LMFDB - Embedded newform 667.2.h.b.59.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(59,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([14, 0]))

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

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

chi := DirichletCharacter("667.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.h (of order $11$, degree $10$, 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:	$5.32602181482$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$28$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			59.16
Character	$\chi$	$=$	667.59
Dual form			667.2.h.b.407.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.240264 + 0.277280i) q^{2} +(-0.500077 - 0.321380i) q^{3} +(0.265473 - 1.84640i) q^{4} +(-1.01259 + 2.21725i) q^{5} +(-0.0310385 - 0.215877i) q^{6} +(0.240790 + 0.0707024i) q^{7} +(1.19306 - 0.766730i) q^{8} +(-1.09945 - 2.40747i) q^{9} +O(q^{10})$	\(q+(0.240264 + 0.277280i) q^{2} +(-0.500077 - 0.321380i) q^{3} +(0.265473 - 1.84640i) q^{4} +(-1.01259 + 2.21725i) q^{5} +(-0.0310385 - 0.215877i) q^{6} +(0.240790 + 0.0707024i) q^{7} +(1.19306 - 0.766730i) q^{8} +(-1.09945 - 2.40747i) q^{9} +(-0.858088 + 0.251957i) q^{10} +(-0.00585983 + 0.00676260i) q^{11} +(-0.726153 + 0.838025i) q^{12} +(1.01240 - 0.297266i) q^{13} +(0.0382490 + 0.0837536i) q^{14} +(1.21895 - 0.783372i) q^{15} +(-3.08041 - 0.904489i) q^{16} +(-0.511197 - 3.55546i) q^{17} +(0.403383 - 0.883285i) q^{18} +(0.529510 - 3.68282i) q^{19} +(3.82513 + 2.45826i) q^{20} +(-0.0976913 - 0.112742i) q^{21} -0.00328304 q^{22} +(-0.375491 - 4.78111i) q^{23} -0.843030 q^{24} +(-0.616579 - 0.711570i) q^{25} +(0.325669 + 0.209295i) q^{26} +(-0.477694 + 3.32243i) q^{27} +(0.194468 - 0.425826i) q^{28} +(0.142315 + 0.989821i) q^{29} +(0.510084 + 0.149774i) q^{30} +(0.633909 - 0.407389i) q^{31} +(-1.66759 - 3.65151i) q^{32} +(0.00510373 - 0.00149859i) q^{33} +(0.863034 - 0.995994i) q^{34} +(-0.400586 + 0.462301i) q^{35} +(-4.73703 + 1.39092i) q^{36} +(-4.00135 - 8.76173i) q^{37} +(1.14839 - 0.738028i) q^{38} +(-0.601811 - 0.176708i) q^{39} +(0.491964 + 3.42169i) q^{40} +(1.42146 - 3.11257i) q^{41} +(0.00778928 - 0.0541756i) q^{42} +(-4.05218 - 2.60418i) q^{43} +(0.0109309 + 0.0126149i) q^{44} +6.45126 q^{45} +(1.23549 - 1.25285i) q^{46} +1.23267 q^{47} +(1.24976 + 1.44229i) q^{48} +(-5.83579 - 3.75044i) q^{49} +(0.0491621 - 0.341930i) q^{50} +(-0.887014 + 1.94229i) q^{51} +(-0.280110 - 1.94821i) q^{52} +(8.62743 + 2.53324i) q^{53} +(-1.03602 + 0.665808i) q^{54} +(-0.00906083 - 0.0198404i) q^{55} +(0.341486 - 0.100269i) q^{56} +(-1.44838 + 1.67152i) q^{57} +(-0.240264 + 0.277280i) q^{58} +(-2.66665 + 0.782998i) q^{59} +(-1.12282 - 2.45864i) q^{60} +(7.85919 - 5.05079i) q^{61} +(0.265267 + 0.0778893i) q^{62} +(-0.0945240 - 0.657429i) q^{63} +(-2.05551 + 4.50095i) q^{64} +(-0.366023 + 2.54575i) q^{65} +(0.00164177 + 0.00105510i) q^{66} +(-8.84327 - 10.2057i) q^{67} -6.70051 q^{68} +(-1.34878 + 2.51160i) q^{69} -0.224433 q^{70} +(9.96556 + 11.5009i) q^{71} +(-3.15759 - 2.02926i) q^{72} +(-1.75276 + 12.1907i) q^{73} +(1.46807 - 3.21462i) q^{74} +(0.0796526 + 0.553996i) q^{75} +(-6.65940 - 1.95538i) q^{76} +(-0.00188912 + 0.00121407i) q^{77} +(-0.0955963 - 0.209327i) q^{78} +(-3.41123 + 1.00163i) q^{79} +(5.12466 - 5.91417i) q^{80} +(-3.89289 + 4.49264i) q^{81} +(1.20458 - 0.353697i) q^{82} +(-0.780913 - 1.70996i) q^{83} +(-0.234101 + 0.150447i) q^{84} +(8.40098 + 2.46675i) q^{85} +(-0.251509 - 1.74928i) q^{86} +(0.246940 - 0.540724i) q^{87} +(-0.00180601 + 0.0125611i) q^{88} +(12.2513 + 7.87341i) q^{89} +(1.55001 + 1.78880i) q^{90} +0.264793 q^{91} +(-8.92753 - 0.575945i) q^{92} -0.447930 q^{93} +(0.296166 + 0.341793i) q^{94} +(7.62957 + 4.90323i) q^{95} +(-0.339599 + 2.36196i) q^{96} +(-4.96695 + 10.8761i) q^{97} +(-0.362213 - 2.51924i) q^{98} +(0.0227234 + 0.00667218i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 2 q^{3} - 32 q^{4} - 4 q^{6} + 6 q^{7} - 26 q^{9}+O(q^{10}) $ 280 * q - 2 * q^3 - 32 * q^4 - 4 * q^6 + 6 * q^7 - 26 * q^9	\( 280 q - 2 q^{3} - 32 q^{4} - 4 q^{6} + 6 q^{7} - 26 q^{9} - 41 q^{10} - 20 q^{11} + 18 q^{12} - 3 q^{15} - 40 q^{16} + 9 q^{17} + 54 q^{18} + 10 q^{19} + 58 q^{20} - 4 q^{21} - 118 q^{22} - 4 q^{23} + 20 q^{24} - 44 q^{25} - 22 q^{26} + 4 q^{27} + 76 q^{28} + 28 q^{29} + 100 q^{30} - 5 q^{31} + 40 q^{32} - 81 q^{33} - 58 q^{34} + 28 q^{35} - 24 q^{36} + 40 q^{37} - 14 q^{38} + 4 q^{39} + 78 q^{40} + 12 q^{41} + 74 q^{42} + 40 q^{43} - 90 q^{44} - 246 q^{45} - 72 q^{46} + 50 q^{47} - 14 q^{48} - 34 q^{49} + 46 q^{50} + 48 q^{51} + 90 q^{52} + 4 q^{53} + 46 q^{54} - 18 q^{55} - 272 q^{56} - 142 q^{57} + 66 q^{59} + 42 q^{60} + 40 q^{61} - 26 q^{62} + 32 q^{63} + 44 q^{64} + 19 q^{65} + 78 q^{66} - 78 q^{67} - 130 q^{68} - 283 q^{69} + 120 q^{70} + 59 q^{71} + 82 q^{72} + 28 q^{73} + 62 q^{74} + 87 q^{75} + 203 q^{76} - 58 q^{77} - 36 q^{78} + 32 q^{79} - 182 q^{80} + 66 q^{81} + 60 q^{82} - 24 q^{83} + 90 q^{84} + 90 q^{85} + 49 q^{86} + 2 q^{87} + 26 q^{88} + 36 q^{89} - 113 q^{90} - 668 q^{91} - 175 q^{92} - 60 q^{93} + 49 q^{94} + 11 q^{95} + 313 q^{96} + 75 q^{97} - 48 q^{98} + 101 q^{99}+O(q^{100}) \) 280 * q - 2 * q^3 - 32 * q^4 - 4 * q^6 + 6 * q^7 - 26 * q^9 - 41 * q^10 - 20 * q^11 + 18 * q^12 - 3 * q^15 - 40 * q^16 + 9 * q^17 + 54 * q^18 + 10 * q^19 + 58 * q^20 - 4 * q^21 - 118 * q^22 - 4 * q^23 + 20 * q^24 - 44 * q^25 - 22 * q^26 + 4 * q^27 + 76 * q^28 + 28 * q^29 + 100 * q^30 - 5 * q^31 + 40 * q^32 - 81 * q^33 - 58 * q^34 + 28 * q^35 - 24 * q^36 + 40 * q^37 - 14 * q^38 + 4 * q^39 + 78 * q^40 + 12 * q^41 + 74 * q^42 + 40 * q^43 - 90 * q^44 - 246 * q^45 - 72 * q^46 + 50 * q^47 - 14 * q^48 - 34 * q^49 + 46 * q^50 + 48 * q^51 + 90 * q^52 + 4 * q^53 + 46 * q^54 - 18 * q^55 - 272 * q^56 - 142 * q^57 + 66 * q^59 + 42 * q^60 + 40 * q^61 - 26 * q^62 + 32 * q^63 + 44 * q^64 + 19 * q^65 + 78 * q^66 - 78 * q^67 - 130 * q^68 - 283 * q^69 + 120 * q^70 + 59 * q^71 + 82 * q^72 + 28 * q^73 + 62 * q^74 + 87 * q^75 + 203 * q^76 - 58 * q^77 - 36 * q^78 + 32 * q^79 - 182 * q^80 + 66 * q^81 + 60 * q^82 - 24 * q^83 + 90 * q^84 + 90 * q^85 + 49 * q^86 + 2 * q^87 + 26 * q^88 + 36 * q^89 - 113 * q^90 - 668 * q^91 - 175 * q^92 - 60 * q^93 + 49 * q^94 + 11 * q^95 + 313 * q^96 + 75 * q^97 - 48 * q^98 + 101 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/667\mathbb{Z}\right)^\times$.

$n$	$465$	$553$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	0.240264	+	0.277280i	0.169893	+	0.196066i	0.834311	−	0.551295i	$-0.185866\pi$
$2$	0.240264	+	0.277280i	0.169893	+	0.196066i	−0.664418	+	0.747361i	$0.731321\pi$
$3$	−0.500077	−	0.321380i	−0.288719	−	0.185549i	0.388262	−	0.921549i	$-0.373076\pi$
$3$	−0.500077	−	0.321380i	−0.288719	−	0.185549i	−0.676981	+	0.736001i	$0.736712\pi$
$4$	0.265473	−	1.84640i	0.132736	−	0.923201i
$5$	−1.01259	+	2.21725i	−0.452842	+	0.991586i	0.536219	+	0.844079i	$0.319852\pi$
$5$	−1.01259	+	2.21725i	−0.452842	+	0.991586i	−0.989061	+	0.147507i	$0.952875\pi$
$6$	−0.0310385	−	0.215877i	−0.0126714	−	0.0881315i
$7$	0.240790	+	0.0707024i	0.0910102	+	0.0267230i	0.326921	−	0.945052i	$-0.393989\pi$
$7$	0.240790	+	0.0707024i	0.0910102	+	0.0267230i	−0.235910	+	0.971775i	$0.575807\pi$
$8$	1.19306	−	0.766730i	0.421809	−	0.271080i
$9$	−1.09945	−	2.40747i	−0.366484	−	0.802489i
$10$	−0.858088	+	0.251957i	−0.271351	+	0.0796759i
$11$	−0.00585983	+	0.00676260i	−0.00176681	+	0.00203900i	−0.756632	−	0.653841i	$-0.773157\pi$
$11$	−0.00585983	+	0.00676260i	−0.00176681	+	0.00203900i	0.754865	+	0.655880i	$0.227702\pi$
$12$	−0.726153	+	0.838025i	−0.209622	+	0.241917i
$13$	1.01240	−	0.297266i	0.280788	−	0.0824469i	−0.138306	−	0.990390i	$-0.544166\pi$
$13$	1.01240	−	0.297266i	0.280788	−	0.0824469i	0.419094	+	0.907943i	$0.362348\pi$
$14$	0.0382490	+	0.0837536i	0.0102225	+	0.0223841i
$15$	1.21895	−	0.783372i	0.314732	−	0.202266i
$16$	−3.08041	−	0.904489i	−0.770102	−	0.226122i
$17$	−0.511197	−	3.55546i	−0.123984	−	0.862325i	−0.952972	−	0.303059i	$-0.901992\pi$
$17$	−0.511197	−	3.55546i	−0.123984	−	0.862325i	0.828988	−	0.559266i	$-0.188917\pi$
$18$	0.403383	−	0.883285i	0.0950782	−	0.208192i
$19$	0.529510	−	3.68282i	0.121478	−	0.844897i	−0.834406	−	0.551151i	$-0.814189\pi$
$19$	0.529510	−	3.68282i	0.121478	−	0.844897i	0.955883	−	0.293746i	$-0.0949020\pi$
$20$	3.82513	+	2.45826i	0.855324	+	0.549684i
$21$	−0.0976913	−	0.112742i	−0.0213180	−	0.0246023i
$22$	−0.00328304			−0.000699947
$23$	−0.375491	−	4.78111i	−0.0782954	−	0.996930i
$23$	−0.375491	−	4.78111i	−0.0782954	−	0.996930i
$24$	−0.843030			−0.172083
$25$	−0.616579	−	0.711570i	−0.123316	−	0.142314i
$26$	0.325669	+	0.209295i	0.0638689	+	0.0410461i
$27$	−0.477694	+	3.32243i	−0.0919323	+	0.639403i
$28$	0.194468	−	0.425826i	0.0367510	−	0.0804736i
$29$	0.142315	+	0.989821i	0.0264272	+	0.183805i
$29$	0.142315	+	0.989821i	0.0264272	+	0.183805i
$30$	0.510084	+	0.149774i	0.0931281	+	0.0273449i
$31$	0.633909	−	0.407389i	0.113853	−	0.0731692i	−0.482475	−	0.875910i	$-0.660262\pi$
$31$	0.633909	−	0.407389i	0.113853	−	0.0731692i	0.596328	+	0.802741i	$0.296626\pi$
$32$	−1.66759	−	3.65151i	−0.294791	−	0.645502i
$33$	0.00510373	−	0.00149859i	0.000888445	−	0.000260871i
$34$	0.863034	−	0.995994i	0.148009	−	0.170812i
$35$	−0.400586	+	0.462301i	−0.0677114	+	0.0781431i
$36$	−4.73703	+	1.39092i	−0.789504	+	0.231819i
$37$	−4.00135	−	8.76173i	−0.657817	−	1.44042i	−0.884542	−	0.466460i	$-0.845529\pi$
$37$	−4.00135	−	8.76173i	−0.657817	−	1.44042i	0.226725	−	0.973959i	$-0.427198\pi$
$38$	1.14839	−	0.738028i	0.186294	−	0.119724i
$39$	−0.601811	−	0.176708i	−0.0963669	−	0.0282959i
$40$	0.491964	+	3.42169i	0.0777864	+	0.541016i
$41$	1.42146	−	3.11257i	0.221995	−	0.486102i	−0.765562	−	0.643362i	$-0.777539\pi$
$41$	1.42146	−	3.11257i	0.221995	−	0.486102i	0.987557	+	0.157260i	$0.0502662\pi$
$42$	0.00778928	−	0.0541756i	0.00120191	−	0.00835948i
$43$	−4.05218	−	2.60418i	−0.617952	−	0.397134i	0.193879	−	0.981025i	$-0.437893\pi$
$43$	−4.05218	−	2.60418i	−0.617952	−	0.397134i	−0.811832	+	0.583892i	$0.801529\pi$
$44$	0.0109309	+	0.0126149i	0.00164789	+	0.00190177i
$45$	6.45126			0.961696
$46$	1.23549	−	1.25285i	0.182163	−	0.184722i
$47$	1.23267			0.179803			0.0899014	−	0.995951i	$-0.471345\pi$
$47$	1.23267			0.179803			0.0899014	+	0.995951i	$0.471345\pi$
$48$	1.24976	+	1.44229i	0.180387	+	0.208177i
$49$	−5.83579	−	3.75044i	−0.833685	−	0.535777i
$50$	0.0491621	−	0.341930i	0.00695257	−	0.0483562i
$51$	−0.887014	+	1.94229i	−0.124207	+	0.271975i
$52$	−0.280110	−	1.94821i	−0.0388442	−	0.270168i
$53$	8.62743	+	2.53324i	1.18507	+	0.347968i	0.814126	−	0.580688i	$-0.197216\pi$
$53$	8.62743	+	2.53324i	1.18507	+	0.347968i	0.370943	+	0.928656i	$0.379035\pi$
$54$	−1.03602	+	0.665808i	−0.140984	+	0.0906050i
$55$	−0.00906083	−	0.0198404i	−0.00122176	−	0.00267528i
$56$	0.341486	−	0.100269i	0.0456329	−	0.0133990i
$57$	−1.44838	+	1.67152i	−0.191843	+	0.221398i
$58$	−0.240264	+	0.277280i	−0.0315483	+	0.0364086i
$59$	−2.66665	+	0.782998i	−0.347168	+	0.101938i	−0.450668	−	0.892692i	$-0.648814\pi$
$59$	−2.66665	+	0.782998i	−0.347168	+	0.101938i	0.103500	+	0.994629i	$0.466996\pi$
$60$	−1.12282	−	2.45864i	−0.144956	−	0.317409i
$61$	7.85919	−	5.05079i	1.00627	−	0.646688i	0.0698416	−	0.997558i	$-0.477751\pi$
$61$	7.85919	−	5.05079i	1.00627	−	0.646688i	0.936424	+	0.350870i	$0.114114\pi$
$62$	0.265267	+	0.0778893i	0.0336889	+	0.00989195i
$63$	−0.0945240	−	0.657429i	−0.0119089	−	0.0828282i
$64$	−2.05551	+	4.50095i	−0.256939	+	0.562618i
$65$	−0.366023	+	2.54575i	−0.0453996	+	0.315761i
$66$	0.00164177	+	0.00105510i	0.000202088	+	0.000129874i
$67$	−8.84327	−	10.2057i	−1.08038	−	1.24682i	−0.967408	−	0.253223i	$-0.918509\pi$
$67$	−8.84327	−	10.2057i	−1.08038	−	1.24682i	−0.112969	−	0.993598i	$-0.536036\pi$
$68$	−6.70051			−0.812556
$69$	−1.34878	+	2.51160i	−0.162374	+	0.302361i
$70$	−0.224433			−0.0268249
$71$	9.96556	+	11.5009i	1.18269	+	1.36490i	0.916029	+	0.401113i	$0.131376\pi$
$71$	9.96556	+	11.5009i	1.18269	+	1.36490i	0.266666	+	0.963789i	$0.414078\pi$
$72$	−3.15759	−	2.02926i	−0.372125	−	0.239150i
$73$	−1.75276	+	12.1907i	−0.205145	+	1.42682i	0.583573	+	0.812061i	$0.301654\pi$
$73$	−1.75276	+	12.1907i	−0.205145	+	1.42682i	−0.788718	+	0.614755i	$0.789255\pi$
$74$	1.46807	−	3.21462i	0.170660	−	0.373692i
$75$	0.0796526	+	0.553996i	0.00919749	+	0.0639699i
$76$	−6.65940	−	1.95538i	−0.763885	−	0.224297i
$77$	−0.00188912	+	0.00121407i	−0.000215285	+	0.000138356i
$78$	−0.0955963	−	0.209327i	−0.0108241	−	0.0237016i
$79$	−3.41123	+	1.00163i	−0.383794	+	0.112692i	−0.467937	−	0.883762i	$-0.655003\pi$
$79$	−3.41123	+	1.00163i	−0.383794	+	0.112692i	0.0841437	+	0.996454i	$0.473185\pi$
$80$	5.12466	−	5.91417i	0.572954	−	0.661224i
$81$	−3.89289	+	4.49264i	−0.432544	+	0.499182i
$82$	1.20458	−	0.353697i	0.133024	−	0.0390593i
$83$	−0.780913	−	1.70996i	−0.0857164	−	0.187693i	0.861920	−	0.507045i	$-0.169262\pi$
$83$	−0.780913	−	1.70996i	−0.0857164	−	0.187693i	−0.947636	+	0.319352i	$0.896535\pi$
$84$	−0.234101	+	0.150447i	−0.0255425	+	0.0164152i
$85$	8.40098	+	2.46675i	0.911214	+	0.267557i
$86$	−0.251509	−	1.74928i	−0.0271209	−	0.188630i
$87$	0.246940	−	0.540724i	0.0264748	−	0.0579717i
$88$	−0.00180601	+	0.0125611i	−0.000192521	+	0.00133901i
$89$	12.2513	+	7.87341i	1.29863	+	0.834580i	0.993062	−	0.117590i	$-0.0375168\pi$
$89$	12.2513	+	7.87341i	1.29863	+	0.834580i	0.305569	+	0.952170i	$0.401153\pi$
$90$	1.55001	+	1.78880i	0.163385	+	0.188556i
$91$	0.264793			0.0277578
$92$	−8.92753	−	0.575945i	−0.930760	−	0.0600464i
$93$	−0.447930			−0.0464482
$94$	0.296166	+	0.341793i	0.0305471	+	0.0352533i
$95$	7.62957	+	4.90323i	0.782778	+	0.503061i
$96$	−0.339599	+	2.36196i	−0.0346602	+	0.241067i
$97$	−4.96695	+	10.8761i	−0.504317	+	1.10430i	0.470725	+	0.882280i	$0.343992\pi$
$97$	−4.96695	+	10.8761i	−0.504317	+	1.10430i	−0.975042	+	0.222020i	$0.928735\pi$
$98$	−0.362213	−	2.51924i	−0.0365890	−	0.254482i
$99$	0.0227234	+	0.00667218i	0.00228378	+	0.000670579i
$100$	−1.47753	+	0.949551i	−0.147753	+	0.0949551i
$101$	0.989616	+	2.16696i	0.0984705	+	0.215620i	0.952456	−	0.304677i	$-0.0985485\pi$
$101$	0.989616	+	2.16696i	0.0984705	+	0.215620i	−0.853985	+	0.520297i	$0.825821\pi$
$102$	−0.751675	+	0.220712i	−0.0744270	+	0.0218537i
$103$	4.36287	−	5.03502i	0.429886	−	0.496115i	−0.498937	−	0.866638i	$-0.666276\pi$
$103$	4.36287	−	5.03502i	0.429886	−	0.496115i	0.928823	+	0.370523i	$0.120822\pi$
$104$	0.979922	−	1.13089i	0.0960892	−	0.110893i
$105$	0.348898	−	0.102446i	0.0340489	−	0.00999767i
$106$	1.37045	+	3.00086i	0.133110	+	0.291469i
$107$	11.8644	−	7.62479i	1.14697	−	0.737116i	0.177940	−	0.984041i	$-0.443057\pi$
$107$	11.8644	−	7.62479i	1.14697	−	0.737116i	0.969035	+	0.246925i	$0.0794202\pi$
$108$	6.00774	+	1.76403i	0.578095	+	0.169744i
$109$	−1.73441	−	12.0631i	−0.166126	−	1.15543i	−0.886798	−	0.462158i	$-0.847075\pi$
$109$	−1.73441	−	12.0631i	−0.166126	−	1.15543i	0.720671	−	0.693277i	$-0.243834\pi$
$110$	0.00332436	−	0.00727934i	0.000316965	−	0.000694058i
$111$	−0.814861	+	5.66749i	−0.0773432	+	0.537934i
$112$	−0.677783	−	0.435584i	−0.0640444	−	0.0411589i
$113$	8.26321	+	9.53625i	0.777337	+	0.897095i	0.996914	−	0.0785004i	$-0.0250132\pi$
$113$	8.26321	+	9.53625i	0.777337	+	0.897095i	−0.219577	+	0.975595i	$0.570468\pi$
$114$	−0.811472			−0.0760014
$115$	10.9811	+	4.00872i	1.02400	+	0.373815i
$116$	1.86539			0.173197
$117$	−1.82874	−	2.11048i	−0.169067	−	0.195114i
$118$	−0.857810	−	0.551281i	−0.0789678	−	0.0507495i
$119$	0.128288	−	0.892262i	0.0117601	−	0.0817935i
$120$	0.853641	−	1.86921i	0.0779264	−	0.170635i
$121$	1.56545	+	10.8880i	0.142314	+	0.989814i
$122$	3.28877	+	0.965669i	0.297751	+	0.0874275i
$123$	−1.71116	+	1.09969i	−0.154290	+	0.0991561i
$124$	−0.583918	−	1.27860i	−0.0524374	−	0.114822i
$125$	−9.49188	+	2.78707i	−0.848980	+	0.249283i
$126$	0.159581	−	0.184166i	0.0142166	−	0.0164068i
$127$	−7.87001	+	9.08248i	−0.698351	+	0.805940i	−0.988529	−	0.151033i	$-0.951740\pi$
$127$	−7.87001	+	9.08248i	−0.698351	+	0.805940i	0.290178	+	0.956973i	$0.406286\pi$
$128$	−9.44522	+	2.77337i	−0.834847	+	0.245133i
$129$	1.18947	+	2.60458i	0.104727	+	0.229320i
$130$	−0.793827	+	0.510161i	−0.0696232	+	0.0447441i
$131$	12.0610	+	3.54143i	1.05378	+	0.309416i	0.762342	−	0.647175i	$-0.224050\pi$
$131$	12.0610	+	3.54143i	1.05378	+	0.309416i	0.291434	+	0.956591i	$0.405868\pi$
$132$	−0.00141210	−	0.00982137i	−0.000122907	−	0.000854840i
$133$	0.387885	−	0.849350i	0.0336339	−	0.0736480i
$134$	0.705106	−	4.90412i	0.0609119	−	0.423652i
$135$	−6.88297	−	4.42342i	−0.592392	−	0.380707i
$136$	−3.33596	−	3.84990i	−0.286056	−	0.330127i
$137$	11.8447			1.01196			0.505982	−	0.862544i	$-0.331130\pi$
$137$	11.8447			1.01196			0.505982	+	0.862544i	$0.331130\pi$
$138$	−1.02048	+	0.229458i	−0.0868689	+	0.0195328i
$139$	18.9933			1.61099			0.805495	−	0.592603i	$-0.201899\pi$
$139$	18.9933			1.61099			0.805495	+	0.592603i	$0.201899\pi$
$140$	0.747248	+	0.862371i	0.0631540	+	0.0728836i
$141$	−0.616427	−	0.396154i	−0.0519125	−	0.0333622i
$142$	−0.794590	+	5.52650i	−0.0666805	+	0.463773i
$143$	−0.00392218	+	0.00858837i	−0.000327989	+	0.000718195i
$144$	1.20924	+	8.41042i	0.100770	+	0.700869i
$145$	−2.33879	−	0.686731i	−0.194226	−	0.0570299i
$146$	−3.80137	+	2.44299i	−0.314603	+	0.202183i
$147$	1.71303	+	3.75101i	0.141288	+	0.309378i
$148$	−17.2399	+	5.06210i	−1.41711	+	0.416102i
$149$	3.56980	−	4.11977i	0.292449	−	0.337504i	−0.590444	−	0.807079i	$-0.701047\pi$
$149$	3.56980	−	4.11977i	0.292449	−	0.337504i	0.882893	+	0.469574i	$0.155593\pi$
$150$	−0.134474	+	0.155191i	−0.0109798	+	0.0126713i
$151$	−11.6157	+	3.41069i	−0.945274	+	0.277558i	−0.717818	−	0.696231i	$-0.754859\pi$
$151$	−11.6157	+	3.41069i	−0.945274	+	0.277558i	−0.227456	+	0.973788i	$0.573041\pi$
$152$	−2.19199	−	4.79980i	−0.177794	−	0.389315i
$153$	−7.99761	+	5.13975i	−0.646568	+	0.415524i
$154$	−0.000790525	0	0.000232119i	−6.37023e−5	0	1.87047e-5i
$155$	0.261397	+	1.81805i	0.0209959	+	0.146030i
$156$	−0.486038	+	1.06427i	−0.0389142	+	0.0852101i
$157$	1.84957	−	12.8640i	0.147611	−	1.02666i	−0.772503	−	0.635011i	$-0.780996\pi$
$157$	1.84957	−	12.8640i	0.147611	−	1.02666i	0.920115	−	0.391649i	$-0.128095\pi$
$158$	−1.09733	−	0.705210i	−0.0872988	−	0.0561035i
$159$	−3.50024	−	4.03950i	−0.277587	−	0.320353i
$160$	9.78490			0.773564
$161$	0.247621	−	1.17779i	0.0195153	−	0.0928231i
$162$	−2.18104			−0.171359
$163$	−12.0112	−	13.8617i	−0.940793	−	1.08573i	−0.996185	−	0.0872683i	$-0.972186\pi$
$163$	−12.0112	−	13.8617i	−0.940793	−	1.08573i	0.0553919	−	0.998465i	$-0.482359\pi$
$164$	−5.36970	−	3.45089i	−0.419303	−	0.269470i
$165$	−0.00184521	+	0.0128337i	−0.000143649	+	0.000999103i
$166$	0.286512	−	0.627374i	0.0222377	−	0.0486937i
$167$	−1.19266	−	8.29516i	−0.0922911	−	0.641899i	−0.982488	−	0.186324i	$-0.940343\pi$
$167$	−1.19266	−	8.29516i	−0.0922911	−	0.641899i	0.890197	−	0.455575i	$-0.150566\pi$
$168$	−0.202994	−	0.0596043i	−0.0156613	−	0.00459857i
$169$	−9.99972	+	6.42643i	−0.769209	+	0.494341i
$170$	1.33448	+	2.92209i	0.102350	+	0.224114i
$171$	−9.44844	+	2.77431i	−0.722540	+	0.212157i
$172$	−5.88411	+	6.79062i	−0.448659	+	0.517780i
$173$	−15.3768	+	17.7458i	−1.16908	+	1.34919i	−0.243833	+	0.969817i	$0.578405\pi$
$173$	−15.3768	+	17.7458i	−1.16908	+	1.34919i	−0.925245	+	0.379370i	$0.876141\pi$
$174$	0.209263	−	0.0614451i	0.0158642	−	0.00465814i
$175$	−0.0981565	−	0.214933i	−0.00741994	−	0.0162474i
$176$	0.0241674	−	0.0155314i	0.00182168	−	0.00117073i
$177$	1.58517	+	0.465447i	0.119148	+	0.0349851i
$178$	0.760405	+	5.28873i	0.0569947	+	0.396407i
$179$	−8.28724	+	18.1465i	−0.619417	+	1.35634i	0.296525	+	0.955025i	$0.404172\pi$
$179$	−8.28724	+	18.1465i	−0.619417	+	1.35634i	−0.915942	+	0.401310i	$0.868555\pi$
$180$	1.71263	−	11.9116i	0.127652	−	0.887839i
$181$	7.92284	+	5.09170i	0.588900	+	0.378463i	0.800892	−	0.598808i	$-0.204359\pi$
$181$	7.92284	+	5.09170i	0.588900	+	0.378463i	−0.211992	+	0.977271i	$0.567995\pi$
$182$	0.0636202	+	0.0734217i	0.00471585	+	0.00544238i
$183$	−5.55342			−0.410520
$184$	−4.11380	−	5.41623i	−0.303274	−	0.399290i
$185$	23.4787			1.72619
$186$	−0.107622	−	0.124202i	−0.00789120	−	0.00910693i
$187$	0.0270397	+	0.0173773i	0.00197734	+	0.00127076i
$188$	0.327239	−	2.27600i	0.0238663	−	0.165994i
$189$	−0.349928	+	0.766236i	−0.0254535	+	0.0557355i
$190$	0.473548	+	3.29360i	0.0343548	+	0.238943i
$191$	−3.12704	−	0.918181i	−0.226264	−	0.0664372i	0.166635	−	0.986019i	$-0.446710\pi$
$191$	−3.12704	−	0.918181i	−0.226264	−	0.0664372i	−0.392900	+	0.919581i	$0.628528\pi$
$192$	2.47443	−	1.59022i	0.178576	−	0.114764i
$193$	8.26918	+	18.1070i	0.595229	+	1.30337i	0.932230	+	0.361865i	$0.117860\pi$
$193$	8.26918	+	18.1070i	0.595229	+	1.30337i	−0.337002	+	0.941504i	$0.609413\pi$
$194$	−4.20910	+	1.23590i	−0.302196	+	0.0887328i
$195$	1.00119	−	1.15544i	0.0716968	−	0.0827425i
$196$	−8.47406	+	9.77958i	−0.605290	+	0.698542i
$197$	−15.4978	+	4.55056i	−1.10417	+	0.324214i	−0.782508	−	0.622640i	$-0.786060\pi$
$197$	−15.4978	+	4.55056i	−1.10417	+	0.324214i	−0.321663	+	0.946854i	$0.604242\pi$
$198$	0.00360955	+	0.00790382i	0.000256520	+	0.000561700i
$199$	15.0143	−	9.64913i	1.06434	−	0.684009i	0.113450	−	0.993544i	$-0.463810\pi$
$199$	15.0143	−	9.64913i	1.06434	−	0.684009i	0.950888	+	0.309535i	$0.100173\pi$
$200$	−1.28120	−	0.376193i	−0.0905942	−	0.0266009i
$201$	1.14241	+	7.94567i	0.0805797	+	0.560444i
$202$	−0.363084	+	0.795043i	−0.0255465	+	0.0559391i
$203$	−0.0357147	+	0.248401i	−0.00250668	+	0.0174344i
$204$	3.35077	+	2.15341i	0.234601	+	0.150769i
$205$	5.46200	+	6.30349i	0.381483	+	0.440255i
$206$	2.44435			0.170306
$207$	−11.0975	+	6.16059i	−0.771331	+	0.428191i
$208$	−3.38747			−0.234879
$209$	0.0218026	+	0.0251616i	0.00150812	+	0.00174046i
$210$	0.112234	+	0.0721283i	0.00774487	+	0.00497732i
$211$	−0.478793	+	3.33008i	−0.0329615	+	0.229252i	−0.999643	−	0.0267313i	$-0.991490\pi$
$211$	−0.478793	+	3.33008i	−0.0329615	+	0.229252i	0.966681	+	0.255983i	$0.0823992\pi$
$212$	6.96773	−	15.2572i	0.478546	−	1.04787i
$213$	−1.28740	−	8.95404i	−0.0882110	−	0.613521i
$214$	4.96479	+	1.45779i	0.339386	+	0.0996528i
$215$	9.87731	−	6.34776i	0.673627	−	0.432914i
$216$	1.97750	+	4.33011i	0.134552	+	0.294627i
$217$	0.181443	−	0.0532763i	0.0123171	−	0.00361663i
$218$	2.92813	−	3.37925i	0.198318	−	0.228872i
$219$	4.79436	−	5.53299i	0.323973	−	0.373885i
$220$	−0.0390388	+	0.0114628i	−0.00263200	+	0.000772824i
$221$	−1.57445	−	3.44757i	−0.105909	−	0.231909i
$222$	−1.76726	+	1.13575i	−0.118611	+	0.0762266i
$223$	2.15167	+	0.631786i	0.144086	+	0.0423075i	0.352980	−	0.935631i	$-0.385168\pi$
$223$	2.15167	+	0.631786i	0.144086	+	0.0423075i	−0.208894	+	0.977938i	$0.566986\pi$
$224$	−0.143369	−	0.997150i	−0.00957921	−	0.0666249i
$225$	−1.03518	+	2.26673i	−0.0690121	+	0.151115i
$226$	−0.658856	+	4.58244i	−0.0438264	+	0.304819i
$227$	−8.63485	−	5.54928i	−0.573115	−	0.368319i	0.221751	−	0.975103i	$-0.428823\pi$
$227$	−8.63485	−	5.54928i	−0.573115	−	0.368319i	−0.794866	+	0.606785i	$0.792459\pi$
$228$	2.70179	+	3.11803i	0.178930	+	0.206497i
$229$	0.542848			0.0358724			0.0179362	−	0.999839i	$-0.494290\pi$
$229$	0.542848			0.0358724			0.0179362	+	0.999839i	$0.494290\pi$
$230$	1.52684	+	4.00800i	0.100677	+	0.264280i
$231$	0.00133488			8.78288e−5
$232$	0.928715	+	1.07179i	0.0609731	+	0.0703668i
$233$	−2.31732	−	1.48925i	−0.151813	−	0.0975640i	0.462529	−	0.886604i	$-0.346942\pi$
$233$	−2.31732	−	1.48925i	−0.151813	−	0.0975640i	−0.614342	+	0.789040i	$0.710578\pi$
$234$	0.145812	−	1.01415i	0.00953205	−	0.0662968i
$235$	−1.24818	+	2.73313i	−0.0814222	+	0.178290i
$236$	0.737808	+	5.13156i	0.0480272	+	0.334036i
$237$	2.02778	+	0.595410i	0.131718	+	0.0386760i
$238$	0.278229	−	0.178807i	0.0180349	−	0.0115903i
$239$	−4.66866	−	10.2229i	−0.301990	−	0.661267i	0.696420	−	0.717635i	$-0.254775\pi$
$239$	−4.66866	−	10.2229i	−0.301990	−	0.661267i	−0.998410	+	0.0563680i	$0.982048\pi$
$240$	−4.46342	+	1.31058i	−0.288112	+	0.0845974i
$241$	11.8134	−	13.6334i	0.760968	−	0.878204i	−0.234615	−	0.972088i	$-0.575383\pi$
$241$	11.8134	−	13.6334i	0.760968	−	0.878204i	0.995583	+	0.0938847i	$0.0299285\pi$
$242$	−2.64289	+	3.05006i	−0.169891	+	0.196065i
$243$	13.0525	−	3.83256i	0.837318	−	0.245859i
$244$	−7.23939	−	15.8521i	−0.463455	−	1.01482i
$245$	14.2249	−	9.14179i	0.908796	−	0.584048i
$246$	−0.716053	−	0.210252i	−0.0456539	−	0.0134052i
$247$	−0.558705	−	3.88588i	−0.0355496	−	0.247253i
$248$	0.443932	−	0.972075i	0.0281897	−	0.0617268i
$249$	−0.159031	+	1.10608i	−0.0100782	+	0.0700951i
$250$	−3.05336	−	1.96227i	−0.193111	−	0.124105i
$251$	−12.1293	−	13.9980i	−0.765596	−	0.883545i	0.230386	−	0.973099i	$-0.426001\pi$
$251$	−12.1293	−	13.9980i	−0.765596	−	0.883545i	−0.995982	+	0.0895546i	$0.971456\pi$
$252$	−1.23897			−0.0780478
$253$	0.0345331	+	0.0254772i	0.00217108	+	0.00160174i
$254$	−4.40927			−0.276662
$255$	−3.40837	−	3.93347i	−0.213440	−	0.246323i
$256$	5.28686	+	3.39766i	0.330429	+	0.212354i
$257$	2.65897	−	18.4936i	0.165862	−	1.15360i	−0.721463	−	0.692453i	$-0.756530\pi$
$257$	2.65897	−	18.4936i	0.165862	−	1.15360i	0.887325	−	0.461144i	$-0.152561\pi$
$258$	−0.436410	+	0.955604i	−0.0271697	+	0.0594933i
$259$	−0.344010	−	2.39264i	−0.0213757	−	0.148672i
$260$	4.60330	+	1.35165i	0.285485	+	0.0838259i
$261$	2.22649	−	1.43088i	0.137817	−	0.0885693i
$262$	1.91586	+	4.19515i	0.118362	+	0.259178i
$263$	18.3069	−	5.37538i	1.12885	−	0.331460i	0.336594	−	0.941650i	$-0.390725\pi$
$263$	18.3069	−	5.37538i	1.12885	−	0.331460i	0.792255	+	0.610190i	$0.208907\pi$
$264$	0.00494002	−	0.00570108i	0.000304037	−	0.000350877i
$265$	−14.3529	+	16.5641i	−0.881689	+	1.01752i
$266$	0.328702	−	0.0965158i	0.0201540	−	0.00591776i
$267$	−3.59622	−	7.87462i	−0.220085	−	0.481919i
$268$	−21.1914	+	13.6189i	−1.29447	+	0.831907i
$269$	8.82354	+	2.59082i	0.537981	+	0.157965i	0.539425	−	0.842034i	$-0.318642\pi$
$269$	8.82354	+	2.59082i	0.537981	+	0.157965i	−0.00144446	+	0.999999i	$0.500460\pi$
$270$	−0.427208	−	2.97130i	−0.0259991	−	0.180828i
$271$	12.6239	−	27.6425i	0.766846	−	1.67916i	0.0333714	−	0.999443i	$-0.489376\pi$
$271$	12.6239	−	27.6425i	0.766846	−	1.67916i	0.733475	−	0.679716i	$-0.237897\pi$
$272$	−1.64118	+	11.4146i	−0.0995109	+	0.692113i
$273$	−0.132417	−	0.0850990i	−0.00801422	−	0.00515042i
$274$	2.84587	+	3.28431i	0.171925	+	0.198412i
$275$	0.00842512			0.000508054
$276$	4.27935	+	3.15714i	0.257587	+	0.190038i
$277$	13.9905			0.840608			0.420304	−	0.907383i	$-0.361923\pi$
$277$	13.9905			0.840608			0.420304	+	0.907383i	$0.361923\pi$
$278$	4.56341	+	5.26646i	0.273695	+	0.315861i
$279$	−1.67773	−	1.07821i	−0.100443	−	0.0645508i
$280$	−0.123461	+	0.858691i	−0.00737822	+	0.0513166i
$281$	3.47795	−	7.61565i	0.207477	−	0.454311i	−0.777074	−	0.629409i	$-0.783297\pi$
$281$	3.47795	−	7.61565i	0.207477	−	0.454311i	0.984551	+	0.175098i	$0.0560242\pi$
$282$	−0.0382600	−	0.266104i	−0.00227835	−	0.0158463i
$283$	−6.43698	−	1.89007i	−0.382638	−	0.112353i	0.0847558	−	0.996402i	$-0.472989\pi$
$283$	−6.43698	−	1.89007i	−0.382638	−	0.112353i	−0.467394	+	0.884049i	$0.654807\pi$
$284$	23.8808	−	15.3473i	1.41707	−	0.910693i
$285$	−2.23957	−	4.90398i	−0.132661	−	0.290487i
$286$	−0.00332374		0.000975938i	−0.000196537		5.77084e-5i
$287$	0.562341	−	0.648976i	0.0331939	−	0.0383078i
$288$	−6.95745	+	8.02933i	−0.409972	+	0.473133i
$289$	3.93144	−	1.15437i	0.231261	−	0.0679043i
$290$	−0.371511	−	0.813497i	−0.0218159	−	0.0477702i
$291$	5.97921	−	3.84261i	0.350508	−	0.225258i
$292$	22.0437	+	6.47260i	1.29001	+	0.378780i
$293$	−0.975663	−	6.78589i	−0.0569989	−	0.396436i	−0.998271	−	0.0587859i	$-0.981277\pi$
$293$	−0.975663	−	6.78589i	−0.0569989	−	0.396436i	0.941272	−	0.337650i	$-0.109632\pi$
$294$	−0.628500	+	1.37622i	−0.0366549	+	0.0802630i
$295$	0.964103	−	6.70548i	0.0561322	−	0.390408i
$296$	−11.4917	−	7.38527i	−0.667942	−	0.429260i
$297$	−0.0196691	−	0.0226994i	−0.00114132	−	0.00131715i
$298$	2.00002			0.115858
$299$	−1.80141	−	4.72876i	−0.104178	−	0.273471i
$300$	1.04404			0.0602779
$301$	−0.791605	−	0.913560i	−0.0456273	−	0.0526567i
$302$	−3.73656	−	2.40134i	−0.215015	−	0.138182i
$303$	0.201532	−	1.40169i	0.0115777	−	0.0805248i
$304$	−4.96218	+	10.8657i	−0.284600	+	0.623188i
$305$	3.24079	+	22.5402i	0.185567	+	1.29065i
$306$	−3.34669	−	0.982676i	−0.191317	−	0.0561759i
$307$	−6.18085	+	3.97219i	−0.352760	+	0.226705i	−0.705004	−	0.709203i	$-0.749055\pi$
$307$	−6.18085	+	3.97219i	−0.352760	+	0.226705i	0.352244	+	0.935908i	$0.385419\pi$
$308$	0.00174014	+	0.00381038i	9.91538e−5	+	0.000217117i
$309$	−3.79992	+	1.11576i	−0.216170	+	0.0634732i
$310$	−0.441305	+	0.509294i	−0.0250645	+	0.0289259i
$311$	10.1482	−	11.7117i	0.575454	−	0.664109i	−0.391167	−	0.920320i	$-0.627929\pi$
$311$	10.1482	−	11.7117i	0.575454	−	0.664109i	0.966621	+	0.256210i	$0.0824740\pi$
$312$	−0.853481	+	0.250605i	−0.0483188	+	0.0141877i
$313$	5.92065	+	12.9644i	0.334655	+	0.732792i	0.999904	−	0.0138292i	$-0.00440210\pi$
$313$	5.92065	+	12.9644i	0.334655	+	0.732792i	−0.665249	+	0.746621i	$0.731675\pi$
$314$	4.01132	−	2.57792i	0.226372	−	0.145480i
$315$	1.55340	+	0.456119i	0.0875241	+	0.0256994i
$316$	0.943820	+	6.56441i	0.0530940	+	0.369277i
$317$	5.80207	−	12.7048i	0.325876	−	0.713570i	−0.673802	−	0.738912i	$-0.735340\pi$
$317$	5.80207	−	12.7048i	0.325876	−	0.713570i	0.999679	+	0.0253417i	$0.00806737\pi$
$318$	0.279087	−	1.94109i	0.0156504	−	0.108851i
$319$	−0.00752771	−	0.00483777i	−0.000421471	−	0.000270863i
$320$	−7.89836	−	9.11519i	−0.441532	−	0.509555i
$321$	−8.38356			−0.467925
$322$	0.386073	−	0.214321i	0.0215150	−	0.0119437i
$323$	−13.3648			−0.743637
$324$	7.26176	+	8.38051i	0.403431	+	0.465584i
$325$	−0.835749	−	0.537103i	−0.0463590	−	0.0297931i
$326$	0.957700	−	6.66095i	0.0530421	−	0.368916i
$327$	−3.00949	+	6.58987i	−0.166425	+	0.364421i
$328$	−0.690617	−	4.80335i	−0.0381329	−	0.265220i
$329$	0.296814	+	0.0871524i	0.0163639	+	0.00480487i
$330$	−0.00400187	+	0.00257184i	−0.000220296	+	0.000141575i
$331$	2.19835	+	4.81372i	0.120832	+	0.264586i	0.960377	−	0.278705i	$-0.0899052\pi$
$331$	2.19835	+	4.81372i	0.120832	+	0.264586i	−0.839544	+	0.543291i	$0.817178\pi$
$332$	−3.36459	+	0.987932i	−0.184656	+	0.0542198i
$333$	−16.6943	+	19.2662i	−0.914840	+	1.05578i
$334$	2.01353	−	2.32373i	0.110175	−	0.127149i
$335$	31.5831	−	9.27365i	1.72557	−	0.506673i
$336$	0.198955	+	0.435651i	0.0108539	+	0.0237667i
$337$	−10.5305	+	6.76756i	−0.573634	+	0.368652i	−0.795065	−	0.606524i	$-0.792564\pi$
$337$	−10.5305	+	6.76756i	−0.573634	+	0.368652i	0.221431	+	0.975176i	$0.428927\pi$
$338$	−4.18449	−	1.22868i	−0.227606	−	0.0668313i
$339$	−1.06748	−	7.42448i	−0.0579775	−	0.403242i
$340$	6.78484	−	14.8567i	0.367960	−	0.805719i
$341$	−0.000959592		0.00667411i	−5.19648e−5		0.000361423i
$342$	−3.03938	−	1.95329i	−0.164351	−	0.105622i
$343$	−2.29042	−	2.64329i	−0.123671	−	0.142724i
$344$	−6.83118			−0.368313
$345$	−4.20309	−	5.53379i	−0.226287	−	0.297929i
$346$	−8.61505			−0.463148
$347$	−12.7683	−	14.7354i	−0.685436	−	0.791035i	0.301272	−	0.953538i	$-0.402589\pi$
$347$	−12.7683	−	14.7354i	−0.685436	−	0.791035i	−0.986708	+	0.162503i	$0.948043\pi$
$348$	−0.932837	−	0.599498i	−0.0500053	−	0.0321365i
$349$	1.65698	−	11.5245i	0.0886959	−	0.616893i	−0.896188	−	0.443675i	$-0.853674\pi$
$349$	1.65698	−	11.5245i	0.0886959	−	0.616893i	0.984883	−	0.173218i	$-0.0554165\pi$
$350$	0.0360130	−	0.0788575i	0.00192498	−	0.00421511i
$351$	0.504033	+	3.50562i	0.0269033	+	0.187116i
$352$	0.0344655	+	0.0101200i	0.00183702	+	0.000539397i
$353$	−15.3236	+	9.84786i	−0.815592	+	0.524149i	−0.880669	−	0.473731i	$-0.842907\pi$
$353$	−15.3236	+	9.84786i	−0.815592	+	0.524149i	0.0650778	+	0.997880i	$0.479270\pi$
$354$	0.251800	+	0.551365i	0.0133830	+	0.0293047i
$355$	−35.5913	+	10.4506i	−1.88899	+	0.554658i
$356$	17.7899	−	20.5306i	0.942860	−	1.08812i
$357$	−0.350909	+	0.404970i	−0.0185721	+	0.0214333i
$358$	−7.02279	+	2.06208i	−0.371166	+	0.108984i
$359$	−2.49948	−	5.47310i	−0.131917	−	0.288859i	0.832134	−	0.554575i	$-0.187119\pi$
$359$	−2.49948	−	5.47310i	−0.131917	−	0.288859i	−0.964051	+	0.265716i	$0.914392\pi$
$360$	7.69670	−	4.94637i	0.405652	−	0.260697i
$361$	4.94758	+	1.45274i	0.260399	+	0.0764600i
$362$	0.491750	+	3.42020i	0.0258458	+	0.179762i
$363$	2.71632	−	5.94792i	0.142570	−	0.312185i
$364$	0.0702952	−	0.488914i	0.00368447	−	0.0256260i
$365$	−25.2551	−	16.2305i	−1.32191	−	0.849541i
$366$	−1.33429	−	1.53985i	−0.0697444	−	0.0804893i
$367$	26.7676			1.39726			0.698629	−	0.715484i	$-0.253794\pi$
$367$	26.7676			1.39726			0.698629	+	0.715484i	$0.253794\pi$
$368$	−3.16780	+	15.0674i	−0.165133	+	0.785442i
$369$	−9.05624			−0.471449
$370$	5.64109	+	6.51016i	0.293266	+	0.338447i
$371$	1.89829	+	1.21996i	0.0985545	+	0.0633372i
$372$	−0.118913	+	0.827058i	−0.00616535	+	0.0428810i
$373$	−7.46363	+	16.3431i	−0.386452	+	0.846212i	0.612014	+	0.790847i	$0.290360\pi$
$373$	−7.46363	+	16.3431i	−0.386452	+	0.846212i	−0.998466	+	0.0553652i	$0.982368\pi$
$374$	0.00167828	+	0.0116727i	8.67819e−5	+	0.000603582i
$375$	5.64238	+	1.65675i	0.291371	+	0.0855543i
$376$	1.47064	−	0.945121i	0.0758424	−	0.0487409i
$377$	0.438320	+	0.959786i	0.0225746	+	0.0494315i
$378$	−0.296537	+	0.0870711i	−0.0152522	+	0.00447846i
$379$	22.2783	−	25.7105i	1.14436	−	1.32066i	0.204593	−	0.978847i	$-0.434413\pi$
$379$	22.2783	−	25.7105i	1.14436	−	1.32066i	0.939767	−	0.341815i	$-0.111042\pi$
$380$	11.0788	−	12.7856i	0.568329	−	0.655887i
$381$	6.85454	−	2.01267i	0.351169	−	0.103112i
$382$	−0.496722	−	1.08767i	−0.0254145	−	0.0556501i
$383$	−0.0255121	+	0.0163956i	−0.00130361	+	0.000837778i	−0.541292	−	0.840834i	$-0.682065\pi$
$383$	−0.0255121	+	0.0163956i	−0.00130361	+	0.000837778i	0.539989	+	0.841672i	$0.318428\pi$
$384$	5.61464	+	1.64861i	0.286521	+	0.0841301i
$385$	−0.000778992	−	0.00541801i	−3.97011e−5	−	0.000276127i
$386$	−3.03391	+	6.64334i	−0.154422	+	0.338137i
$387$	−1.81429	+	12.6187i	−0.0922256	+	0.641443i
$388$	18.7631	+	12.0583i	0.952550	+	0.612167i
$389$	5.94513	+	6.86104i	0.301430	+	0.347869i	0.886177	−	0.463347i	$-0.153352\pi$
$389$	5.94513	+	6.86104i	0.301430	+	0.347869i	−0.584747	+	0.811216i	$0.698806\pi$
$390$	0.560930			0.0284038
$391$	−16.8071	+	3.77913i	−0.849970	+	0.191119i
$392$	−9.83800			−0.496894
$393$	−4.89328	−	5.64715i	−0.246834	−	0.284861i
$394$	−4.98534	−	3.20389i	−0.251158	−	0.161409i
$395$	1.23330	−	8.57780i	0.0620541	−	0.431596i
$396$	0.0183520	−	0.0401852i	0.000922220	−	0.00201938i
$397$	0.132673	+	0.922760i	0.00665866	+	0.0463120i	0.992880	−	0.119120i	$-0.0380073\pi$
$397$	0.132673	+	0.922760i	0.00665866	+	0.0463120i	−0.986221	+	0.165432i	$0.947098\pi$
$398$	6.28292	+	1.84483i	0.314934	+	0.0924731i
$399$	−0.466936	+	0.300082i	−0.0233760	+	0.0150229i
$400$	1.25571	+	2.74962i	0.0627854	+	0.137481i
$401$	−20.3669	+	5.98026i	−1.01707	+	0.298640i	−0.747445	−	0.664324i	$-0.768720\pi$
$401$	−20.3669	+	5.98026i	−1.01707	+	0.298640i	−0.269630	+	0.962964i	$0.586901\pi$
$402$	−1.92869	+	2.22583i	−0.0961944	+	0.111014i
$403$	0.520665	−	0.600879i	0.0259362	−	0.0299319i
$404$	4.26379	−	1.25196i	0.212132	−	0.0622874i
$405$	−6.01943	−	13.1807i	−0.299108	−	0.654955i
$406$	−0.0774577	+	0.0497790i	−0.00384416	+	0.00247049i
$407$	0.0826993	+	0.0242827i	0.00409925	+	0.00120365i
$408$	0.430955	+	2.99736i	0.0213355	+	0.148391i
$409$	4.46800	−	9.78356i	0.220929	−	0.483766i	−0.766418	−	0.642342i	$-0.777963\pi$
$409$	4.46800	−	9.78356i	0.220929	−	0.483766i	0.987347	+	0.158576i	$0.0506902\pi$
$410$	−0.435505	+	3.02901i	−0.0215081	+	0.149592i
$411$	−5.92327	−	3.80666i	−0.292174	−	0.187769i
$412$	−8.13845	−	9.39227i	−0.400953	−	0.462724i
$413$	−0.697462			−0.0343199
$414$	−4.37455	−	1.59695i	−0.214997	−	0.0784858i
$415$	4.58216			0.224929
$416$	−2.77373	−	3.20106i	−0.135993	−	0.156945i
$417$	−9.49810	−	6.10406i	−0.465124	−	0.298917i
$418$	−0.00173840	+	0.0120909i	−8.50281e−5	+	0.000591383i
$419$	−5.26613	+	11.5312i	−0.257267	+	0.563337i	−0.993558	−	0.113329i	$-0.963849\pi$
$419$	−5.26613	+	11.5312i	−0.257267	+	0.563337i	0.736290	+	0.676666i	$0.236576\pi$
$420$	−0.0965330	−	0.671402i	−0.00471033	−	0.0327611i
$421$	20.4979	+	6.01871i	0.999004	+	0.293334i	0.740047	−	0.672555i	$-0.234803\pi$
$421$	20.4979	+	6.01871i	0.999004	+	0.293334i	0.258957	+	0.965889i	$0.416621\pi$
$422$	−1.03840	+	0.667340i	−0.0505486	+	0.0324856i
$423$	−1.35526	−	2.96760i	−0.0658949	−	0.144290i
$424$	12.2353	−	3.59261i	0.594199	−	0.174473i
$425$	−2.21476	+	2.55597i	−0.107432	+	0.123983i
$426$	2.17346	−	2.50831i	0.105304	−	0.121528i
$427$	2.24952	−	0.660518i	0.108862	−	0.0319647i
$428$	−10.9288	−	23.9306i	−0.528261	−	1.15673i
$429$	0.00472152	−	0.00303433i	0.000227957	−	0.000146499i
$430$	4.13327	+	1.21364i	0.199324	+	0.0585268i
$431$	2.18903	+	15.2250i	0.105442	+	0.733364i	0.972118	+	0.234493i	$0.0753429\pi$
$431$	2.18903	+	15.2250i	0.105442	+	0.733364i	−0.866676	+	0.498871i	$0.833748\pi$
$432$	4.47660	−	9.80238i	0.215380	−	0.471617i
$433$	−2.10838	+	14.6641i	−0.101322	+	0.704713i	0.874321	+	0.485349i	$0.161307\pi$
$433$	−2.10838	+	14.6641i	−0.101322	+	0.704713i	−0.975643	+	0.219364i	$0.929602\pi$
$434$	0.0583666	+	0.0375100i	0.00280169	+	0.00180054i
$435$	0.948873	+	1.09506i	0.0454950	+	0.0525040i
$436$	−22.7337			−1.08875
$437$	−17.8068	−	1.14878i	−0.851814	−	0.0549534i
$438$	2.68610			0.128347
$439$	−11.0203	−	12.7181i	−0.525969	−	0.607000i	0.429147	−	0.903235i	$-0.358814\pi$
$439$	−11.0203	−	12.7181i	−0.525969	−	0.607000i	−0.955115	+	0.296235i	$0.904269\pi$
$440$	−0.0260223	−	0.0167235i	−0.00124057	−	0.000797263i
$441$	−2.61287	+	18.1729i	−0.124422	+	0.865377i
$442$	0.577657	−	1.26489i	0.0274763	−	0.0601648i
$443$	−0.410172	−	2.85281i	−0.0194879	−	0.135541i	0.977755	−	0.209751i	$-0.0672655\pi$
$443$	−0.410172	−	2.85281i	−0.0194879	−	0.135541i	−0.997243	+	0.0742104i	$0.976356\pi$
$444$	10.2481	+	3.00912i	0.486355	+	0.142807i
$445$	−29.8628	+	19.1917i	−1.41563	+	0.909772i
$446$	0.341787	+	0.748409i	0.0161841	+	0.0354382i
$447$	−3.10918	+	0.912938i	−0.147059	+	0.0431805i
$448$	−0.813175	+	0.938454i	−0.0384189	+	0.0443378i
$449$	−1.52976	+	1.76544i	−0.0721940	+	0.0833163i	−0.790698	−	0.612207i	$-0.790282\pi$
$449$	−1.52976	+	1.76544i	−0.0721940	+	0.0833163i	0.718504	+	0.695523i	$0.244827\pi$
$450$	−0.877237	+	0.257580i	−0.0413533	+	0.0121424i
$451$	0.0127195	+	0.0278519i	0.000598940	+	0.00131150i
$452$	19.8014	−	12.7256i	0.931380	−	0.598561i
$453$	6.90488	+	2.02746i	0.324419	+	0.0952582i
$454$	−0.535943	−	3.72756i	−0.0251530	−	0.174943i
$455$	−0.268125	+	0.587112i	−0.0125699	+	0.0275243i
$456$	−0.446393	+	3.10473i	−0.0209043	+	0.145392i
$457$	−10.9716	−	7.05100i	−0.513228	−	0.329832i	0.258260	−	0.966076i	$-0.416851\pi$
$457$	−10.9716	−	7.05100i	−0.513228	−	0.329832i	−0.771488	+	0.636244i	$0.780487\pi$
$458$	0.130427	+	0.150521i	0.00609446	+	0.00703338i
$459$	12.0570			0.562771
$460$	10.3169	−	19.2114i	0.481028	−	0.895736i
$461$	−15.2868			−0.711977			−0.355989	−	0.934490i	$-0.615856\pi$
$461$	−15.2868			−0.711977			−0.355989	+	0.934490i	$0.615856\pi$
$462$	0.000320725	0	0.000370136i	1.49215e−5	0	1.72203e-5i
$463$	−23.7807	−	15.2830i	−1.10518	−	0.710259i	−0.144946	−	0.989440i	$-0.546301\pi$
$463$	−23.7807	−	15.2830i	−1.10518	−	0.710259i	−0.960239	+	0.279180i	$0.909937\pi$
$464$	0.456895	−	3.17778i	0.0212108	−	0.147525i
$465$	0.453567	−	0.993174i	0.0210337	−	0.0460573i
$466$	−0.143830	−	1.00036i	−0.00666279	−	0.0463407i
$467$	37.2019	+	10.9235i	1.72150	+	0.505478i	0.985234	−	0.171214i	$-0.0547690\pi$
$467$	37.2019	+	10.9235i	1.72150	+	0.505478i	0.736266	+	0.676692i	$0.236587\pi$
$468$	−4.38228	+	2.81632i	−0.202571	+	0.130184i
$469$	−1.40781	−	3.08267i	−0.0650065	−	0.142344i
$470$	−1.05774	+	0.310579i	−0.0487897	+	0.0143259i
$471$	−5.05916	+	5.83858i	−0.233114	+	0.269028i
$472$	−2.58111	+	2.97876i	−0.118805	+	0.137108i
$473$	0.0413562	−	0.0121433i	0.00190156	−	0.000558348i
$474$	0.322108	+	0.705319i	0.0147949	+	0.0323964i
$475$	−2.94707	+	1.89397i	−0.135221	+	0.0869012i
$476$	−1.61342	−	0.473742i	−0.0739509	−	0.0217139i
$477$	−3.38676	−	23.5554i	−0.155069	−	1.07853i
$478$	1.71290	−	3.75073i	0.0783463	−	0.171554i
$479$	0.568079	−	3.95108i	0.0259562	−	0.180529i	−0.972719	−	0.231987i	$-0.925477\pi$
$479$	0.568079	−	3.95108i	0.0259562	−	0.180529i	0.998675	+	0.0514572i	$0.0163866\pi$
$480$	−4.89320	−	3.14467i	−0.223343	−	0.143534i
$481$	−6.65552	−	7.68087i	−0.303465	−	0.350218i
$482$	6.61860			0.301469
$483$	−0.502348	+	0.509406i	−0.0228576	+	0.0231788i
$484$	20.5191			0.932688
$485$	−19.0856	−	22.0260i	−0.866633	−	1.00015i
$486$	4.19874	+	2.69837i	0.190459	+	0.122400i
$487$	2.08772	−	14.5204i	0.0946038	−	0.657984i	−0.886246	−	0.463216i	$-0.846695\pi$
$487$	2.08772	−	14.5204i	0.0946038	−	0.657984i	0.980849	−	0.194768i	$-0.0623954\pi$
$488$	5.50385	−	12.0517i	0.249148	−	0.545557i
$489$	1.55167	+	10.7921i	0.0701688	+	0.488035i
$490$	5.95257	+	1.74783i	0.268910	+	0.0789591i
$491$	21.6143	−	13.8906i	0.975438	−	0.626876i	0.0472091	−	0.998885i	$-0.484967\pi$
$491$	21.6143	−	13.8906i	0.975438	−	0.626876i	0.928229	+	0.372009i	$0.121331\pi$
$492$	1.57621	+	3.45142i	0.0710611	+	0.155602i
$493$	3.44652	−	1.01199i	0.155223	−	0.0455777i
$494$	0.943239	−	1.08856i	0.0424383	−	0.0489765i
$495$	−0.0378033	+	0.0436273i	−0.00169913	+	0.00196090i
$496$	−2.32118	+	0.681559i	−0.104224	+	0.0306029i
$497$	1.58647	+	3.47389i	0.0711629	+	0.155825i
$498$	−0.344904	+	0.221656i	−0.0154555	+	0.00993265i
$499$	−4.94941	−	1.45328i	−0.221566	−	0.0650576i	0.169065	−	0.985605i	$-0.445925\pi$
$499$	−4.94941	−	1.45328i	−0.221566	−	0.0650576i	−0.390631	+	0.920547i	$0.627743\pi$
$500$	2.62621	+	18.2657i	0.117448	+	0.816868i
$501$	−2.06947	+	4.53152i	−0.0924573	+	0.202453i
$502$	0.967115	−	6.72643i	0.0431644	−	0.300215i
$503$	3.21416	+	2.06561i	0.143312	+	0.0921012i	0.610332	−	0.792146i	$-0.291036\pi$
$503$	3.21416	+	2.06561i	0.143312	+	0.0921012i	−0.467020	+	0.884247i	$0.654672\pi$
$504$	−0.616842	−	0.711874i	−0.0274763	−	0.0317094i
$505$	−5.80677			−0.258398
$506$	0.00123275	+	0.0156966i	5.48026e−5	+	0.000697798i
$507$	7.06595			0.313810
$508$	14.6806	+	16.9424i	0.651348	+	0.751696i
$509$	33.2882	+	21.3930i	1.47547	+	0.948230i	0.997559	+	0.0698244i	$0.0222439\pi$
$509$	33.2882	+	21.3930i	1.47547	+	0.948230i	0.477916	+	0.878406i	$0.341392\pi$
$510$	0.271762	−	1.89014i	0.0120338	−	0.0836970i
$511$	−1.28396	+	2.81148i	−0.0567991	+	0.124373i
$512$	3.13003	+	21.7698i	0.138329	+	0.962099i
$513$	11.9830	+	3.51852i	0.529062	+	0.155347i
$514$	5.76675	−	3.70606i	0.254360	−	0.163468i
$515$	6.74614	+	14.7720i	0.297270	+	0.650931i
$516$	5.12487	−	1.50480i	0.225610	−	0.0662451i
$517$	−0.00722321	+	0.00833603i	−0.000317676	+	0.000366618i
$518$	0.580778	−	0.670254i	0.0255179	−	0.0294493i
$519$	13.3927	−	3.93246i	0.587875	−	0.172616i
$520$	1.51521	+	3.31786i	0.0664466	+	0.145498i
$521$	1.20518	−	0.774524i	0.0528000	−	0.0339325i	−0.513975	−	0.857805i	$-0.671827\pi$
$521$	1.20518	−	0.774524i	0.0528000	−	0.0339325i	0.566775	+	0.823873i	$0.308191\pi$
$522$	0.931702	+	0.273572i	0.0407795	+	0.0119739i
$523$	3.55609	+	24.7331i	0.155497	+	1.08150i	0.906804	+	0.421552i	$0.138514\pi$
$523$	3.55609	+	24.7331i	0.155497	+	1.08150i	−0.751308	+	0.659952i	$0.770577\pi$
$524$	9.74077	−	21.3293i	0.425528	−	0.931776i
$525$	−0.0199893	+	0.139028i	−0.000872403	+	0.00606770i
$526$	5.88897	+	3.78461i	0.256771	+	0.165017i
$527$	−1.77251	−	2.04558i	−0.0772116	−	0.0891069i
$528$	−0.0170770			−0.000743182
$529$	−22.7180	+	3.59053i	−0.987740	+	0.156110i
$530$	−8.04136			−0.349294
$531$	4.81689	+	5.55899i	0.209035	+	0.241240i
$532$	−1.46527	−	0.941671i	−0.0635274	−	0.0408266i
$533$	0.513822	−	3.57371i	0.0222561	−	0.154794i
$534$	1.31943	−	2.88915i	0.0570973	−	0.125026i
$535$	4.89236	+	34.0271i	0.211515	+	1.47112i
$536$	−18.3755	−	5.39554i	−0.793701	−	0.233052i
$537$	9.97618	−	6.41130i	0.430504	−	0.276668i
$538$	1.40160	+	3.06907i	0.0604272	+	0.132317i
$539$	0.0595595	−	0.0174882i	0.00256541	−	0.000753272i
$540$	−9.99465	+	11.5344i	−0.430101	+	0.496363i
$541$	−4.22115	+	4.87147i	−0.181481	+	0.209441i	−0.839200	−	0.543823i	$-0.816976\pi$
$541$	−4.22115	+	4.87147i	−0.181481	+	0.209441i	0.657718	+	0.753264i	$0.271522\pi$
$542$	10.6978	−	3.14115i	0.459508	−	0.134924i
$543$	−2.32566	−	5.09248i	−0.0998035	−	0.218539i
$544$	−12.1303	+	7.79568i	−0.520083	+	0.334237i
$545$	28.5032	+	8.36928i	1.22094	+	0.358501i
$546$	−0.00821876	−	0.0571627i	−0.000351730	−	0.00244634i
$547$	2.03420	−	4.45427i	0.0869760	−	0.190451i	−0.861146	−	0.508358i	$-0.830253\pi$
$547$	2.03420	−	4.45427i	0.0869760	−	0.190451i	0.948122	+	0.317907i	$0.102980\pi$
$548$	3.14445	−	21.8701i	0.134324	−	0.934246i
$549$	−20.8004	−	13.3676i	−0.887740	−	0.570516i
$550$	0.00202426	+	0.00233612i	8.63145e−5	+	9.96123e-5i
$551$	3.72069			0.158507
$552$	0.316551	+	4.03062i	0.0134733	+	0.171555i
$553$	−0.892209			−0.0379406
$554$	3.36142	+	3.87929i	0.142813	+	0.164815i
$555$	−11.7411	−	7.54557i	−0.498383	−	0.320292i
$556$	5.04220	−	35.0693i	0.213837	−	1.48727i
$557$	−13.8579	+	30.3445i	−0.587177	+	1.28574i	0.349956	+	0.936766i	$0.386196\pi$
$557$	−13.8579	+	30.3445i	−0.587177	+	1.28574i	−0.937133	+	0.348972i	$0.886531\pi$
$558$	−0.104132	−	0.724256i	−0.00440827	−	0.0306602i
$559$	−4.87655	−	1.43188i	−0.206256	−	0.0605623i
$560$	1.65211	−	1.06175i	0.0698146	−	0.0448671i
$561$	−0.00793718	−	0.0173800i	−0.000335108	−	0.000733784i
$562$	2.94729	−	0.865403i	0.124324	−	0.0365048i
$563$	1.65697	−	1.91224i	0.0698328	−	0.0805913i	−0.719758	−	0.694225i	$-0.755747\pi$
$563$	1.65697	−	1.91224i	0.0698328	−	0.0805913i	0.789591	+	0.613634i	$0.210293\pi$
$564$	−0.895103	+	1.03300i	−0.0376907	+	0.0434973i
$565$	−29.5115	+	8.66535i	−1.24156	+	0.364554i
$566$	−1.02250	−	2.23896i	−0.0429788	−	0.0941105i
$567$	−1.25501	+	0.806546i	−0.0527055	+	0.0338718i
$568$	20.7075	+	6.08028i	0.868868	+	0.255123i
$569$	6.76685	+	47.0645i	0.283681	+	1.97304i	0.222588	+	0.974913i	$0.428550\pi$
$569$	6.76685	+	47.0645i	0.283681	+	1.97304i	0.0610929	+	0.998132i	$0.480541\pi$
$570$	0.821685	−	1.79924i	0.0344166	−	0.0753619i
$571$	3.06388	−	21.3098i	0.128220	−	0.891786i	−0.819590	−	0.572950i	$-0.805799\pi$
$571$	3.06388	−	21.3098i	0.128220	−	0.891786i	0.947810	−	0.318836i	$-0.103292\pi$
$572$	0.0148163	+	0.00952189i	0.000619503	+	0.000398130i
$573$	1.26867	+	1.46413i	0.0529996	+	0.0611648i
$574$	0.315058			0.0131503
$575$	−3.17058	+	3.21512i	−0.132222	+	0.134080i
$576$	13.0958			0.545659
$577$	−10.3367	−	11.9292i	−0.430323	−	0.496619i	0.498631	−	0.866814i	$-0.333836\pi$
$577$	−10.3367	−	11.9292i	−0.430323	−	0.496619i	−0.928954	+	0.370195i	$0.879291\pi$
$578$	1.26467	+	0.812753i	0.0526033	+	0.0338061i
$579$	1.68399	−	11.7124i	0.0699843	−	0.486752i
$580$	−1.88887	+	4.13604i	−0.0784309	+	0.171740i
$581$	−0.0671379	−	0.466955i	−0.00278535	−	0.0193725i
$582$	2.50207	+	0.734674i	0.103714	+	0.0304532i
$583$	−0.0676866	+	0.0434995i	−0.00280329	+	0.00180157i
$584$	7.25585	+	15.8881i	0.300249	+	0.657454i
$585$	6.53123	−	1.91774i	0.270033	−	0.0792889i
$586$	1.64717	−	1.90094i	0.0680441	−	0.0785271i
$587$	−6.91708	+	7.98274i	−0.285498	+	0.329483i	−0.880325	−	0.474371i	$-0.842675\pi$
$587$	−6.91708	+	7.98274i	−0.285498	+	0.329483i	0.594826	+	0.803854i	$0.297221\pi$
$588$	7.38064	−	2.16715i	0.304372	−	0.0893718i
$589$	−1.16468	−	2.55029i	−0.0479898	−	0.105083i
$590$	2.09093	−	1.34376i	0.0860824	−	0.0553218i
$591$	9.21254	+	2.70505i	0.378953	+	0.111271i
$592$	4.40089	+	30.6089i	0.180875	+	1.25802i
$593$	−2.74806	+	6.01742i	−0.112849	+	0.247106i	−0.957627	−	0.288012i	$-0.907006\pi$
$593$	−2.74806	+	6.01742i	−0.112849	+	0.247106i	0.844777	+	0.535118i	$0.179733\pi$
$594$	0.00156829	−	0.0109077i	6.43477e−5	−	0.000447548i
$595$	1.84847	+	1.18794i	0.0757798	+	0.0487007i
$596$	−6.65906	−	7.68497i	−0.272766	−	0.314789i
$597$	−10.6094			−0.434212
$598$	0.878375	−	1.63565i	0.0359194	−	0.0668866i
$599$	4.67260			0.190917			0.0954586	−	0.995433i	$-0.469568\pi$
$599$	4.67260			0.190917			0.0954586	+	0.995433i	$0.469568\pi$
$600$	0.519795	+	0.599875i	0.0212205	+	0.0244898i
$601$	35.0890	+	22.5503i	1.43131	+	0.919848i	0.999843	+	0.0177192i	$0.00564050\pi$
$601$	35.0890	+	22.5503i	1.43131	+	0.919848i	0.431468	+	0.902128i	$0.357996\pi$
$602$	0.0631175	−	0.438992i	0.00257248	−	0.0178920i
$603$	−14.8471	+	32.5105i	−0.604619	+	1.32393i
$604$	3.21384	+	22.3527i	0.130769	+	0.909520i
$605$	−25.7265	−	7.55399i	−1.04593	−	0.307113i
$606$	0.437081	−	0.280895i	0.0177552	−	0.0114106i
$607$	−6.66883	−	14.6027i	−0.270680	−	0.592706i	0.724663	−	0.689103i	$-0.241995\pi$
$607$	−6.66883	−	14.6027i	−0.270680	−	0.592706i	−0.995343	+	0.0963974i	$0.969268\pi$
$608$	−14.3309	+	4.20792i	−0.581193	+	0.170654i
$609$	0.0976913	−	0.112742i	0.00395865	−	0.00456852i
$610$	−5.47129	+	6.31420i	−0.221526	+	0.255655i
$611$	1.24795	−	0.366430i	0.0504865	−	0.0148242i
$612$	7.36690	+	16.1313i	0.297789	+	0.652067i
$613$	−25.9988	+	16.7084i	−1.05008	+	0.674846i	−0.947460	−	0.319874i	$-0.896359\pi$
$613$	−25.9988	+	16.7084i	−1.05008	+	0.674846i	−0.102621	+	0.994720i	$0.532723\pi$
$614$	−2.58645	−	0.759450i	−0.104381	−	0.0306489i
$615$	−0.705607	−	4.90760i	−0.0284528	−	0.197894i
$616$	−0.00132297	+	0.00289689i	−5.33039e−5	+	0.000116719i
$617$	−4.78762	+	33.2986i	−0.192742	+	1.34055i	0.631967	+	0.774996i	$0.282248\pi$
$617$	−4.78762	+	33.2986i	−0.192742	+	1.34055i	−0.824709	+	0.565557i	$0.808661\pi$
$618$	−1.22236	−	0.785565i	−0.0491707	−	0.0316001i
$619$	−1.44398	−	1.66644i	−0.0580383	−	0.0669798i	0.725988	−	0.687707i	$-0.241383\pi$
$619$	−1.44398	−	1.66644i	−0.0580383	−	0.0669798i	−0.784026	+	0.620728i	$0.786837\pi$
$620$	3.42625			0.137602
$621$	16.0643	+	1.03636i	0.644638	+	0.0415877i
$622$	5.68568			0.227975
$623$	2.39332	+	2.76203i	0.0958862	+	0.110659i
$624$	1.69399	+	1.08866i	0.0678140	+	0.0435814i
$625$	4.10169	−	28.5279i	0.164067	−	1.14111i
$626$	−2.17225	+	4.75656i	−0.0868206	+	0.190111i
$627$	−0.00281656	−	0.0195896i	−0.000112483	−	0.000782335i
$628$	−23.2611	−	6.83008i	−0.928220	−	0.272550i
$629$	−29.1065	+	18.7056i	−1.16055	+	0.745840i
$630$	0.246754	+	0.540316i	0.00983091	+	0.0215267i
$631$	−22.9030	+	6.72492i	−0.911753	+	0.267715i	−0.703779	−	0.710419i	$-0.748505\pi$
$631$	−22.9030	+	6.72492i	−0.911753	+	0.267715i	−0.207975	+	0.978134i	$0.566687\pi$
$632$	−3.30181	+	3.81049i	−0.131339	+	0.151573i
$633$	1.30965	−	1.51142i	0.0520540	−	0.0600736i
$634$	4.91680	−	1.44370i	0.195271	−	0.0573368i
$635$	−12.1691	−	26.6466i	−0.482916	−	1.05744i
$636$	−8.38775	+	5.39048i	−0.332596	+	0.213746i
$637$	−7.02302	−	2.06214i	−0.278262	−	0.0817051i
$638$	−0.000467226	−	0.00324963i	−1.84976e−5	−	0.000128654i
$639$	16.7313	−	36.6364i	0.661880	−	1.44931i
$640$	3.41484	−	23.7507i	0.134983	−	0.938829i
$641$	4.55666	+	2.92839i	0.179977	+	0.115664i	0.627527	−	0.778594i	$-0.284067\pi$
$641$	4.55666	+	2.92839i	0.179977	+	0.115664i	−0.447550	+	0.894259i	$0.647703\pi$
$642$	−2.01427	−	2.32459i	−0.0794969	−	0.0917444i
$643$	−18.1860			−0.717185			−0.358592	−	0.933494i	$-0.616743\pi$
$643$	−18.1860			−0.717185			−0.358592	+	0.933494i	$0.616743\pi$
$644$	−2.10894	−	0.769880i	−0.0831040	−	0.0303375i
$645$	−6.97946			−0.274816
$646$	−3.21108	−	3.70579i	−0.126338	−	0.145802i
$647$	30.3504	+	19.5050i	1.19320	+	0.766821i	0.977766	−	0.209698i	$-0.0672480\pi$
$647$	30.3504	+	19.5050i	1.19320	+	0.766821i	0.215431	+	0.976519i	$0.430884\pi$
$648$	−1.19980	+	8.34476i	−0.0471324	+	0.327813i
$649$	0.0103310	−	0.0226217i	0.000405527	−	0.000887980i
$650$	−0.0518728	−	0.360783i	−0.00203462	−	0.0141511i
$651$	−0.107857	−	0.0316697i	−0.00422725	−	0.00124123i
$652$	−28.7829	+	18.4977i	−1.12723	+	0.724425i
$653$	−6.43484	−	14.0903i	−0.251815	−	0.551397i	0.740938	−	0.671573i	$-0.234381\pi$
$653$	−6.43484	−	14.0903i	−0.251815	−	0.551397i	−0.992753	+	0.120176i	$0.961654\pi$
$654$	−2.55031	+	0.748839i	−0.0997251	+	0.0292819i
$655$	−20.0651	+	23.1563i	−0.784007	+	0.904792i
$656$	−7.19397	+	8.30229i	−0.280877	+	0.324150i
$657$	31.2758	−	9.18341i	1.22019	−	0.358279i
$658$	0.0471482	+	0.103240i	0.00183803	+	0.00402472i
$659$	21.5294	−	13.8361i	0.838668	−	0.538979i	−0.0493535	−	0.998781i	$-0.515716\pi$
$659$	21.5294	−	13.8361i	0.838668	−	0.538979i	0.888021	+	0.459802i	$0.152080\pi$
$660$	0.0232063	+	0.00681399i	0.000903305	+	0.000265234i
$661$	−0.0549746	−	0.382357i	−0.00213826	−	0.0148719i	0.988724	−	0.149747i	$-0.0478459\pi$
$661$	−0.0549746	−	0.382357i	−0.00213826	−	0.0148719i	−0.990863	+	0.134875i	$0.956937\pi$
$662$	−0.806562	+	1.76612i	−0.0313479	+	0.0686424i
$663$	−0.320632	+	2.23005i	−0.0124523	+	0.0866078i
$664$	−2.24275	−	1.44133i	−0.0870357	−	0.0559344i
$665$	1.49046	+	1.72008i	0.0577974	+	0.0667018i
$666$	−9.35317			−0.362428
$667$	4.67901	−	1.05209i	0.181172	−	0.0407372i
$668$	−15.6328			−0.604852
$669$	−0.872954	−	1.00744i	−0.0337504	−	0.0389500i
$670$	10.1597	+	6.52924i	0.392503	+	0.252247i
$671$	−0.0118970	+	0.0827453i	−0.000459278	+	0.00319435i
$672$	−0.248769	+	0.544727i	−0.00959646	+	0.0210133i
$673$	0.420437	+	2.92420i	0.0162066	+	0.112720i	0.996319	−	0.0857241i	$-0.0273204\pi$
$673$	0.420437	+	2.92420i	0.0162066	+	0.112720i	−0.980112	+	0.198444i	$0.936411\pi$
$674$	−4.40662	−	1.29390i	−0.169737	−	0.0498391i
$675$	2.65868	−	1.70863i	0.102333	−	0.0657653i
$676$	9.21112	+	20.1695i	0.354274	+	0.775751i
$677$	−1.81095	+	0.531743i	−0.0696005	+	0.0204365i	−0.316347	−	0.948643i	$-0.602457\pi$
$677$	−1.81095	+	0.531743i	−0.0696005	+	0.0204365i	0.246747	+	0.969080i	$0.420638\pi$
$678$	1.80218	−	2.07983i	0.0692124	−	0.0798753i
$679$	−1.96496	+	2.26768i	−0.0754082	+	0.0870257i
$680$	11.9142	−	3.49831i	0.456887	−	0.134154i
$681$	2.53466	+	5.55013i	0.0971283	+	0.212681i
$682$	−0.00208115	+	0.00133747i	−7.96914e−5	+	5.12146e-5i
$683$	15.8140	+	4.64342i	0.605108	+	0.177676i	0.569913	−	0.821705i	$-0.306977\pi$
$683$	15.8140	+	4.64342i	0.605108	+	0.177676i	0.0351944	+	0.999380i	$0.488795\pi$
$684$	2.61419	+	18.1821i	0.0999562	+	0.695211i
$685$	−11.9938	+	26.2628i	−0.458260	+	1.00345i
$686$	0.182624	−	1.27018i	0.00697261	−	0.0484956i
$687$	−0.271466	−	0.174460i	−0.0103571	−	0.00665608i
$688$	10.1269	+	11.6871i	0.386085	+	0.445566i
$689$	9.48743			0.361442
$690$	0.524554	−	2.49500i	0.0199694	−	0.0949832i
$691$	−34.1145			−1.29778			−0.648888	−	0.760884i	$-0.724766\pi$
$691$	−34.1145			−1.29778			−0.648888	+	0.760884i	$0.724766\pi$
$692$	28.6837	+	33.1028i	1.09039	+	1.25838i
$693$	0.00499982	+	0.00321319i	0.000189928	+	0.000122059i
$694$	1.01806	−	7.08076i	0.0386450	−	0.268782i
$695$	−19.2323	+	42.1129i	−0.729524	+	1.59744i
$696$	−0.119976	−	0.834450i	−0.00454767	−	0.0316297i
$697$	−11.7933	−	3.46281i	−0.446701	−	0.131163i
$698$	3.59363	−	2.30949i	0.136021	−	0.0874153i
$699$	0.680222	+	1.48948i	0.0257283	+	0.0563372i
$700$	−0.422910	+	0.124178i	−0.0159845	+	0.00469347i
$701$	−24.0228	+	27.7238i	−0.907330	+	1.04711i	0.0913535	+	0.995819i	$0.470881\pi$
$701$	−24.0228	+	27.7238i	−0.907330	+	1.04711i	−0.998683	+	0.0512961i	$0.983665\pi$
$702$	−0.850938	+	0.982035i	−0.0321166	+	0.0370645i
$703$	−34.3866	+	10.0968i	−1.29692	+	0.380809i
$704$	−0.0183932	−	0.0402754i	−0.000693218	−	0.00151794i
$705$	1.50256	−	0.965636i	0.0565896	−	0.0363679i
$706$	−6.41232	−	1.88283i	−0.241331	−	0.0708612i
$707$	0.0850809	+	0.591751i	0.00319980	+	0.0222551i
$708$	1.28022	−	2.80329i	0.0481136	−	0.105354i
$709$	4.49050	−	31.2321i	0.168644	−	1.17295i	−0.713045	−	0.701118i	$-0.752685\pi$
$709$	4.49050	−	31.2321i	0.168644	−	1.17295i	0.881690	−	0.471830i	$-0.156406\pi$
$710$	−11.4491	−	7.35786i	−0.429675	−	0.276136i
$711$	6.16188	+	7.11119i	0.231088	+	0.266690i
$712$	20.6532			0.774012
$713$	−2.18580	−	2.87782i	−0.0818588	−	0.107775i
$714$	−0.196601			−0.00735761
$715$	−0.0150710	−	0.0173929i	−0.000563625	−	0.000650458i
$716$	31.3057	+	20.1190i	1.16995	+	0.751882i
$717$	−0.950757	+	6.61266i	−0.0355067	+	0.246954i
$718$	0.917043	−	2.00805i	0.0342238	−	0.0749396i
$719$	−5.11849	−	35.5999i	−0.190888	−	1.32765i	−0.829666	−	0.558261i	$-0.811469\pi$
$719$	−5.11849	−	35.5999i	−0.190888	−	1.32765i	0.638778	−	0.769391i	$-0.279440\pi$
$720$	−19.8725	−	5.83509i	−0.740604	−	0.217461i
$721$	1.40652	−	0.903918i	0.0523817	−	0.0336637i
$722$	0.785911	+	1.72091i	0.0292486	+	0.0640455i
$723$	−10.2891	+	3.02115i	−0.382656	+	0.112358i
$724$	11.5046	−	13.2770i	0.427566	−	0.493437i
$725$	0.616579	−	0.711570i	0.0228992	−	0.0264271i
$726$	2.30187	−	0.675891i	0.0854305	−	0.0250847i
$727$	17.6790	+	38.7116i	0.655678	+	1.43574i	0.886495	+	0.462738i	$0.153133\pi$
$727$	17.6790	+	38.7116i	0.655678	+	1.43574i	−0.230816	+	0.972997i	$0.574140\pi$
$728$	0.315912	−	0.203024i	0.0117085	−	0.00752459i
$729$	9.35248	+	2.74614i	0.346388	+	0.101709i
$730$	−1.56752	−	10.9023i	−0.0580164	−	0.403513i
$731$	−7.18758	+	15.7386i	−0.265842	+	0.582114i
$732$	−1.47428	+	10.2538i	−0.0544909	+	0.378993i
$733$	−8.34177	−	5.36093i	−0.308110	−	0.198010i	0.377443	−	0.926033i	$-0.376803\pi$
$733$	−8.34177	−	5.36093i	−0.308110	−	0.198010i	−0.685553	+	0.728022i	$0.740440\pi$
$734$	6.43131	+	7.42212i	0.237384	+	0.273956i
$735$	−10.0515			−0.370756
$736$	−16.8321	+	9.34403i	−0.620439	+	0.344426i
$737$	0.120837			0.00445109
$738$	−2.17589	−	2.51111i	−0.0800957	−	0.0924354i
$739$	−4.82025	−	3.09779i	−0.177316	−	0.113954i	0.448972	−	0.893546i	$-0.351790\pi$
$739$	−4.82025	−	3.09779i	−0.177316	−	0.113954i	−0.626288	+	0.779592i	$0.715427\pi$
$740$	6.23294	−	43.3511i	0.229128	−	1.59362i
$741$	−0.969448	+	2.12279i	−0.0356135	+	0.0779828i
$742$	0.117822	+	0.819472i	0.00432539	+	0.0300838i
$743$	41.2911	+	12.1242i	1.51482	+	0.444793i	0.930366	−	0.366631i	$-0.119489\pi$
$743$	41.2911	+	12.1242i	1.51482	+	0.444793i	0.584458	+	0.811424i	$0.301307\pi$
$744$	−0.534405	+	0.343441i	−0.0195922	+	0.0125912i
$745$	5.51984	+	12.0868i	0.202231	+	0.442825i
$746$	−6.32485	+	1.85714i	−0.231569	+	0.0679948i
$747$	−3.25810	+	3.76005i	−0.119208	+	0.137573i
$748$	0.0392638	−	0.0453129i	0.00143563	−	0.00165680i
$749$	3.39592	−	0.997133i	0.124084	−	0.0364344i
$750$	0.896278	+	1.96258i	0.0327275	+	0.0716631i
$751$	−1.16955	+	0.751625i	−0.0426775	+	0.0274272i	−0.561806	−	0.827269i	$-0.689893\pi$
$751$	−1.16955	+	0.751625i	−0.0426775	+	0.0274272i	0.519128	+	0.854696i	$0.326257\pi$
$752$	−3.79711	−	1.11493i	−0.138466	−	0.0406574i
$753$	1.56692	+	10.8982i	0.0571018	+	0.397152i
$754$	−0.160817	+	0.352140i	−0.00585660	+	0.0128242i
$755$	4.19957	−	29.2086i	0.152838	−	1.06301i
$756$	1.32188	+	0.849523i	0.0480764	+	0.0308968i
$757$	−2.55282	−	2.94611i	−0.0927839	−	0.107078i	0.707459	−	0.706755i	$-0.249841\pi$
$757$	−2.55282	−	2.94611i	−0.0927839	−	0.107078i	−0.800243	+	0.599676i	$0.795296\pi$
$758$	12.4817			0.453356
$759$	−0.00908133	−	0.0238388i	−0.000329631	−	0.000865293i
$760$	12.8620			0.466552
$761$	−8.50916	−	9.82009i	−0.308457	−	0.355978i	0.580263	−	0.814429i	$-0.302950\pi$
$761$	−8.50916	−	9.82009i	−0.308457	−	0.355978i	−0.888720	+	0.458451i	$0.848404\pi$
$762$	2.20497	+	1.41705i	0.0798778	+	0.0513343i
$763$	0.435260	−	3.02730i	0.0157575	−	0.109596i
$764$	−2.52547	+	5.53001i	−0.0913684	+	0.200069i
$765$	−3.29786	−	22.9372i	−0.119235	−	0.829295i
$766$	−0.0106758	−	0.00313471i	−0.000385733	−	0.000113262i
$767$	−2.46694	+	1.58541i	−0.0890762	+	0.0572458i
$768$	−1.55190	−	3.39818i	−0.0559992	−	0.122621i
$769$	40.7207	−	11.9567i	1.46842	−	0.431168i	0.552838	−	0.833289i	$-0.313545\pi$
$769$	40.7207	−	11.9567i	1.46842	−	0.431168i	0.915587	+	0.402121i	$0.131727\pi$
$770$	0.00131514	−	0.00151775i	4.73944e−5	−	5.46960e-5i
$771$	−7.27315	+	8.39366i	−0.261936	+	0.302290i
$772$	35.6280	−	10.4613i	1.28228	−	0.376511i
$773$	−7.36286	−	16.1224i	−0.264824	−	0.579883i	0.729774	−	0.683689i	$-0.239625\pi$
$773$	−7.36286	−	16.1224i	−0.264824	−	0.579883i	−0.994598	+	0.103806i	$0.966898\pi$
$774$	−3.93481	+	2.52875i	−0.141434	+	0.0908941i
$775$	−0.680741	−	0.199884i	−0.0244529	−	0.00718003i
$776$	2.41319	+	16.7841i	0.0866284	+	0.602514i
$777$	−0.596915	+	1.30706i	−0.0214142	+	0.0468906i
$778$	−0.474027	+	3.29693i	−0.0169947	+	0.118201i
$779$	−10.7104	−	6.88313i	−0.383738	−	0.246614i
$780$	−1.86761	−	2.15534i	−0.0668712	−	0.0771735i
$781$	−0.136172			−0.00487263
$782$	−5.08602	−	3.75227i	−0.181876	−	0.134181i
$783$	−3.35660			−0.119955
$784$	14.5844	+	16.8313i	0.520871	+	0.601117i
$785$	26.6499	+	17.1269i	0.951177	+	0.611284i
$786$	0.390159	−	2.71362i	0.0139165	−	0.0967916i
$787$	2.73211	−	5.98249i	0.0973892	−	0.213253i	−0.854666	−	0.519177i	$-0.826238\pi$
$787$	2.73211	−	5.98249i	0.0973892	−	0.213253i	0.952056	+	0.305925i	$0.0989656\pi$
$788$	4.28793	+	29.8232i	0.152751	+	1.06241i
$789$	−10.8824	−	3.19535i	−0.387423	−	0.113758i
$790$	2.67477	−	1.71897i	0.0951640	−	0.0611582i
$791$	1.31546	+	2.88046i	0.0467725	+	0.102418i
$792$	0.0322260	−	0.00946240i	0.00114510	−	0.000336232i
$793$	6.45518	−	7.44968i	0.229230	−	0.264546i
$794$	−0.223986	+	0.258494i	−0.00794898	+	0.00917361i
$795$	12.5009	−	3.67059i	0.443361	−	0.130182i
$796$	−13.8303	−	30.2841i	−0.490201	−	1.07339i
$797$	3.85073	−	2.47472i	0.136400	−	0.0876590i	−0.470661	−	0.882314i	$-0.655985\pi$
$797$	3.85073	−	2.47472i	0.136400	−	0.0876590i	0.607061	+	0.794655i	$0.292348\pi$
$798$	−0.195395	−	0.0573730i	−0.00691690	−	0.00203098i
$799$	−0.630135	−	4.38269i	−0.0222926	−	0.155048i
$800$	−1.57011	+	3.43805i	−0.0555116	+	0.121553i
$801$	5.48528	−	38.1510i	0.193813	−	1.34800i
$802$	−6.55165	−	4.21049i	−0.231347	−	0.148678i
$803$	−0.0721701	−	0.0832887i	−0.00254683	−	0.00293920i
$804$	14.9742			0.528098
$805$	2.36073	+	1.74165i	0.0832047	+	0.0613853i
$806$	0.291709			0.0102750
$807$	−3.57981	−	4.13132i	−0.126015	−	0.145429i
$808$	2.84214	+	1.82653i	0.0999861	+	0.0642572i
$809$	−2.43309	+	16.9225i	−0.0855429	+	0.594964i	0.901289	+	0.433217i	$0.142622\pi$
$809$	−2.43309	+	16.9225i	−0.0855429	+	0.594964i	−0.986832	+	0.161746i	$0.948287\pi$
$810$	2.20849	−	4.83592i	0.0775985	−	0.169917i
$811$	0.601274	+	4.18195i	0.0211136	+	0.146848i	0.997651	−	0.0684987i	$-0.0218209\pi$
$811$	0.601274	+	4.18195i	0.0211136	+	0.146848i	−0.976538	+	0.215347i	$0.930912\pi$
$812$	0.449167	+	0.131887i	0.0157627	+	0.00462834i
$813$	−15.1966	+	9.76628i	−0.532969	+	0.342519i
$814$	0.0131366	+	0.0287651i	0.000460437	+	0.00100822i
$815$	42.8973	−	12.5958i	1.50263	−	0.441211i
$816$	4.48914	−	5.18075i	0.157151	−	0.181362i
$817$	−11.7364	+	13.5445i	−0.410605	+	0.473863i
$818$	3.78629	−	1.11175i	0.132384	−	0.0388716i
$819$	−0.291127	−	0.637480i	−0.0101728	−	0.0222753i
$820$	13.0888	−	8.41165i	0.457080	−	0.293748i
$821$	31.0682	+	9.12244i	1.08429	+	0.318375i	0.774592	−	0.632461i	$-0.217955\pi$
$821$	31.0682	+	9.12244i	1.08429	+	0.318375i	0.309695	+	0.950836i	$0.399773\pi$
$822$	−0.367642	−	2.55701i	−0.0128230	−	0.0891859i
$823$	20.3022	−	44.4556i	0.707690	−	1.54962i	−0.122702	−	0.992444i	$-0.539156\pi$
$823$	20.3022	−	44.4556i	0.707690	−	1.54962i	0.830391	−	0.557181i	$-0.188117\pi$
$824$	1.34464	−	9.35220i	0.0468429	−	0.325799i
$825$	−0.00421320	−	0.00270766i	−0.000146685	−	9.42687e-5i
$826$	−0.167575	−	0.193392i	−0.00583069	−	0.00672898i
$827$	22.2539			0.773845			0.386922	−	0.922112i	$-0.373538\pi$
$827$	22.2539			0.773845			0.386922	+	0.922112i	$0.373538\pi$
$828$	8.42884	+	22.1260i	0.292922	+	0.768930i
$829$	29.4668			1.02343			0.511713	−	0.859157i	$-0.329011\pi$
$829$	29.4668			1.02343			0.511713	+	0.859157i	$0.329011\pi$
$830$	1.10093	+	1.27054i	0.0382138	+	0.0441011i
$831$	−6.99633	−	4.49627i	−0.242700	−	0.155974i
$832$	−0.743014	+	5.16778i	−0.0257594	+	0.179160i
$833$	−10.3513	+	22.6661i	−0.358650	+	0.785335i
$834$	−0.589523	−	4.10022i	−0.0204135	−	0.141979i
$835$	19.6002	+	5.75512i	0.678291	+	0.199164i
$836$	0.0522464	−	0.0335767i	0.00180698	−	0.00116127i
$837$	1.05071	+	2.30073i	0.0363178	+	0.0795249i
$838$	−4.46264	+	1.31035i	−0.154159	+	0.0452653i
$839$	12.6532	−	14.6025i	0.436836	−	0.504136i	−0.494056	−	0.869430i	$-0.664486\pi$
$839$	12.6532	−	14.6025i	0.436836	−	0.504136i	0.930892	+	0.365294i	$0.119032\pi$
$840$	0.337706	−	0.389734i	0.0116520	−	0.0134471i
$841$	−0.959493	+	0.281733i	−0.0330860	+	0.00971492i
$842$	3.25604	+	7.12973i	0.112210	+	0.245707i
$843$	−4.18676	+	2.69066i	−0.144200	+	0.0926714i
$844$	6.02156	+	1.76809i	0.207271	+	0.0608601i
$845$	−4.12345	−	28.6792i	−0.141851	−	0.986595i
$846$	0.497236	−	1.08879i	0.0170953	−	0.0374335i
$847$	−0.392859	+	2.73239i	−0.0134988	+	0.0938862i
$848$	−24.2847	−	15.6068i	−0.833940	−	0.535941i
$849$	2.61155	+	3.01389i	0.0896282	+	0.103436i
$850$	−1.24085			−0.0425608
$851$	−40.3883	+	22.4208i	−1.38449	+	0.768576i
$852$	−16.8745			−0.578112
$853$	19.1021	+	22.0450i	0.654043	+	0.754806i	0.981792	−	0.189959i	$-0.0608356\pi$
$853$	19.1021	+	22.0450i	0.654043	+	0.754806i	−0.327749	+	0.944765i	$0.606290\pi$
$854$	0.723627	+	0.465047i	0.0247620	+	0.0159136i
$855$	3.41600	−	23.7588i	0.116825	−	0.812534i
$856$	8.30873	−	18.1936i	0.283987	−	0.621844i
$857$	−5.94637	−	41.3579i	−0.203124	−	1.41276i	−0.794940	−	0.606687i	$-0.792498\pi$
$857$	−5.94637	−	41.3579i	−0.203124	−	1.41276i	0.591816	−	0.806073i	$-0.298411\pi$
$858$	0.00197577		0.000580139i	6.74517e−5		1.98056e-5i
$859$	10.2295	−	6.57411i	0.349026	−	0.224306i	−0.354367	−	0.935106i	$-0.615304\pi$
$859$	10.2295	−	6.57411i	0.349026	−	0.224306i	0.703393	+	0.710801i	$0.251667\pi$
$860$	−9.09837	−	19.9226i	−0.310252	−	0.679357i
$861$	−0.489781	+	0.143813i	−0.0166917	+	0.00490112i
$862$	−3.69565	+	4.26501i	−0.125874	+	0.145267i
$863$	−3.93835	+	4.54510i	−0.134063	+	0.154717i	−0.818811	−	0.574063i	$-0.805367\pi$
$863$	−3.93835	+	4.54510i	−0.134063	+	0.154717i	0.684748	+	0.728780i	$0.259912\pi$
$864$	12.9285	−	3.79615i	0.439836	−	0.129148i
$865$	−23.7766	−	52.0634i	−0.808428	−	1.77021i
$866$	−4.57263	+	2.93865i	−0.155384	+	0.0998595i
$867$	−2.33701	−	0.686209i	−0.0793691	−	0.0233049i
$868$	−0.0502015	−	0.349159i	−0.00170395	−	0.0118512i
$869$	0.0132156	−	0.0289382i	0.000448309	−	0.000981661i
$870$	−0.0756571	+	0.526207i	−0.00256502	+	0.0178401i
$871$	−11.9867	−	7.70338i	−0.406154	−	0.261019i
$872$	−11.3184	−	13.0621i	−0.383289	−	0.442339i
$873$	31.6448			1.07101
$874$	−3.95981	−	5.21348i	−0.133942	−	0.176348i
$875$	−2.48261			−0.0839274
$876$	−8.94335	−	10.3212i	−0.302168	−	0.348720i
$877$	−12.3136	−	7.91347i	−0.415801	−	0.267219i	0.315971	−	0.948769i	$-0.397670\pi$
$877$	−12.3136	−	7.91347i	−0.415801	−	0.267219i	−0.731772	+	0.681550i	$0.761306\pi$
$878$	0.878686	−	6.11139i	0.0296542	−	0.206250i
$879$	−1.69294	+	3.70702i	−0.0571015	+	0.125035i
$880$	0.00996557	+	0.0693121i	0.000335939	+	0.00233651i
$881$	−6.40904	−	1.88186i	−0.215926	−	0.0634016i	0.171980	−	0.985100i	$-0.444983\pi$
$881$	−6.40904	−	1.88186i	−0.215926	−	0.0634016i	−0.387906	+	0.921699i	$0.626802\pi$
$882$	−5.66676	+	3.64181i	−0.190810	+	0.122626i
$883$	−13.4016	−	29.3454i	−0.450999	−	0.987550i	−0.989448	−	0.144891i	$-0.953717\pi$
$883$	−13.4016	−	29.3454i	−0.450999	−	0.987550i	0.538449	−	0.842658i	$-0.319011\pi$
$884$	−6.78357	+	1.99184i	−0.228156	+	0.0669927i
$885$	−2.63713	+	3.04341i	−0.0886462	+	0.102303i
$886$	0.692476	−	0.799160i	0.0232642	−	0.0268483i
$887$	−55.4296	+	16.2756i	−1.86115	+	0.546482i	−0.861924	+	0.507038i	$0.830740\pi$
$887$	−55.4296	+	16.2756i	−1.86115	+	0.546482i	−0.999222	+	0.0394436i	$0.987441\pi$
$888$	3.37326	+	7.38640i	0.113199	+	0.247871i
$889$	−2.53718	+	1.63054i	−0.0850942	+	0.0546867i
$890$	−12.4964	−	3.66928i	−0.418881	−	0.122995i
$891$	−0.00757024	−	0.0526522i	−0.000253613	−	0.00176391i
$892$	1.73774	−	3.80512i	0.0581838	−	0.127405i
$893$	0.652708	−	4.53969i	0.0218420	−	0.151915i
$894$	−1.00017	−	0.642767i	−0.0334505	−	0.0214973i
$895$	−31.8439	−	36.7498i	−1.06442	−	1.22841i
$896$	−2.47040			−0.0825303
$897$	−0.618884	+	2.94368i	−0.0206639	+	0.0982865i
$898$	−0.857069			−0.0286008
$899$	0.493457	+	0.569480i	0.0164577	+	0.0189932i
$900$	3.91049	+	2.51312i	0.130350	+	0.0837706i
$901$	4.59651	−	31.9694i	0.153132	−	1.06506i
$902$	−0.00466672	+	0.0102187i	−0.000155385	+	0.000340245i
$903$	0.102263	+	0.711256i	0.00340310	+	0.0236691i
$904$	17.1702	+	5.04162i	0.571072	+	0.167682i
$905$	−19.3121	+	12.4112i	−0.641957	+	0.412561i
$906$	1.09682	+	2.40171i	0.0364395	+	0.0797914i
$907$	20.6004	−	6.04882i	0.684024	−	0.200848i	0.0787855	−	0.996892i	$-0.474896\pi$
$907$	20.6004	−	6.04882i	0.684024	−	0.200848i	0.605239	+	0.796044i	$0.293078\pi$
$908$	−12.5385	+	14.4702i	−0.416105	+	0.480211i
$909$	4.12884	−	4.76494i	0.136945	−	0.158043i
$910$	−0.227215	+	0.0667165i	−0.00753212	+	0.00221163i
$911$	12.6521	+	27.7042i	0.419182	+	0.917881i	0.994960	+	0.100275i	$0.0319722\pi$
$911$	12.6521	+	27.7042i	0.419182	+	0.917881i	−0.575777	+	0.817606i	$0.695301\pi$
$912$	5.97347	−	3.83892i	0.197801	−	0.127119i
$913$	0.0161398	+	0.00473908i	0.000534150	+	0.000156841i
$914$	−0.680977	−	4.73630i	−0.0225247	−	0.156663i
$915$	5.62331	−	12.3133i	0.185901	−	0.407066i
$916$	0.144111	−	1.00232i	0.00476157	−	0.0331175i
$917$	2.65379	+	1.70548i	0.0876357	+	0.0563201i
$918$	2.89686	+	3.34315i	0.0956106	+	0.110341i
$919$	51.7699			1.70773			0.853866	−	0.520493i	$-0.174252\pi$
$919$	51.7699			1.70773			0.853866	+	0.520493i	$0.174252\pi$
$920$	16.1747	−	3.63695i	0.533265	−	0.119907i
$921$	4.36748			0.143913
$922$	−3.67287	−	4.23872i	−0.120960	−	0.139595i
$923$	13.5079	+	8.68101i	0.444619	+	0.285739i
$924$	0.000354374	−	0.00246473i	1.16581e−5	−	8.10836e-5i
$925$	−3.76744	+	8.24954i	−0.123873	+	0.271243i
$926$	−1.47601	−	10.2659i	−0.0485047	−	0.337357i
$927$	−16.9184	−	4.96770i	−0.555674	−	0.163161i
$928$	3.37702	−	2.17028i	0.110856	−	0.0712429i
$929$	15.6444	+	34.2565i	0.513277	+	1.12392i	0.971923	+	0.235301i	$0.0756077\pi$
$929$	15.6444	+	34.2565i	0.513277	+	1.12392i	−0.458645	+	0.888620i	$0.651665\pi$
$930$	0.384363	−	0.112859i	0.0126038	−	0.00370080i
$931$	−16.9023	+	19.5063i	−0.553950	+	0.639293i
$932$	−3.36494	+	3.88334i	−0.110222	+	0.127203i
$933$	−8.83880	+	2.59531i	−0.289369	+	0.0849665i
$934$	5.90944	+	12.9399i	0.193363	+	0.423405i
$935$	−0.0659100	+	0.0423578i	−0.00215549	+	0.00138525i
$936$	−3.79996	−	1.11577i	−0.124206	−	0.0364700i
$937$	0.634004	+	4.40959i	0.0207120	+	0.144055i	0.997553	−	0.0699100i	$-0.0222712\pi$
$937$	0.634004	+	4.40959i	0.0207120	+	0.144055i	−0.976841	+	0.213965i	$0.931362\pi$
$938$	0.516516	−	1.13101i	0.0168648	−	0.0369288i
$939$	1.20572	−	8.38598i	0.0393472	−	0.273666i
$940$	4.71510	+	3.03021i	0.153790	+	0.0988346i
$941$	−29.0606	−	33.5377i	−0.947348	−	1.09330i	−0.995529	−	0.0944592i	$-0.969888\pi$
$941$	−29.0606	−	33.5377i	−0.947348	−	1.09330i	0.0481807	−	0.998839i	$-0.484658\pi$
$942$	−2.83446			−0.0923516
$943$	−15.4153	−	5.62743i	−0.501991	−	0.183254i
$944$	8.92257			0.290405
$945$	−1.34461	−	1.55176i	−0.0437401	−	0.0504787i
$946$	0.0133035	+	0.00854964i	0.000432534	+	0.000277973i
$947$	2.23695	−	15.5583i	0.0726911	−	0.505577i	−0.920652	−	0.390384i	$-0.872342\pi$
$947$	2.23695	−	15.5583i	0.0726911	−	0.505577i	0.993343	−	0.115193i	$-0.0367487\pi$
$948$	1.63769	−	3.58603i	0.0531896	−	0.116469i
$949$	1.84940	+	12.8629i	0.0600341	+	0.417547i
$950$	−1.23323	−	0.362110i	−0.0400114	−	0.0117484i
$951$	−6.98453	+	4.48868i	−0.226489	+	0.145556i
$952$	−0.531069	−	1.16288i	−0.0172121	−	0.0376892i
$953$	47.9492	−	14.0792i	1.55323	−	0.456069i	0.611165	−	0.791503i	$-0.290701\pi$
$953$	47.9492	−	14.0792i	1.55323	−	0.456069i	0.942064	+	0.335434i	$0.108883\pi$
$954$	5.71773	−	6.59861i	0.185118	−	0.213638i
$955$	5.20223	−	6.00369i	0.168340	−	0.194275i
$956$	−20.1150	+	5.90631i	−0.650567	+	0.191024i
$957$	0.00220967	+	0.00483851i	7.14286e−5	+	0.000156407i
$958$	1.23204	−	0.791786i	0.0398055	−	0.0255815i
$959$	2.85210	+	0.837451i	0.0920990	+	0.0270427i
$960$	1.02035	+	7.09666i	0.0329315	+	0.229044i
$961$	−12.6420	+	27.6821i	−0.407806	+	0.892971i
$962$	0.530669	−	3.69088i	0.0171094	−	0.118999i
$963$	−31.4008	−	20.1801i	−1.01188	−	0.650293i
$964$	−22.0366	−	25.4316i	−0.709750	−	0.819096i
$965$	−48.5210			−1.56195
$966$	−0.261944	−	0.0168989i	−0.00842792	−	0.000543714i
$967$	−41.9936			−1.35042			−0.675212	−	0.737623i	$-0.735948\pi$
$967$	−41.9936			−1.35042			−0.675212	+	0.737623i	$0.735948\pi$
$968$	10.2158	+	11.7897i	0.328348	+	0.378934i
$969$	6.68342	+	4.29517i	0.214702	+	0.137981i
$970$	1.52176	−	10.5841i	0.0488609	−	0.339835i
$971$	−6.26191	+	13.7117i	−0.200954	+	0.440029i	−0.983101	−	0.183066i	$-0.941398\pi$
$971$	−6.26191	+	13.7117i	−0.200954	+	0.440029i	0.782146	+	0.623095i	$0.214125\pi$
$972$	−3.61136	−	25.1176i	−0.115835	−	0.805647i
$973$	4.57340	+	1.34287i	0.146616	+	0.0430505i
$974$	4.52783	−	2.90986i	0.145081	−	0.0932379i
$975$	0.245324	+	0.537185i	0.00785667	+	0.0172037i
$976$	−28.7779	+	8.44995i	−0.921158	+	0.270476i
$977$	17.0376	−	19.6624i	0.545081	−	0.629057i	−0.414649	−	0.909981i	$-0.636096\pi$
$977$	17.0376	−	19.6624i	0.545081	−	0.629057i	0.959730	+	0.280925i	$0.0906411\pi$
$978$	−2.61962	+	3.02320i	−0.0837661	+	0.0966713i
$979$	−0.125035	+	0.0367136i	−0.00399614	+	0.00117337i
$980$	−13.1031	−	28.6918i	−0.418563	−	0.916526i
$981$	−27.1346	+	17.4383i	−0.866341	+	0.556763i
$982$	9.04473	+	2.65577i	0.288629	+	0.0847491i
$983$	2.14625	+	14.9275i	0.0684547	+	0.476113i	0.994996	+	0.0999187i	$0.0318583\pi$
$983$	2.14625	+	14.9275i	0.0684547	+	0.476113i	−0.926541	+	0.376194i	$0.877233\pi$
$984$	−1.19834	+	2.62399i	−0.0382016	+	0.0836498i
$985$	5.60309	−	38.9703i	0.178529	−	1.24170i
$986$	1.10868	+	0.712505i	0.0353075	+	0.0226908i
$987$	−0.120421	−	0.138973i	−0.00383303	−	0.00442355i
$988$	−7.32322			−0.232983
$989$	−10.9293	+	20.3518i	−0.347532	+	0.647149i
$990$	−0.0211797			−0.000673136
$991$	−15.4668	−	17.8497i	−0.491320	−	0.567014i	0.454898	−	0.890544i	$-0.349676\pi$
$991$	−15.4668	−	17.8497i	−0.491320	−	0.567014i	−0.946218	+	0.323530i	$0.895130\pi$
$992$	−2.54468	−	1.63537i	−0.0807938	−	0.0519230i
$993$	0.447688	−	3.11374i	0.0142069	−	0.0988114i
$994$	−0.582066	+	1.27455i	−0.0184620	+	0.0404262i
$995$	6.19126	+	43.0612i	0.196276	+	1.36513i
$996$	2.00005	+	0.587269i	0.0633741	+	0.0186083i
$997$	17.6778	−	11.3608i	0.559861	−	0.359801i	−0.229901	−	0.973214i	$-0.573840\pi$
$997$	17.6778	−	11.3608i	0.559861	−	0.359801i	0.789762	+	0.613413i	$0.210204\pi$
$998$	−0.786201	−	1.72154i	−0.0248868	−	0.0544944i
$999$	31.0217	−	9.10879i	0.981483	−	0.288189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.h.b.59.16	✓	280
23.16	even	11	inner	667.2.h.b.407.16	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.h.b.59.16	✓	280	1.1	even	1	trivial
667.2.h.b.407.16	yes	280	23.16	even	11	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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.h (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.240264 + 0.277280i) q^{2} +(-0.500077 - 0.321380i) q^{3} +(0.265473 - 1.84640i) q^{4} +(-1.01259 + 2.21725i) q^{5} +(-0.0310385 - 0.215877i) q^{6} +(0.240790 + 0.0707024i) q^{7} +(1.19306 - 0.766730i) q^{8} +(-1.09945 - 2.40747i) q^{9} +O(q^{10})\)	\(q+(0.240264 + 0.277280i) q^{2} +(-0.500077 - 0.321380i) q^{3} +(0.265473 - 1.84640i) q^{4} +(-1.01259 + 2.21725i) q^{5} +(-0.0310385 - 0.215877i) q^{6} +(0.240790 + 0.0707024i) q^{7} +(1.19306 - 0.766730i) q^{8} +(-1.09945 - 2.40747i) q^{9} +(-0.858088 + 0.251957i) q^{10} +(-0.00585983 + 0.00676260i) q^{11} +(-0.726153 + 0.838025i) q^{12} +(1.01240 - 0.297266i) q^{13} +(0.0382490 + 0.0837536i) q^{14} +(1.21895 - 0.783372i) q^{15} +(-3.08041 - 0.904489i) q^{16} +(-0.511197 - 3.55546i) q^{17} +(0.403383 - 0.883285i) q^{18} +(0.529510 - 3.68282i) q^{19} +(3.82513 + 2.45826i) q^{20} +(-0.0976913 - 0.112742i) q^{21} -0.00328304 q^{22} +(-0.375491 - 4.78111i) q^{23} -0.843030 q^{24} +(-0.616579 - 0.711570i) q^{25} +(0.325669 + 0.209295i) q^{26} +(-0.477694 + 3.32243i) q^{27} +(0.194468 - 0.425826i) q^{28} +(0.142315 + 0.989821i) q^{29} +(0.510084 + 0.149774i) q^{30} +(0.633909 - 0.407389i) q^{31} +(-1.66759 - 3.65151i) q^{32} +(0.00510373 - 0.00149859i) q^{33} +(0.863034 - 0.995994i) q^{34} +(-0.400586 + 0.462301i) q^{35} +(-4.73703 + 1.39092i) q^{36} +(-4.00135 - 8.76173i) q^{37} +(1.14839 - 0.738028i) q^{38} +(-0.601811 - 0.176708i) q^{39} +(0.491964 + 3.42169i) q^{40} +(1.42146 - 3.11257i) q^{41} +(0.00778928 - 0.0541756i) q^{42} +(-4.05218 - 2.60418i) q^{43} +(0.0109309 + 0.0126149i) q^{44} +6.45126 q^{45} +(1.23549 - 1.25285i) q^{46} +1.23267 q^{47} +(1.24976 + 1.44229i) q^{48} +(-5.83579 - 3.75044i) q^{49} +(0.0491621 - 0.341930i) q^{50} +(-0.887014 + 1.94229i) q^{51} +(-0.280110 - 1.94821i) q^{52} +(8.62743 + 2.53324i) q^{53} +(-1.03602 + 0.665808i) q^{54} +(-0.00906083 - 0.0198404i) q^{55} +(0.341486 - 0.100269i) q^{56} +(-1.44838 + 1.67152i) q^{57} +(-0.240264 + 0.277280i) q^{58} +(-2.66665 + 0.782998i) q^{59} +(-1.12282 - 2.45864i) q^{60} +(7.85919 - 5.05079i) q^{61} +(0.265267 + 0.0778893i) q^{62} +(-0.0945240 - 0.657429i) q^{63} +(-2.05551 + 4.50095i) q^{64} +(-0.366023 + 2.54575i) q^{65} +(0.00164177 + 0.00105510i) q^{66} +(-8.84327 - 10.2057i) q^{67} -6.70051 q^{68} +(-1.34878 + 2.51160i) q^{69} -0.224433 q^{70} +(9.96556 + 11.5009i) q^{71} +(-3.15759 - 2.02926i) q^{72} +(-1.75276 + 12.1907i) q^{73} +(1.46807 - 3.21462i) q^{74} +(0.0796526 + 0.553996i) q^{75} +(-6.65940 - 1.95538i) q^{76} +(-0.00188912 + 0.00121407i) q^{77} +(-0.0955963 - 0.209327i) q^{78} +(-3.41123 + 1.00163i) q^{79} +(5.12466 - 5.91417i) q^{80} +(-3.89289 + 4.49264i) q^{81} +(1.20458 - 0.353697i) q^{82} +(-0.780913 - 1.70996i) q^{83} +(-0.234101 + 0.150447i) q^{84} +(8.40098 + 2.46675i) q^{85} +(-0.251509 - 1.74928i) q^{86} +(0.246940 - 0.540724i) q^{87} +(-0.00180601 + 0.0125611i) q^{88} +(12.2513 + 7.87341i) q^{89} +(1.55001 + 1.78880i) q^{90} +0.264793 q^{91} +(-8.92753 - 0.575945i) q^{92} -0.447930 q^{93} +(0.296166 + 0.341793i) q^{94} +(7.62957 + 4.90323i) q^{95} +(-0.339599 + 2.36196i) q^{96} +(-4.96695 + 10.8761i) q^{97} +(-0.362213 - 2.51924i) q^{98} +(0.0227234 + 0.00667218i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 2 q^{3} - 32 q^{4} - 4 q^{6} + 6 q^{7} - 26 q^{9}+O(q^{10}) \) 280 * q - 2 * q^3 - 32 * q^4 - 4 * q^6 + 6 * q^7 - 26 * q^9	\( 280 q - 2 q^{3} - 32 q^{4} - 4 q^{6} + 6 q^{7} - 26 q^{9} - 41 q^{10} - 20 q^{11} + 18 q^{12} - 3 q^{15} - 40 q^{16} + 9 q^{17} + 54 q^{18} + 10 q^{19} + 58 q^{20} - 4 q^{21} - 118 q^{22} - 4 q^{23} + 20 q^{24} - 44 q^{25} - 22 q^{26} + 4 q^{27} + 76 q^{28} + 28 q^{29} + 100 q^{30} - 5 q^{31} + 40 q^{32} - 81 q^{33} - 58 q^{34} + 28 q^{35} - 24 q^{36} + 40 q^{37} - 14 q^{38} + 4 q^{39} + 78 q^{40} + 12 q^{41} + 74 q^{42} + 40 q^{43} - 90 q^{44} - 246 q^{45} - 72 q^{46} + 50 q^{47} - 14 q^{48} - 34 q^{49} + 46 q^{50} + 48 q^{51} + 90 q^{52} + 4 q^{53} + 46 q^{54} - 18 q^{55} - 272 q^{56} - 142 q^{57} + 66 q^{59} + 42 q^{60} + 40 q^{61} - 26 q^{62} + 32 q^{63} + 44 q^{64} + 19 q^{65} + 78 q^{66} - 78 q^{67} - 130 q^{68} - 283 q^{69} + 120 q^{70} + 59 q^{71} + 82 q^{72} + 28 q^{73} + 62 q^{74} + 87 q^{75} + 203 q^{76} - 58 q^{77} - 36 q^{78} + 32 q^{79} - 182 q^{80} + 66 q^{81} + 60 q^{82} - 24 q^{83} + 90 q^{84} + 90 q^{85} + 49 q^{86} + 2 q^{87} + 26 q^{88} + 36 q^{89} - 113 q^{90} - 668 q^{91} - 175 q^{92} - 60 q^{93} + 49 q^{94} + 11 q^{95} + 313 q^{96} + 75 q^{97} - 48 q^{98} + 101 q^{99}+O(q^{100}) \) 280 * q - 2 * q^3 - 32 * q^4 - 4 * q^6 + 6 * q^7 - 26 * q^9 - 41 * q^10 - 20 * q^11 + 18 * q^12 - 3 * q^15 - 40 * q^16 + 9 * q^17 + 54 * q^18 + 10 * q^19 + 58 * q^20 - 4 * q^21 - 118 * q^22 - 4 * q^23 + 20 * q^24 - 44 * q^25 - 22 * q^26 + 4 * q^27 + 76 * q^28 + 28 * q^29 + 100 * q^30 - 5 * q^31 + 40 * q^32 - 81 * q^33 - 58 * q^34 + 28 * q^35 - 24 * q^36 + 40 * q^37 - 14 * q^38 + 4 * q^39 + 78 * q^40 + 12 * q^41 + 74 * q^42 + 40 * q^43 - 90 * q^44 - 246 * q^45 - 72 * q^46 + 50 * q^47 - 14 * q^48 - 34 * q^49 + 46 * q^50 + 48 * q^51 + 90 * q^52 + 4 * q^53 + 46 * q^54 - 18 * q^55 - 272 * q^56 - 142 * q^57 + 66 * q^59 + 42 * q^60 + 40 * q^61 - 26 * q^62 + 32 * q^63 + 44 * q^64 + 19 * q^65 + 78 * q^66 - 78 * q^67 - 130 * q^68 - 283 * q^69 + 120 * q^70 + 59 * q^71 + 82 * q^72 + 28 * q^73 + 62 * q^74 + 87 * q^75 + 203 * q^76 - 58 * q^77 - 36 * q^78 + 32 * q^79 - 182 * q^80 + 66 * q^81 + 60 * q^82 - 24 * q^83 + 90 * q^84 + 90 * q^85 + 49 * q^86 + 2 * q^87 + 26 * q^88 + 36 * q^89 - 113 * q^90 - 668 * q^91 - 175 * q^92 - 60 * q^93 + 49 * q^94 + 11 * q^95 + 313 * q^96 + 75 * q^97 - 48 * q^98 + 101 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more