LMFDB - Embedded newform 966.2.y.c.25.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			25.6
Character	$\chi$	$=$	966.25
Dual form			966.2.y.c.541.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0475819 - 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.244232 + 1.00674i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(0.601440 - 2.57648i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})$	\(q+(0.0475819 - 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.244232 + 1.00674i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(0.601440 - 2.57648i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(1.01722 - 0.196053i) q^{10} +(-0.174359 - 3.66025i) q^{11} +(0.888835 + 0.458227i) q^{12} +(2.40263 + 2.77278i) q^{13} +(-2.54495 - 0.723353i) q^{14} +(0.147429 - 1.02539i) q^{15} +(0.981929 + 0.189251i) q^{16} +(0.246105 + 0.345606i) q^{17} +(0.723734 - 0.690079i) q^{18} +(-0.741084 + 1.04071i) q^{19} +(-0.147429 - 1.02539i) q^{20} +(-1.51594 + 2.16839i) q^{21} -3.66440 q^{22} +(1.05685 - 4.67793i) q^{23} +(0.500000 - 0.866025i) q^{24} +(3.49031 - 1.79938i) q^{25} +(2.88396 - 2.26797i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-0.843627 + 2.50765i) q^{28} +(-0.0701139 + 0.153528i) q^{29} +(-1.01722 - 0.196053i) q^{30} +(-5.39985 - 4.24649i) q^{31} +(0.235759 - 0.971812i) q^{32} +(-1.19851 + 3.46286i) q^{33} +(0.356925 - 0.229382i) q^{34} +(2.74073 - 0.0237674i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(0.476920 + 0.454742i) q^{37} +(1.00427 + 0.789764i) q^{38} +(-1.19998 - 3.46712i) q^{39} +(-1.03125 + 0.0984722i) q^{40} +(-5.75186 - 1.68890i) q^{41} +(2.09381 + 1.61740i) q^{42} +(-0.946223 - 6.58113i) q^{43} +(-0.174359 + 3.66025i) q^{44} +(-0.517969 + 0.897149i) q^{45} +(-4.62235 - 1.27824i) q^{46} +(-2.76086 - 4.78196i) q^{47} +(-0.841254 - 0.540641i) q^{48} +(-6.27654 - 3.09920i) q^{49} +(-1.63126 - 3.57197i) q^{50} +(-0.100027 - 0.412317i) q^{51} +(-2.12818 - 2.98861i) q^{52} +(-2.13778 - 6.17670i) q^{53} +(-0.928368 + 0.371662i) q^{54} +(3.64233 - 1.06948i) q^{55} +(2.46467 + 0.961990i) q^{56} +(1.07479 - 0.690726i) q^{57} +(0.150018 + 0.0773397i) q^{58} +(0.632019 - 0.121812i) q^{59} +(-0.244232 + 1.00674i) q^{60} +(7.64893 - 3.06217i) q^{61} +(-4.49862 + 5.19168i) q^{62} +(2.21326 - 1.44965i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-2.20466 + 3.09601i) q^{65} +(3.40191 + 1.36192i) q^{66} +(1.64969 - 0.850474i) q^{67} +(-0.212139 - 0.367435i) q^{68} +(-2.71976 + 3.95005i) q^{69} +(0.106669 - 2.73876i) q^{70} +(-8.92989 - 5.73889i) q^{71} +(-0.786053 + 0.618159i) q^{72} +(-1.01169 - 0.0966045i) q^{73} +(0.476920 - 0.454742i) q^{74} +(-3.90905 + 0.373269i) q^{75} +(0.836654 - 0.965550i) q^{76} +(-9.53545 - 1.75219i) q^{77} +(-3.52029 + 1.03365i) q^{78} +(-3.38657 + 9.78484i) q^{79} +(0.0492919 + 1.03477i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(-1.96067 + 5.66499i) q^{82} +(-0.513800 + 0.150865i) q^{83} +(1.71519 - 2.01447i) q^{84} +(-0.287828 + 0.332171i) q^{85} +(-6.61869 + 0.632009i) q^{86} +(0.122152 - 0.116472i) q^{87} +(3.64781 + 0.348324i) q^{88} +(0.291575 - 0.229297i) q^{89} +(0.871487 + 0.560071i) q^{90} +(8.58905 - 4.52267i) q^{91} +(-1.49673 + 4.55629i) q^{92} +(3.43479 + 5.94923i) q^{93} +(-4.90791 + 2.53020i) q^{94} +(-1.22872 - 0.491903i) q^{95} +(-0.580057 + 0.814576i) q^{96} +(12.0996 + 3.55277i) q^{97} +(-3.39434 + 6.12196i) q^{98} +(2.39967 - 2.76937i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{12} - 4 q^{13} + 9 q^{14} - 18 q^{15} + 8 q^{16} - 21 q^{17} + 8 q^{18} + 4 q^{19} + 18 q^{20} - 15 q^{21} + 116 q^{22} + 14 q^{23} + 80 q^{24} + 2 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 46 q^{29} - 2 q^{30} + q^{31} + 8 q^{32} - 8 q^{33} - 68 q^{34} - 84 q^{35} - 16 q^{36} + 19 q^{37} - 7 q^{38} - 2 q^{39} - 9 q^{40} + 38 q^{41} + 2 q^{42} + 28 q^{43} + 8 q^{44} + 24 q^{45} - 8 q^{46} - 26 q^{47} + 16 q^{48} - 6 q^{49} - 4 q^{50} + 21 q^{51} + 2 q^{52} - 20 q^{53} - 8 q^{54} + 46 q^{55} - 2 q^{56} - 14 q^{57} - 21 q^{58} + 36 q^{59} - 2 q^{60} + 40 q^{61} - 24 q^{62} - 2 q^{63} - 16 q^{64} - 10 q^{65} - 8 q^{66} + 6 q^{67} + 34 q^{68} + 6 q^{69} - 20 q^{70} + 132 q^{71} + 8 q^{72} - 36 q^{73} + 19 q^{74} - 2 q^{75} - 8 q^{76} - 75 q^{77} - 18 q^{78} + 34 q^{79} + 2 q^{80} + 8 q^{81} + 47 q^{82} + 74 q^{83} + 13 q^{84} + 2 q^{85} + 30 q^{86} + 10 q^{87} - 3 q^{88} - 12 q^{89} - 4 q^{90} - 30 q^{91} - 50 q^{92} + 10 q^{93} - 4 q^{94} + 27 q^{95} - 8 q^{96} + 24 q^{97} + 7 q^{98} - 16 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^12 - 4 * q^13 + 9 * q^14 - 18 * q^15 + 8 * q^16 - 21 * q^17 + 8 * q^18 + 4 * q^19 + 18 * q^20 - 15 * q^21 + 116 * q^22 + 14 * q^23 + 80 * q^24 + 2 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 46 * q^29 - 2 * q^30 + q^31 + 8 * q^32 - 8 * q^33 - 68 * q^34 - 84 * q^35 - 16 * q^36 + 19 * q^37 - 7 * q^38 - 2 * q^39 - 9 * q^40 + 38 * q^41 + 2 * q^42 + 28 * q^43 + 8 * q^44 + 24 * q^45 - 8 * q^46 - 26 * q^47 + 16 * q^48 - 6 * q^49 - 4 * q^50 + 21 * q^51 + 2 * q^52 - 20 * q^53 - 8 * q^54 + 46 * q^55 - 2 * q^56 - 14 * q^57 - 21 * q^58 + 36 * q^59 - 2 * q^60 + 40 * q^61 - 24 * q^62 - 2 * q^63 - 16 * q^64 - 10 * q^65 - 8 * q^66 + 6 * q^67 + 34 * q^68 + 6 * q^69 - 20 * q^70 + 132 * q^71 + 8 * q^72 - 36 * q^73 + 19 * q^74 - 2 * q^75 - 8 * q^76 - 75 * q^77 - 18 * q^78 + 34 * q^79 + 2 * q^80 + 8 * q^81 + 47 * q^82 + 74 * q^83 + 13 * q^84 + 2 * q^85 + 30 * q^86 + 10 * q^87 - 3 * q^88 - 12 * q^89 - 4 * q^90 - 30 * q^91 - 50 * q^92 + 10 * q^93 - 4 * q^94 + 27 * q^95 - 8 * q^96 + 24 * q^97 + 7 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{11}\right)$

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 $

$2$	0.0475819	−	0.998867i	0.0336455	−	0.706306i
$2$	0.0475819	−	0.998867i	0.0336455	−	0.706306i
$3$	−0.928368	−	0.371662i	−0.535993	−	0.214579i
$3$	−0.928368	−	0.371662i	−0.535993	−	0.214579i
$4$	−0.995472	−	0.0950560i	−0.497736	−	0.0475280i
$5$	0.244232	+	1.00674i	0.109224	+	0.450227i	0.999991	−	0.00423321i	$-0.00134748\pi$
$5$	0.244232	+	1.00674i	0.109224	+	0.450227i	−0.890767	+	0.454460i	$0.849832\pi$
$6$	−0.415415	+	0.909632i	−0.169592	+	0.371356i
$7$	0.601440	−	2.57648i	0.227323	−	0.973819i
$7$	0.601440	−	2.57648i	0.227323	−	0.973819i
$8$	−0.142315	+	0.989821i	−0.0503159	+	0.349955i
$9$	0.723734	+	0.690079i	0.241245	+	0.230026i
$10$	1.01722	−	0.196053i	0.321673	−	0.0619973i
$11$	−0.174359	−	3.66025i	−0.0525713	−	1.10361i	−0.858901	−	0.512142i	$-0.828852\pi$
$11$	−0.174359	−	3.66025i	−0.0525713	−	1.10361i	0.806330	−	0.591466i	$-0.201451\pi$
$12$	0.888835	+	0.458227i	0.256585	+	0.132279i
$13$	2.40263	+	2.77278i	0.666369	+	0.769030i	0.983804	−	0.179250i	$-0.0573670\pi$
$13$	2.40263	+	2.77278i	0.666369	+	0.769030i	−0.317435	+	0.948280i	$0.602822\pi$
$14$	−2.54495	−	0.723353i	−0.680166	−	0.193324i
$15$	0.147429	−	1.02539i	0.0380661	−	0.264756i
$16$	0.981929	+	0.189251i	0.245482	+	0.0473128i
$17$	0.246105	+	0.345606i	0.0596892	+	0.0838218i	0.843342	−	0.537378i	$-0.180585\pi$
$17$	0.246105	+	0.345606i	0.0596892	+	0.0838218i	−0.783652	+	0.621200i	$0.786646\pi$
$18$	0.723734	−	0.690079i	0.170586	−	0.162653i
$19$	−0.741084	+	1.04071i	−0.170016	+	0.238755i	−0.890789	−	0.454417i	$-0.849848\pi$
$19$	−0.741084	+	1.04071i	−0.170016	+	0.238755i	0.720773	+	0.693171i	$0.243787\pi$
$20$	−0.147429	−	1.02539i	−0.0329662	−	0.229285i
$21$	−1.51594	+	2.16839i	−0.330805	+	0.473182i
$22$	−3.66440			−0.781253
$23$	1.05685	−	4.67793i	0.220369	−	0.975417i
$23$	1.05685	−	4.67793i	0.220369	−	0.975417i
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	3.49031	−	1.79938i	0.698061	−	0.359876i
$26$	2.88396	−	2.26797i	0.565591	−	0.444786i
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$	−0.843627	+	2.50765i	−0.159431	+	0.473901i
$29$	−0.0701139	+	0.153528i	−0.0130198	+	0.0285094i	−0.916030	−	0.401109i	$-0.868625\pi$
$29$	−0.0701139	+	0.153528i	−0.0130198	+	0.0285094i	0.903010	+	0.429619i	$0.141352\pi$
$30$	−1.01722	−	0.196053i	−0.185718	−	0.0357942i
$31$	−5.39985	−	4.24649i	−0.969842	−	0.762693i	0.00159246	−	0.999999i	$-0.499493\pi$
$31$	−5.39985	−	4.24649i	−0.969842	−	0.762693i	−0.971435	+	0.237306i	$0.923736\pi$
$32$	0.235759	−	0.971812i	0.0416767	−	0.171794i
$33$	−1.19851	+	3.46286i	−0.208634	+	0.602807i
$34$	0.356925	−	0.229382i	0.0612121	−	0.0393386i
$35$	2.74073	−	0.0237674i	0.463268	−	0.00401742i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	0.476920	+	0.454742i	0.0784051	+	0.0747592i	0.728268	−	0.685292i	$-0.240325\pi$
$37$	0.476920	+	0.454742i	0.0784051	+	0.0747592i	−0.649863	+	0.760051i	$0.725174\pi$
$38$	1.00427	+	0.789764i	0.162914	+	0.128117i
$39$	−1.19998	−	3.46712i	−0.192151	−	0.555184i
$40$	−1.03125	+	0.0984722i	−0.163055	+	0.0155698i
$41$	−5.75186	−	1.68890i	−0.898290	−	0.263762i	−0.200186	−	0.979758i	$-0.564155\pi$
$41$	−5.75186	−	1.68890i	−0.898290	−	0.263762i	−0.698104	+	0.715996i	$0.745973\pi$
$42$	2.09381	+	1.61740i	0.323081	+	0.249570i
$43$	−0.946223	−	6.58113i	−0.144298	−	1.00361i	−0.925341	−	0.379136i	$-0.876221\pi$
$43$	−0.946223	−	6.58113i	−0.144298	−	1.00361i	0.781043	−	0.624477i	$-0.214688\pi$
$44$	−0.174359	+	3.66025i	−0.0262857	+	0.551804i
$45$	−0.517969	+	0.897149i	−0.0772143	+	0.133739i
$46$	−4.62235	−	1.27824i	−0.681528	−	0.188466i
$47$	−2.76086	−	4.78196i	−0.402713	−	0.697520i	0.591339	−	0.806423i	$-0.298599\pi$
$47$	−2.76086	−	4.78196i	−0.402713	−	0.697520i	−0.994052	+	0.108903i	$0.965266\pi$
$48$	−0.841254	−	0.540641i	−0.121424	−	0.0780348i
$49$	−6.27654	−	3.09920i	−0.896649	−	0.442743i
$50$	−1.63126	−	3.57197i	−0.230696	−	0.505153i
$51$	−0.100027	−	0.412317i	−0.0140066	−	0.0577360i
$52$	−2.12818	−	2.98861i	−0.295125	−	0.414445i
$53$	−2.13778	−	6.17670i	−0.293646	−	0.848435i	−0.991255	−	0.131957i	$-0.957874\pi$
$53$	−2.13778	−	6.17670i	−0.293646	−	0.848435i	0.697609	−	0.716478i	$-0.254247\pi$
$54$	−0.928368	+	0.371662i	−0.126335	+	0.0505769i
$55$	3.64233	−	1.06948i	0.491132	−	0.144209i
$56$	2.46467	+	0.961990i	0.329355	+	0.128551i
$57$	1.07479	−	0.690726i	0.142360	−	0.0914889i
$58$	0.150018	+	0.0773397i	0.0196983	+	0.0101552i
$59$	0.632019	−	0.121812i	0.0822819	−	0.0158585i	−0.147944	−	0.988996i	$-0.547266\pi$
$59$	0.632019	−	0.121812i	0.0822819	−	0.0158585i	0.230226	+	0.973137i	$0.426053\pi$
$60$	−0.244232	+	1.00674i	−0.0315302	+	0.129969i
$61$	7.64893	−	3.06217i	0.979345	−	0.392071i	0.173914	−	0.984761i	$-0.444358\pi$
$61$	7.64893	−	3.06217i	0.979345	−	0.392071i	0.805431	+	0.592690i	$0.201934\pi$
$62$	−4.49862	+	5.19168i	−0.571325	+	0.659344i
$63$	2.21326	−	1.44965i	0.278845	−	0.182638i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−2.20466	+	3.09601i	−0.273455	+	0.384013i
$66$	3.40191	+	1.36192i	0.418747	+	0.167641i
$67$	1.64969	−	0.850474i	0.201542	−	0.103902i	−0.354501	−	0.935056i	$-0.615349\pi$
$67$	1.64969	−	0.850474i	0.201542	−	0.103902i	0.556043	+	0.831154i	$0.312319\pi$
$68$	−0.212139	−	0.367435i	−0.0257256	−	0.0445580i
$69$	−2.71976	+	3.95005i	−0.327421	+	0.475530i
$70$	0.106669	−	2.73876i	0.0127494	−	0.327344i
$71$	−8.92989	−	5.73889i	−1.05978	−	0.681081i	−0.109981	−	0.993934i	$-0.535079\pi$
$71$	−8.92989	−	5.73889i	−1.05978	−	0.681081i	−0.949802	+	0.312853i	$0.898715\pi$
$72$	−0.786053	+	0.618159i	−0.0926372	+	0.0728507i
$73$	−1.01169	−	0.0966045i	−0.118409	−	0.0113067i	0.0356832	−	0.999363i	$-0.488639\pi$
$73$	−1.01169	−	0.0966045i	−0.118409	−	0.0113067i	−0.154092	+	0.988056i	$0.549245\pi$
$74$	0.476920	−	0.454742i	0.0554408	−	0.0528627i
$75$	−3.90905	+	0.373269i	−0.451378	+	0.0431014i
$76$	0.836654	−	0.965550i	0.0959708	−	0.110756i
$77$	−9.53545	−	1.75219i	−1.08667	−	0.199680i
$78$	−3.52029	+	1.03365i	−0.398595	+	0.117038i
$79$	−3.38657	+	9.78484i	−0.381019	+	1.10088i	0.577633	+	0.816297i	$0.303977\pi$
$79$	−3.38657	+	9.78484i	−0.381019	+	1.10088i	−0.958651	+	0.284584i	$0.908145\pi$
$80$	0.0492919	+	1.03477i	0.00551101	+	0.115690i
$81$	0.0475819	+	0.998867i	0.00528688	+	0.110985i
$82$	−1.96067	+	5.66499i	−0.216520	+	0.625593i
$83$	−0.513800	+	0.150865i	−0.0563969	+	0.0165596i	−0.309809	−	0.950799i	$-0.600265\pi$
$83$	−0.513800	+	0.150865i	−0.0563969	+	0.0165596i	0.253412	+	0.967358i	$0.418447\pi$
$84$	1.71519	−	2.01447i	0.187143	−	0.219797i
$85$	−0.287828	+	0.332171i	−0.0312193	+	0.0360290i
$86$	−6.61869	+	0.632009i	−0.713712	+	0.0681512i
$87$	0.122152	−	0.116472i	0.0130961	−	0.0124871i
$88$	3.64781	+	0.348324i	0.388858	+	0.0371314i
$89$	0.291575	−	0.229297i	0.0309068	−	0.0243054i	−0.602586	−	0.798054i	$-0.705863\pi$
$89$	0.291575	−	0.229297i	0.0309068	−	0.0243054i	0.633493	+	0.773748i	$0.281621\pi$
$90$	0.871487	+	0.560071i	0.0918628	+	0.0590366i
$91$	8.58905	−	4.52267i	0.900378	−	0.474104i
$92$	−1.49673	+	4.55629i	−0.156045	+	0.475026i
$93$	3.43479	+	5.94923i	0.356171	+	0.616906i
$94$	−4.90791	+	2.53020i	−0.506212	+	0.260970i
$95$	−1.22872	−	0.491903i	−0.126064	−	0.0504682i
$96$	−0.580057	+	0.814576i	−0.0592018	+	0.0831373i
$97$	12.0996	+	3.55277i	1.22853	+	0.360729i	0.830695	−	0.556727i	$-0.187943\pi$
$97$	12.0996	+	3.55277i	1.22853	+	0.360729i	0.397836	+	0.917457i	$0.369761\pi$
$98$	−3.39434	+	6.12196i	−0.342880	+	0.618412i
$99$	2.39967	−	2.76937i	0.241176	−	0.278332i
$100$	−3.64554	+	1.45946i	−0.364554	+	0.145946i
$101$	0.990934	−	4.08468i	0.0986016	−	0.406441i	−0.901025	−	0.433767i	$-0.857184\pi$
$101$	0.990934	−	4.08468i	0.0986016	−	0.406441i	0.999627	+	0.0273259i	$0.00869918\pi$
$102$	−0.416610	+	0.0802950i	−0.0412505	+	0.00795039i
$103$	7.81015	+	4.02641i	0.769557	+	0.396734i	0.797843	−	0.602866i	$-0.205975\pi$
$103$	7.81015	+	4.02641i	0.769557	+	0.396734i	−0.0282859	+	0.999600i	$0.509005\pi$
$104$	−3.08648	+	1.98356i	−0.302655	+	0.194504i
$105$	−2.55324	−	0.996563i	−0.249171	−	0.0972546i
$106$	−6.27142	+	1.84146i	−0.609135	+	0.178858i
$107$	−2.70658	+	1.08355i	−0.261655	+	0.104751i	−0.498781	−	0.866728i	$-0.666219\pi$
$107$	−2.70658	+	1.08355i	−0.261655	+	0.104751i	0.237126	+	0.971479i	$0.423795\pi$
$108$	0.327068	+	0.945001i	0.0314721	+	0.0909327i
$109$	5.41183	+	7.59985i	0.518359	+	0.727933i	0.987920	−	0.154967i	$-0.0495271\pi$
$109$	5.41183	+	7.59985i	0.518359	+	0.727933i	−0.469561	+	0.882900i	$0.655588\pi$
$110$	−0.894964	−	3.68909i	−0.0853315	−	0.351741i
$111$	−0.273747	−	0.599421i	−0.0259829	−	0.0568946i
$112$	1.07817	−	2.41610i	0.101878	−	0.228300i
$113$	−15.5948	−	10.0222i	−1.46704	−	0.942809i	−0.998228	−	0.0595109i	$-0.981046\pi$
$113$	−15.5948	−	10.0222i	−1.46704	−	0.942809i	−0.468812	−	0.883298i	$-0.655318\pi$
$114$	−0.638803	−	1.10644i	−0.0598294	−	0.103628i
$115$	4.96757	−	0.0785280i	0.463228	−	0.00732277i
$116$	0.0843902	−	0.146168i	0.00783543	−	0.0135714i
$117$	−0.174574	+	3.66476i	−0.0161394	+	0.338807i
$118$	−0.0916010	−	0.637099i	−0.00843256	−	0.0586497i
$119$	1.03847	−	0.426224i	0.0951960	−	0.0390719i
$120$	0.993976	+	0.291858i	0.0907372	+	0.0266428i
$121$	−2.41686	+	0.230782i	−0.219714	+	0.0209802i
$122$	−2.69475	−	7.78597i	−0.243971	−	0.704909i
$123$	4.71214	+	3.70567i	0.424880	+	0.334129i
$124$	4.97175	+	4.74055i	0.446476	+	0.425714i
$125$	6.05592	+	6.98891i	0.541658	+	0.625107i
$126$	−1.34269	−	2.27973i	−0.119617	−	0.203095i
$127$	−4.06340	+	2.61139i	−0.360568	+	0.231723i	−0.708364	−	0.705847i	$-0.750567\pi$
$127$	−4.06340	+	2.61139i	−0.360568	+	0.231723i	0.347796	+	0.937570i	$0.386930\pi$
$128$	−0.327068	+	0.945001i	−0.0289090	+	0.0835271i
$129$	−1.56751	+	6.46138i	−0.138012	+	0.568893i
$130$	2.98761	+	2.34948i	0.262030	+	0.206063i
$131$	−2.87697	−	0.554491i	−0.251362	−	0.0484461i	0.0620135	−	0.998075i	$-0.480248\pi$
$131$	−2.87697	−	0.554491i	−0.251362	−	0.0484461i	−0.313376	+	0.949629i	$0.601460\pi$
$132$	1.52225	−	3.33326i	0.132495	−	0.290123i
$133$	2.23565	+	2.53532i	0.193855	+	0.219840i
$134$	−0.771016	−	1.68829i	−0.0666056	−	0.145846i
$135$	0.814303	−	0.640375i	0.0700840	−	0.0551147i
$136$	−0.377113	+	0.194415i	−0.0323371	+	0.0166710i
$137$	0.373526	−	0.646966i	0.0319125	−	0.0552740i	−0.849628	−	0.527382i	$-0.823174\pi$
$137$	0.373526	−	0.646966i	0.0319125	−	0.0552740i	0.881541	+	0.472108i	$0.156507\pi$
$138$	3.81617	+	2.90463i	0.324854	+	0.247259i
$139$	16.7440			1.42021			0.710106	−	0.704095i	$-0.248647\pi$
$139$	16.7440			1.42021			0.710106	+	0.704095i	$0.248647\pi$
$140$	−2.73058	−	0.236864i	−0.230776	−	0.0200186i
$141$	0.785824	+	5.46552i	0.0661783	+	0.460280i
$142$	−6.15729	+	8.64671i	−0.516708	+	0.725615i
$143$	9.73015	−	9.27768i	0.813676	−	0.775838i
$144$	0.580057	+	0.814576i	0.0483381	+	0.0678813i
$145$	−0.171686	−	0.0330899i	−0.0142578	−	0.00274796i
$146$	−0.144633	+	1.00595i	−0.0119699	+	0.0832526i
$147$	4.67508	+	5.20995i	0.385594	+	0.429710i
$148$	−0.431534	−	0.498017i	−0.0354719	−	0.0409368i
$149$	−0.674063	−	0.347504i	−0.0552214	−	0.0284686i	0.430395	−	0.902641i	$-0.358374\pi$
$149$	−0.674063	−	0.347504i	−0.0552214	−	0.0284686i	−0.485616	+	0.874172i	$0.661405\pi$
$150$	0.186846	+	3.92238i	0.0152559	+	0.320261i
$151$	16.2055	−	3.12335i	1.31878	−	0.254174i	0.519159	−	0.854678i	$-0.326245\pi$
$151$	16.2055	−	3.12335i	1.31878	−	0.254174i	0.799622	+	0.600503i	$0.205033\pi$
$152$	−0.924647	−	0.881649i	−0.0749988	−	0.0715112i
$153$	−0.0603809	+	0.419959i	−0.00488151	+	0.0339516i
$154$	−2.20392	+	9.44128i	−0.177597	+	0.760800i
$155$	2.95629	−	6.47336i	0.237455	−	0.519953i
$156$	0.864979	+	3.56549i	0.0692537	+	0.285468i
$157$	2.68808	+	0.256680i	0.214532	+	0.0204853i	0.201769	−	0.979433i	$-0.435331\pi$
$157$	2.68808	+	0.256680i	0.214532	+	0.0204853i	0.0127633	+	0.999919i	$0.495937\pi$
$158$	9.61262	+	3.84831i	0.764739	+	0.306155i
$159$	−0.311004	+	6.52878i	−0.0246642	+	0.517766i
$160$	1.03594			0.0818981
$161$	−11.4170	−	5.53646i	−0.899785	−	0.436334i
$162$	1.00000			0.0785674
$163$	0.0319385	−	0.670471i	0.00250161	−	0.0525153i	−0.997271	−	0.0738231i	$-0.976480\pi$
$163$	0.0319385	−	0.670471i	0.00250161	−	0.0525153i	0.999773	+	0.0213078i	$0.00678300\pi$
$164$	5.56528	+	2.22800i	0.434575	+	0.173978i
$165$	−3.77891	−	0.360842i	−0.294188	−	0.0280915i
$166$	0.126247	+	0.520397i	0.00979866	+	0.0403906i
$167$	−7.32902	+	16.0483i	−0.567136	+	1.24186i	0.381172	+	0.924504i	$0.375521\pi$
$167$	−7.32902	+	16.0483i	−0.567136	+	1.24186i	−0.948308	+	0.317351i	$0.897207\pi$
$168$	−1.93058	−	1.80910i	−0.148948	−	0.139575i
$169$	−0.0655947	+	0.456221i	−0.00504574	+	0.0350939i
$170$	0.318099	+	0.303307i	0.0243971	+	0.0232626i
$171$	−1.25452	+	0.241789i	−0.0959354	+	0.0184900i
$172$	0.316363	+	6.64127i	0.0241224	+	0.506392i
$173$	16.5372	+	8.52550i	1.25730	+	0.648182i	0.952588	−	0.304263i	$-0.0984103\pi$
$173$	16.5372	+	8.52550i	1.25730	+	0.648182i	0.304710	+	0.952445i	$0.401441\pi$
$174$	−0.110528	−	0.127556i	−0.00837908	−	0.00966997i
$175$	−2.53686	−	10.0749i	−0.191769	−	0.761594i
$176$	0.521499	−	3.62711i	0.0393095	−	0.273403i
$177$	−0.632019	−	0.121812i	−0.0475055	−	0.00915593i
$178$	−0.215163	−	0.302155i	−0.0161272	−	0.0226475i
$179$	10.7008	−	10.2032i	0.799813	−	0.762620i	−0.175256	−	0.984523i	$-0.556075\pi$
$179$	10.7008	−	10.2032i	0.799813	−	0.762620i	0.975069	+	0.221903i	$0.0712267\pi$
$180$	0.600903	−	0.843851i	0.0447887	−	0.0628969i
$181$	−2.57322	−	17.8971i	−0.191266	−	1.33028i	−0.828664	−	0.559747i	$-0.810898\pi$
$181$	−2.57322	−	17.8971i	−0.191266	−	1.33028i	0.637398	−	0.770535i	$-0.280011\pi$
$182$	−4.10886	−	8.79452i	−0.304569	−	0.651893i
$183$	−8.23911			−0.609053
$184$	4.47991	+	1.71183i	0.330264	+	0.126198i
$185$	−0.341327	+	0.591196i	−0.0250949	+	0.0434656i
$186$	6.10593	−	3.14782i	0.447708	−	0.230810i
$187$	1.22209	−	0.961066i	0.0893684	−	0.0702801i
$188$	2.29381	+	5.02274i	0.167293	+	0.366321i
$189$	−2.59350	+	0.523221i	−0.188649	+	0.0380587i
$190$	−0.549811	+	1.20392i	−0.0398875	+	0.0873414i
$191$	11.0197	+	2.12387i	0.797357	+	0.153678i	0.571629	−	0.820512i	$-0.306312\pi$
$191$	11.0197	+	2.12387i	0.797357	+	0.153678i	0.225728	+	0.974190i	$0.427524\pi$
$192$	0.786053	+	0.618159i	0.0567285	+	0.0446118i
$193$	−1.88634	+	7.77559i	−0.135782	+	0.559699i	0.862755	+	0.505622i	$0.168737\pi$
$193$	−1.88634	+	7.77559i	−0.135782	+	0.559699i	−0.998537	+	0.0540774i	$0.982778\pi$
$194$	4.12447	−	11.9169i	0.296120	−	0.855582i
$195$	3.19741	−	2.05485i	0.228971	−	0.147151i
$196$	5.95352	+	3.68179i	0.425252	+	0.262985i
$197$	−10.1253	−	11.6852i	−0.721400	−	0.832540i	0.270075	−	0.962839i	$-0.412951\pi$
$197$	−10.1253	−	11.6852i	−0.721400	−	0.832540i	−0.991475	+	0.130300i	$0.958406\pi$
$198$	−2.65205	−	2.52873i	−0.188473	−	0.179709i
$199$	20.9957	+	16.5112i	1.48835	+	1.17045i	0.943254	+	0.332072i	$0.107748\pi$
$199$	20.9957	+	16.5112i	1.48835	+	1.17045i	0.545092	+	0.838376i	$0.316495\pi$
$200$	1.28434	+	3.71086i	0.0908166	+	0.262397i
$201$	−1.84761	+	0.176425i	−0.130320	+	0.0124441i
$202$	−4.03291	−	1.18417i	−0.283754	−	0.0833178i
$203$	0.353393	+	0.272985i	0.0248033	+	0.0191598i
$204$	0.0603809	+	0.419959i	0.00422751	+	0.0294030i
$205$	0.295490	−	6.20310i	0.0206379	−	0.433243i
$206$	4.39347	−	7.60972i	0.306108	−	0.530194i
$207$	3.99302	−	2.65627i	0.277534	−	0.184623i
$208$	1.83446	+	3.17737i	0.127197	+	0.220311i
$209$	3.93847	+	2.53110i	0.272429	+	0.175080i
$210$	−1.11692	+	2.50293i	−0.0770750	+	0.172719i
$211$	−4.84551	−	10.6102i	−0.333579	−	0.730435i	0.666305	−	0.745679i	$-0.267875\pi$
$211$	−4.84551	−	10.6102i	−0.333579	−	0.730435i	−0.999884	+	0.0152439i	$0.995148\pi$
$212$	1.54096	+	6.35194i	0.105834	+	0.436253i
$213$	6.15729	+	8.64671i	0.421891	+	0.592463i
$214$	0.953540	+	2.75507i	0.0651827	+	0.188333i
$215$	6.39437	−	2.55992i	0.436092	−	0.174585i
$216$	0.959493	−	0.281733i	0.0652852	−	0.0191695i
$217$	−14.1887	+	11.3586i	−0.963192	+	0.771074i
$218$	7.84874	−	5.04408i	0.531584	−	0.341628i
$219$	0.903314	+	0.465691i	0.0610403	+	0.0314685i
$220$	−3.72750	+	0.718416i	−0.251308	+	0.0484356i
$221$	−0.366991	+	1.51276i	−0.0246865	+	0.101759i
$222$	−0.611768	+	0.244915i	−0.0410592	+	0.0164376i
$223$	−8.41636	+	9.71300i	−0.563601	+	0.650431i	−0.963997	−	0.265912i	$-0.914327\pi$
$223$	−8.41636	+	9.71300i	−0.563601	+	0.650431i	0.400396	+	0.916342i	$0.368873\pi$
$224$	−2.36206	−	1.19192i	−0.157822	−	0.0796382i
$225$	3.76777	+	1.10632i	0.251184	+	0.0737544i
$226$	−10.7529	+	15.1003i	−0.715271	+	1.00446i
$227$	21.6497	+	8.66723i	1.43694	+	0.575265i	0.953844	−	0.300302i	$-0.0970875\pi$
$227$	21.6497	+	8.66723i	1.43694	+	0.575265i	0.483097	+	0.875567i	$0.339512\pi$
$228$	−1.13558	+	0.585433i	−0.0752057	+	0.0387713i
$229$	−3.09450	−	5.35983i	−0.204490	−	0.354188i	0.745480	−	0.666528i	$-0.232220\pi$
$229$	−3.09450	−	5.35983i	−0.204490	−	0.354188i	−0.949970	+	0.312341i	$0.898887\pi$
$230$	0.157927	−	4.96568i	0.0104134	−	0.327427i
$231$	8.20118	+	5.17064i	0.539598	+	0.340203i
$232$	−0.141987	−	0.0912496i	−0.00932191	−	0.00599083i
$233$	12.4742	−	9.80985i	0.817214	−	0.642664i	−0.119471	−	0.992838i	$-0.538120\pi$
$233$	12.4742	−	9.80985i	0.817214	−	0.642664i	0.936685	+	0.350173i	$0.113877\pi$
$234$	3.65230	+	0.348752i	0.238758	+	0.0227986i
$235$	4.13988	−	3.94737i	0.270056	−	0.257498i
$236$	−0.640736	+	0.0611829i	−0.0417084	+	0.00398267i
$237$	6.78064	−	7.82527i	0.440450	−	0.508306i
$238$	−0.376329	−	1.05757i	−0.0243938	−	0.0685521i
$239$	2.34165	−	0.687571i	0.151469	−	0.0444753i	−0.205119	−	0.978737i	$-0.565758\pi$
$239$	2.34165	−	0.687571i	0.151469	−	0.0444753i	0.356588	+	0.934262i	$0.383940\pi$
$240$	0.338822	−	0.978963i	0.0218709	−	0.0631918i
$241$	0.687598	+	14.4345i	0.0442921	+	0.929806i	0.906228	+	0.422789i	$0.138949\pi$
$241$	0.687598	+	14.4345i	0.0442921	+	0.929806i	−0.861936	+	0.507017i	$0.830748\pi$
$242$	0.115522	+	2.42510i	0.00742603	+	0.155891i
$243$	0.327068	−	0.945001i	0.0209814	−	0.0606218i
$244$	−7.90537	+	2.32123i	−0.506090	+	0.148601i
$245$	1.58715	−	7.07575i	0.101399	−	0.452053i
$246$	3.92569	−	4.53048i	0.250293	−	0.288853i
$247$	−4.66620	+	0.445568i	−0.296903	+	0.0283508i
$248$	4.97175	−	4.74055i	0.315706	−	0.301025i
$249$	0.533067	+	0.0509017i	0.0337817	+	0.00322576i
$250$	7.26914	−	5.71652i	0.459741	−	0.361544i
$251$	−5.35407	−	3.44085i	−0.337946	−	0.217185i	0.360650	−	0.932701i	$-0.382555\pi$
$251$	−5.35407	−	3.44085i	−0.337946	−	0.217185i	−0.698596	+	0.715517i	$0.746191\pi$
$252$	−2.34104	+	1.23270i	−0.147471	+	0.0776528i
$253$	−17.3067	−	3.05270i	−1.08806	−	0.191922i
$254$	2.41508	+	4.18305i	0.151536	+	0.262468i
$255$	0.390666	−	0.201402i	0.0244644	−	0.0126123i
$256$	0.928368	+	0.371662i	0.0580230	+	0.0232289i
$257$	−6.03521	+	8.47527i	−0.376466	+	0.528673i	−0.958727	−	0.284330i	$-0.908229\pi$
$257$	−6.03521	+	8.47527i	−0.376466	+	0.528673i	0.582261	+	0.813002i	$0.302168\pi$
$258$	6.37948	+	1.87318i	0.397169	+	0.116619i
$259$	1.45847	−	0.955276i	0.0906252	−	0.0593580i
$260$	2.48897	−	2.87243i	0.154360	−	0.178140i
$261$	−0.156690	+	0.0627293i	−0.00969889	+	0.00388285i
$262$	−0.690755	+	2.84733i	−0.0426750	+	0.175909i
$263$	−11.1621	+	2.15131i	−0.688283	+	0.132656i	−0.521389	−	0.853319i	$-0.674586\pi$
$263$	−11.1621	+	2.15131i	−0.688283	+	0.132656i	−0.166894	+	0.985975i	$0.553374\pi$
$264$	−3.25705	−	1.67913i	−0.200458	−	0.103343i
$265$	5.69620	−	3.66073i	0.349915	−	0.224877i
$266$	2.63882	−	2.11248i	0.161796	−	0.129525i
$267$	−0.355910	+	0.104504i	−0.0217813	+	0.00639557i
$268$	−1.72306	+	0.689810i	−0.105253	+	0.0421369i
$269$	2.59646	+	7.50199i	0.158309	+	0.457404i	0.996063	−	0.0886430i	$-0.0282530\pi$
$269$	2.59646	+	7.50199i	0.158309	+	0.457404i	−0.837754	+	0.546047i	$0.816132\pi$
$270$	−0.600903	−	0.843851i	−0.0365698	−	0.0513551i
$271$	−0.847289	−	3.49257i	−0.0514691	−	0.212159i	0.940270	−	0.340429i	$-0.110572\pi$
$271$	−0.847289	−	3.49257i	−0.0514691	−	0.212159i	−0.991739	+	0.128271i	$0.959057\pi$
$272$	0.176251	+	0.385936i	0.0106868	+	0.0234008i
$273$	−9.65471	+	1.00647i	−0.584330	+	0.0609144i
$274$	−0.628460	−	0.403887i	−0.0379666	−	0.0243997i
$275$	−7.19475	−	12.4617i	−0.433860	−	0.751467i
$276$	3.08292	−	3.67364i	0.185570	−	0.221127i
$277$	0.801268	−	1.38784i	0.0481435	−	0.0833870i	−0.840949	−	0.541114i	$-0.818003\pi$
$277$	0.801268	−	1.38784i	0.0481435	−	0.0833870i	0.889093	+	0.457727i	$0.151336\pi$
$278$	0.796714	−	16.7251i	0.0477837	−	1.00310i
$279$	−0.977643	−	6.79966i	−0.0585300	−	0.407085i
$280$	−0.366522	+	2.71622i	−0.0219039	+	0.162325i
$281$	−4.76881	−	1.40025i	−0.284484	−	0.0835319i	0.136378	−	0.990657i	$-0.456454\pi$
$281$	−4.76881	−	1.40025i	−0.284484	−	0.0835319i	−0.420861	+	0.907125i	$0.638272\pi$
$282$	5.49672	−	0.524873i	0.327325	−	0.0312558i
$283$	0.601457	+	1.73780i	0.0357529	+	0.103301i	0.961465	−	0.274928i	$-0.0886542\pi$
$283$	0.601457	+	1.73780i	0.0357529	+	0.103301i	−0.925712	+	0.378230i	$0.876533\pi$
$284$	8.34394	+	6.56174i	0.495122	+	0.389368i
$285$	0.957878	+	0.913335i	0.0567398	+	0.0541013i
$286$	−8.80419	−	10.1606i	−0.520603	−	0.600808i
$287$	−7.81082	+	13.8038i	−0.461058	+	0.814813i
$288$	0.841254	−	0.540641i	0.0495713	−	0.0318576i
$289$	5.50128	−	15.8949i	0.323605	−	0.934994i
$290$	−0.0412215	+	0.169918i	−0.00242061	+	0.00997790i
$291$	−9.91247	−	7.79526i	−0.581079	−	0.456966i
$292$	0.997924	+	0.192334i	0.0583991	+	0.0112555i
$293$	−11.7626	+	25.7564i	−0.687176	+	1.50471i	0.167681	+	0.985841i	$0.446372\pi$
$293$	−11.7626	+	25.7564i	−0.687176	+	1.50471i	−0.854857	+	0.518864i	$0.826355\pi$
$294$	5.42650	−	4.42189i	0.316480	−	0.257890i
$295$	0.276992	+	0.606527i	0.0161271	+	0.0353134i
$296$	−0.517986	+	0.407349i	−0.0301073	+	0.0236767i
$297$	−3.25705	+	1.67913i	−0.188993	+	0.0974328i
$298$	−0.379183	+	0.656765i	−0.0219655	+	0.0380454i
$299$	15.5101	−	8.30891i	0.896972	−	0.480517i
$300$	3.92683			0.226716
$301$	−17.5253	−	1.52022i	−1.01014	−	0.0876242i
$302$	−2.34872	−	16.3357i	−0.135154	−	0.940015i
$303$	−2.43808	+	3.42380i	−0.140064	+	0.196692i
$304$	−0.924647	+	0.881649i	−0.0530322	+	0.0505661i
$305$	4.95091	+	6.95258i	0.283488	+	0.398104i
$306$	0.416610	+	0.0802950i	0.0238160	+	0.00459016i
$307$	−4.32367	+	30.0718i	−0.246765	+	1.71629i	0.369908	+	0.929068i	$0.379389\pi$
$307$	−4.32367	+	30.0718i	−0.246765	+	1.71629i	−0.616673	+	0.787219i	$0.711520\pi$
$308$	9.32572	+	2.65066i	0.531382	+	0.151035i
$309$	−5.75422	−	6.64073i	−0.327346	−	0.377778i
$310$	−6.32536	−	3.26095i	−0.359257	−	0.185210i
$311$	−1.12696	−	23.6577i	−0.0639039	−	1.34151i	−0.772104	−	0.635496i	$-0.780796\pi$
$311$	−1.12696	−	23.6577i	−0.0639039	−	1.34151i	0.708200	−	0.706012i	$-0.249507\pi$
$312$	3.60261	−	0.694346i	0.203958	−	0.0393096i
$313$	−0.302067	−	0.288020i	−0.0170738	−	0.0162799i	0.681494	−	0.731824i	$-0.261331\pi$
$313$	−0.302067	−	0.288020i	−0.0170738	−	0.0162799i	−0.698568	+	0.715544i	$0.746179\pi$
$314$	0.384293	−	2.67282i	0.0216869	−	0.150836i
$315$	1.99996	+	1.87412i	0.112685	+	0.105595i
$316$	4.30134	−	9.41862i	0.241969	−	0.529839i
$317$	5.02754	+	20.7238i	0.282375	+	1.16396i	0.919464	+	0.393174i	$0.128623\pi$
$317$	5.02754	+	20.7238i	0.282375	+	1.16396i	−0.637089	+	0.770790i	$0.719862\pi$
$318$	6.50659	+	0.621304i	0.364871	+	0.0348410i
$319$	0.574177	+	0.229866i	0.0321477	+	0.0128700i
$320$	0.0492919	−	1.03477i	0.00275550	−	0.0578451i
$321$	2.91542			0.162723
$322$	−6.07343	+	11.1406i	−0.338459	+	0.620843i
$323$	−0.542059			−0.0301610
$324$	0.0475819	−	0.998867i	0.00264344	−	0.0554926i
$325$	13.3752	+	5.35461i	0.741921	+	0.297021i
$326$	−0.668192	−	0.0638046i	−0.0370077	−	0.00353381i
$327$	−2.19959	−	9.06682i	−0.121637	−	0.501397i
$328$	2.49028	−	5.45296i	0.137503	−	0.301089i
$329$	−13.9811	+	4.23726i	−0.770804	+	0.233608i
$330$	−0.540241	+	3.75746i	−0.0297393	+	0.206841i
$331$	−1.41555	−	1.34972i	−0.0778057	−	0.0741876i	0.650178	−	0.759782i	$-0.274694\pi$
$331$	−1.41555	−	1.34972i	−0.0778057	−	0.0741876i	−0.727984	+	0.685594i	$0.759543\pi$
$332$	0.525814	−	0.101342i	0.0288578	−	0.00556189i
$333$	0.0313551	+	0.658225i	0.00171825	+	0.0360705i
$334$	15.6814	+	8.08433i	0.858048	+	0.442355i
$335$	1.25911	+	1.45309i	0.0687926	+	0.0793909i
$336$	−1.89892	+	1.84231i	−0.103594	+	0.100506i
$337$	−4.30124	+	29.9158i	−0.234303	+	1.62962i	0.444840	+	0.895610i	$0.353261\pi$
$337$	−4.30124	+	29.9158i	−0.234303	+	1.62962i	−0.679143	+	0.734006i	$0.737648\pi$
$338$	0.452583	+	0.0872282i	0.0246173	+	0.00474459i
$339$	10.7529	+	15.1003i	0.584016	+	0.820136i
$340$	0.318099	−	0.303307i	0.0172514	−	0.0164491i
$341$	−14.6017	+	20.5052i	−0.790727	+	1.11042i
$342$	0.181822	+	1.26460i	0.00983183	+	0.0683819i
$343$	−11.7600	+	14.3074i	−0.634981	+	0.772528i
$344$	6.64880			0.358479
$345$	−4.64092	−	1.77336i	−0.249859	−	0.0954742i
$346$	9.30272	−	16.1128i	0.500117	−	0.866228i
$347$	9.61685	−	4.95783i	0.516260	−	0.266150i	−0.180348	−	0.983603i	$-0.557722\pi$
$347$	9.61685	−	4.95783i	0.516260	−	0.266150i	0.696607	+	0.717453i	$0.254692\pi$
$348$	−0.132670	+	0.104333i	−0.00711188	+	0.00559284i
$349$	0.538513	+	1.17918i	0.0288259	+	0.0631200i	0.923497	−	0.383605i	$-0.125318\pi$
$349$	0.538513	+	1.17918i	0.0288259	+	0.0631200i	−0.894671	+	0.446725i	$0.852590\pi$
$350$	−10.1842	+	2.05460i	−0.544370	+	0.109823i
$351$	1.52412	−	3.33736i	0.0813516	−	0.178135i
$352$	−3.59818	−	0.693493i	−0.191784	−	0.0369633i
$353$	−10.5803	−	8.32043i	−0.563132	−	0.442852i	0.295574	−	0.955320i	$-0.404489\pi$
$353$	−10.5803	−	8.32043i	−0.563132	−	0.442852i	−0.858706	+	0.512468i	$0.828731\pi$
$354$	−0.151746	+	0.625507i	−0.00806523	+	0.0332453i
$355$	3.59659	−	10.3917i	0.190887	−	0.551533i
$356$	−0.312050	+	0.200543i	−0.0165386	+	0.0106287i
$357$	−1.12249	+	0.00973411i	−0.0594084	+	0.000515184i
$358$	−9.68245	−	11.1741i	−0.511733	−	0.590572i
$359$	21.7019	+	20.6927i	1.14538	+	1.09212i	0.994625	+	0.103548i	$0.0330194\pi$
$359$	21.7019	+	20.6927i	1.14538	+	1.09212i	0.150756	+	0.988571i	$0.451829\pi$
$360$	−0.814303	−	0.640375i	−0.0429175	−	0.0337507i
$361$	5.68043	+	16.4125i	0.298970	+	0.863816i
$362$	−17.9993	+	1.71872i	−0.946021	+	0.0903340i
$363$	2.32951	+	0.684005i	0.122267	+	0.0359009i
$364$	−8.98007	+	3.68575i	−0.470684	+	0.193186i
$365$	−0.149831	−	1.04210i	−0.00784251	−	0.0545459i
$366$	−0.392033	+	8.22978i	−0.0204919	+	0.430178i
$367$	13.2387	−	22.9302i	0.691057	−	1.19695i	−0.280435	−	0.959873i	$-0.590479\pi$
$367$	13.2387	−	22.9302i	0.691057	−	1.19695i	0.971492	−	0.237072i	$-0.0761878\pi$
$368$	1.92306	−	4.39339i	0.100246	−	0.229021i
$369$	−2.99735	−	5.19155i	−0.156036	−	0.270262i
$370$	0.574285	+	0.369070i	0.0298557	+	0.0191871i
$371$	−17.1999	+	1.79303i	−0.892975	+	0.0930897i
$372$	−2.85373	−	6.24879i	−0.147959	−	0.323985i
$373$	−2.94897	−	12.1558i	−0.152692	−	0.629405i	−0.995792	−	0.0916472i	$-0.970787\pi$
$373$	−2.94897	−	12.1558i	−0.152692	−	0.629405i	0.843100	−	0.537757i	$-0.180728\pi$
$374$	−0.901828	−	1.26644i	−0.0466324	−	0.0654860i
$375$	−3.02461	−	8.73904i	−0.156190	−	0.451282i
$376$	5.12619	−	2.05222i	0.264363	−	0.105835i
$377$	−0.594157	+	0.174460i	−0.0306006	+	0.00898516i
$378$	0.399225	+	2.61546i	0.0205339	+	0.134525i
$379$	−17.9011	+	11.5043i	−0.919517	+	0.590938i	−0.912517	−	0.409038i	$-0.865864\pi$
$379$	−17.9011	+	11.5043i	−0.919517	+	0.590938i	−0.00699949	+	0.999976i	$0.502228\pi$
$380$	1.17639	+	0.606473i	0.0603477	+	0.0311114i
$381$	4.74288	−	0.914115i	0.242985	−	0.0468316i
$382$	2.64580	−	10.9062i	0.135371	−	0.558007i
$383$	−27.5680	+	11.0366i	−1.40866	+	0.563942i	−0.946456	−	0.322833i	$-0.895365\pi$
$383$	−27.5680	+	11.0366i	−1.40866	+	0.563942i	−0.462202	+	0.886775i	$0.652941\pi$
$384$	0.654861	−	0.755750i	0.0334182	−	0.0385667i
$385$	−0.564867	−	10.0276i	−0.0287883	−	0.511055i
$386$	7.67703	+	2.25418i	0.390750	+	0.114735i
$387$	3.85668	−	5.41595i	0.196046	−	0.275308i
$388$	−11.7071	−	4.68683i	−0.594339	−	0.237938i
$389$	−25.9366	+	13.3713i	−1.31504	+	0.677950i	−0.965850	−	0.259102i	$-0.916573\pi$
$389$	−25.9366	+	13.3713i	−1.31504	+	0.677950i	−0.349190	+	0.937052i	$0.613543\pi$
$390$	−1.90038	−	3.29156i	−0.0962297	−	0.166675i
$391$	1.87682	−	0.786008i	0.0949148	−	0.0397501i
$392$	3.96090	−	5.77159i	0.200056	−	0.291509i
$393$	2.46481	+	1.58403i	0.124333	+	0.0799040i
$394$	−12.1538	+	9.55785i	−0.612299	+	0.481518i
$395$	−10.6779	−	1.01961i	−0.537262	−	0.0513023i
$396$	−2.65205	+	2.52873i	−0.133271	+	0.127073i
$397$	12.5066	−	1.19424i	0.627688	−	0.0599369i	0.223636	−	0.974673i	$-0.428207\pi$
$397$	12.5066	−	1.19424i	0.627688	−	0.0599369i	0.404052	+	0.914736i	$0.367601\pi$
$398$	17.4915	−	20.1863i	0.876771	−	1.01185i
$399$	−1.13322	−	3.18461i	−0.0567321	−	0.159430i
$400$	3.76777	−	1.10632i	0.188388	−	0.0553158i
$401$	−3.92104	+	11.3291i	−0.195807	+	0.565748i	−0.999574	−	0.0291971i	$-0.990705\pi$
$401$	−3.92104	+	11.3291i	−0.195807	+	0.565748i	0.803766	+	0.594945i	$0.202826\pi$
$402$	0.0883127	+	1.85391i	0.00440463	+	0.0924647i
$403$	−1.19925	−	25.1753i	−0.0597388	−	1.25407i
$404$	−1.37472	+	3.97199i	−0.0683949	+	0.197614i
$405$	−0.993976	+	0.291858i	−0.0493911	+	0.0145025i
$406$	0.289491	−	0.340004i	0.0143672	−	0.0168741i
$407$	1.58132	−	1.82494i	0.0783829	−	0.0904587i
$408$	0.422356	−	0.0403301i	0.0209097	−	0.00199664i
$409$	9.57245	−	9.12731i	0.473327	−	0.451317i	−0.415477	−	0.909604i	$-0.636385\pi$
$409$	9.57245	−	9.12731i	0.473327	−	0.451317i	0.888804	+	0.458287i	$0.151537\pi$
$410$	−6.18201	−	0.590311i	−0.305308	−	0.0291534i
$411$	−0.587222	+	0.461797i	−0.0289655	+	0.0227788i
$412$	−7.39205	−	4.75058i	−0.364180	−	0.234044i
$413$	0.0662756	−	1.70165i	0.00326121	−	0.0837327i
$414$	−2.46326	−	4.11489i	−0.121063	−	0.202236i
$415$	−0.277368	−	0.480416i	−0.0136155	−	0.0235827i
$416$	3.26106	−	1.68119i	0.159887	−	0.0824272i
$417$	−15.5446	−	6.22313i	−0.761224	−	0.304748i
$418$	2.71563	−	3.81357i	0.132826	−	0.186528i
$419$	29.2348	+	8.58412i	1.42822	+	0.419362i	0.902275	−	0.431160i	$-0.141896\pi$
$419$	29.2348	+	8.58412i	1.42822	+	0.419362i	0.525940	+	0.850522i	$0.323714\pi$
$420$	2.44695	+	1.23475i	0.119399	+	0.0602497i
$421$	19.6409	−	22.6668i	0.957238	−	1.10471i	−0.0371913	−	0.999308i	$-0.511841\pi$
$421$	19.6409	−	22.6668i	0.957238	−	1.10471i	0.994430	−	0.105404i	$-0.0336135\pi$
$422$	−10.8287	+	4.33517i	−0.527134	+	0.211033i
$423$	1.30180	−	5.36608i	0.0632955	−	0.260908i
$424$	6.41807	−	1.23698i	0.311689	−	0.0600731i
$425$	1.48086	+	0.763435i	0.0718321	+	0.0370320i
$426$	8.92989	−	5.73889i	0.432654	−	0.278050i
$427$	−3.28926	−	21.5491i	−0.159178	−	1.04283i
$428$	2.79732	−	0.821369i	0.135214	−	0.0397024i
$429$	−12.4813	+	4.99677i	−0.602604	+	0.241246i
$430$	−2.25276	−	6.50893i	−0.108638	−	0.313888i
$431$	−2.23944	−	3.14486i	−0.107870	−	0.151482i	0.757112	−	0.653285i	$-0.226610\pi$
$431$	−2.23944	−	3.14486i	−0.107870	−	0.151482i	−0.864982	+	0.501803i	$0.832670\pi$
$432$	−0.235759	−	0.971812i	−0.0113430	−	0.0467563i
$433$	7.65955	+	16.7721i	0.368094	+	0.806014i	0.999532	+	0.0305875i	$0.00973784\pi$
$433$	7.65955	+	16.7721i	0.368094	+	0.806014i	−0.631438	+	0.775427i	$0.717535\pi$
$434$	10.6706	+	14.7131i	0.512207	+	0.706251i
$435$	0.147090	+	0.0945290i	0.00705242	+	0.00453232i
$436$	−4.66491	−	8.07986i	−0.223409	−	0.386955i
$437$	4.08514	+	4.56662i	0.195419	+	0.218451i
$438$	0.508145	−	0.880133i	0.0242801	−	0.0420544i
$439$	1.34955	−	28.3305i	0.0644104	−	1.35214i	−0.703094	−	0.711097i	$-0.748199\pi$
$439$	1.34955	−	28.3305i	0.0644104	−	1.35214i	0.767505	−	0.641043i	$-0.221498\pi$
$440$	0.540241	+	3.75746i	0.0257550	+	0.179130i
$441$	−2.40385	−	6.57431i	−0.114469	−	0.313062i
$442$	1.49358	+	0.438555i	0.0710424	+	0.0208599i
$443$	33.0911	−	3.15982i	1.57221	−	0.150127i	0.727784	−	0.685807i	$-0.240550\pi$
$443$	33.0911	−	3.15982i	1.57221	−	0.150127i	0.844422	+	0.535679i	$0.179944\pi$
$444$	0.215528	+	0.622728i	0.0102285	+	0.0295534i
$445$	0.302053	+	0.237537i	0.0143187	+	0.0112604i
$446$	9.30153	+	8.86899i	0.440440	+	0.419959i
$447$	0.496624	+	0.573135i	0.0234895	+	0.0271084i
$448$	−1.30296	+	2.30267i	−0.0615589	+	0.108791i
$449$	32.4866	−	20.8779i	1.53314	−	0.985289i	0.543873	−	0.839168i	$-0.316957\pi$
$449$	32.4866	−	20.8779i	1.53314	−	0.985289i	0.989267	−	0.146121i	$-0.0466789\pi$
$450$	1.28434	−	3.71086i	0.0605444	−	0.174932i
$451$	−5.17891	+	21.3477i	−0.243865	+	1.00523i
$452$	14.5716	+	11.4592i	0.685388	+	0.538995i
$453$	−16.2055	−	3.12335i	−0.761399	−	0.146748i
$454$	9.68755	−	21.2128i	0.454659	−	0.995565i
$455$	6.65086	+	7.54234i	0.311797	+	0.353590i
$456$	0.530737	+	1.16215i	0.0248540	+	0.0544227i
$457$	−29.8384	+	23.4652i	−1.39578	+	1.09766i	−0.413448	+	0.910528i	$0.635676\pi$
$457$	−29.8384	+	23.4652i	−1.39578	+	1.09766i	−0.982335	+	0.187129i	$0.940082\pi$
$458$	−5.50100	+	2.83596i	−0.257045	+	0.132516i
$459$	0.212139	−	0.367435i	0.00990178	−	0.0171504i
$460$	−4.95254	−	0.394025i	−0.230913	−	0.0183715i
$461$	−7.28094			−0.339107			−0.169554	−	0.985521i	$-0.554233\pi$
$461$	−7.28094			−0.339107			−0.169554	+	0.985521i	$0.554233\pi$
$462$	5.55502	−	7.94586i	0.258443	−	0.369675i
$463$	5.60900	+	39.0115i	0.260672	+	1.81302i	0.527815	+	0.849359i	$0.323012\pi$
$463$	5.60900	+	39.0115i	0.260672	+	1.81302i	−0.267142	+	0.963657i	$0.586079\pi$
$464$	−0.0979022	+	0.137484i	−0.00454500	+	0.00638256i
$465$	−5.15043	+	4.91092i	−0.238845	+	0.227739i
$466$	−9.20519	−	12.9269i	−0.426422	−	0.598826i
$467$	−32.5044	−	6.26472i	−1.50413	−	0.289896i	−0.630383	−	0.776284i	$-0.717102\pi$
$467$	−32.5044	−	6.26472i	−1.50413	−	0.289896i	−0.873743	+	0.486388i	$0.838314\pi$
$468$	0.522141	−	3.63157i	0.0241360	−	0.167869i
$469$	−1.19904	−	4.76191i	−0.0553667	−	0.219885i
$470$	−3.74591	−	4.32302i	−0.172786	−	0.199406i
$471$	−2.40013	−	1.23735i	−0.110592	−	0.0570141i
$472$	0.0306261	+	0.642922i	0.00140968	+	0.0295929i
$473$	−23.9236	+	4.61090i	−1.10001	+	0.212009i
$474$	−7.49378	−	7.14530i	−0.344201	−	0.328195i
$475$	−0.713986	+	4.96588i	−0.0327599	+	0.227850i
$476$	−1.07428	+	0.325582i	−0.0492395	+	0.0149230i
$477$	2.71523	−	5.94552i	0.124322	−	0.272227i
$478$	−0.575372	−	2.37172i	−0.0263169	−	0.108480i
$479$	3.50498	+	0.334685i	0.160147	+	0.0152922i	0.174821	−	0.984600i	$-0.444065\pi$
$479$	3.50498	+	0.334685i	0.160147	+	0.0152922i	−0.0146747	+	0.999892i	$0.504671\pi$
$480$	−0.961732	−	0.385020i	−0.0438969	−	0.0175737i
$481$	−0.115039	+	2.41497i	−0.00524533	+	0.110113i
$482$	14.4508			0.658217
$483$	8.54147	+	9.38314i	0.388650	+	0.426947i
$484$	2.42785			0.110357
$485$	−0.621593	+	13.0488i	−0.0282251	+	0.592517i
$486$	−0.928368	−	0.371662i	−0.0421116	−	0.0168590i
$487$	−30.8946	−	2.95007i	−1.39997	−	0.133681i	−0.632396	−	0.774645i	$-0.717928\pi$
$487$	−30.8946	−	2.95007i	−1.39997	−	0.133681i	−0.767570	+	0.640965i	$0.778534\pi$
$488$	1.94244	+	8.00687i	0.0879303	+	0.362454i
$489$	−0.278839	+	0.610573i	−0.0126096	+	0.0276111i
$490$	−6.99222	−	1.92203i	−0.315876	−	0.0868285i
$491$	−0.00409056	+	0.0284505i	−0.000184605	+	0.00128395i	−0.989914	−	0.141673i	$-0.954752\pi$
$491$	−0.00409056	+	0.0284505i	−0.000184605	+	0.00128395i	0.989729	+	0.142957i	$0.0456610\pi$
$492$	−4.33856	−	4.13681i	−0.195597	−	0.186502i
$493$	−0.0703156	+	0.0135522i	−0.00316685	+	0.000610361i
$494$	0.223037	+	4.68212i	0.0100349	+	0.210658i
$495$	3.37411	+	1.73947i	0.151655	+	0.0781835i
$496$	−4.49862	−	5.19168i	−0.201994	−	0.233113i
$497$	−20.1570	+	19.5561i	−0.904163	+	0.877212i
$498$	0.0762084	−	0.530041i	0.00341498	−	0.0237517i
$499$	−20.8395	−	4.01649i	−0.932906	−	0.179803i	−0.299919	−	0.953965i	$-0.596959\pi$
$499$	−20.8395	−	4.01649i	−0.932906	−	0.179803i	−0.632988	+	0.774162i	$0.718172\pi$
$500$	−5.36416	−	7.53291i	−0.239893	−	0.336882i
$501$	12.7686	−	12.1748i	0.570458	−	0.543931i
$502$	−3.69171	+	5.18429i	−0.164769	+	0.231386i
$503$	0.668600	+	4.65021i	0.0298114	+	0.207343i	0.999283	−	0.0378607i	$-0.0120543\pi$
$503$	0.668600	+	4.65021i	0.0298114	+	0.207343i	−0.969472	+	0.245203i	$0.921145\pi$
$504$	1.11991	+	2.39704i	0.0498849	+	0.106773i
$505$	4.35422			0.193760
$506$	−3.87273	+	17.1418i	−0.172164	+	0.762048i
$507$	0.230456	−	0.399162i	0.0102349	−	0.0177274i
$508$	4.29323	−	2.21331i	0.190481	−	0.0981998i
$509$	28.1539	−	22.1404i	1.24790	−	0.981358i	0.247978	−	0.968766i	$-0.420234\pi$
$509$	28.1539	−	22.1404i	1.24790	−	0.981358i	0.999921	−	0.0125924i	$-0.00400838\pi$
$510$	−0.182585	−	0.399806i	−0.00808501	−	0.0177037i
$511$	−0.857369	+	2.54850i	−0.0379278	+	0.112739i
$512$	0.415415	−	0.909632i	0.0183589	−	0.0402004i
$513$	1.25452	+	0.241789i	0.0553883	+	0.0106752i
$514$	8.17850	+	6.43164i	0.360738	+	0.283688i
$515$	−2.14605	+	8.84614i	−0.0945663	+	0.389808i
$516$	2.17461	−	6.28312i	0.0957319	−	0.276599i
$517$	−17.0218	+	10.9392i	−0.748617	+	0.481107i
$518$	−0.884797	−	1.50228i	−0.0388758	−	0.0660062i
$519$	−12.1840	−	14.0610i	−0.534817	−	0.617211i
$520$	−2.75074	−	2.62283i	−0.120628	−	0.115019i
$521$	−16.6863	−	13.1223i	−0.731042	−	0.574898i	0.181739	−	0.983347i	$-0.441827\pi$
$521$	−16.6863	−	13.1223i	−0.731042	−	0.574898i	−0.912781	+	0.408449i	$0.866070\pi$
$522$	0.0552027	+	0.159498i	0.00241616	+	0.00698102i
$523$	−24.1610	+	2.30709i	−1.05649	+	0.100882i	−0.608812	−	0.793315i	$-0.708354\pi$
$523$	−24.1610	+	2.30709i	−1.05649	+	0.100882i	−0.447674	+	0.894197i	$0.647748\pi$
$524$	2.81124	+	0.825454i	0.122810	+	0.0360601i
$525$	−1.38934	+	10.2961i	−0.0606356	+	0.449359i
$526$	1.61776	+	11.2518i	0.0705379	+	0.490602i
$527$	0.138683	−	2.91130i	0.00604111	−	0.126818i
$528$	−1.83220	+	3.17347i	−0.0797363	+	0.138107i
$529$	−20.7661	−	9.88777i	−0.902875	−	0.429903i
$530$	−3.38554	−	5.86393i	−0.147059	−	0.254713i
$531$	0.541473	+	0.347984i	0.0234979	+	0.0151012i
$532$	−1.98453	−	2.73635i	−0.0860402	−	0.118636i
$533$	−9.13663	−	20.0064i	−0.395752	−	0.866575i
$534$	0.0874512	+	0.360479i	0.00378439	+	0.0155994i
$535$	−1.75189	−	2.46018i	−0.0757406	−	0.106363i
$536$	0.607042	+	1.75393i	0.0262202	+	0.0757584i
$537$	−13.7264	+	5.49522i	−0.592337	+	0.237136i
$538$	7.61704	−	2.23656i	0.328394	−	0.0964251i
$539$	−10.2495	+	23.5141i	−0.441477	+	1.01282i
$540$	−0.871487	+	0.560071i	−0.0375028	+	0.0241016i
$541$	25.3856	+	13.0872i	1.09141	+	0.562662i	0.907402	−	0.420263i	$-0.138062\pi$
$541$	25.3856	+	13.0872i	1.09141	+	0.562662i	0.184009	+	0.982925i	$0.441092\pi$
$542$	−3.52893	+	0.680146i	−0.151581	+	0.0292148i
$543$	−4.26279	+	17.5715i	−0.182934	+	0.754064i
$544$	0.393885	−	0.157688i	0.0168877	−	0.00676081i
$545$	−6.32931	+	7.30441i	−0.271118	+	0.312887i
$546$	0.545941	+	9.69166i	0.0233641	+	0.414765i
$547$	−36.7485	−	10.7903i	−1.57125	−	0.461361i	−0.623886	−	0.781516i	$-0.714447\pi$
$547$	−36.7485	−	10.7903i	−1.57125	−	0.461361i	−0.947365	+	0.320155i	$0.896265\pi$
$548$	−0.433332	+	0.608530i	−0.0185110	+	0.0259951i
$549$	7.64893	+	3.06217i	0.326448	+	0.130690i
$550$	−12.7899	+	6.59365i	−0.545363	+	0.281154i
$551$	−0.107817	−	0.186745i	−0.00459318	−	0.00795562i
$552$	−3.52278	−	3.25423i	−0.149940	−	0.138509i
$553$	23.1737	+	14.6104i	0.985445	+	0.621299i
$554$	−1.34814	−	0.866396i	−0.0572769	−	0.0368096i
$555$	0.536602	−	0.421989i	0.0227775	−	0.0179124i
$556$	−16.6682	−	1.59162i	−0.706890	−	0.0674998i
$557$	17.6381	−	16.8179i	0.747352	−	0.712598i	−0.217306	−	0.976103i	$-0.569727\pi$
$557$	17.6381	−	16.8179i	0.747352	−	0.712598i	0.964658	+	0.263505i	$0.0848786\pi$
$558$	−6.83847	+	0.652995i	−0.289496	+	0.0276435i
$559$	15.9746	−	18.4357i	0.675653	−	0.779745i
$560$	2.69570	+	0.495349i	0.113914	+	0.0209323i
$561$	−1.49175	+	0.438016i	−0.0629815	+	0.0184930i
$562$	−1.62557	+	4.69679i	−0.0685707	+	0.198122i
$563$	−0.145280	−	3.04981i	−0.00612283	−	0.128534i	−0.999859	−	0.0167837i	$-0.994657\pi$
$563$	−0.145280	−	3.04981i	−0.00612283	−	0.128534i	0.993736	−	0.111750i	$-0.0356457\pi$
$564$	−0.262734	−	5.51547i	−0.0110631	−	0.232243i
$565$	6.28096	−	18.1476i	0.264242	−	0.763477i
$566$	1.76445	−	0.518088i	0.0741653	−	0.0217769i
$567$	2.60218	+	0.478165i	0.109281	+	0.0200810i
$568$	6.95133	−	8.02227i	0.291671	−	0.336607i
$569$	−23.9649	+	2.28837i	−1.00466	+	0.0959333i	−0.584396	−	0.811469i	$-0.698668\pi$
$569$	−23.9649	+	2.28837i	−1.00466	+	0.0959333i	−0.420263	+	0.907402i	$0.638062\pi$
$570$	0.957878	−	0.913335i	0.0401211	−	0.0382554i
$571$	2.35421	+	0.224800i	0.0985205	+	0.00940757i	0.144200	−	0.989549i	$-0.453939\pi$
$571$	2.35421	+	0.224800i	0.0985205	+	0.00940757i	−0.0456793	+	0.998956i	$0.514545\pi$
$572$	−10.5680	+	8.31076i	−0.441870	+	0.347490i
$573$	−9.44097	−	6.06734i	−0.394402	−	0.253467i
$574$	13.4165	+	8.45879i	0.559995	+	0.353063i
$575$	−4.72863	−	18.2291i	−0.197198	−	0.760206i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−18.1568	+	9.36050i	−0.755879	+	0.389683i	−0.792678	−	0.609640i	$-0.791314\pi$
$577$	−18.1568	+	9.36050i	−0.755879	+	0.389683i	0.0367997	+	0.999323i	$0.488284\pi$
$578$	−15.6151	−	6.25136i	−0.649504	−	0.260022i
$579$	4.64111	−	6.51753i	0.192878	−	0.270859i
$580$	0.167764	+	0.0492599i	0.00696601	+	0.00204540i
$581$	0.0796822	+	1.41453i	0.00330577	+	0.0586848i
$582$	−8.25808	+	9.53033i	−0.342308	+	0.395045i
$583$	−22.2355	+	8.90177i	−0.920902	+	0.368674i
$584$	0.239599	−	0.987642i	0.00991469	−	0.0408689i
$585$	−3.73208	+	0.719300i	−0.154303	+	0.0297394i
$586$	25.1676	+	12.9748i	1.03966	+	0.535983i
$587$	−6.12035	+	3.93331i	−0.252614	+	0.162345i	−0.660819	−	0.750545i	$-0.729791\pi$
$587$	−6.12035	+	3.93331i	−0.252614	+	0.162345i	0.408205	+	0.912890i	$0.366155\pi$
$588$	−4.15868	−	5.63076i	−0.171501	−	0.232208i
$589$	8.42110	−	2.47266i	0.346986	−	0.101884i
$590$	0.619020	−	0.247818i	0.0254846	−	0.0102025i
$591$	5.05706	+	14.6114i	0.208020	+	0.601033i
$592$	0.382241	+	0.536782i	0.0157100	+	0.0220616i
$593$	−1.36760	−	5.63734i	−0.0561607	−	0.231498i	0.936813	−	0.349830i	$-0.113760\pi$
$593$	−1.36760	−	5.63734i	−0.0561607	−	0.231498i	−0.992974	+	0.118332i	$0.962245\pi$
$594$	1.52225	+	3.33326i	0.0624586	+	0.136765i
$595$	0.682722	+	0.941364i	0.0279889	+	0.0385922i
$596$	0.637978	+	0.410004i	0.0261326	+	0.0167944i
$597$	−13.3551	−	23.1318i	−0.546590	−	0.946721i
$598$	−7.56150	−	15.8879i	−0.309213	−	0.649704i
$599$	0.778416	−	1.34826i	0.0318052	−	0.0550883i	−0.849685	−	0.527291i	$-0.823208\pi$
$599$	0.778416	−	1.34826i	0.0318052	−	0.0550883i	0.881490	+	0.472203i	$0.156541\pi$
$600$	0.186846	−	3.92238i	0.00762796	−	0.160131i
$601$	−0.106749	−	0.742458i	−0.00435439	−	0.0302855i	0.987528	−	0.157441i	$-0.0503244\pi$
$601$	−0.106749	−	0.742458i	−0.00435439	−	0.0302855i	−0.991883	+	0.127155i	$0.959415\pi$
$602$	−2.35239	+	17.4331i	−0.0958761	+	0.710519i
$603$	1.78083	+	0.522899i	0.0725211	+	0.0212941i
$604$	−16.4290	+	1.56878i	−0.668485	+	0.0638326i
$605$	−0.822611	−	2.37678i	−0.0334439	−	0.0966297i
$606$	3.30391	+	2.59822i	0.134212	+	0.105546i
$607$	−28.1869	−	26.8761i	−1.14407	−	1.09087i	−0.994777	−	0.102076i	$-0.967452\pi$
$607$	−28.1869	−	26.8761i	−1.14407	−	1.09087i	−0.149293	−	0.988793i	$-0.547700\pi$
$608$	0.836654	+	0.965550i	0.0339308	+	0.0391582i
$609$	−0.226621	−	0.384774i	−0.00918313	−	0.0155918i
$610$	7.18028	−	4.61449i	0.290721	−	0.186835i
$611$	6.62598	−	19.1445i	0.268058	−	0.774504i
$612$	0.100027	−	0.412317i	0.00404336	−	0.0166669i
$613$	22.5594	+	17.7409i	0.911164	+	0.716548i	0.959329	−	0.282292i	$-0.0910946\pi$
$613$	22.5594	+	17.7409i	0.911164	+	0.716548i	−0.0481642	+	0.998839i	$0.515337\pi$
$614$	29.8320	+	5.74965i	1.20392	+	0.232037i
$615$	−2.57978	+	5.64893i	−0.104027	+	0.227787i
$616$	3.09139	−	9.18903i	0.124556	−	0.370237i
$617$	12.8231	+	28.0787i	0.516240	+	1.13041i	0.970844	+	0.239713i	$0.0770535\pi$
$617$	12.8231	+	28.0787i	0.516240	+	1.13041i	−0.454604	+	0.890694i	$0.650219\pi$
$618$	−6.90700	+	5.43173i	−0.277840	+	0.218496i
$619$	20.1007	−	10.3626i	0.807916	−	0.416509i	−0.00421062	−	0.999991i	$-0.501340\pi$
$619$	20.1007	−	10.3626i	0.807916	−	0.416509i	0.812126	+	0.583482i	$0.198310\pi$
$620$	−3.55823	+	6.16304i	−0.142902	+	0.247514i
$621$	−4.69423	+	0.981938i	−0.188373	+	0.0394038i
$622$	−23.6846			−0.949665
$623$	−0.415415	−	0.889146i	−0.0166432	−	0.0356229i
$624$	−0.522141	−	3.63157i	−0.0209024	−	0.145379i
$625$	5.83198	−	8.18987i	0.233279	−	0.327595i
$626$	−0.302067	+	0.288020i	−0.0120730	+	0.0115116i
$627$	−2.71563	−	3.81357i	−0.108452	−	0.152299i
$628$	−2.65151	−	0.511036i	−0.105807	−	0.0203925i
$629$	−0.0397893	+	0.276741i	−0.00158650	+	0.0110344i
$630$	1.96716	−	1.90852i	0.0783736	−	0.0760374i
$631$	−0.306585	−	0.353818i	−0.0122050	−	0.0140853i	0.749614	−	0.661875i	$-0.230239\pi$
$631$	−0.306585	−	0.353818i	−0.0122050	−	0.0140853i	−0.761819	+	0.647790i	$0.775694\pi$
$632$	−9.20329	−	4.74463i	−0.366087	−	0.188731i
$633$	0.555008	+	11.6510i	0.0220596	+	0.463088i
$634$	20.9395	−	4.03577i	0.831616	−	0.160281i
$635$	−3.62139	−	3.45299i	−0.143711	−	0.137028i
$636$	0.930196	−	6.46966i	0.0368847	−	0.256539i
$637$	−6.48678	−	24.8497i	−0.257016	−	0.984580i
$638$	0.256926	−	0.562589i	0.0101718	−	0.0222731i
$639$	−2.50258	−	10.3158i	−0.0990004	−	0.408085i
$640$	−1.03125	−	0.0984722i	−0.0407637	−	0.00389246i
$641$	−16.0317	−	6.41811i	−0.633213	−	0.253500i	0.0327750	−	0.999463i	$-0.489566\pi$
$641$	−16.0317	−	6.41811i	−0.633213	−	0.253500i	−0.665988	+	0.745963i	$0.731990\pi$
$642$	0.138721	−	2.91212i	0.00547489	−	0.114932i
$643$	26.5344			1.04641			0.523206	−	0.852206i	$-0.324736\pi$
$643$	26.5344			1.04641			0.523206	+	0.852206i	$0.324736\pi$
$644$	10.8390	+	6.59664i	0.427117	+	0.259944i
$645$	−6.88775			−0.271205
$646$	−0.0257922	+	0.541445i	−0.00101478	+	0.0213029i
$647$	16.1574	+	6.46845i	0.635214	+	0.254301i	0.666843	−	0.745199i	$-0.267645\pi$
$647$	16.1574	+	6.46845i	0.635214	+	0.254301i	−0.0316291	+	0.999500i	$0.510070\pi$
$648$	−0.995472	−	0.0950560i	−0.0391058	−	0.00373415i
$649$	−0.556060	−	2.29211i	−0.0218273	−	0.0899732i
$650$	5.98497	−	13.1052i	0.234750	−	0.514030i
$651$	17.3939	−	5.27158i	0.681721	−	0.206609i
$652$	−0.0955261	+	0.664399i	−0.00374109	+	0.0260199i
$653$	18.2840	+	17.4338i	0.715508	+	0.682236i	0.957627	−	0.288011i	$-0.0929939\pi$
$653$	18.2840	+	17.4338i	0.715508	+	0.682236i	−0.242119	+	0.970247i	$0.577842\pi$
$654$	−9.16122	+	1.76568i	−0.358232	+	0.0690435i
$655$	−0.144421	−	3.03178i	−0.00564301	−	0.118461i
$656$	−5.32829	−	2.74693i	−0.208035	−	0.107249i
$657$	−0.665528	−	0.768060i	−0.0259647	−	0.0299649i
$658$	3.56721	+	14.1669i	0.139064	+	0.552283i
$659$	−1.74501	+	12.1368i	−0.0679758	+	0.472782i	0.927192	+	0.374588i	$0.122216\pi$
$659$	−1.74501	+	12.1368i	−0.0679758	+	0.472782i	−0.995167	+	0.0981942i	$0.968693\pi$
$660$	3.72750	+	0.718416i	0.145093	+	0.0279643i
$661$	−11.5864	−	16.2708i	−0.450659	−	0.632863i	0.525274	−	0.850933i	$-0.323963\pi$
$661$	−11.5864	−	16.2708i	−0.450659	−	0.632863i	−0.975933	+	0.218071i	$0.930024\pi$
$662$	−1.41555	+	1.34972i	−0.0550169	+	0.0524585i
$663$	0.902937	−	1.26800i	0.0350672	−	0.0492449i
$664$	−0.0762084	−	0.530041i	−0.00295746	−	0.0205696i
$665$	−2.00638	+	2.86991i	−0.0778041	+	0.111291i
$666$	0.658971			0.0255346
$667$	0.644094	+	0.490245i	0.0249394	+	0.0189824i
$668$	8.82132	−	15.2790i	0.341307	−	0.591161i
$669$	11.4234	−	5.88919i	0.441656	−	0.227689i
$670$	1.51136	−	1.18854i	0.0583888	−	0.0459175i
$671$	−12.5420	−	27.4631i	−0.484178	−	1.06020i
$672$	1.74987	+	1.98443i	0.0675028	+	0.0765509i
$673$	11.3229	−	24.7937i	0.436465	−	0.955725i	−0.555768	−	0.831337i	$-0.687576\pi$
$673$	11.3229	−	24.7937i	0.436465	−	0.955725i	0.992234	−	0.124388i	$-0.0396968\pi$
$674$	29.6772	+	5.71982i	1.14312	+	0.220319i
$675$	−3.08670	−	2.42741i	−0.118807	−	0.0934309i
$676$	0.108664	−	0.447920i	0.00417939	−	0.0172277i
$677$	8.46214	−	24.4498i	0.325227	−	0.939680i	−0.657312	−	0.753619i	$-0.728306\pi$
$677$	8.46214	−	24.4498i	0.325227	−	0.939680i	0.982538	−	0.186061i	$-0.0595724\pi$
$678$	15.5948	−	10.0222i	0.598916	−	0.384900i
$679$	16.4309	−	29.0377i	0.630558	−	1.11437i
$680$	−0.287828	−	0.332171i	−0.0110377	−	0.0127382i
$681$	−16.8776	−	16.0928i	−0.646751	−	0.616676i
$682$	19.7872	+	15.5609i	0.757693	+	0.595856i
$683$	5.76761	+	16.6644i	0.220692	+	0.637646i	0.999940	+	0.0109316i	$0.00347971\pi$
$683$	5.76761	+	16.6644i	0.220692	+	0.637646i	−0.779249	+	0.626715i	$0.784399\pi$
$684$	1.27182	−	0.121444i	0.0486293	−	0.00464354i
$685$	0.742551	+	0.218033i	0.0283714	+	0.00833060i
$686$	13.7317	+	12.4275i	0.524277	+	0.474483i
$687$	0.880786	+	6.12600i	0.0336041	+	0.233722i
$688$	0.316363	−	6.64127i	0.0120612	−	0.253196i
$689$	11.9903	−	20.7679i	0.456796	−	0.791193i
$690$	−1.99217	+	4.55128i	−0.0758406	+	0.173264i
$691$	16.3043	+	28.2398i	0.620243	+	1.07429i	0.989440	+	0.144942i	$0.0462995\pi$
$691$	16.3043	+	28.2398i	0.620243	+	1.07429i	−0.369197	+	0.929351i	$0.620367\pi$
$692$	−15.6519	−	10.0589i	−0.594995	−	0.382380i
$693$	−5.69198	−	7.84833i	−0.216220	−	0.298133i
$694$	−4.49463	−	9.84186i	−0.170614	−	0.373592i
$695$	4.08943	+	16.8569i	0.155121	+	0.639417i
$696$	0.0979022	+	0.137484i	0.00371098	+	0.00521134i
$697$	−0.831868	−	2.40352i	−0.0315092	−	0.0910400i
$698$	1.20347	−	0.481796i	0.0455519	−	0.0182362i
$699$	−15.2266	+	4.47094i	−0.575924	+	0.169107i
$700$	1.56769	+	10.2705i	0.0592530	+	0.388187i
$701$	28.7553	−	18.4799i	1.08607	−	0.697976i	0.130120	−	0.991498i	$-0.458464\pi$
$701$	28.7553	−	18.4799i	1.08607	−	0.697976i	0.955952	+	0.293522i	$0.0948275\pi$
$702$	−3.26106	−	1.68119i	−0.123081	−	0.0634525i
$703$	−0.826691	+	0.159332i	−0.0311793	+	0.00600931i
$704$	−0.863916	+	3.56111i	−0.0325601	+	0.134214i
$705$	−5.31042	+	2.12597i	−0.200002	+	0.0800688i
$706$	−8.81444	+	10.1724i	−0.331736	+	0.382843i
$707$	−9.92814	−	5.00982i	−0.373386	−	0.188414i
$708$	0.617578	+	0.181337i	0.0232100	+	0.00681507i
$709$	24.5902	−	34.5321i	0.923503	−	1.29688i	−0.0312600	−	0.999511i	$-0.509952\pi$
$709$	24.5902	−	34.5321i	0.923503	−	1.29688i	0.954763	−	0.297367i	$-0.0961086\pi$
$710$	−10.2088	−	4.08697i	−0.383128	−	0.153381i
$711$	−9.20329	+	4.74463i	−0.345150	+	0.177937i
$712$	0.185468	+	0.321239i	0.00695069	+	0.0120389i
$713$	−25.5717	+	20.7722i	−0.957666	+	0.777927i
$714$	−0.0436871	+	1.12168i	−0.00163495	+	0.0419779i
$715$	11.7166	+	7.52980i	0.438176	+	0.281599i
$716$	−11.6222	+	9.13979i	−0.434342	+	0.341570i
$717$	−2.42946	−	0.231985i	−0.0907298	−	0.00866365i
$718$	21.7019	−	20.6927i	0.809907	−	0.772244i
$719$	41.8806	−	3.99911i	1.56188	−	0.149142i	0.721994	−	0.691899i	$-0.243226\pi$
$719$	41.8806	−	3.99911i	1.56188	−	0.149142i	0.839889	+	0.542758i	$0.182620\pi$
$720$	−0.678396	+	0.782910i	−0.0252823	+	0.0291773i
$721$	15.0713	−	17.7011i	0.561285	−	0.659223i
$722$	16.6642	−	4.89305i	0.620178	−	0.182101i
$723$	4.72640	−	13.6560i	0.175777	−	0.507874i
$724$	0.860335	+	18.0607i	0.0319741	+	0.671219i
$725$	0.0315360	+	0.662021i	0.00117122	+	0.0245869i
$726$	0.794073	−	2.29432i	0.0294708	−	0.0851503i
$727$	−26.5624	+	7.79944i	−0.985146	+	0.289265i	−0.734347	−	0.678774i	$-0.762512\pi$
$727$	−26.5624	+	7.79944i	−0.985146	+	0.289265i	−0.250799	+	0.968039i	$0.580693\pi$
$728$	3.25428	+	9.14527i	0.120612	+	0.338946i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	−1.04805	+	0.100076i	−0.0387899	+	0.00370399i
$731$	2.04161	−	1.94667i	0.0755115	−	0.0720001i
$732$	8.20181	+	0.783178i	0.303147	+	0.0289471i
$733$	30.6851	−	24.1311i	1.13338	−	0.891301i	0.138303	−	0.990390i	$-0.455835\pi$
$733$	30.6851	−	24.1311i	1.13338	−	0.891301i	0.995079	+	0.0990888i	$0.0315928\pi$
$734$	−22.2743	−	14.3148i	−0.822158	−	0.528369i
$735$	−4.10325	+	5.97902i	−0.151351	+	0.220539i
$736$	−4.29691	−	2.12993i	−0.158386	−	0.0785101i
$737$	−3.40059	−	5.88999i	−0.125262	−	0.216961i
$738$	−5.32829	+	2.74693i	−0.196137	+	0.101116i
$739$	−4.48598	−	1.79591i	−0.165019	−	0.0660638i	0.287682	−	0.957726i	$-0.407115\pi$
$739$	−4.48598	−	1.79591i	−0.165019	−	0.0660638i	−0.452701	+	0.891662i	$0.649540\pi$
$740$	0.395978	−	0.556073i	0.0145564	−	0.0204417i
$741$	4.49755	+	1.32060i	0.165222	+	0.0485135i
$742$	0.972598	+	17.2658i	0.0357052	+	0.633846i
$743$	6.86454	−	7.92210i	0.251836	−	0.290634i	−0.615729	−	0.787958i	$-0.711138\pi$
$743$	6.86454	−	7.92210i	0.251836	−	0.290634i	0.867565	+	0.497324i	$0.165684\pi$
$744$	−6.37750	+	2.55316i	−0.233810	+	0.0936036i
$745$	0.185217	−	0.763476i	0.00678583	−	0.0279716i
$746$	−12.2824	+	2.36723i	−0.449690	+	0.0866706i
$747$	−0.475964	−	0.245376i	−0.0174146	−	0.00897785i
$748$	−1.30792	+	0.840546i	−0.0478221	+	0.0307334i
$749$	1.16391	+	7.62516i	0.0425283	+	0.278617i
$750$	−8.87306	+	2.60536i	−0.323998	+	0.0951344i
$751$	6.16541	−	2.46826i	0.224979	−	0.0900680i	−0.256434	−	0.966562i	$-0.582548\pi$
$751$	6.16541	−	2.46826i	0.224979	−	0.0900680i	0.481414	+	0.876494i	$0.340124\pi$
$752$	−1.80598	−	5.21804i	−0.0658573	−	0.190282i
$753$	3.69171	+	5.18429i	0.134534	+	0.188926i
$754$	0.145991	+	0.601785i	0.00531670	+	0.0219157i
$755$	7.10228	+	15.5518i	0.258478	+	0.565989i
$756$	2.63149	−	0.274324i	0.0957064	−	0.00997707i
$757$	−25.0962	−	16.1283i	−0.912135	−	0.586194i	−0.00176971	−	0.999998i	$-0.500563\pi$
$757$	−25.0962	−	16.1283i	−0.912135	−	0.586194i	−0.910366	+	0.413805i	$0.864200\pi$
$758$	10.6395	+	18.4282i	0.386445	+	0.669343i
$759$	14.9324	+	9.26628i	0.542012	+	0.336345i
$760$	0.661761	−	1.14620i	0.0240046	−	0.0415772i
$761$	−1.32927	+	27.9048i	−0.0481860	+	1.01155i	0.837260	+	0.546805i	$0.184156\pi$
$761$	−1.32927	+	27.9048i	−0.0481860	+	1.01155i	−0.885446	+	0.464743i	$0.846147\pi$
$762$	−0.687405	−	4.78100i	−0.0249020	−	0.173198i
$763$	22.8358	−	9.37263i	0.826710	−	0.339312i
$764$	−10.7679	−	3.16174i	−0.389569	−	0.114388i
$765$	−0.437535	+	0.0417795i	−0.0158191	+	0.00151054i
$766$	9.71232	+	28.0619i	0.350920	+	1.01392i
$767$	1.85626	+	1.45978i	0.0670257	+	0.0527096i
$768$	−0.723734	−	0.690079i	−0.0261155	−	0.0249011i
$769$	−9.17198	−	10.5850i	−0.330750	−	0.381706i	0.565879	−	0.824488i	$-0.308537\pi$
$769$	−9.17198	−	10.5850i	−0.330750	−	0.381706i	−0.896629	+	0.442782i	$0.853991\pi$
$770$	−10.0432	+	0.0870932i	−0.361930	+	0.00313862i
$771$	8.75283	−	5.62510i	0.315226	−	0.202583i
$772$	2.61691	−	7.56108i	0.0941848	−	0.272129i
$773$	−5.27407	+	21.7400i	−0.189695	+	0.781934i	0.794851	+	0.606805i	$0.207549\pi$
$773$	−5.27407	+	21.7400i	−0.189695	+	0.781934i	−0.984546	+	0.175128i	$0.943966\pi$
$774$	−5.22631	−	4.11002i	−0.187856	−	0.147731i
$775$	−26.4882	−	5.10518i	−0.951484	−	0.183383i
$776$	−5.23857	+	11.4709i	−0.188054	+	0.411780i
$777$	−1.70904	+	0.344788i	−0.0613115	+	0.0123692i
$778$	12.1220	+	26.5435i	0.434595	+	0.951630i
$779$	6.02027	−	4.73439i	0.215698	−	0.169627i
$780$	−3.37826	+	1.74161i	−0.120961	+	0.0623597i
$781$	−19.4488	+	33.6863i	−0.695932	+	1.20539i
$782$	−0.695815	−	1.91209i	−0.0248823	−	0.0683763i
$783$	0.168780			0.00603172
$784$	−5.57659	−	4.23104i	−0.199164	−	0.151108i
$785$	0.398104	+	2.76888i	0.0142090	+	0.0988254i
$786$	1.69952	−	2.38664i	0.0606199	−	0.0851287i
$787$	23.5593	−	22.4638i	0.839799	−	0.800747i	−0.142160	−	0.989844i	$-0.545405\pi$
$787$	23.5593	−	22.4638i	0.839799	−	0.800747i	0.981958	+	0.189097i	$0.0605561\pi$
$788$	8.96872	+	12.5948i	0.319498	+	0.448672i
$789$	11.1621	+	2.15131i	0.397381	+	0.0765888i
$790$	−1.52653	+	10.6173i	−0.0543116	+	0.377745i
$791$	−35.2014	+	34.1521i	−1.25162	+	1.21431i
$792$	2.39967	+	2.76937i	0.0852687	+	0.0984053i
$793$	26.8682	+	13.8515i	0.954119	+	0.491882i
$794$	−0.597795	−	12.5493i	−0.0212149	−	0.445356i
$795$	−6.64873	+	1.28144i	−0.235806	+	0.0454479i
$796$	−19.3311	−	18.4322i	−0.685174	−	0.653312i
$797$	−7.54030	+	52.4439i	−0.267091	+	1.85766i	0.208540	+	0.978014i	$0.433129\pi$
$797$	−7.54030	+	52.4439i	−0.267091	+	1.85766i	−0.475631	+	0.879645i	$0.657780\pi$
$798$	−3.23493	+	0.980409i	−0.114515	+	0.0347061i
$799$	0.973210	−	2.13103i	0.0344297	−	0.0753905i
$800$	−0.925785	−	3.81614i	−0.0327315	−	0.134921i
$801$	0.369255	+	0.0352596i	0.0130470	+	0.00124584i
$802$	11.1297	+	4.45566i	0.393003	+	0.157335i
$803$	−0.177200	+	3.71988i	−0.00625324	+	0.131272i
$804$	1.85601			0.0654565
$805$	2.78537	−	12.8461i	0.0981713	−	0.452765i
$806$	−25.2039			−0.887769
$807$	0.377734	−	7.92962i	0.0132969	−	0.279136i
$808$	3.90208	+	1.56216i	0.137275	+	0.0549566i
$809$	−12.2585	−	1.17054i	−0.430985	−	0.0411541i	−0.122690	−	0.992445i	$-0.539152\pi$
$809$	−12.2585	−	1.17054i	−0.430985	−	0.0411541i	−0.308295	+	0.951291i	$0.599758\pi$
$810$	0.244232	+	1.00674i	0.00858143	+	0.0353731i
$811$	10.8349	−	23.7251i	0.380464	−	0.833099i	−0.618419	−	0.785848i	$-0.712227\pi$
$811$	10.8349	−	23.7251i	0.380464	−	0.833099i	0.998883	−	0.0472510i	$-0.0150461\pi$
$812$	−0.325844	−	0.305341i	−0.0114349	−	0.0107154i
$813$	−0.511462	+	3.55730i	−0.0179378	+	0.124760i
$814$	−1.74763	−	1.66636i	−0.0612543	−	0.0584058i
$815$	0.682788	−	0.131597i	0.0239170	−	0.00460963i
$816$	−0.0201879	−	0.423797i	−0.000706719	−	0.0148358i
$817$	7.55026	+	3.89243i	0.264150	+	0.136179i
$818$	−8.66150	−	9.99590i	−0.302842	−	0.349499i
$819$	9.33719	+	2.65392i	0.326268	+	0.0927354i
$820$	−0.883794	+	6.14692i	−0.0308634	+	0.214660i
$821$	31.6132	+	6.09295i	1.10331	+	0.212646i	0.708216	−	0.705995i	$-0.249500\pi$
$821$	31.6132	+	6.09295i	1.10331	+	0.212646i	0.395093	+	0.918641i	$0.370712\pi$
$822$	0.433332	+	0.608530i	0.0151142	+	0.0212249i
$823$	7.05092	−	6.72304i	0.245780	−	0.234350i	−0.557168	−	0.830400i	$-0.688112\pi$
$823$	7.05092	−	6.72304i	0.245780	−	0.234350i	0.802948	+	0.596049i	$0.203264\pi$
$824$	−5.09693	+	7.15763i	−0.177560	+	0.249348i
$825$	2.04784	+	14.2430i	0.0712966	+	0.495879i
$826$	−1.69657	−	0.147168i	−0.0590312	−	0.00512064i
$827$	52.1901			1.81483			0.907413	−	0.420240i	$-0.138054\pi$
$827$	52.1901			1.81483			0.907413	+	0.420240i	$0.138054\pi$
$828$	−4.22744	+	2.26468i	−0.146914	+	0.0787031i
$829$	−25.0263	+	43.3468i	−0.869198	+	1.50550i	−0.00638126	+	0.999980i	$0.502031\pi$
$829$	−25.0263	+	43.3468i	−0.869198	+	1.50550i	−0.862817	+	0.505516i	$0.831302\pi$
$830$	−0.493069	+	0.254195i	−0.0171147	+	0.00882323i
$831$	−1.25968	+	0.990622i	−0.0436977	+	0.0343643i
$832$	−1.52412	−	3.33736i	−0.0528394	−	0.115702i
$833$	−0.473585	−	2.93194i	−0.0164087	−	0.101586i
$834$	−6.95573	+	15.2309i	−0.240857	+	0.527404i
$835$	−17.9464	−	3.45889i	−0.621061	−	0.119700i
$836$	−3.68004	−	2.89401i	−0.127277	−	0.100092i
$837$	−1.61956	+	6.67594i	−0.0559803	+	0.230754i
$838$	9.96545	−	28.7933i	0.344251	−	0.994647i
$839$	−12.9457	+	8.31972i	−0.446936	+	0.287229i	−0.744685	−	0.667416i	$-0.767401\pi$
$839$	−12.9457	+	8.31972i	−0.446936	+	0.287229i	0.297749	+	0.954644i	$0.403764\pi$
$840$	1.34978	−	2.38543i	0.0465720	−	0.0823051i
$841$	18.9723	+	21.8952i	0.654217	+	0.755007i
$842$	−21.7066	−	20.6972i	−0.748058	−	0.713272i
$843$	3.90679	+	3.07234i	0.134557	+	0.105817i
$844$	3.81501	+	11.0227i	0.131318	+	0.379418i
$845$	−0.475315	+	0.0453871i	−0.0163513	+	0.00156136i
$846$	−5.29806	−	1.55565i	−0.182151	−	0.0534844i
$847$	−0.858989	+	6.36580i	−0.0295152	+	0.218731i
$848$	−0.930196	−	6.46966i	−0.0319431	−	0.222169i
$849$	0.0875002	−	1.83685i	0.00300300	−	0.0630407i
$850$	0.833032	−	1.44285i	0.0285728	−	0.0494895i
$851$	2.63129	−	1.75040i	0.0901994	−	0.0600031i
$852$	−5.30749	−	9.19284i	−0.181832	−	0.314942i
$853$	11.2578	+	7.23494i	0.385459	+	0.247719i	0.718991	−	0.695019i	$-0.244604\pi$
$853$	11.2578	+	7.23494i	0.385459	+	0.247719i	−0.333532	+	0.942739i	$0.608241\pi$
$854$	−21.6812	+	2.26019i	−0.741914	+	0.0773420i
$855$	−0.549811	−	1.20392i	−0.0188031	−	0.0411731i
$856$	−0.687336	−	2.83324i	−0.0234927	−	0.0968381i
$857$	−11.2034	−	15.7330i	−0.382700	−	0.537428i	0.577628	−	0.816300i	$-0.303979\pi$
$857$	−11.2034	−	15.7330i	−0.382700	−	0.537428i	−0.960328	+	0.278873i	$0.910039\pi$
$858$	4.39722	+	12.7049i	0.150119	+	0.433740i
$859$	−27.3423	+	10.9462i	−0.932908	+	0.373480i	−0.787797	−	0.615935i	$-0.788778\pi$
$859$	−27.3423	+	10.9462i	−0.932908	+	0.373480i	−0.145111	+	0.989415i	$0.546354\pi$
$860$	−6.60875	+	1.94050i	−0.225356	+	0.0661706i
$861$	12.3817	−	9.91203i	0.421966	−	0.337801i
$862$	−3.24785	+	2.08727i	−0.110622	+	0.0710926i
$863$	46.7053	+	24.0783i	1.58987	+	0.819634i	0.999926	+	0.0121875i	$0.00387951\pi$
$863$	46.7053	+	24.0783i	1.58987	+	0.819634i	0.589942	+	0.807446i	$0.299151\pi$
$864$	−0.981929	+	0.189251i	−0.0334059	+	0.00643846i
$865$	−4.54404	+	18.7308i	−0.154502	+	0.636866i
$866$	17.1175	−	6.85282i	0.581677	−	0.232868i
$867$	−11.0148	+	12.7117i	−0.374081	+	0.431712i
$868$	15.2042	−	9.95847i	0.516063	−	0.338013i
$869$	36.4055	+	10.6896i	1.23497	+	0.362620i
$870$	0.101421	−	0.142425i	0.00343848	−	0.00482868i
$871$	6.32177	+	2.53085i	0.214205	+	0.0857547i
$872$	−8.29267	+	4.27517i	−0.280825	+	0.144776i
$873$	6.30522	+	10.9210i	0.213399	+	0.369618i
$874$	4.75582	−	3.86323i	0.160868	−	0.130676i
$875$	21.6491	−	11.3996i	0.731873	−	0.385376i
$876$	−0.854957	−	0.549448i	−0.0288863	−	0.0185641i
$877$	31.4809	−	24.7568i	1.06303	−	0.835978i	0.0760985	−	0.997100i	$-0.475754\pi$
$877$	31.4809	−	24.7568i	1.06303	−	0.835978i	0.986935	+	0.161122i	$0.0515112\pi$
$878$	−28.2342	−	2.69604i	−0.952857	−	0.0909868i
$879$	20.4927	−	19.5397i	0.691201	−	0.659058i
$880$	3.77891	−	0.360842i	0.127387	−	0.0121640i
$881$	−15.6774	+	18.0927i	−0.528186	+	0.609560i	−0.955662	−	0.294467i	$-0.904858\pi$
$881$	−15.6774	+	18.0927i	−0.528186	+	0.609560i	0.427475	+	0.904027i	$0.359403\pi$
$882$	−6.68124	+	2.08831i	−0.224969	+	0.0703171i
$883$	−42.9729	+	12.6180i	−1.44615	+	0.424629i	−0.908268	−	0.418389i	$-0.862595\pi$
$883$	−42.9729	+	12.6180i	−1.44615	+	0.424629i	−0.537886	+	0.843018i	$0.680777\pi$
$884$	0.509126	−	1.47102i	0.0171237	−	0.0494758i
$885$	−0.0317268	−	0.666027i	−0.00106648	−	0.0223883i
$886$	−1.58170	−	33.2040i	−0.0531382	−	1.11551i
$887$	−6.66585	+	19.2597i	−0.223817	+	0.646677i	0.776055	+	0.630666i	$0.217218\pi$
$887$	−6.66585	+	19.2597i	−0.223817	+	0.646677i	−0.999872	+	0.0160117i	$0.994903\pi$
$888$	0.632278	−	0.185654i	0.0212179	−	0.00623013i
$889$	4.28431	+	12.0399i	0.143691	+	0.403804i
$890$	0.251641	−	0.290409i	0.00843501	−	0.00973453i
$891$	3.64781	−	0.348324i	0.122206	−	0.0116693i
$892$	9.30153	−	8.86899i	0.311438	−	0.296956i
$893$	7.02265	+	0.670582i	0.235004	+	0.0224402i
$894$	0.596116	−	0.468791i	0.0199371	−	0.0156787i
$895$	12.8854	+	8.28093i	0.430711	+	0.276801i
$896$	2.23807	+	1.41105i	0.0747686	+	0.0471398i
$897$	−17.4872	+	1.94921i	−0.583880	+	0.0650821i
$898$	−19.3085	−	33.4433i	−0.644332	−	1.11602i
$899$	1.03056	−	0.531291i	0.0343711	−	0.0177195i
$900$	−3.64554	−	1.45946i	−0.121518	−	0.0486485i
$901$	1.60859	−	2.25894i	0.0535898	−	0.0752564i
$902$	21.0771	+	6.18881i	0.701792	+	0.206065i
$903$	15.7049	+	7.92481i	0.522626	+	0.263721i
$904$	12.1396	−	14.0098i	0.403756	−	0.465959i
$905$	17.3892	−	6.96159i	0.578037	−	0.231411i
$906$	−3.89090	+	16.0385i	−0.129266	+	0.532843i
$907$	−3.73161	+	0.719208i	−0.123906	+	0.0238809i	−0.250827	−	0.968032i	$-0.580703\pi$
$907$	−3.73161	+	0.719208i	−0.123906	+	0.0238809i	0.126921	+	0.991913i	$0.459490\pi$
$908$	−20.7278	−	10.6859i	−0.687876	−	0.354625i
$909$	3.53593	−	2.27240i	0.117279	−	0.0753708i
$910$	7.85026	−	6.28445i	0.260234	−	0.208327i
$911$	−5.51530	+	1.61944i	−0.182730	+	0.0536544i	−0.371817	−	0.928306i	$-0.621265\pi$
$911$	−5.51530	+	1.61944i	−0.182730	+	0.0536544i	0.189087	+	0.981960i	$0.439447\pi$
$912$	1.18609	−	0.474838i	0.0392753	−	0.0157235i
$913$	0.641791	+	1.85433i	0.0212402	+	0.0613695i
$914$	22.0189	+	30.9212i	0.728319	+	1.02278i
$915$	−2.01225	−	8.29462i	−0.0665231	−	0.274212i
$916$	2.57100	+	5.62971i	0.0849483	+	0.186011i
$917$	−3.15896	+	7.07898i	−0.104318	+	0.233769i
$918$	−0.356925	−	0.229382i	−0.0117803	−	0.00757072i
$919$	16.9999	+	29.4447i	0.560775	+	0.971291i	0.997429	+	0.0716616i	$0.0228302\pi$
$919$	16.9999	+	29.4447i	0.560775	+	0.971291i	−0.436654	+	0.899630i	$0.643837\pi$
$920$	−0.629230	+	4.92818i	−0.0207451	+	0.162477i
$921$	15.1905	−	26.3107i	0.500544	−	0.866968i
$922$	−0.346441	+	7.27269i	−0.0114094	+	0.239513i
$923$	−5.54251	−	38.5490i	−0.182434	−	1.26886i
$924$	−7.67255	−	5.92680i	−0.252408	−	0.194978i
$925$	2.48285	+	0.729030i	0.0816356	+	0.0239704i
$926$	39.2342	−	3.74641i	1.28931	−	0.123115i
$927$	2.87393	+	8.30367i	0.0943922	+	0.272728i
$928$	0.132670	+	0.104333i	0.00435512	+	0.00342490i
$929$	26.7218	+	25.4792i	0.876715	+	0.835946i	0.987455	−	0.157903i	$-0.0504734\pi$
$929$	26.7218	+	25.4792i	0.876715	+	0.835946i	−0.110739	+	0.993849i	$0.535322\pi$
$930$	4.66029	+	5.37826i	0.152817	+	0.176360i
$931$	7.87681	−	4.23527i	0.258152	−	0.138805i
$932$	−13.3502	+	8.57968i	−0.437302	+	0.281037i
$933$	−7.74646	+	22.3819i	−0.253608	+	0.732752i
$934$	−7.80424	+	32.1695i	−0.255363	+	1.05262i
$935$	1.26602	+	0.995605i	0.0414031	+	0.0325598i
$936$	−3.60261	−	0.694346i	−0.117755	−	0.0226954i
$937$	4.95727	−	10.8549i	0.161947	−	0.354615i	−0.811211	−	0.584754i	$-0.801191\pi$
$937$	4.95727	−	10.8549i	0.161947	−	0.354615i	0.973158	+	0.230140i	$0.0739183\pi$
$938$	−4.81357	+	0.971105i	−0.157169	+	0.0317077i
$939$	0.173383	+	0.379656i	0.00565814	+	0.0123896i
$940$	−4.49636	+	3.53597i	−0.146655	+	0.115331i
$941$	9.69335	−	4.99727i	0.315994	−	0.162906i	−0.292932	−	0.956133i	$-0.594631\pi$
$941$	9.69335	−	4.99727i	0.315994	−	0.162906i	0.608926	+	0.793227i	$0.291601\pi$
$942$	−1.35015	+	2.33853i	−0.0439903	+	0.0761935i
$943$	−13.9794	+	25.1219i	−0.455233	+	0.818082i
$944$	0.643651			0.0209490
$945$	−1.16016	−	2.48319i	−0.0377400	−	0.0807780i
$946$	3.46734	+	24.1159i	0.112733	+	0.784075i
$947$	27.4989	−	38.6169i	0.893596	−	1.25488i	−0.0726764	−	0.997356i	$-0.523154\pi$
$947$	27.4989	−	38.6169i	0.893596	−	1.25488i	0.966272	−	0.257524i	$-0.0829066\pi$
$948$	−7.49378	+	7.14530i	−0.243387	+	0.232069i
$949$	−2.16284	−	3.03729i	−0.0702089	−	0.0985946i
$950$	4.92628	+	0.949463i	0.159830	+	0.0308046i
$951$	3.03485	−	21.1079i	0.0984118	−	0.684469i
$952$	0.274097	+	1.08855i	0.00888352	+	0.0352802i
$953$	33.2134	+	38.3303i	1.07589	+	1.24164i	0.968919	+	0.247377i	$0.0795685\pi$
$953$	33.2134	+	38.3303i	1.07589	+	1.24164i	0.106967	+	0.994263i	$0.465886\pi$
$954$	−5.80959	−	2.99505i	−0.188093	−	0.0969684i
$955$	0.553179	+	11.6127i	0.0179004	+	0.375777i
$956$	−2.39641	+	0.461869i	−0.0775053	+	0.0149379i
$957$	−0.447615	−	0.426800i	−0.0144693	−	0.0137965i
$958$	0.501080	−	3.48509i	0.0161892	−	0.112598i
$959$	−1.44224	−	1.35149i	−0.0465725	−	0.0436420i
$960$	−0.430344	+	0.942323i	−0.0138893	+	0.0304133i
$961$	3.81720	+	15.7347i	0.123136	+	0.507572i
$962$	2.40676	+	0.229818i	0.0775970	+	0.00740962i
$963$	−2.70658	−	1.08355i	−0.0872184	−	0.0349170i
$964$	0.687598	−	14.4345i	0.0221460	−	0.464903i
$965$	−8.28868			−0.266822
$966$	9.77893	−	8.08533i	0.314632	−	0.260141i
$967$	−1.11966			−0.0360059			−0.0180030	−	0.999838i	$-0.505731\pi$
$967$	−1.11966			−0.0360059			−0.0180030	+	0.999838i	$0.505731\pi$
$968$	0.115522	−	2.42510i	0.00371301	−	0.0779457i
$969$	0.503230	+	0.201463i	0.0161661	+	0.00647193i
$970$	13.0045	+	1.24178i	0.417549	+	0.0398711i
$971$	8.04077	+	33.1445i	0.258041	+	1.06366i	0.942393	+	0.334507i	$0.108570\pi$
$971$	8.04077	+	33.1445i	0.258041	+	1.06366i	−0.684353	+	0.729151i	$0.739915\pi$
$972$	−0.415415	+	0.909632i	−0.0133244	+	0.0291765i
$973$	10.0705	−	43.1408i	0.322847	−	1.38303i
$974$	−4.41675	+	30.7192i	−0.141522	+	0.984307i
$975$	−10.4270	−	9.94210i	−0.333931	−	0.318402i
$976$	8.09022	−	1.55926i	0.258962	−	0.0499108i
$977$	−1.66857	−	35.0277i	−0.0533824	−	1.12063i	−0.853601	−	0.520927i	$-0.825586\pi$
$977$	−1.66857	−	35.0277i	−0.0533824	−	1.12063i	0.800219	−	0.599708i	$-0.204717\pi$
$978$	0.596614	+	0.307576i	0.0190776	+	0.00983519i
$979$	−0.890123	−	1.02726i	−0.0284485	−	0.0328313i
$980$	−2.25256	+	6.89284i	−0.0719553	+	0.220184i
$981$	−1.32777	+	9.23485i	−0.0423925	+	0.294846i
$982$	0.0282236	+	0.00543966i	0.000900652	+	0.000173586i
$983$	−0.00259074	−	0.00363818i	−8.26317e−5	−	0.000116040i	0.814535	−	0.580115i	$-0.196992\pi$
$983$	−0.00259074	−	0.00363818i	−8.26317e−5	−	0.000116040i	−0.814617	+	0.579999i	$0.803053\pi$
$984$	−4.33856	+	4.13681i	−0.138308	+	0.131877i
$985$	9.29105	−	13.0475i	0.296037	−	0.415726i
$986$	0.0101911	+	0.0708808i	0.000324551	+	0.00225730i
$987$	14.5545	+	1.26252i	0.463274	+	0.0401865i
$988$	4.68742			0.149127
$989$	−31.7861	−	2.52891i	−1.01074	−	0.0804146i
$990$	1.89805	−	3.28752i	0.0603239	−	0.104484i
$991$	−36.9349	+	19.0412i	−1.17327	+	0.604865i	−0.930884	−	0.365314i	$-0.880962\pi$
$991$	−36.9349	+	19.0412i	−1.17327	+	0.604865i	−0.242390	+	0.970179i	$0.577931\pi$
$992$	−5.39985	+	4.24649i	−0.171446	+	0.134826i
$993$	0.812510	+	1.77915i	0.0257842	+	0.0564596i
$994$	18.5749	+	21.0646i	0.589159	+	0.668130i
$995$	−11.4946	+	25.1697i	−0.364404	+	0.797934i
$996$	−0.525814	−	0.101342i	−0.0166611	−	0.00321116i
$997$	19.5000	+	15.3350i	0.617572	+	0.485664i	0.877252	−	0.480031i	$-0.159375\pi$
$997$	19.5000	+	15.3350i	0.617572	+	0.485664i	−0.259680	+	0.965695i	$0.583617\pi$
$998$	−5.00353	+	20.6248i	−0.158384	+	0.652868i
$999$	0.215528	−	0.622728i	0.00681902	−	0.0197023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.c.25.6	✓	160
7.2	even	3	inner	966.2.y.c.163.6	yes	160
23.12	even	11	inner	966.2.y.c.403.6	yes	160
161.58	even	33	inner	966.2.y.c.541.6	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.c.25.6	✓	160	1.1	even	1	trivial
966.2.y.c.163.6	yes	160	7.2	even	3	inner
966.2.y.c.403.6	yes	160	23.12	even	11	inner
966.2.y.c.541.6	yes	160	161.58	even	33	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0475819 - 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.244232 + 1.00674i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(0.601440 - 2.57648i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})\)	\(q+(0.0475819 - 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.244232 + 1.00674i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(0.601440 - 2.57648i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(1.01722 - 0.196053i) q^{10} +(-0.174359 - 3.66025i) q^{11} +(0.888835 + 0.458227i) q^{12} +(2.40263 + 2.77278i) q^{13} +(-2.54495 - 0.723353i) q^{14} +(0.147429 - 1.02539i) q^{15} +(0.981929 + 0.189251i) q^{16} +(0.246105 + 0.345606i) q^{17} +(0.723734 - 0.690079i) q^{18} +(-0.741084 + 1.04071i) q^{19} +(-0.147429 - 1.02539i) q^{20} +(-1.51594 + 2.16839i) q^{21} -3.66440 q^{22} +(1.05685 - 4.67793i) q^{23} +(0.500000 - 0.866025i) q^{24} +(3.49031 - 1.79938i) q^{25} +(2.88396 - 2.26797i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-0.843627 + 2.50765i) q^{28} +(-0.0701139 + 0.153528i) q^{29} +(-1.01722 - 0.196053i) q^{30} +(-5.39985 - 4.24649i) q^{31} +(0.235759 - 0.971812i) q^{32} +(-1.19851 + 3.46286i) q^{33} +(0.356925 - 0.229382i) q^{34} +(2.74073 - 0.0237674i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(0.476920 + 0.454742i) q^{37} +(1.00427 + 0.789764i) q^{38} +(-1.19998 - 3.46712i) q^{39} +(-1.03125 + 0.0984722i) q^{40} +(-5.75186 - 1.68890i) q^{41} +(2.09381 + 1.61740i) q^{42} +(-0.946223 - 6.58113i) q^{43} +(-0.174359 + 3.66025i) q^{44} +(-0.517969 + 0.897149i) q^{45} +(-4.62235 - 1.27824i) q^{46} +(-2.76086 - 4.78196i) q^{47} +(-0.841254 - 0.540641i) q^{48} +(-6.27654 - 3.09920i) q^{49} +(-1.63126 - 3.57197i) q^{50} +(-0.100027 - 0.412317i) q^{51} +(-2.12818 - 2.98861i) q^{52} +(-2.13778 - 6.17670i) q^{53} +(-0.928368 + 0.371662i) q^{54} +(3.64233 - 1.06948i) q^{55} +(2.46467 + 0.961990i) q^{56} +(1.07479 - 0.690726i) q^{57} +(0.150018 + 0.0773397i) q^{58} +(0.632019 - 0.121812i) q^{59} +(-0.244232 + 1.00674i) q^{60} +(7.64893 - 3.06217i) q^{61} +(-4.49862 + 5.19168i) q^{62} +(2.21326 - 1.44965i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-2.20466 + 3.09601i) q^{65} +(3.40191 + 1.36192i) q^{66} +(1.64969 - 0.850474i) q^{67} +(-0.212139 - 0.367435i) q^{68} +(-2.71976 + 3.95005i) q^{69} +(0.106669 - 2.73876i) q^{70} +(-8.92989 - 5.73889i) q^{71} +(-0.786053 + 0.618159i) q^{72} +(-1.01169 - 0.0966045i) q^{73} +(0.476920 - 0.454742i) q^{74} +(-3.90905 + 0.373269i) q^{75} +(0.836654 - 0.965550i) q^{76} +(-9.53545 - 1.75219i) q^{77} +(-3.52029 + 1.03365i) q^{78} +(-3.38657 + 9.78484i) q^{79} +(0.0492919 + 1.03477i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(-1.96067 + 5.66499i) q^{82} +(-0.513800 + 0.150865i) q^{83} +(1.71519 - 2.01447i) q^{84} +(-0.287828 + 0.332171i) q^{85} +(-6.61869 + 0.632009i) q^{86} +(0.122152 - 0.116472i) q^{87} +(3.64781 + 0.348324i) q^{88} +(0.291575 - 0.229297i) q^{89} +(0.871487 + 0.560071i) q^{90} +(8.58905 - 4.52267i) q^{91} +(-1.49673 + 4.55629i) q^{92} +(3.43479 + 5.94923i) q^{93} +(-4.90791 + 2.53020i) q^{94} +(-1.22872 - 0.491903i) q^{95} +(-0.580057 + 0.814576i) q^{96} +(12.0996 + 3.55277i) q^{97} +(-3.39434 + 6.12196i) q^{98} +(2.39967 - 2.76937i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{12} - 4 q^{13} + 9 q^{14} - 18 q^{15} + 8 q^{16} - 21 q^{17} + 8 q^{18} + 4 q^{19} + 18 q^{20} - 15 q^{21} + 116 q^{22} + 14 q^{23} + 80 q^{24} + 2 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 46 q^{29} - 2 q^{30} + q^{31} + 8 q^{32} - 8 q^{33} - 68 q^{34} - 84 q^{35} - 16 q^{36} + 19 q^{37} - 7 q^{38} - 2 q^{39} - 9 q^{40} + 38 q^{41} + 2 q^{42} + 28 q^{43} + 8 q^{44} + 24 q^{45} - 8 q^{46} - 26 q^{47} + 16 q^{48} - 6 q^{49} - 4 q^{50} + 21 q^{51} + 2 q^{52} - 20 q^{53} - 8 q^{54} + 46 q^{55} - 2 q^{56} - 14 q^{57} - 21 q^{58} + 36 q^{59} - 2 q^{60} + 40 q^{61} - 24 q^{62} - 2 q^{63} - 16 q^{64} - 10 q^{65} - 8 q^{66} + 6 q^{67} + 34 q^{68} + 6 q^{69} - 20 q^{70} + 132 q^{71} + 8 q^{72} - 36 q^{73} + 19 q^{74} - 2 q^{75} - 8 q^{76} - 75 q^{77} - 18 q^{78} + 34 q^{79} + 2 q^{80} + 8 q^{81} + 47 q^{82} + 74 q^{83} + 13 q^{84} + 2 q^{85} + 30 q^{86} + 10 q^{87} - 3 q^{88} - 12 q^{89} - 4 q^{90} - 30 q^{91} - 50 q^{92} + 10 q^{93} - 4 q^{94} + 27 q^{95} - 8 q^{96} + 24 q^{97} + 7 q^{98} - 16 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^12 - 4 * q^13 + 9 * q^14 - 18 * q^15 + 8 * q^16 - 21 * q^17 + 8 * q^18 + 4 * q^19 + 18 * q^20 - 15 * q^21 + 116 * q^22 + 14 * q^23 + 80 * q^24 + 2 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 46 * q^29 - 2 * q^30 + q^31 + 8 * q^32 - 8 * q^33 - 68 * q^34 - 84 * q^35 - 16 * q^36 + 19 * q^37 - 7 * q^38 - 2 * q^39 - 9 * q^40 + 38 * q^41 + 2 * q^42 + 28 * q^43 + 8 * q^44 + 24 * q^45 - 8 * q^46 - 26 * q^47 + 16 * q^48 - 6 * q^49 - 4 * q^50 + 21 * q^51 + 2 * q^52 - 20 * q^53 - 8 * q^54 + 46 * q^55 - 2 * q^56 - 14 * q^57 - 21 * q^58 + 36 * q^59 - 2 * q^60 + 40 * q^61 - 24 * q^62 - 2 * q^63 - 16 * q^64 - 10 * q^65 - 8 * q^66 + 6 * q^67 + 34 * q^68 + 6 * q^69 - 20 * q^70 + 132 * q^71 + 8 * q^72 - 36 * q^73 + 19 * q^74 - 2 * q^75 - 8 * q^76 - 75 * q^77 - 18 * q^78 + 34 * q^79 + 2 * q^80 + 8 * q^81 + 47 * q^82 + 74 * q^83 + 13 * q^84 + 2 * q^85 + 30 * q^86 + 10 * q^87 - 3 * q^88 - 12 * q^89 - 4 * q^90 - 30 * q^91 - 50 * q^92 + 10 * q^93 - 4 * q^94 + 27 * q^95 - 8 * q^96 + 24 * q^97 + 7 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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