LMFDB - Embedded newform 224.2.bd.a.37.18

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			37.18
Character	$\chi$	$=$	224.37
Dual form			224.2.bd.a.109.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.361256 - 1.36729i) q^{2} +(0.338207 - 0.440760i) q^{3} +(-1.73899 - 0.987888i) q^{4} +(3.17926 - 2.43953i) q^{5} +(-0.480469 - 0.621656i) q^{6} +(-2.54805 - 0.712336i) q^{7} +(-1.97895 + 2.02083i) q^{8} +(0.696572 + 2.59964i) q^{9} +O(q^{10})$	\(q+(0.361256 - 1.36729i) q^{2} +(0.338207 - 0.440760i) q^{3} +(-1.73899 - 0.987888i) q^{4} +(3.17926 - 2.43953i) q^{5} +(-0.480469 - 0.621656i) q^{6} +(-2.54805 - 0.712336i) q^{7} +(-1.97895 + 2.02083i) q^{8} +(0.696572 + 2.59964i) q^{9} +(-2.18703 - 5.22828i) q^{10} +(-0.556535 + 0.0732692i) q^{11} +(-1.02356 + 0.432366i) q^{12} +(3.73361 - 1.54651i) q^{13} +(-1.89447 + 3.22660i) q^{14} -2.22636i q^{15} +(2.04816 + 3.43585i) q^{16} +(-4.57446 + 2.64107i) q^{17} +(3.80612 - 0.0132815i) q^{18} +(0.214255 - 1.62743i) q^{19} +(-7.93868 + 1.10156i) q^{20} +(-1.17574 + 0.882164i) q^{21} +(-0.100871 + 0.787416i) q^{22} +(-0.771669 - 2.87991i) q^{23} +(0.221404 + 1.55570i) q^{24} +(2.86228 - 10.6822i) q^{25} +(-0.765746 - 5.66363i) q^{26} +(2.92123 + 1.21001i) q^{27} +(3.72733 + 3.75593i) q^{28} +(1.20639 + 2.91247i) q^{29} +(-3.04409 - 0.804287i) q^{30} +(4.93865 + 8.55399i) q^{31} +(5.43773 - 1.55921i) q^{32} +(-0.155930 + 0.270079i) q^{33} +(1.95856 + 7.20874i) q^{34} +(-9.83869 + 3.95136i) q^{35} +(1.35682 - 5.20888i) q^{36} +(-3.72267 + 2.85651i) q^{37} +(-2.14777 - 0.880868i) q^{38} +(0.581093 - 2.16867i) q^{39} +(-1.36174 + 11.2525i) q^{40} +(1.41386 - 1.41386i) q^{41} +(0.781434 + 1.92627i) q^{42} +(1.24801 - 3.01295i) q^{43} +(1.04019 + 0.422380i) q^{44} +(8.55649 + 6.56563i) q^{45} +(-4.21645 + 0.0147133i) q^{46} +(5.29275 + 3.05577i) q^{47} +(2.20709 + 0.259284i) q^{48} +(5.98515 + 3.63014i) q^{49} +(-13.5717 - 7.77259i) q^{50} +(-0.383039 + 2.90947i) q^{51} +(-8.02048 - 0.999023i) q^{52} +(6.70740 - 0.883046i) q^{53} +(2.70976 - 3.55706i) q^{54} +(-1.59063 + 1.59063i) q^{55} +(6.48199 - 3.73950i) q^{56} +(-0.644843 - 0.644843i) q^{57} +(4.41803 - 0.597335i) q^{58} +(0.381583 + 2.89841i) q^{59} +(-2.19939 + 3.87161i) q^{60} +(-3.16459 - 0.416626i) q^{61} +(13.4799 - 3.66240i) q^{62} +(0.0769160 - 7.12022i) q^{63} +(-0.167484 - 7.99825i) q^{64} +(8.09735 - 14.0250i) q^{65} +(0.312946 + 0.310770i) q^{66} +(-3.73546 + 4.86814i) q^{67} +(10.5640 - 0.0737273i) q^{68} +(-1.53033 - 0.633885i) q^{69} +(1.84838 + 14.8798i) q^{70} +(-10.1461 - 10.1461i) q^{71} +(-6.63191 - 3.73692i) q^{72} +(-8.12245 - 2.17640i) q^{73} +(2.56085 + 6.12192i) q^{74} +(-3.74024 - 4.87437i) q^{75} +(-1.98030 + 2.61842i) q^{76} +(1.47027 + 0.209746i) q^{77} +(-2.75528 - 1.57797i) q^{78} +(6.68828 + 3.86148i) q^{79} +(14.8935 + 5.92692i) q^{80} +(-5.47101 + 3.15869i) q^{81} +(-1.42239 - 2.44392i) q^{82} +(-14.6200 + 6.05578i) q^{83} +(2.91608 - 0.372573i) q^{84} +(-8.10044 + 19.5562i) q^{85} +(-3.66874 - 2.79484i) q^{86} +(1.69171 + 0.453293i) q^{87} +(0.953293 - 1.26966i) q^{88} +(2.24106 - 0.600491i) q^{89} +(12.0682 - 9.32737i) q^{90} +(-10.6151 + 1.28101i) q^{91} +(-1.50310 + 5.77045i) q^{92} +(5.44054 + 0.716261i) q^{93} +(6.09018 - 6.13283i) q^{94} +(-3.28899 - 5.69669i) q^{95} +(1.15184 - 2.92407i) q^{96} -4.72776 q^{97} +(7.12565 - 6.87206i) q^{98} +(-0.578140 - 1.39575i) 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 $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.361256	−	1.36729i	0.255447	−	0.966823i
$2$	0.361256	−	1.36729i	0.255447	−	0.966823i
$3$	0.338207	−	0.440760i	0.195264	−	0.254473i	−0.685452	−	0.728118i	$-0.740395\pi$
$3$	0.338207	−	0.440760i	0.195264	−	0.254473i	0.880716	+	0.473645i	$0.157062\pi$
$4$	−1.73899	−	0.987888i	−0.869494	−	0.493944i
$5$	3.17926	−	2.43953i	1.42181	−	1.09099i	0.440673	−	0.897668i	$-0.354740\pi$
$5$	3.17926	−	2.43953i	1.42181	−	1.09099i	0.981135	−	0.193324i	$-0.0619270\pi$
$6$	−0.480469	−	0.621656i	−0.196151	−	0.253790i
$7$	−2.54805	−	0.712336i	−0.963074	−	0.269238i
$7$	−2.54805	−	0.712336i	−0.963074	−	0.269238i
$8$	−1.97895	+	2.02083i	−0.699666	+	0.714470i
$9$	0.696572	+	2.59964i	0.232191	+	0.866547i
$10$	−2.18703	−	5.22828i	−0.691600	−	1.65333i
$11$	−0.556535	+	0.0732692i	−0.167802	+	0.0220915i	−0.213959	−	0.976843i	$-0.568636\pi$
$11$	−0.556535	+	0.0732692i	−0.167802	+	0.0220915i	0.0461572	+	0.998934i	$0.485302\pi$
$12$	−1.02356	+	0.432366i	−0.295476	+	0.124813i
$13$	3.73361	−	1.54651i	1.03552	−	0.428925i	0.200816	−	0.979629i	$-0.435641\pi$
$13$	3.73361	−	1.54651i	1.03552	−	0.428925i	0.834701	+	0.550704i	$0.185641\pi$
$14$	−1.89447	+	3.22660i	−0.506319	+	0.862346i
$15$		−	2.22636i		−	0.574843i
$16$	2.04816	+	3.43585i	0.512039	+	0.858962i
$17$	−4.57446	+	2.64107i	−1.10947	+	0.640553i	−0.938692	−	0.344757i	$-0.887961\pi$
$17$	−4.57446	+	2.64107i	−1.10947	+	0.640553i	−0.170778	+	0.985310i	$0.554628\pi$
$18$	3.80612	−	0.0132815i	0.897110	−	0.00313047i
$19$	0.214255	−	1.62743i	0.0491534	−	0.373357i	−0.949135	−	0.314870i	$-0.898039\pi$
$19$	0.214255	−	1.62743i	0.0491534	−	0.373357i	0.998288	−	0.0584871i	$-0.0186277\pi$
$20$	−7.93868	+	1.10156i	−1.77514	+	0.246317i
$21$	−1.17574	+	0.882164i	−0.256567	+	0.192504i
$22$	−0.100871	+	0.787416i	−0.0215058	+	0.167878i
$23$	−0.771669	−	2.87991i	−0.160904	−	0.600502i	−0.998527	−	0.0542536i	$-0.982722\pi$
$23$	−0.771669	−	2.87991i	−0.160904	−	0.600502i	0.837623	−	0.546249i	$-0.183945\pi$
$24$	0.221404	+	1.55570i	0.0451938	+	0.317556i
$25$	2.86228	−	10.6822i	0.572457	−	2.13644i
$26$	−0.765746	−	5.66363i	−0.150175	−	1.11073i
$27$	2.92123	+	1.21001i	0.562191	+	0.232867i
$28$	3.72733	+	3.75593i	0.704398	+	0.709805i
$29$	1.20639	+	2.91247i	0.224020	+	0.540833i	0.995429	−	0.0955074i	$-0.0304474\pi$
$29$	1.20639	+	2.91247i	0.224020	+	0.540833i	−0.771408	+	0.636340i	$0.780447\pi$
$30$	−3.04409	−	0.804287i	−0.555772	−	0.146842i
$31$	4.93865	+	8.55399i	0.887007	+	1.53634i	0.843396	+	0.537293i	$0.180553\pi$
$31$	4.93865	+	8.55399i	0.887007	+	1.53634i	0.0436113	+	0.999049i	$0.486114\pi$
$32$	5.43773	−	1.55921i	0.961263	−	0.275632i
$33$	−0.155930	+	0.270079i	−0.0271439	+	0.0470147i
$34$	1.95856	+	7.20874i	0.335891	+	1.23629i
$35$	−9.83869	+	3.95136i	−1.66304	+	0.667901i
$36$	1.35682	−	5.20888i	0.226137	−	0.868146i
$37$	−3.72267	+	2.85651i	−0.612003	+	0.469607i	−0.867658	−	0.497161i	$-0.834376\pi$
$37$	−3.72267	+	2.85651i	−0.612003	+	0.469607i	0.255655	+	0.966768i	$0.417709\pi$
$38$	−2.14777	−	0.880868i	−0.348414	−	0.142896i
$39$	0.581093	−	2.16867i	0.0930493	−	0.347265i
$40$	−1.36174	+	11.2525i	−0.215309	+	1.77917i
$41$	1.41386	−	1.41386i	0.220807	−	0.220807i	−0.588031	−	0.808838i	$-0.700097\pi$
$41$	1.41386	−	1.41386i	0.220807	−	0.220807i	0.808838	+	0.588031i	$0.200097\pi$
$42$	0.781434	+	1.92627i	0.120578	+	0.297230i
$43$	1.24801	−	3.01295i	0.190319	−	0.459471i	−0.799701	−	0.600399i	$-0.795009\pi$
$43$	1.24801	−	3.01295i	0.190319	−	0.459471i	0.990020	+	0.140928i	$0.0450085\pi$
$44$	1.04019	+	0.422380i	0.156814	+	0.0636762i
$45$	8.55649	+	6.56563i	1.27553	+	0.978746i
$46$	−4.21645	+	0.0147133i	−0.621682	+	0.00216936i
$47$	5.29275	+	3.05577i	0.772027	+	0.445730i	0.833597	−	0.552373i	$-0.186278\pi$
$47$	5.29275	+	3.05577i	0.772027	+	0.445730i	−0.0615704	+	0.998103i	$0.519611\pi$
$48$	2.20709	+	0.259284i	0.318566	+	0.0374244i
$49$	5.98515	+	3.63014i	0.855022	+	0.518592i
$50$	−13.5717	−	7.77259i	−1.91932	−	1.09921i
$51$	−0.383039	+	2.90947i	−0.0536362	+	0.407407i
$52$	−8.02048	−	0.999023i	−1.11224	−	0.138540i
$53$	6.70740	−	0.883046i	0.921332	−	0.121296i	0.345085	−	0.938571i	$-0.387850\pi$
$53$	6.70740	−	0.883046i	0.921332	−	0.121296i	0.576247	+	0.817276i	$0.304517\pi$
$54$	2.70976	−	3.55706i	0.368752	−	0.484054i
$55$	−1.59063	+	1.59063i	−0.214480	+	0.214480i
$56$	6.48199	−	3.73950i	0.866192	−	0.499711i
$57$	−0.644843	−	0.644843i	−0.0854115	−	0.0854115i
$58$	4.41803	−	0.597335i	0.580115	−	0.0784340i
$59$	0.381583	+	2.89841i	0.0496779	+	0.377341i	0.998166	+	0.0605296i	$0.0192789\pi$
$59$	0.381583	+	2.89841i	0.0496779	+	0.377341i	−0.948489	+	0.316812i	$0.897388\pi$
$60$	−2.19939	+	3.87161i	−0.283940	+	0.499823i
$61$	−3.16459	−	0.416626i	−0.405184	−	0.0533435i	−0.0748199	−	0.997197i	$-0.523838\pi$
$61$	−3.16459	−	0.416626i	−0.405184	−	0.0533435i	−0.330364	+	0.943854i	$0.607172\pi$
$62$	13.4799	−	3.66240i	1.71195	−	0.465125i
$63$	0.0769160	−	7.12022i	0.00969051	−	0.897063i
$64$	−0.167484	−	7.99825i	−0.0209354	−	0.999781i
$65$	8.09735	−	14.0250i	1.00435	−	1.73959i
$66$	0.312946	+	0.310770i	0.0385210	+	0.0382531i
$67$	−3.73546	+	4.86814i	−0.456359	+	0.594738i	−0.963694	−	0.267011i	$-0.913964\pi$
$67$	−3.73546	+	4.86814i	−0.456359	+	0.594738i	0.507335	+	0.861749i	$0.330631\pi$
$68$	10.5640	−	0.0737273i	1.28107	−	0.00894075i
$69$	−1.53033	−	0.633885i	−0.184230	−	0.0763107i
$70$	1.84838	+	14.8798i	0.220923	+	1.77848i
$71$	−10.1461	−	10.1461i	−1.20412	−	1.20412i	−0.972901	−	0.231220i	$-0.925728\pi$
$71$	−10.1461	−	10.1461i	−1.20412	−	1.20412i	−0.231220	−	0.972901i	$-0.574272\pi$
$72$	−6.63191	−	3.73692i	−0.781578	−	0.440400i
$73$	−8.12245	−	2.17640i	−0.950661	−	0.254729i	−0.250018	−	0.968241i	$-0.580437\pi$
$73$	−8.12245	−	2.17640i	−0.950661	−	0.254729i	−0.700643	+	0.713512i	$0.747103\pi$
$74$	2.56085	+	6.12192i	0.297692	+	0.711659i
$75$	−3.74024	−	4.87437i	−0.431885	−	0.562844i
$76$	−1.98030	+	2.61842i	−0.227156	+	0.300353i
$77$	1.47027	+	0.209746i	0.167553	+	0.0239028i
$78$	−2.75528	−	1.57797i	−0.311975	−	0.178670i
$79$	6.68828	+	3.86148i	0.752490	+	0.434450i	0.826593	−	0.562800i	$-0.190276\pi$
$79$	6.68828	+	3.86148i	0.752490	+	0.434450i	−0.0741027	+	0.997251i	$0.523609\pi$
$80$	14.8935	+	5.92692i	1.66514	+	0.662649i
$81$	−5.47101	+	3.15869i	−0.607890	+	0.350966i
$82$	−1.42239	−	2.44392i	−0.157077	−	0.269886i
$83$	−14.6200	+	6.05578i	−1.60475	+	0.664708i	−0.992077	−	0.125630i	$-0.959905\pi$
$83$	−14.6200	+	6.05578i	−1.60475	+	0.664708i	−0.612671	+	0.790338i	$0.709905\pi$
$84$	2.91608	−	0.372573i	0.318170	−	0.0406510i
$85$	−8.10044	+	19.5562i	−0.878616	+	2.12117i
$86$	−3.66874	−	2.79484i	−0.395611	−	0.301375i
$87$	1.69171	+	0.453293i	0.181371	+	0.0485981i
$88$	0.953293	−	1.26966i	0.101621	−	0.135346i
$89$	2.24106	−	0.600491i	0.237552	−	0.0636519i	−0.138079	−	0.990421i	$-0.544093\pi$
$89$	2.24106	−	0.600491i	0.237552	−	0.0636519i	0.375631	+	0.926769i	$0.377426\pi$
$90$	12.0682	−	9.32737i	1.27210	−	0.983191i
$91$	−10.6151	+	1.28101i	−1.11276	+	0.134286i
$92$	−1.50310	+	5.77045i	−0.156709	+	0.601610i
$93$	5.44054	+	0.716261i	0.564158	+	0.0742728i
$94$	6.09018	−	6.13283i	0.628154	−	0.632553i
$95$	−3.28899	−	5.69669i	−0.337443	−	0.584469i
$96$	1.15184	−	2.92407i	0.117559	−	0.298437i
$97$	−4.72776			−0.480031			−0.240016	−	0.970769i	$-0.577153\pi$
$97$	−4.72776			−0.480031			−0.240016	+	0.970769i	$0.577153\pi$
$98$	7.12565	−	6.87206i	0.719799	−	0.694182i
$99$	−0.578140	−	1.39575i	−0.0581053	−	0.140279i
$100$	−15.5303	+	15.7486i	−1.55303	+	1.57486i
$101$	1.55770	+	11.8319i	0.154997	+	1.17732i	0.875272	+	0.483631i	$0.160682\pi$
$101$	1.55770	+	11.8319i	0.154997	+	1.17732i	−0.720275	+	0.693689i	$0.755984\pi$
$102$	3.83973	+	1.57479i	0.380190	+	0.155928i
$103$	2.39676	−	0.642210i	0.236160	−	0.0632788i	−0.138798	−	0.990321i	$-0.544324\pi$
$103$	2.39676	−	0.642210i	0.236160	−	0.0632788i	0.374958	+	0.927042i	$0.377657\pi$
$104$	−4.26341	+	10.6055i	−0.418062	+	1.03995i
$105$	−1.58592	+	5.67288i	−0.154770	+	0.553617i
$106$	1.21571	−	9.49000i	0.118080	−	0.921750i
$107$	−3.78111	−	4.92763i	−0.365533	−	0.476372i	0.573988	−	0.818864i	$-0.305396\pi$
$107$	−3.78111	−	4.92763i	−0.365533	−	0.476372i	−0.939521	+	0.342492i	$0.888729\pi$
$108$	−3.88463	−	4.99005i	−0.373799	−	0.480168i
$109$	−2.66677	−	2.04629i	−0.255431	−	0.195999i	0.473106	−	0.881005i	$-0.343133\pi$
$109$	−2.66677	−	2.04629i	−0.255431	−	0.195999i	−0.728537	+	0.685007i	$0.759799\pi$
$110$	1.60023	+	2.74948i	0.152576	+	0.262153i
$111$			2.60690i			0.247436i
$112$	−2.77133	−	10.2137i	−0.261866	−	0.965104i
$113$		−	12.3092i		−	1.15795i	−0.815345	−	0.578976i	$-0.803453\pi$
$113$		−	12.3092i		−	1.15795i	0.815345	−	0.578976i	$-0.196547\pi$
$114$	−1.11464	+	0.648736i	−0.104396	+	0.0607597i
$115$	−9.47896	−	7.27346i	−0.883918	−	0.678254i
$116$	0.779307	−	6.25653i	0.0723568	−	0.580904i
$117$	6.62110	+	8.62879i	0.612121	+	0.797732i
$118$	4.10083	+	0.525334i	0.377512	+	0.0483609i
$119$	13.5373	−	3.47103i	1.24096	−	0.318188i
$120$	4.49909	+	4.40586i	0.410709	+	0.402198i
$121$	−10.3208	+	2.76546i	−0.938256	+	0.251405i
$122$	−1.71288	+	4.17641i	−0.155077	+	0.378115i
$123$	−0.144995	−	1.10135i	−0.0130738	−	0.0993053i
$124$	−0.137866	−	19.7541i	−0.0123807	−	1.77397i
$125$	−9.29182	−	22.4324i	−0.831086	−	2.00642i
$126$	−9.70765	−	2.67739i	−0.864826	−	0.238521i
$127$	−7.08277			−0.628495			−0.314247	−	0.949341i	$-0.601752\pi$
$127$	−7.08277			−0.628495			−0.314247	+	0.949341i	$0.601752\pi$
$128$	−10.9965	−	2.66042i	−0.971959	−	0.235150i
$129$	−0.905905	−	1.56907i	−0.0797605	−	0.138149i
$130$	−16.2511	−	16.1381i	−1.42532	−	1.41540i
$131$	1.04034	+	0.136963i	0.0908950	+	0.0119666i	0.175836	−	0.984419i	$-0.443737\pi$
$131$	1.04034	+	0.136963i	0.0908950	+	0.0119666i	−0.0849415	+	0.996386i	$0.527070\pi$
$132$	0.537968	−	0.315622i	0.0468241	−	0.0274714i
$133$	−1.70521	+	3.99415i	−0.147860	+	0.346337i
$134$	5.30673	+	6.86612i	0.458431	+	0.593142i
$135$	12.2392	−	3.27949i	1.05338	−	0.282254i
$136$	3.71551	−	14.4707i	0.318602	−	1.24086i
$137$	−17.2446	−	4.62067i	−1.47330	−	0.394771i	−0.569242	−	0.822170i	$-0.692763\pi$
$137$	−17.2446	−	4.62067i	−1.47330	−	0.394771i	−0.904063	+	0.427399i	$0.859430\pi$
$138$	−1.41955	+	1.86342i	−0.120840	+	0.158625i
$139$	−4.76834	+	11.5118i	−0.404445	+	0.976417i	0.582128	+	0.813097i	$0.302220\pi$
$139$	−4.76834	+	11.5118i	−0.404445	+	0.976417i	−0.986573	+	0.163320i	$0.947780\pi$
$140$	21.0129	+	2.84816i	1.77591	+	0.240714i
$141$	3.13691	−	1.29935i	0.264175	−	0.109425i
$142$	−17.5381	+	10.2074i	−1.47176	+	0.856584i
$143$	−1.96457	+	1.13425i	−0.164286	+	0.0948505i
$144$	−7.50529	+	7.71778i	−0.625441	+	0.643149i
$145$	10.9405	+	6.31650i	0.908558	+	0.524556i
$146$	−5.91007	+	10.3195i	−0.489121	+	0.854051i
$147$	3.62424	−	1.41028i	0.298923	−	0.116318i
$148$	9.29559	−	1.28985i	0.764092	−	0.106025i
$149$	−12.8996	−	16.8111i	−1.05678	−	1.37722i	−0.922377	−	0.386291i	$-0.873756\pi$
$149$	−12.8996	−	16.8111i	−1.05678	−	1.37722i	−0.134399	−	0.990927i	$-0.542910\pi$
$150$	−8.01589	+	3.35311i	−0.654494	+	0.273780i
$151$	22.7943	+	6.10770i	1.85497	+	0.497038i	0.999774	−	0.0212667i	$-0.00676992\pi$
$151$	22.7943	+	6.10770i	1.85497	+	0.497038i	0.855196	+	0.518304i	$0.173437\pi$
$152$	2.86475	+	3.65357i	0.232362	+	0.296344i
$153$	−10.0523	−	10.0523i	−0.812678	−	0.812678i
$154$	0.817930	−	1.93452i	0.0659107	−	0.155888i
$155$	36.5690	+	15.1474i	2.93729	+	1.21667i
$156$	−3.15291	+	3.19723i	−0.252435	+	0.255983i
$157$	3.93413	−	5.12705i	0.313977	−	0.409183i	−0.609530	−	0.792763i	$-0.708642\pi$
$157$	3.93413	−	5.12705i	0.313977	−	0.409183i	0.923508	+	0.383579i	$0.125309\pi$
$158$	7.69596	−	7.74986i	0.612258	−	0.616546i
$159$	1.87928	−	3.25501i	0.149037	−	0.258139i
$160$	13.4842	−	18.2226i	1.06602	−	1.44063i
$161$	−0.0852083	+	7.88785i	−0.00671535	+	0.621649i
$162$	2.34242	+	8.62158i	0.184038	+	0.677376i
$163$	22.7332	+	2.99288i	1.78060	+	0.234421i	0.947736	−	0.319055i	$-0.103366\pi$
$163$	22.7332	+	2.99288i	1.78060	+	0.234421i	0.832865	+	0.553476i	$0.186699\pi$
$164$	−3.85541	+	1.06195i	−0.301057	+	0.0829242i
$165$	0.163124	+	1.23905i	0.0126992	+	0.0964597i
$166$	2.99848	+	22.1775i	0.232728	+	1.72131i
$167$	−13.8627	−	13.8627i	−1.07273	−	1.07273i	−0.997139	−	0.0755890i	$-0.975916\pi$
$167$	−13.8627	−	13.8627i	−1.07273	−	1.07273i	−0.0755890	−	0.997139i	$-0.524084\pi$
$168$	0.544035	−	4.12173i	0.0419732	−	0.317998i
$169$	2.35575	−	2.35575i	0.181212	−	0.181212i
$170$	23.8127	+	18.1405i	1.82635	+	1.39131i
$171$	4.37997	−	0.576634i	0.334945	−	0.0440963i
$172$	−5.14673	+	4.00660i	−0.392434	+	0.305500i
$173$	1.37410	−	10.4373i	0.104471	−	0.793534i	−0.856356	−	0.516386i	$-0.827277\pi$
$173$	1.37410	−	10.4373i	0.104471	−	0.793534i	0.960827	−	0.277149i	$-0.0893895\pi$
$174$	1.23093	−	2.14931i	0.0933163	−	0.162939i
$175$	−14.9026	+	25.1799i	−1.12653	+	1.90342i
$176$	−1.39161	−	1.76210i	−0.104897	−	0.132824i
$177$	1.40656	+	0.812077i	0.105723	+	0.0610395i
$178$	−0.0114495	−	3.28112i	−0.000858177	−	0.245931i
$179$	−2.58639	−	1.98460i	−0.193315	−	0.148336i	0.507569	−	0.861611i	$-0.330544\pi$
$179$	−2.58639	−	1.98460i	−0.193315	−	0.148336i	−0.700884	+	0.713275i	$0.747211\pi$
$180$	−8.39353	−	19.8704i	−0.625617	−	1.48105i
$181$	−2.03143	+	4.90431i	−0.150995	+	0.364534i	−0.981219	−	0.192895i	$-0.938212\pi$
$181$	−2.03143	+	4.90431i	−0.150995	+	0.364534i	0.830224	+	0.557429i	$0.188212\pi$
$182$	−2.08325	+	14.9767i	−0.154420	+	1.11015i
$183$	−1.25392	+	1.25392i	−0.0926923	+	0.0926923i
$184$	7.34689	+	4.13979i	0.541620	+	0.305190i
$185$	−4.86680	+	18.1631i	−0.357814	+	1.33538i
$186$	2.94477	−	7.18007i	0.215921	−	0.526468i
$187$	2.35234	−	1.80501i	0.172020	−	0.131996i
$188$	−6.18527	−	10.5426i	−0.451107	−	0.768897i
$189$	−6.58152	−	5.16408i	−0.478735	−	0.375632i
$190$	−8.97723	+	2.43905i	−0.651276	+	0.176947i
$191$	2.21481	−	3.83617i	0.160258	−	0.277575i	−0.774703	−	0.632325i	$-0.782101\pi$
$191$	2.21481	−	3.83617i	0.160258	−	0.277575i	0.934961	+	0.354750i	$0.115434\pi$
$192$	−3.58195	−	2.63124i	−0.258505	−	0.189894i
$193$	6.49249	+	11.2453i	0.467340	+	0.809456i	0.999304	−	0.0373108i	$-0.0118792\pi$
$193$	6.49249	+	11.2453i	0.467340	+	0.809456i	−0.531964	+	0.846767i	$0.678546\pi$
$194$	−1.70793	+	6.46424i	−0.122623	+	0.464106i
$195$	−3.44309	−	8.31236i	−0.246565	−	0.595260i
$196$	−6.82194	−	12.2254i	−0.487281	−	0.873245i
$197$	−2.68825	−	1.11351i	−0.191530	−	0.0793343i	0.284857	−	0.958570i	$-0.408054\pi$
$197$	−2.68825	−	1.11351i	−0.191530	−	0.0793343i	−0.476387	+	0.879236i	$0.658054\pi$
$198$	−2.11726	+	0.286263i	−0.150467	+	0.0203438i
$199$	−5.04984	+	18.8463i	−0.357974	+	1.33598i	0.518727	+	0.854940i	$0.326406\pi$
$199$	−5.04984	+	18.8463i	−0.357974	+	1.33598i	−0.876701	+	0.481037i	$0.840260\pi$
$200$	15.9225	+	26.9237i	1.12589	+	1.90379i
$201$	0.882325	+	3.29288i	0.0622344	+	0.232262i
$202$	16.7404	+	2.14452i	1.17785	+	0.150888i
$203$	−0.999277	−	8.28049i	−0.0701355	−	0.581177i
$204$	3.54033	−	4.68113i	0.247873	−	0.327745i
$205$	1.04587	−	7.94417i	0.0730467	−	0.554845i
$206$	−0.0122450	−	3.50908i	−0.000853147	−	0.244489i
$207$	6.94920	−	4.01212i	0.483003	−	0.278862i
$208$	12.9606	+	9.66062i	0.898656	+	0.669844i
$209$			0.921418i			0.0637359i
$210$	7.18358	+	4.21778i	0.495714	+	0.291054i
$211$	−8.53722	+	3.53623i	−0.587726	+	0.243444i	−0.656672	−	0.754176i	$-0.728036\pi$
$211$	−8.53722	+	3.53623i	−0.587726	+	0.243444i	0.0689458	+	0.997620i	$0.478036\pi$
$212$	−12.5364	−	5.09055i	−0.861006	−	0.349621i
$213$	−7.90349	+	1.04051i	−0.541538	+	0.0712949i
$214$	−8.10347	+	3.38974i	−0.553942	+	0.231718i
$215$	−3.38246	−	12.6235i	−0.230682	−	0.860917i
$216$	−8.22621	+	3.50874i	−0.559723	+	0.238740i
$217$	−6.49062	−	25.3140i	−0.440612	−	1.71843i
$218$	−3.76127	+	2.90703i	−0.254745	+	0.196889i
$219$	−3.70634	+	2.84398i	−0.250452	+	0.192178i
$220$	4.33744	−	1.19472i	0.292430	−	0.0805480i
$221$	−12.9948	+	16.9352i	−0.874126	+	1.13918i
$222$	3.56439	+	0.941758i	0.239227	+	0.0632067i
$223$	17.0402			1.14110			0.570548	−	0.821265i	$-0.306731\pi$
$223$	17.0402			1.14110			0.570548	+	0.821265i	$0.306731\pi$
$224$	−14.9663	+	0.0994588i	−0.999978	+	0.00664537i
$225$	29.7636			1.98424
$226$	−16.8303	−	4.44678i	−1.11953	−	0.295795i
$227$	8.60157	−	11.2098i	0.570906	−	0.744019i	−0.415274	−	0.909696i	$-0.636314\pi$
$227$	8.60157	−	11.2098i	0.570906	−	0.744019i	0.986180	+	0.165677i	$0.0529810\pi$
$228$	0.484341	+	1.75841i	0.0320763	+	0.116453i
$229$	1.73830	−	1.33384i	0.114870	−	0.0881429i	−0.549729	−	0.835343i	$-0.685269\pi$
$229$	1.73830	−	1.33384i	0.114870	−	0.0881429i	0.664599	+	0.747200i	$0.268602\pi$
$230$	−13.3693	+	10.3329i	−0.881546	+	0.681334i
$231$	0.589705	−	0.577101i	0.0387997	−	0.0379704i
$232$	−8.27299	−	3.32575i	−0.543148	−	0.218346i
$233$	4.39508	+	16.4026i	0.287931	+	1.07457i	0.946671	+	0.322202i	$0.104423\pi$
$233$	4.39508	+	16.4026i	0.287931	+	1.07457i	−0.658740	+	0.752371i	$0.728910\pi$
$234$	14.1900	−	5.93579i	0.927630	−	0.388035i
$235$	24.2817	−	3.19674i	1.58396	−	0.208533i
$236$	2.19974	−	5.41726i	0.143191	−	0.352634i
$237$	3.96401	−	1.64195i	0.257490	−	0.106656i
$238$	0.144524	−	19.7634i	0.00936808	−	1.28107i
$239$		−	1.95582i		−	0.126511i	−0.997997	−	0.0632557i	$-0.979852\pi$
$239$		−	1.95582i		−	0.126511i	0.997997	−	0.0632557i	$-0.0201484\pi$
$240$	7.64943	−	4.55993i	0.493769	−	0.294342i
$241$	−4.36354	+	2.51929i	−0.281080	+	0.162282i	−0.633912	−	0.773405i	$-0.718552\pi$
$241$	−4.36354	+	2.51929i	−0.281080	+	0.162282i	0.352832	+	0.935687i	$0.385219\pi$
$242$	0.0527287	+	15.1106i	0.00338953	+	0.971349i
$243$	−1.69625	+	12.8843i	−0.108815	+	0.826529i
$244$	5.09160	+	3.85076i	0.325956	+	0.246520i
$245$	27.8842	−	3.05981i	1.78146	−	0.195484i
$246$	−1.55825	−	0.199618i	−0.0993503	−	0.0127272i
$247$	−1.71689	−	6.40752i	−0.109243	−	0.407701i
$248$	−27.0595	−	6.94779i	−1.71828	−	0.441185i
$249$	−2.27543	+	8.49200i	−0.144199	+	0.538159i
$250$	−34.0285	+	4.60079i	−2.15215	+	0.290980i
$251$	13.8552	+	5.73903i	0.874535	+	0.362244i	0.774375	−	0.632727i	$-0.218065\pi$
$251$	13.8552	+	5.73903i	0.874535	+	0.362244i	0.100160	+	0.994971i	$0.468065\pi$
$252$	−7.16773	+	12.3060i	−0.451525	+	0.775204i
$253$	0.640469	+	1.54623i	0.0402660	+	0.0972106i
$254$	−2.55870	+	9.68424i	−0.160547	+	0.607643i
$255$	5.87996	+	10.1844i	0.368218	+	0.637772i
$256$	−7.61012	+	14.0743i	−0.475632	+	0.879644i
$257$	−8.44559	+	14.6282i	−0.526821	+	0.912482i	0.472690	+	0.881229i	$0.343283\pi$
$257$	−8.44559	+	14.6282i	−0.526821	+	0.912482i	−0.999512	+	0.0312528i	$0.990050\pi$
$258$	−2.47265	+	0.671801i	−0.153941	+	0.0418245i
$259$	11.5204	−	4.62674i	0.715840	−	0.287491i
$260$	−27.9363	+	16.3901i	−1.73254	+	1.01647i
$261$	−6.73105	+	5.16492i	−0.416642	+	0.319700i
$262$	0.563099	−	1.37297i	0.0347884	−	0.0848225i
$263$	6.92554	−	25.8464i	0.427047	−	1.59376i	−0.332366	−	0.943151i	$-0.607847\pi$
$263$	6.92554	−	25.8464i	0.427047	−	1.59376i	0.759412	−	0.650610i	$-0.225487\pi$
$264$	−0.237204	−	0.849581i	−0.0145989	−	0.0522881i
$265$	19.1704	−	19.1704i	1.17763	−	1.17763i
$266$	4.84516	+	3.77443i	0.297076	+	0.231425i
$267$	0.493271	−	1.19086i	0.0301877	−	0.0728795i
$268$	11.3051	−	4.77543i	0.690568	−	0.291706i
$269$	19.9694	+	15.3230i	1.21755	+	0.934261i	0.999135	−	0.0415941i	$-0.0132436\pi$
$269$	19.9694	+	15.3230i	1.21755	+	0.934261i	0.218418	+	0.975855i	$0.429910\pi$
$270$	−0.0625298	−	17.9194i	−0.00380544	−	1.09054i
$271$	−14.4954	−	8.36894i	−0.880534	−	0.508377i	−0.00969976	−	0.999953i	$-0.503088\pi$
$271$	−14.4954	−	8.36894i	−0.880534	−	0.508377i	−0.870835	+	0.491576i	$0.836421\pi$
$272$	−18.4435	−	10.3078i	−1.11830	−	0.625005i
$273$	−3.02548	+	5.11195i	−0.183110	+	0.309389i
$274$	−12.5475	+	21.9092i	−0.758025	+	1.32358i
$275$	−0.810285	+	6.15473i	−0.0488620	+	0.371144i
$276$	2.03502	+	2.61411i	0.122494	+	0.157351i
$277$	−26.5703	+	3.49805i	−1.59646	+	0.210178i	−0.875646	−	0.482954i	$-0.839564\pi$
$277$	−26.5703	+	3.49805i	−1.59646	+	0.210178i	−0.720811	+	0.693131i	$0.756231\pi$
$278$	14.0174	+	10.6784i	0.840708	+	0.640450i
$279$	−18.7972	+	18.7972i	−1.12536	+	1.12536i
$280$	11.4853	−	27.7018i	0.686378	−	1.65550i
$281$	−6.82634	−	6.82634i	−0.407225	−	0.407225i	0.473544	−	0.880770i	$-0.342974\pi$
$281$	−6.82634	−	6.82634i	−0.407225	−	0.407225i	−0.880770	+	0.473544i	$0.842974\pi$
$282$	−0.643365	−	4.75848i	−0.0383119	−	0.283363i
$283$	0.396492	+	3.01166i	0.0235690	+	0.179024i	0.999180	−	0.0404809i	$-0.0128890\pi$
$283$	0.396492	+	3.01166i	0.0235690	+	0.179024i	−0.975611	+	0.219505i	$0.929556\pi$
$284$	7.62074	+	27.6672i	0.452208	+	1.64175i
$285$	−3.62324	−	0.477008i	−0.214622	−	0.0282555i
$286$	0.841135	+	3.09590i	0.0497373	+	0.183065i
$287$	−4.60972	+	2.59544i	−0.272103	+	0.153204i
$288$	7.84115	+	13.0500i	0.462044	+	0.768981i
$289$	5.45047	−	9.44049i	0.320616	−	0.555323i
$290$	12.5888	−	12.6770i	0.739242	−	0.744419i
$291$	−1.59896	+	2.08381i	−0.0937329	+	0.122155i
$292$	11.9748	+	11.8088i	0.700772	+	0.691058i
$293$	15.4007	+	6.37917i	0.899717	+	0.372675i	0.784111	−	0.620620i	$-0.213119\pi$
$293$	15.4007	+	6.37917i	0.899717	+	0.372675i	0.115606	+	0.993295i	$0.463119\pi$
$294$	−0.618984	−	5.46488i	−0.0360999	−	0.318718i
$295$	8.28392	+	8.28392i	0.482309	+	0.482309i
$296$	1.59449	−	13.1758i	0.0926778	−	0.765826i
$297$	−1.71443	−	0.459379i	−0.0994810	−	0.0266559i
$298$	−27.6458	+	11.5644i	−1.60148	+	0.669910i
$299$	−7.33492	−	9.55905i	−0.424189	−	0.552814i
$300$	1.68889	+	12.1714i	0.0975083	+	0.702717i
$301$	−5.32622	+	6.78817i	−0.306998	+	0.391263i
$302$	16.5856	−	28.9600i	0.954394	−	1.66646i
$303$	5.74186	+	3.31507i	0.329861	+	0.190446i
$304$	6.03042	−	2.59708i	0.345868	−	0.148953i
$305$	−11.0774	+	6.39555i	−0.634291	+	0.366208i
$306$	−17.3759	+	10.1130i	−0.993311	+	0.578120i
$307$	15.6767	−	6.49350i	0.894717	−	0.370604i	0.112530	−	0.993648i	$-0.464104\pi$
$307$	15.6767	−	6.49350i	0.894717	−	0.370604i	0.782186	+	0.623044i	$0.214104\pi$
$308$	−2.34958	−	1.81721i	−0.133880	−	0.103545i
$309$	0.527541	−	1.27360i	0.0300107	−	0.0724524i
$310$	33.9217	−	44.5285i	1.92662	−	2.52905i
$311$	−13.1121	−	3.51339i	−0.743521	−	0.199226i	−0.132879	−	0.991132i	$-0.542422\pi$
$311$	−13.1121	−	3.51339i	−0.743521	−	0.199226i	−0.610643	+	0.791906i	$0.709089\pi$
$312$	3.23255	+	5.46598i	0.183007	+	0.309450i
$313$	10.0871	−	2.70284i	0.570158	−	0.152773i	0.0377888	−	0.999286i	$-0.487969\pi$
$313$	10.0871	−	2.70284i	0.570158	−	0.152773i	0.532369	+	0.846512i	$0.321302\pi$
$314$	−5.58896	−	7.23129i	−0.315403	−	0.408085i
$315$	−17.1255	−	22.8247i	−0.964910	−	1.28602i
$316$	−7.81613	−	13.3223i	−0.439691	−	0.749440i
$317$	21.4486	+	2.82376i	1.20467	+	0.158598i	0.706013	−	0.708199i	$-0.250492\pi$
$317$	21.4486	+	2.82376i	1.20467	+	0.158598i	0.498661	+	0.866797i	$0.333825\pi$
$318$	−3.77165	−	3.74542i	−0.211504	−	0.210033i
$319$	−0.884791	−	1.53250i	−0.0495388	−	0.0858037i
$320$	−20.0445	−	25.0199i	−1.12052	−	1.39866i
$321$	−3.45070			−0.192599
$322$	10.7542	+	2.96604i	0.599310	+	0.165291i
$323$	3.31804	+	8.01046i	0.184621	+	0.445714i
$324$	12.6345	−	0.0881772i	0.701914	−	0.00489873i
$325$	−5.83348	−	44.3097i	−0.323583	−	2.45786i
$326$	12.3047	−	30.0018i	0.681492	−	1.66164i
$327$	−1.80384	+	0.483339i	−0.0997528	+	0.0267287i
$328$	0.0592027	+	5.65512i	0.00326892	+	0.312252i
$329$	−11.3095	−	11.5565i	−0.623511	−	0.637129i
$330$	1.75307	+	0.224576i	0.0965034	+	0.0123625i
$331$	−5.94187	−	7.74359i	−0.326595	−	0.425626i	0.600980	−	0.799264i	$-0.294777\pi$
$331$	−5.94187	−	7.74359i	−0.326595	−	0.425626i	−0.927575	+	0.373638i	$0.878110\pi$
$332$	31.4063	+	3.91194i	1.72365	+	0.214696i
$333$	−10.0190	−	7.68785i	−0.549038	−	0.421291i
$334$	−23.9624	+	13.9464i	−1.31116	+	0.763113i
$335$			24.5899i			1.34349i
$336$	−5.43908	−	2.23286i	−0.296726	−	0.121812i
$337$			2.16403i			0.117882i	0.998261	+	0.0589410i	$0.0187724\pi$
$337$			2.16403i			0.117882i	−0.998261	+	0.0589410i	$0.981228\pi$
$338$	−2.36998	−	4.07204i	−0.128910	−	0.221490i
$339$	−5.42541	−	4.16306i	−0.294668	−	0.226106i
$340$	33.4059	−	26.0056i	1.81169	−	1.41035i
$341$	−3.37527	−	4.39874i	−0.182781	−	0.238205i
$342$	0.793864	−	6.19702i	0.0429272	−	0.335096i
$343$	−12.6646	−	13.5132i	−0.683825	−	0.729646i
$344$	3.61891	+	8.48450i	0.195119	+	0.457454i
$345$	−6.41171	+	1.71801i	−0.345195	+	0.0924946i
$346$	−13.7745	−	5.64935i	−0.740521	−	0.303711i
$347$	−2.60144	−	19.7599i	−0.139653	−	1.06077i	−0.907475	−	0.420105i	$-0.861993\pi$
$347$	−2.60144	−	19.7599i	−0.139653	−	1.06077i	0.767823	−	0.640663i	$-0.221340\pi$
$348$	−2.49406	−	2.45949i	−0.133696	−	0.131843i
$349$	−4.76355	−	11.5002i	−0.254987	−	0.615593i	0.743606	−	0.668618i	$-0.233114\pi$
$349$	−4.76355	−	11.5002i	−0.254987	−	0.615593i	−0.998593	+	0.0530250i	$0.983114\pi$
$350$	29.0447	+	29.4726i	1.55250	+	1.57538i
$351$	12.7780			0.682042
$352$	−2.91204	+	1.26617i	−0.155212	+	0.0674872i
$353$	−2.31271	−	4.00574i	−0.123093	−	0.213204i	0.797893	−	0.602799i	$-0.205948\pi$
$353$	−2.31271	−	4.00574i	−0.123093	−	0.213204i	−0.920986	+	0.389596i	$0.872615\pi$
$354$	1.61848	−	1.62981i	0.0860211	−	0.0866235i
$355$	−57.0089	−	7.50536i	−3.02572	−	0.398343i
$356$	−4.49040	−	1.16967i	−0.237991	−	0.0619925i
$357$	3.04852	−	7.14063i	0.161345	−	0.377922i
$358$	−3.64788	+	2.81940i	−0.192797	+	0.149010i
$359$	−8.43576	+	2.26036i	−0.445222	+	0.119297i	−0.474463	−	0.880275i	$-0.657358\pi$
$359$	−8.43576	+	2.26036i	−0.445222	+	0.119297i	0.0292406	+	0.999572i	$0.490691\pi$
$360$	−30.2009	+	4.29812i	−1.59173	+	0.226531i
$361$	15.7500	+	4.22019i	0.828946	+	0.222115i
$362$	5.97177	+	4.54928i	0.313869	+	0.239105i
$363$	−2.27167	+	5.48431i	−0.119232	+	0.287851i
$364$	19.7250	+	8.25884i	1.03387	+	0.432881i
$365$	−31.1328	+	12.8956i	−1.62956	+	0.674988i
$366$	1.26149	+	2.16746i	0.0659391	+	0.113295i
$367$	17.5583	−	10.1373i	0.916538	−	0.529164i	0.0340092	−	0.999422i	$-0.489172\pi$
$367$	17.5583	−	10.1373i	0.916538	−	0.529164i	0.882529	+	0.470258i	$0.155839\pi$
$368$	8.31443	−	8.54984i	0.433420	−	0.445691i
$369$	4.66037	+	2.69067i	0.242609	+	0.140071i
$370$	23.0762	+	13.2159i	1.19967	+	0.687062i
$371$	−17.7198	−	2.52787i	−0.919968	−	0.131241i
$372$	−8.75345	−	6.62022i	−0.453845	−	0.343242i
$373$	9.37162	+	12.2133i	0.485244	+	0.632383i	0.970243	−	0.242132i	$-0.0778467\pi$
$373$	9.37162	+	12.2133i	0.485244	+	0.632383i	−0.484999	+	0.874515i	$0.661180\pi$
$374$	−1.61819	−	3.86841i	−0.0836745	−	0.200031i
$375$	−13.0299	−	3.49135i	−0.672861	−	0.180292i
$376$	−16.6493	+	4.64850i	−0.858622	+	0.239728i
$377$	9.00835	+	9.00835i	0.463954	+	0.463954i
$378$	−9.43843	+	7.13332i	−0.485461	+	0.366898i
$379$	−13.7408	−	5.69163i	−0.705818	−	0.292359i	0.000755097	−	1.00000i	$-0.499760\pi$
$379$	−13.7408	−	5.69163i	−0.705818	−	0.292359i	−0.706573	+	0.707641i	$0.749760\pi$
$380$	0.0918145	+	13.1556i	0.00470999	+	0.674870i
$381$	−2.39545	+	3.12181i	−0.122722	+	0.159935i
$382$	−4.44505	−	4.41414i	−0.227429	−	0.225847i
$383$	7.53510	−	13.0512i	0.385025	−	0.666884i	−0.606747	−	0.794895i	$-0.707526\pi$
$383$	7.53510	−	13.0512i	0.385025	−	0.666884i	0.991773	+	0.128011i	$0.0408594\pi$
$384$	−4.89169	+	3.94703i	−0.249628	+	0.201421i
$385$	5.18606	−	2.91994i	0.264306	−	0.148814i
$386$	17.7211	−	4.81470i	0.901981	−	0.245062i
$387$	8.70192	+	1.14563i	0.442344	+	0.0582356i
$388$	8.22152	+	4.67050i	0.417384	+	0.237109i
$389$	−1.97948	−	15.0357i	−0.100364	−	0.762339i	−0.965427	−	0.260675i	$-0.916055\pi$
$389$	−1.97948	−	15.0357i	−0.100364	−	0.762339i	0.865063	−	0.501664i	$-0.167278\pi$
$390$	−12.6093	+	1.70483i	−0.638495	+	0.0863272i
$391$	11.1360	+	11.1360i	0.563172	+	0.563172i
$392$	−19.1802	+	4.91108i	−0.968748	+	0.248047i
$393$	0.412219	−	0.412219i	0.0207937	−	0.0207937i
$394$	−2.49364	+	3.27337i	−0.125628	+	0.164910i
$395$	30.6840	−	4.03962i	1.54388	−	0.203256i
$396$	−0.373470	+	2.99834i	−0.0187676	+	0.150672i
$397$	1.61784	−	12.2887i	0.0811971	−	0.616754i	−0.901668	−	0.432429i	$-0.857657\pi$
$397$	1.61784	−	12.2887i	0.0811971	−	0.616754i	0.982865	−	0.184325i	$-0.0590099\pi$
$398$	23.9441	+	13.7130i	1.20021	+	0.687369i
$399$	1.18375	+	2.10244i	0.0592616	+	0.105254i
$400$	42.5648	−	12.0444i	2.12824	−	0.602220i
$401$	−19.6055	−	11.3193i	−0.979054	−	0.565257i	−0.0770696	−	0.997026i	$-0.524556\pi$
$401$	−19.6055	−	11.3193i	−0.979054	−	0.565257i	−0.901984	+	0.431769i	$0.857890\pi$
$402$	4.82109	−	0.0168232i	0.240454	−	0.000839066i
$403$	31.6678	+	24.2996i	1.57749	+	1.21045i
$404$	8.97978	−	22.1144i	0.446761	−	1.10023i
$405$	−9.68805	+	23.3890i	−0.481403	+	1.16221i
$406$	−11.6829	−	1.62508i	−0.579811	−	0.0806512i
$407$	1.86250	−	1.86250i	0.0923208	−	0.0923208i
$408$	−5.12152	−	6.53176i	−0.253553	−	0.323370i
$409$	4.94458	−	18.4534i	0.244494	−	0.912462i	−0.729144	−	0.684361i	$-0.760081\pi$
$409$	4.94458	−	18.4534i	0.244494	−	0.912462i	0.973637	−	0.228102i	$-0.0732519\pi$
$410$	−10.4842	−	4.29989i	−0.517777	−	0.212357i
$411$	−7.86885	+	6.03798i	−0.388142	+	0.297832i
$412$	−4.80237	−	1.25093i	−0.236596	−	0.0616291i
$413$	1.09235	−	7.65713i	0.0537510	−	0.376783i
$414$	−2.97531	−	10.9510i	−0.146229	−	0.538213i
$415$	−31.7074	+	54.9187i	−1.55645	+	2.69586i
$416$	17.8910	−	14.2310i	0.877179	−	0.697731i
$417$	3.46125	+	5.99506i	0.169498	+	0.293580i
$418$	1.25985	+	0.332868i	0.0616213	+	0.0162811i
$419$	5.16064	+	12.4589i	0.252114	+	0.608656i	0.998374	−	0.0569976i	$-0.0181527\pi$
$419$	5.16064	+	12.4589i	0.252114	+	0.608656i	−0.746261	+	0.665654i	$0.768153\pi$
$420$	8.36206	−	8.29836i	0.408027	−	0.404919i
$421$	−5.57068	−	2.30745i	−0.271498	−	0.112458i	0.242781	−	0.970081i	$-0.421940\pi$
$421$	−5.57068	−	2.30745i	−0.271498	−	0.112458i	−0.514279	+	0.857623i	$0.671940\pi$
$422$	1.75094	+	12.9504i	0.0852346	+	0.630414i
$423$	−4.25713	+	15.8878i	−0.206989	+	0.772492i
$424$	−11.4892	+	15.3020i	−0.557963	+	0.743131i
$425$	15.1190	+	56.4247i	0.733377	+	2.73700i
$426$	−1.43250	+	11.1823i	−0.0694047	+	0.541784i
$427$	7.76676	+	3.31583i	0.375860	+	0.160464i
$428$	1.70735	+	12.3044i	0.0825277	+	0.594756i
$429$	−0.164502	+	1.24952i	−0.00794223	+	0.0603272i
$430$	−18.4820	+	0.0644931i	−0.891281	+	0.00311013i
$431$	−14.6028	+	8.43095i	−0.703394	+	0.406104i	−0.808610	−	0.588345i	$-0.799780\pi$
$431$	−14.6028	+	8.43095i	−0.703394	+	0.406104i	0.105217	+	0.994449i	$0.466446\pi$
$432$	1.82571	+	12.5152i	0.0878396	+	0.602138i
$433$		−	1.19815i		−	0.0575797i	−0.999585	−	0.0287898i	$-0.990835\pi$
$433$		−	1.19815i		−	0.0575797i	0.999585	−	0.0287898i	$-0.00916535\pi$
$434$	−36.9565	−	0.270251i	−1.77397	−	0.0129725i
$435$	6.48421	−	2.68585i	0.310894	−	0.128777i
$436$	2.61598	+	6.19294i	0.125283	+	0.296588i
$437$	−4.85217	+	0.638801i	−0.232111	+	0.0305580i
$438$	2.54961	+	6.09507i	0.121825	+	0.291234i
$439$	3.50963	+	13.0981i	0.167505	+	0.625139i	0.997707	+	0.0676760i	$0.0215584\pi$
$439$	3.50963	+	13.0981i	0.167505	+	0.625139i	−0.830202	+	0.557463i	$0.811775\pi$
$440$	−0.0666046	−	6.36216i	−0.00317525	−	0.303304i
$441$	−5.26797	+	18.0879i	−0.250856	+	0.861329i
$442$	18.4609	+	23.8857i	0.878096	+	1.13613i
$443$	14.7826	−	11.3431i	0.702342	−	0.538926i	−0.194704	−	0.980862i	$-0.562375\pi$
$443$	14.7826	−	11.3431i	0.702342	−	0.538926i	0.897047	+	0.441936i	$0.145708\pi$
$444$	2.57532	−	4.53336i	0.122219	−	0.215144i
$445$	5.66000	−	7.37626i	0.268310	−	0.349668i
$446$	6.15588	−	23.2989i	0.291489	−	1.10324i
$447$	−11.7724			−0.556815
$448$	−5.27068	+	20.4993i	−0.249016	+	0.968499i
$449$	−11.9642			−0.564628			−0.282314	−	0.959322i	$-0.591102\pi$
$449$	−11.9642			−0.564628			−0.282314	+	0.959322i	$0.591102\pi$
$450$	10.7523	−	40.6956i	0.506868	−	1.91841i
$451$	−0.683269	+	0.890453i	−0.0321739	+	0.0419298i
$452$	−12.1601	+	21.4055i	−0.571963	+	1.00683i
$453$	10.4012	−	7.98113i	0.488692	−	0.374986i
$454$	−12.2197	−	15.8105i	−0.573499	−	0.742022i
$455$	−30.6230	+	29.9685i	−1.43563	+	1.40494i
$456$	2.57923	−	0.0270016i	0.120783	−	0.00126447i
$457$	−4.35925	−	16.2689i	−0.203917	−	0.761028i	−0.989777	−	0.142624i	$-0.954446\pi$
$457$	−4.35925	−	16.2689i	−0.203917	−	0.761028i	0.785860	−	0.618404i	$-0.212221\pi$
$458$	−1.19579	−	2.85863i	−0.0558754	−	0.133575i
$459$	−16.5588	+	2.18001i	−0.772899	+	0.101754i
$460$	9.29843	+	22.0126i	0.433542	+	1.02634i
$461$	20.4085	−	8.45350i	0.950521	−	0.393719i	0.147094	−	0.989122i	$-0.453008\pi$
$461$	20.4085	−	8.45350i	0.950521	−	0.393719i	0.803427	+	0.595404i	$0.203008\pi$
$462$	−0.576032	−	1.01478i	−0.0267994	−	0.0472119i
$463$		−	19.9875i		−	0.928898i	−0.885600	−	0.464449i	$-0.846252\pi$
$463$		−	19.9875i		−	0.928898i	0.885600	−	0.464449i	$-0.153748\pi$
$464$	−7.53596	+	10.1102i	−0.349848	+	0.469353i
$465$	19.0442	−	10.9952i	0.883156	−	0.509890i
$466$	24.0150	−	0.0838006i	1.11247	−	0.00388199i
$467$	0.100100	−	0.760333i	0.00463206	−	0.0351840i	−0.988973	−	0.148098i	$-0.952685\pi$
$467$	0.100100	−	0.760333i	0.00463206	−	0.0351840i	0.993605	+	0.112914i	$0.0360183\pi$
$468$	−2.98974	−	21.5463i	−0.138201	−	0.995976i
$469$	12.9859	−	9.74339i	0.599633	−	0.449908i
$470$	4.40102	−	34.3550i	0.203004	−	1.58468i
$471$	−0.929251	−	3.46801i	−0.0428176	−	0.159798i
$472$	−6.61233	−	4.96471i	−0.304357	−	0.228519i
$473$	−0.473802	+	1.76825i	−0.0217855	+	0.0813044i
$474$	−0.813001	−	6.01313i	−0.0373424	−	0.276192i
$475$	−16.7712	−	6.94687i	−0.769516	−	0.318744i
$476$	−26.9702	−	7.33727i	−1.23618	−	0.336303i
$477$	6.96779	+	16.8217i	0.319033	+	0.770214i
$478$	−2.67418	−	0.706552i	−0.122314	−	0.0323169i
$479$	−15.8658	−	27.4803i	−0.724925	−	1.25561i	−0.959005	−	0.283390i	$-0.908541\pi$
$479$	−15.8658	−	27.4803i	−0.724925	−	1.25561i	0.234079	−	0.972217i	$-0.424792\pi$
$480$	−3.47136	−	12.1063i	−0.158445	−	0.552576i
$481$	−9.48138	+	16.4222i	−0.432314	+	0.748789i
$482$	1.86826	+	6.87636i	0.0850967	+	0.313209i
$483$	3.44783	+	2.70528i	0.156882	+	0.123095i
$484$	20.6797	+	5.38672i	0.939988	+	0.244851i
$485$	−15.0308	+	11.5335i	−0.682513	+	0.523710i
$486$	17.0039	+	6.97381i	0.771311	+	0.316339i
$487$	1.59123	−	5.93855i	0.0721055	−	0.269101i	−0.920456	−	0.390846i	$-0.872182\pi$
$487$	1.59123	−	5.93855i	0.0721055	−	0.269101i	0.992561	+	0.121745i	$0.0388490\pi$
$488$	7.10450	−	5.57060i	0.321606	−	0.252169i
$489$	9.00768	−	9.00768i	0.407341	−	0.407341i
$490$	5.88968	−	39.2313i	0.266069	−	1.77229i
$491$	0.634073	−	1.53079i	0.0286153	−	0.0690835i	−0.908926	−	0.416958i	$-0.863096\pi$
$491$	0.634073	−	1.53079i	0.0286153	−	0.0690835i	0.937541	+	0.347874i	$0.113096\pi$
$492$	−0.835864	+	2.05847i	−0.0376836	+	0.0928030i
$493$	−13.2106	−	10.1369i	−0.594976	−	0.456541i
$494$	−9.38121	+	0.0327358i	−0.422081	+	0.00147285i
$495$	−5.24305	−	3.02707i	−0.235657	−	0.136057i
$496$	−19.2751	+	34.4883i	−0.865477	+	1.54857i
$497$	18.6254	+	33.0803i	0.835463	+	1.48385i
$498$	10.7891	+	6.17897i	0.483469	+	0.276886i
$499$	−0.133870	+	1.01684i	−0.00599285	+	0.0455202i	−0.994180	−	0.107732i	$-0.965641\pi$
$499$	−0.133870	+	1.01684i	−0.00599285	+	0.0455202i	0.988187	+	0.153252i	$0.0489746\pi$
$500$	−6.00237	+	48.1890i	−0.268434	+	2.15508i
$501$	−10.7986	+	1.42166i	−0.482446	+	0.0635152i
$502$	12.8522	−	16.8709i	0.573623	−	0.752986i
$503$	3.89746	−	3.89746i	0.173779	−	0.173779i	−0.614858	−	0.788638i	$-0.710787\pi$
$503$	3.89746	−	3.89746i	0.173779	−	0.173779i	0.788638	+	0.614858i	$0.210787\pi$
$504$	14.2365	+	14.2460i	0.634145	+	0.634568i
$505$	33.8167	+	33.8167i	1.50482	+	1.50482i
$506$	2.34553	−	0.317125i	0.104271	−	0.0140979i
$507$	−0.241590	−	1.83506i	−0.0107294	−	0.0814977i
$508$	12.3169	+	6.99699i	0.546472	+	0.310441i
$509$	−5.51929	−	0.726628i	−0.244638	−	0.0322072i	0.00720994	−	0.999974i	$-0.497705\pi$
$509$	−5.51929	−	0.726628i	−0.244638	−	0.0322072i	−0.251848	+	0.967767i	$0.581038\pi$
$510$	16.0492	−	4.36046i	0.710672	−	0.193085i
$511$	19.1461	+	11.3315i	0.846974	+	0.501276i
$512$	16.4945	+	15.4897i	0.728961	+	0.684555i
$513$	2.59510	−	4.49484i	0.114576	−	0.198452i
$514$	16.9500	+	16.8321i	0.747633	+	0.742434i
$515$	6.05323	−	7.88872i	0.266737	−	0.347619i
$516$	0.0252890	+	3.62353i	0.00111329	+	0.159517i
$517$	−3.16949	−	1.31285i	−0.139394	−	0.0577390i
$518$	−2.16431	−	17.4232i	−0.0950943	−	0.765530i
$519$	−4.13562	−	4.13562i	−0.181534	−	0.181534i
$520$	12.3179	+	44.1182i	0.540174	+	1.93471i
$521$	−4.12707	−	1.10585i	−0.180810	−	0.0484480i	0.167278	−	0.985910i	$-0.446502\pi$
$521$	−4.12707	−	1.10585i	−0.180810	−	0.0484480i	−0.348088	+	0.937462i	$0.613169\pi$
$522$	4.63033	+	11.0692i	0.202664	+	0.484485i
$523$	18.2211	+	23.7462i	0.796752	+	1.03835i	0.998266	+	0.0588622i	$0.0187473\pi$
$523$	18.2211	+	23.7462i	0.796752	+	1.03835i	−0.201514	+	0.979486i	$0.564586\pi$
$524$	−1.67383	−	1.26592i	−0.0731218	−	0.0553019i
$525$	6.05813	+	15.0845i	0.264399	+	0.658340i
$526$	−32.8378	−	18.8064i	−1.43180	−	0.820000i
$527$	−45.1833	−	26.0866i	−1.96822	−	1.13635i
$528$	−1.24732	+	0.0174112i	−0.0542826	+	0.000757725i
$529$	12.2202	−	7.05533i	0.531313	−	0.306754i
$530$	−19.2861	−	33.1369i	−0.837735	−	1.43938i
$531$	−7.26903	+	3.01093i	−0.315449	+	0.130663i
$532$	6.91111	−	5.26122i	0.299634	−	0.228103i
$533$	3.09224	−	7.46534i	0.133940	−	0.323360i
$534$	−1.45006	−	1.10465i	−0.0627503	−	0.0478030i
$535$	−24.0422	−	6.44210i	−1.03944	−	0.278516i
$536$	−2.44538	−	17.1825i	−0.105624	−	0.742173i
$537$	−1.74947	+	0.468769i	−0.0754951	+	0.0202289i
$538$	28.1651	−	21.7684i	1.21429	−	0.938504i
$539$	−3.59693	−	1.58177i	−0.154931	−	0.0681318i
$540$	−24.5236	−	6.38799i	−1.05533	−	0.274895i
$541$	35.9498	+	4.73288i	1.54560	+	0.203482i	0.854568	−	0.519339i	$-0.173822\pi$
$541$	35.9498	+	4.73288i	1.54560	+	0.203482i	0.691034	+	0.722822i	$0.257155\pi$
$542$	−16.6794	+	16.7962i	−0.716440	+	0.721458i
$543$	1.47458	+	2.55405i	0.0632803	+	0.109605i
$544$	−20.7567	+	21.4939i	−0.889936	+	0.921545i
$545$	−13.4704			−0.577006
$546$	5.89657	+	5.98344i	0.252350	+	0.256068i
$547$	−8.08654	−	19.5226i	−0.345756	−	0.834728i	−0.997111	−	0.0759554i	$-0.975799\pi$
$547$	−8.08654	−	19.5226i	−0.345756	−	0.834728i	0.651356	−	0.758773i	$-0.274201\pi$
$548$	25.4234	+	25.0710i	1.08603	+	1.07098i
$549$	−1.12128	−	8.51700i	−0.0478553	−	0.363497i
$550$	8.12260	+	3.33133i	0.346349	+	0.142049i
$551$	4.99831	−	1.33929i	0.212935	−	0.0570559i
$552$	4.30943	−	1.83811i	0.183421	−	0.0782351i
$553$	−14.2914	−	14.6036i	−0.607733	−	0.621007i
$554$	−4.81584	+	37.5932i	−0.204605	+	1.59718i
$555$	6.35961	+	8.28800i	0.269950	+	0.351806i
$556$	19.6644	−	15.3083i	0.833958	−	0.649215i
$557$	−21.0430	−	16.1469i	−0.891621	−	0.684165i	0.0577466	−	0.998331i	$-0.481608\pi$
$557$	−21.0430	−	16.1469i	−0.891621	−	0.684165i	−0.949368	+	0.314166i	$0.898275\pi$
$558$	18.9107	+	32.4919i	0.800552	+	1.37549i
$559$		−	13.1792i		−	0.557423i
$560$	−33.7274	−	25.7113i	−1.42524	−	1.08650i
$561$		−	1.64729i		−	0.0695485i
$562$	−11.7997	+	6.86756i	−0.497739	+	0.289691i
$563$	−9.80683	−	7.52504i	−0.413308	−	0.317143i	0.381092	−	0.924537i	$-0.375548\pi$
$563$	−9.80683	−	7.52504i	−0.413308	−	0.317143i	−0.794400	+	0.607394i	$0.792215\pi$
$564$	−6.73866	−	0.839360i	−0.283749	−	0.0353434i
$565$	−30.0287	−	39.1341i	−1.26332	−	1.64639i
$566$	4.26106	+	0.545859i	0.179106	+	0.0229442i
$567$	16.1905	−	4.15131i	0.679937	−	0.174339i
$568$	40.5822	−	0.424850i	1.70279	−	0.0178263i
$569$	17.5412	−	4.70015i	0.735366	−	0.197041i	0.128348	−	0.991729i	$-0.459032\pi$
$569$	17.5412	−	4.70015i	0.735366	−	0.197041i	0.607017	+	0.794689i	$0.292366\pi$
$570$	−1.96113	+	4.78171i	−0.0821426	+	0.200284i
$571$	4.74969	+	36.0774i	0.198768	+	1.50979i	0.742108	+	0.670281i	$0.233826\pi$
$571$	4.74969	+	36.0774i	0.198768	+	1.50979i	−0.543339	+	0.839513i	$0.682840\pi$
$572$	4.53688	−	0.0316633i	0.189696	−	0.00132391i
$573$	−0.941764	−	2.27362i	−0.0393428	−	0.0949818i
$574$	1.88344	+	7.24047i	0.0786133	+	0.302211i
$575$	−32.9724			−1.37505
$576$	20.6759	−	6.00675i	0.861496	−	0.250281i
$577$	4.06611	+	7.04271i	0.169274	+	0.293192i	0.938165	−	0.346189i	$-0.112524\pi$
$577$	4.06611	+	7.04271i	0.169274	+	0.293192i	−0.768891	+	0.639380i	$0.779191\pi$
$578$	−10.9389	−	10.8628i	−0.454999	−	0.451835i
$579$	7.15230	+	0.941618i	0.297239	+	0.0391323i
$580$	−12.7854	−	21.7923i	−0.530884	−	0.904875i
$581$	41.5662	−	5.01614i	1.72446	−	0.208105i
$582$	2.27155	+	2.93904i	0.0941586	+	0.121827i
$583$	−3.66820	+	0.982892i	−0.151921	+	0.0407072i
$584$	20.4721	−	12.1071i	0.847141	−	0.500994i
$585$	42.1004	+	11.2808i	1.74064	+	0.466402i
$586$	14.2858	−	18.7527i	0.590141	−	0.774669i
$587$	−3.01636	+	7.28213i	−0.124498	+	0.300566i	−0.973824	−	0.227304i	$-0.927009\pi$
$587$	−3.01636	+	7.28213i	−0.124498	+	0.300566i	0.849326	+	0.527869i	$0.177009\pi$
$588$	−7.69571	−	1.12789i	−0.317366	−	0.0465134i
$589$	14.9791	−	6.20455i	0.617204	−	0.255654i
$590$	14.3192	−	8.33394i	0.589511	−	0.343103i
$591$	−1.39998	+	0.808277i	−0.0575874	+	0.0332481i
$592$	−17.4391	−	6.93997i	−0.716744	−	0.285231i
$593$	2.91079	+	1.68054i	0.119532	+	0.0690117i	0.558574	−	0.829455i	$-0.311349\pi$
$593$	2.91079	+	1.68054i	0.119532	+	0.0690117i	−0.439042	+	0.898467i	$0.644682\pi$
$594$	−1.24745	+	2.17817i	−0.0511836	+	0.0893714i
$595$	34.5709	−	44.0600i	1.41727	−	1.80628i
$596$	5.82478	+	41.9776i	0.238592	+	1.71947i
$597$	6.59879	+	8.59972i	0.270071	+	0.351963i
$598$	−15.7198	+	6.57573i	−0.642832	+	0.268901i
$599$	19.4119	+	5.20140i	0.793148	+	0.212523i	0.632574	−	0.774500i	$-0.281999\pi$
$599$	19.4119	+	5.20140i	0.793148	+	0.212523i	0.160575	+	0.987024i	$0.448665\pi$
$600$	17.2520	+	2.08779i	0.704311	+	0.0852335i
$601$	2.01160	+	2.01160i	0.0820547	+	0.0820547i	0.746943	−	0.664888i	$-0.231521\pi$
$601$	2.01160	+	2.01160i	0.0820547	+	0.0820547i	−0.664888	+	0.746943i	$0.731521\pi$
$602$	7.35729	+	9.73478i	0.299861	+	0.396760i
$603$	−15.2574	−	6.31984i	−0.621331	−	0.257364i
$604$	−33.6052	−	33.1394i	−1.36738	−	1.34842i
$605$	−26.0662	+	33.9701i	−1.05974	+	1.38108i
$606$	6.60696	−	6.65323i	0.268389	−	0.270269i
$607$	16.6476	−	28.8345i	0.675706	−	1.17036i	−0.300556	−	0.953764i	$-0.597172\pi$
$607$	16.6476	−	28.8345i	0.675706	−	1.17036i	0.976262	−	0.216593i	$-0.0694943\pi$
$608$	−1.37244	−	9.18357i	−0.0556598	−	0.372443i
$609$	−3.98768	−	2.36008i	−0.161589	−	0.0956353i
$610$	4.74281	+	17.4565i	0.192031	+	0.706794i
$611$	24.4868	+	3.22375i	0.990632	+	0.130419i
$612$	7.55026	+	27.4113i	0.305201	+	1.10804i
$613$	3.99724	+	30.3621i	0.161447	+	1.22631i	0.859827	+	0.510585i	$0.170571\pi$
$613$	3.99724	+	30.3621i	0.161447	+	1.22631i	−0.698380	+	0.715727i	$0.746095\pi$
$614$	−3.21522	−	23.7805i	−0.129756	−	0.959702i
$615$	−3.14775	−	3.14775i	−0.126930	−	0.126930i
$616$	−3.33346	+	2.55609i	−0.134309	+	0.102988i
$617$	−10.8660	+	10.8660i	−0.437450	+	0.437450i	−0.891153	−	0.453703i	$-0.850103\pi$
$617$	−10.8660	+	10.8660i	−0.437450	+	0.437450i	0.453703	+	0.891153i	$0.350103\pi$
$618$	−1.55080	−	1.18140i	−0.0623825	−	0.0475228i
$619$	4.32745	−	0.569719i	0.173935	−	0.0228990i	−0.0430556	−	0.999073i	$-0.513709\pi$
$619$	4.32745	−	0.569719i	0.173935	−	0.0228990i	0.216990	+	0.976174i	$0.430376\pi$
$620$	−48.6291	−	62.4671i	−1.95299	−	2.50874i
$621$	1.23050	−	9.34661i	0.0493784	−	0.375067i
$622$	−9.54068	+	16.6589i	−0.382546	+	0.667962i
$623$	−6.13810	−	0.0663067i	−0.245918	−	0.00265652i
$624$	8.64139	−	2.44522i	0.345932	−	0.0978872i
$625$	−36.3788	−	21.0033i	−1.45515	−	0.840133i
$626$	−0.0515348	−	14.7685i	−0.00205974	−	0.590267i
$627$	0.406125	+	0.311630i	0.0162191	+	0.0124453i
$628$	−11.9064	+	5.02941i	−0.475115	+	0.200695i
$629$	9.48499	−	22.8988i	0.378192	−	0.913035i
$630$	−37.3947	+	15.1700i	−1.48984	+	0.604387i
$631$	8.54432	−	8.54432i	0.340144	−	0.340144i	−0.516278	−	0.856421i	$-0.672683\pi$
$631$	8.54432	−	8.54432i	0.340144	−	0.340144i	0.856421	+	0.516278i	$0.172683\pi$
$632$	−21.0392	+	5.87417i	−0.836894	+	0.233662i
$633$	−1.32872	+	4.95884i	−0.0528118	+	0.197096i
$634$	11.6094	−	28.3065i	0.461067	−	1.12419i
$635$	−22.5180	+	17.2787i	−0.893599	+	0.685683i
$636$	−6.48363	+	3.80390i	−0.257093	+	0.150835i
$637$	27.9603	+	4.29742i	1.10783	+	0.170270i
$638$	−2.41502	+	0.656143i	−0.0956116	+	0.0259770i
$639$	19.3088	−	33.4437i	0.763842	−	1.32301i
$640$	−41.4508	+	18.3681i	−1.63849	+	0.726061i
$641$	−4.04730	−	7.01013i	−0.159859	−	0.276884i	0.774959	−	0.632012i	$-0.217771\pi$
$641$	−4.04730	−	7.01013i	−0.159859	−	0.276884i	−0.934818	+	0.355128i	$0.884437\pi$
$642$	−1.24659	+	4.71812i	−0.0491989	+	0.186210i
$643$	11.3285	+	27.3495i	0.446754	+	1.07856i	0.973531	+	0.228557i	$0.0734006\pi$
$643$	11.3285	+	27.3495i	0.446754	+	1.07856i	−0.526776	+	0.850004i	$0.676599\pi$
$644$	7.94048	−	13.6327i	0.312899	−	0.537203i
$645$	−6.70792	−	2.77851i	−0.264124	−	0.109404i
$646$	12.1513	−	1.64291i	0.478088	−	0.0646394i
$647$	−1.16669	+	4.35413i	−0.0458671	+	0.171178i	−0.985060	−	0.172212i	$-0.944909\pi$
$647$	−1.16669	+	4.35413i	−0.0458671	+	0.171178i	0.939193	+	0.343390i	$0.111575\pi$
$648$	4.44372	−	17.3069i	0.174566	−	0.679878i
$649$	−0.424729	−	1.58511i	−0.0166721	−	0.0622210i
$650$	−62.6917	−	8.03107i	−2.45897	−	0.315004i
$651$	−13.3526	−	5.70057i	−0.523329	−	0.223423i
$652$	−36.5761	−	27.6624i	−1.43243	−	1.08334i
$653$	1.62988	−	12.3802i	0.0637823	−	0.484475i	−0.929506	−	0.368808i	$-0.879766\pi$
$653$	1.62988	−	12.3802i	0.0637823	−	0.484475i	0.993288	−	0.115667i	$-0.0369006\pi$
$654$	0.00921578	+	2.64100i	0.000360366	+	0.103271i
$655$	3.64164	−	2.10250i	0.142291	−	0.0821515i
$656$	7.75360	+	1.96200i	0.302727	+	0.0766032i
$657$		−	22.6315i		−	0.882938i
$658$	−19.8867	+	11.2885i	−0.775266	+	0.440073i
$659$	−9.80661	+	4.06203i	−0.382011	+	0.158234i	−0.565421	−	0.824802i	$-0.691286\pi$
$659$	−9.80661	+	4.06203i	−0.382011	+	0.158234i	0.183410	+	0.983036i	$0.441286\pi$
$660$	0.940369	−	2.31584i	0.0366038	−	0.0901438i
$661$	48.1375	−	6.33743i	1.87233	−	0.246497i	0.893192	−	0.449676i	$-0.148461\pi$
$661$	48.1375	−	6.33743i	1.87233	−	0.246497i	0.979142	+	0.203179i	$0.0651273\pi$
$662$	−12.7343	+	5.32686i	−0.494933	+	0.207034i
$663$	3.06941	+	11.4552i	0.119206	+	0.444883i
$664$	16.6945	−	41.5285i	0.647873	−	1.61162i
$665$	4.32256	+	16.8583i	0.167622	+	0.653739i
$666$	−14.1310	+	10.9216i	−0.547564	+	0.423205i
$667$	7.45673	−	5.72175i	0.288726	−	0.221547i
$668$	10.4123	+	37.8019i	0.402863	+	1.46260i
$669$	5.76311	−	7.51064i	0.222815	−	0.290378i
$670$	33.6216	+	8.88325i	1.29891	+	0.343190i
$671$	1.79173			0.0691690
$672$	−5.01787	+	6.63019i	−0.193569	+	0.255765i
$673$	−27.4685			−1.05883			−0.529416	−	0.848362i	$-0.677589\pi$
$673$	−27.4685			−1.05883			−0.529416	+	0.848362i	$0.677589\pi$
$674$	2.95886	+	0.781768i	0.113971	+	0.0301126i
$675$	21.2870	−	27.7417i	0.819337	−	1.06778i
$676$	−6.42385	+	1.76941i	−0.247071	+	0.0680541i
$677$	−17.0418	+	13.0766i	−0.654968	+	0.502575i	−0.881961	−	0.471322i	$-0.843777\pi$
$677$	−17.0418	+	13.0766i	−0.654968	+	0.502575i	0.226993	+	0.973896i	$0.427110\pi$
$678$	−7.65209	+	5.91419i	−0.293877	+	0.227133i
$679$	12.0466	+	3.36776i	0.462306	+	0.129243i
$680$	−23.4893	−	55.0704i	−0.900773	−	2.11185i
$681$	−2.03171	−	7.58246i	−0.0778554	−	0.290560i
$682$	−7.23372	+	3.02592i	−0.276993	+	0.115868i
$683$	−45.9417	+	6.04834i	−1.75791	+	0.231433i	−0.939343	−	0.342979i	$-0.888564\pi$
$683$	−45.9417	+	6.04834i	−1.75791	+	0.231433i	−0.818566	+	0.574412i	$0.805231\pi$
$684$	−8.18636	−	3.32416i	−0.313013	−	0.127102i
$685$	−66.0973	+	27.3784i	−2.52545	+	1.04608i
$686$	−23.0517	+	12.4345i	−0.880120	+	0.474752i
$687$		−	1.21729i		−	0.0464425i
$688$	12.9082	−	1.88304i	0.492119	−	0.0717901i
$689$	23.6772	−	13.6700i	0.902029	−	0.520786i
$690$	0.0327572	+	9.38733i	0.00124705	+	0.357370i
$691$	−3.06573	+	23.2865i	−0.116626	+	0.885861i	0.828691	+	0.559707i	$0.189086\pi$
$691$	−3.06573	+	23.2865i	−0.116626	+	0.885861i	−0.945317	+	0.326154i	$0.894247\pi$
$692$	−12.7004	+	16.7929i	−0.482798	+	0.638371i
$693$	0.478886	+	3.96829i	0.0181914	+	0.150743i
$694$	−27.9574	−	3.58146i	−1.06125	−	0.135950i
$695$	12.9236	+	48.2315i	0.490219	+	1.82952i
$696$	−4.26385	+	2.52161i	−0.161621	+	0.0955814i
$697$	−2.73354	+	10.2017i	−0.103540	+	0.386418i
$698$	−17.4450	+	2.35864i	−0.660305	+	0.0892759i
$699$	8.71608	+	3.61032i	0.329672	+	0.136555i
$700$	50.7902	−	29.0654i	1.91969	−	1.09857i
$701$	−11.7900	−	28.4636i	−0.445303	−	1.07506i	−0.974062	−	0.226283i	$-0.927342\pi$
$701$	−11.7900	−	28.4636i	−0.445303	−	1.07506i	0.528759	−	0.848772i	$-0.322658\pi$
$702$	4.61615	−	17.4713i	0.174225	−	0.659413i
$703$	3.85115	+	6.67039i	0.145249	+	0.251579i
$704$	0.679236	+	4.43903i	0.0255997	+	0.167302i
$705$	6.80324	−	11.7836i	0.256225	−	0.443795i
$706$	−6.31250	+	1.71506i	−0.237574	+	0.0645472i
$707$	4.45919	−	31.2580i	0.167705	−	1.17558i
$708$	−1.64375	−	2.80171i	−0.0617758	−	0.105295i
$709$	−24.4850	+	18.7880i	−0.919552	+	0.705597i	−0.955885	−	0.293743i	$-0.905099\pi$
$709$	−24.4850	+	18.7880i	−0.919552	+	0.705597i	0.0363323	+	0.999340i	$0.488433\pi$
$710$	−30.8569	+	75.2366i	−1.15804	+	2.82358i
$711$	−5.37960	+	20.0769i	−0.201751	+	0.752943i
$712$	−3.22147	+	5.71714i	−0.120730	+	0.214259i
$713$	20.8237	−	20.8237i	0.779853	−	0.779853i
$714$	−8.66205	−	6.74783i	−0.324169	−	0.252531i
$715$	−3.47886	+	8.39870i	−0.130102	+	0.314094i
$716$	2.53713	+	6.00626i	0.0948169	+	0.224464i
$717$	−0.862047	−	0.661472i	−0.0321937	−	0.0247031i
$718$	0.0430980	+	12.3507i	0.00160840	+	0.460925i
$719$	43.4951	+	25.1119i	1.62209	+	0.936515i	0.986359	+	0.164606i	$0.0526352\pi$
$719$	43.4951	+	25.1119i	1.62209	+	0.936515i	0.635733	+	0.771909i	$0.280698\pi$
$720$	−5.03348	+	42.8462i	−0.187587	+	1.59678i
$721$	−6.56454	−	0.0709133i	−0.244476	−	0.00264095i
$722$	11.4600	−	20.0103i	0.426498	−	0.744706i
$723$	−0.365378	+	2.77532i	−0.0135885	+	0.103215i
$724$	8.37754	−	6.52171i	0.311349	−	0.242377i
$725$	34.5646	−	4.55052i	1.28370	−	0.169002i
$726$	6.67800	+	5.08729i	0.247844	+	0.188807i
$727$	17.9706	−	17.9706i	0.666491	−	0.666491i	−0.290411	−	0.956902i	$-0.593792\pi$
$727$	17.9706	−	17.9706i	0.666491	−	0.666491i	0.956902	+	0.290411i	$0.0937920\pi$
$728$	18.4180	−	23.9863i	0.682618	−	0.888991i
$729$	−8.29599	−	8.29599i	−0.307259	−	0.307259i
$730$	6.38519	+	47.2263i	0.236327	+	1.74792i
$731$	2.24846	+	17.0787i	0.0831621	+	0.631679i
$732$	3.41928	−	0.941818i	0.126380	−	0.0348106i
$733$	13.9446	+	1.83584i	0.515056	+	0.0678084i	0.383574	−	0.923510i	$-0.374693\pi$
$733$	13.9446	+	1.83584i	0.515056	+	0.0678084i	0.131482	+	0.991319i	$0.458026\pi$
$734$	−7.51763	−	27.6696i	−0.277481	−	1.02130i
$735$	8.08200	−	13.3251i	0.298109	−	0.491504i
$736$	−8.68650	−	14.4570i	−0.320189	−	0.532890i
$737$	1.72223	−	2.98299i	0.0634391	−	0.109880i
$738$	5.36252	−	5.40008i	0.197397	−	0.198780i
$739$	−17.5517	+	22.8738i	−0.645650	+	0.841427i	−0.995439	−	0.0954015i	$-0.969587\pi$
$739$	−17.5517	+	22.8738i	−0.645650	+	0.841427i	0.349789	+	0.936828i	$0.386253\pi$
$740$	26.4065	−	26.7776i	0.970721	−	0.984366i
$741$	−3.40485	−	1.41033i	−0.125080	−	0.0518099i
$742$	−9.85776	+	23.3150i	−0.361890	+	0.855922i
$743$	13.7040	+	13.7040i	0.502752	+	0.502752i	0.912292	−	0.409540i	$-0.134311\pi$
$743$	13.7040	+	13.7040i	0.502752	+	0.502752i	−0.409540	+	0.912292i	$0.634311\pi$
$744$	−12.2140	+	9.57695i	−0.447788	+	0.351108i
$745$	−82.0224	−	21.9778i	−3.00507	−	0.805205i
$746$	20.0848	−	8.40162i	0.735356	−	0.307605i
$747$	−25.9267	−	33.7883i	−0.948608	−	1.23625i
$748$	−5.87384	+	0.815049i	−0.214769	+	0.0298011i
$749$	6.12433	+	15.2493i	0.223778	+	0.557197i
$750$	−9.48083	+	16.5544i	−0.346191	+	0.604482i
$751$	−20.2349	−	11.6826i	−0.738381	−	0.426304i	0.0830994	−	0.996541i	$-0.473518\pi$
$751$	−20.2349	−	11.6826i	−0.738381	−	0.426304i	−0.821480	+	0.570237i	$0.806851\pi$
$752$	0.341208	+	24.4438i	0.0124426	+	0.891373i
$753$	7.21548	−	4.16586i	0.262947	−	0.151812i
$754$	15.5714	−	9.06274i	0.567077	−	0.330046i
$755$	87.3688	−	36.1893i	3.17968	−	1.31706i
$756$	6.34365	+	15.4821i	0.230716	+	0.563078i
$757$	−0.172573	+	0.416629i	−0.00627229	+	0.0151426i	−0.926985	−	0.375099i	$-0.877609\pi$
$757$	−0.172573	+	0.416629i	−0.00627229	+	0.0151426i	0.920712	+	0.390242i	$0.127609\pi$
$758$	−12.7461	+	16.7316i	−0.462959	+	0.607718i
$759$	0.898128	+	0.240653i	0.0326000	+	0.00873514i
$760$	18.0208	+	4.62702i	0.653683	+	0.167840i
$761$	7.23293	−	1.93806i	0.262193	−	0.0702545i	−0.125328	−	0.992115i	$-0.539998\pi$
$761$	7.23293	−	1.93806i	0.262193	−	0.0702545i	0.387521	+	0.921861i	$0.373332\pi$
$762$	3.40306	+	4.40305i	0.123280	+	0.159506i
$763$	5.33744	+	7.11369i	0.193228	+	0.257533i
$764$	−7.64123	+	4.48306i	−0.276450	+	0.162191i
$765$	−56.4816	−	7.43594i	−2.04210	−	0.268847i
$766$	−15.1227	−	15.0175i	−0.546405	−	0.542605i
$767$	5.90711	+	10.2314i	0.213293	+	0.369435i
$768$	3.62960	+	8.11427i	0.130972	+	0.292799i
$769$	17.8318			0.643030			0.321515	−	0.946904i	$-0.395808\pi$
$769$	17.8318			0.643030			0.321515	+	0.946904i	$0.395808\pi$
$770$	−2.11892	−	8.14572i	−0.0763606	−	0.293552i
$771$	3.59117	+	8.66984i	0.129333	+	0.312237i
$772$	−0.181243	−	25.9693i	−0.00652307	−	0.934657i
$773$	1.99510	+	15.1543i	0.0717588	+	0.545062i	0.989132	+	0.147033i	$0.0469724\pi$
$773$	1.99510	+	15.1543i	0.0717588	+	0.545062i	−0.917373	+	0.398029i	$0.869694\pi$
$774$	4.71004	−	11.4842i	0.169299	−	0.412792i
$775$	105.511	−	28.2716i	3.79007	−	1.01555i
$776$	9.35602	−	9.55399i	0.335862	−	0.342968i
$777$	1.85699	−	6.64251i	0.0666190	−	0.238299i
$778$	−21.2733	−	2.72520i	−0.762684	−	0.0977030i
$779$	−1.99802	−	2.60387i	−0.0715866	−	0.0932935i
$780$	−2.22418	+	17.8565i	−0.0796385	+	0.639364i
$781$	6.39006	+	4.90327i	0.228655	+	0.175453i
$782$	19.2491	−	11.2032i	0.688348	−	0.400627i
$783$			9.96776i			0.356219i
$784$	−0.214090	+	27.9992i	−0.00764606	+	0.999971i
$785$		−	25.8977i		−	0.924327i
$786$	−0.414708	−	0.712541i	−0.0147921	−	0.0254155i
$787$	−29.2069	−	22.4112i	−1.04111	−	0.798875i	−0.0611656	−	0.998128i	$-0.519482\pi$
$787$	−29.2069	−	22.4112i	−1.04111	−	0.798875i	−0.979948	+	0.199253i	$0.936148\pi$
$788$	3.57481	+	4.59207i	0.127347	+	0.163586i
$789$	−9.04982	−	11.7940i	−0.322182	−	0.419876i
$790$	5.56143	−	43.4134i	0.197867	−	1.54458i
$791$	−8.76829	+	31.3645i	−0.311764	+	1.11519i
$792$	3.96469	+	1.59381i	0.140879	+	0.0566336i
$793$	−12.4597	+	3.33855i	−0.442455	+	0.118556i
$794$	−16.2179	−	6.65145i	−0.575550	−	0.236051i
$795$	−1.96598	−	14.9331i	−0.0697260	−	0.529622i
$796$	27.3996	−	27.7848i	0.971154	−	0.984804i
$797$	16.2989	+	39.3490i	0.577337	+	1.39381i	0.895194	+	0.445676i	$0.147037\pi$
$797$	16.2989	+	39.3490i	0.577337	+	1.39381i	−0.317857	+	0.948139i	$0.602963\pi$
$798$	3.30229	−	0.859014i	0.116900	−	0.0304088i
$799$	−32.2820			−1.14205
$800$	−1.09145	−	62.5497i	−0.0385884	−	2.21147i
$801$	3.12212	+	5.40767i	0.110315	+	0.191071i
$802$	−22.5594	+	22.7174i	−0.796600	+	0.802179i
$803$	4.67989	+	0.616120i	0.165150	+	0.0217424i
$804$	1.71865	−	6.59792i	0.0606120	−	0.232691i
$805$	18.9718	+	25.2854i	0.668666	+	0.891193i
$806$	44.6649	−	34.5209i	1.57325	−	1.21595i
$807$	13.5076	−	3.61934i	0.475489	−	0.127407i
$808$	−26.9929	−	20.2670i	−0.949606	−	0.712989i
$809$	−18.4341	−	4.93941i	−0.648109	−	0.173660i	−0.0802355	−	0.996776i	$-0.525567\pi$
$809$	−18.4341	−	4.93941i	−0.648109	−	0.173660i	−0.567874	+	0.823116i	$0.692234\pi$
$810$	28.4798	+	21.6958i	1.00068	+	0.762314i
$811$	−19.2780	+	46.5412i	−0.676942	+	1.63428i	0.0926129	+	0.995702i	$0.470478\pi$
$811$	−19.2780	+	46.5412i	−0.676942	+	1.63428i	−0.769555	+	0.638581i	$0.779522\pi$
$812$	−6.44247	+	15.3869i	−0.226086	+	0.539973i
$813$	−8.59115	+	3.55857i	−0.301305	+	0.124805i
$814$	−1.87375	−	3.21943i	−0.0656749	−	0.112841i
$815$	79.5760	−	45.9432i	2.78742	−	1.60932i
$816$	−10.7810	+	4.64298i	−0.377411	+	0.162537i
$817$	−4.63597	−	2.67658i	−0.162192	−	0.0936416i
$818$	−23.4450	−	13.4271i	−0.819734	−	0.469468i
$819$	−10.7243	−	26.7031i	−0.374738	−	0.933081i
$820$	−9.66670	+	12.7816i	−0.337576	+	0.446353i
$821$	6.91101	+	9.00660i	0.241196	+	0.314332i	0.898228	−	0.439530i	$-0.144855\pi$
$821$	6.91101	+	9.00660i	0.241196	+	0.314332i	−0.657032	+	0.753863i	$0.728188\pi$
$822$	5.41303	+	12.9403i	0.188801	+	0.451345i
$823$	−37.7050	−	10.1030i	−1.31431	−	0.352170i	−0.467470	−	0.884009i	$-0.654834\pi$
$823$	−37.7050	−	10.1030i	−1.31431	−	0.352170i	−0.846845	+	0.531839i	$0.821501\pi$
$824$	−3.44528	+	6.11434i	−0.120022	+	0.213003i
$825$	2.43872	+	2.43872i	0.0849052	+	0.0849052i
$826$	−10.0749	−	4.25975i	−0.350552	−	0.148216i
$827$	6.23299	+	2.58179i	0.216742	+	0.0897776i	0.488413	−	0.872613i	$-0.337576\pi$
$827$	6.23299	+	2.58179i	0.216742	+	0.0897776i	−0.271670	+	0.962390i	$0.587576\pi$
$828$	−16.0481	+	0.112001i	−0.557710	+	0.00389232i
$829$	−6.91331	+	9.00960i	−0.240109	+	0.312916i	−0.897827	−	0.440348i	$-0.854855\pi$
$829$	−6.91331	+	9.00960i	−0.240109	+	0.312916i	0.657718	+	0.753264i	$0.271522\pi$
$830$	63.6356	+	63.1930i	2.20882	+	2.19346i
$831$	−7.44448	+	12.8942i	−0.258246	+	0.447295i
$832$	−12.9947	−	29.6033i	−0.450510	−	1.02631i
$833$	−36.9663	−	0.798749i	−1.28081	−	0.0276750i
$834$	9.44742	−	2.56679i	0.327137	−	0.0888808i
$835$	−77.8916	−	10.2546i	−2.69555	−	0.354876i
$836$	0.910258	−	1.60234i	0.0314819	−	0.0554179i
$837$	4.07649	+	30.9640i	0.140904	+	1.07027i
$838$	18.8993	−	2.55526i	0.652865	−	0.0882700i
$839$	−17.6350	−	17.6350i	−0.608829	−	0.608829i	0.333811	−	0.942640i	$-0.391665\pi$
$839$	−17.6350	−	17.6350i	−0.608829	−	0.608829i	−0.942640	+	0.333811i	$0.891665\pi$
$840$	−8.32546	−	14.4312i	−0.287256	−	0.497925i
$841$	13.4790	−	13.4790i	0.464792	−	0.464792i
$842$	−5.16741	+	6.78318i	−0.178081	+	0.233764i
$843$	−5.31750	+	0.700062i	−0.183144	+	0.0241114i
$844$	18.3395	+	2.28435i	0.631272	+	0.0786306i
$845$	1.74262	−	13.2365i	0.0599479	−	0.455349i
$846$	20.1854	+	11.5603i	0.693988	+	0.397452i
$847$	28.2679	+	0.305364i	0.971298	+	0.0104924i
$848$	16.7718	+	21.2370i	0.575946	+	0.729282i
$849$	1.46151	+	0.843806i	0.0501591	+	0.0289593i
$850$	82.6110	−	0.288272i	2.83354	−	0.00988765i
$851$	11.0991	+	8.51667i	0.380474	+	0.291948i
$852$	14.7720	+	5.99832i	0.506080	+	0.205499i
$853$	19.6280	−	47.3862i	0.672050	−	1.62247i	−0.106072	−	0.994358i	$-0.533827\pi$
$853$	19.6280	−	47.3862i	0.672050	−	1.62247i	0.778122	−	0.628114i	$-0.216173\pi$
$854$	7.33951	−	9.42158i	0.251153	−	0.322400i
$855$	12.5183	−	12.5183i	0.428118	−	0.428118i
$856$	17.4405	+	2.11060i	0.596105	+	0.0721387i
$857$	−1.98559	+	7.41031i	−0.0678263	+	0.253131i	−0.991511	−	0.130022i	$-0.958495\pi$
$857$	−1.98559	+	7.41031i	−0.0678263	+	0.253131i	0.923685	+	0.383153i	$0.125162\pi$
$858$	1.64903	+	0.676318i	0.0562969	+	0.0230891i
$859$	2.93678	−	2.25347i	0.100202	−	0.0768874i	−0.557446	−	0.830214i	$-0.688218\pi$
$859$	2.93678	−	2.25347i	0.100202	−	0.0768874i	0.657647	+	0.753326i	$0.271552\pi$
$860$	−6.58856	+	25.2936i	−0.224668	+	0.862505i
$861$	−0.415075	+	2.90958i	−0.0141457	+	0.0991582i
$862$	6.25222	+	23.0121i	0.212951	+	0.783795i
$863$	−5.72376	+	9.91385i	−0.194839	+	0.337471i	−0.946848	−	0.321682i	$-0.895752\pi$
$863$	−5.72376	+	9.91385i	−0.194839	+	0.337471i	0.752009	+	0.659153i	$0.229085\pi$
$864$	17.7715	+	2.02491i	0.604600	+	0.0688890i
$865$	−21.0936	−	36.5351i	−0.717202	−	1.24223i
$866$	−1.63823	−	0.432841i	−0.0556693	−	0.0147085i
$867$	−2.31761	−	5.59520i	−0.0787100	−	0.190023i
$868$	−13.7203	+	50.4327i	−0.465696	+	1.71180i
$869$	−4.00519	−	1.65900i	−0.135867	−	0.0562779i
$870$	−1.32988	−	9.83611i	−0.0450872	−	0.333475i
$871$	−6.41810	+	23.9527i	−0.217469	+	0.811605i
$872$	9.41262	−	1.33958i	0.318751	−	0.0453639i
$873$	−3.29322	−	12.2905i	−0.111459	−	0.415970i
$874$	−0.879450	+	6.86512i	−0.0297478	+	0.232216i
$875$	7.69662	+	63.7780i	0.260193	+	2.15609i
$876$	9.25482	−	1.28419i	0.312691	−	0.0433888i
$877$	−4.84668	+	36.8142i	−0.163661	+	1.24313i	0.690582	+	0.723254i	$0.257354\pi$
$877$	−4.84668	+	36.8142i	−0.163661	+	1.24313i	−0.854243	+	0.519874i	$0.825979\pi$
$878$	19.1768	−	0.0669178i	0.647187	−	0.00225837i
$879$	8.02031	−	4.63053i	0.270518	−	0.156184i
$880$	−8.72301	−	2.20730i	−0.294052	−	0.0744082i
$881$			34.4842i			1.16180i	0.813974	+	0.580902i	$0.197300\pi$
$881$			34.4842i			1.16180i	−0.813974	+	0.580902i	$0.802700\pi$
$882$	22.8284	+	13.7372i	0.768672	+	0.462557i
$883$	9.61471	−	3.98254i	0.323561	−	0.134023i	−0.214990	−	0.976616i	$-0.568972\pi$
$883$	9.61471	−	3.98254i	0.323561	−	0.134023i	0.538551	+	0.842593i	$0.318972\pi$
$884$	39.3279	−	16.6126i	1.32274	−	0.558743i
$885$	6.45291	−	0.849541i	0.216912	−	0.0285570i
$886$	−10.1690	−	24.3099i	−0.341635	−	0.816708i
$887$	−3.05918	−	11.4170i	−0.102717	−	0.383346i	0.895359	−	0.445345i	$-0.146919\pi$
$887$	−3.05918	−	11.4170i	−0.102717	−	0.383346i	−0.998076	+	0.0619991i	$0.980252\pi$
$888$	−5.26809	−	5.15893i	−0.176785	−	0.173122i
$889$	18.0473	+	5.04532i	0.605287	+	0.169214i
$890$	−8.04080	−	10.4036i	−0.269528	−	0.348730i
$891$	2.81338	−	2.15878i	0.0942517	−	0.0723218i
$892$	−29.6327	−	16.8338i	−0.992175	−	0.563637i
$893$	6.10704	−	7.95885i	0.204364	−	0.266333i
$894$	−4.25285	+	16.0963i	−0.142237	+	0.538342i
$895$	−13.0643			−0.436691
$896$	26.1245	+	14.6121i	0.872757	+	0.488155i
$897$	−6.69398			−0.223505
$898$	−4.32216	+	16.3587i	−0.144232	+	0.545895i
$899$	−18.9554	+	24.7031i	−0.632196	+	0.823894i
$900$	−51.7586	−	29.4031i	−1.72529	−	0.980104i
$901$	−28.3506	+	21.7542i	−0.944494	+	0.724736i
$902$	0.970676	+	1.25591i	0.0323200	+	0.0418173i
$903$	1.19059	+	4.64339i	0.0396203	+	0.154522i
$904$	24.8748	+	24.3593i	0.827322	+	0.810179i
$905$	5.50577	+	20.5478i	0.183018	+	0.683032i
$906$	−7.15505	−	17.1048i	−0.237711	−	0.568267i
$907$	24.2945	−	3.19843i	0.806685	−	0.106202i	0.284106	−	0.958793i	$-0.408303\pi$
$907$	24.2945	−	3.19843i	0.806685	−	0.106202i	0.522579	+	0.852591i	$0.324970\pi$
$908$	−26.0320	+	10.9963i	−0.863903	+	0.364925i
$909$	−29.6737	+	12.2912i	−0.984214	+	0.407675i
$910$	29.9130	+	52.6970i	0.991605	+	1.74689i
$911$		−	37.4079i		−	1.23938i	−0.784848	−	0.619689i	$-0.787259\pi$
$911$		−	37.4079i		−	1.23938i	0.784848	−	0.619689i	$-0.212741\pi$
$912$	0.894844	−	3.53632i	0.0296312	−	0.117099i
$913$	7.69281	−	4.44145i	0.254595	−	0.146990i
$914$	−23.8192	+	0.0831174i	−0.787870	+	0.00274928i
$915$	−0.927559	+	7.04551i	−0.0306641	+	0.232917i
$916$	−4.34057	+	0.602294i	−0.143416	+	0.0199003i
$917$	−2.55328	−	1.09006i	−0.0843167	−	0.0359970i
$918$	−3.00126	+	23.4283i	−0.0990564	+	0.773249i
$919$	13.6226	+	50.8402i	0.449367	+	1.67706i	0.704140	+	0.710061i	$0.251333\pi$
$919$	13.6226	+	50.8402i	0.449367	+	1.67706i	−0.254773	+	0.967001i	$0.582001\pi$
$920$	33.4568	−	4.76149i	1.10304	−	0.156982i
$921$	2.43990	−	9.10582i	0.0803973	−	0.300047i
$922$	−4.18570	−	30.9584i	−0.137849	−	1.01956i
$923$	−53.5727	−	22.1905i	−1.76337	−	0.730410i
$924$	−1.59560	+	0.421008i	−0.0524914	+	0.0138502i
$925$	19.8584	+	47.9424i	0.652940	+	1.57634i
$926$	−27.3288	−	7.22062i	−0.898080	−	0.237284i
$927$	3.33903	+	5.78337i	0.109668	+	0.189951i
$928$	11.1012	+	13.9562i	0.364413	+	0.458136i
$929$	11.0836	−	19.1973i	0.363640	−	0.629843i	−0.624917	−	0.780691i	$-0.714867\pi$
$929$	11.0836	−	19.1973i	0.363640	−	0.629843i	0.988557	+	0.150849i	$0.0482006\pi$
$930$	−8.15382	−	30.0112i	−0.267374	−	0.984105i
$931$	7.19014	−	8.96263i	0.235647	−	0.293738i
$932$	8.56099	−	32.8658i	0.280425	−	1.07656i
$933$	−5.98318	+	4.59106i	−0.195881	+	0.150304i
$934$	−1.00344	−	0.411541i	−0.0328335	−	0.0134660i
$935$	3.07531	−	11.4772i	0.100573	−	0.375345i
$936$	−30.5401	−	3.69587i	−0.998236	−	0.120803i
$937$	−9.92355	+	9.92355i	−0.324188	+	0.324188i	−0.850371	−	0.526183i	$-0.823623\pi$
$937$	−9.92355	+	9.92355i	−0.324188	+	0.324188i	0.526183	+	0.850371i	$0.323623\pi$
$938$	−8.63084	−	21.2754i	−0.281807	−	0.694667i
$939$	2.22023	−	5.36012i	0.0724546	−	0.174921i
$940$	−45.3836	−	18.4285i	−1.48025	−	0.601071i
$941$	29.9040	+	22.9461i	0.974842	+	0.748023i	0.967740	−	0.251952i	$-0.0810725\pi$
$941$	29.9040	+	22.9461i	0.974842	+	0.748023i	0.00710244	+	0.999975i	$0.497739\pi$
$942$	−5.07749	+	0.0177180i	−0.165434	+	0.000577282i
$943$	−5.16281	−	2.98075i	−0.168124	−	0.0970665i
$944$	−9.17697	+	7.24746i	−0.298685	+	0.235885i
$945$	−33.5223	−	0.362124i	−1.09048	−	0.0117799i
$946$	2.24656	+	1.28662i	0.0730420	+	0.0418317i
$947$	−6.32155	+	48.0169i	−0.205423	+	1.56034i	0.509088	+	0.860715i	$0.329983\pi$
$947$	−6.32155	+	48.0169i	−0.205423	+	1.56034i	−0.714510	+	0.699625i	$0.753350\pi$
$948$	−8.51543	−	1.06067i	−0.276568	−	0.0344490i
$949$	−33.6919	+	4.43562i	−1.09369	+	0.143986i
$950$	−15.5571	+	20.4216i	−0.504740	+	0.662564i
$951$	8.49868	−	8.49868i	0.275589	−	0.275589i
$952$	−19.7754	+	34.2255i	−0.640923	+	1.10926i
$953$	−5.16385	−	5.16385i	−0.167274	−	0.167274i	0.618506	−	0.785780i	$-0.287738\pi$
$953$	−5.16385	−	5.16385i	−0.167274	−	0.167274i	−0.785780	+	0.618506i	$0.787738\pi$
$954$	25.5174	−	3.45006i	0.826157	−	0.111700i
$955$	−2.31699	−	17.5993i	−0.0749760	−	0.569499i
$956$	−1.93213	+	3.40114i	−0.0624895	+	0.110001i
$957$	−0.974709	−	0.128323i	−0.0315079	−	0.00414809i
$958$	−43.3053	+	11.7657i	−1.39913	+	0.380134i
$959$	40.6487	+	24.0577i	1.31261	+	0.776863i
$960$	−17.8070	+	0.372879i	−0.574717	+	0.0120346i
$961$	−33.2805	+	57.6434i	−1.07356	+	1.85947i
$962$	19.0288	+	18.8965i	0.613514	+	0.609247i
$963$	10.1763	−	13.2620i	0.327925	−	0.427361i
$964$	10.0769	−	0.0703279i	0.324556	−	0.00226511i
$965$	48.0746	+	19.9132i	1.54758	+	0.641028i
$966$	4.94447	−	3.73690i	0.159086	−	0.120233i
$967$	−11.0009	−	11.0009i	−0.353766	−	0.353766i	0.507742	−	0.861509i	$-0.330480\pi$
$967$	−11.0009	−	11.0009i	−0.353766	−	0.353766i	−0.861509	+	0.507742i	$0.830480\pi$
$968$	14.8359	−	26.3293i	0.476845	−	0.846256i
$969$	4.65288	+	1.24674i	0.149472	+	0.0400509i
$970$	10.3398	+	24.7181i	0.331990	+	0.793649i
$971$	−3.22448	−	4.20223i	−0.103479	−	0.134856i	0.738743	−	0.673987i	$-0.235420\pi$
$971$	−3.22448	−	4.20223i	−0.103479	−	0.134856i	−0.842222	+	0.539131i	$0.818753\pi$
$972$	15.6780	−	20.7299i	0.502872	−	0.664913i
$973$	20.3502	−	25.9360i	0.652399	−	0.831470i
$974$	−7.54490	−	4.32102i	−0.241754	−	0.138454i
$975$	−21.5029	−	12.4147i	−0.688643	−	0.397588i
$976$	−5.05010	−	11.7264i	−0.161650	−	0.375352i
$977$	−8.12803	+	4.69272i	−0.260039	+	0.150133i	−0.624352	−	0.781143i	$-0.714637\pi$
$977$	−8.12803	+	4.69272i	−0.260039	+	0.150133i	0.364314	+	0.931276i	$0.381304\pi$
$978$	−9.06206	−	15.5702i	−0.289773	−	0.497881i
$979$	−1.20323	+	0.498395i	−0.0384555	+	0.0159288i
$980$	−51.5130	−	22.2255i	−1.64552	−	0.709967i
$981$	3.46201	−	8.35804i	0.110534	−	0.266852i
$982$	−1.86397	−	1.41997i	−0.0594818	−	0.0453131i
$983$	−33.0325	−	8.85104i	−1.05357	−	0.282304i	−0.309846	−	0.950787i	$-0.600278\pi$
$983$	−33.0325	−	8.85104i	−1.05357	−	0.282304i	−0.743728	+	0.668482i	$0.766944\pi$
$984$	2.51257	+	1.88651i	0.0800979	+	0.0601397i
$985$	−11.2631	+	3.01794i	−0.358872	+	0.0961595i
$986$	−18.6325	+	14.4008i	−0.593379	+	0.458615i
$987$	−8.91858	+	1.07628i	−0.283882	+	0.0342584i
$988$	−3.34426	+	12.8387i	−0.106395	+	0.408453i
$989$	−9.64007	−	1.26914i	−0.306537	−	0.0403563i
$990$	−6.03298	+	6.07524i	−0.191741	+	0.193084i
$991$	−20.5345	−	35.5667i	−0.652299	−	1.12981i	−0.982564	−	0.185926i	$-0.940471\pi$
$991$	−20.5345	−	35.5667i	−0.652299	−	1.12981i	0.330265	−	0.943888i	$-0.392862\pi$
$992$	40.1925	+	38.8139i	1.27611	+	1.23234i
$993$	−5.42265			−0.172083
$994$	51.9590	−	13.5159i	1.64804	−	0.428699i
$995$	29.9213	+	72.2364i	0.948570	+	2.29005i
$996$	12.3461	−	12.5196i	0.391201	−	0.396699i
$997$	−7.49250	−	56.9112i	−0.237290	−	1.80240i	−0.531931	−	0.846788i	$-0.678533\pi$
$997$	−7.49250	−	56.9112i	−0.237290	−	1.80240i	0.294641	−	0.955608i	$-0.404800\pi$
$998$	1.34196	+	0.550382i	0.0424791	+	0.0174220i
$999$	−14.3312	+	3.84003i	−0.453419	+	0.121493i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.37.18	✓	240
4.3	odd	2		896.2.bh.a.625.14		240
7.4	even	3	inner	224.2.bd.a.165.23	yes	240
28.11	odd	6		896.2.bh.a.753.17		240
32.13	even	8	inner	224.2.bd.a.205.23	yes	240
32.19	odd	8		896.2.bh.a.401.17		240
224.109	even	24	inner	224.2.bd.a.109.18	yes	240
224.179	odd	24		896.2.bh.a.529.14		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.18	✓	240	1.1	even	1	trivial
224.2.bd.a.109.18	yes	240	224.109	even	24	inner
224.2.bd.a.165.23	yes	240	7.4	even	3	inner
224.2.bd.a.205.23	yes	240	32.13	even	8	inner
896.2.bh.a.401.17		240	32.19	odd	8
896.2.bh.a.529.14		240	224.179	odd	24
896.2.bh.a.625.14		240	4.3	odd	2
896.2.bh.a.753.17		240	28.11	odd	6

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)

\(f(q)\)	\(=\)	\(q+(0.361256 - 1.36729i) q^{2} +(0.338207 - 0.440760i) q^{3} +(-1.73899 - 0.987888i) q^{4} +(3.17926 - 2.43953i) q^{5} +(-0.480469 - 0.621656i) q^{6} +(-2.54805 - 0.712336i) q^{7} +(-1.97895 + 2.02083i) q^{8} +(0.696572 + 2.59964i) q^{9} +O(q^{10})\)	\(q+(0.361256 - 1.36729i) q^{2} +(0.338207 - 0.440760i) q^{3} +(-1.73899 - 0.987888i) q^{4} +(3.17926 - 2.43953i) q^{5} +(-0.480469 - 0.621656i) q^{6} +(-2.54805 - 0.712336i) q^{7} +(-1.97895 + 2.02083i) q^{8} +(0.696572 + 2.59964i) q^{9} +(-2.18703 - 5.22828i) q^{10} +(-0.556535 + 0.0732692i) q^{11} +(-1.02356 + 0.432366i) q^{12} +(3.73361 - 1.54651i) q^{13} +(-1.89447 + 3.22660i) q^{14} -2.22636i q^{15} +(2.04816 + 3.43585i) q^{16} +(-4.57446 + 2.64107i) q^{17} +(3.80612 - 0.0132815i) q^{18} +(0.214255 - 1.62743i) q^{19} +(-7.93868 + 1.10156i) q^{20} +(-1.17574 + 0.882164i) q^{21} +(-0.100871 + 0.787416i) q^{22} +(-0.771669 - 2.87991i) q^{23} +(0.221404 + 1.55570i) q^{24} +(2.86228 - 10.6822i) q^{25} +(-0.765746 - 5.66363i) q^{26} +(2.92123 + 1.21001i) q^{27} +(3.72733 + 3.75593i) q^{28} +(1.20639 + 2.91247i) q^{29} +(-3.04409 - 0.804287i) q^{30} +(4.93865 + 8.55399i) q^{31} +(5.43773 - 1.55921i) q^{32} +(-0.155930 + 0.270079i) q^{33} +(1.95856 + 7.20874i) q^{34} +(-9.83869 + 3.95136i) q^{35} +(1.35682 - 5.20888i) q^{36} +(-3.72267 + 2.85651i) q^{37} +(-2.14777 - 0.880868i) q^{38} +(0.581093 - 2.16867i) q^{39} +(-1.36174 + 11.2525i) q^{40} +(1.41386 - 1.41386i) q^{41} +(0.781434 + 1.92627i) q^{42} +(1.24801 - 3.01295i) q^{43} +(1.04019 + 0.422380i) q^{44} +(8.55649 + 6.56563i) q^{45} +(-4.21645 + 0.0147133i) q^{46} +(5.29275 + 3.05577i) q^{47} +(2.20709 + 0.259284i) q^{48} +(5.98515 + 3.63014i) q^{49} +(-13.5717 - 7.77259i) q^{50} +(-0.383039 + 2.90947i) q^{51} +(-8.02048 - 0.999023i) q^{52} +(6.70740 - 0.883046i) q^{53} +(2.70976 - 3.55706i) q^{54} +(-1.59063 + 1.59063i) q^{55} +(6.48199 - 3.73950i) q^{56} +(-0.644843 - 0.644843i) q^{57} +(4.41803 - 0.597335i) q^{58} +(0.381583 + 2.89841i) q^{59} +(-2.19939 + 3.87161i) q^{60} +(-3.16459 - 0.416626i) q^{61} +(13.4799 - 3.66240i) q^{62} +(0.0769160 - 7.12022i) q^{63} +(-0.167484 - 7.99825i) q^{64} +(8.09735 - 14.0250i) q^{65} +(0.312946 + 0.310770i) q^{66} +(-3.73546 + 4.86814i) q^{67} +(10.5640 - 0.0737273i) q^{68} +(-1.53033 - 0.633885i) q^{69} +(1.84838 + 14.8798i) q^{70} +(-10.1461 - 10.1461i) q^{71} +(-6.63191 - 3.73692i) q^{72} +(-8.12245 - 2.17640i) q^{73} +(2.56085 + 6.12192i) q^{74} +(-3.74024 - 4.87437i) q^{75} +(-1.98030 + 2.61842i) q^{76} +(1.47027 + 0.209746i) q^{77} +(-2.75528 - 1.57797i) q^{78} +(6.68828 + 3.86148i) q^{79} +(14.8935 + 5.92692i) q^{80} +(-5.47101 + 3.15869i) q^{81} +(-1.42239 - 2.44392i) q^{82} +(-14.6200 + 6.05578i) q^{83} +(2.91608 - 0.372573i) q^{84} +(-8.10044 + 19.5562i) q^{85} +(-3.66874 - 2.79484i) q^{86} +(1.69171 + 0.453293i) q^{87} +(0.953293 - 1.26966i) q^{88} +(2.24106 - 0.600491i) q^{89} +(12.0682 - 9.32737i) q^{90} +(-10.6151 + 1.28101i) q^{91} +(-1.50310 + 5.77045i) q^{92} +(5.44054 + 0.716261i) q^{93} +(6.09018 - 6.13283i) q^{94} +(-3.28899 - 5.69669i) q^{95} +(1.15184 - 2.92407i) q^{96} -4.72776 q^{97} +(7.12565 - 6.87206i) q^{98} +(-0.578140 - 1.39575i) 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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