LMFDB - Embedded newform 368.2.j.c.93.3

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			93.3
Root			$1.09121 + 0.899589i$ of defining polynomial
Character	$\chi$	$=$	368.93
Dual form			368.2.j.c.277.3

$q$-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} +(-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} - 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}+ \cdots + 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

Character values

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

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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	0.962438	−	0.271503i	$-0.0875206\pi$
$3$	1.19673	+	1.19673i	0.690935	+	0.690935i	−0.271503	+	0.962438i	$0.587521\pi$
$4$	−1.99080	−	0.191621i	−0.995400	−	0.0958104i
$5$	0.672033	−	0.672033i	0.300542	−	0.300542i	−0.540684	−	0.841226i	$-0.681834\pi$
$5$	0.672033	−	0.672033i	0.300542	−	0.300542i	0.841226	+	0.540684i	$0.181834\pi$
$6$	1.77166	−	1.60932i	0.723277	−	0.657002i
$7$		−	1.79918i		−	0.680026i	−0.940421	−	0.340013i	$-0.889569\pi$
$7$		−	1.79918i		−	0.680026i	0.940421	−	0.340013i	$-0.110431\pi$
$8$	−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	−0.221920	−	0.975065i	$-0.571232\pi$
$11$	2.49790	−	2.49790i	0.753145	−	0.753145i	0.975065	+	0.221920i	$0.0712324\pi$
$12$	−2.15314	−	2.61178i	−0.621558	−	0.753955i
$13$	−0.0311077	−	0.0311077i	−0.00862773	−	0.00862773i	0.702780	−	0.711407i	$-0.251942\pi$
$13$	−0.0311077	−	0.0311077i	−0.00862773	−	0.00862773i	−0.711407	+	0.702780i	$0.751942\pi$
$14$	−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	0.600974	−	0.799269i	$-0.294780\pi$
$19$	−0.864348	−	0.864348i	−0.198295	−	0.198295i	−0.799269	+	0.600974i	$0.794780\pi$
$20$	−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	0.602039	−	0.798467i	$-0.294355\pi$
$29$	−1.05780	−	1.05780i	−0.196428	−	0.196428i	−0.798467	+	0.602039i	$0.794355\pi$
$30$	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	−0.814434	−	0.580257i	$-0.802952\pi$
$37$	−1.42444	+	1.42444i	−0.234177	+	0.234177i	0.580257	+	0.814434i	$0.302952\pi$
$38$	−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	$0.246213\pi$
$41$			8.94702i			1.39729i	−0.715469	+	0.698645i	$0.753787\pi$
$42$	−2.89546	−	3.18753i	−0.446778	−	0.491847i
$43$	−2.22919	+	2.22919i	−0.339948	+	0.339948i	−0.856348	−	0.516400i	$-0.827272\pi$
$43$	−2.22919	+	2.22919i	−0.339948	+	0.339948i	0.516400	+	0.856348i	$0.327272\pi$
$44$	−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	−0.958107	−	0.286411i	$-0.907538\pi$
$53$	−4.89002	+	4.89002i	−0.671696	+	0.671696i	0.286411	+	0.958107i	$0.407538\pi$
$54$	−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	−0.984842	−	0.173453i	$-0.944507\pi$
$59$	−6.23240	+	6.23240i	−0.811389	+	0.811389i	0.173453	+	0.984842i	$0.444507\pi$
$60$	−3.20218	−	0.308220i	−0.413400	−	0.0397911i
$61$	0.841880	+	0.841880i	0.107792	+	0.107792i	0.758946	−	0.651154i	$-0.225715\pi$
$61$	0.841880	+	0.841880i	0.107792	+	0.107792i	−0.651154	+	0.758946i	$0.725715\pi$
$62$	−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	0.190733	−	0.981642i	$-0.438913\pi$
$67$	−6.47387	−	6.47387i	−0.790909	−	0.790909i	−0.981642	+	0.190733i	$0.938913\pi$
$68$	−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	$0.128611\pi$
$71$			6.62529i			0.786278i	−0.919479	+	0.393139i	$0.871389\pi$
$72$	0.379715	+	0.0550354i	0.0447499	+	0.00648599i
$73$		−	0.712123i		−	0.0833477i	−0.999131	−	0.0416739i	$-0.986731\pi$
$73$		−	0.712123i		−	0.0833477i	0.999131	−	0.0416739i	$-0.0132690\pi$
$74$	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	0.988436	−	0.151638i	$-0.0484549\pi$
$83$	7.62359	+	7.62359i	0.836798	+	0.836798i	−0.151638	+	0.988436i	$0.548455\pi$
$84$	−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	$0.0995219\pi$
$89$			5.80356i			0.615176i	−0.951520	+	0.307588i	$0.900478\pi$
$90$	−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	−0.486105	−	0.873900i	$-0.661583\pi$
$101$	3.89729	−	3.89729i	0.387795	−	0.387795i	0.873900	+	0.486105i	$0.161583\pi$
$102$	7.51381	−	6.82531i	0.743978	−	0.675806i
$103$		−	11.3587i		−	1.11920i	−0.828762	−	0.559602i	$-0.810954\pi$
$103$		−	11.3587i		−	1.11920i	0.828762	−	0.559602i	$-0.189046\pi$
$104$	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	−0.148963	+	0.988843i	$0.547594\pi$
$107$	−11.7696	+	11.7696i	−1.13781	+	1.13781i	−0.988843	+	0.148963i	$0.952406\pi$
$108$	−8.18963	+	6.75150i	−0.788047	+	0.649663i
$109$	5.49682	+	5.49682i	0.526500	+	0.526500i	0.919527	−	0.393027i	$-0.128572\pi$
$109$	5.49682	+	5.49682i	0.526500	+	0.526500i	−0.393027	+	0.919527i	$0.628572\pi$
$110$	−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	−0.994656	−	0.103242i	$-0.967079\pi$
$131$	−12.5660	−	12.5660i	−1.09790	−	1.09790i	−0.103242	−	0.994656i	$-0.532921\pi$
$132$	−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	$0.156917\pi$
$137$			11.0784i			0.946488i	−0.880931	+	0.473244i	$0.843083\pi$
$138$	−1.60932	−	1.77166i	−0.136994	−	0.150814i
$139$	−3.40558	+	3.40558i	−0.288857	+	0.288857i	−0.836628	−	0.547771i	$-0.815476\pi$
$139$	−3.40558	+	3.40558i	−0.288857	+	0.288857i	0.547771	+	0.836628i	$0.315476\pi$
$140$	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	−0.706882	−	0.707331i	$-0.749899\pi$
$149$	0.00548598	−	0.00548598i	0.000449429	−	0.000449429i	0.707331	+	0.706882i	$0.249899\pi$
$150$	6.59297	+	7.25804i	0.538314	+	0.592616i
$151$		−	16.7120i		−	1.36000i	−0.733211	−	0.680001i	$-0.761979\pi$
$151$		−	16.7120i		−	1.36000i	0.733211	−	0.680001i	$-0.238021\pi$
$152$	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	0.620789	−	0.783978i	$-0.286812\pi$
$157$	−2.04476	−	2.04476i	−0.163189	−	0.163189i	−0.783978	+	0.620789i	$0.786812\pi$
$158$	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	0.725398	−	0.688330i	$-0.241656\pi$
$163$	0.473260	+	0.473260i	0.0370686	+	0.0370686i	−0.688330	+	0.725398i	$0.741656\pi$
$164$	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	$-0.982587\pi$
$167$		−	1.41315i		−	0.109353i	0.998504	−	0.0546765i	$-0.0174128\pi$
$168$	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	−0.997787	−	0.0664845i	$-0.978822\pi$
$173$	−13.9983	−	13.9983i	−1.06427	−	1.06427i	−0.0664845	−	0.997787i	$-0.521178\pi$
$174$	−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	0.772004	−	0.635618i	$-0.219255\pi$
$179$	1.82472	+	1.82472i	0.136386	+	0.136386i	−0.635618	+	0.772004i	$0.719255\pi$
$180$	0.164018	+	0.198956i	0.0122252	+	0.0148293i
$181$	−2.45441	+	2.45441i	−0.182435	+	0.182435i	−0.792416	−	0.609981i	$-0.791177\pi$
$181$	−2.45441	+	2.45441i	−0.182435	+	0.182435i	0.609981	+	0.792416i	$0.291177\pi$
$182$	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	−0.969893	−	0.243531i	$-0.921694\pi$
$197$	−10.1950	+	10.1950i	−0.726362	+	0.726362i	0.243531	+	0.969893i	$0.421694\pi$
$198$	−0.501632	+	0.455667i	−0.0356494	+	0.0323828i
$199$		−	7.12208i		−	0.504871i	−0.967614	−	0.252435i	$-0.918768\pi$
$199$		−	7.12208i		−	0.504871i	0.967614	−	0.252435i	$-0.0812315\pi$
$200$	−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	0.597194	−	0.802097i	$-0.296282\pi$
$211$	−2.97638	−	2.97638i	−0.204902	−	0.204902i	−0.802097	+	0.597194i	$0.796282\pi$
$212$	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	0.375495	−	0.926824i	$-0.377473\pi$
$227$	−8.30662	−	8.30662i	−0.551330	−	0.551330i	−0.926824	+	0.375495i	$0.877473\pi$
$228$	−0.396423	+	4.11854i	−0.0262538	+	0.272757i
$229$	−16.9537	+	16.9537i	−1.12033	+	1.12033i	−0.128639	+	0.991691i	$0.541061\pi$
$229$	−16.9537	+	16.9537i	−1.12033	+	1.12033i	−0.991691	+	0.128639i	$0.958939\pi$
$230$	−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	$-0.690178\pi$
$233$		−	25.2401i		−	1.65353i	0.562546	−	0.826766i	$-0.309822\pi$
$234$	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	−0.411459	−	0.911428i	$-0.634981\pi$
$251$	7.92099	−	7.92099i	0.499969	−	0.499969i	0.911428	+	0.411459i	$0.134981\pi$
$252$	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	$0.376597\pi$
$263$			30.0275i			1.85158i	−0.378044	+	0.925788i	$0.623403\pi$
$264$	−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	−0.918819	−	0.394680i	$-0.870856\pi$
$269$	−21.5430	−	21.5430i	−1.31350	−	1.31350i	−0.394680	−	0.918819i	$-0.629144\pi$
$270$	−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	−0.0581665	+	0.998307i	$0.518525\pi$
$277$	−17.5832	+	17.5832i	−1.05647	+	1.05647i	−0.998307	+	0.0581665i	$0.981475\pi$
$278$	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	$0.232961\pi$
$281$			22.4042i			1.33652i	−0.743928	+	0.668260i	$0.767039\pi$
$282$	−16.6699	+	15.1424i	−0.992677	+	0.901716i
$283$	−2.23454	+	2.23454i	−0.132830	+	0.132830i	−0.770396	−	0.637566i	$-0.779941\pi$
$283$	−2.23454	+	2.23454i	−0.132830	+	0.132830i	0.637566	+	0.770396i	$0.279941\pi$
$284$	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	−0.546660	−	0.837354i	$-0.684101\pi$
$293$	4.97588	−	4.97588i	0.290694	−	0.290694i	0.837354	+	0.546660i	$0.184101\pi$
$294$	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	0.858646	−	0.512569i	$-0.171306\pi$
$307$	6.06375	+	6.06375i	0.346076	+	0.346076i	−0.512569	+	0.858646i	$0.671306\pi$
$308$	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	$-0.774053\pi$
$311$		−	22.9860i		−	1.30342i	0.758470	−	0.651708i	$-0.225947\pi$
$312$	0.208414	+	0.0302072i	0.0117991	+	0.00171015i
$313$		−	17.5784i		−	0.993589i	−0.867868	−	0.496795i	$-0.834510\pi$
$313$		−	17.5784i		−	0.993589i	0.867868	−	0.496795i	$-0.165490\pi$
$314$	−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	0.984947	+	0.172855i	$0.0552993\pi$
$317$	20.6141	+	20.6141i	1.15780	+	1.15780i	0.172855	+	0.984947i	$0.444701\pi$
$318$	−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	0.184416	−	0.982848i	$-0.440961\pi$
$331$	21.2365	−	21.2365i	1.16726	−	1.16726i	0.982848	−	0.184416i	$-0.0590393\pi$
$332$	−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	−0.746409	−	0.665488i	$-0.768224\pi$
$347$	−1.50740	+	1.50740i	−0.0809215	+	0.0809215i	0.665488	+	0.746409i	$0.268224\pi$
$348$	−0.485145	+	5.04031i	−0.0260065	+	0.270189i
$349$	12.1021	+	12.1021i	0.647810	+	0.647810i	0.952463	−	0.304654i	$-0.0985407\pi$
$349$	12.1021	+	12.1021i	0.647810	+	0.647810i	−0.304654	+	0.952463i	$0.598541\pi$
$350$	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	$0.328570\pi$
$359$			32.5305i			1.71689i	−0.512903	+	0.858447i	$0.671430\pi$
$360$	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	−0.951483	−	0.307703i	$-0.900440\pi$
$373$	−12.4335	+	12.4335i	−0.643780	+	0.643780i	0.307703	+	0.951483i	$0.400440\pi$
$374$	−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	0.0741473	−	0.997247i	$-0.476377\pi$
$379$	20.8578	−	20.8578i	1.07139	−	1.07139i	0.997247	−	0.0741473i	$-0.0236235\pi$
$380$	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	−0.00340262	−	0.999994i	$-0.501083\pi$
$389$	19.6559	−	19.6559i	0.996592	−	0.996592i	0.999994	+	0.00340262i	$0.00108309\pi$
$390$	−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	−0.962712	−	0.270528i	$-0.912802\pi$
$397$	−24.5721	−	24.5721i	−1.23324	−	1.23324i	−0.270528	−	0.962712i	$-0.587198\pi$
$398$	−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	$0.174488\pi$
$409$			21.0782i			1.04225i	−0.853480	+	0.521126i	$0.825512\pi$
$410$	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	0.491115	−	0.871095i	$-0.336589\pi$
$419$	−7.77798	−	7.77798i	−0.379979	−	0.379979i	−0.871095	+	0.491115i	$0.836589\pi$
$420$	−0.554543	+	5.76130i	−0.0270589	+	0.281122i
$421$	12.0592	−	12.0592i	0.587729	−	0.587729i	−0.349287	−	0.937016i	$-0.613576\pi$
$421$	12.0592	−	12.0592i	0.587729	−	0.587729i	0.937016	+	0.349287i	$0.113576\pi$
$422$	−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	$-0.927047\pi$
$439$		−	9.52025i		−	0.454377i	0.973851	−	0.227188i	$-0.0729533\pi$
$440$	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	−0.898759	−	0.438444i	$-0.855530\pi$
$443$	−9.68850	+	9.68850i	−0.460315	+	0.460315i	0.438444	+	0.898759i	$0.355530\pi$
$444$	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	$0.228669\pi$
$457$			28.1401i			1.31634i	−0.752870	+	0.658170i	$0.771331\pi$
$458$	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	0.999592	+	0.0285604i	$0.00909230\pi$
$461$	22.0754	+	22.0754i	1.02815	+	1.02815i	0.0285604	+	0.999592i	$0.490908\pi$
$462$	−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	0.508327	−	0.861164i	$-0.330264\pi$
$467$	−7.62488	−	7.62488i	−0.352837	−	0.352837i	−0.861164	+	0.508327i	$0.830264\pi$
$468$	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	$0.154252\pi$
$487$			20.5609i			0.931701i	−0.884863	+	0.465851i	$0.845748\pi$
$488$	−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	−0.890134	−	0.455699i	$-0.849389\pi$
$491$	−9.62643	+	9.62643i	−0.434435	+	0.434435i	0.455699	+	0.890134i	$0.349389\pi$
$492$	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	0.593098	−	0.805130i	$-0.297905\pi$
$499$	−4.73643	−	4.73643i	−0.212032	−	0.212032i	−0.805130	+	0.593098i	$0.797905\pi$
$500$	−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	$0.305294\pi$
$503$			36.7222i			1.63736i	−0.574250	+	0.818680i	$0.694706\pi$
$504$	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	0.483741	−	0.875211i	$-0.339278\pi$
$509$	−8.83197	−	8.83197i	−0.391470	−	0.391470i	−0.875211	+	0.483741i	$0.839278\pi$
$510$	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	$0.0202685\pi$
$521$			2.90487i			0.127265i	−0.997973	+	0.0636323i	$0.979732\pi$
$522$	0.192963	+	0.212428i	0.00844576	+	0.00929772i
$523$	7.62526	−	7.62526i	0.333430	−	0.333430i	−0.520458	−	0.853887i	$-0.674239\pi$
$523$	7.62526	−	7.62526i	0.333430	−	0.333430i	0.853887	+	0.520458i	$0.174239\pi$
$524$	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	0.671108	−	0.741360i	$-0.265819\pi$
$541$	−1.63403	−	1.63403i	−0.0702524	−	0.0702524i	−0.741360	+	0.671108i	$0.765819\pi$
$542$	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	0.349253	−	0.937028i	$-0.386435\pi$
$547$	−13.7469	−	13.7469i	−0.587776	−	0.587776i	−0.937028	+	0.349253i	$0.886435\pi$
$548$	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	0.213179	−	0.977013i	$-0.431618\pi$
$557$	−18.0271	−	18.0271i	−0.763834	−	0.763834i	−0.977013	+	0.213179i	$0.931618\pi$
$558$	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	0.240914	−	0.970546i	$-0.422553\pi$
$563$	−17.3124	−	17.3124i	−0.729632	−	0.729632i	−0.970546	+	0.240914i	$0.922553\pi$
$564$	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	$-0.836784\pi$
$569$		−	23.4044i		−	0.981164i	0.871395	−	0.490582i	$-0.163216\pi$
$570$	−2.05821	+	1.86961i	−0.0862089	+	0.0783095i
$571$	18.8951	−	18.8951i	0.790736	−	0.790736i	−0.190878	−	0.981614i	$-0.561134\pi$
$571$	18.8951	−	18.8951i	0.790736	−	0.790736i	0.981614	+	0.190878i	$0.0611335\pi$
$572$	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	−0.999874	−	0.0158694i	$-0.994948\pi$
$587$	−23.8405	+	23.8405i	−0.984005	+	0.984005i	0.0158694	+	0.999874i	$0.494948\pi$
$588$	−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	$-0.922889\pi$
$599$		−	11.7422i		−	0.479775i	0.970801	−	0.239887i	$-0.0771105\pi$
$600$	−11.7345	−	15.7126i	−0.479059	−	0.641466i
$601$		−	0.512081i		−	0.0208882i	−0.999945	−	0.0104441i	$-0.996675\pi$
$601$		−	0.512081i		−	0.0208882i	0.999945	−	0.0104441i	$-0.00332452\pi$
$602$	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	0.0244582	−	0.999701i	$-0.492214\pi$
$613$	25.3570	−	25.3570i	1.02416	−	1.02416i	0.999701	−	0.0244582i	$-0.00778608\pi$
$614$	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	$-0.700400\pi$
$617$		−	40.1544i		−	1.61655i	0.588802	−	0.808277i	$-0.299600\pi$
$618$	−18.2798	−	20.1237i	−0.735320	−	0.809495i
$619$	32.8697	−	32.8697i	1.32114	−	1.32114i	0.408293	−	0.912851i	$-0.366124\pi$
$619$	32.8697	−	32.8697i	1.32114	−	1.32114i	0.912851	−	0.408293i	$-0.133876\pi$
$620$	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	$0.103679\pi$
$631$			16.0760i			0.639976i	−0.947422	+	0.319988i	$0.896321\pi$
$632$	−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	−0.962356	−	0.271791i	$-0.912384\pi$
$643$	−31.2948	−	31.2948i	−1.23415	−	1.23415i	−0.271791	−	0.962356i	$-0.587616\pi$
$644$	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	$0.414555\pi$
$647$			49.0505i			1.92837i	−0.265222	+	0.964187i	$0.585445\pi$
$648$	−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	−0.905527	−	0.424288i	$-0.860524\pi$
$653$	−33.9819	−	33.9819i	−1.32982	−	1.32982i	−0.424288	−	0.905527i	$-0.639476\pi$
$654$	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	0.388766	−	0.921337i	$-0.372901\pi$
$659$	−13.6716	−	13.6716i	−0.532570	−	0.532570i	−0.921337	+	0.388766i	$0.872901\pi$
$660$	−8.76863	+	7.22882i	−0.341318	+	0.281382i
$661$	−2.22873	+	2.22873i	−0.0866877	+	0.0866877i	−0.749121	−	0.662433i	$-0.769524\pi$
$661$	−2.22873	+	2.22873i	−0.0866877	+	0.0866877i	0.662433	+	0.749121i	$0.269524\pi$
$662$	−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	−0.910634	−	0.413214i	$-0.864406\pi$
$677$	−12.9425	+	12.9425i	−0.497420	+	0.497420i	0.413214	+	0.910634i	$0.364406\pi$
$678$	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	−0.925766	−	0.378098i	$-0.876578\pi$
$683$	−14.3129	+	14.3129i	−0.547668	+	0.547668i	0.378098	+	0.925766i	$0.376578\pi$
$684$	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	0.595168	−	0.803602i	$-0.297086\pi$
$691$	−5.47908	−	5.47908i	−0.208434	−	0.208434i	−0.803602	+	0.595168i	$0.797086\pi$
$692$	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	0.998887	+	0.0471776i	$0.0150227\pi$
$701$	27.6960	+	27.6960i	1.04606	+	1.04606i	0.0471776	+	0.998887i	$0.484977\pi$
$702$	−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	−0.985832	−	0.167736i	$-0.946354\pi$
$709$	−21.7835	+	21.7835i	−0.818096	+	0.818096i	0.167736	+	0.985832i	$0.446354\pi$
$710$	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	$0.188244\pi$
$727$			30.0643i			1.11502i	−0.830169	+	0.557511i	$0.811756\pi$
$728$	−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	0.616178	−	0.787607i	$-0.288680\pi$
$733$	−4.64126	−	4.64126i	−0.171429	−	0.171429i	−0.787607	+	0.616178i	$0.788680\pi$
$734$	−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	0.831557	−	0.555439i	$-0.187450\pi$
$739$	7.50615	+	7.50615i	0.276118	+	0.276118i	−0.555439	+	0.831557i	$0.687450\pi$
$740$	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	$0.135113\pi$
$743$			22.4518i			0.823678i	−0.911257	+	0.411839i	$0.864887\pi$
$744$	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	−0.666109	−	0.745855i	$-0.732041\pi$
$757$	2.19410	−	2.19410i	0.0797460	−	0.0797460i	0.745855	+	0.666109i	$0.232041\pi$
$758$	−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	$0.0720402\pi$
$761$			12.3804i			0.448788i	−0.974499	+	0.224394i	$0.927960\pi$
$762$	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	+	24.9249i	0.381923	+	0.899398i
$769$	−44.4954			−1.60454			−0.802272	−	0.596958i	$-0.796376\pi$
$769$	−44.4954			−1.60454			−0.802272	+	0.596958i	$0.796376\pi$

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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8} - 6 q^{10} - 4 q^{11} - 8 q^{12} + 18 q^{13} - 2 q^{14} + 8 q^{16} - 8 q^{17} - 4 q^{18} - 8 q^{19} - 32 q^{20} + 8 q^{21} - 34 q^{22} + 12 q^{24} - 14 q^{26}+ \cdots + 36 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

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