LMFDB - Embedded newform 672.2.bo.a.125.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(125,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 4, 4]))

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

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

chi := DirichletCharacter("672.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bo (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$496$
Relative dimension:	$124$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			125.10
Character	$\chi$	$=$	672.125
Dual form			672.2.bo.a.629.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38553 + 0.283382i) q^{2} +(1.72093 - 0.195961i) q^{3} +(1.83939 - 0.785270i) q^{4} +(-0.478704 - 1.15569i) q^{5} +(-2.32887 + 0.759191i) q^{6} +(0.141859 - 2.64195i) q^{7} +(-2.32600 + 1.60927i) q^{8} +(2.92320 - 0.674470i) q^{9} +O(q^{10})$	\(q+(-1.38553 + 0.283382i) q^{2} +(1.72093 - 0.195961i) q^{3} +(1.83939 - 0.785270i) q^{4} +(-0.478704 - 1.15569i) q^{5} +(-2.32887 + 0.759191i) q^{6} +(0.141859 - 2.64195i) q^{7} +(-2.32600 + 1.60927i) q^{8} +(2.92320 - 0.674470i) q^{9} +(0.990761 + 1.46559i) q^{10} +(1.43539 + 3.46534i) q^{11} +(3.01158 - 1.71184i) q^{12} +(0.510390 + 0.211410i) q^{13} +(0.552132 + 3.70070i) q^{14} +(-1.05029 - 1.89506i) q^{15} +(2.76670 - 2.88883i) q^{16} +2.53724i q^{17} +(-3.85905 + 1.76288i) q^{18} +(1.42486 + 0.590197i) q^{19} +(-1.78805 - 1.74986i) q^{20} +(-0.273590 - 4.57440i) q^{21} +(-2.97080 - 4.39458i) q^{22} +(2.12148 - 2.12148i) q^{23} +(-3.68752 + 3.22524i) q^{24} +(2.42907 - 2.42907i) q^{25} +(-0.767071 - 0.148280i) q^{26} +(4.89845 - 1.73355i) q^{27} +(-1.81371 - 4.97096i) q^{28} +(2.21207 - 5.34040i) q^{29} +(1.99223 + 2.32803i) q^{30} -8.32246i q^{31} +(-3.01470 + 4.78660i) q^{32} +(3.14928 + 5.68233i) q^{33} +(-0.719010 - 3.51543i) q^{34} +(-3.12119 + 1.10076i) q^{35} +(4.84726 - 3.53611i) q^{36} +(0.444715 + 1.07364i) q^{37} +(-2.14144 - 0.413955i) q^{38} +(0.919773 + 0.263806i) q^{39} +(2.97328 + 1.91778i) q^{40} +(-5.42285 - 5.42285i) q^{41} +(1.67537 + 6.26044i) q^{42} +(-6.80898 + 2.82037i) q^{43} +(5.36148 + 5.24694i) q^{44} +(-2.17883 - 3.05545i) q^{45} +(-2.33819 + 3.54057i) q^{46} +1.56201i q^{47} +(4.19520 - 5.51365i) q^{48} +(-6.95975 - 0.749565i) q^{49} +(-2.67719 + 4.05390i) q^{50} +(0.497201 + 4.36641i) q^{51} +(1.10482 - 0.0119280i) q^{52} +(1.69351 + 4.08851i) q^{53} +(-6.29569 + 3.79002i) q^{54} +(3.31775 - 3.31775i) q^{55} +(3.92163 + 6.37345i) q^{56} +(2.56774 + 0.736471i) q^{57} +(-1.55151 + 8.02615i) q^{58} +(-4.21269 - 10.1703i) q^{59} +(-3.42002 - 2.66099i) q^{60} +(-0.934435 + 2.25593i) q^{61} +(2.35844 + 11.5310i) q^{62} +(-1.36723 - 7.81861i) q^{63} +(2.82053 - 7.48630i) q^{64} -0.691057i q^{65} +(-5.97370 - 6.98059i) q^{66} +(12.9304 + 5.35594i) q^{67} +(1.99242 + 4.66697i) q^{68} +(3.23520 - 4.06665i) q^{69} +(4.01256 - 2.40963i) q^{70} +(-0.713212 - 0.713212i) q^{71} +(-5.71395 + 6.27302i) q^{72} +(1.51178 - 1.51178i) q^{73} +(-0.920415 - 1.36153i) q^{74} +(3.70425 - 4.65625i) q^{75} +(3.08434 - 0.0332995i) q^{76} +(9.35887 - 3.30064i) q^{77} +(-1.34913 - 0.104863i) q^{78} +13.0505i q^{79} +(-4.66303 - 1.81456i) q^{80} +(8.09018 - 3.94322i) q^{81} +(9.05026 + 5.97678i) q^{82} +(-0.429086 + 1.03591i) q^{83} +(-4.09538 - 8.19926i) q^{84} +(2.93227 - 1.21459i) q^{85} +(8.63481 - 5.83726i) q^{86} +(2.76030 - 9.62393i) q^{87} +(-8.91538 - 5.75045i) q^{88} +(-7.42964 + 7.42964i) q^{89} +(3.88469 + 3.61597i) q^{90} +(0.630938 - 1.31843i) q^{91} +(2.23630 - 5.56817i) q^{92} +(-1.63088 - 14.3224i) q^{93} +(-0.442645 - 2.16421i) q^{94} -1.92923i q^{95} +(-4.25011 + 8.82817i) q^{96} +5.48728i q^{97} +(9.85536 - 0.933727i) q^{98} +(6.53321 + 9.16176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9	$ 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9} - 48 q^{16} - 8 q^{18} - 4 q^{21} - 16 q^{22} - 16 q^{25} - 8 q^{28} - 64 q^{30} - 48 q^{36} - 16 q^{37} - 8 q^{39} + 56 q^{42} - 16 q^{43} - 16 q^{46} + 16 q^{51} - 8 q^{57} - 80 q^{58} + 24 q^{60} - 8 q^{63} - 112 q^{64} + 48 q^{67} - 8 q^{70} - 8 q^{72} - 160 q^{78} + 128 q^{84} + 64 q^{85} - 16 q^{88} - 56 q^{91} + 16 q^{93} - 8 q^{99}+O(q^{100}) $ 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9 - 48 * q^16 - 8 * q^18 - 4 * q^21 - 16 * q^22 - 16 * q^25 - 8 * q^28 - 64 * q^30 - 48 * q^36 - 16 * q^37 - 8 * q^39 + 56 * q^42 - 16 * q^43 - 16 * q^46 + 16 * q^51 - 8 * q^57 - 80 * q^58 + 24 * q^60 - 8 * q^63 - 112 * q^64 + 48 * q^67 - 8 * q^70 - 8 * q^72 - 160 * q^78 + 128 * q^84 + 64 * q^85 - 16 * q^88 - 56 * q^91 + 16 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.38553	+	0.283382i	−0.979718	+	0.200382i
$2$	−1.38553	+	0.283382i	−0.979718	+	0.200382i
$3$	1.72093	−	0.195961i	0.993579	−	0.113138i
$3$	1.72093	−	0.195961i	0.993579	−	0.113138i
$4$	1.83939	−	0.785270i	0.919694	−	0.392635i
$5$	−0.478704	−	1.15569i	−0.214083	−	0.516841i	0.779960	−	0.625829i	$-0.215239\pi$
$5$	−0.478704	−	1.15569i	−0.214083	−	0.516841i	−0.994043	+	0.108987i	$0.965239\pi$
$6$	−2.32887	+	0.759191i	−0.950757	+	0.309939i
$7$	0.141859	−	2.64195i	0.0536175	−	0.998562i
$7$	0.141859	−	2.64195i	0.0536175	−	0.998562i
$8$	−2.32600	+	1.60927i	−0.822364	+	0.568961i
$9$	2.92320	−	0.674470i	0.974400	−	0.224823i
$10$	0.990761	+	1.46559i	0.313306	+	0.463461i
$11$	1.43539	+	3.46534i	0.432787	+	1.04484i	0.978385	+	0.206793i	$0.0663028\pi$
$11$	1.43539	+	3.46534i	0.432787	+	1.04484i	−0.545597	+	0.838047i	$0.683697\pi$
$12$	3.01158	−	1.71184i	0.869367	−	0.494167i
$13$	0.510390	+	0.211410i	0.141557	+	0.0586347i	0.452337	−	0.891847i	$-0.350590\pi$
$13$	0.510390	+	0.211410i	0.141557	+	0.0586347i	−0.310780	+	0.950482i	$0.600590\pi$
$14$	0.552132	+	3.70070i	0.147563	+	0.989053i
$15$	−1.05029	−	1.89506i	−0.271183	−	0.489302i
$16$	2.76670	−	2.88883i	0.691675	−	0.722208i
$17$			2.53724i			0.615371i	0.951488	+	0.307686i	$0.0995545\pi$
$17$			2.53724i			0.615371i	−0.951488	+	0.307686i	$0.900445\pi$
$18$	−3.85905	+	1.76288i	−0.909586	+	0.415515i
$19$	1.42486	+	0.590197i	0.326886	+	0.135401i	0.540090	−	0.841607i	$-0.318390\pi$
$19$	1.42486	+	0.590197i	0.326886	+	0.135401i	−0.213204	+	0.977008i	$0.568390\pi$
$20$	−1.78805	−	1.74986i	−0.399821	−	0.391280i
$21$	−0.273590	−	4.57440i	−0.0597022	−	0.998216i
$22$	−2.97080	−	4.39458i	−0.633376	−	0.936927i
$23$	2.12148	−	2.12148i	0.442360	−	0.442360i	−0.450444	−	0.892804i	$-0.648734\pi$
$23$	2.12148	−	2.12148i	0.442360	−	0.442360i	0.892804	+	0.450444i	$0.148734\pi$
$24$	−3.68752	+	3.22524i	−0.752713	+	0.658349i
$25$	2.42907	−	2.42907i	0.485813	−	0.485813i
$26$	−0.767071	−	0.148280i	−0.150435	−	0.0290801i
$27$	4.89845	−	1.73355i	0.942707	−	0.333622i
$28$	−1.81371	−	4.97096i	−0.342759	−	0.939424i
$29$	2.21207	−	5.34040i	0.410770	−	0.991687i	−0.574161	−	0.818742i	$-0.694672\pi$
$29$	2.21207	−	5.34040i	0.410770	−	0.991687i	0.984931	−	0.172945i	$-0.0553283\pi$
$30$	1.99223	+	2.32803i	0.363730	+	0.425038i
$31$		−	8.32246i		−	1.49476i	−0.664398	−	0.747379i	$-0.731312\pi$
$31$		−	8.32246i		−	1.49476i	0.664398	−	0.747379i	$-0.268688\pi$
$32$	−3.01470	+	4.78660i	−0.532929	+	0.846160i
$33$	3.14928	+	5.68233i	0.548220	+	0.989167i
$34$	−0.719010	−	3.51543i	−0.123309	−	0.602890i
$35$	−3.12119	+	1.10076i	−0.527577	+	0.186063i
$36$	4.84726	−	3.53611i	0.807876	−	0.589352i
$37$	0.444715	+	1.07364i	0.0731106	+	0.176505i	0.956210	−	0.292681i	$-0.0945474\pi$
$37$	0.444715	+	1.07364i	0.0731106	+	0.176505i	−0.883099	+	0.469186i	$0.844547\pi$
$38$	−2.14144	−	0.413955i	−0.347388	−	0.0671524i
$39$	0.919773	+	0.263806i	0.147282	+	0.0422427i
$40$	2.97328	+	1.91778i	0.470117	+	0.303227i
$41$	−5.42285	−	5.42285i	−0.846906	−	0.846906i	0.142839	−	0.989746i	$-0.454377\pi$
$41$	−5.42285	−	5.42285i	−0.846906	−	0.846906i	−0.989746	+	0.142839i	$0.954377\pi$
$42$	1.67537	+	6.26044i	0.258516	+	0.966007i
$43$	−6.80898	+	2.82037i	−1.03836	+	0.430103i	−0.835723	−	0.549151i	$-0.814951\pi$
$43$	−6.80898	+	2.82037i	−1.03836	+	0.430103i	−0.202637	+	0.979254i	$0.564951\pi$
$44$	5.36148	+	5.24694i	0.808273	+	0.791007i
$45$	−2.17883	−	3.05545i	−0.324800	−	0.455479i
$46$	−2.33819	+	3.54057i	−0.344747	+	0.522029i
$47$			1.56201i			0.227842i	0.993490	+	0.113921i	$0.0363411\pi$
$47$			1.56201i			0.227842i	−0.993490	+	0.113921i	$0.963659\pi$
$48$	4.19520	−	5.51365i	0.605525	−	0.795826i
$49$	−6.95975	−	0.749565i	−0.994250	−	0.107081i
$50$	−2.67719	+	4.05390i	−0.378612	+	0.573308i
$51$	0.497201	+	4.36641i	0.0696220	+	0.611420i
$52$	1.10482	−	0.0119280i	0.153211	−	0.00165411i
$53$	1.69351	+	4.08851i	0.232622	+	0.561599i	0.996484	−	0.0837799i	$-0.0266993\pi$
$53$	1.69351	+	4.08851i	0.232622	+	0.561599i	−0.763862	+	0.645379i	$0.776699\pi$
$54$	−6.29569	+	3.79002i	−0.856735	+	0.515756i
$55$	3.31775	−	3.31775i	0.447365	−	0.447365i
$56$	3.92163	+	6.37345i	0.524050	+	0.851688i
$57$	2.56774	+	0.736471i	0.340106	+	0.0975479i
$58$	−1.55151	+	8.02615i	−0.203723	+	1.05388i
$59$	−4.21269	−	10.1703i	−0.548445	−	1.32406i	−0.918635	−	0.395108i	$-0.870707\pi$
$59$	−4.21269	−	10.1703i	−0.548445	−	1.32406i	0.370190	−	0.928956i	$-0.379293\pi$
$60$	−3.42002	−	2.66099i	−0.441522	−	0.343533i
$61$	−0.934435	+	2.25593i	−0.119642	+	0.288842i	−0.972343	−	0.233558i	$-0.924963\pi$
$61$	−0.934435	+	2.25593i	−0.119642	+	0.288842i	0.852701	+	0.522400i	$0.174963\pi$
$62$	2.35844	+	11.5310i	0.299522	+	1.46444i
$63$	−1.36723	−	7.81861i	−0.172255	−	0.985052i
$64$	2.82053	−	7.48630i	0.352566	−	0.935787i
$65$		−	0.691057i		−	0.0857150i
$66$	−5.97370	−	6.98059i	−0.735312	−	0.859252i
$67$	12.9304	+	5.35594i	1.57970	+	0.654332i	0.988366	−	0.152097i	$-0.0486025\pi$
$67$	12.9304	+	5.35594i	1.57970	+	0.654332i	0.591332	+	0.806429i	$0.298602\pi$
$68$	1.99242	+	4.66697i	0.241616	+	0.565954i
$69$	3.23520	−	4.06665i	0.389472	−	0.489567i
$70$	4.01256	−	2.40963i	0.479593	−	0.288006i
$71$	−0.713212	−	0.713212i	−0.0846427	−	0.0846427i	0.663518	−	0.748160i	$-0.269063\pi$
$71$	−0.713212	−	0.713212i	−0.0846427	−	0.0846427i	−0.748160	+	0.663518i	$0.769063\pi$
$72$	−5.71395	+	6.27302i	−0.673395	+	0.739283i
$73$	1.51178	−	1.51178i	0.176940	−	0.176940i	−0.613080	−	0.790021i	$-0.710070\pi$
$73$	1.51178	−	1.51178i	0.176940	−	0.176940i	0.790021	+	0.613080i	$0.210070\pi$
$74$	−0.920415	−	1.36153i	−0.106996	−	0.158275i
$75$	3.70425	−	4.65625i	0.427730	−	0.537658i
$76$	3.08434	−	0.0332995i	0.353798	−	0.00381972i
$77$	9.35887	−	3.30064i	1.06654	−	0.376143i
$78$	−1.34913	−	0.104863i	−0.152759	−	0.0118734i
$79$			13.0505i			1.46830i	0.678987	+	0.734151i	$0.262419\pi$
$79$			13.0505i			1.46830i	−0.678987	+	0.734151i	$0.737581\pi$
$80$	−4.66303	−	1.81456i	−0.521343	−	0.202874i
$81$	8.09018	−	3.94322i	0.898909	−	0.438136i
$82$	9.05026	+	5.97678i	0.999434	+	0.660025i
$83$	−0.429086	+	1.03591i	−0.0470983	+	0.113705i	−0.945678	−	0.325105i	$-0.894600\pi$
$83$	−0.429086	+	1.03591i	−0.0470983	+	0.113705i	0.898579	+	0.438811i	$0.144600\pi$
$84$	−4.09538	−	8.19926i	−0.446842	−	0.894613i
$85$	2.93227	−	1.21459i	0.318049	−	0.131740i
$86$	8.63481	−	5.83726i	0.931115	−	0.629448i
$87$	2.76030	−	9.62393i	0.295935	−	1.03179i
$88$	−8.91538	−	5.75045i	−0.950383	−	0.613000i
$89$	−7.42964	+	7.42964i	−0.787540	+	0.787540i	−0.981090	−	0.193550i	$-0.938000\pi$
$89$	−7.42964	+	7.42964i	−0.787540	+	0.787540i	0.193550	+	0.981090i	$0.438000\pi$
$90$	3.88469	+	3.61597i	0.409482	+	0.381157i
$91$	0.630938	−	1.31843i	0.0661403	−	0.138209i
$92$	2.23630	−	5.56817i	0.233150	−	0.580522i
$93$	−1.63088	−	14.3224i	−0.169114	−	1.48516i
$94$	−0.442645	−	2.16421i	−0.0456554	−	0.223221i
$95$		−	1.92923i		−	0.197935i
$96$	−4.25011	+	8.82817i	−0.433775	+	0.901021i
$97$			5.48728i			0.557149i	0.960415	+	0.278574i	$0.0898619\pi$
$97$			5.48728i			0.557149i	−0.960415	+	0.278574i	$0.910138\pi$
$98$	9.85536	−	0.933727i	0.995542	−	0.0943206i
$99$	6.53321	+	9.16176i	0.656612	+	0.920792i
$100$	2.56052	−	6.37547i	0.256052	−	0.637547i
$101$	−5.31269	−	12.8260i	−0.528632	−	1.27623i	−0.932419	−	0.361378i	$-0.882306\pi$
$101$	−5.31269	−	12.8260i	−0.528632	−	1.27623i	0.403787	−	0.914853i	$-0.367694\pi$
$102$	−1.92625	−	5.90890i	−0.190727	−	0.585068i
$103$	11.8789	+	11.8789i	1.17046	+	1.17046i	0.982100	+	0.188359i	$0.0603170\pi$
$103$	11.8789	+	11.8789i	1.17046	+	1.17046i	0.188359	+	0.982100i	$0.439683\pi$
$104$	−1.52738	+	0.329613i	−0.149772	+	0.0323212i
$105$	−5.15563	+	2.50597i	−0.503138	+	0.244557i
$106$	−3.50503	−	5.18484i	−0.340438	−	0.503596i
$107$	2.20955	+	5.33432i	0.213605	+	0.515688i	0.993972	−	0.109633i	$-0.0349677\pi$
$107$	2.20955	+	5.33432i	0.213605	+	0.515688i	−0.780367	+	0.625322i	$0.784968\pi$
$108$	7.64885	−	7.03528i	0.736011	−	0.676970i
$109$	−3.68219	+	8.88960i	−0.352690	+	0.851469i	0.643596	+	0.765365i	$0.277442\pi$
$109$	−3.68219	+	8.88960i	−0.352690	+	0.851469i	−0.996286	+	0.0861039i	$0.972558\pi$
$110$	−3.65665	+	5.53703i	−0.348648	+	0.527935i
$111$	0.975714	+	1.76051i	0.0926106	+	0.167100i
$112$	−7.23966	−	7.71928i	−0.684084	−	0.729404i
$113$	−2.33142			−0.219322			−0.109661	−	0.993969i	$-0.534977\pi$
$113$	−2.33142			−0.219322			−0.109661	+	0.993969i	$0.534977\pi$
$114$	−3.76639	−	0.292749i	−0.352755	−	0.0274184i
$115$	−3.46735	−	1.43622i	−0.323332	−	0.133928i
$116$	−0.124807	−	11.5601i	−0.0115880	−	1.07333i
$117$	1.63456	+	0.273752i	0.151115	+	0.0253084i
$118$	8.71890	+	12.8975i	0.802640	+	1.18731i
$119$	6.70325	+	0.359929i	0.614486	+	0.0329947i
$120$	5.49262	+	2.71771i	0.501405	+	0.248092i
$121$	−2.17009	+	2.17009i	−0.197281	+	0.197281i
$122$	0.655399	−	3.39046i	0.0593370	−	0.306958i
$123$	−10.3950	−	8.26967i	−0.937286	−	0.745651i
$124$	−6.53538	−	15.3082i	−0.586894	−	1.37472i
$125$	−9.74852	−	4.03797i	−0.871934	−	0.361167i
$126$	4.11000	+	10.4455i	0.366148	+	0.930557i
$127$	−0.796762			−0.0707012			−0.0353506	−	0.999375i	$-0.511255\pi$
$127$	−0.796762			−0.0707012			−0.0353506	+	0.999375i	$0.511255\pi$
$128$	−1.78644	+	11.1718i	−0.157900	+	0.987455i
$129$	−11.1651	+	6.18796i	−0.983032	+	0.544819i
$130$	0.195833	+	0.957480i	0.0171757	+	0.0839765i
$131$	17.5097	+	7.25276i	1.52983	+	0.633677i	0.979532	−	0.201291i	$-0.0645137\pi$
$131$	17.5097	+	7.25276i	1.52983	+	0.633677i	0.550299	+	0.834968i	$0.314514\pi$
$132$	10.2549	+	7.97898i	0.892576	+	0.694481i
$133$	1.76140	−	3.68068i	0.152733	−	0.319156i
$134$	−19.4332	−	3.75657i	−1.67877	−	0.324518i
$135$	−4.34836	−	4.83125i	−0.374247	−	0.415807i
$136$	−4.08310	−	5.90162i	−0.350123	−	0.506059i
$137$	−10.6233	+	10.6233i	−0.907608	+	0.907608i	−0.996079	−	0.0884711i	$-0.971802\pi$
$137$	−10.6233	+	10.6233i	−0.907608	+	0.907608i	0.0884711	+	0.996079i	$0.471802\pi$
$138$	−3.33004	+	6.55127i	−0.283472	+	0.557681i
$139$	5.28995	+	12.7711i	0.448688	+	1.08323i	0.972814	+	0.231587i	$0.0743919\pi$
$139$	5.28995	+	12.7711i	0.448688	+	1.08323i	−0.524127	+	0.851640i	$0.675608\pi$
$140$	−4.87668	+	4.47571i	−0.412154	+	0.378266i
$141$	0.306093	+	2.68810i	0.0257776	+	0.226379i
$142$	1.19029	+	0.786065i	0.0998868	+	0.0659651i
$143$			2.07213i			0.173281i
$144$	6.13919	−	10.3107i	0.511599	−	0.859224i
$145$	−7.23078			−0.600484
$146$	−1.66620	+	2.52303i	−0.137896	+	0.208807i
$147$	−12.1241	+	0.0738911i	−0.999981	+	0.00609444i
$148$	1.66110	+	1.62561i	0.136541	+	0.133625i
$149$	−2.95214	−	7.12711i	−0.241849	−	0.583875i	0.755617	−	0.655013i	$-0.227337\pi$
$149$	−2.95214	−	7.12711i	−0.241849	−	0.583875i	−0.997466	+	0.0711379i	$0.977337\pi$
$150$	−3.81285	+	7.50110i	−0.311318	+	0.612462i
$151$	10.1117	+	10.1117i	0.822882	+	0.822882i	0.986520	−	0.163639i	$-0.0523231\pi$
$151$	10.1117	+	10.1117i	0.822882	+	0.822882i	−0.163639	+	0.986520i	$0.552323\pi$
$152$	−4.26401	+	0.920186i	−0.345857	+	0.0746369i
$153$	1.71129	+	7.41686i	0.138350	+	0.599618i
$154$	−12.0317	+	7.22528i	−0.969539	+	0.582230i
$155$	−9.61820	+	3.98399i	−0.772552	+	0.320002i
$156$	1.89898	−	0.237029i	0.152040	−	0.0189775i
$157$	−9.30918	+	22.4743i	−0.742953	+	1.79365i	−0.149531	+	0.988757i	$0.547776\pi$
$157$	−9.30918	+	22.4743i	−0.742953	+	1.79365i	−0.593422	+	0.804891i	$0.702224\pi$
$158$	−3.69830	−	18.0819i	−0.294221	−	1.43852i
$159$	3.71561	+	6.70417i	0.294667	+	0.531675i
$160$	6.97499	+	1.19271i	0.551421	+	0.0942919i
$161$	−5.30389	−	5.90580i	−0.418005	−	0.465442i
$162$	−10.0917	+	7.75607i	−0.792883	+	0.609374i
$163$	−1.78633	−	0.739924i	−0.139917	−	0.0579553i	0.311626	−	0.950205i	$-0.399126\pi$
$163$	−1.78633	−	0.739924i	−0.139917	−	0.0579553i	−0.451543	+	0.892249i	$0.649126\pi$
$164$	−14.2331	−	5.71632i	−1.11142	−	0.446370i
$165$	5.05946	−	6.35976i	0.393878	−	0.495106i
$166$	0.300954	−	1.55687i	0.0233586	−	0.120837i
$167$	−15.4977	+	15.4977i	−1.19925	+	1.19925i	−0.224853	+	0.974393i	$0.572190\pi$
$167$	−15.4977	+	15.4977i	−1.19925	+	1.19925i	−0.974393	+	0.224853i	$0.927810\pi$
$168$	7.99780	+	10.1998i	0.617044	+	0.786929i
$169$	−8.97658	−	8.97658i	−0.690507	−	0.690507i
$170$	−3.71856	+	2.51380i	−0.285200	+	0.192800i
$171$	4.56323	+	0.764237i	0.348959	+	0.0584426i
$172$	−10.3096	+	10.5347i	−0.786100	+	0.803260i
$173$	0.742301	−	1.79207i	0.0564361	−	0.136249i	−0.893146	−	0.449766i	$-0.851507\pi$
$173$	0.742301	−	1.79207i	0.0564361	−	0.136249i	0.949582	+	0.313517i	$0.101507\pi$
$174$	−1.09723	+	14.1165i	−0.0831804	+	1.07017i
$175$	−6.07287	−	6.76204i	−0.459066	−	0.511162i
$176$	13.9821	+	5.44096i	1.05394	+	0.410128i
$177$	−9.24273	−	16.6769i	−0.694726	−	1.25351i
$178$	8.18856	−	12.3994i	0.613759	−	0.929376i
$179$	11.6567	+	4.82835i	0.871260	+	0.360888i	0.773101	−	0.634283i	$-0.218705\pi$
$179$	11.6567	+	4.82835i	0.871260	+	0.360888i	0.0981592	+	0.995171i	$0.468705\pi$
$180$	−6.40706	−	3.90919i	−0.477554	−	0.291374i
$181$	−3.05312	−	7.37088i	−0.226937	−	0.547873i	0.768865	−	0.639411i	$-0.220822\pi$
$181$	−3.05312	−	7.37088i	−0.226937	−	0.547873i	−0.995802	+	0.0915377i	$0.970822\pi$
$182$	−0.500563	+	2.00552i	−0.0371042	+	0.148659i
$183$	−1.16602	+	4.06540i	−0.0861950	+	0.300523i
$184$	−1.52053	+	8.34860i	−0.112095	+	0.615467i
$185$	1.02791	−	1.02791i	0.0755732	−	0.0755732i
$186$	6.31834	+	19.3819i	0.463283	+	1.42115i
$187$	−8.79242	+	3.64194i	−0.642965	+	0.266325i
$188$	1.22660	+	2.87314i	0.0894588	+	0.209545i
$189$	−3.88506	−	13.1874i	−0.282596	−	0.959239i
$190$	0.546711	+	2.67301i	0.0396626	+	0.193921i
$191$		−	0.533375i		−	0.0385936i	−0.999814	−	0.0192968i	$-0.993857\pi$
$191$		−	0.533375i		−	0.0385936i	0.999814	−	0.0192968i	$-0.00614275\pi$
$192$	3.38690	−	13.4361i	0.244429	−	0.969667i
$193$	−15.0903			−1.08622			−0.543112	−	0.839661i	$-0.682754\pi$
$193$	−15.0903			−1.08622			−0.543112	+	0.839661i	$0.682754\pi$
$194$	−1.55500	−	7.60279i	−0.111642	−	0.545849i
$195$	−0.135420	−	1.18926i	−0.00969764	−	0.0851647i
$196$	−13.3903	+	4.08654i	−0.956450	+	0.291896i
$197$	−2.10402	+	0.871515i	−0.149905	+	0.0620929i	−0.456375	−	0.889788i	$-0.650852\pi$
$197$	−2.10402	+	0.871515i	−0.149905	+	0.0620929i	0.306469	+	0.951881i	$0.400852\pi$
$198$	−11.6482	−	10.8425i	−0.827805	−	0.770543i
$199$	−8.80480	−	8.80480i	−0.624156	−	0.624156i	0.322436	−	0.946591i	$-0.395498\pi$
$199$	−8.80480	−	8.80480i	−0.624156	−	0.624156i	−0.946591	+	0.322436i	$0.895498\pi$
$200$	−1.74099	+	9.55901i	−0.123106	+	0.675924i
$201$	23.3018	+	6.68334i	1.64358	+	0.471407i
$202$	10.9955	+	16.2652i	0.773644	+	1.14442i
$203$	−13.7952	−	6.60174i	−0.968236	−	0.463351i
$204$	4.34336	+	7.64110i	0.304096	+	0.534984i
$205$	−3.67121	+	8.86308i	−0.256408	+	0.619024i
$206$	−19.8248	−	13.0923i	−1.38126	−	0.912182i
$207$	4.77064	−	7.63240i	0.331582	−	0.530488i
$208$	2.02283	−	0.889522i	0.140258	−	0.0616772i
$209$			5.78480i			0.400143i
$210$	6.43314	−	4.93311i	0.443929	−	0.340417i
$211$	−2.12378	+	5.12725i	−0.146207	+	0.352974i	−0.979969	−	0.199149i	$-0.936182\pi$
$211$	−2.12378	+	5.12725i	−0.146207	+	0.352974i	0.833763	+	0.552123i	$0.186182\pi$
$212$	6.32561	+	6.19049i	0.434445	+	0.425164i
$213$	−1.36715	−	1.08763i	−0.0936755	−	0.0745229i
$214$	−4.57305	−	6.76472i	−0.312607	−	0.462427i
$215$	6.51897	+	6.51897i	0.444590	+	0.444590i
$216$	−8.60404	+	11.9151i	−0.585431	+	0.810723i
$217$	−21.9875	−	1.18061i	−1.49261	−	0.0801451i
$218$	2.58263	−	13.3603i	0.174918	−	0.904872i
$219$	2.30542	−	2.89792i	0.155786	−	0.195823i
$220$	3.49730	−	8.70795i	0.235788	−	0.587090i
$221$	−0.536399	+	1.29498i	−0.0360821	+	0.0871099i
$222$	−1.85078	−	2.16273i	−0.124216	−	0.145153i
$223$		−	20.6997i		−	1.38615i	−0.720863	−	0.693077i	$-0.756254\pi$
$223$		−	20.6997i		−	1.38615i	0.720863	−	0.693077i	$-0.243746\pi$
$224$	12.2183	+	8.64370i	0.816368	+	0.577532i
$225$	5.46231	−	8.73897i	0.364154	−	0.582598i
$226$	3.23026	−	0.660685i	0.214874	−	0.0439481i
$227$	23.7254	+	9.82737i	1.57471	+	0.652266i	0.987564	−	0.157217i	$-0.0502522\pi$
$227$	23.7254	+	9.82737i	1.57471	+	0.652266i	0.587144	+	0.809482i	$0.300252\pi$
$228$	5.30141	−	0.661717i	0.351094	−	0.0438233i
$229$	−1.74347	+	0.722169i	−0.115212	+	0.0477223i	−0.439545	−	0.898221i	$-0.644860\pi$
$229$	−1.74347	+	0.722169i	−0.115212	+	0.0477223i	0.324333	+	0.945943i	$0.394860\pi$
$230$	5.21111	+	1.00734i	0.343611	+	0.0664223i
$231$	15.4592	−	7.51415i	1.01714	−	0.494394i
$232$	3.44887	+	15.9816i	0.226429	+	1.04924i
$233$	−19.7108	+	19.7108i	−1.29130	+	1.29130i	−0.357311	+	0.933985i	$0.616306\pi$
$233$	−19.7108	+	19.7108i	−1.29130	+	1.29130i	−0.933985	+	0.357311i	$0.883694\pi$
$234$	−2.34231	+	0.0839146i	−0.153122	+	0.00548567i
$235$	1.80520	−	0.747738i	0.117758	−	0.0487771i
$236$	−15.7352	−	15.3991i	−1.02428	−	1.00240i
$237$	2.55740	+	22.4591i	0.166121	+	1.45887i
$238$	−9.38956	+	1.40089i	−0.608635	+	0.0908063i
$239$	22.8588			1.47862			0.739308	−	0.673368i	$-0.235153\pi$
$239$	22.8588			1.47862			0.739308	+	0.673368i	$0.235153\pi$
$240$	−8.38034	−	2.20896i	−0.540948	−	0.142588i
$241$	−16.5395			−1.06540			−0.532700	−	0.846304i	$-0.678823\pi$
$241$	−16.5395			−1.06540			−0.532700	+	0.846304i	$0.678823\pi$
$242$	2.39176	−	3.62169i	0.153748	−	0.232811i
$243$	13.1499	−	8.37137i	0.843567	−	0.537023i
$244$	0.0527218	+	4.88331i	0.00337517	+	0.312622i
$245$	2.46539	+	8.40215i	0.157508	+	0.536794i
$246$	16.7461	+	8.51212i	1.06769	+	0.542713i
$247$	0.602461	+	0.602461i	0.0383337	+	0.0383337i
$248$	13.3930	+	19.3580i	0.850459	+	1.22923i
$249$	−0.535430	+	1.86680i	−0.0339315	+	0.118304i
$250$	14.6512	+	2.83217i	0.926621	+	0.179122i
$251$	6.48254	+	15.6502i	0.409175	+	0.987835i	0.985355	+	0.170513i	$0.0545424\pi$
$251$	6.48254	+	15.6502i	0.409175	+	0.987835i	−0.576181	+	0.817322i	$0.695458\pi$
$252$	−8.65459	−	13.3078i	−0.545188	−	0.838314i
$253$	10.3968	+	4.30651i	0.653643	+	0.270748i
$254$	1.10394	−	0.225788i	0.0692672	−	0.0141672i
$255$	4.80822	−	2.66483i	0.301103	−	0.166878i
$256$	−0.690723	−	15.9851i	−0.0431702	−	0.999068i
$257$	26.2950			1.64024			0.820119	−	0.572194i	$-0.193907\pi$
$257$	26.2950			1.64024			0.820119	+	0.572194i	$0.193907\pi$
$258$	13.7160	−	11.7376i	0.853922	−	0.730751i
$259$	2.89958	−	1.02261i	0.180171	−	0.0635417i
$260$	−0.542666	−	1.27112i	−0.0336547	−	0.0788316i
$261$	2.86437	−	17.1030i	0.177300	−	1.05865i
$262$	−26.3155	−	5.08697i	−1.62578	−	0.314274i
$263$	−15.9101	−	15.9101i	−0.981058	−	0.981058i	0.0187658	−	0.999824i	$-0.494026\pi$
$263$	−15.9101	−	15.9101i	−0.981058	−	0.981058i	−0.999824	+	0.0187658i	$0.994026\pi$
$264$	−16.4696	−	8.14906i	−1.01363	−	0.501540i
$265$	3.91436	−	3.91436i	0.240458	−	0.240458i
$266$	−1.39743	+	5.59885i	−0.0856819	+	0.343287i
$267$	−11.3300	+	14.2418i	−0.693383	+	0.871584i
$268$	27.9899	−	0.302187i	1.70975	−	0.0184590i
$269$	3.36051	−	8.11298i	0.204894	−	0.494657i	−0.787711	−	0.616044i	$-0.788734\pi$
$269$	3.36051	−	8.11298i	0.204894	−	0.494657i	0.992605	+	0.121387i	$0.0387342\pi$
$270$	7.39387	+	5.46159i	0.449977	+	0.332382i
$271$	−18.9636			−1.15196			−0.575979	−	0.817465i	$-0.695379\pi$
$271$	−18.9636			−1.15196			−0.575979	+	0.817465i	$0.695379\pi$
$272$	7.32967	+	7.01979i	0.444427	+	0.425637i
$273$	0.827438	−	2.39257i	0.0500789	−	0.144805i
$274$	11.7084	−	17.7293i	0.707332	−	1.07107i
$275$	11.9042	+	4.93089i	0.717851	+	0.297344i
$276$	2.75736	−	10.0207i	0.165974	−	0.603173i
$277$	8.04436	−	3.33208i	0.483339	−	0.200205i	−0.127690	−	0.991814i	$-0.540756\pi$
$277$	8.04436	−	3.33208i	0.483339	−	0.200205i	0.611028	+	0.791609i	$0.290756\pi$
$278$	−10.9485	−	16.1956i	−0.656646	−	0.971349i
$279$	−5.61325	−	24.3282i	−0.336056	−	1.45649i
$280$	5.48845	−	7.58319i	0.327997	−	0.453182i
$281$	−12.1142	−	12.1142i	−0.722674	−	0.722674i	0.246475	−	0.969149i	$-0.420728\pi$
$281$	−12.1142	−	12.1142i	−0.722674	−	0.722674i	−0.969149	+	0.246475i	$0.920728\pi$
$282$	−1.18586	−	3.63771i	−0.0706171	−	0.216622i
$283$	5.74249	−	2.37862i	0.341356	−	0.141394i	−0.205419	−	0.978674i	$-0.565856\pi$
$283$	5.74249	−	2.37862i	0.341356	−	0.141394i	0.546774	+	0.837280i	$0.315856\pi$
$284$	−1.87194	−	0.751810i	−0.111079	−	0.0446117i
$285$	−0.378054	−	3.32007i	−0.0223940	−	0.196664i
$286$	−0.587206	−	2.87100i	−0.0347222	−	0.169766i
$287$	−15.0961	+	13.5576i	−0.891097	+	0.800279i
$288$	−5.58416	+	16.0255i	−0.329050	+	0.944313i
$289$	10.5624			0.621318
$290$	10.0185	−	2.04908i	0.588305	−	0.120326i
$291$	1.07529	+	9.44322i	0.0630348	+	0.553572i
$292$	1.59359	−	3.96790i	0.0932581	−	0.232204i
$293$	−5.12453	−	12.3717i	−0.299378	−	0.722763i	−0.999958	−	0.00918885i	$-0.997075\pi$
$293$	−5.12453	−	12.3717i	−0.299378	−	0.722763i	0.700579	−	0.713574i	$-0.252925\pi$
$294$	16.7774	−	3.53814i	0.978479	−	0.206349i
$295$	−9.73714	+	9.73714i	−0.566918	+	0.566918i
$296$	−2.76217	−	1.78161i	−0.160548	−	0.103554i
$297$	13.0385	+	14.4865i	0.756573	+	0.840591i
$298$	6.10998	+	9.03824i	0.353942	+	0.523571i
$299$	1.53129	−	0.634280i	0.0885566	−	0.0366814i
$300$	3.15714	−	11.4735i	0.182277	−	0.662423i
$301$	6.48536	+	18.3891i	0.373810	+	1.05993i
$302$	−16.8756	−	11.1446i	−0.971083	−	0.641302i
$303$	−11.6562	−	21.0315i	−0.669629	−	1.20823i
$304$	5.64715	−	2.48329i	0.323886	−	0.142427i
$305$	3.05448			0.174899
$306$	−4.47286	−	9.79134i	−0.255696	−	0.559733i
$307$	6.66865	+	2.76225i	0.380600	+	0.157650i	0.564777	−	0.825243i	$-0.308962\pi$
$307$	6.66865	+	2.76225i	0.380600	+	0.157650i	−0.184177	+	0.982893i	$0.558962\pi$
$308$	14.6227	−	13.4204i	0.833206	−	0.764699i
$309$	22.7705	+	18.1149i	1.29537	+	1.03052i
$310$	12.1973	−	8.24557i	0.692761	−	0.468317i
$311$	15.0866	+	15.0866i	0.855482	+	0.855482i	0.990802	−	0.135320i	$-0.0432062\pi$
$311$	15.0866	+	15.0866i	0.855482	+	0.855482i	−0.135320	+	0.990802i	$0.543206\pi$
$312$	−2.56392	+	0.866548i	−0.145154	+	0.0490586i
$313$	−4.50825	−	4.50825i	−0.254821	−	0.254821i	0.568123	−	0.822944i	$-0.307670\pi$
$313$	−4.50825	−	4.50825i	−0.254821	−	0.254821i	−0.822944	+	0.568123i	$0.807670\pi$
$314$	6.52931	−	33.7770i	0.368471	−	1.90614i
$315$	−8.38141	+	5.32290i	−0.472239	+	0.299911i
$316$	10.2482	+	24.0050i	0.576506	+	1.35039i
$317$	1.27147	−	3.06960i	0.0714128	−	0.172406i	−0.884143	−	0.467217i	$-0.845257\pi$
$317$	1.27147	−	3.06960i	0.0714128	−	0.172406i	0.955556	+	0.294811i	$0.0952567\pi$
$318$	−7.04793	−	8.23589i	−0.395228	−	0.461846i
$319$	21.6815			1.21393
$320$	−10.0021	+	0.324057i	−0.559132	+	0.0181153i
$321$	4.84780	+	8.74701i	0.270578	+	0.488211i
$322$	9.02231	+	6.67963i	0.502793	+	0.372241i
$323$	−1.49747	+	3.61522i	−0.0833216	+	0.201156i
$324$	11.7845	−	13.6061i	0.654694	−	0.755894i
$325$	1.75330	−	0.726241i	0.0972556	−	0.0402846i
$326$	2.68470	+	0.518971i	0.148692	+	0.0287432i
$327$	−4.59478	+	16.0199i	−0.254092	+	0.885905i
$328$	21.3403	+	3.88672i	1.17832	+	0.214608i
$329$	4.12674	+	0.221584i	0.227514	+	0.0122163i
$330$	−5.20779	+	10.2454i	−0.286679	+	0.563991i
$331$	−14.2486	+	5.90198i	−0.783176	+	0.324402i	−0.738196	−	0.674586i	$-0.764322\pi$
$331$	−14.2486	+	5.90198i	−0.783176	+	0.324402i	−0.0449794	+	0.998988i	$0.514322\pi$
$332$	0.0242095	+	2.24238i	0.00132867	+	0.123067i
$333$	2.02413	+	2.83851i	0.110921	+	0.155549i
$334$	17.0807	−	25.8643i	0.934615	−	1.41523i
$335$		−	17.5075i		−	0.956534i
$336$	−13.9716	−	11.8656i	−0.762215	−	0.647324i
$337$		−	28.1935i		−	1.53580i	−0.640571	−	0.767899i	$-0.721302\pi$
$337$		−	28.1935i		−	1.53580i	0.640571	−	0.767899i	$-0.278698\pi$
$338$	14.9811	+	9.89352i	0.814866	+	0.538137i
$339$	−4.01222	+	0.456868i	−0.217914	+	0.0248137i
$340$	4.43981	−	4.53672i	0.240782	−	0.246038i
$341$	28.8402	−	11.9460i	1.56178	−	0.646912i
$342$	−6.53906	+	0.234266i	−0.353592	+	0.0126676i
$343$	−2.96761	+	18.2810i	−0.160236	+	0.987079i
$344$	11.2989	−	17.5176i	0.609198	−	0.944488i
$345$	−6.24850	−	1.79217i	−0.336408	−	0.0964873i
$346$	−0.520638	+	2.69333i	−0.0279897	+	0.144794i
$347$	2.14020	−	0.886501i	0.114892	−	0.0475899i	−0.324497	−	0.945887i	$-0.605195\pi$
$347$	2.14020	−	0.886501i	0.114892	−	0.0475899i	0.439389	+	0.898297i	$0.355195\pi$
$348$	−2.48012	−	19.8697i	−0.132948	−	1.06513i
$349$	−3.98800	+	9.62788i	−0.213473	+	0.515369i	−0.993952	−	0.109812i	$-0.964975\pi$
$349$	−3.98800	+	9.62788i	−0.213473	+	0.515369i	0.780480	+	0.625181i	$0.214975\pi$
$350$	10.3304	+	7.64807i	0.552183	+	0.408806i
$351$	2.86661	+	0.150797i	0.153008	+	0.00804896i
$352$	−20.9145	−	3.57634i	−1.11475	−	0.190619i
$353$	−13.5602			−0.721735			−0.360868	−	0.932617i	$-0.617519\pi$
$353$	−13.5602			−0.721735			−0.360868	+	0.932617i	$0.617519\pi$
$354$	17.5320	+	20.4871i	0.931816	+	1.08888i
$355$	−0.482837	+	1.16567i	−0.0256263	+	0.0618674i
$356$	−7.83172	+	19.5003i	−0.415080	+	1.03351i
$357$	11.6064	−	0.694163i	0.614274	−	0.0367390i
$358$	−17.5189	−	3.38653i	−0.925905	−	0.178984i
$359$	−12.5317	−	12.5317i	−0.661396	−	0.661396i	0.294313	−	0.955709i	$-0.404909\pi$
$359$	−12.5317	−	12.5317i	−0.661396	−	0.661396i	−0.955709	+	0.294313i	$0.904909\pi$
$360$	9.98497	+	3.60065i	0.526254	+	0.189771i
$361$	−11.7531	−	11.7531i	−0.618586	−	0.618586i
$362$	6.31897	+	9.34738i	0.332118	+	0.491287i
$363$	−3.30931	+	4.15982i	−0.173694	+	0.218334i
$364$	0.125215	−	2.92056i	0.00656305	−	0.153079i
$365$	−2.47085	−	1.02346i	−0.129330	−	0.0535702i
$366$	0.463497	−	5.96317i	0.0242274	−	0.311700i
$367$	−30.5123			−1.59273			−0.796363	−	0.604818i	$-0.793246\pi$
$367$	−30.5123			−1.59273			−0.796363	+	0.604818i	$0.793246\pi$
$368$	−0.259101	−	11.9981i	−0.0135066	−	0.625446i
$369$	−19.5096	−	12.1945i	−1.01563	−	0.634821i
$370$	−1.13291	+	1.71549i	−0.0588970	+	0.0891839i
$371$	11.0418	−	3.89418i	0.573264	−	0.202176i
$372$	−14.2467	−	25.0637i	−0.738659	−	1.29949i
$373$	21.6843	−	8.98192i	1.12277	−	0.465066i	0.257452	−	0.966291i	$-0.417117\pi$
$373$	21.6843	−	8.98192i	1.12277	−	0.465066i	0.865317	+	0.501225i	$0.167117\pi$
$374$	11.1501	−	7.53763i	0.576558	−	0.389762i
$375$	−17.5678	−	5.03873i	−0.907197	−	0.260199i
$376$	−2.51368	−	3.63322i	−0.129633	−	0.187369i
$377$	2.25803	−	2.25803i	0.116295	−	0.116295i
$378$	9.11993	+	17.1705i	0.469078	+	0.883156i
$379$	−8.36733	−	20.2005i	−0.429801	−	1.03763i	−0.979350	−	0.202170i	$-0.935201\pi$
$379$	−8.36733	−	20.2005i	−0.429801	−	1.03763i	0.549549	−	0.835461i	$-0.314799\pi$
$380$	−1.51497	−	3.54861i	−0.0777163	−	0.182040i
$381$	−1.37117	+	0.156134i	−0.0702472	+	0.00799900i
$382$	0.151149	+	0.739007i	0.00773346	+	0.0378109i
$383$	−24.4600			−1.24985			−0.624924	−	0.780686i	$-0.714870\pi$
$383$	−24.4600			−1.24985			−0.624924	+	0.780686i	$0.714870\pi$
$384$	−0.885100	+	19.5759i	−0.0451676	+	0.998979i
$385$	−8.29465	−	9.23595i	−0.422735	−	0.470708i
$386$	20.9081	−	4.27632i	1.06419	−	0.217659i
$387$	−18.0017	+	12.8370i	−0.915080	+	0.652540i
$388$	4.30900	+	10.0932i	0.218756	+	0.512407i
$389$	−6.48661	+	2.68684i	−0.328884	+	0.136228i	−0.541015	−	0.841013i	$-0.681960\pi$
$389$	−6.48661	+	2.68684i	−0.328884	+	0.136228i	0.212131	+	0.977241i	$0.431960\pi$
$390$	0.524644	+	1.60938i	0.0265664	+	0.0814941i
$391$	5.38272	+	5.38272i	0.272216	+	0.272216i
$392$	17.3946	−	9.45661i	0.878561	−	0.477631i
$393$	31.5542	+	9.05027i	1.59170	+	0.456526i
$394$	2.66822	−	1.80375i	0.134423	−	0.0908718i
$395$	15.0824	−	6.24734i	0.758879	−	0.314338i
$396$	19.2116	+	11.7217i	0.965418	+	0.589038i
$397$	3.78913	+	1.56951i	0.190171	+	0.0787713i	0.475737	−	0.879588i	$-0.342182\pi$
$397$	3.78913	+	1.56951i	0.190171	+	0.0787713i	−0.285566	+	0.958359i	$0.592182\pi$
$398$	14.6944	+	9.70419i	0.736566	+	0.486427i
$399$	2.30997	−	6.67936i	0.115643	−	0.334386i
$400$	−0.296667	−	13.7377i	−0.0148334	−	0.686883i
$401$	−8.99760			−0.449318			−0.224659	−	0.974437i	$-0.572127\pi$
$401$	−8.99760			−0.449318			−0.224659	+	0.974437i	$0.572127\pi$
$402$	−34.1793	−	2.65664i	−1.70471	−	0.132501i
$403$	1.75945	−	4.24770i	0.0876446	−	0.211593i
$404$	−19.8439	−	19.4200i	−0.987273	−	0.966183i
$405$	−8.42995	−	7.46213i	−0.418888	−	0.370796i
$406$	20.9845	+	5.23758i	1.04145	+	0.259937i
$407$	−3.08218	+	3.08218i	−0.152778	+	0.152778i
$408$	−8.18321	−	9.35614i	−0.405129	−	0.463198i
$409$	15.8101	+	15.8101i	0.781759	+	0.781759i	0.980127	−	0.198369i	$-0.0635644\pi$
$409$	15.8101	+	15.8101i	0.781759	+	0.781759i	−0.198369	+	0.980127i	$0.563564\pi$
$410$	2.57493	−	13.3204i	0.127167	−	0.657849i
$411$	−16.2002	+	20.3637i	−0.799095	+	1.00447i
$412$	31.1780	+	12.5217i	1.53603	+	0.616902i
$413$	−27.4671	+	9.68694i	−1.35157	+	0.476663i
$414$	−4.44698	+	11.9268i	−0.218557	+	0.586172i
$415$	1.40259			0.0688506
$416$	−2.55061	+	1.80569i	−0.125054	+	0.0885314i
$417$	11.6063	+	20.9415i	0.568361	+	1.02551i
$418$	−1.63931	−	8.01502i	−0.0801814	−	0.392028i
$419$	12.0738	+	5.00115i	0.589846	+	0.244322i	0.657584	−	0.753381i	$-0.271578\pi$
$419$	12.0738	+	5.00115i	0.589846	+	0.244322i	−0.0677386	+	0.997703i	$0.521578\pi$
$420$	−7.51535	+	8.65801i	−0.366712	+	0.422468i
$421$	1.69838	+	4.10026i	0.0827742	+	0.199834i	0.959848	−	0.280522i	$-0.0905074\pi$
$421$	1.69838	+	4.10026i	0.0827742	+	0.199834i	−0.877074	+	0.480356i	$0.840507\pi$
$422$	1.48958	−	7.70580i	0.0725118	−	0.375112i
$423$	1.05353	+	4.56606i	0.0512243	+	0.222009i
$424$	−10.5186	−	6.78454i	−0.510829	−	0.329486i
$425$	6.16313	+	6.16313i	0.298956	+	0.298956i
$426$	2.20244	+	1.11951i	0.106709	+	0.0542405i
$427$	5.82748	+	2.78875i	0.282011	+	0.134957i
$428$	8.25310	+	8.07680i	0.398929	+	0.390407i
$429$	0.406057	+	3.56600i	0.0196046	+	0.172168i
$430$	−10.8796	−	7.18487i	−0.524660	−	0.346485i
$431$	−26.5189			−1.27737			−0.638686	−	0.769467i	$-0.720522\pi$
$431$	−26.5189			−1.27737			−0.638686	+	0.769467i	$0.720522\pi$
$432$	8.54461	−	18.9470i	0.411103	−	0.911589i
$433$	10.3069			0.495320			0.247660	−	0.968847i	$-0.420338\pi$
$433$	10.3069			0.495320			0.247660	+	0.968847i	$0.420338\pi$
$434$	30.7989	−	4.59509i	1.47839	−	0.220571i
$435$	−12.4437	+	1.41695i	−0.596628	+	0.0679377i
$436$	0.207753	+	19.2429i	0.00994957	+	0.921570i
$437$	4.27492	−	1.77073i	0.204497	−	0.0847054i
$438$	−2.37300	+	4.66846i	−0.113387	+	0.223068i
$439$	−0.658500	+	0.658500i	−0.0314285	+	0.0314285i	−0.722646	−	0.691218i	$-0.757074\pi$
$439$	−0.658500	+	0.658500i	−0.0314285	+	0.0314285i	0.691218	+	0.722646i	$0.257074\pi$
$440$	−2.37793	+	13.0562i	−0.113363	+	0.622430i
$441$	−20.8503	+	2.50302i	−0.992871	+	0.119191i
$442$	0.376222	−	1.94624i	0.0178951	−	0.0925734i
$443$	32.4562	−	13.4438i	1.54204	−	0.638735i	0.560187	−	0.828366i	$-0.310729\pi$
$443$	32.4562	−	13.4438i	1.54204	−	0.638735i	0.981855	+	0.189632i	$0.0607294\pi$
$444$	3.17719	+	2.47206i	0.150783	+	0.117319i
$445$	12.1430	+	5.02978i	0.575632	+	0.238435i
$446$	5.86593	+	28.6801i	0.277760	+	1.35804i
$447$	−6.47707	−	11.6867i	−0.306355	−	0.552764i
$448$	−19.3783	−	8.51367i	−0.915537	−	0.402233i
$449$		−	10.4224i		−	0.491864i	−0.969287	−	0.245932i	$-0.920906\pi$
$449$		−	10.4224i		−	0.491864i	0.969287	−	0.245932i	$-0.0790941\pi$
$450$	−5.09172	+	13.6560i	−0.240026	+	0.643752i
$451$	11.0081	−	26.5759i	0.518352	−	1.25141i
$452$	−4.28840	+	1.83080i	−0.201709	+	0.0861135i
$453$	19.3831	+	15.4201i	0.910698	+	0.724499i
$454$	−35.6571	−	6.89277i	−1.67347	−	0.323494i
$455$	−1.82573	−	0.0980323i	−0.0855917	−	0.00459583i
$456$	−7.15774	+	2.41915i	−0.335192	+	0.113287i
$457$	22.4740	+	22.4740i	1.05129	+	1.05129i	0.998612	+	0.0526789i	$0.0167760\pi$
$457$	22.4740	+	22.4740i	1.05129	+	1.05129i	0.0526789	+	0.998612i	$0.483224\pi$
$458$	2.21098	−	1.49466i	0.103312	−	0.0698407i
$459$	4.39843	+	12.4285i	0.205301	+	0.580115i
$460$	−7.50562	+	0.0810331i	−0.349951	+	0.00377819i
$461$	−14.3504	+	34.6450i	−0.668366	+	1.61358i	0.115978	+	0.993252i	$0.463000\pi$
$461$	−14.3504	+	34.6450i	−0.668366	+	1.61358i	−0.784344	+	0.620326i	$0.787000\pi$
$462$	−19.2898	+	14.7919i	−0.897441	+	0.688183i
$463$		−	15.1442i		−	0.703811i	−0.936035	−	0.351906i	$-0.885534\pi$
$463$		−	15.1442i		−	0.703811i	0.936035	−	0.351906i	$-0.114466\pi$
$464$	−9.30740	−	21.1656i	−0.432085	−	0.982588i
$465$	−15.7715	+	8.74096i	−0.731388	+	0.405352i
$466$	21.7242	−	32.8956i	1.00635	−	1.52386i
$467$	−7.88405	+	19.0338i	−0.364830	+	0.880778i	0.629749	+	0.776799i	$0.283158\pi$
$467$	−7.88405	+	19.0338i	−0.364830	+	0.880778i	−0.994579	+	0.103980i	$0.966842\pi$
$468$	3.22156	−	0.780036i	0.148917	−	0.0360572i
$469$	15.9844	−	33.4016i	0.738090	−	1.54234i
$470$	−2.28926	+	1.54758i	−0.105596	+	0.0713844i
$471$	−11.6163	+	40.5010i	−0.535253	+	1.86619i
$472$	26.1655	+	16.8768i	1.20436	+	0.776818i
$473$	−19.5471	−	19.5471i	−0.898778	−	0.898778i
$474$	−9.90786	−	30.3930i	−0.455083	−	1.39600i
$475$	4.89471	−	2.02746i	0.224585	−	0.0930261i
$476$	12.6125	−	4.60181i	0.578094	−	0.210924i
$477$	7.70806	+	10.8093i	0.352928	+	0.494923i
$478$	−31.6716	+	6.47779i	−1.44863	+	0.296287i
$479$	23.1194			1.05635			0.528177	−	0.849135i	$-0.322876\pi$
$479$	23.1194			1.05635			0.528177	+	0.849135i	$0.322876\pi$
$480$	12.2372	+	0.685740i	0.558549	+	0.0312996i
$481$			0.641990i			0.0292722i
$482$	22.9159	−	4.68700i	1.04379	−	0.213487i
$483$	−10.2849	−	9.12410i	−0.467981	−	0.415161i
$484$	−2.28753	+	5.69574i	−0.103979	+	0.258897i
$485$	6.34161	−	2.62678i	0.287958	−	0.119276i
$486$	−15.8473	+	15.3252i	−0.718848	+	0.695167i
$487$	−28.5972	+	28.5972i	−1.29586	+	1.29586i	−0.364760	+	0.931102i	$0.618849\pi$
$487$	−28.5972	+	28.5972i	−1.29586	+	1.29586i	−0.931102	+	0.364760i	$0.881151\pi$
$488$	−1.45689	−	6.75103i	−0.0659504	−	0.305605i
$489$	−3.21915	−	0.923305i	−0.145575	−	0.0417533i
$490$	−5.79690	−	10.9428i	−0.261877	−	0.494345i
$491$	3.30941	+	7.98962i	0.149351	+	0.360566i	0.980795	−	0.195044i	$-0.0624848\pi$
$491$	3.30941	+	7.98962i	0.149351	+	0.360566i	−0.831443	+	0.555610i	$0.812485\pi$
$492$	−25.6144	−	7.04825i	−1.15479	−	0.317760i
$493$	13.5499	+	5.61255i	0.610256	+	0.252776i
$494$	−1.00546	−	0.664002i	−0.0452376	−	0.0298748i
$495$	7.46071	−	11.9362i	0.335334	−	0.536490i
$496$	−24.0422	−	23.0258i	−1.07953	−	1.03389i
$497$	−1.98544	+	1.78309i	−0.0890592	+	0.0799826i
$498$	0.212835	−	2.73825i	0.00953734	−	0.122704i
$499$	13.6511	−	32.9567i	0.611107	−	1.47534i	−0.250679	−	0.968070i	$-0.580654\pi$
$499$	13.6511	−	32.9567i	0.611107	−	1.47534i	0.861786	−	0.507272i	$-0.169346\pi$
$500$	−21.1022	+	0.227826i	−0.943720	+	0.0101887i
$501$	−23.6335	+	29.7073i	−1.05586	+	1.32723i
$502$	−13.4168	−	19.8469i	−0.598820	−	0.885808i
$503$	−21.1291	−	21.1291i	−0.942099	−	0.942099i	0.0563141	−	0.998413i	$-0.482065\pi$
$503$	−21.1291	−	21.1291i	−0.942099	−	0.942099i	−0.998413	+	0.0563141i	$0.982065\pi$
$504$	15.7624	+	15.9858i	0.702113	+	0.712065i
$505$	−12.2797	+	12.2797i	−0.546438	+	0.546438i
$506$	−15.6255	−	3.02052i	−0.694639	−	0.134278i
$507$	−17.2071	−	13.6890i	−0.764196	−	0.607950i
$508$	−1.46555	+	0.625673i	−0.0650235	+	0.0277598i
$509$	4.53224	+	1.87732i	0.200888	+	0.0832106i	0.480859	−	0.876798i	$-0.340325\pi$
$509$	4.53224	+	1.87732i	0.200888	+	0.0832106i	−0.279971	+	0.960008i	$0.590325\pi$
$510$	−5.90677	+	5.05477i	−0.261556	+	0.223829i
$511$	−3.77958	−	4.20850i	−0.167199	−	0.186173i
$512$	5.48691	+	21.9521i	0.242489	+	0.970154i
$513$	8.00275	+	0.420983i	0.353330	+	0.0185868i
$514$	−36.4325	+	7.45154i	−1.60697	+	0.328673i
$515$	8.04186	−	19.4148i	0.354367	−	0.855517i
$516$	−15.6777	+	20.1497i	−0.690174	+	0.887040i
$517$	−5.41289	+	2.24209i	−0.238059	+	0.0986072i
$518$	−3.72766	+	2.23854i	−0.163784	+	0.0983559i
$519$	0.926271	−	3.22949i	0.0406588	−	0.141759i
$520$	1.11209	+	1.60740i	0.0487685	+	0.0704890i
$521$	3.21528	+	3.21528i	0.140864	+	0.140864i	0.774022	−	0.633158i	$-0.218242\pi$
$521$	3.21528	+	3.21528i	0.140864	+	0.140864i	−0.633158	+	0.774022i	$0.718242\pi$
$522$	0.878030	+	24.5085i	0.0384303	+	1.07271i
$523$	17.1222	+	41.3367i	0.748703	+	1.80753i	0.566090	+	0.824344i	$0.308456\pi$
$523$	17.1222	+	41.3367i	0.748703	+	1.80753i	0.182613	+	0.983185i	$0.441544\pi$
$524$	37.9025	−	0.409208i	1.65578	−	0.0178763i
$525$	−11.7761	−	10.4470i	−0.513951	−	0.455942i
$526$	26.5526	+	17.5353i	1.15775	+	0.764574i
$527$	21.1161			0.919831
$528$	25.1284	+	6.62357i	1.09358	+	0.288254i
$529$			13.9986i			0.608635i
$530$	−4.31421	+	6.53273i	−0.187397	+	0.283764i
$531$	−19.1741	−	26.8886i	−0.832085	−	1.16686i
$532$	0.349565	−	8.15338i	0.0151555	−	0.353494i
$533$	−1.62132	−	3.91421i	−0.0702271	−	0.169543i
$534$	11.6621	−	22.9432i	0.504670	−	0.992848i
$535$	5.10712	−	5.10712i	0.220800	−	0.220800i
$536$	−38.6952	+	8.35052i	−1.67138	+	0.360688i
$537$	21.0065	+	6.02500i	0.906496	+	0.259998i
$538$	−2.35701	+	12.1931i	−0.101618	+	0.525682i
$539$	−7.39248	−	25.1939i	−0.318416	−	1.08518i
$540$	−11.7921	−	5.47191i	−0.507453	−	0.235473i
$541$	−34.6837	−	14.3664i	−1.49117	−	0.617662i	−0.519597	−	0.854412i	$-0.673918\pi$
$541$	−34.6837	−	14.3664i	−1.49117	−	0.617662i	−0.971571	+	0.236750i	$0.923918\pi$
$542$	26.2747	−	5.37395i	1.12859	−	0.230831i
$543$	−6.69861	−	12.0865i	−0.287465	−	0.518680i
$544$	−12.1448	−	7.64903i	−0.520703	−	0.327950i
$545$	12.0363			0.515579
$546$	−0.468429	+	3.54946i	−0.0200469	+	0.151903i
$547$	−19.8488	−	8.22165i	−0.848674	−	0.351532i	−0.0844065	−	0.996431i	$-0.526899\pi$
$547$	−19.8488	−	8.22165i	−0.848674	−	0.351532i	−0.764268	+	0.644899i	$0.776899\pi$
$548$	−11.1982	+	27.8825i	−0.478363	+	1.19108i
$549$	−1.20998	+	7.22477i	−0.0516409	+	0.308346i
$550$	−17.8910	−	3.45845i	−0.762874	−	0.147469i
$551$	6.30378	−	6.30378i	0.268550	−	0.268550i
$552$	−0.980731	+	14.6653i	−0.0417427	+	0.624197i
$553$	34.4788	+	1.85133i	1.46619	+	0.0787266i
$554$	−10.2014	+	6.89633i	−0.433418	+	0.292997i
$555$	1.56753	−	1.97039i	0.0665378	−	0.0836382i
$556$	19.7590	+	19.3369i	0.837969	+	0.820068i
$557$	−8.62298	−	3.57176i	−0.365367	−	0.151340i	0.192444	−	0.981308i	$-0.438359\pi$
$557$	−8.62298	−	3.57176i	−0.365367	−	0.151340i	−0.557811	+	0.829968i	$0.688359\pi$
$558$	14.6715	+	32.1167i	0.621095	+	1.35961i
$559$	−4.07149			−0.172206
$560$	−5.45546	+	12.0621i	−0.230535	+	0.509716i
$561$	−14.4175	+	7.99049i	−0.608705	+	0.337359i
$562$	20.2176	+	13.3517i	0.852828	+	0.563206i
$563$	−8.99782	+	21.7227i	−0.379213	+	0.915501i	0.612901	+	0.790160i	$0.290003\pi$
$563$	−8.99782	+	21.7227i	−0.379213	+	0.915501i	−0.992114	+	0.125341i	$0.959997\pi$
$564$	2.67391	+	4.70410i	0.112592	+	0.198078i
$565$	1.11606	+	2.69441i	0.0469530	+	0.113355i
$566$	−7.28234	+	4.92297i	−0.306100	+	0.206928i
$567$	−9.27012	−	21.9332i	−0.389308	−	0.921108i
$568$	2.80668	+	0.511181i	0.117766	+	0.0214487i
$569$	25.2531	+	25.2531i	1.05867	+	1.05867i	0.998168	+	0.0604976i	$0.0192687\pi$
$569$	25.2531	+	25.2531i	1.05867	+	1.05867i	0.0604976	+	0.998168i	$0.480731\pi$
$570$	1.46466	+	4.49293i	0.0613477	+	0.188188i
$571$	−12.7571	−	30.7984i	−0.533868	−	1.28887i	−0.928943	−	0.370223i	$-0.879281\pi$
$571$	−12.7571	−	30.7984i	−0.533868	−	1.28887i	0.395074	−	0.918649i	$-0.370719\pi$
$572$	1.62718	+	3.81146i	0.0680360	+	0.159365i
$573$	−0.104521	−	0.917900i	−0.00436641	−	0.0383458i
$574$	17.0742	−	23.0624i	0.712663	−	0.962607i
$575$		−	10.3064i		−	0.429809i
$576$	3.19567	−	23.7863i	0.133153	−	0.991096i
$577$			10.6776i			0.444514i	0.974988	+	0.222257i	$0.0713424\pi$
$577$			10.6776i			0.444514i	−0.974988	+	0.222257i	$0.928658\pi$
$578$	−14.6345	+	2.99320i	−0.608716	+	0.124501i
$579$	−25.9693	+	2.95711i	−1.07925	+	0.122893i
$580$	−13.3002	+	5.67812i	−0.552262	+	0.235771i
$581$	2.67594	+	1.28057i	0.111017	+	0.0531272i
$582$	−4.16590	−	12.7792i	−0.172682	−	0.529713i
$583$	−11.7372	+	11.7372i	−0.486106	+	0.486106i
$584$	−1.08354	+	5.94925i	−0.0448372	+	0.246182i
$585$	−0.466097	−	2.02010i	−0.0192707	−	0.0835207i
$586$	10.6061	+	15.6892i	0.438135	+	0.648114i
$587$	7.91089	−	3.27680i	0.326517	−	0.135248i	−0.213402	−	0.976964i	$-0.568455\pi$
$587$	7.91089	−	3.27680i	0.326517	−	0.135248i	0.539920	+	0.841716i	$0.318455\pi$
$588$	−22.2430	+	9.65663i	−0.917284	+	0.398233i
$589$	4.91189	−	11.8584i	0.202391	−	0.488615i
$590$	10.7318	−	16.2504i	0.441820	−	0.669020i
$591$	−3.45009	+	1.91212i	−0.141918	+	0.0786542i
$592$	4.33195	+	1.68572i	0.178042	+	0.0692828i
$593$		−	14.4741i		−	0.594381i	−0.954818	−	0.297190i	$-0.903950\pi$
$593$		−	14.4741i		−	0.594381i	0.954818	−	0.297190i	$-0.0960496\pi$
$594$	−22.1705	−	16.3766i	−0.909667	−	0.671939i
$595$	−2.79290	−	7.91920i	−0.114498	−	0.324656i
$596$	−11.0268	−	10.7913i	−0.451677	−	0.442028i
$597$	−16.8778	−	13.4270i	−0.690764	−	0.549532i
$598$	−1.94190	+	1.31275i	−0.0794102	+	0.0536825i
$599$	30.0560	−	30.0560i	1.22806	−	1.22806i	0.263359	−	0.964698i	$-0.415170\pi$
$599$	30.0560	−	30.0560i	1.22806	−	1.22806i	0.964698	−	0.263359i	$-0.0848302\pi$
$600$	−1.12292	+	16.7916i	−0.0458431	+	0.685512i
$601$	1.47409	+	1.47409i	0.0601295	+	0.0601295i	0.736532	−	0.676403i	$-0.236462\pi$
$601$	1.47409	+	1.47409i	0.0601295	+	0.0601295i	−0.676403	+	0.736532i	$0.736462\pi$
$602$	−14.1968	−	23.6408i	−0.578618	−	0.963525i
$603$	41.4105	+	6.93531i	1.68637	+	0.282428i
$604$	26.5399	+	10.6590i	1.07989	+	0.433708i
$605$	3.54678	+	1.46912i	0.144197	+	0.0597284i
$606$	22.1099	+	25.8366i	0.898154	+	1.04954i
$607$			33.6523i			1.36590i	0.730464	+	0.682951i	$0.239304\pi$
$607$			33.6523i			1.36590i	−0.730464	+	0.682951i	$0.760696\pi$
$608$	−7.12058	+	5.04098i	−0.288778	+	0.204439i
$609$	−25.0343	−	8.65780i	−1.01444	−	0.350832i
$610$	−4.23207	+	0.865585i	−0.171351	+	0.0350465i
$611$	−0.330224	+	0.797232i	−0.0133595	+	0.0322526i
$612$	8.97197	+	12.2987i	0.362671	+	0.497144i
$613$	15.7692	+	38.0702i	0.636912	+	1.53764i	0.830773	+	0.556612i	$0.187899\pi$
$613$	15.7692	+	38.0702i	0.636912	+	1.53764i	−0.193861	+	0.981029i	$0.562101\pi$
$614$	−10.0224	−	1.93740i	−0.404471	−	0.0781870i
$615$	−4.58107	+	15.9722i	−0.184727	+	0.644059i
$616$	−16.4571	+	22.7382i	−0.663076	+	0.916148i
$617$	−7.22653	+	7.22653i	−0.290929	+	0.290929i	−0.837447	−	0.546518i	$-0.815953\pi$
$617$	−7.22653	+	7.22653i	−0.290929	+	0.290929i	0.546518	+	0.837447i	$0.315953\pi$
$618$	−36.6827	−	18.6460i	−1.47559	−	0.750052i
$619$	−4.82174	−	11.6407i	−0.193802	−	0.467879i	0.796869	−	0.604152i	$-0.206488\pi$
$619$	−4.82174	−	11.6407i	−0.193802	−	0.467879i	−0.990671	+	0.136272i	$0.956488\pi$
$620$	−14.5631	+	14.8810i	−0.584868	+	0.597635i
$621$	6.71428	−	14.0697i	0.269435	−	0.564597i
$622$	−25.1782	−	16.6277i	−1.00955	−	0.666708i
$623$	18.5747	+	20.6827i	0.744181	+	0.828633i
$624$	3.30683	−	1.92720i	0.132379	−	0.0771497i
$625$		−	3.97681i		−	0.159072i
$626$	7.52387	+	4.96875i	0.300714	+	0.198591i
$627$	1.13360	+	9.95524i	0.0452715	+	0.397574i
$628$	0.525233	+	48.6493i	0.0209591	+	1.94132i
$629$	−2.72407	+	1.12835i	−0.108616	+	0.0449902i
$630$	10.1043	−	9.75018i	0.402564	−	0.388457i
$631$	−16.5810	−	16.5810i	−0.660079	−	0.660079i	0.295319	−	0.955399i	$-0.404574\pi$
$631$	−16.5810	−	16.5810i	−0.660079	−	0.660079i	−0.955399	+	0.295319i	$0.904574\pi$
$632$	−21.0018	−	30.3555i	−0.835407	−	1.20748i
$633$	−2.65013	+	9.23981i	−0.105333	+	0.367249i
$634$	−0.891789	+	4.61333i	−0.0354175	+	0.183219i
$635$	0.381413	+	0.920812i	0.0151359	+	0.0365413i
$636$	12.0990	+	9.41382i	0.479758	+	0.373282i
$637$	−3.39372	−	1.85393i	−0.134464	−	0.0734555i
$638$	−30.0404	+	6.14416i	−1.18931	+	0.243250i
$639$	−2.56590	−	1.60382i	−0.101505	−	0.0634461i
$640$	13.7663	−	3.28340i	0.544161	−	0.129788i
$641$		−	26.5111i		−	1.04713i	−0.851987	−	0.523563i	$-0.824602\pi$
$641$		−	26.5111i		−	1.04713i	0.851987	−	0.523563i	$-0.175398\pi$
$642$	−9.19552	−	10.7455i	−0.362918	−	0.424090i
$643$	4.60715	−	11.1226i	0.181688	−	0.438634i	−0.806627	−	0.591061i	$-0.798709\pi$
$643$	4.60715	−	11.1226i	0.181688	−	0.438634i	0.988315	+	0.152428i	$0.0487091\pi$
$644$	−14.3936	−	6.69806i	−0.567186	−	0.263941i
$645$	12.4961	+	9.94122i	0.492035	+	0.391435i
$646$	1.05030	−	5.43336i	0.0413237	−	0.213773i
$647$	11.9909	−	11.9909i	0.471410	−	0.471410i	−0.430961	−	0.902371i	$-0.641825\pi$
$647$	11.9909	−	11.9909i	0.471410	−	0.471410i	0.902371	+	0.430961i	$0.141825\pi$
$648$	−12.4720	+	22.1912i	−0.489948	+	0.871752i
$649$	29.1968	−	29.1968i	1.14608	−	1.14608i
$650$	−2.22345	+	1.50308i	−0.0872107	+	0.0589558i
$651$	−38.0703	+	2.27694i	−1.49209	+	0.0892403i
$652$	−3.86680	+	0.0417473i	−0.151436	+	0.00163495i
$653$	4.79271	+	1.98521i	0.187553	+	0.0776872i	0.474484	−	0.880264i	$-0.342635\pi$
$653$	4.79271	+	1.98521i	0.187553	+	0.0776872i	−0.286930	+	0.957951i	$0.592635\pi$
$654$	1.82644	−	23.4982i	0.0714193	−	0.918852i
$655$		−	23.7078i		−	0.926339i
$656$	−30.6691	+	0.662304i	−1.19743	+	0.0258586i
$657$	3.39958	−	5.43888i	0.132630	−	0.212191i
$658$	−5.78051	+	0.862434i	−0.225348	+	0.0336212i
$659$	−12.5114	−	5.18239i	−0.487375	−	0.201877i	0.125444	−	0.992101i	$-0.459965\pi$
$659$	−12.5114	−	5.18239i	−0.487375	−	0.201877i	−0.612819	+	0.790223i	$0.709965\pi$
$660$	4.31218	−	15.6711i	0.167852	−	0.609997i
$661$	12.4289	+	30.0061i	0.483430	+	1.16710i	0.957970	+	0.286869i	$0.0926144\pi$
$661$	12.4289	+	30.0061i	0.483430	+	1.16710i	−0.474540	+	0.880234i	$0.657386\pi$
$662$	18.0694	−	12.2152i	0.702287	−	0.474757i
$663$	−0.669339	+	2.33369i	−0.0259950	+	0.0906329i
$664$	−0.668994	−	3.10003i	−0.0259620	−	0.120304i
$665$	−5.09693	−	0.273678i	−0.197650	−	0.0106128i
$666$	−3.60887	−	3.35923i	−0.139841	−	0.130168i
$667$	−6.63671	−	16.0224i	−0.256974	−	0.620391i
$668$	−16.3364	+	40.6761i	−0.632073	+	1.57381i
$669$	−4.05634	−	35.6227i	−0.156827	−	1.37725i
$670$	4.96130	+	24.2571i	0.191672	+	0.937134i
$671$	−9.15885			−0.353573
$672$	22.7206	+	12.4809i	0.876467	+	0.481461i
$673$	−36.8971			−1.42228			−0.711140	−	0.703050i	$-0.751821\pi$
$673$	−36.8971			−1.42228			−0.711140	+	0.703050i	$0.751821\pi$
$674$	7.98954	+	39.0630i	0.307746	+	1.50465i
$675$	7.68775	−	16.1096i	0.295902	−	0.620057i
$676$	−23.5605	−	9.46239i	−0.906172	−	0.363938i
$677$	5.58594	+	13.4856i	0.214685	+	0.518296i	0.994132	−	0.108172i	$-0.0344999\pi$
$677$	5.58594	+	13.4856i	0.214685	+	0.518296i	−0.779447	+	0.626468i	$0.784500\pi$
$678$	5.42958	−	1.77000i	0.208522	−	0.0679763i
$679$	14.4971	+	0.778418i	0.556348	+	0.0298729i
$680$	−4.86586	+	7.54393i	−0.186597	+	0.289297i
$681$	42.7555	+	12.2630i	1.63839	+	0.469918i
$682$	−36.5737	+	24.7243i	−1.40048	+	0.946744i
$683$	−15.8783	−	38.3336i	−0.607566	−	1.46679i	−0.865640	−	0.500668i	$-0.833088\pi$
$683$	−15.8783	−	38.3336i	−0.607566	−	1.46679i	0.258074	−	0.966125i	$-0.416912\pi$
$684$	8.99368	−	2.17764i	0.343882	−	0.0832640i
$685$	17.3626	+	7.19184i	0.663392	+	0.274786i
$686$	−1.06879	−	26.1698i	−0.0408065	−	0.999167i
$687$	−2.85887	+	1.58446i	−0.109073	+	0.0604507i
$688$	−10.6908	+	27.4731i	−0.407584	+	1.04740i
$689$			2.44476i			0.0931379i
$690$	9.16536	+	0.712392i	0.348919	+	0.0271203i
$691$	39.8241	+	16.4957i	1.51498	+	0.627525i	0.976578	−	0.215164i	$-0.0690285\pi$
$691$	39.8241	+	16.4957i	1.51498	+	0.627525i	0.538401	+	0.842689i	$0.319029\pi$
$692$	−0.0418813	−	3.87922i	−0.00159209	−	0.147466i
$693$	25.1317	−	15.9607i	0.954673	−	0.606297i
$694$	−2.71410	+	1.83477i	−0.103026	+	0.0696469i
$695$	12.2271	−	12.2271i	0.463801	−	0.463801i
$696$	9.06702	+	26.8273i	0.343684	+	1.01689i
$697$	13.7591	−	13.7591i	0.521162	−	0.521162i
$698$	2.79712	−	14.4699i	0.105873	−	0.547692i
$699$	−30.0583	+	37.7834i	−1.13691	+	1.42910i
$700$	−16.4804	−	7.66918i	−0.622901	−	0.289868i
$701$	6.50656	−	15.7082i	0.245749	−	0.593292i	−0.752085	−	0.659066i	$-0.770952\pi$
$701$	6.50656	−	15.7082i	0.245749	−	0.593292i	0.997835	+	0.0657743i	$0.0209517\pi$
$702$	−4.01451	+	0.603413i	−0.151518	+	0.0227743i
$703$			1.79225i			0.0675961i
$704$	29.9912	−	0.971685i	1.13033	−	0.0366217i
$705$	2.96009	−	1.64055i	0.111484	−	0.0617868i
$706$	18.7880	−	3.84272i	0.707097	−	0.144623i
$707$	−34.6392	+	12.2164i	−1.30274	+	0.459444i
$708$	−30.0968	−	23.4173i	−1.13111	−	0.880074i
$709$	6.62663	+	15.9981i	0.248868	+	0.600821i	0.998108	−	0.0614770i	$-0.0195811\pi$
$709$	6.62663	+	15.9981i	0.248868	+	0.600821i	−0.749240	+	0.662298i	$0.769581\pi$
$710$	0.338654	−	1.75190i	0.0127095	−	0.0657476i
$711$	8.80221	+	38.1493i	0.330109	+	1.43071i
$712$	5.32505	−	29.2376i	0.199565	−	1.09572i
$713$	−17.6560	−	17.6560i	−0.661221	−	0.661221i
$714$	−15.8843	+	4.25082i	−0.594453	+	0.159083i
$715$	2.39475	−	0.991938i	0.0895585	−	0.0370964i
$716$	25.2327	−	0.272420i	0.942990	−	0.0101808i
$717$	39.3385	−	4.47944i	1.46912	−	0.167288i
$718$	20.9142	+	13.8117i	0.780513	+	0.515449i
$719$		−	24.1493i		−	0.900617i	−0.892873	−	0.450308i	$-0.851314\pi$
$719$		−	24.1493i		−	0.900617i	0.892873	−	0.450308i	$-0.148686\pi$
$720$	−14.8548	−	2.15925i	−0.553607	−	0.0804703i
$721$	33.0684	−	29.6982i	1.23153	−	1.10602i
$722$	19.6149	+	12.9537i	0.729993	+	0.482086i
$723$	−28.4633	+	3.24109i	−1.05856	+	0.120538i
$724$	−11.4040	−	11.1604i	−0.423827	−	0.414773i
$725$	−7.59893	−	18.3454i	−0.282217	−	0.681332i
$726$	3.40634	−	6.70136i	0.126421	−	0.248711i
$727$	−8.15470	+	8.15470i	−0.302441	+	0.302441i	−0.841968	−	0.539527i	$-0.818603\pi$
$727$	−8.15470	+	8.15470i	−0.302441	+	0.302441i	0.539527	+	0.841968i	$0.318603\pi$
$728$	0.654148	+	4.08202i	0.0242443	+	0.151290i
$729$	20.9896	−	16.9834i	0.777393	−	0.629015i
$730$	3.71346	+	0.717837i	0.137441	+	0.0265684i
$731$	−7.15597	−	17.2760i	−0.264673	−	0.638977i
$732$	1.04767	+	8.39350i	0.0387230	+	0.310233i
$733$	15.2009	−	36.6982i	0.561458	−	1.35548i	−0.347142	−	0.937813i	$-0.612848\pi$
$733$	15.2009	−	36.6982i	0.561458	−	1.35548i	0.908600	−	0.417668i	$-0.137152\pi$
$734$	42.2757	−	8.64664i	1.56042	−	0.319153i
$735$	5.88926	+	13.9764i	0.217229	+	0.515527i
$736$	3.75905	+	16.5503i	0.138561	+	0.610054i
$737$			52.4961i			1.93372i
$738$	30.4869	+	11.3672i	1.12224	+	0.418432i
$739$	18.2449	+	7.55728i	0.671149	+	0.277999i	0.692121	−	0.721781i	$-0.256676\pi$
$739$	18.2449	+	7.55728i	0.671149	+	0.277999i	−0.0209725	+	0.999780i	$0.506676\pi$
$740$	1.08354	−	2.69791i	0.0398316	−	0.0991770i
$741$	1.15485	+	0.918735i	0.0424246	+	0.0337506i
$742$	−14.1953	+	8.52458i	−0.521125	+	0.312947i
$743$	20.8459	+	20.8459i	0.764762	+	0.764762i	0.977179	−	0.212417i	$-0.0681336\pi$
$743$	20.8459	+	20.8459i	0.764762	+	0.764762i	−0.212417	+	0.977179i	$0.568134\pi$
$744$	26.8419	+	30.6893i	0.984072	+	1.12512i
$745$	−6.82354	+	6.82354i	−0.249995	+	0.249995i
$746$	−27.4989	+	18.5897i	−1.00681	+	0.680616i
$747$	−0.555616	+	3.31756i	−0.0203289	+	0.121383i
$748$	−13.3128	+	13.6034i	−0.486763	+	0.497388i
$749$	14.4064	−	5.08079i	0.526400	−	0.185648i
$750$	25.7686	+	2.00291i	0.940937	+	0.0731358i
$751$			22.1770i			0.809252i	0.914482	+	0.404626i	$0.132598\pi$
$751$			22.1770i			0.809252i	−0.914482	+	0.404626i	$0.867402\pi$
$752$	4.51238	+	4.32161i	0.164550	+	0.157593i
$753$	14.2228	+	25.6626i	0.518309	+	0.935199i
$754$	−2.48868	+	3.76846i	−0.0906326	+	0.137239i
$755$	6.84554	−	16.5266i	0.249135	−	0.601464i
$756$	−17.5018	−	21.2059i	−0.636533	−	0.771249i
$757$	4.50594	−	1.86642i	0.163771	−	0.0678362i	−0.299292	−	0.954162i	$-0.596750\pi$
$757$	4.50594	−	1.86642i	0.163771	−	0.0678362i	0.463063	+	0.886325i	$0.346750\pi$
$758$	17.3177	+	25.6173i	0.629006	+	0.930462i
$759$	18.7361	+	5.37383i	0.680078	+	0.195058i
$760$	3.10465	+	4.48739i	0.112617	+	0.162775i
$761$	21.1883	−	21.1883i	0.768074	−	0.768074i	−0.209693	−	0.977767i	$-0.567247\pi$
$761$	21.1883	−	21.1883i	0.768074	−	0.768074i	0.977767	+	0.209693i	$0.0672466\pi$
$762$	1.85555	−	0.604895i	0.0672196	−	0.0219130i
$763$	22.9635	+	10.9892i	0.831334	+	0.397836i
$764$	−0.418843	−	0.981083i	−0.0151532	−	0.0354943i
$765$	7.75241	−	5.52821i	0.280289	−	0.199873i
$766$	33.8901	−	6.93154i	1.22450	−	0.250447i
$767$		−	6.08144i		−	0.219588i
$768$	−4.32114	−	27.3739i	−0.155926	−	0.987769i
$769$		−	42.2407i		−	1.52324i	−0.648024	−	0.761620i	$-0.724405\pi$
$769$		−	42.2407i		−	1.52324i	0.648024	−	0.761620i	$-0.275595\pi$
$770$	14.1098	+	10.4461i	0.508482	+	0.376453i
$771$	45.2518	−	5.15280i	1.62971	−	0.185573i
$772$	−27.7569	+	11.8500i	−0.998993	+	0.426489i
$773$	−0.289948	−	0.699995i	−0.0104287	−	0.0251771i	0.918579	−	0.395236i	$-0.129337\pi$
$773$	−0.289948	−	0.699995i	−0.0104287	−	0.0251771i	−0.929008	+	0.370059i	$0.879337\pi$
$774$	21.3042	−	22.8874i	0.765764	−	0.822670i
$775$	−20.2158	−	20.2158i	−0.726173	−	0.726173i
$776$	−8.83050	−	12.7634i	−0.316996	−	0.458179i
$777$	4.78957	−	2.32804i	0.171825	−	0.0835180i
$778$	8.22600	−	5.56090i	0.294916	−	0.199368i
$779$	−4.52626	−	10.9274i	−0.162170	−	0.391513i
$780$	−1.18298	−	2.08117i	−0.0423575	−	0.0745178i
$781$	1.44779	−	3.49526i	0.0518058	−	0.125070i
$782$	−8.98329	−	5.93255i	−0.321242	−	0.212148i
$783$	1.57785	−	29.9944i	0.0563877	−	1.07191i
$784$	−21.4209	+	18.0317i	−0.765033	+	0.643991i
$785$	30.4298			1.08609
$786$	−46.2841	−	3.59750i	−1.65090	−	0.128319i
$787$	15.0203	+	6.22159i	0.535414	+	0.221776i	0.633973	−	0.773355i	$-0.281423\pi$
$787$	15.0203	+	6.22159i	0.535414	+	0.221776i	−0.0985584	+	0.995131i	$0.531423\pi$
$788$	−3.18574	+	3.25528i	−0.113487	+	0.115965i
$789$	−30.4979	−	24.2624i	−1.08575	−	0.863764i
$790$	−19.1268	+	12.9300i	−0.680500	+	0.460028i
$791$	−0.330733	+	6.15950i	−0.0117595	+	0.219006i
$792$	−29.9399	−	10.7966i	−1.06387	−	0.383639i
$793$	−0.953853	+	0.953853i	−0.0338723	+	0.0338723i
$794$	−5.69472	−	1.10083i	−0.202098	−	0.0390669i
$795$	5.96928	−	7.50341i	0.211709	−	0.266119i
$796$	−23.1096	−	9.28131i	−0.819098	−	0.328967i
$797$	−35.1908	−	14.5765i	−1.24652	−	0.516326i	−0.340775	−	0.940145i	$-0.610689\pi$
$797$	−35.1908	−	14.5765i	−1.24652	−	0.516326i	−0.905747	+	0.423819i	$0.860689\pi$
$798$	−1.30772	+	9.90907i	−0.0462928	+	0.350777i
$799$	−3.96319			−0.140208
$800$	4.30406	+	18.9499i	0.152171	+	0.669980i
$801$	−16.7072	+	26.7294i	−0.590321	+	0.944436i
$802$	12.4664	−	2.54976i	0.440205	−	0.0900352i
$803$	7.40883	+	3.06884i	0.261452	+	0.108297i
$804$	48.1093	−	6.00496i	1.69669	−	0.211779i
$805$	−4.28629	+	8.95680i	−0.151072	+	0.315686i
$806$	−1.23405	+	6.38391i	−0.0434677	+	0.224864i
$807$	4.19337	−	14.6204i	0.147614	−	0.514663i
$808$	32.9977	+	21.2836i	1.16085	+	0.748756i
$809$	−13.8688	+	13.8688i	−0.487602	+	0.487602i	−0.907549	−	0.419947i	$-0.862049\pi$
$809$	−13.8688	+	13.8688i	−0.487602	+	0.487602i	0.419947	+	0.907549i	$0.362049\pi$
$810$	13.7946	+	7.95010i	0.484692	+	0.279338i
$811$	0.757911	+	1.82976i	0.0266138	+	0.0642515i	0.936628	−	0.350326i	$-0.113929\pi$
$811$	0.757911	+	1.82976i	0.0266138	+	0.0642515i	−0.910014	+	0.414578i	$0.863929\pi$
$812$	−30.5590	−	1.31017i	−1.07241	−	0.0459780i
$813$	−32.6350	+	3.71613i	−1.14456	+	0.130330i
$814$	3.39702	−	5.14389i	0.119065	−	0.180293i
$815$			2.41866i			0.0847219i
$816$	13.9895	+	10.6442i	0.489729	+	0.372623i
$817$	−11.3664			−0.397661
$818$	−26.3857	−	17.4251i	−0.922553	−	0.609253i
$819$	0.955113	−	4.27959i	0.0333744	−	0.149541i
$820$	0.207133	+	19.1855i	0.00723341	+	0.669988i
$821$	5.45730	+	13.1751i	0.190461	+	0.459814i	0.990047	−	0.140738i	$-0.0449475\pi$
$821$	5.45730	+	13.1751i	0.190461	+	0.459814i	−0.799586	+	0.600552i	$0.794948\pi$
$822$	16.6751	−	32.8053i	0.581611	−	1.14422i
$823$	10.0798	+	10.0798i	0.351361	+	0.351361i	0.860616	−	0.509255i	$-0.170079\pi$
$823$	10.0798	+	10.0798i	0.351361	+	0.351361i	−0.509255	+	0.860616i	$0.670079\pi$
$824$	−46.7465	−	8.51395i	−1.62849	−	0.296598i
$825$	21.4526	+	6.15295i	0.746883	+	0.214218i
$826$	35.3113	−	21.2052i	1.22864	−	0.737824i
$827$	−25.8569	+	10.7103i	−0.899132	+	0.372432i	−0.783886	−	0.620905i	$-0.786765\pi$
$827$	−25.8569	+	10.7103i	−0.899132	+	0.372432i	−0.115245	+	0.993337i	$0.536765\pi$
$828$	2.78157	−	17.7852i	0.0966662	−	0.618078i
$829$	−4.21348	+	10.1722i	−0.146340	+	0.353296i	−0.980005	−	0.198975i	$-0.936239\pi$
$829$	−4.21348	+	10.1722i	−0.146340	+	0.353296i	0.833664	+	0.552271i	$0.186239\pi$
$830$	−1.94334	+	0.397470i	−0.0674542	+	0.0137964i
$831$	13.1908	−	7.31066i	0.457584	−	0.253604i
$832$	3.02225	−	3.22464i	0.104778	−	0.111794i
$833$	1.90183	−	17.6586i	0.0658944	−	0.611833i
$834$	−22.0153	−	25.7260i	−0.762327	−	0.890820i
$835$	25.3293	+	10.4918i	0.876558	+	0.363082i
$836$	4.54263	+	10.6405i	0.157110	+	0.368010i
$837$	−14.4274	−	40.7671i	−0.498683	−	1.40912i
$838$	−18.1459	−	3.50773i	−0.626840	−	0.121172i
$839$	−3.06711	+	3.06711i	−0.105889	+	0.105889i	−0.758066	−	0.652178i	$-0.773856\pi$
$839$	−3.06711	+	3.06711i	−0.105889	+	0.105889i	0.652178	+	0.758066i	$0.273856\pi$
$840$	7.95922	−	14.1257i	0.274619	−	0.487382i
$841$	−3.12053	−	3.12053i	−0.107605	−	0.107605i
$842$	−3.51510	−	5.19974i	−0.121138	−	0.179195i
$843$	−23.2217	−	18.4738i	−0.799796	−	0.636272i
$844$	0.119826	+	11.0987i	0.00412456	+	0.382034i
$845$	−6.07705	+	14.6713i	−0.209057	+	0.504708i
$846$	−2.75363	−	6.02786i	−0.0946719	−	0.207242i
$847$	5.42541	+	6.04110i	0.186419	+	0.207575i
$848$	16.4965	+	6.41939i	0.566491	+	0.220443i
$849$	9.41631	−	5.21874i	0.323167	−	0.179107i
$850$	−10.2857	−	6.79268i	−0.352797	−	0.232987i
$851$	3.22116	+	1.33425i	0.110420	+	0.0457374i
$852$	−3.36880	−	0.926985i	−0.115413	−	0.0317580i
$853$	−21.4023	−	51.6698i	−0.732802	−	1.76914i	−0.633026	−	0.774130i	$-0.718188\pi$
$853$	−21.4023	−	51.6698i	−0.732802	−	1.76914i	−0.0997756	−	0.995010i	$-0.531812\pi$
$854$	−8.86443	−	2.21249i	−0.303335	−	0.0757099i
$855$	−1.30121	−	5.63953i	−0.0445005	−	0.192868i
$856$	−13.7238	−	8.85187i	−0.469068	−	0.302551i
$857$	−28.6340	+	28.6340i	−0.978117	+	0.978117i	−0.999766	−	0.0216483i	$-0.993109\pi$
$857$	−28.6340	+	28.6340i	−0.978117	+	0.978117i	0.0216483	+	0.999766i	$0.493109\pi$
$858$	−1.57315	−	4.82573i	−0.0537063	−	0.164748i
$859$	−44.1192	+	18.2748i	−1.50533	+	0.623528i	−0.974588	−	0.224007i	$-0.928086\pi$
$859$	−44.1192	+	18.2748i	−1.50533	+	0.623528i	−0.530741	+	0.847534i	$0.678086\pi$
$860$	17.1101	+	6.87177i	0.583448	+	0.234325i
$861$	−23.3226	+	26.2899i	−0.794834	+	0.895958i
$862$	36.7428	−	7.51500i	1.25146	−	0.255962i
$863$			22.3970i			0.762403i	0.924492	+	0.381201i	$0.124490\pi$
$863$			22.3970i			0.762403i	−0.924492	+	0.381201i	$0.875510\pi$
$864$	−6.46957	+	28.6731i	−0.220099	+	0.975478i
$865$	−2.42643			−0.0825010
$866$	−14.2806	+	2.92081i	−0.485274	+	0.0992530i
$867$	18.1772	−	2.06982i	0.617329	−	0.0702948i
$868$	−41.3706	+	15.0945i	−1.40421	+	0.512341i
$869$	−45.2246	+	18.7327i	−1.53414	+	0.635462i
$870$	16.8395	−	5.48955i	0.570914	−	0.186113i
$871$	5.46723	+	5.46723i	0.185250	+	0.185250i
$872$	−5.74096	−	26.6028i	−0.194414	−	0.900885i
$873$	3.70101	+	16.0404i	0.125260	+	0.542886i
$874$	−5.42123	+	3.66483i	−0.183376	+	0.123965i
$875$	−12.0510	+	25.1822i	−0.407398	+	0.851315i
$876$	1.96491	−	7.14077i	0.0663881	−	0.241264i
$877$	5.09322	−	12.2961i	0.171986	−	0.415211i	−0.814259	−	0.580502i	$-0.802856\pi$
$877$	5.09322	−	12.2961i	0.171986	−	0.415211i	0.986245	+	0.165291i	$0.0528564\pi$
$878$	0.725764	−	1.09898i	0.0244933	−	0.0370887i
$879$	−11.2433	−	20.2866i	−0.379228	−	0.684251i
$880$	−0.405204	−	18.7636i	−0.0136594	−	0.632522i
$881$		−	46.5697i		−	1.56897i	−0.620146	−	0.784486i	$-0.712927\pi$
$881$		−	46.5697i		−	1.56897i	0.620146	−	0.784486i	$-0.287073\pi$
$882$	28.1794	−	9.37662i	0.948850	−	0.315727i
$883$	1.54878	−	3.73908i	0.0521206	−	0.125830i	−0.895675	−	0.444710i	$-0.853307\pi$
$883$	1.54878	−	3.73908i	0.0521206	−	0.125830i	0.947795	+	0.318880i	$0.103307\pi$
$884$	0.0302642	+	2.80319i	0.00101789	+	0.0942816i
$885$	−14.8488	+	18.6650i	−0.499138	+	0.627418i
$886$	−41.1594	+	27.8243i	−1.38278	+	0.934777i
$887$	6.40060	+	6.40060i	0.214911	+	0.214911i	0.806350	−	0.591439i	$-0.201440\pi$
$887$	6.40060	+	6.40060i	0.214911	+	0.214911i	−0.591439	+	0.806350i	$0.701440\pi$
$888$	−5.10263	−	2.52475i	−0.171233	−	0.0847250i
$889$	−0.113028	+	2.10500i	−0.00379082	+	0.0705995i
$890$	−18.2498	−	3.52781i	−0.611735	−	0.118253i
$891$	25.2772	+	22.3752i	0.846818	+	0.749597i
$892$	−16.2549	−	38.0748i	−0.544253	−	1.27484i
$893$	−0.921892	+	2.22565i	−0.0308500	+	0.0744784i
$894$	12.2860	+	14.3569i	0.410905	+	0.480165i
$895$		−	15.7829i		−	0.527563i
$896$	29.2618	+	6.30448i	0.977568	+	0.210618i
$897$	2.51094	−	1.39162i	0.0838380	−	0.0464650i
$898$	2.95353	+	14.4406i	0.0985606	+	0.481888i
$899$	−44.4452	−	18.4098i	−1.48233	−	0.614002i
$900$	3.18485	−	20.3638i	0.106162	−	0.678792i
$901$	−10.3735	+	4.29686i	−0.345592	+	0.143149i
$902$	−7.72092	+	39.9413i	−0.257079	+	1.32990i
$903$	14.7644	+	30.3754i	0.491328	+	1.01083i
$904$	5.42289	−	3.75188i	0.180363	−	0.124786i
$905$	−7.05694	+	7.05694i	−0.234580	+	0.234580i
$906$	−31.2257	−	15.8722i	−1.03740	−	0.527318i
$907$	−22.3173	+	9.24412i	−0.741033	+	0.306946i	−0.721077	−	0.692855i	$-0.756353\pi$
$907$	−22.3173	+	9.24412i	−0.741033	+	0.306946i	−0.0199559	+	0.999801i	$0.506353\pi$
$908$	51.3573	−	0.554470i	1.70435	−	0.0184007i
$909$	−24.1808	−	33.9096i	−0.802026	−	1.12471i
$910$	2.55739	−	0.381554i	0.0847767	−	0.0126484i
$911$	10.3445			0.342728			0.171364	−	0.985208i	$-0.445183\pi$
$911$	10.3445			0.342728			0.171364	+	0.985208i	$0.445183\pi$
$912$	9.23172	−	5.38019i	0.305693	−	0.178156i
$913$	−4.20568			−0.139188
$914$	−37.5072	−	24.7697i	−1.24063	−	0.819309i
$915$	5.25654	−	0.598558i	0.173776	−	0.0197877i
$916$	−2.63982	+	2.69745i	−0.0872222	+	0.0891261i
$917$	21.6453	−	45.2308i	0.714791	−	1.49365i
$918$	−9.61620	−	15.9737i	−0.317382	−	0.527210i
$919$	−12.8201	−	12.8201i	−0.422897	−	0.422897i	0.463303	−	0.886200i	$-0.346664\pi$
$919$	−12.8201	−	12.8201i	−0.422897	−	0.422897i	−0.886200	+	0.463303i	$0.846664\pi$
$920$	10.3763	−	2.23923i	0.342096	−	0.0738254i
$921$	12.0176	+	3.44684i	0.395992	+	0.113577i
$922$	10.0652	−	52.0683i	0.331479	−	1.71478i
$923$	−0.213236	−	0.514796i	−0.00701874	−	0.0169447i
$924$	22.5348	−	25.9611i	0.741340	−	0.854056i
$925$	3.68817	+	1.52769i	0.121266	+	0.0502302i
$926$	4.29160	+	20.9828i	0.141031	+	0.689537i
$927$	42.7362	+	26.7123i	1.40364	+	0.877348i
$928$	18.8936	+	26.6880i	0.620214	+	0.876077i
$929$	−34.3288			−1.12629			−0.563145	−	0.826358i	$-0.690409\pi$
$929$	−34.3288			−1.12629			−0.563145	+	0.826358i	$0.690409\pi$
$930$	19.3749	−	16.5802i	0.635328	−	0.543688i
$931$	−9.47430	−	5.17565i	−0.310508	−	0.169625i
$932$	−20.7775	+	51.7341i	−0.680590	+	1.69461i
$933$	28.9193	+	23.0066i	0.946777	+	0.753202i
$934$	5.52975	−	28.6061i	0.180939	−	0.936020i
$935$	8.41792	+	8.41792i	0.275296	+	0.275296i
$936$	−4.24252	+	1.99370i	−0.138671	+	0.0651660i
$937$	7.70546	−	7.70546i	0.251726	−	0.251726i	−0.569952	−	0.821678i	$-0.693038\pi$
$937$	7.70546	−	7.70546i	0.251726	−	0.251726i	0.821678	+	0.569952i	$0.193038\pi$
$938$	−12.6814	+	50.8086i	−0.414063	+	1.65896i
$939$	−8.64182	−	6.87493i	−0.282015	−	0.224355i
$940$	2.73329	−	2.79295i	0.0891500	−	0.0910960i
$941$	−4.93205	+	11.9070i	−0.160780	+	0.388158i	−0.983655	−	0.180066i	$-0.942369\pi$
$941$	−4.93205	+	11.9070i	−0.160780	+	0.388158i	0.822874	+	0.568223i	$0.192369\pi$
$942$	4.61753	−	59.4073i	0.150447	−	1.93559i
$943$	−23.0090			−0.749275
$944$	−41.0356	−	15.9685i	−1.33560	−	0.519731i
$945$	−13.3807	+	10.8028i	−0.435275	+	0.351414i
$946$	32.6225	+	21.5438i	1.06065	+	0.700450i
$947$	34.4563	+	14.2723i	1.11968	+	0.463787i	0.864261	−	0.503043i	$-0.167786\pi$
$947$	34.4563	+	14.2723i	1.11968	+	0.463787i	0.255419	+	0.966830i	$0.417786\pi$
$948$	22.3405	+	39.3027i	0.725585	+	1.27649i
$949$	1.09120	−	0.451991i	0.0354219	−	0.0146722i
$950$	−6.20723	+	4.19618i	−0.201389	+	0.136142i
$951$	1.58659	−	5.53172i	0.0514486	−	0.179378i
$952$	−16.1710	+	9.95012i	−0.524104	+	0.322485i
$953$	8.93503	+	8.93503i	0.289434	+	0.289434i	0.836856	−	0.547422i	$-0.184391\pi$
$953$	8.93503	+	8.93503i	0.289434	+	0.289434i	−0.547422	+	0.836856i	$0.684391\pi$
$954$	−13.7429	−	12.7923i	−0.444943	−	0.414165i
$955$	−0.616417	+	0.255328i	−0.0199468	+	0.00826223i
$956$	42.0463	−	17.9504i	1.35987	−	0.580556i
$957$	37.3124	−	4.24873i	1.20614	−	0.137342i
$958$	−32.0327	+	6.55164i	−1.03493	+	0.211674i
$959$	26.5591	+	29.5731i	0.857638	+	0.954966i
$960$	−17.1493	+	2.51769i	−0.553492	+	0.0812582i
$961$	−38.2633			−1.23430
$962$	−0.181929	−	0.889497i	−0.00586562	−	0.0286785i
$963$	10.0568	+	14.1030i	0.324076	+	0.454463i
$964$	−30.4225	+	12.9880i	−0.979843	+	0.418314i
$965$	7.22378	+	17.4397i	0.232542	+	0.561405i
$966$	16.8357	+	9.72715i	0.541680	+	0.312966i
$967$	−16.4468	+	16.4468i	−0.528892	+	0.528892i	−0.920242	−	0.391350i	$-0.872008\pi$
$967$	−16.4468	+	16.4468i	−0.528892	+	0.528892i	0.391350	+	0.920242i	$0.372008\pi$
$968$	1.55537	−	8.53986i	0.0499914	−	0.274482i
$969$	−1.86860	+	6.51499i	−0.0600282	+	0.209292i
$970$	−8.04211	+	5.43659i	−0.258217	+	0.174558i
$971$	6.59321	−	2.73100i	0.211586	−	0.0876419i	−0.274373	−	0.961623i	$-0.588470\pi$
$971$	6.59321	−	2.73100i	0.211586	−	0.0876419i	0.485959	+	0.873981i	$0.338470\pi$
$972$	17.6140	−	25.7244i	0.564970	−	0.825112i
$973$	34.4909	−	12.1641i	1.10573	−	0.389962i
$974$	31.5183	−	47.7262i	1.00991	−	1.52925i
$975$	2.87499	−	1.59339i	0.0920734	−	0.0510292i
$976$	3.93169	+	8.94091i	0.125850	+	0.286191i
$977$	44.8343			1.43438			0.717189	−	0.696879i	$-0.245429\pi$
$977$	44.8343			1.43438			0.717189	+	0.696879i	$0.245429\pi$
$978$	4.72188	+	0.367016i	0.150989	+	0.0117359i
$979$	−36.4107	−	15.0818i	−1.16369	−	0.482017i
$980$	11.1328	+	13.5188i	0.355623	+	0.431843i
$981$	−4.76801	+	28.4696i	−0.152231	+	0.908964i
$982$	−6.84940	−	10.1320i	−0.218573	−	0.323326i
$983$	30.7337	+	30.7337i	0.980253	+	0.980253i	0.999809	−	0.0195562i	$-0.00622534\pi$
$983$	30.7337	+	30.7337i	0.980253	+	0.980253i	−0.0195562	+	0.999809i	$0.506225\pi$
$984$	37.4869	+	2.50690i	1.19504	+	0.0799171i
$985$	2.01441	+	2.01441i	0.0641843	+	0.0641843i
$986$	−20.3643	−	3.93655i	−0.648531	−	0.125365i
$987$	7.14525	−	0.427349i	0.227436	−	0.0136027i
$988$	1.58126	+	0.635066i	0.0503064	+	0.0202041i
$989$	−8.46177	+	20.4285i	−0.269069	+	0.649589i
$990$	−6.95454	+	18.6521i	−0.221030	+	0.592804i
$991$	15.9408			0.506375			0.253187	−	0.967417i	$-0.418521\pi$
$991$	15.9408			0.506375			0.253187	+	0.967417i	$0.418521\pi$
$992$	39.8363	+	25.0897i	1.26480	+	0.796600i
$993$	−23.3643	+	12.9491i	−0.741445	+	0.410926i
$994$	2.24559	−	3.03317i	0.0712259	−	0.0962062i
$995$	−5.96075	+	14.3905i	−0.188969	+	0.456211i
$996$	0.481082	+	3.85424i	0.0152437	+	0.122126i
$997$	2.13804	−	0.885605i	0.0677124	−	0.0280474i	−0.348570	−	0.937283i	$-0.613333\pi$
$997$	2.13804	−	0.885605i	0.0677124	−	0.0280474i	0.416283	+	0.909235i	$0.363333\pi$
$998$	−9.57467	+	49.5309i	−0.303081	+	1.56787i
$999$	4.03961	+	4.48822i	0.127808	+	0.142001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bo.a.125.10	yes	496
3.2	odd	2	inner	672.2.bo.a.125.115	yes	496
7.6	odd	2	inner	672.2.bo.a.125.9	✓	496
21.20	even	2	inner	672.2.bo.a.125.116	yes	496
32.21	even	8	inner	672.2.bo.a.629.116	yes	496
96.53	odd	8	inner	672.2.bo.a.629.9	yes	496
224.181	odd	8	inner	672.2.bo.a.629.115	yes	496
672.629	even	8	inner	672.2.bo.a.629.10	yes	496

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bo.a.125.9	✓	496	7.6	odd	2	inner
672.2.bo.a.125.10	yes	496	1.1	even	1	trivial
672.2.bo.a.125.115	yes	496	3.2	odd	2	inner
672.2.bo.a.125.116	yes	496	21.20	even	2	inner
672.2.bo.a.629.9	yes	496	96.53	odd	8	inner
672.2.bo.a.629.10	yes	496	672.629	even	8	inner
672.2.bo.a.629.115	yes	496	224.181	odd	8	inner
672.2.bo.a.629.116	yes	496	32.21	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bo (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38553 + 0.283382i) q^{2} +(1.72093 - 0.195961i) q^{3} +(1.83939 - 0.785270i) q^{4} +(-0.478704 - 1.15569i) q^{5} +(-2.32887 + 0.759191i) q^{6} +(0.141859 - 2.64195i) q^{7} +(-2.32600 + 1.60927i) q^{8} +(2.92320 - 0.674470i) q^{9} +O(q^{10})\)	\(q+(-1.38553 + 0.283382i) q^{2} +(1.72093 - 0.195961i) q^{3} +(1.83939 - 0.785270i) q^{4} +(-0.478704 - 1.15569i) q^{5} +(-2.32887 + 0.759191i) q^{6} +(0.141859 - 2.64195i) q^{7} +(-2.32600 + 1.60927i) q^{8} +(2.92320 - 0.674470i) q^{9} +(0.990761 + 1.46559i) q^{10} +(1.43539 + 3.46534i) q^{11} +(3.01158 - 1.71184i) q^{12} +(0.510390 + 0.211410i) q^{13} +(0.552132 + 3.70070i) q^{14} +(-1.05029 - 1.89506i) q^{15} +(2.76670 - 2.88883i) q^{16} +2.53724i q^{17} +(-3.85905 + 1.76288i) q^{18} +(1.42486 + 0.590197i) q^{19} +(-1.78805 - 1.74986i) q^{20} +(-0.273590 - 4.57440i) q^{21} +(-2.97080 - 4.39458i) q^{22} +(2.12148 - 2.12148i) q^{23} +(-3.68752 + 3.22524i) q^{24} +(2.42907 - 2.42907i) q^{25} +(-0.767071 - 0.148280i) q^{26} +(4.89845 - 1.73355i) q^{27} +(-1.81371 - 4.97096i) q^{28} +(2.21207 - 5.34040i) q^{29} +(1.99223 + 2.32803i) q^{30} -8.32246i q^{31} +(-3.01470 + 4.78660i) q^{32} +(3.14928 + 5.68233i) q^{33} +(-0.719010 - 3.51543i) q^{34} +(-3.12119 + 1.10076i) q^{35} +(4.84726 - 3.53611i) q^{36} +(0.444715 + 1.07364i) q^{37} +(-2.14144 - 0.413955i) q^{38} +(0.919773 + 0.263806i) q^{39} +(2.97328 + 1.91778i) q^{40} +(-5.42285 - 5.42285i) q^{41} +(1.67537 + 6.26044i) q^{42} +(-6.80898 + 2.82037i) q^{43} +(5.36148 + 5.24694i) q^{44} +(-2.17883 - 3.05545i) q^{45} +(-2.33819 + 3.54057i) q^{46} +1.56201i q^{47} +(4.19520 - 5.51365i) q^{48} +(-6.95975 - 0.749565i) q^{49} +(-2.67719 + 4.05390i) q^{50} +(0.497201 + 4.36641i) q^{51} +(1.10482 - 0.0119280i) q^{52} +(1.69351 + 4.08851i) q^{53} +(-6.29569 + 3.79002i) q^{54} +(3.31775 - 3.31775i) q^{55} +(3.92163 + 6.37345i) q^{56} +(2.56774 + 0.736471i) q^{57} +(-1.55151 + 8.02615i) q^{58} +(-4.21269 - 10.1703i) q^{59} +(-3.42002 - 2.66099i) q^{60} +(-0.934435 + 2.25593i) q^{61} +(2.35844 + 11.5310i) q^{62} +(-1.36723 - 7.81861i) q^{63} +(2.82053 - 7.48630i) q^{64} -0.691057i q^{65} +(-5.97370 - 6.98059i) q^{66} +(12.9304 + 5.35594i) q^{67} +(1.99242 + 4.66697i) q^{68} +(3.23520 - 4.06665i) q^{69} +(4.01256 - 2.40963i) q^{70} +(-0.713212 - 0.713212i) q^{71} +(-5.71395 + 6.27302i) q^{72} +(1.51178 - 1.51178i) q^{73} +(-0.920415 - 1.36153i) q^{74} +(3.70425 - 4.65625i) q^{75} +(3.08434 - 0.0332995i) q^{76} +(9.35887 - 3.30064i) q^{77} +(-1.34913 - 0.104863i) q^{78} +13.0505i q^{79} +(-4.66303 - 1.81456i) q^{80} +(8.09018 - 3.94322i) q^{81} +(9.05026 + 5.97678i) q^{82} +(-0.429086 + 1.03591i) q^{83} +(-4.09538 - 8.19926i) q^{84} +(2.93227 - 1.21459i) q^{85} +(8.63481 - 5.83726i) q^{86} +(2.76030 - 9.62393i) q^{87} +(-8.91538 - 5.75045i) q^{88} +(-7.42964 + 7.42964i) q^{89} +(3.88469 + 3.61597i) q^{90} +(0.630938 - 1.31843i) q^{91} +(2.23630 - 5.56817i) q^{92} +(-1.63088 - 14.3224i) q^{93} +(-0.442645 - 2.16421i) q^{94} -1.92923i q^{95} +(-4.25011 + 8.82817i) q^{96} +5.48728i q^{97} +(9.85536 - 0.933727i) q^{98} +(6.53321 + 9.16176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9	\( 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9} - 48 q^{16} - 8 q^{18} - 4 q^{21} - 16 q^{22} - 16 q^{25} - 8 q^{28} - 64 q^{30} - 48 q^{36} - 16 q^{37} - 8 q^{39} + 56 q^{42} - 16 q^{43} - 16 q^{46} + 16 q^{51} - 8 q^{57} - 80 q^{58} + 24 q^{60} - 8 q^{63} - 112 q^{64} + 48 q^{67} - 8 q^{70} - 8 q^{72} - 160 q^{78} + 128 q^{84} + 64 q^{85} - 16 q^{88} - 56 q^{91} + 16 q^{93} - 8 q^{99}+O(q^{100}) \) 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9 - 48 * q^16 - 8 * q^18 - 4 * q^21 - 16 * q^22 - 16 * q^25 - 8 * q^28 - 64 * q^30 - 48 * q^36 - 16 * q^37 - 8 * q^39 + 56 * q^42 - 16 * q^43 - 16 * q^46 + 16 * q^51 - 8 * q^57 - 80 * q^58 + 24 * q^60 - 8 * q^63 - 112 * q^64 + 48 * q^67 - 8 * q^70 - 8 * q^72 - 160 * q^78 + 128 * q^84 + 64 * q^85 - 16 * q^88 - 56 * q^91 + 16 * q^93 - 8 * q^99

Introduction

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Modular forms

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