LMFDB - Embedded newform 224.2.bd.a.109.20

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			109.20
Character	$\chi$	$=$	224.109
Dual form			224.2.bd.a.37.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.699836 - 1.22891i) q^{2} +(0.666690 + 0.868847i) q^{3} +(-1.02046 - 1.72008i) q^{4} +(-0.367682 - 0.282133i) q^{5} +(1.53431 - 0.211254i) q^{6} +(1.90974 - 1.83109i) q^{7} +(-2.82798 + 0.0502881i) q^{8} +(0.466037 - 1.73928i) q^{9} +O(q^{10})$	\(q+(0.699836 - 1.22891i) q^{2} +(0.666690 + 0.868847i) q^{3} +(-1.02046 - 1.72008i) q^{4} +(-0.367682 - 0.282133i) q^{5} +(1.53431 - 0.211254i) q^{6} +(1.90974 - 1.83109i) q^{7} +(-2.82798 + 0.0502881i) q^{8} +(0.466037 - 1.73928i) q^{9} +(-0.604034 + 0.254404i) q^{10} +(-0.629214 - 0.0828376i) q^{11} +(0.814152 - 2.03338i) q^{12} +(5.18123 + 2.14613i) q^{13} +(-0.913752 - 3.62837i) q^{14} -0.507554i q^{15} +(-1.91732 + 3.51054i) q^{16} +(-2.73539 - 1.57928i) q^{17} +(-1.81127 - 1.78993i) q^{18} +(0.304092 + 2.30981i) q^{19} +(-0.110084 + 0.920347i) q^{20} +(2.86414 + 0.438501i) q^{21} +(-0.542147 + 0.715278i) q^{22} +(-1.86331 + 6.95396i) q^{23} +(-1.92908 - 2.42355i) q^{24} +(-1.23850 - 4.62216i) q^{25} +(6.26342 - 4.86534i) q^{26} +(4.85725 - 2.01194i) q^{27} +(-5.09843 - 1.41634i) q^{28} +(-2.36952 + 5.72053i) q^{29} +(-0.623741 - 0.355205i) q^{30} +(-4.76239 + 8.24871i) q^{31} +(2.97234 + 4.81302i) q^{32} +(-0.347517 - 0.601918i) q^{33} +(-3.85512 + 2.25632i) q^{34} +(-1.21879 + 0.134461i) q^{35} +(-3.46726 + 0.973242i) q^{36} +(-6.27791 - 4.81721i) q^{37} +(3.05137 + 1.24278i) q^{38} +(1.58961 + 5.93250i) q^{39} +(1.05399 + 0.779375i) q^{40} +(-0.188847 - 0.188847i) q^{41} +(2.54331 - 3.21291i) q^{42} +(2.27999 + 5.50439i) q^{43} +(0.499601 + 1.16683i) q^{44} +(-0.662060 + 0.508017i) q^{45} +(7.24181 + 7.15647i) q^{46} +(5.81940 - 3.35983i) q^{47} +(-4.32838 + 0.674581i) q^{48} +(0.294206 - 6.99381i) q^{49} +(-6.54699 - 1.71274i) q^{50} +(-0.451505 - 3.42952i) q^{51} +(-1.59572 - 11.1021i) q^{52} +(-1.46042 - 0.192268i) q^{53} +(0.926775 - 7.37716i) q^{54} +(0.207980 + 0.207980i) q^{55} +(-5.30862 + 5.27433i) q^{56} +(-1.80413 + 1.80413i) q^{57} +(5.37177 + 6.91537i) q^{58} +(0.0666577 - 0.506316i) q^{59} +(-0.873032 + 0.517939i) q^{60} +(12.9961 - 1.71097i) q^{61} +(6.80406 + 11.6253i) q^{62} +(-2.29476 - 4.17492i) q^{63} +(7.99494 - 0.284428i) q^{64} +(-1.29955 - 2.25089i) q^{65} +(-0.982910 + 0.00582560i) q^{66} +(1.35564 + 1.76670i) q^{67} +(0.0748790 + 6.31666i) q^{68} +(-7.28417 + 3.01720i) q^{69} +(-0.687711 + 1.59189i) q^{70} +(-6.37378 + 6.37378i) q^{71} +(-1.23048 + 4.94207i) q^{72} +(-1.07263 + 0.287410i) q^{73} +(-10.3134 + 4.34376i) q^{74} +(3.19025 - 4.15761i) q^{75} +(3.66273 - 2.88013i) q^{76} +(-1.35332 + 0.993951i) q^{77} +(8.40299 + 2.19828i) q^{78} +(5.13736 - 2.96606i) q^{79} +(1.69540 - 0.749824i) q^{80} +(0.308165 + 0.177919i) q^{81} +(-0.364239 + 0.0999150i) q^{82} +(-0.509916 - 0.211214i) q^{83} +(-2.16849 - 5.37401i) q^{84} +(0.560188 + 1.35241i) q^{85} +(8.36004 + 1.05025i) q^{86} +(-6.55000 + 1.75507i) q^{87} +(1.78357 + 0.202621i) q^{88} +(-6.57980 - 1.76305i) q^{89} +(0.160976 + 1.16914i) q^{90} +(13.8246 - 5.38875i) q^{91} +(13.8628 - 3.89121i) q^{92} +(-10.3419 + 1.36154i) q^{93} +(-0.0563225 - 9.50287i) q^{94} +(0.539863 - 0.935070i) q^{95} +(-2.20015 + 5.79130i) q^{96} +6.01128 q^{97} +(-8.38890 - 5.25607i) q^{98} +(-0.437315 + 1.05577i) 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 $

$2$	0.699836	−	1.22891i	0.494858	−	0.868974i
$2$	0.699836	−	1.22891i	0.494858	−	0.868974i
$3$	0.666690	+	0.868847i	0.384913	+	0.501629i	0.945120	−	0.326724i	$-0.105945\pi$
$3$	0.666690	+	0.868847i	0.384913	+	0.501629i	−0.560206	+	0.828353i	$0.689278\pi$
$4$	−1.02046	−	1.72008i	−0.510230	−	0.860038i
$5$	−0.367682	−	0.282133i	−0.164433	−	0.126174i	0.523267	−	0.852169i	$-0.324713\pi$
$5$	−0.367682	−	0.282133i	−0.164433	−	0.126174i	−0.687700	+	0.725995i	$0.741380\pi$
$6$	1.53431	−	0.211254i	0.626380	−	0.0862443i
$7$	1.90974	−	1.83109i	0.721813	−	0.692088i
$7$	1.90974	−	1.83109i	0.721813	−	0.692088i
$8$	−2.82798	+	0.0502881i	−0.999842	+	0.0177795i
$9$	0.466037	−	1.73928i	0.155346	−	0.579759i
$10$	−0.604034	+	0.254404i	−0.191012	+	0.0804495i
$11$	−0.629214	−	0.0828376i	−0.189715	−	0.0249765i	0.0350698	−	0.999385i	$-0.488835\pi$
$11$	−0.629214	−	0.0828376i	−0.189715	−	0.0249765i	−0.224785	+	0.974408i	$0.572168\pi$
$12$	0.814152	−	2.03338i	0.235025	−	0.586986i
$13$	5.18123	+	2.14613i	1.43701	+	0.595231i	0.959072	−	0.283161i	$-0.0913831\pi$
$13$	5.18123	+	2.14613i	1.43701	+	0.595231i	0.477942	+	0.878392i	$0.341383\pi$
$14$	−0.913752	−	3.62837i	−0.244210	−	0.969722i
$15$		−	0.507554i		−	0.131050i
$16$	−1.91732	+	3.51054i	−0.479330	+	0.877635i
$17$	−2.73539	−	1.57928i	−0.663429	−	0.383031i	0.130153	−	0.991494i	$-0.458453\pi$
$17$	−2.73539	−	1.57928i	−0.663429	−	0.383031i	−0.793582	+	0.608463i	$0.791786\pi$
$18$	−1.81127	−	1.78993i	−0.426921	−	0.421890i
$19$	0.304092	+	2.30981i	0.0697635	+	0.529907i	0.990268	+	0.139174i	$0.0444448\pi$
$19$	0.304092	+	2.30981i	0.0697635	+	0.529907i	−0.920504	+	0.390732i	$0.872222\pi$
$20$	−0.110084	+	0.920347i	−0.0246156	+	0.205796i
$21$	2.86414	+	0.438501i	0.625007	+	0.0956887i
$22$	−0.542147	+	0.715278i	−0.115586	+	0.152498i
$23$	−1.86331	+	6.95396i	−0.388527	+	1.45000i	0.444006	+	0.896024i	$0.353557\pi$
$23$	−1.86331	+	6.95396i	−0.388527	+	1.45000i	−0.832532	+	0.553977i	$0.813110\pi$
$24$	−1.92908	−	2.42355i	−0.393771	−	0.494706i
$25$	−1.23850	−	4.62216i	−0.247701	−	0.924432i
$26$	6.26342	−	4.86534i	1.22836	−	0.954172i
$27$	4.85725	−	2.01194i	0.934777	−	0.387198i
$28$	−5.09843	−	1.41634i	−0.963513	−	0.267663i
$29$	−2.36952	+	5.72053i	−0.440009	+	1.06228i	0.535935	+	0.844259i	$0.319959\pi$
$29$	−2.36952	+	5.72053i	−0.440009	+	1.06228i	−0.975945	+	0.218018i	$0.930041\pi$
$30$	−0.623741	−	0.355205i	−0.113879	−	0.0648512i
$31$	−4.76239	+	8.24871i	−0.855351	+	1.48151i	0.0209674	+	0.999780i	$0.493325\pi$
$31$	−4.76239	+	8.24871i	−0.855351	+	1.48151i	−0.876319	+	0.481732i	$0.840008\pi$
$32$	2.97234	+	4.81302i	0.525441	+	0.850830i
$33$	−0.347517	−	0.601918i	−0.0604950	−	0.104780i
$34$	−3.85512	+	2.25632i	−0.661147	+	0.386956i
$35$	−1.21879	+	0.134461i	−0.206013	+	0.0227280i
$36$	−3.46726	+	0.973242i	−0.577876	+	0.162207i
$37$	−6.27791	−	4.81721i	−1.03208	−	0.791944i	−0.0536595	−	0.998559i	$-0.517089\pi$
$37$	−6.27791	−	4.81721i	−1.03208	−	0.791944i	−0.978422	+	0.206615i	$0.933755\pi$
$38$	3.05137	+	1.24278i	0.494998	+	0.201606i
$39$	1.58961	+	5.93250i	0.254541	+	0.949960i
$40$	1.05399	+	0.779375i	0.166650	+	0.123230i
$41$	−0.188847	−	0.188847i	−0.0294930	−	0.0294930i	0.692207	−	0.721699i	$-0.256639\pi$
$41$	−0.188847	−	0.188847i	−0.0294930	−	0.0294930i	−0.721699	+	0.692207i	$0.756639\pi$
$42$	2.54331	−	3.21291i	0.392441	−	0.495762i
$43$	2.27999	+	5.50439i	0.347696	+	0.839411i	0.996891	+	0.0787898i	$0.0251056\pi$
$43$	2.27999	+	5.50439i	0.347696	+	0.839411i	−0.649196	+	0.760621i	$0.724894\pi$
$44$	0.499601	+	1.16683i	0.0753177	+	0.175906i
$45$	−0.662060	+	0.508017i	−0.0986941	+	0.0757306i
$46$	7.24181	+	7.15647i	1.06775	+	1.05516i
$47$	5.81940	−	3.35983i	0.848846	−	0.490082i	−0.0114150	−	0.999935i	$-0.503634\pi$
$47$	5.81940	−	3.35983i	0.848846	−	0.490082i	0.860261	+	0.509853i	$0.170300\pi$
$48$	−4.32838	+	0.674581i	−0.624747	+	0.0973674i
$49$	0.294206	−	6.99381i	0.0420294	−	0.999116i
$50$	−6.54699	−	1.71274i	−0.925884	−	0.242217i
$51$	−0.451505	−	3.42952i	−0.0632233	−	0.480229i
$52$	−1.59572	−	11.1021i	−0.221287	−	1.53959i
$53$	−1.46042	−	0.192268i	−0.200604	−	0.0264100i	0.0295545	−	0.999563i	$-0.490591\pi$
$53$	−1.46042	−	0.192268i	−0.200604	−	0.0264100i	−0.230159	+	0.973153i	$0.573924\pi$
$54$	0.926775	−	7.37716i	0.126118	−	1.00390i
$55$	0.207980	+	0.207980i	0.0280440	+	0.0280440i
$56$	−5.30862	+	5.27433i	−0.709394	+	0.704812i
$57$	−1.80413	+	1.80413i	−0.238964	+	0.238964i
$58$	5.37177	+	6.91537i	0.705348	+	0.908033i
$59$	0.0666577	−	0.506316i	0.00867810	−	0.0659167i	−0.986558	−	0.163412i	$-0.947750\pi$
$59$	0.0666577	−	0.506316i	0.00867810	−	0.0659167i	0.995236	+	0.0974957i	$0.0310832\pi$
$60$	−0.873032	+	0.517939i	−0.112708	+	0.0668657i
$61$	12.9961	−	1.71097i	1.66398	−	0.219067i	0.761000	−	0.648752i	$-0.224709\pi$
$61$	12.9961	−	1.71097i	1.66398	−	0.219067i	0.902979	+	0.429685i	$0.141375\pi$
$62$	6.80406	+	11.6253i	0.864117	+	1.47642i
$63$	−2.29476	−	4.17492i	−0.289113	−	0.525990i
$64$	7.99494	−	0.284428i	0.999368	−	0.0355535i
$65$	−1.29955	−	2.25089i	−0.161190	−	0.279188i
$66$	−0.982910	+	0.00582560i	−0.120988	+	0.000717082i
$67$	1.35564	+	1.76670i	0.165617	+	0.215837i	0.868788	−	0.495185i	$-0.164900\pi$
$67$	1.35564	+	1.76670i	0.165617	+	0.215837i	−0.703171	+	0.711021i	$0.748233\pi$
$68$	0.0748790	+	6.31666i	0.00908042	+	0.766008i
$69$	−7.28417	+	3.01720i	−0.876911	+	0.363229i
$70$	−0.687711	+	1.59189i	−0.0821972	+	0.190267i
$71$	−6.37378	+	6.37378i	−0.756429	+	0.756429i	−0.975671	−	0.219242i	$-0.929642\pi$
$71$	−6.37378	+	6.37378i	−0.756429	+	0.756429i	0.219242	+	0.975671i	$0.429642\pi$
$72$	−1.23048	+	4.94207i	−0.145013	+	0.582429i
$73$	−1.07263	+	0.287410i	−0.125542	+	0.0336388i	−0.321043	−	0.947065i	$-0.604033\pi$
$73$	−1.07263	+	0.287410i	−0.125542	+	0.0336388i	0.195501	+	0.980703i	$0.437367\pi$
$74$	−10.3134	+	4.34376i	−1.19891	+	0.504952i
$75$	3.19025	−	4.15761i	0.368378	−	0.480080i
$76$	3.66273	−	2.88013i	0.420144	−	0.330374i
$77$	−1.35332	+	0.993951i	−0.154225	+	0.113271i
$78$	8.40299	+	2.19828i	0.951452	+	0.248906i
$79$	5.13736	−	2.96606i	0.577998	−	0.333708i	−0.182339	−	0.983236i	$-0.558367\pi$
$79$	5.13736	−	2.96606i	0.577998	−	0.333708i	0.760338	+	0.649528i	$0.225034\pi$
$80$	1.69540	−	0.749824i	0.189552	−	0.0838329i
$81$	0.308165	+	0.177919i	0.0342405	+	0.0197688i
$82$	−0.364239	+	0.0999150i	−0.0402234	+	0.0110338i
$83$	−0.509916	−	0.211214i	−0.0559706	−	0.0231838i	0.354523	−	0.935047i	$-0.384643\pi$
$83$	−0.509916	−	0.211214i	−0.0559706	−	0.0231838i	−0.410493	+	0.911864i	$0.634643\pi$
$84$	−2.16849	−	5.37401i	−0.236601	−	0.586353i
$85$	0.560188	+	1.35241i	0.0607610	+	0.146690i
$86$	8.36004	+	1.05025i	0.901486	+	0.113252i
$87$	−6.55000	+	1.75507i	−0.702234	+	0.188163i
$88$	1.78357	+	0.202621i	0.190129	+	0.0215995i
$89$	−6.57980	−	1.76305i	−0.697458	−	0.186883i	−0.107366	−	0.994220i	$-0.534242\pi$
$89$	−6.57980	−	1.76305i	−0.697458	−	0.186883i	−0.590092	+	0.807336i	$0.700908\pi$
$90$	0.160976	+	1.16914i	0.0169683	+	0.123239i
$91$	13.8246	−	5.38875i	1.44921	−	0.564894i
$92$	13.8628	−	3.89121i	1.44529	−	0.405687i
$93$	−10.3419	+	1.36154i	−1.07241	+	0.141185i
$94$	−0.0563225	−	9.50287i	−0.00580922	−	0.980146i
$95$	0.539863	−	0.935070i	0.0553888	−	0.0959362i
$96$	−2.20015	+	5.79130i	−0.224552	+	0.591072i
$97$	6.01128			0.610353			0.305177	−	0.952296i	$-0.401285\pi$
$97$	6.01128			0.610353			0.305177	+	0.952296i	$0.401285\pi$
$98$	−8.38890	−	5.25607i	−0.847407	−	0.530944i
$99$	−0.437315	+	1.05577i	−0.0439518	+	0.106109i
$100$	−6.68662	+	6.84705i	−0.668662	+	0.684705i
$101$	0.230723	−	1.75252i	0.0229578	−	0.174382i	−0.976125	−	0.217211i	$-0.930304\pi$
$101$	0.230723	−	1.75252i	0.0229578	−	0.174382i	0.999082	+	0.0428295i	$0.0136372\pi$
$102$	−4.53057	−	1.84524i	−0.448593	−	0.182706i
$103$	−11.5972	−	3.10746i	−1.14270	−	0.306187i	−0.362666	−	0.931919i	$-0.618134\pi$
$103$	−11.5972	−	3.10746i	−1.14270	−	0.306187i	−0.780038	+	0.625732i	$0.784800\pi$
$104$	−14.7603	−	5.80867i	−1.44737	−	0.569587i
$105$	−0.929379	−	0.969296i	−0.0906981	−	0.0945937i
$106$	−1.25833	+	1.66017i	−0.122220	+	0.161250i
$107$	0.907191	−	1.18227i	0.0877015	−	0.114295i	−0.747442	−	0.664327i	$-0.768718\pi$
$107$	0.907191	−	1.18227i	0.0877015	−	0.114295i	0.835143	+	0.550033i	$0.185385\pi$
$108$	−8.41731	−	6.30173i	−0.809956	−	0.606384i
$109$	4.62283	−	3.54722i	0.442787	−	0.339762i	−0.363184	−	0.931717i	$-0.618310\pi$
$109$	4.62283	−	3.54722i	0.442787	−	0.339762i	0.805971	+	0.591955i	$0.201644\pi$
$110$	0.401141	−	0.110038i	0.0382473	−	0.0104917i
$111$		−	8.66612i		−	0.822552i
$112$	2.76653	+	10.2150i	0.261413	+	0.965227i
$113$		−	19.8494i		−	1.86728i	−0.358216	−	0.933639i	$-0.616615\pi$
$113$		−	19.8494i		−	1.86728i	0.358216	−	0.933639i	$-0.383385\pi$
$114$	0.954529	+	3.47972i	0.0893999	+	0.325906i
$115$	2.64704	−	2.03115i	0.246838	−	0.189406i
$116$	12.2578	−	1.76182i	1.13810	−	0.163581i
$117$	6.14737	−	8.01140i	0.568324	−	0.740654i
$118$	−0.575569	−	0.436254i	−0.0529854	−	0.0401605i
$119$	−8.11568	+	1.99274i	−0.743963	+	0.182674i
$120$	0.0255240	+	1.43535i	0.00233001	+	0.131029i
$121$	−10.2361	−	2.74276i	−0.930558	−	0.249342i
$122$	6.99250	−	17.1685i	0.633071	−	1.55436i
$123$	0.0381768	−	0.289982i	0.00344229	−	0.0261468i
$124$	19.0482	−	0.225802i	1.71058	−	0.0202776i
$125$	−1.73547	+	4.18978i	−0.155225	+	0.374746i
$126$	−6.73658	−	0.101690i	−0.600142	−	0.00905927i
$127$	−12.2752			−1.08925			−0.544623	−	0.838681i	$-0.683327\pi$
$127$	−12.2752			−1.08925			−0.544623	+	0.838681i	$0.683327\pi$
$128$	5.24561	−	10.0242i	0.463651	−	0.886018i
$129$	−3.26242	+	5.65068i	−0.287240	+	0.497515i
$130$	−3.67562	+	0.0217850i	−0.322373	+	0.00191067i
$131$	−16.9895	+	2.23671i	−1.48438	+	0.195422i	−0.828733	−	0.559644i	$-0.810938\pi$
$131$	−16.9895	+	2.23671i	−1.48438	+	0.195422i	−0.655648	+	0.755067i	$0.727605\pi$
$132$	−0.680716	+	1.21199i	−0.0592487	+	0.105490i
$133$	4.81021	+	3.85431i	0.417098	+	0.334211i
$134$	3.11984	−	0.429561i	0.269513	−	0.0371084i
$135$	−2.35356	−	0.630634i	−0.202562	−	0.0542763i
$136$	7.81504	+	4.32861i	0.670134	+	0.371175i
$137$	−8.60428	+	2.30551i	−0.735113	+	0.196973i	−0.606905	−	0.794774i	$-0.707589\pi$
$137$	−8.60428	+	2.30551i	−0.735113	+	0.196973i	−0.128208	+	0.991747i	$0.540923\pi$
$138$	−1.38984	+	11.0632i	−0.118311	+	0.941760i
$139$	−4.47830	−	10.8116i	−0.379845	−	0.917026i	−0.991994	−	0.126284i	$-0.959695\pi$
$139$	−4.47830	−	10.8116i	−0.379845	−	0.917026i	0.612150	−	0.790742i	$-0.290305\pi$
$140$	1.47501	+	1.95920i	0.124661	+	0.165582i
$141$	6.79891	+	2.81620i	0.572572	+	0.237167i
$142$	3.37223	+	12.2934i	0.282991	+	1.03164i
$143$	−3.08232	−	1.77958i	−0.257757	−	0.148816i
$144$	5.21225	+	4.97079i	0.434354	+	0.414233i
$145$	2.48518	−	1.43482i	0.206383	−	0.119155i
$146$	−0.397462	+	1.51931i	−0.0328942	+	0.125739i
$147$	6.27270	−	4.40708i	0.517363	−	0.363490i
$148$	−1.87961	+	15.7142i	−0.154503	+	1.29170i
$149$	6.34049	−	8.26309i	0.519434	−	0.676939i	−0.457812	−	0.889049i	$-0.651367\pi$
$149$	6.34049	−	8.26309i	0.519434	−	0.676939i	0.977246	+	0.212110i	$0.0680335\pi$
$150$	−2.87670	−	6.83019i	−0.234882	−	0.557683i
$151$	12.9876	−	3.48001i	1.05691	−	0.283199i	0.311807	−	0.950145i	$-0.399066\pi$
$151$	12.9876	−	3.48001i	1.05691	−	0.283199i	0.745106	+	0.666946i	$0.232399\pi$
$152$	−0.976122	−	6.51680i	−0.0791740	−	0.528582i
$153$	−4.02159	+	4.02159i	−0.325126	+	0.325126i
$154$	0.274380	+	2.35871i	0.0221102	+	0.190071i
$155$	4.07828	−	1.68928i	0.327575	−	0.135686i
$156$	8.58221	−	8.78812i	0.687127	−	0.703613i
$157$	10.3643	+	13.5070i	0.827159	+	1.07797i	0.995733	+	0.0922857i	$0.0294173\pi$
$157$	10.3643	+	13.5070i	0.827159	+	1.07797i	−0.168573	+	0.985689i	$0.553916\pi$
$158$	−0.0497215	−	8.38913i	−0.00395563	−	0.667403i
$159$	−0.806595	−	1.39706i	−0.0639671	−	0.110794i
$160$	0.265033	−	2.60826i	0.0209527	−	0.206201i
$161$	9.17491	+	16.6921i	0.723084	+	1.31552i
$162$	0.434312	−	0.254194i	0.0341228	−	0.0199714i
$163$	−1.16061	+	0.152798i	−0.0909063	+	0.0119680i	−0.175842	−	0.984418i	$-0.556265\pi$
$163$	−1.16061	+	0.152798i	−0.0909063	+	0.0119680i	0.0849358	+	0.996386i	$0.472931\pi$
$164$	−0.132120	+	0.517542i	−0.0103169	+	0.0404133i
$165$	−0.0420446	+	0.319360i	−0.00327317	+	0.0248622i
$166$	−0.616422	+	0.478828i	−0.0478436	+	0.0371643i
$167$	5.38648	−	5.38648i	0.416818	−	0.416818i	−0.467287	−	0.884106i	$-0.654769\pi$
$167$	5.38648	−	5.38648i	0.416818	−	0.416818i	0.884106	+	0.467287i	$0.154769\pi$
$168$	−8.12178	−	1.09604i	−0.626609	−	0.0845612i
$169$	13.0468	+	13.0468i	1.00360	+	1.00360i
$170$	2.05404	+	0.258044i	0.157538	+	0.0197911i
$171$	4.15911	+	0.547558i	0.318055	+	0.0418728i
$172$	7.14132	−	9.53877i	0.544521	−	0.727324i
$173$	3.00052	+	22.7912i	0.228125	+	1.73278i	0.596067	+	0.802935i	$0.296729\pi$
$173$	3.00052	+	22.7912i	0.228125	+	1.73278i	−0.367942	+	0.929849i	$0.619937\pi$
$174$	−2.42710	+	9.27765i	−0.183998	+	0.703337i
$175$	−10.8288	−	6.55930i	−0.818582	−	0.495837i
$176$	1.49721	−	2.05005i	0.112856	−	0.154529i
$177$	0.484351	−	0.279640i	0.0364060	−	0.0210190i
$178$	−6.77142	+	6.85217i	−0.507540	+	0.513592i
$179$	2.07819	−	1.59465i	0.155331	−	0.119190i	−0.528172	−	0.849138i	$-0.677122\pi$
$179$	2.07819	−	1.59465i	0.155331	−	0.119190i	0.683503	+	0.729948i	$0.260456\pi$
$180$	1.54943	+	0.620383i	0.115488	+	0.0462406i
$181$	0.833967	+	2.01338i	0.0619883	+	0.149653i	0.951839	−	0.306600i	$-0.0991913\pi$
$181$	0.833967	+	2.01338i	0.0619883	+	0.149653i	−0.889850	+	0.456253i	$0.849191\pi$
$182$	3.05261	−	20.7604i	0.226275	−	1.53887i
$183$	10.1509	+	10.1509i	0.750378	+	0.750378i
$184$	4.91970	−	19.7594i	0.362685	−	1.45668i
$185$	0.949185	+	3.54241i	0.0697854	+	0.260443i
$186$	−5.56442	+	13.6622i	−0.408003	+	1.00176i
$187$	1.59032	+	1.22030i	0.116296	+	0.0892369i
$188$	−11.7176	−	6.58123i	−0.854596	−	0.479986i
$189$	5.59203	−	12.7363i	0.406760	−	0.926432i
$190$	−0.771306	−	1.31784i	−0.0559564	−	0.0956062i
$191$	−6.62256	−	11.4706i	−0.479192	−	0.829984i	0.520524	−	0.853847i	$-0.325737\pi$
$191$	−6.62256	−	11.4706i	−0.479192	−	0.829984i	−0.999715	+	0.0238630i	$0.992403\pi$
$192$	5.57727	+	6.75675i	0.402505	+	0.487627i
$193$	6.06964	−	10.5129i	0.436902	−	0.756737i	−0.560547	−	0.828123i	$-0.689409\pi$
$193$	6.06964	−	10.5129i	0.436902	−	0.756737i	0.997449	+	0.0713860i	$0.0227422\pi$
$194$	4.20691	−	7.38735i	0.302038	−	0.530381i
$195$	1.08928	−	2.62975i	0.0780050	−	0.188321i
$196$	−12.3301	+	6.63085i	−0.880723	+	0.473632i
$197$	−24.0288	+	9.95306i	−1.71198	+	0.709126i	−0.712005	+	0.702174i	$0.752213\pi$
$197$	−24.0288	+	9.95306i	−1.71198	+	0.709126i	−0.999976	+	0.00695193i	$0.997787\pi$
$198$	0.991404	+	1.27629i	0.0704560	+	0.0907019i
$199$	3.60342	+	13.4481i	0.255440	+	0.953314i	0.967845	+	0.251546i	$0.0809390\pi$
$199$	3.60342	+	13.4481i	0.255440	+	0.953314i	−0.712406	+	0.701768i	$0.752394\pi$
$200$	3.73490	+	13.0091i	0.264098	+	0.919882i
$201$	−0.631202	+	2.35568i	−0.0445216	+	0.166157i
$202$	−1.99223	−	1.51001i	−0.140172	−	0.106244i
$203$	5.94965	+	15.2635i	0.417584	+	1.07129i
$204$	−5.43829	+	4.27631i	−0.380757	+	0.299402i
$205$	0.0161558	+	0.122716i	0.00112837	+	0.00857083i
$206$	−11.9349	+	12.0772i	−0.831545	+	0.841461i
$207$	11.2265	+	6.48161i	0.780294	+	0.450503i
$208$	−17.4682	+	14.0741i	−1.21120	+	0.975861i
$209$		−	1.47855i		−	0.102274i
$210$	−1.84159	+	0.463779i	−0.127082	+	0.0320038i
$211$	−17.8191	−	7.38092i	−1.22672	−	0.508124i	−0.327179	−	0.944962i	$-0.606098\pi$
$211$	−17.8191	−	7.38092i	−1.22672	−	0.508124i	−0.899540	+	0.436839i	$0.856098\pi$
$212$	1.15958	+	2.70823i	0.0796406	+	0.186002i
$213$	−9.78717	−	1.28851i	−0.670606	−	0.0882870i
$214$	−0.818029	−	1.94226i	−0.0559193	−	0.132770i
$215$	0.714654	−	2.66713i	0.0487390	−	0.181896i
$216$	−13.6350	+	5.93398i	−0.927746	+	0.403756i
$217$	6.00921	+	24.4733i	0.407932	+	1.66135i
$218$	−1.12401	−	8.16353i	−0.0761276	−	0.552904i
$219$	−0.964827	−	0.740337i	−0.0651969	−	0.0500274i
$220$	0.145506	−	0.569976i	0.00981000	−	0.0384278i
$221$	−10.7833	−	14.0531i	−0.725365	−	0.945314i
$222$	−10.6499	−	6.06486i	−0.714776	−	0.407047i
$223$	11.6359			0.779195			0.389597	−	0.920985i	$-0.372614\pi$
$223$	11.6359			0.779195			0.389597	+	0.920985i	$0.372614\pi$
$224$	14.4895	+	3.74899i	0.968119	+	0.250490i
$225$	−8.61640			−0.574426
$226$	−24.3932	−	13.8913i	−1.62261	−	0.924038i
$227$	6.17424	+	8.04643i	0.409799	+	0.534060i	0.951963	−	0.306212i	$-0.0990617\pi$
$227$	6.17424	+	8.04643i	0.409799	+	0.534060i	−0.542165	+	0.840272i	$0.682395\pi$
$228$	4.94430	+	1.26220i	0.327444	+	0.0835913i
$229$	11.9958	+	9.20473i	0.792707	+	0.608265i	0.923699	−	0.383118i	$-0.125150\pi$
$229$	11.9958	+	9.20473i	0.792707	+	0.608265i	−0.130992	+	0.991383i	$0.541816\pi$
$230$	−0.643612	−	4.67446i	−0.0424385	−	0.308225i
$231$	−1.76583	−	0.513169i	−0.116183	−	0.0337641i
$232$	6.41329	−	16.2967i	0.421053	−	1.06993i
$233$	−4.17950	+	15.5981i	−0.273808	+	1.02187i	0.682828	+	0.730579i	$0.260750\pi$
$233$	−4.17950	+	15.5981i	−0.273808	+	1.02187i	−0.956636	+	0.291286i	$0.905917\pi$
$234$	−5.54318	−	13.1612i	−0.362369	−	0.860378i
$235$	−3.08761	−	0.406491i	−0.201413	−	0.0265166i
$236$	−0.938923	+	0.402019i	−0.0611187	+	0.0261692i
$237$	6.00207	+	2.48614i	0.389877	+	0.161492i
$238$	−3.23073	+	11.3681i	−0.209417	+	0.736882i
$239$		−	4.50768i		−	0.291577i	−0.989316	−	0.145789i	$-0.953428\pi$
$239$		−	4.50768i		−	0.291577i	0.989316	−	0.145789i	$-0.0465720\pi$
$240$	1.78179	+	0.973145i	0.115014	+	0.0628162i
$241$	10.5989	+	6.11926i	0.682734	+	0.394176i	0.800884	−	0.598819i	$-0.204363\pi$
$241$	10.5989	+	6.11926i	0.682734	+	0.394176i	−0.118151	+	0.992996i	$0.537697\pi$
$242$	−10.5342	+	10.6598i	−0.677166	+	0.685241i
$243$	−2.00784	−	15.2510i	−0.128803	−	0.978354i
$244$	−16.2050	−	20.6083i	−1.03742	−	1.31931i
$245$	−2.08136	+	2.48850i	−0.132973	+	0.158984i
$246$	−0.329645	−	0.249855i	−0.0210174	−	0.0159302i
$247$	−3.38159	+	12.6203i	−0.215165	+	0.803008i
$248$	13.0531	−	23.5667i	0.828876	−	1.49649i
$249$	−0.156443	−	0.583853i	−0.00991418	−	0.0370002i
$250$	3.93435	+	5.06490i	0.248830	+	0.320332i
$251$	22.2806	−	9.22892i	1.40634	−	0.582524i	0.454949	−	0.890517i	$-0.349657\pi$
$251$	22.2806	−	9.22892i	1.40634	−	0.582524i	0.951389	+	0.307993i	$0.0996574\pi$
$252$	−4.83946	+	8.20751i	−0.304858	+	0.517024i
$253$	1.74847	−	4.22118i	0.109925	−	0.265383i
$254$	−8.59061	+	15.0852i	−0.539023	+	0.946527i
$255$	−0.801569	+	1.38836i	−0.0501962	+	0.0869424i
$256$	−8.64776	−	13.4617i	−0.540485	−	0.841354i
$257$	−0.744349	−	1.28925i	−0.0464312	−	0.0804212i	0.841876	−	0.539671i	$-0.181451\pi$
$257$	−0.744349	−	1.28925i	−0.0464312	−	0.0804212i	−0.888307	+	0.459250i	$0.848118\pi$
$258$	4.66104	+	7.96378i	0.290184	+	0.495804i
$259$	−20.8099	+	2.29582i	−1.29307	+	0.142655i
$260$	−2.54556	+	4.53227i	−0.157869	+	0.281079i
$261$	8.84530	+	6.78724i	0.547510	+	0.420119i
$262$	−9.14114	+	22.4440i	−0.564742	+	1.38659i
$263$	−4.53078	−	16.9091i	−0.279380	−	1.04266i	−0.952849	−	0.303445i	$-0.901863\pi$
$263$	−4.53078	−	16.9091i	−0.279380	−	1.04266i	0.673469	−	0.739216i	$-0.264804\pi$
$264$	1.01304	+	1.68474i	0.0623484	+	0.103688i
$265$	0.482725	+	0.482725i	0.0296536	+	0.0296536i
$266$	8.10297	−	3.21395i	0.496825	−	0.197060i
$267$	−2.85486	−	6.89225i	−0.174715	−	0.421799i
$268$	1.65548	−	4.13464i	0.101125	−	0.252563i
$269$	−2.50081	+	1.91894i	−0.152477	+	0.117000i	−0.682183	−	0.731182i	$-0.738969\pi$
$269$	−2.50081	+	1.91894i	−0.152477	+	0.117000i	0.529706	+	0.848182i	$0.322302\pi$
$270$	−2.42210	+	2.45098i	−0.147404	+	0.149162i
$271$	−1.38786	+	0.801279i	−0.0843063	+	0.0486742i	−0.541560	−	0.840662i	$-0.682166\pi$
$271$	−1.38786	+	0.801279i	−0.0843063	+	0.0486742i	0.457254	+	0.889336i	$0.348833\pi$
$272$	10.7887	−	6.57470i	0.654163	−	0.398650i
$273$	13.8987	+	8.41880i	0.841187	+	0.509529i
$274$	−3.18831	+	12.1874i	−0.192613	+	0.736268i
$275$	0.396395	+	3.01092i	0.0239035	+	0.181565i
$276$	12.6230	+	9.45039i	0.759817	+	0.568847i
$277$	−6.25584	−	0.823597i	−0.375877	−	0.0494852i	−0.0597789	−	0.998212i	$-0.519040\pi$
$277$	−6.25584	−	0.823597i	−0.375877	−	0.0494852i	−0.316098	+	0.948726i	$0.602373\pi$
$278$	−16.4206	−	2.06288i	−0.984840	−	0.123723i
$279$	12.1273	+	12.1273i	0.726044	+	0.726044i
$280$	3.43995	−	0.441542i	0.205576	−	0.0263872i
$281$	21.8948	−	21.8948i	1.30613	−	1.30613i	0.381949	−	0.924183i	$-0.375253\pi$
$281$	21.8948	−	21.8948i	1.30613	−	1.30613i	0.924183	−	0.381949i	$-0.124747\pi$
$282$	8.21899	−	6.38440i	0.489434	−	0.380185i
$283$	−2.12881	+	16.1699i	−0.126545	+	0.961203i	0.803899	+	0.594766i	$0.202755\pi$
$283$	−2.12881	+	16.1699i	−0.126545	+	0.961203i	−0.930443	+	0.366436i	$0.880578\pi$
$284$	17.4676	+	4.45920i	1.03651	+	0.264605i
$285$	1.17235	−	0.154343i	0.0694442	−	0.00914251i
$286$	−4.34407	+	2.54250i	−0.256870	+	0.150341i
$287$	−0.706445	−	0.0148523i	−0.0417001	−	0.000876703i
$288$	9.75640	−	2.92667i	0.574901	−	0.172456i
$289$	−3.51177	−	6.08256i	−0.206575	−	0.357798i
$290$	−0.0240526	−	4.05821i	−0.00141242	−	0.238306i
$291$	4.00766	+	5.22288i	0.234933	+	0.306171i
$292$	1.58894	+	1.55171i	0.0929859	+	0.0908072i
$293$	−7.36316	+	3.04992i	−0.430161	+	0.178178i	−0.587249	−	0.809406i	$-0.699789\pi$
$293$	−7.36316	+	3.04992i	−0.430161	+	0.178178i	0.157089	+	0.987585i	$0.449789\pi$
$294$	−1.02607	−	10.7928i	−0.0598417	−	0.629451i
$295$	−0.167357	+	0.167357i	−0.00974390	+	0.00974390i
$296$	17.9960	+	13.3073i	1.04600	+	0.773469i
$297$	−3.22291	+	0.863577i	−0.187012	+	0.0501098i
$298$	−5.71733	−	13.5747i	−0.331196	−	0.786363i
$299$	−24.5784	+	32.0311i	−1.42140	+	1.85241i
$300$	−10.4069	−	1.24479i	−0.600845	−	0.0718680i
$301$	14.4332	+	6.33707i	0.831917	+	0.365263i
$302$	4.81253	−	18.3960i	0.276930	−	1.05857i
$303$	1.67649	−	0.967922i	0.0963118	−	0.0556057i
$304$	−8.69172	−	3.36112i	−0.498504	−	0.192773i
$305$	−5.26115	−	3.03753i	−0.301253	−	0.173928i
$306$	2.12774	+	7.75664i	0.121635	+	0.443418i
$307$	−13.4735	−	5.58092i	−0.768975	−	0.318520i	−0.0365181	−	0.999333i	$-0.511627\pi$
$307$	−13.4735	−	5.58092i	−0.768975	−	0.318520i	−0.732457	+	0.680813i	$0.761627\pi$
$308$	3.09068	+	1.31352i	0.176108	+	0.0748449i
$309$	−5.03182	−	12.1479i	−0.286250	−	0.691069i
$310$	0.778146	−	6.19407i	0.0441957	−	0.351800i
$311$	26.0410	−	6.97767i	1.47665	−	0.395668i	0.571445	−	0.820640i	$-0.306383\pi$
$311$	26.0410	−	6.97767i	1.47665	−	0.395668i	0.905206	+	0.424973i	$0.139716\pi$
$312$	−4.79371	−	16.6970i	−0.271391	−	0.945284i
$313$	−16.2943	−	4.36605i	−0.921010	−	0.246784i	−0.232993	−	0.972478i	$-0.574852\pi$
$313$	−16.2943	−	4.36605i	−0.921010	−	0.246784i	−0.688017	+	0.725695i	$0.741519\pi$
$314$	23.8522	−	3.28414i	1.34606	−	0.185335i
$315$	−0.334137	+	2.18247i	−0.0188265	+	0.122968i
$316$	−10.3443	−	5.80991i	−0.581913	−	0.326833i
$317$	−18.6637	+	2.45712i	−1.04826	+	0.138006i	−0.634925	−	0.772574i	$-0.718969\pi$
$317$	−18.6637	+	2.45712i	−1.04826	+	0.138006i	−0.413334	+	0.910580i	$0.635636\pi$
$318$	−2.28136	+	0.0135214i	−0.127932	+	0.000758240i
$319$	1.96481	−	3.40316i	0.110008	−	0.190540i
$320$	−3.01985	−	2.15105i	−0.168814	−	0.120248i
$321$	1.63203			0.0910910
$322$	26.9341	+	0.406576i	1.50098	+	0.0226576i
$323$	2.81602	−	6.79847i	0.156687	−	0.378277i
$324$	−0.00843577	−	0.711626i	−0.000468654	−	0.0395348i
$325$	3.50281	−	26.6065i	0.194301	−	1.47586i
$326$	−0.624463	+	1.53323i	−0.0345858	+	0.0849176i
$327$	6.16398	+	1.65163i	0.340869	+	0.0913356i
$328$	0.543553	+	0.524559i	0.0300127	+	0.0289639i
$329$	4.96137	−	17.0723i	0.273529	−	0.941224i
$330$	0.363042	+	0.275169i	0.0199848	+	0.0151476i
$331$	12.5359	−	16.3371i	0.689035	−	0.897969i	−0.309564	−	0.950879i	$-0.600183\pi$
$331$	12.5359	−	16.3371i	0.689035	−	0.897969i	0.998599	+	0.0529101i	$0.0168497\pi$
$332$	0.157045	+	1.09263i	0.00861896	+	0.0599659i
$333$	−11.3042	+	8.67401i	−0.619466	+	0.475333i
$334$	−2.84987	−	10.3892i	−0.155938	−	0.568470i
$335$		−	1.03205i		−	0.0563871i
$336$	−7.03085	+	9.21393i	−0.383564	+	0.502661i
$337$		−	4.19060i		−	0.228277i	−0.993465	−	0.114138i	$-0.963589\pi$
$337$		−	4.19060i		−	0.228277i	0.993465	−	0.114138i	$-0.0364107\pi$
$338$	25.1641	−	6.90280i	1.36875	−	0.375463i
$339$	17.2461	−	13.2334i	0.936680	−	0.718740i
$340$	1.75461	−	2.34365i	0.0951568	−	0.127102i
$341$	3.67987	−	4.79570i	0.199276	−	0.259702i
$342$	3.58360	−	4.72799i	0.193779	−	0.255661i
$343$	−12.2445	−	13.8951i	−0.661139	−	0.750264i
$344$	−6.72458	−	15.4516i	−0.362565	−	0.833097i
$345$	3.52951	+	0.945730i	0.190023	+	0.0509164i
$346$	30.1083	+	12.2627i	1.61863	+	0.659248i
$347$	−2.80157	+	21.2801i	−0.150396	+	1.14237i	0.735177	+	0.677875i	$0.237099\pi$
$347$	−2.80157	+	21.2801i	−0.150396	+	1.14237i	−0.885574	+	0.464499i	$0.846234\pi$
$348$	9.70287	+	9.47552i	0.520128	+	0.507941i
$349$	0.339165	−	0.818816i	0.0181551	−	0.0438302i	−0.914542	−	0.404491i	$-0.867449\pi$
$349$	0.339165	−	0.818816i	0.0181551	−	0.0438302i	0.932697	+	0.360661i	$0.117449\pi$
$350$	−15.6392	+	8.71725i	−0.835951	+	0.465957i
$351$	29.4844			1.57376
$352$	−1.47154	−	3.27464i	−0.0784333	−	0.174539i
$353$	−4.04793	+	7.01122i	−0.215450	+	0.373170i	−0.953412	−	0.301673i	$-0.902455\pi$
$353$	−4.04793	+	7.01122i	−0.215450	+	0.373170i	0.737962	+	0.674842i	$0.235788\pi$
$354$	−0.00468774	−	0.790928i	−0.000249151	−	0.0420373i
$355$	4.14178	−	0.545275i	0.219823	−	0.0289402i
$356$	3.68184	+	13.1169i	0.195137	+	0.695194i
$357$	−7.14202	−	5.72274i	−0.377996	−	0.302880i
$358$	−0.505299	−	3.66991i	−0.0267059	−	0.193961i
$359$	11.3023	+	3.02843i	0.596511	+	0.159835i	0.544427	−	0.838808i	$-0.316747\pi$
$359$	11.3023	+	3.02843i	0.596511	+	0.159835i	0.0520837	+	0.998643i	$0.483414\pi$
$360$	1.84675	−	1.46995i	0.0973320	−	0.0774734i
$361$	13.1098	−	3.51277i	0.689992	−	0.184883i
$362$	3.05791	+	0.384157i	0.160720	+	0.0201909i
$363$	−4.44128	−	10.7222i	−0.233107	−	0.562770i
$364$	−23.3765	−	18.2803i	−1.22526	−	0.958148i
$365$	0.475475	+	0.196948i	0.0248875	+	0.0103087i
$366$	19.5786	−	5.37064i	1.02339	−	0.280728i
$367$	−19.9559	−	11.5215i	−1.04169	−	0.601420i	−0.121378	−	0.992606i	$-0.538731\pi$
$367$	−19.9559	−	11.5215i	−1.04169	−	0.601420i	−0.920311	+	0.391187i	$0.872065\pi$
$368$	−20.8396	−	19.8742i	−1.08634	−	1.03601i
$369$	−0.416467	+	0.240447i	−0.0216804	+	0.0125172i
$370$	5.01759	+	1.31263i	0.260852	+	0.0682406i
$371$	−3.14108	+	2.30698i	−0.163077	+	0.119772i
$372$	12.8954	+	16.3995i	0.668598	+	0.850272i
$373$	0.132104	−	0.172161i	0.00684008	−	0.00891417i	−0.789921	−	0.613209i	$-0.789878\pi$
$373$	0.132104	−	0.172161i	0.00684008	−	0.00891417i	0.796761	+	0.604295i	$0.206545\pi$
$374$	2.61260	−	1.10036i	0.135094	−	0.0568983i
$375$	−4.79730	+	1.28543i	−0.247731	+	0.0663794i
$376$	−16.2882	+	9.79418i	−0.839999	+	0.505096i
$377$	−24.5541	+	24.5541i	−1.26460	+	1.26460i
$378$	−11.7384	−	15.7855i	−0.603756	−	0.811917i
$379$	−35.3256	+	14.6323i	−1.81455	+	0.751612i	−0.835052	+	0.550171i	$0.814563\pi$
$379$	−35.3256	+	14.6323i	−1.81455	+	0.751612i	−0.979501	+	0.201442i	$0.935437\pi$
$380$	−2.15930	+	0.0255968i	−0.110770	+	0.00131309i
$381$	−8.18374	−	10.6653i	−0.419266	−	0.546398i
$382$	−18.7311	+	0.111017i	−0.958366	+	0.00568014i
$383$	−8.69358	−	15.0577i	−0.444221	−	0.769413i	0.553777	−	0.832665i	$-0.313186\pi$
$383$	−8.69358	−	15.0577i	−0.444221	−	0.769413i	−0.997998	+	0.0632520i	$0.979853\pi$
$384$	12.2066	−	2.12537i	0.622918	−	0.108460i
$385$	0.778017	+	0.0163570i	0.0396514	+	0.000833631i
$386$	−8.67173	−	14.8164i	−0.441380	−	0.754134i
$387$	10.6362	−	1.40028i	0.540669	−	0.0711804i
$388$	−6.13427	−	10.3399i	−0.311421	−	0.524927i
$389$	2.11289	−	16.0490i	0.107128	−	0.813717i	−0.850554	−	0.525888i	$-0.823733\pi$
$389$	2.11289	−	16.0490i	0.107128	−	0.813717i	0.957682	−	0.287829i	$-0.0929335\pi$
$390$	−2.46943	−	3.17903i	−0.125044	−	0.160976i
$391$	16.0791	−	16.0791i	0.813155	−	0.813155i
$392$	−0.480302	+	19.7932i	−0.0242589	+	0.999706i
$393$	−13.2701	−	13.2701i	−0.669388	−	0.669388i
$394$	−4.58476	+	36.4948i	−0.230977	+	1.83858i
$395$	−2.72574	−	0.358850i	−0.137147	−	0.0180557i
$396$	2.26227	−	0.325158i	0.113683	−	0.0163398i
$397$	−3.84235	−	29.1855i	−0.192842	−	1.46478i	−0.764679	−	0.644412i	$-0.777102\pi$
$397$	−3.84235	−	29.1855i	−0.192842	−	1.46478i	0.571837	−	0.820367i	$-0.306231\pi$
$398$	19.0484	+	4.98320i	0.954811	+	0.249785i
$399$	−0.141890	+	6.74896i	−0.00710339	+	0.337871i
$400$	18.6009	+	4.51435i	0.930044	+	0.225717i
$401$	16.3558	−	9.44303i	0.816770	−	0.471563i	−0.0325311	−	0.999471i	$-0.510357\pi$
$401$	16.3558	−	9.44303i	0.816770	−	0.471563i	0.849301	+	0.527908i	$0.177023\pi$
$402$	2.45319	+	2.42428i	0.122354	+	0.120912i
$403$	−42.3779	+	32.5177i	−2.11099	+	1.61982i
$404$	−3.24991	+	1.39151i	−0.161689	+	0.0692304i
$405$	−0.0631100	−	0.152361i	−0.00313596	−	0.00757088i
$406$	22.9214	+	3.37036i	1.13757	+	0.167268i
$407$	3.55110	+	3.55110i	0.176022	+	0.176022i
$408$	1.44931	+	9.67591i	0.0717516	+	0.479029i
$409$	2.72348	+	10.1642i	0.134668	+	0.502586i	0.999999	+	0.00138610i	$0.000441211\pi$
$409$	2.72348	+	10.1642i	0.134668	+	0.502586i	−0.865332	+	0.501200i	$0.832892\pi$
$410$	0.162113	+	0.0660267i	0.00800621	+	0.00326082i
$411$	−7.73952	−	5.93874i	−0.381762	−	0.292936i
$412$	6.48941	+	23.1191i	0.319710	+	1.13899i
$413$	−0.799812	−	1.08899i	−0.0393562	−	0.0535856i
$414$	15.8220	−	9.26032i	0.777611	−	0.455120i
$415$	0.127897	+	0.221524i	0.00627821	+	0.0108742i
$416$	5.07098	+	31.3164i	0.248625	+	1.53541i
$417$	6.40796	−	11.0989i	0.313799	−	0.543516i
$418$	−1.81702	−	1.03475i	−0.0888732	−	0.0506110i
$419$	−4.60368	+	11.1143i	−0.224904	+	0.542967i	−0.995543	−	0.0943047i	$-0.969937\pi$
$419$	−4.60368	+	11.1143i	−0.224904	+	0.542967i	0.770639	+	0.637272i	$0.219937\pi$
$420$	−0.718869	+	2.58773i	−0.0350772	+	0.126268i
$421$	7.44632	−	3.08437i	0.362912	−	0.150323i	−0.193774	−	0.981046i	$-0.562073\pi$
$421$	7.44632	−	3.08437i	0.362912	−	0.150323i	0.556686	+	0.830723i	$0.312073\pi$
$422$	−21.5410	+	16.7327i	−1.04860	+	0.814537i
$423$	−3.13161	−	11.6873i	−0.152264	−	0.568258i
$424$	4.13971	+	0.470288i	0.201042	+	0.0228392i
$425$	−3.91188	+	14.5993i	−0.189754	+	0.708172i
$426$	−8.43287	+	11.1259i	−0.408574	+	0.539049i
$427$	21.6862	−	27.0645i	1.04947	−	1.30974i
$428$	−2.95935	−	0.353973i	−0.143046	−	0.0171099i
$429$	−0.508770	−	3.86449i	−0.0245636	−	0.186579i
$430$	−2.77753	−	2.74480i	−0.133944	−	0.132366i
$431$	17.9328	+	10.3535i	0.863792	+	0.498710i	0.865280	−	0.501288i	$-0.167140\pi$
$431$	17.9328	+	10.3535i	0.863792	+	0.498710i	−0.00148843	+	0.999999i	$0.500474\pi$
$432$	−2.24992	+	20.9091i	−0.108249	+	1.00599i
$433$			32.8821i			1.58021i	0.612968	+	0.790107i	$0.289975\pi$
$433$			32.8821i			1.58021i	−0.612968	+	0.790107i	$0.710025\pi$
$434$	34.2810	+	9.74245i	1.64554	+	0.467653i
$435$	2.90348	+	1.20266i	0.139211	+	0.0576632i
$436$	−10.8189	−	4.33182i	−0.518132	−	0.207456i
$437$	−16.6289	−	2.18924i	−0.795470	−	0.104726i
$438$	−1.58503	+	0.667575i	−0.0757357	+	0.0318979i
$439$	1.98785	−	7.41874i	0.0948747	−	0.354077i	−0.902126	−	0.431473i	$-0.857994\pi$
$439$	1.98785	−	7.41874i	0.0948747	−	0.354077i	0.997000	+	0.0773961i	$0.0246606\pi$
$440$	−0.598622	−	0.577704i	−0.0285382	−	0.0275409i
$441$	−12.0271	−	3.77108i	−0.572717	−	0.179575i
$442$	−24.8166	+	3.41692i	−1.18041	+	0.162526i
$443$	−2.45839	−	1.88639i	−0.116802	−	0.0896250i	0.548709	−	0.836013i	$-0.315119\pi$
$443$	−2.45839	−	1.88639i	−0.116802	−	0.0896250i	−0.665511	+	0.746388i	$0.731786\pi$
$444$	−14.9064	+	8.84344i	−0.707426	+	0.419691i
$445$	1.92186	+	2.50462i	0.0911050	+	0.118730i
$446$	8.14319	−	14.2995i	0.385591	−	0.677100i
$447$	11.4065			0.539509
$448$	14.7474	−	15.1827i	0.696751	−	0.717313i
$449$	14.2618			0.673058			0.336529	−	0.941673i	$-0.390747\pi$
$449$	14.2618			0.673058			0.336529	+	0.941673i	$0.390747\pi$
$450$	−6.03006	+	10.5888i	−0.284260	+	0.499161i
$451$	0.103182	+	0.134469i	0.00485863	+	0.00633189i
$452$	−34.1425	+	20.2556i	−1.60593	+	0.952741i
$453$	11.6823	+	8.96412i	0.548881	+	0.421171i
$454$	14.2093	−	1.95644i	0.666876	−	0.0918201i
$455$	−6.60339	−	1.91901i	−0.309572	−	0.0899647i
$456$	5.01133	−	5.19278i	0.234677	−	0.243174i
$457$	1.44221	−	5.38240i	0.0674638	−	0.251778i	−0.923955	−	0.382501i	$-0.875063\pi$
$457$	1.44221	−	5.38240i	0.0674638	−	0.251778i	0.991419	+	0.130722i	$0.0417297\pi$
$458$	19.7069	−	8.30006i	0.920844	−	0.387836i
$459$	−16.4639	−	2.16751i	−0.768467	−	0.101171i
$460$	−6.19493	−	2.48041i	−0.288840	−	0.115650i
$461$	−35.5395	−	14.7209i	−1.65524	−	0.685622i	−0.657540	−	0.753420i	$-0.728403\pi$
$461$	−35.5395	−	14.7209i	−1.65524	−	0.685622i	−0.997699	+	0.0677971i	$0.978403\pi$
$462$	−1.86643	+	1.81092i	−0.0868344	+	0.0842518i
$463$			7.71929i			0.358746i	0.983781	+	0.179373i	$0.0574069\pi$
$463$			7.71929i			0.358746i	−0.983781	+	0.179373i	$0.942593\pi$
$464$	−15.5390	−	19.2864i	−0.721381	−	0.895349i
$465$	4.18667	+	2.41717i	0.194152	+	0.112094i
$466$	16.2438	+	16.0523i	0.752478	+	0.743611i
$467$	4.51616	+	34.3036i	0.208983	+	1.58738i	0.698644	+	0.715470i	$0.253787\pi$
$467$	4.51616	+	34.3036i	0.208983	+	1.58738i	−0.489661	+	0.871913i	$0.662879\pi$
$468$	−20.0534	−	2.39862i	−0.926967	−	0.110876i
$469$	5.82390	+	0.891640i	0.268922	+	0.0411721i
$470$	−2.66036	+	3.50993i	−0.122713	+	0.161901i
$471$	−4.82575	+	18.0099i	−0.222359	+	0.829854i
$472$	−0.163045	+	1.43520i	−0.00750476	+	0.0660606i
$473$	−0.978633	−	3.65231i	−0.0449976	−	0.167933i
$474$	7.25572	−	5.63614i	0.333266	−	0.258877i
$475$	10.2997	−	4.26627i	0.472582	−	0.195750i
$476$	11.7094	+	11.9261i	0.536699	+	0.546630i
$477$	−1.01502	+	2.45047i	−0.0464744	+	0.112199i
$478$	−5.53955	−	3.15463i	−0.253373	−	0.144290i
$479$	−17.2474	+	29.8733i	−0.788052	+	1.36495i	0.139107	+	0.990277i	$0.455577\pi$
$479$	−17.2474	+	29.8733i	−0.788052	+	1.36495i	−0.927159	+	0.374668i	$0.877757\pi$
$480$	2.44287	−	1.50862i	0.111501	−	0.0688590i
$481$	−22.1889	−	38.4323i	−1.01173	−	1.75236i
$482$	14.9375	−	8.74263i	0.680385	−	0.398216i
$483$	−8.38609	+	19.1001i	−0.381580	+	0.869083i
$484$	5.72781	+	20.4058i	0.260355	+	0.927537i
$485$	−2.21024	−	1.69598i	−0.100362	−	0.0770104i
$486$	−20.1474	−	8.20576i	−0.913903	−	0.372221i
$487$	6.14828	+	22.9457i	0.278605	+	1.03977i	0.953387	+	0.301751i	$0.0975712\pi$
$487$	6.14828	+	22.9457i	0.278605	+	1.03977i	−0.674781	+	0.738018i	$0.735762\pi$
$488$	−36.6667	+	5.49213i	−1.65982	+	0.248617i
$489$	−0.906527	−	0.906527i	−0.0409946	−	0.0409946i
$490$	1.60154	+	4.29935i	0.0723503	+	0.194225i
$491$	−4.28702	−	10.3498i	−0.193470	−	0.467079i	0.797140	−	0.603795i	$-0.206345\pi$
$491$	−4.28702	−	10.3498i	−0.193470	−	0.467079i	−0.990610	+	0.136716i	$0.956345\pi$
$492$	−0.537748	+	0.230248i	−0.0242436	+	0.0103804i
$493$	15.5159	−	11.9057i	0.698800	−	0.536208i
$494$	13.1427	+	12.9878i	0.591317	+	0.584349i
$495$	0.458660	−	0.264808i	0.0206153	−	0.0119022i
$496$	−19.8264	−	32.5340i	−0.890230	−	1.46082i
$497$	−0.501280	+	23.8432i	−0.0224855	+	1.06952i
$498$	−0.826990	−	0.216346i	−0.0370583	−	0.00969471i
$499$	0.893660	+	6.78803i	0.0400057	+	0.303874i	0.999737	+	0.0229525i	$0.00730664\pi$
$499$	0.893660	+	6.78803i	0.0400057	+	0.303874i	−0.959731	+	0.280921i	$0.909360\pi$
$500$	8.97772	−	1.29038i	0.401496	−	0.0577074i
$501$	8.27114	+	1.08892i	0.369527	+	0.0486492i
$502$	4.25119	−	33.8396i	0.189740	−	1.51034i
$503$	−28.5834	−	28.5834i	−1.27447	−	1.27447i	−0.943718	−	0.330751i	$-0.892698\pi$
$503$	−28.5834	−	28.5834i	−1.27447	−	1.27447i	−0.330751	−	0.943718i	$-0.607302\pi$
$504$	6.69949	+	11.6912i	0.298419	+	0.520767i
$505$	−0.579275	+	0.579275i	−0.0257774	+	0.0257774i
$506$	−3.96383	−	5.10285i	−0.176214	−	0.226849i
$507$	−2.63751	+	20.0339i	−0.117136	+	0.889736i
$508$	12.5263	+	21.1143i	0.555767	+	0.936793i
$509$	26.3453	−	3.46843i	1.16774	−	0.153735i	0.478377	−	0.878155i	$-0.341225\pi$
$509$	26.3453	−	3.46843i	1.16774	−	0.153735i	0.689360	+	0.724419i	$0.257892\pi$
$510$	1.14521	+	1.95668i	0.0507106	+	0.0866433i
$511$	−1.52217	+	2.51296i	−0.0673368	+	0.111167i
$512$	−22.5952	+	1.20641i	−0.998578	+	0.0533161i
$513$	6.12424	+	10.6075i	0.270392	+	0.468332i
$514$	−2.10530	+	0.0124779i	−0.0928608	+	0.000550376i
$515$	3.38736	+	4.41450i	0.149265	+	0.194526i
$516$	13.0488	−	0.154683i	0.574440	−	0.00680953i
$517$	−3.93997	+	1.63199i	−0.173280	+	0.0717748i
$518$	−11.7422	+	27.1803i	−0.515921	+	1.19423i
$519$	−17.8017	+	17.8017i	−0.781406	+	0.781406i
$520$	3.78830	+	6.30012i	0.166128	+	0.276278i
$521$	35.6552	−	9.55378i	1.56208	−	0.418559i	0.628760	−	0.777599i	$-0.283563\pi$
$521$	35.6552	−	9.55378i	1.56208	−	0.418559i	0.933322	+	0.359041i	$0.116896\pi$
$522$	14.5312	−	6.12016i	0.636013	−	0.267872i
$523$	−6.36446	+	8.29433i	−0.278299	+	0.362686i	−0.911499	−	0.411302i	$-0.865074\pi$
$523$	−6.36446	+	8.29433i	−0.278299	+	0.362686i	0.633201	+	0.773988i	$0.281741\pi$
$524$	21.1844	+	26.9408i	0.925447	+	1.17691i
$525$	−1.52043	−	13.7816i	−0.0663570	−	0.601478i
$526$	−23.9506	−	6.26565i	−1.04430	−	0.273195i
$527$	26.0540	−	15.0423i	1.13493	−	0.655252i
$528$	2.77936	−	0.0659034i	0.120956	−	0.00286808i
$529$	−24.9671	−	14.4147i	−1.08552	−	0.626728i
$530$	0.931057	−	0.255400i	0.0404425	−	0.0110939i
$531$	−0.849557	−	0.351898i	−0.0368677	−	0.0152711i
$532$	1.72108	−	12.2071i	0.0746183	−	0.529245i
$533$	−0.573168	−	1.38375i	−0.0248267	−	0.0599369i
$534$	−10.4679	−	1.31506i	−0.452991	−	0.0569082i
$535$	−0.667116	+	0.178753i	−0.0288420	+	0.00772818i
$536$	−3.92255	−	4.92801i	−0.169428	−	0.212858i
$537$	2.77102	+	0.742492i	0.119578	+	0.0320409i
$538$	0.608055	+	4.41622i	0.0262151	+	0.190397i
$539$	−0.764469	+	4.37624i	−0.0329280	+	0.188498i
$540$	1.31697	+	4.69183i	0.0566735	+	0.201904i
$541$	−20.9478	+	2.75783i	−0.900615	+	0.118568i	−0.566594	−	0.823997i	$-0.691739\pi$
$541$	−20.9478	+	2.75783i	−0.900615	+	0.118568i	−0.334021	+	0.942566i	$0.608406\pi$
$542$	0.0134322	+	2.26632i	0.000576964	+	0.0973468i
$543$	−1.19332	+	2.06689i	−0.0512101	+	0.0886986i
$544$	−0.529410	−	17.8596i	−0.0226982	−	0.765725i
$545$	−2.70052			−0.115678
$546$	20.0728	−	11.1885i	0.859036	−	0.478824i
$547$	14.3700	−	34.6922i	0.614416	−	1.48333i	−0.243687	−	0.969854i	$-0.578357\pi$
$547$	14.3700	−	34.6922i	0.614416	−	1.48333i	0.858103	−	0.513477i	$-0.171643\pi$
$548$	12.7460	+	12.4473i	0.544481	+	0.531724i
$549$	3.08082	−	23.4012i	0.131486	−	0.998737i
$550$	3.97758	+	1.62001i	0.169604	+	0.0690777i
$551$	−13.9339	−	3.73358i	−0.593604	−	0.159056i
$552$	20.4478	−	8.89890i	0.870315	−	0.378762i
$553$	4.37990	−	15.0714i	0.186252	−	0.640900i
$554$	−5.39019	+	7.11151i	−0.229007	+	0.302139i
$555$	−2.44500	+	3.18638i	−0.103784	+	0.135254i
$556$	−14.0268	+	18.7358i	−0.594869	+	0.794575i
$557$	−6.85705	+	5.26160i	−0.290543	+	0.222941i	−0.743740	−	0.668469i	$-0.766950\pi$
$557$	−6.85705	+	5.26160i	−0.290543	+	0.222941i	0.453197	+	0.891410i	$0.350283\pi$
$558$	23.3906	−	6.41631i	0.990202	−	0.271624i
$559$			33.4127i			1.41320i
$560$	1.86478	−	4.53641i	0.0788013	−	0.191698i
$561$			2.19530i			0.0926858i
$562$	−11.5841	−	42.2295i	−0.488644	−	1.78135i
$563$	24.4301	−	18.7459i	1.02961	−	0.790045i	0.0516102	−	0.998667i	$-0.483565\pi$
$563$	24.4301	−	18.7459i	1.02961	−	0.790045i	0.977996	+	0.208622i	$0.0668980\pi$
$564$	−2.09394	−	14.5685i	−0.0881708	−	0.613443i
$565$	−5.60017	+	7.29828i	−0.235601	+	0.307041i
$566$	18.3816	+	13.9324i	0.772638	+	0.585623i
$567$	0.914301	−	0.224499i	0.0383970	−	0.00942808i
$568$	17.7044	−	18.3455i	0.742860	−	0.769758i
$569$	20.4903	+	5.49037i	0.859000	+	0.230168i	0.661325	−	0.750099i	$-0.269994\pi$
$569$	20.4903	+	5.49037i	0.859000	+	0.230168i	0.197675	+	0.980268i	$0.436661\pi$
$570$	0.630780	−	1.54874i	0.0264205	−	0.0648695i
$571$	3.04816	−	23.1531i	0.127562	−	0.968926i	−0.801239	−	0.598345i	$-0.795825\pi$
$571$	3.04816	−	23.1531i	0.127562	−	0.968926i	0.928800	−	0.370581i	$-0.120841\pi$
$572$	0.0843760	+	7.11782i	0.00352794	+	0.297611i
$573$	5.55101	−	13.4013i	0.231897	−	0.559848i
$574$	−0.512648	+	0.857766i	−0.0213975	+	0.0358025i
$575$	34.4500			1.43667
$576$	3.23124	−	14.0380i	0.134635	−	0.584915i
$577$	−16.7927	+	29.0858i	−0.699089	+	1.21086i	0.269693	+	0.962946i	$0.413078\pi$
$577$	−16.7927	+	29.0858i	−0.699089	+	1.21086i	−0.968783	+	0.247912i	$0.920256\pi$
$578$	−9.93261	+	0.0588695i	−0.413142	+	0.00244865i
$579$	13.1807	−	1.73527i	0.547771	−	0.0721154i
$580$	−5.00403	−	2.81052i	−0.207781	−	0.116701i
$581$	−1.36056	+	0.530339i	−0.0564455	+	0.0220022i
$582$	9.22317	−	1.26991i	0.382313	−	0.0526394i
$583$	0.902990	+	0.241955i	0.0373980	+	0.0100208i
$584$	3.01892	−	0.866731i	0.124924	−	0.0358656i
$585$	−4.52056	+	1.21128i	−0.186902	+	0.0500802i
$586$	−1.40491	+	11.1831i	−0.0580363	+	0.461971i
$587$	6.32050	+	15.2590i	0.260875	+	0.629807i	0.998993	−	0.0448638i	$-0.0142854\pi$
$587$	6.32050	+	15.2590i	0.260875	+	0.629807i	−0.738118	+	0.674671i	$0.764285\pi$
$588$	−13.9816	−	6.29226i	−0.576590	−	0.259488i
$589$	−20.5012	−	8.49185i	−0.844735	−	0.349901i
$590$	0.0885450	+	0.322790i	0.00364534	+	0.0132890i
$591$	−24.6674	−	14.2417i	−1.01468	−	0.585827i
$592$	28.9478	−	12.8027i	1.18975	−	0.526188i
$593$	−7.55272	+	4.36056i	−0.310153	+	0.179067i	−0.646995	−	0.762494i	$-0.723975\pi$
$593$	−7.55272	+	4.36056i	−0.310153	+	0.179067i	0.336842	+	0.941561i	$0.390641\pi$
$594$	−1.19425	+	4.56504i	−0.0490005	+	0.187306i
$595$	3.54621	+	1.55700i	0.145380	+	0.0638309i
$596$	−20.6834	−	2.47397i	−0.847224	−	0.101338i
$597$	−9.28201	+	12.0966i	−0.379888	+	0.495079i
$598$	22.1627	+	52.6212i	0.906301	+	2.15184i
$599$	5.50159	−	1.47415i	0.224789	−	0.0602320i	−0.144667	−	0.989480i	$-0.546211\pi$
$599$	5.50159	−	1.47415i	0.224789	−	0.0602320i	0.369455	+	0.929249i	$0.379544\pi$
$600$	−8.81288	+	11.9181i	−0.359785	+	0.486554i
$601$	21.0920	−	21.0920i	0.860359	−	0.860359i	−0.131021	−	0.991380i	$-0.541825\pi$
$601$	21.0920	−	21.0920i	0.860359	−	0.860359i	0.991380	+	0.131021i	$0.0418255\pi$
$602$	17.8886	−	13.3023i	0.729085	−	0.542161i
$603$	3.70455	−	1.53448i	0.150861	−	0.0624887i
$604$	−19.2392	−	18.7884i	−0.782831	−	0.764488i
$605$	2.98982	+	3.89641i	0.121554	+	0.158412i
$606$	−0.0162258	−	2.73765i	−0.000659126	−	0.111209i
$607$	−3.94704	−	6.83647i	−0.160205	−	0.277484i	0.774737	−	0.632284i	$-0.217882\pi$
$607$	−3.94704	−	6.83647i	−0.160205	−	0.277484i	−0.934942	+	0.354800i	$0.884549\pi$
$608$	−10.2133	+	8.32914i	−0.414204	+	0.337791i
$609$	−9.29511	+	15.3454i	−0.376657	+	0.621826i
$610$	−7.41480	+	4.33974i	−0.300217	+	0.175711i
$611$	37.3623	−	4.91884i	1.51152	−	0.198995i
$612$	11.0213	+	2.81357i	0.445510	+	0.113732i
$613$	−0.852555	+	6.47580i	−0.0344344	+	0.261555i	0.965565	+	0.260163i	$0.0837764\pi$
$613$	−0.852555	+	6.47580i	−0.0344344	+	0.261555i	−0.999999	+	0.00139187i	$0.999557\pi$
$614$	−16.2877	+	12.6521i	−0.657320	+	0.510597i
$615$	−0.0958502	+	0.0958502i	−0.00386505	+	0.00386505i
$616$	3.77717	−	2.87893i	0.152187	−	0.115995i
$617$	33.0437	+	33.0437i	1.33029	+	1.33029i	0.905108	+	0.425183i	$0.139790\pi$
$617$	33.0437	+	33.0437i	1.33029	+	1.33029i	0.425183	+	0.905108i	$0.360210\pi$
$618$	−18.4501	−	2.31785i	−0.742174	−	0.0932375i
$619$	3.90132	+	0.513619i	0.156807	+	0.0206441i	0.208521	−	0.978018i	$-0.433135\pi$
$619$	3.90132	+	0.513619i	0.156807	+	0.0206441i	−0.0517137	+	0.998662i	$0.516468\pi$
$620$	−7.06741	−	5.29111i	−0.283834	−	0.212496i
$621$	4.94039	+	37.5260i	0.198251	+	1.50586i
$622$	9.64948	−	36.8854i	0.386909	−	1.47897i
$623$	−15.7940	+	8.68125i	−0.632774	+	0.347807i
$624$	−23.8740	−	5.79412i	−0.955727	−	0.231951i
$625$	−18.9004	+	10.9121i	−0.756016	+	0.436486i
$626$	−16.7688	+	16.9688i	−0.670218	+	0.678210i
$627$	1.28464	−	0.985737i	0.0513035	−	0.0393665i
$628$	12.6567	−	31.6107i	0.505058	−	1.26140i
$629$	9.56481	+	23.0915i	0.381374	+	0.920718i
$630$	2.44823	+	1.93800i	0.0975398	+	0.0772116i
$631$	11.4028	+	11.4028i	0.453939	+	0.453939i	0.896660	−	0.442721i	$-0.145987\pi$
$631$	11.4028	+	11.4028i	0.453939	+	0.453939i	−0.442721	+	0.896660i	$0.645987\pi$
$632$	−14.3792	+	8.64630i	−0.571974	+	0.343931i
$633$	−5.46693	−	20.4029i	−0.217291	−	0.810941i
$634$	−10.0419	+	24.6557i	−0.398816	+	0.979202i
$635$	4.51337	+	3.46323i	0.179108	+	0.137434i
$636$	−1.57996	+	2.81305i	−0.0626494	+	0.111545i
$637$	16.5340	−	35.6051i	0.655102	−	1.41073i
$638$	−2.80714	−	4.79624i	−0.111136	−	0.189885i
$639$	8.11534	+	14.0562i	0.321038	+	0.556054i
$640$	−4.75686	+	2.20575i	−0.188031	+	0.0871898i
$641$	4.47764	−	7.75550i	0.176856	−	0.306324i	−0.763946	−	0.645280i	$-0.776741\pi$
$641$	4.47764	−	7.75550i	0.176856	−	0.306324i	0.940802	+	0.338956i	$0.110074\pi$
$642$	1.14215	−	2.00562i	0.0450772	−	0.0791557i
$643$	0.840054	−	2.02807i	0.0331285	−	0.0799793i	−0.906449	−	0.422314i	$-0.861218\pi$
$643$	0.840054	−	2.02807i	0.0331285	−	0.0799793i	0.939578	+	0.342335i	$0.111218\pi$
$644$	19.3491	−	32.8152i	0.762462	−	1.29310i
$645$	2.79378	−	1.15722i	0.110005	−	0.0455655i
$646$	−6.38399	−	8.21846i	−0.251175	−	0.323351i
$647$	−5.12780	−	19.1372i	−0.201595	−	0.752361i	−0.990461	−	0.137796i	$-0.955998\pi$
$647$	−5.12780	−	19.1372i	−0.201595	−	0.752361i	0.788866	−	0.614565i	$-0.210669\pi$
$648$	−0.880431	−	0.487655i	−0.0345866	−	0.0191569i
$649$	−0.0838840	+	0.313059i	−0.00329273	+	0.0122887i
$650$	−30.2457	−	22.9248i	−1.18633	−	0.899184i
$651$	−17.2572	+	21.5372i	−0.676364	+	0.844108i
$652$	1.44718	+	1.84042i	0.0566761	+	0.0720764i
$653$	−2.87103	−	21.8077i	−0.112352	−	0.853400i	−0.951101	−	0.308881i	$-0.900046\pi$
$653$	−2.87103	−	21.8077i	−0.112352	−	0.853400i	0.838749	−	0.544519i	$-0.183288\pi$
$654$	6.34349	−	6.41914i	0.248050	−	0.251008i
$655$	6.87780	+	3.97090i	0.268738	+	0.155156i
$656$	1.02504	−	0.300874i	0.0400209	−	0.0117472i
$657$			1.99954i			0.0780096i
$658$	−17.5082	−	18.0449i	−0.682540	−	0.703462i
$659$	11.8981	+	4.92837i	0.463485	+	0.191982i	0.602191	−	0.798352i	$-0.294294\pi$
$659$	11.8981	+	4.92837i	0.463485	+	0.191982i	−0.138706	+	0.990334i	$0.544294\pi$
$660$	0.592229	−	0.253575i	0.0230525	−	0.00987039i
$661$	−42.9148	−	5.64985i	−1.66919	−	0.219754i	−0.764140	−	0.645050i	$-0.776836\pi$
$661$	−42.9148	−	5.64985i	−1.66919	−	0.219754i	−0.905054	+	0.425297i	$0.860170\pi$
$662$	−11.3038	−	26.8388i	−0.439336	−	1.04312i
$663$	5.02086	−	18.7381i	0.194994	−	0.727728i
$664$	1.45265	+	0.571667i	0.0563739	+	0.0221850i
$665$	−0.681202	−	2.77428i	−0.0264159	−	0.107582i
$666$	2.74854	+	19.9623i	0.106504	+	0.773522i
$667$	−35.3652	−	27.1367i	−1.36935	−	1.05074i
$668$	−14.7618	−	3.76846i	−0.571153	−	0.145806i
$669$	7.75751	+	10.1098i	0.299923	+	0.390867i
$670$	−1.26830	−	0.722267i	−0.0489989	−	0.0279036i
$671$	−8.31906			−0.321154
$672$	6.40269	+	15.0885i	0.246989	+	0.582053i
$673$	10.7072			0.412732			0.206366	−	0.978475i	$-0.433836\pi$
$673$	10.7072			0.412732			0.206366	+	0.978475i	$0.433836\pi$
$674$	−5.14989	−	2.93273i	−0.198366	−	0.112965i
$675$	−15.3152	−	19.9592i	−0.589483	−	0.768229i
$676$	9.12777	−	35.7553i	0.351068	−	1.37520i
$677$	15.7969	+	12.1214i	0.607125	+	0.465863i	0.865998	−	0.500048i	$-0.166684\pi$
$677$	15.7969	+	12.1214i	0.607125	+	0.465863i	−0.258873	+	0.965911i	$0.583351\pi$
$678$	−4.19328	−	30.4552i	−0.161042	−	1.16962i
$679$	11.4800	−	11.0072i	0.440561	−	0.422418i
$680$	−1.65221	−	3.79643i	−0.0633594	−	0.145586i
$681$	−2.87481	+	10.7289i	−0.110163	+	0.411134i
$682$	−3.31820	−	7.87845i	−0.127060	−	0.301681i
$683$	33.7033	+	4.43712i	1.28962	+	0.169782i	0.743960	−	0.668224i	$-0.232945\pi$
$683$	33.7033	+	4.43712i	1.28962	+	0.169782i	0.545661	+	0.838006i	$0.316279\pi$
$684$	−3.30237	−	7.71275i	−0.126269	−	0.294904i
$685$	3.81410	+	1.57985i	0.145729	+	0.0603631i
$686$	−25.6450	+	5.32312i	−0.979129	+	0.203238i
$687$			16.5592i			0.631774i
$688$	−23.6948	−	2.54968i	−0.903357	−	0.0972056i
$689$	−7.15413	−	4.13044i	−0.272551	−	0.157357i
$690$	3.63230	−	3.67561i	0.138279	−	0.139928i
$691$	5.55238	+	42.1745i	0.211223	+	1.60440i	0.688228	+	0.725495i	$0.258389\pi$
$691$	5.55238	+	42.1745i	0.211223	+	1.60440i	−0.477005	+	0.878900i	$0.658278\pi$
$692$	36.1407	−	28.4186i	1.37386	−	1.08031i
$693$	1.09806	+	2.81701i	0.0417117	+	0.107009i
$694$	24.1907	+	18.3354i	0.918268	+	0.696004i
$695$	−1.40371	+	5.23870i	−0.0532456	+	0.198715i
$696$	18.4350	−	5.29269i	0.698778	−	0.200619i
$697$	0.218328	+	0.814812i	0.00826977	+	0.0308632i
$698$	−0.768895	−	0.989840i	−0.0291031	−	0.0374660i
$699$	−16.3388	+	6.76775i	−0.617990	+	0.255980i
$700$	−0.232120	+	25.3199i	−0.00877331	+	0.957002i
$701$	−7.07844	+	17.0889i	−0.267349	+	0.645437i	−0.999357	−	0.0358587i	$-0.988583\pi$
$701$	−7.07844	+	17.0889i	−0.267349	+	0.645437i	0.732008	+	0.681296i	$0.238583\pi$
$702$	20.6342	−	36.2338i	0.778788	−	1.36756i
$703$	9.21777	−	15.9656i	0.347655	−	0.602156i
$704$	−5.05409	−	0.483316i	−0.190483	−	0.0182157i
$705$	−1.70530	−	2.95366i	−0.0642252	−	0.111241i
$706$	5.78330	+	9.88126i	0.217657	+	0.371886i
$707$	−2.76840	−	3.76933i	−0.104116	−	0.141760i
$708$	−0.975263	−	0.547758i	−0.0366526	−	0.0205860i
$709$	31.5364	+	24.1988i	1.18438	+	0.908803i	0.997292	−	0.0735406i	$-0.0234299\pi$
$709$	31.5364	+	24.1988i	1.18438	+	0.908803i	0.187083	+	0.982344i	$0.440097\pi$
$710$	2.22847	−	5.47149i	0.0836329	−	0.205341i
$711$	−2.76459	−	10.3176i	−0.103680	−	0.386940i
$712$	18.6962	+	4.65499i	0.700670	+	0.174453i
$713$	−48.4874	−	48.4874i	−1.81587	−	1.81587i
$714$	−12.0310	+	4.77196i	−0.450249	+	0.178586i
$715$	0.631238	+	1.52394i	0.0236070	+	0.0569922i
$716$	−4.86364	−	1.94737i	−0.181763	−	0.0727765i
$717$	3.91648	−	3.00522i	0.146264	−	0.112232i
$718$	11.6314	−	11.7701i	0.434080	−	0.439257i
$719$	27.5576	−	15.9104i	1.02773	−	0.593357i	0.111393	−	0.993776i	$-0.464469\pi$
$719$	27.5576	−	15.9104i	1.02773	−	0.593357i	0.916332	+	0.400419i	$0.131135\pi$
$720$	−0.514030	−	3.29822i	−0.0191568	−	0.122917i
$721$	−27.8376	+	15.3011i	−1.03673	+	0.569842i
$722$	4.85784	−	18.5692i	0.180790	−	0.691075i
$723$	1.74946	+	13.2884i	0.0650630	+	0.494203i
$724$	2.61213	−	3.48906i	0.0970790	−	0.129670i
$725$	29.3759	+	3.86741i	1.09099	+	0.143632i
$726$	−16.2848	−	2.04582i	−0.604387	−	0.0759277i
$727$	−4.45867	−	4.45867i	−0.165363	−	0.165363i	0.619575	−	0.784938i	$-0.287305\pi$
$727$	−4.45867	−	4.45867i	−0.165363	−	0.165363i	−0.784938	+	0.619575i	$0.787305\pi$
$728$	−38.8246	+	15.9345i	−1.43894	+	0.590571i
$729$	12.6671	−	12.6671i	0.469150	−	0.469150i
$730$	0.574787	−	0.446487i	0.0212738	−	0.0165252i
$731$	2.45629	−	18.6574i	0.0908492	−	0.690068i
$732$	7.10175	−	27.8190i	0.262488	−	1.02822i
$733$	−4.69572	+	0.618203i	−0.173440	+	0.0228339i	−0.216746	−	0.976228i	$-0.569544\pi$
$733$	−4.69572	+	0.618203i	−0.173440	+	0.0228339i	0.0433057	+	0.999062i	$0.486211\pi$
$734$	−28.1248	+	16.4609i	−1.03811	+	0.607583i
$735$	−3.54974	−	0.149325i	−0.130934	−	0.00550795i
$736$	−39.0080	+	11.7014i	−1.43785	+	0.431319i
$737$	−0.706636	−	1.22393i	−0.0260293	−	0.0450840i
$738$	0.00403074	+	0.680076i	0.000148373	+	0.0250339i
$739$	6.54792	+	8.53341i	0.240869	+	0.313907i	0.898107	−	0.439776i	$-0.144942\pi$
$739$	6.54792	+	8.53341i	0.240869	+	0.313907i	−0.657238	+	0.753683i	$0.728276\pi$
$740$	5.12460	−	5.24755i	0.188384	−	0.192904i
$741$	−13.2195	+	5.47572i	−0.485632	+	0.201155i
$742$	0.636842	+	5.47462i	0.0233792	+	0.200980i
$743$	10.4838	−	10.4838i	0.384613	−	0.384613i	−0.488148	−	0.872761i	$-0.662327\pi$
$743$	10.4838	−	10.4838i	0.384613	−	0.384613i	0.872761	+	0.488148i	$0.162327\pi$
$744$	29.1782	−	4.37048i	1.06973	−	0.160229i
$745$	−4.66258	+	1.24933i	−0.170824	+	0.0457720i
$746$	−0.119120	−	0.282829i	−0.00436131	−	0.0103551i
$747$	−0.605000	+	0.788451i	−0.0221358	+	0.0288479i
$748$	0.476142	−	3.98074i	0.0174095	−	0.145550i
$749$	−0.432355	−	3.91899i	−0.0157979	−	0.143197i
$750$	−1.77763	+	6.79506i	−0.0649100	+	0.248120i
$751$	−29.2155	+	16.8676i	−1.06609	+	0.615506i	−0.927110	−	0.374789i	$-0.877715\pi$
$751$	−29.2155	+	16.8676i	−1.06609	+	0.615506i	−0.138978	+	0.990295i	$0.544382\pi$
$752$	0.637161	+	26.8711i	0.0232349	+	0.979888i
$753$	22.8727	+	13.2056i	0.833529	+	0.481238i
$754$	12.9910	+	47.3587i	0.473106	+	1.72470i
$755$	−5.75712	−	2.38468i	−0.209523	−	0.0867873i
$756$	−27.6139	+	3.37821i	−1.00431	+	0.122864i
$757$	17.1737	+	41.4610i	0.624189	+	1.50693i	0.846741	+	0.532005i	$0.178561\pi$
$757$	17.1737	+	41.4610i	0.624189	+	1.50693i	−0.222552	+	0.974921i	$0.571439\pi$
$758$	−6.74021	+	53.6523i	−0.244815	+	1.94874i
$759$	4.83324	−	1.29506i	0.175436	−	0.0470078i
$760$	−1.47970	+	2.67151i	−0.0536743	+	0.0969058i
$761$	23.4881	+	6.29361i	0.851442	+	0.228143i	0.658046	−	0.752978i	$-0.271383\pi$
$761$	23.4881	+	6.29361i	0.851442	+	0.228143i	0.193396	+	0.981121i	$0.438050\pi$
$762$	−18.8340	+	2.59319i	−0.682282	+	0.0939413i
$763$	2.33311	−	15.2391i	0.0844642	−	0.551692i
$764$	−12.9723	+	23.0966i	−0.469320	+	0.835606i
$765$	2.61329	−	0.344046i	0.0944837	−	0.0124390i
$766$	−24.5887	+	0.145735i	−0.888426	+	0.00526561i
$767$	1.43199	−	2.48028i	0.0517062	−	0.0895577i
$768$	5.93075	−	16.4883i	0.214007	−	0.594971i
$769$	23.5872			0.850577			0.425288	−	0.905058i	$-0.360173\pi$
$769$	23.5872			0.850577			0.425288	+	0.905058i	$0.360173\pi$
$770$	0.564585	−	0.944669i	0.0203462	−	0.0340435i
$771$	0.623911	−	1.50625i	0.0224696	−	0.0542464i
$772$	−24.2769	+	0.287783i	−0.873743	+	0.0103575i
$773$	5.20276	−	39.5188i	0.187130	−	1.42139i	−0.597718	−	0.801706i	$-0.703926\pi$
$773$	5.20276	−	39.5188i	0.187130	−	1.42139i	0.784848	−	0.619688i	$-0.212741\pi$
$774$	5.72277	−	14.0510i	0.205701	−	0.505051i
$775$	44.0251	+	11.7965i	1.58143	+	0.423742i
$776$	−16.9998	+	0.302296i	−0.610257	+	0.0108518i
$777$	−15.8685	−	16.5500i	−0.569278	−	0.593729i
$778$	−18.2442	−	13.8282i	−0.654085	−	0.495766i
$779$	0.378774	−	0.493628i	0.0135710	−	0.0176860i
$780$	−5.63494	+	0.809916i	−0.201763	+	0.0289997i
$781$	4.53846	−	3.48248i	0.162399	−	0.124613i
$782$	−8.50711	−	31.0126i	−0.304214	−	1.10901i
$783$			32.5534i			1.16336i
$784$	23.9880	+	14.4422i	0.856713	+	0.515793i
$785$		−	7.89038i		−	0.281620i
$786$	−25.5947	+	7.02092i	−0.912932	+	0.250428i
$787$	11.8445	−	9.08861i	0.422211	−	0.323974i	−0.375708	−	0.926738i	$-0.622601\pi$
$787$	11.8445	−	9.08861i	0.422211	−	0.323974i	0.797920	+	0.602764i	$0.205934\pi$
$788$	41.6405	+	31.1747i	1.48338	+	1.11055i
$789$	11.6708	−	15.2097i	0.415491	−	0.541479i
$790$	−2.34857	+	3.09856i	−0.0835582	+	0.110242i
$791$	−36.3461	−	37.9072i	−1.29232	−	1.34783i
$792$	1.18362	−	3.00769i	0.0420583	−	0.106874i
$793$	71.0077	+	19.0265i	2.52156	+	0.675649i
$794$	−38.5555	−	15.7031i	−1.36828	−	0.557284i
$795$	−0.0975864	+	0.741242i	−0.00346103	+	0.0262892i
$796$	19.4547	−	19.9215i	0.689553	−	0.706097i
$797$	−13.5420	+	32.6932i	−0.479682	+	1.15805i	0.480077	+	0.877227i	$0.340609\pi$
$797$	−13.5420	+	32.6932i	−0.479682	+	1.15805i	−0.959758	+	0.280828i	$0.909391\pi$
$798$	8.19460	+	4.89754i	0.290086	+	0.173371i
$799$	−21.2244			−0.750866
$800$	18.5653	−	19.6996i	0.656382	−	0.696485i
$801$	−6.13287	+	10.6224i	−0.216694	+	0.375326i
$802$	−0.158298	−	26.7085i	−0.00558971	−	0.943109i
$803$	0.698722	−	0.0919885i	0.0246574	−	0.00324620i
$804$	4.69606	−	1.31816i	0.165617	−	0.0464879i
$805$	1.33594	−	8.72594i	0.0470858	−	0.307549i
$806$	10.3039	+	74.8358i	0.362940	+	2.63598i
$807$	−3.33453	−	0.893483i	−0.117381	−	0.0314521i
$808$	−0.564350	+	4.96769i	−0.0198538	+	0.174763i
$809$	−24.5165	+	6.56917i	−0.861954	+	0.230960i	−0.662605	−	0.748969i	$-0.730549\pi$
$809$	−24.5165	+	6.56917i	−0.861954	+	0.230960i	−0.199349	+	0.979929i	$0.563883\pi$
$810$	−0.231405	−	0.0290709i	−0.00813075	−	0.00102145i
$811$	−3.58663	−	8.65888i	−0.125943	−	0.304054i	0.848314	−	0.529494i	$-0.177618\pi$
$811$	−3.58663	−	8.65888i	−0.125943	−	0.304054i	−0.974257	+	0.225440i	$0.927618\pi$
$812$	20.1831	−	25.8097i	0.708287	−	0.905743i
$813$	−1.62146	−	0.671630i	−0.0568670	−	0.0235551i
$814$	6.84919	−	1.87881i	0.240064	−	0.0658524i
$815$	0.469846	+	0.271266i	0.0164580	+	0.00950203i
$816$	12.9051	+	4.99047i	0.451770	+	0.174701i
$817$	−12.0208	+	6.94019i	−0.420553	+	0.242806i
$818$	14.3969	+	3.76632i	0.503375	+	0.131686i
$819$	−2.92975	−	26.5561i	−0.102374	−	0.927944i
$820$	0.194594	−	0.153016i	0.00679551	−	0.00534354i
$821$	21.4543	−	27.9598i	0.748762	−	0.975805i	−0.251207	−	0.967933i	$-0.580828\pi$
$821$	21.4543	−	27.9598i	0.748762	−	0.975805i	0.999969	−	0.00787202i	$-0.00250577\pi$
$822$	−12.7146	+	5.35506i	−0.443472	+	0.186779i
$823$	−41.4290	+	11.1009i	−1.44413	+	0.386952i	−0.893976	−	0.448114i	$-0.852096\pi$
$823$	−41.4290	+	11.1009i	−1.44413	+	0.386952i	−0.550149	+	0.835066i	$0.685429\pi$
$824$	32.9529	+	8.20462i	1.14797	+	0.285822i
$825$	−2.35176	+	2.35176i	−0.0818777	+	0.0818777i
$826$	−1.89801	+	0.220788i	−0.0660402	+	0.00768220i
$827$	−10.6775	+	4.42277i	−0.371293	+	0.153795i	−0.560524	−	0.828138i	$-0.689400\pi$
$827$	−10.6775	+	4.42277i	−0.371293	+	0.153795i	0.189231	+	0.981933i	$0.439400\pi$
$828$	−0.307316	−	25.9246i	−0.0106800	−	0.900943i
$829$	29.4623	+	38.3961i	1.02327	+	1.33355i	0.941542	+	0.336896i	$0.109377\pi$
$829$	29.4623	+	38.3961i	1.02327	+	1.33355i	0.0817272	+	0.996655i	$0.473956\pi$
$830$	0.361740	−	0.00214400i	0.0125562	−	7.44192e-5i
$831$	−3.45512	−	5.98445i	−0.119857	−	0.207598i
$832$	42.0340	+	15.6845i	1.45727	+	0.543764i
$833$	−11.8499	+	18.6662i	−0.410576	+	0.646744i
$834$	−9.15510	−	15.6423i	−0.317015	−	0.541647i
$835$	−3.50022	+	0.460812i	−0.121130	+	0.0159471i
$836$	−2.54323	+	1.50881i	−0.0879593	+	0.0521832i
$837$	−6.53624	+	49.6477i	−0.225925	+	1.71607i
$838$	10.4367	+	13.4357i	0.360528	+	0.464128i
$839$	−9.27209	+	9.27209i	−0.320108	+	0.320108i	−0.848808	−	0.528700i	$-0.822679\pi$
$839$	−9.27209	+	9.27209i	−0.320108	+	0.320108i	0.528700	+	0.848808i	$0.322679\pi$
$840$	2.67701	+	2.69441i	0.0923656	+	0.0929661i
$841$	−6.60378	−	6.60378i	−0.227717	−	0.227717i
$842$	1.42078	−	11.3094i	0.0489633	−	0.389749i
$843$	33.6202	+	4.42619i	1.15794	+	0.152446i
$844$	5.48796	+	38.1822i	0.188904	+	1.31429i
$845$	−1.11615	−	8.47803i	−0.0383968	−	0.291653i
$846$	−16.5544	−	4.33073i	−0.569151	−	0.148894i
$847$	−24.5706	+	13.5053i	−0.844256	+	0.464049i
$848$	3.47506	−	4.75822i	0.119334	−	0.163398i
$849$	−15.4684	+	8.93071i	−0.530876	+	0.306501i
$850$	15.2037	+	15.0245i	0.521481	+	0.515336i
$851$	45.1964	−	34.6804i	1.54931	−	1.18883i
$852$	7.77109	+	18.1495i	0.266233	+	0.621793i
$853$	12.5837	+	30.3797i	0.430856	+	1.04018i	0.979012	+	0.203803i	$0.0653302\pi$
$853$	12.5837	+	30.3797i	0.430856	+	1.04018i	−0.548155	+	0.836377i	$0.684670\pi$
$854$	−18.0832	−	45.5912i	−0.618795	−	1.56010i
$855$	−1.37475	−	1.37475i	−0.0470154	−	0.0470154i
$856$	−2.50606	+	3.38907i	−0.0856555	+	0.115836i
$857$	−9.83702	−	36.7123i	−0.336026	−	1.25407i	−0.902752	−	0.430161i	$-0.858457\pi$
$857$	−9.83702	−	36.7123i	−0.336026	−	1.25407i	0.566726	−	0.823906i	$-0.308210\pi$
$858$	−5.10518	−	2.07927i	−0.174288	−	0.0709852i
$859$	−26.3019	−	20.1822i	−0.897409	−	0.688606i	0.0533372	−	0.998577i	$-0.483014\pi$
$859$	−26.3019	−	20.1822i	−0.897409	−	0.688606i	−0.950746	+	0.309970i	$0.899681\pi$
$860$	−5.31694	+	1.49244i	−0.181306	+	0.0508917i
$861$	−0.458075	−	0.623694i	−0.0156112	−	0.0212554i
$862$	25.2736	−	14.7921i	0.860821	−	0.503821i
$863$	−8.38490	−	14.5231i	−0.285425	−	0.494371i	0.687287	−	0.726386i	$-0.258801\pi$
$863$	−8.38490	−	14.5231i	−0.285425	−	0.494371i	−0.972712	+	0.232015i	$0.925468\pi$
$864$	24.1209	+	17.3979i	0.820609	+	0.591888i
$865$	5.32691	−	9.22647i	0.181120	−	0.313709i
$866$	40.4093	+	23.0121i	1.37316	+	0.781983i
$867$	2.94355	−	7.10637i	0.0999684	−	0.241345i
$868$	35.9637	−	35.3103i	1.22069	−	1.19851i
$869$	−3.47820	+	1.44072i	−0.117990	+	0.0488730i
$870$	3.50993	−	2.72647i	0.118998	−	0.0924358i
$871$	3.23228	+	12.0630i	0.109522	+	0.408740i
$872$	−12.8949	+	10.2639i	−0.436676	+	0.347581i
$873$	2.80148	−	10.4553i	0.0948158	−	0.353857i
$874$	−14.3279	+	18.9034i	−0.484649	+	0.639418i
$875$	4.35759	+	11.1792i	0.147314	+	0.377926i
$876$	−0.288869	+	2.41506i	−0.00975999	+	0.0815973i
$877$	4.28406	+	32.5407i	0.144662	+	1.09882i	0.897626	+	0.440758i	$0.145290\pi$
$877$	4.28406	+	32.5407i	0.144662	+	1.09882i	−0.752963	+	0.658062i	$0.771376\pi$
$878$	−7.72583	−	7.63479i	−0.260734	−	0.257662i
$879$	−7.55886	−	4.36411i	−0.254954	−	0.147198i
$880$	−1.12888	+	0.331357i	−0.0380547	+	0.0111700i
$881$		−	27.9606i		−	0.942017i	−0.882129	−	0.471008i	$-0.843890\pi$
$881$		−	27.9606i		−	0.942017i	0.882129	−	0.471008i	$-0.156110\pi$
$882$	−13.0513	+	12.1411i	−0.439460	+	0.408812i
$883$	−3.40229	−	1.40928i	−0.114496	−	0.0474259i	0.324700	−	0.945817i	$-0.394737\pi$
$883$	−3.40229	−	1.40928i	−0.114496	−	0.0474259i	−0.439196	+	0.898391i	$0.644737\pi$
$884$	−13.1684	+	32.8888i	−0.442903	+	1.10617i
$885$	−0.256983	−	0.0338324i	−0.00863838	−	0.00113726i
$886$	−4.03868	+	1.70099i	−0.135682	+	0.0571458i
$887$	9.44426	−	35.2465i	0.317107	−	1.18346i	−0.604904	−	0.796298i	$-0.706789\pi$
$887$	9.44426	−	35.2465i	0.317107	−	1.18346i	0.922012	−	0.387162i	$-0.126545\pi$
$888$	0.435803	+	24.5076i	0.0146246	+	0.822422i
$889$	−23.4424	+	22.4770i	−0.786233	+	0.753854i
$890$	4.42295	−	0.608982i	0.148258	−	0.0204131i
$891$	−0.179163	−	0.137477i	−0.00600220	−	0.00460565i
$892$	−11.8739	−	20.0146i	−0.397569	−	0.670137i
$893$	9.53020	+	12.4200i	0.318916	+	0.415619i
$894$	7.98268	−	14.0176i	0.266981	−	0.468819i
$895$	−1.21402			−0.0405801
$896$	−8.33740	−	28.7487i	−0.278533	−	0.960427i
$897$	−44.2163			−1.47634
$898$	9.98095	−	17.5266i	0.333069	−	0.584870i
$899$	−35.9024	−	46.7889i	−1.19741	−	1.56050i
$900$	8.79269	+	14.8209i	0.293090	+	0.494029i
$901$	3.69117	+	2.83233i	0.122971	+	0.0943587i
$902$	0.237461	−	0.0326952i	0.00790658	−	0.00108863i
$903$	4.11654	+	16.7651i	0.136990	+	0.557908i
$904$	0.998191	+	56.1338i	0.0331993	+	1.86698i
$905$	0.261404	−	0.975572i	0.00868935	−	0.0324291i
$906$	19.1918	−	8.08309i	0.637605	−	0.268543i
$907$	−23.7197	−	3.12276i	−0.787600	−	0.103690i	−0.274012	−	0.961726i	$-0.588351\pi$
$907$	−23.7197	−	3.12276i	−0.787600	−	0.103690i	−0.513588	+	0.858037i	$0.671684\pi$
$908$	7.53990	−	18.8312i	0.250220	−	0.624936i
$909$	−2.94058	−	1.21803i	−0.0975330	−	0.0403995i
$910$	−6.97959	+	6.77200i	−0.231371	+	0.224490i
$911$			9.52571i			0.315601i	0.987471	+	0.157800i	$0.0504403\pi$
$911$			9.52571i			0.315601i	−0.987471	+	0.157800i	$0.949560\pi$
$912$	−2.87438	−	9.79259i	−0.0951802	−	0.324265i
$913$	0.303350	+	0.175139i	0.0100394	+	0.00579626i
$914$	−5.60520	−	5.53915i	−0.185404	−	0.183219i
$915$	−0.868409	−	6.59622i	−0.0287087	−	0.218064i
$916$	3.59155	−	30.0268i	0.118668	−	0.992113i
$917$	−28.3499	+	35.3809i	−0.936197	+	1.16838i
$918$	−14.1857	+	18.7158i	−0.468197	+	0.617712i
$919$	1.32232	−	4.93496i	0.0436192	−	0.162789i	−0.940681	−	0.339293i	$-0.889812\pi$
$919$	1.32232	−	4.93496i	0.0436192	−	0.162789i	0.984300	+	0.176504i	$0.0564788\pi$
$920$	−7.38365	+	5.87716i	−0.243432	+	0.193764i
$921$	−4.13370	−	15.4272i	−0.136210	−	0.508343i
$922$	−42.9626	+	33.3727i	−1.41490	+	1.09907i
$923$	−46.7030	+	19.3450i	−1.53725	+	0.636749i
$924$	0.919273	+	3.56104i	0.0302419	+	0.117150i
$925$	−14.4907	+	34.9836i	−0.476451	+	1.15025i
$926$	9.48634	+	5.40223i	0.311741	+	0.177528i
$927$	−10.8094	+	18.7225i	−0.355029	+	0.614928i
$928$	−34.5761	+	5.59881i	−1.13502	+	0.183790i
$929$	20.3649	+	35.2731i	0.668151	+	1.15727i	0.978421	+	0.206623i	$0.0662474\pi$
$929$	20.3649	+	35.2731i	0.668151	+	1.15727i	−0.310270	+	0.950649i	$0.600419\pi$
$930$	5.90048	−	3.45343i	0.193484	−	0.113243i
$931$	16.2438	−	1.44720i	0.532370	−	0.0474302i
$932$	31.0949	−	8.72819i	1.01855	−	0.285901i
$933$	23.4238	+	17.9737i	0.766861	+	0.588433i
$934$	45.3168	+	18.4569i	1.48281	+	0.603929i
$935$	−0.240448	−	0.897363i	−0.00786348	−	0.0293469i
$936$	−16.9817	+	22.9652i	−0.555066	+	0.750642i
$937$	0.830644	+	0.830644i	0.0271359	+	0.0271359i	0.720545	−	0.693409i	$-0.243892\pi$
$937$	0.830644	+	0.830644i	0.0271359	+	0.0271359i	−0.693409	+	0.720545i	$0.743892\pi$
$938$	5.17152	−	6.53307i	0.168856	−	0.213312i
$939$	−7.06983	−	17.0681i	−0.230715	−	0.556995i
$940$	2.45159	+	5.72573i	0.0799619	+	0.186753i
$941$	−0.366869	+	0.281509i	−0.0119596	+	0.00917692i	−0.614724	−	0.788742i	$-0.710733\pi$
$941$	−0.366869	+	0.281509i	−0.0119596	+	0.00917692i	0.602764	+	0.797919i	$0.294066\pi$
$942$	18.7554	+	18.5344i	0.611085	+	0.603884i
$943$	1.66512	−	0.961355i	0.0542236	−	0.0313060i
$944$	1.64964	+	1.20477i	0.0536911	+	0.0392121i
$945$	−5.64943	+	3.10523i	−0.183776	+	0.101013i
$946$	−5.17326	−	1.35336i	−0.168197	−	0.0440015i
$947$	4.02535	+	30.5756i	0.130806	+	0.993573i	0.923404	+	0.383829i	$0.125395\pi$
$947$	4.02535	+	30.5756i	0.130806	+	0.993573i	−0.792598	+	0.609745i	$0.791272\pi$
$948$	−1.84853	−	12.8610i	−0.0600374	−	0.417707i
$949$	−6.17436	−	0.812870i	−0.200428	−	0.0263869i
$950$	1.96521	−	15.6431i	0.0637597	−	0.507530i
$951$	−14.5778	−	14.5778i	−0.472716	−	0.472716i
$952$	22.8508	−	6.04355i	0.740597	−	0.195873i
$953$	17.7776	−	17.7776i	0.575872	−	0.575872i	−0.357892	−	0.933763i	$-0.616504\pi$
$953$	17.7776	−	17.7776i	0.575872	−	0.575872i	0.933763	+	0.357892i	$0.116504\pi$
$954$	2.30107	+	2.96229i	0.0744999	+	0.0959078i
$955$	−0.801235	+	6.08598i	−0.0259273	+	0.196938i
$956$	−7.75355	+	4.59991i	−0.250768	+	0.148772i
$957$	4.26674	−	0.561727i	0.137924	−	0.0181581i
$958$	24.6414	+	42.1019i	0.796127	+	1.36025i
$959$	−12.2103	+	20.1581i	−0.394292	+	0.650941i
$960$	−0.144363	−	4.05787i	−0.00465928	−	0.130967i
$961$	−29.8608	−	51.7204i	−0.963252	−	1.66840i
$962$	−62.7586	+	0.371963i	−2.02342	+	0.0119926i
$963$	−1.63352	−	2.12884i	−0.0526393	−	0.0686009i
$964$	−0.290136	−	24.4753i	−0.00934464	−	0.788297i
$965$	−5.19774	+	2.15297i	−0.167321	+	0.0693067i
$966$	17.6034	+	23.6727i	0.566382	+	0.761656i
$967$	0.297332	−	0.297332i	0.00956155	−	0.00956155i	−0.702310	−	0.711871i	$-0.747848\pi$
$967$	0.297332	−	0.297332i	0.00956155	−	0.00956155i	0.711871	+	0.702310i	$0.247848\pi$
$968$	29.0855	+	7.24173i	0.934844	+	0.232758i
$969$	7.78424	−	2.08578i	0.250066	−	0.0670049i
$970$	−3.63102	+	1.52929i	−0.116585	+	0.0491026i
$971$	3.48079	−	4.53625i	0.111704	−	0.145575i	−0.734155	−	0.678982i	$-0.762422\pi$
$971$	3.48079	−	4.53625i	0.111704	−	0.145575i	0.845859	+	0.533406i	$0.179088\pi$
$972$	−24.1840	+	19.0167i	−0.775703	+	0.609961i
$973$	−28.3494	−	12.4471i	−0.908839	−	0.399036i
$974$	32.5011	+	8.50251i	1.04140	+	0.272438i
$975$	25.4522	−	14.6948i	0.815123	−	0.470612i
$976$	−18.9113	+	48.9038i	−0.605335	+	1.56537i
$977$	29.3094	+	16.9218i	0.937691	+	0.541376i	0.889236	−	0.457449i	$-0.151237\pi$
$977$	29.3094	+	16.9218i	0.937691	+	0.541376i	0.0484555	+	0.998825i	$0.484570\pi$
$978$	−1.74846	+	0.479624i	−0.0559097	+	0.0153367i
$979$	3.99406	+	1.65439i	0.127651	+	0.0528746i
$980$	6.40435	+	1.04068i	0.204579	+	0.0332433i
$981$	−4.01518	−	9.69351i	−0.128195	−	0.309490i
$982$	−15.7192	−	1.97477i	−0.501620	−	0.0630173i
$983$	19.7773	−	5.29932i	0.630799	−	0.169022i	0.0707668	−	0.997493i	$-0.477455\pi$
$983$	19.7773	−	5.29932i	0.630799	−	0.169022i	0.560032	+	0.828471i	$0.310789\pi$
$984$	−0.0933806	+	0.821982i	−0.00297686	+	0.0262038i
$985$	11.6430	+	3.11975i	0.370978	+	0.0994034i
$986$	−3.77258	−	27.3997i	−0.120144	−	0.872586i
$987$	18.1409	−	7.07122i	0.577430	−	0.225079i
$988$	25.1586	−	7.06189i	0.800402	−	0.224669i
$989$	−42.5256	+	5.59860i	−1.35224	+	0.178025i
$990$	−0.00443910	−	0.748976i	−0.000141084	−	0.0238040i
$991$	1.21819	−	2.10997i	0.0386971	−	0.0670254i	−0.846028	−	0.533138i	$-0.821013\pi$
$991$	1.21819	−	2.10997i	0.0386971	−	0.0670254i	0.884725	+	0.466113i	$0.154346\pi$
$992$	−53.8567	+	1.59646i	−1.70995	+	0.0506878i
$993$	22.5520			0.715666
$994$	28.9505	+	17.3024i	0.918253	+	0.548798i
$995$	2.46925	−	5.96129i	0.0782804	−	0.188986i
$996$	−0.844628	+	0.864893i	−0.0267631	+	0.0274052i
$997$	0.798664	−	6.06645i	0.0252939	−	0.192126i	−0.974133	−	0.225975i	$-0.927443\pi$
$997$	0.798664	−	6.06645i	0.0252939	−	0.192126i	0.999427	+	0.0338488i	$0.0107765\pi$
$998$	8.96732	+	3.65227i	0.283855	+	0.115611i
$999$	−40.1853	−	10.7676i	−1.27141	−	0.340672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.109.20	yes	240
4.3	odd	2		896.2.bh.a.529.10		240
7.2	even	3	inner	224.2.bd.a.205.1	yes	240
28.23	odd	6		896.2.bh.a.401.21		240
32.5	even	8	inner	224.2.bd.a.165.1	yes	240
32.27	odd	8		896.2.bh.a.753.21		240
224.37	even	24	inner	224.2.bd.a.37.20	✓	240
224.219	odd	24		896.2.bh.a.625.10		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.20	✓	240	224.37	even	24	inner
224.2.bd.a.109.20	yes	240	1.1	even	1	trivial
224.2.bd.a.165.1	yes	240	32.5	even	8	inner
224.2.bd.a.205.1	yes	240	7.2	even	3	inner
896.2.bh.a.401.21		240	28.23	odd	6
896.2.bh.a.529.10		240	4.3	odd	2
896.2.bh.a.625.10		240	224.219	odd	24
896.2.bh.a.753.21		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)

\(f(q)\)	\(=\)	\(q+(0.699836 - 1.22891i) q^{2} +(0.666690 + 0.868847i) q^{3} +(-1.02046 - 1.72008i) q^{4} +(-0.367682 - 0.282133i) q^{5} +(1.53431 - 0.211254i) q^{6} +(1.90974 - 1.83109i) q^{7} +(-2.82798 + 0.0502881i) q^{8} +(0.466037 - 1.73928i) q^{9} +O(q^{10})\)	\(q+(0.699836 - 1.22891i) q^{2} +(0.666690 + 0.868847i) q^{3} +(-1.02046 - 1.72008i) q^{4} +(-0.367682 - 0.282133i) q^{5} +(1.53431 - 0.211254i) q^{6} +(1.90974 - 1.83109i) q^{7} +(-2.82798 + 0.0502881i) q^{8} +(0.466037 - 1.73928i) q^{9} +(-0.604034 + 0.254404i) q^{10} +(-0.629214 - 0.0828376i) q^{11} +(0.814152 - 2.03338i) q^{12} +(5.18123 + 2.14613i) q^{13} +(-0.913752 - 3.62837i) q^{14} -0.507554i q^{15} +(-1.91732 + 3.51054i) q^{16} +(-2.73539 - 1.57928i) q^{17} +(-1.81127 - 1.78993i) q^{18} +(0.304092 + 2.30981i) q^{19} +(-0.110084 + 0.920347i) q^{20} +(2.86414 + 0.438501i) q^{21} +(-0.542147 + 0.715278i) q^{22} +(-1.86331 + 6.95396i) q^{23} +(-1.92908 - 2.42355i) q^{24} +(-1.23850 - 4.62216i) q^{25} +(6.26342 - 4.86534i) q^{26} +(4.85725 - 2.01194i) q^{27} +(-5.09843 - 1.41634i) q^{28} +(-2.36952 + 5.72053i) q^{29} +(-0.623741 - 0.355205i) q^{30} +(-4.76239 + 8.24871i) q^{31} +(2.97234 + 4.81302i) q^{32} +(-0.347517 - 0.601918i) q^{33} +(-3.85512 + 2.25632i) q^{34} +(-1.21879 + 0.134461i) q^{35} +(-3.46726 + 0.973242i) q^{36} +(-6.27791 - 4.81721i) q^{37} +(3.05137 + 1.24278i) q^{38} +(1.58961 + 5.93250i) q^{39} +(1.05399 + 0.779375i) q^{40} +(-0.188847 - 0.188847i) q^{41} +(2.54331 - 3.21291i) q^{42} +(2.27999 + 5.50439i) q^{43} +(0.499601 + 1.16683i) q^{44} +(-0.662060 + 0.508017i) q^{45} +(7.24181 + 7.15647i) q^{46} +(5.81940 - 3.35983i) q^{47} +(-4.32838 + 0.674581i) q^{48} +(0.294206 - 6.99381i) q^{49} +(-6.54699 - 1.71274i) q^{50} +(-0.451505 - 3.42952i) q^{51} +(-1.59572 - 11.1021i) q^{52} +(-1.46042 - 0.192268i) q^{53} +(0.926775 - 7.37716i) q^{54} +(0.207980 + 0.207980i) q^{55} +(-5.30862 + 5.27433i) q^{56} +(-1.80413 + 1.80413i) q^{57} +(5.37177 + 6.91537i) q^{58} +(0.0666577 - 0.506316i) q^{59} +(-0.873032 + 0.517939i) q^{60} +(12.9961 - 1.71097i) q^{61} +(6.80406 + 11.6253i) q^{62} +(-2.29476 - 4.17492i) q^{63} +(7.99494 - 0.284428i) q^{64} +(-1.29955 - 2.25089i) q^{65} +(-0.982910 + 0.00582560i) q^{66} +(1.35564 + 1.76670i) q^{67} +(0.0748790 + 6.31666i) q^{68} +(-7.28417 + 3.01720i) q^{69} +(-0.687711 + 1.59189i) q^{70} +(-6.37378 + 6.37378i) q^{71} +(-1.23048 + 4.94207i) q^{72} +(-1.07263 + 0.287410i) q^{73} +(-10.3134 + 4.34376i) q^{74} +(3.19025 - 4.15761i) q^{75} +(3.66273 - 2.88013i) q^{76} +(-1.35332 + 0.993951i) q^{77} +(8.40299 + 2.19828i) q^{78} +(5.13736 - 2.96606i) q^{79} +(1.69540 - 0.749824i) q^{80} +(0.308165 + 0.177919i) q^{81} +(-0.364239 + 0.0999150i) q^{82} +(-0.509916 - 0.211214i) q^{83} +(-2.16849 - 5.37401i) q^{84} +(0.560188 + 1.35241i) q^{85} +(8.36004 + 1.05025i) q^{86} +(-6.55000 + 1.75507i) q^{87} +(1.78357 + 0.202621i) q^{88} +(-6.57980 - 1.76305i) q^{89} +(0.160976 + 1.16914i) q^{90} +(13.8246 - 5.38875i) q^{91} +(13.8628 - 3.89121i) q^{92} +(-10.3419 + 1.36154i) q^{93} +(-0.0563225 - 9.50287i) q^{94} +(0.539863 - 0.935070i) q^{95} +(-2.20015 + 5.79130i) q^{96} +6.01128 q^{97} +(-8.38890 - 5.25607i) q^{98} +(-0.437315 + 1.05577i) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more