LMFDB - Embedded newform 224.2.be.a.115.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(3,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 4]))

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

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

chi := DirichletCharacter("224.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.be (of order $24$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			115.2
Character	$\chi$	$=$	224.115
Dual form			224.2.be.a.187.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41368 + 0.0389436i) q^{2} +(0.788053 + 1.02701i) q^{3} +(1.99697 - 0.110107i) q^{4} +(1.15943 - 1.51100i) q^{5} +(-1.15405 - 1.42117i) q^{6} +(0.624522 - 2.57099i) q^{7} +(-2.81878 + 0.233426i) q^{8} +(0.342734 - 1.27910i) q^{9} +O(q^{10})$	\(q+(-1.41368 + 0.0389436i) q^{2} +(0.788053 + 1.02701i) q^{3} +(1.99697 - 0.110107i) q^{4} +(1.15943 - 1.51100i) q^{5} +(-1.15405 - 1.42117i) q^{6} +(0.624522 - 2.57099i) q^{7} +(-2.81878 + 0.233426i) q^{8} +(0.342734 - 1.27910i) q^{9} +(-1.58022 + 2.18122i) q^{10} +(0.664765 - 5.04939i) q^{11} +(1.68680 + 1.96413i) q^{12} +(-2.64057 + 6.37490i) q^{13} +(-0.782748 + 3.65887i) q^{14} +2.46550 q^{15} +(3.97575 - 0.439762i) q^{16} +(0.520718 - 0.901911i) q^{17} +(-0.434703 + 1.82158i) q^{18} +(-0.185877 - 1.41188i) q^{19} +(2.14897 - 3.14507i) q^{20} +(3.13259 - 1.38468i) q^{21} +(-0.743121 + 7.16409i) q^{22} +(3.16081 + 0.846936i) q^{23} +(-2.46108 - 2.71096i) q^{24} +(0.355257 + 1.32584i) q^{25} +(3.48465 - 9.11488i) q^{26} +(5.17168 - 2.14218i) q^{27} +(0.964064 - 5.20294i) q^{28} +(-1.14636 + 2.76757i) q^{29} +(-3.48542 + 0.0960156i) q^{30} +(-1.53764 + 2.66328i) q^{31} +(-5.60331 + 0.776512i) q^{32} +(5.70964 - 3.29646i) q^{33} +(-0.701004 + 1.29529i) q^{34} +(-3.16067 - 3.92453i) q^{35} +(0.543590 - 2.59206i) q^{36} +(7.90414 + 6.06506i) q^{37} +(0.317754 + 1.98870i) q^{38} +(-8.62799 + 2.31186i) q^{39} +(-2.91547 + 4.52981i) q^{40} +(0.859509 - 0.859509i) q^{41} +(-4.37454 + 2.07949i) q^{42} +(-5.93649 + 2.45898i) q^{43} +(0.771537 - 10.1567i) q^{44} +(-1.53534 - 2.00090i) q^{45} +(-4.50135 - 1.07420i) q^{46} +(-1.27846 + 0.738121i) q^{47} +(3.58474 + 3.73658i) q^{48} +(-6.21995 - 3.21127i) q^{49} +(-0.553852 - 1.86047i) q^{50} +(1.33663 - 0.175970i) q^{51} +(-4.57120 + 13.0212i) q^{52} +(-8.48833 - 1.11751i) q^{53} +(-7.22766 + 3.22975i) q^{54} +(-6.85887 - 6.85887i) q^{55} +(-1.16025 + 7.39282i) q^{56} +(1.30353 - 1.30353i) q^{57} +(1.51281 - 3.95709i) q^{58} +(-1.46984 + 11.1645i) q^{59} +(4.92353 - 0.271470i) q^{60} +(1.68729 + 12.8162i) q^{61} +(2.07001 - 3.82489i) q^{62} +(-3.07451 - 1.67999i) q^{63} +(7.89102 - 1.31595i) q^{64} +(6.57090 + 11.3811i) q^{65} +(-7.94321 + 4.88249i) q^{66} +(7.53594 - 5.78253i) q^{67} +(0.940550 - 1.85842i) q^{68} +(1.62107 + 3.91361i) q^{69} +(4.62100 + 5.42493i) q^{70} +(-8.22460 - 8.22460i) q^{71} +(-0.667517 + 3.68551i) q^{72} +(0.468243 + 1.74751i) q^{73} +(-11.4101 - 8.26622i) q^{74} +(-1.08169 + 1.40968i) q^{75} +(-0.526649 - 2.79901i) q^{76} +(-12.5667 - 4.86255i) q^{77} +(12.1072 - 3.60423i) q^{78} +(-6.23642 - 10.8018i) q^{79} +(3.94513 - 6.51723i) q^{80} +(2.83516 + 1.63688i) q^{81} +(-1.18160 + 1.24854i) q^{82} +(5.52119 + 2.28695i) q^{83} +(6.10321 - 3.11009i) q^{84} +(-0.759049 - 1.83251i) q^{85} +(8.29652 - 3.70739i) q^{86} +(-3.74571 + 1.00366i) q^{87} +(-0.695168 + 14.3883i) q^{88} +(2.58953 - 9.66427i) q^{89} +(2.24840 + 2.76883i) q^{90} +(14.7407 + 10.7701i) q^{91} +(6.40528 + 1.34327i) q^{92} +(-3.94696 + 0.519627i) q^{93} +(1.77859 - 1.09325i) q^{94} +(-2.34886 - 1.35611i) q^{95} +(-5.21319 - 5.14272i) q^{96} -8.78032i q^{97} +(8.91805 + 4.29748i) q^{98} +(-6.23084 - 2.58090i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9	$ 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 12 q^{28} - 16 q^{29} - 52 q^{30} - 4 q^{32} - 24 q^{33} - 32 q^{35} + 64 q^{36} - 4 q^{37} - 12 q^{38} - 4 q^{39} - 12 q^{40} - 28 q^{42} - 32 q^{43} - 52 q^{44} - 48 q^{45} - 4 q^{46} - 24 q^{47} - 40 q^{50} + 20 q^{51} + 60 q^{52} - 20 q^{53} - 12 q^{54} - 48 q^{56} - 16 q^{57} - 36 q^{58} + 84 q^{59} + 28 q^{60} - 12 q^{61} - 136 q^{64} - 8 q^{65} + 132 q^{66} + 36 q^{67} - 12 q^{68} + 28 q^{70} - 80 q^{71} - 4 q^{72} - 12 q^{73} - 20 q^{74} - 72 q^{75} - 8 q^{77} - 216 q^{78} - 8 q^{79} + 24 q^{80} + 108 q^{82} + 12 q^{84} + 24 q^{85} - 4 q^{86} - 12 q^{87} - 48 q^{88} - 12 q^{89} + 40 q^{91} - 80 q^{92} + 20 q^{93} + 60 q^{94} + 312 q^{96} - 16 q^{98} - 40 q^{99}+O(q^{100}) $ 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 12 * q^10 - 4 * q^11 - 12 * q^12 - 40 * q^14 - 32 * q^15 - 24 * q^16 + 16 * q^18 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^29 - 52 * q^30 - 4 * q^32 - 24 * q^33 - 32 * q^35 + 64 * q^36 - 4 * q^37 - 12 * q^38 - 4 * q^39 - 12 * q^40 - 28 * q^42 - 32 * q^43 - 52 * q^44 - 48 * q^45 - 4 * q^46 - 24 * q^47 - 40 * q^50 + 20 * q^51 + 60 * q^52 - 20 * q^53 - 12 * q^54 - 48 * q^56 - 16 * q^57 - 36 * q^58 + 84 * q^59 + 28 * q^60 - 12 * q^61 - 136 * q^64 - 8 * q^65 + 132 * q^66 + 36 * q^67 - 12 * q^68 + 28 * q^70 - 80 * q^71 - 4 * q^72 - 12 * q^73 - 20 * q^74 - 72 * q^75 - 8 * q^77 - 216 * q^78 - 8 * q^79 + 24 * q^80 + 108 * q^82 + 12 * q^84 + 24 * q^85 - 4 * q^86 - 12 * q^87 - 48 * q^88 - 12 * q^89 + 40 * q^91 - 80 * q^92 + 20 * q^93 + 60 * q^94 + 312 * q^96 - 16 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{8}\right)$

Coefficient data

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

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

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

$2$	−1.41368	+	0.0389436i	−0.999621	+	0.0275373i
$2$	−1.41368	+	0.0389436i	−0.999621	+	0.0275373i
$3$	0.788053	+	1.02701i	0.454982	+	0.592945i	0.963367	−	0.268185i	$-0.0864239\pi$
$3$	0.788053	+	1.02701i	0.454982	+	0.592945i	−0.508385	+	0.861130i	$0.669757\pi$
$4$	1.99697	−	0.110107i	0.998483	−	0.0550537i
$5$	1.15943	−	1.51100i	0.518513	−	0.675739i	−0.458555	−	0.888666i	$-0.651633\pi$
$5$	1.15943	−	1.51100i	0.518513	−	0.675739i	0.977068	+	0.212927i	$0.0682996\pi$
$6$	−1.15405	−	1.42117i	−0.471138	−	0.580191i
$7$	0.624522	−	2.57099i	0.236047	−	0.971742i
$7$	0.624522	−	2.57099i	0.236047	−	0.971742i
$8$	−2.81878	+	0.233426i	−0.996589	+	0.0825284i
$9$	0.342734	−	1.27910i	0.114245	−	0.426367i
$10$	−1.58022	+	2.18122i	−0.499708	+	0.689761i
$11$	0.664765	−	5.04939i	0.200434	−	1.52245i	−0.535000	−	0.844852i	$-0.679689\pi$
$11$	0.664765	−	5.04939i	0.200434	−	1.52245i	0.735434	−	0.677596i	$-0.236978\pi$
$12$	1.68680	+	1.96413i	0.486936	+	0.566997i
$13$	−2.64057	+	6.37490i	−0.732362	+	1.76808i	−0.0978003	+	0.995206i	$0.531181\pi$
$13$	−2.64057	+	6.37490i	−0.732362	+	1.76808i	−0.634562	+	0.772872i	$0.718819\pi$
$14$	−0.782748	+	3.65887i	−0.209198	+	0.977873i
$15$	2.46550			0.636590
$16$	3.97575	−	0.439762i	0.993938	−	0.109940i
$17$	0.520718	−	0.901911i	0.126293	−	0.218745i	−0.795945	−	0.605369i	$-0.793025\pi$
$17$	0.520718	−	0.901911i	0.126293	−	0.218745i	0.922238	+	0.386624i	$0.126359\pi$
$18$	−0.434703	+	1.82158i	−0.102460	+	0.429351i
$19$	−0.185877	−	1.41188i	−0.0426432	−	0.323907i	−0.999449	−	0.0331805i	$-0.989436\pi$
$19$	−0.185877	−	1.41188i	−0.0426432	−	0.323907i	0.956806	−	0.290726i	$-0.0938970\pi$
$20$	2.14897	−	3.14507i	0.480524	−	0.703260i
$21$	3.13259	−	1.38468i	0.683586	−	0.302163i
$22$	−0.743121	+	7.16409i	−0.158434	+	1.52739i
$23$	3.16081	+	0.846936i	0.659074	+	0.176598i	0.572828	−	0.819675i	$-0.305846\pi$
$23$	3.16081	+	0.846936i	0.659074	+	0.176598i	0.0862461	+	0.996274i	$0.472513\pi$
$24$	−2.46108	−	2.71096i	−0.502365	−	0.553373i
$25$	0.355257	+	1.32584i	0.0710514	+	0.265168i
$26$	3.48465	−	9.11488i	0.683396	−	1.78758i
$27$	5.17168	−	2.14218i	0.995290	−	0.412263i
$28$	0.964064	−	5.20294i	0.182191	−	0.983263i
$29$	−1.14636	+	2.76757i	−0.212874	+	0.513924i	−0.993863	−	0.110621i	$-0.964716\pi$
$29$	−1.14636	+	2.76757i	−0.212874	+	0.513924i	0.780988	+	0.624546i	$0.214716\pi$
$30$	−3.48542	+	0.0960156i	−0.636348	+	0.0175300i
$31$	−1.53764	+	2.66328i	−0.276169	+	0.478339i	−0.970429	−	0.241385i	$-0.922398\pi$
$31$	−1.53764	+	2.66328i	−0.276169	+	0.478339i	0.694260	+	0.719724i	$0.255732\pi$
$32$	−5.60331	+	0.776512i	−0.990534	+	0.137269i
$33$	5.70964	−	3.29646i	0.993921	−	0.573841i
$34$	−0.701004	+	1.29529i	−0.120221	+	0.222140i
$35$	−3.16067	−	3.92453i	−0.534250	−	0.663366i
$36$	0.543590	−	2.59206i	0.0905983	−	0.432010i
$37$	7.90414	+	6.06506i	1.29943	+	0.997090i	0.999064	+	0.0432669i	$0.0137766\pi$
$37$	7.90414	+	6.06506i	1.29943	+	0.997090i	0.300369	+	0.953823i	$0.402890\pi$
$38$	0.317754	+	1.98870i	0.0515465	+	0.322610i
$39$	−8.62799	+	2.31186i	−1.38158	+	0.370194i
$40$	−2.91547	+	4.52981i	−0.460976	+	0.716226i
$41$	0.859509	−	0.859509i	0.134233	−	0.134233i	−0.636798	−	0.771031i	$-0.719741\pi$
$41$	0.859509	−	0.859509i	0.134233	−	0.134233i	0.771031	+	0.636798i	$0.219741\pi$
$42$	−4.37454	+	2.07949i	−0.675006	+	0.320872i
$43$	−5.93649	+	2.45898i	−0.905307	+	0.374990i	−0.786258	−	0.617898i	$-0.787984\pi$
$43$	−5.93649	+	2.45898i	−0.905307	+	0.374990i	−0.119049	+	0.992888i	$0.537984\pi$
$44$	0.771537	−	10.1567i	0.116314	−	1.53117i
$45$	−1.53534	−	2.00090i	−0.228875	−	0.298276i
$46$	−4.50135	−	1.07420i	−0.663687	−	0.158382i
$47$	−1.27846	+	0.738121i	−0.186483	+	0.107666i	−0.590335	−	0.807158i	$-0.701004\pi$
$47$	−1.27846	+	0.738121i	−0.186483	+	0.107666i	0.403852	+	0.914824i	$0.367671\pi$
$48$	3.58474	+	3.73658i	0.517413	+	0.539329i
$49$	−6.21995	−	3.21127i	−0.888564	−	0.458753i
$50$	−0.553852	−	1.86047i	−0.0783265	−	0.263110i
$51$	1.33663	−	0.175970i	0.187165	−	0.0246407i
$52$	−4.57120	+	13.0212i	−0.633912	+	1.80572i
$53$	−8.48833	−	1.11751i	−1.16596	−	0.153502i	−0.477404	−	0.878684i	$-0.658422\pi$
$53$	−8.48833	−	1.11751i	−1.16596	−	0.153502i	−0.688557	+	0.725182i	$0.741756\pi$
$54$	−7.22766	+	3.22975i	−0.983560	+	0.439514i
$55$	−6.85887	−	6.85887i	−0.924849	−	0.924849i
$56$	−1.16025	+	7.39282i	−0.155045	+	0.987907i
$57$	1.30353	−	1.30353i	0.172657	−	0.172657i
$58$	1.51281	−	3.95709i	0.198642	−	0.519591i
$59$	−1.46984	+	11.1645i	−0.191357	+	1.45350i	0.578709	+	0.815534i	$0.303557\pi$
$59$	−1.46984	+	11.1645i	−0.191357	+	1.45350i	−0.770066	+	0.637965i	$0.779777\pi$
$60$	4.92353	−	0.271470i	0.635624	−	0.0350467i
$61$	1.68729	+	12.8162i	0.216035	+	1.64095i	0.664600	+	0.747199i	$0.268602\pi$
$61$	1.68729	+	12.8162i	0.216035	+	1.64095i	−0.448565	+	0.893750i	$0.648065\pi$
$62$	2.07001	−	3.82489i	0.262892	−	0.485762i
$63$	−3.07451	−	1.67999i	−0.387352	−	0.211659i
$64$	7.89102	−	1.31595i	0.986378	−	0.164494i
$65$	6.57090	+	11.3811i	0.815020	+	1.41166i
$66$	−7.94321	+	4.88249i	−0.977742	+	0.600993i
$67$	7.53594	−	5.78253i	0.920662	−	0.706449i	−0.0354746	−	0.999371i	$-0.511294\pi$
$67$	7.53594	−	5.78253i	0.920662	−	0.706449i	0.956136	+	0.292922i	$0.0946276\pi$
$68$	0.940550	−	1.85842i	0.114058	−	0.225367i
$69$	1.62107	+	3.91361i	0.195154	+	0.471144i
$70$	4.62100	+	5.42493i	0.552315	+	0.648403i
$71$	−8.22460	−	8.22460i	−0.976081	−	0.976081i	0.0236400	−	0.999721i	$-0.492474\pi$
$71$	−8.22460	−	8.22460i	−0.976081	−	0.976081i	−0.999721	+	0.0236400i	$0.992474\pi$
$72$	−0.667517	+	3.68551i	−0.0786676	+	0.434341i
$73$	0.468243	+	1.74751i	0.0548037	+	0.204530i	0.987899	−	0.155099i	$-0.0495698\pi$
$73$	0.468243	+	1.74751i	0.0548037	+	0.204530i	−0.933095	+	0.359629i	$0.882903\pi$
$74$	−11.4101	−	8.26622i	−1.32640	−	0.960929i
$75$	−1.08169	+	1.40968i	−0.124903	+	0.162776i
$76$	−0.526649	−	2.79901i	−0.0604108	−	0.321068i
$77$	−12.5667	−	4.86255i	−1.43211	−	0.554139i
$78$	12.1072	−	3.60423i	1.37087	−	0.408099i
$79$	−6.23642	−	10.8018i	−0.701652	−	1.21530i	−0.967886	−	0.251389i	$-0.919113\pi$
$79$	−6.23642	−	10.8018i	−0.701652	−	1.21530i	0.266234	−	0.963909i	$-0.414221\pi$
$80$	3.94513	−	6.51723i	0.441078	−	0.728648i
$81$	2.83516	+	1.63688i	0.315018	+	0.181876i
$82$	−1.18160	+	1.24854i	−0.130485	+	0.137878i
$83$	5.52119	+	2.28695i	0.606030	+	0.251026i	0.664530	−	0.747262i	$-0.268632\pi$
$83$	5.52119	+	2.28695i	0.606030	+	0.251026i	−0.0585001	+	0.998287i	$0.518632\pi$
$84$	6.10321	−	3.11009i	0.665914	−	0.339338i
$85$	−0.759049	−	1.83251i	−0.0823304	−	0.198763i
$86$	8.29652	−	3.70739i	0.894637	−	0.399778i
$87$	−3.74571	+	1.00366i	−0.401583	+	0.107604i
$88$	−0.695168	+	14.3883i	−0.0741051	+	1.53380i
$89$	2.58953	−	9.66427i	0.274490	−	1.02441i	−0.681692	−	0.731639i	$-0.738756\pi$
$89$	2.58953	−	9.66427i	0.274490	−	1.02441i	0.956182	−	0.292772i	$-0.0945777\pi$
$90$	2.24840	+	2.76883i	0.237002	+	0.291861i
$91$	14.7407	+	10.7701i	1.54524	+	1.12902i
$92$	6.40528	+	1.34327i	0.667797	+	0.140046i
$93$	−3.94696	+	0.519627i	−0.409280	+	0.0538828i
$94$	1.77859	−	1.09325i	0.183447	−	0.112760i
$95$	−2.34886	−	1.35611i	−0.240988	−	0.139134i
$96$	−5.21319	−	5.14272i	−0.532068	−	0.524877i
$97$		−	8.78032i		−	0.891506i	−0.895156	−	0.445753i	$-0.852936\pi$
$97$		−	8.78032i		−	0.891506i	0.895156	−	0.445753i	$-0.147064\pi$
$98$	8.91805	+	4.29748i	0.900860	+	0.434111i
$99$	−6.23084	−	2.58090i	−0.626223	−	0.259390i
$100$	0.855421	+	2.60854i	0.0855421	+	0.260854i
$101$	1.79812	+	0.236727i	0.178919	+	0.0235552i	0.219453	−	0.975623i	$-0.429573\pi$
$101$	1.79812	+	0.236727i	0.178919	+	0.0235552i	−0.0405341	+	0.999178i	$0.512906\pi$
$102$	−1.88270	+	0.300818i	−0.186415	+	0.0297854i
$103$	3.33372	+	0.893268i	0.328481	+	0.0880163i	0.419291	−	0.907852i	$-0.362279\pi$
$103$	3.33372	+	0.893268i	0.328481	+	0.0880163i	−0.0908095	+	0.995868i	$0.528945\pi$
$104$	5.95511	−	18.5858i	0.583947	−	1.82249i
$105$	1.53976	−	6.33877i	0.150265	−	0.618601i
$106$	12.0433	+	1.24923i	1.16975	+	0.121336i
$107$	−3.34486	−	2.56660i	−0.323360	−	0.248123i	0.434306	−	0.900765i	$-0.356994\pi$
$107$	−3.34486	−	2.56660i	−0.323360	−	0.248123i	−0.757666	+	0.652643i	$0.773660\pi$
$108$	10.0918	−	4.84730i	0.971084	−	0.466432i
$109$	2.89312	−	2.21997i	0.277111	−	0.212635i	−0.460850	−	0.887478i	$-0.652455\pi$
$109$	2.89312	−	2.21997i	0.277111	−	0.212635i	0.737961	+	0.674843i	$0.235789\pi$
$110$	9.96333	+	9.42911i	0.949967	+	0.899031i
$111$			12.8972i			1.22415i
$112$	1.35232	−	10.4962i	0.127782	−	0.991802i
$113$			12.3773i			1.16436i	0.813061	+	0.582178i	$0.197800\pi$
$113$			12.3773i			1.16436i	−0.813061	+	0.582178i	$0.802200\pi$
$114$	−1.79201	+	1.89354i	−0.167837	+	0.177346i
$115$	4.94445	−	3.79401i	0.461073	−	0.353794i
$116$	−1.98452	+	5.65296i	−0.184258	+	0.524864i
$117$	7.24913	+	5.56245i	0.670182	+	0.514249i
$118$	1.64309	−	15.8403i	0.151259	−	1.45822i
$119$	−1.99360	−	1.90202i	−0.182753	−	0.174358i
$120$	−6.94970	+	0.575511i	−0.634418	+	0.0525367i
$121$	−14.4292	−	3.86630i	−1.31175	−	0.351482i
$122$	−2.88439	−	18.0523i	−0.261140	−	1.63438i
$123$	1.56006	+	0.205386i	0.140666	+	0.0185190i
$124$	−2.77738	+	5.48778i	−0.249416	+	0.492817i
$125$	11.2132	+	4.64466i	1.00294	+	0.415431i
$126$	4.41179	+	2.25523i	0.393033	+	0.200912i
$127$			2.70749i			0.240251i	0.992759	+	0.120126i	$0.0383297\pi$
$127$			2.70749i			0.240251i	−0.992759	+	0.120126i	$0.961670\pi$
$128$	−11.1041	+	2.16763i	−0.981474	+	0.191594i
$129$	−7.20366	−	4.15904i	−0.634247	−	0.366183i
$130$	−9.73236	−	15.8334i	−0.853584	−	1.38868i
$131$	−4.67087	+	0.614931i	−0.408096	+	0.0537268i	−0.331780	−	0.943357i	$-0.607649\pi$
$131$	−4.67087	+	0.614931i	−0.408096	+	0.0537268i	−0.0763159	+	0.997084i	$0.524316\pi$
$132$	11.0390	−	7.21160i	0.960822	−	0.627689i
$133$	−3.74600	−	0.403860i	−0.324820	−	0.0350191i
$134$	−10.4282	+	8.46811i	−0.900859	+	0.731533i
$135$	2.75937	−	10.2981i	0.237489	−	0.886320i
$136$	−1.25726	+	2.66384i	−0.107809	+	0.228422i
$137$	−2.77832	+	0.744450i	−0.237368	+	0.0636026i	−0.375542	−	0.926805i	$-0.622543\pi$
$137$	−2.77832	+	0.744450i	−0.237368	+	0.0636026i	0.138174	+	0.990408i	$0.455877\pi$
$138$	−2.44408	−	5.46946i	−0.208054	−	0.465591i
$139$	4.39928	+	10.6208i	0.373142	+	0.900844i	0.993214	+	0.116300i	$0.0371033\pi$
$139$	4.39928	+	10.6208i	0.373142	+	0.900844i	−0.620072	+	0.784545i	$0.712897\pi$
$140$	−6.74387	−	7.48914i	−0.569961	−	0.632948i
$141$	−1.76555	−	0.731316i	−0.148686	−	0.0615880i
$142$	11.9472	+	11.3066i	1.00259	+	0.948832i
$143$	30.4340	+	17.5711i	2.54502	+	1.46937i
$144$	0.800126	−	5.23611i	0.0666772	−	0.436343i
$145$	2.85266	+	4.94095i	0.236901	+	0.410324i
$146$	−0.729999	−	2.45217i	−0.0604151	−	0.202943i
$147$	−1.60363	−	8.91860i	−0.132266	−	0.735594i
$148$	16.4521	+	11.2414i	1.35236	+	0.924039i
$149$	1.60857	−	2.09633i	0.131779	−	0.171738i	−0.722803	−	0.691054i	$-0.757147\pi$
$149$	1.60857	−	2.09633i	0.131779	−	0.171738i	0.854582	+	0.519316i	$0.173813\pi$
$150$	1.47426	−	2.03496i	0.120373	−	0.166154i
$151$	0.341777	+	1.27553i	0.0278134	+	0.103801i	0.978437	−	0.206545i	$-0.0662219\pi$
$151$	0.341777	+	1.27553i	0.0278134	+	0.103801i	−0.950624	+	0.310346i	$0.899555\pi$
$152$	0.853515	+	3.93638i	0.0692292	+	0.319283i
$153$	−0.975167	−	0.975167i	−0.0788376	−	0.0788376i
$154$	17.9547	+	6.38468i	1.44683	+	0.514493i
$155$	2.24142	+	5.41126i	0.180035	+	0.434643i
$156$	−16.9753	+	5.56672i	−1.35911	+	0.445694i
$157$	−18.9690	+	14.5554i	−1.51389	+	1.16165i	−0.574646	+	0.818402i	$0.694860\pi$
$157$	−18.9690	+	14.5554i	−1.51389	+	1.16165i	−0.939245	+	0.343247i	$0.888473\pi$
$158$	9.23695	+	15.0274i	0.734852	+	1.19552i
$159$	−5.54156	−	9.59826i	−0.439474	−	0.761191i
$160$	−5.32333	+	9.36689i	−0.420846	+	0.740518i
$161$	4.15146	−	7.59747i	0.327181	−	0.598764i
$162$	−4.07175	−	2.20361i	−0.319907	−	0.173132i
$163$	0.732554	+	5.56430i	0.0573781	+	0.435830i	0.995889	+	0.0905806i	$0.0288723\pi$
$163$	0.732554	+	5.56430i	0.0573781	+	0.435830i	−0.938511	+	0.345249i	$0.887794\pi$
$164$	1.62177	−	1.81105i	0.126639	−	0.141419i
$165$	1.63898	−	12.4493i	0.127594	−	0.969175i
$166$	−7.89425	−	3.01800i	−0.612713	−	0.234242i
$167$	−8.02123	+	8.02123i	−0.620702	+	0.620702i	−0.945711	−	0.325009i	$-0.894633\pi$
$167$	−8.02123	+	8.02123i	−0.620702	+	0.620702i	0.325009	+	0.945711i	$0.394633\pi$
$168$	−8.50684	+	4.63434i	−0.656317	+	0.357547i
$169$	−24.4743	−	24.4743i	−1.88264	−	1.88264i
$170$	1.14441	+	2.56101i	0.0877726	+	0.196421i
$171$	−1.86964	−	0.246143i	−0.142975	−	0.0188230i
$172$	−11.5842	+	5.56415i	−0.883289	+	0.424262i
$173$	2.40205	−	0.316235i	0.182624	−	0.0240429i	−0.0386593	−	0.999252i	$-0.512309\pi$
$173$	2.40205	−	0.316235i	0.182624	−	0.0240429i	0.221284	+	0.975210i	$0.428975\pi$
$174$	5.25615	−	1.56472i	0.398467	−	0.118621i
$175$	3.63058	−	0.0853472i	0.274446	−	0.00645164i
$176$	0.422411	−	20.3675i	0.0318404	−	1.53525i
$177$	−12.6244	+	7.28870i	−0.948908	+	0.547853i
$178$	−3.28440	+	13.7630i	−0.246176	+	1.03158i
$179$	6.72543	+	8.76475i	0.502682	+	0.655108i	0.973918	−	0.226899i	$-0.0728588\pi$
$179$	6.72543	+	8.76475i	0.502682	+	0.655108i	−0.471236	+	0.882007i	$0.656192\pi$
$180$	−3.28634	−	3.82667i	−0.244950	−	0.285223i
$181$	2.76075	−	1.14354i	0.205205	−	0.0849987i	−0.277714	−	0.960664i	$-0.589577\pi$
$181$	2.76075	−	1.14354i	0.205205	−	0.0849987i	0.482919	+	0.875665i	$0.339577\pi$
$182$	−21.2580	−	14.6514i	−1.57575	−	1.08604i
$183$	−11.8327	+	11.8327i	−0.874700	+	0.874700i
$184$	−9.10732	−	1.64951i	−0.671400	−	0.121604i
$185$	18.3286	−	4.91113i	1.34754	−	0.361074i
$186$	5.55949	−	0.888293i	0.407641	−	0.0651328i
$187$	−4.20794	−	3.22887i	−0.307715	−	0.236118i
$188$	−2.47178	+	1.61477i	−0.180273	+	0.117769i
$189$	−2.27769	−	14.6342i	−0.165678	−	1.06448i
$190$	3.37334	+	1.82563i	0.244727	+	0.132445i
$191$	5.51336	−	3.18314i	0.398933	−	0.230324i	−0.287090	−	0.957903i	$-0.592688\pi$
$191$	5.51336	−	3.18314i	0.398933	−	0.230324i	0.686023	+	0.727579i	$0.259355\pi$
$192$	7.57004	+	7.06713i	0.546320	+	0.510026i
$193$	−0.647141	+	1.12088i	−0.0465823	+	0.0806828i	−0.888376	−	0.459116i	$-0.848166\pi$
$193$	−0.647141	+	1.12088i	−0.0465823	+	0.0806828i	0.841794	+	0.539799i	$0.181500\pi$
$194$	0.341938	+	12.4125i	0.0245497	+	0.891168i
$195$	−6.51033	+	15.7173i	−0.466214	+	1.12554i
$196$	−12.7746	−	5.72794i	−0.912472	−	0.409139i
$197$	−1.64133	+	0.679859i	−0.116940	+	0.0484380i	−0.440386	−	0.897808i	$-0.645158\pi$
$197$	−1.64133	+	0.679859i	−0.116940	+	0.0484380i	0.323446	+	0.946246i	$0.395158\pi$
$198$	8.90891	+	3.40591i	0.633128	+	0.242047i
$199$	2.39258	+	8.92924i	0.169606	+	0.632977i	0.997408	+	0.0719569i	$0.0229244\pi$
$199$	2.39258	+	8.92924i	0.169606	+	0.632977i	−0.827802	+	0.561020i	$0.810409\pi$
$200$	−1.31088	−	3.65432i	−0.0926929	−	0.258399i
$201$	11.8774	+	3.18255i	0.837770	+	0.224480i
$202$	−2.55118	−	0.264630i	−0.179500	−	0.0186193i
$203$	6.39945	+	4.67569i	0.449153	+	0.328169i
$204$	2.64982	−	0.498579i	0.185525	−	0.0349075i
$205$	−0.302176	−	2.29526i	−0.0211049	−	0.160308i
$206$	−4.74759	−	1.13297i	−0.330780	−	0.0789374i
$207$	2.16663	−	3.75272i	0.150592	−	0.260832i
$208$	−7.69481	+	26.5062i	−0.533539	+	1.83788i
$209$	−7.25268			−0.501678
$210$	−1.92987	+	9.02094i	−0.133174	+	0.622504i
$211$	7.65203	−	18.4736i	0.526788	−	1.27178i	−0.406829	−	0.913504i	$-0.633365\pi$
$211$	7.65203	−	18.4736i	0.526788	−	1.27178i	0.933617	−	0.358274i	$-0.116635\pi$
$212$	−17.0740	−	1.29700i	−1.17264	−	0.0890784i
$213$	1.96533	−	14.9282i	0.134662	−	1.02286i
$214$	4.82851	+	3.49809i	0.330070	+	0.239124i
$215$	−3.16744	+	11.8210i	−0.216017	+	0.806188i
$216$	−14.0778	+	7.24553i	−0.957871	+	0.492996i
$217$	5.88696	+	5.61653i	0.399633	+	0.381275i
$218$	−4.00349	+	3.25099i	−0.271150	+	0.220185i
$219$	−1.42571	+	1.85802i	−0.0963403	+	0.125553i
$220$	−14.4521	−	12.9417i	−0.974363	−	0.872530i
$221$	4.37460	+	5.70108i	0.294267	+	0.383496i
$222$	−0.502265	−	18.2325i	−0.0337098	−	1.22369i
$223$	5.44239			0.364449			0.182225	−	0.983257i	$-0.441670\pi$
$223$	5.44239			0.364449			0.182225	+	0.983257i	$0.441670\pi$
$224$	−1.50298	+	14.8910i	−0.100422	+	0.994945i
$225$	1.81764			0.121176
$226$	−0.482017	−	17.4975i	−0.0320633	−	1.16392i
$227$	0.130527	+	0.170106i	0.00866337	+	0.0112903i	0.797665	−	0.603101i	$-0.206068\pi$
$227$	0.130527	+	0.170106i	0.00866337	+	0.0112903i	−0.789002	+	0.614391i	$0.789402\pi$
$228$	2.45958	−	2.74664i	0.162890	−	0.181901i
$229$	12.9967	−	16.9376i	0.858844	−	1.11927i	−0.132913	−	0.991128i	$-0.542433\pi$
$229$	12.9967	−	16.9376i	0.858844	−	1.11927i	0.991756	−	0.128139i	$-0.0409003\pi$
$230$	−6.84211	+	5.55607i	−0.451155	+	0.366356i
$231$	−4.90937	−	16.7381i	−0.323013	−	1.10129i
$232$	2.58532	−	8.06875i	0.169735	−	0.529739i
$233$	−1.04716	+	3.90806i	−0.0686017	+	0.256025i	−0.991706	−	0.128523i	$-0.958976\pi$
$233$	−1.04716	+	3.90806i	−0.0686017	+	0.256025i	0.923105	+	0.384549i	$0.125643\pi$
$234$	−10.4645	−	7.58120i	−0.684089	−	0.495599i
$235$	−0.366988	+	2.78755i	−0.0239397	+	0.181840i
$236$	−1.70592	+	22.4571i	−0.111046	+	1.46183i
$237$	6.17893	−	14.9173i	0.401365	−	0.968980i
$238$	2.89238	+	2.61121i	0.187485	+	0.169259i
$239$	−2.73300			−0.176783			−0.0883915	−	0.996086i	$-0.528173\pi$
$239$	−2.73300			−0.176783			−0.0883915	+	0.996086i	$0.528173\pi$
$240$	9.80223	−	1.08423i	0.632731	−	0.0699870i
$241$	7.50863	−	13.0053i	0.483673	−	0.837747i	−0.516151	−	0.856498i	$-0.672636\pi$
$241$	7.50863	−	13.0053i	0.483673	−	0.837747i	0.999824	+	0.0187508i	$0.00596890\pi$
$242$	20.5488	+	4.90377i	1.32093	+	0.315226i
$243$	−1.63881	−	12.4480i	−0.105130	−	0.798539i
$244$	4.78062	+	25.4078i	0.306048	+	1.62657i
$245$	−12.0638	+	5.67508i	−0.770729	+	0.362568i
$246$	−2.21342	−	0.229595i	−0.141123	−	0.0146384i
$247$	9.49140	+	2.54321i	0.603923	+	0.161821i
$248$	3.71260	−	7.86611i	0.235750	−	0.499499i
$249$	2.00227	+	7.47256i	0.126889	+	0.473554i
$250$	−16.0327	−	6.12937i	−1.01400	−	0.387655i
$251$	−22.8325	+	9.45753i	−1.44117	+	0.596954i	−0.960083	−	0.279716i	$-0.909760\pi$
$251$	−22.8325	+	9.45753i	−1.44117	+	0.596954i	−0.481092	+	0.876670i	$0.659760\pi$
$252$	−6.32467	−	3.01636i	−0.398417	−	0.190013i
$253$	6.37770	−	15.3971i	0.400963	−	0.968010i
$254$	−0.105440	−	3.82752i	−0.00661587	−	0.240160i
$255$	1.28383	−	2.22366i	0.0803967	−	0.139251i
$256$	15.6132	−	3.49677i	0.975826	−	0.218548i
$257$	11.9243	−	6.88450i	0.743818	−	0.429443i	−0.0796379	−	0.996824i	$-0.525376\pi$
$257$	11.9243	−	6.88450i	0.743818	−	0.429443i	0.823456	+	0.567380i	$0.192043\pi$
$258$	10.3456	+	5.59900i	0.644090	+	0.348578i
$259$	20.5295	−	16.5337i	1.27564	−	1.02735i
$260$	14.3750	+	22.0042i	0.891501	+	1.36465i
$261$	3.14710	+	2.41486i	0.194801	+	0.149476i
$262$	6.57915	−	1.05122i	0.406461	−	0.0649443i
$263$	−12.6964	+	3.40199i	−0.782894	+	0.209776i	−0.628060	−	0.778165i	$-0.716151\pi$
$263$	−12.6964	+	3.40199i	−0.782894	+	0.209776i	−0.154834	+	0.987941i	$0.549484\pi$
$264$	−15.3247	+	10.6248i	−0.943172	+	0.653910i
$265$	−11.5302	+	11.5302i	−0.708293	+	0.708293i
$266$	5.31137	+	0.425045i	0.325661	+	0.0260612i
$267$	11.9660	−	4.95648i	0.732307	−	0.303332i
$268$	14.4123	−	12.3773i	0.880373	−	0.756063i
$269$	−4.03019	−	5.25225i	−0.245725	−	0.320235i	0.654165	−	0.756352i	$-0.273020\pi$
$269$	−4.03019	−	5.25225i	−0.245725	−	0.320235i	−0.899890	+	0.436117i	$0.856354\pi$
$270$	−3.49981	+	14.6657i	−0.212992	+	0.892523i
$271$	20.6375	−	11.9151i	1.25364	−	0.723789i	0.281809	−	0.959470i	$-0.409065\pi$
$271$	20.6375	−	11.9151i	1.25364	−	0.723789i	0.971830	+	0.235681i	$0.0757320\pi$
$272$	1.67362	−	3.81477i	0.101478	−	0.231304i
$273$	0.555403	+	23.6263i	0.0336145	+	1.42993i
$274$	3.89866	−	1.16061i	0.235527	−	0.0701150i
$275$	6.93083	−	0.912461i	0.417945	−	0.0550235i
$276$	3.66814	+	7.63686i	0.220796	+	0.459685i
$277$	−9.87702	−	1.30034i	−0.593453	−	0.0781296i	−0.172183	−	0.985065i	$-0.555082\pi$
$277$	−9.87702	−	1.30034i	−0.593453	−	0.0781296i	−0.421270	+	0.906935i	$0.638415\pi$
$278$	−6.63277	−	14.8431i	−0.397807	−	0.890227i
$279$	2.87960	+	2.87960i	0.172397	+	0.172397i
$280$	9.82531	+	10.3246i	0.587174	+	0.617013i
$281$	−17.1617	+	17.1617i	−1.02378	+	1.02378i	−0.0240710	+	0.999710i	$0.507663\pi$
$281$	−17.1617	+	17.1617i	−1.02378	+	1.02378i	−0.999710	+	0.0240710i	$0.992337\pi$
$282$	2.52440	+	0.965088i	0.150326	+	0.0574702i
$283$	1.93111	−	14.6682i	0.114793	−	0.871936i	−0.833050	−	0.553198i	$-0.813407\pi$
$283$	1.93111	−	14.6682i	0.114793	−	0.871936i	0.947843	−	0.318739i	$-0.103259\pi$
$284$	−17.3298	−	15.5187i	−1.02834	−	0.920863i
$285$	−0.458281	−	3.48099i	−0.0271462	−	0.206196i
$286$	−43.7081	−	23.6546i	−2.58451	−	1.39873i
$287$	−1.67300	−	2.74657i	−0.0987543	−	0.162125i
$288$	−0.927207	+	7.43333i	−0.0546362	+	0.438013i
$289$	7.95770	+	13.7831i	0.468100	+	0.810773i
$290$	−4.22516	−	6.87382i	−0.248110	−	0.403645i
$291$	9.01748	−	6.91935i	0.528614	−	0.405620i
$292$	1.12748	+	3.43815i	0.0659807	+	0.201203i
$293$	10.4831	+	25.3085i	0.612430	+	1.47854i	0.860323	+	0.509750i	$0.170262\pi$
$293$	10.4831	+	25.3085i	0.612430	+	1.47854i	−0.247892	+	0.968788i	$0.579738\pi$
$294$	2.61434	+	12.5456i	0.152472	+	0.731673i
$295$	15.1654	+	15.1654i	0.882965	+	0.882965i
$296$	−23.6958	−	15.2510i	−1.37729	−	0.886448i
$297$	−7.37875	−	27.5379i	−0.428158	−	1.59791i
$298$	−2.19236	+	3.02617i	−0.127000	+	0.175302i
$299$	−13.7455	+	17.9134i	−0.794921	+	1.03596i
$300$	−2.00488	+	2.93419i	−0.115752	+	0.169406i
$301$	2.61453	+	16.7983i	0.150699	+	0.968240i
$302$	−0.532836	−	1.78988i	−0.0306613	−	0.102996i
$303$	1.17389	+	2.03324i	0.0674382	+	0.116806i
$304$	−1.35989	−	5.53153i	−0.0779951	−	0.317255i
$305$	21.3216	+	12.3100i	1.22087	+	0.704870i
$306$	1.41655	+	1.34060i	0.0809787	+	0.0766367i
$307$	−1.05530	−	0.437118i	−0.0602290	−	0.0249477i	0.352366	−	0.935862i	$-0.385377\pi$
$307$	−1.05530	−	0.437118i	−0.0602290	−	0.0249477i	−0.412595	+	0.910915i	$0.635377\pi$
$308$	−25.6308	−	8.32666i	−1.46045	−	0.474456i
$309$	1.70975	+	4.12771i	0.0972644	+	0.234817i
$310$	−3.37937	−	7.56248i	−0.191935	−	0.429520i
$311$	7.04619	−	1.88802i	0.399553	−	0.107060i	−0.0534464	−	0.998571i	$-0.517021\pi$
$311$	7.04619	−	1.88802i	0.399553	−	0.107060i	0.452999	+	0.891511i	$0.350354\pi$
$312$	23.7807	−	8.53062i	1.34632	−	0.482952i
$313$	1.50768	−	5.62674i	0.0852192	−	0.318042i	−0.910136	−	0.414309i	$-0.864023\pi$
$313$	1.50768	−	5.62674i	0.0852192	−	0.318042i	0.995356	+	0.0962664i	$0.0306901\pi$
$314$	26.2492	−	21.3154i	1.48133	−	1.20290i
$315$	−6.10314	+	2.69774i	−0.343873	+	0.152001i
$316$	−13.6433	−	20.8842i	−0.767495	−	1.17483i
$317$	−20.2421	+	2.66492i	−1.13691	+	0.149677i	−0.675395	−	0.737456i	$-0.736027\pi$
$317$	−20.2421	+	2.66492i	−1.13691	+	0.149677i	−0.461514	+	0.887133i	$0.652693\pi$
$318$	8.20776	+	13.3530i	0.460268	+	0.748801i
$319$	13.2125	+	7.62822i	0.739756	+	0.427098i
$320$	7.16069	−	13.4491i	0.400295	−	0.751826i
$321$		−	5.45782i		−	0.304626i
$322$	−5.57295	+	10.9020i	−0.310568	+	0.607547i
$323$	−1.37018	−	0.567546i	−0.0762387	−	0.0315791i
$324$	5.84196	+	2.95663i	0.324553	+	0.164257i
$325$	−9.39016	−	1.23624i	−0.520872	−	0.0685742i
$326$	−1.25229	−	7.83760i	−0.0693579	−	0.434084i
$327$	4.55987	+	1.22181i	0.252161	+	0.0675664i
$328$	−2.22213	+	2.62340i	−0.122697	+	0.144853i
$329$	1.09927	+	3.74788i	0.0606048	+	0.206628i
$330$	−1.83217	+	17.6631i	−0.100857	+	0.972321i
$331$	−21.7550	−	16.6932i	−1.19576	−	0.917541i	−0.197732	−	0.980256i	$-0.563358\pi$
$331$	−21.7550	−	16.6932i	−1.19576	−	0.917541i	−0.998031	+	0.0627147i	$0.980024\pi$
$332$	11.2775	+	3.95905i	0.618931	+	0.217281i
$333$	10.4668	−	8.03149i	0.573580	−	0.440123i
$334$	11.0271	−	11.6518i	0.603374	−	0.637559i
$335$		−	18.0912i		−	0.988429i
$336$	11.8455	−	6.88275i	0.646223	−	0.375485i
$337$		−	16.1002i		−	0.877036i	−0.898722	−	0.438518i	$-0.855503\pi$
$337$		−	16.1002i		−	0.877036i	0.898722	−	0.438518i	$-0.144497\pi$
$338$	35.5519	+	33.6457i	1.93377	+	1.83008i
$339$	−12.7116	+	9.75395i	−0.690399	+	0.529762i
$340$	−1.71757	−	3.57588i	−0.0931482	−	0.193929i
$341$	12.4257	+	9.53461i	0.672892	+	0.516328i
$342$	2.65265	+	0.275156i	0.143439	+	0.0148787i
$343$	−12.1406	+	13.9859i	−0.655532	+	0.755167i
$344$	16.1597	−	8.31704i	0.871271	−	0.448425i
$345$	7.79298	+	2.08812i	0.419560	+	0.112421i
$346$	−3.38340	+	0.540599i	−0.181893	+	0.0290628i
$347$	−16.6462	−	2.19151i	−0.893612	−	0.117646i	−0.330286	−	0.943881i	$-0.607145\pi$
$347$	−16.6462	−	2.19151i	−0.893612	−	0.117646i	−0.563326	+	0.826235i	$0.690479\pi$
$348$	−7.36956	+	2.41671i	−0.395050	+	0.129549i
$349$	−15.7087	−	6.50674i	−0.840865	−	0.348298i	−0.0796707	−	0.996821i	$-0.525387\pi$
$349$	−15.7087	−	6.50674i	−0.840865	−	0.348298i	−0.761195	+	0.648523i	$0.775387\pi$
$350$	−5.12914	+	0.262041i	−0.274164	+	0.0140067i
$351$			38.6255i			2.06168i
$352$	0.196031	+	28.8095i	0.0104485	+	1.53555i
$353$	12.0664	+	6.96653i	0.642229	+	0.370791i	0.785473	−	0.618897i	$-0.212420\pi$
$353$	12.0664	+	6.96653i	0.642229	+	0.370791i	−0.143244	+	0.989687i	$0.545753\pi$
$354$	17.5630	−	10.7955i	0.933462	−	0.573775i
$355$	−21.9632	+	2.89151i	−1.16569	+	0.153465i
$356$	4.10711	−	19.5844i	0.217676	−	1.03797i
$357$	0.382335	−	3.54634i	0.0202353	−	0.187692i
$358$	−9.84891	−	12.1286i	−0.520531	−	0.641017i
$359$	7.58620	−	28.3121i	0.400384	−	1.49426i	−0.412028	−	0.911171i	$-0.635179\pi$
$359$	7.58620	−	28.3121i	0.400384	−	1.49426i	0.812412	−	0.583084i	$-0.198154\pi$
$360$	4.79485	+	5.28170i	0.252711	+	0.278370i
$361$	16.3937	−	4.39269i	0.862829	−	0.231194i
$362$	−3.85828	+	1.72411i	−0.202787	+	0.0906173i
$363$	−7.40026	−	17.8658i	−0.388413	−	0.937711i
$364$	30.6225	+	19.8845i	1.60506	+	1.04223i
$365$	3.18337	+	1.31860i	0.166625	+	0.0690185i
$366$	16.2668	−	17.1885i	0.850281	−	0.898455i
$367$	−10.1024	−	5.83264i	−0.527343	−	0.304462i	0.212591	−	0.977141i	$-0.431810\pi$
$367$	−10.1024	−	5.83264i	−0.527343	−	0.304462i	−0.739934	+	0.672680i	$0.765143\pi$
$368$	12.9390	+	1.97721i	0.674494	+	0.103069i
$369$	−0.804816	−	1.39398i	−0.0418970	−	0.0725678i
$370$	−25.7195	+	7.65654i	−1.33709	+	0.398044i
$371$	−8.17425	+	21.1255i	−0.424386	+	1.09678i
$372$	−7.82472	+	1.47227i	−0.405693	+	0.0763335i
$373$	1.58394	−	2.06423i	0.0820134	−	0.106882i	−0.750545	−	0.660820i	$-0.770209\pi$
$373$	1.58394	−	2.06423i	0.0820134	−	0.106882i	0.832558	+	0.553938i	$0.186875\pi$
$374$	6.07442	+	4.40070i	0.314101	+	0.227555i
$375$	4.06648	+	15.1763i	0.209992	+	0.783702i
$376$	3.43141	−	2.37903i	0.176961	−	0.122689i
$377$	−14.6159	−	14.6159i	−0.752757	−	0.752757i
$378$	3.78983	+	20.5993i	0.194928	+	1.05951i
$379$	2.88601	+	6.96745i	0.148244	+	0.357894i	0.980506	−	0.196490i	$-0.0629542\pi$
$379$	2.88601	+	6.96745i	0.148244	+	0.357894i	−0.832262	+	0.554383i	$0.812954\pi$
$380$	−4.83990	−	2.44948i	−0.248282	−	0.125656i
$381$	−2.78062	+	2.13365i	−0.142456	+	0.109310i
$382$	−7.67015	+	4.71465i	−0.392439	+	0.241222i
$383$	−11.5792	−	20.0558i	−0.591670	−	1.02480i	−0.994008	−	0.109311i	$-0.965136\pi$
$383$	−11.5792	−	20.0558i	−0.591670	−	1.02480i	0.402338	−	0.915491i	$-0.368198\pi$
$384$	−10.9768	−	9.69583i	−0.560158	−	0.494788i
$385$	−21.9176	+	13.3505i	−1.11702	+	0.680407i
$386$	0.871198	−	1.60977i	0.0443428	−	0.0819350i
$387$	1.11064	+	8.43615i	0.0564570	+	0.428834i
$388$	−0.966779	−	17.5340i	−0.0490807	−	0.890154i
$389$	3.13990	−	23.8499i	0.159199	−	1.20924i	−0.706147	−	0.708065i	$-0.749568\pi$
$389$	3.13990	−	23.8499i	0.159199	−	1.20924i	0.865346	−	0.501174i	$-0.167099\pi$
$390$	8.59141	−	22.4728i	0.435043	−	1.13795i
$391$	2.40975	−	2.40975i	0.121866	−	0.121866i
$392$	18.2822	+	7.59997i	0.923393	+	0.383857i
$393$	−4.31243	−	4.31243i	−0.217533	−	0.217533i
$394$	2.29383	−	1.02502i	0.115561	−	0.0516398i
$395$	−23.5522	−	3.10071i	−1.18504	−	0.156013i
$396$	−12.7270	−	4.46791i	−0.639554	−	0.224521i
$397$	−13.3525	+	1.75790i	−0.670145	+	0.0882262i	−0.457918	−	0.888994i	$-0.651405\pi$
$397$	−13.3525	+	1.75790i	−0.670145	+	0.0882262i	−0.212226	+	0.977221i	$0.568071\pi$
$398$	−3.73008	−	12.5299i	−0.186972	−	0.628067i
$399$	−2.53728	−	4.16545i	−0.127023	−	0.208533i
$400$	1.99547	+	5.11497i	0.0997734	+	0.255749i
$401$	4.45802	−	2.57384i	0.222623	−	0.128531i	−0.384541	−	0.923108i	$-0.625640\pi$
$401$	4.45802	−	2.57384i	0.222623	−	0.128531i	0.607164	+	0.794576i	$0.292307\pi$
$402$	−16.9148	−	4.03655i	−0.843634	−	0.201325i
$403$	−12.9179	−	16.8349i	−0.643484	−	0.838605i
$404$	3.61685	+	0.274749i	0.179945	+	0.0136693i
$405$	5.76050	−	2.38608i	0.286241	−	0.118565i
$406$	−9.22884	−	6.36070i	−0.458020	−	0.315676i
$407$	35.8792	−	35.8792i	1.77847	−	1.77847i
$408$	−3.72657	+	0.808023i	−0.184493	+	0.0400031i
$409$	−1.10573	+	0.296281i	−0.0546751	+	0.0146501i	−0.286053	−	0.958214i	$-0.592343\pi$
$409$	−1.10573	+	0.296281i	−0.0546751	+	0.0146501i	0.231378	+	0.972864i	$0.425677\pi$
$410$	0.516565	+	3.23298i	0.0255113	+	0.159666i
$411$	−2.95402	−	2.26670i	−0.145711	−	0.111808i
$412$	6.75569	+	1.41676i	0.332829	+	0.0697987i
$413$	27.7859	+	10.7514i	1.36726	+	0.529043i
$414$	−2.91678	+	5.38951i	−0.143352	+	0.264880i
$415$	9.85702	−	5.69095i	0.483862	−	0.279358i
$416$	9.84573	−	37.7709i	0.482727	−	1.85187i
$417$	−7.44080	+	12.8879i	−0.364378	+	0.631121i
$418$	10.2530	−	0.282446i	0.501488	−	0.0138149i
$419$	−10.7109	+	25.8583i	−0.523261	+	1.26326i	0.412606	+	0.910909i	$0.364618\pi$
$419$	−10.7109	+	25.8583i	−0.523261	+	1.26326i	−0.935867	+	0.352353i	$0.885382\pi$
$420$	2.37690	−	12.8279i	0.115981	−	0.625935i
$421$	−10.9194	+	4.52297i	−0.532179	+	0.220436i	−0.632557	−	0.774514i	$-0.717995\pi$
$421$	−10.9194	+	4.52297i	−0.532179	+	0.220436i	0.100378	+	0.994949i	$0.467995\pi$
$422$	−10.0981	+	26.4138i	−0.491567	+	1.28580i
$423$	0.505959	+	1.88826i	0.0246005	+	0.0918105i
$424$	24.1876	+	1.16862i	1.17465	+	0.0567532i
$425$	1.38078	+	0.369978i	0.0669775	+	0.0179466i
$426$	−2.19699	+	21.1801i	−0.106444	+	1.02618i
$427$	34.0041	+	3.66601i	1.64557	+	0.177411i
$428$	−6.96218	−	4.75712i	−0.336530	−	0.229944i
$429$	5.93791	+	45.1029i	0.286685	+	2.17759i
$430$	4.01738	−	16.8345i	0.193735	−	0.811831i
$431$	−16.1978	+	28.0554i	−0.780219	+	1.35138i	0.151595	+	0.988443i	$0.451559\pi$
$431$	−16.1978	+	28.0554i	−0.780219	+	1.35138i	−0.931814	+	0.362937i	$0.881774\pi$
$432$	19.6193	−	10.7911i	0.943932	−	0.519186i
$433$	23.2185			1.11581			0.557905	−	0.829905i	$-0.311605\pi$
$433$	23.2185			1.11581			0.557905	+	0.829905i	$0.311605\pi$
$434$	−8.54098	−	7.71071i	−0.409980	−	0.370126i
$435$	−2.82636	+	6.82344i	−0.135514	+	0.327159i
$436$	5.53303	−	4.75176i	0.264984	−	0.227568i
$437$	0.608248	−	4.62010i	0.0290964	−	0.221009i
$438$	1.94313	−	2.68216i	0.0928464	−	0.128158i
$439$	−5.31588	+	19.8391i	−0.253713	+	0.946870i	0.715089	+	0.699034i	$0.246386\pi$
$439$	−5.31588	+	19.8391i	−0.253713	+	0.946870i	−0.968802	+	0.247836i	$0.920280\pi$
$440$	20.9347	+	17.7326i	0.998021	+	0.845368i
$441$	−6.23933	+	6.85533i	−0.297111	+	0.326444i
$442$	−6.40629	−	7.88913i	−0.304716	−	0.375248i
$443$	15.2770	−	19.9093i	0.725830	−	0.945921i	−0.274045	−	0.961717i	$-0.588362\pi$
$443$	15.2770	−	19.9093i	0.725830	−	0.945921i	0.999875	+	0.0157964i	$0.00502835\pi$
$444$	1.42008	+	25.7553i	0.0673940	+	1.22229i
$445$	−11.6003	−	15.1178i	−0.549908	−	0.716654i
$446$	−7.69378	+	0.211946i	−0.364311	+	0.0100360i
$447$	3.42059			0.161788
$448$	1.54483	−	21.1096i	0.0729861	−	0.997333i
$449$	20.2136			0.953938			0.476969	−	0.878920i	$-0.341735\pi$
$449$	20.2136			0.953938			0.476969	+	0.878920i	$0.341735\pi$
$450$	−2.56956	+	0.0707855i	−0.121130	+	0.00333686i
$451$	−3.76862	−	4.91136i	−0.177457	−	0.231267i
$452$	1.36283	+	24.7170i	0.0641022	+	1.16259i
$453$	−1.04064	+	1.35619i	−0.0488937	+	0.0637195i
$454$	−0.191147	−	0.235392i	−0.00897099	−	0.0110475i
$455$	33.3644	−	9.78594i	1.56415	−	0.458772i
$456$	−3.37009	+	3.97864i	−0.157819	+	0.186317i
$457$	−5.73442	+	21.4011i	−0.268245	+	1.00110i	0.691989	+	0.721908i	$0.256734\pi$
$457$	−5.73442	+	21.4011i	−0.268245	+	1.00110i	−0.960234	+	0.279196i	$0.909932\pi$
$458$	−17.7135	+	24.4504i	−0.827696	+	1.14249i
$459$	0.760934	−	5.77986i	0.0355173	−	0.269781i
$460$	9.45616	−	8.12094i	0.440896	−	0.378641i
$461$	9.74244	−	23.5203i	0.453751	−	1.09545i	−0.517134	−	0.855904i	$-0.673001\pi$
$461$	9.74244	−	23.5203i	0.453751	−	1.09545i	0.970885	−	0.239546i	$-0.0769987\pi$
$462$	7.59211	+	23.4711i	0.353217	+	1.09198i
$463$	−12.3133			−0.572248			−0.286124	−	0.958193i	$-0.592367\pi$
$463$	−12.3133			−0.572248			−0.286124	+	0.958193i	$0.592367\pi$
$464$	−3.34059	+	11.5073i	−0.155083	+	0.534213i
$465$	−3.79106	+	6.56631i	−0.175806	+	0.304505i
$466$	1.32815	−	5.56551i	0.0615255	−	0.257817i
$467$	−3.77280	−	28.6573i	−0.174585	−	1.32610i	−0.824399	−	0.566008i	$-0.808487\pi$
$467$	−3.77280	−	28.6573i	−0.174585	−	1.32610i	0.649815	−	0.760092i	$-0.274846\pi$
$468$	15.0887	+	10.3098i	0.697477	+	0.476573i
$469$	−10.1605	−	22.9861i	−0.469166	−	1.06140i
$470$	0.410246	−	3.95499i	0.0189232	−	0.182430i
$471$	−29.8971	−	8.01092i	−1.37759	−	0.369123i
$472$	1.53706	−	31.8135i	0.0707490	−	1.46433i
$473$	8.46995	+	31.6103i	0.389449	+	1.45344i
$474$	−8.15408	+	21.3288i	−0.374529	+	0.979665i
$475$	1.80589	−	0.748023i	0.0828598	−	0.0343216i
$476$	−4.19058	−	3.57877i	−0.192075	−	0.164032i
$477$	−4.33865	+	10.4744i	−0.198653	+	0.479591i
$478$	3.86358	−	0.106433i	0.176716	−	0.00486813i
$479$	−10.5049	+	18.1950i	−0.479980	+	0.831350i	−0.999736	−	0.0229647i	$-0.992689\pi$
$479$	−10.5049	+	18.1950i	−0.479980	+	0.831350i	0.519756	+	0.854315i	$0.326023\pi$
$480$	−13.8150	+	1.91449i	−0.630564	+	0.0873842i
$481$	−59.5356	+	34.3729i	−2.71459	+	1.56727i
$482$	−10.1083	+	18.6778i	−0.460421	+	0.850748i
$483$	11.0742	−	1.72362i	0.503896	−	0.0784273i
$484$	−29.2404	−	6.13210i	−1.32911	−	0.278732i
$485$	−13.2670	−	10.1802i	−0.602425	−	0.462257i
$486$	2.80152	+	17.5336i	0.127079	+	0.795341i
$487$	8.74932	−	2.34437i	0.396469	−	0.106234i	−0.0550752	−	0.998482i	$-0.517540\pi$
$487$	8.74932	−	2.34437i	0.396469	−	0.106234i	0.451545	+	0.892249i	$0.350873\pi$
$488$	−7.74772	−	35.7322i	−0.350723	−	1.61752i
$489$	−5.13730	+	5.13730i	−0.232317	+	0.232317i
$490$	16.8333	−	8.49254i	0.760453	−	0.383654i
$491$	−9.93228	+	4.11409i	−0.448238	+	0.185666i	−0.595372	−	0.803450i	$-0.702995\pi$
$491$	−9.93228	+	4.11409i	−0.448238	+	0.185666i	0.147134	+	0.989117i	$0.452995\pi$
$492$	3.13801	+	0.238375i	0.141472	+	0.0107468i
$493$	1.89917	+	2.47504i	0.0855341	+	0.111470i
$494$	−13.5168	−	3.22565i	−0.608150	−	0.145129i
$495$	−11.1240	+	6.42242i	−0.499985	+	0.288666i
$496$	−4.94208	+	11.2647i	−0.221906	+	0.505801i
$497$	−26.2818	+	16.0089i	−1.17890	+	0.718097i
$498$	−3.12157	−	10.4858i	−0.139881	−	0.469881i
$499$	−9.69348	+	1.27617i	−0.433940	+	0.0571293i	−0.344332	−	0.938848i	$-0.611895\pi$
$499$	−9.69348	+	1.27617i	−0.433940	+	0.0571293i	−0.0896076	+	0.995977i	$0.528561\pi$
$500$	22.9038	+	8.04058i	1.02429	+	0.359586i
$501$	−14.5590	−	1.91673i	−0.650450	−	0.0856334i
$502$	31.9095	−	14.2591i	1.42419	−	0.636414i
$503$	−21.5342	−	21.5342i	−0.960163	−	0.960163i	0.0390731	−	0.999236i	$-0.487559\pi$
$503$	−21.5342	−	21.5342i	−0.960163	−	0.960163i	−0.999236	+	0.0390731i	$0.987559\pi$
$504$	9.05851	+	4.01785i	0.403498	+	0.178969i
$505$	2.44248	−	2.44248i	0.108689	−	0.108689i
$506$	−8.41639	+	22.0150i	−0.374154	+	0.978684i
$507$	5.84832	−	44.4224i	0.259733	−	1.97287i
$508$	0.298115	+	5.40677i	0.0132267	+	0.239887i
$509$	−1.76046	−	13.3721i	−0.0780312	−	0.592706i	−0.985133	−	0.171794i	$-0.945044\pi$
$509$	−1.76046	−	13.3721i	−0.0780312	−	0.592706i	0.907102	−	0.420912i	$-0.138290\pi$
$510$	−1.72833	+	3.19354i	−0.0765316	+	0.141412i
$511$	4.78524	−	0.112491i	0.211687	−	0.00497630i
$512$	−21.9359	+	5.55134i	−0.969438	+	0.245337i
$513$	−3.98579	−	6.90359i	−0.175977	−	0.304801i
$514$	−16.5890	+	10.1968i	−0.731710	+	0.449763i
$515$	5.21494	−	4.00156i	0.229798	−	0.176330i
$516$	−14.8434	−	7.51228i	−0.653445	−	0.330710i
$517$	2.87718	+	6.94613i	0.126538	+	0.305491i
$518$	−28.3782	+	24.1728i	−1.24687	+	1.06209i
$519$	2.21772	+	2.21772i	0.0973469	+	0.0973469i
$520$	−21.1786	−	30.5471i	−0.928742	−	1.33958i
$521$	7.80395	+	29.1247i	0.341897	+	1.27598i	0.896195	+	0.443659i	$0.146320\pi$
$521$	7.80395	+	29.1247i	0.341897	+	1.27598i	−0.554298	+	0.832318i	$0.687013\pi$
$522$	−4.54303	−	3.29127i	−0.198843	−	0.144055i
$523$	−0.0340226	+	0.0443391i	−0.00148770	+	0.00193881i	−0.794097	−	0.607792i	$-0.792056\pi$
$523$	−0.0340226	+	0.0443391i	−0.00148770	+	0.00193881i	0.792609	+	0.609730i	$0.208722\pi$
$524$	−9.25986	+	1.74229i	−0.404519	+	0.0761125i
$525$	2.94874	+	3.66138i	0.128693	+	0.159796i
$526$	17.8161	−	5.30377i	0.776821	−	0.231255i
$527$	1.60136	+	2.77363i	0.0697563	+	0.120821i
$528$	21.2505	−	15.6168i	0.924808	−	0.679634i
$529$	−10.6452	−	6.14599i	−0.462834	−	0.267217i
$530$	15.8509	−	16.7490i	0.688520	−	0.727529i
$531$	13.7768	+	5.70654i	0.597863	+	0.247643i
$532$	−7.52511	−	0.394032i	−0.326255	−	0.0170835i
$533$	3.20969	+	7.74887i	0.139027	+	0.335641i
$534$	−16.7230	+	7.47286i	−0.723677	+	0.323382i
$535$	−7.75626	+	2.07828i	−0.335332	+	0.0898520i
$536$	−19.8924	+	18.0588i	−0.859219	+	0.780019i
$537$	−3.70149	+	13.8142i	−0.159731	+	0.596125i
$538$	5.90193	+	7.26803i	0.254450	+	0.313347i
$539$	−20.3498	+	29.2722i	−0.876526	+	1.26084i
$540$	4.37647	−	20.8688i	0.188333	−	0.898050i
$541$	30.8782	−	4.06519i	1.32756	−	0.174776i	0.566823	−	0.823840i	$-0.308172\pi$
$541$	30.8782	−	4.06519i	1.32756	−	0.174776i	0.760734	+	0.649063i	$0.224839\pi$
$542$	−28.7108	+	17.6478i	−1.23323	+	0.758037i
$543$	3.35005	+	1.93415i	0.143764	+	0.0830023i
$544$	−2.21740	+	5.45803i	−0.0950702	+	0.234011i
$545$		−	6.94540i		−	0.297508i
$546$	−1.70525	−	33.3783i	−0.0729781	−	1.42846i
$547$	−34.0676	−	14.1112i	−1.45662	−	0.603353i	−0.492860	−	0.870109i	$-0.664048\pi$
$547$	−34.0676	−	14.1112i	−1.45662	−	0.603353i	−0.963764	+	0.266755i	$0.914048\pi$
$548$	−5.46625	+	1.79256i	−0.233507	+	0.0765742i
$549$	16.9715	+	2.23435i	0.724328	+	0.0953595i
$550$	−9.76242	+	1.55984i	−0.416271	+	0.0665117i
$551$	4.12055	+	1.10410i	0.175541	+	0.0470361i
$552$	−5.48298	−	10.6532i	−0.233371	−	0.453431i
$553$	−31.6661	+	9.28780i	−1.34658	+	0.394958i
$554$	14.0136	+	1.45361i	0.595379	+	0.0617578i
$555$	19.4877	+	14.9534i	0.827206	+	0.634737i
$556$	9.95464	+	20.7250i	0.422171	+	0.878935i
$557$	8.88642	−	6.81879i	0.376530	−	0.288922i	−0.403108	−	0.915153i	$-0.632070\pi$
$557$	8.88642	−	6.81879i	0.376530	−	0.288922i	0.779638	+	0.626231i	$0.215403\pi$
$558$	−4.18296	−	3.95868i	−0.177079	−	0.167584i
$559$		−	44.3376i		−	1.87528i
$560$	−14.2919	−	14.2130i	−0.603943	−	0.600609i
$561$		−	6.86612i		−	0.289888i
$562$	23.5928	−	24.9294i	0.995201	−	1.05159i
$563$	−2.52674	+	1.93883i	−0.106489	+	0.0817121i	−0.660634	−	0.750709i	$-0.729712\pi$
$563$	−2.52674	+	1.93883i	−0.106489	+	0.0817121i	0.554144	+	0.832421i	$0.313046\pi$
$564$	−3.60628	−	1.26601i	−0.151852	−	0.0533088i
$565$	18.7021	+	14.3506i	0.786801	+	0.603734i
$566$	−2.15873	+	20.8114i	−0.0907383	+	0.874767i
$567$	5.97902	−	6.26690i	0.251095	−	0.263185i
$568$	25.1032	+	21.2635i	1.05331	+	0.892196i
$569$	31.5198	+	8.44569i	1.32138	+	0.354062i	0.849493	−	0.527599i	$-0.176908\pi$
$569$	31.5198	+	8.44569i	1.32138	+	0.354062i	0.471883	+	0.881661i	$0.343574\pi$
$570$	0.783423	+	4.90314i	0.0328140	+	0.205370i
$571$	28.4516	+	3.74573i	1.19066	+	0.156754i	0.699707	−	0.714430i	$-0.253314\pi$
$571$	28.4516	+	3.74573i	1.19066	+	0.156754i	0.490957	+	0.871184i	$0.336647\pi$
$572$	62.7103	+	31.7378i	2.62205	+	1.32702i
$573$	7.61394	+	3.15380i	0.318077	+	0.131752i
$574$	2.47205	+	3.81761i	0.103181	+	0.159344i
$575$			4.49160i			0.187313i
$576$	1.02129	−	10.5444i	0.0425538	−	0.439352i
$577$	−8.18229	−	4.72405i	−0.340633	−	0.196665i	0.319919	−	0.947445i	$-0.396344\pi$
$577$	−8.18229	−	4.72405i	−0.340633	−	0.196665i	−0.660552	+	0.750780i	$0.729678\pi$
$578$	−11.7864	−	19.1750i	−0.490249	−	0.797576i
$579$	−1.66114	+	0.218693i	−0.0690346	+	0.00908857i
$580$	6.24070	+	9.55282i	0.259131	+	0.396659i
$581$	9.32783	−	12.7667i	0.386984	−	0.529651i
$582$	−12.4783	+	10.1329i	−0.517244	+	0.420022i
$583$	−11.2855	+	42.1180i	−0.467397	+	1.74435i
$584$	−1.72779	−	4.81653i	−0.0714963	−	0.199310i
$585$	16.8097	−	4.50415i	0.694996	−	0.186223i
$586$	−15.8053	−	35.3698i	−0.652913	−	1.46111i
$587$	−1.45514	−	3.51303i	−0.0600602	−	0.144998i	0.891000	−	0.454002i	$-0.150004\pi$
$587$	−1.45514	−	3.51303i	−0.0600602	−	0.144998i	−0.951061	+	0.309004i	$0.900004\pi$
$588$	−4.18441	−	17.6336i	−0.172562	−	0.727196i
$589$	4.04603	+	1.67592i	0.166714	+	0.0690551i
$590$	−22.0296	−	20.8484i	−0.906944	−	0.858316i
$591$	−1.99167	−	1.14989i	−0.0819265	−	0.0473003i
$592$	34.0921	+	20.6372i	1.40118	+	0.848185i
$593$	−24.2502	−	42.0026i	−0.995837	−	1.72484i	−0.576860	−	0.816843i	$-0.695722\pi$
$593$	−24.2502	−	42.0026i	−0.995837	−	1.72484i	−0.418976	−	0.907997i	$-0.637611\pi$
$594$	11.5036	+	38.6423i	0.471998	+	1.58551i
$595$	−5.18539	+	0.807065i	−0.212580	+	0.0330864i
$596$	2.98144	−	4.36341i	0.122124	−	0.178732i
$597$	−7.28494	+	9.49392i	−0.298153	+	0.388560i
$598$	18.7340	−	25.8591i	0.766092	−	1.05746i
$599$	−4.20531	−	15.6944i	−0.171824	−	0.641257i	−0.997071	−	0.0764845i	$-0.975630\pi$
$599$	−4.20531	−	15.6944i	−0.171824	−	0.641257i	0.825246	−	0.564773i	$-0.191036\pi$
$600$	2.71998	−	4.22608i	0.111043	−	0.172529i
$601$	−11.9648	−	11.9648i	−0.488053	−	0.488053i	0.419638	−	0.907691i	$-0.362157\pi$
$601$	−11.9648	−	11.9648i	−0.488053	−	0.488053i	−0.907691	+	0.419638i	$0.862157\pi$
$602$	−4.35029	−	23.6456i	−0.177304	−	0.963723i
$603$	−4.81362	−	11.6211i	−0.196026	−	0.473248i
$604$	0.822962	+	2.50956i	0.0334859	+	0.102112i
$605$	−22.5716	+	17.3198i	−0.917667	+	0.704151i
$606$	−1.73868	−	2.82863i	−0.0706292	−	0.114905i
$607$	−1.40684	−	2.43672i	−0.0571020	−	0.0989035i	0.836061	−	0.548636i	$-0.184853\pi$
$607$	−1.40684	−	2.43672i	−0.0571020	−	0.0989035i	−0.893163	+	0.449732i	$0.851519\pi$
$608$	2.13787	+	7.76685i	0.0867019	+	0.314987i
$609$	0.241120	+	10.2570i	0.00977068	+	0.415634i
$610$	−30.6212	−	16.5721i	−1.23982	−	0.670983i
$611$	−1.32958	−	10.0991i	−0.0537889	−	0.408567i
$612$	−2.05475	−	1.84000i	−0.0830583	−	0.0743777i
$613$	0.669238	−	5.08336i	0.0270303	−	0.205315i	−0.972601	−	0.232482i	$-0.925315\pi$
$613$	0.669238	−	5.08336i	0.0270303	−	0.205315i	0.999631	+	0.0271670i	$0.00864860\pi$
$614$	1.50887	+	0.576847i	0.0608931	+	0.0232797i
$615$	2.11912	−	2.11912i	0.0854512	−	0.0854512i
$616$	36.5579	+	10.7731i	1.47296	+	0.434059i
$617$	6.91032	+	6.91032i	0.278199	+	0.278199i	0.832390	−	0.554191i	$-0.186972\pi$
$617$	6.91032	+	6.91032i	0.278199	+	0.278199i	−0.554191	+	0.832390i	$0.686972\pi$
$618$	−2.57779	−	5.76866i	−0.103694	−	0.232050i
$619$	16.1936	+	2.13193i	0.650875	+	0.0856893i	0.448732	−	0.893667i	$-0.351876\pi$
$619$	16.1936	+	2.13193i	0.650875	+	0.0856893i	0.202143	+	0.979356i	$0.435209\pi$
$620$	5.07185	+	10.5593i	0.203691	+	0.424072i
$621$	18.1610	−	2.39094i	0.728775	−	0.0959450i
$622$	−9.88752	+	2.94346i	−0.396453	+	0.118022i
$623$	−23.2295	−	12.6932i	−0.930670	−	0.508543i
$624$	−33.2861	+	12.9857i	−1.33251	+	0.519842i
$625$	14.0754	−	8.12645i	0.563017	−	0.325058i
$626$	−1.91225	+	8.01311i	−0.0764288	+	0.320268i
$627$	−5.71550	−	7.44858i	−0.228255	−	0.297468i
$628$	−36.2778	+	31.1553i	−1.44764	+	1.24323i
$629$	9.58598	−	3.97064i	0.382218	−	0.158320i
$630$	8.52281	−	4.05142i	0.339557	−	0.161412i
$631$	32.1040	−	32.1040i	1.27804	−	1.27804i	0.336278	−	0.941763i	$-0.390832\pi$
$631$	32.1040	−	32.1040i	1.27804	−	1.27804i	0.941763	−	0.336278i	$-0.109168\pi$
$632$	20.1005	+	28.9921i	0.799555	+	1.15325i
$633$	25.0028	−	6.69949i	0.993773	−	0.266281i
$634$	28.5120	−	4.55564i	1.13236	−	0.180928i
$635$	4.09102	+	3.13915i	0.162347	+	0.124573i
$636$	−12.1231	−	18.5572i	−0.480714	−	0.735842i
$637$	36.8957	−	31.1719i	1.46186	−	1.23508i
$638$	−18.9752	−	10.2693i	−0.751236	−	0.406565i
$639$	−13.3389	+	7.70125i	−0.527681	+	0.304657i
$640$	−9.59915	+	19.2915i	−0.379440	+	0.762564i
$641$	4.77006	−	8.26198i	0.188406	−	0.326329i	−0.756313	−	0.654210i	$-0.773001\pi$
$641$	4.77006	−	8.26198i	0.188406	−	0.326329i	0.944719	+	0.327881i	$0.106335\pi$
$642$	0.212547	+	7.71560i	0.00838858	+	0.304510i
$643$	−1.30599	+	3.15294i	−0.0515033	+	0.124340i	−0.947537	−	0.319646i	$-0.896436\pi$
$643$	−1.30599	+	3.15294i	−0.0515033	+	0.124340i	0.896034	+	0.443986i	$0.146436\pi$
$644$	7.45378	−	15.6290i	0.293720	−	0.615869i
$645$	−14.6364	+	6.06261i	−0.576309	+	0.238715i
$646$	1.95909	+	0.748967i	0.0770794	+	0.0294677i
$647$	6.07105	+	22.6575i	0.238678	+	0.890757i	0.976456	+	0.215715i	$0.0692081\pi$
$647$	6.07105	+	22.6575i	0.238678	+	0.890757i	−0.737779	+	0.675043i	$0.764125\pi$
$648$	−8.37379	−	3.95221i	−0.328953	−	0.155257i
$649$	55.3970	+	14.8436i	2.17452	+	0.582661i
$650$	13.3228	+	1.38195i	0.522563	+	0.0542047i
$651$	−1.12901	+	10.4721i	−0.0442492	+	0.410433i
$652$	2.07556	+	11.0311i	0.0812851	+	0.432010i
$653$	−6.33574	−	48.1248i	−0.247937	−	1.88327i	−0.434273	−	0.900781i	$-0.642995\pi$
$653$	−6.33574	−	48.1248i	−0.247937	−	1.88327i	0.186336	−	0.982486i	$-0.440339\pi$
$654$	−6.49376	−	1.54967i	−0.253926	−	0.0605969i
$655$	−4.48638	+	7.77064i	−0.175297	+	0.303624i
$656$	3.03921	−	3.79517i	0.118661	−	0.148177i
$657$	2.39572			0.0934659
$658$	−1.69997	−	5.25549i	−0.0662718	−	0.204880i
$659$	−12.9028	+	31.1501i	−0.502621	+	1.21343i	0.445430	+	0.895317i	$0.353051\pi$
$659$	−12.9028	+	31.1501i	−0.502621	+	1.21343i	−0.948051	+	0.318118i	$0.896949\pi$
$660$	1.90223	−	25.0413i	0.0740441	−	0.974729i
$661$	−4.05812	+	30.8245i	−0.157843	+	1.19893i	0.710763	+	0.703431i	$0.248350\pi$
$661$	−4.05812	+	30.8245i	−0.157843	+	1.19893i	−0.868606	+	0.495503i	$0.834984\pi$
$662$	31.4047	+	22.7516i	1.22058	+	0.884265i
$663$	−2.40766	+	8.98551i	−0.0935057	+	0.348968i
$664$	−16.0969	−	5.15763i	−0.624679	−	0.200155i
$665$	−4.95346	+	5.19196i	−0.192087	+	0.201335i
$666$	−14.4840	+	11.7616i	−0.561242	+	0.455751i
$667$	−5.96739	+	7.77685i	−0.231058	+	0.301121i
$668$	−15.1349	+	16.9013i	−0.585588	+	0.653932i
$669$	4.28889	+	5.58939i	0.165818	+	0.216098i
$670$	0.704538	+	25.5752i	0.0272187	+	0.988055i
$671$	65.8357			2.54156
$672$	−16.4776	+	10.1913i	−0.635638	+	0.393138i
$673$	40.9511			1.57855			0.789274	−	0.614041i	$-0.210457\pi$
$673$	40.9511			1.57855			0.789274	+	0.614041i	$0.210457\pi$
$674$	0.627002	+	22.7606i	0.0241512	+	0.876704i
$675$	4.67746	+	6.09578i	0.180035	+	0.234627i
$676$	−51.5692	−	46.1796i	−1.98343	−	1.77614i
$677$	−10.0454	+	13.0914i	−0.386075	+	0.503142i	−0.945448	−	0.325774i	$-0.894375\pi$
$677$	−10.0454	+	13.0914i	−0.386075	+	0.503142i	0.559373	+	0.828916i	$0.311042\pi$
$678$	17.5902	−	14.2840i	0.675549	−	0.548573i
$679$	−22.5741	−	5.48350i	−0.866314	−	0.210437i
$680$	2.56734	+	4.98825i	0.0984532	+	0.191291i
$681$	−0.0718385	+	0.268105i	−0.00275286	+	0.0102738i
$682$	−17.9373	−	12.9950i	−0.686855	−	0.497603i
$683$	0.239358	−	1.81811i	0.00915880	−	0.0695680i	−0.986255	−	0.165230i	$-0.947163\pi$
$683$	0.239358	−	1.81811i	0.00915880	−	0.0695680i	0.995414	+	0.0956619i	$0.0304967\pi$
$684$	−3.76071	−	0.285678i	−0.143794	−	0.0109232i
$685$	−2.09641	+	5.06118i	−0.0800996	+	0.193378i
$686$	16.6183	−	20.2443i	0.634489	−	0.772932i
$687$	27.6371			1.05442
$688$	−22.5207	+	12.3869i	−0.858592	+	0.472247i
$689$	29.5380	−	51.1614i	1.12531	−	1.94909i
$690$	−11.0981	−	2.64844i	−0.422497	−	0.100825i
$691$	5.74341	+	43.6255i	0.218490	+	1.65959i	0.651832	+	0.758363i	$0.274001\pi$
$691$	5.74341	+	43.6255i	0.218490	+	1.65959i	−0.433343	+	0.901229i	$0.642666\pi$
$692$	4.76199	−	0.895995i	0.181024	−	0.0340606i
$693$	−10.5268	+	14.4076i	−0.399878	+	0.547299i
$694$	23.6176	+	2.44982i	0.896513	+	0.0929940i
$695$	21.1487	+	5.66676i	0.802214	+	0.214953i
$696$	10.3241	−	3.70344i	0.391332	−	0.140379i
$697$	−0.327638	−	1.22276i	−0.0124102	−	0.0463154i
$698$	22.4604	+	8.58668i	0.850138	+	0.325011i
$699$	−4.83883	+	2.00431i	−0.183021	+	0.0758099i
$700$	7.24075	−	0.570189i	0.273674	−	0.0215511i
$701$	17.7520	−	42.8570i	0.670483	−	1.61869i	−0.110309	−	0.993897i	$-0.535184\pi$
$701$	17.7520	−	42.8570i	0.670483	−	1.61869i	0.780792	−	0.624791i	$-0.214816\pi$
$702$	−1.50422	−	54.6040i	−0.0567730	−	2.06089i
$703$	7.09392	−	12.2870i	0.267552	−	0.463414i
$704$	−1.39907	−	40.7196i	−0.0527294	−	1.53468i
$705$	−3.15205	+	1.81984i	−0.118713	+	0.0685391i
$706$	−17.3293	−	9.37851i	−0.652196	−	0.352965i
$707$	1.73158	−	4.47509i	0.0651229	−	0.168303i
$708$	−24.4080	+	15.9453i	−0.917308	+	0.599263i
$709$	−0.950811	−	0.729583i	−0.0357084	−	0.0274001i	0.590753	−	0.806852i	$-0.298831\pi$
$709$	−0.950811	−	0.729583i	−0.0357084	−	0.0274001i	−0.626461	+	0.779452i	$0.715497\pi$
$710$	30.9363	−	4.94299i	1.16102	−	0.185507i
$711$	−15.9540	+	4.27487i	−0.598323	+	0.160320i
$712$	−5.04344	+	27.8459i	−0.189011	+	1.04357i
$713$	−7.11582	+	7.11582i	−0.266490	+	0.266490i
$714$	−0.402390	+	5.02827i	−0.0150591	+	0.188178i
$715$	61.8359	−	25.6133i	2.31253	−	0.957882i
$716$	14.3955	+	16.7624i	0.537986	+	0.626440i
$717$	−2.15375	−	2.80682i	−0.0804332	−	0.104823i
$718$	−9.62187	+	40.3196i	−0.359085	+	1.50471i
$719$	−19.7501	+	11.4027i	−0.736554	+	0.425250i	−0.820815	−	0.571194i	$-0.806480\pi$
$719$	−19.7501	+	11.4027i	−0.736554	+	0.425250i	0.0842609	+	0.996444i	$0.473147\pi$
$720$	−6.98406	−	7.27989i	−0.260281	−	0.271306i
$721$	4.37856	−	8.01309i	0.163066	−	0.298423i
$722$	−23.0044	+	6.84828i	−0.856135	+	0.254867i
$723$	19.2738	−	2.53744i	0.716801	−	0.0943686i
$724$	5.38722	−	2.58759i	0.200214	−	0.0961671i
$725$	−4.07660	−	0.536694i	−0.151401	−	0.0199323i
$726$	11.1573	+	24.9683i	0.414088	+	0.926660i
$727$	−1.25193	−	1.25193i	−0.0464316	−	0.0464316i	0.683510	−	0.729941i	$-0.260453\pi$
$727$	−1.25193	−	1.25193i	−0.0464316	−	0.0464316i	−0.729941	+	0.683510i	$0.760453\pi$
$728$	−44.0647	−	26.9178i	−1.63315	−	0.997638i
$729$	18.4375	−	18.4375i	0.682869	−	0.682869i
$730$	−4.55161	−	1.74010i	−0.168463	−	0.0644039i
$731$	−0.873464	+	6.63462i	−0.0323062	+	0.245390i
$732$	−22.3267	+	24.9324i	−0.825218	+	0.921529i
$733$	3.22720	+	24.5131i	0.119200	+	0.905410i	0.941655	+	0.336580i	$0.109270\pi$
$733$	3.22720	+	24.5131i	0.119200	+	0.905410i	−0.822455	+	0.568830i	$0.807396\pi$
$734$	14.5087	+	7.85205i	0.535527	+	0.289824i
$735$	−15.3353	−	7.91740i	−0.565651	−	0.292038i
$736$	−18.3686	−	2.29124i	−0.677077	−	0.0844561i
$737$	−24.1886	−	41.8959i	−0.890999	−	1.54326i
$738$	1.19204	+	1.93930i	0.0438795	+	0.0713865i
$739$	23.8650	−	18.3122i	0.877887	−	0.673626i	−0.0681536	−	0.997675i	$-0.521711\pi$
$739$	23.8650	−	18.3122i	0.877887	−	0.673626i	0.946040	+	0.324049i	$0.105044\pi$
$740$	36.0608	−	11.8255i	1.32562	−	0.434713i
$741$	4.86781	+	11.7519i	0.178824	+	0.431718i
$742$	10.7330	−	30.1829i	0.394022	−	1.10805i
$743$	−4.91671	−	4.91671i	−0.180377	−	0.180377i	0.611143	−	0.791520i	$-0.290710\pi$
$743$	−4.91671	−	4.91671i	−0.180377	−	0.180377i	−0.791520	+	0.611143i	$0.790710\pi$
$744$	11.0043	−	2.38603i	0.403437	−	0.0874762i
$745$	−1.30252	−	4.86109i	−0.0477208	−	0.178097i
$746$	−2.15879	+	2.97985i	−0.0790391	+	0.109100i
$747$	4.81755	−	6.27835i	0.176265	−	0.229713i
$748$	−8.75864	−	5.98461i	−0.320248	−	0.218819i
$749$	−8.68764	+	6.99669i	−0.317439	+	0.255654i
$750$	−6.33971	−	21.2960i	−0.231494	−	0.777622i
$751$	−7.80945	−	13.5264i	−0.284971	−	0.493584i	0.687631	−	0.726060i	$-0.258651\pi$
$751$	−7.80945	−	13.5264i	−0.284971	−	0.493584i	−0.972602	+	0.232476i	$0.925317\pi$
$752$	−4.75826	+	3.49681i	−0.173516	+	0.127515i
$753$	−27.7062	−	15.9962i	−1.00967	−	0.582933i
$754$	21.2314	+	20.0930i	0.773201	+	0.731743i
$755$	2.32359	+	0.962461i	0.0845640	+	0.0350276i
$756$	−6.15980	−	28.9731i	−0.224030	−	1.05374i
$757$	6.69326	+	16.1590i	0.243271	+	0.587308i	0.997604	−	0.0691842i	$-0.0220396\pi$
$757$	6.69326	+	16.1590i	0.243271	+	0.587308i	−0.754333	+	0.656492i	$0.772040\pi$
$758$	−4.35123	−	9.73733i	−0.158044	−	0.353676i
$759$	20.8390	−	5.58379i	0.756407	−	0.202679i
$760$	6.93746	+	3.27430i	0.251648	+	0.118771i
$761$	5.17487	−	19.3129i	0.187589	−	0.700092i	−0.806472	−	0.591272i	$-0.798626\pi$
$761$	5.17487	−	19.3129i	0.187589	−	0.700092i	0.994061	−	0.108820i	$-0.0347073\pi$
$762$	3.84781	−	3.12458i	0.139391	−	0.113191i
$763$	−3.90070	−	8.82460i	−0.141215	−	0.319472i
$764$	10.6595	−	6.96369i	0.385648	−	0.251938i
$765$	−2.60411	+	0.342838i	−0.0941519	+	0.0123953i
$766$	17.1503	+	27.9015i	0.619666	+	1.00812i
$767$	−67.2916	−	38.8508i	−2.42976	−	1.40282i
$768$	15.8953	+	13.2793i	0.573571	+	0.479175i
$769$		−	46.5336i		−	1.67804i	−0.544098	−	0.839022i	$-0.683128\pi$
$769$		−	46.5336i		−	1.67804i	0.544098	−	0.839022i	$-0.316872\pi$
$770$	30.4644	−	19.7269i	1.09786	−	0.710909i
$771$	16.4674	+	6.82104i	0.593060	+	0.245654i
$772$	−1.16890	+	2.30962i	−0.0420697	+	0.0831250i
$773$	−28.8332	−	3.79596i	−1.03706	−	0.136531i	−0.407278	−	0.913304i	$-0.633522\pi$
$773$	−28.8332	−	3.79596i	−1.03706	−	0.136531i	−0.629781	+	0.776773i	$0.716855\pi$
$774$	−1.89862	−	11.8827i	−0.0682445	−	0.427116i
$775$	−4.07733	−	1.09252i	−0.146462	−	0.0392444i
$776$	2.04955	+	24.7498i	0.0735746	+	0.888465i
$777$	33.1586	+	8.05459i	1.18956	+	0.288957i
$778$	−3.51001	+	33.8384i	−0.125840	+	1.21317i
$779$	−1.37328	−	1.05376i	−0.0492030	−	0.0377548i
$780$	−11.2703	+	32.1038i	−0.403542	+	1.14950i
$781$	−46.9966	+	36.0618i	−1.68167	+	1.29039i
$782$	−3.31277	+	3.50046i	−0.118464	+	0.125176i
$783$			16.7687i			0.599264i
$784$	−26.1412	−	10.0319i	−0.933613	−	0.358283i
$785$			45.5381i			1.62532i
$786$	6.26433	+	5.92844i	0.223441	+	0.211461i
$787$	−8.08180	+	6.20139i	−0.288085	+	0.221056i	−0.742686	−	0.669640i	$-0.766449\pi$
$787$	−8.08180	+	6.20139i	−0.288085	+	0.221056i	0.454601	+	0.890695i	$0.349782\pi$
$788$	−3.20281	+	1.53838i	−0.114096	+	0.0548025i
$789$	−13.4993	−	10.3584i	−0.480589	−	0.368769i
$790$	33.4160	+	3.46619i	1.18889	+	0.123321i
$791$	31.8218	+	7.72988i	1.13145	+	0.274843i
$792$	18.1658	+	5.82054i	0.645494	+	0.206824i
$793$	−86.1575	−	23.0858i	−3.05954	−	0.819802i
$794$	18.8077	−	3.00509i	0.667461	−	0.106647i
$795$	−20.9280	−	2.75522i	−0.742239	−	0.0977177i
$796$	5.76109	+	17.5680i	0.204196	+	0.622680i
$797$	−29.1949	−	12.0929i	−1.03414	−	0.428353i	−0.199932	−	0.979810i	$-0.564072\pi$
$797$	−29.1949	−	12.0929i	−1.03414	−	0.428353i	−0.834204	+	0.551457i	$0.814072\pi$
$798$	3.74911	+	5.78979i	0.132717	+	0.204956i
$799$			1.53741i			0.0543898i
$800$	−3.02014	−	7.15321i	−0.106778	−	0.252904i
$801$	−11.4741	−	6.62455i	−0.405416	−	0.234067i
$802$	−6.20197	+	3.81219i	−0.218999	+	0.134613i
$803$	9.13511	−	1.20266i	0.322371	−	0.0424409i
$804$	24.0693	+	5.04765i	0.848858	+	0.178017i
$805$	−6.66644	−	15.0816i	−0.234961	−	0.531555i
$806$	18.9173	+	23.2960i	0.666333	+	0.820567i
$807$	2.21811	−	8.27810i	0.0780811	−	0.291403i
$808$	−5.12375	−	0.247553i	−0.180253	−	0.00870890i
$809$	17.4026	−	4.66300i	0.611841	−	0.163942i	0.0604253	−	0.998173i	$-0.480754\pi$
$809$	17.4026	−	4.66300i	0.611841	−	0.163942i	0.551416	+	0.834230i	$0.314088\pi$
$810$	−8.05056	+	3.59748i	−0.282868	+	0.126402i
$811$	−3.00766	−	7.26114i	−0.105613	−	0.254973i	0.862235	−	0.506509i	$-0.169064\pi$
$811$	−3.00766	−	7.26114i	−0.105613	−	0.254973i	−0.967848	+	0.251536i	$0.919064\pi$
$812$	13.2943	+	8.63257i	0.466539	+	0.302944i
$813$	28.5004	+	11.8052i	0.999551	+	0.414028i
$814$	−49.3244	+	52.1189i	−1.72882	+	1.82677i
$815$	9.25699	+	5.34453i	0.324258	+	0.187211i
$816$	5.23671	−	1.28741i	0.183321	−	0.0450684i
$817$	4.57523	+	7.92453i	0.160067	+	0.277244i
$818$	1.55161	−	0.461907i	0.0542509	−	0.0161502i
$819$	18.8282	−	15.1635i	0.657911	−	0.529857i
$820$	−0.856160	−	4.55028i	−0.0298984	−	0.158903i
$821$	27.1989	−	35.4463i	0.949250	−	1.23709i	−0.0221790	−	0.999754i	$-0.507060\pi$
$821$	27.1989	−	35.4463i	0.949250	−	1.23709i	0.971429	−	0.237332i	$-0.0762730\pi$
$822$	4.26431	+	3.08934i	0.148735	+	0.107753i
$823$	5.71956	+	21.3457i	0.199371	+	0.744064i	0.991092	+	0.133180i	$0.0425190\pi$
$823$	5.71956	+	21.3457i	0.199371	+	0.744064i	−0.791720	+	0.610884i	$0.790814\pi$
$824$	−9.60553	−	1.73975i	−0.334625	−	0.0606070i
$825$	6.39897	+	6.39897i	0.222783	+	0.222783i
$826$	−39.6990	−	14.1170i	−1.38131	−	0.491192i
$827$	10.4914	+	25.3284i	0.364821	+	0.880755i	0.994581	+	0.103965i	$0.0331532\pi$
$827$	10.4914	+	25.3284i	0.364821	+	0.880755i	−0.629760	+	0.776790i	$0.716847\pi$
$828$	3.91349	−	7.73262i	0.136003	−	0.268727i
$829$	15.2197	−	11.6785i	0.528601	−	0.405610i	−0.309686	−	0.950839i	$-0.600224\pi$
$829$	15.2197	−	11.6785i	0.528601	−	0.405610i	0.838287	+	0.545229i	$0.183557\pi$
$830$	−13.7130	+	8.42904i	−0.475986	+	0.292576i
$831$	−6.44816	−	11.1685i	−0.223684	−	0.387432i
$832$	−12.4477	+	53.7793i	−0.431548	+	1.86446i
$833$	−6.13512	+	3.93767i	−0.212569	+	0.136432i
$834$	10.0170	−	18.5090i	0.346860	−	0.640915i
$835$	2.82001	+	21.4201i	0.0975905	+	0.741274i
$836$	−14.4834	+	0.798575i	−0.500918	+	0.0276193i
$837$	−2.24698	+	17.0675i	−0.0776670	+	0.589940i
$838$	14.1347	−	36.9725i	0.488275	−	1.27719i
$839$	6.91976	−	6.91976i	0.238897	−	0.238897i	−0.577497	−	0.816393i	$-0.695970\pi$
$839$	6.91976	−	6.91976i	0.238897	−	0.238897i	0.816393	+	0.577497i	$0.195970\pi$
$840$	−2.86061	+	18.2270i	−0.0987004	+	0.628892i
$841$	14.1608	+	14.1608i	0.488304	+	0.488304i
$842$	15.2604	−	6.81925i	0.525907	−	0.235007i
$843$	−31.1496	−	4.10092i	−1.07285	−	0.141243i
$844$	13.2468	−	37.7338i	0.455973	−	1.29885i
$845$	−65.3569	+	8.60440i	−2.24835	+	0.296000i
$846$	−0.788798	−	2.64969i	−0.0271194	−	0.0910982i
$847$	−18.9516	+	34.6827i	−0.651183	+	1.19171i
$848$	−34.2389	−	0.710098i	−1.17577	−	0.0243849i
$849$	16.5863	−	9.57608i	0.569239	−	0.328650i
$850$	−1.96638	−	0.469257i	−0.0674463	−	0.0160954i
$851$	19.8468	+	25.8648i	0.680338	+	0.886634i
$852$	2.28100	−	30.0275i	0.0781457	−	1.02872i
$853$	33.0362	−	13.6840i	1.13114	−	0.468532i	0.262970	−	0.964804i	$-0.415298\pi$
$853$	33.0362	−	13.6840i	1.13114	−	0.468532i	0.868167	+	0.496271i	$0.165298\pi$
$854$	−48.2136	−	3.85832i	−1.64983	−	0.132029i
$855$	−2.53964	+	2.53964i	−0.0868538	+	0.0868538i
$856$	10.0275	+	6.45391i	0.342734	+	0.220590i
$857$	−45.0972	+	12.0838i	−1.54049	+	0.412774i	−0.926425	−	0.376480i	$-0.877134\pi$
$857$	−45.0972	+	12.0838i	−1.54049	+	0.412774i	−0.614068	+	0.789253i	$0.710468\pi$
$858$	−10.1508	−	63.5297i	−0.346541	−	2.16887i
$859$	−30.9777	−	23.7700i	−1.05695	−	0.811023i	−0.0744347	−	0.997226i	$-0.523715\pi$
$859$	−30.9777	−	23.7700i	−1.05695	−	0.811023i	−0.982511	+	0.186203i	$0.940382\pi$
$860$	−5.02368	+	23.9550i	−0.171306	+	0.816858i
$861$	1.50234	−	3.88263i	0.0511995	−	0.132320i
$862$	21.8058	−	40.2920i	0.742710	−	1.37235i
$863$	−14.2685	+	8.23794i	−0.485706	+	0.280423i	−0.722792	−	0.691066i	$-0.757141\pi$
$863$	−14.2685	+	8.23794i	−0.485706	+	0.280423i	0.237085	+	0.971489i	$0.423808\pi$
$864$	−27.3151	+	16.0192i	−0.929277	+	0.544983i
$865$	2.30717	−	3.99614i	0.0784462	−	0.135873i
$866$	−32.8235	+	0.904214i	−1.11539	+	0.0307264i
$867$	−7.88434	+	19.0345i	−0.267766	+	0.646445i
$868$	12.3745	+	10.5678i	0.420017	+	0.358696i
$869$	−58.6882	+	24.3095i	−1.99086	+	0.824642i
$870$	3.72983	−	9.75621i	0.126453	−	0.330767i
$871$	16.9639	+	63.3100i	0.574799	+	2.14518i
$872$	−7.63687	+	6.93293i	−0.258617	+	0.234779i
$873$	−11.2309	−	3.00931i	−0.380109	−	0.101850i
$874$	−0.679943	+	6.55502i	−0.0229994	+	0.221727i
$875$	18.9443	−	25.9283i	0.640433	−	0.876537i
$876$	−2.64251	+	3.86738i	−0.0892820	+	0.130667i
$877$	2.96458	+	22.5182i	0.100107	+	0.760385i	0.965704	+	0.259645i	$0.0836055\pi$
$877$	2.96458	+	22.5182i	0.100107	+	0.760385i	−0.865598	+	0.500740i	$0.833061\pi$
$878$	6.74233	−	28.2531i	0.227543	−	0.953497i
$879$	−17.7308	+	30.7107i	−0.598046	+	1.03585i
$880$	−30.2854	−	24.2529i	−1.02092	−	0.817565i
$881$	−22.7253			−0.765636			−0.382818	−	0.923824i	$-0.625046\pi$
$881$	−22.7253			−0.765636			−0.382818	+	0.923824i	$0.625046\pi$
$882$	8.55343	−	9.93420i	0.288009	−	0.334502i
$883$	−17.4587	+	42.1489i	−0.587530	+	1.41842i	0.298326	+	0.954464i	$0.403572\pi$
$883$	−17.4587	+	42.1489i	−0.587530	+	1.41842i	−0.885856	+	0.463960i	$0.846428\pi$
$884$	9.36365	+	10.9032i	0.314934	+	0.366714i
$885$	−3.62389	+	27.5262i	−0.121816	+	0.925283i
$886$	−20.8214	+	28.7403i	−0.699507	+	0.965549i
$887$	0.763209	−	2.84834i	0.0256261	−	0.0956377i	−0.951928	−	0.306321i	$-0.900902\pi$
$887$	0.763209	−	2.84834i	0.0256261	−	0.0956377i	0.977554	+	0.210683i	$0.0675687\pi$
$888$	−3.01054	−	36.3544i	−0.101027	−	1.21997i
$889$	6.96093	+	1.69089i	0.233462	+	0.0567106i
$890$	16.9878	+	20.9200i	0.569434	+	0.701239i
$891$	10.1500	−	13.2277i	0.340037	−	0.443144i
$892$	10.8683	−	0.599248i	0.363897	−	0.0200643i
$893$	1.27977	+	1.66783i	0.0428260	+	0.0558119i
$894$	−4.83561	+	0.133210i	−0.161727	+	0.00445521i
$895$	21.0412			0.703329
$896$	−1.36180	+	29.9023i	−0.0454946	+	0.998965i
$897$	−29.2294			−0.975942
$898$	−28.5755	+	0.787190i	−0.953576	+	0.0262689i
$899$	−5.60810	−	7.30861i	−0.187040	−	0.243756i
$900$	3.62977	−	0.200136i	0.120992	−	0.00667119i
$901$	−5.42792	+	7.07381i	−0.180830	+	0.235663i
$902$	5.51888	+	6.79632i	0.183759	+	0.226293i
$903$	−15.1917	+	15.9231i	−0.505547	+	0.529888i
$904$	−2.88918	−	34.8888i	−0.0960925	−	1.16039i
$905$	1.47301	−	5.49735i	0.0489645	−	0.182738i
$906$	1.41832	−	1.95774i	0.0471204	−	0.0650417i
$907$	−5.55893	+	42.2242i	−0.184581	+	1.40203i	0.608808	+	0.793318i	$0.291648\pi$
$907$	−5.55893	+	42.2242i	−0.184581	+	1.40203i	−0.793389	+	0.608715i	$0.791685\pi$
$908$	0.279388	+	0.325324i	0.00927180	+	0.0107962i
$909$	0.919074	−	2.21884i	0.0304837	−	0.0735943i
$910$	−46.7854	+	15.1335i	−1.55092	+	0.501670i
$911$	−22.9192			−0.759346			−0.379673	−	0.925121i	$-0.623964\pi$
$911$	−22.9192			−0.759346			−0.379673	+	0.925121i	$0.623964\pi$
$912$	4.60928	−	5.75576i	0.152628	−	0.190592i
$913$	15.2180	−	26.3584i	0.503643	−	0.872335i
$914$	7.27318	−	30.4776i	0.240575	−	1.00811i
$915$	4.16001	+	31.5984i	0.137526	+	1.04461i
$916$	24.0889	−	35.2548i	0.795921	−	1.16485i
$917$	−1.33608	+	12.3928i	−0.0441212	+	0.409246i
$918$	−0.850626	+	8.20050i	−0.0280748	+	0.270657i
$919$	−6.56055	−	1.75789i	−0.216413	−	0.0579876i	0.148984	−	0.988840i	$-0.452400\pi$
$919$	−6.56055	−	1.75789i	−0.216413	−	0.0579876i	−0.365396	+	0.930852i	$0.619067\pi$
$920$	−13.0517	+	11.8486i	−0.430302	+	0.390638i
$921$	−0.382705	−	1.42827i	−0.0126105	−	0.0470632i
$922$	−12.8567	+	33.6296i	−0.423413	+	1.10753i
$923$	74.1486	−	30.7134i	2.44063	−	1.01094i
$924$	−11.6468	−	32.8849i	−0.383153	−	1.08183i
$925$	−5.23328	+	12.6343i	−0.172069	+	0.415412i
$926$	17.4071	−	0.479525i	0.572031	−	0.0157582i
$927$	2.28516	−	3.95801i	0.0750545	−	0.129998i
$928$	4.27438	−	16.3977i	0.140313	−	0.538280i
$929$	2.88857	−	1.66772i	0.0947709	−	0.0547160i	−0.451866	−	0.892086i	$-0.649241\pi$
$929$	2.88857	−	1.66772i	0.0947709	−	0.0547160i	0.546636	+	0.837370i	$0.315908\pi$
$930$	5.10362	−	9.43028i	0.167354	−	0.309231i
$931$	−3.37778	+	9.37870i	−0.110702	+	0.307375i
$932$	−1.66084	+	7.91956i	−0.0544026	+	0.259414i
$933$	7.49179	+	5.74865i	0.245270	+	0.188202i
$934$	6.44954	+	40.3652i	0.211036	+	1.32079i
$935$	−9.75762	+	2.61455i	−0.319108	+	0.0855048i
$936$	−21.7321	−	13.9872i	−0.710336	−	0.457185i
$937$	−30.7306	+	30.7306i	−1.00392	+	1.00392i	−0.00393267	+	0.999992i	$0.501252\pi$
$937$	−30.7306	+	30.7306i	−1.00392	+	1.00392i	−0.999992	+	0.00393267i	$0.998748\pi$
$938$	15.2588	+	32.0993i	0.498216	+	1.04808i
$939$	6.96685	−	2.88577i	0.227355	−	0.0941734i
$940$	−0.425933	+	5.60706i	−0.0138924	+	0.182882i
$941$	0.0171643	+	0.0223689i	0.000559540	+	0.000729207i	0.793633	−	0.608397i	$-0.208187\pi$
$941$	0.0171643	+	0.0223689i	0.000559540	+	0.000729207i	−0.793073	+	0.609126i	$0.791520\pi$
$942$	42.5769	+	10.1605i	1.38723	+	0.331048i
$943$	3.44469	−	1.98879i	0.112175	−	0.0647640i
$944$	−0.933979	+	45.0338i	−0.0303984	+	1.46573i
$945$	−24.7530	−	13.5257i	−0.805215	−	0.439991i
$946$	−13.2048	−	44.3569i	−0.429325	−	1.44217i
$947$	−15.5110	+	2.04206i	−0.504040	+	0.0663581i	−0.378259	−	0.925700i	$-0.623477\pi$
$947$	−15.5110	+	2.04206i	−0.504040	+	0.0663581i	−0.125781	+	0.992058i	$0.540144\pi$
$948$	10.6966	−	30.4696i	0.347410	−	0.989607i
$949$	−12.3766	−	1.62941i	−0.401761	−	0.0528929i
$950$	−2.52381	+	1.12779i	−0.0818832	+	0.0365904i
$951$	−18.6887	−	18.6887i	−0.606024	−	0.606024i
$952$	6.06350	+	4.89602i	0.196519	+	0.158681i
$953$	41.4334	−	41.4334i	1.34216	−	1.34216i	0.448251	−	0.893908i	$-0.352047\pi$
$953$	41.4334	−	41.4334i	1.34216	−	1.34216i	0.893908	−	0.448251i	$-0.147953\pi$
$954$	5.72554	−	14.9764i	0.185371	−	0.484879i
$955$	1.58264	−	12.0213i	0.0512129	−	0.389000i
$956$	−5.45771	+	0.300924i	−0.176515	+	0.00973257i
$957$	2.57786	+	19.5808i	0.0833303	+	0.632956i
$958$	14.1419	−	26.1309i	0.456905	−	0.844252i
$959$	0.178847	+	7.60796i	0.00577527	+	0.245674i
$960$	19.4553	−	3.24448i	0.627918	−	0.104715i
$961$	10.7713	+	18.6565i	0.347462	+	0.601821i
$962$	82.8255	−	50.9107i	2.67040	−	1.64143i
$963$	−4.42934	+	3.39875i	−0.142734	+	0.109523i
$964$	13.5625	−	26.7980i	0.436819	−	0.863105i
$965$	0.943335	+	2.27741i	0.0303670	+	0.0733125i
$966$	−15.5883	+	2.86791i	−0.501545	+	0.0922735i
$967$	−42.0180	−	42.0180i	−1.35121	−	1.35121i	−0.884311	−	0.466898i	$-0.845372\pi$
$967$	−42.0180	−	42.0180i	−1.35121	−	1.35121i	−0.466898	−	0.884311i	$-0.654628\pi$
$968$	41.5753	+	7.53009i	1.33628	+	0.242026i
$969$	−0.496896	−	1.85444i	−0.0159626	−	0.0595733i
$970$	19.1518	+	13.8748i	0.614926	+	0.445493i
$971$	−17.2773	+	22.5162i	−0.554455	+	0.722579i	−0.983541	−	0.180684i	$-0.942169\pi$
$971$	−17.2773	+	22.5162i	−0.554455	+	0.722579i	0.429087	+	0.903263i	$0.358836\pi$
$972$	−4.64327	−	24.6778i	−0.148933	−	0.791540i
$973$	30.0534	−	4.67757i	0.963467	−	0.149956i
$974$	−12.2774	+	3.65492i	−0.393394	+	0.117111i
$975$	−6.13031	−	10.6180i	−0.196327	−	0.340049i
$976$	12.3443	+	50.2121i	0.395132	+	1.60725i
$977$	22.2372	+	12.8387i	0.711431	+	0.410745i	0.811591	−	0.584226i	$-0.198602\pi$
$977$	22.2372	+	12.8387i	0.711431	+	0.410745i	−0.100159	+	0.994971i	$0.531935\pi$
$978$	7.06242	−	7.46256i	0.225831	−	0.238626i
$979$	−47.0772	−	19.5000i	−1.50460	−	0.623224i
$980$	−23.4662	+	12.6613i	−0.749599	+	0.404449i
$981$	−1.84800	−	4.46146i	−0.0590020	−	0.142443i
$982$	13.8808	−	6.20279i	0.442955	−	0.197939i
$983$	5.74279	−	1.53877i	0.183166	−	0.0490793i	−0.166070	−	0.986114i	$-0.553108\pi$
$983$	5.74279	−	1.53877i	0.183166	−	0.0490793i	0.349236	+	0.937035i	$0.386441\pi$
$984$	−4.44541	−	0.214779i	−0.141715	−	0.00684692i
$985$	−0.875735	+	3.26829i	−0.0279032	+	0.104136i
$986$	−2.78119	−	3.42495i	−0.0885713	−	0.109073i
$987$	−2.98283	+	4.08249i	−0.0949446	+	0.129947i
$988$	19.2340	+	4.03364i	0.611916	+	0.128327i
$989$	−20.8467	+	2.74452i	−0.662887	+	0.0872707i
$990$	15.4756	−	9.51243i	0.491846	−	0.302325i
$991$	17.8271	+	10.2925i	0.566296	+	0.326951i	0.755669	−	0.654954i	$-0.227312\pi$
$991$	17.8271	+	10.2925i	0.566296	+	0.326951i	−0.189373	+	0.981905i	$0.560645\pi$
$992$	6.54782	−	16.1171i	0.207893	−	0.511720i
$993$		−	35.4977i		−	1.12649i
$994$	36.5305	−	23.6549i	1.15868	−	0.750289i
$995$	16.2661	+	6.73764i	0.515670	+	0.213598i
$996$	4.82125	+	14.7020i	0.152767	+	0.465851i
$997$	−52.9240	−	6.96758i	−1.67612	−	0.220665i	−0.768319	−	0.640067i	$-0.778907\pi$
$997$	−52.9240	−	6.96758i	−1.67612	−	0.220665i	−0.907801	+	0.419401i	$0.862240\pi$
$998$	13.6538	−	2.18159i	0.432202	−	0.0690571i
$999$	53.8701	+	14.4345i	1.70438	+	0.456686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.be.a.115.2	yes	240
4.3	odd	2		896.2.bi.a.367.9		240
7.5	odd	6	inner	224.2.be.a.19.21	✓	240
28.19	even	6		896.2.bi.a.495.9		240
32.5	even	8		896.2.bi.a.143.9		240
32.27	odd	8	inner	224.2.be.a.59.21	yes	240
224.5	odd	24		896.2.bi.a.271.9		240
224.187	even	24	inner	224.2.be.a.187.2	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.be.a.19.21	✓	240	7.5	odd	6	inner
224.2.be.a.59.21	yes	240	32.27	odd	8	inner
224.2.be.a.115.2	yes	240	1.1	even	1	trivial
224.2.be.a.187.2	yes	240	224.187	even	24	inner
896.2.bi.a.143.9		240	32.5	even	8
896.2.bi.a.271.9		240	224.5	odd	24
896.2.bi.a.367.9		240	4.3	odd	2
896.2.bi.a.495.9		240	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.be (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41368 + 0.0389436i) q^{2} +(0.788053 + 1.02701i) q^{3} +(1.99697 - 0.110107i) q^{4} +(1.15943 - 1.51100i) q^{5} +(-1.15405 - 1.42117i) q^{6} +(0.624522 - 2.57099i) q^{7} +(-2.81878 + 0.233426i) q^{8} +(0.342734 - 1.27910i) q^{9} +O(q^{10})\)	\(q+(-1.41368 + 0.0389436i) q^{2} +(0.788053 + 1.02701i) q^{3} +(1.99697 - 0.110107i) q^{4} +(1.15943 - 1.51100i) q^{5} +(-1.15405 - 1.42117i) q^{6} +(0.624522 - 2.57099i) q^{7} +(-2.81878 + 0.233426i) q^{8} +(0.342734 - 1.27910i) q^{9} +(-1.58022 + 2.18122i) q^{10} +(0.664765 - 5.04939i) q^{11} +(1.68680 + 1.96413i) q^{12} +(-2.64057 + 6.37490i) q^{13} +(-0.782748 + 3.65887i) q^{14} +2.46550 q^{15} +(3.97575 - 0.439762i) q^{16} +(0.520718 - 0.901911i) q^{17} +(-0.434703 + 1.82158i) q^{18} +(-0.185877 - 1.41188i) q^{19} +(2.14897 - 3.14507i) q^{20} +(3.13259 - 1.38468i) q^{21} +(-0.743121 + 7.16409i) q^{22} +(3.16081 + 0.846936i) q^{23} +(-2.46108 - 2.71096i) q^{24} +(0.355257 + 1.32584i) q^{25} +(3.48465 - 9.11488i) q^{26} +(5.17168 - 2.14218i) q^{27} +(0.964064 - 5.20294i) q^{28} +(-1.14636 + 2.76757i) q^{29} +(-3.48542 + 0.0960156i) q^{30} +(-1.53764 + 2.66328i) q^{31} +(-5.60331 + 0.776512i) q^{32} +(5.70964 - 3.29646i) q^{33} +(-0.701004 + 1.29529i) q^{34} +(-3.16067 - 3.92453i) q^{35} +(0.543590 - 2.59206i) q^{36} +(7.90414 + 6.06506i) q^{37} +(0.317754 + 1.98870i) q^{38} +(-8.62799 + 2.31186i) q^{39} +(-2.91547 + 4.52981i) q^{40} +(0.859509 - 0.859509i) q^{41} +(-4.37454 + 2.07949i) q^{42} +(-5.93649 + 2.45898i) q^{43} +(0.771537 - 10.1567i) q^{44} +(-1.53534 - 2.00090i) q^{45} +(-4.50135 - 1.07420i) q^{46} +(-1.27846 + 0.738121i) q^{47} +(3.58474 + 3.73658i) q^{48} +(-6.21995 - 3.21127i) q^{49} +(-0.553852 - 1.86047i) q^{50} +(1.33663 - 0.175970i) q^{51} +(-4.57120 + 13.0212i) q^{52} +(-8.48833 - 1.11751i) q^{53} +(-7.22766 + 3.22975i) q^{54} +(-6.85887 - 6.85887i) q^{55} +(-1.16025 + 7.39282i) q^{56} +(1.30353 - 1.30353i) q^{57} +(1.51281 - 3.95709i) q^{58} +(-1.46984 + 11.1645i) q^{59} +(4.92353 - 0.271470i) q^{60} +(1.68729 + 12.8162i) q^{61} +(2.07001 - 3.82489i) q^{62} +(-3.07451 - 1.67999i) q^{63} +(7.89102 - 1.31595i) q^{64} +(6.57090 + 11.3811i) q^{65} +(-7.94321 + 4.88249i) q^{66} +(7.53594 - 5.78253i) q^{67} +(0.940550 - 1.85842i) q^{68} +(1.62107 + 3.91361i) q^{69} +(4.62100 + 5.42493i) q^{70} +(-8.22460 - 8.22460i) q^{71} +(-0.667517 + 3.68551i) q^{72} +(0.468243 + 1.74751i) q^{73} +(-11.4101 - 8.26622i) q^{74} +(-1.08169 + 1.40968i) q^{75} +(-0.526649 - 2.79901i) q^{76} +(-12.5667 - 4.86255i) q^{77} +(12.1072 - 3.60423i) q^{78} +(-6.23642 - 10.8018i) q^{79} +(3.94513 - 6.51723i) q^{80} +(2.83516 + 1.63688i) q^{81} +(-1.18160 + 1.24854i) q^{82} +(5.52119 + 2.28695i) q^{83} +(6.10321 - 3.11009i) q^{84} +(-0.759049 - 1.83251i) q^{85} +(8.29652 - 3.70739i) q^{86} +(-3.74571 + 1.00366i) q^{87} +(-0.695168 + 14.3883i) q^{88} +(2.58953 - 9.66427i) q^{89} +(2.24840 + 2.76883i) q^{90} +(14.7407 + 10.7701i) q^{91} +(6.40528 + 1.34327i) q^{92} +(-3.94696 + 0.519627i) q^{93} +(1.77859 - 1.09325i) q^{94} +(-2.34886 - 1.35611i) q^{95} +(-5.21319 - 5.14272i) q^{96} -8.78032i q^{97} +(8.91805 + 4.29748i) q^{98} +(-6.23084 - 2.58090i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 12 q^{28} - 16 q^{29} - 52 q^{30} - 4 q^{32} - 24 q^{33} - 32 q^{35} + 64 q^{36} - 4 q^{37} - 12 q^{38} - 4 q^{39} - 12 q^{40} - 28 q^{42} - 32 q^{43} - 52 q^{44} - 48 q^{45} - 4 q^{46} - 24 q^{47} - 40 q^{50} + 20 q^{51} + 60 q^{52} - 20 q^{53} - 12 q^{54} - 48 q^{56} - 16 q^{57} - 36 q^{58} + 84 q^{59} + 28 q^{60} - 12 q^{61} - 136 q^{64} - 8 q^{65} + 132 q^{66} + 36 q^{67} - 12 q^{68} + 28 q^{70} - 80 q^{71} - 4 q^{72} - 12 q^{73} - 20 q^{74} - 72 q^{75} - 8 q^{77} - 216 q^{78} - 8 q^{79} + 24 q^{80} + 108 q^{82} + 12 q^{84} + 24 q^{85} - 4 q^{86} - 12 q^{87} - 48 q^{88} - 12 q^{89} + 40 q^{91} - 80 q^{92} + 20 q^{93} + 60 q^{94} + 312 q^{96} - 16 q^{98} - 40 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 12 * q^10 - 4 * q^11 - 12 * q^12 - 40 * q^14 - 32 * q^15 - 24 * q^16 + 16 * q^18 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^29 - 52 * q^30 - 4 * q^32 - 24 * q^33 - 32 * q^35 + 64 * q^36 - 4 * q^37 - 12 * q^38 - 4 * q^39 - 12 * q^40 - 28 * q^42 - 32 * q^43 - 52 * q^44 - 48 * q^45 - 4 * q^46 - 24 * q^47 - 40 * q^50 + 20 * q^51 + 60 * q^52 - 20 * q^53 - 12 * q^54 - 48 * q^56 - 16 * q^57 - 36 * q^58 + 84 * q^59 + 28 * q^60 - 12 * q^61 - 136 * q^64 - 8 * q^65 + 132 * q^66 + 36 * q^67 - 12 * q^68 + 28 * q^70 - 80 * q^71 - 4 * q^72 - 12 * q^73 - 20 * q^74 - 72 * q^75 - 8 * q^77 - 216 * q^78 - 8 * q^79 + 24 * q^80 + 108 * q^82 + 12 * q^84 + 24 * q^85 - 4 * q^86 - 12 * q^87 - 48 * q^88 - 12 * q^89 + 40 * q^91 - 80 * q^92 + 20 * q^93 + 60 * q^94 + 312 * q^96 - 16 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

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