LMFDB - Embedded newform 368.2.j.c.277.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(93,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("368.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.j (of order $4$, degree $2$, 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:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.221124989353984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 2 x^{10} + 2 x^{9} + 12 x^{8} - 8 x^{7} - 14 x^{6} - 16 x^{5} + 48 x^{4} + 16 x^{3} + \cdots + 64 $ x^12 - 2x^11 - 2x^10 + 2x^9 + 12x^8 - 8x^7 - 14x^6 - 16x^5 + 48x^4 + 16x^3 - 32x^2 - 64*x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			277.3
Root			$1.09121 - 0.899589i$ of defining polynomial
Character	$\chi$	$=$	368.277
Dual form			368.2.j.c.93.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0678262 + 1.41259i) q^{2} +(1.19673 - 1.19673i) q^{3} +(-1.99080 + 0.191621i) q^{4} +(0.672033 + 0.672033i) q^{5} +(1.77166 + 1.60932i) q^{6} +1.79918i q^{7} +(-0.405709 - 2.79918i) q^{8} +0.135652i q^{9} +O(q^{10})$	\(q+(0.0678262 + 1.41259i) q^{2} +(1.19673 - 1.19673i) q^{3} +(-1.99080 + 0.191621i) q^{4} +(0.672033 + 0.672033i) q^{5} +(1.77166 + 1.60932i) q^{6} +1.79918i q^{7} +(-0.405709 - 2.79918i) q^{8} +0.135652i q^{9} +(-0.903723 + 0.994886i) q^{10} +(2.49790 + 2.49790i) q^{11} +(-2.15314 + 2.61178i) q^{12} +(-0.0311077 + 0.0311077i) q^{13} +(-2.54149 + 0.122031i) q^{14} +1.60849 q^{15} +(3.92656 - 0.762957i) q^{16} +4.24111 q^{17} +(-0.191621 + 0.00920079i) q^{18} +(-0.864348 + 0.864348i) q^{19} +(-1.46666 - 1.20911i) q^{20} +(2.15314 + 2.15314i) q^{21} +(-3.35907 + 3.69792i) q^{22} +1.00000i q^{23} +(-3.83540 - 2.86435i) q^{24} -4.09674i q^{25} +(-0.0460522 - 0.0418324i) q^{26} +(3.75254 + 3.75254i) q^{27} +(-0.344760 - 3.58180i) q^{28} +(-1.05780 + 1.05780i) q^{29} +(0.109098 + 2.27213i) q^{30} -2.27890 q^{31} +(1.34407 + 5.49486i) q^{32} +5.97864 q^{33} +(0.287658 + 5.99093i) q^{34} +(-1.20911 + 1.20911i) q^{35} +(-0.0259938 - 0.270057i) q^{36} +(-1.42444 - 1.42444i) q^{37} +(-1.27959 - 1.16234i) q^{38} +0.0744553i q^{39} +(1.60849 - 2.15379i) q^{40} -8.94702i q^{41} +(-2.89546 + 3.18753i) q^{42} +(-2.22919 - 2.22919i) q^{43} +(-5.45146 - 4.49417i) q^{44} +(-0.0911629 + 0.0911629i) q^{45} +(-1.41259 + 0.0678262i) q^{46} -9.40918 q^{47} +(3.78600 - 5.61211i) q^{48} +3.76296 q^{49} +(5.78700 - 0.277867i) q^{50} +(5.07548 - 5.07548i) q^{51} +(0.0559683 - 0.0678901i) q^{52} +(-4.89002 - 4.89002i) q^{53} +(-5.04627 + 5.55531i) q^{54} +3.35734i q^{55} +(5.03622 - 0.729943i) q^{56} +2.06879i q^{57} +(-1.56597 - 1.42248i) q^{58} +(-6.23240 - 6.23240i) q^{59} +(-3.20218 + 0.308220i) q^{60} +(0.841880 - 0.841880i) q^{61} +(-0.154569 - 3.21914i) q^{62} -0.244063 q^{63} +(-7.67080 + 2.27130i) q^{64} -0.0418108 q^{65} +(0.405509 + 8.44535i) q^{66} +(-6.47387 + 6.47387i) q^{67} +(-8.44320 + 0.812685i) q^{68} +(1.19673 + 1.19673i) q^{69} +(-1.78998 - 1.62596i) q^{70} -6.62529i q^{71} +(0.379715 - 0.0550354i) q^{72} +0.712123i q^{73} +(1.91554 - 2.10876i) q^{74} +(-4.90271 - 4.90271i) q^{75} +(1.55512 - 1.88637i) q^{76} +(-4.49417 + 4.49417i) q^{77} +(-0.105175 + 0.00505002i) q^{78} +3.84242 q^{79} +(3.15151 + 2.12605i) q^{80} +8.57464 q^{81} +(12.6384 - 0.606842i) q^{82} +(7.62359 - 7.62359i) q^{83} +(-4.69905 - 3.87388i) q^{84} +(2.85017 + 2.85017i) q^{85} +(2.99772 - 3.30012i) q^{86} +2.53180i q^{87} +(5.97864 - 8.00549i) q^{88} -5.80356i q^{89} +(-0.134959 - 0.122592i) q^{90} +(-0.0559683 - 0.0559683i) q^{91} +(-0.191621 - 1.99080i) q^{92} +(-2.72724 + 2.72724i) q^{93} +(-0.638189 - 13.2913i) q^{94} -1.16174 q^{95} +(8.18438 + 4.96740i) q^{96} +19.5071 q^{97} +(0.255227 + 5.31550i) q^{98} +(-0.338846 + 0.338846i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 - 4 * q^8	$ 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8} - 6 q^{10} - 4 q^{11} - 8 q^{12} + 18 q^{13} - 2 q^{14} + 8 q^{16} - 8 q^{17} - 4 q^{18} - 8 q^{19} - 32 q^{20} + 8 q^{21} - 34 q^{22} + 12 q^{24} - 14 q^{26} + 14 q^{27} + 12 q^{28} + 2 q^{29} - 30 q^{30} + 20 q^{31} - 8 q^{32} - 36 q^{33} + 10 q^{34} + 4 q^{35} + 4 q^{36} - 4 q^{37} + 24 q^{38} - 14 q^{42} + 20 q^{43} + 4 q^{44} - 20 q^{45} - 2 q^{46} - 16 q^{47} - 12 q^{48} + 52 q^{49} + 6 q^{50} - 4 q^{51} - 16 q^{53} + 16 q^{54} + 28 q^{56} + 14 q^{58} + 8 q^{59} + 48 q^{60} + 12 q^{61} - 44 q^{62} - 4 q^{63} + 24 q^{64} - 52 q^{65} + 34 q^{66} - 4 q^{67} - 16 q^{68} + 2 q^{69} + 28 q^{70} + 8 q^{72} - 26 q^{74} - 46 q^{75} - 8 q^{76} - 12 q^{77} - 44 q^{78} - 4 q^{79} + 4 q^{80} + 48 q^{81} - 6 q^{82} + 28 q^{83} + 12 q^{84} - 8 q^{85} + 44 q^{86} - 36 q^{88} + 4 q^{90} - 4 q^{92} - 14 q^{93} + 48 q^{95} + 32 q^{96} + 36 q^{97} - 2 q^{98} + 36 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 - 4 * q^8 - 6 * q^10 - 4 * q^11 - 8 * q^12 + 18 * q^13 - 2 * q^14 + 8 * q^16 - 8 * q^17 - 4 * q^18 - 8 * q^19 - 32 * q^20 + 8 * q^21 - 34 * q^22 + 12 * q^24 - 14 * q^26 + 14 * q^27 + 12 * q^28 + 2 * q^29 - 30 * q^30 + 20 * q^31 - 8 * q^32 - 36 * q^33 + 10 * q^34 + 4 * q^35 + 4 * q^36 - 4 * q^37 + 24 * q^38 - 14 * q^42 + 20 * q^43 + 4 * q^44 - 20 * q^45 - 2 * q^46 - 16 * q^47 - 12 * q^48 + 52 * q^49 + 6 * q^50 - 4 * q^51 - 16 * q^53 + 16 * q^54 + 28 * q^56 + 14 * q^58 + 8 * q^59 + 48 * q^60 + 12 * q^61 - 44 * q^62 - 4 * q^63 + 24 * q^64 - 52 * q^65 + 34 * q^66 - 4 * q^67 - 16 * q^68 + 2 * q^69 + 28 * q^70 + 8 * q^72 - 26 * q^74 - 46 * q^75 - 8 * q^76 - 12 * q^77 - 44 * q^78 - 4 * q^79 + 4 * q^80 + 48 * q^81 - 6 * q^82 + 28 * q^83 + 12 * q^84 - 8 * q^85 + 44 * q^86 - 36 * q^88 + 4 * q^90 - 4 * q^92 - 14 * q^93 + 48 * q^95 + 32 * q^96 + 36 * q^97 - 2 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.0678262	+	1.41259i	0.0479604	+	0.998849i
$2$	0.0678262	+	1.41259i	0.0479604	+	0.998849i
$3$	1.19673	−	1.19673i	0.690935	−	0.690935i	−0.271503	−	0.962438i	$-0.587521\pi$
$3$	1.19673	−	1.19673i	0.690935	−	0.690935i	0.962438	+	0.271503i	$0.0875206\pi$
$4$	−1.99080	+	0.191621i	−0.995400	+	0.0958104i
$5$	0.672033	+	0.672033i	0.300542	+	0.300542i	0.841226	−	0.540684i	$-0.181834\pi$
$5$	0.672033	+	0.672033i	0.300542	+	0.300542i	−0.540684	+	0.841226i	$0.681834\pi$
$6$	1.77166	+	1.60932i	0.723277	+	0.657002i
$7$			1.79918i			0.680026i	0.940421	+	0.340013i	$0.110431\pi$
$7$			1.79918i			0.680026i	−0.940421	+	0.340013i	$0.889569\pi$
$8$	−0.405709	−	2.79918i	−0.143440	−	0.989659i
$9$			0.135652i			0.0452175i
$10$	−0.903723	+	0.994886i	−0.285782	+	0.314611i
$11$	2.49790	+	2.49790i	0.753145	+	0.753145i	0.975065	−	0.221920i	$-0.0712324\pi$
$11$	2.49790	+	2.49790i	0.753145	+	0.753145i	−0.221920	+	0.975065i	$0.571232\pi$
$12$	−2.15314	+	2.61178i	−0.621558	+	0.753955i
$13$	−0.0311077	+	0.0311077i	−0.00862773	+	0.00862773i	−0.711407	−	0.702780i	$-0.751942\pi$
$13$	−0.0311077	+	0.0311077i	−0.00862773	+	0.00862773i	0.702780	+	0.711407i	$0.251942\pi$
$14$	−2.54149	+	0.122031i	−0.679243	+	0.0326143i
$15$	1.60849			0.415310
$16$	3.92656	−	0.762957i	0.981641	−	0.190739i
$17$	4.24111			1.02862			0.514310	−	0.857604i	$-0.328048\pi$
$17$	4.24111			1.02862			0.514310	+	0.857604i	$0.328048\pi$
$18$	−0.191621	+	0.00920079i	−0.0451654	+	0.00216865i
$19$	−0.864348	+	0.864348i	−0.198295	+	0.198295i	−0.799269	−	0.600974i	$-0.794780\pi$
$19$	−0.864348	+	0.864348i	−0.198295	+	0.198295i	0.600974	+	0.799269i	$0.294780\pi$
$20$	−1.46666	−	1.20911i	−0.327955	−	0.270365i
$21$	2.15314	+	2.15314i	0.469853	+	0.469853i
$22$	−3.35907	+	3.69792i	−0.716157	+	0.788399i
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	−3.83540	−	2.86435i	−0.782898	−	0.584682i
$25$		−	4.09674i		−	0.819349i
$26$	−0.0460522	−	0.0418324i	−0.00903159	−	0.00820401i
$27$	3.75254	+	3.75254i	0.722177	+	0.722177i
$28$	−0.344760	−	3.58180i	−0.0651535	−	0.676897i
$29$	−1.05780	+	1.05780i	−0.196428	+	0.196428i	−0.798467	−	0.602039i	$-0.794355\pi$
$29$	−1.05780	+	1.05780i	−0.196428	+	0.196428i	0.602039	+	0.798467i	$0.294355\pi$
$30$	0.109098	+	2.27213i	0.0199184	+	0.414833i
$31$	−2.27890			−0.409302			−0.204651	−	0.978835i	$-0.565606\pi$
$31$	−2.27890			−0.409302			−0.204651	+	0.978835i	$0.565606\pi$
$32$	1.34407	+	5.49486i	0.237600	+	0.971363i
$33$	5.97864			1.04075
$34$	0.287658	+	5.99093i	0.0493330	+	1.02744i
$35$	−1.20911	+	1.20911i	−0.204376	+	0.204376i
$36$	−0.0259938	−	0.270057i	−0.00433230	−	0.0450095i
$37$	−1.42444	−	1.42444i	−0.234177	−	0.234177i	0.580257	−	0.814434i	$-0.302952\pi$
$37$	−1.42444	−	1.42444i	−0.234177	−	0.234177i	−0.814434	+	0.580257i	$0.802952\pi$
$38$	−1.27959	−	1.16234i	−0.207577	−	0.188556i
$39$			0.0744553i			0.0119224i
$40$	1.60849	−	2.15379i	0.254325	−	0.340544i
$41$		−	8.94702i		−	1.39729i	−0.715469	−	0.698645i	$-0.753787\pi$
$41$		−	8.94702i		−	1.39729i	0.715469	−	0.698645i	$-0.246213\pi$
$42$	−2.89546	+	3.18753i	−0.446778	+	0.491847i
$43$	−2.22919	−	2.22919i	−0.339948	−	0.339948i	0.516400	−	0.856348i	$-0.327272\pi$
$43$	−2.22919	−	2.22919i	−0.339948	−	0.339948i	−0.856348	+	0.516400i	$0.827272\pi$
$44$	−5.45146	−	4.49417i	−0.821839	−	0.677521i
$45$	−0.0911629	+	0.0911629i	−0.0135898	+	0.0135898i
$46$	−1.41259	+	0.0678262i	−0.208274	+	0.0100004i
$47$	−9.40918			−1.37247			−0.686235	−	0.727380i	$-0.740738\pi$
$47$	−9.40918			−1.37247			−0.686235	+	0.727380i	$0.740738\pi$
$48$	3.78600	−	5.61211i	0.546462	−	0.810038i
$49$	3.76296			0.537565
$50$	5.78700	−	0.277867i	0.818406	−	0.0392963i
$51$	5.07548	−	5.07548i	0.710710	−	0.710710i
$52$	0.0559683	−	0.0678901i	0.00776141	−	0.00941466i
$53$	−4.89002	−	4.89002i	−0.671696	−	0.671696i	0.286411	−	0.958107i	$-0.407538\pi$
$53$	−4.89002	−	4.89002i	−0.671696	−	0.671696i	−0.958107	+	0.286411i	$0.907538\pi$
$54$	−5.04627	+	5.55531i	−0.686710	+	0.755982i
$55$			3.35734i			0.452704i
$56$	5.03622	−	0.729943i	0.672993	−	0.0975428i
$57$			2.06879i			0.274018i
$58$	−1.56597	−	1.42248i	−0.205622	−	0.186781i
$59$	−6.23240	−	6.23240i	−0.811389	−	0.811389i	0.173453	−	0.984842i	$-0.444507\pi$
$59$	−6.23240	−	6.23240i	−0.811389	−	0.811389i	−0.984842	+	0.173453i	$0.944507\pi$
$60$	−3.20218	+	0.308220i	−0.413400	+	0.0397911i
$61$	0.841880	−	0.841880i	0.107792	−	0.107792i	−0.651154	−	0.758946i	$-0.725715\pi$
$61$	0.841880	−	0.841880i	0.107792	−	0.107792i	0.758946	+	0.651154i	$0.225715\pi$
$62$	−0.154569	−	3.21914i	−0.0196303	−	0.408831i
$63$	−0.244063			−0.0307490
$64$	−7.67080	+	2.27130i	−0.958850	+	0.283913i
$65$	−0.0418108			−0.00518599
$66$	0.405509	+	8.44535i	0.0499147	+	1.03955i
$67$	−6.47387	+	6.47387i	−0.790909	+	0.790909i	−0.981642	−	0.190733i	$-0.938913\pi$
$67$	−6.47387	+	6.47387i	−0.790909	+	0.790909i	0.190733	+	0.981642i	$0.438913\pi$
$68$	−8.44320	+	0.812685i	−1.02389	+	0.0985525i
$69$	1.19673	+	1.19673i	0.144070	+	0.144070i
$70$	−1.78998	−	1.62596i	−0.213943	−	0.194339i
$71$		−	6.62529i		−	0.786278i	−0.919479	−	0.393139i	$-0.871389\pi$
$71$		−	6.62529i		−	0.786278i	0.919479	−	0.393139i	$-0.128611\pi$
$72$	0.379715	−	0.0550354i	0.0447499	−	0.00648599i
$73$			0.712123i			0.0833477i	0.999131	+	0.0416739i	$0.0132690\pi$
$73$			0.712123i			0.0833477i	−0.999131	+	0.0416739i	$0.986731\pi$
$74$	1.91554	−	2.10876i	0.222676	−	0.245139i
$75$	−4.90271	−	4.90271i	−0.566117	−	0.566117i
$76$	1.55512	−	1.88637i	0.178384	−	0.216381i
$77$	−4.49417	+	4.49417i	−0.512158	+	0.512158i
$78$	−0.105175	+	0.00505002i	−0.0119087	+	0.000571803i
$79$	3.84242			0.432306			0.216153	−	0.976360i	$-0.430649\pi$
$79$	3.84242			0.432306			0.216153	+	0.976360i	$0.430649\pi$
$80$	3.15151	+	2.12605i	0.352350	+	0.237699i
$81$	8.57464			0.952738
$82$	12.6384	−	0.606842i	1.39568	−	0.0670145i
$83$	7.62359	−	7.62359i	0.836798	−	0.836798i	−0.151638	−	0.988436i	$-0.548455\pi$
$83$	7.62359	−	7.62359i	0.836798	−	0.836798i	0.988436	+	0.151638i	$0.0484549\pi$
$84$	−4.69905	−	3.87388i	−0.512709	−	0.422675i
$85$	2.85017	+	2.85017i	0.309144	+	0.309144i
$86$	2.99772	−	3.30012i	0.323253	−	0.355861i
$87$			2.53180i			0.271437i
$88$	5.97864	−	8.00549i	0.637326	−	0.853388i
$89$		−	5.80356i		−	0.615176i	−0.951520	−	0.307588i	$-0.900478\pi$
$89$		−	5.80356i		−	0.615176i	0.951520	−	0.307588i	$-0.0995219\pi$
$90$	−0.134959	−	0.122592i	−0.0142259	−	0.0129224i
$91$	−0.0559683	−	0.0559683i	−0.00586707	−	0.00586707i
$92$	−0.191621	−	1.99080i	−0.0199778	−	0.207555i
$93$	−2.72724	+	2.72724i	−0.282801	+	0.282801i
$94$	−0.638189	−	13.2913i	−0.0658242	−	1.37089i
$95$	−1.16174			−0.119192
$96$	8.18438	+	4.96740i	0.835315	+	0.506983i
$97$	19.5071			1.98064			0.990322	−	0.138785i	$-0.0443198\pi$
$97$	19.5071			1.98064			0.990322	+	0.138785i	$0.0443198\pi$
$98$	0.255227	+	5.31550i	0.0257818	+	0.536947i
$99$	−0.338846	+	0.338846i	−0.0340553	+	0.0340553i
$100$	0.785021	+	8.15579i	0.0785021	+	0.815579i
$101$	3.89729	+	3.89729i	0.387795	+	0.387795i	0.873900	−	0.486105i	$-0.161583\pi$
$101$	3.89729	+	3.89729i	0.387795	+	0.387795i	−0.486105	+	0.873900i	$0.661583\pi$
$102$	7.51381	+	6.82531i	0.743978	+	0.675806i
$103$			11.3587i			1.11920i	0.828762	+	0.559602i	$0.189046\pi$
$103$			11.3587i			1.11920i	−0.828762	+	0.559602i	$0.810954\pi$
$104$	0.0996967	+	0.0744553i	0.00977607	+	0.00730095i
$105$			2.89396i			0.282422i
$106$	6.57591	−	7.23925i	0.638709	−	0.703138i
$107$	−11.7696	−	11.7696i	−1.13781	−	1.13781i	−0.988843	−	0.148963i	$-0.952406\pi$
$107$	−11.7696	−	11.7696i	−1.13781	−	1.13781i	−0.148963	−	0.988843i	$-0.547594\pi$
$108$	−8.18963	−	6.75150i	−0.788047	−	0.649663i
$109$	5.49682	−	5.49682i	0.526500	−	0.526500i	−0.393027	−	0.919527i	$-0.628572\pi$
$109$	5.49682	−	5.49682i	0.526500	−	0.526500i	0.919527	+	0.393027i	$0.128572\pi$
$110$	−4.74253	+	0.227716i	−0.452183	+	0.0217118i
$111$	−3.40936			−0.323602
$112$	1.37270	+	7.06459i	0.129708	+	0.667541i
$113$	3.27215			0.307818			0.153909	−	0.988085i	$-0.450814\pi$
$113$	3.27215			0.307818			0.153909	+	0.988085i	$0.450814\pi$
$114$	−2.92234	+	0.140318i	−0.273703	+	0.0131420i
$115$	−0.672033	+	0.672033i	−0.0626674	+	0.0626674i
$116$	1.90316	−	2.30855i	0.176704	−	0.214344i
$117$	−0.00421984	−	0.00421984i	−0.000390124	−	0.000390124i
$118$	8.38108	−	9.22652i	0.771541	−	0.849370i
$119$			7.63051i			0.699488i
$120$	−0.652579	−	4.50245i	−0.0595721	−	0.411016i
$121$			1.47900i			0.134455i
$122$	1.24633	+	1.13213i	0.112837	+	0.102498i
$123$	−10.7072	−	10.7072i	−0.965436	−	0.965436i
$124$	4.53683	−	0.436684i	0.407419	−	0.0392154i
$125$	6.11331	−	6.11331i	0.546791	−	0.546791i
$126$	−0.0165539	−	0.344760i	−0.00147474	−	0.0307137i
$127$	5.18531			0.460122			0.230061	−	0.973176i	$-0.426107\pi$
$127$	5.18531			0.460122			0.230061	+	0.973176i	$0.426107\pi$
$128$	−3.72870	−	10.6816i	−0.329573	−	0.944130i
$129$	−5.33549			−0.469764
$130$	−0.00283587	−	0.0590614i	−0.000248722	−	0.00518003i
$131$	−12.5660	+	12.5660i	−1.09790	+	1.09790i	−0.103242	+	0.994656i	$0.532921\pi$
$131$	−12.5660	+	12.5660i	−1.09790	+	1.09790i	−0.994656	+	0.103242i	$0.967079\pi$
$132$	−11.9023	+	1.14563i	−1.03596	+	0.0997145i
$133$	−1.55512	−	1.55512i	−0.134846	−	0.134846i
$134$	−9.58399	−	8.70579i	−0.827931	−	0.752066i
$135$			5.04367i			0.434090i
$136$	−1.72066	−	11.8716i	−0.147545	−	1.01798i
$137$		−	11.0784i		−	0.946488i	−0.880931	−	0.473244i	$-0.843083\pi$
$137$		−	11.0784i		−	0.946488i	0.880931	−	0.473244i	$-0.156917\pi$
$138$	−1.60932	+	1.77166i	−0.136994	+	0.150814i
$139$	−3.40558	−	3.40558i	−0.288857	−	0.288857i	0.547771	−	0.836628i	$-0.315476\pi$
$139$	−3.40558	−	3.40558i	−0.288857	−	0.288857i	−0.836628	+	0.547771i	$0.815476\pi$
$140$	2.17540	−	2.63878i	0.183855	−	0.223018i
$141$	−11.2603	+	11.2603i	−0.948288	+	0.948288i
$142$	9.35880	−	0.449369i	0.785373	−	0.0377102i
$143$	−0.155408			−0.0129959
$144$	0.103497	+	0.532648i	0.00862475	+	0.0443873i
$145$	−1.42175			−0.118070
$146$	−1.00594	+	0.0483006i	−0.0832518	+	0.00399739i
$147$	4.50326	−	4.50326i	0.371423	−	0.371423i
$148$	3.10874	+	2.56283i	0.255536	+	0.210663i
$149$	0.00548598	+	0.00548598i	0.000449429	+	0.000449429i	0.707331	−	0.706882i	$-0.249899\pi$
$149$	0.00548598	+	0.00548598i	0.000449429	+	0.000449429i	−0.706882	+	0.707331i	$0.749899\pi$
$150$	6.59297	−	7.25804i	0.538314	−	0.592616i
$151$			16.7120i			1.36000i	0.733211	+	0.680001i	$0.238021\pi$
$151$			16.7120i			1.36000i	−0.733211	+	0.680001i	$0.761979\pi$
$152$	2.77014	+	2.06879i	0.224688	+	0.167801i
$153$			0.575317i			0.0465116i
$154$	−6.65322	−	6.04357i	−0.536132	−	0.487005i
$155$	−1.53149	−	1.53149i	−0.123013	−	0.123013i
$156$	−0.0142672	−	0.148226i	−0.00114229	−	0.0118675i
$157$	−2.04476	+	2.04476i	−0.163189	+	0.163189i	−0.783978	−	0.620789i	$-0.786812\pi$
$157$	−2.04476	+	2.04476i	−0.163189	+	0.163189i	0.620789	+	0.783978i	$0.286812\pi$
$158$	0.260617	+	5.42775i	0.0207336	+	0.431809i
$159$	−11.7041			−0.928197
$160$	−2.78947	+	4.59598i	−0.220527	+	0.363345i
$161$	−1.79918			−0.141795
$162$	0.581585	+	12.1124i	0.0456937	+	0.951642i
$163$	0.473260	−	0.473260i	0.0370686	−	0.0370686i	−0.688330	−	0.725398i	$-0.741656\pi$
$163$	0.473260	−	0.473260i	0.0370686	−	0.0370686i	0.725398	+	0.688330i	$0.241656\pi$
$164$	1.71443	+	17.8117i	0.133875	+	1.39086i
$165$	4.01785	+	4.01785i	0.312789	+	0.312789i
$166$	11.2861	+	10.2519i	0.875968	+	0.795702i
$167$			1.41315i			0.109353i	0.998504	+	0.0546765i	$0.0174128\pi$
$167$			1.41315i			0.109353i	−0.998504	+	0.0546765i	$0.982587\pi$
$168$	5.15347	−	6.90057i	0.397599	−	0.532390i
$169$			12.9981i			0.999851i
$170$	−3.83279	+	4.21942i	−0.293961	+	0.323615i
$171$	−0.117251	−	0.117251i	−0.00896640	−	0.00896640i
$172$	4.86502	+	4.01071i	0.370955	+	0.305813i
$173$	−13.9983	+	13.9983i	−1.06427	+	1.06427i	−0.0664845	+	0.997787i	$0.521178\pi$
$173$	−13.9983	+	13.9983i	−1.06427	+	1.06427i	−0.997787	+	0.0664845i	$0.978822\pi$
$174$	−3.57639	+	0.171722i	−0.271125	+	0.0130182i
$175$	7.37077			0.557178
$176$	11.7139	+	7.90237i	0.882972	+	0.595663i
$177$	−14.9170			−1.12123
$178$	8.19803	−	0.393634i	0.614468	−	0.0295041i
$179$	1.82472	−	1.82472i	0.136386	−	0.136386i	−0.635618	−	0.772004i	$-0.719255\pi$
$179$	1.82472	−	1.82472i	0.136386	−	0.136386i	0.772004	+	0.635618i	$0.219255\pi$
$180$	0.164018	−	0.198956i	0.0122252	−	0.0148293i
$181$	−2.45441	−	2.45441i	−0.182435	−	0.182435i	0.609981	−	0.792416i	$-0.291177\pi$
$181$	−2.45441	−	2.45441i	−0.182435	−	0.182435i	−0.792416	+	0.609981i	$0.791177\pi$
$182$	0.0752639	−	0.0828562i	0.00557893	−	0.00614171i
$183$		−	2.01501i		−	0.148954i
$184$	2.79918	−	0.405709i	0.206358	−	0.0299093i
$185$		−	1.91455i		−	0.140760i
$186$	−4.03743	−	3.66748i	−0.296039	−	0.268912i
$187$	10.5939	+	10.5939i	0.774700	+	0.774700i
$188$	18.7318	−	1.80299i	1.36616	−	0.131497i
$189$	−6.75150	+	6.75150i	−0.491099	+	0.491099i
$190$	−0.0787965	−	1.64106i	−0.00571650	−	0.119055i
$191$	−0.477663			−0.0345625			−0.0172813	−	0.999851i	$-0.505501\pi$
$191$	−0.477663			−0.0345625			−0.0172813	+	0.999851i	$0.505501\pi$
$192$	−6.46176	+	11.8981i	−0.466338	+	0.858669i
$193$	−5.57344			−0.401185			−0.200593	−	0.979675i	$-0.564287\pi$
$193$	−5.57344			−0.401185			−0.200593	+	0.979675i	$0.564287\pi$
$194$	1.32309	+	27.5554i	0.0949925	+	1.97837i
$195$	−0.0500365	+	0.0500365i	−0.00358318	+	0.00358318i
$196$	−7.49129	+	0.721061i	−0.535092	+	0.0515043i
$197$	−10.1950	−	10.1950i	−0.726362	−	0.726362i	0.243531	−	0.969893i	$-0.421694\pi$
$197$	−10.1950	−	10.1950i	−0.726362	−	0.726362i	−0.969893	+	0.243531i	$0.921694\pi$
$198$	−0.501632	−	0.455667i	−0.0356494	−	0.0323828i
$199$			7.12208i			0.504871i	0.967614	+	0.252435i	$0.0812315\pi$
$199$			7.12208i			0.504871i	−0.967614	+	0.252435i	$0.918768\pi$
$200$	−11.4675	+	1.66209i	−0.810876	+	0.117527i
$201$			15.4950i			1.09293i
$202$	−5.24092	+	5.76960i	−0.368750	+	0.405947i
$203$	−1.90316	−	1.90316i	−0.133576	−	0.133576i
$204$	−9.13170	+	11.0768i	−0.639347	+	0.775533i
$205$	6.01269	−	6.01269i	0.419945	−	0.419945i
$206$	−16.0451	+	0.770416i	−1.11792	+	0.0536774i
$207$	−0.135652			−0.00942850
$208$	−0.0984125	+	0.145880i	−0.00682368	+	0.0101150i
$209$	−4.31811			−0.298690
$210$	−4.08797	+	0.196286i	−0.282097	+	0.0135451i
$211$	−2.97638	+	2.97638i	−0.204902	+	0.204902i	−0.802097	−	0.597194i	$-0.796282\pi$
$211$	−2.97638	+	2.97638i	−0.204902	+	0.204902i	0.597194	+	0.802097i	$0.296282\pi$
$212$	10.6721	+	8.79802i	0.732962	+	0.604251i
$213$	−7.92872	−	7.92872i	−0.543267	−	0.543267i
$214$	15.8272	−	17.4238i	1.08193	−	1.19107i
$215$		−	2.99618i		−	0.204337i
$216$	8.98160	−	12.0265i	0.611120	−	0.818298i
$217$		−	4.10014i		−	0.278336i
$218$	8.13756	+	7.39190i	0.551145	+	0.500643i
$219$	0.852223	+	0.852223i	0.0575879	+	0.0575879i
$220$	−0.643336	−	6.68379i	−0.0433737	−	0.450621i
$221$	−0.131931	+	0.131931i	−0.00887465	+	0.00887465i
$222$	−0.231244	−	4.81602i	−0.0155201	−	0.323230i
$223$	12.5625			0.841247			0.420623	−	0.907235i	$-0.361811\pi$
$223$	12.5625			0.841247			0.420623	+	0.907235i	$0.361811\pi$
$224$	−9.88623	+	2.41821i	−0.660552	+	0.161574i
$225$	0.555733			0.0370489
$226$	0.221938	+	4.62220i	0.0147631	+	0.307464i
$227$	−8.30662	+	8.30662i	−0.551330	+	0.551330i	−0.926824	−	0.375495i	$-0.877473\pi$
$227$	−8.30662	+	8.30662i	−0.551330	+	0.551330i	0.375495	+	0.926824i	$0.377473\pi$
$228$	−0.396423	−	4.11854i	−0.0262538	−	0.272757i
$229$	−16.9537	−	16.9537i	−1.12033	−	1.12033i	−0.991691	−	0.128639i	$-0.958939\pi$
$229$	−16.9537	−	16.9537i	−1.12033	−	1.12033i	−0.128639	−	0.991691i	$-0.541061\pi$
$230$	−0.994886	−	0.903723i	−0.0656008	−	0.0595897i
$231$			10.7566i			0.707736i
$232$	3.39011	+	2.53180i	0.222572	+	0.166221i
$233$			25.2401i			1.65353i	0.562546	+	0.826766i	$0.309822\pi$
$233$			25.2401i			1.65353i	−0.562546	+	0.826766i	$0.690178\pi$
$234$	0.00567467	−	0.00624710i	0.000370965	−	0.000408386i
$235$	−6.32328	−	6.32328i	−0.412485	−	0.412485i
$236$	13.6017	+	11.2132i	0.885396	+	0.729917i
$237$	4.59836	−	4.59836i	0.298695	−	0.298695i
$238$	−10.7788	+	0.517549i	−0.698683	+	0.0335477i
$239$	20.6753			1.33737			0.668687	−	0.743544i	$-0.266857\pi$
$239$	20.6753			1.33737			0.668687	+	0.743544i	$0.266857\pi$
$240$	6.31584	−	1.22721i	0.407686	−	0.0792160i
$241$	16.6390			1.07181			0.535906	−	0.844278i	$-0.319970\pi$
$241$	16.6390			1.07181			0.535906	+	0.844278i	$0.319970\pi$
$242$	−2.08921	+	0.100315i	−0.134300	+	0.00644849i
$243$	−0.996062	+	0.996062i	−0.0638974	+	0.0638974i
$244$	−1.51469	+	1.83734i	−0.0969682	+	0.117623i
$245$	2.52883	+	2.52883i	0.161561	+	0.161561i
$246$	14.3986	−	15.8511i	0.918023	−	1.01063i
$247$		−	0.0537757i		−	0.00342167i
$248$	0.924570	+	6.37904i	0.0587102	+	0.405069i
$249$		−	18.2468i		−	1.15635i
$250$	9.05022	+	8.22094i	0.572386	+	0.519938i
$251$	7.92099	+	7.92099i	0.499969	+	0.499969i	0.911428	−	0.411459i	$-0.134981\pi$
$251$	7.92099	+	7.92099i	0.499969	+	0.499969i	−0.411459	+	0.911428i	$0.634981\pi$
$252$	0.485880	−	0.0467675i	0.0306076	−	0.00294608i
$253$	−2.49790	+	2.49790i	−0.157042	+	0.157042i
$254$	0.351700	+	7.32470i	0.0220676	+	0.459592i
$255$	6.82178			0.427197
$256$	14.8358	−	5.99160i	0.927237	−	0.374475i
$257$	−7.54288			−0.470512			−0.235256	−	0.971933i	$-0.575593\pi$
$257$	−7.54288			−0.470512			−0.235256	+	0.971933i	$0.575593\pi$
$258$	−0.361886	−	7.53684i	−0.0225301	−	0.469223i
$259$	2.56283	−	2.56283i	0.159246	−	0.159246i
$260$	0.0832369	−	0.00801182i	0.00516214	−	0.000496872i
$261$	−0.143492	−	0.143492i	−0.00888196	−	0.00888196i
$262$	−18.6029	−	16.8983i	−1.14929	−	1.04398i
$263$		−	30.0275i		−	1.85158i	−0.378044	−	0.925788i	$-0.623403\pi$
$263$		−	30.0275i		−	1.85158i	0.378044	−	0.925788i	$-0.376597\pi$
$264$	−2.42559	−	16.7353i	−0.149285	−	1.02999i
$265$		−	6.57251i		−	0.403746i
$266$	2.09126	−	2.30221i	0.128223	−	0.141158i
$267$	−6.94532	−	6.94532i	−0.425047	−	0.425047i
$268$	11.6476	−	14.1287i	0.711493	−	0.863047i
$269$	−21.5430	+	21.5430i	−1.31350	+	1.31350i	−0.394680	+	0.918819i	$0.629144\pi$
$269$	−21.5430	+	21.5430i	−1.31350	+	1.31350i	−0.918819	+	0.394680i	$0.870856\pi$
$270$	−7.12461	+	0.342093i	−0.433590	+	0.0208191i
$271$	12.2999			0.747167			0.373584	−	0.927596i	$-0.378129\pi$
$271$	12.2999			0.747167			0.373584	+	0.927596i	$0.378129\pi$
$272$	16.6530	−	3.23578i	1.00974	−	0.196198i
$273$	−0.133958			−0.00810753
$274$	15.6491	−	0.751403i	0.945399	−	0.0453939i
$275$	10.2333	−	10.2333i	0.617088	−	0.617088i
$276$	−2.61178	−	2.15314i	−0.157211	−	0.129604i
$277$	−17.5832	−	17.5832i	−1.05647	−	1.05647i	−0.998307	−	0.0581665i	$-0.981475\pi$
$277$	−17.5832	−	17.5832i	−1.05647	−	1.05647i	−0.0581665	−	0.998307i	$-0.518525\pi$
$278$	4.57968	−	5.04166i	0.274671	−	0.302379i
$279$		−	0.309138i		−	0.0185076i
$280$	3.87505	+	2.89396i	0.231579	+	0.172947i
$281$		−	22.4042i		−	1.33652i	−0.743928	−	0.668260i	$-0.767039\pi$
$281$		−	22.4042i		−	1.33652i	0.743928	−	0.668260i	$-0.232961\pi$
$282$	−16.6699	−	15.1424i	−0.992677	−	0.901716i
$283$	−2.23454	−	2.23454i	−0.132830	−	0.132830i	0.637566	−	0.770396i	$-0.279941\pi$
$283$	−2.23454	−	2.23454i	−0.132830	−	0.132830i	−0.770396	+	0.637566i	$0.779941\pi$
$284$	1.26954	+	13.1896i	0.0753335	+	0.782660i
$285$	−1.39029	+	1.39029i	−0.0823540	+	0.0823540i
$286$	−0.0105407	−	0.219527i	−0.000623286	−	0.0129809i
$287$	16.0973			0.950193
$288$	−0.745391	+	0.182326i	−0.0439226	+	0.0107437i
$289$	0.987008			0.0580593
$290$	−0.0964317	−	2.00834i	−0.00566266	−	0.117934i
$291$	23.3448	−	23.3448i	1.36850	−	1.36850i
$292$	−0.136458	−	1.41769i	−0.00798558	−	0.0829643i
$293$	4.97588	+	4.97588i	0.290694	+	0.290694i	0.837354	−	0.546660i	$-0.184101\pi$
$293$	4.97588	+	4.97588i	0.290694	+	0.290694i	−0.546660	+	0.837354i	$0.684101\pi$
$294$	6.66668	+	6.05580i	0.388809	+	0.353182i
$295$		−	8.37675i		−	0.487713i
$296$	−3.40936	+	4.56518i	−0.198165	+	0.265346i
$297$			18.7470i			1.08781i
$298$	−0.00737732	+	0.00812151i	−0.000427357	+	0.000470466i
$299$	−0.0311077	−	0.0311077i	−0.00179901	−	0.00179901i
$300$	10.6998	+	8.82086i	0.617752	+	0.509272i
$301$	4.01071	−	4.01071i	0.231173	−	0.231173i
$302$	−23.6071	+	1.13351i	−1.35844	+	0.0652262i
$303$	9.32805			0.535882
$304$	−2.73446	+	4.05338i	−0.156832	+	0.232477i
$305$	1.13154			0.0647919
$306$	−0.812685	+	0.0390216i	−0.0464581	+	0.00223071i
$307$	6.06375	−	6.06375i	0.346076	−	0.346076i	−0.512569	−	0.858646i	$-0.671306\pi$
$307$	6.06375	−	6.06375i	0.346076	−	0.346076i	0.858646	+	0.512569i	$0.171306\pi$
$308$	8.08581	−	9.80816i	0.460732	−	0.558872i
$309$	13.5933	+	13.5933i	0.773297	+	0.773297i
$310$	2.05949	−	2.26724i	0.116971	−	0.128771i
$311$			22.9860i			1.30342i	0.758470	+	0.651708i	$0.225947\pi$
$311$			22.9860i			1.30342i	−0.758470	+	0.651708i	$0.774053\pi$
$312$	0.208414	−	0.0302072i	0.0117991	−	0.00171015i
$313$			17.5784i			0.993589i	0.867868	+	0.496795i	$0.165490\pi$
$313$			17.5784i			0.993589i	−0.867868	+	0.496795i	$0.834510\pi$
$314$	−3.02708	−	2.74971i	−0.170828	−	0.155175i
$315$	−0.164018	−	0.164018i	−0.00924139	−	0.00924139i
$316$	−7.64949	+	0.736287i	−0.430317	+	0.0414194i
$317$	20.6141	−	20.6141i	1.15780	−	1.15780i	0.172855	−	0.984947i	$-0.444701\pi$
$317$	20.6141	−	20.6141i	1.15780	−	1.15780i	0.984947	−	0.172855i	$-0.0552993\pi$
$318$	−0.793846	−	16.5331i	−0.0445167	−	0.927129i
$319$	−5.28453			−0.295877
$320$	−6.68142	−	3.62864i	−0.373503	−	0.202847i
$321$	−28.1701			−1.57230
$322$	−0.122031	−	2.54149i	−0.00680055	−	0.141632i
$323$	−3.66579	+	3.66579i	−0.203970	+	0.203970i
$324$	−17.0704	+	1.64308i	−0.948355	+	0.0912822i
$325$	0.127440	+	0.127440i	0.00706911	+	0.00706911i
$326$	0.700619	+	0.636421i	0.0388037	+	0.0352481i
$327$		−	13.1565i		−	0.727554i
$328$	−25.0443	+	3.62989i	−1.38284	+	0.200427i
$329$		−	16.9288i		−	0.933315i
$330$	−5.40304	+	5.94807i	−0.297428	+	0.327431i
$331$	21.2365	+	21.2365i	1.16726	+	1.16726i	0.982848	+	0.184416i	$0.0590393\pi$
$331$	21.2365	+	21.2365i	1.16726	+	1.16726i	0.184416	+	0.982848i	$0.440961\pi$
$332$	−13.7162	+	16.6379i	−0.752774	+	0.913122i
$333$	0.193229	−	0.193229i	0.0105889	−	0.0105889i
$334$	−1.99620	+	0.0958488i	−0.109227	+	0.00524461i
$335$	−8.70130			−0.475403
$336$	10.0972	+	6.81168i	0.550847	+	0.371608i
$337$	16.1040			0.877242			0.438621	−	0.898672i	$-0.355467\pi$
$337$	16.1040			0.877242			0.438621	+	0.898672i	$0.355467\pi$
$338$	−18.3609	+	0.881610i	−0.998701	+	0.0479532i
$339$	3.91590	−	3.91590i	0.212682	−	0.212682i
$340$	−6.22026	−	5.12796i	−0.337341	−	0.278103i
$341$	−5.69246	−	5.69246i	−0.308264	−	0.308264i
$342$	0.157674	−	0.173580i	0.00852605	−	0.00938611i
$343$			19.3645i			1.04558i
$344$	−5.33549	+	7.14430i	−0.287670	+	0.385195i
$345$			1.60849i			0.0865982i
$346$	−20.7233	−	18.8244i	−1.11409	−	1.01200i
$347$	−1.50740	−	1.50740i	−0.0809215	−	0.0809215i	0.665488	−	0.746409i	$-0.268224\pi$
$347$	−1.50740	−	1.50740i	−0.0809215	−	0.0809215i	−0.746409	+	0.665488i	$0.768224\pi$
$348$	−0.485145	−	5.04031i	−0.0260065	−	0.270189i
$349$	12.1021	−	12.1021i	0.647810	−	0.647810i	−0.304654	−	0.952463i	$-0.598541\pi$
$349$	12.1021	−	12.1021i	0.647810	−	0.647810i	0.952463	+	0.304654i	$0.0985407\pi$
$350$	0.499932	+	10.4119i	0.0267225	+	0.556537i
$351$	−0.233466			−0.0124615
$352$	−10.3683	+	17.0829i	−0.552630	+	0.910524i
$353$	−25.8399			−1.37532			−0.687661	−	0.726032i	$-0.741362\pi$
$353$	−25.8399			−1.37532			−0.687661	+	0.726032i	$0.741362\pi$
$354$	−1.01177	−	21.0716i	−0.0537748	−	1.11994i
$355$	4.45242	−	4.45242i	0.236310	−	0.236310i
$356$	1.11208	+	11.5537i	0.0589403	+	0.612346i
$357$	9.13170	+	9.13170i	0.483301	+	0.483301i
$358$	2.70134	+	2.45381i	0.142770	+	0.129688i
$359$		−	32.5305i		−	1.71689i	−0.512903	−	0.858447i	$-0.671430\pi$
$359$		−	32.5305i		−	1.71689i	0.512903	−	0.858447i	$-0.328570\pi$
$360$	0.292167	+	0.218196i	0.0153985	+	0.0114999i
$361$			17.5058i			0.921358i
$362$	3.30059	−	3.63354i	0.173475	−	0.190975i
$363$	1.76997	+	1.76997i	0.0928993	+	0.0928993i
$364$	0.122146	+	0.100697i	0.00640221	+	0.00527796i
$365$	−0.478570	+	0.478570i	−0.0250495	+	0.0250495i
$366$	2.84638	−	0.136671i	0.148783	−	0.00714389i
$367$	−27.7341			−1.44771			−0.723854	−	0.689954i	$-0.757631\pi$
$367$	−27.7341			−1.44771			−0.723854	+	0.689954i	$0.757631\pi$
$368$	0.762957	+	3.92656i	0.0397719	+	0.204686i
$369$	1.21368			0.0631819
$370$	2.70446	−	0.129856i	0.140598	−	0.00675092i
$371$	8.79802	−	8.79802i	0.456771	−	0.456771i
$372$	4.90678	−	5.95197i	0.254405	−	0.308595i
$373$	−12.4335	−	12.4335i	−0.643780	−	0.643780i	0.307703	−	0.951483i	$-0.400440\pi$
$373$	−12.4335	−	12.4335i	−0.643780	−	0.643780i	−0.951483	+	0.307703i	$0.900440\pi$
$374$	−14.2462	+	15.6833i	−0.736654	+	0.810963i
$375$		−	14.6320i		−	0.755595i
$376$	3.81739	+	26.3380i	0.196867	+	1.35828i
$377$		−	0.0658112i		−	0.00338945i
$378$	−9.99500	−	9.07914i	−0.514087	−	0.466981i
$379$	20.8578	+	20.8578i	1.07139	+	1.07139i	0.997247	+	0.0741473i	$0.0236235\pi$
$379$	20.8578	+	20.8578i	1.07139	+	1.07139i	0.0741473	+	0.997247i	$0.476377\pi$
$380$	2.31279	−	0.222614i	0.118644	−	0.0114198i
$381$	6.20544	−	6.20544i	0.317914	−	0.317914i
$382$	−0.0323981	−	0.674741i	−0.00165763	−	0.0345227i
$383$	35.8926			1.83403			0.917013	−	0.398857i	$-0.130593\pi$
$383$	35.8926			1.83403			0.917013	+	0.398857i	$0.130593\pi$
$384$	−17.2453	−	8.32080i	−0.880046	−	0.424619i
$385$	−6.04046			−0.307850
$386$	−0.378026	−	7.87297i	−0.0192410	−	0.400724i
$387$	0.302395	−	0.302395i	0.0153716	−	0.0153716i
$388$	−38.8347	+	3.73796i	−1.97153	+	0.189766i
$389$	19.6559	+	19.6559i	0.996592	+	0.996592i	0.999994	−	0.00340262i	$-0.00108309\pi$
$389$	19.6559	+	19.6559i	0.996592	+	0.996592i	−0.00340262	+	0.999994i	$0.501083\pi$
$390$	−0.0740746	−	0.0672870i	−0.00375091	−	0.00340721i
$391$			4.24111i			0.214482i
$392$	−1.52667	−	10.5332i	−0.0771083	−	0.532006i
$393$			30.0764i			1.51715i
$394$	13.7098	−	15.0928i	0.690689	−	0.760362i
$395$	2.58223	+	2.58223i	0.129926	+	0.129926i
$396$	0.609645	−	0.739504i	0.0306358	−	0.0371615i
$397$	−24.5721	+	24.5721i	−1.23324	+	1.23324i	−0.270528	+	0.962712i	$0.587198\pi$
$397$	−24.5721	+	24.5721i	−1.23324	+	1.23324i	−0.962712	+	0.270528i	$0.912802\pi$
$398$	−10.0606	+	0.483064i	−0.504290	+	0.0242138i
$399$	−3.72212			−0.186339
$400$	−3.12564	−	16.0861i	−0.156282	−	0.804306i
$401$	8.10606			0.404797			0.202399	−	0.979303i	$-0.435126\pi$
$401$	8.10606			0.404797			0.202399	+	0.979303i	$0.435126\pi$
$402$	−21.8880	+	1.05097i	−1.09168	+	0.0524175i
$403$	0.0708913	−	0.0708913i	0.00353135	−	0.00353135i
$404$	−8.50553	−	7.01192i	−0.423166	−	0.348856i
$405$	5.76244	+	5.76244i	0.286338	+	0.286338i
$406$	2.55930	−	2.81747i	0.127016	−	0.139828i
$407$		−	7.11623i		−	0.352739i
$408$	−16.2664	−	12.1480i	−0.805304	−	0.601416i
$409$		−	21.0782i		−	1.04225i	−0.853480	−	0.521126i	$-0.825512\pi$
$409$		−	21.0782i		−	1.04225i	0.853480	−	0.521126i	$-0.174488\pi$
$410$	8.90126	+	8.08563i	0.439602	+	0.399321i
$411$	−13.2579	−	13.2579i	−0.653962	−	0.653962i
$412$	−2.17656	−	22.6128i	−0.107231	−	1.11406i
$413$	11.2132	−	11.2132i	0.551765	−	0.551765i
$414$	−0.00920079	−	0.191621i	−0.000452194	−	0.00941765i
$415$	10.2466			0.502986
$416$	−0.212743	−	0.129122i	−0.0104306	−	0.00633071i
$417$	−8.15114			−0.399163
$418$	−0.292881	−	6.09970i	−0.0143253	−	0.298346i
$419$	−7.77798	+	7.77798i	−0.379979	+	0.379979i	−0.871095	−	0.491115i	$-0.836589\pi$
$419$	−7.77798	+	7.77798i	−0.379979	+	0.379979i	0.491115	+	0.871095i	$0.336589\pi$
$420$	−0.554543	−	5.76130i	−0.0270589	−	0.281122i
$421$	12.0592	+	12.0592i	0.587729	+	0.587729i	0.937016	−	0.349287i	$-0.113576\pi$
$421$	12.0592	+	12.0592i	0.587729	+	0.587729i	−0.349287	+	0.937016i	$0.613576\pi$
$422$	−4.40627	−	4.00251i	−0.214494	−	0.194839i
$423$		−	1.27638i		−	0.0620597i
$424$	−11.7041	+	15.6720i	−0.568402	+	0.761098i
$425$		−	17.3747i		−	0.842798i
$426$	10.6622	−	11.7378i	0.516586	−	0.568697i
$427$	1.51469	+	1.51469i	0.0733011	+	0.0733011i
$428$	25.6861	+	21.1755i	1.24159	+	1.02356i
$429$	−0.185982	+	0.185982i	−0.00897929	+	0.00897929i
$430$	4.23236	−	0.203219i	0.204102	−	0.00980010i
$431$	−29.8754			−1.43905			−0.719525	−	0.694467i	$-0.755640\pi$
$431$	−29.8754			−1.43905			−0.719525	+	0.694467i	$0.755640\pi$
$432$	17.5976	+	11.8716i	0.846666	+	0.571171i
$433$	−15.2159			−0.731227			−0.365614	−	0.930767i	$-0.619141\pi$
$433$	−15.2159			−0.731227			−0.365614	+	0.930767i	$0.619141\pi$
$434$	5.79180	−	0.278097i	0.278016	−	0.0133491i
$435$	−1.70145	+	1.70145i	−0.0815785	+	0.0815785i
$436$	−9.88976	+	11.9964i	−0.473634	+	0.574522i
$437$	−0.864348	−	0.864348i	−0.0413474	−	0.0413474i
$438$	−1.14603	+	1.26164i	−0.0547597	+	0.0602835i
$439$			9.52025i			0.454377i	0.973851	+	0.227188i	$0.0729533\pi$
$439$			9.52025i			0.454377i	−0.973851	+	0.227188i	$0.927047\pi$
$440$	9.39780	−	1.36210i	0.448022	−	0.0649358i
$441$			0.510454i			0.0243073i
$442$	−0.195313	−	0.177416i	−0.00929007	−	0.00843881i
$443$	−9.68850	−	9.68850i	−0.460315	−	0.460315i	0.438444	−	0.898759i	$-0.355530\pi$
$443$	−9.68850	−	9.68850i	−0.460315	−	0.460315i	−0.898759	+	0.438444i	$0.855530\pi$
$444$	6.78736	−	0.653305i	0.322114	−	0.0310045i
$445$	3.90019	−	3.90019i	0.184887	−	0.184887i
$446$	0.852067	+	17.7456i	0.0403465	+	0.840279i
$447$	0.0131305			0.000621052
$448$	−4.08648	−	13.8011i	−0.193068	−	0.652042i
$449$	21.9967			1.03809			0.519045	−	0.854747i	$-0.326288\pi$
$449$	21.9967			1.03809			0.519045	+	0.854747i	$0.326288\pi$
$450$	0.0376933	+	0.785021i	0.00177688	+	0.0370062i
$451$	22.3487	−	22.3487i	1.05236	−	1.05236i
$452$	−6.51420	+	0.627012i	−0.306402	+	0.0294922i
$453$	19.9998	+	19.9998i	0.939673	+	0.939673i
$454$	−12.2972	−	11.1704i	−0.577137	−	0.524253i
$455$		−	0.0752251i		−	0.00352661i
$456$	5.79091	−	0.839327i	0.271184	−	0.0393051i
$457$		−	28.1401i		−	1.31634i	−0.752870	−	0.658170i	$-0.771331\pi$
$457$		−	28.1401i		−	1.31634i	0.752870	−	0.658170i	$-0.228669\pi$
$458$	22.7986	−	25.0984i	1.06531	−	1.17277i
$459$	15.9149	+	15.9149i	0.742846	+	0.742846i
$460$	1.20911	−	1.46666i	0.0563749	−	0.0683833i
$461$	22.0754	−	22.0754i	1.02815	−	1.02815i	0.0285604	−	0.999592i	$-0.490908\pi$
$461$	22.0754	−	22.0754i	1.02815	−	1.02815i	0.999592	−	0.0285604i	$-0.00909230\pi$
$462$	−15.1947	+	0.729583i	−0.706921	+	0.0339433i
$463$	−15.5046			−0.720558			−0.360279	−	0.932845i	$-0.617318\pi$
$463$	−15.5046			−0.720558			−0.360279	+	0.932845i	$0.617318\pi$
$464$	−3.34645	+	4.96055i	−0.155355	+	0.230288i
$465$	−3.66558			−0.169987
$466$	−35.6538	+	1.71194i	−1.65163	+	0.0793040i
$467$	−7.62488	+	7.62488i	−0.352837	+	0.352837i	−0.861164	−	0.508327i	$-0.830264\pi$
$467$	−7.62488	+	7.62488i	−0.352837	+	0.352837i	0.508327	+	0.861164i	$0.330264\pi$
$468$	0.00920945	+	0.00759224i	0.000425707	+	0.000350951i
$469$	−11.6476	−	11.6476i	−0.537838	−	0.537838i
$470$	8.50330	−	9.36107i	0.392228	−	0.431794i
$471$			4.89406i			0.225506i
$472$	−14.9170	+	19.9741i	−0.686613	+	0.919384i
$473$		−	11.1366i		−	0.512060i
$474$	6.80746	+	6.18369i	0.312677	+	0.284026i
$475$	3.54101	+	3.54101i	0.162473	+	0.162473i
$476$	−1.46216	−	15.1908i	−0.0670182	−	0.696270i
$477$	0.663344	−	0.663344i	0.0303724	−	0.0303724i
$478$	1.40233	+	29.2056i	0.0641409	+	1.33583i
$479$	2.43354			0.111191			0.0555957	−	0.998453i	$-0.482294\pi$
$479$	2.43354			0.111191			0.0555957	+	0.998453i	$0.482294\pi$
$480$	2.16192	+	8.83843i	0.0986776	+	0.403417i
$481$	0.0886224			0.00404083
$482$	1.12856	+	23.5040i	0.0514045	+	1.07058i
$483$	−2.15314	+	2.15314i	−0.0979712	+	0.0979712i
$484$	−0.283407	−	2.94439i	−0.0128821	−	0.133836i
$485$	13.1094	+	13.1094i	0.595268	+	0.595268i
$486$	−1.47458	−	1.33946i	−0.0668884	−	0.0607593i
$487$		−	20.5609i		−	0.931701i	−0.884863	−	0.465851i	$-0.845748\pi$
$487$		−	20.5609i		−	0.931701i	0.884863	−	0.465851i	$-0.154252\pi$
$488$	−2.69813	−	2.01501i	−0.122139	−	0.0912154i
$489$		−	1.13273i		−	0.0512239i
$490$	−3.40067	+	3.74371i	−0.153627	+	0.169124i
$491$	−9.62643	−	9.62643i	−0.434435	−	0.434435i	0.455699	−	0.890134i	$-0.349389\pi$
$491$	−9.62643	−	9.62643i	−0.434435	−	0.434435i	−0.890134	+	0.455699i	$0.849389\pi$
$492$	23.3676	+	19.2642i	1.05349	+	0.868496i
$493$	−4.48623	+	4.48623i	−0.202049	+	0.202049i
$494$	0.0759629	−	0.00364740i	0.00341773	−	0.000164105i
$495$	−0.455432			−0.0204701
$496$	−8.94823	+	1.73870i	−0.401788	+	0.0780699i
$497$	11.9201			0.534689
$498$	25.7752	−	1.23761i	1.15502	−	0.0554588i
$499$	−4.73643	+	4.73643i	−0.212032	+	0.212032i	−0.805130	−	0.593098i	$-0.797905\pi$
$499$	−4.73643	+	4.73643i	−0.212032	+	0.212032i	0.593098	+	0.805130i	$0.297905\pi$
$500$	−10.9989	+	13.3418i	−0.491888	+	0.596664i
$501$	1.69117	+	1.69117i	0.0755558	+	0.0755558i
$502$	−10.6518	+	11.7263i	−0.475415	+	0.523372i
$503$		−	36.7222i		−	1.63736i	−0.574250	−	0.818680i	$-0.694706\pi$
$503$		−	36.7222i		−	1.63736i	0.574250	−	0.818680i	$-0.305294\pi$
$504$	0.0990186	+	0.683176i	0.00441064	+	0.0304311i
$505$			5.23822i			0.233098i
$506$	−3.69792	−	3.35907i	−0.164393	−	0.149329i
$507$	15.5552	+	15.5552i	0.690832	+	0.690832i
$508$	−10.3229	+	0.993613i	−0.458005	+	0.0440844i
$509$	−8.83197	+	8.83197i	−0.391470	+	0.391470i	−0.875211	−	0.483741i	$-0.839278\pi$
$509$	−8.83197	+	8.83197i	−0.391470	+	0.391470i	0.483741	+	0.875211i	$0.339278\pi$
$510$	0.462696	+	9.63636i	0.0204885	+	0.426705i
$511$	−1.28124			−0.0566786
$512$	9.46990	+	20.5504i	0.418514	+	0.908210i
$513$	−6.48700			−0.286408
$514$	−0.511605	−	10.6550i	−0.0225659	−	0.469970i
$515$	−7.63341	+	7.63341i	−0.336368	+	0.336368i
$516$	10.6219	−	1.02239i	0.467603	−	0.0450083i
$517$	−23.5032	−	23.5032i	−1.03367	−	1.03367i
$518$	3.79404	+	3.44639i	0.166701	+	0.151426i
$519$			33.5045i			1.47069i
$520$	0.0169630	+	0.117036i	0.000743878	+	0.00513237i
$521$		−	2.90487i		−	0.127265i	−0.997973	−	0.0636323i	$-0.979732\pi$
$521$		−	2.90487i		−	0.127265i	0.997973	−	0.0636323i	$-0.0202685\pi$
$522$	0.192963	−	0.212428i	0.00844576	−	0.00929772i
$523$	7.62526	+	7.62526i	0.333430	+	0.333430i	0.853887	−	0.520458i	$-0.174239\pi$
$523$	7.62526	+	7.62526i	0.333430	+	0.333430i	−0.520458	+	0.853887i	$0.674239\pi$
$524$	22.6085	−	27.4243i	0.987657	−	1.19804i
$525$	8.82086	−	8.82086i	0.384974	−	0.384974i
$526$	42.4164	−	2.03665i	1.84944	−	0.0888022i
$527$	−9.66505			−0.421016
$528$	23.4755	−	4.56145i	1.02164	−	0.198512i
$529$	−1.00000			−0.0434783
$530$	9.28424	−	0.445789i	0.403282	−	0.0193638i
$531$	0.845440	−	0.845440i	0.0366890	−	0.0366890i
$532$	3.39392	+	2.79793i	0.147145	+	0.121306i
$533$	0.278321	+	0.278321i	0.0120554	+	0.0120554i
$534$	9.33979	−	10.2819i	0.404172	−	0.444943i
$535$		−	15.8191i		−	0.683918i
$536$	20.7480	+	15.4950i	0.896178	+	0.669282i
$537$		−	4.36741i		−	0.188468i
$538$	−31.8925	−	28.9701i	−1.37498	−	1.24899i
$539$	9.39949	+	9.39949i	0.404865	+	0.404865i
$540$	−0.966471	−	10.0409i	−0.0415903	−	0.432093i
$541$	−1.63403	+	1.63403i	−0.0702524	+	0.0702524i	−0.741360	−	0.671108i	$-0.765819\pi$
$541$	−1.63403	+	1.63403i	−0.0702524	+	0.0702524i	0.671108	+	0.741360i	$0.265819\pi$
$542$	0.834258	+	17.3747i	0.0358344	+	0.746308i
$543$	−5.87455			−0.252101
$544$	5.70033	+	23.3043i	0.244400	+	0.999164i
$545$	7.38809			0.316471
$546$	−0.00908589	−	0.189228i	−0.000388840	−	0.00809820i
$547$	−13.7469	+	13.7469i	−0.587776	+	0.587776i	−0.937028	−	0.349253i	$-0.886435\pi$
$547$	−13.7469	+	13.7469i	−0.587776	+	0.587776i	0.349253	+	0.937028i	$0.386435\pi$
$548$	2.12284	+	22.0548i	0.0906834	+	0.942134i
$549$	0.114203	+	0.114203i	0.00487407	+	0.00487407i
$550$	15.1494	+	13.7613i	0.645974	+	0.586782i
$551$		−	1.82861i		−	0.0779012i
$552$	2.86435	−	3.83540i	0.121915	−	0.163245i
$553$			6.91320i			0.293979i
$554$	23.6452	−	26.0304i	1.00459	−	1.10593i
$555$	−2.29120	−	2.29120i	−0.0972562	−	0.0972562i
$556$	7.43240	+	6.12724i	0.315204	+	0.259853i
$557$	−18.0271	+	18.0271i	−0.763834	+	0.763834i	−0.977013	−	0.213179i	$-0.931618\pi$
$557$	−18.0271	+	18.0271i	−0.763834	+	0.763834i	0.213179	+	0.977013i	$0.431618\pi$
$558$	0.436684	−	0.0209677i	0.0184863	−	0.000887632i
$559$	0.138690			0.00586595
$560$	−3.82514	+	5.67013i	−0.161642	+	0.239607i
$561$	25.3561			1.07053
$562$	31.6478	−	1.51959i	1.33498	−	0.0641000i
$563$	−17.3124	+	17.3124i	−0.729632	+	0.729632i	−0.970546	−	0.240914i	$-0.922553\pi$
$563$	−17.3124	+	17.3124i	−0.729632	+	0.729632i	0.240914	+	0.970546i	$0.422553\pi$
$564$	20.2593	−	24.5747i	0.853070	−	1.03478i
$565$	2.19899	+	2.19899i	0.0925124	+	0.0925124i
$566$	3.00493	−	3.30805i	0.126306	−	0.139048i
$567$			15.4273i			0.647886i
$568$	−18.5454	+	2.68794i	−0.778147	+	0.112784i
$569$			23.4044i			0.981164i	0.871395	+	0.490582i	$0.163216\pi$
$569$			23.4044i			0.981164i	−0.871395	+	0.490582i	$0.836784\pi$
$570$	−2.05821	−	1.86961i	−0.0862089	−	0.0783095i
$571$	18.8951	+	18.8951i	0.790736	+	0.790736i	0.981614	−	0.190878i	$-0.0611335\pi$
$571$	18.8951	+	18.8951i	0.790736	+	0.790736i	−0.190878	+	0.981614i	$0.561134\pi$
$572$	0.309386	−	0.0297794i	0.0129361	−	0.00124514i
$573$	−0.571636	+	0.571636i	−0.0238804	+	0.0238804i
$574$	1.09182	+	22.7388i	0.0455716	+	0.949099i
$575$	4.09674			0.170846
$576$	−0.308108	−	1.04056i	−0.0128378	−	0.0433568i
$577$	−8.99343			−0.374402			−0.187201	−	0.982322i	$-0.559941\pi$
$577$	−8.99343			−0.374402			−0.187201	+	0.982322i	$0.559941\pi$
$578$	0.0669450	+	1.39423i	0.00278454	+	0.0579925i
$579$	−6.66993	+	6.66993i	−0.277193	+	0.277193i
$580$	2.83041	−	0.272436i	0.117526	−	0.0113123i
$581$	13.7162	+	13.7162i	0.569044	+	0.569044i
$582$	34.5599	+	31.3932i	1.43256	+	1.30129i
$583$		−	24.4296i		−	1.01177i
$584$	1.99336	−	0.288915i	0.0824858	−	0.0119554i
$585$		−	0.00567174i		−	0.000234498i
$586$	−6.69137	+	7.36636i	−0.276418	+	0.304301i
$587$	−23.8405	−	23.8405i	−0.984005	−	0.984005i	0.0158694	−	0.999874i	$-0.494948\pi$
$587$	−23.8405	−	23.8405i	−0.984005	−	0.984005i	−0.999874	+	0.0158694i	$0.994948\pi$
$588$	−8.10217	+	9.82801i	−0.334128	+	0.405300i
$589$	1.96976	−	1.96976i	0.0811625	−	0.0811625i
$590$	11.8329	−	0.568163i	0.487152	−	0.0233909i
$591$	−24.4014			−1.00374
$592$	−6.67996	−	4.50638i	−0.274545	−	0.185211i
$593$	−16.6058			−0.681921			−0.340960	−	0.940078i	$-0.610752\pi$
$593$	−16.6058			−0.681921			−0.340960	+	0.940078i	$0.610752\pi$
$594$	−26.4817	+	1.27153i	−1.08656	+	0.0521717i
$595$	−5.12796	+	5.12796i	−0.210226	+	0.210226i
$596$	−0.0119727	−	0.00987025i	−0.000490421	−	0.000404301i
$597$	8.52324	+	8.52324i	0.348833	+	0.348833i
$598$	0.0418324	−	0.0460522i	0.00171065	−	0.00188322i
$599$			11.7422i			0.479775i	0.970801	+	0.239887i	$0.0771105\pi$
$599$			11.7422i			0.479775i	−0.970801	+	0.239887i	$0.922889\pi$
$600$	−11.7345	+	15.7126i	−0.479059	+	0.641466i
$601$			0.512081i			0.0208882i	0.999945	+	0.0104441i	$0.00332452\pi$
$601$			0.512081i			0.0208882i	−0.999945	+	0.0104441i	$0.996675\pi$
$602$	5.93750	+	5.39344i	0.241994	+	0.219820i
$603$	−0.878196	−	0.878196i	−0.0357629	−	0.0357629i
$604$	−3.20236	−	33.2702i	−0.130302	−	1.35375i
$605$	−0.993937	+	0.993937i	−0.0404093	+	0.0404093i
$606$	0.632686	+	13.1767i	0.0257011	+	0.535266i
$607$	−33.8421			−1.37361			−0.686805	−	0.726842i	$-0.740987\pi$
$607$	−33.8421			−1.37361			−0.686805	+	0.726842i	$0.740987\pi$
$608$	−5.91121	−	3.58773i	−0.239731	−	0.145502i
$609$	−4.55516			−0.184584
$610$	0.0767482	+	1.59840i	0.00310745	+	0.0647174i
$611$	0.292698	−	0.292698i	0.0118413	−	0.0118413i
$612$	−0.110243	−	1.14534i	−0.00445629	−	0.0462976i
$613$	25.3570	+	25.3570i	1.02416	+	1.02416i	0.999701	+	0.0244582i	$0.00778608\pi$
$613$	25.3570	+	25.3570i	1.02416	+	1.02416i	0.0244582	+	0.999701i	$0.492214\pi$
$614$	8.97685	+	8.15429i	0.362276	+	0.329080i
$615$		−	14.3912i		−	0.580309i
$616$	14.4033	+	10.7566i	0.580325	+	0.433398i
$617$			40.1544i			1.61655i	0.588802	+	0.808277i	$0.299600\pi$
$617$			40.1544i			1.61655i	−0.588802	+	0.808277i	$0.700400\pi$
$618$	−18.2798	+	20.1237i	−0.735320	+	0.809495i
$619$	32.8697	+	32.8697i	1.32114	+	1.32114i	0.912851	+	0.408293i	$0.133876\pi$
$619$	32.8697	+	32.8697i	1.32114	+	1.32114i	0.408293	+	0.912851i	$0.366124\pi$
$620$	3.34236	+	2.75543i	0.134233	+	0.110661i
$621$	−3.75254	+	3.75254i	−0.150584	+	0.150584i
$622$	−32.4697	+	1.55905i	−1.30192	+	0.0625124i
$623$	10.4416			0.418336
$624$	0.0568062	+	0.292354i	0.00227407	+	0.0117035i
$625$	−12.2670			−0.490681
$626$	−24.8310	+	1.19228i	−0.992446	+	0.0476529i
$627$	−5.16763	+	5.16763i	−0.206375	+	0.206375i
$628$	3.67888	−	4.46251i	0.146803	−	0.178074i
$629$	−6.04122	−	6.04122i	−0.240879	−	0.240879i
$630$	0.220565	−	0.242815i	0.00878753	−	0.00967397i
$631$		−	16.0760i		−	0.639976i	−0.947422	−	0.319988i	$-0.896321\pi$
$631$		−	16.0760i		−	0.639976i	0.947422	−	0.319988i	$-0.103679\pi$
$632$	−1.55891	−	10.7556i	−0.0620099	−	0.427836i
$633$			7.12387i			0.283148i
$634$	30.5174	+	27.7210i	1.21200	+	1.10094i
$635$	3.48470	+	3.48470i	0.138286	+	0.138286i
$636$	23.3006	−	2.24275i	0.923927	−	0.0889309i
$637$	−0.117057	+	0.117057i	−0.00463797	+	0.00463797i
$638$	−0.358430	−	7.46486i	−0.0141904	−	0.295536i
$639$	0.898737			0.0355535
$640$	4.67259	−	9.68420i	0.184700	−	0.382802i
$641$	11.2505			0.444368			0.222184	−	0.975005i	$-0.428681\pi$
$641$	11.2505			0.444368			0.222184	+	0.975005i	$0.428681\pi$
$642$	−1.91067	−	39.7926i	−0.0754081	−	1.57049i
$643$	−31.2948	+	31.2948i	−1.23415	+	1.23415i	−0.271791	+	0.962356i	$0.587616\pi$
$643$	−31.2948	+	31.2948i	−1.23415	+	1.23415i	−0.962356	+	0.271791i	$0.912384\pi$
$644$	3.58180	−	0.344760i	0.141143	−	0.0135854i
$645$	−3.58563	−	3.58563i	−0.141184	−	0.141184i
$646$	−5.42688	−	4.92961i	−0.213518	−	0.193953i
$647$		−	49.0505i		−	1.92837i	−0.265222	−	0.964187i	$-0.585445\pi$
$647$		−	49.0505i		−	1.92837i	0.265222	−	0.964187i	$-0.414555\pi$
$648$	−3.47881	−	24.0020i	−0.136661	−	0.942886i
$649$		−	31.1358i		−	1.22219i
$650$	−0.171377	+	0.188664i	−0.00672194	+	0.00740002i
$651$	−4.90678	−	4.90678i	−0.192312	−	0.192312i
$652$	−0.851479	+	1.03285i	−0.0333465	+	0.0404496i
$653$	−33.9819	+	33.9819i	−1.32982	+	1.32982i	−0.424288	+	0.905527i	$0.639476\pi$
$653$	−33.9819	+	33.9819i	−1.32982	+	1.32982i	−0.905527	+	0.424288i	$0.860524\pi$
$654$	18.5846	−	0.892354i	0.726717	−	0.0348938i
$655$	−16.8896			−0.659930
$656$	−6.82619	−	35.1310i	−0.266518	−	1.37164i
$657$	−0.0966013			−0.00376877
$658$	23.9134	−	1.14822i	0.932241	−	0.0447621i
$659$	−13.6716	+	13.6716i	−0.532570	+	0.532570i	−0.921337	−	0.388766i	$-0.872901\pi$
$659$	−13.6716	+	13.6716i	−0.532570	+	0.532570i	0.388766	+	0.921337i	$0.372901\pi$
$660$	−8.76863	−	7.22882i	−0.341318	−	0.281382i
$661$	−2.22873	−	2.22873i	−0.0866877	−	0.0866877i	0.662433	−	0.749121i	$-0.269524\pi$
$661$	−2.22873	−	2.22873i	−0.0866877	−	0.0866877i	−0.749121	+	0.662433i	$0.769524\pi$
$662$	−28.5580	+	31.4388i	−1.10994	+	1.22190i
$663$			0.315773i			0.0122636i
$664$	−24.4327	−	18.2468i	−0.948175	−	0.708114i
$665$		−	2.09018i		−	0.0810536i
$666$	0.286059	+	0.259847i	0.0110846	+	0.0100689i
$667$	−1.05780	−	1.05780i	−0.0409580	−	0.0409580i
$668$	−0.270789	−	2.81330i	−0.0104772	−	0.108850i
$669$	15.0340	−	15.0340i	0.581247	−	0.581247i
$670$	−0.590176	−	12.2913i	−0.0228005	−	0.474856i
$671$	4.20586			0.162365
$672$	−8.93724	+	14.7252i	−0.344761	+	0.568035i
$673$	−8.55906			−0.329928			−0.164964	−	0.986300i	$-0.552751\pi$
$673$	−8.55906			−0.329928			−0.164964	+	0.986300i	$0.552751\pi$
$674$	1.09227	+	22.7483i	0.0420728	+	0.876232i
$675$	15.3732	−	15.3732i	0.591715	−	0.591715i
$676$	−2.49070	−	25.8765i	−0.0957961	−	0.995251i
$677$	−12.9425	−	12.9425i	−0.497420	−	0.497420i	0.413214	−	0.910634i	$-0.364406\pi$
$677$	−12.9425	−	12.9425i	−0.497420	−	0.497420i	−0.910634	+	0.413214i	$0.864406\pi$
$678$	5.79714	+	5.26594i	0.222638	+	0.202237i
$679$			35.0967i			1.34689i
$680$	6.82178	−	9.13446i	0.261603	−	0.350291i
$681$			19.8816i			0.761866i
$682$	7.65499	−	8.42718i	0.293125	−	0.322693i
$683$	−14.3129	−	14.3129i	−0.547668	−	0.547668i	0.378098	−	0.925766i	$-0.376578\pi$
$683$	−14.3129	−	14.3129i	−0.547668	−	0.547668i	−0.925766	+	0.378098i	$0.876578\pi$
$684$	0.255891	+	0.210955i	0.00978422	+	0.00806607i
$685$	7.44503	−	7.44503i	0.284460	−	0.284460i
$686$	−27.3540	+	1.31342i	−1.04438	+	0.0501466i
$687$	−40.5781			−1.54815
$688$	−10.4538	−	7.05227i	−0.398548	−	0.268865i
$689$	0.304235			0.0115904
$690$	−2.27213	+	0.109098i	−0.0864986	+	0.00415328i
$691$	−5.47908	+	5.47908i	−0.208434	+	0.208434i	−0.803602	−	0.595168i	$-0.797086\pi$
$691$	−5.47908	+	5.47908i	−0.208434	+	0.208434i	0.595168	+	0.803602i	$0.297086\pi$
$692$	25.1855	−	30.5502i	0.957408	−	1.16134i
$693$	−0.609645	−	0.609645i	−0.0231585	−	0.0231585i
$694$	2.02709	−	2.23157i	0.0769473	−	0.0847094i
$695$		−	4.57732i		−	0.173628i
$696$	7.08696	−	1.02717i	0.268631	−	0.0389350i
$697$		−	37.9453i		−	1.43728i
$698$	17.9161	+	16.2744i	0.678133	+	0.615995i
$699$	30.2057	+	30.2057i	1.14248	+	1.14248i
$700$	−14.6737	+	1.41239i	−0.554615	+	0.0533834i
$701$	27.6960	−	27.6960i	1.04606	−	1.04606i	0.0471776	−	0.998887i	$-0.484977\pi$
$701$	27.6960	−	27.6960i	1.04606	−	1.04606i	0.998887	−	0.0471776i	$-0.0150227\pi$
$702$	−0.0158351	−	0.329791i	−0.000597658	−	0.0124472i
$703$	2.46243			0.0928723
$704$	−24.8344	−	13.4874i	−0.935981	−	0.508325i
$705$	−15.1346			−0.570001
$706$	−1.75263	−	36.5011i	−0.0659609	−	1.37374i
$707$	−7.01192	+	7.01192i	−0.263710	+	0.263710i
$708$	29.6968	−	2.85842i	1.11608	−	0.107426i
$709$	−21.7835	−	21.7835i	−0.818096	−	0.818096i	0.167736	−	0.985832i	$-0.446354\pi$
$709$	−21.7835	−	21.7835i	−0.818096	−	0.818096i	−0.985832	+	0.167736i	$0.946354\pi$
$710$	6.59141	+	5.98743i	0.247371	+	0.224704i
$711$			0.521234i			0.0195478i
$712$	−16.2452	+	2.35456i	−0.608815	+	0.0882408i
$713$		−	2.27890i		−	0.0853454i
$714$	−12.2799	+	13.5187i	−0.459565	+	0.505924i
$715$	−0.104439	−	0.104439i	−0.00390580	−	0.00390580i
$716$	−3.28300	+	3.98231i	−0.122691	+	0.148826i
$717$	24.7428	−	24.7428i	0.924038	−	0.924038i
$718$	45.9521	−	2.20642i	1.71492	−	0.0823429i
$719$	7.79232			0.290605			0.145302	−	0.989387i	$-0.453585\pi$
$719$	7.79232			0.290605			0.145302	+	0.989387i	$0.453585\pi$
$720$	−0.288404	+	0.427510i	−0.0107482	+	0.0159324i
$721$	−20.4363			−0.761087
$722$	−24.7285	+	1.18735i	−0.920298	+	0.0441887i
$723$	19.9125	−	19.9125i	0.740552	−	0.740552i
$724$	5.35655	+	4.41592i	0.199075	+	0.164116i
$725$	4.33352	+	4.33352i	0.160943	+	0.160943i
$726$	−2.38019	+	2.62029i	−0.0883370	+	0.0972479i
$727$		−	30.0643i		−	1.11502i	−0.830169	−	0.557511i	$-0.811756\pi$
$727$		−	30.0643i		−	1.11502i	0.830169	−	0.557511i	$-0.188244\pi$
$728$	−0.133958	+	0.179372i	−0.00496483	+	0.00664797i
$729$			28.1080i			1.04104i
$730$	−0.708482	−	0.643562i	−0.0262221	−	0.0238193i
$731$	−9.45423	−	9.45423i	−0.349677	−	0.349677i
$732$	0.386118	+	4.01149i	0.0142713	+	0.148269i
$733$	−4.64126	+	4.64126i	−0.171429	+	0.171429i	−0.787607	−	0.616178i	$-0.788680\pi$
$733$	−4.64126	+	4.64126i	−0.171429	+	0.171429i	0.616178	+	0.787607i	$0.288680\pi$
$734$	−1.88110	−	39.1768i	−0.0694326	−	1.44604i
$735$	6.05268			0.223256
$736$	−5.49486	+	1.34407i	−0.202543	+	0.0495429i
$737$	−32.3421			−1.19134
$738$	0.0823197	+	1.71443i	0.00303023	+	0.0631092i
$739$	7.50615	−	7.50615i	0.276118	−	0.276118i	−0.555439	−	0.831557i	$-0.687450\pi$
$739$	7.50615	−	7.50615i	0.276118	−	0.276118i	0.831557	+	0.555439i	$0.187450\pi$
$740$	0.366867	+	3.81148i	0.0134863	+	0.140113i
$741$	−0.0643553	−	0.0643553i	−0.00236415	−	0.00236415i
$742$	13.0247	+	11.8312i	0.478152	+	0.434338i
$743$		−	22.4518i		−	0.823678i	−0.911257	−	0.411839i	$-0.864887\pi$
$743$		−	22.4518i		−	0.823678i	0.911257	−	0.411839i	$-0.135113\pi$
$744$	8.74048	+	6.52755i	0.320442	+	0.239312i
$745$			0.00737352i			0.000270145i
$746$	16.7200	−	18.4066i	0.612163	−	0.673915i
$747$	1.03416	+	1.03416i	0.0378379	+	0.0378379i
$748$	−23.1203	−	19.0603i	−0.845360	−	0.696912i
$749$	21.1755	−	21.1755i	0.773737	−	0.773737i
$750$	20.6690	−	0.992435i	0.754725	−	0.0362386i
$751$	22.4533			0.819334			0.409667	−	0.912235i	$-0.365645\pi$
$751$	22.4533			0.819334			0.409667	+	0.912235i	$0.365645\pi$
$752$	−36.9457	+	7.17880i	−1.34727	+	0.261784i
$753$	18.9586			0.690892
$754$	0.0929639	−	0.00446372i	0.00338555	−	0.000162559i
$755$	−11.2310	+	11.2310i	−0.408738	+	0.408738i
$756$	12.1471	−	14.7346i	0.441787	−	0.535892i
$757$	2.19410	+	2.19410i	0.0797460	+	0.0797460i	0.745855	−	0.666109i	$-0.232041\pi$
$757$	2.19410	+	2.19410i	0.0797460	+	0.0797460i	−0.666109	+	0.745855i	$0.732041\pi$
$758$	−28.0488	+	30.8782i	−1.01878	+	1.12155i
$759$			5.97864i			0.217011i
$760$	0.471329	+	3.25192i	0.0170969	+	0.117959i
$761$		−	12.3804i		−	0.448788i	−0.974499	−	0.224394i	$-0.927960\pi$
$761$		−	12.3804i		−	0.448788i	0.974499	−	0.224394i	$-0.0720402\pi$
$762$	9.18661	+	8.34483i	0.332796	+	0.302301i
$763$	9.88976	+	9.88976i	0.358033	+	0.358033i
$764$	0.950932	−	0.0915302i	0.0344035	−	0.00331145i
$765$	−0.386632	+	0.386632i	−0.0139787	+	0.0139787i
$766$	2.43446	+	50.7014i	0.0879606	+	1.83192i
$767$	0.387751			0.0140009
$768$	10.5842	−

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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0678262 + 1.41259i) q^{2} +(1.19673 - 1.19673i) q^{3} +(-1.99080 + 0.191621i) q^{4} +(0.672033 + 0.672033i) q^{5} +(1.77166 + 1.60932i) q^{6} +1.79918i q^{7} +(-0.405709 - 2.79918i) q^{8} +0.135652i q^{9} +O(q^{10})\)	\(q+(0.0678262 + 1.41259i) q^{2} +(1.19673 - 1.19673i) q^{3} +(-1.99080 + 0.191621i) q^{4} +(0.672033 + 0.672033i) q^{5} +(1.77166 + 1.60932i) q^{6} +1.79918i q^{7} +(-0.405709 - 2.79918i) q^{8} +0.135652i q^{9} +(-0.903723 + 0.994886i) q^{10} +(2.49790 + 2.49790i) q^{11} +(-2.15314 + 2.61178i) q^{12} +(-0.0311077 + 0.0311077i) q^{13} +(-2.54149 + 0.122031i) q^{14} +1.60849 q^{15} +(3.92656 - 0.762957i) q^{16} +4.24111 q^{17} +(-0.191621 + 0.00920079i) q^{18} +(-0.864348 + 0.864348i) q^{19} +(-1.46666 - 1.20911i) q^{20} +(2.15314 + 2.15314i) q^{21} +(-3.35907 + 3.69792i) q^{22} +1.00000i q^{23} +(-3.83540 - 2.86435i) q^{24} -4.09674i q^{25} +(-0.0460522 - 0.0418324i) q^{26} +(3.75254 + 3.75254i) q^{27} +(-0.344760 - 3.58180i) q^{28} +(-1.05780 + 1.05780i) q^{29} +(0.109098 + 2.27213i) q^{30} -2.27890 q^{31} +(1.34407 + 5.49486i) q^{32} +5.97864 q^{33} +(0.287658 + 5.99093i) q^{34} +(-1.20911 + 1.20911i) q^{35} +(-0.0259938 - 0.270057i) q^{36} +(-1.42444 - 1.42444i) q^{37} +(-1.27959 - 1.16234i) q^{38} +0.0744553i q^{39} +(1.60849 - 2.15379i) q^{40} -8.94702i q^{41} +(-2.89546 + 3.18753i) q^{42} +(-2.22919 - 2.22919i) q^{43} +(-5.45146 - 4.49417i) q^{44} +(-0.0911629 + 0.0911629i) q^{45} +(-1.41259 + 0.0678262i) q^{46} -9.40918 q^{47} +(3.78600 - 5.61211i) q^{48} +3.76296 q^{49} +(5.78700 - 0.277867i) q^{50} +(5.07548 - 5.07548i) q^{51} +(0.0559683 - 0.0678901i) q^{52} +(-4.89002 - 4.89002i) q^{53} +(-5.04627 + 5.55531i) q^{54} +3.35734i q^{55} +(5.03622 - 0.729943i) q^{56} +2.06879i q^{57} +(-1.56597 - 1.42248i) q^{58} +(-6.23240 - 6.23240i) q^{59} +(-3.20218 + 0.308220i) q^{60} +(0.841880 - 0.841880i) q^{61} +(-0.154569 - 3.21914i) q^{62} -0.244063 q^{63} +(-7.67080 + 2.27130i) q^{64} -0.0418108 q^{65} +(0.405509 + 8.44535i) q^{66} +(-6.47387 + 6.47387i) q^{67} +(-8.44320 + 0.812685i) q^{68} +(1.19673 + 1.19673i) q^{69} +(-1.78998 - 1.62596i) q^{70} -6.62529i q^{71} +(0.379715 - 0.0550354i) q^{72} +0.712123i q^{73} +(1.91554 - 2.10876i) q^{74} +(-4.90271 - 4.90271i) q^{75} +(1.55512 - 1.88637i) q^{76} +(-4.49417 + 4.49417i) q^{77} +(-0.105175 + 0.00505002i) q^{78} +3.84242 q^{79} +(3.15151 + 2.12605i) q^{80} +8.57464 q^{81} +(12.6384 - 0.606842i) q^{82} +(7.62359 - 7.62359i) q^{83} +(-4.69905 - 3.87388i) q^{84} +(2.85017 + 2.85017i) q^{85} +(2.99772 - 3.30012i) q^{86} +2.53180i q^{87} +(5.97864 - 8.00549i) q^{88} -5.80356i q^{89} +(-0.134959 - 0.122592i) q^{90} +(-0.0559683 - 0.0559683i) q^{91} +(-0.191621 - 1.99080i) q^{92} +(-2.72724 + 2.72724i) q^{93} +(-0.638189 - 13.2913i) q^{94} -1.16174 q^{95} +(8.18438 + 4.96740i) q^{96} +19.5071 q^{97} +(0.255227 + 5.31550i) q^{98} +(-0.338846 + 0.338846i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 - 4 * q^8	\( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8} - 6 q^{10} - 4 q^{11} - 8 q^{12} + 18 q^{13} - 2 q^{14} + 8 q^{16} - 8 q^{17} - 4 q^{18} - 8 q^{19} - 32 q^{20} + 8 q^{21} - 34 q^{22} + 12 q^{24} - 14 q^{26} + 14 q^{27} + 12 q^{28} + 2 q^{29} - 30 q^{30} + 20 q^{31} - 8 q^{32} - 36 q^{33} + 10 q^{34} + 4 q^{35} + 4 q^{36} - 4 q^{37} + 24 q^{38} - 14 q^{42} + 20 q^{43} + 4 q^{44} - 20 q^{45} - 2 q^{46} - 16 q^{47} - 12 q^{48} + 52 q^{49} + 6 q^{50} - 4 q^{51} - 16 q^{53} + 16 q^{54} + 28 q^{56} + 14 q^{58} + 8 q^{59} + 48 q^{60} + 12 q^{61} - 44 q^{62} - 4 q^{63} + 24 q^{64} - 52 q^{65} + 34 q^{66} - 4 q^{67} - 16 q^{68} + 2 q^{69} + 28 q^{70} + 8 q^{72} - 26 q^{74} - 46 q^{75} - 8 q^{76} - 12 q^{77} - 44 q^{78} - 4 q^{79} + 4 q^{80} + 48 q^{81} - 6 q^{82} + 28 q^{83} + 12 q^{84} - 8 q^{85} + 44 q^{86} - 36 q^{88} + 4 q^{90} - 4 q^{92} - 14 q^{93} + 48 q^{95} + 32 q^{96} + 36 q^{97} - 2 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 - 4 * q^8 - 6 * q^10 - 4 * q^11 - 8 * q^12 + 18 * q^13 - 2 * q^14 + 8 * q^16 - 8 * q^17 - 4 * q^18 - 8 * q^19 - 32 * q^20 + 8 * q^21 - 34 * q^22 + 12 * q^24 - 14 * q^26 + 14 * q^27 + 12 * q^28 + 2 * q^29 - 30 * q^30 + 20 * q^31 - 8 * q^32 - 36 * q^33 + 10 * q^34 + 4 * q^35 + 4 * q^36 - 4 * q^37 + 24 * q^38 - 14 * q^42 + 20 * q^43 + 4 * q^44 - 20 * q^45 - 2 * q^46 - 16 * q^47 - 12 * q^48 + 52 * q^49 + 6 * q^50 - 4 * q^51 - 16 * q^53 + 16 * q^54 + 28 * q^56 + 14 * q^58 + 8 * q^59 + 48 * q^60 + 12 * q^61 - 44 * q^62 - 4 * q^63 + 24 * q^64 - 52 * q^65 + 34 * q^66 - 4 * q^67 - 16 * q^68 + 2 * q^69 + 28 * q^70 + 8 * q^72 - 26 * q^74 - 46 * q^75 - 8 * q^76 - 12 * q^77 - 44 * q^78 - 4 * q^79 + 4 * q^80 + 48 * q^81 - 6 * q^82 + 28 * q^83 + 12 * q^84 - 8 * q^85 + 44 * q^86 - 36 * q^88 + 4 * q^90 - 4 * q^92 - 14 * q^93 + 48 * q^95 + 32 * q^96 + 36 * q^97 - 2 * q^98 + 36 * q^99

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