LMFDB - Embedded newform 351.2.e.b.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,2,Mod(118,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("351.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.e (of order $3$, degree $2$, not 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:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.487558322307.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 13x^{8} + 43x^{6} + 48x^{4} + 21x^{2} + 3 $ x^10 + 13x^8 + 43x^6 + 48x^4 + 21x^2 + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.1
Root			$-1.65737i$ of defining polynomial
Character	$\chi$	$=$	351.235
Dual form			351.2.e.b.118.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.786226 + 1.36178i) q^{2} +(-0.236304 - 0.409291i) q^{4} +(-0.557959 - 0.966413i) q^{5} +(1.93532 - 3.35208i) q^{7} -2.40175 q^{8} +1.75473 q^{10} +(2.48935 - 4.31168i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(3.04320 + 5.27098i) q^{14} +(2.36093 - 4.08925i) q^{16} +4.37224 q^{17} -6.30588 q^{19} +(-0.263696 + 0.456735i) q^{20} +(3.91439 + 6.77992i) q^{22} +(0.977469 + 1.69303i) q^{23} +(1.87736 - 3.25169i) q^{25} +1.57245 q^{26} -1.82930 q^{28} +(-1.08049 + 1.87146i) q^{29} +(1.25490 + 2.17356i) q^{31} +(1.31070 + 2.27020i) q^{32} +(-3.43757 + 5.95405i) q^{34} -4.31932 q^{35} +7.10248 q^{37} +(4.95785 - 8.58725i) q^{38} +(1.34008 + 2.32108i) q^{40} +(2.75305 + 4.76842i) q^{41} +(-3.94721 + 6.83676i) q^{43} -2.35298 q^{44} -3.07405 q^{46} +(3.99982 - 6.92790i) q^{47} +(-3.99095 - 6.91253i) q^{49} +(2.95207 + 5.11313i) q^{50} +(-0.236304 + 0.409291i) q^{52} -5.68016 q^{53} -5.55582 q^{55} +(-4.64816 + 8.05086i) q^{56} +(-1.69902 - 2.94279i) q^{58} +(-2.34811 - 4.06705i) q^{59} +(-1.06675 + 1.84766i) q^{61} -3.94656 q^{62} +5.32169 q^{64} +(-0.557959 + 0.966413i) q^{65} +(-1.16845 - 2.02382i) q^{67} +(-1.03318 - 1.78952i) q^{68} +(3.39596 - 5.88198i) q^{70} -4.31876 q^{71} +7.66241 q^{73} +(-5.58416 + 9.67205i) q^{74} +(1.49011 + 2.58094i) q^{76} +(-9.63540 - 16.6890i) q^{77} +(1.49553 - 2.59034i) q^{79} -5.26920 q^{80} -8.65808 q^{82} +(6.98114 - 12.0917i) q^{83} +(-2.43953 - 4.22539i) q^{85} +(-6.20679 - 10.7505i) q^{86} +(-5.97881 + 10.3556i) q^{88} -7.98729 q^{89} -3.87065 q^{91} +(0.461960 - 0.800138i) q^{92} +(6.28953 + 10.8938i) q^{94} +(3.51842 + 6.09409i) q^{95} +(-3.82682 + 6.62824i) q^{97} +12.5512 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} - 4 q^{4} + q^{5} + 2 q^{7} - 24 q^{8} - 4 q^{10} + 11 q^{11} - 5 q^{13} - 5 q^{14} - 10 q^{16} - 14 q^{17} + 6 q^{19} - q^{20} + 7 q^{22} + 18 q^{23} + 8 q^{25} - 4 q^{26} - 38 q^{28}+ \cdots + 78 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 - 4 * q^4 + q^5 + 2 * q^7 - 24 * q^8 - 4 * q^10 + 11 * q^11 - 5 * q^13 - 5 * q^14 - 10 * q^16 - 14 * q^17 + 6 * q^19 - q^20 + 7 * q^22 + 18 * q^23 + 8 * q^25 - 4 * q^26 - 38 * q^28 + 4 * q^29 + 16 * q^31 + 31 * q^32 - 13 * q^34 - 22 * q^35 + 10 * q^37 + 24 * q^38 - 18 * q^40 + 12 * q^41 - 2 * q^44 + 12 * q^46 + 15 * q^47 - 3 * q^49 - 5 * q^50 - 4 * q^52 + 6 * q^53 - 34 * q^55 - 24 * q^56 + 2 * q^58 + 3 * q^59 + q^61 + 8 * q^62 + 124 * q^64 + q^65 + 4 * q^67 - 16 * q^68 + 25 * q^70 - 30 * q^71 - 10 * q^73 + 11 * q^74 - 9 * q^76 + q^77 - 13 * q^79 - 64 * q^80 - 42 * q^82 + 26 * q^83 + 7 * q^85 - 6 * q^86 - 3 * q^88 - 58 * q^89 - 4 * q^91 - 6 * q^92 - 12 * q^94 + 12 * q^95 + 16 * q^97 + 78 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.786226	+	1.36178i	−0.555946	+	0.962927i	0.441883	+	0.897073i	$0.354311\pi$
$2$	−0.786226	+	1.36178i	−0.555946	+	0.962927i	−0.997829	+	0.0658542i	$0.979023\pi$
$3$		0			0
$3$		0			0
$4$	−0.236304	−	0.409291i	−0.118152	−	0.204645i
$5$	−0.557959	−	0.966413i	−0.249527	−	0.432193i	0.713868	−	0.700280i	$-0.246942\pi$
$5$	−0.557959	−	0.966413i	−0.249527	−	0.432193i	−0.963395	+	0.268087i	$0.913608\pi$
$6$		0			0
$7$	1.93532	−	3.35208i	0.731483	−	1.26697i	−0.224766	−	0.974413i	$-0.572162\pi$
$7$	1.93532	−	3.35208i	0.731483	−	1.26697i	0.956249	−	0.292553i	$-0.0945049\pi$
$8$	−2.40175			−0.849147
$9$		0			0
$10$	1.75473			0.554894
$11$	2.48935	−	4.31168i	0.750568	−	1.30002i	−0.196980	−	0.980408i	$-0.563113\pi$
$11$	2.48935	−	4.31168i	0.750568	−	1.30002i	0.947548	−	0.319614i	$-0.103553\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	3.04320	+	5.27098i	0.813330	+	1.40873i
$15$		0			0
$16$	2.36093	−	4.08925i	0.590232	−	1.02231i
$17$	4.37224			1.06042			0.530212	−	0.847865i	$-0.322112\pi$
$17$	4.37224			1.06042			0.530212	+	0.847865i	$0.322112\pi$
$18$		0			0
$19$	−6.30588			−1.44667			−0.723335	−	0.690498i	$-0.757392\pi$
$19$	−6.30588			−1.44667			−0.723335	+	0.690498i	$0.757392\pi$
$20$	−0.263696	+	0.456735i	−0.0589642	+	0.102129i
$21$		0			0
$22$	3.91439	+	6.77992i	0.834550	+	1.44548i
$23$	0.977469	+	1.69303i	0.203816	+	0.353020i	0.949755	−	0.312994i	$-0.101332\pi$
$23$	0.977469	+	1.69303i	0.203816	+	0.353020i	−0.745939	+	0.666015i	$0.767999\pi$
$24$		0			0
$25$	1.87736	−	3.25169i	0.375473	−	0.650338i
$26$	1.57245			0.308383
$27$		0			0
$28$	−1.82930			−0.345705
$29$	−1.08049	+	1.87146i	−0.200642	+	0.347522i	−0.948735	−	0.316071i	$-0.897636\pi$
$29$	−1.08049	+	1.87146i	−0.200642	+	0.347522i	0.748094	+	0.663593i	$0.230969\pi$
$30$		0			0
$31$	1.25490	+	2.17356i	0.225388	+	0.390383i	0.956436	−	0.291943i	$-0.0943018\pi$
$31$	1.25490	+	2.17356i	0.225388	+	0.390383i	−0.731048	+	0.682326i	$0.760968\pi$
$32$	1.31070	+	2.27020i	0.231701	+	0.401318i
$33$		0			0
$34$	−3.43757	+	5.95405i	−0.589539	+	1.02111i
$35$	−4.31932			−0.730099
$36$		0			0
$37$	7.10248			1.16764			0.583820	−	0.811883i	$-0.301557\pi$
$37$	7.10248			1.16764			0.583820	+	0.811883i	$0.301557\pi$
$38$	4.95785	−	8.58725i	0.804270	−	1.39304i
$39$		0			0
$40$	1.34008	+	2.32108i	0.211885	+	0.366996i
$41$	2.75305	+	4.76842i	0.429954	+	0.744702i	0.996869	−	0.0790745i	$-0.0251965\pi$
$41$	2.75305	+	4.76842i	0.429954	+	0.744702i	−0.566915	+	0.823776i	$0.691863\pi$
$42$		0			0
$43$	−3.94721	+	6.83676i	−0.601943	+	1.04260i	0.390583	+	0.920568i	$0.372273\pi$
$43$	−3.94721	+	6.83676i	−0.601943	+	1.04260i	−0.992527	+	0.122029i	$0.961060\pi$
$44$	−2.35298			−0.354725
$45$		0			0
$46$	−3.07405			−0.453244
$47$	3.99982	−	6.92790i	0.583434	−	1.01054i	−0.411635	−	0.911349i	$-0.635042\pi$
$47$	3.99982	−	6.92790i	0.583434	−	1.01054i	0.995069	−	0.0991886i	$-0.0316247\pi$
$48$		0			0
$49$	−3.99095	−	6.91253i	−0.570135	−	0.987504i
$50$	2.95207	+	5.11313i	0.417485	+	0.723106i
$51$		0			0
$52$	−0.236304	+	0.409291i	−0.0327695	+	0.0567584i
$53$	−5.68016			−0.780230			−0.390115	−	0.920766i	$-0.627565\pi$
$53$	−5.68016			−0.780230			−0.390115	+	0.920766i	$0.627565\pi$
$54$		0			0
$55$	−5.55582			−0.749147
$56$	−4.64816	+	8.05086i	−0.621137	+	1.07584i
$57$		0			0
$58$	−1.69902	−	2.94279i	−0.223092	−	0.386407i
$59$	−2.34811	−	4.06705i	−0.305699	−	0.529485i	0.671718	−	0.740807i	$-0.265557\pi$
$59$	−2.34811	−	4.06705i	−0.305699	−	0.529485i	−0.977417	+	0.211321i	$0.932223\pi$
$60$		0			0
$61$	−1.06675	+	1.84766i	−0.136583	+	0.236569i	−0.926201	−	0.377030i	$-0.876945\pi$
$61$	−1.06675	+	1.84766i	−0.136583	+	0.236569i	0.789618	+	0.613599i	$0.210279\pi$
$62$	−3.94656			−0.501213
$63$		0			0
$64$	5.32169			0.665212
$65$	−0.557959	+	0.966413i	−0.0692063	+	0.119869i
$66$		0			0
$67$	−1.16845	−	2.02382i	−0.142749	−	0.247249i	0.785782	−	0.618504i	$-0.212261\pi$
$67$	−1.16845	−	2.02382i	−0.142749	−	0.247249i	−0.928531	+	0.371255i	$0.878928\pi$
$68$	−1.03318	−	1.78952i	−0.125291	−	0.217011i
$69$		0			0
$70$	3.39596	−	5.88198i	0.405895	−	0.703032i
$71$	−4.31876			−0.512543			−0.256272	−	0.966605i	$-0.582494\pi$
$71$	−4.31876			−0.512543			−0.256272	+	0.966605i	$0.582494\pi$
$72$		0			0
$73$	7.66241			0.896817			0.448408	−	0.893829i	$-0.351991\pi$
$73$	7.66241			0.896817			0.448408	+	0.893829i	$0.351991\pi$
$74$	−5.58416	+	9.67205i	−0.649145	+	1.12435i
$75$		0			0
$76$	1.49011	+	2.58094i	0.170927	+	0.296054i
$77$	−9.63540	−	16.6890i	−1.09806	−	1.90189i
$78$		0			0
$79$	1.49553	−	2.59034i	0.168260	−	0.291436i	−0.769548	−	0.638589i	$-0.779518\pi$
$79$	1.49553	−	2.59034i	0.168260	−	0.291436i	0.937808	+	0.347154i	$0.112852\pi$
$80$	−5.26920			−0.589115
$81$		0			0
$82$	−8.65808			−0.956125
$83$	6.98114	−	12.0917i	0.766279	−	1.32724i	−0.173288	−	0.984871i	$-0.555439\pi$
$83$	6.98114	−	12.0917i	0.766279	−	1.32724i	0.939567	−	0.342364i	$-0.111228\pi$
$84$		0			0
$85$	−2.43953	−	4.22539i	−0.264604	−	0.458308i
$86$	−6.20679	−	10.7505i	−0.669296	−	1.15925i
$87$		0			0
$88$	−5.97881	+	10.3556i	−0.637343	+	1.10391i
$89$	−7.98729			−0.846651			−0.423325	−	0.905978i	$-0.639137\pi$
$89$	−7.98729			−0.846651			−0.423325	+	0.905978i	$0.639137\pi$
$90$		0			0
$91$	−3.87065			−0.405754
$92$	0.461960	−	0.800138i	0.0481627	−	0.0834202i
$93$		0			0
$94$	6.28953	+	10.8938i	0.648716	+	1.12361i
$95$	3.51842	+	6.09409i	0.360983	+	0.625240i
$96$		0			0
$97$	−3.82682	+	6.62824i	−0.388555	+	0.672996i	−0.992255	−	0.124215i	$-0.960359\pi$
$97$	−3.82682	+	6.62824i	−0.388555	+	0.672996i	0.603701	+	0.797211i	$0.293692\pi$
$98$	12.5512			1.26786
$99$		0			0
$100$	−1.77452			−0.177452
$101$	−5.50684	+	9.53813i	−0.547951	+	0.949080i	0.450463	+	0.892795i	$0.351259\pi$
$101$	−5.50684	+	9.53813i	−0.547951	+	0.949080i	−0.998415	+	0.0562848i	$0.982075\pi$
$102$		0			0
$103$	−2.31923	−	4.01702i	−0.228520	−	0.395809i	0.728849	−	0.684674i	$-0.240055\pi$
$103$	−2.31923	−	4.01702i	−0.228520	−	0.395809i	−0.957370	+	0.288865i	$0.906722\pi$
$104$	1.20088	+	2.07998i	0.117756	+	0.203959i
$105$		0			0
$106$	4.46589	−	7.73515i	0.433766	−	0.751304i
$107$	2.23334			0.215906			0.107953	−	0.994156i	$-0.465570\pi$
$107$	2.23334			0.215906			0.107953	+	0.994156i	$0.465570\pi$
$108$		0			0
$109$	−12.9073			−1.23630			−0.618149	−	0.786061i	$-0.712117\pi$
$109$	−12.9073			−1.23630			−0.618149	+	0.786061i	$0.712117\pi$
$110$	4.36814	−	7.56583i	0.416485	−	0.721374i
$111$		0			0
$112$	−9.13832	−	15.8280i	−0.863490	−	1.49561i
$113$	2.77305	+	4.80306i	0.260867	+	0.451834i	0.966472	−	0.256770i	$-0.0826584\pi$
$113$	2.77305	+	4.80306i	0.260867	+	0.451834i	−0.705606	+	0.708605i	$0.749325\pi$
$114$		0			0
$115$	1.09078	−	1.88928i	0.101715	−	0.176176i
$116$	1.02130			0.0948250
$117$		0			0
$118$	7.38460			0.679808
$119$	8.46170	−	14.6561i	0.775683	−	1.34352i
$120$		0			0
$121$	−6.89375	−	11.9403i	−0.626704	−	1.08548i
$122$	−1.67741	−	2.90537i	−0.151866	−	0.263039i
$123$		0			0
$124$	0.593078	−	1.02724i	0.0532600	−	0.0922490i
$125$	−9.76955			−0.873816
$126$		0			0
$127$	11.0870			0.983809			0.491905	−	0.870649i	$-0.336301\pi$
$127$	11.0870			0.983809			0.491905	+	0.870649i	$0.336301\pi$
$128$	−6.80545	+	11.7874i	−0.601523	+	1.04187i
$129$		0			0
$130$	−0.877364	−	1.51964i	−0.0769499	−	0.133281i
$131$	2.84980	+	4.93599i	0.248988	+	0.431259i	0.963245	−	0.268624i	$-0.0865688\pi$
$131$	2.84980	+	4.93599i	0.248988	+	0.431259i	−0.714257	+	0.699883i	$0.753235\pi$
$132$		0			0
$133$	−12.2039	+	21.1378i	−1.05821	+	1.83288i
$134$	3.67467			0.317443
$135$		0			0
$136$	−10.5010			−0.900457
$137$	3.00702	−	5.20831i	0.256907	−	0.444976i	−0.708505	−	0.705706i	$-0.750630\pi$
$137$	3.00702	−	5.20831i	0.256907	−	0.444976i	0.965412	+	0.260730i	$0.0839632\pi$
$138$		0			0
$139$	5.99085	+	10.3765i	0.508138	+	0.880120i	0.999956	+	0.00942221i	$0.00299923\pi$
$139$	5.99085	+	10.3765i	0.508138	+	0.880120i	−0.491818	+	0.870698i	$0.663667\pi$
$140$	1.02067	+	1.76786i	0.0862626	+	0.149411i
$141$		0			0
$142$	3.39553	−	5.88123i	0.284946	−	0.493541i
$143$	−4.97870			−0.416340
$144$		0			0
$145$	2.41147			0.200262
$146$	−6.02439	+	10.4345i	−0.498582	+	0.863569i
$147$		0			0
$148$	−1.67835	−	2.90698i	−0.137959	−	0.238952i
$149$	10.0766	+	17.4532i	0.825507	+	1.42982i	0.901531	+	0.432715i	$0.142444\pi$
$149$	10.0766	+	17.4532i	0.825507	+	1.42982i	−0.0760235	+	0.997106i	$0.524222\pi$
$150$		0			0
$151$	−0.540200	+	0.935654i	−0.0439608	+	0.0761424i	−0.887169	−	0.461445i	$-0.847331\pi$
$151$	−0.540200	+	0.935654i	−0.0439608	+	0.0761424i	0.843208	+	0.537588i	$0.180664\pi$
$152$	15.1452			1.22844
$153$		0			0
$154$	30.3024			2.44184
$155$	1.40037	−	2.42551i	0.112480	−	0.194822i
$156$		0			0
$157$	10.3978	+	18.0095i	0.829833	+	1.43731i	0.898169	+	0.439650i	$0.144898\pi$
$157$	10.3978	+	18.0095i	0.829833	+	1.43731i	−0.0683361	+	0.997662i	$0.521769\pi$
$158$	2.35165	+	4.07318i	0.187087	+	0.324045i
$159$		0			0
$160$	1.46263	−	2.53335i	0.115631	−	0.200279i
$161$	7.56688			0.596353
$162$		0			0
$163$	23.3112			1.82587			0.912937	−	0.408101i	$-0.133809\pi$
$163$	23.3112			1.82587			0.912937	+	0.408101i	$0.133809\pi$
$164$	1.30111	−	2.25359i	0.101600	−	0.175976i
$165$		0			0
$166$	10.9775	+	19.0136i	0.852020	+	1.47574i
$167$	7.88747	+	13.6615i	0.610351	+	1.05716i	0.991181	+	0.132514i	$0.0423049\pi$
$167$	7.88747	+	13.6615i	0.610351	+	1.05716i	−0.380830	+	0.924645i	$0.624362\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	7.67209			0.588423
$171$		0			0
$172$	3.73096			0.284483
$173$	−5.16995	+	8.95461i	−0.393064	+	0.680806i	−0.992852	−	0.119352i	$-0.961918\pi$
$173$	−5.16995	+	8.95461i	−0.393064	+	0.680806i	0.599788	+	0.800159i	$0.295252\pi$
$174$		0			0
$175$	−7.26661	−	12.5861i	−0.549304	−	0.951423i
$176$	−11.7544	−	20.3592i	−0.886019	−	1.53463i
$177$		0			0
$178$	6.27982	−	10.8770i	0.470692	−	0.815263i
$179$	9.84680			0.735984			0.367992	−	0.929829i	$-0.380045\pi$
$179$	9.84680			0.735984			0.367992	+	0.929829i	$0.380045\pi$
$180$		0			0
$181$	−19.0799			−1.41820			−0.709098	−	0.705110i	$-0.750898\pi$
$181$	−19.0799			−1.41820			−0.709098	+	0.705110i	$0.750898\pi$
$182$	3.04320	−	5.27098i	0.225577	−	0.390711i
$183$		0			0
$184$	−2.34764	−	4.06623i	−0.173070	−	0.299766i
$185$	−3.96289	−	6.86393i	−0.291358	−	0.504646i
$186$		0			0
$187$	10.8840	−	18.8517i	0.795920	−	1.37857i
$188$	−3.78070			−0.275736
$189$		0			0
$190$	−11.0651			−0.802748
$191$	−2.71267	+	4.69848i	−0.196282	+	0.339970i	−0.947320	−	0.320289i	$-0.896220\pi$
$191$	−2.71267	+	4.69848i	−0.196282	+	0.339970i	0.751038	+	0.660259i	$0.229553\pi$
$192$		0			0
$193$	8.90207	+	15.4188i	0.640785	+	1.10987i	0.985258	+	0.171076i	$0.0547243\pi$
$193$	8.90207	+	15.4188i	0.640785	+	1.10987i	−0.344473	+	0.938796i	$0.611942\pi$
$194$	−6.01749	−	10.4226i	−0.432031	−	0.748299i
$195$		0			0
$196$	−1.88615	+	3.26692i	−0.134725	+	0.233351i
$197$	9.90279			0.705545			0.352772	−	0.935709i	$-0.385239\pi$
$197$	9.90279			0.705545			0.352772	+	0.935709i	$0.385239\pi$
$198$		0			0
$199$	9.39752			0.666172			0.333086	−	0.942896i	$-0.391910\pi$
$199$	9.39752			0.666172			0.333086	+	0.942896i	$0.391910\pi$
$200$	−4.50896	+	7.80975i	−0.318832	+	0.552233i
$201$		0			0
$202$	−8.65925	−	14.9983i	−0.609263	−	1.05527i
$203$	4.18219	+	7.24377i	0.293532	+	0.508413i
$204$		0			0
$205$	3.07217	−	5.32116i	0.214570	−	0.371646i
$206$	7.29375			0.508180
$207$		0			0
$208$	−4.72186			−0.327402
$209$	−15.6976	+	27.1890i	−1.08582	+	1.88070i
$210$		0			0
$211$	−11.3713	−	19.6957i	−0.782835	−	1.35591i	−0.930284	−	0.366841i	$-0.880439\pi$
$211$	−11.3713	−	19.6957i	−0.782835	−	1.35591i	0.147448	−	0.989070i	$-0.452894\pi$
$212$	1.34224	+	2.32484i	0.0921857	+	0.159670i
$213$		0			0
$214$	−1.75591	+	3.04133i	−0.120032	+	0.207901i
$215$	8.80951			0.600804
$216$		0			0
$217$	9.71458			0.659469
$218$	10.1481	−	17.5770i	0.687315	−	1.19046i
$219$		0			0
$220$	1.31286	+	2.27395i	0.0885133	+	0.153309i
$221$	−2.18612	−	3.78647i	−0.147054	−	0.254706i
$222$		0			0
$223$	−9.62529	+	16.6715i	−0.644557	+	1.11641i	0.339847	+	0.940481i	$0.389625\pi$
$223$	−9.62529	+	16.6715i	−0.644557	+	1.11641i	−0.984404	+	0.175925i	$0.943708\pi$
$224$	10.1465			0.677941
$225$		0			0
$226$	−8.72098			−0.580111
$227$	−2.57312	+	4.45677i	−0.170784	+	0.295806i	−0.938694	−	0.344751i	$-0.887963\pi$
$227$	−2.57312	+	4.45677i	−0.170784	+	0.295806i	0.767910	+	0.640557i	$0.221297\pi$
$228$		0			0
$229$	−4.52272	−	7.83357i	−0.298869	−	0.517657i	0.677008	−	0.735976i	$-0.263276\pi$
$229$	−4.52272	−	7.83357i	−0.298869	−	0.517657i	−0.975878	+	0.218318i	$0.929943\pi$
$230$	1.71519	+	2.97080i	0.113096	+	0.195889i
$231$		0			0
$232$	2.59507	−	4.49479i	0.170375	−	0.295097i
$233$	−5.69101			−0.372830			−0.186415	−	0.982471i	$-0.559687\pi$
$233$	−5.69101			−0.372830			−0.186415	+	0.982471i	$0.559687\pi$
$234$		0			0
$235$	−8.92695			−0.582330
$236$	−1.10974	+	1.92212i	−0.0722378	+	0.125120i
$237$		0			0
$238$	13.3056	+	23.0460i	0.862475	+	1.49385i
$239$	−5.22578	−	9.05132i	−0.338028	−	0.585481i	0.646034	−	0.763309i	$-0.276426\pi$
$239$	−5.22578	−	9.05132i	−0.338028	−	0.585481i	−0.984062	+	0.177827i	$0.943093\pi$
$240$		0			0
$241$	−7.45124	+	12.9059i	−0.479976	+	0.831343i	−0.999736	−	0.0229690i	$-0.992688\pi$
$241$	−7.45124	+	12.9059i	−0.479976	+	0.831343i	0.519760	+	0.854312i	$0.326021\pi$
$242$	21.6802			1.39365
$243$		0			0
$244$	1.00831			0.0645504
$245$	−4.45357	+	7.71381i	−0.284528	+	0.492817i
$246$		0			0
$247$	3.15294	+	5.46106i	0.200617	+	0.347479i
$248$	−3.01397	−	5.22035i	−0.191387	−	0.331493i
$249$		0			0
$250$	7.68108	−	13.3040i	0.485794	−	0.841420i
$251$	−7.44478			−0.469910			−0.234955	−	0.972006i	$-0.575494\pi$
$251$	−7.44478			−0.469910			−0.234955	+	0.972006i	$0.575494\pi$
$252$		0			0
$253$	9.73306			0.611912
$254$	−8.71687	+	15.0981i	−0.546945	+	0.947336i
$255$		0			0
$256$	−5.37956	−	9.31767i	−0.336222	−	0.582354i
$257$	3.98142	+	6.89602i	0.248354	+	0.430162i	0.963069	−	0.269254i	$-0.0867771\pi$
$257$	3.98142	+	6.89602i	0.248354	+	0.430162i	−0.714715	+	0.699416i	$0.753444\pi$
$258$		0			0
$259$	13.7456	−	23.8081i	0.854110	−	1.47936i
$260$	0.527392			0.0327075
$261$		0			0
$262$	−8.96234			−0.553695
$263$	−1.72097	+	2.98080i	−0.106119	+	0.183804i	−0.914195	−	0.405275i	$-0.867176\pi$
$263$	−1.72097	+	2.98080i	−0.106119	+	0.183804i	0.808076	+	0.589079i	$0.200509\pi$
$264$		0			0
$265$	3.16929	+	5.48938i	0.194688	+	0.337210i
$266$	−19.1901	−	33.2382i	−1.17662	−	2.03797i
$267$		0			0
$268$	−0.552220	+	0.956473i	−0.0337322	+	0.0584259i
$269$	−9.24141			−0.563458			−0.281729	−	0.959494i	$-0.590908\pi$
$269$	−9.24141			−0.563458			−0.281729	+	0.959494i	$0.590908\pi$
$270$		0			0
$271$	−25.6813			−1.56003			−0.780015	−	0.625761i	$-0.784788\pi$
$271$	−25.6813			−1.56003			−0.780015	+	0.625761i	$0.784788\pi$
$272$	10.3226	−	17.8792i	0.625897	−	1.08408i
$273$		0			0
$274$	4.72840	+	8.18983i	0.285653	+	0.494766i
$275$	−9.34684	−	16.1892i	−0.563636	−	0.976245i
$276$		0			0
$277$	5.10462	−	8.84145i	0.306707	−	0.531232i	−0.670933	−	0.741518i	$-0.734106\pi$
$277$	5.10462	−	8.84145i	0.306707	−	0.531232i	0.977640	+	0.210286i	$0.0674396\pi$
$278$	−18.8407			−1.12999
$279$		0			0
$280$	10.3739			0.619961
$281$	9.87570	−	17.1052i	0.589135	−	1.02041i	−0.405211	−	0.914223i	$-0.632802\pi$
$281$	9.87570	−	17.1052i	0.589135	−	1.02041i	0.994346	−	0.106188i	$-0.0338646\pi$
$282$		0			0
$283$	−10.1506	−	17.5814i	−0.603391	−	1.04510i	−0.992304	−	0.123829i	$-0.960482\pi$
$283$	−10.1506	−	17.5814i	−0.603391	−	1.04510i	0.388912	−	0.921275i	$-0.372851\pi$
$284$	1.02054	+	1.76763i	0.0605580	+	0.104890i
$285$		0			0
$286$	3.91439	−	6.77992i	0.231463	−	0.400905i
$287$	21.3121			1.25802
$288$		0			0
$289$	2.11650			0.124500
$290$	−1.89596	+	3.28391i	−0.111335	+	0.192838i
$291$		0			0
$292$	−1.81066	−	3.13615i	−0.105961	−	0.183529i
$293$	−4.05935	−	7.03101i	−0.237150	−	0.410756i	0.722745	−	0.691114i	$-0.242880\pi$
$293$	−4.05935	−	7.03101i	−0.237150	−	0.410756i	−0.959895	+	0.280359i	$0.909547\pi$
$294$		0			0
$295$	−2.62030	+	4.53850i	−0.152560	+	0.264242i
$296$	−17.0584			−0.991499
$297$		0			0
$298$	−31.6900			−1.83575
$299$	0.977469	−	1.69303i	0.0565285	−	0.0979103i
$300$		0			0
$301$	15.2782	+	26.4627i	0.880623	+	1.52528i
$302$	−0.849439	−	1.47127i	−0.0488797	−	0.0846621i
$303$		0			0
$304$	−14.8877	+	25.7863i	−0.853871	+	1.47895i
$305$	2.38081			0.136325
$306$		0			0
$307$	−14.1914			−0.809944			−0.404972	−	0.914329i	$-0.632719\pi$
$307$	−14.1914			−0.809944			−0.404972	+	0.914329i	$0.632719\pi$
$308$	−4.55377	+	7.88736i	−0.259475	+	0.449424i
$309$		0			0
$310$	2.20202	+	3.81400i	0.125066	+	0.216621i
$311$	13.5633	+	23.4923i	0.769102	+	1.33212i	0.938050	+	0.346499i	$0.112630\pi$
$311$	13.5633	+	23.4923i	0.769102	+	1.33212i	−0.168948	+	0.985625i	$0.554037\pi$
$312$		0			0
$313$	13.5933	−	23.5444i	0.768341	−	1.33081i	−0.170121	−	0.985423i	$-0.554416\pi$
$313$	13.5933	−	23.5444i	0.768341	−	1.33081i	0.938462	−	0.345383i	$-0.112251\pi$
$314$	−32.7000			−1.84537
$315$		0			0
$316$	−1.41360			−0.0795212
$317$	12.7249	−	22.0402i	0.714704	−	1.23790i	−0.248370	−	0.968665i	$-0.579895\pi$
$317$	12.7249	−	22.0402i	0.714704	−	1.23790i	0.963074	−	0.269238i	$-0.0867718\pi$
$318$		0			0
$319$	5.37944	+	9.31746i	0.301191	+	0.521677i
$320$	−2.96929	−	5.14295i	−0.165988	−	0.287500i
$321$		0			0
$322$	−5.94928	+	10.3045i	−0.331540	+	0.574245i
$323$	−27.5709			−1.53408
$324$		0			0
$325$	−3.75473			−0.208275
$326$	−18.3279	+	31.7448i	−1.01509	+	1.75818i
$327$		0			0
$328$	−6.61214	−	11.4526i	−0.365094	−	0.632362i
$329$	−15.4819	−	26.8154i	−0.853545	−	1.47838i
$330$		0			0
$331$	1.80139	−	3.12009i	0.0990131	−	0.171496i	−0.812263	−	0.583291i	$-0.801765\pi$
$331$	1.80139	−	3.12009i	0.0990131	−	0.171496i	0.911276	+	0.411795i	$0.135098\pi$
$332$	−6.59869			−0.362150
$333$		0			0
$334$	−24.8054			−1.35729
$335$	−1.30390	+	2.25841i	−0.0712394	+	0.123390i
$336$		0			0
$337$	2.85188	+	4.93960i	0.155352	+	0.269077i	0.933187	−	0.359391i	$-0.117016\pi$
$337$	2.85188	+	4.93960i	0.155352	+	0.269077i	−0.777835	+	0.628468i	$0.783682\pi$
$338$	−0.786226	−	1.36178i	−0.0427651	−	0.0740713i
$339$		0			0
$340$	−1.15294	+	1.99695i	−0.0625271	+	0.108300i
$341$	12.4956			0.676675
$342$		0			0
$343$	−3.80057			−0.205212
$344$	9.48021	−	16.4202i	0.511138	−	0.885318i
$345$		0			0
$346$	−8.12950	−	14.0807i	−0.437045	−	0.756983i
$347$	17.6247	+	30.5268i	0.946142	+	1.63877i	0.753449	+	0.657506i	$0.228389\pi$
$347$	17.6247	+	30.5268i	0.946142	+	1.63877i	0.192693	+	0.981259i	$0.438278\pi$
$348$		0			0
$349$	−5.45273	+	9.44440i	−0.291878	+	0.505547i	−0.974254	−	0.225454i	$-0.927613\pi$
$349$	−5.45273	+	9.44440i	−0.291878	+	0.505547i	0.682376	+	0.731001i	$0.260947\pi$
$350$	22.8528			1.22153
$351$		0			0
$352$	13.0512			0.695629
$353$	−8.19606	+	14.1960i	−0.436232	+	0.755577i	−0.997395	−	0.0721287i	$-0.977021\pi$
$353$	−8.19606	+	14.1960i	−0.436232	+	0.755577i	0.561163	+	0.827705i	$0.310354\pi$
$354$		0			0
$355$	2.40969	+	4.17371i	0.127893	+	0.221518i
$356$	1.88743	+	3.26912i	0.100034	+	0.173263i
$357$		0			0
$358$	−7.74181	+	13.4092i	−0.409168	+	0.708699i
$359$	1.31488			0.0693969			0.0346984	−	0.999398i	$-0.488953\pi$
$359$	1.31488			0.0693969			0.0346984	+	0.999398i	$0.488953\pi$
$360$		0			0
$361$	20.7642			1.09285
$362$	15.0011	−	25.9827i	0.788441	−	1.36562i
$363$		0			0
$364$	0.914649	+	1.58422i	0.0479407	+	0.0830356i
$365$	−4.27531	−	7.40505i	−0.223780	−	0.387598i
$366$		0			0
$367$	11.5784	−	20.0543i	0.604386	−	1.04683i	−0.387762	−	0.921759i	$-0.626752\pi$
$367$	11.5784	−	20.0543i	0.604386	−	1.04683i	0.992148	−	0.125068i	$-0.0399149\pi$
$368$	9.23094			0.481196
$369$		0			0
$370$	12.4629			0.647916
$371$	−10.9929	+	19.0403i	−0.570725	+	0.988524i
$372$		0			0
$373$	15.1931	+	26.3152i	0.786668	+	1.36255i	0.927998	+	0.372586i	$0.121529\pi$
$373$	15.1931	+	26.3152i	0.786668	+	1.36255i	−0.141330	+	0.989963i	$0.545138\pi$
$374$	17.1147	+	29.6435i	0.884978	+	1.53283i
$375$		0			0
$376$	−9.60658	+	16.6391i	−0.495422	+	0.858095i
$377$	2.16098			0.111296
$378$		0			0
$379$	31.9119			1.63920			0.819602	−	0.572933i	$-0.194195\pi$
$379$	31.9119			1.63920			0.819602	+	0.572933i	$0.194195\pi$
$380$	1.66284	−	2.88012i	0.0853017	−	0.147747i
$381$		0			0
$382$	−4.26555	−	7.38814i	−0.218244	−	0.378010i
$383$	−15.4894	−	26.8285i	−0.791473	−	1.37087i	−0.925055	−	0.379834i	$-0.875981\pi$
$383$	−15.4894	−	26.8285i	−0.791473	−	1.37087i	0.133582	−	0.991038i	$-0.457352\pi$
$384$		0			0
$385$	−10.7523	+	18.6235i	−0.547989	+	0.949144i
$386$	−27.9962			−1.42497
$387$		0			0
$388$	3.61717			0.183634
$389$	−10.1003	+	17.4943i	−0.512108	+	0.886997i	0.487794	+	0.872959i	$0.337802\pi$
$389$	−10.1003	+	17.4943i	−0.512108	+	0.886997i	−0.999901	+	0.0140378i	$0.995531\pi$
$390$		0			0
$391$	4.27373	+	7.40232i	0.216132	+	0.374352i
$392$	9.58527	+	16.6022i	0.484129	+	0.838536i
$393$		0			0
$394$	−7.78584	+	13.4855i	−0.392245	+	0.679388i
$395$	−3.33778			−0.167942
$396$		0			0
$397$	−24.3056			−1.21986			−0.609931	−	0.792454i	$-0.708803\pi$
$397$	−24.3056			−1.21986			−0.609931	+	0.792454i	$0.708803\pi$
$398$	−7.38858	+	12.7974i	−0.370356	+	0.641475i
$399$		0			0
$400$	−8.86465	−	15.3540i	−0.443232	−	0.767701i
$401$	12.5171	+	21.6802i	0.625073	+	1.08266i	0.988527	+	0.151046i	$0.0482643\pi$
$401$	12.5171	+	21.6802i	0.625073	+	1.08266i	−0.363453	+	0.931612i	$0.618402\pi$
$402$		0			0
$403$	1.25490	−	2.17356i	0.0625113	−	0.108273i
$404$	5.20516			0.258966
$405$		0			0
$406$	−13.1526			−0.652752
$407$	17.6806	−	30.6237i	0.876393	−	1.51796i
$408$		0			0
$409$	9.30478	+	16.1164i	0.460092	+	0.796902i	0.998965	−	0.0454844i	$-0.0144831\pi$
$409$	9.30478	+	16.1164i	0.460092	+	0.796902i	−0.538873	+	0.842387i	$0.681150\pi$
$410$	4.83085	+	8.36728i	0.238579	+	0.413230i
$411$		0			0
$412$	−1.09609	+	1.89848i	−0.0540003	+	0.0935312i
$413$	−18.1774			−0.894453
$414$		0			0
$415$	−15.5808			−0.764829
$416$	1.31070	−	2.27020i	0.0642623	−	0.111305i
$417$		0			0
$418$	−24.6837	−	42.7534i	−1.20732	−	2.09114i
$419$	−9.88439	−	17.1203i	−0.482884	−	0.836379i	0.516923	−	0.856032i	$-0.327077\pi$
$419$	−9.88439	−	17.1203i	−0.482884	−	0.836379i	−0.999807	+	0.0196526i	$0.993744\pi$
$420$		0			0
$421$	−0.242394	+	0.419838i	−0.0118135	+	0.0204617i	−0.871872	−	0.489734i	$-0.837094\pi$
$421$	−0.242394	+	0.419838i	−0.0118135	+	0.0204617i	0.860058	+	0.510196i	$0.170427\pi$
$422$	35.7618			1.74086
$423$		0			0
$424$	13.6423			0.662530
$425$	8.20829	−	14.2172i	0.398161	−	0.689634i
$426$		0			0
$427$	4.12901	+	7.15166i	0.199817	+	0.346093i
$428$	−0.527748	−	0.914087i	−0.0255097	−	0.0441841i
$429$		0			0
$430$	−6.92627	+	11.9967i	−0.334014	+	0.578530i
$431$	6.71380			0.323392			0.161696	−	0.986841i	$-0.448304\pi$
$431$	6.71380			0.323392			0.161696	+	0.986841i	$0.448304\pi$
$432$		0			0
$433$	1.48138			0.0711905			0.0355953	−	0.999366i	$-0.488667\pi$
$433$	1.48138			0.0711905			0.0355953	+	0.999366i	$0.488667\pi$
$434$	−7.63786	+	13.2292i	−0.366629	+	0.635020i
$435$		0			0
$436$	3.05005	+	5.28285i	0.146071	+	0.253003i
$437$	−6.16381	−	10.6760i	−0.294855	−	0.510704i
$438$		0			0
$439$	−3.73596	+	6.47087i	−0.178308	+	0.308838i	−0.941301	−	0.337568i	$-0.890396\pi$
$439$	−3.73596	+	6.47087i	−0.178308	+	0.308838i	0.762993	+	0.646406i	$0.223729\pi$
$440$	13.3437			0.636136
$441$		0			0
$442$	6.87514			0.327017
$443$	19.9367	−	34.5314i	0.947221	−	1.64063i	0.195978	−	0.980608i	$-0.437212\pi$
$443$	19.9367	−	34.5314i	0.947221	−	1.64063i	0.751242	−	0.660026i	$-0.229455\pi$
$444$		0			0
$445$	4.45658	+	7.71902i	0.211262	+	0.365917i
$446$	−15.1353	−	26.2151i	−0.716678	−	1.24132i
$447$		0			0
$448$	10.2992	−	17.8387i	0.486591	−	0.842801i
$449$	−12.7677			−0.602546			−0.301273	−	0.953538i	$-0.597412\pi$
$449$	−12.7677			−0.602546			−0.301273	+	0.953538i	$0.597412\pi$
$450$		0			0
$451$	27.4132			1.29084
$452$	1.31057	−	2.26997i	0.0616439	−	0.106770i
$453$		0			0
$454$	−4.04611	−	7.00806i	−0.189893	−	0.328905i
$455$	2.15966	+	3.74064i	0.101246	+	0.175364i
$456$		0			0
$457$	4.64821	−	8.05094i	0.217434	−	0.376607i	−0.736589	−	0.676341i	$-0.763565\pi$
$457$	4.64821	−	8.05094i	0.217434	−	0.376607i	0.954023	+	0.299734i	$0.0968979\pi$
$458$	14.2235			0.664621
$459$		0			0
$460$	−1.03102			−0.0480715
$461$	−6.30336	+	10.9177i	−0.293577	+	0.508490i	−0.974653	−	0.223723i	$-0.928179\pi$
$461$	−6.30336	+	10.9177i	−0.293577	+	0.508490i	0.681076	+	0.732213i	$0.261512\pi$
$462$		0			0
$463$	−7.65035	−	13.2508i	−0.355542	−	0.615817i	0.631669	−	0.775238i	$-0.282370\pi$
$463$	−7.65035	−	13.2508i	−0.355542	−	0.615817i	−0.987211	+	0.159422i	$0.949037\pi$
$464$	5.10192	+	8.83678i	0.236851	+	0.410237i
$465$		0			0
$466$	4.47442	−	7.74992i	0.207273	−	0.359008i
$467$	−16.9099			−0.782498			−0.391249	−	0.920285i	$-0.627957\pi$
$467$	−16.9099			−0.782498			−0.391249	+	0.920285i	$0.627957\pi$
$468$		0			0
$469$	−9.04532			−0.417674
$470$	7.01860	−	12.1566i	0.323744	−	0.560741i
$471$		0			0
$472$	5.63959	+	9.76805i	0.259583	+	0.449611i
$473$	19.6520	+	34.0382i	0.903598	+	1.56508i
$474$		0			0
$475$	−11.8384	+	20.5048i	−0.543185	+	0.940824i
$476$	−7.99814			−0.366594
$477$		0			0
$478$	16.4346			0.751701
$479$	−5.06351	+	8.77026i	−0.231358	+	0.400723i	−0.958208	−	0.286073i	$-0.907650\pi$
$479$	−5.06351	+	8.77026i	−0.231358	+	0.400723i	0.726850	+	0.686796i	$0.240983\pi$
$480$		0			0
$481$	−3.55124	−	6.15093i	−0.161923	−	0.280458i
$482$	−11.7167	−	20.2940i	−0.533682	−	0.924364i
$483$		0			0
$484$	−3.25804	+	5.64309i	−0.148093	+	0.256504i
$485$	8.54083			0.387819
$486$		0			0
$487$	0.181885			0.00824202			0.00412101	−	0.999992i	$-0.498688\pi$
$487$	0.181885			0.00824202			0.00412101	+	0.999992i	$0.498688\pi$
$488$	2.56207	−	4.43763i	0.115979	−	0.200882i
$489$		0			0
$490$	−7.00303	−	12.1296i	−0.316365	−	0.547960i
$491$	3.62972	+	6.28685i	0.163807	+	0.283722i	0.936231	−	0.351385i	$-0.114289\pi$
$491$	3.62972	+	6.28685i	0.163807	+	0.283722i	−0.772424	+	0.635107i	$0.780956\pi$
$492$		0			0
$493$	−4.72416	+	8.18249i	−0.212766	+	0.368521i
$494$	−9.91571			−0.446129
$495$		0			0
$496$	11.8510			0.532124
$497$	−8.35820	+	14.4768i	−0.374917	+	0.649375i
$498$		0			0
$499$	−5.49985	−	9.52603i	−0.246207	−	0.426443i	0.716263	−	0.697830i	$-0.245851\pi$
$499$	−5.49985	−	9.52603i	−0.246207	−	0.426443i	−0.962470	+	0.271387i	$0.912518\pi$
$500$	2.30859	+	3.99859i	0.103243	+	0.178822i
$501$		0			0
$502$	5.85328	−	10.1382i	0.261245	−	0.452489i
$503$	29.7279			1.32550			0.662750	−	0.748841i	$-0.269389\pi$
$503$	29.7279			1.32550			0.662750	+	0.748841i	$0.269389\pi$
$504$		0			0
$505$	12.2904			0.546914
$506$	−7.65239	+	13.2543i	−0.340190	+	0.589227i
$507$		0			0
$508$	−2.61990	−	4.53779i	−0.116239	−	0.201332i
$509$	−2.41633	−	4.18521i	−0.107102	−	0.185506i	0.807493	−	0.589877i	$-0.200824\pi$
$509$	−2.41633	−	4.18521i	−0.107102	−	0.185506i	−0.914595	+	0.404371i	$0.867490\pi$
$510$		0			0
$511$	14.8292	−	25.6850i	0.656007	−	1.13624i
$512$	−10.3036			−0.455359
$513$		0			0
$514$	−12.5212			−0.552286
$515$	−2.58807	+	4.48266i	−0.114044	+	0.197530i
$516$		0			0
$517$	−19.9139	−	34.4919i	−0.875814	−	1.51695i
$518$	21.6143	+	37.4371i	0.949678	+	1.64489i
$519$		0			0
$520$	1.34008	−	2.32108i	0.0587663	−	0.101786i
$521$	17.2295			0.754836			0.377418	−	0.926043i	$-0.376812\pi$
$521$	17.2295			0.754836			0.377418	+	0.926043i	$0.376812\pi$
$522$		0			0
$523$	9.49365			0.415128			0.207564	−	0.978221i	$-0.433446\pi$
$523$	9.49365			0.415128			0.207564	+	0.978221i	$0.433446\pi$
$524$	1.34684	−	2.33279i	0.0588368	−	0.101908i
$525$		0			0
$526$	−2.70614	−	4.68717i	−0.117993	−	0.204371i
$527$	5.48675	+	9.50333i	0.239007	+	0.413971i
$528$		0			0
$529$	9.58911	−	16.6088i	0.416918	−	0.722123i
$530$	−9.96713			−0.432944
$531$		0			0
$532$	11.5353			0.500121
$533$	2.75305	−	4.76842i	0.119248	−	0.206543i
$534$		0			0
$535$	−1.24611	−	2.15833i	−0.0538742	−	0.0933129i
$536$	2.80633	+	4.86071i	0.121215	+	0.209951i
$537$		0			0
$538$	7.26584	−	12.5848i	0.313253	−	0.542569i
$539$	−39.7395			−1.71170
$540$		0			0
$541$	−3.51263			−0.151020			−0.0755098	−	0.997145i	$-0.524058\pi$
$541$	−3.51263			−0.151020			−0.0755098	+	0.997145i	$0.524058\pi$
$542$	20.1913	−	34.9724i	0.867292	−	1.50219i
$543$		0			0
$544$	5.73069	+	9.92584i	0.245701	+	0.425567i
$545$	7.20176	+	12.4738i	0.308489	+	0.534319i
$546$		0			0
$547$	10.2324	−	17.7231i	0.437507	−	0.757785i	−0.559989	−	0.828500i	$-0.689195\pi$
$547$	10.2324	−	17.7231i	0.437507	−	0.757785i	0.997497	+	0.0707152i	$0.0225281\pi$
$548$	−2.84229			−0.121416
$549$		0			0
$550$	29.3949			1.25340
$551$	6.81344	−	11.8012i	0.290262	−	0.502749i
$552$		0			0
$553$	−5.78867	−	10.0263i	−0.246159	−	0.426360i
$554$	8.02677	+	13.9028i	0.341025	+	0.590672i
$555$		0			0
$556$	2.83133	−	4.90400i	0.120075	−	0.207976i
$557$	−37.6453			−1.59508			−0.797540	−	0.603266i	$-0.793866\pi$
$557$	−37.6453			−1.59508			−0.797540	+	0.603266i	$0.793866\pi$
$558$		0			0
$559$	7.89441			0.333898
$560$	−10.1976	+	17.6628i	−0.430928	+	0.746389i
$561$		0			0
$562$	15.5291	+	26.8971i	0.655054	+	1.13459i
$563$	19.5488	+	33.8596i	0.823885	+	1.42701i	0.902768	+	0.430127i	$0.141531\pi$
$563$	19.5488	+	33.8596i	0.823885	+	1.42701i	−0.0788832	+	0.996884i	$0.525135\pi$
$564$		0			0
$565$	3.09450	−	5.35982i	0.130186	−	0.225489i
$566$	31.9227			1.34181
$567$		0			0
$568$	10.3726			0.435225
$569$	17.4317	−	30.1926i	0.730774	−	1.26574i	−0.225779	−	0.974179i	$-0.572493\pi$
$569$	17.4317	−	30.1926i	0.730774	−	1.26574i	0.956553	−	0.291559i	$-0.0941740\pi$
$570$		0			0
$571$	5.09367	+	8.82250i	0.213164	+	0.369210i	0.952703	−	0.303903i	$-0.0982899\pi$
$571$	5.09367	+	8.82250i	0.213164	+	0.369210i	−0.739539	+	0.673113i	$0.764957\pi$
$572$	1.17649	+	2.03774i	0.0491914	+	0.0852021i
$573$		0			0
$574$	−16.7562	+	29.0225i	−0.699389	+	1.21138i
$575$	7.34026			0.306110
$576$		0			0
$577$	20.5759			0.856587			0.428293	−	0.903640i	$-0.359115\pi$
$577$	20.5759			0.856587			0.428293	+	0.903640i	$0.359115\pi$
$578$	−1.66405	+	2.88222i	−0.0692153	+	0.119884i
$579$		0			0
$580$	−0.569841	−	0.986994i	−0.0236614	−	0.0409827i
$581$	−27.0215	−	46.8026i	−1.12104	−	1.94170i
$582$		0			0
$583$	−14.1399	+	24.4910i	−0.585615	+	1.01432i
$584$	−18.4032			−0.761530
$585$		0			0
$586$	12.7663			0.527370
$587$	1.25881	−	2.18032i	0.0519567	−	0.0899916i	−0.838877	−	0.544320i	$-0.816788\pi$
$587$	1.25881	−	2.18032i	0.0519567	−	0.0899916i	0.890834	+	0.454329i	$0.150121\pi$
$588$		0			0
$589$	−7.91329	−	13.7062i	−0.326061	−	0.564755i
$590$	−4.12030	−	7.13657i	−0.169630	−	0.293808i
$591$		0			0
$592$	16.7685	−	29.0438i	0.689179	−	1.19369i
$593$	1.33875			0.0549761			0.0274880	−	0.999622i	$-0.491249\pi$
$593$	1.33875			0.0549761			0.0274880	+	0.999622i	$0.491249\pi$
$594$		0			0
$595$	−18.8851			−0.774214
$596$	4.76228	−	8.24852i	0.195071	−	0.337872i
$597$		0			0
$598$	1.53702	+	2.66220i	0.0628536	+	0.108866i
$599$	0.143216	+	0.248057i	0.00585165	+	0.0101354i	0.868936	−	0.494924i	$-0.164804\pi$
$599$	0.143216	+	0.248057i	0.00585165	+	0.0101354i	−0.863085	+	0.505059i	$0.831471\pi$
$600$		0			0
$601$	2.56733	−	4.44675i	0.104724	−	0.181387i	−0.808902	−	0.587944i	$-0.799938\pi$
$601$	2.56733	−	4.44675i	0.104724	−	0.181387i	0.913625	+	0.406557i	$0.133271\pi$
$602$	−48.0486			−1.95831
$603$		0			0
$604$	0.510606			0.0207763
$605$	−7.69285	+	13.3244i	−0.312759	+	0.541714i
$606$		0			0
$607$	−15.8953	−	27.5316i	−0.645172	−	1.11747i	−0.984262	−	0.176717i	$-0.943452\pi$
$607$	−15.8953	−	27.5316i	−0.645172	−	1.11747i	0.339089	−	0.940754i	$-0.389881\pi$
$608$	−8.26511	−	14.3156i	−0.335194	−	0.580574i
$609$		0			0
$610$	−1.87186	+	3.24215i	−0.0757892	+	0.131271i
$611$	−7.99965			−0.323631
$612$		0			0
$613$	−21.8649			−0.883116			−0.441558	−	0.897233i	$-0.645574\pi$
$613$	−21.8649			−0.883116			−0.441558	+	0.897233i	$0.645574\pi$
$614$	11.1576	−	19.3256i	0.450285	−	0.779916i
$615$		0			0
$616$	23.1418	+	40.0828i	0.932411	+	1.61498i
$617$	4.10686	+	7.11329i	0.165336	+	0.286370i	0.936775	−	0.349933i	$-0.113796\pi$
$617$	4.10686	+	7.11329i	0.165336	+	0.286370i	−0.771439	+	0.636304i	$0.780462\pi$
$618$		0			0
$619$	0.346345	−	0.599887i	0.0139208	−	0.0241115i	−0.858981	−	0.512007i	$-0.828902\pi$
$619$	0.346345	−	0.599887i	0.0139208	−	0.0241115i	0.872902	+	0.487896i	$0.162235\pi$
$620$	−1.32365			−0.0531592
$621$		0			0
$622$	−42.6552			−1.71032
$623$	−15.4580	+	26.7740i	−0.619311	+	1.07268i
$624$		0			0
$625$	−3.93581	−	6.81702i	−0.157432	−	0.272681i
$626$	21.3749	+	37.0224i	0.854313	+	1.47971i
$627$		0			0
$628$	4.91407	−	8.51143i	0.196093	−	0.339643i
$629$	31.0538			1.23819
$630$		0			0
$631$	3.59567			0.143141			0.0715707	−	0.997436i	$-0.477199\pi$
$631$	3.59567			0.143141			0.0715707	+	0.997436i	$0.477199\pi$
$632$	−3.59189	+	6.22134i	−0.142878	+	0.247472i
$633$		0			0
$634$	20.0094	+	34.6572i	0.794674	+	1.37641i
$635$	−6.18607	−	10.7146i	−0.245487	−	0.425195i
$636$		0			0
$637$	−3.99095	+	6.91253i	−0.158127	+	0.273884i
$638$	−16.9178			−0.669783
$639$		0			0
$640$	15.1886			0.600384
$641$	11.6855	−	20.2398i	0.461548	−	0.799424i	−0.537491	−	0.843270i	$-0.680628\pi$
$641$	11.6855	−	20.2398i	0.461548	−	0.799424i	0.999038	+	0.0438456i	$0.0139610\pi$
$642$		0			0
$643$	9.86171	+	17.0810i	0.388908	+	0.673608i	0.992303	−	0.123834i	$-0.0395191\pi$
$643$	9.86171	+	17.0810i	0.388908	+	0.673608i	−0.603395	+	0.797442i	$0.706186\pi$
$644$	−1.78808	−	3.09705i	−0.0704604	−	0.122041i
$645$		0			0
$646$	21.6769	−	37.5456i	0.852868	−	1.47721i
$647$	−36.9338			−1.45202			−0.726008	−	0.687686i	$-0.758627\pi$
$647$	−36.9338			−1.45202			−0.726008	+	0.687686i	$0.758627\pi$
$648$		0			0
$649$	−23.3811			−0.917790
$650$	2.95207	−	5.11313i	0.115790	−	0.200553i
$651$		0			0
$652$	−5.50853	−	9.54105i	−0.215731	−	0.373657i
$653$	−12.0573	−	20.8839i	−0.471841	−	0.817252i	0.527640	−	0.849468i	$-0.323077\pi$
$653$	−12.0573	−	20.8839i	−0.471841	−	0.817252i	−0.999481	+	0.0322160i	$0.989744\pi$
$654$		0			0
$655$	3.18014	−	5.50816i	0.124258	−	0.215222i
$656$	25.9990			1.01509
$657$		0			0
$658$	48.6891			1.89810
$659$	0.306111	−	0.530200i	0.0119244	−	0.0206537i	−0.860002	−	0.510291i	$-0.829538\pi$
$659$	0.306111	−	0.530200i	0.0119244	−	0.0206537i	0.871926	+	0.489638i	$0.162871\pi$
$660$		0			0
$661$	−16.5228	−	28.6183i	−0.642663	−	1.11312i	−0.984836	−	0.173488i	$-0.944496\pi$
$661$	−16.5228	−	28.6183i	−0.642663	−	1.11312i	0.342173	−	0.939637i	$-0.388837\pi$
$662$	2.83259	+	4.90620i	0.110092	+	0.190685i
$663$		0			0
$664$	−16.7670	+	29.0412i	−0.650684	+	1.12702i
$665$	27.2371			1.05621
$666$		0			0
$667$	−4.22458			−0.163576
$668$	3.72768	−	6.45654i	0.144228	−	0.249811i
$669$		0			0
$670$	−2.05031	−	3.55125i	−0.0792106	−	0.137197i
$671$	5.31103	+	9.19898i	0.205030	+	0.355123i
$672$		0			0
$673$	−20.7180	+	35.8846i	−0.798619	+	1.38325i	0.121897	+	0.992543i	$0.461102\pi$
$673$	−20.7180	+	35.8846i	−0.798619	+	1.38325i	−0.920516	+	0.390705i	$0.872231\pi$
$674$	−8.96889			−0.345469
$675$		0			0
$676$	0.472608			0.0181772
$677$	−12.7842	+	22.1429i	−0.491336	+	0.851019i	−0.999950	−	0.00997530i	$-0.996825\pi$
$677$	−12.7842	+	22.1429i	−0.491336	+	0.851019i	0.508614	+	0.860995i	$0.330158\pi$
$678$		0			0
$679$	14.8123	+	25.6556i	0.568442	+	0.984571i
$680$	5.85915	+	10.1483i	0.224688	+	0.389171i
$681$		0			0
$682$	−9.82437	+	17.0163i	−0.376195	+	0.651588i
$683$	24.4296			0.934772			0.467386	−	0.884053i	$-0.345196\pi$
$683$	24.4296			0.934772			0.467386	+	0.884053i	$0.345196\pi$
$684$		0			0
$685$	−6.71118			−0.256421
$686$	2.98811	−	5.17556i	0.114087	−	0.197604i
$687$		0			0
$688$	18.6381	+	32.2822i	0.710572	+	1.23075i
$689$	2.84008	+	4.91916i	0.108198	+	0.187405i
$690$		0			0
$691$	2.50550	−	4.33966i	0.0953138	−	0.165088i	−0.814426	−	0.580268i	$-0.802948\pi$
$691$	2.50550	−	4.33966i	0.0953138	−	0.165088i	0.909740	+	0.415179i	$0.136281\pi$
$692$	4.88672			0.185765
$693$		0			0
$694$	−55.4279			−2.10401
$695$	6.68530	−	11.5793i	0.253588	−	0.439227i
$696$		0			0
$697$	12.0370	+	20.8487i	0.455934	+	0.789700i
$698$	−8.57416	−	14.8509i	−0.324537	−	0.562114i
$699$		0			0
$700$	−3.43426	+	5.94831i	−0.129803	+	0.224825i
$701$	50.6694			1.91376			0.956879	−	0.290486i	$-0.0938170\pi$
$701$	50.6694			1.91376			0.956879	+	0.290486i	$0.0938170\pi$
$702$		0			0
$703$	−44.7874			−1.68919
$704$	13.2476	−	22.9455i	0.499287	−	0.864790i
$705$		0			0
$706$	−12.8879	−	22.3225i	−0.485043	−	0.840120i
$707$	21.3150	+	36.9187i	0.801635	+	1.38847i
$708$		0			0
$709$	−11.9738	+	20.7393i	−0.449686	+	0.778879i	−0.998365	−	0.0571538i	$-0.981797\pi$
$709$	−11.9738	+	20.7393i	−0.449686	+	0.778879i	0.548679	+	0.836033i	$0.315131\pi$
$710$	−7.57826			−0.284407
$711$		0			0
$712$	19.1835			0.718931
$713$	−2.45326	+	4.24918i	−0.0918754	+	0.159133i
$714$		0			0
$715$	2.77791	+	4.81148i	0.103888	+	0.179939i
$716$	−2.32684	−	4.03020i	−0.0869580	−	0.150616i
$717$		0			0
$718$	−1.03380	+	1.79059i	−0.0385809	+	0.0668241i
$719$	37.9792			1.41639			0.708193	−	0.706019i	$-0.249511\pi$
$719$	37.9792			1.41639			0.708193	+	0.706019i	$0.249511\pi$
$720$		0			0
$721$	−17.9538			−0.668635
$722$	−16.3253	+	28.2763i	−0.607567	+	1.05234i
$723$		0			0
$724$	4.50865	+	7.80922i	0.167563	+	0.290227i
$725$	4.05694	+	7.02683i	0.150671	+	0.260970i
$726$		0			0
$727$	−14.2552	+	24.6908i	−0.528698	+	0.915731i	0.470742	+	0.882271i	$0.343986\pi$
$727$	−14.2552	+	24.6908i	−0.528698	+	0.915731i	−0.999440	+	0.0334607i	$0.989347\pi$
$728$	9.29633			0.344545
$729$		0			0
$730$	13.4454			0.497638
$731$	−17.2581	+	29.8920i	−0.638315	+	1.10559i
$732$		0			0
$733$	0.489397	+	0.847661i	0.0180763	+	0.0313091i	0.874922	−	0.484264i	$-0.160912\pi$
$733$	0.489397	+	0.847661i	0.0180763	+	0.0313091i	−0.856846	+	0.515573i	$0.827579\pi$
$734$	18.2064	+	31.5345i	0.672012	+	1.16396i
$735$		0			0
$736$	−2.56233	+	4.43809i	−0.0944489	+	0.163590i
$737$	−11.6347			−0.428571
$738$		0			0
$739$	−36.9812			−1.36038			−0.680188	−	0.733038i	$-0.738102\pi$
$739$	−36.9812			−1.36038			−0.680188	+	0.733038i	$0.738102\pi$
$740$	−1.87290	+	3.24395i	−0.0688490	+	0.119250i
$741$		0			0
$742$	−17.2859	−	29.9400i	−0.634584	−	1.09913i
$743$	−14.1476	−	24.5043i	−0.519024	−	0.898975i	−0.999756	−	0.0221077i	$-0.992962\pi$
$743$	−14.1476	−	24.5043i	−0.519024	−	0.898975i	0.480732	−	0.876868i	$-0.340371\pi$
$744$		0			0
$745$	11.2447	−	19.4763i	0.411972	−	0.713557i
$746$	−47.7808			−1.74938
$747$		0			0
$748$	−10.2878			−0.376159
$749$	4.32224	−	7.48634i	0.157931	−	0.273545i
$750$		0			0
$751$	5.30501	+	9.18854i	0.193582	+	0.335295i	0.946435	−	0.322895i	$-0.104656\pi$
$751$	5.30501	+	9.18854i	0.193582	+	0.335295i	−0.752852	+	0.658189i	$0.771323\pi$
$752$	−18.8866	−	32.7125i	−0.688723	−	1.19290i
$753$		0			0
$754$	−1.69902	+	2.94279i	−0.0618746	+	0.107170i
$755$	1.20564			0.0438776
$756$		0			0
$757$	−17.0596			−0.620040			−0.310020	−	0.950730i	$-0.600336\pi$
$757$	−17.0596			−0.620040			−0.310020	+	0.950730i	$0.600336\pi$
$758$	−25.0900	+	43.4571i	−0.911309	+	1.57843i
$759$		0			0
$760$	−8.45038	−	14.6365i	−0.306528	−	0.530921i
$761$	−8.78193	−	15.2108i	−0.318345	−	0.551389i	0.661798	−	0.749682i	$-0.269794\pi$
$761$	−8.78193	−	15.2108i	−0.318345	−	0.551389i	−0.980143	+	0.198293i	$0.936460\pi$
$762$		0			0
$763$	−24.9798	+	43.2664i	−0.904331	+	1.56635i
$764$	2.56406			0.0927645
$765$		0			0
$766$	48.7128			1.76007
$767$	−2.34811	+	4.06705i	−0.0847855	+	0.146853i
$768$		0			0
$769$	4.60704	+	7.97963i	0.166134	+	0.287753i	0.937057	−	0.349175i	$-0.113538\pi$
$769$	4.60704	+	7.97963i	0.166134	+	0.287753i	−0.770923	+	0.636928i	$0.780205\pi$
$770$	−16.9075	−	29.2847i	−0.609304	−	1.05535i
$771$		0			0
$772$	4.20719	−	7.28707i	0.151420	−	0.262267i
$773$	−27.0112			−0.971525			−0.485762	−	0.874091i	$-0.661458\pi$
$773$	−27.0112			−0.971525			−0.485762	+	0.874091i	$0.661458\pi$
$774$		0			0
$775$	9.42365			0.338508
$776$	9.19107	−	15.9194i	0.329940	−	0.571473i
$777$		0			0
$778$	−15.8823	−	27.5090i	−0.569409	−	0.986245i
$779$	−17.3604	−	30.0691i	−0.622001	−	1.07734i
$780$		0			0
$781$	−10.7509	+	18.6211i	−0.384698	+	0.666317i
$782$	−13.4405			−0.480631
$783$		0			0
$784$	−37.6894			−1.34605
$785$	11.6031	−	20.0971i	0.414131	−	0.717296i
$786$		0			0
$787$	−4.00528	−	6.93734i	−0.142773	−	0.247290i	0.785767	−	0.618523i	$-0.212268\pi$
$787$	−4.00528	−	6.93734i	−0.142773	−	0.247290i	−0.928540	+	0.371233i	$0.878935\pi$
$788$	−2.34007	−	4.05312i	−0.0833615	−	0.144386i
$789$		0			0
$790$	2.62425	−	4.54533i	0.0933666	−	0.161716i
$791$	21.4670			0.763278
$792$		0			0
$793$	2.13350			0.0757628
$794$	19.1097	−	33.0990i	0.678178	−	1.17464i
$795$		0			0
$796$	−2.22067	−	3.84632i	−0.0787096	−	0.136329i
$797$	−9.79921	−	16.9727i	−0.347106	−	0.601205i	0.638628	−	0.769515i	$-0.279502\pi$
$797$	−9.79921	−	16.9727i	−0.347106	−	0.601205i	−0.985734	+	0.168311i	$0.946169\pi$
$798$		0			0
$799$	17.4882	−	30.2904i	0.618688	−	1.07160i
$800$	9.84263			0.347989
$801$		0			0
$802$	−39.3651			−1.39003
$803$	19.0744	−	33.0379i	0.673122	−	1.16588i
$804$		0			0
$805$	−4.22200	−	7.31273i	−0.148806	−	0.257740i
$806$	1.97328	+	3.41782i	0.0695058	+	0.120388i
$807$		0			0
$808$	13.2261	−	22.9082i	0.465292	−	0.805909i
$809$	−42.9313			−1.50938			−0.754691	−	0.656080i	$-0.772213\pi$
$809$	−42.9313			−1.50938			−0.754691	+	0.656080i	$0.772213\pi$
$810$		0			0
$811$	21.7459			0.763600			0.381800	−	0.924245i	$-0.375304\pi$
$811$	21.7459			0.763600			0.381800	+	0.924245i	$0.375304\pi$
$812$	1.97654	−	3.42346i	0.0693629	−	0.120140i
$813$		0			0
$814$	27.8019	+	48.1543i	0.974455	+	1.68781i
$815$	−13.0067	−	22.5282i	−0.455604	−	0.789130i
$816$		0			0
$817$	24.8906	−	43.1118i	0.870813	−	1.50829i
$818$	−29.2627			−1.02315
$819$		0			0
$820$	−2.90387			−0.101408
$821$	−4.07220	+	7.05326i	−0.142121	+	0.246161i	−0.928295	−	0.371844i	$-0.878726\pi$
$821$	−4.07220	+	7.05326i	−0.142121	+	0.246161i	0.786174	+	0.618005i	$0.212059\pi$
$822$		0			0
$823$	−0.204811	−	0.354744i	−0.00713928	−	0.0123656i	0.862434	−	0.506170i	$-0.168939\pi$
$823$	−0.204811	−	0.354744i	−0.00713928	−	0.0123656i	−0.869573	+	0.493804i	$0.835606\pi$
$824$	5.57021	+	9.64789i	0.194047	+	0.336100i
$825$		0			0
$826$	14.2916	−	24.7538i	0.497268	−	0.861293i
$827$	−35.2456			−1.22561			−0.612804	−	0.790235i	$-0.709959\pi$
$827$	−35.2456			−1.22561			−0.612804	+	0.790235i	$0.709959\pi$
$828$		0			0
$829$	−10.9615			−0.380710			−0.190355	−	0.981715i	$-0.560964\pi$
$829$	−10.9615			−0.380710			−0.190355	+	0.981715i	$0.560964\pi$
$830$	12.2500	−	21.2176i	0.425204	−	0.736474i
$831$		0			0
$832$	−2.66085	−	4.60872i	−0.0922483	−	0.159779i
$833$	−17.4494	−	30.2232i	−0.604586	−	1.04717i
$834$		0			0
$835$	8.80177	−	15.2451i	0.304598	−	0.527579i
$836$	14.8376			0.513169
$837$		0			0
$838$	31.0855			1.07383
$839$	−12.0475	+	20.8668i	−0.415925	+	0.720403i	−0.995525	−	0.0944981i	$-0.969875\pi$
$839$	−12.0475	+	20.8668i	−0.415925	+	0.720403i	0.579600	+	0.814901i	$0.303209\pi$
$840$		0			0
$841$	12.1651	+	21.0705i	0.419486	+	0.726571i
$842$	−0.381153	−	0.660176i	−0.0131354	−	0.0227512i
$843$		0			0
$844$	−5.37419	+	9.30837i	−0.184987	+	0.320407i
$845$	1.11592			0.0383887
$846$		0			0
$847$	−53.3665			−1.83369
$848$	−13.4104	+	23.2276i	−0.460517	+	0.797638i
$849$		0			0
$850$	12.9071	+	22.3558i	0.442712	+	0.766799i
$851$	6.94246	+	12.0247i	0.237984	+	0.412201i
$852$		0			0
$853$	3.95635	−	6.85260i	0.135463	−	0.234629i	−0.790311	−	0.612705i	$-0.790081\pi$
$853$	3.95635	−	6.85260i	0.135463	−	0.234629i	0.925774	+	0.378077i	$0.123415\pi$
$854$	−12.9853			−0.444349
$855$		0			0
$856$	−5.36394			−0.183336
$857$	−6.01297	+	10.4148i	−0.205399	+	0.355762i	−0.950260	−	0.311458i	$-0.899183\pi$
$857$	−6.01297	+	10.4148i	−0.205399	+	0.355762i	0.744861	+	0.667220i	$0.232516\pi$
$858$		0			0
$859$	−13.0444	−	22.5936i	−0.445070	−	0.770884i	0.552987	−	0.833190i	$-0.313488\pi$
$859$	−13.0444	−	22.5936i	−0.445070	−	0.770884i	−0.998057	+	0.0623058i	$0.980155\pi$
$860$	−2.08172	−	3.60565i	−0.0709862	−	0.122952i
$861$		0			0
$862$	−5.27857	+	9.14275i	−0.179789	+	0.311403i
$863$	−29.5606			−1.00625			−0.503127	−	0.864213i	$-0.667817\pi$
$863$	−29.5606			−1.00625			−0.503127	+	0.864213i	$0.667817\pi$
$864$		0			0
$865$	11.5385			0.392320
$866$	−1.16470	+	2.01732i	−0.0395781	+	0.0685513i
$867$		0			0
$868$	−2.29560	−	3.97609i	−0.0779176	−	0.134957i
$869$	−7.44581	−	12.8965i	−0.252582	−	0.437484i
$870$		0			0
$871$	−1.16845	+	2.02382i	−0.0395915	+	0.0685744i
$872$	31.0002			1.04980
$873$		0			0
$874$	19.3846			0.655694
$875$	−18.9072	+	32.7483i	−0.639181	+	1.10709i
$876$		0			0
$877$	6.96208	+	12.0587i	0.235093	+	0.407193i	0.959300	−	0.282390i	$-0.0911273\pi$
$877$	6.96208	+	12.0587i	0.235093	+	0.407193i	−0.724207	+	0.689583i	$0.757794\pi$
$878$	−5.87462	−	10.1751i	−0.198259	−	0.343394i
$879$		0			0
$880$	−13.1169	+	22.7191i	−0.442171	+	0.765862i
$881$	37.5189			1.26404			0.632022	−	0.774950i	$-0.282225\pi$
$881$	37.5189			1.26404			0.632022	+	0.774950i	$0.282225\pi$
$882$		0			0
$883$	37.4210			1.25932			0.629658	−	0.776872i	$-0.283195\pi$
$883$	37.4210			1.25932			0.629658	+	0.776872i	$0.283195\pi$
$884$	−1.03318	+	1.78952i	−0.0347496	+	0.0601880i
$885$		0			0
$886$	31.3495	+	54.2989i	1.05321	+	1.82421i
$887$	−4.27014	−	7.39609i	−0.143377	−	0.248336i	0.785389	−	0.619002i	$-0.212463\pi$
$887$	−4.27014	−	7.39609i	−0.143377	−	0.248336i	−0.928766	+	0.370666i	$0.879130\pi$
$888$		0			0
$889$	21.4569	−	37.1644i	0.719640	−	1.24645i
$890$	−14.0155			−0.469801
$891$		0			0
$892$	9.09798			0.304623
$893$	−25.2224	+	43.6865i	−0.844036	+	1.46191i
$894$		0			0
$895$	−5.49411	−	9.51607i	−0.183648	−	0.318087i
$896$	26.3415	+	45.6248i	0.880008	+	1.52422i
$897$		0			0
$898$	10.0383	−	17.3869i	0.334983	−	0.580208i
$899$	−5.42365			−0.180889
$900$		0			0
$901$	−24.8350			−0.827374
$902$	−21.5530	+	37.3309i	−0.717636	+	1.24298i
$903$		0			0
$904$	−6.66018	−	11.5358i	−0.221514	−	0.383674i
$905$	10.6458	+	18.4390i	0.353878	+	0.612935i
$906$		0			0
$907$	8.93992	−	15.4844i	0.296845	−	0.514151i	−0.678567	−	0.734538i	$-0.737399\pi$
$907$	8.93992	−	15.4844i	0.296845	−	0.514151i	0.975412	+	0.220388i	$0.0707322\pi$
$908$	2.43215			0.0807138
$909$		0			0
$910$	−6.79193			−0.225150
$911$	23.2627	−	40.2921i	0.770727	−	1.33494i	−0.166438	−	0.986052i	$-0.553227\pi$
$911$	23.2627	−	40.2921i	0.770727	−	1.33494i	0.937165	−	0.348886i	$-0.113440\pi$
$912$		0			0
$913$	−34.7570	−	60.2009i	−1.15029	−	1.99236i
$914$	7.30910	+	12.6597i	0.241763	+	0.418746i
$915$		0			0
$916$	−2.13747	+	3.70221i	−0.0706241	+	0.122324i
$917$	22.0611			0.728521
$918$		0			0
$919$	7.44747			0.245669			0.122835	−	0.992427i	$-0.460802\pi$
$919$	7.44747			0.245669			0.122835	+	0.992427i	$0.460802\pi$
$920$	−2.61977	+	4.53758i	−0.0863713	+	0.149599i
$921$		0			0
$922$	−9.91174	−	17.1676i	−0.326426	−	0.565386i
$923$	2.15938	+	3.74016i	0.0710769	+	0.123109i
$924$		0			0
$925$	13.3339	−	23.0951i	0.438417	−	0.759361i
$926$	24.0596			0.790648
$927$		0			0
$928$	−5.66478			−0.185956
$929$	−13.0210	+	22.5530i	−0.427204	+	0.739938i	−0.996623	−	0.0821086i	$-0.973835\pi$
$929$	−13.0210	+	22.5530i	−0.427204	+	0.739938i	0.569420	+	0.822047i	$0.307168\pi$
$930$		0			0
$931$	25.1665	+	43.5896i	0.824797	+	1.42859i
$932$	1.34481	+	2.32928i	0.0440507	+	0.0762980i
$933$		0			0
$934$	13.2950	−	23.0277i	0.435027	−	0.753488i
$935$	−24.2914			−0.794414
$936$		0			0
$937$	38.7266			1.26514			0.632571	−	0.774502i	$-0.282000\pi$
$937$	38.7266			1.26514			0.632571	+	0.774502i	$0.282000\pi$
$938$	7.11167	−	12.3178i	0.232204	−	0.402190i
$939$		0			0
$940$	2.10947	+	3.65372i	0.0688034	+	0.119171i
$941$	−15.1751	−	26.2840i	−0.494693	−	0.856834i	0.505288	−	0.862951i	$-0.331386\pi$
$941$	−15.1751	−	26.2840i	−0.494693	−	0.856834i	−0.999981	+	0.00611707i	$0.998053\pi$
$942$		0			0
$943$	−5.38204	+	9.32197i	−0.175263	+	0.303565i
$944$	−22.1749			−0.721733
$945$		0			0
$946$	−61.8036			−2.00941
$947$	23.9432	−	41.4709i	0.778050	−	1.34762i	−0.155014	−	0.987912i	$-0.549542\pi$
$947$	23.9432	−	41.4709i	0.778050	−	1.34762i	0.933064	−	0.359710i	$-0.117124\pi$
$948$		0			0
$949$	−3.83120	−	6.63584i	−0.124366	−	0.215408i
$950$	−18.6154	−	32.2428i	−0.603963	−	1.04609i
$951$		0			0
$952$	−20.3229	+	35.2003i	−0.658669	+	1.14085i
$953$	59.0107			1.91154			0.955772	−	0.294109i	$-0.0950229\pi$
$953$	59.0107			1.91154			0.955772	+	0.294109i	$0.0950229\pi$
$954$		0			0
$955$	6.05423			0.195910
$956$	−2.46975	+	4.27773i	−0.0798773	+	0.138352i
$957$		0			0
$958$	−7.96213	−	13.7908i	−0.257245	−	0.445561i
$959$	−11.6391	−	20.1595i	−0.375847	−	0.650985i
$960$		0			0
$961$	12.3504	−	21.3916i	0.398401	−	0.690051i
$962$	11.1683			0.360081
$963$		0			0
$964$	7.04303			0.226841
$965$	9.93397	−	17.2061i	0.319786	−	0.553886i
$966$		0			0
$967$	−13.7859	−	23.8779i	−0.443325	−	0.767862i	0.554609	−	0.832111i	$-0.312868\pi$
$967$	−13.7859	−	23.8779i	−0.443325	−	0.767862i	−0.997934	+	0.0642496i	$0.979535\pi$
$968$	16.5571	+	28.6777i	0.532164	+	0.921735i
$969$		0			0
$970$	−6.71503	+	11.6308i	−0.215606	+	0.373441i
$971$	−2.16029			−0.0693270			−0.0346635	−	0.999399i	$-0.511036\pi$
$971$	−2.16029			−0.0693270			−0.0346635	+	0.999399i	$0.511036\pi$
$972$		0			0
$973$	46.3770			1.48678
$974$	−0.143003	+	0.247689i	−0.00458212	+	0.00793646i
$975$		0			0
$976$	5.03704	+	8.72441i	0.161232	+	0.279262i
$977$	10.1025	+	17.4980i	0.323208	+	0.559812i	0.981148	−	0.193258i	$-0.0619055\pi$
$977$	10.1025	+	17.4980i	0.323208	+	0.559812i	−0.657940	+	0.753070i	$0.728572\pi$
$978$		0			0
$979$	−19.8832	+	34.4387i	−0.635469	+	1.10066i
$980$	4.20959			0.134470
$981$		0			0
$982$	−11.4151			−0.364271
$983$	−4.46476	+	7.73319i	−0.142404	+	0.246650i	−0.928401	−	0.371579i	$-0.878816\pi$
$983$	−4.46476	+	7.73319i	−0.142404	+	0.246650i	0.785998	+	0.618229i	$0.212150\pi$
$984$		0			0
$985$	−5.52535	−	9.57019i	−0.176052	−	0.304931i
$986$	−7.42852	−	12.8666i	−0.236572	−	0.409755i
$987$		0			0
$988$	1.49011	−	2.58094i	0.0474066	−	0.0821106i
$989$	−15.4331			−0.490744
$990$		0			0
$991$	33.6950			1.07036			0.535179	−	0.844739i	$-0.320244\pi$
$991$	33.6950			1.07036			0.535179	+	0.844739i	$0.320244\pi$
$992$	−3.28960	+	5.69776i	−0.104445	+	0.180904i
$993$		0			0
$994$	−13.1429	−	22.7641i	−0.416867	−	0.722035i
$995$	−5.24343	−	9.08188i	−0.166228	−	0.287915i
$996$		0			0
$997$	−7.27953	+	12.6085i	−0.230545	+	0.399315i	−0.957969	−	0.286873i	$-0.907384\pi$
$997$	−7.27953	+	12.6085i	−0.230545	+	0.399315i	0.727424	+	0.686189i	$0.240718\pi$
$998$	17.2965			0.547512
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.e.b.235.1		10
3.2	odd	2		117.2.e.b.79.5	yes	10
9.2	odd	6		1053.2.a.k.1.1		5
9.4	even	3	inner	351.2.e.b.118.1		10
9.5	odd	6		117.2.e.b.40.5	✓	10
9.7	even	3		1053.2.a.j.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.e.b.40.5	✓	10	9.5	odd	6
117.2.e.b.79.5	yes	10	3.2	odd	2
351.2.e.b.118.1		10	9.4	even	3	inner
351.2.e.b.235.1		10	1.1	even	1	trivial
1053.2.a.j.1.5		5	9.7	even	3
1053.2.a.k.1.1		5	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.786226 + 1.36178i) q^{2} +(-0.236304 - 0.409291i) q^{4} +(-0.557959 - 0.966413i) q^{5} +(1.93532 - 3.35208i) q^{7} -2.40175 q^{8} +1.75473 q^{10} +(2.48935 - 4.31168i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(3.04320 + 5.27098i) q^{14} +(2.36093 - 4.08925i) q^{16} +4.37224 q^{17} -6.30588 q^{19} +(-0.263696 + 0.456735i) q^{20} +(3.91439 + 6.77992i) q^{22} +(0.977469 + 1.69303i) q^{23} +(1.87736 - 3.25169i) q^{25} +1.57245 q^{26} -1.82930 q^{28} +(-1.08049 + 1.87146i) q^{29} +(1.25490 + 2.17356i) q^{31} +(1.31070 + 2.27020i) q^{32} +(-3.43757 + 5.95405i) q^{34} -4.31932 q^{35} +7.10248 q^{37} +(4.95785 - 8.58725i) q^{38} +(1.34008 + 2.32108i) q^{40} +(2.75305 + 4.76842i) q^{41} +(-3.94721 + 6.83676i) q^{43} -2.35298 q^{44} -3.07405 q^{46} +(3.99982 - 6.92790i) q^{47} +(-3.99095 - 6.91253i) q^{49} +(2.95207 + 5.11313i) q^{50} +(-0.236304 + 0.409291i) q^{52} -5.68016 q^{53} -5.55582 q^{55} +(-4.64816 + 8.05086i) q^{56} +(-1.69902 - 2.94279i) q^{58} +(-2.34811 - 4.06705i) q^{59} +(-1.06675 + 1.84766i) q^{61} -3.94656 q^{62} +5.32169 q^{64} +(-0.557959 + 0.966413i) q^{65} +(-1.16845 - 2.02382i) q^{67} +(-1.03318 - 1.78952i) q^{68} +(3.39596 - 5.88198i) q^{70} -4.31876 q^{71} +7.66241 q^{73} +(-5.58416 + 9.67205i) q^{74} +(1.49011 + 2.58094i) q^{76} +(-9.63540 - 16.6890i) q^{77} +(1.49553 - 2.59034i) q^{79} -5.26920 q^{80} -8.65808 q^{82} +(6.98114 - 12.0917i) q^{83} +(-2.43953 - 4.22539i) q^{85} +(-6.20679 - 10.7505i) q^{86} +(-5.97881 + 10.3556i) q^{88} -7.98729 q^{89} -3.87065 q^{91} +(0.461960 - 0.800138i) q^{92} +(6.28953 + 10.8938i) q^{94} +(3.51842 + 6.09409i) q^{95} +(-3.82682 + 6.62824i) q^{97} +12.5512 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 4 q^{4} + q^{5} + 2 q^{7} - 24 q^{8} - 4 q^{10} + 11 q^{11} - 5 q^{13} - 5 q^{14} - 10 q^{16} - 14 q^{17} + 6 q^{19} - q^{20} + 7 q^{22} + 18 q^{23} + 8 q^{25} - 4 q^{26} - 38 q^{28}+ \cdots + 78 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 - 4 * q^4 + q^5 + 2 * q^7 - 24 * q^8 - 4 * q^10 + 11 * q^11 - 5 * q^13 - 5 * q^14 - 10 * q^16 - 14 * q^17 + 6 * q^19 - q^20 + 7 * q^22 + 18 * q^23 + 8 * q^25 - 4 * q^26 - 38 * q^28 + 4 * q^29 + 16 * q^31 + 31 * q^32 - 13 * q^34 - 22 * q^35 + 10 * q^37 + 24 * q^38 - 18 * q^40 + 12 * q^41 - 2 * q^44 + 12 * q^46 + 15 * q^47 - 3 * q^49 - 5 * q^50 - 4 * q^52 + 6 * q^53 - 34 * q^55 - 24 * q^56 + 2 * q^58 + 3 * q^59 + q^61 + 8 * q^62 + 124 * q^64 + q^65 + 4 * q^67 - 16 * q^68 + 25 * q^70 - 30 * q^71 - 10 * q^73 + 11 * q^74 - 9 * q^76 + q^77 - 13 * q^79 - 64 * q^80 - 42 * q^82 + 26 * q^83 + 7 * q^85 - 6 * q^86 - 3 * q^88 - 58 * q^89 - 4 * q^91 - 6 * q^92 - 12 * q^94 + 12 * q^95 + 16 * q^97 + 78 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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