LMFDB - Embedded newform 192.2.r.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(13,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("192.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.r (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			109.1
Character	$\chi$	$=$	192.109
Dual form			192.2.r.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40493 + 0.161763i) q^{2} +(-0.555570 - 0.831470i) q^{3} +(1.94767 - 0.454533i) q^{4} +(0.573343 + 2.88239i) q^{5} +(0.915039 + 1.07829i) q^{6} +(-0.457164 - 1.10369i) q^{7} +(-2.66281 + 0.953649i) q^{8} +(-0.382683 + 0.923880i) q^{9} +O(q^{10})$	\(q+(-1.40493 + 0.161763i) q^{2} +(-0.555570 - 0.831470i) q^{3} +(1.94767 - 0.454533i) q^{4} +(0.573343 + 2.88239i) q^{5} +(0.915039 + 1.07829i) q^{6} +(-0.457164 - 1.10369i) q^{7} +(-2.66281 + 0.953649i) q^{8} +(-0.382683 + 0.923880i) q^{9} +(-1.27177 - 3.95682i) q^{10} +(2.40965 + 1.61008i) q^{11} +(-1.46000 - 1.36690i) q^{12} +(-0.448390 + 2.25421i) q^{13} +(0.820822 + 1.47666i) q^{14} +(2.07809 - 2.07809i) q^{15} +(3.58680 - 1.77056i) q^{16} +(4.06310 + 4.06310i) q^{17} +(0.388194 - 1.35989i) q^{18} +(6.07997 + 1.20938i) q^{19} +(2.42682 + 5.35333i) q^{20} +(-0.663700 + 0.993297i) q^{21} +(-3.64585 - 1.87226i) q^{22} +(-3.42652 - 1.41931i) q^{23} +(2.27231 + 1.68423i) q^{24} +(-3.36006 + 1.39178i) q^{25} +(0.265309 - 3.23954i) q^{26} +(0.980785 - 0.195090i) q^{27} +(-1.39207 - 1.94183i) q^{28} +(2.32238 - 1.55176i) q^{29} +(-2.58341 + 3.25573i) q^{30} +5.26463i q^{31} +(-4.75280 + 3.06772i) q^{32} -2.89806i q^{33} +(-6.36564 - 5.05112i) q^{34} +(2.91916 - 1.95052i) q^{35} +(-0.325406 + 1.97335i) q^{36} +(-4.10237 + 0.816012i) q^{37} +(-8.73757 - 0.715581i) q^{38} +(2.12342 - 0.879549i) q^{39} +(-4.27549 - 7.12849i) q^{40} +(-11.6743 - 4.83565i) q^{41} +(0.771774 - 1.50288i) q^{42} +(3.86632 - 5.78635i) q^{43} +(5.42503 + 2.04063i) q^{44} +(-2.88239 - 0.573343i) q^{45} +(5.04363 + 1.43975i) q^{46} +(-6.83938 - 6.83938i) q^{47} +(-3.46488 - 1.99865i) q^{48} +(3.94061 - 3.94061i) q^{49} +(4.49551 - 2.49889i) q^{50} +(1.12101 - 5.63568i) q^{51} +(0.151299 + 4.59425i) q^{52} +(6.84757 + 4.57540i) q^{53} +(-1.34638 + 0.432744i) q^{54} +(-3.25932 + 7.86868i) q^{55} +(2.26988 + 2.50295i) q^{56} +(-2.37229 - 5.72720i) q^{57} +(-3.01176 + 2.55579i) q^{58} +(0.196660 + 0.988678i) q^{59} +(3.10286 - 4.99198i) q^{60} +(1.32785 + 1.98727i) q^{61} +(-0.851624 - 7.39644i) q^{62} +1.19463 q^{63} +(6.18111 - 5.07877i) q^{64} -6.75459 q^{65} +(0.468800 + 4.07158i) q^{66} +(-3.10501 - 4.64698i) q^{67} +(9.76037 + 6.06675i) q^{68} +(0.723559 + 3.63758i) q^{69} +(-3.78570 + 3.21256i) q^{70} +(-3.32085 - 8.01724i) q^{71} +(0.137957 - 2.82506i) q^{72} +(-4.82696 + 11.6533i) q^{73} +(5.63155 - 1.81005i) q^{74} +(3.02397 + 2.02055i) q^{75} +(12.3914 - 0.408077i) q^{76} +(0.675424 - 3.39558i) q^{77} +(-2.84098 + 1.57920i) q^{78} +(-6.87664 + 6.87664i) q^{79} +(7.15990 + 9.32342i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(17.1838 + 4.90528i) q^{82} +(-11.3817 - 2.26396i) q^{83} +(-0.841179 + 2.23628i) q^{84} +(-9.38189 + 14.0410i) q^{85} +(-4.49589 + 8.75486i) q^{86} +(-2.58049 - 1.06887i) q^{87} +(-7.95189 - 1.98937i) q^{88} +(9.91702 - 4.10777i) q^{89} +(4.14231 + 0.339243i) q^{90} +(2.69294 - 0.535659i) q^{91} +(-7.31885 - 1.20688i) q^{92} +(4.37738 - 2.92487i) q^{93} +(10.7152 + 8.50250i) q^{94} +18.2182i q^{95} +(5.19123 + 2.24747i) q^{96} -8.49536i q^{97} +(-4.89884 + 6.17373i) q^{98} +(-2.40965 + 1.61008i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) $ 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{16}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.40493	+	0.161763i	−0.993437	+	0.114384i
$2$	−1.40493	+	0.161763i	−0.993437	+	0.114384i
$3$	−0.555570	−	0.831470i	−0.320759	−	0.480049i
$3$	−0.555570	−	0.831470i	−0.320759	−	0.480049i
$4$	1.94767	−	0.454533i	0.973833	−	0.227266i
$5$	0.573343	+	2.88239i	0.256407	+	1.28904i	0.867481	+	0.497471i	$0.165738\pi$
$5$	0.573343	+	2.88239i	0.256407	+	1.28904i	−0.611074	+	0.791574i	$0.709262\pi$
$6$	0.915039	+	1.07829i	0.373563	+	0.440209i
$7$	−0.457164	−	1.10369i	−0.172792	−	0.417157i	0.813631	−	0.581382i	$-0.197488\pi$
$7$	−0.457164	−	1.10369i	−0.172792	−	0.417157i	−0.986423	+	0.164225i	$0.947488\pi$
$8$	−2.66281	+	0.953649i	−0.941445	+	0.337166i
$9$	−0.382683	+	0.923880i	−0.127561	+	0.307960i
$10$	−1.27177	−	3.95682i	−0.402170	−	1.25125i
$11$	2.40965	+	1.61008i	0.726537	+	0.485457i	0.863010	−	0.505187i	$-0.168577\pi$
$11$	2.40965	+	1.61008i	0.726537	+	0.485457i	−0.136473	+	0.990644i	$0.543577\pi$
$12$	−1.46000	−	1.36690i	−0.421464	−	0.394590i
$13$	−0.448390	+	2.25421i	−0.124361	+	0.625205i	0.867453	+	0.497518i	$0.165755\pi$
$13$	−0.448390	+	2.25421i	−0.124361	+	0.625205i	−0.991815	+	0.127687i	$0.959245\pi$
$14$	0.820822	+	1.47666i	0.219374	+	0.394654i
$15$	2.07809	−	2.07809i	0.536560	−	0.536560i
$16$	3.58680	−	1.77056i	0.896700	−	0.442639i
$17$	4.06310	+	4.06310i	0.985447	+	0.985447i	0.999896	−	0.0144488i	$-0.00459936\pi$
$17$	4.06310	+	4.06310i	0.985447	+	0.985447i	−0.0144488	+	0.999896i	$0.504599\pi$
$18$	0.388194	−	1.35989i	0.0914982	−	0.320530i
$19$	6.07997	+	1.20938i	1.39484	+	0.277451i	0.834590	−	0.550872i	$-0.185705\pi$
$19$	6.07997	+	1.20938i	1.39484	+	0.277451i	0.560251	+	0.828323i	$0.310705\pi$
$20$	2.42682	+	5.35333i	0.542654	+	1.19704i
$21$	−0.663700	+	0.993297i	−0.144831	+	0.216755i
$22$	−3.64585	−	1.87226i	−0.777297	−	0.399166i
$23$	−3.42652	−	1.41931i	−0.714480	−	0.295947i	−0.00432287	−	0.999991i	$-0.501376\pi$
$23$	−3.42652	−	1.41931i	−0.714480	−	0.295947i	−0.710157	+	0.704043i	$0.751376\pi$
$24$	2.27231	+	1.68423i	0.463833	+	0.343791i
$25$	−3.36006	+	1.39178i	−0.672011	+	0.278356i
$26$	0.265309	−	3.23954i	0.0520314	−	0.635327i
$27$	0.980785	−	0.195090i	0.188752	−	0.0375451i
$28$	−1.39207	−	1.94183i	−0.263076	−	0.366971i
$29$	2.32238	−	1.55176i	0.431254	−	0.288155i	−0.320936	−	0.947101i	$-0.603997\pi$
$29$	2.32238	−	1.55176i	0.431254	−	0.288155i	0.752190	+	0.658946i	$0.228997\pi$
$30$	−2.58341	+	3.25573i	−0.471664	+	0.594412i
$31$			5.26463i			0.945555i	0.881182	+	0.472777i	$0.156748\pi$
$31$			5.26463i			0.945555i	−0.881182	+	0.472777i	$0.843252\pi$
$32$	−4.75280	+	3.06772i	−0.840184	+	0.542302i
$33$		−	2.89806i		−	0.504488i
$34$	−6.36564	−	5.05112i	−1.09170	−	0.866260i
$35$	2.91916	−	1.95052i	0.493428	−	0.329698i
$36$	−0.325406	+	1.97335i	−0.0542343	+	0.328892i
$37$	−4.10237	+	0.816012i	−0.674425	+	0.134152i	−0.520409	−	0.853917i	$-0.674221\pi$
$37$	−4.10237	+	0.816012i	−0.674425	+	0.134152i	−0.154016	+	0.988068i	$0.549221\pi$
$38$	−8.73757	−	0.715581i	−1.41742	−	0.116083i
$39$	2.12342	−	0.879549i	0.340019	−	0.140841i
$40$	−4.27549	−	7.12849i	−0.676015	−	1.12711i
$41$	−11.6743	−	4.83565i	−1.82322	−	0.755201i	−0.973772	−	0.227525i	$-0.926937\pi$
$41$	−11.6743	−	4.83565i	−1.82322	−	0.755201i	−0.849445	−	0.527677i	$-0.823063\pi$
$42$	0.771774	−	1.50288i	0.119087	−	0.231899i
$43$	3.86632	−	5.78635i	0.589608	−	0.882410i	−0.409951	−	0.912107i	$-0.634454\pi$
$43$	3.86632	−	5.78635i	0.589608	−	0.882410i	0.999559	+	0.0296971i	$0.00945427\pi$
$44$	5.42503	+	2.04063i	0.817854	+	0.307636i
$45$	−2.88239	−	0.573343i	−0.429681	−	0.0854690i
$46$	5.04363	+	1.43975i	0.743642	+	0.212280i
$47$	−6.83938	−	6.83938i	−0.997627	−	0.997627i	0.00237063	−	0.999997i	$-0.499245\pi$
$47$	−6.83938	−	6.83938i	−0.997627	−	0.997627i	−0.999997	+	0.00237063i	$0.999245\pi$
$48$	−3.46488	−	1.99865i	−0.500113	−	0.288480i
$49$	3.94061	−	3.94061i	0.562944	−	0.562944i
$50$	4.49551	−	2.49889i	0.635761	−	0.353396i
$51$	1.12101	−	5.63568i	0.156972	−	0.789154i
$52$	0.151299	+	4.59425i	0.0209813	+	0.637108i
$53$	6.84757	+	4.57540i	0.940586	+	0.628480i	0.928454	−	0.371447i	$-0.121138\pi$
$53$	6.84757	+	4.57540i	0.940586	+	0.628480i	0.0121320	+	0.999926i	$0.496138\pi$
$54$	−1.34638	+	0.432744i	−0.183219	+	0.0588890i
$55$	−3.25932	+	7.86868i	−0.439486	+	1.06101i
$56$	2.26988	+	2.50295i	0.303325	+	0.334471i
$57$	−2.37229	−	5.72720i	−0.314217	−	0.758587i
$58$	−3.01176	+	2.55579i	−0.395464	+	0.335592i
$59$	0.196660	+	0.988678i	0.0256030	+	0.128715i	0.991473	−	0.130312i	$-0.0415980\pi$
$59$	0.196660	+	0.988678i	0.0256030	+	0.128715i	−0.965870	+	0.259027i	$0.916598\pi$
$60$	3.10286	−	4.99198i	0.400578	−	0.644462i
$61$	1.32785	+	1.98727i	0.170014	+	0.254444i	0.906686	−	0.421807i	$-0.138604\pi$
$61$	1.32785	+	1.98727i	0.170014	+	0.254444i	−0.736672	+	0.676250i	$0.763604\pi$
$62$	−0.851624	−	7.39644i	−0.108156	−	0.939349i
$63$	1.19463			0.150509
$64$	6.18111	−	5.07877i	0.772639	−	0.634846i
$65$	−6.75459			−0.837804
$66$	0.468800	+	4.07158i	0.0577053	+	0.501177i
$67$	−3.10501	−	4.64698i	−0.379337	−	0.567719i	0.591846	−	0.806051i	$-0.298399\pi$
$67$	−3.10501	−	4.64698i	−0.379337	−	0.567719i	−0.971184	+	0.238332i	$0.923399\pi$
$68$	9.76037	+	6.06675i	1.18362	+	0.735701i
$69$	0.723559	+	3.63758i	0.0871063	+	0.437913i
$70$	−3.78570	+	3.21256i	−0.452477	+	0.383975i
$71$	−3.32085	−	8.01724i	−0.394112	−	0.951471i	−0.989034	−	0.147688i	$-0.952817\pi$
$71$	−3.32085	−	8.01724i	−0.394112	−	0.951471i	0.594922	−	0.803784i	$-0.297183\pi$
$72$	0.137957	−	2.82506i	0.0162584	−	0.332937i
$73$	−4.82696	+	11.6533i	−0.564953	+	1.36392i	0.340809	+	0.940133i	$0.389299\pi$
$73$	−4.82696	+	11.6533i	−0.564953	+	1.36392i	−0.905763	+	0.423786i	$0.860701\pi$
$74$	5.63155	−	1.81005i	0.654654	−	0.210414i
$75$	3.02397	+	2.02055i	0.349178	+	0.233313i
$76$	12.3914	−	0.408077i	1.42140	−	0.0468096i
$77$	0.675424	−	3.39558i	0.0769717	−	0.386963i
$78$	−2.84098	+	1.57920i	−0.321678	+	0.178809i
$79$	−6.87664	+	6.87664i	−0.773683	+	0.773683i	−0.978748	−	0.205065i	$-0.934259\pi$
$79$	−6.87664	+	6.87664i	−0.773683	+	0.773683i	0.205065	+	0.978748i	$0.434259\pi$
$80$	7.15990	+	9.32342i	0.800501	+	1.04239i
$81$	−0.707107	−	0.707107i	−0.0785674	−	0.0785674i
$82$	17.1838	+	4.90528i	1.89763	+	0.541698i
$83$	−11.3817	−	2.26396i	−1.24930	−	0.248502i	−0.474246	−	0.880392i	$-0.657279\pi$
$83$	−11.3817	−	2.26396i	−1.24930	−	0.248502i	−0.775058	+	0.631890i	$0.782279\pi$
$84$	−0.841179	+	2.23628i	−0.0917801	+	0.243999i
$85$	−9.38189	+	14.0410i	−1.01761	+	1.52296i
$86$	−4.49589	+	8.75486i	−0.484804	+	0.944060i
$87$	−2.58049	−	1.06887i	−0.276657	−	0.114595i
$88$	−7.95189	−	1.98937i	−0.847674	−	0.212067i
$89$	9.91702	−	4.10777i	1.05120	−	0.435422i	0.210881	−	0.977512i	$-0.432367\pi$
$89$	9.91702	−	4.10777i	1.05120	−	0.435422i	0.840321	+	0.542089i	$0.182367\pi$
$90$	4.14231	+	0.339243i	0.436638	+	0.0357593i
$91$	2.69294	−	0.535659i	0.282297	−	0.0561524i
$92$	−7.31885	−	1.20688i	−0.763043	−	0.125826i
$93$	4.37738	−	2.92487i	0.453913	−	0.303295i
$94$	10.7152	+	8.50250i	1.10519	+	0.876966i
$95$			18.2182i			1.86915i
$96$	5.19123	+	2.24747i	0.529828	+	0.229382i
$97$		−	8.49536i		−	0.862573i	−0.902215	−	0.431287i	$-0.858060\pi$
$97$		−	8.49536i		−	0.862573i	0.902215	−	0.431287i	$-0.141940\pi$
$98$	−4.89884	+	6.17373i	−0.494858	+	0.623641i
$99$	−2.40965	+	1.61008i	−0.242179	+	0.161819i
$100$	−5.91165	+	4.23798i	−0.591165	+	0.423798i
$101$	13.1309	−	2.61189i	1.30657	−	0.259893i	0.507771	−	0.861492i	$-0.330470\pi$
$101$	13.1309	−	2.61189i	1.30657	−	0.259893i	0.798798	+	0.601600i	$0.205470\pi$
$102$	−0.663291	+	8.09909i	−0.0656756	+	0.801929i
$103$	15.9973	−	6.62631i	1.57626	−	0.652910i	0.588448	−	0.808535i	$-0.299739\pi$
$103$	15.9973	−	6.62631i	1.57626	−	0.652910i	0.987816	+	0.155625i	$0.0497393\pi$
$104$	−0.955746	−	6.43014i	−0.0937186	−	0.630527i
$105$	−3.24360	−	1.34354i	−0.316543	−	0.131116i
$106$	−10.3605	−	5.32044i	−1.00630	−	0.516767i
$107$	1.47596	−	2.20893i	0.142687	−	0.213546i	−0.753242	−	0.657743i	$-0.771511\pi$
$107$	1.47596	−	2.20893i	0.142687	−	0.213546i	0.895929	+	0.444198i	$0.146511\pi$
$108$	1.82157	−	0.825770i	0.175280	−	0.0794597i
$109$	−3.65104	−	0.726237i	−0.349706	−	0.0695609i	0.0171119	−	0.999854i	$-0.494553\pi$
$109$	−3.65104	−	0.726237i	−0.349706	−	0.0695609i	−0.366818	+	0.930293i	$0.619553\pi$
$110$	3.30625	−	11.5822i	0.315239	−	1.10432i
$111$	2.95764	+	2.95764i	0.280727	+	0.280727i
$112$	−3.59391	−	3.14929i	−0.339592	−	0.297580i
$113$	11.2901	−	11.2901i	1.06208	−	1.06208i	0.0641425	−	0.997941i	$-0.479569\pi$
$113$	11.2901	−	11.2901i	1.06208	−	1.06208i	0.997941	−	0.0641425i	$-0.0204312\pi$
$114$	4.25935	+	7.66258i	0.398925	+	0.717666i
$115$	2.12644	−	10.6903i	0.198292	−	0.996879i
$116$	3.81788	−	4.07791i	0.354482	−	0.378624i
$117$	−1.91103	−	1.27691i	−0.176674	−	0.118050i
$118$	−0.436226	−	1.35721i	−0.0401579	−	0.124942i
$119$	2.62691	−	6.34192i	0.240808	−	0.581363i
$120$	−3.55179	+	7.51532i	−0.324232	+	0.686051i
$121$	−0.995448	−	2.40322i	−0.0904953	−	0.218475i
$122$	−2.18701	−	2.57718i	−0.198002	−	0.233327i
$123$	2.46519	+	12.3934i	0.222279	+	1.11747i
$124$	2.39295	+	10.2537i	0.214893	+	0.920812i
$125$	2.22560	+	3.33084i	0.199063	+	0.297919i
$126$	−1.67837	+	0.193247i	−0.149521	+	0.0172158i
$127$	−15.5723			−1.38182			−0.690909	−	0.722942i	$-0.742790\pi$
$127$	−15.5723			−1.38182			−0.690909	+	0.722942i	$0.742790\pi$
$128$	−7.86248	+	8.13520i	−0.694951	+	0.719057i
$129$	−6.95919			−0.612722
$130$	9.48974	−	1.09265i	0.832305	−	0.0958314i
$131$	0.279216	+	0.417877i	0.0243952	+	0.0365101i	0.843467	−	0.537181i	$-0.180511\pi$
$131$	0.279216	+	0.417877i	0.0243952	+	0.0365101i	−0.819072	+	0.573691i	$0.805511\pi$
$132$	−1.31726	−	5.64446i	−0.114653	−	0.491287i
$133$	−1.44476	−	7.26330i	−0.125277	−	0.629808i
$134$	5.11404	+	6.02641i	0.441786	+	0.520602i
$135$	1.12465	+	2.71515i	0.0967947	+	0.233683i
$136$	−14.6940	−	6.94449i	−1.26000	−	0.595485i
$137$	4.94499	−	11.9383i	0.422479	−	1.01996i	−0.559135	−	0.829077i	$-0.688866\pi$
$137$	4.94499	−	11.9383i	0.422479	−	1.01996i	0.981614	−	0.190878i	$-0.0611335\pi$
$138$	−1.60498	−	4.99350i	−0.136625	−	0.425075i
$139$	14.7935	+	9.88469i	1.25477	+	0.838408i	0.991974	−	0.126444i	$-0.0403564\pi$
$139$	14.7935	+	9.88469i	1.25477	+	0.838408i	0.262793	+	0.964852i	$0.415356\pi$
$140$	4.79897	−	5.12582i	0.405587	−	0.433211i
$141$	−1.88698	+	9.48650i	−0.158913	+	0.798907i
$142$	5.96246	+	10.7265i	0.500359	+	0.900146i
$143$	−4.70992	+	4.70992i	−0.393863	+	0.393863i
$144$	0.263172	+	3.99133i	0.0219310	+	0.332611i
$145$	5.80430	+	5.80430i	0.482021	+	0.482021i
$146$	4.89647	−	17.1529i	0.405235	−	1.41959i
$147$	−5.46578	−	1.08721i	−0.450810	−	0.0896717i
$148$	−7.61914	+	3.45398i	−0.626289	+	0.283915i
$149$	−0.777282	+	1.16329i	−0.0636775	+	0.0953001i	−0.861942	−	0.507007i	$-0.830752\pi$
$149$	−0.777282	+	1.16329i	−0.0636775	+	0.0953001i	0.798264	+	0.602307i	$0.205752\pi$
$150$	−4.57532	−	2.34957i	−0.373574	−	0.191842i
$151$	−9.74739	−	4.03750i	−0.793231	−	0.328567i	−0.0509894	−	0.998699i	$-0.516237\pi$
$151$	−9.74739	−	4.03750i	−0.793231	−	0.328567i	−0.742242	+	0.670132i	$0.766237\pi$
$152$	−17.3431	+	2.57780i	−1.40671	+	0.209087i
$153$	−5.30870	+	2.19893i	−0.429183	+	0.177773i
$154$	−0.399643	+	4.87982i	−0.0322041	+	0.393227i
$155$	−15.1747	+	3.01844i	−1.21886	+	0.242447i
$156$	3.73593	−	2.67823i	0.299113	−	0.214430i
$157$	4.21665	−	2.81748i	0.336525	−	0.224859i	−0.375813	−	0.926696i	$-0.622636\pi$
$157$	4.21665	−	2.81748i	0.336525	−	0.224859i	0.712338	+	0.701837i	$0.247636\pi$
$158$	8.54883	−	10.7736i	0.680108	−	0.857102i
$159$		−	8.23550i		−	0.653118i
$160$	−11.5674	−	11.9406i	−0.914480	−	0.943984i
$161$			4.43069i			0.349187i
$162$	1.10782	+	0.879053i	0.0870386	+	0.0690649i
$163$	1.42704	−	0.953517i	0.111774	−	0.0746852i	−0.498427	−	0.866932i	$-0.666089\pi$
$163$	1.42704	−	0.953517i	0.111774	−	0.0746852i	0.610201	+	0.792247i	$0.291089\pi$
$164$	−24.9356	−	4.11188i	−1.94714	−	0.321084i
$165$	8.35335	−	1.66158i	0.650307	−	0.129354i
$166$	16.3567	+	1.33957i	1.26953	+	0.103971i
$167$	9.52713	−	3.94627i	0.737231	−	0.305371i	0.0177115	−	0.999843i	$-0.494362\pi$
$167$	9.52713	−	3.94627i	0.737231	−	0.305371i	0.719520	+	0.694472i	$0.244362\pi$
$168$	0.820050	−	3.27790i	0.0632682	−	0.252895i
$169$	7.13003	+	2.95335i	0.548464	+	0.227181i
$170$	10.9096	−	21.2443i	0.836728	−	1.62936i
$171$	−3.44403	+	5.15435i	−0.263371	+	0.394163i
$172$	4.90020	−	13.0272i	0.373637	−	0.993318i
$173$	−9.52608	−	1.89486i	−0.724254	−	0.144063i	−0.180822	−	0.983516i	$-0.557876\pi$
$173$	−9.52608	−	1.89486i	−0.724254	−	0.144063i	−0.543433	+	0.839453i	$0.682876\pi$
$174$	3.79831	+	1.08426i	0.287949	+	0.0821979i
$175$	3.07220	+	3.07220i	0.232236	+	0.232236i
$176$	11.4937	+	1.50860i	0.866368	+	0.113715i
$177$	0.712797	−	0.712797i	0.0535771	−	0.0535771i
$178$	−13.2683	+	7.37534i	−0.994498	+	0.552805i
$179$	−2.75596	+	13.8551i	−0.205990	+	1.03558i	0.729971	+	0.683478i	$0.239534\pi$
$179$	−2.75596	+	13.8551i	−0.205990	+	1.03558i	−0.935961	+	0.352104i	$0.885466\pi$
$180$	−5.87454	+	0.193461i	−0.437862	+	0.0144197i
$181$	−17.5831	−	11.7487i	−1.30694	−	0.873270i	−0.309948	−	0.950754i	$-0.600312\pi$
$181$	−17.5831	−	11.7487i	−1.30694	−	0.873270i	−0.996994	+	0.0774833i	$0.975312\pi$
$182$	−3.69675	+	1.18818i	−0.274021	+	0.0880741i
$183$	0.914639	−	2.20813i	0.0676120	−	0.163230i
$184$	10.4777	+	0.511660i	0.772427	+	0.0377201i
$185$	−4.70413	−	11.3568i	−0.345855	−	0.834967i
$186$	−5.67678	+	4.81734i	−0.416241	+	0.353224i
$187$	3.24875	+	16.3326i	0.237572	+	1.19436i
$188$	−16.4296	−	10.2121i	−1.19825	−	0.744794i
$189$	−0.663700	−	0.993297i	−0.0482771	−	0.0722517i
$190$	−2.94704	−	25.5954i	−0.213801	−	1.85688i
$191$	−14.7446			−1.06688			−0.533441	−	0.845837i	$-0.679101\pi$
$191$	−14.7446			−1.06688			−0.533441	+	0.845837i	$0.679101\pi$
$192$	−7.65688	−	2.31779i	−0.552588	−	0.167272i
$193$	14.2646			1.02679			0.513395	−	0.858152i	$-0.328388\pi$
$193$	14.2646			1.02679			0.513395	+	0.858152i	$0.328388\pi$
$194$	1.37424	+	11.9354i	0.0986646	+	0.856912i
$195$	3.75265	+	5.61624i	0.268733	+	0.402187i
$196$	5.88385	−	9.46613i	0.420275	−	0.676152i
$197$	3.03683	+	15.2672i	0.216365	+	1.08774i	0.924360	+	0.381522i	$0.124600\pi$
$197$	3.03683	+	15.2672i	0.216365	+	1.08774i	−0.707995	+	0.706218i	$0.750400\pi$
$198$	3.12494	−	2.65184i	0.222080	−	0.188458i
$199$	1.86681	+	4.50688i	0.132335	+	0.319484i	0.976132	−	0.217178i	$-0.0696851\pi$
$199$	1.86681	+	4.50688i	0.132335	+	0.319484i	−0.843797	+	0.536662i	$0.819685\pi$
$200$	7.61992	−	6.91036i	0.538810	−	0.488636i
$201$	−2.13877	+	5.16344i	−0.150857	+	0.364201i
$202$	−18.0254	+	5.79362i	−1.26827	+	0.407637i
$203$	−2.77438	−	1.85378i	−0.194723	−	0.130110i
$204$	−0.378257	−	11.4860i	−0.0264833	−	0.804178i
$205$	7.24485	−	36.4223i	0.506003	−	2.54385i
$206$	−21.4033	+	11.8973i	−1.49124	+	0.828924i
$207$	2.62255	−	2.62255i	0.182280	−	0.182280i
$208$	2.38292	+	8.87930i	0.165226	+	0.615668i
$209$	12.7034	+	12.7034i	0.878713	+	0.878713i
$210$	4.77437	+	1.36289i	0.329463	+	0.0940483i
$211$	−20.3138	−	4.04066i	−1.39846	−	0.278170i	−0.562424	−	0.826849i	$-0.690131\pi$
$211$	−20.3138	−	4.04066i	−1.39846	−	0.278170i	−0.836033	+	0.548679i	$0.815131\pi$
$212$	15.4164	+	5.79890i	1.05881	+	0.398270i
$213$	−4.82112	+	7.21532i	−0.330338	+	0.494386i
$214$	−1.71630	+	3.34216i	−0.117324	+	0.228465i
$215$	18.8953	+	7.82667i	1.28865	+	0.533774i
$216$	−2.42560	+	1.45481i	−0.165041	+	0.0989875i
$217$	5.81053	−	2.40680i	0.394444	−	0.163384i
$218$	5.24694	+	0.429709i	0.355368	+	0.0291036i
$219$	12.3711	−	2.46076i	0.835962	−	0.166283i
$220$	−2.77148	+	16.8070i	−0.186853	+	1.13313i
$221$	−10.9809	+	7.33723i	−0.738658	+	0.493555i
$222$	−4.63372	−	3.67685i	−0.310995	−	0.246774i
$223$			10.6299i			0.711833i	0.934518	+	0.355917i	$0.115831\pi$
$223$			10.6299i			0.711833i	−0.934518	+	0.355917i	$0.884169\pi$
$224$	5.55863	+	3.84317i	0.371402	+	0.256783i
$225$		−	3.63690i		−	0.242460i
$226$	−14.0355	+	17.6881i	−0.933627	+	1.17660i
$227$	−0.723182	+	0.483215i	−0.0479993	+	0.0320721i	−0.579338	−	0.815087i	$-0.696689\pi$
$227$	−0.723182	+	0.483215i	−0.0479993	+	0.0320721i	0.531339	+	0.847159i	$0.321689\pi$
$228$	−7.22362	−	10.0764i	−0.478396	−	0.667326i
$229$	16.9691	−	3.37536i	1.12135	−	0.223050i	0.400605	−	0.916251i	$-0.368800\pi$
$229$	16.9691	−	3.37536i	1.12135	−	0.223050i	0.720745	+	0.693200i	$0.243800\pi$
$230$	−1.25820	+	15.3632i	−0.0829631	+	1.01302i
$231$	−3.19857	+	1.32489i	−0.210450	+	0.0871714i
$232$	−4.70421	+	6.34678i	−0.308846	+	0.416686i
$233$	9.97421	+	4.13145i	0.653432	+	0.270660i	0.684672	−	0.728852i	$-0.259946\pi$
$233$	9.97421	+	4.13145i	0.653432	+	0.270660i	−0.0312398	+	0.999512i	$0.509946\pi$
$234$	2.89142	+	1.48483i	0.189018	+	0.0970666i
$235$	15.7925	−	23.6351i	1.03019	−	1.54178i
$236$	0.832415	+	1.83623i	0.0541856	+	0.119528i
$237$	9.53818	+	1.89726i	0.619571	+	0.123240i
$238$	−2.66474	+	9.33490i	−0.172729	+	0.605092i
$239$	−6.58523	−	6.58523i	−0.425963	−	0.425963i	0.461287	−	0.887251i	$-0.347388\pi$
$239$	−6.58523	−	6.58523i	−0.425963	−	0.425963i	−0.887251	+	0.461287i	$0.847388\pi$
$240$	3.77431	−	11.1331i	0.243631	−	0.718636i
$241$	0.615471	−	0.615471i	0.0396460	−	0.0396460i	−0.687006	−	0.726652i	$-0.741075\pi$
$241$	0.615471	−	0.615471i	0.0396460	−	0.0396460i	0.726652	+	0.687006i	$0.241075\pi$
$242$	1.78729	+	3.21534i	0.114891	+	0.206690i
$243$	−0.195090	+	0.980785i	−0.0125150	+	0.0629174i
$244$	3.48949	+	3.26698i	0.223391	+	0.209147i
$245$	13.6177	+	9.09906i	0.870003	+	0.581317i
$246$	−5.46822	−	17.0130i	−0.348641	−	1.08471i
$247$	−5.45239	+	13.1632i	−0.346928	+	0.837557i
$248$	−5.02060	−	14.0187i	−0.318809	−	0.890188i
$249$	4.44092	+	10.7213i	0.281432	+	0.679436i
$250$	−3.66562	−	4.31958i	−0.231834	−	0.273194i
$251$	0.825091	+	4.14801i	0.0520793	+	0.261820i	0.998049	−	0.0624345i	$-0.0198865\pi$
$251$	0.825091	+	4.14801i	0.0520793	+	0.261820i	−0.945970	+	0.324255i	$0.894886\pi$
$252$	2.32674	−	0.542998i	0.146571	−	0.0342056i
$253$	−5.97153	−	8.93702i	−0.375427	−	0.561866i
$254$	21.8780	−	2.51903i	1.37275	−	0.158058i
$255$	16.8870			1.05750
$256$	9.73026	−	12.7013i	0.608141	−	0.793829i
$257$	−15.1916			−0.947627			−0.473813	−	0.880625i	$-0.657123\pi$
$257$	−15.1916			−0.947627			−0.473813	+	0.880625i	$0.657123\pi$
$258$	9.77718	−	1.12574i	0.608701	−	0.0700856i
$259$	2.77608	+	4.15470i	0.172497	+	0.258161i
$260$	−13.1557	+	3.07019i	−0.815881	+	0.190405i
$261$	0.544906	+	2.73943i	0.0337289	+	0.169566i
$262$	−0.459877	−	0.541921i	−0.0284113	−	0.0334800i
$263$	4.97449	+	12.0095i	0.306740	+	0.740536i	0.999807	+	0.0196623i	$0.00625911\pi$
$263$	4.97449	+	12.0095i	0.306740	+	0.740536i	−0.693067	+	0.720873i	$0.743741\pi$
$264$	2.76373	+	7.71699i	0.170096	+	0.474948i
$265$	−9.26209	+	22.3607i	−0.568965	+	1.37360i
$266$	3.20472	+	9.97073i	0.196494	+	0.611345i
$267$	−8.92508	−	5.96355i	−0.546206	−	0.364963i
$268$	−8.15973	−	7.63943i	−0.498435	−	0.466652i
$269$	5.87507	−	29.5360i	0.358209	−	1.80084i	−0.209718	−	0.977762i	$-0.567255\pi$
$269$	5.87507	−	29.5360i	0.358209	−	1.80084i	0.567927	−	0.823079i	$-0.307745\pi$
$270$	−2.01927	−	3.63268i	−0.122889	−	0.221078i
$271$	14.4641	−	14.4641i	0.878634	−	0.878634i	−0.114759	−	0.993393i	$-0.536610\pi$
$271$	14.4641	−	14.4641i	0.878634	−	0.878634i	0.993393	+	0.114759i	$0.0366096\pi$
$272$	21.7675	+	7.37958i	1.31985	+	0.447453i
$273$	−1.94150	−	1.94150i	−0.117505	−	0.117505i
$274$	−5.01620	+	17.5724i	−0.303040	+	1.06159i
$275$	−10.3374	−	2.05624i	−0.623371	−	0.123996i
$276$	3.06265	+	6.75590i	0.184350	+	0.406658i
$277$	−0.431697	+	0.646081i	−0.0259382	+	0.0388192i	−0.844212	−	0.536009i	$-0.819931\pi$
$277$	−0.431697	+	0.646081i	−0.0259382	+	0.0388192i	0.818274	+	0.574828i	$0.194931\pi$
$278$	−22.3828	−	11.4943i	−1.34243	−	0.689380i
$279$	−4.86388	−	2.01468i	−0.291193	−	0.120616i
$280$	−5.91306	+	7.97772i	−0.353373	+	0.476760i
$281$	−19.1511	+	7.93265i	−1.14246	+	0.473222i	−0.871998	−	0.489509i	$-0.837176\pi$
$281$	−19.1511	+	7.93265i	−1.14246	+	0.473222i	−0.270461	+	0.962731i	$0.587176\pi$
$282$	1.11651	−	13.6331i	0.0664873	−	0.811841i
$283$	−10.4218	+	2.07302i	−0.619509	+	0.123228i	−0.494860	−	0.868973i	$-0.664781\pi$
$283$	−10.4218	+	2.07302i	−0.619509	+	0.123228i	−0.124649	+	0.992201i	$0.539781\pi$
$284$	−10.1120	−	14.1055i	−0.600037	−	0.837005i
$285$	15.1479	−	10.1215i	0.897285	−	0.599546i
$286$	5.85522	−	7.37900i	0.346226	−	0.436329i
$287$			15.0955i			0.891060i
$288$	−1.01539	−	5.56498i	−0.0598324	−	0.327919i
$289$			16.0176i			0.942211i
$290$	−9.09357	−	7.21572i	−0.533993	−	0.423722i
$291$	−7.06364	+	4.71977i	−0.414078	+	0.276678i
$292$	−4.10449	+	24.8908i	−0.240197	+	1.45662i
$293$	3.80735	−	0.757329i	0.222428	−	0.0442437i	−0.0826181	−	0.996581i	$-0.526328\pi$
$293$	3.80735	−	0.757329i	0.222428	−	0.0442437i	0.305046	+	0.952338i	$0.401328\pi$
$294$	7.85492	+	0.643295i	0.458108	+	0.0375177i
$295$	−2.73700	+	1.13370i	−0.159354	+	0.0660068i
$296$	10.1456	−	6.08510i	0.589703	−	0.353689i
$297$	2.67746	+	1.10904i	0.155362	+	0.0643531i
$298$	0.903852	−	1.76007i	0.0523587	−	0.101958i
$299$	4.73585	−	7.08770i	0.273881	−	0.409892i
$300$	6.80809	+	2.56087i	0.393065	+	0.147852i
$301$	−8.15389	−	1.62191i	−0.469983	−	0.0934854i
$302$	14.3475	+	4.09564i	0.825608	+	0.235678i
$303$	−9.46682	−	9.46682i	−0.543854	−	0.543854i
$304$	23.9489	−	6.42712i	1.37356	−	0.368620i
$305$	−4.96677	+	4.96677i	−0.284396	+	0.284396i
$306$	7.10265	−	3.94811i	0.406031	−	0.225698i
$307$	1.82304	−	9.16506i	0.104047	−	0.523078i	−0.893248	−	0.449565i	$-0.851579\pi$
$307$	1.82304	−	9.16506i	0.104047	−	0.523078i	0.997294	−	0.0735128i	$-0.0234210\pi$
$308$	−0.227906	−	6.92046i	−0.0129861	−	0.394330i
$309$	−14.3972	−	9.61991i	−0.819029	−	0.547258i
$310$	20.8312	−	6.69541i	1.18313	−	0.380274i
$311$	10.1964	−	24.6163i	0.578186	−	1.39586i	−0.316253	−	0.948675i	$-0.602425\pi$
$311$	10.1964	−	24.6163i	0.578186	−	1.39586i	0.894439	−	0.447190i	$-0.147575\pi$
$312$	−4.81548	+	4.36707i	−0.272623	+	0.247236i
$313$	−11.8022	−	28.4930i	−0.667098	−	1.61052i	−0.786441	−	0.617665i	$-0.788079\pi$
$313$	−11.8022	−	28.4930i	−0.667098	−	1.61052i	0.119343	−	0.992853i	$-0.461921\pi$
$314$	−5.46834	+	4.64046i	−0.308596	+	0.261876i
$315$	0.684932	+	3.44338i	0.0385915	+	0.194013i
$316$	−10.2677	+	16.5191i	−0.577605	+	0.929270i
$317$	8.06770	+	12.0742i	0.453127	+	0.678153i	0.985753	−	0.168198i	$-0.0537947\pi$
$317$	8.06770	+	12.0742i	0.453127	+	0.678153i	−0.532626	+	0.846351i	$0.678795\pi$
$318$	1.33220	+	11.5703i	0.0747062	+	0.648831i
$319$	8.09457			0.453209
$320$	18.1829	+	14.9045i	1.01645	+	0.833187i
$321$	−2.65666			−0.148280
$322$	−0.716723	−	6.22481i	−0.0399414	−	0.346895i
$323$	19.7897	+	29.6174i	1.10113	+	1.64795i
$324$	−1.69861	−	1.05580i	−0.0943673	−	0.0586558i
$325$	−1.63075	−	8.19833i	−0.0904577	−	0.454762i
$326$	−1.85065	+	1.57047i	−0.102498	+	0.0869802i
$327$	1.42457	+	3.43920i	0.0787786	+	0.190188i
$328$	35.6979	+	1.74324i	1.97109	+	0.0962545i
$329$	−4.42185	+	10.6753i	−0.243785	+	0.588548i
$330$	−11.4671	+	3.68568i	−0.631243	+	0.202890i
$331$	−15.0008	−	10.0232i	−0.824517	−	0.550925i	0.0702129	−	0.997532i	$-0.477632\pi$
$331$	−15.0008	−	10.0232i	−0.824517	−	0.550925i	−0.894730	+	0.446607i	$0.852632\pi$
$332$	−23.1968	+	0.763919i	−1.27309	+	0.0419255i
$333$	0.816012	−	4.10237i	0.0447172	−	0.224808i
$334$	−12.7466	+	7.08537i	−0.697463	+	0.387694i
$335$	11.6142	−	11.6142i	0.634550	−	0.634550i
$336$	−0.621870	+	4.73787i	−0.0339258	+	0.258472i
$337$	−1.74612	−	1.74612i	−0.0951174	−	0.0951174i	0.657947	−	0.753064i	$-0.271425\pi$
$337$	−1.74612	−	1.74612i	−0.0951174	−	0.0951174i	−0.753064	+	0.657947i	$0.771425\pi$
$338$	−10.4949	−	2.99588i	−0.570850	−	0.162955i
$339$	−15.6598	−	3.11493i	−0.850525	−	0.169180i
$340$	−11.8907	+	31.6115i	−0.644863	+	1.71438i
$341$	−8.47645	+	12.6859i	−0.459026	+	0.686981i
$342$	4.00483	−	7.79862i	0.216557	−	0.421701i
$343$	−13.8766	−	5.74787i	−0.749265	−	0.310356i
$344$	−4.77712	+	19.0951i	−0.257565	+	1.02954i
$345$	−10.0701	+	4.17116i	−0.542155	+	0.224568i
$346$	13.6900	+	1.12117i	0.735979	+	0.0602745i
$347$	−9.84943	+	1.95917i	−0.528745	+	0.105174i	−0.452242	−	0.891895i	$-0.649376\pi$
$347$	−9.84943	+	1.95917i	−0.528745	+	0.105174i	−0.0765033	+	0.997069i	$0.524376\pi$
$348$	−5.51176	−	0.908890i	−0.295461	−	0.0487216i
$349$	−21.4960	+	14.3632i	−1.15065	+	0.768842i	−0.976424	−	0.215863i	$-0.930744\pi$
$349$	−21.4960	+	14.3632i	−1.15065	+	0.768842i	−0.174230	+	0.984705i	$0.555744\pi$
$350$	−4.81319	−	3.81926i	−0.257276	−	0.204148i
$351$			2.29837i			0.122678i
$352$	−16.3919	−	0.260230i	−0.873689	−	0.0138703i
$353$			24.3940i			1.29836i	0.760633	+	0.649182i	$0.224889\pi$
$353$			24.3940i			1.29836i	−0.760633	+	0.649182i	$0.775111\pi$
$354$	−0.886127	+	1.11674i	−0.0470971	+	0.0593538i
$355$	21.2048	−	14.1686i	1.12544	−	0.751992i
$356$	17.4479	−	12.5082i	0.924738	−	0.662931i
$357$	−6.73255	+	1.33919i	−0.356324	+	0.0708773i
$358$	1.63068	−	19.9113i	0.0861841	−	1.05235i
$359$	17.0195	−	7.04969i	0.898253	−	0.372068i	0.114705	−	0.993400i	$-0.463408\pi$
$359$	17.0195	−	7.04969i	0.898253	−	0.372068i	0.783548	+	0.621331i	$0.213408\pi$
$360$	8.22203	−	1.22208i	0.433339	−	0.0644095i
$361$	17.9497	+	7.43501i	0.944721	+	0.391316i
$362$	26.6036	+	13.6617i	1.39825	+	0.718046i
$363$	−1.44517	+	2.16284i	−0.0758516	+	0.113520i
$364$	5.00147	−	2.26732i	0.262148	−	0.118840i
$365$	−36.3569	−	7.23184i	−1.90301	−	0.378532i
$366$	−0.927810	+	3.25023i	−0.0484974	+	0.169892i
$367$	4.47084	+	4.47084i	0.233376	+	0.233376i	0.814100	−	0.580724i	$-0.197231\pi$
$367$	4.47084	+	4.47084i	0.233376	+	0.233376i	−0.580724	+	0.814100i	$0.697231\pi$
$368$	−14.8032	+	0.976062i	−0.771672	+	0.0508808i
$369$	8.93511	−	8.93511i	0.465143	−	0.465143i
$370$	8.44609	+	15.1945i	0.439091	+	0.789926i
$371$	1.91937	−	9.64932i	0.0996487	−	0.500968i
$372$	7.19621	−	7.68633i	0.373106	−	0.398518i
$373$	6.48135	+	4.33070i	0.335591	+	0.224235i	0.711935	−	0.702245i	$-0.247819\pi$
$373$	6.48135	+	4.33070i	0.335591	+	0.224235i	−0.376344	+	0.926480i	$0.622819\pi$
$374$	−7.20628	−	22.4206i	−0.372628	−	1.15934i
$375$	1.53302	−	3.70103i	0.0791646	−	0.191120i
$376$	24.7343	+	11.6896i	1.27558	+	0.602845i
$377$	2.45667	+	5.93092i	0.126525	+	0.305458i
$378$	1.09313	+	1.28815i	0.0562246	+	0.0662554i
$379$	0.688559	+	3.46162i	0.0353689	+	0.177812i	0.994432	−	0.105381i	$-0.0336063\pi$
$379$	0.688559	+	3.46162i	0.0353689	+	0.177812i	−0.959063	+	0.283193i	$0.908606\pi$
$380$	8.28079	+	35.4830i	0.424795	+	1.82024i
$381$	8.65151	+	12.9479i	0.443230	+	0.663341i
$382$	20.7152	−	2.38514i	1.05988	−	0.122034i
$383$	22.7199			1.16093			0.580467	−	0.814284i	$-0.302870\pi$
$383$	22.7199			1.16093			0.580467	+	0.814284i	$0.302870\pi$
$384$	11.1323	+	2.01774i	0.568094	+	0.102967i
$385$	10.1746			0.518548
$386$	−20.0408	+	2.30749i	−1.02005	+	0.117448i
$387$	3.86632	+	5.78635i	0.196536	+	0.294137i
$388$	−3.86142	−	16.5461i	−0.196034	−	0.840002i
$389$	−5.90069	−	29.6648i	−0.299177	−	1.50406i	−0.779182	−	0.626797i	$-0.784365\pi$
$389$	−5.90069	−	29.6648i	−0.299177	−	1.50406i	0.480006	−	0.877265i	$-0.340635\pi$
$390$	−6.18072	−	7.28339i	−0.312973	−	0.368809i
$391$	−8.15550	−	19.6891i	−0.412442	−	0.995722i
$392$	−6.73514	+	14.2511i	−0.340176	+	0.719787i
$393$	0.192328	−	0.464320i	0.00970164	−	0.0234218i
$394$	−6.73620	−	20.9581i	−0.339365	−	1.05585i
$395$	−23.7639	−	15.8785i	−1.19569	−	0.798934i
$396$	−3.96136	+	4.23116i	−0.199066	+	0.212624i
$397$	1.57498	−	7.91796i	0.0790460	−	0.397391i	−0.920925	−	0.389740i	$-0.872565\pi$
$397$	1.57498	−	7.91796i	0.0790460	−	0.397391i	0.999971	−	0.00765051i	$-0.00243526\pi$
$398$	−3.35179	−	6.02988i	−0.168010	−	0.302250i
$399$	−5.23655	+	5.23655i	−0.262155	+	0.262155i
$400$	−9.58762	+	10.9412i	−0.479381	+	0.547060i
$401$	5.57284	+	5.57284i	0.278294	+	0.278294i	0.832428	−	0.554134i	$-0.186950\pi$
$401$	5.57284	+	5.57284i	0.278294	+	0.278294i	−0.554134	+	0.832428i	$0.686950\pi$
$402$	2.16957	−	7.60026i	0.108208	−	0.379067i
$403$	−11.8676	−	2.36061i	−0.591166	−	0.117590i
$404$	24.3873	−	11.0555i	1.21331	−	0.550031i
$405$	1.63274	−	2.44357i	0.0811317	−	0.121422i
$406$	4.19768	+	2.15564i	0.208327	+	0.106983i
$407$	−11.1991	−	4.63883i	−0.555120	−	0.229938i
$408$	2.38943	+	16.0758i	0.118295	+	0.795871i
$409$	19.0605	−	7.89512i	0.942481	−	0.390389i	0.142081	−	0.989855i	$-0.454621\pi$
$409$	19.0605	−	7.89512i	0.942481	−	0.390389i	0.800400	+	0.599466i	$0.204621\pi$
$410$	−4.28672	+	52.3429i	−0.211706	+	2.58503i
$411$	−12.6736	+	2.52094i	−0.625142	+	0.124349i
$412$	28.1456	−	20.1771i	1.38663	−	0.994057i
$413$	1.00129	−	0.669041i	0.0492703	−	0.0329213i
$414$	−3.26027	+	4.10873i	−0.160233	+	0.201933i
$415$		−	34.1045i		−	1.67413i
$416$	−4.78418	−	12.0893i	−0.234564	−	0.592728i
$417$		−	17.7920i		−	0.871276i
$418$	−19.9024	−	15.7925i	−0.973456	−	0.772435i
$419$	−2.52828	+	1.68934i	−0.123515	+	0.0825298i	−0.615793	−	0.787908i	$-0.711164\pi$
$419$	−2.52828	+	1.68934i	−0.123515	+	0.0825298i	0.492278	+	0.870438i	$0.336164\pi$
$420$	−6.92813	−	1.14245i	−0.338058	−	0.0557458i
$421$	−29.1341	+	5.79514i	−1.41991	+	0.282438i	−0.844556	−	0.535467i	$-0.820136\pi$
$421$	−29.1341	+	5.79514i	−1.41991	+	0.282438i	−0.575354	+	0.817905i	$0.695136\pi$
$422$	29.1931	+	2.39083i	1.42110	+	0.116384i
$423$	8.93608	−	3.70145i	0.434487	−	0.179971i
$424$	−22.5971	−	5.65325i	−1.09741	−	0.274546i
$425$	−19.3072	−	7.99730i	−0.936536	−	0.387926i
$426$	5.60618	−	10.9169i	0.271620	−	0.528926i
$427$	1.58629	−	2.37405i	0.0767658	−	0.114888i
$428$	1.87065	−	4.97313i	0.0904211	−	0.240386i
$429$	6.53284	+	1.29946i	0.315409	+	0.0627387i
$430$	−27.8126	−	7.93938i	−1.34124	−	0.382871i
$431$	−6.95134	−	6.95134i	−0.334834	−	0.334834i	0.519585	−	0.854419i	$-0.326087\pi$
$431$	−6.95134	−	6.95134i	−0.334834	−	0.334834i	−0.854419	+	0.519585i	$0.826087\pi$
$432$	3.17246	−	2.43629i	0.152635	−	0.117216i
$433$	−10.4868	+	10.4868i	−0.503962	+	0.503962i	−0.912667	−	0.408704i	$-0.865981\pi$
$433$	−10.4868	+	10.4868i	−0.503962	+	0.503962i	0.408704	+	0.912667i	$0.365981\pi$
$434$	−7.77406	+	4.32132i	−0.373167	+	0.207430i
$435$	1.60140	−	8.05080i	0.0767814	−	0.386006i
$436$	−7.44110	+	0.245051i	−0.356364	+	0.0117358i
$437$	−19.1167	−	12.7733i	−0.914474	−	0.611032i
$438$	−16.9825	+	5.45840i	−0.811455	+	0.260812i
$439$	−12.9562	+	31.2791i	−0.618367	+	1.49287i	0.235232	+	0.971939i	$0.424415\pi$
$439$	−12.9562	+	31.2791i	−0.618367	+	1.49287i	−0.853599	+	0.520930i	$0.825585\pi$
$440$	1.17498	−	24.0610i	0.0560149	−	1.14707i
$441$	2.13264	+	5.14865i	0.101554	+	0.245174i
$442$	14.2406	−	12.0846i	0.677355	−	0.574806i
$443$	−2.86955	−	14.4262i	−0.136336	−	0.685408i	−0.987131	−	0.159911i	$-0.948879\pi$
$443$	−2.86955	−	14.4262i	−0.136336	−	0.685408i	0.850795	−	0.525497i	$-0.176121\pi$
$444$	7.10484	+	4.41615i	0.337181	+	0.209581i
$445$	17.5260	+	26.2296i	0.830814	+	1.24340i
$446$	−1.71953	−	14.9343i	−0.0814223	−	0.707161i
$447$	1.39907			0.0661738
$448$	−8.43118	−	4.50021i	−0.398336	−	0.212615i
$449$	−22.2364			−1.04940			−0.524701	−	0.851286i	$-0.675823\pi$
$449$	−22.2364			−1.04940			−0.524701	+	0.851286i	$0.675823\pi$
$450$	0.588317	+	5.10959i	0.0277335	+	0.240869i
$451$	−20.3452	−	30.4487i	−0.958018	−	1.43377i
$452$	16.8576	−	27.1211i	0.792915	−	1.27567i
$453$	2.05830	+	10.3478i	0.0967074	+	0.486181i
$454$	0.937854	−	0.795868i	0.0440157	−	0.0373519i
$455$	3.08796	+	7.45499i	0.144766	+	0.349495i
$456$	11.7787	+	12.9881i	0.551587	+	0.608225i
$457$	−6.88982	+	16.6335i	−0.322292	+	0.778082i	0.676828	+	0.736141i	$0.263354\pi$
$457$	−6.88982	+	16.6335i	−0.322292	+	0.778082i	−0.999120	+	0.0419406i	$0.986646\pi$
$458$	−23.2944	+	7.48713i	−1.08848	+	0.349851i
$459$	4.77770	+	3.19236i	0.223004	+	0.149007i
$460$	−0.717516	−	21.7877i	−0.0334544	−	1.01586i
$461$	−6.96437	+	35.0123i	−0.324363	+	1.63068i	0.382940	+	0.923773i	$0.374912\pi$
$461$	−6.96437	+	35.0123i	−0.324363	+	1.63068i	−0.707303	+	0.706910i	$0.750088\pi$
$462$	4.27945	−	2.37879i	0.199098	−	0.110671i
$463$	18.5791	−	18.5791i	0.863443	−	0.863443i	−0.128293	−	0.991736i	$-0.540950\pi$
$463$	18.5791	−	18.5791i	0.863443	−	0.863443i	0.991736	+	0.128293i	$0.0409499\pi$
$464$	5.58242	−	9.67776i	0.259157	−	0.449279i
$465$	10.9404	+	10.9404i	0.507347	+	0.507347i
$466$	−14.6814	−	4.19095i	−0.680102	−	0.194142i
$467$	19.8595	+	3.95031i	0.918990	+	0.182799i	0.631851	−	0.775090i	$-0.282296\pi$
$467$	19.8595	+	3.95031i	0.918990	+	0.182799i	0.287140	+	0.957889i	$0.407296\pi$
$468$	−4.30244	−	1.61836i	−0.198880	−	0.0748089i
$469$	−3.70933	+	5.55141i	−0.171281	+	0.256340i
$470$	−18.3640	+	35.7603i	−0.847070	+	1.64950i
$471$	−4.68529	−	1.94071i	−0.215887	−	0.0894233i
$472$	−1.46652	−	2.44512i	−0.0675021	−	0.112546i
$473$	18.6329	−	7.71802i	0.856744	−	0.354875i
$474$	−13.7074	−	1.12259i	−0.629602	−	0.0515625i
$475$	−22.1122	+	4.39839i	−1.01458	+	0.201812i
$476$	2.23373	−	13.5460i	0.102383	−	0.620878i
$477$	−6.84757	+	4.57540i	−0.313529	+	0.209493i
$478$	10.3171	+	8.18655i	0.471891	+	0.374444i
$479$		−	9.12804i		−	0.417071i	−0.978015	−	0.208535i	$-0.933130\pi$
$479$		−	9.12804i		−	0.417071i	0.978015	−	0.208535i	$-0.0668697\pi$
$480$	−3.50173	+	16.2517i	−0.159831	+	0.741786i
$481$		−	9.61349i		−	0.438337i
$482$	−0.765134	+	0.964255i	−0.0348509	+	0.0439206i
$483$	3.68398	−	2.46156i	0.167627	−	0.112005i
$484$	−3.03114	−	4.22821i	−0.137779	−	0.192191i
$485$	24.4870	−	4.87076i	1.11190	−	0.221170i
$486$	0.115433	−	1.40949i	0.00523617	−	0.0639360i
$487$	−5.23967	+	2.17034i	−0.237432	+	0.0983476i	−0.498227	−	0.867047i	$-0.666015\pi$
$487$	−5.23967	+	2.17034i	−0.237432	+	0.0983476i	0.260795	+	0.965394i	$0.416015\pi$
$488$	−5.43097	−	4.02541i	−0.245848	−	0.182222i
$489$	−1.58564	−	0.656794i	−0.0717051	−	0.0297012i
$490$	−20.6038	−	10.5807i	−0.930786	−	0.477988i
$491$	−1.22036	+	1.82640i	−0.0550742	+	0.0824243i	−0.857985	−	0.513675i	$-0.828284\pi$
$491$	−1.22036	+	1.82640i	−0.0550742	+	0.0824243i	0.802911	+	0.596100i	$0.203284\pi$
$492$	10.4346	+	23.0176i	0.470426	+	1.03771i
$493$	15.7410	+	3.13108i	0.708940	+	0.141017i
$494$	5.53091	−	19.3755i	0.248847	−	0.871743i
$495$	−6.02243	−	6.02243i	−0.270688	−	0.270688i
$496$	9.32131	+	18.8832i	0.418539	+	0.847879i
$497$	−7.33039	+	7.33039i	−0.328813	+	0.328813i
$498$	−7.97350	−	14.3444i	−0.357301	−	0.642786i
$499$	−4.81413	+	24.2023i	−0.215510	+	1.08344i	0.709850	+	0.704353i	$0.248763\pi$
$499$	−4.81413	+	24.2023i	−0.215510	+	1.08344i	−0.925360	+	0.379090i	$0.876237\pi$
$500$	5.84869	+	5.47575i	0.261561	+	0.244883i
$501$	−8.57419	−	5.72909i	−0.383066	−	0.255957i
$502$	−1.83019	−	5.69421i	−0.0816855	−	0.254145i
$503$	12.4204	−	29.9854i	0.553797	−	1.33698i	−0.360810	−	0.932639i	$-0.617500\pi$
$503$	12.4204	−	29.9854i	0.553797	−	1.33698i	0.914607	−	0.404344i	$-0.132500\pi$
$504$	−3.18107	+	1.13926i	−0.141696	+	0.0507465i
$505$	15.0570	+	36.3507i	0.670026	+	1.61759i
$506$	9.83527	+	11.5899i	0.437231	+	0.515235i
$507$	−1.50561	−	7.56920i	−0.0668663	−	0.336160i
$508$	−30.3296	+	7.07812i	−1.34566	+	0.314041i
$509$	−12.7108	−	19.0230i	−0.563394	−	0.843179i	0.434965	−	0.900448i	$-0.356761\pi$
$509$	−12.7108	−	19.0230i	−0.563394	−	0.843179i	−0.998359	+	0.0572685i	$0.981761\pi$
$510$	−23.7250	+	2.73169i	−1.05056	+	0.120961i
$511$	15.0684			0.666587
$512$	−11.6158	+	19.4184i	−0.513349	+	0.858180i
$513$	6.19908			0.273696
$514$	21.3432	−	2.45745i	0.941407	−	0.108393i
$515$	28.2716	+	42.3114i	1.24579	+	1.86446i
$516$	−13.5542	+	3.16318i	−0.596689	+	0.139251i
$517$	−5.46859	−	27.4925i	−0.240508	−	1.20912i
$518$	−4.57228	−	5.38800i	−0.200895	−	0.236735i
$519$	3.71689	+	8.97337i	0.163153	+	0.393887i
$520$	17.9862	−	6.44151i	0.788747	−	0.282479i
$521$	1.76786	−	4.26800i	0.0774515	−	0.186984i	−0.880411	−	0.474211i	$-0.842733\pi$
$521$	1.76786	−	4.26800i	0.0774515	−	0.186984i	0.957863	+	0.287227i	$0.0927333\pi$
$522$	−1.20870	−	3.76056i	−0.0529032	−	0.164595i
$523$	32.4159	+	21.6596i	1.41745	+	0.947108i	0.999249	+	0.0387519i	$0.0123382\pi$
$523$	32.4159	+	21.6596i	1.41745	+	0.947108i	0.418198	+	0.908356i	$0.362662\pi$
$524$	0.733759	+	0.686971i	0.0320544	+	0.0300105i
$525$	0.847617	−	4.26126i	0.0369930	−	0.185977i
$526$	−8.93151	−	16.0678i	−0.389432	−	0.700589i
$527$	−21.3907	+	21.3907i	−0.931794	+	0.931794i
$528$	−5.13118	−	10.3948i	−0.223306	−	0.452374i
$529$	−6.53683	−	6.53683i	−0.284210	−	0.284210i
$530$	9.39546	−	32.9135i	0.408113	−	1.42967i
$531$	−0.988678	−	0.196660i	−0.0429050	−	0.00853433i
$532$	−6.11532	−	13.4898i	−0.265133	−	0.584856i
$533$	16.1352	−	24.1480i	0.698893	−	1.04597i
$534$	13.5038	+	6.93463i	0.584367	+	0.300091i
$535$	7.21324	+	2.98782i	0.311856	+	0.129175i
$536$	12.6996	+	9.41293i	0.548541	+	0.406577i
$537$	13.0513	−	5.40601i	0.563204	−	0.233287i
$538$	−3.47623	+	42.4464i	−0.149871	+	1.82999i
$539$	15.8402	−	3.15081i	0.682285	−	0.135715i
$540$	3.42457	+	4.77702i	0.147370	+	0.205570i
$541$	−6.84771	+	4.57549i	−0.294406	+	0.196716i	−0.693997	−	0.719978i	$-0.744152\pi$
$541$	−6.84771	+	4.57549i	−0.294406	+	0.196716i	0.399591	+	0.916693i	$0.369152\pi$
$542$	−17.9814	+	22.6609i	−0.772366	+	0.973369i
$543$			21.1470i			0.907505i
$544$	−31.7756	−	6.84663i	−1.36237	−	0.293547i
$545$		−	10.9401i		−	0.468623i
$546$	3.04174	+	2.41361i	0.130175	+	0.103293i
$547$	−10.9409	+	7.31045i	−0.467798	+	0.312572i	−0.767034	−	0.641607i	$-0.778268\pi$
$547$	−10.9409	+	7.31045i	−0.467798	+	0.312572i	0.299236	+	0.954179i	$0.403268\pi$
$548$	4.20485	−	25.4994i	0.179622	−	1.08928i
$549$	−2.34414	+	0.466279i	−0.100046	+	0.0199003i
$550$	14.8560	+	1.21666i	0.633463	+	0.0518787i
$551$	15.9966	−	6.62603i	0.681480	−	0.282278i
$552$	−5.39567	−	8.99616i	−0.229655	−	0.382902i
$553$	10.7335	+	4.44594i	0.456433	+	0.189061i
$554$	0.501993	−	0.977532i	0.0213276	−	0.0415314i
$555$	−6.82934	+	10.2208i	−0.289889	+	0.433850i
$556$	33.3057	+	12.5279i	1.41247	+	0.531303i
$557$	6.48843	+	1.29063i	0.274924	+	0.0546857i	0.330627	−	0.943762i	$-0.392740\pi$
$557$	6.48843	+	1.29063i	0.274924	+	0.0546857i	−0.0557028	+	0.998447i	$0.517740\pi$
$558$	7.15932	+	2.04370i	0.303078	+	0.0865166i
$559$	11.3100	+	11.3100i	0.478363	+	0.478363i
$560$	7.01694	−	12.1647i	0.296520	−	0.514051i
$561$	11.7751	−	11.7751i	0.497146	−	0.497146i
$562$	25.6228	−	14.2428i	1.08083	−	0.600795i
$563$	1.73273	−	8.71100i	0.0730257	−	0.367125i	−0.926942	−	0.375206i	$-0.877572\pi$
$563$	1.73273	−	8.71100i	0.0730257	−	0.367125i	0.999967	+	0.00808052i	$0.00257214\pi$
$564$	0.636717	+	19.3342i	0.0268106	+	0.814117i
$565$	39.0156	+	26.0694i	1.64140	+	1.09675i
$566$	14.3065	−	4.59830i	0.601348	−	0.193281i
$567$	−0.457164	+	1.10369i	−0.0191991	+	0.0463507i
$568$	16.4884	+	18.1815i	0.691838	+	0.762877i
$569$	−13.3927	−	32.3327i	−0.561449	−	1.35546i	−0.908607	−	0.417652i	$-0.862853\pi$
$569$	−13.3927	−	32.3327i	−0.561449	−	1.35546i	0.347158	−	0.937807i	$-0.387147\pi$
$570$	−19.6445	+	16.6704i	−0.822817	+	0.698246i
$571$	2.01942	+	10.1523i	0.0845103	+	0.424862i	0.999759	+	0.0219716i	$0.00699434\pi$
$571$	2.01942	+	10.1523i	0.0845103	+	0.424862i	−0.915248	+	0.402890i	$0.868006\pi$
$572$	−7.03253	+	11.3142i	−0.294045	+	0.473068i
$573$	8.19166	+	12.2597i	0.342212	+	0.512156i
$574$	−2.44190	−	21.2082i	−0.101923	−	0.885211i
$575$	13.4887			0.562517
$576$	2.32676	+	7.65416i	0.0969484	+	0.318923i
$577$	−5.26507			−0.219188			−0.109594	−	0.993976i	$-0.534955\pi$
$577$	−5.26507			−0.219188			−0.109594	+	0.993976i	$0.534955\pi$
$578$	−2.59106	−	22.5036i	−0.107774	−	0.936027i
$579$	−7.92500	−	11.8606i	−0.329352	−	0.492910i
$580$	13.9431	+	8.66659i	0.578955	+	0.359861i
$581$	2.70459	+	13.5969i	0.112205	+	0.564094i
$582$	9.16044	−	7.77359i	0.379712	−	0.322226i
$583$	9.13351	+	22.0502i	0.378271	+	0.913228i
$584$	1.74011	−	35.6338i	0.0720064	−	1.47454i
$585$	2.58487	−	6.24043i	0.106871	−	0.258010i
$586$	−5.22656	+	1.67989i	−0.215907	+	0.0693954i
$587$	21.8029	+	14.5682i	0.899902	+	0.601296i	0.917144	−	0.398556i	$-0.130488\pi$
$587$	21.8029	+	14.5682i	0.899902	+	0.601296i	−0.0172417	+	0.999851i	$0.505488\pi$
$588$	−11.1397	+	0.366854i	−0.459393	+	0.0151288i
$589$	−6.36694	+	32.0088i	−0.262345	+	1.31890i
$590$	3.66191	−	2.03552i	0.150758	−	0.0838011i
$591$	11.0070	−	11.0070i	0.452768	−	0.452768i
$592$	−13.2696	+	10.1903i	−0.545376	+	0.418821i
$593$	−7.76835	−	7.76835i	−0.319008	−	0.319008i	0.529378	−	0.848386i	$-0.322425\pi$
$593$	−7.76835	−	7.76835i	−0.319008	−	0.319008i	−0.848386	+	0.529378i	$0.822425\pi$
$594$	−3.94105	−	1.12501i	−0.161703	−	0.0461598i
$595$	19.7860	+	3.93568i	0.811147	+	0.161347i
$596$	−0.985135	+	2.61899i	−0.0403527	+	0.107278i
$597$	2.71019	−	4.05609i	0.110921	−	0.166005i
$598$	−5.50701	+	10.7238i	−0.225199	+	0.438530i
$599$	−10.8021	−	4.47436i	−0.441360	−	0.182817i	0.150926	−	0.988545i	$-0.451774\pi$
$599$	−10.8021	−	4.47436i	−0.441360	−	0.182817i	−0.592286	+	0.805728i	$0.701774\pi$
$600$	−9.97915	−	2.49654i	−0.407397	−	0.101921i
$601$	21.4324	−	8.87760i	0.874247	−	0.362125i	0.0999839	−	0.994989i	$-0.468121\pi$
$601$	21.4324	−	8.87760i	0.874247	−	0.362125i	0.774263	+	0.632864i	$0.218121\pi$
$602$	11.7180	+	0.959672i	0.477591	+	0.0391133i
$603$	5.48148	−	1.09033i	0.223223	−	0.0444019i
$604$	−20.8198	−	3.43319i	−0.847147	−	0.139695i
$605$	6.35630	−	4.24714i	0.258420	−	0.172671i
$606$	14.8316	+	11.7688i	0.602493	+	0.478077i
$607$			41.4568i			1.68268i	0.540506	+	0.841340i	$0.318233\pi$
$607$			41.4568i			1.68268i	−0.540506	+	0.841340i	$0.681767\pi$
$608$	−32.6069	+	12.9037i	−1.32238	+	0.523315i
$609$			3.33671i			0.135210i
$610$	6.17453	−	7.78141i	0.249999	−	0.315060i
$611$	18.4841	−	12.3507i	0.747787	−	0.499655i
$612$	−9.34008	+	6.69577i	−0.377550	+	0.270660i
$613$	−13.6918	+	2.72347i	−0.553006	+	0.110000i	−0.463680	−	0.886003i	$-0.653471\pi$
$613$	−13.6918	+	2.72347i	−0.553006	+	0.110000i	−0.0893261	+	0.996002i	$0.528471\pi$
$614$	−1.07868	+	13.1712i	−0.0435320	+	0.531546i
$615$	−34.3091	+	14.2113i	−1.38348	+	0.573055i
$616$	1.43967	+	9.68591i	0.0580059	+	0.390256i
$617$	10.6574	+	4.41443i	0.429050	+	0.177718i	0.586749	−	0.809769i	$-0.300408\pi$
$617$	10.6574	+	4.41443i	0.429050	+	0.177718i	−0.157699	+	0.987487i	$0.550408\pi$
$618$	21.7833	+	11.1864i	0.876251	+	0.449982i
$619$	−17.5508	+	26.2666i	−0.705427	+	1.05575i	0.289698	+	0.957118i	$0.406445\pi$
$619$	−17.5508	+	26.2666i	−0.705427	+	1.05575i	−0.995124	+	0.0986274i	$0.968555\pi$
$620$	−28.1833	+	12.7763i	−1.13187	+	0.513109i
$621$	−3.63758	−	0.723559i	−0.145971	−	0.0290354i
$622$	−10.3433	+	36.2337i	−0.414727	+	1.45284i
$623$	−9.06742	−	9.06742i	−0.363278	−	0.363278i
$624$	6.05899	−	6.91440i	0.242554	−	0.276797i
$625$	−21.1831	+	21.1831i	−0.847325	+	0.847325i
$626$	21.1904	+	38.1215i	0.846937	+	1.52364i
$627$	3.50486	−	17.6201i	0.139971	−	0.703680i
$628$	6.93199	−	7.40411i	0.276617	−	0.295456i
$629$	−19.9839	−	13.3528i	−0.796809	−	0.532411i
$630$	−1.51930	−	4.72692i	−0.0605302	−	0.188325i
$631$	−11.5277	+	27.8303i	−0.458910	+	1.10791i	0.509930	+	0.860216i	$0.329671\pi$
$631$	−11.5277	+	27.8303i	−0.458910	+	1.10791i	−0.968839	+	0.247690i	$0.920329\pi$
$632$	11.7533	−	24.8691i	0.467521	−	0.989239i
$633$	7.92604	+	19.1351i	0.315032	+	0.760554i
$634$	−13.2877	−	15.6583i	−0.527723	−	0.621872i
$635$	−8.92827	−	44.8855i	−0.354308	−	1.78123i
$636$	−3.74331	−	16.0400i	−0.148432	−	0.636028i
$637$	7.11603	+	10.6499i	0.281947	+	0.421964i
$638$	−11.3723	+	1.30941i	−0.450234	+	0.0518399i
$639$	8.67780			0.343288
$640$	−27.9567	−	17.9985i	−1.10509	−	0.711452i
$641$	−19.2847			−0.761699			−0.380850	−	0.924637i	$-0.624368\pi$
$641$	−19.2847			−0.761699			−0.380850	+	0.924637i	$0.624368\pi$
$642$	3.73243	−	0.429750i	0.147307	−	0.0169609i
$643$	−7.01053	−	10.4920i	−0.276468	−	0.413764i	0.667087	−	0.744980i	$-0.267541\pi$
$643$	−7.01053	−	10.4920i	−0.276468	−	0.413764i	−0.943555	+	0.331216i	$0.892541\pi$
$644$	2.01389	+	8.62950i	0.0793585	+	0.340050i
$645$	−3.99000	−	20.0591i	−0.157106	−	0.789826i
$646$	−32.5942	−	38.4091i	−1.28240	−	1.51119i
$647$	2.18679	+	5.27938i	0.0859717	+	0.207554i	0.961018	−	0.276485i	$-0.0891695\pi$
$647$	2.18679	+	5.27938i	0.0859717	+	0.207554i	−0.875047	+	0.484039i	$0.839169\pi$
$648$	2.55722	+	1.20856i	0.100457	+	0.0474767i
$649$	−1.11797	+	2.69901i	−0.0438840	+	0.105945i
$650$	3.61728	+	11.2543i	0.141881	+	0.441430i
$651$	−5.22934	−	3.49413i	−0.204954	−	0.136946i
$652$	2.34599	−	2.50577i	0.0918760	−	0.0981334i
$653$	−6.17700	+	31.0539i	−0.241725	+	1.21523i	0.649036	+	0.760758i	$0.275173\pi$
$653$	−6.17700	+	31.0539i	−0.241725	+	1.21523i	−0.890760	+	0.454473i	$0.849827\pi$
$654$	−2.55775	−	4.60140i	−0.100016	−	0.179929i
$655$	−1.04440	+	1.04440i	−0.0408080	+	0.0408080i
$656$	−50.4351	+	3.32548i	−1.96916	+	0.129838i
$657$	−8.91907	−	8.91907i	−0.347966	−	0.347966i
$658$	4.48553	−	15.7134i	0.174864	−	0.612570i
$659$	23.0449	+	4.58392i	0.897702	+	0.178564i	0.622313	−	0.782769i	$-0.286193\pi$
$659$	23.0449	+	4.58392i	0.897702	+	0.178564i	0.275389	+	0.961333i	$0.411193\pi$
$660$	15.5143	−	7.03308i	0.603893	−	0.273762i
$661$	13.0036	−	19.4613i	0.505782	−	0.756957i	−0.487444	−	0.873154i	$-0.662071\pi$
$661$	13.0036	−	19.4613i	0.505782	−	0.756957i	0.993226	+	0.116197i	$0.0370705\pi$
$662$	22.6964	+	11.6553i	0.882123	+	0.452997i
$663$	12.2014	+	5.05397i	0.473862	+	0.196280i
$664$	32.4663	−	4.82564i	1.25994	−	0.187271i
$665$	20.1073	−	8.32873i	0.779729	−	0.322974i
$666$	−0.482828	+	5.89555i	−0.0187092	+	0.228448i
$667$	−10.1601	+	2.02097i	−0.393401	+	0.0782524i
$668$	16.7619	−	12.0164i	0.648539	−	0.464928i
$669$	8.83847	−	5.90568i	0.341715	−	0.228327i
$670$	−14.4384	+	18.1959i	−0.557803	+	0.702967i
$671$			6.92656i			0.267397i
$672$	0.107271	−	6.75699i	0.00413806	−	0.260656i
$673$		−	18.8467i		−	0.726488i	−0.931694	−	0.363244i	$-0.881669\pi$
$673$		−	18.8467i		−	0.726488i	0.931694	−	0.363244i	$-0.118331\pi$
$674$	2.73564	+	2.17073i	0.105373	+	0.0836132i
$675$	−3.02397	+	2.02055i	−0.116393	+	0.0777711i
$676$	15.2293	+	2.51131i	0.585742	+	0.0965890i
$677$	22.3610	−	4.44787i	0.859402	−	0.170946i	0.254331	−	0.967117i	$-0.418145\pi$
$677$	22.3610	−	4.44787i	0.859402	−	0.170946i	0.605071	+	0.796171i	$0.293145\pi$
$678$	22.5049	+	1.84308i	0.864294	+	0.0707831i
$679$	−9.37627	+	3.88378i	−0.359828	+	0.149046i
$680$	11.5920	−	46.3355i	0.444534	−	1.77689i
$681$	0.803556	+	0.332844i	0.0307923	+	0.0127546i
$682$	9.85672	−	19.1940i	0.377433	−	0.734977i
$683$	−9.80688	+	14.6770i	−0.375250	+	0.561601i	−0.970244	−	0.242129i	$-0.922154\pi$
$683$	−9.80688	+	14.6770i	−0.375250	+	0.561601i	0.594994	+	0.803730i	$0.297154\pi$
$684$	−4.36499	+	11.6044i	−0.166899	+	0.443704i
$685$	37.2459	+	7.40868i	1.42309	+	0.283071i
$686$	20.4254	+	5.83064i	0.779847	+	0.222615i
$687$	−12.2340	−	12.2340i	−0.466758	−	0.466758i
$688$	3.62264	−	27.6000i	0.138112	−	1.05224i
$689$	−13.3843	+	13.3843i	−0.509901	+	0.509901i
$690$	13.4730	−	7.48917i	0.512909	−	0.285108i
$691$	−7.22341	+	36.3146i	−0.274792	+	1.38147i	0.558898	+	0.829237i	$0.311224\pi$
$691$	−7.22341	+	36.3146i	−0.274792	+	1.38147i	−0.833689	+	0.552234i	$0.813776\pi$
$692$	−19.4149	+	0.639373i	−0.738043	+	0.0243053i
$693$	2.87864	+	1.92344i	0.109350	+	0.0730656i
$694$	13.5208	−	4.34578i	0.513244	−	0.164964i
$695$	−20.0098	+	48.3079i	−0.759015	+	1.83242i
$696$	7.89067	+	0.385327i	0.299095	+	0.0146058i
$697$	−27.7861	−	67.0815i	−1.05247	−	2.54089i
$698$	27.8770	−	23.6565i	1.05516	−	0.895412i
$699$	−2.10620	−	10.5886i	−0.0796636	−	0.400496i
$700$	7.38002	+	4.58719i	0.278939	+	0.173380i
$701$	8.11831	+	12.1499i	0.306624	+	0.458896i	0.952496	−	0.304550i	$-0.0985060\pi$
$701$	8.11831	+	12.1499i	0.306624	+	0.458896i	−0.645872	+	0.763446i	$0.723506\pi$
$702$	−0.371792	−	3.22906i	−0.0140324	−	0.121873i
$703$	−25.9291			−0.977936
$704$	23.0715	−	2.28600i	0.869541	−	0.0861567i
$705$	−28.4257			−1.07057
$706$	−3.94606	−	34.2720i	−0.148512	−	1.28984i
$707$	−8.88568	−	13.2984i	−0.334180	−	0.500136i
$708$	1.06430	−	1.71228i	0.0399989	−	0.0643514i
$709$	−9.51757	−	47.8481i	−0.357440	−	1.79697i	−0.571992	−	0.820259i	$-0.693829\pi$
$709$	−9.51757	−	47.8481i	−0.357440	−	1.79697i	0.214552	−	0.976713i	$-0.431171\pi$
$710$	−27.4994	+	23.3361i	−1.03203	+	0.875788i
$711$	−3.72161	−	8.98477i	−0.139571	−	0.336955i
$712$	−22.4898	+	20.3956i	−0.842840	+	0.764356i
$713$	7.47215	−	18.0394i	0.279834	−	0.675580i
$714$	9.24213	−	2.97054i	0.345878	−	0.111170i
$715$	−16.2762	−	10.8754i	−0.608696	−	0.406718i
$716$	0.929933	+	28.2379i	0.0347532	+	1.05530i
$717$	−1.81686	+	9.13398i	−0.0678520	+	0.341115i
$718$	−22.7708	+	12.6575i	−0.849798	+	0.472372i
$719$	−8.93880	+	8.93880i	−0.333361	+	0.333361i	−0.853861	−	0.520500i	$-0.825745\pi$
$719$	−8.93880	+	8.93880i	−0.333361	+	0.333361i	0.520500	+	0.853861i	$0.325745\pi$
$720$	−11.3537	+	3.04697i	−0.423127	+	0.113554i
$721$	−14.6268	−	14.6268i	−0.544731	−	0.544731i
$722$	−26.4208	−	7.54207i	−0.983280	−	0.280687i
$723$	−0.853683	−	0.169808i	−0.0317488	−	0.00631523i
$724$	−39.5861	−	14.8903i	−1.47121	−	0.553395i
$725$	−5.64360	+	8.44624i	−0.209598	+	0.313686i
$726$	1.68049	−	3.27242i	0.0623689	−	0.121451i
$727$	−25.2747	−	10.4691i	−0.937385	−	0.388278i	−0.138910	−	0.990305i	$-0.544360\pi$
$727$	−25.2747	−	10.4691i	−0.937385	−	0.388278i	−0.798476	+	0.602027i	$0.794360\pi$
$728$	−6.65996	+	3.99448i	−0.246835	+	0.148045i
$729$	0.923880	−	0.382683i	0.0342178	−	0.0141735i
$730$	52.2488	+	4.27903i	1.93382	+	0.158374i
$731$	39.2198	−	7.80130i	1.45060	−	0.288541i
$732$	0.777741	−	4.71644i	0.0287461	−	0.174325i
$733$	−14.4593	+	9.66143i	−0.534068	+	0.356853i	−0.793173	−	0.608996i	$-0.791572\pi$
$733$	−14.4593	+	9.66143i	−0.534068	+	0.356853i	0.259105	+	0.965849i	$0.416572\pi$
$734$	−7.00444	−	5.55800i	−0.258538	−	0.205150i
$735$		−	16.3779i		−	0.604107i
$736$	20.6396	−	3.76592i	0.760787	−	0.138814i
$737$		−	16.1969i		−	0.596621i
$738$	−11.1078	+	13.9986i	−0.408886	+	0.515295i
$739$	−10.9042	+	7.28599i	−0.401119	+	0.268019i	−0.739725	−	0.672909i	$-0.765045\pi$
$739$	−10.9042	+	7.28599i	−0.401119	+	0.268019i	0.338606	+	0.940928i	$0.390045\pi$
$740$	−14.3241	−	19.9810i	−0.526564	−	0.734517i
$741$	13.9740	−	2.77961i	0.513349	−	0.102111i
$742$	−1.13568	+	13.8671i	−0.0416920	+	0.509078i
$743$	−8.77012	+	3.63270i	−0.321745	+	0.133271i	−0.537710	−	0.843130i	$-0.680710\pi$
$743$	−8.77012	+	3.63270i	−0.321745	+	0.133271i	0.215965	+	0.976401i	$0.430710\pi$
$744$	−8.86682	+	11.9628i	−0.325073	+	0.438579i
$745$	−3.79869	−	1.57347i	−0.139173	−	0.0576475i
$746$	−9.80639	−	5.03589i	−0.359038	−	0.184377i
$747$	6.44721	−	9.64894i	0.235891	−	0.353036i
$748$	13.7512	+	30.3337i	0.502792	+	1.10911i
$749$	−3.11274	−	0.619162i	−0.113737	−	0.0226237i
$750$	−1.55509	+	5.44768i	−0.0567839	+	0.198921i
$751$	−13.6101	−	13.6101i	−0.496640	−	0.496640i	0.413750	−	0.910390i	$-0.364219\pi$
$751$	−13.6101	−	13.6101i	−0.496640	−	0.496640i	−0.910390	+	0.413750i	$0.864219\pi$
$752$	−36.6410	−	12.4220i	−1.33616	−	0.452983i
$753$	2.99055	−	2.99055i	0.108982	−	0.108982i
$754$	−4.41085	−	7.93513i	−0.160634	−	0.288980i
$755$	6.04906	−	30.4107i	0.220148	−	1.10676i
$756$	−1.74415	−	1.63294i	−0.0634342	−	0.0593893i
$757$	35.1738	+	23.5024i	1.27841	+	0.854208i	0.994510	−	0.104644i	$-0.0333704\pi$
$757$	35.1738	+	23.5024i	1.27841	+	0.854208i	0.283904	+	0.958853i	$0.408370\pi$
$758$	−1.52734	−	4.75196i	−0.0554756	−	0.172599i
$759$	−4.11326	+	9.93028i	−0.149302	+	0.360446i
$760$	−17.3738	−	48.5117i	−0.630214	−	1.75970i
$761$	6.33249	+	15.2880i	0.229553	+	0.554189i	0.996123	−	0.0879711i	$-0.0280383\pi$
$761$	6.33249	+	15.2880i	0.229553	+	0.554189i	−0.766570	+	0.642160i	$0.778038\pi$
$762$	−14.2493	−	16.7914i	−0.516197	−	0.608289i
$763$	0.867583	+	4.36163i	0.0314086	+	0.157902i
$764$	−28.7175	+	6.70191i	−1.03896	+	0.242466i
$765$	−9.38189	−	14.0410i	−0.339203	−	0.507653i
$766$	−31.9199	+	3.67525i	−1.15331	+	0.132792i
$767$	−2.31687			−0.0836573
$768$	−15.9666	−	1.03398i	−0.576143	−	0.0373104i
$769$	−8.34452			−0.300911			−0.150456	−	0.988617i	$-0.548074\pi$
$769$	−8.34452			−0.300911			−0.150456	+	0.988617i	$0.548074\pi$
$770$	−14.2947	+	1.64589i	−0.515145	+	0.0593136i
$771$	8.44001	+	12.6314i	0.303959	+	0.454907i
$772$	27.7827	−	6.48374i	0.999921	−	0.233355i
$773$	2.48831	+	12.5096i	0.0894983	+	0.449938i	0.999384	+	0.0350805i	$0.0111687\pi$
$773$	2.48831	+	12.5096i	0.0894983	+	0.449938i	−0.909886	+	0.414858i	$0.863831\pi$
$774$	−6.36793	−	7.50400i	−0.228891	−	0.269726i
$775$	−7.32720	−	17.6894i	−0.263201	−	0.635423i
$776$	8.10159	+	22.6215i	0.290830	+	0.812066i
$777$	1.91220	−	4.61646i	0.0685998	−	0.165614i
$778$	13.0887	+	40.7224i	0.469254	+	1.45997i
$779$	−65.1312	−	43.5192i	−2.33357	−	1.55924i
$780$	9.86167	+	9.23285i	0.353105	+	0.330589i
$781$	4.90629	−	24.6656i	0.175561	−	0.882603i
$782$	14.6429	+	26.3426i	0.523629	+	0.942010i
$783$	1.97502	−	1.97502i	0.0705814	−	0.0705814i
$784$	7.15711	−	21.1112i	0.255611	−	0.753973i
$785$	10.5387	+	10.5387i	0.376141	+	0.376141i
$786$	−0.195097	+	0.683449i	−0.00695888	+	0.0243778i
$787$	33.6629	+	6.69597i	1.19995	+	0.238686i	0.754306	−	0.656523i	$-0.227974\pi$
$787$	33.6629	+	6.69597i	1.19995	+	0.238686i	0.445647	+	0.895209i	$0.352974\pi$
$788$	12.8541	+	28.3550i	0.457910	+	1.01010i
$789$	7.22183	−	10.8082i	0.257104	−	0.384784i
$790$	35.9551	+	18.4641i	1.27923	+	0.656923i
$791$	−17.6222	−	7.29937i	−0.626574	−	0.259536i
$792$	4.88099	−	6.58529i	0.173439	−	0.233998i
$793$	−5.07511	+	2.10218i	−0.180223	+	0.0746506i
$794$	−0.931903	+	11.3790i	−0.0330720	+	0.403824i
$795$	23.7379	−	4.72177i	0.841898	−	0.167464i
$796$	5.68445	+	7.92937i	0.201480	+	0.281049i
$797$	14.5288	−	9.70787i	0.514638	−	0.343870i	−0.270977	−	0.962586i	$-0.587347\pi$
$797$	14.5288	−	9.70787i	0.514638	−	0.343870i	0.785615	+	0.618716i	$0.212347\pi$
$798$	6.50991	−	8.20407i	0.230448	−	0.290421i
$799$		−	55.5782i		−	1.96622i
$800$	11.7001	−	16.9226i	0.413660	−	0.598303i
$801$			10.7341i			0.379271i
$802$	−8.73094	−	6.92798i	−0.308300	−	0.244635i
$803$	−30.3941	+	20.3087i	−1.07258	+	0.716677i
$804$	−1.81865	+	11.0288i	−0.0641388	+	0.388956i
$805$	−12.7710	+	2.54030i	−0.450118	+	0.0895340i
$806$	17.0550	+	1.39675i	0.600736	+	0.0491985i
$807$	−27.8223	+	11.5244i	−0.979391	+	0.405677i
$808$	−32.4741	+	19.4772i	−1.14244	+	0.685205i
$809$	14.0556	+	5.82200i	0.494167	+	0.204691i	0.615827	−	0.787881i	$-0.288822\pi$
$809$	14.0556	+	5.82200i	0.494167	+	0.204691i	−0.121660	+	0.992572i	$0.538822\pi$
$810$	−1.89861	+	3.69717i	−0.0667104	+	0.129905i
$811$	27.9559	−	41.8390i	0.981664	−	1.46916i	0.101306	−	0.994855i	$-0.467698\pi$
$811$	27.9559	−	41.8390i	0.981664	−	1.46916i	0.880358	−	0.474309i	$-0.157302\pi$
$812$	−6.24616	−	2.34949i	−0.219197	−	0.0824511i
$813$	−20.0623	−	3.99065i	−0.703617	−	0.139958i
$814$	16.4844	+	4.70563i	0.577778	+	0.164932i
$815$	3.56659	+	3.56659i	0.124932	+	0.124932i
$816$	−5.95746	−	22.1989i	−0.208553	−	0.777116i
$817$	30.5050	−	30.5050i	1.06723	−	1.06723i
$818$	−25.5016	+	14.1754i	−0.891641	+	0.495631i
$819$	−0.535659	+	2.69294i	−0.0187175	+	0.0940990i
$820$	−2.44460	−	74.2316i	−0.0853692	−	2.59228i
$821$	−21.3005	−	14.2326i	−0.743394	−	0.496720i	0.125269	−	0.992123i	$-0.460021\pi$
$821$	−21.3005	−	14.2326i	−0.743394	−	0.496720i	−0.868664	+	0.495403i	$0.835021\pi$
$822$	17.3977	−	5.59187i	0.606816	−	0.195039i
$823$	8.81905	−	21.2911i	0.307413	−	0.742160i	−0.692375	−	0.721538i	$-0.743435\pi$
$823$	8.81905	−	21.2911i	0.307413	−	0.742160i	0.999787	−	0.0206216i	$-0.00656453\pi$
$824$	−36.2787	+	32.9004i	−1.26383	+	1.14614i
$825$	4.03347	+	9.73765i	0.140427	+	0.339022i
$826$	−1.29852	+	1.10193i	−0.0451812	+	0.0383410i
$827$	4.67924	+	23.5241i	0.162713	+	0.818014i	0.972790	+	0.231690i	$0.0744254\pi$
$827$	4.67924	+	23.5241i	0.162713	+	0.818014i	−0.810077	+	0.586324i	$0.800575\pi$
$828$	3.91581	−	6.29988i	0.136084	−	0.218936i
$829$	14.0583	+	21.0397i	0.488265	+	0.730741i	0.991024	−	0.133686i	$-0.0426815\pi$
$829$	14.0583	+	21.0397i	0.488265	+	0.730741i	−0.502758	+	0.864427i	$0.667681\pi$
$830$	5.51686	+	47.9145i	0.191493	+	1.66314i
$831$	0.777035			0.0269550
$832$	8.67706	+	16.2108i	0.300823	+	0.562008i
$833$	32.0222			1.10950
$834$	2.87809	+	24.9965i	0.0996600	+	0.865558i
$835$	16.8370	+	25.1983i	0.582668	+	0.872025i
$836$	30.5161	+	18.9679i	1.05542	+	0.656017i
$837$	1.02708	+	5.16347i	0.0355010	+	0.178476i
$838$	3.27879	−	2.78240i	0.113264	−	0.0961163i
$839$	−1.85977	−	4.48989i	−0.0642065	−	0.155008i	0.888520	−	0.458839i	$-0.151734\pi$
$839$	−1.85977	−	4.48989i	−0.0642065	−	0.155008i	−0.952726	+	0.303830i	$0.901734\pi$
$840$	9.91835	+	0.484345i	0.342216	+	0.0167115i
$841$	−8.11236	+	19.5850i	−0.279736	+	0.675343i
$842$	39.9940	−	12.8546i	1.37828	−	0.442999i
$843$	17.2355	+	11.5164i	0.593624	+	0.396647i
$844$	−41.4010	+	1.36342i	−1.42508	+	0.0469310i
$845$	−4.42477	+	22.2448i	−0.152217	+	0.765245i
$846$	−11.9558	+	6.64581i	−0.411050	+	0.228488i
$847$	−2.19734	+	2.19734i	−0.0755014	+	0.0755014i
$848$	32.6619	+	4.28704i	1.12161	+	0.147218i
$849$	7.51367	+	7.51367i	0.257868	+	0.257868i
$850$	28.4190	+	8.11246i	0.974762	+	0.278255i
$851$	15.2150	+	3.02646i	0.521565	+	0.103746i
$852$	−6.11034	+	16.2444i	−0.209337	+	0.556524i
$853$	1.45109	−	2.17172i	0.0496845	−	0.0743582i	−0.805796	−	0.592194i	$-0.798262\pi$
$853$	1.45109	−	2.17172i	0.0496845	−	0.0743582i	0.855480	+	0.517835i	$0.173262\pi$
$854$	−1.84459	+	3.59197i	−0.0631206	+	0.122915i
$855$	−16.8315	−	6.97182i	−0.575624	−	0.238431i
$856$	−1.82366	+	7.28952i	−0.0623314	+	0.249151i
$857$	−24.2262	+	10.0348i	−0.827553	+	0.342784i	−0.755933	−	0.654649i	$-0.772817\pi$
$857$	−24.2262	+	10.0348i	−0.827553	+	0.342784i	−0.0716192	+	0.997432i	$0.522817\pi$
$858$	−9.38840	−	0.768882i	−0.320515	−	0.0262492i
$859$	−49.0640	+	9.75943i	−1.67404	+	0.332988i	−0.938707	−	0.344717i	$-0.887975\pi$
$859$	−49.0640	+	9.75943i	−1.67404	+	0.332988i	−0.735335	+	0.677704i	$0.762975\pi$
$860$	40.3591	+	6.65522i	1.37623	+	0.226941i
$861$	12.5515	−	8.38662i	0.427753	−	0.285815i
$862$	10.8906	+	8.64169i	0.370936	+	0.294337i
$863$			6.62270i			0.225439i	0.993627	+	0.112720i	$0.0359562\pi$
$863$			6.62270i			0.225439i	−0.993627	+	0.112720i	$0.964044\pi$
$864$	−4.06299	+	3.93600i	−0.138226	+	0.133906i
$865$		−	28.5443i		−	0.970535i
$866$	13.0368	−	16.4296i	0.443009	−	0.558300i
$867$	13.3181	−	8.89889i	0.452308	−	0.302222i
$868$	10.2230	−	7.32871i	0.346991	−	0.248753i
$869$	−27.6422	+	5.49838i	−0.937699	+	0.186520i
$870$	−0.947538	+	11.5699i	−0.0321245	+	0.392255i
$871$	11.8675	−	4.91569i	0.402115	−	0.166562i
$872$	10.4146	−	1.54798i	0.352683	−	0.0524212i
$873$	7.84869	+	3.25103i	0.265638	+	0.110031i
$874$	28.9239	+	14.8533i	0.978365	+	0.502421i
$875$	2.65876	−	3.97911i	0.0898824	−	0.134519i
$876$	22.9763	−	10.4158i	0.776296	−	0.351918i
$877$	14.9106	+	2.96590i	0.503494	+	0.100151i	0.440301	−	0.897850i	$-0.354872\pi$
$877$	14.9106	+	2.96590i	0.503494	+	0.100151i	0.0631928	+	0.998001i	$0.479872\pi$
$878$	13.1428	−	46.0408i	0.443548	−	1.55380i
$879$	−2.74495	−	2.74495i	−0.0925848	−	0.0925848i
$880$	2.24143	+	33.9942i	0.0755587	+	1.14594i
$881$	−12.1970	+	12.1970i	−0.410928	+	0.410928i	−0.882062	−	0.471134i	$-0.843845\pi$
$881$	−12.1970	+	12.1970i	−0.410928	+	0.410928i	0.471134	+	0.882062i	$0.343845\pi$
$882$	−3.82908	−	6.88852i	−0.128932	−	0.231949i
$883$	−2.80083	+	14.0807i	−0.0942553	+	0.473854i	0.904610	+	0.426239i	$0.140162\pi$
$883$	−2.80083	+	14.0807i	−0.0942553	+	0.473854i	−0.998866	+	0.0476143i	$0.984838\pi$
$884$	−18.0522	+	19.2817i	−0.607160	+	0.648512i
$885$	2.46324	+	1.64588i	0.0828008	+	0.0553257i
$886$	6.36514	+	19.8036i	0.213841	+	0.665315i
$887$	−19.3526	+	46.7213i	−0.649796	+	1.56875i	0.163273	+	0.986581i	$0.447795\pi$
$887$	−19.3526	+	46.7213i	−0.649796	+	1.56875i	−0.813070	+	0.582166i	$0.802205\pi$
$888$	−10.6962	−	5.05509i	−0.358941	−	0.169638i
$889$	7.11910	+	17.1870i	0.238767	+	0.576435i
$890$	−28.8659	−	34.0157i	−0.967586	−	1.14021i
$891$	−0.565384	−	2.84238i	−0.0189411	−	0.0952232i
$892$	4.83166	+	20.7036i	0.161776	+	0.693206i
$893$	−33.3118	−	49.8546i	−1.11474	−	1.66832i
$894$	−1.96560	+	0.226319i	−0.0657395	+	0.00756922i
$895$	−41.5161			−1.38773
$896$	12.5732	+	4.95863i	0.420041	+	0.165656i
$897$	−8.52430			−0.284618
$898$	31.2407	−	3.59704i	1.04252	−	0.120035i
$899$	8.16945	+	12.2264i	0.272466	+	0.407775i
$900$	−1.65309	−	7.08346i	−0.0551030	−	0.236115i
$901$	9.23206	+	46.4127i	0.307564	+	1.54623i
$902$	33.5091	+	39.4873i	1.11573	+	1.31478i
$903$	3.18149	+	7.68080i	0.105873	+	0.255601i
$904$	−19.2966	+	40.8302i	−0.641795	+	1.35799i
$905$	23.7831	−	57.4174i	0.790575	−	1.90862i
$906$	−4.56566	−	14.2050i	−0.151684	−	0.471928i
$907$	25.1190	+	16.7840i	0.834062	+	0.557302i	0.897668	−	0.440673i	$-0.145260\pi$
$907$	25.1190	+	16.7840i	0.834062	+	0.557302i	−0.0636060	+	0.997975i	$0.520260\pi$
$908$	−1.18888	+	1.26985i	−0.0394543	+	0.0421415i
$909$	−2.61189	+	13.1309i	−0.0866309	+	0.435523i
$910$	−5.54432	−	9.97424i	−0.183792	−	0.330643i
$911$	6.84516	−	6.84516i	0.226790	−	0.226790i	−0.584560	−	0.811350i	$-0.698733\pi$
$911$	6.84516	−	6.84516i	0.226790	−	0.226790i	0.811350	+	0.584560i	$0.198733\pi$
$912$	−18.6492	−	16.3421i	−0.617538	−	0.541140i
$913$	−23.7808	−	23.7808i	−0.787029	−	0.787029i
$914$	6.98903	−	24.4834i	0.231177	−	0.809840i
$915$	6.88911	+	1.37033i	0.227747	+	0.0453017i
$916$	31.5159	−	14.2871i	1.04132	−	0.472059i
$917$	0.333560	−	0.499207i	0.0110151	−	0.0164853i
$918$	−7.22875	−	3.71219i	−0.238584	−	0.122520i
$919$	36.0413	+	14.9288i	1.18889	+	0.492456i	0.887395	−	0.461010i	$-0.152513\pi$
$919$	36.0413	+	14.9288i	1.18889	+	0.492456i	0.301499	+	0.953466i	$0.402513\pi$
$920$	4.53252	+	30.4942i	0.149433	+	1.00536i
$921$	−8.63330	+	3.57603i	−0.284477	+	0.117834i
$922$	4.12076	−	50.3164i	0.135710	−	1.65708i
$923$	19.5616	−	3.89104i	0.643877	−	0.128075i
$924$	−5.62754	+	4.03430i	−0.185132	+	0.132719i
$925$	12.6485	−	8.45144i	0.415879	−	0.277882i
$926$	−23.0969	+	29.1077i	−0.759012	+	0.956540i
$927$			17.3154i			0.568712i
$928$	−6.27741	+	14.4996i	−0.206066	+	0.475973i
$929$			9.23214i			0.302897i	0.988465	+	0.151448i	$0.0483937\pi$
$929$			9.23214i			0.302897i	−0.988465	+	0.151448i	$0.951606\pi$
$930$	−17.1402	−	13.6007i	−0.562049	−	0.445985i
$931$	28.7245	−	19.1931i	0.941407	−	0.629028i
$932$	21.3043	+	3.51308i	0.697845	+	0.115075i
$933$	−26.1326	+	5.19809i	−0.855542	+	0.170178i
$934$	−28.5403	−	2.33737i	−0.933868	−	0.0764810i
$935$	−45.2142	+	18.7283i	−1.47866	+	0.612482i
$936$	6.30642	+	1.57771i	0.206132	+	0.0515692i
$937$	−47.8893	−	19.8364i	−1.56448	−	0.648027i	−0.578616	−	0.815600i	$-0.696407\pi$
$937$	−47.8893	−	19.8364i	−1.56448	−	0.648027i	−0.985860	+	0.167573i	$0.946407\pi$
$938$	4.31334	−	8.39938i	0.140836	−	0.274250i
$939$	−17.1341	+	25.6430i	−0.559150	+	0.836828i
$940$	20.0155	−	53.2114i	0.652834	−	1.73557i
$941$	−18.0449	−	3.58936i	−0.588248	−	0.117010i	−0.108013	−	0.994149i	$-0.534449\pi$
$941$	−18.0449	−	3.58936i	−0.588248	−	0.117010i	−0.480235	+	0.877140i	$0.659449\pi$
$942$	6.89645	+	1.96866i	0.224699	+	0.0641424i
$943$	33.1389	+	33.1389i	1.07915	+	1.07915i
$944$	2.45589	+	3.19799i	0.0799324	+	0.104086i
$945$	2.48254	−	2.48254i	0.0807571	−	0.0807571i
$946$	−24.9295	+	13.8574i	−0.810529	+	0.450544i
$947$	−7.31607	+	36.7804i	−0.237740	+	1.19520i	0.658827	+	0.752295i	$0.271053\pi$
$947$	−7.31607	+	36.7804i	−0.237740	+	1.19520i	−0.896567	+	0.442908i	$0.853947\pi$
$948$	19.4395	−	0.640186i	0.631367	−	0.0207923i
$949$	−24.1047	−	16.1062i	−0.782471	−	0.522830i
$950$	30.3547	−	9.75639i	0.984835	−	0.316539i
$951$	5.55713	−	13.4161i	0.180202	−	0.435047i
$952$	−0.946996	+	19.3925i	−0.0306923	+	0.628514i
$953$	2.48590	+	6.00150i	0.0805263	+	0.194408i	0.959015	−	0.283356i	$-0.0914477\pi$
$953$	2.48590	+	6.00150i	0.0805263	+	0.194408i	−0.878489	+	0.477763i	$0.841448\pi$
$954$	8.88024	−	7.53581i	0.287508	−	0.243981i
$955$	−8.45372	−	42.4997i	−0.273556	−	1.37526i
$956$	−15.8190	−	9.83263i	−0.511624	−	0.318010i
$957$	−4.49710	−	6.73039i	−0.145371	−	0.217563i
$958$	1.47658	+	12.8243i	0.0477062	+	0.414334i
$959$	−15.4369			−0.498482
$960$	2.29076	−	23.3990i	0.0739340	−	0.755200i
$961$	3.28372			0.105926
$962$	1.55511	+	13.5063i	0.0501388	+	0.435460i
$963$	1.47596	+	2.20893i	0.0475622	+	0.0711819i
$964$	0.918979	−	1.47848i	0.0295983	−	0.0476187i
$965$	8.17852	+	41.1162i	0.263276	+	1.32358i
$966$	−4.77755	+	4.05425i	−0.153715	+	0.130444i
$967$	−18.8539	−	45.5175i	−0.606302	−	1.46374i	−0.866993	−	0.498320i	$-0.833950\pi$
$967$	−18.8539	−	45.5175i	−0.606302	−	1.46374i	0.260691	−	0.965422i	$-0.416050\pi$
$968$	4.94252	+	5.45002i	0.158859	+	0.175170i
$969$	13.6314	−	32.9090i	0.437903	−	1.05719i
$970$	−33.6146	+	10.8042i	−1.07930	+	0.346901i
$971$	−15.3632	−	10.2654i	−0.493029	−	0.329432i	0.284076	−	0.958802i	$-0.408313\pi$
$971$	−15.3632	−	10.2654i	−0.493029	−	0.329432i	−0.777106	+	0.629370i	$0.783313\pi$
$972$	0.0658286	+	1.99892i	0.00211145	+	0.0641153i
$973$	4.14660	−	20.8464i	0.132934	−	0.668304i
$974$	7.01029	−	3.89677i	0.224624	−	0.124860i
$975$	−5.91067	+	5.91067i	−0.189293	+	0.189293i
$976$	8.28130	+	4.77690i	0.265078	+	0.152905i
$977$	−10.4989	−	10.4989i	−0.335889	−	0.335889i	0.518928	−	0.854818i	$-0.326331\pi$
$977$	−10.4989	−	10.4989i	−0.335889	−	0.335889i	−0.854818	+	0.518928i	$0.826331\pi$
$978$	2.33396	+	0.666252i	0.0746318	+	0.0213044i
$979$	30.5104	+	6.06889i	0.975116	+	0.193963i
$980$	30.6585	+	11.5322i	0.979351	+	0.368383i
$981$	2.06815	−	3.09520i	0.0660309	−	0.0988222i
$982$	1.41908	−	2.76338i	0.0452847	−	0.0881829i
$983$	16.7986	+	6.95819i	0.535791	+	0.221932i	0.634137	−	0.773220i	$-0.281355\pi$
$983$	16.7986	+	6.95819i	0.535791	+	0.221932i	−0.0983464	+	0.995152i	$0.531355\pi$
$984$	−18.3832	−	30.6502i	−0.586036	−	0.977094i
$985$	−42.2648	+	17.5066i	−1.34667	+	0.557808i
$986$	−22.6215	−	1.85264i	−0.720417	−	0.0590000i
$987$	11.3328	−	2.25424i	0.360728	−	0.0717533i
$988$	−4.63631	+	28.1159i	−0.147501	+	0.894486i
$989$	−21.4607	+	14.3396i	−0.682410	+	0.455972i
$990$	9.43531	+	7.48689i	0.299874	+	0.237949i
$991$		−	27.7797i		−	0.882452i	−0.897396	−	0.441226i	$-0.854544\pi$
$991$		−	27.7797i		−	0.882452i	0.897396	−	0.441226i	$-0.145456\pi$
$992$	−16.1504	−	25.0217i	−0.512776	−	0.794440i
$993$			18.0413i			0.572523i
$994$	9.11291	−	11.4845i	0.289044	−	0.364266i
$995$	−11.9203	+	7.96487i	−0.377898	+	0.252503i
$996$	13.5226	+	18.8630i	0.428481	+	0.597697i
$997$	13.9113	−	2.76712i	0.440574	−	0.0876356i	0.0301811	−	0.999544i	$-0.490392\pi$
$997$	13.9113	−	2.76712i	0.440574	−	0.0876356i	0.410393	+	0.911909i	$0.365392\pi$
$998$	2.84848	−	34.7813i	0.0901672	−	1.10098i
$999$	−3.86435	+	1.60066i	−0.122263	+	0.0506428i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.r.a.109.1	yes	128
3.2	odd	2		576.2.bd.b.109.16		128
4.3	odd	2		768.2.r.a.529.15		128
64.27	odd	16		768.2.r.a.241.15		128
64.37	even	16	inner	192.2.r.a.37.1	✓	128
192.101	odd	16		576.2.bd.b.37.16		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.37.1	✓	128	64.37	even	16	inner
192.2.r.a.109.1	yes	128	1.1	even	1	trivial
576.2.bd.b.37.16		128	192.101	odd	16
576.2.bd.b.109.16		128	3.2	odd	2
768.2.r.a.241.15		128	64.27	odd	16
768.2.r.a.529.15		128	4.3	odd	2

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40493 + 0.161763i) q^{2} +(-0.555570 - 0.831470i) q^{3} +(1.94767 - 0.454533i) q^{4} +(0.573343 + 2.88239i) q^{5} +(0.915039 + 1.07829i) q^{6} +(-0.457164 - 1.10369i) q^{7} +(-2.66281 + 0.953649i) q^{8} +(-0.382683 + 0.923880i) q^{9} +O(q^{10})\)	\(q+(-1.40493 + 0.161763i) q^{2} +(-0.555570 - 0.831470i) q^{3} +(1.94767 - 0.454533i) q^{4} +(0.573343 + 2.88239i) q^{5} +(0.915039 + 1.07829i) q^{6} +(-0.457164 - 1.10369i) q^{7} +(-2.66281 + 0.953649i) q^{8} +(-0.382683 + 0.923880i) q^{9} +(-1.27177 - 3.95682i) q^{10} +(2.40965 + 1.61008i) q^{11} +(-1.46000 - 1.36690i) q^{12} +(-0.448390 + 2.25421i) q^{13} +(0.820822 + 1.47666i) q^{14} +(2.07809 - 2.07809i) q^{15} +(3.58680 - 1.77056i) q^{16} +(4.06310 + 4.06310i) q^{17} +(0.388194 - 1.35989i) q^{18} +(6.07997 + 1.20938i) q^{19} +(2.42682 + 5.35333i) q^{20} +(-0.663700 + 0.993297i) q^{21} +(-3.64585 - 1.87226i) q^{22} +(-3.42652 - 1.41931i) q^{23} +(2.27231 + 1.68423i) q^{24} +(-3.36006 + 1.39178i) q^{25} +(0.265309 - 3.23954i) q^{26} +(0.980785 - 0.195090i) q^{27} +(-1.39207 - 1.94183i) q^{28} +(2.32238 - 1.55176i) q^{29} +(-2.58341 + 3.25573i) q^{30} +5.26463i q^{31} +(-4.75280 + 3.06772i) q^{32} -2.89806i q^{33} +(-6.36564 - 5.05112i) q^{34} +(2.91916 - 1.95052i) q^{35} +(-0.325406 + 1.97335i) q^{36} +(-4.10237 + 0.816012i) q^{37} +(-8.73757 - 0.715581i) q^{38} +(2.12342 - 0.879549i) q^{39} +(-4.27549 - 7.12849i) q^{40} +(-11.6743 - 4.83565i) q^{41} +(0.771774 - 1.50288i) q^{42} +(3.86632 - 5.78635i) q^{43} +(5.42503 + 2.04063i) q^{44} +(-2.88239 - 0.573343i) q^{45} +(5.04363 + 1.43975i) q^{46} +(-6.83938 - 6.83938i) q^{47} +(-3.46488 - 1.99865i) q^{48} +(3.94061 - 3.94061i) q^{49} +(4.49551 - 2.49889i) q^{50} +(1.12101 - 5.63568i) q^{51} +(0.151299 + 4.59425i) q^{52} +(6.84757 + 4.57540i) q^{53} +(-1.34638 + 0.432744i) q^{54} +(-3.25932 + 7.86868i) q^{55} +(2.26988 + 2.50295i) q^{56} +(-2.37229 - 5.72720i) q^{57} +(-3.01176 + 2.55579i) q^{58} +(0.196660 + 0.988678i) q^{59} +(3.10286 - 4.99198i) q^{60} +(1.32785 + 1.98727i) q^{61} +(-0.851624 - 7.39644i) q^{62} +1.19463 q^{63} +(6.18111 - 5.07877i) q^{64} -6.75459 q^{65} +(0.468800 + 4.07158i) q^{66} +(-3.10501 - 4.64698i) q^{67} +(9.76037 + 6.06675i) q^{68} +(0.723559 + 3.63758i) q^{69} +(-3.78570 + 3.21256i) q^{70} +(-3.32085 - 8.01724i) q^{71} +(0.137957 - 2.82506i) q^{72} +(-4.82696 + 11.6533i) q^{73} +(5.63155 - 1.81005i) q^{74} +(3.02397 + 2.02055i) q^{75} +(12.3914 - 0.408077i) q^{76} +(0.675424 - 3.39558i) q^{77} +(-2.84098 + 1.57920i) q^{78} +(-6.87664 + 6.87664i) q^{79} +(7.15990 + 9.32342i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(17.1838 + 4.90528i) q^{82} +(-11.3817 - 2.26396i) q^{83} +(-0.841179 + 2.23628i) q^{84} +(-9.38189 + 14.0410i) q^{85} +(-4.49589 + 8.75486i) q^{86} +(-2.58049 - 1.06887i) q^{87} +(-7.95189 - 1.98937i) q^{88} +(9.91702 - 4.10777i) q^{89} +(4.14231 + 0.339243i) q^{90} +(2.69294 - 0.535659i) q^{91} +(-7.31885 - 1.20688i) q^{92} +(4.37738 - 2.92487i) q^{93} +(10.7152 + 8.50250i) q^{94} +18.2182i q^{95} +(5.19123 + 2.24747i) q^{96} -8.49536i q^{97} +(-4.89884 + 6.17373i) q^{98} +(-2.40965 + 1.61008i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) \) 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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