LMFDB - Embedded newform 224.2.bd.a.109.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(37,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("224.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.bd (of order $24$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			109.30
Character	$\chi$	$=$	224.109
Dual form			224.2.bd.a.37.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37739 + 0.320624i) q^{2} +(-1.00894 - 1.31488i) q^{3} +(1.79440 + 0.883248i) q^{4} +(-3.47903 - 2.66955i) q^{5} +(-0.968125 - 2.13459i) q^{6} +(1.71027 - 2.01866i) q^{7} +(2.18840 + 1.79190i) q^{8} +(0.0655120 - 0.244494i) q^{9} +O(q^{10})$	\(q+(1.37739 + 0.320624i) q^{2} +(-1.00894 - 1.31488i) q^{3} +(1.79440 + 0.883248i) q^{4} +(-3.47903 - 2.66955i) q^{5} +(-0.968125 - 2.13459i) q^{6} +(1.71027 - 2.01866i) q^{7} +(2.18840 + 1.79190i) q^{8} +(0.0655120 - 0.244494i) q^{9} +(-3.93605 - 4.79247i) q^{10} +(-3.28912 - 0.433021i) q^{11} +(-0.649082 - 3.25057i) q^{12} +(4.67399 + 1.93603i) q^{13} +(3.00293 - 2.23213i) q^{14} +7.26794i q^{15} +(2.43974 + 3.16980i) q^{16} +(1.57403 + 0.908767i) q^{17} +(0.168626 - 0.315759i) q^{18} +(0.0886253 + 0.673176i) q^{19} +(-3.88489 - 7.86309i) q^{20} +(-4.37986 - 0.212081i) q^{21} +(-4.39157 - 1.65101i) q^{22} +(0.695642 - 2.59617i) q^{23} +(0.148173 - 4.68541i) q^{24} +(3.68303 + 13.7453i) q^{25} +(5.81716 + 4.16526i) q^{26} +(-4.98121 + 2.06329i) q^{27} +(4.85188 - 2.11170i) q^{28} +(0.687814 - 1.66053i) q^{29} +(-2.33028 + 10.0108i) q^{30} +(0.418066 - 0.724111i) q^{31} +(2.34416 + 5.14829i) q^{32} +(2.74917 + 4.76170i) q^{33} +(1.87668 + 1.75640i) q^{34} +(-11.3390 + 2.45733i) q^{35} +(0.333504 - 0.380857i) q^{36} +(4.53365 + 3.47879i) q^{37} +(-0.0937650 + 0.955640i) q^{38} +(-2.17014 - 8.09909i) q^{39} +(-2.82991 - 12.0761i) q^{40} +(2.56341 + 2.56341i) q^{41} +(-5.96477 - 1.69641i) q^{42} +(-2.94113 - 7.10052i) q^{43} +(-5.51954 - 3.68213i) q^{44} +(-0.880608 + 0.675714i) q^{45} +(1.79057 - 3.35290i) q^{46} +(-0.538181 + 0.310719i) q^{47} +(1.70635 - 6.40613i) q^{48} +(-1.14998 - 6.90489i) q^{49} +(0.665903 + 20.1134i) q^{50} +(-0.393188 - 2.98656i) q^{51} +(6.67701 + 7.60231i) q^{52} +(8.35206 + 1.09957i) q^{53} +(-7.52261 + 1.24485i) q^{54} +(10.2870 + 10.2870i) q^{55} +(7.35999 - 1.35300i) q^{56} +(0.795729 - 0.795729i) q^{57} +(1.47979 - 2.06667i) q^{58} +(-1.17781 + 8.94637i) q^{59} +(-6.41940 + 13.0416i) q^{60} +(5.00491 - 0.658909i) q^{61} +(0.808007 - 0.863341i) q^{62} +(-0.381508 - 0.550396i) q^{63} +(1.57815 + 7.84279i) q^{64} +(-11.0926 - 19.2130i) q^{65} +(2.25996 + 7.44017i) q^{66} +(-2.75918 - 3.59583i) q^{67} +(2.02177 + 3.02095i) q^{68} +(-4.11552 + 1.70470i) q^{69} +(-16.4061 - 0.250849i) q^{70} +(1.49681 - 1.49681i) q^{71} +(0.581476 - 0.417659i) q^{72} +(-12.2751 + 3.28910i) q^{73} +(5.12921 + 6.24524i) q^{74} +(14.3574 - 18.7110i) q^{75} +(-0.435552 + 1.28623i) q^{76} +(-6.49940 + 5.89904i) q^{77} +(-0.392368 - 11.8514i) q^{78} +(-1.28041 + 0.739243i) q^{79} +(-0.0259858 - 17.5409i) q^{80} +(7.08112 + 4.08829i) q^{81} +(2.70892 + 4.35270i) q^{82} +(5.25757 + 2.17776i) q^{83} +(-7.67190 - 4.24906i) q^{84} +(-3.05010 - 7.36358i) q^{85} +(-1.77448 - 10.7232i) q^{86} +(-2.87737 + 0.770988i) q^{87} +(-6.42197 - 6.84142i) q^{88} +(-1.13014 - 0.302821i) q^{89} +(-1.42959 + 0.648377i) q^{90} +(11.9019 - 6.12407i) q^{91} +(3.54132 - 4.04415i) q^{92} +(-1.37393 + 0.180881i) q^{93} +(-0.840909 + 0.255427i) q^{94} +(1.48875 - 2.57859i) q^{95} +(4.40427 - 8.27663i) q^{96} -8.69153 q^{97} +(0.629904 - 9.87943i) q^{98} +(-0.321348 + 0.775803i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	1.37739	+	0.320624i	0.973961	+	0.226716i
$2$	1.37739	+	0.320624i	0.973961	+	0.226716i
$3$	−1.00894	−	1.31488i	−0.582514	−	0.759147i	0.405402	−	0.914139i	$-0.367132\pi$
$3$	−1.00894	−	1.31488i	−0.582514	−	0.759147i	−0.987916	+	0.154992i	$0.950465\pi$
$4$	1.79440	+	0.883248i	0.897200	+	0.441624i
$5$	−3.47903	−	2.66955i	−1.55587	−	1.19386i	−0.897370	−	0.441278i	$-0.854525\pi$
$5$	−3.47903	−	2.66955i	−1.55587	−	1.19386i	−0.658498	−	0.752582i	$-0.728808\pi$
$6$	−0.968125	−	2.13459i	−0.395236	−	0.871445i
$7$	1.71027	−	2.01866i	0.646420	−	0.762982i
$7$	1.71027	−	2.01866i	0.646420	−	0.762982i
$8$	2.18840	+	1.79190i	0.773715	+	0.633534i
$9$	0.0655120	−	0.244494i	0.0218373	−	0.0814980i
$10$	−3.93605	−	4.79247i	−1.24469	−	1.51551i
$11$	−3.28912	−	0.433021i	−0.991708	−	0.130561i	−0.382825	−	0.923821i	$-0.625049\pi$
$11$	−3.28912	−	0.433021i	−0.991708	−	0.130561i	−0.608883	+	0.793260i	$0.708382\pi$
$12$	−0.649082	−	3.25057i	−0.187374	−	0.938359i
$13$	4.67399	+	1.93603i	1.29633	+	0.536958i	0.920866	−	0.389879i	$-0.127483\pi$
$13$	4.67399	+	1.93603i	1.29633	+	0.536958i	0.375465	+	0.926837i	$0.377483\pi$
$14$	3.00293	−	2.23213i	0.802568	−	0.596561i
$15$			7.26794i			1.87657i
$16$	2.43974	+	3.16980i	0.609936	+	0.792451i
$17$	1.57403	+	0.908767i	0.381759	+	0.220408i	0.678583	−	0.734524i	$-0.262594\pi$
$17$	1.57403	+	0.908767i	0.381759	+	0.220408i	−0.296825	+	0.954932i	$0.595928\pi$
$18$	0.168626	−	0.315759i	0.0397456	−	0.0744250i
$19$	0.0886253	+	0.673176i	0.0203320	+	0.154437i	0.998599	−	0.0529111i	$-0.0168500\pi$
$19$	0.0886253	+	0.673176i	0.0203320	+	0.154437i	−0.978267	+	0.207348i	$0.933517\pi$
$20$	−3.88489	−	7.86309i	−0.868688	−	1.75824i
$21$	−4.37986	−	0.212081i	−0.955764	−	0.0462799i
$22$	−4.39157	−	1.65101i	−0.936285	−	0.351997i
$23$	0.695642	−	2.59617i	0.145051	−	0.541339i	−0.854702	−	0.519119i	$-0.826260\pi$
$23$	0.695642	−	2.59617i	0.145051	−	0.541339i	0.999753	−	0.0222197i	$-0.00707335\pi$
$24$	0.148173	−	4.68541i	0.0302457	−	0.956406i
$25$	3.68303	+	13.7453i	0.736607	+	2.74905i
$26$	5.81716	+	4.16526i	1.14084	+	0.816875i
$27$	−4.98121	+	2.06329i	−0.958635	+	0.397080i
$28$	4.85188	−	2.11170i	0.916919	−	0.399073i
$29$	0.687814	−	1.66053i	0.127724	−	0.308353i	−0.847062	−	0.531494i	$-0.821631\pi$
$29$	0.687814	−	1.66053i	0.127724	−	0.308353i	0.974786	+	0.223141i	$0.0716310\pi$
$30$	−2.33028	+	10.0108i	−0.425448	+	1.82771i
$31$	0.418066	−	0.724111i	0.0750868	−	0.130054i	−0.826037	−	0.563616i	$-0.809410\pi$
$31$	0.418066	−	0.724111i	0.0750868	−	0.130054i	0.901124	+	0.433561i	$0.142743\pi$
$32$	2.34416	+	5.14829i	0.414393	+	0.910098i
$33$	2.74917	+	4.76170i	0.478569	+	0.828906i
$34$	1.87668	+	1.75640i	0.321848	+	0.301220i
$35$	−11.3390	+	2.45733i	−1.91664	+	0.415365i
$36$	0.333504	−	0.380857i	0.0555840	−	0.0634762i
$37$	4.53365	+	3.47879i	0.745327	+	0.571910i	0.910084	−	0.414425i	$-0.136017\pi$
$37$	4.53365	+	3.47879i	0.745327	+	0.571910i	−0.164757	+	0.986334i	$0.552684\pi$
$38$	−0.0937650	+	0.955640i	−0.0152107	+	0.155025i
$39$	−2.17014	−	8.09909i	−0.347501	−	1.29689i
$40$	−2.82991	−	12.0761i	−0.447448	−	1.90940i
$41$	2.56341	+	2.56341i	0.400337	+	0.400337i	0.878352	−	0.478015i	$-0.158643\pi$
$41$	2.56341	+	2.56341i	0.400337	+	0.400337i	−0.478015	+	0.878352i	$0.658643\pi$
$42$	−5.96477	−	1.69641i	−0.920385	−	0.261761i
$43$	−2.94113	−	7.10052i	−0.448519	−	1.08282i	−0.972877	−	0.231322i	$-0.925695\pi$
$43$	−2.94113	−	7.10052i	−0.448519	−	1.08282i	0.524359	−	0.851498i	$-0.324305\pi$
$44$	−5.51954	−	3.68213i	−0.832102	−	0.555102i
$45$	−0.880608	+	0.675714i	−0.131273	+	0.100730i
$46$	1.79057	−	3.35290i	0.264004	−	0.494358i
$47$	−0.538181	+	0.310719i	−0.0785018	+	0.0453231i	−0.538737	−	0.842474i	$-0.681098\pi$
$47$	−0.538181	+	0.310719i	−0.0785018	+	0.0453231i	0.460235	+	0.887797i	$0.347765\pi$
$48$	1.70635	−	6.40613i	0.246290	−	0.924645i
$49$	−1.14998	−	6.90489i	−0.164283	−	0.986413i
$50$	0.665903	+	20.1134i	0.0941730	+	2.84447i
$51$	−0.393188	−	2.98656i	−0.0550573	−	0.418202i
$52$	6.67701	+	7.60231i	0.925935	+	1.05425i
$53$	8.35206	+	1.09957i	1.14724	+	0.151038i	0.680083	−	0.733135i	$-0.261944\pi$
$53$	8.35206	+	1.09957i	1.14724	+	0.151038i	0.467161	+	0.884172i	$0.345277\pi$
$54$	−7.52261	+	1.24485i	−1.02370	+	0.169403i
$55$	10.2870	+	10.2870i	1.38710	+	1.38710i
$56$	7.35999	−	1.35300i	0.983520	−	0.180802i
$57$	0.795729	−	0.795729i	0.105397	−	0.105397i
$58$	1.47979	−	2.06667i	0.194306	−	0.271367i
$59$	−1.17781	+	8.94637i	−0.153338	+	1.16472i	0.725716	+	0.687995i	$0.241509\pi$
$59$	−1.17781	+	8.94637i	−0.153338	+	1.16472i	−0.879054	+	0.476723i	$0.841825\pi$
$60$	−6.41940	+	13.0416i	−0.828740	+	1.68366i
$61$	5.00491	−	0.658909i	0.640813	−	0.0843647i	0.196884	−	0.980427i	$-0.436918\pi$
$61$	5.00491	−	0.658909i	0.640813	−	0.0843647i	0.443929	+	0.896062i	$0.353584\pi$
$62$	0.808007	−	0.863341i	0.102617	−	0.109644i
$63$	−0.381508	−	0.550396i	−0.0480655	−	0.0693434i
$64$	1.57815	+	7.84279i	0.197269	+	0.980349i
$65$	−11.0926	−	19.2130i	−1.37587	−	2.38307i
$66$	2.25996	+	7.44017i	0.278182	+	0.915821i
$67$	−2.75918	−	3.59583i	−0.337087	−	0.439301i	0.593797	−	0.804615i	$-0.297628\pi$
$67$	−2.75918	−	3.59583i	−0.337087	−	0.439301i	−0.930884	+	0.365314i	$0.880962\pi$
$68$	2.02177	+	3.02095i	0.245176	+	0.366344i
$69$	−4.11552	+	1.70470i	−0.495451	+	0.205222i
$70$	−16.4061	−	0.250849i	−1.96090	−	0.0299822i
$71$	1.49681	−	1.49681i	0.177639	−	0.177639i	−0.612687	−	0.790326i	$-0.709911\pi$
$71$	1.49681	−	1.49681i	0.177639	−	0.177639i	0.790326	+	0.612687i	$0.209911\pi$
$72$	0.581476	−	0.417659i	0.0685276	−	0.0492215i
$73$	−12.2751	+	3.28910i	−1.43669	+	0.384960i	−0.891374	−	0.453269i	$-0.850258\pi$
$73$	−12.2751	+	3.28910i	−1.43669	+	0.384960i	−0.545317	+	0.838230i	$0.683591\pi$
$74$	5.12921	+	6.24524i	0.596259	+	0.725995i
$75$	14.3574	−	18.7110i	1.65785	−	2.16056i
$76$	−0.435552	+	1.28623i	−0.0499613	+	0.147540i
$77$	−6.49940	+	5.89904i	−0.740675	+	0.672258i
$78$	−0.392368	−	11.8514i	−0.0444270	−	1.34191i
$79$	−1.28041	+	0.739243i	−0.144057	+	0.0831714i	−0.570296	−	0.821439i	$-0.693172\pi$
$79$	−1.28041	+	0.739243i	−0.144057	+	0.0831714i	0.426239	+	0.904611i	$0.359838\pi$
$80$	−0.0259858	−	17.5409i	−0.00290530	−	1.96113i
$81$	7.08112	+	4.08829i	0.786791	+	0.454254i
$82$	2.70892	+	4.35270i	0.299150	+	0.480675i
$83$	5.25757	+	2.17776i	0.577093	+	0.239040i	0.652087	−	0.758144i	$-0.273894\pi$
$83$	5.25757	+	2.17776i	0.577093	+	0.239040i	−0.0749938	+	0.997184i	$0.523894\pi$
$84$	−7.67190	−	4.24906i	−0.837073	−	0.463611i
$85$	−3.05010	−	7.36358i	−0.330829	−	0.798693i
$86$	−1.77448	−	10.7232i	−0.191348	−	1.15631i
$87$	−2.87737	+	0.770988i	−0.308486	+	0.0826586i
$88$	−6.42197	−	6.84142i	−0.684585	−	0.729298i
$89$	−1.13014	−	0.302821i	−0.119795	−	0.0320990i	0.198423	−	0.980116i	$-0.436418\pi$
$89$	−1.13014	−	0.302821i	−0.119795	−	0.0320990i	−0.318218	+	0.948017i	$0.603085\pi$
$90$	−1.42959	+	0.648377i	−0.150692	+	0.0683449i
$91$	11.9019	−	6.12407i	1.24766	−	0.641977i
$92$	3.54132	−	4.04415i	0.369209	−	0.421631i
$93$	−1.37393	+	0.180881i	−0.142469	+	0.0187565i
$94$	−0.840909	+	0.255427i	−0.0867332	+	0.0263453i
$95$	1.48875	−	2.57859i	0.152742	−	0.264558i
$96$	4.40427	−	8.27663i	0.449509	−	0.844730i
$97$	−8.69153			−0.882491			−0.441245	−	0.897386i	$-0.645463\pi$
$97$	−8.69153			−0.882491			−0.441245	+	0.897386i	$0.645463\pi$
$98$	0.629904	−	9.87943i	0.0636299	−	0.997974i
$99$	−0.321348	+	0.775803i	−0.0322967	+	0.0779712i
$100$	−5.53165	+	27.9175i	−0.553165	+	2.79175i
$101$	0.904031	−	6.86679i	0.0899544	−	0.683272i	−0.885747	−	0.464168i	$-0.846353\pi$
$101$	0.904031	−	6.86679i	0.0899544	−	0.683272i	0.975702	−	0.219104i	$-0.0703133\pi$
$102$	0.415990	−	4.23972i	0.0411892	−	0.419795i
$103$	1.89779	+	0.508511i	0.186995	+	0.0501051i	0.351101	−	0.936338i	$-0.385807\pi$
$103$	1.89779	+	0.508511i	0.186995	+	0.0501051i	−0.164106	+	0.986443i	$0.552474\pi$
$104$	6.75936	+	12.6121i	0.662810	+	1.23672i
$105$	14.6715	+	12.4301i	1.43179	+	1.21305i
$106$	11.1515	+	4.19241i	1.08313	+	0.407203i
$107$	−7.84388	+	10.2223i	−0.758296	+	0.988231i	0.241545	+	0.970390i	$0.422346\pi$
$107$	−7.84388	+	10.2223i	−0.758296	+	0.988231i	−0.999841	+	0.0178412i	$0.994321\pi$
$108$	−10.7607	−	0.697288i	−1.03545	−	0.0670966i
$109$	3.20882	−	2.46221i	0.307349	−	0.235837i	−0.443557	−	0.896246i	$-0.646284\pi$
$109$	3.20882	−	2.46221i	0.307349	−	0.235837i	0.750906	+	0.660409i	$0.229617\pi$
$110$	10.8709	+	17.4674i	1.03650	+	1.66545i
$111$		−	9.47111i		−	0.898958i
$112$	10.5714	+	0.496189i	0.998900	+	0.0468855i
$113$			4.47915i			0.421363i	0.977555	+	0.210682i	$0.0675683\pi$
$113$			4.47915i			0.421363i	−0.977555	+	0.210682i	$0.932432\pi$
$114$	1.35116	−	0.840898i	0.126547	−	0.0787573i
$115$	−9.35077	+	7.17510i	−0.871964	+	0.669082i
$116$	2.70087	−	2.37214i	0.250770	−	0.220248i
$117$	0.779550	−	1.01593i	0.0720694	−	0.0939227i
$118$	−4.49073	+	11.9450i	−0.413405	+	1.09963i
$119$	4.52650	−	1.62320i	0.414944	−	0.148799i
$120$	−13.0235	+	15.9051i	−1.18887	+	1.45193i
$121$	0.00564575	+	0.00151277i	0.000513250	+	0.000137525i
$122$	7.10497	+	0.697122i	0.643254	+	0.0631144i
$123$	0.784242	−	5.95691i	0.0707127	−	0.537117i
$124$	1.38975	−	0.930089i	0.124803	−	0.0835245i
$125$	15.4896	−	37.3952i	1.38543	−	3.34472i
$126$	−0.349014	−	0.880431i	−0.0310926	−	0.0784350i
$127$	−12.4939			−1.10865			−0.554327	−	0.832299i	$-0.687024\pi$
$127$	−12.4939			−1.10865			−0.554327	+	0.832299i	$0.687024\pi$
$128$	−0.340858	+	11.3086i	−0.0301278	+	0.999546i
$129$	−6.36891	+	11.0313i	−0.560751	+	0.971249i
$130$	−9.11869	−	30.0203i	−0.799762	−	2.63295i
$131$	18.9029	−	2.48861i	1.65155	−	0.217431i	0.753541	−	0.657401i	$-0.228344\pi$
$131$	18.9029	−	2.48861i	1.65155	−	0.217431i	0.898013	+	0.439970i	$0.145011\pi$
$132$	0.727345	+	10.9726i	0.0633073	+	0.955042i
$133$	1.51049	+	0.972405i	0.130976	+	0.0843182i
$134$	−2.64755	−	5.83752i	−0.228714	−	0.504285i
$135$	22.8378	+	6.11938i	1.96557	+	0.526672i
$136$	1.81618	+	4.80926i	0.155736	+	0.412390i
$137$	5.46370	−	1.46400i	0.466796	−	0.125078i	−0.0177519	−	0.999842i	$-0.505651\pi$
$137$	5.46370	−	1.46400i	0.466796	−	0.125078i	0.484548	+	0.874765i	$0.338984\pi$
$138$	−6.21524	+	1.02851i	−0.529077	+	0.0875522i
$139$	−1.62276	−	3.91770i	−0.137641	−	0.332295i	0.839997	−	0.542592i	$-0.182557\pi$
$139$	−1.62276	−	3.91770i	−0.137641	−	0.332295i	−0.977638	+	0.210297i	$0.932557\pi$
$140$	−22.5171	−	5.60570i	−1.90304	−	0.473768i
$141$	0.951554	+	0.394147i	0.0801353	+	0.0331931i
$142$	2.54160	−	1.58178i	0.213287	−	0.132740i
$143$	−14.5350	−	8.39178i	−1.21548	−	0.701756i
$144$	0.934831	−	0.388843i	0.0779025	−	0.0324036i
$145$	−6.82580	+	3.94088i	−0.566852	+	0.327272i
$146$	−17.9621	+	0.594679i	−1.48656	+	0.0492160i
$147$	−7.91885	+	8.47874i	−0.653136	+	0.699315i
$148$	5.06254	+	10.2467i	0.416138	+	0.842272i
$149$	−2.98589	+	3.89128i	−0.244613	+	0.318786i	−0.899483	−	0.436955i	$-0.856057\pi$
$149$	−2.98589	+	3.89128i	−0.244613	+	0.318786i	0.654870	+	0.755742i	$0.272723\pi$
$150$	25.7749	−	21.1689i	2.10452	−	1.72844i
$151$	11.7227	−	3.14109i	0.953980	−	0.255618i	0.251929	−	0.967746i	$-0.418935\pi$
$151$	11.7227	−	3.14109i	0.953980	−	0.255618i	0.702050	+	0.712128i	$0.252268\pi$
$152$	−1.01232	+	1.63198i	−0.0821100	+	0.132371i
$153$	0.325306	−	0.325306i	0.0262994	−	0.0262994i
$154$	−10.8436	+	6.04141i	−0.873800	+	0.486831i
$155$	−3.38752	+	1.40315i	−0.272092	+	0.112704i
$156$	3.25940	−	16.4498i	0.260961	−	1.31704i
$157$	−5.47116	−	7.13015i	−0.436646	−	0.569048i	0.522255	−	0.852789i	$-0.325091\pi$
$157$	−5.47116	−	7.13015i	−0.436646	−	0.569048i	−0.958901	+	0.283741i	$0.908424\pi$
$158$	−2.00064	+	0.607696i	−0.159162	+	0.0483457i
$159$	−6.98096	−	12.0914i	−0.553626	−	0.958908i
$160$	5.58823	−	24.1689i	0.441788	−	1.91072i
$161$	−4.05106	−	5.84441i	−0.319268	−	0.460604i
$162$	8.44265	+	7.90154i	0.663317	+	0.620804i
$163$	−10.0624	+	1.32474i	−0.788149	+	0.103762i	−0.513847	−	0.857882i	$-0.671780\pi$
$163$	−10.0624	+	1.32474i	−0.788149	+	0.103762i	−0.274302	+	0.961644i	$0.588447\pi$
$164$	2.33565	+	6.86391i	0.182384	+	0.535981i
$165$	3.14717	−	23.9052i	0.245007	−	1.86101i
$166$	6.54348	+	4.68532i	0.507872	+	0.363651i
$167$	−17.2772	+	17.2772i	−1.33695	+	1.33695i	−0.437947	+	0.899001i	$0.644294\pi$
$167$	−17.2772	+	17.2772i	−1.33695	+	1.33695i	−0.899001	+	0.437947i	$0.855706\pi$
$168$	−9.20484	−	8.31241i	−0.710169	−	0.641317i
$169$	8.90557	+	8.90557i	0.685044	+	0.685044i
$170$	−1.84023	−	11.1205i	−0.141139	−	0.852900i
$171$	0.170394	+	0.0224327i	0.0130303	+	0.00171547i
$172$	0.993957	−	15.3389i	0.0757885	−	1.16958i
$173$	0.515604	+	3.91640i	0.0392007	+	0.297759i	0.999803	+	0.0198332i	$0.00631352\pi$
$173$	0.515604	+	3.91640i	0.0392007	+	0.297759i	−0.960603	+	0.277926i	$0.910353\pi$
$174$	−4.21045	+	0.139397i	−0.319193	+	0.0105677i
$175$	34.0460	+	16.0733i	2.57364	+	1.21502i
$176$	−6.65203	−	11.4823i	−0.501416	−	0.865514i
$177$	12.9518	−	7.47770i	0.973514	−	0.562058i
$178$	−1.45956	−	0.779454i	−0.109398	−	0.0584226i
$179$	−14.1756	+	10.8773i	−1.05954	+	0.813010i	−0.982917	−	0.184050i	$-0.941079\pi$
$179$	−14.1756	+	10.8773i	−1.05954	+	0.813010i	−0.0766188	+	0.997060i	$0.524412\pi$
$180$	−2.17699	+	0.434706i	−0.162263	+	0.0324011i
$181$	8.84752	+	21.3598i	0.657631	+	1.58766i	0.801453	+	0.598058i	$0.204061\pi$
$181$	8.84752	+	21.3598i	0.657631	+	1.58766i	−0.143822	+	0.989604i	$0.545939\pi$
$182$	18.3571	−	4.61918i	1.36072	−	0.342396i
$183$	−5.91606	−	5.91606i	−0.437328	−	0.437328i
$184$	6.17443	−	4.43493i	0.455185	−	0.326947i
$185$	−6.48588	−	24.2056i	−0.476851	−	1.77963i
$186$	−1.95042	−	0.191371i	−0.143012	−	0.0140320i
$187$	−4.78367	−	3.67064i	−0.349816	−	0.268424i
$188$	−1.24016	+	0.0822067i	−0.0904476	+	0.00599554i
$189$	−4.35413	+	13.5841i	−0.316716	+	0.988101i
$190$	2.87734	−	3.07439i	0.208744	−	0.223040i
$191$	−7.38718	−	12.7950i	−0.534518	−	0.925812i	−0.999187	−	0.0403271i	$-0.987160\pi$
$191$	−7.38718	−	12.7950i	−0.534518	−	0.925812i	0.464669	−	0.885484i	$-0.346173\pi$
$192$	8.72008	−	9.98803i	0.629317	−	0.720824i
$193$	−8.40250	+	14.5536i	−0.604825	+	1.04759i	0.387254	+	0.921973i	$0.373424\pi$
$193$	−8.40250	+	14.5536i	−0.604825	+	1.04759i	−0.992079	+	0.125615i	$0.959910\pi$
$194$	−11.9716	−	2.78671i	−0.859512	−	0.200074i
$195$	−14.0709	+	33.9703i	−1.00764	+	2.43266i
$196$	4.03521	−	13.4059i	0.288229	−	0.957561i
$197$	−22.5053	+	9.32202i	−1.60344	+	0.664166i	−0.991897	−	0.127045i	$-0.959451\pi$
$197$	−22.5053	+	9.32202i	−1.60344	+	0.664166i	−0.611542	+	0.791212i	$0.709451\pi$
$198$	−0.691363	+	0.965551i	−0.0491330	+	0.0686187i
$199$	1.28914	+	4.81113i	0.0913846	+	0.341052i	0.996447	−	0.0842277i	$-0.0268423\pi$
$199$	1.28914	+	4.81113i	0.0913846	+	0.341052i	−0.905062	+	0.425280i	$0.860176\pi$
$200$	−16.5703	+	36.6797i	−1.17170	+	2.59365i
$201$	−1.94424	+	7.25599i	−0.137136	+	0.511798i
$202$	3.44686	−	9.16839i	0.242520	−	0.645086i
$203$	−2.17570	−	4.22841i	−0.152704	−	0.296776i
$204$	1.93234	−	5.70636i	0.135291	−	0.399525i
$205$	−2.07502	−	15.7613i	−0.144925	−	1.10082i
$206$	2.45095	+	1.30889i	0.170766	+	0.0911950i
$207$	−0.589176	−	0.340161i	−0.0409505	−	0.0236428i
$208$	5.26651	+	19.5390i	0.365166	+	1.35479i
$209$		−	2.25254i		−	0.155811i
$210$	16.2230	+	21.8251i	1.11949	+	1.50608i
$211$	20.3021	+	8.40942i	1.39766	+	0.578928i	0.949142	−	0.314847i	$-0.101953\pi$
$211$	20.3021	+	8.40942i	1.39766	+	0.578928i	0.448514	+	0.893776i	$0.351953\pi$
$212$	14.0157	+	9.35001i	0.962606	+	0.642162i
$213$	−3.47832	−	0.457930i	−0.238331	−	0.0313769i
$214$	−14.0816	+	11.5652i	−0.962598	+	0.790581i
$215$	−8.72293	+	32.5544i	−0.594899	+	2.22019i
$216$	−14.5981	−	4.41057i	−0.993274	−	0.300102i
$217$	−0.746731	−	2.08236i	−0.0506914	−	0.141359i
$218$	5.20924	−	2.36260i	0.352814	−	0.160016i
$219$	16.7097	+	12.8218i	1.12913	+	0.866415i
$220$	9.37300	+	27.5449i	0.631928	+	1.85708i
$221$	5.59760	+	7.29494i	0.376535	+	0.490711i
$222$	3.03667	−	13.0454i	0.203808	−	0.875550i
$223$	12.7380			0.853000			0.426500	−	0.904487i	$-0.359746\pi$
$223$	12.7380			0.853000			0.426500	+	0.904487i	$0.359746\pi$
$224$	14.4018	+	4.07288i	0.962260	+	0.272131i
$225$	3.60192			0.240128
$226$	−1.43612	+	6.16953i	−0.0955296	+	0.410391i
$227$	−5.04381	−	6.57322i	−0.334769	−	0.436280i	0.595390	−	0.803437i	$-0.296998\pi$
$227$	−5.04381	−	6.57322i	−0.334769	−	0.436280i	−0.930159	+	0.367157i	$0.880331\pi$
$228$	2.13068	−	0.725029i	0.141108	−	0.0480162i
$229$	−13.7028	−	10.5145i	−0.905505	−	0.694818i	0.0471448	−	0.998888i	$-0.484988\pi$
$229$	−13.7028	−	10.5145i	−0.905505	−	0.694818i	−0.952650	+	0.304070i	$0.901654\pi$
$230$	−15.1802	+	6.88482i	−1.00095	+	0.453972i
$231$	14.3141	+	2.59414i	0.941797	+	0.170682i
$232$	4.48072	−	2.40140i	0.294174	−	0.157660i
$233$	−4.62284	+	17.2527i	−0.302852	+	1.13026i	0.631926	+	0.775029i	$0.282265\pi$
$233$	−4.62284	+	17.2527i	−0.302852	+	1.13026i	−0.934778	+	0.355231i	$0.884402\pi$
$234$	1.39948	−	1.14939i	0.0914866	−	0.0751378i
$235$	2.70183	+	0.355703i	0.176248	+	0.0232035i
$236$	−10.0153	+	15.0131i	−0.651942	+	0.977267i
$237$	2.26388	+	0.937728i	0.147055	+	0.0609120i
$238$	6.75519	−	0.784472i	0.437874	−	0.0508498i
$239$		−	17.6428i		−	1.14122i	−0.821222	−	0.570609i	$-0.806707\pi$
$239$		−	17.6428i		−	1.14122i	0.821222	−	0.570609i	$-0.193293\pi$
$240$	−23.0379	+	17.7319i	−1.48709	+	1.14459i
$241$	15.5850	+	8.99801i	1.00392	+	0.579613i	0.909405	−	0.415911i	$-0.136537\pi$
$241$	15.5850	+	8.99801i	1.00392	+	0.579613i	0.0945136	+	0.995524i	$0.469870\pi$
$242$	0.00729136	+	0.00389384i	0.000468706	+	0.000250306i
$243$	0.342404	+	2.60082i	0.0219652	+	0.166842i
$244$	9.56280	+	3.23823i	0.612195	+	0.207307i
$245$	−14.4322	+	27.0923i	−0.922037	+	1.73086i
$246$	2.99014	−	7.95354i	0.190644	−	0.507099i
$247$	−0.889055	+	3.31800i	−0.0565692	+	0.211119i
$248$	2.21243	−	0.835508i	0.140490	−	0.0530548i
$249$	−2.44110	−	9.11031i	−0.154698	−	0.577343i
$250$	33.3250	−	46.5413i	2.10766	−	2.94353i
$251$	0.538924	−	0.223229i	0.0340166	−	0.0140901i	−0.365610	−	0.930768i	$-0.619140\pi$
$251$	0.538924	−	0.223229i	0.0340166	−	0.0140901i	0.399627	+	0.916678i	$0.369140\pi$
$252$	−0.198441	−	1.32460i	−0.0125006	−	0.0834418i
$253$	−3.41225	+	8.23790i	−0.214526	+	0.517912i
$254$	−17.2090	−	4.00585i	−1.07979	−	0.251349i
$255$	−6.60486	+	11.4400i	−0.413613	+	0.716398i
$256$	−4.09530	+	15.4670i	−0.255956	+	0.966688i
$257$	−1.00316	−	1.73753i	−0.0625756	−	0.108384i	0.833040	−	0.553212i	$-0.186598\pi$
$257$	−1.00316	−	1.73753i	−0.0625756	−	0.108384i	−0.895616	+	0.444828i	$0.853265\pi$
$258$	−12.3094	+	13.1523i	−0.766347	+	0.818828i
$259$	14.7762	−	3.20224i	0.918151	−	0.198978i
$260$	−2.93476	−	44.2733i	−0.182006	−	2.74571i
$261$	−0.360930	−	0.276951i	−0.0223410	−	0.0171428i
$262$	26.8345	+	2.63294i	1.65784	+	0.162663i
$263$	−0.324920	−	1.21262i	−0.0200354	−	0.0747732i	0.955184	−	0.296012i	$-0.0956567\pi$
$263$	−0.324920	−	1.21262i	−0.0200354	−	0.0747732i	−0.975220	+	0.221238i	$0.928990\pi$
$264$	−2.51624	+	15.3467i	−0.154864	+	0.944527i
$265$	−26.1217	−	26.1217i	−1.60464	−	1.60464i
$266$	1.76875	+	1.82368i	0.108449	+	0.111817i
$267$	0.742078	+	1.79153i	0.0454144	+	0.109640i
$268$	−1.77506	−	8.88940i	−0.108429	−	0.543007i
$269$	3.57084	−	2.74001i	0.217718	−	0.167061i	−0.494144	−	0.869380i	$-0.664519\pi$
$269$	3.57084	−	2.74001i	0.217718	−	0.167061i	0.711863	+	0.702319i	$0.247852\pi$
$270$	29.4946	+	15.7511i	1.79498	+	0.958583i
$271$	−18.6539	+	10.7698i	−1.13314	+	0.654221i	−0.944724	−	0.327867i	$-0.893670\pi$
$271$	−18.6539	+	10.7698i	−1.13314	+	0.654221i	−0.188421	+	0.982088i	$0.560337\pi$
$272$	0.959620	+	7.20653i	0.0581855	+	0.436960i
$273$	−20.0608	−	9.47081i	−1.21414	−	0.573199i
$274$	7.99504	−	0.264695i	0.482998	−	0.0159908i
$275$	−6.16196	−	46.8047i	−0.371580	−	2.82243i
$276$	−8.89057	−	0.576105i	−0.535149	−	0.0346775i
$277$	−10.9592	−	1.44280i	−0.658473	−	0.0866896i	−0.206117	−	0.978527i	$-0.566083\pi$
$277$	−10.9592	−	1.44280i	−0.658473	−	0.0866896i	−0.452356	+	0.891838i	$0.649416\pi$
$278$	−0.979067	−	5.91649i	−0.0587206	−	0.354847i
$279$	−0.149653	−	0.149653i	−0.00895947	−	0.00895947i
$280$	−29.2175	−	14.9408i	−1.74608	−	0.892881i
$281$	−8.84724	+	8.84724i	−0.527782	+	0.527782i	−0.919910	−	0.392129i	$-0.871739\pi$
$281$	−8.84724	+	8.84724i	−0.527782	+	0.527782i	0.392129	+	0.919910i	$0.371739\pi$
$282$	1.18429	+	0.847984i	0.0705232	+	0.0504967i
$283$	1.74174	−	13.2298i	0.103536	−	0.786431i	−0.858366	−	0.513037i	$-0.828520\pi$
$283$	1.74174	−	13.2298i	0.103536	−	0.786431i	0.961902	−	0.273394i	$-0.0881464\pi$
$284$	4.00793	−	1.36382i	0.237827	−	0.0809279i
$285$	−4.89260	+	0.644123i	−0.289813	+	0.0381546i
$286$	−17.3297	−	16.2190i	−1.02473	−	0.959050i
$287$	9.55876	−	0.790542i	0.564236	−	0.0466642i
$288$	1.41230	−	0.235859i	0.0832204	−	0.0138981i
$289$	−6.84828	−	11.8616i	−0.402840	−	0.697740i
$290$	−10.6653	+	3.23960i	−0.626289	+	0.190236i
$291$	8.76926	+	11.4283i	0.514063	+	0.669940i
$292$	−24.9315	−	4.93999i	−1.45901	−	0.289091i
$293$	3.98516	−	1.65071i	0.232816	−	0.0964354i	−0.263226	−	0.964734i	$-0.584786\pi$
$293$	3.98516	−	1.65071i	0.232816	−	0.0964354i	0.496041	+	0.868299i	$0.334786\pi$
$294$	−13.6258	+	9.13955i	−0.794674	+	0.533029i
$295$	27.9804	−	27.9804i	1.62908	−	1.62908i
$296$	3.68776	+	15.7368i	0.214346	+	0.914685i
$297$	17.2773	−	4.62943i	1.00253	−	0.268627i
$298$	−5.36037	+	4.40246i	−0.310518	+	0.255028i
$299$	8.27769	−	10.7877i	0.478711	−	0.623868i
$300$	42.2894	−	20.8938i	2.44158	−	1.20630i
$301$	−19.3637	−	6.20663i	−1.11610	−	0.357744i
$302$	17.1538	−	0.567918i	0.987091	−	0.0326800i
$303$	−9.94114	+	5.73952i	−0.571103	+	0.329727i
$304$	−1.91761	+	1.92330i	−0.109983	+	0.110309i
$305$	−19.1712	−	11.0685i	−1.09774	−	0.633781i
$306$	0.552374	−	0.343772i	0.0315771	−	0.0196521i
$307$	29.9950	+	12.4243i	1.71191	+	0.709095i	0.999977	+	0.00684451i	$0.00217869\pi$
$307$	29.9950	+	12.4243i	1.71191	+	0.709095i	0.711930	+	0.702250i	$0.247821\pi$
$308$	−16.8728	+	4.84466i	−0.961420	+	0.276050i
$309$	−1.24613	−	3.00843i	−0.0708899	−	0.171143i
$310$	−5.11581	+	0.846570i	−0.290559	+	0.0480820i
$311$	18.3347	−	4.91276i	1.03966	−	0.278577i	0.301690	−	0.953406i	$-0.402449\pi$
$311$	18.3347	−	4.91276i	1.03966	−	0.278577i	0.737974	+	0.674829i	$0.235783\pi$
$312$	9.76366	−	21.6127i	0.552758	−	1.22358i
$313$	−0.835055	−	0.223752i	−0.0472001	−	0.0126472i	0.235142	−	0.971961i	$-0.424445\pi$
$313$	−0.835055	−	0.223752i	−0.0472001	−	0.0126472i	−0.282342	+	0.959314i	$0.591111\pi$
$314$	−5.24981	−	11.5752i	−0.296264	−	0.653225i
$315$	−0.142036	+	2.93330i	−0.00800282	+	0.165273i
$316$	−2.95050	+	0.195581i	−0.165978	+	0.0110023i
$317$	22.3559	−	2.94321i	1.25563	−	0.165307i	0.526795	−	0.849992i	$-0.323394\pi$
$317$	22.3559	−	2.94321i	1.25563	−	0.165307i	0.728839	+	0.684685i	$0.240060\pi$
$318$	−5.73871	−	18.8928i	−0.321811	−	1.05946i
$319$	−2.98135	+	5.16385i	−0.166924	+	0.289120i
$320$	15.4463	−	31.4983i	0.863475	−	1.76081i
$321$	21.3552			1.19193
$322$	−3.70602	−	9.34889i	−0.206528	−	0.520993i
$323$	−0.472261	+	1.14014i	−0.0262773	+	0.0634390i
$324$	9.09539	+	13.5904i	0.505300	+	0.755023i
$325$	−9.39679	+	71.3757i	−0.521240	+	3.95921i
$326$	−14.2846	−	1.40157i	−0.791150	−	0.0776257i
$327$	−6.47504	−	1.73498i	−0.358071	−	0.0959447i
$328$	1.01637	+	10.2031i	0.0561196	+	0.563374i
$329$	−0.293197	+	1.61782i	−0.0161645	+	0.0891932i
$330$	11.9995	−	31.9176i	0.660548	−	1.75701i
$331$	−7.14967	+	9.31763i	−0.392981	+	0.512143i	−0.947381	−	0.320107i	$-0.896281\pi$
$331$	−7.14967	+	9.31763i	−0.392981	+	0.512143i	0.554400	+	0.832250i	$0.312948\pi$
$332$	7.51068	+	8.55151i	0.412202	+	0.469325i
$333$	1.14755	−	0.880548i	0.0628855	−	0.0482537i
$334$	−29.3369	+	18.2579i	−1.60524	+	0.999028i
$335$			19.8758i			1.08593i
$336$	−10.0135	−	14.4007i	−0.546280	−	0.785624i
$337$		−	15.7057i		−	0.855544i	−0.903887	−	0.427772i	$-0.859299\pi$
$337$		−	15.7057i		−	0.855544i	0.903887	−	0.427772i	$-0.140701\pi$
$338$	9.41109	+	15.1218i	0.511896	+	0.822516i
$339$	5.88955	−	4.51921i	0.319877	−	0.245450i
$340$	1.03078	−	15.9072i	0.0559019	−	0.862690i
$341$	−1.68863	+	2.20066i	−0.0914442	+	0.119172i
$342$	0.227506	+	0.0855309i	0.0123021	+	0.00462498i
$343$	−15.9054	−	9.48778i	−0.858811	−	0.512292i
$344$	6.28710	−	20.8090i	0.338978	−	1.12195i
$345$	18.8688	+	5.05588i	1.01586	+	0.272200i
$346$	−0.545506	+	5.55973i	−0.0293266	+	0.298893i
$347$	0.804224	−	6.10869i	0.0431730	−	0.327932i	−0.956206	−	0.292695i	$-0.905448\pi$
$347$	0.804224	−	6.10869i	0.0431730	−	0.327932i	0.999379	−	0.0352369i	$-0.0112186\pi$
$348$	−5.84412	−	1.15797i	−0.313278	−	0.0620736i
$349$	−5.16989	+	12.4812i	−0.276738	+	0.668105i	−0.999741	−	0.0227397i	$-0.992761\pi$
$349$	−5.16989	+	12.4812i	−0.276738	+	0.668105i	0.723003	+	0.690845i	$0.242761\pi$
$350$	41.7411	+	33.0551i	2.23116	+	1.76687i
$351$	−27.2767			−1.45592
$352$	−5.48092	−	17.9484i	−0.292134	−	0.956655i
$353$	10.8994	−	18.8783i	0.580116	−	1.00479i	−0.415349	−	0.909662i	$-0.636341\pi$
$353$	10.8994	−	18.8783i	0.580116	−	1.00479i	0.995465	−	0.0951280i	$-0.0303260\pi$
$354$	20.2371	−	6.14705i	1.07559	−	0.326712i
$355$	−9.20326	+	1.21163i	−0.488458	+	0.0643067i
$356$	−1.76046	−	1.54158i	−0.0933044	−	0.0817036i
$357$	−6.70130	−	4.31410i	−0.354671	−	0.228326i
$358$	−23.0129	+	10.4373i	−1.21627	+	0.551627i
$359$	3.27284	+	0.876956i	0.172734	+	0.0462840i	0.344149	−	0.938915i	$-0.388167\pi$
$359$	3.27284	+	0.876956i	0.172734	+	0.0462840i	−0.171415	+	0.985199i	$0.554834\pi$
$360$	−3.13793	−	0.0992352i	−0.165384	−	0.00523016i
$361$	17.9073	−	4.79824i	0.942488	−	0.252539i
$362$	5.33800	+	32.2575i	0.280559	+	1.69542i
$363$	−0.00370713	−	0.00894979i	−0.000194574	−	0.000469742i
$364$	26.7659	−	0.476657i	1.40292	−	0.0249836i
$365$	51.4858	+	21.3261i	2.69489	+	1.11626i
$366$	−6.25189	−	10.0456i	−0.326791	−	0.525089i
$367$	−7.28755	−	4.20747i	−0.380407	−	0.219628i	0.297588	−	0.954694i	$-0.403818\pi$
$367$	−7.28755	−	4.20747i	−0.380407	−	0.219628i	−0.677995	+	0.735066i	$0.737151\pi$
$368$	9.92654	−	4.12895i	0.517457	−	0.215236i
$369$	0.794672	−	0.458804i	0.0413690	−	0.0238844i
$370$	−1.17267	−	35.4201i	−0.0609640	−	1.84140i
$371$	16.5039	−	14.9794i	0.856840	−	0.777693i
$372$	−2.62513	−	0.888945i	−0.136107	−	0.0460896i
$373$	15.2842	−	19.9188i	0.791388	−	1.03136i	−0.207204	−	0.978298i	$-0.566436\pi$
$373$	15.2842	−	19.9188i	0.791388	−	1.03136i	0.998591	−	0.0530588i	$-0.0168971\pi$
$374$	−5.41207	−	6.58965i	−0.279852	−	0.340743i
$375$	−64.7983	+	17.3627i	−3.34617	+	0.896604i
$376$	−1.73453	−	0.284393i	−0.0894517	−	0.0146665i
$377$	6.42967	−	6.42967i	0.331145	−	0.331145i
$378$	−10.3527	+	17.3146i	−0.532487	+	0.890568i
$379$	−20.3854	+	8.44391i	−1.04713	+	0.433735i	−0.838866	−	0.544338i	$-0.816781\pi$
$379$	−20.3854	+	8.44391i	−1.04713	+	0.433735i	−0.208262	+	0.978073i	$0.566781\pi$
$380$	4.94894	−	3.31208i	0.253875	−	0.169906i
$381$	12.6056	+	16.4280i	0.645807	+	0.841632i
$382$	−6.07264	−	19.9922i	−0.310703	−	1.02289i
$383$	5.40426	+	9.36046i	0.276145	+	0.478297i	0.970423	−	0.241410i	$-0.0776097\pi$
$383$	5.40426	+	9.36046i	0.276145	+	0.478297i	−0.694278	+	0.719706i	$0.744276\pi$
$384$	15.2133	−	10.9615i	0.776352	−	0.559378i
$385$	38.3594	−	3.17245i	1.95498	−	0.161683i
$386$	−16.2397	+	17.3519i	−0.826581	+	0.883187i
$387$	−1.92872	+	0.253920i	−0.0980421	+	0.0129075i
$388$	−15.5961	−	7.67678i	−0.791771	−	0.389729i
$389$	2.13015	−	16.1801i	0.108003	−	0.820362i	−0.848614	−	0.529013i	$-0.822562\pi$
$389$	2.13015	−	16.1801i	0.108003	−	0.820362i	0.956617	−	0.291349i	$-0.0941042\pi$
$390$	−30.2729	+	42.2788i	−1.53293	+	2.14087i
$391$	3.45428	−	3.45428i	0.174690	−	0.174690i
$392$	9.85630	−	17.1713i	0.497818	−	0.867281i
$393$	−22.3442	−	22.3442i	−1.12712	−	1.12712i
$394$	−33.9875	+	5.62429i	−1.71226	+	0.283347i
$395$	6.42802	+	0.846265i	0.323429	+	0.0425802i
$396$	−1.26185	+	1.10827i	−0.0634106	+	0.0556927i
$397$	−0.0155174	−	0.117866i	−0.000778794	−	0.00591553i	0.991051	−	0.133483i	$-0.0426163\pi$
$397$	−0.0155174	−	0.117866i	−0.000778794	−	0.00591553i	−0.991830	+	0.127568i	$0.959283\pi$
$398$	0.233080	+	7.04013i	0.0116833	+	0.352890i
$399$	−0.245399	−	2.96721i	−0.0122853	−	0.148546i
$400$	−34.5841	+	45.2094i	−1.72921	+	2.26047i
$401$	21.6642	−	12.5078i	1.08186	−	0.624611i	0.150461	−	0.988616i	$-0.451924\pi$
$401$	21.6642	−	12.5078i	1.08186	−	0.624611i	0.931397	+	0.364005i	$0.118591\pi$
$402$	−5.00441	+	9.37094i	−0.249597	+	0.467380i
$403$	3.35593	−	2.57510i	0.167171	−	0.128275i
$404$	7.68728	−	11.5233i	0.382456	−	0.573305i
$405$	−13.7215	−	33.1267i	−0.681828	−	1.64608i
$406$	−1.64106	−	6.52175i	−0.0814443	−	0.323669i
$407$	−13.4053	−	13.4053i	−0.664478	−	0.664478i
$408$	4.49118	−	7.24033i	0.222346	−	0.358450i
$409$	−4.51208	−	16.8393i	−0.223108	−	0.832650i	−0.983154	−	0.182780i	$-0.941490\pi$
$409$	−4.51208	−	16.8393i	−0.223108	−	0.832650i	0.760046	−	0.649869i	$-0.225176\pi$
$410$	2.19536	−	22.3748i	0.108421	−	1.10501i
$411$	−7.43755	−	5.70703i	−0.366867	−	0.281507i
$412$	2.95625	+	2.58869i	0.145644	+	0.127536i
$413$	16.0453	+	17.6783i	0.789538	+	0.869891i
$414$	−0.702460	−	0.657438i	−0.0345240	−	0.0323113i
$415$	−12.4776	−	21.6118i	−0.612501	−	1.06088i
$416$	0.989338	+	28.6014i	0.0485063	+	1.40230i
$417$	−3.51403	+	6.08648i	−0.172083	+	0.298056i
$418$	0.722218	−	3.10262i	0.0353248	−	0.151754i
$419$	14.5601	−	35.1512i	0.711308	−	1.71725i	0.0146007	−	0.999893i	$-0.495352\pi$
$419$	14.5601	−	35.1512i	0.711308	−	1.71725i	0.696707	−	0.717356i	$-0.254648\pi$
$420$	15.3477	+	35.2632i	0.748890	+	1.72067i
$421$	13.9825	−	5.79175i	0.681466	−	0.282272i	−0.0149737	−	0.999888i	$-0.504766\pi$
$421$	13.9825	−	5.79175i	0.681466	−	0.282272i	0.696440	+	0.717615i	$0.254766\pi$
$422$	25.2677	+	18.0924i	1.23001	+	0.880724i
$423$	0.0407117	+	0.151938i	0.00197947	+	0.00738748i
$424$	16.3073	+	17.3724i	0.791952	+	0.843678i
$425$	−6.69404	+	24.9825i	−0.324709	+	1.21183i
$426$	−4.64418	−	1.74598i	−0.225011	−	0.0845932i
$427$	7.22962	−	11.2301i	0.349866	−	0.543464i
$428$	−23.1039	+	11.4149i	−1.11677	+	0.551759i
$429$	3.63079	+	27.5786i	0.175296	+	1.33151i
$430$	−22.4526	+	42.0433i	−1.08276	+	2.02751i
$431$	18.4092	+	10.6286i	0.886740	+	0.511960i	0.872875	−	0.487944i	$-0.162253\pi$
$431$	18.4092	+	10.6286i	0.886740	+	0.511960i	0.0138651	+	0.999904i	$0.495586\pi$
$432$	−18.6931	−	10.7556i	−0.899372	−	0.517478i
$433$		−	10.1061i		−	0.485669i	−0.970068	−	0.242835i	$-0.921923\pi$
$433$		−	10.1061i		−	0.485669i	0.970068	−	0.242835i	$-0.0780773\pi$
$434$	−0.360885	−	3.10763i	−0.0173231	−	0.149171i
$435$	12.0686	+	4.99899i	0.578647	+	0.239683i
$436$	7.93266	−	1.58401i	0.379905	−	0.0758605i
$437$	1.80933	+	0.238203i	0.0865521	+	0.0113948i
$438$	18.9047	+	23.0181i	0.903303	+	1.09985i
$439$	7.84728	−	29.2864i	0.374530	−	1.39777i	−0.479500	−	0.877542i	$-0.659182\pi$
$439$	7.84728	−	29.2864i	0.374530	−	1.39777i	0.854030	−	0.520224i	$-0.174151\pi$
$440$	4.07870	+	40.9453i	0.194444	+	1.95199i
$441$	−1.76354	−	0.171190i	−0.0839782	−	0.00815189i
$442$	5.37114	+	11.8427i	0.255479	+	0.563299i
$443$	−2.25768	−	1.73238i	−0.107266	−	0.0823077i	0.553736	−	0.832692i	$-0.313202\pi$
$443$	−2.25768	−	1.73238i	−0.107266	−	0.0823077i	−0.661002	+	0.750385i	$0.729868\pi$
$444$	8.36535	−	16.9950i	0.397002	−	0.806545i
$445$	3.12341	+	4.07050i	0.148064	+	0.192960i
$446$	17.5452	+	4.08412i	0.830789	+	0.193388i
$447$	8.12917			0.384497
$448$	18.5310	+	10.2275i	0.875508	+	0.483204i
$449$	−21.3346			−1.00684			−0.503421	−	0.864041i	$-0.667926\pi$
$449$	−21.3346			−1.00684			−0.503421	+	0.864041i	$0.667926\pi$
$450$	4.96124	+	1.15486i	0.233875	+	0.0544408i
$451$	−7.32136	−	9.54138i	−0.344749	−	0.449286i
$452$	−3.95620	+	8.03739i	−0.186084	+	0.378047i
$453$	−15.9577	−	12.2448i	−0.749758	−	0.575310i
$454$	−4.83975	−	10.6710i	−0.227141	−	0.500817i
$455$	−57.7558	−	10.4671i	−2.70763	−	0.490703i
$456$	3.16724	−	0.315499i	0.148320	−	0.0147746i
$457$	1.06704	−	3.98223i	0.0499139	−	0.186281i	−0.936468	−	0.350754i	$-0.885925\pi$
$457$	1.06704	−	3.98223i	0.0499139	−	0.186281i	0.986382	+	0.164472i	$0.0525922\pi$
$458$	−15.5028	−	18.8760i	−0.724400	−	0.882018i
$459$	−9.71563	−	1.27909i	−0.453487	−	0.0597027i
$460$	−23.1164	+	4.61595i	−1.07781	+	0.215220i
$461$	−33.5146	−	13.8822i	−1.56093	−	0.646560i	−0.575682	−	0.817674i	$-0.695263\pi$
$461$	−33.5146	−	13.8822i	−1.56093	−	0.646560i	−0.985251	+	0.171114i	$0.945263\pi$
$462$	18.8843	+	8.16257i	0.878577	+	0.379757i
$463$		−	33.1517i		−	1.54069i	−0.637626	−	0.770346i	$-0.720084\pi$
$463$		−	33.1517i		−	1.54069i	0.637626	−	0.770346i	$-0.279916\pi$
$464$	6.94164	−	1.87103i	0.322258	−	0.0868606i
$465$	5.26279	+	3.03848i	0.244056	+	0.140906i
$466$	−11.8991	+	22.2814i	−0.551214	+	1.03217i
$467$	−1.05800	−	8.03630i	−0.0489584	−	0.371876i	−0.998332	−	0.0577276i	$-0.981615\pi$
$467$	−1.05800	−	8.03630i	−0.0489584	−	0.371876i	0.949374	−	0.314148i	$-0.101719\pi$
$468$	2.29614	−	1.13445i	0.106139	−	0.0524399i
$469$	−11.9777	−	0.579983i	−0.553078	−	0.0267811i
$470$	3.60742	+	1.35621i	0.166398	+	0.0625574i
$471$	−3.85521	+	14.3878i	−0.177639	+	0.662957i
$472$	−18.6086	+	17.4677i	−0.856528	+	0.804014i
$473$	6.59907	+	24.6281i	0.303426	+	1.13240i
$474$	2.81758	+	2.01747i	0.129416	+	0.0926655i
$475$	−8.92657	+	3.69751i	−0.409579	+	0.169653i
$476$	9.55605	+	1.08536i	0.438001	+	0.0497472i
$477$	0.815999	−	1.97000i	0.0373620	−	0.0901999i
$478$	5.65671	−	24.3010i	0.258732	−	1.11150i
$479$	−9.50011	+	16.4547i	−0.434071	+	0.751833i	−0.997219	−	0.0745228i	$-0.976257\pi$
$479$	−9.50011	+	16.4547i	−0.434071	+	0.751833i	0.563148	+	0.826356i	$0.309590\pi$
$480$	−37.4175	+	17.0372i	−1.70787	+	0.777639i
$481$	14.4552	+	25.0371i	0.659099	+	1.14159i
$482$	18.5816	+	17.3907i	0.846371	+	0.792125i
$483$	−3.59742	+	11.2233i	−0.163688	+	0.510680i
$484$	0.00879458	+	0.00770112i	0.000399754	+	0.000350051i
$485$	30.2381	+	23.2025i	1.37304	+	1.05357i
$486$	−0.362261	+	3.69212i	−0.0164325	+	0.167478i
$487$	1.26183	+	4.70921i	0.0571789	+	0.213395i	0.988604	−	0.150538i	$-0.0481006\pi$
$487$	1.26183	+	4.70921i	0.0571789	+	0.213395i	−0.931425	+	0.363932i	$0.881434\pi$
$488$	12.1334	+	7.52637i	0.549255	+	0.340703i
$489$	11.8943	+	11.8943i	0.537878	+	0.537878i
$490$	−28.5651	+	32.6893i	−1.29044	+	1.47675i
$491$	7.85392	+	18.9610i	0.354442	+	0.855699i	0.996061	+	0.0886752i	$0.0282633\pi$
$491$	7.85392	+	18.9610i	0.354442	+	0.855699i	−0.641618	+	0.767024i	$0.721737\pi$
$492$	6.66868	−	9.99640i	0.300647	−	0.450673i
$493$	2.59168	−	1.98866i	0.116723	−	0.0895649i
$494$	−2.28840	+	4.28512i	−0.102960	+	0.192797i
$495$	3.18903	−	1.84119i	0.143336	−	0.0827552i
$496$	3.31526	−	0.441460i	0.148860	−	0.0198221i
$497$	−0.461608	−	5.58149i	−0.0207060	−	0.250364i
$498$	−0.441358	−	13.3311i	−0.0197777	−	0.597382i
$499$	5.05498	+	38.3964i	0.226292	+	1.71886i	0.607459	+	0.794351i	$0.292189\pi$
$499$	5.05498	+	38.3964i	0.226292	+	1.71886i	−0.381167	+	0.924506i	$0.624478\pi$
$500$	60.8237	−	53.4207i	2.72012	−	2.38905i
$501$	40.1491	+	5.28573i	1.79373	+	0.236149i
$502$	0.813880	−	0.134682i	0.0363252	−	0.00601114i
$503$	−2.96141	−	2.96141i	−0.132043	−	0.132043i	0.637997	−	0.770039i	$-0.279763\pi$
$503$	−2.96141	−	2.96141i	−0.132043	−	0.132043i	−0.770039	+	0.637997i	$0.779763\pi$
$504$	0.151368	−	1.88811i	0.00674247	−	0.0841031i
$505$	−21.4764	+	21.4764i	−0.955688	+	0.955688i
$506$	−7.34127	+	10.2527i	−0.326359	+	0.455790i
$507$	2.72455	−	20.6950i	0.121001	−	0.919097i
$508$	−22.4191	−	11.0352i	−0.994685	−	0.489609i
$509$	−27.3459	+	3.60016i	−1.21209	+	0.159574i	−0.709345	−	0.704862i	$-0.751009\pi$
$509$	−27.3459	+	3.60016i	−1.21209	+	0.159574i	−0.502743	+	0.864436i	$0.667676\pi$
$510$	−12.7654	+	13.6396i	−0.565261	+	0.603971i
$511$	−14.3541	+	30.4045i	−0.634988	+	1.34502i
$512$	−10.5999	+	19.9910i	−0.468454	+	0.883488i
$513$	−1.83042	−	3.17037i	−0.0808149	−	0.139975i
$514$	−0.824652	−	2.71489i	−0.0363738	−	0.119749i
$515$	−5.24496	−	6.83537i	−0.231121	−	0.301202i
$516$	−21.1717	+	14.1692i	−0.932033	+	0.623764i
$517$	1.90469	−	0.788950i	0.0837683	−	0.0346980i
$518$	21.3793	+	0.326891i	0.939354	+	0.0143628i
$519$	4.62939	−	4.62939i	0.203208	−	0.203208i
$520$	10.1528	−	61.9225i	0.445229	−	2.71548i
$521$	8.53602	−	2.28722i	0.373970	−	0.100205i	−0.0669384	−	0.997757i	$-0.521323\pi$
$521$	8.53602	−	2.28722i	0.373970	−	0.100205i	0.440908	+	0.897552i	$0.354656\pi$
$522$	−0.408343	−	0.497192i	−0.0178727	−	0.0217615i
$523$	−4.25147	+	5.54062i	−0.185904	+	0.242275i	−0.877002	−	0.480486i	$-0.840460\pi$
$523$	−4.25147	+	5.54062i	−0.185904	+	0.242275i	0.691099	+	0.722760i	$0.257127\pi$
$524$	36.1174	+	12.2304i	1.57780	+	0.534287i
$525$	−13.2161	−	60.9835i	−0.576796	−	2.66154i
$526$	−0.0587465	−	1.77442i	−0.00256147	−	0.0773685i
$527$	1.31610	−	0.759849i	0.0573301	−	0.0330995i
$528$	−8.38638	+	20.3317i	−0.364971	+	0.884822i
$529$	13.6624	+	7.88799i	0.594017	+	0.342956i
$530$	−27.6045	−	44.3550i	−1.19906	−	1.92666i
$531$	2.11017	+	0.874062i	0.0915737	+	0.0379311i
$532$	1.85154	+	3.07902i	0.0802745	+	0.133492i
$533$	7.01851	+	16.9442i	0.304005	+	0.733934i
$534$	0.447721	+	2.70557i	0.0193748	+	0.117081i
$535$	54.5781	−	14.6242i	2.35962	−	0.632258i
$536$	0.405212	−	12.8133i	0.0175025	−	0.553450i
$537$	28.6048	+	7.66464i	1.23439	+	0.330753i
$538$	5.79695	−	2.62915i	0.249924	−	0.113351i
$539$	0.792465	+	23.2090i	0.0341339	+	0.999683i
$540$	35.5753	+	31.1521i	1.53092	+	1.34057i
$541$	−33.7330	+	4.44103i	−1.45029	+	0.190935i	−0.814159	−	0.580642i	$-0.802801\pi$
$541$	−33.7330	+	4.44103i	−1.45029	+	0.190935i	−0.636136	+	0.771577i	$0.719468\pi$
$542$	−29.1468	+	8.85337i	−1.25196	+	0.380285i
$543$	19.1590	−	33.1843i	0.822189	−	1.42407i
$544$	−0.988816	+	10.2339i	−0.0423952	+	0.438773i
$545$	−17.7366			−0.759752
$546$	−24.5950	−	19.4770i	−1.05257	−	0.833537i
$547$	−3.20036	+	7.72635i	−0.136837	+	0.330355i	−0.977413	−	0.211340i	$-0.932217\pi$
$547$	−3.20036	+	7.72635i	−0.136837	+	0.330355i	0.840575	+	0.541695i	$0.182217\pi$
$548$	11.0971	+	2.19882i	0.474046	+	0.0939287i
$549$	0.166782	−	1.26684i	0.00711810	−	0.0540673i
$550$	6.51931	−	66.4440i	0.277985	−	2.83318i
$551$	1.17879	+	0.315855i	0.0502180	+	0.0134559i
$552$	−12.0611	−	3.64405i	−0.513353	−	0.155101i
$553$	−0.697555	+	3.84901i	−0.0296631	+	0.163677i
$554$	−14.6324	−	5.50108i	−0.621673	−	0.233718i
$555$	−25.2836	+	32.9503i	−1.07323	+	1.39866i
$556$	0.548413	−	8.46322i	0.0232579	−	0.358920i
$557$	−16.8764	+	12.9497i	−0.715074	+	0.548696i	−0.900974	−	0.433873i	$-0.857147\pi$
$557$	−16.8764	+	12.9497i	−0.715074	+	0.548696i	0.185900	+	0.982569i	$0.440480\pi$
$558$	−0.158148	−	0.254112i	−0.00669492	−	0.0107574i
$559$		−	38.8819i		−	1.64453i
$560$	−35.4535	−	29.9471i	−1.49818	−	1.26549i
$561$			9.99342i			0.421923i
$562$	−15.0227	+	9.34945i	−0.633695	+	0.394383i
$563$	−30.8523	+	23.6738i	−1.30027	+	0.997733i	−0.301248	+	0.953546i	$0.597403\pi$
$563$	−30.8523	+	23.6738i	−1.30027	+	0.997733i	−0.999023	+	0.0441873i	$0.985930\pi$
$564$	1.35934	+	1.54772i	0.0572385	+	0.0651706i
$565$	11.9573	−	15.5831i	0.503049	−	0.655586i
$566$	6.64085	−	17.6642i	0.279136	−	0.742480i
$567$	20.3635	−	7.30232i	0.855185	−	0.306669i
$568$	5.95775	−	0.593472i	0.249982	−	0.0249015i
$569$	17.9645	+	4.81356i	0.753110	+	0.201795i	0.614897	−	0.788607i	$-0.289198\pi$
$569$	17.9645	+	4.81356i	0.753110	+	0.201795i	0.138213	+	0.990403i	$0.455864\pi$
$570$	−6.94554	−	0.681478i	−0.290916	−	0.0285440i
$571$	4.51387	−	34.2862i	0.188899	−	1.43483i	−0.589857	−	0.807508i	$-0.700816\pi$
$571$	4.51387	−	34.2862i	0.188899	−	1.43483i	0.778757	−	0.627326i	$-0.215851\pi$
$572$	−18.6696	−	27.8962i	−0.780613	−	1.16640i
$573$	−9.37062	+	22.6227i	−0.391463	+	0.945076i
$574$	13.4196	+	1.97589i	0.560123	+	0.0824719i
$575$	38.2471			1.59502
$576$	2.02091	+	0.127948i	0.0842044	+	0.00533115i
$577$	−3.14916	+	5.45451i	−0.131101	+	0.227074i	−0.924101	−	0.382147i	$-0.875185\pi$
$577$	−3.14916	+	5.45451i	−0.131101	+	0.227074i	0.793000	+	0.609222i	$0.208518\pi$
$578$	−5.62964	−	18.5337i	−0.234162	−	0.770902i
$579$	27.6139	−	3.63543i	1.14759	−	0.151083i
$580$	−15.7290	+	1.04263i	−0.653111	+	0.0432930i
$581$	13.3880	−	6.88870i	0.555427	−	0.285792i
$582$	8.41449	+	18.5529i	0.348792	+	0.769042i
$583$	−26.9948	−	7.23324i	−1.11801	−	0.299570i
$584$	−32.7565	−	14.7979i	−1.35547	−	0.612343i
$585$	−5.42415	+	1.45340i	−0.224261	+	0.0600906i
$586$	6.01838	−	0.995928i	0.248617	−	0.0411414i
$587$	−2.62881	−	6.34651i	−0.108503	−	0.261949i	0.860297	−	0.509793i	$-0.170278\pi$
$587$	−2.62881	−	6.34651i	−0.108503	−	0.261949i	−0.968800	+	0.247844i	$0.920278\pi$
$588$	−21.6984	+	8.21994i	−0.894828	+	0.338985i
$589$	0.524505	+	0.217257i	0.0216119	+	0.00895193i
$590$	47.5111	−	29.5687i	1.95600	−	1.21733i
$591$	34.9640	+	20.1865i	1.43823	+	0.830360i
$592$	0.0338630	+	22.8581i	0.00139176	+	0.939463i
$593$	−4.31425	+	2.49083i	−0.177165	+	0.102286i	−0.585960	−	0.810340i	$-0.699282\pi$
$593$	−4.31425	+	2.49083i	−0.177165	+	0.102286i	0.408795	+	0.912626i	$0.365949\pi$
$594$	25.2818	−	0.837015i	1.03733	−	0.0343432i
$595$	−20.0811	−	6.43658i	−0.823243	−	0.263874i
$596$	−8.79485	+	4.34524i	−0.360251	+	0.177988i
$597$	5.02540	−	6.54923i	0.205676	−	0.268042i
$598$	14.8604	−	12.2048i	0.607687	−	0.499092i
$599$	4.25960	−	1.14136i	0.174043	−	0.0466346i	−0.170745	−	0.985315i	$-0.554618\pi$
$599$	4.25960	−	1.14136i	0.174043	−	0.0466346i	0.344788	+	0.938681i	$0.387951\pi$
$600$	64.9480	−	15.2199i	2.65149	−	0.621348i
$601$	2.31530	−	2.31530i	0.0944429	−	0.0944429i	−0.658307	−	0.752750i	$-0.728727\pi$
$601$	2.31530	−	2.31530i	0.0944429	−	0.0944429i	0.752750	+	0.658307i	$0.228727\pi$
$602$	−24.6813	−	14.7574i	−1.00593	−	0.601467i
$603$	−1.05992	+	0.439033i	−0.0431632	+	0.0178788i
$604$	23.8096	+	4.71769i	0.968798	+	0.191960i
$605$	−0.0156033	−	0.0203346i	−0.000634364	−	0.000826719i
$606$	−15.5330	+	4.71818i	−0.630987	+	0.191663i
$607$	12.8344	+	22.2298i	0.520931	+	0.902279i	0.999704	+	0.0243404i	$0.00774856\pi$
$607$	12.8344	+	22.2298i	0.520931	+	0.902279i	−0.478772	+	0.877939i	$0.658918\pi$
$608$	−3.25795	+	2.03430i	−0.132127	+	0.0825018i
$609$	−3.36470	+	7.12702i	−0.136344	+	0.288801i
$610$	−22.8574	−	21.3924i	−0.925469	−	0.866153i
$611$	−3.11702	+	0.410363i	−0.126101	+	0.0166015i
$612$	0.871055	−	0.296403i	0.0352103	−	0.0119814i
$613$	−4.30735	+	32.7175i	−0.173972	+	1.32145i	0.652207	+	0.758041i	$0.273843\pi$
$613$	−4.30735	+	32.7175i	−0.173972	+	1.32145i	−0.826179	+	0.563408i	$0.809490\pi$
$614$	37.3313	+	26.7303i	1.50657	+	1.07875i
$615$	−18.6307	+	18.6307i	−0.751262	+	0.751262i
$616$	−24.7938	+	1.26314i	−0.998970	+	0.0508933i
$617$	−30.9899	−	30.9899i	−1.24761	−	1.24761i	−0.956774	−	0.290832i	$-0.906068\pi$
$617$	−30.9899	−	30.9899i	−1.24761	−	1.24761i	−0.290832	−	0.956774i	$-0.593932\pi$
$618$	−0.751833	−	4.54331i	−0.0302431	−	0.182759i
$619$	14.8820	+	1.95925i	0.598158	+	0.0787490i	0.423525	−	0.905885i	$-0.360793\pi$
$619$	14.8820	+	1.95925i	0.598158	+	0.0787490i	0.174633	+	0.984634i	$0.444126\pi$
$620$	−7.31789	−	0.474196i	−0.293894	−	0.0190442i
$621$	1.89150	+	14.3674i	0.0759034	+	0.576544i
$622$	26.8291	−	0.888242i	1.07575	−	0.0356153i
$623$	−2.54414	+	1.76347i	−0.101929	+	0.0706520i
$624$	20.3779	−	26.6386i	0.815769	−	1.06640i
$625$	−92.0987	+	53.1732i	−3.68395	+	2.12693i
$626$	−1.07845	−	0.575933i	−0.0431037	−	0.0230189i
$627$	−2.96182	+	2.27268i	−0.118284	+	0.0907622i
$628$	−3.51975	−	17.6267i	−0.140453	−	0.703383i
$629$	3.97469	+	9.59575i	0.158481	+	0.382608i
$630$	−1.13613	+	3.99475i	−0.0452643	+	0.159155i
$631$	−3.73073	−	3.73073i	−0.148518	−	0.148518i	0.628938	−	0.777456i	$-0.283490\pi$
$631$	−3.73073	−	3.73073i	−0.148518	−	0.148518i	−0.777456	+	0.628938i	$0.783490\pi$
$632$	−4.12669	−	0.676610i	−0.164151	−	0.0269141i
$633$	−9.42633	−	35.1795i	−0.374663	−	1.39826i
$634$	31.7365	+	3.11390i	1.26042	+	0.123669i
$635$	43.4666	+	33.3531i	1.72492	+	1.32358i
$636$	−1.84695	−	27.8627i	−0.0732361	−	1.10483i
$637$	7.99308	−	34.4998i	0.316697	−	1.36693i
$638$	−5.76214	+	6.15674i	−0.228125	+	0.243748i
$639$	−0.267902	−	0.464020i	−0.0105980	−	0.0183564i
$640$	31.3747	−	38.4329i	1.24019	−	1.51919i
$641$	6.69941	−	11.6037i	0.264611	−	0.458319i	−0.702851	−	0.711337i	$-0.748090\pi$
$641$	6.69941	−	11.6037i	0.264611	−	0.458319i	0.967462	+	0.253018i	$0.0814232\pi$
$642$	29.4144	+	6.84699i	1.16089	+	0.270229i
$643$	−13.2052	+	31.8802i	−0.520762	+	1.25723i	0.416669	+	0.909058i	$0.363198\pi$
$643$	−13.2052	+	31.8802i	−0.520762	+	1.25723i	−0.937431	+	0.348172i	$0.886802\pi$
$644$	−2.10715	−	14.0653i	−0.0830334	−	0.554250i
$645$	51.6062	−	21.3760i	2.03199	−	0.841678i
$646$	−1.01604	+	1.41900i	−0.0399757	+	0.0558297i
$647$	5.74847	+	21.4536i	0.225996	+	0.843428i	0.982003	+	0.188865i	$0.0604808\pi$
$647$	5.74847	+	21.4536i	0.225996	+	0.843428i	−0.756007	+	0.654563i	$0.772853\pi$
$648$	8.17048	+	21.6355i	0.320967	+	0.849922i
$649$	7.74794	−	28.9157i	0.304133	−	1.13504i
$650$	−35.8278	+	95.2992i	−1.40528	+	3.73794i
$651$	−1.98464	+	3.08284i	−0.0777842	+	0.120826i
$652$	−19.2261	−	6.51049i	−0.752951	−	0.254970i
$653$	4.10108	+	31.1508i	0.160488	+	1.21902i	0.862201	+	0.506566i	$0.169085\pi$
$653$	4.10108	+	31.1508i	0.160488	+	1.21902i	−0.701714	+	0.712459i	$0.747581\pi$
$654$	−8.36237	−	4.46580i	−0.326995	−	0.174627i
$655$	−72.4072	−	41.8043i	−2.82918	−	1.63343i
$656$	−1.87144	+	14.3796i	−0.0730673	+	0.561427i
$657$			3.21666i			0.125494i
$658$	−0.922558	+	2.13436i	−0.0359650	+	0.0832060i
$659$	7.32010	+	3.03209i	0.285151	+	0.118113i	0.520674	−	0.853755i	$-0.325681\pi$
$659$	7.32010	+	3.03209i	0.285151	+	0.118113i	−0.235524	+	0.971869i	$0.575681\pi$
$660$	26.7615	−	40.1157i	1.04169	−	1.56150i
$661$	8.20812	+	1.08062i	0.319259	+	0.0420312i	0.288453	−	0.957494i	$-0.406859\pi$
$661$	8.20812	+	1.08062i	0.319259	+	0.0420312i	0.0308061	+	0.999525i	$0.490193\pi$
$662$	−12.8353	+	10.5416i	−0.498859	+	0.409713i
$663$	3.94431	−	14.7204i	0.153184	−	0.571692i
$664$	7.60331	+	14.1869i	0.295066	+	0.550557i
$665$	−2.65914	−	7.41535i	−0.103117	−	0.287555i
$666$	1.86295	−	0.844924i	0.0721879	−	0.0327401i
$667$	−3.83255	−	2.94082i	−0.148397	−	0.113869i
$668$	−46.2622	+	15.7421i	−1.78994	+	0.609081i
$669$	−12.8519	−	16.7490i	−0.496885	−	0.647553i
$670$	−6.37265	+	27.3767i	−0.246197	+	1.05765i
$671$	−16.7471			−0.646515
$672$	−9.17525	−	23.0460i	−0.353943	−	0.889017i
$673$	−1.35344			−0.0521711			−0.0260856	−	0.999660i	$-0.508304\pi$
$673$	−1.35344			−0.0521711			−0.0260856	+	0.999660i	$0.508304\pi$
$674$	5.03563	−	21.6329i	0.193965	−	0.833267i
$675$	−46.7064	−	60.8690i	−1.79773	−	2.34285i
$676$	8.11433	+	23.8460i	0.312090	+	0.917154i
$677$	1.63971	+	1.25820i	0.0630194	+	0.0483565i	0.639791	−	0.768549i	$-0.279021\pi$
$677$	1.63971	+	1.25820i	0.0630194	+	0.0483565i	−0.576771	+	0.816906i	$0.695688\pi$
$678$	9.56118	−	4.33638i	0.367195	−	0.166538i
$679$	−14.8648	+	17.5452i	−0.570459	+	0.673325i
$680$	6.52002	−	21.5799i	0.250031	−	0.827552i
$681$	−3.55408	+	13.2640i	−0.136193	+	0.508278i
$682$	−3.03148	+	2.48975i	−0.116081	+	0.0953375i
$683$	37.7436	+	4.96905i	1.44422	+	0.190135i	0.811549	−	0.584285i	$-0.198625\pi$
$683$	37.7436	+	4.96905i	1.44422	+	0.190135i	0.632672	+	0.774420i	$0.281958\pi$
$684$	0.285941	+	0.190753i	0.0109332	+	0.00729363i
$685$	−22.9166	−	9.49236i	−0.875598	−	0.362685i
$686$	−18.8659	−	18.1680i	−0.720304	−	0.693658i
$687$			28.6261i			1.09215i
$688$	15.3316	−	26.6463i	0.584513	−	1.01588i
$689$	36.9086	+	21.3092i	1.40611	+	0.811817i
$690$	24.3687	+	13.0137i	0.927699	+	0.495424i
$691$	−5.39800	−	41.0019i	−0.205350	−	1.55979i	−0.714827	−	0.699301i	$-0.753495\pi$
$691$	−5.39800	−	41.0019i	−0.205350	−	1.55979i	0.509477	−	0.860484i	$-0.329839\pi$
$692$	−2.53396	+	7.48300i	−0.0963266	+	0.284461i
$693$	1.01649	+	1.97552i	0.0386134	+	0.0750439i
$694$	3.06632	−	8.15618i	0.116396	−	0.309605i
$695$	−4.81286	+	17.9618i	−0.182562	+	0.681331i
$696$	−7.67835	−	3.46874i	−0.291047	−	0.131482i
$697$	1.70534	+	6.36442i	0.0645944	+	0.241070i
$698$	−11.1227	+	15.5339i	−0.421002	+	0.587967i
$699$	27.3494	−	11.3285i	1.03445	−	0.428483i
$700$	46.8955	+	58.9130i	1.77248	+	2.22670i
$701$	12.6441	−	30.5254i	0.477559	−	1.15293i	−0.483191	−	0.875515i	$-0.660522\pi$
$701$	12.6441	−	30.5254i	0.477559	−	1.15293i	0.960750	−	0.277415i	$-0.0894777\pi$
$702$	−37.5707	−	8.74558i	−1.41801	−	0.330081i
$703$	−1.94004	+	3.36025i	−0.0731701	+	0.126734i
$704$	−1.79465	−	26.4793i	−0.0676383	−	0.997976i
$705$	−2.25829	−	3.91147i	−0.0850520	−	0.147314i
$706$	21.0655	−	22.5081i	0.792812	−	0.847105i
$707$	−12.3156	−	13.5690i	−0.463176	−	0.510314i
$708$	29.8453	−	1.97837i	1.12166	−	0.0743516i
$709$	−33.3690	−	25.6049i	−1.25320	−	0.961613i	−0.253215	−	0.967410i	$-0.581488\pi$
$709$	−33.3690	−	25.6049i	−1.25320	−	0.961613i	−0.999983	+	0.00579720i	$0.998155\pi$
$710$	−13.0649	−	1.28190i	−0.490319	−	0.0481088i
$711$	0.0968586	+	0.361481i	0.00363248	+	0.0135566i
$712$	−1.93058	−	2.68780i	−0.0723514	−	0.100730i
$713$	−1.58909	−	1.58909i	−0.0595120	−	0.0595120i
$714$	−7.84710	−	8.09079i	−0.293670	−	0.302790i
$715$	28.1653	+	67.9971i	1.05332	+	2.54295i
$716$	−35.0441	+	6.99770i	−1.30966	+	0.261516i
$717$	−23.1982	+	17.8006i	−0.866352	+	0.664775i
$718$	4.22680	+	2.25726i	0.157743	+	0.0842403i
$719$	−10.4550	+	6.03622i	−0.389907	+	0.225113i	−0.682120	−	0.731240i	$-0.738942\pi$
$719$	−10.4550	+	6.03622i	−0.389907	+	0.225113i	0.292213	+	0.956353i	$0.405608\pi$
$720$	−4.29034	−	1.14278i	−0.159891	−	0.0425890i
$721$	4.27223	−	2.96130i	0.159106	−	0.110285i
$722$	26.2037	−	0.867536i	0.975201	−	0.0322864i
$723$	−3.89309	−	29.5709i	−0.144785	−	1.09976i
$724$	−2.99002	+	46.1426i	−0.111123	+	1.71488i
$725$	25.3577	+	3.33840i	0.941760	+	0.123985i
$726$	−0.00223663	−	0.0135159i	−8.30092e−5	−	0.000501624i
$727$	−22.5305	−	22.5305i	−0.835609	−	0.835609i	0.152668	−	0.988277i	$-0.451213\pi$
$727$	−22.5305	−	22.5305i	−0.835609	−	0.835609i	−0.988277	+	0.152668i	$0.951213\pi$
$728$	37.0199	+	7.92527i	1.37205	+	0.293730i
$729$	20.4194	−	20.4194i	0.756275	−	0.756275i
$730$	64.0783	+	45.8820i	2.37165	+	1.69817i
$731$	1.82329	−	13.8492i	0.0674367	−	0.512233i
$732$	−5.39043	−	15.8411i	−0.199236	−	0.585505i
$733$	−31.5166	+	4.14924i	−1.16409	+	0.153256i	−0.687712	−	0.725983i	$-0.741385\pi$
$733$	−31.5166	+	4.14924i	−1.16409	+	0.153256i	−0.476381	+	0.879239i	$0.658052\pi$
$734$	−8.68878	−	8.13189i	−0.320709	−	0.300154i
$735$	50.1843	−	8.35799i	1.85108	−	0.308289i
$736$	14.9965	−	2.50448i	0.552780	−	0.0923162i
$737$	7.51821	+	13.0219i	0.276937	+	0.479669i
$738$	1.24168	−	0.377161i	0.0457067	−	0.0138835i
$739$	14.5124	+	18.9129i	0.533847	+	0.695723i	0.979947	−	0.199261i	$-0.0638540\pi$
$739$	14.5124	+	18.9129i	0.533847	+	0.695723i	−0.446100	+	0.894983i	$0.647187\pi$
$740$	9.74132	−	49.1632i	0.358098	−	1.80728i
$741$	5.25978	−	2.17867i	0.193223	−	0.0800355i
$742$	27.5351	−	15.3409i	1.01084	−	0.563184i
$743$	−0.748867	+	0.748867i	−0.0274733	+	0.0274733i	−0.720710	−	0.693237i	$-0.756184\pi$
$743$	−0.748867	+	0.748867i	−0.0274733	+	0.0274733i	0.693237	+	0.720710i	$0.256184\pi$
$744$	−3.33081	−	2.06610i	−0.122114	−	0.0757471i
$745$	20.7760	−	5.56691i	0.761173	−	0.203956i
$746$	27.4388	−	22.5354i	1.00461	−	0.825081i
$747$	0.876882	−	1.14278i	0.0320834	−	0.0418120i
$748$	−5.34173	−	10.8118i	−0.195313	−	0.395317i
$749$	7.22032	+	33.3170i	0.263825	+	1.21738i
$750$	−94.8194	+	3.13922i	−3.46231	+	0.114628i
$751$	−20.3541	+	11.7514i	−0.742730	+	0.428815i	−0.823061	−	0.567953i	$-0.807736\pi$
$751$	−20.3541	+	11.7514i	−0.742730	+	0.428815i	0.0803311	+	0.996768i	$0.474402\pi$
$752$	−2.29794	−	0.947853i	−0.0837974	−	0.0345647i
$753$	−0.837264	−	0.483395i	−0.0305116	−	0.0176159i
$754$	10.9177	−	6.79465i	0.397598	−	0.247447i
$755$	−49.1689	−	20.3664i	−1.78944	−	0.741210i
$756$	−19.8112	+	20.5296i	−0.720527	+	0.746655i
$757$	−13.5497	−	32.7119i	−0.492473	−	1.18893i	−0.953458	−	0.301527i	$-0.902504\pi$
$757$	−13.5497	−	32.7119i	−0.492473	−	1.18893i	0.460985	−	0.887408i	$-0.347496\pi$
$758$	−30.7860	+	5.09449i	−1.11820	+	0.185040i
$759$	14.2746	−	3.82488i	0.518136	−	0.138834i
$760$	7.87856	−	2.97528i	0.285785	−	0.107925i
$761$	−39.8828	−	10.6866i	−1.44575	−	0.387388i	−0.551208	−	0.834368i	$-0.685833\pi$
$761$	−39.8828	−	10.6866i	−1.44575	−	0.387388i	−0.894544	+	0.446980i	$0.852499\pi$
$762$	12.0957	+	26.6694i	0.438180	+	0.966131i
$763$	0.517561	−	10.6886i	0.0187370	−	0.386952i
$764$	−1.95442	−	29.4840i	−0.0707084	−	1.06669i
$765$	−2.00017	+	0.263327i	−0.0723163	+	0.00952063i
$766$	4.44258	+	14.6257i	0.160517	+	0.528449i
$767$	−22.8255	+	39.5349i	−0.824181	+	1.42752i
$768$	24.4692	−	10.2205i	0.882957	−	0.368801i
$769$	18.6008			0.670761			0.335381	−	0.942083i	$-0.391135\pi$
$769$	18.6008			0.670761			0.335381	+	0.942083i	$0.391135\pi$
$770$	53.8530	+	7.92925i	1.94073	+	0.285750i
$771$	−1.27251	+	3.07211i	−0.0458283	+	0.110639i
$772$	−27.9319	+	18.6934i	−1.00529	+	0.672791i
$773$	4.46222	−	33.8939i	0.160495	−	1.21908i	−0.701689	−	0.712484i	$-0.747570\pi$
$773$	4.46222	−	33.8939i	0.160495	−	1.21908i	0.862183	−	0.506596i	$-0.169096\pi$
$774$	−2.73800	−	0.268646i	−0.0984155	−	0.00965628i
$775$	11.4929	+	3.07950i	0.412835	+	0.110619i
$776$	−19.0205	−	15.5744i	−0.682796	−	0.559088i
$777$	−19.1190	−	16.1981i	−0.685889	−	0.581104i
$778$	8.12176	−	21.6033i	0.291179	−	0.774515i
$779$	−1.49844	+	1.95281i	−0.0536872	+	0.0699666i
$780$	−55.2531	+	48.5281i	−1.97838	+	1.73758i
$781$	−5.57134	+	4.27504i	−0.199358	+	0.152973i
$782$	5.86541	−	3.65036i	0.209747	−	0.130537i
$783$			9.69061i			0.346314i
$784$	19.0815	−	20.4914i	0.681482	−	0.731835i
$785$			39.4115i			1.40666i
$786$	−23.6126	−	37.9407i	−0.842232	−	1.35330i
$787$	−10.6267	+	8.15413i	−0.378800	+	0.290663i	−0.780559	−	0.625082i	$-0.785066\pi$
$787$	−10.6267	+	8.15413i	−0.378800	+	0.290663i	0.401759	+	0.915745i	$0.368399\pi$
$788$	−48.6173	−	3.15038i	−1.73192	−	0.112228i
$789$	−1.26662	+	1.65069i	−0.0450929	+	0.0587663i
$790$	8.58255	+	3.22662i	0.305353	+	0.114798i
$791$	9.04189	+	7.66054i	0.321493	+	0.272377i
$792$	−2.09340	+	1.12194i	−0.0743858	+	0.0398664i
$793$	24.6686	+	6.60992i	0.876007	+	0.234725i
$794$	0.0164173	−	0.167323i	0.000582627	−	0.00593806i
$795$	−7.99161	+	60.7023i	−0.283433	+	2.15289i
$796$	−1.93619	+	9.77173i	−0.0686266	+	0.346350i
$797$	−5.73263	+	13.8398i	−0.203060	+	0.490231i	−0.992300	−	0.123854i	$-0.960475\pi$
$797$	−5.73263	+	13.8398i	−0.203060	+	0.490231i	0.789240	+	0.614085i	$0.210475\pi$
$798$	0.613351	−	4.16569i	0.0217124	−	0.147464i
$799$	−1.12949			−0.0399583
$800$	−62.1310	+	51.1825i	−2.19666	+	1.80957i
$801$	−0.148076	+	0.256475i	−0.00523201	+	0.00906210i
$802$	33.8503	−	10.2821i	1.19530	−	0.363073i
$803$	41.7986	−	5.50288i	1.47504	−	0.194193i
$804$	−9.89757	+	11.3029i	−0.349061	+	0.398622i
$805$	−1.50822	+	31.1474i	−0.0531576	+	1.09780i
$806$	5.44807	−	2.47092i	0.191900	−	0.0870344i
$807$	−7.20556	−	1.93072i	−0.253648	−	0.0679647i
$808$	14.2830	−	13.4073i	0.502475	−	0.471668i
$809$	−6.43738	+	1.72489i	−0.226326	+	0.0606440i	−0.370200	−	0.928952i	$-0.620711\pi$
$809$	−6.43738	+	1.72489i	−0.226326	+	0.0606440i	0.143874	+	0.989596i	$0.454044\pi$
$810$	−8.27866	−	50.0278i	−0.290882	−	1.75780i
$811$	−0.976216	−	2.35679i	−0.0342796	−	0.0827583i	0.905813	−	0.423679i	$-0.139261\pi$
$811$	−0.976216	−	2.35679i	−0.0342796	−	0.0827583i	−0.940092	+	0.340920i	$0.889261\pi$
$812$	−0.169342	−	9.50915i	−0.00594274	−	0.333706i
$813$	32.9818	+	13.6615i	1.15672	+	0.479130i
$814$	−14.1663	−	22.7624i	−0.496528	−	0.797823i
$815$	38.5439	+	22.2533i	1.35013	+	0.779500i
$816$	8.50752	−	8.53277i	0.297823	−	0.298707i
$817$	4.51924	−	2.60919i	0.158108	−	0.0912839i
$818$	−0.815797	−	24.6409i	−0.0285237	−	0.861550i
$819$	−0.717579	−	3.31116i	−0.0250742	−	0.115701i
$820$	10.1978	−	30.1149i	0.356121	−	1.05166i
$821$	−3.51694	+	4.58336i	−0.122742	+	0.159960i	−0.850682	−	0.525680i	$-0.823811\pi$
$821$	−3.51694	+	4.58336i	−0.122742	+	0.159960i	0.727941	+	0.685640i	$0.240478\pi$
$822$	−8.41459	−	10.2455i	−0.293492	−	0.357352i
$823$	38.1976	−	10.2350i	1.33149	−	0.356770i	0.478216	−	0.878242i	$-0.341283\pi$
$823$	38.1976	−	10.2350i	1.33149	−	0.356770i	0.853269	+	0.521472i	$0.174617\pi$
$824$	3.24191	+	4.51348i	0.112937	+	0.157235i
$825$	−55.3256	+	55.3256i	−1.92619	+	1.92619i
$826$	16.4325	+	29.4944i	0.571761	+	1.02624i
$827$	−28.9834	+	12.0053i	−1.00785	+	0.417466i	−0.824671	−	0.565613i	$-0.808640\pi$
$827$	−28.9834	+	12.0053i	−1.00785	+	0.417466i	−0.183181	+	0.983079i	$0.558640\pi$
$828$	−0.756771	−	1.13077i	−0.0262996	−	0.0392971i
$829$	−11.1334	−	14.5094i	−0.386681	−	0.503932i	0.558938	−	0.829209i	$-0.311209\pi$
$829$	−11.1334	−	14.5094i	−0.386681	−	0.503932i	−0.945619	+	0.325277i	$0.894542\pi$
$830$	−10.2572	−	33.7685i	−0.356033	−	1.17212i
$831$	9.16008	+	15.8657i	0.317760	+	0.550376i
$832$	−7.80761	+	39.7125i	−0.270680	+	1.37678i
$833$	4.46483	−	11.9136i	0.154697	−	0.412781i
$834$	−6.79166	+	7.25676i	−0.235176	+	0.251281i
$835$	106.230	−	13.9855i	3.67624	−	0.483987i
$836$	1.98955	−	4.04195i	0.0688100	−	0.139794i
$837$	−0.588426	+	4.46954i	−0.0203390	+	0.154490i
$838$	31.3253	−	43.7486i	1.08211	−	1.51127i
$839$	6.60602	−	6.60602i	0.228065	−	0.228065i	−0.583819	−	0.811884i	$-0.698442\pi$
$839$	6.60602	−	6.60602i	0.228065	−	0.228065i	0.811884	+	0.583819i	$0.198442\pi$
$840$	9.83349	+	53.4919i	0.339288	+	1.84565i
$841$	18.2218	+	18.2218i	0.628339	+	0.628339i
$842$	21.1163	−	3.49435i	0.727717	−	0.120423i
$843$	20.5594	+	2.70670i	0.708105	+	0.0932237i
$844$	29.0026	+	33.0217i	0.998309	+	1.13665i
$845$	−7.20885	−	54.7566i	−0.247992	−	1.88369i
$846$	0.00736079	+	0.222331i	0.000253069	+	0.00764389i
$847$	0.0127095	−	0.00880960i	0.000436704	−	0.000302702i
$848$	16.8915	+	29.1571i	0.580056	+	1.00126i
$849$	−19.1530	+	11.0580i	−0.657328	+	0.379509i
$850$	−17.2303	+	32.2643i	−0.590994	+	1.10666i
$851$	12.1853	−	9.35013i	0.417708	−	0.320518i
$852$	−5.83704	−	3.89394i	−0.199974	−	0.133404i
$853$	16.3102	+	39.3763i	0.558450	+	1.34822i	0.910993	+	0.412422i	$0.135317\pi$
$853$	16.3102	+	39.3763i	0.558450	+	1.34822i	−0.352543	+	0.935796i	$0.614683\pi$
$854$	13.5586	−	13.1503i	0.463967	−	0.449993i
$855$	−0.532919	−	0.532919i	−0.0182254	−	0.0182254i
$856$	−35.4830	+	8.31505i	−1.21278	+	0.284202i
$857$	−7.25127	−	27.0621i	−0.247698	−	0.924423i	−0.972008	−	0.234948i	$-0.924508\pi$
$857$	−7.25127	−	27.0621i	−0.247698	−	0.924423i	0.724309	−	0.689475i	$-0.242159\pi$
$858$	−3.84136	+	39.1506i	−0.131142	+	1.33658i
$859$	−33.5563	−	25.7486i	−1.14492	−	0.878532i	−0.150994	−	0.988535i	$-0.548247\pi$
$859$	−33.5563	−	25.7486i	−1.14492	−	0.878532i	−0.993931	+	0.110003i	$0.964914\pi$
$860$	−44.4061	+	50.7112i	−1.51423	+	1.72924i
$861$	−10.6837	−	11.7710i	−0.364100	−	0.401155i
$862$	21.9489	+	20.5421i	0.747581	+	0.699666i
$863$	25.9033	+	44.8658i	0.881757	+	1.52725i	0.849386	+	0.527773i	$0.176973\pi$
$863$	25.9033	+	44.8658i	0.881757	+	1.52725i	0.0323719	+	0.999476i	$0.489694\pi$
$864$	−22.2992	−	20.8081i	−0.758633	−	0.707905i
$865$	8.66125	−	15.0017i	0.294491	−	0.510074i
$866$	3.24027	−	13.9201i	0.110109	−	0.473023i
$867$	−8.68703	+	20.9723i	−0.295027	+	0.712258i
$868$	0.499303	−	4.39613i	0.0169474	−	0.149214i
$869$	4.53153	−	1.87702i	0.153721	−	0.0636735i
$870$	15.0204	+	10.7550i	0.509239	+	0.364630i
$871$	−5.93473	−	22.1487i	−0.201091	−	0.750481i
$872$	11.4342	+	0.361600i	0.387212	+	0.0122453i
$873$	−0.569399	+	2.12503i	−0.0192712	+	0.0719213i
$874$	2.41578	+	0.908214i	0.0817150	+	0.0307208i
$875$	−48.9968	−	95.2239i	−1.65640	−	3.21915i
$876$	18.6590	+	37.7662i	0.630429	+	1.27600i
$877$	−2.30272	−	17.4909i	−0.0777574	−	0.590626i	−0.985321	−	0.170712i	$-0.945393\pi$
$877$	−2.30272	−	17.4909i	−0.0777574	−	0.590626i	0.907564	−	0.419915i	$-0.137940\pi$
$878$	20.1987	−	37.8228i	0.681673	−	1.27646i
$879$	−6.19129	−	3.57454i	−0.208827	−	0.120566i
$880$	−7.51010	+	57.7053i	−0.253165	+	1.94525i
$881$		−	22.9740i		−	0.774015i	−0.922077	−	0.387008i	$-0.873509\pi$
$881$		−	22.9740i		−	0.774015i	0.922077	−	0.387008i	$-0.126491\pi$
$882$	−2.37420	−	0.801229i	−0.0799434	−	0.0269788i
$883$	−53.3636	−	22.1039i	−1.79583	−	0.743856i	−0.988003	−	0.154434i	$-0.950645\pi$
$883$	−53.3636	−	22.1039i	−1.79583	−	0.743856i	−0.807825	−	0.589423i	$-0.799355\pi$
$884$	3.60110	+	18.0341i	0.121118	+	0.606553i
$885$	−65.0216	−	8.56026i	−2.18568	−	0.287750i
$886$	−2.55426	−	3.11002i	−0.0858120	−	0.104483i
$887$	−9.05478	+	33.7929i	−0.304030	+	1.13466i	0.629747	+	0.776800i	$0.283158\pi$
$887$	−9.05478	+	33.7929i	−0.304030	+	1.13466i	−0.933777	+	0.357855i	$0.883508\pi$
$888$	16.9713	−	20.7265i	0.569521	−	0.695537i
$889$	−21.3679	+	25.2209i	−0.716656	+	0.845883i
$890$	2.99704	+	6.60810i	0.100461	+	0.221504i
$891$	−21.5204	−	16.5132i	−0.720959	−	0.553212i
$892$	22.8571	+	11.2508i	0.765312	+	0.376706i
$893$	−0.256865	−	0.334753i	−0.00859567	−	0.0112021i
$894$	11.1970	+	2.60641i	0.374485	+	0.0871714i
$895$	78.3550			2.61912
$896$	22.2452	+	20.0287i	0.743160	+	0.669113i
$897$	−22.5363			−0.752464
$898$	−29.3861	−	6.84039i	−0.980625	−	0.228267i
$899$	−0.914857	−	1.19226i	−0.0305122	−	0.0397642i
$900$	6.46329	+	3.18139i	0.215443	+	0.106046i
$901$	12.1472	+	9.32084i	0.404680	+	0.310522i
$902$	−7.02516	−	15.4896i	−0.233912	−	0.515747i
$903$	11.3759	+	31.7231i	0.378565	+	1.05568i
$904$	−8.02621	+	9.80216i	−0.266948	+	0.326015i
$905$	26.2403	−	97.9303i	0.872258	−	3.25531i
$906$	−18.0540	−	21.9822i	−0.599804	−	0.730311i
$907$	−55.7139	−	7.33488i	−1.84995	−	0.243551i	−0.877987	−	0.478684i	$-0.841114\pi$
$907$	−55.7139	−	7.33488i	−1.84995	−	0.243551i	−0.971963	+	0.235133i	$0.924447\pi$
$908$	−3.24482	−	16.2499i	−0.107683	−	0.539272i
$909$	−1.61967	−	0.670888i	−0.0537209	−	0.0222519i
$910$	−76.1961	−	32.9351i	−2.52588	−	1.09179i
$911$			24.2116i			0.802167i	0.916042	+	0.401083i	$0.131366\pi$
$911$			24.2116i			0.802167i	−0.916042	+	0.401083i	$0.868634\pi$
$912$	4.46368	+	0.580928i	0.147807	+	0.0192365i
$913$	−16.3498	−	9.43955i	−0.541099	−	0.312404i
$914$	2.74653	−	5.14297i	0.0908470	−	0.170114i
$915$	4.78891	+	36.3754i	0.158317	+	1.20253i
$916$	−15.3013	−	30.9702i	−0.505571	−	1.02328i
$917$	27.3053	−	42.4147i	0.901701	−	1.40066i
$918$	−12.9721	−	4.87687i	−0.428143	−	0.160961i
$919$	4.90356	−	18.3003i	0.161754	−	0.603673i	−0.836678	−	0.547695i	$-0.815506\pi$
$919$	4.90356	−	18.3003i	0.161754	−	0.603673i	0.998432	−	0.0559782i	$-0.0178277\pi$
$920$	−33.3203	−	1.05373i	−1.09854	−	0.0347406i
$921$	−13.9268	−	51.9754i	−0.458902	−	1.71265i
$922$	−41.7117	−	29.8668i	−1.37370	−	0.983612i
$923$	9.89394	−	4.09820i	0.325663	−	0.134894i
$924$	23.3939	+	17.2978i	0.769603	+	0.569056i
$925$	−31.1193	+	75.1287i	−1.02320	+	2.47022i
$926$	10.6292	−	45.6628i	0.349299	−	1.50057i
$927$	0.248656	−	0.430685i	0.00816693	−	0.0141455i
$928$	10.1612	−	0.351483i	0.333559	−	0.0115380i
$929$	13.9106	+	24.0939i	0.456392	+	0.790495i	0.998767	−	0.0496420i	$-0.0158080\pi$
$929$	13.9106	+	24.0939i	0.456392	+	0.790495i	−0.542375	+	0.840137i	$0.682475\pi$
$930$	6.27471	+	5.87254i	0.205756	+	0.192568i
$931$	4.54629	−	1.38609i	0.148999	−	0.0454272i
$932$	−23.5336	+	26.8751i	−0.770869	+	0.880322i
$933$	−24.9584	−	19.1512i	−0.817100	−	0.626983i
$934$	1.11936	−	11.4083i	0.0366265	−	0.373292i
$935$	6.84356	+	25.5405i	0.223808	+	0.835264i
$936$	3.52641	−	0.826377i	0.115264	−	0.0270110i
$937$	4.23341	+	4.23341i	0.138299	+	0.138299i	0.772867	−	0.634568i	$-0.218822\pi$
$937$	4.23341	+	4.23341i	0.138299	+	0.138299i	−0.634568	+	0.772867i	$0.718822\pi$
$938$	−16.3120	−	4.63920i	−0.532605	−	0.151475i
$939$	0.548316	+	1.32375i	0.0178936	+	0.0431990i
$940$	4.53399	+	3.02466i	0.147882	+	0.0986535i
$941$	39.5909	−	30.3792i	1.29063	−	0.990333i	0.291195	−	0.956664i	$-0.405947\pi$
$941$	39.5909	−	30.3792i	1.29063	−	0.990333i	0.999433	−	0.0336696i	$-0.0107194\pi$
$942$	−9.92322	+	18.5816i	−0.323316	+	0.605421i
$943$	8.43826	−	4.87183i	0.274788	−	0.158649i
$944$	−31.2318	+	18.0934i	−1.01651	+	0.588890i
$945$	51.4117	−	35.6361i	1.67242	−	1.15924i
$946$	1.19313	+	36.0383i	0.0387921	+	1.17170i
$947$	5.18044	+	39.3494i	0.168342	+	1.27868i	0.841935	+	0.539580i	$0.181417\pi$
$947$	5.18044	+	39.3494i	0.168342	+	1.27868i	−0.673593	+	0.739103i	$0.735250\pi$
$948$	3.23405	+	3.68222i	0.105037	+	0.119593i
$949$	−63.7414	−	8.39172i	−2.06913	−	0.272407i
$950$	−13.4809	+	2.23083i	−0.437377	+	0.0723777i
$951$	−26.4259	−	26.4259i	−0.856917	−	0.856917i
$952$	12.8144	+	4.55886i	0.415317	+	0.147753i
$953$	−32.8371	+	32.8371i	−1.06370	+	1.06370i	−0.0658686	+	0.997828i	$0.520982\pi$
$953$	−32.8371	+	32.8371i	−1.06370	+	1.06370i	−0.997828	+	0.0658686i	$0.979018\pi$
$954$	1.75558	−	2.45182i	0.0568389	−	0.0793806i
$955$	−8.45664	+	64.2345i	−0.273650	+	2.07858i
$956$	15.5830	−	31.6582i	0.503989	−	1.02390i
$957$	9.79787	−	1.28991i	0.316720	−	0.0416970i
$958$	−18.3611	+	19.6185i	−0.593220	+	0.633845i
$959$	6.38908	−	13.5332i	0.206314	−	0.437009i
$960$	−57.0009	+	11.4699i	−1.83970	+	0.370190i
$961$	15.1504	+	26.2413i	0.488724	+	0.846495i
$962$	11.8829	+	39.1205i	0.383120	+	1.26130i
$963$	1.98543	+	2.58747i	0.0639797	+	0.0833800i
$964$	20.0183	+	29.9115i	0.644745	+	0.963384i
$965$	68.0840	−	28.2013i	2.19170	−	0.907833i
$966$	−8.55351	+	14.3055i	−0.275205	+	0.460271i
$967$	7.06718	−	7.06718i	0.227265	−	0.227265i	−0.584284	−	0.811549i	$-0.698625\pi$
$967$	7.06718	−	7.06718i	0.227265	−	0.227265i	0.811549	+	0.584284i	$0.198625\pi$
$968$	0.00964439	+	0.0134272i	0.000309982	+	0.000431566i
$969$	1.97563	−	0.529369i	0.0634665	−	0.0170058i
$970$	34.2103	+	41.6539i	1.09843	+	1.33743i
$971$	−14.9357	+	19.4646i	−0.479311	+	0.624650i	−0.968945	−	0.247278i	$-0.920464\pi$
$971$	−14.9357	+	19.4646i	−0.479311	+	0.624650i	0.489634	+	0.871928i	$0.337130\pi$
$972$	−1.68276	+	4.96933i	−0.0539745	+	0.159391i
$973$	−10.6839	−	3.42449i	−0.342509	−	0.109784i
$974$	0.228142	+	6.89098i	0.00731015	+	0.220801i
$975$	103.331	−	59.6584i	3.30925	−	1.91060i
$976$	14.2993	+	14.2570i	0.457710	+	0.456356i
$977$	−7.82445	−	4.51745i	−0.250326	−	0.144526i	0.369587	−	0.929196i	$-0.379499\pi$
$977$	−7.82445	−	4.51745i	−0.250326	−	0.144526i	−0.619914	+	0.784670i	$0.712832\pi$
$978$	12.5695	+	20.1966i	0.401927	+	0.645818i
$979$	3.58606	+	1.48539i	0.114611	+	0.0474734i
$980$	−49.8263	+	35.8672i	−1.59164	+	1.14573i
$981$	−0.391781	−	0.945842i	−0.0125086	−	0.0301984i
$982$	4.73853	+	28.6349i	0.151213	+	0.913775i
$983$	−28.9091	+	7.74616i	−0.922056	+	0.247064i	−0.688464	−	0.725270i	$-0.741715\pi$
$983$	−28.9091	+	7.74616i	−0.922056	+	0.247064i	−0.233592	+	0.972335i	$0.575048\pi$
$984$	12.3905	−	11.6308i	0.394993	−	0.370776i
$985$	103.182	+	27.6476i	3.28766	+	0.880927i
$986$	4.20736	−	1.90821i	0.133990	−	0.0607697i
$987$	2.42306	−	1.24677i	0.0771268	−	0.0396851i
$988$	−4.52594	+	5.16856i	−0.143989	+	0.164434i
$989$	−20.4802	+	2.69626i	−0.651231	+	0.0857362i
$990$	4.98286	−	1.51355i	0.158366	−	0.0481038i
$991$	6.47693	−	11.2184i	0.205746	−	0.356363i	−0.744624	−	0.667484i	$-0.767371\pi$
$991$	6.47693	−	11.2184i	0.205746	−	0.356363i	0.950370	+	0.311121i	$0.100704\pi$
$992$	4.70795	+	0.454891i	0.149478	+	0.0144428i
$993$	19.4652			0.617709
$994$	1.15375	−	7.83589i	0.0365947	−	0.248539i
$995$	8.35862	−	20.1795i	0.264986	−	0.639733i
$996$	3.66636	−	18.5036i	0.116173	−	0.586310i
$997$	5.84198	−	44.3743i	0.185017	−	1.40535i	−0.606929	−	0.794756i	$-0.707599\pi$
$997$	5.84198	−	44.3743i	0.185017	−	1.40535i	0.791946	−	0.610591i	$-0.209068\pi$
$998$	−5.34813	+	54.5075i	−0.169292	+	1.72540i
$999$	−29.7608	−	7.97439i	−0.941590	−	0.252298i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.109.30	yes	240
4.3	odd	2		896.2.bh.a.529.22		240
7.2	even	3	inner	224.2.bd.a.205.13	yes	240
28.23	odd	6		896.2.bh.a.401.9		240
32.5	even	8	inner	224.2.bd.a.165.13	yes	240
32.27	odd	8		896.2.bh.a.753.9		240
224.37	even	24	inner	224.2.bd.a.37.30	✓	240
224.219	odd	24		896.2.bh.a.625.22		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.30	✓	240	224.37	even	24	inner
224.2.bd.a.109.30	yes	240	1.1	even	1	trivial
224.2.bd.a.165.13	yes	240	32.5	even	8	inner
224.2.bd.a.205.13	yes	240	7.2	even	3	inner
896.2.bh.a.401.9		240	28.23	odd	6
896.2.bh.a.529.22		240	4.3	odd	2
896.2.bh.a.625.22		240	224.219	odd	24
896.2.bh.a.753.9		240	32.27	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37739 + 0.320624i) q^{2} +(-1.00894 - 1.31488i) q^{3} +(1.79440 + 0.883248i) q^{4} +(-3.47903 - 2.66955i) q^{5} +(-0.968125 - 2.13459i) q^{6} +(1.71027 - 2.01866i) q^{7} +(2.18840 + 1.79190i) q^{8} +(0.0655120 - 0.244494i) q^{9} +O(q^{10})\)	\(q+(1.37739 + 0.320624i) q^{2} +(-1.00894 - 1.31488i) q^{3} +(1.79440 + 0.883248i) q^{4} +(-3.47903 - 2.66955i) q^{5} +(-0.968125 - 2.13459i) q^{6} +(1.71027 - 2.01866i) q^{7} +(2.18840 + 1.79190i) q^{8} +(0.0655120 - 0.244494i) q^{9} +(-3.93605 - 4.79247i) q^{10} +(-3.28912 - 0.433021i) q^{11} +(-0.649082 - 3.25057i) q^{12} +(4.67399 + 1.93603i) q^{13} +(3.00293 - 2.23213i) q^{14} +7.26794i q^{15} +(2.43974 + 3.16980i) q^{16} +(1.57403 + 0.908767i) q^{17} +(0.168626 - 0.315759i) q^{18} +(0.0886253 + 0.673176i) q^{19} +(-3.88489 - 7.86309i) q^{20} +(-4.37986 - 0.212081i) q^{21} +(-4.39157 - 1.65101i) q^{22} +(0.695642 - 2.59617i) q^{23} +(0.148173 - 4.68541i) q^{24} +(3.68303 + 13.7453i) q^{25} +(5.81716 + 4.16526i) q^{26} +(-4.98121 + 2.06329i) q^{27} +(4.85188 - 2.11170i) q^{28} +(0.687814 - 1.66053i) q^{29} +(-2.33028 + 10.0108i) q^{30} +(0.418066 - 0.724111i) q^{31} +(2.34416 + 5.14829i) q^{32} +(2.74917 + 4.76170i) q^{33} +(1.87668 + 1.75640i) q^{34} +(-11.3390 + 2.45733i) q^{35} +(0.333504 - 0.380857i) q^{36} +(4.53365 + 3.47879i) q^{37} +(-0.0937650 + 0.955640i) q^{38} +(-2.17014 - 8.09909i) q^{39} +(-2.82991 - 12.0761i) q^{40} +(2.56341 + 2.56341i) q^{41} +(-5.96477 - 1.69641i) q^{42} +(-2.94113 - 7.10052i) q^{43} +(-5.51954 - 3.68213i) q^{44} +(-0.880608 + 0.675714i) q^{45} +(1.79057 - 3.35290i) q^{46} +(-0.538181 + 0.310719i) q^{47} +(1.70635 - 6.40613i) q^{48} +(-1.14998 - 6.90489i) q^{49} +(0.665903 + 20.1134i) q^{50} +(-0.393188 - 2.98656i) q^{51} +(6.67701 + 7.60231i) q^{52} +(8.35206 + 1.09957i) q^{53} +(-7.52261 + 1.24485i) q^{54} +(10.2870 + 10.2870i) q^{55} +(7.35999 - 1.35300i) q^{56} +(0.795729 - 0.795729i) q^{57} +(1.47979 - 2.06667i) q^{58} +(-1.17781 + 8.94637i) q^{59} +(-6.41940 + 13.0416i) q^{60} +(5.00491 - 0.658909i) q^{61} +(0.808007 - 0.863341i) q^{62} +(-0.381508 - 0.550396i) q^{63} +(1.57815 + 7.84279i) q^{64} +(-11.0926 - 19.2130i) q^{65} +(2.25996 + 7.44017i) q^{66} +(-2.75918 - 3.59583i) q^{67} +(2.02177 + 3.02095i) q^{68} +(-4.11552 + 1.70470i) q^{69} +(-16.4061 - 0.250849i) q^{70} +(1.49681 - 1.49681i) q^{71} +(0.581476 - 0.417659i) q^{72} +(-12.2751 + 3.28910i) q^{73} +(5.12921 + 6.24524i) q^{74} +(14.3574 - 18.7110i) q^{75} +(-0.435552 + 1.28623i) q^{76} +(-6.49940 + 5.89904i) q^{77} +(-0.392368 - 11.8514i) q^{78} +(-1.28041 + 0.739243i) q^{79} +(-0.0259858 - 17.5409i) q^{80} +(7.08112 + 4.08829i) q^{81} +(2.70892 + 4.35270i) q^{82} +(5.25757 + 2.17776i) q^{83} +(-7.67190 - 4.24906i) q^{84} +(-3.05010 - 7.36358i) q^{85} +(-1.77448 - 10.7232i) q^{86} +(-2.87737 + 0.770988i) q^{87} +(-6.42197 - 6.84142i) q^{88} +(-1.13014 - 0.302821i) q^{89} +(-1.42959 + 0.648377i) q^{90} +(11.9019 - 6.12407i) q^{91} +(3.54132 - 4.04415i) q^{92} +(-1.37393 + 0.180881i) q^{93} +(-0.840909 + 0.255427i) q^{94} +(1.48875 - 2.57859i) q^{95} +(4.40427 - 8.27663i) q^{96} -8.69153 q^{97} +(0.629904 - 9.87943i) q^{98} +(-0.321348 + 0.775803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

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