LMFDB - Embedded newform 343.2.g.h.116.4

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			116.4
Character	$\chi$	$=$	343.116
Dual form			343.2.g.h.275.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.137969 + 1.84107i) q^{2} +(-1.49877 - 0.462308i) q^{3} +(-1.39283 + 0.209936i) q^{4} +(-1.02018 + 0.946588i) q^{5} +(0.644358 - 2.82312i) q^{6} +(0.242977 + 1.06455i) q^{8} +(-0.446142 - 0.304175i) q^{9} +O(q^{10})$	\(q+(0.137969 + 1.84107i) q^{2} +(-1.49877 - 0.462308i) q^{3} +(-1.39283 + 0.209936i) q^{4} +(-1.02018 + 0.946588i) q^{5} +(0.644358 - 2.82312i) q^{6} +(0.242977 + 1.06455i) q^{8} +(-0.446142 - 0.304175i) q^{9} +(-1.88349 - 1.74762i) q^{10} +(-2.38230 + 1.62423i) q^{11} +(2.18458 + 0.329273i) q^{12} +(-4.03898 - 1.94507i) q^{13} +(1.96663 - 0.947078i) q^{15} +(-4.61836 + 1.42457i) q^{16} +(-0.176220 - 0.449001i) q^{17} +(0.498452 - 0.863344i) q^{18} +(-1.90688 - 3.30281i) q^{19} +(1.22222 - 1.53261i) q^{20} +(-3.31899 - 4.16188i) q^{22} +(2.48708 - 6.33698i) q^{23} +(0.127985 - 1.70784i) q^{24} +(-0.228914 + 3.05464i) q^{25} +(3.02375 - 7.70439i) q^{26} +(3.46178 + 4.34093i) q^{27} +(1.45010 - 1.81836i) q^{29} +(2.01497 + 3.49003i) q^{30} +(-3.94134 + 6.82660i) q^{31} +(-2.46207 - 6.27326i) q^{32} +(4.32141 - 1.33298i) q^{33} +(0.802329 - 0.386381i) q^{34} +(0.685258 + 0.330003i) q^{36} +(-9.48212 - 1.42920i) q^{37} +(5.81760 - 3.96637i) q^{38} +(5.15426 + 4.78246i) q^{39} +(-1.25557 - 0.856034i) q^{40} +(1.56272 + 6.84673i) q^{41} +(0.546589 - 2.39476i) q^{43} +(2.97716 - 2.76240i) q^{44} +(0.743073 - 0.112000i) q^{45} +(12.0099 + 3.70458i) q^{46} +(0.836981 + 11.1687i) q^{47} +7.58043 q^{48} -5.65538 q^{50} +(0.0565357 + 0.754416i) q^{51} +(6.03395 + 1.86123i) q^{52} +(-5.30755 + 0.799985i) q^{53} +(-7.51433 + 6.97228i) q^{54} +(0.892902 - 3.91206i) q^{55} +(1.33105 + 5.83170i) q^{57} +(3.54780 + 2.41885i) q^{58} +(2.74408 + 2.54613i) q^{59} +(-2.54036 + 1.73198i) q^{60} +(0.0400051 + 0.00602980i) q^{61} +(-13.1120 - 6.31441i) q^{62} +(2.50091 - 1.20437i) q^{64} +(5.96166 - 1.83893i) q^{65} +(3.05032 + 7.77209i) q^{66} +(-0.534751 + 0.926216i) q^{67} +(0.339706 + 0.588388i) q^{68} +(-6.65719 + 8.34785i) q^{69} +(4.21712 + 5.28810i) q^{71} +(0.215407 - 0.548848i) q^{72} +(0.613480 - 8.18632i) q^{73} +(1.32301 - 17.6544i) q^{74} +(1.75527 - 4.47236i) q^{75} +(3.34933 + 4.19993i) q^{76} +(-8.09370 + 10.1492i) q^{78} +(6.91827 + 11.9828i) q^{79} +(3.36307 - 5.82500i) q^{80} +(-2.58973 - 6.59853i) q^{81} +(-12.3897 + 3.82171i) q^{82} +(0.465572 - 0.224208i) q^{83} +(0.604795 + 0.291254i) q^{85} +(4.48433 + 0.675905i) q^{86} +(-3.01400 + 2.05491i) q^{87} +(-2.30791 - 2.14143i) q^{88} +(-0.648563 - 0.442183i) q^{89} +(0.308721 + 1.35260i) q^{90} +(-2.13373 + 9.34846i) q^{92} +(9.06315 - 8.40937i) q^{93} +(-20.4469 + 3.08188i) q^{94} +(5.07175 + 1.56443i) q^{95} +(0.789894 + 10.5404i) q^{96} -9.61207 q^{97} +1.55689 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 $\left(\mathbb{Z}/343\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{21}\right)$

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 $

$2$	0.137969	+	1.84107i	0.0975588	+	1.30183i	0.804242	+	0.594301i	$0.202571\pi$
$2$	0.137969	+	1.84107i	0.0975588	+	1.30183i	−0.706684	+	0.707530i	$0.749810\pi$
$3$	−1.49877	−	0.462308i	−0.865314	−	0.266914i	−0.169845	−	0.985471i	$-0.554327\pi$
$3$	−1.49877	−	0.462308i	−0.865314	−	0.266914i	−0.695468	+	0.718557i	$0.744803\pi$
$4$	−1.39283	+	0.209936i	−0.696416	+	0.104968i
$5$	−1.02018	+	0.946588i	−0.456238	+	0.423327i	−0.874520	−	0.484990i	$-0.838823\pi$
$5$	−1.02018	+	0.946588i	−0.456238	+	0.423327i	0.418281	+	0.908318i	$0.362633\pi$
$6$	0.644358	−	2.82312i	0.263058	−	1.15253i
$7$		0			0
$7$		0			0
$8$	0.242977	+	1.06455i	0.0859052	+	0.376375i
$9$	−0.446142	−	0.304175i	−0.148714	−	0.101392i
$10$	−1.88349	−	1.74762i	−0.595611	−	0.552646i
$11$	−2.38230	+	1.62423i	−0.718291	+	0.489722i	−0.866464	−	0.499239i	$-0.833613\pi$
$11$	−2.38230	+	1.62423i	−0.718291	+	0.489722i	0.148173	+	0.988961i	$0.452661\pi$
$12$	2.18458	+	0.329273i	0.630635	+	0.0950530i
$13$	−4.03898	−	1.94507i	−1.12021	−	0.539465i	−0.220253	−	0.975443i	$-0.570688\pi$
$13$	−4.03898	−	1.94507i	−1.12021	−	0.539465i	−0.899957	+	0.435978i	$0.856403\pi$
$14$		0			0
$15$	1.96663	−	0.947078i	0.507781	−	0.244534i
$16$	−4.61836	+	1.42457i	−1.15459	+	0.356144i
$17$	−0.176220	−	0.449001i	−0.0427396	−	0.108899i	0.907910	−	0.419165i	$-0.137677\pi$
$17$	−0.176220	−	0.449001i	−0.0427396	−	0.108899i	−0.950650	+	0.310266i	$0.899582\pi$
$18$	0.498452	−	0.863344i	0.117486	−	0.203492i
$19$	−1.90688	−	3.30281i	−0.437467	−	0.757716i	0.560026	−	0.828475i	$-0.310791\pi$
$19$	−1.90688	−	3.30281i	−0.437467	−	0.757716i	−0.997493	+	0.0707594i	$0.977458\pi$
$20$	1.22222	−	1.53261i	0.273296	−	0.342702i
$21$		0			0
$22$	−3.31899	−	4.16188i	−0.707611	−	0.887317i
$23$	2.48708	−	6.33698i	0.518592	−	1.32135i	−0.396474	−	0.918046i	$-0.629766\pi$
$23$	2.48708	−	6.33698i	0.518592	−	1.32135i	0.915066	−	0.403305i	$-0.132139\pi$
$24$	0.127985	−	1.70784i	0.0261249	−	0.348612i
$25$	−0.228914	+	3.05464i	−0.0457827	+	0.610928i
$26$	3.02375	−	7.70439i	0.593006	−	1.51095i
$27$	3.46178	+	4.34093i	0.666219	+	0.835413i
$28$		0			0
$29$	1.45010	−	1.81836i	0.269276	−	0.337662i	−0.628747	−	0.777610i	$-0.716432\pi$
$29$	1.45010	−	1.81836i	0.269276	−	0.337662i	0.898023	+	0.439948i	$0.145003\pi$
$30$	2.01497	+	3.49003i	0.367881	+	0.637189i
$31$	−3.94134	+	6.82660i	−0.707885	+	1.22609i	0.257755	+	0.966210i	$0.417017\pi$
$31$	−3.94134	+	6.82660i	−0.707885	+	1.22609i	−0.965640	+	0.259883i	$0.916316\pi$
$32$	−2.46207	−	6.27326i	−0.435237	−	1.10897i
$33$	4.32141	−	1.33298i	0.752261	−	0.232042i
$34$	0.802329	−	0.386381i	0.137598	−	0.0662638i
$35$		0			0
$36$	0.685258	+	0.330003i	0.114210	+	0.0550005i
$37$	−9.48212	−	1.42920i	−1.55885	−	0.234959i	−0.687707	−	0.725988i	$-0.741383\pi$
$37$	−9.48212	−	1.42920i	−1.55885	−	0.234959i	−0.871143	+	0.491029i	$0.836621\pi$
$38$	5.81760	−	3.96637i	0.943739	−	0.643430i
$39$	5.15426	+	4.78246i	0.825343	+	0.765806i
$40$	−1.25557	−	0.856034i	−0.198523	−	0.135351i
$41$	1.56272	+	6.84673i	0.244056	+	1.06928i	0.937286	+	0.348562i	$0.113330\pi$
$41$	1.56272	+	6.84673i	0.244056	+	1.06928i	−0.693230	+	0.720717i	$0.743813\pi$
$42$		0			0
$43$	0.546589	−	2.39476i	0.0833541	−	0.365198i	−0.915998	−	0.401182i	$-0.868599\pi$
$43$	0.546589	−	2.39476i	0.0833541	−	0.365198i	0.999352	+	0.0359841i	$0.0114566\pi$
$44$	2.97716	−	2.76240i	0.448824	−	0.416448i
$45$	0.743073	−	0.112000i	0.110771	−	0.0166960i
$46$	12.0099	+	3.70458i	1.77077	+	0.546210i
$47$	0.836981	+	11.1687i	0.122086	+	1.62913i	0.636283	+	0.771455i	$0.280471\pi$
$47$	0.836981	+	11.1687i	0.122086	+	1.62913i	−0.514197	+	0.857672i	$0.671910\pi$
$48$	7.58043			1.09414
$49$		0			0
$50$	−5.65538			−0.799791
$51$	0.0565357	+	0.754416i	0.00791658	+	0.105639i
$52$	6.03395	+	1.86123i	0.836759	+	0.258106i
$53$	−5.30755	+	0.799985i	−0.729049	+	0.109886i	−0.503070	−	0.864246i	$-0.667796\pi$
$53$	−5.30755	+	0.799985i	−0.729049	+	0.109886i	−0.225979	+	0.974132i	$0.572558\pi$
$54$	−7.51433	+	6.97228i	−1.02257	+	0.948807i
$55$	0.892902	−	3.91206i	0.120399	−	0.527502i
$56$		0			0
$57$	1.33105	+	5.83170i	0.176302	+	0.772428i
$58$	3.54780	+	2.41885i	0.465849	+	0.317610i
$59$	2.74408	+	2.54613i	0.357248	+	0.331478i	0.838295	−	0.545217i	$-0.183553\pi$
$59$	2.74408	+	2.54613i	0.357248	+	0.331478i	−0.481047	+	0.876695i	$0.659743\pi$
$60$	−2.54036	+	1.73198i	−0.327958	+	0.223598i
$61$	0.0400051	+	0.00602980i	0.00512213	+	0.000772036i	0.151603	−	0.988441i	$-0.451557\pi$
$61$	0.0400051	+	0.00602980i	0.00512213	+	0.000772036i	−0.146481	+	0.989214i	$0.546795\pi$
$62$	−13.1120	−	6.31441i	−1.66523	−	0.801931i
$63$		0			0
$64$	2.50091	−	1.20437i	0.312614	−	0.150547i
$65$	5.96166	−	1.83893i	0.739453	−	0.228091i
$66$	3.05032	+	7.77209i	0.375469	+	0.956679i
$67$	−0.534751	+	0.926216i	−0.0653302	+	0.113155i	−0.896840	−	0.442354i	$-0.854143\pi$
$67$	−0.534751	+	0.926216i	−0.0653302	+	0.113155i	0.831510	+	0.555509i	$0.187477\pi$
$68$	0.339706	+	0.588388i	0.0411954	+	0.0713525i
$69$	−6.65719	+	8.34785i	−0.801432	+	1.00496i
$70$		0			0
$71$	4.21712	+	5.28810i	0.500480	+	0.627582i	0.966337	−	0.257278i	$-0.0828256\pi$
$71$	4.21712	+	5.28810i	0.500480	+	0.627582i	−0.465858	+	0.884860i	$0.654254\pi$
$72$	0.215407	−	0.548848i	0.0253860	−	0.0646824i
$73$	0.613480	−	8.18632i	0.0718024	−	0.958137i	−0.838690	−	0.544610i	$-0.816678\pi$
$73$	0.613480	−	8.18632i	0.0718024	−	0.958137i	0.910492	−	0.413527i	$-0.135703\pi$
$74$	1.32301	−	17.6544i	0.153797	−	2.05228i
$75$	1.75527	−	4.47236i	0.202682	−	0.516424i
$76$	3.34933	+	4.19993i	0.384195	+	0.481765i
$77$		0			0
$78$	−8.09370	+	10.1492i	−0.916431	+	1.14917i
$79$	6.91827	+	11.9828i	0.778366	+	1.34817i	0.932883	+	0.360180i	$0.117285\pi$
$79$	6.91827	+	11.9828i	0.778366	+	1.34817i	−0.154517	+	0.987990i	$0.549382\pi$
$80$	3.36307	−	5.82500i	0.376002	−	0.651255i
$81$	−2.58973	−	6.59853i	−0.287748	−	0.733170i
$82$	−12.3897	+	3.82171i	−1.36821	+	0.422037i
$83$	0.465572	−	0.224208i	0.0511032	−	0.0246100i	−0.408158	−	0.912911i	$-0.633829\pi$
$83$	0.465572	−	0.224208i	0.0511032	−	0.0246100i	0.459261	+	0.888301i	$0.348114\pi$
$84$		0			0
$85$	0.604795	+	0.291254i	0.0655993	+	0.0315909i
$86$	4.48433	+	0.675905i	0.483558	+	0.0728847i
$87$	−3.01400	+	2.05491i	−0.323135	+	0.220310i
$88$	−2.30791	−	2.14143i	−0.246024	−	0.228277i
$89$	−0.648563	−	0.442183i	−0.0687475	−	0.0468713i	0.528459	−	0.848959i	$-0.322770\pi$
$89$	−0.648563	−	0.442183i	−0.0687475	−	0.0468713i	−0.597206	+	0.802088i	$0.703723\pi$
$90$	0.308721	+	1.35260i	0.0325421	+	0.142576i
$91$		0			0
$92$	−2.13373	+	9.34846i	−0.222456	+	0.974645i
$93$	9.06315	−	8.40937i	0.939804	−	0.872011i
$94$	−20.4469	+	3.08188i	−2.10894	+	0.317871i
$95$	5.07175	+	1.56443i	0.520351	+	0.160507i
$96$	0.789894	+	10.5404i	0.0806182	+	1.07578i
$97$	−9.61207			−0.975958			−0.487979	−	0.872855i	$-0.662266\pi$
$97$	−9.61207			−0.975958			−0.487979	+	0.872855i	$0.662266\pi$
$98$		0			0
$99$	1.55689			0.156474
$100$	−0.322439	−	4.30265i	−0.0322439	−	0.430265i
$101$	6.26182	+	1.93151i	0.623074	+	0.192193i	0.590188	−	0.807266i	$-0.299054\pi$
$101$	6.26182	+	1.93151i	0.623074	+	0.192193i	0.0328866	+	0.999459i	$0.489530\pi$
$102$	−1.38113	+	0.208172i	−0.136752	+	0.0206121i
$103$	−1.82240	+	1.69094i	−0.179566	+	0.166613i	−0.764835	−	0.644226i	$-0.777179\pi$
$103$	−1.82240	+	1.69094i	−0.179566	+	0.166613i	0.585269	+	0.810839i	$0.300989\pi$
$104$	1.08925	−	4.77230i	0.106809	−	0.467962i
$105$		0			0
$106$	−2.20510	−	9.66119i	−0.214179	−	0.938378i
$107$	2.26405	+	1.54360i	0.218874	+	0.149226i	0.667794	−	0.744346i	$-0.267239\pi$
$107$	2.26405	+	1.54360i	0.218874	+	0.149226i	−0.448920	+	0.893572i	$0.648191\pi$
$108$	−5.73299	−	5.31943i	−0.551657	−	0.511863i
$109$	−3.90673	+	2.66357i	−0.374197	+	0.255123i	−0.735786	−	0.677215i	$-0.763187\pi$
$109$	−3.90673	+	2.66357i	−0.374197	+	0.255123i	0.361589	+	0.932338i	$0.382235\pi$
$110$	7.32556	+	1.10415i	0.698465	+	0.105277i
$111$	13.5508	+	6.52570i	1.28618	+	0.619392i
$112$		0			0
$113$	−13.4971	+	6.49986i	−1.26970	+	0.611456i	−0.942723	−	0.333577i	$-0.891744\pi$
$113$	−13.4971	+	6.49986i	−1.26970	+	0.611456i	−0.326977	+	0.945032i	$0.606030\pi$
$114$	−10.5529	+	3.25514i	−0.988371	+	0.304872i
$115$	3.46124	+	8.81909i	0.322762	+	0.822385i
$116$	−1.63800	+	2.83710i	−0.152085	+	0.263418i
$117$	1.21032	+	2.09633i	0.111894	+	0.193806i
$118$	−4.30900	+	5.40331i	−0.396675	+	0.497415i
$119$		0			0
$120$	1.48606	+	1.86346i	0.135658	+	0.170109i
$121$	−0.981500	+	2.50082i	−0.0892273	+	0.227347i
$122$	−0.00558180	+	0.0744840i	−0.000505353	+	0.00674346i
$123$	0.823145	−	10.9841i	0.0742205	−	0.990404i
$124$	4.05647	−	10.3357i	0.364282	−	0.928176i
$125$	−6.99647	−	8.77330i	−0.625783	−	0.784707i
$126$		0			0
$127$	5.35179	−	6.71094i	0.474895	−	0.595499i	−0.485467	−	0.874255i	$-0.661350\pi$
$127$	5.35179	−	6.71094i	0.474895	−	0.595499i	0.960362	+	0.278756i	$0.0899219\pi$
$128$	−4.17673	−	7.23431i	−0.369174	−	0.639429i
$129$	−1.92633	+	3.33650i	−0.169604	+	0.293763i
$130$	4.20812	+	10.7221i	0.369076	+	0.940391i
$131$	8.45061	−	2.60667i	0.738333	−	0.227746i	0.0972958	−	0.995256i	$-0.468981\pi$
$131$	8.45061	−	2.60667i	0.738333	−	0.227746i	0.641037	+	0.767510i	$0.278505\pi$
$132$	−5.73915	+	2.76383i	−0.499529	+	0.240561i
$133$		0			0
$134$	−1.77900	−	0.856723i	−0.153683	−	0.0740096i
$135$	−7.64071	−	1.15165i	−0.657608	−	0.0991184i
$136$	0.435167	−	0.296692i	0.0373153	−	0.0254411i
$137$	4.14733	+	3.84816i	0.354330	+	0.328770i	0.837175	−	0.546936i	$-0.184206\pi$
$137$	4.14733	+	3.84816i	0.354330	+	0.328770i	−0.482844	+	0.875706i	$0.660396\pi$
$138$	−16.2874	−	11.1046i	−1.38648	−	0.945286i
$139$	−0.696319	−	3.05077i	−0.0590610	−	0.258763i	0.936774	−	0.349934i	$-0.113796\pi$
$139$	−0.696319	−	3.05077i	−0.0590610	−	0.258763i	−0.995835	+	0.0911712i	$0.970939\pi$
$140$		0			0
$141$	3.90896	−	17.1263i	0.329194	−	1.44229i
$142$	−9.15391	+	8.49359i	−0.768179	+	0.712766i
$143$	12.7813	−	1.92647i	1.06883	−	0.161099i
$144$	2.49376	+	0.769224i	0.207814	+	0.0641020i
$145$	0.241883	+	3.22770i	0.0200873	+	0.268046i
$146$	15.1562			1.25434
$147$		0			0
$148$	13.5070			1.11027
$149$	−0.148393	−	1.98017i	−0.0121569	−	0.162222i	−0.999978	−	0.00662853i	$-0.997890\pi$
$149$	−0.148393	−	1.98017i	−0.0121569	−	0.162222i	0.987821	−	0.155593i	$-0.0497290\pi$
$150$	8.47609	+	2.61453i	0.692070	+	0.213475i
$151$	11.6101	−	1.74994i	0.944815	−	0.142408i	0.341474	−	0.939891i	$-0.389074\pi$
$151$	11.6101	−	1.74994i	0.944815	−	0.142408i	0.603341	+	0.797483i	$0.293836\pi$
$152$	3.05268	−	2.83247i	0.247605	−	0.229744i
$153$	−0.0579556	+	0.253920i	−0.00468543	+	0.0205282i
$154$		0			0
$155$	−2.44111	−	10.6952i	−0.196074	−	0.859058i
$156$	−8.18303	−	5.57909i	−0.655167	−	0.446685i
$157$	−9.29209	−	8.62180i	−0.741589	−	0.688094i	0.215948	−	0.976405i	$-0.430716\pi$
$157$	−9.29209	−	8.62180i	−0.741589	−	0.688094i	−0.957537	+	0.288311i	$0.906906\pi$
$158$	−21.1066	+	14.3903i	−1.67915	+	1.14483i
$159$	8.32463	+	1.25474i	0.660186	+	0.0995070i
$160$	8.44996	+	4.06928i	0.668028	+	0.321705i
$161$		0			0
$162$	11.7910	−	5.67826i	0.926391	−	0.446126i
$163$	4.23432	−	1.30612i	0.331658	−	0.102303i	−0.124454	−	0.992225i	$-0.539718\pi$
$163$	4.23432	−	1.30612i	0.331658	−	0.102303i	0.456112	+	0.889922i	$0.349242\pi$
$164$	−3.61398	−	9.20827i	−0.282204	−	0.719045i
$165$	−3.14683	+	5.45047i	−0.244981	+	0.424319i
$166$	0.477016	+	0.826216i	0.0370236	+	0.0641268i
$167$	10.0522	−	12.6051i	0.777864	−	0.975411i	−0.222136	−	0.975016i	$-0.571303\pi$
$167$	10.0522	−	12.6051i	0.777864	−	0.975411i	1.00000		0.000394933i	$-0.000125711\pi$
$168$		0			0
$169$	4.42467	+	5.54837i	0.340360	+	0.426797i
$170$	−0.452775	+	1.15365i	−0.0347263	+	0.0884811i
$171$	−0.153892	+	2.05354i	−0.0117684	+	0.157038i
$172$	−0.258561	+	3.45025i	−0.0197151	+	0.263079i
$173$	7.62757	−	19.4347i	0.579914	−	1.47760i	−0.276350	−	0.961057i	$-0.589125\pi$
$173$	7.62757	−	19.4347i	0.579914	−	1.47760i	0.856264	−	0.516539i	$-0.172780\pi$
$174$	−4.19907	−	5.26547i	−0.318331	−	0.399174i
$175$		0			0
$176$	8.68849	−	10.8950i	0.654919	−	0.821243i
$177$	−2.93563	−	5.08467i	−0.220656	−	0.382187i
$178$	0.724606	−	1.25505i	0.0543115	−	0.0940703i
$179$	−1.16205	−	2.96085i	−0.0868555	−	0.221304i	0.880846	−	0.473403i	$-0.156974\pi$
$179$	−1.16205	−	2.96085i	−0.0868555	−	0.221304i	−0.967702	+	0.252099i	$0.918879\pi$
$180$	−1.01146	+	0.311995i	−0.0753900	+	0.0232547i
$181$	15.2545	−	7.34617i	1.13386	−	0.546036i	0.229710	−	0.973259i	$-0.426222\pi$
$181$	15.2545	−	7.34617i	1.13386	−	0.546036i	0.904146	+	0.427223i	$0.140508\pi$
$182$		0			0
$183$	−0.0571707	−	0.0275320i	−0.00422618	−	0.00203522i
$184$	7.35033	+	1.10788i	0.541874	+	0.0816743i
$185$	11.0263	−	7.51762i	0.810672	−	0.552707i
$186$	16.7326	+	15.5256i	1.22690	+	1.13839i
$187$	1.14909	+	0.783435i	0.0840297	+	0.0572905i
$188$	−3.51049	−	15.3805i	−0.256029	−	1.12173i
$189$		0			0
$190$	−2.18047	+	9.55328i	−0.158188	+	0.693068i
$191$	−10.3792	+	9.63045i	−0.751010	+	0.696835i	−0.959662	−	0.281155i	$-0.909283\pi$
$191$	−10.3792	+	9.63045i	−0.751010	+	0.696835i	0.208653	+	0.977990i	$0.433092\pi$
$192$	−4.30507	+	0.648885i	−0.310692	+	0.0468293i
$193$	−14.2403	−	4.39254i	−1.02504	−	0.316182i	−0.263746	−	0.964592i	$-0.584958\pi$
$193$	−14.2403	−	4.39254i	−1.02504	−	0.316182i	−0.761291	+	0.648410i	$0.775434\pi$
$194$	−1.32617	−	17.6965i	−0.0952133	−	1.27053i
$195$	−9.78530			−0.700740
$196$		0			0
$197$	−18.8819			−1.34528			−0.672639	−	0.739971i	$-0.734839\pi$
$197$	−18.8819			−1.34528			−0.672639	+	0.739971i	$0.734839\pi$
$198$	0.214803	+	2.86634i	0.0152654	+	0.203702i
$199$	−7.74578	−	2.38926i	−0.549084	−	0.169370i	0.00778589	−	0.999970i	$-0.497522\pi$
$199$	−7.74578	−	2.38926i	−0.549084	−	0.169370i	−0.556870	+	0.830600i	$0.687998\pi$
$200$	−3.30744	+	0.498516i	−0.233871	+	0.0352504i
$201$	1.22966	−	1.14096i	0.0867338	−	0.0804772i
$202$	−2.69211	+	11.7949i	−0.189416	+	0.829887i
$203$		0			0
$204$	−0.237123	−	1.03891i	−0.0166020	−	0.0727380i
$205$	−8.07529	−	5.50564i	−0.564003	−	0.384531i
$206$	−3.36456	−	3.12186i	−0.234420	−	0.217510i
$207$	−3.03714	+	2.07069i	−0.211096	+	0.143923i
$208$	21.4243	+	3.22920i	1.48551	+	0.223905i
$209$	9.90725	+	4.77108i	0.685299	+	0.330023i
$210$		0			0
$211$	−5.64480	+	2.71839i	−0.388604	+	0.187142i	−0.617976	−	0.786197i	$-0.712047\pi$
$211$	−5.64480	+	2.71839i	−0.388604	+	0.187142i	0.229372	+	0.973339i	$0.426333\pi$
$212$	7.22458	−	2.22849i	0.496186	−	0.153053i
$213$	−3.87575	−	9.87524i	−0.265562	−	0.676640i
$214$	−2.52951	+	4.38124i	−0.172914	+	0.299495i
$215$	1.70924	+	2.96048i	0.116569	+	0.201903i
$216$	−3.78001	+	4.73998i	−0.257197	+	0.322515i
$217$		0			0
$218$	−5.44281	−	6.82507i	−0.368634	−	0.462252i
$219$	−4.70407	+	11.9858i	−0.317872	+	0.809924i
$220$	−0.422382	+	5.63629i	−0.0284770	+	0.379999i
$221$	−0.161590	+	2.15627i	−0.0108697	+	0.145046i
$222$	−10.1447	+	25.8482i	−0.680866	+	1.73482i
$223$	−6.36466	−	7.98103i	−0.426209	−	0.534449i	0.521641	−	0.853165i	$-0.325320\pi$
$223$	−6.36466	−	7.98103i	−0.426209	−	0.534449i	−0.947850	+	0.318716i	$0.896749\pi$
$224$		0			0
$225$	1.03127	−	1.29317i	0.0687514	−	0.0862116i
$226$	−13.8289	−	23.9523i	−0.919882	−	1.59328i
$227$	−13.2110	+	22.8821i	−0.876842	+	1.51874i	−0.0220553	+	0.999757i	$0.507021\pi$
$227$	−13.2110	+	22.8821i	−0.876842	+	1.51874i	−0.854787	+	0.518979i	$0.826312\pi$
$228$	−3.07821	−	7.84314i	−0.203859	−	0.519425i
$229$	−22.8543	+	7.04962i	−1.51026	+	0.465852i	−0.935755	−	0.352651i	$-0.885280\pi$
$229$	−22.8543	+	7.04962i	−1.51026	+	0.465852i	−0.574501	+	0.818504i	$0.694804\pi$
$230$	−15.7590	+	7.58914i	−1.03912	+	0.500413i
$231$		0			0
$232$	2.28808	+	1.10188i	0.150220	+	0.0723420i
$233$	19.0035	+	2.86431i	1.24496	+	0.187647i	0.738284	−	0.674490i	$-0.235637\pi$
$233$	19.0035	+	2.86431i	1.24496	+	0.187647i	0.506674	+	0.862137i	$0.330875\pi$
$234$	−3.69250	+	2.51750i	−0.241386	+	0.164574i
$235$	−11.4261	−	10.6018i	−0.745354	−	0.691588i
$236$	−4.35656	−	2.97025i	−0.283588	−	0.193347i
$237$	−4.82913	−	21.1578i	−0.313686	−	1.37435i
$238$		0			0
$239$	0.0104807	−	0.0459188i	0.000677938	−	0.00297024i	−0.974588	−	0.224006i	$-0.928087\pi$
$239$	0.0104807	−	0.0459188i	0.000677938	−	0.00297024i	0.975266	+	0.221036i	$0.0709437\pi$
$240$	−7.73340	+	7.17555i	−0.499189	+	0.463180i
$241$	1.05291	−	0.158700i	0.0678236	−	0.0102228i	−0.115043	−	0.993361i	$-0.536701\pi$
$241$	1.05291	−	0.158700i	0.0678236	−	0.0102228i	0.182866	+	0.983138i	$0.441462\pi$
$242$	−4.73960	−	1.46197i	−0.304673	−	0.0939791i
$243$	−0.413913	−	5.52329i	−0.0265525	−	0.354319i
$244$	−0.0569862			−0.00364817
$245$		0			0
$246$	20.3361			1.29658
$247$	1.27764	+	17.0490i	0.0812945	+	1.08480i
$248$	−8.22491	−	2.53705i	−0.522282	−	0.161103i
$249$	−0.801437	+	0.120797i	−0.0507890	+	0.00765521i
$250$	15.1869	−	14.0914i	0.960506	−	0.891219i
$251$	−5.44054	+	23.8365i	−0.343404	+	1.50455i	0.448433	+	0.893816i	$0.351982\pi$
$251$	−5.44054	+	23.8365i	−0.343404	+	1.50455i	−0.791837	+	0.610733i	$0.790875\pi$
$252$		0			0
$253$	4.36770	+	19.1362i	0.274595	+	1.20308i
$254$	13.0937	+	8.92711i	0.821570	+	0.560137i
$255$	−0.771798	−	0.716124i	−0.0483319	−	0.0448454i
$256$	17.3295	−	11.8151i	1.08310	−	0.738443i
$257$	−9.66984	−	1.45749i	−0.603188	−	0.0909160i	−0.159653	−	0.987173i	$-0.551038\pi$
$257$	−9.66984	−	1.45749i	−0.603188	−	0.0909160i	−0.443535	+	0.896257i	$0.646276\pi$
$258$	−6.40850	−	3.08617i	−0.398976	−	0.192137i
$259$		0			0
$260$	−7.91753	+	3.81288i	−0.491025	+	0.236465i
$261$	−1.20005	+	0.370166i	−0.0742812	+	0.0229127i
$262$	5.96497	+	15.1985i	0.368517	+	0.938966i
$263$	7.86423	−	13.6213i	0.484929	−	0.839922i	−0.514921	−	0.857238i	$-0.672179\pi$
$263$	7.86423	−	13.6213i	0.484929	−	0.839922i	0.999850	+	0.0173155i	$0.00551197\pi$
$264$	2.46902	+	4.27647i	0.151958	+	0.263199i
$265$	4.65740	−	5.84020i	0.286102	−	0.358761i
$266$		0			0
$267$	0.767620	+	0.962565i	0.0469776	+	0.0589080i
$268$	0.550372	−	1.40233i	0.0336193	−	0.0856607i
$269$	0.883178	−	11.7852i	0.0538483	−	0.718556i	−0.903310	−	0.428989i	$-0.858870\pi$
$269$	0.883178	−	11.7852i	0.0538483	−	0.718556i	0.957158	−	0.289567i	$-0.0935111\pi$
$270$	1.06609	−	14.2260i	0.0648800	−	0.865764i
$271$	−8.86531	+	22.5884i	−0.538529	+	1.37215i	0.359883	+	0.932997i	$0.382816\pi$
$271$	−8.86531	+	22.5884i	−0.538529	+	1.37215i	−0.898413	+	0.439152i	$0.855279\pi$
$272$	1.45348	+	1.82261i	0.0881303	+	0.110512i
$273$		0			0
$274$	−6.51252	+	8.16644i	−0.393436	+	0.493353i
$275$	−4.41608	−	7.64888i	−0.266300	−	0.461245i
$276$	7.51983	−	13.0247i	0.452641	−	0.783997i
$277$	−1.11662	−	2.84510i	−0.0670912	−	0.170945i	0.893396	−	0.449270i	$-0.148316\pi$
$277$	−1.11662	−	2.84510i	−0.0670912	−	0.170945i	−0.960487	+	0.278325i	$0.910221\pi$
$278$	5.52061	−	1.70288i	0.331104	−	0.102132i
$279$	3.83488	−	1.84678i	0.229588	−	0.110564i
$280$		0			0
$281$	−3.77618	−	1.81851i	−0.225268	−	0.108483i	0.317846	−	0.948142i	$-0.397041\pi$
$281$	−3.77618	−	1.81851i	−0.225268	−	0.108483i	−0.543114	+	0.839659i	$0.682755\pi$
$282$	32.0699	+	4.83377i	1.90974	+	0.287847i
$283$	0.927361	−	0.632264i	0.0551259	−	0.0375842i	−0.535444	−	0.844571i	$-0.679856\pi$
$283$	0.927361	−	0.632264i	0.0551259	−	0.0375842i	0.590569	+	0.806987i	$0.298903\pi$
$284$	−6.98389	−	6.48011i	−0.414418	−	0.384524i
$285$	−6.87813	−	4.68943i	−0.407425	−	0.277778i
$286$	5.31018	+	23.2654i	0.313998	+	1.37571i
$287$		0			0
$288$	−0.809732	+	3.54767i	−0.0477139	+	0.209048i
$289$	12.2913	−	11.4047i	0.723020	−	0.670864i
$290$	−5.90905	+	0.890645i	−0.346991	+	0.0523005i
$291$	14.4063	+	4.44374i	0.844510	+	0.260497i
$292$	0.864126	+	11.5310i	0.0505691	+	0.674798i
$293$	−21.7602			−1.27124			−0.635621	−	0.772001i	$-0.719256\pi$
$293$	−21.7602			−1.27124			−0.635621	+	0.772001i	$0.719256\pi$
$294$		0			0
$295$	−5.20959			−0.303314
$296$	−0.782479	−	10.4415i	−0.0454806	−	0.606897i
$297$	−15.2976	−	4.71870i	−0.887659	−	0.273807i
$298$	3.62516	−	0.546404i	0.210000	−	0.0316524i
$299$	−22.3711	+	20.7574i	−1.29375	+	1.20043i
$300$	−1.50589	+	6.59774i	−0.0869427	+	0.380921i
$301$		0			0
$302$	4.82359	+	21.1335i	0.277566	+	1.21610i
$303$	−8.49205	−	5.78978i	−0.487856	−	0.332614i
$304$	13.5117	+	12.5370i	0.774950	+	0.719049i
$305$	−0.0465201	+	0.0317169i	−0.00266373	+	0.00181610i
$306$	−0.475480	−	0.0716671i	−0.0271814	−	0.00409693i
$307$	18.9973	+	9.14861i	1.08423	+	0.522139i	0.888668	−	0.458552i	$-0.151632\pi$
$307$	18.9973	+	9.14861i	1.08423	+	0.522139i	0.195565	+	0.980691i	$0.437346\pi$
$308$		0			0
$309$	3.51308	−	1.69181i	0.199852	−	0.0962438i
$310$	19.3538	−	5.96984i	1.09922	−	0.339064i
$311$	0.303767	+	0.773985i	0.0172250	+	0.0438887i	0.939228	−	0.343295i	$-0.111543\pi$
$311$	0.303767	+	0.773985i	0.0172250	+	0.0438887i	−0.922003	+	0.387184i	$0.873448\pi$
$312$	−3.83880	+	6.64900i	−0.217329	+	0.376425i
$313$	−5.63256	−	9.75588i	−0.318371	−	0.551435i	0.661777	−	0.749701i	$-0.269802\pi$
$313$	−5.63256	−	9.75588i	−0.318371	−	0.551435i	−0.980148	+	0.198266i	$0.936469\pi$
$314$	14.5913	−	18.2969i	0.823434	−	1.03255i
$315$		0			0
$316$	−12.1516	−	15.2376i	−0.683581	−	0.857183i
$317$	−5.40799	+	13.7793i	−0.303743	+	0.773925i	0.694761	+	0.719241i	$0.255510\pi$
$317$	−5.40799	+	13.7793i	−0.303743	+	0.773925i	−0.998504	+	0.0546836i	$0.982585\pi$
$318$	−1.16151	+	15.4993i	−0.0651344	+	0.869159i
$319$	−0.501135	+	6.68718i	−0.0280581	+	0.374410i
$320$	−1.41133	+	3.59601i	−0.0788957	+	0.201023i
$321$	−2.67966	−	3.36019i	−0.149564	−	0.187548i
$322$		0			0
$323$	−1.14693	+	1.43821i	−0.0638171	+	0.0800241i
$324$	4.99233	+	8.64696i	0.277351	+	0.480387i
$325$	6.86606	−	11.8924i	0.380860	−	0.659670i
$326$	2.98885	+	7.61547i	0.165537	+	0.421782i
$327$	7.08667	−	2.18595i	0.391894	−	0.120883i
$328$	−6.90898	+	3.32719i	−0.381485	+	0.183713i
$329$		0			0
$330$	−10.4689	−	5.04153i	−0.576291	−	0.277527i
$331$	−20.8521	−	3.14295i	−1.14614	−	0.172752i	−0.451607	−	0.892217i	$-0.649149\pi$
$331$	−20.8521	−	3.14295i	−1.14614	−	0.172752i	−0.694529	+	0.719464i	$0.744387\pi$
$332$	−0.601394	+	0.410024i	−0.0330058	+	0.0225030i
$333$	3.79565	+	3.52184i	0.208000	+	0.192996i
$334$	24.5937	+	16.7677i	1.34571	+	0.917488i
$335$	−0.331203	−	1.45110i	−0.0180956	−	0.0792818i
$336$		0			0
$337$	−6.25654	+	27.4117i	−0.340815	+	1.49321i	0.456542	+	0.889702i	$0.349088\pi$
$337$	−6.25654	+	27.4117i	−0.340815	+	1.49321i	−0.797357	+	0.603508i	$0.793769\pi$
$338$	−9.60445	+	8.91163i	−0.522413	+	0.484729i
$339$	23.2340	−	3.50196i	1.26190	−	0.190200i
$340$	−0.903523	−	0.278700i	−0.0490004	−	0.0151146i
$341$	−1.69848	−	22.6646i	−0.0919779	−	1.22736i
$342$	−3.80194			−0.205586
$343$		0			0
$344$	2.68216			0.144612
$345$	−1.11045	−	14.8179i	−0.0597846	−	0.797771i
$346$	36.8330	+	11.3615i	1.98016	+	0.610797i
$347$	0.418101	−	0.0630185i	0.0224448	−	0.00338301i	−0.137810	−	0.990459i	$-0.544006\pi$
$347$	0.418101	−	0.0630185i	0.0224448	−	0.00338301i	0.160255	+	0.987076i	$0.448768\pi$
$348$	3.76660	−	3.49489i	0.201911	−	0.187346i
$349$	−1.67026	+	7.31789i	−0.0894070	+	0.391717i	−0.999755	−	0.0221256i	$-0.992957\pi$
$349$	−1.67026	+	7.31789i	−0.0894070	+	0.391717i	0.910348	+	0.413843i	$0.135814\pi$
$350$		0			0
$351$	−5.53863	−	24.2663i	−0.295630	−	1.29524i
$352$	16.0546	+	10.9458i	0.855713	+	0.583415i
$353$	24.9001	+	23.1039i	1.32530	+	1.22970i	0.953504	+	0.301380i	$0.0974474\pi$
$353$	24.9001	+	23.1039i	1.32530	+	1.22970i	0.371793	+	0.928316i	$0.378743\pi$
$354$	8.95618	−	6.10622i	0.476016	−	0.324542i
$355$	−9.30787	−	1.40294i	−0.494010	−	0.0744601i
$356$	0.996168	+	0.479729i	0.0527968	+	0.0254256i
$357$		0			0
$358$	5.29079	−	2.54791i	0.279627	−	0.134661i
$359$	8.28567	−	2.55579i	0.437301	−	0.134889i	−0.0682849	−	0.997666i	$-0.521753\pi$
$359$	8.28567	−	2.55579i	0.437301	−	0.134889i	0.505586	+	0.862776i	$0.331276\pi$
$360$	0.299779	+	0.763825i	0.0157998	+	0.0402571i
$361$	2.22765	−	3.85840i	0.117245	−	0.203074i
$362$	15.6294	+	27.0710i	0.821465	+	1.42282i
$363$	2.62719	−	3.29439i	0.137892	−	0.172911i
$364$		0			0
$365$	7.12322	+	8.93223i	0.372846	+	0.467534i
$366$	0.0428004	−	0.109054i	0.00223721	−	0.00570033i
$367$	2.47903	−	33.0804i	0.129404	−	1.72678i	−0.434268	−	0.900783i	$-0.642993\pi$
$367$	2.47903	−	33.0804i	0.129404	−	1.72678i	0.563673	−	0.825998i	$-0.309388\pi$
$368$	−2.45873	+	32.8094i	−0.128170	+	1.71031i
$369$	1.38540	−	3.52995i	0.0721213	−	0.183762i
$370$	15.3617	+	19.2630i	0.798619	+	1.00144i
$371$		0			0
$372$	−10.8580	+	13.6155i	−0.562961	+	0.705931i
$373$	3.96993	+	6.87613i	0.205555	+	0.356032i	0.950310	−	0.311307i	$-0.100767\pi$
$373$	3.96993	+	6.87613i	0.205555	+	0.356032i	−0.744754	+	0.667339i	$0.767433\pi$
$374$	−1.28382	+	2.22364i	−0.0663847	+	0.114982i
$375$	6.43011	+	16.3837i	0.332049	+	0.846048i
$376$	−11.6863	+	3.60475i	−0.602675	+	0.185901i
$377$	−9.39375	+	4.52379i	−0.483803	+	0.232987i
$378$		0			0
$379$	9.46127	+	4.55631i	0.485993	+	0.234042i	0.660802	−	0.750561i	$-0.270216\pi$
$379$	9.46127	+	4.55631i	0.485993	+	0.234042i	−0.174809	+	0.984602i	$0.555931\pi$
$380$	−7.39253	−	1.11424i	−0.379229	−	0.0571595i
$381$	−11.1236	+	7.58395i	−0.569880	+	0.388538i
$382$	−19.1623	−	17.7800i	−0.980429	−	0.909705i
$383$	2.86105	+	1.95063i	0.146193	+	0.0996724i	0.634208	−	0.773163i	$-0.281326\pi$
$383$	2.86105	+	1.95063i	0.146193	+	0.0996724i	−0.488015	+	0.872835i	$0.662279\pi$
$384$	2.91547	+	12.7735i	0.148779	+	0.651844i
$385$		0			0
$386$	6.12225	−	26.8233i	0.311614	−	1.36527i
$387$	−0.972283	+	0.902147i	−0.0494239	+	0.0458587i
$388$	13.3880	−	2.01792i	0.679672	−	0.102444i
$389$	10.9291	+	3.37119i	0.554129	+	0.170926i	0.559158	−	0.829061i	$-0.311124\pi$
$389$	10.9291	+	3.37119i	0.554129	+	0.170926i	−0.00502864	+	0.999987i	$0.501601\pi$
$390$	−1.35007	−	18.0154i	−0.0683633	−	0.912245i
$391$	−3.28358			−0.166058
$392$		0			0
$393$	−13.8706			−0.699678
$394$	−2.60511	−	34.7628i	−0.131244	−	1.75132i
$395$	−18.4007	−	5.67585i	−0.925837	−	0.285583i
$396$	−2.16849	+	0.326847i	−0.108971	+	0.0164247i
$397$	24.2691	−	22.5184i	1.21803	−	1.13017i	0.230445	−	0.973085i	$-0.425982\pi$
$397$	24.2691	−	22.5184i	1.21803	−	1.13017i	0.987586	−	0.157081i	$-0.0502085\pi$
$398$	3.33011	−	14.5902i	0.166923	−	0.731338i
$399$		0			0
$400$	−3.29435	−	14.4335i	−0.164718	−	0.721676i
$401$	−10.6837	−	7.28404i	−0.533520	−	0.363748i	0.266392	−	0.963865i	$-0.414168\pi$
$401$	−10.6837	−	7.28404i	−0.533520	−	0.363748i	−0.799912	+	0.600117i	$0.795121\pi$
$402$	2.27024	+	2.10648i	0.113229	+	0.105062i
$403$	29.1972	−	19.9063i	1.45442	−	0.991604i
$404$	−9.12715	−	1.37570i	−0.454093	−	0.0684435i
$405$	8.88808	+	4.28027i	0.441652	+	0.212689i
$406$		0			0
$407$	24.9106	−	11.9963i	1.23477	−	0.594635i
$408$	−0.789377	+	0.243491i	−0.0390800	+	0.0120546i
$409$	0.860629	+	2.19285i	0.0425554	+	0.108429i	0.950571	−	0.310506i	$-0.100499\pi$
$409$	0.860629	+	2.19285i	0.0425554	+	0.108429i	−0.908016	+	0.418936i	$0.862403\pi$
$410$	9.02211	−	15.6268i	0.445570	−	0.771751i
$411$	−4.43685	−	7.68484i	−0.218853	−	0.379065i
$412$	2.18330	−	2.73777i	0.107564	−	0.134880i
$413$		0			0
$414$	−4.23130	−	5.30588i	−0.207957	−	0.260770i
$415$	−0.262735	+	0.669437i	−0.0128971	+	0.0328614i
$416$	−2.25767	+	30.1265i	−0.110691	+	1.47707i
$417$	−0.366778	+	4.89431i	−0.0179612	+	0.239676i
$418$	−7.41699	+	18.8982i	−0.362777	+	0.924340i
$419$	9.17670	+	11.5072i	0.448311	+	0.562164i	0.953712	−	0.300720i	$-0.0972270\pi$
$419$	9.17670	+	11.5072i	0.448311	+	0.562164i	−0.505401	+	0.862884i	$0.668656\pi$
$420$		0			0
$421$	1.85359	−	2.32433i	0.0903385	−	0.113281i	−0.734608	−	0.678492i	$-0.762634\pi$
$421$	1.85359	−	2.32433i	0.0903385	−	0.113281i	0.824946	+	0.565211i	$0.191205\pi$
$422$	−5.78355	−	10.0174i	−0.281539	−	0.487639i
$423$	3.02383	−	5.23743i	0.147024	−	0.254653i
$424$	−2.14124	−	5.45578i	−0.103988	−	0.264956i
$425$	1.41188	−	0.435506i	0.0684860	−	0.0211251i
$426$	17.6462	−	8.49798i	0.854963	−	0.411729i
$427$		0			0
$428$	−3.47750	−	1.67467i	−0.168091	−	0.0809484i
$429$	−20.0468	−	3.02157i	−0.967869	−	0.145883i
$430$	−5.21463	+	3.55527i	−0.251472	+	0.171451i
$431$	5.31954	+	4.93581i	0.256233	+	0.237750i	0.797821	−	0.602895i	$-0.205986\pi$
$431$	5.31954	+	4.93581i	0.256233	+	0.237750i	−0.541588	+	0.840644i	$0.682177\pi$
$432$	−22.1717	−	15.1164i	−1.06674	−	0.727288i
$433$	1.04771	+	4.59030i	0.0503495	+	0.220596i	0.993843	−	0.110795i	$-0.0353395\pi$
$433$	1.04771	+	4.59030i	0.0503495	+	0.220596i	−0.943494	+	0.331390i	$0.892482\pi$
$434$		0			0
$435$	1.12967	−	4.94940i	0.0541634	−	0.237306i
$436$	4.88224	−	4.53006i	0.233817	−	0.216950i
$437$	−25.6724	+	3.86948i	−1.22808	+	0.185103i
$438$	−22.7156	−	7.00685i	−1.08540	−	0.334800i
$439$	1.01644	+	13.5635i	0.0485122	+	0.647350i	0.967469	+	0.252991i	$0.0814143\pi$
$439$	1.01644	+	13.5635i	0.0485122	+	0.647350i	−0.918956	+	0.394359i	$0.870967\pi$
$440$	4.38154			0.208882
$441$		0			0
$442$	−3.99212			−0.189886
$443$	1.58647	+	21.1699i	0.0753754	+	1.00581i	0.898791	+	0.438376i	$0.144446\pi$
$443$	1.58647	+	21.1699i	0.0753754	+	1.00581i	−0.823416	+	0.567438i	$0.807935\pi$
$444$	−20.2439	−	6.24441i	−0.960733	−	0.296347i
$445$	1.08022	−	0.162816i	0.0512071	−	0.00771823i
$446$	13.8155	−	12.8189i	0.654182	−	0.606993i
$447$	−0.693043	+	3.03642i	−0.0327798	+	0.143618i
$448$		0			0
$449$	7.08787	+	31.0540i	0.334497	+	1.46553i	0.810320	+	0.585988i	$0.199293\pi$
$449$	7.08787	+	31.0540i	0.334497	+	1.46553i	−0.475822	+	0.879541i	$0.657850\pi$
$450$	2.52310	+	1.72022i	0.118940	+	0.0810920i
$451$	−14.8435	−	13.7728i	−0.698953	−	0.648534i
$452$	17.4346	−	11.8867i	0.820056	−	0.559105i
$453$	−18.2098	−	2.74469i	−0.855572	−	0.128957i
$454$	−43.9501	−	21.1653i	−2.06268	−	0.993335i
$455$		0			0
$456$	−5.88473	+	2.83393i	−0.275578	+	0.132711i
$457$	0.177657	−	0.0547998i	0.00831043	−	0.00256343i	−0.290597	−	0.956845i	$-0.593854\pi$
$457$	0.177657	−	0.0547998i	0.00831043	−	0.00256343i	0.298908	+	0.954282i	$0.403378\pi$
$458$	−16.1320	−	41.1037i	−0.753800	−	1.92065i
$459$	1.33905	−	2.31930i	0.0625014	−	0.108256i
$460$	−6.67236	−	11.5569i	−0.311101	−	0.538842i
$461$	−5.24668	+	6.57913i	−0.244362	+	0.306421i	−0.888854	−	0.458191i	$-0.848498\pi$
$461$	−5.24668	+	6.57913i	−0.244362	+	0.306421i	0.644492	+	0.764611i	$0.277069\pi$
$462$		0			0
$463$	0.463761	+	0.581537i	0.0215528	+	0.0270263i	0.792491	−	0.609883i	$-0.208784\pi$
$463$	0.463761	+	0.581537i	0.0215528	+	0.0270263i	−0.770938	+	0.636910i	$0.780212\pi$
$464$	−4.10667	+	10.4636i	−0.190647	+	0.485761i
$465$	−1.28582	+	17.1581i	−0.0596287	+	0.795690i
$466$	−2.65150	+	35.3818i	−0.122828	+	1.63903i
$467$	−1.29121	+	3.28995i	−0.0597501	+	0.152241i	−0.957631	−	0.287997i	$-0.907011\pi$
$467$	−1.29121	+	3.28995i	−0.0597501	+	0.152241i	0.897881	+	0.440238i	$0.145106\pi$
$468$	−2.12586	−	2.66575i	−0.0982680	−	0.123224i
$469$		0			0
$470$	17.9423	−	22.4989i	0.827615	−	1.03780i
$471$	9.94075	+	17.2179i	0.458046	+	0.793358i
$472$	−2.04374	+	3.53986i	−0.0940706	+	0.162935i
$473$	2.58750	+	6.59283i	0.118973	+	0.303139i
$474$	38.2867	−	11.8099i	1.75856	−	0.542445i
$475$	10.5254	−	5.06876i	0.482938	−	0.232571i
$476$		0			0
$477$	2.61126	+	1.25752i	0.119561	+	0.0575777i
$478$	0.0859856	+	0.0129602i	0.00393289	+	0.000592788i
$479$	−10.2622	+	6.99664i	−0.468891	+	0.319685i	−0.774612	−	0.632437i	$-0.782055\pi$
$479$	−10.2622	+	6.99664i	−0.468891	+	0.319685i	0.305721	+	0.952121i	$0.401103\pi$
$480$	−10.7833	−	10.0054i	−0.492186	−	0.456682i
$481$	35.5182	+	24.2159i	1.61949	+	1.10415i
$482$	0.437446	+	1.91657i	0.0199251	+	0.0872976i
$483$		0			0
$484$	0.842053	−	3.68927i	0.0382751	−	0.167694i
$485$	9.80604	−	9.09868i	0.445269	−	0.413150i
$486$	10.1116	−	1.52408i	0.458673	−	0.0691338i
$487$	−29.6475	−	9.14505i	−1.34346	−	0.414402i	−0.462090	−	0.886833i	$-0.652900\pi$
$487$	−29.6475	−	9.14505i	−1.34346	−	0.414402i	−0.881368	+	0.472431i	$0.843377\pi$
$488$	0.00330128	+	0.0440525i	0.000149442	+	0.00199416i
$489$	−6.95009			−0.314294
$490$		0			0
$491$	−23.1351			−1.04407			−0.522037	−	0.852923i	$-0.674828\pi$
$491$	−23.1351			−1.04407			−0.522037	+	0.852923i	$0.674828\pi$
$492$	1.15945	+	15.4718i	0.0522722	+	0.697524i
$493$	−1.07198	−	0.330663i	−0.0482797	−	0.0148923i
$494$	−31.2120	+	4.70445i	−1.40429	+	0.211663i
$495$	−1.58831	+	1.47374i	−0.0713893	+	0.0662395i
$496$	8.47751	−	37.1424i	0.380651	−	1.66774i
$497$		0			0
$498$	−0.332969	−	1.45883i	−0.0149207	−	0.0653719i
$499$	−7.05070	−	4.80708i	−0.315632	−	0.215195i	0.395133	−	0.918624i	$-0.370699\pi$
$499$	−7.05070	−	4.80708i	−0.315632	−	0.215195i	−0.710765	+	0.703430i	$0.751651\pi$
$500$	11.5867	+	10.7509i	0.518174	+	0.480795i
$501$	−20.8934	+	14.2449i	−0.933447	+	0.636413i
$502$	−44.6353	−	6.72769i	−1.99217	−	0.300271i
$503$	−23.1723	−	11.1592i	−1.03320	−	0.497563i	−0.161124	−	0.986934i	$-0.551512\pi$
$503$	−23.1723	−	11.1592i	−1.03320	−	0.497563i	−0.872076	+	0.489371i	$0.837226\pi$
$504$		0			0
$505$	−8.21653	+	3.95687i	−0.365631	+	0.176078i
$506$	−34.6284	+	10.6814i	−1.53942	+	0.474848i
$507$	−4.06650	−	10.3613i	−0.180600	−	0.460160i
$508$	−6.04528	+	10.4707i	−0.268216	+	0.464564i
$509$	−2.10837	−	3.65180i	−0.0934516	−	0.161863i	0.815510	−	0.578743i	$-0.196457\pi$
$509$	−2.10837	−	3.65180i	−0.0934516	−	0.161863i	−0.908961	+	0.416880i	$0.863123\pi$
$510$	1.21195	−	1.51974i	0.0536660	−	0.0672950i
$511$		0			0
$512$	13.7267	+	17.2127i	0.606640	+	0.760703i
$513$	7.73607	−	19.7112i	0.341556	−	0.870270i
$514$	1.34921	−	18.0039i	0.0595110	−	0.794118i
$515$	0.258551	−	3.45012i	0.0113931	−	0.152030i
$516$	1.98260	−	5.05159i	0.0872792	−	0.222384i
$517$	−20.1345	−	25.2478i	−0.885514	−	1.11040i
$518$		0			0
$519$	−20.4168	+	25.6019i	−0.896198	+	1.12380i
$520$	3.40618	+	5.89967i	0.149371	+	0.258718i
$521$	15.5782	−	26.9823i	0.682494	−	1.18212i	−0.291723	−	0.956503i	$-0.594228\pi$
$521$	15.5782	−	26.9823i	0.682494	−	1.18212i	0.974217	−	0.225612i	$-0.0724382\pi$
$522$	−0.847070	−	2.15830i	−0.0370753	−	0.0944662i
$523$	10.0028	−	3.08545i	0.437391	−	0.134917i	−0.0682367	−	0.997669i	$-0.521737\pi$
$523$	10.0028	−	3.08545i	0.437391	−	0.134917i	0.505627	+	0.862752i	$0.331261\pi$
$524$	−11.2230	+	5.40473i	−0.490281	+	0.236107i
$525$		0			0
$526$	26.1627	+	12.5993i	1.14075	+	0.549354i
$527$	3.75969	+	0.566683i	0.163775	+	0.0246851i
$528$	−18.0589	+	12.3123i	−0.785912	+	0.535826i
$529$	−17.1115	−	15.8772i	−0.743978	−	0.690311i
$530$	11.3948	+	7.76883i	0.494957	+	0.337456i
$531$	−0.449780	−	1.97061i	−0.0195188	−	0.0855173i
$532$		0			0
$533$	7.00556	−	30.6934i	0.303445	−	1.32948i
$534$	−1.66624	+	1.54604i	−0.0721052	+	0.0669039i
$535$	−3.77089	+	0.568371i	−0.163030	+	0.0245728i
$536$	−1.11594	−	0.344220i	−0.0482011	−	0.0148681i
$537$	0.372813	+	4.97485i	0.0160881	+	0.214680i
$538$	21.8192			0.940692
$539$		0			0
$540$	10.8840			0.468372
$541$	2.56621	+	34.2437i	0.110330	+	1.47225i	0.727872	+	0.685713i	$0.240509\pi$
$541$	2.56621	+	34.2437i	0.110330	+	1.47225i	−0.617542	+	0.786538i	$0.711872\pi$
$542$	−42.8100	−	13.2051i	−1.83885	−	0.567209i
$543$	−26.2591	+	3.95792i	−1.12689	+	0.169851i
$544$	−2.38284	+	2.21095i	−0.102163	+	0.0947937i
$545$	1.46427	−	6.41538i	0.0627224	−	0.274805i
$546$		0			0
$547$	−6.10206	−	26.7349i	−0.260905	−	1.14310i	−0.920272	−	0.391279i	$-0.872033\pi$
$547$	−6.10206	−	26.7349i	−0.260905	−	1.14310i	0.659367	−	0.751821i	$-0.270824\pi$
$548$	−6.58440	−	4.48917i	−0.281271	−	0.191768i
$549$	−0.0160138	−	0.0148587i	−0.000683454	−	0.000634153i
$550$	13.4728	−	9.18561i	0.574483	−	0.391676i
$551$	−8.77086	−	1.32199i	−0.373651	−	0.0563188i
$552$	−10.5043	−	5.05858i	−0.447091	−	0.215307i
$553$		0			0
$554$	5.08396	−	2.44831i	0.215997	−	0.104019i
$555$	−20.0014	+	6.16960i	−0.849010	+	0.261885i
$556$	1.61032	+	4.10303i	0.0682928	+	0.174007i
$557$	−4.62629	+	8.01296i	−0.196022	+	0.339520i	−0.947235	−	0.320540i	$-0.896136\pi$
$557$	−4.62629	+	8.01296i	−0.196022	+	0.339520i	0.751213	+	0.660060i	$0.229469\pi$
$558$	3.92914	+	6.80547i	0.166334	+	0.288098i
$559$	−6.86564	+	8.60924i	−0.290386	+	0.364132i
$560$		0			0
$561$	−1.36003	−	1.70542i	−0.0574204	−	0.0720029i
$562$	2.82701	−	7.20310i	0.119250	−	0.303845i
$563$	−2.74709	+	36.6574i	−0.115776	+	1.54492i	0.572761	+	0.819723i	$0.305872\pi$
$563$	−2.74709	+	36.6574i	−0.115776	+	1.54492i	−0.688537	+	0.725202i	$0.741747\pi$
$564$	−1.84911	+	24.6746i	−0.0778615	+	1.03899i
$565$	7.61677	−	19.4072i	0.320440	−	0.816468i
$566$	1.29199	+	1.62010i	0.0543063	+	0.0680979i
$567$		0			0
$568$	−4.60479	+	5.77422i	−0.193212	+	0.242281i
$569$	14.1037	+	24.4283i	0.591256	+	1.02409i	0.994064	+	0.108801i	$0.0347012\pi$
$569$	14.1037	+	24.4283i	0.591256	+	1.02409i	−0.402807	+	0.915285i	$0.631965\pi$
$570$	7.68459	−	13.3101i	0.321872	−	0.557498i
$571$	−0.826570	−	2.10607i	−0.0345909	−	0.0881361i	0.912535	−	0.408999i	$-0.134122\pi$
$571$	−0.826570	−	2.10607i	−0.0345909	−	0.0881361i	−0.947125	+	0.320863i	$0.896027\pi$
$572$	−17.3977	+	5.36649i	−0.727436	+	0.224384i
$573$	20.0082	−	9.63544i	0.835854	−	0.402526i
$574$		0			0
$575$	18.7878	+	9.04775i	0.783507	+	0.377317i
$576$	−1.48210	−	0.223391i	−0.0617542	−	0.00930795i
$577$	10.4382	−	7.11661i	0.434546	−	0.296268i	−0.326221	−	0.945294i	$-0.605775\pi$
$577$	10.4382	−	7.11661i	0.434546	−	0.296268i	0.760767	+	0.649025i	$0.224823\pi$
$578$	22.6926	+	21.0557i	0.943889	+	0.875801i
$579$	19.3121	+	13.1668i	0.802585	+	0.547193i
$580$	−1.01451	−	4.44487i	−0.0421253	−	0.184563i
$581$		0			0
$582$	−6.19361	+	27.1360i	−0.256734	+	1.12482i
$583$	11.3448	−	10.5265i	0.469855	−	0.435962i
$584$	8.86381	−	1.33600i	0.366787	−	0.0552843i
$585$	−3.21910	−	0.992962i	−0.133094	−	0.0410539i
$586$	−3.00223	−	40.0619i	−0.124021	−	1.65494i
$587$	24.3065			1.00324			0.501619	−	0.865089i	$-0.332738\pi$
$587$	24.3065			1.00324			0.501619	+	0.865089i	$0.332738\pi$
$588$		0			0
$589$	30.0626			1.23871
$590$	−0.718761	−	9.59120i	−0.0295909	−	0.394863i
$591$	28.2995	+	8.72925i	1.16409	+	0.359073i
$592$	45.8278	−	6.90743i	1.88351	−	0.283894i
$593$	−32.1173	+	29.8005i	−1.31890	+	1.22376i	−0.362404	+	0.932021i	$0.618044\pi$
$593$	−32.1173	+	29.8005i	−1.31890	+	1.22376i	−0.956498	+	0.291740i	$0.905766\pi$
$594$	6.57684	−	28.8150i	0.269851	−	1.18229i
$595$		0			0
$596$	0.622395	+	2.72689i	0.0254943	+	0.111698i
$597$	10.5046	+	7.16188i	0.429923	+	0.293116i
$598$	−41.3022	−	38.3228i	−1.68897	−	1.56714i
$599$	8.59700	−	5.86133i	0.351264	−	0.239488i	−0.374814	−	0.927100i	$-0.622293\pi$
$599$	8.59700	−	5.86133i	0.351264	−	0.239488i	0.726078	+	0.687612i	$0.241341\pi$
$600$	5.18755	+	0.781897i	0.211781	+	0.0319208i
$601$	19.5049	+	9.39308i	0.795623	+	0.383152i	0.787111	−	0.616812i	$-0.211576\pi$
$601$	19.5049	+	9.39308i	0.795623	+	0.383152i	0.00851252	+	0.999964i	$0.497290\pi$
$602$		0			0
$603$	0.520306	−	0.250566i	0.0211885	−	0.0102038i
$604$	−15.8035	+	4.87474i	−0.643036	+	0.198350i
$605$	−1.36594	−	3.48036i	−0.0555334	−	0.141497i
$606$	9.48774	−	16.4332i	0.385413	−	0.667555i
$607$	−14.3514	−	24.8573i	−0.582505	−	1.00893i	−0.995181	−	0.0980500i	$-0.968739\pi$
$607$	−14.3514	−	24.8573i	−0.582505	−	1.00893i	0.412677	−	0.910877i	$-0.364594\pi$
$608$	−16.0245	+	20.0941i	−0.649879	+	0.814923i
$609$		0			0
$610$	−0.0648112	−	0.0812707i	−0.00262413	−	0.00329056i
$611$	18.3434	−	46.7382i	0.742095	−	1.89083i
$612$	0.0274155	−	0.365835i	0.00110821	−	0.0147880i
$613$	−2.10741	+	28.1214i	−0.0851175	+	1.13581i	0.777134	+	0.629335i	$0.216672\pi$
$613$	−2.10741	+	28.1214i	−0.0851175	+	1.13581i	−0.862252	+	0.506480i	$0.830947\pi$
$614$	−14.2222	+	36.2375i	−0.573960	+	1.46243i
$615$	9.55768	+	11.9849i	0.385403	+	0.483280i
$616$		0			0
$617$	22.5924	−	28.3299i	0.909535	−	1.14052i	−0.0800820	−	0.996788i	$-0.525518\pi$
$617$	22.5924	−	28.3299i	0.909535	−	1.14052i	0.989617	−	0.143732i	$-0.0459104\pi$
$618$	3.59943	+	6.23440i	0.144790	+	0.250784i
$619$	1.79353	−	3.10648i	0.0720880	−	0.124860i	−0.827728	−	0.561129i	$-0.810367\pi$
$619$	1.79353	−	3.10648i	0.0720880	−	0.124860i	0.899816	+	0.436269i	$0.143700\pi$
$620$	5.64535	+	14.3841i	0.226723	+	0.577680i
$621$	36.1181	−	11.1410i	1.44937	−	0.447071i
$622$	−1.38305	+	0.666041i	−0.0554552	+	0.0267058i
$623$		0			0
$624$	−30.6172	−	14.7445i	−1.22567	−	0.590251i
$625$	0.297404	+	0.0448264i	0.0118961	+	0.00179305i
$626$	17.1841	−	11.7159i	0.686815	−	0.468263i
$627$	−12.6430	−	11.7309i	−0.504911	−	0.468489i
$628$	14.7523	+	10.0580i	0.588682	+	0.401357i
$629$	1.02923	+	4.50934i	0.0410379	+	0.179799i
$630$		0			0
$631$	5.01004	−	21.9504i	0.199447	−	0.873833i	−0.771820	−	0.635841i	$-0.780654\pi$
$631$	5.01004	−	21.9504i	0.199447	−	0.873833i	0.971267	−	0.237992i	$-0.0764893\pi$
$632$	−11.0753	+	10.2764i	−0.440552	+	0.408773i
$633$	9.71697	−	1.46460i	0.386215	−	0.0582125i
$634$	−26.1148	−	8.05535i	−1.03715	−	0.319919i
$635$	0.892704	+	11.9123i	0.0354259	+	0.472725i
$636$	−11.8582			−0.470209
$637$		0			0
$638$	−12.3807			−0.490156
$639$	−0.272929	−	3.64198i	−0.0107969	−	0.144075i
$640$	11.1089	+	3.42665i	0.439119	+	0.135450i
$641$	39.8768	−	6.01047i	1.57504	−	0.237399i	0.697387	−	0.716695i	$-0.254346\pi$
$641$	39.8768	−	6.01047i	1.57504	−	0.237399i	0.877653	+	0.479296i	$0.159108\pi$
$642$	5.81663	−	5.39704i	0.229564	−	0.213004i
$643$	0.706670	−	3.09612i	0.0278683	−	0.122099i	−0.959080	−	0.283134i	$-0.908626\pi$
$643$	0.706670	−	3.09612i	0.0278683	−	0.122099i	0.986949	+	0.161035i	$0.0514831\pi$
$644$		0			0
$645$	−1.19309	−	5.22727i	−0.0469779	−	0.205824i
$646$	−2.80608	−	1.91315i	−0.110404	−	0.0752721i
$647$	22.5388	+	20.9129i	0.886090	+	0.822172i	0.984934	−	0.172931i	$-0.0553239\pi$
$647$	22.5388	+	20.9129i	0.886090	+	0.822172i	−0.0988436	+	0.995103i	$0.531514\pi$
$648$	6.39522	−	4.36019i	0.251228	−	0.171284i
$649$	−10.6727	−	1.60865i	−0.418940	−	0.0631451i
$650$	22.8419	+	11.0001i	0.895935	+	0.431459i
$651$		0			0
$652$	−5.62350	+	2.70813i	−0.220233	+	0.106059i
$653$	−30.3074	+	9.34858i	−1.18602	+	0.365838i	−0.824140	−	0.566387i	$-0.808341\pi$
$653$	−30.3074	+	9.34858i	−1.18602	+	0.365838i	−0.361879	+	0.932225i	$0.617865\pi$
$654$	5.00222	+	12.7454i	0.195602	+	0.498386i
$655$	−6.15370	+	10.6585i	−0.240445	+	0.416463i
$656$	−16.9709	−	29.3944i	−0.662601	−	1.14766i
$657$	−2.76377	+	3.46566i	−0.107825	+	0.135208i
$658$		0			0
$659$	−9.00661	−	11.2939i	−0.350848	−	0.439949i	0.574824	−	0.818277i	$-0.305071\pi$
$659$	−9.00661	−	11.2939i	−0.350848	−	0.439949i	−0.925672	+	0.378328i	$0.876499\pi$
$660$	3.23876	−	8.25222i	0.126068	−	0.321217i
$661$	−3.08427	+	41.1567i	−0.119964	+	1.60081i	0.534802	+	0.844977i	$0.320386\pi$
$661$	−3.08427	+	41.1567i	−0.119964	+	1.60081i	−0.654766	+	0.755831i	$0.727233\pi$
$662$	2.90944	−	38.8238i	0.113079	−	1.50893i
$663$	1.23905	−	3.15704i	0.0481205	−	0.122609i
$664$	0.351804	+	0.441148i	0.0136526	+	0.0171198i
$665$		0			0
$666$	−5.96027	+	7.47394i	−0.230956	+	0.289609i
$667$	−7.91642	−	13.7116i	−0.306525	−	0.530917i
$668$	−11.3548	+	19.6671i	−0.439330	+	0.760942i
$669$	5.84945	+	14.9041i	0.226153	+	0.576228i
$670$	2.62587	−	0.809973i	0.101446	−	0.0312920i
$671$	−0.105098	+	0.0506125i	−0.00405726	+	0.00195387i
$672$		0			0
$673$	−27.8881	−	13.4302i	−1.07501	−	0.517697i	−0.189291	−	0.981921i	$-0.560619\pi$
$673$	−27.8881	−	13.4302i	−1.07501	−	0.517697i	−0.885718	+	0.464224i	$0.846333\pi$
$674$	−51.3300	−	7.73675i	−1.97716	−	0.298008i
$675$	−14.0524	+	9.58078i	−0.540878	+	0.368764i
$676$	−7.32762	−	6.79904i	−0.281832	−	0.261502i
$677$	10.3704	+	7.07041i	0.398566	+	0.271738i	0.745972	−	0.665977i	$-0.231985\pi$
$677$	10.3704	+	7.07041i	0.398566	+	0.271738i	−0.347406	+	0.937715i	$0.612937\pi$
$678$	9.65290	+	42.2921i	0.370717	+	1.62422i
$679$		0			0
$680$	−0.163103	+	0.714603i	−0.00625473	+	0.0274038i
$681$	30.3787	−	28.1873i	1.16412	−	1.08014i
$682$	41.4928	−	6.25403i	1.58884	−	0.239479i
$683$	3.36410	+	1.03769i	0.128724	+	0.0397061i	0.358448	−	0.933550i	$-0.383306\pi$
$683$	3.36410	+	1.03769i	0.128724	+	0.0397061i	−0.229724	+	0.973256i	$0.573782\pi$
$684$	−0.216766	−	2.89255i	−0.00828827	−	0.110599i
$685$	−7.87365			−0.300837
$686$		0			0
$687$	37.5124			1.43119
$688$	0.887175	+	11.8385i	0.0338232	+	0.451340i
$689$	22.9931	+	7.09244i	0.875968	+	0.270200i
$690$	27.1276	−	4.08883i	1.03273	−	0.155659i
$691$	27.3082	−	25.3383i	1.03885	−	0.963914i	0.0394753	−	0.999221i	$-0.487431\pi$
$691$	27.3082	−	25.3383i	1.03885	−	0.963914i	0.999377	+	0.0353069i	$0.0112409\pi$
$692$	−6.54388	+	28.6706i	−0.248761	+	1.08989i
$693$		0			0
$694$	0.173706	+	0.761057i	0.00659380	+	0.0288893i
$695$	3.59820	+	2.45321i	0.136487	+	0.0930555i
$696$	−2.91989	−	2.70926i	−0.110678	−	0.102694i
$697$	2.79881	−	1.90819i	0.106012	−	0.0722780i
$698$	−13.7032	−	2.06542i	−0.518672	−	0.0781773i
$699$	−27.1576	−	13.0784i	−1.02719	−	0.494670i
$700$		0			0
$701$	−35.6860	+	17.1855i	−1.34784	+	0.649086i	−0.961891	−	0.273434i	$-0.911840\pi$
$701$	−35.6860	+	17.1855i	−1.34784	+	0.649086i	−0.385949	+	0.922520i	$0.626126\pi$
$702$	43.9118	−	13.5450i	1.65734	−	0.511222i
$703$	13.3609	+	34.0429i	0.503914	+	1.28395i
$704$	−4.00174	+	6.93122i	−0.150821	+	0.261230i
$705$	12.2237	+	21.1721i	0.460371	+	0.797386i
$706$	−39.1004	+	49.0303i	−1.47156	+	1.84528i
$707$		0			0
$708$	5.15629	+	6.46579i	0.193785	+	0.242999i
$709$	8.25019	−	21.0211i	0.309842	−	0.789466i	−0.688116	−	0.725601i	$-0.741562\pi$
$709$	8.25019	−	21.0211i	0.309842	−	0.789466i	0.997959	−	0.0638651i	$-0.0203427\pi$
$710$	1.29870	−	17.3300i	0.0487394	−	0.650382i
$711$	0.558330	−	7.45039i	0.0209390	−	0.279412i
$712$	0.313140	−	0.797868i	0.0117354	−	0.0299014i
$713$	33.4576	+	41.9545i	1.25300	+	1.57121i
$714$		0			0
$715$	−11.2156	+	14.0640i	−0.419441	+	0.525963i
$716$	2.24012	+	3.88001i	0.0837173	+	0.145003i
$717$	−0.0369367	+	0.0639763i	−0.00137943	+	0.00238924i
$718$	5.84854	+	14.9018i	0.218266	+	0.556132i
$719$	19.2415	−	5.93522i	0.717587	−	0.221346i	0.0856049	−	0.996329i	$-0.472718\pi$
$719$	19.2415	−	5.93522i	0.717587	−	0.221346i	0.631982	+	0.774983i	$0.282242\pi$
$720$	−3.27222	+	1.57582i	−0.121949	+	0.0587273i
$721$		0			0
$722$	7.41093	+	3.56891i	0.275806	+	0.132821i
$723$	−1.65143	−	0.248913i	−0.0614173	−	0.00925717i
$724$	−19.7047	+	13.4344i	−0.732319	+	0.499287i
$725$	5.22250	+	4.84577i	0.193959	+	0.179967i
$726$	6.42767	+	4.38231i	0.238553	+	0.162643i
$727$	−6.56471	−	28.7619i	−0.243472	−	1.06672i	−0.937831	−	0.347091i	$-0.887170\pi$
$727$	−6.56471	−	28.7619i	−0.243472	−	1.06672i	0.694360	−	0.719628i	$-0.255688\pi$
$728$		0			0
$729$	−6.66514	+	29.2019i	−0.246857	+	1.08155i
$730$	−15.4621	+	14.3467i	−0.572277	+	0.530995i
$731$	−1.17157	+	0.176586i	−0.0433322	+	0.00653127i
$732$	0.0854091	+	0.0263452i	0.00315681	+	0.000973747i
$733$	1.76036	+	23.4903i	0.0650203	+	0.867636i	0.930406	+	0.366530i	$0.119454\pi$
$733$	1.76036	+	23.4903i	0.0650203	+	0.867636i	−0.865386	+	0.501106i	$0.832927\pi$
$734$	61.2452			2.26060
$735$		0			0
$736$	−45.8769			−1.69104
$737$	−0.230445	−	3.07508i	−0.00848857	−	0.113272i
$738$	6.69002	+	2.06360i	0.246263	+	0.0759621i
$739$	−2.96363	+	0.446695i	−0.109019	+	0.0164319i	−0.203325	−	0.979111i	$-0.565175\pi$
$739$	−2.96363	+	0.446695i	−0.109019	+	0.0164319i	0.0943062	+	0.995543i	$0.469937\pi$
$740$	−13.7796	+	12.7856i	−0.506548	+	0.470008i
$741$	5.96699	−	26.1431i	0.219203	−	0.960390i
$742$		0			0
$743$	−0.0458811	−	0.201018i	−0.00168321	−	0.00737464i	0.974079	−	0.226207i	$-0.0726325\pi$
$743$	−0.0458811	−	0.201018i	−0.00168321	−	0.00737464i	−0.975763	+	0.218832i	$0.929775\pi$
$744$	11.1543	+	7.60489i	0.408938	+	0.278809i
$745$	2.02580	+	1.87966i	0.0742194	+	0.0688656i
$746$	−12.1117	+	8.25761i	−0.443440	+	0.302332i
$747$	−0.275910	−	0.0415867i	−0.0100950	−	0.00152158i
$748$	−1.76496	−	0.849959i	−0.0645332	−	0.0310776i
$749$		0			0
$750$	−29.2763	+	14.0987i	−1.06902	+	0.514812i
$751$	34.2567	−	10.5668i	1.25005	−	0.385588i	0.402063	−	0.915612i	$-0.368293\pi$
$751$	34.2567	−	10.5668i	1.25005	−	0.385588i	0.847983	+	0.530024i	$0.177817\pi$
$752$	−19.7762	−	50.3888i	−0.721163	−	1.83749i
$753$	19.1739	−	33.2102i	0.698737	−	1.21025i
$754$	−9.62465	−	16.6704i	−0.350509	−	0.607100i
$755$	−10.1879	+	12.7752i	−0.370776	+	0.464938i
$756$		0			0
$757$	−23.3107	−	29.2307i	−0.847241	−	1.06241i	−0.997279	−	0.0737258i	$-0.976511\pi$
$757$	−23.3107	−	29.2307i	−0.847241	−	1.06241i	0.150038	−	0.988680i	$-0.452060\pi$
$758$	−7.08310	+	18.0475i	−0.257270	+	0.655513i
$759$	2.30064	−	30.6999i	0.0835079	−	1.11434i
$760$	−0.433095	+	5.77926i	−0.0157100	+	0.209636i
$761$	−2.46343	+	6.27672i	−0.0892993	+	0.227531i	−0.968545	−	0.248837i	$-0.919952\pi$
$761$	−2.46343	+	6.27672i	−0.0892993	+	0.227531i	0.879246	+	0.476368i	$0.158047\pi$
$762$	−15.4973	−	19.4330i	−0.561407	−	0.703982i
$763$		0			0
$764$	12.4346	−	15.5926i	0.449870	−	0.564119i
$765$	−0.181233	−	0.313904i	−0.00655248	−	0.0113492i
$766$	−3.19650	+	5.53650i	−0.115494	+	0.200042i
$767$	−6.13086	−	15.6212i	−0.221372	−	0.564048i
$768$	−31.4352	+	9.69646i	−1.13432	+	0.349891i
$769$	−33.3770	+	16.0735i	−1.20360	+	0.579625i	−0.924701	−	0.380694i	$-0.875685\pi$
$769$	−33.3770	+	16.0735i	−1.20360	+	0.579625i	−0.278903	+	0.960319i	$0.589971\pi$
$770$		0			0
$771$	13.8190	+	6.65489i	0.497680	+	0.239670i
$772$	20.7564	+	3.12853i	0.747040	+	0.112598i
$773$	11.6502	−	7.94298i	0.419029	−	0.285689i	−0.335394	−	0.942078i	$-0.608869\pi$
$773$	11.6502	−	7.94298i	0.419029	−	0.285689i	0.754423	+	0.656389i	$0.227917\pi$
$774$	−1.79506	−	1.66557i	−0.0645220	−	0.0598677i
$775$	−19.9506	−	13.6021i	−0.716646	−	0.488601i
$776$	−2.33551	−	10.2325i	−0.0838399	−	0.367327i
$777$		0			0
$778$	−4.69871	+	20.5864i	−0.168457	+	0.738058i
$779$	19.6335	−	18.2172i	0.703443	−	0.652700i
$780$	13.6293	−	2.05428i	0.488006	−	0.0735551i
$781$	−18.6355	−	5.74829i	−0.666831	−	0.205690i
$782$	−0.453032	−	6.04530i	−0.0162004	−	0.216179i
$783$	12.9133			0.461484
$784$		0			0
$785$	17.6409			0.629631
$786$	−1.91371	−	25.5367i	−0.0682597	−	0.910863i
$787$	−28.7944	−	8.88191i	−1.02641	−	0.316606i	−0.264568	−	0.964367i	$-0.585229\pi$
$787$	−28.7944	−	8.88191i	−1.02641	−	0.316606i	−0.761843	+	0.647761i	$0.775705\pi$
$788$	26.2993	−	3.96397i	0.936872	−	0.141211i
$789$	−18.0839	+	16.7794i	−0.643803	+	0.597362i
$790$	7.91090	−	34.6599i	0.281457	−	1.23315i
$791$		0			0
$792$	0.378289	+	1.65739i	0.0134419	+	0.0588928i
$793$	−0.149851	−	0.102167i	−0.00532137	−	0.00362805i
$794$	44.8063	+	41.5742i	1.59012	+	1.47541i
$795$	−9.68034	+	6.59994i	−0.343326	+	0.234076i
$796$	11.2902	+	1.70172i	0.400169	+	0.0603158i
$797$	−8.43053	−	4.05993i	−0.298625	−	0.143810i	0.278572	−	0.960415i	$-0.410139\pi$
$797$	−8.43053	−	4.05993i	−0.298625	−	0.143810i	−0.577196	+	0.816605i	$0.695853\pi$
$798$		0			0
$799$	4.86728	−	2.34396i	0.172192	−	0.0829233i
$800$	19.7262	−	6.08471i	0.697425	−	0.215127i
$801$	0.154850	+	0.394553i	0.00547137	+	0.0139408i
$802$	11.9364	−	20.6744i	0.421489	−	0.730040i
$803$	11.8349	+	20.4987i	0.417646	+	0.723384i
$804$	−1.47319	+	1.84732i	−0.0519553	+	0.0651499i
$805$		0			0
$806$	40.6771	+	51.0075i	1.43279	+	1.79666i
$807$	−6.77207	+	17.2550i	−0.238388	+	0.607403i
$808$	−0.534719	+	7.13533i	−0.0188114	+	0.251020i
$809$	3.25954	−	43.4956i	0.114599	−	1.52922i	−0.582845	−	0.812584i	$-0.698060\pi$
$809$	3.25954	−	43.4956i	0.114599	−	1.52922i	0.697444	−	0.716639i	$-0.254321\pi$
$810$	−6.65399	+	16.9541i	−0.233798	+	0.595706i
$811$	−12.0587	−	15.1211i	−0.423439	−	0.530975i	0.523656	−	0.851930i	$-0.324568\pi$
$811$	−12.0587	−	15.1211i	−0.423439	−	0.530975i	−0.947095	+	0.320955i	$0.895996\pi$
$812$		0			0
$813$	23.7299	−	29.7563i	0.832242	−	1.04360i
$814$	25.5229	+	44.2070i	0.894578	+	1.54945i
$815$	−3.08342	+	5.34063i	−0.108007	+	0.187074i
$816$	−1.33582	−	3.40362i	−0.0467632	−	0.119151i
$817$	−8.95172	+	2.76124i	−0.313181	+	0.0966035i
$818$	−3.91844	+	1.88702i	−0.137005	+	0.0659781i
$819$		0			0
$820$	12.4033	+	5.97314i	0.433144	+	0.208591i
$821$	−7.78819	−	1.17388i	−0.271810	−	0.0409687i	0.0117230	−	0.999931i	$-0.496268\pi$
$821$	−7.78819	−	1.17388i	−0.271810	−	0.0409687i	−0.283533	+	0.958963i	$0.591506\pi$
$822$	13.5362	−	9.22880i	0.472128	−	0.321891i
$823$	7.52570	+	6.98283i	0.262329	+	0.243406i	0.800361	−	0.599519i	$-0.204641\pi$
$823$	7.52570	+	6.98283i	0.262329	+	0.243406i	−0.538031	+	0.842925i	$0.680832\pi$
$824$	−2.24289	−	1.52917i	−0.0781346	−	0.0532713i
$825$	3.08254	+	13.5055i	0.107320	+	0.470200i
$826$		0			0
$827$	−11.9442	+	52.3311i	−0.415342	+	1.81973i	0.142513	+	0.989793i	$0.454482\pi$
$827$	−11.9442	+	52.3311i	−0.415342	+	1.81973i	−0.557855	+	0.829938i	$0.688375\pi$
$828$	3.79551	−	3.52172i	0.131903	−	0.122388i
$829$	−55.5254	+	8.36911i	−1.92848	+	0.290671i	−0.997271	−	0.0738212i	$-0.976481\pi$
$829$	−55.5254	+	8.36911i	−1.92848	+	0.290671i	−0.931206	+	0.364492i	$0.881242\pi$
$830$	−1.26873	−	0.391351i	−0.0440382	−	0.0135840i
$831$	0.358239	+	4.78037i	0.0124272	+	0.165829i
$832$	−12.4437			−0.431408
$833$		0			0
$834$	−9.06136			−0.313769
$835$	1.67676	+	22.3748i	0.0580266	+	0.774311i
$836$	−14.8008	−	4.56543i	−0.511895	−	0.157899i
$837$	−43.2778	+	6.52308i	−1.49590	+	0.225471i
$838$	−19.9195	+	18.4826i	−0.688106	+	0.638469i
$839$	−11.6602	+	51.0868i	−0.402556	+	1.76371i	0.214430	+	0.976739i	$0.431210\pi$
$839$	−11.6602	+	51.0868i	−0.402556	+	1.76371i	−0.616986	+	0.786974i	$0.711647\pi$
$840$		0			0
$841$	5.24944	+	22.9993i	0.181015	+	0.793079i
$842$	4.53498	+	3.09190i	0.156286	+	0.106554i
$843$	4.81890	+	4.47129i	0.165972	+	0.153999i
$844$	7.29156	−	4.97130i	0.250986	−	0.171119i
$845$	−9.76598	−	1.47199i	−0.335960	−	0.0506378i
$846$	10.0597	+	4.84448i	0.345858	+	0.166557i
$847$		0			0
$848$	23.3725	−	11.2556i	0.802616	−	0.386520i
$849$	−1.68220	+	0.518890i	−0.0577329	+	0.0178082i
$850$	0.996591	+	2.53927i	0.0341828	+	0.0870963i
$851$	−32.6396	+	56.5334i	−1.11887	+	1.93794i
$852$	7.47142	+	12.9409i	0.255967	+	0.443347i
$853$	20.0999	−	25.2045i	0.688209	−	0.862987i	−0.307872	−	0.951428i	$-0.599617\pi$
$853$	20.0999	−	25.2045i	0.688209	−	0.862987i	0.996081	+	0.0884409i	$0.0281884\pi$
$854$		0			0
$855$	−1.78686	−	2.24066i	−0.0611094	−	0.0766288i
$856$	−1.09313	+	2.78525i	−0.0373625	+	0.0951980i
$857$	0.00267714	−	0.0357240i	9.14495e−5	−	0.00122031i	−0.997158	−	0.0753402i	$-0.975996\pi$
$857$	0.00267714	−	0.0357240i	9.14495e−5	−	0.00122031i	0.997249	+	0.0741199i	$0.0236148\pi$
$858$	2.79708	−	37.3244i	0.0954906	−	1.27423i
$859$	−4.21185	+	10.7316i	−0.143706	+	0.366158i	−0.984546	−	0.175126i	$-0.943967\pi$
$859$	−4.21185	+	10.7316i	−0.143706	+	0.366158i	0.840839	+	0.541285i	$0.182062\pi$
$860$	−3.00219	−	3.76463i	−0.102374	−	0.128373i
$861$		0			0
$862$	−8.35323	+	10.4746i	−0.284512	+	0.356767i
$863$	0.570412	+	0.987983i	0.0194171	+	0.0336313i	0.875571	−	0.483090i	$-0.160486\pi$
$863$	0.570412	+	0.987983i	0.0194171	+	0.0336313i	−0.856154	+	0.516721i	$0.827152\pi$
$864$	18.7087	−	32.4043i	0.636481	−	1.10242i
$865$	10.6152	+	27.0471i	0.360928	+	0.919629i
$866$	−8.30649	+	2.56221i	−0.282266	+	0.0870676i
$867$	−23.6943	+	11.4106i	−0.804702	+	0.387524i
$868$		0			0
$869$	−35.9442	−	17.3098i	−1.21932	−	0.587195i
$870$	9.26804	+	1.39693i	0.314216	+	0.0473604i
$871$	3.96140	−	2.70084i	0.134227	−	0.0915144i
$872$	−3.78474	−	3.51173i	−0.128168	−	0.118922i
$873$	4.28835	+	2.92375i	0.145139	+	0.0989539i
$874$	−10.6660	−	46.7307i	−0.360782	−	1.58069i
$875$		0			0
$876$	4.03574	−	17.6817i	0.136355	−	0.597410i
$877$	−24.7084	+	22.9260i	−0.834343	+	0.774157i	−0.976461	−	0.215693i	$-0.930799\pi$
$877$	−24.7084	+	22.9260i	−0.834343	+	0.774157i	0.142119	+	0.989850i	$0.454609\pi$
$878$	−24.8311	+	3.74268i	−0.838008	+	0.126309i
$879$	32.6134	+	10.0599i	1.10002	+	0.339312i
$880$	1.44928	+	19.3393i	0.0488552	+	0.651927i
$881$	−3.43604			−0.115763			−0.0578815	−	0.998323i	$-0.518435\pi$
$881$	−3.43604			−0.115763			−0.0578815	+	0.998323i	$0.518435\pi$
$882$		0			0
$883$	32.7898			1.10346			0.551732	−	0.834022i	$-0.313967\pi$
$883$	32.7898			1.10346			0.551732	+	0.834022i	$0.313967\pi$
$884$	−0.227609	−	3.03724i	−0.00765534	−	0.102153i
$885$	7.80796	+	2.40844i	0.262462	+	0.0809587i
$886$	−38.7564	+	5.84159i	−1.30205	+	0.196252i
$887$	6.90421	−	6.40617i	0.231821	−	0.215098i	−0.555706	−	0.831379i	$-0.687552\pi$
$887$	6.90421	−	6.40617i	0.231821	−	0.215098i	0.787526	+	0.616281i	$0.211361\pi$
$888$	−3.65442	+	16.0111i	−0.122634	+	0.537296i
$889$		0			0
$890$	0.448792	+	1.96629i	0.0150435	+	0.0659100i
$891$	16.8870	+	11.5134i	0.565736	+	0.385713i
$892$	10.5404	+	9.78006i	0.352919	+	0.327461i
$893$	35.2921	−	24.0618i	1.18101	−	0.805197i
$894$	−5.68587	−	0.857007i	−0.190164	−	0.0286626i
$895$	3.98820	+	1.92062i	0.133311	+	0.0641991i
$896$		0			0
$897$	43.1254	−	20.7681i	1.43991	−	0.693426i
$898$	−56.1946	+	17.3337i	−1.87524	+	0.578434i
$899$	6.69792	+	17.0660i	0.223388	+	0.569184i
$900$	−1.16490	+	2.01767i	−0.0388301	+	0.0672558i
$901$	1.29449	+	2.24213i	0.0431258	+	0.0746960i
$902$	23.3086	−	29.2281i	0.776093	−	0.973189i
$903$		0			0
$904$	−10.1989	−	12.7890i	−0.339211	−	0.425357i
$905$	−8.60851	+	21.9341i	−0.286156	+	0.729115i
$906$	2.54077	−	33.9042i	0.0844114	−	1.12639i
$907$	−1.54280	+	20.5873i	−0.0512280	+	0.683590i	0.911185	+	0.411998i	$0.135169\pi$
$907$	−1.54280	+	20.5873i	−0.0512280	+	0.683590i	−0.962413	+	0.271591i	$0.912450\pi$
$908$	13.5969	−	34.6443i	0.451228	−	1.14971i
$909$	−2.20614	−	2.76642i	−0.0731731	−	0.0917562i
$910$		0			0
$911$	−22.0419	+	27.6397i	−0.730282	+	0.915745i	−0.998871	−	0.0475101i	$-0.984871\pi$
$911$	−22.0419	+	27.6397i	−0.730282	+	0.915745i	0.268589	+	0.963255i	$0.413443\pi$
$912$	−14.4549	−	25.0367i	−0.478651	−	0.829048i
$913$	−0.744969	+	1.29032i	−0.0246549	+	0.0427035i
$914$	0.125401	+	0.319517i	0.00414791	+	0.0105687i
$915$	0.0843858	−	0.0260296i	0.00278971	−	0.000860511i
$916$	30.3522	−	14.6169i	1.00287	−	0.482955i
$917$		0			0
$918$	4.45474	+	2.14529i	0.147028	+	0.0708050i
$919$	−6.92670	−	1.04403i	−0.228491	−	0.0344394i	0.0337989	−	0.999429i	$-0.489239\pi$
$919$	−6.92670	−	1.04403i	−0.228491	−	0.0344394i	−0.262289	+	0.964989i	$0.584478\pi$
$920$	−8.54737	+	5.82750i	−0.281798	+	0.192127i
$921$	−24.2430	−	22.4942i	−0.798835	−	0.741211i
$922$	−12.8365	−	8.75178i	−0.422748	−	0.288224i
$923$	−6.74713	−	29.5611i	−0.222084	−	0.973015i
$924$		0			0
$925$	6.53627	−	28.6373i	0.214911	−	0.941588i
$926$	−1.00666	+	0.934049i	−0.0330811	+	0.0306947i
$927$	1.32739	−	0.200071i	0.0435971	−	0.00657121i
$928$	−14.9773	−	4.61989i	−0.491655	−	0.151655i
$929$	1.17182	+	15.6369i	0.0384462	+	0.513029i	0.982870	+	0.184299i	$0.0590016\pi$
$929$	1.17182	+	15.6369i	0.0384462	+	0.513029i	−0.944424	+	0.328730i	$0.893379\pi$
$930$	−31.7667			−1.04167
$931$		0			0
$932$	−27.0699			−0.886705
$933$	−0.0974558	−	1.30046i	−0.00319056	−	0.0425751i
$934$	−6.23516	−	1.92329i	−0.204021	−	0.0629321i
$935$	−1.91387	+	0.288469i	−0.0625902	+	0.00943395i
$936$	−1.93757	+	1.79780i	−0.0633315	+	0.0587630i
$937$	−11.1098	+	48.6753i	−0.362942	+	1.59015i	0.382744	+	0.923855i	$0.374979\pi$
$937$	−11.1098	+	48.6753i	−0.362942	+	1.59015i	−0.745686	+	0.666298i	$0.767878\pi$
$938$		0			0
$939$	3.93167	+	17.2258i	0.128305	+	0.562142i
$940$	18.1403	+	12.3678i	0.591671	+	0.403394i
$941$	−27.7253	−	25.7253i	−0.903820	−	0.838622i	0.0836394	−	0.996496i	$-0.473346\pi$
$941$	−27.7253	−	25.7253i	−0.903820	−	0.838622i	−0.987459	+	0.157874i	$0.949536\pi$
$942$	−30.3278	+	20.6771i	−0.988132	+	0.673697i
$943$	47.2742	+	7.12543i	1.53946	+	0.232036i
$944$	−16.3003	−	7.84979i	−0.530528	−	0.255489i
$945$		0			0
$946$	−11.7809	+	5.67336i	−0.383029	+	0.184457i
$947$	20.4357	−	6.30356i	0.664069	−	0.204838i	0.0556457	−	0.998451i	$-0.482278\pi$
$947$	20.4357	−	6.30356i	0.664069	−	0.204838i	0.608424	+	0.793612i	$0.291802\pi$
$948$	11.1679	+	28.4554i	0.362718	+	0.924190i
$949$	−18.4008	+	31.8711i	−0.597315	+	1.03458i
$950$	10.7841	+	18.6786i	0.349882	+	0.606014i
$951$	14.4756	−	18.1519i	0.469404	−	0.588614i
$952$		0			0
$953$	9.75003	+	12.2262i	0.315835	+	0.396044i	0.914256	−	0.405138i	$-0.132776\pi$
$953$	9.75003	+	12.2262i	0.315835	+	0.396044i	−0.598421	+	0.801182i	$0.704205\pi$
$954$	−1.95490	+	4.98100i	−0.0632922	+	0.161266i
$955$	1.47253	−	19.6496i	0.0476500	−	0.635846i
$956$	−0.00495781	+	0.0661574i	−0.000160347	+	0.00213968i
$957$	3.84262	−	9.79084i	0.124214	−	0.316493i
$958$	−14.2971	−	17.9281i	−0.461920	−	0.579229i
$959$		0			0
$960$	3.77772	−	4.73711i	0.121925	−	0.152890i
$961$	−15.5683	−	26.9651i	−0.502204	−	0.869842i
$962$	−39.6826	+	68.7324i	−1.27942	+	2.21602i
$963$	−0.540563	−	1.37733i	−0.0174194	−	0.0443839i
$964$	−1.43320	+	0.442085i	−0.0461604	+	0.0142386i
$965$	18.6856	−	8.99849i	0.601509	−	0.289672i
$966$		0			0
$967$	−22.6459	−	10.9057i	−0.728243	−	0.350703i	0.0327500	−	0.999464i	$-0.489573\pi$
$967$	−22.6459	−	10.9057i	−0.728243	−	0.350703i	−0.760993	+	0.648760i	$0.775288\pi$
$968$	−2.90073	−	0.437215i	−0.0932330	−	0.0140526i
$969$	2.38388	−	1.62530i	0.0765814	−	0.0522123i
$970$	18.1042	+	16.7982i	0.581291	+	0.539359i
$971$	−36.3940	−	24.8130i	−1.16794	−	0.796286i	−0.185457	−	0.982652i	$-0.559377\pi$
$971$	−36.3940	−	24.8130i	−1.16794	−	0.796286i	−0.982480	+	0.186366i	$0.940329\pi$
$972$	1.73605	+	7.60611i	0.0556837	+	0.243966i
$973$		0			0
$974$	12.7462	−	55.8448i	0.408415	−	1.78938i
$975$	−15.7886	+	14.6496i	−0.505639	+	0.469164i
$976$	−0.193348	+	0.0291425i	−0.00618891	+	0.000932828i
$977$	20.7678	+	6.40603i	0.664422	+	0.204947i	0.608580	−	0.793492i	$-0.291739\pi$
$977$	20.7678	+	6.40603i	0.664422	+	0.204947i	0.0558422	+	0.998440i	$0.482216\pi$
$978$	−0.958897	−	12.7956i	−0.0306621	−	0.409158i
$979$	2.26328			0.0723346
$980$		0			0
$981$	2.55315			0.0815157
$982$	−3.19193	−	42.5934i	−0.101859	−	1.35921i
$983$	−33.3330	−	10.2819i	−1.06316	−	0.327940i	−0.286641	−	0.958038i	$-0.592539\pi$
$983$	−33.3330	−	10.2819i	−1.06316	−	0.327940i	−0.776516	+	0.630098i	$0.783015\pi$
$984$	11.8931	−	1.79260i	0.379140	−	0.0571461i
$985$	19.2629	−	17.8734i	0.613767	−	0.569492i
$986$	0.460873	−	2.01922i	0.0146772	−	0.0643049i
$987$		0			0
$988$	−5.35872	−	23.4781i	−0.170484	−	0.746938i
$989$	−13.8162	−	9.41969i	−0.439328	−	0.299529i
$990$	−2.93239	−	2.72086i	−0.0931974	−	0.0864745i
$991$	−14.2860	+	9.74005i	−0.453811	+	0.309403i	−0.768567	−	0.639770i	$-0.779030\pi$
$991$	−14.2860	+	9.74005i	−0.453811	+	0.309403i	0.314756	+	0.949173i	$0.398077\pi$
$992$	52.5289	+	7.91746i	1.66780	+	0.251380i
$993$	29.7995	+	14.3507i	0.945658	+	0.455405i
$994$		0			0
$995$	10.1637	−	4.89460i	0.322212	−	0.155169i
$996$	1.09091	−	0.336500i	0.0345667	−	0.0106624i
$997$	−7.01382	−	17.8709i	−0.222130	−	0.565978i	0.775751	−	0.631039i	$-0.217371\pi$
$997$	−7.01382	−	17.8709i	−0.222130	−	0.565978i	−0.997881	+	0.0650609i	$0.979276\pi$
$998$	7.87739	−	13.6440i	0.249354	−	0.431894i
$999$	−26.6209	−	46.1088i	−0.842249	−	1.45882i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	343.2.g.h.116.4		48
7.2	even	3		343.2.g.g.30.4		48
7.3	odd	6		343.2.e.d.197.2		48
7.4	even	3		343.2.e.c.197.2		48
7.5	odd	6		49.2.g.a.37.4	yes	48
7.6	odd	2		343.2.g.i.116.4		48
21.5	even	6		441.2.bb.d.37.1		48
28.19	even	6		784.2.bg.c.625.3		48
49.4	even	21		343.2.e.c.148.2		48
49.11	even	21		2401.2.a.i.1.20		24
49.22	even	7		343.2.g.g.263.4		48
49.23	even	21	inner	343.2.g.h.275.4		48
49.26	odd	42		343.2.g.i.275.4		48
49.27	odd	14		49.2.g.a.4.4	✓	48
49.38	odd	42		2401.2.a.h.1.20		24
49.45	odd	42		343.2.e.d.148.2		48
147.125	even	14		441.2.bb.d.298.1		48
196.27	even	14		784.2.bg.c.641.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.4.4	✓	48	49.27	odd	14
49.2.g.a.37.4	yes	48	7.5	odd	6
343.2.e.c.148.2		48	49.4	even	21
343.2.e.c.197.2		48	7.4	even	3
343.2.e.d.148.2		48	49.45	odd	42
343.2.e.d.197.2		48	7.3	odd	6
343.2.g.g.30.4		48	7.2	even	3
343.2.g.g.263.4		48	49.22	even	7
343.2.g.h.116.4		48	1.1	even	1	trivial
343.2.g.h.275.4		48	49.23	even	21	inner
343.2.g.i.116.4		48	7.6	odd	2
343.2.g.i.275.4		48	49.26	odd	42
441.2.bb.d.37.1		48	21.5	even	6
441.2.bb.d.298.1		48	147.125	even	14
784.2.bg.c.625.3		48	28.19	even	6
784.2.bg.c.641.3		48	196.27	even	14
2401.2.a.h.1.20		24	49.38	odd	42
2401.2.a.i.1.20		24	49.11	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)

\(f(q)\)	\(=\)	\(q+(0.137969 + 1.84107i) q^{2} +(-1.49877 - 0.462308i) q^{3} +(-1.39283 + 0.209936i) q^{4} +(-1.02018 + 0.946588i) q^{5} +(0.644358 - 2.82312i) q^{6} +(0.242977 + 1.06455i) q^{8} +(-0.446142 - 0.304175i) q^{9} +O(q^{10})\)	\(q+(0.137969 + 1.84107i) q^{2} +(-1.49877 - 0.462308i) q^{3} +(-1.39283 + 0.209936i) q^{4} +(-1.02018 + 0.946588i) q^{5} +(0.644358 - 2.82312i) q^{6} +(0.242977 + 1.06455i) q^{8} +(-0.446142 - 0.304175i) q^{9} +(-1.88349 - 1.74762i) q^{10} +(-2.38230 + 1.62423i) q^{11} +(2.18458 + 0.329273i) q^{12} +(-4.03898 - 1.94507i) q^{13} +(1.96663 - 0.947078i) q^{15} +(-4.61836 + 1.42457i) q^{16} +(-0.176220 - 0.449001i) q^{17} +(0.498452 - 0.863344i) q^{18} +(-1.90688 - 3.30281i) q^{19} +(1.22222 - 1.53261i) q^{20} +(-3.31899 - 4.16188i) q^{22} +(2.48708 - 6.33698i) q^{23} +(0.127985 - 1.70784i) q^{24} +(-0.228914 + 3.05464i) q^{25} +(3.02375 - 7.70439i) q^{26} +(3.46178 + 4.34093i) q^{27} +(1.45010 - 1.81836i) q^{29} +(2.01497 + 3.49003i) q^{30} +(-3.94134 + 6.82660i) q^{31} +(-2.46207 - 6.27326i) q^{32} +(4.32141 - 1.33298i) q^{33} +(0.802329 - 0.386381i) q^{34} +(0.685258 + 0.330003i) q^{36} +(-9.48212 - 1.42920i) q^{37} +(5.81760 - 3.96637i) q^{38} +(5.15426 + 4.78246i) q^{39} +(-1.25557 - 0.856034i) q^{40} +(1.56272 + 6.84673i) q^{41} +(0.546589 - 2.39476i) q^{43} +(2.97716 - 2.76240i) q^{44} +(0.743073 - 0.112000i) q^{45} +(12.0099 + 3.70458i) q^{46} +(0.836981 + 11.1687i) q^{47} +7.58043 q^{48} -5.65538 q^{50} +(0.0565357 + 0.754416i) q^{51} +(6.03395 + 1.86123i) q^{52} +(-5.30755 + 0.799985i) q^{53} +(-7.51433 + 6.97228i) q^{54} +(0.892902 - 3.91206i) q^{55} +(1.33105 + 5.83170i) q^{57} +(3.54780 + 2.41885i) q^{58} +(2.74408 + 2.54613i) q^{59} +(-2.54036 + 1.73198i) q^{60} +(0.0400051 + 0.00602980i) q^{61} +(-13.1120 - 6.31441i) q^{62} +(2.50091 - 1.20437i) q^{64} +(5.96166 - 1.83893i) q^{65} +(3.05032 + 7.77209i) q^{66} +(-0.534751 + 0.926216i) q^{67} +(0.339706 + 0.588388i) q^{68} +(-6.65719 + 8.34785i) q^{69} +(4.21712 + 5.28810i) q^{71} +(0.215407 - 0.548848i) q^{72} +(0.613480 - 8.18632i) q^{73} +(1.32301 - 17.6544i) q^{74} +(1.75527 - 4.47236i) q^{75} +(3.34933 + 4.19993i) q^{76} +(-8.09370 + 10.1492i) q^{78} +(6.91827 + 11.9828i) q^{79} +(3.36307 - 5.82500i) q^{80} +(-2.58973 - 6.59853i) q^{81} +(-12.3897 + 3.82171i) q^{82} +(0.465572 - 0.224208i) q^{83} +(0.604795 + 0.291254i) q^{85} +(4.48433 + 0.675905i) q^{86} +(-3.01400 + 2.05491i) q^{87} +(-2.30791 - 2.14143i) q^{88} +(-0.648563 - 0.442183i) q^{89} +(0.308721 + 1.35260i) q^{90} +(-2.13373 + 9.34846i) q^{92} +(9.06315 - 8.40937i) q^{93} +(-20.4469 + 3.08188i) q^{94} +(5.07175 + 1.56443i) q^{95} +(0.789894 + 10.5404i) q^{96} -9.61207 q^{97} +1.55689 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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