LMFDB - Embedded newform 250.2.h.a.109.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(9,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("250.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.h (of order $50$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			109.8
Character	$\chi$	$=$	250.109
Dual form			250.2.h.a.39.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.125333 - 0.992115i) q^{2} +(-0.959277 + 0.793583i) q^{3} +(-0.968583 - 0.248690i) q^{4} +(-0.640085 - 2.14250i) q^{5} +(0.667096 + 1.05118i) q^{6} +(-3.55074 + 1.15371i) q^{7} +(-0.368125 + 0.929776i) q^{8} +(-0.271705 + 1.42433i) q^{9} +O(q^{10})$	\(q+(0.125333 - 0.992115i) q^{2} +(-0.959277 + 0.793583i) q^{3} +(-0.968583 - 0.248690i) q^{4} +(-0.640085 - 2.14250i) q^{5} +(0.667096 + 1.05118i) q^{6} +(-3.55074 + 1.15371i) q^{7} +(-0.368125 + 0.929776i) q^{8} +(-0.271705 + 1.42433i) q^{9} +(-2.20583 + 0.366512i) q^{10} +(-1.38299 - 0.174712i) q^{11} +(1.12650 - 0.530089i) q^{12} +(-1.68000 - 0.320477i) q^{13} +(0.699583 + 3.66734i) q^{14} +(2.31427 + 1.54729i) q^{15} +(0.876307 + 0.481754i) q^{16} +(-1.33976 - 5.21800i) q^{17} +(1.37904 + 0.448079i) q^{18} +(-3.02363 + 3.65494i) q^{19} +(0.0871584 + 2.23437i) q^{20} +(2.49058 - 3.92453i) q^{21} +(-0.346669 + 1.35019i) q^{22} +(-2.38312 + 2.53776i) q^{23} +(-0.384721 - 1.18405i) q^{24} +(-4.18058 + 2.74276i) q^{25} +(-0.528510 + 1.62659i) q^{26} +(-2.66901 - 4.85491i) q^{27} +(3.72610 - 0.234427i) q^{28} +(-0.173502 - 2.75773i) q^{29} +(1.82514 - 2.10209i) q^{30} +(7.30163 - 1.87474i) q^{31} +(0.587785 - 0.809017i) q^{32} +(1.46532 - 0.929920i) q^{33} +(-5.34477 + 0.675202i) q^{34} +(4.74459 + 6.86898i) q^{35} +(0.617386 - 1.31201i) q^{36} +(-1.20338 + 2.18894i) q^{37} +(3.24716 + 3.45787i) q^{38} +(1.86591 - 1.02579i) q^{39} +(2.22767 + 0.193570i) q^{40} +(6.71995 - 6.31045i) q^{41} +(-3.58143 - 2.96282i) q^{42} +(-7.32742 - 10.0853i) q^{43} +(1.29609 + 0.513159i) q^{44} +(3.22554 - 0.329564i) q^{45} +(2.21907 + 2.68239i) q^{46} +(3.03232 + 7.65878i) q^{47} +(-1.22293 + 0.233287i) q^{48} +(5.61361 - 4.07853i) q^{49} +(2.19717 + 4.49138i) q^{50} +(5.42611 + 3.94230i) q^{51} +(1.54752 + 0.728209i) q^{52} +(6.78621 + 4.30666i) q^{53} +(-5.15115 + 2.03948i) q^{54} +(0.510911 + 3.07488i) q^{55} +(0.234427 - 3.72610i) q^{56} -5.90560i q^{57} +(-2.75773 - 0.173502i) q^{58} +(-0.502614 - 1.06811i) q^{59} +(-1.85677 - 2.07421i) q^{60} +(-5.28612 - 4.96400i) q^{61} +(-0.944820 - 7.47902i) q^{62} +(-0.678502 - 5.37090i) q^{63} +(-0.728969 - 0.684547i) q^{64} +(0.388722 + 3.80453i) q^{65} +(-0.738934 - 1.57031i) q^{66} +(-0.927036 - 0.0583242i) q^{67} +5.38725i q^{68} +(0.272145 - 4.32562i) q^{69} +(7.40947 - 3.84626i) q^{70} +(-7.89668 + 3.12652i) q^{71} +(-1.22429 - 0.776956i) q^{72} +(-13.1246 - 6.17596i) q^{73} +(2.02085 + 1.46824i) q^{74} +(1.83373 - 5.94871i) q^{75} +(3.83758 - 2.78817i) q^{76} +(5.11221 - 0.975206i) q^{77} +(-0.783845 - 1.97977i) q^{78} +(6.01512 + 7.27103i) q^{79} +(0.471245 - 2.18585i) q^{80} +(2.36853 + 0.937768i) q^{81} +(-5.41846 - 7.45787i) q^{82} +(-6.54238 - 5.41233i) q^{83} +(-3.38833 + 3.18185i) q^{84} +(-10.3220 + 6.21039i) q^{85} +(-10.9242 + 6.00561i) q^{86} +(2.35493 + 2.50774i) q^{87} +(0.671556 - 1.22156i) q^{88} +(-4.51854 + 9.60239i) q^{89} +(0.0773014 - 3.24141i) q^{90} +(6.33499 - 0.800295i) q^{91} +(2.93937 - 1.86538i) q^{92} +(-5.51653 + 7.59285i) q^{93} +(7.97844 - 2.04851i) q^{94} +(9.76607 + 4.13864i) q^{95} +(0.0781732 + 1.24253i) q^{96} +(8.56513 - 0.538873i) q^{97} +(-3.34280 - 6.08052i) q^{98} +(0.624614 - 1.92236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 10 q^{5}+O(q^{10}) $ 240 * q + 10 * q^5	$ 240 q + 10 q^{5} + 10 q^{11} - 40 q^{12} + 20 q^{15} - 10 q^{17} - 20 q^{19} - 20 q^{22} - 60 q^{23} - 10 q^{24} - 110 q^{25} + 30 q^{26} - 10 q^{28} - 20 q^{29} - 20 q^{30} + 10 q^{31} + 30 q^{33} - 10 q^{35} + 10 q^{37} - 20 q^{39} + 30 q^{41} + 10 q^{42} - 160 q^{45} + 20 q^{46} - 220 q^{47} + 10 q^{48} + 40 q^{49} + 20 q^{51} + 10 q^{55} - 30 q^{59} - 50 q^{60} + 40 q^{61} - 20 q^{63} - 50 q^{65} - 10 q^{67} - 20 q^{69} - 50 q^{71} - 50 q^{74} - 10 q^{75} + 10 q^{76} - 40 q^{77} - 170 q^{78} - 40 q^{79} + 50 q^{81} - 200 q^{82} - 50 q^{83} - 30 q^{84} + 20 q^{85} - 20 q^{87} + 10 q^{88} - 40 q^{89} + 30 q^{90} - 240 q^{91} + 10 q^{92} - 100 q^{93} - 100 q^{95} + 20 q^{97} + 40 q^{98} - 30 q^{99}+O(q^{100}) $ 240 * q + 10 * q^5 + 10 * q^11 - 40 * q^12 + 20 * q^15 - 10 * q^17 - 20 * q^19 - 20 * q^22 - 60 * q^23 - 10 * q^24 - 110 * q^25 + 30 * q^26 - 10 * q^28 - 20 * q^29 - 20 * q^30 + 10 * q^31 + 30 * q^33 - 10 * q^35 + 10 * q^37 - 20 * q^39 + 30 * q^41 + 10 * q^42 - 160 * q^45 + 20 * q^46 - 220 * q^47 + 10 * q^48 + 40 * q^49 + 20 * q^51 + 10 * q^55 - 30 * q^59 - 50 * q^60 + 40 * q^61 - 20 * q^63 - 50 * q^65 - 10 * q^67 - 20 * q^69 - 50 * q^71 - 50 * q^74 - 10 * q^75 + 10 * q^76 - 40 * q^77 - 170 * q^78 - 40 * q^79 + 50 * q^81 - 200 * q^82 - 50 * q^83 - 30 * q^84 + 20 * q^85 - 20 * q^87 + 10 * q^88 - 40 * q^89 + 30 * q^90 - 240 * q^91 + 10 * q^92 - 100 * q^93 - 100 * q^95 + 20 * q^97 + 40 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{27}{50}\right)$

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 $

$2$	0.125333	−	0.992115i	0.0886240	−	0.701531i
$2$	0.125333	−	0.992115i	0.0886240	−	0.701531i
$3$	−0.959277	+	0.793583i	−0.553839	+	0.458175i	−0.871754	−	0.489944i	$-0.837017\pi$
$3$	−0.959277	+	0.793583i	−0.553839	+	0.458175i	0.317915	+	0.948119i	$0.397017\pi$
$4$	−0.968583	−	0.248690i	−0.484292	−	0.124345i
$5$	−0.640085	−	2.14250i	−0.286255	−	0.958154i
$5$	−0.640085	−	2.14250i	−0.286255	−	0.958154i
$6$	0.667096	+	1.05118i	0.272341	+	0.429140i
$7$	−3.55074	+	1.15371i	−1.34205	+	0.436060i	−0.890012	−	0.455937i	$-0.849304\pi$
$7$	−3.55074	+	1.15371i	−1.34205	+	0.436060i	−0.452042	+	0.891997i	$0.649304\pi$
$8$	−0.368125	+	0.929776i	−0.130152	+	0.328726i
$9$	−0.271705	+	1.42433i	−0.0905685	+	0.474777i
$10$	−2.20583	+	0.366512i	−0.697543	+	0.115901i
$11$	−1.38299	−	0.174712i	−0.416987	−	0.0526777i	−0.0859591	−	0.996299i	$-0.527395\pi$
$11$	−1.38299	−	0.174712i	−0.416987	−	0.0526777i	−0.331028	+	0.943621i	$0.607395\pi$
$12$	1.12650	−	0.530089i	0.325191	−	0.153023i
$13$	−1.68000	−	0.320477i	−0.465949	−	0.0888845i	−0.0509396	−	0.998702i	$-0.516222\pi$
$13$	−1.68000	−	0.320477i	−0.465949	−	0.0888845i	−0.415009	+	0.909817i	$0.636222\pi$
$14$	0.699583	+	3.66734i	0.186971	+	0.980138i
$15$	2.31427	+	1.54729i	0.597541	+	0.399508i
$16$	0.876307	+	0.481754i	0.219077	+	0.120438i
$17$	−1.33976	−	5.21800i	−0.324938	−	1.26555i	−0.895782	−	0.444493i	$-0.853384\pi$
$17$	−1.33976	−	5.21800i	−0.324938	−	1.26555i	0.570844	−	0.821059i	$-0.306616\pi$
$18$	1.37904	+	0.448079i	0.325044	+	0.105613i
$19$	−3.02363	+	3.65494i	−0.693668	+	0.838501i	−0.993301	−	0.115554i	$-0.963136\pi$
$19$	−3.02363	+	3.65494i	−0.693668	+	0.838501i	0.299633	+	0.954054i	$0.403136\pi$
$20$	0.0871584	+	2.23437i	0.0194892	+	0.499620i
$21$	2.49058	−	3.92453i	0.543490	−	0.856403i
$22$	−0.346669	+	1.35019i	−0.0739101	+	0.287861i
$23$	−2.38312	+	2.53776i	−0.496915	+	0.529160i	−0.927716	−	0.373286i	$-0.878231\pi$
$23$	−2.38312	+	2.53776i	−0.496915	+	0.529160i	0.430801	+	0.902447i	$0.358231\pi$
$24$	−0.384721	−	1.18405i	−0.0785309	−	0.241693i
$25$	−4.18058	+	2.74276i	−0.836116	+	0.548552i
$26$	−0.528510	+	1.62659i	−0.103649	+	0.319000i
$27$	−2.66901	−	4.85491i	−0.513651	−	0.934328i
$28$	3.72610	−	0.234427i	0.704167	−	0.0443025i
$29$	−0.173502	−	2.75773i	−0.0322185	−	0.512098i	−0.980732	−	0.195360i	$-0.937412\pi$
$29$	−0.173502	−	2.75773i	−0.0322185	−	0.512098i	0.948513	−	0.316738i	$-0.102588\pi$
$30$	1.82514	−	2.10209i	0.333224	−	0.383788i
$31$	7.30163	−	1.87474i	1.31141	−	0.336713i	0.472668	−	0.881240i	$-0.343291\pi$
$31$	7.30163	−	1.87474i	1.31141	−	0.336713i	0.838743	+	0.544527i	$0.183291\pi$
$32$	0.587785	−	0.809017i	0.103907	−	0.143015i
$33$	1.46532	−	0.929920i	0.255079	−	0.161878i
$34$	−5.34477	+	0.675202i	−0.916621	+	0.115796i
$35$	4.74459	+	6.86898i	0.801982	+	1.16107i
$36$	0.617386	−	1.31201i	0.102898	−	0.218669i
$37$	−1.20338	+	2.18894i	−0.197834	+	0.359859i	−0.956553	−	0.291560i	$-0.905826\pi$
$37$	−1.20338	+	2.18894i	−0.197834	+	0.359859i	0.758718	+	0.651419i	$0.225826\pi$
$38$	3.24716	+	3.45787i	0.526759	+	0.560941i
$39$	1.86591	−	1.02579i	0.298785	−	0.164259i
$40$	2.22767	+	0.193570i	0.352226	+	0.0306060i
$41$	6.71995	−	6.31045i	1.04948	−	0.985527i	0.0495670	−	0.998771i	$-0.484216\pi$
$41$	6.71995	−	6.31045i	1.04948	−	0.985527i	0.999912	+	0.0132442i	$0.00421588\pi$
$42$	−3.58143	−	2.96282i	−0.552627	−	0.457173i
$43$	−7.32742	−	10.0853i	−1.11742	−	1.53800i	−0.810005	−	0.586422i	$-0.800536\pi$
$43$	−7.32742	−	10.0853i	−1.11742	−	1.53800i	−0.307415	−	0.951575i	$-0.599464\pi$
$44$	1.29609	+	0.513159i	0.195393	+	0.0773616i
$45$	3.22554	−	0.329564i	0.480835	−	0.0491285i
$46$	2.21907	+	2.68239i	0.327184	+	0.395497i
$47$	3.03232	+	7.65878i	0.442310	+	1.11715i	0.964445	+	0.264284i	$0.0851357\pi$
$47$	3.03232	+	7.65878i	0.442310	+	1.11715i	−0.522135	+	0.852863i	$0.674864\pi$
$48$	−1.22293	+	0.233287i	−0.176515	+	0.0336721i
$49$	5.61361	−	4.07853i	0.801945	−	0.582647i
$50$	2.19717	+	4.49138i	0.310726	+	0.635177i
$51$	5.42611	+	3.94230i	0.759808	+	0.552033i
$52$	1.54752	+	0.728209i	0.214603	+	0.100984i
$53$	6.78621	+	4.30666i	0.932158	+	0.591565i	0.912871	−	0.408249i	$-0.133860\pi$
$53$	6.78621	+	4.30666i	0.932158	+	0.591565i	0.0192870	+	0.999814i	$0.493860\pi$
$54$	−5.15115	+	2.03948i	−0.700982	+	0.277538i
$55$	0.510911	+	3.07488i	0.0688912	+	0.414617i
$56$	0.234427	−	3.72610i	0.0313266	−	0.497922i
$57$		−	5.90560i		−	0.782216i
$58$	−2.75773	−	0.173502i	−0.362108	−	0.0227819i
$59$	−0.502614	−	1.06811i	−0.0654347	−	0.139056i	0.869434	−	0.494048i	$-0.164483\pi$
$59$	−0.502614	−	1.06811i	−0.0654347	−	0.139056i	−0.934869	+	0.354992i	$0.884483\pi$
$60$	−1.85677	−	2.07421i	−0.239707	−	0.267780i
$61$	−5.28612	−	4.96400i	−0.676819	−	0.635575i	0.267904	−	0.963446i	$-0.413669\pi$
$61$	−5.28612	−	4.96400i	−0.676819	−	0.635575i	−0.944723	+	0.327871i	$0.893669\pi$
$62$	−0.944820	−	7.47902i	−0.119992	−	0.949837i
$63$	−0.678502	−	5.37090i	−0.0854832	−	0.676669i
$64$	−0.728969	−	0.684547i	−0.0911211	−	0.0855684i
$65$	0.388722	+	3.80453i	0.0482150	+	0.471894i
$66$	−0.738934	−	1.57031i	−0.0909565	−	0.193292i
$67$	−0.927036	−	0.0583242i	−0.113255	−	0.00712543i	0.00606162	−	0.999982i	$-0.498071\pi$
$67$	−0.927036	−	0.0583242i	−0.113255	−	0.00712543i	−0.119317	+	0.992856i	$0.538071\pi$
$68$			5.38725i			0.653300i
$69$	0.272145	−	4.32562i	0.0327624	−	0.520744i
$70$	7.40947	−	3.84626i	0.885601	−	0.459716i
$71$	−7.89668	+	3.12652i	−0.937163	+	0.371049i	−0.786538	−	0.617542i	$-0.788129\pi$
$71$	−7.89668	+	3.12652i	−0.937163	+	0.371049i	−0.150625	+	0.988591i	$0.548129\pi$
$72$	−1.22429	−	0.776956i	−0.144284	−	0.0915651i
$73$	−13.1246	−	6.17596i	−1.53612	−	0.722841i	−0.542973	−	0.839750i	$-0.682702\pi$
$73$	−13.1246	−	6.17596i	−1.53612	−	0.722841i	−0.993143	+	0.116908i	$0.962702\pi$
$74$	2.02085	+	1.46824i	0.234920	+	0.170679i
$75$	1.83373	−	5.94871i	0.211741	−	0.686897i
$76$	3.83758	−	2.78817i	0.440201	−	0.319825i
$77$	5.11221	−	0.975206i	0.582590	−	0.111135i
$78$	−0.783845	−	1.97977i	−0.0887529	−	0.224164i
$79$	6.01512	+	7.27103i	0.676754	+	0.818055i	0.991360	−	0.131167i	$-0.0418725\pi$
$79$	6.01512	+	7.27103i	0.676754	+	0.818055i	−0.314606	+	0.949222i	$0.601873\pi$
$80$	0.471245	−	2.18585i	0.0526868	−	0.244385i
$81$	2.36853	+	0.937768i	0.263170	+	0.104196i
$82$	−5.41846	−	7.45787i	−0.598368	−	0.823584i
$83$	−6.54238	−	5.41233i	−0.718120	−	0.594080i	0.204923	−	0.978778i	$-0.434306\pi$
$83$	−6.54238	−	5.41233i	−0.718120	−	0.594080i	−0.923043	+	0.384698i	$0.874306\pi$
$84$	−3.38833	+	3.18185i	−0.369697	+	0.347169i
$85$	−10.3220	+	6.21039i	−1.11958	+	0.673611i
$86$	−10.9242	+	6.00561i	−1.17798	+	0.647602i
$87$	2.35493	+	2.50774i	0.252475	+	0.268858i
$88$	0.671556	−	1.22156i	0.0715881	−	0.130218i
$89$	−4.51854	+	9.60239i	−0.478965	+	1.01785i	0.508653	+	0.860972i	$0.330144\pi$
$89$	−4.51854	+	9.60239i	−0.478965	+	1.01785i	−0.987618	+	0.156880i	$0.949856\pi$
$90$	0.0773014	−	3.24141i	0.00814828	−	0.341674i
$91$	6.33499	−	0.800295i	0.664087	−	0.0838937i
$92$	2.93937	−	1.86538i	0.306450	−	0.194479i
$93$	−5.51653	+	7.59285i	−0.572037	+	0.787341i
$94$	7.97844	−	2.04851i	0.822913	−	0.211288i
$95$	9.76607	+	4.13864i	1.00198	+	0.424616i
$96$	0.0781732	+	1.24253i	0.00797852	+	0.126815i
$97$	8.56513	−	0.538873i	0.869658	−	0.0547142i	0.378311	−	0.925678i	$-0.376505\pi$
$97$	8.56513	−	0.538873i	0.869658	−	0.0547142i	0.491346	+	0.870964i	$0.336505\pi$
$98$	−3.34280	−	6.08052i	−0.337673	−	0.614226i
$99$	0.624614	−	1.92236i	0.0627760	−	0.193205i
$100$	4.73134	−	1.61692i	0.473134	−	0.161692i
$101$	2.63437	+	8.10774i	0.262129	+	0.806751i	0.992341	+	0.123530i	$0.0394214\pi$
$101$	2.63437	+	8.10774i	0.262129	+	0.806751i	−0.730212	+	0.683221i	$0.760579\pi$
$102$	4.59129	−	4.88923i	0.454605	−	0.484106i
$103$	−2.79493	+	10.8855i	−0.275392	+	1.07258i	0.668868	+	0.743382i	$0.266779\pi$
$103$	−2.79493	+	10.8855i	−0.275392	+	1.07258i	−0.944260	+	0.329201i	$0.893221\pi$
$104$	0.916422	−	1.44405i	0.0898626	−	0.141601i
$105$	−10.0025	−	2.82403i	−0.976142	−	0.275597i
$106$	5.12324	−	6.19293i	0.497613	−	0.601511i
$107$	6.78652	+	2.20508i	0.656078	+	0.213173i	0.618092	−	0.786106i	$-0.287906\pi$
$107$	6.78652	+	2.20508i	0.656078	+	0.213173i	0.0379858	+	0.999278i	$0.487906\pi$
$108$	1.37779	+	5.36614i	0.132578	+	0.516357i
$109$	−7.00320	−	3.85004i	−0.670785	−	0.368767i	0.109680	−	0.993967i	$-0.465018\pi$
$109$	−7.00320	−	3.85004i	−0.670785	−	0.368767i	−0.780465	+	0.625200i	$0.785018\pi$
$110$	3.11467	−	0.121497i	0.296972	−	0.0115843i
$111$	−0.582730	−	3.05478i	−0.0553103	−	0.289947i
$112$	−3.66734	−	0.699583i	−0.346531	−	0.0661044i
$113$	−9.48687	+	4.46418i	−0.892449	+	0.419955i	−0.816627	−	0.577166i	$-0.804158\pi$
$113$	−9.48687	+	4.46418i	−0.892449	+	0.419955i	−0.0758229	+	0.997121i	$0.524158\pi$
$114$	−5.85903	−	0.740168i	−0.548749	−	0.0693231i
$115$	6.96255	+	3.48144i	0.649261	+	0.324646i
$116$	−0.517769	+	2.71424i	−0.0480737	+	0.252011i
$117$	0.912931	−	2.30580i	0.0844005	−	0.213171i
$118$	−1.12268	+	0.364781i	−0.103351	+	0.0335808i
$119$	10.7772	+	16.9821i	0.987941	+	1.55675i
$120$	−2.29057	+	1.58216i	−0.209099	+	0.144431i
$121$	−8.77228	−	2.25234i	−0.797480	−	0.204758i
$122$	−5.58738	+	4.62229i	−0.505858	+	0.418482i
$123$	−1.43842	+	11.3863i	−0.129698	+	1.02667i
$124$	−7.53847			−0.676974
$125$	8.55228	+	7.20128i	0.764939	+	0.644102i
$126$	−5.41358			−0.482280
$127$	−0.750827	+	5.94341i	−0.0666251	+	0.527392i	0.923116	+	0.384521i	$0.125633\pi$
$127$	−0.750827	+	5.94341i	−0.0666251	+	0.527392i	−0.989741	+	0.142871i	$0.954367\pi$
$128$	−0.770513	+	0.637424i	−0.0681044	+	0.0563409i
$129$	15.0326	+	3.85971i	1.32354	+	0.339828i
$130$	3.82325	+	0.0911772i	0.335321	+	0.00799677i
$131$	−1.78374	−	2.81073i	−0.155846	−	0.245575i	0.757429	−	0.652918i	$-0.226455\pi$
$131$	−1.78374	−	2.81073i	−0.155846	−	0.245575i	−0.913275	+	0.407343i	$0.866455\pi$
$132$	−1.65054	+	0.536295i	−0.143661	+	0.0466785i
$133$	6.51940	−	16.4661i	0.565304	−	1.42779i
$134$	−0.174053	+	0.912416i	−0.0150359	+	0.0788208i
$135$	−8.69324	+	8.82590i	−0.748195	+	0.759613i
$136$	5.34477	+	0.675202i	0.458310	+	0.0578981i
$137$	−7.78712	+	3.66434i	−0.665299	+	0.313066i	−0.728611	−	0.684928i	$-0.759834\pi$
$137$	−7.78712	+	3.66434i	−0.665299	+	0.313066i	0.0633119	+	0.997994i	$0.479834\pi$
$138$	−4.25740	−	0.812143i	−0.362414	−	0.0691342i
$139$	1.75636	+	9.20718i	0.148973	+	0.780943i	0.975830	+	0.218531i	$0.0701265\pi$
$139$	1.75636	+	9.20718i	0.148973	+	0.780943i	−0.826857	+	0.562412i	$0.809873\pi$
$140$	−2.88728	−	7.83311i	−0.244020	−	0.662019i
$141$	−8.98671	−	4.94049i	−0.756818	−	0.416064i
$142$	2.11215	+	8.22626i	0.177247	+	0.690333i
$143$	2.26743	+	0.736734i	0.189612	+	0.0616088i
$144$	−0.924273	+	1.11725i	−0.0770228	+	0.0931045i
$145$	−5.79738	+	2.13691i	−0.481446	+	0.177461i
$146$	−7.77221	+	12.2470i	−0.643232	+	1.01357i
$147$	−2.14836	+	8.36731i	−0.177194	+	0.690124i
$148$	1.70994	−	1.82090i	0.140556	−	0.149677i
$149$	−4.88883	−	15.0463i	−0.400509	−	1.23264i	−0.924588	−	0.380969i	$-0.875590\pi$
$149$	−4.88883	−	15.0463i	−0.400509	−	1.23264i	0.524079	−	0.851670i	$-0.324410\pi$
$150$	−5.67197	−	2.56484i	−0.463115	−	0.209418i
$151$	1.04852	−	3.22701i	0.0853273	−	0.262610i	−0.899285	−	0.437363i	$-0.855913\pi$
$151$	1.04852	−	3.22701i	0.0853273	−	0.262610i	0.984612	+	0.174753i	$0.0559126\pi$
$152$	−2.28520	−	4.15677i	−0.185355	−	0.337159i
$153$	7.79617	−	0.490494i	0.630283	−	0.0396541i
$154$	−0.326786	−	5.19412i	−0.0263332	−	0.418554i
$155$	−8.69029	−	14.4437i	−0.698021	−	1.16015i
$156$	−2.06240	+	0.529533i	−0.165124	+	0.0423966i
$157$	1.58917	−	2.18730i	0.126829	−	0.174566i	−0.740880	−	0.671637i	$-0.765591\pi$
$157$	1.58917	−	2.18730i	0.126829	−	0.174566i	0.867710	+	0.497072i	$0.165591\pi$
$158$	7.96759	−	5.05639i	0.633868	−	0.402265i
$159$	−9.92755	+	1.25414i	−0.787306	+	0.0994599i
$160$	−2.10955	−	0.741488i	−0.166774	−	0.0586198i
$161$	5.53401	−	11.7604i	0.436141	−	0.926847i
$162$	1.22723	−	2.23232i	0.0964202	−	0.175388i
$163$	−15.7297	−	16.7504i	−1.23204	−	1.31199i	−0.933927	−	0.357464i	$-0.883642\pi$
$163$	−15.7297	−	16.7504i	−1.23204	−	1.31199i	−0.298117	−	0.954529i	$-0.596358\pi$
$164$	−8.07817	+	4.44101i	−0.630799	+	0.346785i
$165$	−2.93028	−	2.54421i	−0.228122	−	0.198067i
$166$	−6.18963	+	5.81245i	−0.480408	+	0.451134i
$167$	5.50086	+	4.55071i	0.425669	+	0.352144i	0.825459	−	0.564463i	$-0.190917\pi$
$167$	5.50086	+	4.55071i	0.425669	+	0.352144i	−0.399789	+	0.916607i	$0.630917\pi$
$168$	2.73209	+	3.76040i	0.210786	+	0.290121i
$169$	−9.36739	−	3.70881i	−0.720569	−	0.285293i
$170$	4.86773	+	11.0190i	0.373338	+	0.845116i
$171$	−4.38430	−	5.29971i	−0.335276	−	0.405279i
$172$	4.58910	+	11.5907i	0.349915	+	0.883785i
$173$	21.5757	−	4.11579i	1.64037	−	0.312918i	0.717073	−	0.696998i	$-0.245481\pi$
$173$	21.5757	−	4.11579i	1.64037	−	0.312918i	0.923300	+	0.384080i	$0.125481\pi$
$174$	2.78312	−	2.02205i	0.210988	−	0.153291i
$175$	11.6798	−	14.5620i	0.882912	−	1.10078i
$176$	−1.12775	−	0.819362i	−0.0850077	−	0.0617617i
$177$	1.32978	+	0.625746i	0.0999523	+	0.0470340i
$178$	8.96035	+	5.68641i	0.671607	+	0.426215i
$179$	−13.9307	+	5.51556i	−1.04123	+	0.412252i	−0.825620	−	0.564227i	$-0.809174\pi$
$179$	−13.9307	+	5.51556i	−1.04123	+	0.412252i	−0.215611	+	0.976479i	$0.569174\pi$
$180$	−3.20616	−	0.482948i	−0.238973	−	0.0359968i
$181$	−0.812594	+	12.9158i	−0.0603997	+	0.960025i	0.844812	+	0.535064i	$0.179712\pi$
$181$	−0.812594	+	12.9158i	−0.0603997	+	0.960025i	−0.905211	+	0.424961i	$0.860288\pi$
$182$		−	6.38534i		−	0.473313i
$183$	9.01020	+	0.566874i	0.666053	+	0.0419045i
$184$	−1.48227	−	3.14998i	−0.109274	−	0.232220i
$185$	5.46006	+	1.17713i	0.401431	+	0.0865442i
$186$	6.84157	+	6.42466i	0.501648	+	0.471079i
$187$	0.941219	+	7.45051i	0.0688287	+	0.544836i
$188$	−1.03240	−	8.17227i	−0.0752953	−	0.596024i
$189$	15.0781	+	14.1593i	1.09677	+	1.02994i
$190$	5.33002	−	9.17036i	0.386680	−	0.665288i
$191$	−9.45964	−	20.1028i	−0.684475	−	1.45458i	−0.880530	−	0.473991i	$-0.842813\pi$
$191$	−9.45964	−	20.1028i	−0.684475	−	1.45458i	0.196054	−	0.980593i	$-0.437187\pi$
$192$	1.24253	+	0.0781732i	0.0896717	+	0.00564167i
$193$			5.84473i			0.420713i	0.977625	+	0.210357i	$0.0674625\pi$
$193$			5.84473i			0.420713i	−0.977625	+	0.210357i	$0.932537\pi$
$194$	0.538873	−	8.56513i	0.0386888	−	0.614941i
$195$	−3.39210	−	3.34112i	−0.242914	−	0.239262i
$196$	−6.45154	+	2.55435i	−0.460824	+	0.182453i
$197$	8.44013	+	5.35627i	0.601334	+	0.381618i	0.801369	−	0.598171i	$-0.204105\pi$
$197$	8.44013	+	5.35627i	0.601334	+	0.381618i	−0.200035	+	0.979789i	$0.564105\pi$
$198$	−1.82892	−	0.860624i	−0.129976	−	0.0611619i
$199$	−11.1377	−	8.09199i	−0.789528	−	0.573626i	0.118295	−	0.992978i	$-0.462257\pi$
$199$	−11.1377	−	8.09199i	−0.789528	−	0.573626i	−0.907823	+	0.419353i	$0.862257\pi$
$200$	−1.01118	−	4.89668i	−0.0715011	−	0.346248i
$201$	0.935570	−	0.679731i	0.0659900	−	0.0479445i
$202$	8.37398	−	1.59742i	0.589191	−	0.112394i
$203$	3.79767	+	9.59183i	0.266544	+	0.673214i
$204$	−4.27523	−	5.16787i	−0.299326	−	0.361823i
$205$	−17.8215	−	10.3582i	−1.24470	−	0.723451i
$206$	10.4494	+	4.13721i	0.728043	+	0.288253i
$207$	−2.96711	−	4.08387i	−0.206228	−	0.283849i
$208$	−1.31781	−	1.09018i	−0.0913734	−	0.0755906i
$209$	4.82021	−	4.52648i	0.333421	−	0.313103i
$210$	−4.05541	+	9.56967i	−0.279850	+	0.660370i
$211$	5.25744	−	2.89030i	0.361937	−	0.198977i	−0.290400	−	0.956905i	$-0.593788\pi$
$211$	5.25744	−	2.89030i	0.361937	−	0.198977i	0.652338	+	0.757929i	$0.273788\pi$
$212$	−5.50199	−	5.85902i	−0.377878	−	0.402399i
$213$	5.09395	−	9.26586i	0.349032	−	0.634886i
$214$	3.03826	−	6.45664i	0.207691	−	0.441367i
$215$	−16.9176	+	22.1544i	−1.15377	+	1.51092i
$216$	5.49651	−	0.694371i	0.373990	−	0.0472460i
$217$	−23.7633	+	15.0807i	−1.61316	+	1.02374i
$218$	−4.69742	+	6.46544i	−0.318149	+	0.437895i
$219$	17.4912	−	4.49099i	1.18195	−	0.303473i
$220$	0.269832	−	3.10534i	0.0181921	−	0.209362i
$221$	0.578539	+	9.19561i	0.0389167	+	0.618564i
$222$	−3.10373	+	0.195270i	−0.208309	+	0.0131057i
$223$	−1.01268	−	1.84206i	−0.0678140	−	0.123353i	0.840227	−	0.542236i	$-0.182422\pi$
$223$	−1.01268	−	1.84206i	−0.0678140	−	0.123353i	−0.908041	+	0.418882i	$0.862422\pi$
$224$	−1.15371	+	3.55074i	−0.0770852	+	0.237244i
$225$	−2.77071	−	6.69975i	−0.184714	−	0.446650i
$226$	3.23996	+	9.97157i	0.215519	+	0.663299i
$227$	16.6528	−	17.7335i	1.10529	−	1.17701i	0.122462	−	0.992473i	$-0.460921\pi$
$227$	16.6528	−	17.7335i	1.10529	−	1.17701i	0.982825	−	0.184539i	$-0.0590791\pi$
$228$	−1.46866	+	5.72007i	−0.0972646	+	0.378821i
$229$	11.5079	−	18.1336i	0.760464	−	1.19830i	−0.214670	−	0.976687i	$-0.568868\pi$
$229$	11.5079	−	18.1336i	0.760464	−	1.19830i	0.975135	−	0.221614i	$-0.0711324\pi$
$230$	4.32663	−	6.47131i	0.285289	−	0.426705i
$231$	−4.13012	+	4.99245i	−0.271742	+	0.328479i
$232$	2.62795	+	0.853871i	0.172533	+	0.0560594i
$233$	5.83465	+	22.7245i	0.382241	+	1.48873i	0.810858	+	0.585243i	$0.199001\pi$
$233$	5.83465	+	22.7245i	0.382241	+	1.48873i	−0.428617	+	0.903486i	$0.640999\pi$
$234$	−2.17320	−	1.19473i	−0.142066	−	0.0781017i
$235$	14.4680	−	11.3990i	0.943785	−	0.743589i
$236$	0.221195	+	1.15955i	0.0143986	+	0.0754801i
$237$	−11.5403	−	2.20144i	−0.749625	−	0.142999i
$238$	18.1989	−	8.56376i	1.17966	−	0.555106i
$239$	0.913365	+	0.115385i	0.0590807	+	0.00746362i	0.154818	−	0.987943i	$-0.450521\pi$
$239$	0.913365	+	0.115385i	0.0590807	+	0.00746362i	−0.0957373	+	0.995407i	$0.530521\pi$
$240$	1.28260	+	2.47081i	0.0827913	+	0.159490i
$241$	−2.83021	+	14.8365i	−0.182310	+	0.955701i	0.767068	+	0.641565i	$0.221715\pi$
$241$	−2.83021	+	14.8365i	−0.182310	+	0.955701i	−0.949378	+	0.314136i	$0.898285\pi$
$242$	−3.33404	+	8.42081i	−0.214320	+	0.541310i
$243$	12.7908	−	4.15600i	0.820533	−	0.266607i
$244$	3.88555	+	6.12265i	0.248747	+	0.391963i
$245$	−12.3314	−	9.41654i	−0.787826	−	0.601601i
$246$	11.1162	+	2.85416i	0.708745	+	0.181975i
$247$	6.25103	−	5.17130i	0.397743	−	0.329042i
$248$	−0.944820	+	7.47902i	−0.0599962	+	0.474918i
$249$	10.5711			0.669916
$250$	8.21638	−	7.58228i	0.519650	−	0.479546i
$251$	−8.53525			−0.538740			−0.269370	−	0.963037i	$-0.586816\pi$
$251$	−8.53525			−0.538740			−0.269370	+	0.963037i	$0.586816\pi$
$252$	−0.678502	+	5.37090i	−0.0427416	+	0.338335i
$253$	3.73921	−	3.09334i	0.235082	−	0.194477i
$254$	5.80244	+	1.48981i	0.364078	+	0.0934792i
$255$	4.97320	−	14.1488i	0.311434	−	0.886035i
$256$	0.535827	+	0.844328i	0.0334892	+	0.0527705i
$257$	14.1032	−	4.58241i	0.879735	−	0.285843i	0.165888	−	0.986145i	$-0.446951\pi$
$257$	14.1032	−	4.58241i	0.879735	−	0.285843i	0.713847	+	0.700302i	$0.246951\pi$
$258$	5.71335	−	14.4303i	0.355698	−	0.898390i
$259$	1.74750	−	9.16070i	0.108584	−	0.569218i
$260$	0.569639	−	3.78168i	0.0353275	−	0.234530i
$261$	3.97506	+	0.502167i	0.246050	+	0.0310834i
$262$	−3.01213	+	1.41740i	−0.186090	+	0.0875673i
$263$	−6.04727	−	1.15358i	−0.372891	−	0.0711327i	−0.00247030	−	0.999997i	$-0.500786\pi$
$263$	−6.04727	−	1.15358i	−0.372891	−	0.0711327i	−0.370420	+	0.928864i	$0.620786\pi$
$264$	0.325198	+	1.70475i	0.0200145	+	0.104920i
$265$	4.88325	−	17.2961i	0.299976	−	1.06249i
$266$	−15.5192	−	8.53175i	−0.951543	−	0.523115i
$267$	−3.28576	−	12.7972i	−0.201085	−	0.783176i
$268$	0.883407	+	0.287036i	0.0539627	+	0.0175335i
$269$	9.58534	−	11.5867i	0.584428	−	0.706453i	−0.392564	−	0.919724i	$-0.628412\pi$
$269$	9.58534	−	11.5867i	0.584428	−	0.706453i	0.976993	+	0.213272i	$0.0684120\pi$
$270$	7.66676	+	9.73087i	0.466584	+	0.592202i
$271$	−8.62339	+	13.5883i	−0.523833	+	0.825429i	−0.998501	−	0.0547358i	$-0.982568\pi$
$271$	−8.62339	+	13.5883i	−0.523833	+	0.825429i	0.474667	+	0.880165i	$0.342568\pi$
$272$	1.33976	−	5.21800i	0.0812346	−	0.316388i
$273$	−5.44191	+	5.79505i	−0.329359	+	0.350732i
$274$	2.65946	+	8.18498i	0.160664	+	0.494473i
$275$	6.26090	−	3.06281i	0.377546	−	0.184694i
$276$	−1.33933	+	4.12205i	−0.0806184	+	0.248118i
$277$	5.57618	+	10.1430i	0.335040	+	0.609435i	0.989141	−	0.146972i	$-0.0469528\pi$
$277$	5.57618	+	10.1430i	0.335040	+	0.609435i	−0.654101	+	0.756407i	$0.726953\pi$
$278$	9.35471	−	0.588549i	0.561058	−	0.0352988i
$279$	0.686355	+	10.9093i	0.0410910	+	0.653123i
$280$	−8.13322	+	1.88277i	−0.486053	+	0.112517i
$281$	21.1653	−	5.43433i	1.26262	−	0.324185i	0.442701	−	0.896669i	$-0.354020\pi$
$281$	21.1653	−	5.43433i	1.26262	−	0.324185i	0.819915	+	0.572485i	$0.194020\pi$
$282$	−6.02786	+	8.29664i	−0.358954	+	0.494058i
$283$	20.1647	−	12.7969i	1.19867	−	0.760697i	0.221914	−	0.975066i	$-0.428770\pi$
$283$	20.1647	−	12.7969i	1.19867	−	0.760697i	0.976753	+	0.214369i	$0.0687696\pi$
$284$	8.42612	−	1.06447i	0.499998	−	0.0631645i
$285$	−12.6527	+	3.78009i	−0.749483	+	0.223913i
$286$	1.01511	−	2.15722i	0.0600247	−	0.127559i
$287$	−16.5804	+	30.1596i	−0.978710	+	1.78027i
$288$	0.992602	+	1.05701i	0.0584897	+	0.0622852i
$289$	−10.5354	+	5.79188i	−0.619729	+	0.340699i
$290$	1.39346	+	6.01949i	0.0818266	+	0.353477i
$291$	−7.78870	+	7.31407i	−0.456581	+	0.428759i
$292$	11.1764	+	9.24588i	0.654046	+	0.541074i
$293$	−15.0008	−	20.6468i	−0.876354	−	1.20620i	−0.977417	−	0.211318i	$-0.932225\pi$
$293$	−15.0008	−	20.6468i	−0.876354	−	1.20620i	0.101063	−	0.994880i	$-0.467775\pi$
$294$	8.03207	+	3.18012i	0.468440	+	0.185468i
$295$	−1.96670	+	1.76053i	−0.114506	+	0.102502i
$296$	−1.59223	−	1.92468i	−0.0925465	−	0.111869i
$297$	2.84300	+	7.18060i	0.164968	+	0.416661i
$298$	−15.5404	+	2.96448i	−0.900229	+	0.171728i
$299$	4.81694	−	3.49971i	0.278571	−	0.202394i
$300$	−3.25550	+	5.30579i	−0.187957	+	0.306330i
$301$	37.6533	+	27.3567i	2.17030	+	1.57681i
$302$	−3.07015	−	1.44470i	−0.176667	−	0.0831333i
$303$	−8.96125	−	5.68698i	−0.514811	−	0.326709i
$304$	−4.41041	+	1.74620i	−0.252954	+	0.100152i
$305$	−7.25178	+	14.5029i	−0.415236	+	0.830433i
$306$	0.490494	−	7.79617i	0.0280397	−	0.445678i
$307$		−	14.4913i		−	0.827060i	−0.910490	−	0.413530i	$-0.864296\pi$
$307$		−	14.4913i		−	0.827060i	0.910490	−	0.413530i	$-0.135704\pi$
$308$	−5.19412	−	0.326786i	−0.295963	−	0.0186204i
$309$	−5.95746	−	12.6602i	−0.338908	−	0.720216i
$310$	−15.4190	+	6.81148i	−0.875741	+	0.386866i
$311$	−18.6421	−	17.5061i	−1.05709	−	0.992678i	−0.0571109	−	0.998368i	$-0.518189\pi$
$311$	−18.6421	−	17.5061i	−1.05709	−	0.992678i	−0.999984	+	0.00568980i	$0.998189\pi$
$312$	0.266871	+	2.11250i	0.0151086	+	0.119597i
$313$	3.48788	+	27.6094i	0.197147	+	1.56058i	0.711305	+	0.702883i	$0.248104\pi$
$313$	3.48788	+	27.6094i	0.197147	+	1.56058i	−0.514159	+	0.857695i	$0.671896\pi$
$314$	−1.97088	−	1.85078i	−0.111223	−	0.104445i
$315$	−11.0728	+	4.89152i	−0.623883	+	0.275606i
$316$	−4.01791	−	8.53850i	−0.226025	−	0.480328i
$317$	−2.85149	−	0.179400i	−0.160156	−	0.0100761i	−0.0174897	−	0.999847i	$-0.505567\pi$
$317$	−2.85149	−	0.179400i	−0.160156	−	0.0100761i	−0.142666	+	0.989771i	$0.545567\pi$
$318$			10.0065i			0.561134i
$319$	−0.241858	+	3.84423i	−0.0135415	+	0.215236i
$320$	−1.00004	+	1.99998i	−0.0559038	+	0.111802i
$321$	−8.26007	+	3.27039i	−0.461032	+	0.182535i
$322$	−10.9740	−	6.96434i	−0.611559	−	0.388107i
$323$	23.1224	+	10.8806i	1.28656	+	0.605412i
$324$	−2.06091	−	1.49734i	−0.114495	−	0.0831854i
$325$	7.90238	−	3.26806i	0.438345	−	0.181279i
$326$	−18.5898	+	13.5063i	−1.02959	+	0.748043i
$327$	9.77334	−	1.86436i	0.540467	−	0.103100i
$328$	3.39353	+	8.57108i	0.187376	+	0.473259i
$329$	−19.6030	−	23.6959i	−1.08075	−	1.30640i
$330$	−2.89141	+	2.58830i	−0.159167	+	0.142481i
$331$	−18.2038	−	7.20741i	−1.00057	−	0.396155i	−0.189995	−	0.981785i	$-0.560847\pi$
$331$	−18.2038	−	7.20741i	−1.00057	−	0.396155i	−0.810579	+	0.585630i	$0.800847\pi$
$332$	4.99085	+	6.86932i	0.273908	+	0.377003i
$333$	−2.79080	−	2.30875i	−0.152935	−	0.126519i
$334$	5.20427	−	4.88713i	0.284765	−	0.267412i
$335$	0.468423	+	2.02350i	0.0255927	+	0.110556i
$336$	4.07317	−	2.23925i	0.222210	−	0.122161i
$337$	−11.6588	−	12.4154i	−0.635095	−	0.676308i	0.328244	−	0.944593i	$-0.393543\pi$
$337$	−11.6588	−	12.4154i	−0.635095	−	0.676308i	−0.963340	+	0.268285i	$0.913543\pi$
$338$	−4.85361	+	8.82869i	−0.264002	+	0.480218i
$339$	5.55784	−	11.8110i	0.301860	−	0.641486i
$340$	11.5422	−	3.44830i	0.625962	−	0.187010i
$341$	−10.4256	+	1.31706i	−0.564579	+	0.0713229i
$342$	−5.80742	+	3.68550i	−0.314029	+	0.199289i
$343$	0.134284	−	0.184827i	0.00725068	−	0.00997971i
$344$	12.0745	−	3.10021i	0.651014	−	0.167152i
$345$	−9.44183	+	2.18570i	−0.508331	+	0.117674i
$346$	−1.37918	−	21.9215i	−0.0741452	−	1.17850i
$347$	−3.65166	+	0.229743i	−0.196032	+	0.0123333i	−0.160503	−	0.987035i	$-0.551312\pi$
$347$	−3.65166	+	0.229743i	−0.196032	+	0.0123333i	−0.0355288	+	0.999369i	$0.511312\pi$
$348$	−1.65729	−	3.01460i	−0.0888402	−	0.161600i
$349$	10.5158	−	32.3643i	0.562898	−	1.73242i	−0.111219	−	0.993796i	$-0.535476\pi$
$349$	10.5158	−	32.3643i	0.562898	−	1.73242i	0.674117	−	0.738625i	$-0.264524\pi$
$350$	−12.9833	−	13.4128i	−0.693987	−	0.716946i
$351$	2.92805	+	9.01162i	0.156288	+	0.481005i
$352$	−0.954246	+	1.01617i	−0.0508615	+	0.0541620i
$353$	−0.589960	+	2.29774i	−0.0314004	+	0.122296i	−0.982351	−	0.187046i	$-0.940109\pi$
$353$	−0.589960	+	2.29774i	−0.0314004	+	0.122296i	0.950951	+	0.309342i	$0.100109\pi$
$354$	0.787477	−	1.24087i	0.0418539	−	0.0659513i
$355$	11.7531	+	14.9174i	0.623789	+	0.791732i
$356$	6.76460	−	8.17700i	0.358523	−	0.433380i
$357$	−23.8150	−	7.73796i	−1.26042	−	0.409536i
$358$	3.72609	+	14.5122i	0.196930	+	0.766991i
$359$	−5.52561	−	3.03773i	−0.291630	−	0.160325i	0.329222	−	0.944252i	$-0.393213\pi$
$359$	−5.52561	−	3.03773i	−0.291630	−	0.160325i	−0.620853	+	0.783927i	$0.713213\pi$
$360$	−0.880978	+	3.12035i	−0.0464316	+	0.164457i
$361$	−0.656006	−	3.43890i	−0.0345266	−	0.180995i
$362$	12.7121	+	2.42497i	0.668135	+	0.127453i
$363$	10.2025	−	4.80091i	0.535490	−	0.251983i
$364$	−6.33499	−	0.800295i	−0.332044	−	0.0419469i
$365$	−4.83112	+	32.0725i	−0.252873	+	1.67875i
$366$	1.69168	−	8.86811i	0.0884256	−	0.463543i
$367$	−8.99823	+	22.7269i	−0.469704	+	1.18634i	0.481134	+	0.876647i	$0.340225\pi$
$367$	−8.99823	+	22.7269i	−0.469704	+	1.18634i	−0.950838	+	0.309689i	$0.899775\pi$
$368$	−3.31092	+	1.07578i	−0.172594	+	0.0560791i
$369$	7.16231	+	11.2860i	0.372855	+	0.587526i
$370$	1.85217	−	5.26947i	0.0962899	−	0.273947i
$371$	−29.0647	−	7.46255i	−1.50896	−	0.387436i
$372$	7.23148	−	5.98240i	0.374935	−	0.310173i
$373$	−4.23279	+	33.5060i	−0.219166	+	1.73488i	0.371918	+	0.928266i	$0.378700\pi$
$373$	−4.23279	+	33.5060i	−0.219166	+	1.73488i	−0.591084	+	0.806610i	$0.701300\pi$
$374$	7.50973			0.388319
$375$	−13.9188	−	0.121081i	−0.718765	−	0.00625260i
$376$	−8.23722			−0.424802
$377$	−0.592308	+	4.68860i	−0.0305054	+	0.241475i
$378$	15.9374	−	13.1846i	0.819733	−	0.678142i
$379$	−32.7044	−	8.39706i	−1.67991	−	0.431328i	−0.716119	−	0.697978i	$-0.754083\pi$
$379$	−32.7044	−	8.39706i	−1.67991	−	0.431328i	−0.963793	+	0.266650i	$0.914083\pi$
$380$	−8.43002	−	6.43734i	−0.432451	−	0.330229i
$381$	−3.99634	−	6.29722i	−0.204739	−	0.322616i
$382$	−21.1298	+	6.86550i	−1.08110	+	0.351270i
$383$	12.2877	−	31.0352i	0.627872	−	1.58582i	−0.171632	−	0.985161i	$-0.554904\pi$
$383$	12.2877	−	31.0352i	0.627872	−	1.58582i	0.799503	−	0.600662i	$-0.205096\pi$
$384$	0.233287	−	1.22293i	0.0119049	−	0.0624075i
$385$	−5.36162	−	10.3287i	−0.273254	−	0.526398i
$386$	5.79865	+	0.732539i	0.295143	+	0.0372853i
$387$	16.3557	−	7.69642i	0.831408	−	0.391231i
$388$	−8.43006	−	1.60812i	−0.427971	−	0.0816399i
$389$	−0.0124029	−	0.0650180i	−0.000628850	−	0.00329654i	0.981971	−	0.189029i	$-0.0605341\pi$
$389$	−0.0124029	−	0.0650180i	−0.000628850	−	0.00329654i	−0.982600	+	0.185733i	$0.940534\pi$
$390$	−3.73991	+	2.94660i	−0.189378	+	0.149207i
$391$	16.4349	+	9.03514i	0.831146	+	0.456927i
$392$	1.72561	+	6.72081i	0.0871565	+	0.339452i
$393$	3.94165	+	1.28072i	0.198830	+	0.0646038i
$394$	6.37186	−	7.70226i	0.321010	−	0.388034i
$395$	11.7280	−	17.5415i	0.590098	−	0.882606i
$396$	−1.08306	+	1.70663i	−0.0544259	+	0.0857616i
$397$	−7.05738	+	27.4867i	−0.354200	+	1.37952i	0.502890	+	0.864350i	$0.332270\pi$
$397$	−7.05738	+	27.4867i	−0.354200	+	1.37952i	−0.857090	+	0.515167i	$0.827730\pi$
$398$	−9.42410	+	10.0356i	−0.472387	+	0.503042i
$399$	6.81333	+	20.9693i	0.341093	+	1.04978i
$400$	−4.98481	+	0.389488i	−0.249240	+	0.0194744i
$401$	5.41369	−	16.6616i	0.270347	−	0.832042i	−0.720066	−	0.693905i	$-0.755889\pi$
$401$	5.41369	−	16.6616i	0.270347	−	0.832042i	0.990413	−	0.138137i	$-0.0441113\pi$
$402$	−0.557113	−	1.01339i	−0.0277863	−	0.0505431i
$403$	−12.8676	+	0.809559i	−0.640979	+	0.0403270i
$404$	−0.535288	−	8.50816i	−0.0266316	−	0.423297i
$405$	0.493103	−	5.67482i	0.0245025	−	0.281984i
$406$	9.99217	−	2.56555i	0.495903	−	0.127326i
$407$	2.04669	−	2.81703i	0.101451	−	0.139635i
$408$	−5.66295	+	3.59381i	−0.280358	+	0.177920i
$409$	−15.6685	+	1.97939i	−0.774758	+	0.0978747i	−0.502764	−	0.864424i	$-0.667683\pi$
$409$	−15.6685	+	1.97939i	−0.774758	+	0.0978747i	−0.271995	+	0.962299i	$0.587683\pi$
$410$	−12.5102	+	16.3827i	−0.617834	+	0.809084i
$411$	4.56205	−	9.69485i	0.225029	−	0.478212i
$412$	5.41424	−	9.84846i	0.266740	−	0.485199i
$413$	3.01693	+	3.21271i	0.148454	+	0.158087i
$414$	−4.42355	+	2.43187i	−0.217405	+	0.119520i
$415$	−7.40822	+	17.4814i	−0.363655	+	0.858127i
$416$	−1.24675	+	1.17078i	−0.0611270	+	0.0574021i
$417$	−8.99150	−	7.43842i	−0.440316	−	0.364261i
$418$	−3.88665	−	5.34952i	−0.190102	−	0.261654i
$419$	−14.6717	−	5.80894i	−0.716760	−	0.283786i	−0.0187008	−	0.999825i	$-0.505953\pi$
$419$	−14.6717	−	5.80894i	−0.716760	−	0.283786i	−0.698060	+	0.716040i	$0.745953\pi$
$420$	8.98593	+	5.22283i	0.438468	+	0.254848i
$421$	16.6329	+	20.1057i	0.810638	+	0.979893i	0.999998	−	0.00201505i	$-0.000641410\pi$
$421$	16.6329	+	20.1057i	0.810638	+	0.979893i	−0.189360	+	0.981908i	$0.560641\pi$
$422$	−2.20858	−	5.57824i	−0.107512	−	0.271544i
$423$	−11.7325	+	2.23810i	−0.570455	+	0.108820i
$424$	−6.50240	+	4.72427i	−0.315785	+	0.229431i
$425$	19.9127	+	18.1397i	0.965907	+	0.879903i
$426$	−8.55436	−	6.21510i	−0.414460	−	0.301123i
$427$	24.4967	+	11.5273i	1.18548	+	0.557843i
$428$	−6.02493	−	3.82354i	−0.291226	−	0.184818i
$429$	−2.75976	+	1.09267i	−0.133242	+	0.0527544i
$430$	19.8594	+	19.5609i	0.957705	+	0.943310i
$431$	−0.318869	+	5.06828i	−0.0153594	+	0.244130i	0.982854	+	0.184384i	$0.0590291\pi$
$431$	−0.318869	+	5.06828i	−0.0153594	+	0.244130i	−0.998214	+	0.0597461i	$0.980971\pi$
$432$		−	5.54020i		−	0.266553i
$433$	5.97356	+	0.375824i	0.287071	+	0.0180610i	0.205673	−	0.978621i	$-0.434062\pi$
$433$	5.97356	+	0.375824i	0.287071	+	0.0180610i	0.0813977	+	0.996682i	$0.474062\pi$
$434$	11.9834	+	25.4660i	0.575222	+	1.22241i
$435$	3.86548	−	6.65059i	0.185335	−	0.318871i
$436$	5.82572	+	5.47071i	0.279001	+	0.262000i
$437$	−2.06971	−	16.3834i	−0.0990075	−	0.783725i
$438$	−2.26334	−	17.9162i	−0.108147	−	0.856069i
$439$	5.37014	+	5.04289i	0.256303	+	0.240684i	0.802037	−	0.597274i	$-0.203749\pi$
$439$	5.37014	+	5.04289i	0.256303	+	0.240684i	−0.545735	+	0.837958i	$0.683749\pi$
$440$	−3.04703	−	0.656907i	−0.145262	−	0.0313168i
$441$	4.28392	+	9.10380i	0.203996	+	0.433514i
$442$	9.19561	+	0.578539i	0.437391	+	0.0275183i
$443$		−	7.61933i		−	0.362005i	−0.983483	−	0.181003i	$-0.942066\pi$
$443$		−	7.61933i		−	0.362005i	0.983483	−	0.181003i	$-0.0579343\pi$
$444$	−0.195270	+	3.10373i	−0.00926710	+	0.147296i
$445$	23.4653	+	3.53461i	1.11236	+	0.167557i
$446$	−1.95445	+	0.773823i	−0.0925460	+	0.0366416i
$447$	16.6302	+	10.5539i	0.786582	+	0.499180i
$448$	3.37815	+	1.58963i	0.159602	+	0.0751032i
$449$	−1.85687	−	1.34910i	−0.0876311	−	0.0636677i	0.543107	−	0.839663i	$-0.317248\pi$
$449$	−1.85687	−	1.34910i	−0.0876311	−	0.0636677i	−0.630738	+	0.775996i	$0.717248\pi$
$450$	−6.99418	+	1.90916i	−0.329709	+	0.0899986i
$451$	−10.3961	+	7.55323i	−0.489535	+	0.355668i
$452$	10.2990	−	1.96464i	0.484425	−	0.0924090i
$453$	1.55508	+	3.92768i	0.0730640	+	0.184539i
$454$	−15.5065	−	18.7441i	−0.727755	−	0.879705i
$455$	−5.76956	−	13.0604i	−0.270481	−	0.612283i
$456$	5.49089	+	2.17400i	0.257134	+	0.101807i
$457$	−3.18560	−	4.38460i	−0.149016	−	0.205103i	0.727983	−	0.685595i	$-0.240458\pi$
$457$	−3.18560	−	4.38460i	−0.149016	−	0.205103i	−0.876999	+	0.480492i	$0.840458\pi$
$458$	−16.5483	−	13.6899i	−0.773249	−	0.639688i
$459$	−21.7571	+	20.4313i	−1.01554	+	0.953651i
$460$	−5.87801	−	5.10358i	−0.274064	−	0.237956i
$461$	−24.5787	+	13.5122i	−1.14474	+	0.629328i	−0.937164	−	0.348890i	$-0.886559\pi$
$461$	−24.5787	+	13.5122i	−1.14474	+	0.629328i	−0.207580	+	0.978218i	$0.566559\pi$
$462$	4.43544	+	4.72327i	0.206356	+	0.219746i
$463$	−1.05912	+	1.92653i	−0.0492214	+	0.0895335i	−0.899773	−	0.436358i	$-0.856268\pi$
$463$	−1.05912	+	1.92653i	−0.0492214	+	0.0895335i	0.850552	+	0.525891i	$0.176268\pi$
$464$	1.17651	−	2.50020i	0.0546180	−	0.116069i
$465$	19.7987	+	6.95907i	0.918142	+	0.322719i
$466$	23.2765	−	2.94051i	1.07827	−	0.136217i
$467$	−16.2121	+	10.2885i	−0.750207	+	0.476096i	−0.855149	−	0.518382i	$-0.826534\pi$
$467$	−16.2121	+	10.2885i	−0.750207	+	0.476096i	0.104942	+	0.994478i	$0.466534\pi$
$468$	−1.45768	+	2.00632i	−0.0673812	+	0.0927423i
$469$	3.35896	−	0.862433i	0.155102	−	0.0398235i
$470$	−9.49581	−	15.7825i	−0.438009	−	0.727995i
$471$	0.211353	+	3.35936i	0.00973864	+	0.154791i
$472$	1.17813	−	0.0741214i	0.0542277	−	0.00341172i
$473$	8.37171	+	15.2281i	0.384932	+	0.700188i
$474$	−3.63046	+	11.1734i	−0.166753	+	0.513212i
$475$	2.61591	−	23.5729i	0.120026	−	1.08160i
$476$	−6.21531	−	19.1287i	−0.284878	−	0.876765i
$477$	−7.97795	+	8.49566i	−0.365285	+	0.388989i
$478$	0.228950	−	0.891701i	0.0104719	−	0.0407855i
$479$	12.0507	−	18.9888i	0.550609	−	0.867621i	−0.449056	−	0.893504i	$-0.648240\pi$
$479$	12.0507	−	18.9888i	0.550609	−	0.867621i	0.999665	+	0.0258826i	$0.00823961\pi$
$480$	2.61207	−	0.962809i	0.119224	−	0.0439460i
$481$	2.72318	−	3.29176i	0.124167	−	0.150092i
$482$	14.3648	+	4.66739i	0.654297	+	0.212594i
$483$	4.02418	+	15.6731i	0.183107	+	0.713153i
$484$	7.93655	+	4.36315i	0.360752	+	0.198325i
$485$	−6.63695	−	18.0058i	−0.301368	−	0.817603i
$486$	−2.52011	−	13.2109i	−0.114314	−	0.599257i
$487$	12.1017	+	2.30853i	0.548382	+	0.104609i	0.454124	−	0.890938i	$-0.349952\pi$
$487$	12.1017	+	2.30853i	0.548382	+	0.104609i	0.0942575	+	0.995548i	$0.469952\pi$
$488$	6.56136	−	3.08754i	0.297019	−	0.139766i
$489$	28.3820	+	3.58548i	1.28348	+	0.162141i
$490$	−10.8878	+	11.0540i	−0.491862	+	0.499368i
$491$	−2.05943	+	10.7959i	−0.0929406	+	0.487212i	0.905131	+	0.425133i	$0.139773\pi$
$491$	−2.05943	+	10.7959i	−0.0929406	+	0.487212i	−0.998071	+	0.0620783i	$0.980227\pi$
$492$	4.22489	−	10.6709i	0.190473	−	0.481080i
$493$	−14.1574	+	4.60002i	−0.637617	+	0.207174i
$494$	−4.34706	−	6.84987i	−0.195584	−	0.308190i
$495$	−4.51846	−	0.107757i	−0.203090	−	0.00484330i
$496$	7.30163	+	1.87474i	0.327853	+	0.0841783i
$497$	24.4320	−	20.2119i	1.09592	−	0.906627i
$498$	1.32491	−	10.4877i	0.0593706	−	0.469967i
$499$	25.7588			1.15312			0.576562	−	0.817053i	$-0.304394\pi$
$499$	25.7588			1.15312			0.576562	+	0.817053i	$0.304394\pi$
$500$	−6.49271	−	9.10191i	−0.290363	−	0.407050i
$501$	−8.88822			−0.397096
$502$	−1.06975	+	8.46795i	−0.0477453	+	0.377943i
$503$	2.71108	−	2.24280i	0.120881	−	0.100002i	−0.575019	−	0.818140i	$-0.695005\pi$
$503$	2.71108	−	2.24280i	0.120881	−	0.100002i	0.695900	+	0.718138i	$0.255005\pi$
$504$	5.24351	+	1.34630i	0.233564	+	0.0599691i
$505$	15.6846	−	10.8338i	0.697955	−	0.482096i
$506$	−2.60030	−	4.09742i	−0.115598	−	0.182153i
$507$	11.9292	−	3.87603i	0.529793	−	0.172140i
$508$	2.20530	−	5.56996i	0.0978446	−	0.247127i
$509$	−3.65236	+	19.1463i	−0.161888	+	0.848647i	0.804967	+	0.593320i	$0.202183\pi$
$509$	−3.65236	+	19.1463i	−0.161888	+	0.848647i	−0.966855	+	0.255327i	$0.917817\pi$
$510$	−13.4140	−	6.70730i	−0.593980	−	0.297004i
$511$	53.7273	+	6.78733i	2.37675	+	0.300254i
$512$	0.904827	−	0.425779i	0.0399881	−	0.0188170i
$513$	25.8145	+	4.92438i	1.13974	+	0.217417i
$514$	−2.77868	−	14.5663i	−0.122562	−	0.642494i
$515$	25.1112	−	0.979538i	1.10653	−	0.0431636i
$516$	−13.6004	−	7.47690i	−0.598725	−	0.329152i
$517$	−2.85559	−	11.1218i	−0.125589	−	0.489136i
$518$	−8.86945	−	2.88186i	−0.389701	−	0.126622i
$519$	−17.4309	+	21.0703i	−0.765131	+	0.924885i
$520$	−3.68046	−	1.03912i	−0.161399	−	0.0455683i
$521$	23.8909	−	37.6461i	1.04668	−	1.64930i	0.342124	−	0.939655i	$-0.388854\pi$
$521$	23.8909	−	37.6461i	1.04668	−	1.64930i	0.704556	−	0.709649i	$-0.251146\pi$
$522$	0.996415	−	3.88078i	0.0436119	−	0.169857i
$523$	−17.8451	+	19.0031i	−0.780313	+	0.830949i	−0.989136	−	0.147005i	$-0.953037\pi$
$523$	−17.8451	+	19.0031i	−0.780313	+	0.830949i	0.208823	+	0.977953i	$0.433037\pi$
$524$	1.02870	+	3.16603i	0.0449392	+	0.138308i
$525$	0.351958	+	23.2379i	0.0153607	+	1.01419i
$526$	−1.90241	+	5.85500i	−0.0829488	+	0.255290i
$527$	−19.5648	−	35.5882i	−0.852256	−	1.55025i
$528$	1.73206	−	0.108972i	0.0753783	−	0.00474240i
$529$	0.683192	+	10.8590i	0.0297040	+	0.472132i
$530$	−16.5476	−	7.01252i	−0.718784	−	0.304604i
$531$	1.65790	−	0.425677i	0.0719468	−	0.0184728i
$532$	−10.4095	+	14.3275i	−0.451311	+	0.621176i
$533$	−13.3119	+	8.44797i	−0.576601	+	0.365922i
$534$	−13.1081	+	1.65594i	−0.567243	+	0.0716595i
$535$	0.380414	−	15.9515i	0.0164467	−	0.689645i
$536$	0.395493	−	0.840466i	0.0170827	−	0.0363026i
$537$	8.98636	−	16.3461i	0.387790	−	0.705388i
$538$	−10.2940	−	10.9620i	−0.443804	−	0.472603i
$539$	−8.47614	+	4.65980i	−0.365093	+	0.200712i
$540$	10.6150	−	6.38670i	0.456799	−	0.274840i
$541$	−26.7091	+	25.0815i	−1.14832	+	1.07834i	−0.152375	+	0.988323i	$0.548692\pi$
$541$	−26.7091	+	25.0815i	−1.14832	+	1.07834i	−0.995940	+	0.0900172i	$0.971308\pi$
$542$	12.4003	+	10.2585i	0.532640	+	0.440638i
$543$	−9.47027	−	13.0347i	−0.406408	−	0.559373i
$544$	−5.00894	−	1.98318i	−0.214757	−	0.0850281i
$545$	−3.76606	+	17.4687i	−0.161320	+	0.748277i
$546$	5.06730	+	6.12531i	0.216860	+	0.262139i
$547$	−9.94527	−	25.1189i	−0.425229	−	1.07401i	−0.971635	−	0.236486i	$-0.924004\pi$
$547$	−9.94527	−	25.1189i	−0.425229	−	1.07401i	0.546406	−	0.837521i	$-0.315996\pi$
$548$	8.45376	−	1.61264i	0.361127	−	0.0688886i
$549$	8.50664	−	6.18044i	0.363055	−	0.263775i
$550$	−2.25396	−	6.59540i	−0.0961092	−	0.281229i
$551$	10.6040	+	7.70422i	0.451744	+	0.328211i
$552$	3.92168	+	1.84540i	0.166918	+	0.0785455i
$553$	−29.7468	−	18.8779i	−1.26496	−	0.802769i
$554$	10.7619	−	4.26095i	0.457230	−	0.181030i
$555$	−6.17186	+	3.20382i	−0.261981	+	0.135994i
$556$	0.588549	−	9.35471i	0.0249600	−	0.396728i
$557$		−	15.1403i		−	0.641513i	−0.947162	−	0.320757i	$-0.896063\pi$
$557$		−	15.1403i		−	0.641513i	0.947162	−	0.320757i	$-0.103937\pi$
$558$	10.9093	+	0.686355i	0.461828	+	0.0290557i
$559$	9.07796	+	19.2916i	0.383957	+	0.815949i
$560$	0.848557	+	8.30506i	0.0358581	+	0.350953i
$561$	−6.81549	−	6.40017i	−0.287750	−	0.270216i
$562$	−2.73876	−	21.6795i	−0.115528	−	0.914495i
$563$	−1.92439	−	15.2331i	−0.0811035	−	0.642000i	−0.979301	−	0.202408i	$-0.935123\pi$
$563$	−1.92439	−	15.2331i	−0.0811035	−	0.642000i	0.898198	−	0.439592i	$-0.144877\pi$
$564$	7.47573	+	7.02018i	0.314785	+	0.295603i
$565$	15.6369	+	17.4681i	0.657849	+	0.734890i
$566$	−10.1687	−	21.6096i	−0.427422	−	0.908318i
$567$	−9.49196	−	0.597183i	−0.398625	−	0.0250793i
$568$		−	8.49309i		−	0.356362i
$569$	−2.41478	+	38.3819i	−0.101233	+	1.60905i	0.539972	+	0.841683i	$0.318435\pi$
$569$	−2.41478	+	38.3819i	−0.101233	+	1.60905i	−0.641205	+	0.767369i	$0.721565\pi$
$570$	2.16447	+	13.0267i	0.0906598	+	0.545630i
$571$	−13.6126	+	5.38960i	−0.569668	+	0.225548i	−0.635259	−	0.772299i	$-0.719107\pi$
$571$	−13.6126	+	5.38960i	−0.569668	+	0.225548i	0.0655909	+	0.997847i	$0.479107\pi$
$572$	−2.01298	−	1.27748i	−0.0841669	−	0.0534140i
$573$	25.0276	+	11.7771i	1.04554	+	0.491996i
$574$	27.8437	+	20.2297i	1.16217	+	0.844369i
$575$	3.00235	−	17.1457i	0.125207	−	0.715023i
$576$	1.17309	−	0.852297i	0.0488786	−	0.0355124i
$577$	−28.3582	+	5.40961i	−1.18057	+	0.225205i	−0.740058	−	0.672543i	$-0.765202\pi$
$577$	−28.3582	+	5.40961i	−1.18057	+	0.225205i	−0.440509	+	0.897748i	$0.645202\pi$
$578$	4.42577	+	11.1782i	0.184088	+	0.464953i
$579$	−4.63828	−	5.60672i	−0.192760	−	0.233007i
$580$	6.14667	−	0.628027i	0.255227	−	0.0260774i
$581$	29.4746	+	11.6698i	1.22281	+	0.484145i
$582$	6.28022	+	8.64398i	0.260323	+	0.358304i
$583$	−8.63283	−	7.14170i	−0.357535	−	0.295779i
$584$	10.5737	−	9.92941i	0.437545	−	0.410882i
$585$	−5.52452	−	0.480043i	−0.228411	−	0.0198473i
$586$	−22.3641	+	12.2948i	−0.923851	+	0.507891i
$587$	−10.4079	−	11.0833i	−0.429580	−	0.457456i	0.477365	−	0.878705i	$-0.341592\pi$
$587$	−10.4079	−	11.0833i	−0.429580	−	0.457456i	−0.906945	+	0.421249i	$0.861592\pi$
$588$	4.16173	−	7.57016i	0.171627	−	0.312188i
$589$	−15.2254	+	32.3555i	−0.627350	+	1.33319i
$590$	1.50015	+	2.17185i	0.0617603	+	0.0894135i
$591$	−12.3471	+	1.55980i	−0.507890	+	0.0641615i
$592$	−2.10906	+	1.33845i	−0.0866817	+	0.0550099i
$593$	15.3157	−	21.0803i	0.628941	−	0.865663i	−0.369025	−	0.929420i	$-0.620308\pi$
$593$	15.3157	−	21.0803i	0.628941	−	0.865663i	0.997965	+	0.0637569i	$0.0203082\pi$
$594$	7.48030	−	1.92062i	0.306921	−	0.0788038i
$595$	29.4858	−	33.9600i	1.20880	−	1.39223i
$596$	0.993383	+	15.7894i	0.0406906	+	0.646758i
$597$	17.1058	−	1.07620i	0.700093	−	0.0440461i
$598$	−2.86839	−	5.21759i	−0.117297	−	0.213363i
$599$	−8.80268	+	27.0919i	−0.359668	+	1.10694i	0.593586	+	0.804771i	$0.297712\pi$
$599$	−8.80268	+	27.0919i	−0.359668	+	1.10694i	−0.953253	+	0.302172i	$0.902288\pi$
$600$	4.85593	+	3.89482i	0.198242	+	0.159005i
$601$	4.55910	+	14.0315i	0.185970	+	0.572356i	0.999964	−	0.00851750i	$-0.00271124\pi$
$601$	4.55910	+	14.0315i	0.185970	+	0.572356i	−0.813994	+	0.580873i	$0.802711\pi$
$602$	31.8602	−	33.9277i	1.29852	−	1.38279i
$603$	0.334954	−	1.30456i	0.0136404	−	0.0531257i
$604$	−1.81810	+	2.86487i	−0.0739775	+	0.116570i
$605$	0.789377	+	20.2363i	0.0320927	+	0.822721i
$606$	−6.76528	+	8.17782i	−0.274821	+	0.332201i
$607$	19.3931	+	6.30119i	0.787141	+	0.255758i	0.674886	−	0.737922i	$-0.264193\pi$
$607$	19.3931	+	6.30119i	0.787141	+	0.255758i	0.112255	+	0.993679i	$0.464193\pi$
$608$	1.17966	+	4.59449i	0.0478417	+	0.186331i
$609$	−11.2549	−	6.18745i	−0.456073	−	0.250728i
$610$	13.4796	+	9.01229i	0.545774	+	0.364897i
$611$	−2.63984	−	13.8385i	−0.106797	−	0.559848i
$612$	−7.67322	−	1.46375i	−0.310172	−	0.0591684i
$613$	−41.0973	+	19.3389i	−1.65990	+	0.781091i	−0.660357	+	0.750952i	$0.729595\pi$
$613$	−41.0973	+	19.3389i	−1.65990	+	0.781091i	−0.999546	+	0.0301389i	$0.990405\pi$
$614$	−14.3770	−	1.81624i	−0.580209	−	0.0732974i
$615$	25.3158	−	4.20638i	1.02083	−	0.169618i
$616$	−0.975206	+	5.11221i	−0.0392922	+	0.205977i
$617$	9.64364	−	24.3571i	0.388239	−	0.980579i	−0.595881	−	0.803073i	$-0.703197\pi$
$617$	9.64364	−	24.3571i	0.388239	−	0.980579i	0.984120	−	0.177506i	$-0.0568029\pi$
$618$	−13.3071	+	4.32373i	−0.535289	+	0.173926i
$619$	−15.1524	−	23.8763i	−0.609026	−	0.959671i	−0.999241	−	0.0389475i	$-0.987599\pi$
$619$	−15.1524	−	23.8763i	−0.609026	−	0.959671i	0.390216	−	0.920724i	$-0.372401\pi$
$620$	4.82526	+	16.1511i	0.193787	+	0.648645i
$621$	18.6812	+	4.79652i	0.749651	+	0.192478i
$622$	−19.7045	+	16.3010i	−0.790078	+	0.653610i
$623$	4.96584	−	39.3087i	0.198952	−	1.57487i
$624$	2.12929			0.0852399
$625$	9.95454	−	22.9327i	0.398181	−	0.917307i
$626$	27.8289			1.11227
$627$	−1.03178	+	8.16738i	−0.0412053	+	0.326174i
$628$	−2.08320	+	1.72337i	−0.0831287	+	0.0687701i
$629$	13.0341	+	3.34659i	0.519704	+	0.133437i
$630$	3.46515	+	11.5986i	0.138055	+	0.462099i
$631$	−17.2660	−	27.2068i	−0.687347	−	1.08309i	−0.991455	−	0.130448i	$-0.958358\pi$
$631$	−17.2660	−	27.2068i	−0.687347	−	1.08309i	0.304108	−	0.952637i	$-0.401642\pi$
$632$	−8.97475	+	2.91607i	−0.356996	+	0.115995i
$633$	−2.74965	+	6.94482i	−0.109289	+	0.276032i
$634$	−0.535372	+	2.80652i	−0.0212623	+	0.111461i
$635$	13.2143	−	2.19564i	0.524395	−	0.0871314i
$636$	9.92755	+	1.25414i	0.393653	+	0.0497299i
$637$	−10.7380	+	5.05290i	−0.425453	+	0.200203i
$638$	3.78360	+	0.721761i	0.149794	+	0.0285748i
$639$	−2.30762	−	12.0970i	−0.0912880	−	0.478548i
$640$	1.85887	+	1.24282i	0.0734784	+	0.0491266i
$641$	5.62681	+	3.09336i	0.222246	+	0.122181i	0.588987	−	0.808142i	$-0.299527\pi$
$641$	5.62681	+	3.09336i	0.222246	+	0.122181i	−0.366742	+	0.930323i	$0.619527\pi$
$642$	2.20934	+	8.60482i	0.0871958	+	0.339605i
$643$	−32.4685	−	10.5497i	−1.28043	−	0.416038i	−0.411701	−	0.911319i	$-0.635065\pi$
$643$	−32.4685	−	10.5497i	−1.28043	−	0.416038i	−0.868733	+	0.495281i	$0.835065\pi$
$644$	−8.28483	+	10.0146i	−0.326468	+	0.394632i
$645$	−1.35271	−	34.6778i	−0.0532630	−	1.36544i
$646$	13.6928	−	21.5764i	0.538735	−	0.848911i
$647$	−2.99030	+	11.6464i	−0.117561	+	0.457869i	−0.999919	−	0.0127091i	$-0.995954\pi$
$647$	−2.99030	+	11.6464i	−0.117561	+	0.457869i	0.882359	+	0.470578i	$0.155954\pi$
$648$	−1.74383	+	1.85699i	−0.0685041	+	0.0729495i
$649$	0.508498	+	1.56500i	0.0199603	+	0.0614314i
$650$	−2.25186	−	8.24966i	−0.0883252	−	0.323578i
$651$	10.8278	−	33.3247i	0.424377	−	1.30610i
$652$	11.0698	+	20.1360i	0.433529	+	0.788586i
$653$	8.09096	−	0.509040i	0.316624	−	0.0199203i	0.0963163	−	0.995351i	$-0.469294\pi$
$653$	8.09096	−	0.509040i	0.316624	−	0.0199203i	0.220307	+	0.975431i	$0.429294\pi$
$654$	−0.624739	−	9.92994i	−0.0244292	−	0.388291i
$655$	−4.88023	+	5.62077i	−0.190687	+	0.219622i
$656$	8.92882	−	2.29253i	0.348612	−	0.0895083i
$657$	12.3626	−	17.0157i	0.482312	−	0.663845i
$658$	−25.9660	+	16.4785i	−1.01226	+	0.642399i
$659$	22.7107	−	2.86903i	0.884684	−	0.111762i	0.330156	−	0.943927i	$-0.392899\pi$
$659$	22.7107	−	2.86903i	0.884684	−	0.111762i	0.554528	+	0.832165i	$0.312899\pi$
$660$	2.20550	+	3.19301i	0.0858489	+	0.124288i
$661$	13.9639	−	29.6747i	0.543132	−	1.15421i	−0.425327	−	0.905040i	$-0.639841\pi$
$661$	13.9639	−	29.6747i	0.543132	−	1.15421i	0.968459	−	0.249174i	$-0.0801590\pi$
$662$	−9.43212	+	17.1570i	−0.366590	+	0.666825i
$663$	−7.85246	−	8.36202i	−0.304964	−	0.324754i
$664$	7.44067	−	4.09054i	0.288754	−	0.158744i
$665$	−39.4516	−	3.42807i	−1.52987	−	0.132935i
$666$	−2.64033	+	2.47943i	−0.102311	+	0.0960762i
$667$	7.41195	+	6.13170i	0.286992	+	0.237420i
$668$	−4.19633	−	5.77575i	−0.162361	−	0.223470i
$669$	2.43326	+	0.963397i	0.0940754	+	0.0372471i
$670$	2.06626	−	0.211117i	0.0798265	−	0.00815615i
$671$	6.44338	+	7.78871i	0.248744	+	0.300680i
$672$	−1.71108	−	4.32171i	−0.0660065	−	0.166713i
$673$	8.08984	−	1.54322i	0.311840	−	0.0594867i	−0.0290854	−	0.999577i	$-0.509259\pi$
$673$	8.08984	−	1.54322i	0.311840	−	0.0594867i	0.340926	+	0.940090i	$0.389259\pi$
$674$	−13.7787	+	10.0108i	−0.530735	+	0.385602i
$675$	24.4739	+	12.9759i	0.942000	+	0.499443i
$676$	8.15076	+	5.92187i	0.313491	+	0.227764i
$677$	−26.0998	−	12.2816i	−1.00310	−	0.472022i	−0.147167	−	0.989112i	$-0.547015\pi$
$677$	−26.0998	−	12.2816i	−1.00310	−	0.472022i	−0.855931	+	0.517090i	$0.827015\pi$
$678$	−11.0213	−	6.99432i	−0.423270	−	0.268615i
$679$	−29.7909	+	11.7950i	−1.14327	+	0.452652i
$680$	−1.97449	−	11.8833i	−0.0757183	−	0.455705i
$681$	−1.90170	+	30.2267i	−0.0728735	+	1.15829i
$682$			10.5085i			0.402391i
$683$	35.7877	+	2.25157i	1.36938	+	0.0861540i	0.730373	−	0.683048i	$-0.239346\pi$
$683$	35.7877	+	2.25157i	1.36938	+	0.0861540i	0.639006	+	0.769202i	$0.279346\pi$
$684$	2.92858	+	6.22354i	0.111977	+	0.237963i
$685$	12.8353	+	14.3384i	0.490410	+	0.547842i
$686$	−0.166539	−	0.156391i	−0.00635849	−	0.00597102i
$687$	3.35122	+	26.5276i	0.127857	+	1.01209i
$688$	−1.56242	−	12.3678i	−0.0595668	−	0.471520i
$689$	−10.0207	−	9.41002i	−0.381757	−	0.358493i
$690$	0.985087	+	9.64132i	0.0375016	+	0.367039i
$691$	0.871075	+	1.85113i	0.0331373	+	0.0704202i	0.920710	−	0.390247i	$-0.127610\pi$
$691$	0.871075	+	1.85113i	0.0331373	+	0.0704202i	−0.887573	+	0.460667i	$0.847610\pi$
$692$	−21.9215	−	1.37918i	−0.833329	−	0.0524286i
$693$			7.54644i			0.286665i
$694$	−0.229743	+	3.65166i	−0.00872093	+	0.138615i
$695$	18.6021	−	9.65638i	0.705619	−	0.366288i
$696$	−3.19855	+	1.26639i	−0.121241	+	0.0480025i
$697$	−41.9310	−	26.6102i	−1.58825	−	1.00793i
$698$	−30.7911	−	14.4892i	−1.16546	−	0.548424i
$699$	−23.6308	−	17.1688i	−0.893799	−	0.649383i
$700$	−14.9343	+	11.1998i	−0.564464	+	0.423314i
$701$	−0.236445	+	0.171788i	−0.00893042	+	0.00648833i	−0.592242	−	0.805761i	$-0.701757\pi$
$701$	−0.236445	+	0.171788i	−0.00893042	+	0.00648833i	0.583311	+	0.812249i	$0.301757\pi$
$702$	9.30754	−	1.77551i	0.351291	−	0.0670123i
$703$	−4.36187	−	11.0168i	−0.164511	−	0.415507i
$704$	0.888557	+	1.07408i	0.0334888	+	0.0404810i
$705$	−4.83272	+	22.4163i	−0.182011	+	0.844248i
$706$	2.20568	+	0.873291i	0.0830119	+	0.0328668i
$707$	−18.7079	−	25.7492i	−0.703583	−	0.968399i
$708$	−1.13238	−	0.936790i	−0.0425576	−	0.0352067i
$709$	−11.4142	+	10.7186i	−0.428667	+	0.402546i	−0.868623	−	0.495474i	$-0.834994\pi$
$709$	−11.4142	+	10.7186i	−0.428667	+	0.402546i	0.439955	+	0.898020i	$0.354994\pi$
$710$	16.2728	−	9.79077i	0.610707	−	0.367441i
$711$	−11.9907	+	6.59194i	−0.449686	+	0.247217i
$712$	−7.26469	−	7.73611i	−0.272256	−	0.289923i
$713$	−12.6430	+	22.9975i	−0.473484	+	0.861265i
$714$	−10.6618	+	22.6574i	−0.399006	+	0.847931i
$715$	0.127099	−	5.32954i	0.00475325	−	0.199314i
$716$	14.8647	−	1.87785i	0.555521	−	0.0701786i
$717$	−0.967737	+	0.614145i	−0.0361408	+	0.0229357i
$718$	−3.70632	+	5.10131i	−0.138319	+	0.190379i
$719$	−38.7877	+	9.95900i	−1.44654	+	0.371408i	−0.888680	−	0.458528i	$-0.848377\pi$
$719$	−38.7877	+	9.95900i	−1.44654	+	0.371408i	−0.557859	+	0.829936i	$0.688377\pi$
$720$	2.98533	+	1.26511i	0.111257	+	0.0471480i
$721$	−2.63463	−	41.8762i	−0.0981187	−	1.55955i
$722$	−3.49401	+	0.219824i	−0.130033	+	0.00818101i
$723$	−9.05902	−	16.4783i	−0.336908	−	0.612834i
$724$	3.99910	−	12.3080i	0.148625	−	0.457422i
$725$	8.28914	+	11.0531i	0.307851	+	0.410500i
$726$	−3.48435	−	10.7237i	−0.129316	−	0.397995i
$727$	−18.0485	+	19.2197i	−0.669382	+	0.712819i	−0.970590	−	0.240739i	$-0.922610\pi$
$727$	−18.0485	+	19.2197i	−0.669382	+	0.712819i	0.301208	+	0.953559i	$0.402610\pi$
$728$	−1.58797	+	6.18473i	−0.0588541	+	0.229221i
$729$	−13.0668	+	20.5899i	−0.483954	+	0.762590i
$730$	31.2141	+	8.81278i	1.15529	+	0.326176i
$731$	−42.8083	+	51.7464i	−1.58332	+	1.91391i
$732$	−8.58615	−	2.78981i	−0.317353	−	0.103114i
$733$	5.70680	+	22.2265i	0.210785	+	0.820955i	0.982696	+	0.185224i	$0.0593011\pi$
$733$	5.70680	+	22.2265i	0.210785	+	0.820955i	−0.771911	+	0.635731i	$0.780699\pi$
$734$	21.4200	+	11.7757i	0.790625	+	0.434650i
$735$	19.3021	−	0.752936i	0.711967	−	0.0277725i
$736$	0.652332	+	3.41964i	0.0240453	+	0.126050i
$737$	1.27189	+	0.242626i	0.0468507	+	0.00893725i
$738$	12.0947	−	5.69133i	0.445211	−	0.209501i
$739$	−8.86229	−	1.11957i	−0.326005	−	0.0411840i	−0.0393723	−	0.999225i	$-0.512536\pi$
$739$	−8.86229	−	1.11957i	−0.326005	−	0.0411840i	−0.286632	+	0.958041i	$0.592536\pi$
$740$	−4.99578	−	2.49801i	−0.183648	−	0.0918286i
$741$	−1.89261	+	9.92142i	−0.0695268	+	0.364472i
$742$	−11.0465	+	27.9002i	−0.405529	+	1.02425i
$743$	13.5835	−	4.41353i	0.498329	−	0.161917i	−0.0490590	−	0.998796i	$-0.515622\pi$
$743$	13.5835	−	4.41353i	0.498329	−	0.161917i	0.547388	+	0.836879i	$0.315622\pi$
$744$	−5.02888	−	7.92425i	−0.184368	−	0.290517i
$745$	−29.1073	+	20.1052i	−1.06641	+	0.736598i
$746$	32.7113	+	8.39883i	1.19765	+	0.307503i
$747$	9.48654	−	7.84795i	0.347094	−	0.287142i
$748$	0.941219	−	7.45051i	0.0344144	−	0.272418i
$749$	−26.6412			−0.973448
$750$	−1.86462	+	13.7939i	−0.0680862	+	0.503682i
$751$	−4.89817			−0.178737			−0.0893683	−	0.995999i	$-0.528485\pi$
$751$	−4.89817			−0.178737			−0.0893683	+	0.995999i	$0.528485\pi$
$752$	−1.03240	+	8.17227i	−0.0376477	+	0.298012i
$753$	8.18767	−	6.77343i	0.298375	−	0.246838i
$754$	4.57739	+	1.17527i	0.166699	+	0.0428010i
$755$	−7.58500	−	0.180888i	−0.276046	−	0.00658318i
$756$	−11.0831	−	17.4642i	−0.403090	−	0.635168i
$757$	14.2073	−	4.61623i	0.516372	−	0.167780i	−0.0392260	−	0.999230i	$-0.512489\pi$
$757$	14.2073	−	4.61623i	0.516372	−	0.167780i	0.555598	+	0.831451i	$0.312489\pi$
$758$	−12.4298	+	31.3941i	−0.451471	+	1.14028i
$759$	−1.13211	+	5.93474i	−0.0410931	+	0.215418i
$760$	−7.44314	+	7.55673i	−0.269991	+	0.274111i
$761$	13.5174	+	1.70765i	0.490007	+	0.0619023i	0.366455	−	0.930436i	$-0.380571\pi$
$761$	13.5174	+	1.70765i	0.490007	+	0.0619023i	0.123552	+	0.992338i	$0.460571\pi$
$762$	−6.74844	+	3.17557i	−0.244470	+	0.115039i
$763$	29.3084	+	5.59087i	1.06103	+	0.202403i
$764$	4.16309	+	21.8237i	0.150615	+	0.789554i
$765$	−6.04109	−	16.3893i	−0.218416	−	0.592557i
$766$	−29.2504	−	16.0805i	−1.05686	−	0.581013i
$767$	0.502087	+	1.95550i	0.0181293	+	0.0706090i
$768$	−1.18405	−	0.384721i	−0.0427257	−	0.0138824i
$769$	23.2507	−	28.1053i	0.838442	−	1.01350i	−0.161204	−	0.986921i	$-0.551538\pi$
$769$	23.2507	−	28.1053i	0.838442	−	1.01350i	0.999647	−	0.0265817i	$-0.00846222\pi$
$770$	−10.9192	+	4.02482i	−0.393501	+	0.145044i
$771$	−9.89237	+	15.5879i	−0.356265	+	0.561384i
$772$	1.45353	−	5.66111i	0.0523136	−	0.203748i
$773$	−6.67610	+	7.10932i	−0.240123	+	0.255705i	−0.837730	−	0.546084i	$-0.816118\pi$
$773$	−6.67610	+	7.10932i	−0.240123	+	0.255705i	0.597608	+	0.801789i	$0.296118\pi$
$774$	−5.58582	−	17.1914i	−0.200778	−	0.617931i
$775$	−25.3831	+	27.8641i	−0.911788	+	1.00091i
$776$	−2.65200	+	8.16203i	−0.0952014	+	0.293000i
$777$	5.59344	+	10.1744i	0.200664	+	0.365006i
$778$	−0.0660598	+	0.00415613i	−0.00236836	+	0.000149005i
$779$	2.74569	+	43.6415i	0.0983745	+	1.56362i
$780$	2.45463	+	4.07973i	0.0878899	+	0.146078i
$781$	11.4673	−	2.94429i	0.410331	−	0.105355i
$782$	11.0237	−	15.1729i	0.394208	−	0.542580i
$783$	−12.9255	+	8.20276i	−0.461919	+	0.293143i
$784$	6.88409	−	0.869663i	0.245860	−	0.0310594i
$785$	−5.70349	−	2.00473i	−0.203566	−	0.0715518i
$786$	1.76464	−	3.75006i	0.0629427	−	0.133760i
$787$	1.79046	−	3.25683i	0.0638229	−	0.116093i	−0.842471	−	0.538742i	$-0.818900\pi$
$787$	1.79046	−	3.25683i	0.0638229	−	0.116093i	0.906293	+	0.422649i	$0.138900\pi$
$788$	−6.84292	−	7.28696i	−0.243769	−	0.259587i
$789$	6.71647	−	3.69241i	0.239113	−	0.131453i
$790$	−15.9332	−	13.8340i	−0.566879	−	0.492192i
$791$	28.5351	−	26.7962i	1.01459	−	0.952764i
$792$	1.55743	+	1.28842i	0.0553409	+	0.0457820i
$793$	7.28985	+	10.0336i	0.258870	+	0.356304i
$794$	26.3854	+	10.4467i	0.936384	+	0.370740i
$795$	9.04147	+	20.4670i	0.320668	+	0.725889i
$796$	8.77536	+	10.6076i	0.311034	+	0.375976i
$797$	−13.5217	−	34.1519i	−0.478963	−	1.20972i	−0.945617	−	0.325282i	$-0.894541\pi$
$797$	−13.5217	−	34.1519i	−0.478963	−	1.20972i	0.466654	−	0.884440i	$-0.345459\pi$
$798$	21.6579	−	4.13146i	0.766680	−	0.146252i
$799$	35.9009	−	26.0836i	1.27008	−	0.922770i
$800$	−0.238345	+	4.99432i	−0.00842678	+	0.176576i
$801$	−12.4493	−	9.04492i	−0.439873	−	0.319586i
$802$	−15.8517	−	7.45926i	−0.559744	−	0.263395i
$803$	17.0721	+	10.8343i	0.602463	+	0.382335i
$804$	−1.07522	+	0.425709i	−0.0379201	+	0.0150136i
$805$	−28.7388	−	4.32896i	−1.01291	−	0.152576i
$806$	−0.809559	+	12.8676i	−0.0285155	+	0.453241i
$807$			18.7216i			0.659032i
$808$	−8.50816	−	0.535288i	−0.299316	−	0.0188314i
$809$	−12.6919	−	26.9717i	−0.446224	−	0.948275i	−0.993765	−	0.111496i	$-0.964436\pi$
$809$	−12.6919	−	26.9717i	−0.446224	−	0.948275i	0.547541	−	0.836779i	$-0.315564\pi$
$810$	−5.56827	−	1.20046i	−0.195649	−	0.0421798i
$811$	30.8593	+	28.9788i	1.08362	+	1.01758i	0.999777	+	0.0211056i	$0.00671862\pi$
$811$	30.8593	+	28.9788i	1.08362	+	1.01758i	0.0838405	+	0.996479i	$0.473281\pi$
$812$	−1.29297	−	10.2349i	−0.0453744	−	0.359176i
$813$	−2.51121	−	19.8783i	−0.0880721	−	0.697162i
$814$	−2.53830	−	2.38362i	−0.0889674	−	0.0835460i
$815$	−25.8194	+	44.4225i	−0.904413	+	1.55605i
$816$	2.85572	+	6.06872i	0.0999702	+	0.212448i
$817$	59.0167	+	3.71301i	2.06473	+	0.129902i
$818$			15.7931i			0.552191i
$819$	−0.581367	+	9.24056i	−0.0203146	+	0.322891i
$820$	14.6856	+	14.4648i	0.512842	+	0.505134i
$821$	−21.9399	+	8.68663i	−0.765709	+	0.303166i	−0.718322	−	0.695711i	$-0.755089\pi$
$821$	−21.9399	+	8.68663i	−0.765709	+	0.303166i	−0.0473870	+	0.998877i	$0.515089\pi$
$822$	−9.04663	−	5.74116i	−0.315537	−	0.200246i
$823$	18.9751	+	8.92900i	0.661430	+	0.311245i	0.727035	−	0.686600i	$-0.240898\pi$
$823$	18.9751	+	8.92900i	0.661430	+	0.311245i	−0.0656049	+	0.997846i	$0.520898\pi$
$824$	−9.09222	−	6.60589i	−0.316743	−	0.230127i
$825$	−3.57534	+	7.90662i	−0.124477	+	0.275273i
$826$	3.56550	−	2.59049i	0.124060	−	0.0901345i
$827$	−16.1476	+	3.08032i	−0.561506	+	0.107113i	−0.460318	−	0.887754i	$-0.652265\pi$
$827$	−16.1476	+	3.08032i	−0.561506	+	0.107113i	−0.101189	+	0.994867i	$0.532265\pi$
$828$	1.85827	+	4.69346i	0.0645794	+	0.163109i
$829$	10.6588	+	12.8843i	0.370195	+	0.447489i	0.922410	−	0.386213i	$-0.126217\pi$
$829$	10.6588	+	12.8843i	0.370195	+	0.447489i	−0.552214	+	0.833702i	$0.686217\pi$
$830$	16.4150	+	9.54080i	0.569774	+	0.331166i
$831$	−13.3984	−	5.30481i	−0.464786	−	0.184022i
$832$	1.00529	+	1.38366i	0.0348520	+	0.0479697i
$833$	−28.8026	−	23.8276i	−0.997952	−	0.825578i
$834$	−8.50670	+	7.98832i	−0.294563	+	0.276613i
$835$	6.22886	−	14.6984i	0.215559	−	0.508660i
$836$	−5.79446	+	3.18553i	−0.200406	+	0.110174i
$837$	−28.5898	−	30.4451i	−0.988209	−	1.05234i
$838$	−7.60199	+	13.8280i	−0.262607	+	0.477679i
$839$	17.2869	−	36.7366i	0.596811	−	1.26829i	−0.347020	−	0.937858i	$-0.612806\pi$
$839$	17.2869	−	36.7366i	0.596811	−	1.26829i	0.943831	−	0.330430i	$-0.107194\pi$
$840$	6.30788	−	8.26048i	0.217643	−	0.285014i
$841$	21.1963	−	2.67772i	0.730908	−	0.0923352i
$842$	22.0318	−	13.9818i	0.759267	−	0.481846i
$843$	−15.9908	+	22.0094i	−0.550752	+	0.758046i
$844$	−5.81106	+	1.49203i	−0.200025	+	0.0513577i
$845$	−1.95019	+	22.4436i	−0.0670886	+	0.772082i
$846$	0.749975	+	11.9205i	0.0257847	+	0.409836i
$847$	33.7466	−	2.12316i	1.15955	−	0.0729526i
$848$	3.87205	+	7.04324i	0.132967	+	0.241866i
$849$	−9.18812	+	28.2781i	−0.315336	+	0.970503i
$850$	20.4923	−	17.4822i	0.702882	−	0.599633i
$851$	−2.68721	−	8.27039i	−0.0921165	−	0.283505i
$852$	−7.23824	+	7.70794i	−0.247978	+	0.264070i
$853$	6.97434	−	27.1632i	0.238797	−	0.930052i	−0.730251	−	0.683179i	$-0.760597\pi$
$853$	6.97434	−	27.1632i	0.238797	−	0.930052i	0.969048	−	0.246873i	$-0.0794030\pi$
$854$	14.5066	−	22.8587i	0.496406	−	0.782210i
$855$	−8.54829	+	12.7856i	−0.292345	+	0.437259i
$856$	−4.54851	+	5.49821i	−0.155465	+	0.187925i
$857$	48.3279	+	15.7027i	1.65085	+	0.536393i	0.978924	−	0.204225i	$-0.0654675\pi$
$857$	48.3279	+	15.7027i	1.65085	+	0.536393i	0.671925	+	0.740619i	$0.265468\pi$
$858$	0.738160	+	2.87494i	0.0252004	+	0.0981489i
$859$	−0.306792	−	0.168660i	−0.0104676	−	0.00575462i	0.476511	−	0.879168i	$-0.341901\pi$
$859$	−0.306792	−	0.168660i	−0.0104676	−	0.00575462i	−0.486979	+	0.873414i	$0.661901\pi$
$860$	21.8957	−	17.2512i	0.746637	−	0.588260i
$861$	−8.02897	−	42.0894i	−0.273627	−	1.43440i
$862$	4.98835	+	0.951579i	0.169904	+	0.0324109i
$863$	−10.5218	+	4.95117i	−0.358166	+	0.168540i	−0.596439	−	0.802658i	$-0.703418\pi$
$863$	−10.5218	+	4.95117i	−0.358166	+	0.168540i	0.238274	+	0.971198i	$0.423418\pi$
$864$	−5.49651	−	0.694371i	−0.186995	−	0.0236230i
$865$	−22.6284	−	43.5915i	−0.769388	−	1.48216i
$866$	1.12155	−	5.87935i	0.0381117	−	0.199789i
$867$	5.51002	−	13.9167i	0.187130	−	0.472637i
$868$	26.7671	−	8.69717i	0.908536	−	0.295201i
$869$	−7.04851	−	11.1067i	−0.239104	−	0.376768i
$870$	−6.11368	−	4.66853i	−0.207273	−	0.158278i
$871$	1.53873	+	0.395079i	0.0521379	+	0.0133867i
$872$	6.15773	−	5.09412i	0.208527	−	0.172509i
$873$	−1.55966	+	12.3460i	−0.0527865	+	0.417848i
$874$	−16.5136			−0.558582
$875$	−38.6751	−	15.7031i	−1.30746	−	0.530861i
$876$	−18.0586			−0.610143
$877$	1.28304	−	10.1563i	0.0433252	−	0.342954i	−0.955521	−	0.294924i	$-0.904706\pi$
$877$	1.28304	−	10.1563i	0.0433252	−	0.342954i	0.998846	−	0.0480301i	$-0.0152943\pi$
$878$	5.67618	−	4.69575i	0.191562	−	0.158474i
$879$	30.7748	+	7.90163i	1.03801	+	0.266515i
$880$	−1.03362	+	2.94067i	−0.0348434	+	0.0991300i
$881$	0.530164	+	0.835405i	0.0178617	+	0.0281455i	0.853141	−	0.521680i	$-0.174694\pi$
$881$	0.530164	+	0.835405i	0.0178617	+	0.0281455i	−0.835280	+	0.549825i	$0.814694\pi$
$882$	9.56893	−	3.10913i	0.322203	−	0.104690i
$883$	9.50774	−	24.0138i	0.319961	−	0.808129i	−0.677406	−	0.735609i	$-0.736896\pi$
$883$	9.50774	−	24.0138i	0.319961	−	0.808129i	0.997367	−	0.0725196i	$-0.0231040\pi$
$884$	1.72649	−	9.05059i	0.0580682	−	0.304404i
$885$	0.489488	−	3.24958i	0.0164540	−	0.109233i
$886$	−7.55925	−	0.954956i	−0.253958	−	0.0320824i
$887$	−6.21219	+	2.92323i	−0.208585	+	0.0981525i	−0.527234	−	0.849720i	$-0.676771\pi$
$887$	−6.21219	+	2.92323i	−0.208585	+	0.0981525i	0.318649	+	0.947873i	$0.396771\pi$
$888$	3.05478	+	0.582730i	0.102512	+	0.0195551i
$889$	−4.19095	−	21.9697i	−0.140560	−	0.736842i
$890$	6.44773	−	22.8373i	0.216128	−	0.765508i
$891$	−3.11182	−	1.71074i	−0.104250	−	0.0573118i
$892$	0.522763	+	2.03603i	0.0175034	+	0.0681712i
$893$	−37.1610	−	12.0743i	−1.24354	−	0.404052i
$894$	12.5550	−	15.1763i	0.419900	−	0.507573i
$895$	20.7339	+	26.3161i	0.693058	+	0.879650i
$896$	2.00049	−	3.15227i	0.0668318	−	0.105310i
$897$	−1.84347	+	7.17984i	−0.0615516	+	0.239728i
$898$	−1.57118	+	1.67314i	−0.0524311	+	0.0558335i
$899$	−6.43688	−	19.8107i	−0.214682	−	0.660723i
$900$	1.01750	+	7.17831i	0.0339167	+	0.239277i
$901$	13.3803	−	41.1803i	0.445762	−	1.37192i
$902$	6.19069	+	11.2608i	0.206127	+	0.374944i
$903$	−57.8297	+	3.63834i	−1.92445	+	0.121076i
$904$	−0.658342	−	10.4640i	−0.0218961	−	0.348029i
$905$	28.1922	−	6.52624i	0.937141	−	0.216940i
$906$	4.09161	−	1.05055i	0.135935	−	0.0349021i
$907$	−12.0517	+	16.5877i	−0.400170	+	0.550787i	−0.960787	−	0.277289i	$-0.910564\pi$
$907$	−12.0517	+	16.5877i	−0.400170	+	0.550787i	0.560617	+	0.828076i	$0.310564\pi$
$908$	−20.5398	+	13.0349i	−0.681637	+	0.432580i
$909$	−12.2639	+	1.54929i	−0.406767	+	0.0513866i
$910$	−13.6806	+	4.08716i	−0.453506	+	0.135488i
$911$	−11.9437	+	25.3816i	−0.395711	+	0.840928i	0.603345	+	0.797480i	$0.293834\pi$
$911$	−11.9437	+	25.3816i	−0.395711	+	0.840928i	−0.999056	+	0.0434480i	$0.986166\pi$
$912$	2.84504	−	5.17512i	0.0942088	−	0.171365i
$913$	8.10245	+	8.62823i	0.268152	+	0.285553i
$914$	−4.74928	+	2.61094i	−0.157092	+	0.0863623i
$915$	−4.55277	−	19.6672i	−0.150510	−	0.650177i
$916$	−15.6560	+	14.7020i	−0.517289	+	0.485767i
$917$	9.57637	+	7.92227i	0.316240	+	0.261616i
$918$	17.5433	+	24.1463i	0.579015	+	0.796946i
$919$	32.3870	+	12.8229i	1.06835	+	0.422990i	0.835482	−	0.549519i	$-0.185189\pi$
$919$	32.3870	+	12.8229i	1.06835	+	0.422990i	0.232869	+	0.972508i	$0.425189\pi$
$920$	−5.80005	+	5.19201i	−0.191222	+	0.171176i
$921$	11.5000	+	13.9011i	0.378939	+	0.458058i
$922$	10.3252	+	26.0784i	0.340041	+	0.858846i
$923$	14.2684	−	2.72184i	0.469650	−	0.0895906i
$924$	5.24193	−	3.80849i	0.172447	−	0.125290i
$925$	−0.972907	−	12.4516i	−0.0319890	−	0.409407i
$926$	1.77860	+	1.29223i	0.0584483	+	0.0424652i
$927$	−14.7452	−	6.93855i	−0.484295	−	0.227892i
$928$	−2.33303	−	1.48059i	−0.0765856	−	0.0486027i
$929$	3.82788	−	1.51556i	0.125589	−	0.0497240i	−0.304490	−	0.952516i	$-0.598486\pi$
$929$	3.82788	−	1.51556i	0.125589	−	0.0497240i	0.430078	+	0.902792i	$0.358486\pi$
$930$	9.38563	−	18.7704i	0.307767	−	0.615505i
$931$	−2.06671	+	32.8494i	−0.0677336	+	1.07659i
$932$		−	23.4615i		−	0.768509i
$933$	31.7754	+	1.99914i	1.04028	+	0.0654489i
$934$	8.17548	+	17.3738i	0.267510	+	0.568487i
$935$	15.3602	−	6.78552i	0.502334	−	0.221910i
$936$	1.80781	+	1.69764i	0.0590900	+	0.0554892i
$937$	0.0199269	+	0.157738i	0.000650984	+	0.00515307i	0.992437	−	0.122756i	$-0.0391733\pi$
$937$	0.0199269	+	0.157738i	0.000650984	+	0.00515307i	−0.991786	+	0.127909i	$0.959173\pi$
$938$	−0.434644	−	3.44056i	−0.0141916	−	0.112338i
$939$	−25.2562	−	23.7172i	−0.824206	−	0.773981i
$940$	−16.8482	+	7.44286i	−0.549529	+	0.242759i
$941$	−20.6194	−	43.8185i	−0.672173	−	1.42844i	−0.891605	−	0.452813i	$-0.850420\pi$
$941$	−20.6194	−	43.8185i	−0.672173	−	1.42844i	0.219432	−	0.975628i	$-0.429580\pi$
$942$	3.35936	+	0.211353i	0.109454	+	0.00688626i
$943$			32.0922i			1.04507i
$944$	0.0741214	−	1.17813i	0.00241245	−	0.0383447i
$945$	20.6850	−	41.3679i	0.672882	−	1.34570i
$946$	16.1573	−	6.39712i	0.525318	−	0.207988i
$947$	17.8985	+	11.3587i	0.581622	+	0.369108i	0.793852	−	0.608111i	$-0.208073\pi$
$947$	17.8985	+	11.3587i	0.581622	+	0.369108i	−0.212230	+	0.977220i	$0.568073\pi$
$948$	10.6303	+	5.00224i	0.345256	+	0.162465i
$949$	20.0701	+	14.5818i	0.651502	+	0.473344i
$950$	−23.0591	−	5.54974i	−0.748137	−	0.180057i
$951$	2.87774	−	2.09080i	0.0933170	−	0.0677988i
$952$	−19.7569	+	3.76883i	−0.640325	+	0.122148i
$953$	10.9591	+	27.6795i	0.355000	+	0.896626i	0.992055	+	0.125808i	$0.0401524\pi$
$953$	10.9591	+	27.6795i	0.355000	+	0.896626i	−0.637055	+	0.770818i	$0.719848\pi$
$954$	7.42876	+	8.97983i	0.240515	+	0.290733i
$955$	−37.0151	+	33.1347i	−1.19778	+	1.07221i
$956$	−0.855975	−	0.338904i	−0.0276842	−	0.0109610i
$957$	−2.81871	−	3.87962i	−0.0911158	−	0.125410i
$958$	−17.3287	−	14.3356i	−0.559866	−	0.463161i
$959$	23.4225	−	21.9952i	0.756352	−	0.710262i
$960$	−0.627838	−	2.71215i	−0.0202634	−	0.0875342i
$961$	22.6337	−	12.4430i	0.730118	−	0.401386i
$962$	−2.92450	−	3.11428i	−0.0942897	−	0.100408i
$963$	−4.98469	+	9.06712i	−0.160629	+	0.292184i
$964$	6.43097	−	13.6665i	0.207128	−	0.440169i
$965$	12.5223	−	3.74113i	0.403108	−	0.120431i
$966$	16.0539	−	2.02808i	0.516526	−	0.0652525i
$967$	44.8330	−	28.4519i	1.44173	−	0.914951i	0.441892	−	0.897068i	$-0.354307\pi$
$967$	44.8330	−	28.4519i	1.44173	−	0.914951i	0.999840	−	0.0178831i	$-0.00569267\pi$
$968$	5.32346	−	7.32712i	0.171103	−	0.235502i
$969$	−30.8154	+	7.91206i	−0.989934	+	0.254172i
$970$	−18.6957	+	4.32788i	−0.600283	+	0.138960i
$971$	−1.70590	−	27.1144i	−0.0547448	−	0.870144i	−0.925576	−	0.378562i	$-0.876419\pi$
$971$	−1.70590	−	27.1144i	−0.0547448	−	0.870144i	0.870831	−	0.491582i	$-0.163581\pi$
$972$	−13.4226	+	0.844476i	−0.430529	+	0.0270866i
$973$	−16.8588	−	30.6660i	−0.540468	−	0.983107i
$974$	3.80707	−	11.7170i	0.121986	−	0.375436i
$975$	−4.98709	+	9.40617i	−0.159715	+	0.301238i
$976$	−2.24084	−	6.89660i	−0.0717275	−	0.220755i
$977$	−39.7137	+	42.2908i	−1.27055	+	1.35300i	−0.363724	+	0.931507i	$0.618495\pi$
$977$	−39.7137	+	42.2908i	−1.27055	+	1.35300i	−0.906830	+	0.421496i	$0.861505\pi$
$978$	7.11441	−	27.7088i	0.227494	−	0.886029i
$979$	7.92675	−	12.4906i	0.253340	−	0.399200i
$980$	9.60221	+	12.1874i	0.306731	+	0.389312i
$981$	7.38654	−	8.92879i	0.235834	−	0.285074i
$982$	10.4526	+	3.39627i	0.333557	+	0.108379i
$983$	10.5354	+	41.0327i	0.336027	+	1.30874i	0.882124	+	0.471017i	$0.156113\pi$
$983$	10.5354	+	41.0327i	0.336027	+	1.30874i	−0.546097	+	0.837722i	$0.683887\pi$
$984$	−10.0572	−	5.52899i	−0.320612	−	0.176258i
$985$	6.07339	−	21.5114i	0.193514	−	0.685410i
$986$	2.78935	+	14.6223i	0.0888311	+	0.465669i
$987$	37.6094	+	7.17437i	1.19712	+	0.228363i
$988$	−7.34069	+	3.45427i	−0.233538	+	0.109895i
$989$	43.0563	+	5.43927i	1.36911	+	0.172959i
$990$	−0.673220	+	4.46933i	−0.0213964	+	0.142045i
$991$	−2.82493	+	14.8088i	−0.0897367	+	0.470416i	0.908843	+	0.417138i	$0.136967\pi$
$991$	−2.82493	+	14.8088i	−0.0897367	+	0.470416i	−0.998580	+	0.0532780i	$0.983033\pi$
$992$	2.77509	−	7.00909i	0.0881093	−	0.222539i
$993$	23.1822	−	7.53235i	0.735665	−	0.239032i
$994$	−16.9904	−	26.7725i	−0.538902	−	0.849174i
$995$	−10.2080	+	29.0420i	−0.323615	+	0.920692i
$996$	−10.2390	−	2.62892i	−0.324435	−	0.0833006i
$997$	−2.38619	+	1.97403i	−0.0755714	+	0.0625181i	−0.674443	−	0.738327i	$-0.735616\pi$
$997$	−2.38619	+	1.97403i	−0.0755714	+	0.0625181i	0.598871	+	0.800845i	$0.295616\pi$
$998$	3.22844	−	25.5557i	0.102194	−	0.808952i
$999$	13.8389			0.437845

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.h.a.109.8	yes	240
125.39	even	50	inner	250.2.h.a.39.8	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
250.2.h.a.39.8	✓	240	125.39	even	50	inner
250.2.h.a.109.8	yes	240	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.h (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.125333 - 0.992115i) q^{2} +(-0.959277 + 0.793583i) q^{3} +(-0.968583 - 0.248690i) q^{4} +(-0.640085 - 2.14250i) q^{5} +(0.667096 + 1.05118i) q^{6} +(-3.55074 + 1.15371i) q^{7} +(-0.368125 + 0.929776i) q^{8} +(-0.271705 + 1.42433i) q^{9} +O(q^{10})\)	\(q+(0.125333 - 0.992115i) q^{2} +(-0.959277 + 0.793583i) q^{3} +(-0.968583 - 0.248690i) q^{4} +(-0.640085 - 2.14250i) q^{5} +(0.667096 + 1.05118i) q^{6} +(-3.55074 + 1.15371i) q^{7} +(-0.368125 + 0.929776i) q^{8} +(-0.271705 + 1.42433i) q^{9} +(-2.20583 + 0.366512i) q^{10} +(-1.38299 - 0.174712i) q^{11} +(1.12650 - 0.530089i) q^{12} +(-1.68000 - 0.320477i) q^{13} +(0.699583 + 3.66734i) q^{14} +(2.31427 + 1.54729i) q^{15} +(0.876307 + 0.481754i) q^{16} +(-1.33976 - 5.21800i) q^{17} +(1.37904 + 0.448079i) q^{18} +(-3.02363 + 3.65494i) q^{19} +(0.0871584 + 2.23437i) q^{20} +(2.49058 - 3.92453i) q^{21} +(-0.346669 + 1.35019i) q^{22} +(-2.38312 + 2.53776i) q^{23} +(-0.384721 - 1.18405i) q^{24} +(-4.18058 + 2.74276i) q^{25} +(-0.528510 + 1.62659i) q^{26} +(-2.66901 - 4.85491i) q^{27} +(3.72610 - 0.234427i) q^{28} +(-0.173502 - 2.75773i) q^{29} +(1.82514 - 2.10209i) q^{30} +(7.30163 - 1.87474i) q^{31} +(0.587785 - 0.809017i) q^{32} +(1.46532 - 0.929920i) q^{33} +(-5.34477 + 0.675202i) q^{34} +(4.74459 + 6.86898i) q^{35} +(0.617386 - 1.31201i) q^{36} +(-1.20338 + 2.18894i) q^{37} +(3.24716 + 3.45787i) q^{38} +(1.86591 - 1.02579i) q^{39} +(2.22767 + 0.193570i) q^{40} +(6.71995 - 6.31045i) q^{41} +(-3.58143 - 2.96282i) q^{42} +(-7.32742 - 10.0853i) q^{43} +(1.29609 + 0.513159i) q^{44} +(3.22554 - 0.329564i) q^{45} +(2.21907 + 2.68239i) q^{46} +(3.03232 + 7.65878i) q^{47} +(-1.22293 + 0.233287i) q^{48} +(5.61361 - 4.07853i) q^{49} +(2.19717 + 4.49138i) q^{50} +(5.42611 + 3.94230i) q^{51} +(1.54752 + 0.728209i) q^{52} +(6.78621 + 4.30666i) q^{53} +(-5.15115 + 2.03948i) q^{54} +(0.510911 + 3.07488i) q^{55} +(0.234427 - 3.72610i) q^{56} -5.90560i q^{57} +(-2.75773 - 0.173502i) q^{58} +(-0.502614 - 1.06811i) q^{59} +(-1.85677 - 2.07421i) q^{60} +(-5.28612 - 4.96400i) q^{61} +(-0.944820 - 7.47902i) q^{62} +(-0.678502 - 5.37090i) q^{63} +(-0.728969 - 0.684547i) q^{64} +(0.388722 + 3.80453i) q^{65} +(-0.738934 - 1.57031i) q^{66} +(-0.927036 - 0.0583242i) q^{67} +5.38725i q^{68} +(0.272145 - 4.32562i) q^{69} +(7.40947 - 3.84626i) q^{70} +(-7.89668 + 3.12652i) q^{71} +(-1.22429 - 0.776956i) q^{72} +(-13.1246 - 6.17596i) q^{73} +(2.02085 + 1.46824i) q^{74} +(1.83373 - 5.94871i) q^{75} +(3.83758 - 2.78817i) q^{76} +(5.11221 - 0.975206i) q^{77} +(-0.783845 - 1.97977i) q^{78} +(6.01512 + 7.27103i) q^{79} +(0.471245 - 2.18585i) q^{80} +(2.36853 + 0.937768i) q^{81} +(-5.41846 - 7.45787i) q^{82} +(-6.54238 - 5.41233i) q^{83} +(-3.38833 + 3.18185i) q^{84} +(-10.3220 + 6.21039i) q^{85} +(-10.9242 + 6.00561i) q^{86} +(2.35493 + 2.50774i) q^{87} +(0.671556 - 1.22156i) q^{88} +(-4.51854 + 9.60239i) q^{89} +(0.0773014 - 3.24141i) q^{90} +(6.33499 - 0.800295i) q^{91} +(2.93937 - 1.86538i) q^{92} +(-5.51653 + 7.59285i) q^{93} +(7.97844 - 2.04851i) q^{94} +(9.76607 + 4.13864i) q^{95} +(0.0781732 + 1.24253i) q^{96} +(8.56513 - 0.538873i) q^{97} +(-3.34280 - 6.08052i) q^{98} +(0.624614 - 1.92236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 10 q^{5}+O(q^{10}) \) 240 * q + 10 * q^5	\( 240 q + 10 q^{5} + 10 q^{11} - 40 q^{12} + 20 q^{15} - 10 q^{17} - 20 q^{19} - 20 q^{22} - 60 q^{23} - 10 q^{24} - 110 q^{25} + 30 q^{26} - 10 q^{28} - 20 q^{29} - 20 q^{30} + 10 q^{31} + 30 q^{33} - 10 q^{35} + 10 q^{37} - 20 q^{39} + 30 q^{41} + 10 q^{42} - 160 q^{45} + 20 q^{46} - 220 q^{47} + 10 q^{48} + 40 q^{49} + 20 q^{51} + 10 q^{55} - 30 q^{59} - 50 q^{60} + 40 q^{61} - 20 q^{63} - 50 q^{65} - 10 q^{67} - 20 q^{69} - 50 q^{71} - 50 q^{74} - 10 q^{75} + 10 q^{76} - 40 q^{77} - 170 q^{78} - 40 q^{79} + 50 q^{81} - 200 q^{82} - 50 q^{83} - 30 q^{84} + 20 q^{85} - 20 q^{87} + 10 q^{88} - 40 q^{89} + 30 q^{90} - 240 q^{91} + 10 q^{92} - 100 q^{93} - 100 q^{95} + 20 q^{97} + 40 q^{98} - 30 q^{99}+O(q^{100}) \) 240 * q + 10 * q^5 + 10 * q^11 - 40 * q^12 + 20 * q^15 - 10 * q^17 - 20 * q^19 - 20 * q^22 - 60 * q^23 - 10 * q^24 - 110 * q^25 + 30 * q^26 - 10 * q^28 - 20 * q^29 - 20 * q^30 + 10 * q^31 + 30 * q^33 - 10 * q^35 + 10 * q^37 - 20 * q^39 + 30 * q^41 + 10 * q^42 - 160 * q^45 + 20 * q^46 - 220 * q^47 + 10 * q^48 + 40 * q^49 + 20 * q^51 + 10 * q^55 - 30 * q^59 - 50 * q^60 + 40 * q^61 - 20 * q^63 - 50 * q^65 - 10 * q^67 - 20 * q^69 - 50 * q^71 - 50 * q^74 - 10 * q^75 + 10 * q^76 - 40 * q^77 - 170 * q^78 - 40 * q^79 + 50 * q^81 - 200 * q^82 - 50 * q^83 - 30 * q^84 + 20 * q^85 - 20 * q^87 + 10 * q^88 - 40 * q^89 + 30 * q^90 - 240 * q^91 + 10 * q^92 - 100 * q^93 - 100 * q^95 + 20 * q^97 + 40 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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