LMFDB - Embedded newform 348.2.t.a.35.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [348,2,Mod(35,348)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(348, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 7, 3]))

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

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

chi := DirichletCharacter("348.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 348 = 2^{2} \cdot 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	348.t (of order $14$, degree $6$, 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:	$2.77879399034$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			35.4
Character	$\chi$	$=$	348.35
Dual form			348.2.t.a.179.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37991 - 0.309609i) q^{2} +(0.578538 - 1.63257i) q^{3} +(1.80828 + 0.854463i) q^{4} +(-2.25006 - 1.79437i) q^{5} +(-1.30379 + 2.07368i) q^{6} +(0.00145454 + 0.000331989i) q^{7} +(-2.23071 - 1.73894i) q^{8} +(-2.33059 - 1.88901i) q^{9} +O(q^{10})$	\(q+(-1.37991 - 0.309609i) q^{2} +(0.578538 - 1.63257i) q^{3} +(1.80828 + 0.854463i) q^{4} +(-2.25006 - 1.79437i) q^{5} +(-1.30379 + 2.07368i) q^{6} +(0.00145454 + 0.000331989i) q^{7} +(-2.23071 - 1.73894i) q^{8} +(-2.33059 - 1.88901i) q^{9} +(2.54933 + 3.17270i) q^{10} +(0.153025 + 0.317760i) q^{11} +(2.44113 - 2.45782i) q^{12} +(-4.65883 + 2.24357i) q^{13} +(-0.00190434 - 0.000908452i) q^{14} +(-4.23118 + 2.63528i) q^{15} +(2.53979 + 3.09022i) q^{16} +0.768538 q^{17} +(2.63114 + 3.32823i) q^{18} +(-1.34708 - 5.90193i) q^{19} +(-2.53554 - 5.16732i) q^{20} +(0.00138350 - 0.00218257i) q^{21} +(-0.112779 - 0.485856i) q^{22} +(2.25150 + 2.82329i) q^{23} +(-4.12950 + 2.63576i) q^{24} +(0.730434 + 3.20024i) q^{25} +(7.12338 - 1.65351i) q^{26} +(-4.43228 + 2.71199i) q^{27} +(0.00234655 + 0.00184318i) q^{28} +(-3.52633 + 4.07001i) q^{29} +(6.65454 - 2.32643i) q^{30} +(1.25819 - 1.57772i) q^{31} +(-2.54791 - 5.05056i) q^{32} +(0.607296 - 0.0659884i) q^{33} +(-1.06051 - 0.237946i) q^{34} +(-0.00267710 - 0.00335697i) q^{35} +(-2.60028 - 5.40727i) q^{36} +(-1.70022 + 3.53054i) q^{37} +(0.0315499 + 8.56118i) q^{38} +(0.967488 + 8.90387i) q^{39} +(1.89895 + 7.91545i) q^{40} -0.571669 q^{41} +(-0.00258485 + 0.00258340i) q^{42} +(-4.51533 - 5.66205i) q^{43} +(0.00519885 + 0.705354i) q^{44} +(1.85439 + 8.43232i) q^{45} +(-2.23275 - 4.59297i) q^{46} +(-3.16295 - 6.56793i) q^{47} +(6.51438 - 2.35857i) q^{48} +(-6.30678 - 3.03719i) q^{49} +(-0.0171075 - 4.64218i) q^{50} +(0.444628 - 1.25469i) q^{51} +(-10.3415 + 0.0762230i) q^{52} +(-7.74056 - 6.17289i) q^{53} +(6.95579 - 2.37002i) q^{54} +(0.225861 - 0.989562i) q^{55} +(-0.00266735 - 0.00326993i) q^{56} +(-10.4147 - 1.21529i) q^{57} +(6.12612 - 4.52446i) q^{58} +7.91189 q^{59} +(-9.90293 + 1.14996i) q^{60} +(5.42043 + 1.23718i) q^{61} +(-2.22466 + 1.78756i) q^{62} +(-0.00276280 - 0.00352137i) q^{63} +(1.95217 + 7.75816i) q^{64} +(14.5085 + 3.31146i) q^{65} +(-0.858443 - 0.0969666i) q^{66} +(-0.713661 + 1.48193i) q^{67} +(1.38974 + 0.656687i) q^{68} +(5.91181 - 2.04236i) q^{69} +(0.00265479 + 0.00546116i) q^{70} +(10.8320 - 5.21643i) q^{71} +(1.91400 + 8.26660i) q^{72} +(0.163822 - 0.130644i) q^{73} +(3.43923 - 4.34541i) q^{74} +(5.64721 + 0.658974i) q^{75} +(2.60708 - 11.8234i) q^{76} +(0.000117088 + 0.000512996i) q^{77} +(1.42168 - 12.5861i) q^{78} +(6.82625 + 3.28735i) q^{79} +(-0.169687 - 11.5105i) q^{80} +(1.86328 + 8.80501i) q^{81} +(0.788850 + 0.176994i) q^{82} +(-3.05983 - 13.4060i) q^{83} +(0.00436669 - 0.00276456i) q^{84} +(-1.72926 - 1.37904i) q^{85} +(4.47772 + 9.21108i) q^{86} +(4.60448 + 8.11164i) q^{87} +(0.211210 - 0.974932i) q^{88} +(9.57939 - 12.0122i) q^{89} +(0.0518316 - 12.2100i) q^{90} +(-0.00752129 + 0.00171669i) q^{91} +(1.65896 + 7.02915i) q^{92} +(-1.84783 - 2.96686i) q^{93} +(2.33108 + 10.0424i) q^{94} +(-7.55921 + 15.6969i) q^{95} +(-9.71947 + 1.23770i) q^{96} +(15.1893 - 3.46685i) q^{97} +(7.76243 + 6.14367i) q^{98} +(0.243613 - 1.02963i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9}+O(q^{10}) $ 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9	$ 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97}+O(q^{100}) $ 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9 - 14 * q^10 - 20 * q^13 - 26 * q^16 - 56 * q^18 - 14 * q^21 - 40 * q^22 + 3 * q^24 + 40 * q^25 - 36 * q^28 - 6 * q^30 - 22 * q^33 - 8 * q^34 + 9 * q^36 - 28 * q^37 - 14 * q^40 - 74 * q^42 - 22 * q^45 + 14 * q^48 + 4 * q^49 - 4 * q^52 - 31 * q^54 - 12 * q^57 - 106 * q^58 - 42 * q^60 - 28 * q^61 - 94 * q^64 - 7 * q^66 - 14 * q^69 + 70 * q^72 - 28 * q^73 - 84 * q^76 - 9 * q^78 - 50 * q^81 - 46 * q^82 - 35 * q^84 - 168 * q^85 - 60 * q^88 + 119 * q^90 + 122 * q^93 + 36 * q^94 + 2 * q^96 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/348\mathbb{Z}\right)^\times$.

$n$	$175$	$205$	$233$
$\chi(n)$	$-1$	$e\left(\frac{3}{14}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.37991	−	0.309609i	−0.975741	−	0.218927i
$2$	−1.37991	−	0.309609i	−0.975741	−	0.218927i
$3$	0.578538	−	1.63257i	0.334019	−	0.942566i
$3$	0.578538	−	1.63257i	0.334019	−	0.942566i
$4$	1.80828	+	0.854463i	0.904142	+	0.427231i
$5$	−2.25006	−	1.79437i	−1.00626	−	0.802465i	−0.0258959	−	0.999665i	$-0.508244\pi$
$5$	−2.25006	−	1.79437i	−1.00626	−	0.802465i	−0.980363	+	0.197200i	$0.936815\pi$
$6$	−1.30379	+	2.07368i	−0.532269	+	0.846575i
$7$	0.00145454		0.000331989i	0.000549764		0.000125480i	0.222796	−	0.974865i	$-0.428482\pi$
$7$	0.00145454		0.000331989i	0.000549764		0.000125480i	−0.222246	+	0.974991i	$0.571339\pi$
$8$	−2.23071	−	1.73894i	−0.788677	−	0.614808i
$9$	−2.33059	−	1.88901i	−0.776863	−	0.629670i
$10$	2.54933	+	3.17270i	0.806168	+	1.00330i
$11$	0.153025	+	0.317760i	0.0461387	+	0.0958081i	0.922764	−	0.385366i	$-0.125925\pi$
$11$	0.153025	+	0.317760i	0.0461387	+	0.0958081i	−0.876625	+	0.481174i	$0.840211\pi$
$12$	2.44113	−	2.45782i	0.704695	−	0.709511i
$13$	−4.65883	+	2.24357i	−1.29213	+	0.622256i	−0.948478	−	0.316843i	$-0.897377\pi$
$13$	−4.65883	+	2.24357i	−1.29213	+	0.622256i	−0.343649	+	0.939098i	$0.611663\pi$
$14$	−0.00190434		0.000908452i	−0.000508956		0.000242794i
$15$	−4.23118	+	2.63528i	−1.09249	+	0.680428i
$16$	2.53979	+	3.09022i	0.634947	+	0.772556i
$17$	0.768538			0.186398			0.0931989	−	0.995648i	$-0.470291\pi$
$17$	0.768538			0.186398			0.0931989	+	0.995648i	$0.470291\pi$
$18$	2.63114	+	3.32823i	0.620165	+	0.784471i
$19$	−1.34708	−	5.90193i	−0.309041	−	1.35400i	−0.856060	−	0.516876i	$-0.827095\pi$
$19$	−1.34708	−	5.90193i	−0.309041	−	1.35400i	0.547020	−	0.837120i	$-0.315762\pi$
$20$	−2.53554	−	5.16732i	−0.566963	−	1.15545i
$21$	0.00138350	−	0.00218257i	0.000301905	−	0.000476276i
$22$	−0.112779	−	0.485856i	−0.0240445	−	0.103585i
$23$	2.25150	+	2.82329i	0.469471	+	0.588698i	0.959041	−	0.283266i	$-0.0914179\pi$
$23$	2.25150	+	2.82329i	0.469471	+	0.588698i	−0.489571	+	0.871964i	$0.662846\pi$
$24$	−4.12950	+	2.63576i	−0.842931	+	0.538022i
$25$	0.730434	+	3.20024i	0.146087	+	0.640048i
$26$	7.12338	−	1.65351i	1.39701	−	0.324280i
$27$	−4.43228	+	2.71199i	−0.852993	+	0.521923i
$28$	0.00234655	+	0.00184318i	0.000443456	+	0.000348328i
$29$	−3.52633	+	4.07001i	−0.654823	+	0.755783i
$29$	−3.52633	+	4.07001i	−0.654823	+	0.755783i
$30$	6.65454	−	2.32643i	1.21495	−	0.424747i
$31$	1.25819	−	1.57772i	0.225977	−	0.283367i	−0.655898	−	0.754850i	$-0.727710\pi$
$31$	1.25819	−	1.57772i	0.225977	−	0.283367i	0.881875	+	0.471483i	$0.156281\pi$
$32$	−2.54791	−	5.05056i	−0.450410	−	0.892822i
$33$	0.607296	−	0.0659884i	0.105717	−	0.0114871i
$34$	−1.06051	−	0.237946i	−0.181876	−	0.0408074i
$35$	−0.00267710	−	0.00335697i	−0.000452512	−	0.000567432i
$36$	−2.60028	−	5.40727i	−0.433379	−	0.901212i
$37$	−1.70022	+	3.53054i	−0.279514	+	0.580417i	−0.992707	−	0.120551i	$-0.961534\pi$
$37$	−1.70022	+	3.53054i	−0.279514	+	0.580417i	0.713193	+	0.700968i	$0.247248\pi$
$38$	0.0315499	+	8.56118i	0.00511807	+	1.38881i
$39$	0.967488	+	8.90387i	0.154922	+	1.42576i
$40$	1.89895	+	7.91545i	0.300251	+	1.25154i
$41$	−0.571669			−0.0892797			−0.0446398	−	0.999003i	$-0.514214\pi$
$41$	−0.571669			−0.0892797			−0.0446398	+	0.999003i	$0.514214\pi$
$42$	−0.00258485	+	0.00258340i	−0.000398851	+	0.000398627i
$43$	−4.51533	−	5.66205i	−0.688582	−	0.863454i	0.307531	−	0.951538i	$-0.400497\pi$
$43$	−4.51533	−	5.66205i	−0.688582	−	0.863454i	−0.996113	+	0.0880838i	$0.971926\pi$
$44$	0.00519885	+	0.705354i	0.000783757	+	0.106336i
$45$	1.85439	+	8.43232i	0.276437	+	1.25702i
$46$	−2.23275	−	4.59297i	−0.329200	−	0.677196i
$47$	−3.16295	−	6.56793i	−0.461363	−	0.958031i	−0.993760	−	0.111536i	$-0.964423\pi$
$47$	−3.16295	−	6.56793i	−0.461363	−	0.958031i	0.532397	−	0.846495i	$-0.321291\pi$
$48$	6.51438	−	2.35857i	0.940270	−	0.340431i
$49$	−6.30678	−	3.03719i	−0.900969	−	0.433884i
$50$	−0.0171075	−	4.64218i	−0.00241937	−	0.656503i
$51$	0.444628	−	1.25469i	0.0622604	−	0.175692i
$52$	−10.3415	+	0.0762230i	−1.43411	+	0.0105702i
$53$	−7.74056	−	6.17289i	−1.06325	−	0.847911i	−0.0744571	−	0.997224i	$-0.523722\pi$
$53$	−7.74056	−	6.17289i	−1.06325	−	0.847911i	−0.988790	+	0.149313i	$0.952294\pi$
$54$	6.95579	−	2.37002i	0.946563	−	0.322519i
$55$	0.225861	−	0.989562i	0.0304551	−	0.133433i
$56$	−0.00266735	−	0.00326993i	−0.000356440	−	0.000436962i
$57$	−10.4147	−	1.21529i	−1.37946	−	0.160969i
$58$	6.12612	−	4.52446i	0.804398	−	0.594090i
$59$	7.91189			1.03004			0.515020	−	0.857178i	$-0.327784\pi$
$59$	7.91189			1.03004			0.515020	+	0.857178i	$0.327784\pi$
$60$	−9.90293	+	1.14996i	−1.27846	+	0.148459i
$61$	5.42043	+	1.23718i	0.694014	+	0.158404i	0.554956	−	0.831880i	$-0.312735\pi$
$61$	5.42043	+	1.23718i	0.694014	+	0.158404i	0.139059	+	0.990284i	$0.455592\pi$
$62$	−2.22466	+	1.78756i	−0.282532	+	0.227020i
$63$	−0.00276280	−	0.00352137i	−0.000348080	−	0.000443651i
$64$	1.95217	+	7.75816i	0.244022	+	0.969770i
$65$	14.5085	+	3.31146i	1.79955	+	0.410736i
$66$	−0.858443	−	0.0969666i	−0.105667	−	0.0119358i
$67$	−0.713661	+	1.48193i	−0.0871875	+	0.181047i	−0.940004	−	0.341165i	$-0.889179\pi$
$67$	−0.713661	+	1.48193i	−0.0871875	+	0.181047i	0.852816	+	0.522212i	$0.174893\pi$
$68$	1.38974	+	0.656687i	0.168530	+	0.0796350i
$69$	5.91181	−	2.04236i	0.711699	−	0.245871i
$70$	0.00265479	+	0.00546116i	0.000317308	+	0.000652733i
$71$	10.8320	−	5.21643i	1.28552	−	0.619076i	0.338721	−	0.940887i	$-0.390006\pi$
$71$	10.8320	−	5.21643i	1.28552	−	0.619076i	0.946804	+	0.321811i	$0.104291\pi$
$72$	1.91400	+	8.26660i	0.225567	+	0.974228i
$73$	0.163822	−	0.130644i	0.0191739	−	0.0152907i	−0.613856	−	0.789418i	$-0.710382\pi$
$73$	0.163822	−	0.130644i	0.0191739	−	0.0152907i	0.633030	+	0.774127i	$0.281811\pi$
$74$	3.43923	−	4.34541i	0.399802	−	0.505144i
$75$	5.64721	+	0.658974i	0.652083	+	0.0760917i
$76$	2.60708	−	11.8234i	0.299053	−	1.35624i
$77$	0.000117088	0	0.000512996i	1.33434e−5	0	5.84613e-5i
$78$	1.42168	−	12.5861i	0.160973	−	1.42509i
$79$	6.82625	+	3.28735i	0.768013	+	0.369856i	0.776507	−	0.630108i	$-0.216990\pi$
$79$	6.82625	+	3.28735i	0.768013	+	0.369856i	−0.00849430	+	0.999964i	$0.502704\pi$
$80$	−0.169687	−	11.5105i	−0.0189716	−	1.28691i
$81$	1.86328	+	8.80501i	0.207031	+	0.978334i
$82$	0.788850	+	0.176994i	0.0871139	+	0.0195457i
$83$	−3.05983	−	13.4060i	−0.335860	−	1.47150i	−0.807584	−	0.589753i	$-0.799225\pi$
$83$	−3.05983	−	13.4060i	−0.335860	−	1.47150i	0.471724	−	0.881746i	$-0.343632\pi$
$84$	0.00436669	−	0.00276456i	0.000476445	−	0.000301638i
$85$	−1.72926	−	1.37904i	−0.187565	−	0.149578i
$86$	4.47772	+	9.21108i	0.482845	+	0.993257i
$87$	4.60448	+	8.11164i	0.493652	+	0.869659i
$88$	0.211210	−	0.974932i	0.0225151	−	0.103928i
$89$	9.57939	−	12.0122i	1.01541	−	1.27329i	0.0538957	−	0.998547i	$-0.482836\pi$
$89$	9.57939	−	12.0122i	1.01541	−	1.27329i	0.961518	−	0.274742i	$-0.0885924\pi$
$90$	0.0518316	−	12.2100i	0.00546353	−	1.28704i
$91$	−0.00752129	+	0.00171669i	−0.000788445	+	0.000179958i
$92$	1.65896	+	7.02915i	0.172958	+	0.732839i
$93$	−1.84783	−	2.96686i	−0.191611	−	0.307649i
$94$	2.33108	+	10.0424i	0.240433	+	1.03579i
$95$	−7.55921	+	15.6969i	−0.775559	+	1.61046i
$96$	−9.71947	+	1.23770i	−0.991989	+	0.126322i
$97$	15.1893	−	3.46685i	1.54224	−	0.352005i	0.634961	−	0.772544i	$-0.281016\pi$
$97$	15.1893	−	3.46685i	1.54224	−	0.352005i	0.907275	+	0.420539i	$0.138159\pi$
$98$	7.76243	+	6.14367i	0.784124	+	0.620604i
$99$	0.243613	−	1.02963i	0.0244840	−	0.103482i
$100$	−1.41365	+	6.41107i	−0.141365	+	0.641107i
$101$	−1.01341	−	1.27077i	−0.100838	−	0.126447i	0.728852	−	0.684671i	$-0.240054\pi$
$101$	−1.01341	−	1.27077i	−0.100838	−	0.126447i	−0.829690	+	0.558225i	$0.811483\pi$
$102$	−1.00201	+	1.59370i	−0.0992138	+	0.157800i
$103$	−4.89776	−	10.1703i	−0.482591	−	1.00211i	−0.990087	−	0.140456i	$-0.955143\pi$
$103$	−4.89776	−	10.1703i	−0.482591	−	1.00211i	0.507496	−	0.861654i	$-0.330571\pi$
$104$	14.2940	+	3.09665i	1.40164	+	0.303652i
$105$	−0.00702930	+	0.00242842i	−0.000685989	+	0.000236989i
$106$	8.77006	+	10.9146i	0.851824	+	1.06012i
$107$	−12.7581	−	6.14396i	−1.23337	−	0.593959i	−0.300364	−	0.953825i	$-0.597108\pi$
$107$	−12.7581	−	6.14396i	−1.23337	−	0.593959i	−0.933004	+	0.359866i	$0.882823\pi$
$108$	−10.3321	+	1.11683i	−0.994209	+	0.107467i
$109$	4.13850	−	18.1320i	0.396397	−	1.73673i	−0.245004	−	0.969522i	$-0.578789\pi$
$109$	4.13850	−	18.1320i	0.396397	−	1.73673i	0.641401	−	0.767206i	$-0.278354\pi$
$110$	−0.618044	+	1.29557i	−0.0589282	+	0.123528i
$111$	4.78022	+	4.81828i	0.453718	+	0.457331i
$112$	0.00266830	+	0.00533803i	0.000252130	+	0.000504396i
$113$	−3.47830	+	15.2394i	−0.327211	+	1.43361i	0.497211	+	0.867630i	$0.334357\pi$
$113$	−3.47830	+	15.2394i	−0.327211	+	1.43361i	−0.824422	+	0.565976i	$0.808500\pi$
$114$	13.9950	+	4.90146i	1.31075	+	0.459064i
$115$		−	10.3926i		−	0.969116i
$116$	−9.85428	+	4.34663i	−0.914947	+	0.403574i
$117$	15.0959	+	3.57173i	1.39562	+	0.330207i
$118$	−10.9177	−	2.44959i	−1.00505	−	0.225503i
$119$	0.00111787		0.000255146i	0.000102475		2.33892e-5i
$120$	14.0212	+	1.47920i	1.27995	+	0.135032i
$121$	6.78083	−	8.50290i	0.616439	−	0.772991i
$122$	−7.09664	−	3.38540i	−0.642500	−	0.306500i
$123$	−0.330732	+	0.933291i	−0.0298211	+	0.0841520i
$124$	3.62327	−	1.77789i	0.325379	−	0.159659i
$125$	−2.14458	+	4.45326i	−0.191817	+	0.398312i
$126$	0.00272216	+	0.00571455i	0.000242509	+	0.000509092i
$127$	2.60598	−	1.25498i	0.231244	−	0.111361i	−0.314674	−	0.949200i	$-0.601895\pi$
$127$	2.60598	−	1.25498i	0.231244	−	0.111361i	0.545918	+	0.837839i	$0.316181\pi$
$128$	−0.291822	−	11.3099i	−0.0257936	−	0.999667i
$129$	−11.8560	+	4.09590i	−1.04386	+	0.360624i
$130$	−18.9951	−	9.06146i	−1.66598	−	0.794742i
$131$	1.21328	−	0.967559i	0.106005	−	0.0845360i	−0.569053	−	0.822301i	$-0.692690\pi$
$131$	1.21328	−	0.967559i	0.106005	−	0.0845360i	0.675058	+	0.737765i	$0.264119\pi$
$132$	1.15455	+	0.399586i	0.100491	+	0.0347795i
$133$		−	0.00903180i		−	0.000783156i
$134$	1.44360	−	1.82397i	0.124708	−	0.157567i
$135$	14.8392	+	1.85098i	1.27716	+	0.159307i
$136$	−1.71439	−	1.33644i	−0.147008	−	0.114599i
$137$	−6.14626	−	2.95988i	−0.525110	−	0.252880i	0.152497	−	0.988304i	$-0.451269\pi$
$137$	−6.14626	−	2.95988i	−0.525110	−	0.252880i	−0.677607	+	0.735424i	$0.736983\pi$
$138$	−8.79008	+	0.987913i	−0.748262	+	0.0840967i
$139$	−9.86987	+	7.87096i	−0.837152	+	0.667606i	−0.945183	−	0.326541i	$-0.894117\pi$
$139$	−9.86987	+	7.87096i	−0.837152	+	0.667606i	0.108031	+	0.994148i	$0.465545\pi$
$140$	−0.00197254	−	0.00835784i	−0.000166710	−	0.000706366i
$141$	−12.5525	+	1.36395i	−1.05711	+	0.114865i
$142$	−16.5622	+	3.84449i	−1.38987	+	0.322623i
$143$	−1.42583	−	1.13706i	−0.119234	−	0.0950861i
$144$	−0.0817271	−	11.9997i	−0.00681059	−	0.999977i
$145$	15.2376	−	2.83027i	1.26541	−	0.235041i
$146$	−0.266508	+	0.129555i	−0.0220563	+	0.0107221i
$147$	−8.60714	+	8.53915i	−0.709905	+	0.704297i
$148$	−6.09119	+	4.93145i	−0.500693	+	0.405362i
$149$	−9.41130	+	2.14807i	−0.771004	+	0.175977i	−0.589888	−	0.807485i	$-0.700828\pi$
$149$	−9.41130	+	2.14807i	−0.771004	+	0.175977i	−0.181116	+	0.983462i	$0.557971\pi$
$150$	−7.58859	−	2.65775i	−0.619606	−	0.217004i
$151$	−7.42950	+	5.92483i	−0.604604	+	0.482156i	−0.877299	−	0.479945i	$-0.840657\pi$
$151$	−7.42950	+	5.92483i	−0.604604	+	0.482156i	0.272694	+	0.962101i	$0.412085\pi$
$152$	−7.25816	+	15.5080i	−0.588714	+	1.25787i
$153$	−1.79114	−	1.45178i	−0.144805	−	0.117369i
$154$	−2.74232e−6	0	0.000744138i	−2.20983e−7	0	5.99644e-5i
$155$	−5.66201	+	1.29232i	−0.454784	+	0.103801i
$156$	−5.85854	+	16.9274i	−0.469058	+	1.35528i
$157$			24.0857i			1.92225i	0.276110	+	0.961126i	$0.410955\pi$
$157$			24.0857i			1.92225i	−0.276110	+	0.961126i	$0.589045\pi$
$158$	−8.40179	−	6.64970i	−0.668411	−	0.529022i
$159$	−14.5559	+	9.06577i	−1.15436	+	0.718962i
$160$	−3.32960	+	15.9360i	−0.263228	+	1.25985i
$161$	0.00233759	+	0.00485406i	0.000184228	+	0.000382554i
$162$	0.154961	−	12.7270i	0.0121749	−	0.999926i
$163$	10.7692	−	5.18619i	0.843512	−	0.406214i	0.0383468	−	0.999264i	$-0.487791\pi$
$163$	10.7692	−	5.18619i	0.843512	−	0.406214i	0.805165	+	0.593050i	$0.202077\pi$
$164$	−1.03374	−	0.488470i	−0.0807215	−	0.0381431i
$165$	−1.48486	−	0.941234i	−0.115596	−	0.0732750i
$166$	0.0716644	+	19.4464i	0.00556224	+	1.50933i
$167$	−4.05783	+	17.7785i	−0.314004	+	1.37574i	0.533880	+	0.845560i	$0.320733\pi$
$167$	−4.05783	+	17.7785i	−0.314004	+	1.37574i	−0.847884	+	0.530182i	$0.822124\pi$
$168$	−0.00688156	+	0.00246287i	−0.000530924	+	0.000190014i
$169$	8.56571	−	10.7411i	0.658901	−	0.826235i
$170$	1.95925	+	2.43834i	0.150268	+	0.187012i
$171$	−8.00933	+	16.2996i	−0.612489	+	1.24646i
$172$	−3.32700	−	14.0968i	−0.253681	−	1.07487i
$173$		−	17.4421i		−	1.32610i	−0.748575	−	0.663050i	$-0.769262\pi$
$173$		−	17.4421i		−	1.32610i	0.748575	−	0.663050i	$-0.230738\pi$
$174$	−3.84231	−	12.6189i	−0.291285	−	0.956636i
$175$			0.00489737i			0.000370206i
$176$	−0.593298	+	1.27992i	−0.0447215	+	0.0964778i
$177$	4.57733	−	12.9167i	0.344053	−	0.970881i
$178$	−16.9377	+	13.6098i	−1.26954	+	1.02010i
$179$	14.9561	−	18.7544i	1.11787	−	1.40177i	0.212495	−	0.977162i	$-0.431841\pi$
$179$	14.9561	−	18.7544i	1.11787	−	1.40177i	0.905378	−	0.424606i	$-0.139587\pi$
$180$	−3.85183	+	16.8326i	−0.287099	+	1.25462i
$181$	−0.104310	+	0.457013i	−0.00775333	+	0.0339695i	−0.978657	−	0.205502i	$-0.934117\pi$
$181$	−0.104310	+	0.457013i	−0.00775333	+	0.0339695i	0.970903	+	0.239472i	$0.0769743\pi$
$182$	0.0109102		4.02065e-5i	0.000808716		2.98031e-6i
$183$	5.15570	−	8.13349i	0.381121	−	0.601245i
$184$	−0.112918	−	10.2132i	−0.00832443	−	0.752927i
$185$	10.1607	−	4.89312i	0.747028	−	0.359750i
$186$	1.63127	+	4.66609i	0.119610	+	0.342134i
$187$	0.117605	+	0.244210i	0.00860016	+	0.0178584i
$188$	−0.107458	−	14.5793i	−0.00783715	−	1.06330i
$189$	−0.00734727	+	0.00247322i	−0.000534435	+	0.000179901i
$190$	15.2909	−	19.3198i	1.10932	−	1.40161i
$191$			20.9787i			1.51796i	0.651111	+	0.758982i	$0.274303\pi$
$191$			20.9787i			1.51796i	−0.651111	+	0.758982i	$0.725697\pi$
$192$	13.7952	+	1.30132i	0.995580	+	0.0939149i
$193$	−6.35294	+	1.45002i	−0.457294	+	0.104374i	−0.444962	−	0.895549i	$-0.646783\pi$
$193$	−6.35294	+	1.45002i	−0.457294	+	0.104374i	−0.0123325	+	0.999924i	$0.503926\pi$
$194$	−22.0331	+	0.0811972i	−1.58189	+	0.00582962i
$195$	13.7999	−	21.7703i	0.988231	−	1.55900i
$196$	−8.80929	−	10.8810i	−0.629235	−	0.777215i
$197$	−4.66689	+	3.72172i	−0.332502	+	0.265162i	−0.775482	−	0.631370i	$-0.782493\pi$
$197$	−4.66689	+	3.72172i	−0.332502	+	0.265162i	0.442980	+	0.896532i	$0.353921\pi$
$198$	−0.654947	+	1.34537i	−0.0465450	+	0.0956114i
$199$	−15.6850	+	3.58001i	−1.11188	+	0.253780i	−0.738738	−	0.673993i	$-0.764578\pi$
$199$	−15.6850	+	3.58001i	−1.11188	+	0.253780i	−0.373145	+	0.927773i	$0.621721\pi$
$200$	3.93564	−	8.40900i	0.278291	−	0.594606i
$201$	2.00648	+	2.02246i	0.141526	+	0.142653i
$202$	1.00497	+	2.06731i	0.0707091	+	0.145455i
$203$	−0.00648038	+	0.00474929i	−0.000454833	+	0.000333335i
$204$	1.87610	−	1.88893i	0.131354	−	0.132251i
$205$	1.28629	+	1.02578i	0.0898385	+	0.0716438i
$206$	3.60963	+	15.5505i	0.251495	+	1.08345i
$207$	0.0859102	−	10.8330i	0.00597117	−	0.752949i
$208$	−18.7656	−	8.69863i	−1.30116	−	0.603142i
$209$	1.66926	−	1.33119i	0.115465	−	0.0920803i
$210$	0.0104516	−	0.00117465i	0.000721232	−	8.10589e-5i
$211$	17.9140	+	8.62694i	1.23325	+	0.593903i	0.932972	−	0.359948i	$-0.117206\pi$
$211$	17.9140	+	8.62694i	1.23325	+	0.593903i	0.300280	+	0.953851i	$0.402920\pi$
$212$	−8.72262	−	17.7764i	−0.599072	−	1.22089i
$213$	−2.24946	−	20.7020i	−0.154131	−	1.41848i
$214$	15.7027	+	12.4281i	1.07342	+	0.849567i
$215$			20.8421i			1.42142i
$216$	14.6031	+	1.65780i	0.993618	+	0.112799i
$217$	0.00235387	−	0.00187715i	0.000159791	−	0.000127429i
$218$	−11.3246	+	23.7391i	−0.766997	+	1.60782i
$219$	−0.118508	−	0.343034i	−0.00800804	−	0.0231801i
$220$	1.25397	−	1.59642i	0.0845423	−	0.107631i
$221$	−3.58049	+	1.72427i	−0.240850	+	0.115987i
$222$	−5.10448	−	8.12878i	−0.342590	−	0.545568i
$223$	11.9790	−	24.8746i	0.802170	−	1.66572i	0.0574488	−	0.998348i	$-0.481703\pi$
$223$	11.9790	−	24.8746i	0.802170	−	1.66572i	0.744721	−	0.667375i	$-0.232582\pi$
$224$	−0.00202930	−	0.00819211i	−0.000135588	−	0.000547359i
$225$	4.34295	−	8.83823i	0.289530	−	0.589216i
$226$	9.51800	−	19.9521i	0.633128	−	1.32719i
$227$	−1.95720	+	2.45425i	−0.129904	+	0.162894i	−0.842529	−	0.538650i	$-0.818934\pi$
$227$	−1.95720	+	2.45425i	−0.129904	+	0.162894i	0.712626	+	0.701544i	$0.247506\pi$
$228$	−17.7943	−	11.0965i	−1.17845	−	0.734886i
$229$	−7.27987	−	1.66158i	−0.481067	−	0.109801i	−0.0248916	−	0.999690i	$-0.507924\pi$
$229$	−7.27987	−	1.66158i	−0.481067	−	0.109801i	−0.456176	+	0.889890i	$0.650781\pi$
$230$	−3.21765	+	14.3408i	−0.212165	+	0.945607i
$231$	0.000905243	0	0.000105633i	5.95606e−5	0	6.95014e-6i
$232$	14.9437	−	2.94697i	0.981105	−	0.193478i
$233$			3.85720i			0.252694i	0.991986	+	0.126347i	$0.0403252\pi$
$233$			3.85720i			0.252694i	−0.991986	+	0.126347i	$0.959675\pi$
$234$	−19.7252	−	9.60250i	−1.28947	−	0.627735i
$235$	−4.66843	+	20.4537i	−0.304535	+	1.33425i
$236$	14.3069	+	6.76041i	0.931303	+	0.440066i
$237$	9.31608	−	9.24249i	0.605144	−	0.600364i
$238$	−0.00146356		0.000698180i	−9.48684e−5		4.52563e-5i
$239$	−3.63370	+	15.9203i	−0.235045	+	1.02980i	0.710344	+	0.703854i	$0.248539\pi$
$239$	−3.63370	+	15.9203i	−0.235045	+	1.02980i	−0.945389	+	0.325944i	$0.894318\pi$
$240$	−18.8899	−	6.38224i	−1.21934	−	0.411972i
$241$	−16.2889	−	7.84431i	−1.04926	−	0.505296i	−0.171891	−	0.985116i	$-0.554988\pi$
$241$	−16.2889	−	7.84431i	−1.04926	−	0.505296i	−0.877367	+	0.479820i	$0.840702\pi$
$242$	−11.9895	+	9.63380i	−0.770714	+	0.619284i
$243$	15.4528	+	2.05210i	0.991297	+	0.131642i
$244$	8.74455	+	6.86872i	0.559813	+	0.439725i
$245$	8.74084	+	18.1505i	0.558432	+	1.15960i
$246$	0.745335	−	1.18546i	0.0475208	−	0.0755820i
$247$	19.5172	+	24.4738i	1.24185	+	1.55723i
$248$	−5.55022	+	1.33153i	−0.352439	+	0.0845519i
$249$	−23.6565	−	2.76048i	−1.49917	−	0.174938i
$250$	4.33809	−	5.48111i	0.274365	−	0.346656i
$251$	21.0903	−	4.81372i	1.33121	−	0.303839i	0.503012	−	0.864279i	$-0.332225\pi$
$251$	21.0903	−	4.81372i	1.33121	−	0.303839i	0.828195	+	0.560440i	$0.189368\pi$
$252$	−0.00198705	−	0.00872834i	−0.000125172	−	0.000549834i
$253$	−0.552593	+	1.14747i	−0.0347412	+	0.0721409i
$254$	−3.98457	+	0.924913i	−0.250014	+	0.0580342i
$255$	−3.25182	+	2.02532i	−0.203637	+	0.126830i
$256$	−3.09897	+	15.6970i	−0.193686	+	0.981064i
$257$	−1.35034	+	0.308205i	−0.0842316	+	0.0192253i	−0.264429	−	0.964405i	$-0.585183\pi$
$257$	−1.35034	+	0.308205i	−0.0842316	+	0.0192253i	0.180197	+	0.983630i	$0.442326\pi$
$258$	17.6283	−	1.98124i	1.09749	−	0.123346i
$259$	−0.00364513	+	0.00457085i	−0.000226497	+	0.000284019i
$260$	23.4059	+	18.3850i	1.45157	+	1.14019i
$261$	15.9067	−	2.82425i	0.984601	−	0.174817i
$262$	−1.97378	+	0.959498i	−0.121940	+	0.0592780i
$263$	−9.61349	−	7.66650i	−0.592793	−	0.472737i	0.280552	−	0.959839i	$-0.409483\pi$
$263$	−9.61349	−	7.66650i	−0.592793	−	0.472737i	−0.873345	+	0.487102i	$0.838054\pi$
$264$	−1.46945	−	0.908851i	−0.0904387	−	0.0559359i
$265$	6.34033	+	27.7788i	0.389483	+	1.70644i
$266$	−0.00279633	+	0.0124630i	−0.000171454	+	0.000764158i
$267$	−14.0687	−	22.5886i	−0.860991	−	1.38240i
$268$	−2.55676	+	2.06996i	−0.156179	+	0.126443i
$269$	16.9525	+	8.16389i	1.03361	+	0.497761i	0.872212	−	0.489128i	$-0.162685\pi$
$269$	16.9525	+	8.16389i	1.03361	+	0.497761i	0.161400	+	0.986889i	$0.448399\pi$
$270$	−19.9037	−	7.14854i	−1.21130	−	0.435046i
$271$	−1.02758	−	4.50214i	−0.0624213	−	0.273485i	0.934080	−	0.357064i	$-0.116222\pi$
$271$	−1.02758	−	4.50214i	−0.0624213	−	0.273485i	−0.996501	+	0.0835786i	$0.973365\pi$
$272$	1.95192	+	2.37495i	0.118353	+	0.144003i
$273$	−0.00154874	+	0.0132722i	−9.37339e−5	+	0.000803271i
$274$	7.56485	+	5.98729i	0.457009	+	0.361706i
$275$	−0.905132	+	0.721819i	−0.0545815	+	0.0435273i
$276$	12.4354	+	1.35826i	0.748521	+	0.0817577i
$277$	−9.71584	+	4.67890i	−0.583768	+	0.281128i	−0.702368	−	0.711814i	$-0.747874\pi$
$277$	−9.71584	+	4.67890i	−0.583768	+	0.281128i	0.118600	+	0.992942i	$0.462160\pi$
$278$	16.0564	−	7.80539i	0.963000	−	0.468136i
$279$	−5.91265	+	1.30028i	−0.353981	+	0.0778457i
$280$	0.000134262		0.0121438i	8.02372e−6		0.000725728i
$281$	−10.0769	+	20.9249i	−0.601136	+	1.24827i	0.349200	+	0.937048i	$0.386453\pi$
$281$	−10.0769	+	20.9249i	−0.601136	+	1.24827i	−0.950337	+	0.311224i	$0.899261\pi$
$282$	17.7436	+	2.00425i	1.05661	+	0.119351i
$283$	2.44417	+	0.557866i	0.145291	+	0.0331617i	0.294548	−	0.955637i	$-0.404831\pi$
$283$	2.44417	+	0.557866i	0.145291	+	0.0331617i	−0.149257	+	0.988798i	$0.547688\pi$
$284$	24.0446	−	0.177222i	1.42679	−	0.0105162i
$285$	21.2530	+	21.4222i	1.25892	+	1.26894i
$286$	1.61547	+	2.01049i	0.0955249	+	0.118883i
$287$	−0.000831514	0	0.000189788i	−4.90827e−5	0	1.12028e-5i
$288$	−3.60245	+	16.5838i	−0.212276	+	0.977210i
$289$	−16.4093			−0.965256
$290$	−21.9027	−	0.812177i	−1.28617	−	0.0476927i
$291$	3.12768	−	26.8033i	0.183348	−	1.57124i
$292$	0.407867	−	0.0962612i	0.0238686	−	0.00563326i
$293$	−0.554417	+	2.42906i	−0.0323894	+	0.141907i	−0.988537	−	0.150977i	$-0.951758\pi$
$293$	−0.554417	+	2.42906i	−0.0323894	+	0.141907i	0.956148	+	0.292884i	$0.0946151\pi$
$294$	14.5208	−	9.11838i	0.846873	−	0.531795i
$295$	−17.8023	−	14.1968i	−1.03649	−	0.826571i
$296$	9.93210	−	4.91905i	0.577291	−	0.285914i
$297$	−1.54001	−	0.993397i	−0.0893604	−	0.0576428i
$298$	13.6518	−	0.0503099i	0.790826	−	0.00291438i
$299$	−16.8236	−	8.10184i	−0.972936	−	0.468541i
$300$	9.64869	+	6.01694i	0.557067	+	0.347388i
$301$	−0.00468799	−	0.00973470i	−0.000270211	−	0.000561099i
$302$	12.0864	−	5.87547i	0.695494	−	0.338095i
$303$	−2.66092	+	0.919271i	−0.152866	+	0.0528108i
$304$	14.8170	−	19.1524i	0.849813	−	1.09847i
$305$	−9.97636	−	12.5100i	−0.571245	−	0.716318i
$306$	2.02213	+	2.55787i	0.115597	+	0.146224i
$307$	−0.357640			−0.0204116			−0.0102058	−	0.999948i	$-0.503249\pi$
$307$	−0.357640			−0.0204116			−0.0102058	+	0.999948i	$0.503249\pi$
$308$	−0.000226608		0.00102769i	−1.29122e−5		5.85581e-5i
$309$	−19.4373	+	2.11204i	−1.10575	+	0.120150i
$310$	8.21316	−	0.0302674i	0.466476	−	0.00171907i
$311$	6.22808	−	12.9327i	0.353162	−	0.733348i	−0.646398	−	0.763000i	$-0.723726\pi$
$311$	6.22808	−	12.9327i	0.353162	−	0.733348i	0.999560	+	0.0296520i	$0.00943990\pi$
$312$	13.3251	−	21.5444i	0.754386	−	1.21971i
$313$	5.14335	+	6.44956i	0.290720	+	0.364551i	0.905647	−	0.424033i	$-0.139386\pi$
$313$	5.14335	+	6.44956i	0.290720	+	0.364551i	−0.614927	+	0.788584i	$0.710815\pi$
$314$	7.45716	−	33.2361i	0.420832	−	1.87562i
$315$	−0.000102149		0.0128808i	−5.75547e−6		0.000725750i
$316$	9.53488	+	11.7772i	0.536379	+	0.662521i
$317$	11.8165	−	14.8175i	0.663683	−	0.832233i	−0.330055	−	0.943962i	$-0.607067\pi$
$317$	11.8165	−	14.8175i	0.663683	−	0.832233i	0.993739	+	0.111729i	$0.0356388\pi$
$318$	22.8926	−	8.00328i	1.28375	−	0.448802i
$319$	−1.83290	−	0.497711i	−0.102623	−	0.0278664i
$320$	9.52846	−	20.9593i	0.532657	−	1.17166i
$321$	−17.4115	+	17.2740i	−0.971814	+	0.964138i
$322$	−0.00172280	−	0.00742190i	−9.60079e−5	−	0.000413606i
$323$	−1.03528	−	4.53586i	−0.0576045	−	0.252382i
$324$	−4.15422	+	17.5141i	−0.230790	+	0.973004i
$325$	−10.5829	−	13.2706i	−0.587036	−	0.736120i
$326$	−16.4662	+	3.82221i	−0.911981	+	0.211693i
$327$	−27.2075	−	17.2464i	−1.50458	−	0.953731i
$328$	1.27523	+	0.994098i	0.0704128	+	0.0548899i
$329$	−0.00242015	−	0.0106034i	−0.000133427	−	0.000584582i
$330$	1.75756	+	1.75854i	0.0967504	+	0.0968045i
$331$	10.9614			0.602494			0.301247	−	0.953546i	$-0.402597\pi$
$331$	10.9614			0.602494			0.301247	+	0.953546i	$0.402597\pi$
$332$	5.92188	−	26.8564i	0.325005	−	1.47393i
$333$	10.6317	−	5.01650i	0.582615	−	0.274903i
$334$	11.1038	−	23.2763i	0.607573	−	1.27362i
$335$	4.26491	−	2.05387i	0.233017	−	0.112215i
$336$	0.0102584	−	0.00126793i	0.000559643	−	6.91715e-5i
$337$	9.33467	+	19.3836i	0.508492	+	1.05589i	0.984326	+	0.176359i	$0.0564319\pi$
$337$	9.33467	+	19.3836i	0.508492	+	1.05589i	−0.475834	+	0.879535i	$0.657854\pi$
$338$	−15.1454	+	12.1696i	−0.823801	+	0.661941i
$339$	22.8672	+	14.4952i	1.24197	+	0.787270i
$340$	−1.94866	−	3.97128i	−0.105681	−	0.215373i
$341$	0.693870	+	0.158371i	0.0375751	+	0.00857628i
$342$	16.0986	−	20.0122i	0.870514	−	1.08213i
$343$	−0.0163303	−	0.0130230i	−0.000881753	−	0.000703174i
$344$	0.226454	+	20.4823i	0.0122096	+	1.10433i
$345$	−16.9667	−	6.01252i	−0.913456	−	0.323703i
$346$	−5.40024	+	24.0685i	−0.290319	+	1.29393i
$347$	−8.91535			−0.478601			−0.239301	−	0.970946i	$-0.576918\pi$
$347$	−8.91535			−0.478601			−0.239301	+	0.970946i	$0.576918\pi$
$348$	1.39511	+	18.6025i	0.0747858	+	0.997200i
$349$	11.6049			0.621199			0.310599	−	0.950541i	$-0.399470\pi$
$349$	11.6049			0.621199			0.310599	+	0.950541i	$0.399470\pi$
$350$	0.00151627	−	0.00675791i	8.10480e−5	−	0.000361225i
$351$	14.5647	−	22.5789i	0.777406	−	1.20517i
$352$	1.21497	−	1.58248i	0.0647582	−	0.0843466i
$353$	18.4517	+	14.7147i	0.982082	+	0.783185i	0.976216	−	0.216798i	$-0.0695613\pi$
$353$	18.4517	+	14.7147i	0.982082	+	0.783185i	0.00586604	+	0.999983i	$0.498133\pi$
$354$	−10.3154	+	16.4067i	−0.548258	+	0.872006i
$355$	−33.7329	−	7.69932i	−1.79036	−	0.408638i
$356$	27.5862	−	13.5362i	1.46207	−	0.717417i
$357$	0.00106327	−	0.00167739i	5.62744e−5	−	8.87768e-5i
$358$	−26.4446	+	21.2487i	−1.39764	+	1.12303i
$359$	−2.32563	−	4.82921i	−0.122742	−	0.254876i	0.830540	−	0.556960i	$-0.188032\pi$
$359$	−2.32563	−	4.82921i	−0.122742	−	0.254876i	−0.953281	+	0.302083i	$0.902318\pi$
$360$	10.5267	−	22.0348i	0.554805	−	1.16134i
$361$	−15.8997	+	7.65692i	−0.836829	+	0.402996i
$362$	0.285434	−	0.598340i	0.0150021	−	0.0314481i
$363$	−9.95863	−	15.9895i	−0.522692	−	0.839229i
$364$	−0.0150675	−	0.00332241i	−0.000789750	−	0.000174141i
$365$	−0.603033			−0.0315642
$366$	−9.63259	+	9.62720i	−0.503504	+	0.503222i
$367$	−3.59607	−	15.7554i	−0.187714	−	0.822427i	−0.977818	−	0.209455i	$-0.932831\pi$
$367$	−3.59607	−	15.7554i	−0.187714	−	0.822427i	0.790105	−	0.612972i	$-0.210026\pi$
$368$	−3.00628	+	14.1282i	−0.156713	+	0.736484i
$369$	1.33232	+	1.07989i	0.0693580	+	0.0562168i
$370$	−15.5357	+	3.60622i	−0.807665	+	0.187478i
$371$	−0.00920961	−	0.0115485i	−0.000478139	−	0.000599567i
$372$	−0.806336	−	6.94382i	−0.0418066	−	0.360020i
$373$	−4.04156	−	17.7072i	−0.209264	−	0.916846i	−0.965058	−	0.262036i	$-0.915606\pi$
$373$	−4.04156	−	17.7072i	−0.209264	−	0.916846i	0.755794	−	0.654810i	$-0.227251\pi$
$374$	−0.0866749	−	0.373399i	−0.00448185	−	0.0193080i
$375$	6.02956	+	6.07756i	0.311365	+	0.313844i
$376$	−4.36560	+	20.1513i	−0.225139	+	1.03923i
$377$	7.29718	−	26.8731i	0.375824	−	1.38403i
$378$	0.0109043	−	0.00113804i	0.000560856	−	5.85343e-5i
$379$	−2.39271	+	3.00036i	−0.122905	+	0.154118i	−0.839477	−	0.543395i	$-0.817139\pi$
$379$	−2.39271	+	3.00036i	−0.122905	+	0.154118i	0.716572	+	0.697513i	$0.245710\pi$
$380$	−27.0816	+	21.9253i	−1.38926	+	1.12475i
$381$	−0.541179	−	4.98051i	−0.0277254	−	0.255159i
$382$	6.49519	−	28.9486i	0.332323	−	1.48114i
$383$	−3.35831	−	4.21119i	−0.171602	−	0.215182i	0.688592	−	0.725149i	$-0.258229\pi$
$383$	−3.35831	−	4.21119i	−0.171602	−	0.215182i	−0.860194	+	0.509967i	$0.829658\pi$
$384$	−18.6331	−	6.06681i	−0.950868	−	0.309596i
$385$	0.000657047	−	0.00136437i	3.34862e−5	−	6.95349e-5i
$386$	9.21540	−	0.0339609i	0.469051	−	0.00172856i
$387$	−0.172291	+	21.7254i	−0.00875803	+	1.10436i
$388$	30.4288	+	6.70961i	1.54479	+	0.340629i
$389$	−11.9625			−0.606524			−0.303262	−	0.952907i	$-0.598076\pi$
$389$	−11.9625			−0.606524			−0.303262	+	0.952907i	$0.598076\pi$
$390$	−25.7829	+	25.7684i	−1.30557	+	1.30484i
$391$	1.73036	+	2.16981i	0.0875083	+	0.109732i
$392$	8.78714	+	17.7422i	0.443818	+	0.896117i
$393$	−0.877682	−	2.54054i	−0.0442732	−	0.128153i
$394$	7.59215	−	3.69071i	0.382487	−	0.185936i
$395$	−9.46079	−	19.6455i	−0.476024	−	0.988474i
$396$	1.32030	−	1.65371i	0.0663478	−	0.0831020i
$397$	8.99715	+	4.33280i	0.451554	+	0.217457i	0.645817	−	0.763493i	$-0.276517\pi$
$397$	8.99715	+	4.33280i	0.451554	+	0.217457i	−0.194262	+	0.980950i	$0.562231\pi$
$398$	22.7523	−	0.0838475i	1.14047	−	0.00420289i
$399$	−0.0147451	−	0.00522524i	−0.000738177	−	0.000261589i
$400$	−8.03431	+	10.3851i	−0.401716	+	0.519256i
$401$	16.3327	+	13.0249i	0.815616	+	0.650432i	0.939761	−	0.341832i	$-0.111047\pi$
$401$	16.3327	+	13.0249i	0.815616	+	0.650432i	−0.124145	+	0.992264i	$0.539619\pi$
$402$	−2.14259	−	3.41203i	−0.106862	−	0.170176i
$403$	−2.32196	+	10.1732i	−0.115665	+	0.506762i
$404$	−0.746701	−	3.16384i	−0.0371498	−	0.157407i
$405$	11.6069	−	23.1552i	0.576752	−	1.15059i
$406$	0.0104127	−	0.00454719i	0.000516776	−	0.000225673i
$407$	−1.38204			−0.0685051
$408$	−3.17368	+	2.02568i	−0.157120	+	0.100286i
$409$	−7.85966	−	1.79392i	−0.388635	−	0.0887035i	0.0237385	−	0.999718i	$-0.492443\pi$
$409$	−7.85966	−	1.79392i	−0.388635	−	0.0887035i	−0.412374	+	0.911015i	$0.635300\pi$
$410$	−1.45737	−	1.81373i	−0.0719744	−	0.0895739i
$411$	−8.38806	+	8.32181i	−0.413753	+	0.410484i
$412$	−0.166396	−	22.5758i	−0.00819774	−	1.11223i
$413$	0.0115081	+	0.00262666i	0.000566279	+	0.000129249i
$414$	−3.47256	+	14.9220i	−0.170667	+	0.733376i
$415$	−17.1705	+	35.6548i	−0.842864	+	1.75023i
$416$	23.2016	+	17.8133i	1.13755	+	0.873369i
$417$	7.13982	+	20.6669i	0.349639	+	1.01206i
$418$	−2.71557	+	1.32010i	−0.132823	+	0.0645682i
$419$	17.3604	−	8.36034i	0.848112	−	0.408429i	0.0412357	−	0.999149i	$-0.486871\pi$
$419$	17.3604	−	8.36034i	0.848112	−	0.408429i	0.806877	+	0.590720i	$0.201156\pi$
$420$	−0.0147860	−	0.00161501i	−0.000721481	−	7.88043e-5i
$421$	−16.4662	+	13.1314i	−0.802514	+	0.639984i	−0.936369	−	0.351017i	$-0.885836\pi$
$421$	−16.4662	+	13.1314i	−0.802514	+	0.639984i	0.133855	+	0.991001i	$0.457264\pi$
$422$	−22.0487	−	17.4507i	−1.07331	−	0.849488i
$423$	−5.03536	+	21.2820i	−0.244828	+	1.03476i
$424$	6.53269	+	27.2303i	0.317255	+	1.32242i
$425$	0.561366	+	2.45951i	0.0272303	+	0.119304i
$426$	−3.30547	+	29.2632i	−0.160151	+	1.41781i
$427$	0.00747349	+	0.00359904i	0.000361667	+	0.000174170i
$428$	−17.8204	−	22.0113i	−0.861383	−	1.06396i
$429$	−2.68124	+	1.66994i	−0.129452	+	0.0806256i
$430$	6.45291	−	28.7602i	0.311187	−	1.38694i
$431$	−2.99715	−	13.1314i	−0.144368	−	0.632516i	−0.994391	−	0.105770i	$-0.966269\pi$
$431$	−2.99715	−	13.1314i	−0.144368	−	0.632516i	0.850023	−	0.526746i	$-0.176588\pi$
$432$	−19.6377	−	6.80887i	−0.944819	−	0.327592i
$433$	−23.4207	−	18.6774i	−1.12553	−	0.897578i	−0.129949	−	0.991521i	$-0.541481\pi$
$433$	−23.4207	−	18.6774i	−1.12553	−	0.897578i	−0.995578	+	0.0939431i	$0.970053\pi$
$434$	−0.00382930	+	0.00186151i	−0.000183812	+	8.93553e-5i
$435$	4.19489	−	26.5138i	0.201129	−	1.27124i
$436$	22.9767	−	29.2516i	1.10038	−	1.40090i
$437$	13.6299	−	17.0914i	0.652008	−	0.817593i
$438$	0.0573238	+	0.510046i	0.00273904	+	0.0243709i
$439$	32.1394	−	7.33561i	1.53393	−	0.350110i	0.629592	−	0.776926i	$-0.283222\pi$
$439$	32.1394	−	7.33561i	1.53393	−	0.350110i	0.904338	+	0.426816i	$0.140365\pi$
$440$	−2.22462	+	1.81467i	−0.106055	+	0.0865111i
$441$	8.96123	+	18.9920i	0.426725	+	0.904381i
$442$	5.47459	−	1.27078i	0.260400	−	0.0604450i
$443$	−13.4834	+	27.9986i	−0.640617	+	1.33026i	0.287433	+	0.957801i	$0.407198\pi$
$443$	−13.4834	+	27.9986i	−0.640617	+	1.33026i	−0.928050	+	0.372455i	$0.878516\pi$
$444$	4.52696	+	12.7973i	0.214840	+	0.607335i
$445$	−43.1085	+	9.83923i	−2.04354	+	0.466424i
$446$	−24.2312	+	30.6158i	−1.14738	+	1.44970i
$447$	−1.93792	+	16.6074i	−0.0916603	+	0.785501i
$448$	0.000263889		0.0119326i	1.24676e−5		0.000563764i
$449$	−10.7493	−	13.4791i	−0.507289	−	0.636120i	0.460567	−	0.887625i	$-0.347646\pi$
$449$	−10.7493	−	13.4791i	−0.507289	−	0.636120i	−0.967856	+	0.251505i	$0.919075\pi$
$450$	−8.72926	+	10.8513i	−0.411501	+	0.511536i
$451$	−0.0874796	−	0.181653i	−0.00411925	−	0.00855372i
$452$	−19.3113	+	24.5852i	−0.908327	+	1.15639i
$453$	5.37447	+	15.5569i	0.252514	+	0.730929i
$454$	3.46061	−	2.78067i	0.162414	−	0.130503i
$455$	0.0200037	+	0.00963330i	0.000937790	+	0.000451616i
$456$	21.1188	+	20.8214i	0.988980	+	0.975053i
$457$	−0.617311	+	2.70462i	−0.0288766	+	0.126517i	−0.987312	−	0.158794i	$-0.949240\pi$
$457$	−0.617311	+	2.70462i	−0.0288766	+	0.126517i	0.958435	+	0.285310i	$0.0920967\pi$
$458$	9.53110	+	4.54674i	0.445359	+	0.212455i
$459$	−3.40638	+	2.08427i	−0.158996	+	0.0972852i
$460$	8.88010	−	18.7928i	0.414037	−	0.876219i
$461$	−6.56259	+	28.7526i	−0.305650	+	1.33914i	0.555807	+	0.831311i	$0.312409\pi$
$461$	−6.56259	+	28.7526i	−0.305650	+	1.33914i	−0.861457	+	0.507830i	$0.830448\pi$
$462$	−0.00121645		0.000426035i	−5.65942e−5		1.98209e-5i
$463$			11.1962i			0.520330i	0.965564	+	0.260165i	$0.0837770\pi$
$463$			11.1962i			0.520330i	−0.965564	+	0.260165i	$0.916223\pi$
$464$	−21.5334	−	0.560178i	−0.999662	−	0.0260056i
$465$	−1.16589	+	9.99130i	−0.0540667	+	0.463336i
$466$	1.19422	−	5.32258i	0.0553213	−	0.246564i
$467$	19.6141	+	4.47680i	0.907634	+	0.207161i	0.650760	−	0.759284i	$-0.274450\pi$
$467$	19.6141	+	4.47680i	0.907634	+	0.207161i	0.256874	+	0.966445i	$0.417308\pi$
$468$	24.2459	+	19.3576i	1.12077	+	0.894807i
$469$	−0.00153003	+	0.00191860i	−7.06503e−5	+	8.85927e-5i
$470$	12.7747	−	26.7789i	0.589251	−	1.23522i
$471$	39.3217	+	13.9345i	1.81185	+	0.642069i
$472$	−17.6492	−	13.7583i	−0.812368	−	0.633277i
$473$	1.10821	−	2.30122i	0.0509556	−	0.105810i
$474$	−15.7169	+	9.86943i	−0.721900	+	0.453318i
$475$	17.9036	−	8.62194i	0.821475	−	0.395602i
$476$	0.00180341	+	0.00141655i	8.26592e−5	+	6.49276e-5i
$477$	6.37939	+	29.0084i	0.292092	+	1.32821i
$478$	9.94324	−	20.8435i	0.454793	−	0.953359i
$479$	−2.93665	+	2.34190i	−0.134179	+	0.107004i	−0.688280	−	0.725446i	$-0.741634\pi$
$479$	−2.93665	+	2.34190i	−0.134179	+	0.107004i	0.554100	+	0.832450i	$0.313062\pi$
$480$	24.0903	+	14.6554i	1.09957	+	0.668924i
$481$		−	20.2627i		−	0.923902i
$482$	20.0485	+	15.8676i	0.913182	+	0.722749i
$483$	0.00927700	−	0.00100803i	0.000422118	−	4.58670e-5i
$484$	19.5271	−	9.58168i	0.887595	−	0.435531i
$485$	−40.3976	−	19.4545i	−1.83436	−	0.883382i
$486$	−20.6881	−	7.61603i	−0.938430	−	0.345470i
$487$	−0.584914	+	0.466453i	−0.0265050	+	0.0211370i	−0.636653	−	0.771151i	$-0.719682\pi$
$487$	−0.584914	+	0.466453i	−0.0265050	+	0.0211370i	0.610148	+	0.792288i	$0.291110\pi$
$488$	−9.94005	−	12.1856i	−0.449965	−	0.551616i
$489$	−2.23642	−	20.5820i	−0.101135	−	0.930749i
$490$	−6.44197	−	27.7523i	−0.291019	−	1.25372i
$491$	−10.8284	−	8.63533i	−0.488677	−	0.389707i	0.347921	−	0.937524i	$-0.386888\pi$
$491$	−10.8284	−	8.63533i	−0.488677	−	0.389707i	−0.836598	+	0.547817i	$0.815459\pi$
$492$	−1.39552	+	1.40506i	−0.0629149	+	0.0633449i
$493$	−2.71012	+	3.12796i	−0.122058	+	0.140876i
$494$	−19.3546	−	39.8143i	−0.870806	−	1.79133i
$495$	−2.39568	+	1.87961i	−0.107678	+	0.0844821i
$496$	8.07104	−	0.118983i	0.362400	−	0.00534248i
$497$	0.0174874	−	0.00399138i	0.000784417	−	0.000179038i
$498$	31.7891	+	11.1335i	1.42450	+	0.498903i
$499$	−4.11280	+	3.27985i	−0.184114	+	0.146826i	−0.711210	−	0.702980i	$-0.751852\pi$
$499$	−4.11280	+	3.27985i	−0.184114	+	0.146826i	0.527096	+	0.849806i	$0.323281\pi$
$500$	−7.68316	+	6.22030i	−0.343601	+	0.278180i
$501$	26.6771	+	16.9102i	1.19184	+	0.755494i
$502$	−30.5930	+	0.112742i	−1.36543	+	0.00503194i
$503$	15.9855	−	3.64858i	0.712756	−	0.162682i	0.149257	−	0.988798i	$-0.452312\pi$
$503$	15.9855	−	3.64858i	0.712756	−	0.162682i	0.563499	+	0.826116i	$0.309455\pi$
$504$	3.95665e−5		0.0126595i	1.76243e−6		0.000563899i
$505$			4.67775i			0.208157i
$506$	1.11779	−	1.41231i	0.0496920	−	0.0627850i
$507$	−12.5800	−	20.1982i	−0.558696	−	0.897036i
$508$	5.78469	−	0.0426364i	0.256654	−	0.00189169i
$509$	−12.8618	−	26.7077i	−0.570088	−	1.18380i	−0.964308	−	0.264784i	$-0.914699\pi$
$509$	−12.8618	−	26.7077i	−0.570088	−	1.18380i	0.394220	−	0.919016i	$-0.371015\pi$
$510$	5.11427	−	1.78795i	0.226464	−	0.0791719i
$511$	0.000281658	0	0.000135639i	1.24598e−5	0	6.00033e-6i
$512$	9.13623	−	20.7009i	0.403768	−	0.914861i
$513$	21.9766	+	22.5058i	0.970290	+	0.993653i
$514$	1.95876	−	0.00721848i	0.0863972	−	0.000318394i
$515$	−7.22897	+	31.6722i	−0.318547	+	1.39564i
$516$	−24.9388	−	2.72396i	−1.09787	−	0.119916i
$517$	1.60301	−	2.01011i	0.0705004	−	0.0884047i
$518$	0.00644512	−	0.00517878i	0.000283182	−	0.000227543i
$519$	−28.4755	−	10.0909i	−1.24994	−	0.442943i
$520$	−26.6058	−	32.6163i	−1.16674	−	1.43032i
$521$		−	15.4473i		−	0.676758i	−0.941010	−	0.338379i	$-0.890121\pi$
$521$		−	15.4473i		−	0.676758i	0.941010	−	0.338379i	$-0.109879\pi$
$522$	−22.8242	−	1.02765i	−0.998988	−	0.0449792i
$523$			10.9418i			0.478452i	0.970964	+	0.239226i	$0.0768937\pi$
$523$			10.9418i			0.478452i	−0.970964	+	0.239226i	$0.923106\pi$
$524$	3.02070	−	0.712919i	0.131960	−	0.0311440i
$525$	0.00799531	+	0.00283331i	0.000348944	+	0.000123656i
$526$	10.8921	+	13.5555i	0.474918	+	0.591047i
$527$	0.966966	−	1.21254i	0.0421217	−	0.0528189i
$528$	1.74632	+	1.70909i	0.0759989	+	0.0743784i
$529$	2.21625	−	9.71003i	0.0963588	−	0.422175i
$530$	−0.148497	−	40.2952i	−0.00645030	−	1.75031i
$531$	−18.4393	−	14.9456i	−0.800200	−	0.648586i
$532$	0.00771734	−	0.0163321i	0.000334589	−	0.000708085i
$533$	2.66331	−	1.28258i	0.115361	−	0.0555548i
$534$	12.4199	+	35.5259i	0.537461	+	1.53736i
$535$	17.6819	+	36.7169i	0.764457	+	1.58741i
$536$	4.16896	−	2.06475i	0.180072	−	0.0891838i
$537$	−21.9652	−	35.2671i	−0.947869	−	1.52189i
$538$	−20.8653	−	16.5141i	−0.899565	−	0.711972i
$539$		−	2.46880i		−	0.106339i
$540$	25.2519	+	16.0267i	1.08667	+	0.689678i
$541$	37.2563	−	8.50350i	1.60177	−	0.365594i	0.673997	−	0.738734i	$-0.264576\pi$
$541$	37.2563	−	8.50350i	1.60177	−	0.365594i	0.927775	+	0.373140i	$0.121719\pi$
$542$	0.0240671	+	6.53068i	0.00103377	+	0.280517i
$543$	0.685760	+	0.434694i	0.0294288	+	0.0186545i
$544$	−1.95816	−	3.88155i	−0.0839555	−	0.166420i
$545$	−41.8473	+	33.3721i	−1.79254	+	1.42950i
$546$	0.00624631	−	0.0178349i	0.000267317	−	0.000763264i
$547$	14.1959	−	3.24013i	0.606975	−	0.138538i	0.0920225	−	0.995757i	$-0.470667\pi$
$547$	14.1959	−	3.24013i	0.606975	−	0.138538i	0.514952	+	0.857219i	$0.327810\pi$
$548$	−8.58507	−	10.6041i	−0.366736	−	0.452983i
$549$	−10.2957	−	13.1226i	−0.439411	−	0.560059i
$550$	1.47248	−	0.715805i	0.0627867	−	0.0305220i
$551$	28.7712	+	15.3295i	1.22569	+	0.653059i
$552$	−16.7391	−	5.72437i	−0.712464	−	0.243645i
$553$	0.00883768	+	0.00704781i	0.000375816	+	0.000299703i
$554$	14.8556	−	3.44834i	0.631153	−	0.146506i
$555$	−2.11004	−	19.4189i	−0.0895664	−	0.824287i
$556$	−24.5730	+	5.79950i	−1.04213	+	0.245953i
$557$	11.5770	−	9.23237i	0.490534	−	0.391188i	−0.346748	−	0.937958i	$-0.612714\pi$
$557$	11.5770	−	9.23237i	0.490534	−	0.391188i	0.837283	+	0.546770i	$0.184143\pi$
$558$	8.56148	+	0.0363437i	0.362436	+	0.00153855i
$559$	33.7394	+	16.2480i	1.42702	+	0.687219i
$560$	0.00357454	−	0.0167988i	0.000151052	−	0.000709879i
$561$	0.466730	−	0.0507146i	0.0197054	−	0.00214117i
$562$	20.3837	−	25.7545i	0.859833	−	1.08639i
$563$		−	44.8773i		−	1.89135i	−0.325109	−	0.945677i	$-0.605401\pi$
$563$		−	44.8773i		−	1.89135i	0.325109	−	0.945677i	$-0.394599\pi$
$564$	−23.8639	−	8.25925i	−1.00485	−	0.347777i
$565$	35.1715	−	28.0484i	1.47968	−	1.18000i
$566$	−3.20000	−	1.52654i	−0.134506	−	0.0641652i
$567$	−0.000212957		0.0134258i	−8.94335e−6		0.000563831i
$568$	−33.2342	−	7.19988i	−1.39448	−	0.302100i
$569$	−8.83873	+	4.25651i	−0.370539	+	0.178442i	−0.609881	−	0.792493i	$-0.708783\pi$
$569$	−8.83873	+	4.25651i	−0.370539	+	0.178442i	0.239342	+	0.970935i	$0.423068\pi$
$570$	−22.6946	−	36.1408i	−0.950574	−	1.51377i
$571$	−12.1506	+	25.2310i	−0.508487	+	1.05588i	0.475841	+	0.879532i	$0.342144\pi$
$571$	−12.1506	+	25.2310i	−0.508487	+	1.05588i	−0.984327	+	0.176352i	$0.943570\pi$
$572$	−1.60673	−	3.27446i	−0.0671809	−	0.136912i
$573$	34.2492	+	12.1370i	1.43078	+	0.507029i
$574$	0.00108865		0.000519334i	4.54395e−5		2.16766e-5i
$575$	−7.39064	+	9.26758i	−0.308211	+	0.386485i
$576$	10.1055	−	21.7687i	0.421064	−	0.907031i
$577$	3.20231	+	0.730906i	0.133314	+	0.0304280i	0.288657	−	0.957433i	$-0.406791\pi$
$577$	3.20231	+	0.730906i	0.133314	+	0.0304280i	−0.155343	+	0.987861i	$0.549648\pi$
$578$	22.6434	+	5.08048i	0.941840	+	0.211320i
$579$	−1.30816	+	11.2105i	−0.0543652	+	0.465893i
$580$	29.9722	+	7.90200i	1.24453	+	0.328113i
$581$		−	0.0205154i		−	0.000851121i
$582$	−12.6144	+	36.0177i	−0.522885	+	1.49298i
$583$	0.776996	−	3.40424i	0.0321799	−	0.140989i
$584$	−0.592622	+	0.00655208i	−0.0245229	+	0.000271127i
$585$	−27.5579	−	35.1243i	−1.13938	−	1.45221i
$586$	1.51710	−	3.18022i	0.0626709	−	0.131374i
$587$	4.11563	−	18.0318i	0.169870	−	0.744250i	−0.816179	−	0.577799i	$-0.803912\pi$
$587$	4.11563	−	18.0318i	0.169870	−	0.744250i	0.986050	−	0.166452i	$-0.0532310\pi$
$588$	−22.8605	+	8.08673i	−0.942753	+	0.333491i
$589$	−11.0065	−	5.30043i	−0.453513	−	0.218401i
$590$	20.1700	+	25.1020i	0.830385	+	1.03343i
$591$	3.37601	+	9.77219i	0.138870	+	0.401974i
$592$	−15.2283	+	3.71276i	−0.625881	+	0.152593i
$593$	6.97238	+	14.4783i	0.286321	+	0.594552i	0.993673	−	0.112309i	$-0.0358247\pi$
$593$	6.97238	+	14.4783i	0.286321	+	0.594552i	−0.707352	+	0.706861i	$0.750110\pi$
$594$	1.81751	+	1.84760i	0.0745731	+	0.0758078i
$595$	−0.00205745	−	0.00257996i	−8.43472e−5	−	0.000105768i
$596$	−18.8537	−	4.15729i	−0.772280	−	0.170289i
$597$	−3.22977	+	27.6781i	−0.132186	+	1.13279i
$598$	20.7066	+	16.3885i	0.846758	+	0.670177i
$599$	−16.0215	+	3.65681i	−0.654622	+	0.149413i	−0.536917	−	0.843635i	$-0.680411\pi$
$599$	−16.0215	+	3.65681i	−0.654622	+	0.149413i	−0.117706	+	0.993049i	$0.537554\pi$
$600$	−11.4514	−	11.2901i	−0.467501	−	0.460918i
$601$	−12.6750	+	26.3200i	−0.517026	+	1.07361i	0.465077	+	0.885270i	$0.346027\pi$
$601$	−12.6750	+	26.3200i	−0.517026	+	1.07361i	−0.982103	+	0.188345i	$0.939688\pi$
$602$	0.00345503	+	0.0148844i	0.000140817	+	0.000606644i
$603$	4.46263	−	2.10566i	0.181732	−	0.0857491i
$604$	−18.4972	+	4.36554i	−0.752640	+	0.177631i
$605$	−30.5146	+	6.96476i	−1.24060	+	0.283158i
$606$	3.95644	−	0.444663i	0.160719	−	0.0180632i
$607$	−17.6193	+	22.0939i	−0.715146	+	0.896765i	−0.998052	−	0.0623830i	$-0.980130\pi$
$607$	−17.6193	+	22.0939i	−0.715146	+	0.896765i	0.282906	+	0.959148i	$0.408701\pi$
$608$	−26.3758	+	21.8411i	−1.06968	+	0.885772i
$609$	0.00400442	+	0.0133273i	0.000162267	+	0.000540051i
$610$	9.89325	+	20.3513i	0.400566	+	0.824002i
$611$	29.4713	+	23.5025i	1.19228	+	0.950811i
$612$	−1.99841	−	4.15569i	−0.0807810	−	0.167984i
$613$	5.66437	+	24.8172i	0.228782	+	1.00236i	0.950635	+	0.310312i	$0.100433\pi$
$613$	5.66437	+	24.8172i	0.228782	+	1.00236i	−0.721853	+	0.692046i	$0.756709\pi$
$614$	0.493510	+	0.110729i	0.0199165	+	0.00446865i
$615$	2.41883	−	1.50651i	0.0975368	−	0.0607484i
$616$	0.000630879	−	0.00134796i	2.54189e−5	−	5.43107e-5i
$617$	16.3022	+	7.85073i	0.656302	+	0.316059i	0.732233	−	0.681055i	$-0.238478\pi$
$617$	16.3022	+	7.85073i	0.656302	+	0.316059i	−0.0759303	+	0.997113i	$0.524193\pi$
$618$	27.4756	+	3.10354i	1.10523	+	0.124843i
$619$	−8.77408	−	38.4417i	−0.352660	−	1.54510i	−0.771013	−	0.636820i	$-0.780250\pi$
$619$	−8.77408	−	38.4417i	−0.352660	−	1.54510i	0.418353	−	0.908285i	$-0.362608\pi$
$620$	−11.3428	−	2.50110i	−0.455536	−	0.100447i
$621$	−17.6360	−	6.40758i	−0.707710	−	0.257127i
$622$	−12.5983	+	15.9177i	−0.505144	+	0.638241i
$623$	0.0179215	−	0.0142919i	0.000718010	−	0.000572594i
$624$	−25.0578	+	25.6037i	−1.00311	+	1.02497i
$625$	27.6036	−	13.2932i	1.10414	−	0.531727i
$626$	−5.10051	−	10.4922i	−0.203857	−	0.419354i
$627$	−1.20753	−	3.49533i	−0.0482242	−	0.139590i
$628$	−20.5804	+	43.5539i	−0.821247	+	1.73799i
$629$	−1.30668	+	2.71335i	−0.0521008	+	0.108188i
$630$	0.00412896	−	0.0177426i	0.000164502	−	0.000706884i
$631$	−28.6497	−	6.53910i	−1.14052	−	0.260317i	−0.389779	−	0.920908i	$-0.627449\pi$
$631$	−28.6497	−	6.53910i	−1.14052	−	0.260317i	−0.750746	+	0.660591i	$0.770306\pi$
$632$	−9.51091	−	19.2036i	−0.378324	−	0.763877i
$633$	24.4481	−	24.2549i	0.971723	−	0.964047i
$634$	−20.8934	+	16.7882i	−0.829781	+	0.666746i
$635$	−8.11552	−	1.85231i	−0.322055	−	0.0735068i
$636$	−34.0676	+	3.95602i	−1.35087	+	0.156866i
$637$	36.1964			1.43415
$638$	2.37514	+	1.25428i	0.0940326	+	0.0496573i
$639$	−35.0989	−	8.30447i	−1.38849	−	0.328520i
$640$	−19.6376	+	25.9717i	−0.776243	+	1.02662i
$641$	3.13643	−	13.7416i	0.123882	−	0.542761i	−0.874455	−	0.485107i	$-0.838781\pi$
$641$	3.13643	−	13.7416i	0.123882	−	0.542761i	0.998337	−	0.0576542i	$-0.0183621\pi$
$642$	29.3744	−	18.4457i	1.15931	−	0.727993i
$643$	12.8935	+	10.2822i	0.508469	+	0.405490i	0.843839	−	0.536596i	$-0.180290\pi$
$643$	12.8935	+	10.2822i	0.508469	+	0.405490i	−0.335371	+	0.942086i	$0.608862\pi$
$644$	7.94172e−5		0.0107749i	3.12948e−6		0.000424591i
$645$	34.0263	+	12.0580i	1.33978	+	0.474782i
$646$	0.0242473	+	6.57959i	0.000953998	+	0.258871i
$647$	37.6619	+	18.1370i	1.48064	+	0.713039i	0.987604	−	0.156969i	$-0.0501722\pi$
$647$	37.6619	+	18.1370i	1.48064	+	0.713039i	0.493038	+	0.870008i	$0.335887\pi$
$648$	11.1549	−	22.8816i	0.438208	−	0.898874i
$649$	1.21072	+	2.51408i	0.0475248	+	0.0986862i
$650$	10.4948	+	21.5887i	0.411639	+	0.846780i
$651$	−0.00170278	−	0.00492886i	−6.67371e−5	−	0.000193177i
$652$	23.9053	−	0.176195i	0.936202	−	0.00690034i
$653$	1.74073	+	2.18280i	0.0681199	+	0.0854196i	0.814724	−	0.579849i	$-0.196888\pi$
$653$	1.74073	+	2.18280i	0.0681199	+	0.0854196i	−0.746604	+	0.665269i	$0.768317\pi$
$654$	32.2041	+	32.2222i	1.25928	+	1.25999i
$655$	−4.46611			−0.174506
$656$	−1.45192	−	1.76659i	−0.0566878	−	0.0689736i
$657$	−0.628589	−	0.00498495i	−0.0245236	−	0.000194481i
$658$	5.66824e−5		0.0153810i	2.20971e−6		0.000599612i
$659$	0.344621	−	0.715613i	0.0134245	−	0.0278763i	−0.894149	−	0.447770i	$-0.852218\pi$
$659$	0.344621	−	0.715613i	0.0134245	−	0.0278763i	0.907573	+	0.419894i	$0.137933\pi$
$660$	−1.88081	−	2.97078i	−0.0732102	−	0.115637i
$661$	−18.3121	−	22.9626i	−0.712257	−	0.893142i	0.285615	−	0.958344i	$-0.407802\pi$
$661$	−18.3121	−	22.9626i	−0.712257	−	0.893142i	−0.997872	+	0.0652025i	$0.979231\pi$
$662$	−15.1257	−	3.39375i	−0.587878	−	0.131902i
$663$	0.743551	+	6.84296i	0.0288771	+	0.265759i
$664$	−16.4866	+	35.2258i	−0.639805	+	1.36703i
$665$	−0.0162064	+	0.0203221i	−0.000628455	+	0.000788058i
$666$	−16.2240	+	3.63062i	−0.628665	+	0.140684i
$667$	−19.4304	−	0.792215i	−0.752347	−	0.0306747i
$668$	−22.5288	+	28.6813i	−0.871665	+	1.10971i
$669$	−33.6792	−	33.9474i	−1.30212	−	1.31248i
$670$	−6.52108	+	1.51370i	−0.251931	+	0.0584793i
$671$	0.436336	+	1.91171i	0.0168445	+	0.0738008i
$672$	−0.0145482	−	0.00142647i	−0.000561211	−	5.50274e-5i
$673$	−7.13716	−	8.94971i	−0.275117	−	0.344986i	0.625007	−	0.780619i	$-0.285096\pi$
$673$	−7.13716	−	8.94971i	−0.275117	−	0.344986i	−0.900124	+	0.435633i	$0.856525\pi$
$674$	−6.87962	−	29.6377i	−0.264993	−	1.14160i
$675$	−11.9165	−	12.2034i	−0.458666	−	0.469710i
$676$	24.6671	−	12.1038i	0.948734	−	0.465531i
$677$	−7.22347	−	31.6481i	−0.277620	−	1.21633i	−0.900792	−	0.434250i	$-0.857013\pi$
$677$	−7.22347	−	31.6481i	−0.277620	−	1.21633i	0.623172	−	0.782085i	$-0.285844\pi$
$678$	−27.0667	−	27.0819i	−1.03949	−	1.04007i
$679$	0.0232443			0.000892035
$680$	1.45942	+	6.08332i	0.0559662	+	0.233285i
$681$	2.87442	+	4.61514i	0.110148	+	0.176853i
$682$	−0.908442	−	0.433366i	−0.0347860	−	0.0165944i
$683$	−15.7741	+	7.59640i	−0.603579	+	0.290668i	−0.710609	−	0.703588i	$-0.751580\pi$
$683$	−15.7741	+	7.59640i	−0.603579	+	0.290668i	0.107030	+	0.994256i	$0.465866\pi$
$684$	−28.4106	+	22.6307i	−1.08630	+	0.865305i
$685$	8.51836	+	17.6886i	0.325470	+	0.675845i
$686$	0.0185022	+	0.0230265i	0.000706419	+	0.000879155i
$687$	−6.92434	+	10.9236i	−0.264180	+	0.416763i
$688$	6.02902	−	28.3338i	0.229854	−	1.08022i
$689$	49.9113	+	11.3919i	1.90147	+	0.433998i
$690$	21.5509	+	13.5498i	0.820430	+	0.515831i
$691$	−27.1283	−	21.6341i	−1.03201	−	0.823001i	−0.0475959	−	0.998867i	$-0.515156\pi$
$691$	−27.1283	−	21.6341i	−1.03201	−	0.823001i	−0.984414	+	0.175866i	$0.943727\pi$
$692$	14.9036	−	31.5403i	0.566552	−	1.19898i
$693$	0.000696171	−	0.00141676i	2.64454e−5	−	5.38184e-5i
$694$	12.3024	+	2.76027i	0.466991	+	0.104779i
$695$	36.3312			1.37812
$696$	3.83438	−	26.1017i	0.145342	−	0.989381i
$697$	−0.439349			−0.0166415
$698$	−16.0137	−	3.59300i	−0.606129	−	0.135997i
$699$	6.29716	+	2.23154i	0.238180	+	0.0844045i
$700$	−0.00418462	+	0.00885583i	−0.000158164	+	0.000334719i
$701$	−6.43611	−	5.13262i	−0.243088	−	0.193856i	0.494365	−	0.869254i	$-0.335401\pi$
$701$	−6.43611	−	5.13262i	−0.243088	−	0.193856i	−0.737454	+	0.675398i	$0.763972\pi$
$702$	−27.0885	+	26.6473i	−1.02239	+	1.00574i
$703$	23.1273	+	5.27866i	0.872263	+	0.199088i
$704$	−2.16650	+	1.80751i	−0.0816529	+	0.0681232i
$705$	30.6914	+	19.4548i	1.15590	+	0.732711i
$706$	−20.9058	−	26.0177i	−0.786799	−	0.979190i
$707$	−0.00105216	−	0.00218483i	−3.95705e−5	−	8.21689e-5i
$708$	19.3140	−	19.4460i	0.725864	−	0.730824i
$709$	21.9107	−	10.5516i	0.822873	−	0.396275i	0.0254358	−	0.999676i	$-0.491903\pi$
$709$	21.9107	−	10.5516i	0.822873	−	0.396275i	0.797437	+	0.603402i	$0.206188\pi$
$710$	44.1645	+	21.0684i	1.65746	+	0.790682i
$711$	−9.69933	−	20.5563i	−0.363753	−	0.770922i
$712$	−42.2574	+	10.1377i	−1.58366	+	0.379928i
$713$	7.28718			0.272907
$714$	−0.00198655	+	0.00198544i	−7.43449e−5	+	7.43033e-5i
$715$	1.16791	+	5.11694i	0.0436773	+	0.191363i
$716$	43.0698	−	21.1338i	1.60960	−	0.789807i
$717$	23.8888	+	15.1428i	0.892144	+	0.565517i
$718$	1.71398	+	7.38390i	0.0639651	+	0.275565i
$719$	−22.9378	−	28.7631i	−0.855436	−	1.07268i	−0.996575	−	0.0826932i	$-0.973648\pi$
$719$	−22.9378	−	28.7631i	−0.855436	−	1.07268i	0.141139	−	0.989990i	$-0.454924\pi$
$720$	−21.3480	+	27.1468i	−0.795593	+	1.01170i
$721$	−0.00374755	−	0.0164191i	−0.000139566	−	0.000611479i
$722$	24.3108	−	5.64312i	0.904755	−	0.210015i
$723$	−22.2301	+	22.0545i	−0.826747	+	0.820217i
$724$	−0.579124	+	0.737281i	−0.0215230	+	0.0274008i
$725$	−15.6008	−	8.31222i	−0.579398	−	0.308708i
$726$	8.79150	+	25.1472i	0.326283	+	0.933301i
$727$	4.89634	−	6.13982i	0.181595	−	0.227713i	−0.682699	−	0.730700i	$-0.739194\pi$
$727$	4.89634	−	6.13982i	0.181595	−	0.227713i	0.864294	+	0.502986i	$0.167765\pi$
$728$	0.0197631	+	0.00924964i	0.000732468	+	0.000342814i
$729$	12.2902	−	24.0406i	0.455194	−	0.890393i
$730$	0.832129	+	0.186704i	0.0307985	+	0.00691024i
$731$	−3.47020	−	4.35150i	−0.128350	−	0.160946i
$732$	16.2727	−	10.3023i	0.601458	−	0.380784i
$733$	2.87283	−	5.96549i	0.106110	−	0.220340i	−0.841153	−	0.540798i	$-0.818122\pi$
$733$	2.87283	−	5.96549i	0.106110	−	0.220340i	0.947263	+	0.320457i	$0.103837\pi$
$734$	0.0842237	+	22.8544i	0.00310875	+	0.843571i
$735$	34.6890	−	3.76928i	1.27952	−	0.139032i
$736$	8.52261	−	18.5648i	0.314147	−	0.684309i
$737$	−0.580106			−0.0213685
$738$	−1.50414	−	1.90265i	−0.0553682	−	0.0700373i
$739$	10.9022	+	13.6710i	0.401045	+	0.502894i	0.940816	−	0.338917i	$-0.110061\pi$
$739$	10.9022	+	13.6710i	0.401045	+	0.502894i	−0.539771	+	0.841812i	$0.681489\pi$
$740$	22.5544	−	0.166239i	0.829116	−	0.00611105i
$741$	51.2467	−	17.7042i	1.88260	−	0.650382i
$742$	0.00913288	+	0.0187872i	0.000335279	+	0.000689700i
$743$	−7.46456	−	15.5003i	−0.273848	−	0.568651i	0.718005	−	0.696038i	$-0.245055\pi$
$743$	−7.46456	−	15.5003i	−0.273848	−	0.568651i	−0.991853	+	0.127387i	$0.959341\pi$
$744$	−1.03720	+	9.83148i	−0.0380256	+	0.360439i
$745$	25.0304	+	12.0540i	0.917044	+	0.441625i
$746$	0.0946575	+	25.6856i	0.00346566	+	0.940418i
$747$	−18.1929	+	37.0239i	−0.665642	+	1.35463i
$748$	0.00399552	+	0.542091i	0.000146091	+	0.0198208i
$749$	−0.0165174	−	0.0131722i	−0.000603531	−	0.000481300i
$750$	−6.43856	−	10.2533i	−0.235103	−	0.374397i
$751$	3.12867	−	13.7076i	0.114167	−	0.500197i	−0.885220	−	0.465173i	$-0.845992\pi$
$751$	3.12867	−	13.7076i	0.114167	−	0.500197i	0.999386	−	0.0350242i	$-0.0111508\pi$
$752$	12.2632	−	26.4553i	0.447191	−	0.964727i
$753$	4.34278	−	37.2164i	0.158260	−	1.35624i
$754$	−18.3896	+	34.8231i	−0.669709	+	1.26818i
$755$	27.3482			0.995302
$756$	−0.0153992	−	0.00180568i	−0.000560065	−	6.56719e-5i
$757$	4.79159	+	1.09365i	0.174153	+	0.0397494i	0.308708	−	0.951157i	$-0.400103\pi$
$757$	4.79159	+	1.09365i	0.174153	+	0.0397494i	−0.134555	+	0.990906i	$0.542960\pi$
$758$	4.23065	−	3.39942i	0.153664	−	0.123472i
$759$	1.55363	+	1.56600i	0.0563933	+	0.0568423i
$760$	44.1584	−	21.8702i	1.60179	−	0.793316i
$761$	40.7996	+	9.31224i	1.47898	+	0.337569i	0.884501	−	0.466539i	$-0.154499\pi$
$761$	40.7996	+	9.31224i	1.47898	+	0.337569i	0.594484	+	0.804107i	$0.297356\pi$
$762$	−0.795235	+	7.04019i	−0.0288083	+	0.255039i
$763$	0.0120392	−	0.0249997i	0.000435849	−	0.000905050i
$764$	−17.9255	+	37.9354i	−0.648522	+	1.37246i
$765$	1.42517	+	6.48056i	0.0515272	+	0.234305i
$766$	3.33034	+	6.85082i	0.120330	+	0.247530i
$767$	−36.8601	+	17.7509i	−1.33094	+	0.640948i
$768$	23.8336	+	14.1406i	0.860023	+	0.510256i
$769$	12.4195	−	9.90421i	0.447858	−	0.357155i	−0.373440	−	0.927654i	$-0.621822\pi$
$769$	12.4195	−	9.90421i	0.447858	−	0.357155i	0.821298	+	0.570499i	$0.193250\pi$
$770$	−0.00132909	+	0.00167928i	−4.78969e−5	+	6.05170e-5i
$771$	−0.278053	+	2.38283i	−0.0100138	+	0.0858155i
$772$	−12.7269	−	2.80631i	−0.458051	−	0.101001i
$773$	4.82576	+	21.1430i	0.173571	+	0.760462i	0.984509	+	0.175331i	$0.0560997\pi$
$773$	4.82576	+	21.1430i	0.173571	+	0.760462i	−0.810939	+	0.585131i	$0.801043\pi$
$774$	6.96413	−	29.9257i	0.250320	−	1.07566i
$775$	5.96810	+	2.87409i	0.214381	+	0.103240i
$776$	−39.9115	−	18.6797i	−1.43274	−	0.670561i
$777$	0.00535340	+	0.00859535i	0.000192052	+	0.000308357i
$778$	16.5072	+	3.70371i	0.591811	+	0.132784i
$779$	0.770082	+	3.37395i	0.0275911	+	0.120884i
$780$	43.5561	−	27.5754i	1.55956	−	0.987358i
$781$	3.31514	+	2.64374i	0.118625	+	0.0946003i
$782$	−1.71595	−	3.52987i	−0.0613622	−	0.126228i
$783$	4.59184	−	27.6028i	0.164099	−	0.986444i
$784$	−6.63229	−	27.2032i	−0.236867	−	0.971542i
$785$	43.2187	−	54.1945i	1.54254	−	1.93428i
$786$	0.424545	+	3.77744i	0.0151430	+	0.134737i
$787$	−23.8848	+	5.45156i	−0.851402	+	0.194327i	−0.625888	−	0.779913i	$-0.715263\pi$
$787$	−23.8848	+	5.45156i	−0.851402	+	0.194327i	−0.225514	+	0.974240i	$0.572406\pi$
$788$	−11.6191	+	2.74224i	−0.413915	+	0.0976884i
$789$	−18.0779	+	11.2594i	−0.643590	+	0.400844i
$790$	6.97257	+	30.0381i	0.248073	+	1.06871i
$791$	−0.0101186	+	0.0210116i	−0.000359778	+	0.000747086i
$792$	−2.33390	+	1.87319i	−0.0829315	+	0.0665608i
$793$	−28.0285	+	6.39733i	−0.995323	+	0.227176i
$794$	−11.0738	−	8.76446i	−0.392993	−	0.311039i
$795$	49.0190	+	5.72004i	1.73853	+	0.202869i
$796$	−31.4220	−	6.92861i	−1.11372	−	0.245578i
$797$	−5.96457	−	7.47934i	−0.211276	−	0.264932i	0.664890	−	0.746941i	$-0.268478\pi$
$797$	−5.96457	−	7.47934i	−0.211276	−	0.264932i	−0.876166	+	0.482010i	$0.839907\pi$
$798$	0.0187290	+	0.0117755i	0.000663001	+	0.000416850i
$799$	−2.43084	−	5.04770i	−0.0859971	−	0.178575i
$800$	14.3019	−	11.8430i	0.505650	−	0.418714i
$801$	−45.0168	+	9.89986i	−1.59059	+	0.349794i
$802$	−18.5050	−	23.0299i	−0.653433	−	0.813213i
$803$	0.0665822	+	0.0320643i	0.00234963	+	0.00113152i
$804$	1.90018	+	5.37164i	0.0670140	+	0.189443i
$805$	0.00345023	−	0.0151165i	0.000121605	−	0.000532785i
$806$	6.35379	−	13.3191i	0.223803	−	0.469146i
$807$	23.1358	−	22.9531i	0.814419	−	0.807986i
$808$	0.0508247	+	4.59699i	0.00178801	+	0.161721i
$809$	−10.3923	+	45.5317i	−0.365374	+	1.60081i	0.373943	+	0.927452i	$0.378006\pi$
$809$	−10.3923	+	45.5317i	−0.365374	+	1.60081i	−0.739317	+	0.673358i	$0.764851\pi$
$810$	−23.1855	+	28.3585i	−0.814657	+	0.996415i
$811$		−	5.21562i		−	0.183145i	−0.995798	−	0.0915726i	$-0.970811\pi$
$811$		−	5.21562i		−	0.183145i	0.995798	−	0.0915726i	$-0.0291894\pi$
$812$	−0.0157765	+	0.00305083i	−0.000553645	+	0.000107063i
$813$	−7.94456	−	0.927053i	−0.278628	−	0.0325132i
$814$	1.90708	+	0.427891i	0.0668432	+	0.0149976i
$815$	−33.5374	−	7.65470i	−1.17476	−	0.268132i
$816$	5.00655	−	1.81265i	0.175264	−	0.0634555i
$817$	−27.3345	+	34.2764i	−0.956313	+	1.19918i
$818$	10.2902	+	4.90886i	0.359788	+	0.171634i
$819$	0.0207719	+	0.0102069i	0.000725828	+	0.000356658i
$820$	1.44949	+	2.95400i	0.0506183	+	0.103158i
$821$	−5.49064	+	11.4014i	−0.191625	+	0.397913i	−0.974539	−	0.224216i	$-0.928018\pi$
$821$	−5.49064	+	11.4014i	−0.191625	+	0.397913i	0.782915	+	0.622129i	$0.213732\pi$
$822$	14.1512	−	8.88629i	0.493581	−	0.309945i
$823$	3.96604	−	1.90995i	0.138248	−	0.0665765i	−0.363481	−	0.931602i	$-0.618412\pi$
$823$	3.96604	−	1.90995i	0.138248	−	0.0665765i	0.501729	+	0.865025i	$0.332698\pi$
$824$	−6.76004	+	31.2039i	−0.235497	+	1.08704i
$825$	0.654768	+	1.89529i	0.0227961	+	0.0659856i
$826$	−0.0150669	−	0.00718757i	−0.000524245	−	0.000250087i
$827$	19.7164	−	15.7233i	0.685606	−	0.546753i	−0.217558	−	0.976047i	$-0.569809\pi$
$827$	19.7164	−	15.7233i	0.685606	−	0.546753i	0.903164	+	0.429295i	$0.141238\pi$
$828$	9.41179	−	19.5158i	0.327082	−	0.678222i
$829$		−	0.0389868i		−	0.00135407i	−1.00000		0.000677033i	$-0.999784\pi$
$829$		−	0.0389868i		−	0.00135407i	1.00000		0.000677033i	$-0.000215506\pi$
$830$	34.7327	−	43.8842i	1.20559	−	1.52324i
$831$	2.01767	+	18.5687i	0.0699920	+	0.644142i
$832$	−26.5009	−	31.7641i	−0.918752	−	1.10122i
$833$	−4.84700	−	2.33419i	−0.167939	−	0.0808750i
$834$	−3.45362	−	30.7290i	−0.119589	−	1.06406i
$835$	41.0315	−	32.7215i	1.41995	−	1.13238i
$836$	4.15594	−	0.980849i	0.143736	−	0.0339234i
$837$	−1.29789	+	10.4051i	−0.0448616	+	0.359653i
$838$	−26.5442	+	6.16155i	−0.916954	+	0.212847i
$839$	−12.6116	−	10.0574i	−0.435401	−	0.347220i	0.381131	−	0.924521i	$-0.375535\pi$
$839$	−12.6116	−	10.0574i	−0.435401	−	0.347220i	−0.816532	+	0.577301i	$0.804106\pi$
$840$	0.0199032	+	0.00680643i	0.000686727	+	0.000234844i
$841$	−4.13003	−	28.7044i	−0.142415	−	0.989807i
$842$	26.7874	−	13.0220i	0.923156	−	0.448767i
$843$	28.3315	+	28.5571i	0.975788	+	0.983557i
$844$	25.0223	+	30.9068i	0.861302	+	1.06386i
$845$	−38.5468	+	8.79805i	−1.32605	+	0.302662i
$846$	13.5374	−	27.8081i	0.465426	−	0.956063i
$847$	0.0126858	−	0.0101166i	0.000435891	−	0.000347611i
$848$	−0.583749	−	39.5979i	−0.0200460	−	1.35980i
$849$	2.32480	−	3.66754i	0.0797869	−	0.125870i
$850$	−0.0131478	−	3.56769i	−0.000450965	−	0.122371i
$851$	−13.7958	+	3.14880i	−0.472914	+	0.107939i
$852$	13.6214	−	39.3571i	0.466662	−	1.34835i
$853$		−	10.9855i		−	0.376137i	−0.982156	−	0.188069i	$-0.939777\pi$
$853$		−	10.9855i		−	0.376137i	0.982156	−	0.188069i	$-0.0602228\pi$
$854$	−0.00919842	−	0.00728020i	−0.000314763	−	0.000249123i
$855$	47.2690	−	22.3035i	1.61656	−	0.762763i
$856$	17.7756	+	35.8909i	0.607558	+	1.22673i
$857$	18.9074	+	39.2616i	0.645865	+	1.34115i	0.924657	+	0.380800i	$0.124351\pi$
$857$	18.9074	+	39.2616i	0.645865	+	1.34115i	−0.278793	+	0.960351i	$0.589934\pi$
$858$	4.21689	−	1.47423i	0.143962	−	0.0503294i
$859$	23.3926	−	11.2653i	0.798144	−	0.384366i	0.0100721	−	0.999949i	$-0.496794\pi$
$859$	23.3926	−	11.2653i	0.798144	−	0.384366i	0.788072	+	0.615583i	$0.211080\pi$
$860$	−17.8088	+	37.6885i	−0.607276	+	1.28517i
$861$	−0.000790905		0.00124771i	−2.69540e−5		4.25218e-5i
$862$	0.0701963	+	19.0480i	0.00239090	+	0.648778i
$863$	6.08033	−	26.6397i	0.206977	−	0.906825i	−0.759588	−	0.650404i	$-0.774600\pi$
$863$	6.08033	−	26.6397i	0.206977	−	0.906825i	0.966565	−	0.256421i	$-0.0825433\pi$
$864$	24.9901	+	15.4756i	0.850181	+	0.526491i
$865$	−31.2976	+	39.2459i	−1.06415	+	1.33440i
$866$	26.5357	+	33.0243i	0.901719	+	1.12221i
$867$	−9.49343	+	26.7895i	−0.322414	+	0.909818i
$868$	0.00586042	−	0.00138312i	0.000198916	−	4.69463e-5i
$869$			2.67215i			0.0906465i
$870$	−13.9975	+	35.2879i	−0.474559	+	1.19637i
$871$		−	8.50522i		−	0.288188i
$872$	−40.7622	+	33.2506i	−1.38038	+	1.12601i
$873$	−41.9488	−	20.6129i	−1.41975	−	0.697640i
$874$	−24.0997	+	19.3646i	−0.815184	+	0.655017i
$875$	−0.00459781	+	0.00576547i	−0.000155434	+	0.000194908i
$876$	0.0788133	−	0.721564i	0.00266285	−	0.0243794i
$877$	−1.36283	+	5.97094i	−0.0460194	+	0.201624i	−0.992711	−	0.120516i	$-0.961545\pi$
$877$	−1.36283	+	5.97094i	−0.0460194	+	0.201624i	0.946692	+	0.322140i	$0.104402\pi$
$878$	−46.6206	+	0.171808i	−1.57337	+	0.00579822i
$879$	3.64487	+	2.31043i	0.122938	+	0.0779289i
$880$	3.63161	−	1.81531i	0.122421	−	0.0611942i
$881$	28.6281	−	13.7866i	0.964506	−	0.464482i	0.115757	−	0.993278i	$-0.463071\pi$
$881$	28.6281	−	13.7866i	0.964506	−	0.464482i	0.848749	+	0.528796i	$0.177356\pi$
$882$	−6.48556	−	28.9817i	−0.218380	−	0.975863i
$883$	13.6794	+	28.4055i	0.460348	+	0.955923i	0.993913	+	0.110164i	$0.0351376\pi$
$883$	13.6794	+	28.4055i	0.460348	+	0.955923i	−0.533565	+	0.845759i	$0.679148\pi$
$884$	−7.94787	+	0.0585803i	−0.267316	+	0.00197027i
$885$	−33.4766	+	20.8501i	−1.12530	+	0.700868i
$886$	27.2745	−	34.4609i	0.916305	−	1.15774i
$887$		−	53.8189i		−	1.80706i	−0.428523	−	0.903531i	$-0.640966\pi$
$887$		−	53.8189i		−	1.80706i	0.428523	−	0.903531i	$-0.359034\pi$
$888$	−2.28461	−	19.0607i	−0.0766664	−	0.639636i
$889$	0.00420714		0.000960253i	0.000141103		3.22058e-5i
$890$	62.5320	−	0.230445i	2.09608	−	0.00772453i
$891$	−2.51275	+	1.93946i	−0.0841802	+	0.0649744i
$892$	42.9158	−	34.7447i	1.43693	−	1.16334i
$893$	−34.5027	+	27.5150i	−1.15459	+	0.920754i
$894$	7.81593	−	22.3166i	0.261404	−	0.746379i
$895$	−67.3045	+	15.3618i	−2.24974	+	0.513488i
$896$	0.00333031	−	0.0165476i	0.000111258	−	0.000552818i
$897$	−22.9600	+	22.7786i	−0.766611	+	0.760555i
$898$	10.6597	+	21.9280i	0.355719	+	0.731748i
$899$	1.98455	+	10.6844i	0.0661885	+	0.356345i
$900$	15.4052	−	12.2712i	0.513508	−	0.409039i
$901$	−5.94891	−	4.74410i	−0.198187	−	0.158049i
$902$	0.0644722	+	0.277749i	0.00214669	+	0.00924803i
$903$	−0.0186048	+	0.00202158i	−0.000619129	+	6.72741e-5i
$904$	34.2596	−	27.9463i	1.13946	−	0.929479i
$905$	1.05475	−	0.841139i	0.0350612	−	0.0279604i
$906$	−2.59969	−	23.1311i	−0.0863690	−	0.768480i
$907$	24.7136	+	11.9014i	0.820601	+	0.395181i	0.796582	−	0.604531i	$-0.206639\pi$
$907$	24.7136	+	11.9014i	0.820601	+	0.395181i	0.0240195	+	0.999711i	$0.492354\pi$
$908$	−5.63623	+	2.76562i	−0.187045	+	0.0917805i
$909$	−0.0386684	+	4.87599i	−0.00128255	+	0.161726i
$910$	−0.0246207	−	0.0194864i	−0.000816170	−	0.000645968i
$911$			1.41627i			0.0469233i	0.999725	+	0.0234616i	$0.00746876\pi$
$911$			1.41627i			0.0469233i	−0.999725	+	0.0234616i	$0.992531\pi$
$912$	−22.6955	−	35.2702i	−0.751523	−	1.16791i
$913$	3.79165	−	3.02374i	0.125485	−	0.100071i
$914$	1.68921	−	3.54099i	0.0558740	−	0.117126i
$915$	−26.1951	+	9.04965i	−0.865984	+	0.299172i
$916$	−11.7443	−	9.22500i	−0.388043	−	0.304802i
$917$	0.00208598	−	0.00100456i	6.88852e−5	−	3.31734e-5i
$918$	5.34579	−	1.82145i	0.176437	−	0.0601168i
$919$	20.0787	−	41.6937i	0.662334	−	1.37535i	−0.250940	−	0.968003i	$-0.580740\pi$
$919$	20.0787	−	41.6937i	0.662334	−	1.37535i	0.913273	−	0.407347i	$-0.133546\pi$
$920$	−18.0721	+	23.1830i	−0.595821	+	0.764319i
$921$	−0.206909	+	0.583874i	−0.00681787	+	0.0192393i
$922$	17.9578	−	37.6440i	0.591409	−	1.23974i
$923$	−38.7611	+	48.6049i	−1.27584	+	1.59985i
$924$	0.00154668		0.000964511i	5.08820e−5		3.17301e-5i
$925$	−12.5405	−	2.86228i	−0.412328	−	0.0941112i
$926$	3.46644	−	15.4497i	0.113914	−	0.507708i
$927$	−7.79715	+	32.9547i	−0.256092	+	1.08237i
$928$	29.5406	+	7.43992i	0.969718	+	0.244227i
$929$			15.7737i			0.517518i	0.965942	+	0.258759i	$0.0833136\pi$
$929$			15.7737i			0.517518i	−0.965942	+	0.258759i	$0.916686\pi$
$930$	4.70221	−	13.4261i	0.154192	−	0.440259i
$931$	−9.42954	+	41.3135i	−0.309041	+	1.35400i
$932$	−3.29583	+	6.97492i	−0.107959	+	0.228471i
$933$	−17.5104	−	17.6499i	−0.573266	−	0.577831i
$934$	−25.6796	−	12.2503i	−0.840262	−	0.400841i
$935$	0.173583	−	0.760516i	0.00567676	−	0.0248715i
$936$	−27.4637	−	34.2185i	−0.897680	−	1.11847i
$937$	6.25310	+	3.01134i	0.204280	+	0.0983760i	0.533227	−	0.845972i	$-0.320979\pi$
$937$	6.25310	+	3.01134i	0.204280	+	0.0983760i	−0.328947	+	0.944349i	$0.606694\pi$
$938$	0.00270532	−	0.00217378i	8.83317e−5	−	7.09763e-5i
$939$	13.5050	−	4.66558i	0.440719	−	0.152256i
$940$	−25.9188	+	32.9972i	−0.845379	+	1.07625i
$941$	−14.4151	−	29.9333i	−0.469920	−	0.975799i	−0.992389	−	0.123141i	$-0.960703\pi$
$941$	−14.4151	−	29.9333i	−0.469920	−	0.975799i	0.522469	−	0.852658i	$-0.325011\pi$
$942$	−49.9461	−	31.4027i	−1.62733	−	1.02316i
$943$	−1.28711	−	1.61399i	−0.0419142	−	0.0525587i
$944$	20.0945	+	24.4495i	0.654020	+	0.795764i
$945$	0.0209697	+	0.00761878i	0.000682145	+	0.000247839i
$946$	−2.24171	+	2.83236i	−0.0728842	+	0.0920880i
$947$	−16.3069	+	3.72194i	−0.529903	+	0.120947i	−0.479097	−	0.877762i	$-0.659036\pi$
$947$	−16.3069	+	3.72194i	−0.529903	+	0.120947i	−0.0508053	+	0.998709i	$0.516179\pi$
$948$	24.7435	−	8.75281i	0.803631	−	0.284278i
$949$	−0.470110	+	0.976194i	−0.0152604	+	0.0316886i
$950$	−27.3748	+	6.35434i	−0.888155	+	0.206162i
$951$	−17.3543	−	27.8638i	−0.562752	−	0.903547i
$952$	−0.00204996	−	0.00251306i	−6.64396e−5	−	8.14489e-5i
$953$	−11.1415	+	2.54297i	−0.360908	+	0.0823749i	−0.399130	−	0.916894i	$-0.630688\pi$
$953$	−11.1415	+	2.54297i	−0.360908	+	0.0823749i	0.0382219	+	0.999269i	$0.487831\pi$
$954$	0.178308	−	42.0041i	0.00577294	−	1.35993i
$955$	37.6435	−	47.2034i	1.21811	−	1.52747i
$956$	−20.1741	+	25.6836i	−0.652476	+	0.830666i
$957$	−1.87295	+	2.70440i	−0.0605439	+	0.0874209i
$958$	4.77738	−	2.32239i	0.154350	−	0.0750331i
$959$	−0.00795732	−	0.00634575i	−0.000256955	−	0.000204915i
$960$	−28.7050	−	27.6816i	−0.926448	−	0.893421i
$961$	5.99199	+	26.2526i	0.193290	+	0.846859i
$962$	−6.27353	+	27.9607i	−0.202267	+	0.901489i
$963$	18.1278	+	38.4191i	0.584159	+	1.23804i
$964$	−22.7522	−	28.1030i	−0.732800	−	0.905136i
$965$	16.8964	+	8.13687i	0.543914	+	0.261935i
$966$	−0.0131135	−	0.00148125i	−0.000421920	−	4.76585e-5i
$967$	−12.2790	−	53.7977i	−0.394865	−	1.73002i	−0.647149	−	0.762363i	$-0.724039\pi$
$967$	−12.2790	−	53.7977i	−0.394865	−	1.73002i	0.252284	−	0.967653i	$-0.418818\pi$
$968$	−29.9121	+	7.17607i	−0.961412	+	0.230648i
$969$	−8.00406	−	0.933996i	−0.257128	−	0.0300043i
$970$	49.7217	+	39.3528i	1.59647	+	1.26354i
$971$	−36.3001	+	28.9484i	−1.16493	+	0.928998i	−0.998372	−	0.0570342i	$-0.981836\pi$
$971$	−36.3001	+	28.9484i	−1.16493	+	0.928998i	−0.166555	+	0.986032i	$0.553264\pi$
$972$	26.1896	+	16.9146i	0.840032	+	0.542537i
$973$	−0.0169692	+	0.00817193i	−0.000544007	+	0.000261980i
$974$	0.951544	−	0.462567i	0.0304895	−	0.0148216i
$975$	−27.7878	+	9.59988i	−0.889923	+	0.307442i
$976$	9.94357	+	19.8925i	0.318286	+	0.636743i
$977$	23.1021	−	47.9721i	0.739103	−	1.53476i	−0.102540	−	0.994729i	$-0.532697\pi$
$977$	23.1021	−	47.9721i	0.739103	−	1.53476i	0.841643	−	0.540035i	$-0.181589\pi$
$978$	−3.28631	+	29.0936i	−0.105085	+	0.930312i
$979$	5.28287	+	1.20578i	0.168841	+	0.0385369i
$980$	0.296960	+	40.2901i	0.00948605	+	1.28702i
$981$	−43.8966	+	34.4405i	−1.40151	+	1.09960i
$982$	12.2685	+	15.2685i	0.391505	+	0.487238i
$983$	4.39673	+	1.00353i	0.140234	+	0.0320075i	0.292062	−	0.956399i	$-0.405659\pi$
$983$	4.39673	+	1.00353i	0.140234	+	0.0320075i	−0.151828	+	0.988407i	$0.548516\pi$
$984$	2.36071	−	1.50678i	0.0752566	−	0.0480345i
$985$	17.1789			0.547366
$986$	4.70815	−	3.47722i	0.149938	−	0.110737i
$987$	−0.0187109	−	0.00218338i	−0.000595575	−	6.94977e-5i
$988$	14.3807	+	60.9324i	0.457512	+	1.93852i
$989$	5.81935	−	25.4962i	0.185044	−	0.810733i
$990$	3.88776	−	1.85196i	0.123561	−	0.0588591i
$991$	−39.4750	−	31.4802i	−1.25396	−	1.00000i	−0.999458	−	0.0329315i	$-0.989516\pi$
$991$	−39.4750	−	31.4802i	−1.25396	−	1.00000i	−0.254506	−	0.967071i	$-0.581913\pi$
$992$	−11.1741	−	2.33468i	−0.354779	−	0.0741262i
$993$	6.34159	−	17.8953i	0.201244	−	0.567890i
$994$	−0.0253667		9.34823e-5i	−0.000804584		2.96508e-6i
$995$	41.7162	+	20.0895i	1.32249	+	0.636879i
$996$	−40.4189	−	25.2053i	−1.28072	−	0.798662i
$997$	24.7026	+	51.2955i	0.782340	+	1.62455i	0.780987	+	0.624547i	$0.214716\pi$
$997$	24.7026	+	51.2955i	0.782340	+	1.62455i	0.00135309	+	0.999999i	$0.499569\pi$
$998$	6.69076	−	3.25253i	0.211792	−	0.102957i
$999$	−2.03894	−	20.2593i	−0.0645092	−	0.640976i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	348.2.t.a.35.4	✓	336
3.2	odd	2	inner	348.2.t.a.35.53	yes	336
4.3	odd	2	inner	348.2.t.a.35.36	yes	336
12.11	even	2	inner	348.2.t.a.35.21	yes	336
29.5	even	14	inner	348.2.t.a.179.21	yes	336
87.5	odd	14	inner	348.2.t.a.179.36	yes	336
116.63	odd	14	inner	348.2.t.a.179.53	yes	336
348.179	even	14	inner	348.2.t.a.179.4	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
348.2.t.a.35.4	✓	336	1.1	even	1	trivial
348.2.t.a.35.21	yes	336	12.11	even	2	inner
348.2.t.a.35.36	yes	336	4.3	odd	2	inner
348.2.t.a.35.53	yes	336	3.2	odd	2	inner
348.2.t.a.179.4	yes	336	348.179	even	14	inner
348.2.t.a.179.21	yes	336	29.5	even	14	inner
348.2.t.a.179.36	yes	336	87.5	odd	14	inner
348.2.t.a.179.53	yes	336	116.63	odd	14	inner

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:	\( N \)	\(=\)	\( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	348.t (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37991 - 0.309609i) q^{2} +(0.578538 - 1.63257i) q^{3} +(1.80828 + 0.854463i) q^{4} +(-2.25006 - 1.79437i) q^{5} +(-1.30379 + 2.07368i) q^{6} +(0.00145454 + 0.000331989i) q^{7} +(-2.23071 - 1.73894i) q^{8} +(-2.33059 - 1.88901i) q^{9} +O(q^{10})\)	\(q+(-1.37991 - 0.309609i) q^{2} +(0.578538 - 1.63257i) q^{3} +(1.80828 + 0.854463i) q^{4} +(-2.25006 - 1.79437i) q^{5} +(-1.30379 + 2.07368i) q^{6} +(0.00145454 + 0.000331989i) q^{7} +(-2.23071 - 1.73894i) q^{8} +(-2.33059 - 1.88901i) q^{9} +(2.54933 + 3.17270i) q^{10} +(0.153025 + 0.317760i) q^{11} +(2.44113 - 2.45782i) q^{12} +(-4.65883 + 2.24357i) q^{13} +(-0.00190434 - 0.000908452i) q^{14} +(-4.23118 + 2.63528i) q^{15} +(2.53979 + 3.09022i) q^{16} +0.768538 q^{17} +(2.63114 + 3.32823i) q^{18} +(-1.34708 - 5.90193i) q^{19} +(-2.53554 - 5.16732i) q^{20} +(0.00138350 - 0.00218257i) q^{21} +(-0.112779 - 0.485856i) q^{22} +(2.25150 + 2.82329i) q^{23} +(-4.12950 + 2.63576i) q^{24} +(0.730434 + 3.20024i) q^{25} +(7.12338 - 1.65351i) q^{26} +(-4.43228 + 2.71199i) q^{27} +(0.00234655 + 0.00184318i) q^{28} +(-3.52633 + 4.07001i) q^{29} +(6.65454 - 2.32643i) q^{30} +(1.25819 - 1.57772i) q^{31} +(-2.54791 - 5.05056i) q^{32} +(0.607296 - 0.0659884i) q^{33} +(-1.06051 - 0.237946i) q^{34} +(-0.00267710 - 0.00335697i) q^{35} +(-2.60028 - 5.40727i) q^{36} +(-1.70022 + 3.53054i) q^{37} +(0.0315499 + 8.56118i) q^{38} +(0.967488 + 8.90387i) q^{39} +(1.89895 + 7.91545i) q^{40} -0.571669 q^{41} +(-0.00258485 + 0.00258340i) q^{42} +(-4.51533 - 5.66205i) q^{43} +(0.00519885 + 0.705354i) q^{44} +(1.85439 + 8.43232i) q^{45} +(-2.23275 - 4.59297i) q^{46} +(-3.16295 - 6.56793i) q^{47} +(6.51438 - 2.35857i) q^{48} +(-6.30678 - 3.03719i) q^{49} +(-0.0171075 - 4.64218i) q^{50} +(0.444628 - 1.25469i) q^{51} +(-10.3415 + 0.0762230i) q^{52} +(-7.74056 - 6.17289i) q^{53} +(6.95579 - 2.37002i) q^{54} +(0.225861 - 0.989562i) q^{55} +(-0.00266735 - 0.00326993i) q^{56} +(-10.4147 - 1.21529i) q^{57} +(6.12612 - 4.52446i) q^{58} +7.91189 q^{59} +(-9.90293 + 1.14996i) q^{60} +(5.42043 + 1.23718i) q^{61} +(-2.22466 + 1.78756i) q^{62} +(-0.00276280 - 0.00352137i) q^{63} +(1.95217 + 7.75816i) q^{64} +(14.5085 + 3.31146i) q^{65} +(-0.858443 - 0.0969666i) q^{66} +(-0.713661 + 1.48193i) q^{67} +(1.38974 + 0.656687i) q^{68} +(5.91181 - 2.04236i) q^{69} +(0.00265479 + 0.00546116i) q^{70} +(10.8320 - 5.21643i) q^{71} +(1.91400 + 8.26660i) q^{72} +(0.163822 - 0.130644i) q^{73} +(3.43923 - 4.34541i) q^{74} +(5.64721 + 0.658974i) q^{75} +(2.60708 - 11.8234i) q^{76} +(0.000117088 + 0.000512996i) q^{77} +(1.42168 - 12.5861i) q^{78} +(6.82625 + 3.28735i) q^{79} +(-0.169687 - 11.5105i) q^{80} +(1.86328 + 8.80501i) q^{81} +(0.788850 + 0.176994i) q^{82} +(-3.05983 - 13.4060i) q^{83} +(0.00436669 - 0.00276456i) q^{84} +(-1.72926 - 1.37904i) q^{85} +(4.47772 + 9.21108i) q^{86} +(4.60448 + 8.11164i) q^{87} +(0.211210 - 0.974932i) q^{88} +(9.57939 - 12.0122i) q^{89} +(0.0518316 - 12.2100i) q^{90} +(-0.00752129 + 0.00171669i) q^{91} +(1.65896 + 7.02915i) q^{92} +(-1.84783 - 2.96686i) q^{93} +(2.33108 + 10.0424i) q^{94} +(-7.55921 + 15.6969i) q^{95} +(-9.71947 + 1.23770i) q^{96} +(15.1893 - 3.46685i) q^{97} +(7.76243 + 6.14367i) q^{98} +(0.243613 - 1.02963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9}+O(q^{10}) \) 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9	\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97}+O(q^{100}) \) 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9 - 14 * q^10 - 20 * q^13 - 26 * q^16 - 56 * q^18 - 14 * q^21 - 40 * q^22 + 3 * q^24 + 40 * q^25 - 36 * q^28 - 6 * q^30 - 22 * q^33 - 8 * q^34 + 9 * q^36 - 28 * q^37 - 14 * q^40 - 74 * q^42 - 22 * q^45 + 14 * q^48 + 4 * q^49 - 4 * q^52 - 31 * q^54 - 12 * q^57 - 106 * q^58 - 42 * q^60 - 28 * q^61 - 94 * q^64 - 7 * q^66 - 14 * q^69 + 70 * q^72 - 28 * q^73 - 84 * q^76 - 9 * q^78 - 50 * q^81 - 46 * q^82 - 35 * q^84 - 168 * q^85 - 60 * q^88 + 119 * q^90 + 122 * q^93 + 36 * q^94 + 2 * q^96 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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