LMFDB - Embedded newform 343.2.g.h.30.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [343,2,Mod(30,343)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(343, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([32]))

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

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

chi := DirichletCharacter("343.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 343 = 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	343.g (of order $21$, degree $12$, not 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:	$2.73886878933$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			30.4
Character	$\chi$	$=$	343.30
Dual form			343.2.g.h.263.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.12492 - 1.44875i) q^{2} +(-0.595824 + 0.552844i) q^{3} +(1.68574 - 4.29521i) q^{4} +(2.35776 + 0.727274i) q^{5} +(-0.465149 + 2.03795i) q^{6} +(-1.49604 - 6.55456i) q^{8} +(-0.174820 + 2.33282i) q^{9} +O(q^{10})$	\(q+(2.12492 - 1.44875i) q^{2} +(-0.595824 + 0.552844i) q^{3} +(1.68574 - 4.29521i) q^{4} +(2.35776 + 0.727274i) q^{5} +(-0.465149 + 2.03795i) q^{6} +(-1.49604 - 6.55456i) q^{8} +(-0.174820 + 2.33282i) q^{9} +(6.06370 - 1.87040i) q^{10} +(-0.0412523 - 0.550473i) q^{11} +(1.37017 + 3.49114i) q^{12} +(-1.06432 - 0.512550i) q^{13} +(-1.80688 + 0.870148i) q^{15} +(-5.91002 - 5.48369i) q^{16} +(-7.42426 - 1.11903i) q^{17} +(3.00818 + 5.21032i) q^{18} +(0.499767 - 0.865623i) q^{19} +(7.09838 - 8.90108i) q^{20} +(-0.885154 - 1.10995i) q^{22} +(2.25110 - 0.339299i) q^{23} +(4.51502 + 3.07829i) q^{24} +(0.898926 + 0.612877i) q^{25} +(-3.00415 + 0.452803i) q^{26} +(-2.70584 - 3.39301i) q^{27} +(-3.55438 + 4.45705i) q^{29} +(-2.57886 + 4.46671i) q^{30} +(2.90369 + 5.02934i) q^{31} +(-7.20676 - 1.08624i) q^{32} +(0.328905 + 0.305179i) q^{33} +(-17.3972 + 8.37803i) q^{34} +(9.72523 + 4.68342i) q^{36} +(-1.34391 - 3.42423i) q^{37} +(-0.192102 - 2.56342i) q^{38} +(0.917508 - 0.283014i) q^{39} +(1.23966 - 16.5421i) q^{40} +(0.206089 + 0.902934i) q^{41} +(-0.949065 + 4.15812i) q^{43} +(-2.43394 - 0.750770i) q^{44} +(-2.10878 + 5.37308i) q^{45} +(4.29186 - 3.98227i) q^{46} +(7.96926 - 5.43335i) q^{47} +6.55296 q^{48} +2.79805 q^{50} +(5.04220 - 3.43771i) q^{51} +(-3.99568 + 3.70745i) q^{52} +(-2.85905 + 7.28475i) q^{53} +(-10.6653 - 3.28981i) q^{54} +(0.303081 - 1.32789i) q^{55} +(0.180781 + 0.792052i) q^{57} +(-1.09564 + 14.6203i) q^{58} +(2.65234 - 0.818137i) q^{59} +(0.691526 + 9.22778i) q^{60} +(2.60511 + 6.63771i) q^{61} +(13.4564 + 6.48024i) q^{62} +(-2.35990 + 1.13647i) q^{64} +(-2.13665 - 1.98252i) q^{65} +(1.14102 + 0.171982i) q^{66} +(-1.62615 - 2.81657i) q^{67} +(-17.3219 + 30.0023i) q^{68} +(-1.15368 + 1.44667i) q^{69} +(0.0286915 + 0.0359779i) q^{71} +(15.5521 - 2.34410i) q^{72} +(-6.90892 - 4.71043i) q^{73} +(-7.81656 - 5.32924i) q^{74} +(-0.874427 + 0.131799i) q^{75} +(-2.87555 - 3.60582i) q^{76} +(1.53962 - 1.93062i) q^{78} +(-2.93822 + 5.08914i) q^{79} +(-9.94627 - 17.2275i) q^{80} +(-3.45167 - 0.520256i) q^{81} +(1.74605 + 1.62009i) q^{82} +(10.6979 - 5.15183i) q^{83} +(-16.6908 - 8.03787i) q^{85} +(4.00738 + 10.2106i) q^{86} +(-0.346269 - 4.62064i) q^{87} +(-3.54639 + 1.09392i) q^{88} +(0.337316 - 4.50117i) q^{89} +(3.30325 + 14.4725i) q^{90} +(2.33743 - 10.2409i) q^{92} +(-4.51053 - 1.39131i) q^{93} +(9.06251 - 23.0909i) q^{94} +(1.80788 - 1.67747i) q^{95} +(4.89448 - 3.33700i) q^{96} -1.37110 q^{97} +1.29136 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} - 7 q^{3} + 12 q^{4} - 7 q^{5} - 20 q^{8} - 15 q^{9}+O(q^{10}) $ 48 * q + 8 * q^2 - 7 * q^3 + 12 * q^4 - 7 * q^5 - 20 * q^8 - 15 * q^9	$ 48 q + 8 q^{2} - 7 q^{3} + 12 q^{4} - 7 q^{5} - 20 q^{8} - 15 q^{9} - 7 q^{10} - 3 q^{11} + 63 q^{12} + 14 q^{13} - 12 q^{15} + 18 q^{16} - 14 q^{17} + 2 q^{18} - 21 q^{19} - 14 q^{20} - 20 q^{22} - 27 q^{23} + 77 q^{24} + 17 q^{25} + 21 q^{26} - 7 q^{27} + 12 q^{29} + 11 q^{30} - 35 q^{31} - 60 q^{32} - 7 q^{33} - 70 q^{34} - 12 q^{36} - 6 q^{37} - 35 q^{38} + 35 q^{39} - 105 q^{40} + 42 q^{41} - 30 q^{43} + 13 q^{44} + 35 q^{45} + 69 q^{46} + 42 q^{47} + 84 q^{48} + 40 q^{50} + 53 q^{51} + 7 q^{52} - 31 q^{53} - 70 q^{54} + 7 q^{55} - 12 q^{57} - 47 q^{58} - 35 q^{59} - 91 q^{60} + 14 q^{61} + 28 q^{62} - 32 q^{64} + 35 q^{65} + 35 q^{66} + 11 q^{67} - 77 q^{68} - 70 q^{69} + 19 q^{71} - 124 q^{72} + 35 q^{73} + 13 q^{74} + 119 q^{75} - 119 q^{76} + 28 q^{78} + 15 q^{79} - 70 q^{80} - 125 q^{81} + 98 q^{82} - 26 q^{85} + 9 q^{86} - 35 q^{87} + 49 q^{88} + 14 q^{89} + 182 q^{90} - 38 q^{92} + 46 q^{93} - 14 q^{94} + 128 q^{95} - 98 q^{96} - 16 q^{99}+O(q^{100}) $ 48 * q + 8 * q^2 - 7 * q^3 + 12 * q^4 - 7 * q^5 - 20 * q^8 - 15 * q^9 - 7 * q^10 - 3 * q^11 + 63 * q^12 + 14 * q^13 - 12 * q^15 + 18 * q^16 - 14 * q^17 + 2 * q^18 - 21 * q^19 - 14 * q^20 - 20 * q^22 - 27 * q^23 + 77 * q^24 + 17 * q^25 + 21 * q^26 - 7 * q^27 + 12 * q^29 + 11 * q^30 - 35 * q^31 - 60 * q^32 - 7 * q^33 - 70 * q^34 - 12 * q^36 - 6 * q^37 - 35 * q^38 + 35 * q^39 - 105 * q^40 + 42 * q^41 - 30 * q^43 + 13 * q^44 + 35 * q^45 + 69 * q^46 + 42 * q^47 + 84 * q^48 + 40 * q^50 + 53 * q^51 + 7 * q^52 - 31 * q^53 - 70 * q^54 + 7 * q^55 - 12 * q^57 - 47 * q^58 - 35 * q^59 - 91 * q^60 + 14 * q^61 + 28 * q^62 - 32 * q^64 + 35 * q^65 + 35 * q^66 + 11 * q^67 - 77 * q^68 - 70 * q^69 + 19 * q^71 - 124 * q^72 + 35 * q^73 + 13 * q^74 + 119 * q^75 - 119 * q^76 + 28 * q^78 + 15 * q^79 - 70 * q^80 - 125 * q^81 + 98 * q^82 - 26 * q^85 + 9 * q^86 - 35 * q^87 + 49 * q^88 + 14 * q^89 + 182 * q^90 - 38 * q^92 + 46 * q^93 - 14 * q^94 + 128 * q^95 - 98 * q^96 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/343\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{16}{21}\right)$

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 $

$2$	2.12492	−	1.44875i	1.50255	−	1.02442i	0.516815	−	0.856097i	$-0.327117\pi$
$2$	2.12492	−	1.44875i	1.50255	−	1.02442i	0.985732	−	0.168323i	$-0.0538350\pi$
$3$	−0.595824	+	0.552844i	−0.343999	+	0.319185i	−0.833184	−	0.552995i	$-0.813485\pi$
$3$	−0.595824	+	0.552844i	−0.343999	+	0.319185i	0.489185	+	0.872180i	$0.337294\pi$
$4$	1.68574	−	4.29521i	0.842872	−	2.14760i
$5$	2.35776	+	0.727274i	1.05442	+	0.325247i	0.773046	−	0.634350i	$-0.218732\pi$
$5$	2.35776	+	0.727274i	1.05442	+	0.325247i	0.281378	+	0.959597i	$0.409209\pi$
$6$	−0.465149	+	2.03795i	−0.189896	+	0.831990i
$7$		0			0
$7$		0			0
$8$	−1.49604	−	6.55456i	−0.528928	−	2.31739i
$9$	−0.174820	+	2.33282i	−0.0582735	+	0.777605i
$10$	6.06370	−	1.87040i	1.91751	−	0.591474i
$11$	−0.0412523	−	0.550473i	−0.0124380	−	0.165974i	−0.999964	−	0.00851606i	$-0.997289\pi$
$11$	−0.0412523	−	0.550473i	−0.0124380	−	0.165974i	0.987526	−	0.157458i	$-0.0503298\pi$
$12$	1.37017	+	3.49114i	0.395535	+	1.00781i
$13$	−1.06432	−	0.512550i	−0.295189	−	0.142156i	0.280428	−	0.959875i	$-0.409524\pi$
$13$	−1.06432	−	0.512550i	−0.295189	−	0.142156i	−0.575617	+	0.817720i	$0.695238\pi$
$14$		0			0
$15$	−1.80688	+	0.870148i	−0.466535	+	0.224671i
$16$	−5.91002	−	5.48369i	−1.47750	−	1.37092i
$17$	−7.42426	−	1.11903i	−1.80065	−	0.271404i	−0.838691	−	0.544608i	$-0.816679\pi$
$17$	−7.42426	−	1.11903i	−1.80065	−	0.271404i	−0.961956	+	0.273204i	$0.911917\pi$
$18$	3.00818	+	5.21032i	0.709035	+	1.22809i
$19$	0.499767	−	0.865623i	0.114655	−	0.198587i	−0.802987	−	0.595996i	$-0.796757\pi$
$19$	0.499767	−	0.865623i	0.114655	−	0.198587i	0.917642	+	0.397409i	$0.130091\pi$
$20$	7.09838	−	8.90108i	1.58725	−	1.99034i
$21$		0			0
$22$	−0.885154	−	1.10995i	−0.188716	−	0.236642i
$23$	2.25110	−	0.339299i	0.469387	−	0.0707488i	0.0899103	−	0.995950i	$-0.471342\pi$
$23$	2.25110	−	0.339299i	0.469387	−	0.0707488i	0.379477	+	0.925201i	$0.376104\pi$
$24$	4.51502	+	3.07829i	0.921625	+	0.628354i
$25$	0.898926	+	0.612877i	0.179785	+	0.122575i
$26$	−3.00415	+	0.452803i	−0.589163	+	0.0888020i
$27$	−2.70584	−	3.39301i	−0.520739	−	0.652986i
$28$		0			0
$29$	−3.55438	+	4.45705i	−0.660032	+	0.827654i	−0.993347	−	0.115162i	$-0.963261\pi$
$29$	−3.55438	+	4.45705i	−0.660032	+	0.827654i	0.333315	+	0.942816i	$0.391833\pi$
$30$	−2.57886	+	4.46671i	−0.470833	+	0.815506i
$31$	2.90369	+	5.02934i	0.521518	+	0.903295i	0.999687	+	0.0250274i	$0.00796731\pi$
$31$	2.90369	+	5.02934i	0.521518	+	0.903295i	−0.478169	+	0.878268i	$0.658699\pi$
$32$	−7.20676	−	1.08624i	−1.27399	−	0.192023i
$33$	0.328905	+	0.305179i	0.0572550	+	0.0531249i
$34$	−17.3972	+	8.37803i	−2.98359	+	1.43682i
$35$		0			0
$36$	9.72523	+	4.68342i	1.62087	+	0.780570i
$37$	−1.34391	−	3.42423i	−0.220938	−	0.562940i	0.776831	−	0.629710i	$-0.216826\pi$
$37$	−1.34391	−	3.42423i	−0.220938	−	0.562940i	−0.997768	+	0.0667693i	$0.978731\pi$
$38$	−0.192102	−	2.56342i	−0.0311630	−	0.415841i
$39$	0.917508	−	0.283014i	0.146919	−	0.0453184i
$40$	1.23966	−	16.5421i	0.196008	−	2.61554i
$41$	0.206089	+	0.902934i	0.0321857	+	0.141015i	0.988468	−	0.151431i	$-0.0483881\pi$
$41$	0.206089	+	0.902934i	0.0321857	+	0.141015i	−0.956282	+	0.292446i	$0.905531\pi$
$42$		0			0
$43$	−0.949065	+	4.15812i	−0.144731	+	0.634108i	0.849568	+	0.527479i	$0.176863\pi$
$43$	−0.949065	+	4.15812i	−0.144731	+	0.634108i	−0.994299	+	0.106629i	$0.965994\pi$
$44$	−2.43394	−	0.750770i	−0.366930	−	0.113183i
$45$	−2.10878	+	5.37308i	−0.314358	+	0.800972i
$46$	4.29186	−	3.98227i	0.632801	−	0.587153i
$47$	7.96926	−	5.43335i	1.16244	−	0.792536i	0.180842	−	0.983512i	$-0.442118\pi$
$47$	7.96926	−	5.43335i	1.16244	−	0.792536i	0.981595	+	0.190977i	$0.0611654\pi$
$48$	6.55296			0.945838
$49$		0			0
$50$	2.79805			0.395704
$51$	5.04220	−	3.43771i	0.706049	−	0.481376i
$52$	−3.99568	+	3.70745i	−0.554101	+	0.514131i
$53$	−2.85905	+	7.28475i	−0.392721	+	1.00064i	0.588628	+	0.808404i	$0.299668\pi$
$53$	−2.85905	+	7.28475i	−0.392721	+	1.00064i	−0.981349	+	0.192233i	$0.938427\pi$
$54$	−10.6653	−	3.28981i	−1.45137	−	0.447687i
$55$	0.303081	−	1.32789i	0.0408675	−	0.179052i
$56$		0			0
$57$	0.180781	+	0.792052i	0.0239450	+	0.104910i
$58$	−1.09564	+	14.6203i	−0.143864	+	1.91974i
$59$	2.65234	−	0.818137i	0.345305	−	0.106512i	−0.117252	−	0.993102i	$-0.537408\pi$
$59$	2.65234	−	0.818137i	0.345305	−	0.106512i	0.462556	+	0.886590i	$0.346932\pi$
$60$	0.691526	+	9.22778i	0.0892757	+	1.19130i
$61$	2.60511	+	6.63771i	0.333550	+	0.849872i	0.994999	+	0.0998821i	$0.0318466\pi$
$61$	2.60511	+	6.63771i	0.333550	+	0.849872i	−0.661449	+	0.749990i	$0.730058\pi$
$62$	13.4564	+	6.48024i	1.70896	+	0.822991i
$63$		0			0
$64$	−2.35990	+	1.13647i	−0.294988	+	0.142059i
$65$	−2.13665	−	1.98252i	−0.265019	−	0.245902i
$66$	1.14102	+	0.171982i	0.140450	+	0.0211695i
$67$	−1.62615	−	2.81657i	−0.198665	−	0.344098i	0.749431	−	0.662083i	$-0.230327\pi$
$67$	−1.62615	−	2.81657i	−0.198665	−	0.344098i	−0.948096	+	0.317985i	$0.896994\pi$
$68$	−17.3219	+	30.0023i	−2.10058	+	3.63832i
$69$	−1.15368	+	1.44667i	−0.138887	+	0.174159i
$70$		0			0
$71$	0.0286915	+	0.0359779i	0.00340505	+	0.00426980i	0.783531	−	0.621353i	$-0.213417\pi$
$71$	0.0286915	+	0.0359779i	0.00340505	+	0.00426980i	−0.780126	+	0.625622i	$0.784845\pi$
$72$	15.5521	−	2.34410i	1.83283	−	0.276255i
$73$	−6.90892	−	4.71043i	−0.808628	−	0.551314i	0.0869523	−	0.996212i	$-0.472287\pi$
$73$	−6.90892	−	4.71043i	−0.808628	−	0.551314i	−0.895581	+	0.444899i	$0.853240\pi$
$74$	−7.81656	−	5.32924i	−0.908656	−	0.619511i
$75$	−0.874427	+	0.131799i	−0.100970	+	0.0152188i
$76$	−2.87555	−	3.60582i	−0.329848	−	0.413616i
$77$		0			0
$78$	1.53962	−	1.93062i	0.174327	−	0.218600i
$79$	−2.93822	+	5.08914i	−0.330575	+	0.572573i	−0.982625	−	0.185603i	$-0.940576\pi$
$79$	−2.93822	+	5.08914i	−0.330575	+	0.572573i	0.652049	+	0.758176i	$0.273909\pi$
$80$	−9.94627	−	17.2275i	−1.11203	−	1.92609i
$81$	−3.45167	−	0.520256i	−0.383519	−	0.0578063i
$82$	1.74605	+	1.62009i	0.192819	+	0.178909i
$83$	10.6979	−	5.15183i	1.17425	−	0.565487i	0.258016	−	0.966141i	$-0.416931\pi$
$83$	10.6979	−	5.15183i	1.17425	−	0.565487i	0.916230	+	0.400654i	$0.131217\pi$
$84$		0			0
$85$	−16.6908	−	8.03787i	−1.81037	−	0.871829i
$86$	4.00738	+	10.2106i	0.432127	+	1.10104i
$87$	−0.346269	−	4.62064i	−0.0371239	−	0.495384i
$88$	−3.54639	+	1.09392i	−0.378047	+	0.116612i
$89$	0.337316	−	4.50117i	0.0357555	−	0.477124i	−0.950370	−	0.311122i	$-0.899295\pi$
$89$	0.337316	−	4.50117i	0.0357555	−	0.477124i	0.986125	−	0.166002i	$-0.0530857\pi$
$90$	3.30325	+	14.4725i	0.348193	+	1.52553i
$91$		0			0
$92$	2.33743	−	10.2409i	0.243693	−	1.06769i
$93$	−4.51053	−	1.39131i	−0.467720	−	0.144272i
$94$	9.06251	−	23.0909i	0.934727	−	2.38164i
$95$	1.80788	−	1.67747i	0.185484	−	0.172104i
$96$	4.89448	−	3.33700i	0.499541	−	0.340581i
$97$	−1.37110			−0.139214			−0.0696070	−	0.997574i	$-0.522175\pi$
$97$	−1.37110			−0.139214			−0.0696070	+	0.997574i	$0.522175\pi$
$98$		0			0
$99$	1.29136			0.129787
$100$	4.14779	−	2.82792i	0.414779	−	0.282792i
$101$	−0.224525	+	0.208329i	−0.0223411	+	0.0207295i	−0.691264	−	0.722602i	$-0.742946\pi$
$101$	−0.224525	+	0.208329i	−0.0223411	+	0.0207295i	0.668923	+	0.743332i	$0.266755\pi$
$102$	5.73391	−	14.6098i	0.567741	−	1.44658i
$103$	−0.785456	−	0.242281i	−0.0773933	−	0.0238727i	0.255817	−	0.966725i	$-0.417656\pi$
$103$	−0.785456	−	0.242281i	−0.0773933	−	0.0238727i	−0.333210	+	0.942853i	$0.608132\pi$
$104$	−1.76728	+	7.74294i	−0.173296	+	0.759258i
$105$		0			0
$106$	4.47850	+	19.6216i	0.434990	+	1.90582i
$107$	0.445973	−	5.95110i	0.0431139	−	0.575314i	−0.933257	−	0.359211i	$-0.883046\pi$
$107$	0.445973	−	5.95110i	0.0431139	−	0.575314i	0.976370	−	0.216104i	$-0.0693350\pi$
$108$	−19.1350	+	5.90238i	−1.84127	+	0.567957i
$109$	−0.445456	−	5.94420i	−0.0426670	−	0.569351i	−0.977040	−	0.213055i	$-0.931659\pi$
$109$	−0.445456	−	5.94420i	−0.0426670	−	0.569351i	0.934373	−	0.356296i	$-0.115960\pi$
$110$	−1.27975	−	3.26075i	−0.122019	−	0.310900i
$111$	2.69380	+	1.29727i	0.255684	+	0.123131i
$112$		0			0
$113$	9.88796	−	4.76179i	0.930181	−	0.447951i	0.0934859	−	0.995621i	$-0.470199\pi$
$113$	9.88796	−	4.76179i	0.930181	−	0.447951i	0.836695	+	0.547669i	$0.184485\pi$
$114$	1.53163	+	1.42114i	0.143450	+	0.133102i
$115$	5.55433	+	0.837181i	0.517944	+	0.0780675i
$116$	13.1522	+	22.7802i	1.22115	+	2.11509i
$117$	1.38175	−	2.39326i	0.127743	−	0.221257i
$118$	4.45074	−	5.58105i	0.409723	−	0.513777i
$119$		0			0
$120$	8.40660	+	10.5415i	0.767414	+	0.962306i
$121$	10.5758	−	1.59405i	0.961438	−	0.144913i
$122$	15.1520	+	10.3305i	1.37180	+	0.935278i
$123$	−0.621974	−	0.424055i	−0.0560815	−	0.0382357i
$124$	26.4969	−	3.99377i	2.37949	−	0.358651i
$125$	−6.01821	−	7.54660i	−0.538285	−	0.674988i
$126$		0			0
$127$	12.7459	−	15.9829i	1.13102	−	1.41825i	0.236265	−	0.971689i	$-0.424077\pi$
$127$	12.7459	−	15.9829i	1.13102	−	1.41825i	0.894752	−	0.446563i	$-0.147352\pi$
$128$	3.92001	−	6.78965i	0.346483	−	0.600126i
$129$	−1.73332	−	3.00220i	−0.152610	−	0.264329i
$130$	−7.41239	−	1.11724i	−0.650110	−	0.0979883i
$131$	−9.33535	−	8.66194i	−0.815633	−	0.756797i	0.157382	−	0.987538i	$-0.449695\pi$
$131$	−9.33535	−	8.66194i	−0.815633	−	0.756797i	−0.973015	+	0.230741i	$0.925885\pi$
$132$	1.86526	−	0.898260i	0.162350	−	0.0781835i
$133$		0			0
$134$	−7.53593	−	3.62911i	−0.651005	−	0.313507i
$135$	−3.91207	−	9.96780i	−0.336698	−	0.857892i
$136$	3.77223	+	50.3369i	0.323466	+	4.31635i
$137$	−8.97416	+	2.76816i	−0.766714	+	0.236500i	−0.653352	−	0.757054i	$-0.726638\pi$
$137$	−8.97416	+	2.76816i	−0.766714	+	0.236500i	−0.113362	+	0.993554i	$0.536162\pi$
$138$	−0.355623	+	4.74546i	−0.0302726	+	0.403960i
$139$	2.74110	+	12.0095i	0.232497	+	1.01864i	0.947560	+	0.319577i	$0.103541\pi$
$139$	2.74110	+	12.0095i	0.232497	+	1.01864i	−0.715063	+	0.699060i	$0.753602\pi$
$140$		0			0
$141$	−1.74448	+	7.64308i	−0.146912	+	0.643663i
$142$	0.113090	+	0.0348837i	0.00949031	+	0.00292737i
$143$	−0.238239	+	0.607023i	−0.0199226	+	0.0507618i
$144$	13.8256	−	12.8283i	1.15214	−	1.06903i
$145$	−11.6219	+	7.92366i	−0.965145	+	0.658024i
$146$	−21.5052			−1.77978
$147$		0			0
$148$	−16.9733			−1.39519
$149$	−15.2145	+	10.3731i	−1.24642	+	0.849796i	−0.993064	−	0.117577i	$-0.962487\pi$
$149$	−15.2145	+	10.3731i	−1.24642	+	0.849796i	−0.253358	+	0.967373i	$0.581535\pi$
$150$	−1.66715	+	1.54689i	−0.136122	+	0.126303i
$151$	4.31025	−	10.9823i	0.350763	−	0.893730i	−0.641220	−	0.767358i	$-0.721571\pi$
$151$	4.31025	−	10.9823i	0.350763	−	0.893730i	0.991983	−	0.126373i	$-0.0403336\pi$
$152$	−6.42145	−	1.98075i	−0.520848	−	0.160660i
$153$	3.90840	−	17.1238i	0.315975	−	1.38438i
$154$		0			0
$155$	3.18851	+	13.9698i	0.256107	+	1.12208i
$156$	0.331081	−	4.41797i	0.0265077	−	0.353721i
$157$	18.7135	−	5.77236i	1.49350	−	0.460685i	0.562841	−	0.826565i	$-0.309708\pi$
$157$	18.7135	−	5.77236i	1.49350	−	0.460685i	0.930662	+	0.365880i	$0.119232\pi$
$158$	1.12940	+	15.0708i	0.0898501	+	1.19897i
$159$	−2.32384	−	5.92104i	−0.184292	−	0.469569i
$160$	−16.2018	−	7.80239i	−1.28087	−	0.616833i
$161$		0			0
$162$	−8.08826	+	3.89510i	−0.635474	+	0.306028i
$163$	−5.29847	−	4.91626i	−0.415008	−	0.385071i	0.444849	−	0.895605i	$-0.353257\pi$
$163$	−5.29847	−	4.91626i	−0.415008	−	0.385071i	−0.859858	+	0.510534i	$0.829448\pi$
$164$	4.22570	+	0.636922i	0.329972	+	0.0497353i
$165$	0.553531	+	0.958744i	0.0430923	+	0.0746381i
$166$	15.2685	−	26.4458i	1.18506	−	2.05259i
$167$	−11.4043	+	14.3005i	−0.882489	+	1.10661i	0.111128	+	0.993806i	$0.464554\pi$
$167$	−11.4043	+	14.3005i	−0.882489	+	1.10661i	−0.993618	+	0.112801i	$0.964018\pi$
$168$		0			0
$169$	−7.23530	−	9.07278i	−0.556561	−	0.697906i
$170$	−47.1115	+	7.10092i	−3.61329	+	0.544616i
$171$	1.93197	+	1.31719i	0.147741	+	0.100728i
$172$	16.2601	+	11.0860i	1.23982	+	0.845297i
$173$	−10.7762	+	1.62425i	−0.819299	+	0.123489i	−0.545300	−	0.838241i	$-0.683584\pi$
$173$	−10.7762	+	1.62425i	−0.819299	+	0.123489i	−0.273999	+	0.961730i	$0.588346\pi$
$174$	−7.42993	−	9.31684i	−0.563262	−	0.706308i
$175$		0			0
$176$	−2.77482	+	3.47952i	−0.209160	+	0.262279i
$177$	−1.12802	+	1.95379i	−0.0847874	+	0.146856i
$178$	−5.80430	−	10.0533i	−0.435050	−	0.753529i
$179$	−14.2413	−	2.14653i	−1.06444	−	0.160439i	−0.406610	−	0.913602i	$-0.633289\pi$
$179$	−14.2413	−	2.14653i	−1.06444	−	0.160439i	−0.657835	+	0.753162i	$0.728527\pi$
$180$	19.5236	+	18.1153i	1.45521	+	1.35023i
$181$	16.2838	−	7.84185i	1.21036	−	0.582880i	0.283751	−	0.958898i	$-0.408421\pi$
$181$	16.2838	−	7.84185i	1.21036	−	0.582880i	0.926613	+	0.376017i	$0.122707\pi$
$182$		0			0
$183$	−5.22181	−	2.51469i	−0.386007	−	0.185891i
$184$	−5.59169	−	14.2474i	−0.412225	−	1.05033i
$185$	−0.678273	−	9.05092i	−0.0498676	−	0.665437i
$186$	−11.6002	+	3.57818i	−0.850566	+	0.262365i
$187$	−0.309727	+	4.13302i	−0.0226495	+	0.302236i
$188$	−9.90323	−	43.3889i	−0.722267	−	3.16446i
$189$		0			0
$190$	1.41138	−	6.18364i	0.102392	−	0.448609i
$191$	−0.692252	−	0.213531i	−0.0500896	−	0.0154506i	0.269609	−	0.962970i	$-0.413106\pi$
$191$	−0.692252	−	0.213531i	−0.0500896	−	0.0154506i	−0.319699	+	0.947519i	$0.603582\pi$
$192$	0.777797	−	1.98179i	0.0561327	−	0.143024i
$193$	−8.36896	+	7.76526i	−0.602411	+	0.558955i	−0.921308	−	0.388834i	$-0.872878\pi$
$193$	−8.36896	+	7.76526i	−0.602411	+	0.558955i	0.318897	+	0.947789i	$0.396688\pi$
$194$	−2.91348	+	1.98638i	−0.209176	+	0.142614i
$195$	2.36909			0.169654
$196$		0			0
$197$	−0.639392			−0.0455548			−0.0227774	−	0.999741i	$-0.507251\pi$
$197$	−0.639392			−0.0455548			−0.0227774	+	0.999741i	$0.507251\pi$
$198$	2.74405	−	1.87086i	0.195011	−	0.132956i
$199$	−13.3455	+	12.3828i	−0.946036	+	0.877793i	−0.992638	−	0.121121i	$-0.961351\pi$
$199$	−13.3455	+	12.3828i	−0.946036	+	0.877793i	0.0466021	+	0.998914i	$0.485161\pi$
$200$	2.67232	−	6.80895i	0.188961	−	0.481465i
$201$	2.52602	+	0.779173i	0.178172	+	0.0549587i
$202$	−0.175283	+	0.767964i	−0.0123328	+	0.0540337i
$203$		0			0
$204$	−6.26583	−	27.4524i	−0.438696	−	1.92205i
$205$	−0.170771	+	2.27879i	−0.0119272	+	0.159157i
$206$	−2.02004	+	0.623099i	−0.140743	+	0.0434134i
$207$	0.397984	+	5.31073i	0.0276618	+	0.369121i
$208$	3.47948	+	8.86558i	0.241259	+	0.614718i
$209$	−0.497118	−	0.239400i	−0.0343864	−	0.0165596i
$210$		0			0
$211$	20.9321	−	10.0804i	1.44102	−	0.693960i	0.460013	−	0.887912i	$-0.347845\pi$
$211$	20.9321	−	10.0804i	1.44102	−	0.693960i	0.981011	+	0.193952i	$0.0621306\pi$
$212$	26.4699	+	24.5604i	1.81796	+	1.68682i
$213$	−0.0369853	−	0.00557463i	−0.00253419	−	0.000381967i
$214$	−7.67398	−	13.2917i	−0.524583	−	0.908604i
$215$	−5.26176	+	9.11364i	−0.358849	+	0.621545i
$216$	−18.1917	+	22.8116i	−1.23779	+	1.55214i
$217$		0			0
$218$	−9.55821	−	11.9856i	−0.647364	−	0.811768i
$219$	6.72063	−	1.01297i	0.454138	−	0.0684504i
$220$	−5.19263	−	3.54028i	−0.350087	−	0.238685i
$221$	7.32823	+	4.99630i	0.492950	+	0.336088i
$222$	7.60353	−	1.14605i	0.510316	−	0.0769177i
$223$	17.3419	+	21.7461i	1.16130	+	1.45622i	0.865453	+	0.500990i	$0.167031\pi$
$223$	17.3419	+	21.7461i	1.16130	+	1.45622i	0.295847	+	0.955235i	$0.404398\pi$
$224$		0			0
$225$	−1.58688	+	1.98988i	−0.105792	+	0.132659i
$226$	14.1125	−	24.4436i	0.938751	−	1.62596i
$227$	11.7659	+	20.3791i	0.780930	+	1.35261i	0.931401	+	0.363996i	$0.118588\pi$
$227$	11.7659	+	20.3791i	0.780930	+	1.35261i	−0.150471	+	0.988614i	$0.548079\pi$
$228$	3.70678	+	0.558707i	0.245487	+	0.0370013i
$229$	4.54440	+	4.21659i	0.300302	+	0.278640i	0.815903	−	0.578189i	$-0.196241\pi$
$229$	4.54440	+	4.21659i	0.300302	+	0.278640i	−0.515600	+	0.856829i	$0.672431\pi$
$230$	13.0154	−	6.26788i	0.858209	−	0.413292i
$231$		0			0
$232$	34.5315	+	16.6295i	2.26710	+	1.09178i
$233$	7.42816	+	18.9266i	0.486635	+	1.23993i	0.937704	+	0.347436i	$0.112948\pi$
$233$	7.42816	+	18.9266i	0.486635	+	1.23993i	−0.451069	+	0.892489i	$0.648957\pi$
$234$	−0.531119	−	7.08730i	−0.0347204	−	0.463311i
$235$	22.7412	−	7.01472i	1.48347	−	0.457590i
$236$	0.957092	−	12.7715i	0.0623014	−	0.831354i
$237$	−1.06284	−	4.65661i	−0.0690389	−	0.302479i
$238$		0			0
$239$	−2.07422	+	9.08775i	−0.134170	+	0.587838i	0.862483	+	0.506087i	$0.168908\pi$
$239$	−2.07422	+	9.08775i	−0.134170	+	0.587838i	−0.996653	+	0.0817510i	$0.973949\pi$
$240$	15.4503	+	4.76579i	0.997314	+	0.307631i
$241$	1.49189	−	3.80128i	0.0961013	−	0.244862i	−0.874737	−	0.484598i	$-0.838966\pi$
$241$	1.49189	−	3.80128i	0.0961013	−	0.244862i	0.970838	+	0.239736i	$0.0770610\pi$
$242$	20.1634	−	18.7089i	1.29615	−	1.20266i
$243$	13.1014	−	8.93239i	0.840456	−	0.573013i
$244$	32.9019			2.10633
$245$		0			0
$246$	−1.93600			−0.123435
$247$	−0.975587	+	0.665144i	−0.0620751	+	0.0423221i
$248$	28.6211	−	26.5565i	1.81744	−	1.68634i
$249$	−3.52590	+	8.98385i	−0.223445	+	0.569328i
$250$	−23.7214	−	7.31707i	−1.50027	−	0.462772i
$251$	−1.62926	+	7.13827i	−0.102838	+	0.450563i	0.897123	+	0.441780i	$0.145653\pi$
$251$	−1.62926	+	7.13827i	−0.102838	+	0.450563i	−0.999961	+	0.00878312i	$0.997204\pi$
$252$		0			0
$253$	−0.279638	−	1.22517i	−0.0175807	−	0.0770261i
$254$	3.92894	−	52.4280i	0.246523	−	3.28963i
$255$	14.3885	−	4.43826i	0.901041	−	0.277934i
$256$	−1.89826	−	25.3305i	−0.118641	−	1.58316i
$257$	1.83738	+	4.68156i	0.114612	+	0.292028i	0.976657	−	0.214805i	$-0.0689115\pi$
$257$	1.83738	+	4.68156i	0.114612	+	0.292028i	−0.862045	+	0.506832i	$0.830816\pi$
$258$	−8.03259	−	3.86829i	−0.500087	−	0.240829i
$259$		0			0
$260$	−12.1172	+	5.83533i	−0.751476	+	0.361892i
$261$	−9.77610	−	9.07090i	−0.605125	−	0.561474i
$262$	−32.3859	−	4.88138i	−2.00081	−	0.301573i
$263$	−8.22314	−	14.2429i	−0.507061	−	0.878255i	−0.999967	−	0.00817206i	$-0.997399\pi$
$263$	−8.22314	−	14.2429i	−0.507061	−	0.878255i	0.492906	−	0.870083i	$-0.335935\pi$
$264$	1.50826	−	2.61239i	0.0928271	−	0.160781i
$265$	−12.0390	+	15.0964i	−0.739548	+	0.927364i
$266$		0			0
$267$	2.28747	+	2.86839i	0.139991	+	0.175543i
$268$	−14.8390	+	2.23662i	−0.906436	+	0.136623i
$269$	−5.42331	−	3.69755i	−0.330665	−	0.225444i	0.386594	−	0.922250i	$-0.373651\pi$
$269$	−5.42331	−	3.69755i	−0.330665	−	0.225444i	−0.717259	+	0.696806i	$0.754604\pi$
$270$	−22.7537	−	15.5132i	−1.38475	−	0.944104i
$271$	4.40911	−	0.664566i	0.267834	−	0.0403695i	−0.0137520	−	0.999905i	$-0.504378\pi$
$271$	4.40911	−	0.664566i	0.267834	−	0.0403695i	0.281586	+	0.959536i	$0.409139\pi$
$272$	37.7411	+	47.3258i	2.28839	+	2.86955i
$273$		0			0
$274$	−15.0590	+	18.8834i	−0.909749	+	1.14079i
$275$	0.300290	−	0.520117i	0.0181081	−	0.0313642i
$276$	4.26894	+	7.39402i	0.256960	+	0.445068i
$277$	25.8937	+	3.90285i	1.55580	+	0.234499i	0.869912	−	0.493206i	$-0.164175\pi$
$277$	25.8937	+	3.90285i	1.55580	+	0.234499i	0.685890	+	0.727706i	$0.259413\pi$
$278$	23.2234	+	21.5482i	1.39285	+	1.29237i
$279$	−12.2401	+	5.89454i	−0.732798	+	0.352897i
$280$		0			0
$281$	−0.748290	−	0.360358i	−0.0446393	−	0.0214971i	0.411431	−	0.911441i	$-0.365029\pi$
$281$	−0.748290	−	0.360358i	−0.0446393	−	0.0214971i	−0.456070	+	0.889944i	$0.650743\pi$
$282$	7.36600	+	18.7683i	0.438639	+	1.11763i
$283$	−2.22171	−	29.6466i	−0.132067	−	1.76231i	−0.532919	−	0.846166i	$-0.678905\pi$
$283$	−2.22171	−	29.6466i	−0.132067	−	1.76231i	0.400852	−	0.916143i	$-0.368714\pi$
$284$	0.202899	−	0.0625861i	0.0120399	−	0.00371380i
$285$	−0.149800	+	1.99895i	−0.00887341	+	0.118407i
$286$	0.373184	+	1.63503i	0.0220668	+	0.0966811i
$287$		0			0
$288$	3.79390	−	16.6221i	0.223557	−	0.979469i
$289$	37.6227	+	11.6051i	2.21310	+	0.682650i
$290$	−13.2162	+	33.6743i	−0.776082	+	1.97743i
$291$	0.816934	−	0.758004i	0.0478895	−	0.0444350i
$292$	−31.8789	+	21.7347i	−1.86557	+	1.27193i
$293$	−13.1758			−0.769740			−0.384870	−	0.922971i	$-0.625754\pi$
$293$	−13.1758			−0.769740			−0.384870	+	0.922971i	$0.625754\pi$
$294$		0			0
$295$	6.84859			0.398740
$296$	−20.4338	+	13.9315i	−1.18769	+	0.809753i
$297$	−1.75614	+	1.62946i	−0.101902	+	0.0945509i
$298$	−17.3017	+	44.0840i	−1.00226	+	2.55372i
$299$	−2.56980	−	0.792679i	−0.148615	−	0.0458418i
$300$	−0.907958	+	3.97802i	−0.0524210	+	0.229671i
$301$		0			0
$302$	−6.75169	−	29.5811i	−0.388516	−	1.70220i
$303$	0.0186041	−	0.248255i	0.00106878	−	0.0142619i
$304$	−7.70044	+	2.37527i	−0.441651	+	0.136231i
$305$	1.31480	+	17.5448i	0.0752852	+	1.00461i
$306$	−16.5030	−	42.0490i	−0.943415	−	2.40378i
$307$	−16.6155	−	8.00162i	−0.948299	−	0.456677i	−0.105210	−	0.994450i	$-0.533551\pi$
$307$	−16.6155	−	8.00162i	−0.948299	−	0.456677i	−0.843089	+	0.537773i	$0.819266\pi$
$308$		0			0
$309$	0.601938	−	0.289878i	0.0342430	−	0.0164906i
$310$	27.0140	+	25.0653i	1.53429	+	1.42361i
$311$	−7.77870	−	1.17245i	−0.441089	−	0.0664835i	−0.0752568	−	0.997164i	$-0.523978\pi$
$311$	−7.77870	−	1.17245i	−0.441089	−	0.0664835i	−0.365833	+	0.930681i	$0.619216\pi$
$312$	−3.22765	−	5.59046i	−0.182730	−	0.316497i
$313$	−7.71392	+	13.3609i	−0.436017	+	0.755203i	−0.997378	−	0.0723677i	$-0.976944\pi$
$313$	−7.71392	+	13.3609i	−0.436017	+	0.755203i	0.561361	+	0.827571i	$0.310278\pi$
$314$	31.4021	−	39.3770i	1.77213	−	2.22217i
$315$		0			0
$316$	16.9058	+	21.1992i	0.951028	+	1.19255i
$317$	−8.72413	+	1.31495i	−0.489996	+	0.0738550i	−0.389393	−	0.921072i	$-0.627315\pi$
$317$	−8.72413	+	1.31495i	−0.489996	+	0.0738550i	−0.100603	+	0.994927i	$0.532077\pi$
$318$	−13.5161	−	9.21510i	−0.757943	−	0.516757i
$319$	2.60011	+	1.77273i	0.145578	+	0.0992536i
$320$	−6.39062	+	0.963230i	−0.357246	+	0.0538462i
$321$	3.02431	+	3.79236i	0.168800	+	0.211669i
$322$		0			0
$323$	−4.67906	+	5.86735i	−0.260350	+	0.326468i
$324$	−8.05325	+	13.9486i	−0.447403	+	0.774924i
$325$	−0.642615	−	1.11304i	−0.0356459	−	0.0617404i
$326$	−18.3813	−	2.77053i	−1.01804	−	0.153445i
$327$	3.55163	+	3.29543i	0.196406	+	0.182238i
$328$	5.61002	−	2.70164i	0.309761	−	0.149173i
$329$		0			0
$330$	2.56519	+	1.23533i	0.141209	+	0.0680027i
$331$	−2.97975	−	7.59227i	−0.163782	−	0.417309i	0.825297	−	0.564699i	$-0.191008\pi$
$331$	−2.97975	−	7.59227i	−0.163782	−	0.417309i	−0.989078	+	0.147390i	$0.952913\pi$
$332$	−4.09428	−	54.6343i	−0.224703	−	2.99845i
$333$	8.22304	−	2.53647i	0.450620	−	0.138998i
$334$	−3.51537	+	46.9094i	−0.192353	+	2.56677i
$335$	−1.78565	−	7.82345i	−0.0975605	−	0.427441i
$336$		0			0
$337$	−3.49358	+	15.3064i	−0.190307	+	0.833791i	0.786142	+	0.618046i	$0.212075\pi$
$337$	−3.49358	+	15.3064i	−0.190307	+	0.833791i	−0.976450	+	0.215745i	$0.930782\pi$
$338$	−28.5186	−	8.79683i	−1.55121	−	0.478484i
$339$	−3.25896	+	8.30369i	−0.177002	+	0.450994i
$340$	−62.6607	+	58.1407i	−3.39826	+	3.15312i
$341$	2.64873	−	1.80587i	0.143437	−	0.0977935i
$342$	6.01357			0.325176
$343$		0			0
$344$	28.6745			1.54603
$345$	−3.77224	+	2.57187i	−0.203090	+	0.138465i
$346$	−20.5455	+	19.0634i	−1.10453	+	1.02485i
$347$	6.15304	−	15.6777i	0.330313	−	0.841623i	−0.665171	−	0.746691i	$-0.731641\pi$
$347$	6.15304	−	15.6777i	0.330313	−	0.841623i	0.995484	−	0.0949318i	$-0.0302633\pi$
$348$	−20.4303	−	6.30192i	−1.09518	−	0.337818i
$349$	3.59731	−	15.7608i	0.192559	−	0.843658i	−0.782666	−	0.622443i	$-0.786140\pi$
$349$	3.59731	−	15.7608i	0.192559	−	0.843658i	0.975225	−	0.221215i	$-0.0710024\pi$
$350$		0			0
$351$	1.14079	+	4.99813i	0.0608909	+	0.266780i
$352$	−0.300653	+	4.01194i	−0.0160249	+	0.213837i
$353$	0.440212	−	0.135787i	0.0234301	−	0.00722723i	−0.283018	−	0.959115i	$-0.591336\pi$
$353$	0.440212	−	0.135787i	0.0234301	−	0.00722723i	0.306448	+	0.951887i	$0.400859\pi$
$354$	0.433592	+	5.78588i	0.0230452	+	0.307516i
$355$	0.0414818	+	0.105694i	0.00220163	+	0.00560966i
$356$	−18.7649	−	9.03668i	−0.994535	−	0.478943i
$357$		0			0
$358$	−33.3714	+	16.0708i	−1.76374	+	0.849370i
$359$	17.9508	+	16.6559i	0.947405	+	0.879063i	0.992785	−	0.119906i	$-0.0382594\pi$
$359$	17.9508	+	16.6559i	0.947405	+	0.879063i	−0.0453802	+	0.998970i	$0.514450\pi$
$360$	38.3730	+	5.78380i	2.02244	+	0.304833i
$361$	9.00047	+	15.5893i	0.473709	+	0.820488i
$362$	23.2409	−	40.2544i	1.22151	−	2.11573i
$363$	−5.42007	+	6.79655i	−0.284480	+	0.356726i
$364$		0			0
$365$	−12.8638	−	16.1307i	−0.673324	−	0.844322i
$366$	−14.7391	+	2.22156i	−0.770425	+	0.116123i
$367$	13.0124	+	8.87168i	0.679240	+	0.463098i	0.853151	−	0.521663i	$-0.174688\pi$
$367$	13.0124	+	8.87168i	0.679240	+	0.463098i	−0.173912	+	0.984761i	$0.555641\pi$
$368$	−15.1647	−	10.3391i	−0.790513	−	0.538963i
$369$	−2.14241	+	0.322916i	−0.111529	+	0.0168103i
$370$	−14.5538	−	18.2499i	−0.756615	−	0.948765i
$371$		0			0
$372$	−13.5796	+	17.0282i	−0.704068	+	0.882873i
$373$	−13.3984	+	23.2067i	−0.693744	+	1.20160i	0.276858	+	0.960911i	$0.410707\pi$
$373$	−13.3984	+	23.2067i	−0.693744	+	1.20160i	−0.970602	+	0.240689i	$0.922627\pi$
$374$	5.32955	+	9.23106i	0.275585	+	0.477327i
$375$	7.75789	+	1.16931i	0.400616	+	0.0603831i
$376$	−47.5355	−	44.1065i	−2.45146	−	2.27462i
$377$	6.06746	−	2.92193i	0.312490	−	0.150487i
$378$		0			0
$379$	21.1837	+	10.2015i	1.08813	+	0.524018i	0.889909	−	0.456139i	$-0.150768\pi$
$379$	21.1837	+	10.2015i	1.08813	+	0.524018i	0.198226	+	0.980156i	$0.436482\pi$
$380$	−4.15744	−	10.5930i	−0.213272	−	0.543409i
$381$	1.24171	+	16.5695i	0.0636148	+	0.848881i
$382$	−1.78034	+	0.549161i	−0.0910899	+	0.0280975i
$383$	1.80659	−	24.1073i	0.0923125	−	1.23182i	−0.738106	−	0.674685i	$-0.764280\pi$
$383$	1.80659	−	24.1073i	0.0923125	−	1.23182i	0.830419	−	0.557140i	$-0.188101\pi$
$384$	1.41798	+	6.21259i	0.0723612	+	0.317035i
$385$		0			0
$386$	−6.53349	+	28.6251i	−0.332546	+	1.45698i
$387$	−9.53422	−	2.94092i	−0.484652	−	0.149495i
$388$	−2.31132	+	5.88916i	−0.117340	+	0.298977i
$389$	7.15107	−	6.63523i	0.362574	−	0.336419i	−0.477758	−	0.878491i	$-0.658550\pi$
$389$	7.15107	−	6.63523i	0.362574	−	0.336419i	0.840332	+	0.542072i	$0.182360\pi$
$390$	5.03414	−	3.43222i	0.254914	−	0.173797i
$391$	−17.0925			−0.864403
$392$		0			0
$393$	10.3509			0.522135
$394$	−1.35866	+	0.926318i	−0.0684482	+	0.0466672i
$395$	−10.6288	+	9.86210i	−0.534794	+	0.496216i
$396$	2.17691	−	5.54668i	0.109394	−	0.278731i
$397$	28.3414	+	8.74217i	1.42241	+	0.438757i	0.908067	−	0.418825i	$-0.137558\pi$
$397$	28.3414	+	8.74217i	1.42241	+	0.438757i	0.514347	+	0.857582i	$0.328034\pi$
$398$	−10.4186	+	45.6467i	−0.522235	+	2.28806i
$399$		0			0
$400$	−1.95183	−	8.55155i	−0.0975917	−	0.427577i
$401$	−1.36159	+	18.1692i	−0.0679947	+	0.907326i	0.854037	+	0.520212i	$0.174147\pi$
$401$	−1.36159	+	18.1692i	−0.0679947	+	0.907326i	−0.922032	+	0.387114i	$0.873472\pi$
$402$	6.49642	−	2.00388i	0.324012	−	0.0999445i
$403$	−0.512670	−	6.84111i	−0.0255379	−	0.340780i
$404$	0.516324	+	1.31557i	0.0256881	+	0.0654522i
$405$	−7.75986	−	3.73695i	−0.385591	−	0.185691i
$406$		0			0
$407$	−1.82951	+	0.881044i	−0.0906853	+	0.0436718i
$408$	−30.0760	−	27.9065i	−1.48898	−	1.38158i
$409$	−27.7664	−	4.18511i	−1.37296	−	0.206940i	−0.579207	−	0.815181i	$-0.696638\pi$
$409$	−27.7664	−	4.18511i	−1.37296	−	0.206940i	−0.793753	+	0.608240i	$0.791876\pi$
$410$	2.93851	+	5.08965i	0.145123	+	0.251360i
$411$	3.81666	−	6.61065i	0.188262	−	0.326079i
$412$	−2.36473	+	2.96527i	−0.116502	+	0.146089i
$413$		0			0
$414$	8.53959	+	10.7083i	0.419698	+	0.526284i
$415$	28.9699	−	4.36651i	1.42208	−	0.214343i
$416$	7.11354	+	4.84993i	0.348770	+	0.237787i
$417$	−8.27262	−	5.64018i	−0.405112	−	0.276201i
$418$	−1.40317	+	0.211494i	−0.0686312	+	0.0103445i
$419$	5.06020	+	6.34529i	0.247207	+	0.309988i	0.889918	−	0.456121i	$-0.150762\pi$
$419$	5.06020	+	6.34529i	0.247207	+	0.309988i	−0.642711	+	0.766109i	$0.722190\pi$
$420$		0			0
$421$	4.02881	−	5.05197i	0.196352	−	0.246218i	−0.673902	−	0.738821i	$-0.735383\pi$
$421$	4.02881	−	5.05197i	0.196352	−	0.246218i	0.870254	+	0.492603i	$0.163954\pi$
$422$	29.8752	−	51.7453i	1.45430	−	2.51892i
$423$	11.2818	+	19.5407i	0.548541	+	0.950100i
$424$	52.0256	+	7.84159i	2.52658	+	0.380821i
$425$	−5.98803	−	5.55608i	−0.290462	−	0.269509i
$426$	−0.0866671	+	0.0417367i	−0.00419903	+	0.00202215i
$427$		0			0
$428$	−24.8094	−	11.9476i	−1.19921	−	0.577508i
$429$	−0.193641	−	0.493388i	−0.00934906	−	0.0238210i
$430$	2.02253	+	26.9888i	0.0975349	+	1.30151i
$431$	−25.0647	+	7.73142i	−1.20732	+	0.372409i	−0.832152	−	0.554547i	$-0.812892\pi$
$431$	−25.0647	+	7.73142i	−1.20732	+	0.372409i	−0.375169	+	0.926956i	$0.622415\pi$
$432$	−2.61470	+	34.8908i	−0.125800	+	1.67868i
$433$	0.0249686	+	0.109395i	0.00119992	+	0.00525717i	0.975524	−	0.219892i	$-0.0705703\pi$
$433$	0.0249686	+	0.109395i	0.00119992	+	0.00525717i	−0.974324	+	0.225149i	$0.927713\pi$
$434$		0			0
$435$	2.54405	−	11.1462i	0.121978	−	0.534419i
$436$	−26.2825	−	8.10708i	−1.25870	−	0.388259i
$437$	0.831323	−	2.11818i	0.0397676	−	0.101326i
$438$	12.8133	−	11.8890i	0.612243	−	0.568078i
$439$	−24.4148	+	16.6457i	−1.16526	+	0.794458i	−0.982051	−	0.188616i	$-0.939600\pi$
$439$	−24.4148	+	16.6457i	−1.16526	+	0.794458i	−0.183205	+	0.983075i	$0.558647\pi$
$440$	−9.15713			−0.436549
$441$		0			0
$442$	22.8103			1.08498
$443$	19.6443	−	13.3933i	0.933331	−	0.636334i	0.00180064	−	0.999998i	$-0.499427\pi$
$443$	19.6443	−	13.3933i	0.933331	−	0.636334i	0.931530	+	0.363664i	$0.118474\pi$
$444$	10.1131	−	9.38357i	0.479946	−	0.445325i
$445$	4.06890	−	10.3674i	0.192884	−	0.491461i
$446$	68.3548	+	21.0847i	3.23669	+	0.998388i
$447$	3.33048	−	14.5918i	0.157526	−	0.690168i
$448$		0			0
$449$	6.76384	+	29.6343i	0.319205	+	1.39853i	0.838950	+	0.544208i	$0.183170\pi$
$449$	6.76384	+	29.6343i	0.319205	+	1.39853i	−0.519745	+	0.854321i	$0.673973\pi$
$450$	−0.489156	+	6.52734i	−0.0230591	+	0.307702i
$451$	0.488539	−	0.150694i	0.0230044	−	0.00709592i
$452$	−3.78430	−	50.4980i	−0.177999	−	2.37523i
$453$	3.50337	+	8.92644i	0.164603	+	0.419401i
$454$	54.5258	+	26.2583i	2.55902	+	1.23236i
$455$		0			0
$456$	4.92110	−	2.36988i	0.230452	−	0.110980i
$457$	−14.1243	−	13.1055i	−0.660708	−	0.613048i	0.276835	−	0.960918i	$-0.410715\pi$
$457$	−14.1243	−	13.1055i	−0.660708	−	0.613048i	−0.937543	+	0.347870i	$0.886905\pi$
$458$	15.7653	+	2.37623i	0.736663	+	0.111034i
$459$	16.2920	+	28.2185i	0.760444	+	1.31713i
$460$	12.9591	−	22.4457i	0.604219	−	1.04654i
$461$	−11.4345	+	14.3384i	−0.532558	+	0.667807i	−0.973223	−	0.229865i	$-0.926172\pi$
$461$	−11.4345	+	14.3384i	−0.532558	+	0.667807i	0.440664	+	0.897672i	$0.354743\pi$
$462$		0			0
$463$	4.26160	+	5.34387i	0.198053	+	0.248351i	0.870934	−	0.491400i	$-0.163515\pi$
$463$	4.26160	+	5.34387i	0.198053	+	0.248351i	−0.672881	+	0.739751i	$0.734943\pi$
$464$	45.4475	−	6.85012i	2.10985	−	0.318009i
$465$	−9.62288	−	6.56077i	−0.446251	−	0.304249i
$466$	43.2042	+	29.4561i	2.00140	+	1.36453i
$467$	−19.9763	+	3.01094i	−0.924392	+	0.139330i	−0.593955	−	0.804498i	$-0.702434\pi$
$467$	−19.9763	+	3.01094i	−0.924392	+	0.139330i	−0.330437	+	0.943828i	$0.607196\pi$
$468$	−7.95027	−	9.96932i	−0.367501	−	0.460832i
$469$		0			0
$470$	38.1607	−	47.8520i	1.76022	−	2.20725i
$471$	−7.95876	+	13.7850i	−0.366721	+	0.635179i
$472$	−9.33052	−	16.1609i	−0.429472	−	0.743867i
$473$	2.32809	+	0.350903i	0.107046	+	0.0161345i
$474$	−9.00471	−	8.35515i	−0.413600	−	0.383765i
$475$	0.979774	−	0.471834i	0.0449551	−	0.0216492i
$476$		0			0
$477$	−16.4942	−	7.94317i	−0.755215	−	0.363693i
$478$	8.75830	+	22.3158i	0.400595	+	1.02070i
$479$	0.144231	+	1.92463i	0.00659007	+	0.0879384i	0.999529	−	0.0306882i	$-0.00976989\pi$
$479$	0.144231	+	1.92463i	0.00659007	+	0.0879384i	−0.992939	+	0.118627i	$0.962151\pi$
$480$	13.9669	−	4.30823i	0.637501	−	0.196643i
$481$	−0.324736	+	4.33330i	−0.0148067	+	0.197581i
$482$	−2.33694	−	10.2388i	−0.106445	−	0.466365i
$483$		0			0
$484$	10.9814	−	48.1125i	0.499153	−	2.18693i
$485$	−3.23273	−	0.997164i	−0.146791	−	0.0452789i
$486$	14.8987	−	37.9613i	0.675819	−	1.72196i
$487$	7.45216	−	6.91459i	0.337689	−	0.313330i	−0.493040	−	0.870007i	$-0.664114\pi$
$487$	7.45216	−	6.91459i	0.337689	−	0.313330i	0.830729	+	0.556677i	$0.187924\pi$
$488$	39.6100	−	27.0056i	1.79306	−	1.22249i
$489$	5.87488			0.265671
$490$		0			0
$491$	−39.8079			−1.79650			−0.898252	−	0.439481i	$-0.855162\pi$
$491$	−39.8079			−1.79650			−0.898252	+	0.439481i	$0.855162\pi$
$492$	−2.86989	+	1.95666i	−0.129385	+	0.0882131i
$493$	31.3762	−	29.1129i	1.41311	−	1.31118i
$494$	−1.10942	+	2.82676i	−0.0499152	+	0.127182i
$495$	3.04473	+	0.939175i	0.136850	+	0.0422128i
$496$	10.4185	−	45.6464i	0.467804	−	2.04958i
$497$		0			0
$498$	5.52307	+	24.1981i	0.247494	+	1.08434i
$499$	−0.0390685	+	0.521333i	−0.00174895	+	0.0233381i	−0.998010	−	0.0630559i	$-0.979915\pi$
$499$	−0.0390685	+	0.521333i	−0.00174895	+	0.0233381i	0.996261	+	0.0863940i	$0.0275344\pi$
$500$	−42.5594	+	13.1278i	−1.90331	+	0.587094i
$501$	−1.11101	−	14.8254i	−0.0496362	−	0.662349i
$502$	6.87949	+	17.5287i	0.307047	+	0.782342i
$503$	8.65152	+	4.16635i	0.385752	+	0.185768i	0.616701	−	0.787197i	$-0.288469\pi$
$503$	8.65152	+	4.16635i	0.385752	+	0.185768i	−0.230949	+	0.972966i	$0.574183\pi$
$504$		0			0
$505$	−0.680890	+	0.327899i	−0.0302992	+	0.0145913i
$506$	−2.36918	−	2.19828i	−0.105323	−	0.0977253i
$507$	9.32679	+	1.40579i	0.414217	+	0.0624332i
$508$	−47.1634	−	81.6894i	−2.09254	−	3.62438i
$509$	−7.64275	+	13.2376i	−0.338759	+	0.586747i	−0.984200	−	0.177063i	$-0.943340\pi$
$509$	−7.64275	+	13.2376i	−0.338759	+	0.586747i	0.645441	+	0.763810i	$0.276674\pi$
$510$	24.1445	−	30.2762i	1.06914	−	1.34065i
$511$		0			0
$512$	−30.9549	−	38.8162i	−1.36803	−	1.71545i
$513$	−4.28936	+	0.646517i	−0.189380	+	0.0285444i
$514$	10.6867	+	7.28606i	0.471369	+	0.321374i
$515$	−1.67572	−	1.14248i	−0.0738408	−	0.0503438i
$516$	−15.8170	+	2.38403i	−0.696304	+	0.104951i
$517$	−3.31966	−	4.16273i	−0.145999	−	0.183076i
$518$		0			0
$519$	5.52276	−	6.92532i	0.242422	−	0.303988i
$520$	−9.79806	+	16.9707i	−0.429673	+	0.744216i
$521$	−15.8646	−	27.4783i	−0.695041	−	1.20385i	−0.970167	−	0.242439i	$-0.922053\pi$
$521$	−15.8646	−	27.4783i	−0.695041	−	1.20385i	0.275125	−	0.961408i	$-0.411281\pi$
$522$	−33.9149	−	5.11185i	−1.48441	−	0.223740i
$523$	−11.3120	−	10.4960i	−0.494640	−	0.458959i	0.392972	−	0.919550i	$-0.371447\pi$
$523$	−11.3120	−	10.4960i	−0.494640	−	0.458959i	−0.887612	+	0.460592i	$0.847637\pi$
$524$	−52.9418	+	25.4954i	−2.31278	+	1.11377i
$525$		0			0
$526$	−38.1079	−	18.3518i	−1.66158	−	0.800176i
$527$	−15.9298	−	40.5884i	−0.693912	−	1.76806i
$528$	−0.270324	−	3.60723i	−0.0117644	−	0.156984i
$529$	−17.0258	+	5.25177i	−0.740254	+	0.228338i
$530$	−3.71102	+	49.5201i	−0.161196	+	2.15102i
$531$	1.44488	+	6.33044i	0.0627025	+	0.274718i
$532$		0			0
$533$	0.243454	−	1.06664i	0.0105452	−	0.0462014i
$534$	9.01627	+	2.78115i	0.390172	+	0.120352i
$535$	5.37958	−	13.7069i	0.232579	−	0.592603i
$536$	−16.0286	+	14.8723i	−0.692329	+	0.642388i
$537$	9.67201	−	6.59426i	0.417378	−	0.284563i
$538$	−16.8809			−0.727789
$539$		0			0
$540$	−49.4085			−2.12621
$541$	12.1064	−	8.25402i	0.520496	−	0.354868i	−0.274398	−	0.961616i	$-0.588479\pi$
$541$	12.1064	−	8.25402i	0.520496	−	0.354868i	0.794894	+	0.606748i	$0.207526\pi$
$542$	8.40623	−	7.79984i	0.361078	−	0.335032i
$543$	−5.36695	+	13.6748i	−0.230318	+	0.586840i
$544$	52.2893	+	16.1291i	2.24189	+	0.691530i
$545$	3.27278	−	14.3390i	0.140190	−	0.614215i
$546$		0			0
$547$	−7.66606	−	33.5872i	−0.327777	−	1.43608i	−0.823358	−	0.567523i	$-0.807902\pi$
$547$	−7.66606	−	33.5872i	−0.327777	−	1.43608i	0.495581	−	0.868562i	$-0.334955\pi$
$548$	−3.23831	+	43.2123i	−0.138334	+	1.84594i
$549$	−15.9400	+	4.91684i	−0.680302	+	0.209845i
$550$	−0.115426	−	1.54025i	−0.00492178	−	0.0656766i
$551$	2.08176	+	5.30424i	0.0886860	+	0.225968i
$552$	11.2082	+	5.39761i	0.477055	+	0.229737i
$553$		0			0
$554$	60.6764	−	29.2202i	2.57789	−	1.24145i
$555$	5.40788	+	5.01778i	0.229552	+	0.212993i
$556$	56.2043	+	8.47143i	2.38359	+	0.359269i
$557$	−2.52513	−	4.37365i	−0.106993	−	0.185318i	0.807558	−	0.589789i	$-0.200789\pi$
$557$	−2.52513	−	4.37365i	−0.106993	−	0.185318i	−0.914551	+	0.404471i	$0.867456\pi$
$558$	−17.4696	+	30.2583i	−0.739549	+	1.28094i
$559$	3.14135	−	3.93913i	0.132865	−	0.166608i
$560$		0			0
$561$	−2.10037	−	2.63378i	−0.0886777	−	0.111198i
$562$	−2.11213	+	0.318352i	−0.0890947	+	0.0134289i
$563$	−13.9797	−	9.53118i	−0.589173	−	0.401691i	0.231712	−	0.972784i	$-0.425567\pi$
$563$	−13.9797	−	9.53118i	−0.589173	−	0.401691i	−0.820885	+	0.571093i	$0.806520\pi$
$564$	29.8879	+	20.3772i	1.25851	+	0.858035i
$565$	26.7766	−	4.03592i	1.12650	−	0.169792i
$566$	−47.6714	−	59.7781i	−2.00378	−	2.51266i
$567$		0			0
$568$	0.192896	−	0.241884i	0.00809374	−	0.0101492i
$569$	−5.08278	+	8.80364i	−0.213081	+	0.369068i	−0.952677	−	0.303983i	$-0.901683\pi$
$569$	−5.08278	+	8.80364i	−0.213081	+	0.369068i	0.739596	+	0.673051i	$0.235017\pi$
$570$	2.57766	+	4.46463i	0.107966	+	0.187003i
$571$	−1.55583	−	0.234504i	−0.0651094	−	0.00981367i	0.116407	−	0.993202i	$-0.462862\pi$
$571$	−1.55583	−	0.234504i	−0.0651094	−	0.00981367i	−0.181516	+	0.983388i	$0.558100\pi$
$572$	2.20568	+	2.04657i	0.0922241	+	0.0855715i
$573$	0.530510	−	0.255480i	0.0221624	−	0.0106728i
$574$		0			0
$575$	2.23152	+	1.07464i	0.0930610	+	0.0448158i
$576$	−2.23861	−	5.70390i	−0.0932756	−	0.237662i
$577$	2.28930	+	30.5485i	0.0953047	+	1.27175i	0.815817	+	0.578310i	$0.196288\pi$
$577$	2.28930	+	30.5485i	0.0953047	+	1.27175i	−0.720512	+	0.693442i	$0.756093\pi$
$578$	96.7580	−	29.8459i	4.02460	−	1.24143i
$579$	0.693451	−	9.25345i	0.0288188	−	0.384560i
$580$	14.4423	+	63.2757i	0.599682	+	2.62738i
$581$		0			0
$582$	0.637765	−	2.79423i	0.0264362	−	0.115825i
$583$	4.12800	+	1.27332i	0.170964	+	0.0527355i
$584$	−20.5388	+	52.3319i	−0.849900	+	2.16551i
$585$	4.99839	−	4.63783i	0.206658	−	0.191751i
$586$	−27.9976	+	19.0885i	−1.15657	+	0.788537i
$587$	39.4658			1.62893			0.814463	−	0.580215i	$-0.197032\pi$
$587$	39.4658			1.62893			0.814463	+	0.580215i	$0.197032\pi$
$588$		0			0
$589$	5.80467			0.239177
$590$	14.5527	−	9.92188i	0.599126	−	0.408477i
$591$	0.380965	−	0.353484i	0.0156708	−	0.0145404i
$592$	−10.8349	+	27.6069i	−0.445312	+	1.13464i
$593$	−25.9590	−	8.00730i	−1.06601	−	0.328820i	−0.288363	−	0.957521i	$-0.593111\pi$
$593$	−25.9590	−	8.00730i	−1.06601	−	0.328820i	−0.777647	+	0.628701i	$0.783587\pi$
$594$	−1.37099	+	6.00668i	−0.0562522	+	0.246457i
$595$		0			0
$596$	18.9067	+	82.8359i	0.774450	+	3.39309i
$597$	1.10580	−	14.7559i	0.0452576	−	0.603920i
$598$	−6.60902	+	2.03861i	−0.270263	+	0.0833651i
$599$	1.03248	+	13.7775i	0.0421860	+	0.562933i	0.977750	+	0.209775i	$0.0672731\pi$
$599$	1.03248	+	13.7775i	0.0421860	+	0.562933i	−0.935564	+	0.353158i	$0.885108\pi$
$600$	2.17206	+	5.53431i	0.0886738	+	0.225937i
$601$	27.6964	+	13.3379i	1.12976	+	0.544063i	0.902894	−	0.429864i	$-0.141438\pi$
$601$	27.6964	+	13.3379i	1.12976	+	0.544063i	0.226864	+	0.973926i	$0.427153\pi$
$602$		0			0
$603$	6.85481	−	3.30110i	0.279150	−	0.134431i
$604$	−39.9055	−	37.0269i	−1.62373	−	1.50660i
$605$	26.0946	+	3.93313i	1.06090	+	0.159904i
$606$	−0.320126	−	0.554475i	−0.0130042	−	0.0225240i
$607$	4.20387	−	7.28132i	0.170630	−	0.295540i	−0.768010	−	0.640437i	$-0.778753\pi$
$607$	4.20387	−	7.28132i	0.170630	−	0.295540i	0.938640	+	0.344898i	$0.112086\pi$
$608$	−4.54198	+	5.69546i	−0.184202	+	0.230982i
$609$		0			0
$610$	28.2118	+	35.3765i	1.14226	+	1.43235i
$611$	−11.2667	+	1.69818i	−0.455802	+	0.0687011i
$612$	−66.9617	−	45.6537i	−2.70677	−	1.84544i
$613$	−33.6447	−	22.9386i	−1.35890	−	0.926480i	−0.358921	−	0.933368i	$-0.616855\pi$
$613$	−33.6447	−	22.9386i	−1.35890	−	0.926480i	−0.999976	+	0.00688794i	$0.997807\pi$
$614$	−46.8991	+	7.06890i	−1.89269	+	0.285278i
$615$	−1.15806	−	1.45217i	−0.0466976	−	0.0585570i
$616$		0			0
$617$	−12.6776	+	15.8972i	−0.510381	+	0.639997i	−0.968536	−	0.248875i	$-0.919939\pi$
$617$	−12.6776	+	15.8972i	−0.510381	+	0.639997i	0.458155	+	0.888872i	$0.348511\pi$
$618$	0.859111	−	1.48802i	0.0345585	−	0.0598571i
$619$	−0.831657	−	1.44047i	−0.0334271	−	0.0578975i	0.848828	−	0.528669i	$-0.177309\pi$
$619$	−0.831657	−	1.44047i	−0.0334271	−	0.0578975i	−0.882255	+	0.470772i	$0.843976\pi$
$620$	65.3780	+	9.85415i	2.62564	+	0.395752i
$621$	−7.24237	−	6.71993i	−0.290626	−	0.269662i
$622$	−18.2277	+	8.77800i	−0.730865	+	0.351966i
$623$		0			0
$624$	−6.97445	−	3.35872i	−0.279201	−	0.134456i
$625$	−10.6885	−	27.2338i	−0.427539	−	1.08935i
$626$	2.96509	+	39.5664i	0.118509	+	1.58139i
$627$	0.428546	−	0.132189i	0.0171145	−	0.00527911i
$628$	6.75276	−	90.1093i	0.269464	−	3.59575i
$629$	6.14574	+	26.9263i	0.245047	+	1.07362i
$630$		0			0
$631$	5.45794	−	23.9128i	0.217277	−	0.951953i	−0.742203	−	0.670176i	$-0.766219\pi$
$631$	5.45794	−	23.9128i	0.217277	−	0.951953i	0.959480	−	0.281778i	$-0.0909240\pi$
$632$	37.7528	+	11.6452i	1.50172	+	0.463221i
$633$	−6.89897	+	17.5783i	−0.274210	+	0.698674i
$634$	−16.6331	+	15.4332i	−0.660584	+	0.612932i
$635$	41.6758	−	28.4141i	1.65385	−	1.12758i
$636$	−29.3495			−1.16378
$637$		0			0
$638$	8.09327			0.320416
$639$	−0.0889458	+	0.0606422i	−0.00351864	+	0.00239897i
$640$	14.1804	−	13.1575i	0.560529	−	0.520095i
$641$	−4.98600	+	12.7041i	−0.196935	+	0.501783i	−0.994894	−	0.100930i	$-0.967818\pi$
$641$	−4.98600	+	12.7041i	−0.196935	+	0.501783i	0.797958	+	0.602713i	$0.205914\pi$
$642$	11.9206	+	3.67702i	0.470468	+	0.145120i
$643$	−0.0325384	+	0.142560i	−0.00128319	+	0.00562202i	−0.975565	−	0.219709i	$-0.929489\pi$
$643$	−0.0325384	+	0.142560i	−0.00128319	+	0.00562202i	0.974282	+	0.225331i	$0.0723464\pi$
$644$		0			0
$645$	−1.90334	−	8.33906i	−0.0749438	−	0.328350i
$646$	−1.44232	+	19.2464i	−0.0567474	+	0.757241i
$647$	−0.0919828	+	0.0283729i	−0.00361622	+	0.00111546i	−0.296563	−	0.955013i	$-0.595840\pi$
$647$	−0.0919828	+	0.0283729i	−0.00361622	+	0.00111546i	0.292947	+	0.956129i	$0.405364\pi$
$648$	1.75378	+	23.4025i	0.0688949	+	0.919338i
$649$	−0.559777	−	1.42629i	−0.0219732	−	0.0559868i
$650$	−2.97802	−	1.43414i	−0.116808	−	0.0562516i
$651$		0			0
$652$	−30.0482	+	14.4705i	−1.17678	+	0.566707i
$653$	−21.7519	−	20.1828i	−0.851216	−	0.789813i	0.128182	−	0.991751i	$-0.459086\pi$
$653$	−21.7519	−	20.1828i	−0.851216	−	0.789813i	−0.979398	+	0.201937i	$0.935276\pi$
$654$	12.3212	+	1.85712i	0.481797	+	0.0726191i
$655$	−15.7109	−	27.2122i	−0.613877	−	1.06327i
$656$	3.73343	−	6.46648i	0.145766	−	0.252474i
$657$	12.1964	−	15.2938i	0.475826	−	0.596667i
$658$		0			0
$659$	22.4578	+	28.1612i	0.874833	+	1.09701i	0.994556	+	0.104199i	$0.0332279\pi$
$659$	22.4578	+	28.1612i	0.874833	+	1.09701i	−0.119723	+	0.992807i	$0.538201\pi$
$660$	5.05111	−	0.761333i	0.196614	−	0.0296349i
$661$	23.1913	+	15.8115i	0.902036	+	0.614998i	0.923007	−	0.384783i	$-0.125724\pi$
$661$	23.1913	+	15.8115i	0.902036	+	0.614998i	−0.0209715	+	0.999780i	$0.506676\pi$
$662$	−17.3310	−	11.8161i	−0.673590	−	0.459246i
$663$	−7.12851	+	1.07445i	−0.276849	+	0.0417282i
$664$	−49.7724	−	62.4126i	−1.93154	−	2.42208i
$665$		0			0
$666$	13.7986	−	17.3029i	0.534686	−	0.670475i
$667$	−6.48900	+	11.2393i	−0.251255	+	0.435187i
$668$	42.1990	+	73.0907i	1.63273	+	2.82797i
$669$	−22.3549	−	3.36946i	−0.864291	−	0.130271i
$670$	−15.1286	−	14.0373i	−0.584468	−	0.542307i
$671$	3.54642	−	1.70786i	0.136908	−	0.0659314i
$672$		0			0
$673$	10.1804	+	4.90261i	0.392425	+	0.188982i	0.619682	−	0.784853i	$-0.287262\pi$
$673$	10.1804	+	4.90261i	0.392425	+	0.188982i	−0.227257	+	0.973835i	$0.572976\pi$
$674$	14.7515	+	37.5862i	0.568206	+	1.44776i
$675$	−0.352847	−	4.70841i	−0.0135811	−	0.181227i
$676$	−51.1663	+	15.7827i	−1.96794	+	0.607028i
$677$	1.27901	−	17.0671i	0.0491562	−	0.655943i	−0.917149	−	0.398544i	$-0.869515\pi$
$677$	1.27901	−	17.0671i	0.0491562	−	0.655943i	0.966305	−	0.257399i	$-0.0828655\pi$
$678$	5.10492	+	22.3661i	0.196053	+	0.858965i
$679$		0			0
$680$	−27.7147	+	121.426i	−1.06281	+	4.65647i
$681$	−18.2769	−	5.63767i	−0.700372	−	0.216036i
$682$	3.01209	−	7.67468i	0.115339	−	0.293879i
$683$	−25.5911	+	23.7450i	−0.979214	+	0.908578i	−0.995825	−	0.0912838i	$-0.970903\pi$
$683$	−25.5911	+	23.7450i	−0.979214	+	0.908578i	0.0166104	+	0.999862i	$0.494712\pi$
$684$	8.91443	−	6.07775i	0.340852	−	0.232389i
$685$	−23.1721			−0.885362
$686$		0			0
$687$	−5.03878			−0.192241
$688$	28.4109	−	19.3702i	1.08315	−	0.738482i
$689$	6.77674	−	6.28790i	0.258173	−	0.239550i
$690$	−4.28972	+	10.9300i	−0.163307	+	0.416099i
$691$	0.669008	+	0.206362i	0.0254503	+	0.00785037i	0.307454	−	0.951563i	$-0.400523\pi$
$691$	0.669008	+	0.206362i	0.0254503	+	0.00785037i	−0.282004	+	0.959413i	$0.590999\pi$
$692$	−11.1894	+	49.0241i	−0.425358	+	1.86362i
$693$		0			0
$694$	−9.63829	−	42.2281i	−0.365864	−	1.60296i
$695$	−2.27136	+	30.3092i	−0.0861576	+	1.14969i
$696$	−29.7682	+	9.18228i	−1.12836	+	0.348053i
$697$	−0.519649	−	6.93423i	−0.0196831	−	0.262653i
$698$	−15.1895	−	38.7021i	−0.574930	−	1.46490i
$699$	−14.8894	−	7.17034i	−0.563167	−	0.271207i
$700$		0			0
$701$	−4.92502	+	2.37177i	−0.186016	+	0.0895803i	−0.524573	−	0.851365i	$-0.675775\pi$
$701$	−4.92502	+	2.37177i	−0.186016	+	0.0895803i	0.338558	+	0.940946i	$0.390061\pi$
$702$	9.66512	+	8.96792i	0.364786	+	0.338472i
$703$	−3.63574	−	0.547999i	−0.137124	−	0.0206682i
$704$	0.722947	+	1.25218i	0.0272471	+	0.0471933i
$705$	−9.67169	+	16.7519i	−0.364257	+	0.630911i
$706$	0.738695	−	0.926294i	0.0278011	−	0.0348615i
$707$		0			0
$708$	6.49039	+	8.13869i	0.243924	+	0.305871i
$709$	4.57436	−	0.689473i	0.171794	−	0.0258937i	−0.0625821	−	0.998040i	$-0.519934\pi$
$709$	4.57436	−	0.689473i	0.171794	−	0.0258937i	0.234376	+	0.972146i	$0.424695\pi$
$710$	0.241270	+	0.164495i	0.00905469	+	0.00617338i
$711$	−11.3584	−	7.74401i	−0.425972	−	0.290423i
$712$	−30.0079	+	4.52296i	−1.12459	+	0.169505i
$713$	8.24295	+	10.3363i	0.308701	+	0.387099i
$714$		0			0
$715$	−1.00318	+	1.25795i	−0.0375169	+	0.0470447i
$716$	−33.2270	+	57.5508i	−1.24175	+	2.15078i
$717$	−3.78824	−	6.56142i	−0.141474	−	0.245041i
$718$	62.2741	+	9.38632i	2.32405	+	0.350294i
$719$	6.36517	+	5.90602i	0.237381	+	0.220257i	0.789888	−	0.613251i	$-0.210138\pi$
$719$	6.36517	+	5.90602i	0.237381	+	0.220257i	−0.552507	+	0.833508i	$0.686329\pi$
$720$	41.9273	−	20.1911i	1.56254	−	0.752478i
$721$		0			0
$722$	41.7102	+	20.0866i	1.55229	+	0.747545i
$723$	1.21261	+	3.08968i	0.0450974	+	0.114906i
$724$	−6.23210	−	83.1616i	−0.231614	−	3.09068i
$725$	−5.92675	+	1.82816i	−0.220114	+	0.0678961i
$726$	−1.67074	+	22.2945i	−0.0620069	+	0.827425i
$727$	−11.7882	−	51.6473i	−0.437199	−	1.91549i	−0.400822	−	0.916156i	$-0.631276\pi$
$727$	−11.7882	−	51.6473i	−0.437199	−	1.91549i	−0.0363767	−	0.999338i	$-0.511582\pi$
$728$		0			0
$729$	−0.537682	+	2.35574i	−0.0199141	+	0.0872495i
$730$	−50.7040	−	15.6401i	−1.87664	−	0.578867i
$731$	11.6992	−	29.8090i	0.432709	−	1.10252i
$732$	−19.6038	+	18.1896i	−0.724576	+	0.672308i
$733$	9.91140	−	6.75748i	0.366086	−	0.249593i	−0.366280	−	0.930505i	$-0.619369\pi$
$733$	9.91140	−	6.75748i	0.366086	−	0.249593i	0.732366	+	0.680912i	$0.238416\pi$
$734$	40.5031			1.49500
$735$		0			0
$736$	−16.5917			−0.611579
$737$	−1.48336	+	1.01134i	−0.0546403	+	0.0372531i
$738$	−4.08463	+	3.78998i	−0.150357	+	0.139511i
$739$	−2.17541	+	5.54286i	−0.0800239	+	0.203897i	−0.965286	−	0.261195i	$-0.915884\pi$
$739$	−2.17541	+	5.54286i	−0.0800239	+	0.203897i	0.885262	+	0.465092i	$0.153979\pi$
$740$	−40.0190	−	12.3442i	−1.47113	−	0.453782i
$741$	0.213557	−	0.935656i	0.00784523	−	0.0343722i
$742$		0			0
$743$	−2.49333	−	10.9240i	−0.0914713	−	0.400762i	0.908378	−	0.418151i	$-0.137322\pi$
$743$	−2.49333	−	10.9240i	−0.0914713	−	0.400762i	−0.999849	+	0.0173892i	$0.994465\pi$
$744$	−2.37154	+	31.6460i	−0.0869448	+	1.16020i
$745$	−43.4163	+	13.3922i	−1.59065	+	0.490650i
$746$	5.15011	+	68.7235i	0.188559	+	2.51615i
$747$	10.1481	+	25.8569i	0.371298	+	0.946053i
$748$	17.2300	+	8.29755i	0.629993	+	0.303389i
$749$		0			0
$750$	18.1790	−	8.75452i	0.663802	−	0.319670i
$751$	−21.7877	−	20.2160i	−0.795043	−	0.737692i	0.173957	−	0.984753i	$-0.444345\pi$
$751$	−21.7877	−	20.2160i	−0.795043	−	0.737692i	−0.969000	+	0.247061i	$0.920535\pi$
$752$	−76.8933	−	11.5898i	−2.80401	−	0.422637i
$753$	−2.97559	−	5.15388i	−0.108437	−	0.187818i
$754$	8.65973	−	14.9991i	0.315369	−	0.546235i
$755$	18.1497	−	22.7590i	0.660536	−	0.828286i
$756$		0			0
$757$	−21.0101	−	26.3458i	−0.763626	−	0.957556i	0.236275	−	0.971686i	$-0.424074\pi$
$757$	−21.0101	−	26.3458i	−0.763626	−	0.957556i	−0.999900	+	0.0141302i	$0.995502\pi$
$758$	59.7932	−	9.01238i	2.17179	−	0.327344i
$759$	0.843946	+	0.575392i	0.0306333	+	0.0208854i
$760$	−13.6997	−	9.34029i	−0.496940	−	0.338808i
$761$	−39.1368	+	5.89892i	−1.41871	+	0.213836i	−0.813191	−	0.581997i	$-0.802272\pi$
$761$	−39.1368	+	5.89892i	−1.41871	+	0.213836i	−0.605517	+	0.795833i	$0.707033\pi$
$762$	26.6436	+	33.4100i	0.965194	+	1.21032i
$763$		0			0
$764$	−2.08412	+	2.61341i	−0.0754009	+	0.0945497i
$765$	21.6688	−	37.5314i	0.783436	−	1.35695i
$766$	−31.0865	−	53.8434i	−1.12320	−	1.94544i
$767$	−3.24227	−	0.488694i	−0.117072	−	0.0176457i
$768$	15.1349	+	14.0431i	0.546132	+	0.506737i
$769$	24.4950	−	11.7962i	0.883313	−	0.425381i	0.0634795	−	0.997983i	$-0.479780\pi$
$769$	24.4950	−	11.7962i	0.883313	−	0.425381i	0.819833	+	0.572602i	$0.194066\pi$
$770$		0			0
$771$	−3.68293	−	1.77360i	−0.132637	−	0.0638748i
$772$	19.2455	+	49.0366i	0.692659	+	1.76487i
$773$	−0.141892	−	1.89342i	−0.00510351	−	0.0681016i	0.994071	−	0.108737i	$-0.0346807\pi$
$773$	−0.141892	−	1.89342i	−0.00510351	−	0.0681016i	−0.999174	+	0.0406357i	$0.987062\pi$
$774$	−24.5201	+	7.56346i	−0.881358	+	0.271863i
$775$	−0.472165	+	6.30060i	−0.0169607	+	0.226324i
$776$	2.05121	+	8.98695i	0.0736343	+	0.322613i
$777$		0			0
$778$	5.58271	−	24.4594i	0.200150	−	0.876914i
$779$	0.884596	+	0.272862i	0.0316940	+	0.00977629i
$780$	3.99369	−	10.1757i	0.142997	−	0.364350i
$781$	0.0186213	−	0.0172780i	0.000666323	−	0.000618257i
$782$	−36.3202	+	24.7627i	−1.29881	+	0.885511i
$783$	24.7404			0.884150
$784$		0			0
$785$	48.3202			1.72462
$786$	21.9949	−	14.9959i	0.784533	−	0.534886i
$787$	−22.3454	+	20.7335i	−0.796526	+	0.739068i	−0.969297	−	0.245894i	$-0.920919\pi$
$787$	−22.3454	+	20.7335i	−0.796526	+	0.739068i	0.172770	+	0.984962i	$0.444728\pi$
$788$	−1.07785	+	2.74632i	−0.0383969	+	0.0978336i
$789$	12.7736	+	3.94015i	0.454754	+	0.140273i
$790$	−8.29772	+	36.3547i	−0.295220	+	1.29344i
$791$		0			0
$792$	−1.93193	−	8.46432i	−0.0686480	−	0.300767i
$793$	0.629486	−	8.39990i	0.0223537	−	0.298289i
$794$	72.8885	−	22.4831i	2.58672	−	0.797896i
$795$	−1.17284	−	15.6505i	−0.0415964	−	0.555065i
$796$	30.6896	+	78.1958i	1.08776	+	2.77158i
$797$	−38.6850	−	18.6297i	−1.37029	−	0.659899i	−0.403387	−	0.915030i	$-0.632167\pi$
$797$	−38.6850	−	18.6297i	−1.37029	−	0.659899i	−0.966906	+	0.255131i	$0.917881\pi$
$798$		0			0
$799$	−65.2459	+	31.4208i	−2.30824	+	1.11159i
$800$	−5.81261	−	5.39331i	−0.205507	−	0.190682i
$801$	10.4414	+	1.57379i	0.368930	+	0.0556073i
$802$	23.4293	+	40.5807i	0.827317	+	1.43296i
$803$	−2.30795	+	3.99749i	−0.0814459	+	0.141068i
$804$	7.60493	−	9.53628i	0.268205	−	0.336319i
$805$		0			0
$806$	−11.0004	−	13.7941i	−0.387473	−	0.485876i
$807$	5.27551	−	0.795155i	0.185707	−	0.0279908i
$808$	1.70140	+	1.16000i	0.0598552	+	0.0408086i
$809$	26.0228	+	17.7421i	0.914914	+	0.623778i	0.926557	−	0.376154i	$-0.122754\pi$
$809$	26.0228	+	17.7421i	0.914914	+	0.623778i	−0.0116430	+	0.999932i	$0.503706\pi$
$810$	−21.9030	+	3.30135i	−0.769593	+	0.115998i
$811$	9.32495	+	11.6931i	0.327443	+	0.410601i	0.918117	−	0.396310i	$-0.129709\pi$
$811$	9.32495	+	11.6931i	0.327443	+	0.410601i	−0.590674	+	0.806911i	$0.701138\pi$
$812$		0			0
$813$	−2.25965	+	2.83351i	−0.0792495	+	0.0993757i
$814$	−2.61115	+	4.52265i	−0.0915208	+	0.158519i
$815$	−8.91707	−	15.4448i	−0.312351	−	0.541008i
$816$	−48.6509	−	7.33294i	−1.70312	−	0.256704i
$817$	3.12505	+	2.89963i	0.109332	+	0.101445i
$818$	−65.0646	+	31.3335i	−2.27493	+	1.09555i
$819$		0			0
$820$	9.49999	+	4.57495i	0.331754	+	0.159764i
$821$	1.13007	+	2.87936i	0.0394396	+	0.100490i	0.949237	−	0.314563i	$-0.101858\pi$
$821$	1.13007	+	2.87936i	0.0394396	+	0.100490i	−0.909797	+	0.415054i	$0.863763\pi$
$822$	−1.46706	−	19.5765i	−0.0511694	−	0.682809i
$823$	17.4726	−	5.38960i	0.609058	−	0.187870i	0.0251425	−	0.999684i	$-0.491996\pi$
$823$	17.4726	−	5.38960i	0.609058	−	0.187870i	0.583916	+	0.811814i	$0.301520\pi$
$824$	−0.412976	+	5.51078i	−0.0143867	+	0.191977i
$825$	0.108624	+	0.475912i	0.00378179	+	0.0165691i
$826$		0			0
$827$	6.82739	−	29.9127i	0.237412	−	1.04017i	−0.705913	−	0.708298i	$-0.749463\pi$
$827$	6.82739	−	29.9127i	0.237412	−	1.04017i	0.943325	−	0.331870i	$-0.107680\pi$
$828$	23.4816	+	7.24310i	0.816041	+	0.251715i
$829$	−2.29689	+	5.85239i	−0.0797744	+	0.203262i	−0.965196	−	0.261526i	$-0.915774\pi$
$829$	−2.29689	+	5.85239i	−0.0797744	+	0.203262i	0.885422	+	0.464788i	$0.153869\pi$
$830$	55.2328	−	51.2485i	1.91716	−	1.77886i
$831$	−17.5858	+	11.9898i	−0.610043	+	0.415920i
$832$	3.09419			0.107272
$833$		0			0
$834$	−25.7499			−0.891645
$835$	−37.2890	+	25.4232i	−1.29044	+	0.879806i
$836$	−1.86629	+	1.73166i	−0.0645468	+	0.0598907i
$837$	9.20769	−	23.4608i	0.318264	−	0.810924i
$838$	19.9453	+	6.15230i	0.688998	+	0.212528i
$839$	−5.38717	+	23.6027i	−0.185986	+	0.814857i	0.792720	+	0.609586i	$0.208664\pi$
$839$	−5.38717	+	23.6027i	−0.185986	+	0.814857i	−0.978705	+	0.205270i	$0.934193\pi$
$840$		0			0
$841$	−0.778582	−	3.41119i	−0.0268477	−	0.117627i
$842$	1.24188	−	16.5718i	0.0427981	−	0.571101i
$843$	0.645071	−	0.198978i	0.0222174	−	0.00685317i
$844$	−8.01109	−	106.901i	−0.275753	−	3.67967i
$845$	−10.4607	−	26.6535i	−0.359860	−	0.916908i
$846$	52.2825	+	25.1779i	1.79751	+	0.865635i
$847$		0			0
$848$	56.8444	−	27.3748i	1.95204	−	0.940055i
$849$	17.7137	+	16.4359i	0.607933	+	0.564079i
$850$	−20.7735	−	3.13110i	−0.712524	−	0.107396i
$851$	−4.18712	−	7.25231i	−0.143533	−	0.248606i
$852$	−0.0862919	+	0.149462i	−0.00295631	+	0.00512048i
$853$	−2.13074	+	2.67187i	−0.0729553	+	0.0914830i	−0.816970	−	0.576680i	$-0.804348\pi$
$853$	−2.13074	+	2.67187i	−0.0729553	+	0.0914830i	0.744015	+	0.668163i	$0.232919\pi$
$854$		0			0
$855$	3.59716	+	4.51070i	0.123020	+	0.154263i
$856$	−39.6740	+	5.97990i	−1.35603	+	0.204389i
$857$	31.0664	+	21.1807i	1.06121	+	0.723518i	0.962413	−	0.271590i	$-0.0875494\pi$
$857$	31.0664	+	21.1807i	1.06121	+	0.723518i	0.0987933	+	0.995108i	$0.468502\pi$
$858$	−1.12627	−	0.767875i	−0.0384501	−	0.0262148i
$859$	15.5104	−	2.33781i	0.529207	−	0.0797652i	0.120997	−	0.992653i	$-0.461391\pi$
$859$	15.5104	−	2.33781i	0.529207	−	0.0797652i	0.408211	+	0.912888i	$0.366153\pi$
$860$	30.2750	+	37.9636i	1.03237	+	1.29455i
$861$		0			0
$862$	−42.0596	+	52.7410i	−1.43255	+	1.79637i
$863$	7.37672	−	12.7769i	0.251107	−	0.434929i	−0.712724	−	0.701444i	$-0.752539\pi$
$863$	7.37672	−	12.7769i	0.251107	−	0.434929i	0.963831	+	0.266515i	$0.0858722\pi$
$864$	15.8147	+	27.3918i	0.538026	+	0.931889i
$865$	−26.5890	−	4.00765i	−0.904053	−	0.136264i
$866$	0.211542	+	0.196282i	0.00718848	+	0.00666994i
$867$	−28.8323	+	13.8849i	−0.979195	+	0.471556i
$868$		0			0
$869$	2.92264	+	1.40747i	0.0991439	+	0.0477452i
$870$	−10.7421	−	27.3705i	−0.364192	−	0.927947i
$871$	0.287109	+	3.83121i	0.00972833	+	0.129816i
$872$	−38.2952	+	11.8125i	−1.29684	+	0.400022i
$873$	0.239696	−	3.19852i	0.00811248	−	0.108254i
$874$	−1.30221	−	5.70534i	−0.0440478	−	0.192986i
$875$		0			0
$876$	6.97835	−	30.5741i	0.235776	−	1.03300i
$877$	19.4153	+	5.98883i	0.655608	+	0.202228i	0.604673	−	0.796474i	$-0.293304\pi$
$877$	19.4153	+	5.98883i	0.655608	+	0.202228i	0.0509349	+	0.998702i	$0.483780\pi$
$878$	−27.7641	+	70.7419i	−0.936994	+	2.38742i
$879$	7.85048	−	7.28418i	0.264790	−	0.245689i
$880$	−9.07294	+	6.18583i	−0.305849	+	0.208524i
$881$	35.6191			1.20004			0.600019	−	0.799986i	$-0.295160\pi$
$881$	35.6191			1.20004			0.600019	+	0.799986i	$0.295160\pi$
$882$		0			0
$883$	−33.7765			−1.13667			−0.568335	−	0.822797i	$-0.692412\pi$
$883$	−33.7765			−1.13667			−0.568335	+	0.822797i	$0.692412\pi$
$884$	33.8137	−	23.0538i	1.13728	−	0.775383i
$885$	−4.08056	+	3.78620i	−0.137166	+	0.127272i
$886$	22.3392	−	56.9194i	0.750501	−	1.91224i
$887$	13.4953	+	4.16275i	0.453128	+	0.139772i	0.512915	−	0.858440i	$-0.328566\pi$
$887$	13.4953	+	4.16275i	0.453128	+	0.139772i	−0.0597863	+	0.998211i	$0.519042\pi$
$888$	4.47299	−	19.5974i	0.150104	−	0.657647i
$889$		0			0
$890$	−6.37363	−	27.9247i	−0.213645	−	0.936038i
$891$	−0.143998	+	1.92152i	−0.00482410	+	0.0643732i
$892$	122.638	−	37.8288i	4.10622	−	1.26660i
$893$	−0.720454	−	9.61378i	−0.0241091	−	0.321713i
$894$	−14.0628	−	35.8314i	−0.470331	−	1.19838i
$895$	−32.0165	−	15.4183i	−1.07019	−	0.515378i
$896$		0			0
$897$	1.96938	−	0.948402i	0.0657556	−	0.0316662i
$898$	57.3053	+	53.1715i	1.91230	+	1.77436i
$899$	−32.7368	−	4.93428i	−1.09183	−	0.164567i
$900$	5.87189	+	10.1704i	0.195730	+	0.339014i
$901$	29.3782	−	50.8845i	0.978729	−	1.69521i
$902$	0.819790	−	1.02798i	0.0272960	−	0.0342281i
$903$		0			0
$904$	−46.0042	−	57.6874i	−1.53008	−	1.91865i
$905$	44.0965	−	6.64647i	1.46582	−	0.220936i
$906$	20.3766	+	13.8925i	0.676966	+	0.461547i
$907$	45.2475	+	30.8492i	1.50242	+	1.02433i	0.985763	+	0.168139i	$0.0537757\pi$
$907$	45.2475	+	30.8492i	1.50242	+	1.02433i	0.516656	+	0.856193i	$0.327177\pi$
$908$	107.367	−	16.1830i	3.56309	−	0.537050i
$909$	−0.446742	−	0.560196i	−0.0148175	−	0.0185805i
$910$		0			0
$911$	−4.83611	+	6.06430i	−0.160228	+	0.200919i	−0.855464	−	0.517862i	$-0.826728\pi$
$911$	−4.83611	+	6.06430i	−0.160228	+	0.200919i	0.695237	+	0.718781i	$0.255300\pi$
$912$	3.27496	−	5.67239i	0.108445	−	0.187832i
$913$	−3.27726	−	5.67637i	−0.108461	−	0.187861i
$914$	−48.9996	−	7.38550i	−1.62076	−	0.244291i
$915$	−10.4829	−	9.72673i	−0.346555	−	0.321556i
$916$	25.7718	−	12.4110i	0.851525	−	0.410073i
$917$		0			0
$918$	75.5007	+	36.3592i	2.49189	+	1.20003i
$919$	1.45073	+	3.69640i	0.0478551	+	0.121933i	0.952803	−	0.303590i	$-0.0981854\pi$
$919$	1.45073	+	3.69640i	0.0478551	+	0.121933i	−0.904948	+	0.425523i	$0.860090\pi$
$920$	−2.82213	−	37.6587i	−0.0930427	−	1.24157i
$921$	14.3236	−	4.41824i	0.471978	−	0.145586i
$922$	−3.52469	+	47.0338i	−0.116080	+	1.54897i
$923$	−0.0120964	−	0.0529978i	−0.000398158	−	0.00174445i
$924$		0			0
$925$	0.890556	−	3.90178i	0.0292813	−	0.128290i
$926$	16.7975	+	5.18134i	0.552000	+	0.170269i
$927$	0.702511	−	1.78997i	0.0230735	−	0.0587903i
$928$	30.4570	−	28.2600i	0.999800	−	0.927679i
$929$	−1.98320	+	1.35212i	−0.0650667	+	0.0443617i	−0.595417	−	0.803417i	$-0.703013\pi$
$929$	−1.98320	+	1.35212i	−0.0650667	+	0.0443617i	0.530350	+	0.847779i	$0.322061\pi$
$930$	−29.9528			−0.982191
$931$		0			0
$932$	93.8158			3.07304
$933$	5.28292	−	3.60183i	0.172955	−	0.117919i
$934$	−38.0860	+	35.3386i	−1.24621	+	1.15631i
$935$	−3.73610	+	9.51942i	−0.122183	+	0.311318i
$936$	−17.7539	−	5.47635i	−0.580304	−	0.179000i
$937$	−8.08320	+	35.4148i	−0.264067	+	1.15695i	0.652728	+	0.757592i	$0.273624\pi$
$937$	−8.08320	+	35.4148i	−0.264067	+	1.15695i	−0.916795	+	0.399359i	$0.869233\pi$
$938$		0			0
$939$	−2.79036	−	12.2253i	−0.0910598	−	0.398959i
$940$	8.20612	−	109.503i	0.267654	−	3.57160i
$941$	−33.7983	+	10.4254i	−1.10179	+	0.339858i	−0.791738	−	0.610861i	$-0.790823\pi$
$941$	−33.7983	+	10.4254i	−1.10179	+	0.339858i	−0.310054	+	0.950719i	$0.600347\pi$
$942$	3.05921	+	40.8223i	0.0996743	+	1.33006i
$943$	0.770292	+	1.96267i	0.0250842	+	0.0639134i
$944$	−20.1618	−	9.70940i	−0.656210	−	0.316014i
$945$		0			0
$946$	5.45537	−	2.62717i	0.177369	−	0.0854166i
$947$	−11.9780	−	11.1140i	−0.389234	−	0.361156i	0.461147	−	0.887324i	$-0.347438\pi$
$947$	−11.9780	−	11.1140i	−0.389234	−	0.361156i	−0.850381	+	0.526167i	$0.823628\pi$
$948$	−21.7928	−	3.28473i	−0.707797	−	0.106683i
$949$	4.93898	+	8.55457i	0.160326	+	0.277693i
$950$	1.39838	−	2.42206i	0.0453693	−	0.0785819i
$951$	4.47109	−	5.60657i	0.144985	−	0.181805i
$952$		0			0
$953$	25.4951	+	31.9699i	0.825869	+	1.03561i	0.998716	+	0.0506581i	$0.0161319\pi$
$953$	25.4951	+	31.9699i	0.825869	+	1.03561i	−0.172847	+	0.984949i	$0.555297\pi$
$954$	−46.5564	+	7.01726i	−1.50732	+	0.227192i
$955$	−1.47687	−	1.00691i	−0.0477904	−	0.0325829i
$956$	35.5372	+	24.2288i	1.14935	+	0.783616i
$957$	−2.52925	+	0.381223i	−0.0817591	+	0.0123232i
$958$	3.09478	+	3.88073i	0.0999877	+	0.125381i
$959$		0			0
$960$	3.27517	−	4.10693i	0.105706	−	0.132551i
$961$	−1.36281	+	2.36045i	−0.0439616	+	0.0761437i
$962$	5.58782	+	9.67839i	0.180159	+	0.312044i
$963$	13.8049	+	2.08075i	0.444855	+	0.0670511i
$964$	−13.8123	−	12.8160i	−0.444866	−	0.412775i
$965$	−25.3795	+	12.2221i	−0.816994	+	0.393444i
$966$		0			0
$967$	34.8489	+	16.7823i	1.12066	+	0.539683i	0.900097	−	0.435689i	$-0.143495\pi$
$967$	34.8489	+	16.7823i	1.12066	+	0.539683i	0.220566	+	0.975372i	$0.429209\pi$
$968$	−26.2701	−	66.9351i	−0.844353	−	2.15138i
$969$	−0.455835	−	6.08270i	−0.0146435	−	0.195404i
$970$	−8.31394	+	2.56451i	−0.266944	+	0.0823414i
$971$	−4.37077	+	58.3239i	−0.140265	+	1.87170i	0.274249	+	0.961659i	$0.411571\pi$
$971$	−4.37077	+	58.3239i	−0.140265	+	1.87170i	−0.414514	+	0.910043i	$0.636048\pi$
$972$	−16.2808	−	71.3310i	−0.522208	−	2.28794i
$973$		0			0
$974$	5.81776	−	25.4893i	0.186413	−	0.816729i
$975$	0.998224	+	0.307911i	0.0319687	+	0.00986105i
$976$	21.0029	−	53.5146i	0.672288	−	1.71296i
$977$	9.69217	−	8.99302i	0.310080	−	0.287712i	−0.509746	−	0.860325i	$-0.670261\pi$
$977$	9.69217	−	8.99302i	0.310080	−	0.287712i	0.819826	+	0.572613i	$0.194070\pi$
$978$	12.4837	−	8.51122i	0.399184	−	0.272159i
$979$	−2.49169			−0.0796348
$980$		0			0
$981$	13.9446			0.445217
$982$	−84.5886	+	57.6715i	−2.69933	+	1.84037i
$983$	−10.0208	+	9.29798i	−0.319615	+	0.296559i	−0.823621	−	0.567141i	$-0.808049\pi$
$983$	−10.0208	+	9.29798i	−0.319615	+	0.296559i	0.504006	+	0.863700i	$0.331859\pi$
$984$	−1.84900	+	4.71117i	−0.0589439	+	0.150187i
$985$	−1.50753	−	0.465013i	−0.0480340	−	0.0148165i
$986$	24.4948	−	107.319i	0.780074	−	3.41773i
$987$		0			0
$988$	1.21234	+	5.31161i	0.0385697	+	0.168985i
$989$	−0.725594	+	9.68238i	−0.0230726	+	0.307882i
$990$	7.83044	−	2.41537i	0.248868	−	0.0767656i
$991$	2.04651	+	27.3088i	0.0650097	+	0.867494i	0.930435	+	0.366456i	$0.119429\pi$
$991$	2.04651	+	27.3088i	0.0650097	+	0.867494i	−0.865426	+	0.501037i	$0.832952\pi$
$992$	−15.4631	−	39.3993i	−0.490954	−	1.25093i
$993$	5.97275	+	2.87632i	0.189539	+	0.0912774i
$994$		0			0
$995$	−40.4711	+	19.4899i	−1.28302	+	0.617871i
$996$	32.6437	+	30.2890i	1.03436	+	0.959742i
$997$	35.0653	+	5.28525i	1.11053	+	0.167385i	0.678590	−	0.734517i	$-0.262591\pi$
$997$	35.0653	+	5.28525i	1.11053	+	0.167385i	0.431940	+	0.901903i	$0.357829\pi$
$998$	0.672262	+	1.16439i	0.0212801	+	0.0368582i
$999$	−7.98205	+	13.8253i	−0.252541	+	0.437414i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	343.2.g.h.30.4		48
7.2	even	3		343.2.e.c.197.1		48
7.3	odd	6		49.2.g.a.32.4	yes	48
7.4	even	3		343.2.g.g.116.4		48
7.5	odd	6		343.2.e.d.197.1		48
7.6	odd	2		343.2.g.i.30.4		48
21.17	even	6		441.2.bb.d.424.1		48
28.3	even	6		784.2.bg.c.81.3		48
49.2	even	21		2401.2.a.i.1.23		24
49.4	even	21	inner	343.2.g.h.263.4		48
49.22	even	7		343.2.g.g.275.4		48
49.23	even	21		343.2.e.c.148.1		48
49.26	odd	42		343.2.e.d.148.1		48
49.27	odd	14		49.2.g.a.23.4	✓	48
49.45	odd	42		343.2.g.i.263.4		48
49.47	odd	42		2401.2.a.h.1.23		24
147.125	even	14		441.2.bb.d.415.1		48
196.27	even	14		784.2.bg.c.513.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.23.4	✓	48	49.27	odd	14
49.2.g.a.32.4	yes	48	7.3	odd	6
343.2.e.c.148.1		48	49.23	even	21
343.2.e.c.197.1		48	7.2	even	3
343.2.e.d.148.1		48	49.26	odd	42
343.2.e.d.197.1		48	7.5	odd	6
343.2.g.g.116.4		48	7.4	even	3
343.2.g.g.275.4		48	49.22	even	7
343.2.g.h.30.4		48	1.1	even	1	trivial
343.2.g.h.263.4		48	49.4	even	21	inner
343.2.g.i.30.4		48	7.6	odd	2
343.2.g.i.263.4		48	49.45	odd	42
441.2.bb.d.415.1		48	147.125	even	14
441.2.bb.d.424.1		48	21.17	even	6
784.2.bg.c.81.3		48	28.3	even	6
784.2.bg.c.513.3		48	196.27	even	14
2401.2.a.h.1.23		24	49.47	odd	42
2401.2.a.i.1.23		24	49.2	even	21

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:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	343.g (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.12492 - 1.44875i) q^{2} +(-0.595824 + 0.552844i) q^{3} +(1.68574 - 4.29521i) q^{4} +(2.35776 + 0.727274i) q^{5} +(-0.465149 + 2.03795i) q^{6} +(-1.49604 - 6.55456i) q^{8} +(-0.174820 + 2.33282i) q^{9} +O(q^{10})\)	\(q+(2.12492 - 1.44875i) q^{2} +(-0.595824 + 0.552844i) q^{3} +(1.68574 - 4.29521i) q^{4} +(2.35776 + 0.727274i) q^{5} +(-0.465149 + 2.03795i) q^{6} +(-1.49604 - 6.55456i) q^{8} +(-0.174820 + 2.33282i) q^{9} +(6.06370 - 1.87040i) q^{10} +(-0.0412523 - 0.550473i) q^{11} +(1.37017 + 3.49114i) q^{12} +(-1.06432 - 0.512550i) q^{13} +(-1.80688 + 0.870148i) q^{15} +(-5.91002 - 5.48369i) q^{16} +(-7.42426 - 1.11903i) q^{17} +(3.00818 + 5.21032i) q^{18} +(0.499767 - 0.865623i) q^{19} +(7.09838 - 8.90108i) q^{20} +(-0.885154 - 1.10995i) q^{22} +(2.25110 - 0.339299i) q^{23} +(4.51502 + 3.07829i) q^{24} +(0.898926 + 0.612877i) q^{25} +(-3.00415 + 0.452803i) q^{26} +(-2.70584 - 3.39301i) q^{27} +(-3.55438 + 4.45705i) q^{29} +(-2.57886 + 4.46671i) q^{30} +(2.90369 + 5.02934i) q^{31} +(-7.20676 - 1.08624i) q^{32} +(0.328905 + 0.305179i) q^{33} +(-17.3972 + 8.37803i) q^{34} +(9.72523 + 4.68342i) q^{36} +(-1.34391 - 3.42423i) q^{37} +(-0.192102 - 2.56342i) q^{38} +(0.917508 - 0.283014i) q^{39} +(1.23966 - 16.5421i) q^{40} +(0.206089 + 0.902934i) q^{41} +(-0.949065 + 4.15812i) q^{43} +(-2.43394 - 0.750770i) q^{44} +(-2.10878 + 5.37308i) q^{45} +(4.29186 - 3.98227i) q^{46} +(7.96926 - 5.43335i) q^{47} +6.55296 q^{48} +2.79805 q^{50} +(5.04220 - 3.43771i) q^{51} +(-3.99568 + 3.70745i) q^{52} +(-2.85905 + 7.28475i) q^{53} +(-10.6653 - 3.28981i) q^{54} +(0.303081 - 1.32789i) q^{55} +(0.180781 + 0.792052i) q^{57} +(-1.09564 + 14.6203i) q^{58} +(2.65234 - 0.818137i) q^{59} +(0.691526 + 9.22778i) q^{60} +(2.60511 + 6.63771i) q^{61} +(13.4564 + 6.48024i) q^{62} +(-2.35990 + 1.13647i) q^{64} +(-2.13665 - 1.98252i) q^{65} +(1.14102 + 0.171982i) q^{66} +(-1.62615 - 2.81657i) q^{67} +(-17.3219 + 30.0023i) q^{68} +(-1.15368 + 1.44667i) q^{69} +(0.0286915 + 0.0359779i) q^{71} +(15.5521 - 2.34410i) q^{72} +(-6.90892 - 4.71043i) q^{73} +(-7.81656 - 5.32924i) q^{74} +(-0.874427 + 0.131799i) q^{75} +(-2.87555 - 3.60582i) q^{76} +(1.53962 - 1.93062i) q^{78} +(-2.93822 + 5.08914i) q^{79} +(-9.94627 - 17.2275i) q^{80} +(-3.45167 - 0.520256i) q^{81} +(1.74605 + 1.62009i) q^{82} +(10.6979 - 5.15183i) q^{83} +(-16.6908 - 8.03787i) q^{85} +(4.00738 + 10.2106i) q^{86} +(-0.346269 - 4.62064i) q^{87} +(-3.54639 + 1.09392i) q^{88} +(0.337316 - 4.50117i) q^{89} +(3.30325 + 14.4725i) q^{90} +(2.33743 - 10.2409i) q^{92} +(-4.51053 - 1.39131i) q^{93} +(9.06251 - 23.0909i) q^{94} +(1.80788 - 1.67747i) q^{95} +(4.89448 - 3.33700i) q^{96} -1.37110 q^{97} +1.29136 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} - 7 q^{3} + 12 q^{4} - 7 q^{5} - 20 q^{8} - 15 q^{9}+O(q^{10}) \) 48 * q + 8 * q^2 - 7 * q^3 + 12 * q^4 - 7 * q^5 - 20 * q^8 - 15 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} + 12 q^{4} - 7 q^{5} - 20 q^{8} - 15 q^{9} - 7 q^{10} - 3 q^{11} + 63 q^{12} + 14 q^{13} - 12 q^{15} + 18 q^{16} - 14 q^{17} + 2 q^{18} - 21 q^{19} - 14 q^{20} - 20 q^{22} - 27 q^{23} + 77 q^{24} + 17 q^{25} + 21 q^{26} - 7 q^{27} + 12 q^{29} + 11 q^{30} - 35 q^{31} - 60 q^{32} - 7 q^{33} - 70 q^{34} - 12 q^{36} - 6 q^{37} - 35 q^{38} + 35 q^{39} - 105 q^{40} + 42 q^{41} - 30 q^{43} + 13 q^{44} + 35 q^{45} + 69 q^{46} + 42 q^{47} + 84 q^{48} + 40 q^{50} + 53 q^{51} + 7 q^{52} - 31 q^{53} - 70 q^{54} + 7 q^{55} - 12 q^{57} - 47 q^{58} - 35 q^{59} - 91 q^{60} + 14 q^{61} + 28 q^{62} - 32 q^{64} + 35 q^{65} + 35 q^{66} + 11 q^{67} - 77 q^{68} - 70 q^{69} + 19 q^{71} - 124 q^{72} + 35 q^{73} + 13 q^{74} + 119 q^{75} - 119 q^{76} + 28 q^{78} + 15 q^{79} - 70 q^{80} - 125 q^{81} + 98 q^{82} - 26 q^{85} + 9 q^{86} - 35 q^{87} + 49 q^{88} + 14 q^{89} + 182 q^{90} - 38 q^{92} + 46 q^{93} - 14 q^{94} + 128 q^{95} - 98 q^{96} - 16 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 + 12 * q^4 - 7 * q^5 - 20 * q^8 - 15 * q^9 - 7 * q^10 - 3 * q^11 + 63 * q^12 + 14 * q^13 - 12 * q^15 + 18 * q^16 - 14 * q^17 + 2 * q^18 - 21 * q^19 - 14 * q^20 - 20 * q^22 - 27 * q^23 + 77 * q^24 + 17 * q^25 + 21 * q^26 - 7 * q^27 + 12 * q^29 + 11 * q^30 - 35 * q^31 - 60 * q^32 - 7 * q^33 - 70 * q^34 - 12 * q^36 - 6 * q^37 - 35 * q^38 + 35 * q^39 - 105 * q^40 + 42 * q^41 - 30 * q^43 + 13 * q^44 + 35 * q^45 + 69 * q^46 + 42 * q^47 + 84 * q^48 + 40 * q^50 + 53 * q^51 + 7 * q^52 - 31 * q^53 - 70 * q^54 + 7 * q^55 - 12 * q^57 - 47 * q^58 - 35 * q^59 - 91 * q^60 + 14 * q^61 + 28 * q^62 - 32 * q^64 + 35 * q^65 + 35 * q^66 + 11 * q^67 - 77 * q^68 - 70 * q^69 + 19 * q^71 - 124 * q^72 + 35 * q^73 + 13 * q^74 + 119 * q^75 - 119 * q^76 + 28 * q^78 + 15 * q^79 - 70 * q^80 - 125 * q^81 + 98 * q^82 - 26 * q^85 + 9 * q^86 - 35 * q^87 + 49 * q^88 + 14 * q^89 + 182 * q^90 - 38 * q^92 + 46 * q^93 - 14 * q^94 + 128 * q^95 - 98 * q^96 - 16 * q^99

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