LMFDB - Embedded newform 168.2.ba.c.101.15

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			101.15
Character	$\chi$	$=$	168.101
Dual form			168.2.ba.c.5.15

$q$-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 $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

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

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	−0.804636	−	0.593769i	$-0.797639\pi$
$5$	−1.54900	+	0.894317i	−0.692735	+	0.399951i	0.111901	+	0.993719i	$0.464306\pi$
$6$	−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	−0.931655	−	0.363345i	$-0.881635\pi$
$11$	−0.501346	+	0.868358i	−0.151162	+	0.261820i	0.780493	+	0.625164i	$0.214968\pi$
$12$	−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	0.107001	+	0.994259i	$0.465875\pi$
$17$	−3.32963	+	5.76708i	−0.807553	+	1.39872i	−0.914554	+	0.404464i	$0.867458\pi$
$18$	0.807221	−	4.16514i	0.190264	−	0.981733i
$19$	1.85941	+	3.22059i	0.426577	+	0.738854i	0.996566	−	0.0827988i	$-0.0263859\pi$
$19$	1.85941	+	3.22059i	0.426577	+	0.738854i	−0.569989	+	0.821652i	$0.693053\pi$
$20$	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	0.431803	−	0.901968i	$-0.357877\pi$
$23$	6.85244	−	3.95626i	1.42883	−	0.824936i	0.997029	+	0.0770314i	$0.0245442\pi$
$24$	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	0.735265	−	0.677779i	$-0.237058\pi$
$31$	2.87254	+	1.65846i	0.515924	+	0.297869i	−0.219341	+	0.975648i	$0.570391\pi$
$32$	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	−0.741045	−	0.671455i	$-0.765670\pi$
$37$	−3.22429	+	1.86155i	−0.530071	+	0.306036i	0.210975	+	0.977492i	$0.432336\pi$
$38$	−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	$-0.752636\pi$
$43$		−	9.19651i		−	1.40245i	0.712938	−	0.701227i	$-0.247364\pi$
$44$	−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	0.940094	−	0.340916i	$-0.110737\pi$
$47$	1.19840	+	2.07569i	0.174805	+	0.302771i	−0.765289	+	0.643687i	$0.777404\pi$
$48$	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	0.00943963	−	0.999955i	$-0.496995\pi$
$53$	6.33884	−	10.9792i	0.870707	−	1.50811i	0.861267	−	0.508153i	$-0.169671\pi$
$54$	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	0.895183	−	0.445699i	$-0.147045\pi$
$59$	7.34922	+	4.24308i	0.956787	+	0.552401i	0.0616046	+	0.998101i	$0.480378\pi$
$60$	4.54308	+	4.21319i	0.586508	+	0.543921i
$61$	−2.02442	−	3.50640i	−0.259200	−	0.448948i	0.706828	−	0.707386i	$-0.250126\pi$
$61$	−2.02442	−	3.50640i	−0.259200	−	0.448948i	−0.966028	+	0.258438i	$0.916792\pi$
$62$	−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	0.0154303	−	0.999881i	$-0.495088\pi$
$67$	−6.89843	−	3.98281i	−0.842777	−	0.486577i	−0.858207	+	0.513303i	$0.828422\pi$
$68$	−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	$-0.894807\pi$
$71$		−	5.46843i		−	0.648984i	0.945889	−	0.324492i	$-0.105193\pi$
$72$	2.79341	+	8.01229i	0.329207	+	0.944258i
$73$	−5.68546	−	3.28250i	−0.665433	−	0.384188i	0.128911	−	0.991656i	$-0.458852\pi$
$73$	−5.68546	−	3.28250i	−0.665433	−	0.384188i	−0.794344	+	0.607468i	$0.792185\pi$
$74$	−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	0.972793	−	0.231676i	$-0.0744210\pi$
$79$	2.53988	+	4.39920i	0.285759	+	0.494949i	−0.687034	+	0.726625i	$0.741088\pi$
$80$	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	$0.100441\pi$
$83$			5.65457i			0.620669i	−0.950627	+	0.310335i	$0.899559\pi$
$84$	−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	−0.929676	−	0.368379i	$-0.879913\pi$
$89$	−7.39495	−	12.8084i	−0.783863	−	1.35769i	0.145812	−	0.989312i	$-0.453420\pi$
$90$	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	$-0.971590\pi$
$97$		−	1.75577i		−	0.178271i	0.996019	−	0.0891356i	$-0.0284105\pi$
$98$	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	−0.288330	−	0.957531i	$-0.593100\pi$
$101$	−12.6803	−	7.32100i	−1.26174	−	0.728467i	−0.973411	+	0.229064i	$0.926433\pi$
$102$	7.64204	−	14.4109i	0.756675	−	1.42689i
$103$	−8.54056	+	4.93089i	−0.841526	+	0.485855i	−0.857783	−	0.514013i	$-0.828158\pi$
$103$	−8.54056	+	4.93089i	−0.841526	+	0.485855i	0.0162566	+	0.999868i	$0.494825\pi$
$104$	−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	0.983778	−	0.179392i	$-0.0574130\pi$
$107$	3.48110	+	6.02945i	0.336531	+	0.582889i	−0.647247	+	0.762281i	$0.724080\pi$
$108$	−1.60871	+	10.2670i	−0.154798	+	0.987946i
$109$	2.36373	+	1.36470i	0.226404	+	0.130715i	0.608912	−	0.793238i	$-0.291606\pi$
$109$	2.36373	+	1.36470i	0.226404	+	0.130715i	−0.382508	+	0.923952i	$0.624939\pi$
$110$	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	$0.00795328\pi$
$113$			0.531154i			0.0499667i	−0.999688	+	0.0249834i	$0.992047\pi$
$114$	−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	0.216416	−	0.976301i	$-0.430563\pi$
$131$	13.3927	−	7.73228i	1.17013	−	0.675573i	0.953710	+	0.300729i	$0.0972298\pi$
$132$	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	0.853766	−	0.520657i	$-0.174313\pi$
$137$	9.71195	+	5.60719i	0.829748	+	0.479055i	−0.0240187	+	0.999712i	$0.507646\pi$
$138$	−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	0.884348	−	0.466828i	$-0.154603\pi$
$149$	0.462495	+	0.801066i	0.0378891	+	0.0656258i	−0.846459	+	0.532454i	$0.821270\pi$
$150$	2.06655	−	3.89697i	0.168733	−	0.318186i
$151$	9.56720	−	16.5709i	0.778568	−	1.34852i	−0.154200	−	0.988040i	$-0.549280\pi$
$151$	9.56720	−	16.5709i	0.778568	−	1.34852i	0.932767	−	0.360479i	$-0.117387\pi$
$152$	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	−0.997413	−	0.0718851i	$-0.977099\pi$
$157$	−5.46873	+	9.47212i	−0.436452	+	0.755957i	0.560961	+	0.827842i	$0.310432\pi$
$158$	−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	−0.815316	−	0.579017i	$-0.803437\pi$
$163$	−9.21188	+	5.31848i	−0.721530	+	0.416576i	0.0937855	+	0.995592i	$0.470103\pi$
$164$	−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	−0.633974	−	0.773354i	$-0.718577\pi$
$173$	−3.69882	+	2.13552i	−0.281216	+	0.162360i	0.352758	+	0.935715i	$0.385244\pi$
$174$	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	−0.971975	−	0.235083i	$-0.924464\pi$
$179$	−3.77825	+	6.54412i	−0.282399	+	0.489130i	0.689576	+	0.724214i	$0.257797\pi$
$180$	−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	−0.0699601	−	0.997550i	$-0.522287\pi$
$191$	10.4891	−	6.05587i	0.758963	−	0.438188i	0.828923	+	0.559362i	$0.188954\pi$
$192$	−13.5298	−	2.99078i	−0.976429	−	0.215841i
$193$	0.592437	−	1.02613i	0.0426445	−	0.0738625i	−0.843915	−	0.536476i	$-0.819755\pi$
$193$	0.592437	−	1.02613i	0.0426445	−	0.0738625i	0.886560	+	0.462614i	$0.153088\pi$
$194$	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	−0.0260186	−	0.999661i	$-0.508283\pi$
$199$	−12.7632	−	7.36884i	−0.904760	−	0.522363i	−0.878741	+	0.477298i	$0.841616\pi$
$200$	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	$0.171727\pi$
$211$			14.9240i			1.02741i	−0.857967	+	0.513704i	$0.828273\pi$
$212$	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	$-0.917859\pi$
$223$		−	7.62187i		−	0.510398i	0.966889	−	0.255199i	$-0.0821410\pi$
$224$	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	−0.0269870	−	0.999636i	$-0.508591\pi$
$227$	−13.6531	−	7.88264i	−0.906190	−	0.523189i	−0.879203	+	0.476446i	$0.841925\pi$
$228$	8.75981	−	9.44567i	0.580132	−	0.625555i
$229$	8.82193	+	15.2800i	0.582970	+	1.00973i	0.995125	+	0.0986198i	$0.0314428\pi$
$229$	8.82193	+	15.2800i	0.582970	+	1.00973i	−0.412155	+	0.911114i	$0.635224\pi$
$230$	−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	−0.916715	−	0.399542i	$-0.869169\pi$
$233$	−15.7079	+	9.06896i	−1.02906	+	0.594127i	−0.112344	+	0.993669i	$0.535836\pi$
$234$	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	$0.0559877\pi$
$239$			5.41040i			0.349970i	−0.984571	+	0.174985i	$0.944012\pi$
$240$	−12.0910	−	2.71456i	−0.780473	−	0.175224i
$241$	−18.6025	−	10.7401i	−1.19829	−	0.691834i	−0.238117	−	0.971236i	$-0.576530\pi$
$241$	−18.6025	−	10.7401i	−1.19829	−	0.691834i	−0.960174	+	0.279403i	$0.909863\pi$
$242$	−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	$0.215565\pi$
$251$			19.8553i			1.25325i	−0.779319	+	0.626627i	$0.784435\pi$
$252$	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	0.697111	−	0.716964i	$-0.254469\pi$
$257$	−4.36616	−	7.56240i	−0.272353	−	0.471730i	−0.969464	+	0.245234i	$0.921135\pi$
$258$	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	−0.132455	−	0.991189i	$-0.542286\pi$
$263$	−17.1429	−	9.89747i	−1.05708	−	0.610304i	−0.924623	+	0.380885i	$0.875619\pi$
$264$	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	0.524357	−	0.851498i	$-0.324306\pi$
$269$	0.805574	+	0.465098i	0.0491167	+	0.0283575i	−0.475241	+	0.879856i	$0.657639\pi$
$270$	−13.0717	+	1.37401i	−0.795519	+	0.0836197i
$271$	−7.45646	+	4.30499i	−0.452948	+	0.261509i	−0.709074	−	0.705134i	$-0.750887\pi$
$271$	−7.45646	+	4.30499i	−0.452948	+	0.261509i	0.256127	+	0.966643i	$0.417554\pi$
$272$	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	−0.999086	−	0.0427456i	$-0.986390\pi$
$277$	−25.5583	−	14.7561i	−1.53565	−	0.886607i	−0.536562	−	0.843861i	$-0.680277\pi$
$278$	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	$0.219454\pi$
$281$			21.3260i			1.27220i	−0.771605	+	0.636102i	$0.780546\pi$
$282$	−3.11661	−	4.97542i	−0.185592	−	0.296282i
$283$	10.4247	−	18.0561i	0.619684	−	1.07332i	−0.369860	−	0.929088i	$-0.620594\pi$
$283$	10.4247	−	18.0561i	0.619684	−	1.07332i	0.989543	−	0.144236i	$-0.0460724\pi$
$284$	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	$-0.874951\pi$
$293$		−	13.1058i		−	0.765652i	0.923821	−	0.382826i	$-0.125049\pi$
$294$	−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	−0.434211	−	0.900811i	$-0.642973\pi$
$311$	9.92896	−	17.1975i	0.563020	−	0.975179i	0.997231	−	0.0743677i	$-0.0236939\pi$
$312$	10.2460	−	6.46522i	0.580065	−	0.366021i
$313$	2.33108	−	1.34585i	0.131760	−	0.0760718i	−0.432671	−	0.901552i	$-0.642429\pi$
$313$	2.33108	−	1.34585i	0.131760	−	0.0760718i	0.564431	+	0.825480i	$0.309096\pi$
$314$	−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	0.976283	−	0.216499i	$-0.0694638\pi$
$317$	5.35288	+	9.27147i	0.300648	+	0.520737i	−0.675635	+	0.737236i	$0.736130\pi$
$318$	−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	0.117465	−	0.993077i	$-0.462523\pi$
$331$	18.8525	−	10.8845i	1.03623	−	0.598266i	0.918762	+	0.394811i	$0.129190\pi$
$332$	−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	−0.465604	−	0.884993i	$-0.654163\pi$
$347$	9.94032	−	17.2171i	0.533624	−	0.924265i	0.999229	−	0.0392715i	$-0.0125037\pi$
$348$	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	−0.998474	−	0.0552182i	$-0.982415\pi$
$353$	−8.48135	+	14.6901i	−0.451417	+	0.781877i	0.547057	+	0.837095i	$0.315748\pi$
$354$	−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	0.0648056	−	0.997898i	$-0.479357\pi$
$359$	18.2162	−	10.5171i	0.961413	−	0.555072i	0.896608	+	0.442826i	$0.146024\pi$
$360$	−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	0.532238	−	0.846595i	$-0.321351\pi$
$367$	1.24875	+	0.720966i	0.0651842	+	0.0376341i	−0.467054	+	0.884229i	$0.654685\pi$
$368$	−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	0.0744535	−	0.997224i	$-0.476279\pi$
$373$	18.8362	−	10.8751i	0.975302	−	0.563091i	0.900848	+	0.434134i	$0.142945\pi$
$374$	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	$-0.985091\pi$
$379$		−	1.82298i		−	0.0936402i	0.998903	−	0.0468201i	$-0.0149087\pi$
$380$	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	0.716546	−	0.697540i	$-0.245722\pi$
$383$	−4.81069	−	8.33236i	−0.245815	−	0.425763i	−0.962360	+	0.271777i	$0.912389\pi$
$384$	−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	0.250703	+	0.968064i	$0.419338\pi$
$389$	−14.0629	+	24.3576i	−0.713017	+	1.23498i	−0.963719	+	0.266917i	$0.913995\pi$
$390$	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	0.526425	−	0.850221i	$-0.323532\pi$
$397$	−9.42646	−	16.3271i	−0.473101	−	0.819434i	−0.999526	+	0.0307871i	$0.990199\pi$
$398$	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	−0.624806	−	0.780780i	$-0.714822\pi$
$401$	−5.22718	+	3.01791i	−0.261033	+	0.150707i	0.363773	+	0.931488i	$0.381488\pi$
$402$	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	0.941556	−	0.336856i	$-0.109364\pi$
$409$	22.6629	+	13.0844i	1.12061	+	0.646984i	0.179052	+	0.983840i	$0.442697\pi$
$410$	−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	$-0.980404\pi$
$419$		−	2.51866i		−	0.123045i	0.998106	−	0.0615223i	$-0.0195955\pi$
$420$	12.9436	+	10.0597i	0.631581	+	0.490864i
$421$			33.4873i			1.63207i	0.578003	+	0.816034i	$0.303832\pi$
$421$			33.4873i			1.63207i	−0.578003	+	0.816034i	$0.696168\pi$
$422$	−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	0.182319	−	0.983240i	$-0.441640\pi$
$431$	−12.0003	−	6.92836i	−0.578033	−	0.333727i	−0.760351	+	0.649512i	$0.774973\pi$
$432$	−7.54454	−	19.3670i	−0.362987	−	0.931794i
$433$		−	9.79368i		−	0.470654i	−0.971916	−	0.235327i	$-0.924384\pi$
$433$		−	9.79368i		−	0.470654i	0.971916	−	0.235327i	$-0.0756161\pi$
$434$	−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	−0.323707	−	0.946157i	$-0.604929\pi$
$439$	6.99463	−	4.03835i	0.333835	−	0.192740i	0.657543	+	0.753417i	$0.271596\pi$
$440$	−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	0.575559	−	0.817760i	$-0.304784\pi$
$443$	−8.84884	−	15.3266i	−0.420421	−	0.728191i	−0.995981	+	0.0895692i	$0.971451\pi$
$444$	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	$-0.848099\pi$
$449$		−	19.4650i		−	0.918609i	0.888279	−	0.459305i	$-0.151901\pi$
$450$	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	0.988424	−	0.151715i	$-0.0484797\pi$
$457$	7.75626	+	13.4342i	0.362823	+	0.628427i	−0.625601	+	0.780143i	$0.715146\pi$
$458$	−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	$0.00635516\pi$
$461$			0.857290i			0.0399280i	−0.999801	+	0.0199640i	$0.993645\pi$
$462$	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	−0.687431	−	0.726249i	$-0.741262\pi$
$467$	−8.69155	+	5.01807i	−0.402197	+	0.232208i	0.285235	+	0.958458i	$0.407928\pi$
$468$	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	0.494663	+	0.869085i	$0.335292\pi$
$479$	−11.0594	+	19.1555i	−0.505318	+	0.875237i	−0.999981	+	0.00615194i	$0.998042\pi$
$480$	−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	−0.489419	−	0.872049i	$-0.662791\pi$
$487$	11.2659	−	19.5131i	0.510506	−	0.884223i	0.999926	−	0.0121746i	$-0.00387541\pi$
$488$	−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	−0.279813	−	0.960054i	$-0.590273\pi$
$499$	9.19695	−	5.30986i	0.411712	−	0.237702i	0.691525	+	0.722353i	$0.256939\pi$
$500$	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	−0.876546	−	0.481318i	$-0.840158\pi$
$509$	−20.2595	+	11.6968i	−0.897985	+	0.518452i	−0.0214392	+	0.999770i	$0.506825\pi$
$510$	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	−0.849460	−	0.527654i	$-0.823072\pi$
$521$	0.735700	−	1.27427i	0.0322316	−	0.0558267i	0.881691	+	0.471827i	$0.156405\pi$
$522$	−0.604127	+	3.11720i	−0.0264419	+	0.136436i
$523$	5.30372	+	9.18631i	0.231915	+	0.401689i	0.958372	−	0.285523i	$-0.0921674\pi$
$523$	5.30372	+	9.18631i	0.231915	+	0.401689i	−0.726456	+	0.687213i	$0.758834\pi$
$524$	−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	−0.769807	−	0.638277i	$-0.779647\pi$
$541$	−14.0009	+	8.08343i	−0.601946	+	0.347534i	0.167861	+	0.985811i	$0.446314\pi$
$542$	−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	$0.0855228\pi$
$547$			12.4170i			0.530914i	−0.964123	+	0.265457i	$0.914477\pi$
$548$	−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	−0.544554	−	0.838726i	$-0.683301\pi$
$557$	10.7167	−	18.5619i	0.454081	−	0.786492i	0.998635	+	0.0522341i	$0.0166342\pi$
$558$	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	0.827932	−	0.560829i	$-0.189517\pi$
$563$	17.9430	+	10.3594i	0.756205	+	0.436595i	−0.0717262	+	0.997424i	$0.522851\pi$
$564$	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	0.0922056	−	0.995740i	$-0.470608\pi$
$569$	23.8691	−	13.7808i	1.00064	−	0.577722i	0.908439	+	0.418018i	$0.137275\pi$
$570$	14.3943	+	7.63326i	0.602911	+	0.319722i
$571$	−0.339940	−	0.196264i	−0.0142260	−	0.00821340i	0.492870	−	0.870103i	$-0.335948\pi$
$571$	−0.339940	−	0.196264i	−0.0142260	−	0.00821340i	−0.507096	+	0.861889i	$0.669281\pi$
$572$	−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	0.209493	−	0.977810i	$-0.432819\pi$
$577$	−12.7927	−	7.38589i	−0.532569	−	0.307479i	−0.742062	+	0.670331i	$0.766152\pi$
$578$	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	$-0.976895\pi$
$587$		−	3.51421i		−	0.145047i	0.997367	−	0.0725236i	$-0.0231052\pi$
$588$	−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	0.955012	+	0.296568i	$0.0958423\pi$
$593$	17.8824	+	30.9732i	0.734342	+	1.27192i	−0.220670	+	0.975349i	$0.570824\pi$
$594$	−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	0.998466	−	0.0553669i	$-0.0176328\pi$
$599$	35.4819	+	20.4855i	1.44975	+	0.837014i	0.451284	+	0.892380i	$0.350966\pi$
$600$	0.346647	+	8.81521i	0.0141518	+	0.359879i
$601$			36.1540i			1.47475i	0.675482	+	0.737377i	$0.263936\pi$
$601$			36.1540i			1.47475i	−0.675482	+	0.737377i	$0.736064\pi$
$602$	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	−0.305182	−	0.952294i	$-0.598717\pi$
$607$	9.04038	−	5.21946i	0.366938	−	0.211851i	0.672120	+	0.740443i	$0.265384\pi$
$608$	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	0.387418	−	0.921904i	$-0.373367\pi$
$613$	−5.37925	−	3.10571i	−0.217266	−	0.125439i	−0.604684	+	0.796466i	$0.706700\pi$
$614$	−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	$-0.850413\pi$
$617$		−	22.4963i		−	0.905669i	0.891595	−	0.452834i	$-0.149587\pi$
$618$	20.4716	−	12.8235i	0.823490	−	0.515836i
$619$	−14.1624	+	24.5300i	−0.569235	+	0.985943i	0.427407	+	0.904059i	$0.359427\pi$
$619$	−14.1624	+	24.5300i	−0.569235	+	0.985943i	−0.996642	+	0.0818842i	$0.973906\pi$
$620$	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	0.501566	−	0.865119i	$-0.332757\pi$
$641$	0.0793494	+	0.0458124i	0.00313411	+	0.00180948i	−0.498432	+	0.866929i	$0.666091\pi$
$642$	−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	−0.934716	−	0.355395i	$-0.884346\pi$
$647$	−4.05903	+	7.03045i	−0.159577	+	0.276396i	0.775139	+	0.631791i	$0.217680\pi$
$648$	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	−0.981959	−	0.189095i	$-0.939444\pi$
$653$	−16.7312	−	28.9792i	−0.654741	−	1.13404i	0.327218	−	0.944949i	$-0.393889\pi$
$654$	−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	−0.393130	−	0.919483i	$-0.628608\pi$
$661$	15.4190	−	26.7065i	0.599731	−	1.03876i	0.992861	−	0.119281i	$-0.0380590\pi$
$662$	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	−0.971305	−	0.237836i	$-0.923562\pi$
$677$	−32.5497	+	18.7926i	−1.25099	+	0.722257i	−0.279680	+	0.960093i	$0.590228\pi$
$678$	−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	−0.884889	−	0.465802i	$-0.845766\pi$
$683$	−1.02051	+	1.76757i	−0.0390487	+	0.0676343i	0.845841	+	0.533436i	$0.179099\pi$
$684$	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	0.551786	−	0.833986i	$-0.313947\pi$
$691$	−11.7334	−	20.3229i	−0.446360	−	0.773119i	−0.998146	+	0.0608673i	$0.980613\pi$
$692$	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	0.570093	−	0.821580i	$-0.306907\pi$
$709$	41.7153	−	24.0843i	1.56665	−	0.904505i	0.996556	−	0.0829254i	$-0.0264263\pi$
$710$	−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	0.961296	−	0.275517i	$-0.0888489\pi$
$719$	6.49021	+	11.2414i	0.242044	+	0.419232i	−0.719252	+	0.694749i	$0.755516\pi$
$720$	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	$0.0714880\pi$
$727$			12.0095i			0.445406i	−0.974886	+	0.222703i	$0.928512\pi$
$728$	−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	0.775666	−	0.631143i	$-0.217414\pi$
$733$	−4.29808	−	7.44449i	−0.158753	−	0.274968i	−0.934419	+	0.356175i	$0.884081\pi$
$734$	−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	0.540875	−	0.841103i	$-0.318093\pi$
$739$	2.25350	+	1.30106i	0.0828963	+	0.0478602i	−0.457979	+	0.888963i	$0.651426\pi$
$740$	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	$0.0790872\pi$
$743$			13.4061i			0.491823i	−0.969292	+	0.245911i	$0.920913\pi$
$744$	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	0.686182	−	0.727430i	$-0.259285\pi$
$751$	−7.86182	−	13.6171i	−0.286882	−	0.496894i	−0.973064	+	0.230536i	$0.925952\pi$
$752$	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	$-0.653367\pi$
$757$		−	48.7626i		−	1.77231i	0.463391	−	0.886154i	$-0.346633\pi$
$758$	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	0.927652	+	0.373447i	$0.121824\pi$
$761$	21.7170	+	37.6149i	0.787240	+	1.36354i	−0.140411	+	0.990093i	$0.544842\pi$
$762$	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	$-0.858043\pi$
$769$		−	23.9226i		−	0.862670i	0.902192	−	0.431335i	$-0.141957\pi$
$770$	6.30247	−	2.30421i	0.227125	−	0.0830379i
$771$	14.4663	−	4.41417i	0.520993	−	0.158972i
$772$	0.00780924	+	2.36974i	0.000281061	+	0.0852886i
$773$	−14.3402	−	8.27930i	−0.515780	−	0.297786i	0.219427	−	0.975629i	$-0.429581\pi$
$773$	−14.3402	−	8.27930i	−0.515780	−	0.297786i	−0.735206	+	0.677843i	$0.762915\pi$
$774$	−38.3047	−	7.42361i	−1.37684	−	0.266836i
$775$	−5.17284	+	2.98654i	−0.185814	+	0.107280i
$776$	−3.49414	+	3.52885i	−0.125432	+	0.126678i
$777$	−6.37940	−	15.8238i	−0.228860	−	0.567676i
$778$	−38.4374	−	10.2314i	−1.37805	−	0.366815i
$779$	3.73823	+	6.47480i	0.133936	+	0.231984i
$780$	11.2351	+	10.4193i	0.402281	+	0.373071i
$781$	4.74856	+	2.74158i	0.169917	+	0.0981014i
$782$	−71.9460	+	19.4050i	−2.57278	+	0.693920i
$783$	−2.45226	+	3.01816i	−0.0876366	+	0.107860i
$784$	9.41381	−	26.3701i	0.336208	−	0.941788i
$785$		−	19.5631i		−	0.698237i
$786$	−32.1022	+	20.1089i	−1.14505	+	0.717260i
$787$	5.81161	−	10.0660i	0.207162	−	0.358814i	−0.743658	−	0.668561i	$-0.766911\pi$
$787$	5.81161	−	10.0660i	0.207162	−	0.358814i	0.950819	+	0.309746i	$0.100244\pi$
$788$	−33.7297	+	19.6224i	−1.20157	+	0.699018i
$789$	23.3966	−	25.0623i	0.832940	−	0.892242i
$790$	3.30519	−	12.4169i	0.117593	−	0.441775i
$791$	0.122192	+	1.39998i	0.00434463	+	0.0497775i
$792$	−8.35800	−	1.59126i	−0.296989	−	0.0565428i
$793$	−5.00642	−	8.67137i	−0.177783	−	0.307930i
$794$	18.8218	−	18.8840i	0.667962	−	0.670167i
$795$	−38.2641	−	8.85597i	−1.35709	−	0.314089i
$796$	29.4752	−	0.0971328i	1.04472	−	0.00344278i
$797$		−	2.35681i		−	0.0834824i	−0.999128	−	0.0417412i	$-0.986709\pi$
$797$		−	2.35681i		−	0.0834824i	0.999128	−	0.0417412i	$-0.0132905\pi$
$798$	−14.5214	−	19.2347i	−0.514051	−	0.680899i
$799$	−15.9609			−0.564657
$800$	−7.14357	+	7.26225i	−0.252563	+	0.256759i
$801$	3.04672	+	44.2650i	0.107651	+	1.56403i
$802$	−6.04577	−	6.02587i	−0.213483	−	0.212781i
$803$	5.70077	−	3.29134i	0.201176	−	0.116149i
$804$	−6.13329	+	26.9034i	−0.216305	+	0.948811i
$805$	−15.8316	+	33.9327i	−0.557991	+	1.19597i
$806$	−2.98397	+	11.2102i	−0.105106	+	0.394862i
$807$	−1.09944	+	1.17772i	−0.0387022	+	0.0414576i
$808$	10.9163	+	39.9492i	0.384034	+	1.40541i
$809$	−39.6070	−	22.8671i	−1.39251	−	0.803964i	−0.398914	−	0.916988i	$-0.630613\pi$
$809$	−39.6070	−	22.8671i	−1.39251	−	0.803964i	−0.993592	+	0.113024i	$0.963946\pi$
$810$	2.78656	−	22.5944i	0.0979098	−	0.793887i
$811$	−0.844573			−0.0296570			−0.0148285	−	0.999890i	$-0.504720\pi$
$811$	−0.844573			−0.0296570			−0.0148285	+	0.999890i	$0.504720\pi$
$812$	3.23695	−	2.28148i	0.113595	−	0.0800641i
$813$	−4.35233	−	14.2637i	−0.152643	−	0.500249i
$814$	5.09728	−	1.37482i	0.178660	−	0.0481873i
$815$	9.51282	−	16.4767i	0.333219	−	0.577153i
$816$	−44.0384	+	13.7555i	−1.54165	+	0.481539i
$817$	29.6182	−	17.1000i	1.03621	−	0.598255i
$818$	−9.51956	+	35.7631i	−0.332844	+	1.25043i
$819$	−18.3161	−	7.05818i	−0.640015	−	0.246633i
$820$	3.57540	−	6.24017i	0.124858	−	0.217916i
$821$	18.4890	+	32.0239i	0.645272	+	1.11764i	0.984239	+	0.176845i	$0.0565892\pi$
$821$	18.4890	+	32.0239i	0.645272	+	1.11764i	−0.338967	+	0.940798i	$0.610078\pi$
$822$	−24.2683	−	12.8694i	−0.846456	−	0.448873i
$823$	−3.62518	+	6.27899i	−0.126366	+	0.218872i	−0.922266	−	0.386556i	$-0.873665\pi$
$823$	−3.62518	+	6.27899i	−0.126366	+	0.218872i	0.795900	+	0.605428i	$0.206998\pi$
$824$	26.9783	+	7.08606i	0.939832	+	0.246855i
$825$	2.99130	−	0.912746i	0.104144	−	0.0317777i
$826$	−5.46864	+	31.2778i	−0.190278	+	1.08829i
$827$	−43.4014			−1.50921			−0.754607	−	0.656176i	$-0.772173\pi$
$827$	−43.4014			−1.50921			−0.754607	+	0.656176i	$0.772173\pi$
$828$	39.3000	−	26.6344i	1.36577	−	0.925608i
$829$	−12.7789	+	22.1338i	−0.443830	+	0.768737i	−0.997970	−	0.0636869i	$-0.979714\pi$
$829$	−12.7789	+	22.1338i	−0.443830	+	0.768737i	0.554139	+	0.832424i	$0.313047\pi$
$830$	10.0973	−	10.1306i	0.350481	−	0.351638i
$831$	34.8818	−	37.3652i	1.21004	−	1.29619i
$832$	0.195586	+	19.7832i	0.00678073	+	0.685858i
$833$	−15.9612	+	43.7970i	−0.553024	+	1.51748i
$834$	−44.0193	+	1.58573i	−1.52426	+	0.0549095i
$835$	12.2842	−	7.09229i	0.425113	−	0.245439i
$836$	6.44620	−	3.75009i	0.222946	−	0.129700i
$837$	16.1006	−	6.15019i	0.556518	−	0.212582i
$838$	3.43903	−	0.927561i	0.118799	−	0.0320421i
$839$	19.2288			0.663854			0.331927	−	0.943305i	$-0.392301\pi$
$839$	19.2288			0.663854			0.331927	+	0.943305i	$0.392301\pi$
$840$	−8.96894	+	21.3782i	−0.309458	+	0.737617i
$841$	−28.4399			−0.980686
$842$	−45.7242	+	12.3325i	−1.57576	+	0.425007i
$843$	−35.9865	−	8.32884i	−1.23944	−	0.286860i
$844$	−15.0091	−	25.7998i	−0.516634	−	0.888064i
$845$	10.6636	−	6.15665i	0.366840	−	0.211795i
$846$	9.61294	−	3.31597i	0.330500	−	0.114005i
$847$	15.1628	+	21.6642i	0.520999	+	0.744389i
$848$	−25.6443	−	43.7487i	−0.880627	−	1.50234i
$849$	26.3973	+	24.6429i	0.905954	+	0.845741i
$850$	11.9721	−	12.0116i	0.410641	−	0.411996i
$851$	−14.7295	+	25.5123i	−0.504921	+	0.874549i
$852$	−18.1002	+	5.58824i	−0.620102	+	0.191450i
$853$	−43.5472			−1.49103			−0.745514	−	0.666489i	$-0.767796\pi$
$853$	−43.5472			−1.49103			−0.745514	+	0.666489i	$0.767796\pi$
$854$	9.72108	−	11.6191i	0.332649	−	0.397598i
$855$	11.1405	+	16.5555i	0.380997	+	0.566185i
$856$	5.00261	−	19.0461i	0.170986	−	0.650981i
$857$	−4.41603	+	7.64878i	−0.150849	+	0.261277i	−0.931540	−	0.363640i	$-0.881534\pi$
$857$	−4.41603	+	7.64878i	−0.150849	+	0.261277i	0.780691	+	0.624917i	$0.214867\pi$
$858$	2.84563	−	5.36611i	0.0971483	−	0.183196i
$859$	2.94564	+	5.10200i	0.100504	+	0.174078i	0.911892	−	0.410429i	$-0.134621\pi$
$859$	2.94564	+	5.10200i	0.100504	+	0.174078i	−0.811388	+	0.584507i	$0.801288\pi$
$860$	−28.5449	−	16.3552i	−0.973372	−	0.557708i
$861$	−1.28906	+	9.12236i	−0.0439311	+	0.310889i
$862$	5.04071	−	18.9370i	0.171687	−	0.644995i
$863$	−2.80835	+	1.62140i	−0.0955974	+	0.0551932i	−0.547037	−	0.837109i	$-0.684244\pi$
$863$	−2.80835	+	1.62140i	−0.0955974	+	0.0551932i	0.451439	+	0.892302i	$0.350911\pi$
$864$	23.6656	−	17.4339i	0.805120	−	0.593112i
$865$	3.81966	−	6.61584i	0.129872	−	0.224945i
$866$	13.3725	−	3.60677i	0.454416	−	0.122563i
$867$	45.3020	−	13.8232i	1.53854	−	0.469460i
$868$	−17.4799	+	1.58373i	−0.593307	+	0.0537552i
$869$	−5.09344			−0.172783
$870$	−2.77878	+	1.74063i	−0.0942094	+	0.0590130i
$871$	−17.0599	−	9.84955i	−0.578053	−	0.333739i
$872$	−2.03490	−	7.44690i	−0.0689103	−	0.252184i
$873$	−2.31420	+	4.73170i	−0.0783240	+	0.160144i
$874$	−10.7041	+	40.2132i	−0.362072	+	1.36023i
$875$	−2.79835	−	32.0614i	−0.0946015	−	1.08387i
$876$	−5.05486	+	22.1729i	−0.170788	+	0.749154i
$877$	−39.1526	+	22.6048i	−1.32209	+	0.763309i	−0.984062	−	0.177828i	$-0.943093\pi$
$877$	−39.1526	+	22.6048i	−1.32209	+	0.763309i	−0.338028	+	0.941136i	$0.609760\pi$
$878$	8.09000	+	8.06338i	0.273024	+	0.272126i
$879$	22.1154	+	5.11847i	0.745934	+	0.172642i
$880$	−6.23620	−	3.54588i	−0.210222	−	0.119532i
$881$	−28.1014			−0.946759			−0.473380	−	0.880859i	$-0.656966\pi$
$881$	−28.1014			−0.946759			−0.473380	+	0.880859i	$0.656966\pi$
$882$	0.514055	−	29.6940i	0.0173091	−	0.999850i
$883$		−	5.45102i		−	0.183442i	−0.995785	−	0.0917208i	$-0.970763\pi$
$883$		−	5.45102i		−	0.183442i	0.995785	−	0.0917208i	$-0.0292367\pi$
$884$	−0.108540	−	32.9367i	−0.00365059	−	1.10778i
$885$	5.92799	−	25.6131i	0.199267	−	0.860975i
$886$	17.6685	−	17.7268i	0.593585	−	0.595544i
$887$	−25.3783	−	43.9566i	−0.852122	−	1.47592i	−0.879290	−	0.476287i	$-0.841982\pi$
$887$	−25.3783	−	43.9566i	−0.852122	−	1.47592i	0.0271684	−	0.999631i	$-0.491351\pi$
$888$	−8.49197	+	16.1419i	−0.284972	+	0.541687i
$889$	−11.9239	+	1.04073i	−0.399914	+	0.0349049i
$890$	−9.62318	+	36.1524i	−0.322570	+	1.21183i
$891$	−8.93914	+	1.23640i	−0.299472	+	0.0414211i
$892$	7.66533	+	13.1763i	0.256654	+	0.441174i
$893$	−4.45664	+	7.71912i	−0.149136	+	0.258311i
$894$	−1.20278	−	1.92015i	−0.0402271	−	0.0642193i
$895$		−	13.5158i		−	0.451783i
$896$	−28.0103	+	10.5557i	−0.935758	+	0.352643i
$897$	9.89147	+	32.4168i	0.330266	+	1.08237i
$898$	26.5779	−	7.16848i	0.886915	−	0.239215i
$899$	−2.14982	−	1.24120i	−0.0717005	−	0.0413963i
$900$	−4.71508	+	9.72164i	−0.157169	+	0.324055i
$901$	42.2119	+	73.1132i	1.40628	+	2.43575i
$902$	−2.75492	−	0.733315i	−0.0917288	−	0.0244167i
$903$	41.7291	+	5.89666i	1.38866	+	0.196228i
$904$	1.05704	−	1.06755i	0.0351567	−	0.0355060i
$905$	−7.74871	+	4.47372i	−0.257576	+	0.148711i
$906$	−21.9583	+	41.4075i	−0.729516	+	1.37567i
$907$	−8.66652	−	5.00362i	−0.287767	−	0.166142i	0.349167	−	0.937060i	$-0.386464\pi$
$907$	−8.66652	−	5.00362i	−0.287767	−	0.166142i	−0.636934	+	0.770918i	$0.719798\pi$
$908$	31.5304	−	0.103905i	1.04637	−	0.00344822i
$909$	24.5233	+	36.4431i	0.813387	+	1.20874i
$910$	−12.6938	−	10.6202i	−0.420795	−	0.352056i
$911$		−	14.5940i		−	0.483521i	−0.970336	−	0.241761i	$-0.922275\pi$
$911$		−	14.5940i		−	0.483521i	0.970336	−	0.241761i	$-0.0777249\pi$
$912$	−5.64395	+	25.1389i	−0.186890	+	0.832433i
$913$	−4.91019	−	2.83490i	−0.162503	−	0.0938214i
$914$	−15.4869	+	15.5381i	−0.512263	+	0.513954i
$915$	−8.55953	+	9.16893i	−0.282969	+	0.303115i
$916$	−30.6181	−	17.5431i	−1.01165	−	0.579639i
$917$	33.5208	−	23.4612i	1.10695	−	0.774757i
$918$	−39.5892	+	28.7638i	−1.30664	+	0.949348i
$919$	−1.14316	−	1.98001i	−0.0377093	−	0.0653145i	0.846555	−	0.532302i	$-0.178673\pi$
$919$	−1.14316	−	1.98001i	−0.0377093	−	0.0653145i	−0.884264	+	0.466987i	$0.845339\pi$
$920$	38.6139	−	10.5514i	1.27306	−	0.347870i
$921$	7.28079	−	31.4582i	0.239910	−	1.03658i
$922$	−1.17056	+	0.315719i	−0.0385504	+	0.0103977i
$923$		−	13.5235i		−	0.445132i
$924$	9.10362	+	1.25583i	0.299487	+	0.0413138i
$925$		−	6.70450i		−	0.220443i
$926$	13.8373	+	51.3031i	0.454721	+	1.68593i
$927$	29.5155	−	2.03153i	0.969417	−	0.0667242i
$928$	−4.09824	−	1.06201i	−0.134531	−	0.0348622i
$929$	9.71753	+	16.8313i	0.318822	+	0.552216i	0.980242	−	0.197799i	$-0.0633795\pi$
$929$	9.71753	+	16.8313i	0.318822	+	0.552216i	−0.661421	+	0.750015i	$0.730046\pi$
$930$	14.5228	−	0.523166i	0.476223	−	0.0171553i
$931$	16.7246	+	19.9483i	0.548128	+	0.653780i
$932$	18.0343	−	31.4754i	0.590733	−	1.03101i
$933$	25.1420	+	23.4710i	0.823114	+	0.768407i
$934$	−10.0527	−	10.0196i	−0.328933	−	0.327851i
$935$	10.3430	+	5.97152i	0.338252	+	0.195290i
$936$	6.90815	+	19.8145i	0.225800	+	0.647658i
$937$		−	21.6552i		−	0.707445i	−0.935350	−	0.353723i	$-0.884916\pi$
$937$		−	21.6552i		−	0.707445i	0.935350	−	0.353723i	$-0.115084\pi$
$938$	5.13319	−	29.3592i	0.167605	−	0.958613i
$939$	1.36065	+	4.45918i	0.0444030	+	0.145520i
$940$	8.57397	−	0.0282547i	0.279652	−	0.000921567i
$941$	−5.82024	−	3.36032i	−0.189735	−	0.109543i	0.402124	−	0.915585i	$-0.368272\pi$
$941$	−5.82024	−	3.36032i	−0.189735	−	0.109543i	−0.591858	+	0.806042i	$0.701605\pi$
$942$	12.5516	−	23.6691i	0.408955	−	0.771180i
$943$	13.7764	−	7.95381i	0.448622	−	0.259012i
$944$	29.2844	−	17.1657i	0.953126	−	0.558695i
$945$	−1.76053	+	24.5265i	−0.0572701	+	0.797849i
$946$	−3.35446	+	12.6020i	−0.109063	+	0.409728i
$947$	10.5673	+	18.3031i	0.343392	+	0.594772i	0.985060	−	0.172210i	$-0.0550908\pi$
$947$	10.5673	+	18.3031i	0.343392	+	0.594772i	−0.641668	+	0.766982i	$0.721757\pi$
$948$	11.9656	−	12.9024i	0.388624	−	0.419052i
$949$	−14.0602	−	8.11768i	−0.456414	−	0.263511i
$950$	−2.46627	−	9.14394i	−0.0800163	−	0.296669i
$951$	−17.7357	+	5.41174i	−0.575118	+	0.175488i
$952$	46.7467	−	17.2656i	1.51507	−	0.559582i
$953$			2.18327i			0.0707230i	0.999375	+	0.0353615i	$0.0112583\pi$
$953$			2.18327i			0.0707230i	−0.999375	+	0.0353615i	$0.988742\pi$
$954$	−40.6130	−	35.2648i	−1.31490	−	1.14174i
$955$	−10.8317	+	18.7611i	−0.350507	+	0.607096i
$956$	−5.44125	−	9.35321i	−0.175983	−	0.302504i
$957$	0.950102	+	0.886955i	0.0307124	+	0.0286712i
$958$	−30.2282	−	8.04627i	−0.976630	−	0.259963i
$959$	26.8880	+	12.5448i	0.868259	+	0.405094i
$960$	23.6324	−	7.46720i	0.762732	−	0.241003i
$961$	−9.99900	−	17.3188i	−0.322548	−	0.558670i
$962$	−9.22243	−	9.19209i	−0.297343	−	0.296365i
$963$	−1.43422	−	20.8373i	−0.0462170	−	0.671473i
$964$	42.9603	−	0.141572i	1.38366	−	0.00455972i
$965$			2.11931i			0.0682229i
$966$	−40.9255	+	30.8971i	−1.31676	+	0.994098i
$967$	−25.1413			−0.808490			−0.404245	−	0.914651i	$-0.632466\pi$
$967$	−25.1413			−0.808490			−0.404245	+	0.914651i	$0.632466\pi$
$968$	7.18150	−	27.3416i	0.230822	−	0.878793i
$969$	9.67175	−	41.7888i	0.310701	−	1.34245i
$970$	−3.13525	+	3.14560i	−0.100667	+	0.100999i
$971$	−30.0100	+	17.3263i	−0.963065	+	0.556026i	−0.897115	−	0.441797i	$-0.854341\pi$
$971$	−30.0100	+	17.3263i	−0.963065	+	0.556026i	−0.0659503	+	0.997823i	$0.521008\pi$
$972$	17.8679	−	25.5487i	0.573114	−	0.819476i
$973$	47.3969	−	4.13685i	1.51947	−	0.132621i
$974$	30.7925	+	8.19648i	0.986657	+	0.262632i
$975$	−5.63841	−	5.26366i	−0.180574	−	0.168572i
$976$	−16.1950	+	0.106739i	−0.518389	+	0.00341664i
$977$	3.22538	+	1.86218i	0.103189	+	0.0595763i	0.550706	−	0.834699i	$-0.314358\pi$
$977$	3.22538	+	1.86218i	0.103189	+	0.0595763i	−0.447517	+	0.894275i	$0.647692\pi$
$978$	22.0808	−	13.8314i	0.706065	−	0.442281i
$979$	14.8297			0.473960
$980$	8.49660	−	23.5553i	0.271414	−	0.752447i
$981$	−4.57137	−	6.79333i	−0.145953	−	0.216894i
$982$	−9.24685	−	34.2837i	−0.295079	−	1.09404i
$983$	27.3018	−	47.2881i	0.870792	−	1.50826i	0.00961355	−	0.999954i	$-0.496940\pi$
$983$	27.3018	−	47.2881i	0.870792	−	1.50826i	0.861179	−	0.508302i	$-0.169727\pi$
$984$	8.32948	−	5.25590i	0.265534	−	0.167552i
$985$	−30.2227	+	17.4491i	−0.962977	+	0.555975i
$986$	6.81100	+	1.81298i	0.216906	+	0.0577370i
$987$	−10.1869	+	4.10685i	−0.324251	+	0.130722i
$988$	−15.9594	−	9.14415i	−0.507735	−	0.290914i
$989$	−36.3837	−	63.0185i	−1.15694	−	2.00387i
$990$	−7.46997	−	1.44771i	−0.237411	−	0.0460113i
$991$	−25.1790	+	43.6114i	−0.799839	+	1.38536i	0.119882	+	0.992788i	$0.461748\pi$
$991$	−25.1790	+	43.6114i	−0.799839	+	1.38536i	−0.919721	+	0.392573i	$0.871585\pi$
$992$	13.3766	+	13.1580i	0.424706	+	0.417765i
$993$	11.0042	+	36.0635i	0.349207	+	1.14444i
$994$	19.2169	−	7.02579i	0.609525	−	0.222844i
$995$	26.3603			0.835679
$996$	18.7163	−	5.77845i	0.593048	−	0.183097i
$997$	−12.7609	+	22.1025i	−0.404141	+	0.699993i	−0.994221	−	0.107352i	$-0.965763\pi$
$997$	−12.7609	+	22.1025i	−0.404141	+	0.699993i	0.590080	+	0.807345i	$0.299096\pi$
$998$	10.6372	+	10.6022i	0.336715	+	0.335607i
$999$	−3.05765	+	19.1026i	−0.0967398	+	0.604380i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.ba.c.101.15	yes	48
3.2	odd	2	inner	168.2.ba.c.101.10	yes	48
4.3	odd	2		672.2.bi.c.17.14		48
7.5	odd	6	inner	168.2.ba.c.5.18	yes	48
8.3	odd	2		672.2.bi.c.17.11		48
8.5	even	2	inner	168.2.ba.c.101.7	yes	48
12.11	even	2		672.2.bi.c.17.20		48
21.5	even	6	inner	168.2.ba.c.5.7	✓	48
24.5	odd	2	inner	168.2.ba.c.101.18	yes	48
24.11	even	2		672.2.bi.c.17.5		48
28.19	even	6		672.2.bi.c.593.5		48
56.5	odd	6	inner	168.2.ba.c.5.10	yes	48
56.19	even	6		672.2.bi.c.593.20		48
84.47	odd	6		672.2.bi.c.593.11		48
168.5	even	6	inner	168.2.ba.c.5.15	yes	48
168.131	odd	6		672.2.bi.c.593.14		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.7	✓	48	21.5	even	6	inner
168.2.ba.c.5.10	yes	48	56.5	odd	6	inner
168.2.ba.c.5.15	yes	48	168.5	even	6	inner
168.2.ba.c.5.18	yes	48	7.5	odd	6	inner
168.2.ba.c.101.7	yes	48	8.5	even	2	inner
168.2.ba.c.101.10	yes	48	3.2	odd	2	inner
168.2.ba.c.101.15	yes	48	1.1	even	1	trivial
168.2.ba.c.101.18	yes	48	24.5	odd	2	inner
672.2.bi.c.17.5		48	24.11	even	2
672.2.bi.c.17.11		48	8.3	odd	2
672.2.bi.c.17.14		48	4.3	odd	2
672.2.bi.c.17.20		48	12.11	even	2
672.2.bi.c.593.5		48	28.19	even	6
672.2.bi.c.593.11		48	84.47	odd	6
672.2.bi.c.593.14		48	168.131	odd	6
672.2.bi.c.593.20		48	56.19	even	6

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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