LMFDB - Embedded newform 512.2.o.a.157.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(5,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(128))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("512.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.o (of order $128$, degree $64$, 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$4032$
Relative dimension:	$63$ over $\Q(\zeta_{128})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{128}]$

Embedding invariants

Embedding label			157.21
Character	$\chi$	$=$	512.157
Dual form			512.2.o.a.437.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.813297 + 1.15696i) q^{2} +(2.77078 - 1.06881i) q^{3} +(-0.677096 - 1.88190i) q^{4} +(2.43553 - 3.12085i) q^{5} +(-1.01690 + 4.07493i) q^{6} +(-0.0546682 + 0.152787i) q^{7} +(2.72795 + 0.747171i) q^{8} +(4.31203 - 3.90820i) q^{9} +O(q^{10})$	\(q+(-0.813297 + 1.15696i) q^{2} +(2.77078 - 1.06881i) q^{3} +(-0.677096 - 1.88190i) q^{4} +(2.43553 - 3.12085i) q^{5} +(-1.01690 + 4.07493i) q^{6} +(-0.0546682 + 0.152787i) q^{7} +(2.72795 + 0.747171i) q^{8} +(4.31203 - 3.90820i) q^{9} +(1.62987 + 5.35598i) q^{10} +(0.865624 + 3.85480i) q^{11} +(-3.88748 - 4.49064i) q^{12} +(-3.86101 + 1.06849i) q^{13} +(-0.132307 - 0.187510i) q^{14} +(3.41275 - 11.2503i) q^{15} +(-3.08308 + 2.54845i) q^{16} +(-4.28239 + 1.29905i) q^{17} +(1.01465 + 8.16736i) q^{18} +(1.72161 + 3.42025i) q^{19} +(-7.52221 - 2.47031i) q^{20} +(0.0118268 + 0.481771i) q^{21} +(-5.16384 - 2.13361i) q^{22} +(4.90652 - 0.727814i) q^{23} +(8.35715 - 0.845414i) q^{24} +(-2.59297 - 10.3517i) q^{25} +(1.90396 - 5.33602i) q^{26} +(3.76485 - 7.47947i) q^{27} +(0.324546 - 0.000571809i) q^{28} +(-0.640296 - 3.69011i) q^{29} +(10.2406 + 13.0982i) q^{30} +(-0.986656 + 1.47663i) q^{31} +(-0.440989 - 5.63964i) q^{32} +(6.51850 + 9.75562i) q^{33} +(1.97991 - 6.01105i) q^{34} +(0.343680 + 0.542731i) q^{35} +(-10.2745 - 5.46858i) q^{36} +(-3.25314 + 2.80618i) q^{37} +(-5.35725 - 0.789851i) q^{38} +(-9.55602 + 7.08723i) q^{39} +(8.97584 - 6.69377i) q^{40} +(-2.26451 + 9.04044i) q^{41} +(-0.567007 - 0.378140i) q^{42} +(-4.89316 - 11.0388i) q^{43} +(6.66823 - 4.23909i) q^{44} +(-1.69479 - 22.9758i) q^{45} +(-3.14841 + 6.26856i) q^{46} +(-6.16130 - 7.50756i) q^{47} +(-5.81874 + 10.3564i) q^{48} +(5.39072 + 4.42405i) q^{49} +(14.0853 + 5.41907i) q^{50} +(-10.4771 + 8.17644i) q^{51} +(4.62506 + 6.54256i) q^{52} +(-0.0866272 + 0.499245i) q^{53} +(5.59148 + 10.4388i) q^{54} +(14.1385 + 6.68701i) q^{55} +(-0.263291 + 0.375951i) q^{56} +(8.42579 + 7.63669i) q^{57} +(4.79005 + 2.26036i) q^{58} +(-2.03885 + 7.36745i) q^{59} +(-23.4827 + 1.19511i) q^{60} +(4.10943 + 0.100881i) q^{61} +(-0.905958 - 2.34246i) q^{62} +(0.361393 + 0.872479i) q^{63} +(6.88347 + 4.07650i) q^{64} +(-6.06905 + 14.6520i) q^{65} +(-16.5883 - 0.392598i) q^{66} +(-2.19338 + 2.08827i) q^{67} +(5.34427 + 7.17944i) q^{68} +(12.8170 - 7.26075i) q^{69} +(-0.907430 - 0.0437779i) q^{70} +(3.42338 - 0.168180i) q^{71} +(14.6831 - 7.43956i) q^{72} +(3.75418 + 10.4922i) q^{73} +(-0.600856 - 6.04599i) q^{74} +(-18.2486 - 25.9110i) q^{75} +(5.27086 - 5.55572i) q^{76} +(-0.636287 - 0.0784785i) q^{77} +(-0.427732 - 16.8199i) q^{78} +(6.39581 - 0.629932i) q^{79} +(0.444387 + 15.8287i) q^{80} +(0.726196 - 7.37319i) q^{81} +(-8.61767 - 9.97250i) q^{82} +(-3.20299 - 2.76291i) q^{83} +(0.898636 - 0.348462i) q^{84} +(-6.37578 + 16.5286i) q^{85} +(16.7510 + 3.31664i) q^{86} +(-5.71815 - 9.54015i) q^{87} +(-0.518810 + 11.1625i) q^{88} +(-17.2844 - 2.56389i) q^{89} +(27.9603 + 16.7253i) q^{90} +(0.0478234 - 0.648327i) q^{91} +(-4.69186 - 8.74077i) q^{92} +(-1.15557 + 5.14598i) q^{93} +(13.6969 - 1.02248i) q^{94} +(14.8671 + 2.95725i) q^{95} +(-7.24958 - 15.1549i) q^{96} +(13.6465 - 2.71445i) q^{97} +(-9.50268 + 2.63876i) q^{98} +(18.7979 + 13.2390i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) $ 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{91}{128}\right)$	$1$

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 $

$2$	−0.813297	+	1.15696i	−0.575088	+	0.818092i
$2$	−0.813297	+	1.15696i	−0.575088	+	0.818092i
$3$	2.77078	−	1.06881i	1.59971	−	0.617077i	0.614577	−	0.788857i	$-0.289327\pi$
$3$	2.77078	−	1.06881i	1.59971	−	0.617077i	0.985135	+	0.171780i	$0.0549517\pi$
$4$	−0.677096	−	1.88190i	−0.338548	−	0.940949i
$5$	2.43553	−	3.12085i	1.08920	−	1.39569i	0.177853	−	0.984057i	$-0.443085\pi$
$5$	2.43553	−	3.12085i	1.08920	−	1.39569i	0.911351	−	0.411629i	$-0.135040\pi$
$6$	−1.01690	+	4.07493i	−0.415149	+	1.66358i
$7$	−0.0546682	+	0.152787i	−0.0206627	+	0.0577482i	−0.951433	−	0.307857i	$-0.900388\pi$
$7$	−0.0546682	+	0.152787i	−0.0206627	+	0.0577482i	0.930770	+	0.365606i	$0.119138\pi$
$8$	2.72795	+	0.747171i	0.964478	+	0.264165i
$9$	4.31203	−	3.90820i	1.43734	−	1.30273i
$10$	1.62987	+	5.35598i	0.515411	+	1.69371i
$11$	0.865624	+	3.85480i	0.260995	+	1.16227i	0.914258	+	0.405134i	$0.132775\pi$
$11$	0.865624	+	3.85480i	0.260995	+	1.16227i	−0.653262	+	0.757132i	$0.726600\pi$
$12$	−3.88748	−	4.49064i	−1.12222	−	1.29634i
$13$	−3.86101	+	1.06849i	−1.07085	+	0.296345i	−0.757193	−	0.653191i	$-0.773430\pi$
$13$	−3.86101	+	1.06849i	−1.07085	+	0.296345i	−0.313659	+	0.949536i	$0.601555\pi$
$14$	−0.132307	−	0.187510i	−0.0353605	−	0.0501143i
$15$	3.41275	−	11.2503i	0.881167	−	2.90482i
$16$	−3.08308	+	2.54845i	−0.770770	+	0.637113i
$17$	−4.28239	+	1.29905i	−1.03863	+	0.315066i	−0.763137	−	0.646237i	$-0.776342\pi$
$17$	−4.28239	+	1.29905i	−1.03863	+	0.315066i	−0.275495	+	0.961302i	$0.588842\pi$
$18$	1.01465	+	8.16736i	0.239156	+	1.92507i
$19$	1.72161	+	3.42025i	0.394964	+	0.784658i	0.999933	−	0.0115908i	$-0.00368955\pi$
$19$	1.72161	+	3.42025i	0.394964	+	0.784658i	−0.604969	+	0.796249i	$0.706815\pi$
$20$	−7.52221	−	2.47031i	−1.68202	−	0.552379i
$21$	0.0118268	+	0.481771i	0.00258082	+	0.105131i
$22$	−5.16384	−	2.13361i	−1.10094	−	0.454886i
$23$	4.90652	−	0.727814i	1.02308	−	0.151760i	0.385953	−	0.922518i	$-0.373873\pi$
$23$	4.90652	−	0.727814i	1.02308	−	0.151760i	0.637127	+	0.770759i	$0.280123\pi$
$24$	8.35715	−	0.845414i	1.70590	−	0.172569i
$25$	−2.59297	−	10.3517i	−0.518594	−	2.07034i
$26$	1.90396	−	5.33602i	0.373397	−	1.04648i
$27$	3.76485	−	7.47947i	0.724546	−	1.43943i
$28$	0.324546		0.000571809i	0.0613335		0.000108062i
$29$	−0.640296	−	3.69011i	−0.118900	−	0.685237i	−0.983238	−	0.182326i	$-0.941637\pi$
$29$	−0.640296	−	3.69011i	−0.118900	−	0.685237i	0.864338	−	0.502911i	$-0.167738\pi$
$30$	10.2406	+	13.0982i	1.86966	+	2.39140i
$31$	−0.986656	+	1.47663i	−0.177209	+	0.265211i	−0.909432	−	0.415854i	$-0.863483\pi$
$31$	−0.986656	+	1.47663i	−0.177209	+	0.265211i	0.732223	+	0.681065i	$0.238483\pi$
$32$	−0.440989	−	5.63964i	−0.0779566	−	0.996957i
$33$	6.51850	+	9.75562i	1.13473	+	1.69824i
$34$	1.97991	−	6.01105i	0.339552	−	1.03089i
$35$	0.343680	+	0.542731i	0.0580926	+	0.0917382i
$36$	−10.2745	−	5.46858i	−1.71242	−	0.911430i
$37$	−3.25314	+	2.80618i	−0.534812	+	0.461332i	−0.878494	−	0.477754i	$-0.841451\pi$
$37$	−3.25314	+	2.80618i	−0.534812	+	0.461332i	0.343681	+	0.939086i	$0.388326\pi$
$38$	−5.35725	−	0.789851i	−0.869061	−	0.128131i
$39$	−9.55602	+	7.08723i	−1.53019	+	1.13486i
$40$	8.97584	−	6.69377i	1.41920	−	1.05838i
$41$	−2.26451	+	9.04044i	−0.353657	+	1.41188i	0.488461	+	0.872586i	$0.337559\pi$
$41$	−2.26451	+	9.04044i	−0.353657	+	1.41188i	−0.842118	+	0.539293i	$0.818691\pi$
$42$	−0.567007	−	0.378140i	−0.0874910	−	0.0583482i
$43$	−4.89316	−	11.0388i	−0.746200	−	1.68340i	−0.729919	−	0.683534i	$-0.760442\pi$
$43$	−4.89316	−	11.0388i	−0.746200	−	1.68340i	−0.0162813	−	0.999867i	$-0.505183\pi$
$44$	6.66823	−	4.23909i	1.00527	−	0.639066i
$45$	−1.69479	−	22.9758i	−0.252645	−	3.42502i
$46$	−3.14841	+	6.26856i	−0.464208	+	0.924249i
$47$	−6.16130	−	7.50756i	−0.898718	−	1.09509i	−0.995014	−	0.0997378i	$-0.968200\pi$
$47$	−6.16130	−	7.50756i	−0.898718	−	1.09509i	0.0962962	−	0.995353i	$-0.469300\pi$
$48$	−5.81874	+	10.3564i	−0.839863	+	1.49482i
$49$	5.39072	+	4.42405i	0.770103	+	0.632007i
$50$	14.0853	+	5.41907i	1.99197	+	0.766372i
$51$	−10.4771	+	8.17644i	−1.46709	+	1.14493i
$52$	4.62506	+	6.54256i	0.641380	+	0.907290i
$53$	−0.0866272	+	0.499245i	−0.0118992	+	0.0685765i	−0.990630	−	0.136570i	$-0.956392\pi$
$53$	−0.0866272	+	0.499245i	−0.0118992	+	0.0685765i	0.978731	+	0.205147i	$0.0657671\pi$
$54$	5.59148	+	10.4388i	0.760904	+	1.42054i
$55$	14.1385	+	6.68701i	1.90644	+	0.901677i
$56$	−0.263291	+	0.375951i	−0.0351837	+	0.0502385i
$57$	8.42579	+	7.63669i	1.11602	+	1.01150i
$58$	4.79005	+	2.26036i	0.628965	+	0.296800i
$59$	−2.03885	+	7.36745i	−0.265435	+	0.959160i	0.703265	+	0.710928i	$0.251725\pi$
$59$	−2.03885	+	7.36745i	−0.265435	+	0.959160i	−0.968700	+	0.248233i	$0.920150\pi$
$60$	−23.4827	+	1.19511i	−3.03160	+	0.154288i
$61$	4.10943	+	0.100881i	0.526159	+	0.0129165i	0.286756	−	0.958004i	$-0.407423\pi$
$61$	4.10943	+	0.100881i	0.526159	+	0.0129165i	0.239403	+	0.970920i	$0.423048\pi$
$62$	−0.905958	−	2.34246i	−0.115057	−	0.297493i
$63$	0.361393	+	0.872479i	0.0455312	+	0.109922i
$64$	6.88347	+	4.07650i	0.860434	+	0.509562i
$65$	−6.06905	+	14.6520i	−0.752772	+	1.81735i
$66$	−16.5883	−	0.392598i	−2.04188	−	0.0483255i
$67$	−2.19338	+	2.08827i	−0.267964	+	0.255123i	−0.811621	−	0.584185i	$-0.801414\pi$
$67$	−2.19338	+	2.08827i	−0.267964	+	0.255123i	0.543657	+	0.839308i	$0.317039\pi$
$68$	5.34427	+	7.17944i	0.648088	+	0.870635i
$69$	12.8170	−	7.26075i	1.54299	−	0.874091i
$70$	−0.907430	−	0.0437779i	−0.108459	−	0.00523246i
$71$	3.42338	−	0.168180i	0.406280	−	0.0199593i	0.155098	−	0.987899i	$-0.450431\pi$
$71$	3.42338	−	0.168180i	0.406280	−	0.0199593i	0.251182	+	0.967940i	$0.419181\pi$
$72$	14.6831	−	7.43956i	1.73042	−	0.876761i
$73$	3.75418	+	10.4922i	0.439393	+	1.22802i	0.933487	+	0.358612i	$0.116750\pi$
$73$	3.75418	+	10.4922i	0.439393	+	1.22802i	−0.494094	+	0.869409i	$0.664500\pi$
$74$	−0.600856	−	6.04599i	−0.0698481	−	0.702832i
$75$	−18.2486	−	25.9110i	−2.10716	−	2.99194i
$76$	5.27086	−	5.55572i	0.604609	−	0.637285i
$77$	−0.636287	−	0.0784785i	−0.0725116	−	0.00894346i
$78$	−0.427732	−	16.8199i	−0.0484311	−	1.90448i
$79$	6.39581	−	0.629932i	0.719585	−	0.0708729i	0.268405	−	0.963306i	$-0.413503\pi$
$79$	6.39581	−	0.629932i	0.719585	−	0.0708729i	0.451180	+	0.892433i	$0.351003\pi$
$80$	0.444387	+	15.8287i	0.0496840	+	1.76970i
$81$	0.726196	−	7.37319i	0.0806885	−	0.819244i
$82$	−8.61767	−	9.97250i	−0.951663	−	1.10128i
$83$	−3.20299	−	2.76291i	−0.351573	−	0.303269i	0.459541	−	0.888156i	$-0.348014\pi$
$83$	−3.20299	−	2.76291i	−0.351573	−	0.303269i	−0.811115	+	0.584887i	$0.801139\pi$
$84$	0.898636	−	0.348462i	0.0980492	−	0.0380203i
$85$	−6.37578	+	16.5286i	−0.691550	+	1.79278i
$86$	16.7510	+	3.31664i	1.80631	+	0.357643i
$87$	−5.71815	−	9.54015i	−0.613050	−	1.02281i
$88$	−0.518810	+	11.1625i	−0.0553053	+	1.18992i
$89$	−17.2844	−	2.56389i	−1.83214	−	0.271772i	−0.860710	−	0.509096i	$-0.829980\pi$
$89$	−17.2844	−	2.56389i	−1.83214	−	0.271772i	−0.971431	+	0.237324i	$0.923730\pi$
$90$	27.9603	+	16.7253i	2.94728	+	1.76300i
$91$	0.0478234	−	0.648327i	0.00501326	−	0.0679631i
$92$	−4.69186	−	8.74077i	−0.489160	−	0.911288i
$93$	−1.15557	+	5.14598i	−0.119827	+	0.533613i
$94$	13.6969	−	1.02248i	1.41273	−	0.105460i
$95$	14.8671	+	2.95725i	1.52533	+	0.303408i
$96$	−7.24958	−	15.1549i	−0.739907	−	1.54674i
$97$	13.6465	−	2.71445i	1.38559	−	0.275611i	0.554702	−	0.832049i	$-0.312832\pi$
$97$	13.6465	−	2.71445i	1.38559	−	0.275611i	0.830889	+	0.556438i	$0.187832\pi$
$98$	−9.50268	+	2.63876i	−0.959916	+	0.266555i
$99$	18.7979	+	13.2390i	1.88926	+	1.33057i
$100$	−17.7252	+	11.8888i	−1.77252	+	1.18888i
$101$	−3.30748	+	1.09265i	−0.329107	+	0.108722i	−0.473489	−	0.880800i	$-0.657006\pi$
$101$	−3.30748	+	1.09265i	−0.329107	+	0.108722i	0.144382	+	0.989522i	$0.453881\pi$
$102$	−0.938760	−	18.7715i	−0.0929511	−	1.85865i
$103$	−1.40780	−	0.843804i	−0.138715	−	0.0831425i	0.443062	−	0.896491i	$-0.353892\pi$
$103$	−1.40780	−	0.843804i	−0.138715	−	0.0831425i	−0.581777	+	0.813349i	$0.697642\pi$
$104$	−11.3310	+	0.0299457i	−1.11110	+	0.00293642i
$105$	1.53234	+	1.13646i	0.149541	+	0.110907i
$106$	−0.507151	−	0.506258i	−0.0492588	−	0.0491721i
$107$	12.0662	+	11.4880i	1.16648	+	1.11058i	0.992041	+	0.125916i	$0.0401870\pi$
$107$	12.0662	+	11.4880i	1.16648	+	1.11058i	0.174441	+	0.984668i	$0.444188\pi$
$108$	−16.6248	−	2.02074i	−1.59972	−	0.194446i
$109$	4.16288	−	12.6012i	0.398731	−	1.20698i	−0.533714	−	0.845665i	$-0.679204\pi$
$109$	4.16288	−	12.6012i	0.398731	−	1.20698i	0.932445	−	0.361312i	$-0.117671\pi$
$110$	−19.2354	+	10.9191i	−1.83402	+	1.04110i
$111$	−6.01447	+	11.2523i	−0.570868	+	1.06802i
$112$	−0.220825	−	0.610376i	−0.0208660	−	0.0576751i
$113$	−7.73402	+	4.13392i	−0.727555	+	0.388886i	−0.793204	−	0.608957i	$-0.791588\pi$
$113$	−7.73402	+	4.13392i	−0.727555	+	0.388886i	0.0656486	+	0.997843i	$0.479088\pi$
$114$	−15.6880	+	3.53737i	−1.46931	+	0.331305i
$115$	9.67860	−	17.0851i	0.902535	−	1.59320i
$116$	−6.51088	+	3.70353i	−0.604520	+	0.343865i
$117$	−12.4730	+	19.6970i	−1.15313	+	1.82098i
$118$	−6.86563	−	8.35078i	−0.632032	−	0.768752i
$119$	0.0356323	−	0.725313i	0.00326641	−	0.0664893i
$120$	17.7157	−	28.1405i	1.61722	−	2.56886i
$121$	−4.16628	+	1.97051i	−0.378753	+	0.179137i
$122$	−3.45890	+	4.67239i	−0.313154	+	0.423018i
$123$	3.38803	+	27.4694i	0.305488	+	2.47683i
$124$	3.44694	+	0.856962i	0.309544	+	0.0769574i
$125$	−20.5259	−	9.09850i	−1.83589	−	0.813794i
$126$	−1.30334	−	0.291469i	−0.116111	−	0.0259661i
$127$	5.52155	−	5.52155i	0.489959	−	0.489959i	−0.418334	−	0.908293i	$-0.637386\pi$
$127$	5.52155	−	5.52155i	0.489959	−	0.489959i	0.908293	+	0.418334i	$0.137386\pi$
$128$	−10.3146	+	4.64848i	−0.911693	+	0.410871i
$129$	−25.3563	−	25.3563i	−2.23249	−	2.23249i
$130$	−12.0158	−	18.9380i	−1.05385	−	1.66097i
$131$	5.77787	−	13.0347i	0.504815	−	1.13884i	−0.462811	−	0.886457i	$-0.653159\pi$
$131$	5.77787	−	13.0347i	0.504815	−	1.13884i	0.967626	−	0.252387i	$-0.0812158\pi$
$132$	13.9454	−	18.8726i	1.21379	−	1.64265i
$133$	−0.616688	+	0.0760612i	−0.0534736	+	0.00659534i
$134$	−0.632169	−	4.23603i	−0.0546111	−	0.365937i
$135$	−14.1729	−	29.9660i	−1.21981	−	2.57907i
$136$	−12.6528	+	0.344070i	−1.08497	+	0.0295037i
$137$	0.378031	+	0.0185715i	0.0322974	+	0.00158667i	0.0652099	−	0.997872i	$-0.479228\pi$
$137$	0.378031	+	0.0185715i	0.0322974	+	0.00158667i	−0.0329126	+	0.999458i	$0.510478\pi$
$138$	−2.02367	+	20.7339i	−0.172266	+	1.76498i
$139$	−4.97458	−	3.15012i	−0.421938	−	0.267189i	0.307080	−	0.951684i	$-0.400648\pi$
$139$	−4.97458	−	3.15012i	−0.421938	−	0.267189i	−0.729018	+	0.684494i	$0.760023\pi$
$140$	0.788659	−	1.01425i	0.0666538	−	0.0857200i
$141$	−25.0958	−	14.2166i	−2.11345	−	1.19725i
$142$	−2.58964	+	4.09748i	−0.217318	+	0.343853i
$143$	−7.46098	−	13.9585i	−0.623919	−	1.16727i
$144$	−3.33449	+	23.0383i	−0.277874	+	1.91986i
$145$	−13.0758	−	6.98914i	−1.08588	−	0.580416i
$146$	−15.1923	−	4.18987i	−1.25732	−	0.346756i
$147$	19.6650	+	6.49643i	1.62194	+	0.535816i
$148$	7.48362	+	4.22202i	0.615150	+	0.347048i
$149$	−14.5596	+	15.2924i	−1.19277	+	1.25280i	−0.232851	+	0.972512i	$0.574805\pi$
$149$	−14.5596	+	15.2924i	−1.19277	+	1.25280i	−0.959916	+	0.280289i	$0.909570\pi$
$150$	44.8194	−	0.0394830i	3.65949	−	0.00322377i
$151$	−0.730524	+	0.984998i	−0.0594492	+	0.0801580i	−0.831932	−	0.554878i	$-0.812765\pi$
$151$	−0.730524	+	0.984998i	−0.0594492	+	0.0801580i	0.772482	+	0.635036i	$0.219015\pi$
$152$	2.14096	+	10.6166i	0.173655	+	0.861121i
$153$	−13.3889	+	22.3380i	−1.08243	+	1.80592i
$154$	0.608287	−	0.672330i	0.0490171	−	0.0541779i
$155$	2.20532	+	6.67560i	0.177136	+	0.536197i
$156$	19.8078	+	13.1847i	1.58589	+	1.05562i
$157$	12.2272	−	17.3614i	0.975840	−	1.38559i	0.0537747	−	0.998553i	$-0.482875\pi$
$157$	12.2272	−	17.3614i	0.975840	−	1.38559i	0.922066	−	0.387034i	$-0.126500\pi$
$158$	−4.47289	+	7.91200i	−0.355844	+	0.629445i
$159$	0.293572	+	1.47589i	0.0232818	+	0.117045i
$160$	−18.6745	−	12.3593i	−1.47635	−	0.977087i
$161$	−0.157030	+	0.789443i	−0.0123757	+	0.0622168i
$162$	7.93985	+	6.83677i	0.623814	+	0.537148i
$163$	2.26105	+	0.507735i	0.177099	+	0.0397689i	0.306747	−	0.951791i	$-0.400760\pi$
$163$	2.26105	+	0.507735i	0.177099	+	0.0397689i	−0.129648	+	0.991560i	$0.541385\pi$
$164$	18.5465	−	1.85967i	1.44824	−	0.145216i
$165$	46.3219	+	3.41691i	3.60615	+	0.266006i
$166$	5.80155	−	1.45865i	0.450288	−	0.113213i
$167$	−0.210775	+	1.42093i	−0.0163102	+	0.109955i	−0.995803	−	0.0915264i	$-0.970825\pi$
$167$	−0.210775	+	1.42093i	−0.0163102	+	0.109955i	0.979492	+	0.201481i	$0.0645754\pi$
$168$	−0.327702	+	1.32309i	−0.0252828	+	0.102078i
$169$	2.61528	−	1.56754i	0.201175	−	0.120580i
$170$	−13.9374	−	20.8191i	−1.06895	−	1.59675i
$171$	20.7906	+	8.01983i	1.58990	+	0.613292i
$172$	−17.4608	+	16.6828i	−1.33137	+	1.27205i
$173$	−2.68108	+	3.10812i	−0.203839	+	0.236306i	−0.849853	−	0.527019i	$-0.823310\pi$
$173$	−2.68108	+	3.10812i	−0.203839	+	0.236306i	0.646015	+	0.763325i	$0.276435\pi$
$174$	15.6881	+	1.14333i	1.18931	+	0.0866755i
$175$	1.72337	+	0.169737i	0.130274	+	0.0128309i
$176$	−12.4926	−	9.67865i	−0.941662	−	0.729556i
$177$	2.22519	+	22.5927i	0.167256	+	1.69817i
$178$	17.0236	−	17.9121i	1.27598	−	1.34257i
$179$	1.11116	−	9.00908i	0.0830523	−	0.673370i	−0.892101	−	0.451837i	$-0.850769\pi$
$179$	1.11116	−	9.00908i	0.0830523	−	0.673370i	0.975153	−	0.221533i	$-0.0711061\pi$
$180$	−42.0905	+	18.7462i	−3.13724	+	1.39726i
$181$	−6.23081	+	4.38823i	−0.463132	+	0.326174i	−0.783796	−	0.621019i	$-0.786719\pi$
$181$	−6.23081	+	4.38823i	−0.463132	+	0.326174i	0.320664	+	0.947193i	$0.396094\pi$
$182$	0.711191	+	0.582612i	0.0527170	+	0.0431861i
$183$	11.4942	−	4.11268i	0.849673	−	0.304018i
$184$	13.9286	+	1.68057i	1.02683	+	0.123893i
$185$	0.834522	+	16.9871i	0.0613553	+	1.24892i
$186$	−5.01386	−	5.52215i	−0.367634	−	0.404904i
$187$	−8.71451	−	15.3833i	−0.637268	−	1.12494i
$188$	−9.95668	+	16.6783i	−0.726165	+	1.21639i
$189$	0.936952	+	0.984112i	0.0681532	+	0.0715836i
$190$	−15.5128	+	14.7955i	−1.12542	+	1.07338i
$191$	−14.0715	−	5.82860i	−1.01818	−	0.421743i	−0.189746	−	0.981833i	$-0.560766\pi$
$191$	−14.0715	−	5.82860i	−1.01818	−	0.421743i	−0.828431	+	0.560091i	$0.810766\pi$
$192$	23.4296	+	3.93797i	1.69089	+	0.284198i
$193$	9.63596	−	3.99134i	0.693611	−	0.287303i	−0.00789257	−	0.999969i	$-0.502512\pi$
$193$	9.63596	−	3.99134i	0.693611	−	0.287303i	0.701504	+	0.712666i	$0.252512\pi$
$194$	−7.95814	+	17.9960i	−0.571361	+	1.29204i
$195$	−1.15585	+	47.0841i	−0.0827721	+	3.37176i
$196$	4.67557	−	13.1403i	0.333969	−	0.938592i
$197$	−2.30855	−	0.638863i	−0.164478	−	0.0455171i	0.183501	−	0.983019i	$-0.441257\pi$
$197$	−2.30855	−	0.638863i	−0.164478	−	0.0455171i	−0.347979	+	0.937502i	$0.613132\pi$
$198$	−30.6052	+	10.9811i	−2.17502	+	0.780396i
$199$	−1.17415	+	1.29547i	−0.0832332	+	0.0918336i	−0.781144	−	0.624351i	$-0.785363\pi$
$199$	−1.17415	+	1.29547i	−0.0832332	+	0.0918336i	0.697910	+	0.716185i	$0.254113\pi$
$200$	0.660996	−	30.1764i	0.0467395	−	2.13379i
$201$	−3.84541	+	8.13045i	−0.271235	+	0.573477i
$202$	1.42582	−	4.71526i	0.100321	−	0.331765i
$203$	0.598807	+	0.103903i	0.0420280	+	0.00729255i
$204$	22.4813	+	14.1807i	1.57400	+	0.992846i
$205$	22.6985	+	29.0855i	1.58534	+	2.03142i
$206$	2.12121	−	0.942503i	0.147791	−	0.0656673i
$207$	18.3126	−	22.3140i	1.27282	−	1.55093i
$208$	9.18083	−	13.1338i	0.636576	−	0.910668i
$209$	−11.6941	+	9.59709i	−0.808897	+	0.663845i
$210$	−2.56108	+	0.848570i	−0.176731	+	0.0585569i
$211$	8.43622	−	0.622293i	0.580774	−	0.0428404i	0.220010	−	0.975498i	$-0.429391\pi$
$211$	8.43622	−	0.622293i	0.580774	−	0.0428404i	0.360764	+	0.932657i	$0.382516\pi$
$212$	0.998183	−	0.175013i	0.0685555	−	0.0120200i
$213$	9.30568	−	4.12492i	0.637615	−	0.282635i
$214$	−23.1045	+	4.61693i	−1.57939	+	0.315607i
$215$	−46.3679	−	11.6146i	−3.16226	−	0.792106i
$216$	15.8588	−	17.5907i	1.07905	−	1.19689i
$217$	−0.171673	−	0.231474i	−0.0116539	−	0.0157135i
$218$	11.1934	+	15.0648i	0.758112	+	1.02032i
$219$	21.6162	+	25.0592i	1.46069	+	1.69334i
$220$	3.01115	−	31.1350i	0.203012	−	2.09912i
$221$	15.1463	−	9.59132i	1.01885	−	0.645182i
$222$	−8.12685	−	16.1099i	−0.545439	−	1.08123i
$223$	6.42542	−	4.29333i	0.430278	−	0.287502i	−0.321512	−	0.946906i	$-0.604191\pi$
$223$	6.42542	−	4.29333i	0.430278	−	0.287502i	0.751790	+	0.659403i	$0.229191\pi$
$224$	0.885774	+	0.240932i	0.0591833	+	0.0160979i
$225$	−51.6375	−	34.5031i	−3.44250	−	2.30021i
$226$	1.50729	−	12.3100i	0.100263	−	0.818850i
$227$	12.0121	−	2.08429i	0.797268	−	0.138339i	0.242290	−	0.970204i	$-0.422102\pi$
$227$	12.0121	−	2.08429i	0.797268	−	0.138339i	0.554978	+	0.831865i	$0.312727\pi$
$228$	8.66640	−	21.0273i	0.573946	−	1.39256i
$229$	11.9332	+	6.00668i	0.788569	+	0.396932i	0.797722	−	0.603026i	$-0.206038\pi$
$229$	11.9332	+	6.00668i	0.788569	+	0.396932i	−0.00915263	+	0.999958i	$0.502913\pi$
$230$	11.8952	+	25.0930i	0.784344	+	1.65458i
$231$	−1.84689	+	0.462622i	−0.121517	+	0.0304383i
$232$	1.01045	−	10.5449i	0.0663392	−	0.692305i
$233$	−2.19353	−	14.7876i	−0.143703	−	0.968767i	−0.934315	−	0.356449i	$-0.883987\pi$
$233$	−2.19353	−	14.7876i	−0.143703	−	0.968767i	0.790612	−	0.612318i	$-0.209763\pi$
$234$	−12.6443	−	30.4501i	−0.826584	−	1.99059i
$235$	−38.4360	+	0.943551i	−2.50729	+	0.0615505i
$236$	15.2453	−	1.15157i	0.992384	−	0.0749608i
$237$	17.0481	−	8.58131i	1.10739	−	0.557416i
$238$	0.810175	+	0.631120i	0.0525159	+	0.0409094i
$239$	−0.983494	−	3.24215i	−0.0636169	−	0.209717i	0.919369	−	0.393395i	$-0.128700\pi$
$239$	−0.983494	−	3.24215i	−0.0636169	−	0.209717i	−0.982986	+	0.183678i	$0.941200\pi$
$240$	18.1491	+	43.3829i	1.17152	+	2.80035i
$241$	8.57122	+	2.60005i	0.552121	+	0.167484i	0.554004	−	0.832514i	$-0.313099\pi$
$241$	8.57122	+	2.60005i	0.552121	+	0.167484i	−0.00188298	+	0.999998i	$0.500599\pi$
$242$	1.10864	−	6.42281i	0.0712659	−	0.412874i
$243$	0.831606	+	3.00504i	0.0533475	+	0.192773i
$244$	−2.59263	−	7.80184i	−0.165976	−	0.499462i
$245$	26.9361	−	6.04870i	1.72088	−	0.386437i
$246$	−34.5364	−	18.4210i	−2.20196	−	1.17448i
$247$	−10.3016	−	11.3661i	−0.655477	−	0.723207i
$248$	−3.79485	+	3.29099i	−0.240973	+	0.208978i
$249$	−11.8278	−	4.23206i	−0.749557	−	0.268196i
$250$	27.2202	−	16.3478i	1.72156	−	1.03392i
$251$	−0.142160	−	0.110942i	−0.00897304	−	0.00700263i	0.610735	−	0.791835i	$-0.290874\pi$
$251$	−0.142160	−	0.110942i	−0.00897304	−	0.00700263i	−0.619708	+	0.784832i	$0.712749\pi$
$252$	1.39722	−	1.27086i	0.0880165	−	0.0800564i
$253$	7.05278	+	18.2836i	0.443404	+	1.14948i
$254$	1.89753	+	10.8789i	0.119062	+	0.682600i
$255$			52.6116i			3.29467i
$256$	3.01078	−	15.7142i	0.188173	−	0.982136i
$257$			9.65470i			0.602244i	0.953586	+	0.301122i	$0.0973611\pi$
$257$			9.65470i			0.602244i	−0.953586	+	0.301122i	$0.902639\pi$
$258$	49.9583	−	8.71392i	3.11027	−	0.542505i
$259$	−0.250905	−	0.650447i	−0.0155905	−	0.0404168i
$260$	31.6828	+	1.50053i	1.96489	+	0.0930588i
$261$	−17.1827	−	13.4095i	−1.06358	−	0.830027i
$262$	10.3814	+	17.2858i	0.641366	+	1.06792i
$263$	28.8202	+	10.3120i	1.77713	+	0.635868i	0.999978	+	0.00655760i	$0.00208736\pi$
$263$	28.8202	+	10.3120i	1.77713	+	0.635868i	0.777154	+	0.629311i	$0.216663\pi$
$264$	10.4931	+	31.4833i	0.645803	+	1.93766i
$265$	1.34708	+	1.48628i	0.0827507	+	0.0913013i
$266$	0.413551	−	0.775341i	0.0253564	−	0.0475392i
$267$	−50.6316	+	11.3697i	−3.09860	+	0.695814i
$268$	5.41504	+	2.71375i	0.330776	+	0.165769i
$269$	−0.831650	−	3.00520i	−0.0507066	−	0.183230i	0.934059	−	0.357120i	$-0.116241\pi$
$269$	−0.831650	−	3.00520i	−0.0507066	−	0.183230i	−0.984765	+	0.173890i	$0.944366\pi$
$270$	46.1962	+	7.97388i	2.81141	+	0.485275i
$271$	−8.25095	−	2.50290i	−0.501209	−	0.152040i	0.0295491	−	0.999563i	$-0.490593\pi$
$271$	−8.25095	−	2.50290i	−0.501209	−	0.152040i	−0.530758	+	0.847523i	$0.678093\pi$
$272$	9.89239	−	14.9185i	0.599814	−	0.904570i
$273$	−0.560429	−	1.84749i	−0.0339187	−	0.111815i
$274$	−0.328938	+	0.422261i	−0.0198719	+	0.0255097i
$275$	37.6592	−	18.9561i	2.27094	−	1.14309i
$276$	−22.3423	−	19.2041i	−1.34485	−	1.15595i
$277$	−29.7468	+	0.730243i	−1.78731	+	0.0438760i	−0.904656	−	0.426143i	$-0.859872\pi$
$277$	−29.7468	+	0.730243i	−1.78731	+	0.0438760i	−0.882656	+	0.470019i	$0.844247\pi$
$278$	7.69035	−	3.19339i	0.461237	−	0.191527i
$279$	1.51649	+	10.2233i	0.0907899	+	0.612056i
$280$	0.532032	+	1.73733i	0.0317950	+	0.103825i
$281$	−20.8383	+	5.21971i	−1.24311	+	0.311382i	−0.808100	−	0.589046i	$-0.799504\pi$
$281$	−20.8383	+	5.21971i	−1.24311	+	0.311382i	−0.435006	+	0.900427i	$0.643254\pi$
$282$	36.8583	−	17.4724i	2.19488	−	1.04047i
$283$	14.0429	+	7.06862i	0.834766	+	0.420186i	0.814889	−	0.579617i	$-0.196798\pi$
$283$	14.0429	+	7.06862i	0.834766	+	0.420186i	0.0198767	+	0.999802i	$0.493673\pi$
$284$	−2.63445	−	6.32857i	−0.156326	−	0.375532i
$285$	44.3543	−	7.69619i	2.62732	−	0.455883i
$286$	22.2174	+	2.72039i	1.31374	+	0.160860i
$287$	−1.25747	−	0.840214i	−0.0742261	−	0.0495963i
$288$	−23.9424	−	22.5948i	−1.41082	−	1.33141i
$289$	2.51636	−	1.68138i	0.148021	−	0.0989047i
$290$	18.7206	−	9.44383i	1.09931	−	0.554561i
$291$	34.9102	−	22.1067i	2.04647	−	1.29591i
$292$	17.2033	−	14.1692i	1.00675	−	0.829191i
$293$	−17.2648	−	20.0147i	−1.00862	−	1.16927i	−0.985523	−	0.169539i	$-0.945772\pi$
$293$	−17.2648	−	20.0147i	−1.00862	−	1.16927i	−0.0230979	−	0.999733i	$-0.507353\pi$
$294$	−23.5095	+	17.4680i	−1.37110	+	1.01875i
$295$	18.0270	+	24.3066i	1.04957	+	1.41519i
$296$	−10.9711	+	5.22447i	−0.637682	+	0.303666i
$297$	32.0908	+	8.03833i	1.86210	+	0.466431i
$298$	−5.85138	−	29.2820i	−0.338961	−	1.69626i
$299$	−18.1665	+	8.05265i	−1.05059	+	0.465697i
$300$	−36.4058	+	51.8862i	−2.10189	+	2.99565i
$301$	1.95409	−	0.144142i	0.112632	−	0.00830823i
$302$	−0.545467	−	1.64628i	−0.0313881	−	0.0947328i
$303$	−7.99649	+	6.56255i	−0.459387	+	0.377009i
$304$	−14.0242	−	6.15746i	−0.804342	−	0.353155i
$305$	10.3235	−	12.5792i	0.591122	−	0.720284i
$306$	−14.9549	−	33.6577i	−0.854917	−	1.92409i
$307$	13.1778	+	16.8858i	0.752099	+	0.963725i	0.999987	−	0.00506324i	$-0.00161169\pi$
$307$	13.1778	+	16.8858i	0.752099	+	0.963725i	−0.247889	+	0.968789i	$0.579737\pi$
$308$	0.283139	+	1.25057i	0.0161333	+	0.0712576i
$309$	−4.80258	−	0.833327i	−0.273209	−	0.0474063i
$310$	−9.51696	−	2.87779i	−0.540527	−	0.163447i
$311$	−9.32414	+	19.7142i	−0.528723	+	1.11789i	0.446114	+	0.894976i	$0.352808\pi$
$311$	−9.32414	+	19.7142i	−0.528723	+	1.11789i	−0.974838	+	0.222916i	$0.928442\pi$
$312$	−31.3638	+	12.1937i	−1.77562	+	0.690330i
$313$	2.49382	−	2.75150i	0.140959	−	0.155524i	−0.666380	−	0.745612i	$-0.732157\pi$
$313$	2.49382	−	2.75150i	0.140959	−	0.155524i	0.807339	+	0.590088i	$0.200907\pi$
$314$	10.1419	+	28.2663i	0.572343	+	1.59516i
$315$	3.60306	+	0.997101i	0.203009	+	0.0561803i
$316$	−5.51605	−	11.6097i	−0.310302	−	0.653099i
$317$	0.216453	−	8.81733i	0.0121572	−	0.495231i	−0.962469	−	0.271392i	$-0.912516\pi$
$317$	0.216453	−	8.81733i	0.0121572	−	0.495231i	0.974626	−	0.223839i	$-0.0718589\pi$
$318$	−1.94630	−	0.860684i	−0.109143	−	0.0482648i
$319$	13.6704	−	5.66246i	0.765395	−	0.317037i
$320$	29.4871	−	11.5538i	1.64838	−	0.645879i
$321$	45.7112	+	18.9342i	2.55135	+	1.05680i
$322$	−0.785639	−	0.823729i	−0.0437820	−	0.0459046i
$323$	−11.8157	−	12.4104i	−0.657441	−	0.690532i
$324$	−14.3673	+	3.62574i	−0.798184	+	0.201430i
$325$	21.0722	+	37.1976i	1.16887	+	2.06335i
$326$	−2.42633	+	2.20299i	−0.134382	+	0.122013i
$327$	−1.93386	−	39.3645i	−0.106942	−	2.17686i
$328$	−12.9322	+	22.9699i	−0.714063	+	1.26830i
$329$	1.48389	−	0.530944i	0.0818094	−	0.0292719i
$330$	−41.6266	+	50.8134i	−2.29147	+	2.79719i
$331$	21.0375	−	14.8163i	1.15633	−	0.814378i	0.171037	−	0.985265i	$-0.445288\pi$
$331$	21.0375	−	14.8163i	1.15633	−	0.814378i	0.985291	+	0.170887i	$0.0546632\pi$
$332$	−3.03079	+	7.89845i	−0.166336	+	0.433484i
$333$	−3.06054	+	24.8142i	−0.167717	+	1.35981i
$334$	−1.47253	−	1.39949i	−0.0805732	−	0.0765768i
$335$	1.17513	+	11.9313i	0.0642040	+	0.651874i
$336$	−1.26423	−	1.45520i	−0.0689696	−	0.0793876i
$337$	−24.0059	−	2.36437i	−1.30768	−	0.128796i	−0.579949	−	0.814653i	$-0.696927\pi$
$337$	−24.0059	−	2.36437i	−1.30768	−	0.128796i	−0.727736	+	0.685857i	$0.759427\pi$
$338$	−0.313425	+	4.30064i	−0.0170481	+	0.233924i
$339$	−17.0109	+	19.7204i	−0.923906	+	1.07106i
$340$	35.4221	+	0.807120i	1.92103	+	0.0437722i
$341$	−6.54620	−	2.52515i	−0.354497	−	0.136744i
$342$	−26.1875	+	17.5313i	−1.41606	+	0.947987i
$343$	−1.94495	+	1.16576i	−0.105017	+	0.0629449i
$344$	−5.10046	−	33.7694i	−0.274998	−	1.82072i
$345$	8.55658	−	57.6838i	0.460671	−	3.10559i
$346$	−1.41544	−	5.62971i	−0.0760946	−	0.302655i
$347$	−7.05922	−	0.520720i	−0.378959	−	0.0279537i	−0.117255	−	0.993102i	$-0.537409\pi$
$347$	−7.05922	−	0.520720i	−0.378959	−	0.0279537i	−0.261704	+	0.965148i	$0.584284\pi$
$348$	−14.0819	+	17.2206i	−0.754867	+	0.923120i
$349$	−32.1828	−	7.22689i	−1.72271	−	0.386846i	−0.758431	−	0.651753i	$-0.774034\pi$
$349$	−32.1828	−	7.22689i	−1.72271	−	0.386846i	−0.964274	+	0.264907i	$0.914659\pi$
$350$	−1.59799	+	1.85581i	−0.0854160	+	0.0991974i
$351$	−6.54442	+	32.9010i	−0.349315	+	1.75613i
$352$	21.3579	−	6.58173i	1.13838	−	0.350807i
$353$	−3.96545	−	19.9357i	−0.211060	−	1.06107i	−0.930438	−	0.366450i	$-0.880573\pi$
$353$	−3.96545	−	19.9357i	−0.211060	−	1.06107i	0.719378	−	0.694619i	$-0.244427\pi$
$354$	−27.9486	−	15.8002i	−1.48545	−	0.839769i
$355$	7.81289	−	11.0934i	0.414665	−	0.588779i
$356$	6.87820	+	34.2634i	0.364544	+	1.81596i
$357$	−0.676491	−	2.04777i	−0.0358037	−	0.108379i
$358$	9.51940	+	8.61262i	0.503116	+	0.455191i
$359$	−12.6551	+	21.1137i	−0.667910	+	1.11434i	0.318165	+	0.948035i	$0.396933\pi$
$359$	−12.6551	+	21.1137i	−0.667910	+	1.11434i	−0.986074	+	0.166304i	$0.946817\pi$
$360$	12.5435	−	63.9431i	0.661100	−	3.37010i
$361$	2.58414	−	3.48431i	0.136007	−	0.183385i
$362$	−0.00949446	−	10.7777i	−0.000499018	−	0.566463i
$363$	−9.43777	+	9.91280i	−0.495355	+	0.520287i
$364$	−1.25247	+	0.348981i	−0.0656470	+	0.0182916i
$365$	41.8881	+	13.8379i	2.19252	+	0.724311i
$366$	−4.58998	+	16.6431i	−0.239922	+	0.869948i
$367$	−32.0216	−	17.1159i	−1.67152	−	0.893444i	−0.986272	−	0.165131i	$-0.947195\pi$
$367$	−32.0216	−	17.1159i	−1.67152	−	0.893444i	−0.685244	−	0.728313i	$-0.740305\pi$
$368$	−13.2724	+	14.7479i	−0.691872	+	0.768790i
$369$	25.5672	+	47.8328i	1.33097	+	2.49008i
$370$	−20.3320	−	12.8500i	−1.05701	−	0.668042i
$371$	−0.0715426	−	0.0405284i	−0.00371431	−	0.00210413i
$372$	10.4666	−	1.30966i	0.542670	−	0.0679029i
$373$	−4.97848	−	3.15259i	−0.257776	−	0.163235i	0.399847	−	0.916582i	$-0.369063\pi$
$373$	−4.97848	−	3.15259i	−0.257776	−	0.163235i	−0.657623	+	0.753347i	$0.728438\pi$
$374$	24.8853	+	2.42885i	1.28679	+	0.125593i
$375$	−66.5973	−	3.27172i	−3.43907	−	0.168951i
$376$	−11.1983	−	25.0838i	−0.577509	−	1.29360i
$377$	6.41502	+	13.5634i	0.330391	+	0.698552i
$378$	−1.90059	+	0.283638i	−0.0977560	+	0.0145888i
$379$	9.07478	−	1.11927i	0.466140	−	0.0574929i	0.114082	−	0.993471i	$-0.463607\pi$
$379$	9.07478	−	1.11927i	0.466140	−	0.0574929i	0.352057	+	0.935978i	$0.385482\pi$
$380$	−4.50122	−	29.9807i	−0.230908	−	1.53798i
$381$	9.39754	−	21.2005i	0.481451	−	1.08613i
$382$	18.1877	−	11.5397i	0.930565	−	0.590423i
$383$	3.35586	+	3.35586i	0.171476	+	0.171476i	0.787628	−	0.616151i	$-0.211309\pi$
$383$	3.35586	+	3.35586i	0.171476	+	0.171476i	−0.616151	+	0.787628i	$0.711309\pi$
$384$	−23.6113	+	23.9043i	−1.20491	+	1.21986i
$385$	−1.79462	+	1.79462i	−0.0914623	+	0.0914623i
$386$	−3.21908	+	14.3945i	−0.163847	+	0.732662i
$387$	−64.2413	−	28.4762i	−3.26557	−	1.44753i
$388$	−14.3483	−	23.8433i	−0.728425	−	1.21046i
$389$	1.84464	+	14.9559i	0.0935268	+	0.758295i	0.963967	+	0.266021i	$0.0857092\pi$
$389$	1.84464	+	14.9559i	0.0935268	+	0.758295i	−0.870440	+	0.492274i	$0.836166\pi$
$390$	−53.5342	−	39.6306i	−2.71081	−	2.00677i
$391$	−20.0662	+	9.49059i	−1.01479	+	0.479960i
$392$	11.4001	+	16.0964i	0.575793	+	0.812990i
$393$	2.07766	−	42.2917i	0.104804	−	2.13333i
$394$	2.61668	−	2.15131i	0.131826	−	0.108381i
$395$	13.6113	−	21.4946i	0.684859	−	1.08151i
$396$	12.1864	−	44.3398i	0.612391	−	2.22816i
$397$	−2.35325	+	4.15407i	−0.118106	+	0.208487i	−0.922873	−	0.385105i	$-0.874165\pi$
$397$	−2.35325	+	4.15407i	−0.118106	+	0.208487i	0.804767	+	0.593591i	$0.202290\pi$
$398$	−0.543875	−	2.41204i	−0.0272620	−	0.120905i
$399$	−1.62741	+	0.869871i	−0.0814726	+	0.0435480i
$400$	34.3752	+	25.3071i	1.71876	+	1.26536i
$401$	7.55767	−	14.1394i	0.377412	−	0.706089i	−0.619468	−	0.785022i	$-0.712651\pi$
$401$	7.55767	−	14.1394i	0.377412	−	0.706089i	0.996880	+	0.0789336i	$0.0251515\pi$
$402$	−6.27911	−	11.0614i	−0.313173	−	0.551695i
$403$	2.23173	−	6.75553i	0.111170	−	0.336517i
$404$	4.29573	+	5.48452i	0.213721	+	0.272865i
$405$	−21.2420	−	20.2240i	−1.05552	−	1.00494i
$406$	−0.607219	+	0.608290i	−0.0301358	+	0.0301889i
$407$	−13.6332	−	10.1111i	−0.675774	−	0.501188i
$408$	−34.6904	+	14.4767i	−1.71743	+	0.716706i
$409$	15.3006	+	9.17085i	0.756568	+	0.453469i	0.839687	−	0.543070i	$-0.182738\pi$
$409$	15.3006	+	9.17085i	0.756568	+	0.453469i	−0.0831195	+	0.996540i	$0.526488\pi$
$410$	−52.1113	+	2.60608i	−2.57359	+	0.128705i
$411$	1.06729	−	0.352585i	0.0526456	−	0.0173918i
$412$	−0.634736	+	3.22068i	−0.0312712	+	0.158671i
$413$	−1.01419	−	0.714276i	−0.0499052	−	0.0351472i
$414$	10.9227	+	39.3348i	0.536823	+	1.93320i
$415$	−16.4236	+	3.26686i	−0.806204	+	0.160364i
$416$	7.72854	+	21.3035i	0.378923	+	1.04449i
$417$	−17.1503	−	3.41142i	−0.839856	−	0.167058i
$418$	−1.59265	−	21.3348i	−0.0778991	−	1.04352i
$419$	4.68123	−	20.8465i	0.228693	−	1.01842i	−0.717941	−	0.696104i	$-0.754915\pi$
$419$	4.68123	−	20.8465i	0.228693	−	1.01842i	0.946634	−	0.322312i	$-0.104460\pi$
$420$	1.10116	−	3.65320i	0.0537311	−	0.178258i
$421$	−0.276904	+	3.75389i	−0.0134955	+	0.182954i	0.986338	+	0.164731i	$0.0526757\pi$
$421$	−0.276904	+	3.75389i	−0.0134955	+	0.182954i	−0.999834	+	0.0182224i	$0.994199\pi$
$422$	−6.14119	+	10.2665i	−0.298948	+	0.499763i
$423$	−55.9088	−	8.29328i	−2.71838	−	0.403233i
$424$	−0.609336	+	1.29719i	−0.0295920	+	0.0629972i
$425$	24.5515	+	40.9617i	1.19092	+	1.98693i
$426$	−2.79592	+	14.1211i	−0.135463	+	0.684167i
$427$	−0.240069	+	0.622355i	−0.0116177	+	0.0301179i
$428$	13.4492	−	30.4858i	0.650092	−	1.47359i
$429$	−35.5918	−	30.7017i	−1.71839	−	1.48229i
$430$	51.1484	−	44.1996i	2.46659	−	2.13149i
$431$	−1.04513	+	10.6114i	−0.0503420	+	0.511131i	0.936639	+	0.350296i	$0.113919\pi$
$431$	−1.04513	+	10.6114i	−0.0503420	+	0.511131i	−0.986981	+	0.160836i	$0.948581\pi$
$432$	7.45375	+	32.6544i	0.358619	+	1.57108i
$433$	4.58747	−	0.451826i	0.220460	−	0.0217134i	0.0128158	−	0.999918i	$-0.495920\pi$
$433$	4.58747	−	0.451826i	0.220460	−	0.0217134i	0.207644	+	0.978204i	$0.433420\pi$
$434$	0.407426	−	0.0103609i	0.0195571	−	0.000497338i
$435$	−43.7001	−	5.38990i	−2.09526	−	0.258426i
$436$	−26.5329	+	0.698123i	−1.27069	+	0.0334340i
$437$	10.9364	+	15.5285i	0.523159	+	0.742829i
$438$	−46.5727	+	4.62844i	−2.22533	+	0.221156i
$439$	6.69461	+	18.7102i	0.319516	+	0.892988i	0.988702	+	0.149893i	$0.0478929\pi$
$439$	6.69461	+	18.7102i	0.319516	+	0.892988i	−0.669186	+	0.743095i	$0.733357\pi$
$440$	33.5728	+	28.8057i	1.60052	+	1.37326i
$441$	40.5350	−	1.99136i	1.93024	−	0.0948265i
$442$	−1.22174	+	25.3243i	−0.0581122	+	1.20455i
$443$	−8.09107	+	4.58353i	−0.384418	+	0.217770i	−0.672930	−	0.739706i	$-0.734965\pi$
$443$	−8.09107	+	4.58353i	−0.384418	+	0.217770i	0.288512	+	0.957476i	$0.406840\pi$
$444$	25.2480	+	3.69974i	1.19822	+	0.175582i
$445$	−50.0982	+	47.6975i	−2.37488	+	2.26108i
$446$	−0.258580	+	10.9257i	−0.0122441	+	0.517346i
$447$	−23.9968	+	57.9333i	−1.13501	+	2.74015i
$448$	−0.999145	+	0.828854i	−0.0472052	+	0.0391596i
$449$	−8.22495	−	19.8568i	−0.388159	−	0.937099i	−0.990330	−	0.138732i	$-0.955697\pi$
$449$	−8.22495	−	19.8568i	−0.388159	−	0.937099i	0.602171	−	0.798367i	$-0.294303\pi$
$450$	81.9152	−	31.6811i	3.86152	−	1.49346i
$451$	−36.8093	−	0.903617i	−1.73328	−	0.0425497i
$452$	13.0163	+	11.7556i	0.612235	+	0.552935i
$453$	−0.971350	+	3.51001i	−0.0456380	+	0.164914i
$454$	−7.35793	+	15.5926i	−0.345325	+	0.731795i
$455$	−1.90685	−	1.72827i	−0.0893947	−	0.0810226i
$456$	17.2793	+	27.1280i	0.809175	+	1.27039i
$457$	−28.6780	−	13.5637i	−1.34150	−	0.634482i	−0.384111	−	0.923287i	$-0.625492\pi$
$457$	−28.6780	−	13.5637i	−1.34150	−	0.634482i	−0.957388	+	0.288805i	$0.906742\pi$
$458$	−16.6547	+	8.92100i	−0.778223	+	0.416851i
$459$	−6.40636	+	36.9208i	−0.299023	+	1.72331i
$460$	−38.7058	−	6.64587i	−1.80467	−	0.309865i
$461$	18.8709	−	14.7270i	0.878907	−	0.685906i	−0.0713233	−	0.997453i	$-0.522722\pi$
$461$	18.8709	−	14.7270i	0.878907	−	0.685906i	0.950231	+	0.311547i	$0.100847\pi$
$462$	0.966838	−	2.51302i	0.0449814	−	0.116916i
$463$	10.8362	+	8.89301i	0.503599	+	0.413293i	0.851593	−	0.524204i	$-0.175637\pi$
$463$	10.8362	+	8.89301i	0.503599	+	0.413293i	−0.347994	+	0.937497i	$0.613137\pi$
$464$	11.3782	+	9.74516i	0.528218	+	0.452408i
$465$	13.2454	+	16.1396i	0.614241	+	0.748455i
$466$	18.8926	+	9.48888i	0.875182	+	0.439564i
$467$	−2.35424	−	31.9157i	−0.108941	−	1.47688i	−0.724764	−	0.688997i	$-0.758051\pi$
$467$	−2.35424	−	31.9157i	−0.108941	−	1.47688i	0.615823	−	0.787885i	$-0.288824\pi$
$468$	45.5130	+	10.1361i	2.10384	+	0.468541i
$469$	−0.199153	−	0.449283i	−0.00919605	−	0.0207460i
$470$	30.1683	−	45.2362i	1.39156	−	2.08659i
$471$	15.3231	−	61.1731i	0.706050	−	2.81871i
$472$	−11.0666	+	18.5747i	−0.509383	+	0.854970i
$473$	38.3167	−	28.4176i	1.76180	−	1.30664i
$474$	−3.93699	+	26.7031i	−0.180832	+	1.22651i
$475$	30.9413	−	26.6902i	1.41969	−	1.22463i
$476$	−1.38909	+	0.424050i	−0.0636689	+	0.0194363i
$477$	1.57761	+	2.49132i	0.0722337	+	0.114070i
$478$	4.55089	+	1.49897i	0.208153	+	0.0685612i
$479$	18.1793	+	27.2072i	0.830633	+	1.24313i	0.967583	+	0.252553i	$0.0812702\pi$
$479$	18.1793	+	27.2072i	0.830633	+	1.24313i	−0.136950	+	0.990578i	$0.543730\pi$
$480$	−64.9527	−	14.2854i	−2.96467	−	0.652036i
$481$	9.56204	−	14.3106i	0.435992	−	0.652508i
$482$	−9.97909	+	7.80191i	−0.454535	+	0.355367i
$483$	0.408668	+	2.35521i	0.0185950	+	0.107166i
$484$	6.52927	+	6.50630i	0.296785	+	0.295741i
$485$	24.7651	−	49.1998i	1.12452	−	2.23405i
$486$	−4.15304	−	1.48186i	−0.188386	−	0.0672183i
$487$	−3.81734	−	15.2397i	−0.172980	−	0.690575i	−0.992987	−	0.118222i	$-0.962281\pi$
$487$	−3.81734	−	15.2397i	−0.172980	−	0.690575i	0.820007	−	0.572353i	$-0.193969\pi$
$488$	11.1350	+	3.34565i	0.504056	+	0.151450i
$489$	6.80755	−	1.00980i	0.307848	−	0.0456649i
$490$	−14.9089	+	36.0832i	−0.673517	+	1.63007i
$491$	−0.391508	−	15.9483i	−0.0176685	−	0.719735i	−0.941515	−	0.336971i	$-0.890597\pi$
$491$	−0.391508	−	15.9483i	−0.0176685	−	0.719735i	0.923846	−	0.382763i	$-0.125028\pi$
$492$	49.4006	−	24.9754i	2.22715	−	1.12598i
$493$	7.53564	+	14.9707i	0.339388	+	0.674248i
$494$	21.5284	−	2.67453i	0.968607	−	0.120333i
$495$	87.0999	−	26.4215i	3.91485	−	1.18756i
$496$	−0.721195	−	7.06703i	−0.0323826	−	0.317319i
$497$	−0.161454	+	0.532243i	−0.00724221	+	0.0238744i
$498$	14.5158	−	10.2423i	0.650470	−	0.458970i
$499$	10.4480	−	2.89136i	0.467718	−	0.129435i	−0.0248826	−	0.999690i	$-0.507921\pi$
$499$	10.4480	−	2.89136i	0.467718	−	0.129435i	0.492601	+	0.870255i	$0.336046\pi$
$500$	−3.22444	+	44.7882i	−0.144202	+	2.00299i
$501$	0.934689	+	4.16236i	0.0417588	+	0.185960i
$502$	0.243974	−	0.0742434i	0.0108891	−	0.00331364i
$503$	11.7304	−	10.6319i	0.523034	−	0.474051i	−0.366822	−	0.930291i	$-0.619554\pi$
$503$	11.7304	−	10.6319i	0.523034	−	0.474051i	0.889857	+	0.456240i	$0.150804\pi$
$504$	0.333972	+	2.65011i	0.0148763	+	0.118045i
$505$	−4.64551	+	12.9833i	−0.206723	+	0.577751i
$506$	−26.8894	−	6.71027i	−1.19538	−	0.298308i
$507$	5.57098	−	7.13855i	0.247416	−	0.317034i
$508$	−14.1296	−	6.65238i	−0.626901	−	0.295151i
$509$	20.3305	−	7.84235i	0.901135	−	0.347606i	0.135422	−	0.990788i	$-0.456761\pi$
$509$	20.3305	−	7.84235i	0.901135	−	0.347606i	0.765713	+	0.643182i	$0.222386\pi$
$510$	−60.8693	−	42.7888i	−2.69534	−	1.89472i
$511$	−1.80831			−0.0799951
$512$	15.7320	+	16.2636i	0.695261	+	0.718757i
$513$	32.0632			1.41563
$514$	−11.1701	−	7.85214i	−0.492691	−	0.346343i
$515$	−6.06214	+	2.33842i	−0.267130	+	0.103043i
$516$	−30.5493	+	64.8865i	−1.34486	+	2.85647i
$517$	23.6068	−	30.2493i	1.03822	−	1.33036i
$518$	0.956600	+	0.238720i	0.0420306	+	0.0104888i
$519$	−4.10671	+	11.4775i	−0.180264	+	0.503805i
$520$	−27.5036	+	35.4353i	−1.20611	+	1.55394i
$521$	−14.2593	+	12.9238i	−0.624710	+	0.566204i	−0.921325	−	0.388793i	$-0.872892\pi$
$521$	−14.2593	+	12.9238i	−0.624710	+	0.566204i	0.296615	+	0.954997i	$0.404142\pi$
$522$	29.4888	−	8.97371i	1.29069	−	0.392769i
$523$	5.09384	+	22.6839i	0.222738	+	0.991897i	0.951625	+	0.307263i	$0.0994131\pi$
$523$	5.09384	+	22.6839i	0.222738	+	0.991897i	−0.728887	+	0.684634i	$0.759962\pi$
$524$	−28.4421	−	2.04764i	−1.24250	−	0.0894515i
$525$	4.95649	−	1.37165i	0.216319	−	0.0598635i
$526$	−35.3700	+	24.9570i	−1.54221	+	1.08818i
$527$	2.30703	−	7.60524i	0.100496	−	0.331290i
$528$	−44.9588	−	13.4653i	−1.95658	−	0.586001i
$529$	1.53461	−	0.465517i	0.0667220	−	0.0202399i
$530$	−2.81514	+	0.349732i	−0.122282	+	0.0151914i
$531$	20.0019	+	39.7369i	0.868008	+	1.72444i
$532$	0.560697	+	1.10904i	0.0243093	+	0.0480831i
$533$	−0.916274	−	37.3248i	−0.0396882	−	1.61672i
$534$	28.0242	−	67.8255i	1.21273	−	2.93509i
$535$	65.2398	−	9.67741i	2.82056	−	0.418391i
$536$	−7.54373	+	4.05788i	−0.325840	+	0.175274i
$537$	−6.55019	−	26.1498i	−0.282662	−	1.12845i
$538$	4.15326	+	1.48193i	0.179060	+	0.0638907i
$539$	−12.3875	+	24.6097i	−0.533566	+	1.06001i
$540$	−46.7966	+	46.9618i	−2.01381	+	2.02092i
$541$	0.0620205	+	0.357433i	0.00266647	+	0.0153672i	0.986581	−	0.163273i	$-0.0522052\pi$
$541$	0.0620205	+	0.357433i	0.00266647	+	0.0153672i	−0.983914	+	0.178640i	$0.942830\pi$
$542$	9.60621	−	7.51039i	0.412622	−	0.322599i
$543$	−12.5740	+	18.8184i	−0.539603	+	0.807574i
$544$	9.21466	+	23.5783i	0.395075	+	1.01091i
$545$	−29.1876	−	43.6824i	−1.25026	−	1.87115i
$546$	2.59326	+	0.854163i	0.110981	+	0.0365548i
$547$	−22.8448	−	36.0758i	−0.976772	−	1.54249i	−0.833288	−	0.552839i	$-0.813545\pi$
$547$	−22.8448	−	36.0758i	−0.976772	−	1.54249i	−0.143484	−	0.989653i	$-0.545830\pi$
$548$	−0.221014	−	0.723991i	−0.00944124	−	0.0309273i
$549$	18.1143	−	15.6255i	0.773098	−	0.666879i
$550$	−8.69680	+	58.9870i	−0.370833	+	2.51521i
$551$	11.5188	−	8.54289i	0.490716	−	0.363940i
$552$	40.3892	−	10.2305i	1.71908	−	0.435439i
$553$	−0.253402	+	1.01164i	−0.0107757	+	0.0430192i
$554$	23.3481	−	35.0097i	0.991967	−	1.48742i
$555$	20.4682	+	46.1756i	0.868828	+	1.96004i
$556$	−2.55993	+	11.4946i	−0.108565	+	0.487479i
$557$	0.141163	+	1.91370i	0.00598127	+	0.0810861i	0.999457	−	0.0329607i	$-0.0104936\pi$
$557$	0.141163	+	1.91370i	0.00598127	+	0.0810861i	−0.993475	+	0.114047i	$0.963619\pi$
$558$	−13.0613	−	6.56010i	−0.552930	−	0.277711i
$559$	30.6874	+	37.3927i	1.29794	+	1.58154i
$560$	−2.44272	−	0.797429i	−0.103224	−	0.0336975i
$561$	−40.5878	−	33.3095i	−1.71362	−	1.40633i
$562$	10.9087	−	28.3541i	0.460156	−	1.19605i
$563$	15.2532	−	11.9038i	0.642848	−	0.501683i	−0.240349	−	0.970687i	$-0.577262\pi$
$563$	15.2532	−	11.9038i	0.642848	−	0.501683i	0.883196	+	0.469003i	$0.155387\pi$
$564$	−9.76189	+	56.8537i	−0.411050	+	2.39397i
$565$	−5.93513	+	34.2050i	−0.249693	+	1.43902i
$566$	−19.5992	+	10.4982i	−0.823814	+	0.441271i
$567$	1.08683	+	0.514033i	0.0456427	+	0.0215874i
$568$	9.46447	+	2.09906i	0.397120	+	0.0880746i
$569$	−18.2987	−	16.5850i	−0.767123	−	0.695279i	0.191015	−	0.981587i	$-0.438822\pi$
$569$	−18.2987	−	16.5850i	−0.767123	−	0.695279i	−0.958138	+	0.286308i	$0.907572\pi$
$570$	−27.1690	+	57.5752i	−1.13798	+	2.41156i
$571$	6.83004	−	24.6806i	0.285828	−	1.03285i	−0.670824	−	0.741617i	$-0.734059\pi$
$571$	6.83004	−	24.6806i	0.285828	−	1.03285i	0.956652	−	0.291234i	$-0.0940657\pi$
$572$	−21.2167	+	23.4921i	−0.887115	+	0.982253i
$573$	−45.2187	−	1.11006i	−1.88904	−	0.0463733i
$574$	1.99479	−	0.771494i	0.0832608	−	0.0322015i
$575$	−20.2566	−	48.9037i	−0.844758	−	2.03943i
$576$	45.6135	−	9.32399i	1.90056	−	0.388500i
$577$	−4.13419	+	9.98081i	−0.172108	+	0.415506i	−0.986272	−	0.165129i	$-0.947196\pi$
$577$	−4.13419	+	9.98081i	−0.172108	+	0.415506i	0.814164	+	0.580636i	$0.197196\pi$
$578$	−0.101267	+	4.27878i	−0.00421214	+	0.177974i
$579$	22.4332	−	21.3581i	0.932290	−	0.887614i
$580$	−4.29930	+	29.3396i	−0.178519	+	1.21826i
$581$	0.597240	−	0.338332i	0.0247777	−	0.0140364i
$582$	−2.81594	+	58.3689i	−0.116724	+	2.41947i
$583$	−1.99947	+	0.0982279i	−0.0828098	+	0.00406818i
$584$	2.40174	+	31.4273i	0.0993848	+	1.30047i
$585$	31.0929	+	86.8988i	1.28553	+	3.59282i
$586$	37.1976	−	3.69673i	1.53662	−	0.152711i
$587$	19.6155	+	27.8519i	0.809619	+	1.14957i	0.986244	+	0.165293i	$0.0528570\pi$
$587$	19.6155	+	27.8519i	0.809619	+	1.14957i	−0.176625	+	0.984278i	$0.556518\pi$
$588$	−1.08946	−	41.4062i	−0.0449287	−	1.70756i
$589$	−6.74909	−	0.832421i	−0.278091	−	0.0342993i
$590$	−42.7830	+	1.08798i	−1.76135	+	0.0447913i
$591$	−7.07932	+	0.697252i	−0.291204	+	0.0286811i
$592$	2.87828	−	16.9421i	0.118297	−	0.696317i
$593$	1.02052	−	10.3616i	0.0419079	−	0.425498i	−0.951224	−	0.308500i	$-0.900173\pi$
$593$	1.02052	−	10.3616i	0.0419079	−	0.425498i	0.993132	−	0.116998i	$-0.0373271\pi$
$594$	−35.3993	+	30.5901i	−1.45245	+	1.25513i
$595$	−2.17681	−	1.87773i	−0.0892404	−	0.0769793i
$596$	38.6370	+	17.0452i	1.58263	+	0.698199i
$597$	−1.86870	+	4.84441i	−0.0764807	+	0.198269i
$598$	5.45818	−	27.5670i	0.223202	−	1.12730i
$599$	−13.4782	−	22.4870i	−0.550704	−	0.918795i	−0.999681	−	0.0252511i	$-0.991961\pi$
$599$	−13.4782	−	22.4870i	−0.550704	−	0.918795i	0.448977	−	0.893543i	$-0.351789\pi$
$600$	−30.4213	−	84.3187i	−1.24195	−	3.44230i
$601$	−5.11533	−	0.758788i	−0.208659	−	0.0309516i	0.0415827	−	0.999135i	$-0.486760\pi$
$601$	−5.11533	−	0.758788i	−0.208659	−	0.0309516i	−0.250241	+	0.968183i	$0.580510\pi$
$602$	−1.42249	+	2.37803i	−0.0579763	+	0.0969212i
$603$	−1.29655	+	17.5768i	−0.0527994	+	0.715785i
$604$	2.34830	+	0.707834i	0.0955510	+	0.0288013i
$605$	−3.99748	+	17.8016i	−0.162521	+	0.723737i
$606$	−1.08906	−	14.5889i	−0.0442402	−	0.592634i
$607$	−14.8062	−	2.94514i	−0.600967	−	0.119540i	−0.114774	−	0.993392i	$-0.536615\pi$
$607$	−14.8062	−	2.94514i	−0.600967	−	0.119540i	−0.486192	+	0.873852i	$0.661615\pi$
$608$	18.5297	−	11.2175i	0.751480	−	0.454931i
$609$	1.77022	−	0.352118i	0.0717328	−	0.0142685i
$610$	6.15754	+	22.1745i	0.249311	+	0.897818i
$611$	31.8106	+	22.4035i	1.28692	+	0.906350i
$612$	51.1034	+	10.0715i	2.06573	+	0.407117i
$613$	32.3120	−	10.6745i	1.30507	−	0.431137i	0.424662	−	0.905352i	$-0.360393\pi$
$613$	32.3120	−	10.6745i	1.30507	−	0.431137i	0.880409	+	0.474215i	$0.157268\pi$
$614$	−30.2537	+	1.51298i	−1.22094	+	0.0610591i
$615$	93.9796	+	56.3292i	3.78962	+	2.27141i
$616$	−1.67713	−	0.689501i	−0.0675733	−	0.0277808i
$617$	−7.57909	−	5.62103i	−0.305123	−	0.226294i	0.432294	−	0.901733i	$-0.357704\pi$
$617$	−7.57909	−	5.62103i	−0.305123	−	0.226294i	−0.737416	+	0.675439i	$0.763954\pi$
$618$	4.87005	−	4.87863i	0.195902	−	0.196247i
$619$	−5.25842	−	5.00643i	−0.211354	−	0.201225i	0.576484	−	0.817109i	$-0.304424\pi$
$619$	−5.25842	−	5.00643i	−0.211354	−	0.201225i	−0.787838	+	0.615883i	$0.788799\pi$
$620$	11.0696	−	8.67021i	0.444565	−	0.348204i
$621$	13.0287	−	39.4383i	0.522822	−	1.58260i
$622$	−15.2252	−	26.8212i	−0.610476	−	1.07543i
$623$	1.33664	−	2.50067i	0.0535512	−	0.100187i
$624$	11.4005	−	46.2036i	0.456386	−	1.84962i
$625$	−31.3293	+	16.7458i	−1.25317	+	0.669834i
$626$	1.15516	+	5.12303i	0.0461693	+	0.204757i
$627$	−22.1443	+	39.0902i	−0.884360	+	1.56111i
$628$	−40.9513	−	11.2551i	−1.63414	−	0.449128i
$629$	10.2858	−	16.2431i	0.410124	−	0.647656i
$630$	−4.08396	+	3.35764i	−0.162709	+	0.133772i
$631$	−0.842188	+	17.1431i	−0.0335270	+	0.682457i	0.921935	+	0.387344i	$0.126607\pi$
$631$	−0.842188	+	17.1431i	−0.0335270	+	0.682457i	−0.955462	+	0.295113i	$0.904643\pi$
$632$	17.9181	+	3.06034i	0.712746	+	0.121734i
$633$	22.7098	−	10.7410i	0.902635	−	0.426914i
$634$	10.0252	+	7.42153i	0.398153	+	0.294747i
$635$	−3.78400	−	30.6799i	−0.150163	−	1.21749i
$636$	2.57869	−	1.55179i	0.102252	−	0.0615325i
$637$	−25.5407	−	11.3214i	−1.01196	−	0.448570i
$638$	−4.56687	+	20.4213i	−0.180804	+	0.808487i
$639$	14.1044	−	14.1044i	0.557963	−	0.557963i
$640$	−10.6145	+	43.5119i	−0.419573	+	1.71996i
$641$	11.2750	+	11.2750i	0.445335	+	0.445335i	0.893800	−	0.448465i	$-0.148029\pi$
$641$	11.2750	+	11.2750i	0.445335	+	0.445335i	−0.448465	+	0.893800i	$0.648029\pi$
$642$	−59.0829	+	37.4868i	−2.33181	+	1.47948i
$643$	9.86812	−	22.2621i	0.389161	−	0.877933i	−0.607347	−	0.794436i	$-0.707766\pi$
$643$	9.86812	−	22.2621i	0.389161	−	0.877933i	0.996508	−	0.0834962i	$-0.0266086\pi$
$644$	1.59198	−	0.239015i	0.0627327	−	0.00941850i
$645$	−140.889	+	17.3770i	−5.54750	+	0.684219i
$646$	23.9679	−	3.57688i	0.943005	−	0.140731i
$647$	−15.6094	−	33.0034i	−0.613670	−	1.29750i	−0.936376	−	0.350998i	$-0.885842\pi$
$647$	−15.6094	−	33.0034i	−0.613670	−	1.29750i	0.322706	−	0.946499i	$-0.395408\pi$
$648$	7.49007	−	19.5711i	0.294238	−	0.768827i
$649$	−30.1649	−	1.48191i	−1.18408	−	0.0581699i
$650$	−60.1739	−	5.87309i	−2.36021	−	0.230362i
$651$	−0.723069	−	0.457878i	−0.0283393	−	0.0179457i
$652$	−0.575441	−	4.59885i	−0.0225360	−	0.180105i
$653$	−22.7660	−	12.8968i	−0.890903	−	0.504690i	−0.0220482	−	0.999757i	$-0.507019\pi$
$653$	−22.7660	−	12.8968i	−0.890903	−	0.504690i	−0.868855	+	0.495066i	$0.835144\pi$
$654$	47.1159	+	29.7777i	1.84238	+	1.16440i
$655$	−26.6070	−	49.7783i	−1.03962	−	1.94500i
$656$	−16.0575	−	33.6434i	−0.626938	−	1.31355i
$657$	57.1938	+	30.5707i	2.23134	+	1.19268i
$658$	−0.592563	+	2.14861i	−0.0231005	+	0.0837615i
$659$	−12.4782	−	4.12224i	−0.486081	−	0.160580i	0.0601915	−	0.998187i	$-0.480829\pi$
$659$	−12.4782	−	4.12224i	−0.486081	−	0.160580i	−0.546273	+	0.837607i	$0.683954\pi$
$660$	−24.9341	−	89.4866i	−0.970558	−	3.48326i
$661$	−19.1955	+	20.1616i	−0.746617	+	0.784197i	−0.982236	−	0.187649i	$-0.939913\pi$
$661$	−19.1955	+	20.1616i	−0.746617	+	0.784197i	0.235619	+	0.971846i	$0.424288\pi$
$662$	0.0320569	+	36.3896i	0.00124593	+	1.41432i
$663$	31.7160	−	42.7640i	1.23175	−	1.66082i
$664$	−6.67323	−	9.93028i	−0.258972	−	0.385370i
$665$	−1.26459	+	2.10984i	−0.0490387	+	0.0818161i
$666$	−26.2199	−	23.7222i	−1.01600	−	0.919218i
$667$	−5.82734	−	17.6396i	−0.225635	−	0.683008i
$668$	2.81675	−	0.565448i	0.108983	−	0.0218778i
$669$	13.2147	−	18.7634i	0.510910	−	0.725436i
$670$	−14.7597	−	8.34408i	−0.570216	−	0.322360i
$671$	3.16835	+	15.9284i	0.122313	+	0.614907i
$672$	2.71180	−	0.279155i	0.104610	−	0.0107686i
$673$	−2.90465	+	14.6027i	−0.111966	+	0.562892i	0.883553	+	0.468331i	$0.155145\pi$
$673$	−2.90465	+	14.6027i	−0.111966	+	0.562892i	−0.995519	+	0.0945606i	$0.969855\pi$
$674$	22.2594	−	25.8508i	0.857400	−	0.995737i
$675$	−87.1875	−	19.5786i	−3.35585	−	0.753581i
$676$	−4.72075	−	3.86032i	−0.181567	−	0.148474i
$677$	−13.7597	−	1.01497i	−0.528827	−	0.0390086i	−0.193481	−	0.981104i	$-0.561978\pi$
$677$	−13.7597	−	1.01497i	−0.528827	−	0.0390086i	−0.335345	+	0.942095i	$0.608853\pi$
$678$	−8.98069	−	35.7194i	−0.344901	−	1.37180i
$679$	−0.331295	+	2.23341i	−0.0127139	+	0.0857103i
$680$	−29.7425	+	40.3254i	−1.14057	+	1.54641i
$681$	31.0551	−	18.6137i	1.19003	−	0.713279i
$682$	8.24549	−	5.51998i	0.315736	−	0.211371i
$683$	37.2092	+	14.3532i	1.42377	+	0.549209i	0.944516	−	0.328466i	$-0.106532\pi$
$683$	37.2092	+	14.3532i	1.42377	+	0.549209i	0.479256	+	0.877675i	$0.340907\pi$
$684$	1.01524	−	44.5560i	0.0388188	−	1.70364i
$685$	0.978667	−	1.13455i	0.0373929	−	0.0433488i
$686$	0.233090	−	3.19832i	0.00889941	−	0.122113i
$687$	39.4843	+	3.88887i	1.50642	+	0.148370i
$688$	43.2179	+	21.5635i	1.64767	+	0.822101i
$689$	−0.198967	−	2.02015i	−0.00758005	−	0.0769616i
$690$	59.7786	+	56.8136i	2.27573	+	2.16286i
$691$	−2.24799	+	18.2262i	−0.0855176	+	0.693358i	0.887203	+	0.461379i	$0.152645\pi$
$691$	−2.24799	+	18.2262i	−0.0855176	+	0.693358i	−0.972721	+	0.231979i	$0.925480\pi$
$692$	7.66451	+	2.94102i	0.291361	+	0.111801i
$693$	−3.05040	+	2.14833i	−0.115875	+	0.0816085i
$694$	6.34369	−	7.74371i	0.240803	−	0.293947i
$695$	−21.9468	+	7.85269i	−0.832489	+	0.297869i
$696$	−8.47072	−	30.2975i	−0.321082	−	1.14843i
$697$	−2.04645	−	41.6564i	−0.0775148	−	1.57785i
$698$	34.5354	−	31.3565i	1.30718	−	1.18686i
$699$	−21.8829	−	38.6287i	−0.827687	−	1.46107i
$700$	−0.847458	−	3.35813i	−0.0320309	−	0.126925i
$701$	25.2069	+	26.4757i	0.952052	+	0.999972i	0.999999	+	0.00112182i	$0.000357085\pi$
$701$	25.2069	+	26.4757i	0.952052	+	0.999972i	−0.0479472	+	0.998850i	$0.515268\pi$
$702$	−32.7425	−	34.3299i	−1.23579	−	1.29570i
$703$	−15.1984	−	6.29540i	−0.573220	−	0.237435i
$704$	−9.75557	+	30.0631i	−0.367677	+	1.13305i
$705$	−105.489	+	43.6951i	−3.97296	+	1.64565i
$706$	26.2898	+	11.6258i	0.989429	+	0.437541i
$707$	0.0138718	−	0.565075i	0.000521704	−	0.0212518i
$708$	41.0106	−	19.4850i	1.54127	−	0.732293i
$709$	16.9360	+	4.68682i	0.636044	+	0.176017i	0.569796	−	0.821786i	$-0.307022\pi$
$709$	16.9360	+	4.68682i	0.636044	+	0.176017i	0.0662479	+	0.997803i	$0.478897\pi$
$710$	6.48044	+	18.0614i	0.243206	+	0.677834i
$711$	25.1170	−	27.7124i	0.941963	−	1.03930i
$712$	−45.2353	−	19.9086i	−1.69527	−	0.746105i
$713$	−3.76633	+	7.96324i	−0.141050	+	0.298226i
$714$	2.91937	+	0.882772i	0.109255	+	0.0330369i
$715$	−61.7339	−	10.7118i	−2.30872	−	0.400600i
$716$	−17.7065	+	4.00892i	−0.661724	+	0.149820i
$717$	−6.19028	−	7.93212i	−0.231180	−	0.296230i
$718$	−14.1353	−	31.8131i	−0.527526	−	1.18725i
$719$	−31.7146	+	38.6444i	−1.18276	+	1.44119i	−0.311581	+	0.950220i	$0.600858\pi$
$719$	−31.7146	+	38.6444i	−1.18276	+	1.44119i	−0.871175	+	0.490972i	$0.836642\pi$
$720$	63.7778	+	66.5170i	2.37686	+	2.47894i
$721$	0.205885	−	0.168965i	0.00766755	−	0.00629260i
$722$	1.92952	+	5.82351i	0.0718093	+	0.216729i
$723$	26.5279	−	1.95682i	0.986585	−	0.0727749i
$724$	12.4771	+	8.75449i	0.463706	+	0.325358i
$725$	−36.5388	+	16.1965i	−1.35702	+	0.601523i
$726$	−3.79297	−	18.9811i	−0.140770	−	0.704456i
$727$	13.0632	+	3.27216i	0.484487	+	0.121358i	0.477525	−	0.878618i	$-0.341534\pi$
$727$	13.0632	+	3.27216i	0.484487	+	0.121358i	0.00696197	+	0.999976i	$0.497784\pi$
$728$	0.614871	−	1.73287i	0.0227886	−	0.0642246i
$729$	18.7564	+	25.2901i	0.694681	+	0.936669i
$730$	−50.0773	+	37.2083i	−1.85344	+	1.37714i
$731$	35.2944	+	40.9160i	1.30541	+	1.51333i
$732$	−15.5223	−	18.8462i	−0.573721	−	0.696575i
$733$	28.9631	−	18.3407i	1.06978	−	0.677428i	0.120768	−	0.992681i	$-0.461464\pi$
$733$	28.9631	−	18.3407i	1.06978	−	0.677428i	0.949008	+	0.315253i	$0.102089\pi$
$734$	45.8455	−	23.1273i	1.69219	−	0.853645i
$735$	68.1691	−	45.5491i	2.51445	−	1.68011i
$736$	−6.26833	−	27.3500i	−0.231054	−	1.00814i
$737$	−9.94850	−	6.64738i	−0.366458	−	0.244859i
$738$	−76.1342	−	9.32218i	−2.80254	−	0.343154i
$739$	5.37986	−	0.933494i	0.197901	−	0.0343391i	−0.0711469	−	0.997466i	$-0.522666\pi$
$739$	5.37986	−	0.933494i	0.197901	−	0.0343391i	0.269048	+	0.963127i	$0.413291\pi$
$740$	31.4029	−	13.0724i	1.15439	−	0.480550i
$741$	−40.6918	−	20.4825i	−1.49485	−	0.752444i
$742$	0.105075	−	0.0498101i	0.00385742	−	0.00182858i
$743$	−1.18532	+	0.296907i	−0.0434851	+	0.0108925i	−0.264662	−	0.964341i	$-0.585260\pi$
$743$	−1.18532	+	0.296907i	−0.0434851	+	0.0108925i	0.221177	+	0.975234i	$0.429010\pi$
$744$	−6.99727	+	13.1746i	−0.256532	+	0.483004i
$745$	12.2649	+	82.6834i	0.449352	+	3.02928i
$746$	7.69640	−	3.19590i	0.281785	−	0.117010i
$747$	−24.6094	+	0.604127i	−0.900411	+	0.0221038i
$748$	−23.0492	+	26.8158i	−0.842761	+	0.980482i
$749$	−2.41485	+	1.21554i	−0.0882369	+	0.0444147i
$750$	57.9486	−	74.3893i	2.11598	−	2.71631i
$751$	9.95133	+	32.8051i	0.363129	+	1.19708i	0.928215	+	0.372044i	$0.121343\pi$
$751$	9.95133	+	32.8051i	0.363129	+	1.19708i	−0.565086	+	0.825032i	$0.691157\pi$
$752$	38.1284	+	7.44465i	1.39040	+	0.271478i
$753$	−0.512470	−	0.155456i	−0.0186754	−	0.00566513i
$754$	−20.9096	−	3.60919i	−0.761483	−	0.131439i
$755$	1.29481	+	4.67885i	0.0471231	+	0.170281i
$756$	1.21759	−	2.42959i	0.0442833	−	0.0883632i
$757$	42.0557	−	9.44393i	1.52854	−	0.343245i	0.628069	−	0.778158i	$-0.283846\pi$
$757$	42.0557	−	9.44393i	1.52854	−	0.343245i	0.900473	+	0.434913i	$0.143221\pi$
$758$	−6.08554	+	11.4094i	−0.221037	+	0.414409i
$759$	39.0834	+	43.1219i	1.41864	+	1.56523i
$760$	38.3472	+	19.1755i	1.39100	+	0.695569i
$761$	1.66999	+	0.597533i	0.0605372	+	0.0216606i	0.366984	−	0.930227i	$-0.380390\pi$
$761$	1.66999	+	0.597533i	0.0605372	+	0.0216606i	−0.306447	+	0.951888i	$0.599140\pi$
$762$	16.8851	+	28.1149i	0.611682	+	1.01849i
$763$	1.69773	+	1.32492i	0.0614620	+	0.0479654i
$764$	−1.44108	+	30.4276i	−0.0521364	+	1.10083i
$765$	37.1044	+	96.1896i	1.34151	+	3.47774i
$766$	−6.61189	+	1.15327i	−0.238897	+	0.0416694i
$767$		−	30.6243i		−	1.10578i
$768$	−8.45324	−	46.7585i	−0.305030	−	1.68725i
$769$			10.3798i			0.374305i	0.982331	+	0.187153i	$0.0599259\pi$
$769$			10.3798i			0.374305i	−0.982331	+	0.187153i	$0.940074\pi$
$770$	−0.616738	−	3.53585i	−0.0222257	−	0.127423i
$771$	10.3190	+	26.7511i	0.371631	+	0.963417i
$772$	−14.0358	−	15.4314i	−0.505159	−	0.555387i
$773$	29.5365	+	23.0505i	1.06236	+	0.829070i	0.985788	−	0.167994i	$-0.0537290\pi$
$773$	29.5365	+	23.0505i	1.06236	+	0.829070i	0.0765674	+	0.997064i	$0.475604\pi$
$774$	85.1930	−	51.1648i	3.06220	−	1.83908i
$775$	17.8441	+	6.38471i	0.640978	+	0.229346i
$776$	39.2552	+	2.79135i	1.40918	+	0.100203i
$777$	−1.39041	−	1.53408i	−0.0498806	−	0.0550348i
$778$	−18.8036	−	10.0294i	−0.674141	−	0.359573i
$779$	−34.8191	+	7.81889i	−1.24752	+	0.280141i
$780$	89.3901	−	29.7053i	3.20068	−	1.06362i
$781$	3.61165	+	13.0508i	0.129235	+	0.466996i
$782$	5.33955	−	30.9344i	0.190942	−	1.10621i
$783$	−30.0107	−	9.10365i	−1.07250	−	0.325338i
$784$	−27.8945	+	0.0982933i	−0.996232	+	0.00351048i
$785$	−24.4023	−	80.4436i	−0.870955	−	2.87115i
$786$	47.2399	+	36.7995i	1.68499	+	1.31259i
$787$	0.949195	−	0.477784i	0.0338351	−	0.0170312i	−0.432613	−	0.901580i	$-0.642408\pi$
$787$	0.949195	−	0.477784i	0.0338351	−	0.0170312i	0.466448	+	0.884548i	$0.345533\pi$
$788$	0.360839	+	4.77703i	0.0128543	+	0.170175i
$789$	90.8763	−	2.23089i	3.23528	−	0.0794217i
$790$	13.7983	+	33.2292i	0.490921	+	1.18224i
$791$	−0.208806	−	1.40765i	−0.00742428	−	0.0500504i
$792$	41.3881	+	50.1606i	1.47066	+	1.78238i
$793$	−15.9744	+	4.00137i	−0.567266	+	0.142093i
$794$	−2.89218	−	6.10110i	−0.102640	−	0.216520i
$795$	5.32103	+	2.67838i	0.188717	+	0.0949923i
$796$	3.23296	+	1.33247i	0.114589	+	0.0472281i
$797$	−19.8493	+	3.44418i	−0.703098	+	0.121999i	−0.511258	−	0.859427i	$-0.670820\pi$
$797$	−19.8493	+	3.44418i	−0.703098	+	0.121999i	−0.191840	+	0.981426i	$0.561445\pi$
$798$	0.317168	−	2.59031i	0.0112276	−	0.0916960i
$799$	36.1378	+	24.1465i	1.27846	+	0.854242i
$800$	−57.2365	+	19.1884i	−2.02362	+	0.678413i
$801$	−84.5510	+	56.4952i	−2.98746	+	1.99616i
$802$	10.2121	+	20.2434i	0.360600	+	0.714821i
$803$	−37.1957	+	23.5539i	−1.31261	+	0.831199i
$804$	17.9044	+	1.73158i	0.631439	+	0.0610682i
$805$	2.08128	+	2.41278i	0.0733555	+	0.0850394i
$806$	6.00080	+	8.07627i	0.211369	+	0.284474i
$807$	−5.51630	−	7.43787i	−0.194183	−	0.261826i
$808$	−9.83906	+	0.509431i	−0.346137	+	0.0179217i
$809$	−25.7286	−	6.44468i	−0.904569	−	0.226583i	−0.237332	−	0.971428i	$-0.576273\pi$
$809$	−25.7286	−	6.44468i	−0.904569	−	0.226583i	−0.667237	+	0.744846i	$0.732523\pi$
$810$	40.6743	−	8.12788i	1.42915	−	0.285585i
$811$	−0.548697	+	0.243221i	−0.0192673	+	0.00854063i	−0.414852	−	0.909889i	$-0.636167\pi$
$811$	−0.548697	+	0.243221i	−0.0192673	+	0.00854063i	0.395585	+	0.918429i	$0.370542\pi$
$812$	−0.209916	−	1.19725i	−0.00736659	−	0.0420151i
$813$	−25.5367	+	1.88370i	−0.895611	+	0.0660643i
$814$	22.7860	−	7.54974i	0.798648	−	0.264618i
$815$	7.09143	−	5.81978i	0.248402	−	0.203858i
$816$	11.4646	−	51.9091i	0.401341	−	1.81718i
$817$	29.3313	−	35.7403i	1.02617	−	1.25039i
$818$	−23.0542	+	10.2435i	−0.806072	+	0.358157i
$819$	−2.32757	−	2.98251i	−0.0813320	−	0.104217i
$820$	39.3668	−	62.4100i	1.37475	−	2.17945i
$821$	−54.2684	−	9.41647i	−1.89398	−	0.328637i	−0.899796	−	0.436311i	$-0.856285\pi$
$821$	−54.2684	−	9.41647i	−1.89398	−	0.328637i	−0.994186	+	0.107674i	$0.965660\pi$
$822$	−0.460099	+	1.52157i	−0.0160478	+	0.0530707i
$823$	13.6365	−	28.8319i	0.475337	−	1.00502i	−0.513785	−	0.857919i	$-0.671757\pi$
$823$	13.6365	−	28.8319i	0.475337	−	1.00502i	0.989122	−	0.147097i	$-0.0469929\pi$
$824$	−3.20995	−	3.35373i	−0.111824	−	0.116833i
$825$	84.0852	−	92.7737i	2.92747	−	3.22997i
$826$	1.65123	−	0.592460i	0.0574535	−	0.0206143i
$827$	−31.7626	−	8.78991i	−1.10450	−	0.305655i	−0.333663	−	0.942693i	$-0.608285\pi$
$827$	−31.7626	−	8.78991i	−1.10450	−	0.305655i	−0.770833	+	0.637038i	$0.780160\pi$
$828$	−54.3921	−	19.3538i	−1.89026	−	0.672590i
$829$	−0.0426984	+	1.73934i	−0.00148298	+	0.0604098i	0.998501	+	0.0547349i	$0.0174314\pi$
$829$	−0.0426984	+	1.73934i	−0.00148298	+	0.0604098i	−0.999984	+	0.00567485i	$0.998194\pi$
$830$	9.57766	−	21.6583i	0.332446	−	0.751772i
$831$	−81.6414	+	33.8170i	−2.83211	+	1.17310i
$832$	−30.9328	−	8.38451i	−1.07240	−	0.290680i
$833$	−28.8322	−	11.9427i	−0.998977	−	0.413790i
$834$	17.8952	−	17.0677i	0.619659	−	0.591006i
$835$	3.92115	+	4.11851i	0.135697	+	0.142527i
$836$	25.9788	+	15.5089i	0.898495	+	0.536388i
$837$	7.32984	+	12.9390i	0.253356	+	0.447236i
$838$	20.3112	+	22.3703i	0.701639	+	0.772770i
$839$	2.64723	+	53.8855i	0.0913924	+	1.86034i	0.409537	+	0.912293i	$0.365690\pi$
$839$	2.64723	+	53.8855i	0.0913924	+	1.86034i	−0.318145	+	0.948042i	$0.603060\pi$
$840$	3.33102	+	4.24513i	0.114931	+	0.146471i
$841$	14.0978	−	5.04428i	0.486131	−	0.173941i
$842$	−4.11789	−	3.37340i	−0.141912	−	0.116255i
$843$	−52.1594	+	36.7348i	−1.79647	+	1.26521i
$844$	−6.88323	−	15.4548i	−0.236931	−	0.531975i
$845$	1.47755	−	11.9797i	0.0508294	−	0.412114i
$846$	55.0654	−	57.9391i	1.89319	−	1.99199i
$847$	−0.0733052	−	0.744280i	−0.00251880	−	0.0255738i
$848$	−1.00522	−	1.75998i	−0.0345195	−	0.0604379i
$849$	46.4649	+	4.57640i	1.59467	+	0.157062i
$850$	−67.3586	−	4.90901i	−2.31038	−	0.168378i
$851$	−13.9192	+	16.1362i	−0.477144	+	0.553143i
$852$	−14.0635	−	14.7194i	−0.481809	−	0.504277i
$853$	−32.6590	−	12.5980i	−1.11822	−	0.431346i	−0.270997	−	0.962580i	$-0.587353\pi$
$853$	−32.6590	−	12.5980i	−1.11822	−	0.431346i	−0.847225	+	0.531234i	$0.821728\pi$
$854$	−0.524790	−	0.783908i	−0.0179580	−	0.0268248i
$855$	75.6650	−	45.3518i	2.58769	−	1.55100i
$856$	24.3325	+	40.3542i	0.831669	+	1.37928i
$857$	2.52236	−	17.0044i	0.0861623	−	0.580859i	−0.902499	−	0.430693i	$-0.858269\pi$
$857$	2.52236	−	17.0044i	0.0861623	−	0.580859i	0.988661	−	0.150166i	$-0.0479808\pi$
$858$	64.4671	−	16.2085i	2.20087	−	0.553351i
$859$	−1.06165	−	0.0783120i	−0.0362230	−	0.00267197i	0.0554409	−	0.998462i	$-0.482344\pi$
$859$	−1.06165	−	0.0783120i	−0.0362230	−	0.00267197i	−0.0916639	+	0.995790i	$0.529219\pi$
$860$	9.53813	+	95.1238i	0.325248	+	3.24370i
$861$	−4.38220	−	0.984056i	−0.149345	−	0.0335366i
$862$	−11.4269	−	9.83935i	−0.389201	−	0.335130i
$863$	0.0148687	−	0.0747501i	0.000506137	−	0.00254452i	−0.980531	−	0.196362i	$-0.937087\pi$
$863$	0.0148687	−	0.0747501i	0.000506137	−	0.00254452i	0.981038	+	0.193818i	$0.0620871\pi$
$864$	−43.8418	−	17.9340i	−1.49153	−	0.610128i
$865$	3.17010	+	15.9372i	0.107787	+	0.541880i
$866$	−3.20823	+	5.67497i	−0.109020	+	0.192843i
$867$	5.17522	−	7.34825i	0.175760	−	0.249560i
$868$	−0.319371	+	0.479800i	−0.0108402	+	0.0162855i
$869$	7.96463	+	24.1093i	0.270182	+	0.817851i
$870$	41.7771	−	46.1756i	1.41637	−	1.56550i
$871$	6.23737	−	10.4064i	0.211345	−	0.352608i
$872$	20.7714	−	31.2651i	0.703408	−	1.05877i
$873$	48.2355	−	65.0380i	1.63252	−	2.20120i
$874$	−26.8603	+	0.0236622i	−0.908564	+	0.000800386i
$875$	2.51225	−	2.63870i	0.0849295	−	0.0892043i
$876$	32.5226	−	57.6469i	1.09884	−	1.94771i
$877$	−34.9445	−	11.5441i	−1.17999	−	0.389817i	−0.344218	−	0.938890i	$-0.611856\pi$
$877$	−34.9445	−	11.5441i	−1.17999	−	0.389817i	−0.835774	+	0.549073i	$0.814981\pi$
$878$	−27.0916	−	7.47156i	−0.914296	−	0.252153i
$879$	−69.2290	−	37.0037i	−2.33504	−	1.24810i
$880$	−60.6317	+	15.4147i	−2.04389	+	0.519630i
$881$	7.49031	+	14.0134i	0.252355	+	0.472123i	0.975919	−	0.218135i	$-0.0699972\pi$
$881$	7.49031	+	14.0134i	0.252355	+	0.472123i	−0.723564	+	0.690258i	$0.757497\pi$
$882$	−30.6631	+	48.5168i	−1.03248	+	1.63365i
$883$	50.8387	+	28.7998i	1.71086	+	0.969189i	0.945522	+	0.325560i	$0.105553\pi$
$883$	50.8387	+	28.7998i	1.71086	+	0.969189i	0.765337	+	0.643630i	$0.222572\pi$
$884$	−28.3054	−	22.0096i	−0.952015	−	0.740264i
$885$	75.9281	+	48.0809i	2.55229	+	1.61622i
$886$	1.27749	−	13.0888i	0.0429182	−	0.439726i
$887$	−15.8433	−	0.778330i	−0.531965	−	0.0261338i	−0.218687	−	0.975795i	$-0.570177\pi$
$887$	−15.8433	−	0.778330i	−0.531965	−	0.0261338i	−0.313278	+	0.949661i	$0.601427\pi$
$888$	−24.8146	+	26.2019i	−0.832723	+	0.879278i
$889$	0.541771	+	1.14548i	0.0181704	+	0.0384181i
$890$	−14.4392	−	96.7537i	−0.484002	−	3.24319i
$891$	29.0508	−	3.58307i	0.973238	−	0.120037i
$892$	−12.4302	−	9.18499i	−0.416195	−	0.307536i
$893$	15.0704	−	33.9982i	0.504311	−	1.13771i
$894$	−47.5098	−	74.8802i	−1.58897	−	2.50437i
$895$	−25.4097	−	25.4097i	−0.849352	−	0.849352i
$896$	−0.146346	−	1.83007i	−0.00488908	−	0.0611384i
$897$	−41.7286	+	41.7286i	−1.39328	+	1.39328i
$898$	29.6627	+	6.63355i	0.989859	+	0.221364i
$899$	6.08070	+	2.69539i	0.202803	+	0.0898963i
$900$	−29.9677	+	120.539i	−0.998924	+	4.01795i
$901$	−0.277572	−	2.25049i	−0.00924726	−	0.0749748i
$902$	30.9823	−	41.8518i	1.03160	−	1.39351i
$903$	5.26030	−	2.48794i	0.175052	−	0.0827934i
$904$	−24.1868	+	5.49851i	−0.804441	+	0.182878i
$905$	−1.48034	+	30.1331i	−0.0492083	+	1.00166i
$906$	−3.27093	−	3.97849i	−0.108669	−	0.132176i
$907$	25.5710	−	40.3810i	0.849070	−	1.34083i	−0.0895883	−	0.995979i	$-0.528555\pi$
$907$	25.5710	−	40.3810i	0.849070	−	1.34083i	0.938658	−	0.344849i	$-0.112070\pi$
$908$	−12.0557	−	21.1942i	−0.400084	−	0.703354i
$909$	−9.99171	+	17.6378i	−0.331404	+	0.585010i
$910$	3.55037	−	0.800549i	0.117694	−	0.0265379i
$911$	7.69021	−	4.11051i	0.254788	−	0.136187i	−0.339059	−	0.940765i	$-0.610109\pi$
$911$	7.69021	−	4.11051i	0.254788	−	0.136187i	0.593847	+	0.804578i	$0.297609\pi$
$912$	−45.4391	−	2.07181i	−1.50464	−	0.0686044i
$913$	7.87790	−	14.7385i	0.260720	−	0.487773i
$914$	39.0163	−	22.1479i	1.29054	−	0.732587i
$915$	15.1594	−	45.8881i	0.501154	−	1.51701i
$916$	3.22401	−	26.5242i	0.106524	−	0.876384i
$917$	1.67567	+	1.59537i	0.0553354	+	0.0526837i
$918$	−37.5054	−	37.4394i	−1.23786	−	1.23568i
$919$	−22.1592	−	16.4344i	−0.730964	−	0.542120i	0.164974	−	0.986298i	$-0.447246\pi$
$919$	−22.1592	−	16.4344i	−0.730964	−	0.542120i	−0.895939	+	0.444178i	$0.853496\pi$
$920$	39.1683	−	39.3759i	1.29134	−	1.29818i
$921$	54.5606	+	32.7024i	1.79783	+	1.07758i
$922$	1.69085	+	33.8103i	0.0556852	+	1.11348i
$923$	−13.0380	+	4.30717i	−0.429151	+	0.141772i
$924$	2.12113	+	3.16242i	0.0697801	+	0.104036i
$925$	37.4840	+	26.3992i	1.23247	+	0.868001i
$926$	−19.1018	+	5.30431i	−0.627726	+	0.174311i
$927$	−9.36824	+	1.86346i	−0.307693	+	0.0612040i
$928$	−20.5286	+	5.23834i	−0.673883	+	0.171957i
$929$	−1.15273	−	0.229293i	−0.0378199	−	0.00752285i	0.176144	−	0.984364i	$-0.443638\pi$
$929$	−1.15273	−	0.229293i	−0.0378199	−	0.00752285i	−0.213964	+	0.976842i	$0.568638\pi$
$930$	−29.4452	+	2.19809i	−0.965547	+	0.0720783i
$931$	−5.85063	+	26.0540i	−0.191747	+	0.853887i
$932$	−26.3435	+	14.1406i	−0.862910	+	0.463192i
$933$	−4.76442	+	64.5896i	−0.155980	+	2.11457i
$934$	38.8398	+	23.2332i	1.27088	+	0.760213i
$935$	−69.2334	−	10.2698i	−2.26417	−	0.335858i
$936$	−48.7426	+	44.4130i	−1.59320	+	1.45168i
$937$	8.62480	+	14.3896i	0.281760	+	0.470088i	0.965775	−	0.259379i	$-0.0835180\pi$
$937$	8.62480	+	14.3896i	0.281760	+	0.470088i	−0.684016	+	0.729467i	$0.739768\pi$
$938$	0.681772	+	0.134989i	0.0222606	+	0.00440753i
$939$	3.96900	−	10.2892i	0.129523	−	0.335777i
$940$	27.8006	+	71.6938i	0.906754	+	2.33839i
$941$	0.270267	+	0.233134i	0.00881044	+	0.00759994i	0.657567	−	0.753396i	$-0.271586\pi$
$941$	0.270267	+	0.233134i	0.00881044	+	0.00759994i	−0.648757	+	0.760996i	$0.724711\pi$
$942$	58.3124	+	67.4800i	1.89992	+	2.19862i
$943$	−4.53112	+	46.0052i	−0.147554	+	1.49814i
$944$	−12.4897	−	27.9104i	−0.406504	−	0.908405i
$945$	5.35324	−	0.527248i	0.174141	−	0.0171514i
$946$	1.71508	+	67.4427i	0.0557619	+	2.19275i
$947$	−20.0768	−	2.47624i	−0.652408	−	0.0804669i	−0.210594	−	0.977574i	$-0.567540\pi$
$947$	−20.0768	−	2.47624i	−0.652408	−	0.0804669i	−0.441814	+	0.897107i	$0.645665\pi$
$948$	−27.6924	−	26.2725i	−0.899406	−	0.853290i
$949$	−25.7057	−	36.4993i	−0.834443	−	1.18482i
$950$	5.71488	+	57.5048i	0.185415	+	1.86570i
$951$	−8.82430	−	24.6623i	−0.286147	−	0.799728i
$952$	0.639136	−	1.95200i	0.0207145	−	0.0632646i
$953$	−5.16764	+	0.253870i	−0.167396	+	0.00822365i	−0.132593	−	0.991171i	$-0.542330\pi$
$953$	−5.16764	+	0.253870i	−0.167396	+	0.00822365i	−0.0348031	+	0.999394i	$0.511080\pi$
$954$	−4.16541	−	0.200955i	−0.134860	−	0.00650617i
$955$	−52.4618	+	29.7192i	−1.69762	+	0.961691i
$956$	−5.43547	+	4.04608i	−0.175796	+	0.130860i
$957$	31.8256	−	30.3005i	1.02878	−	0.979476i
$958$	−46.2628	−	1.09491i	−1.49468	−	0.0353749i
$959$	−0.0235038	+	0.0567432i	−0.000758977	+	0.00183233i
$960$	69.3534	−	63.5292i	2.23837	−	2.05040i
$961$	10.6562	+	25.7264i	0.343749	+	0.829884i
$962$	8.77997	+	22.7016i	0.283078	+	0.731930i
$963$	96.9271	+	2.37943i	3.12343	+	0.0766759i
$964$	−0.910511	−	17.8906i	−0.0293256	−	0.576219i
$965$	11.0123	−	39.7934i	0.354499	−	1.28100i
$966$	−3.05725	−	1.44267i	−0.0983653	−	0.0464173i
$967$	24.9451	+	22.6089i	0.802181	+	0.727054i	0.965749	−	0.259478i	$-0.0835504\pi$
$967$	24.9451	+	22.6089i	0.802181	+	0.727054i	−0.163568	+	0.986532i	$0.552300\pi$
$968$	−12.8377	+	2.26252i	−0.412620	+	0.0727203i
$969$	−46.0030	−	21.7578i	−1.47783	−	0.698961i
$970$	36.7806	+	68.6661i	1.18095	+	2.20474i
$971$	6.61600	−	38.1289i	0.212317	−	1.22362i	−0.666152	−	0.745816i	$-0.732060\pi$
$971$	6.61600	−	38.1289i	0.212317	−	1.22362i	0.878469	−	0.477799i	$-0.158565\pi$
$972$	5.09210	−	3.59970i	0.163329	−	0.115460i
$973$	0.753250	−	0.587842i	0.0241481	−	0.0188453i
$974$	20.7362	+	7.97787i	0.664432	+	0.255628i
$975$	98.1434	+	80.5442i	3.14311	+	2.57948i
$976$	−12.9268	+	10.1617i	−0.413777	+	0.325267i
$977$	30.4031	+	37.0463i	0.972682	+	1.18522i	0.982688	+	0.185266i	$0.0593148\pi$
$977$	30.4031	+	37.0463i	0.972682	+	1.18522i	−0.0100064	+	0.999950i	$0.503185\pi$
$978$	−4.36826	+	8.69730i	−0.139681	+	0.278109i
$979$	−5.07847	−	68.8471i	−0.162309	−	2.20036i
$980$	−29.6213	−	46.5954i	−0.946219	−	1.48843i
$981$	−31.2976	−	70.6062i	−0.999254	−	2.25428i
$982$	18.7698	+	12.5177i	0.598970	+	0.399456i
$983$	−14.3457	+	57.2712i	−0.457556	+	1.82667i	0.0979985	+	0.995187i	$0.468756\pi$
$983$	−14.3457	+	57.2712i	−0.457556	+	1.82667i	−0.555555	+	0.831480i	$0.687494\pi$
$984$	−11.2820	+	77.4668i	−0.359656	+	2.46955i
$985$	−7.61636	+	5.64867i	−0.242677	+	0.179982i
$986$	−23.4492	−	3.45725i	−0.746775	−	0.110101i
$987$	3.54406	−	3.05712i	0.112809	−	0.0973093i
$988$	−14.4146	+	27.0826i	−0.458591	+	0.861611i
$989$	−32.0426	−	50.6008i	−1.01890	−	1.60901i
$990$	−40.2696	+	122.259i	−1.27985	+	3.88565i
$991$	−1.74020	−	2.60440i	−0.0552793	−	0.0827314i	0.802800	−	0.596248i	$-0.203342\pi$
$991$	−1.74020	−	2.60440i	−0.0552793	−	0.0827314i	−0.858080	+	0.513517i	$0.828342\pi$
$992$	8.76279	+	4.91320i	0.278219	+	0.155994i
$993$	42.4547	−	63.5379i	1.34726	−	2.01631i
$994$	−0.484472	−	0.619667i	−0.0153665	−	0.0196546i
$995$	1.18330	+	6.81951i	0.0375130	+	0.216193i
$996$	0.0442657	+	25.1242i	0.00140261	+	0.796092i
$997$	−19.1602	+	38.0649i	−0.606811	+	1.20553i	0.355780	+	0.934570i	$0.384215\pi$
$997$	−19.1602	+	38.0649i	−0.606811	+	1.20553i	−0.962591	+	0.270957i	$0.912660\pi$
$998$	−5.15218	+	14.4395i	−0.163089	+	0.457073i
$999$	8.74114	+	34.8966i	0.276557	+	1.10408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.o.a.157.21	✓	4032
512.437	even	128	inner	512.2.o.a.437.21	yes	4032

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.o.a.157.21	✓	4032	1.1	even	1	trivial
512.2.o.a.437.21	yes	4032	512.437	even	128	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.o (of order \(128\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.813297 + 1.15696i) q^{2} +(2.77078 - 1.06881i) q^{3} +(-0.677096 - 1.88190i) q^{4} +(2.43553 - 3.12085i) q^{5} +(-1.01690 + 4.07493i) q^{6} +(-0.0546682 + 0.152787i) q^{7} +(2.72795 + 0.747171i) q^{8} +(4.31203 - 3.90820i) q^{9} +O(q^{10})\)	\(q+(-0.813297 + 1.15696i) q^{2} +(2.77078 - 1.06881i) q^{3} +(-0.677096 - 1.88190i) q^{4} +(2.43553 - 3.12085i) q^{5} +(-1.01690 + 4.07493i) q^{6} +(-0.0546682 + 0.152787i) q^{7} +(2.72795 + 0.747171i) q^{8} +(4.31203 - 3.90820i) q^{9} +(1.62987 + 5.35598i) q^{10} +(0.865624 + 3.85480i) q^{11} +(-3.88748 - 4.49064i) q^{12} +(-3.86101 + 1.06849i) q^{13} +(-0.132307 - 0.187510i) q^{14} +(3.41275 - 11.2503i) q^{15} +(-3.08308 + 2.54845i) q^{16} +(-4.28239 + 1.29905i) q^{17} +(1.01465 + 8.16736i) q^{18} +(1.72161 + 3.42025i) q^{19} +(-7.52221 - 2.47031i) q^{20} +(0.0118268 + 0.481771i) q^{21} +(-5.16384 - 2.13361i) q^{22} +(4.90652 - 0.727814i) q^{23} +(8.35715 - 0.845414i) q^{24} +(-2.59297 - 10.3517i) q^{25} +(1.90396 - 5.33602i) q^{26} +(3.76485 - 7.47947i) q^{27} +(0.324546 - 0.000571809i) q^{28} +(-0.640296 - 3.69011i) q^{29} +(10.2406 + 13.0982i) q^{30} +(-0.986656 + 1.47663i) q^{31} +(-0.440989 - 5.63964i) q^{32} +(6.51850 + 9.75562i) q^{33} +(1.97991 - 6.01105i) q^{34} +(0.343680 + 0.542731i) q^{35} +(-10.2745 - 5.46858i) q^{36} +(-3.25314 + 2.80618i) q^{37} +(-5.35725 - 0.789851i) q^{38} +(-9.55602 + 7.08723i) q^{39} +(8.97584 - 6.69377i) q^{40} +(-2.26451 + 9.04044i) q^{41} +(-0.567007 - 0.378140i) q^{42} +(-4.89316 - 11.0388i) q^{43} +(6.66823 - 4.23909i) q^{44} +(-1.69479 - 22.9758i) q^{45} +(-3.14841 + 6.26856i) q^{46} +(-6.16130 - 7.50756i) q^{47} +(-5.81874 + 10.3564i) q^{48} +(5.39072 + 4.42405i) q^{49} +(14.0853 + 5.41907i) q^{50} +(-10.4771 + 8.17644i) q^{51} +(4.62506 + 6.54256i) q^{52} +(-0.0866272 + 0.499245i) q^{53} +(5.59148 + 10.4388i) q^{54} +(14.1385 + 6.68701i) q^{55} +(-0.263291 + 0.375951i) q^{56} +(8.42579 + 7.63669i) q^{57} +(4.79005 + 2.26036i) q^{58} +(-2.03885 + 7.36745i) q^{59} +(-23.4827 + 1.19511i) q^{60} +(4.10943 + 0.100881i) q^{61} +(-0.905958 - 2.34246i) q^{62} +(0.361393 + 0.872479i) q^{63} +(6.88347 + 4.07650i) q^{64} +(-6.06905 + 14.6520i) q^{65} +(-16.5883 - 0.392598i) q^{66} +(-2.19338 + 2.08827i) q^{67} +(5.34427 + 7.17944i) q^{68} +(12.8170 - 7.26075i) q^{69} +(-0.907430 - 0.0437779i) q^{70} +(3.42338 - 0.168180i) q^{71} +(14.6831 - 7.43956i) q^{72} +(3.75418 + 10.4922i) q^{73} +(-0.600856 - 6.04599i) q^{74} +(-18.2486 - 25.9110i) q^{75} +(5.27086 - 5.55572i) q^{76} +(-0.636287 - 0.0784785i) q^{77} +(-0.427732 - 16.8199i) q^{78} +(6.39581 - 0.629932i) q^{79} +(0.444387 + 15.8287i) q^{80} +(0.726196 - 7.37319i) q^{81} +(-8.61767 - 9.97250i) q^{82} +(-3.20299 - 2.76291i) q^{83} +(0.898636 - 0.348462i) q^{84} +(-6.37578 + 16.5286i) q^{85} +(16.7510 + 3.31664i) q^{86} +(-5.71815 - 9.54015i) q^{87} +(-0.518810 + 11.1625i) q^{88} +(-17.2844 - 2.56389i) q^{89} +(27.9603 + 16.7253i) q^{90} +(0.0478234 - 0.648327i) q^{91} +(-4.69186 - 8.74077i) q^{92} +(-1.15557 + 5.14598i) q^{93} +(13.6969 - 1.02248i) q^{94} +(14.8671 + 2.95725i) q^{95} +(-7.24958 - 15.1549i) q^{96} +(13.6465 - 2.71445i) q^{97} +(-9.50268 + 2.63876i) q^{98} +(18.7979 + 13.2390i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Introduction

L-functions

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