LMFDB - Embedded newform 192.2.s.a.11.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(11,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8]))

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

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

chi := DirichletCharacter("192.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.s (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			11.20
Character	$\chi$	$=$	192.11
Dual form			192.2.s.a.35.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.640805 - 1.26070i) q^{2} +(-1.16480 - 1.28189i) q^{3} +(-1.17874 - 1.61573i) q^{4} +(3.57797 - 2.39072i) q^{5} +(-2.36249 + 0.647019i) q^{6} +(-0.994439 + 2.40079i) q^{7} +(-2.79229 + 0.450669i) q^{8} +(-0.286494 + 2.98629i) q^{9} +O(q^{10})$	\(q+(0.640805 - 1.26070i) q^{2} +(-1.16480 - 1.28189i) q^{3} +(-1.17874 - 1.61573i) q^{4} +(3.57797 - 2.39072i) q^{5} +(-2.36249 + 0.647019i) q^{6} +(-0.994439 + 2.40079i) q^{7} +(-2.79229 + 0.450669i) q^{8} +(-0.286494 + 2.98629i) q^{9} +(-0.721207 - 6.04274i) q^{10} +(0.714367 - 3.59136i) q^{11} +(-0.698199 + 3.39301i) q^{12} +(-1.38986 + 2.08008i) q^{13} +(2.38944 + 2.79213i) q^{14} +(-7.23226 - 1.80186i) q^{15} +(-1.22116 + 3.80904i) q^{16} +(0.951204 + 0.951204i) q^{17} +(3.58123 + 2.27481i) q^{18} +(-0.214739 + 0.321380i) q^{19} +(-8.08025 - 2.96299i) q^{20} +(4.23587 - 1.52167i) q^{21} +(-4.06987 - 3.20197i) q^{22} +(1.14288 + 2.75916i) q^{23} +(3.83016 + 3.05448i) q^{24} +(5.17290 - 12.4885i) q^{25} +(1.73173 + 3.08513i) q^{26} +(4.16181 - 3.11117i) q^{27} +(5.05121 - 1.22316i) q^{28} +(2.53398 - 0.504039i) q^{29} +(-6.90608 + 7.96308i) q^{30} +2.03735 q^{31} +(4.01954 + 3.98037i) q^{32} +(-5.43583 + 3.26747i) q^{33} +(1.80872 - 0.589648i) q^{34} +(2.18155 + 10.9674i) q^{35} +(5.16273 - 3.05715i) q^{36} +(4.28668 - 2.86427i) q^{37} +(0.267558 + 0.476664i) q^{38} +(4.28535 - 0.641215i) q^{39} +(-8.91331 + 8.28808i) q^{40} +(-4.29457 + 1.77887i) q^{41} +(0.795999 - 6.31526i) q^{42} +(-1.88124 + 9.45763i) q^{43} +(-6.64472 + 3.07905i) q^{44} +(6.11432 + 11.3698i) q^{45} +(4.21083 + 0.327251i) q^{46} +(5.57116 - 5.57116i) q^{47} +(6.30518 - 2.87137i) q^{48} +(0.174869 + 0.174869i) q^{49} +(-12.4294 - 14.5242i) q^{50} +(0.111381 - 2.32730i) q^{51} +(4.99913 - 0.206223i) q^{52} +(-1.47041 - 0.292483i) q^{53} +(-1.25534 - 7.24045i) q^{54} +(-6.02998 - 14.5576i) q^{55} +(1.69480 - 7.15187i) q^{56} +(0.662102 - 0.0990701i) q^{57} +(0.988343 - 3.51758i) q^{58} +(-3.66506 - 5.48515i) q^{59} +(5.61361 + 13.8093i) q^{60} +(-4.09381 + 0.814309i) q^{61} +(1.30554 - 2.56849i) q^{62} +(-6.88455 - 3.65750i) q^{63} +(7.59380 - 2.51680i) q^{64} +10.7652i q^{65} +(0.635995 + 8.94678i) q^{66} +(1.50936 + 7.58806i) q^{67} +(0.415668 - 2.65811i) q^{68} +(2.20572 - 4.67890i) q^{69} +(15.2245 + 4.27767i) q^{70} +(-6.27514 - 2.59925i) q^{71} +(-0.545851 - 8.46771i) q^{72} +(-15.4732 + 6.40920i) q^{73} +(-0.864060 - 7.23966i) q^{74} +(-22.0342 + 7.91545i) q^{75} +(0.772384 - 0.0318623i) q^{76} +(7.91171 + 5.28644i) q^{77} +(1.93769 - 5.81344i) q^{78} +(2.31400 - 2.31400i) q^{79} +(4.73710 + 16.5481i) q^{80} +(-8.83584 - 1.71111i) q^{81} +(-0.509359 + 6.55408i) q^{82} +(1.62719 + 1.08726i) q^{83} +(-7.45158 - 5.05037i) q^{84} +(5.67744 + 1.12931i) q^{85} +(10.7177 + 8.43218i) q^{86} +(-3.59769 - 2.66118i) q^{87} +(-0.376205 + 10.3501i) q^{88} +(-4.04231 - 1.67438i) q^{89} +(18.2520 - 0.422520i) q^{90} +(-3.61170 - 5.40528i) q^{91} +(3.11089 - 5.09890i) q^{92} +(-2.37310 - 2.61166i) q^{93} +(-3.45354 - 10.5936i) q^{94} +1.66327i q^{95} +(0.420453 - 9.78893i) q^{96} +1.86899i q^{97} +(0.332515 - 0.108401i) q^{98} +(10.5202 + 3.16221i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{16}\right)$

Coefficient data

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

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

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

$2$	0.640805	−	1.26070i	0.453118	−	0.891451i
$2$	0.640805	−	1.26070i	0.453118	−	0.891451i
$3$	−1.16480	−	1.28189i	−0.672496	−	0.740101i
$3$	−1.16480	−	1.28189i	−0.672496	−	0.740101i
$4$	−1.17874	−	1.61573i	−0.589369	−	0.807864i
$5$	3.57797	−	2.39072i	1.60012	−	1.06916i	0.648796	−	0.760963i	$-0.275273\pi$
$5$	3.57797	−	2.39072i	1.60012	−	1.06916i	0.951321	−	0.308201i	$-0.0997270\pi$
$6$	−2.36249	+	0.647019i	−0.964483	+	0.264144i
$7$	−0.994439	+	2.40079i	−0.375863	+	0.907413i	0.616869	+	0.787066i	$0.288401\pi$
$7$	−0.994439	+	2.40079i	−0.375863	+	0.907413i	−0.992732	+	0.120347i	$0.961599\pi$
$8$	−2.79229	+	0.450669i	−0.987224	+	0.159336i
$9$	−0.286494	+	2.98629i	−0.0954981	+	0.995430i
$10$	−0.721207	−	6.04274i	−0.228066	−	1.91088i
$11$	0.714367	−	3.59136i	0.215390	−	1.08284i	−0.710111	−	0.704090i	$-0.751355\pi$
$11$	0.714367	−	3.59136i	0.215390	−	1.08284i	0.925500	−	0.378747i	$-0.123645\pi$
$12$	−0.698199	+	3.39301i	−0.201553	+	0.979478i
$13$	−1.38986	+	2.08008i	−0.385479	+	0.576910i	−0.972570	−	0.232611i	$-0.925273\pi$
$13$	−1.38986	+	2.08008i	−0.385479	+	0.576910i	0.587091	+	0.809521i	$0.300273\pi$
$14$	2.38944	+	2.79213i	0.638604	+	0.746228i
$15$	−7.23226	−	1.80186i	−1.86736	−	0.465239i
$16$	−1.22116	+	3.80904i	−0.305289	+	0.952260i
$17$	0.951204	+	0.951204i	0.230701	+	0.230701i	0.812985	−	0.582284i	$-0.197841\pi$
$17$	0.951204	+	0.951204i	0.230701	+	0.230701i	−0.582284	+	0.812985i	$0.697841\pi$
$18$	3.58123	+	2.27481i	0.844105	+	0.536179i
$19$	−0.214739	+	0.321380i	−0.0492646	+	0.0737297i	−0.855284	−	0.518159i	$-0.826618\pi$
$19$	−0.214739	+	0.321380i	−0.0492646	+	0.0737297i	0.806020	+	0.591889i	$0.201618\pi$
$20$	−8.08025	−	2.96299i	−1.80680	−	0.662545i
$21$	4.23587	−	1.52167i	0.924343	−	0.332055i
$22$	−4.06987	−	3.20197i	−0.867699	−	0.682662i
$23$	1.14288	+	2.75916i	0.238307	+	0.575324i	0.997108	−	0.0759988i	$-0.0242145\pi$
$23$	1.14288	+	2.75916i	0.238307	+	0.575324i	−0.758801	+	0.651322i	$0.774215\pi$
$24$	3.83016	+	3.05448i	0.781829	+	0.623493i
$25$	5.17290	−	12.4885i	1.03458	−	2.49769i
$26$	1.73173	+	3.08513i	0.339620	+	0.605044i
$27$	4.16181	−	3.11117i	0.800940	−	0.598744i
$28$	5.05121	−	1.22316i	0.954588	−	0.231155i
$29$	2.53398	−	0.504039i	0.470548	−	0.0935978i	0.0458799	−	0.998947i	$-0.485391\pi$
$29$	2.53398	−	0.504039i	0.470548	−	0.0935978i	0.424668	+	0.905349i	$0.360391\pi$
$30$	−6.90608	+	7.96308i	−1.26087	+	1.45385i
$31$	2.03735			0.365919			0.182959	−	0.983120i	$-0.441432\pi$
$31$	2.03735			0.365919			0.182959	+	0.983120i	$0.441432\pi$
$32$	4.01954	+	3.98037i	0.710561	+	0.703636i
$33$	−5.43583	+	3.26747i	−0.946257	+	0.568794i
$34$	1.80872	−	0.589648i	0.310193	−	0.101124i
$35$	2.18155	+	10.9674i	0.368749	+	1.85383i
$36$	5.16273	−	3.05715i	0.860456	−	0.509526i
$37$	4.28668	−	2.86427i	0.704726	−	0.470883i	−0.150852	−	0.988556i	$-0.548202\pi$
$37$	4.28668	−	2.86427i	0.704726	−	0.470883i	0.855578	+	0.517674i	$0.173202\pi$
$38$	0.267558	+	0.476664i	0.0434037	+	0.0773252i
$39$	4.28535	−	0.641215i	0.686205	−	0.102676i
$40$	−8.91331	+	8.28808i	−1.40932	+	1.31046i
$41$	−4.29457	+	1.77887i	−0.670699	+	0.277813i	−0.691933	−	0.721962i	$-0.743241\pi$
$41$	−4.29457	+	1.77887i	−0.670699	+	0.277813i	0.0212338	+	0.999775i	$0.493241\pi$
$42$	0.795999	−	6.31526i	0.122825	−	0.974467i
$43$	−1.88124	+	9.45763i	−0.286886	+	1.44228i	0.521312	+	0.853366i	$0.325443\pi$
$43$	−1.88124	+	9.45763i	−0.286886	+	1.44228i	−0.808199	+	0.588910i	$0.799557\pi$
$44$	−6.64472	+	3.07905i	−1.00173	+	0.464185i
$45$	6.11432	+	11.3698i	0.911469	+	1.69491i
$46$	4.21083	+	0.327251i	0.620854	+	0.0482505i
$47$	5.57116	−	5.57116i	0.812637	−	0.812637i	−0.172392	−	0.985028i	$-0.555150\pi$
$47$	5.57116	−	5.57116i	0.812637	−	0.812637i	0.985028	+	0.172392i	$0.0551495\pi$
$48$	6.30518	−	2.87137i	0.910074	−	0.414446i
$49$	0.174869	+	0.174869i	0.0249813	+	0.0249813i
$50$	−12.4294	−	14.5242i	−1.75779	−	2.05403i
$51$	0.111381	−	2.32730i	0.0155965	−	0.325887i
$52$	4.99913	−	0.206223i	0.693254	−	0.0285981i
$53$	−1.47041	−	0.292483i	−0.201977	−	0.0401757i	0.0930650	−	0.995660i	$-0.470334\pi$
$53$	−1.47041	−	0.292483i	−0.201977	−	0.0401757i	−0.295042	+	0.955484i	$0.595334\pi$
$54$	−1.25534	−	7.24045i	−0.170831	−	0.985300i
$55$	−6.02998	−	14.5576i	−0.813082	−	1.96295i
$56$	1.69480	−	7.15187i	0.226478	−	0.955709i
$57$	0.662102	−	0.0990701i	0.0876976	−	0.0131222i
$58$	0.988343	−	3.51758i	0.129776	−	0.461881i
$59$	−3.66506	−	5.48515i	−0.477150	−	0.714105i	0.512328	−	0.858790i	$-0.328783\pi$
$59$	−3.66506	−	5.48515i	−0.477150	−	0.714105i	−0.989478	+	0.144685i	$0.953783\pi$
$60$	5.61361	+	13.8093i	0.724714	+	1.78277i
$61$	−4.09381	+	0.814309i	−0.524158	+	0.104262i	−0.450075	−	0.892991i	$-0.648603\pi$
$61$	−4.09381	+	0.814309i	−0.524158	+	0.104262i	−0.0740827	+	0.997252i	$0.523603\pi$
$62$	1.30554	−	2.56849i	0.165804	−	0.326199i
$63$	−6.88455	−	3.65750i	−0.867372	−	0.460801i
$64$	7.59380	−	2.51680i	0.949224	−	0.314600i
$65$			10.7652i			1.33526i
$66$	0.635995	+	8.94678i	0.0782855	+	1.10127i
$67$	1.50936	+	7.58806i	0.184398	+	0.927029i	0.956545	+	0.291585i	$0.0941827\pi$
$67$	1.50936	+	7.58806i	0.184398	+	0.927029i	−0.772147	+	0.635444i	$0.780817\pi$
$68$	0.415668	−	2.65811i	0.0504071	−	0.322343i
$69$	2.20572	−	4.67890i	0.265537	−	0.563274i
$70$	15.2245	+	4.27767i	1.81968	+	0.511280i
$71$	−6.27514	−	2.59925i	−0.744722	−	0.308474i	−0.0221361	−	0.999755i	$-0.507047\pi$
$71$	−6.27514	−	2.59925i	−0.744722	−	0.308474i	−0.722586	+	0.691281i	$0.757047\pi$
$72$	−0.545851	−	8.46771i	−0.0643292	−	0.997929i
$73$	−15.4732	+	6.40920i	−1.81100	+	0.750140i	−0.829543	+	0.558443i	$0.811399\pi$
$73$	−15.4732	+	6.40920i	−1.81100	+	0.750140i	−0.981454	+	0.191697i	$0.938601\pi$
$74$	−0.864060	−	7.23966i	−0.100445	−	0.841593i
$75$	−22.0342	+	7.91545i	−2.54430	+	0.913997i
$76$	0.772384	−	0.0318623i	0.0885985	−	0.00365486i
$77$	7.91171	+	5.28644i	0.901623	+	0.602446i
$78$	1.93769	−	5.81344i	0.219401	−	0.658242i
$79$	2.31400	−	2.31400i	0.260345	−	0.260345i	−0.564849	−	0.825194i	$-0.691066\pi$
$79$	2.31400	−	2.31400i	0.260345	−	0.260345i	0.825194	+	0.564849i	$0.191066\pi$
$80$	4.73710	+	16.5481i	0.529623	+	1.85013i
$81$	−8.83584	−	1.71111i	−0.981760	−	0.190123i
$82$	−0.509359	+	6.55408i	−0.0562493	+	0.723777i
$83$	1.62719	+	1.08726i	0.178608	+	0.119342i	0.641660	−	0.766989i	$-0.278246\pi$
$83$	1.62719	+	1.08726i	0.178608	+	0.119342i	−0.463053	+	0.886331i	$0.653246\pi$
$84$	−7.45158	−	5.05037i	−0.813035	−	0.551041i
$85$	5.67744	+	1.12931i	0.615805	+	0.122491i
$86$	10.7177	+	8.43218i	1.15572	+	0.909266i
$87$	−3.59769	−	2.66118i	−0.385713	−	0.285309i
$88$	−0.376205	+	10.3501i	−0.0401036	+	1.10332i
$89$	−4.04231	−	1.67438i	−0.428484	−	0.177484i	0.158010	−	0.987438i	$-0.449492\pi$
$89$	−4.04231	−	1.67438i	−0.428484	−	0.177484i	−0.586494	+	0.809954i	$0.699492\pi$
$90$	18.2520	−	0.422520i	1.92393	−	0.0445376i
$91$	−3.61170	−	5.40528i	−0.378609	−	0.566628i
$92$	3.11089	−	5.09890i	0.324333	−	0.531597i
$93$	−2.37310	−	2.61166i	−0.246079	−	0.270817i
$94$	−3.45354	−	10.5936i	−0.356205	−	1.09265i
$95$			1.66327i			0.170648i
$96$	0.420453	−	9.78893i	0.0429123	−	0.999079i
$97$			1.86899i			0.189767i	0.995488	+	0.0948834i	$0.0302478\pi$
$97$			1.86899i			0.189767i	−0.995488	+	0.0948834i	$0.969752\pi$
$98$	0.332515	−	0.108401i	0.0335891	−	0.0109501i
$99$	10.5202	+	3.16221i	1.05732	+	0.317814i
$100$	−26.2755	+	6.36264i	−2.62755	+	0.636264i
$101$	7.63182	+	11.4218i	0.759395	+	1.13651i	0.986678	+	0.162686i	$0.0520157\pi$
$101$	7.63182	+	11.4218i	0.759395	+	1.13651i	−0.227283	+	0.973829i	$0.572984\pi$
$102$	−2.86266	−	1.63176i	−0.283445	−	0.161569i
$103$	13.4251	+	5.56087i	1.32282	+	0.547929i	0.928598	−	0.371087i	$-0.121015\pi$
$103$	13.4251	+	5.56087i	1.32282	+	0.547929i	0.394220	+	0.919016i	$0.371015\pi$
$104$	2.94348	−	6.43456i	0.288632	−	0.630960i
$105$	11.5179	−	15.5713i	1.12404	−	1.51960i
$106$	−1.31098	+	1.66633i	−0.127334	+	0.161848i
$107$	−2.15026	−	0.427713i	−0.207874	−	0.0413486i	0.0900550	−	0.995937i	$-0.471296\pi$
$107$	−2.15026	−	0.427713i	−0.207874	−	0.0413486i	−0.297929	+	0.954588i	$0.596296\pi$
$108$	−9.93248	−	3.05710i	−0.955753	−	0.294170i
$109$	−14.2766	−	9.53929i	−1.36745	−	0.913698i	−0.367579	−	0.929992i	$-0.619813\pi$
$109$	−14.2766	−	9.53929i	−1.36745	−	0.913698i	−0.999867	+	0.0162943i	$0.994813\pi$
$110$	−22.2169	−	1.72662i	−2.11830	−	0.164626i
$111$	−8.66479	−	2.15877i	−0.822426	−	0.204901i
$112$	−7.93033	−	6.71960i	−0.749346	−	0.634942i
$113$	−8.95069	+	8.95069i	−0.842010	+	0.842010i	−0.989120	−	0.147110i	$-0.953003\pi$
$113$	−8.95069	+	8.95069i	−0.842010	+	0.842010i	0.147110	+	0.989120i	$0.453003\pi$
$114$	0.299381	−	0.898198i	0.0280396	−	0.0841240i
$115$	10.6856	+	7.13987i	0.996434	+	0.665796i
$116$	−3.80128	−	3.50009i	−0.352940	−	0.324975i
$117$	−5.81353	−	4.74647i	−0.537461	−	0.438811i
$118$	−9.26372	+	1.10563i	−0.852795	+	0.101782i
$119$	−3.22955	+	1.33773i	−0.296053	+	0.122629i
$120$	21.0066	+	1.77198i	1.91763	+	0.161758i
$121$	−2.22490	−	0.921585i	−0.202264	−	0.0837805i
$122$	−1.59673	+	5.68288i	−0.144561	+	0.514504i
$123$	7.28262	+	3.43315i	0.656652	+	0.309557i
$124$	−2.40150	−	3.29180i	−0.215661	−	0.295613i
$125$	−7.15047	−	35.9478i	−0.639557	−	3.21527i
$126$	−9.02267	+	6.33562i	−0.803803	+	0.564422i
$127$			17.0863i			1.51617i	0.652158	+	0.758083i	$0.273864\pi$
$127$			17.0863i			1.51617i	−0.652158	+	0.758083i	$0.726136\pi$
$128$	1.69321	−	11.1863i	0.149660	−	0.988737i
$129$	14.3149	−	8.60468i	1.26036	−	0.757600i
$130$	13.5718	+	6.89842i	1.19032	+	0.605032i
$131$	1.56358	−	0.311016i	0.136611	−	0.0271736i	−0.126311	−	0.991991i	$-0.540314\pi$
$131$	1.56358	−	0.311016i	0.136611	−	0.0271736i	0.262922	+	0.964817i	$0.415314\pi$
$132$	11.6868	+	4.93134i	1.01720	+	0.429218i
$133$	−0.558021	−	0.835137i	−0.0483865	−	0.0724155i
$134$	10.5335	+	2.95962i	0.909954	+	0.255672i
$135$	7.45289	−	21.0814i	0.641442	−	1.81440i
$136$	−3.08472	−	2.22736i	−0.264512	−	0.190995i
$137$	5.56434	+	13.4335i	0.475393	+	1.14770i	0.961747	+	0.273939i	$0.0883267\pi$
$137$	5.56434	+	13.4335i	0.475393	+	1.14770i	−0.486354	+	0.873762i	$0.661673\pi$
$138$	−4.48527	−	5.77902i	−0.381811	−	0.491943i
$139$	−4.94256	−	0.983137i	−0.419223	−	0.0833886i	−0.0190285	−	0.999819i	$-0.506057\pi$
$139$	−4.94256	−	0.983137i	−0.419223	−	0.0833886i	−0.400194	+	0.916430i	$0.631057\pi$
$140$	15.1488	−	16.4524i	1.28031	−	1.39049i
$141$	−13.6309	−	0.652353i	−1.14793	−	0.0549380i
$142$	−7.29802	+	6.24547i	−0.612436	+	0.524108i
$143$	6.47745	+	6.47745i	0.541672	+	0.541672i
$144$	−11.0250	−	4.73799i	−0.918753	−	0.394833i
$145$	7.86148	−	7.86148i	0.652860	−	0.652860i
$146$	−1.83520	+	23.6141i	−0.151882	+	1.95432i
$147$	0.0204763	−	0.427850i	0.00168885	−	0.0352885i
$148$	−9.68075	−	3.54989i	−0.795752	−	0.291799i
$149$	0.473681	−	2.38135i	0.0388054	−	0.195088i	−0.956520	−	0.291667i	$-0.905790\pi$
$149$	0.473681	−	2.38135i	0.0388054	−	0.195088i	0.995325	+	0.0965790i	$0.0307900\pi$
$150$	−4.14064	+	32.8509i	−0.338082	+	2.68226i
$151$	−1.17767	+	0.487807i	−0.0958374	+	0.0396972i	−0.430087	−	0.902787i	$-0.641517\pi$
$151$	−1.17767	+	0.487807i	−0.0958374	+	0.0396972i	0.334250	+	0.942485i	$0.391517\pi$
$152$	0.454779	−	0.994164i	0.0368874	−	0.0806373i
$153$	−3.11308	+	2.56806i	−0.251678	+	0.207615i
$154$	11.7345	−	6.58673i	0.945592	−	0.530774i
$155$	7.28958	−	4.87074i	0.585513	−	0.391227i
$156$	−6.08733	−	6.16813i	−0.487376	−	0.493846i
$157$	2.08481	+	10.4811i	0.166386	+	0.836479i	0.970332	+	0.241777i	$0.0777302\pi$
$157$	2.08481	+	10.4811i	0.166386	+	0.836479i	−0.803946	+	0.594703i	$0.797270\pi$
$158$	−1.43444	−	4.40008i	−0.114118	−	0.350052i
$159$	1.33780	+	2.22559i	0.106094	+	0.176501i
$160$	23.8977	+	4.63203i	1.88928	+	0.366194i
$161$	−7.76067			−0.611627
$162$	−7.81925	+	10.0429i	−0.614339	+	0.789043i
$163$	−7.80064	+	1.55164i	−0.610993	+	0.121534i	−0.490882	−	0.871226i	$-0.663325\pi$
$163$	−7.80064	+	1.55164i	−0.610993	+	0.121534i	−0.120112	+	0.992760i	$0.538325\pi$
$164$	7.93634	+	4.84204i	0.619724	+	0.378100i
$165$	−11.6376	+	24.6865i	−0.905989	+	1.92184i
$166$	2.41342	−	1.35469i	0.187318	−	0.105144i
$167$	6.86336	−	16.5696i	0.531103	−	1.28220i	−0.399691	−	0.916650i	$-0.630882\pi$
$167$	6.86336	−	16.5696i	0.531103	−	1.28220i	0.930793	−	0.365545i	$-0.119118\pi$
$168$	−11.1420	+	6.15792i	−0.859626	+	0.475094i
$169$	2.57988	+	6.22838i	0.198452	+	0.479106i
$170$	5.06186	−	6.43389i	0.388227	−	0.493457i
$171$	−0.898212	−	0.733347i	−0.0686880	−	0.0560805i
$172$	17.4985	−	8.10849i	1.33424	−	0.618267i
$173$	7.24199	−	10.8384i	0.550598	−	0.824029i	−0.446910	−	0.894579i	$-0.647476\pi$
$173$	7.24199	−	10.8384i	0.550598	−	0.824029i	0.997508	+	0.0705503i	$0.0224755\pi$
$174$	−5.66038	+	2.83032i	−0.429112	+	0.214566i
$175$	24.8381	+	24.8381i	1.87758	+	1.87758i
$176$	12.8073	+	7.10667i	0.965386	+	0.535685i
$177$	−2.76232	+	11.0873i	−0.207628	+	0.833372i
$178$	−4.70122	+	4.02319i	−0.352372	+	0.301551i
$179$	−3.45085	+	5.16456i	−0.257929	+	0.386018i	−0.937722	−	0.347386i	$-0.887069\pi$
$179$	−3.45085	+	5.16456i	−0.257929	+	0.386018i	0.679794	+	0.733404i	$0.262069\pi$
$180$	11.1633	−	23.2811i	0.832063	−	1.73527i
$181$	2.65101	−	13.3275i	0.197048	−	0.990627i	−0.748001	−	0.663698i	$-0.768986\pi$
$181$	2.65101	−	13.3275i	0.197048	−	0.990627i	0.945049	−	0.326929i	$-0.106014\pi$
$182$	−9.12884	+	1.08954i	−0.676675	+	0.0807618i
$183$	5.81231	+	4.29931i	0.429658	+	0.317814i
$184$	−4.43472	−	7.18931i	−0.326932	−	0.530003i
$185$	8.48994	−	20.4965i	0.624193	−	1.50693i
$186$	−4.81322	+	1.31820i	−0.352923	+	0.0966554i
$187$	4.09563	−	2.73661i	0.299502	−	0.200121i
$188$	−15.5684	−	2.43455i	−1.13544	−	0.177557i
$189$	3.33059	+	13.0855i	0.242265	+	0.951829i
$190$	2.09689	+	1.06583i	0.152124	+	0.0773236i
$191$	−13.5497			−0.980420			−0.490210	−	0.871604i	$-0.663080\pi$
$191$	−13.5497			−0.980420			−0.490210	+	0.871604i	$0.663080\pi$
$192$	−12.0715	−	6.80286i	−0.871185	−	0.490954i
$193$	−20.6394			−1.48566			−0.742830	−	0.669480i	$-0.766517\pi$
$193$	−20.6394			−1.48566			−0.742830	+	0.669480i	$0.766517\pi$
$194$	2.35623	+	1.19766i	0.169168	+	0.0859867i
$195$	13.7999	−	12.5393i	0.988230	−	0.897960i
$196$	0.0764163	−	0.488666i	0.00545830	−	0.0349047i
$197$	−2.97611	+	1.98857i	−0.212039	+	0.141680i	−0.657055	−	0.753843i	$-0.728198\pi$
$197$	−2.97611	+	1.98857i	−0.212039	+	0.141680i	0.445016	+	0.895523i	$0.353198\pi$
$198$	10.7280	−	11.2365i	0.762406	−	0.798540i
$199$	5.60732	−	13.5373i	0.397492	−	0.959631i	−0.590767	−	0.806842i	$-0.701175\pi$
$199$	5.60732	−	13.5373i	0.397492	−	0.959631i	0.988259	−	0.152788i	$-0.0488253\pi$
$200$	−8.81607	+	37.2027i	−0.623390	+	2.63063i
$201$	7.96898	−	10.7734i	0.562088	−	0.759896i
$202$	19.2900	−	2.30228i	1.35724	−	0.161988i
$203$	−1.30979	+	6.58478i	−0.0919295	+	0.462161i
$204$	−3.89157	+	2.56331i	−0.272465	+	0.179468i
$205$	−11.1131	+	16.6319i	−0.776169	+	1.16162i
$206$	15.6135	−	13.3617i	1.08784	−	0.930951i
$207$	−8.56706	+	2.62249i	−0.595452	+	0.182275i
$208$	−6.22586	−	7.83415i	−0.431686	−	0.543201i
$209$	1.00079	+	1.00079i	0.0692261	+	0.0692261i
$210$	−12.2500	−	24.4988i	−0.845330	−	1.69058i
$211$	10.2740	−	15.3761i	0.707289	−	1.05853i	−0.287619	−	0.957745i	$-0.592864\pi$
$211$	10.2740	−	15.3761i	0.707289	−	1.05853i	0.994908	−	0.100788i	$-0.0321362\pi$
$212$	1.26066	+	2.72055i	0.0865823	+	0.186848i
$213$	3.97731	+	11.0717i	0.272521	+	0.758617i
$214$	−1.91712	+	2.43676i	−0.131051	+	0.166573i
$215$	15.8796	+	38.3367i	1.08298	+	2.61454i
$216$	−10.2189	+	10.5629i	−0.695307	+	0.718713i
$217$	−2.02602	+	4.89125i	−0.137535	+	0.332040i
$218$	−21.1747	+	11.8856i	−1.43413	+	0.804998i
$219$	26.2390	+	12.3695i	1.77307	+	0.835854i
$220$	−16.4134	+	26.9024i	−1.10659	+	1.81376i
$221$	−3.30062	+	0.656535i	−0.222024	+	0.0441633i
$222$	−8.27401	+	9.54037i	−0.555315	+	0.640308i
$223$	−19.2274			−1.28756			−0.643782	−	0.765209i	$-0.722636\pi$
$223$	−19.2274			−1.28756			−0.643782	+	0.765209i	$0.722636\pi$
$224$	−13.5532	+	5.69183i	−0.905562	+	0.380301i
$225$	35.8122	+	19.0256i	2.38748	+	1.26838i
$226$	5.54850	+	17.0198i	0.369081	+	1.13214i
$227$	−1.97234	−	9.91561i	−0.130909	−	0.658122i	−0.989391	−	0.145279i	$-0.953592\pi$
$227$	−1.97234	−	9.91561i	−0.130909	−	0.658122i	0.858482	−	0.512844i	$-0.171408\pi$
$228$	−0.940515	−	0.953000i	−0.0622871	−	0.0631140i
$229$	14.4937	−	9.68436i	0.957768	−	0.639960i	0.0247136	−	0.999695i	$-0.492133\pi$
$229$	14.4937	−	9.68436i	0.957768	−	0.639960i	0.933055	+	0.359734i	$0.117133\pi$
$230$	15.8486	−	8.89605i	1.04503	−	0.586588i
$231$	−2.43890	−	16.2996i	−0.160468	−	1.07243i
$232$	−6.84845	+	2.54941i	−0.449623	+	0.167377i
$233$	−7.39105	+	3.06147i	−0.484203	+	0.200564i	−0.611412	−	0.791312i	$-0.709398\pi$
$233$	−7.39105	+	3.06147i	−0.484203	+	0.200564i	0.127209	+	0.991876i	$0.459398\pi$
$234$	−9.70922	+	4.28756i	−0.634712	+	0.280287i
$235$	6.61434	−	33.2525i	0.431472	−	2.16916i
$236$	−4.54237	+	12.3873i	−0.295683	+	0.806344i
$237$	−5.66163	−	0.270957i	−0.367763	−	0.0176005i
$238$	−0.383043	+	4.92873i	−0.0248290	+	0.319482i
$239$	−8.30613	+	8.30613i	−0.537279	+	0.537279i	−0.922729	−	0.385450i	$-0.874046\pi$
$239$	−8.30613	+	8.30613i	−0.537279	+	0.537279i	0.385450	+	0.922729i	$0.374046\pi$
$240$	15.6951	−	25.3476i	1.01311	−	1.63618i
$241$	3.01268	+	3.01268i	0.194063	+	0.194063i	0.797449	−	0.603386i	$-0.206182\pi$
$241$	3.01268	+	3.01268i	0.194063	+	0.194063i	−0.603386	+	0.797449i	$0.706182\pi$
$242$	−2.58757	+	2.21438i	−0.166336	+	0.142346i
$243$	8.09851	+	13.3197i	0.519519	+	0.854459i
$244$	6.14122	+	5.65462i	0.393152	+	0.362000i
$245$	1.04374	+	0.207613i	0.0666821	+	0.0132639i
$246$	8.99492	−	6.98123i	0.573495	−	0.445107i
$247$	−0.370038	−	0.893350i	−0.0235449	−	0.0568425i
$248$	−5.68888	+	0.918170i	−0.361244	+	0.0583039i
$249$	−0.501606	−	3.35232i	−0.0317880	−	0.212445i
$250$	−49.9015	−	14.0209i	−3.15605	−	0.886763i
$251$	−7.23109	−	10.8221i	−0.456422	−	0.683085i	0.529872	−	0.848077i	$-0.322240\pi$
$251$	−7.23109	−	10.8221i	−0.456422	−	0.683085i	−0.986295	+	0.164993i	$0.947240\pi$
$252$	2.20555	+	15.4348i	0.138937	+	0.972300i
$253$	10.7256	−	2.13345i	0.674311	−	0.134129i
$254$	21.5408	+	10.9490i	1.35159	+	0.687002i
$255$	−5.16541	−	8.59329i	−0.323471	−	0.538133i
$256$	−13.0176	−	9.30287i	−0.813597	−	0.581429i
$257$		−	27.8550i		−	1.73755i	−0.495210	−	0.868773i	$-0.664909\pi$
$257$		−	27.8550i		−	1.73755i	0.495210	−	0.868773i	$-0.335091\pi$
$258$	−1.67485	−	23.5608i	−0.104272	−	1.46683i
$259$	2.61366	+	13.1398i	0.162405	+	0.816464i
$260$	17.3937	−	12.6894i	1.07871	−	0.786963i
$261$	0.779237	+	7.71159i	0.0482336	+	0.477336i
$262$	0.609854	−	2.17051i	0.0376769	−	0.134095i
$263$	10.8728	+	4.50368i	0.670448	+	0.277709i	0.691828	−	0.722063i	$-0.256806\pi$
$263$	10.8728	+	4.50368i	0.670448	+	0.277709i	−0.0213794	+	0.999771i	$0.506806\pi$
$264$	13.7059	−	11.5735i	0.843539	−	0.712299i
$265$	−5.96034	+	2.46885i	−0.366141	+	0.151660i
$266$	−1.41044	+	0.168337i	−0.0864797	+	0.0103214i
$267$	2.56210	+	7.13211i	0.156798	+	0.436478i
$268$	10.4811	−	11.3830i	0.640235	−	0.695330i
$269$	−3.40585	−	2.27572i	−0.207658	−	0.138753i	0.447392	−	0.894338i	$-0.352353\pi$
$269$	−3.40585	−	2.27572i	−0.207658	−	0.138753i	−0.655051	+	0.755585i	$0.727353\pi$
$270$	−21.8015	−	22.9049i	−1.32680	−	1.39395i
$271$	−1.68641	+	1.68641i	−0.102442	+	0.102442i	−0.756470	−	0.654028i	$-0.773078\pi$
$271$	−1.68641	+	1.68641i	−0.102442	+	0.102442i	0.654028	+	0.756470i	$0.273078\pi$
$272$	−4.78474	+	2.46160i	−0.290118	+	0.149257i
$273$	−2.72210	+	10.9259i	−0.164749	+	0.661263i
$274$	20.5013	+	1.59329i	1.23853	+	0.0962540i
$275$	−41.1553	−	27.4991i	−2.48176	−	1.65826i
$276$	−10.1598	+	1.95136i	−0.611548	+	0.117458i
$277$	3.18127	+	0.632795i	0.191144	+	0.0380210i	0.289734	−	0.957107i	$-0.406433\pi$
$277$	3.18127	+	0.632795i	0.191144	+	0.0380210i	−0.0985898	+	0.995128i	$0.531433\pi$
$278$	−4.40666	+	5.60110i	−0.264294	+	0.335931i
$279$	−0.583689	+	6.08412i	−0.0349446	+	0.364246i
$280$	−11.0342	−	29.6410i	−0.659418	−	1.77139i
$281$	−22.6232	−	9.37084i	−1.34959	−	0.559018i	−0.413410	−	0.910545i	$-0.635662\pi$
$281$	−22.6232	−	9.37084i	−1.34959	−	0.559018i	−0.936178	+	0.351527i	$0.885662\pi$
$282$	−9.55717	+	16.7665i	−0.569121	+	0.998428i
$283$	1.43456	+	2.14698i	0.0852760	+	0.127625i	0.871655	−	0.490119i	$-0.163047\pi$
$283$	1.43456	+	2.14698i	0.0852760	+	0.127625i	−0.786379	+	0.617744i	$0.788047\pi$
$284$	3.19706	+	13.2028i	0.189711	+	0.783439i
$285$	2.13213	−	1.93737i	0.126297	−	0.114760i
$286$	12.3169	−	4.01535i	0.728314	−	0.237433i
$287$		−	12.0793i		−	0.713020i
$288$	−13.0381	+	10.8631i	−0.768277	+	0.640117i
$289$		−	15.1904i		−	0.893554i
$290$	−4.87330	−	14.9487i	−0.286170	−	0.877815i
$291$	2.39584	−	2.17699i	0.140447	−	0.127617i
$292$	28.5943	+	17.4457i	1.67336	+	1.02093i
$293$	−9.50218	−	14.2210i	−0.555123	−	0.830800i	0.442705	−	0.896667i	$-0.354019\pi$
$293$	−9.50218	−	14.2210i	−0.555123	−	0.830800i	−0.997828	+	0.0658668i	$0.979019\pi$
$294$	−0.526271	−	0.299983i	−0.0306927	−	0.0174954i
$295$	−26.2269	−	10.8636i	−1.52699	−	0.632500i
$296$	−10.6788	+	9.92975i	−0.620694	+	0.577155i
$297$	−8.20028	−	17.1691i	−0.475828	−	0.996251i
$298$	−2.69864	−	2.12315i	−0.156328	−	0.122991i
$299$	−7.32771	−	1.45757i	−0.423772	−	0.0842936i
$300$	38.7618	+	26.2711i	2.23791	+	1.51676i
$301$	−20.8350	−	13.9215i	−1.20091	−	0.802422i
$302$	−0.139678	+	1.79728i	−0.00803757	+	0.103422i
$303$	5.75203	−	23.0873i	0.330445	−	1.32633i
$304$	−0.961919	−	1.21041i	−0.0551698	−	0.0694215i
$305$	−12.7007	+	12.7007i	−0.727242	+	0.727242i
$306$	1.24267	+	5.57029i	0.0710388	+	0.318432i
$307$	−6.85681	−	4.58157i	−0.391339	−	0.261484i	0.344298	−	0.938860i	$-0.388117\pi$
$307$	−6.85681	−	4.58157i	−0.391339	−	0.261484i	−0.735637	+	0.677376i	$0.763117\pi$
$308$	−0.784384	−	19.0145i	−0.0446944	−	1.08345i
$309$	−8.50912	−	23.6869i	−0.484067	−	1.34750i
$310$	−1.46935	−	12.3112i	−0.0834535	−	0.699228i
$311$	30.1840	−	12.5026i	1.71157	−	0.708958i	0.711595	−	0.702590i	$-0.247973\pi$
$311$	30.1840	−	12.5026i	1.71157	−	0.708958i	0.999980	−	0.00636791i	$-0.00202698\pi$
$312$	−11.6770	+	3.72173i	−0.661078	+	0.210702i
$313$	−6.61643	−	2.74061i	−0.373982	−	0.154909i	0.187772	−	0.982213i	$-0.439873\pi$
$313$	−6.61643	−	2.74061i	−0.373982	−	0.154909i	−0.561754	+	0.827304i	$0.689873\pi$
$314$	14.5494	+	4.08799i	0.821073	+	0.230699i
$315$	−33.3768	+	3.37264i	−1.88057	+	0.190027i
$316$	−6.46639	−	1.01120i	−0.363763	−	0.0568842i
$317$	3.68607	+	18.5311i	0.207031	+	1.04081i	0.934850	+	0.355044i	$0.115534\pi$
$317$	3.68607	+	18.5311i	0.207031	+	1.04081i	−0.727819	+	0.685769i	$0.759466\pi$
$318$	3.66308	−	0.260395i	0.205415	−	0.0146022i
$319$		−	9.46050i		−	0.529687i
$320$	21.1534	−	27.1597i	1.18251	−	1.51827i
$321$	1.95634	+	3.25460i	0.109192	+	0.181654i
$322$	−4.97308	+	9.78389i	−0.277139	+	0.545235i
$323$	−0.509959	+	0.101437i	−0.0283749	+	0.00564411i
$324$	7.65045	+	16.2933i	0.425025	+	0.905182i
$325$	18.7874	+	28.1173i	1.04214	+	1.55967i
$326$	−3.04253	+	10.8286i	−0.168510	+	0.599740i
$327$	4.40095	+	29.4123i	0.243373	+	1.62651i
$328$	11.1900	−	6.90255i	0.617865	−	0.381130i
$329$	7.83499	+	18.9153i	0.431957	+	1.04284i
$330$	23.6648	+	30.4908i	1.30271	+	1.67846i
$331$	19.6169	+	3.90204i	1.07824	+	0.214476i	0.702094	−	0.712084i	$-0.252249\pi$
$331$	19.6169	+	3.90204i	1.07824	+	0.214476i	0.376147	+	0.926560i	$0.377249\pi$
$332$	−0.161323	−	3.91069i	−0.00885377	−	0.214627i
$333$	7.32542	+	13.6219i	0.401431	+	0.746473i
$334$	−16.4913	−	19.2705i	−0.902362	−	1.05444i
$335$	23.5414	+	23.5414i	1.28620	+	1.28620i
$336$	0.623431	+	17.9928i	0.0340110	+	0.981588i
$337$	3.84192	−	3.84192i	0.209283	−	0.209283i	−0.594680	−	0.803963i	$-0.702721\pi$
$337$	3.84192	−	3.84192i	0.209283	−	0.209283i	0.803963	+	0.594680i	$0.202721\pi$
$338$	9.50532	+	0.738720i	0.517021	+	0.0401811i
$339$	21.8996	+	1.04808i	1.18942	+	0.0569238i
$340$	−4.86755	−	10.5044i	−0.263980	−	0.569680i
$341$	1.45542	−	7.31687i	0.0788152	−	0.396231i
$342$	−1.50011	+	0.662445i	−0.0811167	+	0.0358209i
$343$	−17.3992	+	7.20700i	−0.939471	+	0.389142i
$344$	0.990712	−	27.2563i	0.0534156	−	1.46956i
$345$	−3.29398	−	22.0142i	−0.177342	−	1.18521i
$346$	−9.02329	−	16.0753i	−0.485095	−	0.864213i
$347$	−14.6437	+	9.78460i	−0.786114	+	0.525265i	−0.882631	−	0.470067i	$-0.844230\pi$
$347$	−14.6437	+	9.78460i	−0.786114	+	0.525265i	0.0965168	+	0.995331i	$0.469230\pi$
$348$	−0.0590103	+	8.94973i	−0.00316328	+	0.479756i
$349$	−0.173660	−	0.873047i	−0.00929580	−	0.0467332i	0.975859	−	0.218402i	$-0.0700842\pi$
$349$	−0.173660	−	0.873047i	−0.00929580	−	0.0467332i	−0.985155	+	0.171668i	$0.945084\pi$
$350$	47.2297	−	15.3970i	2.52454	−	0.823006i
$351$	0.687124	+	12.9810i	0.0366760	+	0.692874i
$352$	17.1664	−	11.5922i	0.914971	−	0.617866i
$353$	33.0774			1.76053			0.880266	−	0.474481i	$-0.157364\pi$
$353$	33.0774			1.76053			0.880266	+	0.474481i	$0.157364\pi$
$354$	12.2077	+	10.5873i	0.648830	+	0.562706i
$355$	−28.6663	+	5.70209i	−1.52145	+	0.302636i
$356$	2.05948	+	8.50492i	0.109152	+	0.450760i
$357$	5.47660	+	2.58176i	0.289852	+	0.136641i
$358$	4.29965	+	7.65997i	0.227244	+	0.404842i
$359$	−4.91221	+	11.8591i	−0.259257	+	0.625901i	−0.998890	−	0.0471093i	$-0.984999\pi$
$359$	−4.91221	+	11.8591i	−0.259257	+	0.625901i	0.739633	+	0.673010i	$0.234999\pi$
$360$	−22.1970	−	28.9922i	−1.16988	−	1.52802i
$361$	7.21381	+	17.4157i	0.379674	+	0.916615i
$362$	−15.1032	−	11.8825i	−0.793809	−	0.624529i
$363$	1.41019	+	3.92555i	0.0740157	+	0.206038i
$364$	−4.47623	+	12.2069i	−0.234618	+	0.639817i
$365$	−40.0399	+	59.9240i	−2.09579	+	3.13656i
$366$	9.14471	−	4.57257i	0.478002	−	0.239012i
$367$	0.647822	+	0.647822i	0.0338161	+	0.0338161i	0.723813	−	0.689997i	$-0.242388\pi$
$367$	0.647822	+	0.647822i	0.0338161	+	0.0338161i	−0.689997	+	0.723813i	$0.742388\pi$
$368$	−11.9054	+	0.983912i	−0.620610	+	0.0512899i
$369$	−4.08185	−	13.3345i	−0.212492	−	0.694164i
$370$	−20.3996	−	23.8376i	−1.06053	−	1.23926i
$371$	2.16443	−	3.23929i	0.112371	−	0.168176i
$372$	−1.42248	+	6.91275i	−0.0737520	+	0.358409i
$373$	3.01645	−	15.1647i	0.156186	−	0.785200i	−0.820687	−	0.571378i	$-0.806409\pi$
$373$	3.01645	−	15.1647i	0.156186	−	0.785200i	0.976873	−	0.213821i	$-0.0685911\pi$
$374$	−0.825550	−	6.91700i	−0.0426882	−	0.357670i
$375$	−37.7524	+	51.0381i	−1.94952	+	2.63559i
$376$	−13.0456	+	18.0670i	−0.672773	+	0.931737i
$377$	−2.47344	+	5.97142i	−0.127389	+	0.307544i
$378$	18.6312	+	4.18637i	0.958283	+	0.215324i
$379$	−2.79369	+	1.86669i	−0.143502	+	0.0958852i	−0.625249	−	0.780425i	$-0.715003\pi$
$379$	−2.79369	+	1.86669i	−0.143502	+	0.0958852i	0.481747	+	0.876311i	$0.340003\pi$
$380$	2.68739	−	1.96056i	0.137860	−	0.100575i
$381$	21.9028	−	19.9021i	1.12212	−	1.01962i
$382$	−8.68271	+	17.0821i	−0.444246	+	0.873996i
$383$	−23.3643			−1.19386			−0.596931	−	0.802293i	$-0.703613\pi$
$383$	−23.3643			−1.19386			−0.596931	+	0.802293i	$0.703613\pi$
$384$	−16.3119	+	10.8592i	−0.832411	+	0.554158i
$385$	40.9463			2.08682
$386$	−13.2259	+	26.0202i	−0.673179	+	1.32439i
$387$	−27.7043	−	8.32749i	−1.40829	−	0.423310i
$388$	3.01977	−	2.20304i	0.153306	−	0.111843i
$389$	10.1512	−	6.78284i	0.514688	−	0.343904i	−0.270946	−	0.962594i	$-0.587337\pi$
$389$	10.1512	−	6.78284i	0.514688	−	0.343904i	0.785635	+	0.618691i	$0.212337\pi$
$390$	−6.96531	−	25.4328i	−0.352702	−	1.28784i
$391$	−1.53741	+	3.71163i	−0.0777501	+	0.187705i
$392$	−0.567094	−	0.409478i	−0.0286426	−	0.0206817i
$393$	−2.21995	−	1.64207i	−0.111981	−	0.0828316i
$394$	0.599890	+	5.02627i	0.0302220	+	0.253220i
$395$	2.74729	−	13.8115i	0.138231	−	0.694934i
$396$	−7.29127	−	20.7252i	−0.366400	−	1.04148i
$397$	15.0250	−	22.4865i	0.754083	−	1.12856i	−0.233636	−	0.972324i	$-0.575062\pi$
$397$	15.0250	−	22.4865i	0.754083	−	1.12856i	0.987719	−	0.156241i	$-0.0499376\pi$
$398$	−13.4732	−	15.7439i	−0.675353	−	0.789170i
$399$	−0.420574	+	1.68809i	−0.0210551	+	0.0845101i
$400$	41.2522	+	34.9541i	2.06261	+	1.74771i
$401$	1.77953	+	1.77953i	0.0888656	+	0.0888656i	0.750142	−	0.661277i	$-0.229985\pi$
$401$	1.77953	+	1.77953i	0.0888656	+	0.0888656i	−0.661277	+	0.750142i	$0.729985\pi$
$402$	−8.47546	−	16.9501i	−0.422718	−	0.845396i
$403$	−2.83164	+	4.23785i	−0.141054	+	0.211102i
$404$	9.45866	−	25.7943i	0.470586	−	1.28331i
$405$	−35.7052	+	15.0018i	−1.77420	+	0.745443i
$406$	7.46212	+	5.87082i	0.370339	+	0.291364i
$407$	−7.22437	−	17.4412i	−0.358099	−	0.864526i
$408$	0.737834	+	6.54870i	0.0365282	+	0.324209i
$409$	−7.30266	+	17.6302i	−0.361093	+	0.871756i	0.634048	+	0.773294i	$0.281392\pi$
$409$	−7.30266	+	17.6302i	−0.361093	+	0.871756i	−0.995141	+	0.0984620i	$0.968608\pi$
$410$	13.8465	+	24.6680i	0.683831	+	1.21827i
$411$	10.7390	−	22.7802i	0.529714	−	1.12366i
$412$	−6.83985	−	28.2462i	−0.336975	−	1.39159i
$413$	16.8134	−	3.34439i	0.827331	−	0.164566i
$414$	−2.18365	+	12.4810i	−0.107320	+	0.613408i
$415$	8.42137			0.413389
$416$	−13.8661	+	2.82879i	−0.679841	+	0.138693i
$417$	4.49681	+	7.48099i	0.220210	+	0.366345i
$418$	1.90301	−	0.620386i	0.0930793	−	0.0303441i
$419$	2.89265	+	14.5424i	0.141315	+	0.710440i	0.984856	+	0.173375i	$0.0554672\pi$
$419$	2.89265	+	14.5424i	0.141315	+	0.710440i	−0.843541	+	0.537066i	$0.819533\pi$
$420$	−38.7356	−	0.255404i	−1.89010	−	0.0124624i
$421$	−9.40305	+	6.28291i	−0.458276	+	0.306211i	−0.763195	−	0.646168i	$-0.776371\pi$
$421$	−9.40305	+	6.28291i	−0.458276	+	0.306211i	0.304919	+	0.952378i	$0.401371\pi$
$422$	−12.8010	−	22.8055i	−0.623144	−	1.11015i
$423$	15.0410	+	18.2332i	0.731317	+	0.886528i
$424$	4.23764	+	0.154030i	0.205798	+	0.00748034i
$425$	16.7996	−	6.95861i	0.814898	−	0.337542i
$426$	16.5067	+	2.08057i	0.799754	+	0.100804i
$427$	2.11606	−	10.6381i	0.102403	−	0.514816i
$428$	1.84352	+	3.97840i	0.0891101	+	0.192303i
$429$	0.758475	−	15.8483i	0.0366195	−	0.765164i
$430$	58.5068	+	4.54694i	2.82145	+	0.219273i
$431$	0.840930	−	0.840930i	0.0405062	−	0.0405062i	−0.686564	−	0.727070i	$-0.740882\pi$
$431$	0.840930	−	0.840930i	0.0405062	−	0.0405062i	0.727070	+	0.686564i	$0.240882\pi$
$432$	6.76833	+	19.6517i	0.325642	+	0.945493i
$433$	0.498959	+	0.498959i	0.0239785	+	0.0239785i	0.718994	−	0.695016i	$-0.244603\pi$
$433$	0.498959	+	0.498959i	0.0239785	+	0.0239785i	−0.695016	+	0.718994i	$0.744603\pi$
$434$	4.86812	+	5.68854i	0.233677	+	0.273059i
$435$	−19.2346	−	0.920537i	−0.922228	−	0.0441364i
$436$	1.41541	+	34.3113i	0.0677857	+	1.64322i
$437$	−1.13216	−	0.225200i	−0.0541585	−	0.0107728i
$438$	32.4084	−	25.1531i	1.54853	−	1.20186i
$439$	−5.55530	−	13.4117i	−0.265140	−	0.640105i	0.734102	−	0.679040i	$-0.237604\pi$
$439$	−5.55530	−	13.4117i	−0.265140	−	0.640105i	−0.999242	+	0.0389347i	$0.987604\pi$
$440$	23.3981	+	37.9317i	1.11546	+	1.80832i
$441$	−0.572309	+	0.472111i	−0.0272528	+	0.0224815i
$442$	−1.28736	+	4.58181i	−0.0612336	+	0.217935i
$443$	−1.97447	−	2.95500i	−0.0938100	−	0.140397i	0.781596	−	0.623785i	$-0.214406\pi$
$443$	−1.97447	−	2.95500i	−0.0938100	−	0.140397i	−0.875406	+	0.483388i	$0.839406\pi$
$444$	6.72553	+	16.5446i	0.319180	+	0.785171i
$445$	−18.4662	+	3.67316i	−0.875383	+	0.174125i
$446$	−12.3210	+	24.2400i	−0.583418	+	1.14780i
$447$	−3.60438	+	2.16659i	−0.170481	+	0.102476i
$448$	−1.50927	+	20.7339i	−0.0713061	+	0.979585i
$449$			5.09669i			0.240527i	0.992742	+	0.120264i	$0.0383740\pi$
$449$			5.09669i			0.240527i	−0.992742	+	0.120264i	$0.961626\pi$
$450$	46.9343	−	32.9568i	2.21250	−	1.55360i
$451$	3.32067	+	16.6941i	0.156364	+	0.786096i
$452$	25.0124	+	3.91137i	1.17648	+	0.183975i
$453$	1.99706	+	0.941450i	0.0938302	+	0.0442332i
$454$	−13.7645	−	3.86745i	−0.646001	−	0.181508i
$455$	−25.8451	−	10.7054i	−1.21164	−	0.501876i
$456$	−1.80414	+	0.575022i	−0.0844864	+	0.0269279i
$457$	32.8641	−	13.6128i	1.53732	−	0.636779i	0.556351	−	0.830947i	$-0.312201\pi$
$457$	32.8641	−	13.6128i	1.53732	−	0.636779i	0.980968	+	0.194169i	$0.0622009\pi$
$458$	−2.92147	−	24.4780i	−0.136511	−	1.14378i
$459$	6.91808	+	0.999374i	0.322908	+	0.0466468i
$460$	−1.05939	−	25.6810i	−0.0493943	−	1.19738i
$461$	8.02408	+	5.36152i	0.373719	+	0.249711i	0.728218	−	0.685345i	$-0.240349\pi$
$461$	8.02408	+	5.36152i	0.373719	+	0.249711i	−0.354500	+	0.935056i	$0.615349\pi$
$462$	−22.1118	−	7.37014i	−1.02873	−	0.342890i
$463$	−13.9676	+	13.9676i	−0.649129	+	0.649129i	−0.952782	−	0.303654i	$-0.901793\pi$
$463$	−13.9676	+	13.9676i	−0.649129	+	0.649129i	0.303654	+	0.952782i	$0.401793\pi$
$464$	−1.17448	+	10.2675i	−0.0545237	+	0.476658i
$465$	−14.7346	−	3.67103i	−0.683303	−	0.170240i
$466$	−0.876619	+	11.2797i	−0.0406086	+	0.522522i
$467$	−26.7190	−	17.8531i	−1.23641	−	0.826141i	−0.246678	−	0.969097i	$-0.579339\pi$
$467$	−26.7190	−	17.8531i	−1.23641	−	0.826141i	−0.989729	+	0.142957i	$0.954339\pi$
$468$	−0.816379	+	14.9879i	−0.0377371	+	0.692817i
$469$	−19.7183	−	3.92221i	−0.910506	−	0.181111i
$470$	−37.6830	−	29.6471i	−1.73819	−	1.36752i
$471$	11.0072	−	14.8808i	0.507185	−	0.685672i
$472$	12.7059	+	13.6644i	0.584836	+	0.628955i
$473$	32.6219	+	13.5124i	1.49996	+	0.621303i
$474$	−3.96960	+	6.96400i	−0.182330	+	0.319867i
$475$	2.90272	+	4.34423i	0.133186	+	0.199327i
$476$	5.96820	+	3.64126i	0.273552	+	0.166897i
$477$	1.29470	−	4.30728i	0.0592804	−	0.197217i
$478$	5.14894	+	15.7942i	0.235507	+	0.722408i
$479$		−	6.21762i		−	0.284090i	−0.989860	−	0.142045i	$-0.954632\pi$
$479$		−	6.21762i		−	0.284090i	0.989860	−	0.142045i	$-0.0453678\pi$
$480$	−21.8983	−	36.0297i	−0.999514	−	1.64452i
$481$			12.8976i			0.588079i
$482$	5.72862	−	1.86755i	0.260932	−	0.0850644i
$483$	9.03961	+	9.94835i	0.411317	+	0.452665i
$484$	1.13355	+	4.68115i	0.0515248	+	0.212779i
$485$	4.46823	+	6.68717i	0.202892	+	0.303649i
$486$	21.9817	−	1.67447i	0.997111	−	0.0759557i
$487$	1.30351	+	0.539930i	0.0590676	+	0.0244666i	0.412022	−	0.911174i	$-0.364823\pi$
$487$	1.30351	+	0.539930i	0.0590676	+	0.0244666i	−0.352954	+	0.935641i	$0.614823\pi$
$488$	11.0641	−	4.11874i	0.500849	−	0.186447i
$489$	11.0752	+	8.19223i	0.500838	+	0.370465i
$490$	0.930572	−	1.18281i	0.0420390	−	0.0534337i
$491$	10.3424	+	2.05722i	0.466744	+	0.0928411i	0.422859	−	0.906195i	$-0.361027\pi$
$491$	10.3424	+	2.05722i	0.466744	+	0.0928411i	0.0438848	+	0.999037i	$0.486027\pi$
$492$	−3.03725	−	15.8135i	−0.136930	−	0.712929i
$493$	2.88977	+	1.93088i	0.130149	+	0.0869627i
$494$	−1.36337	−	0.105956i	−0.0613409	−	0.00476719i
$495$	45.2009	−	13.8366i	2.03163	−	0.621907i
$496$	−2.48792	+	7.76034i	−0.111711	+	0.348450i
$497$	12.4805	−	12.4805i	0.559827	−	0.559827i
$498$	−4.54770	−	1.51581i	−0.203788	−	0.0679250i
$499$	−10.5229	−	7.03120i	−0.471071	−	0.314760i	0.297277	−	0.954791i	$-0.403921\pi$
$499$	−10.5229	−	7.03120i	−0.471071	−	0.314760i	−0.768349	+	0.640031i	$0.778921\pi$
$500$	−49.6534	+	53.9263i	−2.22057	+	2.41166i
$501$	−29.2349	+	10.5022i	−1.30612	+	0.469202i
$502$	−18.2772	+	2.18140i	−0.815749	+	0.0973604i
$503$	6.66908	−	2.76242i	0.297360	−	0.123170i	−0.229016	−	0.973423i	$-0.573551\pi$
$503$	6.66908	−	2.76242i	0.297360	−	0.123170i	0.526375	+	0.850252i	$0.323551\pi$
$504$	20.8720	+	7.11015i	0.929712	+	0.316711i
$505$	54.6129	+	22.6214i	2.43024	+	1.00664i
$506$	4.18336	−	14.8889i	0.185973	−	0.661891i
$507$	4.97907	−	10.5619i	0.221128	−	0.469071i
$508$	27.6069	−	20.1403i	1.22486	−	0.893581i
$509$	−1.85153	−	9.30829i	−0.0820678	−	0.412583i	−0.999879	−	0.0155653i	$-0.995045\pi$
$509$	−1.85153	−	9.30829i	−0.0820678	−	0.412583i	0.917811	−	0.397018i	$-0.129955\pi$
$510$	−14.1436	+	1.00542i	−0.626289	+	0.0445207i
$511$		−	43.5214i		−	1.92527i
$512$	−20.0699	+	10.4499i	−0.886971	+	0.461826i
$513$	0.106163	+	2.00561i	0.00468722	+	0.0885499i
$514$	−35.1168	−	17.8496i	−1.54894	−	0.787313i
$515$	61.3293	−	12.1991i	2.70249	−	0.537559i
$516$	−30.7764	−	12.9864i	−1.35485	−	0.571694i
$517$	−16.0282	−	23.9879i	−0.704920	−	1.05499i
$518$	18.2402	+	5.12498i	0.801426	+	0.225179i
$519$	−22.3291	+	3.34110i	−0.980140	+	0.146658i
$520$	−4.85156	−	30.0597i	−0.212755	−	1.31821i
$521$	6.13573	+	14.8130i	0.268811	+	0.648968i	0.999428	−	0.0338199i	$-0.0107673\pi$
$521$	6.13573	+	14.8130i	0.268811	+	0.648968i	−0.730617	+	0.682788i	$0.760767\pi$
$522$	10.2214	+	3.95924i	0.447377	+	0.173291i
$523$	−31.6109	−	6.28780i	−1.38225	−	0.274946i	−0.552699	−	0.833381i	$-0.686402\pi$
$523$	−31.6109	−	6.28780i	−1.38225	−	0.274946i	−0.829548	+	0.558435i	$0.811402\pi$
$524$	−2.34557	−	2.15972i	−0.102467	−	0.0943477i
$525$	2.90841	−	60.7710i	0.126933	−	2.65226i
$526$	12.6452	−	10.8214i	0.551356	−	0.471837i
$527$	1.93794	+	1.93794i	0.0844178	+	0.0844178i
$528$	−5.80792	−	24.6954i	−0.252757	−	1.07473i
$529$	9.95669	−	9.95669i	0.432900	−	0.432900i
$530$	−0.706929	+	9.09626i	−0.0307070	+	0.395116i
$531$	17.4303	−	9.37346i	0.756409	−	0.406773i
$532$	−0.691595	+	1.88602i	−0.0299844	+	0.0817692i
$533$	2.26868	−	11.4054i	0.0982675	−	0.494024i
$534$	10.6333	+	1.34026i	0.460147	+	0.0579986i
$535$	−8.71611	+	3.61033i	−0.376830	+	0.156088i
$536$	−7.63427	−	20.5079i	−0.329750	−	0.885805i
$537$	10.6400	−	1.59205i	0.459148	−	0.0687021i
$538$	−5.05149	+	2.83547i	−0.217785	+	0.122246i
$539$	0.752940	−	0.503098i	0.0324314	−	0.0216700i
$540$	−42.8468	+	12.8076i	−1.84383	+	0.551151i
$541$	5.30294	+	26.6597i	0.227991	+	1.14619i	0.909924	+	0.414774i	$0.136139\pi$
$541$	5.30294	+	26.6597i	0.227991	+	1.14619i	−0.681933	+	0.731414i	$0.738861\pi$
$542$	1.04540	+	3.20673i	0.0449039	+	0.137741i
$543$	−20.1723	+	12.1256i	−0.865678	+	0.520357i
$544$	0.0372604	+	7.60954i	0.00159753	+	0.326256i
$545$	−73.8869			−3.16497
$546$	12.0299	+	10.4331i	0.514833	+	0.446496i
$547$	2.89843	−	0.576533i	0.123928	−	0.0246508i	−0.132737	−	0.991151i	$-0.542376\pi$
$547$	2.89843	−	0.576533i	0.123928	−	0.0246508i	0.256664	+	0.966501i	$0.417376\pi$
$548$	15.1460	−	24.8250i	0.647005	−	1.06047i
$549$	−1.25891	−	12.4586i	−0.0537289	−	0.531719i
$550$	−61.0407	+	34.2630i	−2.60278	+	1.46098i
$551$	−0.382156	+	0.922607i	−0.0162804	+	0.0393044i
$552$	−4.05037	+	14.0589i	−0.172395	+	0.598387i
$553$	3.25429	+	7.85655i	0.138386	+	0.334095i
$554$	2.83634	−	3.60514i	0.120505	−	0.153168i
$555$	−36.1634	+	12.9911i	−1.53505	+	0.551442i
$556$	4.23750	+	9.14470i	0.179710	+	0.387822i
$557$	9.09602	−	13.6132i	0.385411	−	0.576808i	−0.587144	−	0.809483i	$-0.699748\pi$
$557$	9.09602	−	13.6132i	0.385411	−	0.576808i	0.972555	+	0.232675i	$0.0747477\pi$
$558$	7.29622	+	4.63459i	0.308874	+	0.196198i
$559$	−17.0580	−	17.0580i	−0.721475	−	0.721475i
$560$	−44.4392	−	5.08329i	−1.87790	−	0.214808i
$561$	−8.27862	−	2.06256i	−0.349524	−	0.0870812i
$562$	−26.3109	+	22.5162i	−1.10986	+	0.949790i
$563$	19.5452	−	29.2515i	0.823732	−	1.23280i	−0.146159	−	0.989261i	$-0.546691\pi$
$563$	19.5452	−	29.2515i	0.823732	−	1.23280i	0.969891	−	0.243541i	$-0.0783089\pi$
$564$	15.0132	+	22.7928i	0.632170	+	0.959749i
$565$	−10.6267	+	53.4239i	−0.447068	+	2.24756i
$566$	3.62598	−	0.432764i	0.152411	−	0.0181904i
$567$	12.8947	−	19.5114i	0.541527	−	0.819402i
$568$	18.6934	+	4.42985i	0.784359	+	0.185872i
$569$	7.42318	−	17.9211i	0.311196	−	0.751293i	−0.688465	−	0.725269i	$-0.741715\pi$
$569$	7.42318	−	17.9211i	0.311196	−	0.751293i	0.999661	−	0.0260241i	$-0.00828468\pi$
$570$	−1.07617	−	3.92946i	−0.0450757	−	0.164587i
$571$	25.4369	−	16.9964i	1.06450	−	0.711277i	0.105426	−	0.994427i	$-0.466379\pi$
$571$	25.4369	−	16.9964i	1.06450	−	0.711277i	0.959076	+	0.283150i	$0.0913794\pi$
$572$	2.83059	−	18.1010i	0.118353	−	0.756841i
$573$	15.7826	+	17.3692i	0.659329	+	0.725610i
$574$	−15.2284	−	7.74050i	−0.635622	−	0.323082i
$575$	40.3696			1.68353
$576$	5.34031	+	23.3983i	0.222513	+	0.974930i
$577$	−13.6429			−0.567963			−0.283982	−	0.958830i	$-0.591655\pi$
$577$	−13.6429			−0.567963			−0.283982	+	0.958830i	$0.591655\pi$
$578$	−19.1506	−	9.73410i	−0.796560	−	0.404885i
$579$	24.0408	+	26.4575i	0.999100	+	1.09954i
$580$	−21.9686	−	3.43539i	−0.912198	−	0.142647i
$581$	−4.22842	+	2.82534i	−0.175424	+	0.117215i
$582$	−1.20927	−	4.41546i	−0.0501258	−	0.183027i
$583$	−2.10083	+	5.07185i	−0.0870074	+	0.210054i
$584$	40.3172	−	24.8696i	1.66834	−	1.02911i
$585$	−32.1481	−	3.08418i	−1.32916	−	0.127515i
$586$	−24.0175	+	2.86651i	−0.992154	+	0.118414i
$587$	−4.83875	+	24.3260i	−0.199717	+	1.00404i	0.742706	+	0.669618i	$0.233542\pi$
$587$	−4.83875	+	24.3260i	−0.199717	+	1.00404i	−0.942422	+	0.334425i	$0.891458\pi$
$588$	−0.715426	+	0.471239i	−0.0295037	+	0.0194336i
$589$	−0.437499	+	0.654764i	−0.0180268	+	0.0269791i
$590$	−30.5021	+	26.1029i	−1.25575	+	1.07464i
$591$	6.01569	+	1.49877i	0.247453	+	0.0616510i
$592$	5.67540	+	19.8258i	0.233257	+	0.814837i
$593$	9.31734	+	9.31734i	0.382617	+	0.382617i	0.872044	−	0.489427i	$-0.162794\pi$
$593$	9.31734	+	9.31734i	0.382617	+	0.382617i	−0.489427	+	0.872044i	$0.662794\pi$
$594$	−26.8999	−	0.663937i	−1.10372	−	0.0272417i
$595$	−8.35712	+	12.5073i	−0.342608	+	0.512750i
$596$	−4.40597	+	2.04165i	−0.180475	+	0.0836293i
$597$	−23.8847	+	8.58019i	−0.977535	+	0.351164i
$598$	−6.53320	+	8.30404i	−0.267162	+	0.339577i
$599$	0.450558	+	1.08774i	0.0184093	+	0.0444440i	0.932817	−	0.360351i	$-0.117343\pi$
$599$	0.450558	+	1.08774i	0.0184093	+	0.0444440i	−0.914408	+	0.404795i	$0.867343\pi$
$600$	57.9588	−	32.0324i	2.36616	−	1.30772i
$601$	−9.25984	+	22.3552i	−0.377717	+	0.911889i	0.614676	+	0.788780i	$0.289287\pi$
$601$	−9.25984	+	22.3552i	−0.377717	+	0.911889i	−0.992393	+	0.123110i	$0.960713\pi$
$602$	−30.9020	+	17.3458i	−1.25947	+	0.706960i
$603$	−23.0926	+	2.33345i	−0.940402	+	0.0950252i
$604$	2.17633	+	1.32780i	0.0885535	+	0.0540274i
$605$	−10.1639	+	2.02172i	−0.413221	+	0.0821948i
$606$	−25.4203	−	22.0460i	−1.03263	−	0.895559i
$607$	47.3452			1.92168			0.960840	−	0.277103i	$-0.0893743\pi$
$607$	47.3452			1.92168			0.960840	+	0.277103i	$0.0893743\pi$
$608$	−2.14236	+	0.437058i	−0.0868843	+	0.0177251i
$609$	9.96662	−	5.99092i	0.403868	−	0.242764i
$610$	7.87314	+	24.1505i	0.318774	+	0.977826i
$611$	3.84529	+	19.3316i	0.155564	+	0.782073i
$612$	7.81879	+	2.00284i	0.316056	+	0.0809599i
$613$	0.532520	−	0.355818i	0.0215083	−	0.0143714i	−0.544770	−	0.838586i	$-0.683383\pi$
$613$	0.532520	−	0.355818i	0.0215083	−	0.0143714i	0.566278	+	0.824214i	$0.308383\pi$
$614$	−10.1699	+	5.70850i	−0.410423	+	0.230376i
$615$	34.2647	−	5.12701i	1.38169	−	0.206741i
$616$	−24.4743	−	11.1957i	−0.986096	−	0.451088i
$617$	−15.4604	+	6.40389i	−0.622411	+	0.257811i	−0.671525	−	0.740982i	$-0.734360\pi$
$617$	−15.4604	+	6.40389i	−0.622411	+	0.257811i	0.0491140	+	0.998793i	$0.484360\pi$
$618$	−35.3148	−	4.45120i	−1.42057	−	0.179054i
$619$	−8.36961	+	42.0769i	−0.336403	+	1.69121i	0.328678	+	0.944442i	$0.393397\pi$
$619$	−8.36961	+	42.0769i	−0.336403	+	1.69121i	−0.665081	+	0.746771i	$0.731603\pi$
$620$	−16.4623	−	6.03665i	−0.661141	−	0.242438i
$621$	13.3406	+	7.92739i	0.535341	+	0.318115i
$622$	3.57998	−	46.0647i	0.143544	−	1.84703i
$623$	8.03966	−	8.03966i	0.322102	−	0.322102i
$624$	−2.79067	+	17.1061i	−0.111716	+	0.684791i
$625$	−63.7341	−	63.7341i	−2.54937	−	2.54937i
$626$	−7.69494	+	6.58514i	−0.307551	+	0.263195i
$627$	0.117187	−	2.44862i	0.00468001	−	0.0977886i
$628$	14.4771	−	15.7229i	0.577699	−	0.627412i
$629$	6.80201	+	1.35300i	0.271214	+	0.0539478i
$630$	−17.1361	+	44.2393i	−0.682719	+	1.76254i
$631$	8.07387	+	19.4920i	0.321416	+	0.775966i	0.999172	+	0.0406796i	$0.0129523\pi$
$631$	8.07387	+	19.4920i	0.321416	+	0.775966i	−0.677757	+	0.735286i	$0.737048\pi$
$632$	−5.41851	+	7.50421i	−0.215537	+	0.298501i
$633$	−31.6775	+	4.73990i	−1.25907	+	0.188394i
$634$	25.7243	+	7.22782i	1.02164	+	0.287053i
$635$	40.8487	+	61.1344i	1.62103	+	2.42604i
$636$	2.01904	−	4.78491i	0.0800601	−	0.189734i
$637$	−0.606786	+	0.120697i	−0.0240417	+	0.00478220i
$638$	−11.9269	−	6.06234i	−0.472189	−	0.240010i
$639$	9.55990	−	17.9947i	0.378184	−	0.711860i
$640$	−20.6851	−	44.0722i	−0.817649	−	1.74211i
$641$		−	37.3054i		−	1.47347i	−0.676180	−	0.736736i	$-0.736366\pi$
$641$		−	37.3054i		−	1.47347i	0.676180	−	0.736736i	$-0.263634\pi$
$642$	5.35671	−	0.380790i	0.211413	−	0.0150286i
$643$	−0.437593	−	2.19993i	−0.0172570	−	0.0867567i	0.971197	−	0.238278i	$-0.0765829\pi$
$643$	−0.437593	−	2.19993i	−0.0172570	−	0.0867567i	−0.988454	+	0.151521i	$0.951583\pi$
$644$	9.14780	+	12.5391i	0.360474	+	0.494111i
$645$	30.6470	−	65.0103i	1.20672	−	2.55978i
$646$	−0.198902	+	0.707907i	−0.00782571	+	0.0278522i
$647$	−13.8914	−	5.75400i	−0.546126	−	0.226213i	0.0925234	−	0.995711i	$-0.470507\pi$
$647$	−13.8914	−	5.75400i	−0.546126	−	0.226213i	−0.638650	+	0.769498i	$0.720507\pi$
$648$	25.4434	+	0.795880i	0.999511	+	0.0312651i
$649$	−22.3174	+	9.24415i	−0.876033	+	0.362865i
$650$	47.4866	−	5.66757i	1.86258	−	0.222300i
$651$	8.62995	−	3.10017i	0.338235	−	0.121505i
$652$	11.7019	+	10.7747i	0.458283	+	0.421971i
$653$	20.8375	+	13.9232i	0.815433	+	0.544855i	0.891908	−	0.452216i	$-0.149367\pi$
$653$	20.8375	+	13.9232i	0.815433	+	0.544855i	−0.0764751	+	0.997071i	$0.524367\pi$
$654$	39.9003	+	13.2993i	1.56023	+	0.520043i
$655$	4.85090	−	4.85090i	0.189540	−	0.189540i
$656$	−1.53144	−	18.5305i	−0.0597926	−	0.723493i
$657$	−14.7067	−	48.0435i	−0.573764	−	1.87436i
$658$	28.8673	+	2.24346i	1.12537	+	0.0874593i
$659$	24.4240	+	16.3196i	0.951426	+	0.635722i	0.931369	−	0.364076i	$-0.118615\pi$
$659$	24.4240	+	16.3196i	0.951426	+	0.635722i	0.0200567	+	0.999799i	$0.493615\pi$
$660$	53.6044	−	10.2956i	2.08655	−	0.400757i
$661$	37.5355	+	7.46628i	1.45996	+	0.290405i	0.860275	−	0.509830i	$-0.170292\pi$
$661$	37.5355	+	7.46628i	1.45996	+	0.290405i	0.599687	+	0.800235i	$0.295292\pi$
$662$	17.4899	−	22.2306i	0.679765	−	0.864016i
$663$	4.68617	+	3.46631i	0.181996	+	0.134620i
$664$	−5.03359	−	2.30261i	−0.195341	−	0.0893586i
$665$	−3.99316	−	1.65402i	−0.154848	−	0.0641402i
$666$	21.8673	−	0.506212i	0.847339	−	0.0196153i
$667$	4.28675	+	6.41558i	0.165984	+	0.248412i
$668$	−34.8621	+	8.44190i	−1.34886	+	0.326627i
$669$	22.3961	+	24.6475i	0.865881	+	0.952927i
$670$	44.7641	−	14.5932i	1.72939	−	0.563785i
$671$			15.2841i			0.590035i
$672$	23.0830	+	10.7439i	0.890448	+	0.414456i
$673$			17.2901i			0.666486i	0.942841	+	0.333243i	$0.108143\pi$
$673$			17.2901i			0.666486i	−0.942841	+	0.333243i	$0.891857\pi$
$674$	−2.38159	−	7.30544i	−0.0917356	−	0.281395i
$675$	−17.3251	−	68.0684i	−0.666844	−	2.61995i
$676$	7.02237	−	11.5100i	0.270091	−	0.442692i
$677$	−0.0350577	−	0.0524676i	−0.00134738	−	0.00201649i	0.830795	−	0.556578i	$-0.187886\pi$
$677$	−0.0350577	−	0.0524676i	−0.00134738	−	0.00201649i	−0.832143	+	0.554562i	$0.812886\pi$
$678$	15.3547	−	26.9372i	0.589692	−	1.03452i
$679$	−4.48704	−	1.85859i	−0.172197	−	0.0713263i
$680$	−16.3620	−	0.594727i	−0.627455	−	0.0228067i
$681$	−10.4134	+	14.0780i	−0.399041	+	0.539470i
$682$	−8.29175	−	6.52353i	−0.317507	−	0.249799i
$683$	−25.4364	−	5.05961i	−0.973297	−	0.193601i	−0.317267	−	0.948336i	$-0.602765\pi$
$683$	−25.4364	−	5.05961i	−0.973297	−	0.193601i	−0.656029	+	0.754735i	$0.727765\pi$
$684$	−0.126134	+	2.31569i	−0.00482284	+	0.0885426i
$685$	52.0248	+	34.7619i	1.98777	+	1.32818i
$686$	−2.06365	+	26.5535i	−0.0787904	+	1.01382i
$687$	−29.2965	−	7.29900i	−1.11773	−	0.278474i
$688$	−33.7272	−	18.7150i	−1.28584	−	0.713502i
$689$	2.65206	−	2.65206i	0.101036	−	0.101036i
$690$	−29.8642	−	9.95411i	−1.13691	−	0.378947i
$691$	−31.0818	−	20.7682i	−1.18241	−	0.790059i	−0.200550	−	0.979683i	$-0.564273\pi$
$691$	−31.0818	−	20.7682i	−1.18241	−	0.790059i	−0.981857	+	0.189624i	$0.939273\pi$
$692$	−26.0483	+	1.07454i	−0.990209	+	0.0408480i
$693$	−18.0535	+	22.1121i	−0.685795	+	0.839970i
$694$	2.95171	+	24.7313i	0.112045	+	0.938789i
$695$	−20.0347	+	8.29866i	−0.759961	+	0.314786i
$696$	11.2451	+	5.80943i	0.426245	+	0.220206i
$697$	−5.77708	−	2.39294i	−0.218822	−	0.0906392i
$698$	−1.21193	−	0.340520i	−0.0458724	−	0.0128889i
$699$	12.5335	+	5.90853i	0.474062	+	0.223481i
$700$	10.8540	−	69.4091i	0.410243	−	2.62342i
$701$	−6.43348	−	32.3433i	−0.242989	−	1.22159i	−0.888873	−	0.458154i	$-0.848511\pi$
$701$	−6.43348	−	32.3433i	−0.242989	−	1.22159i	0.645884	−	0.763436i	$-0.276489\pi$
$702$	16.8055	+	7.45203i	0.634282	+	0.281259i
$703$			1.99272i			0.0751570i
$704$	−3.61399	−	29.0700i	−0.136207	−	1.09562i
$705$	−50.3305	+	30.2536i	−1.89556	+	1.13942i
$706$	21.1962	−	41.7007i	0.797728	−	1.56943i
$707$	−35.0108	+	6.96408i	−1.31672	+	0.261911i
$708$	21.1701	−	8.60585i	0.795621	−	0.323428i
$709$	13.2204	+	19.7857i	0.496502	+	0.743067i	0.992095	−	0.125487i	$-0.0400494\pi$
$709$	13.2204	+	19.7857i	0.496502	+	0.743067i	−0.495593	+	0.868555i	$0.665049\pi$
$710$	−11.1809	+	39.7936i	−0.419612	+	1.49343i
$711$	6.24732	+	7.57321i	0.234293	+	0.284018i
$712$	12.0419	+	2.85361i	0.451289	+	0.106944i
$713$	2.32845	+	5.62136i	0.0872010	+	0.210522i
$714$	6.76426	−	5.24995i	0.253146	−	0.196474i
$715$	38.6619	+	7.69033i	1.44587	+	0.287602i
$716$	12.4122	−	0.512026i	0.463865	−	0.0191353i
$717$	20.3225	+	0.972604i	0.758958	+	0.0363226i
$718$	11.8031	+	13.7922i	0.440486	+	0.514722i
$719$	−17.8047	−	17.8047i	−0.664002	−	0.664002i	0.292319	−	0.956321i	$-0.405573\pi$
$719$	−17.8047	−	17.8047i	−0.664002	−	0.664002i	−0.956321	+	0.292319i	$0.905573\pi$
$720$	−50.7745	+	9.40541i	−1.89225	+	0.350519i
$721$	−26.7010	+	26.7010i	−0.994396	+	0.994396i
$722$	26.5786	+	2.06560i	0.989154	+	0.0768735i
$723$	0.352768	−	7.37108i	0.0131196	−	0.274133i
$724$	−24.6585	+	11.4263i	−0.916426	+	0.424656i
$725$	6.81332	−	34.2529i	0.253040	−	1.27212i
$726$	5.85260	+	0.737683i	0.217210	+	0.0273780i
$727$	22.6315	−	9.37426i	0.839355	−	0.347672i	0.0787556	−	0.996894i	$-0.474905\pi$
$727$	22.6315	−	9.37426i	0.839355	−	0.347672i	0.760599	+	0.649222i	$0.224905\pi$
$728$	12.5209	+	13.4655i	0.464056	+	0.499063i
$729$	7.64129	−	25.8962i	0.283011	−	0.959117i
$730$	49.8885	+	88.8780i	1.84645	+	3.28952i
$731$	−10.7856	+	7.20670i	−0.398919	+	0.266549i
$732$	0.0953349	−	14.4589i	0.00352368	−	0.534415i
$733$	−9.77199	−	49.1271i	−0.360937	−	1.81455i	−0.553015	−	0.833171i	$-0.686523\pi$
$733$	−9.77199	−	49.1271i	−0.360937	−	1.81455i	0.192078	−	0.981380i	$-0.438477\pi$
$734$	1.23184	−	0.401583i	0.0454680	−	0.0148227i
$735$	−0.949609	−	1.57979i	−0.0350268	−	0.0582714i
$736$	−6.38860	+	15.6396i	−0.235487	+	0.576484i
$737$	28.3297			1.04354
$738$	−19.4264	−	3.39880i	−0.715097	−	0.125112i
$739$	28.8194	−	5.73254i	1.06014	−	0.210875i	0.365926	−	0.930644i	$-0.380752\pi$
$739$	28.8194	−	5.73254i	1.06014	−	0.210875i	0.694214	+	0.719769i	$0.255752\pi$
$740$	−43.1242	+	10.4426i	−1.58528	+	0.383877i
$741$	−0.714159	+	1.51492i	−0.0262353	+	0.0556520i
$742$	−2.69681	−	4.80445i	−0.0990029	−	0.176377i
$743$	−15.3189	+	36.9832i	−0.561997	+	1.35678i	0.346169	+	0.938172i	$0.387482\pi$
$743$	−15.3189	+	36.9832i	−0.561997	+	1.35678i	−0.908166	+	0.418609i	$0.862518\pi$
$744$	7.80338	+	6.22304i	0.286086	+	0.228148i
$745$	−3.99834	−	9.65285i	−0.146488	−	0.353653i
$746$	−17.1852	−	13.5205i	−0.629196	−	0.495020i
$747$	−3.71304	+	4.54778i	−0.135853	+	0.166394i
$748$	−9.24929	−	3.39168i	−0.338188	−	0.124012i
$749$	3.16515	−	4.73699i	0.115652	−	0.173086i
$750$	40.1518	+	80.2999i	1.46614	+	2.93214i
$751$	−0.644925	−	0.644925i	−0.0235337	−	0.0235337i	0.695242	−	0.718776i	$-0.255297\pi$
$751$	−0.644925	−	0.644925i	−0.0235337	−	0.0235337i	−0.718776	+	0.695242i	$0.755297\pi$
$752$	14.4175	+	28.0240i	0.525752	+	1.02193i
$753$	−5.45000	+	21.8750i	−0.198609	+	0.797170i
$754$	5.94318	+	6.94479i	0.216438	+	0.252914i
$755$	−3.04746	+	4.56084i	−0.110908	+	0.165986i
$756$	17.2167	−	20.8057i	0.626166	−	0.756695i
$757$	2.74459	−	13.7980i	0.0997538	−	0.501496i	−0.898314	−	0.439355i	$-0.855207\pi$
$757$	2.74459	−	13.7980i	0.0997538	−	0.501496i	0.998067	−	0.0621412i	$-0.0197929\pi$
$758$	0.563121	+	4.71820i	0.0204535	+	0.171373i
$759$	−15.2280	−	11.2640i	−0.552740	−	0.408857i
$760$	−0.749584	−	4.64434i	−0.0271903	−	0.168468i
$761$	0.456572	−	1.10226i	0.0165507	−	0.0399570i	−0.915388	−	0.402572i	$-0.868116\pi$
$761$	0.456572	−	1.10226i	0.0165507	−	0.0399570i	0.931939	+	0.362615i	$0.118116\pi$
$762$	−11.0552	−	40.3663i	−0.400487	−	1.46232i
$763$	37.0990	−	24.7888i	1.34307	−	0.897413i
$764$	15.9715	+	21.8926i	0.577829	+	0.792047i
$765$	−4.99901	+	16.6309i	−0.180740	+	0.601293i
$766$	−14.9720	+	29.4555i	−0.540960	+	1.06427i
$767$	16.5035			0.595906
$768$	3.23754	+	27.5231i	0.116825	+	0.993153i
$769$	17.8345			0.643128			0.321564	−	0.946888i	$-0.395792\pi$
$769$	17.8345			0.643128			0.321564	+	0.946888i	$0.395792\pi$
$770$	26.2386	−	51.6210i	0.945573	−	1.86029i
$771$	−35.7071	+	32.4454i	−1.28596	+	1.16849i
$772$	24.3285	+	33.3477i	0.875601	+	1.20021i
$773$	−30.0410	+	20.0728i	−1.08050	+	0.721968i	−0.962564	−	0.271053i	$-0.912628\pi$
$773$	−30.0410	+	20.0728i	−1.08050	+	0.721968i	−0.117937	+	0.993021i	$0.537628\pi$
$774$	−28.2515	+	29.5905i	−1.01548	+	1.06361i
$775$	10.5390	−	25.4434i	0.378572	−	0.913954i
$776$	−0.842294	−	5.21875i	−0.0302366	−	0.187342i
$777$	13.7994	−	18.6556i	0.495049	−	0.669265i
$778$	−2.04617	−	17.1442i	−0.0733588	−	0.614648i
$779$	0.350520	−	1.76218i	0.0125587	−	0.0631367i
$780$	−36.5266	−	7.51628i	−1.30786	−	0.269126i
$781$	−13.8176	+	20.6795i	−0.494433	+	0.739971i
$782$	3.69408	+	4.31665i	0.132100	+	0.154363i
$783$	8.97778	−	9.98134i	0.320840	−	0.356704i
$784$	−0.879626	+	0.452541i	−0.0314152	+	0.0161622i
$785$	32.5167	+	32.5167i	1.16057	+	1.16057i
$786$	−3.49272	+	1.74644i	−0.124581	+	0.0622934i
$787$	−28.9404	+	43.3124i	−1.03161	+	1.54392i	−0.206906	+	0.978361i	$0.566339\pi$
$787$	−28.9404	+	43.3124i	−1.03161	+	1.54392i	−0.824708	+	0.565558i	$0.808661\pi$
$788$	6.72104	+	2.46458i	0.239427	+	0.0877969i
$789$	−6.89143	−	19.1837i	−0.245341	−	0.682957i
$790$	−15.6518	−	12.3140i	−0.556865	−	0.438113i
$791$	−12.5878	−	30.3896i	−0.447571	−	1.08053i
$792$	−30.8006	−	4.08870i	−1.09445	−	0.145286i
$793$	3.99601	−	9.64722i	0.141902	−	0.342583i
$794$	−18.7207	−	33.3515i	−0.664372	−	1.18360i
$795$	10.1074	+	4.76480i	0.358472	+	0.168990i
$796$	−28.4821	+	6.89697i	−1.00952	+	0.244457i
$797$	16.5418	−	3.29037i	0.585942	−	0.116551i	0.106788	−	0.994282i	$-0.465944\pi$
$797$	16.5418	−	3.29037i	0.585942	−	0.116551i	0.479154	+	0.877731i	$0.340944\pi$
$798$	1.85867	+	1.61195i	0.0657961	+	0.0570626i
$799$	10.5986			0.374952
$800$	70.5013	−	29.6079i	2.49260	−	1.04680i
$801$	6.15828	−	11.5918i	0.217592	−	0.409576i
$802$	3.38379	−	1.10313i	0.119486	−	0.0389527i
$803$	11.9642	+	60.1483i	0.422209	+	2.12259i
$804$	−26.8002	−	0.176708i	−0.945170	−	0.00623200i
$805$	−27.7675	+	18.5536i	−0.978674	+	0.653929i
$806$	3.52813	+	6.28549i	0.124273	+	0.221397i
$807$	1.04990	+	7.01668i	0.0369583	+	0.246999i
$808$	−26.4577	−	28.4537i	−0.930780	−	1.00100i
$809$	−39.8340	+	16.4998i	−1.40049	+	0.580102i	−0.949879	−	0.312619i	$-0.898794\pi$
$809$	−39.8340	+	16.4998i	−1.40049	+	0.580102i	−0.450611	+	0.892721i	$0.648794\pi$
$810$	−3.96732	+	54.6268i	−0.139398	+	1.91939i
$811$	9.67058	−	48.6173i	0.339580	−	1.70718i	−0.313243	−	0.949673i	$-0.601416\pi$
$811$	9.67058	−	48.6173i	0.339580	−	1.70718i	0.652823	−	0.757510i	$-0.273584\pi$
$812$	12.1831	−	5.64546i	0.427544	−	0.198117i
$813$	4.12613	+	0.197470i	0.144710	+	0.00692558i
$814$	−26.6175	−	2.06862i	−0.932943	−	0.0725050i
$815$	−24.2009	+	24.2009i	−0.847721	+	0.847721i
$816$	8.72876	+	3.26625i	0.305568	+	0.114342i
$817$	−2.63552	−	2.63552i	−0.0922051	−	0.0922051i
$818$	17.5468	+	20.5040i	0.613510	+	0.716905i
$819$	17.1765	−	9.23698i	0.600194	−	0.322766i
$820$	39.9719	−	1.64892i	1.39588	−	0.0575827i
$821$	17.9426	+	3.56901i	0.626203	+	0.124559i	0.497984	−	0.867186i	$-0.334074\pi$
$821$	17.9426	+	3.56901i	0.626203	+	0.124559i	0.128219	+	0.991746i	$0.459074\pi$
$822$	−21.8374	−	28.1363i	−0.761668	−	0.981366i
$823$	5.19727	+	12.5473i	0.181165	+	0.437372i	0.988207	−	0.153122i	$-0.0489329\pi$
$823$	5.19727	+	12.5473i	0.181165	+	0.437372i	−0.807042	+	0.590494i	$0.798933\pi$
$824$	−39.9930	−	9.47730i	−1.39322	−	0.330157i
$825$	12.6867	+	84.7876i	0.441695	+	2.95192i
$826$	6.55782	−	23.3397i	0.228176	−	0.812093i
$827$	−16.4642	−	24.6404i	−0.572516	−	0.856831i	0.426344	−	0.904561i	$-0.359801\pi$
$827$	−16.4642	−	24.6404i	−0.572516	−	0.856831i	−0.998860	+	0.0477298i	$0.984801\pi$
$828$	14.3355	+	10.7508i	0.498195	+	0.373617i
$829$	−16.2671	+	3.23572i	−0.564979	+	0.112381i	−0.469312	−	0.883032i	$-0.655498\pi$
$829$	−16.2671	+	3.23572i	−0.564979	+	0.112381i	−0.0956663	+	0.995413i	$0.530498\pi$
$830$	5.39646	−	10.6168i	0.187314	−	0.368516i
$831$	−2.89436	−	4.81513i	−0.100404	−	0.167035i
$832$	−5.31921	+	19.2937i	−0.184410	+	0.668889i
$833$			0.332672i			0.0115264i
$834$	12.3129	−	0.875278i	0.426360	−	0.0303084i
$835$	−15.0565	−	75.6940i	−0.521051	−	2.61950i
$836$	0.437336	−	2.79667i	0.0151256	−	0.0967250i
$837$	8.47906	−	6.33853i	0.293079	−	0.219092i
$838$	20.1872	+	5.67204i	0.697355	+	0.195937i
$839$	−45.1745	−	18.7119i	−1.55960	−	0.646006i	−0.574578	−	0.818450i	$-0.694834\pi$
$839$	−45.1745	−	18.7119i	−1.55960	−	0.646006i	−0.985019	+	0.172444i	$0.944834\pi$
$840$	−25.1440	+	48.6704i	−0.867549	+	1.67929i
$841$	−20.6255	+	8.54337i	−0.711225	+	0.294599i
$842$	1.89536	+	15.8806i	0.0653184	+	0.547280i
$843$	14.3391	+	39.9157i	0.493863	+	1.37477i
$844$	−36.9539	+	1.52442i	−1.27200	+	0.0524726i
$845$	24.1211	+	16.1172i	0.829789	+	0.554448i
$846$	32.6249	−	7.27826i	1.12167	−	0.250232i
$847$	4.42506	−	4.42506i	0.152047	−	0.152047i
$848$	2.90968	−	5.24369i	0.0999190	−	0.180069i
$849$	1.08122	−	4.33975i	0.0371073	−	0.148940i
$850$	1.99252	−	25.6383i	0.0683429	−	0.879388i
$851$	12.8021	+	8.55410i	0.438851	+	0.293231i
$852$	13.2006	−	19.4768i	0.452244	−	0.667265i
$853$	25.6899	+	5.11004i	0.879606	+	0.174965i	0.614179	−	0.789166i	$-0.289487\pi$
$853$	25.6899	+	5.11004i	0.879606	+	0.174965i	0.265427	+	0.964131i	$0.414487\pi$
$854$	−12.0555	−	9.48470i	−0.412532	−	0.324560i
$855$	−4.96701	−	0.476518i	−0.169868	−	0.0162966i
$856$	6.19691	+	0.225245i	0.211806	+	0.00769873i
$857$	−30.8971	−	12.7980i	−1.05543	−	0.437172i	−0.213600	−	0.976921i	$-0.568519\pi$
$857$	−30.8971	−	12.7980i	−1.05543	−	0.437172i	−0.841826	+	0.539749i	$0.818519\pi$
$858$	−19.4940	−	11.1119i	−0.665513	−	0.379354i
$859$	16.0686	+	24.0483i	0.548252	+	0.820517i	0.997334	−	0.0729736i	$-0.0232489\pi$
$859$	16.0686	+	24.0483i	0.548252	+	0.820517i	−0.449082	+	0.893491i	$0.648249\pi$
$860$	43.2238	−	70.8459i	1.47392	−	2.41583i
$861$	−15.4844	+	14.0700i	−0.527707	+	0.479503i
$862$	−0.521290	−	1.59904i	−0.0177552	−	0.0544634i
$863$		−	44.8567i		−	1.52694i	−0.645843	−	0.763470i	$-0.723494\pi$
$863$		−	44.8567i		−	1.52694i	0.645843	−	0.763470i	$-0.276506\pi$
$864$	29.1121	+	4.06007i	0.990415	+	0.138126i
$865$		−	56.0931i		−	1.90722i
$866$	0.948775	−	0.309303i	0.0322407	−	0.0105105i
$867$	−19.4725	+	17.6938i	−0.661320	+	0.600912i
$868$	10.2911	−	2.49200i	0.349302	−	0.0845839i
$869$	−6.65737	−	9.96345i	−0.225836	−	0.337987i
$870$	−13.4861	+	23.6592i	−0.457223	+	0.802122i
$871$	−17.8816	−	7.40679i	−0.605894	−	0.250969i
$872$	44.1634	+	20.2025i	1.49556	+	0.684142i
$873$	−5.58133	−	0.535454i	−0.188899	−	0.0181224i
$874$	−1.00940	+	1.28300i	−0.0341436	+	0.0433983i
$875$	93.4139	+	18.5812i	3.15796	+	0.628158i
$876$	−10.9431	−	56.9755i	−0.369733	−	1.92502i
$877$	−16.5425	−	11.0534i	−0.558602	−	0.373246i	0.243987	−	0.969779i	$-0.421545\pi$
$877$	−16.5425	−	11.0534i	−0.558602	−	0.373246i	−0.802589	+	0.596533i	$0.796545\pi$
$878$	−20.4680	−	1.59070i	−0.690762	−	0.0536835i
$879$	−7.16169	+	28.7454i	−0.241558	+	0.969557i
$880$	62.8142	−	5.19124i	2.11747	−	0.174997i
$881$	29.6126	−	29.6126i	0.997673	−	0.997673i	−0.00232406	−	0.999997i	$-0.500740\pi$
$881$	29.6126	−	29.6126i	0.997673	−	0.997673i	0.999997	+	0.00232406i	$0.000739773\pi$
$882$	0.228452	+	1.02404i	0.00769239	+	0.0344813i
$883$	−34.3003	−	22.9187i	−1.15430	−	0.771277i	−0.177222	−	0.984171i	$-0.556711\pi$
$883$	−34.3003	−	22.9187i	−1.15430	−	0.771277i	−0.977075	+	0.212894i	$0.931711\pi$
$884$	4.95135	+	4.55903i	0.166532	+	0.153337i
$885$	16.6232	+	46.2739i	0.558782	+	1.55548i
$886$	−4.99063	+	0.595636i	−0.167664	+	0.0200108i
$887$	17.2802	−	7.15771i	0.580214	−	0.240332i	−0.0732204	−	0.997316i	$-0.523328\pi$
$887$	17.2802	−	7.15771i	0.580214	−	0.240332i	0.653434	+	0.756983i	$0.273328\pi$
$888$	25.1675	+	2.12296i	0.844567	+	0.0712419i
$889$	−41.0207	−	16.9913i	−1.37579	−	0.569871i
$890$	−7.20250	+	25.6342i	−0.241428	+	0.859260i
$891$	−12.4573	+	30.5104i	−0.417334	+	1.02214i
$892$	22.6641	+	31.0663i	0.758850	+	1.04018i
$893$	0.594112	+	2.98680i	0.0198812	+	0.0999496i
$894$	0.421714	+	5.93241i	0.0141042	+	0.198409i
$895$			26.7287i			0.893441i
$896$	25.1721	+	15.1891i	0.840942	+	0.507433i
$897$	6.66685	+	11.0911i	0.222600	+	0.370321i
$898$	6.42540	+	3.26598i	0.214418	+	0.108987i
$899$	5.16260	−	1.02690i	0.172182	−	0.0342492i
$900$	−11.4729	−	80.2890i	−0.382430	−	2.67630i
$901$	−1.12045	−	1.67687i	−0.0373276	−	0.0558648i
$902$	23.1742	+	6.51131i	0.771617	+	0.216803i
$903$	6.42269	+	42.9240i	0.213734	+	1.42842i
$904$	20.9592	−	29.0267i	0.697091	−	0.965415i
$905$	−22.3772	−	54.0233i	−0.743843	−	1.79580i
$906$	2.46661	−	1.91441i	0.0819478	−	0.0636021i
$907$	−6.74321	−	1.34131i	−0.223905	−	0.0445374i	0.0818628	−	0.996644i	$-0.473913\pi$
$907$	−6.74321	−	1.34131i	−0.223905	−	0.0445374i	−0.305768	+	0.952106i	$0.598913\pi$
$908$	−13.6961	+	14.8747i	−0.454520	+	0.493633i
$909$	−36.2954	+	19.5185i	−1.20384	+	0.647389i
$910$	−30.0580	+	25.7229i	−0.996411	+	0.852705i
$911$	−7.04481	−	7.04481i	−0.233405	−	0.233405i	0.580707	−	0.814112i	$-0.302776\pi$
$911$	−7.04481	−	7.04481i	−0.233405	−	0.233405i	−0.814112	+	0.580707i	$0.802776\pi$
$912$	−0.431169	+	2.64295i	−0.0142774	+	0.0875169i
$913$	5.06714	−	5.06714i	0.167698	−	0.167698i
$914$	3.89787	−	50.1550i	0.128930	−	1.65898i
$915$	31.0747	+	1.48719i	1.02730	+	0.0491649i
$916$	−32.7315	−	12.0025i	−1.08148	−	0.396574i
$917$	−0.808204	+	4.06312i	−0.0266893	+	0.134176i
$918$	5.69306	−	8.08123i	0.187899	−	0.266720i
$919$	−47.5960	+	19.7149i	−1.57005	+	0.650335i	−0.986798	−	0.161959i	$-0.948219\pi$
$919$	−47.5960	+	19.7149i	−1.57005	+	0.650335i	−0.583249	+	0.812293i	$0.698219\pi$
$920$	−33.0549	−	15.1209i	−1.08979	−	0.498523i
$921$	2.11371	+	14.1263i	0.0696491	+	0.465477i
$922$	11.9011	−	6.68028i	0.391943	−	0.220003i
$923$	14.1282	−	9.44019i	0.465037	−	0.310728i
$924$	−23.4609	+	23.1535i	−0.771807	+	0.761695i
$925$	−13.5958	−	68.3506i	−0.447027	−	2.24735i
$926$	8.65846	+	26.5595i	0.284534	+	0.872798i
$927$	−20.4526	+	38.4982i	−0.671752	+	1.26445i
$928$	12.1917	+	8.06015i	0.400211	+	0.264587i
$929$	2.02612			0.0664748			0.0332374	−	0.999447i	$-0.489418\pi$
$929$	2.02612			0.0664748			0.0332374	+	0.999447i	$0.489418\pi$
$930$	−14.0701	+	16.2236i	−0.461377	+	0.531992i
$931$	−0.0937507	+	0.0186482i	−0.00307256	+	0.000611169i
$932$	13.6586	+	8.33325i	0.447403	+	0.272965i
$933$	−51.1852	−	24.1296i	−1.67573	−	0.789967i
$934$	−39.6290	+	22.2443i	−1.29670	+	0.727857i
$935$	8.11156	−	19.5830i	0.265276	−	0.640433i
$936$	18.3722	+	10.6336i	0.600513	+	0.347568i
$937$	−0.987795	−	2.38475i	−0.0322699	−	0.0779063i	0.906923	−	0.421296i	$-0.138425\pi$
$937$	−0.987795	−	2.38475i	−0.0322699	−	0.0779063i	−0.939193	+	0.343390i	$0.888425\pi$
$938$	−17.5803	+	22.3455i	−0.574018	+	0.729607i
$939$	4.19362	+	11.6738i	0.136854	+	0.380960i
$940$	−61.5236	+	28.5090i	−2.00668	+	0.929862i
$941$	2.09080	−	3.12910i	0.0681580	−	0.102006i	−0.795825	−	0.605527i	$-0.792962\pi$
$941$	2.09080	−	3.12910i	0.0681580	−	0.102006i	0.863983	+	0.503521i	$0.167962\pi$
$942$	−11.7068	−	23.4125i	−0.381428	−	0.762820i
$943$	−9.81635	−	9.81635i	−0.319664	−	0.319664i
$944$	25.3687	−	7.26212i	0.825682	−	0.236362i
$945$	43.2005	+	38.8570i	1.40531	+	1.26402i
$946$	37.9395	−	32.4677i	1.23352	−	1.05561i
$947$	−16.2924	+	24.3833i	−0.529432	+	0.792352i	−0.995734	−	0.0922743i	$-0.970586\pi$
$947$	−16.2924	+	24.3833i	−0.529432	+	0.792352i	0.466301	+	0.884626i	$0.345586\pi$
$948$	6.23579	+	9.46705i	0.202529	+	0.307475i
$949$	8.17397	−	41.0933i	0.265338	−	1.33395i
$950$	7.33686	−	0.875661i	0.238039	−	0.0284102i
$951$	19.4614	−	26.3102i	0.631079	−	0.853166i
$952$	8.41499	−	5.19078i	0.272731	−	0.168234i
$953$	−12.0888	+	29.1848i	−0.391593	+	0.945389i	0.598000	+	0.801496i	$0.295962\pi$
$953$	−12.0888	+	29.1848i	−0.391593	+	0.945389i	−0.989593	+	0.143893i	$0.954038\pi$
$954$	−4.60054	−	4.39236i	−0.148948	−	0.142208i
$955$	−48.4803	+	32.3935i	−1.56879	+	1.04823i
$956$	23.2112	+	3.62971i	0.750704	+	0.117393i
$957$	−12.1273	+	11.0196i	−0.392021	+	0.356212i
$958$	−7.83856	−	3.98428i	−0.253253	−	0.128726i
$959$	−37.7844			−1.22012
$960$	−59.4552	+	4.51916i	−1.91891	+	0.145855i
$961$	−26.8492			−0.866103
$962$	16.2600	+	8.26483i	0.524243	+	0.266469i
$963$	1.89331	−	6.29876i	0.0610112	−	0.202975i
$964$	1.31651	−	8.41882i	0.0424020	−	0.271152i
$965$	−73.8473	+	49.3432i	−2.37723	+	1.58841i
$966$	18.3345	−	5.02130i	0.589904	−	0.161558i
$967$	−16.2050	+	39.1222i	−0.521116	+	1.25809i	0.416094	+	0.909321i	$0.363399\pi$
$967$	−16.2050	+	39.1222i	−0.521116	+	1.25809i	−0.937210	+	0.348764i	$0.886601\pi$
$968$	6.62791	+	1.57064i	0.213029	+	0.0504823i
$969$	0.724030	+	0.535559i	0.0232592	+	0.0172046i
$970$	11.2938	−	1.34793i	0.362622	−	0.0432793i
$971$	8.80545	−	44.2680i	0.282580	−	1.42063i	−0.535019	−	0.844840i	$-0.679696\pi$
$971$	8.80545	−	44.2680i	0.282580	−	1.42063i	0.817600	−	0.575787i	$-0.195304\pi$
$972$	11.9750	−	28.7854i	0.384098	−	0.923292i
$973$	7.27538	−	10.8884i	0.233238	−	0.349065i
$974$	1.51599	−	1.29734i	0.0485753	−	0.0415696i
$975$	14.1599	−	56.8344i	0.453479	−	1.82016i
$976$	1.89744	−	16.5879i	0.0607357	−	0.530965i
$977$	−8.81730	−	8.81730i	−0.282090	−	0.282090i	0.551852	−	0.833942i	$-0.313921\pi$
$977$	−8.81730	−	8.81730i	−0.282090	−	0.282090i	−0.833942	+	0.551852i	$0.813921\pi$
$978$	17.4250	−	8.71291i	0.557190	−	0.278608i
$979$	−8.90099	+	13.3213i	−0.284477	+	0.425750i
$980$	−0.894850	−	1.93112i	−0.0285849	−	0.0616874i
$981$	32.5772	−	39.9010i	1.04011	−	1.27394i
$982$	9.22098	−	11.7203i	0.294253	−	0.374011i
$983$	16.0320	+	38.7047i	0.511341	+	1.23449i	0.943103	+	0.332500i	$0.107892\pi$
$983$	16.0320	+	38.7047i	0.511341	+	1.23449i	−0.431762	+	0.901988i	$0.642108\pi$
$984$	−21.8824	−	6.30431i	−0.697586	−	0.200974i
$985$	−5.89430	+	14.2301i	−0.187808	+	0.453408i
$986$	4.28605	−	2.40582i	0.136496	−	0.0766169i
$987$	15.1213	−	32.0762i	0.481315	−	1.02100i
$988$	−1.00723	+	1.65090i	−0.0320444	+	0.0525223i
$989$	−28.2451	+	5.61830i	−0.898142	+	0.178652i
$990$	11.5212	−	65.8514i	0.366167	−	2.09289i
$991$	30.3970			0.965592			0.482796	−	0.875733i	$-0.339621\pi$
$991$	30.3970			0.965592			0.482796	+	0.875733i	$0.339621\pi$
$992$	8.18921	+	8.10940i	0.260008	+	0.257474i
$993$	−17.8477	−	29.6918i	−0.566380	−	0.942241i
$994$	−7.73661	−	23.7317i	−0.245390	−	0.752725i
$995$	−12.3010	−	61.8414i	−0.389969	−	1.96051i
$996$	−4.82517	+	4.76196i	−0.152891	+	0.150889i
$997$	−2.67064	+	1.78447i	−0.0845801	+	0.0565146i	−0.597141	−	0.802136i	$-0.703697\pi$
$997$	−2.67064	+	1.78447i	−0.0845801	+	0.0565146i	0.512561	+	0.858651i	$0.328697\pi$
$998$	−15.6074	+	8.76065i	−0.494044	+	0.277314i
$999$	8.92912	−	25.2571i	0.282505	−	0.799099i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.s.a.11.20	yes	240
3.2	odd	2	inner	192.2.s.a.11.11	✓	240
4.3	odd	2		768.2.s.a.719.23		240
12.11	even	2		768.2.s.a.719.12		240
64.29	even	16		768.2.s.a.47.12		240
64.35	odd	16	inner	192.2.s.a.35.11	yes	240
192.29	odd	16		768.2.s.a.47.23		240
192.35	even	16	inner	192.2.s.a.35.20	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.11.11	✓	240	3.2	odd	2	inner
192.2.s.a.11.20	yes	240	1.1	even	1	trivial
192.2.s.a.35.11	yes	240	64.35	odd	16	inner
192.2.s.a.35.20	yes	240	192.35	even	16	inner
768.2.s.a.47.12		240	64.29	even	16
768.2.s.a.47.23		240	192.29	odd	16
768.2.s.a.719.12		240	12.11	even	2
768.2.s.a.719.23		240	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.640805 - 1.26070i) q^{2} +(-1.16480 - 1.28189i) q^{3} +(-1.17874 - 1.61573i) q^{4} +(3.57797 - 2.39072i) q^{5} +(-2.36249 + 0.647019i) q^{6} +(-0.994439 + 2.40079i) q^{7} +(-2.79229 + 0.450669i) q^{8} +(-0.286494 + 2.98629i) q^{9} +O(q^{10})\)	\(q+(0.640805 - 1.26070i) q^{2} +(-1.16480 - 1.28189i) q^{3} +(-1.17874 - 1.61573i) q^{4} +(3.57797 - 2.39072i) q^{5} +(-2.36249 + 0.647019i) q^{6} +(-0.994439 + 2.40079i) q^{7} +(-2.79229 + 0.450669i) q^{8} +(-0.286494 + 2.98629i) q^{9} +(-0.721207 - 6.04274i) q^{10} +(0.714367 - 3.59136i) q^{11} +(-0.698199 + 3.39301i) q^{12} +(-1.38986 + 2.08008i) q^{13} +(2.38944 + 2.79213i) q^{14} +(-7.23226 - 1.80186i) q^{15} +(-1.22116 + 3.80904i) q^{16} +(0.951204 + 0.951204i) q^{17} +(3.58123 + 2.27481i) q^{18} +(-0.214739 + 0.321380i) q^{19} +(-8.08025 - 2.96299i) q^{20} +(4.23587 - 1.52167i) q^{21} +(-4.06987 - 3.20197i) q^{22} +(1.14288 + 2.75916i) q^{23} +(3.83016 + 3.05448i) q^{24} +(5.17290 - 12.4885i) q^{25} +(1.73173 + 3.08513i) q^{26} +(4.16181 - 3.11117i) q^{27} +(5.05121 - 1.22316i) q^{28} +(2.53398 - 0.504039i) q^{29} +(-6.90608 + 7.96308i) q^{30} +2.03735 q^{31} +(4.01954 + 3.98037i) q^{32} +(-5.43583 + 3.26747i) q^{33} +(1.80872 - 0.589648i) q^{34} +(2.18155 + 10.9674i) q^{35} +(5.16273 - 3.05715i) q^{36} +(4.28668 - 2.86427i) q^{37} +(0.267558 + 0.476664i) q^{38} +(4.28535 - 0.641215i) q^{39} +(-8.91331 + 8.28808i) q^{40} +(-4.29457 + 1.77887i) q^{41} +(0.795999 - 6.31526i) q^{42} +(-1.88124 + 9.45763i) q^{43} +(-6.64472 + 3.07905i) q^{44} +(6.11432 + 11.3698i) q^{45} +(4.21083 + 0.327251i) q^{46} +(5.57116 - 5.57116i) q^{47} +(6.30518 - 2.87137i) q^{48} +(0.174869 + 0.174869i) q^{49} +(-12.4294 - 14.5242i) q^{50} +(0.111381 - 2.32730i) q^{51} +(4.99913 - 0.206223i) q^{52} +(-1.47041 - 0.292483i) q^{53} +(-1.25534 - 7.24045i) q^{54} +(-6.02998 - 14.5576i) q^{55} +(1.69480 - 7.15187i) q^{56} +(0.662102 - 0.0990701i) q^{57} +(0.988343 - 3.51758i) q^{58} +(-3.66506 - 5.48515i) q^{59} +(5.61361 + 13.8093i) q^{60} +(-4.09381 + 0.814309i) q^{61} +(1.30554 - 2.56849i) q^{62} +(-6.88455 - 3.65750i) q^{63} +(7.59380 - 2.51680i) q^{64} +10.7652i q^{65} +(0.635995 + 8.94678i) q^{66} +(1.50936 + 7.58806i) q^{67} +(0.415668 - 2.65811i) q^{68} +(2.20572 - 4.67890i) q^{69} +(15.2245 + 4.27767i) q^{70} +(-6.27514 - 2.59925i) q^{71} +(-0.545851 - 8.46771i) q^{72} +(-15.4732 + 6.40920i) q^{73} +(-0.864060 - 7.23966i) q^{74} +(-22.0342 + 7.91545i) q^{75} +(0.772384 - 0.0318623i) q^{76} +(7.91171 + 5.28644i) q^{77} +(1.93769 - 5.81344i) q^{78} +(2.31400 - 2.31400i) q^{79} +(4.73710 + 16.5481i) q^{80} +(-8.83584 - 1.71111i) q^{81} +(-0.509359 + 6.55408i) q^{82} +(1.62719 + 1.08726i) q^{83} +(-7.45158 - 5.05037i) q^{84} +(5.67744 + 1.12931i) q^{85} +(10.7177 + 8.43218i) q^{86} +(-3.59769 - 2.66118i) q^{87} +(-0.376205 + 10.3501i) q^{88} +(-4.04231 - 1.67438i) q^{89} +(18.2520 - 0.422520i) q^{90} +(-3.61170 - 5.40528i) q^{91} +(3.11089 - 5.09890i) q^{92} +(-2.37310 - 2.61166i) q^{93} +(-3.45354 - 10.5936i) q^{94} +1.66327i q^{95} +(0.420453 - 9.78893i) q^{96} +1.86899i q^{97} +(0.332515 - 0.108401i) q^{98} +(10.5202 + 3.16221i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more