LMFDB - Embedded newform 336.2.s.d.155.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(155,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))

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

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

chi := DirichletCharacter("336.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			155.7
Character	$\chi$	$=$	336.155
Dual form			336.2.s.d.323.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809995 - 1.15927i) q^{2} +(0.594785 + 1.62672i) q^{3} +(-0.687816 + 1.87801i) q^{4} +(0.0563417 - 0.0563417i) q^{5} +(1.40404 - 2.00716i) q^{6} +1.00000 q^{7} +(2.73425 - 0.723812i) q^{8} +(-2.29246 + 1.93510i) q^{9} +O(q^{10})$	\(q+(-0.809995 - 1.15927i) q^{2} +(0.594785 + 1.62672i) q^{3} +(-0.687816 + 1.87801i) q^{4} +(0.0563417 - 0.0563417i) q^{5} +(1.40404 - 2.00716i) q^{6} +1.00000 q^{7} +(2.73425 - 0.723812i) q^{8} +(-2.29246 + 1.93510i) q^{9} +(-0.110952 - 0.0196788i) q^{10} +(0.982600 + 0.982600i) q^{11} +(-3.46410 - 0.00187549i) q^{12} +(-0.649283 + 0.649283i) q^{13} +(-0.809995 - 1.15927i) q^{14} +(0.125164 + 0.0581412i) q^{15} +(-3.05382 - 2.58345i) q^{16} +4.55146i q^{17} +(4.10019 + 1.09016i) q^{18} +(2.11045 + 2.11045i) q^{19} +(0.0670574 + 0.144563i) q^{20} +(0.594785 + 1.62672i) q^{21} +(0.343198 - 1.93500i) q^{22} +2.24104i q^{23} +(2.80373 + 4.01735i) q^{24} +4.99365i q^{25} +(1.27861 + 0.226778i) q^{26} +(-4.51140 - 2.57823i) q^{27} +(-0.687816 + 1.87801i) q^{28} +(4.36474 + 4.36474i) q^{29} +(-0.0339806 - 0.192193i) q^{30} -4.82864i q^{31} +(-0.521333 + 5.63278i) q^{32} +(-1.01398 + 2.18285i) q^{33} +(5.27637 - 3.68666i) q^{34} +(0.0563417 - 0.0563417i) q^{35} +(-2.05735 - 5.63625i) q^{36} +(-1.58919 - 1.58919i) q^{37} +(0.737130 - 4.15605i) q^{38} +(-1.44239 - 0.670020i) q^{39} +(0.113271 - 0.194833i) q^{40} -5.28555 q^{41} +(1.40404 - 2.00716i) q^{42} +(7.65146 - 7.65146i) q^{43} +(-2.52118 + 1.16948i) q^{44} +(-0.0201342 + 0.238188i) q^{45} +(2.59797 - 1.81523i) q^{46} +1.18584 q^{47} +(2.38619 - 6.50432i) q^{48} +1.00000 q^{49} +(5.78899 - 4.04483i) q^{50} +(-7.40397 + 2.70714i) q^{51} +(-0.772771 - 1.66595i) q^{52} +(9.36864 - 9.36864i) q^{53} +(0.665345 + 7.31829i) q^{54} +0.110723 q^{55} +(2.73425 - 0.723812i) q^{56} +(-2.17786 + 4.68839i) q^{57} +(1.52449 - 8.59533i) q^{58} +(-3.21595 - 3.21595i) q^{59} +(-0.195279 + 0.195068i) q^{60} +(0.0261719 - 0.0261719i) q^{61} +(-5.59770 + 3.91117i) q^{62} +(-2.29246 + 1.93510i) q^{63} +(6.95219 - 3.95816i) q^{64} +0.0731635i q^{65} +(3.35184 - 0.592621i) q^{66} +(-7.39154 - 7.39154i) q^{67} +(-8.54767 - 3.13056i) q^{68} +(-3.64555 + 1.33293i) q^{69} +(-0.110952 - 0.0196788i) q^{70} +2.08674i q^{71} +(-4.86750 + 6.95036i) q^{72} +14.0696i q^{73} +(-0.555063 + 3.12953i) q^{74} +(-8.12329 + 2.97015i) q^{75} +(-5.41505 + 2.51184i) q^{76} +(0.982600 + 0.982600i) q^{77} +(0.391593 + 2.21483i) q^{78} -14.7926i q^{79} +(-0.317613 + 0.0265017i) q^{80} +(1.51076 - 8.87229i) q^{81} +(4.28127 + 6.12738i) q^{82} +(-2.06238 + 2.06238i) q^{83} +(-3.46410 - 0.00187549i) q^{84} +(0.256437 + 0.256437i) q^{85} +(-15.0678 - 2.67247i) q^{86} +(-4.50414 + 9.69630i) q^{87} +(3.39789 + 1.97545i) q^{88} -6.33792 q^{89} +(0.292433 - 0.169590i) q^{90} +(-0.649283 + 0.649283i) q^{91} +(-4.20868 - 1.54142i) q^{92} +(7.85486 - 2.87200i) q^{93} +(-0.960528 - 1.37471i) q^{94} +0.237813 q^{95} +(-9.47306 + 2.50223i) q^{96} -7.26847 q^{97} +(-0.809995 - 1.15927i) q^{98} +(-4.15400 - 0.351140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{6} + 48 q^{7}+O(q^{10}) $ 48 * q + 6 * q^6 + 48 * q^7	$ 48 q + 6 q^{6} + 48 q^{7} - 16 q^{10} + 6 q^{12} - 28 q^{16} - 20 q^{18} + 8 q^{19} - 8 q^{22} - 38 q^{24} - 12 q^{27} - 24 q^{30} + 12 q^{34} - 4 q^{36} + 16 q^{37} - 24 q^{39} + 60 q^{40} + 6 q^{42} - 48 q^{43} + 20 q^{45} + 52 q^{46} + 62 q^{48} + 48 q^{49} + 12 q^{52} + 14 q^{54} - 32 q^{55} - 100 q^{58} - 16 q^{60} + 8 q^{61} - 60 q^{64} - 96 q^{66} - 16 q^{67} - 28 q^{69} - 16 q^{70} - 80 q^{72} - 12 q^{75} + 4 q^{76} - 56 q^{78} + 4 q^{82} + 6 q^{84} - 48 q^{85} + 56 q^{87} + 116 q^{88} + 68 q^{90} - 64 q^{93} + 48 q^{94} + 62 q^{96} + 32 q^{99}+O(q^{100}) $ 48 * q + 6 * q^6 + 48 * q^7 - 16 * q^10 + 6 * q^12 - 28 * q^16 - 20 * q^18 + 8 * q^19 - 8 * q^22 - 38 * q^24 - 12 * q^27 - 24 * q^30 + 12 * q^34 - 4 * q^36 + 16 * q^37 - 24 * q^39 + 60 * q^40 + 6 * q^42 - 48 * q^43 + 20 * q^45 + 52 * q^46 + 62 * q^48 + 48 * q^49 + 12 * q^52 + 14 * q^54 - 32 * q^55 - 100 * q^58 - 16 * q^60 + 8 * q^61 - 60 * q^64 - 96 * q^66 - 16 * q^67 - 28 * q^69 - 16 * q^70 - 80 * q^72 - 12 * q^75 + 4 * q^76 - 56 * q^78 + 4 * q^82 + 6 * q^84 - 48 * q^85 + 56 * q^87 + 116 * q^88 + 68 * q^90 - 64 * q^93 + 48 * q^94 + 62 * q^96 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$1$

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 $

$2$	−0.809995	−	1.15927i	−0.572753	−	0.819728i
$2$	−0.809995	−	1.15927i	−0.572753	−	0.819728i
$3$	0.594785	+	1.62672i	0.343399	+	0.939189i
$3$	0.594785	+	1.62672i	0.343399	+	0.939189i
$4$	−0.687816	+	1.87801i	−0.343908	+	0.939003i
$5$	0.0563417	−	0.0563417i	0.0251968	−	0.0251968i	−0.694396	−	0.719593i	$-0.744328\pi$
$5$	0.0563417	−	0.0563417i	0.0251968	−	0.0251968i	0.719593	+	0.694396i	$0.244328\pi$
$6$	1.40404	−	2.00716i	0.573197	−	0.819418i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	2.73425	−	0.723812i	0.966702	−	0.255906i
$9$	−2.29246	+	1.93510i	−0.764154	+	0.645034i
$10$	−0.110952	−	0.0196788i	−0.0350860	−	0.00622297i
$11$	0.982600	+	0.982600i	0.296265	+	0.296265i	0.839549	−	0.543284i	$-0.182819\pi$
$11$	0.982600	+	0.982600i	0.296265	+	0.296265i	−0.543284	+	0.839549i	$0.682819\pi$
$12$	−3.46410	−	0.00187549i	−1.00000	−	0.000541407i
$13$	−0.649283	+	0.649283i	−0.180079	+	0.180079i	−0.791390	−	0.611311i	$-0.790642\pi$
$13$	−0.649283	+	0.649283i	−0.180079	+	0.180079i	0.611311	+	0.791390i	$0.290642\pi$
$14$	−0.809995	−	1.15927i	−0.216480	−	0.309828i
$15$	0.125164	+	0.0581412i	0.0323171	+	0.0150120i
$16$	−3.05382	−	2.58345i	−0.763455	−	0.645861i
$17$			4.55146i			1.10389i	0.833880	+	0.551945i	$0.186114\pi$
$17$			4.55146i			1.10389i	−0.833880	+	0.551945i	$0.813886\pi$
$18$	4.10019	+	1.09016i	0.966424	+	0.256953i
$19$	2.11045	+	2.11045i	0.484172	+	0.484172i	0.906461	−	0.422289i	$-0.138773\pi$
$19$	2.11045	+	2.11045i	0.484172	+	0.484172i	−0.422289	+	0.906461i	$0.638773\pi$
$20$	0.0670574	+	0.144563i	0.0149945	+	0.0323252i
$21$	0.594785	+	1.62672i	0.129793	+	0.354980i
$22$	0.343198	−	1.93500i	0.0731700	−	0.412543i
$23$			2.24104i			0.467288i	0.972322	+	0.233644i	$0.0750651\pi$
$23$			2.24104i			0.467288i	−0.972322	+	0.233644i	$0.924935\pi$
$24$	2.80373	+	4.01735i	0.572309	+	0.820038i
$25$			4.99365i			0.998730i
$26$	1.27861	+	0.226778i	0.250756	+	0.0444749i
$27$	−4.51140	−	2.57823i	−0.868219	−	0.496181i
$28$	−0.687816	+	1.87801i	−0.129985	+	0.354910i
$29$	4.36474	+	4.36474i	0.810511	+	0.810511i	0.984710	−	0.174199i	$-0.0557336\pi$
$29$	4.36474	+	4.36474i	0.810511	+	0.810511i	−0.174199	+	0.984710i	$0.555734\pi$
$30$	−0.0339806	−	0.192193i	−0.00620398	−	0.0350894i
$31$		−	4.82864i		−	0.867249i	−0.901094	−	0.433625i	$-0.857234\pi$
$31$		−	4.82864i		−	0.867249i	0.901094	−	0.433625i	$-0.142766\pi$
$32$	−0.521333	+	5.63278i	−0.0921595	+	0.995744i
$33$	−1.01398	+	2.18285i	−0.176512	+	0.379986i
$34$	5.27637	−	3.68666i	0.904890	−	0.632257i
$35$	0.0563417	−	0.0563417i	0.00952349	−	0.00952349i
$36$	−2.05735	−	5.63625i	−0.342891	−	0.939375i
$37$	−1.58919	−	1.58919i	−0.261261	−	0.261261i	0.564305	−	0.825566i	$-0.309144\pi$
$37$	−1.58919	−	1.58919i	−0.261261	−	0.261261i	−0.825566	+	0.564305i	$0.809144\pi$
$38$	0.737130	−	4.15605i	0.119578	−	0.674200i
$39$	−1.44239	−	0.670020i	−0.230967	−	0.107289i
$40$	0.113271	−	0.194833i	0.0179098	−	0.0308058i
$41$	−5.28555			−0.825464			−0.412732	−	0.910852i	$-0.635425\pi$
$41$	−5.28555			−0.825464			−0.412732	+	0.910852i	$0.635425\pi$
$42$	1.40404	−	2.00716i	0.216648	−	0.309711i
$43$	7.65146	−	7.65146i	1.16684	−	1.16684i	0.183890	−	0.982947i	$-0.441131\pi$
$43$	7.65146	−	7.65146i	1.16684	−	1.16684i	0.982947	−	0.183890i	$-0.0588691\pi$
$44$	−2.52118	+	1.16948i	−0.380082	+	0.176306i
$45$	−0.0201342	+	0.238188i	−0.00300143	+	0.0355070i
$46$	2.59797	−	1.81523i	0.383049	−	0.267641i
$47$	1.18584			0.172973			0.0864866	−	0.996253i	$-0.472436\pi$
$47$	1.18584			0.172973			0.0864866	+	0.996253i	$0.472436\pi$
$48$	2.38619	−	6.50432i	0.344416	−	0.938817i
$49$	1.00000			0.142857
$50$	5.78899	−	4.04483i	0.818687	−	0.572026i
$51$	−7.40397	+	2.70714i	−1.03676	+	0.379075i
$52$	−0.772771	−	1.66595i	−0.107164	−	0.231025i
$53$	9.36864	−	9.36864i	1.28688	−	1.28688i	0.350210	−	0.936671i	$-0.386110\pi$
$53$	9.36864	−	9.36864i	1.28688	−	1.28688i	0.936671	−	0.350210i	$-0.113890\pi$
$54$	0.665345	+	7.31829i	0.0905420	+	0.995893i
$55$	0.110723			0.0149299
$56$	2.73425	−	0.723812i	0.365379	−	0.0967235i
$57$	−2.17786	+	4.68839i	−0.288465	+	0.620993i
$58$	1.52449	−	8.59533i	0.200176	−	1.12862i
$59$	−3.21595	−	3.21595i	−0.418681	−	0.418681i	0.466068	−	0.884749i	$-0.345670\pi$
$59$	−3.21595	−	3.21595i	−0.418681	−	0.418681i	−0.884749	+	0.466068i	$0.845670\pi$
$60$	−0.195279	+	0.195068i	−0.0252104	+	0.0251831i
$61$	0.0261719	−	0.0261719i	0.00335097	−	0.00335097i	−0.705429	−	0.708780i	$-0.749246\pi$
$61$	0.0261719	−	0.0261719i	0.00335097	−	0.00335097i	0.708780	+	0.705429i	$0.249246\pi$
$62$	−5.59770	+	3.91117i	−0.710909	+	0.496720i
$63$	−2.29246	+	1.93510i	−0.288823	+	0.243800i
$64$	6.95219	−	3.95816i	0.869024	−	0.494770i
$65$			0.0731635i			0.00907481i
$66$	3.35184	−	0.592621i	0.412583	−	0.0729467i
$67$	−7.39154	−	7.39154i	−0.903020	−	0.903020i	0.0926761	−	0.995696i	$-0.470458\pi$
$67$	−7.39154	−	7.39154i	−0.903020	−	0.903020i	−0.995696	+	0.0926761i	$0.970458\pi$
$68$	−8.54767	−	3.13056i	−1.03656	−	0.379637i
$69$	−3.64555	+	1.33293i	−0.438872	+	0.160466i
$70$	−0.110952	−	0.0196788i	−0.0132613	−	0.00235206i
$71$			2.08674i			0.247650i	0.992304	+	0.123825i	$0.0395161\pi$
$71$			2.08674i			0.247650i	−0.992304	+	0.123825i	$0.960484\pi$
$72$	−4.86750	+	6.95036i	−0.573640	+	0.819107i
$73$			14.0696i			1.64672i	0.567522	+	0.823359i	$0.307902\pi$
$73$			14.0696i			1.64672i	−0.567522	+	0.823359i	$0.692098\pi$
$74$	−0.555063	+	3.12953i	−0.0645248	+	0.363800i
$75$	−8.12329	+	2.97015i	−0.937997	+	0.342963i
$76$	−5.41505	+	2.51184i	−0.621149	+	0.288128i
$77$	0.982600	+	0.982600i	0.111978	+	0.111978i
$78$	0.391593	+	2.21483i	0.0443392	+	0.250780i
$79$		−	14.7926i		−	1.66429i	−0.554555	−	0.832147i	$-0.687111\pi$
$79$		−	14.7926i		−	1.66429i	0.554555	−	0.832147i	$-0.312889\pi$
$80$	−0.317613	+	0.0265017i	−0.0355102	+	0.00296298i
$81$	1.51076	−	8.87229i	0.167862	−	0.985811i
$82$	4.28127	+	6.12738i	0.472787	+	0.676656i
$83$	−2.06238	+	2.06238i	−0.226376	+	0.226376i	−0.811177	−	0.584801i	$-0.801173\pi$
$83$	−2.06238	+	2.06238i	−0.226376	+	0.226376i	0.584801	+	0.811177i	$0.301173\pi$
$84$	−3.46410	−	0.00187549i	−0.377964	−	0.000204633i
$85$	0.256437	+	0.256437i	0.0278145	+	0.0278145i
$86$	−15.0678	−	2.67247i	−1.62480	−	0.288179i
$87$	−4.50414	+	9.69630i	−0.482895	+	1.03955i
$88$	3.39789	+	1.97545i	0.362216	+	0.210584i
$89$	−6.33792			−0.671818			−0.335909	−	0.941894i	$-0.609044\pi$
$89$	−6.33792			−0.671818			−0.335909	+	0.941894i	$0.609044\pi$
$90$	0.292433	−	0.169590i	0.0308252	−	0.0178764i
$91$	−0.649283	+	0.649283i	−0.0680634	+	0.0680634i
$92$	−4.20868	−	1.54142i	−0.438785	−	0.160704i
$93$	7.85486	−	2.87200i	0.814511	−	0.297813i
$94$	−0.960528	−	1.37471i	−0.0990709	−	0.141791i
$95$	0.237813			0.0243991
$96$	−9.47306	+	2.50223i	−0.966840	+	0.255383i
$97$	−7.26847			−0.738001			−0.369000	−	0.929429i	$-0.620300\pi$
$97$	−7.26847			−0.738001			−0.369000	+	0.929429i	$0.620300\pi$
$98$	−0.809995	−	1.15927i	−0.0818219	−	0.117104i
$99$	−4.15400	−	0.351140i	−0.417493	−	0.0352909i
$100$	−9.37811	−	3.43471i	−0.937811	−	0.343471i
$101$	11.1168	−	11.1168i	1.10616	−	1.10616i	0.112507	−	0.993651i	$-0.464112\pi$
$101$	11.1168	−	11.1168i	1.10616	−	1.10616i	0.993651	−	0.112507i	$-0.0358882\pi$
$102$	9.13548	+	6.39043i	0.904548	+	0.632747i
$103$	12.0433			1.18666			0.593332	−	0.804958i	$-0.297812\pi$
$103$	12.0433			1.18666			0.593332	+	0.804958i	$0.297812\pi$
$104$	−1.30534	+	2.24526i	−0.127999	+	0.220166i
$105$	0.125164	+	0.0581412i	0.0122147	+	0.00567400i
$106$	−18.4493	−	3.27223i	−1.79196	−	0.317827i
$107$	−5.01344	−	5.01344i	−0.484667	−	0.484667i	0.421951	−	0.906618i	$-0.361345\pi$
$107$	−5.01344	−	5.01344i	−0.484667	−	0.484667i	−0.906618	+	0.421951i	$0.861345\pi$
$108$	7.94495	−	6.69909i	0.764503	−	0.644620i
$109$	−2.25726	+	2.25726i	−0.216207	+	0.216207i	−0.806898	−	0.590691i	$-0.798855\pi$
$109$	−2.25726	+	2.25726i	−0.216207	+	0.216207i	0.590691	+	0.806898i	$0.298855\pi$
$110$	−0.0896849	−	0.128358i	−0.00855112	−	0.0122384i
$111$	1.63994	−	3.53039i	0.155656	−	0.335090i
$112$	−3.05382	−	2.58345i	−0.288559	−	0.244113i
$113$			8.08089i			0.760186i	0.924948	+	0.380093i	$0.124108\pi$
$113$			8.08089i			0.760186i	−0.924948	+	0.380093i	$0.875892\pi$
$114$	7.19917	−	1.27285i	0.674264	−	0.119213i
$115$	0.126264	+	0.126264i	0.0117742	+	0.0117742i
$116$	−11.1991	+	5.19487i	−1.03981	+	0.482332i
$117$	0.232027	−	2.74489i	0.0214509	−	0.253765i
$118$	−1.12325	+	6.33307i	−0.103404	+	0.583006i
$119$			4.55146i			0.417232i
$120$	0.384311	+	0.0683773i	0.0350827	+	0.00624197i
$121$		−	9.06899i		−	0.824454i
$122$	−0.0515395	−	0.00914121i	−0.00466617	−	0.000827606i
$123$	−3.14377	−	8.59813i	−0.283464	−	0.775267i
$124$	9.06822	+	3.32121i	0.814350	+	0.298254i
$125$	0.563060	+	0.563060i	0.0503616	+	0.0503616i
$126$	4.10019	+	1.09016i	0.365274	+	0.0971190i
$127$		−	5.44459i		−	0.483129i	−0.970385	−	0.241565i	$-0.922339\pi$
$127$		−	5.44459i		−	0.483129i	0.970385	−	0.241565i	$-0.0776606\pi$
$128$	−10.2198	−	4.85338i	−0.903313	−	0.428982i
$129$	16.9978	+	7.89584i	1.49657	+	0.695190i
$130$	0.0848162	−	0.0592621i	0.00743888	−	0.00519763i
$131$	13.7844	−	13.7844i	1.20435	−	1.20435i	0.231521	−	0.972830i	$-0.425630\pi$
$131$	13.7844	−	13.7844i	1.20435	−	1.20435i	0.972830	−	0.231521i	$-0.0743702\pi$
$132$	−3.40198	−	3.40567i	−0.296105	−	0.296425i
$133$	2.11045	+	2.11045i	0.183000	+	0.183000i
$134$	−2.58168	+	14.5559i	−0.223023	+	1.25744i
$135$	−0.399442	+	0.108918i	−0.0343785	+	0.00937418i
$136$	3.29440	+	12.4448i	0.282493	+	1.06713i
$137$	16.5058			1.41019			0.705094	−	0.709114i	$-0.250905\pi$
$137$	16.5058			1.41019			0.705094	+	0.709114i	$0.250905\pi$
$138$	4.49811	+	3.14650i	0.382904	+	0.267848i
$139$	−4.01774	+	4.01774i	−0.340780	+	0.340780i	−0.856661	−	0.515880i	$-0.827465\pi$
$139$	−4.01774	+	4.01774i	−0.340780	+	0.340780i	0.515880	+	0.856661i	$0.327465\pi$
$140$	0.0670574	+	0.144563i	0.00566739	+	0.0122178i
$141$	0.705323	+	1.92904i	0.0593989	+	0.162455i
$142$	2.41909	−	1.69025i	0.203006	−	0.141842i
$143$	−1.27597			−0.106702
$144$	12.0000	+	0.0129938i	0.999999	+	0.00108281i
$145$	0.491834			0.0408446
$146$	16.3104	−	11.3963i	1.34986	−	0.943162i
$147$	0.594785	+	1.62672i	0.0490571	+	0.134170i
$148$	4.07757	−	1.89144i	0.335174	−	0.155475i
$149$	10.7088	−	10.7088i	0.877297	−	0.877297i	−0.115957	−	0.993254i	$-0.536993\pi$
$149$	10.7088	−	10.7088i	0.877297	−	0.877297i	0.993254	+	0.115957i	$0.0369934\pi$
$150$	10.0230	+	7.01128i	0.818377	+	0.572469i
$151$	−3.21595			−0.261710			−0.130855	−	0.991402i	$-0.541772\pi$
$151$	−3.21595			−0.261710			−0.130855	+	0.991402i	$0.541772\pi$
$152$	7.29807	+	4.24293i	0.591952	+	0.344147i
$153$	−8.80754	−	10.4340i	−0.712047	−	0.843542i
$154$	0.343198	−	1.93500i	0.0276557	−	0.155927i
$155$	−0.272054	−	0.272054i	−0.0218519	−	0.0218519i
$156$	2.25040	−	2.24796i	0.180176	−	0.179981i
$157$	−14.4819	+	14.4819i	−1.15578	+	1.15578i	−0.170411	+	0.985373i	$0.554509\pi$
$157$	−14.4819	+	14.4819i	−1.15578	+	1.15578i	−0.985373	+	0.170411i	$0.945491\pi$
$158$	−17.1486	+	11.9819i	−1.36427	+	0.953230i
$159$	20.8125	+	9.66786i	1.65054	+	0.766711i
$160$	0.287988	+	0.346733i	0.0227674	+	0.0274117i
$161$			2.24104i			0.176618i
$162$	−11.5091	+	5.43514i	−0.904240	+	0.427025i
$163$	2.86616	+	2.86616i	0.224495	+	0.224495i	0.810388	−	0.585893i	$-0.199256\pi$
$163$	2.86616	+	2.86616i	0.224495	+	0.224495i	−0.585893	+	0.810388i	$0.699256\pi$
$164$	3.63548	−	9.92630i	0.283884	−	0.775114i
$165$	0.0658563	+	0.180115i	0.00512690	+	0.0140220i
$166$	4.06138	+	0.720339i	0.315224	+	0.0559092i
$167$			4.32740i			0.334864i	0.985884	+	0.167432i	$0.0535475\pi$
$167$			4.32740i			0.334864i	−0.985884	+	0.167432i	$0.946453\pi$
$168$	2.80373	+	4.01735i	0.216313	+	0.309945i
$169$			12.1569i			0.935143i
$170$	0.0895671	−	0.504993i	0.00686948	−	0.0387312i
$171$	−8.92208	−	0.754189i	−0.682289	−	0.0576743i
$172$	9.10670	+	19.6323i	0.694380	+	1.49695i
$173$	−9.37126	−	9.37126i	−0.712483	−	0.712483i	0.254571	−	0.967054i	$-0.418066\pi$
$173$	−9.37126	−	9.37126i	−0.712483	−	0.712483i	−0.967054	+	0.254571i	$0.918066\pi$
$174$	14.8890	−	2.63244i	1.12873	−	0.199565i
$175$			4.99365i			0.377485i
$176$	−0.462190	−	5.53918i	−0.0348388	−	0.417531i
$177$	3.31867	−	7.14427i	0.249446	−	0.536996i
$178$	5.13369	+	7.34736i	0.384786	+	0.550708i
$179$	15.4721	−	15.4721i	1.15644	−	1.15644i	0.171203	−	0.985236i	$-0.445235\pi$
$179$	15.4721	−	15.4721i	1.15644	−	1.15644i	0.985236	−	0.171203i	$-0.0547653\pi$
$180$	−0.433471	−	0.201642i	−0.0323090	−	0.0150295i
$181$	0.740768	+	0.740768i	0.0550609	+	0.0550609i	0.734101	−	0.679040i	$-0.237604\pi$
$181$	0.740768	+	0.740768i	0.0550609	+	0.0550609i	−0.679040	+	0.734101i	$0.737604\pi$
$182$	1.27861	+	0.226778i	0.0947769	+	0.0168099i
$183$	0.0581412	+	0.0270078i	0.00429792	+	0.00199648i
$184$	1.62209	+	6.12754i	0.119582	+	0.451728i
$185$	−0.179075			−0.0131659
$186$	−9.69183	−	6.77960i	−0.710639	−	0.497105i
$187$	−4.47226	+	4.47226i	−0.327044	+	0.327044i
$188$	−0.815642	+	2.22702i	−0.0594868	+	0.162422i
$189$	−4.51140	−	2.57823i	−0.328156	−	0.187539i
$190$	−0.192628	−	0.275690i	−0.0139747	−	0.0200007i
$191$	16.9588			1.22710			0.613548	−	0.789658i	$-0.289742\pi$
$191$	16.9588			1.22710			0.613548	+	0.789658i	$0.289742\pi$
$192$	10.5739	+	8.95504i	0.763105	+	0.646275i
$193$	−10.7909			−0.776743			−0.388371	−	0.921503i	$-0.626962\pi$
$193$	−10.7909			−0.776743			−0.388371	+	0.921503i	$0.626962\pi$
$194$	5.88742	+	8.42612i	0.422692	+	0.604960i
$195$	−0.119017	+	0.0435165i	−0.00852297	+	0.00311628i
$196$	−0.687816	+	1.87801i	−0.0491297	+	0.134143i
$197$	−1.95292	+	1.95292i	−0.139140	+	0.139140i	−0.773246	−	0.634106i	$-0.781368\pi$
$197$	−1.95292	+	1.95292i	−0.139140	+	0.139140i	0.634106	+	0.773246i	$0.281368\pi$
$198$	2.95766	+	5.10004i	0.210192	+	0.362444i
$199$	20.5617			1.45758			0.728791	−	0.684736i	$-0.240082\pi$
$199$	20.5617			1.45758			0.728791	+	0.684736i	$0.240082\pi$
$200$	3.61446	+	13.6539i	0.255581	+	0.965474i
$201$	7.62762	−	16.4204i	0.538010	−	1.15820i
$202$	−21.8918	−	3.88281i	−1.54030	−	0.273193i
$203$	4.36474	+	4.36474i	0.306345	+	0.306345i
$204$	0.00853621	−	15.7667i	0.000597654	−	1.10389i
$205$	−0.297797	+	0.297797i	−0.0207990	+	0.0207990i
$206$	−9.75504	−	13.9615i	−0.679666	−	0.972742i
$207$	−4.33663	−	5.13749i	−0.301417	−	0.357080i
$208$	3.66018	−	0.305406i	0.253788	−	0.0211761i
$209$			4.14747i			0.286886i
$210$	−0.0339806	−	0.192193i	−0.00234488	−	0.0132626i
$211$	−4.98675	−	4.98675i	−0.343302	−	0.343302i	0.514305	−	0.857607i	$-0.328050\pi$
$211$	−4.98675	−	4.98675i	−0.343302	−	0.343302i	−0.857607	+	0.514305i	$0.828050\pi$
$212$	11.1505	+	24.0383i	0.765817	+	1.65095i
$213$	−3.39454	+	1.24116i	−0.232590	+	0.0850428i
$214$	−1.75107	+	9.87279i	−0.119701	+	0.674890i
$215$		−	0.862193i		−	0.0588011i
$216$	−14.2014	−	3.78411i	−0.966285	−	0.257476i
$217$		−	4.82864i		−	0.327789i
$218$	4.44515	+	0.788406i	0.301064	+	0.0533976i
$219$	−22.8873	+	8.36836i	−1.54658	+	0.565482i
$220$	−0.0761569	+	0.207938i	−0.00513449	+	0.0140192i
$221$	−2.95518	−	2.95518i	−0.198787	−	0.198787i
$222$	−5.42102	+	0.958463i	−0.363835	+	0.0643278i
$223$			21.1250i			1.41463i	0.706896	+	0.707317i	$0.250095\pi$
$223$			21.1250i			1.41463i	−0.706896	+	0.707317i	$0.749905\pi$
$224$	−0.521333	+	5.63278i	−0.0348330	+	0.376356i
$225$	−9.66323	−	11.4478i	−0.644215	−	0.763183i
$226$	9.36794	−	6.54548i	0.623146	−	0.435399i
$227$	−3.90366	+	3.90366i	−0.259095	+	0.259095i	−0.824686	−	0.565591i	$-0.808648\pi$
$227$	−3.90366	+	3.90366i	−0.259095	+	0.259095i	0.565591	+	0.824686i	$0.308648\pi$
$228$	−7.30687	−	7.31479i	−0.483909	−	0.484434i
$229$	−18.5720	−	18.5720i	−1.22727	−	1.22727i	−0.964991	−	0.262283i	$-0.915525\pi$
$229$	−18.5720	−	18.5720i	−1.22727	−	1.22727i	−0.262283	−	0.964991i	$-0.584475\pi$
$230$	0.0441008	−	0.248647i	0.00290792	−	0.0163953i
$231$	−1.01398	+	2.18285i	−0.0667152	+	0.143621i
$232$	15.0935	+	8.77501i	0.990938	+	0.576108i
$233$	−15.2870			−1.00149			−0.500743	−	0.865596i	$-0.666940\pi$
$233$	−15.2870			−1.00149			−0.500743	+	0.865596i	$0.666940\pi$
$234$	−3.37001	+	1.95436i	−0.220304	+	0.127761i
$235$	0.0668125	−	0.0668125i	0.00435837	−	0.00435837i
$236$	8.25157	−	3.82760i	0.537131	−	0.249155i
$237$	24.0634	−	8.79840i	1.56309	−	0.571518i
$238$	5.27637	−	3.68666i	0.342016	−	0.238971i
$239$	−22.5869			−1.46103			−0.730513	−	0.682899i	$-0.760719\pi$
$239$	−22.5869			−1.46103			−0.730513	+	0.682899i	$0.760719\pi$
$240$	−0.232023	−	0.500906i	−0.0149770	−	0.0323334i
$241$	13.8440			0.891770			0.445885	−	0.895090i	$-0.352889\pi$
$241$	13.8440			0.891770			0.445885	+	0.895090i	$0.352889\pi$
$242$	−10.5134	+	7.34584i	−0.675828	+	0.472209i
$243$	15.3313	−	2.81953i	0.983506	−	0.180873i
$244$	0.0311496	+	0.0671526i	0.00199415	+	0.00429900i
$245$	0.0563417	−	0.0563417i	0.00359954	−	0.00359954i
$246$	−7.42112	+	10.6089i	−0.473153	+	0.676400i
$247$	−2.74057			−0.174378
$248$	−3.49503	−	13.2027i	−0.221934	−	0.838371i
$249$	−4.58160	−	2.12825i	−0.290347	−	0.134872i
$250$	0.196663	−	1.10881i	0.0124380	−	0.0701275i
$251$	10.9389	+	10.9389i	0.690457	+	0.690457i	0.962332	−	0.271876i	$-0.0876439\pi$
$251$	10.9389	+	10.9389i	0.690457	+	0.690457i	−0.271876	+	0.962332i	$0.587644\pi$
$252$	−2.05735	−	5.63625i	−0.129601	−	0.355050i
$253$	−2.20204	+	2.20204i	−0.138441	+	0.138441i
$254$	−6.31175	+	4.41009i	−0.396035	+	0.276714i
$255$	−0.264627	+	0.569677i	−0.0165716	+	0.0356746i
$256$	2.65162	+	15.7787i	0.165726	+	0.986172i
$257$			22.3890i			1.39659i	0.715811	+	0.698295i	$0.246057\pi$
$257$			22.3890i			1.39659i	−0.715811	+	0.698295i	$0.753943\pi$
$258$	−4.61472	−	26.1006i	−0.287300	−	1.62495i
$259$	−1.58919	−	1.58919i	−0.0987472	−	0.0987472i
$260$	−0.137401	−	0.0503230i	−0.00852128	−	0.00312090i
$261$	−18.4522	−	1.55978i	−1.14216	−	0.0965477i
$262$	−27.1452	−	4.81456i	−1.67704	−	0.297444i
$263$		−	4.94524i		−	0.304936i	−0.988308	−	0.152468i	$-0.951278\pi$
$263$		−	4.94524i		−	0.304936i	0.988308	−	0.152468i	$-0.0487222\pi$
$264$	−1.19250	+	6.70239i	−0.0733934	+	0.412504i
$265$		−	1.05569i		−	0.0648505i
$266$	0.737130	−	4.15605i	0.0451963	−	0.254824i
$267$	−3.76970	−	10.3100i	−0.230702	−	0.630965i
$268$	18.9654	−	8.79734i	1.15849	−	0.537383i
$269$	−18.3940	−	18.3940i	−1.12150	−	1.12150i	−0.991515	−	0.129989i	$-0.958506\pi$
$269$	−18.3940	−	18.3940i	−1.12150	−	1.12150i	−0.129989	−	0.991515i	$-0.541494\pi$
$270$	0.449812	+	0.374838i	0.0273747	+	0.0228119i
$271$			11.8486i			0.719753i	0.933000	+	0.359877i	$0.117181\pi$
$271$			11.8486i			0.719753i	−0.933000	+	0.359877i	$0.882819\pi$
$272$	11.7584	−	13.8993i	0.712960	−	0.842771i
$273$	−1.44239	−	0.670020i	−0.0872973	−	0.0405515i
$274$	−13.3696	−	19.1347i	−0.807690	−	1.15597i
$275$	−4.90676	+	4.90676i	−0.295889	+	0.295889i
$276$	0.00420304	−	7.76317i	0.000252993	−	0.467288i
$277$	6.50973	+	6.50973i	0.391132	+	0.391132i	0.875091	−	0.483959i	$-0.160802\pi$
$277$	6.50973	+	6.50973i	0.391132	+	0.391132i	−0.483959	+	0.875091i	$0.660802\pi$
$278$	7.91200	+	1.40330i	0.474530	+	0.0841642i
$279$	9.34391	+	11.0695i	0.559405	+	0.662712i
$280$	0.113271	−	0.194833i	0.00676925	−	0.0116435i
$281$	−15.0704			−0.899024			−0.449512	−	0.893274i	$-0.648402\pi$
$281$	−15.0704			−0.899024			−0.449512	+	0.893274i	$0.648402\pi$
$282$	1.66497	−	2.38017i	0.0991477	−	0.141737i
$283$	−1.15006	+	1.15006i	−0.0683637	+	0.0683637i	−0.740462	−	0.672098i	$-0.765393\pi$
$283$	−1.15006	+	1.15006i	−0.0683637	+	0.0683637i	0.672098	+	0.740462i	$0.265393\pi$
$284$	−3.91890	−	1.43529i	−0.232544	−	0.0851687i
$285$	0.141448	+	0.386857i	0.00837865	+	0.0229154i
$286$	1.03353	+	1.47920i	0.0611139	+	0.0874667i
$287$	−5.28555			−0.311996
$288$	−9.70487	−	13.9218i	−0.571865	−	0.820348i
$289$	−3.71578			−0.218575
$290$	−0.398383	−	0.570168i	−0.0233939	−	0.0334814i
$291$	−4.32318	−	11.8238i	−0.253429	−	0.693123i
$292$	−26.4227	−	9.67726i	−1.54627	−	0.566319i
$293$	−18.7265	+	18.7265i	−1.09401	+	1.09401i	−0.0989165	+	0.995096i	$0.531538\pi$
$293$	−18.7265	+	18.7265i	−1.09401	+	1.09401i	−0.995096	+	0.0989165i	$0.968462\pi$
$294$	1.40404	−	2.00716i	0.0818853	−	0.117060i
$295$	−0.362385			−0.0210989
$296$	−5.49550	−	3.19495i	−0.319419	−	0.185703i
$297$	−1.89953	−	6.96627i	−0.110222	−	0.404224i
$298$	−21.0884	−	3.74031i	−1.22162	−	0.216670i
$299$	−1.45507	−	1.45507i	−0.0841487	−	0.0841487i
$300$	0.00936554	−	17.2985i	0.000540720	−	0.998730i
$301$	7.65146	−	7.65146i	0.441023	−	0.441023i
$302$	2.60490	+	3.72815i	0.149895	+	0.214531i
$303$	24.6960	+	11.4718i	1.41875	+	0.659038i
$304$	−0.992703	−	11.8972i	−0.0569354	−	0.682351i
$305$		−	0.00294915i		−	0.000168868i
$306$	−4.96181	+	18.6618i	−0.283648	+	1.06683i
$307$	19.5045	+	19.5045i	1.11318	+	1.11318i	0.992718	+	0.120465i	$0.0384385\pi$
$307$	19.5045	+	19.5045i	1.11318	+	1.11318i	0.120465	+	0.992718i	$0.461562\pi$
$308$	−2.52118	+	1.16948i	−0.143657	+	0.0666374i
$309$	7.16320	+	19.5912i	0.407500	+	1.11450i
$310$	−0.0950217	+	0.535746i	−0.00539687	+	0.0304284i
$311$			17.5380i			0.994487i	0.867611	+	0.497243i	$0.165654\pi$
$311$			17.5380i			0.994487i	−0.867611	+	0.497243i	$0.834346\pi$
$312$	−4.42881	−	0.787982i	−0.250732	−	0.0446107i
$313$		−	17.6529i		−	0.997804i	−0.866659	−	0.498902i	$-0.833737\pi$
$313$		−	17.6529i		−	0.997804i	0.866659	−	0.498902i	$-0.166263\pi$
$314$	28.5188	+	5.05818i	1.60941	+	0.285450i
$315$	−0.0201342	+	0.238188i	−0.00113443	+	0.0134204i
$316$	27.7806	+	10.1746i	1.56278	+	0.572364i
$317$	14.2180	+	14.2180i	0.798562	+	0.798562i	0.982869	−	0.184307i	$-0.0590039\pi$
$317$	14.2180	+	14.2180i	0.798562	+	0.798562i	−0.184307	+	0.982869i	$0.559004\pi$
$318$	−5.65037	−	31.9582i	−0.316857	−	1.79213i
$319$			8.57758i			0.480252i
$320$	0.168689	−	0.614708i	0.00943000	−	0.0343632i
$321$	5.17356	−	11.1374i	0.288760	−	0.621629i
$322$	2.59797	−	1.81523i	0.144779	−	0.101159i
$323$	−9.60565	+	9.60565i	−0.534473	+	0.534473i
$324$	15.6231	+	8.93971i	0.867951	+	0.496651i
$325$	−3.24229	−	3.24229i	−0.179850	−	0.179850i
$326$	1.00108	−	5.64423i	0.0554446	−	0.312605i
$327$	−5.01453	−	2.32936i	−0.277304	−	0.128814i
$328$	−14.4520	+	3.82575i	−0.797978	+	0.211241i
$329$	1.18584			0.0653777
$330$	0.155459	−	0.222238i	0.00855775	−	0.0122338i
$331$	2.53027	−	2.53027i	0.139076	−	0.139076i	−0.634141	−	0.773217i	$-0.718646\pi$
$331$	2.53027	−	2.53027i	0.139076	−	0.139076i	0.773217	+	0.634141i	$0.218646\pi$
$332$	−2.45463	−	5.29171i	−0.134715	−	0.290420i
$333$	6.71839	+	0.567909i	0.368165	+	0.0311212i
$334$	5.01662	−	3.50517i	0.274497	−	0.191794i
$335$	−0.832904			−0.0455064
$336$	2.38619	−	6.50432i	0.130177	−	0.354840i
$337$	−12.4339			−0.677318			−0.338659	−	0.940909i	$-0.609973\pi$
$337$	−12.4339			−0.677318			−0.338659	+	0.940909i	$0.609973\pi$
$338$	14.0931	−	9.84700i	0.766563	−	0.535606i
$339$	−13.1454	+	4.80639i	−0.713959	+	0.261048i
$340$	−0.657972	+	0.305209i	−0.0356835	+	0.0165523i
$341$	4.74462	−	4.74462i	0.256936	−	0.256936i
$342$	6.35254	+	10.9540i	0.343506	+	0.592324i
$343$	1.00000			0.0539949
$344$	15.3828	−	26.4592i	0.829382	−	1.42658i
$345$	−0.130297	+	0.280496i	−0.00701493	+	0.0151014i
$346$	−3.27315	+	18.4545i	−0.175966	+	0.992120i
$347$	15.4354	+	15.4354i	0.828615	+	0.828615i	0.987325	−	0.158710i	$-0.0507334\pi$
$347$	15.4354	+	15.4354i	0.828615	+	0.828615i	−0.158710	+	0.987325i	$0.550733\pi$
$348$	−15.1117	−	15.1281i	−0.810072	−	0.810950i
$349$	10.3679	−	10.3679i	0.554980	−	0.554980i	−0.372894	−	0.927874i	$-0.621635\pi$
$349$	10.3679	−	10.3679i	0.554980	−	0.554980i	0.927874	+	0.372894i	$0.121635\pi$
$350$	5.78899	−	4.04483i	0.309435	−	0.216205i
$351$	4.60318	−	1.25517i	0.245699	−	0.0669962i
$352$	−6.04703	+	5.02251i	−0.322308	+	0.267701i
$353$			36.7135i			1.95406i	0.213099	+	0.977031i	$0.431644\pi$
$353$			36.7135i			1.95406i	−0.213099	+	0.977031i	$0.568356\pi$
$354$	−10.9702	+	1.93959i	−0.583062	+	0.103088i
$355$	0.117570	+	0.117570i	0.00623998	+	0.00623998i
$356$	4.35932	−	11.9027i	0.231044	−	0.630840i
$357$	−7.40397	+	2.70714i	−0.391859	+	0.143277i
$358$	−30.4687	−	5.40402i	−1.61032	−	0.285611i
$359$		−	23.9524i		−	1.26416i	−0.774904	−	0.632080i	$-0.782202\pi$
$359$		−	23.9524i		−	1.26416i	0.774904	−	0.632080i	$-0.217798\pi$
$360$	0.117352	+	0.665838i	0.00618498	+	0.0350928i
$361$		−	10.0920i		−	0.531156i
$362$	0.258732	−	1.45877i	0.0135987	−	0.0766712i
$363$	14.7527	−	5.39410i	0.774319	−	0.283117i
$364$	−0.772771	−	1.66595i	−0.0405042	−	0.0873192i
$365$	0.792703	+	0.792703i	0.0414920	+	0.0414920i
$366$	−0.0157847	−	0.0892776i	−0.000825080	−	0.00466661i
$367$		−	28.1683i		−	1.47037i	−0.677866	−	0.735186i	$-0.737095\pi$
$367$		−	28.1683i		−	1.47037i	0.677866	−	0.735186i	$-0.262905\pi$
$368$	5.78959	−	6.84372i	0.301803	−	0.356753i
$369$	12.1169	−	10.2281i	0.630782	−	0.532453i
$370$	0.145050	+	0.207596i	0.00754079	+	0.0107924i
$371$	9.36864	−	9.36864i	0.486395	−	0.486395i
$372$	−0.00905606	+	16.7269i	−0.000469535	+	0.867249i
$373$	−5.06355	−	5.06355i	−0.262180	−	0.262180i	0.563759	−	0.825939i	$-0.309355\pi$
$373$	−5.06355	−	5.06355i	−0.262180	−	0.262180i	−0.825939	+	0.563759i	$0.809355\pi$
$374$	8.80707	+	1.56205i	0.455403	+	0.0807717i
$375$	−0.581043	+	1.25084i	−0.0300049	+	0.0645932i
$376$	3.24239	−	0.858328i	0.167213	−	0.0442649i
$377$	−5.66790			−0.291912
$378$	0.665345	+	7.31829i	0.0342217	+	0.376412i
$379$	5.88744	−	5.88744i	0.302417	−	0.302417i	−0.539542	−	0.841959i	$-0.681402\pi$
$379$	5.88744	−	5.88744i	0.302417	−	0.302417i	0.841959	+	0.539542i	$0.181402\pi$
$380$	−0.163572	+	0.446615i	−0.00839105	+	0.0229109i
$381$	8.85685	−	3.23836i	0.453750	−	0.165906i
$382$	−13.7365	−	19.6598i	−0.702823	−	1.00588i
$383$	−30.2815			−1.54731			−0.773657	−	0.633605i	$-0.781575\pi$
$383$	−30.2815			−1.54731			−0.773657	+	0.633605i	$0.781575\pi$
$384$	1.81651	−	19.5115i	0.0926986	−	0.995694i
$385$	0.110723			0.00564295
$386$	8.74054	+	12.5095i	0.444882	+	0.636718i
$387$	−2.73431	+	32.3470i	−0.138993	+	1.64429i
$388$	4.99936	−	13.6502i	0.253804	−	0.692985i
$389$	3.35714	−	3.35714i	0.170214	−	0.170214i	−0.616860	−	0.787073i	$-0.711595\pi$
$389$	3.35714	−	3.35714i	0.170214	−	0.170214i	0.787073	+	0.616860i	$0.211595\pi$
$390$	0.146850	+	0.102724i	0.00743606	+	0.00520165i
$391$	−10.2000			−0.515835
$392$	2.73425	−	0.723812i	0.138100	−	0.0365580i
$393$	30.6222	+	14.2247i	1.54469	+	0.717540i
$394$	3.84583	+	0.682108i	0.193750	+	0.0343641i
$395$	−0.833439	−	0.833439i	−0.0419349	−	0.0419349i
$396$	3.51663	−	7.55973i	0.176717	−	0.379891i
$397$	2.69541	−	2.69541i	0.135279	−	0.135279i	−0.636225	−	0.771504i	$-0.719505\pi$
$397$	2.69541	−	2.69541i	0.135279	−	0.135279i	0.771504	+	0.636225i	$0.219505\pi$
$398$	−16.6549	−	23.8366i	−0.834835	−	1.19482i
$399$	−2.17786	+	4.68839i	−0.109029	+	0.234713i
$400$	12.9008	−	15.2497i	0.645041	−	0.762485i
$401$		−	25.6205i		−	1.27943i	−0.768614	−	0.639713i	$-0.779053\pi$
$401$		−	25.6205i		−	1.27943i	0.768614	−	0.639713i	$-0.220947\pi$
$402$	−25.2140	+	4.45795i	−1.25756	+	0.222343i
$403$	3.13515	+	3.13515i	0.156173	+	0.156173i
$404$	13.2311	+	28.5236i	0.658270	+	1.41910i
$405$	−0.414762	−	0.584999i	−0.0206097	−	0.0290688i
$406$	1.52449	−	8.59533i	0.0756594	−	0.426579i
$407$		−	3.12307i		−	0.154805i
$408$	−18.2848	+	12.7611i	−0.905232	+	0.631767i
$409$			6.21409i			0.307267i	0.988128	+	0.153633i	$0.0490975\pi$
$409$			6.21409i			0.307267i	−0.988128	+	0.153633i	$0.950903\pi$
$410$	0.586442	+	0.104013i	0.0289623	+	0.00513684i
$411$	9.81742	+	26.8504i	0.484258	+	1.32443i
$412$	−8.28359	+	22.6175i	−0.408103	+	1.11428i
$413$	−3.21595	−	3.21595i	−0.158247	−	0.158247i
$414$	−2.44308	+	9.18867i	−0.120071	+	0.451598i
$415$			0.232396i			0.0114079i
$416$	−3.31878	−	3.99576i	−0.162716	−	0.195908i
$417$	−8.92545	−	4.14606i	−0.437081	−	0.203034i
$418$	4.80803	−	3.35943i	0.235169	−	0.164315i
$419$	−20.7299	+	20.7299i	−1.01272	+	1.01272i	−0.0128038	+	0.999918i	$0.504076\pi$
$419$	−20.7299	+	20.7299i	−1.01272	+	1.01272i	−0.999918	+	0.0128038i	$0.995924\pi$
$420$	−0.195279	+	0.195068i	−0.00952865	+	0.00951833i
$421$	28.1216	+	28.1216i	1.37056	+	1.37056i	0.859610	+	0.510950i	$0.170706\pi$
$421$	28.1216	+	28.1216i	1.37056	+	1.37056i	0.510950	+	0.859610i	$0.329294\pi$
$422$	−1.74175	+	9.82023i	−0.0847869	+	0.478041i
$423$	−2.71850	+	2.29473i	−0.132178	+	0.111574i
$424$	18.8350	−	32.3973i	0.914709	−	1.57335i
$425$	−22.7284			−1.10249
$426$	4.18840	+	2.92986i	0.202929	+	0.141952i
$427$	0.0261719	−	0.0261719i	0.00126655	−	0.00126655i
$428$	12.8636	−	5.96695i	0.621785	−	0.288423i
$429$	−0.758929	−	2.07565i	−0.0366414	−	0.100213i
$430$	−0.999515	+	0.698372i	−0.0482009	+	0.0336785i
$431$	−19.0430			−0.917267			−0.458633	−	0.888626i	$-0.651661\pi$
$431$	−19.0430			−0.917267			−0.458633	+	0.888626i	$0.651661\pi$
$432$	7.11628	+	19.5284i	0.342382	+	0.939561i
$433$	7.59170			0.364834			0.182417	−	0.983221i	$-0.441608\pi$
$433$	7.59170			0.364834			0.182417	+	0.983221i	$0.441608\pi$
$434$	−5.59770	+	3.91117i	−0.268698	+	0.187742i
$435$	0.292535	+	0.800078i	0.0140260	+	0.0383608i
$436$	−2.68657	−	5.79174i	−0.128664	−	0.277374i
$437$	−4.72960	+	4.72960i	−0.226248	+	0.226248i
$438$	28.2398	+	19.7542i	1.34935	+	0.943893i
$439$	−26.6302			−1.27099			−0.635494	−	0.772106i	$-0.719204\pi$
$439$	−26.6302			−1.27099			−0.635494	+	0.772106i	$0.719204\pi$
$440$	0.302743	−	0.0801425i	0.0144327	−	0.00382064i
$441$	−2.29246	+	1.93510i	−0.109165	+	0.0921477i
$442$	−1.03217	+	5.81954i	−0.0490955	+	0.276807i
$443$	14.6242	+	14.6242i	0.694815	+	0.694815i	0.963287	−	0.268473i	$-0.0865189\pi$
$443$	14.6242	+	14.6242i	0.694815	+	0.694815i	−0.268473	+	0.963287i	$0.586519\pi$
$444$	5.50212	+	5.50808i	0.261119	+	0.261402i
$445$	−0.357089	+	0.357089i	−0.0169277	+	0.0169277i
$446$	24.4896	−	17.1111i	1.15962	−	0.810236i
$447$	23.7897	+	11.0508i	1.12521	+	0.522685i
$448$	6.95219	−	3.95816i	0.328460	−	0.187005i
$449$		−	22.3877i		−	1.05654i	−0.849077	−	0.528270i	$-0.822841\pi$
$449$		−	22.3877i		−	1.05654i	0.849077	−	0.528270i	$-0.177159\pi$
$450$	−5.44387	+	20.4749i	−0.256627	+	0.965197i
$451$	−5.19358	−	5.19358i	−0.244556	−	0.244556i
$452$	−15.1760	−	5.55816i	−0.713817	−	0.261434i
$453$	−1.91280	−	5.23146i	−0.0898711	−	0.245795i
$454$	7.68735	+	1.36345i	0.360785	+	0.0639900i
$455$			0.0731635i			0.00342996i
$456$	−2.56129	+	14.3956i	−0.119943	+	0.674135i
$457$			22.2962i			1.04297i	0.853260	+	0.521485i	$0.174622\pi$
$457$			22.2962i			1.04297i	−0.853260	+	0.521485i	$0.825378\pi$
$458$	−6.48675	+	36.5732i	−0.303106	+	1.70896i
$459$	11.7347	−	20.5334i	0.547729	−	0.958419i
$460$	−0.323971	+	0.150278i	−0.0151052	+	0.00700675i
$461$	−1.27616	−	1.27616i	−0.0594365	−	0.0594365i	0.676764	−	0.736200i	$-0.263382\pi$
$461$	−1.27616	−	1.27616i	−0.0594365	−	0.0594365i	−0.736200	+	0.676764i	$0.763382\pi$
$462$	3.35184	−	0.592621i	0.155942	−	0.0275712i
$463$		−	20.8408i		−	0.968556i	−0.874914	−	0.484278i	$-0.839082\pi$
$463$		−	20.8408i		−	0.968556i	0.874914	−	0.484278i	$-0.160918\pi$
$464$	−2.05306	−	24.6052i	−0.0953109	−	1.14227i
$465$	0.280743	−	0.604370i	0.0130191	−	0.0280270i
$466$	12.3824	+	17.7218i	0.573604	+	0.820945i
$467$	−6.49727	+	6.49727i	−0.300658	+	0.300658i	−0.841271	−	0.540613i	$-0.818192\pi$
$467$	−6.49727	+	6.49727i	−0.300658	+	0.300658i	0.540613	+	0.841271i	$0.318192\pi$
$468$	4.99532	+	2.32372i	0.230909	+	0.107414i
$469$	−7.39154	−	7.39154i	−0.341310	−	0.341310i
$470$	−0.131572	−	0.0233360i	−0.00606894	−	0.00107641i
$471$	−32.1717	−	14.9445i	−1.48240	−	0.688604i
$472$	−11.1210	−	6.46546i	−0.511883	−	0.297597i
$473$	15.0367			0.691386
$474$	−29.6910	−	20.7694i	−1.36375	−	0.953968i
$475$	−10.5389	+	10.5389i	−0.483557	+	0.483557i
$476$	−8.54767	−	3.13056i	−0.391782	−	0.143489i
$477$	−3.34796	+	39.6065i	−0.153293	+	1.81346i
$478$	18.2953	+	26.1843i	0.836807	+	1.19764i
$479$	−27.0082			−1.23404			−0.617019	−	0.786948i	$-0.711660\pi$
$479$	−27.0082			−1.23404			−0.617019	+	0.786948i	$0.711660\pi$
$480$	−0.392749	+	0.674709i	−0.0179264	+	0.0307961i
$481$	2.06366			0.0940950
$482$	−11.2136	−	16.0489i	−0.510764	−	0.731009i
$483$	−3.64555	+	1.33293i	−0.165878	+	0.0606506i
$484$	17.0316	+	6.23780i	0.774165	+	0.283536i
$485$	−0.409518	+	0.409518i	−0.0185953	+	0.0185953i
$486$	−15.6869	−	15.4894i	−0.711573	−	0.702612i
$487$	−6.20042			−0.280968			−0.140484	−	0.990083i	$-0.544866\pi$
$487$	−6.20042			−0.280968			−0.140484	+	0.990083i	$0.544866\pi$
$488$	0.0526169	−	0.0905041i	0.00238186	−	0.00409693i
$489$	−2.95770	+	6.36720i	−0.133752	+	0.287935i
$490$	−0.110952	−	0.0196788i	−0.00501229	−	0.000888996i
$491$	1.63824	+	1.63824i	0.0739327	+	0.0739327i	0.743106	−	0.669174i	$-0.233352\pi$
$491$	1.63824	+	1.63824i	0.0739327	+	0.0739327i	−0.669174	+	0.743106i	$0.733352\pi$
$492$	18.3097	+	0.00991300i	0.825464	+	0.000446912i
$493$	−19.8659	+	19.8659i	−0.894716	+	0.894716i
$494$	2.21984	+	3.17706i	0.0998755	+	0.142943i
$495$	−0.253828	+	0.214260i	−0.0114087	+	0.00963027i
$496$	−12.4745	+	14.7458i	−0.560123	+	0.662106i
$497$			2.08674i			0.0936029i
$498$	1.24386	+	7.03519i	0.0557385	+	0.315254i
$499$	25.2847	+	25.2847i	1.13190	+	1.13190i	0.989861	+	0.142037i	$0.0453652\pi$
$499$	25.2847	+	25.2847i	1.13190	+	1.13190i	0.142037	+	0.989861i	$0.454635\pi$
$500$	−1.44471	+	0.670149i	−0.0646094	+	0.0299700i
$501$	−7.03948	+	2.57387i	−0.314501	+	0.114992i
$502$	3.82068	−	21.5416i	0.170525	−	0.961448i
$503$		−	42.2889i		−	1.88557i	−0.333400	−	0.942785i	$-0.608196\pi$
$503$		−	42.2889i		−	1.88557i	0.333400	−	0.942785i	$-0.391804\pi$
$504$	−4.86750	+	6.95036i	−0.216816	+	0.309593i
$505$		−	1.25267i		−	0.0557433i
$506$	4.33640	+	0.769119i	0.192777	+	0.0341915i
$507$	−19.7759	+	7.23072i	−0.878277	+	0.321128i
$508$	10.2250	+	3.74487i	0.453660	+	0.166152i
$509$	−27.6287	−	27.6287i	−1.22462	−	1.22462i	−0.965972	−	0.258647i	$-0.916723\pi$
$509$	−27.6287	−	27.6287i	−1.22462	−	1.22462i	−0.258647	−	0.965972i	$-0.583277\pi$
$510$	0.874757	−	0.154661i	0.0387349	−	0.00684851i
$511$			14.0696i			0.622401i
$512$	16.1440	−	15.8547i	0.713472	−	0.700683i
$513$	−4.07987	−	14.9623i	−0.180130	−	0.660604i
$514$	25.9549	−	18.1350i	1.14482	−	0.799901i
$515$	0.678542	−	0.678542i	0.0299001	−	0.0299001i
$516$	−26.5198	+	26.4911i	−1.16747	+	1.16621i
$517$	1.16521	+	1.16521i	0.0512459	+	0.0512459i
$518$	−0.555063	+	3.12953i	−0.0243881	+	0.137504i
$519$	9.67056	−	20.8183i	0.424491	−	0.913823i
$520$	0.0529566	+	0.200047i	0.00232230	+	0.00877263i
$521$	30.3995			1.33183			0.665914	−	0.746028i	$-0.268042\pi$
$521$	30.3995			1.33183			0.665914	+	0.746028i	$0.268042\pi$
$522$	13.1380	+	22.6545i	0.575034	+	0.991561i
$523$	18.8182	−	18.8182i	0.822861	−	0.822861i	−0.163657	−	0.986517i	$-0.552329\pi$
$523$	18.8182	−	18.8182i	0.822861	−	0.822861i	0.986517	+	0.163657i	$0.0523289\pi$
$524$	16.4061	+	35.3684i	0.716704	+	1.54508i
$525$	−8.12329	+	2.97015i	−0.354530	+	0.129628i
$526$	−5.73287	+	4.00562i	−0.249965	+	0.174653i
$527$	21.9774			0.957349
$528$	8.73581	−	4.04647i	0.380177	−	0.176100i
$529$	17.9778			0.781642
$530$	−1.22383	+	0.855104i	−0.0531598	+	0.0371433i
$531$	13.5956	+	1.14925i	0.590001	+	0.0498731i
$532$	−5.41505	+	2.51184i	−0.234772	+	0.108902i
$533$	3.43182	−	3.43182i	0.148649	−	0.148649i
$534$	−8.89869	+	12.7212i	−0.385084	+	0.550500i
$535$	−0.564931			−0.0244241
$536$	−25.5604	−	14.8602i	−1.10404	−	0.641863i
$537$	34.3714	+	15.9663i	1.48324	+	0.688995i
$538$	−6.42458	+	36.2228i	−0.276983	+	1.56167i
$539$	0.982600	+	0.982600i	0.0423236	+	0.0423236i
$540$	0.0701936	−	0.825070i	0.00302065	−	0.0355054i
$541$	21.8506	−	21.8506i	0.939431	−	0.939431i	−0.0588371	−	0.998268i	$-0.518739\pi$
$541$	21.8506	−	21.8506i	0.939431	−	0.939431i	0.998268	+	0.0588371i	$0.0187392\pi$
$542$	13.7358	−	9.59734i	0.590002	−	0.412241i
$543$	−0.764427	+	1.64562i	−0.0328047	+	0.0706205i
$544$	−25.6374	−	2.37282i	−1.09919	−	0.101734i
$545$			0.254356i			0.0108954i
$546$	0.391593	+	2.21483i	0.0167586	+	0.0947860i
$547$	−23.4318	−	23.4318i	−1.00187	−	1.00187i	−0.999998	−	0.00187110i	$-0.999404\pi$
$547$	−23.4318	−	23.4318i	−1.00187	−	1.00187i	−0.00187110	−	0.999998i	$-0.500596\pi$
$548$	−11.3530	+	30.9981i	−0.484975	+	1.32417i
$549$	−0.00935276	+	0.110644i	−0.000399166	+	0.00472215i
$550$	9.66272	+	1.71381i	0.412020	+	0.0730771i
$551$			18.4232i			0.784853i
$552$	−9.00302	+	6.28326i	−0.383194	+	0.267433i
$553$		−	14.7926i		−	0.629044i
$554$	2.27369	−	12.8194i	0.0965997	−	0.544644i
$555$	−0.106511	−	0.291306i	−0.00452115	−	0.0123652i
$556$	−4.78188	−	10.3088i	−0.202797	−	0.437191i
$557$	−9.90604	−	9.90604i	−0.419733	−	0.419733i	0.465379	−	0.885112i	$-0.345918\pi$
$557$	−9.90604	−	9.90604i	−0.419733	−	0.419733i	−0.885112	+	0.465379i	$0.845918\pi$
$558$	5.26398	−	19.7983i	0.222842	−	0.838131i
$559$			9.93593i			0.420245i
$560$	−0.317613	+	0.0265017i	−0.0134216	+	0.00111990i
$561$	−9.93517	−	4.61510i	−0.419463	−	0.194850i
$562$	12.2069	+	17.4707i	0.514919	+	0.736955i
$563$	22.6353	−	22.6353i	0.953963	−	0.953963i	−0.0450232	−	0.998986i	$-0.514336\pi$
$563$	22.6353	−	22.6353i	0.953963	−	0.953963i	0.998986	+	0.0450232i	$0.0143362\pi$
$564$	−4.10788	−	0.00222404i	−0.172973	−	9.36489e-5i
$565$	0.455291	+	0.455291i	0.0191543	+	0.0191543i
$566$	2.26476	+	0.401686i	0.0951951	+	0.0168841i
$567$	1.51076	−	8.87229i	0.0634458	−	0.372601i
$568$	1.51040	+	5.70564i	0.0633751	+	0.239404i
$569$	−15.6200			−0.654824			−0.327412	−	0.944882i	$-0.606177\pi$
$569$	−15.6200			−0.654824			−0.327412	+	0.944882i	$0.606177\pi$
$570$	0.333899	−	0.477328i	0.0139855	−	0.0199931i
$571$	2.78108	−	2.78108i	0.116384	−	0.116384i	−0.646516	−	0.762900i	$-0.723775\pi$
$571$	2.78108	−	2.78108i	0.116384	−	0.116384i	0.762900	+	0.646516i	$0.223775\pi$
$572$	0.877633	−	2.39628i	0.0366957	−	0.100194i
$573$	10.0868	+	27.5873i	0.421384	+	1.15248i
$574$	4.28127	+	6.12738i	0.178697	+	0.255752i
$575$	−11.1909			−0.466695
$576$	−8.27819	+	22.5271i	−0.344924	+	0.938630i
$577$	−19.0714			−0.793954			−0.396977	−	0.917829i	$-0.629941\pi$
$577$	−19.0714			−0.793954			−0.396977	+	0.917829i	$0.629941\pi$
$578$	3.00976	+	4.30759i	0.125190	+	0.179172i
$579$	−6.41824	−	17.5537i	−0.266733	−	0.729509i
$580$	−0.338291	+	0.923667i	−0.0140468	+	0.0383532i
$581$	−2.06238	+	2.06238i	−0.0855620	+	0.0855620i
$582$	−10.2052	+	14.5889i	−0.423020	+	0.604731i
$583$	18.4112			0.762516
$584$	10.1837	+	38.4696i	0.421405	+	1.59188i
$585$	−0.141579	−	0.167724i	−0.00585356	−	0.00693455i
$586$	36.8774	+	6.54069i	1.52339	+	0.270194i
$587$	6.44050	+	6.44050i	0.265828	+	0.265828i	0.827417	−	0.561589i	$-0.189810\pi$
$587$	6.44050	+	6.44050i	0.265828	+	0.265828i	−0.561589	+	0.827417i	$0.689810\pi$
$588$	−3.46410	−	0.00187549i	−0.142857	−	7.73439e-5i
$589$	10.1906	−	10.1906i	0.419897	−	0.419897i
$590$	0.293530	+	0.420102i	0.0120844	+	0.0172953i
$591$	−4.33844	−	2.01530i	−0.178460	−	0.0828983i
$592$	0.747512	+	8.95866i	0.0307226	+	0.368199i
$593$		−	5.00130i		−	0.205379i	−0.994713	−	0.102689i	$-0.967255\pi$
$593$		−	5.00130i		−	0.205379i	0.994713	−	0.102689i	$-0.0327448\pi$
$594$	−6.53718	+	7.84472i	−0.268224	+	0.321873i
$595$	0.256437	+	0.256437i	0.0105129	+	0.0105129i
$596$	12.7455	+	27.4768i	0.522076	+	1.12549i
$597$	12.2298	+	33.4483i	0.500533	+	1.36895i
$598$	−0.508219	+	2.86541i	−0.0207826	+	0.117175i
$599$		−	17.5253i		−	0.716064i	−0.933709	−	0.358032i	$-0.883448\pi$
$599$		−	17.5253i		−	0.716064i	0.933709	−	0.358032i	$-0.116552\pi$
$600$	−20.0612	+	14.0009i	−0.818997	+	0.571582i
$601$			5.76128i			0.235008i	0.993072	+	0.117504i	$0.0374892\pi$
$601$			5.76128i			0.235008i	−0.993072	+	0.117504i	$0.962511\pi$
$602$	−15.0678	−	2.67247i	−0.614116	−	0.108922i
$603$	31.2482	+	2.64143i	1.27253	+	0.107567i
$604$	2.21198	−	6.03957i	0.0900042	−	0.245747i
$605$	−0.510963	−	0.510963i	−0.0207736	−	0.0207736i
$606$	−6.70469	−	37.9214i	−0.272359	−	1.54045i
$607$			3.28937i			0.133511i	0.997769	+	0.0667557i	$0.0212648\pi$
$607$			3.28937i			0.133511i	−0.997769	+	0.0667557i	$0.978735\pi$
$608$	−12.9880	+	10.7875i	−0.526732	+	0.437490i
$609$	−4.50414	+	9.69630i	−0.182517	+	0.392914i
$610$	−0.00341886	+	0.00238879i	−0.000138425	+	9.67194e-5i
$611$	−0.769949	+	0.769949i	−0.0311488	+	0.0311488i
$612$	25.6532	−	9.36392i	1.03697	−	0.378514i
$613$	3.34086	+	3.34086i	0.134936	+	0.134936i	0.771349	−	0.636413i	$-0.219582\pi$
$613$	3.34086	+	3.34086i	0.134936	+	0.134936i	−0.636413	+	0.771349i	$0.719582\pi$
$614$	6.81245	−	38.4096i	0.274928	−	1.55009i
$615$	−0.661559	−	0.307308i	−0.0266766	−	0.0123919i
$616$	3.39789	+	1.97545i	0.136905	+	0.0795932i
$617$	24.5463			0.988198			0.494099	−	0.869406i	$-0.335498\pi$
$617$	24.5463			0.988198			0.494099	+	0.869406i	$0.335498\pi$
$618$	16.9093	−	24.1728i	0.680192	−	0.972374i
$619$	33.6427	−	33.6427i	1.35221	−	1.35221i	0.469034	−	0.883180i	$-0.344602\pi$
$619$	33.6427	−	33.6427i	1.35221	−	1.35221i	0.883180	−	0.469034i	$-0.155398\pi$
$620$	0.698042	−	0.323796i	0.0280340	−	0.0130040i
$621$	5.77791	−	10.1102i	0.231859	−	0.405709i
$622$	20.3312	−	14.2057i	0.815208	−	0.569595i
$623$	−6.33792			−0.253923
$624$	2.67383	+	5.77245i	0.107039	+	0.231083i
$625$	−24.9048			−0.996192
$626$	−20.4645	+	14.2988i	−0.817928	+	0.571495i
$627$	−6.74678	+	2.46685i	−0.269441	+	0.0985166i
$628$	−17.2363	−	37.1581i	−0.687802	−	1.48277i
$629$	7.23312	−	7.23312i	0.288403	−	0.288403i
$630$	0.292433	−	0.169590i	0.0116508	−	0.00675664i
$631$	−9.04985			−0.360269			−0.180134	−	0.983642i	$-0.557653\pi$
$631$	−9.04985			−0.360269			−0.180134	+	0.983642i	$0.557653\pi$
$632$	−10.7070	−	40.4465i	−0.425903	−	1.60888i
$633$	5.14602	−	11.0781i	0.204536	−	0.440315i
$634$	4.96599	−	27.9990i	0.197225	−	1.11198i
$635$	−0.306758	−	0.306758i	−0.0121733	−	0.0121733i
$636$	−32.4715	+	32.4363i	−1.28758	+	1.28618i
$637$	−0.649283	+	0.649283i	−0.0257255	+	0.0257255i
$638$	9.94374	−	6.94780i	0.393676	−	0.275066i
$639$	−4.03805	−	4.78376i	−0.159743	−	0.189243i
$640$	−0.849250	+	0.302354i	−0.0335696	+	0.0119516i
$641$			4.29829i			0.169772i	0.996391	+	0.0848860i	$0.0270526\pi$
$641$			4.29829i			0.169772i	−0.996391	+	0.0848860i	$0.972947\pi$
$642$	−17.1018	+	3.02368i	−0.674954	+	0.119335i
$643$	−8.10913	−	8.10913i	−0.319793	−	0.319793i	0.528895	−	0.848688i	$-0.322607\pi$
$643$	−8.10913	−	8.10913i	−0.319793	−	0.319793i	−0.848688	+	0.528895i	$0.822607\pi$
$644$	−4.20868	−	1.54142i	−0.165845	−	0.0607404i
$645$	1.40255	−	0.512820i	0.0552254	−	0.0201923i
$646$	18.9161	+	3.35502i	0.744243	+	0.132001i
$647$		−	27.3981i		−	1.07713i	−0.842584	−	0.538565i	$-0.818967\pi$
$647$		−	27.3981i		−	1.07713i	0.842584	−	0.538565i	$-0.181033\pi$
$648$	−2.29110	−	25.3525i	−0.0900028	−	0.995942i
$649$		−	6.31999i		−	0.248081i
$650$	−1.13245	+	6.38494i	−0.0444184	+	0.250438i
$651$	7.85486	−	2.87200i	0.307856	−	0.112563i
$652$	−7.35406	+	3.41128i	−0.288007	+	0.133596i
$653$	34.6921	+	34.6921i	1.35761	+	1.35761i	0.876859	+	0.480747i	$0.159635\pi$
$653$	34.6921	+	34.6921i	1.35761	+	1.35761i	0.480747	+	0.876859i	$0.340365\pi$
$654$	1.36139	+	7.69996i	0.0532346	+	0.301092i
$655$		−	1.55328i		−	0.0606916i
$656$	16.1411	+	13.6549i	0.630205	+	0.533135i
$657$	−27.2260	−	32.2539i	−1.06219	−	1.25834i
$658$	−0.960528	−	1.37471i	−0.0374453	−	0.0535919i
$659$	−1.03430	+	1.03430i	−0.0402906	+	0.0402906i	−0.726965	−	0.686674i	$-0.759070\pi$
$659$	−1.03430	+	1.03430i	−0.0402906	+	0.0402906i	0.686674	+	0.726965i	$0.259070\pi$
$660$	−0.383555		0.000207659i	−0.0149299		8.08313e-6i
$661$	−1.42359	−	1.42359i	−0.0553711	−	0.0553711i	0.678879	−	0.734250i	$-0.262466\pi$
$661$	−1.42359	−	1.42359i	−0.0553711	−	0.0553711i	−0.734250	+	0.678879i	$0.762466\pi$
$662$	−4.98277	−	0.883759i	−0.193661	−	0.0343483i
$663$	3.04957	−	6.56497i	0.118435	−	0.254962i
$664$	−4.14628	+	7.13184i	−0.160907	+	0.276769i
$665$	0.237813			0.00922201
$666$	−4.78350	−	8.24843i	−0.185357	−	0.319620i
$667$	−9.78153	+	9.78153i	−0.378742	+	0.378742i
$668$	−8.12688	−	2.97645i	−0.314438	−	0.115162i
$669$	−34.3645	+	12.5648i	−1.32861	+	0.485785i
$670$	0.674648	+	0.965561i	0.0260639	+	0.0373029i
$671$	0.0514331			0.00198555
$672$	−9.47306	+	2.50223i	−0.365431	+	0.0965256i
$673$	10.7072			0.412733			0.206367	−	0.978475i	$-0.433836\pi$
$673$	10.7072			0.412733			0.206367	+	0.978475i	$0.433836\pi$
$674$	10.0714	+	14.4143i	0.387936	+	0.555216i
$675$	12.8748	−	22.5284i	0.495551	−	0.867117i
$676$	−22.8307	−	8.36168i	−0.878103	−	0.321603i
$677$	−12.6999	+	12.6999i	−0.488098	+	0.488098i	−0.907706	−	0.419607i	$-0.862168\pi$
$677$	−12.6999	+	12.6999i	−0.488098	+	0.488098i	0.419607	+	0.907706i	$0.362168\pi$
$678$	16.2196	+	11.3459i	0.622910	+	0.435736i
$679$	−7.26847			−0.278938
$680$	0.886774	+	0.515550i	0.0340062	+	0.0197704i
$681$	−8.67202	−	4.02834i	−0.332313	−	0.154366i
$682$	−9.34342	−	1.65718i	−0.357778	−	0.0634567i
$683$	7.64233	+	7.64233i	0.292426	+	0.292426i	0.838038	−	0.545612i	$-0.183703\pi$
$683$	7.64233	+	7.64233i	0.292426	+	0.292426i	−0.545612	+	0.838038i	$0.683703\pi$
$684$	7.55312	−	16.2370i	0.288801	−	0.620837i
$685$	0.929967	−	0.929967i	0.0355322	−	0.0355322i
$686$	−0.809995	−	1.15927i	−0.0309258	−	0.0442611i
$687$	19.1652	−	41.2579i	0.731197	−	1.57409i
$688$	−43.1333	+	3.59905i	−1.64444	+	0.137212i
$689$			12.1658i			0.463480i
$690$	0.430710	−	0.0761517i	0.0163969	−	0.00289905i
$691$	−12.1159	−	12.1159i	−0.460911	−	0.460911i	0.438043	−	0.898954i	$-0.355672\pi$
$691$	−12.1159	−	12.1159i	−0.460911	−	0.460911i	−0.898954	+	0.438043i	$0.855672\pi$
$692$	24.0450	−	11.1536i	0.914053	−	0.423996i
$693$	−4.15400	−	0.351140i	−0.157798	−	0.0133387i
$694$	5.39120	−	30.3964i	0.204647	−	1.15383i
$695$			0.452733i			0.0171731i
$696$	−5.29712	+	29.7722i	−0.200787	+	1.12851i
$697$		−	24.0570i		−	0.911222i
$698$	−20.4171	−	3.62124i	−0.772798	−	0.137066i
$699$	−9.09249	−	24.8677i	−0.343909	−	0.940584i
$700$	−9.37811	−	3.43471i	−0.354459	−	0.129820i
$701$	16.9921	+	16.9921i	0.641783	+	0.641783i	0.950994	−	0.309211i	$-0.100065\pi$
$701$	16.9921	+	16.9921i	0.641783	+	0.641783i	−0.309211	+	0.950994i	$0.600065\pi$
$702$	−5.18364	−	4.31964i	−0.195644	−	0.163034i
$703$		−	6.70781i		−	0.252990i
$704$	10.7205	+	2.94194i	0.404044	+	0.110878i
$705$	0.148425	+	0.0689464i	0.00558999	+	0.00259667i
$706$	42.5608	−	29.7377i	1.60180	−	1.11919i
$707$	11.1168	−	11.1168i	0.418089	−	0.418089i
$708$	11.1344	+	11.1464i	0.418455	+	0.418908i
$709$	2.15033	+	2.15033i	0.0807575	+	0.0807575i	0.746332	−	0.665574i	$-0.231813\pi$
$709$	2.15033	+	2.15033i	0.0807575	+	0.0807575i	−0.665574	+	0.746332i	$0.731813\pi$
$710$	0.0410644	−	0.231527i	0.00154112	−	0.00868906i
$711$	28.6251	+	33.9114i	1.07353	+	1.27178i
$712$	−17.3294	+	4.58746i	−0.649448	+	0.171922i
$713$	10.8212			0.405255
$714$	9.13548	+	6.39043i	0.341887	+	0.239156i
$715$	−0.0718904	+	0.0718904i	−0.00268855	+	0.00268855i
$716$	18.4147	+	39.6986i	0.688191	+	1.48361i
$717$	−13.4344	−	36.7427i	−0.501715	−	1.37218i
$718$	−27.7673	+	19.4013i	−1.03627	+	0.724051i
$719$	−40.9574			−1.52745			−0.763726	−	0.645540i	$-0.776632\pi$
$719$	−40.9574			−1.52745			−0.763726	+	0.645540i	$0.776632\pi$
$720$	0.676832	−	0.675368i	0.0252241	−	0.0251695i
$721$	12.0433			0.448517
$722$	−11.6993	+	8.17444i	−0.435403	+	0.304221i
$723$	8.23420	+	22.5204i	0.306233	+	0.837541i
$724$	−1.90068	+	0.881656i	−0.0706382	+	0.0327665i
$725$	−21.7960	+	21.7960i	−0.809482	+	0.809482i
$726$	−18.2029	−	12.7332i	−0.675572	−	0.472574i
$727$	−32.5137			−1.20587			−0.602933	−	0.797791i	$-0.706002\pi$
$727$	−32.5137			−1.20587			−0.602933	+	0.797791i	$0.706002\pi$
$728$	−1.30534	+	2.24526i	−0.0483791	+	0.0832148i
$729$	13.7055	+	23.2629i	0.507609	+	0.861587i
$730$	0.276872	−	1.56104i	0.0102475	−	0.0577768i
$731$	34.8253	+	34.8253i	1.28806	+	1.28806i
$732$	−0.0907113	+	0.0906132i	−0.00335279	+	0.00334916i
$733$	−7.24114	+	7.24114i	−0.267458	+	0.267458i	−0.828075	−	0.560617i	$-0.810564\pi$
$733$	−7.24114	+	7.24114i	−0.267458	+	0.267458i	0.560617	+	0.828075i	$0.310564\pi$
$734$	−32.6546	+	22.8162i	−1.20530	+	0.842160i
$735$	0.125164	+	0.0581412i	0.00461673	+	0.00214457i
$736$	−12.6233	−	1.16832i	−0.465300	−	0.0430650i
$737$		−	14.5259i		−	0.535067i
$738$	−21.6718	−	5.76209i	−0.797748	−	0.212105i
$739$	−18.5151	−	18.5151i	−0.681087	−	0.681087i	0.279158	−	0.960245i	$-0.409945\pi$
$739$	−18.5151	−	18.5151i	−0.681087	−	0.681087i	−0.960245	+	0.279158i	$0.909945\pi$
$740$	0.123171	−	0.336304i	0.00452784	−	0.0123628i
$741$	−1.63005	−	4.45814i	−0.0598813	−	0.163774i
$742$	−18.4493	−	3.27223i	−0.677296	−	0.120127i
$743$			10.3358i			0.379185i	0.981863	+	0.189593i	$0.0607168\pi$
$743$			10.3358i			0.379185i	−0.981863	+	0.189593i	$0.939283\pi$
$744$	19.3983	−	13.5382i	0.711177	−	0.496335i
$745$		−	1.20670i		−	0.0442102i
$746$	−1.76857	+	9.97147i	−0.0647520	+	0.365081i
$747$	0.737010	−	8.71885i	0.0269658	−	0.319006i
$748$	−5.32285	−	11.4750i	−0.194623	−	0.419569i
$749$	−5.01344	−	5.01344i	−0.183187	−	0.183187i
$750$	1.92071	−	0.339590i	0.0701343	−	0.0124001i
$751$			6.62437i			0.241727i	0.992669	+	0.120863i	$0.0385663\pi$
$751$			6.62437i			0.241727i	−0.992669	+	0.120863i	$0.961434\pi$
$752$	−3.62135	−	3.06356i	−0.132057	−	0.111717i
$753$	−11.2883	+	24.3009i	−0.411367	+	0.885572i
$754$	4.59097	+	6.57063i	0.167193	+	0.239288i
$755$	−0.181192	+	0.181192i	−0.00659425	+	0.00659425i
$756$	7.94495	−	6.69909i	0.288955	−	0.243644i
$757$	3.54651	+	3.54651i	0.128900	+	0.128900i	0.768613	−	0.639713i	$-0.220947\pi$
$757$	3.54651	+	3.54651i	0.128900	+	0.128900i	−0.639713	+	0.768613i	$0.720947\pi$
$758$	−11.5939	−	2.05634i	−0.421111	−	0.0746895i
$759$	−4.89185	−	2.27237i	−0.177563	−	0.0824819i
$760$	0.650240	−	0.172132i	0.0235867	−	0.00624389i
$761$	19.0393			0.690175			0.345088	−	0.938570i	$-0.387849\pi$
$761$	19.0393			0.690175			0.345088	+	0.938570i	$0.387849\pi$
$762$	−10.9281	−	7.64442i	−0.395885	−	0.276928i
$763$	−2.25726	+	2.25726i	−0.0817184	+	0.0817184i
$764$	−11.6645	+	31.8487i	−0.422008	+	1.15225i
$765$	−1.08410	−	0.0916399i	−0.0391959	−	0.00331325i
$766$	24.5279	+	35.1045i	0.886229	+	1.26838i
$767$	4.17613			0.150791
$768$	−24.0905	+	13.6984i	−0.869292	+	0.494299i
$769$	−11.4937			−0.414475			−0.207237	−	0.978291i	$-0.566447\pi$
$769$	−11.4937			−0.414475			−0.207237	+	0.978291i	$0.566447\pi$
$770$	−0.0896849	−	0.128358i	−0.00323202	−	0.00462569i
$771$	−36.4208	+	13.3167i	−1.31166	+	0.479588i
$772$	7.42212	−	20.2653i	0.267128	−	0.729364i
$773$	14.8126	−	14.8126i	0.532774	−	0.532774i	−0.388623	−	0.921397i	$-0.627049\pi$
$773$	14.8126	−	14.8126i	0.532774	−	0.532774i	0.921397	+	0.388623i	$0.127049\pi$
$774$	39.7138	−	23.0311i	1.42748	−	0.827837i
$775$	24.1125			0.866148
$776$	−19.8738	+	5.26100i	−0.713427	+	0.188859i
$777$	1.63994	−	3.53039i	0.0588326	−	0.126652i
$778$	−6.61110	−	1.17257i	−0.237019	−	0.0420385i
$779$	−11.1549	−	11.1549i	−0.399666	−	0.399666i
$780$	0.000137217	−	0.253446i	4.91317e−6	−	0.00907481i
$781$	−2.05043	+	2.05043i	−0.0733700	+	0.0733700i
$782$	8.26193	+	11.8245i	0.295446	+	0.422844i
$783$	−8.43778	−	30.9444i	−0.301541	−	1.10586i
$784$	−3.05382	−	2.58345i	−0.109065	−	0.0922659i
$785$			1.63187i			0.0582441i
$786$	−8.31360	−	47.0214i	−0.296536	−	1.67720i
$787$	−9.51896	−	9.51896i	−0.339314	−	0.339314i	0.516795	−	0.856109i	$-0.327125\pi$
$787$	−9.51896	−	9.51896i	−0.339314	−	0.339314i	−0.856109	+	0.516795i	$0.827125\pi$
$788$	−2.32435	−	5.01086i	−0.0828016	−	0.178504i
$789$	8.04453	−	2.94135i	0.286393	−	0.104715i
$790$	−0.291100	+	1.64126i	−0.0103569	+	0.0583935i
$791$			8.08089i			0.287323i
$792$	−11.6122	+	2.04661i	−0.412622	+	0.0727233i
$793$			0.0339860i			0.00120688i
$794$	−5.30798	−	0.941441i	−0.188373	−	0.0334105i
$795$	1.71732	−	0.627909i	0.0609069	−	0.0222696i
$796$	−14.1427	+	38.6151i	−0.501274	+	1.36868i
$797$	−26.3275	−	26.3275i	−0.932567	−	0.932567i	0.0652984	−	0.997866i	$-0.479200\pi$
$797$	−26.3275	−	26.3275i	−0.932567	−	0.932567i	−0.997866	+	0.0652984i	$0.979200\pi$
$798$	7.19917	−	1.27285i	0.254848	−	0.0450583i
$799$			5.39732i			0.190943i
$800$	−28.1281	−	2.60335i	−0.994480	−	0.0920425i
$801$	14.5294	−	12.2645i	0.513372	−	0.433346i
$802$	−29.7011	+	20.7525i	−1.04878	+	0.732795i
$803$	−13.8247	+	13.8247i	−0.487865	+	0.487865i
$804$	25.5912	+	25.6189i	0.902531	+	0.903509i
$805$	0.126264	+	0.126264i	0.00445021	+	0.00445021i
$806$	1.09503	−	6.17395i	0.0385708	−	0.217468i
$807$	18.9815	−	40.8625i	0.668181	−	1.43843i
$808$	22.3495	−	38.4424i	0.786252	−	1.35240i
$809$	7.86550			0.276536			0.138268	−	0.990395i	$-0.455846\pi$
$809$	7.86550			0.276536			0.138268	+	0.990395i	$0.455846\pi$
$810$	−0.342217	+	0.954668i	−0.0120243	+	0.0335436i
$811$	−19.4695	+	19.4695i	−0.683668	+	0.683668i	−0.960825	−	0.277157i	$-0.910608\pi$
$811$	−19.4695	+	19.4695i	−0.683668	+	0.683668i	0.277157	+	0.960825i	$0.410608\pi$
$812$	−11.1991	+	5.19487i	−0.393013	+	0.182304i
$813$	−19.2745	+	7.04739i	−0.675985	+	0.247163i
$814$	−3.62048	+	2.52967i	−0.126898	+	0.0886649i
$815$	0.322969			0.0113131
$816$	29.6041	+	10.8606i	1.03635	+	0.380198i
$817$	32.2961			1.12990
$818$	7.20381	−	5.03338i	0.251875	−	0.175988i
$819$	0.232027	−	2.74489i	0.00810767	−	0.0959141i
$820$	−0.354435	−	0.764094i	−0.0123774	−	0.0266833i
$821$	−18.0960	+	18.0960i	−0.631555	+	0.631555i	−0.948458	−	0.316903i	$-0.897357\pi$
$821$	−18.0960	+	18.0960i	−0.631555	+	0.631555i	0.316903	+	0.948458i	$0.397357\pi$
$822$	23.1748	−	33.1298i	0.808315	−	1.15553i
$823$	−5.02770			−0.175255			−0.0876273	−	0.996153i	$-0.527928\pi$
$823$	−5.02770			−0.175255			−0.0876273	+	0.996153i	$0.527928\pi$
$824$	32.9294	−	8.71711i	1.14715	−	0.303675i
$825$	−10.9004	−	5.06348i	−0.379504	−	0.176288i
$826$	−1.12325	+	6.33307i	−0.0390830	+	0.220356i
$827$	−28.7697	−	28.7697i	−1.00042	−	1.00042i	−1.00000		0.000419119i	$-0.999867\pi$
$827$	−28.7697	−	28.7697i	−1.00042	−	1.00042i	−0.000419119	−	1.00000i	$-0.500133\pi$
$828$	12.6310	−	4.61058i	0.438959	−	0.160229i
$829$	−24.0228	+	24.0228i	−0.834348	+	0.834348i	−0.988108	−	0.153760i	$-0.950862\pi$
$829$	−24.0228	+	24.0228i	−0.834348	+	0.834348i	0.153760	+	0.988108i	$0.450862\pi$
$830$	0.269410	−	0.188240i	0.00935137	−	0.00653390i
$831$	−6.71764	+	14.4614i	−0.233032	+	0.501661i
$832$	−1.94398	+	7.08391i	−0.0673952	+	0.245590i
$833$			4.55146i			0.157699i
$834$	2.42316	+	13.7053i	0.0839073	+	0.474576i
$835$	0.243813	+	0.243813i	0.00843750	+	0.00843750i
$836$	−7.78897	−	2.85269i	−0.269387	−	0.0986624i
$837$	−12.4493	+	21.7839i	−0.430312	+	0.752963i
$838$	40.8227	+	7.24044i	1.41020	+	0.250117i
$839$		−	36.4629i		−	1.25884i	−0.777066	−	0.629419i	$-0.783293\pi$
$839$		−	36.4629i		−	1.25884i	0.777066	−	0.629419i	$-0.216707\pi$
$840$	0.384311	+	0.0683773i	0.0132600	+	0.00235924i
$841$			9.10187i			0.313857i
$842$	9.82216	−	55.3788i	0.338494	−	1.90848i
$843$	−8.96365	−	24.5154i	−0.308724	−	0.844354i
$844$	12.7951	−	5.93518i	0.440426	−	0.204297i
$845$	0.684939	+	0.684939i	0.0235626	+	0.0235626i
$846$	4.86219	+	1.29276i	0.167165	+	0.0444459i
$847$		−	9.06899i		−	0.311614i
$848$	−52.8135	+	4.40676i	−1.81362	+	0.151329i
$849$	−2.55486	−	1.18679i	−0.0876825	−	0.0407304i
$850$	18.4099	+	26.3484i	0.631454	+	0.903741i
$851$	3.56142	−	3.56142i	0.122084	−	0.122084i
$852$	0.00391365	−	7.22866i	0.000134079	−	0.247650i
$853$	1.06625	+	1.06625i	0.0365077	+	0.0365077i	0.725125	−	0.688617i	$-0.241782\pi$
$853$	1.06625	+	1.06625i	0.0365077	+	0.0365077i	−0.688617	+	0.725125i	$0.741782\pi$
$854$	−0.0515395	−	0.00914121i	−0.00176365	−	0.000312806i
$855$	−0.545178	+	0.460193i	−0.0186447	+	0.0157383i
$856$	−17.3367	−	10.0792i	−0.592558	−	0.344499i
$857$	33.9677			1.16032			0.580158	−	0.814504i	$-0.302991\pi$
$857$	33.9677			1.16032			0.580158	+	0.814504i	$0.302991\pi$
$858$	−1.79151	+	2.56107i	−0.0611613	+	0.0874336i
$859$	−22.4121	+	22.4121i	−0.764692	+	0.764692i	−0.977167	−	0.212475i	$-0.931848\pi$
$859$	−22.4121	+	22.4121i	−0.764692	+	0.764692i	0.212475	+	0.977167i	$0.431848\pi$
$860$	1.61920	+	0.593030i	0.0552144	+	0.0202222i
$861$	−3.14377	−	8.59813i	−0.107139	−	0.293024i
$862$	15.4247	+	22.0759i	0.525367	+	0.751909i
$863$	44.7992			1.52498			0.762491	−	0.646999i	$-0.223976\pi$
$863$	44.7992			1.52498			0.762491	+	0.646999i	$0.223976\pi$
$864$	16.8745	−	24.0676i	0.574084	−	0.818797i
$865$	−1.05599			−0.0359046
$866$	−6.14924	−	8.80083i	−0.208960	−	0.299064i
$867$	−2.21009	−	6.04454i	−0.0750585	−	0.205283i
$868$	9.06822	+	3.32121i	0.307795	+	0.112729i
$869$	14.5352	−	14.5352i	0.493072	−	0.493072i
$870$	0.690554	−	0.987187i	0.0234120	−	0.0334688i
$871$	9.59840			0.325229
$872$	−4.53808	+	7.80574i	−0.153679	+	0.264336i
$873$	16.6627	−	14.0652i	0.563946	−	0.476036i
$874$	9.31385	+	1.65193i	0.315046	+	0.0558775i
$875$	0.563060	+	0.563060i	0.0190349	+	0.0190349i
$876$	0.0263873	−	48.7384i	0.000891545	−	1.64672i
$877$	−6.84684	+	6.84684i	−0.231201	+	0.231201i	−0.813194	−	0.581993i	$-0.802273\pi$
$877$	−6.84684	+	6.84684i	−0.231201	+	0.231201i	0.581993	+	0.813194i	$0.302273\pi$
$878$	21.5703	+	30.8716i	0.727963	+	1.04186i
$879$	−41.6010	−	19.3246i	−1.40317	−	0.651802i
$880$	−0.338127	−	0.286046i	−0.0113983	−	0.00964262i
$881$		−	41.0576i		−	1.38327i	−0.722249	−	0.691633i	$-0.756892\pi$
$881$		−	41.0576i		−	1.38327i	0.722249	−	0.691633i	$-0.243108\pi$
$882$	4.10019	+	1.09016i	0.138061	+	0.0367075i
$883$	19.6591	+	19.6591i	0.661583	+	0.661583i	0.955753	−	0.294170i	$-0.0950432\pi$
$883$	19.6591	+	19.6591i	0.661583	+	0.661583i	−0.294170	+	0.955753i	$0.595043\pi$
$884$	7.58248	−	3.51723i	0.255026	−	0.118297i
$885$	−0.215541	−	0.589500i	−0.00724533	−	0.0198158i
$886$	5.10786	−	28.7988i	0.171602	−	0.967516i
$887$			52.5972i			1.76604i	0.469334	+	0.883021i	$0.344494\pi$
$887$			52.5972i			1.76604i	−0.469334	+	0.883021i	$0.655506\pi$
$888$	1.92867	−	10.8400i	0.0647218	−	0.363766i
$889$		−	5.44459i		−	0.182606i
$890$	0.703204	+	0.124722i	0.0235714	+	0.00418071i
$891$	10.2024	−	7.23345i	0.341793	−	0.242330i
$892$	−39.6729	−	14.5301i	−1.32835	−	0.486504i
$893$	2.50267	+	2.50267i	0.0837487	+	0.0837487i
$894$	−6.45863	−	36.5297i	−0.216009	−	1.22174i
$895$		−	1.74345i		−	0.0582771i
$896$	−10.2198	−	4.85338i	−0.341420	−	0.162140i
$897$	1.50154	−	3.23244i	0.0501349	−	0.107928i
$898$	−25.9534	+	18.1339i	−0.866075	+	0.605136i
$899$	21.0757	−	21.0757i	0.702915	−	0.702915i
$900$	28.1455	−	10.2737i	0.938182	−	0.342455i
$901$	42.6410	+	42.6410i	1.42058	+	1.42058i
$902$	−1.81399	+	10.2275i	−0.0603992	+	0.340540i
$903$	16.9978	+	7.89584i	0.565651	+	0.262757i
$904$	5.84905	+	22.0951i	0.194536	+	0.734873i
$905$	0.0834723			0.00277471
$906$	−4.51532	+	6.45491i	−0.150011	+	0.214450i
$907$	−20.1032	+	20.1032i	−0.667515	+	0.667515i	−0.957140	−	0.289625i	$-0.906469\pi$
$907$	−20.1032	+	20.1032i	−0.667515	+	0.667515i	0.289625	+	0.957140i	$0.406469\pi$
$908$	−4.64611	−	10.0161i	−0.154186	−	0.332396i
$909$	−3.97267	+	46.9968i	−0.131765	+	1.55878i
$910$	0.0848162	−	0.0592621i	0.00281163	−	0.00196452i
$911$	−19.5030			−0.646165			−0.323082	−	0.946371i	$-0.604719\pi$
$911$	−19.5030			−0.646165			−0.323082	+	0.946371i	$0.604719\pi$
$912$	18.7630	−	8.69113i	0.621305	−	0.287792i
$913$	−4.05299			−0.134135
$914$	25.8473	−	18.0598i	0.854952	−	0.597365i
$915$	0.00479744	−	0.00175411i	0.000158599	−	5.79890e-5i
$916$	47.6525	−	22.1043i	1.57448	−	0.730345i
$917$	13.7844	−	13.7844i	0.455202	−	0.455202i
$918$	−33.3089	+	3.02829i	−1.09936	+	0.0999485i
$919$	−20.6131			−0.679963			−0.339982	−	0.940432i	$-0.610421\pi$
$919$	−20.6131			−0.679963			−0.339982	+	0.940432i	$0.610421\pi$
$920$	0.436627	+	0.253845i	0.0143952	+	0.00836902i
$921$	−20.1275	+	43.3295i	−0.663223	+	1.42776i
$922$	−0.445730	+	2.51309i	−0.0146793	+	0.0827642i
$923$	−1.35488	−	1.35488i	−0.0445965	−	0.0445965i
$924$	−3.40198	−	3.40567i	−0.111917	−	0.112038i
$925$	7.93584	−	7.93584i	0.260929	−	0.260929i
$926$	−24.1602	+	16.8810i	−0.793953	+	0.554744i
$927$	−27.6089	+	23.3051i	−0.906794	+	0.765439i
$928$	−26.8611	+	22.3101i	−0.881758	+	0.732366i
$929$			26.0927i			0.856072i	0.903762	+	0.428036i	$0.140794\pi$
$929$			26.0927i			0.856072i	−0.903762	+	0.428036i	$0.859206\pi$
$930$	−0.928029	+	0.164080i	−0.0304313	+	0.00538040i
$931$	2.11045	+	2.11045i	0.0691674	+	0.0691674i
$932$	10.5146	−	28.7091i	0.344419	−	0.940398i
$933$	−28.5294	+	10.4313i	−0.934011	+	0.341506i
$934$	12.7949	+	2.26934i	0.418661	+	0.0742550i
$935$			0.503950i			0.0164809i
$936$	−1.35236	−	7.67313i	−0.0442034	−	0.250804i
$937$		−	27.2654i		−	0.890723i	−0.895351	−	0.445362i	$-0.853075\pi$
$937$		−	27.2654i		−	0.890723i	0.895351	−	0.445362i	$-0.146925\pi$
$938$	−2.58168	+	14.5559i	−0.0842949	+	0.475267i
$939$	28.7165	−	10.4997i	0.937127	−	0.342645i
$940$	0.0795197	+	0.171429i	0.00259365	+	0.00559140i
$941$	−7.49253	−	7.49253i	−0.244249	−	0.244249i	0.574356	−	0.818606i	$-0.305252\pi$
$941$	−7.49253	−	7.49253i	−0.244249	−	0.244249i	−0.818606	+	0.574356i	$0.805252\pi$
$942$	8.73428	+	49.4007i	0.284578	+	1.60956i
$943$		−	11.8451i		−	0.385730i
$944$	1.51270	+	18.1292i	0.0492342	+	0.590055i
$945$	−0.399442	+	0.108918i	−0.0129939	+	0.00354311i
$946$	−12.1796	−	17.4315i	−0.395994	−	0.566749i
$947$	−29.5988	+	29.5988i	−0.961831	+	0.961831i	−0.999298	−	0.0374672i	$-0.988071\pi$
$947$	−29.5988	+	29.5988i	−0.961831	+	0.961831i	0.0374672	+	0.999298i	$0.488071\pi$
$948$	−0.0277433	+	51.2430i	−0.000901061	+	1.66429i
$949$	−9.13512	−	9.13512i	−0.296539	−	0.296539i
$950$	20.7538	+	3.68097i	0.673344	+	0.119426i
$951$	−14.6721	+	31.5854i	−0.475775	+	1.02423i
$952$	3.29440	+	12.4448i	0.106772	+	0.403338i
$953$	−32.9359			−1.06690			−0.533449	−	0.845833i	$-0.679104\pi$
$953$	−32.9359			−1.06690			−0.533449	+	0.845833i	$0.679104\pi$
$954$	48.6265	−	28.1999i	1.57434	−	0.913005i
$955$	0.955488	−	0.955488i	0.0309189	−	0.0309189i
$956$	15.5356	−	42.4184i	0.502458	−	1.37191i
$957$	−13.9534	+	5.10182i	−0.451048	+	0.164918i
$958$	21.8765	+	31.3098i	0.706799	+	1.01158i
$959$	16.5058			0.533001
$960$	1.10029	−	0.0912088i	0.0355118	−	0.00294375i
$961$	7.68424			0.247879
$962$	−1.67156	−	2.39234i	−0.0538932	−	0.0771323i
$963$	21.1946	+	1.79159i	0.682987	+	0.0577333i
$964$	−9.52212	+	25.9991i	−0.306687	+	0.837375i
$965$	−0.607976	+	0.607976i	−0.0195714	+	0.0195714i
$966$	4.49811	+	3.14650i	0.144724	+	0.101237i
$967$	−22.2307			−0.714892			−0.357446	−	0.933934i	$-0.616352\pi$
$967$	−22.2307			−0.714892			−0.357446	+	0.933934i	$0.616352\pi$
$968$	−6.56425	−	24.7969i	−0.210983	−	0.797001i
$969$	−21.3390	−	9.91244i	−0.685509	−	0.318433i
$970$	0.806450	+	0.143034i	0.0258935	+	0.00459256i
$971$	8.19661	+	8.19661i	0.263042	+	0.263042i	0.826289	−	0.563247i	$-0.190448\pi$
$971$	8.19661	+	8.19661i	0.263042	+	0.263042i	−0.563247	+	0.826289i	$0.690448\pi$
$972$	−5.25005	+	30.7317i	−0.168395	+	0.985720i
$973$	−4.01774	+	4.01774i	−0.128803	+	0.128803i
$974$	5.02231	+	7.18796i	0.160925	+	0.230317i
$975$	3.34585	−	7.20278i	0.107153	−	0.230674i
$976$	−0.147538	+	0.0123106i	−0.00472258	+	0.000394053i
$977$			55.0238i			1.76037i	0.474633	+	0.880184i	$0.342581\pi$
$977$			55.0238i			1.76037i	−0.474633	+	0.880184i	$0.657419\pi$
$978$	9.77703	−	1.72863i	0.312635	−	0.0552754i
$979$	−6.22764	−	6.22764i	−0.199036	−	0.199036i
$980$	0.0670574	+	0.144563i	0.00214207	+	0.00461789i
$981$	0.806652	−	9.54272i	0.0257544	−	0.304676i
$982$	0.572196	−	3.22613i	0.0182595	−	0.102950i
$983$			28.7272i			0.916255i	0.888887	+	0.458127i	$0.151480\pi$
$983$			28.7272i			0.916255i	−0.888887	+	0.458127i	$0.848520\pi$
$984$	−14.8193	−	21.2339i	−0.472421	−	0.676912i
$985$			0.220062i			0.00701177i
$986$	39.1213	+	6.93867i	1.24588	+	0.220972i
$987$	0.705323	+	1.92904i	0.0224507	+	0.0614020i
$988$	1.88500	−	5.14680i	0.0599700	−	0.163742i
$989$	17.1472	+	17.1472i	0.545249	+	0.545249i
$990$	0.453984	+	0.120705i	0.0144286	+	0.00383627i
$991$			54.1532i			1.72023i	0.510098	+	0.860116i	$0.329609\pi$
$991$			54.1532i			1.72023i	−0.510098	+	0.860116i	$0.670391\pi$
$992$	27.1987	+	2.51733i	0.863559	+	0.0799252i
$993$	5.62101	+	2.61108i	0.178377	+	0.0828601i
$994$	2.41909	−	1.69025i	0.0767289	−	0.0536113i
$995$	1.15848	−	1.15848i	0.0367264	−	0.0367264i
$996$	7.14817	−	7.14043i	0.226498	−	0.226253i
$997$	19.5787	+	19.5787i	0.620064	+	0.620064i	0.945548	−	0.325484i	$-0.105527\pi$
$997$	19.5787	+	19.5787i	0.620064	+	0.620064i	−0.325484	+	0.945548i	$0.605527\pi$
$998$	8.83132	−	49.7923i	0.279550	−	1.57615i
$999$	3.07217	+	11.2667i	0.0971990	+	0.356464i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.s.d.155.7	✓	48
3.2	odd	2	inner	336.2.s.d.155.18	yes	48
4.3	odd	2		1344.2.s.d.911.9		48
12.11	even	2		1344.2.s.d.911.3		48
16.3	odd	4	inner	336.2.s.d.323.18	yes	48
16.13	even	4		1344.2.s.d.239.3		48
48.29	odd	4		1344.2.s.d.239.9		48
48.35	even	4	inner	336.2.s.d.323.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.d.155.7	✓	48	1.1	even	1	trivial
336.2.s.d.155.18	yes	48	3.2	odd	2	inner
336.2.s.d.323.7	yes	48	48.35	even	4	inner
336.2.s.d.323.18	yes	48	16.3	odd	4	inner
1344.2.s.d.239.3		48	16.13	even	4
1344.2.s.d.239.9		48	48.29	odd	4
1344.2.s.d.911.3		48	12.11	even	2
1344.2.s.d.911.9		48	4.3	odd	2

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809995 - 1.15927i) q^{2} +(0.594785 + 1.62672i) q^{3} +(-0.687816 + 1.87801i) q^{4} +(0.0563417 - 0.0563417i) q^{5} +(1.40404 - 2.00716i) q^{6} +1.00000 q^{7} +(2.73425 - 0.723812i) q^{8} +(-2.29246 + 1.93510i) q^{9} +O(q^{10})\)	\(q+(-0.809995 - 1.15927i) q^{2} +(0.594785 + 1.62672i) q^{3} +(-0.687816 + 1.87801i) q^{4} +(0.0563417 - 0.0563417i) q^{5} +(1.40404 - 2.00716i) q^{6} +1.00000 q^{7} +(2.73425 - 0.723812i) q^{8} +(-2.29246 + 1.93510i) q^{9} +(-0.110952 - 0.0196788i) q^{10} +(0.982600 + 0.982600i) q^{11} +(-3.46410 - 0.00187549i) q^{12} +(-0.649283 + 0.649283i) q^{13} +(-0.809995 - 1.15927i) q^{14} +(0.125164 + 0.0581412i) q^{15} +(-3.05382 - 2.58345i) q^{16} +4.55146i q^{17} +(4.10019 + 1.09016i) q^{18} +(2.11045 + 2.11045i) q^{19} +(0.0670574 + 0.144563i) q^{20} +(0.594785 + 1.62672i) q^{21} +(0.343198 - 1.93500i) q^{22} +2.24104i q^{23} +(2.80373 + 4.01735i) q^{24} +4.99365i q^{25} +(1.27861 + 0.226778i) q^{26} +(-4.51140 - 2.57823i) q^{27} +(-0.687816 + 1.87801i) q^{28} +(4.36474 + 4.36474i) q^{29} +(-0.0339806 - 0.192193i) q^{30} -4.82864i q^{31} +(-0.521333 + 5.63278i) q^{32} +(-1.01398 + 2.18285i) q^{33} +(5.27637 - 3.68666i) q^{34} +(0.0563417 - 0.0563417i) q^{35} +(-2.05735 - 5.63625i) q^{36} +(-1.58919 - 1.58919i) q^{37} +(0.737130 - 4.15605i) q^{38} +(-1.44239 - 0.670020i) q^{39} +(0.113271 - 0.194833i) q^{40} -5.28555 q^{41} +(1.40404 - 2.00716i) q^{42} +(7.65146 - 7.65146i) q^{43} +(-2.52118 + 1.16948i) q^{44} +(-0.0201342 + 0.238188i) q^{45} +(2.59797 - 1.81523i) q^{46} +1.18584 q^{47} +(2.38619 - 6.50432i) q^{48} +1.00000 q^{49} +(5.78899 - 4.04483i) q^{50} +(-7.40397 + 2.70714i) q^{51} +(-0.772771 - 1.66595i) q^{52} +(9.36864 - 9.36864i) q^{53} +(0.665345 + 7.31829i) q^{54} +0.110723 q^{55} +(2.73425 - 0.723812i) q^{56} +(-2.17786 + 4.68839i) q^{57} +(1.52449 - 8.59533i) q^{58} +(-3.21595 - 3.21595i) q^{59} +(-0.195279 + 0.195068i) q^{60} +(0.0261719 - 0.0261719i) q^{61} +(-5.59770 + 3.91117i) q^{62} +(-2.29246 + 1.93510i) q^{63} +(6.95219 - 3.95816i) q^{64} +0.0731635i q^{65} +(3.35184 - 0.592621i) q^{66} +(-7.39154 - 7.39154i) q^{67} +(-8.54767 - 3.13056i) q^{68} +(-3.64555 + 1.33293i) q^{69} +(-0.110952 - 0.0196788i) q^{70} +2.08674i q^{71} +(-4.86750 + 6.95036i) q^{72} +14.0696i q^{73} +(-0.555063 + 3.12953i) q^{74} +(-8.12329 + 2.97015i) q^{75} +(-5.41505 + 2.51184i) q^{76} +(0.982600 + 0.982600i) q^{77} +(0.391593 + 2.21483i) q^{78} -14.7926i q^{79} +(-0.317613 + 0.0265017i) q^{80} +(1.51076 - 8.87229i) q^{81} +(4.28127 + 6.12738i) q^{82} +(-2.06238 + 2.06238i) q^{83} +(-3.46410 - 0.00187549i) q^{84} +(0.256437 + 0.256437i) q^{85} +(-15.0678 - 2.67247i) q^{86} +(-4.50414 + 9.69630i) q^{87} +(3.39789 + 1.97545i) q^{88} -6.33792 q^{89} +(0.292433 - 0.169590i) q^{90} +(-0.649283 + 0.649283i) q^{91} +(-4.20868 - 1.54142i) q^{92} +(7.85486 - 2.87200i) q^{93} +(-0.960528 - 1.37471i) q^{94} +0.237813 q^{95} +(-9.47306 + 2.50223i) q^{96} -7.26847 q^{97} +(-0.809995 - 1.15927i) q^{98} +(-4.15400 - 0.351140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} + 48 q^{7}+O(q^{10}) \) 48 * q + 6 * q^6 + 48 * q^7	\( 48 q + 6 q^{6} + 48 q^{7} - 16 q^{10} + 6 q^{12} - 28 q^{16} - 20 q^{18} + 8 q^{19} - 8 q^{22} - 38 q^{24} - 12 q^{27} - 24 q^{30} + 12 q^{34} - 4 q^{36} + 16 q^{37} - 24 q^{39} + 60 q^{40} + 6 q^{42} - 48 q^{43} + 20 q^{45} + 52 q^{46} + 62 q^{48} + 48 q^{49} + 12 q^{52} + 14 q^{54} - 32 q^{55} - 100 q^{58} - 16 q^{60} + 8 q^{61} - 60 q^{64} - 96 q^{66} - 16 q^{67} - 28 q^{69} - 16 q^{70} - 80 q^{72} - 12 q^{75} + 4 q^{76} - 56 q^{78} + 4 q^{82} + 6 q^{84} - 48 q^{85} + 56 q^{87} + 116 q^{88} + 68 q^{90} - 64 q^{93} + 48 q^{94} + 62 q^{96} + 32 q^{99}+O(q^{100}) \) 48 * q + 6 * q^6 + 48 * q^7 - 16 * q^10 + 6 * q^12 - 28 * q^16 - 20 * q^18 + 8 * q^19 - 8 * q^22 - 38 * q^24 - 12 * q^27 - 24 * q^30 + 12 * q^34 - 4 * q^36 + 16 * q^37 - 24 * q^39 + 60 * q^40 + 6 * q^42 - 48 * q^43 + 20 * q^45 + 52 * q^46 + 62 * q^48 + 48 * q^49 + 12 * q^52 + 14 * q^54 - 32 * q^55 - 100 * q^58 - 16 * q^60 + 8 * q^61 - 60 * q^64 - 96 * q^66 - 16 * q^67 - 28 * q^69 - 16 * q^70 - 80 * q^72 - 12 * q^75 + 4 * q^76 - 56 * q^78 + 4 * q^82 + 6 * q^84 - 48 * q^85 + 56 * q^87 + 116 * q^88 + 68 * q^90 - 64 * q^93 + 48 * q^94 + 62 * q^96 + 32 * q^99

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