LMFDB - Embedded newform 168.2.ba.c.5.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(5,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

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

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

chi := DirichletCharacter("168.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.ba (of order $6$, 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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.15
Character	$\chi$	$=$	168.5
Dual form			168.2.ba.c.101.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.368276 - 1.36542i) q^{2} +(-0.390548 - 1.68745i) q^{3} +(-1.72875 - 1.00570i) q^{4} +(-1.54900 - 0.894317i) q^{5} +(-2.44790 - 0.0881824i) q^{6} +(2.63573 + 0.230049i) q^{7} +(-2.00986 + 1.99009i) q^{8} +(-2.69494 + 1.31806i) q^{9} +O(q^{10})$	\(q+(0.368276 - 1.36542i) q^{2} +(-0.390548 - 1.68745i) q^{3} +(-1.72875 - 1.00570i) q^{4} +(-1.54900 - 0.894317i) q^{5} +(-2.44790 - 0.0881824i) q^{6} +(2.63573 + 0.230049i) q^{7} +(-2.00986 + 1.99009i) q^{8} +(-2.69494 + 1.31806i) q^{9} +(-1.79158 + 1.78568i) q^{10} +(-0.501346 - 0.868358i) q^{11} +(-1.02191 + 3.30994i) q^{12} +2.47302 q^{13} +(1.28479 - 3.51416i) q^{14} +(-0.904151 + 2.96313i) q^{15} +(1.97713 + 3.47721i) q^{16} +(-3.32963 - 5.76708i) q^{17} +(0.807221 + 4.16514i) q^{18} +(1.85941 - 3.22059i) q^{19} +(1.77842 + 3.10388i) q^{20} +(-0.641185 - 4.53750i) q^{21} +(-1.37031 + 0.364754i) q^{22} +(6.85244 + 3.95626i) q^{23} +(4.14312 + 2.61431i) q^{24} +(-0.900394 - 1.55953i) q^{25} +(0.910752 - 3.37671i) q^{26} +(3.27666 + 4.03281i) q^{27} +(-4.32515 - 3.04846i) q^{28} -0.748403 q^{29} +(3.71294 + 2.32580i) q^{30} +(2.87254 - 1.65846i) q^{31} +(5.47598 - 1.41904i) q^{32} +(-1.26951 + 1.18513i) q^{33} +(-9.10071 + 2.42246i) q^{34} +(-3.87702 - 2.71353i) q^{35} +(5.98445 + 0.431724i) q^{36} +(-3.22429 - 1.86155i) q^{37} +(-3.71268 - 3.72494i) q^{38} +(-0.965832 - 4.17308i) q^{39} +(4.89305 - 1.28520i) q^{40} +2.01044 q^{41} +(-6.43172 - 0.795563i) q^{42} +9.19651i q^{43} +(-0.00660852 + 2.00538i) q^{44} +(5.35324 + 0.368459i) q^{45} +(7.92554 - 7.89946i) q^{46} +(1.19840 - 2.07569i) q^{47} +(5.09544 - 4.69431i) q^{48} +(6.89415 + 1.21270i) q^{49} +(-2.46101 + 0.655080i) q^{50} +(-8.43126 + 7.87089i) q^{51} +(-4.27522 - 2.48712i) q^{52} +(6.33884 + 10.9792i) q^{53} +(6.71319 - 2.98883i) q^{54} +1.79345i q^{55} +(-5.75527 + 4.78297i) q^{56} +(-6.16075 - 1.87985i) q^{57} +(-0.275619 + 1.02188i) q^{58} +(7.34922 - 4.24308i) q^{59} +(4.54308 - 4.21319i) q^{60} +(-2.02442 + 3.50640i) q^{61} +(-1.20661 - 4.53300i) q^{62} +(-7.40637 + 2.85408i) q^{63} +(0.0790881 - 7.99961i) q^{64} +(-3.83071 - 2.21166i) q^{65} +(1.15067 + 2.16986i) q^{66} +(-6.89843 + 3.98281i) q^{67} +(-0.0438896 + 13.3184i) q^{68} +(3.99976 - 13.1082i) q^{69} +(-5.13292 + 4.29443i) q^{70} +5.46843i q^{71} +(2.79341 - 8.01229i) q^{72} +(-5.68546 + 3.28250i) q^{73} +(-3.72922 + 3.71695i) q^{74} +(-2.27997 + 2.12844i) q^{75} +(-6.45340 + 3.69757i) q^{76} +(-1.12165 - 2.40409i) q^{77} +(-6.05370 - 0.218077i) q^{78} +(2.53988 - 4.39920i) q^{79} +(0.0471537 - 7.15438i) q^{80} +(5.52545 - 7.10419i) q^{81} +(0.740396 - 2.74510i) q^{82} -5.65457i q^{83} +(-3.45493 + 8.48902i) q^{84} +11.9110i q^{85} +(12.5571 + 3.38685i) q^{86} +(0.292288 + 1.26289i) q^{87} +(2.73575 + 0.747554i) q^{88} +(-7.39495 + 12.8084i) q^{89} +(2.47457 - 7.17372i) q^{90} +(6.51821 + 0.568916i) q^{91} +(-7.86731 - 13.7309i) q^{92} +(-3.92043 - 4.19955i) q^{93} +(-2.39285 - 2.40075i) q^{94} +(-5.76045 + 3.32580i) q^{95} +(-4.53318 - 8.68621i) q^{96} +1.75577i q^{97} +(4.19479 - 8.96681i) q^{98} +(2.49565 + 1.67937i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.368276	−	1.36542i	0.260410	−	0.965498i
$2$	0.368276	−	1.36542i	0.260410	−	0.965498i
$3$	−0.390548	−	1.68745i	−0.225483	−	0.974247i
$3$	−0.390548	−	1.68745i	−0.225483	−	0.974247i
$4$	−1.72875	−	1.00570i	−0.864373	−	0.502851i
$5$	−1.54900	−	0.894317i	−0.692735	−	0.399951i	0.111901	−	0.993719i	$-0.464306\pi$
$5$	−1.54900	−	0.894317i	−0.692735	−	0.399951i	−0.804636	+	0.593769i	$0.797639\pi$
$6$	−2.44790	−	0.0881824i	−0.999352	−	0.0360003i
$7$	2.63573	+	0.230049i	0.996213	+	0.0869505i
$7$	2.63573	+	0.230049i	0.996213	+	0.0869505i
$8$	−2.00986	+	1.99009i	−0.710593	+	0.703603i
$9$	−2.69494	+	1.31806i	−0.898315	+	0.439353i
$10$	−1.79158	+	1.78568i	−0.566547	+	0.564683i
$11$	−0.501346	−	0.868358i	−0.151162	−	0.261820i	0.780493	−	0.625164i	$-0.214968\pi$
$11$	−0.501346	−	0.868358i	−0.151162	−	0.261820i	−0.931655	+	0.363345i	$0.881635\pi$
$12$	−1.02191	+	3.30994i	−0.295000	+	0.955497i
$13$	2.47302			0.685891			0.342946	−	0.939355i	$-0.388575\pi$
$13$	2.47302			0.685891			0.342946	+	0.939355i	$0.388575\pi$
$14$	1.28479	−	3.51416i	0.343375	−	0.939199i
$15$	−0.904151	+	2.96313i	−0.233451	+	0.765077i
$16$	1.97713	+	3.47721i	0.494281	+	0.869302i
$17$	−3.32963	−	5.76708i	−0.807553	−	1.39872i	−0.914554	−	0.404464i	$-0.867458\pi$
$17$	−3.32963	−	5.76708i	−0.807553	−	1.39872i	0.107001	−	0.994259i	$-0.465875\pi$
$18$	0.807221	+	4.16514i	0.190264	+	0.981733i
$19$	1.85941	−	3.22059i	0.426577	−	0.738854i	−0.569989	−	0.821652i	$-0.693053\pi$
$19$	1.85941	−	3.22059i	0.426577	−	0.738854i	0.996566	+	0.0827988i	$0.0263859\pi$
$20$	1.77842	+	3.10388i	0.397666	+	0.694049i
$21$	−0.641185	−	4.53750i	−0.139918	−	0.990163i
$22$	−1.37031	+	0.364754i	−0.292150	+	0.0777658i
$23$	6.85244	+	3.95626i	1.42883	+	0.824936i	0.997029	−	0.0770314i	$-0.0245442\pi$
$23$	6.85244	+	3.95626i	1.42883	+	0.824936i	0.431803	+	0.901968i	$0.357877\pi$
$24$	4.14312	+	2.61431i	0.845710	+	0.533643i
$25$	−0.900394	−	1.55953i	−0.180079	−	0.311906i
$26$	0.910752	−	3.37671i	0.178613	−	0.662227i
$27$	3.27666	+	4.03281i	0.630593	+	0.776114i
$28$	−4.32515	−	3.04846i	−0.817376	−	0.576104i
$29$	−0.748403			−0.138975			−0.0694875	−	0.997583i	$-0.522136\pi$
$29$	−0.748403			−0.138975			−0.0694875	+	0.997583i	$0.522136\pi$
$30$	3.71294	+	2.32580i	0.677888	+	0.424630i
$31$	2.87254	−	1.65846i	0.515924	−	0.297869i	−0.219341	−	0.975648i	$-0.570391\pi$
$31$	2.87254	−	1.65846i	0.515924	−	0.297869i	0.735265	+	0.677779i	$0.237058\pi$
$32$	5.47598	−	1.41904i	0.968025	−	0.250853i
$33$	−1.26951	+	1.18513i	−0.220993	+	0.206305i
$34$	−9.10071	+	2.42246i	−1.56076	+	0.415449i
$35$	−3.87702	−	2.71353i	−0.655335	−	0.458670i
$36$	5.98445	+	0.431724i	0.997408	+	0.0719540i
$37$	−3.22429	−	1.86155i	−0.530071	−	0.306036i	0.210975	−	0.977492i	$-0.432336\pi$
$37$	−3.22429	−	1.86155i	−0.530071	−	0.306036i	−0.741045	+	0.671455i	$0.765670\pi$
$38$	−3.71268	−	3.72494i	−0.602277	−	0.604265i
$39$	−0.965832	−	4.17308i	−0.154657	−	0.668228i
$40$	4.89305	−	1.28520i	0.773659	−	0.203208i
$41$	2.01044			0.313978			0.156989	−	0.987600i	$-0.449821\pi$
$41$	2.01044			0.313978			0.156989	+	0.987600i	$0.449821\pi$
$42$	−6.43172	−	0.795563i	−0.992437	−	0.122758i
$43$			9.19651i			1.40245i	0.712938	+	0.701227i	$0.247364\pi$
$43$			9.19651i			1.40245i	−0.712938	+	0.701227i	$0.752636\pi$
$44$	−0.00660852	+	2.00538i	−0.000996272	+	0.302322i
$45$	5.35324	+	0.368459i	0.798013	+	0.0549266i
$46$	7.92554	−	7.89946i	1.16856	−	1.16471i
$47$	1.19840	−	2.07569i	0.174805	−	0.302771i	−0.765289	−	0.643687i	$-0.777404\pi$
$47$	1.19840	−	2.07569i	0.174805	−	0.302771i	0.940094	+	0.340916i	$0.110737\pi$
$48$	5.09544	−	4.69431i	0.735463	−	0.677565i
$49$	6.89415	+	1.21270i	0.984879	+	0.173242i
$50$	−2.46101	+	0.655080i	−0.348039	+	0.0926423i
$51$	−8.43126	+	7.87089i	−1.18061	+	1.10214i
$52$	−4.27522	−	2.48712i	−0.592866	−	0.344901i
$53$	6.33884	+	10.9792i	0.870707	+	1.50811i	0.861267	+	0.508153i	$0.169671\pi$
$53$	6.33884	+	10.9792i	0.870707	+	1.50811i	0.00943963	+	0.999955i	$0.496995\pi$
$54$	6.71319	−	2.98883i	0.913549	−	0.406728i
$55$			1.79345i			0.241829i
$56$	−5.75527	+	4.78297i	−0.769081	+	0.639152i
$57$	−6.16075	−	1.87985i	−0.816012	−	0.248993i
$58$	−0.275619	+	1.02188i	−0.0361905	+	0.134180i
$59$	7.34922	−	4.24308i	0.956787	−	0.552401i	0.0616046	−	0.998101i	$-0.480378\pi$
$59$	7.34922	−	4.24308i	0.956787	−	0.552401i	0.895183	+	0.445699i	$0.147045\pi$
$60$	4.54308	−	4.21319i	0.586508	−	0.543921i
$61$	−2.02442	+	3.50640i	−0.259200	+	0.448948i	−0.966028	−	0.258438i	$-0.916792\pi$
$61$	−2.02442	+	3.50640i	−0.259200	+	0.448948i	0.706828	+	0.707386i	$0.250126\pi$
$62$	−1.20661	−	4.53300i	−0.153240	−	0.575692i
$63$	−7.40637	+	2.85408i	−0.933114	+	0.359580i
$64$	0.0790881	−	7.99961i	0.00988602	−	0.999951i
$65$	−3.83071	−	2.21166i	−0.475141	−	0.274323i
$66$	1.15067	+	2.16986i	0.141638	+	0.267092i
$67$	−6.89843	+	3.98281i	−0.842777	+	0.486577i	−0.858207	−	0.513303i	$-0.828422\pi$
$67$	−6.89843	+	3.98281i	−0.842777	+	0.486577i	0.0154303	+	0.999881i	$0.495088\pi$
$68$	−0.0438896	+	13.3184i	−0.00532240	+	1.61510i
$69$	3.99976	−	13.1082i	0.481514	−	1.57804i
$70$	−5.13292	+	4.29443i	−0.613501	+	0.513283i
$71$			5.46843i			0.648984i	0.945889	+	0.324492i	$0.105193\pi$
$71$			5.46843i			0.648984i	−0.945889	+	0.324492i	$0.894807\pi$
$72$	2.79341	−	8.01229i	0.329207	−	0.944258i
$73$	−5.68546	+	3.28250i	−0.665433	+	0.384188i	−0.794344	−	0.607468i	$-0.792185\pi$
$73$	−5.68546	+	3.28250i	−0.665433	+	0.384188i	0.128911	+	0.991656i	$0.458852\pi$
$74$	−3.72922	+	3.71695i	−0.433513	+	0.432087i
$75$	−2.27997	+	2.12844i	−0.263268	+	0.245771i
$76$	−6.45340	+	3.69757i	−0.740255	+	0.424140i
$77$	−1.12165	−	2.40409i	−0.127824	−	0.273972i
$78$	−6.05370	−	0.218077i	−0.685447	−	0.0246923i
$79$	2.53988	−	4.39920i	0.285759	−	0.494949i	−0.687034	−	0.726625i	$-0.741088\pi$
$79$	2.53988	−	4.39920i	0.285759	−	0.494949i	0.972793	+	0.231676i	$0.0744210\pi$
$80$	0.0471537	−	7.15438i	0.00527194	−	0.799884i
$81$	5.52545	−	7.10419i	0.613938	−	0.789354i
$82$	0.740396	−	2.74510i	0.0817631	−	0.303145i
$83$		−	5.65457i		−	0.620669i	−0.950627	−	0.310335i	$-0.899559\pi$
$83$		−	5.65457i		−	0.620669i	0.950627	−	0.310335i	$-0.100441\pi$
$84$	−3.45493	+	8.48902i	−0.376963	+	0.926228i
$85$			11.9110i			1.29193i
$86$	12.5571	+	3.38685i	1.35407	+	0.365213i
$87$	0.292288	+	1.26289i	0.0313365	+	0.135396i
$88$	2.73575	+	0.747554i	0.291632	+	0.0796896i
$89$	−7.39495	+	12.8084i	−0.783863	+	1.35769i	0.145812	+	0.989312i	$0.453420\pi$
$89$	−7.39495	+	12.8084i	−0.783863	+	1.35769i	−0.929676	+	0.368379i	$0.879913\pi$
$90$	2.47457	−	7.17372i	0.260842	−	0.756177i
$91$	6.51821	+	0.568916i	0.683294	+	0.0596386i
$92$	−7.86731	−	13.7309i	−0.820223	−	1.43154i
$93$	−3.92043	−	4.19955i	−0.406530	−	0.435473i
$94$	−2.39285	−	2.40075i	−0.246804	−	0.247619i
$95$	−5.76045	+	3.32580i	−0.591010	+	0.341220i
$96$	−4.53318	−	8.68621i	−0.462666	−	0.886533i
$97$			1.75577i			0.178271i	0.996019	+	0.0891356i	$0.0284105\pi$
$97$			1.75577i			0.178271i	−0.996019	+	0.0891356i	$0.971590\pi$
$98$	4.19479	−	8.96681i	0.423738	−	0.905785i
$99$	2.49565	+	1.67937i	0.250822	+	0.168783i
$100$	−0.0118686	+	3.60156i	−0.00118686	+	0.360156i
$101$	−12.6803	+	7.32100i	−1.26174	+	0.728467i	−0.973411	−	0.229064i	$-0.926433\pi$
$101$	−12.6803	+	7.32100i	−1.26174	+	0.728467i	−0.288330	+	0.957531i	$0.593100\pi$
$102$	7.64204	+	14.4109i	0.756675	+	1.42689i
$103$	−8.54056	−	4.93089i	−0.841526	−	0.485855i	0.0162566	−	0.999868i	$-0.494825\pi$
$103$	−8.54056	−	4.93089i	−0.841526	−	0.485855i	−0.857783	+	0.514013i	$0.828158\pi$
$104$	−4.97042	+	4.92152i	−0.487390	+	0.482595i
$105$	−3.06476	+	7.60202i	−0.299090	+	0.741881i
$106$	17.3257	−	4.61181i	1.68282	−	0.447939i
$107$	3.48110	−	6.02945i	0.336531	−	0.582889i	−0.647247	−	0.762281i	$-0.724080\pi$
$107$	3.48110	−	6.02945i	0.336531	−	0.582889i	0.983778	+	0.179392i	$0.0574130\pi$
$108$	−1.60871	−	10.2670i	−0.154798	−	0.987946i
$109$	2.36373	−	1.36470i	0.226404	−	0.130715i	−0.382508	−	0.923952i	$-0.624939\pi$
$109$	2.36373	−	1.36470i	0.226404	−	0.130715i	0.608912	+	0.793238i	$0.291606\pi$
$110$	2.44881	+	0.660484i	0.233485	+	0.0629747i
$111$	−1.88202	+	6.16785i	−0.178633	+	0.585426i
$112$	4.41124	+	9.61982i	0.416823	+	0.908988i
$113$		−	0.531154i		−	0.0499667i	−0.999688	−	0.0249834i	$-0.992047\pi$
$113$		−	0.531154i		−	0.0499667i	0.999688	−	0.0249834i	$-0.00795328\pi$
$114$	−4.83565	+	7.71972i	−0.452900	+	0.723018i
$115$	−7.07629	−	12.2565i	−0.659868	−	1.14292i
$116$	1.29380	+	0.752671i	0.120126	+	0.0698837i
$117$	−6.66464	+	3.25958i	−0.616146	+	0.301348i
$118$	−3.08704	−	11.5974i	−0.284185	−	1.06763i
$119$	−7.44929	−	15.9665i	−0.682875	−	1.46364i
$120$	−4.07968	−	7.75482i	−0.372422	−	0.707915i
$121$	4.99730	−	8.65558i	0.454300	−	0.786871i
$122$	4.04216	+	4.05550i	0.365960	+	0.367168i
$123$	−0.785174	−	3.39251i	−0.0707967	−	0.305892i
$124$	−6.63382	−	0.0218611i	−0.595734	−	0.00196319i
$125$			12.1641i			1.08799i
$126$	1.16943	+	11.1639i	0.104181	+	0.994558i
$127$	−4.52393			−0.401434			−0.200717	−	0.979649i	$-0.564327\pi$
$127$	−4.52393			−0.401434			−0.200717	+	0.979649i	$0.564327\pi$
$128$	−10.8937	−	3.05405i	−0.962876	−	0.269942i
$129$	15.5186	−	3.59168i	1.36634	−	0.316230i
$130$	−4.43060	+	4.41603i	−0.388590	+	0.387311i
$131$	13.3927	+	7.73228i	1.17013	+	0.675573i	0.953710	−	0.300729i	$-0.0972298\pi$
$131$	13.3927	+	7.73228i	1.17013	+	0.675573i	0.216416	+	0.976301i	$0.430563\pi$
$132$	3.38654	−	0.772044i	0.294761	−	0.0671978i
$133$	5.64179	−	8.06085i	0.489205	−	0.698964i
$134$	2.89768	+	10.8860i	0.250322	+	0.940409i
$135$	−1.46894	−	9.17720i	−0.126427	−	0.789847i
$136$	18.1691	+	4.96478i	1.55799	+	0.425727i
$137$	9.71195	−	5.60719i	0.829748	−	0.479055i	−0.0240187	−	0.999712i	$-0.507646\pi$
$137$	9.71195	−	5.60719i	0.829748	−	0.479055i	0.853766	+	0.520657i	$0.174313\pi$
$138$	−16.4252	−	10.2888i	−1.39821	−	0.875840i
$139$	17.9824			1.52525			0.762625	−	0.646840i	$-0.223910\pi$
$139$	17.9824			1.52525			0.762625	+	0.646840i	$0.223910\pi$
$140$	3.97338	+	8.59012i	0.335812	+	0.725998i
$141$	−3.97066	−	1.21158i	−0.334390	−	0.102033i
$142$	7.46671	+	2.01389i	0.626592	+	0.169002i
$143$	−1.23984	−	2.14746i	−0.103680	−	0.179580i
$144$	−9.91140	−	6.76491i	−0.825950	−	0.563743i
$145$	1.15928	+	0.669310i	0.0962728	+	0.0555831i
$146$	2.38818	+	8.97191i	0.197647	+	0.742520i
$147$	−0.646141	−	12.1071i	−0.0532928	−	0.998579i
$148$	3.70182	+	6.46082i	0.304288	+	0.531076i
$149$	0.462495	−	0.801066i	0.0378891	−	0.0656258i	−0.846459	−	0.532454i	$-0.821270\pi$
$149$	0.462495	−	0.801066i	0.0378891	−	0.0656258i	0.884348	+	0.466828i	$0.154603\pi$
$150$	2.06655	+	3.89697i	0.168733	+	0.318186i
$151$	9.56720	+	16.5709i	0.778568	+	1.34852i	0.932767	+	0.360479i	$0.117387\pi$
$151$	9.56720	+	16.5709i	0.778568	+	1.34852i	−0.154200	+	0.988040i	$0.549280\pi$
$152$	2.67211	+	10.1733i	0.216736	+	0.825165i
$153$	16.5745	+	11.1533i	1.33997	+	0.901693i
$154$	−3.69567	+	0.646154i	−0.297806	+	0.0520686i
$155$	−5.93277			−0.476531
$156$	−2.52720	+	8.18553i	−0.202338	+	0.655367i
$157$	−5.46873	−	9.47212i	−0.436452	−	0.755957i	0.560961	−	0.827842i	$-0.310432\pi$
$157$	−5.46873	−	9.47212i	−0.436452	−	0.755957i	−0.997413	+	0.0718851i	$0.977099\pi$
$158$	−5.07139	−	5.08813i	−0.403458	−	0.404790i
$159$	16.0512	−	14.9844i	1.27294	−	1.18834i
$160$	−9.75137	−	2.69917i	−0.770914	−	0.213388i
$161$	17.1510	+	12.0040i	1.35169	+	0.946050i
$162$	−7.66531	−	10.1609i	−0.602244	−	0.798312i
$163$	−9.21188	−	5.31848i	−0.721530	−	0.416576i	0.0937855	−	0.995592i	$-0.470103\pi$
$163$	−9.21188	−	5.31848i	−0.721530	−	0.416576i	−0.815316	+	0.579017i	$0.803437\pi$
$164$	−3.47554	−	2.02190i	−0.271394	−	0.157884i
$165$	3.02635	−	0.700429i	0.235601	−	0.0545283i
$166$	−7.72086	−	2.08244i	−0.599255	−	0.161629i
$167$	−7.93040			−0.613673			−0.306836	−	0.951762i	$-0.599270\pi$
$167$	−7.93040			−0.613673			−0.306836	+	0.951762i	$0.599270\pi$
$168$	10.3187	+	7.84373i	0.796106	+	0.605157i
$169$	−6.88419			−0.529553
$170$	16.2635	+	4.38652i	1.24735	+	0.336431i
$171$	−0.766076	+	11.1301i	−0.0585833	+	0.851141i
$172$	9.24895	−	15.8984i	0.705226	−	1.21224i
$173$	−3.69882	−	2.13552i	−0.281216	−	0.162360i	0.352758	−	0.935715i	$-0.385244\pi$
$173$	−3.69882	−	2.13552i	−0.281216	−	0.162360i	−0.633974	+	0.773354i	$0.718577\pi$
$174$	1.83202	+	0.0659960i	0.138885	+	0.00500314i
$175$	−2.01443	−	4.31763i	−0.152276	−	0.326382i
$176$	2.02823	−	3.46014i	0.152884	−	0.260818i
$177$	−10.0302	−	10.7443i	−0.753915	−	0.807590i
$178$	14.7655	+	14.8143i	1.10672	+	1.11038i
$179$	−3.77825	−	6.54412i	−0.282399	−	0.489130i	0.689576	−	0.724214i	$-0.257797\pi$
$179$	−3.77825	−	6.54412i	−0.282399	−	0.489130i	−0.971975	+	0.235083i	$0.924464\pi$
$180$	−8.88383	−	6.02073i	−0.662161	−	0.448759i
$181$	5.00239			0.371824			0.185912	−	0.982566i	$-0.440476\pi$
$181$	5.00239			0.371824			0.185912	+	0.982566i	$0.440476\pi$
$182$	3.17731	−	8.69057i	0.235518	−	0.644188i
$183$	6.70749	+	2.04668i	0.495832	+	0.151295i
$184$	−21.6458	+	5.68543i	−1.59575	+	0.419136i
$185$	3.32963	+	5.76708i	0.244799	+	0.424004i
$186$	−7.17795	+	3.80645i	−0.526313	+	0.279102i
$187$	−3.33859	+	5.78261i	−0.244142	+	0.422867i
$188$	−4.15927	+	2.38311i	−0.303346	+	0.173806i
$189$	7.70864	+	11.3832i	0.560721	+	0.828005i
$190$	2.41968	+	9.09025i	0.175542	+	0.659476i
$191$	10.4891	+	6.05587i	0.758963	+	0.438188i	0.828923	−	0.559362i	$-0.188954\pi$
$191$	10.4891	+	6.05587i	0.758963	+	0.438188i	−0.0699601	+	0.997550i	$0.522287\pi$
$192$	−13.5298	+	2.99078i	−0.976429	+	0.215841i
$193$	0.592437	+	1.02613i	0.0426445	+	0.0738625i	0.886560	−	0.462614i	$-0.153088\pi$
$193$	0.592437	+	1.02613i	0.0426445	+	0.0738625i	−0.843915	+	0.536476i	$0.819755\pi$
$194$	2.39736	+	0.646607i	0.172121	+	0.0464237i
$195$	−2.23598	+	7.32787i	−0.160122	+	0.524760i
$196$	−10.6986	−	9.02991i	−0.764188	−	0.644994i
$197$	19.5111			1.39011			0.695054	−	0.718957i	$-0.255380\pi$
$197$	19.5111			1.39011			0.695054	+	0.718957i	$0.255380\pi$
$198$	3.21213	−	2.78914i	0.228276	−	0.198215i
$199$	−12.7632	+	7.36884i	−0.904760	+	0.522363i	−0.878741	−	0.477298i	$-0.841616\pi$
$199$	−12.7632	+	7.36884i	−0.904760	+	0.522363i	−0.0260186	+	0.999661i	$0.508283\pi$
$200$	4.91327	+	1.34257i	0.347421	+	0.0949341i
$201$	9.41494	+	10.0852i	0.664079	+	0.711358i
$202$	5.32638	+	20.0101i	0.374763	+	1.40791i
$203$	−1.97259	−	0.172170i	−0.138449	−	0.0120839i
$204$	22.4913	−	5.12743i	1.57470	−	0.358992i
$205$	−3.11418	−	1.79797i	−0.217503	−	0.125576i
$206$	−9.87802	+	9.84552i	−0.688234	+	0.685970i
$207$	−23.6815	−	1.62998i	−1.64598	−	0.113291i
$208$	4.88946	+	8.59919i	0.339023	+	0.596247i
$209$	−3.72883			−0.257929
$210$	9.25127	+	6.98433i	0.638398	+	0.481965i
$211$		−	14.9240i		−	1.02741i	−0.857967	−	0.513704i	$-0.828273\pi$
$211$		−	14.9240i		−	1.02741i	0.857967	−	0.513704i	$-0.171727\pi$
$212$	0.0835557	−	25.3552i	0.00573863	−	1.74140i
$213$	9.22768	−	2.13569i	0.632270	−	0.146335i
$214$	−6.95073	−	6.97367i	−0.475142	−	0.476710i
$215$	8.22459	−	14.2454i	0.560913	−	0.971529i
$216$	−14.6113	−	1.58454i	−0.994171	−	0.107814i
$217$	7.95278	−	3.71044i	0.539870	−	0.251881i
$218$	−0.992886	−	3.73007i	−0.0672467	−	0.252633i
$219$	7.75949	+	8.31193i	0.524338	+	0.561668i
$220$	1.80368	−	3.10042i	0.121604	−	0.209030i
$221$	−8.23422	−	14.2621i	−0.553894	−	0.959372i
$222$	7.72860	+	4.84121i	0.518710	+	0.324921i
$223$			7.62187i			0.510398i	0.966889	+	0.255199i	$0.0821410\pi$
$223$			7.62187i			0.510398i	−0.966889	+	0.255199i	$0.917859\pi$
$224$	14.7597	−	2.48045i	0.986171	−	0.165732i
$225$	4.48206	+	3.01607i	0.298804	+	0.201071i
$226$	−0.725248	−	0.195611i	−0.0482428	−	0.0130118i
$227$	−13.6531	+	7.88264i	−0.906190	+	0.523189i	−0.879203	−	0.476446i	$-0.841925\pi$
$227$	−13.6531	+	7.88264i	−0.906190	+	0.523189i	−0.0269870	+	0.999636i	$0.508591\pi$
$228$	8.75981	+	9.44567i	0.580132	+	0.625555i
$229$	8.82193	−	15.2800i	0.582970	−	1.00973i	−0.412155	−	0.911114i	$-0.635224\pi$
$229$	8.82193	−	15.2800i	0.582970	−	1.00973i	0.995125	−	0.0986198i	$-0.0314428\pi$
$230$	−19.3413	+	5.14835i	−1.27533	+	0.339472i
$231$	−3.61871	+	2.83164i	−0.238094	+	0.186308i
$232$	1.50419	−	1.48939i	0.0987547	−	0.0977832i
$233$	−15.7079	−	9.06896i	−1.02906	−	0.594127i	−0.112344	−	0.993669i	$-0.535836\pi$
$233$	−15.7079	−	9.06896i	−1.02906	−	0.594127i	−0.916715	+	0.399542i	$0.869169\pi$
$234$	1.99627	+	10.3005i	0.130500	+	0.673362i
$235$	−3.71266	+	2.14350i	−0.242187	+	0.139827i
$236$	−16.9722	−	0.0559303i	−1.10480	−	0.00364075i
$237$	−8.41536	−	2.56781i	−0.546637	−	0.166797i
$238$	−24.5443	+	4.29135i	−1.59097	+	0.278167i
$239$		−	5.41040i		−	0.349970i	−0.984571	−	0.174985i	$-0.944012\pi$
$239$		−	5.41040i		−	0.349970i	0.984571	−	0.174985i	$-0.0559877\pi$
$240$	−12.0910	+	2.71456i	−0.780473	+	0.175224i
$241$	−18.6025	+	10.7401i	−1.19829	+	0.691834i	−0.960174	−	0.279403i	$-0.909863\pi$
$241$	−18.6025	+	10.7401i	−1.19829	+	0.691834i	−0.238117	+	0.971236i	$0.576530\pi$
$242$	−9.97813	−	10.0111i	−0.641418	−	0.643535i
$243$	−14.1459	−	6.54936i	−0.907459	−	0.420142i
$244$	7.02610	−	4.02571i	0.449800	−	0.257719i
$245$	−9.59453	−	8.04403i	−0.612972	−	0.513914i
$246$	−4.92136	−	0.177285i	−0.313774	−	0.0113033i
$247$	4.59834	−	7.96457i	0.292586	−	0.506773i
$248$	−2.47292	+	9.04990i	−0.157031	+	0.574669i
$249$	−9.54177	+	2.20838i	−0.604685	+	0.139951i
$250$	16.6091	+	4.47975i	1.05045	+	0.283324i
$251$		−	19.8553i		−	1.25325i	−0.779319	−	0.626627i	$-0.784435\pi$
$251$		−	19.8553i		−	1.25325i	0.779319	−	0.626627i	$-0.215565\pi$
$252$	15.6741	+	2.51463i	0.987374	+	0.158407i
$253$		−	7.93382i		−	0.498795i
$254$	−1.66605	+	6.17707i	−0.104538	+	0.387584i
$255$	20.0991	−	4.65181i	1.25865	−	0.291308i
$256$	−8.18195	+	13.7498i	−0.511372	+	0.859360i
$257$	−4.36616	+	7.56240i	−0.272353	+	0.471730i	−0.969464	−	0.245234i	$-0.921135\pi$
$257$	−4.36616	+	7.56240i	−0.272353	+	0.471730i	0.697111	+	0.716964i	$0.254469\pi$
$258$	0.810970	−	22.5121i	0.0504888	−	1.40154i
$259$	−8.07012	−	5.64828i	−0.501453	−	0.350967i
$260$	4.39805	+	7.67595i	0.272755	+	0.476042i
$261$	2.01690	−	0.986439i	0.124843	−	0.0610590i
$262$	15.4900	−	15.4391i	0.956977	−	0.953828i
$263$	−17.1429	+	9.89747i	−1.05708	+	0.610304i	−0.924623	−	0.380885i	$-0.875619\pi$
$263$	−17.1429	+	9.89747i	−1.05708	+	0.610304i	−0.132455	+	0.991189i	$0.542286\pi$
$264$	0.193016	−	4.90838i	0.0118793	−	0.302090i
$265$		−	22.6757i		−	1.39296i
$266$	−8.92871	−	10.6720i	−0.547454	−	0.654344i
$267$	24.5016	+	7.47627i	1.49947	+	0.457540i
$268$	15.9311	+	0.0524996i	0.973150	+	0.00320692i
$269$	0.805574	−	0.465098i	0.0491167	−	0.0283575i	−0.475241	−	0.879856i	$-0.657639\pi$
$269$	0.805574	−	0.465098i	0.0491167	−	0.0283575i	0.524357	+	0.851498i	$0.324306\pi$
$270$	−13.0717	−	1.37401i	−0.795519	−	0.0836197i
$271$	−7.45646	−	4.30499i	−0.452948	−	0.261509i	0.256127	−	0.966643i	$-0.417554\pi$
$271$	−7.45646	−	4.30499i	−0.452948	−	0.261509i	−0.709074	+	0.705134i	$0.750887\pi$
$272$	13.4703	−	22.9801i	0.816754	−	1.39337i
$273$	−1.58566	−	11.2213i	−0.0959685	−	0.679144i
$274$	−4.07950	−	15.3259i	−0.246452	−	0.925870i
$275$	−0.902819	+	1.56373i	−0.0544420	+	0.0942964i
$276$	−20.0975	+	18.6382i	−1.20973	+	1.12189i
$277$	−25.5583	+	14.7561i	−1.53565	+	0.886607i	−0.536562	+	0.843861i	$0.680277\pi$
$277$	−25.5583	+	14.7561i	−1.53565	+	0.886607i	−0.999086	+	0.0427456i	$0.986390\pi$
$278$	6.62250	−	24.5536i	0.397191	−	1.47263i
$279$	−5.55539	+	8.25565i	−0.332593	+	0.494253i
$280$	13.1924	−	2.26180i	0.788398	−	0.135168i
$281$		−	21.3260i		−	1.27220i	−0.771605	−	0.636102i	$-0.780546\pi$
$281$		−	21.3260i		−	1.27220i	0.771605	−	0.636102i	$-0.219454\pi$
$282$	−3.11661	+	4.97542i	−0.185592	+	0.296282i
$283$	10.4247	+	18.0561i	0.619684	+	1.07332i	0.989543	+	0.144236i	$0.0460724\pi$
$283$	10.4247	+	18.0561i	0.619684	+	1.07332i	−0.369860	+	0.929088i	$0.620594\pi$
$284$	5.49962	−	9.45353i	0.326342	−	0.560964i
$285$	7.86184	+	8.42156i	0.465695	+	0.498850i
$286$	−3.38879	+	0.902042i	−0.200383	+	0.0533389i
$287$	5.29898	+	0.462500i	0.312789	+	0.0273005i
$288$	−12.8871	+	11.0419i	−0.759379	+	0.650649i
$289$	−13.6728	+	23.6820i	−0.804284	+	1.39306i
$290$	1.34082	−	1.33641i	0.0787358	−	0.0784768i
$291$	2.96276	−	0.685712i	0.173680	−	0.0401972i
$292$	13.1299	+	0.0432684i	0.768371	+	0.00253209i
$293$			13.1058i			0.765652i	0.923821	+	0.382826i	$0.125049\pi$
$293$			13.1058i			0.765652i	−0.923821	+	0.382826i	$0.874951\pi$
$294$	−16.7693	−	3.57651i	−0.978004	−	0.208586i
$295$	−15.1786			−0.883733
$296$	10.1850	−	2.67518i	0.591993	−	0.155492i
$297$	1.85918	−	4.86714i	0.107880	−	0.282420i
$298$	−0.923465	−	0.926514i	−0.0534949	−	0.0536715i
$299$	16.9462	+	9.78389i	0.980023	+	0.565817i
$300$	6.08207	−	1.38655i	0.351148	−	0.0800528i
$301$	−2.11565	+	24.2395i	−0.121944	+	1.39714i
$302$	26.1496	−	6.96060i	1.50474	−	0.400537i
$303$	17.3061	+	18.5382i	0.994208	+	1.06499i
$304$	14.8749	+	0.0980389i	0.853136	+	0.00562292i
$305$	6.27166	−	3.62094i	0.359114	−	0.207335i
$306$	21.3330	−	18.5237i	1.21952	−	1.05893i
$307$	−18.6425			−1.06398			−0.531992	−	0.846750i	$-0.678556\pi$
$307$	−18.6425			−1.06398			−0.531992	+	0.846750i	$0.678556\pi$
$308$	−0.478754	+	5.28411i	−0.0272795	+	0.301090i
$309$	−4.98511	+	16.3375i	−0.283593	+	0.929406i
$310$	−2.18489	+	8.10072i	−0.124094	+	0.460090i
$311$	9.92896	+	17.1975i	0.563020	+	0.975179i	0.997231	+	0.0743677i	$0.0236939\pi$
$311$	9.92896	+	17.1975i	0.563020	+	0.975179i	−0.434211	+	0.900811i	$0.642973\pi$
$312$	10.2460	+	6.46522i	0.580065	+	0.366021i
$313$	2.33108	+	1.34585i	0.131760	+	0.0760718i	0.564431	−	0.825480i	$-0.309096\pi$
$313$	2.33108	+	1.34585i	0.131760	+	0.0760718i	−0.432671	+	0.901552i	$0.642429\pi$
$314$	−14.9474	+	3.97876i	−0.843532	+	0.224535i
$315$	14.0249	+	2.20267i	0.790215	+	0.124106i
$316$	−8.81510	+	5.05074i	−0.495888	+	0.284126i
$317$	5.35288	−	9.27147i	0.300648	−	0.520737i	−0.675635	−	0.737236i	$-0.736130\pi$
$317$	5.35288	−	9.27147i	0.300648	−	0.520737i	0.976283	+	0.216499i	$0.0694638\pi$
$318$	−14.5487	−	27.4350i	−0.815850	−	1.53848i
$319$	0.375209	+	0.649881i	0.0210077	+	0.0363864i
$320$	−7.27669	+	12.3207i	−0.406780	+	0.688747i
$321$	−11.5339	−	3.51938i	−0.643760	−	0.196433i
$322$	22.7069	−	18.9976i	1.26540	−	1.05869i
$323$	−24.7645			−1.37794
$324$	−16.6968	+	6.72438i	−0.927599	+	0.373577i
$325$	−2.22669	−	3.85674i	−0.123514	−	0.213933i
$326$	−10.6545	+	10.6194i	−0.590097	+	0.588155i
$327$	−3.22601	−	3.45569i	−0.178399	−	0.191100i
$328$	−4.04071	+	4.00095i	−0.223111	+	0.220916i
$329$	3.63618	−	5.19528i	0.200469	−	0.286425i
$330$	0.158151	−	4.39019i	0.00870592	−	0.241672i
$331$	18.8525	+	10.8845i	1.03623	+	0.598266i	0.918762	−	0.394811i	$-0.129190\pi$
$331$	18.8525	+	10.8845i	1.03623	+	0.598266i	0.117465	+	0.993077i	$0.462523\pi$
$332$	−5.68681	+	9.77531i	−0.312104	+	0.536490i
$333$	11.1429	+	0.766958i	0.610628	+	0.0420290i
$334$	−2.92057	+	10.8283i	−0.159807	+	0.592500i
$335$	14.2476			0.778428
$336$	14.5101	−	11.2007i	0.791592	−	0.611050i
$337$	−11.3104			−0.616116			−0.308058	−	0.951368i	$-0.599679\pi$
$337$	−11.3104			−0.616116			−0.308058	+	0.951368i	$0.599679\pi$
$338$	−2.53528	+	9.39982i	−0.137901	+	0.511283i
$339$	−0.896293	+	0.207441i	−0.0486799	+	0.0112667i
$340$	11.9789	−	20.5910i	0.649646	−	1.11671i
$341$	−2.88028	−	1.66293i	−0.155976	−	0.0900527i
$342$	14.9152	+	5.14497i	0.806519	+	0.278208i
$343$	17.8922	+	4.78234i	0.966086	+	0.258222i
$344$	−18.3019	−	18.4837i	−0.986771	−	0.996575i
$345$	−17.9185	+	16.7276i	−0.964702	+	0.900585i
$346$	−4.27806	+	4.26399i	−0.229990	+	0.229233i
$347$	9.94032	+	17.2171i	0.533624	+	0.924265i	0.999229	+	0.0392715i	$0.0125037\pi$
$347$	9.94032	+	17.2171i	0.533624	+	0.924265i	−0.465604	+	0.884993i	$0.654163\pi$
$348$	0.764800	−	2.47717i	0.0409976	−	0.132790i
$349$	9.45348			0.506033			0.253017	−	0.967462i	$-0.418577\pi$
$349$	9.45348			0.506033			0.253017	+	0.967462i	$0.418577\pi$
$350$	−6.63725	+	1.16046i	−0.354776	+	0.0620293i
$351$	8.10323	+	9.97319i	0.432518	+	0.532330i
$352$	−3.97759	−	4.04368i	−0.212006	−	0.215529i
$353$	−8.48135	−	14.6901i	−0.451417	−	0.781877i	0.547057	−	0.837095i	$-0.315748\pi$
$353$	−8.48135	−	14.6901i	−0.451417	−	0.781877i	−0.998474	+	0.0552182i	$0.982415\pi$
$354$	−18.3643	+	9.73856i	−0.976054	+	0.517599i
$355$	4.89051	−	8.47062i	0.259561	−	0.449574i
$356$	25.6655	−	14.7054i	1.36027	−	0.779385i
$357$	−24.0332	+	18.8059i	−1.27197	+	0.995316i
$358$	−10.3269	+	2.74886i	−0.545794	+	0.145282i
$359$	18.2162	+	10.5171i	0.961413	+	0.555072i	0.896608	−	0.442826i	$-0.146024\pi$
$359$	18.2162	+	10.5171i	0.961413	+	0.555072i	0.0648056	+	0.997898i	$0.479357\pi$
$360$	−11.4925	+	9.91287i	−0.605710	+	0.522454i
$361$	2.58521	+	4.47771i	0.136064	+	0.235669i
$362$	1.84226	−	6.83036i	0.0968269	−	0.358996i
$363$	−16.5575	−	5.05225i	−0.869044	−	0.265174i
$364$	−10.6962	−	7.53889i	−0.560631	−	0.395145i
$365$	11.7424			0.614625
$366$	5.26478	−	8.40480i	0.275195	−	0.439326i
$367$	1.24875	−	0.720966i	0.0651842	−	0.0376341i	−0.467054	−	0.884229i	$-0.654685\pi$
$367$	1.24875	−	0.720966i	0.0651842	−	0.0376341i	0.532238	+	0.846595i	$0.321351\pi$
$368$	−0.208597	+	31.6494i	−0.0108739	+	1.64984i
$369$	−5.41802	+	2.64988i	−0.282051	+	0.137947i
$370$	9.10071	−	2.42246i	0.473124	−	0.125938i
$371$	14.1817	+	30.3964i	0.736278	+	1.57810i
$372$	2.55394	+	11.2027i	0.132415	+	0.580835i
$373$	18.8362	+	10.8751i	0.975302	+	0.563091i	0.900848	−	0.434134i	$-0.142945\pi$
$373$	18.8362	+	10.8751i	0.975302	+	0.563091i	0.0744535	+	0.997224i	$0.476279\pi$
$374$	6.66618	+	6.68818i	0.344700	+	0.345838i
$375$	20.5263	−	4.75068i	1.05997	−	0.245324i
$376$	1.72219	+	6.55679i	0.0888154	+	0.338141i
$377$	−1.85081			−0.0953217
$378$	18.3817	−	6.33339i	0.945454	−	0.325754i
$379$			1.82298i			0.0936402i	0.998903	+	0.0468201i	$0.0149087\pi$
$379$			1.82298i			0.0936402i	−0.998903	+	0.0468201i	$0.985091\pi$
$380$	13.3031	+	0.0438392i	0.682436	+	0.00224890i
$381$	1.76681	+	7.63389i	0.0905167	+	0.391096i
$382$	12.1317	−	12.0918i	0.620711	−	0.618669i
$383$	−4.81069	+	8.33236i	−0.245815	+	0.425763i	−0.962360	−	0.271777i	$-0.912389\pi$
$383$	−4.81069	+	8.33236i	−0.245815	+	0.425763i	0.716546	+	0.697540i	$0.245722\pi$
$384$	−0.899025	+	19.5753i	−0.0458782	+	0.998947i
$385$	−0.412582	+	4.72705i	−0.0210271	+	0.240913i
$386$	1.61928	−	0.431026i	0.0824192	−	0.0219387i
$387$	−12.1215	−	24.7841i	−0.616172	−	1.25984i
$388$	1.76578	−	3.03528i	0.0896439	−	0.154093i
$389$	−14.0629	−	24.3576i	−0.713017	−	1.23498i	−0.963719	−	0.266917i	$-0.913995\pi$
$389$	−14.0629	−	24.3576i	−0.713017	−	1.23498i	0.250703	−	0.968064i	$-0.419338\pi$
$390$	9.18217	+	5.75173i	0.464957	+	0.291250i
$391$		−	52.6914i		−	2.66472i
$392$	−16.2697	+	11.2826i	−0.821743	+	0.569859i
$393$	7.81730	−	25.6193i	0.394331	−	1.29232i
$394$	7.18546	−	26.6409i	0.361998	−	1.34215i
$395$	−7.86857	+	4.54292i	−0.395911	+	0.228579i
$396$	−2.62539	−	5.41308i	−0.131931	−	0.272018i
$397$	−9.42646	+	16.3271i	−0.473101	+	0.819434i	−0.999526	−	0.0307871i	$-0.990199\pi$
$397$	−9.42646	+	16.3271i	−0.473101	+	0.819434i	0.526425	+	0.850221i	$0.323532\pi$
$398$	5.36119	+	20.1409i	0.268732	+	1.00957i
$399$	−15.8056	−	6.37206i	−0.791271	−	0.319002i
$400$	3.64261	−	6.21424i	0.182131	−	0.310712i
$401$	−5.22718	−	3.01791i	−0.261033	−	0.150707i	0.363773	−	0.931488i	$-0.381488\pi$
$401$	−5.22718	−	3.01791i	−0.261033	−	0.150707i	−0.624806	+	0.780780i	$0.714822\pi$
$402$	17.2379	−	9.14120i	0.859748	−	0.455922i
$403$	7.10385	−	4.10141i	0.353868	−	0.204306i
$404$	29.2838	+	0.0965021i	1.45693	+	0.00480116i
$405$	−14.9123	+	6.06290i	−0.740999	+	0.301268i
$406$	−0.961541	+	2.63001i	−0.0477205	+	0.130525i
$407$			3.73312i			0.185044i
$408$	1.28189	−	32.5984i	0.0634630	−	1.61386i
$409$	22.6629	−	13.0844i	1.12061	−	0.646984i	0.179052	−	0.983840i	$-0.442697\pi$
$409$	22.6629	−	13.0844i	1.12061	−	0.646984i	0.941556	+	0.336856i	$0.109364\pi$
$410$	−3.60186	+	3.59001i	−0.177883	+	0.177298i
$411$	−13.2548	−	14.1985i	−0.653812	−	0.700360i
$412$	9.80544	+	17.1135i	0.483080	+	0.843123i
$413$	20.3467	−	9.49292i	1.00120	−	0.467116i
$414$	−10.9469	+	31.7349i	−0.538012	+	1.55969i
$415$	−5.05698	+	8.75894i	−0.248237	+	0.429959i
$416$	13.5422	−	3.50930i	0.663960	−	0.172058i
$417$	−7.02301	−	30.3444i	−0.343918	−	1.48597i
$418$	−1.37324	+	5.09142i	−0.0671672	+	0.249029i
$419$			2.51866i			0.123045i	0.998106	+	0.0615223i	$0.0195955\pi$
$419$			2.51866i			0.123045i	−0.998106	+	0.0615223i	$0.980404\pi$
$420$	12.9436	−	10.0597i	0.631581	−	0.490864i
$421$		−	33.4873i		−	1.63207i	−0.578003	−	0.816034i	$-0.696168\pi$
$421$		−	33.4873i		−	1.63207i	0.578003	−	0.816034i	$-0.303832\pi$
$422$	−20.3775	−	5.49614i	−0.991961	−	0.267548i
$423$	−0.493742	+	7.17345i	−0.0240066	+	0.348785i
$424$	−34.5898	−	9.45180i	−1.67983	−	0.459020i
$425$	−5.99595	+	10.3853i	−0.290846	+	0.503761i
$426$	0.482220	−	13.3862i	0.0233636	−	0.648563i
$427$	−6.14247	+	8.77620i	−0.297255	+	0.424710i
$428$	−12.0818	+	6.92243i	−0.583995	+	0.334608i
$429$	−3.13951	+	2.93085i	−0.151577	+	0.141503i
$430$	−16.4221	−	16.4763i	−0.791942	−	0.794556i
$431$	−12.0003	+	6.92836i	−0.578033	+	0.333727i	−0.760351	−	0.649512i	$-0.774973\pi$
$431$	−12.0003	+	6.92836i	−0.578033	+	0.333727i	0.182319	+	0.983240i	$0.441640\pi$
$432$	−7.54454	+	19.3670i	−0.362987	+	0.931794i
$433$			9.79368i			0.470654i	0.971916	+	0.235327i	$0.0756161\pi$
$433$			9.79368i			0.470654i	−0.971916	+	0.235327i	$0.924384\pi$
$434$	−2.13749	−	12.2254i	−0.102603	−	0.586836i
$435$	0.676669	−	2.21762i	0.0324438	−	0.106327i
$436$	−5.45878	−	0.0179889i	−0.261428	−	0.000861511i
$437$	25.4829	−	14.7126i	1.21901	−	0.703798i
$438$	14.2069	−	7.53388i	0.678832	−	0.359983i
$439$	6.99463	+	4.03835i	0.333835	+	0.192740i	0.657543	−	0.753417i	$-0.271596\pi$
$439$	6.99463	+	4.03835i	0.333835	+	0.192740i	−0.323707	+	0.946157i	$0.604929\pi$
$440$	−3.56913	−	3.60459i	−0.170151	−	0.171842i
$441$	−20.1778	+	5.81875i	−0.960846	+	0.277083i
$442$	−22.5062	+	5.99079i	−1.07051	+	0.284953i
$443$	−8.84884	+	15.3266i	−0.420421	+	0.728191i	−0.995981	−	0.0895692i	$-0.971451\pi$
$443$	−8.84884	+	15.3266i	−0.420421	+	0.728191i	0.575559	+	0.817760i	$0.304784\pi$
$444$	9.45654	−	8.76989i	0.448788	−	0.416201i
$445$	22.9096	−	13.2269i	1.08602	−	0.627014i
$446$	10.4071	+	2.80695i	0.492788	+	0.132913i
$447$	−1.53238	−	0.467581i	−0.0724791	−	0.0221158i
$448$	2.04876	−	21.0666i	0.0967948	−	0.995304i
$449$			19.4650i			0.918609i	0.888279	+	0.459305i	$0.151901\pi$
$449$			19.4650i			0.918609i	−0.888279	+	0.459305i	$0.848099\pi$
$450$	5.76884	−	5.00915i	0.271946	−	0.236134i
$451$	−1.00793	−	1.74578i	−0.0474614	−	0.0822056i
$452$	−0.534182	+	0.918230i	−0.0251258	+	0.0431899i
$453$	24.2260	−	22.6159i	1.13824	−	1.06259i
$454$	5.73500	+	21.5453i	0.269157	+	1.01117i
$455$	−9.58793	−	6.71059i	−0.449489	−	0.314597i
$456$	16.1233	−	8.48221i	0.755045	−	0.397216i
$457$	7.75626	−	13.4342i	0.362823	−	0.628427i	−0.625601	−	0.780143i	$-0.715146\pi$
$457$	7.75626	−	13.4342i	0.362823	−	0.628427i	0.988424	+	0.151715i	$0.0484797\pi$
$458$	−17.6148	−	17.6729i	−0.823084	−	0.825801i
$459$	12.3475	−	32.3245i	0.576331	−	1.50878i
$460$	−0.0932765	+	28.3050i	−0.00434904	+	1.31973i
$461$		−	0.857290i		−	0.0399280i	−0.999801	−	0.0199640i	$-0.993645\pi$
$461$		−	0.857290i		−	0.0399280i	0.999801	−	0.0199640i	$-0.00635516\pi$
$462$	2.53369	+	5.98389i	0.117878	+	0.278396i
$463$	37.5731			1.74617			0.873086	−	0.487566i	$-0.162115\pi$
$463$	37.5731			1.74617			0.873086	+	0.487566i	$0.162115\pi$
$464$	−1.47969	−	2.60235i	−0.0686927	−	0.120811i
$465$	2.31703	+	10.0112i	0.107450	+	0.464259i
$466$	−18.1678	+	18.1080i	−0.841606	+	0.838837i
$467$	−8.69155	−	5.01807i	−0.402197	−	0.232208i	0.285235	−	0.958458i	$-0.407928\pi$
$467$	−8.69155	−	5.01807i	−0.402197	−	0.232208i	−0.687431	+	0.726249i	$0.741262\pi$
$468$	14.7996	+	1.06766i	0.684113	+	0.0493526i
$469$	−19.0986	+	8.91063i	−0.881893	+	0.411455i
$470$	1.55950	+	5.85874i	0.0719345	+	0.270244i
$471$	−13.8479	+	12.9275i	−0.638076	+	0.595668i
$472$	−6.32682	+	23.1536i	−0.291216	+	1.06573i
$473$	7.98586	−	4.61064i	0.367190	−	0.211997i
$474$	−6.60531	+	10.5448i	−0.303392	+	0.484341i
$475$	−6.69680			−0.307270
$476$	−3.17958	+	35.0937i	−0.145736	+	1.60852i
$477$	−31.5540	−	21.2333i	−1.44476	−	0.972208i
$478$	−7.38747	−	1.99252i	−0.337895	−	0.0911357i
$479$	−11.0594	−	19.1555i	−0.505318	−	0.875237i	−0.999981	−	0.00615194i	$-0.998042\pi$
$479$	−11.0594	−	19.1555i	−0.505318	−	0.875237i	0.494663	−	0.869085i	$-0.335292\pi$
$480$	−0.746318	+	17.5091i	−0.0340646	+	0.799176i
$481$	−7.97373	−	4.60364i	−0.363571	−	0.209908i
$482$	7.81397	+	29.3555i	0.355917	+	1.33711i
$483$	13.5578	−	33.6296i	0.616902	−	1.53020i
$484$	−17.3440	+	9.93751i	−0.788364	+	0.451705i
$485$	1.57021	−	2.71969i	0.0712997	−	0.123495i
$486$	−14.1522	+	16.9031i	−0.641957	+	0.766740i
$487$	11.2659	+	19.5131i	0.510506	+	0.884223i	0.999926	+	0.0121746i	$0.00387541\pi$
$487$	11.2659	+	19.5131i	0.510506	+	0.884223i	−0.489419	+	0.872049i	$0.662791\pi$
$488$	−2.90924	−	11.0761i	−0.131695	−	0.501394i
$489$	−5.37696	+	17.6217i	−0.243155	+	0.796879i
$490$	−14.5169	+	10.1381i	−0.655807	+	0.457995i
$491$	−25.1085			−1.13313			−0.566565	−	0.824017i	$-0.691728\pi$
$491$	−25.1085			−1.13313			−0.566565	+	0.824017i	$0.691728\pi$
$492$	−2.05449	+	6.65443i	−0.0926234	+	0.300005i
$493$	2.49190	+	4.31610i	0.112230	+	0.194387i
$494$	−9.18152	−	9.21183i	−0.413096	−	0.414460i
$495$	−2.36387	−	4.83325i	−0.106248	−	0.217238i
$496$	11.4462	+	6.70944i	0.513950	+	0.301263i
$497$	−1.25801	+	14.4133i	−0.0564295	+	0.646526i
$498$	−0.498633	+	13.8418i	−0.0223443	+	0.620267i
$499$	9.19695	+	5.30986i	0.411712	+	0.237702i	0.691525	−	0.722353i	$-0.256939\pi$
$499$	9.19695	+	5.30986i	0.411712	+	0.237702i	−0.279813	+	0.960054i	$0.590273\pi$
$500$	12.2335	−	21.0287i	0.547098	−	0.940431i
$501$	3.09721	+	13.3821i	0.138373	+	0.597869i
$502$	−27.1108	−	7.31222i	−1.21001	−	0.326360i
$503$	−13.3046			−0.593223			−0.296612	−	0.954998i	$-0.595857\pi$
$503$	−13.3046			−0.593223			−0.296612	+	0.954998i	$0.595857\pi$
$504$	9.20590	−	20.4756i	0.410064	−	0.912057i
$505$	26.1892			1.16540
$506$	−10.8330	−	2.92183i	−0.481586	−	0.129891i
$507$	2.68861	+	11.6167i	0.119405	+	0.515916i
$508$	7.82073	+	4.54973i	0.346989	+	0.201862i
$509$	−20.2595	−	11.6968i	−0.897985	−	0.518452i	−0.0214392	−	0.999770i	$-0.506825\pi$
$509$	−20.2595	−	11.6968i	−0.897985	−	0.518452i	−0.876546	+	0.481318i	$0.840158\pi$
$510$	1.05034	−	29.1569i	0.0465097	−	1.29109i
$511$	−15.7405	+	7.34385i	−0.696318	+	0.324873i
$512$	15.7610	+	16.2355i	0.696544	+	0.717515i
$513$	19.0806	−	3.05413i	0.842431	−	0.134843i
$514$	8.71791	+	8.74669i	0.384531	+	0.385800i
$515$	8.81956	+	15.2759i	0.388636	+	0.673138i
$516$	−30.4399	−	9.39799i	−1.34004	−	0.413723i
$517$	−2.40326			−0.105695
$518$	−10.6843	+	8.93899i	−0.469442	+	0.392757i
$519$	−2.15900	+	7.07558i	−0.0947695	+	0.310584i
$520$	12.1006	−	3.17832i	0.530646	−	0.139379i
$521$	0.735700	+	1.27427i	0.0322316	+	0.0558267i	0.881691	−	0.471827i	$-0.156405\pi$
$521$	0.735700	+	1.27427i	0.0322316	+	0.0558267i	−0.849460	+	0.527654i	$0.823072\pi$
$522$	−0.604127	−	3.11720i	−0.0264419	−	0.136436i
$523$	5.30372	−	9.18631i	0.231915	−	0.401689i	−0.726456	−	0.687213i	$-0.758834\pi$
$523$	5.30372	−	9.18631i	0.231915	−	0.401689i	0.958372	+	0.285523i	$0.0921674\pi$
$524$	−15.3762	−	26.8362i	−0.671713	−	1.17235i
$525$	−6.49904	+	5.08548i	−0.283641	+	0.221949i
$526$	7.20089	+	27.0523i	0.313974	+	1.17954i
$527$	−19.1290	−	11.0441i	−0.833272	−	0.481090i
$528$	−6.63092	−	2.07118i	−0.288574	−	0.0901367i
$529$	19.8039	+	34.3014i	0.861040	+	1.49137i
$530$	−30.9619	−	8.35092i	−1.34490	−	0.362741i
$531$	−14.2131	+	21.1216i	−0.616797	+	0.916597i
$532$	−17.8600	+	8.26119i	−0.774331	+	0.358168i
$533$	4.97185			0.215355
$534$	19.2316	−	30.7017i	0.832233	−	1.32859i
$535$	−10.7845	+	6.22642i	−0.466254	+	0.269192i
$536$	5.93874	−	21.7334i	0.256514	−	0.938739i
$537$	−9.56725	+	8.93138i	−0.412857	+	0.385417i
$538$	−0.338381	−	1.27123i	−0.0145887	−	0.0548067i
$539$	−2.40331	−	6.59457i	−0.103518	−	0.284048i
$540$	−6.69010	+	17.3424i	−0.287896	+	0.746296i
$541$	−14.0009	−	8.08343i	−0.601946	−	0.347534i	0.167861	−	0.985811i	$-0.446314\pi$
$541$	−14.0009	−	8.08343i	−0.601946	−	0.347534i	−0.769807	+	0.638277i	$0.779647\pi$
$542$	−8.62415	+	8.59578i	−0.370439	+	0.369220i
$543$	−1.95367	−	8.44125i	−0.0838402	−	0.362249i
$544$	−26.4167	−	26.8556i	−1.13261	−	1.15142i
$545$	−4.88190			−0.209118
$546$	−15.9058	−	1.96744i	−0.680704	−	0.0841987i
$547$		−	12.4170i		−	0.530914i	−0.964123	−	0.265457i	$-0.914477\pi$
$547$		−	12.4170i		−	0.530914i	0.964123	−	0.265457i	$-0.0855228\pi$
$548$	−22.4287	−	0.0739115i	−0.958105	−	0.00315734i
$549$	0.834061	−	12.1178i	0.0355969	−	0.517177i
$550$	1.80266	+	1.80861i	0.0768657	+	0.0771194i
$551$	−1.39159	+	2.41030i	−0.0592836	+	0.102682i
$552$	18.0476	+	34.3056i	0.768156	+	1.46014i
$553$	7.70648	−	11.0108i	0.327713	−	0.468228i
$554$	10.7358	+	40.3321i	0.456119	+	1.71355i
$555$	8.43126	−	7.87089i	0.357887	−	0.334101i
$556$	−31.0871	−	18.0850i	−1.31839	−	0.766974i
$557$	10.7167	+	18.5619i	0.454081	+	0.786492i	0.998635	−	0.0522341i	$-0.0166342\pi$
$557$	10.7167	+	18.5619i	0.454081	+	0.786492i	−0.544554	+	0.838726i	$0.683301\pi$
$558$	9.22651	+	10.6258i	0.390589	+	0.449826i
$559$			22.7431i			0.961931i
$560$	1.77015	−	18.8462i	0.0748023	−	0.796396i
$561$	11.0617	+	3.37530i	0.467026	+	0.142505i
$562$	−29.1190	−	7.85385i	−1.22831	−	0.331295i
$563$	17.9430	−	10.3594i	0.756205	−	0.436595i	−0.0717262	−	0.997424i	$-0.522851\pi$
$563$	17.9430	−	10.3594i	0.756205	−	0.436595i	0.827932	+	0.560829i	$0.189517\pi$
$564$	5.64577	+	6.08781i	0.237730	+	0.256343i
$565$	−0.475020	+	0.822758i	−0.0199842	+	0.0346137i
$566$	28.4933	−	7.58447i	1.19766	−	0.318799i
$567$	16.1979	−	17.4536i	0.680248	−	0.732982i
$568$	−10.8827	−	10.9908i	−0.456627	−	0.461164i
$569$	23.8691	+	13.7808i	1.00064	+	0.577722i	0.908439	−	0.418018i	$-0.137275\pi$
$569$	23.8691	+	13.7808i	1.00064	+	0.577722i	0.0922056	+	0.995740i	$0.470608\pi$
$570$	14.3943	−	7.63326i	0.602911	−	0.319722i
$571$	−0.339940	+	0.196264i	−0.0142260	+	0.00821340i	−0.507096	−	0.861889i	$-0.669281\pi$
$571$	−0.339940	+	0.196264i	−0.0142260	+	0.00821340i	0.492870	+	0.870103i	$0.335948\pi$
$572$	−0.0163430	+	4.95933i	−0.000683334	+	0.207360i
$573$	6.12246	−	20.0649i	0.255770	−	0.838222i
$574$	2.58299	−	7.06500i	0.107812	−	0.294888i
$575$		−	14.2488i		−	0.594214i
$576$	10.3308	+	21.6627i	0.430450	+	0.902614i
$577$	−12.7927	+	7.38589i	−0.532569	+	0.307479i	−0.742062	−	0.670331i	$-0.766152\pi$
$577$	−12.7927	+	7.38589i	−0.532569	+	0.307479i	0.209493	+	0.977810i	$0.432819\pi$
$578$	27.3006	+	27.3907i	1.13555	+	1.13930i
$579$	1.50016	−	1.40046i	0.0623447	−	0.0582011i
$580$	−1.33097	−	2.32296i	−0.0552656	−	0.0964555i
$581$	1.30083	−	14.9039i	0.0539675	−	0.618319i
$582$	0.154828	−	4.29795i	0.00641782	−	0.178156i
$583$	6.35591	−	11.0088i	0.263235	−	0.455936i
$584$	4.89452	−	17.9119i	0.202536	−	0.741202i
$585$	13.2386	+	0.911205i	0.547350	+	0.0376737i
$586$	17.8950	+	4.82656i	0.739235	+	0.199384i
$587$			3.51421i			0.145047i	0.997367	+	0.0725236i	$0.0231052\pi$
$587$			3.51421i			0.145047i	−0.997367	+	0.0725236i	$0.976895\pi$
$588$	−11.0592	+	21.5800i	−0.456072	+	0.889943i
$589$		−	12.3350i		−	0.508256i
$590$	−5.58992	+	20.7252i	−0.230133	+	0.853243i
$591$	−7.62003	−	32.9239i	−0.313446	−	1.35431i
$592$	0.0981518	−	14.8921i	0.00403401	−	0.612060i
$593$	17.8824	−	30.9732i	0.734342	−	1.27192i	−0.220670	−	0.975349i	$-0.570824\pi$
$593$	17.8824	−	30.9732i	0.734342	−	1.27192i	0.955012	−	0.296568i	$-0.0958423\pi$
$594$	−5.96101	−	4.33101i	−0.244583	−	0.177703i
$595$	−2.74011	+	31.3941i	−0.112334	+	1.28703i
$596$	−1.60517	+	0.919706i	−0.0657504	+	0.0376726i
$597$	17.4192	+	18.6593i	0.712919	+	0.763676i
$598$	19.6000	−	19.5355i	0.801503	−	0.798866i
$599$	35.4819	−	20.4855i	1.44975	−	0.837014i	0.451284	−	0.892380i	$-0.350966\pi$
$599$	35.4819	−	20.4855i	1.44975	−	0.837014i	0.998466	+	0.0553669i	$0.0176328\pi$
$600$	0.346647	−	8.81521i	0.0141518	−	0.359879i
$601$		−	36.1540i		−	1.47475i	−0.675482	−	0.737377i	$-0.736064\pi$
$601$		−	36.1540i		−	1.47475i	0.675482	−	0.737377i	$-0.263936\pi$
$602$	32.3180	+	11.8156i	1.31718	+	0.481567i
$603$	13.3413	−	19.8260i	0.543300	−	0.807376i
$604$	0.126110	−	38.2686i	0.00513136	−	1.55713i
$605$	−15.4817	+	8.93835i	−0.629419	+	0.363395i
$606$	31.6858	−	16.8029i	1.28715	−	0.682571i
$607$	9.04038	+	5.21946i	0.366938	+	0.211851i	0.672120	−	0.740443i	$-0.265384\pi$
$607$	9.04038	+	5.21946i	0.366938	+	0.211851i	−0.305182	+	0.952294i	$0.598717\pi$
$608$	5.61194	−	20.2744i	0.227594	−	0.822237i
$609$	0.479865	+	3.39588i	0.0194451	+	0.137608i
$610$	−2.63441	−	9.89696i	−0.106664	−	0.400716i
$611$	2.96367	−	5.13323i	0.119897	−	0.207668i
$612$	−17.4362	−	35.9503i	−0.704816	−	1.45320i
$613$	−5.37925	+	3.10571i	−0.217266	+	0.125439i	−0.604684	−	0.796466i	$-0.706700\pi$
$613$	−5.37925	+	3.10571i	−0.217266	+	0.125439i	0.387418	+	0.921904i	$0.373367\pi$
$614$	−6.86558	+	25.4548i	−0.277072	+	1.02727i
$615$	−1.81774	+	5.95720i	−0.0732984	+	0.240217i
$616$	7.03872	+	2.59971i	0.283598	+	0.104745i
$617$			22.4963i			0.905669i	0.891595	+	0.452834i	$0.149587\pi$
$617$			22.4963i			0.905669i	−0.891595	+	0.452834i	$0.850413\pi$
$618$	20.4716	+	12.8235i	0.823490	+	0.515836i
$619$	−14.1624	−	24.5300i	−0.569235	−	0.985943i	−0.996642	−	0.0818842i	$-0.973906\pi$
$619$	−14.1624	−	24.5300i	−0.569235	−	0.985943i	0.427407	−	0.904059i	$-0.359427\pi$
$620$	10.2563	+	5.96660i	0.411901	+	0.239624i
$621$	6.49827	+	40.5978i	0.260767	+	1.62914i
$622$	27.1384	−	7.22380i	1.08815	−	0.289648i
$623$	−22.4377	+	32.0584i	−0.898947	+	1.28439i
$624$	12.6011	−	11.6091i	0.504447	−	0.464736i
$625$	6.37661	−	11.0446i	0.255064	−	0.441785i
$626$	2.69613	−	2.68726i	0.107759	−	0.107404i
$627$	1.45629	+	6.29220i	0.0581585	+	0.251286i
$628$	−0.0720863	+	21.8748i	−0.00287656	+	0.872899i
$629$			24.7930i			0.988563i
$630$	8.17261	−	18.3387i	0.325604	−	0.730633i
$631$	8.51542			0.338993			0.169497	−	0.985531i	$-0.445786\pi$
$631$	8.51542			0.338993			0.169497	+	0.985531i	$0.445786\pi$
$632$	3.65000	+	13.8964i	0.145189	+	0.552768i
$633$	−25.1834	+	5.82853i	−1.00095	+	0.231663i
$634$	−10.6881	−	10.7234i	−0.424479	−	0.425880i
$635$	7.00758	+	4.04583i	0.278087	+	0.160554i
$636$	−42.8182	+	9.76145i	−1.69785	+	0.387066i
$637$	17.0494	+	2.99902i	0.675520	+	0.118825i
$638$	1.02554	−	0.272983i	0.0406016	−	0.0108075i
$639$	−7.20771	−	14.7371i	−0.285133	−	0.582992i
$640$	14.1431	+	14.4732i	0.559055	+	0.572102i
$641$	0.0793494	−	0.0458124i	0.00313411	−	0.00180948i	−0.498432	−	0.866929i	$-0.666091\pi$
$641$	0.0793494	−	0.0458124i	0.00313411	−	0.00180948i	0.501566	+	0.865119i	$0.332757\pi$
$642$	−9.05309	+	14.4525i	−0.357297	+	0.570396i
$643$	5.89351			0.232417			0.116209	−	0.993225i	$-0.462926\pi$
$643$	5.89351			0.232417			0.116209	+	0.993225i	$0.462926\pi$
$644$	−17.5773	−	38.0008i	−0.692644	−	1.49744i
$645$	−27.2505	−	8.31503i	−1.07299	−	0.327404i
$646$	−9.12017	+	33.8140i	−0.358828	+	1.33039i
$647$	−4.05903	−	7.03045i	−0.159577	−	0.276396i	0.775139	−	0.631791i	$-0.217680\pi$
$647$	−4.05903	−	7.03045i	−0.159577	−	0.276396i	−0.934716	+	0.355395i	$0.884346\pi$
$648$	3.03258	+	25.2746i	0.119131	+	0.992879i
$649$	−7.36901	−	4.25450i	−0.289259	−	0.167004i
$650$	−6.08611	+	1.62002i	−0.238717	+	0.0635426i
$651$	−9.36710	−	11.9708i	−0.367126	−	0.469172i
$652$	10.5762	+	18.4587i	0.414196	+	0.722899i
$653$	−16.7312	+	28.9792i	−0.654741	+	1.13404i	0.327218	+	0.944949i	$0.393889\pi$
$653$	−16.7312	+	28.9792i	−0.654741	+	1.13404i	−0.981959	+	0.189095i	$0.939444\pi$
$654$	−5.90653	+	3.13222i	−0.230964	+	0.122479i
$655$	−13.8302	−	23.9547i	−0.540392	−	0.935986i
$656$	3.97489	+	6.99072i	0.155193	+	0.272942i
$657$	10.9955	−	16.3399i	0.428974	−	0.637481i
$658$	−5.75463	−	6.87821i	−0.224339	−	0.268141i
$659$	15.5448			0.605540			0.302770	−	0.953064i	$-0.402089\pi$
$659$	15.5448			0.605540			0.302770	+	0.953064i	$0.402089\pi$
$660$	−5.93621	−	1.83274i	−0.231067	−	0.0713394i
$661$	15.4190	+	26.7065i	0.599731	+	1.03876i	0.992861	+	0.119281i	$0.0380590\pi$
$661$	15.4190	+	26.7065i	0.599731	+	1.03876i	−0.393130	+	0.919483i	$0.628608\pi$
$662$	21.8048	−	21.7331i	0.847469	−	0.844681i
$663$	−20.8506	+	19.4648i	−0.809772	+	0.755952i
$664$	11.2531	+	11.3649i	0.436705	+	0.441044i
$665$	−15.9481	+	7.44072i	−0.618441	+	0.288539i
$666$	5.15089	−	14.9323i	0.199593	−	0.578616i
$667$	−5.12838	−	2.96087i	−0.198572	−	0.114646i
$668$	13.7096	+	7.97562i	0.530442	+	0.308586i
$669$	12.8615	−	2.97671i	0.497254	−	0.115086i
$670$	5.24703	−	19.4539i	0.202711	−	0.751571i
$671$	4.05974			0.156725
$672$	−9.94999	−	23.9374i	−0.383829	−	0.923404i
$673$	3.84855			0.148351			0.0741753	−	0.997245i	$-0.476368\pi$
$673$	3.84855			0.148351			0.0741753	+	0.997245i	$0.476368\pi$
$674$	−4.16534	+	15.4434i	−0.160443	+	0.594858i
$675$	3.33899	−	8.74115i	0.128518	−	0.336447i
$676$	11.9010	+	6.92345i	0.457731	+	0.266286i
$677$	−32.5497	−	18.7926i	−1.25099	−	0.722257i	−0.279680	−	0.960093i	$-0.590228\pi$
$677$	−32.5497	−	18.7926i	−1.25099	−	0.722257i	−0.971305	+	0.237836i	$0.923562\pi$
$678$	−0.0468384	+	1.30021i	−0.00179882	+	0.0499343i
$679$	−0.403913	+	4.62773i	−0.0155008	+	0.177596i
$680$	−23.7039	−	23.9394i	−0.909003	−	0.918034i
$681$	18.6337	+	19.9604i	0.714046	+	0.764883i
$682$	−3.33134	+	3.32038i	−0.127563	+	0.127144i
$683$	−1.02051	−	1.76757i	−0.0390487	−	0.0676343i	0.845841	−	0.533436i	$-0.179099\pi$
$683$	−1.02051	−	1.76757i	−0.0390487	−	0.0676343i	−0.884889	+	0.465802i	$0.845766\pi$
$684$	12.5179	−	18.4707i	0.478635	−	0.706244i
$685$	−20.0584			−0.766394
$686$	13.1191	−	22.6691i	0.500891	−	0.865510i
$687$	−29.2296	−	8.91894i	−1.11518	−	0.340279i
$688$	−31.9782	+	18.1826i	−1.21916	+	0.693207i
$689$	15.6761	+	27.1517i	0.597210	+	1.03440i
$690$	16.2413	+	30.6267i	0.618295	+	1.16594i
$691$	−11.7334	+	20.3229i	−0.446360	+	0.773119i	−0.998146	−	0.0608673i	$-0.980613\pi$
$691$	−11.7334	+	20.3229i	−0.446360	+	0.773119i	0.551786	+	0.833986i	$0.313947\pi$
$692$	4.24663	+	7.41168i	0.161433	+	0.281750i
$693$	6.19151	+	5.00049i	0.235196	+	0.189953i
$694$	27.1694	−	7.23206i	1.03134	−	0.274525i
$695$	−27.8548	−	16.0820i	−1.05659	−	0.610025i
$696$	−3.10072	−	1.95655i	−0.117532	−	0.0741630i
$697$	−6.69401	−	11.5944i	−0.253554	−	0.439168i
$698$	3.48149	−	12.9080i	0.131776	−	0.488574i
$699$	−9.16868	+	30.0481i	−0.346791	+	1.13652i
$700$	−0.859818	+	9.49000i	−0.0324981	+	0.358688i
$701$	15.4603			0.583926			0.291963	−	0.956430i	$-0.405692\pi$
$701$	15.4603			0.583926			0.291963	+	0.956430i	$0.405692\pi$
$702$	16.6018	−	7.39143i	0.626595	−	0.278971i
$703$	−11.9906	+	6.92275i	−0.452232	+	0.261096i
$704$	−6.98617	+	3.94190i	−0.263301	+	0.148566i
$705$	5.06702	+	5.42777i	0.190835	+	0.204421i
$706$	−23.1817	+	6.17059i	−0.872454	+	0.232233i
$707$	−35.1062	+	16.3791i	−1.32030	+	0.615999i
$708$	6.53409	+	28.6615i	0.245566	+	1.07717i
$709$	41.7153	+	24.0843i	1.56665	+	0.904505i	0.996556	+	0.0829254i	$0.0264263\pi$
$709$	41.7153	+	24.0843i	1.56665	+	0.904505i	0.570093	+	0.821580i	$0.306907\pi$
$710$	−9.76490	−	9.79713i	−0.366470	−	0.367680i
$711$	−1.04643	+	15.2033i	−0.0392443	+	0.570169i
$712$	−10.6271	−	40.4598i	−0.398267	−	1.51630i
$713$	26.2452			0.982891
$714$	16.8272	+	39.7412i	0.629741	+	1.48728i
$715$			4.43523i			0.165868i
$716$	−0.0498031	+	15.1129i	−0.00186123	+	0.564796i
$717$	−9.12976	+	2.11302i	−0.340957	+	0.0789123i
$718$	21.0689	−	20.9995i	0.786283	−	0.783696i
$719$	6.49021	−	11.2414i	0.242044	−	0.419232i	−0.719252	−	0.694749i	$-0.755516\pi$
$719$	6.49021	−	11.2414i	0.242044	−	0.419232i	0.961296	+	0.275517i	$0.0888489\pi$
$720$	9.30281	+	19.3428i	0.346695	+	0.720864i
$721$	−21.3763	−	14.9613i	−0.796094	−	0.557186i
$722$	7.06603	−	1.88086i	0.262970	−	0.0699985i
$723$	25.3886	+	27.1961i	0.944211	+	1.01143i
$724$	−8.64786	−	5.03091i	−0.321395	−	0.186972i
$725$	0.673858	+	1.16716i	0.0250264	+	0.0433471i
$726$	−12.9962	+	20.7473i	−0.482333	+	0.770006i
$727$		−	12.0095i		−	0.445406i	−0.974886	−	0.222703i	$-0.928512\pi$
$727$		−	12.0095i		−	0.445406i	0.974886	−	0.222703i	$-0.0714880\pi$
$728$	−14.2329	+	11.8284i	−0.527506	+	0.438389i
$729$	−5.52704	+	26.4282i	−0.204705	+	0.978824i
$730$	4.32444	−	16.0333i	0.160055	−	0.593419i
$731$	53.0370	−	30.6209i	1.96164	−	1.13256i
$732$	−9.53719	−	10.2839i	−0.352505	−	0.380105i
$733$	−4.29808	+	7.44449i	−0.158753	+	0.274968i	−0.934419	−	0.356175i	$-0.884081\pi$
$733$	−4.29808	+	7.44449i	−0.158753	+	0.274968i	0.775666	+	0.631143i	$0.217414\pi$
$734$	−0.524538	−	1.97058i	−0.0193610	−	0.0727355i
$735$	−9.82673	+	19.3318i	−0.362465	+	0.713065i
$736$	43.1379	+	11.9405i	1.59008	+	0.440133i
$737$	6.91700	+	3.99353i	0.254791	+	0.147104i
$738$	1.62287	+	8.37376i	0.0597386	+	0.308242i
$739$	2.25350	−	1.30106i	0.0828963	−	0.0478602i	−0.457979	−	0.888963i	$-0.651426\pi$
$739$	2.25350	−	1.30106i	0.0828963	−	0.0478602i	0.540875	+	0.841103i	$0.318093\pi$
$740$	0.0438896	−	13.3184i	0.00161342	−	0.489595i
$741$	−15.2356	−	4.64891i	−0.559695	−	0.170782i
$742$	46.7267	−	8.16974i	1.71539	−	0.299921i
$743$		−	13.4061i		−	0.491823i	−0.969292	−	0.245911i	$-0.920913\pi$
$743$		−	13.4061i		−	0.491823i	0.969292	−	0.245911i	$-0.0790872\pi$
$744$	16.2370	+	0.638500i	0.595278	+	0.0234085i
$745$	−1.43281	+	0.827235i	−0.0524942	+	0.0303075i
$746$	21.7860	−	21.7143i	0.797642	−	0.795018i
$747$	7.45305	+	15.2387i	0.272693	+	0.557556i
$748$	11.5872	−	6.63904i	0.423669	−	0.242747i
$749$	10.5623	−	15.0912i	0.385939	−	0.551420i
$750$	1.07266	−	29.7766i	0.0391681	−	1.08729i
$751$	−7.86182	+	13.6171i	−0.286882	+	0.496894i	−0.973064	−	0.230536i	$-0.925952\pi$
$751$	−7.86182	+	13.6171i	−0.286882	+	0.496894i	0.686182	+	0.727430i	$0.259285\pi$
$752$	9.58701	+	0.0631869i	0.349602	+	0.00230419i
$753$	−33.5047	+	7.75445i	−1.22098	+	0.282588i
$754$	−0.681609	+	2.52714i	−0.0248228	+	0.0920329i
$755$		−	34.2244i		−	1.24555i
$756$	−1.87819	−	27.4312i	−0.0683091	−	0.997664i
$757$			48.7626i			1.77231i	0.463391	+	0.886154i	$0.346633\pi$
$757$			48.7626i			1.77231i	−0.463391	+	0.886154i	$0.653367\pi$
$758$	2.48913	+	0.671359i	0.0904094	+	0.0243849i
$759$	−13.3879	+	3.09854i	−0.485950	+	0.112470i
$760$	4.95908	−	18.1482i	0.179885	−	0.658305i
$761$	21.7170	−	37.6149i	0.787240	−	1.36354i	−0.140411	−	0.990093i	$-0.544842\pi$
$761$	21.7170	−	37.6149i	0.787240	−	1.36354i	0.927652	−	0.373447i	$-0.121824\pi$
$762$	11.0741	+	0.398931i	0.401174	+	0.0144518i
$763$	6.54411	−	3.05321i	0.236913	−	0.110534i
$764$	−12.0426	−	21.0180i	−0.435684	−	0.760403i
$765$	−15.6993	−	32.0994i	−0.567611	−	1.16056i
$766$	9.60551	+	9.63722i	0.347061	+	0.348207i
$767$	18.1747	−	10.4932i	0.656252	−	0.378887i
$768$	26.3974	+	8.43665i	0.952534	+	0.304431i
$769$			23.9226i			0.862670i	0.902192	+	0.431335i	$0.141957\pi$
$769$			23.9226i			0.862670i	−0.902192	+	0.431335i	$0.858043\pi$

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.368276 - 1.36542i) q^{2} +(-0.390548 - 1.68745i) q^{3} +(-1.72875 - 1.00570i) q^{4} +(-1.54900 - 0.894317i) q^{5} +(-2.44790 - 0.0881824i) q^{6} +(2.63573 + 0.230049i) q^{7} +(-2.00986 + 1.99009i) q^{8} +(-2.69494 + 1.31806i) q^{9} +O(q^{10})\)	\(q+(0.368276 - 1.36542i) q^{2} +(-0.390548 - 1.68745i) q^{3} +(-1.72875 - 1.00570i) q^{4} +(-1.54900 - 0.894317i) q^{5} +(-2.44790 - 0.0881824i) q^{6} +(2.63573 + 0.230049i) q^{7} +(-2.00986 + 1.99009i) q^{8} +(-2.69494 + 1.31806i) q^{9} +(-1.79158 + 1.78568i) q^{10} +(-0.501346 - 0.868358i) q^{11} +(-1.02191 + 3.30994i) q^{12} +2.47302 q^{13} +(1.28479 - 3.51416i) q^{14} +(-0.904151 + 2.96313i) q^{15} +(1.97713 + 3.47721i) q^{16} +(-3.32963 - 5.76708i) q^{17} +(0.807221 + 4.16514i) q^{18} +(1.85941 - 3.22059i) q^{19} +(1.77842 + 3.10388i) q^{20} +(-0.641185 - 4.53750i) q^{21} +(-1.37031 + 0.364754i) q^{22} +(6.85244 + 3.95626i) q^{23} +(4.14312 + 2.61431i) q^{24} +(-0.900394 - 1.55953i) q^{25} +(0.910752 - 3.37671i) q^{26} +(3.27666 + 4.03281i) q^{27} +(-4.32515 - 3.04846i) q^{28} -0.748403 q^{29} +(3.71294 + 2.32580i) q^{30} +(2.87254 - 1.65846i) q^{31} +(5.47598 - 1.41904i) q^{32} +(-1.26951 + 1.18513i) q^{33} +(-9.10071 + 2.42246i) q^{34} +(-3.87702 - 2.71353i) q^{35} +(5.98445 + 0.431724i) q^{36} +(-3.22429 - 1.86155i) q^{37} +(-3.71268 - 3.72494i) q^{38} +(-0.965832 - 4.17308i) q^{39} +(4.89305 - 1.28520i) q^{40} +2.01044 q^{41} +(-6.43172 - 0.795563i) q^{42} +9.19651i q^{43} +(-0.00660852 + 2.00538i) q^{44} +(5.35324 + 0.368459i) q^{45} +(7.92554 - 7.89946i) q^{46} +(1.19840 - 2.07569i) q^{47} +(5.09544 - 4.69431i) q^{48} +(6.89415 + 1.21270i) q^{49} +(-2.46101 + 0.655080i) q^{50} +(-8.43126 + 7.87089i) q^{51} +(-4.27522 - 2.48712i) q^{52} +(6.33884 + 10.9792i) q^{53} +(6.71319 - 2.98883i) q^{54} +1.79345i q^{55} +(-5.75527 + 4.78297i) q^{56} +(-6.16075 - 1.87985i) q^{57} +(-0.275619 + 1.02188i) q^{58} +(7.34922 - 4.24308i) q^{59} +(4.54308 - 4.21319i) q^{60} +(-2.02442 + 3.50640i) q^{61} +(-1.20661 - 4.53300i) q^{62} +(-7.40637 + 2.85408i) q^{63} +(0.0790881 - 7.99961i) q^{64} +(-3.83071 - 2.21166i) q^{65} +(1.15067 + 2.16986i) q^{66} +(-6.89843 + 3.98281i) q^{67} +(-0.0438896 + 13.3184i) q^{68} +(3.99976 - 13.1082i) q^{69} +(-5.13292 + 4.29443i) q^{70} +5.46843i q^{71} +(2.79341 - 8.01229i) q^{72} +(-5.68546 + 3.28250i) q^{73} +(-3.72922 + 3.71695i) q^{74} +(-2.27997 + 2.12844i) q^{75} +(-6.45340 + 3.69757i) q^{76} +(-1.12165 - 2.40409i) q^{77} +(-6.05370 - 0.218077i) q^{78} +(2.53988 - 4.39920i) q^{79} +(0.0471537 - 7.15438i) q^{80} +(5.52545 - 7.10419i) q^{81} +(0.740396 - 2.74510i) q^{82} -5.65457i q^{83} +(-3.45493 + 8.48902i) q^{84} +11.9110i q^{85} +(12.5571 + 3.38685i) q^{86} +(0.292288 + 1.26289i) q^{87} +(2.73575 + 0.747554i) q^{88} +(-7.39495 + 12.8084i) q^{89} +(2.47457 - 7.17372i) q^{90} +(6.51821 + 0.568916i) q^{91} +(-7.86731 - 13.7309i) q^{92} +(-3.92043 - 4.19955i) q^{93} +(-2.39285 - 2.40075i) q^{94} +(-5.76045 + 3.32580i) q^{95} +(-4.53318 - 8.68621i) q^{96} +1.75577i q^{97} +(4.19479 - 8.96681i) q^{98} +(2.49565 + 1.67937i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

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