LMFDB - Embedded newform 192.2.r.a.37.1

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			37.1
Character	$\chi$	$=$	192.37
Dual form			192.2.r.a.109.1

$q$-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 $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{16}\right)$

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	−0.611074	−	0.791574i	$-0.709262\pi$
$5$	0.573343	−	2.88239i	0.256407	−	1.28904i	0.867481	−	0.497471i	$-0.165738\pi$
$6$	0.915039	−	1.07829i	0.373563	−	0.440209i
$7$	−0.457164	+	1.10369i	−0.172792	+	0.417157i	−0.986423	−	0.164225i	$-0.947488\pi$
$7$	−0.457164	+	1.10369i	−0.172792	+	0.417157i	0.813631	+	0.581382i	$0.197488\pi$
$8$	−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	−0.136473	−	0.990644i	$-0.543577\pi$
$11$	2.40965	−	1.61008i	0.726537	−	0.485457i	0.863010	+	0.505187i	$0.168577\pi$
$12$	−1.46000	+	1.36690i	−0.421464	+	0.394590i
$13$	−0.448390	−	2.25421i	−0.124361	−	0.625205i	−0.991815	−	0.127687i	$-0.959245\pi$
$13$	−0.448390	−	2.25421i	−0.124361	−	0.625205i	0.867453	−	0.497518i	$-0.165755\pi$
$14$	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	−0.0144488	−	0.999896i	$-0.504599\pi$
$17$	4.06310	−	4.06310i	0.985447	−	0.985447i	0.999896	+	0.0144488i	$0.00459936\pi$
$18$	0.388194	+	1.35989i	0.0914982	+	0.320530i
$19$	6.07997	−	1.20938i	1.39484	−	0.277451i	0.560251	−	0.828323i	$-0.310705\pi$
$19$	6.07997	−	1.20938i	1.39484	−	0.277451i	0.834590	+	0.550872i	$0.185705\pi$
$20$	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	−0.710157	−	0.704043i	$-0.751376\pi$
$23$	−3.42652	+	1.41931i	−0.714480	+	0.295947i	−0.00432287	+	0.999991i	$0.501376\pi$
$24$	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	0.752190	−	0.658946i	$-0.228997\pi$
$29$	2.32238	+	1.55176i	0.431254	+	0.288155i	−0.320936	+	0.947101i	$0.603997\pi$
$30$	−2.58341	−	3.25573i	−0.471664	−	0.594412i
$31$		−	5.26463i		−	0.945555i	−0.881182	−	0.472777i	$-0.843252\pi$
$31$		−	5.26463i		−	0.945555i	0.881182	−	0.472777i	$-0.156748\pi$
$32$	−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	−0.154016	−	0.988068i	$-0.549221\pi$
$37$	−4.10237	−	0.816012i	−0.674425	−	0.134152i	−0.520409	+	0.853917i	$0.674221\pi$
$38$	−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	−0.849445	+	0.527677i	$0.823063\pi$
$41$	−11.6743	+	4.83565i	−1.82322	+	0.755201i	−0.973772	+	0.227525i	$0.926937\pi$
$42$	0.771774	+	1.50288i	0.119087	+	0.231899i
$43$	3.86632	+	5.78635i	0.589608	+	0.882410i	0.999559	−	0.0296971i	$-0.00945427\pi$
$43$	3.86632	+	5.78635i	0.589608	+	0.882410i	−0.409951	+	0.912107i	$0.634454\pi$
$44$	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	−0.999997	−	0.00237063i	$-0.999245\pi$
$47$	−6.83938	+	6.83938i	−0.997627	+	0.997627i	0.00237063	+	0.999997i	$0.499245\pi$
$48$	−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	0.0121320	−	0.999926i	$-0.496138\pi$
$53$	6.84757	−	4.57540i	0.940586	−	0.628480i	0.928454	+	0.371447i	$0.121138\pi$
$54$	−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	−0.965870	−	0.259027i	$-0.916598\pi$
$59$	0.196660	−	0.988678i	0.0256030	−	0.128715i	0.991473	+	0.130312i	$0.0415980\pi$
$60$	3.10286	+	4.99198i	0.400578	+	0.644462i
$61$	1.32785	−	1.98727i	0.170014	−	0.254444i	−0.736672	−	0.676250i	$-0.763604\pi$
$61$	1.32785	−	1.98727i	0.170014	−	0.254444i	0.906686	+	0.421807i	$0.138604\pi$
$62$	−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	−0.971184	−	0.238332i	$-0.923399\pi$
$67$	−3.10501	+	4.64698i	−0.379337	+	0.567719i	0.591846	+	0.806051i	$0.298399\pi$
$68$	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	0.594922	+	0.803784i	$0.297183\pi$
$71$	−3.32085	+	8.01724i	−0.394112	+	0.951471i	−0.989034	+	0.147688i	$0.952817\pi$
$72$	0.137957	+	2.82506i	0.0162584	+	0.332937i
$73$	−4.82696	−	11.6533i	−0.564953	−	1.36392i	−0.905763	−	0.423786i	$-0.860701\pi$
$73$	−4.82696	−	11.6533i	−0.564953	−	1.36392i	0.340809	−	0.940133i	$-0.389299\pi$
$74$	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	0.205065	−	0.978748i	$-0.434259\pi$
$79$	−6.87664	−	6.87664i	−0.773683	−	0.773683i	−0.978748	+	0.205065i	$0.934259\pi$
$80$	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	−0.775058	−	0.631890i	$-0.782279\pi$
$83$	−11.3817	+	2.26396i	−1.24930	+	0.248502i	−0.474246	+	0.880392i	$0.657279\pi$
$84$	−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	0.840321	−	0.542089i	$-0.182367\pi$
$89$	9.91702	+	4.10777i	1.05120	+	0.435422i	0.210881	+	0.977512i	$0.432367\pi$
$90$	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	$0.141940\pi$
$97$			8.49536i			0.862573i	−0.902215	+	0.431287i	$0.858060\pi$
$98$	−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	0.798798	−	0.601600i	$-0.205470\pi$
$101$	13.1309	+	2.61189i	1.30657	+	0.259893i	0.507771	+	0.861492i	$0.330470\pi$
$102$	−0.663291	−	8.09909i	−0.0656756	−	0.801929i
$103$	15.9973	+	6.62631i	1.57626	+	0.652910i	0.987816	−	0.155625i	$-0.0497393\pi$
$103$	15.9973	+	6.62631i	1.57626	+	0.652910i	0.588448	+	0.808535i	$0.299739\pi$
$104$	−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	0.895929	−	0.444198i	$-0.146511\pi$
$107$	1.47596	+	2.20893i	0.142687	+	0.213546i	−0.753242	+	0.657743i	$0.771511\pi$
$108$	1.82157	+	0.825770i	0.175280	+	0.0794597i
$109$	−3.65104	+	0.726237i	−0.349706	+	0.0695609i	−0.366818	−	0.930293i	$-0.619553\pi$
$109$	−3.65104	+	0.726237i	−0.349706	+	0.0695609i	0.0171119	+	0.999854i	$0.494553\pi$
$110$	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	0.997941	+	0.0641425i	$0.0204312\pi$
$113$	11.2901	+	11.2901i	1.06208	+	1.06208i	0.0641425	+	0.997941i	$0.479569\pi$
$114$	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	−0.819072	−	0.573691i	$-0.805511\pi$
$131$	0.279216	−	0.417877i	0.0243952	−	0.0365101i	0.843467	+	0.537181i	$0.180511\pi$
$132$	−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	0.981614	+	0.190878i	$0.0611335\pi$
$137$	4.94499	+	11.9383i	0.422479	+	1.01996i	−0.559135	+	0.829077i	$0.688866\pi$
$138$	−1.60498	+	4.99350i	−0.136625	+	0.425075i
$139$	14.7935	−	9.88469i	1.25477	−	0.838408i	0.262793	−	0.964852i	$-0.415356\pi$
$139$	14.7935	−	9.88469i	1.25477	−	0.838408i	0.991974	+	0.126444i	$0.0403564\pi$
$140$	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	0.798264	−	0.602307i	$-0.205752\pi$
$149$	−0.777282	−	1.16329i	−0.0636775	−	0.0953001i	−0.861942	+	0.507007i	$0.830752\pi$
$150$	−4.57532	+	2.34957i	−0.373574	+	0.191842i
$151$	−9.74739	+	4.03750i	−0.793231	+	0.328567i	−0.742242	−	0.670132i	$-0.766237\pi$
$151$	−9.74739	+	4.03750i	−0.793231	+	0.328567i	−0.0509894	+	0.998699i	$0.516237\pi$
$152$	−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	0.712338	−	0.701837i	$-0.247636\pi$
$157$	4.21665	+	2.81748i	0.336525	+	0.224859i	−0.375813	+	0.926696i	$0.622636\pi$
$158$	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	0.610201	−	0.792247i	$-0.291089\pi$
$163$	1.42704	+	0.953517i	0.111774	+	0.0746852i	−0.498427	+	0.866932i	$0.666089\pi$
$164$	−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	0.719520	−	0.694472i	$-0.244362\pi$
$167$	9.52713	+	3.94627i	0.737231	+	0.305371i	0.0177115	+	0.999843i	$0.494362\pi$
$168$	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	−0.543433	−	0.839453i	$-0.682876\pi$
$173$	−9.52608	+	1.89486i	−0.724254	+	0.144063i	−0.180822	+	0.983516i	$0.557876\pi$
$174$	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	−0.935961	−	0.352104i	$-0.885466\pi$
$179$	−2.75596	−	13.8551i	−0.205990	−	1.03558i	0.729971	−	0.683478i	$-0.239534\pi$
$180$	−5.87454	−	0.193461i	−0.437862	−	0.0144197i
$181$	−17.5831	+	11.7487i	−1.30694	+	0.873270i	−0.996994	−	0.0774833i	$-0.975312\pi$
$181$	−17.5831	+	11.7487i	−1.30694	+	0.873270i	−0.309948	+	0.950754i	$0.600312\pi$
$182$	−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	−0.707995	−	0.706218i	$-0.750400\pi$
$197$	3.03683	−	15.2672i	0.216365	−	1.08774i	0.924360	−	0.381522i	$-0.124600\pi$
$198$	3.12494	+	2.65184i	0.222080	+	0.188458i
$199$	1.86681	−	4.50688i	0.132335	−	0.319484i	−0.843797	−	0.536662i	$-0.819685\pi$
$199$	1.86681	−	4.50688i	0.132335	−	0.319484i	0.976132	+	0.217178i	$0.0696851\pi$
$200$	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	−0.836033	−	0.548679i	$-0.815131\pi$
$211$	−20.3138	+	4.04066i	−1.39846	+	0.278170i	−0.562424	+	0.826849i	$0.690131\pi$
$212$	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	$-0.884169\pi$
$223$		−	10.6299i		−	0.711833i	0.934518	−	0.355917i	$-0.115831\pi$
$224$	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	0.531339	−	0.847159i	$-0.321689\pi$
$227$	−0.723182	−	0.483215i	−0.0479993	−	0.0320721i	−0.579338	+	0.815087i	$0.696689\pi$
$228$	−7.22362	+	10.0764i	−0.478396	+	0.667326i
$229$	16.9691	+	3.37536i	1.12135	+	0.223050i	0.720745	−	0.693200i	$-0.243800\pi$
$229$	16.9691	+	3.37536i	1.12135	+	0.223050i	0.400605	+	0.916251i	$0.368800\pi$
$230$	−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	−0.0312398	−	0.999512i	$-0.509946\pi$
$233$	9.97421	−	4.13145i	0.653432	−	0.270660i	0.684672	+	0.728852i	$0.259946\pi$
$234$	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	−0.887251	−	0.461287i	$-0.847388\pi$
$239$	−6.58523	+	6.58523i	−0.425963	+	0.425963i	0.461287	+	0.887251i	$0.347388\pi$
$240$	3.77431	+	11.1331i	0.243631	+	0.718636i
$241$	0.615471	+	0.615471i	0.0396460	+	0.0396460i	0.726652	−	0.687006i	$-0.241075\pi$
$241$	0.615471	+	0.615471i	0.0396460	+	0.0396460i	−0.687006	+	0.726652i	$0.741075\pi$
$242$	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	−0.945970	−	0.324255i	$-0.894886\pi$
$251$	0.825091	−	4.14801i	0.0520793	−	0.261820i	0.998049	+	0.0624345i	$0.0198865\pi$
$252$	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	−0.693067	−	0.720873i	$-0.743741\pi$
$263$	4.97449	−	12.0095i	0.306740	−	0.740536i	0.999807	−	0.0196623i	$-0.00625911\pi$
$264$	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	0.567927	+	0.823079i	$0.307745\pi$
$269$	5.87507	+	29.5360i	0.358209	+	1.80084i	−0.209718	+	0.977762i	$0.567255\pi$
$270$	−2.01927	+	3.63268i	−0.122889	+	0.221078i
$271$	14.4641	+	14.4641i	0.878634	+	0.878634i	0.993393	−	0.114759i	$-0.0366096\pi$
$271$	14.4641	+	14.4641i	0.878634	+	0.878634i	−0.114759	+	0.993393i	$0.536610\pi$
$272$	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	0.818274	−	0.574828i	$-0.194931\pi$
$277$	−0.431697	−	0.646081i	−0.0259382	−	0.0388192i	−0.844212	+	0.536009i	$0.819931\pi$
$278$	−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	−0.270461	−	0.962731i	$-0.587176\pi$
$281$	−19.1511	−	7.93265i	−1.14246	−	0.473222i	−0.871998	+	0.489509i	$0.837176\pi$
$282$	1.11651	+	13.6331i	0.0664873	+	0.811841i
$283$	−10.4218	−	2.07302i	−0.619509	−	0.123228i	−0.124649	−	0.992201i	$-0.539781\pi$
$283$	−10.4218	−	2.07302i	−0.619509	−	0.123228i	−0.494860	+	0.868973i	$0.664781\pi$
$284$	−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	0.305046	−	0.952338i	$-0.401328\pi$
$293$	3.80735	+	0.757329i	0.222428	+	0.0442437i	−0.0826181	+	0.996581i	$0.526328\pi$
$294$	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	0.997294	+	0.0735128i	$0.0234210\pi$
$307$	1.82304	+	9.16506i	0.104047	+	0.523078i	−0.893248	+	0.449565i	$0.851579\pi$
$308$	−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	0.894439	+	0.447190i	$0.147575\pi$
$311$	10.1964	+	24.6163i	0.578186	+	1.39586i	−0.316253	+	0.948675i	$0.602425\pi$
$312$	−4.81548	−	4.36707i	−0.272623	−	0.247236i
$313$	−11.8022	+	28.4930i	−0.667098	+	1.61052i	0.119343	+	0.992853i	$0.461921\pi$
$313$	−11.8022	+	28.4930i	−0.667098	+	1.61052i	−0.786441	+	0.617665i	$0.788079\pi$
$314$	−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	−0.532626	−	0.846351i	$-0.678795\pi$
$317$	8.06770	−	12.0742i	0.453127	−	0.678153i	0.985753	+	0.168198i	$0.0537947\pi$
$318$	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	−0.894730	−	0.446607i	$-0.852632\pi$
$331$	−15.0008	+	10.0232i	−0.824517	+	0.550925i	0.0702129	+	0.997532i	$0.477632\pi$
$332$	−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	−0.753064	−	0.657947i	$-0.771425\pi$
$337$	−1.74612	+	1.74612i	−0.0951174	+	0.0951174i	0.657947	+	0.753064i	$0.271425\pi$
$338$	−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	−0.0765033	−	0.997069i	$-0.524376\pi$
$347$	−9.84943	−	1.95917i	−0.528745	−	0.105174i	−0.452242	+	0.891895i	$0.649376\pi$
$348$	−5.51176	+	0.908890i	−0.295461	+	0.0487216i
$349$	−21.4960	−	14.3632i	−1.15065	−	0.768842i	−0.174230	−	0.984705i	$-0.555744\pi$
$349$	−21.4960	−	14.3632i	−1.15065	−	0.768842i	−0.976424	+	0.215863i	$0.930744\pi$
$350$	−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	$-0.775111\pi$
$353$		−	24.3940i		−	1.29836i	0.760633	−	0.649182i	$-0.224889\pi$
$354$	−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	0.783548	−	0.621331i	$-0.213408\pi$
$359$	17.0195	+	7.04969i	0.898253	+	0.372068i	0.114705	+	0.993400i	$0.463408\pi$
$360$	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	−0.580724	−	0.814100i	$-0.697231\pi$
$367$	4.47084	−	4.47084i	0.233376	−	0.233376i	0.814100	+	0.580724i	$0.197231\pi$
$368$	−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	−0.376344	−	0.926480i	$-0.622819\pi$
$373$	6.48135	−	4.33070i	0.335591	−	0.224235i	0.711935	+	0.702245i	$0.247819\pi$
$374$	−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	−0.959063	−	0.283193i	$-0.908606\pi$
$379$	0.688559	−	3.46162i	0.0353689	−	0.177812i	0.994432	+	0.105381i	$0.0336063\pi$
$380$	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	0.480006	+	0.877265i	$0.340635\pi$
$389$	−5.90069	+	29.6648i	−0.299177	+	1.50406i	−0.779182	+	0.626797i	$0.784365\pi$
$390$	−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	0.999971	+	0.00765051i	$0.00243526\pi$
$397$	1.57498	+	7.91796i	0.0790460	+	0.397391i	−0.920925	+	0.389740i	$0.872565\pi$
$398$	−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	−0.554134	−	0.832428i	$-0.686950\pi$
$401$	5.57284	−	5.57284i	0.278294	−	0.278294i	0.832428	+	0.554134i	$0.186950\pi$
$402$	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	0.800400	−	0.599466i	$-0.204621\pi$
$409$	19.0605	+	7.89512i	0.942481	+	0.390389i	0.142081	+	0.989855i	$0.454621\pi$
$410$	−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	0.492278	−	0.870438i	$-0.336164\pi$
$419$	−2.52828	−	1.68934i	−0.123515	−	0.0825298i	−0.615793	+	0.787908i	$0.711164\pi$
$420$	−6.92813	+	1.14245i	−0.338058	+	0.0557458i
$421$	−29.1341	−	5.79514i	−1.41991	−	0.282438i	−0.575354	−	0.817905i	$-0.695136\pi$
$421$	−29.1341	−	5.79514i	−1.41991	−	0.282438i	−0.844556	+	0.535467i	$0.820136\pi$
$422$	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	−0.854419	−	0.519585i	$-0.826087\pi$
$431$	−6.95134	+	6.95134i	−0.334834	+	0.334834i	0.519585	+	0.854419i	$0.326087\pi$
$432$	3.17246	+	2.43629i	0.152635	+	0.117216i
$433$	−10.4868	−	10.4868i	−0.503962	−	0.503962i	0.408704	−	0.912667i	$-0.365981\pi$
$433$	−10.4868	−	10.4868i	−0.503962	−	0.503962i	−0.912667	+	0.408704i	$0.865981\pi$
$434$	−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	−0.853599	−	0.520930i	$-0.825585\pi$
$439$	−12.9562	−	31.2791i	−0.618367	−	1.49287i	0.235232	−	0.971939i	$-0.424415\pi$
$440$	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	0.850795	+	0.525497i	$0.176121\pi$
$443$	−2.86955	+	14.4262i	−0.136336	+	0.685408i	−0.987131	+	0.159911i	$0.948879\pi$
$444$	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	−0.999120	−	0.0419406i	$-0.986646\pi$
$457$	−6.88982	−	16.6335i	−0.322292	−	0.778082i	0.676828	−	0.736141i	$-0.263354\pi$
$458$	−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	−0.707303	−	0.706910i	$-0.750088\pi$
$461$	−6.96437	−	35.0123i	−0.324363	−	1.63068i	0.382940	−	0.923773i	$-0.374912\pi$
$462$	4.27945	+	2.37879i	0.199098	+	0.110671i
$463$	18.5791	+	18.5791i	0.863443	+	0.863443i	0.991736	−	0.128293i	$-0.0409499\pi$
$463$	18.5791	+	18.5791i	0.863443	+	0.863443i	−0.128293	+	0.991736i	$0.540950\pi$
$464$	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	0.287140	−	0.957889i	$-0.407296\pi$
$467$	19.8595	−	3.95031i	0.918990	−	0.182799i	0.631851	+	0.775090i	$0.282296\pi$
$468$	−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	$0.0668697\pi$
$479$			9.12804i			0.417071i	−0.978015	+	0.208535i	$0.933130\pi$
$480$	−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	0.260795	−	0.965394i	$-0.416015\pi$
$487$	−5.23967	−	2.17034i	−0.237432	−	0.0983476i	−0.498227	+	0.867047i	$0.666015\pi$
$488$	−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	0.802911	−	0.596100i	$-0.203284\pi$
$491$	−1.22036	−	1.82640i	−0.0550742	−	0.0824243i	−0.857985	+	0.513675i	$0.828284\pi$
$492$	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	−0.925360	−	0.379090i	$-0.876237\pi$
$499$	−4.81413	−	24.2023i	−0.215510	−	1.08344i	0.709850	−	0.704353i	$-0.248763\pi$
$500$	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	0.914607	+	0.404344i	$0.132500\pi$
$503$	12.4204	+	29.9854i	0.553797	+	1.33698i	−0.360810	+	0.932639i	$0.617500\pi$
$504$	−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	−0.998359	−	0.0572685i	$-0.981761\pi$
$509$	−12.7108	+	19.0230i	−0.563394	+	0.843179i	0.434965	+	0.900448i	$0.356761\pi$
$510$	−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	0.957863	−	0.287227i	$-0.0927333\pi$
$521$	1.76786	+	4.26800i	0.0774515	+	0.186984i	−0.880411	+	0.474211i	$0.842733\pi$
$522$	−1.20870	+	3.76056i	−0.0529032	+	0.164595i
$523$	32.4159	−	21.6596i	1.41745	−	0.947108i	0.418198	−	0.908356i	$-0.362662\pi$
$523$	32.4159	−	21.6596i	1.41745	−	0.947108i	0.999249	−	0.0387519i	$-0.0123382\pi$
$524$	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	0.399591	−	0.916693i	$-0.369152\pi$
$541$	−6.84771	−	4.57549i	−0.294406	−	0.196716i	−0.693997	+	0.719978i	$0.744152\pi$
$542$	−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	0.299236	−	0.954179i	$-0.403268\pi$
$547$	−10.9409	−	7.31045i	−0.467798	−	0.312572i	−0.767034	+	0.641607i	$0.778268\pi$
$548$	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	−0.0557028	−	0.998447i	$-0.517740\pi$
$557$	6.48843	−	1.29063i	0.274924	−	0.0546857i	0.330627	+	0.943762i	$0.392740\pi$
$558$	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	0.999967	−	0.00808052i	$-0.00257214\pi$
$563$	1.73273	+	8.71100i	0.0730257	+	0.367125i	−0.926942	+	0.375206i	$0.877572\pi$
$564$	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	0.347158	+	0.937807i	$0.387147\pi$
$569$	−13.3927	+	32.3327i	−0.561449	+	1.35546i	−0.908607	+	0.417652i	$0.862853\pi$
$570$	−19.6445	−	16.6704i	−0.822817	−	0.698246i
$571$	2.01942	−	10.1523i	0.0845103	−	0.424862i	−0.915248	−	0.402890i	$-0.868006\pi$
$571$	2.01942	−	10.1523i	0.0845103	−	0.424862i	0.999759	−	0.0219716i	$-0.00699434\pi$
$572$	−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	−0.0172417	−	0.999851i	$-0.505488\pi$
$587$	21.8029	−	14.5682i	0.899902	−	0.601296i	0.917144	+	0.398556i	$0.130488\pi$
$588$	−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	−0.848386	−	0.529378i	$-0.822425\pi$
$593$	−7.76835	+	7.76835i	−0.319008	+	0.319008i	0.529378	+	0.848386i	$0.322425\pi$
$594$	−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	−0.592286	−	0.805728i	$-0.701774\pi$
$599$	−10.8021	+	4.47436i	−0.441360	+	0.182817i	0.150926	+	0.988545i	$0.451774\pi$
$600$	−9.97915	+	2.49654i	−0.407397	+	0.101921i
$601$	21.4324	+	8.87760i	0.874247	+	0.362125i	0.774263	−	0.632864i	$-0.218121\pi$
$601$	21.4324	+	8.87760i	0.874247	+	0.362125i	0.0999839	+	0.994989i	$0.468121\pi$
$602$	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	$-0.681767\pi$
$607$		−	41.4568i		−	1.68268i	0.540506	−	0.841340i	$-0.318233\pi$
$608$	−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	−0.0893261	−	0.996002i	$-0.528471\pi$
$613$	−13.6918	−	2.72347i	−0.553006	−	0.110000i	−0.463680	+	0.886003i	$0.653471\pi$
$614$	−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	−0.157699	−	0.987487i	$-0.550408\pi$
$617$	10.6574	−	4.41443i	0.429050	−	0.177718i	0.586749	+	0.809769i	$0.300408\pi$
$618$	21.7833	−	11.1864i	0.876251	−	0.449982i
$619$	−17.5508	−	26.2666i	−0.705427	−	1.05575i	−0.995124	−	0.0986274i	$-0.968555\pi$
$619$	−17.5508	−	26.2666i	−0.705427	−	1.05575i	0.289698	−	0.957118i	$-0.406445\pi$
$620$	−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	−0.968839	−	0.247690i	$-0.920329\pi$
$631$	−11.5277	−	27.8303i	−0.458910	−	1.10791i	0.509930	−	0.860216i	$-0.329671\pi$
$632$	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	−0.943555	−	0.331216i	$-0.892541\pi$
$643$	−7.01053	+	10.4920i	−0.276468	+	0.413764i	0.667087	+	0.744980i	$0.267541\pi$
$644$	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	−0.875047	−	0.484039i	$-0.839169\pi$
$647$	2.18679	−	5.27938i	0.0859717	−	0.207554i	0.961018	+	0.276485i	$0.0891695\pi$
$648$	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	−0.890760	−	0.454473i	$-0.849827\pi$
$653$	−6.17700	−	31.0539i	−0.241725	−	1.21523i	0.649036	−	0.760758i	$-0.275173\pi$
$654$	−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	0.275389	−	0.961333i	$-0.411193\pi$
$659$	23.0449	−	4.58392i	0.897702	−	0.178564i	0.622313	+	0.782769i	$0.286193\pi$
$660$	15.5143	+	7.03308i	0.603893	+	0.273762i
$661$	13.0036	+	19.4613i	0.505782	+	0.756957i	0.993226	−	0.116197i	$-0.0370705\pi$
$661$	13.0036	+	19.4613i	0.505782	+	0.756957i	−0.487444	+	0.873154i	$0.662071\pi$
$662$	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	$0.118331\pi$
$673$			18.8467i			0.726488i	−0.931694	+	0.363244i	$0.881669\pi$
$674$	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	0.605071	−	0.796171i	$-0.293145\pi$
$677$	22.3610	+	4.44787i	0.859402	+	0.170946i	0.254331	+	0.967117i	$0.418145\pi$
$678$	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	0.594994	−	0.803730i	$-0.297154\pi$
$683$	−9.80688	−	14.6770i	−0.375250	−	0.561601i	−0.970244	+	0.242129i	$0.922154\pi$
$684$	−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	−0.833689	−	0.552234i	$-0.813776\pi$
$691$	−7.22341	−	36.3146i	−0.274792	−	1.38147i	0.558898	−	0.829237i	$-0.311224\pi$
$692$	−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	−0.645872	−	0.763446i	$-0.723506\pi$
$701$	8.11831	−	12.1499i	0.306624	−	0.458896i	0.952496	+	0.304550i	$0.0985060\pi$
$702$	−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	0.214552	+	0.976713i	$0.431171\pi$
$709$	−9.51757	+	47.8481i	−0.357440	+	1.79697i	−0.571992	+	0.820259i	$0.693829\pi$
$710$	−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	0.520500	−	0.853861i	$-0.325745\pi$
$719$	−8.93880	−	8.93880i	−0.333361	−	0.333361i	−0.853861	+	0.520500i	$0.825745\pi$
$720$	−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	−0.798476	−	0.602027i	$-0.794360\pi$
$727$	−25.2747	+	10.4691i	−0.937385	+	0.388278i	−0.138910	+	0.990305i	$0.544360\pi$
$728$	−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	0.259105	−	0.965849i	$-0.416572\pi$
$733$	−14.4593	−	9.66143i	−0.534068	−	0.356853i	−0.793173	+	0.608996i	$0.791572\pi$
$734$	−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	0.338606	−	0.940928i	$-0.390045\pi$
$739$	−10.9042	−	7.28599i	−0.401119	−	0.268019i	−0.739725	+	0.672909i	$0.765045\pi$
$740$	−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	0.215965	−	0.976401i	$-0.430710\pi$
$743$	−8.77012	−	3.63270i	−0.321745	−	0.133271i	−0.537710	+	0.843130i	$0.680710\pi$
$744$	−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	−0.910390	−	0.413750i	$-0.864219\pi$
$751$	−13.6101	+	13.6101i	−0.496640	+	0.496640i	0.413750	+	0.910390i	$0.364219\pi$
$752$	−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	0.283904	−	0.958853i	$-0.408370\pi$
$757$	35.1738	−	23.5024i	1.27841	−	0.854208i	0.994510	+	0.104644i	$0.0333704\pi$
$758$	−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	−0.766570	−	0.642160i	$-0.778038\pi$
$761$	6.33249	−	15.2880i	0.229553	−	0.554189i	0.996123	+	0.0879711i	$0.0280383\pi$
$762$	−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	−0.909886	−	0.414858i	$-0.863831\pi$
$773$	2.48831	−	12.5096i	0.0894983	−	0.449938i	0.999384	−	0.0350805i	$-0.0111687\pi$
$774$	−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	0.445647	−	0.895209i	$-0.352974\pi$
$787$	33.6629	−	6.69597i	1.19995	−	0.238686i	0.754306	+	0.656523i	$0.227974\pi$
$788$	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	0.785615	−	0.618716i	$-0.212347\pi$
$797$	14.5288	+	9.70787i	0.514638	+	0.343870i	−0.270977	+	0.962586i	$0.587347\pi$
$798$	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	−0.121660	−	0.992572i	$-0.538822\pi$
$809$	14.0556	−	5.82200i	0.494167	−	0.204691i	0.615827	+	0.787881i	$0.288822\pi$
$810$	−1.89861	−	3.69717i	−0.0667104	−	0.129905i
$811$	27.9559	+	41.8390i	0.981664	+	1.46916i	0.880358	+	0.474309i	$0.157302\pi$
$811$	27.9559	+	41.8390i	0.981664	+	1.46916i	0.101306	+	0.994855i	$0.467698\pi$
$812$	−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	−0.868664	−	0.495403i	$-0.835021\pi$
$821$	−21.3005	+	14.2326i	−0.743394	+	0.496720i	0.125269	+	0.992123i	$0.460021\pi$
$822$	17.3977	+	5.59187i	0.606816	+	0.195039i
$823$	8.81905	+	21.2911i	0.307413	+	0.742160i	0.999787	+	0.0206216i	$0.00656453\pi$
$823$	8.81905	+	21.2911i	0.307413	+	0.742160i	−0.692375	+	0.721538i	$0.743435\pi$
$824$	−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	−0.810077	−	0.586324i	$-0.800575\pi$
$827$	4.67924	−	23.5241i	0.162713	−	0.818014i	0.972790	−	0.231690i	$-0.0744254\pi$
$828$	3.91581	+	6.29988i	0.136084	+	0.218936i
$829$	14.0583	−	21.0397i	0.488265	−	0.730741i	−0.502758	−	0.864427i	$-0.667681\pi$
$829$	14.0583	−	21.0397i	0.488265	−	0.730741i	0.991024	+	0.133686i	$0.0426815\pi$
$830$	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	−0.952726	−	0.303830i	$-0.901734\pi$
$839$	−1.85977	+	4.48989i	−0.0642065	+	0.155008i	0.888520	+	0.458839i	$0.151734\pi$
$840$	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	0.855480	−	0.517835i	$-0.173262\pi$
$853$	1.45109	+	2.17172i	0.0496845	+	0.0743582i	−0.805796	+	0.592194i	$0.798262\pi$
$854$	−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	−0.0716192	−	0.997432i	$-0.522817\pi$
$857$	−24.2262	−	10.0348i	−0.827553	−	0.342784i	−0.755933	+	0.654649i	$0.772817\pi$
$858$	−9.38840	+	0.768882i	−0.320515	+	0.0262492i
$859$	−49.0640	−	9.75943i	−1.67404	−	0.332988i	−0.735335	−	0.677704i	$-0.762975\pi$
$859$	−49.0640	−	9.75943i	−1.67404	−	0.332988i	−0.938707	+	0.344717i	$0.887975\pi$
$860$	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	$-0.964044\pi$
$863$		−	6.62270i		−	0.225439i	0.993627	−	0.112720i	$-0.0359562\pi$
$864$	−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	0.0631928	−	0.998001i	$-0.479872\pi$
$877$	14.9106	−	2.96590i	0.503494	−	0.100151i	0.440301	+	0.897850i	$0.354872\pi$
$878$	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	0.471134	−	0.882062i	$-0.343845\pi$
$881$	−12.1970	−	12.1970i	−0.410928	−	0.410928i	−0.882062	+	0.471134i	$0.843845\pi$
$882$	−3.82908	+	6.88852i	−0.128932	+	0.231949i
$883$	−2.80083	−	14.0807i	−0.0942553	−	0.473854i	−0.998866	−	0.0476143i	$-0.984838\pi$
$883$	−2.80083	−	14.0807i	−0.0942553	−	0.473854i	0.904610	−	0.426239i	$-0.140162\pi$
$884$	−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	−0.813070	−	0.582166i	$-0.802205\pi$
$887$	−19.3526	−	46.7213i	−0.649796	−	1.56875i	0.163273	−	0.986581i	$-0.447795\pi$
$888$	−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	−0.0636060	−	0.997975i	$-0.520260\pi$
$907$	25.1190	−	16.7840i	0.834062	−	0.557302i	0.897668	+	0.440673i	$0.145260\pi$
$908$	−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	0.811350	−	0.584560i	$-0.198733\pi$
$911$	6.84516	+	6.84516i	0.226790	+	0.226790i	−0.584560	+	0.811350i	$0.698733\pi$
$912$	−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	0.301499	−	0.953466i	$-0.402513\pi$
$919$	36.0413	−	14.9288i	1.18889	−	0.492456i	0.887395	+	0.461010i	$0.152513\pi$
$920$	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	$-0.951606\pi$
$929$		−	9.23214i		−	0.302897i	0.988465	−	0.151448i	$-0.0483937\pi$
$930$	−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	−0.985860	−	0.167573i	$-0.946407\pi$
$937$	−47.8893	+	19.8364i	−1.56448	+	0.648027i	−0.578616	+	0.815600i	$0.696407\pi$
$938$	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	−0.480235	−	0.877140i	$-0.659449\pi$
$941$	−18.0449	+	3.58936i	−0.588248	+	0.117010i	−0.108013	+	0.994149i	$0.534449\pi$
$942$	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	−0.896567	−	0.442908i	$-0.853947\pi$
$947$	−7.31607	−	36.7804i	−0.237740	−	1.19520i	0.658827	−	0.752295i	$-0.271053\pi$
$948$	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	−0.878489	−	0.477763i	$-0.841448\pi$
$953$	2.48590	−	6.00150i	0.0805263	−	0.194408i	0.959015	+	0.283356i	$0.0914477\pi$
$954$	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	0.260691	+	0.965422i	$0.416050\pi$
$967$	−18.8539	+	45.5175i	−0.606302	+	1.46374i	−0.866993	+	0.498320i	$0.833950\pi$
$968$	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	−0.777106	−	0.629370i	$-0.783313\pi$
$971$	−15.3632	+	10.2654i	−0.493029	+	0.329432i	0.284076	+	0.958802i	$0.408313\pi$
$972$	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	−0.854818	−	0.518928i	$-0.826331\pi$
$977$	−10.4989	+	10.4989i	−0.335889	+	0.335889i	0.518928	+	0.854818i	$0.326331\pi$
$978$	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	−0.0983464	−	0.995152i	$-0.531355\pi$
$983$	16.7986	−	6.95819i	0.535791	−	0.221932i	0.634137	+	0.773220i	$0.281355\pi$
$984$	−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	$0.145456\pi$
$991$			27.7797i			0.882452i	−0.897396	+	0.441226i	$0.854544\pi$
$992$	−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	0.410393	−	0.911909i	$-0.365392\pi$
$997$	13.9113	+	2.76712i	0.440574	+	0.0876356i	0.0301811	+	0.999544i	$0.490392\pi$
$998$	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.37.1	✓	128
3.2	odd	2		576.2.bd.b.37.16		128
4.3	odd	2		768.2.r.a.241.15		128
64.19	odd	16		768.2.r.a.529.15		128
64.45	even	16	inner	192.2.r.a.109.1	yes	128
192.173	odd	16		576.2.bd.b.109.16		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.37.1	✓	128	1.1	even	1	trivial
192.2.r.a.109.1	yes	128	64.45	even	16	inner
576.2.bd.b.37.16		128	3.2	odd	2
576.2.bd.b.109.16		128	192.173	odd	16
768.2.r.a.241.15		128	4.3	odd	2
768.2.r.a.529.15		128	64.19	odd	16

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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