LMFDB - Embedded newform 418.2.v.a.13.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(13,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.v (of order $90$, degree $24$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$10$ over $\Q(\zeta_{90})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			13.5
Character	$\chi$	$=$	418.13
Dual form			418.2.v.a.193.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.374607 + 0.927184i) q^{2} +(-0.0175505 - 0.0612060i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(2.65042 - 1.40925i) q^{5} +(0.0501746 - 0.0392007i) q^{6} +(1.63684 + 3.67640i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(2.54071 - 1.58761i) q^{9} +O(q^{10})$	\(q+(0.374607 + 0.927184i) q^{2} +(-0.0175505 - 0.0612060i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(2.65042 - 1.40925i) q^{5} +(0.0501746 - 0.0392007i) q^{6} +(1.63684 + 3.67640i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(2.54071 - 1.58761i) q^{9} +(2.29950 + 1.92951i) q^{10} +(-2.41034 - 2.27821i) q^{11} +(0.0551420 + 0.0318363i) q^{12} +(-0.142958 - 4.09378i) q^{13} +(-2.79553 + 2.89485i) q^{14} +(-0.132771 - 0.137489i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(0.195087 - 0.312204i) q^{17} +(2.42377 + 1.76097i) q^{18} +(0.467294 + 4.33378i) q^{19} +(-0.927604 + 2.85487i) q^{20} +(0.196290 - 0.164707i) q^{21} +(1.20939 - 3.08826i) q^{22} +(-1.50133 + 8.51449i) q^{23} +(-0.00886150 + 0.0630529i) q^{24} +(2.24278 - 3.32505i) q^{25} +(3.74213 - 1.66610i) q^{26} +(-0.283716 - 0.255459i) q^{27} +(-3.73128 - 1.50754i) q^{28} +(1.06365 + 4.26608i) q^{29} +(0.0777402 - 0.174607i) q^{30} +(6.85905 - 6.17592i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.0971372 + 0.187511i) q^{33} +(0.362552 + 0.0639276i) q^{34} +(9.51930 + 7.43729i) q^{35} +(-0.724785 + 2.90695i) q^{36} +(2.26201 - 3.11339i) q^{37} +(-3.84316 + 2.05673i) q^{38} +(-0.248055 + 0.0805978i) q^{39} +(-2.99448 + 0.209394i) q^{40} +(-10.0518 + 2.88230i) q^{41} +(0.226245 + 0.120297i) q^{42} +(-0.832840 + 0.146852i) q^{43} +(3.31643 - 0.0355587i) q^{44} +(4.49660 - 7.78834i) q^{45} +(-8.45691 + 1.79757i) q^{46} +(-12.1111 - 0.846887i) q^{47} +(-0.0617812 + 0.0154038i) q^{48} +(-6.15275 + 6.83333i) q^{49} +(3.92310 + 0.833880i) q^{50} +(-0.0225326 - 0.00646113i) q^{51} +(2.94661 + 2.84551i) q^{52} +(-0.0252505 + 0.0474892i) q^{53} +(0.130575 - 0.358753i) q^{54} +(-9.59901 - 2.64143i) q^{55} -4.02432i q^{56} +(0.257052 - 0.104661i) q^{57} +(-3.55699 + 2.58430i) q^{58} +(-0.719059 - 10.2830i) q^{59} +(0.191015 + 0.00667039i) q^{60} +(-0.181401 - 1.29073i) q^{61} +(8.29566 + 4.04606i) q^{62} +(9.99541 + 6.74199i) q^{63} +(0.669131 + 0.743145i) q^{64} +(-6.14807 - 10.6488i) q^{65} +(-0.210246 - 0.0198211i) q^{66} +(1.25912 - 1.50056i) q^{67} +(0.0765415 + 0.360100i) q^{68} +(0.547487 - 0.0575432i) q^{69} +(-3.32974 + 11.6122i) q^{70} +(-5.69130 - 10.7038i) q^{71} +(-2.96679 + 0.416955i) q^{72} +(-6.47399 + 4.36676i) q^{73} +(3.73405 + 0.931002i) q^{74} +(-0.242875 - 0.0789149i) q^{75} +(-3.34664 - 2.79285i) q^{76} +(4.43026 - 12.5904i) q^{77} +(-0.167652 - 0.199800i) q^{78} +(2.64619 - 3.38697i) q^{79} +(-1.31590 - 2.69799i) q^{80} +(3.92935 - 8.05637i) q^{81} +(-6.43788 - 8.24012i) q^{82} +(-2.19361 + 10.3201i) q^{83} +(-0.0267842 + 0.254835i) q^{84} +(0.0770873 - 1.10240i) q^{85} +(-0.448146 - 0.717184i) q^{86} +(0.242442 - 0.139974i) q^{87} +(1.27533 + 3.06162i) q^{88} +(-1.91326 - 5.25664i) q^{89} +(8.90568 + 1.25161i) q^{90} +(14.8164 - 7.22642i) q^{91} +(-4.83469 - 7.16773i) q^{92} +(-0.498383 - 0.311424i) q^{93} +(-3.75166 - 11.5464i) q^{94} +(7.34592 + 10.8278i) q^{95} +(-0.0374258 - 0.0515122i) q^{96} +(-14.5724 + 5.88762i) q^{97} +(-8.64061 - 3.14493i) q^{98} +(-9.74088 - 1.96158i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9}+O(q^{10}) $ 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9	$ 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{13} - 18 q^{14} + 21 q^{15} + 21 q^{17} - 60 q^{18} + 45 q^{19} + 12 q^{20} + 48 q^{21} - 12 q^{22} + 12 q^{24} - 18 q^{25} - 96 q^{26} - 9 q^{27} - 6 q^{28} + 18 q^{29} + 9 q^{31} + 87 q^{33} - 24 q^{34} - 36 q^{35} - 12 q^{36} - 36 q^{38} + 60 q^{41} - 6 q^{42} - 12 q^{43} + 18 q^{44} + 48 q^{45} + 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} - 21 q^{50} - 75 q^{51} + 3 q^{52} - 39 q^{53} + 27 q^{54} - 126 q^{55} - 90 q^{57} - 24 q^{58} + 69 q^{59} - 42 q^{60} + 66 q^{61} - 45 q^{62} - 9 q^{63} + 30 q^{64} - 12 q^{66} - 9 q^{67} + 12 q^{68} - 54 q^{69} + 9 q^{70} + 48 q^{71} + 6 q^{72} - 12 q^{74} + 72 q^{77} - 36 q^{79} - 27 q^{81} + 45 q^{82} + 36 q^{83} + 36 q^{84} - 210 q^{85} + 3 q^{86} + 216 q^{87} + 3 q^{88} + 18 q^{89} - 96 q^{90} - 108 q^{91} - 30 q^{92} + 147 q^{93} - 18 q^{94} + 66 q^{95} - 9 q^{97} - 12 q^{98} - 42 q^{99}+O(q^{100}) $ 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^13 - 18 * q^14 + 21 * q^15 + 21 * q^17 - 60 * q^18 + 45 * q^19 + 12 * q^20 + 48 * q^21 - 12 * q^22 + 12 * q^24 - 18 * q^25 - 96 * q^26 - 9 * q^27 - 6 * q^28 + 18 * q^29 + 9 * q^31 + 87 * q^33 - 24 * q^34 - 36 * q^35 - 12 * q^36 - 36 * q^38 + 60 * q^41 - 6 * q^42 - 12 * q^43 + 18 * q^44 + 48 * q^45 + 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 - 21 * q^50 - 75 * q^51 + 3 * q^52 - 39 * q^53 + 27 * q^54 - 126 * q^55 - 90 * q^57 - 24 * q^58 + 69 * q^59 - 42 * q^60 + 66 * q^61 - 45 * q^62 - 9 * q^63 + 30 * q^64 - 12 * q^66 - 9 * q^67 + 12 * q^68 - 54 * q^69 + 9 * q^70 + 48 * q^71 + 6 * q^72 - 12 * q^74 + 72 * q^77 - 36 * q^79 - 27 * q^81 + 45 * q^82 + 36 * q^83 + 36 * q^84 - 210 * q^85 + 3 * q^86 + 216 * q^87 + 3 * q^88 + 18 * q^89 - 96 * q^90 - 108 * q^91 - 30 * q^92 + 147 * q^93 - 18 * q^94 + 66 * q^95 - 9 * q^97 - 12 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.374607	+	0.927184i	0.264887	+	0.655618i
$2$	0.374607	+	0.927184i	0.264887	+	0.655618i
$3$	−0.0175505	−	0.0612060i	−0.0101328	−	0.0353373i	0.956033	−	0.293259i	$-0.0947400\pi$
$3$	−0.0175505	−	0.0612060i	−0.0101328	−	0.0353373i	−0.966166	+	0.257922i	$0.916962\pi$
$4$	−0.719340	+	0.694658i	−0.359670	+	0.347329i
$5$	2.65042	−	1.40925i	1.18531	−	0.630238i	0.244653	−	0.969611i	$-0.421326\pi$
$5$	2.65042	−	1.40925i	1.18531	−	0.630238i	0.940652	+	0.339373i	$0.110215\pi$
$6$	0.0501746	−	0.0392007i	0.0204837	−	0.0160036i
$7$	1.63684	+	3.67640i	0.618667	+	1.38955i	0.902506	+	0.430676i	$0.141725\pi$
$7$	1.63684	+	3.67640i	0.618667	+	1.38955i	−0.283840	+	0.958872i	$0.591608\pi$
$8$	−0.913545	−	0.406737i	−0.322987	−	0.143803i
$9$	2.54071	−	1.58761i	0.846902	−	0.529203i
$10$	2.29950	+	1.92951i	0.727167	+	0.610166i
$11$	−2.41034	−	2.27821i	−0.726746	−	0.686906i
$11$	−2.41034	−	2.27821i	−0.726746	−	0.686906i
$12$	0.0551420	+	0.0318363i	0.0159181	+	0.00919034i
$13$	−0.142958	−	4.09378i	−0.0396494	−	1.13541i	−0.842317	−	0.538983i	$-0.818809\pi$
$13$	−0.142958	−	4.09378i	−0.0396494	−	1.13541i	0.802668	−	0.596427i	$-0.203413\pi$
$14$	−2.79553	+	2.89485i	−0.747136	+	0.773682i
$15$	−0.132771	−	0.137489i	−0.0342814	−	0.0354994i
$16$	0.0348995	−	0.999391i	0.00872487	−	0.249848i
$17$	0.195087	−	0.312204i	0.0473155	−	0.0757206i	−0.823545	−	0.567251i	$-0.808007\pi$
$17$	0.195087	−	0.312204i	0.0473155	−	0.0757206i	0.870860	+	0.491531i	$0.163562\pi$
$18$	2.42377	+	1.76097i	0.571288	+	0.415065i
$19$	0.467294	+	4.33378i	0.107205	+	0.994237i
$19$	0.467294	+	4.33378i	0.107205	+	0.994237i
$20$	−0.927604	+	2.85487i	−0.207419	+	0.638369i
$21$	0.196290	−	0.164707i	0.0428340	−	0.0359420i
$22$	1.20939	−	3.08826i	0.257843	−	0.658420i
$23$	−1.50133	+	8.51449i	−0.313050	+	1.77539i	0.269902	+	0.962888i	$0.413009\pi$
$23$	−1.50133	+	8.51449i	−0.313050	+	1.77539i	−0.582952	+	0.812507i	$0.698102\pi$
$24$	−0.00886150	+	0.0630529i	−0.00180885	+	0.0128706i
$25$	2.24278	−	3.32505i	0.448555	−	0.665011i
$26$	3.74213	−	1.66610i	0.733892	−	0.326750i
$27$	−0.283716	−	0.255459i	−0.0546011	−	0.0491631i
$28$	−3.73128	−	1.50754i	−0.705146	−	0.284898i
$29$	1.06365	+	4.26608i	0.197515	+	0.792191i	0.984524	+	0.175249i	$0.0560731\pi$
$29$	1.06365	+	4.26608i	0.197515	+	0.792191i	−0.787009	+	0.616942i	$0.788371\pi$
$30$	0.0777402	−	0.174607i	0.0141934	−	0.0318788i
$31$	6.85905	−	6.17592i	1.23192	−	1.10923i	0.241609	−	0.970374i	$-0.422325\pi$
$31$	6.85905	−	6.17592i	1.23192	−	1.10923i	0.990313	−	0.138854i	$-0.0443418\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−0.0971372	+	0.187511i	−0.0169094	+	0.0326415i
$34$	0.362552	+	0.0639276i	0.0621771	+	0.0109635i
$35$	9.51930	+	7.43729i	1.60905	+	1.25713i
$36$	−0.724785	+	2.90695i	−0.120797	+	0.484492i
$37$	2.26201	−	3.11339i	0.371872	−	0.511838i	−0.581536	−	0.813520i	$-0.697548\pi$
$37$	2.26201	−	3.11339i	0.371872	−	0.511838i	0.953408	+	0.301682i	$0.0975482\pi$
$38$	−3.84316	+	2.05673i	−0.623443	+	0.333646i
$39$	−0.248055	+	0.0805978i	−0.0397205	+	0.0129060i
$40$	−2.99448	+	0.209394i	−0.473468	+	0.0331081i
$41$	−10.0518	+	2.88230i	−1.56982	+	0.450140i	−0.944033	−	0.329851i	$-0.893001\pi$
$41$	−10.0518	+	2.88230i	−1.56982	+	0.450140i	−0.625791	+	0.779991i	$0.715224\pi$
$42$	0.226245	+	0.120297i	0.0349104	+	0.0185622i
$43$	−0.832840	+	0.146852i	−0.127007	+	0.0223947i	−0.236790	−	0.971561i	$-0.576095\pi$
$43$	−0.832840	+	0.146852i	−0.127007	+	0.0223947i	0.109783	+	0.993956i	$0.464984\pi$
$44$	3.31643	−	0.0355587i	0.499971	−	0.00536068i
$45$	4.49660	−	7.78834i	0.670313	−	1.16102i
$46$	−8.45691	+	1.79757i	−1.24690	+	0.265038i
$47$	−12.1111	−	0.846887i	−1.76658	−	0.123531i	−0.850871	−	0.525375i	$-0.823925\pi$
$47$	−12.1111	−	0.846887i	−1.76658	−	0.123531i	−0.915708	+	0.401844i	$0.868369\pi$
$48$	−0.0617812	+	0.0154038i	−0.00891735	+	0.00222334i
$49$	−6.15275	+	6.83333i	−0.878965	+	0.976190i
$50$	3.92310	+	0.833880i	0.554810	+	0.117928i
$51$	−0.0225326	−	0.00646113i	−0.00315520	−	0.000904739i
$52$	2.94661	+	2.84551i	0.408621	+	0.394601i
$53$	−0.0252505	+	0.0474892i	−0.00346842	+	0.00652315i	−0.884676	−	0.466207i	$-0.845620\pi$
$53$	−0.0252505	+	0.0474892i	−0.00346842	+	0.00652315i	0.881207	+	0.472730i	$0.156731\pi$
$54$	0.130575	−	0.358753i	0.0177691	−	0.0488201i
$55$	−9.59901	−	2.64143i	−1.29433	−	0.356170i
$56$		−	4.02432i		−	0.537772i
$57$	0.257052	−	0.104661i	0.0340474	−	0.0138627i
$58$	−3.55699	+	2.58430i	−0.467056	+	0.339336i
$59$	−0.719059	−	10.2830i	−0.0936136	−	1.33874i	−0.786456	−	0.617647i	$-0.788086\pi$
$59$	−0.719059	−	10.2830i	−0.0936136	−	1.33874i	0.692842	−	0.721089i	$-0.256358\pi$
$60$	0.191015	+	0.00667039i	0.0246599	+	0.000861144i
$61$	−0.181401	−	1.29073i	−0.0232260	−	0.165261i	0.975202	−	0.221318i	$-0.0710360\pi$
$61$	−0.181401	−	1.29073i	−0.0232260	−	0.165261i	−0.998428	+	0.0560570i	$0.982147\pi$
$62$	8.29566	+	4.04606i	1.05355	+	0.513850i
$63$	9.99541	+	6.74199i	1.25930	+	0.849411i
$64$	0.669131	+	0.743145i	0.0836413	+	0.0928931i
$65$	−6.14807	−	10.6488i	−0.762575	−	1.32082i
$66$	−0.210246	−	0.0198211i	−0.0258795	−	0.00243981i
$67$	1.25912	−	1.50056i	0.153826	−	0.183322i	−0.683628	−	0.729831i	$-0.739599\pi$
$67$	1.25912	−	1.50056i	0.153826	−	0.183322i	0.837454	+	0.546508i	$0.184043\pi$
$68$	0.0765415	+	0.360100i	0.00928202	+	0.0436685i
$69$	0.547487	−	0.0575432i	0.0659097	−	0.00692739i
$70$	−3.32974	+	11.6122i	−0.397980	+	1.38792i
$71$	−5.69130	−	10.7038i	−0.675433	−	1.27030i	−0.951050	−	0.309037i	$-0.899993\pi$
$71$	−5.69130	−	10.7038i	−0.675433	−	1.27030i	0.275617	−	0.961268i	$-0.411118\pi$
$72$	−2.96679	+	0.416955i	−0.349639	+	0.0491386i
$73$	−6.47399	+	4.36676i	−0.757723	+	0.511091i	−0.876248	−	0.481860i	$-0.839961\pi$
$73$	−6.47399	+	4.36676i	−0.757723	+	0.511091i	0.118525	+	0.992951i	$0.462183\pi$
$74$	3.73405	+	0.931002i	0.434074	+	0.108227i
$75$	−0.242875	−	0.0789149i	−0.0280448	−	0.00911231i
$76$	−3.34664	−	2.79285i	−0.383886	−	0.320362i
$77$	4.43026	−	12.5904i	0.504876	−	1.43481i
$78$	−0.167652	−	0.199800i	−0.0189828	−	0.0226229i
$79$	2.64619	−	3.38697i	0.297719	−	0.381063i	−0.615770	−	0.787926i	$-0.711155\pi$
$79$	2.64619	−	3.38697i	0.297719	−	0.381063i	0.913489	+	0.406862i	$0.133377\pi$
$80$	−1.31590	−	2.69799i	−0.147122	−	0.301645i
$81$	3.92935	−	8.05637i	0.436595	−	0.895152i
$82$	−6.43788	−	8.24012i	−0.710945	−	0.909968i
$83$	−2.19361	+	10.3201i	−0.240780	+	1.13278i	0.677091	+	0.735900i	$0.263241\pi$
$83$	−2.19361	+	10.3201i	−0.240780	+	1.13278i	−0.917870	+	0.396880i	$0.870093\pi$
$84$	−0.0267842	+	0.254835i	−0.00292240	+	0.0278048i
$85$	0.0770873	−	1.10240i	0.00836129	−	0.119572i
$86$	−0.448146	−	0.717184i	−0.0483249	−	0.0773360i
$87$	0.242442	−	0.139974i	0.0259925	−	0.0150068i
$88$	1.27533	+	3.06162i	0.135950	+	0.326370i
$89$	−1.91326	−	5.25664i	−0.202805	−	0.557203i	0.796040	−	0.605244i	$-0.206924\pi$
$89$	−1.91326	−	5.25664i	−0.202805	−	0.557203i	−0.998845	+	0.0480408i	$0.984702\pi$
$90$	8.90568	+	1.25161i	0.938741	+	0.131931i
$91$	14.8164	−	7.22642i	1.55318	−	0.757535i
$92$	−4.83469	−	7.16773i	−0.504052	−	0.747287i
$93$	−0.498383	−	0.311424i	−0.0516799	−	0.0322932i
$94$	−3.75166	−	11.5464i	−0.386954	−	1.19092i
$95$	7.34592	+	10.8278i	0.753676	+	1.11091i
$96$	−0.0374258	−	0.0515122i	−0.00381975	−	0.00525744i
$97$	−14.5724	+	5.88762i	−1.47960	+	0.597797i	−0.965609	−	0.259999i	$-0.916278\pi$
$97$	−14.5724	+	5.88762i	−1.47960	+	0.597797i	−0.513990	+	0.857796i	$0.671833\pi$
$98$	−8.64061	−	3.14493i	−0.872834	−	0.317685i
$99$	−9.74088	−	1.96158i	−0.978996	−	0.197146i
$100$	0.696458	+	3.94981i	0.0696458	+	0.394981i
$101$	9.05110	−	0.316071i	0.900618	−	0.0314503i	0.419153	−	0.907915i	$-0.362327\pi$
$101$	9.05110	−	0.316071i	0.900618	−	0.0314503i	0.481465	+	0.876465i	$0.340105\pi$
$102$	−0.00245022	−	0.0233123i	−0.000242608	−	0.00230826i
$103$	1.63048	+	0.171370i	0.160656	+	0.0168856i	0.184515	−	0.982830i	$-0.440929\pi$
$103$	1.63048	+	0.171370i	0.160656	+	0.0168856i	−0.0238591	+	0.999715i	$0.507595\pi$
$104$	−1.53449	+	3.79800i	−0.150469	+	0.372424i
$105$	0.288138	−	0.713166i	0.0281194	−	0.0695979i
$106$	−0.0534902	−	0.00562205i	−0.00519543	−	0.000546062i
$107$	−1.16717	−	11.1049i	−0.112834	−	1.07355i	−0.893643	−	0.448778i	$-0.851860\pi$
$107$	−1.16717	−	11.1049i	−0.112834	−	1.07355i	0.780809	−	0.624770i	$-0.214807\pi$
$108$	0.381545	−	0.0133238i	0.0367141	−	0.00128209i
$109$	−0.0498198	−	0.282542i	−0.00477187	−	0.0270626i	0.982329	−	0.187163i	$-0.0599293\pi$
$109$	−0.0498198	−	0.282542i	−0.00477187	−	0.0270626i	−0.987101	+	0.160100i	$0.948818\pi$
$110$	−1.14676	−	9.88954i	−0.109339	−	0.942931i
$111$	−0.230257	−	0.0838068i	−0.0218551	−	0.00795459i
$112$	3.73128	−	1.50754i	0.352573	−	0.142449i
$113$	2.94067	+	4.04748i	0.276635	+	0.380755i	0.924616	−	0.380902i	$-0.124386\pi$
$113$	2.94067	+	4.04748i	0.276635	+	0.380755i	−0.647981	+	0.761657i	$0.724386\pi$
$114$	0.193334	+	0.199128i	0.0181073	+	0.0186500i
$115$	8.01992	+	24.6828i	0.747861	+	2.30168i
$116$	−3.72860	−	2.32989i	−0.346191	−	0.216324i
$117$	−6.86253	−	10.1741i	−0.634441	−	0.940598i
$118$	9.26489	−	4.51879i	0.852903	−	0.415988i
$119$	1.46711	+	0.206189i	0.134490	+	0.0189013i
$120$	0.0653708	+	0.179605i	0.00596751	+	0.0163956i
$121$	0.619519	+	10.9825i	0.0563199	+	0.998413i
$122$	1.12879	−	0.651709i	0.102196	−	0.0590030i
$123$	0.352828	+	0.564643i	0.0318134	+	0.0509121i
$124$	−0.643836	+	9.20728i	−0.0578182	+	0.826838i
$125$	−0.310403	+	2.95328i	−0.0277632	+	0.264150i
$126$	−2.50672	+	11.7932i	−0.223316	+	1.05062i
$127$	9.23605	+	11.8216i	0.819567	+	1.04900i	0.997884	+	0.0650250i	$0.0207127\pi$
$127$	9.23605	+	11.8216i	0.819567	+	1.04900i	−0.178316	+	0.983973i	$0.557065\pi$
$128$	−0.438371	+	0.898794i	−0.0387469	+	0.0794429i
$129$	0.0236050	+	0.0483975i	0.00207831	+	0.00426116i
$130$	7.57026	−	9.68950i	0.663956	−	0.849825i
$131$	−9.47774	−	11.2951i	−0.828074	−	0.986860i	−0.999998	−	0.00175009i	$-0.999443\pi$
$131$	−9.47774	−	11.2951i	−0.828074	−	0.986860i	0.171924	−	0.985110i	$-0.445002\pi$
$132$	−0.0603816	−	0.202362i	−0.00525554	−	0.0176133i
$133$	−15.1678	+	8.81165i	−1.31522	+	0.764067i
$134$	1.86297	+	0.605314i	0.160936	+	0.0522912i
$135$	−1.11197	−	0.277246i	−0.0957034	−	0.0238615i
$136$	−0.305206	+	0.205864i	−0.0261712	+	0.0176527i
$137$	12.0177	−	1.68898i	1.02674	−	0.144299i	0.394360	−	0.918956i	$-0.370966\pi$
$137$	12.0177	−	1.68898i	1.02674	−	0.144299i	0.632381	+	0.774657i	$0.282078\pi$
$138$	0.258445	+	0.486065i	0.0220003	+	0.0413766i
$139$	1.59058	−	5.54701i	0.134911	−	0.470492i	−0.864576	−	0.502502i	$-0.832413\pi$
$139$	1.59058	−	5.54701i	0.134911	−	0.470492i	0.999488	+	0.0320100i	$0.0101909\pi$
$140$	−12.0140	+	1.26272i	−1.01537	+	0.106719i
$141$	0.160721	+	0.756132i	0.0135351	+	0.0636778i
$142$	7.79237	−	9.28659i	0.653921	−	0.779313i
$143$	−8.98190	+	10.1931i	−0.751105	+	0.852390i
$144$	−1.49797	−	2.59457i	−0.124831	−	0.216214i
$145$	8.83112	+	9.80796i	0.733385	+	0.814507i
$146$	−6.47399	−	4.36676i	−0.535791	−	0.361396i
$147$	0.526225	+	0.256657i	0.0434023	+	0.0211687i
$148$	0.535588	+	3.81091i	0.0440251	+	0.313255i
$149$	−6.26267	−	0.218697i	−0.513058	−	0.0179164i	−0.222799	−	0.974864i	$-0.571519\pi$
$149$	−6.26267	−	0.218697i	−0.513058	−	0.0179164i	−0.290259	+	0.956948i	$0.593741\pi$
$150$	−0.0178140	−	0.254752i	−0.00145451	−	0.0208004i
$151$	−3.31994	+	2.41208i	−0.270173	+	0.196292i	−0.714620	−	0.699513i	$-0.753400\pi$
$151$	−3.31994	+	2.41208i	−0.270173	+	0.196292i	0.444447	+	0.895805i	$0.353400\pi$
$152$	1.33581	−	4.14917i	0.108349	−	0.336542i
$153$		−	1.10294i		−	0.0891675i
$154$	13.3333	−	0.608795i	1.07443	−	0.0490581i
$155$	9.47594	−	26.0349i	0.761126	−	2.09118i
$156$	0.122448	−	0.230290i	0.00980365	−	0.0184380i
$157$	−3.82194	−	3.69080i	−0.305024	−	0.294558i	0.526354	−	0.850265i	$-0.323559\pi$
$157$	−3.82194	−	3.69080i	−0.305024	−	0.294558i	−0.831378	+	0.555707i	$0.812447\pi$
$158$	4.13162	+	1.18472i	0.328694	+	0.0942515i
$159$	0.00334978		0.000712018i	0.000265655		5.64667e-5i
$160$	2.00859	−	2.23076i	0.158793	−	0.176357i
$161$	−33.7601	+	8.41734i	−2.66067	+	0.663379i
$162$	8.94169	+	0.625264i	0.702526	+	0.0491254i
$163$	6.39622	−	1.35956i	0.500990	−	0.106489i	0.0495169	−	0.998773i	$-0.484232\pi$
$163$	6.39622	−	1.35956i	0.500990	−	0.106489i	0.451474	+	0.892284i	$0.350899\pi$
$164$	5.22843	−	9.05590i	0.408272	−	0.707147i
$165$	0.00679639	+	0.633875i	0.000529098	+	0.0493471i
$166$	−10.3904	+	1.83211i	−0.806450	+	0.142199i
$167$	−4.16449	−	2.21430i	−0.322258	−	0.171347i	0.300459	−	0.953795i	$-0.402860\pi$
$167$	−4.16449	−	2.21430i	−0.322258	−	0.171347i	−0.622717	+	0.782447i	$0.713971\pi$
$168$	−0.246312	+	0.0706289i	−0.0190034	+	0.00544914i
$169$	−3.77024	+	0.263641i	−0.290018	+	0.0202800i
$170$	1.05101	−	0.341492i	0.0806084	−	0.0261913i
$171$	8.06760	+	10.2690i	0.616945	+	0.785288i
$172$	0.497083	−	0.684176i	0.0379022	−	0.0521679i
$173$	1.68642	−	6.76386i	0.128216	−	0.514247i	−0.871499	−	0.490397i	$-0.836852\pi$
$173$	1.68642	−	6.76386i	0.128216	−	0.514247i	0.999716	−	0.0238503i	$-0.00759251\pi$
$174$	0.220602	+	0.172353i	0.0167238	+	0.0130661i
$175$	15.8953	+	2.80277i	1.20157	+	0.211869i
$176$	−2.36094	+	2.32937i	−0.177963	+	0.175583i
$177$	−0.616763	+	0.224483i	−0.0463587	+	0.0168732i
$178$	4.15716	−	3.74312i	0.311592	−	0.280559i
$179$	−10.0204	+	22.5062i	−0.748960	+	1.68219i	−0.0179372	+	0.999839i	$0.505710\pi$
$179$	−10.0204	+	22.5062i	−0.748960	+	1.68219i	−0.731023	+	0.682353i	$0.760957\pi$
$180$	2.17565	+	8.72606i	0.162163	+	0.650402i
$181$	1.58505	+	0.640401i	0.117816	+	0.0476006i	0.432758	−	0.901510i	$-0.357541\pi$
$181$	1.58505	+	0.640401i	0.117816	+	0.0476006i	−0.314942	+	0.949111i	$0.601985\pi$
$182$	12.2505	+	11.0304i	0.908069	+	0.817629i
$183$	−0.0758169	+	0.0337559i	−0.00560455	+	0.00249530i
$184$	4.83469	−	7.16773i	0.356418	−	0.528412i
$185$	1.60772	−	11.4395i	0.118202	−	0.841052i
$186$	0.102050	−	0.578754i	0.00748267	−	0.0424363i
$187$	−1.18149	+	0.308071i	−0.0863993	+	0.0225284i
$188$	9.30026	−	7.80384i	0.678291	−	0.569154i
$189$	0.474772	−	1.46120i	0.0345345	−	0.106286i
$190$	−7.28754	+	10.8672i	−0.528694	+	0.788389i
$191$	−17.4720	−	12.6942i	−1.26423	−	0.918517i	−0.265273	−	0.964173i	$-0.585462\pi$
$191$	−17.4720	−	12.6942i	−1.26423	−	0.918517i	−0.998957	+	0.0456561i	$0.985462\pi$
$192$	0.0337413	−	0.0539974i	0.00243507	−	0.00389692i
$193$	0.806226	−	23.0873i	0.0580334	−	1.66186i	−0.526265	−	0.850320i	$-0.676408\pi$
$193$	0.806226	−	23.0873i	0.0580334	−	1.66186i	0.584299	−	0.811539i	$-0.301370\pi$
$194$	−10.9178	−	11.3057i	−0.783853	−	0.811703i
$195$	−0.543867	+	0.563190i	−0.0389471	+	0.0403309i
$196$	−0.320906	−	9.18955i	−0.0229219	−	0.656396i
$197$	9.58085	+	5.53151i	0.682607	+	0.394104i	0.800837	−	0.598883i	$-0.204388\pi$
$197$	9.58085	+	5.53151i	0.682607	+	0.394104i	−0.118229	+	0.992986i	$0.537722\pi$
$198$	−1.83026	−	9.76641i	−0.130071	−	0.694069i
$199$	12.0290	+	10.0936i	0.852716	+	0.715513i	0.960386	−	0.278673i	$-0.0898946\pi$
$199$	12.0290	+	10.0936i	0.852716	+	0.715513i	−0.107670	+	0.994187i	$0.534339\pi$
$200$	−3.40130	+	2.12537i	−0.240508	+	0.150286i
$201$	−0.113941	−	0.0507299i	−0.00803680	−	0.00357821i
$202$	3.68366	+	8.27363i	0.259181	+	0.582131i
$203$	−13.9428	+	10.8933i	−0.978592	+	0.764560i
$204$	0.0206969	−	0.0110047i	0.00144907	−	0.000770486i
$205$	−22.5796	+	21.8048i	−1.57702	+	1.52292i
$206$	0.451896	+	1.57595i	0.0314851	+	0.109802i
$207$	9.70324	+	24.0164i	0.674422	+	1.66925i
$208$	−4.09627			−0.284025
$209$	8.74692	−	11.5105i	0.605037	−	0.796197i
$210$	0.769174			0.0530781
$211$	5.09189	+	12.6029i	0.350540	+	0.867617i	0.994709	+	0.102734i	$0.0327590\pi$
$211$	5.09189	+	12.6029i	0.350540	+	0.867617i	−0.644169	+	0.764883i	$0.722797\pi$
$212$	−0.0148251	−	0.0517013i	−0.00101819	−	0.00355086i
$213$	−0.555250	+	0.536198i	−0.0380451	+	0.0367397i
$214$	9.85902	−	5.24213i	0.673949	−	0.358345i
$215$	−2.00043	+	1.56290i	−0.136428	+	0.106589i
$216$	0.155283	+	0.348771i	0.0105657	+	0.0237308i
$217$	33.9323	+	15.1076i	2.30347	+	1.02557i
$218$	0.243306	−	0.152034i	0.0164788	−	0.0102971i
$219$	0.380894	+	0.319608i	0.0257384	+	0.0215971i
$220$	8.73984	−	4.76795i	0.589240	−	0.321455i
$221$	−1.30598	−	0.754010i	−0.0878500	−	0.0507202i
$222$	−0.00855159	−	0.244886i	−0.000573945	−	0.0164356i
$223$	−6.74628	+	6.98597i	−0.451764	+	0.467815i	−0.906130	−	0.423000i	$-0.860977\pi$
$223$	−6.74628	+	6.98597i	−0.451764	+	0.467815i	0.454366	+	0.890815i	$0.349866\pi$
$224$	2.79553	+	2.89485i	0.186784	+	0.193421i
$225$	0.419351	−	12.0086i	0.0279567	−	0.800576i
$226$	−2.65116	+	4.24275i	−0.176353	+	0.282224i
$227$	14.1242	+	10.2619i	0.937459	+	0.681104i	0.947808	−	0.318842i	$-0.103294\pi$
$227$	14.1242	+	10.2619i	0.937459	+	0.681104i	−0.0103485	+	0.999946i	$0.503294\pi$
$228$	−0.112204	+	0.253850i	−0.00743088	+	0.0168116i
$229$	1.74287	−	5.36400i	0.115172	−	0.354463i	−0.876811	−	0.480835i	$-0.840333\pi$
$229$	1.74287	−	5.36400i	0.115172	−	0.354463i	0.991983	+	0.126373i	$0.0403335\pi$
$230$	−19.8812	+	16.6823i	−1.31092	+	1.10000i
$231$	−0.848364	−	0.0501896i	−0.0558183	−	0.00330224i
$232$	0.763476	−	4.32988i	0.0501246	−	0.284271i
$233$	−2.11024	+	15.0151i	−0.138246	+	0.983673i	0.790370	+	0.612630i	$0.209889\pi$
$233$	−2.11024	+	15.0151i	−0.138246	+	0.983673i	−0.928616	+	0.371043i	$0.879000\pi$
$234$	6.86253	−	10.1741i	0.448618	−	0.665103i
$235$	−33.2929	+	14.8230i	−2.17179	+	0.966943i
$236$	7.66044	+	6.89749i	0.498652	+	0.448988i
$237$	−0.253745	−	0.102519i	−0.0164825	−	0.00665935i
$238$	0.358415	+	1.43752i	0.0232326	+	0.0931808i
$239$	−4.76930	+	10.7120i	−0.308500	+	0.692903i	−0.999553	−	0.0299013i	$-0.990481\pi$
$239$	−4.76930	+	10.7120i	−0.308500	+	0.692903i	0.691052	+	0.722805i	$0.257147\pi$
$240$	−0.142038	+	0.127892i	−0.00916854	+	0.00825539i
$241$	10.4211	−	3.79296i	0.671280	−	0.244326i	0.0161809	−	0.999869i	$-0.494849\pi$
$241$	10.4211	−	3.79296i	0.671280	−	0.244326i	0.655099	+	0.755543i	$0.272627\pi$
$242$	−9.95076	+	4.68854i	−0.639659	+	0.301391i
$243$	−1.68999	−	0.297991i	−0.108413	−	0.0191161i
$244$	1.02711	+	0.802464i	0.0657538	+	0.0513725i
$245$	−6.67750	+	26.7820i	−0.426610	+	1.71104i
$246$	−0.391356	+	0.538655i	−0.0249519	+	0.0343434i
$247$	17.6747	−	2.53254i	1.12462	−	0.161142i
$248$	−8.77803	+	2.85215i	−0.557405	+	0.181112i
$249$	0.670152	−	0.0468616i	0.0424691	−	0.00296973i
$250$	−2.85452	+	0.818519i	−0.180535	+	0.0517677i
$251$	−5.86260	−	3.11720i	−0.370044	−	0.196756i	0.274026	−	0.961722i	$-0.411644\pi$
$251$	−5.86260	−	3.11720i	−0.370044	−	0.196756i	−0.644070	+	0.764966i	$0.722756\pi$
$252$	−11.8735	+	2.09361i	−0.747959	+	0.131885i
$253$	23.0165	−	17.1025i	1.44704	−	1.07523i
$254$	−7.50092	+	12.9920i	−0.470650	+	0.815189i
$255$	−0.0688264	+	0.0146295i	−0.00431008	+	0.000916135i
$256$	−0.997564	−	0.0697565i	−0.0623478	−	0.00435978i
$257$	−3.13362	+	0.781300i	−0.195470	+	0.0487361i	−0.338426	−	0.940993i	$-0.609895\pi$
$257$	−3.13362	+	0.781300i	−0.195470	+	0.0487361i	0.142957	+	0.989729i	$0.454339\pi$
$258$	−0.0360307	+	0.0400162i	−0.00224318	+	0.00249130i
$259$	15.1486	+	3.21993i	0.941288	+	0.200077i
$260$	11.8198	+	3.38928i	0.733034	+	0.210194i
$261$	9.47530	+	9.15019i	0.586506	+	0.566383i
$262$	6.92224	−	13.0188i	0.427657	−	0.804307i
$263$	−1.28484	+	3.53007i	−0.0792268	+	0.217674i	−0.972982	−	0.230881i	$-0.925839\pi$
$263$	−1.28484	+	3.53007i	−0.0792268	+	0.217674i	0.893755	+	0.448555i	$0.148061\pi$
$264$	0.165007	−	0.131791i	0.0101555	−	0.00811116i
$265$			0.161451i			0.00991785i
$266$	−13.8520	−	10.7624i	−0.849320	−	0.659888i
$267$	−0.288159	+	0.209360i	−0.0176351	+	0.0128126i
$268$	0.136642	+	1.95407i	0.00834672	+	0.119364i
$269$	16.4651	+	0.574973i	1.00389	+	0.0350567i	0.532125	−	0.846666i	$-0.321394\pi$
$269$	16.4651	+	0.574973i	1.00389	+	0.0350567i	0.471768	+	0.881723i	$0.343616\pi$
$270$	−0.159494	−	1.13486i	−0.00970652	−	0.0690655i
$271$	−14.7368	−	7.18760i	−0.895195	−	0.436616i	−0.0674515	−	0.997723i	$-0.521487\pi$
$271$	−14.7368	−	7.18760i	−0.895195	−	0.436616i	−0.827743	+	0.561107i	$0.810376\pi$
$272$	−0.305206	−	0.205864i	−0.0185058	−	0.0124823i
$273$	−0.702335	−	0.780022i	−0.0425072	−	0.0472091i
$274$	6.06790	+	10.5099i	0.366575	+	0.634927i
$275$	−12.9810	+	2.90501i	−0.782786	+	0.175179i
$276$	−0.353856	+	0.421710i	−0.0212996	+	0.0253839i
$277$	1.96676	+	9.25289i	0.118171	+	0.555952i	0.996903	+	0.0786369i	$0.0250568\pi$
$277$	1.96676	+	9.25289i	0.118171	+	0.555952i	−0.878732	+	0.477316i	$0.841610\pi$
$278$	5.73894	−	0.603187i	0.344199	−	0.0361768i
$279$	7.62189	−	26.5807i	0.456310	−	1.59134i
$280$	−5.67129	−	10.6661i	−0.338925	−	0.637424i
$281$	9.00385	−	1.26541i	0.537125	−	0.0754880i	0.134605	−	0.990899i	$-0.457023\pi$
$281$	9.00385	−	1.26541i	0.537125	−	0.0754880i	0.402520	+	0.915411i	$0.368135\pi$
$282$	−0.640866	+	0.432270i	−0.0381630	+	0.0257413i
$283$	3.46031	+	0.862753i	0.205694	+	0.0512853i	0.343406	−	0.939187i	$-0.388419\pi$
$283$	3.46031	+	0.862753i	0.205694	+	0.0512853i	−0.137712	+	0.990472i	$0.543975\pi$
$284$	11.5294	+	3.74614i	0.684147	+	0.222293i
$285$	0.533802	−	0.639648i	0.0316197	−	0.0378895i
$286$	−12.8156	−	4.50948i	−0.757800	−	0.266651i
$287$	−27.0496	−	32.2365i	−1.59669	−	1.90286i
$288$	1.84449	−	2.36084i	0.108688	−	0.139114i
$289$	7.39290	+	15.1577i	0.434876	+	0.891629i
$290$	−5.78558	+	11.8622i	−0.339741	+	0.696572i
$291$	0.616110	+	0.788585i	0.0361170	+	0.0462277i
$292$	1.62359	−	7.63839i	0.0950135	−	0.447003i
$293$	3.11174	−	29.6062i	0.181790	−	1.72961i	−0.400211	−	0.916423i	$-0.631063\pi$
$293$	3.11174	−	29.6062i	0.181790	−	1.72961i	0.582000	−	0.813189i	$-0.302270\pi$
$294$	−0.0408409	+	0.584052i	−0.00238189	+	0.0340626i
$295$	−16.3972	−	26.2410i	−0.954683	−	1.52781i
$296$	−3.33278	+	1.92418i	−0.193714	+	0.111841i
$297$	0.101864	+	1.26211i	0.00591074	+	0.0732349i
$298$	−2.14326	−	5.88857i	−0.124156	−	0.341116i
$299$	35.0711	+	4.92892i	2.02821	+	0.285047i
$300$	0.229529	−	0.111949i	0.0132518	−	0.00646335i
$301$	−1.90311	−	2.82148i	−0.109694	−	0.162627i
$302$	−3.48012	−	2.17462i	−0.200258	−	0.125135i
$303$	−0.178197	−	0.548434i	−0.0102372	−	0.0315067i
$304$	4.34745	−	0.315762i	0.249343	−	0.0181102i
$305$	−2.29976	−	3.16535i	−0.131684	−	0.181247i
$306$	1.02263	−	0.413169i	0.0584598	−	0.0236193i
$307$	16.2013	+	5.89678i	0.924655	+	0.336547i	0.760089	−	0.649819i	$-0.225155\pi$
$307$	16.2013	+	5.89678i	0.924655	+	0.336547i	0.164566	+	0.986366i	$0.447378\pi$
$308$	5.55919	+	12.1343i	0.316764	+	0.691418i
$309$	−0.0181269	−	0.102803i	−0.00103120	−	0.00584823i
$310$	27.6889	−	0.966919i	1.57263	−	0.0549173i
$311$	1.50327	+	14.3027i	0.0852429	+	0.811032i	0.950713	+	0.310072i	$0.100353\pi$
$311$	1.50327	+	14.3027i	0.0852429	+	0.811032i	−0.865470	+	0.500960i	$0.832980\pi$
$312$	0.259391	+	0.0272631i	0.0146851	+	0.00154347i
$313$	9.70345	−	24.0169i	0.548471	−	1.35751i	−0.357396	−	0.933953i	$-0.616335\pi$
$313$	9.70345	−	24.0169i	0.548471	−	1.35751i	0.905867	−	0.423561i	$-0.139220\pi$
$314$	1.99033	−	4.92624i	0.112321	−	0.278004i
$315$	35.9932	+	3.78304i	2.02799	+	0.213150i
$316$	0.449276	+	4.27458i	0.0252738	+	0.240464i
$317$	7.09208	−	0.247661i	0.398331	−	0.0139100i	0.164966	−	0.986299i	$-0.447249\pi$
$317$	7.09208	−	0.247661i	0.398331	−	0.0139100i	0.233365	+	0.972389i	$0.425026\pi$
$318$	0.000594679		0.00337259i	3.33479e−5		0.000189126i
$319$	7.15526	−	12.7059i	0.400617	−	0.711396i
$320$	2.82076	+	1.02667i	0.157685	+	0.0573927i
$321$	−0.659199	+	0.266334i	−0.0367929	+	0.0148653i
$322$	−20.4512	−	28.1486i	−1.13970	−	1.56866i
$323$	1.44419	+	0.699572i	0.0803567	+	0.0389252i
$324$	2.76988	+	8.52482i	0.153882	+	0.473601i
$325$	−13.9327	−	8.70609i	−0.772844	−	0.482927i
$326$	3.65663	+	5.42117i	0.202522	+	0.300251i
$327$	−0.0164189	+	0.00800804i	−0.000907968	+	0.000442846i
$328$	10.3551	+	1.45531i	0.571764	+	0.0803562i
$329$	−16.7103	−	45.9113i	−0.921271	−	2.53117i
$330$	−0.585173	+	0.243755i	−0.0322127	+	0.0134183i
$331$	−9.20190	+	5.31272i	−0.505782	+	0.292013i	−0.731098	−	0.682272i	$-0.760992\pi$
$331$	−9.20190	+	5.31272i	−0.505782	+	0.292013i	0.225316	+	0.974286i	$0.427659\pi$
$332$	−5.59101	−	8.94748i	−0.306846	−	0.491057i
$333$	0.804256	−	11.5014i	0.0440729	−	0.630272i
$334$	0.493016	−	4.69073i	0.0269766	−	0.256666i
$335$	1.22253	−	5.75153i	0.0667937	−	0.314240i
$336$	−0.157756	−	0.201919i	−0.00860631	−	0.0110156i
$337$	−8.36881	+	17.1586i	−0.455878	+	0.934688i	0.539798	+	0.841794i	$0.318501\pi$
$337$	−8.36881	+	17.1586i	−0.455878	+	0.934688i	−0.995676	+	0.0928937i	$0.970388\pi$
$338$	−1.65680	−	3.39694i	−0.0901180	−	0.184769i
$339$	0.196120	−	0.251022i	0.0106518	−	0.0136336i
$340$	0.710340	+	0.846550i	0.0385236	+	0.0459106i
$341$	−30.6027	−	0.740271i	−1.65723	−	0.0400879i
$342$	−6.49905	+	11.3270i	−0.351429	+	0.612493i
$343$	−8.40161	−	2.72985i	−0.453644	−	0.147398i
$344$	0.820568	+	0.204590i	0.0442420	+	0.0110308i
$345$	1.36998	−	0.924063i	0.0737572	−	0.0497499i
$346$	6.90309	−	0.970166i	0.371112	−	0.0521564i
$347$	3.16248	+	5.94777i	0.169771	+	0.319293i	0.953280	−	0.302087i	$-0.0976834\pi$
$347$	3.16248	+	5.94777i	0.169771	+	0.319293i	−0.783509	+	0.621380i	$0.786572\pi$
$348$	−0.0771641	+	0.269103i	−0.00413643	+	0.0144254i
$349$	−15.9048	+	1.67166i	−0.851363	+	0.0894819i	−0.520151	−	0.854074i	$-0.674124\pi$
$349$	−15.9048	+	1.67166i	−0.851363	+	0.0894819i	−0.331212	+	0.943556i	$0.607458\pi$
$350$	3.35580	+	15.7878i	0.179375	+	0.843893i
$351$	−1.00523	+	1.19799i	−0.0536553	+	0.0639439i
$352$	−3.04418	−	1.31643i	−0.162255	−	0.0701660i
$353$	12.0997	+	20.9574i	0.644004	+	1.11545i	0.984531	+	0.175213i	$0.0560614\pi$
$353$	12.0997	+	20.9574i	0.644004	+	1.11545i	−0.340526	+	0.940235i	$0.610605\pi$
$354$	−0.439181	−	0.487760i	−0.0233422	−	0.0259241i
$355$	−30.1687	−	20.3490i	−1.60119	−	1.08002i
$356$	5.02786	+	2.45225i	0.266476	+	0.129969i
$357$	−0.0131286	−	0.0934148i	−0.000694839	−	0.00494404i
$358$	−24.6211	−	0.859787i	−1.30127	−	0.0454412i
$359$	1.12020	+	16.0197i	0.0591221	+	0.845485i	0.933122	+	0.359560i	$0.117073\pi$
$359$	1.12020	+	16.0197i	0.0591221	+	0.845485i	−0.874000	+	0.485926i	$0.838483\pi$
$360$	−7.27565	+	5.28607i	−0.383460	+	0.278600i
$361$	−18.5633	+	4.05029i	−0.977014	+	0.213173i
$362$			1.70953i			0.0898508i
$363$	0.661324	−	0.230668i	0.0347105	−	0.0121069i
$364$	−5.63810	+	15.4906i	−0.295517	+	0.811926i
$365$	−11.0049	+	20.6973i	−0.576024	+	1.08334i
$366$	−0.0596994	−	0.0576510i	−0.00312054	−	0.00301347i
$367$	−0.383059	−	0.109840i	−0.0199955	−	0.00573362i	0.265625	−	0.964077i	$-0.414422\pi$
$367$	−0.383059	−	0.109840i	−0.0199955	−	0.00573362i	−0.285620	+	0.958343i	$0.592200\pi$
$368$	8.45691	+	1.79757i	0.440847	+	0.0937049i
$369$	−20.9626	+	23.2814i	−1.09127	+	1.21198i
$370$	11.2088	−	2.79467i	0.582719	−	0.145288i
$371$	−0.215920	−	0.0150986i	−0.0112100	−	0.000783881i
$372$	0.574840	−	0.122186i	0.0298041	−	0.00633505i
$373$	−8.37708	+	14.5095i	−0.433749	+	0.751275i	−0.997193	−	0.0748792i	$-0.976143\pi$
$373$	−8.37708	+	14.5095i	−0.433749	+	0.751275i	0.563444	+	0.826155i	$0.309476\pi$
$374$	−0.728233	−	0.980056i	−0.0376561	−	0.0506775i
$375$	0.186206	−	0.0328332i	0.00961565	−	0.00169550i
$376$	10.7195	+	5.69968i	0.552818	+	0.293939i
$377$	17.3123	−	4.96423i	0.891630	−	0.255671i
$378$	1.53265	−	0.107173i	0.0788310	−	0.00551240i
$379$	−14.8990	+	4.84097i	−0.765308	+	0.248664i	−0.665555	−	0.746349i	$-0.731805\pi$
$379$	−14.8990	+	4.84097i	−0.765308	+	0.248664i	−0.0997529	+	0.995012i	$0.531805\pi$
$380$	−12.8058	−	2.68597i	−0.656926	−	0.137787i
$381$	0.561455	−	0.772777i	0.0287642	−	0.0395906i
$382$	5.22469	−	20.9551i	0.267318	−	1.07216i
$383$	−14.9258	−	11.6613i	−0.762675	−	0.595867i	0.157434	−	0.987530i	$-0.449678\pi$
$383$	−14.9258	−	11.6613i	−0.762675	−	0.595867i	−0.920109	+	0.391663i	$0.871900\pi$
$384$	0.0627052	+	0.0110566i	0.00319991	+	0.000564231i
$385$	−6.00107	−	39.6134i	−0.305843	−	2.01888i
$386$	21.7082	−	7.90113i	1.10492	−	0.402157i
$387$	−1.88286	+	1.69533i	−0.0957111	+	0.0861786i
$388$	6.39260	−	14.3580i	0.324535	−	0.728918i
$389$	−3.83066	−	15.3640i	−0.194222	−	0.778983i	−0.985801	−	0.167916i	$-0.946296\pi$
$389$	−3.83066	−	15.3640i	−0.194222	−	0.778983i	0.791579	−	0.611067i	$-0.209259\pi$
$390$	−0.725917	−	0.293290i	−0.0367582	−	0.0148513i
$391$	2.36537	+	2.12979i	0.119622	+	0.107708i
$392$	8.40019	−	3.74000i	0.424273	−	0.188899i
$393$	−0.524990	+	0.778330i	−0.0264822	+	0.0392615i
$394$	−1.53967	+	10.9553i	−0.0775676	+	0.551922i
$395$	2.24042	−	12.7060i	0.112728	−	0.639310i
$396$	8.36963	−	5.35555i	0.420590	−	0.269126i
$397$	−4.06264	+	3.40896i	−0.203898	+	0.171091i	−0.739019	−	0.673685i	$-0.764711\pi$
$397$	−4.06264	+	3.40896i	−0.203898	+	0.171091i	0.535121	+	0.844776i	$0.320266\pi$
$398$	−4.85243	+	14.9342i	−0.243230	+	0.748586i
$399$	0.805529	+	0.773712i	0.0403269	+	0.0387340i
$400$	−3.24476	−	2.35745i	−0.162238	−	0.117873i
$401$	3.64079	−	5.82648i	0.181812	−	0.290961i	−0.744570	−	0.667544i	$-0.767346\pi$
$401$	3.64079	−	5.82648i	0.181812	−	0.290961i	0.926383	+	0.376583i	$0.122901\pi$
$402$	0.00435281	−	0.124648i	0.000217099	−	0.00621689i
$403$	−26.2634	−	27.1965i	−1.30827	−	1.35476i
$404$	−6.29126	+	6.51479i	−0.313002	+	0.324123i
$405$	−0.939028	−	26.8902i	−0.0466607	−	1.33619i
$406$	−15.3231	−	8.84682i	−0.760475	−	0.439060i
$407$	−12.5452	+	2.35101i	−0.621841	+	0.116535i
$408$	0.0179566	+	0.0150674i	0.000888985	+	0.000745947i
$409$	16.4219	−	10.2615i	0.812010	−	0.507400i	−0.0592376	−	0.998244i	$-0.518867\pi$
$409$	16.4219	−	10.2615i	0.812010	−	0.507400i	0.871248	+	0.490844i	$0.163311\pi$
$410$	−28.6755	−	12.7672i	−1.41618	−	0.630526i
$411$	−0.314292	−	0.705912i	−0.0155029	−	0.0348201i
$412$	−1.29191	+	1.00935i	−0.0636479	+	0.0497272i
$413$	36.6275	−	19.4752i	1.80232	−	0.958312i
$414$	−18.6327	+	17.9934i	−0.915746	+	0.884326i
$415$	8.72968	+	30.4440i	0.428523	+	1.49444i
$416$	−1.53449	−	3.79800i	−0.0752346	−	0.186212i
$417$	−0.367426			−0.0179929
$418$	13.9490	+	3.79810i	0.682268	+	0.185771i
$419$	40.5302			1.98003			0.990014	−	0.140967i	$-0.0450212\pi$
$419$	40.5302			1.98003			0.990014	+	0.140967i	$0.0450212\pi$
$420$	0.288138	+	0.713166i	0.0140597	+	0.0347989i
$421$	−1.03006	−	3.59226i	−0.0502023	−	0.175076i	0.932166	−	0.362030i	$-0.117916\pi$
$421$	−1.03006	−	3.59226i	−0.0502023	−	0.175076i	−0.982369	+	0.186954i	$0.940138\pi$
$422$	−9.77772	+	9.44223i	−0.475972	+	0.459641i
$423$	−32.1152	+	17.0759i	−1.56149	+	0.830260i
$424$	0.0423831	−	0.0331133i	0.00205830	−	0.00160812i
$425$	−0.600560	−	1.34888i	−0.0291314	−	0.0654302i
$426$	−0.705155	−	0.313955i	−0.0341649	−	0.0152112i
$427$	4.44833	−	2.77962i	0.215270	−	0.134515i
$428$	8.55367	+	7.17738i	0.413457	+	0.346932i
$429$	0.781516	+	0.370852i	0.0377319	+	0.0179049i
$430$	−2.19847	−	1.26929i	−0.106020	−	0.0612105i
$431$	0.488204	+	13.9803i	0.0235159	+	0.673408i	0.952721	+	0.303845i	$0.0982705\pi$
$431$	0.488204	+	13.9803i	0.0235159	+	0.673408i	−0.929206	+	0.369563i	$0.879507\pi$
$432$	−0.265205	+	0.274627i	−0.0127597	+	0.0132130i
$433$	20.8396	+	21.5800i	1.00149	+	1.03707i	0.999313	+	0.0370724i	$0.0118032\pi$
$433$	20.8396	+	21.5800i	1.00149	+	1.03707i	0.00217434	+	0.999998i	$0.499308\pi$
$434$	−1.29629	+	37.1209i	−0.0622239	+	1.78186i
$435$	0.445315	−	0.712652i	0.0213512	−	0.0341691i
$436$	0.232108	+	0.168636i	0.0111159	+	0.00807621i
$437$	−37.6015	−	2.52768i	−1.79872	−	0.120916i
$438$	−0.153650	+	0.472886i	−0.00734168	+	0.0225954i
$439$	−9.97487	+	8.36991i	−0.476075	+	0.399474i	−0.849005	−	0.528385i	$-0.822798\pi$
$439$	−9.97487	+	8.36991i	−0.476075	+	0.399474i	0.372930	+	0.927859i	$0.378353\pi$
$440$	7.69477	+	6.31734i	0.366834	+	0.301167i
$441$	−4.78369	+	27.1296i	−0.227795	+	1.29189i
$442$	0.209876	−	1.49334i	0.00998277	−	0.0710311i
$443$	−1.30828	+	1.93961i	−0.0621585	+	0.0921538i	−0.858835	−	0.512252i	$-0.828812\pi$
$443$	−1.30828	+	1.93961i	−0.0621585	+	0.0921538i	0.796677	+	0.604405i	$0.206589\pi$
$444$	0.223850	−	0.0996646i	0.0106235	−	0.00472987i
$445$	−12.4789	−	11.2361i	−0.591557	−	0.532640i
$446$	−9.00448	−	3.63805i	−0.426375	−	0.172267i
$447$	0.0965275	+	0.387151i	0.00456560	+	0.0183116i
$448$	−1.63684	+	3.67640i	−0.0773333	+	0.173694i
$449$	4.95744	−	4.46370i	0.233956	−	0.210655i	−0.543811	−	0.839208i	$-0.683019\pi$
$449$	4.95744	−	4.46370i	0.233956	−	0.210655i	0.777767	+	0.628553i	$0.216352\pi$
$450$	11.2913	−	4.10970i	0.532277	−	0.193733i
$451$	30.7947	+	15.9527i	1.45007	+	0.751184i
$452$	−4.92695	−	0.868755i	−0.231744	−	0.0408628i
$453$	0.205901	+	0.160867i	0.00967405	+	0.00755820i
$454$	−4.22360	+	16.9399i	−0.198223	+	0.795031i
$455$	29.0857	−	40.0331i	1.36356	−	1.87678i
$456$	−0.277398	−	0.00893958i	−0.0129904	−	0.000418634i
$457$	24.5476	−	7.97600i	1.14829	−	0.373102i	0.327790	−	0.944750i	$-0.393696\pi$
$457$	24.5476	−	7.97600i	1.14829	−	0.373102i	0.820498	+	0.571649i	$0.193696\pi$
$458$	5.62630	−	0.393429i	0.262900	−	0.0183837i
$459$	−0.135104	+	0.0387406i	−0.00630614	+	0.00180826i
$460$	−22.9151	−	12.1842i	−1.06842	−	0.568091i
$461$	−0.962167	+	0.169656i	−0.0448126	+	0.00790167i	−0.196010	−	0.980602i	$-0.562798\pi$
$461$	−0.962167	+	0.169656i	−0.0448126	+	0.00790167i	0.151197	+	0.988504i	$0.451687\pi$
$462$	−0.271268	−	0.805391i	−0.0126205	−	0.0374702i
$463$	−8.31716	+	14.4057i	−0.386531	+	0.669491i	−0.991980	−	0.126393i	$-0.959660\pi$
$463$	−8.31716	+	14.4057i	−0.386531	+	0.669491i	0.605449	+	0.795884i	$0.292993\pi$
$464$	4.30060	−	0.914121i	0.199650	−	0.0424370i
$465$	−1.75980	−	0.123057i	−0.0816088	−	0.00570665i
$466$	−14.7123	+	3.66818i	−0.681533	+	0.169925i
$467$	15.5332	−	17.2514i	0.718793	−	0.798300i	−0.267456	−	0.963570i	$-0.586183\pi$
$467$	15.5332	−	17.2514i	0.718793	−	0.798300i	0.986248	+	0.165270i	$0.0528496\pi$
$468$	12.0040	+	2.55154i	0.554887	+	0.117945i
$469$	7.57762	+	2.17285i	0.349902	+	0.100333i
$470$	−26.2153	−	25.3159i	−1.20922	−	1.16773i
$471$	−0.158822	+	0.298701i	−0.00731814	+	0.0137634i
$472$	−3.52559	+	9.68648i	−0.162278	+	0.445856i
$473$	2.34199	+	1.54342i	0.107685	+	0.0709665i
$474$		−	0.273672i		−	0.0125702i
$475$	15.4581	+	8.16592i	0.709266	+	0.374678i
$476$	−1.19858	+	0.870822i	−0.0549370	+	0.0399141i
$477$	0.0112403	+	0.160744i	0.000514659	+	0.00735996i
$478$	−11.7186	−	0.409224i	−0.535998	−	0.0187174i
$479$	−5.43591	−	38.6785i	−0.248373	−	1.76727i	−0.571201	−	0.820810i	$-0.693522\pi$
$479$	−5.43591	−	38.6785i	−0.248373	−	1.76727i	0.322828	−	0.946458i	$-0.395366\pi$
$480$	−0.171788	−	0.0837866i	−0.00784101	−	0.00382432i
$481$	−13.0689	−	8.81508i	−0.595890	−	0.401933i
$482$	7.42057	+	8.24137i	0.337998	+	0.375384i
$483$	1.10770	+	1.91859i	0.0504021	+	0.0872990i
$484$	−8.07476	−	7.46982i	−0.367034	−	0.339537i
$485$	−30.3258	+	36.1408i	−1.37702	+	1.64107i
$486$	−0.356789	−	1.67856i	−0.0161843	−	0.0761411i
$487$	15.7562	−	1.65605i	0.713983	−	0.0750426i	0.259430	−	0.965762i	$-0.416465\pi$
$487$	15.7562	−	1.65605i	0.713983	−	0.0750426i	0.454554	+	0.890719i	$0.349799\pi$
$488$	−0.359271	+	1.25293i	−0.0162634	+	0.0567173i
$489$	−0.195470	−	0.367626i	−0.00883946	−	0.0166246i
$490$	−27.3333	+	3.84144i	−1.23479	+	0.173539i
$491$	14.8337	−	10.0054i	0.669434	−	0.451539i	−0.176874	−	0.984234i	$-0.556598\pi$
$491$	14.8337	−	10.0054i	0.669434	−	0.451539i	0.846308	+	0.532695i	$0.178821\pi$
$492$	−0.646037	−	0.161075i	−0.0291256	−	0.00726183i
$493$	1.53939	+	0.500179i	0.0693308	+	0.0225269i
$494$	8.96920	+	15.4390i	0.403543	+	0.694634i
$495$	−28.5818	+	8.52838i	−1.28466	+	0.383322i
$496$	−5.93278	−	7.07041i	−0.266390	−	0.317471i
$497$	30.0356	−	38.4438i	1.34728	−	1.72444i
$498$	0.294493	+	0.603799i	0.0131965	+	0.0270569i
$499$	9.63770	−	19.7602i	0.431443	−	0.884589i	−0.566715	−	0.823914i	$-0.691786\pi$
$499$	9.63770	−	19.7602i	0.431443	−	0.884589i	0.998158	−	0.0606747i	$-0.0193252\pi$
$500$	−1.82824	−	2.34004i	−0.0817613	−	0.104650i
$501$	−0.0624392	+	0.293753i	−0.00278958	+	0.0131239i
$502$	0.694048	−	6.60343i	0.0309769	−	0.294725i
$503$	0.897598	−	12.8362i	0.0400219	−	0.572340i	−0.935625	−	0.352995i	$-0.885163\pi$
$503$	0.897598	−	12.8362i	0.0400219	−	0.572340i	0.975647	−	0.219345i	$-0.0703922\pi$
$504$	−6.38905	−	10.2246i	−0.284591	−	0.455440i
$505$	23.5438	−	13.5930i	1.04769	−	0.604882i
$506$	24.4793	+	14.9339i	1.08824	+	0.663891i
$507$	0.0823060	+	0.226134i	0.00365534	+	0.0100430i
$508$	−14.8558	−	2.08785i	−0.659121	−	0.0926335i
$509$	−19.4482	+	9.48552i	−0.862026	+	0.420438i	−0.815691	−	0.578488i	$-0.803643\pi$
$509$	−19.4482	+	9.48552i	−0.862026	+	0.420438i	−0.0463350	+	0.998926i	$0.514754\pi$
$510$	−0.0393471	−	0.0583344i	−0.00174232	−	0.00258309i
$511$	−26.6508	−	16.6533i	−1.17896	−	0.736698i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	0.974523	−	1.34894i	0.0430262	−	0.0595569i
$514$	−1.89828	−	2.61276i	−0.0837297	−	0.115244i
$515$	4.56296	−	1.84355i	0.201068	−	0.0812367i
$516$	−0.0505997	−	0.0184168i	−0.00222753	−	0.000810754i
$517$	27.2624	+	29.6328i	1.19900	+	1.30325i
$518$	2.68929	+	15.2517i	0.118161	+	0.670123i
$519$	−0.443586	+	0.0154904i	−0.0194713	+	0.000679952i
$520$	1.28530	+	12.2288i	0.0563640	+	0.536268i
$521$	−37.5955	−	3.95145i	−1.64709	−	0.173116i	−0.764945	−	0.644096i	$-0.777234\pi$
$521$	−37.5955	−	3.95145i	−1.64709	−	0.173116i	−0.882144	+	0.470980i	$0.843900\pi$
$522$	−4.93440	+	12.2131i	−0.215973	+	0.534551i
$523$	−8.07672	+	19.9906i	−0.353170	+	0.874128i	0.641122	+	0.767439i	$0.278469\pi$
$523$	−8.07672	+	19.9906i	−0.353170	+	0.874128i	−0.994292	+	0.106689i	$0.965975\pi$
$524$	14.6640	+	1.54125i	0.640599	+	0.0673296i
$525$	−0.107425	−	1.02208i	−0.00468839	−	0.0446071i
$526$	−3.75434	+	0.131104i	−0.163697	+	0.00571642i
$527$	−0.590037	−	3.34626i	−0.0257024	−	0.145766i
$528$	0.184007	+	0.103622i	0.00800788	+	0.00450957i
$529$	−48.6297	−	17.6997i	−2.11433	−	0.769554i
$530$	−0.149695	+	0.0604805i	−0.00650232	+	0.00262711i
$531$	−18.1524	−	24.9846i	−0.787745	−	1.08424i
$532$	4.78972	−	16.8750i	0.207661	−	0.731625i
$533$	13.2365	+	40.7377i	0.573335	+	1.76454i
$534$	−0.302062	−	0.188749i	−0.0130715	−	0.00816797i
$535$	−18.7431	−	27.7877i	−0.810333	−	1.20137i
$536$	−1.76059	+	0.858698i	−0.0760460	+	0.0370901i
$537$	1.55338	+	0.218313i	0.0670332	+	0.00942090i
$538$	5.63482	+	15.4815i	0.242934	+	0.667457i
$539$	30.3980	−	2.45340i	1.30934	−	0.105676i
$540$	0.992478	−	0.573007i	0.0427094	−	0.0246583i
$541$	−10.1665	−	16.2698i	−0.437093	−	0.699495i	0.554022	−	0.832502i	$-0.313092\pi$
$541$	−10.1665	−	16.2698i	−0.437093	−	0.699495i	−0.991115	+	0.133007i	$0.957537\pi$
$542$	1.14374	−	16.3562i	0.0491278	−	0.702560i
$543$	0.0113779	−	0.108254i	0.000488274	−	0.00464561i
$544$	0.0765415	−	0.360100i	0.00328169	−	0.0154391i
$545$	−0.530218	−	0.678648i	−0.0227120	−	0.0290701i
$546$	0.460124	−	0.943395i	0.0196915	−	0.0403736i
$547$	6.89746	+	14.1419i	0.294914	+	0.604664i	0.993877	−	0.110494i	$-0.0352434\pi$
$547$	6.89746	+	14.1419i	0.294914	+	0.604664i	−0.698962	+	0.715158i	$0.746355\pi$
$548$	−7.47154	+	9.56314i	−0.319169	+	0.408517i
$549$	−2.51007	−	2.99138i	−0.107127	−	0.127669i
$550$	−7.55626	−	10.9476i	−0.322200	−	0.466806i
$551$	−17.9912	+	6.60315i	−0.766451	+	0.281304i
$552$	−0.523559	−	0.170115i	−0.0222842	−	0.00724056i
$553$	16.7832	+	4.18453i	0.713695	+	0.177944i
$554$	−7.84237	+	5.28975i	−0.333190	+	0.224740i
$555$	−0.728385	+	0.102368i	−0.0309182	+	0.00434527i
$556$	2.70911	+	5.09510i	0.114892	+	0.216080i
$557$	−8.12629	+	28.3397i	−0.344322	+	1.20079i	0.578537	+	0.815656i	$0.303624\pi$
$557$	−8.12629	+	28.3397i	−0.344322	+	1.20079i	−0.922859	+	0.385137i	$0.874154\pi$
$558$	27.5004	−	2.89041i	1.16418	−	0.122361i
$559$	0.720241	+	3.38847i	0.0304630	+	0.143317i
$560$	7.76498	−	9.25394i	0.328130	−	0.391050i
$561$	0.0395916	+	0.0669076i	0.00167156	+	0.00282484i
$562$	4.54617	+	7.87420i	0.191769	+	0.332153i
$563$	−9.49719	−	10.5477i	−0.400259	−	0.444532i	0.508998	−	0.860768i	$-0.330016\pi$
$563$	−9.49719	−	10.5477i	−0.400259	−	0.444532i	−0.909257	+	0.416235i	$0.863349\pi$
$564$	−0.640866	−	0.432270i	−0.0269853	−	0.0182018i
$565$	13.4979	+	6.58338i	0.567863	+	0.276965i
$566$	0.496326	+	3.53154i	0.0208621	+	0.148442i
$567$	36.0501	+	1.25890i	1.51396	+	0.0528688i
$568$	0.845642	+	12.0932i	0.0354824	+	0.507421i
$569$	−11.0443	+	8.02412i	−0.462999	+	0.336389i	−0.794707	−	0.606994i	$-0.792375\pi$
$569$	−11.0443	+	8.02412i	−0.462999	+	0.336389i	0.331707	+	0.943382i	$0.392375\pi$
$570$	0.793037	+	0.255316i	0.0332167	+	0.0106940i
$571$		−	15.3279i		−	0.641453i	−0.947172	−	0.320727i	$-0.896073\pi$
$571$		−	15.3279i		−	0.641453i	0.947172	−	0.320727i	$-0.103927\pi$
$572$	−0.619680	−	13.5717i	−0.0259101	−	0.567459i
$573$	−0.470315	+	1.29218i	−0.0196477	+	0.0539816i
$574$	19.7562	−	37.1560i	0.824607	−	1.55086i
$575$	24.9440	+	24.0881i	1.04024	+	1.00454i
$576$	2.87989	+	0.825795i	0.119995	+	0.0344081i
$577$	39.4735	+	8.39036i	1.64330	+	0.349295i	0.934460	−	0.356069i	$-0.115883\pi$
$577$	39.4735	+	8.39036i	1.64330	+	0.349295i	0.708845	+	0.705364i	$0.249217\pi$
$578$	−11.2845	+	12.5327i	−0.469375	+	0.521293i
$579$	−1.42723	+	0.355848i	−0.0593136	+	0.0147885i
$580$	−13.1658	−	0.920640i	−0.546678	−	0.0382275i
$581$	−41.5315	+	8.82778i	−1.72301	+	0.366238i
$582$	−0.500364	+	0.866656i	−0.0207408	+	0.0359241i
$583$	0.169053	−	0.0569395i	0.00700145	−	0.00235819i
$584$	7.69040	−	1.35603i	0.318231	−	0.0561127i
$585$	−32.5265	−	17.2947i	−1.34481	−	0.715047i
$586$	28.6161	−	8.20552i	1.18212	−	0.338967i
$587$	28.0883	−	1.96412i	1.15933	−	0.0810680i	0.522892	−	0.852399i	$-0.324853\pi$
$587$	28.0883	−	1.96412i	1.15933	−	0.0810680i	0.636434	+	0.771331i	$0.280409\pi$
$588$	−0.556823	+	0.180923i	−0.0229630	+	0.00746113i
$589$	29.9702	+	26.8396i	1.23490	+	1.10591i
$590$	18.1878	−	25.0333i	0.748778	−	1.03060i
$591$	0.170412	−	0.683486i	0.00700982	−	0.0281149i
$592$	−3.03255	−	2.36929i	−0.124637	−	0.0973771i
$593$	14.4383	+	2.54587i	0.592912	+	0.104546i	0.462049	−	0.886854i	$-0.347114\pi$
$593$	14.4383	+	2.54587i	0.592912	+	0.104546i	0.130862	+	0.991401i	$0.458225\pi$
$594$	−1.13205	+	0.567240i	−0.0464484	+	0.0232741i
$595$	4.17904	−	1.52105i	0.171324	−	0.0623568i
$596$	4.65691	−	4.19310i	0.190754	−	0.171756i
$597$	0.406670	−	0.913396i	0.0166439	−	0.0373828i
$598$	8.56784	+	34.3637i	0.350365	+	1.40524i
$599$	−19.6096	−	7.92278i	−0.801226	−	0.323716i	−0.0627784	−	0.998027i	$-0.519996\pi$
$599$	−19.6096	−	7.92278i	−0.801226	−	0.323716i	−0.738447	+	0.674311i	$0.764441\pi$
$600$	0.189780	+	0.170879i	0.00774773	+	0.00697609i
$601$	−7.95521	+	3.54189i	−0.324500	+	0.144477i	−0.562520	−	0.826783i	$-0.690168\pi$
$601$	−7.95521	+	3.54189i	−0.324500	+	0.144477i	0.238020	+	0.971260i	$0.423502\pi$
$602$	1.90311	−	2.82148i	0.0775650	−	0.114995i
$603$	0.816748	−	5.81146i	0.0332605	−	0.236661i
$604$	0.712596	−	4.04133i	0.0289951	−	0.164440i
$605$	17.1192	+	28.2353i	0.695994	+	1.14793i
$606$	0.441746	−	0.370669i	0.0179447	−	0.0150574i
$607$	10.1368	−	31.1979i	0.411440	−	1.26628i	−0.503956	−	0.863729i	$-0.668123\pi$
$607$	10.1368	−	31.1979i	0.411440	−	1.26628i	0.915396	−	0.402554i	$-0.131877\pi$
$608$	1.92135	+	3.91260i	0.0779211	+	0.158677i
$609$	0.911438	+	0.662199i	0.0369333	+	0.0268336i
$610$	2.07335	−	3.31806i	0.0839477	−	0.134344i
$611$	−1.73560	+	49.7010i	−0.0702148	+	2.01069i
$612$	0.766167	+	0.793389i	0.0309705	+	0.0320709i
$613$	19.2484	−	19.9323i	0.777434	−	0.805057i	−0.207454	−	0.978245i	$-0.566518\pi$
$613$	19.2484	−	19.9323i	0.777434	−	0.805057i	0.984889	+	0.173188i	$0.0554068\pi$
$614$	0.601703	+	17.2305i	0.0242828	+	0.695367i
$615$	1.73087	+	0.999318i	0.0697954	+	0.0402964i
$616$	−9.16824	+	9.70000i	−0.369399	+	0.390824i
$617$	32.5199	+	27.2874i	1.30920	+	1.09855i	0.988476	+	0.151379i	$0.0483713\pi$
$617$	32.5199	+	27.2874i	1.30920	+	1.09855i	0.320726	+	0.947172i	$0.396073\pi$
$618$	0.0885264	−	0.0553174i	0.00356106	−	0.00222519i
$619$	42.0553	+	18.7242i	1.69035	+	0.752591i	0.999564	+	0.0295280i	$0.00940041\pi$
$619$	42.0553	+	18.7242i	1.69035	+	0.752591i	0.690782	+	0.723063i	$0.257266\pi$
$620$	11.2690	+	25.3105i	0.452573	+	1.01649i
$621$	2.60105	−	2.03217i	0.104377	−	0.0815480i
$622$	−12.6981	+	6.75170i	−0.509147	+	0.270719i
$623$	16.1938	−	15.6382i	0.648792	−	0.626531i
$624$	0.0718917	+	0.250716i	0.00287797	+	0.0100367i
$625$	10.8515	+	26.8584i	0.434059	+	1.07433i
$626$	25.9030			1.03529
$627$	−0.858024	−	0.333348i	−0.0342662	−	0.0133127i
$628$	5.31312			0.212016
$629$	−0.530725	−	1.31359i	−0.0211614	−	0.0523763i
$630$	9.97573	+	34.7895i	0.397443	+	1.38605i
$631$	−9.48565	+	9.16019i	−0.377618	+	0.364661i	−0.859112	−	0.511788i	$-0.828983\pi$
$631$	−9.48565	+	9.16019i	−0.377618	+	0.364661i	0.481494	+	0.876449i	$0.340094\pi$
$632$	−3.79502	+	2.01785i	−0.150958	+	0.0802656i
$633$	0.682005	−	0.532841i	0.0271073	−	0.0211785i
$634$	2.88637	+	6.48289i	0.114632	+	0.257468i
$635$	41.1391	+	18.3163i	1.63256	+	0.726861i
$636$	−0.00290424	+	0.00181477i	−0.000115161	+	7.19604e-5i
$637$	28.8537	+	24.2111i	1.14323	+	0.959280i
$638$	14.4612	+	1.87451i	0.572523	+	0.0742124i
$639$	−31.4533	−	18.1596i	−1.24427	−	0.718382i
$640$	0.104761	+	2.99996i	0.00414104	+	0.118584i
$641$	17.6935	−	18.3222i	0.698853	−	0.723684i	−0.272281	−	0.962218i	$-0.587778\pi$
$641$	17.6935	−	18.3222i	0.698853	−	0.723684i	0.971134	+	0.238534i	$0.0766669\pi$
$642$	−0.493881	−	0.511429i	−0.0194919	−	0.0201845i
$643$	0.437278	−	12.5220i	0.0172446	−	0.493819i	−0.959788	−	0.280727i	$-0.909424\pi$
$643$	0.437278	−	12.5220i	0.0172446	−	0.493819i	0.977032	−	0.213092i	$-0.0683534\pi$
$644$	18.4378	−	29.5067i	0.726552	−	1.16273i
$645$	0.130768	+	0.0950082i	0.00514897	+	0.00374095i
$646$	−0.107630	+	1.60109i	−0.00423465	+	0.0629941i
$647$	−3.04556	+	9.37327i	−0.119733	+	0.368501i	−0.992905	−	0.118912i	$-0.962059\pi$
$647$	−3.04556	+	9.37327i	−0.119733	+	0.368501i	0.873172	+	0.487413i	$0.162059\pi$
$648$	−6.86646	+	5.76165i	−0.269740	+	0.226339i
$649$	−21.6937	+	26.4238i	−0.851553	+	1.03723i
$650$	2.85288	−	16.1795i	0.111899	−	0.634612i
$651$	0.329147	−	2.34201i	0.0129003	−	0.0917904i
$652$	−3.65663	+	5.42117i	−0.143205	+	0.212309i
$653$	6.75129	−	3.00587i	0.264198	−	0.117629i	−0.270363	−	0.962759i	$-0.587144\pi$
$653$	6.75129	−	3.00587i	0.264198	−	0.117629i	0.534561	+	0.845130i	$0.320477\pi$
$654$	−0.0135756	−	0.0122235i	−0.000530846	−	0.000477976i
$655$	−41.0377	−	16.5803i	−1.60348	−	0.647847i
$656$	2.52974	+	10.1462i	0.0987698	+	0.396144i
$657$	−9.51579	+	21.3728i	−0.371246	+	0.833833i
$658$	36.3084	−	32.6922i	1.41545	−	1.27448i
$659$	−33.1656	+	12.0713i	−1.29195	+	0.470230i	−0.894366	−	0.447336i	$-0.852373\pi$
$659$	−33.1656	+	12.0713i	−1.29195	+	0.470230i	−0.397582	+	0.917567i	$0.630150\pi$
$660$	−0.445216	−	0.451250i	−0.0173300	−	0.0175649i
$661$	31.8536	+	5.61665i	1.23896	+	0.218462i	0.754471	−	0.656334i	$-0.227894\pi$
$661$	31.8536	+	5.61665i	1.23896	+	0.218462i	0.484491	+	0.874796i	$0.339005\pi$
$662$	−8.37296	−	6.54167i	−0.325424	−	0.254249i
$663$	−0.0232292	+	0.0931673i	−0.000902148	+	0.00361832i
$664$	6.20153	−	8.53568i	0.240666	−	0.331248i
$665$	−27.7833	+	44.7299i	−1.07739	+	1.73455i
$666$	10.9652	−	3.56280i	0.424892	−	0.138056i
$667$	−37.9204	+	2.65165i	−1.46828	+	0.102672i
$668$	4.53386	−	1.30006i	0.175420	−	0.0503010i
$669$	0.545984	+	0.290305i	0.0211090	+	0.0112238i
$670$	5.79069	−	1.02105i	0.223714	−	0.0394468i
$671$	−2.50332	+	3.52438i	−0.0966397	+	0.136057i
$672$	0.128119	−	0.221909i	0.00494231	−	0.00856033i
$673$	−21.8836	+	4.65151i	−0.843551	+	0.179302i	−0.609365	−	0.792890i	$-0.708576\pi$
$673$	−21.8836	+	4.65151i	−0.843551	+	0.179302i	−0.234186	+	0.972192i	$0.575242\pi$
$674$	−19.0442	−	1.33170i	−0.733554	−	0.0512951i
$675$	−1.48573	+	0.370433i	−0.0571856	+	0.0142580i
$676$	2.52894	−	2.80867i	0.0972670	−	0.108026i
$677$	−15.6937	−	3.33580i	−0.603158	−	0.128205i	−0.103796	−	0.994599i	$-0.533099\pi$
$677$	−15.6937	−	3.33580i	−0.603158	−	0.128205i	−0.499362	+	0.866393i	$0.666432\pi$
$678$	0.306211	+	0.0878046i	0.0117600	+	0.00337212i
$679$	−45.4978	−	43.9367i	−1.74605	−	1.68614i
$680$	−0.518809	+	0.975738i	−0.0198954	+	0.0374179i
$681$	0.380199	−	1.04459i	0.0145693	−	0.0400288i
$682$	−10.7776	−	28.6516i	−0.412696	−	1.09713i
$683$		−	5.19873i		−	0.198924i	−0.995041	−	0.0994619i	$-0.968288\pi$
$683$		−	5.19873i		−	0.198924i	0.995041	−	0.0994619i	$-0.0317121\pi$
$684$	−12.9368	−	1.78266i	−0.494650	−	0.0681616i
$685$	29.4718	−	21.4125i	1.12606	−	0.818130i
$686$	−0.616227	−	8.81246i	−0.0235277	−	0.336461i
$687$	−0.358897	−	0.0125330i	−0.0136928	−	0.000478162i
$688$	0.117697	+	0.837458i	0.00448716	+	0.0319278i
$689$	0.198020	+	0.0965808i	0.00754396	+	0.00367944i
$690$	1.36998	+	0.924063i	0.0521542	+	0.0351785i
$691$	14.2712	+	15.8497i	0.542901	+	0.602953i	0.950697	−	0.310120i	$-0.100369\pi$
$691$	14.2712	+	15.8497i	0.542901	+	0.602953i	−0.407796	+	0.913073i	$0.633703\pi$
$692$	3.48546	+	6.03700i	0.132497	+	0.229492i
$693$	−8.73271	−	39.0222i	−0.331728	−	1.48233i
$694$	−4.32999	+	5.16028i	−0.164364	+	0.195881i
$695$	−3.60145	−	16.9435i	−0.136611	−	0.642702i
$696$	−0.278414	+	0.0292625i	−0.0105533	+	0.00110919i
$697$	−1.06110	+	3.70051i	−0.0401921	+	0.140167i
$698$	−7.50797	−	14.1204i	−0.284181	−	0.534466i
$699$	0.956050	−	0.134364i	0.0361611	−	0.00508212i
$700$	−13.3811	+	9.02565i	−0.505757	+	0.341138i
$701$	24.6362	+	6.14249i	0.930496	+	0.231999i	0.677546	−	0.735480i	$-0.263043\pi$
$701$	24.6362	+	6.14249i	0.930496	+	0.231999i	0.252950	+	0.967479i	$0.418599\pi$
$702$	−1.48732	−	0.483260i	−0.0561353	−	0.0182395i
$703$	14.5498	+	8.34818i	0.548755	+	0.314858i
$704$	0.0802048	−	3.31565i	0.00302283	−	0.124963i
$705$	1.49156	+	1.77757i	0.0561754	+	0.0669473i
$706$	−14.8987	+	19.0695i	−0.560720	+	0.717688i
$707$	15.9772	+	32.7581i	0.600884	+	1.23200i
$708$	0.287723	−	0.589919i	0.0108133	−	0.0221705i
$709$	12.2195	+	15.6402i	0.458913	+	0.587382i	0.960693	−	0.277614i	$-0.0895435\pi$
$709$	12.2195	+	15.6402i	0.458913	+	0.587382i	−0.501780	+	0.864995i	$0.667321\pi$
$710$	7.56591	−	35.5948i	0.283944	−	1.33585i
$711$	1.34601	−	12.8064i	0.0504792	−	0.480277i
$712$	−0.390218	+	5.58038i	−0.0146240	+	0.209133i
$713$	42.2871	+	67.6735i	1.58366	+	2.53439i
$714$	0.0816946	−	0.0471664i	0.00305734	−	0.00176516i
$715$	−9.44117	+	39.6738i	−0.353080	+	1.48372i
$716$	−8.42604	−	23.1504i	−0.314896	−	0.865170i
$717$	0.739344	+	0.103908i	0.0276113	+	0.00388051i
$718$	−14.4335	+	7.03971i	−0.538655	+	0.262719i
$719$	−17.2610	−	25.5905i	−0.643726	−	0.954363i	−0.999802	−	0.0199058i	$-0.993663\pi$
$719$	−17.2610	−	25.5905i	−0.643726	−	0.954363i	0.356076	−	0.934457i	$-0.384114\pi$
$720$	−7.62666	−	4.76567i	−0.284229	−	0.177606i
$721$	2.03880	+	6.27479i	0.0759290	+	0.233685i
$722$	−10.7093	−	15.6943i	−0.398559	−	0.584081i
$723$	−0.415047	−	0.571263i	−0.0154358	−	0.0212455i
$724$	−1.58505	+	0.640401i	−0.0589078	+	0.0238003i
$725$	16.5705	+	6.03116i	0.615412	+	0.223992i
$726$	0.461608	+	0.526759i	0.0171319	+	0.0195499i
$727$	−5.24135	−	29.7252i	−0.194391	−	1.10245i	−0.913284	−	0.407324i	$-0.866462\pi$
$727$	−5.24135	−	29.7252i	−0.194391	−	1.10245i	0.718893	−	0.695121i	$-0.244649\pi$
$728$	−16.4747	+	0.575308i	−0.610592	+	0.0213223i
$729$	−2.79941	−	26.6346i	−0.103682	−	0.986467i
$730$	−23.3127	−	2.45026i	−0.862841	−	0.0906883i
$731$	−0.116628	+	0.288665i	−0.00431365	+	0.0106767i
$732$	0.0310893	−	0.0769488i	0.00114909	−	0.00284411i
$733$	42.1041	+	4.42532i	1.55515	+	0.163453i	0.842743	−	0.538315i	$-0.180939\pi$
$733$	42.1041	+	4.42532i	1.55515	+	0.163453i	0.712405	+	0.701768i	$0.247606\pi$
$734$	−0.0416542	−	0.396313i	−0.00153748	−	0.0146282i
$735$	1.75641	−	0.0613353i	0.0647862	−	0.00226239i
$736$	1.50133	+	8.51449i	0.0553399	+	0.313848i
$737$	−6.45349	+	0.748327i	−0.237717	+	0.0275650i
$738$	−29.4389	−	10.7149i	−1.08366	−	0.394420i
$739$	−45.4211	+	18.3513i	−1.67084	+	0.675063i	−0.997909	−	0.0646409i	$-0.979410\pi$
$739$	−45.4211	+	18.3513i	−1.67084	+	0.675063i	−0.672932	+	0.739704i	$0.734965\pi$
$740$	6.79007	+	9.34574i	0.249608	+	0.343556i
$741$	−0.465207	−	1.03735i	−0.0170898	−	0.0381080i
$742$	−0.0668859	−	0.205854i	−0.00245546	−	0.00755713i
$743$	−39.2758	−	24.5422i	−1.44089	−	0.900367i	−0.999996	−	0.00280706i	$-0.999106\pi$
$743$	−39.2758	−	24.5422i	−1.44089	−	0.900367i	−0.440892	−	0.897560i	$-0.645338\pi$
$744$	0.328628	+	0.487211i	0.0120481	+	0.0178620i
$745$	−16.9069	+	8.24605i	−0.619421	+	0.302112i
$746$	−16.5911	−	2.33173i	−0.607444	−	0.0853707i
$747$	10.8110	+	29.7030i	0.395554	+	1.08678i
$748$	0.635891	−	1.04234i	0.0232505	−	0.0381118i
$749$	38.9154	−	22.4678i	1.42194	−	0.820957i
$750$	0.100197	+	0.160348i	0.00365866	+	0.00585508i
$751$	0.554682	−	7.93233i	0.0202406	−	0.289455i	−0.976889	−	0.213746i	$-0.931434\pi$
$751$	0.554682	−	7.93233i	0.0202406	−	0.289455i	0.997130	−	0.0757089i	$-0.0241220\pi$
$752$	−1.26904	+	12.0741i	−0.0462772	+	0.440298i
$753$	−0.0878994	+	0.413534i	−0.00320323	+	0.0150700i
$754$	11.0881	+	14.1921i	0.403803	+	0.516845i
$755$	−5.40002	+	11.0717i	−0.196527	+	0.402940i
$756$	0.673510	+	1.38090i	0.0244953	+	0.0502229i
$757$	16.1512	−	20.6727i	0.587027	−	0.751360i	−0.399181	−	0.916872i	$-0.630705\pi$
$757$	16.1512	−	20.6727i	0.587027	−	0.751360i	0.986208	+	0.165512i	$0.0529276\pi$
$758$	−10.0697	−	12.0006i	−0.365749	−	0.435882i
$759$	−1.45073	−	1.10859i	−0.0526581	−	0.0402393i
$760$	−2.30677	−	12.8796i	−0.0836753	−	0.467190i
$761$	7.56852	+	2.45916i	0.274358	+	0.0891445i	0.442965	−	0.896539i	$-0.353927\pi$
$761$	7.56852	+	2.45916i	0.274358	+	0.0891445i	−0.168606	+	0.985683i	$0.553927\pi$
$762$	0.926831	+	0.231085i	0.0335756	+	0.00837133i
$763$	0.957191	−	0.645634i	0.0346527	−	0.0233735i
$764$	21.3864	−	3.00567i	0.773733	−	0.108741i
$765$	−1.55432	−	2.92326i	−0.0561967	−	0.105691i
$766$	5.22089	−	18.2074i	0.188639	−	0.657861i
$767$	−41.9936	+	4.41371i	−1.51630	+	0.159370i
$768$	0.0132383	+	0.0622811i	0.000477695	+	0.00224738i
$769$	−7.81330	+	9.31152i	−0.281755	+	0.335782i	−0.888297	−	0.459269i	$-0.848111\pi$
$769$	−7.81330	+	9.31152i	−0.281755	+	0.335782i	0.606543	+	0.795051i	$0.292556\pi$
$770$	34.4808	−	20.4035i	1.24260	−	0.735292i
$771$	0.102817	+	0.178084i	0.00370286	+	0.00641354i
$772$	15.4578	+	17.1677i	0.556339	+	0.617877i
$773$	−26.8065	−	18.0812i	−0.964163	−	0.650336i	−0.0271499	−	0.999631i	$-0.508643\pi$
$773$	−26.8065	−	18.0812i	−0.964163	−	0.650336i	−0.937013	+	0.349296i	$0.886421\pi$
$774$	−2.27722	−	1.11067i	−0.0818529	−	0.0399223i
$775$	−5.15193	−	36.6579i	−0.185063	−	1.31679i
$776$	15.7072	+	0.548508i	0.563857	+	0.0196903i
$777$	−0.0687867	−	0.983696i	−0.00246771	−	0.0352899i
$778$	12.8102	−	9.30717i	0.459269	−	0.333678i
$779$	−17.1884	−	42.2153i	−0.615838	−	1.51252i
$780$		−	0.782927i		−	0.0280333i
$781$	−10.6675	+	38.7658i	−0.381712	+	1.38715i
$782$	−1.08862	+	2.99097i	−0.0389291	+	0.106957i
$783$	0.788032	−	1.48207i	0.0281620	−	0.0529650i
$784$	6.61444	+	6.38749i	0.236230	+	0.228125i
$785$	−15.3310	−	4.39610i	−0.547188	−	0.156904i
$786$	−0.918320	−	0.195195i	−0.0327554	−	0.00696237i
$787$	9.85413	−	10.9441i	0.351262	−	0.390116i	−0.541458	−	0.840728i	$-0.682128\pi$
$787$	9.85413	−	10.9441i	0.351262	−	0.390116i	0.892720	+	0.450612i	$0.148794\pi$
$788$	−10.7344	+	2.67638i	−0.382397	+	0.0953423i
$789$	0.238611	+	0.0166853i	0.00849479	+	0.000594013i
$790$	12.6201	−	2.68249i	0.449004	−	0.0954386i
$791$	−10.0668	+	17.4361i	−0.357933	+	0.619957i
$792$	8.10090	+	5.75396i	0.287853	+	0.204458i
$793$	−5.25804	+	0.927134i	−0.186718	+	0.0329235i
$794$	−4.68263	−	2.48980i	−0.166180	−	0.0883596i
$795$	0.00988176	−	0.00283355i	0.000350470	−	0.000100496i
$796$	−15.6645	+	1.09537i	−0.555215	+	0.0388244i
$797$	18.8180	−	6.11434i	0.666567	−	0.216581i	0.0438624	−	0.999038i	$-0.486034\pi$
$797$	18.8180	−	6.11434i	0.666567	−	0.216581i	0.622705	+	0.782457i	$0.286034\pi$
$798$	−0.415616	+	1.03671i	−0.0147127	+	0.0366992i
$799$	−2.62711	+	3.61591i	−0.0929404	+	0.127922i
$800$	0.970286	−	3.89160i	0.0343048	−	0.137589i
$801$	−13.2065	−	10.3181i	−0.466630	−	0.364571i
$802$	6.76608	+	1.19304i	0.238919	+	0.0421278i
$803$	25.5529	+	4.22371i	0.901744	+	0.149051i
$804$	0.117202	−	0.0426582i	0.00413341	−	0.00150444i
$805$	−77.6164	+	69.8861i	−2.73562	+	2.46316i
$806$	15.3777	−	34.5390i	0.541658	−	1.21658i
$807$	−0.253779	−	1.01785i	−0.00893344	−	0.0358301i
$808$	−8.39715	−	3.39267i	−0.295411	−	0.119354i
$809$	21.5942	+	19.4435i	0.759211	+	0.683597i	0.954853	−	0.297079i	$-0.0960123\pi$
$809$	21.5942	+	19.4435i	0.759211	+	0.683597i	−0.195642	+	0.980675i	$0.562679\pi$
$810$	24.5804	−	10.9439i	0.863668	−	0.384530i
$811$	6.01242	−	8.91378i	0.211125	−	0.313005i	−0.708569	−	0.705641i	$-0.750659\pi$
$811$	6.01242	−	8.91378i	0.211125	−	0.313005i	0.919694	+	0.392636i	$0.128437\pi$
$812$	2.46248	−	17.5215i	0.0864161	−	0.614882i
$813$	−0.181286	+	1.02812i	−0.00635798	+	0.0360579i
$814$	−6.87932	−	10.7510i	−0.241120	−	0.376822i
$815$	15.0367	−	12.6173i	0.526713	−	0.441965i
$816$	−0.00724357	+	0.0222934i	−0.000253576	+	0.000780426i
$817$	−1.02561	−	3.54072i	−0.0358814	−	0.123874i
$818$	15.6661	+	11.3821i	0.547752	+	0.397965i
$819$	26.1713	−	41.8828i	0.914498	−	1.46350i
$820$	1.09547	−	31.3702i	0.0382555	−	1.09549i
$821$	−36.1644	−	37.4493i	−1.26215	−	1.30699i	−0.931728	−	0.363157i	$-0.881699\pi$
$821$	−36.1644	−	37.4493i	−1.26215	−	1.30699i	−0.330419	−	0.943834i	$-0.607190\pi$
$822$	0.536774	−	0.555846i	0.0187222	−	0.0193874i
$823$	1.20809	+	34.5952i	0.0421114	+	1.20591i	0.818066	+	0.575124i	$0.195046\pi$
$823$	1.20809	+	34.5952i	0.0421114	+	1.20591i	−0.775955	+	0.630788i	$0.782732\pi$
$824$	−1.41981	−	0.819729i	−0.0494615	−	0.0285566i
$825$	0.405628	+	0.743533i	0.0141222	+	0.0258865i
$826$	31.7780	+	26.6649i	1.10570	+	0.927791i
$827$	32.9275	−	20.5754i	1.14500	−	0.715475i	0.181555	−	0.983381i	$-0.441887\pi$
$827$	32.9275	−	20.5754i	1.14500	−	0.715475i	0.963445	+	0.267906i	$0.0863315\pi$
$828$	−23.6631	−	10.5355i	−0.822349	−	0.366133i
$829$	4.39599	+	9.87355i	0.152679	+	0.342922i	0.973650	−	0.228047i	$-0.0732341\pi$
$829$	4.39599	+	9.87355i	0.152679	+	0.342922i	−0.820971	+	0.570970i	$0.806567\pi$
$830$	−24.9570	+	19.4986i	−0.866271	+	0.676805i
$831$	0.531815	−	0.282771i	0.0184484	−	0.00980921i
$832$	2.94661	−	2.84551i	0.102155	−	0.0986503i
$833$	0.933072	+	3.25401i	0.0323290	+	0.112745i
$834$	−0.137640	−	0.340671i	−0.00476609	−	0.0117965i
$835$	−14.1582			−0.489963
$836$	1.70385	+	14.3561i	0.0589290	+	0.496515i
$837$	−3.52371			−0.121797
$838$	15.1829	+	37.5789i	0.524484	+	1.29814i
$839$	−11.4026	−	39.7657i	−0.393663	−	1.37287i	−0.869761	−	0.493473i	$-0.835727\pi$
$839$	−11.4026	−	39.7657i	−0.393663	−	1.37287i	0.476098	−	0.879392i	$-0.342051\pi$
$840$	−0.553298	+	0.534313i	−0.0190906	+	0.0184356i
$841$	8.53740	−	4.53942i	0.294393	−	0.156532i
$842$	2.94482	−	2.30074i	0.101485	−	0.0792889i
$843$	−0.235473	−	0.528881i	−0.00811012	−	0.0182156i
$844$	−12.4175	−	5.52862i	−0.427427	−	0.190303i
$845$	−9.62118	+	6.01198i	−0.330979	+	0.206819i
$846$	−27.8631	−	23.3799i	−0.957952	−	0.803817i
$847$	−39.3621	+	20.2542i	−1.35250	+	0.695944i
$848$	0.0465791	+	0.0268924i	0.00159953	+	0.000923490i
$849$	−0.00792470	−	0.226934i	−0.000271975	−	0.00778834i
$850$	1.02569	−	1.06213i	0.0351807	−	0.0364307i
$851$	23.1129	+	23.9341i	0.792300	+	0.820450i
$852$	0.0269385	−	0.771418i	0.000922898	−	0.0264283i
$853$	−8.26685	+	13.2297i	−0.283052	+	0.452977i	−0.958770	−	0.284182i	$-0.908278\pi$
$853$	−8.26685	+	13.2297i	−0.283052	+	0.452977i	0.675719	+	0.737160i	$0.263833\pi$
$854$	4.24359	+	3.08315i	0.145213	+	0.105503i
$855$	35.8542	+	15.8478i	1.22619	+	0.541984i
$856$	−3.45049	+	10.6195i	−0.117935	+	0.362968i
$857$	0.805615	−	0.675991i	0.0275193	−	0.0230914i	−0.628924	−	0.777467i	$-0.716504\pi$
$857$	0.805615	−	0.675991i	0.0275193	−	0.0230914i	0.656444	+	0.754375i	$0.272060\pi$
$858$	−0.0510870	+	0.863532i	−0.00174408	+	0.0294805i
$859$	4.68001	−	26.5417i	0.159680	−	0.905590i	−0.794702	−	0.607000i	$-0.792373\pi$
$859$	4.68001	−	26.5417i	0.159680	−	0.905590i	0.954382	−	0.298590i	$-0.0965162\pi$
$860$	0.353302	−	2.51387i	0.0120475	−	0.0857223i
$861$	−1.49833	+	2.22137i	−0.0510629	+	0.0757039i
$862$	−12.7794	+	5.68977i	−0.435270	+	0.193794i
$863$	−6.34745	−	5.71527i	−0.216070	−	0.194550i	0.553987	−	0.832525i	$-0.313106\pi$
$863$	−6.34745	−	5.71527i	−0.216070	−	0.194550i	−0.770057	+	0.637975i	$0.779772\pi$
$864$	−0.353978	−	0.143016i	−0.0120426	−	0.00486551i
$865$	−5.06228	−	20.3037i	−0.172123	−	0.690346i
$866$	−12.2020	+	27.4062i	−0.414641	+	0.931299i
$867$	0.797992	−	0.718515i	0.0271012	−	0.0244020i
$868$	−34.9035	+	12.7038i	−1.18470	+	0.431196i
$869$	−14.0944	+	2.13518i	−0.478121	+	0.0724311i
$870$	0.827578	+	0.145924i	0.0280575	+	0.00494730i
$871$	−6.32295	−	4.94003i	−0.214245	−	0.167386i
$872$	−0.0694076	+	0.278379i	−0.00235044	+	0.00942710i
$873$	−27.6769	+	38.0939i	−0.936720	+	1.28928i
$874$	−11.7421	−	35.8104i	−0.397184	−	1.21130i
$875$	−11.3655	+	3.69288i	−0.384225	+	0.124842i
$876$	−0.496010	+	0.0346844i	−0.0167586	+	0.00117188i
$877$	−13.4373	+	3.85308i	−0.453745	+	0.130109i	−0.494723	−	0.869051i	$-0.664731\pi$
$877$	−13.4373	+	3.85308i	−0.453745	+	0.130109i	0.0409777	+	0.999160i	$0.486953\pi$
$878$	−11.4971	−	6.11312i	−0.388008	−	0.206308i
$879$	−1.86669	+	0.329147i	−0.0629618	+	0.0111019i
$880$	−2.97482	+	9.50098i	−0.100281	+	0.320278i
$881$	−10.6461	+	18.4395i	−0.358675	+	0.621244i	−0.987740	−	0.156109i	$-0.950105\pi$
$881$	−10.6461	+	18.4395i	−0.358675	+	0.621244i	0.629064	+	0.777353i	$0.283438\pi$
$882$	−26.9462	+	5.72759i	−0.907325	+	0.192858i
$883$	14.1221	+	0.987516i	0.475248	+	0.0332325i	0.305372	−	0.952233i	$-0.401219\pi$
$883$	14.1221	+	0.987516i	0.475248	+	0.0332325i	0.169875	+	0.985466i	$0.445664\pi$
$884$	1.46323	−	0.364823i	0.0492136	−	0.0122703i
$885$	−1.31833	+	1.46415i	−0.0443151	+	0.0492169i
$886$	−2.28847	−	0.486429i	−0.0768826	−	0.0163419i
$887$	5.43359	+	1.55806i	0.182442	+	0.0523144i	0.365614	−	0.930766i	$-0.380859\pi$
$887$	5.43359	+	1.55806i	0.182442	+	0.0523144i	−0.183172	+	0.983081i	$0.558637\pi$
$888$	0.176263	+	0.170215i	0.00591501	+	0.00571206i
$889$	−28.3430	+	53.3055i	−0.950595	+	1.78781i
$890$	5.74321	−	15.7793i	0.192513	−	0.528925i
$891$	−27.8252	+	10.4667i	−0.932179	+	0.350649i
$892$		−	9.71165i		−	0.325170i
$893$	−1.98920	−	52.8824i	−0.0665659	−	1.76964i
$894$	−0.322800	+	0.234528i	−0.0107961	+	0.00784379i
$895$	5.15866	+	73.7722i	0.172435	+	2.46593i
$896$	−4.02187	−	0.140447i	−0.134361	−	0.00469200i
$897$	−0.313837	−	2.23306i	−0.0104787	−	0.0745598i
$898$	5.99576	+	2.92433i	0.200081	+	0.0975861i
$899$	33.6426	+	22.6922i	1.12204	+	0.756828i
$900$	8.04025	+	8.92960i	0.268008	+	0.297653i
$901$	0.00990030	+	0.0171478i	0.000329827	+	0.000571277i
$902$	−3.25520	+	34.5284i	−0.108386	+	1.14967i
$903$	−0.139291	+	0.166000i	−0.00463531	+	0.00552414i
$904$	−1.04017	−	4.89363i	−0.0345957	−	0.162760i
$905$	5.10353	−	0.536403i	0.169647	−	0.0178306i
$906$	−0.0720217	+	0.251170i	−0.00239276	+	0.00834455i
$907$	−7.45994	−	14.0301i	−0.247703	−	0.465862i	0.727817	−	0.685771i	$-0.240535\pi$
$907$	−7.45994	−	14.0301i	−0.247703	−	0.465862i	−0.975520	+	0.219909i	$0.929424\pi$
$908$	−17.2886	+	2.42976i	−0.573743	+	0.0806343i
$909$	22.4944	−	15.1727i	0.746092	−	0.503245i
$910$	48.0137	+	11.9712i	1.59164	+	0.396840i
$911$	16.7839	+	5.45342i	0.556076	+	0.180680i	0.573555	−	0.819167i	$-0.305564\pi$
$911$	16.7839	+	5.45342i	0.556076	+	0.180680i	−0.0174790	+	0.999847i	$0.505564\pi$
$912$	−0.0956265	−	0.260548i	−0.00316651	−	0.00862760i
$913$	28.7987	−	19.8775i	0.953099	−	0.657850i
$914$	16.5909	+	19.7723i	0.548779	+	0.654009i
$915$	−0.153376	+	0.196313i	−0.00507046	+	0.00648989i
$916$	2.47243	+	5.06923i	0.0816914	+	0.167492i
$917$	26.0119	−	53.3323i	0.858988	−	1.76119i
$918$	−0.0865307	−	0.110754i	−0.00285594	−	0.00365543i
$919$	5.66321	−	26.6433i	0.186812	−	0.878881i	−0.780473	−	0.625189i	$-0.785022\pi$
$919$	5.66321	−	26.6433i	0.186812	−	0.878881i	0.967285	−	0.253692i	$-0.0816449\pi$
$920$	2.71283	−	25.8108i	0.0894393	−	0.850958i
$921$	0.0765772	−	1.09511i	0.00252331	−	0.0360850i
$922$	−0.517736	−	0.828551i	−0.0170507	−	0.0272869i
$923$	−43.0053	+	24.8291i	−1.41554	+	0.817260i
$924$	0.645127	−	0.553220i	0.0212231	−	0.0181996i
$925$	−5.27900	−	14.5039i	−0.173573	−	0.476887i
$926$	−16.4724	−	2.31505i	−0.541318	−	0.0760772i
$927$	4.41463	−	2.15316i	0.144996	−	0.0707190i
$928$	2.45859	+	3.64501i	0.0807073	+	0.119653i
$929$	−11.4602	−	7.16110i	−0.375996	−	0.234948i	0.328736	−	0.944422i	$-0.393377\pi$
$929$	−11.4602	−	7.16110i	−0.375996	−	0.234948i	−0.704732	+	0.709474i	$0.748933\pi$
$930$	−0.545137	−	1.67776i	−0.0178757	−	0.0550158i
$931$	−32.4893	−	23.4715i	−1.06479	−	0.769248i
$932$	−8.91240	−	12.2669i	−0.291935	−	0.401814i
$933$	0.849028	−	0.343029i	0.0277959	−	0.0112303i
$934$	21.8141	+	7.93968i	0.713779	+	0.259794i
$935$	−2.69731	+	2.48154i	−0.0882113	+	0.0811551i
$936$	2.13105	+	12.0858i	0.0696554	+	0.395036i
$937$	−33.1070	+	1.15612i	−1.08156	+	0.0377688i	−0.570127	−	0.821556i	$-0.693106\pi$
$937$	−33.1070	+	1.15612i	−1.08156	+	0.0377688i	−0.511430	+	0.859325i	$0.670884\pi$
$938$	0.823997	+	7.83981i	0.0269045	+	0.255979i
$939$	−1.64028	−	0.172400i	−0.0535284	−	0.00562606i
$940$	13.6520	−	33.7899i	0.445280	−	1.10211i
$941$	−6.62732	+	16.4032i	−0.216045	+	0.534729i	−0.995821	−	0.0913293i	$-0.970888\pi$
$941$	−6.62732	+	16.4032i	−0.216045	+	0.534729i	0.779776	+	0.626058i	$0.215333\pi$
$942$	−0.336446	−	0.0353619i	−0.0109620	−	0.00115215i
$943$	−9.45024	−	89.9131i	−0.307742	−	2.92797i
$944$	−10.3019	+	0.359749i	−0.335297	+	0.0117088i
$945$	−0.800853	−	4.54186i	−0.0260517	−	0.147747i
$946$	−0.553709	+	2.74963i	−0.0180026	+	0.0893983i
$947$	45.8750	+	16.6971i	1.49074	+	0.542584i	0.953644	−	0.300938i	$-0.0972996\pi$
$947$	45.8750	+	16.6971i	1.49074	+	0.542584i	0.537094	+	0.843522i	$0.319522\pi$
$948$	0.253745	−	0.102519i	0.00824124	−	0.00332968i
$949$	18.8020	+	25.8788i	0.610340	+	0.840061i
$950$	−1.78061	+	17.3915i	−0.0577707	+	0.564255i
$951$	−0.139628	−	0.429731i	−0.00452775	−	0.0139350i
$952$	−1.25641	−	0.785092i	−0.0407205	−	0.0254450i
$953$	−1.61313	−	2.39156i	−0.0522543	−	0.0774702i	0.802005	−	0.597317i	$-0.203767\pi$
$953$	−1.61313	−	2.39156i	−0.0522543	−	0.0774702i	−0.854259	+	0.519847i	$0.825989\pi$
$954$	−0.144829	+	0.0706376i	−0.00468900	+	0.00228698i
$955$	−64.1975	−	9.02237i	−2.07738	−	0.291957i
$956$	−4.01045	−	11.0186i	−0.129707	−	0.356368i
$957$	−0.903258	−	0.214948i	−0.0291982	−	0.00694829i
$958$	33.8258	−	19.5293i	1.09286	−	0.630964i
$959$	25.8804	+	41.4173i	0.835721	+	1.33743i
$960$	0.0133327	−	0.190666i	0.000430310	−	0.00615372i
$961$	5.66424	−	53.8917i	0.182717	−	1.73844i
$962$	3.27750	−	15.4194i	0.105671	−	0.497143i
$963$	−20.5956	−	26.3612i	−0.663684	−	0.849477i
$964$	−4.86148	+	9.96750i	−0.156578	+	0.321032i
$965$	−30.3990	−	62.3272i	−0.978579	−	2.00638i
$966$	−1.36394	+	1.74576i	−0.0438839	+	0.0561689i
$967$	−16.6780	−	19.8761i	−0.536329	−	0.639172i	0.428032	−	0.903764i	$-0.359207\pi$
$967$	−16.6780	−	19.8761i	−0.536329	−	0.639172i	−0.964360	+	0.264592i	$0.914763\pi$
$968$	3.90104	−	10.2850i	0.125384	−	0.330573i
$969$	0.0174717	−	0.100671i	0.000561273	−	0.00323401i
$970$	−44.8694	−	14.5790i	−1.44067	−	0.468102i
$971$	−15.4977	−	3.86400i	−0.497344	−	0.124002i	−0.0148297	−	0.999890i	$-0.504721\pi$
$971$	−15.4977	−	3.86400i	−0.497344	−	0.124002i	−0.482514	+	0.875888i	$0.660276\pi$
$972$	1.42268	−	0.959610i	0.0456325	−	0.0307795i
$973$	22.9966	−	3.23196i	0.737236	−	0.103612i
$974$	7.43785	+	13.9886i	0.238324	+	0.448222i
$975$	−0.288339	+	1.00556i	−0.00923424	+	0.0322036i
$976$	−1.29628	+	0.136244i	−0.0414928	+	0.00436107i
$977$	4.91039	+	23.1016i	0.157097	+	0.739084i	0.984204	+	0.177039i	$0.0566519\pi$
$977$	4.91039	+	23.1016i	0.157097	+	0.739084i	−0.827107	+	0.562045i	$0.810015\pi$
$978$	0.267632	−	0.318952i	0.00855794	−	0.0101990i
$979$	−7.36412	+	17.0291i	−0.235358	+	0.544254i
$980$	−13.8009	−	23.9039i	−0.440855	−	0.763584i
$981$	−0.575144	−	0.638763i	−0.0183629	−	0.0203941i
$982$	14.8337	+	10.0054i	0.473361	+	0.319286i
$983$	17.4887	+	8.52980i	0.557803	+	0.272059i	0.695633	−	0.718397i	$-0.255124\pi$
$983$	17.4887	+	8.52980i	0.557803	+	0.272059i	−0.137830	+	0.990456i	$0.544013\pi$
$984$	−0.0926635	−	0.659335i	−0.00295400	−	0.0210188i
$985$	33.1886	+	1.15897i	1.05748	+	0.0369279i
$986$	0.112909	+	1.61467i	0.00359575	+	0.0514216i
$987$	−2.51677	+	1.82854i	−0.0801096	+	0.0582031i
$988$	−10.9549	+	14.0996i	−0.348521	+	0.448570i
$989$		−	7.31169i		−	0.232498i
$990$	−18.6143	−	23.3058i	−0.591602	−	0.740707i
$991$	3.76618	−	10.3475i	0.119637	−	0.328699i	−0.865391	−	0.501098i	$-0.832930\pi$
$991$	3.76618	−	10.3475i	0.119637	−	0.328699i	0.985027	+	0.172399i	$0.0551519\pi$
$992$	4.33311	−	8.14940i	0.137576	−	0.258744i
$993$	0.486668	+	0.469970i	0.0154440	+	0.0149141i
$994$	46.8960	+	13.4472i	1.48745	+	0.426520i
$995$	46.1064	+	9.80022i	1.46167	+	0.310688i
$996$	−0.449514	+	0.499236i	−0.0142434	+	0.0158189i
$997$	−4.76976	+	1.18923i	−0.151060	+	0.0376634i	−0.316718	−	0.948520i	$-0.602581\pi$
$997$	−4.76976	+	1.18923i	−0.151060	+	0.0376634i	0.165658	+	0.986183i	$0.447025\pi$
$998$	21.9317	+	1.53361i	0.694236	+	0.0485457i
$999$	−1.43711	+	0.305467i	−0.0454681	+	0.00966455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.v.a.13.5	✓	240
11.6	odd	10		418.2.v.b.127.6	yes	240
19.3	odd	18		418.2.v.b.79.6	yes	240
209.193	even	90	inner	418.2.v.a.193.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.v.a.13.5	✓	240	1.1	even	1	trivial
418.2.v.a.193.5	yes	240	209.193	even	90	inner
418.2.v.b.79.6	yes	240	19.3	odd	18
418.2.v.b.127.6	yes	240	11.6	odd	10

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.v (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.374607 + 0.927184i) q^{2} +(-0.0175505 - 0.0612060i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(2.65042 - 1.40925i) q^{5} +(0.0501746 - 0.0392007i) q^{6} +(1.63684 + 3.67640i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(2.54071 - 1.58761i) q^{9} +O(q^{10})\)	\(q+(0.374607 + 0.927184i) q^{2} +(-0.0175505 - 0.0612060i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(2.65042 - 1.40925i) q^{5} +(0.0501746 - 0.0392007i) q^{6} +(1.63684 + 3.67640i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(2.54071 - 1.58761i) q^{9} +(2.29950 + 1.92951i) q^{10} +(-2.41034 - 2.27821i) q^{11} +(0.0551420 + 0.0318363i) q^{12} +(-0.142958 - 4.09378i) q^{13} +(-2.79553 + 2.89485i) q^{14} +(-0.132771 - 0.137489i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(0.195087 - 0.312204i) q^{17} +(2.42377 + 1.76097i) q^{18} +(0.467294 + 4.33378i) q^{19} +(-0.927604 + 2.85487i) q^{20} +(0.196290 - 0.164707i) q^{21} +(1.20939 - 3.08826i) q^{22} +(-1.50133 + 8.51449i) q^{23} +(-0.00886150 + 0.0630529i) q^{24} +(2.24278 - 3.32505i) q^{25} +(3.74213 - 1.66610i) q^{26} +(-0.283716 - 0.255459i) q^{27} +(-3.73128 - 1.50754i) q^{28} +(1.06365 + 4.26608i) q^{29} +(0.0777402 - 0.174607i) q^{30} +(6.85905 - 6.17592i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.0971372 + 0.187511i) q^{33} +(0.362552 + 0.0639276i) q^{34} +(9.51930 + 7.43729i) q^{35} +(-0.724785 + 2.90695i) q^{36} +(2.26201 - 3.11339i) q^{37} +(-3.84316 + 2.05673i) q^{38} +(-0.248055 + 0.0805978i) q^{39} +(-2.99448 + 0.209394i) q^{40} +(-10.0518 + 2.88230i) q^{41} +(0.226245 + 0.120297i) q^{42} +(-0.832840 + 0.146852i) q^{43} +(3.31643 - 0.0355587i) q^{44} +(4.49660 - 7.78834i) q^{45} +(-8.45691 + 1.79757i) q^{46} +(-12.1111 - 0.846887i) q^{47} +(-0.0617812 + 0.0154038i) q^{48} +(-6.15275 + 6.83333i) q^{49} +(3.92310 + 0.833880i) q^{50} +(-0.0225326 - 0.00646113i) q^{51} +(2.94661 + 2.84551i) q^{52} +(-0.0252505 + 0.0474892i) q^{53} +(0.130575 - 0.358753i) q^{54} +(-9.59901 - 2.64143i) q^{55} -4.02432i q^{56} +(0.257052 - 0.104661i) q^{57} +(-3.55699 + 2.58430i) q^{58} +(-0.719059 - 10.2830i) q^{59} +(0.191015 + 0.00667039i) q^{60} +(-0.181401 - 1.29073i) q^{61} +(8.29566 + 4.04606i) q^{62} +(9.99541 + 6.74199i) q^{63} +(0.669131 + 0.743145i) q^{64} +(-6.14807 - 10.6488i) q^{65} +(-0.210246 - 0.0198211i) q^{66} +(1.25912 - 1.50056i) q^{67} +(0.0765415 + 0.360100i) q^{68} +(0.547487 - 0.0575432i) q^{69} +(-3.32974 + 11.6122i) q^{70} +(-5.69130 - 10.7038i) q^{71} +(-2.96679 + 0.416955i) q^{72} +(-6.47399 + 4.36676i) q^{73} +(3.73405 + 0.931002i) q^{74} +(-0.242875 - 0.0789149i) q^{75} +(-3.34664 - 2.79285i) q^{76} +(4.43026 - 12.5904i) q^{77} +(-0.167652 - 0.199800i) q^{78} +(2.64619 - 3.38697i) q^{79} +(-1.31590 - 2.69799i) q^{80} +(3.92935 - 8.05637i) q^{81} +(-6.43788 - 8.24012i) q^{82} +(-2.19361 + 10.3201i) q^{83} +(-0.0267842 + 0.254835i) q^{84} +(0.0770873 - 1.10240i) q^{85} +(-0.448146 - 0.717184i) q^{86} +(0.242442 - 0.139974i) q^{87} +(1.27533 + 3.06162i) q^{88} +(-1.91326 - 5.25664i) q^{89} +(8.90568 + 1.25161i) q^{90} +(14.8164 - 7.22642i) q^{91} +(-4.83469 - 7.16773i) q^{92} +(-0.498383 - 0.311424i) q^{93} +(-3.75166 - 11.5464i) q^{94} +(7.34592 + 10.8278i) q^{95} +(-0.0374258 - 0.0515122i) q^{96} +(-14.5724 + 5.88762i) q^{97} +(-8.64061 - 3.14493i) q^{98} +(-9.74088 - 1.96158i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9}+O(q^{10}) \) 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9	\( 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{13} - 18 q^{14} + 21 q^{15} + 21 q^{17} - 60 q^{18} + 45 q^{19} + 12 q^{20} + 48 q^{21} - 12 q^{22} + 12 q^{24} - 18 q^{25} - 96 q^{26} - 9 q^{27} - 6 q^{28} + 18 q^{29} + 9 q^{31} + 87 q^{33} - 24 q^{34} - 36 q^{35} - 12 q^{36} - 36 q^{38} + 60 q^{41} - 6 q^{42} - 12 q^{43} + 18 q^{44} + 48 q^{45} + 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} - 21 q^{50} - 75 q^{51} + 3 q^{52} - 39 q^{53} + 27 q^{54} - 126 q^{55} - 90 q^{57} - 24 q^{58} + 69 q^{59} - 42 q^{60} + 66 q^{61} - 45 q^{62} - 9 q^{63} + 30 q^{64} - 12 q^{66} - 9 q^{67} + 12 q^{68} - 54 q^{69} + 9 q^{70} + 48 q^{71} + 6 q^{72} - 12 q^{74} + 72 q^{77} - 36 q^{79} - 27 q^{81} + 45 q^{82} + 36 q^{83} + 36 q^{84} - 210 q^{85} + 3 q^{86} + 216 q^{87} + 3 q^{88} + 18 q^{89} - 96 q^{90} - 108 q^{91} - 30 q^{92} + 147 q^{93} - 18 q^{94} + 66 q^{95} - 9 q^{97} - 12 q^{98} - 42 q^{99}+O(q^{100}) \) 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^13 - 18 * q^14 + 21 * q^15 + 21 * q^17 - 60 * q^18 + 45 * q^19 + 12 * q^20 + 48 * q^21 - 12 * q^22 + 12 * q^24 - 18 * q^25 - 96 * q^26 - 9 * q^27 - 6 * q^28 + 18 * q^29 + 9 * q^31 + 87 * q^33 - 24 * q^34 - 36 * q^35 - 12 * q^36 - 36 * q^38 + 60 * q^41 - 6 * q^42 - 12 * q^43 + 18 * q^44 + 48 * q^45 + 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 - 21 * q^50 - 75 * q^51 + 3 * q^52 - 39 * q^53 + 27 * q^54 - 126 * q^55 - 90 * q^57 - 24 * q^58 + 69 * q^59 - 42 * q^60 + 66 * q^61 - 45 * q^62 - 9 * q^63 + 30 * q^64 - 12 * q^66 - 9 * q^67 + 12 * q^68 - 54 * q^69 + 9 * q^70 + 48 * q^71 + 6 * q^72 - 12 * q^74 + 72 * q^77 - 36 * q^79 - 27 * q^81 + 45 * q^82 + 36 * q^83 + 36 * q^84 - 210 * q^85 + 3 * q^86 + 216 * q^87 + 3 * q^88 + 18 * q^89 - 96 * q^90 - 108 * q^91 - 30 * q^92 + 147 * q^93 - 18 * q^94 + 66 * q^95 - 9 * q^97 - 12 * q^98 - 42 * q^99

Introduction

L-functions

Modular forms

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