LMFDB - Embedded newform 224.2.u.c.85.11

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			85.11
Character	$\chi$	$=$	224.85
Dual form			224.2.u.c.29.11

$q$-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 $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{8}\right)$

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	−0.0751212	−	0.997174i	$-0.523934\pi$
$3$	0.999166	−	0.413868i	0.576869	−	0.238947i	0.651990	+	0.758228i	$0.273934\pi$
$4$	−0.467486	−	1.94460i	−0.233743	−	0.972298i
$5$	0.523077	−	1.26282i	0.233927	−	0.564750i	−0.762705	−	0.646746i	$-0.776129\pi$
$5$	0.523077	−	1.26282i	0.233927	−	0.564750i	0.996633	+	0.0819958i	$0.0261294\pi$
$6$	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	0.514861	−	0.857274i	$-0.327843\pi$
$11$	0.904574	+	0.374687i	0.272739	+	0.112972i	−0.242122	+	0.970246i	$0.577843\pi$
$12$	−1.27190	−	1.74950i	−0.367167	−	0.505037i
$13$	0.430806	+	1.04006i	0.119484	+	0.288460i	0.972294	−	0.233761i	$-0.0751034\pi$
$13$	0.430806	+	1.04006i	0.119484	+	0.288460i	−0.852810	+	0.522222i	$0.825103\pi$
$14$	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	$0.131541\pi$
$17$			3.31157i			0.803175i	−0.915821	+	0.401587i	$0.868459\pi$
$18$	0.304644	+	2.57056i	0.0718054	+	0.605887i
$19$	−1.25398	−	3.02738i	−0.287684	−	0.694530i	0.712289	−	0.701886i	$-0.247658\pi$
$19$	−1.25398	−	3.02738i	−0.287684	−	0.694530i	−0.999973	+	0.00735628i	$0.997658\pi$
$20$	−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	−0.343503	−	0.939152i	$-0.611614\pi$
$23$	2.85663	−	2.85663i	0.595649	−	0.595649i	0.939152	+	0.343503i	$0.111614\pi$
$24$	−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	0.383126	−	0.923696i	$-0.374848\pi$
$29$	7.03942	−	2.91582i	1.30719	−	0.541455i	0.924063	+	0.382241i	$0.124848\pi$
$30$	−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	−0.999837	−	0.0180612i	$-0.994251\pi$
$37$	−1.70363	+	4.11292i	−0.280074	+	0.676159i	0.719763	+	0.694220i	$0.244251\pi$
$38$	−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	−0.154670	+	0.987966i	$0.549432\pi$
$41$	−7.31644	+	7.31644i	−1.14264	+	1.14264i	−0.987966	+	0.154670i	$0.950568\pi$
$42$	1.33433	−	0.747529i	0.205892	−	0.115346i
$43$	0.902235	+	0.373718i	0.137590	+	0.0569915i	0.450416	−	0.892819i	$-0.351276\pi$
$43$	0.902235	+	0.373718i	0.137590	+	0.0569915i	−0.312826	+	0.949810i	$0.601276\pi$
$44$	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	$-0.713867\pi$
$47$		−	10.7312i		−	1.56530i	0.622462	−	0.782650i	$-0.286133\pi$
$48$	−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	0.715608	−	0.698502i	$-0.246150\pi$
$53$	5.29777	+	2.19441i	0.727704	+	0.301425i	0.0120961	+	0.999927i	$0.496150\pi$
$54$	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	−0.956288	−	0.292426i	$-0.905538\pi$
$59$	−0.563137	+	1.35953i	−0.0733142	+	0.176996i	0.882974	+	0.469422i	$0.155538\pi$
$60$	−2.87460	+	0.691061i	−0.371110	+	0.0892156i
$61$	−0.0893244	+	0.0369994i	−0.0114368	+	0.00473729i	−0.388395	−	0.921493i	$-0.626970\pi$
$61$	−0.0893244	+	0.0369994i	−0.0114368	+	0.00473729i	0.376958	+	0.926230i	$0.376970\pi$
$62$	−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	−0.662882	−	0.748724i	$-0.730667\pi$
$67$	−4.92908	+	2.04169i	−0.602184	+	0.249433i	0.0606989	+	0.998156i	$0.480667\pi$
$68$	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	0.739173	−	0.673516i	$-0.235217\pi$
$71$	0.553232	+	0.553232i	0.0656565	+	0.0656565i	−0.673516	+	0.739173i	$0.735217\pi$
$72$	4.85628	−	1.79411i	0.572319	−	0.211438i
$73$	−6.76325	+	6.76325i	−0.791579	+	0.791579i	−0.981751	−	0.190172i	$-0.939095\pi$
$73$	−6.76325	+	6.76325i	−0.791579	+	0.791579i	0.190172	+	0.981751i	$0.439095\pi$
$74$	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	$-0.766820\pi$
$79$		−	11.8884i		−	1.33755i	0.743466	−	0.668773i	$-0.233180\pi$
$80$	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	0.728156	−	0.685411i	$-0.240378\pi$
$83$	−2.47245	−	5.96903i	−0.271387	−	0.655187i	−0.999543	+	0.0302249i	$0.990378\pi$
$84$	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	0.586280	−	0.810109i	$-0.300592\pi$
$89$	−2.11160	−	2.11160i	−0.223829	−	0.223829i	−0.810109	+	0.586280i	$0.800592\pi$
$90$	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	−0.998268	−	0.0588340i	$-0.981262\pi$
$101$	−2.52035	+	6.08466i	−0.250784	+	0.605446i	0.747484	+	0.664280i	$0.231262\pi$
$102$	4.87496	+	1.37408i	0.482693	+	0.136054i
$103$	−8.52867	−	8.52867i	−0.840355	−	0.840355i	0.148550	−	0.988905i	$-0.452539\pi$
$103$	−8.52867	−	8.52867i	−0.840355	−	0.840355i	−0.988905	+	0.148550i	$0.952539\pi$
$104$	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	0.843585	−	0.536995i	$-0.180441\pi$
$107$	10.9686	+	4.54336i	1.06038	+	0.439223i	0.216792	+	0.976218i	$0.430441\pi$
$108$	10.3199	+	1.63127i	0.993031	+	0.156969i
$109$	−4.93652	−	11.9178i	−0.472833	−	1.14152i	−0.962906	−	0.269837i	$-0.913030\pi$
$109$	−4.93652	−	11.9178i	−0.472833	−	1.14152i	0.490073	−	0.871681i	$-0.336970\pi$
$110$	−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	$-0.731273\pi$
$113$		−	15.8912i		−	1.49492i	0.664305	−	0.747461i	$-0.268727\pi$
$114$	−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	0.455646	−	0.890161i	$-0.349408\pi$
$131$	16.1070	−	6.67174i	1.40728	−	0.582913i	0.951629	+	0.307248i	$0.0994082\pi$
$132$	−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	−0.991497	−	0.130126i	$-0.958462\pi$
$137$	−10.0821	+	10.0821i	−0.861372	+	0.861372i	0.130126	+	0.991497i	$0.458462\pi$
$138$	−3.01993	−	5.39055i	−0.257074	−	0.458874i
$139$	−10.0075	−	4.14525i	−0.848826	−	0.351595i	−0.0844986	−	0.996424i	$-0.526929\pi$
$139$	−10.0075	−	4.14525i	−0.848826	−	0.351595i	−0.764327	+	0.644828i	$0.776929\pi$
$140$	−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	0.964697	−	0.263364i	$-0.0848320\pi$
$149$	17.8291	+	7.38504i	1.46061	+	0.605006i	0.495917	+	0.868370i	$0.334832\pi$
$150$	4.17869	−	2.34102i	0.341189	−	0.191144i
$151$	−6.37361	+	6.37361i	−0.518677	+	0.518677i	−0.917171	−	0.398494i	$-0.869533\pi$
$151$	−6.37361	+	6.37361i	−0.518677	+	0.518677i	0.398494	+	0.917171i	$0.369533\pi$
$152$	−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	−0.412474	−	0.910969i	$-0.635335\pi$
$157$	−0.751603	+	0.311324i	−0.0599844	+	0.0248464i	0.352490	+	0.935816i	$0.385335\pi$
$158$	−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	−0.341515	−	0.939876i	$-0.610940\pi$
$163$	1.04167	−	0.431475i	0.0815901	−	0.0337957i	0.423105	+	0.906081i	$0.360940\pi$
$164$	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	0.937118	−	0.349011i	$-0.113483\pi$
$167$	7.60002	+	7.60002i	0.588107	+	0.588107i	−0.349011	+	0.937118i	$0.613483\pi$
$168$	−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	−0.828003	−	0.560723i	$-0.810523\pi$
$173$	−8.40483	−	20.2911i	−0.639008	−	1.54270i	0.188996	−	0.981978i	$-0.439477\pi$
$174$	−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	0.880332	+	0.474358i	$0.157320\pi$
$179$	7.93735	+	19.1624i	0.593265	+	1.43227i	−0.287067	+	0.957911i	$0.592680\pi$
$180$	4.04723	−	2.94238i	0.301663	−	0.219312i
$181$	−0.349364	−	0.144711i	−0.0259680	−	0.0107563i	0.369662	−	0.929166i	$-0.379474\pi$
$181$	−0.349364	−	0.144711i	−0.0259680	−	0.0107563i	−0.395630	+	0.918410i	$0.629474\pi$
$182$	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	−0.940554	−	0.339644i	$-0.889693\pi$
$197$	−0.495698	+	1.19672i	−0.0353171	+	0.0852629i	0.905237	+	0.424907i	$0.139693\pi$
$198$	−0.687581	+	2.43941i	−0.0488642	+	0.173361i
$199$	10.1613	+	10.1613i	0.720317	+	0.720317i	0.968670	−	0.248353i	$-0.0798893\pi$
$199$	10.1613	+	10.1613i	0.720317	+	0.720317i	−0.248353	+	0.968670i	$0.579889\pi$
$200$	−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	0.991263	−	0.131897i	$-0.0421069\pi$
$211$	2.86259	+	6.91091i	0.197069	+	0.475766i	−0.794195	+	0.607664i	$0.792107\pi$
$212$	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	0.206388	−	0.978470i	$-0.433829\pi$
$227$	15.7326	−	6.51665i	1.04421	−	0.432525i	0.837821	+	0.545945i	$0.183829\pi$
$228$	−3.70146	+	6.04438i	−0.245135	+	0.400299i
$229$	−7.45055	+	17.9872i	−0.492346	+	1.18863i	0.461177	+	0.887308i	$0.347427\pi$
$229$	−7.45055	+	17.9872i	−0.492346	+	1.18863i	−0.953523	+	0.301321i	$0.902573\pi$
$230$	−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	−0.805848	−	0.592122i	$-0.798290\pi$
$233$	−3.26240	+	3.26240i	−0.213727	+	0.213727i	0.592122	+	0.805848i	$0.298290\pi$
$234$	−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	$0.0292138\pi$
$239$			2.83372i			0.183298i	−0.995791	+	0.0916491i	$0.970786\pi$
$240$	2.68767	+	5.26688i	0.173488	+	0.339976i
$241$			22.5209i			1.45070i	0.688380	+	0.725350i	$0.258322\pi$
$241$			22.5209i			1.45070i	−0.688380	+	0.725350i	$0.741678\pi$
$242$	−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	0.382025	+	0.924152i	$0.375227\pi$
$251$	−8.58026	+	20.7146i	−0.541581	+	1.30749i	−0.923607	+	0.383341i	$0.874773\pi$
$252$	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	0.998150	−	0.0608073i	$-0.0193675\pi$
$263$	15.2011	+	15.2011i	0.937342	+	0.937342i	−0.0608073	+	0.998150i	$0.519367\pi$
$264$	−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	0.783999	−	0.620762i	$-0.213177\pi$
$269$	−3.43306	−	8.28813i	−0.209317	−	0.505337i	−0.993316	+	0.115426i	$0.963177\pi$
$270$	10.0280	−	1.18845i	0.610287	−	0.0723269i
$271$			16.2410i			0.986571i	0.869867	+	0.493285i	$0.164204\pi$
$271$			16.2410i			0.986571i	−0.869867	+	0.493285i	$0.835796\pi$
$272$	−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	0.614748	−	0.788724i	$-0.289258\pi$
$277$	8.18398	+	3.38992i	0.491728	+	0.203680i	−0.123020	+	0.992404i	$0.539258\pi$
$278$	−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	0.931678	−	0.363286i	$-0.118345\pi$
$281$	9.52799	+	9.52799i	0.568392	+	0.568392i	−0.363286	+	0.931678i	$0.618345\pi$
$282$	−15.7973	−	4.45269i	−0.940716	−	0.265154i
$283$	9.29050	−	22.4293i	0.552263	−	1.33328i	−0.363512	−	0.931589i	$-0.618422\pi$
$283$	9.29050	−	22.4293i	0.552263	−	1.33328i	0.915775	−	0.401691i	$-0.131578\pi$
$284$	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	−0.450782	−	0.892634i	$-0.648855\pi$
$293$	8.54419	−	20.6275i	0.499157	−	1.20507i	0.949939	−	0.312437i	$-0.101145\pi$
$294$	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	−0.679679	−	0.733510i	$-0.737881\pi$
$307$	−12.5759	−	30.3608i	−0.717743	−	1.73278i	−0.0380638	−	0.999275i	$-0.512119\pi$
$308$	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	−0.381197	−	0.924494i	$-0.624488\pi$
$311$	9.58114	−	9.58114i	0.543297	−	0.543297i	0.924494	+	0.381197i	$0.124488\pi$
$312$	−1.19336	−	3.23019i	−0.0675609	−	0.182873i
$313$	9.48170	+	9.48170i	0.535937	+	0.535937i	0.922333	−	0.386396i	$-0.126280\pi$
$313$	9.48170	+	9.48170i	0.535937	+	0.535937i	−0.386396	+	0.922333i	$0.626280\pi$
$314$	−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	−0.962054	−	0.272860i	$-0.912030\pi$
$317$	−25.8056	+	10.6890i	−1.44939	+	0.600356i	−0.487333	+	0.873216i	$0.662030\pi$
$318$	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	0.0415418	−	0.999137i	$-0.486773\pi$
$331$	−11.5634	−	4.78970i	−0.635580	−	0.263266i	−0.677122	+	0.735871i	$0.736773\pi$
$332$	−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	$-0.820822\pi$
$337$		−	19.5928i		−	1.06729i	0.845709	−	0.533645i	$-0.179178\pi$
$338$	−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	−0.130097	−	0.991501i	$-0.541529\pi$
$347$	12.3502	−	29.8160i	0.662993	−	1.60061i	0.793090	−	0.609105i	$-0.208471\pi$
$348$	−14.0547	−	8.60681i	−0.753411	−	0.461374i
$349$	23.5509	−	9.75512i	1.26065	−	0.522179i	0.350543	−	0.936547i	$-0.385997\pi$
$349$	23.5509	−	9.75512i	1.26065	−	0.522179i	0.910110	+	0.414367i	$0.135997\pi$
$350$	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	0.222815	−	0.974861i	$-0.428476\pi$
$359$	−14.2492	−	14.2492i	−0.752046	−	0.752046i	−0.974861	+	0.222815i	$0.928476\pi$
$360$	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	$-0.821637\pi$
$367$		−	20.3633i		−	1.06296i	0.847072	−	0.531478i	$-0.178363\pi$
$368$	−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	0.109151	−	0.994025i	$-0.465187\pi$
$373$	−9.97623	−	4.13229i	−0.516550	−	0.213962i	−0.625701	+	0.780063i	$0.715187\pi$
$374$	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	0.552349	+	0.833613i	$0.313731\pi$
$379$	−8.32592	+	20.1006i	−0.427674	+	1.03250i	−0.980023	+	0.198883i	$0.936269\pi$
$380$	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	−0.418045	−	0.908426i	$-0.637285\pi$
$389$	10.2543	−	24.7560i	0.519912	−	1.25518i	0.937957	−	0.346751i	$-0.112715\pi$
$390$	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	0.909266	+	0.416215i	$0.136644\pi$
$397$	11.1704	+	26.9677i	0.560627	+	1.35347i	−0.348639	+	0.937257i	$0.613356\pi$
$398$	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	$0.00267305\pi$
$401$			0.336321i			0.0167951i	−0.999965	+	0.00839753i	$0.997327\pi$
$402$	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	0.622568	−	0.782566i	$-0.286089\pi$
$409$	−3.23576	−	3.23576i	−0.159998	−	0.159998i	−0.782566	+	0.622568i	$0.786089\pi$
$410$	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	−0.756851	−	0.653588i	$-0.773263\pi$
$419$	−16.9870	+	7.03624i	−0.829869	+	0.343743i	−0.0730182	+	0.997331i	$0.523263\pi$
$420$	−2.52131	−	1.54400i	−0.123027	−	0.0753394i
$421$	−15.0999	+	36.4544i	−0.735924	+	1.77668i	−0.114173	+	0.993461i	$0.536422\pi$
$421$	−15.0999	+	36.4544i	−0.735924	+	1.77668i	−0.621750	+	0.783216i	$0.713578\pi$
$422$	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	$0.102567\pi$
$431$			13.1488i			0.633354i	−0.948533	+	0.316677i	$0.897433\pi$
$432$	−1.65223	−	20.8306i	−0.0794928	−	1.00221i
$433$			40.2052i			1.93214i	0.258282	+	0.966069i	$0.416844\pi$
$433$			40.2052i			1.93214i	−0.258282	+	0.966069i	$0.583156\pi$
$434$	−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	−0.383068	+	0.923720i	$0.625133\pi$
$439$	−27.3803	+	27.3803i	−1.30679	+	1.30679i	−0.923720	+	0.383068i	$0.874867\pi$
$440$	−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	−0.161581	−	0.986859i	$-0.551659\pi$
$443$	13.6912	−	33.0535i	0.650489	−	1.57042i	0.812070	−	0.583560i	$-0.198341\pi$
$444$	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	−0.290159	−	0.956978i	$-0.593708\pi$
$457$	14.2550	−	14.2550i	0.666819	−	0.666819i	0.956978	+	0.290159i	$0.0937082\pi$
$458$	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	0.741535	−	0.670914i	$-0.234098\pi$
$461$	−5.52269	−	13.3330i	−0.257217	−	0.620978i	−0.998752	+	0.0499365i	$0.984098\pi$
$462$	1.48709	−	0.176239i	0.0691857	−	0.00819940i
$463$			2.24545i			0.104355i	0.998638	+	0.0521775i	$0.0166162\pi$
$463$			2.24545i			0.104355i	−0.998638	+	0.0521775i	$0.983384\pi$
$464$	−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	0.751637	−	0.659577i	$-0.229264\pi$
$467$	−5.32133	−	12.8468i	−0.246242	−	0.594480i	−0.997879	+	0.0650968i	$0.979264\pi$
$468$	−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	0.647869	−	0.761752i	$-0.275660\pi$
$487$	−2.51318	−	2.51318i	−0.113883	−	0.113883i	−0.761752	+	0.647869i	$0.775660\pi$
$488$	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	0.895794	−	0.444470i	$-0.146608\pi$
$491$	26.9210	+	11.1510i	1.21493	+	0.503239i	0.319134	+	0.947710i	$0.396608\pi$
$492$	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	0.999801	−	0.0199245i	$-0.00634260\pi$
$499$	6.22672	+	15.0326i	0.278746	+	0.672953i	−0.721055	+	0.692878i	$0.756343\pi$
$500$	−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	−0.865291	−	0.501271i	$-0.832866\pi$
$503$	−8.16412	+	8.16412i	−0.364020	+	0.364020i	0.501271	+	0.865291i	$0.332866\pi$
$504$	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	−0.0514074	−	0.998678i	$-0.516371\pi$
$509$	13.9521	−	5.77913i	0.618414	−	0.256155i	0.669821	+	0.742522i	$0.266371\pi$
$510$	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	−0.715427	−	0.698687i	$-0.753768\pi$
$521$	−0.382095	+	0.382095i	−0.0167399	+	0.0167399i	0.698687	+	0.715427i	$0.253768\pi$
$522$	9.63982	+	17.2070i	0.421924	+	0.753128i
$523$	0.581817	+	0.240997i	0.0254411	+	0.0105380i	0.395368	−	0.918523i	$-0.370617\pi$
$523$	0.581817	+	0.240997i	0.0254411	+	0.0105380i	−0.369927	+	0.929061i	$0.620617\pi$
$524$	−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	−0.577824	−	0.816162i	$-0.696098\pi$
$541$	−9.51992	+	3.94328i	−0.409293	+	0.169535i	0.168530	+	0.985696i	$0.446098\pi$
$542$	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	−0.229186	−	0.973383i	$-0.573606\pi$
$547$	6.94719	−	2.87762i	0.297040	−	0.123038i	0.526226	+	0.850344i	$0.323606\pi$
$548$	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	0.797321	−	0.603555i	$-0.206250\pi$
$557$	−4.56082	−	11.0108i	−0.193248	−	0.466542i	−0.990569	+	0.137013i	$0.956250\pi$
$558$	−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	0.956907	−	0.290396i	$-0.0937870\pi$
$563$	1.77792	+	4.29228i	0.0749304	+	0.180898i	−0.881976	+	0.471294i	$0.843787\pi$
$564$	−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	0.269758	−	0.962928i	$-0.413056\pi$
$569$	−16.5347	−	16.5347i	−0.693170	−	0.693170i	−0.962928	+	0.269758i	$0.913056\pi$
$570$	−1.85847	+	6.59348i	−0.0778426	+	0.276171i
$571$	14.8785	−	35.9199i	0.622646	−	1.50320i	−0.225939	−	0.974141i	$-0.572545\pi$
$571$	14.8785	−	35.9199i	0.622646	−	1.50320i	0.848585	−	0.529059i	$-0.177455\pi$
$572$	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	0.595077	−	0.803669i	$-0.297122\pi$
$587$	10.8440	+	4.49173i	0.447579	+	0.185393i	−0.147497	+	0.989062i	$0.547122\pi$
$588$	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	$-0.832063\pi$
$593$		−	24.5197i		−	1.00690i	0.864024	−	0.503451i	$-0.167937\pi$
$594$	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	−0.874090	−	0.485764i	$-0.838541\pi$
$599$	−9.50408	+	9.50408i	−0.388326	+	0.388326i	0.485764	+	0.874090i	$0.338541\pi$
$600$	−6.50582	−	7.03148i	−0.265599	−	0.287059i
$601$	22.7018	+	22.7018i	0.926024	+	0.926024i	0.997446	−	0.0714221i	$-0.0227537\pi$
$601$	22.7018	+	22.7018i	0.926024	+	0.926024i	−0.0714221	+	0.997446i	$0.522754\pi$
$602$	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	−0.765885	−	0.642977i	$-0.777699\pi$
$613$	5.70272	−	13.7676i	0.230331	−	0.556068i	0.996216	+	0.0869094i	$0.0276991\pi$
$614$	−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	−0.954841	−	0.297118i	$-0.903975\pi$
$617$	−16.3375	+	16.3375i	−0.657723	+	0.657723i	0.297118	+	0.954841i	$0.403975\pi$
$618$	−16.0938	+	9.01622i	−0.647389	+	0.362686i
$619$	−0.207481	−	0.0859413i	−0.00833935	−	0.00345427i	0.378510	−	0.925597i	$-0.376437\pi$
$619$	−0.207481	−	0.0859413i	−0.00833935	−	0.00345427i	−0.386849	+	0.922143i	$0.626437\pi$
$620$	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	−0.963092	−	0.269173i	$-0.913250\pi$
$631$	−17.4310	+	17.4310i	−0.693919	+	0.693919i	0.269173	+	0.963092i	$0.413250\pi$
$632$	−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	−0.856435	−	0.516255i	$-0.827326\pi$
$643$	−27.8166	+	11.5220i	−1.09698	+	0.454383i	−0.240543	+	0.970638i	$0.577326\pi$
$644$	−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	0.356281	−	0.934379i	$-0.384045\pi$
$647$	−14.7046	−	14.7046i	−0.578098	−	0.578098i	−0.934379	+	0.356281i	$0.884045\pi$
$648$	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	0.950410	−	0.310999i	$-0.100664\pi$
$653$	1.49385	+	3.60648i	0.0584590	+	0.141133i	−0.891951	+	0.452132i	$0.850664\pi$
$654$	−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	0.978229	−	0.207527i	$-0.0665414\pi$
$659$	3.58812	+	8.66248i	0.139773	+	0.337442i	−0.838456	+	0.544969i	$0.816541\pi$
$660$	−2.85922	−	0.451960i	−0.111295	−	0.0175925i
$661$	4.73950	+	1.96317i	0.184345	+	0.0763583i	0.472947	−	0.881091i	$-0.343190\pi$
$661$	4.73950	+	1.96317i	0.184345	+	0.0763583i	−0.288602	+	0.957449i	$0.593190\pi$
$662$	−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	0.303799	+	0.952736i	$0.401745\pi$
$677$	−15.2136	+	36.7288i	−0.584706	+	1.41160i	−0.888504	+	0.458868i	$0.848255\pi$
$678$	−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	0.496754	−	0.867891i	$-0.334525\pi$
$683$	6.12378	+	2.53655i	0.234320	+	0.0970585i	−0.262434	+	0.964950i	$0.584525\pi$
$684$	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	0.889716	+	0.456515i	$0.150903\pi$
$691$	15.3357	+	37.0236i	0.583397	+	1.40844i	−0.306319	+	0.951929i	$0.599097\pi$
$692$	−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	0.303447	−	0.952848i	$-0.401862\pi$
$701$	31.5541	−	13.0701i	1.19178	−	0.493652i	0.888335	+	0.459196i	$0.151862\pi$
$702$	−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	−0.277907	−	0.960608i	$-0.589641\pi$
$709$	15.9191	−	38.4322i	0.597856	−	1.44335i	0.875762	−	0.482743i	$-0.160359\pi$
$710$	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	$-0.989973\pi$
$719$		−	1.68899i		−	0.0629887i	0.999504	−	0.0314943i	$-0.0100266\pi$
$720$	−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	−0.515029	−	0.857173i	$-0.672219\pi$
$727$	9.22518	−	9.22518i	0.342143	−	0.342143i	0.857173	+	0.515029i	$0.172219\pi$
$728$	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	0.662601	−	0.748973i	$-0.269453\pi$
$733$	44.9627	−	18.6241i	1.66073	−	0.687898i	0.998133	+	0.0610744i	$0.0194527\pi$
$734$	−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	−0.938081	−	0.346415i	$-0.887399\pi$
$739$	−36.8745	+	15.2739i	−1.35645	+	0.561861i	−0.418371	+	0.908276i	$0.637399\pi$
$740$	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	0.324063	−	0.946035i	$-0.394951\pi$
$743$	−16.9537	−	16.9537i	−0.621972	−	0.621972i	−0.946035	+	0.324063i	$0.894951\pi$
$744$	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	$-0.974037\pi$
$751$		−	4.46547i		−	0.162947i	0.996675	−	0.0814737i	$-0.0259626\pi$
$752$	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	−0.308040	−	0.951373i	$-0.599673\pi$
$757$	−32.9773	−	13.6596i	−1.19858	−	0.496468i	−0.890540	+	0.454905i	$0.849673\pi$
$758$	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	0.982732	+	0.185034i	$0.0592395\pi$
$761$	32.2143	+	32.2143i	1.16777	+	1.16777i	0.185034	+	0.982732i	$0.440761\pi$
$762$	−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	−0.0234209	−	0.999726i	$-0.507456\pi$
$773$	19.4635	−	46.9890i	0.700053	−	1.69008i	0.723474	−	0.690352i	$-0.242544\pi$
$774$	−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	0.776136	+	0.630565i	$0.217177\pi$
$787$	18.8857	+	45.5941i	0.673202	+	1.62525i	−0.102934	+	0.994688i	$0.532823\pi$
$788$	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	−0.277442	−	0.960743i	$-0.589486\pi$
$797$	5.80787	−	2.40570i	0.205725	−	0.0852142i	0.483167	+	0.875528i	$0.339486\pi$
$798$	−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	−0.852986	−	0.521934i	$-0.825211\pi$
$809$	−9.41608	+	9.41608i	−0.331052	+	0.331052i	0.521934	+	0.852986i	$0.325211\pi$
$810$	0.267413	−	0.149812i	0.00939595	−	0.00526387i
$811$	−45.3813	−	18.7976i	−1.59355	−	0.660072i	−0.603068	−	0.797690i	$-0.706055\pi$
$811$	−45.3813	−	18.7976i	−1.59355	−	0.660072i	−0.990485	+	0.137618i	$0.956055\pi$
$812$	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	−0.227678	−	0.973736i	$-0.573113\pi$
$821$	−30.8653	−	12.7848i	−1.07721	−	0.446194i	−0.849528	+	0.527543i	$0.823113\pi$
$822$	10.6585	+	19.0252i	0.371756	+	0.663580i
$823$	0.854721	−	0.854721i	0.0297937	−	0.0297937i	−0.692053	−	0.721847i	$-0.743294\pi$
$823$	0.854721	−	0.854721i	0.0297937	−	0.0297937i	0.721847	+	0.692053i	$0.243294\pi$
$824$	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	−0.999931	−	0.0117158i	$-0.996271\pi$
$827$	−8.18409	+	19.7581i	−0.284589	+	0.687058i	0.715343	+	0.698774i	$0.246271\pi$
$828$	14.3794	−	3.45684i	0.499718	−	0.120133i
$829$	22.1565	−	9.17751i	0.769526	−	0.318748i	0.0368457	−	0.999321i	$-0.488269\pi$
$829$	22.1565	−	9.17751i	0.769526	−	0.318748i	0.732680	+	0.680573i	$0.238269\pi$
$830$	−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	0.827803	−	0.561018i	$-0.189590\pi$
$839$	7.72755	+	7.72755i	0.266785	+	0.266785i	−0.561018	+	0.827803i	$0.689590\pi$
$840$	−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	0.135964	−	0.990714i	$-0.456587\pi$
$853$	−13.6812	−	5.66694i	−0.468436	−	0.194032i	−0.604400	+	0.796681i	$0.706587\pi$
$854$	−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	0.0532590	−	0.998581i	$-0.483039\pi$
$857$	−27.6739	−	27.6739i	−0.945322	−	0.945322i	−0.998581	+	0.0532590i	$0.983039\pi$
$858$	1.62259	+	0.457348i	0.0553941	+	0.0156136i
$859$	−13.1026	+	31.6326i	−0.447056	+	1.07929i	0.526363	+	0.850260i	$0.323555\pi$
$859$	−13.1026	+	31.6326i	−0.447056	+	1.07929i	−0.973419	+	0.229030i	$0.926445\pi$
$860$	−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	0.947131	−	0.320847i	$-0.103968\pi$
$877$	1.49656	+	3.61301i	0.0505352	+	0.122003i	−0.896596	+	0.442850i	$0.853968\pi$
$878$	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	$0.290203\pi$
$881$			46.9294i			1.58109i	−0.612403	+	0.790546i	$0.709797\pi$
$882$	−2.57056	+	0.304644i	−0.0865552	+	0.0102579i
$883$	9.05346	+	21.8570i	0.304673	+	0.735546i	0.999860	+	0.0167174i	$0.00532155\pi$
$883$	9.05346	+	21.8570i	0.304673	+	0.735546i	−0.695187	+	0.718829i	$0.744678\pi$
$884$	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	−0.764211	−	0.644967i	$-0.776871\pi$
$887$	−3.55140	+	3.55140i	−0.119244	+	0.119244i	0.644967	+	0.764211i	$0.276871\pi$
$888$	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	0.129942	−	0.991522i	$-0.458521\pi$
$907$	−14.4344	−	5.97893i	−0.479287	−	0.198527i	−0.609229	+	0.792994i	$0.708521\pi$
$908$	−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	$-0.970146\pi$
$911$		−	5.65334i		−	0.187303i	0.995605	−	0.0936517i	$-0.0298540\pi$
$912$	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	−0.650021	−	0.759916i	$-0.725240\pi$
$919$	3.33146	−	3.33146i	0.109895	−	0.109895i	0.759916	+	0.650021i	$0.225240\pi$
$920$	−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	−0.951131	−	0.308787i	$-0.900077\pi$
$937$	−19.6625	+	19.6625i	−0.642345	+	0.642345i	0.308787	+	0.951131i	$0.400077\pi$
$938$	−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	0.708293	−	0.705919i	$-0.249466\pi$
$941$	−8.94829	−	21.6031i	−0.291706	−	0.704240i	−0.999999	+	0.00167870i	$0.999466\pi$
$942$	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	0.868432	−	0.495808i	$-0.165128\pi$
$947$	−2.96135	−	7.14933i	−0.0962309	−	0.232322i	−0.964663	+	0.263486i	$0.915128\pi$
$948$	−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	0.973431	−	0.228983i	$-0.0735399\pi$
$953$	22.9816	+	22.9816i	0.744448	+	0.744448i	−0.228983	+	0.973431i	$0.573540\pi$
$954$	−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	−0.970400	−	0.241503i	$-0.922360\pi$
$967$	−37.6861	−	37.6861i	−1.21190	−	1.21190i	−0.241503	−	0.970400i	$-0.577640\pi$
$968$	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	0.460986	−	0.887408i	$-0.347496\pi$
$971$	4.96890	+	2.05819i	0.159460	+	0.0660504i	−0.301526	+	0.953458i	$0.597496\pi$
$972$	−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	$0.148916\pi$
$977$			28.1908i			0.901905i	−0.892548	+	0.450952i	$0.851084\pi$
$978$	−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	−0.955422	−	0.295243i	$-0.904599\pi$
$983$	−20.6985	+	20.6985i	−0.660179	+	0.660179i	0.295243	+	0.955422i	$0.404599\pi$
$984$	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	−0.647562	−	0.762013i	$-0.724211\pi$
$997$	11.0248	−	26.6162i	0.349158	−	0.842942i	0.996720	−	0.0809291i	$-0.0257887\pi$
$998$	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.85.11	yes	52
4.3	odd	2		896.2.u.c.561.5		52
32.3	odd	8		896.2.u.c.337.5		52
32.29	even	8	inner	224.2.u.c.29.11	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.29.11	✓	52	32.29	even	8	inner
224.2.u.c.85.11	yes	52	1.1	even	1	trivial
896.2.u.c.337.5		52	32.3	odd	8
896.2.u.c.561.5		52	4.3	odd	2

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