LMFDB - Embedded newform 352.2.n.a.45.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [352,2,Mod(45,352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(352, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("352.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.n (of order $8$, degree $4$, 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:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			45.7
Character	$\chi$	$=$	352.45
Dual form			352.2.n.a.133.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21532 + 0.723188i) q^{2} +(0.443524 - 1.07076i) q^{3} +(0.953999 - 1.75781i) q^{4} +(2.95283 - 1.22310i) q^{5} +(0.235339 + 1.62207i) q^{6} +(-0.544294 + 0.544294i) q^{7} +(0.111813 + 2.82622i) q^{8} +(1.17150 + 1.17150i) q^{9} +(-2.70410 + 3.62191i) q^{10} +(0.382683 + 0.923880i) q^{11} +(-1.45907 - 1.80114i) q^{12} +(2.32285 + 0.962156i) q^{13} +(0.267864 - 1.05512i) q^{14} -3.70425i q^{15} +(-2.17977 - 3.35389i) q^{16} -3.46265i q^{17} +(-2.27096 - 0.576532i) q^{18} +(-1.89621 - 0.785436i) q^{19} +(0.667018 - 6.35734i) q^{20} +(0.341402 + 0.824218i) q^{21} +(-1.13322 - 0.846056i) q^{22} +(-0.669534 - 0.669534i) q^{23} +(3.07580 + 1.13377i) q^{24} +(3.68769 - 3.68769i) q^{25} +(-3.51882 + 0.510531i) q^{26} +(4.98628 - 2.06538i) q^{27} +(0.437509 + 1.47602i) q^{28} +(-0.762793 + 1.84154i) q^{29} +(2.67887 + 4.50185i) q^{30} -4.05527 q^{31} +(5.07461 + 2.49966i) q^{32} +1.15898 q^{33} +(2.50415 + 4.20822i) q^{34} +(-0.941481 + 2.27294i) q^{35} +(3.17689 - 0.941664i) q^{36} +(5.37371 - 2.22586i) q^{37} +(2.87252 - 0.416761i) q^{38} +(2.06048 - 2.06048i) q^{39} +(3.78692 + 8.20858i) q^{40} +(-3.07787 - 3.07787i) q^{41} +(-1.01098 - 0.754789i) q^{42} +(3.30436 + 7.97743i) q^{43} +(1.98908 + 0.208696i) q^{44} +(4.89211 + 2.02638i) q^{45} +(1.29790 + 0.329498i) q^{46} -6.97739i q^{47} +(-4.55800 + 0.846487i) q^{48} +6.40749i q^{49} +(-1.81483 + 7.14862i) q^{50} +(-3.70767 - 1.53577i) q^{51} +(3.90728 - 3.16523i) q^{52} +(-4.90560 - 11.8432i) q^{53} +(-4.56625 + 6.11611i) q^{54} +(2.26000 + 2.26000i) q^{55} +(-1.59915 - 1.47743i) q^{56} +(-1.68203 + 1.68203i) q^{57} +(-0.404746 - 2.78971i) q^{58} +(-10.1996 + 4.22479i) q^{59} +(-6.51137 - 3.53385i) q^{60} +(-2.45277 + 5.92151i) q^{61} +(4.92844 - 2.93272i) q^{62} -1.27528 q^{63} +(-7.97500 + 0.632013i) q^{64} +8.03580 q^{65} +(-1.40854 + 0.838164i) q^{66} +(-3.06636 + 7.40285i) q^{67} +(-6.08667 - 3.30336i) q^{68} +(-1.01387 + 0.419957i) q^{69} +(-0.499561 - 3.44321i) q^{70} +(5.63181 - 5.63181i) q^{71} +(-3.17993 + 3.44191i) q^{72} +(1.23542 + 1.23542i) q^{73} +(-4.92105 + 6.59133i) q^{74} +(-2.31306 - 5.58422i) q^{75} +(-3.18963 + 2.58387i) q^{76} +(-0.711155 - 0.294570i) q^{77} +(-1.01403 + 3.99426i) q^{78} -5.32846i q^{79} +(-10.5387 - 7.23739i) q^{80} -1.28490i q^{81} +(5.96647 + 1.51471i) q^{82} +(-4.83109 - 2.00110i) q^{83} +(1.77451 + 0.186183i) q^{84} +(-4.23518 - 10.2246i) q^{85} +(-9.78503 - 7.30545i) q^{86} +(1.63354 + 1.63354i) q^{87} +(-2.56829 + 1.18485i) q^{88} +(-4.28348 + 4.28348i) q^{89} +(-7.41093 + 1.07522i) q^{90} +(-1.78801 + 0.740618i) q^{91} +(-1.81565 + 0.538177i) q^{92} +(-1.79861 + 4.34223i) q^{93} +(5.04596 + 8.47975i) q^{94} -6.55985 q^{95} +(4.92726 - 4.32504i) q^{96} +13.1781 q^{97} +(-4.63382 - 7.78714i) q^{98} +(-0.634012 + 1.53064i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 16 q^{10} - 16 q^{14} - 16 q^{20} + 24 q^{24} - 48 q^{27} + 40 q^{28} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 56 q^{36} - 16 q^{38} - 48 q^{39} - 64 q^{40} - 104 q^{48} - 80 q^{50} + 32 q^{51} + 64 q^{54}+ \cdots + 56 q^{98}+O(q^{100}) $ 160 * q - 16 * q^10 - 16 * q^14 - 16 * q^20 + 24 * q^24 - 48 * q^27 + 40 * q^28 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 56 * q^36 - 16 * q^38 - 48 * q^39 - 64 * q^40 - 104 * q^48 - 80 * q^50 + 32 * q^51 + 64 * q^54 - 40 * q^56 + 8 * q^58 + 32 * q^59 - 8 * q^60 - 64 * q^61 + 24 * q^62 - 24 * q^64 + 48 * q^68 - 64 * q^69 - 24 * q^70 + 32 * q^71 + 72 * q^72 - 128 * q^78 - 16 * q^80 + 40 * q^82 - 80 * q^83 - 152 * q^84 - 64 * q^86 - 112 * q^87 + 144 * q^90 - 72 * q^92 + 96 * q^94 + 56 * q^96 + 56 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.21532	+	0.723188i	−0.859360	+	0.511371i
$2$	−1.21532	+	0.723188i	−0.859360	+	0.511371i
$3$	0.443524	−	1.07076i	0.256069	−	0.618205i	−0.742603	−	0.669732i	$-0.766409\pi$
$3$	0.443524	−	1.07076i	0.256069	−	0.618205i	0.998672	+	0.0515273i	$0.0164089\pi$
$4$	0.953999	−	1.75781i	0.476999	−	0.878904i
$5$	2.95283	−	1.22310i	1.32055	−	0.546988i	0.392602	−	0.919708i	$-0.371575\pi$
$5$	2.95283	−	1.22310i	1.32055	−	0.546988i	0.927944	+	0.372720i	$0.121575\pi$
$6$	0.235339	+	1.62207i	0.0960767	+	0.662207i
$7$	−0.544294	+	0.544294i	−0.205724	+	0.205724i	−0.802447	−	0.596723i	$-0.796469\pi$
$7$	−0.544294	+	0.544294i	−0.205724	+	0.205724i	0.596723	+	0.802447i	$0.296469\pi$
$8$	0.111813	+	2.82622i	0.0395317	+	0.999218i
$9$	1.17150	+	1.17150i	0.390501	+	0.390501i
$10$	−2.70410	+	3.62191i	−0.855110	+	1.14535i
$11$	0.382683	+	0.923880i	0.115383	+	0.278560i
$11$	0.382683	+	0.923880i	0.115383	+	0.278560i
$12$	−1.45907	−	1.80114i	−0.421198	−	0.519943i
$13$	2.32285	+	0.962156i	0.644243	+	0.266854i	0.680791	−	0.732478i	$-0.261636\pi$
$13$	2.32285	+	0.962156i	0.644243	+	0.266854i	−0.0365481	+	0.999332i	$0.511636\pi$
$14$	0.267864	−	1.05512i	0.0715897	−	0.281992i
$15$		−	3.70425i		−	0.956434i
$16$	−2.17977	−	3.35389i	−0.544943	−	0.838473i
$17$		−	3.46265i		−	0.839816i	−0.907567	−	0.419908i	$-0.862062\pi$
$17$		−	3.46265i		−	0.839816i	0.907567	−	0.419908i	$-0.137938\pi$
$18$	−2.27096	−	0.576532i	−0.535272	−	0.135890i
$19$	−1.89621	−	0.785436i	−0.435020	−	0.180191i	0.154416	−	0.988006i	$-0.450650\pi$
$19$	−1.89621	−	0.785436i	−0.435020	−	0.180191i	−0.589437	+	0.807815i	$0.700650\pi$
$20$	0.667018	−	6.35734i	0.149150	−	1.42155i
$21$	0.341402	+	0.824218i	0.0745000	+	0.179859i
$22$	−1.13322	−	0.846056i	−0.241603	−	0.180380i
$23$	−0.669534	−	0.669534i	−0.139607	−	0.139607i	0.633849	−	0.773457i	$-0.281474\pi$
$23$	−0.669534	−	0.669534i	−0.139607	−	0.139607i	−0.773457	+	0.633849i	$0.781474\pi$
$24$	3.07580	+	1.13377i	0.627844	+	0.231430i
$25$	3.68769	−	3.68769i	0.737539	−	0.737539i
$26$	−3.51882	+	0.510531i	−0.690098	+	0.100123i
$27$	4.98628	−	2.06538i	0.959609	−	0.397483i
$28$	0.437509	+	1.47602i	0.0826813	+	0.278942i
$29$	−0.762793	+	1.84154i	−0.141647	+	0.341966i	−0.978743	−	0.205090i	$-0.934251\pi$
$29$	−0.762793	+	1.84154i	−0.141647	+	0.341966i	0.837096	+	0.547056i	$0.184251\pi$
$30$	2.67887	+	4.50185i	0.489093	+	0.821922i
$31$	−4.05527			−0.728347			−0.364174	−	0.931331i	$-0.618649\pi$
$31$	−4.05527			−0.728347			−0.364174	+	0.931331i	$0.618649\pi$
$32$	5.07461	+	2.49966i	0.897073	+	0.441882i
$33$	1.15898			0.201753
$34$	2.50415	+	4.20822i	0.429458	+	0.721704i
$35$	−0.941481	+	2.27294i	−0.159139	+	0.384196i
$36$	3.17689	−	0.941664i	0.529481	−	0.156944i
$37$	5.37371	−	2.22586i	0.883432	−	0.365930i	0.105605	−	0.994408i	$-0.466322\pi$
$37$	5.37371	−	2.22586i	0.883432	−	0.365930i	0.777827	+	0.628478i	$0.216322\pi$
$38$	2.87252	−	0.416761i	0.465984	−	0.0676076i
$39$	2.06048	−	2.06048i	0.329941	−	0.329941i
$40$	3.78692	+	8.20858i	0.598764	+	1.29789i
$41$	−3.07787	−	3.07787i	−0.480683	−	0.480683i	0.424667	−	0.905350i	$-0.360391\pi$
$41$	−3.07787	−	3.07787i	−0.480683	−	0.480683i	−0.905350	+	0.424667i	$0.860391\pi$
$42$	−1.01098	−	0.754789i	−0.155997	−	0.116466i
$43$	3.30436	+	7.97743i	0.503910	+	1.21655i	0.947338	+	0.320236i	$0.103762\pi$
$43$	3.30436	+	7.97743i	0.503910	+	1.21655i	−0.443428	+	0.896310i	$0.646238\pi$
$44$	1.98908	+	0.208696i	0.299865	+	0.0314621i
$45$	4.89211	+	2.02638i	0.729273	+	0.302075i
$46$	1.29790	+	0.329498i	0.191364	+	0.0485819i
$47$		−	6.97739i		−	1.01776i	−0.860839	−	0.508878i	$-0.830060\pi$
$47$		−	6.97739i		−	1.01776i	0.860839	−	0.508878i	$-0.169940\pi$
$48$	−4.55800	+	0.846487i	−0.657891	+	0.122180i
$49$			6.40749i			0.915355i
$50$	−1.81483	+	7.14862i	−0.256655	+	1.01097i
$51$	−3.70767	−	1.53577i	−0.519178	−	0.215051i
$52$	3.90728	−	3.16523i	0.541842	−	0.438938i
$53$	−4.90560	−	11.8432i	−0.673836	−	1.62678i	−0.775035	−	0.631919i	$-0.782268\pi$
$53$	−4.90560	−	11.8432i	−0.673836	−	1.62678i	0.101198	−	0.994866i	$-0.467732\pi$
$54$	−4.56625	+	6.11611i	−0.621389	+	0.832298i
$55$	2.26000	+	2.26000i	0.304738	+	0.304738i
$56$	−1.59915	−	1.47743i	−0.213696	−	0.197430i
$57$	−1.68203	+	1.68203i	−0.222790	+	0.222790i
$58$	−0.404746	−	2.78971i	−0.0531458	−	0.366306i
$59$	−10.1996	+	4.22479i	−1.32787	+	0.550021i	−0.930047	−	0.367441i	$-0.880234\pi$
$59$	−10.1996	+	4.22479i	−1.32787	+	0.550021i	−0.397822	+	0.917462i	$0.630234\pi$
$60$	−6.51137	−	3.53385i	−0.840614	−	0.456219i
$61$	−2.45277	+	5.92151i	−0.314045	+	0.758172i	0.685502	+	0.728071i	$0.259583\pi$
$61$	−2.45277	+	5.92151i	−0.314045	+	0.758172i	−0.999547	+	0.0301010i	$0.990417\pi$
$62$	4.92844	−	2.93272i	0.625912	−	0.372456i
$63$	−1.27528			−0.160671
$64$	−7.97500	+	0.632013i	−0.996874	+	0.0790017i
$65$	8.03580			0.996718
$66$	−1.40854	+	0.838164i	−0.173379	+	0.103171i
$67$	−3.06636	+	7.40285i	−0.374615	+	0.904402i	0.618340	+	0.785911i	$0.287806\pi$
$67$	−3.06636	+	7.40285i	−0.374615	+	0.904402i	−0.992955	+	0.118491i	$0.962194\pi$
$68$	−6.08667	−	3.30336i	−0.738117	−	0.400592i
$69$	−1.01387	+	0.419957i	−0.122055	+	0.0505569i
$70$	−0.499561	−	3.44321i	−0.0597089	−	0.411542i
$71$	5.63181	−	5.63181i	0.668373	−	0.668373i	−0.288966	−	0.957339i	$-0.593312\pi$
$71$	5.63181	−	5.63181i	0.668373	−	0.668373i	0.957339	+	0.288966i	$0.0933116\pi$
$72$	−3.17993	+	3.44191i	−0.374758	+	0.405633i
$73$	1.23542	+	1.23542i	0.144595	+	0.144595i	0.775699	−	0.631103i	$-0.217398\pi$
$73$	1.23542	+	1.23542i	0.144595	+	0.144595i	−0.631103	+	0.775699i	$0.717398\pi$
$74$	−4.92105	+	6.59133i	−0.572061	+	0.766227i
$75$	−2.31306	−	5.58422i	−0.267089	−	0.644811i
$76$	−3.18963	+	2.58387i	−0.365875	+	0.296390i
$77$	−0.711155	−	0.294570i	−0.0810436	−	0.0335694i
$78$	−1.01403	+	3.99426i	−0.114816	+	0.452260i
$79$		−	5.32846i		−	0.599499i	−0.954018	−	0.299749i	$-0.903097\pi$
$79$		−	5.32846i		−	0.599499i	0.954018	−	0.299749i	$-0.0969031\pi$
$80$	−10.5387	−	7.23739i	−1.17826	−	0.809164i
$81$		−	1.28490i		−	0.142767i
$82$	5.96647	+	1.51471i	0.658887	+	0.167272i
$83$	−4.83109	−	2.00110i	−0.530281	−	0.219650i	0.101445	−	0.994841i	$-0.467653\pi$
$83$	−4.83109	−	2.00110i	−0.530281	−	0.219650i	−0.631726	+	0.775192i	$0.717653\pi$
$84$	1.77451	+	0.186183i	0.193615	+	0.0203143i
$85$	−4.23518	−	10.2246i	−0.459369	−	1.10902i
$86$	−9.78503	−	7.30545i	−1.05515	−	0.787767i
$87$	1.63354	+	1.63354i	0.175134	+	0.175134i
$88$	−2.56829	+	1.18485i	−0.273781	+	0.126305i
$89$	−4.28348	+	4.28348i	−0.454048	+	0.454048i	−0.896696	−	0.442648i	$-0.854039\pi$
$89$	−4.28348	+	4.28348i	−0.454048	+	0.454048i	0.442648	+	0.896696i	$0.354039\pi$
$90$	−7.41093	+	1.07522i	−0.781181	+	0.113338i
$91$	−1.78801	+	0.740618i	−0.187434	+	0.0776379i
$92$	−1.81565	+	0.538177i	−0.189294	+	0.0561089i
$93$	−1.79861	+	4.34223i	−0.186507	+	0.450268i
$94$	5.04596	+	8.47975i	0.520451	+	0.874619i
$95$	−6.55985			−0.673027
$96$	4.92726	−	4.32504i	0.502886	−	0.441423i
$97$	13.1781			1.33804			0.669018	−	0.743246i	$-0.266715\pi$
$97$	13.1781			1.33804			0.669018	+	0.743246i	$0.266715\pi$
$98$	−4.63382	−	7.78714i	−0.468086	−	0.786620i
$99$	−0.634012	+	1.53064i	−0.0637207	+	0.153835i
$100$	−2.96420	−	10.0003i	−0.296420	−	1.00003i
$101$	−9.78129	+	4.05154i	−0.973275	+	0.403144i	−0.811930	−	0.583755i	$-0.801583\pi$
$101$	−9.78129	+	4.05154i	−0.973275	+	0.403144i	−0.161344	+	0.986898i	$0.551583\pi$
$102$	5.61666	−	0.814897i	0.556132	−	0.0806868i
$103$	−6.75733	+	6.75733i	−0.665819	+	0.665819i	−0.956745	−	0.290926i	$-0.906037\pi$
$103$	−6.75733	+	6.75733i	−0.665819	+	0.665819i	0.290926	+	0.956745i	$0.406037\pi$
$104$	−2.45954	+	6.67246i	−0.241178	+	0.654288i
$105$	2.01620	+	2.01620i	0.196761	+	0.196761i
$106$	14.5267	+	10.8456i	1.41096	+	1.05341i
$107$	−6.37055	−	15.3799i	−0.615864	−	1.48683i	−0.856466	−	0.516204i	$-0.827345\pi$
$107$	−6.37055	−	15.3799i	−0.615864	−	1.48683i	0.240601	−	0.970624i	$-0.422655\pi$
$108$	1.12636	−	10.7353i	0.108384	−	1.03300i
$109$	−1.19440	−	0.494736i	−0.114403	−	0.0473871i	0.324748	−	0.945801i	$-0.394721\pi$
$109$	−1.19440	−	0.494736i	−0.114403	−	0.0473871i	−0.439151	+	0.898413i	$0.644721\pi$
$110$	−4.38102	−	1.11221i	−0.417714	−	0.106046i
$111$		−	6.74119i		−	0.639845i
$112$	3.01194	+	0.639066i	0.284602	+	0.0603861i
$113$			19.3552i			1.82079i	0.413744	+	0.910393i	$0.364221\pi$
$113$			19.3552i			1.82079i	−0.413744	+	0.910393i	$0.635779\pi$
$114$	0.827779	−	3.26063i	0.0775286	−	0.305386i
$115$	−2.79593	−	1.15811i	−0.260722	−	0.107994i
$116$	2.50938	+	3.09767i	0.232990	+	0.287612i
$117$	1.59406	+	3.84839i	0.147371	+	0.355784i
$118$	9.34039	−	12.5107i	0.859853	−	1.15170i
$119$	1.88470	+	1.88470i	0.172770	+	0.172770i
$120$	10.4690	−	0.414182i	0.955687	−	0.0378095i
$121$	−0.707107	+	0.707107i	−0.0642824	+	0.0642824i
$122$	−1.30147	−	8.97034i	−0.117829	−	0.812136i
$123$	−4.66078	+	1.93056i	−0.420248	+	0.174072i
$124$	−3.86872	+	7.12838i	−0.347421	+	0.640147i
$125$	0.263194	−	0.635405i	0.0235407	−	0.0568324i
$126$	1.54988	−	0.922270i	0.138074	−	0.0821623i
$127$	−1.19298			−0.105860			−0.0529298	−	0.998598i	$-0.516856\pi$
$127$	−1.19298			−0.105860			−0.0529298	+	0.998598i	$0.516856\pi$
$128$	9.23510	−	6.53552i	0.816275	−	0.577664i
$129$	10.0075			0.881111
$130$	−9.76606	+	5.81139i	−0.856540	+	0.509693i
$131$	−7.77233	+	18.7641i	−0.679071	+	1.63942i	0.0866409	+	0.996240i	$0.472387\pi$
$131$	−7.77233	+	18.7641i	−0.679071	+	1.63942i	−0.765712	+	0.643183i	$0.777613\pi$
$132$	1.10567	−	2.03727i	0.0962362	−	0.177322i
$133$	1.45960	−	0.604588i	0.126564	−	0.0524244i
$134$	−1.62705	−	11.2144i	−0.140555	−	0.968774i
$135$	12.1975	−	12.1975i	1.04979	−	1.04979i
$136$	9.78620	−	0.387168i	0.839160	−	0.0331994i
$137$	11.2859	+	11.2859i	0.964218	+	0.964218i	0.999382	−	0.0351637i	$-0.0111953\pi$
$137$	11.2859	+	11.2859i	0.964218	+	0.964218i	−0.0351637	+	0.999382i	$0.511195\pi$
$138$	0.928463	−	1.24360i	0.0790360	−	0.105862i
$139$	5.49063	+	13.2556i	0.465709	+	1.12432i	0.966018	+	0.258475i	$0.0832198\pi$
$139$	5.49063	+	13.2556i	0.465709	+	1.12432i	−0.500309	+	0.865847i	$0.666780\pi$
$140$	3.09721	+	3.82332i	0.261762	+	0.323130i
$141$	−7.47112	−	3.09464i	−0.629182	−	0.260616i
$142$	−2.77159	+	10.9173i	−0.232586	+	0.916159i
$143$			2.51424i			0.210251i
$144$	1.37548	−	6.48270i	0.114624	−	0.540225i
$145$			6.37074i			0.529061i
$146$	−2.39488	−	0.607990i	−0.198201	−	0.0503176i
$147$	6.86090	+	2.84188i	0.565877	+	0.234394i
$148$	1.21387	−	11.5694i	0.0997797	−	0.951000i
$149$	−3.77221	−	9.10692i	−0.309031	−	0.746068i	−0.999737	−	0.0229316i	$-0.992700\pi$
$149$	−3.77221	−	9.10692i	−0.309031	−	0.746068i	0.690706	−	0.723136i	$-0.257300\pi$
$150$	6.84955	+	5.11383i	0.559263	+	0.417543i
$151$	−5.85800	−	5.85800i	−0.476717	−	0.476717i	0.427363	−	0.904080i	$-0.359443\pi$
$151$	−5.85800	−	5.85800i	−0.476717	−	0.476717i	−0.904080	+	0.427363i	$0.859443\pi$
$152$	2.00779	−	5.44692i	0.162853	−	0.441804i
$153$	4.05650	−	4.05650i	0.327949	−	0.327949i
$154$	1.07731	−	0.156302i	0.0868120	−	0.0125952i
$155$	−11.9745	+	4.96000i	−0.961816	+	0.398397i
$156$	−1.65623	−	5.58763i	−0.132605	−	0.447368i
$157$	−6.12539	+	14.7880i	−0.488860	+	1.18021i	0.466435	+	0.884556i	$0.345538\pi$
$157$	−6.12539	+	14.7880i	−0.488860	+	1.18021i	−0.955294	+	0.295656i	$0.904462\pi$
$158$	3.85348	+	6.47578i	0.306566	+	0.515185i
$159$	−14.8570			−1.17823
$160$	18.0418	+	1.17431i	1.42633	+	0.0928370i
$161$	0.728847			0.0574412
$162$	0.929225	+	1.56156i	0.0730068	+	0.122688i
$163$	−2.27774	+	5.49896i	−0.178407	+	0.430711i	−0.987633	−	0.156786i	$-0.949887\pi$
$163$	−2.27774	+	5.49896i	−0.178407	+	0.430711i	0.809226	+	0.587497i	$0.199887\pi$
$164$	−8.34659	+	2.47402i	−0.651759	+	0.193188i
$165$	3.42228	−	1.41756i	0.266425	−	0.110357i
$166$	7.31849	−	1.06181i	0.568025	−	0.0824123i
$167$	14.6563	−	14.6563i	1.13414	−	1.13414i	0.144658	−	0.989482i	$-0.453792\pi$
$167$	14.6563	−	14.6563i	1.13414	−	1.13414i	0.989482	−	0.144658i	$-0.0462082\pi$
$168$	−2.29124	+	1.05703i	−0.176773	+	0.0815519i
$169$	−4.72250	−	4.72250i	−0.363269	−	0.363269i
$170$	12.5414	+	9.36334i	0.961882	+	0.718135i
$171$	−1.30127	−	3.14155i	−0.0995109	−	0.240241i
$172$	17.1751	+	1.80203i	1.30959	+	0.137403i
$173$	−16.8952	−	6.99823i	−1.28452	−	0.532066i	−0.367172	−	0.930153i	$-0.619674\pi$
$173$	−16.8952	−	6.99823i	−1.28452	−	0.532066i	−0.917348	+	0.398087i	$0.869674\pi$
$174$	−3.16663	−	0.803915i	−0.240061	−	0.0609446i
$175$			4.01438i			0.303459i
$176$	2.26443	−	3.29733i	0.170688	−	0.248545i
$177$			12.7951i			0.961739i
$178$	2.10803	−	8.30355i	0.158004	−	0.622377i
$179$	10.7599	+	4.45688i	0.804230	+	0.333123i	0.746649	−	0.665218i	$-0.231661\pi$
$179$	10.7599	+	4.45688i	0.804230	+	0.333123i	0.0575808	+	0.998341i	$0.481661\pi$
$180$	8.22906	−	6.66623i	0.613358	−	0.496872i
$181$	2.71805	+	6.56194i	0.202031	+	0.487745i	0.992127	−	0.125238i	$-0.0399694\pi$
$181$	2.71805	+	6.56194i	0.202031	+	0.487745i	−0.790096	+	0.612983i	$0.789969\pi$
$182$	1.63740	−	2.19315i	0.121372	−	0.162567i
$183$	5.25267	+	5.25267i	0.388288	+	0.388288i
$184$	1.81739	−	1.96711i	0.133979	−	0.145017i
$185$	13.1452	−	13.1452i	0.966454	−	0.966454i
$186$	−0.954362	−	6.57792i	−0.0699772	−	0.482316i
$187$	3.19907	−	1.32510i	0.233939	−	0.0969008i
$188$	−12.2649	−	6.65642i	−0.894510	−	0.485469i
$189$	−1.58983	+	3.83818i	−0.115643	+	0.279186i
$190$	7.97231	−	4.74401i	0.578372	−	0.344166i
$191$	0.926541			0.0670422			0.0335211	−	0.999438i	$-0.489328\pi$
$191$	0.926541			0.0670422			0.0335211	+	0.999438i	$0.489328\pi$
$192$	−2.86037	+	8.81964i	−0.206429	+	0.636503i
$193$	−4.31258			−0.310426			−0.155213	−	0.987881i	$-0.549606\pi$
$193$	−4.31258			−0.310426			−0.155213	+	0.987881i	$0.549606\pi$
$194$	−16.0156	+	9.53026i	−1.14985	+	0.684233i
$195$	3.56407	−	8.60443i	0.255228	−	0.616176i
$196$	11.2631	+	6.11273i	0.804509	+	0.436624i
$197$	24.1259	−	9.99329i	1.71890	−	0.711992i	0.719047	−	0.694962i	$-0.244579\pi$
$197$	24.1259	−	9.99329i	1.71890	−	0.711992i	0.999855	−	0.0170305i	$-0.00542123\pi$
$198$	−0.336414	−	2.31873i	−0.0239079	−	0.164785i
$199$	5.51477	−	5.51477i	0.390932	−	0.390932i	−0.484088	−	0.875019i	$-0.660848\pi$
$199$	5.51477	−	5.51477i	0.390932	−	0.390932i	0.875019	+	0.484088i	$0.160848\pi$
$200$	10.8345	+	10.0099i	0.766118	+	0.707806i
$201$	6.56668	+	6.56668i	0.463178	+	0.463178i
$202$	8.95736	−	11.9976i	0.630237	−	0.844150i
$203$	−0.587158	−	1.41753i	−0.0412104	−	0.0994908i
$204$	−6.23670	+	5.05226i	−0.436657	+	0.353729i
$205$	−12.8530	−	5.32388i	−0.897691	−	0.371836i
$206$	3.32549	−	13.0991i	0.231698	−	0.912659i
$207$		−	1.56872i		−	0.109034i
$208$	−1.83632	−	9.88787i	−0.127326	−	0.685601i
$209$		−	2.05244i		−	0.141970i
$210$	−3.90843	−	0.992236i	−0.269707	−	0.0684708i
$211$	6.47376	+	2.68152i	0.445672	+	0.184603i	0.594221	−	0.804302i	$-0.297460\pi$
$211$	6.47376	+	2.68152i	0.445672	+	0.184603i	−0.148549	+	0.988905i	$0.547460\pi$
$212$	−25.4980	−	2.67527i	−1.75121	−	0.183738i
$213$	−3.53248	−	8.52817i	−0.242042	−	0.584341i
$214$	18.8648	+	14.0843i	1.28957	+	0.962786i
$215$	19.5144	+	19.5144i	1.33087	+	1.33087i
$216$	6.39475	+	13.8614i	0.435108	+	0.943146i
$217$	2.20726	−	2.20726i	0.149838	−	0.149838i
$218$	1.80936	−	0.262513i	0.122545	−	0.0177796i
$219$	1.87078	−	0.774904i	0.126416	−	0.0523632i
$220$	6.12868	−	1.81661i	0.413195	−	0.122476i
$221$	3.33161	−	8.04322i	0.224108	−	0.541045i
$222$	4.87515	+	8.19269i	0.327198	+	0.549858i
$223$	3.43663			0.230133			0.115067	−	0.993358i	$-0.463292\pi$
$223$	3.43663			0.230133			0.115067	+	0.993358i	$0.463292\pi$
$224$	−4.12263	+	1.40153i	−0.275455	+	0.0936438i
$225$	8.64028			0.576019
$226$	−13.9975	−	23.5228i	−0.931098	−	1.56471i
$227$	−6.05107	+	14.6086i	−0.401623	+	0.969605i	0.585649	+	0.810565i	$0.300840\pi$
$227$	−6.05107	+	14.6086i	−0.401623	+	0.969605i	−0.987272	+	0.159040i	$0.949160\pi$
$228$	1.35203	+	4.56134i	0.0895404	+	0.302082i
$229$	−22.0262	+	9.12353i	−1.45553	+	0.602900i	−0.963507	−	0.267683i	$-0.913742\pi$
$229$	−22.0262	+	9.12353i	−1.45553	+	0.602900i	−0.492022	+	0.870583i	$0.663742\pi$
$230$	4.23548	−	0.614507i	0.279279	−	0.0405194i
$231$	−0.630829	+	0.630829i	−0.0415055	+	0.0415055i
$232$	−5.28989	−	1.94991i	−0.347298	−	0.128018i
$233$	−19.5904	−	19.5904i	−1.28341	−	1.28341i	−0.938715	−	0.344693i	$-0.887983\pi$
$233$	−19.5904	−	19.5904i	−1.28341	−	1.28341i	−0.344693	−	0.938715i	$-0.612017\pi$
$234$	−4.72040	−	3.52422i	−0.308582	−	0.230386i
$235$	−8.53406	−	20.6030i	−0.556701	−	1.34399i
$236$	−2.30399	+	21.9593i	−0.149977	+	1.42943i
$237$	−5.70552	−	2.36330i	−0.370613	−	0.153513i
$238$	−3.65350	−	0.927519i	−0.236822	−	0.0601221i
$239$			24.5821i			1.59008i	0.606556	+	0.795041i	$0.292551\pi$
$239$			24.5821i			1.59008i	−0.606556	+	0.795041i	$0.707449\pi$
$240$	−12.4237	+	8.07443i	−0.801944	+	0.521203i
$241$		−	10.7978i		−	0.695547i	−0.937579	−	0.347774i	$-0.886938\pi$
$241$		−	10.7978i		−	0.695547i	0.937579	−	0.347774i	$-0.113062\pi$
$242$	0.347989	−	1.37073i	0.0223696	−	0.0881139i
$243$	13.5830	+	5.62627i	0.871350	+	0.360925i
$244$	8.06894	+	9.96061i	0.516561	+	0.637663i
$245$	7.83701	+	18.9202i	0.500688	+	1.20877i
$246$	4.26817	−	5.71686i	0.272129	−	0.364494i
$247$	−3.64890	−	3.64890i	−0.232174	−	0.232174i
$248$	−0.453430	−	11.4611i	−0.0287928	−	0.727778i
$249$	−4.28541	+	4.28541i	−0.271577	+	0.271577i
$250$	0.139653	+	0.962558i	0.00883246	+	0.0608775i
$251$	15.4615	−	6.40436i	0.975920	−	0.404239i	0.163008	−	0.986625i	$-0.447881\pi$
$251$	15.4615	−	6.40436i	0.975920	−	0.404239i	0.812913	+	0.582385i	$0.197881\pi$
$252$	−1.21662	+	2.24170i	−0.0766398	+	0.141214i
$253$	0.362349	−	0.874788i	0.0227807	−	0.0549975i
$254$	1.44985	−	0.862747i	0.0909715	−	0.0541335i
$255$	−12.8265			−0.803229
$256$	−6.49718	+	14.6214i	−0.406074	+	0.913840i
$257$	−20.7719			−1.29572			−0.647858	−	0.761761i	$-0.724335\pi$
$257$	−20.7719			−1.29572			−0.647858	+	0.761761i	$0.724335\pi$
$258$	−12.1623	+	7.23730i	−0.757191	+	0.450575i
$259$	−1.71335	+	4.13640i	−0.106463	+	0.257024i
$260$	7.66614	−	14.1254i	0.475434	−	0.876019i
$261$	−3.05099	+	1.26376i	−0.188851	+	0.0782248i
$262$	−4.12408	−	28.4252i	−0.254787	−	1.75611i
$263$	14.3138	−	14.3138i	0.882624	−	0.882624i	−0.111176	−	0.993801i	$-0.535462\pi$
$263$	14.3138	−	14.3138i	0.882624	−	0.882624i	0.993801	+	0.111176i	$0.0354619\pi$
$264$	0.129589	+	3.27554i	0.00797566	+	0.201596i
$265$	−28.9708	−	28.9708i	−1.77966	−	1.77966i
$266$	−1.33665	+	1.79034i	−0.0819555	+	0.109773i
$267$	2.68676	+	6.48641i	0.164427	+	0.396962i
$268$	10.0875	+	12.4524i	0.616191	+	0.760650i
$269$	−18.8459	−	7.80622i	−1.14905	−	0.475953i	−0.274837	−	0.961491i	$-0.588624\pi$
$269$	−18.8459	−	7.80622i	−1.14905	−	0.475953i	−0.874216	+	0.485537i	$0.838624\pi$
$270$	−6.00274	+	23.6448i	−0.365315	+	1.43898i
$271$			1.27900i			0.0776939i	0.999245	+	0.0388469i	$0.0123685\pi$
$271$			1.27900i			0.0776939i	−0.999245	+	0.0388469i	$0.987632\pi$
$272$	−11.6134	+	7.54779i	−0.704163	+	0.457652i
$273$			2.24302i			0.135754i
$274$	−21.8778	−	5.55413i	−1.32168	−	0.335537i
$275$	4.81820	+	1.99576i	0.290549	+	0.120349i
$276$	−0.229023	+	2.18282i	−0.0137856	+	0.131390i
$277$	−8.25944	−	19.9400i	−0.496261	−	1.19808i	−0.951483	−	0.307703i	$-0.900440\pi$
$277$	−8.25944	−	19.9400i	−0.496261	−	1.19808i	0.455221	−	0.890378i	$-0.349560\pi$
$278$	−16.2591	−	12.1390i	−0.975157	−	0.728047i
$279$	−4.75075	−	4.75075i	−0.284420	−	0.284420i
$280$	−6.52908	−	2.40669i	−0.390187	−	0.143827i
$281$	3.33569	−	3.33569i	0.198990	−	0.198990i	−0.600577	−	0.799567i	$-0.705062\pi$
$281$	3.33569	−	3.33569i	0.198990	−	0.198990i	0.799567	+	0.600577i	$0.205062\pi$
$282$	11.3178	−	1.64205i	0.673965	−	0.0977827i
$283$	0.585643	−	0.242581i	0.0348128	−	0.0144199i	−0.365209	−	0.930926i	$-0.619003\pi$
$283$	0.585643	−	0.242581i	0.0348128	−	0.0144199i	0.400022	+	0.916506i	$0.369003\pi$
$284$	−4.52690	−	15.2724i	−0.268622	−	0.906249i
$285$	−2.90945	+	7.02404i	−0.172341	+	0.416068i
$286$	−1.81826	−	3.05560i	−0.107516	−	0.180681i
$287$	3.35053			0.197776
$288$	3.01656	+	8.87328i	0.177753	+	0.522863i
$289$	5.01005			0.294709
$290$	−4.60724	−	7.74248i	−0.270547	−	0.454654i
$291$	5.84482	−	14.1106i	0.342629	−	0.827180i
$292$	3.35023	−	0.993044i	0.196057	−	0.0581135i
$293$	8.66842	−	3.59058i	0.506415	−	0.209764i	−0.114823	−	0.993386i	$-0.536630\pi$
$293$	8.66842	−	3.59058i	0.506415	−	0.209764i	0.621238	+	0.783622i	$0.286630\pi$
$294$	−10.3934	+	1.50793i	−0.606154	+	0.0879444i
$295$	−24.9502	+	24.9502i	−1.45266	+	1.45266i
$296$	6.89162	+	14.9384i	0.400567	+	0.868276i
$297$	3.81633	+	3.81633i	0.221446	+	0.221446i
$298$	11.1704	+	8.33979i	0.647087	+	0.483111i
$299$	−0.911031	−	2.19942i	−0.0526863	−	0.127196i
$300$	−12.0226	−	1.26143i	−0.694128	−	0.0728285i
$301$	−6.14061	−	2.54353i	−0.353939	−	0.146606i
$302$	11.3558	+	2.88290i	0.653451	+	0.165892i
$303$			12.2704i			0.704916i
$304$	1.49904	+	8.07175i	0.0859759	+	0.462947i
$305$			20.4852i			1.17298i
$306$	−1.99633	+	7.86356i	−0.114123	+	0.449530i
$307$	5.10875	+	2.11611i	0.291572	+	0.120773i	0.523675	−	0.851918i	$-0.324561\pi$
$307$	5.10875	+	2.11611i	0.291572	+	0.120773i	−0.232103	+	0.972691i	$0.574561\pi$
$308$	−1.19624	+	0.969054i	−0.0681620	+	0.0552170i
$309$	4.23845	+	10.2325i	0.241117	+	0.582108i
$310$	10.9658	−	14.6878i	0.622817	−	0.834211i
$311$	7.05432	+	7.05432i	0.400014	+	0.400014i	0.878238	−	0.478224i	$-0.158719\pi$
$311$	7.05432	+	7.05432i	0.400014	+	0.400014i	−0.478224	+	0.878238i	$0.658719\pi$
$312$	6.05375	+	5.59298i	0.342726	+	0.316640i
$313$	−10.7947	+	10.7947i	−0.610154	+	0.610154i	−0.942986	−	0.332832i	$-0.891996\pi$
$313$	−10.7947	+	10.7947i	−0.610154	+	0.610154i	0.332832	+	0.942986i	$0.391996\pi$
$314$	−3.25020	−	22.4020i	−0.183420	−	1.26422i
$315$	−3.76570	+	1.55980i	−0.212173	+	0.0878849i
$316$	−9.36641	−	5.08335i	−0.526902	−	0.285961i
$317$	9.61563	−	23.2142i	0.540068	−	1.30384i	−0.384607	−	0.923081i	$-0.625663\pi$
$317$	9.61563	−	23.2142i	0.540068	−	1.30384i	0.924675	−	0.380758i	$-0.124337\pi$
$318$	18.0560	−	10.7444i	1.01253	−	0.602515i
$319$	−1.99327			−0.111602
$320$	−22.7758	+	11.6205i	−1.27321	+	0.649604i
$321$	−19.2937			−1.07687
$322$	−0.885781	+	0.527093i	−0.0493627	+	0.0293738i
$323$	−2.71969	+	6.56591i	−0.151328	+	0.365337i
$324$	−2.25861	−	1.22579i	−0.125478	−	0.0680997i
$325$	12.1141	−	5.01782i	0.671969	−	0.278339i
$326$	−1.20860	−	8.33022i	−0.0669379	−	0.461368i
$327$	−1.05949	+	1.05949i	−0.0585899	+	0.0585899i
$328$	8.35458	−	9.04287i	0.461305	−	0.499309i
$329$	3.79775	+	3.79775i	0.209377	+	0.209377i
$330$	−3.13401	+	4.19774i	−0.172521	+	0.231078i
$331$	−9.54415	−	23.0416i	−0.524594	−	1.26648i	−0.935022	−	0.354589i	$-0.884621\pi$
$331$	−9.54415	−	23.0416i	−0.524594	−	1.26648i	0.410428	−	0.911893i	$-0.365379\pi$
$332$	−8.12641	+	6.58308i	−0.445995	+	0.361293i
$333$	8.90292	+	3.68771i	0.487877	+	0.202085i
$334$	−7.21282	+	28.4114i	−0.394668	+	1.55460i
$335$			25.6098i			1.39921i
$336$	2.02016	−	2.94163i	0.110209	−	0.160479i
$337$		−	25.2384i		−	1.37482i	−0.726269	−	0.687410i	$-0.758747\pi$
$337$		−	25.2384i		−	1.37482i	0.726269	−	0.687410i	$-0.241253\pi$
$338$	9.15459	+	2.32409i	0.497944	+	0.126414i
$339$	20.7249	+	8.58451i	1.12562	+	0.466247i
$340$	−22.0133	−	2.30965i	−1.19384	−	0.125258i
$341$	−1.55188	−	3.74658i	−0.0840392	−	0.202889i
$342$	3.85340	+	2.87692i	0.208368	+	0.155566i
$343$	−7.29762	−	7.29762i	−0.394034	−	0.394034i
$344$	−22.1765	+	10.2308i	−1.19568	+	0.551608i
$345$	−2.48012	+	2.48012i	−0.133525	+	0.133525i
$346$	25.5941	−	3.71334i	1.37595	−	0.199630i
$347$	14.3160	−	5.92989i	0.768524	−	0.318333i	0.0362498	−	0.999343i	$-0.488459\pi$
$347$	14.3160	−	5.92989i	0.768524	−	0.318333i	0.732275	+	0.681010i	$0.238459\pi$
$348$	4.42984	−	1.31305i	0.237464	−	0.0703870i
$349$	−11.3291	+	27.3509i	−0.606433	+	1.46406i	0.260419	+	0.965496i	$0.416139\pi$
$349$	−11.3291	+	27.3509i	−0.606433	+	1.46406i	−0.866853	+	0.498564i	$0.833861\pi$
$350$	−2.90315	−	4.87875i	−0.155180	−	0.260780i
$351$	13.5696			0.724292
$352$	−0.367416	+	5.64491i	−0.0195833	+	0.300875i
$353$	6.76267			0.359941			0.179970	−	0.983672i	$-0.442400\pi$
$353$	6.76267			0.359941			0.179970	+	0.983672i	$0.442400\pi$
$354$	−9.25326	−	15.5501i	−0.491805	−	0.826480i
$355$	9.74150	−	23.5181i	0.517025	−	1.24821i
$356$	3.44310	+	11.6160i	0.182484	+	0.615645i
$357$	2.85398	−	1.18216i	0.151048	−	0.0625663i
$358$	−16.2998	+	2.36487i	−0.861473	+	0.124987i
$359$	17.8241	−	17.8241i	0.940720	−	0.940720i	−0.0576185	−	0.998339i	$-0.518351\pi$
$359$	17.8241	−	17.8241i	0.940720	−	0.940720i	0.998339	+	0.0576185i	$0.0183507\pi$
$360$	−5.17999	+	14.0527i	−0.273009	+	0.740645i
$361$	−10.4563	−	10.4563i	−0.550333	−	0.550333i
$362$	−8.04881	−	6.00919i	−0.423036	−	0.315836i
$363$	0.443524	+	1.07076i	0.0232790	+	0.0562004i
$364$	−0.403896	+	3.84953i	−0.0211699	+	0.201770i
$365$	5.15904	+	2.13695i	0.270037	+	0.111853i
$366$	−10.1823	−	2.58500i	−0.532239	−	0.135120i
$367$		−	20.7924i		−	1.08536i	−0.839941	−	0.542678i	$-0.817411\pi$
$367$		−	20.7924i		−	1.08536i	0.839941	−	0.542678i	$-0.182589\pi$
$368$	−0.786112	+	3.70498i	−0.0409789	+	0.193135i
$369$		−	7.21146i		−	0.375414i
$370$	−6.46915	+	25.4820i	−0.336315	+	1.32475i
$371$	9.11626	+	3.77608i	0.473293	+	0.196044i
$372$	5.91693	+	7.30408i	0.306778	+	0.378699i
$373$	10.1172	+	24.4251i	0.523850	+	1.26468i	0.935495	+	0.353341i	$0.114954\pi$
$373$	10.1172	+	24.4251i	0.523850	+	1.26468i	−0.411645	+	0.911344i	$0.635046\pi$
$374$	−2.92960	+	3.92395i	−0.151486	+	0.202902i
$375$	−0.563635	−	0.563635i	−0.0291060	−	0.0291060i
$376$	19.7196	−	0.780160i	1.01696	−	0.0402337i
$377$	−3.54371	+	3.54371i	−0.182510	+	0.182510i
$378$	−0.843580	−	5.81435i	−0.0433891	−	0.299058i
$379$	11.0476	−	4.57605i	0.567475	−	0.235056i	−0.0804519	−	0.996758i	$-0.525636\pi$
$379$	11.0476	−	4.57605i	0.567475	−	0.235056i	0.647927	+	0.761703i	$0.275636\pi$
$380$	−6.25809	+	11.5310i	−0.321033	+	0.591526i
$381$	−0.529114	+	1.27740i	−0.0271074	+	0.0654429i
$382$	−1.12604	+	0.670063i	−0.0576134	+	0.0342834i
$383$	18.3152			0.935864			0.467932	−	0.883764i	$-0.344999\pi$
$383$	18.3152			0.935864			0.467932	+	0.883764i	$0.344999\pi$
$384$	−2.90200	−	12.7873i	−0.148092	−	0.652547i
$385$	−2.46021			−0.125384
$386$	5.24116	−	3.11881i	0.266768	−	0.158743i
$387$	−5.47451	+	13.2166i	−0.278285	+	0.671840i
$388$	12.5719	−	23.1646i	0.638242	−	1.17600i
$389$	−13.5344	+	5.60611i	−0.686219	+	0.284241i	−0.698424	−	0.715684i	$-0.746115\pi$
$389$	−13.5344	+	5.60611i	−0.686219	+	0.284241i	0.0122048	+	0.999926i	$0.496115\pi$
$390$	1.89114	+	13.0346i	0.0957614	+	0.660034i
$391$	−2.31836	+	2.31836i	−0.117245	+	0.117245i
$392$	−18.1089	+	0.716438i	−0.914640	+	0.0361856i
$393$	16.6446	+	16.6446i	0.839610	+	0.839610i
$394$	−22.0937	+	29.5926i	−1.11306	+	1.49085i
$395$	−6.51726	−	15.7340i	−0.327919	−	0.791666i
$396$	2.08573	+	2.57470i	0.104812	+	0.129384i
$397$	31.9998	+	13.2548i	1.60602	+	0.665237i	0.992251	−	0.124246i	$-0.0396511\pi$
$397$	31.9998	+	13.2548i	1.60602	+	0.665237i	0.613773	+	0.789483i	$0.289651\pi$
$398$	−2.71399	+	10.6904i	−0.136040	+	0.535862i
$399$		−	1.83104i		−	0.0916666i
$400$	−20.4065	−	4.32979i	−1.02032	−	0.216489i
$401$		−	13.0539i		−	0.651879i	−0.945391	−	0.325939i	$-0.894319\pi$
$401$		−	13.0539i		−	0.651879i	0.945391	−	0.325939i	$-0.105681\pi$
$402$	−12.7296	−	3.23167i	−0.634893	−	0.161181i
$403$	−9.41978	−	3.90180i	−0.469232	−	0.194362i
$404$	−2.20951	+	21.0588i	−0.109927	+	1.04771i
$405$	−1.57157	−	3.79410i	−0.0780917	−	0.188530i
$406$	1.73872	+	1.29812i	0.0862913	+	0.0644246i
$407$	4.11286	+	4.11286i	0.203867	+	0.203867i
$408$	3.92585	−	10.6504i	0.194359	−	0.527274i
$409$	13.9131	−	13.9131i	0.687958	−	0.687958i	−0.273822	−	0.961780i	$-0.588288\pi$
$409$	13.9131	−	13.9131i	0.687958	−	0.687958i	0.961780	+	0.273822i	$0.0882880\pi$
$410$	19.4706	−	2.82491i	0.961586	−	0.139512i
$411$	17.0901	−	7.07893i	0.842990	−	0.349178i
$412$	5.43160	+	18.3246i	0.267596	+	0.902786i
$413$	3.25203	−	7.85109i	0.160022	−	0.386327i
$414$	1.13448	+	1.90650i	0.0557567	+	0.0936992i
$415$	−16.7129			−0.820406
$416$	9.38250	+	10.6889i	0.460015	+	0.524067i
$417$	16.6288			0.814315
$418$	1.48430	+	2.49437i	0.0725996	+	0.122004i
$419$	−12.0802	+	29.1643i	−0.590158	+	1.42477i	0.293191	+	0.956054i	$0.405283\pi$
$419$	−12.0802	+	29.1643i	−0.590158	+	1.42477i	−0.883350	+	0.468715i	$0.844717\pi$
$420$	5.46756	−	1.62064i	0.266789	−	0.0790793i
$421$	18.8663	−	7.81469i	0.919489	−	0.380865i	0.127808	−	0.991799i	$-0.459206\pi$
$421$	18.8663	−	7.81469i	0.919489	−	0.380865i	0.791681	+	0.610934i	$0.209206\pi$
$422$	−9.80693	+	1.42285i	−0.477394	+	0.0692630i
$423$	8.17402	−	8.17402i	0.397435	−	0.397435i
$424$	32.9229	−	15.1885i	1.59888	−	0.737619i
$425$	−12.7692	−	12.7692i	−0.619397	−	0.619397i
$426$	10.4606	+	7.80980i	0.506816	+	0.378386i
$427$	−1.88802	−	4.55808i	−0.0913675	−	0.220581i
$428$	−33.1123	−	3.47417i	−1.60055	−	0.167931i
$429$	2.69215	+	1.11512i	0.129978	+	0.0538387i
$430$	−37.8288	−	9.60365i	−1.82427	−	0.463129i
$431$		−	36.5150i		−	1.75887i	−0.476022	−	0.879433i	$-0.657922\pi$
$431$		−	36.5150i		−	1.75887i	0.476022	−	0.879433i	$-0.342078\pi$
$432$	−17.7960	−	12.2214i	−0.856212	−	0.588001i
$433$			15.4998i			0.744871i	0.928058	+	0.372436i	$0.121477\pi$
$433$			15.4998i			0.744871i	−0.928058	+	0.372436i	$0.878523\pi$
$434$	−1.08626	+	4.27878i	−0.0521421	+	0.205388i
$435$	6.82155	+	2.82558i	0.327068	+	0.135476i
$436$	−2.00910	+	1.62754i	−0.0962187	+	0.0779453i
$437$	0.743701	+	1.79545i	0.0355760	+	0.0858882i
$438$	−1.71320	+	2.29468i	−0.0818597	+	0.109644i
$439$	−2.92729	−	2.92729i	−0.139712	−	0.139712i	0.633792	−	0.773504i	$-0.281498\pi$
$439$	−2.92729	−	2.92729i	−0.139712	−	0.139712i	−0.773504	+	0.633792i	$0.781498\pi$
$440$	−6.13455	+	6.63994i	−0.292453	+	0.316547i
$441$	−7.50639	+	7.50639i	−0.357447	+	0.357447i
$442$	1.76779	+	12.1845i	0.0840852	+	0.579555i
$443$	27.6395	−	11.4487i	1.31319	−	0.543943i	0.387379	−	0.921921i	$-0.373381\pi$
$443$	27.6395	−	11.4487i	1.31319	−	0.543943i	0.925815	+	0.377978i	$0.123381\pi$
$444$	−11.8497	−	6.43109i	−0.562362	−	0.305206i
$445$	−7.40925	+	17.8875i	−0.351232	+	0.847950i
$446$	−4.17660	+	2.48533i	−0.197768	+	0.117684i
$447$	−11.4244			−0.540356
$448$	3.99674	−	4.68475i	0.188828	−	0.221333i
$449$	15.2099			0.717800			0.358900	−	0.933376i	$-0.383152\pi$
$449$	15.2099			0.717800			0.358900	+	0.933376i	$0.383152\pi$
$450$	−10.5007	+	6.24855i	−0.495007	+	0.294559i
$451$	1.66573	−	4.02143i	0.0784362	−	0.189362i
$452$	34.0228	+	18.4649i	1.60030	+	0.868514i
$453$	−8.87069	+	3.67436i	−0.416781	+	0.172636i
$454$	−3.21076	−	22.1301i	−0.150689	−	1.03862i
$455$	−4.37384	+	4.37384i	−0.205049	+	0.205049i
$456$	−4.94185	−	4.56571i	−0.231423	−	0.213809i
$457$	−18.5887	−	18.5887i	−0.869542	−	0.869542i	0.122880	−	0.992422i	$-0.460787\pi$
$457$	−18.5887	−	18.5887i	−0.869542	−	0.869542i	−0.992422	+	0.122880i	$0.960787\pi$
$458$	20.1708	−	27.0170i	0.942518	−	1.26242i
$459$	−7.15170	−	17.2657i	−0.333813	−	0.805895i
$460$	−4.70305	+	3.80987i	−0.219281	+	0.177636i
$461$	−11.2192	−	4.64714i	−0.522530	−	0.216439i	0.105798	−	0.994388i	$-0.466260\pi$
$461$	−11.2192	−	4.64714i	−0.522530	−	0.216439i	−0.628328	+	0.777949i	$0.716260\pi$
$462$	0.310450	−	1.22287i	0.0144435	−	0.0568929i
$463$		−	18.8259i		−	0.874915i	−0.899239	−	0.437458i	$-0.855879\pi$
$463$		−	18.8259i		−	0.874915i	0.899239	−	0.437458i	$-0.144121\pi$
$464$	7.83905	−	1.45582i	0.363919	−	0.0675850i
$465$			15.0217i			0.696616i
$466$	37.9761	+	9.64103i	1.75921	+	0.446612i
$467$	−35.1913	−	14.5767i	−1.62846	−	0.674531i	−0.633403	−	0.773822i	$-0.718342\pi$
$467$	−35.1913	−	14.5767i	−1.62846	−	0.674531i	−0.995058	+	0.0992914i	$0.968342\pi$
$468$	8.28546	+	0.869317i	0.382996	+	0.0401842i
$469$	−2.36033	−	5.69833i	−0.108990	−	0.263124i
$470$	25.2715	+	18.8675i	1.16569	+	0.870294i
$471$	13.1177	+	13.1177i	0.604431	+	0.604431i
$472$	−13.0806	−	28.3538i	−0.602084	−	1.30509i
$473$	−6.10566	+	6.10566i	−0.280739	+	0.280739i
$474$	8.64313	−	1.25400i	0.396992	−	0.0575979i
$475$	−9.88909	+	4.09619i	−0.453742	+	0.187946i
$476$	5.11094	−	1.51494i	0.234260	−	0.0694371i
$477$	8.12738	−	19.6212i	0.372127	−	0.898394i
$478$	−17.7775	−	29.8751i	−0.813122	−	1.36645i
$479$	2.83141			0.129371			0.0646853	−	0.997906i	$-0.479396\pi$
$479$	2.83141			0.129371			0.0646853	+	0.997906i	$0.479396\pi$
$480$	9.25938	−	18.7977i	0.422631	−	0.857992i
$481$	14.6240			0.666795
$482$	7.80883	+	13.1228i	0.355683	+	0.597725i
$483$	0.323261	−	0.780422i	0.0147089	−	0.0355104i
$484$	0.568379	+	1.91754i	0.0258354	+	0.0871607i
$485$	38.9128	−	16.1182i	1.76694	−	0.731889i
$486$	−20.5765	+	2.98536i	−0.933370	+	0.135419i
$487$	−0.948636	+	0.948636i	−0.0429868	+	0.0429868i	−0.728273	−	0.685287i	$-0.759677\pi$
$487$	−0.948636	+	0.948636i	−0.0429868	+	0.0429868i	0.685287	+	0.728273i	$0.259677\pi$
$488$	−17.0097	−	6.26996i	−0.769994	−	0.283828i
$489$	4.87784	+	4.87784i	0.220584	+	0.220584i
$490$	−23.2073	−	17.3265i	−1.04840	−	0.782730i
$491$	14.3747	+	34.7036i	0.648721	+	1.56615i	0.814612	+	0.580007i	$0.196950\pi$
$491$	14.3747	+	34.7036i	0.648721	+	1.56615i	−0.165891	+	0.986144i	$0.553050\pi$
$492$	−1.05283	+	10.0345i	−0.0474651	+	0.452390i
$493$	6.37662	+	2.64128i	0.287189	+	0.118957i
$494$	7.07342	+	1.79574i	0.318248	+	0.0807940i
$495$			5.29519i			0.238001i
$496$	8.83956	+	13.6009i	0.396908	+	0.610699i
$497$			6.13072i			0.275001i
$498$	2.10898	−	8.30730i	0.0945058	−	0.372259i
$499$	−26.9875	−	11.1786i	−1.20813	−	0.500422i	−0.314510	−	0.949254i	$-0.601840\pi$
$499$	−26.9875	−	11.1786i	−1.20813	−	0.500422i	−0.893616	+	0.448832i	$0.851840\pi$
$500$	−0.865834	−	1.06882i	−0.0387213	−	0.0477991i
$501$	−9.19300	−	22.1939i	−0.410713	−	0.991548i
$502$	−14.1591	+	18.9649i	−0.631951	+	0.846445i
$503$	11.9194	+	11.9194i	0.531459	+	0.531459i	0.921006	−	0.389548i	$-0.127369\pi$
$503$	11.9194	+	11.9194i	0.531459	+	0.531459i	−0.389548	+	0.921006i	$0.627369\pi$
$504$	−0.142593	−	3.60423i	−0.00635159	−	0.160545i
$505$	−23.9270	+	23.9270i	−1.06474	+	1.06474i
$506$	0.192267	+	1.32519i	0.00854729	+	0.0589120i
$507$	−7.15121	+	2.96213i	−0.317597	+	0.131553i
$508$	−1.13810	+	2.09702i	−0.0504950	+	0.0930404i
$509$	0.380641	−	0.918948i	0.0168716	−	0.0407316i	−0.915219	−	0.402956i	$-0.867983\pi$
$509$	0.380641	−	0.918948i	0.0168716	−	0.0407316i	0.932091	+	0.362225i	$0.117983\pi$
$510$	15.5883	−	9.27600i	0.690263	−	0.410748i
$511$	−1.34487			−0.0594934
$512$	−2.67791	−	22.4684i	−0.118348	−	0.992972i
$513$	−11.0773			−0.489073
$514$	25.2445	−	15.0220i	1.11349	−	0.662592i
$515$	−11.6883	+	28.2181i	−0.515050	+	1.24344i
$516$	9.54714	−	17.5912i	0.420289	−	0.774411i
$517$	6.44626	−	2.67013i	0.283506	−	0.117432i
$518$	−0.909125	−	6.26613i	−0.0399447	−	0.275318i
$519$	−14.9869	+	14.9869i	−0.657851	+	0.657851i
$520$	0.898504	+	22.7109i	0.0394020	+	0.995939i
$521$	−9.33168	−	9.33168i	−0.408828	−	0.408828i	0.472502	−	0.881330i	$-0.343351\pi$
$521$	−9.33168	−	9.33168i	−0.408828	−	0.408828i	−0.881330	+	0.472502i	$0.843351\pi$
$522$	2.79398	−	3.74231i	0.122289	−	0.163796i
$523$	11.0568	+	26.6934i	0.483480	+	1.16722i	0.957946	+	0.286949i	$0.0926411\pi$
$523$	11.0568	+	26.6934i	0.483480	+	1.16722i	−0.474466	+	0.880274i	$0.657359\pi$
$524$	25.5688	+	31.5631i	1.11698	+	1.37884i
$525$	4.29845	+	1.78048i	0.187600	+	0.0777063i
$526$	−7.04424	+	27.7473i	−0.307144	+	1.20984i
$527$			14.0420i			0.611678i
$528$	−2.52632	−	3.88711i	−0.109944	−	0.169165i
$529$		−	22.1034i		−	0.961020i
$530$	56.1601	+	14.2574i	2.43944	+	0.619303i
$531$	−16.8982	−	6.99945i	−0.733318	−	0.303750i
$532$	0.329712	−	3.14248i	0.0142948	−	0.136244i
$533$	−4.18804	−	10.1108i	−0.181404	−	0.437948i
$534$	−7.95617	−	5.94003i	−0.344297	−	0.257050i
$535$	−37.6223	−	37.6223i	−1.62655	−	1.62655i
$536$	−21.2649	−	7.83846i	−0.918504	−	0.338570i
$537$	9.54452	−	9.54452i	0.411877	−	0.411877i
$538$	28.5491	−	4.14207i	1.23084	−	0.178577i
$539$	−5.91975	+	2.45204i	−0.254982	+	0.105617i
$540$	−9.80442	−	33.0771i	−0.421915	−	1.42341i
$541$	−6.48221	+	15.6494i	−0.278692	+	0.672822i	−0.999800	−	0.0200006i	$-0.993633\pi$
$541$	−6.48221	+	15.6494i	−0.278692	+	0.672822i	0.721108	+	0.692823i	$0.243633\pi$
$542$	−0.924959	−	1.55440i	−0.0397304	−	0.0667670i
$543$	8.23180			0.353260
$544$	8.65545	−	17.5716i	0.371099	−	0.753376i
$545$	−4.13197			−0.176994
$546$	−1.62212	−	2.72598i	−0.0694204	−	0.116661i
$547$	8.37376	−	20.2160i	0.358036	−	0.864376i	−0.637540	−	0.770417i	$-0.720048\pi$
$547$	8.37376	−	20.2160i	0.358036	−	0.864376i	0.995576	−	0.0939585i	$-0.0299521\pi$
$548$	30.6051	−	9.07169i	1.30739	−	0.387523i
$549$	−9.81049	+	4.06364i	−0.418702	+	0.173432i
$550$	−7.29896	+	1.05898i	−0.311229	+	0.0451549i
$551$	2.89283	−	2.89283i	0.123239	−	0.123239i
$552$	−1.30025	−	2.81845i	−0.0553424	−	0.119961i
$553$	2.90025	+	2.90025i	0.123331	+	0.123331i
$554$	24.4582	+	18.2604i	1.03913	+	0.775809i
$555$	−8.24516	−	19.9056i	−0.349988	−	0.844945i
$556$	28.5388	+	2.99431i	1.21031	+	0.126987i
$557$	−22.4053	−	9.28058i	−0.949344	−	0.393231i	−0.146360	−	0.989231i	$-0.546756\pi$
$557$	−22.4053	−	9.28058i	−0.949344	−	0.393231i	−0.802984	+	0.596000i	$0.796756\pi$
$558$	9.20937	+	2.33799i	0.389864	+	0.0989751i
$559$			21.7097i			0.918222i
$560$	9.67540	−	1.79686i	0.408860	−	0.0759312i
$561$		−	4.01316i		−	0.169436i
$562$	−1.64159	+	6.46625i	−0.0692464	+	0.272762i
$563$	15.2112	+	6.30068i	0.641075	+	0.265542i	0.679450	−	0.733722i	$-0.262218\pi$
$563$	15.2112	+	6.30068i	0.641075	+	0.265542i	−0.0383755	+	0.999263i	$0.512218\pi$
$564$	−12.5672	+	10.1805i	−0.529175	+	0.428677i
$565$	23.6734	+	57.1527i	0.995949	+	2.40443i
$566$	−0.536311	+	0.718343i	−0.0225428	+	0.0301942i
$567$	0.699364	+	0.699364i	0.0293705	+	0.0293705i
$568$	16.5464	+	15.2870i	0.694272	+	0.641428i
$569$	−17.8883	+	17.8883i	−0.749915	+	0.749915i	−0.974463	−	0.224548i	$-0.927910\pi$
$569$	−17.8883	+	17.8883i	−0.749915	+	0.749915i	0.224548	+	0.974463i	$0.427910\pi$
$570$	−1.54379	−	10.6405i	−0.0646622	−	0.445683i
$571$	19.2874	−	7.98909i	0.807151	−	0.334333i	0.0593344	−	0.998238i	$-0.481102\pi$
$571$	19.2874	−	7.98909i	0.807151	−	0.334333i	0.747817	+	0.663905i	$0.231102\pi$
$572$	4.41954	+	2.39858i	0.184790	+	0.100290i
$573$	0.410943	−	0.992105i	0.0171674	−	0.0414458i
$574$	−4.07197	+	2.42307i	−0.169961	+	0.101137i
$575$	−4.93807			−0.205932
$576$	−10.0831	−	8.60232i	−0.420130	−	0.358430i
$577$	19.2320			0.800638			0.400319	−	0.916376i	$-0.368899\pi$
$577$	19.2320			0.800638			0.400319	+	0.916376i	$0.368899\pi$
$578$	−6.08881	+	3.62321i	−0.253261	+	0.150706i
$579$	−1.91273	+	4.61775i	−0.0794905	+	0.191907i
$580$	11.1985	+	6.07768i	0.464994	+	0.252362i
$581$	3.71872	−	1.54035i	0.154279	−	0.0639043i
$582$	3.10133	+	21.3758i	0.128554	+	0.886056i
$583$	9.06437	−	9.06437i	0.375408	−	0.375408i
$584$	−3.35344	+	3.62971i	−0.138766	+	0.150198i
$585$	9.41396	+	9.41396i	0.389219	+	0.389219i
$586$	−7.93823	+	10.6326i	−0.327925	+	0.439228i
$587$	−9.27341	−	22.3880i	−0.382755	−	0.924051i	−0.991431	−	0.130633i	$-0.958299\pi$
$587$	−9.27341	−	22.3880i	−0.382755	−	0.924051i	0.608676	−	0.793419i	$-0.291701\pi$
$588$	11.5408	−	9.34899i	0.475933	−	0.385546i
$589$	7.68963	+	3.18515i	0.316846	+	0.131242i
$590$	12.2788	−	48.3661i	0.505509	−	1.99120i
$591$		−	30.2654i		−	1.24495i
$592$	−19.1788	−	13.1710i	−0.788243	−	0.541323i
$593$		−	16.9693i		−	0.696847i	−0.937337	−	0.348423i	$-0.886717\pi$
$593$		−	16.9693i		−	0.696847i	0.937337	−	0.348423i	$-0.113283\pi$
$594$	−7.39798	−	1.87813i	−0.303543	−	0.0770608i
$595$	7.87038	+	3.26002i	0.322654	+	0.133648i
$596$	−19.6069	−	2.05717i	−0.803129	−	0.0842650i
$597$	−3.45907	−	8.35094i	−0.141570	−	0.341781i
$598$	2.69779	+	2.01415i	0.110321	+	0.0823649i
$599$	10.9763	+	10.9763i	0.448480	+	0.448480i	0.894849	−	0.446369i	$-0.147283\pi$
$599$	10.9763	+	10.9763i	0.448480	+	0.448480i	−0.446369	+	0.894849i	$0.647283\pi$
$600$	15.5236	−	7.16160i	0.633748	−	0.292371i
$601$	−24.1575	+	24.1575i	−0.985407	+	0.985407i	−0.999895	−	0.0144882i	$-0.995388\pi$
$601$	−24.1575	+	24.1575i	−0.985407	+	0.985407i	0.0144882	+	0.999895i	$0.495388\pi$
$602$	9.30225	−	1.34962i	0.379131	−	0.0550065i
$603$	−12.2647	+	5.08021i	−0.499457	+	0.206882i
$604$	−15.8858	+	4.70871i	−0.646382	+	0.191595i
$605$	−1.22310	+	2.95283i	−0.0497262	+	0.120050i
$606$	−8.87380	−	14.9124i	−0.360473	−	0.605776i
$607$	−11.5860			−0.470261			−0.235131	−	0.971964i	$-0.575552\pi$
$607$	−11.5860			−0.470261			−0.235131	+	0.971964i	$0.575552\pi$
$608$	−7.65921	−	8.72567i	−0.310622	−	0.353872i
$609$	−1.77825			−0.0720584
$610$	−14.8147	−	24.8961i	−0.599828	−	1.00801i
$611$	6.71334	−	16.2074i	0.271593	−	0.655682i
$612$	−3.26065	−	11.0004i	−0.131804	−	0.444667i
$613$	−6.31913	+	2.61747i	−0.255227	+	0.105719i	−0.506629	−	0.862164i	$-0.669109\pi$
$613$	−6.31913	+	2.61747i	−0.255227	+	0.105719i	0.251402	+	0.967883i	$0.419109\pi$
$614$	−7.73911	+	1.12283i	−0.312325	+	0.0453139i
$615$	−11.4012	+	11.4012i	−0.459741	+	0.459741i
$616$	0.753002	−	2.04281i	0.0303393	−	0.0823073i
$617$	−14.5350	−	14.5350i	−0.585158	−	0.585158i	0.351158	−	0.936316i	$-0.385788\pi$
$617$	−14.5350	−	14.5350i	−0.585158	−	0.585158i	−0.936316	+	0.351158i	$0.885788\pi$
$618$	−12.5511	−	9.37059i	−0.504880	−	0.376940i
$619$	6.68173	+	16.1311i	0.268561	+	0.648364i	0.999416	−	0.0341686i	$-0.0108783\pi$
$619$	6.68173	+	16.1311i	0.268561	+	0.648364i	−0.730855	+	0.682533i	$0.760878\pi$
$620$	−2.70493	+	25.7807i	−0.108633	+	1.03538i
$621$	−4.72133	−	1.95564i	−0.189460	−	0.0784770i
$622$	−13.6748	−	3.47165i	−0.548311	−	0.139200i
$623$		−	4.66295i		−	0.186817i
$624$	−11.4020	−	2.41925i	−0.456446	−	0.0968475i
$625$			23.8778i			0.955111i
$626$	5.31242	−	20.9257i	0.212327	−	0.836357i
$627$	−2.19768	−	0.910308i	−0.0877668	−	0.0363542i
$628$	20.1509	+	24.8750i	0.804107	+	0.992621i
$629$	−7.70739	−	18.6073i	−0.307314	−	0.741921i
$630$	3.44849	−	4.61896i	0.137391	−	0.184024i
$631$	7.73226	+	7.73226i	0.307817	+	0.307817i	0.844062	−	0.536245i	$-0.180158\pi$
$631$	7.73226	+	7.73226i	0.307817	+	0.307817i	−0.536245	+	0.844062i	$0.680158\pi$
$632$	15.0594	−	0.595789i	0.599030	−	0.0236992i
$633$	5.74254	−	5.74254i	0.228246	−	0.228246i
$634$	5.10216	+	35.1666i	0.202633	+	1.39664i
$635$	−3.52266	+	1.45913i	−0.139792	+	0.0579039i
$636$	−14.1735	+	26.1157i	−0.562017	+	1.03555i
$637$	−6.16500	+	14.8836i	−0.244266	+	0.589711i
$638$	2.42246	−	1.44151i	0.0959062	−	0.0570700i
$639$	13.1954			0.522000
$640$	19.2761	−	30.5937i	0.761953	−	1.20932i
$641$	−25.2046			−0.995522			−0.497761	−	0.867314i	$-0.665844\pi$
$641$	−25.2046			−0.995522			−0.497761	+	0.867314i	$0.665844\pi$
$642$	23.4480	−	13.9530i	0.925417	−	0.550679i
$643$	−1.80757	+	4.36386i	−0.0712837	+	0.172094i	−0.955506	−	0.294973i	$-0.904689\pi$
$643$	−1.80757	+	4.36386i	−0.0712837	+	0.172094i	0.884222	+	0.467067i	$0.154689\pi$
$644$	0.695319	−	1.28117i	0.0273994	−	0.0504853i
$645$	29.5504	−	12.2402i	1.16355	−	0.481957i
$646$	−1.44310	−	9.94652i	−0.0567779	−	0.391341i
$647$	−29.4720	+	29.4720i	−1.15866	+	1.15866i	−0.173902	+	0.984763i	$0.555638\pi$
$647$	−29.4720	+	29.4720i	−1.15866	+	1.15866i	−0.984763	+	0.173902i	$0.944362\pi$
$648$	3.63141	−	0.143668i	0.142655	−	0.00564382i
$649$	−7.80640	−	7.80640i	−0.306428	−	0.306428i
$650$	−11.0937	+	14.8590i	−0.435129	+	0.582819i
$651$	−1.38448	−	3.34242i	−0.0542619	−	0.131000i
$652$	7.49314	+	9.24983i	0.293454	+	0.362251i
$653$	33.9870	+	14.0779i	1.33002	+	0.550910i	0.930660	−	0.365886i	$-0.119234\pi$
$653$	33.9870	+	14.0779i	1.33002	+	0.550910i	0.399355	+	0.916796i	$0.369234\pi$
$654$	0.521407	−	2.05383i	0.0203886	−	0.0803110i
$655$			64.9134i			2.53638i
$656$	−3.61378	+	17.0319i	−0.141095	+	0.664984i
$657$			2.89460i			0.112929i
$658$	−7.36197	−	1.86899i	−0.286999	−	0.0728608i
$659$	1.06355	+	0.440539i	0.0414302	+	0.0171610i	0.403302	−	0.915067i	$-0.367862\pi$
$659$	1.06355	+	0.440539i	0.0414302	+	0.0171610i	−0.361872	+	0.932228i	$0.617862\pi$
$660$	0.773063	−	7.36806i	0.0300915	−	0.286802i
$661$	−5.03257	−	12.1497i	−0.195744	−	0.472569i	0.795281	−	0.606241i	$-0.207323\pi$
$661$	−5.03257	−	12.1497i	−0.195744	−	0.472569i	−0.991026	+	0.133672i	$0.957323\pi$
$662$	28.2626	+	21.1007i	1.09846	+	0.820102i
$663$	−7.13473	−	7.13473i	−0.277090	−	0.277090i
$664$	5.11537	−	13.8775i	0.198515	−	0.538550i
$665$	3.57049	−	3.57049i	0.138458	−	0.138458i
$666$	−13.4868	+	1.95674i	−0.522602	+	0.0758221i
$667$	1.74369	−	0.722261i	0.0675160	−	0.0279660i
$668$	−11.7809	−	39.7451i	−0.455816	−	1.53778i
$669$	1.52423	−	3.67981i	0.0589300	−	0.142270i
$670$	−18.5207	−	31.1241i	−0.715518	−	1.20243i
$671$	−6.40940			−0.247432
$672$	−0.327781	+	5.03597i	−0.0126444	+	0.194267i
$673$	16.3757			0.631237			0.315618	−	0.948886i	$-0.397788\pi$
$673$	16.3757			0.631237			0.315618	+	0.948886i	$0.397788\pi$
$674$	18.2521	+	30.6726i	0.703044	+	1.18147i
$675$	10.7714	−	26.0044i	0.414590	−	1.00091i
$676$	−12.8065	+	3.79598i	−0.492558	+	0.145999i
$677$	−7.18701	+	2.97696i	−0.276219	+	0.114414i	−0.516493	−	0.856291i	$-0.672763\pi$
$677$	−7.18701	+	2.97696i	−0.276219	+	0.114414i	0.240274	+	0.970705i	$0.422763\pi$
$678$	−31.3955	+	4.55504i	−1.20574	+	0.174935i
$679$	−7.17278	+	7.17278i	−0.275266	+	0.275266i
$680$	28.4234	−	13.1128i	1.08999	−	0.502851i
$681$	12.9585	+	12.9585i	0.496571	+	0.496571i
$682$	4.59551	+	3.43098i	0.175971	+	0.131379i
$683$	8.98311	+	21.6872i	0.343729	+	0.829836i	0.997332	+	0.0729982i	$0.0232567\pi$
$683$	8.98311	+	21.6872i	0.343729	+	0.829836i	−0.653603	+	0.756838i	$0.726743\pi$
$684$	−6.76366	−	0.709649i	−0.258615	−	0.0271341i
$685$	47.1291	+	19.5215i	1.80071	+	0.745878i
$686$	14.1465	+	3.59138i	0.540115	+	0.137120i
$687$			27.6313i			1.05420i
$688$	19.5527	−	28.4715i	0.745439	−	1.08546i
$689$		−	32.2299i		−	1.22786i
$690$	1.22055	−	4.80774i	0.0464654	−	0.183027i
$691$	22.5022	+	9.32071i	0.856023	+	0.354577i	0.767151	−	0.641467i	$-0.221674\pi$
$691$	22.5022	+	9.32071i	0.856023	+	0.354577i	0.0888724	+	0.996043i	$0.471674\pi$
$692$	−28.4196	+	23.0222i	−1.08035	+	0.875174i
$693$	−0.488030	−	1.17821i	−0.0185387	−	0.0447565i
$694$	−13.1101	+	17.5599i	−0.497653	+	0.666564i
$695$	32.4258	+	32.4258i	1.22998	+	1.22998i
$696$	−4.43408	+	4.79938i	−0.168074	+	0.181920i
$697$	−10.6576	+	10.6576i	−0.403685	+	0.403685i
$698$	−6.01136	−	41.4331i	−0.227533	−	1.56827i
$699$	−29.6654	+	12.2878i	−1.12205	+	0.464768i
$700$	7.05651	+	3.82971i	0.266711	+	0.144750i
$701$	−7.18195	+	17.3388i	−0.271259	+	0.654876i	−0.999538	−	0.0304044i	$-0.990320\pi$
$701$	−7.18195	+	17.3388i	−0.271259	+	0.654876i	0.728279	+	0.685281i	$0.240320\pi$
$702$	−16.4914	+	9.81337i	−0.622427	+	0.370382i
$703$	−11.9380			−0.450248
$704$	−3.63580	−	7.12607i	−0.137029	−	0.268574i
$705$	−25.8460			−0.973417
$706$	−8.21880	+	4.89068i	−0.309319	+	0.184063i
$707$	3.11867	−	7.52913i	0.117290	−	0.283162i
$708$	22.4913	+	12.2065i	0.845276	+	0.458749i
$709$	−4.87997	+	2.02135i	−0.183271	+	0.0759134i	−0.472432	−	0.881367i	$-0.656624\pi$
$709$	−4.87997	+	2.02135i	−0.183271	+	0.0759134i	0.289161	+	0.957281i	$0.406624\pi$
$710$	5.16895	+	35.6269i	0.193987	+	1.33705i
$711$	6.24231	−	6.24231i	0.234105	−	0.234105i
$712$	−12.5850	−	11.6271i	−0.471642	−	0.435744i
$713$	2.71514	+	2.71514i	0.101683	+	0.101683i
$714$	−2.61357	+	3.50066i	−0.0978104	+	0.131009i
$715$	3.07517	+	7.42411i	0.115005	+	0.277646i
$716$	18.0992	−	14.6619i	0.676400	−	0.547941i
$717$	26.3216	+	10.9027i	0.982997	+	0.407171i
$718$	−8.77179	+	34.5521i	−0.327360	+	1.28947i
$719$		−	12.6660i		−	0.472363i	−0.971709	−	0.236182i	$-0.924104\pi$
$719$		−	12.6660i		−	0.472363i	0.971709	−	0.236182i	$-0.0758960\pi$
$720$	−3.86744	−	20.8247i	−0.144131	−	0.776090i
$721$		−	7.35595i		−	0.273950i
$722$	20.2697	+	5.14588i	0.754358	+	0.191510i
$723$	−11.5619	−	4.78908i	−0.429991	−	0.178108i
$724$	14.1276	+	1.48228i	0.525050	+	0.0550886i
$725$	3.97810	+	9.60399i	0.147743	+	0.356683i
$726$	−1.31339	−	0.980566i	−0.0487443	−	0.0363922i
$727$	−29.3015	−	29.3015i	−1.08673	−	1.08673i	−0.995863	−	0.0908704i	$-0.971035\pi$
$727$	−29.3015	−	29.3015i	−1.08673	−	1.08673i	−0.0908704	−	0.995863i	$-0.528965\pi$
$728$	−2.29307	−	4.97049i	−0.0849868	−	0.184219i
$729$	14.7745	−	14.7745i	0.547203	−	0.547203i
$730$	−7.81529	+	1.13389i	−0.289257	+	0.0419671i
$731$	27.6230	−	11.4418i	1.02168	−	0.423192i
$732$	14.2442	−	4.22214i	0.526481	−	0.156055i
$733$	7.21333	−	17.4145i	0.266430	−	0.643220i	−0.732880	−	0.680358i	$-0.761824\pi$
$733$	7.21333	−	17.4145i	0.266430	−	0.643220i	0.999310	+	0.0371385i	$0.0118243\pi$
$734$	15.0368	+	25.2694i	0.555019	+	0.932711i
$735$	23.7350			0.875477
$736$	−1.72402	−	5.07123i	−0.0635481	−	0.186928i
$737$	−8.01278			−0.295155
$738$	5.21524	+	8.76423i	0.191976	+	0.322616i
$739$	5.51588	−	13.3165i	0.202905	−	0.489855i	−0.789370	−	0.613918i	$-0.789592\pi$
$739$	5.51588	−	13.3165i	0.202905	−	0.489855i	0.992274	+	0.124063i	$0.0395924\pi$
$740$	−10.5662	−	35.6472i	−0.388422	−	1.31042i
$741$	−5.52548	+	2.28873i	−0.202984	+	0.0840786i
$742$	−13.8100	+	2.00363i	−0.506980	+	0.0735556i
$743$	−35.4362	+	35.4362i	−1.30003	+	1.30003i	−0.371657	+	0.928370i	$0.621210\pi$
$743$	−35.4362	+	35.4362i	−1.30003	+	1.30003i	−0.928370	+	0.371657i	$0.878790\pi$
$744$	−12.4732	−	4.59774i	−0.457289	−	0.168561i
$745$	−22.2774	−	22.2774i	−0.816180	−	0.816180i
$746$	−29.9596	−	22.3677i	−1.09690	−	0.818938i
$747$	−3.31534	−	8.00393i	−0.121302	−	0.292848i
$748$	0.722641	−	6.88749i	0.0264224	−	0.251832i
$749$	11.8386	+	4.90372i	0.432574	+	0.179178i
$750$	1.09261	+	0.277382i	0.0398965	+	0.0101286i
$751$		−	36.4981i		−	1.33184i	−0.746025	−	0.665918i	$-0.768040\pi$
$751$		−	36.4981i		−	1.33184i	0.746025	−	0.665918i	$-0.231960\pi$
$752$	−23.4014	+	15.2091i	−0.853361	+	0.554620i
$753$		−	19.3961i		−	0.706832i
$754$	1.74397	−	6.86950i	0.0635115	−	0.250172i
$755$	−24.4626	−	10.1327i	−0.890286	−	0.368768i
$756$	5.23009	+	6.45622i	0.190216	+	0.234811i
$757$	11.4221	+	27.5754i	0.415144	+	1.00225i	0.983735	+	0.179626i	$0.0574888\pi$
$757$	11.4221	+	27.5754i	0.415144	+	1.00225i	−0.568591	+	0.822620i	$0.692511\pi$
$758$	−10.1170	+	13.5508i	−0.367464	+	0.492188i
$759$	−0.775980	−	0.775980i	−0.0281663	−	0.0281663i
$760$	−0.733474	−	18.5396i	−0.0266059	−	0.672501i
$761$	25.9070	−	25.9070i	0.939128	−	0.939128i	−0.0591223	−	0.998251i	$-0.518830\pi$
$761$	25.9070	−	25.9070i	0.939128	−	0.939128i	0.998251	+	0.0591223i	$0.0188302\pi$
$762$	−0.280754	−	1.93509i	−0.0101706	−	0.0701010i
$763$	0.919386	−	0.380822i	0.0332840	−	0.0137867i
$764$	0.883919	−	1.62868i	0.0319791	−	0.0589236i
$765$	7.01665	−	16.9397i	0.253687	−	0.612455i
$766$	−22.2588	+	13.2454i	−0.804244	+	0.478574i
$767$	−27.7570			−1.00225
$768$	12.7744	+	13.4419i	0.460958	+	0.485043i
$769$	11.7538			0.423855			0.211927	−	0.977285i	$-0.432026\pi$
$769$	11.7538			0.423855			0.211927	+	0.977285i	$0.432026\pi$
$770$	2.98994	−	1.77919i	0.107750	−	0.0641177i
$771$	−9.21285	+	22.2418i	−0.331793	+	0.801018i
$772$	−4.11420	+	7.58069i	−0.148073	+	0.272835i
$773$	−17.1842	+	7.11792i	−0.618072	+	0.256014i	−0.669676	−	0.742654i	$-0.733567\pi$
$773$	−17.1842	+	7.11792i	−0.618072	+	0.256014i	0.0516034	+	0.998668i	$0.483567\pi$
$774$	−2.90484	−	20.0215i	−0.104412	−	0.719659i
$775$	−14.9546	+	14.9546i	−0.537184	+	0.537184i
$776$	1.47348	+	37.2442i	0.0528949	+	1.33699i
$777$	3.66919	+	3.66919i	0.131632	+	0.131632i
$778$	12.3943	−	16.6011i	0.444357	−	0.595178i
$779$	3.41882	+	8.25376i	0.122492	+	0.295722i
$780$	−11.7248	−	14.4736i	−0.419816	−	0.518237i
$781$	7.35831	+	3.04791i	0.263301	+	0.109063i
$782$	1.14094	−	4.49416i	0.0407998	−	0.160711i
$783$			10.7579i			0.384456i
$784$	21.4900	−	13.9669i	0.767501	−	0.498817i
$785$			51.1585i			1.82592i
$786$	−32.2657	−	8.19133i	−1.15088	−	0.292175i
$787$	−23.7898	−	9.85404i	−0.848013	−	0.351259i	−0.0840052	−	0.996465i	$-0.526771\pi$
$787$	−23.7898	−	9.85404i	−0.848013	−	0.351259i	−0.764008	+	0.645207i	$0.776771\pi$
$788$	5.44983	−	51.9423i	0.194142	−	1.85037i
$789$	−8.97813	−	21.6751i	−0.319630	−	0.771655i
$790$	19.2992	+	14.4087i	0.686635	+	0.512638i
$791$	−10.5349	−	10.5349i	−0.374579	−	0.374579i
$792$	−4.39681	−	1.62071i	−0.156234	−	0.0575895i
$793$	−11.3948	+	11.3948i	−0.404643	+	0.404643i
$794$	−48.4756	+	7.03312i	−1.72034	+	0.249596i
$795$	−43.8701	+	18.1716i	−1.55591	+	0.644480i
$796$	−4.43282	−	14.9550i	−0.157117	−	0.530065i
$797$	5.34885	−	12.9133i	0.189466	−	0.457411i	−0.800391	−	0.599478i	$-0.795375\pi$
$797$	5.34885	−	12.9133i	0.189466	−	0.457411i	0.989857	+	0.142067i	$0.0453749\pi$
$798$	1.32419	+	2.22530i	0.0468756	+	0.0787746i
$799$	−24.1602			−0.854728
$800$	27.9316	−	9.49563i	0.987531	−	0.335721i
$801$	−10.0362			−0.354612
$802$	9.44039	+	15.8646i	0.333352	+	0.560198i
$803$	−0.668606	+	1.61416i	−0.0235946	+	0.0569624i
$804$	17.8076	−	5.27836i	0.628025	−	0.186153i
$805$	2.15216	−	0.891455i	0.0758537	−	0.0314196i
$806$	14.2698	−	2.07034i	0.502631	−	0.0729246i
$807$	−16.7172	+	16.7172i	−0.588473	+	0.588473i
$808$	−12.5442	−	27.1910i	−0.441304	−	0.956577i
$809$	2.78835	+	2.78835i	0.0980333	+	0.0980333i	0.754422	−	0.656389i	$-0.227917\pi$
$809$	2.78835	+	2.78835i	0.0980333	+	0.0980333i	−0.656389	+	0.754422i	$0.727917\pi$
$810$	4.65380	+	3.47450i	0.163518	+	0.122081i
$811$	−21.3595	−	51.5664i	−0.750034	−	1.81074i	−0.559019	−	0.829155i	$-0.688822\pi$
$811$	−21.3595	−	51.5664i	−0.750034	−	1.81074i	−0.191015	−	0.981587i	$-0.561178\pi$
$812$	−3.05189	−	0.320206i	−0.107100	−	0.0112370i
$813$	1.36951	+	0.567268i	0.0480307	+	0.0198950i
$814$	−7.97280	−	2.02406i	−0.279447	−	0.0709434i
$815$			19.0234i			0.666360i
$816$	2.93109	+	15.7828i	0.102609	+	0.552507i
$817$		−	17.7222i		−	0.620023i
$818$	−6.84706	+	26.9706i	−0.239402	+	0.943005i
$819$	−2.96229	−	1.22702i	−0.103511	−	0.0428756i
$820$	−21.6201	+	17.5141i	−0.755006	+	0.611618i
$821$	12.3726	+	29.8701i	0.431806	+	1.04247i	0.978705	+	0.205273i	$0.0658083\pi$
$821$	12.3726	+	29.8701i	0.431806	+	1.04247i	−0.546899	+	0.837199i	$0.684192\pi$
$822$	−15.6505	+	20.9625i	−0.545873	+	0.731150i
$823$	−6.06607	−	6.06607i	−0.211450	−	0.211450i	0.593433	−	0.804883i	$-0.297772\pi$
$823$	−6.06607	−	6.06607i	−0.211450	−	0.211450i	−0.804883	+	0.593433i	$0.797772\pi$
$824$	−19.8532	−	18.3421i	−0.691620	−	0.638978i
$825$	4.27398	−	4.27398i	0.148801	−	0.148801i
$826$	1.72556	+	11.8934i	0.0600400	+	0.413825i
$827$	−28.5678	+	11.8332i	−0.993399	+	0.411479i	−0.819372	−	0.573262i	$-0.805678\pi$
$827$	−28.5678	+	11.8332i	−0.993399	+	0.411479i	−0.174027	+	0.984741i	$0.555678\pi$
$828$	−2.75751	−	1.49656i	−0.0958301	−	0.0520090i
$829$	−7.99577	+	19.3035i	−0.277704	+	0.670438i	−0.999771	−	0.0213854i	$-0.993192\pi$
$829$	−7.99577	+	19.3035i	−0.277704	+	0.670438i	0.722067	+	0.691823i	$0.243192\pi$
$830$	20.3115	−	12.0866i	0.705024	−	0.419532i
$831$	−25.0143			−0.867737
$832$	−19.1328	−	6.20512i	−0.663311	−	0.215124i
$833$	22.1869			0.768730
$834$	−20.2093	+	12.0257i	−0.699790	+	0.416417i
$835$	25.3514	−	61.2038i	0.877323	−	2.11804i
$836$	−3.60780	−	1.95803i	−0.124778	−	0.0677198i
$837$	−20.2207	+	8.37568i	−0.698929	+	0.289506i
$838$	−6.40991	−	44.1802i	−0.221427	−	1.52618i
$839$	−0.981871	+	0.981871i	−0.0338980	+	0.0338980i	−0.723853	−	0.689955i	$-0.757630\pi$
$839$	−0.981871	+	0.981871i	−0.0338980	+	0.0338980i	0.689955	+	0.723853i	$0.257630\pi$
$840$	−5.47279	+	5.92367i	−0.188829	+	0.204386i
$841$	17.6967	+	17.6967i	0.610230	+	0.610230i
$842$	−17.2771	+	23.1412i	−0.595409	+	0.797500i
$843$	−2.09227	−	5.05118i	−0.0720616	−	0.173972i
$844$	10.8896	−	8.82146i	0.374834	−	0.303647i
$845$	−19.7208	−	8.16864i	−0.678417	−	0.281010i
$846$	−4.02269	+	15.8454i	−0.138303	+	0.544776i
$847$		−	0.769748i		−	0.0264489i
$848$	−29.0276	+	42.2683i	−0.996812	+	1.45150i
$849$		−	0.734674i		−	0.0252140i
$850$	24.7532	+	6.28411i	0.849026	+	0.215543i
$851$	−5.08817	−	2.10759i	−0.174420	−	0.0722472i
$852$	−18.3609	−	1.92644i	−0.629033	−	0.0659987i
$853$	−2.73939	−	6.61346i	−0.0937948	−	0.226441i	0.870018	−	0.493019i	$-0.164107\pi$
$853$	−2.73939	−	6.61346i	−0.0937948	−	0.226441i	−0.963813	+	0.266579i	$0.914107\pi$
$854$	5.59089	+	4.17412i	0.191316	+	0.142836i
$855$	−7.68488	−	7.68488i	−0.262817	−	0.262817i
$856$	42.7545	−	19.7242i	1.46132	−	0.674160i
$857$	10.5144	−	10.5144i	0.359165	−	0.359165i	−0.504340	−	0.863505i	$-0.668264\pi$
$857$	10.5144	−	10.5144i	0.359165	−	0.359165i	0.863505	+	0.504340i	$0.168264\pi$
$858$	−4.07826	+	0.591698i	−0.139230	+	0.0202002i
$859$	19.3962	−	8.03415i	0.661789	−	0.274122i	−0.0264024	−	0.999651i	$-0.508405\pi$
$859$	19.3962	−	8.03415i	0.661789	−	0.274122i	0.688191	+	0.725530i	$0.258405\pi$
$860$	52.9193	−	15.6859i	1.80453	−	0.534884i
$861$	1.48604	−	3.58763i	0.0506442	−	0.122266i
$862$	26.4072	+	44.3774i	0.899433	+	1.51150i
$863$	−24.2050			−0.823948			−0.411974	−	0.911196i	$-0.635161\pi$
$863$	−24.2050			−0.823948			−0.411974	+	0.911196i	$0.635161\pi$
$864$	30.4662	+	1.98298i	1.03648	+	0.0674624i
$865$	−58.4483			−1.98730
$866$	−11.2092	−	18.8372i	−0.380906	−	0.640113i
$867$	2.22208	−	5.36458i	0.0754658	−	0.182191i
$868$	−1.77421	−	5.98566i	−0.0602207	−	0.203166i
$869$	4.92286	−	2.03911i	0.166997	−	0.0691722i
$870$	−10.3338	+	1.49928i	−0.350348	+	0.0508305i
$871$	−14.2454	+	14.2454i	−0.482687	+	0.482687i
$872$	1.26468	−	3.43095i	0.0428275	−	0.116186i
$873$	15.4382	+	15.4382i	0.522504	+	0.522504i
$874$	−2.20228	−	1.64421i	−0.0744933	−	0.0556163i
$875$	0.202593	+	0.489102i	0.00684889	+	0.0165347i
$876$	0.422593	−	4.02774i	0.0142781	−	0.136085i
$877$	22.9668	+	9.51317i	0.775534	+	0.321237i	0.735112	−	0.677946i	$-0.237130\pi$
$877$	22.9668	+	9.51317i	0.775534	+	0.321237i	0.0404224	+	0.999183i	$0.487130\pi$
$878$	5.67458	+	1.44061i	0.191508	+	0.0486183i
$879$		−	10.8743i		−	0.366782i
$880$	2.65351	−	12.5061i	0.0894497	−	0.421580i
$881$			8.10838i			0.273178i	0.990628	+	0.136589i	$0.0436140\pi$
$881$			8.10838i			0.273178i	−0.990628	+	0.136589i	$0.956386\pi$
$882$	3.69412	−	14.5512i	0.124388	−	0.489964i
$883$	−15.8996	−	6.58581i	−0.535063	−	0.221630i	0.0987563	−	0.995112i	$-0.468514\pi$
$883$	−15.8996	−	6.58581i	−0.535063	−	0.221630i	−0.633819	+	0.773481i	$0.718514\pi$
$884$	−10.9601	−	13.5295i	−0.368627	−	0.455048i
$885$	15.6497	+	37.7818i	0.526059	+	1.27002i
$886$	−25.3113	+	33.9023i	−0.850349	+	1.13897i
$887$	7.11744	+	7.11744i	0.238980	+	0.238980i	0.816428	−	0.577448i	$-0.195951\pi$
$887$	7.11744	+	7.11744i	0.238980	+	0.238980i	−0.577448	+	0.816428i	$0.695951\pi$
$888$	19.0521	−	0.753750i	0.639345	−	0.0252942i
$889$	0.649331	−	0.649331i	0.0217779	−	0.0217779i
$890$	−3.93143	−	27.0973i	−0.131782	−	0.908304i
$891$	1.18709	−	0.491710i	0.0397691	−	0.0164729i
$892$	3.27854	−	6.04093i	0.109774	−	0.202265i
$893$	−5.48029	+	13.2306i	−0.183391	+	0.442745i
$894$	13.8843	−	8.26199i	0.464360	−	0.276322i
$895$	37.2233			1.24424
$896$	−1.46937	+	8.58386i	−0.0490881	+	0.286767i
$897$	−2.75912			−0.0921245
$898$	−18.4849	+	10.9996i	−0.616848	+	0.367062i
$899$	3.09333	−	7.46795i	0.103168	−	0.249070i
$900$	8.24282	−	15.1879i	0.274761	−	0.506265i
$901$	−41.0088	+	16.9864i	−1.36620	+	0.565899i
$902$	0.883856	+	6.09196i	0.0294292	+	0.202840i
$903$	−5.44702	+	5.44702i	−0.181266	+	0.181266i
$904$	−54.7021	+	2.16416i	−1.81936	+	0.0719789i
$905$	16.0519	+	16.0519i	0.533582	+	0.533582i
$906$	8.12346	−	10.8807i	0.269884	−	0.361487i
$907$	−0.0171283	−	0.0413514i	−0.000568736	−	0.00137305i	0.923595	−	0.383370i	$-0.125237\pi$
$907$	−0.0171283	−	0.0413514i	−0.000568736	−	0.00137305i	−0.924164	+	0.381997i	$0.875237\pi$
$908$	19.9063	+	24.5732i	0.660615	+	0.815489i
$909$	−16.2052	−	6.71241i	−0.537492	−	0.222637i
$910$	2.15250	−	8.47872i	0.0713547	−	0.281067i
$911$		−	16.2134i		−	0.537173i	−0.963256	−	0.268586i	$-0.913443\pi$
$911$		−	16.2134i		−	0.537173i	0.963256	−	0.268586i	$-0.0865565\pi$
$912$	9.30779	+	1.97490i	0.308212	+	0.0653956i
$913$		−	5.22913i		−	0.173059i
$914$	36.0343	+	9.14806i	1.19191	+	0.302591i
$915$	21.9348	+	9.08569i	0.725142	+	0.300364i
$916$	−4.97551	+	47.4216i	−0.164395	+	1.56685i
$917$	−5.98274	−	14.4436i	−0.197567	−	0.476970i
$918$	21.1780	+	15.8113i	0.698977	+	0.521852i
$919$	30.4938	+	30.4938i	1.00590	+	1.00590i	0.999983	+	0.00591395i	$0.00188248\pi$
$919$	30.4938	+	30.4938i	1.00590	+	1.00590i	0.00591395	+	0.999983i	$0.498118\pi$
$920$	2.96045	−	8.03139i	0.0976033	−	0.264787i
$921$	4.53171	−	4.53171i	0.149325	−	0.149325i
$922$	16.9957	−	2.46583i	0.559722	−	0.0812077i
$923$	18.5005	−	7.66317i	0.608952	−	0.252236i
$924$	0.507066	+	1.71069i	0.0166812	+	0.0562774i
$925$	11.6083	−	28.0249i	0.381678	−	0.921453i
$926$	13.6147	+	22.8795i	0.447406	+	0.751867i
$927$	−15.8324			−0.520006
$928$	−8.47411	+	7.43840i	−0.278176	+	0.244177i
$929$	16.0909			0.527926			0.263963	−	0.964533i	$-0.414970\pi$
$929$	16.0909			0.527926			0.263963	+	0.964533i	$0.414970\pi$
$930$	−10.8635	−	18.2562i	−0.356229	−	0.598644i
$931$	5.03267	−	12.1499i	0.164939	−	0.398198i
$932$	−53.1253	+	15.7469i	−1.74018	+	0.515807i
$933$	10.6823	−	4.42474i	0.349721	−	0.144859i
$934$	53.3104	−	7.73458i	1.74437	−	0.253083i
$935$	7.82558	−	7.82558i	0.255924	−	0.255924i
$936$	−10.6982	+	4.93545i	−0.349680	+	0.161320i
$937$	18.5678	+	18.5678i	0.606584	+	0.606584i	0.942052	−	0.335468i	$-0.108894\pi$
$937$	18.5678	+	18.5678i	0.606584	+	0.606584i	−0.335468	+	0.942052i	$0.608894\pi$
$938$	6.98951	+	5.21833i	0.228216	+	0.170384i
$939$	6.77086	+	16.3463i	0.220959	+	0.533442i
$940$	−44.3576	−	4.65404i	−1.44679	−	0.151798i
$941$	−46.9249	−	19.4369i	−1.52971	−	0.633626i	−0.550201	−	0.835033i	$-0.685449\pi$
$941$	−46.9249	−	19.4369i	−1.52971	−	0.633626i	−0.979508	+	0.201407i	$0.935449\pi$
$942$	−25.4287	−	6.45561i	−0.828512	−	0.210335i
$943$			4.12148i			0.134214i
$944$	36.4022	+	24.9991i	1.18479	+	0.813652i
$945$			13.2780i			0.431934i
$946$	3.00478	−	11.8359i	0.0976939	−	0.384817i
$947$	30.9941	+	12.8382i	1.00717	+	0.417185i	0.824423	−	0.565975i	$-0.191500\pi$
$947$	30.9941	+	12.8382i	1.00717	+	0.417185i	0.182750	+	0.983159i	$0.441500\pi$
$948$	−9.59729	+	7.77461i	−0.311705	+	0.252508i
$949$	1.68103	+	4.05837i	0.0545686	+	0.131740i
$950$	9.05607	−	12.1298i	0.293818	−	0.393544i
$951$	−20.5921	−	20.5921i	−0.667745	−	0.667745i
$952$	−5.11584	+	5.53731i	−0.165805	+	0.179465i
$953$	21.3166	−	21.3166i	0.690513	−	0.690513i	−0.271832	−	0.962345i	$-0.587629\pi$
$953$	21.3166	−	21.3166i	0.690513	−	0.690513i	0.962345	+	0.271832i	$0.0876294\pi$
$954$	4.31248	+	29.7237i	0.139622	+	0.962339i
$955$	2.73592	−	1.13325i	0.0885322	−	0.0366713i
$956$	43.2106	+	23.4513i	1.39753	+	0.758468i
$957$	−0.884065	+	2.13432i	−0.0285778	+	0.0689928i
$958$	−3.44107	+	2.04764i	−0.111176	+	0.0661564i
$959$	−12.2857			−0.396725
$960$	2.34114	+	29.5414i	0.0755599	+	0.953445i
$961$	−14.5548			−0.469510
$962$	−17.7728	+	10.5759i	−0.573017	+	0.340980i
$963$	10.5544	−	25.4807i	0.340112	−	0.821103i
$964$	−18.9804	−	10.3011i	−0.611319	−	0.331775i
$965$	−12.7343	+	5.27473i	−0.409932	+	0.169799i
$966$	0.171526	+	1.18224i	0.00551876	+	0.0380380i
$967$	2.35492	−	2.35492i	0.0757292	−	0.0757292i	−0.668228	−	0.743957i	$-0.732947\pi$
$967$	2.35492	−	2.35492i	0.0757292	−	0.0757292i	0.743957	+	0.668228i	$0.232947\pi$
$968$	−2.07750	−	1.91937i	−0.0667734	−	0.0616910i
$969$	5.82428	+	5.82428i	0.187103	+	0.187103i
$970$	−35.6349	+	47.7300i	−1.14417	+	1.53252i
$971$	2.59167	+	6.25684i	0.0831706	+	0.200792i	0.959994	−	0.280021i	$-0.0903416\pi$
$971$	2.59167	+	6.25684i	0.0831706	+	0.200792i	−0.876823	+	0.480813i	$0.840342\pi$
$972$	22.8481	−	18.5089i	0.732852	−	0.593672i
$973$	−10.2034	−	4.22640i	−0.327107	−	0.135492i
$974$	0.466853	−	1.83894i	0.0149589	−	0.0589234i
$975$		−	15.1968i		−	0.486688i
$976$	25.2066	−	4.68123i	0.806843	−	0.149842i
$977$		−	31.7772i		−	1.01664i	−0.861167	−	0.508322i	$-0.830266\pi$
$977$		−	31.7772i		−	1.01664i	0.861167	−	0.508322i	$-0.169734\pi$
$978$	−9.45572	−	2.40054i	−0.302361	−	0.0767606i
$979$	−5.59663	−	2.31820i	−0.178869	−	0.0740901i
$980$	40.7346	+	4.27391i	1.30122	+	0.136525i
$981$	−0.819656	−	1.97882i	−0.0261696	−	0.0631790i
$982$	−42.5670	−	31.7803i	−1.35837	−	1.01415i
$983$	−11.1801	−	11.1801i	−0.356589	−	0.356589i	0.505965	−	0.862554i	$-0.331137\pi$
$983$	−11.1801	−	11.1801i	−0.356589	−	0.356589i	−0.862554	+	0.505965i	$0.831137\pi$
$984$	−5.97731	−	12.9565i	−0.190550	−	0.413038i
$985$	59.0170	−	59.0170i	1.88044	−	1.88044i
$986$	−9.65977	+	1.40149i	−0.307630	+	0.0446327i
$987$	5.75088	−	2.38209i	0.183053	−	0.0758229i
$988$	−9.89511	+	2.93302i	−0.314805	+	0.0933117i
$989$	3.12878	−	7.55354i	0.0994894	−	0.240189i
$990$	−3.82941	−	6.43534i	−0.121707	−	0.204528i
$991$	41.8311			1.32881			0.664404	−	0.747374i	$-0.268686\pi$
$991$	41.8311			1.32881			0.664404	+	0.747374i	$0.268686\pi$
$992$	−20.5789	−	10.1368i	−0.653381	−	0.321843i
$993$	−28.9052			−0.917278
$994$	−4.43366	−	7.45078i	−0.140627	−	0.236324i
$995$	9.53905	−	23.0293i	0.302408	−	0.730078i
$996$	3.44465	+	11.6212i	0.109148	+	0.368232i
$997$	45.5709	−	18.8761i	1.44324	−	0.597811i	0.482662	−	0.875807i	$-0.339670\pi$
$997$	45.5709	−	18.8761i	1.44324	−	0.597811i	0.960582	+	0.277996i	$0.0896701\pi$
$998$	40.8826	−	5.93148i	1.29412	−	0.187758i
$999$	22.1975	−	22.1975i	0.702299	−	0.702299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.n.a.45.7	✓	160
32.5	even	8	inner	352.2.n.a.133.7	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.n.a.45.7	✓	160	1.1	even	1	trivial
352.2.n.a.133.7	yes	160	32.5	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21532 + 0.723188i) q^{2} +(0.443524 - 1.07076i) q^{3} +(0.953999 - 1.75781i) q^{4} +(2.95283 - 1.22310i) q^{5} +(0.235339 + 1.62207i) q^{6} +(-0.544294 + 0.544294i) q^{7} +(0.111813 + 2.82622i) q^{8} +(1.17150 + 1.17150i) q^{9} +(-2.70410 + 3.62191i) q^{10} +(0.382683 + 0.923880i) q^{11} +(-1.45907 - 1.80114i) q^{12} +(2.32285 + 0.962156i) q^{13} +(0.267864 - 1.05512i) q^{14} -3.70425i q^{15} +(-2.17977 - 3.35389i) q^{16} -3.46265i q^{17} +(-2.27096 - 0.576532i) q^{18} +(-1.89621 - 0.785436i) q^{19} +(0.667018 - 6.35734i) q^{20} +(0.341402 + 0.824218i) q^{21} +(-1.13322 - 0.846056i) q^{22} +(-0.669534 - 0.669534i) q^{23} +(3.07580 + 1.13377i) q^{24} +(3.68769 - 3.68769i) q^{25} +(-3.51882 + 0.510531i) q^{26} +(4.98628 - 2.06538i) q^{27} +(0.437509 + 1.47602i) q^{28} +(-0.762793 + 1.84154i) q^{29} +(2.67887 + 4.50185i) q^{30} -4.05527 q^{31} +(5.07461 + 2.49966i) q^{32} +1.15898 q^{33} +(2.50415 + 4.20822i) q^{34} +(-0.941481 + 2.27294i) q^{35} +(3.17689 - 0.941664i) q^{36} +(5.37371 - 2.22586i) q^{37} +(2.87252 - 0.416761i) q^{38} +(2.06048 - 2.06048i) q^{39} +(3.78692 + 8.20858i) q^{40} +(-3.07787 - 3.07787i) q^{41} +(-1.01098 - 0.754789i) q^{42} +(3.30436 + 7.97743i) q^{43} +(1.98908 + 0.208696i) q^{44} +(4.89211 + 2.02638i) q^{45} +(1.29790 + 0.329498i) q^{46} -6.97739i q^{47} +(-4.55800 + 0.846487i) q^{48} +6.40749i q^{49} +(-1.81483 + 7.14862i) q^{50} +(-3.70767 - 1.53577i) q^{51} +(3.90728 - 3.16523i) q^{52} +(-4.90560 - 11.8432i) q^{53} +(-4.56625 + 6.11611i) q^{54} +(2.26000 + 2.26000i) q^{55} +(-1.59915 - 1.47743i) q^{56} +(-1.68203 + 1.68203i) q^{57} +(-0.404746 - 2.78971i) q^{58} +(-10.1996 + 4.22479i) q^{59} +(-6.51137 - 3.53385i) q^{60} +(-2.45277 + 5.92151i) q^{61} +(4.92844 - 2.93272i) q^{62} -1.27528 q^{63} +(-7.97500 + 0.632013i) q^{64} +8.03580 q^{65} +(-1.40854 + 0.838164i) q^{66} +(-3.06636 + 7.40285i) q^{67} +(-6.08667 - 3.30336i) q^{68} +(-1.01387 + 0.419957i) q^{69} +(-0.499561 - 3.44321i) q^{70} +(5.63181 - 5.63181i) q^{71} +(-3.17993 + 3.44191i) q^{72} +(1.23542 + 1.23542i) q^{73} +(-4.92105 + 6.59133i) q^{74} +(-2.31306 - 5.58422i) q^{75} +(-3.18963 + 2.58387i) q^{76} +(-0.711155 - 0.294570i) q^{77} +(-1.01403 + 3.99426i) q^{78} -5.32846i q^{79} +(-10.5387 - 7.23739i) q^{80} -1.28490i q^{81} +(5.96647 + 1.51471i) q^{82} +(-4.83109 - 2.00110i) q^{83} +(1.77451 + 0.186183i) q^{84} +(-4.23518 - 10.2246i) q^{85} +(-9.78503 - 7.30545i) q^{86} +(1.63354 + 1.63354i) q^{87} +(-2.56829 + 1.18485i) q^{88} +(-4.28348 + 4.28348i) q^{89} +(-7.41093 + 1.07522i) q^{90} +(-1.78801 + 0.740618i) q^{91} +(-1.81565 + 0.538177i) q^{92} +(-1.79861 + 4.34223i) q^{93} +(5.04596 + 8.47975i) q^{94} -6.55985 q^{95} +(4.92726 - 4.32504i) q^{96} +13.1781 q^{97} +(-4.63382 - 7.78714i) q^{98} +(-0.634012 + 1.53064i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 16 q^{10} - 16 q^{14} - 16 q^{20} + 24 q^{24} - 48 q^{27} + 40 q^{28} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 56 q^{36} - 16 q^{38} - 48 q^{39} - 64 q^{40} - 104 q^{48} - 80 q^{50} + 32 q^{51} + 64 q^{54}+ \cdots + 56 q^{98}+O(q^{100}) \) 160 * q - 16 * q^10 - 16 * q^14 - 16 * q^20 + 24 * q^24 - 48 * q^27 + 40 * q^28 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 56 * q^36 - 16 * q^38 - 48 * q^39 - 64 * q^40 - 104 * q^48 - 80 * q^50 + 32 * q^51 + 64 * q^54 - 40 * q^56 + 8 * q^58 + 32 * q^59 - 8 * q^60 - 64 * q^61 + 24 * q^62 - 24 * q^64 + 48 * q^68 - 64 * q^69 - 24 * q^70 + 32 * q^71 + 72 * q^72 - 128 * q^78 - 16 * q^80 + 40 * q^82 - 80 * q^83 - 152 * q^84 - 64 * q^86 - 112 * q^87 + 144 * q^90 - 72 * q^92 + 96 * q^94 + 56 * q^96 + 56 * q^98

Introduction

L-functions

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