LMFDB - Embedded newform 783.2.bf.a.544.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [783,2,Mod(4,783)] 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("783.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(783, base_ring=CyclotomicField(126)) chi = DirichletCharacter(H, H._module([14, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.bf (of order $126$, degree $36$, 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:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$3168$
Relative dimension:	$88$ over $\Q(\zeta_{126})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{126}]$

Embedding invariants

Embedding label			544.3
Character	$\chi$	$=$	783.544
Dual form			783.2.bf.a.439.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.61370 - 0.327539i) q^{2} +(-1.34920 - 1.08612i) q^{3} +(4.78597 + 1.21866i) q^{4} +(-1.64960 + 0.0823283i) q^{5} +(3.17065 + 3.28071i) q^{6} +(-1.92918 + 0.491229i) q^{7} +(-7.20581 - 2.82807i) q^{8} +(0.640675 + 2.93079i) q^{9} +(4.33853 + 0.325128i) q^{10} +(-1.72144 + 3.16110i) q^{11} +(-5.13361 - 6.84236i) q^{12} +(-0.716813 + 2.13348i) q^{13} +(5.20318 - 0.652043i) q^{14} +(2.31506 + 1.68060i) q^{15} +(9.23297 + 5.02801i) q^{16} +(-1.92349 - 1.11053i) q^{17} +(-0.714581 - 7.87004i) q^{18} +(2.36093 - 3.46284i) q^{19} +(-7.99529 - 1.61628i) q^{20} +(3.13638 + 1.43256i) q^{21} +(5.53471 - 7.69831i) q^{22} +(-5.66316 + 4.28968i) q^{23} +(6.65044 + 11.6420i) q^{24} +(-2.26074 + 0.226221i) q^{25} +(2.57233 - 5.34149i) q^{26} +(2.31880 - 4.65007i) q^{27} -9.83163 q^{28} +(5.31950 - 0.838397i) q^{29} +(-5.50041 - 5.15084i) q^{30} +(6.06284 + 3.10823i) q^{31} +(-9.91502 - 7.12842i) q^{32} +(5.75591 - 2.39525i) q^{33} +(4.66369 + 3.53261i) q^{34} +(3.14194 - 0.969160i) q^{35} +(-0.505382 + 14.8074i) q^{36} +(0.0363647 + 0.241264i) q^{37} +(-7.30495 + 8.27752i) q^{38} +(3.28435 - 2.09995i) q^{39} +(12.1196 + 4.07196i) q^{40} +(-0.883220 - 2.42663i) q^{41} +(-7.72832 - 4.77156i) q^{42} +(-0.568206 + 11.3851i) q^{43} +(-12.0911 + 13.0311i) q^{44} +(-1.29815 - 4.78190i) q^{45} +(16.2068 - 9.35701i) q^{46} +(7.74144 - 0.193059i) q^{47} +(-6.99607 - 16.8119i) q^{48} +(-2.66713 + 1.45244i) q^{49} +(5.98297 + 0.149206i) q^{50} +(1.38900 + 3.58748i) q^{51} +(-6.03063 + 9.33724i) q^{52} +(-1.80849 - 7.92352i) q^{53} +(-7.58372 + 11.3944i) q^{54} +(2.57945 - 5.35629i) q^{55} +(15.2905 + 1.91615i) q^{56} +(-6.94643 + 2.10781i) q^{57} +(-14.1782 + 0.448972i) q^{58} +(0.184823 - 1.04818i) q^{59} +(9.03175 + 10.8645i) q^{60} +(-2.54100 - 9.97913i) q^{61} +(-14.8283 - 10.1098i) q^{62} +(-2.67566 - 5.33930i) q^{63} +(8.16650 + 7.57740i) q^{64} +(1.00681 - 3.57842i) q^{65} +(-15.8287 + 4.37518i) q^{66} +(-4.70480 - 2.87505i) q^{67} +(-7.85243 - 7.65905i) q^{68} +(12.2999 + 0.363260i) q^{69} +(-8.52951 + 1.50398i) q^{70} +(-1.64173 - 4.18305i) q^{71} +(3.67191 - 22.9306i) q^{72} +(-3.14141 - 10.1842i) q^{73} +(-0.0160230 - 0.642502i) q^{74} +(3.29589 + 2.15022i) q^{75} +(15.5193 - 13.6959i) q^{76} +(1.76815 - 6.94395i) q^{77} +(-9.27210 + 4.41287i) q^{78} +(-4.25062 + 1.42813i) q^{79} +(-15.6447 - 7.53409i) q^{80} +(-8.17907 + 3.75537i) q^{81} +(1.51365 + 6.63175i) q^{82} +(4.51902 - 0.452196i) q^{83} +(13.2648 + 10.6784i) q^{84} +(3.26443 + 1.67358i) q^{85} +(5.21417 - 29.5710i) q^{86} +(-8.08767 - 4.64647i) q^{87} +(21.3442 - 17.9099i) q^{88} +(-7.35013 - 7.92156i) q^{89} +(1.82670 + 12.9236i) q^{90} +(0.334830 - 4.46799i) q^{91} +(-32.3314 + 13.6288i) q^{92} +(-4.80405 - 10.7786i) q^{93} +(-20.2970 - 2.03102i) q^{94} +(-3.60950 + 5.90669i) q^{95} +(5.63500 + 20.3866i) q^{96} +(5.77091 - 4.14900i) q^{97} +(7.44680 - 2.92265i) q^{98} +(-10.3674 - 3.01995i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3168 q - 42 q^{2} - 42 q^{3} - 30 q^{4} - 30 q^{5} - 60 q^{6} - 30 q^{7} - 21 q^{8} - 42 q^{9} - 21 q^{10} - 42 q^{11} - 30 q^{13} - 42 q^{14} - 42 q^{15} - 18 q^{16} - 189 q^{18} - 21 q^{19} + 24 q^{20}+ \cdots - 21 q^{98}+O(q^{100}) $ 3168 * q - 42 * q^2 - 42 * q^3 - 30 * q^4 - 30 * q^5 - 60 * q^6 - 30 * q^7 - 21 * q^8 - 42 * q^9 - 21 * q^10 - 42 * q^11 - 30 * q^13 - 42 * q^14 - 42 * q^15 - 18 * q^16 - 189 * q^18 - 21 * q^19 + 24 * q^20 - 42 * q^21 - 30 * q^22 + 60 * q^23 + 60 * q^24 - 30 * q^25 - 84 * q^26 - 168 * q^27 - 144 * q^28 - 72 * q^29 - 54 * q^30 - 42 * q^31 - 42 * q^32 + 60 * q^33 - 60 * q^34 - 45 * q^35 + 60 * q^36 - 21 * q^37 - 42 * q^39 - 42 * q^40 - 30 * q^42 - 42 * q^43 - 21 * q^44 + 12 * q^45 - 42 * q^47 - 105 * q^48 - 120 * q^49 - 42 * q^50 - 57 * q^51 - 132 * q^53 - 12 * q^54 - 84 * q^55 - 126 * q^56 - 36 * q^57 - 63 * q^58 - 66 * q^59 - 42 * q^60 - 42 * q^61 + 3 * q^62 + 150 * q^63 - 237 * q^64 + 66 * q^65 - 42 * q^66 - 30 * q^67 - 126 * q^68 - 42 * q^69 - 111 * q^71 - 42 * q^72 - 21 * q^73 + 270 * q^74 - 42 * q^76 - 42 * q^77 - 66 * q^78 - 42 * q^79 - 246 * q^80 - 42 * q^81 - 60 * q^82 - 228 * q^83 - 168 * q^84 - 147 * q^85 + 36 * q^86 + 39 * q^87 - 12 * q^88 - 21 * q^89 - 42 * q^90 - 15 * q^91 + 120 * q^92 - 24 * q^93 + 96 * q^94 - 210 * q^95 - 258 * q^96 - 42 * q^97 - 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−2.61370	−	0.327539i	−1.84816	−	0.231605i	−0.878791	−	0.477207i	$-0.841649\pi$
$2$	−2.61370	−	0.327539i	−1.84816	−	0.231605i	−0.969371	+	0.245602i	$0.921014\pi$
$3$	−1.34920	−	1.08612i	−0.778960	−	0.627073i
$3$	−1.34920	−	1.08612i	−0.778960	−	0.627073i
$4$	4.78597	+	1.21866i	2.39298	+	0.609329i
$5$	−1.64960	+	0.0823283i	−0.737726	+	0.0368184i	−0.415185	−	0.909737i	$-0.636283\pi$
$5$	−1.64960	+	0.0823283i	−0.737726	+	0.0368184i	−0.322541	+	0.946556i	$0.604537\pi$
$6$	3.17065	+	3.28071i	1.29441	+	1.33934i
$7$	−1.92918	+	0.491229i	−0.729161	+	0.185667i	−0.593209	−	0.805048i	$-0.702139\pi$
$7$	−1.92918	+	0.491229i	−0.729161	+	0.185667i	−0.135951	+	0.990715i	$0.543409\pi$
$8$	−7.20581	−	2.82807i	−2.54764	−	0.999874i
$9$	0.640675	+	2.93079i	0.213558	+	0.976930i
$10$	4.33853	+	0.325128i	1.37196	+	0.102814i
$11$	−1.72144	+	3.16110i	−0.519035	+	0.953108i	0.478161	+	0.878272i	$0.341303\pi$
$11$	−1.72144	+	3.16110i	−0.519035	+	0.953108i	−0.997196	+	0.0748354i	$0.976157\pi$
$12$	−5.13361	−	6.84236i	−1.48195	−	1.97522i
$13$	−0.716813	+	2.13348i	−0.198808	+	0.591722i	−0.999977	−	0.00671556i	$-0.997862\pi$
$13$	−0.716813	+	2.13348i	−0.198808	+	0.591722i	0.801169	+	0.598438i	$0.204212\pi$
$14$	5.20318	−	0.652043i	1.39061	−	0.174266i
$15$	2.31506	+	1.68060i	0.597747	+	0.433928i
$16$	9.23297	+	5.02801i	2.30824	+	1.25700i
$17$	−1.92349	−	1.11053i	−0.466516	−	0.269343i	0.248264	−	0.968692i	$-0.420140\pi$
$17$	−1.92349	−	1.11053i	−0.466516	−	0.269343i	−0.714780	+	0.699349i	$0.753473\pi$
$18$	−0.714581	−	7.87004i	−0.168428	−	1.85499i
$19$	2.36093	−	3.46284i	0.541633	−	0.794430i	−0.453677	−	0.891166i	$-0.649888\pi$
$19$	2.36093	−	3.46284i	0.541633	−	0.794430i	0.995310	+	0.0967361i	$0.0308403\pi$
$20$	−7.99529	−	1.61628i	−1.78780	−	0.361412i
$21$	3.13638	+	1.43256i	0.684414	+	0.312610i
$22$	5.53471	−	7.69831i	1.18000	−	1.64129i
$23$	−5.66316	+	4.28968i	−1.18085	+	0.894460i	−0.996092	−	0.0883236i	$-0.971849\pi$
$23$	−5.66316	+	4.28968i	−1.18085	+	0.894460i	−0.184760	+	0.982784i	$0.559151\pi$
$24$	6.65044	+	11.6420i	1.35751	+	2.37642i
$25$	−2.26074	+	0.226221i	−0.452147	+	0.0452442i
$26$	2.57233	−	5.34149i	0.504475	−	1.04755i
$27$	2.31880	−	4.65007i	0.446254	−	0.894907i
$28$	−9.83163			−1.85800
$29$	5.31950	−	0.838397i	0.987807	−	0.155686i
$29$	5.31950	−	0.838397i	0.987807	−	0.155686i
$30$	−5.50041	−	5.15084i	−1.00423	−	0.940410i
$31$	6.06284	+	3.10823i	1.08892	+	0.558255i	0.905313	−	0.424745i	$-0.139636\pi$
$31$	6.06284	+	3.10823i	1.08892	+	0.558255i	0.183604	+	0.983000i	$0.441223\pi$
$32$	−9.91502	−	7.12842i	−1.75274	−	1.26014i
$33$	5.75591	−	2.39525i	1.00198	−	0.416960i
$34$	4.66369	+	3.53261i	0.799816	+	0.605837i
$35$	3.14194	−	0.969160i	0.531085	−	0.163818i
$36$	−0.505382	+	14.8074i	−0.0842303	+	2.46791i
$37$	0.0363647	+	0.241264i	0.00597832	+	0.0396636i	0.991621	−	0.129180i	$-0.0412347\pi$
$37$	0.0363647	+	0.241264i	0.00597832	+	0.0396636i	−0.985643	+	0.168844i	$0.945997\pi$
$38$	−7.30495	+	8.27752i	−1.18502	+	1.34279i
$39$	3.28435	−	2.09995i	0.525917	−	0.336261i
$40$	12.1196	+	4.07196i	1.91627	+	0.643833i
$41$	−0.883220	−	2.42663i	−0.137936	−	0.378976i	0.851421	−	0.524482i	$-0.175741\pi$
$41$	−0.883220	−	2.42663i	−0.137936	−	0.378976i	−0.989357	+	0.145507i	$0.953519\pi$
$42$	−7.72832	−	4.77156i	−1.19251	−	0.736267i
$43$	−0.568206	+	11.3851i	−0.0866505	+	1.73621i	0.450548	+	0.892752i	$0.351229\pi$
$43$	−0.568206	+	11.3851i	−0.0866505	+	1.73621i	−0.537199	+	0.843456i	$0.680517\pi$
$44$	−12.0911	+	13.0311i	−1.82280	+	1.96451i
$45$	−1.29815	−	4.78190i	−0.193516	−	0.712844i
$46$	16.2068	−	9.35701i	2.38957	−	1.37962i
$47$	7.74144	−	0.193059i	1.12921	−	0.0281606i	0.544029	−	0.839067i	$-0.316898\pi$
$47$	7.74144	−	0.193059i	1.12921	−	0.0281606i	0.585177	+	0.810906i	$0.301025\pi$
$48$	−6.99607	−	16.8119i	−1.00980	−	2.42659i
$49$	−2.66713	+	1.45244i	−0.381019	+	0.207492i
$50$	5.98297	+	0.149206i	0.846120	+	0.0211009i
$51$	1.38900	+	3.58748i	0.194500	+	0.502347i
$52$	−6.03063	+	9.33724i	−0.836298	+	1.29484i
$53$	−1.80849	−	7.92352i	−0.248415	−	1.08838i	−0.933122	−	0.359560i	$-0.882927\pi$
$53$	−1.80849	−	7.92352i	−0.248415	−	1.08838i	0.684707	−	0.728819i	$-0.259930\pi$
$54$	−7.58372	+	11.3944i	−1.03201	+	1.55058i
$55$	2.57945	−	5.35629i	0.347813	−	0.722242i
$56$	15.2905	+	1.91615i	2.04328	+	0.256056i
$57$	−6.94643	+	2.10781i	−0.920077	+	0.279186i
$58$	−14.1782	+	0.448972i	−1.86168	+	0.0589529i
$59$	0.184823	−	1.04818i	0.0240619	−	0.136462i	−0.970410	−	0.241462i	$-0.922373\pi$
$59$	0.184823	−	1.04818i	0.0240619	−	0.136462i	0.994472	+	0.105000i	$0.0334842\pi$
$60$	9.03175	+	10.8645i	1.16599	+	1.40261i
$61$	−2.54100	−	9.97913i	−0.325341	−	1.27770i	−0.891357	−	0.453302i	$-0.850246\pi$
$61$	−2.54100	−	9.97913i	−0.325341	−	1.27770i	0.566016	−	0.824394i	$-0.308484\pi$
$62$	−14.8283	−	10.1098i	−1.88320	−	1.28394i
$63$	−2.67566	−	5.33930i	−0.337102	−	0.672688i
$64$	8.16650	+	7.57740i	1.02081	+	0.947175i
$65$	1.00681	−	3.57842i	0.124880	−	0.443848i
$66$	−15.8287	+	4.37518i	−1.94838	+	0.538547i
$67$	−4.70480	−	2.87505i	−0.574783	−	0.351243i	0.203579	−	0.979059i	$-0.434743\pi$
$67$	−4.70480	−	2.87505i	−0.574783	−	0.351243i	−0.778362	+	0.627816i	$0.783949\pi$
$68$	−7.85243	−	7.65905i	−0.952247	−	0.928796i
$69$	12.2999	+	0.363260i	1.48073	+	0.0437314i
$70$	−8.52951	+	1.50398i	−1.01947	+	0.179760i
$71$	−1.64173	−	4.18305i	−0.194837	−	0.496437i	0.799751	−	0.600332i	$-0.204965\pi$
$71$	−1.64173	−	4.18305i	−0.194837	−	0.496437i	−0.994588	+	0.103895i	$0.966869\pi$
$72$	3.67191	−	22.9306i	0.432738	−	2.70240i
$73$	−3.14141	−	10.1842i	−0.367675	−	1.19197i	−0.930778	−	0.365585i	$-0.880869\pi$
$73$	−3.14141	−	10.1842i	−0.367675	−	1.19197i	0.563103	−	0.826386i	$-0.309607\pi$
$74$	−0.0160230	−	0.642502i	−0.00186264	−	0.0746893i
$75$	3.29589	+	2.15022i	0.380576	+	0.248286i
$76$	15.5193	−	13.6959i	1.78019	−	1.57103i
$77$	1.76815	−	6.94395i	0.201499	−	0.791336i
$78$	−9.27210	+	4.41287i	−1.04986	+	0.499660i
$79$	−4.25062	+	1.42813i	−0.478232	+	0.160677i	−0.547303	−	0.836934i	$-0.684346\pi$
$79$	−4.25062	+	1.42813i	−0.478232	+	0.160677i	0.0690715	+	0.997612i	$0.477996\pi$
$80$	−15.6447	−	7.53409i	−1.74913	−	0.842336i
$81$	−8.17907	+	3.75537i	−0.908786	+	0.417263i
$82$	1.51365	+	6.63175i	0.167155	+	0.732355i
$83$	4.51902	−	0.452196i	0.496026	−	0.0496349i	0.151588	−	0.988444i	$-0.451561\pi$
$83$	4.51902	−	0.452196i	0.496026	−	0.0496349i	0.344439	+	0.938809i	$0.388069\pi$
$84$	13.2648	+	10.6784i	1.44731	+	1.16510i
$85$	3.26443	+	1.67358i	0.354078	+	0.181525i
$86$	5.21417	−	29.5710i	0.562258	−	3.18872i
$87$	−8.08767	−	4.64647i	−0.867089	−	0.498154i
$88$	21.3442	−	17.9099i	2.27530	−	1.90920i
$89$	−7.35013	−	7.92156i	−0.779112	−	0.839683i	0.211358	−	0.977409i	$-0.432211\pi$
$89$	−7.35013	−	7.92156i	−0.779112	−	0.839683i	−0.990470	+	0.137725i	$0.956021\pi$
$90$	1.82670	+	12.9236i	0.192552	+	1.36227i
$91$	0.334830	−	4.46799i	0.0350997	−	0.468373i
$92$	−32.3314	+	13.6288i	−3.37078	+	1.42090i
$93$	−4.80405	−	10.7786i	−0.498156	−	1.11769i
$94$	−20.2970	−	2.03102i	−2.09348	−	0.209484i
$95$	−3.60950	+	5.90669i	−0.370327	+	0.606014i
$96$	5.63500	+	20.3866i	0.575120	+	2.08070i
$97$	5.77091	−	4.14900i	0.585948	−	0.421268i	−0.251443	−	0.967872i	$-0.580905\pi$
$97$	5.77091	−	4.14900i	0.585948	−	0.421268i	0.837391	+	0.546604i	$0.184080\pi$
$98$	7.44680	−	2.92265i	0.752240	−	0.295232i
$99$	−10.3674	−	3.01995i	−1.04196	−	0.303517i
$100$	−11.0955	−	1.67238i	−1.10955	−	0.167238i
$101$	−5.88681	+	3.01799i	−0.585759	+	0.300301i	−0.723673	−	0.690143i	$-0.757548\pi$
$101$	−5.88681	+	3.01799i	−0.585759	+	0.300301i	0.137914	+	0.990444i	$0.455960\pi$
$102$	−2.45540	−	9.83153i	−0.243121	−	0.973466i
$103$	−8.37867	−	9.49419i	−0.825575	−	0.935490i	0.173204	−	0.984886i	$-0.444588\pi$
$103$	−8.37867	−	9.49419i	−0.825575	−	0.935490i	−0.998779	+	0.0493959i	$0.984270\pi$
$104$	11.1989	−	13.3463i	1.09814	−	1.30871i
$105$	−5.29173	−	2.10494i	−0.516420	−	0.205421i
$106$	2.13159	+	21.3020i	0.207038	+	2.06903i
$107$	11.1808	+	14.0203i	1.08089	+	1.35540i	0.930300	+	0.366801i	$0.119547\pi$
$107$	11.1808	+	14.0203i	1.08089	+	1.35540i	0.150593	+	0.988596i	$0.451882\pi$
$108$	16.7646	−	19.4293i	1.61317	−	1.86958i
$109$	−9.69776	−	4.67019i	−0.928877	−	0.447324i	−0.0926448	−	0.995699i	$-0.529532\pi$
$109$	−9.69776	−	4.67019i	−0.928877	−	0.447324i	−0.836232	+	0.548376i	$0.815246\pi$
$110$	−8.49630	+	13.1548i	−0.810090	+	1.25426i
$111$	0.212979	−	0.365010i	0.0202151	−	0.0346452i
$112$	−20.2819	−	5.16441i	−1.91646	−	0.487991i
$113$	10.0356	+	7.21511i	0.944071	+	0.678741i	0.946993	−	0.321255i	$-0.104105\pi$
$113$	10.0356	+	7.21511i	0.944071	+	0.678741i	−0.00292174	+	0.999996i	$0.500930\pi$
$114$	18.8462	−	3.23394i	1.76511	−	0.302886i
$115$	8.98882	−	7.54252i	0.838212	−	0.703343i
$116$	26.4807	+	2.47011i	2.45867	+	0.229344i
$117$	−6.71204	−	0.733959i	−0.620528	−	0.0678545i
$118$	−0.826393	+	2.67910i	−0.0760756	+	0.246631i
$119$	4.25629	+	1.19753i	0.390173	+	0.109778i
$120$	−11.9291	−	18.6572i	−1.08897	−	1.70316i
$121$	−1.06118	−	1.64302i	−0.0964707	−	0.149366i
$122$	3.37285	+	26.9147i	0.305363	+	2.43674i
$123$	−1.44398	+	4.23329i	−0.130199	+	0.381703i
$124$	25.2287	+	22.2644i	2.26560	+	1.99941i
$125$	11.8767	−	1.79013i	1.06229	−	0.160114i
$126$	5.24455	+	14.8317i	0.467221	+	1.32131i
$127$	3.16776	−	21.0167i	0.281094	−	1.86493i	−0.188530	−	0.982067i	$-0.560372\pi$
$127$	3.16776	−	21.0167i	0.281094	−	1.86493i	0.469624	−	0.882867i	$-0.344390\pi$
$128$	−3.16398	−	3.77069i	−0.279659	−	0.333285i
$129$	13.1322	−	14.7436i	1.15623	−	1.29810i
$130$	−3.80357	+	9.02313i	−0.333595	+	0.791381i
$131$	−10.0726	−	13.2976i	−0.880045	−	1.16182i	−0.985883	−	0.167437i	$-0.946451\pi$
$131$	−10.0726	−	13.2976i	−0.880045	−	1.16182i	0.105838	−	0.994383i	$-0.466248\pi$
$132$	30.4666	−	4.44912i	2.65178	−	0.387247i
$133$	−2.85360	+	7.84019i	−0.247438	+	0.679831i
$134$	11.3552	+	9.05550i	0.980943	+	0.782276i
$135$	−3.44227	+	7.86168i	−0.296264	+	0.676626i
$136$	10.7197	+	13.4421i	0.919205	+	1.15265i
$137$	6.88434	−	2.31301i	0.588169	−	0.197614i	−0.00868774	−	0.999962i	$-0.502765\pi$
$137$	6.88434	−	2.31301i	0.588169	−	0.197614i	0.596856	+	0.802348i	$0.296416\pi$
$138$	−32.0291	−	4.97813i	−2.72650	−	0.423766i
$139$	−0.0464842	+	0.0352104i	−0.00394274	+	0.00298651i	−0.605774	−	0.795637i	$-0.707136\pi$
$139$	−0.0464842	+	0.0352104i	−0.00394274	+	0.00298651i	0.601831	+	0.798623i	$0.294438\pi$
$140$	16.2183	−	0.809421i	1.37070	−	0.0684086i
$141$	−10.6544	−	8.14768i	−0.897265	−	0.686158i
$142$	2.92086	+	11.4709i	0.245113	+	0.962621i
$143$	−5.51020	−	5.93859i	−0.460786	−	0.496610i
$144$	−8.82071	+	30.2812i	−0.735059	+	2.52343i
$145$	−8.70605	+	1.82097i	−0.722998	+	0.151223i
$146$	4.87498	+	27.6474i	0.403456	+	2.28811i
$147$	5.17602	+	0.937198i	0.426911	+	0.0772988i
$148$	−0.119978	+	1.19900i	−0.00986213	+	0.0985571i
$149$	3.03303	−	3.10961i	0.248475	−	0.254749i	−0.580206	−	0.814470i	$-0.697028\pi$
$149$	3.03303	−	3.10961i	0.248475	−	0.254749i	0.828681	+	0.559721i	$0.189092\pi$
$150$	−7.91016	−	6.69955i	−0.645862	−	0.547016i
$151$	−1.50208	−	0.0749656i	−0.122237	−	0.00610062i	−0.0113662	−	0.999935i	$-0.503618\pi$
$151$	−1.50208	−	0.0749656i	−0.122237	−	0.00610062i	−0.110871	+	0.993835i	$0.535364\pi$
$152$	−26.8055	+	18.2757i	−2.17422	+	1.48236i
$153$	2.02240	−	6.34885i	0.163501	−	0.513274i
$154$	−6.89581	+	17.5702i	−0.555680	+	1.41585i
$155$	−10.2572	−	4.62821i	−0.823876	−	0.371747i
$156$	18.2779	−	6.04779i	1.46340	−	0.484211i
$157$	−10.2535	−	1.80797i	−0.818319	−	0.144292i	−0.251208	−	0.967933i	$-0.580828\pi$
$157$	−10.2535	−	1.80797i	−0.818319	−	0.144292i	−0.567111	+	0.823641i	$0.691939\pi$
$158$	11.5776	−	2.34046i	0.921063	−	0.186197i
$159$	−6.16590	+	12.6546i	−0.488987	+	1.00358i
$160$	16.9427	+	10.9428i	1.33944	+	0.865103i
$161$	8.81804	−	11.0575i	0.694959	−	0.871450i
$162$	22.6076	−	7.13642i	1.77622	−	0.560690i
$163$	4.16815	+	3.32399i	0.326475	+	0.260355i	0.772986	−	0.634423i	$-0.218762\pi$
$163$	4.16815	+	3.32399i	0.326475	+	0.260355i	−0.446511	+	0.894778i	$0.647334\pi$
$164$	−1.26984	−	12.6901i	−0.0991576	−	0.990931i
$165$	−9.29778	+	4.42510i	−0.723831	+	0.344493i
$166$	−11.9594	−	0.298250i	−0.928233	−	0.0231487i
$167$	−0.145514	+	0.202398i	−0.0112602	+	0.0156620i	−0.817530	−	0.575886i	$-0.804657\pi$
$167$	−0.145514	+	0.202398i	−0.0112602	+	0.0156620i	0.806270	+	0.591548i	$0.201483\pi$
$168$	−18.5488	−	19.1926i	−1.43107	−	1.48074i
$169$	6.32479	+	4.79084i	0.486522	+	0.368526i
$170$	−7.98408	−	5.44345i	−0.612351	−	0.417494i
$171$	11.6614	+	4.70082i	0.891773	+	0.359481i
$172$	−16.5939	+	53.7962i	−1.26527	+	4.10192i
$173$	−0.220636	−	1.25129i	−0.0167746	−	0.0951336i	0.975271	−	0.221012i	$-0.0709361\pi$
$173$	−0.220636	−	1.25129i	−0.0167746	−	0.0951336i	−0.992046	+	0.125879i	$0.959825\pi$
$174$	19.6168	+	14.7935i	1.48715	+	1.12149i
$175$	4.25024	−	1.54696i	0.321288	−	0.116939i
$176$	−31.7881	+	20.5309i	−2.39611	+	1.54758i
$177$	−1.38782	+	1.21347i	−0.104315	+	0.0912099i
$178$	16.6164	+	23.1120i	1.24545	+	1.73232i
$179$	11.6443	+	3.59179i	0.870336	+	0.268463i	0.697585	−	0.716502i	$-0.254258\pi$
$179$	11.6443	+	3.59179i	0.870336	+	0.268463i	0.172752	+	0.984965i	$0.444734\pi$
$180$	−0.385392	−	24.4680i	−0.0287254	−	1.82374i
$181$	1.28829	+	17.1910i	0.0957575	+	1.27780i	0.813532	+	0.581520i	$0.197542\pi$
$181$	1.28829	+	17.1910i	0.0957575	+	1.27780i	−0.717775	+	0.696275i	$0.754839\pi$
$182$	−2.33858	+	11.5683i	−0.173347	+	0.857499i
$183$	−7.41024	+	16.2237i	−0.547781	+	1.19929i
$184$	52.9392	−	14.8948i	3.90273	−	1.09806i
$185$	−0.0798503	−	0.394997i	−0.00587071	−	0.0290407i
$186$	9.02590	+	29.7455i	0.661811	+	2.18105i
$187$	6.82169	−	4.16865i	0.498851	−	0.304842i
$188$	37.2856	+	8.51019i	2.71933	+	0.620669i
$189$	−2.18913	+	10.1099i	−0.159236	+	0.735385i
$190$	11.3688	−	14.2560i	0.824780	−	1.03424i
$191$	−1.98061	+	5.44169i	−0.143312	+	0.393747i	−0.990494	−	0.137556i	$-0.956075\pi$
$191$	−1.98061	+	5.44169i	−0.143312	+	0.393747i	0.847182	+	0.531303i	$0.178297\pi$
$192$	−2.78824	−	19.0932i	−0.201224	−	1.37794i
$193$	6.35322	−	24.9507i	0.457315	−	1.79599i	−0.135646	−	0.990757i	$-0.543311\pi$
$193$	6.35322	−	24.9507i	0.457315	−	1.79599i	0.592961	−	0.805231i	$-0.297959\pi$
$194$	−16.4424	+	8.95404i	−1.18049	+	0.642862i
$195$	−5.24499	+	3.73448i	−0.375602	+	0.267432i
$196$	−14.5348	+	3.70102i	−1.03820	+	0.264359i
$197$	−15.8725	+	4.89601i	−1.13087	+	0.348826i	−0.803048	−	0.595914i	$-0.796790\pi$
$197$	−15.8725	+	4.89601i	−1.13087	+	0.348826i	−0.327819	+	0.944741i	$0.606314\pi$
$198$	26.1081	+	11.2890i	1.85542	+	0.802272i
$199$	−0.690187	+	9.20990i	−0.0489261	+	0.652873i	0.917797	+	0.397049i	$0.129966\pi$
$199$	−0.690187	+	9.20990i	−0.0489261	+	0.652873i	−0.966723	+	0.255824i	$0.917653\pi$
$200$	16.9302	+	4.76342i	1.19715	+	0.336825i
$201$	3.22506	+	8.98900i	0.227478	+	0.634035i
$202$	16.3748	−	5.95995i	1.15213	−	0.419341i
$203$	−9.85042	+	4.23051i	−0.691364	+	0.296924i
$204$	2.27583	+	18.8623i	0.159340	+	1.32062i
$205$	1.65674	+	3.93026i	0.115712	+	0.274501i
$206$	18.7896	+	27.5593i	1.30913	+	1.92014i
$207$	−16.2004	−	13.8493i	−1.12601	−	0.962590i
$208$	−17.3455	+	16.0942i	−1.20269	+	1.11594i
$209$	6.88219	+	13.4242i	0.476051	+	0.928572i
$210$	13.1415	+	7.23492i	0.906850	+	0.499257i
$211$	10.2273	+	18.7804i	0.704074	+	1.29290i	0.946493	+	0.322725i	$0.104599\pi$
$211$	10.2273	+	18.7804i	0.704074	+	1.29290i	−0.242419	+	0.970172i	$0.577941\pi$
$212$	1.00067	−	40.1256i	0.0687263	−	2.75584i
$213$	−2.32829	+	7.42688i	−0.159532	+	0.508882i
$214$	−24.6311	−	40.3070i	−1.68375	−	2.75533i
$215$		−	18.8277i		−	1.28404i
$216$	−29.8596	+	26.9498i	−2.03169	+	1.83370i
$217$	−13.2231	−	3.01810i	−0.897645	−	0.204882i
$218$	23.8173	+	15.3829i	1.61311	+	1.04186i
$219$	−6.82291	+	17.1525i	−0.461050	+	1.15906i
$220$	18.8727	−	22.4916i	1.27239	−	1.51638i
$221$	3.74808	−	3.30770i	0.252123	−	0.222500i
$222$	−0.676218	+	0.884266i	−0.0453848	+	0.0593480i
$223$	6.41211	+	1.29624i	0.429386	+	0.0868024i	0.408028	−	0.912970i	$-0.366217\pi$
$223$	6.41211	+	1.29624i	0.429386	+	0.0868024i	0.0213587	+	0.999772i	$0.493201\pi$
$224$	22.6295	+	8.88143i	1.51200	+	0.593416i
$225$	−2.11140	−	6.48081i	−0.140760	−	0.432054i
$226$	−23.8668	−	22.1452i	−1.58760	−	1.47307i
$227$	2.39701	−	1.01042i	0.159095	−	0.0670642i	−0.307437	−	0.951568i	$-0.599471\pi$
$227$	2.39701	−	1.01042i	0.159095	−	0.0670642i	0.466532	+	0.884504i	$0.345503\pi$
$228$	−35.8141	+	1.62258i	−2.37185	+	0.107458i
$229$	1.60103	−	15.9999i	0.105799	−	1.05730i	−0.790079	−	0.613005i	$-0.789960\pi$
$229$	1.60103	−	15.9999i	0.105799	−	1.05730i	0.895878	−	0.444300i	$-0.146547\pi$
$230$	−25.9645	+	16.7697i	−1.71205	+	1.10576i
$231$	−9.92756	+	7.44834i	−0.653185	+	0.490065i
$232$	−40.7024	−	9.00260i	−2.67224	−	0.591050i
$233$	11.6453	−	20.1702i	0.762908	−	1.32139i	−0.178438	−	0.983951i	$-0.557104\pi$
$233$	11.6453	−	20.1702i	0.762908	−	1.32139i	0.941346	−	0.337444i	$-0.109562\pi$
$234$	17.3028	+	4.11680i	1.13112	+	0.269123i
$235$	−12.7544	+	0.955812i	−0.832007	+	0.0623503i
$236$	2.16194	−	4.79134i	0.140730	−	0.311890i
$237$	7.28605	+	2.68986i	0.473280	+	0.174725i
$238$	−10.7324	−	4.52409i	−0.695678	−	0.293253i
$239$	0.723487	+	1.60341i	0.0467985	+	0.103716i	0.933429	−	0.358763i	$-0.116801\pi$
$239$	0.723487	+	1.60341i	0.0467985	+	0.103716i	−0.886630	+	0.462479i	$0.846960\pi$
$240$	12.9249	+	27.1570i	0.834296	+	1.75298i
$241$	−8.00528	−	23.8265i	−0.515666	−	1.53480i	−0.814307	−	0.580435i	$-0.802883\pi$
$241$	−8.00528	−	23.8265i	−0.515666	−	1.53480i	0.298641	−	0.954366i	$-0.403467\pi$
$242$	2.23544	+	4.64194i	0.143700	+	0.298395i
$243$	15.1140	+	3.81674i	0.969562	+	0.244844i
$244$		−	50.8564i		−	3.25575i
$245$	4.28013	−	2.61553i	0.273448	−	0.167100i
$246$	5.16068	−	10.5916i	0.329033	−	0.675294i
$247$	5.69558	+	7.51920i	0.362401	+	0.478435i
$248$	−34.8973	−	39.5435i	−2.21598	−	2.51101i
$249$	−6.58819	−	4.29810i	−0.417510	−	0.272381i
$250$	−31.6285	+	0.788767i	−2.00036	+	0.0498860i
$251$	5.00292	−	7.33794i	0.315782	−	0.463167i	−0.635229	−	0.772324i	$-0.719094\pi$
$251$	5.00292	−	7.33794i	0.315782	−	0.463167i	0.951011	+	0.309157i	$0.100047\pi$
$252$	−6.29887	−	28.8144i	−0.396792	−	1.81514i
$253$	−3.81129	−	25.2863i	−0.239614	−	1.58973i
$254$	−15.1634	+	53.8938i	−0.951434	+	3.38160i
$255$	−2.58666	−	5.80357i	−0.161983	−	0.363433i
$256$	−5.05373	−	7.82470i	−0.315858	−	0.489044i
$257$	−0.298599	+	0.306138i	−0.0186261	+	0.0190964i	−0.725116	−	0.688627i	$-0.758214\pi$
$257$	−0.298599	+	0.306138i	−0.0186261	+	0.0190964i	0.706490	+	0.707723i	$0.250277\pi$
$258$	−39.1527	+	34.2340i	−2.43754	+	2.13131i
$259$	−0.188670	−	0.447578i	−0.0117234	−	0.0278111i
$260$	9.17943	−	15.8992i	0.569284	−	0.986029i
$261$	5.86523	+	15.0532i	0.363049	+	0.931770i
$262$	21.9712	+	38.0552i	1.35738	+	2.35106i
$263$	8.41588	−	11.1105i	0.518945	−	0.685103i	−0.460304	−	0.887761i	$-0.652260\pi$
$263$	8.41588	−	11.1105i	0.518945	−	0.685103i	0.979249	+	0.202658i	$0.0649581\pi$
$264$	−48.2499	+	0.981607i	−2.96958	+	0.0604138i
$265$	3.63562	+	12.9218i	0.223335	+	0.793778i
$266$	10.0264	−	19.5572i	0.614758	−	1.19913i
$267$	1.31300	+	18.6709i	0.0803545	+	1.14264i
$268$	−19.0134	−	19.4934i	−1.16143	−	1.19075i
$269$	−0.457044	+	0.364480i	−0.0278664	+	0.0222228i	−0.637324	−	0.770596i	$-0.719959\pi$
$269$	−0.457044	+	0.364480i	−0.0278664	+	0.0222228i	0.609458	+	0.792819i	$0.291387\pi$
$270$	11.5721	−	19.4206i	0.704253	−	1.18190i
$271$	9.92481	+	20.6091i	0.602889	+	1.25191i	0.949460	+	0.313889i	$0.101632\pi$
$271$	9.92481	+	20.6091i	0.602889	+	1.25191i	−0.346570	+	0.938024i	$0.612654\pi$
$272$	−12.1758	−	19.9248i	−0.738267	−	1.20812i
$273$	−5.30454	+	5.66454i	−0.321045	+	0.342834i
$274$	−18.7512	+	3.79063i	−1.13280	+	0.229000i
$275$	3.17662	−	7.53584i	0.191558	−	0.454428i
$276$	58.4240	+	16.7279i	3.51671	+	1.00690i
$277$	−0.00214607	−	0.0860548i	−0.000128945	−	0.00517053i	0.999621	−	0.0275159i	$-0.00875968\pi$
$277$	−0.00214607	−	0.0860548i	−0.000128945	−	0.00517053i	−0.999750	+	0.0223453i	$0.992887\pi$
$278$	0.133028	−	0.0768040i	0.00797851	−	0.00460640i
$279$	−5.22528	+	19.7603i	−0.312829	+	1.18302i
$280$	−25.3811	−	1.90205i	−1.51681	−	0.113669i
$281$	6.53933	−	7.40996i	0.390103	−	0.442041i	−0.521413	−	0.853304i	$-0.674595\pi$
$281$	6.53933	−	7.40996i	0.390103	−	0.442041i	0.911517	+	0.411263i	$0.134912\pi$
$282$	25.1788	+	24.7853i	1.49937	+	1.47594i
$283$	30.5097	+	3.05295i	1.81361	+	0.181479i	0.947795	−	0.318882i	$-0.103307\pi$
$283$	30.5097	+	3.05295i	1.81361	+	0.181479i	0.865817	+	0.500361i	$0.166799\pi$
$284$	−2.75955	−	22.0207i	−0.163749	−	1.30669i
$285$	11.2853	−	4.04894i	0.668485	−	0.239838i
$286$	12.4569	+	17.3265i	0.736591	+	1.02454i
$287$	2.89592	+	4.24753i	0.170941	+	0.250724i
$288$	14.5396	−	33.6259i	0.856754	−	1.98142i
$289$	−6.03344	−	10.4502i	−0.354909	−	0.614720i
$290$	23.3514	−	1.90789i	1.37124	−	0.112035i
$291$	−12.2924	−	0.670089i	−0.720595	−	0.0392813i
$292$	−2.62364	−	52.5696i	−0.153537	−	3.07640i
$293$	20.4708	−	9.23678i	1.19592	−	0.539619i	0.287540	−	0.957769i	$-0.407163\pi$
$293$	20.4708	−	9.23678i	1.19592	−	0.539619i	0.908378	+	0.418150i	$0.137321\pi$
$294$	−13.2216	−	4.14490i	−0.771098	−	0.241735i
$295$	−0.218590	+	1.74431i	−0.0127268	+	0.101557i
$296$	0.420275	−	1.84135i	0.0244280	−	0.107026i
$297$	10.7077	+	15.3348i	0.621321	+	0.889815i
$298$	−8.94592	+	7.13413i	−0.518223	+	0.413269i
$299$	−5.09254	−	15.1572i	−0.294509	−	0.876562i
$300$	13.1536	+	14.3074i	0.759425	+	0.826041i
$301$	−4.49651	−	22.2430i	−0.259175	−	1.28206i
$302$	3.90142	+	0.687926i	0.224502	+	0.0395857i
$303$	11.2204	+	2.32193i	0.644594	+	0.133391i
$304$	39.2095	−	20.1015i	2.24882	−	1.15290i
$305$	5.01321	+	16.2524i	0.287055	+	0.930611i
$306$	−7.36543	+	15.9315i	−0.421053	+	0.910746i
$307$	22.9372	+	13.2428i	1.30910	+	0.755806i	0.981945	−	0.189166i	$-0.0605785\pi$
$307$	22.9372	+	13.2428i	1.30910	+	0.755806i	0.327150	+	0.944972i	$0.393912\pi$
$308$	16.9246	−	31.0788i	0.964368	−	1.77088i
$309$	0.992638	+	21.9098i	0.0564692	+	1.24641i
$310$	25.2932	+	15.4564i	1.43656	+	0.877863i
$311$	−7.02469	+	11.4954i	−0.398334	+	0.651844i	−0.987761	−	0.155978i	$-0.950147\pi$
$311$	−7.02469	+	11.4954i	−0.398334	+	0.651844i	0.589427	+	0.807822i	$0.299354\pi$
$312$	−29.6052	+	5.84345i	−1.67606	+	0.330820i
$313$	−19.6678	−	0.981581i	−1.11169	−	0.0554823i	−0.514433	−	0.857530i	$-0.671998\pi$
$313$	−19.6678	−	0.981581i	−1.11169	−	0.0554823i	−0.597259	+	0.802048i	$0.703744\pi$
$314$	26.2074	+	8.08391i	1.47897	+	0.456201i
$315$	4.85336	+	8.58745i	0.273456	+	0.483848i
$316$	−22.0837	+	1.65495i	−1.24231	+	0.0930980i
$317$	−10.7495	+	14.1914i	−0.603755	+	0.797067i	−0.992233	−	0.124391i	$-0.960302\pi$
$317$	−10.7495	+	14.1914i	−0.603755	+	0.797067i	0.388479	+	0.921458i	$0.373001\pi$
$318$	20.2607	−	31.0558i	1.13616	−	1.74152i
$319$	−6.50696	+	18.2587i	−0.364320	+	1.02229i
$320$	−14.0953	−	11.8274i	−0.787953	−	0.661171i
$321$	0.142624	−	31.0600i	0.00796051	−	1.73360i
$322$	−26.6694	+	26.0126i	−1.48623	+	1.44963i
$323$	−8.38682	+	4.03888i	−0.466655	+	0.224729i
$324$	−43.7213	+	8.00558i	−2.42896	+	0.444755i
$325$	1.13789	−	4.98540i	0.0631185	−	0.276540i
$326$	−9.80554	−	10.0531i	−0.543079	−	0.556791i
$327$	8.01180	+	16.8340i	0.443054	+	0.930921i
$328$	−0.498360	+	19.9836i	−0.0275173	+	1.10341i
$329$	−14.8398	+	4.17527i	−0.818144	+	0.230190i
$330$	25.7510	−	8.52047i	1.41754	−	0.469037i
$331$	−17.6966	−	21.0900i	−0.972694	−	1.15921i	−0.987228	−	0.159317i	$-0.949071\pi$
$331$	−17.6966	−	21.0900i	−0.972694	−	1.15921i	0.0145338	−	0.999894i	$-0.495374\pi$
$332$	22.1789	+	3.34294i	1.21723	+	0.183468i
$333$	−0.683797	+	0.261149i	−0.0374718	+	0.0143109i
$334$	0.446623	−	0.481346i	0.0244381	−	0.0263381i
$335$	7.99777	+	4.35535i	0.436965	+	0.237958i
$336$	21.7552	+	28.9965i	1.18684	+	1.58189i
$337$	23.8719	+	8.02052i	1.30038	+	0.436906i	0.881950	−	0.471342i	$-0.156230\pi$
$337$	23.8719	+	8.02052i	1.30038	+	0.436906i	0.418433	+	0.908248i	$0.362579\pi$
$338$	−14.9619	−	14.5934i	−0.813819	−	0.793777i
$339$	−5.70354	−	20.6345i	−0.309774	−	1.12071i
$340$	13.5840	+	11.9879i	0.736694	+	0.650136i
$341$	−20.2623	+	13.8146i	−1.09726	+	0.748101i
$342$	−28.9398	−	16.1061i	−1.56488	−	0.870918i
$343$	14.6471	−	13.5905i	0.790868	−	0.733818i
$344$	36.2922	−	80.4318i	1.95674	−	4.33659i
$345$	−20.3198	+	0.413390i	−1.09398	+	0.0222562i
$346$	0.166830	+	3.34275i	0.00896883	+	0.179707i
$347$	−10.4794	−	8.79325i	−0.562563	−	0.472046i	0.316606	−	0.948557i	$-0.397457\pi$
$347$	−10.4794	−	8.79325i	−0.562563	−	0.472046i	−0.879169	+	0.476511i	$0.841901\pi$
$348$	−33.0449	−	32.0939i	−1.77139	−	1.72042i
$349$	15.5251	+	5.65068i	0.831040	+	0.302474i	0.722286	−	0.691595i	$-0.243092\pi$
$349$	15.5251	+	5.65068i	0.831040	+	0.302474i	0.108754	+	0.994069i	$0.465314\pi$
$350$	−11.6155	+	2.65117i	−0.620875	+	0.141711i
$351$	8.25871	+	8.28036i	0.440817	+	0.441973i
$352$	39.6018	−	19.0712i	2.11078	−	1.01650i
$353$	−0.880979	+	7.03004i	−0.0468898	+	0.374171i	0.950997	+	0.309199i	$0.100061\pi$
$353$	−0.880979	+	7.03004i	−0.0468898	+	0.374171i	−0.997887	+	0.0649723i	$0.979304\pi$
$354$	4.02480	−	2.71707i	0.213916	−	0.144411i
$355$	3.05258	+	6.76522i	0.162014	+	0.359061i
$356$	−25.5238	−	46.8696i	−1.35276	−	2.48408i
$357$	−4.44191	−	6.23856i	−0.235091	−	0.330180i
$358$	−29.2582	−	13.2018i	−1.54635	−	0.697738i
$359$	3.49097	−	23.1611i	0.184247	−	1.22240i	−0.685195	−	0.728360i	$-0.740283\pi$
$359$	3.49097	−	23.1611i	0.184247	−	1.22240i	0.869441	−	0.494036i	$-0.164479\pi$
$360$	−4.16936	+	38.1287i	−0.219744	+	2.00956i
$361$	0.524178	+	1.33558i	0.0275883	+	0.0702939i
$362$	2.26352	−	45.3539i	0.118968	−	2.38375i
$363$	−0.352787	+	3.36934i	−0.0185165	+	0.176844i
$364$	7.04743	−	20.9756i	0.369386	−	1.09942i
$365$	6.02054	+	16.5413i	0.315129	+	0.865811i
$366$	24.6820	−	39.9766i	1.29015	−	2.08961i
$367$	1.40581	−	1.01071i	0.0733827	−	0.0527586i	−0.546456	−	0.837488i	$-0.684023\pi$
$367$	1.40581	−	1.01071i	0.0733827	−	0.0527586i	0.619839	+	0.784729i	$0.287198\pi$
$368$	−73.8563	+	11.1321i	−3.85003	+	0.580298i
$369$	6.54608	−	4.14321i	0.340775	−	0.215687i
$370$	0.0793277	+	1.05855i	0.00412405	+	0.0550317i
$371$	7.38116	+	14.3975i	0.383211	+	0.747480i
$372$	−9.85658	−	57.4406i	−0.511040	−	2.97816i
$373$	−0.230386	−	0.818841i	−0.0119289	−	0.0423980i	0.956426	−	0.291974i	$-0.0943120\pi$
$373$	−0.230386	−	0.818841i	−0.0119289	−	0.0423980i	−0.968355	+	0.249576i	$0.919709\pi$
$374$	−19.1952	+	8.66120i	−0.992560	+	0.447860i
$375$	−17.9684	−	10.4844i	−0.927884	−	0.541410i
$376$	−56.3293	−	20.5022i	−2.90496	−	1.05732i
$377$	−2.02438	+	11.9500i	−0.104261	+	0.615459i
$378$	9.03310	−	25.7071i	0.464612	−	1.32223i
$379$	−33.6036	+	7.66981i	−1.72610	+	0.393971i	−0.966551	−	0.256476i	$-0.917438\pi$
$379$	−33.6036	+	7.66981i	−1.72610	+	0.393971i	−0.759551	+	0.650448i	$0.774581\pi$
$380$	−24.4732	+	23.8705i	−1.25545	+	1.22453i
$381$	−27.1007	+	24.9152i	−1.38841	+	1.27644i
$382$	6.95909	−	13.5742i	0.356058	−	0.694516i
$383$	−13.7203	−	5.78358i	−0.701073	−	0.295527i	0.00869509	−	0.999962i	$-0.497232\pi$
$383$	−13.7203	−	5.78358i	−0.701073	−	0.295527i	−0.709769	+	0.704435i	$0.751200\pi$
$384$	0.173412	+	8.52389i	0.00884938	+	0.434983i
$385$	−2.34506	+	11.6003i	−0.119515	+	0.591208i
$386$	−24.7777	+	63.1325i	−1.26115	+	3.21336i
$387$	−33.7313	+	5.62884i	−1.71466	+	0.286130i
$388$	32.6756	−	12.8242i	1.65885	−	0.651052i
$389$	4.77867	−	0.842609i	0.242288	−	0.0427220i	−0.0511852	−	0.998689i	$-0.516300\pi$
$389$	4.77867	−	0.842609i	0.242288	−	0.0427220i	0.293473	+	0.955967i	$0.405189\pi$
$390$	14.9320	−	8.04285i	0.756111	−	0.407266i
$391$	15.6569	−	1.96206i	0.791803	−	0.0992258i
$392$	23.3264	−	2.92318i	1.17816	−	0.147643i
$393$	−0.852970	+	28.8812i	−0.0430266	+	1.45686i
$394$	43.0894	−	7.59783i	2.17081	−	0.382773i
$395$	6.89426	−	2.70580i	0.346888	−	0.136143i
$396$	−45.9378	−	27.0877i	−2.30846	−	1.36121i
$397$	4.68766	−	11.9440i	0.235267	−	0.599450i	−0.763667	−	0.645610i	$-0.776603\pi$
$397$	4.68766	−	11.9440i	0.235267	−	0.599450i	0.998934	+	0.0461600i	$0.0146984\pi$
$398$	4.82054	−	23.8458i	0.241632	−	1.19528i
$399$	12.3655	−	7.47862i	0.619048	−	0.374399i
$400$	−22.0107	−	9.27831i	−1.10054	−	0.463915i
$401$	12.1587	−	23.7165i	0.607178	−	1.18434i	−0.360643	−	0.932704i	$-0.617443\pi$
$401$	12.1587	−	23.7165i	0.607178	−	1.18434i	0.967821	−	0.251641i	$-0.0809701\pi$
$402$	−5.48509	−	24.5509i	−0.273571	−	1.22449i
$403$	−10.9773	+	10.7069i	−0.546818	+	0.533351i
$404$	−31.8520	+	7.27000i	−1.58469	+	0.361696i
$405$	13.1831	−	6.86824i	0.655072	−	0.341286i
$406$	27.1317	−	7.83087i	1.34652	−	0.388640i
$407$	−0.825260	−	0.300370i	−0.0409066	−	0.0148888i
$408$	0.136742	−	29.7789i	0.00676971	−	1.47427i
$409$	19.3055	−	8.71099i	0.954597	−	0.430731i	0.126906	−	0.991915i	$-0.459495\pi$
$409$	19.3055	−	8.71099i	0.954597	−	0.430731i	0.827691	+	0.561184i	$0.189654\pi$
$410$	−3.04291	−	10.8152i	−0.150279	−	0.534122i
$411$	−11.8006	−	4.35652i	−0.582079	−	0.214891i
$412$	−28.5299	−	55.6496i	−1.40557	−	2.74166i
$413$	0.158342	+	2.11293i	0.00779150	+	0.103970i
$414$	37.8068	+	41.5040i	1.85810	+	2.03981i
$415$	−7.41736	+	1.11799i	−0.364104	+	0.0548798i
$416$	22.3156	−	16.0438i	1.09411	−	0.786612i
$417$	0.100959	+	0.00298170i	0.00494400	+	0.000146015i
$418$	−13.5910	−	37.3410i	−0.664758	−	1.82641i
$419$	−8.31753	+	24.7559i	−0.406338	+	1.20940i	0.526832	+	0.849969i	$0.323380\pi$
$419$	−8.31753	+	24.7559i	−0.406338	+	1.20940i	−0.933170	+	0.359435i	$0.882970\pi$
$420$	−22.7608	−	16.5230i	−1.11061	−	0.806239i
$421$	−0.986040	+	19.7572i	−0.0480566	+	0.962906i	0.851025	+	0.525125i	$0.175981\pi$
$421$	−0.986040	+	19.7572i	−0.0480566	+	0.962906i	−0.899082	+	0.437781i	$0.855765\pi$
$422$	−20.5796	−	52.4361i	−1.00180	−	2.55255i
$423$	5.52556	+	22.5649i	0.268662	+	1.09714i
$424$	−9.37663	+	62.2099i	−0.455369	+	3.02118i
$425$	4.59974	+	2.07548i	0.223120	+	0.100676i
$426$	8.51803	−	18.6490i	0.412700	−	0.903547i
$427$	9.80407	+	18.0033i	0.474452	+	0.871241i
$428$	36.4252	+	80.7265i	1.76068	+	3.90206i
$429$	0.984325	+	13.9971i	0.0475237	+	0.675786i
$430$	−6.16678	+	49.2098i	−0.297389	+	2.37311i
$431$	19.7311	−	9.50199i	0.950413	−	0.457695i	0.106582	−	0.994304i	$-0.466009\pi$
$431$	19.7311	−	9.50199i	0.950413	−	0.457695i	0.843831	+	0.536609i	$0.180295\pi$
$432$	44.7900	−	31.2750i	2.15496	−	1.50472i
$433$	2.21657	−	0.505918i	0.106522	−	0.0243128i	−0.168928	−	0.985628i	$-0.554030\pi$
$433$	2.21657	−	0.505918i	0.106522	−	0.0243128i	0.275449	+	0.961316i	$0.411173\pi$
$434$	33.5727	+	12.2195i	1.61154	+	0.586554i
$435$	13.7240	+	6.99899i	0.658015	+	0.335576i
$436$	−40.7218	−	34.1697i	−1.95022	−	1.63643i
$437$	1.48417	+	29.7383i	0.0709977	+	1.42257i
$438$	23.4511	−	42.5966i	1.12054	−	2.03534i
$439$	2.92814	−	6.48943i	0.139753	−	0.309724i	−0.828378	−	0.560170i	$-0.810736\pi$
$439$	2.92814	−	6.48943i	0.139753	−	0.309724i	0.968131	+	0.250446i	$0.0805772\pi$
$440$	−33.7350	+	31.3015i	−1.60825	+	1.49224i
$441$	−5.96557	−	6.88626i	−0.284075	−	0.327917i
$442$	−10.8798	+	7.41769i	−0.517497	+	0.352824i
$443$	−10.7442	−	9.48178i	−0.510471	−	0.450493i	0.366932	−	0.930248i	$-0.380408\pi$
$443$	−10.7442	−	9.48178i	−0.510471	−	0.450493i	−0.877403	+	0.479755i	$0.840726\pi$
$444$	1.46413	−	1.48738i	0.0694847	−	0.0705878i
$445$	12.7770	+	12.4623i	0.605687	+	0.590770i
$446$	−16.3347	−	5.48818i	−0.773472	−	0.259873i
$447$	−7.46957	+	0.901240i	−0.353299	+	0.0426272i
$448$	−19.4769	−	10.6065i	−0.920196	−	0.501112i
$449$	19.4894	−	21.0046i	0.919764	−	0.991270i	−0.0802210	−	0.996777i	$-0.525563\pi$
$449$	19.4894	−	21.0046i	0.919764	−	0.991270i	0.999985	+	0.00550747i	$0.00175309\pi$
$450$	3.39585	+	17.6304i	0.160082	+	0.831107i
$451$	9.19123	+	1.38535i	0.432798	+	0.0652338i
$452$	39.2374	+	46.7613i	1.84557	+	2.19947i
$453$	1.94518	+	1.73259i	0.0913926	+	0.0814040i
$454$	−6.59601	+	1.85583i	−0.309566	+	0.0870983i
$455$	−0.184494	+	7.39798i	−0.00864922	+	0.346823i
$456$	56.0157	+	4.45654i	2.62317	+	0.208697i
$457$	−20.4588	−	20.9754i	−0.957024	−	0.981189i	0.0428155	−	0.999083i	$-0.486367\pi$
$457$	−20.4588	−	20.9754i	−0.957024	−	0.981189i	−0.999840	+	0.0178944i	$0.994304\pi$
$458$	−9.42521	+	41.2945i	−0.440411	+	1.92957i
$459$	−9.62425	+	6.36929i	−0.449221	+	0.297293i
$460$	52.2120	−	25.1440i	2.43440	−	1.17234i
$461$	11.6779	−	11.3903i	0.543894	−	0.530500i	−0.373945	−	0.927451i	$-0.621995\pi$
$461$	11.6779	−	11.3903i	0.543894	−	0.530500i	0.917840	+	0.396951i	$0.129932\pi$
$462$	28.3872	−	16.2160i	1.32069	−	0.754438i
$463$	0.858265	+	0.720170i	0.0398870	+	0.0334691i	0.662513	−	0.749050i	$-0.269490\pi$
$463$	0.858265	+	0.720170i	0.0398870	+	0.0334691i	−0.622626	+	0.782519i	$0.713934\pi$
$464$	53.3302	+	19.0056i	2.47579	+	0.882312i
$465$	8.81216	+	17.3849i	0.408654	+	0.806207i
$466$	−37.0437	+	48.9045i	−1.71602	+	2.26546i
$467$	29.3822	−	2.20189i	1.35965	−	0.101891i	0.625150	−	0.780504i	$-0.285038\pi$
$467$	29.3822	−	2.20189i	1.35965	−	0.101891i	0.734496	+	0.678613i	$0.237419\pi$
$468$	−31.2292	−	11.6924i	−1.44357	−	0.540481i
$469$	10.4887	+	3.23534i	0.484324	+	0.149394i
$470$	33.6492	+	1.67936i	1.55212	+	0.0774633i
$471$	11.8703	+	13.5759i	0.546957	+	0.625544i
$472$	−4.29614	+	7.03033i	−0.197746	+	0.323597i
$473$	−35.0112	−	21.3949i	−1.60982	−	0.983739i
$474$	−18.1625	−	9.41693i	−0.834231	−	0.432534i
$475$	−4.55406	+	8.36266i	−0.208955	+	0.383705i
$476$	18.9111	+	10.9183i	0.866788	+	0.500440i
$477$	22.0635	−	10.3767i	1.01022	−	0.475117i
$478$	−1.36580	−	4.42780i	−0.0624700	−	0.202523i
$479$	−7.51752	+	3.85401i	−0.343484	+	0.176094i	−0.619376	−	0.785095i	$-0.712614\pi$
$479$	−7.51752	+	3.85401i	−0.343484	+	0.176094i	0.275892	+	0.961189i	$0.411027\pi$
$480$	−10.9739	−	33.1659i	−0.500888	−	1.51381i
$481$	−0.540800	−	0.0953576i	−0.0246584	−	0.00434793i
$482$	13.1193	+	64.8973i	0.597566	+	2.95599i
$483$	−23.9070	+	5.34125i	−1.08781	+	0.243035i
$484$	−3.07648	−	9.15668i	−0.139840	−	0.416213i
$485$	−9.17815	+	7.31933i	−0.416758	+	0.332354i
$486$	−38.2532	−	14.9262i	−1.73520	−	0.677067i
$487$	−2.99793	+	13.1348i	−0.135849	+	0.595193i	0.860472	+	0.509497i	$0.170169\pi$
$487$	−2.99793	+	13.1348i	−0.135849	+	0.595193i	−0.996321	+	0.0856962i	$0.972689\pi$
$488$	−9.91174	+	79.0938i	−0.448683	+	3.58041i
$489$	−2.01340	−	9.01185i	−0.0910493	−	0.407530i
$490$	−12.0437	+	5.43430i	−0.544077	+	0.245497i
$491$	−2.04172	−	40.9098i	−0.0921416	−	1.84623i	−0.427348	−	0.904087i	$-0.640552\pi$
$491$	−2.04172	−	40.9098i	−0.0921416	−	1.84623i	0.335206	−	0.942145i	$-0.391194\pi$
$492$	−12.0698	+	18.5007i	−0.544146	+	0.834075i
$493$	−11.1631	−	4.29482i	−0.502761	−	0.193429i
$494$	−12.4237	−	21.5184i	−0.558967	−	0.968160i
$495$	17.3508	+	4.12820i	0.779858	+	0.185549i
$496$	40.3497	+	59.1822i	1.81176	+	2.65736i
$497$	5.22202	+	7.26338i	0.234239	+	0.325807i
$498$	15.8117	+	13.3918i	0.708541	+	0.600102i
$499$	4.10572	+	32.7629i	0.183797	+	1.46667i	0.760300	+	0.649572i	$0.225052\pi$
$499$	4.10572	+	32.7629i	0.183797	+	1.46667i	−0.576503	+	0.817095i	$0.695583\pi$
$500$	59.0233	+	5.90617i	2.63960	+	0.264132i
$501$	0.416157	−	0.115029i	0.0185925	−	0.00513911i
$502$	−15.4796	+	17.5405i	−0.690888	+	0.782871i
$503$	−40.5229	−	3.03677i	−1.80683	−	0.135403i	−0.871774	−	0.489908i	$-0.837030\pi$
$503$	−40.5229	−	3.03677i	−1.80683	−	0.135403i	−0.935054	+	0.354505i	$0.884649\pi$
$504$	4.18041	+	46.0409i	0.186210	+	2.05083i
$505$	9.46244	−	5.46314i	0.421073	−	0.243107i
$506$	1.67933	+	67.3390i	0.0746553	+	2.99358i
$507$	−3.32996	−	13.3333i	−0.147888	−	0.592152i
$508$	40.7730	−	96.7251i	1.80901	−	4.29148i
$509$	−38.2902	+	7.74052i	−1.69718	+	0.343093i	−0.947756	−	0.318996i	$-0.896654\pi$
$509$	−38.2902	+	7.74052i	−1.69718	+	0.343093i	−0.749426	+	0.662089i	$0.769670\pi$
$510$	4.85985	+	16.0160i	0.215198	+	0.709200i
$511$	11.0631	+	18.1040i	0.489404	+	0.800874i
$512$	14.9174	+	30.9763i	0.659263	+	1.36897i
$513$	−10.6279	−	19.0081i	−0.469235	−	0.839229i
$514$	0.880718	−	0.702349i	0.0388468	−	0.0309793i
$515$	14.6031	+	14.9719i	0.643491	+	0.659739i
$516$	80.8178	−	54.5587i	3.55780	−	2.40181i
$517$	−12.7162	+	24.8038i	−0.559257	+	1.09087i
$518$	0.346527	+	1.23163i	0.0152255	+	0.0541147i
$519$	−1.06137	+	1.92787i	−0.0465890	+	0.0846243i
$520$	−17.3749	+	22.9381i	−0.761940	+	1.00590i
$521$	14.4628	+	25.0503i	0.633627	+	1.09747i	0.986804	+	0.161918i	$0.0517680\pi$
$521$	14.4628	+	25.0503i	0.633627	+	1.09747i	−0.353177	+	0.935556i	$0.614899\pi$
$522$	−10.3994	−	41.2656i	−0.455171	−	1.80615i
$523$	4.53552	−	7.85575i	0.198325	−	0.343508i	−0.749661	−	0.661822i	$-0.769783\pi$
$523$	4.53552	−	7.85575i	0.198325	−	0.343508i	0.947985	+	0.318314i	$0.103117\pi$
$524$	−32.0018	−	75.9171i	−1.39800	−	3.31646i
$525$	−7.41460	−	2.52912i	−0.323600	−	0.110380i
$526$	−25.6357	+	26.2829i	−1.11777	+	1.14599i
$527$	−8.21005	−	12.7116i	−0.357635	−	0.553728i
$528$	65.1875	+	6.82546i	2.83692	+	0.297040i
$529$	7.44074	−	26.4460i	0.323511	−	1.14982i
$530$	−5.27004	−	34.9644i	−0.228916	−	1.51876i
$531$	3.19042	−	0.129867i	0.138453	−	0.00563575i
$532$	−23.2117	+	34.0454i	−1.00636	+	1.47605i
$533$	5.81027	−	0.144899i	0.251671	−	0.00627628i
$534$	2.68365	−	49.2301i	0.116133	−	2.13039i
$535$	−19.5982	−	22.2075i	−0.847306	−	0.960114i
$536$	25.7711	+	34.0226i	1.11314	+	1.46955i
$537$	−11.8094	−	17.4932i	−0.509611	−	0.754887i
$538$	1.31395	−	0.802941i	0.0566486	−	0.0346172i
$539$		−	10.9314i		−	0.470847i
$540$	−26.0553	+	33.4308i	−1.12124	+	1.43863i
$541$	−2.45727	−	5.10258i	−0.105646	−	0.219377i	0.841444	−	0.540345i	$-0.181706\pi$
$541$	−2.45727	−	5.10258i	−0.105646	−	0.219377i	−0.947090	+	0.320968i	$0.895992\pi$
$542$	−19.1902	−	57.1166i	−0.824288	−	2.45337i
$543$	16.9334	−	24.5933i	0.726680	−	1.05540i
$544$	11.1552	+	24.7224i	0.478274	+	1.05996i
$545$	16.3820	+	6.90557i	0.701726	+	0.295802i
$546$	15.7198	−	13.0679i	0.672745	−	0.559256i
$547$	−12.3030	+	27.2662i	−0.526037	+	1.16582i	0.437739	+	0.899102i	$0.355779\pi$
$547$	−12.3030	+	27.2662i	−0.526037	+	1.16582i	−0.963776	+	0.266715i	$0.914062\pi$
$548$	35.7670	−	2.68037i	1.52789	−	0.114500i
$549$	27.6188	−	13.8405i	1.17874	−	0.590698i
$550$	−10.7710	+	18.6559i	−0.459277	+	0.795491i
$551$	9.65571	−	20.4000i	0.411347	−	0.869068i
$552$	−87.6031	−	37.4025i	−3.72863	−	1.59195i
$553$	7.49865	−	4.84314i	0.318875	−	0.205951i
$554$	−0.0225771	+	0.225624i	−0.000959209	+	0.00958585i
$555$	−0.321281	+	0.619656i	−0.0136376	+	0.0263029i
$556$	−0.265382	+	0.111868i	−0.0112547	+	0.00474425i
$557$	31.9859	+	29.6786i	1.35529	+	1.25752i	0.937055	+	0.349183i	$0.113541\pi$
$557$	31.9859	+	29.6786i	1.35529	+	1.25752i	0.418232	+	0.908340i	$0.362650\pi$
$558$	20.1295	−	49.9359i	0.852152	−	2.11395i
$559$	−23.8826	−	9.37322i	−1.01013	−	0.396445i
$560$	33.8823	+	6.84946i	1.43179	+	0.289443i
$561$	−13.7315	−	1.78486i	−0.579743	−	0.0753567i
$562$	−19.5189	+	17.2255i	−0.823353	+	0.726613i
$563$	−13.9311	+	16.6025i	−0.587127	+	0.699711i	−0.975051	−	0.221980i	$-0.928748\pi$
$563$	−13.9311	+	16.6025i	−0.587127	+	0.699711i	0.387924	+	0.921691i	$0.373192\pi$
$564$	−41.0625	−	51.9786i	−1.72904	−	2.18870i
$565$	−17.1488	−	11.0759i	−0.721456	−	0.465965i
$566$	−78.7430	−	17.9726i	−3.30982	−	0.755444i
$567$	13.9341	−	11.2626i	0.585179	−	0.472983i
$568$			34.7852i			1.45955i
$569$	−15.6942	−	25.6824i	−0.657934	−	1.07666i	−0.991013	−	0.133763i	$-0.957294\pi$
$569$	−15.6942	−	25.6824i	−0.657934	−	1.07666i	0.333079	−	0.942899i	$-0.391912\pi$
$570$	−30.8226	+	6.88630i	−1.29102	+	0.288436i
$571$	−0.958789	+	38.4462i	−0.0401241	+	1.60892i	0.573418	+	0.819263i	$0.305617\pi$
$571$	−0.958789	+	38.4462i	−0.0401241	+	1.60892i	−0.613543	+	0.789662i	$0.710256\pi$
$572$	−19.1346	−	35.1370i	−0.800056	−	1.46915i
$573$	8.58259	−	5.19073i	0.358543	−	0.216846i
$574$	−6.17782	−	12.0503i	−0.257857	−	0.502969i
$575$	11.8325	−	10.9790i	0.493450	−	0.457854i
$576$	−16.9757	+	28.7890i	−0.707322	+	1.19954i
$577$	−13.8265	−	20.2797i	−0.575604	−	0.844256i	0.422465	−	0.906379i	$-0.361165\pi$
$577$	−13.8265	−	20.2797i	−0.575604	−	0.844256i	−0.998068	+	0.0621237i	$0.980213\pi$
$578$	12.3467	+	29.2899i	0.513556	+	1.21830i
$579$	−35.6712	+	26.7630i	−1.48245	+	1.11223i
$580$	−43.8860	−	1.89459i	−1.82227	−	0.0786686i
$581$	−8.49585	+	3.09224i	−0.352467	+	0.128288i
$582$	31.9092	+	5.77766i	1.32268	+	0.239492i
$583$	28.1602	+	7.92306i	1.16628	+	0.328140i
$584$	−6.16525	+	82.2696i	−0.255120	+	3.40434i
$585$	11.1326	+	0.658150i	0.460278	+	0.0272112i
$586$	−56.5299	+	17.4372i	−2.33523	+	0.720322i
$587$	−16.6251	+	4.23328i	−0.686193	+	0.174726i	−0.573871	−	0.818946i	$-0.694559\pi$
$587$	−16.6251	+	4.23328i	−0.686193	+	0.174726i	−0.112322	+	0.993672i	$0.535829\pi$
$588$	23.6301	+	10.7932i	0.974491	+	0.445104i
$589$	25.0772	−	13.6563i	1.03329	−	0.562699i
$590$	1.14266	−	4.48749i	0.0470424	−	0.184747i
$591$	26.7328	+	10.6338i	1.09964	+	0.437415i
$592$	−0.877323	+	2.41043i	−0.0360578	+	0.0990679i
$593$	15.4838	−	19.4161i	0.635845	−	0.797325i	−0.354631	−	0.935006i	$-0.615394\pi$
$593$	15.4838	−	19.4161i	0.635845	−	0.797325i	0.990477	+	0.137681i	$0.0439650\pi$
$594$	−22.9638	−	43.5877i	−0.942217	−	1.78842i
$595$	−7.11978	−	1.62504i	−0.291883	−	0.0666203i
$596$	18.3055	−	11.1863i	0.749823	−	0.458207i
$597$	10.9343	−	11.6764i	0.447511	−	0.477882i
$598$	8.34579	+	41.2842i	0.341285	+	1.68824i
$599$	−17.6872	+	4.97640i	−0.722679	+	0.203330i	−0.612375	−	0.790568i	$-0.709786\pi$
$599$	−17.6872	+	4.97640i	−0.722679	+	0.203330i	−0.110304	+	0.993898i	$0.535182\pi$
$600$	−17.6685	−	24.8151i	−0.721315	−	1.01307i
$601$	−2.01427	+	9.96400i	−0.0821637	+	0.406440i	0.917792	+	0.397061i	$0.129970\pi$
$601$	−2.01427	+	9.96400i	−0.0821637	+	0.406440i	−0.999956	+	0.00937952i	$0.997014\pi$
$602$	4.46708	+	59.6091i	0.182065	+	2.42949i
$603$	5.41191	−	15.6308i	0.220390	−	0.636534i
$604$	−7.09754	−	2.18930i	−0.288795	−	0.0890815i
$605$	1.88579	+	2.62298i	0.0766683	+	0.106639i
$606$	−28.5661	−	9.74392i	−1.16042	−	0.395820i
$607$	−25.5305	+	16.4894i	−1.03625	+	0.669282i	−0.945176	−	0.326562i	$-0.894110\pi$
$607$	−25.5305	+	16.4894i	−1.03625	+	0.669282i	−0.0910756	+	0.995844i	$0.529030\pi$
$608$	−48.0932	+	17.5045i	−1.95044	+	0.709901i
$609$	17.8850	+	4.99097i	0.724738	+	0.202244i
$610$	−7.77970	−	44.1209i	−0.314991	−	1.78640i
$611$	−5.13727	+	16.6546i	−0.207832	+	0.673774i
$612$	17.4162	−	27.9208i	0.704008	−	1.12863i
$613$	−38.2993	−	26.1120i	−1.54689	−	1.05465i	−0.971577	−	0.236725i	$-0.923926\pi$
$613$	−38.2993	−	26.1120i	−1.54689	−	1.05465i	−0.575318	−	0.817930i	$-0.695122\pi$
$614$	−55.6133	−	42.1255i	−2.24437	−	1.70005i
$615$	2.03347	−	7.10213i	0.0819974	−	0.286386i
$616$	−32.3789	+	45.0363i	−1.30458	+	1.81456i
$617$	−0.612936	−	0.0152857i	−0.0246759	−	0.000615378i	0.0125909	−	0.999921i	$-0.495992\pi$
$617$	−0.612936	−	0.0152857i	−0.0246759	−	0.000615378i	−0.0372667	+	0.999305i	$0.511865\pi$
$618$	4.58185	−	57.5907i	0.184309	−	2.31664i
$619$	−4.63243	−	46.2941i	−0.186193	−	1.86072i	−0.445967	−	0.895049i	$-0.647140\pi$
$619$	−4.63243	−	46.2941i	−0.186193	−	1.86072i	0.259774	−	0.965669i	$-0.416352\pi$
$620$	−43.4503	−	34.6505i	−1.74501	−	1.39160i
$621$	6.81556	+	36.2810i	0.273499	+	1.45591i
$622$	22.1256	−	27.7446i	0.887155	−	1.11246i
$623$	18.0710	+	11.6715i	0.723999	+	0.467608i
$624$	40.8828	−	2.87503i	1.63662	−	0.115093i
$625$	−8.30967	+	1.67984i	−0.332387	+	0.0671934i
$626$	51.0843	+	9.00753i	2.04174	+	0.360013i
$627$	5.29489	−	25.5868i	0.211458	−	1.02184i
$628$	−46.8697	−	21.1484i	−1.87030	−	0.843913i
$629$	0.197984	−	0.504454i	0.00789413	−	0.0201139i
$630$	−9.87250	−	24.0346i	−0.393330	−	0.957563i
$631$	25.8578	−	17.6296i	1.02938	−	0.701821i	0.0740201	−	0.997257i	$-0.476417\pi$
$631$	25.8578	−	17.6296i	1.02938	−	0.701821i	0.955363	+	0.295435i	$0.0954647\pi$
$632$	34.6680	+	1.73021i	1.37902	+	0.0688239i
$633$	6.59921	−	36.4466i	0.262295	−	1.44862i
$634$	32.7443	−	33.5710i	1.30044	−	1.33328i
$635$	−3.49528	+	34.9301i	−0.138706	+	1.38616i
$636$	−44.9315	+	53.0506i	−1.78165	+	2.10359i
$637$	−1.18693	−	6.73141i	−0.0470278	−	0.266708i
$638$	22.9877	−	45.5915i	0.910090	−	1.80498i
$639$	11.2078	−	7.49153i	0.443375	−	0.296360i
$640$	5.52976	+	5.95966i	0.218583	+	0.235576i
$641$	−7.29240	−	28.6391i	−0.288033	−	1.13118i	−0.930922	−	0.365217i	$-0.880995\pi$
$641$	−7.29240	−	28.6391i	−0.288033	−	1.13118i	0.642890	−	0.765959i	$-0.277735\pi$
$642$	−10.5461	+	81.1346i	−0.416222	+	3.20213i
$643$	15.1912	−	0.758161i	0.599082	−	0.0298989i	0.251990	−	0.967730i	$-0.418915\pi$
$643$	15.1912	−	0.758161i	0.599082	−	0.0298989i	0.347092	+	0.937831i	$0.387169\pi$
$644$	55.6781	−	42.1745i	2.19402	−	1.66191i
$645$	−20.4491	+	25.4022i	−0.805184	+	1.00021i
$646$	23.2435	−	7.80939i	0.914502	−	0.307256i
$647$	28.8803	+	36.2147i	1.13540	+	1.42375i	0.890959	+	0.454083i	$0.150033\pi$
$647$	28.8803	+	36.2147i	1.13540	+	1.42375i	0.244441	+	0.969664i	$0.421396\pi$
$648$	69.5573	−	3.92945i	2.73247	−	0.154364i
$649$	2.99525	+	2.38864i	0.117574	+	0.0937622i
$650$	−4.60700	+	12.6576i	−0.180701	+	0.496473i
$651$	14.5626	+	18.4340i	0.570754	+	0.722484i
$652$	15.8978	+	20.9881i	0.622607	+	0.821956i
$653$	−17.8639	+	42.3781i	−0.699067	+	1.65838i	0.0524115	+	0.998626i	$0.483309\pi$
$653$	−17.8639	+	42.3781i	−0.699067	+	1.65838i	−0.751479	+	0.659757i	$0.770659\pi$
$654$	−15.4266	−	46.6231i	−0.603229	−	1.82311i
$655$	17.7105	+	21.1066i	0.692008	+	0.824703i
$656$	4.04635	−	26.8458i	0.157984	−	1.04815i
$657$	27.8352	−	15.7316i	1.08595	−	0.613748i
$658$	40.1542	−	6.05228i	1.56537	−	0.235942i
$659$	−22.2506	−	19.6362i	−0.866759	−	0.764920i	0.106576	−	0.994305i	$-0.466011\pi$
$659$	−22.2506	−	19.6362i	−0.866759	−	0.764920i	−0.973336	+	0.229385i	$0.926329\pi$
$660$	−49.8916	+	9.84756i	−1.94203	+	0.383316i
$661$	1.88358	+	15.0306i	0.0732628	+	0.584623i	0.984836	+	0.173486i	$0.0555032\pi$
$661$	1.88358	+	15.0306i	0.0732628	+	0.584623i	−0.911573	+	0.411137i	$0.865132\pi$
$662$	39.3458	+	60.9192i	1.52922	+	2.36769i
$663$	−8.64948	+	0.391870i	−0.335918	+	0.0152190i
$664$	−33.8420	−	9.52166i	−1.31332	−	0.369512i
$665$	4.06184	−	13.1681i	0.157511	−	0.510639i
$666$	1.87277	−	0.458595i	0.0725685	−	0.0177702i
$667$	−26.5288	+	27.5669i	−1.02720	+	1.06740i
$668$	−0.943081	+	0.791339i	−0.0364889	+	0.0306178i
$669$	−7.24334	−	8.71322i	−0.280044	−	0.336872i
$670$	−19.4772	−	14.0031i	−0.752469	−	0.540988i
$671$	35.9192	+	9.14615i	1.38665	+	0.353083i
$672$	−20.8854	−	36.5613i	−0.805672	−	1.41038i
$673$	1.54859	−	2.39768i	0.0596936	−	0.0924238i	−0.808907	−	0.587937i	$-0.799940\pi$
$673$	1.54859	−	2.39768i	0.0596936	−	0.0924238i	0.868601	+	0.495513i	$0.165020\pi$
$674$	−59.7668	−	28.7822i	−2.30213	−	1.10865i
$675$	−4.19026	+	11.0371i	−0.161283	+	0.424820i
$676$	24.4318	+	30.6366i	0.939686	+	1.17833i
$677$	2.08410	+	20.8275i	0.0800986	+	0.800465i	0.951038	+	0.309075i	$0.100019\pi$
$677$	2.08410	+	20.8275i	0.0800986	+	0.800465i	−0.870939	+	0.491391i	$0.836489\pi$
$678$	8.14870	+	55.8005i	0.312949	+	2.14301i
$679$	−9.09501	+	10.8390i	−0.349034	+	0.415963i
$680$	−18.7899	−	21.2915i	−0.720559	−	0.816493i
$681$	−4.33149	−	1.24018i	−0.165983	−	0.0475239i
$682$	57.4842	−	29.4704i	2.20118	−	1.12848i
$683$	−8.96790	−	1.35169i	−0.343147	−	0.0517211i	−0.0247920	−	0.999693i	$-0.507892\pi$
$683$	−8.96790	−	1.35169i	−0.343147	−	0.0517211i	−0.318355	+	0.947972i	$0.603130\pi$
$684$	50.0826	+	36.7093i	1.91496	+	1.40362i
$685$	−11.1660	+	4.38233i	−0.426631	+	0.167440i
$686$	−42.7344	+	30.7240i	−1.63161	+	1.17305i
$687$	−19.5380	+	19.8482i	−0.745421	+	0.757255i
$688$	−62.4904	+	102.261i	−2.38243	+	3.89867i
$689$	18.2010	+	1.82129i	0.693405	+	0.0693856i
$690$	53.2452	+	5.57504i	2.02701	+	0.212238i
$691$	−1.47055	+	0.619891i	−0.0559425	+	0.0235818i	−0.416227	−	0.909261i	$-0.636648\pi$
$691$	−1.47055	+	0.619891i	−0.0559425	+	0.0235818i	0.360285	+	0.932842i	$0.382680\pi$
$692$	0.468935	−	6.25750i	0.0178262	−	0.237875i
$693$	21.4841	+	0.733256i	0.816112	+	0.0278541i
$694$	24.5098	+	26.4153i	0.930379	+	1.00271i
$695$	0.0737818	−	0.0619103i	0.00279870	−	0.00234839i
$696$	45.1376	+	56.3541i	1.71094	+	2.13609i
$697$	−0.995974	+	5.64845i	−0.0377252	+	0.213950i
$698$	−38.7271	−	19.8542i	−1.46584	−	0.751494i
$699$	−37.6191	+	14.5654i	−1.42289	+	0.550915i
$700$	22.2267	−	2.22412i	0.840091	−	0.0840638i
$701$	−0.745110	−	3.26454i	−0.0281424	−	0.123300i	0.958906	−	0.283726i	$-0.0915705\pi$
$701$	−0.745110	−	3.26454i	−0.0281424	−	0.123300i	−0.987048	+	0.160426i	$0.948713\pi$
$702$	−18.8736	−	24.3474i	−0.712339	−	0.918932i
$703$	0.921314	+	0.443681i	0.0347480	+	0.0167338i
$704$	−38.0111	+	12.7710i	−1.43260	+	0.481327i
$705$	18.2464	+	12.5633i	0.687198	+	0.473161i
$706$	4.60522	−	18.0858i	0.173320	−	0.680670i
$707$	9.87417	−	8.71401i	0.371356	−	0.327724i
$708$	−8.12087	+	4.11635i	−0.305201	+	0.154702i
$709$	−0.0818181	−	3.28080i	−0.00307274	−	0.123213i	−0.999325	−	0.0367233i	$-0.988308\pi$
$709$	−0.0818181	−	3.28080i	−0.00307274	−	0.123213i	0.996253	−	0.0864899i	$-0.0275650\pi$
$710$	−5.76265	−	18.6821i	−0.216268	−	0.701125i
$711$	−6.90882	−	11.5427i	−0.259101	−	0.432885i
$712$	30.5609	+	77.8679i	1.14532	+	2.91822i
$713$	−47.6682	+	8.40518i	−1.78519	+	0.314777i
$714$	9.56643	+	17.7606i	0.358015	+	0.664674i
$715$	9.57857	+	9.34268i	0.358218	+	0.349396i
$716$	51.3521	+	31.3806i	1.91912	+	1.17275i
$717$	0.765375	−	2.94912i	0.0285834	−	0.110137i
$718$	−16.7105	+	59.3926i	−0.623630	+	2.21651i
$719$	−11.1296	−	10.3268i	−0.415065	−	0.385124i	0.444813	−	0.895624i	$-0.353270\pi$
$719$	−11.1296	−	10.3268i	−0.415065	−	0.385124i	−0.859878	+	0.510499i	$0.829461\pi$
$720$	12.0577	−	50.6782i	0.449363	−	1.88867i
$721$	20.8278	+	14.2001i	0.775666	+	0.528840i
$722$	−0.932587	−	3.66250i	−0.0347073	−	0.136304i
$723$	−15.0778	+	40.8414i	−0.560749	+	1.51891i
$724$	−14.7842	+	83.8455i	−0.549451	+	3.11609i
$725$	−11.8363	+	3.09878i	−0.439590	+	0.115086i
$726$	2.02566	−	8.69087i	0.0751795	−	0.322548i
$727$	14.6685	+	1.83820i	0.544025	+	0.0681752i	0.391593	−	0.920139i	$-0.371924\pi$
$727$	14.6685	+	1.83820i	0.544025	+	0.0681752i	0.152433	+	0.988314i	$0.451289\pi$
$728$	−15.0485	+	31.2486i	−0.557735	+	1.15815i
$729$	−16.2463	−	21.5652i	−0.601716	−	0.798710i
$730$	−10.3179	−	45.2059i	−0.381884	−	1.67314i
$731$	13.7364	−	21.2681i	0.508060	−	0.786630i
$732$	−55.2363	+	68.6154i	−2.04159	+	2.53610i
$733$	46.1933	+	1.15199i	1.70619	+	0.0425497i	0.866091	−	0.499886i	$-0.166625\pi$
$733$	46.1933	+	1.15199i	1.70619	+	0.0425497i	0.840098	+	0.542435i	$0.182498\pi$
$734$	−4.00541	+	2.18123i	−0.147842	+	0.0805106i
$735$	−8.61554	−	1.11987i	−0.317789	−	0.0413072i
$736$	86.7290	−	2.16289i	3.19687	−	0.0797251i
$737$	17.1874	−	9.92313i	0.633105	−	0.365523i
$738$	−18.4665	+	8.68500i	−0.679762	+	0.319699i
$739$	27.3478	−	29.4739i	1.00601	−	1.08422i	0.00956159	−	0.999954i	$-0.496956\pi$
$739$	27.3478	−	29.4739i	1.00601	−	1.08422i	0.996444	−	0.0842615i	$-0.0268531\pi$
$740$	0.0992046	−	1.98775i	0.00364683	−	0.0730712i
$741$	0.482315	−	16.3310i	0.0177183	−	0.599934i
$742$	−14.5764	−	40.0483i	−0.535116	−	1.47022i
$743$	−31.3969	−	10.5488i	−1.15184	−	0.386998i	−0.322953	−	0.946415i	$-0.604676\pi$
$743$	−31.3969	−	10.5488i	−1.15184	−	0.386998i	−0.828886	+	0.559417i	$0.811025\pi$
$744$	4.13436	+	91.2548i	0.151573	+	3.34556i
$745$	−4.74728	+	5.37933i	−0.173927	+	0.197083i
$746$	0.333957	+	2.21566i	0.0122270	+	0.0811211i
$747$	4.22051	+	12.9546i	0.154420	+	0.473983i
$748$	37.7285	−	11.6377i	1.37949	−	0.425517i
$749$	−28.4570	−	21.5554i	−1.03980	−	0.787616i
$750$	43.5299	+	33.2883i	1.58949	+	1.21552i
$751$	−16.0767	−	11.5584i	−0.586647	−	0.421771i	0.250996	−	0.967988i	$-0.419242\pi$
$751$	−16.0767	−	11.5584i	−0.586647	−	0.421771i	−0.837643	+	0.546217i	$0.816067\pi$
$752$	72.4472	+	37.1415i	2.64188	+	1.35441i
$753$	−14.7198	+	4.46655i	−0.536421	+	0.162770i
$754$	9.20521	−	30.5707i	0.335234	−	1.11332i
$755$	2.48401			0.0904023
$756$	−22.7976	+	45.7178i	−0.829140	+	1.66274i
$757$	6.03800	−	12.5380i	0.219455	−	0.455702i	−0.761954	−	0.647631i	$-0.775760\pi$
$757$	6.03800	−	12.5380i	0.219455	−	0.455702i	0.981409	+	0.191929i	$0.0614742\pi$
$758$	90.3418	−	9.04006i	3.28136	−	0.328350i
$759$	−22.3218	+	38.2557i	−0.810230	+	1.38860i
$760$	42.7139	−	32.3545i	1.54940	−	1.17362i
$761$	12.1980	−	16.9664i	0.442177	−	0.615031i	−0.530362	−	0.847772i	$-0.677944\pi$
$761$	12.1980	−	16.9664i	0.442177	−	0.615031i	0.972539	+	0.232740i	$0.0747692\pi$
$762$	78.9937	−	56.2442i	2.86164	−	2.03751i
$763$	21.0028	+	4.24581i	0.760354	+	0.153709i
$764$	−16.1107	+	23.6301i	−0.582865	+	0.854906i
$765$	−2.81347	+	10.6396i	−0.101721	+	0.384675i
$766$	33.9663	+	19.6104i	1.22725	+	0.708554i
$767$	2.10380	+	1.14567i	0.0759639	+	0.0413677i
$768$	−1.68010	+	16.0461i	−0.0606255	+	0.579012i
$769$	7.88422	−	0.988021i	0.284312	−	0.0356290i	0.0190952	−	0.999818i	$-0.493921\pi$
$769$	7.88422	−	0.988021i	0.284312	−	0.0356290i	0.265217	+	0.964189i	$0.414556\pi$
$770$	9.92883	−	29.5516i	0.357810	−	1.06497i
$771$	0.735373	−	0.0887263i	0.0264838	−	0.00319540i
$772$	60.8126	−	111.671i	2.18869	−	4.01912i
$773$	−12.0890	−	0.905946i	−0.434812	−	0.0325846i	−0.144473	−	0.989509i	$-0.546149\pi$
$773$	−12.0890	−	0.905946i	−0.434812	−	0.0325846i	−0.290338	+	0.956924i	$0.593768\pi$
$774$	90.0071	−	3.66376i	3.23524	−	0.131691i
$775$	−14.4096	−	5.65536i	−0.517609	−	0.203147i
$776$	−53.3178	+	13.5764i	−1.91400	+	0.487363i
$777$	−0.231571	+	0.808790i	−0.00830758	+	0.0290152i
$778$	−12.7660	+	0.637124i	−0.457683	+	0.0228420i
$779$	−10.4882	−	2.67063i	−0.375780	−	0.0956854i
$780$	−29.6534	+	11.4813i	−1.06176	+	0.411095i
$781$	16.0492	+	2.01122i	0.574285	+	0.0719672i
$782$	−41.5650			−1.48636
$783$	8.43626	−	26.6801i	0.301487	−	0.953470i
$784$	−31.9284			−1.14030
$785$	17.0631	+	2.13828i	0.609008	+	0.0763186i
$786$	11.6891	−	75.2073i	0.416937	−	2.68256i
$787$	41.7580	+	10.6329i	1.48851	+	0.379022i	0.902290	−	0.431129i	$-0.141885\pi$
$787$	41.7580	+	10.6329i	1.48851	+	0.379022i	0.586222	+	0.810151i	$0.300615\pi$
$788$	−81.9317	+	4.08904i	−2.91870	+	0.145666i
$789$	−23.4221	+	5.84960i	−0.833847	+	0.208251i
$790$	−18.9058	+	4.81400i	−0.672636	+	0.171274i
$791$	−22.9048	−	8.98945i	−0.814399	−	0.319628i
$792$	66.1649	+	51.0810i	2.35107	+	1.81508i
$793$	23.1117	+	1.73198i	0.820721	+	0.0615046i
$794$	−16.1642	+	29.6825i	−0.573647	+	1.05339i
$795$	9.12946	−	21.3828i	0.323788	−	0.758369i
$796$	−14.5269	+	43.2372i	−0.514893	+	1.53250i
$797$	−36.5891	+	4.58521i	−1.29605	+	0.162416i	−0.742189	−	0.670191i	$-0.766212\pi$
$797$	−36.5891	+	4.58521i	−1.29605	+	0.162416i	−0.553863	+	0.832608i	$0.686847\pi$
$798$	−34.7691	+	15.4967i	−1.23081	+	0.548576i
$799$	−15.1050	−	8.22576i	−0.534377	−	0.291006i
$800$	24.0278	+	13.8725i	0.849513	+	0.490466i
$801$	18.5074	−	26.6168i	0.653926	−	0.940459i
$802$	−39.5473	+	58.0052i	−1.39646	+	2.04824i
$803$	37.6011	+	7.60122i	1.32691	+	0.268241i
$804$	4.48054	+	46.9513i	0.158016	+	1.65585i
$805$	−13.6359	+	18.9664i	−0.480603	+	0.668479i
$806$	32.1982	−	24.3892i	1.13413	−	0.859073i
$807$	1.01251	+	0.00464936i	0.0356421	+	0.000163665i
$808$	50.9543	−	5.09875i	1.79257	−	0.179373i
$809$	15.9705	−	33.1630i	0.561492	−	1.16595i	−0.406193	−	0.913787i	$-0.633144\pi$
$809$	15.9705	−	33.1630i	0.561492	−	1.16595i	0.967685	−	0.252162i	$-0.0811417\pi$
$810$	−36.7061	+	13.6335i	−1.28972	+	0.479033i
$811$	32.4803			1.14054			0.570269	−	0.821458i	$-0.306839\pi$
$811$	32.4803			1.14054			0.570269	+	0.821458i	$0.306839\pi$
$812$	−52.2993	+	8.24280i	−1.83535	+	0.289266i
$813$	8.99345	−	38.5853i	0.315414	−	1.35325i
$814$	2.05860	+	1.05538i	0.0721537	+	0.0369911i
$815$	−7.14946	−	5.14011i	−0.250435	−	0.180050i
$816$	−5.21322	+	40.1070i	−0.182499	+	1.40403i
$817$	38.0832	+	28.8469i	1.33236	+	1.00923i
$818$	−53.3120	+	16.4446i	−1.86401	+	0.574971i
$819$	13.3093	−	1.88121i	0.465063	−	0.0657349i
$820$	3.13948	+	20.8291i	0.109636	+	0.727384i
$821$	−22.6407	+	25.6550i	−0.790166	+	0.895367i	−0.996541	−	0.0831058i	$-0.973516\pi$
$821$	−22.6407	+	25.6550i	−0.790166	+	0.895367i	0.206374	+	0.978473i	$0.433834\pi$
$822$	29.4161	+	15.2518i	1.02601	+	0.531966i
$823$	−15.0913	−	5.07041i	−0.526050	−	0.176743i	0.0429558	−	0.999077i	$-0.486323\pi$
$823$	−15.0913	−	5.07041i	−0.526050	−	0.176743i	−0.569006	+	0.822334i	$0.692672\pi$
$824$	33.5248	+	92.1088i	1.16789	+	3.20876i
$825$	−12.4707	+	6.71714i	−0.434176	+	0.233861i
$826$	0.278207	−	5.57441i	0.00968006	−	0.193958i
$827$	27.9763	−	30.1513i	0.972831	−	1.04846i	−0.0259773	−	0.999663i	$-0.508270\pi$
$827$	27.9763	−	30.1513i	0.972831	−	1.04846i	0.998809	−	0.0488002i	$-0.0155398\pi$
$828$	−60.6571	−	86.0249i	−2.10798	−	2.98957i
$829$	14.8196	−	8.55610i	0.514706	−	0.297166i	−0.220060	−	0.975486i	$-0.570625\pi$
$829$	14.8196	−	8.55610i	0.514706	−	0.297166i	0.734766	+	0.678321i	$0.237292\pi$
$830$	19.7529	−	0.492607i	0.685633	−	0.0170986i
$831$	−0.0905706	+	0.118436i	−0.00314186	+	0.00410850i
$832$	−22.0201	+	11.9915i	−0.763410	+	0.415731i
$833$	6.74319	+	0.168165i	0.233638	+	0.00582656i
$834$	−0.262900	−	0.0408613i	−0.00910349	−	0.00141491i
$835$	0.223378	−	0.345857i	0.00773032	−	0.0119689i
$836$	16.5784	+	72.6349i	0.573377	+	2.51213i
$837$	28.5120	−	20.9852i	0.985520	−	0.725356i
$838$	29.8480	−	61.9800i	1.03108	−	2.14106i
$839$	−24.8693	−	3.11653i	−0.858585	−	0.107595i	−0.317189	−	0.948362i	$-0.602739\pi$
$839$	−24.8693	−	3.11653i	−0.858585	−	0.107595i	−0.541396	+	0.840768i	$0.682104\pi$
$840$	32.1782	+	30.1332i	1.11025	+	1.03969i
$841$	27.5942	−	8.91970i	0.951524	−	0.307576i
$842$	9.04844	−	51.3163i	0.311830	−	1.76848i
$843$	−16.8710	+	2.89499i	−0.581067	+	0.0997089i
$844$	26.0605	+	102.346i	0.897039	+	3.52289i
$845$	−10.8278	−	7.38228i	−0.372488	−	0.253958i
$846$	−7.05128	−	60.7875i	−0.242428	−	2.08992i
$847$	2.85430	+	2.64840i	0.0980750	+	0.0910003i
$848$	23.1417	−	82.2506i	0.794691	−	2.82450i
$849$	−37.8477	−	37.2563i	−1.29893	−	1.27863i
$850$	−11.3425	−	6.93127i	−0.389045	−	0.237741i
$851$	−1.24089	−	1.21033i	−0.0425370	−	0.0414894i
$852$	−20.1940	+	32.7074i	−0.691834	+	1.12054i
$853$	15.2099	−	2.68191i	0.520777	−	0.0918270i	0.0929201	−	0.995674i	$-0.470380\pi$
$853$	15.2099	−	2.68191i	0.520777	−	0.0918270i	0.427857	+	0.903847i	$0.359269\pi$
$854$	−19.7281	−	50.2663i	−0.675081	−	1.72008i
$855$	−19.6238	−	6.79443i	−0.671119	−	0.232365i
$856$	−40.9165	−	132.648i	−1.39850	−	4.53382i
$857$	−0.323870	−	12.9868i	−0.0110632	−	0.443620i	−0.980303	−	0.197501i	$-0.936717\pi$
$857$	−0.323870	−	12.9868i	−0.0110632	−	0.443620i	0.969239	−	0.246119i	$-0.0791556\pi$
$858$	2.01186	−	36.9066i	0.0686838	−	1.25997i
$859$	−12.0382	+	10.6238i	−0.410739	+	0.362479i	−0.841750	−	0.539867i	$-0.818474\pi$
$859$	−12.0382	+	10.6238i	−0.410739	+	0.362479i	0.431011	+	0.902347i	$0.358157\pi$
$860$	22.9445	−	90.1086i	0.782400	−	3.07268i
$861$	0.706172	−	8.87609i	0.0240663	−	0.302496i
$862$	−54.6833	+	18.3726i	−1.86252	+	0.625774i
$863$	−25.4044	−	12.2341i	−0.864776	−	0.416454i	−0.0517349	−	0.998661i	$-0.516475\pi$
$863$	−25.4044	−	12.2341i	−0.864776	−	0.416454i	−0.813041	+	0.582207i	$0.802189\pi$
$864$	−56.1386	+	29.5762i	−1.90987	+	1.00620i
$865$	0.466978	+	2.04597i	0.0158777	+	0.0695649i
$866$	−5.95915	+	0.596302i	−0.202500	+	0.0202632i
$867$	−3.20992	+	20.6525i	−0.109015	+	0.701396i
$868$	−59.6075	−	30.5590i	−2.02321	−	1.03724i
$869$	2.80273	−	15.8951i	0.0950761	−	0.539203i
$870$	−33.5779	−	22.7884i	−1.13840	−	0.772598i
$871$	9.50633	−	7.97676i	0.322110	−	0.270282i
$872$	56.6726	+	61.0785i	1.91917	+	2.06838i
$873$	15.8571	+	14.2552i	0.536683	+	0.482465i
$874$	5.86124	−	78.2129i	0.198260	−	2.64559i
$875$	−22.0330	+	9.28769i	−0.744851	+	0.313981i
$876$	−53.5572	+	73.7765i	−1.80953	+	2.49268i
$877$	−47.4129	−	4.74437i	−1.60102	−	0.160206i	−0.741371	−	0.671095i	$-0.765824\pi$
$877$	−47.4129	−	4.74437i	−1.60102	−	0.160206i	−0.859647	+	0.510889i	$0.829316\pi$
$878$	−9.77881	+	16.0023i	−0.330019	+	0.540052i
$879$	−37.6515	−	9.77156i	−1.26995	−	0.329587i
$880$	50.7474	−	36.4849i	1.71070	−	1.22991i
$881$	−17.0415	+	6.68830i	−0.574143	+	0.225335i	−0.634606	−	0.772836i	$-0.718838\pi$
$881$	−17.0415	+	6.68830i	−0.574143	+	0.225335i	0.0604628	+	0.998170i	$0.480742\pi$
$882$	13.3367	+	19.9525i	0.449069	+	0.671837i
$883$	0.175364	+	0.0264319i	0.00590148	+	0.000889505i	0.151992	−	0.988382i	$-0.451431\pi$
$883$	0.175364	+	0.0264319i	0.00590148	+	0.000889505i	−0.146091	+	0.989271i	$0.546669\pi$
$884$	21.9692	−	11.2629i	0.738903	−	0.378814i
$885$	2.18945	−	2.11600i	0.0735977	−	0.0711286i
$886$	24.9763	+	28.3016i	0.839096	+	0.950811i
$887$	−18.0930	+	21.5623i	−0.607502	+	0.723993i	−0.978868	−	0.204494i	$-0.934445\pi$
$887$	−18.0930	+	21.5623i	−0.607502	+	0.723993i	0.371366	+	0.928487i	$0.378890\pi$
$888$	−2.56696	+	2.02787i	−0.0861416	+	0.0680509i
$889$	4.21285	+	42.1011i	0.141295	+	1.41203i
$890$	−29.3132	−	36.7576i	−0.982582	−	1.23212i
$891$	2.20872	−	32.3195i	0.0739949	−	1.08274i
$892$	29.1085	+	14.0179i	0.974624	+	0.469354i
$893$	17.6084	−	27.2632i	0.589244	−	0.912328i
$894$	19.8184	+	0.0910039i	0.662826	+	0.00304363i
$895$	−19.5042	−	4.96638i	−0.651954	−	0.166008i
$896$	7.95616	+	5.72009i	0.265797	+	0.191095i
$897$	−9.59170	+	25.9812i	−0.320258	+	0.867485i
$898$	−57.8193	+	48.5162i	−1.92946	+	1.61901i
$899$	34.8572	+	11.4512i	1.16255	+	0.381919i
$900$	−2.20722	−	33.5900i	−0.0735739	−	1.11967i
$901$	−5.32068	+	17.2492i	−0.177258	+	0.574655i
$902$	−23.5693	−	6.63138i	−0.784772	−	0.220801i
$903$	−18.0919	+	34.8939i	−0.602061	+	1.16120i
$904$	−51.9098	−	80.3722i	−1.72650	−	2.67314i
$905$	−3.54047	−	28.2523i	−0.117689	−	0.939137i
$906$	−4.51662	−	5.16557i	−0.150055	−	0.171615i
$907$	−14.7249	−	12.9948i	−0.488932	−	0.431485i	0.381060	−	0.924550i	$-0.375559\pi$
$907$	−14.7249	−	12.9948i	−0.488932	−	0.431485i	−0.869993	+	0.493065i	$0.835877\pi$
$908$	12.7034	−	1.91473i	0.421576	−	0.0635424i
$909$	−12.6166	−	15.3195i	−0.418467	−	0.508114i
$910$	2.90534	−	19.2756i	0.0963109	−	0.638981i
$911$	22.3758	+	26.6665i	0.741344	+	0.883500i	0.996517	−	0.0833958i	$-0.0265766\pi$
$911$	22.3758	+	26.6665i	0.741344	+	0.883500i	−0.255172	+	0.966896i	$0.582132\pi$
$912$	−74.7342	−	15.4654i	−2.47470	−	0.512110i
$913$	−6.34979	+	15.0635i	−0.210147	+	0.498529i
$914$	46.6029	+	61.5244i	1.54149	+	2.03505i
$915$	10.8883	−	27.3727i	0.359956	−	0.904913i
$916$	27.1609	−	74.6240i	0.897422	−	2.46565i
$917$	25.9640	+	20.7056i	0.857406	+	0.683758i
$918$	27.2410	−	13.4951i	0.899088	−	0.445404i
$919$	3.47562	+	4.35829i	0.114650	+	0.143767i	0.835845	−	0.548965i	$-0.184978\pi$
$919$	3.47562	+	4.35829i	0.114650	+	0.143767i	−0.721195	+	0.692732i	$0.756407\pi$
$920$	−86.1025	+	28.9289i	−2.83871	+	0.953757i
$921$	−16.5635	−	42.7798i	−0.545787	−	1.40964i
$922$	−34.2533	+	25.9458i	−1.12807	+	0.854481i
$923$	10.1013	−	0.504134i	0.332488	−	0.0165938i
$924$	−56.5900	+	23.5492i	−1.86167	+	0.774713i
$925$	−0.136790	−	0.537208i	−0.00449763	−	0.0176633i
$926$	−2.00736	−	2.16342i	−0.0659660	−	0.0710944i
$927$	22.4575	−	30.6388i	0.737600	−	1.00631i
$928$	−58.7194	−	29.6069i	−1.92756	−	0.971894i
$929$	5.25395	+	29.7966i	0.172377	+	0.977596i	0.941129	+	0.338049i	$0.109767\pi$
$929$	5.25395	+	29.7966i	0.172377	+	0.977596i	−0.768752	+	0.639547i	$0.779122\pi$
$930$	−17.3381	−	48.3253i	−0.568538	−	1.58465i
$931$	−1.26732	+	12.6650i	−0.0415347	+	0.415077i
$932$	80.3145	−	82.3424i	2.63079	−	2.69722i
$933$	21.9631	−	7.87990i	0.719040	−	0.257976i
$934$	−77.5174	−	3.86873i	−2.53645	−	0.126589i
$935$	−10.9099	+	7.43823i	−0.356791	+	0.243256i
$936$	46.2900	+	24.2709i	1.51304	+	0.793319i
$937$	3.97186	−	10.1201i	0.129755	−	0.330610i	−0.851201	−	0.524839i	$-0.824125\pi$
$937$	3.97186	−	10.1201i	0.129755	−	0.330610i	0.980956	+	0.194229i	$0.0622206\pi$
$938$	−26.3546	−	11.8916i	−0.860508	−	0.388276i
$939$	25.4697	+	22.6860i	0.831173	+	0.740331i
$940$	−62.2071	−	10.9688i	−2.02897	−	0.357762i
$941$	−11.9820	+	2.42221i	−0.390601	+	0.0789618i	−0.389474	−	0.921038i	$-0.627343\pi$
$941$	−11.9820	+	2.42221i	−0.390601	+	0.0789618i	−0.00112763	+	0.999999i	$0.500359\pi$
$942$	−26.5788	−	39.3712i	−0.865986	−	1.28278i
$943$	15.4113	+	9.95366i	0.501860	+	0.324136i
$944$	6.97675	−	8.74856i	0.227074	−	0.284741i
$945$	2.77887	−	16.8575i	0.0903967	−	0.548375i
$946$	84.5010	+	67.3873i	2.74737	+	2.19095i
$947$	2.15837	+	21.5696i	0.0701374	+	0.700918i	0.966339	+	0.257271i	$0.0828234\pi$
$947$	2.15837	+	21.5696i	0.0701374	+	0.700918i	−0.896202	+	0.443647i	$0.853684\pi$
$948$	31.5928	+	21.7528i	1.02609	+	0.706497i
$949$	23.9797	+	0.598015i	0.778413	+	0.0194124i
$950$	14.6420	−	20.3658i	0.475050	−	0.660754i
$951$	29.9168	−	7.47165i	0.970120	−	0.242285i
$952$	−27.2833	−	20.6663i	−0.884256	−	0.669798i
$953$	−22.7671	−	15.5223i	−0.737499	−	0.502818i	0.135357	−	0.990797i	$-0.456782\pi$
$953$	−22.7671	−	15.5223i	−0.737499	−	0.502818i	−0.872856	+	0.487979i	$0.837734\pi$
$954$	−61.0661	+	19.8949i	−1.97709	+	0.644121i
$955$	2.81922	−	9.13970i	0.0912280	−	0.295754i
$956$	1.50858	+	8.55556i	0.0487909	+	0.276707i
$957$	28.6104	−	17.5673i	0.924843	−	0.567870i
$958$	20.9108	−	7.61092i	0.675598	−	0.245898i
$959$	−12.1449	+	7.84400i	−0.392179	+	0.253296i
$960$	6.17141	+	31.2668i	0.199181	+	1.00913i
$961$	9.00080	+	12.5194i	0.290348	+	0.403850i
$962$	1.38225	+	0.426369i	0.0445656	+	0.0137467i
$963$	−33.9274	+	41.7512i	−1.09329	+	1.34541i
$964$	−9.27668	−	123.789i	−0.298782	−	3.98696i
$965$	−8.42615	+	41.6818i	−0.271248	+	1.34178i
$966$	64.2352	−	6.12992i	2.06673	−	0.197227i
$967$	−12.2105	+	3.43551i	−0.392664	+	0.110478i	−0.461479	−	0.887151i	$-0.652681\pi$
$967$	−12.2105	+	3.43551i	−0.392664	+	0.110478i	0.0688156	+	0.997629i	$0.478078\pi$
$968$	3.00005	+	14.8404i	0.0964253	+	0.476989i
$969$	15.7022	+	3.65986i	0.504427	+	0.117572i
$970$	26.3862	−	16.1243i	0.847211	−	0.517720i
$971$	−26.7584	−	6.10742i	−0.858717	−	0.195996i	−0.229579	−	0.973290i	$-0.573735\pi$
$971$	−26.7584	−	6.10742i	−0.858717	−	0.195996i	−0.629138	+	0.777294i	$0.716592\pi$
$972$	67.6838	+	36.6856i	2.17096	+	1.17669i
$973$	0.0723799	−	0.0907616i	0.00232039	−	0.00290968i
$974$	12.1378	−	33.3484i	0.388921	−	1.06855i
$975$	−6.94999	+	5.49042i	−0.222578	+	0.175834i
$976$	26.7142	−	104.913i	0.855099	−	3.35819i
$977$	−9.67338	+	5.26784i	−0.309479	+	0.168533i	−0.625511	−	0.780215i	$-0.715110\pi$
$977$	−9.67338	+	5.26784i	−0.309479	+	0.168533i	0.316032	+	0.948748i	$0.397649\pi$
$978$	2.31070	+	24.2137i	0.0738879	+	0.774269i
$979$	37.6937	−	9.59799i	1.20469	−	0.306753i
$980$	23.6720	−	7.30185i	0.756175	−	0.233249i
$981$	7.47426	−	31.4142i	0.238635	−	1.00298i
$982$	−8.06309	+	107.594i	−0.257303	+	3.43348i
$983$	−50.6417	−	14.2484i	−1.61522	−	0.454452i	−0.660223	−	0.751069i	$-0.729538\pi$
$983$	−50.6417	−	14.2484i	−1.61522	−	0.454452i	−0.954996	+	0.296617i	$0.904141\pi$
$984$	22.3771	−	26.4206i	0.713354	−	0.842258i
$985$	25.7802	−	9.38323i	0.821426	−	0.298975i
$986$	27.7702	+	14.8817i	0.884384	+	0.473929i
$987$	24.5567	+	10.4846i	0.781647	+	0.333727i
$988$	18.0955	+	42.9276i	0.575695	+	1.36571i
$989$	−45.6205	−	66.9130i	−1.45065	−	2.12771i
$990$	−43.9974	−	16.4729i	−1.39833	−	0.523543i
$991$	−36.7832	+	34.1298i	−1.16846	+	1.08417i	−0.173401	+	0.984851i	$0.555476\pi$
$991$	−36.7832	+	34.1298i	−1.16846	+	1.08417i	−0.995056	+	0.0993179i	$0.968334\pi$
$992$	−37.9564	−	74.0366i	−1.20512	−	2.35067i
$993$	0.969917	+	47.6753i	0.0307794	+	1.51293i
$994$	−11.2697	−	20.6947i	−0.357454	−	0.656396i
$995$	0.380299	−	15.2495i	0.0120563	−	0.483442i
$996$	−26.2930	−	28.5993i	−0.833124	−	0.906205i
$997$	21.6295	+	35.3950i	0.685012	+	1.12097i	0.985904	+	0.167314i	$0.0535094\pi$
$997$	21.6295	+	35.3950i	0.685012	+	1.12097i	−0.300892	+	0.953658i	$0.597284\pi$
$998$		−	86.9769i		−	2.75321i
$999$	1.20622	+	0.390345i	0.0381630	+	0.0123500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.bf.a.544.3	yes	3168
27.7	even	9	inner	783.2.bf.a.196.3	yes	3168
29.4	even	14	inner	783.2.bf.a.4.3	✓	3168
783.439	even	126	inner	783.2.bf.a.439.3	yes	3168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
783.2.bf.a.4.3	✓	3168	29.4	even	14	inner
783.2.bf.a.196.3	yes	3168	27.7	even	9	inner
783.2.bf.a.439.3	yes	3168	783.439	even	126	inner
783.2.bf.a.544.3	yes	3168	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:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.bf (of order \(126\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.61370 - 0.327539i) q^{2} +(-1.34920 - 1.08612i) q^{3} +(4.78597 + 1.21866i) q^{4} +(-1.64960 + 0.0823283i) q^{5} +(3.17065 + 3.28071i) q^{6} +(-1.92918 + 0.491229i) q^{7} +(-7.20581 - 2.82807i) q^{8} +(0.640675 + 2.93079i) q^{9} +(4.33853 + 0.325128i) q^{10} +(-1.72144 + 3.16110i) q^{11} +(-5.13361 - 6.84236i) q^{12} +(-0.716813 + 2.13348i) q^{13} +(5.20318 - 0.652043i) q^{14} +(2.31506 + 1.68060i) q^{15} +(9.23297 + 5.02801i) q^{16} +(-1.92349 - 1.11053i) q^{17} +(-0.714581 - 7.87004i) q^{18} +(2.36093 - 3.46284i) q^{19} +(-7.99529 - 1.61628i) q^{20} +(3.13638 + 1.43256i) q^{21} +(5.53471 - 7.69831i) q^{22} +(-5.66316 + 4.28968i) q^{23} +(6.65044 + 11.6420i) q^{24} +(-2.26074 + 0.226221i) q^{25} +(2.57233 - 5.34149i) q^{26} +(2.31880 - 4.65007i) q^{27} -9.83163 q^{28} +(5.31950 - 0.838397i) q^{29} +(-5.50041 - 5.15084i) q^{30} +(6.06284 + 3.10823i) q^{31} +(-9.91502 - 7.12842i) q^{32} +(5.75591 - 2.39525i) q^{33} +(4.66369 + 3.53261i) q^{34} +(3.14194 - 0.969160i) q^{35} +(-0.505382 + 14.8074i) q^{36} +(0.0363647 + 0.241264i) q^{37} +(-7.30495 + 8.27752i) q^{38} +(3.28435 - 2.09995i) q^{39} +(12.1196 + 4.07196i) q^{40} +(-0.883220 - 2.42663i) q^{41} +(-7.72832 - 4.77156i) q^{42} +(-0.568206 + 11.3851i) q^{43} +(-12.0911 + 13.0311i) q^{44} +(-1.29815 - 4.78190i) q^{45} +(16.2068 - 9.35701i) q^{46} +(7.74144 - 0.193059i) q^{47} +(-6.99607 - 16.8119i) q^{48} +(-2.66713 + 1.45244i) q^{49} +(5.98297 + 0.149206i) q^{50} +(1.38900 + 3.58748i) q^{51} +(-6.03063 + 9.33724i) q^{52} +(-1.80849 - 7.92352i) q^{53} +(-7.58372 + 11.3944i) q^{54} +(2.57945 - 5.35629i) q^{55} +(15.2905 + 1.91615i) q^{56} +(-6.94643 + 2.10781i) q^{57} +(-14.1782 + 0.448972i) q^{58} +(0.184823 - 1.04818i) q^{59} +(9.03175 + 10.8645i) q^{60} +(-2.54100 - 9.97913i) q^{61} +(-14.8283 - 10.1098i) q^{62} +(-2.67566 - 5.33930i) q^{63} +(8.16650 + 7.57740i) q^{64} +(1.00681 - 3.57842i) q^{65} +(-15.8287 + 4.37518i) q^{66} +(-4.70480 - 2.87505i) q^{67} +(-7.85243 - 7.65905i) q^{68} +(12.2999 + 0.363260i) q^{69} +(-8.52951 + 1.50398i) q^{70} +(-1.64173 - 4.18305i) q^{71} +(3.67191 - 22.9306i) q^{72} +(-3.14141 - 10.1842i) q^{73} +(-0.0160230 - 0.642502i) q^{74} +(3.29589 + 2.15022i) q^{75} +(15.5193 - 13.6959i) q^{76} +(1.76815 - 6.94395i) q^{77} +(-9.27210 + 4.41287i) q^{78} +(-4.25062 + 1.42813i) q^{79} +(-15.6447 - 7.53409i) q^{80} +(-8.17907 + 3.75537i) q^{81} +(1.51365 + 6.63175i) q^{82} +(4.51902 - 0.452196i) q^{83} +(13.2648 + 10.6784i) q^{84} +(3.26443 + 1.67358i) q^{85} +(5.21417 - 29.5710i) q^{86} +(-8.08767 - 4.64647i) q^{87} +(21.3442 - 17.9099i) q^{88} +(-7.35013 - 7.92156i) q^{89} +(1.82670 + 12.9236i) q^{90} +(0.334830 - 4.46799i) q^{91} +(-32.3314 + 13.6288i) q^{92} +(-4.80405 - 10.7786i) q^{93} +(-20.2970 - 2.03102i) q^{94} +(-3.60950 + 5.90669i) q^{95} +(5.63500 + 20.3866i) q^{96} +(5.77091 - 4.14900i) q^{97} +(7.44680 - 2.92265i) q^{98} +(-10.3674 - 3.01995i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3168 q - 42 q^{2} - 42 q^{3} - 30 q^{4} - 30 q^{5} - 60 q^{6} - 30 q^{7} - 21 q^{8} - 42 q^{9} - 21 q^{10} - 42 q^{11} - 30 q^{13} - 42 q^{14} - 42 q^{15} - 18 q^{16} - 189 q^{18} - 21 q^{19} + 24 q^{20}+ \cdots - 21 q^{98}+O(q^{100}) \) 3168 * q - 42 * q^2 - 42 * q^3 - 30 * q^4 - 30 * q^5 - 60 * q^6 - 30 * q^7 - 21 * q^8 - 42 * q^9 - 21 * q^10 - 42 * q^11 - 30 * q^13 - 42 * q^14 - 42 * q^15 - 18 * q^16 - 189 * q^18 - 21 * q^19 + 24 * q^20 - 42 * q^21 - 30 * q^22 + 60 * q^23 + 60 * q^24 - 30 * q^25 - 84 * q^26 - 168 * q^27 - 144 * q^28 - 72 * q^29 - 54 * q^30 - 42 * q^31 - 42 * q^32 + 60 * q^33 - 60 * q^34 - 45 * q^35 + 60 * q^36 - 21 * q^37 - 42 * q^39 - 42 * q^40 - 30 * q^42 - 42 * q^43 - 21 * q^44 + 12 * q^45 - 42 * q^47 - 105 * q^48 - 120 * q^49 - 42 * q^50 - 57 * q^51 - 132 * q^53 - 12 * q^54 - 84 * q^55 - 126 * q^56 - 36 * q^57 - 63 * q^58 - 66 * q^59 - 42 * q^60 - 42 * q^61 + 3 * q^62 + 150 * q^63 - 237 * q^64 + 66 * q^65 - 42 * q^66 - 30 * q^67 - 126 * q^68 - 42 * q^69 - 111 * q^71 - 42 * q^72 - 21 * q^73 + 270 * q^74 - 42 * q^76 - 42 * q^77 - 66 * q^78 - 42 * q^79 - 246 * q^80 - 42 * q^81 - 60 * q^82 - 228 * q^83 - 168 * q^84 - 147 * q^85 + 36 * q^86 + 39 * q^87 - 12 * q^88 - 21 * q^89 - 42 * q^90 - 15 * q^91 + 120 * q^92 - 24 * q^93 + 96 * q^94 - 210 * q^95 - 258 * q^96 - 42 * q^97 - 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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