\pi$
$619$	−46.2066	−	15.0134i	−1.85720	−	0.603441i	−0.861844	−	0.507173i	$-0.830691\pi$
$620$	10.2892	+	5.42290i	0.413224	+	0.217789i
$621$	0.529881	+	0.335158i	0.0212634	+	0.0134494i
$622$	11.7836	−	3.82872i	0.472478	−	0.153518i
$623$	34.7225	−	26.2554i	1.39113	−	1.05190i
$624$	3.50418	−	0.823748i	0.140279	−	0.0329763i
$625$	−9.02656	+	23.3135i	−0.361062	+	0.932542i
$626$	22.5871			0.902761
$627$	−2.78306	+	6.62994i	−0.111145	+	0.264774i
$628$	−0.727634	+	0.236423i	−0.0290358	+	0.00943429i
$629$	4.26891	+	13.1383i	0.170213	+	0.523860i
$630$	9.36494	−	28.4179i	0.373108	−	1.13220i
$631$	2.80561	−	8.63478i	0.111690	−	0.343745i	−0.879553	−	0.475802i	$-0.842158\pi$
$631$	2.80561	−	8.63478i	0.111690	−	0.343745i	0.991242	+	0.132056i	$0.0421580\pi$
$632$		−	22.5155i		−	0.895617i
$633$	−38.7103	−	3.23108i	−1.53860	−	0.128424i
$634$	14.2209	−	10.3321i	0.564783	−	0.410339i
$635$	28.7430	−	14.1487i	1.14063	−	0.561474i
$636$	14.5831	+	6.12156i	0.578256	+	0.242736i
$637$	0.111711	+	2.92204i	0.00442616	+	0.115775i
$638$	−15.1047	−	20.7899i	−0.598002	−	0.823079i
$639$	−1.68712	+	10.0359i	−0.0667412	+	0.397015i
$640$	4.94309	−	28.6432i	0.195393	−	1.13222i
$641$	15.0417	+	20.7031i	0.594111	+	0.817724i	0.995153	−	0.0983355i	$-0.0313518\pi$
$641$	15.0417	+	20.7031i	0.594111	+	0.817724i	−0.401042	+	0.916060i	$0.631352\pi$
$642$	27.9707	+	2.33467i	1.10392	+	0.0921420i
$643$			1.01208i			0.0399127i	0.999801	+	0.0199563i	$0.00635272\pi$
$643$			1.01208i			0.0399127i	−0.999801	+	0.0199563i	$0.993647\pi$
$644$	0.153843	−	0.220486i	0.00606228	−	0.00868836i
$645$	−0.633188	−	10.5418i	−0.0249317	−	0.415082i
$646$	3.39494	+	10.4486i	0.133572	+	0.411093i
$647$	0.352200	+	1.08396i	0.0138464	+	0.0426148i	0.957741	−	0.287632i	$-0.0928680\pi$
$647$	0.352200	+	1.08396i	0.0138464	+	0.0426148i	−0.943895	+	0.330247i	$0.892868\pi$
$648$	5.11130	+	16.8077i	0.200791	+	0.660271i
$649$		−	27.6770i		−	1.08642i
$650$	−1.99027	−	2.90484i	−0.0780650	−	0.113937i
$651$	1.81497	−	28.2453i	0.0711343	−	1.10702i
$652$	−8.22762	−	5.97772i	−0.322219	−	0.234105i
$653$	−35.8425	+	11.6459i	−1.40263	+	0.455741i	−0.910039	−	0.414522i	$-0.863949\pi$
$653$	−35.8425	+	11.6459i	−1.40263	+	0.455741i	−0.492588	+	0.870263i	$0.663949\pi$
$654$	28.5870	+	47.1495i	1.11784	+	1.84369i
$655$	−1.98905	−	2.04477i	−0.0777188	−	0.0798959i
$656$	−4.00005	+	12.3109i	−0.156176	+	0.480659i
$657$	13.7761	+	27.6822i	0.537458	+	1.07999i
$658$	−10.2399	+	14.6756i	−0.399192	+	0.572115i
$659$	−13.7944	−	18.9863i	−0.537352	−	0.739602i	0.450876	−	0.892586i	$-0.351112\pi$
$659$	−13.7944	−	18.9863i	−0.537352	−	0.739602i	−0.988229	+	0.152984i	$0.951112\pi$
$660$	2.88176	−	11.0929i	0.112172	−	0.431789i
$661$	−9.79667	+	13.4840i	−0.381046	+	0.524465i	−0.955861	−	0.293818i	$-0.905074\pi$
$661$	−9.79667	+	13.4840i	−0.381046	+	0.524465i	0.574815	+	0.818283i	$0.305074\pi$
$662$	−22.0877	−	30.4011i	−0.858463	−	1.18157i
$663$	−2.60632	+	3.02251i	−0.101221	+	0.117384i
$664$	−13.6720	+	18.8179i	−0.530576	+	0.730275i
$665$	3.20604	+	6.21069i	0.124325	+	0.240840i
$666$	11.2310	+	5.85712i	0.435193	+	0.226959i
$667$	0.161748	−	0.497809i	0.00626290	−	0.0192752i
$668$	−7.65185			−0.296059
$669$	−0.0175349	+	0.210078i	−0.000677938	+	0.00812210i
$670$	37.9525	−	5.47488i	1.46623	−	0.211513i
$671$	15.7309	+	48.4146i	0.607283	+	1.86903i
$672$	19.9069	−	5.08285i	0.767924	−	0.196075i
$673$	−14.3317	−	10.4126i	−0.552447	−	0.401376i	0.276240	−	0.961089i	$-0.410912\pi$
$673$	−14.3317	−	10.4126i	−0.552447	−	0.401376i	−0.828687	+	0.559713i	$0.810912\pi$
$674$			45.4555i			1.75088i
$675$	20.4442	−	16.0322i	0.786899	−	0.617081i
$676$	−10.8011			−0.415426
$677$	−3.70392	−	2.69106i	−0.142353	−	0.103426i	0.514329	−	0.857593i	$-0.328041\pi$
$677$	−3.70392	−	2.69106i	−0.142353	−	0.103426i	−0.656683	+	0.754167i	$0.728041\pi$
$678$	−26.5844	+	16.1183i	−1.02097	+	0.619019i
$679$	−0.150640	−	7.88347i	−0.00578103	−	0.302540i
$680$	10.6328	+	21.6006i	0.407751	+	0.828344i
$681$	12.3516	+	1.03097i	0.473315	+	0.0395068i
$682$		−	36.5883i		−	1.40104i
$683$	−3.73053	−	1.21212i	−0.142745	−	0.0463806i	0.236773	−	0.971565i	$-0.423910\pi$
$683$	−3.73053	−	1.21212i	−0.142745	−	0.0463806i	−0.379518	+	0.925184i	$0.623910\pi$
$684$	2.64655	+	1.38021i	0.101193	+	0.0527736i
$685$	32.2605	−	4.65377i	1.23261	−	0.177812i
$686$	1.78865	+	31.1715i	0.0682908	+	1.19013i
$687$	−7.03678	+	8.16044i	−0.268470	+	0.311340i
$688$	10.9751	−	7.97388i	0.418422	−	0.304001i
$689$	−3.66437	−	2.66232i	−0.139601	−	0.101426i
$690$	0.733342	−	0.287945i	0.0279179	−	0.0109619i
$691$	−2.51582	−	3.46273i	−0.0957062	−	0.131728i	0.758478	−	0.651698i	$-0.225943\pi$
$691$	−2.51582	−	3.46273i	−0.0957062	−	0.131728i	−0.854185	+	0.519970i	$0.825943\pi$
$692$	1.74041	−	5.35642i	0.0661603	−	0.203621i
$693$	−27.5038	+	4.62825i	−1.04478	+	0.175813i
$694$	17.4474	−	53.6975i	0.662294	−	2.03833i
$695$	−5.20656	−	10.5771i	−0.197496	−	0.401212i
$696$	12.5412	−	7.60377i	0.475371	−	0.288220i
$697$	−4.43492	−	13.6493i	−0.167985	−	0.517004i
$698$	−33.7815	−	24.5437i	−1.27865	−	0.928992i
$699$	−9.07046	+	2.13225i	−0.343076	+	0.0806490i
$700$	−6.47133	−	9.06846i	−0.244593	−	0.342756i
$701$			1.39262i			0.0525987i	0.999654	+	0.0262994i	$0.00837231\pi$
$701$			1.39262i			0.0525987i	−0.999654	+	0.0262994i	$0.991628\pi$
$702$	0.235260	+	3.65184i	0.00887933	+	0.137830i
$703$	−2.81400	+	0.914324i	−0.106132	+	0.0344844i
$704$	−7.99294	+	2.59706i	−0.301245	+	0.0978805i
$705$	−14.4633	+	5.67898i	−0.544720	+	0.213883i
$706$	35.0310	+	11.3823i	1.31841	+	0.428377i
$707$	−3.65240	+	12.0175i	−0.137363	+	0.451963i
$708$	−11.4493	−	0.955653i	−0.430291	−	0.0359156i
$709$	1.84127	−	1.33776i	0.0691504	−	0.0502407i	−0.552673	−	0.833398i	$-0.686392\pi$
$709$	1.84127	−	1.33776i	0.0691504	−	0.0502407i	0.621823	+	0.783157i	$0.286392\pi$
$710$	8.91660	+	9.16638i	0.334634	+	0.344008i
$711$	34.1253	+	5.73673i	1.27980	+	0.215144i
$712$	18.8776	+	25.9828i	0.707469	+	0.973747i
$713$	0.602922	−	0.438049i	0.0225796	−	0.0164050i
$714$	−27.2072	+	32.7985i	−1.01821	+	1.22745i
$715$	−1.53038	+	2.90368i	−0.0572328	+	0.108591i
$716$	−9.85112	−	13.5589i	−0.368154	−	0.506720i
$717$	−0.614821	+	7.36592i	−0.0229609	+	0.275085i
$718$	−14.0948			−0.526012
$719$	12.3047	−	37.8699i	0.458887	−	1.41231i	−0.407623	−	0.913150i	$-0.633642\pi$
$719$	12.3047	−	37.8699i	0.458887	−	1.41231i	0.866510	−	0.499159i	$-0.166358\pi$
$720$	31.4918	+	11.0492i	1.17363	+	0.411781i
$721$	−0.863114	−	45.1695i	−0.0321440	−	1.68220i
$722$	28.2259	−	9.17115i	1.05046	−	0.341315i
$723$	3.43096	+	1.44022i	0.127599	+	0.0535624i
$724$			14.7028i			0.546425i
$725$	−17.1885	−	13.2287i	−0.638366	−	0.491301i
$726$	−3.82982	+	0.900299i	−0.142138	+	0.0334132i
$727$	19.7364	−	27.1649i	0.731984	−	1.00749i	−0.267056	−	0.963681i	$-0.586051\pi$
$727$	19.7364	−	27.1649i	0.731984	−	1.00749i	0.999040	−	0.0438082i	$-0.0139490\pi$
$728$	−2.15699	+	0.0412164i	−0.0799434	+	0.00152758i
$729$	−26.7768	+	3.46443i	−0.991734	+	0.128312i
$730$	38.2881	+	6.60755i	1.41710	+	0.244557i
$731$	−4.64787	+	14.3047i	−0.171908	+	0.529078i
$732$	20.5711	−	4.83578i	0.760330	−	0.178735i
$733$	27.4160	+	8.90801i	1.01263	+	0.329025i	0.767903	−	0.640566i	$-0.221300\pi$
$733$	27.4160	+	8.90801i	1.01263	+	0.329025i	0.244731	+	0.969591i	$0.421300\pi$
$734$	1.97440	−	1.43449i	0.0728766	−	0.0529480i
$735$	−13.7081	+	23.3899i	−0.505632	+	0.862749i
$736$	0.437661	+	0.317979i	0.0161324	+	0.0117209i
$737$	−21.0092	−	28.9167i	−0.773883	−	1.06516i
$738$	−11.6678	−	6.08490i	−0.429497	−	0.223988i
$739$	−33.2141	−	24.1315i	−1.22180	−	0.887691i	−0.225554	−	0.974231i	$-0.572419\pi$
$739$	−33.2141	−	24.1315i	−1.22180	−	0.887691i	−0.996248	+	0.0865395i	$0.972419\pi$
$740$	4.23133	−	2.08286i	0.155547	−	0.0765676i
$741$	−0.647367	−	0.558227i	−0.0237816	−	0.0205070i
$742$	−39.6621	−	27.6742i	−1.45604	−	1.01595i
$743$			24.6620i			0.904761i	0.891825	+	0.452380i	$0.149425\pi$
$743$			24.6620i			0.904761i	−0.891825	+	0.452380i	$0.850575\pi$
$744$	20.8093	+	1.73692i	0.762907	+	0.0636785i
$745$	−38.7277	−	20.4113i	−1.41887	−	0.747814i
$746$	20.5736	−	6.68476i	0.753252	−	0.244746i
$747$	−25.0376	−	25.5164i	−0.916079	−	0.933597i
$748$	−9.59444	+	13.2056i	−0.350808	+	0.482845i
$749$	−24.3327	−	7.39531i	−0.889099	−	0.270219i
$750$	−1.05655	−	32.6296i	−0.0385797	−	1.19147i
$751$	−5.24745			−0.191482			−0.0957411	−	0.995406i	$-0.530522\pi$
$751$	−5.24745			−0.191482			−0.0957411	+	0.995406i	$0.530522\pi$
$752$	−16.1479	−	11.7321i	−0.588852	−	0.427826i
$753$	−22.8505	+	13.8544i	−0.832719	+	0.504883i
$754$	2.90549	−	0.944050i	0.105812	−	0.0343803i
$755$	13.1770	−	25.0016i	0.479561	−	0.909901i
$756$	0.964922	+	11.5375i	0.0350939	+	0.419614i
$757$	15.2999			0.556085			0.278043	−	0.960569i	$-0.410314\pi$
$757$	15.2999			0.556085			0.278043	+	0.960569i	$0.410314\pi$
$758$	−18.6506	−	6.05996i	−0.677422	−	0.220108i
$759$	−0.556160	−	0.479579i	−0.0201873	−	0.0174076i
$760$	−4.62645	+	2.27736i	−0.167819	+	0.0826087i
$761$	−30.0535	−	21.8351i	−1.08944	−	0.791523i	−0.110134	−	0.993917i	$-0.535128\pi$
$761$	−30.0535	−	21.8351i	−1.08944	−	0.791523i	−0.979304	+	0.202394i	$0.935128\pi$
$762$	−27.3204	+	31.6831i	−0.989715	+	1.14776i
$763$	−16.3434	−	47.2111i	−0.591671	−	1.70916i
$764$	2.83325	−	3.89963i	0.102503	−	0.141084i
$765$	−35.4479	+	10.6119i	−1.28162	+	0.383675i
$766$	−34.4905	−	47.4721i	−1.24619	−	1.71524i
$767$	3.12927	+	1.01676i	0.112991	+	0.0367132i
$768$	6.79007	+	28.8846i	0.245015	+	1.04228i
$769$	−7.09111	−	2.30404i	−0.255712	−	0.0830859i	0.178356	−	0.983966i	$-0.442922\pi$
$769$	−7.09111	−	2.30404i	−0.255712	−	0.0830859i	−0.434068	+	0.900880i	$0.642922\pi$
$770$	−15.7452	+	31.3105i	−0.567419	+	1.12835i
$771$	5.86281	−	3.55466i	0.211144	−	0.128018i
$772$	−3.50807	−	10.7967i	−0.126258	−	0.388583i
$773$	24.2937	+	17.6504i	0.873784	+	0.634841i	0.931600	−	0.363486i	$-0.118413\pi$
$773$	24.2937	+	17.6504i	0.873784	+	0.634841i	−0.0578154	+	0.998327i	$0.518413\pi$
$774$	6.14433	+	12.3466i	0.220853	+	0.443790i
$775$	−8.72812	−	29.6226i	−0.313523	−	1.06408i
$776$	5.81730			0.208829
$777$	−8.83327	−	7.32744i	−0.316892	−	0.262870i
$778$	6.17069	+	18.9914i	0.221230	+	0.680876i
$779$	2.92343	−	0.949881i	0.104743	−	0.0340330i
$780$	1.14834	+	0.733339i	0.0411171	+	0.0262578i
$781$	3.68346	−	11.3365i	0.131805	−	0.405653i
$782$	−1.12206			−0.0401249
$783$	8.32921	+	20.9452i	0.297662	+	0.748522i
$784$	−34.8002	+	1.33043i	−1.24286	+	0.0475154i
$785$	1.79709	+	0.947153i	0.0641410	+	0.0338054i
$786$	3.43480	+	1.44183i	0.122515	+	0.0514285i
$787$	14.1655	+	19.4972i	0.504946	+	0.694999i	0.983057	−	0.183301i	$-0.0586783\pi$
$787$	14.1655	+	19.4972i	0.504946	+	0.694999i	−0.478111	+	0.878300i	$0.658678\pi$
$788$	0.129756	+	0.178594i	0.00462237	+	0.00636215i
$789$	−10.9209	−	4.58430i	−0.388795	−	0.163205i
$790$	31.1686	−	30.3193i	1.10893	−	1.07871i
$791$	26.6191	−	9.21494i	0.946468	−	0.327646i
$792$	−3.02632	−	20.3532i	−0.107536	−	0.723220i
$793$	−6.05186			−0.214908
$794$	1.73621	−	5.34349i	0.0616156	−	0.189633i
$795$	−15.3479	−	39.0883i	−0.544335	−	1.38632i
$796$	14.7729	−	4.80000i	0.523611	−	0.170132i
$797$	8.71833	+	26.8323i	0.308819	+	0.950448i	0.978224	+	0.207550i	$0.0665491\pi$
$797$	8.71833	+	26.8323i	0.308819	+	0.950448i	−0.669405	+	0.742898i	$0.733451\pi$
$798$	−7.02485	−	5.82730i	−0.248677	−	0.206284i
$799$	22.1299			0.782898
$800$	18.4928	−	12.6704i	0.653818	−	0.447968i
$801$	−44.1904	+	21.9915i	−1.56139	+	0.777031i
$802$	51.5691	+	37.4671i	1.82097	+	1.32301i
$803$	−11.1917	−	34.4445i	−0.394946	−	1.21552i
$804$	−12.6875	+	7.69253i	−0.447455	+	0.271295i
$805$	−0.704459	+	0.115402i	−0.0248289	+	0.00406737i
$806$	4.13682	+	1.34413i	0.145713	+	0.0473451i
$807$	0.0517952	+	0.220334i	0.00182328	+	0.00775612i
$808$	−8.81309	−	2.86355i	−0.310044	−	0.100739i
$809$	17.8912	+	24.6252i	0.629022	+	0.865775i	0.997971	−	0.0636750i	$-0.0202821\pi$
$809$	17.8912	+	24.6252i	0.629022	+	0.865775i	−0.368948	+	0.929450i	$0.620282\pi$
$810$	−16.3844	+	29.7090i	−0.575691	+	1.04387i
$811$	−1.87862	+	2.58569i	−0.0659671	+	0.0907959i	−0.840726	−	0.541461i	$-0.817871\pi$
$811$	−1.87862	+	2.58569i	−0.0659671	+	0.0907959i	0.774759	+	0.632257i	$0.217871\pi$
$812$	9.13373	−	3.16189i	0.320531	−	0.110961i
$813$	22.4519	−	26.0371i	0.787423	−	0.913162i
$814$	−12.0028	−	8.72052i	−0.420697	−	0.305654i
$815$	3.85541	+	26.7261i	0.135049	+	0.936175i
$816$	−35.9967	−	31.0401i	−1.26014	−	1.08662i
$817$	−3.06380	−	0.995491i	−0.107189	−	0.0348278i
$818$	−51.4978			−1.80058
$819$	0.487112	−	3.27972i	0.0170211	−	0.114603i
$820$	−4.39588	+	2.16387i	−0.153511	+	0.0755654i
$821$	−38.7748	+	12.5987i	−1.35325	+	0.439698i	−0.893784	−	0.448497i	$-0.851960\pi$
$821$	−38.7748	+	12.5987i	−1.35325	+	0.439698i	−0.459467	+	0.888195i	$0.651960\pi$
$822$	−36.3968	+	22.0676i	−1.26948	+	0.769695i
$823$	−37.4214	−	27.1882i	−1.30443	−	0.947722i	−0.304439	−	0.952532i	$-0.598469\pi$
$823$	−37.4214	−	27.1882i	−1.30443	−	0.947722i	−0.999988	+	0.00481034i	$0.998469\pi$
$824$	33.3311			1.16114
$825$	−26.4476	+	15.0524i	−0.920787	+	0.524057i
$826$	33.6140	+	10.2161i	1.16958	+	0.355464i
$827$	6.15415	−	8.47046i	0.214001	−	0.294547i	−0.688499	−	0.725237i	$-0.741730\pi$
$827$	6.15415	−	8.47046i	0.214001	−	0.294547i	0.902500	+	0.430691i	$0.141730\pi$
$828$	−0.217594	+	0.213511i	−0.00756190	+	0.00742001i
$829$	−16.4045	+	5.33013i	−0.569750	+	0.185123i	−0.579704	−	0.814827i	$-0.696832\pi$
$829$	−16.4045	+	5.33013i	−0.569750	+	0.185123i	0.00995337	+	0.999950i	$0.496832\pi$
$830$	−44.4606	+	6.41372i	−1.54325	+	0.222623i
$831$	12.2044	+	1.01868i	0.423367	+	0.0353377i
$832$		−	0.999121i		−	0.0346383i
$833$	30.3477	−	23.8722i	1.05149	−	0.827123i
$834$	11.6590	+	10.0536i	0.403718	+	0.348128i
$835$	14.1665	+	14.5633i	0.490250	+	0.503984i
$836$	−2.82841	−	2.05496i	−0.0978225	−	0.0710722i
$837$	−7.93457	+	31.0969i	−0.274259	+	1.07487i
$838$	−26.9804	−	37.1353i	−0.932021	−	1.28282i
$839$	19.3538	+	14.0614i	0.668168	+	0.485452i	0.869411	−	0.494089i	$-0.164498\pi$
$839$	19.3538	+	14.0614i	0.668168	+	0.485452i	−0.201244	+	0.979541i	$0.564498\pi$
$840$	−17.0601	−	10.4414i	−0.588631	−	0.360261i
$841$	−8.23762	+	5.98498i	−0.284056	+	0.206379i
$842$	−21.2118	−	6.89212i	−0.731006	−	0.237518i
$843$	13.9635	−	3.28247i	0.480927	−	0.113054i
$844$	5.83646	−	17.9628i	0.200899	−	0.618304i
$845$	19.9969	+	20.5570i	0.687913	+	0.707183i
$846$	14.4831	−	14.2113i	0.497940	−	0.488596i
$847$	3.56405	−	0.0681029i	0.122462	−	0.00234004i
$848$	31.7071	−	43.6410i	1.08883	−	1.49864i
$849$	−20.0809	+	4.72053i	−0.689173	+	0.162008i
$850$	−15.5839	+	43.8066i	−0.534525	+	1.50255i
$851$		−	0.302194i		−	0.0103591i
$852$	−4.56246	−	1.91519i	−0.156307	−	0.0656135i
$853$	−8.60932	+	2.79734i	−0.294777	+	0.0957790i	−0.452672	−	0.891677i	$-0.649529\pi$
$853$	−8.60932	+	2.79734i	−0.294777	+	0.0957790i	0.157895	+	0.987456i	$0.449529\pi$
$854$	−64.6067	+	1.23453i	−2.21080	+	0.0422446i
$855$	−2.27289	−	7.59229i	−0.0777311	−	0.259651i
$856$	5.79806	−	17.8446i	0.198174	−	0.609916i
$857$	−41.4563			−1.41612			−0.708061	−	0.706151i	$-0.750430\pi$
$857$	−41.4563			−1.41612			−0.708061	+	0.706151i	$0.750430\pi$
$858$	0.356525	−	4.27138i	0.0121716	−	0.145823i
$859$	−17.7311	−	24.4048i	−0.604977	−	0.832680i	0.391175	−	0.920316i	$-0.372069\pi$
$859$	−17.7311	−	24.4048i	−0.604977	−	0.832680i	−0.996153	+	0.0876366i	$0.972069\pi$
$860$	5.06006	+	0.873239i	0.172547	+	0.0297772i
$861$	9.17680	+	7.61240i	0.312744	+	0.259430i
$862$	36.1445	−	26.2605i	1.23109	−	0.894437i
$863$	−2.99463	−	4.12175i	−0.101938	−	0.140306i	0.755001	−	0.655724i	$-0.227637\pi$
$863$	−2.99463	−	4.12175i	−0.101938	−	0.140306i	−0.856939	+	0.515418i	$0.827637\pi$
$864$	−23.2483	+	1.49771i	−0.790922	+	0.0509531i
$865$	−13.4167	+	6.60434i	−0.456181	+	0.224554i
$866$	6.30697	−	4.58228i	0.214319	−	0.155712i
$867$	23.1737	+	1.93427i	0.787019	+	0.0656911i
$868$	13.1671	+	4.00179i	0.446919	+	0.135830i
$869$	−38.5478	−	12.5250i	−1.30765	−	0.424880i
$870$	27.4140	+	7.12174i	0.929421	+	0.241450i
$871$	4.04124	−	1.31308i	0.136932	−	0.0444920i
$872$	35.0552	−	11.3901i	1.18712	−	0.385718i
$873$	−1.48219	+	8.81693i	−0.0501647	+	0.298408i
$874$		−	0.240326i		−	0.00812915i
$875$	−5.27857	+	29.1056i	−0.178448	+	0.983949i
$876$	−14.6353	+	3.44040i	−0.494480	+	0.116240i
$877$	16.2649	+	11.8172i	0.549227	+	0.399037i	0.827500	−	0.561465i	$-0.189762\pi$
$877$	16.2649	+	11.8172i	0.549227	+	0.399037i	−0.278273	+	0.960502i	$0.589762\pi$
$878$	17.1990	+	52.9332i	0.580439	+	1.78641i
$879$	−4.42892	+	2.68528i	−0.149384	+	0.0905722i
$880$	−34.5815	−	18.2261i	−1.16574	−	0.614402i
$881$	5.99905	−	18.4632i	0.202113	−	0.622040i	−0.797707	−	0.603046i	$-0.793954\pi$
$881$	5.99905	−	18.4632i	0.202113	−	0.622040i	0.999820	−	0.0189942i	$-0.00604640\pi$
$882$	4.53114	−	35.1121i	0.152571	−	1.18229i
$883$	4.29831	−	13.2289i	0.144650	−	0.445186i	−0.852316	−	0.523027i	$-0.824803\pi$
$883$	4.29831	−	13.2289i	0.144650	−	0.445186i	0.996966	+	0.0778409i	$0.0248026\pi$
$884$	−1.14061	−	1.56992i	−0.0383629	−	0.0528021i
$885$	19.3781	+	23.5600i	0.651388	+	0.791961i
$886$	−32.4130	−	23.5494i	−1.08893	−	0.791157i
$887$	26.0849	−	18.9518i	0.875846	−	0.636340i	−0.0563031	−	0.998414i	$-0.517931\pi$
$887$	26.0849	−	18.9518i	0.875846	−	0.636340i	0.932149	+	0.362074i	$0.117931\pi$
$888$	5.52953	−	6.41251i	0.185559	−	0.215190i
$889$	30.2356	−	22.8626i	1.01407	−	0.766786i
$890$	−10.5480	+	61.1211i	−0.353568	+	2.04878i
$891$	31.6192	+	0.598993i	1.05928	+	0.0200670i
$892$	−0.0974828	−	0.0316741i	−0.00326397	−	0.00106053i
$893$			4.73982i			0.158612i
$894$	56.9694	+	4.75514i	1.90534	+	0.159036i
$895$	−7.56769	+	43.8517i	−0.252960	+	1.46580i
$896$	−0.657054	−	34.3857i	−0.0219506	−	1.14875i
$897$	0.0746547	−	0.0452636i	0.00249265	−	0.00151131i
$898$	−35.2829	−	25.6345i	−1.17740	−	0.855434i
$899$	26.7926			0.893584
$900$	5.31360	+	11.4605i	0.177120	+	0.382015i
$901$			59.8079i			1.99249i
$902$	12.4695	+	9.05966i	0.415190	+	0.301654i
$903$	−3.09136	−	12.1073i	−0.102874	−	0.402904i
$904$	6.42213	+	19.7653i	0.213597	+	0.657383i
$905$	27.9829	−	27.2204i	0.930184	−	0.904837i
$906$	−3.06979	+	36.7779i	−0.101987	+	1.22187i
$907$	20.6725			0.686420			0.343210	−	0.939259i	$-0.388486\pi$
$907$	20.6725			0.686420			0.343210	+	0.939259i	$0.388486\pi$
$908$	−1.86229	+	5.73153i	−0.0618022	+	0.190208i
$909$	6.58560	−	12.6279i	0.218431	−	0.418840i
$910$	−2.96166	−	2.93046i	−0.0981780	−	0.0971439i
$911$	−7.63311	+	10.5061i	−0.252896	+	0.348082i	−0.916523	−	0.399982i	$-0.869016\pi$
$911$	−7.63311	+	10.5061i	−0.252896	+	0.348082i	0.663627	+	0.748064i	$0.269016\pi$
$912$	6.64824	−	7.70986i	0.220145	−	0.255299i
$913$	24.6119	+	33.8753i	0.814533	+	1.12111i
$914$	−21.1451	+	29.1037i	−0.699418	+	0.962666i
$915$	−47.2885	−	30.1989i	−1.56331	−	0.998344i
$916$	−3.07953	−	4.23861i	−0.101751	−	0.140048i
$917$	−2.76805	−	1.93140i	−0.0914091	−	0.0637804i
$918$	37.1849	−	30.8562i	1.22729	−	1.01841i
$919$	−5.17872	+	15.9385i	−0.170830	+	0.525762i	−0.999419	−	0.0340969i	$-0.989145\pi$
$919$	−5.17872	+	15.9385i	−0.170830	+	0.525762i	0.828588	+	0.559859i	$0.189145\pi$
$920$	−0.0751956	−	0.521265i	−0.00247913	−	0.0171856i
$921$	15.0284	+	24.7868i	0.495202	+	0.816753i
$922$	7.16657	−	2.32856i	0.236018	−	0.0766870i
$923$	1.14644	+	0.832934i	0.0377354	+	0.0274164i
$924$	0.869597	−	13.5330i	0.0286077	−	0.445204i
$925$	−11.7980	−	4.19706i	−0.387915	−	0.137998i
$926$		−	63.3306i		−	2.08117i
$927$	−8.49245	+	50.5179i	−0.278929	+	1.65923i
$928$	6.00999	+	18.4969i	0.197288	+	0.607189i
$929$	11.5409	+	35.5191i	0.378643	+	1.16534i	0.940988	+	0.338441i	$0.109900\pi$
$929$	11.5409	+	35.5191i	0.378643	+	1.16534i	−0.562344	+	0.826903i	$0.690100\pi$
$930$	25.6174	+	31.1457i	0.840026	+	1.02131i
$931$	5.11300	+	6.49994i	0.167572	+	0.213027i
$932$		−	4.53045i		−	0.148400i
$933$	12.6853	+	1.05882i	0.415297	+	0.0346641i
$934$	−8.92065	−	12.2782i	−0.291893	−	0.401756i
$935$	42.8964	−	6.18806i	1.40286	−	0.202371i
$936$	2.41239	+	0.405542i	0.0788515	+	0.0132556i
$937$	7.62771	+	10.4986i	0.249186	+	0.342976i	0.915226	−	0.402941i	$-0.132012\pi$
$937$	7.62771	+	10.4986i	0.249186	+	0.342976i	−0.666040	+	0.745916i	$0.732012\pi$
$938$	42.8745	−	14.8422i	1.39990	−	0.484615i
$939$	21.3971	+	8.98190i	0.698267	+	0.293113i
$940$	−1.07869	−	7.47761i	−0.0351830	−	0.243893i
$941$	18.1772	−	13.2065i	0.592561	−	0.430521i	−0.250670	−	0.968073i	$-0.580651\pi$
$941$	18.1772	−	13.2065i	0.592561	−	0.430521i	0.843231	+	0.537552i	$0.180651\pi$
$942$	−2.64357	−	0.220654i	−0.0861321	−	0.00718930i
$943$			0.313946i			0.0102235i
$944$	−12.1092	+	37.2683i	−0.394121	+	1.21298i
$945$	20.1721	−	23.1967i	0.656199	−	0.754588i
$946$	−4.99164	−	15.3627i	−0.162292	−	0.499484i
$947$	11.2507	−	3.65557i	0.365598	−	0.118790i	−0.120456	−	0.992719i	$-0.538436\pi$
$947$	11.2507	−	3.65557i	0.365598	−	0.118790i	0.486054	+	0.873929i	$0.338436\pi$
$948$	−6.51227	+	15.5138i	−0.211509	+	0.503866i
$949$	4.30558			0.139765
$950$	−9.38258	−	3.33780i	−0.304411	−	0.108293i
$951$	17.5803	−	4.13270i	0.570079	−	0.134012i
$952$	17.1814	+	22.7222i	0.556852	+	0.736432i
$953$	0.779187	−	0.253173i	0.0252403	−	0.00820108i	−0.296370	−	0.955073i	$-0.595776\pi$
$953$	0.779187	−	0.253173i	0.0252403	−	0.00820108i	0.321610	+	0.946872i	$0.395776\pi$
$954$	38.4074	+	39.1419i	1.24349	+	1.26727i
$955$	−12.6673	+	1.82734i	−0.409905	+	0.0591313i
$956$	−3.41801	−	1.11058i	−0.110546	−	0.0359187i
$957$	−6.04170	−	25.7011i	−0.195301	−	0.830797i
$958$	49.0349	+	15.9324i	1.58424	+	0.514752i
$959$	36.4443	−	12.6162i	1.17685	−	0.407398i
$960$	4.98564	−	7.80702i	0.160911	−	0.251970i
$961$	5.78219	+	4.20101i	0.186522	+	0.135516i
$962$	1.42692	−	1.03672i	0.0460057	−	0.0334251i
$963$	25.5687	+	13.3344i	0.823940	+	0.429695i
$964$	−1.06343	+	1.46369i	−0.0342508	+	0.0471421i
$965$	−14.0540	+	26.6655i	−0.452414	+	0.858392i
$966$	0.787744	−	0.498441i	0.0253453	−	0.0160371i
$967$	−10.8965	+	33.5361i	−0.350409	+	1.07845i	0.608215	+	0.793772i	$0.291886\pi$
$967$	−10.8965	+	33.5361i	−0.350409	+	1.07845i	−0.958624	+	0.284675i	$0.908114\pi$
$968$			2.62995i			0.0845297i
$969$	−0.938859	+	11.2481i	−0.0301605	+	0.361341i
$970$	7.83357	+	8.05301i	0.251521	+	0.258567i
$971$	−2.70493	−	8.32491i	−0.0868052	−	0.267159i	0.898226	−	0.439533i	$-0.144856\pi$
$971$	−2.70493	−	8.32491i	−0.0868052	−	0.267159i	−0.985032	+	0.172374i	$0.944856\pi$
$972$	1.33956	−	13.0594i	0.0429665	−	0.418881i
$973$	−8.41316	−	11.1263i	−0.269713	−	0.356694i
$974$		−	69.0527i		−	2.21259i
$975$	−0.730286	−	3.54325i	−0.0233879	−	0.113475i
$976$		−	72.0750i		−	2.30706i
$977$	−10.7209	+	14.7561i	−0.342993	+	0.472090i	−0.945313	−	0.326165i	$-0.894243\pi$
$977$	−10.7209	+	14.7561i	−0.342993	+	0.472090i	0.602319	+	0.798255i	$0.294243\pi$
$978$	−18.2818	−	30.1528i	−0.584588	−	0.964180i
$979$	54.9854	−	17.8659i	1.75734	−	0.570995i
$980$	−9.54561	−	9.09079i	−0.304923	−	0.290395i
$981$	8.33159	+	56.0332i	0.266007	+	1.78900i
$982$	−40.4932			−1.29219
$983$	−6.41859	+	19.7544i	−0.204721	+	0.630067i	0.795003	+	0.606605i	$0.207469\pi$
$983$	−6.41859	+	19.7544i	−0.204721	+	0.630067i	−0.999725	+	0.0234623i	$0.992531\pi$
$984$	−5.74457	+	6.66189i	−0.183130	+	0.212373i
$985$	0.0996794	−	0.577601i	0.00317605	−	0.0184039i
$986$	−32.6352	−	23.7109i	−1.03932	−	0.755109i
$987$	−15.5362	+	9.83048i	−0.494524	+	0.312908i
$988$	0.336248	−	0.244299i	0.0106975	−	0.00777217i
$989$	0.193393	−	0.266183i	0.00614955	−	0.00846413i
$990$	24.1001	−	31.5970i	0.765952	−	1.00422i
$991$	−31.8186	+	23.1176i	−1.01075	+	0.734354i	−0.964367	−	0.264569i	$-0.914770\pi$
$991$	−31.8186	+	23.1176i	−1.01075	+	0.734354i	−0.0463854	+	0.998924i	$0.514770\pi$
$992$	−8.55700	+	26.3357i	−0.271685	+	0.836160i
$993$	−8.83480	−	37.5827i	−0.280364	−	1.19265i
$994$	12.4087	+	8.65814i	0.393580	+	0.274620i
$995$	−36.4857	−	19.2297i	−1.15668	−	0.609623i
$996$	14.8632	−	9.01165i	0.470959	−	0.285545i
$997$	40.3361	−	13.1060i	1.27746	−	0.415071i	0.409773	−	0.912187i	$-0.365608\pi$
$997$	40.3361	−	13.1060i	1.27746	−	0.415071i	0.867684	+	0.497116i	$0.165608\pi$
$998$	−34.5933	+	47.6136i	−1.09503	+	1.50718i
$999$	8.31018	+	10.0146i	0.262923	+	0.316849i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bb.a.41.19	✓	304
3.2	odd	2	inner	525.2.bb.a.41.57	yes	304
7.6	odd	2	inner	525.2.bb.a.41.20	yes	304
21.20	even	2	inner	525.2.bb.a.41.58	yes	304
25.11	even	5	inner	525.2.bb.a.461.58	yes	304
75.11	odd	10	inner	525.2.bb.a.461.20	yes	304
175.111	odd	10	inner	525.2.bb.a.461.57	yes	304
525.461	even	10	inner	525.2.bb.a.461.19	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bb.a.41.19	✓	304	1.1	even	1	trivial
525.2.bb.a.41.20	yes	304	7.6	odd	2	inner
525.2.bb.a.41.57	yes	304	3.2	odd	2	inner
525.2.bb.a.41.58	yes	304	21.20	even	2	inner
525.2.bb.a.461.19	yes	304	525.461	even	10	inner
525.2.bb.a.461.20	yes	304	75.11	odd	10	inner
525.2.bb.a.461.57	yes	304	175.111	odd	10	inner
525.2.bb.a.461.58	yes	304	25.11	even	5	inner

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.990929 + 1.36390i) q^{2} +(-1.48109 + 0.897991i) q^{3} +(-0.260241 - 0.800939i) q^{4} +(-1.04257 + 1.97814i) q^{5} +(0.242884 - 2.90989i) q^{6} +(-0.769360 + 2.53142i) q^{7} +(-1.85644 - 0.603193i) q^{8} +(1.38723 - 2.66000i) q^{9} +O(q^{10})\)	\(q+(-0.990929 + 1.36390i) q^{2} +(-1.48109 + 0.897991i) q^{3} +(-0.260241 - 0.800939i) q^{4} +(-1.04257 + 1.97814i) q^{5} +(0.242884 - 2.90989i) q^{6} +(-0.769360 + 2.53142i) q^{7} +(-1.85644 - 0.603193i) q^{8} +(1.38723 - 2.66000i) q^{9} +(-1.66486 - 3.38216i) q^{10} +(-2.06540 + 2.84279i) q^{11} +(1.10467 + 0.952565i) q^{12} +(-0.245541 - 0.337958i) q^{13} +(-2.69021 - 3.55779i) q^{14} +(-0.232211 - 3.86602i) q^{15} +(4.02493 - 2.92428i) q^{16} +(-1.70453 + 5.24599i) q^{17} +(2.25333 + 4.52791i) q^{18} +(-1.12360 - 0.365079i) q^{19} +(1.85569 + 0.320245i) q^{20} +(-1.13370 - 4.44013i) q^{21} +(-1.83060 - 5.63400i) q^{22} +(0.0709236 - 0.0976180i) q^{23} +(3.29120 - 0.773682i) q^{24} +(-2.82608 - 4.12472i) q^{25} +0.704253 q^{26} +(0.334056 + 5.18540i) q^{27} +(2.22773 - 0.0425682i) q^{28} +(4.12563 - 1.34050i) q^{29} +(5.50295 + 3.51424i) q^{30} +(5.87405 + 1.90859i) q^{31} +4.48340i q^{32} +(0.506245 - 6.06512i) q^{33} +(-5.46593 - 7.52321i) q^{34} +(-4.20539 - 4.16109i) q^{35} +(-2.49151 - 0.418842i) q^{36} +(2.02615 - 1.47208i) q^{37} +(1.61134 - 1.17070i) q^{38} +(0.667149 + 0.280051i) q^{39} +(3.12867 - 3.04342i) q^{40} +(-2.10494 + 1.52933i) q^{41} +(7.17930 + 2.85360i) q^{42} +2.72678 q^{43} +(2.81440 + 0.914454i) q^{44} +(3.81557 + 5.51738i) q^{45} +(0.0628606 + 0.193465i) q^{46} +(-1.23977 - 3.81561i) q^{47} +(-3.33528 + 7.94546i) q^{48} +(-5.81617 - 3.89515i) q^{49} +(8.42613 + 0.232821i) q^{50} +(-2.18630 - 9.30041i) q^{51} +(-0.206784 + 0.284614i) q^{52} +(10.3120 - 3.35057i) q^{53} +(-7.40338 - 4.68275i) q^{54} +(-3.47009 - 7.04948i) q^{55} +(2.95520 - 4.23535i) q^{56} +(1.99198 - 0.468267i) q^{57} +(-2.25991 + 6.95527i) q^{58} +(-6.37221 + 4.62968i) q^{59} +(-3.03601 + 1.19208i) q^{60} +(8.51535 - 11.7204i) q^{61} +(-8.42390 + 6.12032i) q^{62} +(5.66630 + 5.55815i) q^{63} +(1.93496 + 1.40583i) q^{64} +(0.924522 - 0.133368i) q^{65} +(7.77055 + 6.70057i) q^{66} +(-3.14330 + 9.67410i) q^{67} +4.64531 q^{68} +(-0.0173839 + 0.208269i) q^{69} +(9.84255 - 1.61237i) q^{70} +(-3.22622 + 1.04826i) q^{71} +(-4.17979 + 4.10136i) q^{72} +(-6.05823 + 8.33844i) q^{73} +4.22218i q^{74} +(7.88962 + 3.57126i) q^{75} +0.994942i q^{76} +(-5.60724 - 7.41553i) q^{77} +(-1.04306 + 0.632413i) q^{78} +(3.56443 + 10.9702i) q^{79} +(1.58835 + 11.0107i) q^{80} +(-5.15121 - 7.38004i) q^{81} -4.38638i q^{82} +(3.68232 - 11.3330i) q^{83} +(-3.26123 + 2.06353i) q^{84} +(-8.60022 - 8.84113i) q^{85} +(-2.70205 + 3.71905i) q^{86} +(-4.90665 + 5.69017i) q^{87} +(5.54904 - 4.03161i) q^{88} +(-13.3111 - 9.67105i) q^{89} +(-11.3061 - 0.263284i) q^{90} +(1.04442 - 0.361555i) q^{91} +(-0.0966433 - 0.0314013i) q^{92} +(-10.4139 + 2.44805i) q^{93} +(6.43262 + 2.09008i) q^{94} +(1.89361 - 1.84201i) q^{95} +(-4.02605 - 6.64030i) q^{96} +(-2.83435 + 0.920938i) q^{97} +(11.0760 - 4.07284i) q^{98} +(4.69663 + 9.43756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9}+O(q^{10}) \) 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9	\( 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9} + 8 q^{15} - 92 q^{16} - 16 q^{18} + 12 q^{21} - 48 q^{22} - 32 q^{25} - 36 q^{28} - 14 q^{30} - 8 q^{36} - 4 q^{37} - 26 q^{39} - 11 q^{42} - 20 q^{49} + 20 q^{51} - 168 q^{57} + 32 q^{58} + 76 q^{60} + 29 q^{63} + 68 q^{64} - 44 q^{67} + 30 q^{70} - 114 q^{72} - 124 q^{78} - 68 q^{79} - 2 q^{81} + 102 q^{84} + 72 q^{85} - 156 q^{88} + 70 q^{91} - 32 q^{93} - 36 q^{99}+O(q^{100}) \) 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9 + 8 * q^15 - 92 * q^16 - 16 * q^18 + 12 * q^21 - 48 * q^22 - 32 * q^25 - 36 * q^28 - 14 * q^30 - 8 * q^36 - 4 * q^37 - 26 * q^39 - 11 * q^42 - 20 * q^49 + 20 * q^51 - 168 * q^57 + 32 * q^58 + 76 * q^60 + 29 * q^63 + 68 * q^64 - 44 * q^67 + 30 * q^70 - 114 * q^72 - 124 * q^78 - 68 * q^79 - 2 * q^81 + 102 * q^84 + 72 * q^85 - 156 * q^88 + 70 * q^91 - 32 * q^93 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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