LMFDB - Embedded newform 345.2.m.a.211.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [345,2,Mod(16,345)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("345.16"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(345, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.m (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [30,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			211.1
Character	$\chi$	$=$	345.211
Dual form			345.2.m.a.121.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.883723 - 1.93508i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-1.65386 + 1.90866i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(-1.39310 - 1.60773i) q^{6} +(-0.350847 - 2.44020i) q^{7} +(1.07266 + 0.314961i) q^{8} +(0.841254 - 0.540641i) q^{9} +(-0.302750 + 2.10567i) q^{10} +(1.03763 - 2.27210i) q^{11} +(-1.04914 + 2.29729i) q^{12} +(-0.0750447 + 0.521948i) q^{13} +(-4.41193 + 2.83538i) q^{14} +(-0.959493 - 0.281733i) q^{15} +(0.380379 + 2.64560i) q^{16} +(-2.99343 - 3.45460i) q^{17} +(-1.78962 - 1.15012i) q^{18} +(-3.29988 + 3.80827i) q^{19} +(2.42321 - 0.711520i) q^{20} +(-1.02412 - 2.24251i) q^{21} -5.31368 q^{22} +(-2.17254 - 4.27552i) q^{23} +1.11794 q^{24} +(0.415415 + 0.909632i) q^{25} +(1.07633 - 0.316039i) q^{26} +(0.654861 - 0.755750i) q^{27} +(5.23775 + 3.36610i) q^{28} +(-0.853849 - 0.985395i) q^{29} +(0.302750 + 2.10567i) q^{30} +(1.00958 + 0.296440i) q^{31} +(6.66425 - 4.28285i) q^{32} +(0.355477 - 2.47240i) q^{33} +(-4.03958 + 8.84544i) q^{34} +(-1.02412 + 2.24251i) q^{35} +(-0.359418 + 2.49981i) q^{36} +(-3.98079 + 2.55830i) q^{37} +(10.2855 + 3.02009i) q^{38} +(0.0750447 + 0.521948i) q^{39} +(-0.732097 - 0.844885i) q^{40} +(-2.07680 - 1.33468i) q^{41} +(-3.43440 + 3.96351i) q^{42} +(11.7472 - 3.44928i) q^{43} +(2.62056 + 5.73822i) q^{44} -1.00000 q^{45} +(-6.35356 + 7.98243i) q^{46} +6.76385 q^{47} +(1.11032 + 2.43127i) q^{48} +(0.884988 - 0.259856i) q^{49} +(1.39310 - 1.60773i) q^{50} +(-3.84545 - 2.47132i) q^{51} +(-0.872106 - 1.00646i) q^{52} +(0.343110 + 2.38638i) q^{53} +(-2.04115 - 0.599337i) q^{54} +(-2.10130 + 1.35042i) q^{55} +(0.392227 - 2.72800i) q^{56} +(-2.09330 + 4.58369i) q^{57} +(-1.15225 + 2.52309i) q^{58} +(-0.213111 + 1.48222i) q^{59} +(2.12460 - 1.36540i) q^{60} +(6.19515 + 1.81906i) q^{61} +(-0.318554 - 2.21559i) q^{62} +(-1.61442 - 1.86314i) q^{63} +(-9.68002 - 6.22097i) q^{64} +(0.345318 - 0.398518i) q^{65} +(-5.09844 + 1.49704i) q^{66} +(-3.70195 - 8.10614i) q^{67} +11.5444 q^{68} +(-3.28909 - 3.49025i) q^{69} +5.24447 q^{70} +(1.17562 + 2.57426i) q^{71} +(1.07266 - 0.314961i) q^{72} +(9.74573 - 11.2472i) q^{73} +(8.46844 + 5.44234i) q^{74} +(0.654861 + 0.755750i) q^{75} +(-1.81113 - 12.5967i) q^{76} +(-5.90841 - 1.73487i) q^{77} +(0.943694 - 0.606475i) q^{78} +(2.16388 - 15.0501i) q^{79} +(1.11032 - 2.43127i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-0.747397 + 5.19826i) q^{82} +(-0.591590 + 0.380192i) q^{83} +(5.97392 + 1.75410i) q^{84} +(0.650534 + 4.52456i) q^{85} +(-17.0559 - 19.6835i) q^{86} +(-1.09688 - 0.704922i) q^{87} +(1.82865 - 2.11037i) q^{88} +(6.81425 - 2.00085i) q^{89} +(0.883723 + 1.93508i) q^{90} +1.29998 q^{91} +(11.7536 + 2.92447i) q^{92} +1.05220 q^{93} +(-5.97737 - 13.0886i) q^{94} +(4.83494 - 1.41967i) q^{95} +(5.18768 - 5.98690i) q^{96} +(2.79860 + 1.79855i) q^{97} +(-1.28493 - 1.48288i) q^{98} +(-0.355477 - 2.47240i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9} - 7 q^{11} - 2 q^{12} + 7 q^{13} - 47 q^{14} - 3 q^{15} + 26 q^{16} + 15 q^{17} - 7 q^{19} - 2 q^{20} - 12 q^{21} - 18 q^{22}+ \cdots + 4 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9 - 7 * q^11 - 2 * q^12 + 7 * q^13 - 47 * q^14 - 3 * q^15 + 26 * q^16 + 15 * q^17 - 7 * q^19 - 2 * q^20 - 12 * q^21 - 18 * q^22 + 12 * q^23 - 3 * q^25 - 18 * q^26 + 3 * q^27 + 2 * q^28 - 6 * q^29 + 22 * q^31 + 33 * q^32 - 4 * q^33 - 53 * q^34 - 12 * q^35 - 9 * q^36 - 23 * q^37 + 21 * q^38 - 7 * q^39 + 11 * q^40 + 26 * q^41 + 3 * q^42 - 19 * q^43 - 47 * q^44 - 30 * q^45 - 44 * q^46 + 14 * q^47 + 7 * q^48 + 2 * q^49 - 11 * q^50 - 15 * q^51 + 55 * q^52 - 14 * q^53 - 11 * q^54 - 4 * q^55 + 6 * q^56 - 26 * q^57 - 18 * q^58 + 40 * q^59 - 9 * q^60 + 37 * q^61 + 19 * q^62 - 10 * q^63 + 14 * q^64 + 4 * q^65 - 4 * q^66 - 108 * q^67 + 54 * q^68 + 21 * q^69 - 30 * q^70 + 39 * q^71 + 22 * q^72 + 57 * q^73 - 11 * q^74 + 3 * q^75 + 22 * q^76 + 2 * q^77 + 7 * q^78 + 55 * q^79 + 7 * q^80 - 3 * q^81 - 26 * q^82 - 79 * q^83 - 2 * q^84 + 18 * q^85 - 44 * q^86 - 5 * q^87 - 8 * q^88 - 30 * q^89 + 40 * q^91 + 35 * q^92 + 44 * q^93 - 29 * q^94 + 7 * q^95 + 22 * q^96 - 52 * q^97 + 28 * q^98 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{2}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.883723	−	1.93508i	−0.624887	−	1.36831i	−0.911911	−	0.410388i	$-0.865393\pi$
$2$	−0.883723	−	1.93508i	−0.624887	−	1.36831i	0.287025	−	0.957923i	$-0.407334\pi$
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$4$	−1.65386	+	1.90866i	−0.826930	+	0.954329i
$5$	−0.841254	−	0.540641i	−0.376220	−	0.241782i
$5$	−0.841254	−	0.540641i	−0.376220	−	0.241782i
$6$	−1.39310	−	1.60773i	−0.568732	−	0.656351i
$7$	−0.350847	−	2.44020i	−0.132608	−	0.922307i	−0.942137	−	0.335228i	$-0.891187\pi$
$7$	−0.350847	−	2.44020i	−0.132608	−	0.922307i	0.809529	−	0.587080i	$-0.199722\pi$
$8$	1.07266	+	0.314961i	0.379242	+	0.111356i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	−0.302750	+	2.10567i	−0.0957380	+	0.665872i
$11$	1.03763	−	2.27210i	0.312858	−	0.685063i	−0.686247	−	0.727369i	$-0.740743\pi$
$11$	1.03763	−	2.27210i	0.312858	−	0.685063i	0.999105	+	0.0423057i	$0.0134703\pi$
$12$	−1.04914	+	2.29729i	−0.302860	+	0.663170i
$13$	−0.0750447	+	0.521948i	−0.0208137	+	0.144762i	−0.997578	−	0.0695527i	$-0.977843\pi$
$13$	−0.0750447	+	0.521948i	−0.0208137	+	0.144762i	0.976765	+	0.214315i	$0.0687519\pi$
$14$	−4.41193	+	2.83538i	−1.17914	+	0.757786i
$15$	−0.959493	−	0.281733i	−0.247740	−	0.0727430i
$16$	0.380379	+	2.64560i	0.0950949	+	0.661399i
$17$	−2.99343	−	3.45460i	−0.726013	−	0.837864i	0.266004	−	0.963972i	$-0.414297\pi$
$17$	−2.99343	−	3.45460i	−0.726013	−	0.837864i	−0.992016	+	0.126108i	$0.959751\pi$
$18$	−1.78962	−	1.15012i	−0.421818	−	0.271086i
$19$	−3.29988	+	3.80827i	−0.757045	+	0.873676i	−0.995231	−	0.0975433i	$-0.968902\pi$
$19$	−3.29988	+	3.80827i	−0.757045	+	0.873676i	0.238187	+	0.971219i	$0.423447\pi$
$20$	2.42321	−	0.711520i	0.541847	−	0.159101i
$21$	−1.02412	−	2.24251i	−0.223481	−	0.489355i
$22$	−5.31368			−1.13288
$23$	−2.17254	−	4.27552i	−0.453007	−	0.891507i
$23$	−2.17254	−	4.27552i	−0.453007	−	0.891507i
$24$	1.11794			0.228199
$25$	0.415415	+	0.909632i	0.0830830	+	0.181926i
$26$	1.07633	−	0.316039i	0.211086	−	0.0619804i
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$	5.23775	+	3.36610i	0.989842	+	0.636133i
$29$	−0.853849	−	0.985395i	−0.158556	−	0.182983i	0.670913	−	0.741536i	$-0.265902\pi$
$29$	−0.853849	−	0.985395i	−0.158556	−	0.182983i	−0.829469	+	0.558553i	$0.811357\pi$
$30$	0.302750	+	2.10567i	0.0552743	+	0.384442i
$31$	1.00958	+	0.296440i	0.181326	+	0.0532421i	0.371135	−	0.928579i	$-0.378969\pi$
$31$	1.00958	+	0.296440i	0.181326	+	0.0532421i	−0.189809	+	0.981821i	$0.560787\pi$
$32$	6.66425	−	4.28285i	1.17808	−	0.757108i
$33$	0.355477	−	2.47240i	0.0618806	−	0.430389i
$34$	−4.03958	+	8.84544i	−0.692782	+	1.51698i
$35$	−1.02412	+	2.24251i	−0.173108	+	0.379053i
$36$	−0.359418	+	2.49981i	−0.0599031	+	0.416635i
$37$	−3.98079	+	2.55830i	−0.654438	+	0.420582i	−0.825286	−	0.564716i	$-0.808986\pi$
$37$	−3.98079	+	2.55830i	−0.654438	+	0.420582i	0.170847	+	0.985298i	$0.445350\pi$
$38$	10.2855	+	3.02009i	1.66853	+	0.489924i
$39$	0.0750447	+	0.521948i	0.0120168	+	0.0835785i
$40$	−0.732097	−	0.844885i	−0.115755	−	0.133588i
$41$	−2.07680	−	1.33468i	−0.324341	−	0.208441i	0.368330	−	0.929695i	$-0.379930\pi$
$41$	−2.07680	−	1.33468i	−0.324341	−	0.208441i	−0.692671	+	0.721254i	$0.743566\pi$
$42$	−3.43440	+	3.96351i	−0.529939	+	0.611583i
$43$	11.7472	−	3.44928i	1.79142	−	0.526010i	0.794708	−	0.606991i	$-0.207624\pi$
$43$	11.7472	−	3.44928i	1.79142	−	0.526010i	0.996716	+	0.0809818i	$0.0258056\pi$
$44$	2.62056	+	5.73822i	0.395064	+	0.865069i
$45$	−1.00000			−0.149071
$46$	−6.35356	+	7.98243i	−0.936781	+	1.17694i
$47$	6.76385			0.986608			0.493304	−	0.869857i	$-0.335789\pi$
$47$	6.76385			0.986608			0.493304	+	0.869857i	$0.335789\pi$
$48$	1.11032	+	2.43127i	0.160261	+	0.350923i
$49$	0.884988	−	0.259856i	0.126427	−	0.0371223i
$50$	1.39310	−	1.60773i	0.197014	−	0.227367i
$51$	−3.84545	−	2.47132i	−0.538470	−	0.346054i
$52$	−0.872106	−	1.00646i	−0.120939	−	0.139571i
$53$	0.343110	+	2.38638i	0.0471298	+	0.327795i	0.999723	+	0.0235471i	$0.00749597\pi$
$53$	0.343110	+	2.38638i	0.0471298	+	0.327795i	−0.952593	+	0.304248i	$0.901595\pi$
$54$	−2.04115	−	0.599337i	−0.277766	−	0.0815594i
$55$	−2.10130	+	1.35042i	−0.283339	+	0.182091i
$56$	0.392227	−	2.72800i	0.0524136	−	0.364544i
$57$	−2.09330	+	4.58369i	−0.277264	+	0.607124i
$58$	−1.15225	+	2.52309i	−0.151298	+	0.331297i
$59$	−0.213111	+	1.48222i	−0.0277447	+	0.192968i	−0.998980	−	0.0451529i	$-0.985623\pi$
$59$	−0.213111	+	1.48222i	−0.0277447	+	0.192968i	0.971235	+	0.238121i	$0.0765316\pi$
$60$	2.12460	−	1.36540i	0.274285	−	0.176272i
$61$	6.19515	+	1.81906i	0.793208	+	0.232907i	0.653142	−	0.757235i	$-0.273450\pi$
$61$	6.19515	+	1.81906i	0.793208	+	0.232907i	0.140066	+	0.990142i	$0.455269\pi$
$62$	−0.318554	−	2.21559i	−0.0404564	−	0.281381i
$63$	−1.61442	−	1.86314i	−0.203398	−	0.234734i
$64$	−9.68002	−	6.22097i	−1.21000	−	0.777621i
$65$	0.345318	−	0.398518i	0.0428314	−	0.0494301i
$66$	−5.09844	+	1.49704i	−0.627574	+	0.184272i
$67$	−3.70195	−	8.10614i	−0.452265	−	0.990323i	−0.989183	−	0.146688i	$-0.953139\pi$
$67$	−3.70195	−	8.10614i	−0.452265	−	0.990323i	0.536918	−	0.843635i	$-0.319589\pi$
$68$	11.5444			1.39996
$69$	−3.28909	−	3.49025i	−0.395960	−	0.420177i
$70$	5.24447			0.626834
$71$	1.17562	+	2.57426i	0.139521	+	0.305508i	0.966475	−	0.256762i	$-0.0826555\pi$
$71$	1.17562	+	2.57426i	0.139521	+	0.305508i	−0.826954	+	0.562270i	$0.809928\pi$
$72$	1.07266	−	0.314961i	0.126414	−	0.0371185i
$73$	9.74573	−	11.2472i	1.14065	−	1.31638i	0.198920	−	0.980016i	$-0.436256\pi$
$73$	9.74573	−	11.2472i	1.14065	−	1.31638i	0.941731	−	0.336366i	$-0.109198\pi$
$74$	8.46844	+	5.44234i	0.984436	+	0.632659i
$75$	0.654861	+	0.755750i	0.0756168	+	0.0872664i
$76$	−1.81113	−	12.5967i	−0.207751	−	1.44494i
$77$	−5.90841	−	1.73487i	−0.673326	−	0.197706i
$78$	0.943694	−	0.606475i	0.106852	−	0.0686698i
$79$	2.16388	−	15.0501i	0.243455	−	1.69327i	−0.391065	−	0.920363i	$-0.627893\pi$
$79$	2.16388	−	15.0501i	0.243455	−	1.69327i	0.634520	−	0.772906i	$-0.281198\pi$
$80$	1.11032	−	2.43127i	0.124138	−	0.271824i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	−0.747397	+	5.19826i	−0.0825361	+	0.574051i
$83$	−0.591590	+	0.380192i	−0.0649355	+	0.0417315i	−0.572706	−	0.819761i	$-0.694106\pi$
$83$	−0.591590	+	0.380192i	−0.0649355	+	0.0417315i	0.507770	+	0.861493i	$0.330470\pi$
$84$	5.97392	+	1.75410i	0.651809	+	0.191388i
$85$	0.650534	+	4.52456i	0.0705603	+	0.490758i
$86$	−17.0559	−	19.6835i	−1.83918	−	2.12253i
$87$	−1.09688	−	0.704922i	−0.117598	−	0.0755756i
$88$	1.82865	−	2.11037i	0.194934	−	0.224966i
$89$	6.81425	−	2.00085i	0.722309	−	0.212089i	0.100142	−	0.994973i	$-0.468070\pi$
$89$	6.81425	−	2.00085i	0.722309	−	0.212089i	0.622168	+	0.782884i	$0.286252\pi$
$90$	0.883723	+	1.93508i	0.0931526	+	0.203976i
$91$	1.29998			0.136275
$92$	11.7536	+	2.92447i	1.22540	+	0.304897i
$93$	1.05220			0.109108
$94$	−5.97737	−	13.0886i	−0.616518	−	1.34999i
$95$	4.83494	−	1.41967i	0.496054	−	0.145655i
$96$	5.18768	−	5.98690i	0.529465	−	0.611036i
$97$	2.79860	+	1.79855i	0.284155	+	0.182615i	0.674952	−	0.737862i	$-0.264164\pi$
$97$	2.79860	+	1.79855i	0.284155	+	0.182615i	−0.390797	+	0.920477i	$0.627801\pi$
$98$	−1.28493	−	1.48288i	−0.129797	−	0.149794i
$99$	−0.355477	−	2.47240i	−0.0357268	−	0.248485i
$100$	−2.42321	−	0.711520i	−0.242321	−	0.0711520i
$101$	−2.25245	+	1.44756i	−0.224127	+	0.144038i	−0.647886	−	0.761737i	$-0.724347\pi$
$101$	−2.25245	+	1.44756i	−0.224127	+	0.144038i	0.423759	+	0.905775i	$0.360710\pi$
$102$	−1.38390	+	9.62522i	−0.137026	+	0.953039i
$103$	−2.36702	+	5.18305i	−0.233229	+	0.510701i	−0.989671	−	0.143361i	$-0.954209\pi$
$103$	−2.36702	+	5.18305i	−0.233229	+	0.510701i	0.756441	+	0.654062i	$0.226936\pi$
$104$	−0.244890	+	0.536235i	−0.0240135	+	0.0525822i
$105$	−0.350847	+	2.44020i	−0.0342392	+	0.238139i
$106$	4.31464	−	2.77285i	0.419074	−	0.269323i
$107$	16.5418	+	4.85711i	1.59916	+	0.469555i	0.955312	−	0.295600i	$-0.0955197\pi$
$107$	16.5418	+	4.85711i	1.59916	+	0.469555i	0.643846	+	0.765155i	$0.277338\pi$
$108$	0.359418	+	2.49981i	0.0345850	+	0.240544i
$109$	−11.1168	−	12.8295i	−1.06480	−	1.22884i	−0.972449	−	0.233114i	$-0.925109\pi$
$109$	−11.1168	−	12.8295i	−1.06480	−	1.22884i	−0.0923470	−	0.995727i	$-0.529437\pi$
$110$	4.47015	+	2.87279i	0.426212	+	0.273910i
$111$	−3.09879	+	3.57619i	−0.294124	+	0.339437i
$112$	6.32232	−	1.85640i	0.597403	−	0.175413i
$113$	−2.23536	−	4.89475i	−0.210285	−	0.460459i	0.774872	−	0.632119i	$-0.217814\pi$
$113$	−2.23536	−	4.89475i	−0.210285	−	0.460459i	−0.985156	+	0.171659i	$0.945087\pi$
$114$	10.7197			1.00399
$115$	−0.483859	+	4.77136i	−0.0451201	+	0.444932i
$116$	3.29293			0.305741
$117$	0.219055	+	0.479663i	0.0202516	+	0.0443448i
$118$	3.05655	−	0.897484i	0.281378	−	0.0826201i
$119$	−7.37967	+	8.51659i	−0.676493	+	0.780714i
$120$	−0.940473	−	0.604406i	−0.0858531	−	0.0551744i
$121$	3.11772	+	3.59805i	0.283429	+	0.327095i
$122$	−1.95476	−	13.5957i	−0.176976	−	1.23090i
$123$	−2.36869	−	0.695511i	−0.213578	−	0.0627121i
$124$	−2.23551	+	1.43667i	−0.200754	+	0.129017i
$125$	0.142315	−	0.989821i	0.0127290	−	0.0885323i
$126$	−2.17863	+	4.77054i	−0.194088	+	0.424994i
$127$	−8.28989	+	18.1523i	−0.735609	+	1.61076i	0.0550366	+	0.998484i	$0.482472\pi$
$127$	−8.28989	+	18.1523i	−0.735609	+	1.61076i	−0.790645	+	0.612274i	$0.790255\pi$
$128$	−1.22886	+	8.54692i	−0.108617	+	0.755448i
$129$	10.2995	−	6.61911i	0.906824	−	0.582780i
$130$	−1.07633	−	0.316039i	−0.0944005	−	0.0277185i
$131$	3.04018	+	21.1449i	0.265622	+	1.84744i	0.488460	+	0.872586i	$0.337559\pi$
$131$	3.04018	+	21.1449i	0.265622	+	1.84744i	−0.222838	+	0.974856i	$0.571532\pi$
$132$	4.13105	+	4.76748i	0.359561	+	0.414956i
$133$	10.4507	+	6.71624i	0.906188	+	0.582372i
$134$	−12.4146	+	14.3272i	−1.07245	+	1.23768i
$135$	−0.959493	+	0.281733i	−0.0825800	+	0.0242477i
$136$	−2.12286	−	4.64842i	−0.182034	−	0.398599i
$137$	−11.7144			−1.00083			−0.500413	−	0.865787i	$-0.666818\pi$
$137$	−11.7144			−1.00083			−0.500413	+	0.865787i	$0.666818\pi$
$138$	−3.84728	+	9.44909i	−0.327503	+	0.804360i
$139$	5.99314			0.508331			0.254166	−	0.967161i	$-0.418199\pi$
$139$	5.99314			0.508331			0.254166	+	0.967161i	$0.418199\pi$
$140$	−2.58643	−	5.66348i	−0.218593	−	0.478652i
$141$	6.48986	−	1.90560i	0.546545	−	0.160480i
$142$	3.94248	−	4.54987i	0.330846	−	0.381816i
$143$	1.10805	+	0.712098i	0.0926595	+	0.0595487i
$144$	1.75031	+	2.01997i	0.145859	+	0.168331i
$145$	0.185559	+	1.29059i	0.0154099	+	0.107178i
$146$	−30.3768	−	8.91942i	−2.51400	−	0.738176i
$147$	0.775930	−	0.498660i	0.0639976	−	0.0411288i
$148$	1.70076	−	11.8290i	0.139802	−	0.972341i
$149$	−0.123833	+	0.271157i	−0.0101448	+	0.0222140i	−0.914637	−	0.404277i	$-0.867523\pi$
$149$	−0.123833	+	0.271157i	−0.0101448	+	0.0222140i	0.904492	+	0.426491i	$0.140250\pi$
$150$	0.883723	−	1.93508i	0.0721557	−	0.157999i
$151$	1.04748	−	7.28540i	0.0852429	−	0.592877i	−0.901768	−	0.432221i	$-0.857730\pi$
$151$	1.04748	−	7.28540i	0.0852429	−	0.592877i	0.987010	−	0.160656i	$-0.0513609\pi$
$152$	−4.73910	+	3.04563i	−0.384392	+	0.247034i
$153$	−4.38593	−	1.28783i	−0.354581	−	0.104114i
$154$	1.86429	+	12.9664i	0.150229	+	1.04486i
$155$	−0.689046	−	0.795201i	−0.0553455	−	0.0638721i
$156$	−1.12033	−	0.719994i	−0.0896984	−	0.0576457i
$157$	9.40424	−	10.8531i	0.750540	−	0.866169i	−0.244081	−	0.969755i	$-0.578486\pi$
$157$	9.40424	−	10.8531i	0.750540	−	0.866169i	0.994621	+	0.103586i	$0.0330316\pi$
$158$	−31.0355	+	9.11284i	−2.46905	+	0.724979i
$159$	1.00153	+	2.19305i	0.0794268	+	0.173920i
$160$	−7.92181			−0.626274
$161$	−9.67087	+	6.80149i	−0.762171	+	0.536032i
$162$	−2.12733			−0.167139
$163$	3.91075	+	8.56335i	0.306314	+	0.670733i	0.998710	−	0.0507843i	$-0.0161721\pi$
$163$	3.91075	+	8.56335i	0.306314	+	0.670733i	−0.692396	+	0.721518i	$0.743445\pi$
$164$	5.98217	−	1.75652i	0.467129	−	0.137161i
$165$	−1.63572	+	1.88773i	−0.127341	+	0.146959i
$166$	1.25851	+	0.808792i	0.0976790	+	0.0627745i
$167$	−13.2031	−	15.2372i	−1.02169	−	1.17909i	−0.983701	−	0.179813i	$-0.942451\pi$
$167$	−13.2031	−	15.2372i	−1.02169	−	1.17909i	−0.0379878	−	0.999278i	$-0.512095\pi$
$168$	−0.392227	−	2.72800i	−0.0302610	−	0.210470i
$169$	12.2066	+	3.58418i	0.938970	+	0.275706i
$170$	8.18052	−	5.25730i	0.627417	−	0.403216i
$171$	−0.717133	+	4.98777i	−0.0548405	+	0.381424i
$172$	−12.8447	+	28.1259i	−0.979397	+	2.14458i
$173$	−4.98287	+	10.9110i	−0.378841	+	0.829546i	0.620144	+	0.784488i	$0.287074\pi$
$173$	−4.98287	+	10.9110i	−0.378841	+	0.829546i	−0.998984	+	0.0450574i	$0.985653\pi$
$174$	−0.394745	+	2.74551i	−0.0299255	+	0.208137i
$175$	2.07393	−	1.33284i	0.156775	−	0.100753i
$176$	6.40575	+	1.88090i	0.482851	+	0.141778i
$177$	0.213111	+	1.48222i	0.0160184	+	0.111410i
$178$	−9.89372	−	11.4180i	−0.741565	−	0.855812i
$179$	3.43974	+	2.21059i	0.257098	+	0.165227i	0.662841	−	0.748760i	$-0.269351\pi$
$179$	3.43974	+	2.21059i	0.257098	+	0.165227i	−0.405743	+	0.913987i	$0.632987\pi$
$180$	1.65386	−	1.90866i	0.123272	−	0.142263i
$181$	−15.0022	+	4.40504i	−1.11510	+	0.327424i	−0.786837	−	0.617161i	$-0.788283\pi$
$181$	−15.0022	+	4.40504i	−1.11510	+	0.327424i	−0.328267	+	0.944585i	$0.606465\pi$
$182$	−1.14883	−	2.51558i	−0.0851566	−	0.186467i
$183$	6.45669			0.477292
$184$	−0.983776	−	5.27044i	−0.0725250	−	0.388542i
$185$	4.73198			0.347902
$186$	−0.929855	−	2.03610i	−0.0681803	−	0.149294i
$187$	−10.9553	+	3.21676i	−0.801128	+	0.235232i
$188$	−11.1865	+	12.9099i	−0.815857	+	0.941549i
$189$	−2.07393	−	1.33284i	−0.150856	−	0.0969495i
$190$	−7.01992	−	8.10142i	−0.509279	−	0.587739i
$191$	3.16815	+	22.0350i	0.229239	+	1.59440i	0.701324	+	0.712842i	$0.252592\pi$
$191$	3.16815	+	22.0350i	0.229239	+	1.59440i	−0.472085	+	0.881553i	$0.656498\pi$
$192$	−11.0406	−	3.24180i	−0.796784	−	0.233957i
$193$	−4.00702	+	2.57515i	−0.288432	+	0.185364i	−0.676853	−	0.736118i	$-0.736657\pi$
$193$	−4.00702	+	2.57515i	−0.288432	+	0.185364i	0.388422	+	0.921482i	$0.373020\pi$
$194$	1.00716	−	7.00494i	0.0723098	−	0.502926i
$195$	0.219055	−	0.479663i	0.0156868	−	0.0343493i
$196$	−0.967671	+	2.11890i	−0.0691194	+	0.151350i
$197$	1.95714	−	13.6122i	0.139440	−	0.969828i	−0.793185	−	0.608981i	$-0.791579\pi$
$197$	1.95714	−	13.6122i	0.139440	−	0.969828i	0.932625	−	0.360847i	$-0.117512\pi$
$198$	−4.47015	+	2.87279i	−0.317680	+	0.204160i
$199$	−2.55596	−	0.750498i	−0.181187	−	0.0532014i	0.189880	−	0.981807i	$-0.439190\pi$
$199$	−2.55596	−	0.750498i	−0.181187	−	0.0532014i	−0.371068	+	0.928606i	$0.621008\pi$
$200$	0.159100	+	1.10656i	0.0112501	+	0.0782459i
$201$	−5.83576	−	6.73483i	−0.411623	−	0.475038i
$202$	4.79170	+	3.07944i	0.337143	+	0.216669i
$203$	−2.10499	+	2.42928i	−0.147741	+	0.170502i
$204$	11.0767	−	3.25242i	0.775526	−	0.227715i
$205$	1.02553	+	2.24560i	0.0716262	+	0.156840i
$206$	12.1214			0.844540
$207$	−4.13918	−	2.42223i	−0.287693	−	0.168357i
$208$	−1.40941			−0.0977249
$209$	5.22869	+	11.4492i	0.361676	+	0.791960i
$210$	5.03204	−	1.47754i	0.347243	−	0.101960i
$211$	1.11398	−	1.28560i	0.0766893	−	0.0885042i	−0.716108	−	0.697989i	$-0.754078\pi$
$211$	1.11398	−	1.28560i	0.0766893	−	0.0885042i	0.792798	+	0.609485i	$0.208624\pi$
$212$	−5.12224	−	3.29187i	−0.351797	−	0.226086i
$213$	1.85326	+	2.13877i	0.126983	+	0.146546i
$214$	−5.21946	−	36.3021i	−0.356795	−	2.48156i
$215$	−11.7472	−	3.44928i	−0.801149	−	0.235239i
$216$	0.940473	−	0.604406i	0.0639911	−	0.0411246i
$217$	0.369162	−	2.56758i	0.0250604	−	0.174299i
$218$	−15.0019	+	32.8496i	−1.01606	+	2.22486i
$219$	6.18227	−	13.5373i	0.417759	−	0.914764i
$220$	0.897762	−	6.24407i	0.0605271	−	0.420975i
$221$	2.02776	−	1.30316i	0.136402	−	0.0876602i
$222$	9.65870	+	2.83605i	0.648249	+	0.190343i
$223$	3.60908	+	25.1017i	0.241682	+	1.68093i	0.643680	+	0.765295i	$0.277407\pi$
$223$	3.60908	+	25.1017i	0.241682	+	1.68093i	−0.401998	+	0.915640i	$0.631684\pi$
$224$	−12.7891	−	14.7594i	−0.854510	−	0.986157i
$225$	0.841254	+	0.540641i	0.0560836	+	0.0360427i
$226$	−7.49631	+	8.65120i	−0.498647	+	0.575470i
$227$	4.92441	−	1.44594i	0.326844	−	0.0959702i	−0.114194	−	0.993458i	$-0.536429\pi$
$227$	4.92441	−	1.44594i	0.326844	−	0.0959702i	0.441038	+	0.897488i	$0.354610\pi$
$228$	−5.28666	−	11.5762i	−0.350118	−	0.766651i
$229$	8.56535			0.566014			0.283007	−	0.959118i	$-0.408668\pi$
$229$	8.56535			0.566014			0.283007	+	0.959118i	$0.408668\pi$
$230$	9.66058	−	3.28025i	0.637000	−	0.216294i
$231$	−6.15785			−0.405157
$232$	−0.605528	−	1.32592i	−0.0397549	−	0.0870510i
$233$	1.71900	−	0.504745i	0.112616	−	0.0330669i	−0.224939	−	0.974373i	$-0.572218\pi$
$233$	1.71900	−	0.504745i	0.112616	−	0.0330669i	0.337555	+	0.941306i	$0.390400\pi$
$234$	0.734604	−	0.847778i	0.0480225	−	0.0554210i
$235$	−5.69011	−	3.65681i	−0.371182	−	0.238544i
$236$	−2.47659	−	2.85814i	−0.161212	−	0.186049i
$237$	−2.16388	−	15.0501i	−0.140559	−	0.977610i
$238$	23.0019	+	6.75396i	1.49099	+	0.437795i
$239$	3.88919	−	2.49943i	0.251571	−	0.161675i	−0.408778	−	0.912634i	$-0.634045\pi$
$239$	3.88919	−	2.49943i	0.251571	−	0.161675i	0.660348	+	0.750959i	$0.270409\pi$
$240$	0.380379	−	2.64560i	0.0245534	−	0.170773i
$241$	8.77574	−	19.2162i	0.565295	−	1.23782i	−0.383970	−	0.923346i	$-0.625443\pi$
$241$	8.77574	−	19.2162i	0.565295	−	1.23782i	0.949265	−	0.314478i	$-0.101829\pi$
$242$	4.20731	−	9.21273i	0.270456	−	0.592217i
$243$	0.142315	−	0.989821i	0.00912950	−	0.0634971i
$244$	−13.7179	+	8.81595i	−0.878197	+	0.564383i
$245$	−0.884988	−	0.259856i	−0.0565398	−	0.0166016i
$246$	0.747397	+	5.19826i	0.0476523	+	0.331429i
$247$	−1.74008	−	2.00816i	−0.110718	−	0.127776i
$248$	0.989568	+	0.635957i	0.0628376	+	0.0403833i
$249$	−0.460514	+	0.531462i	−0.0291839	+	0.0336800i
$250$	−2.04115	+	0.599337i	−0.129094	+	0.0379054i
$251$	12.9558	+	28.3693i	0.817763	+	1.79065i	0.569575	+	0.821939i	$0.307108\pi$
$251$	12.9558	+	28.3693i	0.817763	+	1.79065i	0.248188	+	0.968712i	$0.420165\pi$
$252$	6.22613			0.392209
$253$	−11.9687	+	0.499817i	−0.752465	+	0.0314232i
$254$	42.4522			2.66369
$255$	1.89890	+	4.15801i	0.118914	+	0.260385i
$256$	−4.45615	+	1.30844i	−0.278510	+	0.0817778i
$257$	−14.4220	+	16.6439i	−0.899622	+	1.03822i	0.0994456	+	0.995043i	$0.468293\pi$
$257$	−14.4220	+	16.6439i	−0.899622	+	1.03822i	−0.999067	+	0.0431760i	$0.986252\pi$
$258$	−21.9105	−	14.0810i	−1.36409	−	0.876645i
$259$	7.63940	+	8.81634i	0.474689	+	0.547821i
$260$	0.189527	+	1.31819i	0.0117539	+	0.0817505i
$261$	−1.25105	−	0.367341i	−0.0774380	−	0.0227378i
$262$	38.2306	−	24.5693i	2.36189	−	1.51790i
$263$	3.33442	−	23.1914i	0.205609	−	1.43004i	−0.581658	−	0.813433i	$-0.697596\pi$
$263$	3.33442	−	23.1914i	0.205609	−	1.43004i	0.787268	−	0.616611i	$-0.211495\pi$
$264$	1.16001	−	2.54007i	0.0713939	−	0.156331i
$265$	1.00153	−	2.19305i	0.0615237	−	0.134718i
$266$	3.76098	−	26.1582i	0.230601	−	1.60386i
$267$	5.97452	−	3.83959i	0.365635	−	0.234979i
$268$	21.5944	+	6.34068i	1.31909	+	0.387318i
$269$	−1.76466	−	12.2735i	−0.107593	−	0.748327i	−0.970174	−	0.242408i	$-0.922063\pi$
$269$	−1.76466	−	12.2735i	−0.107593	−	0.748327i	0.862581	−	0.505919i	$-0.168846\pi$
$270$	1.39310	+	1.60773i	0.0847815	+	0.0978431i
$271$	21.3169	+	13.6995i	1.29491	+	0.832186i	0.992648	−	0.121040i	$-0.0386228\pi$
$271$	21.3169	+	13.6995i	1.29491	+	0.832186i	0.302259	+	0.953226i	$0.402259\pi$
$272$	8.00084	−	9.23346i	0.485122	−	0.559861i
$273$	1.24733	−	0.366248i	0.0754916	−	0.0221663i
$274$	10.3523	+	22.6683i	0.625402	+	1.36944i
$275$	2.49782			0.150624
$276$	12.1014	−	0.505359i	0.728419	−	0.0304190i
$277$	−12.9940			−0.780736			−0.390368	−	0.920659i	$-0.627652\pi$
$277$	−12.9940			−0.780736			−0.390368	+	0.920659i	$0.627652\pi$
$278$	−5.29627	−	11.5972i	−0.317649	−	0.695555i
$279$	1.00958	−	0.296440i	0.0604420	−	0.0177474i
$280$	−1.80483	+	2.08289i	−0.107859	+	0.124476i
$281$	7.53520	+	4.84258i	0.449513	+	0.288884i	0.745745	−	0.666232i	$-0.232094\pi$
$281$	7.53520	+	4.84258i	0.449513	+	0.288884i	−0.296232	+	0.955116i	$0.595730\pi$
$282$	−9.42273	−	10.8744i	−0.561115	−	0.647562i
$283$	−2.21449	−	15.4021i	−0.131638	−	0.915559i	−0.943420	−	0.331600i	$-0.892412\pi$
$283$	−2.21449	−	15.4021i	−0.131638	−	0.915559i	0.811783	−	0.583960i	$-0.198497\pi$
$284$	−6.85770	−	2.01360i	−0.406930	−	0.119485i
$285$	4.23912	−	2.72432i	0.251104	−	0.161375i
$286$	0.398763	−	2.77346i	0.0235794	−	0.163998i
$287$	−2.52823	+	5.53606i	−0.149237	+	0.326783i
$288$	3.29084	−	7.20593i	0.193914	−	0.424613i
$289$	−0.554298	+	3.85523i	−0.0326058	+	0.226778i
$290$	2.33342	−	1.49960i	0.137023	−	0.0880595i
$291$	3.19195	+	0.937240i	0.187115	+	0.0549420i
$292$	5.34892	+	37.2025i	0.313022	+	2.17711i
$293$	−14.4347	−	16.6585i	−0.843284	−	0.973202i	0.156611	−	0.987660i	$-0.449943\pi$
$293$	−14.4347	−	16.6585i	−0.843284	−	0.973202i	−0.999895	+	0.0144583i	$0.995398\pi$
$294$	−1.65066	−	1.06081i	−0.0962682	−	0.0618678i
$295$	0.980628	−	1.13171i	0.0570944	−	0.0658904i
$296$	−5.07579	+	1.49039i	−0.295025	+	0.0866270i
$297$	−1.03763	−	2.27210i	−0.0602095	−	0.131840i
$298$	0.634145			0.0367350
$299$	2.39463	−	0.813099i	0.138485	−	0.0470227i
$300$	−2.52552			−0.145811
$301$	−12.5384	−	27.4552i	−0.722699	−	1.58249i
$302$	−15.0235	+	4.41131i	−0.864507	+	0.253842i
$303$	−1.75339	+	2.02352i	−0.100729	+	0.116248i
$304$	−11.3303	−	7.28157i	−0.649840	−	0.417627i
$305$	−4.22823	−	4.87964i	−0.242108	−	0.279407i
$306$	1.38390	+	9.62522i	0.0791122	+	0.550237i
$307$	13.6699	+	4.01383i	0.780180	+	0.229081i	0.647488	−	0.762076i	$-0.275820\pi$
$307$	13.6699	+	4.01383i	0.780180	+	0.229081i	0.132692	+	0.991157i	$0.457638\pi$
$308$	13.0830	−	8.40791i	0.745471	−	0.479085i
$309$	−0.810905	+	5.63997i	−0.0461308	+	0.320847i
$310$	−0.929855	+	2.03610i	−0.0528122	+	0.115643i
$311$	−4.59277	+	10.0568i	−0.260432	+	0.570266i	−0.994004	−	0.109346i	$-0.965124\pi$
$311$	−4.59277	+	10.0568i	−0.260432	+	0.570266i	0.733572	+	0.679612i	$0.237852\pi$
$312$	−0.0838957	+	0.583508i	−0.00474966	+	0.0330346i
$313$	−15.1590	+	9.74208i	−0.856836	+	0.550655i	−0.893700	−	0.448665i	$-0.851900\pi$
$313$	−15.1590	+	9.74208i	−0.856836	+	0.550655i	0.0368638	+	0.999320i	$0.488263\pi$
$314$	−29.3123	−	8.60688i	−1.65419	−	0.485714i
$315$	0.350847	+	2.44020i	0.0197680	+	0.137489i
$316$	25.1467	+	29.0209i	1.41462	+	1.63255i
$317$	−16.9552	−	10.8964i	−0.952298	−	0.612005i	−0.0304417	−	0.999537i	$-0.509691\pi$
$317$	−16.9552	−	10.8964i	−0.952298	−	0.612005i	−0.921856	+	0.387532i	$0.873328\pi$
$318$	3.35866	−	3.87610i	0.188344	−	0.217361i
$319$	−3.12489	+	0.917552i	−0.174960	+	0.0513730i
$320$	4.78004	+	10.4668i	0.267212	+	0.585113i
$321$	17.2402			0.962252
$322$	21.7078	+	12.7033i	1.20973	+	0.707928i
$323$	23.0340			1.28165
$324$	1.04914	+	2.29729i	0.0582854	+	0.127627i
$325$	−0.505955	+	0.148562i	−0.0280653	+	0.00824072i
$326$	13.1148	−	15.1353i	0.726360	−	0.838265i
$327$	−14.2810	−	9.17782i	−0.789740	−	0.507535i
$328$	−1.80732	−	2.08576i	−0.0997926	−	0.115167i
$329$	−2.37308	−	16.5051i	−0.130832	−	0.909956i
$330$	5.09844	+	1.49704i	0.280660	+	0.0824091i
$331$	−1.25007	+	0.803374i	−0.0687103	+	0.0441574i	−0.574545	−	0.818473i	$-0.694821\pi$
$331$	−1.25007	+	0.803374i	−0.0687103	+	0.0441574i	0.505835	+	0.862630i	$0.331185\pi$
$332$	0.252752	−	1.75793i	0.0138716	−	0.0964788i
$333$	−1.96573	+	4.30436i	−0.107722	+	0.235877i
$334$	−17.8174	+	39.0146i	−0.974924	+	2.13479i
$335$	−1.26823	+	8.82075i	−0.0692909	+	0.481929i
$336$	5.54321	−	3.56241i	0.302407	−	0.194345i
$337$	−9.33212	−	2.74016i	−0.508353	−	0.149266i	0.0174910	−	0.999847i	$-0.494432\pi$
$337$	−9.33212	−	2.74016i	−0.508353	−	0.149266i	−0.525844	+	0.850581i	$0.676250\pi$
$338$	−3.85157	−	26.7882i	−0.209498	−	1.45709i
$339$	−3.52382	−	4.06670i	−0.191388	−	0.220873i
$340$	−9.71173	−	6.24135i	−0.526693	−	0.338485i
$341$	1.72111	−	1.98627i	0.0932034	−	0.107562i
$342$	10.2855	−	3.02009i	0.556176	−	0.163308i
$343$	−8.11342	−	17.7659i	−0.438084	−	0.959269i
$344$	13.6871			0.737957
$345$	0.879988	+	4.71441i	0.0473770	+	0.253815i
$346$	25.5171			1.37181
$347$	14.0492	+	30.7635i	0.754201	+	1.65147i	0.758667	+	0.651479i	$0.225851\pi$
$347$	14.0492	+	30.7635i	0.754201	+	1.65147i	−0.00446632	+	0.999990i	$0.501422\pi$
$348$	3.15954	−	0.927725i	0.169369	−	0.0497313i
$349$	−3.48851	+	4.02596i	−0.186736	+	0.215505i	−0.841397	−	0.540418i	$-0.818266\pi$
$349$	−3.48851	+	4.02596i	−0.186736	+	0.215505i	0.654661	+	0.755923i	$0.272812\pi$
$350$	−4.41193	−	2.83538i	−0.235828	−	0.151557i
$351$	0.345318	+	0.398518i	0.0184317	+	0.0212713i
$352$	−2.81602	−	19.5858i	−0.150094	−	1.04393i
$353$	−28.8958	−	8.48457i	−1.53797	−	0.451588i	−0.600490	−	0.799633i	$-0.705028\pi$
$353$	−28.8958	−	8.48457i	−1.53797	−	0.451588i	−0.937478	+	0.348045i	$0.886846\pi$
$354$	2.67989	−	1.72226i	0.142434	−	0.0915370i
$355$	0.402751	−	2.80120i	0.0213758	−	0.148672i
$356$	−7.45090	+	16.3152i	−0.394897	+	0.864704i
$357$	−4.68134	+	10.2507i	−0.247763	+	0.542524i
$358$	1.23789	−	8.60973i	0.0654246	−	0.455038i
$359$	−10.2212	+	6.56878i	−0.539456	+	0.346687i	−0.781826	−	0.623497i	$-0.785711\pi$
$359$	−10.2212	+	6.56878i	−0.539456	+	0.346687i	0.242370	+	0.970184i	$0.422075\pi$
$360$	−1.07266	−	0.314961i	−0.0565341	−	0.0165999i
$361$	−0.909691	−	6.32704i	−0.0478785	−	0.333002i
$362$	21.7819	+	25.1377i	1.14483	+	1.32121i
$363$	4.00512	+	2.57393i	0.210214	+	0.135097i
$364$	−2.14999	+	2.48122i	−0.112690	+	0.130051i
$365$	−14.2793	+	4.19278i	−0.747413	+	0.219460i
$366$	−5.70593	−	12.4942i	−0.298254	−	0.653084i
$367$	−29.2358			−1.52610			−0.763048	−	0.646342i	$-0.776298\pi$
$367$	−29.2358			−1.52610			−0.763048	+	0.646342i	$0.776298\pi$
$368$	10.4849	−	7.37399i	0.546563	−	0.384396i
$369$	−2.46869			−0.128515
$370$	−4.18176	−	9.15677i	−0.217399	−	0.476038i
$371$	5.70286	−	1.67451i	0.296078	−	0.0869363i
$372$	−1.74020	+	2.00829i	−0.0902249	+	0.104125i
$373$	6.91416	+	4.44346i	0.358002	+	0.230074i	0.707261	−	0.706952i	$-0.249930\pi$
$373$	6.91416	+	4.44346i	0.358002	+	0.230074i	−0.349260	+	0.937026i	$0.613567\pi$
$374$	15.9061	+	18.3566i	0.822485	+	0.949199i
$375$	−0.142315	−	0.989821i	−0.00734911	−	0.0511142i
$376$	7.25530	+	2.13035i	0.374163	+	0.109864i
$377$	0.578401	−	0.371716i	0.0297892	−	0.0191443i
$378$	−0.746366	+	5.19109i	−0.0383889	+	0.267001i
$379$	0.751785	−	1.64618i	0.0386166	−	0.0845585i	−0.889341	−	0.457245i	$-0.848836\pi$
$379$	0.751785	−	1.64618i	0.0386166	−	0.0845585i	0.927957	+	0.372687i	$0.121563\pi$
$380$	−5.28666	+	11.5762i	−0.271200	+	0.593845i
$381$	−2.83999	+	19.7526i	−0.145497	+	1.01195i
$382$	39.8398	−	25.6035i	2.03838	−	1.30999i
$383$	−27.6144	−	8.10832i	−1.41103	−	0.414316i	−0.514573	−	0.857447i	$-0.672050\pi$
$383$	−27.6144	−	8.10832i	−1.41103	−	0.414316i	−0.896457	+	0.443131i	$0.853868\pi$
$384$	1.22886	+	8.54692i	0.0627100	+	0.436158i
$385$	4.03253	+	4.65379i	0.205517	+	0.237179i
$386$	8.52423	+	5.47819i	0.433872	+	0.278833i
$387$	8.01751	−	9.25271i	0.407553	−	0.470341i
$388$	−8.06131	+	2.36701i	−0.409251	+	0.120167i
$389$	5.54123	+	12.1336i	0.280951	+	0.615198i	0.996521	−	0.0833438i	$-0.0265600\pi$
$389$	5.54123	+	12.1336i	0.280951	+	0.615198i	−0.715569	+	0.698542i	$0.753833\pi$
$390$	−1.12177			−0.0568031
$391$	−8.26685	+	20.3037i	−0.418073	+	1.02680i
$392$	1.03113			0.0520801
$393$	8.87425	+	19.4319i	0.447647	+	0.980210i
$394$	−28.0703	+	8.24218i	−1.41416	+	0.415235i
$395$	−9.95707	+	11.4911i	−0.500995	+	0.578179i
$396$	5.30687	+	3.41052i	0.266680	+	0.171385i
$397$	16.7651	+	19.3480i	0.841418	+	0.971048i	0.999867	−	0.0163190i	$-0.00519473\pi$
$397$	16.7651	+	19.3480i	0.841418	+	0.971048i	−0.158449	+	0.987367i	$0.550649\pi$
$398$	0.806485	+	5.60923i	0.0404255	+	0.281165i
$399$	11.9195	+	3.49989i	0.596723	+	0.175214i
$400$	−2.24850	+	1.44503i	−0.112425	+	0.0722513i
$401$	4.12306	−	28.6765i	0.205896	−	1.43203i	−0.580474	−	0.814279i	$-0.697133\pi$
$401$	4.12306	−	28.6765i	0.205896	−	1.43203i	0.786370	−	0.617756i	$-0.211958\pi$
$402$	−7.87526	+	17.2444i	−0.392782	+	0.860073i
$403$	−0.230490	+	0.504702i	−0.0114815	+	0.0251410i
$404$	0.962341	−	6.69323i	0.0478782	−	0.333001i
$405$	−0.841254	+	0.540641i	−0.0418022	+	0.0268647i
$406$	6.56109	+	1.92651i	0.325621	+	0.0956111i
$407$	1.68211	+	11.6993i	0.0833790	+	0.579914i
$408$	−3.34648	−	3.86205i	−0.165676	−	0.191200i
$409$	−13.1140	−	8.42783i	−0.648444	−	0.416730i	0.174653	−	0.984630i	$-0.444119\pi$
$409$	−13.1140	−	8.42783i	−0.648444	−	0.416730i	−0.823097	+	0.567900i	$0.807756\pi$
$410$	3.43914	−	3.96898i	0.169847	−	0.196014i
$411$	−11.2398	+	3.30032i	−0.554421	+	0.162793i
$412$	−5.97795	−	13.0899i	−0.294512	−	0.644892i
$413$	3.69167			0.181655
$414$	−1.02933	+	10.1502i	−0.0505886	+	0.498857i
$415$	0.703225			0.0345199
$416$	1.73531	+	3.79979i	0.0850805	+	0.186300i
$417$	5.75037	−	1.68846i	0.281597	−	0.0826843i
$418$	17.5345	−	20.2359i	0.857640	−	0.989770i
$419$	7.33134	+	4.71156i	0.358159	+	0.230175i	0.707329	−	0.706885i	$-0.249900\pi$
$419$	7.33134	+	4.71156i	0.358159	+	0.230175i	−0.349170	+	0.937059i	$0.613536\pi$
$420$	−4.07725	−	4.70539i	−0.198949	−	0.229600i
$421$	−3.80998	−	26.4990i	−0.185687	−	1.29148i	−0.843020	−	0.537882i	$-0.819225\pi$
$421$	−3.80998	−	26.4990i	−0.185687	−	1.29148i	0.657333	−	0.753600i	$-0.271684\pi$
$422$	−3.47218	−	1.01953i	−0.169023	−	0.0496297i
$423$	5.69011	−	3.65681i	0.276663	−	0.177800i
$424$	−0.383577	+	2.66784i	−0.0186282	+	0.129562i
$425$	1.89890	−	4.15801i	0.0921102	−	0.201693i
$426$	2.50094	−	5.47629i	0.121171	−	0.265327i
$427$	2.26531	−	15.7556i	0.109626	−	0.762467i
$428$	−36.6284	+	23.5397i	−1.77050	+	1.13783i
$429$	1.26378	+	0.371081i	0.0610161	+	0.0179159i
$430$	3.70659	+	25.7799i	0.178748	+	1.24322i
$431$	9.27477	+	10.7037i	0.446750	+	0.515577i	0.933799	−	0.357798i	$-0.116472\pi$
$431$	9.27477	+	10.7037i	0.446750	+	0.515577i	−0.487049	+	0.873375i	$0.661927\pi$
$432$	2.24850	+	1.44503i	0.108181	+	0.0695238i
$433$	8.54867	−	9.86570i	0.410823	−	0.474115i	−0.512196	−	0.858868i	$-0.671168\pi$
$433$	8.54867	−	9.86570i	0.410823	−	0.474115i	0.923019	+	0.384753i	$0.125713\pi$
$434$	−5.29472	+	1.55467i	−0.254155	+	0.0746265i
$435$	0.541645	+	1.18604i	0.0259699	+	0.0568661i
$436$	42.8727			2.05323
$437$	23.4514	+	5.83508i	1.12183	+	0.279130i
$438$	−31.6592			−1.51273
$439$	−2.04513	−	4.47820i	−0.0976086	−	0.213733i	0.854528	−	0.519405i	$-0.173846\pi$
$439$	−2.04513	−	4.47820i	−0.0976086	−	0.213733i	−0.952137	+	0.305672i	$0.901119\pi$
$440$	−2.67931	+	0.786716i	−0.127731	+	0.0375052i
$441$	0.604010	−	0.697065i	0.0287624	−	0.0331936i
$442$	−4.31371	−	2.77225i	−0.205182	−	0.131863i
$443$	19.8741	+	22.9359i	0.944247	+	1.08972i	0.995846	+	0.0910512i	$0.0290227\pi$
$443$	19.8741	+	22.9359i	0.944247	+	1.08972i	−0.0515992	+	0.998668i	$0.516432\pi$
$444$	−1.70076	−	11.8290i	−0.0807145	−	0.561381i
$445$	−6.81425	−	2.00085i	−0.323027	−	0.0948492i
$446$	45.3845	−	29.1668i	2.14902	−	1.38109i
$447$	−0.0424233	+	0.295061i	−0.00200656	+	0.0139559i
$448$	−11.7842	+	25.8038i	−0.556750	+	1.21911i
$449$	6.67276	−	14.6113i	0.314907	−	0.689550i	−0.684307	−	0.729194i	$-0.739895\pi$
$449$	6.67276	−	14.6113i	0.314907	−	0.689550i	0.999214	+	0.0396440i	$0.0126224\pi$
$450$	0.302750	−	2.10567i	0.0142718	−	0.0992624i
$451$	−5.18746	+	3.33378i	−0.244268	+	0.156982i
$452$	13.0394	+	3.82870i	0.613320	+	0.180087i
$453$	−1.04748	−	7.28540i	−0.0492150	−	0.342298i
$454$	−7.14982	−	8.25133i	−0.335558	−	0.387254i
$455$	−1.09362	−	0.702824i	−0.0512695	−	0.0329489i
$456$	−3.68908	+	4.25742i	−0.172757	+	0.199372i
$457$	−9.74581	+	2.86163i	−0.455890	+	0.133861i	−0.501612	−	0.865093i	$-0.667259\pi$
$457$	−9.74581	+	2.86163i	−0.455890	+	0.133861i	0.0457220	+	0.998954i	$0.485441\pi$
$458$	−7.56940	−	16.5747i	−0.353695	−	0.774483i
$459$	−4.57109			−0.213360
$460$	−8.30666	−	8.81469i	−0.387300	−	0.410987i
$461$	−14.9033			−0.694116			−0.347058	−	0.937844i	$-0.612819\pi$
$461$	−14.9033			−0.694116			−0.347058	+	0.937844i	$0.612819\pi$
$462$	5.44183	+	11.9160i	0.253177	+	0.554380i
$463$	25.4210	−	7.46427i	1.18141	−	0.346894i	0.368694	−	0.929551i	$-0.379805\pi$
$463$	25.4210	−	7.46427i	1.18141	−	0.346894i	0.812718	+	0.582657i	$0.197987\pi$
$464$	2.28217	−	2.63377i	0.105947	−	0.122269i
$465$	−0.885168	−	0.568863i	−0.0410487	−	0.0263804i
$466$	−2.49585	−	2.88036i	−0.115618	−	0.133430i
$467$	5.02112	+	34.9227i	0.232350	+	1.61603i	0.687891	+	0.725814i	$0.258537\pi$
$467$	5.02112	+	34.9227i	0.232350	+	1.61603i	−0.455541	+	0.890215i	$0.650554\pi$
$468$	−1.27780	−	0.375195i	−0.0590662	−	0.0173434i
$469$	−18.4818	+	11.8775i	−0.853408	+	0.548452i
$470$	−2.04775	+	14.2424i	−0.0944559	+	0.656955i
$471$	5.96564	−	13.0629i	0.274882	−	0.601908i
$472$	−0.695436	+	1.52279i	−0.0320100	+	0.0700922i
$473$	4.35213	−	30.2697i	0.200111	−	1.39180i
$474$	−27.2110	+	17.4874i	−1.24984	+	0.803224i
$475$	−4.83494	−	1.41967i	−0.221842	−	0.0651388i
$476$	−4.05031	−	28.1705i	−0.185646	−	1.29119i
$477$	1.57882	+	1.82205i	0.0722891	+	0.0834261i
$478$	−8.27357	−	5.31710i	−0.378424	−	0.243198i
$479$	−7.44170	+	8.58818i	−0.340020	+	0.392404i	−0.899847	−	0.436205i	$-0.856322\pi$
$479$	−7.44170	+	8.58818i	−0.340020	+	0.392404i	0.559827	+	0.828609i	$0.310868\pi$
$480$	−7.60092	+	2.23183i	−0.346933	+	0.101869i
$481$	−1.03656	−	2.26975i	−0.0472631	−	0.103492i
$482$	−44.9403			−2.04697
$483$	−7.36293	+	9.25058i	−0.335025	+	0.420916i
$484$	−12.0237			−0.546533
$485$	−1.38196	−	3.02607i	−0.0627516	−	0.137407i
$486$	−2.04115	+	0.599337i	−0.0925886	+	0.0271865i
$487$	−21.0211	+	24.2597i	−0.952559	+	1.09931i	0.0424074	+	0.999100i	$0.486497\pi$
$487$	−21.0211	+	24.2597i	−0.952559	+	1.09931i	−0.994966	+	0.100211i	$0.968048\pi$
$488$	6.07235	+	3.90246i	0.274882	+	0.176656i
$489$	6.16491	+	7.11469i	0.278787	+	0.321737i
$490$	0.279241	+	1.94217i	0.0126148	+	0.0877381i
$491$	−28.0899	−	8.24795i	−1.26768	−	0.372225i	−0.422333	−	0.906441i	$-0.638789\pi$
$491$	−28.0899	−	8.24795i	−1.26768	−	0.372225i	−0.845348	+	0.534216i	$0.820607\pi$
$492$	5.24498	−	3.37074i	0.236462	−	0.151965i
$493$	−0.848208	+	5.89942i	−0.0382014	+	0.265696i
$494$	−2.34820	+	5.14185i	−0.105651	+	0.231343i
$495$	−1.03763	+	2.27210i	−0.0466381	+	0.102123i
$496$	−0.400236	+	2.78370i	−0.0179711	+	0.124992i
$497$	5.86923	−	3.77193i	0.263271	−	0.169194i
$498$	1.43539	+	0.421469i	0.0643214	+	0.0188865i
$499$	−4.22640	−	29.3953i	−0.189200	−	1.31591i	−0.834086	−	0.551634i	$-0.814004\pi$
$499$	−4.22640	−	29.3953i	−0.189200	−	1.31591i	0.644886	−	0.764278i	$-0.276905\pi$
$500$	1.65386	+	1.90866i	0.0739629	+	0.0853578i
$501$	−16.9611	−	10.9003i	−0.757767	−	0.486987i
$502$	43.4475	−	50.1411i	1.93916	−	2.23791i
$503$	13.9424	−	4.09385i	0.621660	−	0.182536i	0.0442905	−	0.999019i	$-0.485897\pi$
$503$	13.9424	−	4.09385i	0.621660	−	0.182536i	0.577370	+	0.816483i	$0.304079\pi$
$504$	−1.14491	−	2.50699i	−0.0509982	−	0.111670i
$505$	2.67750			0.119147
$506$	11.5442	+	22.7187i	0.513202	+	1.00997i
$507$	12.7219			0.565001
$508$	−20.9362	−	45.8440i	−0.928896	−	2.03400i
$509$	32.5553	−	9.55911i	1.44299	−	0.423700i	0.535773	−	0.844362i	$-0.320020\pi$
$509$	32.5553	−	9.55911i	1.44299	−	0.423700i	0.907217	+	0.420662i	$0.138202\pi$
$510$	6.36800	−	7.34906i	0.281980	−	0.325422i
$511$	−30.8646	−	19.8355i	−1.36537	−	0.877469i
$512$	17.7791	+	20.5182i	0.785735	+	0.906786i
$513$	0.717133	+	4.98777i	0.0316622	+	0.220215i
$514$	44.9525	+	13.1992i	1.98277	+	0.582193i
$515$	4.79343	−	3.08055i	0.211224	−	0.135745i
$516$	−4.40039	+	30.6054i	−0.193716	+	1.34733i
$517$	7.01838	−	15.3681i	0.308668	−	0.675889i
$518$	10.3092	−	22.5741i	0.452962	−	0.991849i
$519$	−1.70706	+	11.8728i	−0.0749315	+	0.521160i
$520$	0.495926	−	0.318712i	0.0217478	−	0.0139764i
$521$	13.7279	+	4.03086i	0.601428	+	0.176595i	0.568253	−	0.822854i	$-0.307620\pi$
$521$	13.7279	+	4.03086i	0.601428	+	0.176595i	0.0331759	+	0.999450i	$0.489438\pi$
$522$	0.394745	+	2.74551i	0.0172775	+	0.120168i
$523$	−9.98115	−	11.5189i	−0.436445	−	0.503685i	0.494331	−	0.869274i	$-0.335413\pi$
$523$	−9.98115	−	11.5189i	−0.436445	−	0.503685i	−0.930776	+	0.365589i	$0.880868\pi$
$524$	−45.3865	−	29.1681i	−1.98272	−	1.27422i
$525$	1.61442	−	1.86314i	0.0704591	−	0.0813141i
$526$	−47.8241	+	14.0424i	−2.08523	+	0.612278i
$527$	−1.99803	−	4.37507i	−0.0870354	−	0.190581i
$528$	6.67618			0.290543
$529$	−13.5601	+	18.5775i	−0.589570	+	0.807717i
$530$	−5.12882			−0.222782
$531$	0.622068	+	1.36214i	0.0269954	+	0.0591118i
$532$	−30.1029	+	8.83902i	−1.30513	+	0.383220i
$533$	0.852483	−	0.983818i	0.0369251	−	0.0426139i
$534$	−12.7098	−	8.16807i	−0.550005	−	0.353467i
$535$	−11.2899	−	13.0292i	−0.488105	−	0.563303i
$536$	−1.41781	−	9.86109i	−0.0612401	−	0.425934i
$537$	3.92320	+	1.15196i	0.169299	+	0.0497105i
$538$	−22.1907	+	14.2611i	−0.956710	+	0.614840i
$539$	0.327874	−	2.28041i	0.0141225	−	0.0982243i
$540$	1.04914	−	2.29729i	0.0451477	−	0.0988596i
$541$	13.6235	−	29.8314i	0.585722	−	1.28255i	−0.352271	−	0.935898i	$-0.614590\pi$
$541$	13.6235	−	29.8314i	0.585722	−	1.28255i	0.937993	−	0.346654i	$-0.112682\pi$
$542$	7.67150	−	53.3565i	0.329519	−	2.29186i
$543$	−13.1535	+	8.45321i	−0.564469	+	0.362762i
$544$	−34.7445	−	10.2019i	−1.48966	−	0.437403i
$545$	2.41591	+	16.8030i	0.103486	+	0.719763i
$546$	−1.81101	−	2.09002i	−0.0775041	−	0.0894445i
$547$	−9.94003	−	6.38807i	−0.425005	−	0.273134i	0.310605	−	0.950539i	$-0.399468\pi$
$547$	−9.94003	−	6.38807i	−0.425005	−	0.273134i	−0.735610	+	0.677405i	$0.763105\pi$
$548$	19.3739	−	22.3587i	0.827613	−	0.955116i
$549$	6.19515	−	1.81906i	0.264403	−	0.0776356i
$550$	−2.20738	−	4.83349i	−0.0941230	−	0.206101i
$551$	6.57025			0.279902
$552$	−2.42878	−	4.77979i	−0.103376	−	0.203441i
$553$	−37.4844			−1.59400
$554$	11.4831	+	25.1445i	0.487871	+	1.06829i
$555$	4.54030	−	1.33315i	0.192725	−	0.0565892i
$556$	−9.91181	+	11.4388i	−0.420355	+	0.485115i
$557$	−0.422686	−	0.271644i	−0.0179098	−	0.0115099i	0.531655	−	0.846961i	$-0.321570\pi$
$557$	−0.422686	−	0.271644i	−0.0179098	−	0.0115099i	−0.549565	+	0.835451i	$0.685207\pi$
$558$	−1.46582	−	1.69165i	−0.0620533	−	0.0716133i
$559$	0.918779	+	6.39025i	0.0388602	+	0.270279i
$560$	−6.32232	−	1.85640i	−0.267167	−	0.0784472i
$561$	−9.60523	+	6.17291i	−0.405533	+	0.260620i
$562$	2.71177	−	18.8608i	0.114389	−	0.795593i
$563$	11.5514	−	25.2941i	0.486835	−	1.06602i	−0.493692	−	0.869637i	$-0.664353\pi$
$563$	11.5514	−	25.2941i	0.486835	−	1.06602i	0.980527	−	0.196384i	$-0.0629198\pi$
$564$	−7.09620	+	15.5385i	−0.298804	+	0.654290i
$565$	−0.765799	+	5.32625i	−0.0322174	+	0.224077i
$566$	−27.8473	+	17.8964i	−1.17051	+	0.752242i
$567$	−2.36543	−	0.694552i	−0.0993386	−	0.0291685i
$568$	0.450253	+	3.13158i	0.0188922	+	0.131398i
$569$	−13.5324	−	15.6172i	−0.567306	−	0.654706i	0.397520	−	0.917593i	$-0.369871\pi$
$569$	−13.5324	−	15.6172i	−0.567306	−	0.654706i	−0.964827	+	0.262887i	$0.915325\pi$
$570$	−9.01800	−	5.79552i	−0.377722	−	0.242747i
$571$	20.2805	−	23.4050i	0.848714	−	0.979468i	−0.151245	−	0.988496i	$-0.548328\pi$
$571$	20.2805	−	23.4050i	0.848714	−	0.979468i	0.999959	+	0.00902808i	$0.00287377\pi$
$572$	−3.19171	+	0.937170i	−0.133452	+	0.0391850i
$573$	9.24779	+	20.2498i	0.386332	+	0.845949i
$574$	12.9470			0.540397
$575$	2.98664	−	3.75233i	0.124552	−	0.156483i
$576$	−11.5067			−0.479444
$577$	5.02728	+	11.0082i	0.209288	+	0.458277i	0.984943	−	0.172880i	$-0.0553074\pi$
$577$	5.02728	+	11.0082i	0.209288	+	0.458277i	−0.775655	+	0.631158i	$0.782580\pi$
$578$	7.95004	−	2.33434i	0.330678	−	0.0970958i
$579$	−3.11920	+	3.59975i	−0.129630	+	0.149601i
$580$	−2.77019	−	1.78029i	−0.115026	−	0.0739226i
$581$	1.13530	+	1.31021i	0.0471002	+	0.0543565i
$582$	−1.00716	−	7.00494i	−0.0417481	−	0.290364i
$583$	5.77811	+	1.69661i	0.239305	+	0.0702663i
$584$	13.9963	−	8.99485i	0.579169	−	0.372210i
$585$	0.0750447	−	0.521948i	0.00310272	−	0.0215799i
$586$	−19.4794	+	42.6539i	−0.804686	+	1.76202i
$587$	−10.2867	+	22.5248i	−0.424579	+	0.929698i	0.569597	+	0.821924i	$0.307099\pi$
$587$	−10.2867	+	22.5248i	−0.424579	+	0.929698i	−0.994175	+	0.107774i	$0.965628\pi$
$588$	−0.331509	+	2.30570i	−0.0136712	+	0.0950854i
$589$	−4.46041	+	2.86653i	−0.183788	+	0.118114i
$590$	−3.05655	−	0.897484i	−0.125836	−	0.0369488i
$591$	−1.95714	−	13.6122i	−0.0805058	−	0.559930i
$592$	−8.28244	−	9.55845i	−0.340406	−	0.392850i
$593$	34.5940	+	22.2322i	1.42061	+	0.912968i	0.999984	+	0.00573182i	$0.00182451\pi$
$593$	34.5940	+	22.2322i	1.42061	+	0.912968i	0.420622	+	0.907236i	$0.361812\pi$
$594$	−3.47972	+	4.01581i	−0.142775	+	0.164771i
$595$	10.8126	−	3.17486i	0.443273	−	0.130157i
$596$	−0.312743	−	0.684811i	−0.0128104	−	0.0280509i
$597$	−2.66387			−0.109025
$598$	−3.68961	−	3.91526i	−0.150879	−	0.160107i
$599$	37.8782			1.54766			0.773830	−	0.633393i	$-0.218338\pi$
$599$	37.8782			1.54766			0.773830	+	0.633393i	$0.218338\pi$
$600$	0.464410	+	1.01692i	0.0189595	+	0.0415154i
$601$	39.1663	−	11.5003i	1.59763	−	0.469105i	0.642742	−	0.766083i	$-0.277797\pi$
$601$	39.1663	−	11.5003i	1.59763	−	0.469105i	0.954885	+	0.296977i	$0.0959786\pi$
$602$	−42.0476	+	48.5256i	−1.71373	+	1.97775i
$603$	−7.49679	−	4.81789i	−0.305293	−	0.196200i
$604$	12.1729	+	14.0483i	0.495310	+	0.571618i
$605$	−0.677546	−	4.71244i	−0.0275462	−	0.191588i
$606$	5.46518	+	1.60472i	0.222008	+	0.0651874i
$607$	−32.1856	+	20.6845i	−1.30637	+	0.839556i	−0.993891	−	0.110367i	$-0.964797\pi$
$607$	−32.1856	+	20.6845i	−1.30637	+	0.839556i	−0.312484	+	0.949923i	$0.601161\pi$
$608$	−5.68099	+	39.5121i	−0.230394	+	1.60243i
$609$	−1.33531	+	2.92392i	−0.0541095	+	0.118483i
$610$	−5.70593	+	12.4942i	−0.231026	+	0.505877i
$611$	−0.507591	+	3.53037i	−0.0205349	+	0.142824i
$612$	9.71173	−	6.24135i	0.392574	−	0.252292i
$613$	9.37643	+	2.75317i	0.378710	+	0.111199i	0.465547	−	0.885023i	$-0.345858\pi$
$613$	9.37643	+	2.75317i	0.378710	+	0.111199i	−0.0868366	+	0.996223i	$0.527676\pi$
$614$	−4.31327	−	29.9994i	−0.174069	−	1.21068i
$615$	1.61665	+	1.86571i	0.0651896	+	0.0752328i
$616$	−5.79129	−	3.72184i	−0.233338	−	0.149957i
$617$	−15.6047	+	18.0088i	−0.628222	+	0.725007i	−0.977247	−	0.212107i	$-0.931968\pi$
$617$	−15.6047	+	18.0088i	−0.628222	+	0.725007i	0.349024	+	0.937114i	$0.386513\pi$
$618$	11.6304	−	3.41500i	0.467844	−	0.137371i
$619$	10.2883	+	22.5283i	0.413523	+	0.905488i	0.995718	+	0.0924395i	$0.0294665\pi$
$619$	10.2883	+	22.5283i	0.413523	+	0.905488i	−0.582196	+	0.813049i	$0.697806\pi$
$620$	2.65735			0.106722
$621$	−4.65393	−	1.15797i	−0.186756	−	0.0464677i
$622$	23.5194			0.943042
$623$	−7.27322	−	15.9261i	−0.291395	−	0.638067i
$624$	−1.35232	+	0.397076i	−0.0541360	+	0.0158958i
$625$	−0.654861	+	0.755750i	−0.0261944	+	0.0302300i
$626$	32.2481	+	20.7246i	1.28889	+	0.828321i
$627$	8.24251	+	9.51236i	0.329174	+	0.379887i
$628$	5.16149	+	35.8989i	0.205966	+	1.43252i
$629$	20.7541	+	6.09396i	0.827521	+	0.242982i
$630$	4.41193	−	2.83538i	0.175776	−	0.112964i
$631$	−4.64935	+	32.3369i	−0.185088	+	1.28731i	0.659423	+	0.751772i	$0.270801\pi$
$631$	−4.64935	+	32.3369i	−0.185088	+	1.28731i	−0.844510	+	0.535540i	$0.820108\pi$
$632$	7.06130	−	15.4621i	0.280883	−	0.615049i
$633$	0.706658	−	1.54736i	0.0280871	−	0.0615022i
$634$	−6.10183	+	42.4391i	−0.242334	+	1.68547i
$635$	16.7878	−	10.7889i	0.666203	−	0.428143i
$636$	−5.84218	−	1.71542i	−0.231658	−	0.0680208i
$637$	0.0692175	+	0.481418i	0.00274250	+	0.0190745i
$638$	4.53708	+	5.23607i	0.179625	+	0.207298i
$639$	2.38075	+	1.53001i	0.0941809	+	0.0605264i
$640$	5.65459	−	6.52575i	0.223517	−	0.257953i
$641$	−5.36068	+	1.57404i	−0.211734	+	0.0621708i	−0.385879	−	0.922549i	$-0.626102\pi$
$641$	−5.36068	+	1.57404i	−0.211734	+	0.0621708i	0.174145	+	0.984720i	$0.444284\pi$
$642$	−15.2355	−	33.3612i	−0.601298	−	1.31666i
$643$	22.4403			0.884959			0.442479	−	0.896779i	$-0.354099\pi$
$643$	22.4403			0.884959			0.442479	+	0.896779i	$0.354099\pi$
$644$	3.01257	−	29.7071i	0.118712	−	1.17062i
$645$	−12.2431			−0.482071
$646$	−20.3557	−	44.5727i	−0.800883	−	1.75369i
$647$	25.6724	−	7.53811i	1.00929	−	0.296354i	0.265026	−	0.964241i	$-0.414620\pi$
$647$	25.6724	−	7.53811i	1.00929	−	0.296354i	0.744262	+	0.667888i	$0.232801\pi$
$648$	0.732097	−	0.844885i	0.0287595	−	0.0331902i
$649$	3.14661	+	2.02221i	0.123515	+	0.0793785i
$650$	0.734604	+	0.847778i	0.0288135	+	0.0332526i
$651$	−0.369162	−	2.56758i	−0.0144686	−	0.100631i
$652$	−22.8123	−	6.69831i	−0.893400	−	0.262326i
$653$	−28.6015	+	18.3811i	−1.11926	+	0.719308i	−0.963293	−	0.268454i	$-0.913487\pi$
$653$	−28.6015	+	18.3811i	−1.11926	+	0.719308i	−0.155972	+	0.987762i	$0.549851\pi$
$654$	−5.13943	+	35.7455i	−0.200968	+	1.39776i
$655$	8.87425	−	19.4319i	0.346746	−	0.759267i
$656$	2.74104	−	6.00205i	0.107020	−	0.234341i
$657$	2.11795	−	14.7307i	0.0826291	−	0.574698i
$658$	−29.8416	+	19.1781i	−1.16335	+	0.747638i
$659$	11.4973	+	3.37591i	0.447871	+	0.131507i	0.497887	−	0.867242i	$-0.334109\pi$
$659$	11.4973	+	3.37591i	0.447871	+	0.131507i	−0.0500168	+	0.998748i	$0.515927\pi$
$660$	−0.897762	−	6.24407i	−0.0349453	−	0.243050i
$661$	25.9724	+	29.9738i	1.01021	+	1.16584i	0.986103	+	0.166135i	$0.0531289\pi$
$661$	25.9724	+	29.9738i	1.01021	+	1.16584i	0.0241073	+	0.999709i	$0.492326\pi$
$662$	2.65931	+	1.70904i	0.103357	+	0.0664236i
$663$	1.57848	−	1.82166i	0.0613031	−	0.0707475i
$664$	−0.754320	+	0.221488i	−0.0292733	+	0.00859541i
$665$	−5.16059	−	11.3001i	−0.200119	−	0.438200i
$666$	10.0665			0.390067
$667$	−2.35805	+	5.79146i	−0.0913040	+	0.224246i
$668$	50.9188			1.97011
$669$	10.5349	+	23.0681i	0.407301	+	0.891865i
$670$	18.1896	−	5.34096i	0.702727	−	0.206339i
$671$	10.5614	−	12.1885i	0.407717	−	0.470531i
$672$	−16.4293	−	10.5585i	−0.633774	−	0.407302i
$673$	20.4490	+	23.5994i	0.788252	+	0.909692i	0.997676	−	0.0681334i	$-0.0217043\pi$
$673$	20.4490	+	23.5994i	0.788252	+	0.909692i	−0.209424	+	0.977825i	$0.567159\pi$
$674$	2.94457	+	20.4800i	0.113421	+	0.788859i
$675$	0.959493	+	0.281733i	0.0369309	+	0.0108439i
$676$	−27.0290	+	17.3705i	−1.03958	+	0.668096i
$677$	−1.22047	+	8.48857i	−0.0469065	+	0.326242i	0.952835	+	0.303490i	$0.0981519\pi$
$677$	−1.22047	+	8.48857i	−0.0469065	+	0.326242i	−0.999741	+	0.0227521i	$0.992757\pi$
$678$	−4.75533	+	10.4127i	−0.182627	+	0.399898i
$679$	3.40693	−	7.46015i	0.130746	−	0.286294i
$680$	−0.727260	+	5.05820i	−0.0278891	+	0.193973i
$681$	4.31757	−	2.77473i	0.165449	−	0.106328i
$682$	−5.36458	−	1.57518i	−0.205421	−	0.0603169i
$683$	−4.06286	−	28.2578i	−0.155461	−	1.08126i	−0.906867	−	0.421416i	$-0.861533\pi$
$683$	−4.06286	−	28.2578i	−0.155461	−	1.08126i	0.751406	−	0.659840i	$-0.229376\pi$
$684$	−8.33390	−	9.61783i	−0.318655	−	0.367747i
$685$	9.85475	+	6.33326i	0.376531	+	0.241981i
$686$	−27.2085	+	31.4003i	−1.03883	+	1.19887i
$687$	8.21839	−	2.41314i	0.313551	−	0.0920669i
$688$	13.5938	+	29.7662i	0.518258	+	1.13483i
$689$	−1.27132			−0.0484333
$690$	8.34510	−	5.86908i	0.317693	−	0.223432i
$691$	13.9817			0.531891			0.265945	−	0.963988i	$-0.414316\pi$
$691$	13.9817			0.531891			0.265945	+	0.963988i	$0.414316\pi$
$692$	−12.5843	−	27.5558i	−0.478384	−	1.04752i
$693$	−5.90841	+	1.73487i	−0.224442	+	0.0659021i
$694$	47.1143	−	54.3728i	1.78843	−	2.06396i
$695$	−5.04175	−	3.24013i	−0.191244	−	0.122905i
$696$	−0.954555	−	1.10162i	−0.0361823	−	0.0417566i
$697$	1.60597	+	11.1698i	0.0608304	+	0.423085i
$698$	10.8734	+	3.19273i	0.411566	+	0.120847i
$699$	1.50717	−	0.968598i	0.0570063	−	0.0366357i
$700$	−0.886070	+	6.16275i	−0.0334903	+	0.232930i
$701$	12.7278	−	27.8700i	0.480723	−	1.05264i	−0.501541	−	0.865134i	$-0.667233\pi$
$701$	12.7278	−	27.8700i	0.480723	−	1.05264i	0.982264	−	0.187502i	$-0.0600393\pi$
$702$	0.466000	−	1.02040i	0.0175881	−	0.0385125i
$703$	3.39346	−	23.6020i	0.127987	−	0.890166i
$704$	−24.1789	+	15.5389i	−0.911278	+	0.585643i
$705$	−6.48986	−	1.90560i	−0.244422	−	0.0717689i
$706$	9.11752	+	63.4138i	0.343143	+	2.38661i
$707$	4.32260	+	4.98855i	0.162568	+	0.187614i
$708$	−3.18150	−	2.04463i	−0.119568	−	0.0768418i
$709$	−9.42406	+	10.8760i	−0.353928	+	0.408455i	−0.904596	−	0.426269i	$-0.859828\pi$
$709$	−9.42406	+	10.8760i	−0.353928	+	0.408455i	0.550668	+	0.834724i	$0.314373\pi$
$710$	−5.77647	+	1.69612i	−0.216787	+	0.0636544i
$711$	−6.31633	−	13.8308i	−0.236881	−	0.518697i
$712$	7.93955			0.297547
$713$	−0.925925	−	4.96051i	−0.0346762	−	0.185772i
$714$	23.9730			0.897166
$715$	−0.547159	−	1.19811i	−0.0204626	−	0.0448068i
$716$	−9.90810	+	2.90928i	−0.370283	+	0.108725i
$717$	3.02748	−	3.49389i	0.113063	−	0.130482i
$718$	21.7439	+	13.9739i	0.811474	+	0.521503i
$719$	0.301694	+	0.348173i	0.0112513	+	0.0129847i	0.761347	−	0.648344i	$-0.224538\pi$
$719$	0.301694	+	0.348173i	0.0112513	+	0.0129847i	−0.750096	+	0.661329i	$0.769993\pi$
$720$	−0.380379	−	2.64560i	−0.0141759	−	0.0985956i
$721$	13.4781	+	3.95753i	0.501951	+	0.147386i
$722$	−11.4394	+	7.35168i	−0.425732	+	0.273601i
$723$	3.00643	−	20.9102i	0.111811	−	0.777659i
$724$	16.4038	−	35.9194i	0.609644	−	1.33493i
$725$	0.541645	−	1.18604i	0.0201162	−	0.0440483i
$726$	1.44136	−	10.0249i	0.0534939	−	0.372059i
$727$	41.3244	−	26.5576i	1.53264	−	0.984966i	0.543265	−	0.839562i	$-0.317188\pi$
$727$	41.3244	−	26.5576i	1.53264	−	0.984966i	0.989372	−	0.145404i	$-0.0464483\pi$
$728$	1.39444	+	0.409444i	0.0516813	+	0.0151750i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	20.7323	+	23.9264i	0.767339	+	0.885556i
$731$	−47.0801	−	30.2566i	−1.74132	−	1.11908i
$732$	−10.6785	+	12.3236i	−0.394688	+	0.455494i
$733$	−19.6996	+	5.78431i	−0.727620	+	0.213648i	−0.624505	−	0.781021i	$-0.714699\pi$
$733$	−19.6996	+	5.78431i	−0.727620	+	0.213648i	−0.103115	+	0.994669i	$0.532881\pi$
$734$	25.8363	+	56.5737i	0.953637	+	2.08817i
$735$	−0.922350			−0.0340214
$736$	−32.7898	−	19.1884i	−1.20865	−	0.707295i
$737$	−22.2592			−0.819928
$738$	2.18164	+	4.77713i	0.0803073	+	0.175848i
$739$	3.15804	−	0.927283i	0.116170	−	0.0341107i	−0.223131	−	0.974789i	$-0.571628\pi$
$739$	3.15804	−	0.927283i	0.116170	−	0.0341107i	0.339301	+	0.940678i	$0.389809\pi$
$740$	−7.82603	+	9.03172i	−0.287691	+	0.332013i
$741$	−2.23535	−	1.43657i	−0.0821178	−	0.0527739i
$742$	−8.28007	−	9.55571i	−0.303971	−	0.350801i
$743$	4.89836	+	34.0688i	0.179703	+	1.24986i	0.857449	+	0.514568i	$0.172048\pi$
$743$	4.89836	+	34.0688i	0.179703	+	1.24986i	−0.677746	+	0.735296i	$0.737043\pi$
$744$	1.12865	+	0.331402i	0.0413784	+	0.0121498i
$745$	0.250773	−	0.161162i	0.00918763	−	0.00590453i
$746$	2.48827	−	17.3063i	0.0911019	−	0.633628i
$747$	−0.292130	+	0.639676i	−0.0106885	+	0.0234045i
$748$	11.9788	−	26.2299i	0.437988	−	0.959060i
$749$	6.04866	−	42.0694i	0.221013	−	1.53718i
$750$	−1.78962	+	1.15012i	−0.0653477	+	0.0419964i
$751$	−19.2016	−	5.63809i	−0.700675	−	0.205737i	−0.0880567	−	0.996115i	$-0.528066\pi$
$751$	−19.2016	−	5.63809i	−0.700675	−	0.205737i	−0.612619	+	0.790379i	$0.709884\pi$
$752$	2.57283	+	17.8944i	0.0938214	+	0.652542i
$753$	20.4235	+	23.5700i	0.744275	+	0.858939i
$754$	−1.23045	−	0.790761i	−0.0448103	−	0.0287978i
$755$	−4.81998	+	5.56255i	−0.175417	+	0.202442i
$756$	5.97392	−	1.75410i	0.217270	−	0.0637961i
$757$	−19.8642	−	43.4965i	−0.721976	−	1.58091i	−0.811115	−	0.584887i	$-0.801139\pi$
$757$	−19.8642	−	43.4965i	−0.721976	−	1.58091i	0.0891389	−	0.996019i	$-0.471589\pi$
$758$	−3.84986			−0.139833
$759$	−11.3431	+	3.85154i	−0.411727	+	0.139802i
$760$	5.63338			0.204344
$761$	−12.4722	−	27.3102i	−0.452115	−	0.989994i	−0.989214	−	0.146475i	$-0.953207\pi$
$761$	−12.4722	−	27.3102i	−0.452115	−	0.989994i	0.537099	−	0.843519i	$-0.319520\pi$
$762$	40.7326	−	11.9602i	1.47559	−	0.433272i
$763$	−27.4061	+	31.6284i	−0.992169	+	1.14502i
$764$	−47.2969	−	30.3959i	−1.71114	−	1.09968i
$765$	2.99343	+	3.45460i	0.108228	+	0.124901i
$766$	8.71321	+	60.6017i	0.314821	+	2.18963i
$767$	−0.757648	−	0.222465i	−0.0273571	−	0.00803276i
$768$	−3.90702	+	2.51089i	−0.140982	+	0.0906038i
$769$	−1.42942	+	9.94186i	−0.0515463	+	0.358512i	0.947681	+	0.319218i	$0.103420\pi$
$769$	−1.42942	+	9.94186i	−0.0515463	+	0.358512i	−0.999228	+	0.0392946i	$0.987489\pi$
$770$	5.44183	−	11.9160i	0.196110	−	0.429421i
$771$	−9.14871	+	20.0329i	−0.329483	+	0.721466i
$772$	1.71196	−	11.9070i	0.0616149	−	0.428541i
$773$	10.5376	−	6.77209i	0.379011	−	0.243575i	−0.337240	−	0.941419i	$-0.609493\pi$
$773$	10.5376	−	6.77209i	0.379011	−	0.243575i	0.716250	+	0.697844i	$0.245857\pi$
$774$	−24.9900	−	7.33773i	−0.898248	−	0.263749i
$775$	0.149744	+	1.04149i	0.00537896	+	0.0374115i
$776$	2.43547	+	2.81068i	0.0874282	+	0.100898i
$777$	9.81380	+	6.30695i	0.352068	+	0.226261i
$778$	18.5826	−	21.4455i	0.666219	−	0.768858i
$779$	11.9360	−	3.50472i	0.427651	−	0.125570i
$780$	0.553226	+	1.21140i	0.0198087	+	0.0433749i
$781$	7.06883			0.252943
$782$	46.5950	−	1.94582i	1.66623	−	0.0695825i
$783$	−1.30386			−0.0465963
$784$	1.02411	+	2.24248i	0.0365752	+	0.0800885i
$785$	−13.7790	+	4.04587i	−0.491792	+	0.144403i
$786$	29.7600	−	34.3448i	1.06150	−	1.22504i
$787$	32.4055	+	20.8257i	1.15513	+	0.742357i	0.970654	−	0.240480i	$-0.0773049\pi$
$787$	32.4055	+	20.8257i	1.15513	+	0.742357i	0.184476	+	0.982837i	$0.440941\pi$
$788$	22.7442	+	26.2482i	0.810227	+	0.935052i
$789$	−3.33442	−	23.1914i	−0.118709	−	0.825637i
$790$	31.0355	+	9.11284i	1.10419	+	0.324220i
$791$	−11.1599	+	7.17202i	−0.396800	+	0.255008i
$792$	0.397403	−	2.76400i	0.0141211	−	0.0982144i
$793$	−1.41437	+	3.09703i	−0.0502257	+	0.109979i
$794$	22.6243	−	49.5402i	0.802905	−	1.75812i
$795$	0.343110	−	2.38638i	0.0121689	−	0.0846363i
$796$	5.65965	−	3.63723i	0.200601	−	0.128918i
$797$	28.1737	+	8.27254i	0.997964	+	0.293029i	0.739620	−	0.673025i	$-0.235005\pi$
$797$	28.1737	+	8.27254i	0.997964	+	0.293029i	0.258344	+	0.966053i	$0.416823\pi$
$798$	−3.76098	−	26.1582i	−0.133137	−	0.925991i
$799$	−20.2471	−	23.3664i	−0.716290	−	0.826643i
$800$	6.66425	+	4.28285i	0.235617	+	0.151422i
$801$	4.65078	−	5.36728i	0.164327	−	0.189644i
$802$	−59.1350	+	17.3636i	−2.08813	+	0.613130i
$803$	−15.4422	−	33.8137i	−0.544943	−	1.19326i
$804$	22.5060			0.793726
$805$	11.8128	−	0.493307i	0.416347	−	0.0173868i
$806$	1.18033			0.0415753
$807$	−5.15101	−	11.2791i	−0.181324	−	0.397045i
$808$	−2.87204	+	0.843306i	−0.101038	+	0.0296674i
$809$	18.4660	−	21.3109i	0.649229	−	0.749251i	−0.331749	−	0.943368i	$-0.607639\pi$
$809$	18.4660	−	21.3109i	0.649229	−	0.749251i	0.980978	+	0.194117i	$0.0621842\pi$
$810$	1.78962	+	1.15012i	0.0628809	+	0.0404111i
$811$	13.5896	+	15.6832i	0.477194	+	0.550712i	0.942399	−	0.334492i	$-0.108565\pi$
$811$	13.5896	+	15.6832i	0.477194	+	0.550712i	−0.465204	+	0.885203i	$0.654019\pi$
$812$	−1.15532	−	8.03539i	−0.0405436	−	0.281987i
$813$	24.3130	+	7.13893i	0.852693	+	0.250373i
$814$	21.1526	−	13.5940i	0.741400	−	0.476469i
$815$	1.33976	−	9.31826i	0.0469299	−	0.326404i
$816$	5.07538	−	11.1135i	0.177674	−	0.389052i
$817$	−25.6284	+	56.1185i	−0.896626	+	1.96334i
$818$	−4.71945	+	32.8245i	−0.165012	+	1.14768i
$819$	1.09362	−	0.702824i	0.0382140	−	0.0245587i
$820$	−5.98217	−	1.75652i	−0.208906	−	0.0613405i
$821$	−2.84960	−	19.8194i	−0.0994517	−	0.691702i	−0.977160	−	0.212506i	$-0.931837\pi$
$821$	−2.84960	−	19.8194i	−0.0994517	−	0.691702i	0.877708	−	0.479196i	$-0.159072\pi$
$822$	16.3193	+	18.8335i	0.569201	+	0.656893i
$823$	−35.0802	−	22.5447i	−1.22282	−	0.785858i	−0.240062	−	0.970758i	$-0.577168\pi$
$823$	−35.0802	−	22.5447i	−1.22282	−	0.785858i	−0.982757	+	0.184900i	$0.940804\pi$
$824$	−4.17146	+	4.81412i	−0.145320	+	0.167708i
$825$	2.39664	−	0.703717i	0.0834403	−	0.0245003i
$826$	−3.26242	−	7.14370i	−0.113514	−	0.248561i
$827$	−37.3800			−1.29983			−0.649914	−	0.760008i	$-0.725195\pi$
$827$	−37.3800			−1.29983			−0.649914	+	0.760008i	$0.725195\pi$
$828$	11.4688	−	3.89425i	0.398569	−	0.135334i
$829$	6.16093			0.213978			0.106989	−	0.994260i	$-0.465879\pi$
$829$	6.16093			0.213978			0.106989	+	0.994260i	$0.465879\pi$
$830$	−0.621456	−	1.36080i	−0.0215711	−	0.0472340i
$831$	−12.4677	+	3.66084i	−0.432499	+	0.126993i
$832$	3.97346	−	4.58561i	0.137755	−	0.158977i
$833$	−3.54685	−	2.27942i	−0.122891	−	0.0789772i
$834$	−8.34905	−	9.63532i	−0.289104	−	0.333644i
$835$	2.86931	+	19.9565i	0.0992967	+	0.690624i
$836$	−30.5002	−	8.95566i	−1.05487	−	0.309738i
$837$	0.885168	−	0.568863i	0.0305959	−	0.0196628i
$838$	2.63840	−	18.3505i	0.0911420	−	0.633906i
$839$	8.54438	−	18.7096i	0.294985	−	0.645927i	−0.702875	−	0.711313i	$-0.748101\pi$
$839$	8.54438	−	18.7096i	0.294985	−	0.645927i	0.997860	+	0.0653864i	$0.0208280\pi$
$840$	−1.14491	+	2.50699i	−0.0395030	+	0.0864995i
$841$	3.88519	−	27.0221i	0.133972	−	0.931795i
$842$	−47.9108	+	30.7904i	−1.65111	+	1.06111i
$843$	8.59429	+	2.52351i	0.296003	+	0.0869143i
$844$	0.611403	+	4.25240i	0.0210453	+	0.146374i
$845$	−8.33110	−	9.61460i	−0.286598	−	0.330752i
$846$	−12.1047	−	7.77923i	−0.416169	−	0.267455i
$847$	7.68609	−	8.87022i	0.264097	−	0.304784i
$848$	−6.18289	+	1.81546i	−0.212321	+	0.0623432i
$849$	−6.46406	−	14.1543i	−0.221846	−	0.485775i
$850$	−9.72420			−0.333537
$851$	19.5865	+	11.4619i	0.671417	+	0.392910i
$852$	−7.14721			−0.244859
$853$	20.8101	+	45.5678i	0.712525	+	1.56021i	0.824092	+	0.566456i	$0.191686\pi$
$853$	20.8101	+	45.5678i	0.712525	+	1.56021i	−0.111567	+	0.993757i	$0.535587\pi$
$854$	−32.4903	+	9.54001i	−1.11180	+	0.326453i
$855$	3.29988	−	3.80827i	0.112854	−	0.130240i
$856$	16.2139	+	10.4200i	0.554180	+	0.356150i
$857$	−10.5289	−	12.1510i	−0.359660	−	0.415069i	0.546866	−	0.837220i	$-0.315821\pi$
$857$	−10.5289	−	12.1510i	−0.359660	−	0.415069i	−0.906526	+	0.422151i	$0.861275\pi$
$858$	−0.398763	−	2.77346i	−0.0136136	−	0.0946844i
$859$	35.9411	+	10.5533i	1.22629	+	0.360072i	0.829850	−	0.557987i	$-0.188426\pi$
$859$	35.9411	+	10.5533i	1.22629	+	0.360072i	0.396444	+	0.918059i	$0.370244\pi$
$860$	26.0116	−	16.7167i	0.886990	−	0.570034i
$861$	−0.866134	+	6.02409i	−0.0295178	+	0.205300i
$862$	12.5161	−	27.4065i	0.426302	−	0.933470i
$863$	6.50452	−	14.2429i	0.221416	−	0.484834i	−0.766027	−	0.642809i	$-0.777769\pi$
$863$	6.50452	−	14.2429i	0.221416	−	0.484834i	0.987443	+	0.157974i	$0.0504964\pi$
$864$	1.12739	−	7.84117i	0.0383546	−	0.266762i
$865$	10.0908	−	6.48495i	0.343097	−	0.220495i
$866$	−26.6456	−	7.82386i	−0.905455	−	0.265865i
$867$	0.554298	+	3.85523i	0.0188250	+	0.130930i
$868$	4.29009	+	4.95102i	0.145615	+	0.168049i
$869$	−31.9500	−	20.5330i	−1.08383	−	0.696535i
$870$	1.81642	−	2.09626i	0.0615823	−	0.0710697i
$871$	4.50879	−	1.32390i	0.152775	−	0.0448587i
$872$	−7.88375	−	17.2630i	−0.266977	−	0.584599i
$873$	3.32670			0.112592
$874$	−9.43322	−	50.5371i	−0.319084	−	1.70944i
$875$	−2.46529			−0.0833420
$876$	15.6134	+	34.1886i	0.527528	+	1.15513i
$877$	8.59425	−	2.52350i	0.290207	−	0.0852125i	−0.133389	−	0.991064i	$-0.542586\pi$
$877$	8.59425	−	2.52350i	0.290207	−	0.0852125i	0.423596	+	0.905851i	$0.360768\pi$
$878$	−6.85837	+	7.91499i	−0.231459	+	0.267118i
$879$	−18.5432	−	11.9170i	−0.625448	−	0.401951i
$880$	−4.37197	−	5.04552i	−0.147379	−	0.170084i
$881$	1.15997	+	8.06779i	0.0390805	+	0.271811i	0.999987	−	0.00506158i	$-0.00161116\pi$
$881$	1.15997	+	8.06779i	0.0390805	+	0.271811i	−0.960907	+	0.276872i	$0.910702\pi$
$882$	−1.88266	−	0.552798i	−0.0633924	−	0.0186137i
$883$	−19.2114	+	12.3464i	−0.646515	+	0.415490i	−0.822391	−	0.568923i	$-0.807360\pi$
$883$	−19.2114	+	12.3464i	−0.646515	+	0.415490i	0.175876	+	0.984412i	$0.443724\pi$
$884$	−0.866344	+	6.02555i	−0.0291383	+	0.202661i
$885$	0.622068	−	1.36214i	0.0209106	−	0.0457878i
$886$	26.8198	−	58.7271i	0.901027	−	1.97297i
$887$	6.85654	−	47.6883i	0.230220	−	1.60122i	−0.466933	−	0.884293i	$-0.654641\pi$
$887$	6.85654	−	47.6883i	0.230220	−	1.60122i	0.697153	−	0.716923i	$-0.254450\pi$
$888$	−4.45030	+	2.86003i	−0.149342	+	0.0959764i
$889$	47.2037	+	13.8603i	1.58316	+	0.464858i
$890$	2.15011	+	14.9543i	0.0720719	+	0.501271i
$891$	−1.63572	−	1.88773i	−0.0547988	−	0.0632412i
$892$	−53.8795	−	34.6262i	−1.80402	−	1.15937i
$893$	−22.3199	+	25.7585i	−0.746907	+	0.861976i
$894$	0.608458	−	0.178659i	0.0203499	−	0.00597526i
$895$	−1.69856	−	3.71933i	−0.0567766	−	0.124323i
$896$	21.2873			0.711158
$897$	2.06856	−	1.45481i	0.0690672	−	0.0485747i
$898$	−34.1710			−1.14030
$899$	−0.569920	−	1.24795i	−0.0190079	−	0.0416215i
$900$	−2.42321	+	0.711520i	−0.0807738	+	0.0237173i
$901$	7.21692	−	8.32877i	0.240431	−	0.277472i
$902$	11.0354	+	7.09203i	0.367439	+	0.236139i
$903$	−19.7655	−	22.8106i	−0.657754	−	0.759089i
$904$	−0.856120	−	5.95444i	−0.0284741	−	0.198042i
$905$	15.0022	+	4.40504i	0.498690	+	0.146429i
$906$	−13.1722	+	8.46524i	−0.437616	+	0.281239i
$907$	1.43107	−	9.95330i	0.0475179	−	0.330494i	−0.952171	−	0.305565i	$-0.901155\pi$
$907$	1.43107	−	9.95330i	0.0475179	−	0.330494i	0.999689	−	0.0249294i	$-0.00793611\pi$
$908$	−5.38449	+	11.7904i	−0.178690	+	0.391278i
$909$	−1.11227	+	2.43554i	−0.0368917	+	0.0807816i
$910$	−0.393570	+	2.73734i	−0.0130467	+	0.0907419i
$911$	−40.8947	+	26.2814i	−1.35490	+	0.870742i	−0.997988	−	0.0633955i	$-0.979807\pi$
$911$	−40.8947	+	26.2814i	−1.35490	+	0.870742i	−0.356913	+	0.934138i	$0.616171\pi$
$912$	−12.9228	−	3.79449i	−0.427918	−	0.125648i
$913$	0.249980	+	1.73865i	0.00827313	+	0.0575409i
$914$	14.1501	+	16.3301i	0.468043	+	0.540151i
$915$	−5.43171	−	3.49075i	−0.179567	−	0.115401i
$916$	−14.1659	+	16.3483i	−0.468054	+	0.540164i
$917$	50.5312	−	14.8373i	1.66869	−	0.489970i
$918$	4.03958	+	8.84544i	0.133326	+	0.291943i
$919$	21.6332			0.713613			0.356806	−	0.934178i	$-0.383866\pi$
$919$	21.6332			0.713613			0.356806	+	0.934178i	$0.383866\pi$
$920$	−2.02181	+	4.96564i	−0.0666570	+	0.163712i
$921$	14.2470			0.469453
$922$	13.1704	+	28.8392i	0.433744	+	0.949767i
$923$	−1.43185	+	0.420430i	−0.0471300	+	0.0138386i
$924$	10.1842	−	11.7532i	0.335036	−	0.386653i
$925$	−3.98079	−	2.55830i	−0.130888	−	0.0841164i
$926$	−36.9091	−	42.5953i	−1.21291	−	1.39977i
$927$	0.810905	+	5.63997i	0.0266336	+	0.185241i
$928$	−9.91057	−	2.91000i	−0.325330	−	0.0955256i
$929$	−38.3397	+	24.6394i	−1.25789	+	0.808394i	−0.987993	−	0.154497i	$-0.950624\pi$
$929$	−38.3397	+	24.6394i	−1.25789	+	0.808394i	−0.269892	+	0.962891i	$0.586988\pi$
$930$	−0.318554	+	2.21559i	−0.0104458	+	0.0726521i
$931$	−1.93075	+	4.22776i	−0.0632779	+	0.138559i
$932$	−1.87961	+	4.11576i	−0.0615686	+	0.134816i
$933$	−1.57341	+	10.9433i	−0.0515112	+	0.358268i
$934$	63.1410	−	40.5783i	2.06604	−	1.32776i
$935$	10.9553	+	3.21676i	0.358275	+	0.105199i
$936$	0.0838957	+	0.583508i	0.00274222	+	0.0190725i
$937$	38.4672	+	44.3935i	1.25667	+	1.45027i	0.841254	+	0.540640i	$0.181818\pi$
$937$	38.4672	+	44.3935i	1.25667	+	1.45027i	0.415414	+	0.909632i	$0.363637\pi$
$938$	39.3167	+	25.2673i	1.28374	+	0.825007i
$939$	−11.8003	+	13.6182i	−0.385087	+	0.444414i
$940$	16.3903	−	4.81261i	0.534591	−	0.156970i
$941$	19.7565	+	43.2608i	0.644045	+	1.41026i	0.896671	+	0.442698i	$0.145979\pi$
$941$	19.7565	+	43.2608i	0.644045	+	1.41026i	−0.252626	+	0.967564i	$0.581294\pi$
$942$	−30.5498			−0.995367
$943$	−1.19450	+	11.7790i	−0.0388982	+	0.383578i
$944$	−4.00242			−0.130268
$945$	1.02412	+	2.24251i	0.0333146	+	0.0729487i
$946$	−62.4206	+	18.3283i	−2.02947	+	0.595906i
$947$	−0.672581	+	0.776200i	−0.0218559	+	0.0252231i	−0.766572	−	0.642158i	$-0.778039\pi$
$947$	−0.672581	+	0.776200i	−0.0218559	+	0.0252231i	0.744716	+	0.667381i	$0.232585\pi$
$948$	32.3043	+	20.7607i	1.04919	+	0.674276i
$949$	5.13907	+	5.93080i	0.166821	+	0.192522i
$950$	1.52557	+	10.6106i	0.0494962	+	0.344254i
$951$	−19.3383	−	5.67823i	−0.627086	−	0.184129i
$952$	−10.5983	+	6.81108i	−0.343491	+	0.220748i
$953$	−5.35926	+	37.2745i	−0.173603	+	1.20744i	0.697589	+	0.716498i	$0.254256\pi$
$953$	−5.35926	+	37.2745i	−0.173603	+	1.20744i	−0.871193	+	0.490941i	$0.836653\pi$
$954$	2.13059	−	4.66534i	0.0689803	−	0.151046i
$955$	9.24779	−	20.2498i	0.299251	−	0.655269i
$956$	−1.66162	+	11.5568i	−0.0537407	+	0.373775i
$957$	−2.73981	+	1.76077i	−0.0885655	+	0.0569176i
$958$	23.1953	+	6.81074i	0.749405	+	0.220045i
$959$	4.10995	+	28.5853i	0.132717	+	0.923069i
$960$	7.53526	+	8.69615i	0.243199	+	0.280667i
$961$	−25.1475	−	16.1613i	−0.811209	−	0.521332i
$962$	−3.47613	+	4.01166i	−0.112075	+	0.129341i
$963$	16.5418	−	4.85711i	0.533052	−	0.156518i
$964$	22.1633	+	48.5308i	0.713831	+	1.56307i
$965$	4.76315			0.153331
$966$	24.4074	+	6.07294i	0.785296	+	0.195394i
$967$	−54.8151			−1.76273			−0.881367	−	0.472433i	$-0.843376\pi$
$967$	−54.8151			−1.76273			−0.881367	+	0.472433i	$0.843376\pi$
$968$	2.21101	+	4.84143i	0.0710645	+	0.155610i
$969$	22.1010	−	6.48942i	0.709985	−	0.208470i
$970$	−4.63443	+	5.34842i	−0.148803	+	0.171727i
$971$	29.7976	+	19.1498i	0.956251	+	0.614545i	0.922958	−	0.384900i	$-0.125764\pi$
$971$	29.7976	+	19.1498i	0.956251	+	0.614545i	0.0332931	+	0.999446i	$0.489401\pi$
$972$	1.65386	+	1.90866i	0.0530476	+	0.0612202i
$973$	−2.10268	−	14.6244i	−0.0674087	−	0.468838i
$974$	65.5214	+	19.2388i	2.09944	+	0.616452i
$975$	−0.443606	+	0.285088i	−0.0142067	+	0.00913012i
$976$	−2.45599	+	17.0818i	−0.0786144	+	0.546775i
$977$	−1.51072	+	3.30801i	−0.0483321	+	0.105833i	−0.932258	−	0.361795i	$-0.882164\pi$
$977$	−1.51072	+	3.30801i	−0.0483321	+	0.105833i	0.883925	+	0.467628i	$0.154891\pi$
$978$	8.31944	−	18.2170i	0.266026	−	0.582517i
$979$	2.52457	−	17.5588i	0.0806857	−	0.561181i
$980$	1.95962	−	1.25937i	0.0625979	−	0.0402292i
$981$	−16.2882	−	4.78264i	−0.520042	−	0.152698i
$982$	8.86325	+	61.6453i	0.282838	+	1.96718i
$983$	−39.5157	−	45.6035i	−1.26035	−	1.45453i	−0.835715	−	0.549164i	$-0.814946\pi$
$983$	−39.5157	−	45.6035i	−1.26035	−	1.45453i	−0.424639	−	0.905363i	$-0.639599\pi$
$984$	−2.32174	−	1.49209i	−0.0740143	−	0.0475661i
$985$	−9.00575	+	10.3932i	−0.286947	+	0.331154i
$986$	12.1654	−	3.57210i	0.387427	−	0.113759i
$987$	−6.92698	−	15.1680i	−0.220488	−	0.482802i
$988$	6.71072			0.213497
$989$	−40.2686	−	42.7315i	−1.28047	−	1.35878i
$990$	5.31368			0.168880
$991$	−11.8443	−	25.9353i	−0.376246	−	0.823863i	−0.999136	−	0.0415539i	$-0.986769\pi$
$991$	−11.8443	−	25.9353i	−0.376246	−	0.823863i	0.622891	−	0.782309i	$-0.285958\pi$
$992$	7.99770	−	2.34834i	0.253927	−	0.0745598i
$993$	−0.973100	+	1.12302i	−0.0308804	+	0.0356379i
$994$	−12.4858	−	8.02412i	−0.396025	−	0.254510i
$995$	1.74446	+	2.01322i	0.0553031	+	0.0638232i
$996$	−0.252752	−	1.75793i	−0.00800875	−	0.0557021i
$997$	−4.51995	−	1.32718i	−0.143148	−	0.0420322i	0.209373	−	0.977836i	$-0.432858\pi$
$997$	−4.51995	−	1.32718i	−0.143148	−	0.0420322i	−0.352522	+	0.935804i	$0.614676\pi$
$998$	−53.1473	+	34.1557i	−1.68235	+	1.08118i
$999$	−0.673431	+	4.68381i	−0.0213064	+	0.148189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.m.a.211.1	yes	30
23.6	even	11	inner	345.2.m.a.121.1	✓	30
23.11	odd	22		7935.2.a.bq.1.3		15
23.12	even	11		7935.2.a.bp.1.3		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.a.121.1	✓	30	23.6	even	11	inner
345.2.m.a.211.1	yes	30	1.1	even	1	trivial
7935.2.a.bp.1.3		15	23.12	even	11
7935.2.a.bq.1.3		15	23.11	odd	22

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.883723 - 1.93508i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-1.65386 + 1.90866i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(-1.39310 - 1.60773i) q^{6} +(-0.350847 - 2.44020i) q^{7} +(1.07266 + 0.314961i) q^{8} +(0.841254 - 0.540641i) q^{9} +(-0.302750 + 2.10567i) q^{10} +(1.03763 - 2.27210i) q^{11} +(-1.04914 + 2.29729i) q^{12} +(-0.0750447 + 0.521948i) q^{13} +(-4.41193 + 2.83538i) q^{14} +(-0.959493 - 0.281733i) q^{15} +(0.380379 + 2.64560i) q^{16} +(-2.99343 - 3.45460i) q^{17} +(-1.78962 - 1.15012i) q^{18} +(-3.29988 + 3.80827i) q^{19} +(2.42321 - 0.711520i) q^{20} +(-1.02412 - 2.24251i) q^{21} -5.31368 q^{22} +(-2.17254 - 4.27552i) q^{23} +1.11794 q^{24} +(0.415415 + 0.909632i) q^{25} +(1.07633 - 0.316039i) q^{26} +(0.654861 - 0.755750i) q^{27} +(5.23775 + 3.36610i) q^{28} +(-0.853849 - 0.985395i) q^{29} +(0.302750 + 2.10567i) q^{30} +(1.00958 + 0.296440i) q^{31} +(6.66425 - 4.28285i) q^{32} +(0.355477 - 2.47240i) q^{33} +(-4.03958 + 8.84544i) q^{34} +(-1.02412 + 2.24251i) q^{35} +(-0.359418 + 2.49981i) q^{36} +(-3.98079 + 2.55830i) q^{37} +(10.2855 + 3.02009i) q^{38} +(0.0750447 + 0.521948i) q^{39} +(-0.732097 - 0.844885i) q^{40} +(-2.07680 - 1.33468i) q^{41} +(-3.43440 + 3.96351i) q^{42} +(11.7472 - 3.44928i) q^{43} +(2.62056 + 5.73822i) q^{44} -1.00000 q^{45} +(-6.35356 + 7.98243i) q^{46} +6.76385 q^{47} +(1.11032 + 2.43127i) q^{48} +(0.884988 - 0.259856i) q^{49} +(1.39310 - 1.60773i) q^{50} +(-3.84545 - 2.47132i) q^{51} +(-0.872106 - 1.00646i) q^{52} +(0.343110 + 2.38638i) q^{53} +(-2.04115 - 0.599337i) q^{54} +(-2.10130 + 1.35042i) q^{55} +(0.392227 - 2.72800i) q^{56} +(-2.09330 + 4.58369i) q^{57} +(-1.15225 + 2.52309i) q^{58} +(-0.213111 + 1.48222i) q^{59} +(2.12460 - 1.36540i) q^{60} +(6.19515 + 1.81906i) q^{61} +(-0.318554 - 2.21559i) q^{62} +(-1.61442 - 1.86314i) q^{63} +(-9.68002 - 6.22097i) q^{64} +(0.345318 - 0.398518i) q^{65} +(-5.09844 + 1.49704i) q^{66} +(-3.70195 - 8.10614i) q^{67} +11.5444 q^{68} +(-3.28909 - 3.49025i) q^{69} +5.24447 q^{70} +(1.17562 + 2.57426i) q^{71} +(1.07266 - 0.314961i) q^{72} +(9.74573 - 11.2472i) q^{73} +(8.46844 + 5.44234i) q^{74} +(0.654861 + 0.755750i) q^{75} +(-1.81113 - 12.5967i) q^{76} +(-5.90841 - 1.73487i) q^{77} +(0.943694 - 0.606475i) q^{78} +(2.16388 - 15.0501i) q^{79} +(1.11032 - 2.43127i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-0.747397 + 5.19826i) q^{82} +(-0.591590 + 0.380192i) q^{83} +(5.97392 + 1.75410i) q^{84} +(0.650534 + 4.52456i) q^{85} +(-17.0559 - 19.6835i) q^{86} +(-1.09688 - 0.704922i) q^{87} +(1.82865 - 2.11037i) q^{88} +(6.81425 - 2.00085i) q^{89} +(0.883723 + 1.93508i) q^{90} +1.29998 q^{91} +(11.7536 + 2.92447i) q^{92} +1.05220 q^{93} +(-5.97737 - 13.0886i) q^{94} +(4.83494 - 1.41967i) q^{95} +(5.18768 - 5.98690i) q^{96} +(2.79860 + 1.79855i) q^{97} +(-1.28493 - 1.48288i) q^{98} +(-0.355477 - 2.47240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9} - 7 q^{11} - 2 q^{12} + 7 q^{13} - 47 q^{14} - 3 q^{15} + 26 q^{16} + 15 q^{17} - 7 q^{19} - 2 q^{20} - 12 q^{21} - 18 q^{22}+ \cdots + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9 - 7 * q^11 - 2 * q^12 + 7 * q^13 - 47 * q^14 - 3 * q^15 + 26 * q^16 + 15 * q^17 - 7 * q^19 - 2 * q^20 - 12 * q^21 - 18 * q^22 + 12 * q^23 - 3 * q^25 - 18 * q^26 + 3 * q^27 + 2 * q^28 - 6 * q^29 + 22 * q^31 + 33 * q^32 - 4 * q^33 - 53 * q^34 - 12 * q^35 - 9 * q^36 - 23 * q^37 + 21 * q^38 - 7 * q^39 + 11 * q^40 + 26 * q^41 + 3 * q^42 - 19 * q^43 - 47 * q^44 - 30 * q^45 - 44 * q^46 + 14 * q^47 + 7 * q^48 + 2 * q^49 - 11 * q^50 - 15 * q^51 + 55 * q^52 - 14 * q^53 - 11 * q^54 - 4 * q^55 + 6 * q^56 - 26 * q^57 - 18 * q^58 + 40 * q^59 - 9 * q^60 + 37 * q^61 + 19 * q^62 - 10 * q^63 + 14 * q^64 + 4 * q^65 - 4 * q^66 - 108 * q^67 + 54 * q^68 + 21 * q^69 - 30 * q^70 + 39 * q^71 + 22 * q^72 + 57 * q^73 - 11 * q^74 + 3 * q^75 + 22 * q^76 + 2 * q^77 + 7 * q^78 + 55 * q^79 + 7 * q^80 - 3 * q^81 - 26 * q^82 - 79 * q^83 - 2 * q^84 + 18 * q^85 - 44 * q^86 - 5 * q^87 - 8 * q^88 - 30 * q^89 + 40 * q^91 + 35 * q^92 + 44 * q^93 - 29 * q^94 + 7 * q^95 + 22 * q^96 - 52 * q^97 + 28 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

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