LMFDB - Embedded newform 164.2.o.b.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [164,2,Mod(7,164)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(164, base_ring=CyclotomicField(40))

chi = DirichletCharacter(H, H._module([20, 39]))

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

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

chi := DirichletCharacter("164.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 164 = 2^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	164.o (of order $40$, degree $16$, 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:	$1.30954659315$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	164.11
Dual form			164.2.o.b.15.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26038 - 0.641434i) q^{2} +(-1.13045 + 2.72914i) q^{3} +(1.17712 + 1.61690i) q^{4} +(-0.430197 + 0.844309i) q^{5} +(3.17535 - 2.71465i) q^{6} +(-0.0257188 - 0.107126i) q^{7} +(-0.446489 - 2.79296i) q^{8} +(-4.04896 - 4.04896i) q^{9} +O(q^{10})$	\(q+(-1.26038 - 0.641434i) q^{2} +(-1.13045 + 2.72914i) q^{3} +(1.17712 + 1.61690i) q^{4} +(-0.430197 + 0.844309i) q^{5} +(3.17535 - 2.71465i) q^{6} +(-0.0257188 - 0.107126i) q^{7} +(-0.446489 - 2.79296i) q^{8} +(-4.04896 - 4.04896i) q^{9} +(1.08378 - 0.788209i) q^{10} +(-3.23203 + 3.78422i) q^{11} +(-5.74343 + 1.38471i) q^{12} +(-2.01034 - 3.28058i) q^{13} +(-0.0362991 + 0.151517i) q^{14} +(-1.81792 - 2.12851i) q^{15} +(-1.22876 + 3.80659i) q^{16} +(0.108842 + 1.38297i) q^{17} +(2.50610 + 7.70038i) q^{18} +(3.34801 + 2.05166i) q^{19} +(-1.87156 + 0.298270i) q^{20} +(0.321437 + 0.0509106i) q^{21} +(6.50093 - 2.69643i) q^{22} +(-6.86039 - 4.98437i) q^{23} +(8.12711 + 1.93876i) q^{24} +(2.41114 + 3.31865i) q^{25} +(0.429523 + 5.42429i) q^{26} +(7.43989 - 3.08170i) q^{27} +(0.142939 - 0.167686i) q^{28} +(-0.498000 + 6.32769i) q^{29} +(0.925974 + 3.84881i) q^{30} +(0.564960 - 1.73877i) q^{31} +(3.99038 - 4.00960i) q^{32} +(-6.67403 - 13.0985i) q^{33} +(0.749902 - 1.81289i) q^{34} +(0.101512 + 0.0243709i) q^{35} +(1.78065 - 11.3129i) q^{36} +(0.756379 + 2.32790i) q^{37} +(-2.90376 - 4.73340i) q^{38} +(11.2257 - 1.77798i) q^{39} +(2.55020 + 0.824550i) q^{40} +(-0.811348 + 6.35151i) q^{41} +(-0.372477 - 0.270347i) q^{42} +(0.666293 + 4.20681i) q^{43} +(-9.92323 - 0.771383i) q^{44} +(5.16043 - 1.67672i) q^{45} +(5.44957 + 10.6827i) q^{46} +(-0.398882 + 1.66146i) q^{47} +(-8.99968 - 7.65659i) q^{48} +(6.22623 - 3.17242i) q^{49} +(-0.910261 - 5.72935i) q^{50} +(-3.89736 - 1.26633i) q^{51} +(2.93796 - 7.11218i) q^{52} +(9.27788 + 0.730185i) q^{53} +(-11.3538 - 0.888077i) q^{54} +(-1.80464 - 4.35680i) q^{55} +(-0.287717 + 0.119662i) q^{56} +(-9.38400 + 6.81788i) q^{57} +(4.68646 - 7.65587i) q^{58} +(4.07424 - 5.60771i) q^{59} +(1.30168 - 5.44493i) q^{60} +(-1.41047 + 8.90534i) q^{61} +(-1.82737 + 1.82913i) q^{62} +(-0.329617 + 0.537885i) q^{63} +(-7.60130 + 2.49406i) q^{64} +(3.63467 - 0.286055i) q^{65} +(0.00998733 + 20.7901i) q^{66} +(-10.1475 + 8.66675i) q^{67} +(-2.10801 + 1.80392i) q^{68} +(21.3583 - 13.0884i) q^{69} +(-0.112312 - 0.0958299i) q^{70} +(6.45694 + 5.51475i) q^{71} +(-9.50079 + 13.1164i) q^{72} +(-6.92317 + 6.92317i) q^{73} +(0.539865 - 3.41920i) q^{74} +(-11.7827 + 2.82878i) q^{75} +(0.623682 + 7.82846i) q^{76} +(0.488515 + 0.248911i) q^{77} +(-15.2892 - 4.95964i) q^{78} +(7.44955 + 3.08571i) q^{79} +(-2.68534 - 2.67503i) q^{80} +6.60990i q^{81} +(5.09668 - 7.48491i) q^{82} +3.71433i q^{83} +(0.296053 + 0.579660i) q^{84} +(-1.21448 - 0.503053i) q^{85} +(1.85861 - 5.72957i) q^{86} +(-16.7062 - 8.51221i) q^{87} +(12.0123 + 7.33734i) q^{88} +(-15.9169 + 3.82130i) q^{89} +(-7.57962 - 1.19676i) q^{90} +(-0.299734 + 0.299734i) q^{91} +(-0.0162946 - 16.9598i) q^{92} +(4.10668 + 3.50744i) q^{93} +(1.56846 - 1.83822i) q^{94} +(-3.17254 + 1.94413i) q^{95} +(6.43183 + 15.4229i) q^{96} +(5.75058 - 4.91146i) q^{97} +(-9.88233 + 0.00474736i) q^{98} +(28.4086 - 2.23580i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9}+O(q^{10}) $ 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9	$ 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9} - 12 q^{10} - 8 q^{12} - 24 q^{13} - 4 q^{14} - 28 q^{16} - 12 q^{18} - 44 q^{20} - 32 q^{21} - 40 q^{22} + 8 q^{24} - 40 q^{25} + 4 q^{26} - 48 q^{29} - 44 q^{30} + 108 q^{32} - 72 q^{33} + 12 q^{34} - 20 q^{36} - 24 q^{37} + 56 q^{38} + 8 q^{41} - 112 q^{42} - 40 q^{45} - 48 q^{46} - 68 q^{48} - 16 q^{49} - 60 q^{50} - 124 q^{52} - 64 q^{53} + 64 q^{54} - 84 q^{56} - 24 q^{57} + 40 q^{60} - 8 q^{61} - 44 q^{62} - 20 q^{64} + 64 q^{65} + 60 q^{66} - 28 q^{68} - 8 q^{69} + 128 q^{70} + 160 q^{72} - 32 q^{73} + 80 q^{74} + 288 q^{76} - 32 q^{77} + 116 q^{78} + 176 q^{80} + 212 q^{82} + 152 q^{84} - 56 q^{85} + 180 q^{86} + 144 q^{88} - 72 q^{89} + 224 q^{90} + 36 q^{92} - 8 q^{93} + 52 q^{94} + 136 q^{96} - 88 q^{97} + 104 q^{98}+O(q^{100}) $ 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9 - 12 * q^10 - 8 * q^12 - 24 * q^13 - 4 * q^14 - 28 * q^16 - 12 * q^18 - 44 * q^20 - 32 * q^21 - 40 * q^22 + 8 * q^24 - 40 * q^25 + 4 * q^26 - 48 * q^29 - 44 * q^30 + 108 * q^32 - 72 * q^33 + 12 * q^34 - 20 * q^36 - 24 * q^37 + 56 * q^38 + 8 * q^41 - 112 * q^42 - 40 * q^45 - 48 * q^46 - 68 * q^48 - 16 * q^49 - 60 * q^50 - 124 * q^52 - 64 * q^53 + 64 * q^54 - 84 * q^56 - 24 * q^57 + 40 * q^60 - 8 * q^61 - 44 * q^62 - 20 * q^64 + 64 * q^65 + 60 * q^66 - 28 * q^68 - 8 * q^69 + 128 * q^70 + 160 * q^72 - 32 * q^73 + 80 * q^74 + 288 * q^76 - 32 * q^77 + 116 * q^78 + 176 * q^80 + 212 * q^82 + 152 * q^84 - 56 * q^85 + 180 * q^86 + 144 * q^88 - 72 * q^89 + 224 * q^90 + 36 * q^92 - 8 * q^93 + 52 * q^94 + 136 * q^96 - 88 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/164\mathbb{Z}\right)^\times$.

$n$	$83$	$129$
$\chi(n)$	$-1$	$e\left(\frac{3}{40}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.26038	−	0.641434i	−0.891225	−	0.453562i
$2$	−1.26038	−	0.641434i	−0.891225	−	0.453562i
$3$	−1.13045	+	2.72914i	−0.652663	+	1.57567i	0.156235	+	0.987720i	$0.450064\pi$
$3$	−1.13045	+	2.72914i	−0.652663	+	1.57567i	−0.808899	+	0.587948i	$0.799936\pi$
$4$	1.17712	+	1.61690i	0.588562	+	0.808452i
$5$	−0.430197	+	0.844309i	−0.192390	+	0.377587i	−0.966970	−	0.254889i	$-0.917961\pi$
$5$	−0.430197	+	0.844309i	−0.192390	+	0.377587i	0.774580	+	0.632475i	$0.217961\pi$
$6$	3.17535	−	2.71465i	1.29633	−	1.10825i
$7$	−0.0257188	−	0.107126i	−0.00972079	−	0.0404900i	0.967299	−	0.253640i	$-0.0816278\pi$
$7$	−0.0257188	−	0.107126i	−0.00972079	−	0.0404900i	−0.977020	+	0.213150i	$0.931628\pi$
$8$	−0.446489	−	2.79296i	−0.157858	−	0.987462i
$9$	−4.04896	−	4.04896i	−1.34965	−	1.34965i
$10$	1.08378	−	0.788209i	0.342722	−	0.249254i
$11$	−3.23203	+	3.78422i	−0.974494	+	1.14099i	0.0154999	+	0.999880i	$0.495066\pi$
$11$	−3.23203	+	3.78422i	−0.974494	+	1.14099i	−0.989994	+	0.141107i	$0.954934\pi$
$12$	−5.74343	+	1.38471i	−1.65798	+	0.399732i
$13$	−2.01034	−	3.28058i	−0.557569	−	0.909870i	−0.999915	−	0.0130254i	$-0.995854\pi$
$13$	−2.01034	−	3.28058i	−0.557569	−	0.909870i	0.442346	−	0.896844i	$-0.354146\pi$
$14$	−0.0362991	+	0.151517i	−0.00970134	+	0.0404947i
$15$	−1.81792	−	2.12851i	−0.469385	−	0.549579i
$16$	−1.22876	+	3.80659i	−0.307189	+	0.951649i
$17$	0.108842	+	1.38297i	0.0263981	+	0.335420i	0.995908	+	0.0903689i	$0.0288046\pi$
$17$	0.108842	+	1.38297i	0.0263981	+	0.335420i	−0.969510	+	0.245051i	$0.921195\pi$
$18$	2.50610	+	7.70038i	0.590692	+	1.81500i
$19$	3.34801	+	2.05166i	0.768085	+	0.470683i	0.850539	−	0.525912i	$-0.176276\pi$
$19$	3.34801	+	2.05166i	0.768085	+	0.470683i	−0.0824541	+	0.996595i	$0.526276\pi$
$20$	−1.87156	+	0.298270i	−0.418494	+	0.0666952i
$21$	0.321437	+	0.0509106i	0.0701432	+	0.0111096i
$22$	6.50093	−	2.69643i	1.38600	−	0.574881i
$23$	−6.86039	−	4.98437i	−1.43049	−	1.03931i	−0.989925	−	0.141592i	$-0.954778\pi$
$23$	−6.86039	−	4.98437i	−1.43049	−	1.03931i	−0.440565	−	0.897720i	$-0.645222\pi$
$24$	8.12711	+	1.93876i	1.65894	+	0.395749i
$25$	2.41114	+	3.31865i	0.482228	+	0.663729i
$26$	0.429523	+	5.42429i	0.0842363	+	1.06379i
$27$	7.43989	−	3.08170i	1.43181	−	0.593074i
$28$	0.142939	−	0.167686i	0.0270129	−	0.0316897i
$29$	−0.498000	+	6.32769i	−0.0924762	+	1.17502i	0.759166	+	0.650898i	$0.225607\pi$
$29$	−0.498000	+	6.32769i	−0.0924762	+	1.17502i	−0.851642	+	0.524124i	$0.824393\pi$
$30$	0.925974	+	3.84881i	0.169059	+	0.702694i
$31$	0.564960	−	1.73877i	0.101470	−	0.312292i	−0.887416	−	0.460970i	$-0.847502\pi$
$31$	0.564960	−	1.73877i	0.101470	−	0.312292i	0.988886	+	0.148678i	$0.0475017\pi$
$32$	3.99038	−	4.00960i	0.705406	−	0.708803i
$33$	−6.67403	−	13.0985i	−1.16180	−	2.28016i
$34$	0.749902	−	1.81289i	0.128607	−	0.310907i
$35$	0.101512	+	0.0243709i	0.0171587	+	0.00411943i
$36$	1.78065	−	11.3129i	0.296775	−	1.88549i
$37$	0.756379	+	2.32790i	0.124348	+	0.382704i	0.993782	−	0.111346i	$-0.0355161\pi$
$37$	0.756379	+	2.32790i	0.124348	+	0.382704i	−0.869434	+	0.494050i	$0.835516\pi$
$38$	−2.90376	−	4.73340i	−0.471052	−	0.767859i
$39$	11.2257	−	1.77798i	1.79756	−	0.284705i
$40$	2.55020	+	0.824550i	0.403223	+	0.130373i
$41$	−0.811348	+	6.35151i	−0.126711	+	0.991940i
$41$	−0.811348	+	6.35151i	−0.126711	+	0.991940i
$42$	−0.372477	−	0.270347i	−0.0574745	−	0.0417155i
$43$	0.666293	+	4.20681i	0.101609	+	0.641532i	0.984955	+	0.172811i	$0.0552850\pi$
$43$	0.666293	+	4.20681i	0.101609	+	0.641532i	−0.883346	+	0.468721i	$0.844715\pi$
$44$	−9.92323	−	0.771383i	−1.49598	−	0.116290i
$45$	5.16043	−	1.67672i	0.769271	−	0.249951i
$46$	5.44957	+	10.6827i	0.803495	+	1.57508i
$47$	−0.398882	+	1.66146i	−0.0581828	+	0.242349i	−0.993882	−	0.110451i	$-0.964770\pi$
$47$	−0.398882	+	1.66146i	−0.0581828	+	0.242349i	0.935699	+	0.352800i	$0.114770\pi$
$48$	−8.99968	−	7.65659i	−1.29899	−	1.10513i
$49$	6.22623	−	3.17242i	0.889462	−	0.453203i
$50$	−0.910261	−	5.72935i	−0.128730	−	0.810252i
$51$	−3.89736	−	1.26633i	−0.545739	−	0.177321i
$52$	2.93796	−	7.11218i	0.407422	−	0.986283i
$53$	9.27788	+	0.730185i	1.27441	+	0.100299i	0.697547	−	0.716539i	$-0.254275\pi$
$53$	9.27788	+	0.730185i	1.27441	+	0.100299i	0.576868	+	0.816838i	$0.304275\pi$
$54$	−11.3538	−	0.888077i	−1.54506	−	0.120852i
$55$	−1.80464	−	4.35680i	−0.243338	−	0.587470i
$56$	−0.287717	+	0.119662i	−0.0384478	+	0.0159906i
$57$	−9.38400	+	6.81788i	−1.24294	+	0.903050i
$58$	4.68646	−	7.65587i	0.615363	−	1.00526i
$59$	4.07424	−	5.60771i	0.530421	−	0.730061i	−0.456774	−	0.889583i	$-0.650995\pi$
$59$	4.07424	−	5.60771i	0.530421	−	0.730061i	0.987194	+	0.159521i	$0.0509951\pi$
$60$	1.30168	−	5.44493i	0.168046	−	0.702937i
$61$	−1.41047	+	8.90534i	−0.180592	+	1.14021i	0.716245	+	0.697849i	$0.245860\pi$
$61$	−1.41047	+	8.90534i	−0.180592	+	1.14021i	−0.896836	+	0.442363i	$0.854140\pi$
$62$	−1.82737	+	1.82913i	−0.232076	+	0.232299i
$63$	−0.329617	+	0.537885i	−0.0415278	+	0.0677672i
$64$	−7.60130	+	2.49406i	−0.950162	+	0.311757i
$65$	3.63467	−	0.286055i	0.450825	−	0.0354807i
$66$	0.00998733	+	20.7901i	0.00122935	+	2.55908i
$67$	−10.1475	+	8.66675i	−1.23971	+	1.05881i	−0.243673	+	0.969857i	$0.578352\pi$
$67$	−10.1475	+	8.66675i	−1.23971	+	1.05881i	−0.996036	+	0.0889542i	$0.971648\pi$
$68$	−2.10801	+	1.80392i	−0.255634	+	0.218757i
$69$	21.3583	−	13.0884i	2.57124	−	1.57566i
$70$	−0.112312	−	0.0958299i	−0.0134238	−	0.0114539i
$71$	6.45694	+	5.51475i	0.766298	+	0.654480i	0.944127	−	0.329581i	$-0.106907\pi$
$71$	6.45694	+	5.51475i	0.766298	+	0.654480i	−0.177829	+	0.984061i	$0.556907\pi$
$72$	−9.50079	+	13.1164i	−1.11968	+	1.54579i
$73$	−6.92317	+	6.92317i	−0.810295	+	0.810295i	−0.984678	−	0.174383i	$-0.944207\pi$
$73$	−6.92317	+	6.92317i	−0.810295	+	0.810295i	0.174383	+	0.984678i	$0.444207\pi$
$74$	0.539865	−	3.41920i	0.0627580	−	0.397474i
$75$	−11.7827	+	2.82878i	−1.36055	+	0.326639i
$76$	0.623682	+	7.82846i	0.0715412	+	0.897986i
$77$	0.488515	+	0.248911i	0.0556714	+	0.0283660i
$78$	−15.2892	−	4.95964i	−1.73116	−	0.561568i
$79$	7.44955	+	3.08571i	0.838140	+	0.347169i	0.760120	−	0.649783i	$-0.225140\pi$
$79$	7.44955	+	3.08571i	0.838140	+	0.347169i	0.0780202	+	0.996952i	$0.475140\pi$
$80$	−2.68534	−	2.67503i	−0.300230	−	0.299078i
$81$			6.60990i			0.734433i
$82$	5.09668	−	7.48491i	0.562835	−	0.826569i
$83$			3.71433i			0.407701i	0.979002	+	0.203851i	$0.0653457\pi$
$83$			3.71433i			0.407701i	−0.979002	+	0.203851i	$0.934654\pi$
$84$	0.296053	+	0.579660i	0.0323021	+	0.0632461i
$85$	−1.21448	−	0.503053i	−0.131729	−	0.0545638i
$86$	1.85861	−	5.72957i	0.200419	−	0.617835i
$87$	−16.7062	−	8.51221i	−1.79109	−	0.912605i
$88$	12.0123	+	7.33734i	1.28051	+	0.782163i
$89$	−15.9169	+	3.82130i	−1.68718	+	0.405057i	−0.959691	−	0.281058i	$-0.909315\pi$
$89$	−15.9169	+	3.82130i	−1.68718	+	0.405057i	−0.727493	+	0.686115i	$0.759315\pi$
$90$	−7.57962	−	1.19676i	−0.798962	−	0.126150i
$91$	−0.299734	+	0.299734i	−0.0314206	+	0.0314206i
$92$	−0.0162946	−	16.9598i	−0.00169883	−	1.76818i
$93$	4.10668	+	3.50744i	0.425843	+	0.363704i
$94$	1.56846	−	1.83822i	0.161774	−	0.189598i
$95$	−3.17254	+	1.94413i	−0.325495	+	0.199464i
$96$	6.43183	+	15.4229i	0.656446	+	1.57410i
$97$	5.75058	−	4.91146i	0.583883	−	0.498683i	−0.307735	−	0.951472i	$-0.599571\pi$
$97$	5.75058	−	4.91146i	0.583883	−	0.498683i	0.891618	+	0.452789i	$0.149571\pi$
$98$	−9.88233	+	0.00474736i	−0.998266	+	0.000479556i
$99$	28.4086	−	2.23580i	2.85517	−	0.224707i
$100$	−2.52772	+	7.80504i	−0.252772	+	0.780504i
$101$	3.89513	−	6.35627i	0.387580	−	0.632473i	−0.598037	−	0.801468i	$-0.704052\pi$
$101$	3.89513	−	6.35627i	0.387580	−	0.632473i	0.985617	+	0.168996i	$0.0540524\pi$
$102$	4.09989	+	4.09595i	0.405950	+	0.405560i
$103$	2.40382	−	15.1771i	0.236855	−	1.49545i	−0.526893	−	0.849932i	$-0.676643\pi$
$103$	2.40382	−	15.1771i	0.236855	−	1.49545i	0.763748	−	0.645514i	$-0.223357\pi$
$104$	−8.26495	+	7.07956i	−0.810445	+	0.694208i
$105$	−0.181265	+	0.249490i	−0.0176897	+	0.0243478i
$106$	−11.2253	−	6.87146i	−1.09030	−	0.667415i
$107$	5.85895	−	4.25677i	0.566406	−	0.411518i	−0.267392	−	0.963588i	$-0.586162\pi$
$107$	5.85895	−	4.25677i	0.566406	−	0.411518i	0.833798	+	0.552070i	$0.186162\pi$
$108$	13.7405	+	8.40204i	1.32218	+	0.808487i
$109$	−4.95764	−	11.9688i	−0.474855	−	1.14640i	−0.961992	−	0.273077i	$-0.911959\pi$
$109$	−4.95764	−	11.9688i	−0.474855	−	1.14640i	0.487137	−	0.873326i	$-0.338041\pi$
$110$	−0.520057	+	6.64879i	−0.0495855	+	0.633937i
$111$	−7.20819	−	0.567297i	−0.684171	−	0.0538454i
$112$	0.439389	+	0.0337313i	0.0415184	+	0.00318730i
$113$	−3.06692	−	0.996502i	−0.288511	−	0.0937430i	0.161186	−	0.986924i	$-0.448468\pi$
$113$	−3.06692	−	0.996502i	−0.288511	−	0.0937430i	−0.449697	+	0.893181i	$0.648468\pi$
$114$	16.2006	−	2.57391i	1.51733	−	0.241069i
$115$	7.15967	−	3.64803i	0.667642	−	0.340181i
$116$	−10.8175	+	6.64326i	−1.00438	+	0.616811i
$117$	−5.14315	+	21.4228i	−0.475484	+	1.98053i
$118$	−8.73207	+	4.45450i	−0.803852	+	0.410070i
$119$	0.145353	−	0.0472282i	0.0133245	−	0.00432940i
$120$	−5.13318	+	6.02775i	−0.468593	+	0.550255i
$121$	−2.15354	−	13.5969i	−0.195776	−	1.23608i
$122$	7.48992	−	10.3194i	0.678105	−	0.934275i
$123$	−16.4170	−	9.39432i	−1.48027	−	0.847057i
$124$	3.47645	−	1.13326i	0.312194	−	0.101770i
$125$	−8.51885	+	1.34925i	−0.761949	+	0.120681i
$126$	0.760461	−	0.466514i	0.0677472	−	0.0415603i
$127$	0.905346	+	2.78637i	0.0803365	+	0.247250i	0.983156	−	0.182770i	$-0.0585064\pi$
$127$	0.905346	+	2.78637i	0.0803365	+	0.247250i	−0.902819	+	0.430020i	$0.858506\pi$
$128$	11.1803	+	1.73227i	0.988209	+	0.153112i
$129$	−12.2342	−	2.93716i	−1.07716	−	0.258603i
$130$	−4.76456	−	1.97086i	−0.417879	−	0.172856i
$131$	−4.10398	−	8.05451i	−0.358566	−	0.703725i	0.639304	−	0.768954i	$-0.279222\pi$
$131$	−4.10398	−	8.05451i	−0.358566	−	0.703725i	−0.997870	+	0.0652284i	$0.979222\pi$
$132$	13.3229	−	26.2099i	1.15961	−	2.28127i
$133$	0.133681	−	0.411426i	0.0115916	−	0.0356752i
$134$	18.3488	−	4.41448i	1.58510	−	0.381353i
$135$	−0.598708	+	7.60731i	−0.0515286	+	0.654733i
$136$	3.81399	−	0.921473i	0.327047	−	0.0790157i
$137$	12.5549	−	5.20040i	1.07264	−	0.444300i	0.224715	−	0.974424i	$-0.427855\pi$
$137$	12.5549	−	5.20040i	1.07264	−	0.444300i	0.847920	+	0.530124i	$0.177855\pi$
$138$	−35.3150	+	2.79642i	−3.00621	+	0.238047i
$139$	−2.32378	−	3.19841i	−0.197101	−	0.271286i	0.699014	−	0.715108i	$-0.253622\pi$
$139$	−2.32378	−	3.19841i	−0.197101	−	0.271286i	−0.896115	+	0.443822i	$0.853622\pi$
$140$	0.0800869	+	0.192823i	0.00676858	+	0.0162965i
$141$	−4.08344	−	2.96679i	−0.343888	−	0.249849i
$142$	−4.60086	−	11.0924i	−0.386096	−	0.930853i
$143$	18.9120	+	2.99536i	1.58150	+	0.250484i
$144$	20.3879	−	10.4376i	1.69900	−	0.869798i
$145$	−5.12828	−	3.14262i	−0.425881	−	0.260980i
$146$	13.1666	−	4.28508i	1.08967	−	0.354636i
$147$	1.61956	+	20.5785i	0.133579	+	1.69729i
$148$	−2.87363	+	3.96321i	−0.236211	+	0.325774i
$149$	8.27531	+	9.68914i	0.677940	+	0.793765i	0.987585	−	0.157087i	$-0.0502103\pi$
$149$	8.27531	+	9.68914i	0.677940	+	0.793765i	−0.309645	+	0.950852i	$0.600210\pi$
$150$	16.6652	+	3.99249i	1.36071	+	0.325985i
$151$	7.81477	+	12.7525i	0.635957	+	1.03779i	0.994547	+	0.104292i	$0.0332577\pi$
$151$	7.81477	+	12.7525i	0.635957	+	1.03779i	−0.358590	+	0.933495i	$0.616742\pi$
$152$	4.23537	−	10.2669i	0.343534	−	0.832756i
$153$	5.15890	−	6.04029i	0.417072	−	0.488329i
$154$	−0.456055	−	0.627072i	−0.0367500	−	0.0505309i
$155$	1.22501	+	1.22501i	0.0983955	+	0.0983955i
$156$	16.0889	+	16.0580i	1.28814	+	1.28567i
$157$	−1.14320	−	4.76179i	−0.0912377	−	0.380032i	0.908004	−	0.418961i	$-0.137606\pi$
$157$	−1.14320	−	4.76179i	−0.0912377	−	0.380032i	−0.999242	+	0.0389285i	$0.987606\pi$
$158$	−7.41000	−	8.66756i	−0.589508	−	0.689554i
$159$	−12.4809	+	24.4952i	−0.989801	+	1.94259i
$160$	1.66869	+	5.09403i	0.131921	+	0.402719i
$161$	−0.357517	+	0.863122i	−0.0281763	+	0.0680235i
$162$	4.23981	−	8.33099i	0.333111	−	0.654545i
$163$	−6.62149			−0.518635			−0.259318	−	0.965792i	$-0.583498\pi$
$163$	−6.62149			−0.518635			−0.259318	+	0.965792i	$0.583498\pi$
$164$	−11.2248	+	6.16465i	−0.876513	+	0.481378i
$165$	13.9303			1.08448
$166$	2.38250	−	4.68148i	0.184918	−	0.363353i
$167$	−3.27435	+	7.90498i	−0.253377	+	0.611706i	−0.998472	−	0.0552519i	$-0.982404\pi$
$167$	−3.27435	+	7.90498i	−0.253377	+	0.611706i	0.745096	+	0.666958i	$0.232404\pi$
$168$	−0.00132658	−	0.920492i	−0.000102348	−	0.0710175i
$169$	−0.818862	+	1.60711i	−0.0629893	+	0.123624i
$170$	1.20803	+	1.41305i	0.0926517	+	0.108376i
$171$	−5.24885	−	21.8630i	−0.401390	−	1.67191i
$172$	−6.01769	+	6.02927i	−0.458845	+	0.459727i
$173$	5.98965	+	5.98965i	0.455385	+	0.455385i	0.897137	−	0.441752i	$-0.145643\pi$
$173$	5.98965	+	5.98965i	0.455385	+	0.455385i	−0.441752	+	0.897137i	$0.645643\pi$
$174$	15.5961	+	21.4445i	1.18234	+	1.62571i
$175$	0.293503	−	0.343648i	0.0221868	−	0.0259774i
$176$	−10.4336	−	16.9529i	−0.786464	−	1.27787i
$177$	10.6985	+	17.4584i	0.804149	+	1.31225i
$178$	22.5124	+	5.39332i	1.68738	+	0.404247i
$179$	1.56153	+	1.82832i	0.116715	+	0.136655i	0.815687	−	0.578493i	$-0.196359\pi$
$179$	1.56153	+	1.82832i	0.116715	+	0.136655i	−0.698973	+	0.715148i	$0.746359\pi$
$180$	8.78557	+	6.37020i	0.654837	+	0.474807i
$181$	−0.649867	−	8.25734i	−0.0483042	−	0.613763i	−0.972660	−	0.232232i	$-0.925397\pi$
$181$	−0.649867	−	8.25734i	−0.0483042	−	0.613763i	0.924356	−	0.381531i	$-0.124603\pi$
$182$	0.570038	−	0.185519i	0.0422540	−	0.0137516i
$183$	−22.7094	−	13.9164i	−1.67873	−	1.02873i
$184$	−10.8581	+	21.3863i	−0.800467	+	1.57662i
$185$	−2.29086	−	0.362836i	−0.168427	−	0.0266762i
$186$	−2.92620	−	7.05488i	−0.214559	−	0.517289i
$187$	−5.58525	−	4.05792i	−0.408434	−	0.296745i
$188$	−3.15596	+	1.31079i	−0.230172	+	0.0955994i
$189$	−0.521477	−	0.717752i	−0.0379319	−	0.0522088i
$190$	5.24564	−	0.415377i	0.380559	−	0.0301346i
$191$	24.5630	−	10.1743i	1.77732	−	0.736190i	0.784005	−	0.620755i	$-0.213174\pi$
$191$	24.5630	−	10.1743i	1.77732	−	0.736190i	0.993315	−	0.115435i	$-0.0368263\pi$
$192$	1.78623	−	23.5644i	0.128910	−	1.70061i
$193$	−1.32777	+	16.8709i	−0.0955751	+	1.21440i	0.742879	+	0.669425i	$0.233460\pi$
$193$	−1.32777	+	16.8709i	−0.0955751	+	1.21440i	−0.838454	+	0.544972i	$0.816540\pi$
$194$	−10.3983	+	2.50170i	−0.746555	+	0.179611i
$195$	−3.32811	+	10.2429i	−0.238331	+	0.733508i
$196$	12.4586	+	6.33288i	0.889897	+	0.452349i
$197$	−4.03538	−	7.91989i	−0.287509	−	0.564269i	0.701404	−	0.712764i	$-0.252557\pi$
$197$	−4.03538	−	7.91989i	−0.287509	−	0.564269i	−0.988913	+	0.148495i	$0.952557\pi$
$198$	−37.2397	−	15.4043i	−2.64651	−	1.09473i
$199$	−9.16997	−	2.20152i	−0.650042	−	0.156061i	−0.105003	−	0.994472i	$-0.533485\pi$
$199$	−9.16997	−	2.20152i	−0.650042	−	0.156061i	−0.545039	+	0.838411i	$0.683485\pi$
$200$	8.19231	−	8.21596i	0.579284	−	0.580956i
$201$	−12.1816	−	37.4911i	−0.859223	−	2.64442i
$202$	−8.98648	+	5.51286i	−0.632286	+	0.387884i
$203$	0.690671	−	0.109391i	0.0484756	−	0.00767778i
$204$	−2.54014	−	7.79228i	−0.177846	−	0.545568i
$205$	−5.01360	−	3.41743i	−0.350165	−	0.238684i
$206$	−12.7648	+	17.5871i	−0.889369	+	1.22535i
$207$	7.59596	+	47.9590i	0.527955	+	3.33338i
$208$	14.9581	−	3.62153i	1.03716	−	0.251108i
$209$	−18.5848	+	6.03857i	−1.28554	+	0.417697i
$210$	0.388495	−	0.198183i	0.0268087	−	0.0136759i
$211$	−0.983550	+	4.09678i	−0.0677103	+	0.282034i	−0.995945	−	0.0899605i	$-0.971326\pi$
$211$	−0.983550	+	4.09678i	−0.0677103	+	0.282034i	0.928235	+	0.371994i	$0.121326\pi$
$212$	9.74058	+	15.8610i	0.668986	+	1.08934i
$213$	−22.3497	+	11.3878i	−1.53138	+	0.780276i
$214$	−10.1149	+	1.60703i	−0.691444	+	0.109854i
$215$	−3.83848	−	1.24720i	−0.261782	−	0.0850583i
$216$	−11.9289	−	19.4034i	−0.811660	−	1.32023i
$217$	−0.200798	−	0.0158032i	−0.0136311	−	0.00107279i
$218$	−1.42868	+	18.2652i	−0.0967622	+	1.23708i
$219$	−11.0680	−	26.7205i	−0.747907	−	1.80561i
$220$	4.92023	−	8.04643i	0.331722	−	0.542490i
$221$	4.31814	−	3.13731i	0.290469	−	0.211038i
$222$	8.72119	+	5.33859i	0.585328	+	0.358303i
$223$	−1.84038	+	2.53307i	−0.123241	+	0.169627i	−0.866179	−	0.499733i	$-0.833431\pi$
$223$	−1.84038	+	2.53307i	−0.123241	+	0.169627i	0.742939	+	0.669360i	$0.233431\pi$
$224$	−0.532162	−	0.324353i	−0.0355566	−	0.0216718i
$225$	3.67447	−	23.1997i	0.244965	−	1.54665i
$226$	3.22630	+	3.22320i	0.214610	+	0.214404i
$227$	7.99793	−	13.0514i	0.530842	−	0.866255i	−0.469015	−	0.883190i	$-0.655391\pi$
$227$	7.99793	−	13.0514i	0.530842	−	0.866255i	0.999857	+	0.0169355i	$0.00539101\pi$
$228$	−22.0700	−	7.14754i	−1.46162	−	0.473357i
$229$	−8.90411	+	0.700769i	−0.588400	+	0.0463081i	−0.369165	−	0.929364i	$-0.620356\pi$
$229$	−8.90411	+	0.700769i	−0.588400	+	0.0463081i	−0.219235	+	0.975672i	$0.570356\pi$
$230$	−11.3639	+	0.00545908i	−0.749312	+	0.000359961i
$231$	−1.23155	+	1.05184i	−0.0810301	+	0.0692062i
$232$	17.8953	−	1.43435i	1.17489	−	0.0941695i
$233$	−1.78024	+	1.09093i	−0.116627	+	0.0714692i	−0.579589	−	0.814909i	$-0.696787\pi$
$233$	−1.78024	+	1.09093i	−0.116627	+	0.0714692i	0.462962	+	0.886378i	$0.346787\pi$
$234$	20.2236	−	23.7019i	1.32206	−	1.54944i
$235$	−1.23119	−	1.05153i	−0.0803139	−	0.0685946i
$236$	13.8630	−	0.0133193i	0.902405	−	0.000867011i
$237$	−16.8426	+	16.8426i	−1.09405	+	1.09405i
$238$	−0.213495	−	0.0337091i	−0.0138388	−	0.00218504i
$239$	19.7634	−	4.74478i	1.27839	−	0.306915i	0.463276	−	0.886214i	$-0.346674\pi$
$239$	19.7634	−	4.74478i	1.27839	−	0.306915i	0.815115	+	0.579299i	$0.196674\pi$
$240$	10.3362	−	4.30467i	0.667196	−	0.277865i
$241$	−8.50914	−	4.33563i	−0.548122	−	0.279282i	0.157920	−	0.987452i	$-0.449521\pi$
$241$	−8.50914	−	4.33563i	−0.548122	−	0.279282i	−0.706042	+	0.708170i	$0.749521\pi$
$242$	−6.00724	+	18.5186i	−0.386160	+	1.19042i
$243$	4.28036	+	1.77298i	0.274585	+	0.113737i
$244$	−16.0594	+	8.20210i	−1.02810	+	0.525086i
$245$			6.62163i			0.423040i
$246$	14.6658	+	22.3708i	0.935058	+	1.42631i
$247$		−	15.1079i		−	0.961296i
$248$	−5.10857	−	0.801572i	−0.324394	−	0.0508999i
$249$	−10.1369	−	4.19885i	−0.642402	−	0.266091i
$250$	11.6025	+	3.76371i	0.733804	+	0.238038i
$251$	9.26570	+	4.72111i	0.584846	+	0.297994i	0.721267	−	0.692657i	$-0.243560\pi$
$251$	9.26570	+	4.72111i	0.584846	+	0.297994i	−0.136421	+	0.990651i	$0.543560\pi$
$252$	−1.25771	+	0.100200i	−0.0792282	+	0.00631199i
$253$	41.0350	−	9.85162i	2.57985	−	0.619366i
$254$	0.646190	−	4.09261i	0.0405456	−	0.256793i
$255$	2.74580	−	2.74580i	0.171949	−	0.171949i
$256$	−12.9803	−	9.35475i	−0.811270	−	0.584672i
$257$	19.7721	+	16.8870i	1.23335	+	1.05338i	0.996649	+	0.0818005i	$0.0260670\pi$
$257$	19.7721	+	16.8870i	1.23335	+	1.05338i	0.236704	+	0.971582i	$0.423933\pi$
$258$	13.5357	+	11.5494i	0.842697	+	0.719032i
$259$	0.229926	−	0.140899i	0.0142869	−	0.00875503i
$260$	4.74098	+	5.54019i	0.294023	+	0.343588i
$261$	27.6369	−	23.6042i	1.71068	−	1.46106i
$262$	0.00614138	+	12.7842i	0.000379416	+	0.789809i
$263$	−3.23130	+	0.254309i	−0.199251	+	0.0156814i	−0.177692	−	0.984086i	$-0.556863\pi$
$263$	−3.23130	+	0.254309i	−0.199251	+	0.0156814i	−0.0215590	+	0.999768i	$0.506863\pi$
$264$	−33.6038	+	24.4887i	−2.06817	+	1.50717i
$265$	−4.60782	+	7.51928i	−0.283056	+	0.461905i
$266$	−0.432391	+	0.432807i	−0.0265116	+	0.0265371i
$267$	7.56430	−	47.7591i	0.462927	−	2.92281i
$268$	−25.9581	−	6.20562i	−1.58564	−	0.379069i
$269$	−7.88353	+	10.8508i	−0.480667	+	0.661582i	−0.978633	−	0.205615i	$-0.934081\pi$
$269$	−7.88353	+	10.8508i	−0.480667	+	0.661582i	0.497966	+	0.867197i	$0.334081\pi$
$270$	5.63419	−	9.20408i	0.342886	−	0.560143i
$271$	−8.08598	+	5.87481i	−0.491188	+	0.356869i	−0.805641	−	0.592404i	$-0.798179\pi$
$271$	−8.08598	+	5.87481i	−0.491188	+	0.356869i	0.314453	+	0.949273i	$0.398179\pi$
$272$	−5.39815	−	1.28501i	−0.327311	−	0.0779155i
$273$	−0.479182	−	1.15685i	−0.0290014	−	0.0700155i
$274$	−19.1596	−	1.49864i	−1.15748	−	0.0905359i
$275$	−20.3514	−	1.60169i	−1.22723	−	0.0965854i
$276$	46.3041	+	19.1277i	2.78718	+	1.15135i
$277$	3.36369	+	1.09293i	0.202104	+	0.0656677i	0.408320	−	0.912839i	$-0.366115\pi$
$277$	3.36369	+	1.09293i	0.202104	+	0.0656677i	−0.206215	+	0.978507i	$0.566115\pi$
$278$	0.877283	+	5.52178i	0.0526159	+	0.331174i
$279$	−9.32771	+	4.75271i	−0.558435	+	0.284537i
$280$	0.0227430	−	0.294401i	0.00135915	−	0.0175938i
$281$	−0.411301	+	1.71319i	−0.0245361	+	0.102200i	−0.983294	−	0.182023i	$-0.941736\pi$
$281$	−0.411301	+	1.71319i	−0.0245361	+	0.102200i	0.958758	+	0.284223i	$0.0917356\pi$
$282$	3.24369	+	6.35855i	0.193159	+	0.378646i
$283$	−10.7902	+	3.50594i	−0.641410	+	0.208407i	−0.611623	−	0.791150i	$-0.709483\pi$
$283$	−10.7902	+	3.50594i	−0.641410	+	0.208407i	−0.0297871	+	0.999556i	$0.509483\pi$
$284$	−1.31619	+	16.9318i	−0.0781018	+	1.00472i
$285$	−1.71943	−	10.8560i	−0.101850	−	0.643056i
$286$	−21.9150	−	15.9061i	−1.29586	−	0.940545i
$287$	0.701282	−	0.0764364i	0.0413954	−	0.00451190i
$288$	−32.3916	+	0.0778030i	−1.90869	+	0.00458458i
$289$	14.8899	−	2.35833i	0.875879	−	0.138726i
$290$	4.44781	+	7.25035i	0.261185	+	0.425755i
$291$	6.90333	+	21.2463i	0.404680	+	1.24548i
$292$	−19.3435	−	3.04466i	−1.13199	−	0.178176i
$293$	5.13617	+	1.23309i	0.300058	+	0.0720376i	0.380679	−	0.924707i	$-0.375690\pi$
$293$	5.13617	+	1.23309i	0.300058	+	0.0720376i	−0.0806208	+	0.996745i	$0.525690\pi$
$294$	11.1585	−	26.9756i	0.650776	−	1.57325i
$295$	2.98191	+	5.85234i	0.173614	+	0.340736i
$296$	6.16401	−	3.15192i	0.358276	−	0.183202i
$297$	−12.3841	+	38.1144i	−0.718599	+	2.21162i
$298$	−4.21510	−	17.5201i	−0.244174	−	1.01491i
$299$	−2.55988	+	32.5264i	−0.148042	+	1.88105i
$300$	−18.4436	−	15.7217i	−1.06484	−	0.907691i
$301$	0.433524	−	0.179572i	0.0249879	−	0.0103503i
$302$	−1.66968	−	21.0857i	−0.0960790	−	1.21335i
$303$	12.9439	+	17.8158i	0.743608	+	1.02349i
$304$	−11.9237	+	10.2235i	−0.683872	+	0.586358i
$305$	−6.91208	−	5.02192i	−0.395785	−	0.287554i
$306$	−10.3766	+	4.30398i	−0.593192	+	0.246042i
$307$	10.1809	+	1.61250i	0.581057	+	0.0920304i	0.440042	−	0.897977i	$-0.354964\pi$
$307$	10.1809	+	1.61250i	0.581057	+	0.0920304i	0.141015	+	0.990007i	$0.454964\pi$
$308$	0.172578	+	1.08288i	0.00983354	+	0.0617028i
$309$	38.7030	+	23.7173i	2.20174	+	1.34923i
$310$	−0.758220	−	2.32975i	−0.0430640	−	0.132321i
$311$	−0.705236	−	8.96087i	−0.0399902	−	0.508124i	−0.983995	−	0.178194i	$-0.942975\pi$
$311$	−0.705236	−	8.96087i	−0.0399902	−	0.508124i	0.944005	−	0.329931i	$-0.107025\pi$
$312$	−9.97801	−	30.5592i	−0.564894	−	1.73008i
$313$	−5.49854	−	6.43796i	−0.310796	−	0.363895i	0.582919	−	0.812530i	$-0.301910\pi$
$313$	−5.49854	−	6.43796i	−0.310796	−	0.363895i	−0.893715	+	0.448635i	$0.851910\pi$
$314$	−1.61350	+	6.73496i	−0.0910551	+	0.380076i
$315$	−0.312342	−	0.509695i	−0.0175985	−	0.0287181i
$316$	3.77976	+	15.6775i	0.212628	+	0.881927i
$317$	−6.57852	+	7.70246i	−0.369486	+	0.432613i	−0.913735	−	0.406311i	$-0.866815\pi$
$317$	−6.57852	+	7.70246i	−0.369486	+	0.432613i	0.544248	+	0.838924i	$0.316815\pi$
$318$	31.4428	−	22.8676i	1.76322	−	1.28235i
$319$	−22.3358	−	22.3358i	−1.25057	−	1.25057i
$320$	1.16430	−	7.49078i	0.0650864	−	0.418747i
$321$	4.99410	+	20.8019i	0.278743	+	1.16105i
$322$	1.00424	−	0.858539i	0.0559643	−	0.0478445i
$323$	−2.47298	+	4.85350i	−0.137600	+	0.270056i
$324$	−10.6876	+	7.78067i	−0.593754	+	0.432260i
$325$	6.03988	−	14.5816i	0.335032	−	0.808839i
$326$	8.34561	+	4.24725i	0.462220	+	0.235233i
$327$	38.2688			2.11627
$328$	18.1018	−	0.569817i	0.999505	−	0.0314629i
$329$	0.188245			0.0103783
$330$	−17.5576	−	8.93540i	−0.966512	−	0.491878i
$331$	−3.03644	+	7.33061i	−0.166898	+	0.402927i	−0.985095	−	0.172011i	$-0.944974\pi$
$331$	−3.03644	+	7.33061i	−0.166898	+	0.402927i	0.818197	+	0.574937i	$0.194974\pi$
$332$	−6.00572	+	4.37223i	−0.329607	+	0.239958i
$333$	6.36301	−	12.4881i	0.348691	−	0.684344i
$334$	9.19745	−	7.86301i	0.503262	−	0.430245i
$335$	−2.95201	−	12.2960i	−0.161285	−	0.671802i
$336$	−0.588763	+	1.16102i	−0.0321196	+	0.0633389i
$337$	23.3619	+	23.3619i	1.27260	+	1.27260i	0.944717	+	0.327887i	$0.106337\pi$
$337$	23.3619	+	23.3619i	1.27260	+	1.27260i	0.327887	+	0.944717i	$0.393663\pi$
$338$	2.06293	−	1.50032i	0.112209	−	0.0816067i
$339$	6.18658	−	7.24355i	0.336009	−	0.393416i
$340$	−0.616203	−	2.55585i	−0.0334183	−	0.138610i
$341$	4.75392	+	7.75769i	0.257439	+	0.420103i
$342$	−7.40814	+	30.9226i	−0.400587	+	1.67210i
$343$	−1.00083	−	1.17182i	−0.0540398	−	0.0632725i
$344$	11.4520	−	3.73923i	0.617449	−	0.201606i
$345$	1.86237	+	23.6636i	0.100266	+	1.27401i
$346$	−3.70728	−	11.3912i	−0.199305	−	0.612396i
$347$	13.0145	+	7.97528i	0.698653	+	0.428135i	0.825961	−	0.563728i	$-0.190633\pi$
$347$	13.0145	+	7.97528i	0.698653	+	0.428135i	−0.127307	+	0.991863i	$0.540633\pi$
$348$	−5.90180	−	37.0322i	−0.316370	−	1.98513i
$349$	−23.7479	−	3.76130i	−1.27120	−	0.201338i	−0.515859	−	0.856673i	$-0.672527\pi$
$349$	−23.7479	−	3.76130i	−1.27120	−	0.201338i	−0.755338	+	0.655336i	$0.772527\pi$
$350$	−0.590354	+	0.244865i	−0.0315558	+	0.0130886i
$351$	−25.0665	−	18.2119i	−1.33795	−	0.972079i
$352$	2.27617	+	28.0596i	0.121320	+	1.49558i
$353$	−20.0986	−	27.6633i	−1.06974	−	1.47237i	−0.870340	−	0.492452i	$-0.836101\pi$
$353$	−20.0986	−	27.6633i	−1.06974	−	1.47237i	−0.199400	−	0.979918i	$-0.563899\pi$
$354$	−2.28580	−	28.8666i	−0.121489	−	1.53424i
$355$	−7.43391	+	3.07923i	−0.394551	+	0.163428i
$356$	−24.9148	−	21.2379i	−1.32048	−	1.12561i
$357$	−0.0354219	+	0.450079i	−0.00187473	+	0.0238207i
$358$	−0.795381	−	3.30600i	−0.0420372	−	0.174728i
$359$	−1.48719	+	4.57709i	−0.0784907	+	0.241570i	−0.982601	−	0.185730i	$-0.940535\pi$
$359$	−1.48719	+	4.57709i	−0.0784907	+	0.241570i	0.904110	+	0.427300i	$0.140535\pi$
$360$	−6.98710	−	13.6642i	−0.368253	−	0.720169i
$361$	−1.62599	−	3.19118i	−0.0855784	−	0.167957i
$362$	−4.47746	+	10.8242i	−0.235330	+	0.568910i
$363$	39.5423	+	9.49326i	2.07543	+	0.498267i
$364$	−0.837464	−	0.131817i	−0.0438951	−	0.00690907i
$365$	−2.86697	−	8.82362i	−0.150064	−	0.461849i
$366$	19.6961	+	32.1065i	1.02953	+	1.67824i
$367$	10.0180	−	1.58670i	0.522936	−	0.0828250i	0.110615	−	0.993863i	$-0.464718\pi$
$367$	10.0180	−	1.58670i	0.522936	−	0.0828250i	0.412322	+	0.911038i	$0.364718\pi$
$368$	27.4032	−	19.9902i	1.42849	−	1.04206i
$369$	29.0022	−	22.4319i	1.50979	−	1.16776i
$370$	2.65462	+	1.92674i	0.138007	+	0.100167i
$371$	−0.160394	−	1.01269i	−0.00832723	−	0.0525761i
$372$	−0.837113	+	10.7688i	−0.0434023	+	0.558336i
$373$	−29.6452	+	9.63233i	−1.53497	+	0.498743i	−0.949984	−	0.312299i	$-0.898901\pi$
$373$	−29.6452	+	9.63233i	−1.53497	+	0.498743i	−0.584989	+	0.811041i	$0.698901\pi$
$374$	4.43666	+	8.69710i	0.229414	+	0.449716i
$375$	5.94780	−	24.7744i	0.307143	−	1.27934i
$376$	4.81850	+	0.372237i	0.248495	+	0.0191967i
$377$	21.7596	−	11.0871i	1.12068	−	0.571014i
$378$	0.196870	+	1.23913i	0.0101259	+	0.0637342i
$379$	0.241807	+	0.0785680i	0.0124208	+	0.00403577i	0.315221	−	0.949018i	$-0.397921\pi$
$379$	0.241807	+	0.0785680i	0.0124208	+	0.00403577i	−0.302800	+	0.953054i	$0.597921\pi$
$380$	−6.87795	−	2.84120i	−0.352831	−	0.145751i
$381$	−8.62782	−	0.679025i	−0.442017	−	0.0347875i
$382$	−37.4850	−	2.93201i	−1.91790	−	0.150015i
$383$	−11.4673	−	27.6845i	−0.585951	−	1.41461i	−0.887343	−	0.461110i	$-0.847451\pi$
$383$	−11.4673	−	27.6845i	−0.585951	−	1.41461i	0.301392	−	0.953500i	$-0.402549\pi$
$384$	−17.3663	+	28.5544i	−0.886222	+	1.45716i
$385$	−0.420315	+	0.305377i	−0.0214212	+	0.0155634i
$386$	12.4951	−	20.4121i	0.635984	−	1.03895i
$387$	14.3354	−	19.7310i	0.728710	−	1.00298i
$388$	14.7105	+	3.51674i	0.746813	+	0.178535i
$389$	−1.74698	+	11.0300i	−0.0885752	+	0.559242i	0.902993	+	0.429655i	$0.141365\pi$
$389$	−1.74698	+	11.0300i	−0.0885752	+	0.559242i	−0.991568	+	0.129586i	$0.958635\pi$
$390$	10.7648	−	10.7752i	0.545098	−	0.545622i
$391$	6.14653	−	10.0302i	0.310843	−	0.507250i
$392$	−11.6404	−	15.9732i	−0.587929	−	0.806768i
$393$	26.6212	−	2.09513i	1.34286	−	0.105685i
$394$	0.00603874	+	12.5705i	0.000304227	+	0.633293i
$395$	−5.81006	+	4.96226i	−0.292336	+	0.249679i
$396$	37.0555	+	43.3021i	1.86211	+	2.17601i
$397$	−20.3417	+	12.4654i	−1.02092	+	0.625621i	−0.928975	−	0.370143i	$-0.879309\pi$
$397$	−20.3417	+	12.4654i	−1.02092	+	0.625621i	−0.0919456	+	0.995764i	$0.529309\pi$
$398$	10.1455	+	8.65668i	0.508550	+	0.433920i
$399$	0.971720	+	0.829927i	0.0486469	+	0.0415483i
$400$	−15.5954	+	5.10042i	−0.779772	+	0.255021i
$401$	16.2986	−	16.2986i	0.813915	−	0.813915i	−0.171304	−	0.985218i	$-0.554798\pi$
$401$	16.2986	−	16.2986i	0.813915	−	0.813915i	0.985218	+	0.171304i	$0.0547979\pi$
$402$	−8.69460	+	55.0668i	−0.433647	+	2.74648i
$403$	−6.83994	+	1.64212i	−0.340722	+	0.0818000i
$404$	14.8625	−	1.18408i	0.739439	−	0.0589100i
$405$	−5.58080	−	2.84356i	−0.277312	−	0.141298i
$406$	−0.940676	−	0.305145i	−0.0466850	−	0.0151441i
$407$	−11.2539	−	4.66153i	−0.557836	−	0.231063i
$408$	−1.79668	+	11.4506i	−0.0889490	+	0.566888i
$409$			2.09592i			0.103637i	0.998657	+	0.0518183i	$0.0165017\pi$
$409$			2.09592i			0.103637i	−0.998657	+	0.0518183i	$0.983498\pi$
$410$	4.12700	+	7.52316i	0.203818	+	0.371542i
$411$			40.1427i			1.98010i
$412$	27.3695	−	13.9786i	1.34840	−	0.688677i
$413$	−0.705519	−	0.292235i	−0.0347163	−	0.0143800i
$414$	21.1887	−	65.3189i	1.04137	−	3.21025i
$415$	−3.13605	−	1.59790i	−0.153942	−	0.0784376i
$416$	−21.1758	−	5.03011i	−1.03823	−	0.246621i
$417$	11.3558	−	2.72629i	0.556097	−	0.133507i
$418$	27.2973	+	4.31003i	1.33515	+	0.210810i
$419$	0.354319	−	0.354319i	0.0173096	−	0.0173096i	−0.698399	−	0.715709i	$-0.746104\pi$
$419$	0.354319	−	0.354319i	0.0173096	−	0.0173096i	0.715709	+	0.698399i	$0.246104\pi$
$420$	−0.616774		0.000592582i	−0.0300955		2.89151e-5i
$421$	6.03143	+	5.15133i	0.293954	+	0.251060i	0.784178	−	0.620536i	$-0.213085\pi$
$421$	6.03143	+	5.15133i	0.293954	+	0.251060i	−0.490224	+	0.871596i	$0.663085\pi$
$422$	3.86746	−	4.53262i	0.188265	−	0.220645i
$423$	8.34225	−	5.11214i	0.405614	−	0.248561i
$424$	−2.10309	−	26.2388i	−0.102135	−	1.27427i
$425$	−4.32716	+	3.69574i	−0.209898	+	0.179270i
$426$	35.4737	−	0.0170412i	1.71871	−	0.000825647i
$427$	0.990273	−	0.0779362i	0.0479227	−	0.00377160i
$428$	13.7795	+	4.46260i	0.666057	+	0.215708i
$429$	−29.5537	+	48.2272i	−1.42687	+	2.32843i
$430$	4.03796	+	4.03408i	0.194728	+	0.194541i
$431$	−1.10663	+	6.98701i	−0.0533047	+	0.336553i	0.946595	+	0.322424i	$0.104498\pi$
$431$	−1.10663	+	6.98701i	−0.0533047	+	0.336553i	−0.999900	+	0.0141290i	$0.995502\pi$
$432$	2.58899	+	32.1073i	0.124563	+	1.54476i
$433$	16.3579	−	22.5147i	0.786111	−	1.08199i	−0.208470	−	0.978029i	$-0.566848\pi$
$433$	16.3579	−	22.5147i	0.786111	−	1.08199i	0.994581	−	0.103961i	$-0.0331516\pi$
$434$	0.242946	+	0.148717i	0.0116618	+	0.00713864i
$435$	14.3739	−	10.4432i	0.689175	−	0.500715i
$436$	13.5166	−	22.1048i	0.647329	−	1.05863i
$437$	−12.7424	−	30.7629i	−0.609552	−	1.47159i
$438$	−3.18955	+	40.7775i	−0.152402	+	1.94842i
$439$	29.8248	+	2.34727i	1.42346	+	0.112029i	0.766669	−	0.642042i	$-0.221913\pi$
$439$	29.8248	+	2.34727i	1.42346	+	0.112029i	0.656793	+	0.754071i	$0.271913\pi$
$440$	−11.3626	+	6.98557i	−0.541692	+	0.333024i
$441$	−38.0548	−	12.3648i	−1.81213	−	0.588798i
$442$	−7.45488	+	1.18441i	−0.354593	+	0.0563366i
$443$	−30.5437	+	15.5628i	−1.45118	+	0.739411i	−0.989075	−	0.147416i	$-0.952905\pi$
$443$	−30.5437	+	15.5628i	−1.45118	+	0.739411i	−0.462102	+	0.886827i	$0.652905\pi$
$444$	−7.56767	−	12.3227i	−0.359146	−	0.584811i
$445$	3.62103	−	15.0827i	0.171653	−	0.714987i
$446$	3.94438	−	2.01215i	0.186772	−	0.0952779i
$447$	−35.7978	+	11.6314i	−1.69318	+	0.550146i
$448$	0.462676	+	0.750156i	0.0218594	+	0.0354415i
$449$	4.91546	+	31.0350i	0.231975	+	1.46463i	0.778741	+	0.627346i	$0.215859\pi$
$449$	4.91546	+	31.0350i	0.231975	+	1.46463i	−0.546766	+	0.837286i	$0.684141\pi$
$450$	−19.5123	+	26.8835i	−0.919819	+	1.26730i
$451$	−21.4132	−	23.5986i	−1.00831	−	1.11122i
$452$	−1.99890	−	6.13192i	−0.0940202	−	0.288421i
$453$	−43.6376	+	6.91152i	−2.05027	+	0.324732i
$454$	−18.4521	+	11.3197i	−0.866000	+	0.531258i
$455$	−0.124123	−	0.382012i	−0.00581899	−	0.0179090i
$456$	23.2319	+	23.1651i	1.08793	+	1.08480i
$457$	−4.83920	−	1.16179i	−0.226368	−	0.0543462i	0.118674	−	0.992933i	$-0.462136\pi$
$457$	−4.83920	−	1.16179i	−0.226368	−	0.0543462i	−0.345043	+	0.938587i	$0.612136\pi$
$458$	11.6721	+	4.82816i	0.545400	+	0.225605i
$459$	5.07168	+	9.95373i	0.236726	+	0.464600i
$460$	14.3263	+	7.28230i	0.667969	+	0.339539i
$461$	7.65411	−	23.5569i	0.356487	−	1.09716i	−0.598655	−	0.801007i	$-0.704298\pi$
$461$	7.65411	−	23.5569i	0.356487	−	1.09716i	0.955142	−	0.296148i	$-0.0957022\pi$
$462$	2.22691	−	0.535766i	0.103605	−	0.0249261i
$463$	0.293479	−	3.72901i	0.0136391	−	0.173302i	−0.986325	−	0.164813i	$-0.947298\pi$
$463$	0.293479	−	3.72901i	0.0136391	−	0.173302i	0.999964	−	0.00848865i	$-0.00270205\pi$
$464$	−23.4750	−	9.67086i	−1.08980	−	0.448959i
$465$	−4.72804	+	1.95842i	−0.219258	+	0.0908195i
$466$	2.94354	−	0.233084i	0.136357	−	0.0107974i
$467$	9.14071	+	12.5811i	0.422982	+	0.582185i	0.966325	−	0.257326i	$-0.0828416\pi$
$467$	9.14071	+	12.5811i	0.422982	+	0.582185i	−0.543343	+	0.839511i	$0.682842\pi$
$468$	−40.6927	+	16.9013i	−1.88102	+	0.781262i
$469$	1.18942	+	0.864163i	0.0549222	+	0.0399033i
$470$	0.877278	+	2.11506i	0.0404658	+	0.0975605i
$471$	14.2879	+	2.26298i	0.658352	+	0.104273i
$472$	−17.4812	−	8.87542i	−0.804639	−	0.408524i
$473$	−18.0730	−	11.0751i	−0.830997	−	0.509235i
$474$	32.0316	−	10.4247i	1.47126	−	0.478823i
$475$	1.26377	+	16.0577i	0.0579856	+	0.736777i
$476$	0.247463	+	0.179429i	0.0113424	+	0.00822412i
$477$	−34.6093	−	40.5223i	−1.58465	−	1.85539i
$478$	−27.9530	−	6.69671i	−1.27854	−	0.306300i
$479$	−19.4789	−	31.7867i	−0.890015	−	1.45237i	−0.891828	−	0.452375i	$-0.850577\pi$
$479$	−19.4789	−	31.7867i	−0.890015	−	1.45237i	0.00181276	−	0.999998i	$-0.499423\pi$
$480$	−15.7887	−	1.20444i	−0.720651	−	0.0549751i
$481$	6.11627	−	7.16123i	0.278878	−	0.326524i
$482$	7.94375	+	10.9226i	0.361828	+	0.497511i
$483$	−1.95142	−	1.95142i	−0.0887929	−	0.0887929i
$484$	19.4499	−	19.4873i	0.884086	−	0.885787i
$485$	1.67291	+	6.96817i	0.0759629	+	0.316408i
$486$	−4.25764	−	4.98021i	−0.193130	−	0.225907i
$487$	−10.2958	+	20.2067i	−0.466548	+	0.915652i	0.531114	+	0.847301i	$0.321774\pi$
$487$	−10.2958	+	20.2067i	−0.466548	+	0.915652i	−0.997661	+	0.0683509i	$0.978226\pi$
$488$	25.5021	−	0.0367527i	1.15442	−	0.00166372i
$489$	7.48523	−	18.0710i	0.338494	−	0.817197i
$490$	4.24734	−	8.34578i	0.191875	−	0.377024i
$491$	−22.9478			−1.03562			−0.517810	−	0.855496i	$-0.673252\pi$
$491$	−22.9478			−1.03562			−0.517810	+	0.855496i	$0.673252\pi$
$492$	−4.13510	−	37.6029i	−0.186425	−	1.69527i
$493$	−8.80521			−0.396567
$494$	−9.69075	+	19.0418i	−0.436008	+	0.856730i
$495$	−10.3336	+	24.9474i	−0.464459	+	1.12130i
$496$	5.92459	+	4.28710i	0.266022	+	0.192496i
$497$	0.424711	−	0.833542i	0.0190509	−	0.0373895i
$498$	10.0831	+	11.7943i	0.451835	+	0.528517i
$499$	1.68620	+	7.02354i	0.0754848	+	0.314417i	0.997320	−	0.0731657i	$-0.0233102\pi$
$499$	1.68620	+	7.02354i	0.0754848	+	0.314417i	−0.921835	+	0.387583i	$0.873310\pi$
$500$	−12.2094	−	12.1859i	−0.546019	−	0.544971i
$501$	−17.8723	−	17.8723i	−0.798475	−	0.798475i
$502$	−8.65004	−	11.8937i	−0.386070	−	0.530843i
$503$	−4.46515	+	5.22802i	−0.199091	+	0.233106i	−0.850966	−	0.525221i	$-0.823983\pi$
$503$	−4.46515	+	5.22802i	−0.199091	+	0.233106i	0.651875	+	0.758327i	$0.273983\pi$
$504$	1.64947	+	0.680447i	0.0734730	+	0.0303095i
$505$	3.69099	+	6.02314i	0.164247	+	0.268026i
$506$	−58.0389	−	13.9044i	−2.58014	−	0.618127i
$507$	−3.46033	−	4.05153i	−0.153679	−	0.179935i
$508$	−3.43958	+	4.74376i	−0.152607	+	0.210470i
$509$	0.426718	+	5.42196i	0.0189139	+	0.240324i	0.999106	+	0.0422751i	$0.0134606\pi$
$509$	0.426718	+	5.42196i	0.0189139	+	0.240324i	−0.980192	+	0.198049i	$0.936539\pi$
$510$	−5.22201	+	1.69951i	−0.231235	+	0.0752555i
$511$	0.919710	+	0.563599i	0.0406856	+	0.0249321i
$512$	10.3597	+	20.1166i	0.457839	+	0.889035i
$513$	31.2314	+	4.94657i	1.37890	+	0.218396i
$514$	−14.0885	−	33.9666i	−0.621419	−	1.49820i
$515$	11.7801	+	8.55872i	0.519092	+	0.377142i
$516$	−9.65203	−	23.2389i	−0.424907	−	1.02303i
$517$	−4.99814	−	6.87935i	−0.219818	−	0.302554i
$518$	−0.380172	+	0.0301040i	−0.0167038	+	0.00132269i
$519$	−23.1176	+	9.57561i	−1.01475	+	0.420323i
$520$	−2.42178	−	10.0238i	−0.106202	−	0.439572i
$521$	−1.89934	+	24.1334i	−0.0832115	+	1.05730i	0.803600	+	0.595170i	$0.202915\pi$
$521$	−1.89934	+	24.1334i	−0.0832115	+	1.05730i	−0.886811	+	0.462132i	$0.847085\pi$
$522$	−49.9736	+	12.0230i	−2.18729	+	0.526232i
$523$	−2.24199	+	6.90014i	−0.0980355	+	0.301722i	−0.988033	−	0.154243i	$-0.950706\pi$
$523$	−2.24199	+	6.90014i	−0.0980355	+	0.301722i	0.889997	+	0.455966i	$0.150706\pi$
$524$	8.19247	−	16.1169i	0.357890	−	0.704070i
$525$	0.606074	+	1.18949i	0.0264512	+	0.0519135i
$526$	4.23580	+	1.75214i	0.184690	+	0.0763970i
$527$	2.46616	+	0.592072i	0.107428	+	0.0257911i
$528$	58.0615	−	9.31044i	2.52680	−	0.405185i
$529$	15.1137	+	46.5151i	0.657116	+	2.02240i
$530$	10.6307	−	6.52155i	0.461769	−	0.283278i
$531$	−39.2018	+	6.20896i	−1.70121	+	0.269446i
$532$	0.822595	−	0.268151i	0.0356640	−	0.0116258i
$533$	22.4677	−	10.1070i	0.973186	−	0.437784i
$534$	−40.1682	+	55.3427i	−1.73825	+	2.39491i
$535$	1.07353	+	6.77801i	0.0464128	+	0.293039i
$536$	28.7366	+	24.4719i	1.24123	+	1.05702i
$537$	−6.75497	+	2.19482i	−0.291498	+	0.0947136i
$538$	16.8963	−	8.61932i	0.728451	−	0.371605i
$539$	−8.11822	+	33.8148i	−0.349677	+	1.45651i
$540$	−13.0050	+	7.98670i	−0.559648	+	0.343693i
$541$	10.7836	−	5.49452i	0.463623	−	0.236228i	−0.206545	−	0.978437i	$-0.566222\pi$
$541$	10.7836	−	5.49452i	0.463623	−	0.236228i	0.670168	+	0.742209i	$0.266222\pi$
$542$	13.9597	−	2.21788i	0.599622	−	0.0952660i
$543$	23.2700	+	7.56090i	0.998613	+	0.324469i
$544$	5.97947	+	5.08217i	0.256368	+	0.217896i
$545$	12.2381	+	0.963161i	0.524223	+	0.0412573i
$546$	−0.138089	+	1.76543i	−0.00590967	+	0.0755535i
$547$	15.6448	+	37.7699i	0.668924	+	1.61493i	0.783413	+	0.621501i	$0.213477\pi$
$547$	15.6448	+	37.7699i	0.668924	+	1.61493i	−0.114490	+	0.993424i	$0.536523\pi$
$548$	23.1872	+	14.1785i	0.990508	+	0.605676i
$549$	41.7683	−	30.3465i	1.78263	−	1.29516i
$550$	24.6231	+	15.0728i	1.04993	+	0.642707i
$551$	−14.6496	+	20.1634i	−0.624093	+	0.858990i
$552$	−46.0917	−	53.8092i	−1.96179	−	2.29027i
$553$	0.138967	−	0.877405i	0.00590949	−	0.0373111i
$554$	−3.53849	−	3.53509i	−0.150336	−	0.150192i
$555$	3.57992	−	5.84189i	0.151959	−	0.247975i
$556$	2.43615	−	7.52227i	0.103316	−	0.319015i
$557$	−24.1211	+	1.89837i	−1.02204	+	0.0804365i	−0.578388	−	0.815762i	$-0.696318\pi$
$557$	−24.1211	+	1.89837i	−1.02204	+	0.0804365i	−0.443654	+	0.896198i	$0.646318\pi$
$558$	14.8050	−	0.00711217i	0.626747	−	0.000301082i
$559$	12.4613	−	10.6430i	0.527057	−	0.450149i
$560$	−0.217504	+	0.356469i	−0.00919120	+	0.0150636i
$561$	17.3885	−	10.6557i	0.734141	−	0.449882i
$562$	1.61730	−	1.89545i	0.0682215	−	0.0799548i
$563$	−15.8758	−	13.5592i	−0.669085	−	0.571452i	0.248676	−	0.968587i	$-0.420005\pi$
$563$	−15.8758	−	13.5592i	−0.669085	−	0.571452i	−0.917760	+	0.397135i	$0.870005\pi$
$564$	−0.00969888	−	10.0948i	−0.000408396	−	0.425068i
$565$	2.16074	−	2.16074i	0.0909028	−	0.0909028i
$566$	15.8486	+	2.50236i	0.666165	+	0.105182i
$567$	0.708095	−	0.169999i	0.0297372	−	0.00713927i
$568$	12.5195	−	20.4963i	0.525308	−	0.860005i
$569$	−6.92099	−	3.52642i	−0.290143	−	0.147835i	0.302861	−	0.953035i	$-0.402058\pi$
$569$	−6.92099	−	3.52642i	−0.290143	−	0.147835i	−0.593004	+	0.805199i	$0.702058\pi$
$570$	−4.79629	+	14.7856i	−0.200895	+	0.619302i
$571$	11.2416	+	4.65642i	0.470446	+	0.194865i	0.605295	−	0.796001i	$-0.293055\pi$
$571$	11.2416	+	4.65642i	0.470446	+	0.194865i	−0.134849	+	0.990866i	$0.543055\pi$
$572$	17.4185	+	34.1047i	0.728305	+	1.42599i
$573$			78.5375i			3.28095i
$574$	−0.932912	−	0.353487i	−0.0389390	−	0.0147543i
$575$		−	34.7852i		−	1.45064i
$576$	40.8757	+	20.6790i	1.70315	+	0.861626i
$577$	−15.7081	−	6.50651i	−0.653937	−	0.270869i	0.0309479	−	0.999521i	$-0.490147\pi$
$577$	−15.7081	−	6.50651i	−0.653937	−	0.270869i	−0.684885	+	0.728652i	$0.740147\pi$
$578$	−20.2797	−	6.57851i	−0.843525	−	0.273630i
$579$	−44.5421	−	22.6954i	−1.85111	−	0.943187i
$580$	−0.955321	−	11.9912i	−0.0396675	−	0.497907i
$581$	0.397904	−	0.0955282i	0.0165078	−	0.00396318i
$582$	4.92725	−	31.2064i	0.204241	−	1.29355i
$583$	−32.7496	+	32.7496i	−1.35635	+	1.35635i
$584$	22.4273	+	16.2450i	0.928047	+	0.672224i
$585$	−15.8749	−	13.5584i	−0.656345	−	0.560571i
$586$	−5.68259	−	4.84867i	−0.234746	−	0.200297i
$587$	6.79937	−	4.16666i	0.280640	−	0.171977i	−0.375054	−	0.927003i	$-0.622376\pi$
$587$	6.79937	−	4.16666i	0.280640	−	0.171977i	0.655694	+	0.755026i	$0.272376\pi$
$588$	−31.3670	+	26.8421i	−1.29355	+	1.10695i
$589$	5.45885	−	4.66230i	0.224928	−	0.192107i
$590$	−0.00446227	−	9.28888i	−0.000183709	−	0.382417i
$591$	26.1762	−	2.06012i	1.07675	−	0.0847418i
$592$	−9.79076	+	0.0188135i	−0.402398	+	0.000773230i
$593$	11.6907	−	19.0776i	0.480081	−	0.783421i	−0.517296	−	0.855807i	$-0.673061\pi$
$593$	11.6907	−	19.0776i	0.480081	−	0.783421i	0.997377	+	0.0723856i	$0.0230612\pi$
$594$	40.0566	−	40.0951i	1.64354	−	1.64512i
$595$	−0.0226554	+	0.143041i	−0.000928782	+	0.00586410i
$596$	−5.92534	+	24.7857i	−0.242711	+	1.01526i
$597$	16.3744	−	22.5374i	0.670159	−	0.922395i
$598$	24.0899	−	39.3536i	0.985111	−	1.60929i
$599$	12.7730	−	9.28014i	0.521891	−	0.379176i	−0.295425	−	0.955366i	$-0.595461\pi$
$599$	12.7730	−	9.28014i	0.521891	−	0.379176i	0.817316	+	0.576190i	$0.195461\pi$
$600$	13.1615	+	31.6456i	0.537317	+	1.29193i
$601$	10.4928	+	25.3318i	0.428009	+	1.03330i	0.979918	+	0.199400i	$0.0638994\pi$
$601$	10.4928	+	25.3318i	0.428009	+	1.03330i	−0.551909	+	0.833904i	$0.686101\pi$
$602$	−0.661590	−	0.0517485i	−0.0269644	−	0.00210911i
$603$	76.1780	+	5.99534i	3.10221	+	0.244149i
$604$	−11.4207	+	27.6471i	−0.464701	+	1.12494i
$605$	12.4064	+	4.03109i	0.504393	+	0.163887i
$606$	−4.88663	−	30.7573i	−0.198506	−	1.24943i
$607$	30.9083	−	15.7486i	1.25453	−	0.639215i	0.304840	−	0.952404i	$-0.401397\pi$
$607$	30.9083	−	15.7486i	1.25453	−	0.639215i	0.949691	+	0.313188i	$0.101397\pi$
$608$	21.5861	−	5.23724i	0.875434	−	0.212398i
$609$	−0.482221	+	2.00860i	−0.0195406	+	0.0813924i
$610$	5.49063	+	10.7632i	0.222309	+	0.435788i
$611$	6.25245	−	2.03154i	0.252947	−	0.0821874i
$612$	15.8392	+	1.23126i	0.640263	+	0.0497709i
$613$	3.15528	+	19.9217i	0.127441	+	0.804629i	0.965758	+	0.259446i	$0.0835399\pi$
$613$	3.15528	+	19.9217i	0.127441	+	0.804629i	−0.838317	+	0.545183i	$0.816460\pi$
$614$	−11.7976	−	8.56277i	−0.476111	−	0.345565i
$615$	14.9942	−	9.81959i	0.604626	−	0.395964i
$616$	0.477082	−	1.47554i	0.0192222	−	0.0594512i
$617$	−13.0740	+	2.07072i	−0.526339	+	0.0833640i	−0.413949	−	0.910300i	$-0.635851\pi$
$617$	−13.0740	+	2.07072i	−0.526339	+	0.0833640i	−0.112391	+	0.993664i	$0.535851\pi$
$618$	−33.5676	−	54.7182i	−1.35029	−	2.20109i
$619$	−3.89259	−	11.9801i	−0.156456	−	0.481523i	0.841849	−	0.539713i	$-0.181467\pi$
$619$	−3.89259	−	11.9801i	−0.156456	−	0.481523i	−0.998306	+	0.0581899i	$0.981467\pi$
$620$	−0.538736	+	3.42272i	−0.0216361	+	0.137460i
$621$	−66.4009	−	15.9415i	−2.66458	−	0.639708i
$622$	−4.85894	+	11.7465i	−0.194826	+	0.470991i
$623$	0.818725	+	1.60684i	0.0328015	+	0.0643766i
$624$	−7.02563	+	44.9166i	−0.281250	+	1.79810i
$625$	−3.81246	+	11.7335i	−0.152498	+	0.469341i
$626$	2.80073	+	11.6412i	0.111940	+	0.465278i
$627$	4.52903	−	57.5468i	0.180872	−	2.29820i
$628$	6.35366	−	7.45367i	0.253539	−	0.297434i
$629$	−3.13708	+	1.29942i	−0.125084	+	0.0518114i
$630$	0.0667338	+	0.842757i	0.00265874	+	0.0335762i
$631$	−12.4346	−	17.1148i	−0.495014	−	0.681329i	0.486289	−	0.873798i	$-0.338350\pi$
$631$	−12.4346	−	17.1148i	−0.495014	−	0.681329i	−0.981303	+	0.192470i	$0.938350\pi$
$632$	5.29212	−	22.1841i	0.210509	−	0.882435i
$633$	−10.0688	−	7.31543i	−0.400200	−	0.290762i
$634$	13.2321	−	5.48835i	0.525512	−	0.217970i
$635$	−2.74203	−	0.434295i	−0.108814	−	0.0172345i
$636$	−54.2979	+	8.65343i	−2.15305	+	0.343131i
$637$	−22.9243	−	14.0480i	−0.908292	−	0.556602i
$638$	13.8247	+	42.4786i	0.547325	+	1.68175i
$639$	−3.81490	−	48.4729i	−0.150915	−	1.91756i
$640$	−6.27230	+	8.69442i	−0.247935	+	0.343677i
$641$	−17.5831	−	20.5872i	−0.694492	−	0.813145i	0.295339	−	0.955392i	$-0.404567\pi$
$641$	−17.5831	−	20.5872i	−0.694492	−	0.813145i	−0.989831	+	0.142247i	$0.954567\pi$
$642$	7.04859	−	29.4217i	0.278186	−	1.16118i
$643$	−4.92157	−	8.03127i	−0.194088	−	0.316722i	0.740761	−	0.671769i	$-0.234465\pi$
$643$	−4.92157	−	8.03127i	−0.194088	−	0.316722i	−0.934849	+	0.355046i	$0.884465\pi$
$644$	−1.81643	+	0.437932i	−0.0715772	+	0.0172569i
$645$	7.74297	−	9.06586i	0.304879	−	0.356968i
$646$	6.23010	−	4.53101i	0.245120	−	0.178270i
$647$	28.7170	+	28.7170i	1.12898	+	1.12898i	0.990343	+	0.138638i	$0.0442724\pi$
$647$	28.7170	+	28.7170i	1.12898	+	1.12898i	0.138638	+	0.990343i	$0.455728\pi$
$648$	18.4612	−	2.95125i	0.725225	−	0.115936i
$649$	8.05275	+	33.5421i	0.316098	+	1.31664i
$650$	−16.9657	+	14.5041i	−0.665448	+	0.568899i
$651$	0.270121	−	0.530141i	0.0105869	−	0.0207779i
$652$	−7.79432	−	10.7063i	−0.305249	−	0.419292i
$653$	9.22147	−	22.2626i	0.360864	−	0.871203i	−0.634310	−	0.773079i	$-0.718716\pi$
$653$	9.22147	−	22.2626i	0.360864	−	0.871203i	0.995174	−	0.0981243i	$-0.0312843\pi$
$654$	−48.2333	−	24.5469i	−1.88607	−	0.959861i
$655$	8.56601			0.334702
$656$	−23.1807	−	10.8929i	−0.905054	−	0.425297i
$657$	56.0633			2.18724
$658$	−0.237261	−	0.120747i	−0.00924939	−	0.00470720i
$659$	0.838779	−	2.02499i	0.0326742	−	0.0788825i	−0.906700	−	0.421776i	$-0.861407\pi$
$659$	0.838779	−	2.02499i	0.0326742	−	0.0788825i	0.939374	+	0.342893i	$0.111407\pi$
$660$	16.3978	+	22.5240i	0.638282	+	0.876747i
$661$	12.9735	−	25.4619i	0.504610	−	0.990354i	−0.488433	−	0.872602i	$-0.662431\pi$
$661$	12.9735	−	25.4619i	0.504610	−	0.990354i	0.993043	−	0.117752i	$-0.0375688\pi$
$662$	8.52917	−	7.29169i	0.331496	−	0.283400i
$663$	3.68073	+	15.3314i	0.142948	+	0.595420i
$664$	10.3740	−	1.65841i	0.402589	−	0.0643588i
$665$	0.289862	+	0.289862i	0.0112404	+	0.0112404i
$666$	−16.0301	+	11.6583i	−0.621155	+	0.451751i
$667$	34.9560	−	40.9282i	1.35350	−	1.58475i
$668$	−16.6359	+	4.01084i	−0.643663	+	0.155184i
$669$	−4.83263	−	7.88614i	−0.186840	−	0.304896i
$670$	−4.16642	+	17.3912i	−0.160963	+	0.671879i
$671$	−29.1411	−	34.1199i	−1.12498	−	1.31718i
$672$	1.48679	−	1.08568i	0.0573540	−	0.0418810i
$673$	3.92773	+	49.9065i	0.151403	+	1.92375i	0.337686	+	0.941259i	$0.390356\pi$
$673$	3.92773	+	49.9065i	0.151403	+	1.92375i	−0.186283	+	0.982496i	$0.559644\pi$
$674$	−14.4598	−	44.4300i	−0.556971	−	1.71138i
$675$	28.1657	+	17.2600i	1.08410	+	0.664336i
$676$	−3.56244	+	0.567744i	−0.137017	+	0.0218363i
$677$	18.0913	+	2.86537i	0.695303	+	0.110125i	0.494075	−	0.869419i	$-0.335507\pi$
$677$	18.0913	+	2.86537i	0.695303	+	0.110125i	0.201228	+	0.979544i	$0.435507\pi$
$678$	−12.4437	+	5.16136i	−0.477898	+	0.198221i
$679$	−0.674046	−	0.489723i	−0.0258675	−	0.0187938i
$680$	−0.862759	+	3.61660i	−0.0330853	+	0.138690i
$681$	26.5779	+	36.5814i	1.01847	+	1.40180i
$682$	−1.01571	−	12.8270i	−0.0388934	−	0.491171i
$683$	−7.99419	+	3.31130i	−0.305889	+	0.126703i	−0.530348	−	0.847780i	$-0.677939\pi$
$683$	−7.99419	+	3.31130i	−0.305889	+	0.126703i	0.224459	+	0.974484i	$0.427939\pi$
$684$	29.1719	−	34.2224i	1.11541	−	1.30853i
$685$	−1.01032	+	12.8374i	−0.0386025	+	0.490491i
$686$	0.509783	+	2.11891i	0.0194636	+	0.0809005i
$687$	8.15312	−	25.0927i	0.311061	−	0.957347i
$688$	−16.8323	−	2.63283i	−0.641726	−	0.100376i
$689$	−16.2563	−	31.9048i	−0.619315	−	1.21548i
$690$	12.8314	−	31.0198i	0.488481	−	1.18090i
$691$	5.55028	+	1.33250i	0.211143	+	0.0506909i	0.337637	−	0.941276i	$-0.390372\pi$
$691$	5.55028	+	1.33250i	0.211143	+	0.0506909i	−0.126494	+	0.991967i	$0.540372\pi$
$692$	−2.63412	+	16.7353i	−0.100134	+	0.636179i
$693$	−0.970147	−	2.98581i	−0.0368529	−	0.113421i
$694$	−11.2876	−	18.3998i	−0.428471	−	0.698448i
$695$	3.70014	−	0.586044i	0.140354	−	0.0222299i
$696$	−16.3152	+	50.4603i	−0.618426	+	1.91269i
$697$	−8.87226	−	0.430757i	−0.336061	−	0.0163161i
$698$	27.5188	+	19.9734i	1.04160	+	0.756004i
$699$	−0.964838	−	6.09174i	−0.0364935	−	0.230411i
$700$	0.901136	+	0.0700499i	0.0340598	+	0.00264764i
$701$	8.28337	−	2.69143i	0.312859	−	0.101654i	−0.148379	−	0.988931i	$-0.547406\pi$
$701$	8.28337	−	2.69143i	0.312859	−	0.101654i	0.461238	+	0.887277i	$0.347406\pi$
$702$	19.9117	+	39.0325i	0.751517	+	1.47319i
$703$	−2.24369	+	9.34564i	−0.0846223	+	0.352477i
$704$	15.1296	−	36.8259i	0.570217	−	1.38793i
$705$	4.26157	−	2.17138i	0.160500	−	0.0817789i
$706$	7.58768	+	47.7583i	0.285566	+	1.79741i
$707$	−0.781103	−	0.253796i	−0.0293764	−	0.00954497i
$708$	−15.6350	+	37.8491i	−0.587600	+	1.42246i
$709$	−7.50583	−	0.590722i	−0.281887	−	0.0221850i	−0.0632727	−	0.997996i	$-0.520154\pi$
$709$	−7.50583	−	0.590722i	−0.281887	−	0.0221850i	−0.218615	+	0.975811i	$0.570154\pi$
$710$	11.3447	+	0.887363i	0.425759	+	0.0333021i
$711$	−17.6690	−	42.6569i	−0.662641	−	1.59976i
$712$	17.7795	+	42.7491i	0.666314	+	1.60209i
$713$	−12.5425	+	9.11267i	−0.469721	+	0.341272i
$714$	0.333341	−	0.544550i	0.0124750	−	0.0203793i
$715$	−10.6649	+	14.6789i	−0.398844	+	0.548961i
$716$	−1.11810	+	4.67701i	−0.0417853	+	0.174788i
$717$	−9.39234	+	59.3009i	−0.350763	+	2.21463i
$718$	4.81032	−	4.81495i	0.179520	−	0.179692i
$719$	−28.0153	+	45.7169i	−1.04480	+	1.70495i	−0.505640	+	0.862745i	$0.668743\pi$
$719$	−28.0153	+	45.7169i	−1.04480	+	1.70495i	−0.539156	+	0.842206i	$0.681257\pi$
$720$	0.0417054	+	21.7039i	0.00155427	+	0.808858i
$721$	−1.68769	+	0.132824i	−0.0628530	+	0.00494664i
$722$	0.00243321	+	5.06508i	9.05546e−5	+	0.188503i
$723$	21.4516	−	18.3214i	0.797795	−	0.681381i
$724$	12.5863	−	10.7707i	0.467768	−	0.400289i
$725$	−22.2001	+	13.6042i	−0.824491	+	0.505249i
$726$	−43.7490	−	37.3289i	−1.62368	−	1.38540i
$727$	12.9403	+	11.0521i	0.479930	+	0.409899i	0.856227	−	0.516600i	$-0.172803\pi$
$727$	12.9403	+	11.0521i	0.479930	+	0.409899i	−0.376297	+	0.926499i	$0.622803\pi$
$728$	0.970973	+	0.703317i	0.0359867	+	0.0260667i
$729$	−23.6991	+	23.6991i	−0.877746	+	0.877746i
$730$	−2.04630	+	12.9601i	−0.0757368	+	0.479675i
$731$	−5.74537	+	1.37934i	−0.212500	+	0.0510168i
$732$	−4.23042	−	53.1003i	−0.156361	−	1.96264i
$733$	30.1213	+	15.3476i	1.11255	+	0.566875i	0.910919	−	0.412586i	$-0.135374\pi$
$733$	30.1213	+	15.3476i	1.11255	+	0.566875i	0.201636	+	0.979461i	$0.435374\pi$
$734$	−13.6443	−	4.42605i	−0.503620	−	0.163369i
$735$	−18.0713	−	7.48539i	−0.666571	−	0.276103i
$736$	−47.3609	+	7.61788i	−1.74574	+	0.280799i
$737$		−	66.4115i		−	2.44630i
$738$	−50.9424	+	9.66981i	−1.87521	+	0.355951i
$739$		−	37.7525i		−	1.38875i	−0.719614	−	0.694375i	$-0.755681\pi$
$739$		−	37.7525i		−	1.38875i	0.719614	−	0.694375i	$-0.244319\pi$
$740$	−2.10995	−	4.13120i	−0.0775634	−	0.151866i
$741$	41.2317	+	17.0787i	1.51468	+	0.627402i
$742$	−0.447414	+	1.37925i	−0.0164251	+	0.0506340i
$743$	34.9323	+	17.7989i	1.28154	+	0.652979i	0.956227	−	0.292626i	$-0.0945292\pi$
$743$	34.9323	+	17.7989i	1.28154	+	0.652979i	0.325316	+	0.945605i	$0.394529\pi$
$744$	7.96256	−	13.0358i	0.291922	−	0.477917i
$745$	−11.7406	+	2.81868i	−0.430144	+	0.103268i
$746$	43.5428	+	6.87507i	1.59422	+	0.251714i
$747$	15.0392	−	15.0392i	0.550256	−	0.550256i
$748$	−0.0132659	−	13.8075i	−0.000485051	−	0.504852i
$749$	−0.606698	−	0.518169i	−0.0221683	−	0.0189335i
$750$	−23.3876	+	27.4100i	−0.853995	+	1.00087i
$751$	3.18419	−	1.95127i	0.116193	−	0.0712030i	−0.463188	−	0.886260i	$-0.653294\pi$
$751$	3.18419	−	1.95127i	0.116193	−	0.0712030i	0.579381	+	0.815057i	$0.303294\pi$
$752$	−5.83438	−	3.55991i	−0.212758	−	0.129817i
$753$	−23.3589	+	19.9504i	−0.851247	+	0.727033i
$754$	−34.5371	+	0.0165912i	−1.25777	+	0.000604217i
$755$	−14.1290	+	1.11197i	−0.514206	+	0.0404689i
$756$	0.546692	−	1.68806i	0.0198830	−	0.0613942i
$757$	13.4231	−	21.9044i	0.487869	−	0.796130i	−0.510081	−	0.860126i	$-0.670385\pi$
$757$	13.4231	−	21.9044i	0.487869	−	0.796130i	0.997950	+	0.0639961i	$0.0203845\pi$
$758$	−0.254373	−	0.254129i	−0.00923926	−	0.00923039i
$759$	−19.5014	+	123.127i	−0.707855	+	4.46922i
$760$	6.84640	+	7.99275i	0.248345	+	0.289927i
$761$	24.8723	−	34.2337i	0.901619	−	1.24097i	−0.0683303	−	0.997663i	$-0.521767\pi$
$761$	24.8723	−	34.2337i	0.901619	−	1.24097i	0.969949	−	0.243309i	$-0.0782328\pi$
$762$	10.4388	+	6.39001i	0.378158	+	0.231486i
$763$	−1.15467	+	0.838917i	−0.0418019	+	0.0303708i
$764$	45.3647	+	27.7396i	1.64124	+	1.00358i
$765$	2.88053	+	6.95422i	0.104146	+	0.251430i
$766$	−3.30461	+	42.2485i	−0.119400	+	1.52650i
$767$	−26.5872	−	2.09246i	−0.960007	−	0.0755542i
$768$	40.2039	−	24.8500i	1.45073	−	0.896698i
$769$	27.8884	+	9.06148i	1.00568	+	0.326765i	0.765133	−	0.643872i	$-0.222673\pi$
$769$	27.8884	+	9.06148i	1.00568	+	0.326765i	0.240547	+	0.970638i	$0.422673\pi$
$770$	0.725636	−	0.115287i	0.0261501	−	0.00415465i
$771$	−68.4383	+	34.8710i	−2.46474	+	1.25585i
$772$	−28.8416	+	17.7123i	−1.03803	+	0.637480i
$773$	−7.17856	+	29.9008i	−0.258195	+	1.07546i	0.681057	+	0.732230i	$0.261520\pi$
$773$	−7.17856	+	29.9008i	−0.258195	+	1.07546i	−0.939252	+	0.343228i	$0.888480\pi$
$774$	−30.7242	+	15.6734i	−1.10436	+	0.563368i
$775$	7.13256	−	2.31751i	0.256209	−	0.0832473i
$776$	−16.2851	−	13.8683i	−0.584601	−	0.497841i
$777$	0.124613	+	0.786778i	0.00447048	+	0.0282255i
$778$	9.27686	−	12.7814i	0.332591	−	0.458236i
$779$	−15.7475	+	19.6003i	−0.564214	+	0.702253i
$780$	−20.4794	+	6.67591i	−0.733278	+	0.239036i
$781$	−41.7381	+	6.61067i	−1.49351	+	0.236548i
$782$	−14.1807	+	8.69932i	−0.507101	+	0.311087i
$783$	15.7950	+	48.6120i	0.564467	+	1.73725i
$784$	4.42561	+	27.5989i	0.158058	+	0.985674i
$785$	4.51223	+	1.08329i	0.161048	+	0.0386643i
$786$	−34.8967	−	14.4351i	−1.24473	−	0.514882i
$787$	6.15270	+	12.0753i	0.219320	+	0.430440i	0.974283	−	0.225328i	$-0.0723453\pi$
$787$	6.15270	+	12.0753i	0.219320	+	0.430440i	−0.754963	+	0.655767i	$0.772345\pi$
$788$	8.05555	−	15.8475i	0.286967	−	0.564545i
$789$	2.95877	−	9.10616i	0.105335	−	0.324188i
$790$	10.5059	−	2.52757i	0.373782	−	0.0899270i
$791$	−0.0278743	+	0.354177i	−0.000991097	+	0.0125931i
$792$	−18.9286	−	78.3458i	−0.672599	−	2.78390i
$793$	32.0502	−	13.2756i	1.13814	−	0.471432i
$794$	33.6340	−	2.66331i	1.19363	−	0.0945175i
$795$	−15.3122	−	21.0755i	−0.543069	−	0.747471i
$796$	−7.23456	−	17.4184i	−0.256422	−	0.617380i
$797$	32.5159	+	23.6242i	1.15177	+	0.836812i	0.988716	−	0.149804i	$-0.0478643\pi$
$797$	32.5159	+	23.6242i	1.15177	+	0.836812i	0.163058	+	0.986617i	$0.447864\pi$
$798$	−0.692395	−	1.66932i	−0.0245105	−	0.0590933i
$799$	−2.34117	−	0.370804i	−0.0828245	−	0.0131181i
$800$	22.9278	+	3.57497i	0.810620	+	0.126394i
$801$	79.9191	+	48.9745i	2.82380	+	1.73043i
$802$	−30.9970	+	10.0880i	−1.09454	+	0.356220i
$803$	−3.82291	−	48.5747i	−0.134908	−	1.71416i
$804$	46.2802	−	63.8281i	1.63218	−	2.25104i
$805$	−0.574939	−	0.673167i	−0.0202639	−	0.0237260i
$806$	9.67425	+	2.31767i	0.340761	+	0.0816363i
$807$	−20.7013	−	33.7814i	−0.728720	−	1.18916i
$808$	−19.4920	−	8.04095i	−0.685725	−	0.282880i
$809$	23.2708	−	27.2466i	0.818156	−	0.957938i	−0.181520	−	0.983387i	$-0.558102\pi$
$809$	23.2708	−	27.2466i	0.818156	−	0.957938i	0.999676	+	0.0254494i	$0.00810166\pi$
$810$	5.20998	+	7.16368i	0.183060	+	0.251706i
$811$	26.6597	+	26.6597i	0.936150	+	0.936150i	0.998080	−	0.0619308i	$-0.0197258\pi$
$811$	26.6597	+	26.6597i	0.936150	+	0.936150i	−0.0619308	+	0.998080i	$0.519726\pi$
$812$	0.989881	+	0.987981i	0.0347380	+	0.0346713i
$813$	−6.89240	−	28.7089i	−0.241727	−	1.00687i
$814$	11.1942	+	13.0939i	0.392356	+	0.458943i
$815$	2.84854	−	5.59058i	0.0997802	−	0.195830i
$816$	9.60930	−	13.2796i	0.336393	−	0.464881i
$817$	−6.40019	+	15.4514i	−0.223914	+	0.540577i
$818$	1.34439	−	2.64166i	0.0470056	−	0.0923634i
$819$	2.42722			0.0848139
$820$	−0.375978	−	12.1293i	−0.0131297	−	0.423572i
$821$	−14.2574			−0.497587			−0.248794	−	0.968557i	$-0.580034\pi$
$821$	−14.2574			−0.497587			−0.248794	+	0.968557i	$0.580034\pi$
$822$	25.7489	−	50.5952i	0.898097	−	1.76471i
$823$	16.5169	−	39.8752i	0.575741	−	1.38996i	−0.320861	−	0.947126i	$-0.603972\pi$
$823$	16.5169	−	39.8752i	0.575741	−	1.38996i	0.896602	−	0.442837i	$-0.146028\pi$
$824$	−43.4624	+	0.0626366i	−1.51408	+	0.00218205i
$825$	27.3774	−	53.7311i	0.953157	−	1.87068i
$826$	0.701773	+	0.820872i	0.0244178	+	0.0285618i
$827$	−1.18082	−	4.91849i	−0.0410613	−	0.171033i	0.948072	−	0.318057i	$-0.103030\pi$
$827$	−1.18082	−	4.91849i	−0.0410613	−	0.171033i	−0.989133	+	0.147024i	$0.953030\pi$
$828$	−68.6037	+	68.7356i	−2.38414	+	2.38873i
$829$	−38.3739	−	38.3739i	−1.33278	−	1.33278i	−0.902874	−	0.429905i	$-0.858547\pi$
$829$	−38.3739	−	38.3739i	−1.33278	−	1.33278i	−0.429905	−	0.902874i	$-0.641453\pi$
$830$	2.92767	+	4.02553i	0.101621	+	0.139728i
$831$	−6.78522	+	7.94447i	−0.235377	+	0.275591i
$832$	23.4632	+	19.9228i	0.813439	+	0.690698i
$833$	5.06504	+	8.26540i	0.175493	+	0.286379i
$834$	−16.0614	−	3.84784i	−0.556161	−	0.133240i
$835$	−5.26563	−	6.16526i	−0.182225	−	0.213358i
$836$	−31.6404	−	22.9417i	−1.09431	−	0.793455i
$837$	−1.15513	−	14.6773i	−0.0399271	−	0.507321i
$838$	−0.673850	+	0.219305i	−0.0232777	+	0.00757576i
$839$	28.1847	+	17.2716i	0.973042	+	0.596281i	0.915610	−	0.402068i	$-0.131709\pi$
$839$	28.1847	+	17.2716i	0.973042	+	0.596281i	0.0574327	+	0.998349i	$0.481709\pi$
$840$	0.777750	+	0.394873i	0.0268349	+	0.0136244i
$841$	−11.1486	−	1.76577i	−0.384436	−	0.0608887i
$842$	−4.29766	−	10.3614i	−0.148107	−	0.357077i
$843$	−4.21058	−	3.05917i	−0.145020	−	0.105363i
$844$	−7.78186	+	3.23211i	−0.267863	+	0.111254i
$845$	−1.00462	−	1.38274i	−0.0345601	−	0.0475679i
$846$	−13.7935	+	1.09224i	−0.474231	+	0.0375520i
$847$	−1.40120	+	0.580397i	−0.0481459	+	0.0199427i
$848$	−14.1798	+	34.4199i	−0.486935	+	1.18198i
$849$	2.62952	−	33.4112i	0.0902447	−	1.14667i
$850$	7.82444	−	1.88246i	0.268376	−	0.0645678i
$851$	6.41403	−	19.7403i	0.219870	−	0.676690i
$852$	−44.7213	−	22.7326i	−1.53213	−	0.778805i
$853$	−2.37991	−	4.67083i	−0.0814865	−	0.159926i	0.846668	−	0.532122i	$-0.178605\pi$
$853$	−2.37991	−	4.67083i	−0.0814865	−	0.159926i	−0.928154	+	0.372195i	$0.878605\pi$
$854$	−1.29811	−	0.536966i	−0.0444205	−	0.0183746i
$855$	20.7172	+	4.97376i	0.708513	+	0.170099i
$856$	−14.5050	−	14.4632i	−0.495770	−	0.494343i
$857$	9.04358	+	27.8333i	0.308923	+	0.950767i	0.978184	+	0.207740i	$0.0666107\pi$
$857$	9.04358	+	27.8333i	0.308923	+	0.950767i	−0.669261	+	0.743027i	$0.733389\pi$
$858$	68.1835	−	41.8280i	2.32775	−	1.42798i
$859$	−26.5021	+	4.19753i	−0.904241	+	0.143218i	−0.591203	−	0.806523i	$-0.701347\pi$
$859$	−26.5021	+	4.19753i	−0.904241	+	0.143218i	−0.313038	+	0.949741i	$0.601347\pi$
$860$	−2.50177	−	7.67457i	−0.0853097	−	0.261701i
$861$	−0.584156	+	2.00030i	−0.0199080	+	0.0681701i
$862$	5.87649	−	8.09647i	0.200154	−	0.275767i
$863$	2.59351	+	16.3748i	0.0882841	+	0.557404i	0.991693	+	0.128625i	$0.0410563\pi$
$863$	2.59351	+	16.3748i	0.0882841	+	0.557404i	−0.903409	+	0.428779i	$0.858944\pi$
$864$	17.3316	−	42.1281i	0.589633	−	1.43323i
$865$	−7.63385	+	2.48039i	−0.259559	+	0.0843357i
$866$	−35.0589	+	17.8846i	−1.19135	+	0.607745i
$867$	−10.3960	+	43.3027i	−0.353068	+	1.47064i
$868$	−0.210812	−	0.343274i	−0.00715544	−	0.0116515i
$869$	−35.7542	+	18.2177i	−1.21288	+	0.617992i
$870$	−24.8152	+	3.94257i	−0.841315	+	0.133666i
$871$	48.8318	+	15.8664i	1.65460	+	0.537613i
$872$	−31.2149	+	19.1904i	−1.05707	+	0.649870i
$873$	−43.1702	−	3.39757i	−1.46109	−	0.114990i
$874$	−3.67207	+	46.9464i	−0.124210	+	1.58799i
$875$	0.363635	+	0.877893i	0.0122931	+	0.0296782i
$876$	30.1761	−	49.3493i	1.01956	−	1.66736i
$877$	−24.8517	+	18.0558i	−0.839182	+	0.609701i	−0.922142	−	0.386852i	$-0.873563\pi$
$877$	−24.8517	+	18.0558i	−0.839182	+	0.609701i	0.0829603	+	0.996553i	$0.473563\pi$
$878$	−36.0851	−	22.0891i	−1.21781	−	0.745472i
$879$	−9.17142	+	12.6234i	−0.309344	+	0.425776i
$880$	18.8020	−	1.51611i	0.633816	−	0.0511080i
$881$	1.50040	−	9.47314i	0.0505497	−	0.319158i	−0.949437	−	0.313958i	$-0.898345\pi$
$881$	1.50040	−	9.47314i	0.0505497	−	0.319158i	0.999986	−	0.00519991i	$-0.00165519\pi$
$882$	40.0324	+	39.9940i	1.34796	+	1.34667i
$883$	−4.97743	+	8.12243i	−0.167504	+	0.273342i	−0.925367	−	0.379072i	$-0.876243\pi$
$883$	−4.97743	+	8.12243i	−0.167504	+	0.273342i	0.757863	+	0.652413i	$0.226243\pi$
$884$	10.1557	+	3.28901i	0.341574	+	0.110621i
$885$	−19.3427	+	1.52231i	−0.650198	+	0.0511717i
$886$	48.4793	−	0.0232889i	1.62869	−	0.000782406i
$887$	−29.9820	+	25.6071i	−1.00670	+	0.859801i	−0.990143	−	0.140062i	$-0.955270\pi$
$887$	−29.9820	+	25.6071i	−1.00670	+	0.859801i	−0.0165547	+	0.999863i	$0.505270\pi$
$888$	1.63394	+	20.3855i	0.0548314	+	0.684093i
$889$	0.275209	−	0.168649i	0.00923023	−	0.00565629i
$890$	−14.2384	+	16.6873i	−0.477273	+	0.559358i
$891$	−25.0133	−	21.3634i	−0.837978	−	0.715701i
$892$	−6.26208	+	0.00601647i	−0.209670	+	0.000201446i
$893$	−4.74421	+	4.74421i	−0.158759	+	0.158759i
$894$	52.5796	+	8.30191i	1.75853	+	0.277657i
$895$	−2.21544	+	0.531879i	−0.0740538	+	0.0177788i
$896$	−0.101972	−	1.24226i	−0.00340665	−	0.0415010i
$897$	−85.8751	−	43.7556i	−2.86729	−	1.46096i
$898$	13.7115	−	42.2689i	0.457560	−	1.41053i
$899$	10.7210	+	4.44080i	0.357566	+	0.148109i
$900$	41.8370	−	21.3677i	1.39457	−	0.712255i
$901$			12.9105i			0.430111i
$902$	11.8519	+	43.4785i	0.394625	+	1.44767i
$903$			1.38614i			0.0461280i
$904$	−1.41385	+	9.01072i	−0.0470239	+	0.299692i
$905$	7.25132	+	3.00359i	0.241042	+	0.0998428i
$906$	59.4333	+	19.2795i	1.97454	+	0.640519i
$907$	8.22924	+	4.19301i	0.273247	+	0.139226i	0.585245	−	0.810856i	$-0.300998\pi$
$907$	8.22924	+	4.19301i	0.273247	+	0.139226i	−0.311998	+	0.950083i	$0.600998\pi$
$908$	30.5175	−	2.43128i	1.01276	−	0.0806850i
$909$	−41.5075	+	9.96508i	−1.37672	+	0.330521i
$910$	−0.0885930	+	0.561098i	−0.00293683	+	0.0186002i
$911$	25.3510	−	25.3510i	0.839916	−	0.839916i	−0.148932	−	0.988847i	$-0.547583\pi$
$911$	25.3510	−	25.3510i	0.839916	−	0.839916i	0.988847	+	0.148932i	$0.0475835\pi$
$912$	−14.4222	−	44.0986i	−0.477568	−	1.46025i
$913$	−14.0559	−	12.0048i	−0.465181	−	0.397303i
$914$	5.35403	+	4.56833i	0.177096	+	0.151107i
$915$	21.5192	−	13.1870i	0.711404	−	0.435949i
$916$	−11.6143	−	13.5722i	−0.383748	−	0.448438i
$917$	−0.757302	+	0.646797i	−0.0250083	+	0.0213591i
$918$	−0.00758950	−	15.7987i	−0.000250491	−	0.521433i
$919$	−41.1320	+	3.23716i	−1.35682	+	0.106784i	−0.735900	−	0.677090i	$-0.763241\pi$
$919$	−41.1320	+	3.23716i	−1.35682	+	0.106784i	−0.620920	+	0.783874i	$0.713241\pi$
$920$	−13.3855	−	18.3679i	−0.441308	−	0.605571i
$921$	−15.9097	+	25.9623i	−0.524244	+	0.855488i
$922$	−24.7573	+	24.7811i	−0.815339	+	0.816122i
$923$	5.11092	−	32.2691i	0.168228	−	1.06215i
$924$	−3.15042	−	0.753148i	−0.103641	−	0.0247767i
$925$	−5.90173	+	8.12303i	−0.194048	+	0.267084i
$926$	−2.76181	+	4.51172i	−0.0907586	+	0.148264i
$927$	−71.1845	+	51.7186i	−2.33801	+	1.69866i
$928$	23.3843	+	27.2467i	0.767626	+	0.894415i
$929$	−1.82622	−	4.40889i	−0.0599164	−	0.144651i	0.891086	−	0.453834i	$-0.149944\pi$
$929$	−1.82622	−	4.40889i	−0.0599164	−	0.144651i	−0.951002	+	0.309184i	$0.899944\pi$
$930$	7.21534	+	0.564372i	0.236600	+	0.0185065i
$931$	27.3542	+	2.15282i	0.896497	+	0.0705559i
$932$	−3.85949	−	1.59431i	−0.126422	−	0.0522233i
$933$	25.2527	+	8.20509i	0.826735	+	0.268623i
$934$	−3.45083	−	21.7202i	−0.112915	−	0.710706i
$935$	5.82890	−	2.96997i	0.190625	−	0.0971285i
$936$	62.1293	+	4.79960i	2.03076	+	0.156880i
$937$	7.65210	−	31.8733i	0.249983	−	1.04125i	−0.696258	−	0.717792i	$-0.745153\pi$
$937$	7.65210	−	31.8733i	0.249983	−	1.04125i	0.946241	−	0.323463i	$-0.104847\pi$
$938$	−0.944818	−	1.85211i	−0.0308494	−	0.0604735i
$939$	23.7859	−	7.72850i	0.776223	−	0.252210i
$940$	0.250968	−	3.22850i	0.00818567	−	0.105302i
$941$	−2.48502	−	15.6898i	−0.0810093	−	0.511472i	−0.994511	−	0.104637i	$-0.966632\pi$
$941$	−2.48502	−	15.6898i	−0.0810093	−	0.511472i	0.913501	−	0.406836i	$-0.133368\pi$
$942$	−16.5567	−	12.0170i	−0.539445	−	0.391534i
$943$	37.2244	−	39.5298i	1.21219	−	1.28727i
$944$	16.3400	+	22.3995i	0.531823	+	0.729041i
$945$	0.830342	−	0.131513i	0.0270110	−	0.00427813i
$946$	15.6749	+	25.5515i	0.509635	+	0.830752i
$947$	−11.9316	−	36.7217i	−0.387725	−	1.19329i	−0.934484	−	0.356004i	$-0.884139\pi$
$947$	−11.9316	−	36.7217i	−0.387725	−	1.19329i	0.546760	−	0.837289i	$-0.315861\pi$
$948$	−47.0588	−	7.40704i	−1.52840	−	0.240569i
$949$	36.6300	+	8.79407i	1.18906	+	0.285468i
$950$	8.70712	−	21.0494i	0.282496	−	0.682934i
$951$	−13.5844	−	26.6609i	−0.440504	−	0.864538i
$952$	−0.196805	−	0.384880i	−0.00637850	−	0.0124740i
$953$	−2.81289	+	8.65718i	−0.0911184	+	0.280434i	−0.986223	−	0.165423i	$-0.947101\pi$
$953$	−2.81289	+	8.65718i	−0.0911184	+	0.280434i	0.895104	+	0.445857i	$0.147101\pi$
$954$	17.6286	+	73.2731i	0.570746	+	2.37231i
$955$	−1.97665	+	25.1158i	−0.0639630	+	0.812728i
$956$	30.9359	+	26.3704i	1.00054	+	0.852879i
$957$	86.2070	−	35.7081i	2.78668	−	1.15428i
$958$	4.16180	+	52.5579i	0.134462	+	1.69807i
$959$	−0.879997	−	1.21121i	−0.0284166	−	0.0391121i
$960$	19.1272	+	11.6455i	0.617327	+	0.375855i
$961$	22.3754	+	16.2567i	0.721787	+	0.524409i
$962$	−12.3023	+	5.10270i	−0.396642	+	0.164518i
$963$	−40.9582	−	6.48714i	−1.31986	−	0.209045i
$964$	−3.00603	−	18.8620i	−0.0968178	−	0.607505i
$965$	−13.6731	−	8.37888i	−0.440152	−	0.269726i
$966$	1.20783	+	3.71125i	0.0388613	+	0.119407i
$967$	2.00306	+	25.4512i	0.0644139	+	0.818457i	0.941259	+	0.337684i	$0.109644\pi$
$967$	2.00306	+	25.4512i	0.0644139	+	0.818457i	−0.876845	+	0.480772i	$0.840356\pi$
$968$	−37.0141	+	12.0856i	−1.18968	+	0.388446i
$969$	−10.4503	−	12.2357i	−0.335712	−	0.393068i
$970$	2.36112	−	9.85561i	0.0758109	−	0.316445i
$971$	−6.28006	−	10.2481i	−0.201537	−	0.328878i	0.735865	−	0.677128i	$-0.236776\pi$
$971$	−6.28006	−	10.2481i	−0.201537	−	0.328878i	−0.937401	+	0.348251i	$0.886776\pi$
$972$	2.17178	+	9.00796i	0.0696597	+	0.288930i
$973$	−0.282870	+	0.331198i	−0.00906840	+	0.0106177i
$974$	25.9379	−	18.8640i	0.831104	−	0.604443i
$975$	32.9673	+	32.9673i	1.05580	+	1.05580i
$976$	−32.1659	−	16.3116i	−1.02961	−	0.522120i
$977$	1.37335	+	5.72040i	0.0439373	+	0.183012i	0.990023	−	0.140903i	$-0.0450007\pi$
$977$	1.37335	+	5.72040i	0.0439373	+	0.183012i	−0.946086	+	0.323915i	$0.895001\pi$
$978$	−21.0256	+	17.9750i	−0.672324	+	0.574778i
$979$	36.9832	−	72.5836i	1.18199	−	2.31978i
$980$	−10.7065	+	7.79448i	−0.342008	+	0.248986i
$981$	−28.3879	+	68.5345i	−0.906356	+	2.18814i
$982$	28.9230	+	14.7195i	0.922969	+	0.469718i
$983$	−4.67885			−0.149232			−0.0746161	−	0.997212i	$-0.523773\pi$
$983$	−4.67885			−0.149232			−0.0746161	+	0.997212i	$0.523773\pi$
$984$	−18.9080	+	50.0465i	−0.602765	+	1.59542i
$985$	8.42284			0.268374
$986$	11.0979	+	5.64796i	0.353430	+	0.179868i
$987$	−0.212801	+	0.513747i	−0.00677353	+	0.0163527i
$988$	24.4281	−	17.7839i	0.777161	−	0.565782i
$989$	16.3972	−	32.1814i	0.521402	−	1.02331i
$990$	29.0264	−	24.8150i	0.922519	−	0.788672i
$991$	−2.27738	−	9.48596i	−0.0723433	−	0.301331i	0.924455	−	0.381292i	$-0.124521\pi$
$991$	−2.27738	−	9.48596i	−0.0723433	−	0.301331i	−0.996798	+	0.0799603i	$0.974521\pi$
$992$	−4.71735	−	9.20361i	−0.149776	−	0.292215i
$993$	−16.5737	−	16.5737i	−0.525951	−	0.525951i
$994$	−1.06996	+	0.778157i	−0.0339371	+	0.0246817i
$995$	5.80365	−	6.79521i	0.183988	−	0.215422i
$996$	−5.14329	−	21.3330i	−0.162971	−	0.675962i
$997$	6.10450	+	9.96164i	0.193332	+	0.315488i	0.934587	−	0.355735i	$-0.115769\pi$
$997$	6.10450	+	9.96164i	0.193332	+	0.315488i	−0.741255	+	0.671223i	$0.765769\pi$
$998$	2.37988	−	9.93393i	0.0753337	−	0.314453i
$999$	12.8013	+	14.9884i	0.405014	+	0.474211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	164.2.o.b.11.2	✓	288
4.3	odd	2	inner	164.2.o.b.11.5	yes	288
41.15	odd	40	inner	164.2.o.b.15.5	yes	288
164.15	even	40	inner	164.2.o.b.15.2	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
164.2.o.b.11.2	✓	288	1.1	even	1	trivial
164.2.o.b.11.5	yes	288	4.3	odd	2	inner
164.2.o.b.15.2	yes	288	164.15	even	40	inner
164.2.o.b.15.5	yes	288	41.15	odd	40	inner

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:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	164.o (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26038 - 0.641434i) q^{2} +(-1.13045 + 2.72914i) q^{3} +(1.17712 + 1.61690i) q^{4} +(-0.430197 + 0.844309i) q^{5} +(3.17535 - 2.71465i) q^{6} +(-0.0257188 - 0.107126i) q^{7} +(-0.446489 - 2.79296i) q^{8} +(-4.04896 - 4.04896i) q^{9} +O(q^{10})\)	\(q+(-1.26038 - 0.641434i) q^{2} +(-1.13045 + 2.72914i) q^{3} +(1.17712 + 1.61690i) q^{4} +(-0.430197 + 0.844309i) q^{5} +(3.17535 - 2.71465i) q^{6} +(-0.0257188 - 0.107126i) q^{7} +(-0.446489 - 2.79296i) q^{8} +(-4.04896 - 4.04896i) q^{9} +(1.08378 - 0.788209i) q^{10} +(-3.23203 + 3.78422i) q^{11} +(-5.74343 + 1.38471i) q^{12} +(-2.01034 - 3.28058i) q^{13} +(-0.0362991 + 0.151517i) q^{14} +(-1.81792 - 2.12851i) q^{15} +(-1.22876 + 3.80659i) q^{16} +(0.108842 + 1.38297i) q^{17} +(2.50610 + 7.70038i) q^{18} +(3.34801 + 2.05166i) q^{19} +(-1.87156 + 0.298270i) q^{20} +(0.321437 + 0.0509106i) q^{21} +(6.50093 - 2.69643i) q^{22} +(-6.86039 - 4.98437i) q^{23} +(8.12711 + 1.93876i) q^{24} +(2.41114 + 3.31865i) q^{25} +(0.429523 + 5.42429i) q^{26} +(7.43989 - 3.08170i) q^{27} +(0.142939 - 0.167686i) q^{28} +(-0.498000 + 6.32769i) q^{29} +(0.925974 + 3.84881i) q^{30} +(0.564960 - 1.73877i) q^{31} +(3.99038 - 4.00960i) q^{32} +(-6.67403 - 13.0985i) q^{33} +(0.749902 - 1.81289i) q^{34} +(0.101512 + 0.0243709i) q^{35} +(1.78065 - 11.3129i) q^{36} +(0.756379 + 2.32790i) q^{37} +(-2.90376 - 4.73340i) q^{38} +(11.2257 - 1.77798i) q^{39} +(2.55020 + 0.824550i) q^{40} +(-0.811348 + 6.35151i) q^{41} +(-0.372477 - 0.270347i) q^{42} +(0.666293 + 4.20681i) q^{43} +(-9.92323 - 0.771383i) q^{44} +(5.16043 - 1.67672i) q^{45} +(5.44957 + 10.6827i) q^{46} +(-0.398882 + 1.66146i) q^{47} +(-8.99968 - 7.65659i) q^{48} +(6.22623 - 3.17242i) q^{49} +(-0.910261 - 5.72935i) q^{50} +(-3.89736 - 1.26633i) q^{51} +(2.93796 - 7.11218i) q^{52} +(9.27788 + 0.730185i) q^{53} +(-11.3538 - 0.888077i) q^{54} +(-1.80464 - 4.35680i) q^{55} +(-0.287717 + 0.119662i) q^{56} +(-9.38400 + 6.81788i) q^{57} +(4.68646 - 7.65587i) q^{58} +(4.07424 - 5.60771i) q^{59} +(1.30168 - 5.44493i) q^{60} +(-1.41047 + 8.90534i) q^{61} +(-1.82737 + 1.82913i) q^{62} +(-0.329617 + 0.537885i) q^{63} +(-7.60130 + 2.49406i) q^{64} +(3.63467 - 0.286055i) q^{65} +(0.00998733 + 20.7901i) q^{66} +(-10.1475 + 8.66675i) q^{67} +(-2.10801 + 1.80392i) q^{68} +(21.3583 - 13.0884i) q^{69} +(-0.112312 - 0.0958299i) q^{70} +(6.45694 + 5.51475i) q^{71} +(-9.50079 + 13.1164i) q^{72} +(-6.92317 + 6.92317i) q^{73} +(0.539865 - 3.41920i) q^{74} +(-11.7827 + 2.82878i) q^{75} +(0.623682 + 7.82846i) q^{76} +(0.488515 + 0.248911i) q^{77} +(-15.2892 - 4.95964i) q^{78} +(7.44955 + 3.08571i) q^{79} +(-2.68534 - 2.67503i) q^{80} +6.60990i q^{81} +(5.09668 - 7.48491i) q^{82} +3.71433i q^{83} +(0.296053 + 0.579660i) q^{84} +(-1.21448 - 0.503053i) q^{85} +(1.85861 - 5.72957i) q^{86} +(-16.7062 - 8.51221i) q^{87} +(12.0123 + 7.33734i) q^{88} +(-15.9169 + 3.82130i) q^{89} +(-7.57962 - 1.19676i) q^{90} +(-0.299734 + 0.299734i) q^{91} +(-0.0162946 - 16.9598i) q^{92} +(4.10668 + 3.50744i) q^{93} +(1.56846 - 1.83822i) q^{94} +(-3.17254 + 1.94413i) q^{95} +(6.43183 + 15.4229i) q^{96} +(5.75058 - 4.91146i) q^{97} +(-9.88233 + 0.00474736i) q^{98} +(28.4086 - 2.23580i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9}+O(q^{10}) \) 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9	\( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9} - 12 q^{10} - 8 q^{12} - 24 q^{13} - 4 q^{14} - 28 q^{16} - 12 q^{18} - 44 q^{20} - 32 q^{21} - 40 q^{22} + 8 q^{24} - 40 q^{25} + 4 q^{26} - 48 q^{29} - 44 q^{30} + 108 q^{32} - 72 q^{33} + 12 q^{34} - 20 q^{36} - 24 q^{37} + 56 q^{38} + 8 q^{41} - 112 q^{42} - 40 q^{45} - 48 q^{46} - 68 q^{48} - 16 q^{49} - 60 q^{50} - 124 q^{52} - 64 q^{53} + 64 q^{54} - 84 q^{56} - 24 q^{57} + 40 q^{60} - 8 q^{61} - 44 q^{62} - 20 q^{64} + 64 q^{65} + 60 q^{66} - 28 q^{68} - 8 q^{69} + 128 q^{70} + 160 q^{72} - 32 q^{73} + 80 q^{74} + 288 q^{76} - 32 q^{77} + 116 q^{78} + 176 q^{80} + 212 q^{82} + 152 q^{84} - 56 q^{85} + 180 q^{86} + 144 q^{88} - 72 q^{89} + 224 q^{90} + 36 q^{92} - 8 q^{93} + 52 q^{94} + 136 q^{96} - 88 q^{97} + 104 q^{98}+O(q^{100}) \) 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9 - 12 * q^10 - 8 * q^12 - 24 * q^13 - 4 * q^14 - 28 * q^16 - 12 * q^18 - 44 * q^20 - 32 * q^21 - 40 * q^22 + 8 * q^24 - 40 * q^25 + 4 * q^26 - 48 * q^29 - 44 * q^30 + 108 * q^32 - 72 * q^33 + 12 * q^34 - 20 * q^36 - 24 * q^37 + 56 * q^38 + 8 * q^41 - 112 * q^42 - 40 * q^45 - 48 * q^46 - 68 * q^48 - 16 * q^49 - 60 * q^50 - 124 * q^52 - 64 * q^53 + 64 * q^54 - 84 * q^56 - 24 * q^57 + 40 * q^60 - 8 * q^61 - 44 * q^62 - 20 * q^64 + 64 * q^65 + 60 * q^66 - 28 * q^68 - 8 * q^69 + 128 * q^70 + 160 * q^72 - 32 * q^73 + 80 * q^74 + 288 * q^76 - 32 * q^77 + 116 * q^78 + 176 * q^80 + 212 * q^82 + 152 * q^84 - 56 * q^85 + 180 * q^86 + 144 * q^88 - 72 * q^89 + 224 * q^90 + 36 * q^92 - 8 * q^93 + 52 * q^94 + 136 * q^96 - 88 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more