LMFDB - Embedded newform 196.2.j.a.111.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,2,Mod(27,196)] 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("196.27"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.j (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.18
Character	$\chi$	$=$	196.111
Dual form			196.2.j.a.83.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.739436 + 1.20550i) q^{2} +(0.576591 + 0.723022i) q^{3} +(-0.906467 + 1.78278i) q^{4} +(2.88506 - 2.30076i) q^{5} +(-0.445252 + 1.22971i) q^{6} +(2.64328 - 0.114420i) q^{7} +(-2.81942 + 0.225507i) q^{8} +(0.477259 - 2.09101i) q^{9} +(4.90688 + 1.77668i) q^{10} +(-6.29614 + 1.43705i) q^{11} +(-1.81165 + 0.372541i) q^{12} +(-3.30359 + 0.754023i) q^{13} +(2.09247 + 3.10187i) q^{14} +(3.32699 + 0.759365i) q^{15} +(-2.35663 - 3.23207i) q^{16} +(-1.32426 + 2.74986i) q^{17} +(2.87362 - 0.970832i) q^{18} -3.15336 q^{19} +(1.48654 + 7.22899i) q^{20} +(1.60682 + 1.84517i) q^{21} +(-6.38796 - 6.52739i) q^{22} +(-0.0319146 - 0.0662714i) q^{23} +(-1.78870 - 1.90848i) q^{24} +(1.91747 - 8.40098i) q^{25} +(-3.35177 - 3.42493i) q^{26} +(4.28662 - 2.06433i) q^{27} +(-2.19206 + 4.81611i) q^{28} +(0.122716 + 0.0590968i) q^{29} +(1.54469 + 4.57220i) q^{30} +1.68084 q^{31} +(2.15368 - 5.23084i) q^{32} +(-4.66931 - 3.72365i) q^{33} +(-4.29417 + 0.436946i) q^{34} +(7.36275 - 6.41164i) q^{35} +(3.29520 + 2.74628i) q^{36} +(3.94364 + 1.89916i) q^{37} +(-2.33171 - 3.80138i) q^{38} +(-2.44999 - 1.95380i) q^{39} +(-7.61536 + 7.13741i) q^{40} +(-3.34485 + 2.66743i) q^{41} +(-1.03622 + 3.30141i) q^{42} +(5.02623 + 4.00829i) q^{43} +(3.14529 - 12.5273i) q^{44} +(-3.43398 - 7.13074i) q^{45} +(0.0562914 - 0.0874766i) q^{46} +(0.166245 + 0.728365i) q^{47} +(0.978044 - 3.56748i) q^{48} +(6.97382 - 0.604889i) q^{49} +(11.5452 - 3.90048i) q^{50} +(-2.75177 + 0.628073i) q^{51} +(1.65034 - 6.57308i) q^{52} +(1.78996 - 0.861998i) q^{53} +(5.65823 + 3.64109i) q^{54} +(-14.8584 + 18.6318i) q^{55} +(-7.42671 + 0.918678i) q^{56} +(-1.81820 - 2.27995i) q^{57} +(0.0194993 + 0.191632i) q^{58} +(0.754424 - 0.946018i) q^{59} +(-4.36959 + 5.24297i) q^{60} +(-4.12089 + 8.55712i) q^{61} +(1.24288 + 2.02626i) q^{62} +(1.02227 - 5.58172i) q^{63} +(7.89829 - 1.27160i) q^{64} +(-7.79622 + 9.77615i) q^{65} +(1.03621 - 8.38227i) q^{66} -7.13583i q^{67} +(-3.70201 - 4.85354i) q^{68} +(0.0295140 - 0.0612864i) q^{69} +(13.1735 + 4.13480i) q^{70} +(-2.54779 - 5.29054i) q^{71} +(-0.874057 + 6.00306i) q^{72} +(13.2990 + 3.03541i) q^{73} +(0.626634 + 6.15837i) q^{74} +(7.17969 - 3.45756i) q^{75} +(2.85842 - 5.62176i) q^{76} +(-16.4780 + 4.51893i) q^{77} +(0.543700 - 4.39818i) q^{78} -16.0338i q^{79} +(-14.2352 - 3.90267i) q^{80} +(-1.83297 - 0.882711i) q^{81} +(-5.68890 - 2.05983i) q^{82} +(0.852941 - 3.73698i) q^{83} +(-4.74607 + 1.19202i) q^{84} +(2.50619 + 10.9803i) q^{85} +(-1.11542 + 9.02300i) q^{86} +(0.0280285 + 0.122801i) q^{87} +(17.4274 - 5.47148i) q^{88} +(5.47805 + 1.25033i) q^{89} +(6.05690 - 9.41240i) q^{90} +(-8.64602 + 2.37109i) q^{91} +(0.147077 + 0.00317600i) q^{92} +(0.969158 + 1.21529i) q^{93} +(-0.755118 + 0.738988i) q^{94} +(-9.09762 + 7.25511i) q^{95} +(5.02380 - 1.45889i) q^{96} +0.0207508i q^{97} +(5.88589 + 7.95967i) q^{98} +13.8511i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26}+ \cdots + 105 q^{98}+O(q^{100}) $ 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{11}{14}\right)$

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 $

$2$	0.739436	+	1.20550i	0.522861	+	0.852418i
$2$	0.739436	+	1.20550i	0.522861	+	0.852418i
$3$	0.576591	+	0.723022i	0.332895	+	0.417437i	0.919904	−	0.392143i	$-0.128266\pi$
$3$	0.576591	+	0.723022i	0.332895	+	0.417437i	−0.587009	+	0.809580i	$0.699695\pi$
$4$	−0.906467	+	1.78278i	−0.453234	+	0.891392i
$5$	2.88506	−	2.30076i	1.29024	−	1.02893i	0.292889	−	0.956146i	$-0.405383\pi$
$5$	2.88506	−	2.30076i	1.29024	−	1.02893i	0.997348	−	0.0727829i	$-0.0231880\pi$
$6$	−0.445252	+	1.22971i	−0.181773	+	0.502027i
$7$	2.64328	−	0.114420i	0.999064	−	0.0432468i
$7$	2.64328	−	0.114420i	0.999064	−	0.0432468i
$8$	−2.81942	+	0.225507i	−0.996817	+	0.0797289i
$9$	0.477259	−	2.09101i	0.159086	−	0.697003i
$10$	4.90688	+	1.77668i	1.55169	+	0.561835i
$11$	−6.29614	+	1.43705i	−1.89836	+	0.433287i	−0.999982	−	0.00594367i	$-0.998108\pi$
$11$	−6.29614	+	1.43705i	−1.89836	+	0.433287i	−0.898374	+	0.439231i	$0.855251\pi$
$12$	−1.81165	+	0.372541i	−0.522979	+	0.107543i
$13$	−3.30359	+	0.754023i	−0.916251	+	0.209128i	−0.654548	−	0.756020i	$-0.727141\pi$
$13$	−3.30359	+	0.754023i	−0.916251	+	0.209128i	−0.261703	+	0.965149i	$0.584284\pi$
$14$	2.09247	+	3.10187i	0.559236	+	0.829009i
$15$	3.32699	+	0.759365i	0.859026	+	0.196067i
$16$	−2.35663	−	3.23207i	−0.589158	−	0.808018i
$17$	−1.32426	+	2.74986i	−0.321181	+	0.666939i	−0.997575	−	0.0696007i	$-0.977827\pi$
$17$	−1.32426	+	2.74986i	−0.321181	+	0.666939i	0.676394	+	0.736540i	$0.263542\pi$
$18$	2.87362	−	0.970832i	0.677318	−	0.228827i
$19$	−3.15336			−0.723430			−0.361715	−	0.932289i	$-0.617809\pi$
$19$	−3.15336			−0.723430			−0.361715	+	0.932289i	$0.617809\pi$
$20$	1.48654	+	7.22899i	0.332400	+	1.61645i
$21$	1.60682	+	1.84517i	0.350636	+	0.402650i
$22$	−6.38796	−	6.52739i	−1.36192	−	1.39164i
$23$	−0.0319146	−	0.0662714i	−0.00665466	−	0.0138185i	0.897615	−	0.440780i	$-0.145298\pi$
$23$	−0.0319146	−	0.0662714i	−0.00665466	−	0.0138185i	−0.904270	+	0.426962i	$0.859584\pi$
$24$	−1.78870	−	1.90848i	−0.365117	−	0.389567i
$25$	1.91747	−	8.40098i	0.383494	−	1.68020i
$26$	−3.35177	−	3.42493i	−0.657336	−	0.671684i
$27$	4.28662	−	2.06433i	0.824960	−	0.397280i
$28$	−2.19206	+	4.81611i	−0.414260	+	0.910159i
$29$	0.122716	+	0.0590968i	0.0227878	+	0.0109740i	0.445243	−	0.895410i	$-0.353117\pi$
$29$	0.122716	+	0.0590968i	0.0227878	+	0.0109740i	−0.422455	+	0.906384i	$0.638832\pi$
$30$	1.54469	+	4.57220i	0.282020	+	0.834765i
$31$	1.68084			0.301888			0.150944	−	0.988542i	$-0.451769\pi$
$31$	1.68084			0.301888			0.150944	+	0.988542i	$0.451769\pi$
$32$	2.15368	−	5.23084i	0.380721	−	0.924690i
$33$	−4.66931	−	3.72365i	−0.812823	−	0.648205i
$34$	−4.29417	+	0.436946i	−0.736444	+	0.0749357i
$35$	7.36275	−	6.41164i	1.24453	−	1.08377i
$36$	3.29520	+	2.74628i	0.549199	+	0.457713i
$37$	3.94364	+	1.89916i	0.648330	+	0.312219i	0.728992	−	0.684522i	$-0.239989\pi$
$37$	3.94364	+	1.89916i	0.648330	+	0.312219i	−0.0806620	+	0.996742i	$0.525703\pi$
$38$	−2.33171	−	3.80138i	−0.378253	−	0.616665i
$39$	−2.44999	−	1.95380i	−0.392313	−	0.312859i
$40$	−7.61536	+	7.13741i	−1.20409	+	1.12852i
$41$	−3.34485	+	2.66743i	−0.522378	+	0.416583i	−0.848858	−	0.528622i	$-0.822709\pi$
$41$	−3.34485	+	2.66743i	−0.522378	+	0.416583i	0.326479	+	0.945204i	$0.394138\pi$
$42$	−1.03622	+	3.30141i	−0.159892	+	0.509418i
$43$	5.02623	+	4.00829i	0.766493	+	0.611258i	0.926690	−	0.375827i	$-0.122641\pi$
$43$	5.02623	+	4.00829i	0.766493	+	0.611258i	−0.160196	+	0.987085i	$0.551213\pi$
$44$	3.14529	−	12.5273i	0.474170	−	1.88856i
$45$	−3.43398	−	7.13074i	−0.511908	−	1.06299i
$46$	0.0562914	−	0.0874766i	0.00829972	−	0.0128977i
$47$	0.166245	+	0.728365i	0.0242493	+	0.106243i	0.985604	−	0.169069i	$-0.0540760\pi$
$47$	0.166245	+	0.728365i	0.0242493	+	0.106243i	−0.961355	+	0.275312i	$0.911219\pi$
$48$	0.978044	−	3.56748i	0.141169	−	0.514921i
$49$	6.97382	−	0.604889i	0.996259	−	0.0864128i
$50$	11.5452	−	3.90048i	1.63274	−	0.551611i
$51$	−2.75177	+	0.628073i	−0.385325	+	0.0879478i
$52$	1.65034	−	6.57308i	0.228860	−	0.911522i
$53$	1.78996	−	0.861998i	0.245870	−	0.118405i	−0.306891	−	0.951745i	$-0.599289\pi$
$53$	1.78996	−	0.861998i	0.245870	−	0.118405i	0.552761	+	0.833340i	$0.313574\pi$
$54$	5.65823	+	3.64109i	0.769988	+	0.495489i
$55$	−14.8584	+	18.6318i	−2.00351	+	2.51232i
$56$	−7.42671	+	0.918678i	−0.992436	+	0.122763i
$57$	−1.81820	−	2.27995i	−0.240826	−	0.301986i
$58$	0.0194993	+	0.191632i	0.00256038	+	0.0251626i
$59$	0.754424	−	0.946018i	0.0982176	−	0.123161i	−0.730294	−	0.683133i	$-0.760617\pi$
$59$	0.754424	−	0.946018i	0.0982176	−	0.123161i	0.828511	+	0.559972i	$0.189188\pi$
$60$	−4.36959	+	5.24297i	−0.564112	+	0.676864i
$61$	−4.12089	+	8.55712i	−0.527626	+	1.09563i	0.451481	+	0.892281i	$0.350896\pi$
$61$	−4.12089	+	8.55712i	−0.527626	+	1.09563i	−0.979107	+	0.203346i	$0.934818\pi$
$62$	1.24288	+	2.02626i	0.157846	+	0.257335i
$63$	1.02227	−	5.58172i	0.128794	−	0.703231i
$64$	7.89829	−	1.27160i	0.987287	−	0.158950i
$65$	−7.79622	+	9.77615i	−0.967002	+	1.21258i
$66$	1.03621	−	8.38227i	0.127548	−	1.03179i
$67$		−	7.13583i		−	0.871780i	−0.900000	−	0.435890i	$-0.856434\pi$
$67$		−	7.13583i		−	0.871780i	0.900000	−	0.435890i	$-0.143566\pi$
$68$	−3.70201	−	4.85354i	−0.448934	−	0.588578i
$69$	0.0295140	−	0.0612864i	0.00355307	−	0.00737802i
$70$	13.1735	+	4.13480i	1.57454	+	0.494203i
$71$	−2.54779	−	5.29054i	−0.302367	−	0.627871i	0.693322	−	0.720628i	$-0.256146\pi$
$71$	−2.54779	−	5.29054i	−0.302367	−	0.627871i	−0.995689	+	0.0927568i	$0.970432\pi$
$72$	−0.874057	+	6.00306i	−0.103009	+	0.707468i
$73$	13.2990	+	3.03541i	1.55653	+	0.355268i	0.912286	−	0.409553i	$-0.134315\pi$
$73$	13.2990	+	3.03541i	1.55653	+	0.355268i	0.644243	+	0.764821i	$0.277173\pi$
$74$	0.626634	+	6.15837i	0.0728448	+	0.715895i
$75$	7.17969	−	3.45756i	0.829039	−	0.399244i
$76$	2.85842	−	5.62176i	0.327883	−	0.644860i
$77$	−16.4780	+	4.51893i	−1.87784	+	0.514980i
$78$	0.543700	−	4.39818i	0.0615619	−	0.497996i
$79$		−	16.0338i		−	1.80394i	−0.431794	−	0.901972i	$-0.642119\pi$
$79$		−	16.0338i		−	1.80394i	0.431794	−	0.901972i	$-0.357881\pi$
$80$	−14.2352	−	3.90267i	−1.59155	−	0.436331i
$81$	−1.83297	−	0.882711i	−0.203663	−	0.0980790i
$82$	−5.68890	−	2.05983i	−0.628234	−	0.227470i
$83$	0.852941	−	3.73698i	0.0936224	−	0.410187i	−0.906300	−	0.422635i	$-0.861105\pi$
$83$	0.852941	−	3.73698i	0.0936224	−	0.410187i	0.999923	+	0.0124481i	$0.00396246\pi$
$84$	−4.74607	+	1.19202i	−0.517839	+	0.130060i
$85$	2.50619	+	10.9803i	0.271834	+	1.19098i
$86$	−1.11542	+	9.02300i	−0.120278	+	0.972976i
$87$	0.0280285	+	0.122801i	0.00300497	+	0.0131656i
$88$	17.4274	−	5.47148i	1.85777	−	0.583262i
$89$	5.47805	+	1.25033i	0.580672	+	0.132535i	0.502761	−	0.864426i	$-0.332318\pi$
$89$	5.47805	+	1.25033i	0.580672	+	0.132535i	0.0779116	+	0.996960i	$0.475175\pi$
$90$	6.05690	−	9.41240i	0.638453	−	0.992154i
$91$	−8.64602	+	2.37109i	−0.906349	+	0.248558i
$92$	0.147077	+	0.00317600i	0.0153338	+	0.000331121i
$93$	0.969158	+	1.21529i	0.100497	+	0.126019i
$94$	−0.755118	+	0.738988i	−0.0778844	+	0.0762208i
$95$	−9.09762	+	7.25511i	−0.933396	+	0.744358i
$96$	5.02380	−	1.45889i	0.512740	−	0.148897i
$97$			0.0207508i			0.00210693i	0.999999	+	0.00105346i	$0.000335328\pi$
$97$			0.0207508i			0.00210693i	−0.999999	+	0.00105346i	$0.999665\pi$
$98$	5.88589	+	7.95967i	0.594565	+	0.804048i
$99$			13.8511i			1.39209i
$100$	13.2390	+	11.0337i	1.32390	+	1.10337i
$101$	−8.88336	+	7.08424i	−0.883927	+	0.704909i	−0.956274	−	0.292471i	$-0.905523\pi$
$101$	−8.88336	+	7.08424i	−0.883927	+	0.704909i	0.0723471	+	0.997380i	$0.476951\pi$
$102$	−2.79190	−	2.85284i	−0.276439	−	0.282473i
$103$	8.28982	+	10.3951i	0.816820	+	1.02426i	0.999158	+	0.0410242i	$0.0130621\pi$
$103$	8.28982	+	10.3951i	0.816820	+	1.02426i	−0.182338	+	0.983236i	$0.558366\pi$
$104$	9.14418	−	2.87089i	0.896660	−	0.281514i
$105$	8.88105	+	1.62653i	0.866702	+	0.158733i
$106$	2.36270	+	1.52040i	0.229486	+	0.147675i
$107$	−11.7807	−	2.68886i	−1.13888	−	0.259942i	−0.388821	−	0.921313i	$-0.627118\pi$
$107$	−11.7807	−	2.68886i	−1.13888	−	0.259942i	−0.750059	+	0.661371i	$0.769975\pi$
$108$	−0.205432	+	9.51336i	−0.0197678	+	0.915424i
$109$	1.68605	+	7.38706i	0.161494	+	0.707552i	0.989222	+	0.146422i	$0.0467758\pi$
$109$	1.68605	+	7.38706i	0.161494	+	0.707552i	−0.827728	+	0.561129i	$0.810367\pi$
$110$	−33.4476	−	4.13476i	−3.18910	−	0.394234i
$111$	0.900733	+	3.94637i	0.0854938	+	0.374573i
$112$	−6.59905	−	8.27361i	−0.623551	−	0.781782i
$113$	0.424656	−	1.86054i	0.0399482	−	0.175025i	−0.951018	−	0.309135i	$-0.899961\pi$
$113$	0.424656	−	1.86054i	0.0399482	−	0.175025i	0.990966	+	0.134110i	$0.0428177\pi$
$114$	1.40404	−	3.87771i	0.131500	−	0.363181i
$115$	−0.244550	−	0.117769i	−0.0228044	−	0.0109820i
$116$	−0.216595	+	0.165206i	−0.0201103	+	0.0153390i
$117$			7.26770i			0.671899i
$118$	1.69827	+	0.209939i	0.156339	+	0.0193265i
$119$	−3.18575	+	7.42017i	−0.292038	+	0.680206i
$120$	−9.55144	−	1.39071i	−0.871924	−	0.126954i
$121$	27.6656	−	13.3230i	2.51505	−	1.21118i
$122$	−13.3628	+	1.35971i	−1.20981	+	0.123102i
$123$	−3.85722	−	0.880386i	−0.347794	−	0.0793817i
$124$	−1.52363	+	2.99658i	−0.136826	+	0.269101i
$125$	−5.79118	−	12.0255i	−0.517979	−	1.07559i
$126$	7.48468	−	2.89498i	0.666788	−	0.257905i
$127$	−3.53156	+	7.33336i	−0.313375	+	0.650731i	−0.996856	−	0.0792382i	$-0.974751\pi$
$127$	−3.53156	+	7.33336i	−0.313375	+	0.650731i	0.683480	+	0.729969i	$0.260466\pi$
$128$	7.37320	+	8.58113i	0.651705	+	0.758472i
$129$			5.94522i			0.523447i
$130$	−17.5500	−	2.16951i	−1.53923	−	0.190279i
$131$	2.41824	−	3.03237i	0.211282	−	0.264940i	−0.664886	−	0.746945i	$-0.731520\pi$
$131$	2.41824	−	3.03237i	0.211282	−	0.264940i	0.876168	+	0.482005i	$0.160091\pi$
$132$	10.8710	−	4.94900i	0.946203	−	0.430755i
$133$	−8.33520	+	0.360809i	−0.722753	+	0.0312861i
$134$	8.60225	−	5.27649i	0.743121	−	0.455819i
$135$	7.61763	−	15.8182i	0.655621	−	1.36141i
$136$	3.11355	−	8.05166i	0.266984	−	0.690424i
$137$	2.29764	−	2.88115i	0.196301	−	0.246153i	−0.673933	−	0.738792i	$-0.735396\pi$
$137$	2.29764	−	2.88115i	0.196301	−	0.246153i	0.870234	+	0.492639i	$0.163968\pi$
$138$	0.0957046	−	0.00973826i	0.00814691	−	0.000828976i
$139$	10.7748	+	13.5112i	0.913909	+	1.14601i	0.988864	+	0.148819i	$0.0475472\pi$
$139$	10.7748	+	13.5112i	0.913909	+	1.14601i	−0.0749552	+	0.997187i	$0.523881\pi$
$140$	4.75648	+	18.9381i	0.401996	+	1.60056i
$141$	−0.430769	+	0.540167i	−0.0362773	+	0.0454903i
$142$	4.49382	−	6.98338i	0.377113	−	0.586032i
$143$	19.7163	−	9.49486i	1.64876	−	0.794000i
$144$	−7.88301	+	3.38521i	−0.656918	+	0.282101i
$145$	0.490010	−	0.111841i	0.0406931	−	0.00928793i
$146$	6.17457	+	18.2764i	0.511011	+	1.51257i
$147$	4.45838	+	4.69345i	0.367721	+	0.387109i
$148$	−6.96056	+	5.30913i	−0.572155	+	0.436408i
$149$	−3.60339	−	15.7875i	−0.295201	−	1.29336i	−0.877182	−	0.480159i	$-0.840579\pi$
$149$	−3.60339	−	15.7875i	−0.295201	−	1.29336i	0.581980	−	0.813203i	$-0.302278\pi$
$150$	9.47701	+	6.09848i	0.773795	+	0.497939i
$151$	2.00329	+	4.15987i	0.163025	+	0.338526i	0.966439	−	0.256895i	$-0.0826996\pi$
$151$	2.00329	+	4.15987i	0.163025	+	0.338526i	−0.803414	+	0.595421i	$0.796985\pi$
$152$	8.89065	−	0.711106i	0.721127	−	0.0576783i
$153$	5.11797	+	4.08144i	0.413763	+	0.329965i
$154$	−17.6320	−	16.5228i	−1.42083	−	1.33144i
$155$	4.84933	−	3.86721i	0.389507	−	0.310622i
$156$	5.70405	−	2.59675i	0.456689	−	0.207906i
$157$	−7.33426	−	5.84888i	−0.585338	−	0.466791i	0.285488	−	0.958382i	$-0.407844\pi$
$157$	−7.33426	−	5.84888i	−0.585338	−	0.466791i	−0.870826	+	0.491591i	$0.836416\pi$
$158$	19.3288	−	11.8560i	1.53772	−	0.943212i
$159$	1.65532	+	0.797158i	0.131275	+	0.0632187i
$160$	−5.82138	−	20.0464i	−0.460220	−	1.58480i
$161$	−0.0919419	−	0.171522i	−0.00724604	−	0.0135178i
$162$	−0.291254	−	2.86236i	−0.0228831	−	0.224888i
$163$	−10.9548	−	8.73616i	−0.858046	−	0.684269i	0.0922096	−	0.995740i	$-0.470607\pi$
$163$	−10.9548	−	8.73616i	−0.858046	−	0.684269i	−0.950256	+	0.311471i	$0.899178\pi$
$164$	−1.72345	−	8.38109i	−0.134579	−	0.654453i
$165$	−22.0384			−1.71569
$166$	5.13563	−	1.73504i	0.398602	−	0.134665i
$167$	−9.86284	−	4.74969i	−0.763210	−	0.367542i	0.0114388	−	0.999935i	$-0.496359\pi$
$167$	−9.86284	−	4.74969i	−0.763210	−	0.367542i	−0.774648	+	0.632392i	$0.782073\pi$
$168$	−4.94640	−	4.83997i	−0.381623	−	0.373412i
$169$	−1.36745	+	0.658528i	−0.105188	+	0.0506560i
$170$	−11.3836	+	11.1405i	−0.873084	+	0.854434i
$171$	−1.50497	+	6.59370i	−0.115088	+	0.504233i
$172$	−11.7020	+	5.32730i	−0.892271	+	0.406203i
$173$	−4.61562	−	9.58444i	−0.350919	−	0.728692i	0.648553	−	0.761169i	$-0.275374\pi$
$173$	−4.61562	−	9.58444i	−0.350919	−	0.728692i	−0.999472	+	0.0324778i	$0.989660\pi$
$174$	−0.127311	+	0.124592i	−0.00965145	+	0.00944529i
$175$	4.10716	−	22.4255i	0.310472	−	1.69521i
$176$	19.4823	+	16.9629i	1.46854	+	1.27863i
$177$	1.11899			0.0841081
$178$	2.54340	+	7.52834i	0.190636	+	0.564273i
$179$	−2.88308	+	5.98677i	−0.215491	+	0.447472i	−0.980492	−	0.196557i	$-0.937024\pi$
$179$	−2.88308	+	5.98677i	−0.215491	+	0.447472i	0.765001	+	0.644029i	$0.222738\pi$
$180$	15.8253	+	0.341734i	1.17955	+	0.0254714i
$181$	−14.3390	−	3.27279i	−1.06581	−	0.243265i	−0.346570	−	0.938024i	$-0.612654\pi$
$181$	−14.3390	−	3.27279i	−1.06581	−	0.243265i	−0.719242	+	0.694760i	$0.755511\pi$
$182$	−9.25153	−	8.66952i	−0.685769	−	0.642628i
$183$	−8.56305	+	1.95446i	−0.632999	+	0.144478i
$184$	0.104925	+	0.179650i	0.00773521	+	0.0132440i
$185$	15.7471	−	3.59418i	1.15775	−	0.264249i
$186$	−0.748398	+	2.06695i	−0.0548752	+	0.151556i
$187$	4.38605	−	19.2165i	0.320740	−	1.40525i
$188$	−1.44921	−	0.363861i	−0.105695	−	0.0265373i
$189$	11.0945	−	5.94706i	0.807008	−	0.432585i
$190$	−15.4732	−	5.60250i	−1.12254	−	0.406448i
$191$	−1.35444	+	1.08013i	−0.0980036	+	0.0781553i	−0.671266	−	0.741217i	$-0.734249\pi$
$191$	−1.35444	+	1.08013i	−0.0980036	+	0.0781553i	0.573262	+	0.819372i	$0.305678\pi$
$192$	5.47348	+	4.97744i	0.395014	+	0.359216i
$193$	−0.440447	−	0.552303i	−0.0317040	−	0.0397556i	0.765727	−	0.643166i	$-0.222380\pi$
$193$	−0.440447	−	0.552303i	−0.0317040	−	0.0397556i	−0.797431	+	0.603410i	$0.793808\pi$
$194$	−0.0250152	+	0.0153439i	−0.00179598	+	0.00110163i
$195$	−11.5636			−0.828086
$196$	−5.24315	+	12.9811i	−0.374511	+	0.927223i
$197$	−14.5205			−1.03454			−0.517271	−	0.855822i	$-0.673052\pi$
$197$	−14.5205			−1.03454			−0.517271	+	0.855822i	$0.673052\pi$
$198$	−16.6975	+	10.2420i	−1.18664	+	0.727869i
$199$	7.80846	+	9.79150i	0.553527	+	0.694101i	0.977346	−	0.211646i	$-0.0678823\pi$
$199$	7.80846	+	9.79150i	0.553527	+	0.694101i	−0.423819	+	0.905747i	$0.639311\pi$
$200$	−3.51167	+	24.1183i	−0.248313	+	1.70542i
$201$	5.15936	−	4.11445i	0.363913	−	0.290211i
$202$	−15.1087	−	5.47056i	−1.06305	−	0.384907i
$203$	0.331134	+	0.142168i	0.0232410	+	0.00997824i
$204$	1.37467	−	5.47513i	0.0962461	−	0.383336i
$205$	−3.51298	+	15.3914i	−0.245357	+	1.07498i
$206$	−6.40152	+	17.6799i	−0.446015	+	1.23182i
$207$	−0.153806	+	0.0351051i	−0.0106902	+	0.00243997i
$208$	10.2224	+	8.90048i	0.708796	+	0.617137i
$209$	19.8540	−	4.53154i	1.37333	−	0.313453i
$210$	4.60618	+	11.9088i	0.317857	+	0.821788i
$211$	5.59063	+	1.27603i	0.384875	+	0.0878452i	0.410581	−	0.911824i	$-0.365326\pi$
$211$	5.59063	+	1.27603i	0.384875	+	0.0878452i	−0.0257054	+	0.999670i	$0.508183\pi$
$212$	−0.0857821	+	3.97248i	−0.00589154	+	0.272831i
$213$	2.35614	−	4.89258i	0.161440	−	0.335234i
$214$	−5.46963	−	16.1898i	−0.373896	−	1.10672i
$215$	23.7231			1.61790
$216$	−11.6203	+	6.78688i	−0.790660	+	0.461789i
$217$	4.44293	−	0.192323i	0.301606	−	0.0130557i
$218$	−7.65838	+	7.49479i	−0.518691	+	0.507611i
$219$	5.47341	+	11.3656i	0.369859	+	0.768019i
$220$	−19.7479	−	43.3785i	−1.33140	−	2.92458i
$221$	2.30136	−	10.0829i	0.154807	−	0.678252i
$222$	−4.09132	+	4.00393i	−0.274591	+	0.268726i
$223$	−5.10312	+	2.45753i	−0.341730	+	0.164568i	−0.596875	−	0.802334i	$-0.703591\pi$
$223$	−5.10312	+	2.45753i	−0.341730	+	0.164568i	0.255145	+	0.966903i	$0.417877\pi$
$224$	5.09427	−	14.0730i	0.340375	−	0.940290i
$225$	−16.6514	−	8.01889i	−1.11009	−	0.534593i
$226$	2.55689	−	0.863826i	0.170082	−	0.0574609i
$227$	−14.0310			−0.931268			−0.465634	−	0.884977i	$-0.654174\pi$
$227$	−14.0310			−0.931268			−0.465634	+	0.884977i	$0.654174\pi$
$228$	5.71279	−	1.17475i	0.378339	−	0.0778000i
$229$	17.4379	+	13.9063i	1.15233	+	0.918954i	0.997616	−	0.0690049i	$-0.0219824\pi$
$229$	17.4379	+	13.9063i	1.15233	+	0.918954i	0.154716	+	0.987959i	$0.450554\pi$
$230$	−0.0388584	−	0.381888i	−0.00256224	−	0.0251809i
$231$	−12.7683	−	9.30838i	−0.840095	−	0.612446i
$232$	−0.359315	−	0.138946i	−0.0235902	−	0.00912223i
$233$	−21.6283	−	10.4156i	−1.41692	−	0.682351i	−0.440401	−	0.897801i	$-0.645164\pi$
$233$	−21.6283	−	10.4156i	−1.41692	−	0.682351i	−0.976515	+	0.215450i	$0.930878\pi$
$234$	−8.76122	+	5.37400i	−0.572739	+	0.351309i
$235$	2.15541	+	1.71889i	0.140604	+	0.112128i
$236$	1.00268	+	2.20251i	0.0652692	+	0.143371i
$237$	11.5928	−	9.24494i	0.753033	−	0.600524i
$238$	−11.3007	+	1.64631i	−0.732515	+	0.106714i
$239$	5.78128	+	4.61042i	0.373960	+	0.298223i	0.792377	−	0.610032i	$-0.208843\pi$
$239$	5.78128	+	4.61042i	0.373960	+	0.298223i	−0.418417	+	0.908255i	$0.637415\pi$
$240$	−5.38619	−	12.5426i	−0.347677	−	0.809623i
$241$	−6.40816	−	13.3067i	−0.412786	−	0.857159i	−0.998898	−	0.0469292i	$-0.985056\pi$
$241$	−6.40816	−	13.3067i	−0.412786	−	0.857159i	0.586112	−	0.810230i	$-0.300658\pi$
$242$	36.5178	+	23.4993i	2.34746	+	1.51059i
$243$	−3.59478	−	15.7497i	−0.230605	−	1.01035i
$244$	−11.5200	−	15.1034i	−0.737495	−	0.966896i
$245$	18.7282	−	17.7902i	1.19650	−	1.13657i
$246$	−1.79086	−	5.30087i	−0.114181	−	0.337971i
$247$	10.4174	−	2.37770i	0.662843	−	0.151290i
$248$	−4.73901	+	0.379043i	−0.300927	+	0.0240692i
$249$	3.19371	−	1.53801i	0.202393	−	0.0974675i
$250$	10.2146	−	15.8734i	0.646025	−	1.00392i
$251$	8.66048	−	10.8599i	0.546645	−	0.685471i	−0.429382	−	0.903123i	$-0.641269\pi$
$251$	8.66048	−	10.8599i	0.546645	−	0.685471i	0.976026	+	0.217653i	$0.0698399\pi$
$252$	9.02434	+	6.88214i	0.568480	+	0.433534i
$253$	0.296174	+	0.371391i	0.0186203	+	0.0233491i
$254$	−11.4517	+	1.16525i	−0.718547	+	0.0731145i
$255$	−6.49396	+	8.14317i	−0.406668	+	0.509945i
$256$	−4.89255	+	15.2336i	−0.305785	+	0.952101i
$257$	−6.15132	+	12.7734i	−0.383709	+	0.796780i	0.616248	+	0.787552i	$0.288652\pi$
$257$	−6.15132	+	12.7734i	−0.383709	+	0.796780i	−0.999957	+	0.00922816i	$0.997063\pi$
$258$	−7.16697	+	4.39611i	−0.446196	+	0.273690i
$259$	10.6414	+	4.56876i	0.661226	+	0.283889i
$260$	−10.3617	−	22.7607i	−0.642608	−	1.41156i
$261$	0.182139	−	0.228395i	0.0112741	−	0.0141373i
$262$	5.44366	+	0.672941i	0.336311	+	0.0415744i
$263$		−	17.0275i		−	1.04996i	−0.851114	−	0.524981i	$-0.824072\pi$
$263$		−	17.0275i		−	1.04996i	0.851114	−	0.524981i	$-0.175928\pi$
$264$	14.0045	+	9.44559i	0.861916	+	0.581336i
$265$	3.18088	−	6.60517i	0.195400	−	0.405752i
$266$	−6.59830	−	9.78130i	−0.404568	−	0.599730i
$267$	2.25458	+	4.68168i	0.137978	+	0.286514i
$268$	12.7216	+	6.46839i	0.777097	+	0.395120i
$269$	9.29869	+	2.12236i	0.566951	+	0.129403i	0.496382	−	0.868104i	$-0.334661\pi$
$269$	9.29869	+	2.12236i	0.566951	+	0.129403i	0.0705688	+	0.997507i	$0.477519\pi$
$270$	24.7016	−	2.51347i	1.50329	−	0.152965i
$271$	−15.3410	+	7.38785i	−0.931901	+	0.448780i	−0.837305	−	0.546736i	$-0.815870\pi$
$271$	−15.3410	+	7.38785i	−0.931901	+	0.448780i	−0.0945960	+	0.995516i	$0.530156\pi$
$272$	12.0086	−	2.20030i	0.728125	−	0.133413i
$273$	−6.69956	−	4.88411i	−0.405476	−	0.295600i
$274$	5.17219	+	0.639381i	0.312463	+	0.0386264i
$275$			55.6492i			3.35578i
$276$	0.0825069	+	0.108171i	0.00496633	+	0.00651114i
$277$	16.6096	+	7.99876i	0.997973	+	0.480599i	0.860250	−	0.509872i	$-0.170307\pi$
$277$	16.6096	+	7.99876i	0.997973	+	0.480599i	0.137723	+	0.990471i	$0.456022\pi$
$278$	−8.32048	+	22.9798i	−0.499029	+	1.37823i
$279$	0.802198	−	3.51466i	0.0480263	−	0.210417i
$280$	−19.3128	+	19.7375i	−1.15416	+	1.17954i
$281$	0.889293	+	3.89625i	0.0530508	+	0.232431i	0.994502	−	0.104719i	$-0.0333943\pi$
$281$	0.889293	+	3.89625i	0.0530508	+	0.232431i	−0.941451	+	0.337150i	$0.890537\pi$
$282$	−0.969698	−	0.119873i	−0.0577447	−	0.00713834i
$283$	4.24407	+	18.5945i	0.252284	+	1.10533i	0.929290	+	0.369350i	$0.120420\pi$
$283$	4.24407	+	18.5945i	0.252284	+	1.10533i	−0.677007	+	0.735977i	$0.736723\pi$
$284$	11.7414	+	0.253544i	0.696722	+	0.0150451i
$285$	−10.4912	−	2.39455i	−0.621445	−	0.141841i
$286$	26.0250	+	16.7472i	1.53889	+	0.990280i
$287$	−8.53616	+	7.43348i	−0.503874	+	0.438784i
$288$	−9.90986	−	6.99984i	−0.583944	−	0.412469i
$289$	4.79126	+	6.00805i	0.281839	+	0.353415i
$290$	0.497156	+	0.508008i	0.0291940	+	0.0298312i
$291$	−0.0150033	+	0.0119647i	−0.000879509	+	0.000701385i
$292$	−17.4666	+	20.9577i	−1.02215	+	1.22646i
$293$			30.5428i			1.78433i	0.451712	+	0.892164i	$0.350813\pi$
$293$			30.5428i			1.78433i	−0.451712	+	0.892164i	$0.649187\pi$
$294$	−2.36126	+	8.84510i	−0.137712	+	0.515856i
$295$		−	4.46506i		−	0.259966i
$296$	−11.5471	−	4.46520i	−0.671159	−	0.259535i
$297$	−24.0226	+	19.1574i	−1.39393	+	1.11162i
$298$	16.3674	−	16.0177i	0.948136	−	0.927883i
$299$	0.155403	+	0.194869i	0.00898718	+	0.0112696i
$300$	−0.344080	+	15.9340i	−0.0198655	+	0.919950i
$301$	13.7444	+	10.0199i	0.792211	+	0.577538i
$302$	−3.53343	+	5.49093i	−0.203326	+	0.315967i
$303$	−10.2441	−	2.33815i	−0.588510	−	0.134323i
$304$	7.43131	+	10.1919i	0.426215	+	0.584544i
$305$	7.79884	+	34.1689i	0.446560	+	1.95651i
$306$	−1.13577	+	9.18769i	−0.0649278	+	0.525225i
$307$	−5.68808	−	24.9211i	−0.324636	−	1.42232i	−0.829202	−	0.558949i	$-0.811205\pi$
$307$	−5.68808	−	24.9211i	−0.324636	−	1.42232i	0.504566	−	0.863373i	$-0.331652\pi$
$308$	6.88049	−	33.4730i	0.392052	−	1.90730i
$309$	−2.73605	+	11.9874i	−0.155649	+	0.681942i
$310$	8.24770	+	2.98632i	0.468438	+	0.169611i
$311$	26.2309	+	12.6321i	1.48742	+	0.716302i	0.988623	−	0.150418i	$-0.0480618\pi$
$311$	26.2309	+	12.6321i	1.48742	+	0.716302i	0.498795	+	0.866720i	$0.333776\pi$
$312$	7.34816	+	4.95611i	0.416008	+	0.280584i
$313$		−	31.8341i		−	1.79937i	−0.436539	−	0.899685i	$-0.643796\pi$
$313$		−	31.8341i		−	1.79937i	0.436539	−	0.899685i	$-0.356204\pi$
$314$	1.62761	−	13.1663i	0.0918514	−	0.743020i
$315$	−9.89286	−	18.4556i	−0.557400	−	1.03985i
$316$	28.5848	+	14.5341i	1.60802	+	0.817609i
$317$	−13.1758	+	6.34511i	−0.740024	+	0.356377i	−0.765618	−	0.643296i	$-0.777567\pi$
$317$	−13.1758	+	6.34511i	−0.740024	+	0.356377i	0.0255938	+	0.999672i	$0.491852\pi$
$318$	0.263026	+	2.58493i	0.0147497	+	0.144956i
$319$	−0.857561	−	0.195733i	−0.0480142	−	0.0109589i
$320$	19.8614	−	21.8407i	1.11028	−	1.22093i
$321$	−4.84852	−	10.0680i	−0.270618	−	0.561944i
$322$	0.138785	−	0.237666i	0.00773416	−	0.0132446i
$323$	4.17588	−	8.67130i	0.232352	−	0.482484i
$324$	3.23521	−	2.46764i	0.179734	−	0.137091i
$325$			29.1992i			1.61968i
$326$	2.43108	−	19.6659i	0.134645	−	1.08919i
$327$	−4.36884	+	5.47836i	−0.241598	+	0.302954i
$328$	8.82903	−	8.27491i	0.487502	−	0.456905i
$329$	0.522770	+	1.90625i	0.0288212	+	0.105095i
$330$	−16.2960	−	26.5674i	−0.897067	−	1.46249i
$331$	−6.88686	+	14.3007i	−0.378536	+	0.786039i	0.621460	+	0.783446i	$0.286540\pi$
$331$	−6.88686	+	14.3007i	−0.378536	+	0.786039i	−0.999997	+	0.00259297i	$0.999175\pi$
$332$	5.88906	+	4.90806i	0.323204	+	0.269365i
$333$	5.85329	−	7.33979i	0.320758	−	0.402218i
$334$	−1.56718	−	15.4018i	−0.0857524	−	0.842747i
$335$	−16.4178	−	20.5873i	−0.897000	−	1.12480i
$336$	2.17705	−	9.54174i	0.118768	−	0.520545i
$337$	12.9483	−	16.2367i	0.705339	−	0.884467i	−0.292071	−	0.956397i	$-0.594344\pi$
$337$	12.9483	−	16.2367i	0.705339	−	0.884467i	0.997410	+	0.0719296i	$0.0229157\pi$
$338$	−1.80500	−	1.16152i	−0.0981789	−	0.0631784i
$339$	1.59006	−	0.765733i	0.0863603	−	0.0415889i
$340$	−21.8473	−	5.48531i	−1.18484	−	0.297483i
$341$	−10.5828	+	2.41546i	−0.573092	+	0.130804i
$342$	−9.06154	+	3.06138i	−0.489992	+	0.165540i
$343$	18.3645	−	2.39684i	0.991590	−	0.129417i
$344$	−15.0750	−	10.1676i	−0.812788	−	0.548200i
$345$	−0.0558556	−	0.244719i	−0.00300716	−	0.0131752i
$346$	8.14110	−	12.6512i	0.437668	−	0.680134i
$347$	0.913487	+	1.89687i	0.0490385	+	0.101830i	0.924048	−	0.382276i	$-0.124859\pi$
$347$	0.913487	+	1.89687i	0.0490385	+	0.101830i	−0.875010	+	0.484105i	$0.839145\pi$
$348$	−0.244334	−	0.0613463i	−0.0130977	−	0.00328850i
$349$	7.68260	+	6.12667i	0.411240	+	0.327953i	0.807161	−	0.590332i	$-0.201003\pi$
$349$	7.68260	+	6.12667i	0.411240	+	0.327953i	−0.395921	+	0.918285i	$0.629574\pi$
$350$	30.0710	−	11.6311i	1.60736	−	0.621706i
$351$	−12.6047	+	10.0519i	−0.672788	+	0.536531i
$352$	−6.04291	+	36.0290i	−0.322088	+	1.92035i
$353$	−12.6303	−	10.0724i	−0.672245	−	0.536097i	0.226807	−	0.973940i	$-0.427171\pi$
$353$	−12.6303	−	10.0724i	−0.672245	−	0.536097i	−0.899052	+	0.437842i	$0.855743\pi$
$354$	0.827418	+	1.34894i	0.0439768	+	0.0716953i
$355$	−19.5227	−	9.40166i	−1.03616	−	0.498988i
$356$	−7.19474	+	8.63280i	−0.381321	+	0.457537i
$357$	−7.20182	+	1.97503i	−0.381161	+	0.104530i
$358$	−9.34891	+	0.951283i	−0.494105	+	0.0502769i
$359$	1.72458	+	1.37531i	0.0910199	+	0.0725859i	0.667943	−	0.744213i	$-0.267175\pi$
$359$	1.72458	+	1.37531i	0.0910199	+	0.0725859i	−0.576923	+	0.816799i	$0.695747\pi$
$360$	11.2899	+	19.3302i	0.595029	+	1.01879i
$361$	−9.05633			−0.476649
$362$	−6.65745	−	19.7057i	−0.349908	−	1.03571i
$363$	25.5845	+	12.3209i	1.34284	+	0.646678i
$364$	3.61020	−	17.5633i	0.189226	−	0.920567i
$365$	45.3521	−	21.8404i	2.37384	−	1.14318i
$366$	−8.68794	−	8.87757i	−0.454126	−	0.464038i
$367$	−3.04611	+	13.3459i	−0.159006	+	0.696649i	0.831076	+	0.556158i	$0.187725\pi$
$367$	−3.04611	+	13.3459i	−0.159006	+	0.696649i	−0.990082	+	0.140491i	$0.955132\pi$
$368$	−0.138983	+	0.259328i	−0.00724497	+	0.0135184i
$369$	3.98126	+	8.26717i	0.207256	+	0.430372i
$370$	15.9768	+	16.3255i	0.830593	+	0.848722i
$371$	4.63272	−	2.48331i	0.240519	−	0.128927i
$372$	−3.04510	+	0.626182i	−0.157881	+	0.0324660i
$373$	−26.6728			−1.38107			−0.690534	−	0.723300i	$-0.742624\pi$
$373$	−26.6728			−1.38107			−0.690534	+	0.723300i	$0.742624\pi$
$374$	26.4088	−	8.92202i	1.36557	−	0.461347i
$375$	5.35556	−	11.1209i	0.276560	−	0.574283i
$376$	−0.632965	−	2.01608i	−0.0326427	−	0.103971i
$377$	−0.449963	−	0.102701i	−0.0231743	−	0.00528938i
$378$	15.3729	+	8.97698i	0.790696	+	0.461726i
$379$	−12.4333	+	2.83782i	−0.638656	+	0.145769i	−0.529574	−	0.848264i	$-0.677648\pi$
$379$	−12.4333	+	2.83782i	−0.638656	+	0.145769i	−0.109082	+	0.994033i	$0.534791\pi$
$380$	−4.68759	−	22.7956i	−0.240468	−	1.16939i
$381$	−7.33845	+	1.67495i	−0.375960	+	0.0858104i
$382$	−2.30361	−	0.834090i	−0.117863	−	0.0426757i
$383$	−2.28378	+	10.0059i	−0.116696	+	0.511277i	0.882467	+	0.470374i	$0.155881\pi$
$383$	−2.28378	+	10.0059i	−0.116696	+	0.511277i	−0.999163	+	0.0409038i	$0.986976\pi$
$384$	−1.95303	+	10.2788i	−0.0996650	+	0.524537i
$385$	−37.1430	+	50.9492i	−1.89298	+	2.59661i
$386$	0.340119	−	0.939352i	0.0173116	−	0.0478118i
$387$	10.7802	−	8.59691i	0.547987	−	0.437005i
$388$	−0.0369942	−	0.0188099i	−0.00187810	−	0.000954930i
$389$	−1.61330	−	2.02302i	−0.0817976	−	0.102571i	0.739249	−	0.673432i	$-0.235181\pi$
$389$	−1.61330	−	2.02302i	−0.0817976	−	0.102571i	−0.821046	+	0.570861i	$0.806609\pi$
$390$	−8.55054	−	13.9399i	−0.432974	−	0.705876i
$391$	0.224500			0.0113535
$392$	−19.5257	+	3.27809i	−0.986198	+	0.165568i
$393$	3.58680			0.180930
$394$	−10.7370	−	17.5045i	−0.540921	−	0.881862i
$395$	−36.8899	−	46.2585i	−1.85613	−	2.32752i
$396$	−24.6935	−	12.5556i	−1.24090	−	0.630942i
$397$	11.5515	−	9.21205i	0.579756	−	0.462340i	−0.289173	−	0.957277i	$-0.593380\pi$
$397$	11.5515	−	9.21205i	0.579756	−	0.462340i	0.868929	+	0.494937i	$0.164809\pi$
$398$	−6.02980	+	16.6533i	−0.302247	+	0.834754i
$399$	−5.06687	−	5.81849i	−0.253661	−	0.291289i
$400$	−31.6713	+	13.6006i	−1.58357	+	0.680032i
$401$	1.51328	−	6.63010i	0.0755694	−	0.331091i	−0.922985	−	0.384835i	$-0.874258\pi$
$401$	1.51328	−	6.63010i	0.0755694	−	0.331091i	0.998555	+	0.0537439i	$0.0171155\pi$
$402$	8.77499	+	3.17724i	0.437657	+	0.158466i
$403$	−5.55281	+	1.26739i	−0.276605	+	0.0631334i
$404$	−4.57720	−	22.2587i	−0.227724	−	1.10741i
$405$	−7.31912	+	1.67054i	−0.363690	+	0.0830099i
$406$	0.0734686	+	0.504306i	0.00364618	+	0.0250283i
$407$	−27.5589	−	6.29013i	−1.36604	−	0.311790i
$408$	7.61676	−	2.39135i	0.377086	−	0.118389i
$409$	4.60703	−	9.56660i	0.227803	−	0.473038i	−0.755468	−	0.655185i	$-0.772591\pi$
$409$	4.60703	−	9.56660i	0.227803	−	0.473038i	0.983271	+	0.182148i	$0.0583048\pi$
$410$	−21.1520	+	7.14604i	−1.04462	+	0.352918i
$411$	3.40793			0.168101
$412$	−26.0467	+	5.35613i	−1.28323	+	0.263878i
$413$	1.88591	−	2.58691i	0.0927994	−	0.127293i
$414$	−0.156049	−	0.159455i	−0.00766938	−	0.00783678i
$415$	−6.13709	−	12.7438i	−0.301258	−	0.625569i
$416$	−3.17072	+	18.9045i	−0.155457	+	0.926867i
$417$	−3.55623	+	15.5809i	−0.174149	+	0.762999i
$418$	20.1435	+	20.5832i	0.985252	+	1.00676i
$419$	22.4529	−	10.8127i	1.09690	−	0.528237i	0.204215	−	0.978926i	$-0.434536\pi$
$419$	22.4529	−	10.8127i	1.09690	−	0.528237i	0.892681	+	0.450689i	$0.148822\pi$
$420$	−10.9501	+	14.3586i	−0.534312	+	0.700627i
$421$	−28.7493	−	13.8449i	−1.40115	−	0.674761i	−0.427759	−	0.903893i	$-0.640697\pi$
$421$	−28.7493	−	13.8449i	−1.40115	−	0.674761i	−0.973395	+	0.229132i	$0.926411\pi$
$422$	2.59567	+	7.68306i	0.126355	+	0.374005i
$423$	1.60236			0.0779094
$424$	−4.85226	+	2.83399i	−0.235647	+	0.137631i
$425$	20.5623	+	16.3979i	0.997419	+	0.795415i
$426$	7.64023	−	0.777419i	0.370170	−	0.0376661i
$427$	−9.91354	+	23.0903i	−0.479750	+	1.11742i
$428$	15.4724	−	18.5650i	0.747889	−	0.897374i
$429$	18.2332	+	8.78065i	0.880307	+	0.423934i
$430$	17.5417	+	28.5982i	0.845936	+	1.37913i
$431$	25.7001	+	20.4951i	1.23793	+	0.987215i	0.999873	+	0.0159637i	$0.00508161\pi$
$431$	25.7001	+	20.4951i	1.23793	+	0.987215i	0.238056	+	0.971251i	$0.423490\pi$
$432$	−16.7740	−	8.98979i	−0.807042	−	0.432522i
$433$	−12.5837	+	10.0352i	−0.604734	+	0.482259i	−0.877342	−	0.479866i	$-0.840685\pi$
$433$	−12.5837	+	10.0352i	−0.604734	+	0.482259i	0.272608	+	0.962125i	$0.412114\pi$
$434$	3.51711	+	5.21375i	0.168827	+	0.250268i
$435$	0.363399	+	0.289801i	0.0174236	+	0.0138949i
$436$	−14.6979	−	3.69027i	−0.703900	−	0.176732i
$437$	0.100638	+	0.208977i	0.00481418	+	0.00999675i
$438$	−9.65407	+	15.0024i	−0.461289	+	0.716841i
$439$	−7.01383	−	30.7296i	−0.334752	−	1.46664i	−0.809811	−	0.586691i	$-0.800430\pi$
$439$	−7.01383	−	30.7296i	−0.334752	−	1.46664i	0.475059	−	0.879954i	$-0.342427\pi$
$440$	37.6905	−	55.8817i	1.79682	−	2.66406i
$441$	2.06349	−	14.8710i	0.0982613	−	0.708143i
$442$	13.8567	−	4.68139i	0.659096	−	0.222671i
$443$	28.8464	−	6.58401i	1.37054	−	0.312816i	0.526989	−	0.849872i	$-0.323321\pi$
$443$	28.8464	−	6.58401i	1.37054	−	0.312816i	0.843547	+	0.537056i	$0.180464\pi$
$444$	−7.85201	−	1.97144i	−0.372640	−	0.0935606i
$445$	18.6812	−	8.99639i	0.885574	−	0.426470i
$446$	−6.73599	−	4.33463i	−0.318958	−	0.205251i
$447$	9.33702	−	11.7083i	0.441626	−	0.553781i
$448$	20.7319	−	4.26492i	0.979489	−	0.201499i
$449$	2.38390	+	2.98932i	0.112503	+	0.141075i	0.834895	−	0.550410i	$-0.185528\pi$
$449$	2.38390	+	2.98932i	0.112503	+	0.141075i	−0.722391	+	0.691484i	$0.756957\pi$
$450$	−2.64587	−	26.0027i	−0.124727	−	1.22578i
$451$	17.2264	−	21.6012i	0.811160	−	1.01716i
$452$	2.93200	+	2.44359i	0.137910	+	0.114937i
$453$	−1.85260	+	3.84696i	−0.0870428	+	0.180746i
$454$	−10.3750	−	16.9143i	−0.486923	−	0.793829i
$455$	−19.4890	+	26.7331i	−0.913657	+	1.25327i
$456$	5.64041	+	6.01812i	0.264136	+	0.281824i
$457$	2.28262	−	2.86232i	0.106777	−	0.133894i	−0.725572	−	0.688147i	$-0.758425\pi$
$457$	2.28262	−	2.86232i	0.106777	−	0.133894i	0.832348	+	0.554253i	$0.186996\pi$
$458$	−3.86981	+	31.3043i	−0.180824	+	1.46275i
$459$			14.5213i			0.677798i
$460$	0.431633	−	0.329226i	0.0201250	−	0.0153502i
$461$	−5.12861	+	10.6497i	−0.238863	+	0.496005i	−0.985595	−	0.169120i	$-0.945907\pi$
$461$	−5.12861	+	10.6497i	−0.238863	+	0.496005i	0.746732	+	0.665125i	$0.231622\pi$
$462$	1.77988	−	22.2752i	0.0828076	−	1.03634i
$463$	−1.87583	−	3.89520i	−0.0871771	−	0.181025i	0.852822	−	0.522201i	$-0.174889\pi$
$463$	−1.87583	−	3.89520i	−0.0871771	−	0.181025i	−0.939999	+	0.341176i	$0.889175\pi$
$464$	−0.0981912	−	0.535896i	−0.00455841	−	0.0248783i
$465$	5.59215	+	1.27637i	0.259330	+	0.0591904i
$466$	−3.43668	−	33.7746i	−0.159201	−	1.56458i
$467$	−19.3485	+	9.31777i	−0.895344	+	0.431175i	−0.824205	−	0.566292i	$-0.808378\pi$
$467$	−19.3485	+	9.31777i	−0.895344	+	0.431175i	−0.0711387	+	0.997466i	$0.522663\pi$
$468$	−12.9567	−	6.58793i	−0.598925	−	0.304527i
$469$	−0.816484	−	18.8620i	−0.0377017	−	0.870964i
$470$	−0.478327	+	3.86936i	−0.0220636	+	0.178480i
$471$		−	8.67524i		−	0.399734i
$472$	−1.91371	+	2.83735i	−0.0880855	+	0.130600i
$473$	−37.4060	−	18.0138i	−1.71993	−	0.828274i
$474$	19.7169	+	7.13908i	0.905629	+	0.327909i
$475$	−6.04647	+	26.4913i	−0.277431	+	1.21551i
$476$	−10.3408	−	12.4056i	−0.473968	−	0.568612i
$477$	−0.948172	−	4.15421i	−0.0434138	−	0.190208i
$478$	−1.28298	+	10.3785i	−0.0586819	+	0.474700i
$479$	0.301045	+	1.31896i	0.0137551	+	0.0602650i	0.981340	−	0.192282i	$-0.0615889\pi$
$479$	0.301045	+	1.31896i	0.0137551	+	0.0602650i	−0.967585	+	0.252547i	$0.918732\pi$
$480$	11.1374	−	15.7675i	0.508351	−	0.719686i
$481$	−14.4602	−	3.30044i	−0.659327	−	0.150487i
$482$	11.3028	−	17.5645i	0.514829	−	0.800041i
$483$	0.0710012	−	0.165374i	0.00323067	−	0.00752477i
$484$	−1.32585	+	61.3986i	−0.0602658	+	2.79084i
$485$	0.0477426	+	0.0598673i	0.00216788	+	0.00271843i
$486$	16.3282	−	15.9794i	0.740664	−	0.724842i
$487$	19.1513	−	15.2727i	0.867830	−	0.692071i	−0.0847361	−	0.996403i	$-0.527005\pi$
$487$	19.1513	−	15.2727i	0.867830	−	0.692071i	0.952566	+	0.304332i	$0.0984333\pi$
$488$	9.68884	−	25.0554i	0.438593	−	1.13421i
$489$		−	12.9577i		−	0.585970i
$490$	35.2944	+	9.42210i	1.59444	+	0.425647i
$491$		−	35.9095i		−	1.62057i	−0.586035	−	0.810285i	$-0.699312\pi$
$491$		−	35.9095i		−	1.62057i	0.586035	−	0.810285i	$-0.300688\pi$
$492$	5.06598	−	6.07855i	0.228392	−	0.274042i
$493$	−0.325016	+	0.259192i	−0.0146380	+	0.0116734i
$494$	10.5693	+	10.8000i	0.475537	+	0.485916i
$495$	31.8681	+	39.9613i	1.43236	+	1.79613i
$496$	−3.96113	−	5.43260i	−0.177860	−	0.243931i
$497$	−7.33985	−	13.6928i	−0.329237	−	0.614207i
$498$	4.21562	+	2.71277i	0.188907	+	0.121562i
$499$	−16.5536	−	3.77824i	−0.741039	−	0.169137i	−0.164695	−	0.986345i	$-0.552664\pi$
$499$	−16.5536	−	3.77824i	−0.741039	−	0.169137i	−0.576344	+	0.817207i	$0.695521\pi$
$500$	26.6884	+	0.576312i	1.19354	+	0.0257734i
$501$	−2.25269	−	9.86968i	−0.100643	−	0.440945i
$502$	19.4955	+	2.41002i	0.870126	+	0.107564i
$503$	7.99820	+	35.0424i	0.356622	+	1.56246i	0.761544	+	0.648113i	$0.224441\pi$
$503$	7.99820	+	35.0424i	0.356622	+	1.56246i	−0.404922	+	0.914351i	$0.632701\pi$
$504$	−1.62350	+	15.9678i	−0.0723165	+	0.711261i
$505$	−9.32988	+	40.8769i	−0.415174	+	1.81900i
$506$	−0.228710	+	0.631658i	−0.0101674	+	0.0280806i
$507$	−1.26459	−	0.608993i	−0.0561623	−	0.0270463i
$508$	−9.87255	−	12.9435i	−0.438024	−	0.574273i
$509$			0.698915i			0.0309788i	0.999880	+	0.0154894i	$0.00493063\pi$
$509$			0.698915i			0.0309788i	−0.999880	+	0.0154894i	$0.995069\pi$
$510$	−14.6185	−	1.80712i	−0.647317	−	0.0800208i
$511$	35.5002	+	6.50175i	1.57044	+	0.287620i
$512$	−21.9819	+	5.36631i	−0.971471	+	0.237159i
$513$	−13.5173	+	6.50957i	−0.596801	+	0.287404i
$514$	−19.9468	+	2.02966i	−0.879816	+	0.0895243i
$515$	47.8332	+	10.9176i	2.10778	+	0.481088i
$516$	−10.5990	−	5.38914i	−0.466596	−	0.237244i
$517$	−2.09340	−	4.34698i	−0.0920675	−	0.191180i
$518$	2.36101	+	16.2066i	0.103737	+	0.712075i
$519$	4.26843	−	8.86350i	0.187363	−	0.389064i
$520$	19.7762	−	29.3212i	0.867246	−	1.28582i
$521$			15.8242i			0.693270i	0.938000	+	0.346635i	$0.112676\pi$
$521$			15.8242i			0.693270i	−0.938000	+	0.346635i	$0.887324\pi$
$522$	0.410011	+	0.0506852i	0.0179457	+	0.00221843i
$523$	−24.2933	+	30.4628i	−1.06227	+	1.33205i	−0.121655	+	0.992572i	$0.538820\pi$
$523$	−24.2933	+	30.4628i	−1.06227	+	1.33205i	−0.940616	+	0.339473i	$0.889751\pi$
$524$	3.21401	+	7.05994i	0.140405	+	0.308415i
$525$	18.5823	−	9.96078i	0.810997	−	0.434724i
$526$	20.5267	−	12.5908i	0.895007	−	0.548984i
$527$	−2.22588	+	4.62209i	−0.0969608	+	0.201341i
$528$	−1.03125	+	23.8668i	−0.0448792	+	1.03867i
$529$	14.3369	−	17.9779i	0.623343	−	0.781648i
$530$	10.3146	−	1.04955i	0.448038	−	0.0455893i
$531$	−1.61808	−	2.02900i	−0.0702185	−	0.0880512i
$532$	6.91234	−	15.1869i	0.299688	−	0.658436i
$533$	9.03871	−	11.3342i	0.391510	−	0.490938i
$534$	−3.97665	+	6.17970i	−0.172087	+	0.267422i
$535$	−40.1743	+	19.3469i	−1.73689	+	0.836440i
$536$	1.60918	+	20.1189i	0.0695061	+	0.869005i
$537$	−5.99092	+	1.36739i	−0.258527	+	0.0590071i
$538$	4.31728	+	12.7789i	0.186131	+	0.550939i
$539$	−43.0388	+	13.8302i	−1.85381	+	0.595709i
$540$	21.2952	+	27.9192i	0.916401	+	1.20145i
$541$	1.18246	+	5.18070i	0.0508379	+	0.222735i	0.993965	−	0.109697i	$-0.0349879\pi$
$541$	1.18246	+	5.18070i	0.0508379	+	0.222735i	−0.943127	+	0.332432i	$0.892131\pi$
$542$	−20.2498	−	13.0308i	−0.869803	−	0.559720i
$543$	−5.90145	−	12.2545i	−0.253255	−	0.525890i
$544$	11.5320	+	12.8493i	0.494432	+	0.550911i
$545$	21.8602	+	17.4329i	0.936386	+	0.746743i
$546$	0.933906	−	11.6878i	0.0399675	−	0.500193i
$547$	23.4023	−	18.6627i	1.00061	−	0.797960i	0.0211867	−	0.999776i	$-0.493256\pi$
$547$	23.4023	−	18.6627i	1.00061	−	0.797960i	0.979424	+	0.201815i	$0.0646841\pi$
$548$	3.05373	+	6.70786i	0.130449	+	0.286546i
$549$	15.9263	+	12.7008i	0.679717	+	0.542056i
$550$	−67.0852	+	41.1491i	−2.86052	+	1.75460i
$551$	−0.386967	−	0.186354i	−0.0164854	−	0.00793893i
$552$	−0.0693919	+	0.179448i	−0.00295351	+	0.00763781i
$553$	−1.83459	−	42.3818i	−0.0780149	−	1.80226i
$554$	2.63922	+	25.9375i	0.112130	+	1.10198i
$555$	11.6783	+	9.31314i	0.495716	+	0.395321i
$556$	−33.8546	+	6.96172i	−1.43575	+	0.295243i
$557$	5.13577			0.217610			0.108805	−	0.994063i	$-0.465298\pi$
$557$	5.13577			0.217610			0.108805	+	0.994063i	$0.465298\pi$
$558$	4.83010	−	1.63182i	0.204474	−	0.0690803i
$559$	−19.6269	−	9.45184i	−0.830131	−	0.399770i
$560$	−38.0742	−	8.68702i	−1.60893	−	0.367094i
$561$	16.4229	−	7.90887i	0.693377	−	0.333913i
$562$	−4.03936	+	3.95307i	−0.170390	+	0.166750i
$563$	8.55628	−	37.4875i	0.360604	−	1.57991i	−0.391060	−	0.920365i	$-0.627892\pi$
$563$	8.55628	−	37.4875i	0.360604	−	1.57991i	0.751664	−	0.659546i	$-0.229251\pi$
$564$	−0.572523	−	1.25761i	−0.0241076	−	0.0529550i
$565$	−3.05549	−	6.34478i	−0.128545	−	0.266927i
$566$	−19.2774	+	18.8657i	−0.810292	+	0.792983i
$567$	−4.94604	−	2.12352i	−0.207714	−	0.0891795i
$568$	8.37635	+	14.3417i	0.351464	+	0.601765i
$569$	38.1102			1.59766			0.798832	−	0.601554i	$-0.205452\pi$
$569$	38.1102			1.59766			0.798832	+	0.601554i	$0.205452\pi$
$570$	−4.87095	−	14.4178i	−0.204022	−	0.603894i
$571$	14.1050	−	29.2893i	0.590276	−	1.22572i	−0.365276	−	0.930899i	$-0.619025\pi$
$571$	14.1050	−	29.2893i	0.590276	−	1.22572i	0.955552	−	0.294822i	$-0.0952603\pi$
$572$	−0.944885	+	43.7566i	−0.0395076	+	1.82956i
$573$	−1.56191	−	0.356496i	−0.0652498	−	0.0148928i
$574$	−15.2730	−	4.79377i	−0.637483	−	0.200088i
$575$	−0.617940	+	0.141041i	−0.0257699	+	0.00588181i
$576$	1.11060	−	17.1223i	0.0462751	−	0.713428i
$577$	12.4254	−	2.83602i	0.517276	−	0.118065i	0.0440903	−	0.999028i	$-0.485961\pi$
$577$	12.4254	−	2.83602i	0.517276	−	0.118065i	0.473186	+	0.880963i	$0.343104\pi$
$578$	−3.69988	+	10.2184i	−0.153895	+	0.425031i
$579$	0.145369	−	0.636905i	0.00604135	−	0.0264689i
$580$	−0.244789	+	0.974962i	−0.0101643	+	0.0404831i
$581$	1.82697	−	9.97546i	0.0757956	−	0.413852i
$582$	−0.0255175	−	0.00923934i	−0.00105773	−	0.000382983i
$583$	−10.0311	+	7.99952i	−0.415445	+	0.331306i
$584$	−38.1800	−	5.55908i	−1.57990	−	0.230036i
$585$	16.7212	+	20.9677i	0.691336	+	0.866908i
$586$	−36.8194	+	22.5844i	−1.52099	+	0.932955i
$587$	20.0395			0.827119			0.413559	−	0.910477i	$-0.364285\pi$
$587$	20.0395			0.827119			0.413559	+	0.910477i	$0.364285\pi$
$588$	−12.4088	+	3.69388i	−0.511729	+	0.152333i
$589$	−5.30030			−0.218395
$590$	5.38264	−	3.30163i	0.221600	−	0.135926i
$591$	−8.37238	−	10.4986i	−0.344394	−	0.431856i
$592$	−3.15550	−	17.2217i	−0.129690	−	0.707809i
$593$	5.56296	−	4.43631i	0.228443	−	0.182178i	−0.502578	−	0.864532i	$-0.667615\pi$
$593$	5.56296	−	4.43631i	0.228443	−	0.182178i	0.731022	+	0.682354i	$0.239044\pi$
$594$	−40.8574	−	14.7936i	−1.67640	−	0.606989i
$595$	7.88091	+	28.7372i	0.323086	+	1.17811i
$596$	31.4120	+	7.88678i	1.28669	+	0.323055i
$597$	−2.57718	+	11.2914i	−0.105477	+	0.462125i
$598$	−0.120004	+	0.331432i	−0.00490734	+	0.0135532i
$599$	−18.9146	+	4.31714i	−0.772831	+	0.176394i	−0.590711	−	0.806883i	$-0.701153\pi$
$599$	−18.9146	+	4.31714i	−0.772831	+	0.176394i	−0.182119	+	0.983276i	$0.558296\pi$
$600$	−19.4629	+	11.3674i	−0.794569	+	0.464072i
$601$	−4.54718	+	1.03786i	−0.185483	+	0.0423354i	−0.314254	−	0.949339i	$-0.601754\pi$
$601$	−4.54718	+	1.03786i	−0.185483	+	0.0423354i	0.128770	+	0.991674i	$0.458897\pi$
$602$	−1.91594	+	23.9779i	−0.0780877	+	0.977267i
$603$	−14.9211	−	3.40564i	−0.607633	−	0.138688i
$604$	−9.23207	−	0.199358i	−0.375647	−	0.00811177i
$605$	49.1637	−	102.089i	1.99879	−	4.15052i
$606$	−4.75623	−	14.0782i	−0.193209	−	0.571889i
$607$	1.95223			0.0792387			0.0396193	−	0.999215i	$-0.487385\pi$
$607$	1.95223			0.0792387			0.0396193	+	0.999215i	$0.487385\pi$
$608$	−6.79134	+	16.4947i	−0.275425	+	0.668948i
$609$	0.0881380	+	0.321390i	0.00357153	+	0.0130234i
$610$	−35.4240	+	34.6673i	−1.43427	+	1.40364i
$611$	−1.09841	−	2.28087i	−0.0444368	−	0.0922740i
$612$	−11.9156	+	5.42453i	−0.481660	+	0.219274i
$613$	0.0117640	−	0.0515413i	0.000475142	−	0.00208173i	−0.974690	−	0.223562i	$-0.928232\pi$
$613$	0.0117640	−	0.0515413i	0.000475142	−	0.00208173i	0.975165	+	0.221480i	$0.0710887\pi$
$614$	25.8364	−	25.2845i	1.04267	−	1.02040i
$615$	−13.1539	+	6.33456i	−0.530415	+	0.255434i
$616$	45.4394	−	16.4567i	1.83081	−	0.663059i
$617$	−0.0762730	−	0.0367311i	−0.00307063	−	0.00147874i	0.432348	−	0.901707i	$-0.357685\pi$
$617$	−0.0762730	−	0.0367311i	−0.00307063	−	0.00147874i	−0.435418	+	0.900228i	$0.643400\pi$
$618$	−16.4740	+	5.56563i	−0.662682	+	0.223883i
$619$	−8.46533			−0.340250			−0.170125	−	0.985422i	$-0.554417\pi$
$619$	−8.46533			−0.340250			−0.170125	+	0.985422i	$0.554417\pi$
$620$	2.49864	+	12.1508i	0.100348	+	0.487988i
$621$	−0.273612	−	0.218198i	−0.0109797	−	0.00875598i
$622$	4.16803	+	40.9620i	0.167123	+	1.64243i
$623$	14.6231	+	2.67817i	0.585861	+	0.107298i
$624$	−0.541096	+	12.5229i	−0.0216612	+	0.501319i
$625$	−5.55724	−	2.67623i	−0.222290	−	0.107049i
$626$	38.3761	−	23.5393i	1.53382	−	0.940820i
$627$	14.7240	+	11.7420i	0.588021	+	0.468931i
$628$	17.0756	−	7.77358i	0.681389	−	0.310200i
$629$	−10.4448	+	8.32948i	−0.416463	+	0.332118i
$630$	14.9331	−	25.5726i	0.594949	−	1.01884i
$631$	7.63577	+	6.08932i	0.303975	+	0.242412i	0.763583	−	0.645710i	$-0.223438\pi$
$631$	7.63577	+	6.08932i	0.303975	+	0.242412i	−0.459608	+	0.888122i	$0.652010\pi$
$632$	3.61574	+	45.2061i	0.143827	+	1.79820i
$633$	2.30091	+	4.77789i	0.0914531	+	0.189904i
$634$	−17.3917	−	11.1916i	−0.690712	−	0.444475i
$635$	6.68352	+	29.2824i	0.265228	+	1.16204i
$636$	−2.92165	+	2.22847i	−0.115851	+	0.0883647i
$637$	−22.5825	+	7.25672i	−0.894752	+	0.287522i
$638$	−0.398156	−	1.17852i	−0.0157631	−	0.0466582i
$639$	−12.2785	+	2.80249i	−0.485730	+	0.110865i
$640$	41.0152	+	7.79312i	1.62127	+	0.308050i
$641$	−33.3571	+	16.0639i	−1.31753	+	0.634487i	−0.954756	−	0.297391i	$-0.903883\pi$
$641$	−33.3571	+	16.0639i	−1.31753	+	0.634487i	−0.362771	+	0.931878i	$0.618169\pi$
$642$	8.55188	−	13.2896i	0.337516	−	0.524498i
$643$	−3.60642	+	4.52230i	−0.142223	+	0.178342i	−0.847841	−	0.530250i	$-0.822098\pi$
$643$	−3.60642	+	4.52230i	−0.142223	+	0.178342i	0.705618	+	0.708592i	$0.250669\pi$
$644$	0.389129	−	0.00843358i	0.0153338	−	0.000332330i
$645$	13.6785	+	17.1523i	0.538590	+	0.675371i
$646$	13.5411	−	1.37785i	0.532766	−	0.0542107i
$647$	−8.59670	+	10.7799i	−0.337971	+	0.423802i	−0.921553	−	0.388252i	$-0.873079\pi$
$647$	−8.59670	+	10.7799i	−0.337971	+	0.423802i	0.583582	+	0.812054i	$0.301651\pi$
$648$	5.36697	+	2.07539i	0.210835	+	0.0815290i
$649$	−3.39048	+	7.04040i	−0.133088	+	0.276360i
$650$	−35.1997	+	21.5910i	−1.38065	+	0.846867i
$651$	2.70081	+	3.10145i	0.105853	+	0.121555i
$652$	25.5049	−	11.6110i	0.998847	−	0.454722i
$653$	10.6189	−	13.3156i	0.415548	−	0.521081i	−0.529369	−	0.848392i	$-0.677571\pi$
$653$	10.6189	−	13.3156i	0.415548	−	0.521081i	0.944917	+	0.327311i	$0.106143\pi$
$654$	−9.83465	−	1.21575i	−0.384565	−	0.0475396i
$655$		−	14.3123i		−	0.559229i
$656$	16.5039	+	4.52464i	0.644370	+	0.176658i
$657$	12.6941	−	26.3596i	0.495245	−	1.02839i
$658$	−1.91143	+	2.03975i	−0.0745153	+	0.0795177i
$659$	11.8943	+	24.6987i	0.463335	+	0.962124i	0.993457	+	0.114203i	$0.0364316\pi$
$659$	11.8943	+	24.6987i	0.463335	+	0.962124i	−0.530123	+	0.847921i	$0.677854\pi$
$660$	19.9771	−	39.2898i	0.777609	−	1.52935i
$661$	−20.6258	−	4.70770i	−0.802249	−	0.183108i	−0.198311	−	0.980139i	$-0.563546\pi$
$661$	−20.6258	−	4.70770i	−0.802249	−	0.183108i	−0.603938	+	0.797031i	$0.706403\pi$
$662$	−22.3319	+	2.27235i	−0.867955	+	0.0883174i
$663$	8.61713	−	4.14979i	0.334662	−	0.161164i
$664$	−1.56208	+	10.7285i	−0.0606207	+	0.416345i
$665$	−23.2174	+	20.2182i	−0.900332	+	0.784029i
$666$	13.1763	+	1.62884i	0.510570	+	0.0631162i
$667$		−	0.0100186i		−	0.000387922i
$668$	17.4080	−	13.2779i	0.673536	−	0.513736i
$669$	−4.71926	−	2.27268i	−0.182457	−	0.0878667i
$670$	12.6781	−	35.0147i	0.489796	−	1.35273i
$671$	13.6487	−	59.7987i	0.526901	−	2.30850i
$672$	13.1124	−	4.43108i	0.505821	−	0.170932i
$673$	5.67225	+	24.8517i	0.218649	+	0.957965i	0.958477	+	0.285169i	$0.0920496\pi$
$673$	5.67225	+	24.8517i	0.218649	+	0.957965i	−0.739828	+	0.672796i	$0.765093\pi$
$674$	29.1478	+	3.60322i	1.12273	+	0.138791i
$675$	−9.12292	−	39.9701i	−0.351141	−	1.53845i
$676$	0.0655337	−	3.03480i	0.00252053	−	0.116723i
$677$	−24.3338	−	5.55403i	−0.935223	−	0.213459i	−0.272357	−	0.962196i	$-0.587803\pi$
$677$	−24.3338	−	5.55403i	−0.935223	−	0.213459i	−0.662866	+	0.748738i	$0.730660\pi$
$678$	2.09884	+	1.35061i	0.0806055	+	0.0518699i
$679$	0.00237432	+	0.0548502i	9.11180e−5	+	0.00210496i
$680$	−9.54214	−	30.3930i	−0.365924	−	1.16552i
$681$	−8.09012	−	10.1447i	−0.310014	−	0.388745i
$682$	−10.7372	−	10.9715i	−0.411147	−	0.420121i
$683$	−25.3873	+	20.2457i	−0.971419	+	0.774681i	−0.974286	−	0.225315i	$-0.927659\pi$
$683$	−25.3873	+	20.2457i	−0.971419	+	0.774681i	0.00286675	+	0.999996i	$0.499087\pi$
$684$	−10.3909	−	8.66001i	−0.397307	−	0.331124i
$685$		−	13.5986i		−	0.519575i
$686$	16.4688	+	20.3661i	0.628781	+	0.777583i
$687$			20.6263i			0.786941i
$688$	1.11007	−	25.6912i	0.0423212	−	0.979468i
$689$	−5.26332	+	4.19735i	−0.200516	+	0.159906i
$690$	0.253708	−	0.248288i	0.00965849	−	0.00945217i
$691$	−21.5649	−	27.0416i	−0.820369	−	1.02871i	−0.998996	−	0.0447931i	$-0.985737\pi$
$691$	−21.5649	−	27.0416i	−0.820369	−	1.02871i	0.178628	−	0.983917i	$-0.442834\pi$
$692$	21.2709	+	0.459326i	0.808598	+	0.0174610i
$693$	1.58485	+	36.6123i	0.0602035	+	1.39079i
$694$	−1.61122	+	2.50383i	−0.0611611	+	0.0950440i
$695$	62.1720	+	14.1904i	2.35832	+	0.538271i
$696$	−0.106717	−	0.339907i	−0.00404509	−	0.0128841i
$697$	−2.90560	−	12.7303i	−0.110057	−	0.482193i
$698$	−1.70491	+	13.7917i	−0.0645319	+	0.522022i
$699$	−4.93994	−	21.6433i	−0.186846	−	0.818624i
$700$	36.2568	+	27.6502i	1.37038	+	1.04508i
$701$	1.73982	−	7.62266i	0.0657121	−	0.287904i	−0.931386	−	0.364034i	$-0.881399\pi$
$701$	1.73982	−	7.62266i	0.0657121	−	0.287904i	0.997098	+	0.0761300i	$0.0242564\pi$
$702$	−21.4379	−	7.76222i	−0.809123	−	0.292966i
$703$	−12.4357	−	5.98872i	−0.469021	−	0.225869i
$704$	−47.9014	+	19.3564i	−1.80535	+	0.729523i
$705$			2.54951i			0.0960199i
$706$	2.80291	−	22.6738i	0.105489	−	0.853338i
$707$	−22.6706	+	19.7420i	−0.852615	+	0.742476i
$708$	−1.01432	+	1.99491i	−0.0381206	+	0.0749732i
$709$	−4.04001	+	1.94557i	−0.151726	+	0.0730673i	−0.508206	−	0.861236i	$-0.669691\pi$
$709$	−4.04001	+	1.94557i	−0.151726	+	0.0730673i	0.356480	+	0.934303i	$0.383977\pi$
$710$	−3.10212	−	30.4866i	−0.116420	−	1.14414i
$711$	−33.5268	−	7.65228i	−1.25735	−	0.286983i
$712$	−15.7269	−	2.28987i	−0.589391	−	0.0858164i
$713$	−0.0536435	−	0.111392i	−0.00200896	−	0.00417166i
$714$	−7.70619	−	7.22139i	−0.288397	−	0.270254i
$715$	35.0372	−	72.7555i	1.31032	−	2.72090i
$716$	−8.05970	−	10.5667i	−0.301205	−	0.394896i
$717$			6.83832i			0.255382i
$718$	−0.382717	+	3.09594i	−0.0142829	+	0.115539i
$719$	−8.63837	+	10.8322i	−0.322157	+	0.403972i	−0.916368	−	0.400337i	$-0.868893\pi$
$719$	−8.63837	+	10.8322i	−0.322157	+	0.403972i	0.594211	+	0.804309i	$0.297464\pi$
$720$	−14.9544	+	27.9034i	−0.557318	+	1.03990i
$721$	23.1017	+	26.5286i	0.860352	+	0.987977i
$722$	−6.69658	−	10.9174i	−0.249221	−	0.406304i
$723$	5.92614	−	12.3058i	0.220395	−	0.457656i
$724$	18.8325	−	22.5967i	0.699906	−	0.839800i
$725$	0.731776	−	0.917618i	0.0271775	−	0.0340795i
$726$	4.06532	+	39.9527i	0.150878	+	1.48278i
$727$	4.51607	+	5.66297i	0.167492	+	0.210028i	0.858493	−	0.512826i	$-0.171401\pi$
$727$	4.51607	+	5.66297i	0.167492	+	0.210028i	−0.691001	+	0.722854i	$0.742830\pi$
$728$	23.8421	−	8.63484i	0.883647	−	0.320028i
$729$	5.50933	−	6.90848i	0.204049	−	0.255870i
$730$	59.8636	+	38.5224i	2.21565	+	1.42578i
$731$	−17.6783	+	8.51342i	−0.653855	+	0.314880i
$732$	4.27775	−	17.0377i	0.158110	−	0.629732i
$733$	17.8387	−	4.07158i	0.658889	−	0.150387i	0.120013	−	0.992772i	$-0.461706\pi$
$733$	17.8387	−	4.07158i	0.658889	−	0.150387i	0.538876	+	0.842385i	$0.318849\pi$
$734$	−18.3409	+	6.19634i	−0.676974	+	0.228711i
$735$	23.6612	+	3.28321i	0.872755	+	0.121103i
$736$	−0.415389	+	0.0242125i	−0.0153114	+	0.000892484i
$737$	10.2546	+	44.9281i	0.377731	+	1.65495i
$738$	−7.02220	+	10.9125i	−0.258491	+	0.401693i
$739$	20.8029	+	43.1978i	0.765249	+	1.58906i	0.807443	+	0.589946i	$0.200851\pi$
$739$	20.8029	+	43.1978i	0.765249	+	1.58906i	−0.0421941	+	0.999109i	$0.513435\pi$
$740$	−7.86661	+	31.3317i	−0.289182	+	1.15178i
$741$	7.72571	+	6.16105i	0.283811	+	0.226332i
$742$	6.41923	+	3.74850i	0.235657	+	0.137612i
$743$	18.3337	−	14.6206i	0.672599	−	0.536379i	−0.226563	−	0.973997i	$-0.572749\pi$
$743$	18.3337	−	14.6206i	0.672599	−	0.536379i	0.899161	+	0.437617i	$0.144177\pi$
$744$	−3.00652	−	3.20785i	−0.110224	−	0.117606i
$745$	−46.7192	−	37.2573i	−1.71166	−	1.36500i
$746$	−19.7229	−	32.1541i	−0.722106	−	1.17725i
$747$	−7.40698	−	3.56701i	−0.271007	−	0.130510i
$748$	30.2831	+	25.2385i	1.10726	+	0.922813i
$749$	−31.4472	−	5.75945i	−1.14906	−	0.210446i
$750$	17.3664	−	1.76709i	0.634132	−	0.0645250i
$751$	22.7595	+	18.1501i	0.830504	+	0.662305i	0.943530	−	0.331287i	$-0.107483\pi$
$751$	22.7595	+	18.1501i	0.830504	+	0.662305i	−0.113026	+	0.993592i	$0.536054\pi$
$752$	1.96235	−	2.25380i	0.0715595	−	0.0821878i
$753$	12.8455			0.468116
$754$	−0.208913	−	0.618372i	−0.00760815	−	0.0225198i
$755$	15.3505	+	7.39239i	0.558660	+	0.269037i
$756$	0.545508	+	25.1699i	0.0198399	+	0.915422i
$757$	11.8143	−	5.68947i	0.429399	−	0.206787i	−0.206685	−	0.978408i	$-0.566268\pi$
$757$	11.8143	−	5.68947i	0.429399	−	0.206787i	0.636084	+	0.771620i	$0.280553\pi$
$758$	−12.6146	−	12.8900i	−0.458184	−	0.468185i
$759$	−0.0977523	+	0.428281i	−0.00354818	+	0.0155456i
$760$	24.0140	−	22.5068i	0.871078	−	0.816408i
$761$	−17.8610	−	37.0887i	−0.647459	−	1.34446i	−0.923604	−	0.383347i	$-0.874771\pi$
$761$	−17.8610	−	37.0887i	−0.647459	−	1.34446i	0.276145	−	0.961116i	$-0.410943\pi$
$762$	−7.44547	−	7.60799i	−0.269721	−	0.275608i
$763$	5.30192	+	19.3331i	0.191942	+	0.699906i
$764$	−0.697880	−	3.39377i	−0.0252484	−	0.122782i
$765$	24.1560			0.873363
$766$	−13.7508	+	4.64562i	−0.496838	+	0.167853i
$767$	−1.77899	+	3.69411i	−0.0642355	+	0.133386i
$768$	−13.8352	+	5.24613i	−0.499236	+	0.189304i
$769$	−33.0195	−	7.53649i	−1.19071	−	0.271773i	−0.419146	−	0.907919i	$-0.637670\pi$
$769$	−33.0195	−	7.53649i	−1.19071	−	0.271773i	−0.771569	+	0.636146i	$0.780528\pi$
$770$	−88.8843	−	7.10222i	−3.20317	−	0.255946i
$771$	−12.7822	+	2.91746i	−0.460340	+	0.105070i
$772$	1.38389	−	0.284577i	0.0498072	−	0.0102421i
$773$	−40.7221	+	9.29456i	−1.46467	+	0.334302i	−0.879225	−	0.476407i	$-0.841939\pi$
$773$	−40.7221	+	9.29456i	−1.46467	+	0.334302i	−0.585449	+	0.810709i	$0.699082\pi$
$774$	18.3348	+	6.63865i	0.659032	+	0.238622i
$775$	3.22297	−	14.1207i	0.115772	−	0.507232i
$776$	−0.00467947	−	0.0585054i	−0.000167983	−	0.00210022i
$777$	2.83243	+	10.3283i	0.101613	+	0.370525i
$778$	1.24581	−	3.44073i	0.0446646	−	0.123356i
$779$	10.5475	−	8.41137i	0.377904	−	0.301368i
$780$	10.4820	−	20.6154i	0.375317	−	0.738149i
$781$	23.6440	+	29.6486i	0.846049	+	1.06091i
$782$	0.166004	+	0.270636i	0.00593629	+	0.00967791i
$783$	0.648032			0.0231588
$784$	−18.3898	−	21.1144i	−0.656778	−	0.754084i
$785$	−34.6166			−1.23552
$786$	2.65221	+	4.32390i	0.0946013	+	0.154228i
$787$	23.9800	+	30.0700i	0.854794	+	1.07188i	0.996633	+	0.0819883i	$0.0261270\pi$
$787$	23.9800	+	30.0700i	0.854794	+	1.07188i	−0.141839	+	0.989890i	$0.545302\pi$
$788$	13.1623	−	25.8869i	0.468889	−	0.922182i
$789$	12.3113	−	9.81791i	0.438293	−	0.349527i
$790$	28.4869	−	78.6760i	1.01352	−	2.79917i
$791$	0.909598	−	4.96650i	0.0323416	−	0.176589i
$792$	−3.12353	−	39.0522i	−0.110990	−	1.38766i
$793$	7.16147	−	31.3764i	0.254311	−	1.11421i
$794$	19.6468	+	7.11368i	0.697238	+	0.252455i
$795$	6.60975	−	1.50863i	0.234424	−	0.0535056i
$796$	−24.5342	+	5.04512i	−0.869593	+	0.178819i
$797$	51.6081	−	11.7792i	1.82805	−	0.417241i	0.836611	−	0.547797i	$-0.184533\pi$
$797$	51.6081	−	11.7792i	1.82805	−	0.417241i	0.991441	+	0.130556i	$0.0416761\pi$
$798$	3.26757	−	10.4105i	0.115671	−	0.368528i
$799$	−2.22305	−	0.507398i	−0.0786460	−	0.0179504i
$800$	−39.8145	−	28.1230i	−1.40766	−	0.994300i
$801$	5.22890	−	10.8579i	0.184754	−	0.383646i
$802$	9.11156	−	3.07828i	0.321740	−	0.108698i
$803$	−88.0943			−3.10878
$804$	2.65838	+	12.9276i	0.0937540	+	0.455922i
$805$	−0.659888	−	0.283314i	−0.0232580	−	0.00998552i
$806$	−5.63380	−	5.75677i	−0.198442	−	0.202774i
$807$	3.82702	+	7.94689i	0.134717	+	0.279744i
$808$	23.4484	−	21.9767i	0.824912	−	0.773139i
$809$	−4.89749	+	21.4573i	−0.172187	+	0.754399i	0.812909	+	0.582391i	$0.197883\pi$
$809$	−4.89749	+	21.4573i	−0.172187	+	0.754399i	−0.985096	+	0.172008i	$0.944974\pi$
$810$	−7.42587	−	7.58795i	−0.260918	−	0.266613i
$811$	19.6919	−	9.48313i	0.691477	−	0.332998i	−0.0549277	−	0.998490i	$-0.517493\pi$
$811$	19.6919	−	9.48313i	0.691477	−	0.332998i	0.746404	+	0.665493i	$0.231779\pi$
$812$	−0.553617	+	0.461469i	−0.0194281	+	0.0161944i
$813$	−14.1871	−	6.83213i	−0.497562	−	0.239613i
$814$	−12.7953	−	37.8734i	−0.448474	−	1.32746i
$815$	−51.7050			−1.81115
$816$	8.51489	+	7.41377i	0.298081	+	0.259534i
$817$	−15.8495	−	12.6396i	−0.554504	−	0.442202i
$818$	14.9392	−	1.52011i	0.522335	−	0.0531494i
$819$	0.831573	+	19.2105i	0.0290575	+	0.671270i
$820$	−24.2551	−	20.2147i	−0.847025	−	0.705927i
$821$	21.0119	+	10.1188i	0.733321	+	0.353149i	0.762989	−	0.646411i	$-0.223731\pi$
$821$	21.0119	+	10.1188i	0.733321	+	0.353149i	−0.0296686	+	0.999560i	$0.509445\pi$
$822$	2.51995	+	4.10826i	0.0878933	+	0.143292i
$823$	−23.1352	−	18.4497i	−0.806443	−	0.643117i	0.130950	−	0.991389i	$-0.458197\pi$
$823$	−23.1352	−	18.4497i	−0.806443	−	0.643117i	−0.937394	+	0.348272i	$0.886769\pi$
$824$	−25.7167	−	27.4388i	−0.895883	−	0.955875i
$825$	−40.2356	+	32.0868i	−1.40082	+	1.11712i
$826$	4.51303	+	0.360610i	0.157028	+	0.0125472i
$827$	−14.0089	−	11.1717i	−0.487137	−	0.388479i	0.348893	−	0.937163i	$-0.386558\pi$
$827$	−14.0089	−	11.1717i	−0.487137	−	0.388479i	−0.836030	+	0.548684i	$0.815129\pi$
$828$	0.0768349	−	0.306024i	0.00267020	−	0.0106351i
$829$	22.9695	+	47.6966i	0.797763	+	1.65657i	0.753406	+	0.657556i	$0.228410\pi$
$829$	22.9695	+	47.6966i	0.797763	+	1.65657i	0.0443567	+	0.999016i	$0.485876\pi$
$830$	10.8247	−	16.8215i	0.375730	−	0.583883i
$831$	3.79366	+	16.6211i	0.131601	+	0.576580i
$832$	−25.1339	+	10.1563i	−0.871361	+	0.352108i
$833$	−7.57181	+	19.9781i	−0.262348	+	0.692199i
$834$	−21.4124	+	7.23402i	−0.741450	+	0.250494i
$835$	−39.3827	+	8.98885i	−1.36290	+	0.311072i
$836$	−9.91823	+	39.5030i	−0.343029	+	1.36624i
$837$	7.20514	−	3.46981i	0.249046	−	0.119934i
$838$	29.6373	+	19.0717i	1.02380	+	0.658820i
$839$	8.93086	−	11.1990i	0.308328	−	0.386631i	−0.603391	−	0.797445i	$-0.706184\pi$
$839$	8.93086	−	11.1990i	0.308328	−	0.386631i	0.911719	+	0.410815i	$0.134756\pi$
$840$	−25.4062	−	2.58315i	−0.876598	−	0.0891270i
$841$	−18.0696	−	22.6586i	−0.623091	−	0.781331i
$842$	−4.56819	−	44.8948i	−0.157430	−	1.54718i
$843$	−2.30431	+	2.88952i	−0.0793648	+	0.0995203i
$844$	−7.34261	+	8.81021i	−0.252743	+	0.303260i
$845$	−2.43005	+	5.04605i	−0.0835963	+	0.173590i
$846$	1.18484	+	1.93165i	0.0407357	+	0.0664114i
$847$	71.6033	−	38.3819i	2.46032	−	1.31882i
$848$	−7.00431	−	3.75385i	−0.240529	−	0.128908i
$849$	−10.9971	+	13.7900i	−0.377420	+	0.473270i
$850$	−4.56316	+	36.9131i	−0.156515	+	1.26611i
$851$		−	0.321961i		−	0.0110367i
$852$	6.58664	+	8.63546i	0.225655	+	0.295846i
$853$	17.9730	−	37.3214i	0.615385	−	1.27786i	−0.327535	−	0.944839i	$-0.606218\pi$
$853$	17.9730	−	37.3214i	0.615385	−	1.27786i	0.942920	−	0.333020i	$-0.108068\pi$
$854$	−35.1659	+	5.12305i	−1.20335	+	0.175307i
$855$	10.8286	+	22.4858i	0.370329	+	0.768997i
$856$	33.8210	+	4.92441i	1.15598	+	0.168313i
$857$	48.0746	+	10.9727i	1.64220	+	0.374821i	0.941069	−	0.338215i	$-0.109823\pi$
$857$	48.0746	+	10.9727i	1.64220	+	0.374821i	0.701128	+	0.713036i	$0.252680\pi$
$858$	2.89721	+	28.4729i	0.0989092	+	0.972048i
$859$	36.7574	−	17.7014i	1.25415	−	0.603965i	0.315526	−	0.948917i	$-0.397819\pi$
$859$	36.7574	−	17.7014i	1.25415	−	0.603965i	0.938620	+	0.344952i	$0.112105\pi$
$860$	−21.5042	+	42.2931i	−0.733286	+	1.44218i
$861$	−10.2964	−	1.88576i	−0.350902	−	0.0642664i
$862$	−5.70333	+	46.1363i	−0.194256	+	1.57141i
$863$		−	51.6283i		−	1.75745i	−0.477329	−	0.878725i	$-0.658395\pi$
$863$		−	51.6283i		−	1.75745i	0.477329	−	0.878725i	$-0.341605\pi$
$864$	−1.56613	−	26.8685i	−0.0532809	−	0.914086i
$865$	−35.3678	−	17.0322i	−1.20254	−	0.579113i
$866$	−21.4023	−	7.74930i	−0.727278	−	0.263332i
$867$	−1.58136	+	6.92837i	−0.0537056	+	0.235300i
$868$	−3.68450	+	8.09512i	−0.125060	+	0.274766i
$869$	23.0414	+	100.951i	0.781627	+	3.42453i
$870$	−0.0806450	+	0.652367i	−0.00273412	+	0.0221173i
$871$	5.38057	+	23.5738i	0.182314	+	0.798769i
$872$	−6.41952	−	20.4470i	−0.217392	−	0.692423i
$873$	0.0433902	+	0.00990352i	0.00146853	+	0.000335183i
$874$	−0.177507	+	0.275845i	−0.00600426	+	0.00933060i
$875$	−16.6836	−	31.1241i	−0.564010	−	1.05219i
$876$	−25.2240	−	0.544689i	−0.852238	−	0.0184033i
$877$	−30.9616	−	38.8246i	−1.04550	−	1.31101i	−0.948861	−	0.315693i	$-0.897763\pi$
$877$	−30.9616	−	38.8246i	−1.04550	−	1.31101i	−0.0966364	−	0.995320i	$-0.530808\pi$
$878$	31.8583	−	31.1778i	1.07517	−	1.05220i
$879$	−22.0831	+	17.6107i	−0.744844	+	0.593993i
$880$	95.2353	+	4.11496i	3.21038	+	0.138715i
$881$			48.6937i			1.64053i	0.571981	+	0.820267i	$0.306175\pi$
$881$			48.6937i			1.64053i	−0.571981	+	0.820267i	$0.693825\pi$
$882$	19.4528	−	8.50862i	0.655011	−	0.286500i
$883$		−	22.8933i		−	0.770422i	−0.922829	−	0.385211i	$-0.874129\pi$
$883$		−	22.8933i		−	0.770422i	0.922829	−	0.385211i	$-0.125871\pi$
$884$	15.8896	+	13.2427i	0.534424	+	0.445400i
$885$	3.22834	−	2.57451i	0.108519	−	0.0865413i
$886$	29.2672	+	29.9060i	0.983249	+	1.00471i
$887$	−20.6967	−	25.9529i	−0.694928	−	0.871412i	0.301706	−	0.953401i	$-0.402444\pi$
$887$	−20.6967	−	25.9529i	−0.694928	−	0.871412i	−0.996633	+	0.0819895i	$0.973873\pi$
$888$	−3.42948	−	10.9234i	−0.115086	−	0.366564i
$889$	−8.49581	+	19.7882i	−0.284940	+	0.663675i
$890$	24.6587	+	15.8679i	0.826562	+	0.531895i
$891$	12.8091	+	2.92360i	0.429122	+	0.0979442i
$892$	0.244562	−	11.3254i	0.00818855	−	0.379203i
$893$	−0.524229	−	2.29680i	−0.0175426	−	0.0768593i
$894$	21.0184	+	2.59828i	0.702962	+	0.0868995i
$895$	5.45626	+	23.9054i	0.182383	+	0.799070i
$896$	20.4713	+	21.8387i	0.683897	+	0.729579i
$897$	−0.0512907	+	0.224719i	−0.00171255	+	0.00750316i
$898$	−1.84088	+	5.08421i	−0.0614311	+	0.169662i
$899$	0.206266	+	0.0993325i	0.00687936	+	0.00331292i
$900$	29.3899	−	22.4170i	0.979663	−	0.747233i
$901$			6.06365i			0.202009i
$902$	38.7782	+	4.79372i	1.29117	+	0.159613i
$903$	0.680254	+	15.7148i	0.0226374	+	0.522957i
$904$	−0.777719	+	5.34141i	−0.0258665	+	0.177652i
$905$	−48.8988	+	23.5484i	−1.62545	+	0.782776i
$906$	−6.00740	+	0.611273i	−0.199583	+	0.0203082i
$907$	−7.64236	−	1.74432i	−0.253760	−	0.0579192i	0.0937482	−	0.995596i	$-0.470115\pi$
$907$	−7.64236	−	1.74432i	−0.253760	−	0.0579192i	−0.347509	+	0.937677i	$0.612972\pi$
$908$	12.7186	−	25.0142i	0.422082	−	0.830124i
$909$	10.5735	+	21.9562i	0.350702	+	0.728241i
$910$	−46.6377	−	3.72654i	−1.54602	−	0.123534i
$911$	−25.0671	+	52.0523i	−0.830509	+	1.72457i	−0.154086	+	0.988057i	$0.549243\pi$
$911$	−25.0671	+	52.0523i	−0.830509	+	1.72457i	−0.676424	+	0.736513i	$0.736471\pi$
$912$	−3.08412	+	11.2495i	−0.102126	+	0.372509i
$913$			24.7542i			0.819246i
$914$	5.13838	+	0.635202i	0.169963	+	0.0210106i
$915$	−20.2081	+	25.3402i	−0.668061	+	0.837722i
$916$	−40.5989	+	18.4825i	−1.34142	+	0.610678i
$917$	6.04510	−	8.29209i	0.199627	−	0.273829i
$918$	−17.5055	+	10.7376i	−0.577767	+	0.354394i
$919$	−2.53282	+	5.25945i	−0.0835499	+	0.173493i	−0.938558	−	0.345121i	$-0.887838\pi$
$919$	−2.53282	+	5.25945i	−0.0835499	+	0.173493i	0.855008	+	0.518615i	$0.173552\pi$
$920$	0.716047	+	0.276893i	0.0236074	+	0.00912888i
$921$	14.7388	−	18.4819i	0.485660	−	0.608998i
$922$	−16.6305	+	1.69221i	−0.547696	+	0.0557299i
$923$	12.4060	+	15.5567i	0.408349	+	0.512054i
$924$	28.1689	−	14.3255i	0.926689	−	0.471273i
$925$	23.5166	−	29.4889i	0.773220	−	0.969588i
$926$	3.30861	−	5.14157i	0.108728	−	0.168962i
$927$	25.6926	−	12.3729i	0.843857	−	0.406380i
$928$	0.573417	−	0.514631i	0.0188233	−	0.0168936i
$929$	12.6295	−	2.88261i	0.414361	−	0.0945753i	−0.0102577	−	0.999947i	$-0.503265\pi$
$929$	12.6295	−	2.88261i	0.414361	−	0.0945753i	0.424619	+	0.905372i	$0.360408\pi$
$930$	2.59637	+	7.68515i	0.0851384	+	0.252006i
$931$	−21.9909	+	1.90743i	−0.720724	+	0.0625136i
$932$	38.1742	−	29.1171i	1.25044	−	0.953763i
$933$	5.99118	+	26.2491i	0.196142	+	0.859356i
$934$	−25.5396	−	16.4348i	−0.835681	−	0.537763i
$935$	−31.5586	−	65.5320i	−1.03208	−	2.14313i
$936$	−1.63892	−	20.4907i	−0.0535698	−	0.669760i
$937$	11.7522	+	9.37206i	0.383927	+	0.306172i	0.796368	−	0.604813i	$-0.206752\pi$
$937$	11.7522	+	9.37206i	0.383927	+	0.306172i	−0.412440	+	0.910985i	$0.635323\pi$
$938$	22.1344	−	14.9315i	0.722713	−	0.487531i
$939$	23.0168	−	18.3553i	0.751124	−	0.599001i
$940$	−5.01822	+	2.28452i	−0.163676	+	0.0745130i
$941$	13.4249	+	10.7060i	0.437639	+	0.349006i	0.817392	−	0.576082i	$-0.195419\pi$
$941$	13.4249	+	10.7060i	0.437639	+	0.349006i	−0.379752	+	0.925088i	$0.623991\pi$
$942$	10.4580	−	6.41479i	0.340741	−	0.209005i
$943$	0.283524	+	0.136538i	0.00923281	+	0.00444629i
$944$	−4.83550	−	0.208934i	−0.157382	−	0.00680022i
$945$	18.3256	−	42.6834i	0.596131	−	1.38849i
$946$	−5.94372	−	58.4130i	−0.193247	−	1.89917i
$947$	11.8517	+	9.45145i	0.385130	+	0.307131i	0.796847	−	0.604181i	$-0.206499\pi$
$947$	11.8517	+	9.45145i	0.385130	+	0.307131i	−0.411717	+	0.911312i	$0.635071\pi$
$948$	5.97324	+	29.0477i	0.194002	+	0.943425i
$949$	−46.2232			−1.50047
$950$	−36.4063	+	12.2996i	−1.18118	+	0.399052i
$951$	−12.1847	−	5.86783i	−0.395115	−	0.190277i
$952$	7.30869	−	21.6390i	0.236876	−	0.701324i
$953$	−12.9076	+	6.21599i	−0.418120	+	0.201356i	−0.631101	−	0.775700i	$-0.717397\pi$
$953$	−12.9076	+	6.21599i	−0.418120	+	0.201356i	0.212982	+	0.977056i	$0.431683\pi$
$954$	4.30680	−	4.21480i	0.139438	−	0.136459i
$955$	−1.42252	+	6.23246i	−0.0460316	+	0.201678i
$956$	−13.4599	+	6.12758i	−0.435325	+	0.198180i
$957$	−0.352943	−	0.732893i	−0.0114090	−	0.0236911i
$958$	−1.36741	+	1.33820i	−0.0441790	+	0.0432353i
$959$	5.74363	−	7.87857i	0.185472	−	0.254412i
$960$	27.2432	+	1.76707i	0.879270	+	0.0570320i
$961$	−28.1748			−0.908863
$962$	−6.71369	−	19.8722i	−0.216458	−	0.640706i
$963$	−11.2449	+	23.3502i	−0.362360	+	0.752449i
$964$	29.5317	+	0.637711i	0.951153	+	0.0205393i
$965$	−2.54143	−	0.580064i	−0.0818114	−	0.0186729i
$966$	0.251859	−	0.0366915i	0.00810344	−	0.00118053i
$967$	−22.4883	+	5.13280i	−0.723174	+	0.165060i	−0.568238	−	0.822865i	$-0.692375\pi$
$967$	−22.4883	+	5.13280i	−0.723174	+	0.165060i	−0.154937	+	0.987924i	$0.549517\pi$
$968$	−74.9965	+	43.8020i	−2.41048	+	1.40785i
$969$	8.67731	−	1.98054i	0.278755	−	0.0636241i
$970$	−0.0368675	+	0.101822i	−0.00118374	+	0.00326930i
$971$	0.700907	−	3.07088i	0.0224932	−	0.0985491i	−0.962435	−	0.271511i	$-0.912477\pi$
$971$	0.700907	−	3.07088i	0.0224932	−	0.0985491i	0.984929	+	0.172962i	$0.0553338\pi$
$972$	31.3369	+	7.86792i	1.00513	+	0.252364i
$973$	30.0268	+	34.4810i	0.962615	+	1.10541i
$974$	32.5724	+	11.7938i	1.04369	+	0.377897i
$975$	−21.1117	+	16.8360i	−0.676114	+	0.539183i
$976$	37.3686	−	6.84698i	1.19614	−	0.219167i
$977$	4.61173	+	5.78292i	0.147542	+	0.185012i	0.850111	−	0.526604i	$-0.176535\pi$
$977$	4.61173	+	5.78292i	0.147542	+	0.185012i	−0.702568	+	0.711616i	$0.747964\pi$
$978$	15.6206	−	9.58143i	0.499491	−	0.306380i
$979$	−36.2873			−1.15975
$980$	14.7396	+	49.5145i	0.470839	+	1.58168i
$981$	16.2511			0.518857
$982$	43.2889	−	26.5528i	1.38140	−	0.847333i
$983$	−10.3836	−	13.0206i	−0.331184	−	0.415292i	0.588161	−	0.808744i	$-0.299852\pi$
$983$	−10.3836	−	13.0206i	−0.331184	−	0.415292i	−0.919345	+	0.393452i	$0.871281\pi$
$984$	11.0737	+	1.61235i	0.353016	+	0.0513998i
$985$	−41.8924	+	33.4081i	−1.33480	+	1.06447i
$986$	−0.552785	−	0.200152i	−0.0176043	−	0.00637413i
$987$	−1.07683	+	1.47710i	−0.0342760	+	0.0470166i
$988$	−5.20410	+	20.7273i	−0.165565	+	0.659423i
$989$	0.105224	−	0.461018i	0.00334594	−	0.0146595i
$990$	−24.6090	+	67.9658i	−0.782124	+	2.16009i
$991$	1.39714	−	0.318889i	0.0443818	−	0.0101298i	−0.200272	−	0.979740i	$-0.564183\pi$
$991$	1.39714	−	0.318889i	0.0443818	−	0.0101298i	0.244654	+	0.969610i	$0.421326\pi$
$992$	3.62001	−	8.79221i	0.114935	−	0.279153i
$993$	−14.3106	+	3.26631i	−0.454134	+	0.103653i
$994$	11.0794	−	18.9732i	0.351416	−	0.601793i
$995$	45.0557	+	10.2837i	1.42836	+	0.326014i
$996$	−0.153056	+	7.08786i	−0.00484976	+	0.224587i
$997$	17.8347	−	37.0342i	0.564831	−	1.17288i	−0.401566	−	0.915830i	$-0.631534\pi$
$997$	17.8347	−	37.0342i	0.564831	−	1.17288i	0.966397	−	0.257054i	$-0.0827518\pi$
$998$	−7.68563	−	22.7491i	−0.243284	−	0.720111i
$999$	20.8254			0.658885

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.2.j.a.111.18	yes	156
4.3	odd	2	inner	196.2.j.a.111.13	yes	156
49.34	odd	14	inner	196.2.j.a.83.13	✓	156
196.83	even	14	inner	196.2.j.a.83.18	yes	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.2.j.a.83.13	✓	156	49.34	odd	14	inner
196.2.j.a.83.18	yes	156	196.83	even	14	inner
196.2.j.a.111.13	yes	156	4.3	odd	2	inner
196.2.j.a.111.18	yes	156	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.739436 + 1.20550i) q^{2} +(0.576591 + 0.723022i) q^{3} +(-0.906467 + 1.78278i) q^{4} +(2.88506 - 2.30076i) q^{5} +(-0.445252 + 1.22971i) q^{6} +(2.64328 - 0.114420i) q^{7} +(-2.81942 + 0.225507i) q^{8} +(0.477259 - 2.09101i) q^{9} +(4.90688 + 1.77668i) q^{10} +(-6.29614 + 1.43705i) q^{11} +(-1.81165 + 0.372541i) q^{12} +(-3.30359 + 0.754023i) q^{13} +(2.09247 + 3.10187i) q^{14} +(3.32699 + 0.759365i) q^{15} +(-2.35663 - 3.23207i) q^{16} +(-1.32426 + 2.74986i) q^{17} +(2.87362 - 0.970832i) q^{18} -3.15336 q^{19} +(1.48654 + 7.22899i) q^{20} +(1.60682 + 1.84517i) q^{21} +(-6.38796 - 6.52739i) q^{22} +(-0.0319146 - 0.0662714i) q^{23} +(-1.78870 - 1.90848i) q^{24} +(1.91747 - 8.40098i) q^{25} +(-3.35177 - 3.42493i) q^{26} +(4.28662 - 2.06433i) q^{27} +(-2.19206 + 4.81611i) q^{28} +(0.122716 + 0.0590968i) q^{29} +(1.54469 + 4.57220i) q^{30} +1.68084 q^{31} +(2.15368 - 5.23084i) q^{32} +(-4.66931 - 3.72365i) q^{33} +(-4.29417 + 0.436946i) q^{34} +(7.36275 - 6.41164i) q^{35} +(3.29520 + 2.74628i) q^{36} +(3.94364 + 1.89916i) q^{37} +(-2.33171 - 3.80138i) q^{38} +(-2.44999 - 1.95380i) q^{39} +(-7.61536 + 7.13741i) q^{40} +(-3.34485 + 2.66743i) q^{41} +(-1.03622 + 3.30141i) q^{42} +(5.02623 + 4.00829i) q^{43} +(3.14529 - 12.5273i) q^{44} +(-3.43398 - 7.13074i) q^{45} +(0.0562914 - 0.0874766i) q^{46} +(0.166245 + 0.728365i) q^{47} +(0.978044 - 3.56748i) q^{48} +(6.97382 - 0.604889i) q^{49} +(11.5452 - 3.90048i) q^{50} +(-2.75177 + 0.628073i) q^{51} +(1.65034 - 6.57308i) q^{52} +(1.78996 - 0.861998i) q^{53} +(5.65823 + 3.64109i) q^{54} +(-14.8584 + 18.6318i) q^{55} +(-7.42671 + 0.918678i) q^{56} +(-1.81820 - 2.27995i) q^{57} +(0.0194993 + 0.191632i) q^{58} +(0.754424 - 0.946018i) q^{59} +(-4.36959 + 5.24297i) q^{60} +(-4.12089 + 8.55712i) q^{61} +(1.24288 + 2.02626i) q^{62} +(1.02227 - 5.58172i) q^{63} +(7.89829 - 1.27160i) q^{64} +(-7.79622 + 9.77615i) q^{65} +(1.03621 - 8.38227i) q^{66} -7.13583i q^{67} +(-3.70201 - 4.85354i) q^{68} +(0.0295140 - 0.0612864i) q^{69} +(13.1735 + 4.13480i) q^{70} +(-2.54779 - 5.29054i) q^{71} +(-0.874057 + 6.00306i) q^{72} +(13.2990 + 3.03541i) q^{73} +(0.626634 + 6.15837i) q^{74} +(7.17969 - 3.45756i) q^{75} +(2.85842 - 5.62176i) q^{76} +(-16.4780 + 4.51893i) q^{77} +(0.543700 - 4.39818i) q^{78} -16.0338i q^{79} +(-14.2352 - 3.90267i) q^{80} +(-1.83297 - 0.882711i) q^{81} +(-5.68890 - 2.05983i) q^{82} +(0.852941 - 3.73698i) q^{83} +(-4.74607 + 1.19202i) q^{84} +(2.50619 + 10.9803i) q^{85} +(-1.11542 + 9.02300i) q^{86} +(0.0280285 + 0.122801i) q^{87} +(17.4274 - 5.47148i) q^{88} +(5.47805 + 1.25033i) q^{89} +(6.05690 - 9.41240i) q^{90} +(-8.64602 + 2.37109i) q^{91} +(0.147077 + 0.00317600i) q^{92} +(0.969158 + 1.21529i) q^{93} +(-0.755118 + 0.738988i) q^{94} +(-9.09762 + 7.25511i) q^{95} +(5.02380 - 1.45889i) q^{96} +0.0207508i q^{97} +(5.88589 + 7.95967i) q^{98} +13.8511i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26}+ \cdots + 105 q^{98}+O(q^{100}) \) 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Introduction

L-functions

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