LMFDB - Embedded newform 462.2.bc.b.305.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(95,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 20, 21]))

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

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

chi := DirichletCharacter("462.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bc (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			305.12
Character	$\chi$	$=$	462.305
Dual form			462.2.bc.b.359.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.913545 + 0.406737i) q^{2} +(0.974501 - 1.43190i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.273885 + 0.0287865i) q^{5} +(1.47266 - 0.911743i) q^{6} +(-1.73400 - 1.99831i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.10069 - 2.79078i) q^{9} +O(q^{10})$	\(q+(0.913545 + 0.406737i) q^{2} +(0.974501 - 1.43190i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.273885 + 0.0287865i) q^{5} +(1.47266 - 0.911743i) q^{6} +(-1.73400 - 1.99831i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.10069 - 2.79078i) q^{9} +(0.238498 + 0.137697i) q^{10} +(3.20872 - 0.839120i) q^{11} +(1.71618 - 0.233935i) q^{12} +(0.376661 + 0.518429i) q^{13} +(-0.771302 - 2.53083i) q^{14} +(0.308121 - 0.364124i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(5.58406 - 2.48618i) q^{17} +(0.129580 - 2.99720i) q^{18} +(0.818342 + 0.736838i) q^{19} +(0.161872 + 0.222798i) q^{20} +(-4.55117 + 0.535564i) q^{21} +(3.27261 + 0.538529i) q^{22} +(1.05359 - 0.608290i) q^{23} +(1.66296 + 0.484323i) q^{24} +(-4.81655 - 1.02379i) q^{25} +(0.133233 + 0.626810i) q^{26} +(-5.06876 - 1.14353i) q^{27} +(0.324762 - 2.62574i) q^{28} +(-2.73094 + 8.40497i) q^{29} +(0.429585 - 0.207320i) q^{30} +(0.523104 + 4.97700i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.92536 - 5.41230i) q^{33} +6.11252 q^{34} +(-0.417392 - 0.597223i) q^{35} +(1.33745 - 2.68537i) q^{36} +(-7.07372 + 1.50357i) q^{37} +(0.447893 + 1.00598i) q^{38} +(1.10940 - 0.0341320i) q^{39} +(0.0572575 + 0.269376i) q^{40} +(0.939549 + 2.89164i) q^{41} +(-4.37554 - 1.36187i) q^{42} -1.12509i q^{43} +(2.77064 + 1.82306i) q^{44} +(-0.221127 - 0.796039i) q^{45} +(1.20992 - 0.127167i) q^{46} +(1.77335 + 1.59673i) q^{47} +(1.32220 + 1.11884i) q^{48} +(-0.986490 + 6.93014i) q^{49} +(-3.98373 - 2.89435i) q^{50} +(1.88170 - 10.4186i) q^{51} +(-0.133233 + 0.626810i) q^{52} +(-8.15168 + 0.856777i) q^{53} +(-4.16543 - 3.10632i) q^{54} +(0.902975 - 0.137455i) q^{55} +(1.36467 - 2.26664i) q^{56} +(1.85256 - 0.453736i) q^{57} +(-5.91345 + 6.56755i) q^{58} +(6.57511 - 5.92026i) q^{59} +(0.476770 - 0.0146684i) q^{60} +(4.40502 + 0.462986i) q^{61} +(-1.54645 + 4.75948i) q^{62} +(-3.66825 + 7.03875i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.0882380 + 0.152833i) q^{65} +(3.96029 - 4.16127i) q^{66} +(-5.31001 + 9.19720i) q^{67} +(5.58406 + 2.48618i) q^{68} +(0.155712 - 2.10142i) q^{69} +(-0.138394 - 0.715359i) q^{70} +(6.62602 - 9.11993i) q^{71} +(2.31406 - 1.90922i) q^{72} +(8.47349 - 7.62957i) q^{73} +(-7.07372 - 1.50357i) q^{74} +(-6.15971 + 5.89915i) q^{75} +1.10119i q^{76} +(-7.24074 - 4.95698i) q^{77} +(1.02737 + 0.420051i) q^{78} +(-5.05145 + 11.3457i) q^{79} +(-0.0572575 + 0.269376i) q^{80} +(-6.57694 + 6.14360i) q^{81} +(-0.317813 + 3.02379i) q^{82} +(3.41598 + 2.48186i) q^{83} +(-3.44333 - 3.02382i) q^{84} +(1.60096 - 0.520183i) q^{85} +(0.457617 - 1.02783i) q^{86} +(9.37380 + 12.1011i) q^{87} +(1.78960 + 2.79237i) q^{88} +(-15.7235 + 9.07797i) q^{89} +(0.121769 - 0.817158i) q^{90} +(0.382853 - 1.65164i) q^{91} +(1.15704 + 0.375944i) q^{92} +(7.63635 + 4.10106i) q^{93} +(0.970588 + 2.17998i) q^{94} +(0.202920 + 0.225366i) q^{95} +(0.752814 + 1.55989i) q^{96} +(-8.14146 + 5.91512i) q^{97} +(-3.71994 + 5.92976i) q^{98} +(-5.87362 - 8.03122i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 + 38 * q^29 + 6 * q^30 - 3 * q^31 - 64 * q^32 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.913545	+	0.406737i	0.645974	+	0.287606i
$2$	0.913545	+	0.406737i	0.645974	+	0.287606i
$3$	0.974501	−	1.43190i	0.562629	−	0.826710i
$3$	0.974501	−	1.43190i	0.562629	−	0.826710i
$4$	0.669131	+	0.743145i	0.334565	+	0.371572i
$5$	0.273885	+	0.0287865i	0.122485	+	0.0128737i	0.165573	−	0.986198i	$-0.447053\pi$
$5$	0.273885	+	0.0287865i	0.122485	+	0.0128737i	−0.0430876	+	0.999071i	$0.513719\pi$
$6$	1.47266	−	0.911743i	0.601210	−	0.372218i
$7$	−1.73400	−	1.99831i	−0.655390	−	0.755290i
$7$	−1.73400	−	1.99831i	−0.655390	−	0.755290i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−1.10069	−	2.79078i	−0.366898	−	0.930261i
$10$	0.238498	+	0.137697i	0.0754196	+	0.0435435i
$11$	3.20872	−	0.839120i	0.967465	−	0.253004i
$11$	3.20872	−	0.839120i	0.967465	−	0.253004i
$12$	1.71618	−	0.233935i	0.495419	−	0.0675311i
$13$	0.376661	+	0.518429i	0.104467	+	0.143786i	0.858050	−	0.513567i	$-0.171676\pi$
$13$	0.376661	+	0.518429i	0.104467	+	0.143786i	−0.753583	+	0.657353i	$0.771676\pi$
$14$	−0.771302	−	2.53083i	−0.206139	−	0.676392i
$15$	0.308121	−	0.364124i	0.0795564	−	0.0940165i
$16$	−0.104528	+	0.994522i	−0.0261321	+	0.248630i
$17$	5.58406	−	2.48618i	1.35433	−	0.602988i	0.404154	−	0.914691i	$-0.367566\pi$
$17$	5.58406	−	2.48618i	1.35433	−	0.602988i	0.950180	+	0.311703i	$0.100899\pi$
$18$	0.129580	−	2.99720i	0.0305422	−	0.706447i
$19$	0.818342	+	0.736838i	0.187740	+	0.169042i	0.757641	−	0.652671i	$-0.226352\pi$
$19$	0.818342	+	0.736838i	0.187740	+	0.169042i	−0.569901	+	0.821714i	$0.693018\pi$
$20$	0.161872	+	0.222798i	0.0361957	+	0.0498192i
$21$	−4.55117	+	0.535564i	−0.993147	+	0.116870i
$22$	3.27261	+	0.538529i	0.697723	+	0.114815i
$23$	1.05359	−	0.608290i	0.219689	−	0.126837i	−0.386117	−	0.922450i	$-0.626184\pi$
$23$	1.05359	−	0.608290i	0.219689	−	0.126837i	0.605806	+	0.795612i	$0.292851\pi$
$24$	1.66296	+	0.484323i	0.339450	+	0.0988621i
$25$	−4.81655	−	1.02379i	−0.963311	−	0.204758i
$26$	0.133233	+	0.626810i	0.0261291	+	0.122928i
$27$	−5.06876	−	1.14353i	−0.975483	−	0.220073i
$28$	0.324762	−	2.62574i	0.0613742	−	0.496219i
$29$	−2.73094	+	8.40497i	−0.507123	+	1.56076i	0.290049	+	0.957012i	$0.406328\pi$
$29$	−2.73094	+	8.40497i	−0.507123	+	1.56076i	−0.797172	+	0.603752i	$0.793672\pi$
$30$	0.429585	−	0.207320i	0.0784311	−	0.0378513i
$31$	0.523104	+	4.97700i	0.0939522	+	0.893896i	0.935408	+	0.353570i	$0.115032\pi$
$31$	0.523104	+	4.97700i	0.0939522	+	0.893896i	−0.841456	+	0.540326i	$0.818301\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.92536	−	5.41230i	0.335162	−	0.942160i
$34$	6.11252			1.04829
$35$	−0.417392	−	0.597223i	−0.0705521	−	0.100949i
$36$	1.33745	−	2.68537i	0.222908	−	0.447562i
$37$	−7.07372	+	1.50357i	−1.16291	+	0.247185i	−0.748645	−	0.662971i	$-0.769295\pi$
$37$	−7.07372	+	1.50357i	−1.16291	+	0.247185i	−0.414267	+	0.910155i	$0.635962\pi$
$38$	0.447893	+	1.00598i	0.0726579	+	0.163192i
$39$	1.10940	−	0.0341320i	0.177646	−	0.00546549i
$40$	0.0572575	+	0.269376i	0.00905321	+	0.0425920i
$41$	0.939549	+	2.89164i	0.146733	+	0.451598i	0.997230	−	0.0743826i	$-0.0236986\pi$
$41$	0.939549	+	2.89164i	0.146733	+	0.451598i	−0.850497	+	0.525980i	$0.823699\pi$
$42$	−4.37554	−	1.36187i	−0.675160	−	0.210141i
$43$		−	1.12509i		−	0.171575i	−0.996313	−	0.0857877i	$-0.972659\pi$
$43$		−	1.12509i		−	0.171575i	0.996313	−	0.0857877i	$-0.0273407\pi$
$44$	2.77064	+	1.82306i	0.417690	+	0.274837i
$45$	−0.221127	−	0.796039i	−0.0329636	−	0.118666i
$46$	1.20992	−	0.127167i	0.178392	−	0.0187498i
$47$	1.77335	+	1.59673i	0.258670	+	0.232908i	0.788254	−	0.615350i	$-0.210985\pi$
$47$	1.77335	+	1.59673i	0.258670	+	0.232908i	−0.529584	+	0.848258i	$0.677652\pi$
$48$	1.32220	+	1.11884i	0.190843	+	0.161490i
$49$	−0.986490	+	6.93014i	−0.140927	+	0.990020i
$50$	−3.98373	−	2.89435i	−0.563384	−	0.409323i
$51$	1.88170	−	10.4186i	0.263491	−	1.45890i
$52$	−0.133233	+	0.626810i	−0.0184760	+	0.0869229i
$53$	−8.15168	+	0.856777i	−1.11972	+	0.117687i	−0.646252	−	0.763124i	$-0.723665\pi$
$53$	−8.15168	+	0.856777i	−1.11972	+	0.117687i	−0.473468	+	0.880811i	$0.656998\pi$
$54$	−4.16543	−	3.10632i	−0.566843	−	0.422717i
$55$	0.902975	−	0.137455i	0.121757	−	0.0185344i
$56$	1.36467	−	2.26664i	0.182362	−	0.302893i
$57$	1.85256	−	0.453736i	0.245377	−	0.0600988i
$58$	−5.91345	+	6.56755i	−0.776474	+	0.862361i
$59$	6.57511	−	5.92026i	0.856007	−	0.770752i	−0.119007	−	0.992893i	$-0.537971\pi$
$59$	6.57511	−	5.92026i	0.856007	−	0.770752i	0.975015	+	0.222141i	$0.0713046\pi$
$60$	0.476770	−	0.0146684i	0.0615507	−	0.00189369i
$61$	4.40502	+	0.462986i	0.564005	+	0.0592793i	0.382241	−	0.924063i	$-0.375153\pi$
$61$	4.40502	+	0.462986i	0.564005	+	0.0592793i	0.181764	+	0.983342i	$0.441819\pi$
$62$	−1.54645	+	4.75948i	−0.196399	+	0.604455i
$63$	−3.66825	+	7.03875i	−0.462156	+	0.886799i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	0.0882380	+	0.152833i	0.0109446	+	0.0189566i
$66$	3.96029	−	4.16127i	0.487477	−	0.512216i
$67$	−5.31001	+	9.19720i	−0.648721	+	1.12362i	0.334708	+	0.942322i	$0.391362\pi$
$67$	−5.31001	+	9.19720i	−0.648721	+	1.12362i	−0.983429	+	0.181295i	$0.941971\pi$
$68$	5.58406	+	2.48618i	0.677167	+	0.301494i
$69$	0.155712	−	2.10142i	0.0187455	−	0.252981i
$70$	−0.138394	−	0.715359i	−0.0165413	−	0.0855017i
$71$	6.62602	−	9.11993i	0.786363	−	1.08234i	−0.208188	−	0.978089i	$-0.566757\pi$
$71$	6.62602	−	9.11993i	0.786363	−	1.08234i	0.994551	−	0.104248i	$-0.0332434\pi$
$72$	2.31406	−	1.90922i	0.272715	−	0.225004i
$73$	8.47349	−	7.62957i	0.991747	−	0.892973i	−0.00250924	−	0.999997i	$-0.500799\pi$
$73$	8.47349	−	7.62957i	0.991747	−	0.892973i	0.994256	+	0.107024i	$0.0341321\pi$
$74$	−7.07372	−	1.50357i	−0.822303	−	0.174786i
$75$	−6.15971	+	5.89915i	−0.711262	+	0.681176i
$76$			1.10119i			0.126315i
$77$	−7.24074	−	4.95698i	−0.825159	−	0.564901i
$78$	1.02737	+	0.420051i	0.116326	+	0.0475614i
$79$	−5.05145	+	11.3457i	−0.568332	+	1.27650i	0.369443	+	0.929253i	$0.379548\pi$
$79$	−5.05145	+	11.3457i	−0.568332	+	1.27650i	−0.937776	+	0.347242i	$0.887118\pi$
$80$	−0.0572575	+	0.269376i	−0.00640159	+	0.0301171i
$81$	−6.57694	+	6.14360i	−0.730772	+	0.682622i
$82$	−0.317813	+	3.02379i	−0.0350966	+	0.333922i
$83$	3.41598	+	2.48186i	0.374953	+	0.272419i	0.759262	−	0.650785i	$-0.225560\pi$
$83$	3.41598	+	2.48186i	0.374953	+	0.272419i	−0.384309	+	0.923205i	$0.625560\pi$
$84$	−3.44333	−	3.02382i	−0.375698	−	0.329926i
$85$	1.60096	−	0.520183i	0.173648	−	0.0564218i
$86$	0.457617	−	1.02783i	0.0493461	−	0.110833i
$87$	9.37380	+	12.1011i	1.00498	+	1.29737i
$88$	1.78960	+	2.79237i	0.190772	+	0.297668i
$89$	−15.7235	+	9.07797i	−1.66669	+	0.962263i	−0.697284	+	0.716795i	$0.745608\pi$
$89$	−15.7235	+	9.07797i	−1.66669	+	0.962263i	−0.969405	+	0.245468i	$0.921058\pi$
$90$	0.121769	−	0.817158i	0.0128355	−	0.0861360i
$91$	0.382853	−	1.65164i	0.0401339	−	0.173139i
$92$	1.15704	+	0.375944i	0.120629	+	0.0391949i
$93$	7.63635	+	4.10106i	0.791853	+	0.425260i
$94$	0.970588	+	2.17998i	0.100109	+	0.224847i
$95$	0.202920	+	0.225366i	0.0208192	+	0.0231221i
$96$	0.752814	+	1.55989i	0.0768338	+	0.159206i
$97$	−8.14146	+	5.91512i	−0.826640	+	0.600589i	−0.918607	−	0.395173i	$-0.870685\pi$
$97$	−8.14146	+	5.91512i	−0.826640	+	0.600589i	0.0919669	+	0.995762i	$0.470685\pi$
$98$	−3.71994	+	5.92976i	−0.375771	+	0.598996i
$99$	−5.87362	−	8.03122i	−0.590321	−	0.807168i
$100$	−2.46208	−	4.26445i	−0.246208	−	0.426445i
$101$	0.550141	+	5.23424i	0.0547411	+	0.520826i	0.987193	+	0.159532i	$0.0509984\pi$
$101$	0.550141	+	5.23424i	0.0547411	+	0.520826i	−0.932452	+	0.361295i	$0.882335\pi$
$102$	5.95666	−	8.75253i	0.589797	−	0.866630i
$103$	12.9556	−	2.75380i	1.27655	−	0.271340i	0.480730	−	0.876869i	$-0.340372\pi$
$103$	12.9556	−	2.75380i	1.27655	−	0.271340i	0.795823	+	0.605529i	$0.207038\pi$
$104$	−0.376661	+	0.518429i	−0.0369346	+	0.0508362i
$105$	−1.26191	+	0.0156707i	−0.123150	+	0.00152930i
$106$	−7.79542	−	2.53288i	−0.757158	−	0.246015i
$107$	4.55472	−	5.05853i	0.440322	−	0.489027i	−0.481607	−	0.876388i	$-0.659947\pi$
$107$	4.55472	−	5.05853i	0.440322	−	0.489027i	0.921928	+	0.387361i	$0.126613\pi$
$108$	−2.54185	−	4.53200i	−0.244590	−	0.436092i
$109$	−4.10671	−	2.37101i	−0.393352	−	0.227102i	0.290260	−	0.956948i	$-0.406258\pi$
$109$	−4.10671	−	2.37101i	−0.393352	−	0.227102i	−0.683611	+	0.729846i	$0.739592\pi$
$110$	0.880817	+	0.241702i	0.0839826	+	0.0230454i
$111$	−4.74039	+	11.5941i	−0.449938	+	1.10046i
$112$	2.16862	−	1.51562i	0.204915	−	0.143213i
$113$	1.41966	−	0.461276i	0.133550	−	0.0433932i	−0.241479	−	0.970406i	$-0.577633\pi$
$113$	1.41966	−	0.461276i	0.133550	−	0.0433932i	0.375030	+	0.927013i	$0.377633\pi$
$114$	1.87695	+	0.338994i	0.175792	+	0.0317497i
$115$	0.306073	−	0.136272i	0.0285414	−	0.0127075i
$116$	−8.07347	+	3.59454i	−0.749603	+	0.333745i
$117$	1.03223	−	1.62181i	0.0954302	−	0.149936i
$118$	8.41465	−	2.73409i	0.774632	−	0.251693i
$119$	−14.6509	−	6.84765i	−1.34305	−	0.627723i
$120$	0.441517	+	0.180520i	0.0403048	+	0.0164791i
$121$	9.59175	−	5.38500i	0.871978	−	0.489546i
$122$	3.83587	+	2.21464i	0.347284	+	0.200504i
$123$	5.05613	+	1.47256i	0.455896	+	0.132776i
$124$	−3.34861	+	3.71901i	−0.300714	+	0.333977i
$125$	−2.59928	−	0.844559i	−0.232487	−	0.0755396i
$126$	−6.21403	+	4.93820i	−0.553590	+	0.439930i
$127$	0.0509999	−	0.0701953i	0.00452551	−	0.00622883i	−0.806748	−	0.590895i	$-0.798775\pi$
$127$	0.0509999	−	0.0701953i	0.00452551	−	0.00622883i	0.811274	+	0.584666i	$0.198775\pi$
$128$	−0.978148	+	0.207912i	−0.0864569	+	0.0183770i
$129$	−1.61103	−	1.09641i	−0.141843	−	0.0965332i
$130$	0.0184468	+	0.175509i	0.00161789	+	0.0153932i
$131$	−5.90912	−	10.2349i	−0.516282	−	0.894227i	−0.999821	−	0.0189040i	$-0.993982\pi$
$131$	−5.90912	−	10.2349i	−0.516282	−	0.894227i	0.483539	−	0.875323i	$-0.339351\pi$
$132$	5.31044	−	2.19071i	0.462215	−	0.190677i
$133$	0.0534271	−	2.91298i	0.00463272	−	0.252587i
$134$	−8.59177	+	6.24229i	−0.742216	+	0.539251i
$135$	−1.35534	−	0.459109i	−0.116649	−	0.0395138i
$136$	4.09007	+	4.54248i	0.350721	+	0.389515i
$137$	−3.49972	−	7.86051i	−0.299001	−	0.671568i	0.700096	−	0.714049i	$-0.253141\pi$
$137$	−3.49972	−	7.86051i	−0.299001	−	0.671568i	−0.999097	+	0.0424806i	$0.986474\pi$
$138$	0.996974	−	1.85641i	0.0848680	−	0.158028i
$139$	8.90966	+	2.89492i	0.755707	+	0.245544i	0.661435	−	0.750002i	$-0.269948\pi$
$139$	8.90966	+	2.89492i	0.755707	+	0.245544i	0.0942720	+	0.995546i	$0.469948\pi$
$140$	0.164533	−	0.709803i	0.0139056	−	0.0599893i
$141$	4.01450	−	0.983250i	0.338082	−	0.0828046i
$142$	9.76258	−	5.63643i	0.819257	−	0.472998i
$143$	1.64362	+	1.34743i	0.137447	+	0.112678i
$144$	2.89055	−	0.802948i	0.240879	−	0.0669123i
$145$	−0.989913	+	2.22338i	−0.0822078	+	0.184642i
$146$	10.8441	−	3.52348i	0.897468	−	0.291605i
$147$	8.96195	+	8.16599i	0.739170	+	0.673519i
$148$	−5.85061	−	4.25072i	−0.480917	−	0.349407i
$149$	1.48963	−	14.1729i	0.122035	−	1.16109i	−0.746473	−	0.665416i	$-0.768254\pi$
$149$	1.48963	−	14.1729i	0.122035	−	1.16109i	0.868509	−	0.495674i	$-0.165079\pi$
$150$	−8.02657	+	2.88377i	−0.655367	+	0.235459i
$151$	−2.17633	+	10.2388i	−0.177107	+	0.833223i	0.796437	+	0.604722i	$0.206716\pi$
$151$	−2.17633	+	10.2388i	−0.177107	+	0.833223i	−0.973544	+	0.228501i	$0.926618\pi$
$152$	−0.447893	+	1.00598i	−0.0363289	+	0.0815961i
$153$	−13.0847	−	12.8474i	−1.05784	−	1.03865i
$154$	−4.59856	−	7.47350i	−0.370562	−	0.602232i
$155$			1.37818i			0.110698i
$156$	0.767696	+	0.801604i	0.0614649	+	0.0641797i
$157$	−14.7416	−	3.13343i	−1.17651	−	0.250075i	−0.422144	−	0.906529i	$-0.638722\pi$
$157$	−14.7416	−	3.13343i	−1.17651	−	0.250075i	−0.754366	+	0.656454i	$0.772056\pi$
$158$	−9.22945	+	8.31024i	−0.734256	+	0.661127i
$159$	−6.71701	+	12.5074i	−0.532693	+	0.991898i
$160$	−0.161872	+	0.222798i	−0.0127971	+	0.0176137i
$161$	−3.04248	−	1.05062i	−0.239781	−	0.0828008i
$162$	−8.50716	+	2.93737i	−0.668386	+	0.230782i
$163$	−19.3931	−	8.63435i	−1.51898	−	0.676295i	−0.533458	−	0.845827i	$-0.679108\pi$
$163$	−19.3931	−	8.63435i	−1.51898	−	0.676295i	−0.985525	+	0.169532i	$0.945774\pi$
$164$	−1.52022	+	2.63310i	−0.118709	+	0.205611i
$165$	0.683128	−	1.42692i	0.0531815	−	0.111086i
$166$	2.11119	+	3.65669i	0.163860	+	0.283815i
$167$	3.23429	−	2.34985i	0.250277	−	0.181837i	−0.455573	−	0.890199i	$-0.650566\pi$
$167$	3.23429	−	2.34985i	0.250277	−	0.181837i	0.705849	+	0.708362i	$0.250566\pi$
$168$	−1.91574	−	4.16292i	−0.147803	−	0.321177i
$169$	3.89033	−	11.9732i	0.299256	−	0.921015i
$170$	1.67413	+	0.175958i	0.128400	+	0.0134953i
$171$	1.15561	−	3.09485i	0.0883718	−	0.236669i
$172$	0.836108	−	0.752835i	0.0637527	−	0.0574031i
$173$	−0.506043	+	0.562018i	−0.0384738	+	0.0427294i	−0.762075	−	0.647489i	$-0.775819\pi$
$173$	−0.506043	+	0.562018i	−0.0384738	+	0.0427294i	0.723601	+	0.690219i	$0.242486\pi$
$174$	3.64143	+	14.8676i	0.276056	+	1.12711i
$175$	6.30605	+	11.4002i	0.476693	+	0.861776i
$176$	0.499121	+	3.27885i	0.0376227	+	0.247153i
$177$	−2.06978	−	15.1842i	−0.155574	−	1.14132i
$178$	−18.0565	+	1.89781i	−1.35339	+	0.142247i
$179$	−0.377761	+	1.77722i	−0.0282352	+	0.132836i	−0.990008	−	0.141014i	$-0.954964\pi$
$179$	−0.377761	+	1.77722i	−0.0282352	+	0.132836i	0.961772	+	0.273850i	$0.0882971\pi$
$180$	0.443609	−	0.696983i	0.0330647	−	0.0519500i
$181$	16.7786	+	12.1904i	1.24714	+	0.906102i	0.998053	−	0.0623784i	$-0.0198686\pi$
$181$	16.7786	+	12.1904i	1.24714	+	0.906102i	0.249090	+	0.968480i	$0.419869\pi$
$182$	1.02154	−	1.35313i	0.0757213	−	0.100301i
$183$	4.95565	−	5.85638i	0.366332	−	0.432916i
$184$	0.904096	+	0.814051i	0.0666508	+	0.0600127i
$185$	−1.98067	+	0.208176i	−0.145622	+	0.0153054i
$186$	5.30810	+	6.85249i	0.389209	+	0.502449i
$187$	15.8315	−	12.6632i	1.15771	−	0.926022i
$188$			2.38628i			0.174037i
$189$	6.50409	+	12.1118i	0.473103	+	0.881007i
$190$	0.0937124	+	0.288417i	0.00679862	+	0.0209240i
$191$	−2.38801	−	11.2347i	−0.172790	−	0.812915i	−0.976095	−	0.217346i	$-0.930260\pi$
$191$	−2.38801	−	11.2347i	−0.172790	−	0.812915i	0.803304	−	0.595569i	$-0.203073\pi$
$192$	0.0532635	+	1.73123i	0.00384396	+	0.124941i
$193$	−1.77211	−	3.98021i	−0.127559	−	0.286502i	0.838465	−	0.544956i	$-0.183454\pi$
$193$	−1.77211	−	3.98021i	−0.127559	−	0.286502i	−0.966024	+	0.258454i	$0.916787\pi$
$194$	−9.84349	+	2.09230i	−0.706721	+	0.150218i
$195$	0.304830	+	0.0225874i	0.0218293	+	0.00161752i
$196$	−5.81019	+	3.90406i	−0.415013	+	0.278862i
$197$	16.6705			1.18773			0.593863	−	0.804566i	$-0.297602\pi$
$197$	16.6705			1.18773			0.593863	+	0.804566i	$0.297602\pi$
$198$	−2.09923	−	9.72591i	−0.149186	−	0.691190i
$199$	2.72284	−	4.71610i	0.193017	−	0.334315i	−0.753232	−	0.657755i	$-0.771506\pi$
$199$	2.72284	−	4.71610i	0.193017	−	0.334315i	0.946249	+	0.323440i	$0.104839\pi$
$200$	−0.514715	−	4.89718i	−0.0363958	−	0.346283i
$201$	7.99489	+	16.5661i	0.563916	+	1.16848i
$202$	−1.62638	+	5.00548i	−0.114432	+	0.352184i
$203$	21.5312	−	9.11695i	1.51119	−	0.639884i
$204$	9.00165	−	5.57305i	0.630242	−	0.390191i
$205$	0.174088	+	0.819021i	0.0121589	+	0.0572029i
$206$	12.9556	+	2.75380i	0.902659	+	0.191866i
$207$	−2.85729	−	2.27080i	−0.198595	−	0.157831i
$208$	−0.554961	+	0.320407i	−0.0384796	+	0.0222162i
$209$	3.24412	+	1.67762i	0.224401	+	0.116043i
$210$	−1.15919	−	0.498951i	−0.0799917	−	0.0344309i
$211$	12.1580	+	16.7340i	0.836989	+	1.15202i	0.986582	+	0.163269i	$0.0522037\pi$
$211$	12.1580	+	16.7340i	0.836989	+	1.15202i	−0.149593	+	0.988748i	$0.547796\pi$
$212$	−6.09125	−	5.48459i	−0.418349	−	0.376683i
$213$	−6.60179	−	18.3752i	−0.452348	−	1.25905i
$214$	6.21844	−	2.76863i	0.425084	−	0.189259i
$215$	0.0323875	−	0.308146i	0.00220881	−	0.0210154i
$216$	−0.478767	−	5.17405i	−0.0325760	−	0.352049i
$217$	9.03853	−	9.67544i	0.613575	−	0.656812i
$218$	−2.78729	−	3.83638i	−0.188779	−	0.259832i
$219$	−2.66737	−	19.5682i	−0.180244	−	1.32230i
$220$	0.706357	+	0.579066i	0.0476226	+	0.0390406i
$221$	3.39221	+	1.95849i	0.228185	+	0.131742i
$222$	−9.04631	+	8.66365i	−0.607148	+	0.581466i
$223$	1.74306	+	5.36460i	0.116724	+	0.359240i	0.992303	−	0.123836i	$-0.0395196\pi$
$223$	1.74306	+	5.36460i	0.116724	+	0.359240i	−0.875579	+	0.483076i	$0.839520\pi$
$224$	2.59759	−	0.502533i	0.173559	−	0.0335769i
$225$	2.44438	+	14.5688i	0.162958	+	0.971256i
$226$	1.48454	+	0.156032i	0.0987503	+	0.0103791i
$227$	16.0742	+	17.8522i	1.06688	+	1.18489i	0.982075	+	0.188492i	$0.0603601\pi$
$227$	16.0742	+	17.8522i	1.06688	+	1.18489i	0.0848051	+	0.996398i	$0.472973\pi$
$228$	1.57679	+	1.07311i	0.104426	+	0.0710683i
$229$	−23.6841	−	10.5448i	−1.56509	−	0.696822i	−0.572676	−	0.819782i	$-0.694095\pi$
$229$	−23.6841	−	10.5448i	−1.56509	−	0.696822i	−0.992412	+	0.122960i	$0.960761\pi$
$230$	0.335038			0.0220918
$231$	−14.1540	+	5.53745i	−0.931267	+	0.364338i
$232$	−8.83751			−0.580211
$233$	15.3975	+	6.85542i	1.00873	+	0.449113i	0.843492	−	0.537141i	$-0.180496\pi$
$233$	15.3975	+	6.85542i	1.00873	+	0.449113i	0.165233	+	0.986255i	$0.447162\pi$
$234$	1.60264	−	1.06175i	0.104768	−	0.0694088i
$235$	0.439730	+	0.488370i	0.0286848	+	0.0318577i
$236$	8.79922	+	0.924835i	0.572781	+	0.0602017i
$237$	11.3234	+	18.2896i	0.735531	+	1.18804i
$238$	−10.5991	−	12.2147i	−0.687038	−	0.791762i
$239$	4.22887	+	13.0151i	0.273543	+	0.841877i	0.989601	+	0.143837i	$0.0459442\pi$
$239$	4.22887	+	13.0151i	0.273543	+	0.841877i	−0.716059	+	0.698040i	$0.754056\pi$
$240$	0.329922	+	0.344494i	0.0212964	+	0.0222370i
$241$	−2.75040	−	1.58794i	−0.177169	−	0.102288i	0.408793	−	0.912627i	$-0.365950\pi$
$241$	−2.75040	−	1.58794i	−0.177169	−	0.102288i	−0.585962	+	0.810339i	$0.699283\pi$
$242$	10.9528	−	1.01813i	0.704071	−	0.0654477i
$243$	2.38780	+	15.4045i	0.153177	+	0.988199i
$244$	2.60347	+	3.58337i	0.166670	+	0.229401i
$245$	−0.469679	+	1.86966i	−0.0300067	+	0.119448i
$246$	4.02006	+	3.40176i	0.256310	+	0.216889i
$247$	−0.0737611	+	0.701790i	−0.00469331	+	0.0446538i
$248$	−4.57176	+	2.03548i	−0.290307	+	0.129253i
$249$	6.88266	−	2.47278i	0.436171	−	0.156706i
$250$	−2.03105	−	1.82877i	−0.128455	−	0.115661i
$251$	5.83265	+	8.02796i	0.368154	+	0.506720i	0.952398	−	0.304858i	$-0.0986089\pi$
$251$	5.83265	+	8.02796i	0.368154	+	0.506720i	−0.584244	+	0.811578i	$0.698609\pi$
$252$	−7.68535	+	1.98380i	−0.484131	+	0.124968i
$253$	2.87024	−	2.83592i	0.180451	−	0.178293i
$254$	0.0751417	−	0.0433831i	0.00471481	−	0.00272210i
$255$	0.815285	−	2.79934i	0.0510551	−	0.175301i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	−4.34288	−	20.4316i	−0.270901	−	1.27449i	−0.877536	−	0.479510i	$-0.840814\pi$
$257$	−4.34288	−	20.4316i	−0.270901	−	1.27449i	0.606635	−	0.794980i	$-0.292519\pi$
$258$	−1.02580	−	1.65688i	−0.0638634	−	0.103153i
$259$	15.2704	+	11.5283i	0.948858	+	0.716334i
$260$	−0.0545341	+	0.167839i	−0.00338206	+	0.0104089i
$261$	26.4624	−	1.62984i	1.63798	−	0.100885i
$262$	−1.23534	−	11.7535i	−0.0763197	−	0.726133i
$263$	9.65220	−	16.7181i	0.595180	−	1.03088i	−0.398341	−	0.917237i	$-0.630414\pi$
$263$	9.65220	−	16.7181i	0.595180	−	1.03088i	0.993521	−	0.113645i	$-0.0362526\pi$
$264$	5.74237	+	0.158635i	0.353419	+	0.00976333i
$265$	−2.25729			−0.138664
$266$	1.23362	−	2.63941i	0.0756383	−	0.161832i
$267$	−2.32380	+	31.3610i	−0.142214	+	1.91926i
$268$	−10.3879	+	2.20802i	−0.634544	+	0.134877i
$269$	−8.80112	−	19.7676i	−0.536614	−	1.20525i	−0.954897	−	0.296938i	$-0.904035\pi$
$269$	−8.80112	−	19.7676i	−0.536614	−	1.20525i	0.418283	−	0.908317i	$-0.362632\pi$
$270$	−1.05143	−	0.970682i	−0.0639878	−	0.0590738i
$271$	−4.78009	−	22.4886i	−0.290370	−	1.36608i	−0.845347	−	0.534217i	$-0.820606\pi$
$271$	−4.78009	−	22.4886i	−0.290370	−	1.36608i	0.554977	−	0.831865i	$-0.312727\pi$
$272$	1.88887	+	5.81335i	0.114530	+	0.352486i
$273$	−1.99190	−	2.15773i	−0.120555	−	0.130592i
$274$		−	8.60439i		−	0.519810i
$275$	−16.3141	+	0.756614i	−0.983774	+	0.0456255i
$276$	1.66585	−	1.29041i	0.100272	−	0.0776734i
$277$	−30.5816	+	3.21426i	−1.83747	+	0.193126i	−0.958758	−	0.284223i	$-0.908265\pi$
$277$	−30.5816	+	3.21426i	−1.83747	+	0.193126i	−0.878714	+	0.477349i	$0.841598\pi$
$278$	6.96190	+	6.26853i	0.417547	+	0.375961i
$279$	13.3140	−	6.93803i	0.797086	−	0.415369i
$280$	0.439011	−	0.581515i	0.0262359	−	0.0347522i
$281$	−5.30840	−	3.85678i	−0.316673	−	0.230076i	0.418082	−	0.908409i	$-0.362703\pi$
$281$	−5.30840	−	3.85678i	−0.316673	−	0.230076i	−0.734754	+	0.678333i	$0.762703\pi$
$282$	4.06736	+	0.734602i	0.242207	+	0.0437449i
$283$	4.24111	−	19.9528i	0.252108	−	1.18607i	−0.651815	−	0.758378i	$-0.725992\pi$
$283$	4.24111	−	19.9528i	0.252108	−	1.18607i	0.903923	−	0.427695i	$-0.140674\pi$
$284$	11.2111	−	1.17833i	0.665256	−	0.0699213i
$285$	0.520449	−	0.0709430i	0.0308287	−	0.00420230i
$286$	0.953475	+	1.89946i	0.0563802	+	0.112317i
$287$	4.14921	−	6.89161i	0.244920	−	0.406799i
$288$	2.96724	+	0.442163i	0.174846	+	0.0260547i
$289$	13.6254	−	15.1325i	0.801495	−	0.890150i
$290$	−1.80866	+	1.62853i	−0.106208	+	0.0956303i
$291$	0.536012	+	17.4221i	0.0314216	+	1.02130i
$292$	11.3397	+	1.19186i	0.663608	+	0.0697481i
$293$	−2.75468	+	8.47805i	−0.160930	+	0.495293i	−0.998713	−	0.0507105i	$-0.983851\pi$
$293$	−2.75468	+	8.47805i	−0.160930	+	0.495293i	0.837783	+	0.546003i	$0.183851\pi$
$294$	4.86575	+	11.1052i	0.283776	+	0.647666i
$295$	1.97125	−	1.43220i	0.114770	−	0.0833856i
$296$	−3.61587	−	6.26288i	−0.210168	−	0.364022i
$297$	−17.2238	+	0.584019i	−0.999426	+	0.0338882i
$298$	7.12549	−	12.3417i	0.412768	−	0.714936i
$299$	0.712201	+	0.317092i	0.0411877	+	0.0183379i
$300$	−8.50557	−	0.630249i	−0.491070	−	0.0363875i
$301$	−2.24829	+	1.95091i	−0.129589	+	0.112449i
$302$	−6.15267	+	8.46843i	−0.354047	+	0.487303i
$303$	8.03104	+	4.31303i	0.461371	+	0.247777i
$304$	−0.818342	+	0.736838i	−0.0469351	+	0.0422606i
$305$	1.19314	+	0.253610i	0.0683190	+	0.0145217i
$306$	−6.72801	−	17.0587i	−0.384615	−	0.975181i
$307$		−	18.1321i		−	1.03485i	−0.855728	−	0.517426i	$-0.826890\pi$
$307$		−	18.1321i		−	1.03485i	0.855728	−	0.517426i	$-0.173110\pi$
$308$	−1.16125	−	8.69779i	−0.0661681	−	0.495602i
$309$	8.68208	−	21.2347i	0.493906	−	1.20800i
$310$	−0.560558	+	1.25903i	−0.0318375	+	0.0715083i
$311$	−4.14726	+	19.5113i	−0.235170	+	1.10639i	0.689106	+	0.724661i	$0.258003\pi$
$311$	−4.14726	+	19.5113i	−0.235170	+	1.10639i	−0.924276	+	0.381726i	$0.875330\pi$
$312$	0.375284	+	1.04455i	0.0212463	+	0.0591361i
$313$	2.56985	−	24.4505i	0.145257	−	1.38202i	−0.642617	−	0.766188i	$-0.722151\pi$
$313$	2.56985	−	24.4505i	0.145257	−	1.38202i	0.787874	−	0.615837i	$-0.211182\pi$
$314$	−12.1927	−	8.85849i	−0.688072	−	0.499913i
$315$	−1.20730	+	1.82221i	−0.0680236	+	0.102670i
$316$	−11.8116	+	3.83782i	−0.664455	+	0.215894i
$317$	−6.43740	+	14.4586i	−0.361561	+	0.812078i	0.637570	+	0.770392i	$0.279940\pi$
$317$	−6.43740	+	14.4586i	−0.361561	+	0.812078i	−0.999131	+	0.0416861i	$0.986727\pi$
$318$	−11.2235	+	8.69398i	−0.629382	+	0.487534i
$319$	−1.71004	+	29.2608i	−0.0957438	+	1.63829i
$320$	−0.238498	+	0.137697i	−0.0133324	+	0.00769748i
$321$	−2.80475	−	11.4515i	−0.156546	−	0.639159i
$322$	−2.35211	−	2.19728i	−0.131078	−	0.122450i
$323$	6.40158	+	2.08000i	0.356194	+	0.115734i
$324$	−8.96642	−	0.776753i	−0.498134	−	0.0431529i
$325$	−1.28344	−	2.88266i	−0.0711927	−	0.159901i
$326$	−14.2045	−	15.7757i	−0.786717	−	0.873738i
$327$	−7.39706	+	3.56986i	−0.409058	+	0.197414i
$328$	−2.45977	+	1.78713i	−0.135818	+	0.0986777i
$329$	0.115777	−	6.31245i	0.00638299	−	0.348016i
$330$	1.20445	−	1.02571i	0.0663028	−	0.0564632i
$331$	2.50319	+	4.33564i	0.137588	+	0.238309i	0.926583	−	0.376091i	$-0.122732\pi$
$331$	2.50319	+	4.33564i	0.137588	+	0.238309i	−0.788995	+	0.614399i	$0.789399\pi$
$332$	0.441360	+	4.19926i	0.0242228	+	0.230464i
$333$	11.9821	+	18.0863i	0.656616	+	0.991120i
$334$	3.91044	−	0.831189i	0.213970	−	0.0454806i
$335$	−1.71909	+	2.36612i	−0.0939237	+	0.129275i
$336$	−0.0569028	−	4.58222i	−0.00310430	−	0.249981i
$337$	−33.0515	−	10.7391i	−1.80043	−	0.584996i	−0.800534	−	0.599287i	$-0.795451\pi$
$337$	−33.0515	−	10.7391i	−1.80043	−	0.584996i	−0.999898	+	0.0142910i	$0.995451\pi$
$338$	8.42392	−	9.35572i	0.458201	−	0.508884i
$339$	0.722959	−	2.48233i	0.0392657	−	0.134822i
$340$	1.45782	+	0.841674i	0.0790615	+	0.0456462i
$341$	5.85480	+	15.5309i	0.317055	+	0.841043i
$342$	2.31449	−	2.35725i	0.125153	−	0.127466i
$343$	15.5591	−	10.0455i	0.840115	−	0.542409i
$344$	1.07003	−	0.347673i	0.0576921	−	0.0187453i
$345$	0.103139	−	0.571064i	0.00555284	−	0.0307451i
$346$	−0.690887	+	0.307603i	−0.0371423	+	0.0165368i
$347$	−5.20227	+	2.31620i	−0.279272	+	0.124340i	−0.541593	−	0.840641i	$-0.682179\pi$
$347$	−5.20227	+	2.31620i	−0.279272	+	0.124340i	0.262321	+	0.964981i	$0.415512\pi$
$348$	−2.72057	+	15.0633i	−0.145838	+	0.807478i
$349$	1.53551	−	0.498918i	0.0821941	−	0.0267065i	−0.267631	−	0.963521i	$-0.586241\pi$
$349$	1.53551	−	0.498918i	0.0821941	−	0.0267065i	0.349825	+	0.936815i	$0.386241\pi$
$350$	1.12398	+	12.9795i	0.0600791	+	0.693785i
$351$	−1.31636	−	3.05852i	−0.0702622	−	0.163252i
$352$	−0.877660	+	3.19839i	−0.0467794	+	0.170475i
$353$	3.35330	+	1.93603i	0.178478	+	0.103044i	0.586578	−	0.809893i	$-0.300475\pi$
$353$	3.35330	+	1.93603i	0.178478	+	0.103044i	−0.408099	+	0.912938i	$0.633808\pi$
$354$	4.28514	−	14.7133i	0.227753	−	0.782005i
$355$	2.07730	−	2.30707i	0.110251	−	0.122447i
$356$	−17.2673	−	5.61050i	−0.915167	−	0.297356i
$357$	−24.0825	+	14.3057i	−1.27458	+	0.757137i
$358$	−1.06796	+	1.46993i	−0.0564436	+	0.0776880i
$359$	−12.9606	+	2.75487i	−0.684037	+	0.145396i	−0.536806	−	0.843706i	$-0.680369\pi$
$359$	−12.9606	+	2.75487i	−0.684037	+	0.145396i	−0.147231	+	0.989102i	$0.547036\pi$
$360$	0.688746	−	0.456293i	0.0363001	−	0.0240488i
$361$	−1.85929	−	17.6899i	−0.0978573	−	0.931050i
$362$	10.3697	+	17.9609i	0.545021	+	0.944004i
$363$	1.63637	−	18.9822i	0.0858874	−	0.996305i
$364$	1.48359	−	0.820649i	0.0777611	−	0.0430137i
$365$	2.54039	−	1.84570i	0.132970	−	0.0966084i
$366$	6.90922	−	3.33443i	0.361150	−	0.174293i
$367$	6.27128	+	6.96497i	0.327358	+	0.363568i	0.884248	−	0.467019i	$-0.154672\pi$
$367$	6.27128	+	6.96497i	0.327358	+	0.363568i	−0.556889	+	0.830587i	$0.688005\pi$
$368$	0.494828	+	1.11140i	0.0257947	+	0.0579358i
$369$	7.03577	−	5.80488i	0.366268	−	0.302190i
$370$	−1.89410	−	0.615431i	−0.0984697	−	0.0319947i
$371$	15.8471	+	14.8039i	0.822742	+	0.768583i
$372$	2.06203	+	8.41906i	0.106911	+	0.436508i
$373$	11.2890	−	6.51770i	0.584522	−	0.337474i	−0.178406	−	0.983957i	$-0.557094\pi$
$373$	11.2890	−	6.51770i	0.584522	−	0.337474i	0.762928	+	0.646483i	$0.223761\pi$
$374$	19.6133	−	5.12914i	1.01418	−	0.265221i
$375$	−3.74233	+	2.89890i	−0.193253	+	0.149699i
$376$	−0.970588	+	2.17998i	−0.0500543	+	0.112424i
$377$	−5.38602	+	1.75002i	−0.277394	+	0.0901308i
$378$	1.01545	+	13.7102i	0.0522292	+	0.705175i
$379$	3.50425	+	2.54599i	0.180001	+	0.130778i	0.674137	−	0.738606i	$-0.264516\pi$
$379$	3.50425	+	2.54599i	0.180001	+	0.130778i	−0.494136	+	0.869385i	$0.664516\pi$
$380$	−0.0316993	+	0.301599i	−0.00162614	+	0.0154717i
$381$	−0.0508135	−	0.141432i	−0.00260325	−	0.00724580i
$382$	2.38801	−	11.2347i	0.122181	−	0.574818i
$383$	7.58306	−	17.0318i	0.387476	−	0.870286i	−0.609515	−	0.792774i	$-0.708636\pi$
$383$	7.58306	−	17.0318i	0.387476	−	0.870286i	0.996991	−	0.0775114i	$-0.0246974\pi$
$384$	−0.655497	+	1.60322i	−0.0334507	+	0.0818141i
$385$	−1.84044	−	1.56608i	−0.0937973	−	0.0798147i
$386$		−	4.35689i		−	0.221760i
$387$	−3.13990	+	1.23839i	−0.159610	+	0.0629507i
$388$	−9.84349	−	2.09230i	−0.499727	−	0.106220i
$389$	−23.0397	+	20.7451i	−1.16816	+	1.05182i	−0.170371	+	0.985380i	$0.554497\pi$
$389$	−23.0397	+	20.7451i	−1.16816	+	1.05182i	−0.997791	+	0.0664373i	$0.978837\pi$
$390$	0.269289	+	0.144620i	0.0136360	+	0.00732312i
$391$	4.37099	−	6.01615i	0.221050	−	0.304250i
$392$	−6.89580	+	1.20332i	−0.348290	+	0.0607770i
$393$	−20.4138	−	1.51263i	−1.02974	−	0.0763021i
$394$	15.2293	+	6.78051i	0.767240	+	0.341597i
$395$	−1.71012	+	2.96201i	−0.0860454	+	0.149035i
$396$	2.03814	−	9.73889i	0.102421	−	0.489398i
$397$	−0.560544	−	0.970891i	−0.0281329	−	0.0487276i	0.851616	−	0.524166i	$-0.175623\pi$
$397$	−0.560544	−	0.970891i	−0.0281329	−	0.0487276i	−0.879749	+	0.475438i	$0.842289\pi$
$398$	4.40565	−	3.20089i	0.220835	−	0.160446i
$399$	−4.11904	−	2.91520i	−0.206210	−	0.145943i
$400$	1.52165	−	4.68315i	0.0760824	−	0.234158i
$401$	−11.5154	−	1.21032i	−0.575054	−	0.0604406i	−0.187462	−	0.982272i	$-0.560026\pi$
$401$	−11.5154	−	1.21032i	−0.575054	−	0.0604406i	−0.387592	+	0.921831i	$0.626693\pi$
$402$	0.565659	+	18.3857i	0.0282125	+	0.916996i
$403$	−2.38319	+	2.14583i	−0.118715	+	0.106892i
$404$	−3.52168	+	3.91122i	−0.175210	+	0.194591i
$405$	−1.97818	+	1.49331i	−0.0982965	+	0.0742033i
$406$	23.3779	+	0.428776i	1.16023	+	0.0212798i
$407$	−21.4359	+	10.7602i	−1.06254	+	0.533364i
$408$	10.4902	−	1.42993i	0.519341	−	0.0707921i
$409$	−18.0373	+	1.89579i	−0.891886	+	0.0937410i	−0.539374	−	0.842066i	$-0.681339\pi$
$409$	−18.0373	+	1.89579i	−0.891886	+	0.0937410i	−0.352512	+	0.935807i	$0.614672\pi$
$410$	−0.174088	+	0.819021i	−0.00859761	+	0.0404486i
$411$	−14.6660	−	2.64881i	−0.723419	−	0.130656i
$412$	10.7155	+	7.78523i	0.527913	+	0.383551i
$413$	−23.2318	−	2.87339i	−1.14316	−	0.141390i
$414$	−1.68664	−	3.23664i	−0.0828940	−	0.159072i
$415$	0.864142	+	0.778077i	0.0424191	+	0.0381943i
$416$	−0.637303	+	0.0669833i	−0.0312464	+	0.00328412i
$417$	12.8277	−	9.93666i	0.628176	−	0.486600i
$418$	2.28131	+	2.85209i	0.111582	+	0.139500i
$419$		−	11.8865i		−	0.580692i	−0.956922	−	0.290346i	$-0.906230\pi$
$419$		−	11.8865i		−	0.580692i	0.956922	−	0.290346i	$-0.0937704\pi$
$420$	−0.856031	−	0.927299i	−0.0417700	−	0.0452476i
$421$	8.22765	+	25.3221i	0.400991	+	1.23412i	0.924197	+	0.381917i	$0.124736\pi$
$421$	8.22765	+	25.3221i	0.400991	+	1.23412i	−0.523206	+	0.852206i	$0.675264\pi$
$422$	4.30052	+	20.2324i	0.209346	+	0.984896i
$423$	2.50422	−	6.70656i	0.121759	−	0.326084i
$424$	−3.33385	−	7.48795i	−0.161906	−	0.363647i
$425$	−29.4413	+	6.25793i	−1.42811	+	0.303554i
$426$	1.44283	−	19.4718i	0.0699052	−	0.943410i
$427$	−6.71311	−	9.60541i	−0.324870	−	0.464839i
$428$	6.80693			0.329025
$429$	3.53110	−	1.04044i	0.170483	−	0.0502328i
$430$	0.154922	−	0.268333i	0.00747100	−	0.0129401i
$431$	−0.480468	−	4.57134i	−0.0231433	−	0.220194i	−0.999981	−	0.00621097i	$-0.998023\pi$
$431$	−0.480468	−	4.57134i	−0.0231433	−	0.220194i	0.976837	−	0.213983i	$-0.0686437\pi$
$432$	1.66710	−	4.92146i	0.0802084	−	0.236784i
$433$	−5.62756	+	17.3199i	−0.270443	+	0.832339i	0.719946	+	0.694030i	$0.244167\pi$
$433$	−5.62756	+	17.3199i	−0.270443	+	0.832339i	−0.990389	+	0.138309i	$0.955833\pi$
$434$	12.1925	−	5.16265i	0.585257	−	0.247815i
$435$	2.21899	+	3.58415i	0.106393	+	0.171847i
$436$	−0.985922	−	4.63840i	−0.0472171	−	0.222139i
$437$	1.31041	+	0.278536i	0.0626853	+	0.0133242i
$438$	5.52236	−	18.9614i	0.263868	−	0.906011i
$439$	−19.3916	+	11.1958i	−0.925513	+	0.534345i	−0.885390	−	0.464850i	$-0.846108\pi$
$439$	−19.3916	+	11.1958i	−0.925513	+	0.534345i	−0.0401231	+	0.999195i	$0.512775\pi$
$440$	0.409762	+	0.816304i	0.0195346	+	0.0389158i
$441$	20.4263	−	4.87489i	0.972683	−	0.232137i
$442$	2.30234	+	3.16891i	0.109511	+	0.150729i
$443$	11.5716	+	10.4191i	0.549783	+	0.495027i	0.896561	−	0.442920i	$-0.146058\pi$
$443$	11.5716	+	10.4191i	0.549783	+	0.495027i	−0.346778	+	0.937947i	$0.612724\pi$
$444$	−11.7880	+	4.23518i	−0.559436	+	0.200993i
$445$	−4.56775	+	2.03370i	−0.216532	+	0.0964064i
$446$	−0.589611	+	5.60977i	−0.0279189	+	0.265630i
$447$	−18.8426	−	15.9445i	−0.891224	−	0.754150i
$448$	2.57741	+	0.597448i	0.121771	+	0.0282267i
$449$	10.9616	+	15.0873i	0.517309	+	0.712014i	0.985130	−	0.171809i	$-0.0549610\pi$
$449$	10.9616	+	15.0873i	0.517309	+	0.712014i	−0.467822	+	0.883823i	$0.654961\pi$
$450$	−3.69263	+	14.3035i	−0.174072	+	0.674274i
$451$	5.44118	+	8.49005i	0.256215	+	0.399781i
$452$	1.29273	+	0.746360i	0.0608050	+	0.0351058i
$453$	12.5402	+	13.0940i	0.589188	+	0.615211i
$454$	7.42335	+	22.8467i	0.348395	+	1.07225i
$455$	0.152402	−	0.441339i	0.00714474	−	0.0206903i
$456$	1.00400	+	1.62167i	0.0470166	+	0.0759418i
$457$	19.0672	+	2.00405i	0.891927	+	0.0937453i	0.539394	−	0.842054i	$-0.318653\pi$
$457$	19.0672	+	2.00405i	0.891927	+	0.0937453i	0.352534	+	0.935799i	$0.385320\pi$
$458$	−17.3475	−	19.2664i	−0.810596	−	0.900258i
$459$	−31.1473	+	6.21630i	−1.45383	+	0.290152i
$460$	0.306073	+	0.136272i	0.0142707	+	0.00635373i
$461$	23.8811			1.11225			0.556126	−	0.831098i	$-0.312287\pi$
$461$	23.8811			1.11225			0.556126	+	0.831098i	$0.312287\pi$
$462$	−15.1826	−	0.698246i	−0.706360	−	0.0324854i
$463$	−9.27277			−0.430942			−0.215471	−	0.976510i	$-0.569129\pi$
$463$	−9.27277			−0.430942			−0.215471	+	0.976510i	$0.569129\pi$
$464$	−8.07347	−	3.59454i	−0.374801	−	0.166872i
$465$	1.97343	+	1.34304i	0.0915154	+	0.0622821i
$466$	11.2780	+	12.5255i	0.522443	+	0.580231i
$467$	28.7854	+	3.02546i	1.33203	+	0.140002i	0.743642	−	0.668578i	$-0.233097\pi$
$467$	28.7854	+	3.02546i	1.33203	+	0.140002i	0.588386	+	0.808580i	$0.299764\pi$
$468$	1.89594	−	0.318103i	0.0876399	−	0.0147043i
$469$	27.5864	−	5.33690i	1.27382	−	0.246435i
$470$	0.203076	+	0.625002i	0.00936718	+	0.0288292i
$471$	−18.8525	+	18.0550i	−0.868677	+	0.831933i
$472$	7.66232	+	4.42384i	0.352687	+	0.203624i
$473$	−0.944090	−	3.61011i	−0.0434093	−	0.165993i
$474$	2.90534	+	21.3140i	0.133447	+	0.978986i
$475$	−3.18722	−	4.38683i	−0.146240	−	0.201282i
$476$	−4.71459	−	15.4697i	−0.216093	−	0.709054i
$477$	11.3636	+	21.8065i	0.520303	+	0.998453i
$478$	−1.43046	+	13.6099i	−0.0654278	+	0.622504i
$479$	−29.1402	+	12.9741i	−1.33145	+	0.592800i	−0.944260	−	0.329200i	$-0.893221\pi$
$479$	−29.1402	+	12.9741i	−1.33145	+	0.592800i	−0.387190	+	0.922000i	$0.626554\pi$
$480$	0.161281	+	0.448902i	0.00736142	+	0.0204895i
$481$	−3.44388	−	3.10089i	−0.157028	−	0.141388i
$482$	−1.86674	−	2.56934i	−0.0850275	−	0.117030i
$483$	−4.46929	+	3.33270i	−0.203360	+	0.151643i
$484$	10.4200	+	3.52479i	0.473635	+	0.160218i
$485$	−2.40010	+	1.38570i	−0.108983	+	0.0629213i
$486$	−4.08421	+	15.0439i	−0.185264	+	0.682406i
$487$	−18.7142	−	3.97782i	−0.848021	−	0.180252i	−0.236648	−	0.971595i	$-0.576049\pi$
$487$	−18.7142	−	3.97782i	−0.848021	−	0.180252i	−0.611372	+	0.791343i	$0.709382\pi$
$488$	0.920900	+	4.33249i	0.0416872	+	0.196123i
$489$	−31.2621	+	19.3548i	−1.41372	+	0.875255i
$490$	−1.18953	+	1.51699i	−0.0537376	+	0.0685305i
$491$	8.01785	−	24.6764i	0.361841	−	1.11363i	−0.590095	−	0.807334i	$-0.700910\pi$
$491$	8.01785	−	24.6764i	0.361841	−	1.11363i	0.951936	−	0.306297i	$-0.0990901\pi$
$492$	2.28889	+	4.74277i	0.103191	+	0.213821i
$493$	5.64657	+	53.7235i	0.254309	+	2.41958i
$494$	−0.352828	+	0.611116i	−0.0158745	+	0.0274954i
$495$	−1.37751	−	2.36871i	−0.0619143	−	0.106466i
$496$	−5.00442			−0.224705
$497$	−29.7140	+	2.57312i	−1.33285	+	0.115420i
$498$	7.29339	+	0.540429i	0.326825	+	0.0242172i
$499$	−20.8583	+	4.43356i	−0.933744	+	0.198473i	−0.649572	−	0.760300i	$-0.725052\pi$
$499$	−20.8583	+	4.43356i	−0.933744	+	0.198473i	−0.284172	+	0.958773i	$0.591719\pi$
$500$	−1.11163	−	2.49676i	−0.0497137	−	0.111659i
$501$	−0.212937	−	6.92111i	−0.00951331	−	0.309213i
$502$	2.06313	+	9.70626i	0.0920820	+	0.433212i
$503$	−10.3394	−	31.8215i	−0.461013	−	1.41885i	−0.863929	−	0.503614i	$-0.832003\pi$
$503$	−10.3394	−	31.8215i	−0.461013	−	1.41885i	0.402916	−	0.915237i	$-0.367997\pi$
$504$	−7.82780	−	1.31362i	−0.348678	−	0.0585132i
$505$			1.44942i			0.0644982i
$506$	3.77557	−	1.42331i	0.167845	−	0.0632738i
$507$	−13.3533	−	17.2385i	−0.593042	−	0.765587i
$508$	0.0862909	−	0.00906954i	0.00382854	−	0.000402396i
$509$	4.31420	+	3.88452i	0.191223	+	0.172178i	0.759181	−	0.650879i	$-0.225600\pi$
$509$	4.31420	+	3.88452i	0.191223	+	0.172178i	−0.567958	+	0.823058i	$0.692266\pi$
$510$	1.88339	−	2.22572i	0.0833980	−	0.0985563i
$511$	−29.9393	−	3.70300i	−1.32444	−	0.163811i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−3.30538	−	4.67066i	−0.145936	−	0.206215i
$514$	4.34288	−	20.4316i	0.191556	−	0.901201i
$515$	3.62761	−	0.381278i	0.159852	−	0.0168011i
$516$	−0.263199	−	1.93087i	−0.0115867	−	0.0850016i
$517$	7.03004	+	3.63541i	0.309181	+	0.159885i
$518$	9.26124	+	16.7427i	0.406915	+	0.735631i
$519$	0.311616	+	1.27229i	0.0136784	+	0.0558474i
$520$	−0.118085	+	0.131147i	−0.00517839	+	0.00575118i
$521$	6.06631	−	5.46213i	0.265770	−	0.239300i	−0.525461	−	0.850818i	$-0.676107\pi$
$521$	6.06631	−	5.46213i	0.265770	−	0.239300i	0.791231	+	0.611517i	$0.209441\pi$
$522$	24.8375	+	9.27429i	1.08711	+	0.405925i
$523$	−5.89173	−	0.619246i	−0.257627	−	0.0270777i	−0.0251658	−	0.999683i	$-0.508011\pi$
$523$	−5.89173	−	0.619246i	−0.257627	−	0.0270777i	−0.232462	+	0.972606i	$0.574678\pi$
$524$	3.65204	−	11.2398i	0.159540	−	0.491013i
$525$	22.4693	+	2.07987i	0.980639	+	0.0907731i
$526$	15.6176	−	11.3468i	0.680959	−	0.494746i
$527$	15.2948	+	26.4913i	0.666251	+	1.15398i
$528$	5.18139	+	2.48055i	0.225491	+	0.107952i
$529$	−10.7600	+	18.6368i	−0.467825	+	0.810296i
$530$	−2.06213	−	0.918121i	−0.0895734	−	0.0398806i
$531$	−23.7594	−	11.8333i	−1.03107	−	0.513523i
$532$	2.20051	−	1.90946i	0.0954044	−	0.0827855i
$533$	−1.14522	+	1.57626i	−0.0496048	+	0.0682752i
$534$	−14.8786	+	27.7046i	−0.643859	+	1.19889i
$535$	1.39309	−	1.25434i	0.0602284	−	0.0542299i
$536$	−10.3879	−	2.20802i	−0.448691	−	0.0953721i
$537$	2.17668	+	2.27282i	0.0939309	+	0.0980796i
$538$		−	21.6384i		−	0.932897i
$539$	2.64985	+	23.0647i	0.114137	+	0.993465i
$540$	−0.565714	−	1.31442i	−0.0243445	−	0.0565635i
$541$	−6.32423	+	14.2045i	−0.271900	+	0.610697i	−0.996954	−	0.0779949i	$-0.975148\pi$
$541$	−6.32423	+	14.2045i	−0.271900	+	0.610697i	0.725054	+	0.688692i	$0.241815\pi$
$542$	4.78009	−	22.4886i	0.205322	−	0.965966i
$543$	33.8062	−	12.1458i	1.45076	−	0.521226i
$544$	−0.638932	+	6.07903i	−0.0273940	+	0.260636i
$545$	−1.05651	−	0.767602i	−0.0452561	−	0.0328805i
$546$	−0.942062	−	2.78137i	−0.0403165	−	0.119032i
$547$	−17.7453	+	5.76579i	−0.758734	+	0.246527i	−0.662735	−	0.748854i	$-0.730604\pi$
$547$	−17.7453	+	5.76579i	−0.758734	+	0.246527i	−0.0959986	+	0.995381i	$0.530604\pi$
$548$	3.49972	−	7.86051i	0.149501	−	0.335784i
$549$	−3.55649	−	12.8031i	−0.151787	−	0.546421i
$550$	−15.2114	−	5.94432i	−0.648615	−	0.253467i
$551$	−8.42794	+	4.86588i	−0.359043	+	0.207293i
$552$	2.04669	−	0.501283i	0.0871127	−	0.0213360i
$553$	31.4315	−	9.57914i	1.33660	−	0.407347i
$554$	−29.2451	−	9.50230i	−1.24250	−	0.403714i
$555$	−1.63207	+	3.03899i	−0.0692777	+	0.128998i
$556$	3.81038	+	8.55825i	0.161596	+	0.362950i
$557$	30.7492	+	34.1504i	1.30288	+	1.44700i	0.821185	+	0.570661i	$0.193313\pi$
$557$	30.7492	+	34.1504i	1.30288	+	1.44700i	0.481698	+	0.876337i	$0.340020\pi$
$558$	14.9849	−	0.922929i	0.634359	−	0.0390707i
$559$	0.583282	−	0.423779i	0.0246702	−	0.0179239i
$560$	0.637580	−	0.352679i	0.0269427	−	0.0149034i
$561$	−2.70464	−	35.0094i	−0.114190	−	1.47810i
$562$	−3.28077	−	5.68246i	−0.138391	−	0.239700i
$563$	−0.336644	−	3.20295i	−0.0141879	−	0.134988i	0.985135	−	0.171782i	$-0.0549524\pi$
$563$	−0.336644	−	3.20295i	−0.0141879	−	0.134988i	−0.999323	+	0.0367933i	$0.988286\pi$
$564$	3.41692	+	2.32543i	0.143878	+	0.0979185i
$565$	0.402102	−	0.0854694i	0.0169166	−	0.00359573i
$566$	11.9900	−	16.5028i	0.503977	−	0.693665i
$567$	23.6812	+	2.48978i	0.994518	+	0.104561i
$568$	10.7211	+	3.48350i	0.449848	+	0.146165i
$569$	−10.9310	+	12.1401i	−0.458251	+	0.508939i	−0.927344	−	0.374209i	$-0.877914\pi$
$569$	−10.9310	+	12.1401i	−0.458251	+	0.508939i	0.469093	+	0.883149i	$0.344581\pi$
$570$	0.504309	+	0.146876i	0.0211232	+	0.00615195i
$571$	−36.1012	−	20.8430i	−1.51079	−	0.872253i	−0.999921	−	0.0125921i	$-0.995992\pi$
$571$	−36.1012	−	20.8430i	−1.51079	−	0.872253i	−0.510865	−	0.859661i	$-0.670675\pi$
$572$	0.0984632	+	2.12306i	0.00411695	+	0.0887694i
$573$	−18.4141	−	7.52884i	−0.769261	−	0.314522i
$574$	6.59356	−	4.60816i	0.275210	−	0.192341i
$575$	−5.69743	+	1.85121i	−0.237599	+	0.0772007i
$576$	2.53086	+	1.61082i	0.105453	+	0.0671175i
$577$	35.4712	−	15.7928i	1.47669	−	0.657463i	0.498823	−	0.866704i	$-0.333766\pi$
$577$	35.4712	−	15.7928i	1.47669	−	0.657463i	0.977864	+	0.209241i	$0.0670992\pi$
$578$	18.6024	−	8.28232i	0.773757	−	0.344499i
$579$	−7.42620	−	1.34124i	−0.308622	−	0.0557401i
$580$	−2.31467	+	0.752083i	−0.0961116	+	0.0312286i
$581$	−0.963793	−	11.1297i	−0.0399849	−	0.461739i
$582$	−6.59652	+	16.1339i	−0.273435	+	0.668770i
$583$	−25.4375	+	9.58940i	−1.05351	+	0.397152i
$584$	9.87460	+	5.70110i	0.408614	+	0.235913i
$585$	0.329400	−	0.414475i	0.0136190	−	0.0171364i
$586$	−5.96486	+	6.62465i	−0.246406	+	0.273662i
$587$	−19.6492	−	6.38441i	−0.811009	−	0.263513i	−0.125984	−	0.992032i	$-0.540209\pi$
$587$	−19.6492	−	6.38441i	−0.811009	−	0.263513i	−0.685025	+	0.728520i	$0.740209\pi$
$588$	−0.0717939	+	12.1241i	−0.00296073	+	0.499991i
$589$	−3.23917	+	4.45833i	−0.133468	+	0.183702i
$590$	2.38335	−	0.506597i	0.0981210	−	0.0208563i
$591$	16.2455	−	23.8706i	0.668249	−	0.981905i
$592$	−0.755924	−	7.19213i	−0.0310683	−	0.295595i
$593$	−4.92618	−	8.53239i	−0.202294	−	0.350383i	0.746973	−	0.664854i	$-0.231506\pi$
$593$	−4.92618	−	8.53239i	−0.202294	−	0.350383i	−0.949267	+	0.314471i	$0.898173\pi$
$594$	−15.9723	−	6.47202i	−0.655350	−	0.265550i
$595$	−3.81555	−	2.29721i	−0.156422	−	0.0941766i
$596$	11.5293	−	8.37651i	0.472258	−	0.343115i
$597$	−4.09958	−	8.49469i	−0.167785	−	0.347664i
$598$	0.521655	+	0.579357i	0.0213321	+	0.0236917i
$599$	−1.17629	−	2.64199i	−0.0480620	−	0.107949i	0.887919	−	0.460001i	$-0.152151\pi$
$599$	−1.17629	−	2.64199i	−0.0480620	−	0.107949i	−0.935981	+	0.352052i	$0.885484\pi$
$600$	−7.51388	−	4.03529i	−0.306753	−	0.164740i
$601$	3.36832	+	1.09443i	0.137396	+	0.0446428i	0.376908	−	0.926251i	$-0.376987\pi$
$601$	3.36832	+	1.09443i	0.137396	+	0.0446428i	−0.239512	+	0.970894i	$0.576987\pi$
$602$	−2.84742	+	0.867787i	−0.116052	+	0.0353684i
$603$	31.5121	+	4.69577i	1.28327	+	0.191227i
$604$	−9.06517	+	5.23378i	−0.368856	+	0.212959i
$605$	2.78205	−	1.19876i	0.113106	−	0.0487365i
$606$	5.58245	+	7.20666i	0.226772	+	0.292751i
$607$	4.53573	−	10.1874i	0.184100	−	0.413494i	−0.797793	−	0.602931i	$-0.793999\pi$
$607$	4.53573	−	10.1874i	0.184100	−	0.413494i	0.981893	+	0.189437i	$0.0606661\pi$
$608$	−1.04729	+	0.340286i	−0.0424733	+	0.0138004i
$609$	7.92758	−	39.7151i	0.321242	−	1.60934i
$610$	0.986836	+	0.716978i	0.0399558	+	0.0290296i
$611$	−0.159841	+	1.52078i	−0.00646647	+	0.0615244i
$612$	0.792058	−	18.3204i	0.0320170	−	0.740560i
$613$	1.62987	−	7.66792i	0.0658297	−	0.309705i	−0.932897	−	0.360142i	$-0.882728\pi$
$613$	1.62987	−	7.66792i	0.0658297	−	0.309705i	0.998727	+	0.0504375i	$0.0160616\pi$
$614$	7.37498	−	16.5645i	0.297630	−	0.668488i
$615$	1.34241	+	0.548860i	0.0541312	+	0.0221322i
$616$	2.47686	−	8.41815i	0.0997955	−	0.339177i
$617$		−	31.5067i		−	1.26841i	−0.773165	−	0.634205i	$-0.781327\pi$
$617$		−	31.5067i		−	1.26841i	0.773165	−	0.634205i	$-0.218673\pi$
$618$	16.5684	−	15.8676i	0.666480	−	0.638288i
$619$	−12.2442	−	2.60260i	−0.492138	−	0.104607i	−0.0448437	−	0.998994i	$-0.514279\pi$
$619$	−12.2442	−	2.60260i	−0.492138	−	0.104607i	−0.447294	+	0.894387i	$0.647612\pi$
$620$	−1.02419	+	0.922185i	−0.0411325	+	0.0370358i
$621$	−6.03600	+	1.87846i	−0.242216	+	0.0753801i
$622$	−11.7247	+	16.1376i	−0.470117	+	0.647061i
$623$	45.4052	+	15.6793i	1.81912	+	0.628176i
$624$	−0.0820185	+	1.10689i	−0.00328337	+	0.0443109i
$625$	21.8046	+	9.70804i	0.872185	+	0.388322i
$626$	12.2926	−	21.2914i	0.491311	−	0.850975i
$627$	5.56359	−	3.01043i	0.222188	−	0.120225i
$628$	−7.53548	−	13.0518i	−0.300698	−	0.520825i
$629$	−35.7619	+	25.9826i	−1.42592	+	1.03599i
$630$	−1.84408	+	1.17362i	−0.0734700	+	0.0467581i
$631$	11.8671	−	36.5231i	0.472420	−	1.45396i	−0.376985	−	0.926219i	$-0.623039\pi$
$631$	11.8671	−	36.5231i	0.472420	−	1.45396i	0.849405	−	0.527741i	$-0.176961\pi$
$632$	−12.3514	−	1.29819i	−0.491313	−	0.0516391i
$633$	35.8094	−	1.10172i	1.42330	−	0.0437895i
$634$	−11.7617	+	10.5903i	−0.467118	+	0.420595i
$635$	0.0159888	−	0.0177573i	0.000634495	−	0.000704678i
$636$	−13.7893	+	3.37734i	−0.546782	+	0.133920i
$637$	−3.96436	+	2.09889i	−0.157074	+	0.0831609i
$638$	−13.4636	+	26.0355i	−0.533030	+	1.03076i
$639$	−32.7450	−	8.45352i	−1.29537	−	0.334416i
$640$	−0.273885	+	0.0287865i	−0.0108263	+	0.00113788i
$641$	−4.80811	+	22.6204i	−0.189909	+	0.893452i	0.775223	+	0.631688i	$0.217638\pi$
$641$	−4.80811	+	22.6204i	−0.189909	+	0.893452i	−0.965132	+	0.261764i	$0.915696\pi$
$642$	2.09547	−	11.6022i	0.0827016	−	0.457904i
$643$	−2.06467	−	1.50007i	−0.0814226	−	0.0591570i	0.546329	−	0.837570i	$-0.316025\pi$
$643$	−2.06467	−	1.50007i	−0.0814226	−	0.0591570i	−0.627752	+	0.778414i	$0.716025\pi$
$644$	−1.25505	−	2.96401i	−0.0494559	−	0.116798i
$645$	−0.409674	−	0.346665i	−0.0161309	−	0.0136499i
$646$	5.00213	+	4.50393i	0.196806	+	0.177205i
$647$	−27.4748	+	2.88772i	−1.08015	+	0.113528i	−0.627847	−	0.778337i	$-0.716063\pi$
$647$	−27.4748	+	2.88772i	−1.08015	+	0.113528i	−0.452301	+	0.891865i	$0.649397\pi$
$648$	−7.87530	−	4.35657i	−0.309371	−	0.171142i
$649$	16.1299	−	24.5138i	0.633153	−	0.962249i
$650$		−	3.15547i		−	0.123768i
$651$	−5.04624	−	22.3710i	−0.197778	−	0.876790i
$652$	−6.55992	−	20.1894i	−0.256906	−	0.790677i
$653$	2.34905	+	11.0514i	0.0919253	+	0.432475i	0.999909	+	0.0134697i	$0.00428767\pi$
$653$	2.34905	+	11.0514i	0.0919253	+	0.432475i	−0.907984	+	0.419005i	$0.862379\pi$
$654$	−8.20954	+	0.252577i	−0.321019	+	0.00987653i
$655$	−1.32379	−	2.97328i	−0.0517248	−	0.116176i
$656$	−2.97400	+	0.632144i	−0.116115	+	0.0246811i
$657$	−30.6192	−	15.2499i	−1.19457	−	0.594954i
$658$	2.67327	−	5.71962i	0.104215	−	0.222974i
$659$	34.2568			1.33445			0.667227	−	0.744855i	$-0.267481\pi$
$659$	34.2568			1.33445			0.667227	+	0.744855i	$0.267481\pi$
$660$	1.51751	−	0.447134i	0.0590691	−	0.0174047i
$661$	−14.5364	+	25.1779i	−0.565402	+	0.979306i	0.431610	+	0.902060i	$0.357946\pi$
$661$	−14.5364	+	25.1779i	−0.565402	+	0.979306i	−0.997012	+	0.0772451i	$0.975388\pi$
$662$	0.523308	+	4.97895i	0.0203390	+	0.193512i
$663$	6.11008	−	2.94876i	0.237296	−	0.114520i
$664$	−1.30479	+	4.01573i	−0.0506356	+	0.155840i
$665$	0.0984872	−	0.796283i	0.00381917	−	0.0308785i
$666$	3.58988	+	21.3962i	0.139105	+	0.829085i
$667$	2.23537	+	10.5166i	0.0865539	+	0.407204i
$668$	3.91044	+	0.831189i	0.151299	+	0.0321597i
$669$	9.38020	+	2.73191i	0.362660	+	0.105622i
$670$	−2.53285	+	1.46234i	−0.0978525	+	0.0564952i
$671$	14.5230	−	2.21075i	0.560653	−	0.0853450i
$672$	1.81177	−	4.20921i	0.0698907	−	0.162374i
$673$	6.21543	+	8.55481i	0.239587	+	0.329764i	0.911831	−	0.410567i	$-0.134669\pi$
$673$	6.21543	+	8.55481i	0.239587	+	0.329764i	−0.672243	+	0.740330i	$0.734669\pi$
$674$	−25.8261	−	23.2539i	−0.994784	−	0.895708i
$675$	23.2432	+	10.6972i	0.894632	+	0.411737i
$676$	11.5010	−	5.12055i	0.442344	−	0.196944i
$677$	4.49816	−	42.7972i	0.172878	−	1.64483i	−0.472764	−	0.881189i	$-0.656744\pi$
$677$	4.49816	−	42.7972i	0.172878	−	1.64483i	0.645643	−	0.763640i	$-0.276590\pi$
$678$	1.67011	−	1.97367i	0.0641402	−	0.0757982i
$679$	25.9375	+	6.01235i	0.995391	+	0.230733i
$680$	0.989447	+	1.36186i	0.0379436	+	0.0522248i
$681$	41.2269	−	5.61969i	1.57982	−	0.215347i
$682$	−0.968343	+	16.5695i	−0.0370798	+	0.634479i
$683$	7.54826	+	4.35799i	0.288826	+	0.166754i	0.637412	−	0.770523i	$-0.280005\pi$
$683$	7.54826	+	4.35799i	0.288826	+	0.166754i	−0.348586	+	0.937277i	$0.613338\pi$
$684$	3.07318	−	1.21207i	0.117506	−	0.0463447i
$685$	−0.732245	−	2.25362i	−0.0279776	−	0.0861063i
$686$	18.2999	−	2.84859i	0.698693	−	0.108760i
$687$	−38.1793	+	23.6374i	−1.45663	+	0.901821i
$688$	1.11893	+	0.117604i	0.0426589	+	0.00448363i
$689$	−3.51460	−	3.90336i	−0.133895	−	0.148706i
$690$	0.326495	−	0.479743i	0.0124295	−	0.0182635i
$691$	−1.33728	−	0.595395i	−0.0508725	−	0.0226499i	0.381143	−	0.924516i	$-0.375531\pi$
$691$	−1.33728	−	0.595395i	−0.0508725	−	0.0226499i	−0.432015	+	0.901866i	$0.642197\pi$
$692$	−0.756270			−0.0287491
$693$	−5.86402	+	25.6635i	−0.222756	+	0.974874i
$694$	−5.69459			−0.216164
$695$	2.35689	+	1.04935i	0.0894018	+	0.0398042i
$696$	−8.61216	+	12.6545i	−0.326443	+	0.479666i
$697$	12.4356	+	13.8112i	0.471033	+	0.523136i
$698$	1.60569	+	0.168765i	0.0607762	+	0.00638784i
$699$	24.8212	−	15.3671i	0.938824	−	0.581239i
$700$	−4.25244	+	12.3145i	−0.160727	+	0.465446i
$701$	2.37893	+	7.32158i	0.0898508	+	0.276532i	0.985878	−	0.167468i	$-0.0535590\pi$
$701$	2.37893	+	7.32158i	0.0898508	+	0.276532i	−0.896027	+	0.444000i	$0.853559\pi$
$702$	0.0414549	−	3.32951i	0.00156462	−	0.125664i
$703$	−6.89660	−	3.98176i	−0.260110	−	0.150175i
$704$	−2.10269	+	2.56490i	−0.0792479	+	0.0966683i
$705$	1.12782	−	0.153734i	0.0424760	−	0.00578996i
$706$	2.27594	+	3.13256i	0.0856561	+	0.117896i
$707$	9.50569	−	10.1755i	0.357498	−	0.382690i
$708$	9.89913	−	11.6984i	0.372032	−	0.439652i
$709$	−4.77994	+	45.4781i	−0.179514	+	1.70797i	0.419936	+	0.907554i	$0.362052\pi$
$709$	−4.77994	+	45.4781i	−0.179514	+	1.70797i	−0.599450	+	0.800412i	$0.704614\pi$
$710$	2.83607	−	1.26270i	0.106436	−	0.0473884i
$711$	37.2236	+	1.60931i	1.39599	+	0.0603538i
$712$	−13.4925	−	12.1487i	−0.505653	−	0.455292i
$713$	3.57860	+	4.92552i	0.134020	+	0.184462i
$714$	−27.8191	+	3.27364i	−1.04110	+	0.122513i
$715$	0.411376	+	0.416355i	0.0153846	+	0.0155708i
$716$	−1.57351	+	0.908464i	−0.0588047	+	0.0339509i
$717$	22.7574	+	6.62791i	0.849891	+	0.247524i
$718$	−12.9606	−	2.75487i	−0.483687	−	0.102811i
$719$	−5.35628	−	25.1993i	−0.199755	−	0.939775i	−0.957770	−	0.287537i	$-0.907164\pi$
$719$	−5.35628	−	25.1993i	−0.199755	−	0.939775i	0.758014	−	0.652238i	$-0.226170\pi$
$720$	0.814792	−	0.136707i	0.0303655	−	0.00509476i
$721$	−27.9679	−	21.1142i	−1.04158	−	0.786335i
$722$	5.49660	−	16.9168i	0.204562	−	0.629578i
$723$	−4.95404	+	2.39085i	−0.184243	+	0.0889166i
$724$	2.16787	+	20.6259i	0.0805681	+	0.766554i
$725$	21.7586	−	37.6871i	0.808096	−	1.39966i
$726$	9.21564	−	16.6755i	0.342025	−	0.618885i
$727$	48.6736			1.80521			0.902603	−	0.430474i	$-0.141654\pi$
$727$	48.6736			1.80521			0.902603	+	0.430474i	$0.141654\pi$
$728$	1.68911	−	0.146271i	0.0626027	−	0.00542115i
$729$	24.3847	+	11.5926i	0.903135	+	0.429356i
$730$	3.07148	−	0.652862i	0.113680	−	0.0241635i
$731$	−2.79719	−	6.28260i	−0.103458	−	0.232370i
$732$	7.66812	−	0.235919i	0.283422	−	0.00871982i
$733$	8.72047	+	41.0266i	0.322098	+	1.51535i	0.779677	+	0.626182i	$0.215383\pi$
$733$	8.72047	+	41.0266i	0.322098	+	1.51535i	−0.457579	+	0.889169i	$0.651283\pi$
$734$	2.89620	+	8.91357i	0.106901	+	0.329006i
$735$	2.21947	+	2.49452i	0.0818665	+	0.0920119i
$736$			1.21658i			0.0448438i
$737$	−9.32076	+	33.9670i	−0.343335	+	1.25119i
$738$	8.78856	−	2.44132i	0.323511	−	0.0898662i
$739$	17.8704	−	1.87825i	0.657373	−	0.0690927i	0.230032	−	0.973183i	$-0.426117\pi$
$739$	17.8704	−	1.87825i	0.657373	−	0.0690927i	0.427341	+	0.904090i	$0.359450\pi$
$740$	−1.48003	−	1.33263i	−0.0544070	−	0.0489883i
$741$	0.933015	+	0.789514i	0.0342752	+	0.0290035i
$742$	8.45576	+	19.9697i	0.310421	+	0.733110i
$743$	−16.6041	−	12.0636i	−0.609145	−	0.442570i	0.239968	−	0.970781i	$-0.422863\pi$
$743$	−16.6041	−	12.0636i	−0.609145	−	0.442570i	−0.849113	+	0.528211i	$0.822863\pi$
$744$	−1.54058	+	8.52990i	−0.0564803	+	0.312721i
$745$	0.815976	−	3.83886i	0.0298950	−	0.140645i
$746$	12.9640	−	1.36257i	0.474646	−	0.0498873i
$747$	3.16637	−	12.2650i	0.115852	−	0.448754i
$748$	20.0039	+	3.29177i	0.731415	+	0.120359i
$749$	−18.0064	−	0.330257i	−0.657940	−	0.0120673i
$750$	−4.59788	+	1.12613i	−0.167891	+	0.0411206i
$751$	−3.98139	+	4.42179i	−0.145283	+	0.161353i	−0.811394	−	0.584499i	$-0.801291\pi$
$751$	−3.98139	+	4.42179i	−0.145283	+	0.161353i	0.666111	+	0.745853i	$0.267958\pi$
$752$	−1.77335	+	1.59673i	−0.0646675	+	0.0582269i
$753$	17.1792	−	0.528539i	0.626045	−	0.0192610i
$754$	−5.63217	−	0.591965i	−0.205112	−	0.0215581i
$755$	−0.890802	+	2.74161i	−0.0324196	+	0.0997773i
$756$	−4.64877	+	12.9379i	−0.169074	+	0.470546i
$757$	29.7626	−	21.6238i	1.08174	−	0.785930i	0.103754	−	0.994603i	$-0.466914\pi$
$757$	29.7626	−	21.6238i	1.08174	−	0.785930i	0.977985	+	0.208673i	$0.0669145\pi$
$758$	2.16574	+	3.75118i	0.0786634	+	0.136249i
$759$	−1.26371	−	6.87352i	−0.0458697	−	0.249493i
$760$	−0.151630	+	0.262631i	−0.00550020	+	0.00952662i
$761$	12.8340	+	5.71405i	0.465231	+	0.207134i	0.625945	−	0.779867i	$-0.284713\pi$
$761$	12.8340	+	5.71405i	0.465231	+	0.207134i	−0.160715	+	0.987001i	$0.551380\pi$
$762$	0.0111053	−	0.149873i	0.000402303	−	0.00542931i
$763$	2.38302	+	12.3178i	0.0862712	+	0.445935i
$764$	6.75112	−	9.29212i	0.244247	−	0.336177i
$765$	−3.21388	−	3.89537i	−0.116198	−	0.140837i
$766$	13.8549	−	12.4750i	0.500599	−	0.450742i
$767$	5.54582	+	1.17880i	0.200248	+	0.0425640i
$768$	−1.25092	+	1.19800i	−0.0451385	+	0.0432292i
$769$			46.4499i			1.67503i	0.546416	+	0.837514i	$0.315992\pi$
$769$			46.4499i			1.67503i	−0.546416	+	0.837514i	$0.684008\pi$
$770$	−1.04434	−	2.17926i	−0.0376354	−	0.0785349i
$771$	−33.4883	−	13.6921i	−1.20605	−	0.493108i
$772$	1.77211	−	3.98021i	0.0637795	−	0.143251i
$773$	2.42515	−	11.4094i	0.0872265	−	0.410369i	−0.912772	−	0.408470i	$-0.866062\pi$
$773$	2.42515	−	11.4094i	0.0872265	−	0.410369i	0.999998	−	0.00189841i	$-0.000604282\pi$
$774$	−3.37213	−	0.145789i	−0.121209	−	0.00524029i
$775$	2.57585	−	24.5075i	0.0925271	−	0.880337i
$776$	−8.14146	−	5.91512i	−0.292261	−	0.212340i
$777$	31.3885	−	10.6314i	1.12605	−	0.381400i
$778$	−29.4856	+	9.58047i	−1.05711	+	0.343476i
$779$	−1.36179	+	3.05864i	−0.0487914	+	0.109587i
$780$	0.187185	+	0.241646i	0.00670230	+	0.00865233i
$781$	13.6083	−	34.8233i	0.486943	−	1.24608i
$782$	6.44008	−	3.71818i	0.230297	−	0.132962i
$783$	23.4539	−	39.4799i	0.838172	−	1.41089i
$784$	−6.78906	−	1.70548i	−0.242466	−	0.0609101i
$785$	−3.94731	−	1.28256i	−0.140885	−	0.0457765i
$786$	−18.0337	−	9.68491i	−0.643241	−	0.345449i
$787$	−12.6944	−	28.5121i	−0.452507	−	1.01635i	−0.985414	−	0.170174i	$-0.945567\pi$
$787$	−12.6944	−	28.5121i	−0.452507	−	1.01635i	0.532907	−	0.846174i	$-0.321100\pi$
$788$	11.1548	+	12.3886i	0.397372	+	0.441326i
$789$	−14.5326	−	30.1128i	−0.517375	−	1.07204i
$790$	−2.76703	+	2.01037i	−0.0984465	+	0.0715256i
$791$	−3.38346	−	2.03707i	−0.120302	−	0.0724299i
$792$	5.82310	−	8.06793i	0.206915	−	0.286681i
$793$	1.41917	+	2.45808i	0.0503963	+	0.0872889i
$794$	−0.117186	−	1.11495i	−0.00415876	−	0.0395680i
$795$	−2.19973	+	3.23222i	−0.0780163	+	0.114635i
$796$	5.32668	−	1.13222i	0.188799	−	0.0401305i
$797$	15.3391	−	21.1125i	0.543339	−	0.747842i	−0.445751	−	0.895157i	$-0.647063\pi$
$797$	15.3391	−	21.1125i	0.543339	−	0.747842i	0.989090	+	0.147315i	$0.0470632\pi$
$798$	−2.57721	−	4.33853i	−0.0912322	−	0.153582i
$799$	13.8723	+	4.50738i	0.490766	+	0.159460i
$800$	3.29491	−	3.65936i	0.116492	−	0.129378i
$801$	42.6414	+	33.8888i	1.50666	+	1.19740i
$802$	−10.0276	−	5.78944i	−0.354087	−	0.204432i
$803$	20.7869	−	31.5914i	0.733555	−	1.11484i
$804$	−6.96138	+	17.0262i	−0.245509	+	0.600470i
$805$	−0.803045	−	0.375332i	−0.0283036	−	0.0132287i
$806$	−3.04994	+	0.990986i	−0.107430	+	0.0349060i
$807$	−36.8821	−	6.66124i	−1.29831	−	0.234487i
$808$	−4.80806	+	2.14068i	−0.169147	+	0.0753090i
$809$	42.1204	−	18.7532i	1.48087	−	0.659327i	0.502200	−	0.864751i	$-0.332524\pi$
$809$	42.1204	−	18.7532i	1.48087	−	0.659327i	0.978673	+	0.205424i	$0.0658573\pi$
$810$	−2.41454	+	0.559611i	−0.0848383	+	0.0196627i
$811$	13.2059	−	4.29084i	0.463720	−	0.150672i	−0.0678331	−	0.997697i	$-0.521609\pi$
$811$	13.2059	−	4.29084i	0.463720	−	0.150672i	0.531553	+	0.847025i	$0.321609\pi$
$812$	21.1824	+	9.90036i	0.743356	+	0.347435i
$813$	−36.8596	−	15.0705i	−1.29272	−	0.528546i
$814$	−23.9592	+	1.11118i	−0.839771	+	0.0389469i
$815$	−5.06292	−	2.92308i	−0.177346	−	0.102391i
$816$	10.1649	+	2.96043i	0.355841	+	0.103636i
$817$	0.829013	−	0.920712i	0.0290035	−	0.0322116i
$818$	−17.2490	−	5.60453i	−0.603096	−	0.195958i
$819$	−5.03078	+	0.749493i	−0.175790	+	0.0261894i
$820$	−0.492164	+	0.677405i	−0.0171871	+	0.0236560i
$821$	−9.35280	+	1.98800i	−0.326415	+	0.0693817i	−0.368205	−	0.929745i	$-0.620027\pi$
$821$	−9.35280	+	1.98800i	−0.326415	+	0.0693817i	0.0417896	+	0.999126i	$0.486694\pi$
$822$	−12.3207	−	8.38499i	−0.429732	−	0.292460i
$823$	1.58953	+	15.1233i	0.0554074	+	0.527166i	0.986660	+	0.162793i	$0.0520501\pi$
$823$	1.58953	+	15.1233i	0.0554074	+	0.527166i	−0.931253	+	0.364373i	$0.881283\pi$
$824$	6.62252	+	11.4705i	0.230706	+	0.399595i
$825$	−14.8147	+	24.0975i	−0.515780	+	0.838966i
$826$	−20.0546	−	12.0742i	−0.697787	−	0.420115i
$827$	14.2074	−	10.3223i	0.494039	−	0.358940i	−0.312697	−	0.949853i	$-0.601232\pi$
$827$	14.2074	−	10.3223i	0.494039	−	0.358940i	0.806735	+	0.590913i	$0.201232\pi$
$828$	−0.224365	−	3.64284i	−0.00779723	−	0.126597i
$829$	−0.166037	−	0.184403i	−0.00576672	−	0.00640459i	0.740255	−	0.672327i	$-0.234705\pi$
$829$	−0.166037	−	0.184403i	−0.00576672	−	0.00640459i	−0.746021	+	0.665922i	$0.768038\pi$
$830$	0.472961	+	1.06229i	0.0164167	+	0.0368725i
$831$	−25.1993	+	46.9222i	−0.874155	+	1.62771i
$832$	−0.609450	−	0.198022i	−0.0211289	−	0.00686519i
$833$	11.7210	+	41.1509i	0.406108	+	1.42579i
$834$	15.7603	−	3.86009i	0.545735	−	0.133664i
$835$	0.953466	−	0.550484i	0.0329961	−	0.0190503i
$836$	0.924029	+	3.53340i	0.0319582	+	0.122205i
$837$	3.03988	−	25.8254i	0.105074	−	0.892657i
$838$	4.83466	−	10.8588i	0.167011	−	0.375112i
$839$	−15.1848	+	4.93383i	−0.524236	+	0.170335i	−0.559167	−	0.829055i	$-0.688879\pi$
$839$	−15.1848	+	4.93383i	−0.524236	+	0.170335i	0.0349307	+	0.999390i	$0.488879\pi$
$840$	−0.404857	−	1.19531i	−0.0139689	−	0.0412421i
$841$	−39.7240	−	28.8612i	−1.36979	−	0.995213i
$842$	−2.78309	+	26.4794i	−0.0959118	+	0.912539i
$843$	−10.6956	+	3.84268i	−0.368375	+	0.132349i
$844$	−4.30052	+	20.2324i	−0.148030	+	0.696427i
$845$	1.41017	−	3.16729i	0.0485112	−	0.108958i
$846$	5.01552	−	5.10819i	0.172437	−	0.175623i
$847$	−27.3930	−	9.82971i	−0.941235	−	0.337753i
$848$		−	8.19659i		−	0.281472i
$849$	−24.4376	−	25.5169i	−0.838695	−	0.875738i
$850$	−29.4413	−	6.25793i	−1.00983	−	0.214645i
$851$	−6.53819	+	5.88702i	−0.224126	+	0.201804i
$852$	9.23797	−	17.2015i	0.316488	−	0.589314i
$853$	−24.3236	+	33.4786i	−0.832825	+	1.14628i	0.154566	+	0.987982i	$0.450602\pi$
$853$	−24.3236	+	33.4786i	−0.832825	+	1.14628i	−0.987391	+	0.158303i	$0.949398\pi$
$854$	−2.22586	−	11.5055i	−0.0761673	−	0.393708i
$855$	0.405594	−	0.814366i	0.0138710	−	0.0278507i
$856$	6.21844	+	2.76863i	0.212542	+	0.0946297i
$857$	−27.7853	+	48.1256i	−0.949128	+	1.64394i	−0.201861	+	0.979414i	$0.564699\pi$
$857$	−27.7853	+	48.1256i	−0.949128	+	1.64394i	−0.747267	+	0.664524i	$0.768634\pi$
$858$	3.64901	+	0.485742i	0.124575	+	0.0165829i
$859$	24.3875	+	42.2404i	0.832092	+	1.44123i	0.896376	+	0.443294i	$0.146190\pi$
$859$	24.3875	+	42.2404i	0.832092	+	1.44123i	−0.0642847	+	0.997932i	$0.520477\pi$
$860$	0.250669	−	0.182122i	0.00854774	−	0.00621030i
$861$	−5.82471	−	12.6571i	−0.198505	−	0.431354i
$862$	1.42040	−	4.37155i	0.0483792	−	0.148896i
$863$	41.6386	+	4.37640i	1.41740	+	0.148974i	0.782032	−	0.623239i	$-0.214183\pi$
$863$	41.6386	+	4.37640i	1.41740	+	0.148974i	0.635364	+	0.772213i	$0.280850\pi$
$864$	3.52471	−	3.81791i	0.119913	−	0.129888i
$865$	−0.154776	+	0.139361i	−0.00526255	+	0.00473842i
$866$	−12.1857	+	13.5335i	−0.414085	+	0.459888i
$867$	−8.39037	−	34.2570i	−0.284952	−	1.16343i
$868$	13.2382	+	0.242803i	0.449334	+	0.00824127i
$869$	−6.68824	+	40.6441i	−0.226883	+	1.37876i
$870$	0.569349	+	4.17683i	0.0193027	+	0.141608i
$871$	−6.76817	+	0.711363i	−0.229331	+	0.0241036i
$872$	0.985922	−	4.63840i	0.0333875	−	0.157076i
$873$	25.4691	+	16.2103i	0.861997	+	0.548636i
$874$	1.08383	+	0.787446i	0.0366610	+	0.0266358i
$875$	2.81947	+	6.65864i	0.0953154	+	0.225103i
$876$	12.7572	−	15.0760i	0.431026	−	0.509369i
$877$	34.9581	+	31.4764i	1.18045	+	1.06288i	0.996804	+	0.0798919i	$0.0254575\pi$
$877$	34.9581	+	31.4764i	1.18045	+	1.06288i	0.183649	+	0.982992i	$0.441209\pi$
$878$	−22.2689	+	2.34055i	−0.751538	+	0.0789899i
$879$	9.45530	+	12.2063i	0.318919	+	0.411709i
$880$	0.0423151	+	0.912396i	0.00142644	+	0.0307569i
$881$		−	40.9648i		−	1.38014i	−0.723744	−	0.690069i	$-0.757580\pi$
$881$		−	40.9648i		−	1.38014i	0.723744	−	0.690069i	$-0.242420\pi$
$882$	20.6432	+	3.85471i	0.695092	+	0.129795i
$883$	8.15181	+	25.0887i	0.274330	+	0.844302i	0.989396	+	0.145245i	$0.0463969\pi$
$883$	8.15181	+	25.0887i	0.274330	+	0.844302i	−0.715065	+	0.699058i	$0.753603\pi$
$884$	0.814387	+	3.83139i	0.0273908	+	0.128864i
$885$	−0.129782	−	4.21831i	−0.00436256	−	0.141797i
$886$	6.33334	+	14.2249i	0.212773	+	0.477896i
$887$	11.6765	−	2.48191i	0.392058	−	0.0833345i	−0.00766474	−	0.999971i	$-0.502440\pi$
$887$	11.6765	−	2.48191i	0.392058	−	0.0833345i	0.399723	+	0.916636i	$0.369106\pi$
$888$	−12.4915	−	0.925601i	−0.419188	−	0.0310611i
$889$	−0.228706	+	0.0198051i	−0.00767055	+	0.000664241i
$890$	−5.00003			−0.167601
$891$	−15.9483	+	25.2319i	−0.534290	+	0.845301i
$892$	−2.82034	+	4.88497i	−0.0944318	+	0.163561i
$893$	0.274674	+	2.61335i	0.00919161	+	0.0874524i
$894$	−10.7283	−	22.2300i	−0.358809	−	0.743483i
$895$	−0.154623	+	0.475880i	−0.00516847	+	0.0159069i
$896$	2.11158	+	1.59412i	0.0705429	+	0.0532559i
$897$	1.14809	−	0.710796i	0.0383335	−	0.0237328i
$898$	3.87733	+	18.2414i	0.129388	+	0.608724i
$899$	−43.2601	−	9.19522i	−1.44281	−	0.306678i
$900$	−9.19115	+	11.5650i	−0.306372	+	0.385499i
$901$	−43.3894	+	25.0509i	−1.44551	+	0.834566i
$902$	1.51755	+	9.96917i	0.0505289	+	0.331937i
$903$	0.602560	+	5.12050i	0.0200519	+	0.170400i
$904$	0.877398	+	1.20764i	0.0291818	+	0.0401653i
$905$	4.24448	+	3.82175i	0.141091	+	0.127039i
$906$	6.13018	+	17.0625i	0.203662	+	0.566865i
$907$	6.56460	−	2.92275i	0.217974	−	0.0970482i	−0.294845	−	0.955545i	$-0.595268\pi$
$907$	6.56460	−	2.92275i	0.217974	−	0.0970482i	0.512819	+	0.858497i	$0.328601\pi$
$908$	−2.51103	+	23.8909i	−0.0833315	+	0.792846i
$909$	14.0021	−	7.29662i	0.464420	−	0.242014i
$910$	0.318735	−	0.341195i	0.0105660	−	0.0113105i
$911$	−27.3013	−	37.5770i	−0.904531	−	1.24498i	−0.969000	−	0.247061i	$-0.920535\pi$
$911$	−27.3013	−	37.5770i	−0.904531	−	1.24498i	0.0644688	−	0.997920i	$-0.479465\pi$
$912$	0.257606	+	1.88984i	0.00853018	+	0.0625787i
$913$	13.0435	+	5.09716i	0.431677	+	0.168691i
$914$	16.6037	+	9.58613i	0.549200	+	0.317081i
$915$	1.52586	−	1.46132i	0.0504434	−	0.0483097i
$916$	−8.01141	−	24.6566i	−0.264704	−	0.814676i
$917$	−10.2061	+	29.5556i	−0.337035	+	0.976010i
$918$	−30.9829	−	6.98987i	−1.02259	−	0.230700i
$919$	−17.2514	−	1.81319i	−0.569070	−	0.0598117i	−0.184376	−	0.982856i	$-0.559026\pi$
$919$	−17.2514	−	1.81319i	−0.569070	−	0.0598117i	−0.384694	+	0.923044i	$0.625693\pi$
$920$	0.224184	+	0.248982i	0.00739114	+	0.00820870i
$921$	−25.9634	−	17.6697i	−0.855523	−	0.582238i
$922$	21.8164	+	9.71330i	0.718486	+	0.319891i
$923$	7.22380			0.237774
$924$	−13.5860	−	6.81321i	−0.446947	−	0.224138i
$925$	35.6103			1.17086
$926$	−8.47109	−	3.77157i	−0.278377	−	0.123942i
$927$	−21.9454	−	33.1252i	−0.720782	−	1.08797i
$928$	−5.91345	−	6.56755i	−0.194118	−	0.215590i
$929$	−55.7676	−	5.86141i	−1.82968	−	0.192307i	−0.873842	−	0.486210i	$-0.838379\pi$
$929$	−55.7676	−	5.86141i	−1.82968	−	0.192307i	−0.955835	+	0.293904i	$0.905046\pi$
$930$	1.25655	+	2.02959i	0.0412039	+	0.0665530i
$931$	−5.91368	+	4.94434i	−0.193813	+	0.162044i
$932$	5.20838	+	16.0298i	0.170606	+	0.525072i
$933$	23.8968	+	24.9523i	0.782347	+	0.816902i
$934$	25.0662	+	14.4720i	0.820190	+	0.473537i
$935$	4.70053	−	3.01252i	0.153724	−	0.0985199i
$936$	1.86141	+	0.480547i	0.0608421	+	0.0157072i
$937$	−16.3941	−	22.5645i	−0.535572	−	0.737151i	0.452395	−	0.891818i	$-0.350570\pi$
$937$	−16.3941	−	22.5645i	−0.535572	−	0.737151i	−0.987967	+	0.154666i	$0.950570\pi$
$938$	27.3722	+	6.34490i	0.893733	+	0.207168i
$939$	−32.5064	−	27.5068i	−1.06081	−	0.897652i
$940$	−0.0686926	+	0.653566i	−0.00224051	+	0.0213170i
$941$	−22.9421	+	10.2145i	−0.747893	+	0.332983i	−0.745046	−	0.667013i	$-0.767573\pi$
$941$	−22.9421	+	10.2145i	−0.747893	+	0.332983i	−0.00284621	+	0.999996i	$0.500906\pi$
$942$	−24.5663	+	8.82611i	−0.800412	+	0.287570i
$943$	2.74885	+	2.47508i	0.0895150	+	0.0805996i
$944$	5.20054	+	7.15793i	0.169263	+	0.232971i
$945$	1.43272	+	3.50448i	0.0466062	+	0.114001i
$946$	0.605896	−	3.68200i	0.0196994	−	0.119712i
$947$	−31.8795	+	18.4056i	−1.03594	+	0.598102i	−0.918682	−	0.394999i	$-0.870745\pi$
$947$	−31.8795	+	18.4056i	−1.03594	+	0.598102i	−0.117262	+	0.993101i	$0.537412\pi$
$948$	−6.01503	+	20.6530i	−0.195359	+	0.670780i
$949$	7.14702	+	1.51915i	0.232002	+	0.0493136i
$950$	−1.12738	−	5.30393i	−0.0365772	−	0.172082i
$951$	14.4301	+	23.3077i	0.467929	+	0.755804i
$952$	1.98511	−	16.0499i	0.0643378	−	0.520180i
$953$	−4.53556	+	13.9590i	−0.146921	+	0.452177i	−0.997253	−	0.0740700i	$-0.976401\pi$
$953$	−4.53556	+	13.9590i	−0.146921	+	0.452177i	0.850332	+	0.526247i	$0.176401\pi$
$954$	1.51164	+	24.5433i	0.0489411	+	0.794617i
$955$	−0.330633	−	3.14576i	−0.0106990	−	0.101794i
$956$	−6.84245	+	11.8515i	−0.221301	+	0.383304i
$957$	40.2322	+	30.9633i	1.30052	+	1.00090i
$958$	−31.8979			−1.03058
$959$	−9.63921	+	20.6236i	−0.311266	+	0.665972i
$960$	−0.0352480	+	0.475691i	−0.00113762	+	0.0153529i
$961$	5.82567	−	1.23829i	0.187925	−	0.0399447i
$962$	−1.88490	−	4.23356i	−0.0607716	−	0.136495i
$963$	−19.1306	−	7.14335i	−0.616476	−	0.230191i
$964$	−0.660303	−	3.10648i	−0.0212669	−	0.100053i
$965$	−0.370777	−	1.14113i	−0.0119357	−	0.0367344i
$966$	−5.43843	+	1.22675i	−0.174979	+	0.0394700i
$967$		−	14.2865i		−	0.459422i	−0.973259	−	0.229711i	$-0.926222\pi$
$967$		−	14.2865i		−	0.459422i	0.973259	−	0.229711i	$-0.0737781\pi$
$968$	8.08546	+	7.45824i	0.259876	+	0.239717i
$969$	9.21671	−	7.13949i	0.296083	−	0.229353i
$970$	−2.75621	+	0.289690i	−0.0884966	+	0.00930137i
$971$	−11.3787	−	10.2454i	−0.365159	−	0.328790i	0.466042	−	0.884762i	$-0.345679\pi$
$971$	−11.3787	−	10.2454i	−0.365159	−	0.328790i	−0.831201	+	0.555972i	$0.812346\pi$
$972$	−9.85002	+	12.0821i	−0.315940	+	0.387533i
$973$	−9.66439	−	22.8241i	−0.309826	−	0.731706i
$974$	−15.4783	−	11.2457i	−0.495958	−	0.360334i
$975$	−5.37841	−	0.971391i	−0.172247	−	0.0311094i
$976$	−0.920900	+	4.33249i	−0.0294773	+	0.138680i
$977$	−18.3818	+	1.93201i	−0.588087	+	0.0618104i	−0.393899	−	0.919154i	$-0.628874\pi$
$977$	−18.3818	+	1.93201i	−0.588087	+	0.0618104i	−0.194188	+	0.980964i	$0.562207\pi$
$978$	−36.4317	+	4.96605i	−1.16496	+	0.158797i
$979$	−42.8348	+	42.3226i	−1.36901	+	1.35264i
$980$	−1.70371	+	0.902009i	−0.0544229	+	0.0288136i
$981$	−2.09675	+	14.0707i	−0.0669439	+	0.449243i
$982$	17.3615	−	19.2819i	0.554027	−	0.615309i
$983$	28.2701	−	25.4545i	0.901677	−	0.811874i	−0.0810927	−	0.996707i	$-0.525841\pi$
$983$	28.2701	−	25.4545i	0.901677	−	0.811874i	0.982770	+	0.184833i	$0.0591743\pi$
$984$	0.161945	+	5.26371i	0.00516261	+	0.167801i
$985$	4.56581	+	0.479886i	0.145479	+	0.0152904i
$986$	−16.6929	+	51.3755i	−0.531611	+	1.63613i
$987$	−8.92599	−	6.31727i	−0.284117	−	0.201081i
$988$	−0.570887	+	0.414774i	−0.0181623	+	0.0131957i
$989$	−0.684384	−	1.18539i	−0.0217622	−	0.0376932i
$990$	−0.294972	−	2.72421i	−0.00937483	−	0.0865810i
$991$	11.0674	−	19.1694i	0.351569	−	0.608936i	−0.634955	−	0.772549i	$-0.718982\pi$
$991$	11.0674	−	19.1694i	0.351569	−	0.608936i	0.986525	+	0.163613i	$0.0523149\pi$
$992$	−4.57176	−	2.03548i	−0.145154	−	0.0646265i
$993$	8.64758	+	0.640772i	0.274423	+	0.0203343i
$994$	−28.1916	−	9.73510i	−0.894184	−	0.308779i
$995$	0.881505	−	1.21329i	0.0279456	−	0.0384638i
$996$	6.44303	+	3.46020i	0.204155	+	0.109641i
$997$	−26.7008	+	24.0415i	−0.845623	+	0.761402i	−0.973086	−	0.230441i	$-0.925983\pi$
$997$	−26.7008	+	24.0415i	−0.845623	+	0.761402i	0.127463	+	0.991843i	$0.459316\pi$
$998$	−20.8583	−	4.43356i	−0.660257	−	0.140342i
$999$	37.5744	+	0.467830i	1.18880	+	0.0148015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.b.305.12	yes	128
3.2	odd	2		462.2.bc.a.305.8	yes	128
7.2	even	3	inner	462.2.bc.b.107.11	yes	128
11.7	odd	10		462.2.bc.a.95.2	✓	128
21.2	odd	6		462.2.bc.a.107.2	yes	128
33.29	even	10	inner	462.2.bc.b.95.11	yes	128
77.51	odd	30		462.2.bc.a.359.8	yes	128
231.128	even	30	inner	462.2.bc.b.359.12	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.2	✓	128	11.7	odd	10
462.2.bc.a.107.2	yes	128	21.2	odd	6
462.2.bc.a.305.8	yes	128	3.2	odd	2
462.2.bc.a.359.8	yes	128	77.51	odd	30
462.2.bc.b.95.11	yes	128	33.29	even	10	inner
462.2.bc.b.107.11	yes	128	7.2	even	3	inner
462.2.bc.b.305.12	yes	128	1.1	even	1	trivial
462.2.bc.b.359.12	yes	128	231.128	even	30	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.bc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.913545 + 0.406737i) q^{2} +(0.974501 - 1.43190i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.273885 + 0.0287865i) q^{5} +(1.47266 - 0.911743i) q^{6} +(-1.73400 - 1.99831i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.10069 - 2.79078i) q^{9} +O(q^{10})\)	\(q+(0.913545 + 0.406737i) q^{2} +(0.974501 - 1.43190i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.273885 + 0.0287865i) q^{5} +(1.47266 - 0.911743i) q^{6} +(-1.73400 - 1.99831i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.10069 - 2.79078i) q^{9} +(0.238498 + 0.137697i) q^{10} +(3.20872 - 0.839120i) q^{11} +(1.71618 - 0.233935i) q^{12} +(0.376661 + 0.518429i) q^{13} +(-0.771302 - 2.53083i) q^{14} +(0.308121 - 0.364124i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(5.58406 - 2.48618i) q^{17} +(0.129580 - 2.99720i) q^{18} +(0.818342 + 0.736838i) q^{19} +(0.161872 + 0.222798i) q^{20} +(-4.55117 + 0.535564i) q^{21} +(3.27261 + 0.538529i) q^{22} +(1.05359 - 0.608290i) q^{23} +(1.66296 + 0.484323i) q^{24} +(-4.81655 - 1.02379i) q^{25} +(0.133233 + 0.626810i) q^{26} +(-5.06876 - 1.14353i) q^{27} +(0.324762 - 2.62574i) q^{28} +(-2.73094 + 8.40497i) q^{29} +(0.429585 - 0.207320i) q^{30} +(0.523104 + 4.97700i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.92536 - 5.41230i) q^{33} +6.11252 q^{34} +(-0.417392 - 0.597223i) q^{35} +(1.33745 - 2.68537i) q^{36} +(-7.07372 + 1.50357i) q^{37} +(0.447893 + 1.00598i) q^{38} +(1.10940 - 0.0341320i) q^{39} +(0.0572575 + 0.269376i) q^{40} +(0.939549 + 2.89164i) q^{41} +(-4.37554 - 1.36187i) q^{42} -1.12509i q^{43} +(2.77064 + 1.82306i) q^{44} +(-0.221127 - 0.796039i) q^{45} +(1.20992 - 0.127167i) q^{46} +(1.77335 + 1.59673i) q^{47} +(1.32220 + 1.11884i) q^{48} +(-0.986490 + 6.93014i) q^{49} +(-3.98373 - 2.89435i) q^{50} +(1.88170 - 10.4186i) q^{51} +(-0.133233 + 0.626810i) q^{52} +(-8.15168 + 0.856777i) q^{53} +(-4.16543 - 3.10632i) q^{54} +(0.902975 - 0.137455i) q^{55} +(1.36467 - 2.26664i) q^{56} +(1.85256 - 0.453736i) q^{57} +(-5.91345 + 6.56755i) q^{58} +(6.57511 - 5.92026i) q^{59} +(0.476770 - 0.0146684i) q^{60} +(4.40502 + 0.462986i) q^{61} +(-1.54645 + 4.75948i) q^{62} +(-3.66825 + 7.03875i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.0882380 + 0.152833i) q^{65} +(3.96029 - 4.16127i) q^{66} +(-5.31001 + 9.19720i) q^{67} +(5.58406 + 2.48618i) q^{68} +(0.155712 - 2.10142i) q^{69} +(-0.138394 - 0.715359i) q^{70} +(6.62602 - 9.11993i) q^{71} +(2.31406 - 1.90922i) q^{72} +(8.47349 - 7.62957i) q^{73} +(-7.07372 - 1.50357i) q^{74} +(-6.15971 + 5.89915i) q^{75} +1.10119i q^{76} +(-7.24074 - 4.95698i) q^{77} +(1.02737 + 0.420051i) q^{78} +(-5.05145 + 11.3457i) q^{79} +(-0.0572575 + 0.269376i) q^{80} +(-6.57694 + 6.14360i) q^{81} +(-0.317813 + 3.02379i) q^{82} +(3.41598 + 2.48186i) q^{83} +(-3.44333 - 3.02382i) q^{84} +(1.60096 - 0.520183i) q^{85} +(0.457617 - 1.02783i) q^{86} +(9.37380 + 12.1011i) q^{87} +(1.78960 + 2.79237i) q^{88} +(-15.7235 + 9.07797i) q^{89} +(0.121769 - 0.817158i) q^{90} +(0.382853 - 1.65164i) q^{91} +(1.15704 + 0.375944i) q^{92} +(7.63635 + 4.10106i) q^{93} +(0.970588 + 2.17998i) q^{94} +(0.202920 + 0.225366i) q^{95} +(0.752814 + 1.55989i) q^{96} +(-8.14146 + 5.91512i) q^{97} +(-3.71994 + 5.92976i) q^{98} +(-5.87362 - 8.03122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 + 38 * q^29 + 6 * q^30 - 3 * q^31 - 64 * q^32 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

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