LMFDB - Embedded newform 224.2.u.c.29.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(29,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("224.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.u (of order $8$, degree $4$, 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:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			29.11
Character	$\chi$	$=$	224.29
Dual form			224.2.u.c.85.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.875361 + 1.11074i) q^{2} +(0.999166 + 0.413868i) q^{3} +(-0.467486 + 1.94460i) q^{4} +(0.523077 + 1.26282i) q^{5} +(0.414931 + 1.47210i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.56916 + 1.18297i) q^{8} +(-1.29427 - 1.29427i) q^{9} +O(q^{10})$	\(q+(0.875361 + 1.11074i) q^{2} +(0.999166 + 0.413868i) q^{3} +(-0.467486 + 1.94460i) q^{4} +(0.523077 + 1.26282i) q^{5} +(0.414931 + 1.47210i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.56916 + 1.18297i) q^{8} +(-1.29427 - 1.29427i) q^{9} +(-0.944783 + 1.68643i) q^{10} +(0.904574 - 0.374687i) q^{11} +(-1.27190 + 1.74950i) q^{12} +(0.430806 - 1.04006i) q^{13} +(1.40439 + 0.166438i) q^{14} +1.47825i q^{15} +(-3.56291 - 1.81814i) q^{16} -3.31157i q^{17} +(0.304644 - 2.57056i) q^{18} +(-1.25398 + 3.02738i) q^{19} +(-2.70021 + 0.426824i) q^{20} +(0.999166 - 0.413868i) q^{21} +(1.20801 + 0.676760i) q^{22} +(2.85663 + 2.85663i) q^{23} +(-3.05661 + 0.118690i) q^{24} +(2.21443 - 2.21443i) q^{25} +(1.53235 - 0.431913i) q^{26} +(-1.99914 - 4.82635i) q^{27} +(1.04448 + 1.70560i) q^{28} +(7.03942 + 2.91582i) q^{29} +(-1.64195 + 1.29400i) q^{30} -5.90990 q^{31} +(-1.09935 - 5.54900i) q^{32} +1.05889 q^{33} +(3.67830 - 2.89882i) q^{34} +(1.26282 + 0.523077i) q^{35} +(3.12190 - 1.91179i) q^{36} +(-1.70363 - 4.11292i) q^{37} +(-4.46033 + 1.25721i) q^{38} +(0.860894 - 0.860894i) q^{39} +(-2.83775 - 2.62560i) q^{40} +(-7.31644 - 7.31644i) q^{41} +(1.33433 + 0.747529i) q^{42} +(0.902235 - 0.373718i) q^{43} +(0.305739 + 1.93419i) q^{44} +(0.957430 - 2.31144i) q^{45} +(-0.672390 + 5.67356i) q^{46} +10.7312i q^{47} +(-2.80747 - 3.29120i) q^{48} -1.00000i q^{49} +(4.39808 + 0.521229i) q^{50} +(1.37055 - 3.30881i) q^{51} +(1.82110 + 1.32396i) q^{52} +(5.29777 - 2.19441i) q^{53} +(3.61085 - 6.44533i) q^{54} +(0.946323 + 0.946323i) q^{55} +(-0.980184 + 2.65316i) q^{56} +(-2.50588 + 2.50588i) q^{57} +(2.92332 + 10.3714i) q^{58} +(-0.563137 - 1.35953i) q^{59} +(-2.87460 - 0.691061i) q^{60} +(-0.0893244 - 0.0369994i) q^{61} +(-5.17330 - 6.56436i) q^{62} -1.83038 q^{63} +(5.20116 - 6.07848i) q^{64} +1.53875 q^{65} +(0.926911 + 1.17615i) q^{66} +(-4.92908 - 2.04169i) q^{67} +(6.43968 + 1.54811i) q^{68} +(1.67198 + 4.03652i) q^{69} +(0.524421 + 1.86055i) q^{70} +(0.553232 - 0.553232i) q^{71} +(4.85628 + 1.79411i) q^{72} +(-6.76325 - 6.76325i) q^{73} +(3.07709 - 5.49257i) q^{74} +(3.12907 - 1.29610i) q^{75} +(-5.30082 - 3.85375i) q^{76} +(0.374687 - 0.904574i) q^{77} +(1.70982 + 0.202636i) q^{78} +11.8884i q^{79} +(0.432307 - 5.45035i) q^{80} -0.158568i q^{81} +(1.72213 - 14.5312i) q^{82} +(-2.47245 + 5.96903i) q^{83} +(0.337711 + 2.13645i) q^{84} +(4.18192 - 1.73221i) q^{85} +(1.20489 + 0.675010i) q^{86} +(5.82679 + 5.82679i) q^{87} +(-1.88075 + 2.03271i) q^{88} +(-2.11160 + 2.11160i) q^{89} +(3.40551 - 0.959890i) q^{90} +(-0.430806 - 1.04006i) q^{91} +(-6.89043 + 4.21956i) q^{92} +(-5.90497 - 2.44592i) q^{93} +(-11.9195 + 9.39364i) q^{94} -4.47897 q^{95} +(1.19812 - 5.99936i) q^{96} -6.12164 q^{97} +(1.11074 - 0.875361i) q^{98} +(-1.65571 - 0.685819i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 20 q^{6}+O(q^{10}) $ 52 * q - 20 * q^6	$ 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) $ 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.875361	+	1.11074i	0.618974	+	0.785412i
$2$	0.875361	+	1.11074i	0.618974	+	0.785412i
$3$	0.999166	+	0.413868i	0.576869	+	0.238947i	0.651990	−	0.758228i	$-0.273934\pi$
$3$	0.999166	+	0.413868i	0.576869	+	0.238947i	−0.0751212	+	0.997174i	$0.523934\pi$
$4$	−0.467486	+	1.94460i	−0.233743	+	0.972298i
$5$	0.523077	+	1.26282i	0.233927	+	0.564750i	0.996633	−	0.0819958i	$-0.0261294\pi$
$5$	0.523077	+	1.26282i	0.233927	+	0.564750i	−0.762705	+	0.646746i	$0.776129\pi$
$6$	0.414931	+	1.47210i	0.169395	+	0.600981i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	−2.56916	+	1.18297i	−0.908335	+	0.418243i
$9$	−1.29427	−	1.29427i	−0.431425	−	0.431425i
$10$	−0.944783	+	1.68643i	−0.298767	+	0.533295i
$11$	0.904574	−	0.374687i	0.272739	−	0.112972i	−0.242122	−	0.970246i	$-0.577843\pi$
$11$	0.904574	−	0.374687i	0.272739	−	0.112972i	0.514861	+	0.857274i	$0.327843\pi$
$12$	−1.27190	+	1.74950i	−0.367167	+	0.505037i
$13$	0.430806	−	1.04006i	0.119484	−	0.288460i	−0.852810	−	0.522222i	$-0.825103\pi$
$13$	0.430806	−	1.04006i	0.119484	−	0.288460i	0.972294	+	0.233761i	$0.0751034\pi$
$14$	1.40439	+	0.166438i	0.375338	+	0.0444824i
$15$			1.47825i			0.381683i
$16$	−3.56291	−	1.81814i	−0.890729	−	0.454536i
$17$		−	3.31157i		−	0.803175i	−0.915821	−	0.401587i	$-0.868459\pi$
$17$		−	3.31157i		−	0.803175i	0.915821	−	0.401587i	$-0.131541\pi$
$18$	0.304644	−	2.57056i	0.0718054	−	0.605887i
$19$	−1.25398	+	3.02738i	−0.287684	+	0.694530i	−0.999973	−	0.00735628i	$-0.997658\pi$
$19$	−1.25398	+	3.02738i	−0.287684	+	0.694530i	0.712289	+	0.701886i	$0.247658\pi$
$20$	−2.70021	+	0.426824i	−0.603785	+	0.0954408i
$21$	0.999166	−	0.413868i	0.218036	−	0.0903134i
$22$	1.20801	+	0.676760i	0.257548	+	0.144286i
$23$	2.85663	+	2.85663i	0.595649	+	0.595649i	0.939152	−	0.343503i	$-0.111614\pi$
$23$	2.85663	+	2.85663i	0.595649	+	0.595649i	−0.343503	+	0.939152i	$0.611614\pi$
$24$	−3.05661	+	0.118690i	−0.623928	+	0.0242275i
$25$	2.21443	−	2.21443i	0.442886	−	0.442886i
$26$	1.53235	−	0.431913i	0.300518	−	0.0847051i
$27$	−1.99914	−	4.82635i	−0.384735	−	0.928832i
$28$	1.04448	+	1.70560i	0.197387	+	0.322328i
$29$	7.03942	+	2.91582i	1.30719	+	0.541455i	0.924063	−	0.382241i	$-0.124848\pi$
$29$	7.03942	+	2.91582i	1.30719	+	0.541455i	0.383126	+	0.923696i	$0.374848\pi$
$30$	−1.64195	+	1.29400i	−0.299778	+	0.236252i
$31$	−5.90990			−1.06145			−0.530725	−	0.847544i	$-0.678080\pi$
$31$	−5.90990			−1.06145			−0.530725	+	0.847544i	$0.678080\pi$
$32$	−1.09935	−	5.54900i	−0.194340	−	0.980934i
$33$	1.05889			0.184329
$34$	3.67830	−	2.89882i	0.630823	−	0.497144i
$35$	1.26282	+	0.523077i	0.213455	+	0.0884162i
$36$	3.12190	−	1.91179i	0.520316	−	0.318631i
$37$	−1.70363	−	4.11292i	−0.280074	−	0.676159i	0.719763	−	0.694220i	$-0.244251\pi$
$37$	−1.70363	−	4.11292i	−0.280074	−	0.676159i	−0.999837	+	0.0180612i	$0.994251\pi$
$38$	−4.46033	+	1.25721i	−0.723560	+	0.203946i
$39$	0.860894	−	0.860894i	0.137853	−	0.137853i
$40$	−2.83775	−	2.62560i	−0.448687	−	0.415144i
$41$	−7.31644	−	7.31644i	−1.14264	−	1.14264i	−0.987966	−	0.154670i	$-0.950568\pi$
$41$	−7.31644	−	7.31644i	−1.14264	−	1.14264i	−0.154670	−	0.987966i	$-0.549432\pi$
$42$	1.33433	+	0.747529i	0.205892	+	0.115346i
$43$	0.902235	−	0.373718i	0.137590	−	0.0569915i	−0.312826	−	0.949810i	$-0.601276\pi$
$43$	0.902235	−	0.373718i	0.137590	−	0.0569915i	0.450416	+	0.892819i	$0.351276\pi$
$44$	0.305739	+	1.93419i	0.0460919	+	0.291590i
$45$	0.957430	−	2.31144i	0.142725	−	0.344569i
$46$	−0.672390	+	5.67356i	−0.0991385	+	0.836520i
$47$			10.7312i			1.56530i	0.622462	+	0.782650i	$0.286133\pi$
$47$			10.7312i			1.56530i	−0.622462	+	0.782650i	$0.713867\pi$
$48$	−2.80747	−	3.29120i	−0.405224	−	0.475044i
$49$		−	1.00000i		−	0.142857i
$50$	4.39808	+	0.521229i	0.621983	+	0.0737130i
$51$	1.37055	−	3.30881i	0.191916	−	0.463326i
$52$	1.82110	+	1.32396i	0.252541	+	0.183600i
$53$	5.29777	−	2.19441i	0.727704	−	0.301425i	0.0120961	−	0.999927i	$-0.496150\pi$
$53$	5.29777	−	2.19441i	0.727704	−	0.301425i	0.715608	+	0.698502i	$0.246150\pi$
$54$	3.61085	−	6.44533i	0.491375	−	0.877098i
$55$	0.946323	+	0.946323i	0.127602	+	0.127602i
$56$	−0.980184	+	2.65316i	−0.130983	+	0.354543i
$57$	−2.50588	+	2.50588i	−0.331911	+	0.331911i
$58$	2.92332	+	10.3714i	0.383850	+	1.36183i
$59$	−0.563137	−	1.35953i	−0.0733142	−	0.176996i	0.882974	−	0.469422i	$-0.155538\pi$
$59$	−0.563137	−	1.35953i	−0.0733142	−	0.176996i	−0.956288	+	0.292426i	$0.905538\pi$
$60$	−2.87460	−	0.691061i	−0.371110	−	0.0892156i
$61$	−0.0893244	−	0.0369994i	−0.0114368	−	0.00473729i	0.376958	−	0.926230i	$-0.376970\pi$
$61$	−0.0893244	−	0.0369994i	−0.0114368	−	0.00473729i	−0.388395	+	0.921493i	$0.626970\pi$
$62$	−5.17330	−	6.56436i	−0.657009	−	0.833674i
$63$	−1.83038			−0.230606
$64$	5.20116	−	6.07848i	0.650146	−	0.759810i
$65$	1.53875			0.190859
$66$	0.926911	+	1.17615i	0.114095	+	0.144774i
$67$	−4.92908	−	2.04169i	−0.602184	−	0.249433i	0.0606989	−	0.998156i	$-0.480667\pi$
$67$	−4.92908	−	2.04169i	−0.602184	−	0.249433i	−0.662882	+	0.748724i	$0.730667\pi$
$68$	6.43968	+	1.54811i	0.780925	+	0.187736i
$69$	1.67198	+	4.03652i	0.201283	+	0.485940i
$70$	0.524421	+	1.86055i	0.0626803	+	0.222378i
$71$	0.553232	−	0.553232i	0.0656565	−	0.0656565i	−0.673516	−	0.739173i	$-0.735217\pi$
$71$	0.553232	−	0.553232i	0.0656565	−	0.0656565i	0.739173	+	0.673516i	$0.235217\pi$
$72$	4.85628	+	1.79411i	0.572319	+	0.211438i
$73$	−6.76325	−	6.76325i	−0.791579	−	0.791579i	0.190172	−	0.981751i	$-0.439095\pi$
$73$	−6.76325	−	6.76325i	−0.791579	−	0.791579i	−0.981751	+	0.190172i	$0.939095\pi$
$74$	3.07709	−	5.49257i	0.357705	−	0.638498i
$75$	3.12907	−	1.29610i	0.361313	−	0.149661i
$76$	−5.30082	−	3.85375i	−0.608046	−	0.442056i
$77$	0.374687	−	0.904574i	0.0426995	−	0.103086i
$78$	1.70982	+	0.202636i	0.193599	+	0.0229440i
$79$			11.8884i			1.33755i	0.743466	+	0.668773i	$0.233180\pi$
$79$			11.8884i			1.33755i	−0.743466	+	0.668773i	$0.766820\pi$
$80$	0.432307	−	5.45035i	0.0483334	−	0.609367i
$81$		−	0.158568i		−	0.0176187i
$82$	1.72213	−	14.5312i	0.190178	−	1.60470i
$83$	−2.47245	+	5.96903i	−0.271387	+	0.655187i	−0.999543	−	0.0302249i	$-0.990378\pi$
$83$	−2.47245	+	5.96903i	−0.271387	+	0.655187i	0.728156	+	0.685411i	$0.240378\pi$
$84$	0.337711	+	2.13645i	0.0368473	+	0.233106i
$85$	4.18192	−	1.73221i	0.453593	−	0.187884i
$86$	1.20489	+	0.675010i	0.129926	+	0.0727882i
$87$	5.82679	+	5.82679i	0.624697	+	0.624697i
$88$	−1.88075	+	2.03271i	−0.200489	+	0.216688i
$89$	−2.11160	+	2.11160i	−0.223829	+	0.223829i	−0.810109	−	0.586280i	$-0.800592\pi$
$89$	−2.11160	+	2.11160i	−0.223829	+	0.223829i	0.586280	+	0.810109i	$0.300592\pi$
$90$	3.40551	−	0.959890i	0.358972	−	0.101181i
$91$	−0.430806	−	1.04006i	−0.0451608	−	0.109028i
$92$	−6.89043	+	4.21956i	−0.718377	+	0.439920i
$93$	−5.90497	−	2.44592i	−0.612317	−	0.253630i
$94$	−11.9195	+	9.39364i	−1.22940	+	0.968880i
$95$	−4.47897			−0.459533
$96$	1.19812	−	5.99936i	0.122282	−	0.612307i
$97$	−6.12164			−0.621559			−0.310779	−	0.950482i	$-0.600590\pi$
$97$	−6.12164			−0.621559			−0.310779	+	0.950482i	$0.600590\pi$
$98$	1.11074	−	0.875361i	0.112202	−	0.0884248i
$99$	−1.65571	−	0.685819i	−0.166405	−	0.0689274i
$100$	3.27096	+	5.34139i	0.327096	+	0.534139i
$101$	−2.52035	−	6.08466i	−0.250784	−	0.605446i	0.747484	−	0.664280i	$-0.231262\pi$
$101$	−2.52035	−	6.08466i	−0.250784	−	0.605446i	−0.998268	+	0.0588340i	$0.981262\pi$
$102$	4.87496	−	1.37408i	0.482693	−	0.136054i
$103$	−8.52867	+	8.52867i	−0.840355	+	0.840355i	−0.988905	−	0.148550i	$-0.952539\pi$
$103$	−8.52867	+	8.52867i	−0.840355	+	0.840355i	0.148550	+	0.988905i	$0.452539\pi$
$104$	0.123547	+	3.18171i	0.0121148	+	0.311992i
$105$	1.04528	+	1.04528i	0.102009	+	0.102009i
$106$	7.07488	+	3.96354i	0.687173	+	0.384973i
$107$	10.9686	−	4.54336i	1.06038	−	0.439223i	0.216792	−	0.976218i	$-0.430441\pi$
$107$	10.9686	−	4.54336i	1.06038	−	0.439223i	0.843585	+	0.536995i	$0.180441\pi$
$108$	10.3199	−	1.63127i	0.993031	−	0.156969i
$109$	−4.93652	+	11.9178i	−0.472833	+	1.14152i	0.490073	+	0.871681i	$0.336970\pi$
$109$	−4.93652	+	11.9178i	−0.472833	+	1.14152i	−0.962906	+	0.269837i	$0.913030\pi$
$110$	−0.222744	+	1.87949i	−0.0212378	+	0.179203i
$111$		−	4.81456i		−	0.456978i
$112$	−3.80498	+	1.23374i	−0.359537	+	0.116578i
$113$			15.8912i			1.49492i	0.664305	+	0.747461i	$0.268727\pi$
$113$			15.8912i			1.49492i	−0.664305	+	0.747461i	$0.731273\pi$
$114$	−4.97692	−	0.589830i	−0.466132	−	0.0552426i
$115$	−2.11317	+	5.10165i	−0.197054	+	0.475731i
$116$	−8.96093	+	12.3257i	−0.832002	+	1.14442i
$117$	−1.90370	+	0.788539i	−0.175997	+	0.0729005i
$118$	1.01714	−	1.81558i	0.0936353	−	0.167138i
$119$	−2.34164	−	2.34164i	−0.214657	−	0.214657i
$120$	−1.74873	−	3.79786i	−0.159636	−	0.346696i
$121$	−7.10031	+	7.10031i	−0.645483	+	0.645483i
$122$	−0.0370944	−	0.131604i	−0.00335837	−	0.0119149i
$123$	−4.28230	−	10.3384i	−0.386122	−	0.932181i
$124$	2.76279	−	11.4924i	0.248106	−	1.03205i
$125$	10.2688	+	4.25349i	0.918473	+	0.380444i
$126$	−1.60224	−	2.03308i	−0.142739	−	0.181121i
$127$	−17.0952			−1.51695			−0.758476	−	0.651702i	$-0.774055\pi$
$127$	−17.0952			−1.51695			−0.758476	+	0.651702i	$0.774055\pi$
$128$	11.3045	+	0.456277i	0.999186	+	0.0403296i
$129$	1.05615			0.0929891
$130$	1.34696	+	1.70915i	0.118136	+	0.149903i
$131$	16.1070	+	6.67174i	1.40728	+	0.582913i	0.951629	−	0.307248i	$-0.0994082\pi$
$131$	16.1070	+	6.67174i	1.40728	+	0.582913i	0.455646	+	0.890161i	$0.349408\pi$
$132$	−0.495016	+	2.05911i	−0.0430856	+	0.179223i
$133$	1.25398	+	3.02738i	0.108734	+	0.262508i
$134$	−2.04694	−	7.26215i	−0.176829	−	0.627354i
$135$	5.04911	−	5.04911i	0.434558	−	0.434558i
$136$	3.91749	+	8.50796i	0.335922	+	0.729552i
$137$	−10.0821	−	10.0821i	−0.861372	−	0.861372i	0.130126	−	0.991497i	$-0.458462\pi$
$137$	−10.0821	−	10.0821i	−0.861372	−	0.861372i	−0.991497	+	0.130126i	$0.958462\pi$
$138$	−3.01993	+	5.39055i	−0.257074	+	0.458874i
$139$	−10.0075	+	4.14525i	−0.848826	+	0.351595i	−0.764327	−	0.644828i	$-0.776929\pi$
$139$	−10.0075	+	4.14525i	−0.848826	+	0.351595i	−0.0844986	+	0.996424i	$0.526929\pi$
$140$	−1.60752	+	2.21114i	−0.135861	+	0.186876i
$141$	−4.44128	+	10.7222i	−0.374024	+	0.902973i
$142$	1.09877	+	0.130219i	0.0922070	+	0.0109277i
$143$		−	1.10223i		−	0.0921728i
$144$	2.25821	+	6.96456i	0.188184	+	0.580380i
$145$			10.4147i			0.864896i
$146$	1.59192	−	13.4325i	0.131749	−	1.11168i
$147$	0.413868	−	0.999166i	0.0341353	−	0.0824098i
$148$	8.79438	−	1.39014i	0.722894	−	0.114268i
$149$	17.8291	−	7.38504i	1.46061	−	0.605006i	0.495917	−	0.868370i	$-0.334832\pi$
$149$	17.8291	−	7.38504i	1.46061	−	0.605006i	0.964697	+	0.263364i	$0.0848320\pi$
$150$	4.17869	+	2.34102i	0.341189	+	0.191144i
$151$	−6.37361	−	6.37361i	−0.518677	−	0.518677i	0.398494	−	0.917171i	$-0.369533\pi$
$151$	−6.37361	−	6.37361i	−0.518677	−	0.518677i	−0.917171	+	0.398494i	$0.869533\pi$
$152$	−0.359620	−	9.26126i	−0.0291690	−	0.751187i
$153$	−4.28608	+	4.28608i	−0.346509	+	0.346509i
$154$	1.33273	−	0.375649i	0.107395	−	0.0302707i
$155$	−3.09133	−	7.46314i	−0.248302	−	0.599454i
$156$	1.27164	+	2.07655i	0.101812	+	0.166257i
$157$	−0.751603	−	0.311324i	−0.0599844	−	0.0248464i	0.352490	−	0.935816i	$-0.385335\pi$
$157$	−0.751603	−	0.311324i	−0.0599844	−	0.0248464i	−0.412474	+	0.910969i	$0.635335\pi$
$158$	−13.2049	+	10.4066i	−1.05052	+	0.827906i
$159$	6.20155			0.491815
$160$	6.43234	−	4.29084i	0.508521	−	0.339221i
$161$	4.03989			0.318388
$162$	0.176128	−	0.138804i	0.0138379	−	0.0109055i
$163$	1.04167	+	0.431475i	0.0815901	+	0.0337957i	0.423105	−	0.906081i	$-0.360940\pi$
$163$	1.04167	+	0.431475i	0.0815901	+	0.0337957i	−0.341515	+	0.939876i	$0.610940\pi$
$164$	17.6479	−	10.8072i	1.37807	−	0.843901i
$165$	0.553881	+	1.33719i	0.0431196	+	0.104100i
$166$	−8.79433	+	2.47881i	−0.682573	+	0.192393i
$167$	7.60002	−	7.60002i	0.588107	−	0.588107i	−0.349011	−	0.937118i	$-0.613483\pi$
$167$	7.60002	−	7.60002i	0.588107	−	0.588107i	0.937118	+	0.349011i	$0.113483\pi$
$168$	−2.07742	+	2.24528i	−0.160277	+	0.173227i
$169$	8.29626	+	8.29626i	0.638174	+	0.638174i
$170$	5.58472	+	3.12872i	0.428329	+	0.239962i
$171$	5.54126	−	2.29527i	0.423751	−	0.175523i
$172$	0.304949	+	1.92919i	0.0232521	+	0.147099i
$173$	−8.40483	+	20.2911i	−0.639008	+	1.54270i	0.188996	+	0.981978i	$0.439477\pi$
$173$	−8.40483	+	20.2911i	−0.639008	+	1.54270i	−0.828003	+	0.560723i	$0.810523\pi$
$174$	−1.37150	+	11.5726i	−0.103973	+	0.877316i
$175$		−	3.13168i		−	0.236733i
$176$	−3.90415	−	0.309667i	−0.294286	−	0.0233420i
$177$		−	1.59146i		−	0.119622i
$178$	−4.19385	−	0.497025i	−0.314342	−	0.0372536i
$179$	7.93735	−	19.1624i	0.593265	−	1.43227i	−0.287067	−	0.957911i	$-0.592680\pi$
$179$	7.93735	−	19.1624i	0.593265	−	1.43227i	0.880332	−	0.474358i	$-0.157320\pi$
$180$	4.04723	+	2.94238i	0.301663	+	0.219312i
$181$	−0.349364	+	0.144711i	−0.0259680	+	0.0107563i	−0.395630	−	0.918410i	$-0.629474\pi$
$181$	−0.349364	+	0.144711i	−0.0259680	+	0.0107563i	0.369662	+	0.929166i	$0.379474\pi$
$182$	0.778123	−	1.38894i	0.0576783	−	0.102955i
$183$	−0.0739371	−	0.0739371i	−0.00546559	−	0.00546559i
$184$	−10.7185	−	3.95983i	−0.790175	−	0.291923i
$185$	4.30274	−	4.30274i	0.316344	−	0.316344i
$186$	−2.45220	−	8.69995i	−0.179804	−	0.637911i
$187$	−1.24080	−	2.99556i	−0.0907365	−	0.219057i
$188$	−20.8678	−	5.01666i	−1.52194	−	0.365878i
$189$	−4.82635	−	1.99914i	−0.351065	−	0.145416i
$190$	−3.92072	−	4.97497i	−0.284439	−	0.360922i
$191$	−7.61375			−0.550912			−0.275456	−	0.961314i	$-0.588829\pi$
$191$	−7.61375			−0.550912			−0.275456	+	0.961314i	$0.588829\pi$
$192$	7.71252	−	3.92081i	0.556603	−	0.282960i
$193$	23.7442			1.70914			0.854571	−	0.519334i	$-0.173820\pi$
$193$	23.7442			1.70914			0.854571	+	0.519334i	$0.173820\pi$
$194$	−5.35865	−	6.79955i	−0.384728	−	0.488179i
$195$	1.53747	+	0.636840i	0.110100	+	0.0456051i
$196$	1.94460	+	0.467486i	0.138900	+	0.0333918i
$197$	−0.495698	−	1.19672i	−0.0353171	−	0.0852629i	0.905237	−	0.424907i	$-0.139693\pi$
$197$	−0.495698	−	1.19672i	−0.0353171	−	0.0852629i	−0.940554	+	0.339644i	$0.889693\pi$
$198$	−0.687581	−	2.43941i	−0.0488642	−	0.173361i
$199$	10.1613	−	10.1613i	0.720317	−	0.720317i	−0.248353	−	0.968670i	$-0.579889\pi$
$199$	10.1613	−	10.1613i	0.720317	−	0.720317i	0.968670	+	0.248353i	$0.0798893\pi$
$200$	−3.06962	+	8.30883i	−0.217055	+	0.587523i
$201$	−4.07998	−	4.07998i	−0.287780	−	0.287780i
$202$	4.55226	−	8.12572i	0.320296	−	0.571724i
$203$	7.03942	−	2.91582i	0.494071	−	0.204651i
$204$	5.79359	+	4.21200i	0.405633	+	0.294899i
$205$	5.41229	−	13.0664i	0.378010	−	0.912598i
$206$	−16.9388	−	2.00747i	−1.18018	−	0.139867i
$207$		−	7.39453i		−	0.513955i
$208$	−3.42590	+	2.92237i	−0.237543	+	0.202630i
$209$			3.20834i			0.221926i
$210$	−0.246037	+	2.07604i	−0.0169782	+	0.143260i
$211$	2.86259	−	6.91091i	0.197069	−	0.475766i	−0.794195	−	0.607664i	$-0.792107\pi$
$211$	2.86259	−	6.91091i	0.197069	−	0.475766i	0.991263	+	0.131897i	$0.0421069\pi$
$212$	1.79061	+	11.3279i	0.122979	+	0.778002i
$213$	0.781735	−	0.323805i	0.0535636	−	0.0221868i
$214$	14.6480	+	8.20622i	1.00132	+	0.560966i
$215$	0.943877	+	0.943877i	0.0643719	+	0.0643719i
$216$	10.8455	+	10.0347i	0.737946	+	0.682778i
$217$	−4.17893	+	4.17893i	−0.283684	+	0.283684i
$218$	−17.5588	+	4.94920i	−1.18923	+	0.335202i
$219$	−3.95852	−	9.55671i	−0.267492	−	0.645782i
$220$	−2.28261	+	1.39782i	−0.153894	+	0.0942413i
$221$	−3.44423	−	1.42665i	−0.231684	−	0.0959666i
$222$	5.34773	−	4.21448i	0.358916	−	0.282857i
$223$	9.85085			0.659662			0.329831	−	0.944040i	$-0.393008\pi$
$223$	9.85085			0.659662			0.329831	+	0.944040i	$0.393008\pi$
$224$	−4.70110	−	3.14638i	−0.314105	−	0.210226i
$225$	−5.73216			−0.382144
$226$	−17.6510	+	13.9106i	−1.17413	+	0.925318i
$227$	15.7326	+	6.51665i	1.04421	+	0.432525i	0.837821	−	0.545945i	$-0.183829\pi$
$227$	15.7326	+	6.51665i	1.04421	+	0.432525i	0.206388	+	0.978470i	$0.433829\pi$
$228$	−3.70146	−	6.04438i	−0.245135	−	0.400299i
$229$	−7.45055	−	17.9872i	−0.492346	−	1.18863i	−0.953523	−	0.301321i	$-0.902573\pi$
$229$	−7.45055	−	17.9872i	−0.492346	−	1.18863i	0.461177	−	0.887308i	$-0.347427\pi$
$230$	−7.51639	+	2.11860i	−0.495616	+	0.139696i
$231$	0.748748	−	0.748748i	0.0492640	−	0.0492640i
$232$	−21.5347	+	0.836206i	−1.41382	+	0.0548996i
$233$	−3.26240	−	3.26240i	−0.213727	−	0.213727i	0.592122	−	0.805848i	$-0.298290\pi$
$233$	−3.26240	−	3.26240i	−0.213727	−	0.213727i	−0.805848	+	0.592122i	$0.798290\pi$
$234$	−2.54229	−	1.42426i	−0.166195	−	0.0931069i
$235$	−13.5515	+	5.61322i	−0.884003	+	0.366166i
$236$	2.90700	−	0.459513i	0.189230	−	0.0299117i
$237$	−4.92022	+	11.8785i	−0.319603	+	0.771589i
$238$	0.551171	−	4.65073i	0.0357271	−	0.301462i
$239$		−	2.83372i		−	0.183298i	−0.995791	−	0.0916491i	$-0.970786\pi$
$239$		−	2.83372i		−	0.183298i	0.995791	−	0.0916491i	$-0.0292138\pi$
$240$	2.68767	−	5.26688i	0.173488	−	0.339976i
$241$		−	22.5209i		−	1.45070i	−0.688380	−	0.725350i	$-0.741678\pi$
$241$		−	22.5209i		−	1.45070i	0.688380	−	0.725350i	$-0.258322\pi$
$242$	−14.1019	−	1.67126i	−0.906507	−	0.107433i
$243$	−5.93180	+	14.3206i	−0.380525	+	0.918668i
$244$	0.113707	−	0.156403i	0.00727933	−	0.0100127i
$245$	1.26282	−	0.523077i	0.0806786	−	0.0334182i
$246$	7.73470	−	13.8063i	0.493146	−	0.880260i
$247$	2.60843	+	2.60843i	0.165971	+	0.165971i
$248$	15.1835	−	6.99123i	0.964152	−	0.443944i
$249$	−4.94079	+	4.94079i	−0.313110	+	0.313110i
$250$	4.26442	+	15.1294i	0.269706	+	0.956864i
$251$	−8.58026	−	20.7146i	−0.541581	−	1.30749i	−0.923607	−	0.383341i	$-0.874773\pi$
$251$	−8.58026	−	20.7146i	−0.541581	−	1.30749i	0.382025	−	0.924152i	$-0.375227\pi$
$252$	0.855676	−	3.55935i	0.0539025	−	0.224218i
$253$	3.65437	+	1.51369i	0.229749	+	0.0951650i
$254$	−14.9644	−	18.9883i	−0.938953	−	1.19143i
$255$	4.89534			0.306558
$256$	9.38872	+	12.9558i	0.586795	+	0.809736i
$257$	8.00130			0.499108			0.249554	−	0.968361i	$-0.419716\pi$
$257$	8.00130			0.499108			0.249554	+	0.968361i	$0.419716\pi$
$258$	0.924515	+	1.17311i	0.0575578	+	0.0730347i
$259$	−4.11292	−	1.70363i	−0.255564	−	0.105858i
$260$	−0.719344	+	2.99225i	−0.0446118	+	0.185572i
$261$	−5.33707	−	12.8848i	−0.330356	−	0.797550i
$262$	6.68888	+	23.7309i	0.413240	+	1.46610i
$263$	15.2011	−	15.2011i	0.937342	−	0.937342i	−0.0608073	−	0.998150i	$-0.519367\pi$
$263$	15.2011	−	15.2011i	0.937342	−	0.937342i	0.998150	+	0.0608073i	$0.0193675\pi$
$264$	−2.72046	+	1.25264i	−0.167433	+	0.0770944i
$265$	5.54228	+	5.54228i	0.340460	+	0.340460i
$266$	−2.26495	+	4.04290i	−0.138873	+	0.247886i
$267$	−2.98376	+	1.23591i	−0.182603	+	0.0756367i
$268$	6.27455	−	8.63062i	0.383279	−	0.527199i
$269$	−3.43306	+	8.28813i	−0.209317	+	0.505337i	−0.993316	−	0.115426i	$-0.963177\pi$
$269$	−3.43306	+	8.28813i	−0.209317	+	0.505337i	0.783999	+	0.620762i	$0.213177\pi$
$270$	10.0280	+	1.18845i	0.610287	+	0.0723269i
$271$		−	16.2410i		−	0.986571i	−0.869867	−	0.493285i	$-0.835796\pi$
$271$		−	16.2410i		−	0.986571i	0.869867	−	0.493285i	$-0.164204\pi$
$272$	−6.02091	+	11.7989i	−0.365071	+	0.715411i
$273$		−	1.21749i		−	0.0736857i
$274$	2.37311	−	20.0241i	0.143365	−	1.20970i
$275$	1.17340	−	2.83283i	0.0707585	−	0.170826i
$276$	−8.63103	+	1.36431i	−0.519527	+	0.0821221i
$277$	8.18398	−	3.38992i	0.491728	−	0.203680i	−0.123020	−	0.992404i	$-0.539258\pi$
$277$	8.18398	−	3.38992i	0.491728	−	0.203680i	0.614748	+	0.788724i	$0.289258\pi$
$278$	−13.3645	−	7.48715i	−0.801548	−	0.449050i
$279$	7.64903	+	7.64903i	0.457935	+	0.457935i
$280$	−3.86317	+	0.150009i	−0.230869	+	0.00896476i
$281$	9.52799	−	9.52799i	0.568392	−	0.568392i	−0.363286	−	0.931678i	$-0.618345\pi$
$281$	9.52799	−	9.52799i	0.568392	−	0.568392i	0.931678	+	0.363286i	$0.118345\pi$
$282$	−15.7973	+	4.45269i	−0.940716	+	0.265154i
$283$	9.29050	+	22.4293i	0.552263	+	1.33328i	0.915775	+	0.401691i	$0.131578\pi$
$283$	9.29050	+	22.4293i	0.552263	+	1.33328i	−0.363512	+	0.931589i	$0.618422\pi$
$284$	0.817185	+	1.33444i	0.0484910	+	0.0791844i
$285$	−4.47524	−	1.85370i	−0.265090	−	0.109804i
$286$	1.22429	−	0.964846i	0.0723936	−	0.0570526i
$287$	−10.3470			−0.610765
$288$	−5.75906	+	8.60480i	−0.339356	+	0.507042i
$289$	6.03348			0.354911
$290$	−11.5680	+	9.11665i	−0.679299	+	0.535348i
$291$	−6.11654	−	2.53355i	−0.358558	−	0.148519i
$292$	16.3135	−	9.99007i	0.954676	−	0.584625i
$293$	8.54419	+	20.6275i	0.499157	+	1.20507i	0.949939	+	0.312437i	$0.101145\pi$
$293$	8.54419	+	20.6275i	0.499157	+	1.20507i	−0.450782	+	0.892634i	$0.648855\pi$
$294$	1.47210	−	0.414931i	0.0858545	−	0.0241993i
$295$	1.42228	−	1.42228i	0.0828085	−	0.0828085i
$296$	9.24234	+	8.55140i	0.537200	+	0.497040i
$297$	−3.61674	−	3.61674i	−0.209864	−	0.209864i
$298$	23.8097	+	13.3389i	1.37926	+	0.772700i
$299$	4.20172	−	1.74041i	0.242992	−	0.100650i
$300$	1.05760	+	6.69068i	0.0610607	+	0.386287i
$301$	0.373718	−	0.902235i	0.0215408	−	0.0520040i
$302$	1.50021	−	12.6586i	0.0863274	−	0.728422i
$303$		−	7.12267i		−	0.409187i
$304$	9.97205	−	8.50639i	0.571936	−	0.487875i
$305$		−	0.132154i		−	0.00756713i
$306$	−8.51260	−	1.00885i	−0.486633	−	0.0576723i
$307$	−12.5759	+	30.3608i	−0.717743	+	1.73278i	−0.0380638	+	0.999275i	$0.512119\pi$
$307$	−12.5759	+	30.3608i	−0.717743	+	1.73278i	−0.679679	+	0.733510i	$0.737881\pi$
$308$	1.58387	+	1.15149i	0.0902494	+	0.0656122i
$309$	−12.0513	+	4.99181i	−0.685574	+	0.283974i
$310$	5.58357	−	9.96661i	0.317125	−	0.566065i
$311$	9.58114	+	9.58114i	0.543297	+	0.543297i	0.924494	−	0.381197i	$-0.124488\pi$
$311$	9.58114	+	9.58114i	0.543297	+	0.543297i	−0.381197	+	0.924494i	$0.624488\pi$
$312$	−1.19336	+	3.23019i	−0.0675609	+	0.182873i
$313$	9.48170	−	9.48170i	0.535937	−	0.535937i	−0.386396	−	0.922333i	$-0.626280\pi$
$313$	9.48170	−	9.48170i	0.535937	−	0.535937i	0.922333	+	0.386396i	$0.126280\pi$
$314$	−0.312124	−	1.10736i	−0.0176142	−	0.0624917i
$315$	−0.957430	−	2.31144i	−0.0539451	−	0.130235i
$316$	−23.1181	−	5.55764i	−1.30049	−	0.312642i
$317$	−25.8056	−	10.6890i	−1.44939	−	0.600356i	−0.487333	−	0.873216i	$-0.662030\pi$
$317$	−25.8056	−	10.6890i	−1.44939	−	0.600356i	−0.962054	+	0.272860i	$0.912030\pi$
$318$	5.42859	+	6.88830i	0.304420	+	0.386277i
$319$	7.46020			0.417691
$320$	10.3966	+	3.38862i	0.581189	+	0.189430i
$321$	12.8398			0.716650
$322$	3.53636	+	4.48726i	0.197074	+	0.250065i
$323$	10.0254	+	4.15266i	0.557829	+	0.231060i
$324$	0.308351	+	0.0741283i	0.0171306	+	0.00411824i
$325$	−1.34915	−	3.25713i	−0.0748371	−	0.180673i
$326$	0.432584	+	1.53472i	0.0239586	+	0.0850005i
$327$	−9.86480	+	9.86480i	−0.545525	+	0.545525i
$328$	27.4522	+	10.1420i	1.51580	+	0.559997i
$329$	7.58807	+	7.58807i	0.418344	+	0.418344i
$330$	−1.00042	+	1.78574i	−0.0550714	+	0.0983017i
$331$	−11.5634	+	4.78970i	−0.635580	+	0.263266i	−0.677122	−	0.735871i	$-0.736773\pi$
$331$	−11.5634	+	4.78970i	−0.635580	+	0.263266i	0.0415418	+	0.999137i	$0.486773\pi$
$332$	−10.4515	−	7.59837i	−0.573602	−	0.417014i
$333$	−3.11828	+	7.52820i	−0.170881	+	0.412543i
$334$	15.0944	+	1.78888i	0.825929	+	0.0978832i
$335$		−	7.29251i		−	0.398432i
$336$	−4.31241	−	0.342049i	−0.235262	−	0.0186603i
$337$			19.5928i			1.06729i	0.845709	+	0.533645i	$0.179178\pi$
$337$			19.5928i			1.06729i	−0.845709	+	0.533645i	$0.820822\pi$
$338$	−1.95276	+	16.4772i	−0.106216	+	0.896242i
$339$	−6.57688	+	15.8780i	−0.357207	+	0.862374i
$340$	1.41346	+	8.94193i	0.0766556	+	0.484944i
$341$	−5.34594	+	2.21436i	−0.289499	+	0.119914i
$342$	7.40005	+	4.14572i	0.400149	+	0.224175i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−1.87589	+	2.02746i	−0.101141	+	0.109313i
$345$	−4.22282	+	4.22282i	−0.227349	+	0.227349i
$346$	−29.8954	+	8.42643i	−1.60718	+	0.453008i
$347$	12.3502	+	29.8160i	0.662993	+	1.60061i	0.793090	+	0.609105i	$0.208471\pi$
$347$	12.3502	+	29.8160i	0.662993	+	1.60061i	−0.130097	+	0.991501i	$0.541529\pi$
$348$	−14.0547	+	8.60681i	−0.753411	+	0.461374i
$349$	23.5509	+	9.75512i	1.26065	+	0.522179i	0.910110	−	0.414367i	$-0.135997\pi$
$349$	23.5509	+	9.75512i	1.26065	+	0.522179i	0.350543	+	0.936547i	$0.385997\pi$
$350$	3.47848	−	2.74135i	0.185932	−	0.146531i
$351$	−5.88093			−0.313901
$352$	−3.07358	−	4.60757i	−0.163823	−	0.245584i
$353$	−24.8851			−1.32450			−0.662251	−	0.749282i	$-0.730399\pi$
$353$	−24.8851			−1.32450			−0.662251	+	0.749282i	$0.730399\pi$
$354$	1.76770	−	1.39311i	0.0939524	−	0.0740428i
$355$	0.988014	+	0.409249i	0.0524384	+	0.0217207i
$356$	−3.11907	−	5.09335i	−0.165310	−	0.269947i
$357$	−1.37055	−	3.30881i	−0.0725375	−	0.175121i
$358$	28.2325	−	7.95774i	1.49214	−	0.420580i
$359$	−14.2492	+	14.2492i	−0.752046	+	0.752046i	−0.974861	−	0.222815i	$-0.928476\pi$
$359$	−14.2492	+	14.2492i	−0.752046	+	0.752046i	0.222815	+	0.974861i	$0.428476\pi$
$360$	0.274574	+	7.07107i	0.0144713	+	0.372678i
$361$	5.84245	+	5.84245i	0.307497	+	0.307497i
$362$	−0.466557	−	0.261378i	−0.0245217	−	0.0137377i
$363$	−10.0330	+	4.15580i	−0.526595	+	0.218123i
$364$	2.22389	−	0.351532i	0.116564	−	0.0184253i
$365$	5.00307	−	12.0785i	0.261872	−	0.632216i
$366$	0.0174032	−	0.146847i	0.000909680	−	0.00767579i
$367$			20.3633i			1.06296i	0.847072	+	0.531478i	$0.178363\pi$
$367$			20.3633i			1.06296i	−0.847072	+	0.531478i	$0.821637\pi$
$368$	−4.98417	−	15.3717i	−0.259818	−	0.801305i
$369$			18.9390i			0.985923i
$370$	8.54568	+	1.01277i	0.444269	+	0.0526516i
$371$	2.19441	−	5.29777i	0.113928	−	0.275046i
$372$	7.51681	−	10.3394i	0.389729	−	0.536071i
$373$	−9.97623	+	4.13229i	−0.516550	+	0.213962i	−0.625701	−	0.780063i	$-0.715187\pi$
$373$	−9.97623	+	4.13229i	−0.516550	+	0.213962i	0.109151	+	0.994025i	$0.465187\pi$
$374$	2.24114	−	4.00041i	0.115887	−	0.206856i
$375$	8.49989	+	8.49989i	0.438933	+	0.438933i
$376$	−12.6946	−	27.5701i	−0.654676	−	1.42182i
$377$	6.06526	−	6.06526i	0.312377	−	0.312377i
$378$	−2.00428	−	7.11079i	−0.103089	−	0.365740i
$379$	−8.32592	−	20.1006i	−0.427674	−	1.03250i	−0.980023	−	0.198883i	$-0.936269\pi$
$379$	−8.32592	−	20.1006i	−0.427674	−	1.03250i	0.552349	−	0.833613i	$-0.313731\pi$
$380$	2.09385	−	8.70979i	0.107412	−	0.446803i
$381$	−17.0809	−	7.07515i	−0.875082	−	0.362471i
$382$	−6.66478	−	8.45690i	−0.341000	−	0.432692i
$383$	5.23566			0.267529			0.133765	−	0.991013i	$-0.457293\pi$
$383$	5.23566			0.267529			0.133765	+	0.991013i	$0.457293\pi$
$384$	11.1062	+	5.13447i	0.566763	+	0.262017i
$385$	1.33830			0.0682063
$386$	20.7847	+	26.3736i	1.05791	+	1.34238i
$387$	−1.65143	−	0.684046i	−0.0839471	−	0.0347720i
$388$	2.86178	−	11.9041i	0.145285	−	0.604340i
$389$	10.2543	+	24.7560i	0.519912	+	1.25518i	0.937957	+	0.346751i	$0.112715\pi$
$389$	10.2543	+	24.7560i	0.519912	+	1.25518i	−0.418045	+	0.908426i	$0.637285\pi$
$390$	0.638476	+	2.26519i	0.0323305	+	0.114702i
$391$	9.45994	−	9.45994i	0.478410	−	0.478410i
$392$	1.18297	+	2.56916i	0.0597490	+	0.129762i
$393$	13.3324	+	13.3324i	0.672528	+	0.672528i
$394$	0.895331	−	1.59816i	0.0451061	−	0.0805139i
$395$	−15.0129	+	6.21854i	−0.755380	+	0.312889i
$396$	2.10766	−	2.89908i	0.105914	−	0.145684i
$397$	11.1704	−	26.9677i	0.560627	−	1.35347i	−0.348639	−	0.937257i	$-0.613356\pi$
$397$	11.1704	−	26.9677i	0.560627	−	1.35347i	0.909266	−	0.416215i	$-0.136644\pi$
$398$	20.1814	+	2.39176i	1.01160	+	0.119888i
$399$			3.54384i			0.177414i
$400$	−11.9160	+	3.86368i	−0.595799	+	0.193184i
$401$		−	0.336321i		−	0.0167951i	−0.999965	−	0.00839753i	$-0.997327\pi$
$401$		−	0.336321i		−	0.0167951i	0.999965	−	0.00839753i	$-0.00267305\pi$
$402$	0.960340	−	8.10326i	0.0478974	−	0.404154i
$403$	−2.54602	+	6.14664i	−0.126826	+	0.306186i
$404$	13.0104	−	2.05657i	0.647293	−	0.102318i
$405$	0.200243	−	0.0829433i	0.00995015	−	0.00412149i
$406$	9.40076	+	5.26657i	0.466552	+	0.261375i
$407$	−3.08211	−	3.08211i	−0.152774	−	0.152774i
$408$	0.393051	+	10.1222i	0.0194589	+	0.501123i
$409$	−3.23576	+	3.23576i	−0.159998	+	0.159998i	−0.782566	−	0.622568i	$-0.786089\pi$
$409$	−3.23576	+	3.23576i	−0.159998	+	0.159998i	0.622568	+	0.782566i	$0.286089\pi$
$410$	19.2511	−	5.42619i	0.950744	−	0.267980i
$411$	−5.90103	−	14.2463i	−0.291076	−	0.702721i
$412$	−12.5978	−	20.5718i	−0.620649	−	1.01350i
$413$	−1.35953	−	0.563137i	−0.0668983	−	0.0277102i
$414$	8.21340	−	6.47288i	0.403666	−	0.318125i
$415$	−8.83110			−0.433502
$416$	−6.24489	−	1.24715i	−0.306181	−	0.0611467i
$417$	−11.7148			−0.573674
$418$	−3.56363	+	2.80846i	−0.174303	+	0.137366i
$419$	−16.9870	−	7.03624i	−0.829869	−	0.343743i	−0.0730182	−	0.997331i	$-0.523263\pi$
$419$	−16.9870	−	7.03624i	−0.829869	−	0.343743i	−0.756851	+	0.653588i	$0.773263\pi$
$420$	−2.52131	+	1.54400i	−0.123027	+	0.0753394i
$421$	−15.0999	−	36.4544i	−0.735924	−	1.77668i	−0.621750	−	0.783216i	$-0.713578\pi$
$421$	−15.0999	−	36.4544i	−0.735924	−	1.77668i	−0.114173	−	0.993461i	$-0.536422\pi$
$422$	10.1820	−	2.86995i	0.495653	−	0.139707i
$423$	13.8891	−	13.8891i	0.675309	−	0.675309i
$424$	−11.0149	+	11.9049i	−0.534931	+	0.578152i
$425$	−7.33325	−	7.33325i	−0.355715	−	0.355715i
$426$	1.04396	+	0.584858i	0.0505802	+	0.0283364i
$427$	−0.0893244	+	0.0369994i	−0.00432271	+	0.00179053i
$428$	3.70732	+	23.4535i	0.179200	+	1.13367i
$429$	0.456176	−	1.10131i	0.0220244	−	0.0531716i
$430$	−0.222168	+	1.87464i	−0.0107139	+	0.0904029i
$431$		−	13.1488i		−	0.633354i	−0.948533	−	0.316677i	$-0.897433\pi$
$431$		−	13.1488i		−	0.633354i	0.948533	−	0.316677i	$-0.102567\pi$
$432$	−1.65223	+	20.8306i	−0.0794928	+	1.00221i
$433$		−	40.2052i		−	1.93214i	−0.258282	−	0.966069i	$-0.583156\pi$
$433$		−	40.2052i		−	1.93214i	0.258282	−	0.966069i	$-0.416844\pi$
$434$	−8.29977	−	0.983630i	−0.398402	−	0.0472158i
$435$	−4.31032	+	10.4060i	−0.206664	+	0.498931i
$436$	−20.8676	−	15.1709i	−0.999376	−	0.726556i
$437$	−12.2303	+	5.06595i	−0.585054	+	0.242337i
$438$	7.14988	−	12.7625i	0.341635	−	0.609814i
$439$	−27.3803	−	27.3803i	−1.30679	−	1.30679i	−0.923720	−	0.383068i	$-0.874867\pi$
$439$	−27.3803	−	27.3803i	−1.30679	−	1.30679i	−0.383068	−	0.923720i	$-0.625133\pi$
$440$	−3.55073	−	1.31178i	−0.169274	−	0.0625368i
$441$	−1.29427	+	1.29427i	−0.0616321	+	0.0616321i
$442$	−1.43031	−	5.07447i	−0.0680330	−	0.241368i
$443$	13.6912	+	33.0535i	0.650489	+	1.57042i	0.812070	+	0.583560i	$0.198341\pi$
$443$	13.6912	+	33.0535i	0.650489	+	1.57042i	−0.161581	+	0.986859i	$0.551659\pi$
$444$	9.36238	+	2.25074i	0.444319	+	0.106815i
$445$	−3.77110	−	1.56204i	−0.178767	−	0.0740478i
$446$	8.62306	+	10.9417i	0.408314	+	0.518106i
$447$	20.8706			0.987147
$448$	−0.620354	−	7.97591i	−0.0293090	−	0.376826i
$449$	12.5452			0.592044			0.296022	−	0.955181i	$-0.404340\pi$
$449$	12.5452			0.592044			0.296022	+	0.955181i	$0.404340\pi$
$450$	−5.01771	−	6.36694i	−0.236537	−	0.300140i
$451$	−9.35963	−	3.87689i	−0.440728	−	0.182556i
$452$	−30.9021	−	7.42893i	−1.45351	−	0.349427i
$453$	−3.73046	−	9.00613i	−0.175272	−	0.423145i
$454$	6.53339	+	23.1792i	0.306627	+	1.08786i
$455$	1.08806	−	1.08806i	0.0510091	−	0.0510091i
$456$	3.47362	−	9.40237i	0.162667	−	0.440306i
$457$	14.2550	+	14.2550i	0.666819	+	0.666819i	0.956978	−	0.290159i	$-0.0937082\pi$
$457$	14.2550	+	14.2550i	0.666819	+	0.666819i	−0.290159	+	0.956978i	$0.593708\pi$
$458$	13.4572	−	24.0209i	0.628814	−	1.12242i
$459$	−15.9828	+	6.62030i	−0.746014	+	0.309009i
$460$	−8.93277	−	6.49421i	−0.416493	−	0.302794i
$461$	−5.52269	+	13.3330i	−0.257217	+	0.620978i	−0.998752	−	0.0499365i	$-0.984098\pi$
$461$	−5.52269	+	13.3330i	−0.257217	+	0.620978i	0.741535	+	0.670914i	$0.234098\pi$
$462$	1.48709	+	0.176239i	0.0691857	+	0.00819940i
$463$		−	2.24545i		−	0.104355i	−0.998638	−	0.0521775i	$-0.983384\pi$
$463$		−	2.24545i		−	0.104355i	0.998638	−	0.0521775i	$-0.0166162\pi$
$464$	−19.7795	−	23.1875i	−0.918239	−	1.07645i
$465$		−	8.73632i		−	0.405137i
$466$	0.767898	−	6.47945i	0.0355722	−	0.300155i
$467$	−5.32133	+	12.8468i	−0.246242	+	0.594480i	−0.997879	−	0.0650968i	$-0.979264\pi$
$467$	−5.32133	+	12.8468i	−0.246242	+	0.594480i	0.751637	+	0.659577i	$0.229264\pi$
$468$	−0.643438	−	4.07056i	−0.0297429	−	0.188162i
$469$	−4.92908	+	2.04169i	−0.227604	+	0.0942767i
$470$	−18.0973	−	10.1386i	−0.834766	−	0.467659i
$471$	−0.622129	−	0.622129i	−0.0286662	−	0.0286662i
$472$	3.05508	+	2.82669i	0.140621	+	0.130109i
$473$	0.676111	−	0.676111i	0.0310876	−	0.0310876i
$474$	−17.5008	+	4.93286i	−0.803841	+	0.226574i
$475$	3.92707	+	9.48079i	0.180186	+	0.435008i
$476$	5.64822	−	3.45886i	0.258886	−	0.158536i
$477$	−9.69693	−	4.01660i	−0.443992	−	0.183907i
$478$	3.14753	−	2.48053i	0.143965	−	0.113457i
$479$	−15.6342			−0.714346			−0.357173	−	0.934038i	$-0.616259\pi$
$479$	−15.6342			−0.714346			−0.357173	+	0.934038i	$0.616259\pi$
$480$	8.20282	−	1.62512i	0.374406	−	0.0741764i
$481$	−5.01160			−0.228509
$482$	25.0149	−	19.7139i	1.13940	−	0.897946i
$483$	4.03652	+	1.67198i	0.183668	+	0.0760777i
$484$	−10.4880	−	17.1265i	−0.476725	−	0.778479i
$485$	−3.20209	−	7.73053i	−0.145399	−	0.351025i
$486$	−21.0989	+	5.94703i	−0.957068	+	0.269763i
$487$	−2.51318	+	2.51318i	−0.113883	+	0.113883i	−0.761752	−	0.647869i	$-0.775660\pi$
$487$	−2.51318	+	2.51318i	−0.113883	+	0.113883i	0.647869	+	0.761752i	$0.275660\pi$
$488$	0.273258	−	0.0106108i	0.0123698	−	0.000480327i
$489$	0.862231	+	0.862231i	0.0389914	+	0.0389914i
$490$	1.68643	+	0.944783i	0.0761850	+	0.0426809i
$491$	26.9210	−	11.1510i	1.21493	−	0.503239i	0.319134	−	0.947710i	$-0.396608\pi$
$491$	26.9210	−	11.1510i	1.21493	−	0.503239i	0.895794	+	0.444470i	$0.146608\pi$
$492$	22.1059	−	3.49430i	0.996611	−	0.157535i
$493$	9.65597	−	23.3116i	0.434883	−	1.04990i
$494$	−0.613969	+	5.18061i	−0.0276238	+	0.233087i
$495$		−	2.44960i		−	0.110102i
$496$	21.0565	+	10.7450i	0.945463	+	0.482466i
$497$		−	0.782388i		−	0.0350949i
$498$	−9.81290	−	1.16296i	−0.439727	−	0.0521133i
$499$	6.22672	−	15.0326i	0.278746	−	0.672953i	−0.721055	−	0.692878i	$-0.756343\pi$
$499$	6.22672	−	15.0326i	0.278746	−	0.672953i	0.999801	+	0.0199245i	$0.00634260\pi$
$500$	−13.0719	+	17.9803i	−0.584592	+	0.804104i
$501$	10.7391	−	4.44828i	0.479787	−	0.198734i
$502$	15.4977	−	27.6632i	0.691696	−	1.23467i
$503$	−8.16412	−	8.16412i	−0.364020	−	0.364020i	0.501271	−	0.865291i	$-0.332866\pi$
$503$	−8.16412	−	8.16412i	−0.364020	−	0.364020i	−0.865291	+	0.501271i	$0.832866\pi$
$504$	4.70254	−	2.16528i	0.209468	−	0.0964494i
$505$	6.36549	−	6.36549i	0.283261	−	0.283261i
$506$	1.51758	+	5.38409i	0.0674647	+	0.239352i
$507$	4.85578	+	11.7229i	0.215653	+	0.520632i
$508$	7.99175	−	33.2432i	0.354576	−	1.47493i
$509$	13.9521	+	5.77913i	0.618414	+	0.256155i	0.669821	−	0.742522i	$-0.266371\pi$
$509$	13.9521	+	5.77913i	0.618414	+	0.256155i	−0.0514074	+	0.998678i	$0.516371\pi$
$510$	4.28519	+	5.43745i	0.189751	+	0.240774i
$511$	−9.56468			−0.423117
$512$	−6.17197	+	21.7694i	−0.272765	+	0.962081i
$513$	17.1181			0.755783
$514$	7.00403	+	8.88736i	0.308935	+	0.392005i
$515$	−15.2313	−	6.30902i	−0.671172	−	0.278009i
$516$	−0.493736	+	2.05379i	−0.0217355	+	0.0904131i
$517$	4.02082	+	9.70712i	0.176835	+	0.426919i
$518$	−1.70800	−	6.05967i	−0.0750453	−	0.266246i
$519$	−16.7957	+	16.7957i	−0.737247	+	0.737247i
$520$	−3.95330	+	1.82030i	−0.173364	+	0.0798253i
$521$	−0.382095	−	0.382095i	−0.0167399	−	0.0167399i	0.698687	−	0.715427i	$-0.253768\pi$
$521$	−0.382095	−	0.382095i	−0.0167399	−	0.0167399i	−0.715427	+	0.698687i	$0.753768\pi$
$522$	9.63982	−	17.2070i	0.421924	−	0.753128i
$523$	0.581817	−	0.240997i	0.0254411	−	0.0105380i	−0.369927	−	0.929061i	$-0.620617\pi$
$523$	0.581817	−	0.240997i	0.0254411	−	0.0105380i	0.395368	+	0.918523i	$0.370617\pi$
$524$	−20.5036	+	28.2027i	−0.895706	+	1.23204i
$525$	1.29610	−	3.12907i	0.0565665	−	0.136564i
$526$	30.1910	+	3.57802i	1.31639	+	0.156009i
$527$			19.5711i			0.852529i
$528$	−3.77273	−	1.92521i	−0.164187	−	0.0837841i
$529$		−	6.67932i		−	0.290405i
$530$	−1.30453	+	11.0075i	−0.0566654	+	0.478137i
$531$	−1.03076	+	2.48846i	−0.0447310	+	0.107990i
$532$	−6.47326	+	1.02323i	−0.280652	+	0.0443628i
$533$	−10.7615	+	4.45756i	−0.466132	+	0.193078i
$534$	−3.98465	−	2.23231i	−0.172433	−	0.0966015i
$535$	11.4749	+	11.4749i	0.496102	+	0.496102i
$536$	15.0789	−	0.585521i	0.651308	−	0.0252907i
$537$	15.8615	−	15.8615i	0.684472	−	0.684472i
$538$	−12.2111	+	3.44188i	−0.526459	+	0.148390i
$539$	−0.374687	−	0.904574i	−0.0161389	−	0.0389627i
$540$	7.45810	+	12.1789i	0.320945	+	0.524095i
$541$	−9.51992	−	3.94328i	−0.409293	−	0.169535i	0.168530	−	0.985696i	$-0.446098\pi$
$541$	−9.51992	−	3.94328i	−0.409293	−	0.169535i	−0.577824	+	0.816162i	$0.696098\pi$
$542$	18.0395	−	14.2167i	0.774864	−	0.610662i
$543$	−0.408965			−0.0175503
$544$	−18.3759	+	3.64059i	−0.787861	+	0.156089i
$545$	−17.6322			−0.755281
$546$	1.35231	−	1.06574i	0.0578736	−	0.0456095i
$547$	6.94719	+	2.87762i	0.297040	+	0.123038i	0.526226	−	0.850344i	$-0.323606\pi$
$547$	6.94719	+	2.87762i	0.297040	+	0.123038i	−0.229186	+	0.973383i	$0.573606\pi$
$548$	24.3188	−	14.8924i	1.03885	−	0.636171i
$549$	0.0677230	+	0.163498i	0.00289035	+	0.00697791i
$550$	4.17369	−	1.17641i	0.177967	−	0.0501624i
$551$	−17.6546	+	17.6546i	−0.752113	+	0.752113i
$552$	−9.07066	−	8.39256i	−0.386073	−	0.357211i
$553$	8.40635	+	8.40635i	0.357474	+	0.357474i
$554$	10.9293	+	6.12287i	0.464340	+	0.260136i
$555$	6.07992	−	2.51839i	0.258078	−	0.106900i
$556$	−3.38247	−	21.3984i	−0.143449	−	0.907495i
$557$	−4.56082	+	11.0108i	−0.193248	+	0.466542i	−0.990569	−	0.137013i	$-0.956250\pi$
$557$	−4.56082	+	11.0108i	−0.193248	+	0.466542i	0.797321	+	0.603555i	$0.206250\pi$
$558$	−1.80042	+	15.1917i	−0.0762177	+	0.643118i
$559$		−	1.09938i		−	0.0464987i
$560$	−3.54829	−	4.15966i	−0.149943	−	0.175778i
$561$		−	3.50659i		−	0.148048i
$562$	18.9235	+	2.24268i	0.798242	+	0.0946019i
$563$	1.77792	−	4.29228i	0.0749304	−	0.180898i	−0.881976	−	0.471294i	$-0.843787\pi$
$563$	1.77792	−	4.29228i	0.0749304	−	0.180898i	0.956907	+	0.290396i	$0.0937870\pi$
$564$	−18.7741	−	13.6490i	−0.790534	−	0.574726i
$565$	−20.0678	+	8.31235i	−0.844258	+	0.349703i
$566$	−16.7805	+	29.9530i	−0.705338	+	1.25902i
$567$	−0.112125	−	0.112125i	−0.00470879	−	0.00470879i
$568$	−0.766884	+	2.07580i	−0.0321777	+	0.0870985i
$569$	−16.5347	+	16.5347i	−0.693170	+	0.693170i	−0.962928	−	0.269758i	$-0.913056\pi$
$569$	−16.5347	+	16.5347i	−0.693170	+	0.693170i	0.269758	+	0.962928i	$0.413056\pi$
$570$	−1.85847	−	6.59348i	−0.0778426	−	0.276171i
$571$	14.8785	+	35.9199i	0.622646	+	1.50320i	0.848585	+	0.529059i	$0.177455\pi$
$571$	14.8785	+	35.9199i	0.622646	+	1.50320i	−0.225939	+	0.974141i	$0.572545\pi$
$572$	2.14339	+	0.515275i	0.0896195	+	0.0215447i
$573$	−7.60740	−	3.15109i	−0.317804	−	0.131639i
$574$	−9.05737	−	11.4928i	−0.378047	−	0.479702i
$575$	12.6516			0.527609
$576$	−14.5989	+	1.13548i	−0.608290	+	0.0473118i
$577$	23.0638			0.960160			0.480080	−	0.877225i	$-0.340608\pi$
$577$	23.0638			0.960160			0.480080	+	0.877225i	$0.340608\pi$
$578$	5.28147	+	6.70163i	0.219680	+	0.278751i
$579$	23.7244	+	9.82696i	0.985951	+	0.408394i
$580$	−20.2524	−	4.86873i	−0.840937	−	0.202163i
$581$	2.47245	+	5.96903i	0.102575	+	0.247637i
$582$	−2.54006	−	9.01165i	−0.105289	−	0.373545i
$583$	3.97001	−	3.97001i	0.164421	−	0.164421i
$584$	25.3766	+	9.37515i	1.05009	+	0.387946i
$585$	−1.99157	−	1.99157i	−0.0823411	−	0.0823411i
$586$	−15.4325	+	27.5469i	−0.637512	+	1.13795i
$587$	10.8440	−	4.49173i	0.447579	−	0.185393i	−0.147497	−	0.989062i	$-0.547122\pi$
$587$	10.8440	−	4.49173i	0.447579	−	0.185393i	0.595077	+	0.803669i	$0.297122\pi$
$588$	1.74950	+	1.27190i	0.0721481	+	0.0524524i
$589$	7.41092	−	17.8915i	0.305362	−	0.737208i
$590$	2.82480	+	0.334775i	0.116295	+	0.0137825i
$591$		−	1.40088i		−	0.0576244i
$592$	−1.40799	+	17.7514i	−0.0578682	+	0.729578i
$593$			24.5197i			1.00690i	0.864024	+	0.503451i	$0.167937\pi$
$593$			24.5197i			1.00690i	−0.864024	+	0.503451i	$0.832063\pi$
$594$	0.851303	−	7.18321i	0.0349294	−	0.294731i
$595$	1.73221	−	4.18192i	0.0710136	−	0.171442i
$596$	6.02609	+	38.1227i	0.246838	+	1.56157i
$597$	14.3583	−	5.94740i	0.587646	−	0.243411i
$598$	5.61116	+	3.14353i	0.229457	+	0.128548i
$599$	−9.50408	−	9.50408i	−0.388326	−	0.388326i	0.485764	−	0.874090i	$-0.338541\pi$
$599$	−9.50408	−	9.50408i	−0.388326	−	0.388326i	−0.874090	+	0.485764i	$0.838541\pi$
$600$	−6.50582	+	7.03148i	−0.265599	+	0.287059i
$601$	22.7018	−	22.7018i	0.926024	−	0.926024i	−0.0714221	−	0.997446i	$-0.522754\pi$
$601$	22.7018	−	22.7018i	0.926024	−	0.926024i	0.997446	+	0.0714221i	$0.0227537\pi$
$602$	1.32929	−	0.374678i	0.0541777	−	0.0152707i
$603$	3.73708	+	9.02210i	0.152185	+	0.367408i
$604$	15.3737	−	9.41453i	0.625546	−	0.383072i
$605$	−12.6804	−	5.25240i	−0.515533	−	0.213541i
$606$	7.91144	−	6.23491i	0.321380	−	0.253276i
$607$	46.3175			1.87997			0.939985	−	0.341216i	$-0.110839\pi$
$607$	46.3175			1.87997			0.939985	+	0.341216i	$0.110839\pi$
$608$	18.1775	+	3.63019i	0.737196	+	0.147224i
$609$	8.24032			0.333915
$610$	0.146789	−	0.115683i	0.00594331	−	0.00468385i
$611$	11.1610	+	4.62305i	0.451527	+	0.187029i
$612$	−6.33102	−	10.3384i	−0.255916	−	0.417905i
$613$	5.70272	+	13.7676i	0.230331	+	0.556068i	0.996216	−	0.0869094i	$-0.0276991\pi$
$613$	5.70272	+	13.7676i	0.230331	+	0.556068i	−0.765885	+	0.642977i	$0.777699\pi$
$614$	−44.7314	+	12.6082i	−1.80521	+	0.508825i
$615$	10.8155	−	10.8155i	0.436125	−	0.436125i
$616$	0.107453	+	2.76724i	0.00432942	+	0.111495i
$617$	−16.3375	−	16.3375i	−0.657723	−	0.657723i	0.297118	−	0.954841i	$-0.403975\pi$
$617$	−16.3375	−	16.3375i	−0.657723	−	0.657723i	−0.954841	+	0.297118i	$0.903975\pi$
$618$	−16.0938	−	9.01622i	−0.647389	−	0.362686i
$619$	−0.207481	+	0.0859413i	−0.00833935	+	0.00345427i	−0.386849	−	0.922143i	$-0.626437\pi$
$619$	−0.207481	+	0.0859413i	−0.00833935	+	0.00345427i	0.378510	+	0.925597i	$0.376437\pi$
$620$	15.9579	−	2.52249i	0.640886	−	0.101305i
$621$	8.07630	−	19.4979i	0.324091	−	0.782424i
$622$	−2.25519	+	19.0291i	−0.0904251	+	0.762998i
$623$			2.98625i			0.119642i
$624$	−4.63252	+	1.50206i	−0.185449	+	0.0601307i
$625$		−	0.465782i		−	0.0186313i
$626$	18.8316	+	2.23179i	0.752662	+	0.0892002i
$627$	−1.32783	+	3.20567i	−0.0530285	+	0.128022i
$628$	0.956763	−	1.31602i	0.0381790	−	0.0525151i
$629$	−13.6202	+	5.64168i	−0.543074	+	0.224949i
$630$	1.72931	−	3.08680i	0.0688974	−	0.122981i
$631$	−17.4310	−	17.4310i	−0.693919	−	0.693919i	0.269173	−	0.963092i	$-0.413250\pi$
$631$	−17.4310	−	17.4310i	−0.693919	−	0.693919i	−0.963092	+	0.269173i	$0.913250\pi$
$632$	−14.0636	−	30.5431i	−0.559420	−	1.21494i
$633$	5.72041	−	5.72041i	0.227366	−	0.227366i
$634$	−10.7165	−	38.0201i	−0.425606	−	1.50997i
$635$	−8.94209	−	21.5881i	−0.354856	−	0.856698i
$636$	−2.89913	+	12.0595i	−0.114958	+	0.478191i
$637$	−1.04006	−	0.430806i	−0.0412086	−	0.0170692i
$638$	6.53037	+	8.28634i	0.258540	+	0.328059i
$639$	−1.43207			−0.0566517
$640$	5.33693	+	14.5142i	0.210961	+	0.573725i
$641$	3.65877			0.144513			0.0722563	−	0.997386i	$-0.476980\pi$
$641$	3.65877			0.144513			0.0722563	+	0.997386i	$0.476980\pi$
$642$	11.2395	+	14.2617i	0.443587	+	0.562865i
$643$	−27.8166	−	11.5220i	−1.09698	−	0.454383i	−0.240543	−	0.970638i	$-0.577326\pi$
$643$	−27.8166	−	11.5220i	−1.09698	−	0.454383i	−0.856435	+	0.516255i	$0.827326\pi$
$644$	−1.88859	+	7.85595i	−0.0744208	+	0.309568i
$645$	0.552449	+	1.33373i	0.0217527	+	0.0525156i
$646$	4.16333	+	14.7707i	0.163804	+	0.581145i
$647$	−14.7046	+	14.7046i	−0.578098	+	0.578098i	−0.934379	−	0.356281i	$-0.884045\pi$
$647$	−14.7046	+	14.7046i	−0.578098	+	0.578098i	0.356281	+	0.934379i	$0.384045\pi$
$648$	0.187581	+	0.407387i	0.00736889	+	0.0160037i
$649$	−1.01880	−	1.01880i	−0.0399913	−	0.0399913i
$650$	2.43683	−	4.34971i	0.0955803	−	0.170610i
$651$	−5.90497	+	2.44592i	−0.231434	+	0.0958631i
$652$	−1.32601	+	1.82393i	−0.0519306	+	0.0714304i
$653$	1.49385	−	3.60648i	0.0584590	−	0.141133i	−0.891951	−	0.452132i	$-0.850664\pi$
$653$	1.49385	−	3.60648i	0.0584590	−	0.141133i	0.950410	+	0.310999i	$0.100664\pi$
$654$	−19.5925	−	2.32196i	−0.766127	−	0.0907959i
$655$			23.8301i			0.931118i
$656$	12.7655	+	39.3702i	0.498410	+	1.53715i
$657$			17.5070i			0.683013i
$658$	−1.78607	+	15.0707i	−0.0696282	+	0.587516i
$659$	3.58812	−	8.66248i	0.139773	−	0.337442i	−0.838456	−	0.544969i	$-0.816541\pi$
$659$	3.58812	−	8.66248i	0.139773	−	0.337442i	0.978229	+	0.207527i	$0.0665414\pi$
$660$	−2.85922	+	0.451960i	−0.111295	+	0.0175925i
$661$	4.73950	−	1.96317i	0.184345	−	0.0763583i	−0.288602	−	0.957449i	$-0.593190\pi$
$661$	4.73950	−	1.96317i	0.184345	−	0.0763583i	0.472947	+	0.881091i	$0.343190\pi$
$662$	−15.4422	−	8.65117i	−0.600180	−	0.336237i
$663$	−2.85091	−	2.85091i	−0.110720	−	0.110720i
$664$	−0.709056	−	18.2602i	−0.0275167	−	0.708635i
$665$	−3.16711	+	3.16711i	−0.122815	+	0.122815i
$666$	−11.0915	+	3.12629i	−0.429787	+	0.121141i
$667$	11.7796	+	28.4385i	0.456108	+	1.10114i
$668$	11.2261	+	18.3319i	0.434350	+	0.709281i
$669$	9.84264	+	4.07696i	0.380538	+	0.157624i
$670$	8.10008	−	6.38358i	0.312933	−	0.246619i
$671$	−0.0946637			−0.00365445
$672$	−3.39499	−	5.08939i	−0.130965	−	0.196327i
$673$	−20.7432			−0.799592			−0.399796	−	0.916604i	$-0.630919\pi$
$673$	−20.7432			−0.799592			−0.399796	+	0.916604i	$0.630919\pi$
$674$	−21.7625	+	17.1508i	−0.838262	+	0.660624i
$675$	−15.1146	−	6.26066i	−0.581760	−	0.240973i
$676$	−20.0113	+	12.2545i	−0.769664	+	0.471327i
$677$	−15.2136	−	36.7288i	−0.584706	−	1.41160i	−0.888504	−	0.458868i	$-0.848255\pi$
$677$	−15.2136	−	36.7288i	−0.584706	−	1.41160i	0.303799	−	0.952736i	$-0.401745\pi$
$678$	−23.3935	+	6.59378i	−0.898421	+	0.253232i
$679$	−4.32865	+	4.32865i	−0.166118	+	0.166118i
$680$	−8.69487	+	9.39741i	−0.333433	+	0.360374i
$681$	13.0224	+	13.0224i	0.499021	+	0.499021i
$682$	−7.13920	−	3.99958i	−0.273374	−	0.153152i
$683$	6.12378	−	2.53655i	0.234320	−	0.0970585i	−0.262434	−	0.964950i	$-0.584525\pi$
$683$	6.12378	−	2.53655i	0.234320	−	0.0970585i	0.496754	+	0.867891i	$0.334525\pi$
$684$	1.87291	+	11.8485i	0.0716124	+	0.453040i
$685$	7.45816	−	18.0056i	0.284962	−	0.687958i
$686$	0.166438	−	1.40439i	0.00635462	−	0.0536197i
$687$		−	21.0558i		−	0.803328i
$688$	−3.89406	−	0.308866i	−0.148460	−	0.0117754i
$689$		−	6.45535i		−	0.245929i
$690$	−8.38695	−	0.993961i	−0.319286	−	0.0378395i
$691$	15.3357	−	37.0236i	0.583397	−	1.40844i	−0.306319	−	0.951929i	$-0.599097\pi$
$691$	15.3357	−	37.0236i	0.583397	−	1.40844i	0.889716	−	0.456515i	$-0.150903\pi$
$692$	−35.5288	−	25.8298i	−1.35060	−	0.981902i
$693$	−1.65571	+	0.685819i	−0.0628954	+	0.0260521i
$694$	−22.3069	+	39.8176i	−0.846759	+	1.51146i
$695$	−10.4694	−	10.4694i	−0.397127	−	0.397127i
$696$	−21.8629	−	8.07703i	−0.828710	−	0.306159i
$697$	−24.2289	+	24.2289i	−0.917737	+	0.917737i
$698$	9.78018	+	34.6982i	0.370185	+	1.31335i
$699$	−1.90947	−	4.60988i	−0.0722229	−	0.174362i
$700$	6.08985	+	1.46401i	0.230175	+	0.0553345i
$701$	31.5541	+	13.0701i	1.19178	+	0.493652i	0.888335	−	0.459196i	$-0.151862\pi$
$701$	31.5541	+	13.0701i	1.19178	+	0.493652i	0.303447	+	0.952848i	$0.401862\pi$
$702$	−5.14794	−	6.53218i	−0.194296	−	0.246541i
$703$	14.5877			0.550185
$704$	2.42731	−	7.44724i	0.0914828	−	0.280678i
$705$	−15.8633			−0.597448
$706$	−21.7835	−	27.6409i	−0.819832	−	1.04028i
$707$	−6.08466	−	2.52035i	−0.228837	−	0.0947874i
$708$	3.09476	+	0.743987i	0.116308	+	0.0279607i
$709$	15.9191	+	38.4322i	0.597856	+	1.44335i	0.875762	+	0.482743i	$0.160359\pi$
$709$	15.9191	+	38.4322i	0.597856	+	1.44335i	−0.277907	+	0.960608i	$0.589641\pi$
$710$	0.410300	+	1.45567i	0.0153983	+	0.0546302i
$711$	15.3868	−	15.3868i	0.577051	−	0.577051i
$712$	2.92708	−	7.92299i	0.109697	−	0.296927i
$713$	−16.8824	−	16.8824i	−0.632251	−	0.632251i
$714$	2.47550	−	4.41874i	0.0926432	−	0.165367i
$715$	1.39191	−	0.576549i	0.0520546	−	0.0215617i
$716$	33.5526	+	24.3931i	1.25392	+	0.911613i
$717$	1.17279	−	2.83136i	0.0437985	−	0.105739i
$718$	−28.3004	−	3.35397i	−1.05616	−	0.125169i
$719$			1.68899i			0.0629887i	0.999504	+	0.0314943i	$0.0100266\pi$
$719$			1.68899i			0.0629887i	−0.999504	+	0.0314943i	$0.989973\pi$
$720$	−7.61377	+	6.49472i	−0.283748	+	0.242044i
$721$			12.0614i			0.449188i
$722$	−1.37519	+	11.6037i	−0.0511791	+	0.431845i
$723$	9.32070	−	22.5021i	0.346640	−	0.836864i
$724$	−0.118083	−	0.747023i	−0.00438851	−	0.0277629i
$725$	22.0452	−	9.13142i	0.818738	−	0.339132i
$726$	−13.3985	−	7.50621i	−0.497265	−	0.278582i
$727$	9.22518	+	9.22518i	0.342143	+	0.342143i	0.857173	−	0.515029i	$-0.172219\pi$
$727$	9.22518	+	9.22518i	0.342143	+	0.342143i	−0.515029	+	0.857173i	$0.672219\pi$
$728$	2.33717	+	2.16245i	0.0866212	+	0.0801456i
$729$	−12.1901	+	12.1901i	−0.451484	+	0.451484i
$730$	17.7955	−	5.01592i	0.658642	−	0.185647i
$731$	−1.23759	−	2.98782i	−0.0457741	−	0.110508i
$732$	0.178342	−	0.109213i	0.00659172	−	0.00403664i
$733$	44.9627	+	18.6241i	1.66073	+	0.687898i	0.998133	−	0.0610744i	$-0.0194527\pi$
$733$	44.9627	+	18.6241i	1.66073	+	0.687898i	0.662601	+	0.748973i	$0.269453\pi$
$734$	−22.6183	+	17.8253i	−0.834858	+	0.657942i
$735$	1.47825			0.0545261
$736$	12.7110	−	18.9919i	0.468534	−	0.700051i
$737$	−5.22371			−0.192418
$738$	−21.0363	+	16.5784i	−0.774356	+	0.610261i
$739$	−36.8745	−	15.2739i	−1.35645	−	0.561861i	−0.418371	−	0.908276i	$-0.637399\pi$
$739$	−36.8745	−	15.2739i	−1.35645	−	0.561861i	−0.938081	+	0.346415i	$0.887399\pi$
$740$	6.35563	+	10.3786i	0.233638	+	0.381524i
$741$	1.52671	+	3.68580i	0.0560851	+	0.135401i
$742$	7.80534	−	2.20005i	0.286543	−	0.0807662i
$743$	−16.9537	+	16.9537i	−0.621972	+	0.621972i	−0.946035	−	0.324063i	$-0.894951\pi$
$743$	−16.9537	+	16.9537i	−0.621972	+	0.621972i	0.324063	+	0.946035i	$0.394951\pi$
$744$	18.0643	−	0.701446i	0.662268	−	0.0257162i
$745$	18.6519	+	18.6519i	0.683354	+	0.683354i
$746$	−13.3227	−	7.46375i	−0.487779	−	0.273267i
$747$	10.9256	−	4.52553i	0.399747	−	0.165581i
$748$	6.40522	−	1.01248i	0.234198	−	0.0370199i
$749$	4.54336	−	10.9686i	0.166011	−	0.400785i
$750$	−2.00069	+	16.8816i	−0.0730550	+	0.616431i
$751$			4.46547i			0.162947i	0.996675	+	0.0814737i	$0.0259626\pi$
$751$			4.46547i			0.162947i	−0.996675	+	0.0814737i	$0.974037\pi$
$752$	19.5108	−	38.2342i	0.711484	−	1.39426i
$753$		−	24.2484i		−	0.883661i
$754$	12.0462	+	1.42763i	0.438697	+	0.0519913i
$755$	4.71483	−	11.3826i	0.171590	−	0.414255i
$756$	6.14377	−	8.45074i	0.223447	−	0.307350i
$757$	−32.9773	+	13.6596i	−1.19858	+	0.496468i	−0.890540	−	0.454905i	$-0.849673\pi$
$757$	−32.9773	+	13.6596i	−1.19858	+	0.496468i	−0.308040	+	0.951373i	$0.599673\pi$
$758$	15.0383	−	26.8432i	0.546215	−	0.974988i
$759$	3.02486	+	3.02486i	0.109795	+	0.109795i
$760$	11.5072	−	5.29849i	0.417410	−	0.192196i
$761$	32.2143	−	32.2143i	1.16777	−	1.16777i	0.185034	−	0.982732i	$-0.440761\pi$
$761$	32.2143	−	32.2143i	1.16777	−	1.16777i	0.982732	−	0.185034i	$-0.0592395\pi$
$762$	−7.09332	−	25.1658i	−0.256964	−	0.911659i
$763$	4.93652	+	11.9178i	0.178714	+	0.431454i
$764$	3.55932	−	14.8057i	0.128772	−	0.535651i
$765$	−7.65450	−	3.17060i	−0.276749	−	0.114633i
$766$	4.58309	+	5.81545i	0.165594	+	0.210121i
$767$	−1.65660			−0.0598163
$768$	4.01891	+	16.8307i	0.145020	+	0.607324i
$769$	−46.4889			−1.67643			−0.838217	−	0.545337i	$-0.816402\pi$
$769$	−46.4889			−1.67643			−0.838217	+	0.545337i	$0.816402\pi$
$770$	1.17150	+	1.48651i	0.0422179	+	0.0535700i
$771$	7.99463	+	3.31148i	0.287920	+	0.119260i
$772$	−11.1001	+	46.1728i	−0.399500	+	1.66180i
$773$	19.4635	+	46.9890i	0.700053	+	1.69008i	0.723474	+	0.690352i	$0.242544\pi$
$773$	19.4635	+	46.9890i	0.700053	+	1.69008i	−0.0234209	+	0.999726i	$0.507456\pi$
$774$	−0.685803	−	2.43310i	−0.0246507	−	0.0874560i
$775$	−13.0871	+	13.0871i	−0.470101	+	0.470101i
$776$	15.7275	−	7.24172i	0.564583	−	0.259962i
$777$	−3.40441	−	3.40441i	−0.122133	−	0.122133i
$778$	−18.5213	+	33.0602i	−0.664019	+	1.18527i
$779$	31.3244	−	12.9750i	1.12231	−	0.464877i
$780$	−1.95714	+	2.69204i	−0.0700769	+	0.0963906i
$781$	0.293150	−	0.707727i	0.0104897	−	0.0253245i
$782$	18.7884	+	2.22667i	0.671872	+	0.0796255i
$783$		−	39.8039i		−	1.42247i
$784$	−1.81814	+	3.56291i	−0.0649336	+	0.127247i
$785$		−	1.11198i		−	0.0396884i
$786$	−3.13815	+	26.4794i	−0.111934	+	0.944489i
$787$	18.8857	−	45.5941i	0.673202	−	1.62525i	−0.102934	−	0.994688i	$-0.532823\pi$
$787$	18.8857	−	45.5941i	0.673202	−	1.62525i	0.776136	−	0.630565i	$-0.217177\pi$
$788$	2.55887	−	0.404483i	0.0911561	−	0.0144091i
$789$	21.4797	−	8.89719i	0.764699	−	0.316749i
$790$	−20.0489	−	11.2319i	−0.713307	−	0.399614i
$791$	11.2368	+	11.2368i	0.399535	+	0.399535i
$792$	5.06510	−	0.196681i	0.179980	−	0.00698874i
$793$	−0.0769631	+	0.0769631i	−0.00273304	+	0.00273304i
$794$	39.7323	−	11.1991i	1.41005	−	0.397441i
$795$	3.24389	+	7.83143i	0.115049	+	0.277752i
$796$	15.0094	+	24.5099i	0.531994	+	0.868731i
$797$	5.80787	+	2.40570i	0.205725	+	0.0852142i	0.483167	−	0.875528i	$-0.339486\pi$
$797$	5.80787	+	2.40570i	0.205725	+	0.0852142i	−0.277442	+	0.960743i	$0.589486\pi$
$798$	−3.93629	+	3.10214i	−0.139343	+	0.109815i
$799$	35.5370			1.25721
$800$	−14.7223	−	9.85343i	−0.520513	−	0.348371i
$801$	5.46597			0.193131
$802$	0.373565	−	0.294402i	0.0131910	−	0.0103957i
$803$	−8.65196	−	3.58376i	−0.305321	−	0.126468i
$804$	9.84125	−	6.02659i	0.347074	−	0.212541i
$805$	2.11317	+	5.10165i	0.0744795	+	0.179809i
$806$	−9.05600	+	2.55256i	−0.318984	+	0.0899102i
$807$	−6.86039	+	6.86039i	−0.241497	+	0.241497i
$808$	13.6731	+	12.6510i	0.481019	+	0.445059i
$809$	−9.41608	−	9.41608i	−0.331052	−	0.331052i	0.521934	−	0.852986i	$-0.325211\pi$
$809$	−9.41608	−	9.41608i	−0.331052	−	0.331052i	−0.852986	+	0.521934i	$0.825211\pi$
$810$	0.267413	+	0.149812i	0.00939595	+	0.00526387i
$811$	−45.3813	+	18.7976i	−1.59355	+	0.660072i	−0.990485	−	0.137618i	$-0.956055\pi$
$811$	−45.3813	+	18.7976i	−1.59355	+	0.660072i	−0.603068	+	0.797690i	$0.706055\pi$
$812$	2.37927	+	15.0519i	0.0834962	+	0.528220i
$813$	6.72164	−	16.2275i	0.235738	−	0.569122i
$814$	0.725462	−	6.12138i	0.0254274	−	0.214554i
$815$			1.54114i			0.0539838i
$816$	−10.8991	+	9.29715i	−0.381543	+	0.325465i
$817$			3.20005i			0.111956i
$818$	−6.42654	−	0.761628i	−0.224699	−	0.0266297i
$819$	−0.788539	+	1.90370i	−0.0275538	+	0.0665207i
$820$	22.8787	+	16.6331i	0.798960	+	0.580852i
$821$	−30.8653	+	12.7848i	−1.07721	+	0.446194i	−0.849528	−	0.527543i	$-0.823113\pi$
$821$	−30.8653	+	12.7848i	−1.07721	+	0.446194i	−0.227678	+	0.973736i	$0.573113\pi$
$822$	10.6585	−	19.0252i	0.371756	−	0.663580i
$823$	0.854721	+	0.854721i	0.0297937	+	0.0297937i	0.721847	−	0.692053i	$-0.243294\pi$
$823$	0.854721	+	0.854721i	0.0297937	+	0.0297937i	−0.692053	+	0.721847i	$0.743294\pi$
$824$	11.8224	−	32.0007i	0.411851	−	1.11480i
$825$	2.34484	−	2.34484i	0.0816368	−	0.0816368i
$826$	−0.564584	−	2.00304i	−0.0196444	−	0.0696946i
$827$	−8.18409	−	19.7581i	−0.284589	−	0.687058i	0.715343	−	0.698774i	$-0.246271\pi$
$827$	−8.18409	−	19.7581i	−0.284589	−	0.687058i	−0.999931	+	0.0117158i	$0.996271\pi$
$828$	14.3794	+	3.45684i	0.499718	+	0.120133i
$829$	22.1565	+	9.17751i	0.769526	+	0.318748i	0.732680	−	0.680573i	$-0.238269\pi$
$829$	22.1565	+	9.17751i	0.769526	+	0.318748i	0.0368457	+	0.999321i	$0.488269\pi$
$830$	−7.73040	−	9.80905i	−0.268326	−	0.340477i
$831$	9.58014			0.332331
$832$	−4.08128	−	8.02816i	−0.141493	−	0.278326i
$833$	−3.31157			−0.114739
$834$	−10.2546	−	13.0120i	−0.355089	−	0.450570i
$835$	13.5728	+	5.62206i	0.469708	+	0.194559i
$836$	−6.23893	−	1.49985i	−0.215778	−	0.0518735i
$837$	11.8147	+	28.5233i	0.408376	+	0.985908i
$838$	−7.05432	−	25.0274i	−0.243687	−	0.864557i
$839$	7.72755	−	7.72755i	0.266785	−	0.266785i	−0.561018	−	0.827803i	$-0.689590\pi$
$839$	7.72755	−	7.72755i	0.266785	−	0.266785i	0.827803	+	0.561018i	$0.189590\pi$
$840$	−3.92203	−	1.44896i	−0.135323	−	0.0499938i
$841$	20.5454	+	20.5454i	0.708461	+	0.708461i
$842$	27.2734	−	48.6828i	0.939905	−	1.67772i
$843$	13.4634	−	5.57671i	0.463703	−	0.192072i
$844$	12.1007	+	8.79733i	0.416523	+	0.302817i
$845$	−6.13710	+	14.8163i	−0.211123	+	0.509695i
$846$	27.5851	+	3.26919i	0.948394	+	0.112397i
$847$			10.0414i			0.345025i
$848$	−22.8652	−	1.81361i	−0.785196	−	0.0622796i
$849$			26.2556i			0.901090i
$850$	1.72609	−	14.5646i	0.0592044	−	0.499561i
$851$	6.88245	−	16.6157i	0.235927	−	0.569579i
$852$	0.264221	+	1.67153i	0.00905206	+	0.0572658i
$853$	−13.6812	+	5.66694i	−0.468436	+	0.194032i	−0.604400	−	0.796681i	$-0.706587\pi$
$853$	−13.6812	+	5.66694i	−0.468436	+	0.194032i	0.135964	+	0.990714i	$0.456587\pi$
$854$	−0.119288	−	0.0668284i	−0.00408195	−	0.00228682i
$855$	5.79702	+	5.79702i	0.198254	+	0.198254i
$856$	−22.8055	+	24.6482i	−0.779477	+	0.842457i
$857$	−27.6739	+	27.6739i	−0.945322	+	0.945322i	−0.998581	−	0.0532590i	$-0.983039\pi$
$857$	−27.6739	+	27.6739i	−0.945322	+	0.945322i	0.0532590	+	0.998581i	$0.483039\pi$
$858$	1.62259	−	0.457348i	0.0553941	−	0.0156136i
$859$	−13.1026	−	31.6326i	−0.447056	−	1.07929i	−0.973419	−	0.229030i	$-0.926445\pi$
$859$	−13.1026	−	31.6326i	−0.447056	−	1.07929i	0.526363	−	0.850260i	$-0.323555\pi$
$860$	−2.27671	+	1.39421i	−0.0776351	+	0.0475422i
$861$	−10.3384	−	4.28230i	−0.352331	−	0.145940i
$862$	14.6049	−	11.5099i	0.497444	−	0.392030i
$863$	−42.2413			−1.43791			−0.718955	−	0.695056i	$-0.755380\pi$
$863$	−42.2413			−1.43791			−0.718955	+	0.695056i	$0.755380\pi$
$864$	−24.5837	+	16.3991i	−0.836354	+	0.557909i
$865$	−30.0203			−1.02072
$866$	44.6575	−	35.1941i	1.51752	−	1.19594i
$867$	6.02845	+	2.49707i	0.204737	+	0.0848048i
$868$	−6.17274	−	10.0799i	−0.209517	−	0.342135i
$869$	4.45442	+	10.7539i	0.151106	+	0.364801i
$870$	−15.3315	+	4.32140i	−0.519786	+	0.146509i
$871$	−4.24696	+	4.24696i	−0.143903	+	0.143903i
$872$	−1.41570	−	36.4585i	−0.0479418	−	1.23464i
$873$	7.92308	+	7.92308i	0.268156	+	0.268156i
$874$	−16.3329	−	9.15013i	−0.552468	−	0.309508i
$875$	10.2688	−	4.25349i	0.347150	−	0.143794i
$876$	20.4345	−	3.23010i	0.690417	−	0.109135i
$877$	1.49656	−	3.61301i	0.0505352	−	0.122003i	−0.896596	−	0.442850i	$-0.853968\pi$
$877$	1.49656	−	3.61301i	0.0505352	−	0.122003i	0.947131	+	0.320847i	$0.103968\pi$
$878$	6.44473	−	54.3800i	0.217499	−	1.83523i
$879$			24.1465i			0.814440i
$880$	−1.65112	−	5.09222i	−0.0556592	−	0.171659i
$881$		−	46.9294i		−	1.58109i	−0.612403	−	0.790546i	$-0.709797\pi$
$881$		−	46.9294i		−	1.58109i	0.612403	−	0.790546i	$-0.290203\pi$
$882$	−2.57056	−	0.304644i	−0.0865552	−	0.0102579i
$883$	9.05346	−	21.8570i	0.304673	−	0.735546i	−0.695187	−	0.718829i	$-0.744678\pi$
$883$	9.05346	−	21.8570i	0.304673	−	0.735546i	0.999860	−	0.0167174i	$-0.00532155\pi$
$884$	4.38438	−	6.03070i	0.147463	−	0.202834i
$885$	2.00973	−	0.832459i	0.0675564	−	0.0279828i
$886$	−24.7291	+	44.1411i	−0.830790	+	1.48295i
$887$	−3.55140	−	3.55140i	−0.119244	−	0.119244i	0.644967	−	0.764211i	$-0.276871\pi$
$887$	−3.55140	−	3.55140i	−0.119244	−	0.119244i	−0.764211	+	0.644967i	$0.776871\pi$
$888$	5.69548	+	12.3694i	0.191128	+	0.415089i
$889$	−12.0881	+	12.0881i	−0.405422	+	0.405422i
$890$	−1.56605	−	5.55605i	−0.0524942	−	0.186239i
$891$	−0.0594133	−	0.143436i	−0.00199042	−	0.00480530i
$892$	−4.60513	+	19.1559i	−0.154191	+	0.641388i
$893$	−32.4873	−	13.4567i	−1.08715	−	0.450311i
$894$	18.2693	+	23.1818i	0.611018	+	0.775317i
$895$	28.3506			0.947655
$896$	8.31613	−	7.67085i	0.277822	−	0.256265i
$897$	4.91851			0.164224
$898$	10.9816	+	13.9344i	0.366460	+	0.464998i
$899$	−41.6023	−	17.2322i	−1.38751	−	0.574727i
$900$	2.67970	−	11.1467i	0.0893234	−	0.371558i
$901$	−7.26694	−	17.5439i	−0.242097	−	0.584474i
$902$	−3.88685	−	13.7898i	−0.129418	−	0.459150i
$903$	0.746813	−	0.746813i	0.0248524	−	0.0248524i
$904$	−18.7989	−	40.8271i	−0.625241	−	1.35789i
$905$	−0.365489	−	0.365489i	−0.0121493	−	0.0121493i
$906$	6.73796	−	12.0272i	0.223854	−	0.399576i
$907$	−14.4344	+	5.97893i	−0.479287	+	0.198527i	−0.609229	−	0.792994i	$-0.708521\pi$
$907$	−14.4344	+	5.97893i	−0.479287	+	0.198527i	0.129942	+	0.991522i	$0.458521\pi$
$908$	−20.0270	+	27.5471i	−0.664620	+	0.914183i
$909$	−4.61319	+	11.1372i	−0.153010	+	0.369399i
$910$	2.16100	+	0.256106i	0.0716364	+	0.00848984i
$911$			5.65334i			0.187303i	0.995605	+	0.0936517i	$0.0298540\pi$
$911$			5.65334i			0.187303i	−0.995605	+	0.0936517i	$0.970146\pi$
$912$	13.4843	−	4.37218i	0.446509	−	0.144777i
$913$			6.32583i			0.209354i
$914$	−3.35531	+	28.3118i	−0.110984	+	0.936471i
$915$	0.0546944	−	0.132044i	0.00180814	−	0.00436524i
$916$	38.4609	−	6.07955i	1.27078	−	0.200874i
$917$	16.1070	−	6.67174i	0.531900	−	0.220320i
$918$	−21.3442	−	11.9576i	−0.704463	−	0.394660i
$919$	3.33146	+	3.33146i	0.109895	+	0.109895i	0.759916	−	0.650021i	$-0.225240\pi$
$919$	3.33146	+	3.33146i	0.109895	+	0.109895i	−0.650021	+	0.759916i	$0.725240\pi$
$920$	−0.606020	−	15.6068i	−0.0199799	−	0.514540i
$921$	−25.1308	+	25.1308i	−0.828087	+	0.828087i
$922$	−19.6438	+	5.53688i	−0.646934	+	0.182347i
$923$	−0.337057	−	0.813729i	−0.0110944	−	0.0267842i
$924$	1.10598	+	1.80604i	0.0363842	+	0.0594144i
$925$	−12.8803	−	5.33520i	−0.423502	−	0.175420i
$926$	2.49411	−	1.96558i	0.0819617	−	0.0645930i
$927$	22.0769			0.725099
$928$	8.44110	−	42.2673i	0.277093	−	1.38749i
$929$	−56.0336			−1.83840			−0.919202	−	0.393787i	$-0.871165\pi$
$929$	−56.0336			−1.83840			−0.919202	+	0.393787i	$0.871165\pi$
$930$	9.70377	−	7.64743i	0.318199	−	0.250769i
$931$	3.02738	+	1.25398i	0.0992185	+	0.0410977i
$932$	7.86917	−	4.81892i	0.257763	−	0.157849i
$933$	5.60782	+	13.5385i	0.183592	+	0.443230i
$934$	−18.9276	+	5.33500i	−0.619328	+	0.174566i
$935$	3.13382	−	3.13382i	0.102487	−	0.102487i
$936$	3.95810	−	4.27791i	0.129374	−	0.139828i
$937$	−19.6625	−	19.6625i	−0.642345	−	0.642345i	0.308787	−	0.951131i	$-0.400077\pi$
$937$	−19.6625	−	19.6625i	−0.642345	−	0.642345i	−0.951131	+	0.308787i	$0.900077\pi$
$938$	−6.58252	−	3.68771i	−0.214927	−	0.120408i
$939$	13.3980	−	5.54962i	0.437226	−	0.181105i
$940$	−4.58032	−	28.9763i	−0.149393	−	0.945104i
$941$	−8.94829	+	21.6031i	−0.291706	+	0.704240i	−0.999999	−	0.00167870i	$-0.999466\pi$
$941$	−8.94829	+	21.6031i	−0.291706	+	0.704240i	0.708293	+	0.705919i	$0.249466\pi$
$942$	0.146436	−	1.23561i	0.00477114	−	0.0402584i
$943$		−	41.8008i		−	1.36122i
$944$	−0.465415	+	5.86777i	−0.0151480	+	0.190980i
$945$		−	7.14052i		−	0.232281i
$946$	1.34282	+	0.159142i	0.0436590	+	0.00517415i
$947$	−2.96135	+	7.14933i	−0.0962309	+	0.232322i	−0.964663	−	0.263486i	$-0.915128\pi$
$947$	−2.96135	+	7.14933i	−0.0962309	+	0.232322i	0.868432	+	0.495808i	$0.165128\pi$
$948$	−20.7987	−	15.1209i	−0.675510	−	0.491103i
$949$	−9.94783	+	4.12052i	−0.322920	+	0.133758i
$950$	−7.09308	+	12.6611i	−0.230130	+	0.410779i
$951$	−21.3602	−	21.3602i	−0.692653	−	0.692653i
$952$	8.78612	+	3.24595i	0.284760	+	0.105202i
$953$	22.9816	−	22.9816i	0.744448	−	0.744448i	−0.228983	−	0.973431i	$-0.573540\pi$
$953$	22.9816	−	22.9816i	0.744448	−	0.744448i	0.973431	+	0.228983i	$0.0735399\pi$
$954$	−4.02692	−	14.2867i	−0.130376	−	0.462550i
$955$	−3.98258	−	9.61479i	−0.128873	−	0.311127i
$956$	5.51045	+	1.32472i	0.178221	+	0.0428446i
$957$	7.45398	+	3.08754i	0.240953	+	0.0998059i
$958$	−13.6856	−	17.3656i	−0.442161	−	0.561056i
$959$	−14.2582			−0.460422
$960$	8.98552	+	7.68863i	0.290006	+	0.248149i
$961$	3.92690			0.126674
$962$	−4.38696	−	5.56659i	−0.141441	−	0.179474i
$963$	−20.0768	−	8.31607i	−0.646965	−	0.267982i
$964$	43.7941	+	10.5282i	1.41051	+	0.339091i
$965$	12.4200	+	29.9846i	0.399815	+	0.965239i
$966$	1.67628	+	5.94711i	0.0539333	+	0.191345i
$967$	−37.6861	+	37.6861i	−1.21190	+	1.21190i	−0.241503	+	0.970400i	$0.577640\pi$
$967$	−37.6861	+	37.6861i	−1.21190	+	1.21190i	−0.970400	+	0.241503i	$0.922360\pi$
$968$	9.84238	−	26.6413i	0.316346	−	0.856283i
$969$	8.29839	+	8.29839i	0.266583	+	0.266583i
$970$	5.78362	−	10.3237i	0.185701	−	0.331474i
$971$	4.96890	−	2.05819i	0.159460	−	0.0660504i	−0.301526	−	0.953458i	$-0.597496\pi$
$971$	4.96890	−	2.05819i	0.159460	−	0.0660504i	0.460986	+	0.887408i	$0.347496\pi$
$972$	−25.0748	−	18.2296i	−0.804275	−	0.584716i
$973$	−4.14525	+	10.0075i	−0.132891	+	0.320826i
$974$	−4.99143	−	0.591549i	−0.159936	−	0.0189544i
$975$		−	3.81278i		−	0.122107i
$976$	0.250985	+	0.294230i	0.00803384	+	0.00941808i
$977$		−	28.1908i		−	0.901905i	−0.892548	−	0.450952i	$-0.851084\pi$
$977$		−	28.1908i		−	0.901905i	0.892548	−	0.450952i	$-0.148916\pi$
$978$	−0.202951	+	1.71248i	−0.00648964	+	0.0547590i
$979$	−1.11891	+	2.70128i	−0.0357605	+	0.0863334i
$980$	0.426824	+	2.70021i	0.0136344	+	0.0862549i
$981$	21.8141	−	9.03570i	0.696471	−	0.288488i
$982$	35.9515	+	20.1410i	1.14726	+	0.642726i
$983$	−20.6985	−	20.6985i	−0.660179	−	0.660179i	0.295243	−	0.955422i	$-0.404599\pi$
$983$	−20.6985	−	20.6985i	−0.660179	−	0.660179i	−0.955422	+	0.295243i	$0.904599\pi$
$984$	23.2319	+	21.4951i	0.740606	+	0.685240i
$985$	1.25196	−	1.25196i	0.0398906	−	0.0398906i
$986$	34.3455	−	9.68078i	1.09379	−	0.308299i
$987$	4.44128	+	10.7222i	0.141368	+	0.341292i
$988$	−6.29175	+	3.85295i	−0.200167	+	0.122579i
$989$	3.64493	+	1.50978i	0.115902	+	0.0480082i
$990$	2.72087	−	2.14429i	0.0864750	−	0.0681499i
$991$	13.1949			0.419149			0.209575	−	0.977793i	$-0.432792\pi$
$991$	13.1949			0.419149			0.209575	+	0.977793i	$0.432792\pi$
$992$	6.49707	+	32.7940i	0.206282	+	1.04121i
$993$	−13.5360			−0.429553
$994$	0.869029	−	0.684872i	0.0275639	−	0.0217228i
$995$	18.1471	+	7.51676i	0.575301	+	0.238297i
$996$	−7.29809	−	11.9176i	−0.231249	−	0.377623i
$997$	11.0248	+	26.6162i	0.349158	+	0.842942i	0.996720	+	0.0809291i	$0.0257887\pi$
$997$	11.0248	+	26.6162i	0.349158	+	0.842942i	−0.647562	+	0.762013i	$0.724211\pi$
$998$	22.1480	−	6.24272i	0.701082	−	0.197610i
$999$	−16.4446	+	16.4446i	−0.520284	+	0.520284i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.u.c.29.11	✓	52
4.3	odd	2		896.2.u.c.337.5		52
32.11	odd	8		896.2.u.c.561.5		52
32.21	even	8	inner	224.2.u.c.85.11	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.29.11	✓	52	1.1	even	1	trivial
224.2.u.c.85.11	yes	52	32.21	even	8	inner
896.2.u.c.337.5		52	4.3	odd	2
896.2.u.c.561.5		52	32.11	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.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.875361 + 1.11074i) q^{2} +(0.999166 + 0.413868i) q^{3} +(-0.467486 + 1.94460i) q^{4} +(0.523077 + 1.26282i) q^{5} +(0.414931 + 1.47210i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.56916 + 1.18297i) q^{8} +(-1.29427 - 1.29427i) q^{9} +O(q^{10})\)	\(q+(0.875361 + 1.11074i) q^{2} +(0.999166 + 0.413868i) q^{3} +(-0.467486 + 1.94460i) q^{4} +(0.523077 + 1.26282i) q^{5} +(0.414931 + 1.47210i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.56916 + 1.18297i) q^{8} +(-1.29427 - 1.29427i) q^{9} +(-0.944783 + 1.68643i) q^{10} +(0.904574 - 0.374687i) q^{11} +(-1.27190 + 1.74950i) q^{12} +(0.430806 - 1.04006i) q^{13} +(1.40439 + 0.166438i) q^{14} +1.47825i q^{15} +(-3.56291 - 1.81814i) q^{16} -3.31157i q^{17} +(0.304644 - 2.57056i) q^{18} +(-1.25398 + 3.02738i) q^{19} +(-2.70021 + 0.426824i) q^{20} +(0.999166 - 0.413868i) q^{21} +(1.20801 + 0.676760i) q^{22} +(2.85663 + 2.85663i) q^{23} +(-3.05661 + 0.118690i) q^{24} +(2.21443 - 2.21443i) q^{25} +(1.53235 - 0.431913i) q^{26} +(-1.99914 - 4.82635i) q^{27} +(1.04448 + 1.70560i) q^{28} +(7.03942 + 2.91582i) q^{29} +(-1.64195 + 1.29400i) q^{30} -5.90990 q^{31} +(-1.09935 - 5.54900i) q^{32} +1.05889 q^{33} +(3.67830 - 2.89882i) q^{34} +(1.26282 + 0.523077i) q^{35} +(3.12190 - 1.91179i) q^{36} +(-1.70363 - 4.11292i) q^{37} +(-4.46033 + 1.25721i) q^{38} +(0.860894 - 0.860894i) q^{39} +(-2.83775 - 2.62560i) q^{40} +(-7.31644 - 7.31644i) q^{41} +(1.33433 + 0.747529i) q^{42} +(0.902235 - 0.373718i) q^{43} +(0.305739 + 1.93419i) q^{44} +(0.957430 - 2.31144i) q^{45} +(-0.672390 + 5.67356i) q^{46} +10.7312i q^{47} +(-2.80747 - 3.29120i) q^{48} -1.00000i q^{49} +(4.39808 + 0.521229i) q^{50} +(1.37055 - 3.30881i) q^{51} +(1.82110 + 1.32396i) q^{52} +(5.29777 - 2.19441i) q^{53} +(3.61085 - 6.44533i) q^{54} +(0.946323 + 0.946323i) q^{55} +(-0.980184 + 2.65316i) q^{56} +(-2.50588 + 2.50588i) q^{57} +(2.92332 + 10.3714i) q^{58} +(-0.563137 - 1.35953i) q^{59} +(-2.87460 - 0.691061i) q^{60} +(-0.0893244 - 0.0369994i) q^{61} +(-5.17330 - 6.56436i) q^{62} -1.83038 q^{63} +(5.20116 - 6.07848i) q^{64} +1.53875 q^{65} +(0.926911 + 1.17615i) q^{66} +(-4.92908 - 2.04169i) q^{67} +(6.43968 + 1.54811i) q^{68} +(1.67198 + 4.03652i) q^{69} +(0.524421 + 1.86055i) q^{70} +(0.553232 - 0.553232i) q^{71} +(4.85628 + 1.79411i) q^{72} +(-6.76325 - 6.76325i) q^{73} +(3.07709 - 5.49257i) q^{74} +(3.12907 - 1.29610i) q^{75} +(-5.30082 - 3.85375i) q^{76} +(0.374687 - 0.904574i) q^{77} +(1.70982 + 0.202636i) q^{78} +11.8884i q^{79} +(0.432307 - 5.45035i) q^{80} -0.158568i q^{81} +(1.72213 - 14.5312i) q^{82} +(-2.47245 + 5.96903i) q^{83} +(0.337711 + 2.13645i) q^{84} +(4.18192 - 1.73221i) q^{85} +(1.20489 + 0.675010i) q^{86} +(5.82679 + 5.82679i) q^{87} +(-1.88075 + 2.03271i) q^{88} +(-2.11160 + 2.11160i) q^{89} +(3.40551 - 0.959890i) q^{90} +(-0.430806 - 1.04006i) q^{91} +(-6.89043 + 4.21956i) q^{92} +(-5.90497 - 2.44592i) q^{93} +(-11.9195 + 9.39364i) q^{94} -4.47897 q^{95} +(1.19812 - 5.99936i) q^{96} -6.12164 q^{97} +(1.11074 - 0.875361i) q^{98} +(-1.65571 - 0.685819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 20 q^{6}+O(q^{10}) \) 52 * q - 20 * q^6	\( 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) \) 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more