LMFDB - Embedded newform 98.2.g.a.39.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,2,Mod(9,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("98.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	98.g (of order $21$, degree $12$, 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:	$0.782533939809$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			39.2
Character	$\chi$	$=$	98.39
Dual form			98.2.g.a.93.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.988831 + 0.149042i) q^{2} +(0.520118 - 0.354611i) q^{3} +(0.955573 + 0.294755i) q^{4} +(-0.0807922 - 1.07810i) q^{5} +(0.567161 - 0.273130i) q^{6} +(-2.64324 - 0.115218i) q^{7} +(0.900969 + 0.433884i) q^{8} +(-0.951249 + 2.42374i) q^{9} +O(q^{10})$	\(q+(0.988831 + 0.149042i) q^{2} +(0.520118 - 0.354611i) q^{3} +(0.955573 + 0.294755i) q^{4} +(-0.0807922 - 1.07810i) q^{5} +(0.567161 - 0.273130i) q^{6} +(-2.64324 - 0.115218i) q^{7} +(0.900969 + 0.433884i) q^{8} +(-0.951249 + 2.42374i) q^{9} +(0.0807922 - 1.07810i) q^{10} +(0.249160 + 0.634849i) q^{11} +(0.601534 - 0.185549i) q^{12} +(0.00686501 - 0.00860846i) q^{13} +(-2.59655 - 0.507886i) q^{14} +(-0.424326 - 0.532088i) q^{15} +(0.826239 + 0.563320i) q^{16} +(0.289279 + 0.268411i) q^{17} +(-1.30186 + 2.25490i) q^{18} +(-3.12770 - 5.41734i) q^{19} +(0.240572 - 1.05401i) q^{20} +(-1.41566 + 0.877394i) q^{21} +(0.151758 + 0.664893i) q^{22} +(-4.89692 + 4.54368i) q^{23} +(0.622470 - 0.0938223i) q^{24} +(3.78839 - 0.571008i) q^{25} +(0.00807136 - 0.00748913i) q^{26} +(0.784954 + 3.43911i) q^{27} +(-2.49185 - 0.889208i) q^{28} +(0.591698 - 2.59240i) q^{29} +(-0.340283 - 0.589387i) q^{30} +(2.87561 - 4.98071i) q^{31} +(0.733052 + 0.680173i) q^{32} +(0.354717 + 0.241842i) q^{33} +(0.246043 + 0.308528i) q^{34} +(0.0893369 + 2.85898i) q^{35} +(-1.62340 + 2.03568i) q^{36} +(-1.53038 + 0.472058i) q^{37} +(-2.28536 - 5.82300i) q^{38} +(0.000517969 - 0.00691182i) q^{39} +(0.394977 - 1.00639i) q^{40} +(7.12216 + 3.42985i) q^{41} +(-1.53061 + 0.656602i) q^{42} +(7.84159 - 3.77631i) q^{43} +(0.0509653 + 0.680085i) q^{44} +(2.68988 + 0.829719i) q^{45} +(-5.51943 + 3.76308i) q^{46} +(-11.1729 - 1.68405i) q^{47} +0.629501 q^{48} +(6.97345 + 0.609099i) q^{49} +3.83118 q^{50} +(0.245640 + 0.0370243i) q^{51} +(0.00909741 - 0.00620251i) q^{52} +(7.53046 + 2.32284i) q^{53} +(0.263614 + 3.51769i) q^{54} +(0.664298 - 0.319909i) q^{55} +(-2.33149 - 1.25067i) q^{56} +(-3.54782 - 1.70854i) q^{57} +(0.971466 - 2.47525i) q^{58} +(-0.377607 + 5.03882i) q^{59} +(-0.248639 - 0.633521i) q^{60} +(5.40858 - 1.66833i) q^{61} +(3.58583 - 4.49649i) q^{62} +(2.79364 - 6.29694i) q^{63} +(0.623490 + 0.781831i) q^{64} +(-0.00983539 - 0.00670565i) q^{65} +(0.314710 + 0.292008i) q^{66} +(-3.11565 + 5.39646i) q^{67} +(0.197311 + 0.341753i) q^{68} +(-0.935742 + 4.09975i) q^{69} +(-0.337769 + 2.84036i) q^{70} +(-0.529515 - 2.31996i) q^{71} +(-1.90867 + 1.77099i) q^{72} +(-2.11439 + 0.318694i) q^{73} +(-1.58364 + 0.238695i) q^{74} +(1.76792 - 1.64039i) q^{75} +(-1.39196 - 6.09857i) q^{76} +(-0.585443 - 1.70677i) q^{77} +(0.00154234 - 0.00675742i) q^{78} +(-5.18436 - 8.97958i) q^{79} +(0.540560 - 0.936277i) q^{80} +(-4.09819 - 3.80257i) q^{81} +(6.53142 + 4.45305i) q^{82} +(2.01070 + 2.52134i) q^{83} +(-1.61138 + 0.421142i) q^{84} +(0.266002 - 0.333556i) q^{85} +(8.31684 - 2.56540i) q^{86} +(-0.611538 - 1.55817i) q^{87} +(-0.0509653 + 0.680085i) q^{88} +(-5.92296 + 15.0915i) q^{89} +(2.53618 + 1.22136i) q^{90} +(-0.0191377 + 0.0219633i) q^{91} +(-6.01864 + 2.89842i) q^{92} +(-0.270553 - 3.61028i) q^{93} +(-10.7971 - 3.33048i) q^{94} +(-5.58772 + 3.80965i) q^{95} +(0.622470 + 0.0938223i) q^{96} -19.2879 q^{97} +(6.80478 + 1.64163i) q^{98} -1.77572 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9	$ 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9} - 7 q^{11} + 14 q^{13} - 7 q^{15} + 2 q^{16} - 7 q^{17} + 5 q^{18} - 7 q^{20} + 7 q^{21} - 7 q^{22} - 21 q^{23} + 4 q^{25} - 7 q^{26} - 35 q^{27} - 14 q^{28} - 11 q^{29} + 28 q^{31} - 2 q^{32} + 14 q^{33} + 7 q^{34} + 21 q^{35} + 3 q^{36} - 24 q^{37} - 7 q^{38} - 40 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 10 q^{43} + 21 q^{44} + 7 q^{45} + 42 q^{46} - 70 q^{47} - 14 q^{48} + 84 q^{49} + 8 q^{50} + 60 q^{51} - 7 q^{52} + 26 q^{53} + 63 q^{54} + 56 q^{55} + 21 q^{56} - 33 q^{57} - 30 q^{58} - 7 q^{59} + 14 q^{60} + 14 q^{61} + 28 q^{62} - 14 q^{63} - 4 q^{64} - 21 q^{66} - 36 q^{67} - 14 q^{68} - 35 q^{69} + 14 q^{70} - 2 q^{72} - 7 q^{73} - 11 q^{74} - 28 q^{75} - 91 q^{77} - 24 q^{78} - 26 q^{79} + 55 q^{81} + 14 q^{82} - 7 q^{83} - 21 q^{84} + 49 q^{85} - 16 q^{86} + 35 q^{87} - 21 q^{88} - 56 q^{89} - 21 q^{90} + 7 q^{91} + 21 q^{92} + 72 q^{93} - 35 q^{94} - 14 q^{95} - 126 q^{97} - 56 q^{98} - 14 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9 - 7 * q^11 + 14 * q^13 - 7 * q^15 + 2 * q^16 - 7 * q^17 + 5 * q^18 - 7 * q^20 + 7 * q^21 - 7 * q^22 - 21 * q^23 + 4 * q^25 - 7 * q^26 - 35 * q^27 - 14 * q^28 - 11 * q^29 + 28 * q^31 - 2 * q^32 + 14 * q^33 + 7 * q^34 + 21 * q^35 + 3 * q^36 - 24 * q^37 - 7 * q^38 - 40 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 10 * q^43 + 21 * q^44 + 7 * q^45 + 42 * q^46 - 70 * q^47 - 14 * q^48 + 84 * q^49 + 8 * q^50 + 60 * q^51 - 7 * q^52 + 26 * q^53 + 63 * q^54 + 56 * q^55 + 21 * q^56 - 33 * q^57 - 30 * q^58 - 7 * q^59 + 14 * q^60 + 14 * q^61 + 28 * q^62 - 14 * q^63 - 4 * q^64 - 21 * q^66 - 36 * q^67 - 14 * q^68 - 35 * q^69 + 14 * q^70 - 2 * q^72 - 7 * q^73 - 11 * q^74 - 28 * q^75 - 91 * q^77 - 24 * q^78 - 26 * q^79 + 55 * q^81 + 14 * q^82 - 7 * q^83 - 21 * q^84 + 49 * q^85 - 16 * q^86 + 35 * q^87 - 21 * q^88 - 56 * q^89 - 21 * q^90 + 7 * q^91 + 21 * q^92 + 72 * q^93 - 35 * q^94 - 14 * q^95 - 126 * q^97 - 56 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{17}{21}\right)$

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 $

$2$	0.988831	+	0.149042i	0.699209	+	0.105389i
$2$	0.988831	+	0.149042i	0.699209	+	0.105389i
$3$	0.520118	−	0.354611i	0.300290	−	0.204734i	−0.403796	−	0.914849i	$-0.632309\pi$
$3$	0.520118	−	0.354611i	0.300290	−	0.204734i	0.704086	+	0.710115i	$0.251357\pi$
$4$	0.955573	+	0.294755i	0.477786	+	0.147378i
$5$	−0.0807922	−	1.07810i	−0.0361314	−	0.482139i	−0.985692	−	0.168556i	$-0.946090\pi$
$5$	−0.0807922	−	1.07810i	−0.0361314	−	0.482139i	0.949561	−	0.313583i	$-0.101529\pi$
$6$	0.567161	−	0.273130i	0.231542	−	0.111505i
$7$	−2.64324	−	0.115218i	−0.999051	−	0.0435484i
$7$	−2.64324	−	0.115218i	−0.999051	−	0.0435484i
$8$	0.900969	+	0.433884i	0.318541	+	0.153401i
$9$	−0.951249	+	2.42374i	−0.317083	+	0.807914i
$10$	0.0807922	−	1.07810i	0.0255487	−	0.340924i
$11$	0.249160	+	0.634849i	0.0751245	+	0.191414i	0.963503	−	0.267698i	$-0.0862629\pi$
$11$	0.249160	+	0.634849i	0.0751245	+	0.191414i	−0.888378	+	0.459112i	$0.848168\pi$
$12$	0.601534	−	0.185549i	0.173648	−	0.0535633i
$13$	0.00686501	−	0.00860846i	0.00190401	−	0.00238756i	−0.780879	−	0.624683i	$-0.785228\pi$
$13$	0.00686501	−	0.00860846i	0.00190401	−	0.00238756i	0.782783	+	0.622295i	$0.213800\pi$
$14$	−2.59655	−	0.507886i	−0.693956	−	0.135738i
$15$	−0.424326	−	0.532088i	−0.109560	−	0.137384i
$16$	0.826239	+	0.563320i	0.206560	+	0.140830i
$17$	0.289279	+	0.268411i	0.0701603	+	0.0650993i	0.714474	−	0.699662i	$-0.246666\pi$
$17$	0.289279	+	0.268411i	0.0701603	+	0.0650993i	−0.644313	+	0.764762i	$0.722857\pi$
$18$	−1.30186	+	2.25490i	−0.306852	+	0.531484i
$19$	−3.12770	−	5.41734i	−0.717545	−	1.24282i	−0.961970	−	0.273156i	$-0.911933\pi$
$19$	−3.12770	−	5.41734i	−0.717545	−	1.24282i	0.244425	−	0.969668i	$-0.421401\pi$
$20$	0.240572	−	1.05401i	0.0537935	−	0.235685i
$21$	−1.41566	+	0.877394i	−0.308921	+	0.191463i
$22$	0.151758	+	0.664893i	0.0323548	+	0.141756i
$23$	−4.89692	+	4.54368i	−1.02108	+	0.947423i	−0.998630	−	0.0523250i	$-0.983337\pi$
$23$	−4.89692	+	4.54368i	−1.02108	+	0.947423i	−0.0224490	+	0.999748i	$0.507146\pi$
$24$	0.622470	−	0.0938223i	0.127061	−	0.0191514i
$25$	3.78839	−	0.571008i	0.757678	−	0.114202i
$26$	0.00807136	−	0.00748913i	0.00158292	−	0.00146874i
$27$	0.784954	+	3.43911i	0.151065	+	0.661857i
$28$	−2.49185	−	0.889208i	−0.470915	−	0.168045i
$29$	0.591698	−	2.59240i	0.109875	−	0.481396i	−0.889810	−	0.456331i	$-0.849163\pi$
$29$	0.591698	−	2.59240i	0.109875	−	0.481396i	0.999686	−	0.0250654i	$-0.00797940\pi$
$30$	−0.340283	−	0.589387i	−0.0621269	−	0.107607i
$31$	2.87561	−	4.98071i	0.516475	−	0.894562i	−0.483342	−	0.875432i	$-0.660577\pi$
$31$	2.87561	−	4.98071i	0.516475	−	0.894562i	0.999817	−	0.0191298i	$-0.00608959\pi$
$32$	0.733052	+	0.680173i	0.129586	+	0.120239i
$33$	0.354717	+	0.241842i	0.0617482	+	0.0420992i
$34$	0.246043	+	0.308528i	0.0421960	+	0.0529121i
$35$	0.0893369	+	2.85898i	0.0151007	+	0.483256i
$36$	−1.62340	+	2.03568i	−0.270566	+	0.339279i
$37$	−1.53038	+	0.472058i	−0.251592	+	0.0776059i	−0.417986	−	0.908453i	$-0.637264\pi$
$37$	−1.53038	+	0.472058i	−0.251592	+	0.0776059i	0.166394	+	0.986059i	$0.446788\pi$
$38$	−2.28536	−	5.82300i	−0.370734	−	0.944615i
$39$	0.000517969	−	0.00691182i	8.29415e−5	−	0.00110678i
$40$	0.394977	−	1.00639i	0.0624514	−	0.159124i
$41$	7.12216	+	3.42985i	1.11230	+	0.535653i	0.897504	−	0.441007i	$-0.145379\pi$
$41$	7.12216	+	3.42985i	1.11230	+	0.535653i	0.214791	+	0.976660i	$0.431093\pi$
$42$	−1.53061	+	0.656602i	−0.236179	+	0.101316i
$43$	7.84159	−	3.77631i	1.19583	−	0.575882i	0.273347	−	0.961916i	$-0.411869\pi$
$43$	7.84159	−	3.77631i	1.19583	−	0.575882i	0.922485	+	0.386034i	$0.126155\pi$
$44$	0.0509653	+	0.680085i	0.00768331	+	0.102527i
$45$	2.68988	+	0.829719i	0.400984	+	0.123687i
$46$	−5.51943	+	3.76308i	−0.813795	+	0.554836i
$47$	−11.1729	−	1.68405i	−1.62974	−	0.245644i	−0.730440	−	0.682977i	$-0.760685\pi$
$47$	−11.1729	−	1.68405i	−1.62974	−	0.245644i	−0.899299	+	0.437333i	$0.855923\pi$
$48$	0.629501			0.0908606
$49$	6.97345	+	0.609099i	0.996207	+	0.0870141i
$50$	3.83118			0.541811
$51$	0.245640	+	0.0370243i	0.0343965	+	0.00518444i
$52$	0.00909741	−	0.00620251i	0.00126158	−	0.000860133i
$53$	7.53046	+	2.32284i	1.03439	+	0.319066i	0.765044	−	0.643978i	$-0.222717\pi$
$53$	7.53046	+	2.32284i	1.03439	+	0.319066i	0.269344	+	0.963044i	$0.413193\pi$
$54$	0.263614	+	3.51769i	0.0358734	+	0.478697i
$55$	0.664298	−	0.319909i	0.0895739	−	0.0431365i
$56$	−2.33149	−	1.25067i	−0.311558	−	0.167127i
$57$	−3.54782	−	1.70854i	−0.469921	−	0.226302i
$58$	0.971466	−	2.47525i	0.127560	−	0.325017i
$59$	−0.377607	+	5.03882i	−0.0491603	+	0.655999i	0.917137	+	0.398571i	$0.130494\pi$
$59$	−0.377607	+	5.03882i	−0.0491603	+	0.655999i	−0.966298	+	0.257427i	$0.917125\pi$
$60$	−0.248639	−	0.633521i	−0.0320991	−	0.0817872i
$61$	5.40858	−	1.66833i	0.692498	−	0.213607i	0.0715243	−	0.997439i	$-0.477214\pi$
$61$	5.40858	−	1.66833i	0.692498	−	0.213607i	0.620974	+	0.783832i	$0.286737\pi$
$62$	3.58583	−	4.49649i	0.455401	−	0.571055i
$63$	2.79364	−	6.29694i	0.351965	−	0.793339i
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	−0.00983539	−	0.00670565i	−0.00121993	−	0.000831734i
$66$	0.314710	+	0.292008i	0.0387381	+	0.0359437i
$67$	−3.11565	+	5.39646i	−0.380637	+	0.659283i	−0.991153	−	0.132721i	$-0.957629\pi$
$67$	−3.11565	+	5.39646i	−0.380637	+	0.659283i	0.610516	+	0.792004i	$0.290962\pi$
$68$	0.197311	+	0.341753i	0.0239275	+	0.0414436i
$69$	−0.935742	+	4.09975i	−0.112650	+	0.493552i
$70$	−0.337769	+	2.84036i	−0.0403712	+	0.339488i
$71$	−0.529515	−	2.31996i	−0.0628419	−	0.275328i	0.933739	−	0.357955i	$-0.116526\pi$
$71$	−0.529515	−	2.31996i	−0.0628419	−	0.275328i	−0.996581	+	0.0826273i	$0.973669\pi$
$72$	−1.90867	+	1.77099i	−0.224939	+	0.208713i
$73$	−2.11439	+	0.318694i	−0.247471	+	0.0373003i	−0.271606	−	0.962408i	$-0.587555\pi$
$73$	−2.11439	+	0.318694i	−0.247471	+	0.0373003i	0.0241352	+	0.999709i	$0.492317\pi$
$74$	−1.58364	+	0.238695i	−0.184094	+	0.0277478i
$75$	1.76792	−	1.64039i	0.204142	−	0.189416i
$76$	−1.39196	−	6.09857i	−0.159669	−	0.699554i
$77$	−0.585443	−	1.70677i	−0.0667174	−	0.194504i
$78$	0.00154234	−	0.00675742i	0.000174635	−	0.000765127i
$79$	−5.18436	−	8.97958i	−0.583286	−	1.01028i	−0.995087	−	0.0990072i	$-0.968433\pi$
$79$	−5.18436	−	8.97958i	−0.583286	−	1.01028i	0.411801	−	0.911274i	$-0.364900\pi$
$80$	0.540560	−	0.936277i	0.0604364	−	0.104679i
$81$	−4.09819	−	3.80257i	−0.455355	−	0.422507i
$82$	6.53142	+	4.45305i	0.721275	+	0.491757i
$83$	2.01070	+	2.52134i	0.220703	+	0.276753i	0.879840	−	0.475270i	$-0.157650\pi$
$83$	2.01070	+	2.52134i	0.220703	+	0.276753i	−0.659137	+	0.752023i	$0.729078\pi$
$84$	−1.61138	+	0.421142i	−0.175816	+	0.0459504i
$85$	0.266002	−	0.333556i	0.0288519	−	0.0361792i
$86$	8.31684	−	2.56540i	0.896828	−	0.276635i
$87$	−0.611538	−	1.55817i	−0.0655638	−	0.167054i
$88$	−0.0509653	+	0.680085i	−0.00543292	+	0.0724973i
$89$	−5.92296	+	15.0915i	−0.627833	+	1.59969i	0.162291	+	0.986743i	$0.448112\pi$
$89$	−5.92296	+	15.0915i	−0.627833	+	1.59969i	−0.790123	+	0.612948i	$0.789983\pi$
$90$	2.53618	+	1.22136i	0.267336	+	0.128742i
$91$	−0.0191377	+	0.0219633i	−0.00200618	+	0.00230237i
$92$	−6.01864	+	2.89842i	−0.627487	+	0.302182i
$93$	−0.270553	−	3.61028i	−0.0280550	−	0.374369i
$94$	−10.7971	−	3.33048i	−1.11364	−	0.343513i
$95$	−5.58772	+	3.80965i	−0.573288	+	0.390861i
$96$	0.622470	+	0.0938223i	0.0635306	+	0.00957569i
$97$	−19.2879			−1.95839			−0.979194	−	0.202926i	$-0.934955\pi$
$97$	−19.2879			−1.95839			−0.979194	+	0.202926i	$0.934955\pi$
$98$	6.80478	+	1.64163i	0.687387	+	0.165830i
$99$	−1.77572			−0.178467
$100$	3.78839	+	0.571008i	0.378839	+	0.0571008i
$101$	−10.5624	+	7.20131i	−1.05100	+	0.716557i	−0.960200	−	0.279312i	$-0.909894\pi$
$101$	−10.5624	+	7.20131i	−1.05100	+	0.716557i	−0.0907961	+	0.995870i	$0.528941\pi$
$102$	0.237379	+	0.0732216i	0.0235040	+	0.00725002i
$103$	−0.556558	−	7.42675i	−0.0548393	−	0.731779i	−0.955073	−	0.296372i	$-0.904223\pi$
$103$	−0.556558	−	7.42675i	−0.0548393	−	0.731779i	0.900233	−	0.435408i	$-0.143396\pi$
$104$	0.00992023	−	0.00477733i	0.000972759	−	0.000468456i
$105$	1.06029	+	1.45533i	0.103474	+	0.142025i
$106$	7.10015	+	3.41925i	0.689627	+	0.332107i
$107$	−3.42964	+	8.73859i	−0.331556	+	0.844791i	0.663745	+	0.747959i	$0.268966\pi$
$107$	−3.42964	+	8.73859i	−0.331556	+	0.844791i	−0.995301	+	0.0968319i	$0.969129\pi$
$108$	−0.263614	+	3.51769i	−0.0253663	+	0.338490i
$109$	−4.85252	−	12.3640i	−0.464788	−	1.18426i	−0.950661	−	0.310230i	$-0.899594\pi$
$109$	−4.85252	−	12.3640i	−0.464788	−	1.18426i	0.485874	−	0.874029i	$-0.338501\pi$
$110$	0.704558	−	0.217327i	0.0671770	−	0.0207214i
$111$	−0.628579	+	0.788213i	−0.0596621	+	0.0748139i
$112$	−2.11904	−	1.58419i	−0.200231	−	0.149692i
$113$	−4.75557	−	5.96330i	−0.447367	−	0.560980i	0.506101	−	0.862474i	$-0.331086\pi$
$113$	−4.75557	−	5.96330i	−0.447367	−	0.560980i	−0.953468	+	0.301494i	$0.902515\pi$
$114$	−3.25355	−	2.21823i	−0.304723	−	0.207757i
$115$	5.29416	+	4.91226i	0.493683	+	0.458071i
$116$	1.32953	−	2.30282i	0.123444	−	0.213811i
$117$	0.0143343	+	0.0248278i	0.00132521	+	0.00229533i
$118$	−1.12439	+	4.92626i	−0.103508	+	0.453499i
$119$	−0.733707	−	0.742806i	−0.0672588	−	0.0680929i
$120$	−0.151440	−	0.663503i	−0.0138245	−	0.0605692i
$121$	7.72262	−	7.16554i	0.702056	−	0.651413i
$122$	5.59682	−	0.843585i	0.506713	−	0.0763746i
$123$	4.92063	−	0.741665i	0.443678	−	0.0668737i
$124$	4.21595	−	3.91183i	0.378603	−	0.351293i
$125$	−2.12453	−	9.30818i	−0.190024	−	0.832549i
$126$	3.70095	−	5.81023i	0.329706	−	0.517617i
$127$	−1.38846	+	6.08324i	−0.123206	+	0.539800i	0.875221	+	0.483724i	$0.160716\pi$
$127$	−1.38846	+	6.08324i	−0.123206	+	0.539800i	−0.998426	+	0.0560761i	$0.982141\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	2.73943	−	4.74484i	0.241194	−	0.417760i
$130$	−0.00872611	−	0.00809664i	−0.000765330	−	0.000710123i
$131$	17.1022	+	11.6601i	1.49423	+	1.01875i	0.987671	+	0.156541i	$0.0500344\pi$
$131$	17.1022	+	11.6601i	1.49423	+	1.01875i	0.506557	+	0.862207i	$0.330918\pi$
$132$	0.267673	+	0.335652i	0.0232980	+	0.0292147i
$133$	7.64310	+	14.6797i	0.662741	+	1.27289i
$134$	−3.88515	+	4.87182i	−0.335626	+	0.420861i
$135$	3.64427	−	1.12411i	0.313649	−	0.0967480i
$136$	0.144172	+	0.367343i	0.0123626	+	0.0314994i
$137$	1.56443	−	20.8759i	0.133659	−	1.78355i	−0.379436	−	0.925218i	$-0.623882\pi$
$137$	1.56443	−	20.8759i	0.133659	−	1.78355i	0.513095	−	0.858332i	$-0.328499\pi$
$138$	−1.53633	+	3.91450i	−0.130781	+	0.333224i
$139$	4.34700	+	2.09341i	0.368708	+	0.177560i	0.609058	−	0.793126i	$-0.291548\pi$
$139$	4.34700	+	2.09341i	0.368708	+	0.177560i	−0.240350	+	0.970686i	$0.577262\pi$
$140$	−0.757331	+	2.75829i	−0.0640061	+	0.233118i
$141$	−6.40842	+	3.08613i	−0.539687	+	0.259899i
$142$	−0.177829	−	2.37296i	−0.0149231	−	0.199135i
$143$	0.00717555	+	0.00221336i	0.000600050	+	0.000185091i
$144$	−2.15130	+	1.46673i	−0.179275	+	0.122228i
$145$	−2.84266	−	0.428462i	−0.236070	−	0.0355818i
$146$	−2.13828			−0.176965
$147$	3.84301	−	2.15606i	0.316966	−	0.177828i
$148$	−1.60153			−0.131645
$149$	10.9493	+	1.65034i	0.897000	+	0.135201i	0.581330	−	0.813668i	$-0.302533\pi$
$149$	10.9493	+	1.65034i	0.897000	+	0.135201i	0.315670	+	0.948869i	$0.397771\pi$
$150$	1.99267	−	1.35858i	0.162701	−	0.110927i
$151$	14.0180	+	4.32398i	1.14077	+	0.351880i	0.806870	−	0.590729i	$-0.201160\pi$
$151$	14.0180	+	4.32398i	1.14077	+	0.351880i	0.333898	+	0.942609i	$0.391636\pi$
$152$	−0.467467	−	6.23792i	−0.0379166	−	0.505962i
$153$	−0.925736	+	0.445811i	−0.0748413	+	0.0360417i
$154$	−0.324524	−	1.77496i	−0.0261509	−	0.143030i
$155$	−5.60201	−	2.69779i	−0.449964	−	0.216691i
$156$	0.00253225	−	0.00645207i	0.000202742	−	0.000516579i
$157$	−1.47938	+	19.7410i	−0.118068	+	1.57550i	0.552411	+	0.833572i	$0.313708\pi$
$157$	−1.47938	+	19.7410i	−0.118068	+	1.57550i	−0.670478	+	0.741929i	$0.733911\pi$
$158$	−3.78812	−	9.65197i	−0.301367	−	0.767869i
$159$	4.74043	−	1.46223i	0.375941	−	0.115962i
$160$	0.674067	−	0.845253i	0.0532897	−	0.0668231i
$161$	13.4673	−	11.4458i	1.06137	−	0.902058i
$162$	−3.48567	−	4.37090i	−0.273860	−	0.343410i
$163$	−1.86633	−	1.27244i	−0.146182	−	0.0996653i	0.488020	−	0.872832i	$-0.337719\pi$
$163$	−1.86633	−	1.27244i	−0.146182	−	0.0996653i	−0.634203	+	0.773167i	$0.718672\pi$
$164$	5.79478	+	5.37677i	0.452496	+	0.419855i
$165$	0.232070	−	0.401958i	0.0180666	−	0.0312924i
$166$	1.61246	+	2.79286i	0.125151	+	0.216768i
$167$	0.0383315	−	0.167941i	0.00296618	−	0.0129957i	−0.973423	−	0.229014i	$-0.926450\pi$
$167$	0.0383315	−	0.167941i	0.00296618	−	0.0129957i	0.976389	+	0.216018i	$0.0693070\pi$
$168$	−1.65615	+	0.176275i	−0.127775	+	0.0135999i
$169$	2.89275	+	12.6739i	0.222519	+	0.974919i
$170$	0.312745	−	0.290185i	0.0239864	−	0.0222561i
$171$	16.1055	−	2.42751i	1.23162	−	0.185636i
$172$	8.60630	−	1.29719i	0.656224	−	0.0989099i
$173$	1.85059	−	1.71710i	0.140698	−	0.130549i	−0.606684	−	0.794943i	$-0.707501\pi$
$173$	1.85059	−	1.71710i	0.140698	−	0.130549i	0.747382	+	0.664394i	$0.231310\pi$
$174$	−0.372474	−	1.63192i	−0.0282372	−	0.123715i
$175$	−10.0794	+	1.07282i	−0.761932	+	0.0810976i
$176$	−0.151758	+	0.664893i	−0.0114392	+	0.0501182i
$177$	1.59042	+	2.75469i	0.119543	+	0.207055i
$178$	−8.10607	+	14.0401i	−0.607576	+	1.05235i
$179$	0.168598	+	0.156436i	0.0126016	+	0.0116926i	0.686448	−	0.727178i	$-0.259169\pi$
$179$	0.168598	+	0.156436i	0.0126016	+	0.0116926i	−0.673847	+	0.738871i	$0.735359\pi$
$180$	2.32581	+	1.58571i	0.173356	+	0.118192i
$181$	−14.6668	−	18.3915i	−1.09017	−	1.36703i	−0.924647	−	0.380826i	$-0.875640\pi$
$181$	−14.6668	−	18.3915i	−1.09017	−	1.36703i	−0.165524	−	0.986206i	$-0.552932\pi$
$182$	−0.0221974	+	0.0188656i	−0.00164538	+	0.00139841i
$183$	2.22149	−	2.78567i	0.164218	−	0.205922i
$184$	−6.38340	+	1.96902i	−0.470591	+	0.145158i
$185$	0.632567	+	1.61175i	0.0465072	+	0.118499i
$186$	0.270553	−	3.61028i	0.0198379	−	0.264719i
$187$	−0.0983240	+	0.250525i	−0.00719016	+	0.0183202i
$188$	−10.1802	−	4.90251i	−0.742465	−	0.357552i
$189$	−1.67858	−	9.18084i	−0.122098	−	0.667808i
$190$	−6.09311	+	2.93429i	−0.442041	+	0.212876i
$191$	0.00227420	+	0.0303470i	0.000164555	+	0.00219583i	0.997285	−	0.0736321i	$-0.0234591\pi$
$191$	0.00227420	+	0.0303470i	0.000164555	+	0.00219583i	−0.997121	+	0.0758280i	$0.975840\pi$
$192$	0.601534	+	0.185549i	0.0434120	+	0.0133908i
$193$	−11.6324	+	7.93085i	−0.837320	+	0.570875i	−0.904309	−	0.426879i	$-0.859613\pi$
$193$	−11.6324	+	7.93085i	−0.837320	+	0.570875i	0.0669889	+	0.997754i	$0.478661\pi$
$194$	−19.0725	−	2.87471i	−1.36932	−	0.206392i
$195$	−0.00749346			−0.000536618
$196$	6.48410	+	2.63750i	0.463150	+	0.188393i
$197$	−20.7339			−1.47723			−0.738616	−	0.674126i	$-0.764520\pi$
$197$	−20.7339			−1.47723			−0.738616	+	0.674126i	$0.764520\pi$
$198$	−1.75589	−	0.264658i	−0.124786	−	0.0188084i
$199$	−10.3634	+	7.06563i	−0.734640	+	0.500869i	−0.871911	−	0.489664i	$-0.837119\pi$
$199$	−10.3634	+	7.06563i	−0.734640	+	0.500869i	0.137271	+	0.990534i	$0.456167\pi$
$200$	3.66097	+	1.12926i	0.258870	+	0.0798508i
$201$	0.293137	+	3.91164i	0.0206763	+	0.275906i
$202$	−11.5177	+	5.54664i	−0.810383	+	0.390260i
$203$	−1.86269	+	6.78416i	−0.130735	+	0.476154i
$204$	0.223814	+	0.107783i	0.0156701	+	0.00754634i
$205$	3.12230	−	7.95549i	0.218071	−	0.555635i
$206$	0.556558	−	7.42675i	0.0387772	−	0.517446i
$207$	−6.35452	−	16.1911i	−0.441670	−	1.12536i
$208$	0.0105215	−	0.00324544i	0.000729532	−	0.000225031i
$209$	2.65989	−	3.33540i	0.183989	−	0.230715i
$210$	0.831542	+	1.59710i	0.0573818	+	0.110210i
$211$	13.6037	+	17.0586i	0.936520	+	1.17436i	0.984478	+	0.175510i	$0.0561574\pi$
$211$	13.6037	+	17.0586i	0.936520	+	1.17436i	−0.0479575	+	0.998849i	$0.515271\pi$
$212$	6.51123	+	4.43928i	0.447193	+	0.304891i
$213$	−1.09809	−	1.01888i	−0.0752400	−	0.0698125i
$214$	−4.69376	+	8.12982i	−0.320859	+	0.555743i
$215$	−4.70477	−	8.14890i	−0.320862	−	0.555750i
$216$	−0.784954	+	3.43911i	−0.0534094	+	0.234002i
$217$	−8.17481	+	12.8339i	−0.554942	+	0.871221i
$218$	−2.95556	−	12.9492i	−0.200176	−	0.877028i
$219$	−0.986723	+	0.915545i	−0.0666765	+	0.0618668i
$220$	0.729080	−	0.109891i	0.0491546	−	0.00740886i
$221$	0.00429651		0.000647594i	0.000289014		4.35619e-5i
$222$	−0.739036	+	0.685725i	−0.0496008	+	0.0460228i
$223$	1.32746	+	5.81596i	0.0888930	+	0.389466i	0.999728	−	0.0233041i	$-0.00741859\pi$
$223$	1.32746	+	5.81596i	0.0888930	+	0.389466i	−0.910835	+	0.412770i	$0.864561\pi$
$224$	−1.85926	−	1.88232i	−0.124227	−	0.125768i
$225$	−2.21973	+	9.72525i	−0.147982	+	0.648350i
$226$	−3.81367	−	6.60548i	−0.253682	−	0.439390i
$227$	11.9268	−	20.6578i	0.791609	−	1.37111i	−0.133361	−	0.991068i	$-0.542577\pi$
$227$	11.9268	−	20.6578i	0.791609	−	1.37111i	0.924970	−	0.380040i	$-0.124090\pi$
$228$	−2.88660	−	2.67837i	−0.191170	−	0.177380i
$229$	14.9468	+	10.1905i	0.987711	+	0.673410i	0.945474	−	0.325698i	$-0.105599\pi$
$229$	14.9468	+	10.1905i	0.987711	+	0.673410i	0.0422369	+	0.999108i	$0.486552\pi$
$230$	4.50289	+	5.64645i	0.296912	+	0.372316i
$231$	−0.909737	−	0.680116i	−0.0598563	−	0.0447483i
$232$	1.65790	−	2.07894i	0.108846	−	0.136489i
$233$	3.82105	−	1.17864i	0.250325	−	0.0772150i	−0.167053	−	0.985948i	$-0.553425\pi$
$233$	3.82105	−	1.17864i	0.250325	−	0.0772150i	0.417378	+	0.908733i	$0.362949\pi$
$234$	0.0104738	+	0.0266869i	0.000684697	+	0.00174458i
$235$	−0.912881	+	12.1816i	−0.0595498	+	0.794637i
$236$	−1.84605	+	4.70366i	−0.120168	+	0.306182i
$237$	−5.88073	−	2.83201i	−0.381995	−	0.183959i
$238$	−0.614803	−	0.843863i	−0.0398517	−	0.0546995i
$239$	9.95638	−	4.79474i	0.644025	−	0.310146i	−0.0832127	−	0.996532i	$-0.526518\pi$
$239$	9.95638	−	4.79474i	0.644025	−	0.310146i	0.727238	+	0.686386i	$0.240804\pi$
$240$	−0.0508587	−	0.678663i	−0.00328292	−	0.0438075i
$241$	−16.6454	−	5.13443i	−1.07223	−	0.330738i	−0.292118	−	0.956382i	$-0.594360\pi$
$241$	−16.6454	−	5.13443i	−1.07223	−	0.330738i	−0.780108	+	0.625644i	$0.784836\pi$
$242$	8.70433	−	5.93451i	0.559536	−	0.381485i
$243$	−13.9444	−	2.10178i	−0.894536	−	0.134830i
$244$	5.66004			0.362347
$245$	0.0932671	−	7.56726i	0.00595862	−	0.483455i
$246$	4.97621			0.317272
$247$	−0.0681067	−	0.0102654i	−0.00433353	−	0.000653174i
$248$	4.75189	−	3.23978i	0.301745	−	0.205726i
$249$	1.93990	+	0.598379i	0.122936	+	0.0379207i
$250$	−0.713490	−	9.52087i	−0.0451251	−	0.602152i
$251$	11.2713	−	5.42795i	0.711435	−	0.342609i	−0.0429172	−	0.999079i	$-0.513665\pi$
$251$	11.2713	−	5.42795i	0.711435	−	0.342609i	0.754353	+	0.656469i	$0.227951\pi$
$252$	4.52558	−	5.19374i	0.285085	−	0.327175i
$253$	−4.10467	−	1.97670i	−0.258058	−	0.124274i
$254$	−2.27961	+	5.80835i	−0.143035	+	0.364448i
$255$	0.0200700	−	0.267815i	0.00125683	−	0.0167712i
$256$	0.365341	+	0.930874i	0.0228338	+	0.0581796i
$257$	−2.58909	+	0.798629i	−0.161503	+	0.0498171i	−0.374452	−	0.927246i	$-0.622169\pi$
$257$	−2.58909	+	0.798629i	−0.161503	+	0.0498171i	0.212949	+	0.977063i	$0.431693\pi$
$258$	3.41602	−	4.28355i	0.212672	−	0.266682i
$259$	4.09954	−	1.07144i	0.254733	−	0.0665759i
$260$	−0.00742190	−	0.00930677i	−0.000460287	−	0.000577181i
$261$	5.72045	+	3.90014i	0.354087	+	0.241412i
$262$	15.1734	+	14.0788i	0.937413	+	0.869792i
$263$	−12.5591	+	21.7530i	−0.774428	+	1.34135i	0.160687	+	0.987005i	$0.448629\pi$
$263$	−12.5591	+	21.7530i	−0.774428	+	1.34135i	−0.935115	+	0.354344i	$0.884704\pi$
$264$	0.214657	+	0.371797i	0.0132112	+	0.0228826i
$265$	1.89584	−	8.30623i	0.116461	−	0.510248i
$266$	5.36984	+	15.6549i	0.329246	+	0.959863i
$267$	2.27095	+	9.94968i	0.138980	+	0.608911i
$268$	−4.56786	+	4.23836i	−0.279027	+	0.258899i
$269$	−2.64628	+	0.398863i	−0.161347	+	0.0243191i	−0.229219	−	0.973375i	$-0.573617\pi$
$269$	−2.64628	+	0.398863i	−0.161347	+	0.0243191i	0.0678721	+	0.997694i	$0.478379\pi$
$270$	3.77111	−	0.568403i	0.229502	−	0.0345919i
$271$	16.1177	−	14.9550i	0.979078	−	0.908452i	−0.0167354	−	0.999860i	$-0.505327\pi$
$271$	16.1177	−	14.9550i	0.979078	−	0.908452i	0.995814	+	0.0914083i	$0.0291368\pi$
$272$	0.0878117	+	0.384728i	0.00532437	+	0.0233276i
$273$	−0.00216549	+	0.0182099i	−0.000131061	+	0.00110212i
$274$	4.65835	−	20.4096i	0.281421	−	1.23299i
$275$	1.30642	+	2.26278i	0.0787799	+	0.136451i
$276$	−2.10259	+	3.64180i	−0.126561	+	0.219210i
$277$	12.9354	+	12.0023i	0.777213	+	0.721148i	0.965340	−	0.260997i	$-0.0840511\pi$
$277$	12.9354	+	12.0023i	0.777213	+	0.721148i	−0.188127	+	0.982145i	$0.560242\pi$
$278$	3.98644	+	2.71791i	0.239091	+	0.163009i
$279$	9.33653	+	11.7076i	0.558964	+	0.700918i
$280$	−1.15997	+	2.61461i	−0.0693217	+	0.156253i
$281$	6.73336	−	8.44337i	0.401679	−	0.503689i	−0.539319	−	0.842101i	$-0.681318\pi$
$281$	6.73336	−	8.44337i	0.401679	−	0.503689i	0.940998	+	0.338412i	$0.109890\pi$
$282$	−6.79681	+	2.09654i	−0.404744	+	0.124847i
$283$	−8.61087	−	21.9401i	−0.511863	−	1.30421i	−0.920226	−	0.391386i	$-0.871996\pi$
$283$	−8.61087	−	21.9401i	−0.511863	−	1.30421i	0.408363	−	0.912819i	$-0.366100\pi$
$284$	0.177829	−	2.37296i	0.0105522	−	0.140810i
$285$	−1.55534	+	3.96293i	−0.0921302	+	0.234744i
$286$	0.00676552	+	0.00325810i	0.000400054	+	0.000192656i
$287$	−18.4304	−	9.88653i	−1.08791	−	0.583584i
$288$	−2.34588	+	1.12972i	−0.138232	+	0.0665691i
$289$	−1.25877	−	16.7972i	−0.0740455	−	0.988069i
$290$	−2.74705	−	0.847353i	−0.161312	−	0.0497583i
$291$	−10.0320	+	6.83969i	−0.588085	+	0.400950i
$292$	−2.11439	−	0.318694i	−0.123736	−	0.0186501i
$293$	24.4377			1.42766			0.713832	−	0.700317i	$-0.246958\pi$
$293$	24.4377			1.42766			0.713832	+	0.700317i	$0.246958\pi$
$294$	4.12143	−	1.55920i	0.240367	−	0.0909346i
$295$	5.46284			0.318059
$296$	−1.58364	−	0.238695i	−0.0920472	−	0.0138739i
$297$	−1.98774	+	1.35521i	−0.115340	+	0.0786375i
$298$	10.5810	+	3.26381i	0.612942	+	0.189067i
$299$	0.00549663	+	0.0733474i	0.000317878	+	0.00424179i
$300$	2.17290	−	1.04641i	0.125452	−	0.0604146i
$301$	−21.1623	+	9.07821i	−1.21978	+	0.523259i
$302$	13.2170	+	6.36496i	0.760551	+	0.366262i
$303$	−2.94003	+	7.49106i	−0.168900	+	0.430350i
$304$	0.467467	−	6.23792i	0.0268111	−	0.357769i
$305$	−2.23559	−	5.69618i	−0.128009	−	0.326163i
$306$	−0.981840	+	0.302858i	−0.0561281	+	0.0173132i
$307$	−5.03491	+	6.31357i	−0.287357	+	0.360335i	−0.904468	−	0.426542i	$-0.859732\pi$
$307$	−5.03491	+	6.31357i	−0.287357	+	0.360335i	0.617111	+	0.786876i	$0.288303\pi$
$308$	−0.0563555	−	1.80350i	−0.00321116	−	0.102764i
$309$	−2.92308	−	3.66543i	−0.166288	−	0.208519i
$310$	−5.13736	−	3.50259i	−0.291782	−	0.198934i
$311$	−13.7558	−	12.7635i	−0.780017	−	0.723750i	0.185909	−	0.982567i	$-0.440477\pi$
$311$	−13.7558	−	12.7635i	−0.780017	−	0.723750i	−0.965926	+	0.258817i	$0.916667\pi$
$312$	0.00346560	−	0.00600260i	0.000196201	−	0.000339830i
$313$	4.71554	+	8.16755i	0.266538	+	0.461657i	0.967965	−	0.251084i	$-0.0807869\pi$
$313$	4.71554	+	8.16755i	0.266538	+	0.461657i	−0.701427	+	0.712741i	$0.747454\pi$
$314$	−4.40510	+	19.3000i	−0.248594	+	1.08916i
$315$	−7.01441	−	2.50307i	−0.395217	−	0.141032i
$316$	−2.30726	−	10.1088i	−0.129793	−	0.568662i
$317$	−8.32013	+	7.71996i	−0.467305	+	0.433596i	−0.878349	−	0.478020i	$-0.841355\pi$
$317$	−8.32013	+	7.71996i	−0.467305	+	0.433596i	0.411044	+	0.911616i	$0.365164\pi$
$318$	4.90542	−	0.739373i	0.275082	−	0.0414620i
$319$	1.79321	−	0.270282i	0.100400	−	0.0151329i
$320$	0.792517	−	0.735348i	0.0443030	−	0.0411072i
$321$	1.31498	+	5.76128i	0.0733948	+	0.321564i
$322$	15.0228	−	9.31080i	0.837186	−	0.518871i
$323$	0.549298	−	2.40663i	0.0305638	−	0.133909i
$324$	−2.79529	−	4.84159i	−0.155294	−	0.268977i
$325$	0.0210919	−	0.0365322i	0.00116997	−	0.00202644i
$326$	−1.65584	−	1.53639i	−0.0917083	−	0.0850928i
$327$	−6.90830	−	4.71000i	−0.382030	−	0.260464i
$328$	4.92869	+	6.18038i	0.272141	+	0.341255i
$329$	29.3387	+	5.73867i	1.61750	+	0.316383i
$330$	0.289387	−	0.362880i	0.0159302	−	0.0199759i
$331$	−8.20937	+	2.53225i	−0.451228	+	0.139185i	−0.512036	−	0.858964i	$-0.671108\pi$
$331$	−8.20937	+	2.53225i	−0.451228	+	0.139185i	0.0608081	+	0.998149i	$0.480632\pi$
$332$	1.17819	+	3.00199i	0.0646618	+	0.164756i
$333$	0.311620	−	4.15828i	0.0170767	−	0.227872i
$334$	0.0629337	−	0.160353i	0.00344358	−	0.00877410i
$335$	6.06963	+	2.92298i	0.331619	+	0.159699i
$336$	−1.66392	−	0.0725299i	−0.0907744	−	0.00395683i
$337$	12.3332	−	5.93937i	0.671834	−	0.323538i	−0.0666821	−	0.997774i	$-0.521241\pi$
$337$	12.3332	−	5.93937i	0.671834	−	0.323538i	0.738516	+	0.674236i	$0.235527\pi$
$338$	0.971482	+	12.9635i	0.0528417	+	0.705123i
$339$	−4.58811	−	1.41524i	−0.249192	−	0.0768655i
$340$	0.352501	−	0.240331i	0.0191171	−	0.0130338i
$341$	3.87848	+	0.584587i	0.210032	+	0.0316572i
$342$	16.2874			0.880721
$343$	−18.3623	−	2.41346i	−0.991473	−	0.130315i
$344$	8.70351			0.469262
$345$	4.49553	+	0.677592i	0.242031	+	0.0364803i
$346$	2.08585	−	1.42211i	0.112136	−	0.0764529i
$347$	6.51213	+	2.00873i	0.349590	+	0.107834i	0.464577	−	0.885533i	$-0.346206\pi$
$347$	6.51213	+	2.00873i	0.349590	+	0.107834i	−0.114987	+	0.993367i	$0.536683\pi$
$348$	−0.125090	−	1.66920i	−0.00670550	−	0.0894787i
$349$	9.42498	−	4.53883i	0.504507	−	0.242958i	−0.164277	−	0.986414i	$-0.552529\pi$
$349$	9.42498	−	4.53883i	0.504507	−	0.242958i	0.668785	+	0.743456i	$0.266815\pi$
$350$	−10.1267	−	0.441421i	−0.541297	−	0.0235950i
$351$	0.0349941	+	0.0168523i	0.00186785	+	0.000899509i
$352$	−0.249160	+	0.634849i	−0.0132803	+	0.0338375i
$353$	0.803203	−	10.7180i	0.0427502	−	0.570461i	−0.934166	−	0.356839i	$-0.883855\pi$
$353$	0.803203	−	10.7180i	0.0427502	−	0.570461i	0.976916	−	0.213623i	$-0.0685263\pi$
$354$	1.16209	+	2.96096i	0.0617644	+	0.157373i
$355$	−2.45836	+	0.758303i	−0.130476	+	0.0402465i
$356$	−10.1081	+	12.6752i	−0.535728	+	0.671782i
$357$	−0.645021	−	0.126166i	−0.0341381	−	0.00667744i
$358$	0.143400	+	0.179817i	0.00757890	+	0.00950365i
$359$	−9.88293	−	6.73807i	−0.521601	−	0.355622i	0.273721	−	0.961809i	$-0.411746\pi$
$359$	−9.88293	−	6.73807i	−0.521601	−	0.355622i	−0.795322	+	0.606188i	$0.792698\pi$
$360$	2.06350	+	1.91465i	0.108756	+	0.100911i
$361$	−10.0651	+	17.4332i	−0.529741	+	0.917538i
$362$	−11.7618	−	20.3721i	−0.618188	−	1.07073i
$363$	1.47570	−	6.46545i	0.0774540	−	0.339348i
$364$	−0.0247613	+	0.0153465i	−0.00129784	+	0.000804377i
$365$	0.514409	+	2.25377i	0.0269254	+	0.117968i
$366$	2.61186	−	2.42346i	0.136524	−	0.126676i
$367$	12.2412	−	1.84507i	0.638986	−	0.0963117i	0.178445	−	0.983950i	$-0.442893\pi$
$367$	12.2412	−	1.84507i	0.638986	−	0.0963117i	0.460541	+	0.887638i	$0.347655\pi$
$368$	−6.60557	+	0.995630i	−0.344339	+	0.0519008i
$369$	−15.0880	+	13.9996i	−0.785452	+	0.728793i
$370$	0.385282	+	1.68803i	0.0200299	+	0.0877566i
$371$	−19.6372	−	7.00747i	−1.01951	−	0.363810i
$372$	0.805615	−	3.52963i	0.0417692	−	0.183003i
$373$	7.88597	+	13.6589i	0.408320	+	0.707231i	0.994702	−	0.102804i	$-0.0327814\pi$
$373$	7.88597	+	13.6589i	0.408320	+	0.707231i	−0.586382	+	0.810035i	$0.699448\pi$
$374$	−0.134565	+	0.233073i	−0.00695817	+	0.0120519i
$375$	−4.40579	−	4.08797i	−0.227514	−	0.211102i
$376$	−9.33578	−	6.36503i	−0.481456	−	0.328251i
$377$	−0.0182545	−	0.0228904i	−0.000940156	−	0.00117892i
$378$	−0.291495	−	9.32847i	−0.0149929	−	0.479805i
$379$	20.2615	−	25.4071i	1.04076	−	1.30508i	0.0897381	−	0.995965i	$-0.471397\pi$
$379$	20.2615	−	25.4071i	1.04076	−	1.30508i	0.951026	−	0.309111i	$-0.100032\pi$
$380$	−6.46239	+	1.99338i	−0.331514	+	0.102258i
$381$	1.43502	+	3.65636i	0.0735181	+	0.187321i
$382$	−0.00227420	+	0.0303470i	−0.000116358	+	0.00155269i
$383$	−9.24838	+	23.5645i	−0.472570	+	1.20409i	0.473692	+	0.880690i	$0.342921\pi$
$383$	−9.24838	+	23.5645i	−0.472570	+	1.20409i	−0.946263	+	0.323399i	$0.895174\pi$
$384$	0.567161	+	0.273130i	0.0289428	+	0.0139381i
$385$	−1.79276	+	0.769058i	−0.0913675	+	0.0391948i
$386$	−12.6845	+	6.10855i	−0.645626	+	0.310917i
$387$	1.69350	+	22.5982i	0.0860855	+	1.14873i
$388$	−18.4310	−	5.68520i	−0.935691	−	0.288623i
$389$	−10.2324	+	6.97632i	−0.518802	+	0.353713i	−0.794239	−	0.607606i	$-0.792130\pi$
$389$	−10.2324	+	6.97632i	−0.518802	+	0.353713i	0.275436	+	0.961319i	$0.411178\pi$
$390$	−0.00740976	−	0.00111684i	−0.000375208	−	5.65535e-5i
$391$	−2.63615			−0.133316
$392$	6.01858	+	3.57445i	0.303984	+	0.180537i
$393$	13.0300			0.657275
$394$	−20.5024	−	3.09023i	−1.03289	−	0.155684i
$395$	−9.26199	+	6.31472i	−0.466021	+	0.317728i
$396$	−1.69683	−	0.523403i	−0.0852690	−	0.0263020i
$397$	−2.21539	−	29.5624i	−0.111187	−	1.48369i	−0.721986	−	0.691907i	$-0.756771\pi$
$397$	−2.21539	−	29.5624i	−0.111187	−	1.48369i	0.610799	−	0.791786i	$-0.290848\pi$
$398$	−11.3007	+	5.44213i	−0.566453	+	0.272789i
$399$	9.18090	+	4.92486i	0.459620	+	0.246551i
$400$	3.45177	+	1.66229i	0.172589	+	0.0831143i
$401$	5.70057	−	14.5248i	0.284673	−	0.725335i	−0.714984	−	0.699141i	$-0.753566\pi$
$401$	5.70057	−	14.5248i	0.284673	−	0.725335i	0.999657	−	0.0261938i	$-0.00833871\pi$
$402$	−0.293137	+	3.91164i	−0.0146203	+	0.195095i
$403$	−0.0231351	−	0.0589472i	−0.00115244	−	0.00293637i
$404$	−12.2158	+	3.76806i	−0.607756	+	0.187468i
$405$	−3.76843	+	4.72546i	−0.187255	+	0.234810i
$406$	−2.85301	+	6.43076i	−0.141593	+	0.319153i
$407$	−0.680994	−	0.853939i	−0.0337556	−	0.0423282i
$408$	0.205250	+	0.139937i	0.0101614	+	0.00692792i
$409$	−10.0742	−	9.34748i	−0.498136	−	0.462203i	0.390640	−	0.920543i	$-0.372254\pi$
$409$	−10.0742	−	9.34748i	−0.498136	−	0.462203i	−0.888777	+	0.458340i	$0.848444\pi$
$410$	4.27313	−	7.40128i	0.211035	−	0.365523i
$411$	−6.58913	−	11.4127i	−0.325018	−	0.562947i
$412$	1.65724	−	7.26085i	0.0816464	−	0.357716i
$413$	1.57867	−	13.2753i	0.0776813	−	0.653236i
$414$	−3.87039	−	16.9573i	−0.190219	−	0.833406i
$415$	2.55580	−	2.37144i	0.125459	−	0.116409i
$416$	0.0108876	−	0.00164105i	0.000533811	−	8.04590e-5i
$417$	3.00330	−	0.452674i	0.147072	−	0.0221676i
$418$	3.12730	−	2.90171i	0.152961	−	0.141927i
$419$	4.63704	+	20.3162i	0.226534	+	0.992510i	0.952442	+	0.304719i	$0.0985625\pi$
$419$	4.63704	+	20.3162i	0.226534	+	0.992510i	−0.725908	+	0.687791i	$0.758580\pi$
$420$	0.584219	+	1.70320i	0.0285070	+	0.0831075i
$421$	−0.933055	+	4.08798i	−0.0454743	+	0.199236i	−0.992562	−	0.121738i	$-0.961153\pi$
$421$	−0.933055	+	4.08798i	−0.0454743	+	0.199236i	0.947088	+	0.320974i	$0.104010\pi$
$422$	10.9094	+	18.8956i	0.531059	+	0.919821i
$423$	14.7099	−	25.4784i	0.715221	−	1.23880i
$424$	5.77687	+	5.36015i	0.280549	+	0.260312i
$425$	1.24916	+	0.851666i	0.0605934	+	0.0413119i
$426$	−0.933970	−	1.17116i	−0.0452510	−	0.0567430i
$427$	−14.4884	+	3.78662i	−0.701143	+	0.183248i
$428$	−5.85302	+	7.33945i	−0.282916	+	0.354766i
$429$	0.00451702	−	0.00139332i	0.000218084	−	6.72699e-5i
$430$	−3.43769	−	8.75909i	−0.165780	−	0.422401i
$431$	−1.75992	+	23.4845i	−0.0847724	+	1.13121i	0.778897	+	0.627151i	$0.215779\pi$
$431$	−1.75992	+	23.4845i	−0.0847724	+	1.13121i	−0.863670	+	0.504058i	$0.831840\pi$
$432$	−1.28876	+	3.28371i	−0.0620055	+	0.157987i
$433$	2.94913	+	1.42023i	0.141726	+	0.0682518i	0.503403	−	0.864052i	$-0.332081\pi$
$433$	2.94913	+	1.42023i	0.141726	+	0.0682518i	−0.361676	+	0.932304i	$0.617795\pi$
$434$	−9.99630	+	11.4722i	−0.479838	+	0.550681i
$435$	−1.63046	+	0.785186i	−0.0781743	+	0.0376468i
$436$	−0.992578	−	13.2450i	−0.0475359	−	0.634322i
$437$	39.9308	+	12.3170i	1.91015	+	0.589203i
$438$	−1.11216	+	0.758256i	−0.0531409	+	0.0362309i
$439$	0.544213	+	0.0820270i	0.0259739	+	0.00391493i	0.162016	−	0.986788i	$-0.448200\pi$
$439$	0.544213	+	0.0820270i	0.0259739	+	0.00391493i	−0.136042	+	0.990703i	$0.543438\pi$
$440$	0.737315			0.0351501
$441$	−8.10978	+	16.3224i	−0.386180	+	0.777259i
$442$	0.00434504			0.000206672
$443$	−22.0646	−	3.32570i	−1.04832	−	0.158009i	−0.397780	−	0.917481i	$-0.630219\pi$
$443$	−22.0646	−	3.32570i	−1.04832	−	0.158009i	−0.650540	+	0.759472i	$0.725457\pi$
$444$	−0.832983	+	0.567918i	−0.0395316	+	0.0269522i
$445$	16.7486	+	5.16625i	0.793959	+	0.244904i
$446$	0.445805	+	5.94885i	0.0211095	+	0.281686i
$447$	6.28014	−	3.02436i	0.297041	−	0.143047i
$448$	−1.55795	−	2.13841i	−0.0736064	−	0.101030i
$449$	−13.9116	−	6.69946i	−0.656527	−	0.316167i	0.0757966	−	0.997123i	$-0.475850\pi$
$449$	−13.9116	−	6.69946i	−0.656527	−	0.316167i	−0.732324	+	0.680956i	$0.761564\pi$
$450$	−3.64441	+	9.28579i	−0.171799	+	0.437737i
$451$	−0.402881	+	5.37608i	−0.0189709	+	0.253150i
$452$	−2.78658	−	7.10010i	−0.131070	−	0.333960i
$453$	8.82434	−	2.72195i	0.414604	−	0.127888i
$454$	14.8725	−	18.6495i	0.698000	−	0.875264i
$455$	0.0252247	+	0.0188579i	0.00118255	+	0.000884071i
$456$	−2.45517	−	3.07869i	−0.114974	−	0.144173i
$457$	8.10392	+	5.52516i	0.379085	+	0.258456i	0.737840	−	0.674976i	$-0.235846\pi$
$457$	8.10392	+	5.52516i	0.379085	+	0.258456i	−0.358754	+	0.933432i	$0.616798\pi$
$458$	13.2610	+	12.3044i	0.619646	+	0.574948i
$459$	−0.696025	+	1.20555i	−0.0324877	+	0.0562703i
$460$	3.61104	+	6.25451i	0.168366	+	0.291618i
$461$	4.25075	−	18.6237i	0.197977	−	0.867394i	−0.774162	−	0.632988i	$-0.781828\pi$
$461$	4.25075	−	18.6237i	0.197977	−	0.867394i	0.972139	−	0.234406i	$-0.0753146\pi$
$462$	−0.798210	−	0.808108i	−0.0371361	−	0.0375966i
$463$	3.90205	+	17.0960i	0.181344	+	0.794518i	0.980992	+	0.194049i	$0.0621622\pi$
$463$	3.90205	+	17.0960i	0.181344	+	0.794518i	−0.799648	+	0.600469i	$0.794981\pi$
$464$	1.94923	−	1.80862i	0.0904908	−	0.0839632i
$465$	−3.87037	+	0.583365i	−0.179484	+	0.0270529i
$466$	3.95403	−	0.595975i	0.183167	−	0.0276080i
$467$	27.3276	−	25.3563i	1.26457	−	1.17335i	0.288124	−	0.957593i	$-0.406968\pi$
$467$	27.3276	−	25.3563i	1.26457	−	1.17335i	0.976447	−	0.215757i	$-0.0692220\pi$
$468$	0.00637938	+	0.0279499i	0.000294887	+	0.00129198i
$469$	8.85718	−	13.9052i	0.408987	−	0.642081i
$470$	−2.71825	+	11.9094i	−0.125384	+	0.549341i
$471$	6.23090	+	10.7922i	0.287105	+	0.497280i
$472$	−2.52648	+	4.37598i	−0.116290	+	0.201421i
$473$	4.35119	+	4.03732i	0.200068	+	0.185636i
$474$	−5.39296	−	3.67686i	−0.247707	−	0.168884i
$475$	−14.9423	−	18.7371i	−0.685600	−	0.859715i
$476$	−0.482165	−	0.926069i	−0.0221000	−	0.0424463i
$477$	−12.7933	+	16.0423i	−0.585765	+	0.734526i
$478$	10.5598	−	3.25727i	0.482994	−	0.148984i
$479$	2.67326	+	6.81135i	0.122144	+	0.311219i	0.978848	−	0.204591i	$-0.0655864\pi$
$479$	2.67326	+	6.81135i	0.122144	+	0.311219i	−0.856703	+	0.515810i	$0.827491\pi$
$480$	0.0508587	−	0.678663i	0.00232137	−	0.0309766i
$481$	−0.00644236	+	0.0164149i	−0.000293746	+	0.000748453i
$482$	−15.6943	−	7.55796i	−0.714854	−	0.344256i
$483$	2.94576	−	10.7288i	0.134037	−	0.488178i
$484$	9.49160	−	4.57092i	0.431437	−	0.207769i
$485$	1.55831	+	20.7942i	0.0707592	+	0.944216i
$486$	−13.4754	−	4.15662i	−0.611258	−	0.188548i
$487$	25.5226	−	17.4010i	1.15654	−	0.788514i	0.175912	−	0.984406i	$-0.443713\pi$
$487$	25.5226	−	17.4010i	1.15654	−	0.788514i	0.980625	+	0.195892i	$0.0627603\pi$
$488$	5.59682	+	0.843585i	0.253356	+	0.0381873i
$489$	−1.42193			−0.0643020
$490$	1.22007	−	7.46884i	0.0551170	−	0.337408i
$491$	8.72387			0.393703			0.196851	−	0.980433i	$-0.436928\pi$
$491$	8.72387			0.393703			0.196851	+	0.980433i	$0.436928\pi$
$492$	4.92063	+	0.741665i	0.221839	+	0.0334369i
$493$	0.866994	−	0.591106i	0.0390474	−	0.0266221i
$494$	−0.0658160	−	0.0203016i	−0.00296120	−	0.000913410i
$495$	0.143464	+	1.91440i	0.00644825	+	0.0860459i
$496$	5.18168	−	2.49536i	0.232664	−	0.112045i
$497$	1.13233	+	6.19321i	0.0507921	+	0.277804i
$498$	1.82905	+	0.880822i	0.0819615	+	0.0394706i
$499$	9.00455	−	22.9432i	0.403099	−	1.02708i	−0.574854	−	0.818256i	$-0.694941\pi$
$499$	9.00455	−	22.9432i	0.403099	−	1.02708i	0.977953	−	0.208824i	$-0.0669634\pi$
$500$	0.713490	−	9.52087i	0.0319083	−	0.425786i
$501$	−0.0396169	−	0.100942i	−0.00176995	−	0.00450976i
$502$	11.9544	−	3.68743i	0.533549	−	0.164578i
$503$	−3.06417	+	3.84234i	−0.136624	+	0.171322i	−0.845437	−	0.534075i	$-0.820660\pi$
$503$	−3.06417	+	3.84234i	−0.136624	+	0.171322i	0.708812	+	0.705397i	$0.249231\pi$
$504$	5.24912	−	4.46123i	0.233814	−	0.198719i
$505$	8.61707	+	10.8055i	0.383454	+	0.480837i
$506$	−3.76421	−	2.56639i	−0.167339	−	0.114090i
$507$	5.99888	+	5.56615i	0.266420	+	0.247201i
$508$	−3.11984	+	5.40372i	−0.138420	+	0.239751i
$509$	11.6080	+	20.1056i	0.514514	+	0.891165i	0.999858	+	0.0168414i	$0.00536105\pi$
$509$	11.6080	+	20.1056i	0.514514	+	0.891165i	−0.485344	+	0.874323i	$0.661306\pi$
$510$	0.0597616	−	0.261833i	0.00264629	−	0.0115942i
$511$	5.62557	−	0.598768i	0.248861	−	0.0264879i
$512$	0.222521	+	0.974928i	0.00983413	+	0.0430861i
$513$	16.1757	−	15.0089i	0.714176	−	0.662658i
$514$	−2.67920	+	0.403825i	−0.118175	+	0.0178119i
$515$	−7.96179	+	1.20005i	−0.350838	+	0.0528804i
$516$	4.01629	−	3.72658i	0.176807	−	0.164053i
$517$	−1.71473	−	7.51272i	−0.0754137	−	0.330409i
$518$	4.21344	−	0.448465i	0.185128	−	0.0197044i
$519$	0.353626	−	1.54934i	0.0155224	−	0.0680083i
$520$	−0.00595190	−	0.0103090i	−0.000261008	−	0.000452080i
$521$	−2.56906	+	4.44974i	−0.112553	+	0.194947i	−0.916799	−	0.399350i	$-0.869236\pi$
$521$	−2.56906	+	4.44974i	−0.112553	+	0.194947i	0.804246	+	0.594296i	$0.202569\pi$
$522$	5.07527	+	4.70916i	0.222139	+	0.206115i
$523$	−12.5791	−	8.57629i	−0.550046	−	0.375015i	0.256174	−	0.966631i	$-0.417538\pi$
$523$	−12.5791	−	8.57629i	−0.550046	−	0.375015i	−0.806220	+	0.591616i	$0.798490\pi$
$524$	12.9055	+	16.1830i	0.563781	+	0.706960i
$525$	−4.86205	+	4.13226i	−0.212197	+	0.180347i
$526$	−15.6610	+	19.6382i	−0.682851	+	0.856268i
$527$	2.16873	−	0.668965i	0.0944714	−	0.0291406i
$528$	0.156846	+	0.399638i	0.00682586	+	0.0173920i
$529$	1.61603	−	21.5644i	0.0702622	−	0.937584i
$530$	3.11265	−	7.93090i	0.135205	−	0.344496i
$531$	−11.8536	−	5.70840i	−0.514403	−	0.247723i
$532$	2.97662	+	16.2804i	0.129053	+	0.705844i
$533$	0.0784195	−	0.0377648i	0.00339673	−	0.00163578i
$534$	0.762662	+	10.1770i	0.0330036	+	0.440403i
$535$	9.69813	+	2.99148i	0.419287	+	0.129333i
$536$	−5.14854	+	3.51021i	−0.222383	+	0.151618i
$537$	0.143165	+	0.0215787i	0.00617803	+	0.000931188i
$538$	−2.67617			−0.115378
$539$	1.35082	+	4.57885i	0.0581838	+	0.197225i
$540$	3.81371			0.164116
$541$	−19.8799	−	2.99641i	−0.854704	−	0.128826i	−0.292948	−	0.956128i	$-0.594636\pi$
$541$	−19.8799	−	2.99641i	−0.854704	−	0.128826i	−0.561757	+	0.827303i	$0.689874\pi$
$542$	18.1666	−	12.3858i	0.780321	−	0.532014i
$543$	−14.1503	−	4.36478i	−0.607246	−	0.187311i
$544$	0.0294901	+	0.393519i	0.00126438	+	0.0168720i
$545$	−12.9376	+	6.23041i	−0.554185	+	0.266881i
$546$	−0.00485535	+	0.0176838i	−0.000207790	+	0.000756796i
$547$	−24.8597	−	11.9718i	−1.06292	−	0.511877i	−0.181104	−	0.983464i	$-0.557967\pi$
$547$	−24.8597	−	11.9718i	−1.06292	−	0.511877i	−0.881819	+	0.471587i	$0.843681\pi$
$548$	7.64821	−	19.4873i	0.326716	−	0.832458i
$549$	−1.10131	+	14.6960i	−0.0470029	+	0.627210i
$550$	0.954576	+	2.43222i	0.0407033	+	0.103710i
$551$	−15.8946	+	4.90282i	−0.677131	+	0.208867i
$552$	−2.62189	+	3.28775i	−0.111595	+	0.139936i
$553$	12.6689	+	24.3325i	0.538737	+	1.03472i
$554$	11.0021	+	13.7962i	0.467433	+	0.586143i
$555$	0.900554	+	0.613988i	0.0382264	+	0.0260623i
$556$	3.53683	+	3.28170i	0.149995	+	0.139175i
$557$	21.1662	−	36.6610i	0.896843	−	1.55338i	0.0653351	−	0.997863i	$-0.479188\pi$
$557$	21.1662	−	36.6610i	0.896843	−	1.55338i	0.831508	−	0.555514i	$-0.187478\pi$
$558$	7.48732	+	12.9684i	0.316963	+	0.548997i
$559$	0.0213244	−	0.0934284i	0.000901927	−	0.00395160i
$560$	−1.53671	+	2.41252i	−0.0649377	+	0.101948i
$561$	0.0376989	+	0.165169i	0.00159165	+	0.00697346i
$562$	7.91657	−	7.34550i	0.333940	−	0.309851i
$563$	−17.5040	+	2.63830i	−0.737705	+	0.111191i	−0.507137	−	0.861865i	$-0.669296\pi$
$563$	−17.5040	+	2.63830i	−0.737705	+	0.111191i	−0.230568	+	0.973056i	$0.574058\pi$
$564$	−7.03337	+	1.06011i	−0.296158	+	0.0446387i
$565$	−6.04480	+	5.60875i	−0.254307	+	0.235962i
$566$	−5.24469	−	22.9785i	−0.220451	−	0.965857i
$567$	10.3944	+	10.5233i	0.436523	+	0.441936i
$568$	0.529515	−	2.31996i	0.0222180	−	0.0973432i
$569$	−9.79214	−	16.9605i	−0.410508	−	0.711021i	0.584437	−	0.811439i	$-0.301315\pi$
$569$	−9.79214	−	16.9605i	−0.410508	−	0.711021i	−0.994945	+	0.100418i	$0.967982\pi$
$570$	−2.12861	+	3.68686i	−0.0891576	+	0.154426i
$571$	−15.0837	−	13.9957i	−0.631235	−	0.585701i	0.298283	−	0.954478i	$-0.403586\pi$
$571$	−15.0837	−	13.9957i	−0.631235	−	0.585701i	−0.929518	+	0.368777i	$0.879777\pi$
$572$	0.00620436	+	0.00423006i	0.000259417	+	0.000176868i
$573$	0.0119442	+	0.0149776i	0.000498977	+	0.000625698i
$574$	−16.7511	−	12.5230i	−0.699175	−	0.522701i
$575$	−15.9570	+	20.0094i	−0.665452	+	0.834450i
$576$	−2.48805	+	0.767462i	−0.103669	+	0.0319776i
$577$	−1.39031	−	3.54244i	−0.0578792	−	0.147474i	0.899009	−	0.437930i	$-0.144288\pi$
$577$	−1.39031	−	3.54244i	−0.0578792	−	0.147474i	−0.956888	+	0.290456i	$0.906193\pi$
$578$	1.25877	−	16.7972i	0.0523581	−	0.698670i
$579$	−3.23787	+	8.24996i	−0.134561	+	0.342857i
$580$	−2.59008	−	1.24731i	−0.107547	−	0.0517919i
$581$	−5.02427	−	6.89618i	−0.208442	−	0.286102i
$582$	−10.9393	+	5.26810i	−0.453450	+	0.218370i
$583$	0.401636	+	5.35946i	0.0166341	+	0.221966i
$584$	−2.04328	−	0.630268i	−0.0845515	−	0.0260807i
$585$	0.0256087	−	0.0174597i	0.00105879	−	0.000721870i
$586$	24.1647	+	3.64225i	0.998235	+	0.150460i
$587$	−12.5101			−0.516346			−0.258173	−	0.966099i	$-0.583120\pi$
$587$	−12.5101			−0.516346			−0.258173	+	0.966099i	$0.583120\pi$
$588$	4.30778	−	0.927521i	0.177650	−	0.0382503i
$589$	−35.9763			−1.48238
$590$	5.40183	+	0.814195i	0.222390	+	0.0335199i
$591$	−10.7841	+	7.35247i	−0.443599	+	0.302440i
$592$	−1.53038	−	0.472058i	−0.0628980	−	0.0194015i
$593$	−0.156210	−	2.08448i	−0.00641480	−	0.0855995i	0.993077	−	0.117461i	$-0.0374755\pi$
$593$	−0.156210	−	2.08448i	−0.00641480	−	0.0855995i	−0.999492	+	0.0318615i	$0.989856\pi$
$594$	−2.16752	+	1.04382i	−0.0889343	+	0.0428285i
$595$	−0.741539	+	0.851020i	−0.0304001	+	0.0348884i
$596$	9.97639	+	4.80437i	0.408649	+	0.196795i
$597$	−2.88463	+	7.34993i	−0.118060	+	0.300812i
$598$	−0.00549663	+	0.0733474i	−0.000224774	+	0.00299940i
$599$	5.29866	+	13.5008i	0.216497	+	0.551626i	0.997323	−	0.0731228i	$-0.0232965\pi$
$599$	5.29866	+	13.5008i	0.216497	+	0.551626i	−0.780826	+	0.624749i	$0.785201\pi$
$600$	2.30459	−	0.710870i	0.0940843	−	0.0290212i
$601$	−24.7475	+	31.0324i	−1.00947	+	1.26584i	−0.0457419	+	0.998953i	$0.514565\pi$
$601$	−24.7475	+	31.0324i	−1.00947	+	1.26584i	−0.963729	+	0.266883i	$0.914006\pi$
$602$	−22.2790	+	5.82273i	−0.908024	+	0.237317i
$603$	−10.1159	−	12.6849i	−0.411950	−	0.516569i
$604$	12.1207	+	8.26375i	0.493184	+	0.336247i
$605$	−8.34907	−	7.74681i	−0.339438	−	0.314953i
$606$	−4.02367	+	6.96921i	−0.163451	+	0.283105i
$607$	2.90744	+	5.03583i	0.118009	+	0.204398i	0.918979	−	0.394307i	$-0.129015\pi$
$607$	2.90744	+	5.03583i	0.118009	+	0.204398i	−0.800969	+	0.598705i	$0.795682\pi$
$608$	1.39196	−	6.09857i	0.0564514	−	0.247330i
$609$	1.43691	+	4.18909i	0.0582267	+	0.169751i
$610$	−1.36165	−	5.96576i	−0.0551314	−	0.241547i
$611$	−0.0911994	+	0.0846207i	−0.00368953	+	0.00342339i
$612$	−1.01601	+	0.153139i	−0.0410699	+	0.00619029i
$613$	−0.169613	+	0.0255650i	−0.00685059	+	0.00103256i	−0.152467	−	0.988309i	$-0.548722\pi$
$613$	−0.169613	+	0.0255650i	−0.00685059	+	0.00103256i	0.145616	+	0.989341i	$0.453484\pi$
$614$	−5.91966	+	5.49264i	−0.238898	+	0.221665i
$615$	−1.19714	−	5.24499i	−0.0482732	−	0.211499i
$616$	0.213072	−	1.79176i	0.00858491	−	0.0721920i
$617$	−2.59407	+	11.3654i	−0.104433	+	0.457552i	0.895489	+	0.445084i	$0.146826\pi$
$617$	−2.59407	+	11.3654i	−0.104433	+	0.457552i	−0.999922	+	0.0124683i	$0.996031\pi$
$618$	−2.34413	−	4.06015i	−0.0942946	−	0.163323i
$619$	−13.0419	+	22.5892i	−0.524199	+	0.907939i	0.475405	+	0.879767i	$0.342302\pi$
$619$	−13.0419	+	22.5892i	−0.524199	+	0.907939i	−0.999603	+	0.0281713i	$0.991032\pi$
$620$	−4.55794	−	4.22915i	−0.183051	−	0.169847i
$621$	−19.4701	−	13.2745i	−0.781307	−	0.532686i
$622$	−11.6998	−	14.6711i	−0.469120	−	0.588258i
$623$	17.3946	−	39.2079i	0.696901	−	1.57083i
$624$	0.00432153	−	0.00541903i	0.000173000	−	0.000216935i
$625$	8.44138	−	2.60382i	0.337655	−	0.104153i
$626$	3.44556	+	8.77914i	0.137712	+	0.350885i
$627$	0.200691	−	2.67803i	0.00801481	−	0.106950i
$628$	−7.23241	+	18.4279i	−0.288605	+	0.735353i
$629$	−0.569410	−	0.274214i	−0.0227039	−	0.0109336i
$630$	−6.56300	−	3.52056i	−0.261476	−	0.140262i
$631$	3.79775	−	1.82890i	0.151186	−	0.0728075i	−0.356761	−	0.934196i	$-0.616119\pi$
$631$	3.79775	−	1.82890i	0.151186	−	0.0728075i	0.507947	+	0.861388i	$0.330405\pi$
$632$	−0.774855	−	10.3397i	−0.0308221	−	0.411292i
$633$	13.1247	+	4.04843i	0.521660	+	0.160911i
$634$	−9.37780	+	6.39368i	−0.372440	+	0.253925i
$635$	6.67049	+	1.00541i	0.264710	+	0.0398987i
$636$	4.96083			0.196710
$637$	0.0531162	−	0.0558492i	0.00210454	−	0.00221282i
$638$	1.81346			0.0717956
$639$	6.12668	+	0.923448i	0.242368	+	0.0365310i
$640$	0.893263	−	0.609016i	0.0353093	−	0.0240735i
$641$	−30.3221	−	9.35314i	−1.19765	−	0.369427i	−0.369127	−	0.929379i	$-0.620343\pi$
$641$	−30.3221	−	9.35314i	−1.19765	−	0.369427i	−0.828525	+	0.559952i	$0.810820\pi$
$642$	0.441614	+	5.89292i	0.0174291	+	0.232575i
$643$	3.93846	−	1.89666i	0.155318	−	0.0747970i	−0.354610	−	0.935014i	$-0.615386\pi$
$643$	3.93846	−	1.89666i	0.155318	−	0.0747970i	0.509928	+	0.860217i	$0.329672\pi$
$644$	16.2427	−	6.96778i	0.640051	−	0.274569i
$645$	−5.33672	−	2.57003i	−0.210133	−	0.101195i
$646$	0.901853	−	2.29788i	0.0354829	−	0.0904090i
$647$	−3.13859	+	41.8816i	−0.123391	+	1.64654i	0.501017	+	0.865437i	$0.332959\pi$
$647$	−3.13859	+	41.8816i	−0.123391	+	1.64654i	−0.624408	+	0.781098i	$0.714660\pi$
$648$	−2.04247	−	5.20413i	−0.0802358	−	0.204438i
$649$	−3.29297	+	1.01575i	−0.129261	+	0.0398716i
$650$	0.0263011	−	0.0329805i	0.00103161	−	0.00129360i
$651$	0.299167	+	9.57401i	0.0117253	+	0.375235i
$652$	−1.40835	−	1.76602i	−0.0551554	−	0.0691627i
$653$	−17.1008	−	11.6591i	−0.669205	−	0.456256i	0.180458	−	0.983583i	$-0.442242\pi$
$653$	−17.1008	−	11.6591i	−0.669205	−	0.456256i	−0.849663	+	0.527326i	$0.823194\pi$
$654$	−6.12915	−	5.68702i	−0.239669	−	0.222380i
$655$	11.1890	−	19.3799i	0.437190	−	0.757235i
$656$	3.95250	+	6.84594i	0.154319	+	0.267289i
$657$	1.23888	−	5.42790i	0.0483335	−	0.211763i
$658$	28.1557	+	10.0473i	1.09762	+	0.391684i
$659$	−1.37169	−	6.00977i	−0.0534335	−	0.234107i	0.941159	−	0.337965i	$-0.109739\pi$
$659$	−1.37169	−	6.00977i	−0.0534335	−	0.234107i	−0.994592	+	0.103858i	$0.966881\pi$
$660$	0.340239	−	0.315696i	0.0132438	−	0.0122884i
$661$	−12.7764	+	1.92573i	−0.496944	+	0.0749022i	−0.392732	−	0.919653i	$-0.628470\pi$
$661$	−12.7764	+	1.92573i	−0.496944	+	0.0749022i	−0.104212	+	0.994555i	$0.533232\pi$
$662$	−8.49509	+	1.28043i	−0.330171	+	0.0497653i
$663$	0.00200505	−	0.00186041i	7.78696e−5	−	7.22524e-5i
$664$	0.717611	+	3.14406i	0.0278487	+	0.122013i
$665$	15.2086	−	9.42601i	0.589766	−	0.365525i
$666$	0.927899	−	4.06539i	0.0359554	−	0.157531i
$667$	8.88153	+	15.3833i	0.343894	+	0.595642i
$668$	0.0861301	−	0.149182i	0.00333248	−	0.00577202i
$669$	2.75283	+	2.55426i	0.106431	+	0.0987533i
$670$	5.56619	+	3.79496i	0.215041	+	0.146612i
$671$	2.40674	+	3.01795i	0.0929110	+	0.116507i
$672$	−1.63453	−	0.319715i	−0.0630533	−	0.0123333i
$673$	23.5703	−	29.5562i	0.908569	−	1.13931i	−0.0812098	−	0.996697i	$-0.525878\pi$
$673$	23.5703	−	29.5562i	0.908569	−	1.13931i	0.989779	−	0.142612i	$-0.0455502\pi$
$674$	13.0807	−	4.03486i	0.503849	−	0.155417i
$675$	4.93747	+	12.5805i	0.190043	+	0.484223i
$676$	−0.971482	+	12.9635i	−0.0373647	+	0.498597i
$677$	7.68598	−	19.5836i	0.295396	−	0.752657i	−0.703714	−	0.710483i	$-0.748476\pi$
$677$	7.68598	−	19.5836i	0.295396	−	0.752657i	0.999110	−	0.0421739i	$-0.0134283\pi$
$678$	−4.32593	−	2.08326i	−0.166136	−	0.0800071i
$679$	50.9825	+	2.22231i	1.95653	+	0.0852846i
$680$	0.384384	−	0.185109i	0.0147404	−	0.00709862i
$681$	−1.12214	−	14.9739i	−0.0430004	−	0.573800i
$682$	3.74804	+	1.15612i	0.143520	+	0.0442700i
$683$	18.8900	−	12.8790i	0.722804	−	0.492800i	−0.145171	−	0.989407i	$-0.546373\pi$
$683$	18.8900	−	12.8790i	0.722804	−	0.492800i	0.867976	+	0.496607i	$0.165421\pi$
$684$	16.1055	+	2.42751i	0.615808	+	0.0928181i
$685$	−22.6326			−0.864749
$686$	−17.7975	−	5.12327i	−0.679513	−	0.195607i
$687$	11.3878			0.434470
$688$	8.60630	+	1.29719i	0.328112	+	0.0494549i
$689$	0.0716928	−	0.0488793i	0.00273128	−	0.00186215i
$690$	4.34433	+	1.34005i	0.165386	+	0.0510147i
$691$	1.67889	+	22.4033i	0.0638681	+	0.852261i	0.933504	+	0.358567i	$0.116735\pi$
$691$	1.67889	+	22.4033i	0.0638681	+	0.852261i	−0.869636	+	0.493694i	$0.835646\pi$
$692$	2.27450	−	1.09534i	0.0864636	−	0.0416387i
$693$	4.69366	+	0.204595i	0.178298	+	0.00777194i
$694$	6.14001	+	2.95687i	0.233072	+	0.112241i
$695$	1.90569	−	4.85562i	0.0722869	−	0.184184i
$696$	0.125090	−	1.66920i	0.00474151	−	0.0632710i
$697$	1.13968	+	2.90385i	0.0431684	+	0.109991i
$698$	9.99619	−	3.08341i	0.378361	−	0.116709i
$699$	1.56944	−	1.96801i	0.0593616	−	0.0744371i
$700$	−9.94784	−	1.94580i	−0.375993	−	0.0735444i
$701$	−24.3083	−	30.4817i	−0.918113	−	1.15128i	−0.988113	−	0.153730i	$-0.950871\pi$
$701$	−24.3083	−	30.4817i	−0.918113	−	1.15128i	0.0699999	−	0.997547i	$-0.477700\pi$
$702$	0.0320916	+	0.0218797i	0.00121122	+	0.000825795i
$703$	7.34386	+	6.81411i	0.276979	+	0.256999i
$704$	−0.340996	+	0.590623i	−0.0128518	+	0.0222599i
$705$	3.84490	+	6.65956i	0.144807	+	0.250814i
$706$	2.39167	−	10.4786i	0.0900115	−	0.394366i
$707$	28.7487	−	17.8178i	1.08120	−	0.670108i
$708$	0.707803	+	3.10109i	0.0266009	+	0.116546i
$709$	−2.64319	+	2.45252i	−0.0992670	+	0.0921063i	−0.728245	−	0.685316i	$-0.759664\pi$
$709$	−2.64319	+	2.45252i	−0.0992670	+	0.0921063i	0.628978	+	0.777423i	$0.283473\pi$
$710$	−2.54392	+	0.383434i	−0.0954715	+	0.0143900i
$711$	26.6958	−	4.02374i	1.00117	−	0.150902i
$712$	−11.8843	+	11.0271i	−0.445384	+	0.413256i
$713$	8.54909	+	37.4560i	0.320166	+	1.40274i
$714$	−0.619013	−	0.220893i	−0.0231660	−	0.00826670i
$715$	0.00180649	−	0.00791476i	6.75590e−5	−	0.000295995i
$716$	0.114998	+	0.199182i	0.00429766	+	0.00744377i
$717$	3.47823	−	6.02447i	0.129897	−	0.224988i
$718$	−8.76829	−	8.13578i	−0.327230	−	0.303625i
$719$	31.7639	+	21.6563i	1.18459	+	0.807642i	0.985054	−	0.172248i	$-0.0551029\pi$
$719$	31.7639	+	21.6563i	1.18459	+	0.807642i	0.199540	+	0.979890i	$0.436055\pi$
$720$	1.75509	+	2.20081i	0.0654083	+	0.0820194i
$721$	0.615421	+	19.6948i	0.0229195	+	0.733473i
$722$	−12.5509	+	15.7384i	−0.467098	+	0.585722i
$723$	−10.4783	+	3.23213i	−0.389693	+	0.120204i
$724$	−8.59415	−	21.8975i	−0.319399	−	0.813816i
$725$	0.761302	−	10.1589i	0.0282741	−	0.377291i
$726$	2.42284	−	6.17330i	0.0899200	−	0.229112i
$727$	−0.0311157	−	0.0149845i	−0.00115402	−	0.000555745i	0.433307	−	0.901247i	$-0.357347\pi$
$727$	−0.0311157	−	0.0149845i	−0.00115402	−	0.000555745i	−0.434461	+	0.900691i	$0.643061\pi$
$728$	−0.0267720	+	0.0114847i	−0.000992237	+	0.000425650i
$729$	7.11277	−	3.42533i	0.263436	−	0.126864i
$730$	0.172756	+	2.30527i	0.00639399	+	0.0853218i
$731$	3.28201	+	1.01237i	0.121389	+	0.0374437i
$732$	2.94389	−	2.00711i	0.108809	−	0.0741849i
$733$	22.2194	+	3.34904i	0.820692	+	0.123699i	0.545949	−	0.837818i	$-0.316169\pi$
$733$	22.2194	+	3.34904i	0.820692	+	0.123699i	0.274743	+	0.961518i	$0.411407\pi$
$734$	12.3795			0.456935
$735$	−2.63492	−	3.96894i	−0.0971905	−	0.146397i
$736$	−6.68019			−0.246235
$737$	−4.20223	−	0.633384i	−0.154791	−	0.0233310i
$738$	−17.0061	+	11.5945i	−0.626001	+	0.426801i
$739$	−34.7970	−	10.7335i	−1.28003	−	0.394837i	−0.421139	−	0.906996i	$-0.638369\pi$
$739$	−34.7970	−	10.7335i	−1.28003	−	0.394837i	−0.858890	+	0.512159i	$0.828846\pi$
$740$	0.129391	+	1.72660i	0.00475650	+	0.0634711i
$741$	−0.0390638	+	0.0188121i	−0.00143504	+	0.000691080i
$742$	−18.3734	−	9.85597i	−0.674511	−	0.361824i
$743$	4.59773	+	2.21415i	0.168675	+	0.0812294i	0.516316	−	0.856398i	$-0.327303\pi$
$743$	4.59773	+	2.21415i	0.168675	+	0.0812294i	−0.347641	+	0.937628i	$0.613017\pi$
$744$	1.32268	−	3.37014i	0.0484919	−	0.123555i
$745$	0.894608	−	11.9377i	0.0327759	−	0.437364i
$746$	5.76214	+	14.6817i	0.210967	+	0.537535i
$747$	−8.02376	+	2.47500i	−0.293574	+	0.0905556i
$748$	−0.167799	+	0.210414i	−0.00613535	+	0.00769349i
$749$	10.0722	−	22.7030i	0.368031	−	0.829551i
$750$	−3.74730	−	4.69896i	−0.136832	−	0.171582i
$751$	17.7313	+	12.0890i	0.647025	+	0.441134i	0.841856	−	0.539703i	$-0.181463\pi$
$751$	17.7313	+	12.0890i	0.647025	+	0.441134i	−0.194831	+	0.980837i	$0.562416\pi$
$752$	−8.28285	−	7.68536i	−0.302044	−	0.280256i
$753$	3.93758	−	6.82008i	0.143493	−	0.248538i
$754$	−0.0146390	−	0.0253555i	−0.000533121	−	0.000923392i
$755$	3.52912	−	15.4621i	0.128438	−	0.562723i
$756$	1.10210	−	9.26773i	0.0400829	−	0.337064i
$757$	6.35502	+	27.8432i	0.230977	+	1.01198i	0.948831	+	0.315783i	$0.102267\pi$
$757$	6.35502	+	27.8432i	0.230977	+	1.01198i	−0.717854	+	0.696193i	$0.754876\pi$
$758$	23.8219	−	22.1035i	0.865252	−	0.802837i
$759$	−2.83587	+	0.427439i	−0.102936	+	0.0155150i
$760$	−6.68731	+	1.00795i	−0.242574	+	0.0365622i
$761$	−21.4867	+	19.9367i	−0.778892	+	0.722706i	−0.965691	−	0.259692i	$-0.916379\pi$
$761$	−21.4867	+	19.9367i	−0.778892	+	0.722706i	0.186800	+	0.982398i	$0.440188\pi$
$762$	0.874036	+	3.82940i	0.0316630	+	0.138725i
$763$	11.4018	+	33.2402i	0.412774	+	1.20338i
$764$	−0.00677179	+	0.0296691i	−0.000244995	+	0.00107339i
$765$	0.555419	+	0.962014i	0.0200812	+	0.0347817i
$766$	−12.6572	+	21.9229i	−0.457323	+	0.792106i
$767$	0.0407842	+	0.0378422i	0.00147263	+	0.00136640i
$768$	0.520118	+	0.354611i	0.0187681	+	0.0127959i
$769$	6.96694	+	8.73627i	0.251234	+	0.315038i	0.891416	−	0.453185i	$-0.149712\pi$
$769$	6.96694	+	8.73627i	0.251234	+	0.315038i	−0.640182	+	0.768223i	$0.721141\pi$
$770$	−1.88736	+	0.493271i	−0.0680157	+	0.0177763i
$771$	−1.06343	+	1.33350i	−0.0382985	+	0.0480248i
$772$	−13.4533	+	4.14979i	−0.484194	+	0.149354i
$773$	18.9066	+	48.1731i	0.680022	+	1.73267i	0.680587	+	0.732667i	$0.261725\pi$
$773$	18.9066	+	48.1731i	0.680022	+	1.73267i	−0.000565417		1.00000i	$0.500180\pi$
$774$	−1.69350	+	22.5982i	−0.0608717	+	0.812276i
$775$	8.04992	−	20.5109i	0.289162	−	0.736772i
$776$	−17.3778	−	8.36870i	−0.623826	−	0.300419i
$777$	1.75230	−	2.01101i	0.0628635	−	0.0721447i
$778$	−11.1579	+	5.37334i	−0.400029	+	0.192644i
$779$	−3.69533	−	49.3108i	−0.132399	−	1.76674i
$780$	−0.00716054	−	0.00220874i	−0.000256389	−	7.90854e-5i
$781$	1.34089	−	0.914202i	0.0479807	−	0.0327127i
$782$	−2.60671	−	0.392898i	−0.0932156	−	0.0140500i
$783$	9.37999			0.335214
$784$	5.41862	+	4.43154i	0.193522	+	0.158269i
$785$	21.4022			0.763877
$786$	12.8844	+	1.94202i	0.459573	+	0.0692694i
$787$	30.6135	−	20.8720i	1.09126	−	0.744005i	0.122610	−	0.992455i	$-0.460873\pi$
$787$	30.6135	−	20.8720i	1.09126	−	0.744005i	0.968645	+	0.248450i	$0.0799211\pi$
$788$	−19.8128	−	6.11144i	−0.705801	−	0.217711i
$789$	1.18163	+	15.7677i	0.0420671	+	0.561346i
$790$	−10.0997	+	4.86376i	−0.359331	+	0.173045i
$791$	11.8830	+	16.3104i	0.422512	+	0.579930i
$792$	−1.59987	−	0.770457i	−0.0568489	−	0.0273770i
$793$	0.0227683	−	0.0580126i	0.000808525	−	0.00206009i
$794$	2.21539	−	29.5624i	0.0786214	−	1.04913i
$795$	−1.95941	−	4.99251i	−0.0694933	−	0.177066i
$796$	−11.9856	+	3.69707i	−0.424818	+	0.131039i
$797$	2.48887	−	3.12094i	0.0881601	−	0.110549i	−0.735795	−	0.677204i	$-0.763191\pi$
$797$	2.48887	−	3.12094i	0.0881601	−	0.110549i	0.823955	+	0.566655i	$0.191763\pi$
$798$	8.34434	+	6.23820i	0.295386	+	0.220830i
$799$	−2.78007	−	3.48610i	−0.0983518	−	0.123329i
$800$	3.16547	+	2.15818i	0.111916	+	0.0763032i
$801$	−30.9436	−	28.7115i	−1.09334	−	1.01447i
$802$	7.80171	−	13.5130i	0.275488	−	0.477159i
$803$	−0.729144	−	1.26291i	−0.0257309	−	0.0445673i
$804$	−0.872862	+	3.82426i	−0.0307835	+	0.134871i
$805$	−13.4278	−	13.5943i	−0.473266	−	0.479135i
$806$	−0.0140911	−	0.0617369i	−0.000496336	−	0.00217459i
$807$	−1.23494	+	1.14585i	−0.0434719	+	0.0403360i
$808$	−12.6409	+	1.90531i	−0.444706	+	0.0670286i
$809$	−46.4527	+	7.00162i	−1.63319	+	0.246164i	−0.900645	−	0.434556i	$-0.856905\pi$
$809$	−46.4527	+	7.00162i	−1.63319	+	0.246164i	−0.732544	+	0.680719i	$0.761667\pi$
$810$	−4.43063	+	4.11103i	−0.155677	+	0.144447i
$811$	7.86353	+	34.4524i	0.276126	+	1.20979i	0.902647	+	0.430382i	$0.141621\pi$
$811$	7.86353	+	34.4524i	0.276126	+	1.20979i	−0.626521	+	0.779405i	$0.715522\pi$
$812$	−3.77960	+	5.93372i	−0.132638	+	0.208233i
$813$	3.07989	−	13.4939i	0.108016	−	0.473250i
$814$	−0.546114	−	0.945898i	−0.0191413	−	0.0331537i
$815$	−1.22103	+	2.11489i	−0.0427708	+	0.0740812i
$816$	0.182101	+	0.168965i	0.00637481	+	0.00591496i
$817$	−44.9837	−	30.6694i	−1.57378	−	1.07299i
$818$	−8.56849	−	10.7446i	−0.299590	−	0.375674i
$819$	−0.0350285	−	0.0672775i	−0.00122400	−	0.00235087i
$820$	5.32850	−	6.68173i	0.186079	−	0.233336i
$821$	−27.0343	+	8.33899i	−0.943505	+	0.291033i	−0.728083	−	0.685488i	$-0.759589\pi$
$821$	−27.0343	+	8.33899i	−0.943505	+	0.291033i	−0.215421	+	0.976521i	$0.569113\pi$
$822$	−4.81456	−	12.2673i	−0.167927	−	0.427871i
$823$	−1.83529	+	24.4903i	−0.0639742	+	0.853677i	0.869248	+	0.494377i	$0.164604\pi$
$823$	−1.83529	+	24.4903i	−0.0639742	+	0.853677i	−0.933222	+	0.359300i	$0.883015\pi$
$824$	2.72090	−	6.93275i	0.0947872	−	0.241514i
$825$	1.48190	+	0.713644i	0.0515931	+	0.0248459i
$826$	3.53962	−	12.8918i	0.123159	−	0.448561i
$827$	1.90378	−	0.916813i	0.0662010	−	0.0318807i	−0.400490	−	0.916301i	$-0.631160\pi$
$827$	1.90378	−	0.916813i	0.0662010	−	0.0318807i	0.466691	+	0.884420i	$0.345446\pi$
$828$	−1.29981	−	17.3448i	−0.0451715	−	0.602772i
$829$	−1.18045	−	0.364120i	−0.0409987	−	0.0126464i	0.274188	−	0.961676i	$-0.411591\pi$
$829$	−1.18045	−	0.364120i	−0.0409987	−	0.0126464i	−0.315187	+	0.949030i	$0.602067\pi$
$830$	2.88070	−	1.96403i	0.0999905	−	0.0681724i
$831$	10.9841	+	1.65558i	0.381033	+	0.0574315i
$832$	0.0110106			0.000381725
$833$	1.85378	+	2.04795i	0.0642297	+	0.0709573i
$834$	3.03722			0.105170
$835$	−0.184154	−	0.0277567i	−0.00637291	−	0.000960561i
$836$	3.52485	−	2.40320i	0.121910	−	0.0831165i
$837$	19.3864	+	5.97992i	0.670093	+	0.206696i
$838$	1.55727	+	20.7804i	0.0537951	+	0.717846i
$839$	−18.9497	+	9.12567i	−0.654215	+	0.315053i	−0.731385	−	0.681965i	$-0.761126\pi$
$839$	−18.9497	+	9.12567i	−0.654215	+	0.315053i	0.0771704	+	0.997018i	$0.475411\pi$
$840$	0.323845	+	1.77125i	0.0111737	+	0.0611138i
$841$	19.7577	+	9.51480i	0.681299	+	0.328097i
$842$	−1.53192	+	3.90326i	−0.0527933	+	0.134515i
$843$	0.508036	−	6.77927i	0.0174977	−	0.233490i
$844$	7.97127	+	20.3105i	0.274382	+	0.699115i
$845$	13.4300	−	4.14261i	0.462007	−	0.142510i
$846$	18.3430	−	23.0014i	0.630645	−	0.790804i
$847$	−21.2383	+	18.0505i	−0.729758	+	0.620222i
$848$	4.91346	+	6.16128i	0.168729	+	0.211579i
$849$	−12.2589	−	8.35796i	−0.420723	−	0.286844i
$850$	1.10828	+	1.02833i	0.0380136	+	0.0352715i
$851$	5.34925	−	9.26517i	0.183370	−	0.317606i
$852$	−0.748986	−	1.29728i	−0.0256598	−	0.0444441i
$853$	3.41222	−	14.9499i	0.116832	−	0.511876i	−0.882318	−	0.470654i	$-0.844018\pi$
$853$	3.41222	−	14.9499i	0.116832	−	0.511876i	0.999150	−	0.0412215i	$-0.0131249\pi$
$854$	−14.8909	+	1.58494i	−0.509558	+	0.0542357i
$855$	−3.91828	−	17.1671i	−0.134003	−	0.587103i
$856$	−6.88153	+	6.38513i	−0.235206	+	0.218239i
$857$	−14.0583	+	2.11895i	−0.480223	+	0.0723820i	−0.384693	−	0.923045i	$-0.625693\pi$
$857$	−14.0583	+	2.11895i	−0.480223	+	0.0723820i	−0.0955300	+	0.995427i	$0.530455\pi$
$858$	0.00467423		0.000704527i	0.000159576		2.40521e-5i
$859$	−26.7490	+	24.8194i	−0.912664	+	0.846829i	−0.988643	−	0.150281i	$-0.951982\pi$
$859$	−26.7490	+	24.8194i	−0.912664	+	0.846829i	0.0759791	+	0.997109i	$0.475792\pi$
$860$	−2.09382	−	9.17362i	−0.0713986	−	0.312818i
$861$	−13.0919	+	1.39346i	−0.446169	+	0.0474888i
$862$	−5.24045	+	22.9599i	−0.178490	+	0.782018i
$863$	−11.4975	−	19.9143i	−0.391381	−	0.677892i	0.601251	−	0.799060i	$-0.294669\pi$
$863$	−11.4975	−	19.9143i	−0.391381	−	0.677892i	−0.992632	+	0.121168i	$0.961336\pi$
$864$	−1.76378	+	3.05495i	−0.0600049	+	0.103932i
$865$	−2.00071	−	1.85639i	−0.0680263	−	0.0631192i
$866$	2.70452	+	1.84391i	0.0919034	+	0.0626586i
$867$	−6.61117	−	8.29014i	−0.224527	−	0.281548i
$868$	−11.5945	+	9.85415i	−0.393542	+	0.334472i
$869$	4.40894	−	5.52863i	0.149563	−	0.187546i
$870$	−1.72927	+	0.533409i	−0.0586278	+	0.0180843i
$871$	0.0250662	+	0.0638677i	0.000849337	+	0.00216407i
$872$	0.992578	−	13.2450i	0.0336129	−	0.448534i
$873$	18.3476	−	46.7489i	0.620971	−	1.58221i
$874$	37.6491	+	18.1308i	1.27350	+	0.613284i
$875$	4.54318	+	24.8486i	0.153588	+	0.840035i
$876$	−1.21275	+	0.584028i	−0.0409749	+	0.0197325i
$877$	3.52533	+	47.0422i	0.119042	+	1.58850i	0.662497	+	0.749065i	$0.269497\pi$
$877$	3.52533	+	47.0422i	0.119042	+	1.58850i	−0.543455	+	0.839438i	$0.682884\pi$
$878$	0.525909	+	0.162222i	0.0177486	+	0.00547471i
$879$	12.7105	−	8.66585i	0.428714	−	0.292292i
$880$	0.729080	+	0.109891i	0.0245773	+	0.00370443i
$881$	21.5789			0.727013			0.363507	−	0.931592i	$-0.381579\pi$
$881$	21.5789			0.727013			0.363507	+	0.931592i	$0.381579\pi$
$882$	−10.4519	+	14.9314i	−0.351935	+	0.502768i
$883$	−51.2025			−1.72310			−0.861551	−	0.507671i	$-0.830507\pi$
$883$	−51.2025			−1.72310			−0.861551	+	0.507671i	$0.830507\pi$
$884$	0.00429651		0.000647594i	0.000144507		2.17810e-5i
$885$	2.84132	−	1.93718i	0.0955101	−	0.0651177i
$886$	−21.3225	−	6.57711i	−0.716342	−	0.220962i
$887$	−0.583395	−	7.78486i	−0.0195885	−	0.261390i	−0.998396	−	0.0566095i	$-0.981971\pi$
$887$	−0.583395	−	7.78486i	−0.0195885	−	0.261390i	0.978808	−	0.204780i	$-0.0656481\pi$
$888$	−0.908323	+	0.437425i	−0.0304813	+	0.0146790i
$889$	4.37093	−	15.9195i	0.146596	−	0.533922i
$890$	15.7915	+	7.60479i	0.529333	+	0.254913i
$891$	1.39295	−	3.54918i	0.0466656	−	0.118902i
$892$	−0.445805	+	5.94885i	−0.0149266	+	0.199182i
$893$	25.8226	+	65.7948i	0.864119	+	2.20174i
$894$	6.66076	−	2.05457i	0.222769	−	0.0687152i
$895$	0.155032	−	0.194404i	0.00518215	−	0.00649821i
$896$	−1.22184	−	2.34672i	−0.0408188	−	0.0783985i
$897$	0.0288687	+	0.0362001i	0.000963896	+	0.00120869i
$898$	−12.7577	−	8.69804i	−0.425729	−	0.290257i
$899$	−11.2105	−	10.4018i	−0.373890	−	0.346920i
$900$	−4.98768	+	8.63891i	−0.166256	+	0.287964i
$901$	1.55492	+	2.69321i	0.0518020	+	0.0897237i
$902$	−1.19964	+	5.25599i	−0.0399438	+	0.175005i
$903$	−7.78768	+	12.2261i	−0.259158	+	0.406860i
$904$	−1.69724	−	7.43611i	−0.0564495	−	0.247321i
$905$	−18.6429	+	17.2981i	−0.619710	+	0.575007i
$906$	9.13147	−	1.37635i	0.303373	−	0.0457261i
$907$	30.0997	−	4.53681i	0.999446	−	0.150642i	0.371114	−	0.928587i	$-0.378976\pi$
$907$	30.0997	−	4.53681i	0.999446	−	0.150642i	0.628332	+	0.777945i	$0.283738\pi$
$908$	17.4859	−	16.2246i	0.580291	−	0.538431i
$909$	−7.40667	−	32.4507i	−0.245664	−	1.07632i
$910$	0.0221323	+	0.0224068i	0.000733680	+	0.000742778i
$911$	−2.79711	+	12.2550i	−0.0926725	+	0.406025i	−0.999893	−	0.0146306i	$-0.995343\pi$
$911$	−2.79711	+	12.2550i	−0.0926725	+	0.406025i	0.907220	+	0.420656i	$0.138200\pi$
$912$	−1.96889	−	3.41022i	−0.0651966	−	0.112924i
$913$	−1.09968	+	1.90471i	−0.0363942	+	0.0630366i
$914$	7.18992	+	6.67127i	0.237821	+	0.220666i
$915$	−3.18270	−	2.16993i	−0.105217	−	0.0717355i
$916$	11.2790	+	14.1434i	0.372669	+	0.467312i
$917$	−43.8619	−	32.7909i	−1.44845	−	1.08285i
$918$	−0.867929	+	1.08835i	−0.0286459	+	0.0359209i
$919$	5.91172	−	1.82352i	0.195010	−	0.0601525i	−0.195712	−	0.980661i	$-0.562702\pi$
$919$	5.91172	−	1.82352i	0.195010	−	0.0601525i	0.390722	+	0.920509i	$0.372226\pi$
$920$	2.63852	+	6.72285i	0.0869895	+	0.221646i
$921$	−0.379887	+	5.06923i	−0.0125177	+	0.167037i
$922$	6.97900	−	17.7822i	0.229841	−	0.585625i
$923$	−0.0236064	−	0.0113682i	−0.000777013	−	0.000374190i
$924$	−0.668852	−	0.918050i	−0.0220036	−	0.0302016i
$925$	−5.52811	+	2.66220i	−0.181763	+	0.0875325i
$926$	1.31044	+	17.4866i	0.0430637	+	0.574646i
$927$	18.5300	+	5.71573i	0.608603	+	0.187729i
$928$	2.19702	−	1.49790i	0.0721208	−	0.0491711i
$929$	−5.86214	−	0.883575i	−0.192331	−	0.0289892i	0.0521705	−	0.998638i	$-0.483386\pi$
$929$	−5.86214	−	0.883575i	−0.192331	−	0.0289892i	−0.244501	+	0.969649i	$0.578624\pi$
$930$	−3.91409			−0.128348
$931$	−18.5112	−	39.6826i	−0.606680	−	1.30055i
$932$	3.99870			0.130982
$933$	−11.6807	−	1.76058i	−0.382408	−	0.0576388i
$934$	30.8015	−	21.0001i	1.00786	−	0.687146i
$935$	0.278034	+	0.0857622i	0.00909269	+	0.00280472i
$936$	0.00214241	+	0.0285885i	7.00270e−5	+	0.000934445i
$937$	18.6799	−	8.99578i	0.610246	−	0.293879i	−0.103122	−	0.994669i	$-0.532883\pi$
$937$	18.6799	−	8.99578i	0.610246	−	0.293879i	0.713368	+	0.700790i	$0.247169\pi$
$938$	10.8307	−	12.4298i	0.353635	−	0.405846i
$939$	5.34894	+	2.57591i	0.174556	+	0.0840617i
$940$	−4.46290	+	11.3713i	−0.145564	+	0.370890i
$941$	3.84524	−	51.3111i	0.125351	−	1.67269i	−0.480407	−	0.877046i	$-0.659511\pi$
$941$	3.84524	−	51.3111i	0.125351	−	1.67269i	0.605758	−	0.795649i	$-0.292870\pi$
$942$	4.55281	+	11.6004i	0.148339	+	0.377961i
$943$	−50.4609	+	15.5651i	−1.64323	+	0.506870i
$944$	−3.15046	+	3.95056i	−0.102539	+	0.128580i
$945$	−9.76221	+	2.55141i	−0.317565	+	0.0829973i
$946$	3.70086	+	4.64074i	0.120325	+	0.150883i
$947$	25.8849	+	17.6480i	0.841145	+	0.573483i	0.905453	−	0.424447i	$-0.139531\pi$
$947$	25.8849	+	17.6480i	0.841145	+	0.573483i	−0.0643074	+	0.997930i	$0.520484\pi$
$948$	−4.78472	−	4.43957i	−0.155400	−	0.144190i
$949$	−0.0117719	+	0.0203895i	−0.000382132	+	0.000661871i
$950$	−11.9828	−	20.7548i	−0.388773	−	0.673375i
$951$	−1.58987	+	6.96570i	−0.0515552	+	0.225878i
$952$	−0.338756	−	0.987588i	−0.0109791	−	0.0320079i
$953$	−1.64325	−	7.19953i	−0.0532300	−	0.233216i	0.941314	−	0.337531i	$-0.109592\pi$
$953$	−1.64325	−	7.19953i	−0.0532300	−	0.233216i	−0.994544	+	0.104316i	$0.966735\pi$
$954$	−15.0414	+	13.9564i	−0.486983	+	0.451854i
$955$	0.0325333	−	0.00490361i	0.00105275	−	0.000158677i
$956$	10.9273	−	1.64703i	0.353415	−	0.0532687i
$957$	0.836834	−	0.776469i	0.0270510	−	0.0250997i
$958$	1.62822	+	7.13370i	0.0526054	+	0.230479i
$959$	−6.54046	+	54.9998i	−0.211202	+	1.77604i
$960$	0.151440	−	0.663503i	0.00488771	−	0.0214145i
$961$	−1.03831	−	1.79840i	−0.0334938	−	0.0580129i
$962$	−0.00881691	+	0.0152713i	−0.000284269	+	0.000492368i
$963$	−17.9176	−	16.6251i	−0.577388	−	0.535738i
$964$	−14.3925	−	9.81265i	−0.463552	−	0.316044i
$965$	9.49003	+	11.9001i	0.305495	+	0.383079i
$966$	4.51190	−	10.1699i	0.145168	−	0.327213i
$967$	5.83702	−	7.31939i	0.187706	−	0.235376i	−0.679070	−	0.734073i	$-0.737617\pi$
$967$	5.83702	−	7.31939i	0.187706	−	0.235376i	0.866776	+	0.498698i	$0.166188\pi$
$968$	10.0669	−	3.10521i	0.323561	−	0.0998053i
$969$	−0.567717	−	1.44652i	−0.0182377	−	0.0464689i
$970$	−1.55831	+	20.7942i	−0.0500343	+	0.667662i
$971$	9.08082	−	23.1375i	0.291417	−	0.742519i	−0.707926	−	0.706286i	$-0.750369\pi$
$971$	9.08082	−	23.1375i	0.291417	−	0.742519i	0.999343	−	0.0362325i	$-0.0115357\pi$
$972$	−12.7054	−	6.11860i	−0.407526	−	0.196254i
$973$	−11.2490	−	6.03423i	−0.360626	−	0.193449i
$974$	27.8310	−	13.4027i	0.891762	−	0.429450i
$975$	−0.00198443	−	0.0264804i	−6.35527e−5	−	0.000848053i
$976$	5.40858	+	1.66833i	0.173124	+	0.0534018i
$977$	−15.2635	+	10.4065i	−0.488323	+	0.332933i	−0.782323	−	0.622872i	$-0.785966\pi$
$977$	−15.2635	+	10.4065i	−0.488323	+	0.332933i	0.294001	+	0.955805i	$0.405013\pi$
$978$	−1.40605	−	0.211928i	−0.0449605	−	0.00677671i
$979$	−11.0566			−0.353369
$980$	2.31961	−	7.20358i	0.0740973	−	0.230110i
$981$	34.5832			1.10416
$982$	8.62643	+	1.30022i	0.275280	+	0.0414918i
$983$	−16.7339	+	11.4090i	−0.533729	+	0.363890i	−0.799993	−	0.600010i	$-0.795163\pi$
$983$	−16.7339	+	11.4090i	−0.533729	+	0.363890i	0.266263	+	0.963900i	$0.414211\pi$
$984$	4.75513	+	1.46676i	0.151588	+	0.0467587i
$985$	1.67514	+	22.3532i	0.0533744	+	0.712232i
$986$	0.945410	−	0.455285i	0.0301080	−	0.0144992i
$987$	17.2946	−	7.41903i	0.550493	−	0.236150i
$988$	−0.0620551	−	0.0298842i	−0.00197424	−	0.000950742i
$989$	−21.2413	+	54.1220i	−0.675435	+	1.72098i
$990$	−0.143464	+	1.91440i	−0.00455960	+	0.0608436i
$991$	−1.26226	−	3.21618i	−0.0400970	−	0.102165i	0.909423	−	0.415873i	$-0.136524\pi$
$991$	−1.26226	−	3.21618i	−0.0400970	−	0.102165i	−0.949520	+	0.313708i	$0.898429\pi$
$992$	5.49572	−	1.69520i	0.174489	−	0.0538228i
$993$	−3.37188	+	4.22820i	−0.107003	+	0.134178i
$994$	0.196637	+	6.29281i	0.00623694	+	0.199596i
$995$	8.45471	+	10.6019i	0.268032	+	0.336102i
$996$	1.67734	+	1.14359i	0.0531485	+	0.0362360i
$997$	25.0004	+	23.1970i	0.791771	+	0.734656i	0.968341	−	0.249632i	$-0.0803096\pi$
$997$	25.0004	+	23.1970i	0.791771	+	0.734656i	−0.176569	+	0.984288i	$0.556500\pi$
$998$	12.3235	−	21.3449i	0.390093	−	0.675661i
$999$	−2.82473	−	4.89258i	−0.0893707	−	0.154795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.2.g.a.39.2	✓	24
3.2	odd	2		882.2.z.d.235.2		24
4.3	odd	2		784.2.bg.a.529.1		24
7.2	even	3		686.2.g.a.569.2		24
7.3	odd	6		686.2.e.e.295.3		24
7.4	even	3		686.2.e.f.295.2		24
7.5	odd	6		686.2.g.c.569.1		24
7.6	odd	2		686.2.g.b.165.1		24
49.3	odd	42		686.2.e.e.393.3		24
49.5	odd	42		686.2.g.b.79.1		24
49.8	even	7		686.2.g.a.557.2		24
49.17	odd	42		4802.2.a.k.1.4		12
49.32	even	21		4802.2.a.i.1.9		12
49.41	odd	14		686.2.g.c.557.1		24
49.44	even	21	inner	98.2.g.a.93.2	yes	24
49.46	even	21		686.2.e.f.393.2		24
147.44	odd	42		882.2.z.d.289.2		24
196.191	odd	42		784.2.bg.a.289.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.a.39.2	✓	24	1.1	even	1	trivial
98.2.g.a.93.2	yes	24	49.44	even	21	inner
686.2.e.e.295.3		24	7.3	odd	6
686.2.e.e.393.3		24	49.3	odd	42
686.2.e.f.295.2		24	7.4	even	3
686.2.e.f.393.2		24	49.46	even	21
686.2.g.a.557.2		24	49.8	even	7
686.2.g.a.569.2		24	7.2	even	3
686.2.g.b.79.1		24	49.5	odd	42
686.2.g.b.165.1		24	7.6	odd	2
686.2.g.c.557.1		24	49.41	odd	14
686.2.g.c.569.1		24	7.5	odd	6
784.2.bg.a.289.1		24	196.191	odd	42
784.2.bg.a.529.1		24	4.3	odd	2
882.2.z.d.235.2		24	3.2	odd	2
882.2.z.d.289.2		24	147.44	odd	42
4802.2.a.i.1.9		12	49.32	even	21
4802.2.a.k.1.4		12	49.17	odd	42

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	98.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.988831 + 0.149042i) q^{2} +(0.520118 - 0.354611i) q^{3} +(0.955573 + 0.294755i) q^{4} +(-0.0807922 - 1.07810i) q^{5} +(0.567161 - 0.273130i) q^{6} +(-2.64324 - 0.115218i) q^{7} +(0.900969 + 0.433884i) q^{8} +(-0.951249 + 2.42374i) q^{9} +O(q^{10})\)	\(q+(0.988831 + 0.149042i) q^{2} +(0.520118 - 0.354611i) q^{3} +(0.955573 + 0.294755i) q^{4} +(-0.0807922 - 1.07810i) q^{5} +(0.567161 - 0.273130i) q^{6} +(-2.64324 - 0.115218i) q^{7} +(0.900969 + 0.433884i) q^{8} +(-0.951249 + 2.42374i) q^{9} +(0.0807922 - 1.07810i) q^{10} +(0.249160 + 0.634849i) q^{11} +(0.601534 - 0.185549i) q^{12} +(0.00686501 - 0.00860846i) q^{13} +(-2.59655 - 0.507886i) q^{14} +(-0.424326 - 0.532088i) q^{15} +(0.826239 + 0.563320i) q^{16} +(0.289279 + 0.268411i) q^{17} +(-1.30186 + 2.25490i) q^{18} +(-3.12770 - 5.41734i) q^{19} +(0.240572 - 1.05401i) q^{20} +(-1.41566 + 0.877394i) q^{21} +(0.151758 + 0.664893i) q^{22} +(-4.89692 + 4.54368i) q^{23} +(0.622470 - 0.0938223i) q^{24} +(3.78839 - 0.571008i) q^{25} +(0.00807136 - 0.00748913i) q^{26} +(0.784954 + 3.43911i) q^{27} +(-2.49185 - 0.889208i) q^{28} +(0.591698 - 2.59240i) q^{29} +(-0.340283 - 0.589387i) q^{30} +(2.87561 - 4.98071i) q^{31} +(0.733052 + 0.680173i) q^{32} +(0.354717 + 0.241842i) q^{33} +(0.246043 + 0.308528i) q^{34} +(0.0893369 + 2.85898i) q^{35} +(-1.62340 + 2.03568i) q^{36} +(-1.53038 + 0.472058i) q^{37} +(-2.28536 - 5.82300i) q^{38} +(0.000517969 - 0.00691182i) q^{39} +(0.394977 - 1.00639i) q^{40} +(7.12216 + 3.42985i) q^{41} +(-1.53061 + 0.656602i) q^{42} +(7.84159 - 3.77631i) q^{43} +(0.0509653 + 0.680085i) q^{44} +(2.68988 + 0.829719i) q^{45} +(-5.51943 + 3.76308i) q^{46} +(-11.1729 - 1.68405i) q^{47} +0.629501 q^{48} +(6.97345 + 0.609099i) q^{49} +3.83118 q^{50} +(0.245640 + 0.0370243i) q^{51} +(0.00909741 - 0.00620251i) q^{52} +(7.53046 + 2.32284i) q^{53} +(0.263614 + 3.51769i) q^{54} +(0.664298 - 0.319909i) q^{55} +(-2.33149 - 1.25067i) q^{56} +(-3.54782 - 1.70854i) q^{57} +(0.971466 - 2.47525i) q^{58} +(-0.377607 + 5.03882i) q^{59} +(-0.248639 - 0.633521i) q^{60} +(5.40858 - 1.66833i) q^{61} +(3.58583 - 4.49649i) q^{62} +(2.79364 - 6.29694i) q^{63} +(0.623490 + 0.781831i) q^{64} +(-0.00983539 - 0.00670565i) q^{65} +(0.314710 + 0.292008i) q^{66} +(-3.11565 + 5.39646i) q^{67} +(0.197311 + 0.341753i) q^{68} +(-0.935742 + 4.09975i) q^{69} +(-0.337769 + 2.84036i) q^{70} +(-0.529515 - 2.31996i) q^{71} +(-1.90867 + 1.77099i) q^{72} +(-2.11439 + 0.318694i) q^{73} +(-1.58364 + 0.238695i) q^{74} +(1.76792 - 1.64039i) q^{75} +(-1.39196 - 6.09857i) q^{76} +(-0.585443 - 1.70677i) q^{77} +(0.00154234 - 0.00675742i) q^{78} +(-5.18436 - 8.97958i) q^{79} +(0.540560 - 0.936277i) q^{80} +(-4.09819 - 3.80257i) q^{81} +(6.53142 + 4.45305i) q^{82} +(2.01070 + 2.52134i) q^{83} +(-1.61138 + 0.421142i) q^{84} +(0.266002 - 0.333556i) q^{85} +(8.31684 - 2.56540i) q^{86} +(-0.611538 - 1.55817i) q^{87} +(-0.0509653 + 0.680085i) q^{88} +(-5.92296 + 15.0915i) q^{89} +(2.53618 + 1.22136i) q^{90} +(-0.0191377 + 0.0219633i) q^{91} +(-6.01864 + 2.89842i) q^{92} +(-0.270553 - 3.61028i) q^{93} +(-10.7971 - 3.33048i) q^{94} +(-5.58772 + 3.80965i) q^{95} +(0.622470 + 0.0938223i) q^{96} -19.2879 q^{97} +(6.80478 + 1.64163i) q^{98} -1.77572 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9	\( 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9} - 7 q^{11} + 14 q^{13} - 7 q^{15} + 2 q^{16} - 7 q^{17} + 5 q^{18} - 7 q^{20} + 7 q^{21} - 7 q^{22} - 21 q^{23} + 4 q^{25} - 7 q^{26} - 35 q^{27} - 14 q^{28} - 11 q^{29} + 28 q^{31} - 2 q^{32} + 14 q^{33} + 7 q^{34} + 21 q^{35} + 3 q^{36} - 24 q^{37} - 7 q^{38} - 40 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 10 q^{43} + 21 q^{44} + 7 q^{45} + 42 q^{46} - 70 q^{47} - 14 q^{48} + 84 q^{49} + 8 q^{50} + 60 q^{51} - 7 q^{52} + 26 q^{53} + 63 q^{54} + 56 q^{55} + 21 q^{56} - 33 q^{57} - 30 q^{58} - 7 q^{59} + 14 q^{60} + 14 q^{61} + 28 q^{62} - 14 q^{63} - 4 q^{64} - 21 q^{66} - 36 q^{67} - 14 q^{68} - 35 q^{69} + 14 q^{70} - 2 q^{72} - 7 q^{73} - 11 q^{74} - 28 q^{75} - 91 q^{77} - 24 q^{78} - 26 q^{79} + 55 q^{81} + 14 q^{82} - 7 q^{83} - 21 q^{84} + 49 q^{85} - 16 q^{86} + 35 q^{87} - 21 q^{88} - 56 q^{89} - 21 q^{90} + 7 q^{91} + 21 q^{92} + 72 q^{93} - 35 q^{94} - 14 q^{95} - 126 q^{97} - 56 q^{98} - 14 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9 - 7 * q^11 + 14 * q^13 - 7 * q^15 + 2 * q^16 - 7 * q^17 + 5 * q^18 - 7 * q^20 + 7 * q^21 - 7 * q^22 - 21 * q^23 + 4 * q^25 - 7 * q^26 - 35 * q^27 - 14 * q^28 - 11 * q^29 + 28 * q^31 - 2 * q^32 + 14 * q^33 + 7 * q^34 + 21 * q^35 + 3 * q^36 - 24 * q^37 - 7 * q^38 - 40 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 10 * q^43 + 21 * q^44 + 7 * q^45 + 42 * q^46 - 70 * q^47 - 14 * q^48 + 84 * q^49 + 8 * q^50 + 60 * q^51 - 7 * q^52 + 26 * q^53 + 63 * q^54 + 56 * q^55 + 21 * q^56 - 33 * q^57 - 30 * q^58 - 7 * q^59 + 14 * q^60 + 14 * q^61 + 28 * q^62 - 14 * q^63 - 4 * q^64 - 21 * q^66 - 36 * q^67 - 14 * q^68 - 35 * q^69 + 14 * q^70 - 2 * q^72 - 7 * q^73 - 11 * q^74 - 28 * q^75 - 91 * q^77 - 24 * q^78 - 26 * q^79 + 55 * q^81 + 14 * q^82 - 7 * q^83 - 21 * q^84 + 49 * q^85 - 16 * q^86 + 35 * q^87 - 21 * q^88 - 56 * q^89 - 21 * q^90 + 7 * q^91 + 21 * q^92 + 72 * q^93 - 35 * q^94 - 14 * q^95 - 126 * q^97 - 56 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

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