LMFDB - Embedded newform 825.2.n.n.751.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (of order $5$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 9 x^{14} - 15 x^{13} + 44 x^{12} - 61 x^{11} + 208 x^{10} - 281 x^{9} + 851 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 9x^14 - 15x^13 + 44x^12 - 61x^11 + 208x^10 - 281x^9 + 851x^8 - 1252x^7 + 1929x^6 - 1320x^5 + 1261x^4 + 45x^3 + 640x^2 + 200*x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			751.2
Root			$-0.211561 + 0.651117i$ of defining polynomial
Character	$\chi$	$=$	825.751
Dual form			825.2.n.n.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.553874 + 0.402413i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.473194 + 1.45634i) q^{4} +(0.553874 + 0.402413i) q^{6} +(1.30626 - 4.02026i) q^{7} +(-0.747082 - 2.29928i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.553874 + 0.402413i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.473194 + 1.45634i) q^{4} +(0.553874 + 0.402413i) q^{6} +(1.30626 - 4.02026i) q^{7} +(-0.747082 - 2.29928i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-2.63707 + 2.01144i) q^{11} +1.53129 q^{12} +(-5.07554 + 3.68760i) q^{13} +(0.894299 + 2.75237i) q^{14} +(-1.13863 - 0.827260i) q^{16} +(5.01149 + 3.64106i) q^{17} +(0.211561 - 0.651117i) q^{18} +(-0.868508 - 2.67299i) q^{19} -4.22715 q^{21} +(0.651174 - 2.17527i) q^{22} +0.456579 q^{23} +(-1.95589 + 1.42104i) q^{24} +(1.32727 - 4.08493i) q^{26} +(0.809017 + 0.587785i) q^{27} +(5.23675 + 3.80472i) q^{28} +(-2.18554 + 6.72639i) q^{29} +(-2.87124 + 2.08608i) q^{31} +5.79877 q^{32} +(2.72789 + 1.88643i) q^{33} -4.24094 q^{34} +(-0.473194 - 1.45634i) q^{36} +(-1.95446 + 6.01521i) q^{37} +(1.55669 + 1.13100i) q^{38} +(5.07554 + 3.68760i) q^{39} +(2.71142 + 8.34490i) q^{41} +(2.34131 - 1.70106i) q^{42} -9.83046 q^{43} +(-1.68150 - 4.79227i) q^{44} +(-0.252887 + 0.183733i) q^{46} +(-3.44014 - 10.5877i) q^{47} +(-0.434916 + 1.33853i) q^{48} +(-8.79304 - 6.38851i) q^{49} +(1.91422 - 5.89136i) q^{51} +(-2.96868 - 9.13667i) q^{52} +(-1.52969 + 1.11139i) q^{53} -0.684625 q^{54} -10.2196 q^{56} +(-2.27378 + 1.65200i) q^{57} +(-1.49627 - 4.60505i) q^{58} +(-2.65096 + 8.15882i) q^{59} +(3.39592 + 2.46728i) q^{61} +(0.750840 - 2.31085i) q^{62} +(1.30626 + 4.02026i) q^{63} +(-0.934536 + 0.678980i) q^{64} +(-2.27003 + 0.0528928i) q^{66} -10.0915 q^{67} +(-7.67403 + 5.57551i) q^{68} +(-0.141091 - 0.434233i) q^{69} +(1.16522 + 0.846580i) q^{71} +(1.95589 + 1.42104i) q^{72} +(0.435409 - 1.34005i) q^{73} +(-1.33807 - 4.11817i) q^{74} +4.30377 q^{76} +(4.64180 + 13.2291i) q^{77} -4.29514 q^{78} +(-6.19218 + 4.49888i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-4.85988 - 3.53091i) q^{82} +(-1.39266 - 1.01182i) q^{83} +(2.00026 - 6.15617i) q^{84} +(5.44483 - 3.95590i) q^{86} +7.07254 q^{87} +(6.59497 + 4.56065i) q^{88} -12.6663 q^{89} +(8.19511 + 25.2219i) q^{91} +(-0.216051 + 0.664935i) q^{92} +(2.87124 + 2.08608i) q^{93} +(6.16602 + 4.47988i) q^{94} +(-1.79192 - 5.51496i) q^{96} +(2.94580 - 2.14025i) q^{97} +7.44105 q^{98} +(0.951139 - 3.17732i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 4 q^{3} - 6 q^{4} - 2 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 - 2 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	$ 16 q + 2 q^{2} + 4 q^{3} - 6 q^{4} - 2 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 3 q^{11} - 14 q^{12} - 11 q^{13} + 4 q^{14} + 16 q^{16} - 17 q^{17} - 3 q^{18} + 8 q^{19} - 16 q^{21} - 23 q^{22} - 14 q^{23} - q^{24} + 33 q^{26} + 4 q^{27} + 7 q^{28} + 4 q^{29} - 5 q^{31} + 24 q^{32} + 12 q^{33} - 16 q^{34} - 6 q^{36} + 2 q^{37} - 3 q^{38} + 11 q^{39} + 2 q^{41} - 4 q^{42} + 22 q^{43} - 40 q^{46} - 20 q^{47} + 9 q^{48} - 26 q^{49} - 18 q^{51} - 43 q^{52} + 40 q^{53} - 2 q^{54} - 8 q^{56} + 2 q^{57} + 26 q^{58} + 6 q^{59} - 2 q^{61} + 26 q^{62} - 4 q^{63} + 4 q^{64} - 7 q^{66} - 12 q^{67} - 56 q^{68} + 4 q^{69} + 11 q^{71} + q^{72} - 21 q^{73} + 66 q^{74} - 10 q^{76} + 23 q^{77} + 2 q^{78} - 7 q^{79} - 4 q^{81} + 20 q^{82} + 13 q^{83} + 18 q^{84} + 37 q^{86} + 56 q^{87} + 26 q^{88} + 42 q^{89} + 2 q^{91} + 92 q^{92} + 5 q^{93} + 88 q^{94} + 11 q^{96} - 27 q^{97} - 54 q^{98} + 8 q^{99}+O(q^{100}) $ 16 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 - 2 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 3 * q^11 - 14 * q^12 - 11 * q^13 + 4 * q^14 + 16 * q^16 - 17 * q^17 - 3 * q^18 + 8 * q^19 - 16 * q^21 - 23 * q^22 - 14 * q^23 - q^24 + 33 * q^26 + 4 * q^27 + 7 * q^28 + 4 * q^29 - 5 * q^31 + 24 * q^32 + 12 * q^33 - 16 * q^34 - 6 * q^36 + 2 * q^37 - 3 * q^38 + 11 * q^39 + 2 * q^41 - 4 * q^42 + 22 * q^43 - 40 * q^46 - 20 * q^47 + 9 * q^48 - 26 * q^49 - 18 * q^51 - 43 * q^52 + 40 * q^53 - 2 * q^54 - 8 * q^56 + 2 * q^57 + 26 * q^58 + 6 * q^59 - 2 * q^61 + 26 * q^62 - 4 * q^63 + 4 * q^64 - 7 * q^66 - 12 * q^67 - 56 * q^68 + 4 * q^69 + 11 * q^71 + q^72 - 21 * q^73 + 66 * q^74 - 10 * q^76 + 23 * q^77 + 2 * q^78 - 7 * q^79 - 4 * q^81 + 20 * q^82 + 13 * q^83 + 18 * q^84 + 37 * q^86 + 56 * q^87 + 26 * q^88 + 42 * q^89 + 2 * q^91 + 92 * q^92 + 5 * q^93 + 88 * q^94 + 11 * q^96 - 27 * q^97 - 54 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	−0.553874	+	0.402413i	−0.391648	+	0.284549i	−0.766130	−	0.642685i	$-0.777820\pi$
$2$	−0.553874	+	0.402413i	−0.391648	+	0.284549i	0.374483	+	0.927234i	$0.377820\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−0.473194	+	1.45634i	−0.236597	+	0.728171i
$5$		0			0
$5$		0			0
$6$	0.553874	+	0.402413i	0.226118	+	0.164284i
$7$	1.30626	−	4.02026i	0.493720	−	1.51951i	−0.325221	−	0.945638i	$-0.605439\pi$
$7$	1.30626	−	4.02026i	0.493720	−	1.51951i	0.818942	−	0.573877i	$-0.194561\pi$
$8$	−0.747082	−	2.29928i	−0.264134	−	0.812919i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	−2.63707	+	2.01144i	−0.795106	+	0.606471i
$11$	−2.63707	+	2.01144i	−0.795106	+	0.606471i
$12$	1.53129			0.442045
$13$	−5.07554	+	3.68760i	−1.40770	+	1.02276i	−0.414050	+	0.910254i	$0.635886\pi$
$13$	−5.07554	+	3.68760i	−1.40770	+	1.02276i	−0.993652	+	0.112501i	$0.964114\pi$
$14$	0.894299	+	2.75237i	0.239012	+	0.735602i
$15$		0			0
$16$	−1.13863	−	0.827260i	−0.284656	−	0.206815i
$17$	5.01149	+	3.64106i	1.21546	+	0.883086i	0.995715	−	0.0924702i	$-0.0294763\pi$
$17$	5.01149	+	3.64106i	1.21546	+	0.883086i	0.219749	+	0.975557i	$0.429476\pi$
$18$	0.211561	−	0.651117i	0.0498654	−	0.153470i
$19$	−0.868508	−	2.67299i	−0.199250	−	0.613227i	−0.999901	−	0.0140961i	$-0.995513\pi$
$19$	−0.868508	−	2.67299i	−0.199250	−	0.613227i	0.800651	−	0.599131i	$-0.204487\pi$
$20$		0			0
$21$	−4.22715			−0.922440
$22$	0.651174	−	2.17527i	0.138831	−	0.463769i
$23$	0.456579			0.0952034			0.0476017	−	0.998866i	$-0.484842\pi$
$23$	0.456579			0.0952034			0.0476017	+	0.998866i	$0.484842\pi$
$24$	−1.95589	+	1.42104i	−0.399244	+	0.290068i
$25$		0			0
$26$	1.32727	−	4.08493i	0.260300	−	0.801120i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	5.23675	+	3.80472i	0.989653	+	0.719025i
$29$	−2.18554	+	6.72639i	−0.405844	+	1.24906i	0.514345	+	0.857583i	$0.328035\pi$
$29$	−2.18554	+	6.72639i	−0.405844	+	1.24906i	−0.920189	+	0.391475i	$0.871965\pi$
$30$		0			0
$31$	−2.87124	+	2.08608i	−0.515690	+	0.374671i	−0.814978	−	0.579492i	$-0.803251\pi$
$31$	−2.87124	+	2.08608i	−0.515690	+	0.374671i	0.299288	+	0.954163i	$0.403251\pi$
$32$	5.79877			1.02509
$33$	2.72789	+	1.88643i	0.474864	+	0.328386i
$34$	−4.24094			−0.727315
$35$		0			0
$36$	−0.473194	−	1.45634i	−0.0788657	−	0.242724i
$37$	−1.95446	+	6.01521i	−0.321311	+	0.988895i	0.651767	+	0.758420i	$0.274028\pi$
$37$	−1.95446	+	6.01521i	−0.321311	+	0.988895i	−0.973078	+	0.230475i	$0.925972\pi$
$38$	1.55669	+	1.13100i	0.252529	+	0.183473i
$39$	5.07554	+	3.68760i	0.812737	+	0.590488i
$40$		0			0
$41$	2.71142	+	8.34490i	0.423453	+	1.30325i	0.904468	+	0.426542i	$0.140268\pi$
$41$	2.71142	+	8.34490i	0.423453	+	1.30325i	−0.481015	+	0.876712i	$0.659732\pi$
$42$	2.34131	−	1.70106i	0.361271	−	0.262479i
$43$	−9.83046			−1.49913			−0.749565	−	0.661931i	$-0.769737\pi$
$43$	−9.83046			−1.49913			−0.749565	+	0.661931i	$0.769737\pi$
$44$	−1.68150	−	4.79227i	−0.253495	−	0.722462i
$45$		0			0
$46$	−0.252887	+	0.183733i	−0.0372862	+	0.0270900i
$47$	−3.44014	−	10.5877i	−0.501797	−	1.54437i	−0.806090	−	0.591793i	$-0.798420\pi$
$47$	−3.44014	−	10.5877i	−0.501797	−	1.54437i	0.304294	−	0.952578i	$-0.401580\pi$
$48$	−0.434916	+	1.33853i	−0.0627748	+	0.193201i
$49$	−8.79304	−	6.38851i	−1.25615	−	0.912645i
$50$		0			0
$51$	1.91422	−	5.89136i	0.268044	−	0.824955i
$52$	−2.96868	−	9.13667i	−0.411682	−	1.26703i
$53$	−1.52969	+	1.11139i	−0.210119	+	0.152660i	−0.687868	−	0.725836i	$-0.741453\pi$
$53$	−1.52969	+	1.11139i	−0.210119	+	0.152660i	0.477748	+	0.878497i	$0.341453\pi$
$54$	−0.684625			−0.0931657
$55$		0			0
$56$	−10.2196			−1.36565
$57$	−2.27378	+	1.65200i	−0.301170	+	0.218813i
$58$	−1.49627	−	4.60505i	−0.196470	−	0.604673i
$59$	−2.65096	+	8.15882i	−0.345126	+	1.06219i	0.616391	+	0.787440i	$0.288594\pi$
$59$	−2.65096	+	8.15882i	−0.345126	+	1.06219i	−0.961516	+	0.274747i	$0.911406\pi$
$60$		0			0
$61$	3.39592	+	2.46728i	0.434804	+	0.315903i	0.783567	−	0.621308i	$-0.213398\pi$
$61$	3.39592	+	2.46728i	0.434804	+	0.315903i	−0.348763	+	0.937211i	$0.613398\pi$
$62$	0.750840	−	2.31085i	0.0953568	−	0.293478i
$63$	1.30626	+	4.02026i	0.164573	+	0.506505i
$64$	−0.934536	+	0.678980i	−0.116817	+	0.0848725i
$65$		0			0
$66$	−2.27003	+	0.0528928i	−0.279421	+	0.00651065i
$67$	−10.0915			−1.23287			−0.616434	−	0.787406i	$-0.711423\pi$
$67$	−10.0915			−1.23287			−0.616434	+	0.787406i	$0.711423\pi$
$68$	−7.67403	+	5.57551i	−0.930613	+	0.676130i
$69$	−0.141091	−	0.434233i	−0.0169853	−	0.0522755i
$70$		0			0
$71$	1.16522	+	0.846580i	0.138286	+	0.100471i	0.654778	−	0.755822i	$-0.272762\pi$
$71$	1.16522	+	0.846580i	0.138286	+	0.100471i	−0.516492	+	0.856292i	$0.672762\pi$
$72$	1.95589	+	1.42104i	0.230504	+	0.167471i
$73$	0.435409	−	1.34005i	0.0509608	−	0.156841i	−0.922337	−	0.386385i	$-0.873724\pi$
$73$	0.435409	−	1.34005i	0.0509608	−	0.156841i	0.973298	+	0.229544i	$0.0737235\pi$
$74$	−1.33807	−	4.11817i	−0.155548	−	0.478727i
$75$		0			0
$76$	4.30377			0.493676
$77$	4.64180	+	13.2291i	0.528982	+	1.50760i
$78$	−4.29514			−0.486329
$79$	−6.19218	+	4.49888i	−0.696675	+	0.506164i	−0.878848	−	0.477103i	$-0.841687\pi$
$79$	−6.19218	+	4.49888i	−0.696675	+	0.506164i	0.182173	+	0.983267i	$0.441687\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−4.85988	−	3.53091i	−0.536684	−	0.389924i
$83$	−1.39266	−	1.01182i	−0.152864	−	0.111062i	0.508724	−	0.860930i	$-0.330117\pi$
$83$	−1.39266	−	1.01182i	−0.152864	−	0.111062i	−0.661588	+	0.749867i	$0.730117\pi$
$84$	2.00026	−	6.15617i	0.218246	−	0.671693i
$85$		0			0
$86$	5.44483	−	3.95590i	0.587131	−	0.426576i
$87$	7.07254			0.758256
$88$	6.59497	+	4.56065i	0.703026	+	0.486167i
$89$	−12.6663			−1.34262			−0.671310	−	0.741176i	$-0.734268\pi$
$89$	−12.6663			−1.34262			−0.671310	+	0.741176i	$0.734268\pi$
$90$		0			0
$91$	8.19511	+	25.2219i	0.859081	+	2.64398i
$92$	−0.216051	+	0.664935i	−0.0225248	+	0.0693243i
$93$	2.87124	+	2.08608i	0.297734	+	0.216316i
$94$	6.16602	+	4.47988i	0.635976	+	0.462064i
$95$		0			0
$96$	−1.79192	−	5.51496i	−0.182887	−	0.562868i
$97$	2.94580	−	2.14025i	0.299101	−	0.217310i	−0.428105	−	0.903729i	$-0.640819\pi$
$97$	2.94580	−	2.14025i	0.299101	−	0.217310i	0.727206	+	0.686420i	$0.240819\pi$
$98$	7.44105			0.751660
$99$	0.951139	−	3.17732i	0.0955930	−	0.319332i
$100$		0			0
$101$	0.944734	−	0.686389i	0.0940045	−	0.0682983i	−0.539790	−	0.841800i	$-0.681496\pi$
$101$	0.944734	−	0.686389i	0.0940045	−	0.0682983i	0.633795	+	0.773501i	$0.281496\pi$
$102$	1.31052	+	4.03337i	0.129761	+	0.399363i
$103$	4.25301	−	13.0894i	0.419061	−	1.28974i	−0.489506	−	0.872000i	$-0.662823\pi$
$103$	4.25301	−	13.0894i	0.419061	−	1.28974i	0.908567	−	0.417738i	$-0.137177\pi$
$104$	12.2707	+	8.91517i	1.20324	+	0.874204i
$105$		0			0
$106$	0.400020	−	1.23113i	0.0388533	−	0.119578i
$107$	3.97078	+	12.2208i	0.383870	+	1.18143i	0.937297	+	0.348532i	$0.113320\pi$
$107$	3.97078	+	12.2208i	0.383870	+	1.18143i	−0.553427	+	0.832898i	$0.686680\pi$
$108$	−1.23884	+	0.900069i	−0.119207	+	0.0866091i
$109$	1.58733			0.152039			0.0760196	−	0.997106i	$-0.475779\pi$
$109$	1.58733			0.152039			0.0760196	+	0.997106i	$0.475779\pi$
$110$		0			0
$111$	6.32477			0.600321
$112$	−4.81314	+	3.49695i	−0.454799	+	0.330431i
$113$	0.899155	+	2.76731i	0.0845854	+	0.260327i	0.984400	−	0.175946i	$-0.0562983\pi$
$113$	0.899155	+	2.76731i	0.0845854	+	0.260327i	−0.899814	+	0.436273i	$0.856298\pi$
$114$	0.594603	−	1.83000i	0.0556897	−	0.171395i
$115$		0			0
$116$	−8.76173	−	6.36577i	−0.813506	−	0.591047i
$117$	1.93868	−	5.96666i	0.179231	−	0.551618i
$118$	−1.81492	−	5.58574i	−0.167077	−	0.514209i
$119$	21.1843	−	15.3913i	1.94196	−	1.41092i
$120$		0			0
$121$	2.90824	−	10.6086i	0.264386	−	0.964417i
$122$	−2.87378			−0.260180
$123$	7.09859	−	5.15743i	0.640059	−	0.465030i
$124$	−1.67939	−	5.16863i	−0.150814	−	0.464156i
$125$		0			0
$126$	−2.34131	−	1.70106i	−0.208580	−	0.151542i
$127$	−13.8503	−	10.0628i	−1.22901	−	0.892931i	−0.232198	−	0.972668i	$-0.574592\pi$
$127$	−13.8503	−	10.0628i	−1.22901	−	0.892931i	−0.996816	+	0.0797374i	$0.974592\pi$
$128$	−3.33945	+	10.2778i	−0.295169	+	0.908436i
$129$	3.03778	+	9.34932i	0.267461	+	0.823162i
$130$		0			0
$131$	8.11280			0.708818			0.354409	−	0.935090i	$-0.384682\pi$
$131$	8.11280			0.708818			0.354409	+	0.935090i	$0.384682\pi$
$132$	−4.03811	+	3.08009i	−0.351472	+	0.268087i
$133$	−11.8806			−1.03018
$134$	5.58940	−	4.06093i	0.482850	−	0.350811i
$135$		0			0
$136$	4.62783	−	14.2430i	0.396833	−	1.22133i
$137$	7.32401	+	5.32120i	0.625732	+	0.454621i	0.854919	−	0.518761i	$-0.173607\pi$
$137$	7.32401	+	5.32120i	0.625732	+	0.454621i	−0.229187	+	0.973382i	$0.573607\pi$
$138$	0.252887	+	0.183733i	0.0215272	+	0.0156404i
$139$	−1.52989	+	4.70850i	−0.129763	+	0.399370i	−0.994739	−	0.102444i	$-0.967334\pi$
$139$	−1.52989	+	4.70850i	−0.129763	+	0.399370i	0.864976	+	0.501814i	$0.167334\pi$
$140$		0			0
$141$	−9.00641	+	6.54354i	−0.758477	+	0.551066i
$142$	−0.986058			−0.0827482
$143$	5.96717	−	19.9336i	0.499000	−	1.66693i
$144$	1.40742			0.117285
$145$		0			0
$146$	0.298092	+	0.917433i	0.0246703	+	0.0759273i
$147$	−3.35864	+	10.3368i	−0.277016	+	0.852568i
$148$	−7.83536	−	5.69273i	−0.644063	−	0.467939i
$149$	16.0477	+	11.6593i	1.31468	+	0.955170i	0.999982	+	0.00597828i	$0.00190296\pi$
$149$	16.0477	+	11.6593i	1.31468	+	0.955170i	0.314697	+	0.949192i	$0.398097\pi$
$150$		0			0
$151$	−2.16437	−	6.66124i	−0.176134	−	0.542084i	0.823550	−	0.567244i	$-0.191990\pi$
$151$	−2.16437	−	6.66124i	−0.176134	−	0.542084i	−0.999683	+	0.0251602i	$0.991990\pi$
$152$	−5.49712	+	3.99389i	−0.445876	+	0.323948i
$153$	−6.19454			−0.500799
$154$	−7.89455	−	5.45936i	−0.636161	−	0.439928i
$155$		0			0
$156$	−7.77212	+	5.64677i	−0.622267	+	0.452104i
$157$	−0.987852	−	3.04030i	−0.0788392	−	0.242642i	0.903867	−	0.427813i	$-0.140716\pi$
$157$	−0.987852	−	3.04030i	−0.0788392	−	0.242642i	−0.982706	+	0.185171i	$0.940716\pi$
$158$	1.61928	−	4.98363i	0.128823	−	0.396476i
$159$	1.52969	+	1.11139i	0.121312	+	0.0881386i
$160$		0			0
$161$	0.596412	−	1.83557i	0.0470038	−	0.144663i
$162$	0.211561	+	0.651117i	0.0166218	+	0.0511566i
$163$	7.75631	−	5.63529i	0.607521	−	0.441390i	−0.241019	−	0.970520i	$-0.577482\pi$
$163$	7.75631	−	5.63529i	0.607521	−	0.441390i	0.848541	+	0.529130i	$0.177482\pi$
$164$	−13.4360			−1.04918
$165$		0			0
$166$	1.17853			0.0914715
$167$	2.68262	−	1.94904i	0.207588	−	0.150821i	−0.479134	−	0.877742i	$-0.659049\pi$
$167$	2.68262	−	1.94904i	0.207588	−	0.150821i	0.686722	+	0.726921i	$0.259049\pi$
$168$	3.15803	+	9.71941i	0.243647	+	0.749869i
$169$	8.14553	−	25.0694i	0.626579	−	1.92841i
$170$		0			0
$171$	2.27378	+	1.65200i	0.173881	+	0.126332i
$172$	4.65171	−	14.3165i	0.354690	−	1.09162i
$173$	−3.91697	−	12.0552i	−0.297802	−	0.916541i	−0.982266	−	0.187494i	$-0.939964\pi$
$173$	−3.91697	−	12.0552i	−0.297802	−	0.916541i	0.684464	−	0.729047i	$-0.260036\pi$
$174$	−3.91729	+	2.84608i	−0.296969	+	0.215761i
$175$		0			0
$176$	4.66661	−	0.108734i	0.351759	−	0.00819616i
$177$	8.57869			0.644814
$178$	7.01551	−	5.09706i	0.525834	−	0.382041i
$179$	−4.13485	−	12.7258i	−0.309053	−	0.951167i	−0.978134	−	0.207977i	$-0.933312\pi$
$179$	−4.13485	−	12.7258i	−0.309053	−	0.951167i	0.669081	−	0.743190i	$-0.266688\pi$
$180$		0			0
$181$	2.81681	+	2.04653i	0.209372	+	0.152118i	0.687529	−	0.726157i	$-0.258695\pi$
$181$	2.81681	+	2.04653i	0.209372	+	0.152118i	−0.478158	+	0.878274i	$0.658695\pi$
$182$	−14.6887	−	10.6720i	−1.08880	−	0.791058i
$183$	1.29713	−	3.99215i	0.0958864	−	0.295108i
$184$	−0.341102	−	1.04981i	−0.0251464	−	0.0773927i
$185$		0			0
$186$	−2.42977			−0.178159
$187$	−20.5394	+	0.478577i	−1.50199	+	0.0349970i
$188$	17.0471			1.24329
$189$	3.41984	−	2.48466i	0.248756	−	0.180732i
$190$		0			0
$191$	1.79769	−	5.53271i	0.130076	−	0.400333i	−0.864716	−	0.502262i	$-0.832501\pi$
$191$	1.79769	−	5.53271i	0.130076	−	0.400333i	0.994792	+	0.101929i	$0.0325014\pi$
$192$	0.934536	+	0.678980i	0.0674443	+	0.0490012i
$193$	−0.0777131	−	0.0564619i	−0.00559391	−	0.00406421i	0.584985	−	0.811044i	$-0.301100\pi$
$193$	−0.0777131	−	0.0564619i	−0.00559391	−	0.00406421i	−0.590579	+	0.806980i	$0.701100\pi$
$194$	−0.770338	+	2.37086i	−0.0553071	+	0.170218i
$195$		0			0
$196$	13.4647	−	9.78266i	0.961762	−	0.698761i
$197$	−7.33166			−0.522359			−0.261179	−	0.965290i	$-0.584111\pi$
$197$	−7.33166			−0.522359			−0.261179	+	0.965290i	$0.584111\pi$
$198$	0.751782	+	2.14258i	0.0534268	+	0.152267i
$199$	10.5380			0.747020			0.373510	−	0.927626i	$-0.378154\pi$
$199$	10.5380			0.747020			0.373510	+	0.927626i	$0.378154\pi$
$200$		0			0
$201$	3.11843	+	9.59755i	0.219957	+	0.676959i
$202$	−0.247051	+	0.760346i	−0.0173825	+	0.0534977i
$203$	24.1869	+	17.5728i	1.69759	+	1.23337i
$204$	7.67403	+	5.57551i	0.537290	+	0.390364i
$205$		0			0
$206$	2.91172	+	8.96134i	0.202869	+	0.624366i
$207$	−0.369380	+	0.268371i	−0.0256737	+	0.0186530i
$208$	8.82974			0.612233
$209$	7.66687	+	5.30191i	0.530329	+	0.366741i
$210$		0			0
$211$	−2.05421	+	1.49247i	−0.141417	+	0.102746i	−0.656245	−	0.754548i	$-0.727856\pi$
$211$	−2.05421	+	1.49247i	−0.141417	+	0.102746i	0.514827	+	0.857294i	$0.327856\pi$
$212$	−0.894716	−	2.75365i	−0.0614493	−	0.189122i
$213$	0.445074	−	1.36980i	0.0304959	−	0.0938569i
$214$	−7.11712	−	5.17089i	−0.486516	−	0.353475i
$215$		0			0
$216$	0.747082	−	2.29928i	0.0508325	−	0.156446i
$217$	4.63598	+	14.2681i	0.314711	+	0.968581i
$218$	−0.879183	+	0.638764i	−0.0595458	+	0.0432625i
$219$	−1.40901			−0.0952123
$220$		0			0
$221$	−38.8628			−2.61419
$222$	−3.50312	+	2.54517i	−0.235114	+	0.170820i
$223$	3.70247	+	11.3950i	0.247936	+	0.763069i	0.995140	+	0.0984735i	$0.0313960\pi$
$223$	3.70247	+	11.3950i	0.247936	+	0.763069i	−0.747204	+	0.664595i	$0.768604\pi$
$224$	7.57471	−	23.3126i	0.506107	−	1.55764i
$225$		0			0
$226$	−1.61162	−	1.17091i	−0.107203	−	0.0778878i
$227$	−2.58090	+	7.94321i	−0.171301	+	0.527209i	−0.999445	−	0.0333054i	$-0.989397\pi$
$227$	−2.58090	+	7.94321i	−0.171301	+	0.527209i	0.828145	+	0.560515i	$0.189397\pi$
$228$	−1.32994	−	4.09312i	−0.0880772	−	0.271074i
$229$	12.2199	−	8.87827i	0.807513	−	0.586693i	−0.105595	−	0.994409i	$-0.533675\pi$
$229$	12.2199	−	8.87827i	0.807513	−	0.586693i	0.913109	+	0.407716i	$0.133675\pi$
$230$		0			0
$231$	11.1473	−	8.50264i	0.733437	−	0.559433i
$232$	17.0986			1.12258
$233$	−12.9073	+	9.37772i	−0.845587	+	0.614355i	−0.923926	−	0.382572i	$-0.875038\pi$
$233$	−12.9073	+	9.37772i	−0.845587	+	0.614355i	0.0783385	+	0.996927i	$0.475038\pi$
$234$	1.32727	+	4.08493i	0.0867665	+	0.267040i
$235$		0			0
$236$	−10.6276	−	7.72141i	−0.691798	−	0.502621i
$237$	6.19218	+	4.49888i	0.402226	+	0.292234i
$238$	−5.53977	+	17.0497i	−0.359090	+	1.10517i
$239$	2.22323	+	6.84241i	0.143809	+	0.442599i	0.996856	−	0.0792355i	$-0.0252479\pi$
$239$	2.22323	+	6.84241i	0.143809	+	0.442599i	−0.853047	+	0.521834i	$0.825248\pi$
$240$		0			0
$241$	−0.529998			−0.0341402			−0.0170701	−	0.999854i	$-0.505434\pi$
$241$	−0.529998			−0.0341402			−0.0170701	+	0.999854i	$0.505434\pi$
$242$	2.65823	+	7.04613i	0.170878	+	0.452942i
$243$	−1.00000			−0.0641500
$244$	−5.20014	+	3.77812i	−0.332905	+	0.241869i
$245$		0			0
$246$	−1.85631	+	5.71313i	−0.118354	+	0.364256i
$247$	14.2651	+	10.3642i	0.907665	+	0.659457i
$248$	6.94154	+	5.04332i	0.440788	+	0.320251i
$249$	−0.531948	+	1.63717i	−0.0337108	+	0.103751i
$250$		0			0
$251$	7.83108	−	5.68962i	0.494294	−	0.359125i	−0.312539	−	0.949905i	$-0.601180\pi$
$251$	7.83108	−	5.68962i	0.494294	−	0.359125i	0.806833	+	0.590779i	$0.201180\pi$
$252$	−6.47298			−0.407760
$253$	−1.20403	+	0.918380i	−0.0756967	+	0.0577381i
$254$	11.7207			0.735423
$255$		0			0
$256$	−3.00020	−	9.23366i	−0.187512	−	0.577104i
$257$	2.50018	−	7.69477i	0.155957	−	0.479987i	−0.842300	−	0.539010i	$-0.818799\pi$
$257$	2.50018	−	7.69477i	0.155957	−	0.479987i	0.998257	+	0.0590232i	$0.0187986\pi$
$258$	−5.44483	−	3.95590i	−0.338980	−	0.246284i
$259$	21.6297	+	15.7149i	1.34400	+	0.976475i
$260$		0			0
$261$	−2.18554	−	6.72639i	−0.135281	−	0.416353i
$262$	−4.49346	+	3.26469i	−0.277607	+	0.201693i
$263$	−12.7851			−0.788360			−0.394180	−	0.919033i	$-0.628971\pi$
$263$	−12.7851			−0.788360			−0.394180	+	0.919033i	$0.628971\pi$
$264$	2.29948	−	7.68151i	0.141523	−	0.472764i
$265$		0			0
$266$	6.58036	−	4.78091i	0.403468	−	0.293137i
$267$	3.91409	+	12.0463i	0.239538	+	0.737223i
$268$	4.77522	−	14.6966i	0.291693	−	0.897739i
$269$	−13.6976	−	9.95186i	−0.835155	−	0.606775i	0.0858582	−	0.996307i	$-0.472637\pi$
$269$	−13.6976	−	9.95186i	−0.835155	−	0.606775i	−0.921013	+	0.389532i	$0.872637\pi$
$270$		0			0
$271$	−7.14098	+	21.9777i	−0.433784	+	1.33505i	0.460544	+	0.887637i	$0.347654\pi$
$271$	−7.14098	+	21.9777i	−0.433784	+	1.33505i	−0.894328	+	0.447412i	$0.852346\pi$
$272$	−2.69411	−	8.29161i	−0.163354	−	0.502752i
$273$	21.4551	−	15.5880i	1.29852	−	0.943430i
$274$	−6.19790			−0.374429
$275$		0			0
$276$	0.699154			0.0420841
$277$	−7.64680	+	5.55573i	−0.459452	+	0.333811i	−0.793316	−	0.608810i	$-0.791647\pi$
$277$	−7.64680	+	5.55573i	−0.459452	+	0.333811i	0.333864	+	0.942621i	$0.391647\pi$
$278$	−1.04740	−	3.22356i	−0.0628188	−	0.193336i
$279$	1.09672	−	3.37535i	0.0656587	−	0.202077i
$280$		0			0
$281$	18.1452	+	13.1833i	1.08245	+	0.786449i	0.978109	−	0.208092i	$-0.0667254\pi$
$281$	18.1452	+	13.1833i	1.08245	+	0.786449i	0.104345	+	0.994541i	$0.466725\pi$
$282$	2.35521	−	7.24859i	0.140251	−	0.431647i
$283$	2.77383	+	8.53697i	0.164887	+	0.507470i	0.999028	−	0.0440812i	$-0.0140360\pi$
$283$	2.77383	+	8.53697i	0.164887	+	0.507470i	−0.834141	+	0.551551i	$0.814036\pi$
$284$	−1.78428	+	1.29636i	−0.105878	+	0.0769247i
$285$		0			0
$286$	4.71646	+	13.4419i	0.278890	+	0.794839i
$287$	37.0905			2.18938
$288$	−4.69131	+	3.40843i	−0.276438	+	0.200844i
$289$	6.60441	+	20.3263i	0.388494	+	1.19566i
$290$		0			0
$291$	−2.94580	−	2.14025i	−0.172686	−	0.125464i
$292$	1.74554	+	1.26821i	0.102150	+	0.0742163i
$293$	0.834337	−	2.56782i	0.0487425	−	0.150014i	−0.923723	−	0.383061i	$-0.874870\pi$
$293$	0.834337	−	2.56782i	0.0487425	−	0.150014i	0.972465	+	0.233048i	$0.0748698\pi$
$294$	−2.29941	−	7.07686i	−0.134104	−	0.412731i
$295$		0			0
$296$	15.2908			0.888761
$297$	−3.31572	+	0.0772580i	−0.192398	+	0.00448296i
$298$	−13.5803			−0.786684
$299$	−2.31739	+	1.68368i	−0.134018	+	0.0973697i
$300$		0			0
$301$	−12.8411	+	39.5210i	−0.740151	+	2.27795i
$302$	3.87935	+	2.81852i	0.223232	+	0.162187i
$303$	−0.944734	−	0.686389i	−0.0542735	−	0.0394320i
$304$	−1.22236	+	3.76202i	−0.0701069	+	0.215767i
$305$		0			0
$306$	3.43099	−	2.49276i	0.196137	−	0.142502i
$307$	−6.23363			−0.355772			−0.177886	−	0.984051i	$-0.556926\pi$
$307$	−6.23363			−0.355772			−0.177886	+	0.984051i	$0.556926\pi$
$308$	−21.4626	+	0.500089i	−1.22295	+	0.0284952i
$309$	−13.7630			−0.782951
$310$		0			0
$311$	−6.97254	−	21.4593i	−0.395376	−	1.21684i	−0.928668	−	0.370912i	$-0.879045\pi$
$311$	−6.97254	−	21.4593i	−0.395376	−	1.21684i	0.533292	−	0.845931i	$-0.320955\pi$
$312$	4.68698	−	14.4250i	0.265348	−	0.816657i
$313$	1.33282	+	0.968354i	0.0753357	+	0.0547346i	0.624816	−	0.780772i	$-0.285174\pi$
$313$	1.33282	+	0.968354i	0.0753357	+	0.0547346i	−0.549480	+	0.835507i	$0.685174\pi$
$314$	1.77060	+	1.28642i	0.0999207	+	0.0725966i
$315$		0			0
$316$	−3.62181	−	11.1468i	−0.203743	−	0.627055i
$317$	−3.14995	+	2.28857i	−0.176919	+	0.128539i	−0.672720	−	0.739897i	$-0.734874\pi$
$317$	−3.14995	+	2.28857i	−0.176919	+	0.128539i	0.495802	+	0.868436i	$0.334874\pi$
$318$	−1.29449			−0.0725914
$319$	−7.76630	−	22.1340i	−0.434829	−	1.23927i
$320$		0			0
$321$	10.3956	−	7.55287i	0.580228	−	0.421560i
$322$	0.408319	+	1.25668i	0.0227547	+	0.0700318i
$323$	5.38001	−	16.5580i	0.299352	−	0.921310i
$324$	1.23884	+	0.900069i	0.0688243	+	0.0500038i
$325$		0			0
$326$	−2.02830	+	6.24248i	−0.112337	+	0.345739i
$327$	−0.490513	−	1.50965i	−0.0271255	−	0.0834836i
$328$	17.1616	−	12.4687i	0.947592	−	0.688466i
$329$	−47.0589			−2.59444
$330$		0			0
$331$	7.67417			0.421811			0.210905	−	0.977506i	$-0.432359\pi$
$331$	7.67417			0.421811			0.210905	+	0.977506i	$0.432359\pi$
$332$	2.13256	−	1.54939i	0.117039	−	0.0850341i
$333$	−1.95446	−	6.01521i	−0.107104	−	0.329632i
$334$	−0.701516	+	2.15904i	−0.0383853	+	0.118138i
$335$		0			0
$336$	4.81314	+	3.49695i	0.262578	+	0.190774i
$337$	5.70797	−	17.5673i	0.310933	−	0.956954i	−0.666463	−	0.745538i	$-0.732193\pi$
$337$	5.70797	−	17.5673i	0.310933	−	0.956954i	0.977396	−	0.211416i	$-0.0678074\pi$
$338$	5.57664	+	17.1631i	0.303329	+	0.933551i
$339$	2.35402	−	1.71029i	0.127853	−	0.0928904i
$340$		0			0
$341$	3.37564	−	11.2764i	0.182801	−	0.610654i
$342$	−1.92418			−0.104048
$343$	−13.2306	+	9.61261i	−0.714387	+	0.519032i
$344$	7.34416	+	22.6030i	0.395971	+	1.21867i
$345$		0			0
$346$	7.02068	+	5.10082i	0.377434	+	0.274222i
$347$	−16.9208	−	12.2937i	−0.908356	−	0.659959i	0.0322427	−	0.999480i	$-0.489735\pi$
$347$	−16.9208	−	12.2937i	−0.908356	−	0.659959i	−0.940598	+	0.339521i	$0.889735\pi$
$348$	−3.34668	+	10.3000i	−0.179401	+	0.552140i
$349$	2.57836	+	7.93536i	0.138016	+	0.424770i	0.996047	−	0.0888281i	$-0.0283122\pi$
$349$	2.57836	+	7.93536i	0.138016	+	0.424770i	−0.858031	+	0.513598i	$0.828312\pi$
$350$		0			0
$351$	−6.27371			−0.334866
$352$	−15.2918	+	11.6639i	−0.815053	+	0.621686i
$353$	−22.8476			−1.21606			−0.608028	−	0.793915i	$-0.708039\pi$
$353$	−22.8476			−1.21606			−0.608028	+	0.793915i	$0.708039\pi$
$354$	−4.75151	+	3.45217i	−0.252540	+	0.183481i
$355$		0			0
$356$	5.99360	−	18.4464i	0.317660	−	0.977657i
$357$	−21.1843	−	15.3913i	−1.12119	−	0.814594i
$358$	7.41119	+	5.38454i	0.391693	+	0.284582i
$359$	−9.86049	+	30.3475i	−0.520417	+	1.60168i	0.252788	+	0.967522i	$0.418653\pi$
$359$	−9.86049	+	30.3475i	−0.520417	+	1.60168i	−0.773205	+	0.634156i	$0.781347\pi$
$360$		0			0
$361$	8.98073	−	6.52488i	0.472670	−	0.343415i
$362$	−2.38371			−0.125285
$363$	−10.9881	+	0.512332i	−0.576724	+	0.0268905i
$364$	−40.6096			−2.12852
$365$		0			0
$366$	0.888047	+	2.73313i	0.0464189	+	0.142863i
$367$	−8.09458	+	24.9126i	−0.422534	+	1.30042i	0.482803	+	0.875729i	$0.339619\pi$
$367$	−8.09458	+	24.9126i	−0.422534	+	1.30042i	−0.905336	+	0.424695i	$0.860381\pi$
$368$	−0.519873	−	0.377710i	−0.0271002	−	0.0196895i
$369$	−7.09859	−	5.15743i	−0.369538	−	0.268485i
$370$		0			0
$371$	2.46988	+	7.60151i	0.128230	+	0.394651i
$372$	−4.39670	+	3.19439i	−0.227958	+	0.165621i
$373$	−27.5995			−1.42905			−0.714523	−	0.699612i	$-0.753356\pi$
$373$	−27.5995			−1.42905			−0.714523	+	0.699612i	$0.753356\pi$
$374$	11.1836	−	8.53038i	0.578292	−	0.441096i
$375$		0			0
$376$	−21.7740	+	15.8197i	−1.12291	+	0.815840i
$377$	−13.7114	−	42.1994i	−0.706174	−	2.17338i
$378$	−0.894299	+	2.75237i	−0.0459978	+	0.141567i
$379$	18.5010	+	13.4418i	0.950332	+	0.690457i	0.950885	−	0.309543i	$-0.100176\pi$
$379$	18.5010	+	13.4418i	0.950332	+	0.690457i	−0.000553130		1.00000i	$0.500176\pi$
$380$		0			0
$381$	−5.29034	+	16.2820i	−0.271032	+	0.834152i
$382$	1.23074	+	3.78783i	0.0629702	+	0.193802i
$383$	1.68687	−	1.22558i	0.0861950	−	0.0626243i	−0.543853	−	0.839180i	$-0.683035\pi$
$383$	1.68687	−	1.22558i	0.0861950	−	0.0626243i	0.630048	+	0.776556i	$0.283035\pi$
$384$	10.8067			0.551477
$385$		0			0
$386$	0.0657642			0.00334731
$387$	7.95301	−	5.77820i	0.404274	−	0.293722i
$388$	1.72300	+	5.30285i	0.0874721	+	0.269211i
$389$	7.21589	−	22.2082i	0.365860	−	1.12600i	−0.583581	−	0.812055i	$-0.698349\pi$
$389$	7.21589	−	22.2082i	0.365860	−	1.12600i	0.949441	−	0.313946i	$-0.101651\pi$
$390$		0			0
$391$	2.28814	+	1.66243i	0.115716	+	0.0840728i
$392$	−8.11988	+	24.9904i	−0.410116	+	1.26221i
$393$	−2.50699	−	7.71573i	−0.126461	−	0.389207i
$394$	4.06081	−	2.95035i	0.204581	−	0.148637i
$395$		0			0
$396$	4.17718	+	2.88867i	0.209911	+	0.145161i
$397$	27.5109			1.38073			0.690365	−	0.723461i	$-0.257450\pi$
$397$	27.5109			1.38073			0.690365	+	0.723461i	$0.257450\pi$
$398$	−5.83673	+	4.24063i	−0.292569	+	0.212564i
$399$	3.67131	+	11.2991i	0.183796	+	0.565665i
$400$		0			0
$401$	7.01763	+	5.09861i	0.350444	+	0.254612i	0.749055	−	0.662508i	$-0.230508\pi$
$401$	7.01763	+	5.09861i	0.350444	+	0.254612i	−0.398611	+	0.917120i	$0.630508\pi$
$402$	−5.58940	−	4.06093i	−0.278774	−	0.202541i
$403$	6.88049	−	21.1760i	0.342741	−	1.05485i
$404$	0.552575	+	1.70065i	0.0274916	+	0.0846105i
$405$		0			0
$406$	−20.4680			−1.01581
$407$	−6.94518	−	19.7938i	−0.344260	−	0.981142i
$408$	−14.9760			−0.741421
$409$	−4.54845	+	3.30464i	−0.224906	+	0.163404i	−0.694533	−	0.719461i	$-0.744389\pi$
$409$	−4.54845	+	3.30464i	−0.224906	+	0.163404i	0.469626	+	0.882865i	$0.344389\pi$
$410$		0			0
$411$	2.79752	−	8.60989i	0.137992	−	0.424694i
$412$	17.0502	+	12.3877i	0.840001	+	0.610296i
$413$	29.3377	+	21.3151i	1.44361	+	1.04885i
$414$	0.0965943	−	0.297287i	0.00474735	−	0.0146108i
$415$		0			0
$416$	−29.4319	+	21.3835i	−1.44302	+	1.04841i
$417$	4.95081			0.242442
$418$	−6.38004	+	0.148658i	−0.312058	+	0.00727109i
$419$	−19.3628			−0.945937			−0.472968	−	0.881079i	$-0.656817\pi$
$419$	−19.3628			−0.945937			−0.472968	+	0.881079i	$0.656817\pi$
$420$		0			0
$421$	−8.82438	−	27.1586i	−0.430074	−	1.32363i	−0.898051	−	0.439891i	$-0.855017\pi$
$421$	−8.82438	−	27.1586i	−0.430074	−	1.32363i	0.467978	−	0.883740i	$-0.344983\pi$
$422$	0.537183	−	1.65328i	0.0261496	−	0.0804803i
$423$	9.00641	+	6.54354i	0.437907	+	0.318158i
$424$	3.69819	+	2.68690i	0.179600	+	0.130487i
$425$		0			0
$426$	0.304709	+	0.937797i	0.0147632	+	0.0454364i
$427$	14.3551	−	10.4296i	0.694691	−	0.504722i
$428$	−19.6766			−0.951105
$429$	−20.8019	+	0.484694i	−1.00433	+	0.0234013i
$430$		0			0
$431$	4.24147	−	3.08161i	0.204304	−	0.148436i	−0.480929	−	0.876760i	$-0.659700\pi$
$431$	4.24147	−	3.08161i	0.204304	−	0.148436i	0.685233	+	0.728324i	$0.259700\pi$
$432$	−0.434916	−	1.33853i	−0.0209249	−	0.0644003i
$433$	−7.50382	+	23.0944i	−0.360610	+	1.10984i	0.592074	+	0.805884i	$0.298309\pi$
$433$	−7.50382	+	23.0944i	−0.360610	+	1.10984i	−0.952684	+	0.303961i	$0.901691\pi$
$434$	−8.30941	−	6.03714i	−0.398864	−	0.289792i
$435$		0			0
$436$	−0.751117	+	2.31170i	−0.0359720	+	0.110710i
$437$	−0.396543	−	1.22043i	−0.0189692	−	0.0583813i
$438$	0.780415	−	0.567005i	0.0372897	−	0.0270925i
$439$	−12.2291			−0.583661			−0.291831	−	0.956470i	$-0.594264\pi$
$439$	−12.2291			−0.583661			−0.291831	+	0.956470i	$0.594264\pi$
$440$		0			0
$441$	10.8688			0.517561
$442$	21.5251	−	15.6389i	1.02384	−	0.743865i
$443$	−5.60285	−	17.2438i	−0.266199	−	0.819277i	−0.991415	−	0.130755i	$-0.958260\pi$
$443$	−5.60285	−	17.2438i	−0.266199	−	0.819277i	0.725215	−	0.688522i	$-0.241740\pi$
$444$	−2.99284	+	9.21102i	−0.142034	+	0.437136i
$445$		0			0
$446$	−6.63621	−	4.82149i	−0.314234	−	0.228304i
$447$	6.12968	−	18.8652i	0.289924	−	0.892294i
$448$	1.50893	+	4.64400i	0.0712901	+	0.219408i
$449$	−32.6646	+	23.7322i	−1.54154	+	1.11999i	−0.592177	+	0.805808i	$0.701732\pi$
$449$	−32.6646	+	23.7322i	−1.54154	+	1.11999i	−0.949362	+	0.314186i	$0.898268\pi$
$450$		0			0
$451$	−23.9354	−	16.5522i	−1.12708	−	0.779413i
$452$	−4.45563			−0.209575
$453$	−5.66639	+	4.11687i	−0.266230	+	0.193428i
$454$	−1.76695	−	5.43812i	−0.0829272	−	0.255224i
$455$		0			0
$456$	5.49712	+	3.99389i	0.257426	+	0.187031i
$457$	4.73352	+	3.43910i	0.221425	+	0.160874i	0.692968	−	0.720969i	$-0.256303\pi$
$457$	4.73352	+	3.43910i	0.221425	+	0.160874i	−0.471543	+	0.881843i	$0.656303\pi$
$458$	−3.19555	+	9.83488i	−0.149318	+	0.459554i
$459$	1.91422	+	5.89136i	0.0893480	+	0.274985i
$460$		0			0
$461$	−11.3973			−0.530824			−0.265412	−	0.964135i	$-0.585508\pi$
$461$	−11.3973			−0.530824			−0.265412	+	0.964135i	$0.585508\pi$
$462$	−2.75261	+	9.19520i	−0.128063	+	0.427799i
$463$	13.3271			0.619363			0.309681	−	0.950840i	$-0.399778\pi$
$463$	13.3271			0.619363			0.309681	+	0.950840i	$0.399778\pi$
$464$	8.05298	−	5.85083i	0.373850	−	0.271618i
$465$		0			0
$466$	3.37531	−	10.3881i	0.156358	−	0.481222i
$467$	13.6268	+	9.90043i	0.630572	+	0.458137i	0.856598	−	0.515984i	$-0.172574\pi$
$467$	13.6268	+	9.90043i	0.630572	+	0.458137i	−0.226026	+	0.974121i	$0.572574\pi$
$468$	7.77212	+	5.64677i	0.359266	+	0.261022i
$469$	−13.1821	+	40.5703i	−0.608692	+	1.87336i
$470$		0			0
$471$	−2.58623	+	1.87901i	−0.119167	+	0.0865800i
$472$	20.7399			0.954632
$473$	25.9236	−	19.7733i	1.19197	−	0.909179i
$474$	−5.24010			−0.240686
$475$		0			0
$476$	12.3907	+	38.1346i	0.567927	+	1.74790i
$477$	0.584290	−	1.79826i	0.0267528	−	0.0823366i
$478$	−3.98487	−	2.89517i	−0.182264	−	0.132422i
$479$	20.9309	+	15.2072i	0.956358	+	0.694835i	0.952302	−	0.305157i	$-0.0987090\pi$
$479$	20.9309	+	15.2072i	0.956358	+	0.694835i	0.00405575	+	0.999992i	$0.498709\pi$
$480$		0			0
$481$	−12.2617	−	37.7377i	−0.559087	−	1.72069i
$482$	0.293552	−	0.213278i	0.0133709	−	0.00971454i
$483$	−1.93003			−0.0878193
$484$	14.0736	+	9.25531i	0.639707	+	0.420696i
$485$		0			0
$486$	0.553874	−	0.402413i	0.0251242	−	0.0182538i
$487$	1.68681	+	5.19147i	0.0764367	+	0.235248i	0.981973	−	0.189021i	$-0.0605313\pi$
$487$	1.68681	+	5.19147i	0.0764367	+	0.235248i	−0.905536	+	0.424269i	$0.860531\pi$
$488$	3.13595	−	9.65146i	0.141958	−	0.436901i
$489$	−7.75631	−	5.63529i	−0.350753	−	0.254837i
$490$		0			0
$491$	4.01732	−	12.3641i	0.181299	−	0.557982i	−0.818566	−	0.574413i	$-0.805230\pi$
$491$	4.01732	−	12.3641i	0.181299	−	0.557982i	0.999865	+	0.0164310i	$0.00523038\pi$
$492$	4.15197	+	12.7784i	0.187185	+	0.576097i
$493$	−35.4439	+	25.7515i	−1.59631	+	1.15979i
$494$	−12.0717			−0.543133
$495$		0			0
$496$	4.99500			0.224282
$497$	4.92555	−	3.57862i	0.220941	−	0.160523i
$498$	−0.364185	−	1.12085i	−0.0163195	−	0.0502263i
$499$	1.57545	−	4.84874i	0.0705269	−	0.217059i	−0.909580	−	0.415528i	$-0.863597\pi$
$499$	1.57545	−	4.84874i	0.0705269	−	0.217059i	0.980107	+	0.198469i	$0.0635968\pi$
$500$		0			0
$501$	−2.68262	−	1.94904i	−0.119851	−	0.0870767i
$502$	−2.04786	+	6.30266i	−0.0914003	+	0.281301i
$503$	4.47813	+	13.7823i	0.199670	+	0.614521i	0.999890	+	0.0148151i	$0.00471596\pi$
$503$	4.47813	+	13.7823i	0.199670	+	0.614521i	−0.800220	+	0.599706i	$0.795284\pi$
$504$	8.26783	−	6.00693i	0.368278	−	0.267570i
$505$		0			0
$506$	0.297312	−	0.993184i	0.0132171	−	0.0441524i
$507$	−26.3595			−1.17067
$508$	21.2088	−	15.4091i	0.940987	−	0.683667i
$509$	−9.65742	−	29.7225i	−0.428058	−	1.31743i	−0.900036	−	0.435816i	$-0.856460\pi$
$509$	−9.65742	−	29.7225i	−0.428058	−	1.31743i	0.471978	−	0.881610i	$-0.343540\pi$
$510$		0			0
$511$	−4.81859	−	3.50091i	−0.213162	−	0.154871i
$512$	−12.1081	−	8.79708i	−0.535109	−	0.388780i
$513$	0.868508	−	2.67299i	0.0383456	−	0.118016i
$514$	1.71169	+	5.26804i	0.0754993	+	0.232363i
$515$		0			0
$516$	−15.0533			−0.662683
$517$	30.3683	+	21.0008i	1.33560	+	0.923613i
$518$	−18.3040			−0.804230
$519$	−10.2548	+	7.45053i	−0.450135	+	0.327042i
$520$		0			0
$521$	−1.80789	+	5.56411i	−0.0792050	+	0.243768i	−0.982817	−	0.184585i	$-0.940906\pi$
$521$	−1.80789	+	5.56411i	−0.0792050	+	0.243768i	0.903612	+	0.428353i	$0.140906\pi$
$522$	3.91729	+	2.84608i	0.171455	+	0.124570i
$523$	23.5204	+	17.0885i	1.02847	+	0.747230i	0.968003	−	0.250940i	$-0.0807398\pi$
$523$	23.5204	+	17.0885i	1.02847	+	0.747230i	0.0604707	+	0.998170i	$0.480740\pi$
$524$	−3.83893	+	11.8150i	−0.167704	+	0.516141i
$525$		0			0
$526$	7.08131	−	5.14487i	0.308760	−	0.224327i
$527$	−21.9847			−0.957669
$528$	−1.54548	−	4.40461i	−0.0672582	−	0.191686i
$529$	−22.7915			−0.990936
$530$		0			0
$531$	−2.65096	−	8.15882i	−0.115042	−	0.354063i
$532$	5.62184	−	17.3022i	0.243738	−	0.750147i
$533$	−44.5346	−	32.3562i	−1.92901	−	1.40150i
$534$	−7.01551	−	5.09706i	−0.303591	−	0.220572i
$535$		0			0
$536$	7.53916	+	23.2031i	0.325642	+	1.00222i
$537$	−10.8252	+	7.86495i	−0.467141	+	0.339397i
$538$	11.5915			0.499744
$539$	36.0379	−	0.839700i	1.55226	−	0.0361685i
$540$		0			0
$541$	20.7843	−	15.1007i	0.893585	−	0.649228i	−0.0432251	−	0.999065i	$-0.513763\pi$
$541$	20.7843	−	15.1007i	0.893585	−	0.649228i	0.936810	+	0.349838i	$0.113763\pi$
$542$	−4.88890	−	15.0465i	−0.209996	−	0.646302i
$543$	1.07593	−	3.31136i	0.0461724	−	0.142104i
$544$	29.0605	+	21.1137i	1.24596	+	0.905241i
$545$		0			0
$546$	−5.61058	+	17.2676i	−0.240111	+	0.738985i
$547$	−6.03771	−	18.5822i	−0.258154	−	0.794516i	−0.993192	−	0.116490i	$-0.962836\pi$
$547$	−6.03771	−	18.5822i	−0.258154	−	0.794516i	0.735038	−	0.678026i	$-0.237164\pi$
$548$	−11.2152	+	8.14830i	−0.479088	+	0.348078i
$549$	−4.19759			−0.179149
$550$		0			0
$551$	19.8777			0.846820
$552$	−0.893018	+	0.648815i	−0.0380093	+	0.0276154i
$553$	9.99807	+	30.7709i	0.425161	+	1.30851i
$554$	1.99967	−	6.15434i	0.0849577	−	0.261473i
$555$		0			0
$556$	−6.13326	−	4.45607i	−0.260108	−	0.188980i
$557$	−2.18870	+	6.73611i	−0.0927380	+	0.285418i	−0.986658	−	0.162809i	$-0.947945\pi$
$557$	−2.18870	+	6.73611i	−0.0927380	+	0.285418i	0.893920	+	0.448227i	$0.147945\pi$
$558$	0.750840	+	2.31085i	0.0317856	+	0.0978260i
$559$	49.8949	−	36.2508i	2.11033	−	1.53324i
$560$		0			0
$561$	6.80217	+	19.3862i	0.287188	+	0.818487i
$562$	−15.3553			−0.647724
$563$	3.06013	−	2.22332i	0.128969	−	0.0937016i	−0.521430	−	0.853294i	$-0.674601\pi$
$563$	3.06013	−	2.22332i	0.128969	−	0.0937016i	0.650400	+	0.759592i	$0.274601\pi$
$564$	−5.26785	−	16.2128i	−0.221817	−	0.682681i
$565$		0			0
$566$	−4.97174	−	3.61218i	−0.208978	−	0.151831i
$567$	−3.41984	−	2.48466i	−0.143620	−	0.104346i
$568$	1.07601	−	3.31163i	0.0451486	−	0.138953i
$569$	−13.3153	−	40.9802i	−0.558206	−	1.71798i	−0.687324	−	0.726351i	$-0.741215\pi$
$569$	−13.3153	−	40.9802i	−0.558206	−	1.71798i	0.129118	−	0.991629i	$-0.458785\pi$
$570$		0			0
$571$	−23.2838			−0.974398			−0.487199	−	0.873291i	$-0.661981\pi$
$571$	−23.2838			−0.974398			−0.487199	+	0.873291i	$0.661981\pi$
$572$	26.2065	+	18.1227i	1.09575	+	0.757748i
$573$	−5.81744			−0.243027
$574$	−20.5434	+	14.9257i	−0.857466	+	0.622986i
$575$		0			0
$576$	0.356961	−	1.09861i	0.0148734	−	0.0457756i
$577$	−32.8129	−	23.8399i	−1.36602	−	0.992470i	−0.998036	−	0.0626367i	$-0.980049\pi$
$577$	−32.8129	−	23.8399i	−1.36602	−	0.992470i	−0.367981	−	0.929833i	$-0.619951\pi$
$578$	−11.8376	−	8.60049i	−0.492377	−	0.357733i
$579$	−0.0296838	+	0.0913572i	−0.00123362	+	0.00379668i
$580$		0			0
$581$	−5.88697	+	4.27713i	−0.244233	+	0.177445i
$582$	2.49287			0.103333
$583$	1.79841	−	6.00767i	0.0744827	−	0.248812i
$584$	−3.40644			−0.140960
$585$		0			0
$586$	0.571208	+	1.75800i	0.0235964	+	0.0726222i
$587$	−12.8630	+	39.5883i	−0.530914	+	1.63399i	0.221402	+	0.975183i	$0.428937\pi$
$587$	−12.8630	+	39.5883i	−0.530914	+	1.63399i	−0.752316	+	0.658803i	$0.771063\pi$
$588$	−13.4647	−	9.78266i	−0.555274	−	0.403430i
$589$	8.06977	+	5.86303i	0.332509	+	0.241582i
$590$		0			0
$591$	2.26561	+	6.97282i	0.0931946	+	0.286823i
$592$	7.20155	−	5.23223i	0.295982	−	0.215043i
$593$	38.6530			1.58729			0.793644	−	0.608383i	$-0.208182\pi$
$593$	38.6530			1.58729			0.793644	+	0.608383i	$0.208182\pi$
$594$	1.80540	−	1.37708i	0.0740766	−	0.0565023i
$595$		0			0
$596$	−24.5737	+	17.8538i	−1.00658	+	0.731320i
$597$	−3.25643	−	10.0222i	−0.133277	−	0.410183i
$598$	0.606005	−	1.86509i	0.0247814	−	0.0762693i
$599$	1.76280	+	1.28075i	0.0720262	+	0.0523301i	0.623216	−	0.782050i	$-0.285826\pi$
$599$	1.76280	+	1.28075i	0.0720262	+	0.0523301i	−0.551189	+	0.834380i	$0.685826\pi$
$600$		0			0
$601$	−12.1057	+	37.2575i	−0.493801	+	1.51976i	0.325015	+	0.945709i	$0.394631\pi$
$601$	−12.1057	+	37.2575i	−0.493801	+	1.51976i	−0.818817	+	0.574055i	$0.805369\pi$
$602$	−8.79137	−	27.0571i	−0.358310	−	1.10276i
$603$	8.16417	−	5.93161i	0.332471	−	0.241554i
$604$	10.7252			0.436402
$605$		0			0
$606$	0.799475			0.0324764
$607$	0.205259	−	0.149129i	0.00833119	−	0.00605297i	−0.583612	−	0.812033i	$-0.698361\pi$
$607$	0.205259	−	0.149129i	0.00833119	−	0.00605297i	0.591943	+	0.805980i	$0.298361\pi$
$608$	−5.03628	−	15.5001i	−0.204248	−	0.628612i
$609$	9.23858	−	28.4334i	0.374366	−	1.15218i
$610$		0			0
$611$	56.5037	+	41.0523i	2.28589	+	1.66080i
$612$	2.93122	−	9.02136i	0.118487	−	0.364667i
$613$	−0.699908	−	2.15410i	−0.0282690	−	0.0870031i	0.935927	−	0.352195i	$-0.114565\pi$
$613$	−0.699908	−	2.15410i	−0.0282690	−	0.0870031i	−0.964196	+	0.265192i	$0.914565\pi$
$614$	3.45265	−	2.50849i	0.139337	−	0.101235i
$615$		0			0
$616$	26.9498	−	20.5561i	1.08584	−	0.828228i
$617$	46.7095			1.88045			0.940226	−	0.340550i	$-0.110613\pi$
$617$	46.7095			1.88045			0.940226	+	0.340550i	$0.110613\pi$
$618$	7.62298	−	5.53842i	0.306641	−	0.222788i
$619$	8.11167	+	24.9652i	0.326036	+	1.00343i	0.970971	+	0.239197i	$0.0768842\pi$
$619$	8.11167	+	24.9652i	0.326036	+	1.00343i	−0.644936	+	0.764237i	$0.723116\pi$
$620$		0			0
$621$	0.369380	+	0.268371i	0.0148227	+	0.0107693i
$622$	12.4974	+	9.07988i	0.501100	+	0.364070i
$623$	−16.5454	+	50.9216i	−0.662879	+	2.04013i
$624$	−2.72854	−	8.39759i	−0.109229	−	0.336172i
$625$		0			0
$626$	−1.12789			−0.0450797
$627$	2.67322	−	8.93001i	0.106758	−	0.356630i
$628$	4.89515			0.195338
$629$	−31.6965	+	23.0289i	−1.26382	+	0.918221i
$630$		0			0
$631$	13.3110	−	40.9672i	0.529904	−	1.63088i	−0.224505	−	0.974473i	$-0.572077\pi$
$631$	13.3110	−	40.9672i	0.529904	−	1.63088i	0.754409	−	0.656404i	$-0.227923\pi$
$632$	14.9703	+	10.8765i	0.595486	+	0.432646i
$633$	2.05421	+	1.49247i	0.0816474	+	0.0593203i
$634$	0.823724	−	2.53516i	0.0327142	−	0.100684i
$635$		0			0
$636$	−2.34240	+	1.70185i	−0.0928821	+	0.0674828i
$637$	68.1877			2.70169
$638$	13.2085	+	9.13418i	0.522931	+	0.361626i
$639$	−1.44029			−0.0569769
$640$		0			0
$641$	5.61478	+	17.2805i	0.221770	+	0.682539i	0.998603	+	0.0528323i	$0.0168249\pi$
$641$	5.61478	+	17.2805i	0.221770	+	0.682539i	−0.776833	+	0.629707i	$0.783175\pi$
$642$	−2.71850	+	8.36667i	−0.107291	+	0.330206i
$643$	−15.1832	−	11.0312i	−0.598765	−	0.435028i	0.246675	−	0.969098i	$-0.420662\pi$
$643$	−15.1832	−	11.0312i	−0.598765	−	0.435028i	−0.845440	+	0.534070i	$0.820662\pi$
$644$	2.39099	+	1.73716i	0.0942183	+	0.0684536i
$645$		0			0
$646$	3.68329	+	11.3360i	0.144917	+	0.446009i
$647$	−39.3636	+	28.5993i	−1.54754	+	1.12436i	−0.602170	+	0.798368i	$0.705697\pi$
$647$	−39.3636	+	28.5993i	−1.54754	+	1.12436i	−0.945374	+	0.325988i	$0.894303\pi$
$648$	−2.41761			−0.0949727
$649$	−9.42019	−	26.8476i	−0.369775	−	1.05386i
$650$		0			0
$651$	12.1372	−	8.81816i	0.475693	−	0.345611i
$652$	4.53667	+	13.9624i	0.177670	+	0.546811i
$653$	0.876662	−	2.69809i	0.0343064	−	0.105584i	−0.932437	−	0.361333i	$-0.882322\pi$
$653$	0.876662	−	2.69809i	0.0343064	−	0.105584i	0.966743	+	0.255748i	$0.0823219\pi$
$654$	0.879183	+	0.638764i	0.0343788	+	0.0249776i
$655$		0			0
$656$	3.81611	−	11.7448i	0.148994	−	0.458556i
$657$	0.435409	+	1.34005i	0.0169869	+	0.0522804i
$658$	26.0647	−	18.9371i	1.01611	−	0.738245i
$659$	26.9059			1.04811			0.524053	−	0.851686i	$-0.324420\pi$
$659$	26.9059			1.04811			0.524053	+	0.851686i	$0.324420\pi$
$660$		0			0
$661$	−21.5973			−0.840037			−0.420018	−	0.907516i	$-0.637976\pi$
$661$	−21.5973			−0.840037			−0.420018	+	0.907516i	$0.637976\pi$
$662$	−4.25052	+	3.08819i	−0.165201	+	0.120026i
$663$	12.0093	+	36.9607i	0.466401	+	1.43543i
$664$	−1.28604	+	3.95803i	−0.0499081	+	0.153601i
$665$		0			0
$666$	3.50312	+	2.54517i	0.135743	+	0.0986232i
$667$	−0.997870	+	3.07113i	−0.0386377	+	0.118915i
$668$	1.56907	+	4.82909i	0.0607090	+	0.186843i
$669$	9.69321	−	7.04253i	0.374761	−	0.272280i
$670$		0			0
$671$	−13.9181	+	0.324297i	−0.537301	+	0.0125194i
$672$	−24.5123			−0.945582
$673$	1.50744	−	1.09522i	0.0581075	−	0.0422176i	−0.558352	−	0.829604i	$-0.688566\pi$
$673$	1.50744	−	1.09522i	0.0581075	−	0.0422176i	0.616460	+	0.787386i	$0.288566\pi$
$674$	3.90782	+	12.0270i	0.150524	+	0.463264i
$675$		0			0
$676$	32.6551	+	23.7253i	1.25597	+	0.912513i
$677$	−8.97236	−	6.51880i	−0.344836	−	0.250538i	0.401864	−	0.915700i	$-0.368363\pi$
$677$	−8.97236	−	6.51880i	−0.344836	−	0.250538i	−0.746699	+	0.665162i	$0.768363\pi$
$678$	−0.615584	+	1.89457i	−0.0236414	+	0.0727607i
$679$	−4.75637	−	14.6386i	−0.182533	−	0.561778i
$680$		0			0
$681$	8.35198			0.320049
$682$	2.66811	+	7.60413i	0.102167	+	0.291177i
$683$	4.37404			0.167368			0.0836840	−	0.996492i	$-0.473331\pi$
$683$	4.37404			0.167368			0.0836840	+	0.996492i	$0.473331\pi$
$684$	−3.48182	+	2.52969i	−0.133131	+	0.0967251i
$685$		0			0
$686$	3.45986	−	10.6483i	0.132098	−	0.406556i
$687$	−12.2199	−	8.87827i	−0.466218	−	0.338727i
$688$	11.1932	+	8.13234i	0.426737	+	0.310043i
$689$	3.66567	−	11.2818i	0.139651	−	0.429801i
$690$		0			0
$691$	−27.2007	+	19.7624i	−1.03476	+	0.751798i	−0.969256	−	0.246054i	$-0.920866\pi$
$691$	−27.2007	+	19.7624i	−1.03476	+	0.751798i	−0.0655055	+	0.997852i	$0.520866\pi$
$692$	19.4100			0.737857
$693$	−11.5312	−	7.97423i	−0.438034	−	0.302916i
$694$	14.3191			0.543546
$695$		0			0
$696$	−5.28377	−	16.2618i	−0.200281	−	0.616401i
$697$	−16.7960	+	51.6928i	−0.636194	+	1.95800i
$698$	−4.62137	−	3.35762i	−0.174922	−	0.127088i
$699$	12.9073	+	9.37772i	0.488200	+	0.354698i
$700$		0			0
$701$	−6.85901	−	21.1099i	−0.259061	−	0.797308i	−0.993002	−	0.118095i	$-0.962321\pi$
$701$	−6.85901	−	21.1099i	−0.259061	−	0.797308i	0.733941	−	0.679213i	$-0.237679\pi$
$702$	3.47484	−	2.52462i	0.131150	−	0.0952857i
$703$	17.7761			0.670438
$704$	1.09871	−	3.67028i	0.0414091	−	0.138329i
$705$		0			0
$706$	12.6547	−	9.19418i	0.476266	−	0.346028i
$707$	−1.52539	−	4.69468i	−0.0573683	−	0.176561i
$708$	−4.05939	+	12.4935i	−0.152561	+	0.469535i
$709$	−14.3275	−	10.4095i	−0.538080	−	0.390938i	0.285291	−	0.958441i	$-0.407910\pi$
$709$	−14.3275	−	10.4095i	−0.538080	−	0.390938i	−0.823372	+	0.567503i	$0.807910\pi$
$710$		0			0
$711$	2.36520	−	7.27935i	0.0887021	−	0.272997i
$712$	9.46274	+	29.1233i	0.354631	+	1.09144i
$713$	−1.31095	+	0.952460i	−0.0490954	+	0.0356699i
$714$	17.9271			0.670904
$715$		0			0
$716$	20.4896			0.765733
$717$	5.82050	−	4.22884i	0.217371	−	0.157929i
$718$	−6.75074	−	20.7767i	−0.251935	−	0.775378i
$719$	−8.91388	+	27.4341i	−0.332432	+	1.02312i	0.635542	+	0.772067i	$0.280777\pi$
$719$	−8.91388	+	27.4341i	−0.332432	+	1.02312i	−0.967973	+	0.251053i	$0.919223\pi$
$720$		0			0
$721$	−47.0673	−	34.1964i	−1.75288	−	1.27354i
$722$	−2.34849	+	7.22792i	−0.0874019	+	0.268995i
$723$	0.163778	+	0.504058i	0.00609098	+	0.0187461i
$724$	−4.31335	+	3.13383i	−0.160304	+	0.116468i
$725$		0			0
$726$	5.87983	−	4.70550i	0.218221	−	0.174638i
$727$	−21.7927			−0.808245			−0.404122	−	0.914705i	$-0.632423\pi$
$727$	−21.7927			−0.808245			−0.404122	+	0.914705i	$0.632423\pi$
$728$	51.8700	−	37.6858i	1.92243	−	1.39673i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−49.2652	−	35.7933i	−1.82214	−	1.32386i
$732$	5.20014	+	3.77812i	0.192203	+	0.139643i
$733$	4.94940	−	15.2327i	0.182810	−	0.562632i	−0.817093	−	0.576505i	$-0.804416\pi$
$733$	4.94940	−	15.2327i	0.182810	−	0.562632i	0.999904	+	0.0138730i	$0.00441606\pi$
$734$	−5.54175	−	17.0558i	−0.204550	−	0.629540i
$735$		0			0
$736$	2.64760			0.0975918
$737$	26.6119	−	20.2983i	0.980261	−	0.747699i
$738$	6.00714			0.221126
$739$	31.1394	−	22.6241i	1.14548	−	0.832240i	0.157607	−	0.987502i	$-0.449622\pi$
$739$	31.1394	−	22.6241i	1.14548	−	0.832240i	0.987873	+	0.155262i	$0.0496221\pi$
$740$		0			0
$741$	5.44877	−	16.7696i	0.200166	−	0.616047i
$742$	−4.42694	−	3.21636i	−0.162518	−	0.118076i
$743$	−3.00157	−	2.18077i	−0.110117	−	0.0800046i	0.531364	−	0.847144i	$-0.321680\pi$
$743$	−3.00157	−	2.18077i	−0.110117	−	0.0800046i	−0.641481	+	0.767139i	$0.721680\pi$
$744$	2.65143	−	8.16027i	0.0972062	−	0.299170i
$745$		0			0
$746$	15.2866	−	11.1064i	0.559683	−	0.406634i
$747$	1.72142			0.0629834
$748$	9.02214	−	30.1388i	0.329882	−	1.10198i
$749$	54.3177			1.98472
$750$		0			0
$751$	−3.60115	−	11.0832i	−0.131408	−	0.404432i	0.863606	−	0.504167i	$-0.168200\pi$
$751$	−3.60115	−	11.0832i	−0.131408	−	0.404432i	−0.995014	+	0.0997351i	$0.968200\pi$
$752$	−4.84172	+	14.9013i	−0.176559	+	0.543394i
$753$	−7.83108	−	5.68962i	−0.285381	−	0.207341i
$754$	24.5760	+	17.8555i	0.895004	+	0.650259i
$755$		0			0
$756$	2.00026	+	6.15617i	0.0727488	+	0.223898i
$757$	−16.6849	+	12.1223i	−0.606423	+	0.440592i	−0.848153	−	0.529752i	$-0.822285\pi$
$757$	−16.6849	+	12.1223i	−0.606423	+	0.440592i	0.241730	+	0.970344i	$0.422285\pi$
$758$	−15.6563			−0.568664
$759$	1.24550	+	0.861305i	0.0452087	+	0.0312634i
$760$		0			0
$761$	−1.88428	+	1.36901i	−0.0683049	+	0.0496264i	−0.621414	−	0.783483i	$-0.713441\pi$
$761$	−1.88428	+	1.36901i	−0.0683049	+	0.0496264i	0.553109	+	0.833109i	$0.313441\pi$
$762$	−3.62190	−	11.1471i	−0.131208	−	0.403815i
$763$	2.07347	−	6.38150i	0.0750648	−	0.231026i
$764$	7.20686	+	5.23609i	0.260735	+	0.189435i
$765$		0			0
$766$	−0.441122	+	1.35764i	−0.0159384	+	0.0490534i
$767$	−16.6314	−	51.1861i	−0.600524	−	1.84822i
$768$	−7.85462	+	5.70672i	−0.283429	+	0.205923i
$769$	29.3154			1.05714			0.528571	−	0.848889i	$-0.322728\pi$
$769$	29.3154			1.05714			0.528571	+	0.848889i	$0.322728\pi$
$770$		0			0
$771$	−8.09076			−0.291382
$772$	0.119001	−	0.0864594i	0.00428294	−	0.00311174i
$773$	3.46542	+	10.6655i	0.124643	+	0.383611i	0.993836	−	0.110862i	$-0.0353612\pi$
$773$	3.46542	+	10.6655i	0.124643	+	0.383611i	−0.869193	+	0.494473i	$0.835361\pi$
$774$	−2.07974	+	6.40078i	−0.0747547	+	0.230071i
$775$		0			0
$776$	−7.12180	−	5.17429i	−0.255658	−	0.185746i
$777$	8.26180	−	25.4272i	0.296390	−	0.912196i
$778$	4.94018	+	15.2043i	0.177114	+	0.545101i
$779$	19.9510	−	14.4952i	0.714818	−	0.519345i
$780$		0			0
$781$	−4.77560	+	0.111274i	−0.170884	+	0.00398169i
$782$	−1.93632			−0.0692428
$783$	−5.72180	+	4.15713i	−0.204481	+	0.148564i
$784$	4.72701	+	14.5483i	0.168822	+	0.519581i
$785$		0			0
$786$	4.49346	+	3.26469i	0.160277	+	0.116448i
$787$	−24.3741	−	17.7089i	−0.868845	−	0.631253i	0.0614321	−	0.998111i	$-0.480433\pi$
$787$	−24.3741	−	17.7089i	−0.868845	−	0.631253i	−0.930277	+	0.366859i	$0.880433\pi$
$788$	3.46930	−	10.6774i	0.123589	−	0.380366i
$789$	3.95080	+	12.1593i	0.140652	+	0.432883i
$790$		0			0
$791$	12.2998			0.437332
$792$	−8.01613	+	0.186780i	−0.284841	+	0.00663692i
$793$	−26.3345			−0.935165
$794$	−15.2375	+	11.0707i	−0.540760	+	0.392885i
$795$		0			0
$796$	−4.98653	+	15.3469i	−0.176743	+	0.543958i
$797$	−28.7200	−	20.8663i	−1.01732	−	0.739123i	−0.0515850	−	0.998669i	$-0.516427\pi$
$797$	−28.7200	−	20.8663i	−1.01732	−	0.739123i	−0.965731	+	0.259545i	$0.916427\pi$
$798$	−6.58036	−	4.78091i	−0.232942	−	0.169243i
$799$	21.3101	−	65.5858i	0.753897	−	2.32026i
$800$		0			0
$801$	10.2472	−	7.44504i	0.362068	−	0.263058i
$802$	−5.93863			−0.209700
$803$	1.54723	+	4.40960i	0.0546004	+	0.155611i
$804$	−15.4529			−0.544983
$805$		0			0
$806$	4.71056	+	14.4976i	0.165922	+	0.510656i
$807$	−5.23200	+	16.1024i	−0.184175	+	0.566833i
$808$	−2.28400	−	1.65942i	−0.0803507	−	0.0583782i
$809$	3.01028	+	2.18710i	0.105836	+	0.0768942i	0.639444	−	0.768837i	$-0.279164\pi$
$809$	3.01028	+	2.18710i	0.105836	+	0.0768942i	−0.533609	+	0.845732i	$0.679164\pi$
$810$		0			0
$811$	15.8315	+	48.7244i	0.555920	+	1.71095i	0.693501	+	0.720456i	$0.256067\pi$
$811$	15.8315	+	48.7244i	0.555920	+	1.71095i	−0.137581	+	0.990491i	$0.543933\pi$
$812$	−37.0371	+	26.9091i	−1.29975	+	0.944323i
$813$	23.1087			0.810457
$814$	11.8120	+	8.16843i	0.414011	+	0.286303i
$815$		0			0
$816$	−7.05326	+	5.12449i	−0.246914	+	0.179393i
$817$	8.53783	+	26.2767i	0.298701	+	0.919307i
$818$	1.18944	−	3.66071i	0.0415877	−	0.127994i
$819$	−21.4551	−	15.5880i	−0.749701	−	0.544690i
$820$		0			0
$821$	9.84302	−	30.2937i	0.343524	−	1.05726i	−0.618846	−	0.785513i	$-0.712399\pi$
$821$	9.84302	−	30.2937i	0.343524	−	1.05726i	0.962369	−	0.271745i	$-0.0876007\pi$
$822$	1.91525	+	5.89455i	0.0668022	+	0.205596i
$823$	−4.58787	+	3.33328i	−0.159923	+	0.116191i	−0.664869	−	0.746960i	$-0.731513\pi$
$823$	−4.58787	+	3.33328i	−0.159923	+	0.116191i	0.504946	+	0.863151i	$0.331513\pi$
$824$	−33.2736			−1.15914
$825$		0			0
$826$	−24.8268			−0.863837
$827$	−7.07002	+	5.13667i	−0.245849	+	0.178620i	−0.703885	−	0.710314i	$-0.748553\pi$
$827$	−7.07002	+	5.13667i	−0.245849	+	0.178620i	0.458036	+	0.888934i	$0.348553\pi$
$828$	−0.216051	−	0.664935i	−0.00750828	−	0.0231081i
$829$	−2.21685	+	6.82277i	−0.0769945	+	0.236965i	−0.982145	−	0.188127i	$-0.939758\pi$
$829$	−2.21685	+	6.82277i	−0.0769945	+	0.236965i	0.905150	+	0.425092i	$0.139758\pi$
$830$		0			0
$831$	7.64680	+	5.55573i	0.265265	+	0.192726i
$832$	2.23947	−	6.89239i	0.0776397	−	0.238951i
$833$	−20.8052	−	64.0319i	−0.720858	−	2.21857i
$834$	−2.74213	+	1.99227i	−0.0949520	+	0.0689867i
$835$		0			0
$836$	−11.3493	+	8.65675i	−0.392524	+	0.299400i
$837$	−3.54905			−0.122673
$838$	10.7246	−	7.79185i	0.370474	−	0.269165i
$839$	−3.29368	−	10.1369i	−0.113710	−	0.349965i	0.877965	−	0.478724i	$-0.158901\pi$
$839$	−3.29368	−	10.1369i	−0.113710	−	0.349965i	−0.991676	+	0.128759i	$0.958901\pi$
$840$		0			0
$841$	−17.0062	−	12.3557i	−0.586421	−	0.426060i
$842$	15.8166	+	11.4914i	0.545075	+	0.396020i
$843$	6.93087	−	21.3310i	0.238712	−	0.734679i
$844$	−1.20151	−	3.69786i	−0.0413575	−	0.127285i
$845$		0			0
$846$	−7.62162			−0.262037
$847$	−38.8503	−	25.5495i	−1.33491	−	0.877890i
$848$	2.66115			0.0913842
$849$	7.26198	−	5.27614i	0.249231	−	0.181077i
$850$		0			0
$851$	−0.892366	+	2.74642i	−0.0305899	+	0.0941461i
$852$	1.78428	+	1.29636i	0.0611286	+	0.0444125i
$853$	32.8676	+	23.8797i	1.12536	+	0.817625i	0.985014	−	0.172476i	$-0.0551769\pi$
$853$	32.8676	+	23.8797i	1.12536	+	0.817625i	0.140351	+	0.990102i	$0.455177\pi$
$854$	−3.75391	+	11.5533i	−0.128456	+	0.395347i
$855$		0			0
$856$	25.1326	−	18.2599i	0.859014	−	0.624110i
$857$	−56.5172			−1.93059			−0.965295	−	0.261162i	$-0.915894\pi$
$857$	−56.5172			−1.93059			−0.965295	+	0.261162i	$0.915894\pi$
$858$	11.3266	−	8.63941i	0.386683	−	0.294945i
$859$	−34.5324			−1.17823			−0.589116	−	0.808048i	$-0.700524\pi$
$859$	−34.5324			−1.17823			−0.589116	+	0.808048i	$0.700524\pi$
$860$		0			0
$861$	−11.4616	−	35.2751i	−0.390610	−	1.20217i
$862$	−1.10916	+	3.41364i	−0.0377781	+	0.116269i
$863$	41.8812	+	30.4285i	1.42565	+	1.03580i	0.990805	+	0.135295i	$0.0431981\pi$
$863$	41.8812	+	30.4285i	1.42565	+	1.03580i	0.434849	+	0.900504i	$0.356802\pi$
$864$	4.69131	+	3.40843i	0.159601	+	0.115957i
$865$		0			0
$866$	−5.13730	−	15.8110i	−0.174573	−	0.537280i
$867$	17.2906	−	12.5623i	0.587218	−	0.426639i
$868$	−22.9729			−0.779752
$869$	7.27998	−	24.3190i	0.246956	−	0.824967i
$870$		0			0
$871$	51.2196	−	37.2132i	1.73551	−	1.26092i
$872$	−1.18587	−	3.64973i	−0.0401586	−	0.123596i
$873$	−1.12520	+	3.46300i	−0.0380821	+	0.117205i
$874$	0.710753	+	0.516392i	0.0240416	+	0.0174672i
$875$		0			0
$876$	0.666736	−	2.05200i	0.0225269	−	0.0693308i
$877$	6.50323	+	20.0149i	0.219599	+	0.675855i	0.998795	+	0.0490751i	$0.0156274\pi$
$877$	6.50323	+	20.0149i	0.219599	+	0.675855i	−0.779197	+	0.626780i	$0.784373\pi$
$878$	6.77336	−	4.92113i	0.228590	−	0.166080i
$879$	−2.69997			−0.0910677
$880$		0			0
$881$	38.9312			1.31162			0.655812	−	0.754924i	$-0.272326\pi$
$881$	38.9312			1.31162			0.655812	+	0.754924i	$0.272326\pi$
$882$	−6.01994	+	4.37374i	−0.202702	+	0.147271i
$883$	−0.118104	−	0.363486i	−0.00397451	−	0.0122323i	0.949050	−	0.315127i	$-0.102047\pi$
$883$	−0.118104	−	0.363486i	−0.00397451	−	0.0122323i	−0.953024	+	0.302894i	$0.902047\pi$
$884$	18.3896	−	56.5975i	0.618510	−	1.90358i
$885$		0			0
$886$	10.0424	+	7.29622i	0.337381	+	0.245121i
$887$	−12.9149	+	39.7481i	−0.433641	+	1.33461i	0.460832	+	0.887487i	$0.347551\pi$
$887$	−12.9149	+	39.7481i	−0.433641	+	1.33461i	−0.894473	+	0.447122i	$0.852449\pi$
$888$	−4.72512	−	14.5424i	−0.158565	−	0.488012i
$889$	−58.5472	+	42.5370i	−1.96361	+	1.42665i
$890$		0			0
$891$	1.09809	+	3.12957i	0.0367875	+	0.104844i
$892$	−18.3471			−0.614305
$893$	−25.3130	+	18.3910i	−0.847067	+	0.615430i
$894$	4.19653	+	12.9156i	0.140353	+	0.431962i
$895$		0			0
$896$	36.9571	+	26.8509i	1.23465	+	0.897027i
$897$	2.31739	+	1.68368i	0.0773753	+	0.0562164i
$898$	8.54192	−	26.2893i	0.285047	−	0.877286i
$899$	−7.75657	−	23.8723i	−0.258696	−	0.796185i
$900$		0			0
$901$	−11.7126			−0.390205
$902$	19.9180	−	0.464099i	0.663198	−	0.0154528i
$903$	41.5548			1.38286
$904$	5.69110	−	4.13482i	0.189283	−	0.137522i
$905$		0			0
$906$	1.48178	−	4.56045i	0.0492289	−	0.151511i
$907$	−17.7234	−	12.8768i	−0.588497	−	0.427568i	0.253281	−	0.967393i	$-0.418490\pi$
$907$	−17.7234	−	12.8768i	−0.588497	−	0.427568i	−0.841777	+	0.539825i	$0.818490\pi$
$908$	−10.3468	−	7.51736i	−0.343369	−	0.249472i
$909$	−0.360856	+	1.11060i	−0.0119688	+	0.0368363i
$910$		0			0
$911$	10.3434	−	7.51495i	0.342694	−	0.248981i	−0.403104	−	0.915154i	$-0.632069\pi$
$911$	10.3434	−	7.51495i	0.342694	−	0.248981i	0.745797	+	0.666173i	$0.232069\pi$
$912$	3.95562			0.130984
$913$	5.70775	−	0.132993i	0.188899	−	0.00440144i
$914$	−4.00571			−0.132497
$915$		0			0
$916$	7.14742	+	21.9975i	0.236157	+	0.726817i
$917$	10.5974	−	32.6155i	0.349958	−	1.07706i
$918$	−3.43099	−	2.49276i	−0.113240	−	0.0822734i
$919$	−42.6029	−	30.9529i	−1.40534	−	1.02104i	−0.993979	−	0.109569i	$-0.965053\pi$
$919$	−42.6029	−	30.9529i	−1.40534	−	1.02104i	−0.411362	−	0.911472i	$-0.634947\pi$
$920$		0			0
$921$	1.92630	+	5.92854i	0.0634737	+	0.195352i
$922$	6.31265	−	4.58641i	0.207896	−	0.151045i
$923$	−9.03596			−0.297422
$924$	7.10793	+	20.2576i	0.233834	+	0.666427i
$925$		0			0
$926$	−7.38153	+	5.36300i	−0.242572	+	0.176239i
$927$	4.25301	+	13.0894i	0.139687	+	0.429913i
$928$	−12.6734	+	39.0048i	−0.416026	+	1.28039i
$929$	28.2292	+	20.5097i	0.926170	+	0.672902i	0.945052	−	0.326920i	$-0.106011\pi$
$929$	28.2292	+	20.5097i	0.926170	+	0.672902i	−0.0188824	+	0.999822i	$0.506011\pi$
$930$		0			0
$931$	−9.43964	+	29.0522i	−0.309372	+	0.952148i
$932$	−7.54950	−	23.2350i	−0.247292	−	0.761086i
$933$	−18.2543	+	13.2626i	−0.597620	+	0.434197i
$934$	−11.5316			−0.377325
$935$		0			0
$936$	−15.1674			−0.495762
$937$	17.5675	−	12.7636i	0.573906	−	0.416967i	−0.262616	−	0.964900i	$-0.584585\pi$
$937$	17.5675	−	12.7636i	0.573906	−	0.416967i	0.836522	+	0.547933i	$0.184585\pi$
$938$	−9.02479	−	27.7754i	−0.294670	−	0.906901i
$939$	0.509094	−	1.56683i	0.0166136	−	0.0511315i
$940$		0			0
$941$	32.4320	+	23.5632i	1.05725	+	0.768140i	0.973578	−	0.228353i	$-0.0733341\pi$
$941$	32.4320	+	23.5632i	1.05725	+	0.768140i	0.0836754	+	0.996493i	$0.473334\pi$
$942$	0.676308	−	2.08146i	0.0220353	−	0.0678177i
$943$	1.23798	+	3.81011i	0.0403141	+	0.124074i
$944$	9.76792	−	7.09681i	0.317919	−	0.230981i
$945$		0			0
$946$	−6.40133	+	21.3839i	−0.208125	+	0.695251i
$947$	52.3489			1.70111			0.850555	−	0.525887i	$-0.176266\pi$
$947$	52.3489			1.70111			0.850555	+	0.525887i	$0.176266\pi$
$948$	−9.48202	+	6.88909i	−0.307962	+	0.223747i
$949$	2.73163	+	8.40710i	0.0886725	+	0.272906i
$950$		0			0
$951$	3.14995	+	2.28857i	0.102144	+	0.0742121i
$952$	−51.2154	−	37.2101i	−1.65990	−	1.20599i
$953$	−10.0299	+	30.8689i	−0.324901	+	0.999943i	0.646584	+	0.762843i	$0.276197\pi$
$953$	−10.0299	+	30.8689i	−0.324901	+	0.999943i	−0.971485	+	0.237100i	$0.923803\pi$
$954$	0.400020	+	1.23113i	0.0129511	+	0.0398594i
$955$		0			0
$956$	−11.0169			−0.356312
$957$	−18.6508	+	14.2260i	−0.602893	+	0.459860i
$958$	−17.7126			−0.572270
$959$	30.9597	−	22.4935i	0.999740	−	0.726354i
$960$		0			0
$961$	−5.68723	+	17.5035i	−0.183459	+	0.564629i
$962$	21.9776	+	15.9677i	0.708586	+	0.514818i
$963$	−10.3956	−	7.55287i	−0.334995	−	0.243388i
$964$	0.250792	−	0.771858i	0.00807746	−	0.0248599i
$965$		0			0
$966$	1.06899	−	0.776668i	0.0343942	−	0.0249889i
$967$	18.8006			0.604587			0.302294	−	0.953215i	$-0.402248\pi$
$967$	18.8006			0.604587			0.302294	+	0.953215i	$0.402248\pi$
$968$	−26.5648	+	1.23862i	−0.853826	+	0.0398107i
$969$	−17.4101			−0.559292
$970$		0			0
$971$	−2.17330	−	6.68872i	−0.0697444	−	0.214651i	0.910109	−	0.414369i	$-0.135998\pi$
$971$	−2.17330	−	6.68872i	−0.0697444	−	0.214651i	−0.979854	+	0.199717i	$0.935998\pi$
$972$	0.473194	−	1.45634i	0.0151777	−	0.0467122i
$973$	16.9310	+	12.3011i	0.542782	+	0.394354i
$974$	−3.02339	−	2.19662i	−0.0968758	−	0.0703844i
$975$		0			0
$976$	−1.82560	−	5.61862i	−0.0584361	−	0.179848i
$977$	−3.75126	+	2.72545i	−0.120013	+	0.0871949i	−0.646173	−	0.763191i	$-0.723632\pi$
$977$	−3.75126	+	2.72545i	−0.120013	+	0.0871949i	0.526159	+	0.850386i	$0.323632\pi$
$978$	6.56373			0.209885
$979$	33.4018	−	25.4774i	1.06753	−	0.814261i
$980$		0			0
$981$	−1.28418	+	0.933012i	−0.0410007	+	0.0297888i
$982$	2.75036	+	8.46475i	0.0877676	+	0.270121i
$983$	0.951319	−	2.92786i	0.0303423	−	0.0933841i	−0.934738	−	0.355336i	$-0.884366\pi$
$983$	0.951319	−	2.92786i	0.0303423	−	0.0933841i	0.965081	+	0.261952i	$0.0843663\pi$
$984$	−17.1616	−	12.4687i	−0.547093	−	0.397486i
$985$		0			0
$986$	9.26872	−	28.5262i	0.295176	−	0.908459i
$987$	14.5420	+	44.7557i	0.462877	+	1.42459i
$988$	−21.8439	+	15.8706i	−0.694948	+	0.504909i
$989$	−4.48838			−0.142722
$990$		0			0
$991$	35.0952			1.11484			0.557418	−	0.830232i	$-0.311792\pi$
$991$	35.0952			1.11484			0.557418	+	0.830232i	$0.311792\pi$
$992$	−16.6497	+	12.0967i	−0.528628	+	0.384071i
$993$	−2.37145	−	7.29857i	−0.0752557	−	0.231613i
$994$	−1.28805	+	3.96421i	−0.0408544	+	0.125737i
$995$		0			0
$996$	−2.13256	−	1.54939i	−0.0675727	−	0.0490945i
$997$	−7.48329	+	23.0312i	−0.236998	+	0.729405i	0.759852	+	0.650096i	$0.225271\pi$
$997$	−7.48329	+	23.0312i	−0.236998	+	0.729405i	−0.996850	+	0.0793090i	$0.974729\pi$
$998$	1.07859	+	3.31957i	0.0341423	+	0.105079i
$999$	−5.11685	+	3.71761i	−0.161890	+	0.117620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.n.751.2	yes	16
5.2	odd	4		825.2.bx.j.124.4		32
5.3	odd	4		825.2.bx.j.124.5		32
5.4	even	2		825.2.n.m.751.3	yes	16
11.2	odd	10		9075.2.a.dt.1.4		8
11.4	even	5	inner	825.2.n.n.301.2	yes	16
11.9	even	5		9075.2.a.dv.1.5		8
55.4	even	10		825.2.n.m.301.3	✓	16
55.9	even	10		9075.2.a.du.1.4		8
55.24	odd	10		9075.2.a.dw.1.5		8
55.37	odd	20		825.2.bx.j.499.5		32
55.48	odd	20		825.2.bx.j.499.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.n.m.301.3	✓	16	55.4	even	10
825.2.n.m.751.3	yes	16	5.4	even	2
825.2.n.n.301.2	yes	16	11.4	even	5	inner
825.2.n.n.751.2	yes	16	1.1	even	1	trivial
825.2.bx.j.124.4		32	5.2	odd	4
825.2.bx.j.124.5		32	5.3	odd	4
825.2.bx.j.499.4		32	55.48	odd	20
825.2.bx.j.499.5		32	55.37	odd	20
9075.2.a.dt.1.4		8	11.2	odd	10
9075.2.a.du.1.4		8	55.9	even	10
9075.2.a.dv.1.5		8	11.9	even	5
9075.2.a.dw.1.5		8	55.24	odd	10

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.553874 + 0.402413i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.473194 + 1.45634i) q^{4} +(0.553874 + 0.402413i) q^{6} +(1.30626 - 4.02026i) q^{7} +(-0.747082 - 2.29928i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.553874 + 0.402413i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.473194 + 1.45634i) q^{4} +(0.553874 + 0.402413i) q^{6} +(1.30626 - 4.02026i) q^{7} +(-0.747082 - 2.29928i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-2.63707 + 2.01144i) q^{11} +1.53129 q^{12} +(-5.07554 + 3.68760i) q^{13} +(0.894299 + 2.75237i) q^{14} +(-1.13863 - 0.827260i) q^{16} +(5.01149 + 3.64106i) q^{17} +(0.211561 - 0.651117i) q^{18} +(-0.868508 - 2.67299i) q^{19} -4.22715 q^{21} +(0.651174 - 2.17527i) q^{22} +0.456579 q^{23} +(-1.95589 + 1.42104i) q^{24} +(1.32727 - 4.08493i) q^{26} +(0.809017 + 0.587785i) q^{27} +(5.23675 + 3.80472i) q^{28} +(-2.18554 + 6.72639i) q^{29} +(-2.87124 + 2.08608i) q^{31} +5.79877 q^{32} +(2.72789 + 1.88643i) q^{33} -4.24094 q^{34} +(-0.473194 - 1.45634i) q^{36} +(-1.95446 + 6.01521i) q^{37} +(1.55669 + 1.13100i) q^{38} +(5.07554 + 3.68760i) q^{39} +(2.71142 + 8.34490i) q^{41} +(2.34131 - 1.70106i) q^{42} -9.83046 q^{43} +(-1.68150 - 4.79227i) q^{44} +(-0.252887 + 0.183733i) q^{46} +(-3.44014 - 10.5877i) q^{47} +(-0.434916 + 1.33853i) q^{48} +(-8.79304 - 6.38851i) q^{49} +(1.91422 - 5.89136i) q^{51} +(-2.96868 - 9.13667i) q^{52} +(-1.52969 + 1.11139i) q^{53} -0.684625 q^{54} -10.2196 q^{56} +(-2.27378 + 1.65200i) q^{57} +(-1.49627 - 4.60505i) q^{58} +(-2.65096 + 8.15882i) q^{59} +(3.39592 + 2.46728i) q^{61} +(0.750840 - 2.31085i) q^{62} +(1.30626 + 4.02026i) q^{63} +(-0.934536 + 0.678980i) q^{64} +(-2.27003 + 0.0528928i) q^{66} -10.0915 q^{67} +(-7.67403 + 5.57551i) q^{68} +(-0.141091 - 0.434233i) q^{69} +(1.16522 + 0.846580i) q^{71} +(1.95589 + 1.42104i) q^{72} +(0.435409 - 1.34005i) q^{73} +(-1.33807 - 4.11817i) q^{74} +4.30377 q^{76} +(4.64180 + 13.2291i) q^{77} -4.29514 q^{78} +(-6.19218 + 4.49888i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-4.85988 - 3.53091i) q^{82} +(-1.39266 - 1.01182i) q^{83} +(2.00026 - 6.15617i) q^{84} +(5.44483 - 3.95590i) q^{86} +7.07254 q^{87} +(6.59497 + 4.56065i) q^{88} -12.6663 q^{89} +(8.19511 + 25.2219i) q^{91} +(-0.216051 + 0.664935i) q^{92} +(2.87124 + 2.08608i) q^{93} +(6.16602 + 4.47988i) q^{94} +(-1.79192 - 5.51496i) q^{96} +(2.94580 - 2.14025i) q^{97} +7.44105 q^{98} +(0.951139 - 3.17732i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 4 q^{3} - 6 q^{4} - 2 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 - 2 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 16 q + 2 q^{2} + 4 q^{3} - 6 q^{4} - 2 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 3 q^{11} - 14 q^{12} - 11 q^{13} + 4 q^{14} + 16 q^{16} - 17 q^{17} - 3 q^{18} + 8 q^{19} - 16 q^{21} - 23 q^{22} - 14 q^{23} - q^{24} + 33 q^{26} + 4 q^{27} + 7 q^{28} + 4 q^{29} - 5 q^{31} + 24 q^{32} + 12 q^{33} - 16 q^{34} - 6 q^{36} + 2 q^{37} - 3 q^{38} + 11 q^{39} + 2 q^{41} - 4 q^{42} + 22 q^{43} - 40 q^{46} - 20 q^{47} + 9 q^{48} - 26 q^{49} - 18 q^{51} - 43 q^{52} + 40 q^{53} - 2 q^{54} - 8 q^{56} + 2 q^{57} + 26 q^{58} + 6 q^{59} - 2 q^{61} + 26 q^{62} - 4 q^{63} + 4 q^{64} - 7 q^{66} - 12 q^{67} - 56 q^{68} + 4 q^{69} + 11 q^{71} + q^{72} - 21 q^{73} + 66 q^{74} - 10 q^{76} + 23 q^{77} + 2 q^{78} - 7 q^{79} - 4 q^{81} + 20 q^{82} + 13 q^{83} + 18 q^{84} + 37 q^{86} + 56 q^{87} + 26 q^{88} + 42 q^{89} + 2 q^{91} + 92 q^{92} + 5 q^{93} + 88 q^{94} + 11 q^{96} - 27 q^{97} - 54 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 - 2 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 3 * q^11 - 14 * q^12 - 11 * q^13 + 4 * q^14 + 16 * q^16 - 17 * q^17 - 3 * q^18 + 8 * q^19 - 16 * q^21 - 23 * q^22 - 14 * q^23 - q^24 + 33 * q^26 + 4 * q^27 + 7 * q^28 + 4 * q^29 - 5 * q^31 + 24 * q^32 + 12 * q^33 - 16 * q^34 - 6 * q^36 + 2 * q^37 - 3 * q^38 + 11 * q^39 + 2 * q^41 - 4 * q^42 + 22 * q^43 - 40 * q^46 - 20 * q^47 + 9 * q^48 - 26 * q^49 - 18 * q^51 - 43 * q^52 + 40 * q^53 - 2 * q^54 - 8 * q^56 + 2 * q^57 + 26 * q^58 + 6 * q^59 - 2 * q^61 + 26 * q^62 - 4 * q^63 + 4 * q^64 - 7 * q^66 - 12 * q^67 - 56 * q^68 + 4 * q^69 + 11 * q^71 + q^72 - 21 * q^73 + 66 * q^74 - 10 * q^76 + 23 * q^77 + 2 * q^78 - 7 * q^79 - 4 * q^81 + 20 * q^82 + 13 * q^83 + 18 * q^84 + 37 * q^86 + 56 * q^87 + 26 * q^88 + 42 * q^89 + 2 * q^91 + 92 * q^92 + 5 * q^93 + 88 * q^94 + 11 * q^96 - 27 * q^97 - 54 * q^98 + 8 * q^99

Introduction

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