LMFDB - Embedded newform 847.2.f.p.729.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			729.1
Root			$1.43801 - 1.04478i$ of defining polynomial
Character	$\chi$	$=$	847.729
Dual form			847.2.f.p.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43801 + 1.04478i) q^{2} +(0.190983 + 0.587785i) q^{3} +(0.358290 - 1.10270i) q^{4} +(2.24703 + 1.63256i) q^{5} +(-0.888742 - 0.645709i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.461691 - 1.42094i) q^{8} +(2.11803 - 1.53884i) q^{9} +O(q^{10})$	\(q+(-1.43801 + 1.04478i) q^{2} +(0.190983 + 0.587785i) q^{3} +(0.358290 - 1.10270i) q^{4} +(2.24703 + 1.63256i) q^{5} +(-0.888742 - 0.645709i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.461691 - 1.42094i) q^{8} +(2.11803 - 1.53884i) q^{9} -4.93693 q^{10} +0.716580 q^{12} +(3.47350 - 2.52364i) q^{13} +(-0.549273 - 1.69049i) q^{14} +(-0.530452 + 1.63256i) q^{15} +(4.02452 + 2.92398i) q^{16} +(2.22929 + 1.61968i) q^{17} +(-1.43801 + 4.42575i) q^{18} +(0.599213 + 1.84419i) q^{19} +(2.60532 - 1.89288i) q^{20} -0.618034 q^{21} +4.37009 q^{23} +(0.747032 - 0.542750i) q^{24} +(0.838802 + 2.58157i) q^{25} +(-2.35829 + 7.25807i) q^{26} +(2.80902 + 2.04087i) q^{27} +(0.938015 + 0.681508i) q^{28} +(2.66623 - 8.20580i) q^{29} +(-0.942871 - 2.90186i) q^{30} +(0.162279 - 0.117903i) q^{31} -5.85410 q^{32} -4.89796 q^{34} +(-2.24703 + 1.63256i) q^{35} +(-0.938015 - 2.88691i) q^{36} +(0.319981 - 0.984800i) q^{37} +(-2.78845 - 2.02593i) q^{38} +(2.14674 + 1.55970i) q^{39} +(1.28234 - 3.94664i) q^{40} +(2.96847 + 9.13600i) q^{41} +(0.888742 - 0.645709i) q^{42} -4.70820 q^{43} +7.27155 q^{45} +(-6.28426 + 4.56578i) q^{46} +(-4.03129 - 12.4070i) q^{47} +(-0.950059 + 2.92398i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-3.90337 - 2.83597i) q^{50} +(-0.526264 + 1.61968i) q^{51} +(-1.53831 - 4.73443i) q^{52} +(3.15526 - 2.29243i) q^{53} -6.17167 q^{54} +1.49406 q^{56} +(-0.969548 + 0.704418i) q^{57} +(4.73918 + 14.5857i) q^{58} +(-2.64430 + 8.13831i) q^{59} +(1.61018 + 1.16986i) q^{60} +(0.799801 + 0.581090i) q^{61} +(-0.110177 + 0.339091i) q^{62} +(0.809017 + 2.48990i) q^{63} +(0.369254 - 0.268279i) q^{64} +11.9251 q^{65} -5.41745 q^{67} +(2.58475 - 1.87793i) q^{68} +(0.834614 + 2.56868i) q^{69} +(1.52560 - 4.69530i) q^{70} +(1.63183 + 1.18559i) q^{71} +(-3.16448 - 2.29913i) q^{72} +(-3.08123 + 9.48306i) q^{73} +(0.568761 + 1.75047i) q^{74} +(-1.35721 + 0.986070i) q^{75} +2.24828 q^{76} -4.71658 q^{78} +(-5.09153 + 3.69921i) q^{79} +(4.26963 + 13.1406i) q^{80} +(1.76393 - 5.42882i) q^{81} +(-13.8138 - 10.0363i) q^{82} +(1.39269 + 1.01185i) q^{83} +(-0.221435 + 0.681508i) q^{84} +(2.36507 + 7.27892i) q^{85} +(6.77047 - 4.91903i) q^{86} +5.33245 q^{87} -15.3035 q^{89} +(-10.4566 + 7.59716i) q^{90} +(1.32676 + 4.08334i) q^{91} +(1.56576 - 4.81891i) q^{92} +(0.100294 + 0.0728678i) q^{93} +(18.7597 + 13.6297i) q^{94} +(-1.66431 + 5.12221i) q^{95} +(-1.11803 - 3.44095i) q^{96} +(-9.39772 + 6.82784i) q^{97} +1.77748 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 6 q^{3} - 7 q^{4} + 3 q^{5} - 2 q^{6} + 2 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - q^2 + 6 * q^3 - 7 * q^4 + 3 * q^5 - 2 * q^6 + 2 * q^7 - 12 * q^8 + 8 * q^9	$ 8 q - q^{2} + 6 q^{3} - 7 q^{4} + 3 q^{5} - 2 q^{6} + 2 q^{7} - 12 q^{8} + 8 q^{9} - 28 q^{10} - 14 q^{12} - 5 q^{13} + q^{14} - 9 q^{15} + 7 q^{16} + 14 q^{17} - q^{18} + 6 q^{19} - 4 q^{20} + 4 q^{21} - 16 q^{23} - 9 q^{24} - 5 q^{25} - 9 q^{26} + 18 q^{27} - 3 q^{28} + 6 q^{29} - 26 q^{30} + 14 q^{31} - 20 q^{32} - 24 q^{34} - 3 q^{35} + 3 q^{36} + q^{37} - 15 q^{38} + 29 q^{40} + 18 q^{41} + 2 q^{42} + 16 q^{43} + 18 q^{45} - 26 q^{46} + 7 q^{47} - q^{48} - 2 q^{49} + q^{50} + 8 q^{51} - 4 q^{52} + 7 q^{53} + 4 q^{54} - 18 q^{56} - 3 q^{57} + 36 q^{58} + 17 q^{60} + 12 q^{61} - 5 q^{62} + 2 q^{63} - 4 q^{64} + 24 q^{65} - 30 q^{67} - 7 q^{68} - 22 q^{69} - 12 q^{70} + 21 q^{71} + 3 q^{72} + 8 q^{73} + q^{74} - 52 q^{76} - 18 q^{78} + q^{79} + 37 q^{80} + 32 q^{81} - 34 q^{82} - 22 q^{83} - 11 q^{84} - 5 q^{85} + 13 q^{86} + 12 q^{87} - 34 q^{89} - 18 q^{90} - 5 q^{91} + 51 q^{92} + 3 q^{93} + 50 q^{94} - 41 q^{95} - 15 q^{97} + 4 q^{98}+O(q^{100}) $ 8 * q - q^2 + 6 * q^3 - 7 * q^4 + 3 * q^5 - 2 * q^6 + 2 * q^7 - 12 * q^8 + 8 * q^9 - 28 * q^10 - 14 * q^12 - 5 * q^13 + q^14 - 9 * q^15 + 7 * q^16 + 14 * q^17 - q^18 + 6 * q^19 - 4 * q^20 + 4 * q^21 - 16 * q^23 - 9 * q^24 - 5 * q^25 - 9 * q^26 + 18 * q^27 - 3 * q^28 + 6 * q^29 - 26 * q^30 + 14 * q^31 - 20 * q^32 - 24 * q^34 - 3 * q^35 + 3 * q^36 + q^37 - 15 * q^38 + 29 * q^40 + 18 * q^41 + 2 * q^42 + 16 * q^43 + 18 * q^45 - 26 * q^46 + 7 * q^47 - q^48 - 2 * q^49 + q^50 + 8 * q^51 - 4 * q^52 + 7 * q^53 + 4 * q^54 - 18 * q^56 - 3 * q^57 + 36 * q^58 + 17 * q^60 + 12 * q^61 - 5 * q^62 + 2 * q^63 - 4 * q^64 + 24 * q^65 - 30 * q^67 - 7 * q^68 - 22 * q^69 - 12 * q^70 + 21 * q^71 + 3 * q^72 + 8 * q^73 + q^74 - 52 * q^76 - 18 * q^78 + q^79 + 37 * q^80 + 32 * q^81 - 34 * q^82 - 22 * q^83 - 11 * q^84 - 5 * q^85 + 13 * q^86 + 12 * q^87 - 34 * q^89 - 18 * q^90 - 5 * q^91 + 51 * q^92 + 3 * q^93 + 50 * q^94 - 41 * q^95 - 15 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.43801	+	1.04478i	−1.01683	+	0.738770i	−0.965631	−	0.259918i	$-0.916304\pi$
$2$	−1.43801	+	1.04478i	−1.01683	+	0.738770i	−0.0511995	+	0.998688i	$0.516304\pi$
$3$	0.190983	+	0.587785i	0.110264	+	0.339358i	0.990930	−	0.134380i	$-0.0429043\pi$
$3$	0.190983	+	0.587785i	0.110264	+	0.339358i	−0.880666	+	0.473738i	$0.842904\pi$
$4$	0.358290	−	1.10270i	0.179145	−	0.551351i
$5$	2.24703	+	1.63256i	1.00490	+	0.730105i	0.963134	−	0.269022i	$-0.0867005\pi$
$5$	2.24703	+	1.63256i	1.00490	+	0.730105i	0.0417693	+	0.999127i	$0.486701\pi$
$6$	−0.888742	−	0.645709i	−0.362827	−	0.263610i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	−0.461691	−	1.42094i	−0.163232	−	0.502378i
$9$	2.11803	−	1.53884i	0.706011	−	0.512947i
$10$	−4.93693			−1.56120
$11$		0			0
$11$		0			0
$12$	0.716580			0.206859
$13$	3.47350	−	2.52364i	0.963374	−	0.699932i	0.00944228	−	0.999955i	$-0.496994\pi$
$13$	3.47350	−	2.52364i	0.963374	−	0.699932i	0.953932	+	0.300023i	$0.0969944\pi$
$14$	−0.549273	−	1.69049i	−0.146799	−	0.451802i
$15$	−0.530452	+	1.63256i	−0.136962	+	0.421526i
$16$	4.02452	+	2.92398i	1.00613	+	0.730996i
$17$	2.22929	+	1.61968i	0.540683	+	0.392829i	0.824339	−	0.566097i	$-0.191547\pi$
$17$	2.22929	+	1.61968i	0.540683	+	0.392829i	−0.283656	+	0.958926i	$0.591547\pi$
$18$	−1.43801	+	4.42575i	−0.338943	+	1.04316i
$19$	0.599213	+	1.84419i	0.137469	+	0.423086i	0.995966	−	0.0897327i	$-0.0286013\pi$
$19$	0.599213	+	1.84419i	0.137469	+	0.423086i	−0.858497	+	0.512819i	$0.828601\pi$
$20$	2.60532	−	1.89288i	0.582568	−	0.423260i
$21$	−0.618034			−0.134866
$22$		0			0
$23$	4.37009			0.911228			0.455614	−	0.890178i	$-0.349420\pi$
$23$	4.37009			0.911228			0.455614	+	0.890178i	$0.349420\pi$
$24$	0.747032	−	0.542750i	0.152487	−	0.110788i
$25$	0.838802	+	2.58157i	0.167760	+	0.516313i
$26$	−2.35829	+	7.25807i	−0.462499	+	1.42342i
$27$	2.80902	+	2.04087i	0.540596	+	0.392766i
$28$	0.938015	+	0.681508i	0.177268	+	0.128793i
$29$	2.66623	−	8.20580i	0.495106	−	1.52378i	−0.321686	−	0.946846i	$-0.604250\pi$
$29$	2.66623	−	8.20580i	0.495106	−	1.52378i	0.816792	−	0.576933i	$-0.195750\pi$
$30$	−0.942871	−	2.90186i	−0.172144	−	0.529804i
$31$	0.162279	−	0.117903i	0.0291462	−	0.0211759i	−0.573117	−	0.819474i	$-0.694266\pi$
$31$	0.162279	−	0.117903i	0.0291462	−	0.0211759i	0.602263	+	0.798298i	$0.294266\pi$
$32$	−5.85410			−1.03487
$33$		0			0
$34$	−4.89796			−0.839993
$35$	−2.24703	+	1.63256i	−0.379818	+	0.275954i
$36$	−0.938015	−	2.88691i	−0.156336	−	0.481152i
$37$	0.319981	−	0.984800i	0.0526045	−	0.161900i	−0.921303	−	0.388846i	$-0.872874\pi$
$37$	0.319981	−	0.984800i	0.0526045	−	0.161900i	0.973907	+	0.226946i	$0.0728739\pi$
$38$	−2.78845	−	2.02593i	−0.452346	−	0.328649i
$39$	2.14674	+	1.55970i	0.343753	+	0.249751i
$40$	1.28234	−	3.94664i	0.202756	−	0.624018i
$41$	2.96847	+	9.13600i	0.463597	+	1.42680i	0.860739	+	0.509047i	$0.170002\pi$
$41$	2.96847	+	9.13600i	0.463597	+	1.42680i	−0.397142	+	0.917757i	$0.629998\pi$
$42$	0.888742	−	0.645709i	0.137136	−	0.0996351i
$43$	−4.70820			−0.717994			−0.358997	−	0.933339i	$-0.616881\pi$
$43$	−4.70820			−0.717994			−0.358997	+	0.933339i	$0.616881\pi$
$44$		0			0
$45$	7.27155			1.08398
$46$	−6.28426	+	4.56578i	−0.926564	+	0.673188i
$47$	−4.03129	−	12.4070i	−0.588024	−	1.80975i	−0.586770	−	0.809754i	$-0.699601\pi$
$47$	−4.03129	−	12.4070i	−0.588024	−	1.80975i	−0.00125473	−	0.999999i	$-0.500399\pi$
$48$	−0.950059	+	2.92398i	−0.137129	+	0.422040i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−3.90337	−	2.83597i	−0.552021	−	0.401066i
$51$	−0.526264	+	1.61968i	−0.0736918	+	0.226800i
$52$	−1.53831	−	4.73443i	−0.213325	−	0.656547i
$53$	3.15526	−	2.29243i	0.433409	−	0.314890i	−0.349602	−	0.936898i	$-0.613683\pi$
$53$	3.15526	−	2.29243i	0.433409	−	0.314890i	0.783010	+	0.622009i	$0.213683\pi$
$54$	−6.17167			−0.839857
$55$		0			0
$56$	1.49406			0.199653
$57$	−0.969548	+	0.704418i	−0.128420	+	0.0933024i
$58$	4.73918	+	14.5857i	0.622284	+	1.91519i
$59$	−2.64430	+	8.13831i	−0.344258	+	1.05952i	0.617721	+	0.786397i	$0.288056\pi$
$59$	−2.64430	+	8.13831i	−0.344258	+	1.05952i	−0.961980	+	0.273121i	$0.911944\pi$
$60$	1.61018	+	1.16986i	0.207873	+	0.151029i
$61$	0.799801	+	0.581090i	0.102404	+	0.0744009i	0.637809	−	0.770195i	$-0.279841\pi$
$61$	0.799801	+	0.581090i	0.102404	+	0.0744009i	−0.535405	+	0.844596i	$0.679841\pi$
$62$	−0.110177	+	0.339091i	−0.0139925	+	0.0430646i
$63$	0.809017	+	2.48990i	0.101927	+	0.313698i
$64$	0.369254	−	0.268279i	0.0461567	−	0.0335348i
$65$	11.9251			1.47912
$66$		0			0
$67$	−5.41745			−0.661846			−0.330923	−	0.943658i	$-0.607360\pi$
$67$	−5.41745			−0.661846			−0.330923	+	0.943658i	$0.607360\pi$
$68$	2.58475	−	1.87793i	0.313447	−	0.227733i
$69$	0.834614	+	2.56868i	0.100476	+	0.309232i
$70$	1.52560	−	4.69530i	0.182344	−	0.561196i
$71$	1.63183	+	1.18559i	0.193662	+	0.140704i	0.680391	−	0.732849i	$-0.261810\pi$
$71$	1.63183	+	1.18559i	0.193662	+	0.140704i	−0.486729	+	0.873553i	$0.661810\pi$
$72$	−3.16448	−	2.29913i	−0.372937	−	0.270955i
$73$	−3.08123	+	9.48306i	−0.360631	+	1.10991i	0.592041	+	0.805908i	$0.298322\pi$
$73$	−3.08123	+	9.48306i	−0.360631	+	1.10991i	−0.952672	+	0.304000i	$0.901678\pi$
$74$	0.568761	+	1.75047i	0.0661171	+	0.203488i
$75$	−1.35721	+	0.986070i	−0.156717	+	0.113862i
$76$	2.24828			0.257896
$77$		0			0
$78$	−4.71658			−0.534047
$79$	−5.09153	+	3.69921i	−0.572842	+	0.416194i	−0.836136	−	0.548522i	$-0.815191\pi$
$79$	−5.09153	+	3.69921i	−0.572842	+	0.416194i	0.263295	+	0.964715i	$0.415191\pi$
$80$	4.26963	+	13.1406i	0.477359	+	1.46916i
$81$	1.76393	−	5.42882i	0.195992	−	0.603203i
$82$	−13.8138	−	10.0363i	−1.52548	−	1.10833i
$83$	1.39269	+	1.01185i	0.152868	+	0.111065i	0.661590	−	0.749866i	$-0.269882\pi$
$83$	1.39269	+	1.01185i	0.152868	+	0.111065i	−0.508722	+	0.860931i	$0.669882\pi$
$84$	−0.221435	+	0.681508i	−0.0241606	+	0.0743586i
$85$	2.36507	+	7.27892i	0.256527	+	0.789510i
$86$	6.77047	−	4.91903i	0.730078	−	0.530433i
$87$	5.33245			0.571699
$88$		0			0
$89$	−15.3035			−1.62217			−0.811086	−	0.584928i	$-0.801123\pi$
$89$	−15.3035			−1.62217			−0.811086	+	0.584928i	$0.801123\pi$
$90$	−10.4566	+	7.59716i	−1.10222	+	0.800811i
$91$	1.32676	+	4.08334i	0.139082	+	0.428050i
$92$	1.56576	−	4.81891i	0.163242	−	0.502407i
$93$	0.100294	+	0.0728678i	0.0104000	+	0.00755604i
$94$	18.7597	+	13.6297i	1.93491	+	1.40580i
$95$	−1.66431	+	5.12221i	−0.170754	+	0.525527i
$96$	−1.11803	−	3.44095i	−0.114109	−	0.351191i
$97$	−9.39772	+	6.82784i	−0.954194	+	0.693262i	−0.951795	−	0.306735i	$-0.900764\pi$
$97$	−9.39772	+	6.82784i	−0.954194	+	0.693262i	−0.00239864	+	0.999997i	$0.500764\pi$
$98$	1.77748			0.179553
$99$		0			0
$100$	3.14723			0.314723
$101$	−2.76020	+	2.00540i	−0.274650	+	0.199545i	−0.716580	−	0.697505i	$-0.754294\pi$
$101$	−2.76020	+	2.00540i	−0.274650	+	0.199545i	0.441931	+	0.897049i	$0.354294\pi$
$102$	−0.935427	−	2.87895i	−0.0926210	−	0.285058i
$103$	−5.61873	+	17.2927i	−0.553629	+	1.70390i	0.145906	+	0.989298i	$0.453390\pi$
$103$	−5.61873	+	17.2927i	−0.553629	+	1.70390i	−0.699536	+	0.714598i	$0.746610\pi$
$104$	−5.18962	−	3.77048i	−0.508884	−	0.369726i
$105$	−1.38874	−	1.00898i	−0.135527	−	0.0984664i
$106$	−2.14223	+	6.59310i	−0.208072	+	0.640379i
$107$	1.00352	+	3.08852i	0.0970140	+	0.298578i	0.987773	−	0.155897i	$-0.0498268\pi$
$107$	1.00352	+	3.08852i	0.0970140	+	0.298578i	−0.890759	+	0.454475i	$0.849827\pi$
$108$	3.25692	−	2.36629i	0.313397	−	0.227696i
$109$	12.6912			1.21559			0.607796	−	0.794093i	$-0.292054\pi$
$109$	12.6912			1.21559			0.607796	+	0.794093i	$0.292054\pi$
$110$		0			0
$111$	0.639962			0.0607425
$112$	−4.02452	+	2.92398i	−0.380281	+	0.276290i
$113$	−5.70076	−	17.5451i	−0.536282	−	1.65051i	−0.740862	−	0.671658i	$-0.765583\pi$
$113$	−5.70076	−	17.5451i	−0.536282	−	1.65051i	0.204579	−	0.978850i	$-0.434417\pi$
$114$	0.658263	−	2.02593i	0.0616520	−	0.189745i
$115$	9.81974	+	7.13446i	0.915696	+	0.665292i
$116$	−8.09328	−	5.88011i	−0.751442	−	0.545955i
$117$	3.47350	−	10.6903i	0.321125	−	0.988320i
$118$	−4.70020	−	14.4657i	−0.432688	−	1.33168i
$119$	−2.22929	+	1.61968i	−0.204359	+	0.148475i
$120$	2.56468			0.234122
$121$		0			0
$122$	−1.75724			−0.159093
$123$	−4.80308	+	3.48964i	−0.433079	+	0.314650i
$124$	−0.0718686	−	0.221189i	−0.00645399	−	0.0198633i
$125$	1.96169	−	6.03746i	0.175459	−	0.540007i
$126$	−3.76477	−	2.73527i	−0.335393	−	0.243677i
$127$	−15.7834	−	11.4673i	−1.40055	−	1.01756i	−0.994613	−	0.103653i	$-0.966947\pi$
$127$	−15.7834	−	11.4673i	−1.40055	−	1.01756i	−0.405933	−	0.913903i	$-0.633053\pi$
$128$	3.36733	−	10.3636i	0.297633	−	0.916020i
$129$	−0.899187	−	2.76741i	−0.0791690	−	0.243657i
$130$	−17.1484	+	12.4591i	−1.50402	+	1.09273i
$131$	−6.89796			−0.602677			−0.301339	−	0.953517i	$-0.597433\pi$
$131$	−6.89796			−0.602677			−0.301339	+	0.953517i	$0.597433\pi$
$132$		0			0
$133$	−1.93910			−0.168141
$134$	7.79037	−	5.66003i	0.672985	−	0.488952i
$135$	2.98010	+	9.17180i	0.256486	+	0.789383i
$136$	1.27222	−	3.91548i	0.109092	−	0.335749i
$137$	2.11210	+	1.53453i	0.180449	+	0.131104i	0.674343	−	0.738418i	$-0.264427\pi$
$137$	2.11210	+	1.53453i	0.180449	+	0.131104i	−0.493894	+	0.869522i	$0.664427\pi$
$138$	−3.88389	−	2.82181i	−0.330618	−	0.240208i
$139$	−0.309430	+	0.952327i	−0.0262455	+	0.0807753i	−0.963321	−	0.268351i	$-0.913521\pi$
$139$	−0.309430	+	0.952327i	−0.0262455	+	0.0807753i	0.937076	+	0.349126i	$0.113521\pi$
$140$	0.995144	+	3.06274i	0.0841051	+	0.258849i
$141$	6.52277	−	4.73907i	0.549316	−	0.399102i
$142$	−3.58527			−0.300869
$143$		0			0
$144$	13.0236			1.08530
$145$	19.3876	−	14.0859i	1.61005	−	1.16977i
$146$	−5.47684	−	16.8560i	−0.453267	−	1.39501i
$147$	0.190983	−	0.587785i	0.0157520	−	0.0484797i
$148$	−0.971296	−	0.705688i	−0.0798400	−	0.0580072i
$149$	12.0501	+	8.75492i	0.987184	+	0.717231i	0.959303	−	0.282380i	$-0.0911240\pi$
$149$	12.0501	+	8.75492i	0.987184	+	0.717231i	0.0278812	+	0.999611i	$0.491124\pi$
$150$	0.921462	−	2.83597i	0.0752370	−	0.231556i
$151$	4.88389	+	15.0311i	0.397445	+	1.22321i	0.927041	+	0.374960i	$0.122344\pi$
$151$	4.88389	+	15.0311i	0.397445	+	1.22321i	−0.529596	+	0.848250i	$0.677656\pi$
$152$	2.34383	−	1.70289i	0.190110	−	0.138123i
$153$	7.21414			0.583229
$154$		0			0
$155$	0.557129			0.0447497
$156$	2.48904	−	1.80839i	0.199282	−	0.144787i
$157$	1.41877	+	4.36652i	0.113230	+	0.348486i	0.991574	−	0.129544i	$-0.0413512\pi$
$157$	1.41877	+	4.36652i	0.113230	+	0.348486i	−0.878344	+	0.478029i	$0.841351\pi$
$158$	3.45684	−	10.6390i	0.275011	−	0.846397i
$159$	1.95006	+	1.41680i	0.154650	+	0.112360i
$160$	−13.1544	−	9.55720i	−1.03994	−	0.755563i
$161$	−1.35043	+	4.15621i	−0.106429	+	0.327555i
$162$	3.13536	+	9.64965i	0.246337	+	0.758148i
$163$	−6.50259	+	4.72441i	−0.509322	+	0.370044i	−0.812566	−	0.582869i	$-0.801930\pi$
$163$	−6.50259	+	4.72441i	−0.509322	+	0.370044i	0.303244	+	0.952913i	$0.401930\pi$
$164$	11.1379			0.869721
$165$		0			0
$166$	−3.05987			−0.237492
$167$	10.8464	−	7.88038i	0.839321	−	0.609802i	−0.0828599	−	0.996561i	$-0.526405\pi$
$167$	10.8464	−	7.88038i	0.839321	−	0.609802i	0.922181	+	0.386759i	$0.126405\pi$
$168$	0.285341	+	0.878189i	0.0220145	+	0.0677537i
$169$	1.67918	−	5.16798i	0.129168	−	0.397537i
$170$	−11.0059	−	7.99623i	−0.844112	−	0.613283i
$171$	4.10707	+	2.98396i	0.314075	+	0.228189i
$172$	−1.68690	+	5.19175i	−0.128625	+	0.395867i
$173$	−6.36021	−	19.5747i	−0.483558	−	1.48824i	−0.834059	−	0.551676i	$-0.813989\pi$
$173$	−6.36021	−	19.5747i	−0.483558	−	1.48824i	0.350501	−	0.936562i	$-0.386011\pi$
$174$	−7.66815	+	5.57123i	−0.581321	+	0.422354i
$175$	−2.71442			−0.205191
$176$		0			0
$177$	−5.28860			−0.397515
$178$	22.0067	−	15.9888i	1.64947	−	1.19841i
$179$	−1.14806	−	3.53336i	−0.0858100	−	0.264096i	0.898940	−	0.438072i	$-0.144338\pi$
$179$	−1.14806	−	3.53336i	−0.0858100	−	0.264096i	−0.984750	+	0.173976i	$0.944338\pi$
$180$	2.60532	−	8.01836i	0.194189	−	0.597653i
$181$	−3.86049	−	2.80481i	−0.286948	−	0.208480i	0.434994	−	0.900433i	$-0.356750\pi$
$181$	−3.86049	−	2.80481i	−0.286948	−	0.208480i	−0.721942	+	0.691953i	$0.756750\pi$
$182$	−6.17408	−	4.48573i	−0.457653	−	0.332505i
$183$	−0.188807	+	0.581090i	−0.0139570	+	0.0429554i
$184$	−2.01763	−	6.20964i	−0.148742	−	0.457781i
$185$	2.32676	−	1.69049i	0.171067	−	0.124287i
$186$	−0.220355			−0.0161572
$187$		0			0
$188$	−15.1257			−1.10315
$189$	−2.80902	+	2.04087i	−0.204326	+	0.148451i
$190$	−2.95828	−	9.10464i	−0.214616	−	0.660520i
$191$	−0.256224	+	0.788577i	−0.0185397	+	0.0570594i	−0.959898	−	0.280348i	$-0.909550\pi$
$191$	−0.256224	+	0.788577i	−0.0185397	+	0.0570594i	0.941359	+	0.337408i	$0.109550\pi$
$192$	0.228211	+	0.165805i	0.0164697	+	0.0119660i
$193$	5.45118	+	3.96051i	0.392384	+	0.285084i	0.766432	−	0.642326i	$-0.222030\pi$
$193$	5.45118	+	3.96051i	0.392384	+	0.285084i	−0.374047	+	0.927410i	$0.622030\pi$
$194$	6.38047	−	19.6371i	0.458091	−	1.40986i
$195$	2.27748	+	7.00938i	0.163094	+	0.501952i
$196$	−0.938015	+	0.681508i	−0.0670011	+	0.0486791i
$197$	−10.9216			−0.778129			−0.389065	−	0.921210i	$-0.627202\pi$
$197$	−10.9216			−0.778129			−0.389065	+	0.921210i	$0.627202\pi$
$198$		0			0
$199$	20.9746			1.48685			0.743424	−	0.668820i	$-0.233200\pi$
$199$	20.9746			1.48685			0.743424	+	0.668820i	$0.233200\pi$
$200$	3.28098	−	2.38377i	0.232000	−	0.168558i
$201$	−1.03464	−	3.18429i	−0.0729779	−	0.224603i
$202$	1.87400	−	5.76759i	0.131854	−	0.405806i
$203$	6.98027	+	5.07146i	0.489919	+	0.355947i
$204$	1.59747	+	1.16063i	0.111845	+	0.0812601i
$205$	−8.24487	+	25.3751i	−0.575847	+	1.77227i
$206$	−9.98720	−	30.7374i	−0.695841	−	2.14158i
$207$	9.25601	−	6.72488i	0.643337	−	0.467412i
$208$	21.3582			1.48093
$209$		0			0
$210$	3.05119			0.210552
$211$	4.87320	−	3.54059i	0.335485	−	0.243744i	−0.407269	−	0.913308i	$-0.633519\pi$
$211$	4.87320	−	3.54059i	0.335485	−	0.243744i	0.742754	+	0.669564i	$0.233519\pi$
$212$	−1.39737	−	4.30067i	−0.0959720	−	0.295371i
$213$	−0.385222	+	1.18559i	−0.0263950	+	0.0812354i
$214$	−4.66990	−	3.39288i	−0.319227	−	0.231932i
$215$	−10.5795	−	7.68645i	−0.721515	−	0.524211i
$216$	1.60305	−	4.93369i	0.109074	−	0.335695i
$217$	0.0619850	+	0.190770i	0.00420782	+	0.0129503i
$218$	−18.2501	+	13.2595i	−1.23605	+	0.898043i
$219$	−6.16247			−0.416421
$220$		0			0
$221$	11.8309			0.795833
$222$	−0.920275	+	0.668619i	−0.0617648	+	0.0448748i
$223$	−1.42923	−	4.39871i	−0.0957081	−	0.294559i	0.891729	−	0.452569i	$-0.149492\pi$
$223$	−1.42923	−	4.39871i	−0.0957081	−	0.294559i	−0.987438	+	0.158010i	$0.949492\pi$
$224$	1.80902	−	5.56758i	0.120870	−	0.372000i
$225$	5.74923	+	4.17706i	0.383282	+	0.278471i
$226$	26.5286	+	19.2741i	1.76465	+	1.28210i
$227$	5.34610	−	16.4536i	0.354833	−	1.09206i	−0.601273	−	0.799043i	$-0.705340\pi$
$227$	5.34610	−	16.4536i	0.354833	−	1.09206i	0.956106	−	0.293020i	$-0.0946603\pi$
$228$	0.429384	+	1.32151i	0.0284367	+	0.0875190i
$229$	3.58081	−	2.60161i	0.236626	−	0.171919i	−0.463153	−	0.886279i	$-0.653282\pi$
$229$	3.58081	−	2.60161i	0.236626	−	0.171919i	0.699779	+	0.714359i	$0.253282\pi$
$230$	−21.5749			−1.42260
$231$		0			0
$232$	−12.8909			−0.846330
$233$	8.52141	−	6.19117i	0.558256	−	0.405597i	−0.272564	−	0.962138i	$-0.587872\pi$
$233$	8.52141	−	6.19117i	0.558256	−	0.405597i	0.830820	+	0.556541i	$0.187872\pi$
$234$	6.17408	+	19.0019i	0.403612	+	1.24219i
$235$	11.1969	−	34.4604i	0.730402	−	2.24795i
$236$	8.02672	+	5.83175i	0.522495	+	0.379615i
$237$	−3.14674	−	2.28624i	−0.204403	−	0.148507i
$238$	1.51355	−	4.65823i	0.0981090	−	0.301949i
$239$	−3.01491	−	9.27894i	−0.195018	−	0.600205i	−0.999976	−	0.00687311i	$-0.997812\pi$
$239$	−3.01491	−	9.27894i	−0.195018	−	0.600205i	0.804958	−	0.593332i	$-0.202188\pi$
$240$	−6.90840	+	5.01925i	−0.445935	+	0.323991i
$241$	12.5501			0.808422			0.404211	−	0.914666i	$-0.367546\pi$
$241$	12.5501			0.808422			0.404211	+	0.914666i	$0.367546\pi$
$242$		0			0
$243$	13.9443			0.894525
$244$	0.927330	−	0.673744i	0.0593662	−	0.0431321i
$245$	−0.858290	−	2.64154i	−0.0548341	−	0.168762i
$246$	3.26100	−	10.0363i	0.207914	−	0.639892i
$247$	6.73544	+	4.89358i	0.428566	+	0.311371i
$248$	−0.242455	−	0.176154i	−0.0153959	−	0.0111858i
$249$	−0.328769	+	1.01185i	−0.0208349	+	0.0641233i
$250$	3.48688	+	10.7315i	0.220529	+	0.678720i
$251$	8.89206	−	6.46046i	0.561262	−	0.407781i	−0.270659	−	0.962675i	$-0.587241\pi$
$251$	8.89206	−	6.46046i	0.561262	−	0.407781i	0.831921	+	0.554895i	$0.187241\pi$
$252$	3.03548			0.191217
$253$		0			0
$254$	34.6775			2.17586
$255$	−3.82676	+	2.78030i	−0.239641	+	0.174109i
$256$	6.26747	+	19.2893i	0.391717	+	1.20558i
$257$	1.64792	−	5.07179i	0.102795	−	0.316370i	−0.886412	−	0.462898i	$-0.846810\pi$
$257$	1.64792	−	5.07179i	0.102795	−	0.316370i	0.989207	+	0.146528i	$0.0468098\pi$
$258$	4.18438	+	3.04013i	0.260508	+	0.189270i
$259$	0.837721	+	0.608640i	0.0520535	+	0.0378190i
$260$	4.27263	−	13.1498i	0.264977	−	0.815516i
$261$	−6.98027	−	21.4831i	−0.432068	−	1.32977i
$262$	9.91937	−	7.20684i	0.612821	−	0.445240i
$263$	−8.18034			−0.504421			−0.252211	−	0.967672i	$-0.581158\pi$
$263$	−8.18034			−0.504421			−0.252211	+	0.967672i	$0.581158\pi$
$264$		0			0
$265$	10.8325			0.665436
$266$	2.78845	−	2.02593i	0.170971	−	0.124218i
$267$	−2.92271	−	8.99519i	−0.178867	−	0.550497i
$268$	−1.94102	+	5.97383i	−0.118566	+	0.364910i
$269$	−10.3909	−	7.54946i	−0.633547	−	0.460299i	0.224080	−	0.974571i	$-0.428062\pi$
$269$	−10.3909	−	7.54946i	−0.633547	−	0.460299i	−0.857627	+	0.514272i	$0.828062\pi$
$270$	−13.8679	−	10.0756i	−0.843976	−	0.613184i
$271$	−6.81296	+	20.9681i	−0.413858	+	1.27372i	0.499410	+	0.866366i	$0.333550\pi$
$271$	−6.81296	+	20.9681i	−0.413858	+	1.27372i	−0.913268	+	0.407359i	$0.866450\pi$
$272$	4.23592	+	13.0368i	0.256840	+	0.790473i
$273$	−2.14674	+	1.55970i	−0.129926	+	0.0943971i
$274$	−4.64047			−0.280341
$275$		0			0
$276$	3.13152			0.188495
$277$	−19.4787	+	14.1521i	−1.17036	+	0.850316i	−0.991052	−	0.133477i	$-0.957386\pi$
$277$	−19.4787	+	14.1521i	−1.17036	+	0.850316i	−0.179308	+	0.983793i	$0.557386\pi$
$278$	−0.550006	−	1.69275i	−0.0329872	−	0.101524i
$279$	0.162279	−	0.499443i	0.00971539	−	0.0299009i
$280$	3.35721	+	2.43916i	0.200632	+	0.145767i
$281$	−12.4927	−	9.07648i	−0.745252	−	0.541457i	0.149099	−	0.988822i	$-0.452363\pi$
$281$	−12.4927	−	9.07648i	−0.745252	−	0.541457i	−0.894352	+	0.447365i	$0.852363\pi$
$282$	−4.42856	+	13.6297i	−0.263717	+	0.811637i
$283$	−1.03747	−	3.19300i	−0.0616711	−	0.189804i	0.915474	−	0.402377i	$-0.131816\pi$
$283$	−1.03747	−	3.19300i	−0.0616711	−	0.189804i	−0.977145	+	0.212573i	$0.931816\pi$
$284$	1.89202	−	1.37463i	0.112271	−	0.0815695i
$285$	−3.32861			−0.197170
$286$		0			0
$287$	−9.60616			−0.567034
$288$	−12.3992	+	9.00854i	−0.730629	+	0.530833i
$289$	−2.90689	−	8.94650i	−0.170994	−	0.526265i
$290$	−13.1630	+	40.5115i	−0.772957	+	2.37892i
$291$	−5.80811	−	4.21984i	−0.340477	−	0.247371i
$292$	9.35302	+	6.79537i	0.547344	+	0.397669i
$293$	2.11277	−	6.50242i	0.123429	−	0.379876i	−0.870183	−	0.492730i	$-0.835999\pi$
$293$	2.11277	−	6.50242i	0.123429	−	0.379876i	0.993612	+	0.112854i	$0.0359992\pi$
$294$	0.339469	+	1.04478i	0.0197983	+	0.0609328i
$295$	−19.2281	+	13.9701i	−1.11951	+	0.813369i
$296$	−1.54707			−0.0899218
$297$		0			0
$298$	−26.4752			−1.53367
$299$	15.1795	−	11.0286i	0.877853	−	0.637798i
$300$	0.601068	+	1.84990i	0.0347027	+	0.106804i
$301$	1.45492	−	4.47777i	0.0838599	−	0.258094i
$302$	−22.7272	−	16.5123i	−1.30781	−	0.950176i
$303$	−1.70589	−	1.23940i	−0.0980011	−	0.0712019i
$304$	−2.98083	+	9.17406i	−0.170962	+	0.526168i
$305$	0.848513	+	2.61145i	0.0485857	+	0.149531i
$306$	−10.3740	+	7.53718i	−0.593044	+	0.430872i
$307$	−11.7970			−0.673293			−0.336646	−	0.941631i	$-0.609293\pi$
$307$	−11.7970			−0.673293			−0.336646	+	0.941631i	$0.609293\pi$
$308$		0			0
$309$	−11.2375			−0.639276
$310$	−0.801160	+	0.582077i	−0.0455029	+	0.0330598i
$311$	7.82242	+	24.0749i	0.443569	+	1.36516i	0.884046	+	0.467400i	$0.154809\pi$
$311$	7.82242	+	24.0749i	0.443569	+	1.36516i	−0.440477	+	0.897764i	$0.645191\pi$
$312$	1.22510	−	3.77048i	0.0693579	−	0.213462i
$313$	15.9007	+	11.5525i	0.898760	+	0.652988i	0.938147	−	0.346236i	$-0.112540\pi$
$313$	15.9007	+	11.5525i	0.898760	+	0.652988i	−0.0393869	+	0.999224i	$0.512540\pi$
$314$	−6.60225	−	4.79682i	−0.372587	−	0.270700i
$315$	−2.24703	+	6.91565i	−0.126606	+	0.389653i
$316$	2.25489	+	6.93983i	0.126847	+	0.390396i
$317$	−2.92100	+	2.12223i	−0.164060	+	0.119197i	−0.666786	−	0.745249i	$-0.732330\pi$
$317$	−2.92100	+	2.12223i	−0.164060	+	0.119197i	0.502726	+	0.864446i	$0.332330\pi$
$318$	−4.28446			−0.240261
$319$		0			0
$320$	1.26771			0.0708670
$321$	−1.62373	+	1.17971i	−0.0906278	+	0.0658449i
$322$	−2.40037	−	7.38759i	−0.133768	−	0.411694i
$323$	−1.65117	+	5.08177i	−0.0918734	+	0.282757i
$324$	−5.35438	−	3.89019i	−0.297466	−	0.216121i
$325$	9.42852	+	6.85022i	0.523000	+	0.379982i
$326$	4.41486	−	13.5875i	0.244516	−	0.752544i
$327$	2.42379	+	7.45967i	0.134036	+	0.412521i
$328$	11.6112	−	8.43602i	0.641121	−	0.465801i
$329$	13.0455			0.719224
$330$		0			0
$331$	−26.5335			−1.45841			−0.729205	−	0.684295i	$-0.760110\pi$
$331$	−26.5335			−1.45841			−0.729205	+	0.684295i	$0.760110\pi$
$332$	1.61475	−	1.17319i	0.0886212	−	0.0643870i
$333$	−0.837721	−	2.57824i	−0.0459068	−	0.141287i
$334$	−7.36405	+	22.6642i	−0.402943	+	1.24013i
$335$	−12.1732	−	8.84433i	−0.665092	−	0.483217i
$336$	−2.48729	−	1.80712i	−0.135693	−	0.0985865i
$337$	−0.211979	+	0.652405i	−0.0115472	+	0.0355387i	−0.956664	−	0.291194i	$-0.905948\pi$
$337$	−0.211979	+	0.652405i	−0.0115472	+	0.0355387i	0.945117	+	0.326732i	$0.105948\pi$
$338$	2.98471	+	9.18601i	0.162347	+	0.499653i
$339$	9.22402	−	6.70165i	0.500980	−	0.363983i
$340$	8.87387			0.481253
$341$		0			0
$342$	−9.02361			−0.487941
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	2.17374	+	6.69007i	0.117200	+	0.360704i
$345$	−2.31813	+	7.13446i	−0.124804	+	0.384106i
$346$	29.5973	+	21.5037i	1.59116	+	1.15605i
$347$	−17.3983	−	12.6406i	−0.933989	−	0.678582i	0.0129776	−	0.999916i	$-0.495869\pi$
$347$	−17.3983	−	12.6406i	−0.933989	−	0.678582i	−0.946966	+	0.321333i	$0.895869\pi$
$348$	1.91056	−	5.88011i	0.102417	−	0.315207i
$349$	6.00818	+	18.4913i	0.321610	+	0.989815i	0.972947	+	0.231026i	$0.0742084\pi$
$349$	6.00818	+	18.4913i	0.321610	+	0.989815i	−0.651337	+	0.758788i	$0.725792\pi$
$350$	3.90337	−	2.83597i	0.208644	−	0.151589i
$351$	14.9075			0.795705
$352$		0			0
$353$	−20.9307			−1.11403			−0.557015	−	0.830502i	$-0.688053\pi$
$353$	−20.9307			−1.11403			−0.557015	+	0.830502i	$0.688053\pi$
$354$	7.60508	−	5.52542i	0.404206	−	0.293672i
$355$	1.73121	+	5.32812i	0.0918832	+	0.282787i
$356$	−5.48310	+	16.8752i	−0.290604	+	0.894386i
$357$	−1.37778	−	1.00101i	−0.0729198	−	0.0529793i
$358$	5.34251	+	3.88156i	0.282360	+	0.205147i
$359$	3.01949	−	9.29303i	0.159362	−	0.490467i	−0.839214	−	0.543801i	$-0.816985\pi$
$359$	3.01949	−	9.29303i	0.159362	−	0.490467i	0.998577	+	0.0533336i	$0.0169847\pi$
$360$	−3.35721	−	10.3324i	−0.176940	−	0.544567i
$361$	12.3293	−	8.95779i	0.648913	−	0.471463i
$362$	8.48185			0.445796
$363$		0			0
$364$	4.97807			0.260922
$365$	−22.4053	+	16.2784i	−1.17275	+	0.852052i
$366$	−0.335602	−	1.03288i	−0.0175422	−	0.0539894i
$367$	3.05917	−	9.41516i	0.159687	−	0.491467i	−0.838918	−	0.544258i	$-0.816811\pi$
$367$	3.05917	−	9.41516i	0.159687	−	0.491467i	0.998606	+	0.0527902i	$0.0168114\pi$
$368$	17.5875	+	12.7781i	0.916813	+	0.666103i
$369$	20.3462	+	14.7824i	1.05918	+	0.769539i
$370$	−1.57973	+	4.86189i	−0.0821260	+	0.252758i
$371$	1.20520	+	3.70923i	0.0625710	+	0.192574i
$372$	0.116286	−	0.0844866i	0.00602914	−	0.00438042i
$373$	−4.27475			−0.221338			−0.110669	−	0.993857i	$-0.535299\pi$
$373$	−4.27475			−0.221338			−0.110669	+	0.993857i	$0.535299\pi$
$374$		0			0
$375$	3.92338			0.202603
$376$	−15.7684	+	11.4564i	−0.813195	+	0.590821i
$377$	−11.4474	−	35.2314i	−0.589570	−	1.81451i
$378$	1.90715	−	5.86960i	0.0980932	−	0.301900i
$379$	−3.49976	−	2.54272i	−0.179771	−	0.130611i	0.494261	−	0.869314i	$-0.335439\pi$
$379$	−3.49976	−	2.54272i	−0.179771	−	0.130611i	−0.674031	+	0.738703i	$0.735439\pi$
$380$	5.05197	+	3.67047i	0.259160	+	0.188291i
$381$	3.72594	−	11.4673i	0.190886	−	0.587486i
$382$	−0.455434	−	1.40168i	−0.0233020	−	0.0717163i
$383$	1.06960	−	0.777111i	0.0546541	−	0.0397085i	−0.560123	−	0.828410i	$-0.689246\pi$
$383$	1.06960	−	0.777111i	0.0546541	−	0.0397085i	0.614777	+	0.788701i	$0.289246\pi$
$384$	6.73467			0.343677
$385$		0			0
$386$	−11.9767			−0.609600
$387$	−9.97214	+	7.24518i	−0.506912	+	0.368293i
$388$	4.16197	+	12.8092i	0.211292	+	0.650290i
$389$	−11.9000	+	36.6244i	−0.603353	+	1.85693i	−0.0956157	+	0.995418i	$0.530482\pi$
$389$	−11.9000	+	36.6244i	−0.603353	+	1.85693i	−0.507737	+	0.861512i	$0.669518\pi$
$390$	−10.5983	−	7.70012i	−0.536666	−	0.389911i
$391$	9.74221	+	7.07813i	0.492685	+	0.357957i
$392$	−0.461691	+	1.42094i	−0.0233189	+	0.0717683i
$393$	−1.31739	−	4.05452i	−0.0664537	−	0.204523i
$394$	15.7054	−	11.4106i	0.791225	−	0.574859i
$395$	−17.4800			−0.879516
$396$		0			0
$397$	−0.410109			−0.0205828			−0.0102914	−	0.999947i	$-0.503276\pi$
$397$	−0.410109			−0.0205828			−0.0102914	+	0.999947i	$0.503276\pi$
$398$	−30.1618	+	21.9138i	−1.51187	+	1.09844i
$399$	−0.370334	−	1.13977i	−0.0185399	−	0.0570600i
$400$	−4.17268	+	12.8422i	−0.208634	+	0.642110i
$401$	1.26760	+	0.920966i	0.0633010	+	0.0459908i	0.618986	−	0.785402i	$-0.287544\pi$
$401$	1.26760	+	0.920966i	0.0633010	+	0.0459908i	−0.555685	+	0.831393i	$0.687544\pi$
$402$	4.81471	+	3.49809i	0.240136	+	0.174469i
$403$	0.266131	−	0.819068i	0.0132569	−	0.0408007i
$404$	1.22241	+	3.76219i	0.0608171	+	0.187176i
$405$	12.8265	−	9.31901i	0.637355	−	0.463065i
$406$	−15.3363			−0.761127
$407$		0			0
$408$	2.54443			0.125968
$409$	5.48394	−	3.98432i	0.271163	−	0.197012i	−0.443891	−	0.896081i	$-0.646402\pi$
$409$	5.48394	−	3.98432i	0.271163	−	0.197012i	0.715054	+	0.699069i	$0.246402\pi$
$410$	−14.6551	−	45.1038i	−0.723765	−	2.22752i
$411$	−0.498599	+	1.53453i	−0.0245941	+	0.0756927i
$412$	17.0555	+	12.3916i	0.840266	+	0.610489i
$413$	−6.92286	−	5.02975i	−0.340652	−	0.247498i
$414$	−6.28426	+	19.3410i	−0.308855	+	0.950557i
$415$	1.47751	+	4.54731i	0.0725282	+	0.223219i
$416$	−20.3342	+	14.7737i	−0.996966	+	0.724338i
$417$	−0.618859			−0.0303057
$418$		0			0
$419$	28.7218			1.40315			0.701577	−	0.712594i	$-0.252480\pi$
$419$	28.7218			1.40315			0.701577	+	0.712594i	$0.252480\pi$
$420$	−1.61018	+	1.16986i	−0.0785686	+	0.0570834i
$421$	3.77791	+	11.6272i	0.184124	+	0.566676i	0.999932	−	0.0116470i	$-0.00370742\pi$
$421$	3.77791	+	11.6272i	0.184124	+	0.566676i	−0.815808	+	0.578323i	$0.803707\pi$
$422$	−3.30860	+	10.1828i	−0.161060	+	0.495693i
$423$	−27.6309	−	20.0750i	−1.34346	−	0.976081i
$424$	−4.71416	−	3.42504i	−0.228940	−	0.166335i
$425$	−2.31136	+	7.11365i	−0.112118	+	0.345063i
$426$	−0.684726	−	2.10737i	−0.0331751	−	0.102102i
$427$	−0.799801	+	0.581090i	−0.0387051	+	0.0281209i
$428$	3.76527			0.182001
$429$		0			0
$430$	23.2441			1.12093
$431$	−2.98632	+	2.16969i	−0.143846	+	0.104510i	−0.657381	−	0.753559i	$-0.728336\pi$
$431$	−2.98632	+	2.16969i	−0.143846	+	0.104510i	0.513535	+	0.858069i	$0.328336\pi$
$432$	5.33747	+	16.4270i	0.256799	+	0.790346i
$433$	8.98463	−	27.6519i	0.431774	−	1.32886i	−0.464583	−	0.885530i	$-0.653796\pi$
$433$	8.98463	−	27.6519i	0.431774	−	1.32886i	0.896357	−	0.443334i	$-0.146204\pi$
$434$	−0.288448	−	0.209570i	−0.0138460	−	0.0100597i
$435$	11.9822	+	8.70557i	0.574502	+	0.417400i
$436$	4.54711	−	13.9946i	0.217767	−	0.670218i
$437$	2.61862	+	8.05928i	0.125266	+	0.385528i
$438$	8.86172	−	6.43842i	0.423429	−	0.307639i
$439$	−14.2017			−0.677811			−0.338905	−	0.940820i	$-0.610057\pi$
$439$	−14.2017			−0.677811			−0.338905	+	0.940820i	$0.610057\pi$
$440$		0			0
$441$	−2.61803			−0.124668
$442$	−17.0130	+	12.3607i	−0.809227	+	0.587938i
$443$	8.41626	+	25.9026i	0.399869	+	1.23067i	0.925105	+	0.379712i	$0.123977\pi$
$443$	8.41626	+	25.9026i	0.399869	+	1.23067i	−0.525236	+	0.850957i	$0.676023\pi$
$444$	0.229292	−	0.705688i	0.0108817	−	0.0334905i
$445$	−34.3875	−	24.9840i	−1.63013	−	1.18436i
$446$	6.65093	+	4.83218i	0.314930	+	0.228810i
$447$	−2.84465	+	8.75492i	−0.134547	+	0.414093i
$448$	0.141042	+	0.434084i	0.00666363	+	0.0205085i
$449$	33.9107	−	24.6376i	1.60034	−	1.16272i	0.713493	−	0.700662i	$-0.247112\pi$
$449$	33.9107	−	24.6376i	1.60034	−	1.16272i	0.886851	−	0.462056i	$-0.152888\pi$
$450$	−12.6316			−0.595459
$451$		0			0
$452$	−21.3896			−1.00608
$453$	−7.90229	+	5.74135i	−0.371282	+	0.269752i
$454$	9.50260	+	29.2460i	0.445979	+	1.37258i
$455$	−3.68505	+	11.3414i	−0.172758	+	0.531693i
$456$	1.44857	+	1.05244i	0.0678353	+	0.0492853i
$457$	−15.7740	−	11.4605i	−0.737875	−	0.536097i	0.154170	−	0.988044i	$-0.450730\pi$
$457$	−15.7740	−	11.4605i	−0.737875	−	0.536097i	−0.892045	+	0.451947i	$0.850730\pi$
$458$	−2.43115	+	7.48230i	−0.113600	+	0.349625i
$459$	2.95657	+	9.09939i	0.138001	+	0.424723i
$460$	11.3855	−	8.27205i	0.530852	−	0.385686i
$461$	12.2251			0.569380			0.284690	−	0.958620i	$-0.408109\pi$
$461$	12.2251			0.569380			0.284690	+	0.958620i	$0.408109\pi$
$462$		0			0
$463$	13.8550			0.643894			0.321947	−	0.946758i	$-0.395663\pi$
$463$	13.8550			0.643894			0.321947	+	0.946758i	$0.395663\pi$
$464$	34.7239	−	25.2284i	1.61202	−	1.17120i
$465$	0.106402	+	0.327472i	0.00493429	+	0.0151862i
$466$	−5.78551	+	17.8060i	−0.268009	+	0.824846i
$467$	13.2846	+	9.65186i	0.614740	+	0.446635i	0.851080	−	0.525035i	$-0.175948\pi$
$467$	13.2846	+	9.65186i	0.614740	+	0.446635i	−0.236340	+	0.971670i	$0.575948\pi$
$468$	−10.5437	−	7.66047i	−0.487384	−	0.354105i
$469$	1.67408	−	5.15230i	0.0773020	−	0.237911i
$470$	19.9022	+	61.2528i	0.918021	+	2.82538i
$471$	−2.29561	+	1.66786i	−0.105776	+	0.0768510i
$472$	12.7849			0.588473
$473$		0			0
$474$	6.91367			0.317555
$475$	−4.25827	+	3.09382i	−0.195383	+	0.141954i
$476$	0.987288	+	3.03856i	0.0452523	+	0.139272i
$477$	3.15526	−	9.71090i	0.144470	−	0.444632i
$478$	14.0299	+	10.1933i	0.641714	+	0.466233i
$479$	20.0566	+	14.5720i	0.916412	+	0.665812i	0.942628	−	0.333844i	$-0.108346\pi$
$479$	20.0566	+	14.5720i	0.916412	+	0.665812i	−0.0262166	+	0.999656i	$0.508346\pi$
$480$	3.10532	−	9.55720i	0.141738	−	0.436224i
$481$	−1.37383	−	4.22822i	−0.0626413	−	0.192790i
$482$	−18.0472	+	13.1121i	−0.822028	+	0.597238i
$483$	−2.70087			−0.122894
$484$		0			0
$485$	−32.2639			−1.46503
$486$	−20.0521	+	14.5687i	−0.909580	+	0.660849i
$487$	−4.42951	−	13.6326i	−0.200720	−	0.617753i	−0.999862	−	0.0166105i	$-0.994712\pi$
$487$	−4.42951	−	13.6326i	−0.200720	−	0.617753i	0.799142	−	0.601142i	$-0.205288\pi$
$488$	0.456432	−	1.40475i	0.0206617	−	0.0635902i
$489$	−4.01882	−	2.91984i	−0.181737	−	0.132040i
$490$	3.99406	+	2.90186i	0.180433	+	0.131093i
$491$	−6.80435	+	20.9416i	−0.307076	+	0.945083i	0.671818	+	0.740716i	$0.265514\pi$
$491$	−6.80435	+	20.9416i	−0.307076	+	0.945083i	−0.978894	+	0.204367i	$0.934486\pi$
$492$	2.12714	+	6.54667i	0.0958990	+	0.295147i
$493$	19.2345	−	13.9747i	0.866280	−	0.629389i
$494$	−14.7984			−0.665810
$495$		0			0
$496$	0.997839			0.0448043
$497$	−1.63183	+	1.18559i	−0.0731974	+	0.0531810i
$498$	−0.584382	−	1.79854i	−0.0261868	−	0.0805947i
$499$	−7.82175	+	24.0729i	−0.350150	+	1.07765i	0.608619	+	0.793463i	$0.291724\pi$
$499$	−7.82175	+	24.0729i	−0.350150	+	1.07765i	−0.958769	+	0.284187i	$0.908276\pi$
$500$	−5.95467	−	4.32632i	−0.266301	−	0.193479i
$501$	6.70345	+	4.87034i	0.299488	+	0.217591i
$502$	−6.03716	+	18.5805i	−0.269452	+	0.829287i
$503$	−8.04107	−	24.7479i	−0.358534	−	1.10345i	−0.953932	−	0.300022i	$-0.903006\pi$
$503$	−8.04107	−	24.7479i	−0.358534	−	1.10345i	0.595399	−	0.803430i	$-0.296994\pi$
$504$	3.16448	−	2.29913i	0.140957	−	0.102411i
$505$	−9.47619			−0.421685
$506$		0			0
$507$	3.35836			0.149150
$508$	−18.3000	+	13.2957i	−0.811932	+	0.589903i
$509$	11.7819	+	36.2608i	0.522222	+	1.60723i	0.769745	+	0.638351i	$0.220383\pi$
$509$	11.7819	+	36.2608i	0.522222	+	1.60723i	−0.247523	+	0.968882i	$0.579617\pi$
$510$	2.59813	−	7.99623i	0.115047	−	0.354079i
$511$	−8.06677	−	5.86085i	−0.356853	−	0.259269i
$512$	−11.5342	−	8.38006i	−0.509743	−	0.370350i
$513$	−2.08055	+	6.40328i	−0.0918585	+	0.282712i
$514$	2.92916	+	9.01503i	0.129200	+	0.397636i
$515$	−40.8568	+	29.6842i	−1.80037	+	1.30804i
$516$	−3.37380			−0.148523
$517$		0			0
$518$	−1.84055			−0.0808691
$519$	10.2910	−	7.47688i	0.451726	−	0.328198i
$520$	−5.50570	−	16.9448i	−0.241441	−	0.743078i
$521$	−8.04742	+	24.7674i	−0.352564	+	1.08508i	0.604845	+	0.796343i	$0.293235\pi$
$521$	−8.04742	+	24.7674i	−0.352564	+	1.08508i	−0.957409	+	0.288736i	$0.906765\pi$
$522$	32.4828	+	23.6001i	1.42173	+	1.03295i
$523$	−15.4708	−	11.2402i	−0.676492	−	0.491500i	0.195700	−	0.980664i	$-0.437302\pi$
$523$	−15.4708	−	11.2402i	−0.676492	−	0.491500i	−0.872192	+	0.489164i	$0.837302\pi$
$524$	−2.47147	+	7.60640i	−0.107967	+	0.332287i
$525$	−0.518408	−	1.59550i	−0.0226252	−	0.0696331i
$526$	11.7635	−	8.54665i	0.512911	−	0.372652i
$527$	0.552731			0.0240773
$528$		0			0
$529$	−3.90228			−0.169664
$530$	−15.5773	+	11.3176i	−0.676636	+	0.491605i
$531$	6.92286	+	21.3064i	0.300427	+	0.924618i
$532$	−0.694758	+	2.13825i	−0.0301216	+	0.0927047i
$533$	33.3670	+	24.2425i	1.44528	+	1.05006i
$534$	13.6009	+	9.88163i	0.588568	+	0.427620i
$535$	−2.78726	+	8.57831i	−0.120504	+	0.370873i
$536$	2.50119	+	7.69786i	0.108035	+	0.332497i
$537$	1.85760	−	1.34962i	0.0801613	−	0.0582406i
$538$	22.8298			0.984265
$539$		0			0
$540$	11.1815			0.481176
$541$	−8.80699	+	6.39865i	−0.378642	+	0.275100i	−0.760785	−	0.649003i	$-0.775186\pi$
$541$	−8.80699	+	6.39865i	−0.378642	+	0.275100i	0.382143	+	0.924103i	$0.375186\pi$
$542$	−12.1099	−	37.2706i	−0.520166	−	1.60091i
$543$	0.911338	−	2.80481i	0.0391093	−	0.120366i
$544$	−13.0505	−	9.48174i	−0.559536	−	0.406526i
$545$	28.5174	+	20.7191i	1.22155	+	0.887510i
$546$	1.45750	−	4.48573i	0.0623754	−	0.191972i
$547$	−3.98912	−	12.2772i	−0.170562	−	0.524937i	0.828841	−	0.559485i	$-0.189001\pi$
$547$	−3.98912	−	12.2772i	−0.170562	−	0.524937i	−0.999403	+	0.0345478i	$0.989001\pi$
$548$	2.44887	−	1.77921i	0.104611	−	0.0760041i
$549$	2.58821			0.110462
$550$		0			0
$551$	16.7307			0.712751
$552$	3.26460	−	2.37187i	0.138951	−	0.100954i
$553$	−1.94479	−	5.98545i	−0.0827009	−	0.254527i
$554$	13.2248	−	40.7018i	0.561869	−	1.72925i
$555$	1.43801	+	1.04478i	0.0610403	+	0.0443484i
$556$	0.939268	+	0.682418i	0.0398338	+	0.0289410i
$557$	−0.235664	+	0.725300i	−0.00998542	+	0.0307320i	−0.955925	−	0.293611i	$-0.905143\pi$
$557$	−0.235664	+	0.725300i	−0.00998542	+	0.0307320i	0.945940	+	0.324343i	$0.105143\pi$
$558$	0.288448	+	0.887752i	0.0122110	+	0.0375816i
$559$	−16.3539	+	11.8818i	−0.691697	+	0.502547i
$560$	−13.8168			−0.583867
$561$		0			0
$562$	27.4476			1.15781
$563$	17.9829	−	13.0654i	0.757890	−	0.550639i	−0.140373	−	0.990099i	$-0.544830\pi$
$563$	17.9829	−	13.0654i	0.757890	−	0.550639i	0.898262	+	0.439460i	$0.144830\pi$
$564$	−2.88874	−	8.89063i	−0.121638	−	0.374363i
$565$	15.8338	−	48.7313i	0.666132	−	2.05014i
$566$	4.82788	+	3.50766i	0.202931	+	0.147438i
$567$	4.61803	+	3.35520i	0.193939	+	0.140905i
$568$	0.931253	−	2.86610i	0.0390745	−	0.120259i
$569$	−6.33891	−	19.5092i	−0.265741	−	0.817866i	−0.991522	−	0.129940i	$-0.958521\pi$
$569$	−6.33891	−	19.5092i	−0.265741	−	0.817866i	0.725781	−	0.687926i	$-0.241479\pi$
$570$	4.78659	−	3.47766i	0.200488	−	0.145663i
$571$	−19.5654			−0.818785			−0.409393	−	0.912358i	$-0.634259\pi$
$571$	−19.5654			−0.818785			−0.409393	+	0.912358i	$0.634259\pi$
$572$		0			0
$573$	−0.512448			−0.0214078
$574$	13.8138	−	10.0363i	0.576577	−	0.418908i
$575$	3.66564	+	11.2817i	0.152868	+	0.470479i
$576$	0.369254	−	1.13645i	0.0153856	−	0.0473519i
$577$	15.8337	+	11.5039i	0.659167	+	0.478913i	0.866382	−	0.499382i	$-0.166440\pi$
$577$	15.8337	+	11.5039i	0.659167	+	0.478913i	−0.207214	+	0.978296i	$0.566440\pi$
$578$	13.5273	+	9.82814i	0.562661	+	0.408797i
$579$	−1.28685	+	3.96051i	−0.0534796	+	0.164593i
$580$	−8.58620	−	26.4256i	−0.356522	−	1.09726i
$581$	−1.39269	+	1.01185i	−0.0577785	+	0.0419785i
$582$	12.7609			0.528958
$583$		0			0
$584$	14.8974			0.616460
$585$	25.2577	−	18.3508i	1.04428	−	0.758712i
$586$	3.75541	+	11.5580i	0.155134	+	0.477455i
$587$	0.485367	−	1.49381i	0.0200333	−	0.0616560i	−0.940540	−	0.339683i	$-0.889680\pi$
$587$	0.485367	−	1.49381i	0.0200333	−	0.0616560i	0.960573	+	0.278027i	$0.0896803\pi$
$588$	−0.579725	−	0.421195i	−0.0239075	−	0.0173698i
$589$	0.314674	+	0.228624i	0.0129659	+	0.00942030i
$590$	13.0547	−	40.1783i	0.537455	−	1.65412i
$591$	−2.08583	−	6.41954i	−0.0857997	−	0.264064i
$592$	4.16731	−	3.02773i	0.171275	−	0.124439i
$593$	−30.1230			−1.23700			−0.618502	−	0.785783i	$-0.712260\pi$
$593$	−30.1230			−1.23700			−0.618502	+	0.785783i	$0.712260\pi$
$594$		0			0
$595$	−7.65351			−0.313763
$596$	13.9715	−	10.1509i	0.572295	−	0.415797i
$597$	4.00579	+	12.3285i	0.163946	+	0.504574i
$598$	−10.3059	+	31.7184i	−0.421442	+	1.29706i
$599$	−4.67443	−	3.39617i	−0.190992	−	0.138764i	0.488180	−	0.872743i	$-0.337661\pi$
$599$	−4.67443	−	3.39617i	−0.190992	−	0.138764i	−0.679172	+	0.733979i	$0.737661\pi$
$600$	2.02776	+	1.47325i	0.0827829	+	0.0601453i
$601$	14.0802	−	43.3345i	0.574344	−	1.76765i	−0.0640579	−	0.997946i	$-0.520404\pi$
$601$	14.0802	−	43.3345i	0.574344	−	1.76765i	0.638402	−	0.769703i	$-0.279596\pi$
$602$	2.58609	+	7.95916i	0.105401	+	0.324391i
$603$	−11.4743	+	8.33659i	−0.467271	+	0.339492i
$604$	18.3246			0.745619
$605$		0			0
$606$	3.74801			0.152252
$607$	−28.0899	+	20.4085i	−1.14013	+	0.828356i	−0.987138	−	0.159870i	$-0.948892\pi$
$607$	−28.0899	+	20.4085i	−1.14013	+	0.828356i	−0.152997	+	0.988227i	$0.548892\pi$
$608$	−3.50786	−	10.7961i	−0.142262	−	0.437839i
$609$	−1.64782	+	5.07146i	−0.0667730	+	0.205506i
$610$	−3.94857	−	2.86880i	−0.159873	−	0.116154i
$611$	−45.3136	−	32.9223i	−1.83319	−	1.33189i
$612$	2.58475	−	7.95505i	0.104482	−	0.321564i
$613$	−7.46037	−	22.9607i	−0.301322	−	0.927372i	−0.981024	−	0.193885i	$-0.937891\pi$
$613$	−7.46037	−	22.9607i	−0.301322	−	0.927372i	0.679703	−	0.733488i	$-0.262109\pi$
$614$	16.9643	−	12.3253i	0.684624	−	0.497409i
$615$	−16.4897			−0.664931
$616$		0			0
$617$	−13.4967			−0.543358			−0.271679	−	0.962388i	$-0.587579\pi$
$617$	−13.4967			−0.543358			−0.271679	+	0.962388i	$0.587579\pi$
$618$	16.1596	−	11.7407i	0.650035	−	0.472278i
$619$	−13.4378	−	41.3573i	−0.540111	−	1.66229i	−0.732339	−	0.680940i	$-0.761572\pi$
$619$	−13.4378	−	41.3573i	−0.540111	−	1.66229i	0.192229	−	0.981350i	$-0.438428\pi$
$620$	0.199614	−	0.614348i	0.00801668	−	0.0246728i
$621$	12.2757	+	8.91879i	0.492606	+	0.357899i
$622$	−36.4017	−	26.4474i	−1.45958	−	1.06044i
$623$	4.72905	−	14.5545i	0.189465	−	0.583115i
$624$	4.07906	+	12.5540i	0.163293	+	0.502564i
$625$	25.2446	−	18.3413i	1.00978	−	0.733651i
$626$	−34.9353			−1.39629
$627$		0			0
$628$	5.32330			0.212423
$629$	2.30839	−	1.67714i	0.0920414	−	0.0668720i
$630$	−3.99406	−	12.2925i	−0.159127	−	0.489744i
$631$	1.98393	−	6.10589i	0.0789788	−	0.243072i	−0.903770	−	0.428019i	$-0.859212\pi$
$631$	1.98393	−	6.10589i	0.0789788	−	0.243072i	0.982748	+	0.184948i	$0.0592115\pi$
$632$	7.60707	+	5.52686i	0.302593	+	0.219847i
$633$	3.01180	+	2.18820i	0.119708	+	0.0869733i
$634$	1.98318	−	6.10361i	0.0787622	−	0.242405i
$635$	−16.7446	−	51.5347i	−0.664490	−	2.04509i
$636$	2.26100	−	1.64271i	0.0896544	−	0.0651377i
$637$	−4.29348			−0.170114
$638$		0			0
$639$	5.28070			0.208901
$640$	24.4857	−	17.7899i	0.967883	−	0.703208i
$641$	−1.97647	−	6.08296i	−0.0780660	−	0.240262i	0.904406	−	0.426673i	$-0.140314\pi$
$641$	−1.97647	−	6.08296i	−0.0780660	−	0.240262i	−0.982472	+	0.186411i	$0.940314\pi$
$642$	1.10241	−	3.39288i	0.0435088	−	0.133906i
$643$	−0.528013	−	0.383624i	−0.0208228	−	0.0151286i	0.577325	−	0.816514i	$-0.304097\pi$
$643$	−0.528013	−	0.383624i	−0.0208228	−	0.0151286i	−0.598148	+	0.801386i	$0.704097\pi$
$644$	4.09921	+	2.97825i	0.161532	+	0.117360i
$645$	2.49748	−	7.68645i	0.0983381	−	0.302653i
$646$	−2.93492	−	9.03276i	−0.115473	−	0.355389i
$647$	−14.5317	+	10.5579i	−0.571299	+	0.415073i	−0.835577	−	0.549373i	$-0.814866\pi$
$647$	−14.5317	+	10.5579i	−0.571299	+	0.415073i	0.264278	+	0.964447i	$0.414866\pi$
$648$	−8.52842			−0.335028
$649$		0			0
$650$	−20.7153			−0.812522
$651$	−0.100294	+	0.0728678i	−0.00393083	+	0.00285591i
$652$	2.87981	+	8.86313i	0.112782	+	0.347107i
$653$	−5.22797	+	16.0900i	−0.204586	+	0.629652i	0.795144	+	0.606421i	$0.207395\pi$
$653$	−5.22797	+	16.0900i	−0.204586	+	0.629652i	−0.999730	+	0.0232310i	$0.992605\pi$
$654$	−11.2792	−	8.19479i	−0.441050	−	0.320442i
$655$	−15.4999	−	11.2614i	−0.605632	−	0.440018i
$656$	−14.7669	+	45.4477i	−0.576549	+	1.77444i
$657$	8.06677	+	24.8270i	0.314715	+	0.968592i
$658$	−18.7597	+	13.6297i	−0.731328	+	0.531341i
$659$	23.6249			0.920297			0.460148	−	0.887842i	$-0.347796\pi$
$659$	23.6249			0.920297			0.460148	+	0.887842i	$0.347796\pi$
$660$		0			0
$661$	−20.9819			−0.816103			−0.408051	−	0.912959i	$-0.633792\pi$
$661$	−20.9819			−0.816103			−0.408051	+	0.912959i	$0.633792\pi$
$662$	38.1555	−	27.7216i	1.48296	−	1.07743i
$663$	2.25950	+	6.95404i	0.0877519	+	0.270072i
$664$	0.794782	−	2.44609i	0.0308435	−	0.0949266i
$665$	−4.35721	−	3.16570i	−0.168965	−	0.122760i
$666$	3.89835	+	2.83231i	0.151058	+	0.109750i
$667$	11.6517	−	35.8601i	0.451154	−	1.38851i
$668$	−4.80356	−	14.7838i	−0.185855	−	0.572004i
$669$	2.31254	−	1.68016i	0.0894078	−	0.0649586i
$670$	26.7456			1.03327
$671$		0			0
$672$	3.61803			0.139569
$673$	−9.78799	+	7.11139i	−0.377299	+	0.274124i	−0.760231	−	0.649653i	$-0.774914\pi$
$673$	−9.78799	+	7.11139i	−0.377299	+	0.274124i	0.382932	+	0.923777i	$0.374914\pi$
$674$	−0.376790	−	1.15964i	−0.0145134	−	0.0446676i
$675$	−2.91243	+	8.96355i	−0.112100	+	0.345007i
$676$	−5.09711	−	3.70327i	−0.196043	−	0.142433i
$677$	7.62893	+	5.54274i	0.293204	+	0.213025i	0.724656	−	0.689111i	$-0.241999\pi$
$677$	7.62893	+	5.54274i	0.293204	+	0.213025i	−0.431452	+	0.902136i	$0.641999\pi$
$678$	−6.26255	+	19.2741i	−0.240512	+	0.740219i
$679$	−3.58961	−	11.0477i	−0.137757	−	0.423971i
$680$	9.25098	−	6.72123i	0.354759	−	0.257747i
$681$	10.6922			0.409726
$682$		0			0
$683$	−15.2986			−0.585385			−0.292692	−	0.956207i	$-0.594551\pi$
$683$	−15.2986			−0.585385			−0.292692	+	0.956207i	$0.594551\pi$
$684$	4.76194	−	3.45975i	0.182077	−	0.132287i
$685$	2.24073	+	6.89627i	0.0856141	+	0.263493i
$686$	−0.549273	+	1.69049i	−0.0209713	+	0.0645431i
$687$	2.21306	+	1.60788i	0.0844335	+	0.0613445i
$688$	−18.9482	−	13.7667i	−0.722395	−	0.524851i
$689$	5.17451	−	15.9255i	0.197133	−	0.606713i
$690$	−4.12043	−	12.6814i	−0.156862	−	0.482772i
$691$	−18.4612	+	13.4128i	−0.702296	+	0.510248i	−0.880679	−	0.473713i	$-0.842913\pi$
$691$	−18.4612	+	13.4128i	−0.702296	+	0.510248i	0.178383	+	0.983961i	$0.442913\pi$
$692$	−23.8639			−0.907169
$693$		0			0
$694$	38.2256			1.45102
$695$	−2.25003	+	1.63474i	−0.0853486	+	0.0620094i
$696$	−2.46195	−	7.57709i	−0.0933198	−	0.287209i
$697$	−8.17978	+	25.1748i	−0.309831	+	0.953562i
$698$	−27.9591	−	20.3135i	−1.05827	−	0.768877i
$699$	5.26652	+	3.82635i	0.199198	+	0.144726i
$700$	−0.972549	+	2.99320i	−0.0367589	+	0.113132i
$701$	−9.98872	−	30.7421i	−0.377269	−	1.16111i	−0.941935	−	0.335794i	$-0.890995\pi$
$701$	−9.98872	−	30.7421i	−0.377269	−	1.16111i	0.564667	−	0.825319i	$-0.309005\pi$
$702$	−21.4373	+	15.5751i	−0.809097	+	0.587843i
$703$	2.00789			0.0757292
$704$		0			0
$705$	22.3937			0.843396
$706$	30.0987	−	21.8680i	1.13278	−	0.823012i
$707$	−1.05430	−	3.24480i	−0.0396511	−	0.122033i
$708$	−1.89485	+	5.83175i	−0.0712128	+	0.219171i
$709$	−11.7791	−	8.55802i	−0.442373	−	0.321403i	0.344204	−	0.938895i	$-0.388149\pi$
$709$	−11.7791	−	8.55802i	−0.442373	−	0.321403i	−0.786577	+	0.617492i	$0.788149\pi$
$710$	−8.05622	−	5.85319i	−0.302345	−	0.219666i
$711$	−5.09153	+	15.6701i	−0.190947	+	0.587675i
$712$	7.06551	+	21.7454i	0.264791	+	0.814943i
$713$	0.709174	−	0.515245i	0.0265588	−	0.0192961i
$714$	3.02710			0.113287
$715$		0			0
$716$	−4.30759			−0.160982
$717$	4.87823	−	3.54424i	0.182181	−	0.132362i
$718$	5.36709	+	16.5182i	0.200298	+	0.616454i
$719$	13.8626	−	42.6646i	0.516986	−	1.59112i	−0.262653	−	0.964890i	$-0.584597\pi$
$719$	13.8626	−	42.6646i	0.516986	−	1.59112i	0.779639	−	0.626229i	$-0.215403\pi$
$720$	29.2645	+	21.2619i	1.09062	+	0.792383i
$721$	−14.7100	−	10.6875i	−0.547830	−	0.398021i
$722$	−8.37087	+	25.7629i	−0.311531	+	0.958795i
$723$	2.39685	+	7.37676i	0.0891400	+	0.274345i
$724$	−4.47605	+	3.25204i	−0.166351	+	0.120861i
$725$	23.4202			0.869806
$726$		0			0
$727$	28.3582			1.05175			0.525874	−	0.850562i	$-0.323738\pi$
$727$	28.3582			1.05175			0.525874	+	0.850562i	$0.323738\pi$
$728$	5.18962	−	3.77048i	0.192340	−	0.139743i
$729$	−2.62868	−	8.09024i	−0.0973584	−	0.299638i
$730$	15.2118	−	46.8172i	0.563016	−	1.73278i
$731$	−10.4960	−	7.62576i	−0.388207	−	0.282049i
$732$	0.573121	+	0.416397i	0.0211832	+	0.0153905i
$733$	1.93351	−	5.95072i	0.0714157	−	0.219795i	−0.908978	−	0.416844i	$-0.863136\pi$
$733$	1.93351	−	5.95072i	0.0714157	−	0.219795i	0.980394	+	0.197050i	$0.0631360\pi$
$734$	5.43763	+	16.7353i	0.200707	+	0.617711i
$735$	1.38874	−	1.00898i	0.0512245	−	0.0372168i
$736$	−25.5830			−0.943001
$737$		0			0
$738$	−44.7024			−1.64552
$739$	−7.56593	+	5.49697i	−0.278317	+	0.202209i	−0.718183	−	0.695854i	$-0.755026\pi$
$739$	−7.56593	+	5.49697i	−0.278317	+	0.202209i	0.439866	+	0.898064i	$0.355026\pi$
$740$	−1.03045	−	3.17141i	−0.0378802	−	0.116583i
$741$	−1.59002	+	4.89358i	−0.0584109	+	0.179770i
$742$	−5.60843	−	4.07476i	−0.205892	−	0.149589i
$743$	−20.3926	−	14.8161i	−0.748130	−	0.543549i	0.147116	−	0.989119i	$-0.453001\pi$
$743$	−20.3926	−	14.8161i	−0.748130	−	0.543549i	−0.895247	+	0.445571i	$0.853001\pi$
$744$	0.0572359	−	0.176154i	0.00209837	−	0.00645812i
$745$	12.7840	+	39.3452i	0.468370	+	1.44150i
$746$	6.14715	−	4.46617i	0.225063	−	0.163518i
$747$	4.50684			0.164897
$748$		0			0
$749$	−3.24746			−0.118660
$750$	−5.64188	+	4.09907i	−0.206012	+	0.149677i
$751$	−10.7381	−	33.0485i	−0.391840	−	1.20596i	−0.931396	−	0.364008i	$-0.881408\pi$
$751$	−10.7381	−	33.0485i	−0.391840	−	1.20596i	0.539556	−	0.841950i	$-0.318592\pi$
$752$	20.0540	−	61.7198i	0.731293	−	2.25069i
$753$	5.49560	+	3.99278i	0.200271	+	0.145505i
$754$	53.2705	+	38.7033i	1.94000	+	1.40949i
$755$	−13.5649	+	41.7485i	−0.493678	+	1.51938i
$756$	1.24403	+	3.82873i	0.0452450	+	0.139250i
$757$	−28.1505	+	20.4526i	−1.02315	+	0.743361i	−0.966926	−	0.255057i	$-0.917906\pi$
$757$	−28.1505	+	20.4526i	−1.02315	+	0.743361i	−0.0562231	+	0.998418i	$0.517906\pi$
$758$	7.68929			0.279288
$759$		0			0
$760$	8.04674			0.291886
$761$	9.89060	−	7.18594i	0.358534	−	0.260490i	−0.393906	−	0.919151i	$-0.628877\pi$
$761$	9.89060	−	7.18594i	0.358534	−	0.260490i	0.752440	+	0.658660i	$0.228877\pi$
$762$	6.62281	+	20.3829i	0.239919	+	0.738395i
$763$	−3.92178	+	12.0700i	−0.141978	+	0.436964i
$764$	0.777763	+	0.565078i	0.0281385	+	0.0204438i
$765$	16.2104	+	11.7775i	0.586088	+	0.425818i
$766$	−0.726193	+	2.23499i	−0.0262384	+	0.0807536i
$767$	11.3532	+	34.9417i	0.409941	+	1.26167i
$768$	−10.1410	+	7.36785i	−0.365931	+	0.265864i
$769$	−2.61946			−0.0944603			−0.0472301	−	0.998884i	$-0.515039\pi$
$769$	−2.61946			−0.0944603			−0.0472301	+	0.998884i	$0.515039\pi$
$770$		0			0
$771$	3.29585			0.118697
$772$	6.32037	−	4.59202i	0.227475	−	0.165270i
$773$	−0.0657602	−	0.202389i	−0.00236523	−	0.00727943i	0.949867	−	0.312654i	$-0.101218\pi$
$773$	−0.0657602	−	0.202389i	−0.00236523	−	0.00727943i	−0.952232	+	0.305375i	$0.901218\pi$
$774$	6.77047	−	20.8374i	0.243359	−	0.748983i
$775$	0.440493	+	0.320037i	0.0158230	+	0.0114961i
$776$	14.0408	+	10.2012i	0.504035	+	0.366203i
$777$	−0.197759	+	0.608640i	−0.00709457	+	0.0218348i
$778$	−21.1520	−	65.0993i	−0.758337	−	2.33392i
$779$	−15.0698	+	10.9488i	−0.539931	+	0.392283i
$780$	8.54526			0.305969
$781$		0			0
$782$	−21.4045			−0.765425
$783$	24.2365	−	17.6088i	0.866140	−	0.629288i
$784$	−1.53723	−	4.73110i	−0.0549010	−	0.168968i
$785$	−3.94060	+	12.1279i	−0.140646	+	0.432864i
$786$	6.13051	+	4.45407i	0.218668	+	0.158872i
$787$	−23.5728	−	17.1266i	−0.840278	−	0.610498i	0.0821704	−	0.996618i	$-0.473815\pi$
$787$	−23.5728	−	17.1266i	−0.840278	−	0.610498i	−0.922448	+	0.386121i	$0.873815\pi$
$788$	−3.91309	+	12.0432i	−0.139398	+	0.429023i
$789$	−1.56231	−	4.80828i	−0.0556196	−	0.171179i
$790$	25.1365	−	18.2628i	0.894318	−	0.649760i
$791$	18.4480			0.655937
$792$		0			0
$793$	4.24457			0.150729
$794$	0.589743	−	0.428473i	0.0209292	−	0.0152059i
$795$	2.06883	+	6.36719i	0.0733737	+	0.225821i
$796$	7.51498	−	23.1287i	0.266361	−	0.819776i
$797$	−26.0733	−	18.9434i	−0.923565	−	0.671009i	0.0208440	−	0.999783i	$-0.493365\pi$
$797$	−26.0733	−	18.9434i	−0.923565	−	0.671009i	−0.944409	+	0.328774i	$0.893365\pi$
$798$	1.72336	+	1.25209i	0.0610061	+	0.0443236i
$799$	11.1085	−	34.1883i	0.392989	−	1.20950i
$800$	−4.91043	−	15.1127i	−0.173610	−	0.534316i
$801$	−32.4134	+	23.5497i	−1.14527	+	0.832088i
$802$	−2.78503			−0.0983430
$803$		0			0
$804$	−3.88203			−0.136909
$805$	−9.81974	+	7.13446i	−0.346100	+	0.251457i
$806$	0.473044	+	1.45588i	0.0166623	+	0.0512812i
$807$	2.45297	−	7.54946i	0.0863486	−	0.265754i
$808$	4.12391	+	2.99619i	0.145079	+	0.105406i
$809$	23.7415	+	17.2492i	0.834706	+	0.606450i	0.920887	−	0.389830i	$-0.127466\pi$
$809$	23.7415	+	17.2492i	0.834706	+	0.606450i	−0.0861807	+	0.996280i	$0.527466\pi$
$810$	−8.70842	+	26.8018i	−0.305983	+	0.941718i
$811$	0.321192	+	0.988526i	0.0112786	+	0.0347118i	0.956537	−	0.291610i	$-0.0941908\pi$
$811$	0.321192	+	0.988526i	0.0112786	+	0.0347118i	−0.945259	+	0.326321i	$0.894191\pi$
$812$	8.09328	−	5.88011i	0.284018	−	0.206351i
$813$	−13.6259			−0.477882
$814$		0			0
$815$	−22.3244			−0.781990
$816$	−6.85386	+	4.97962i	−0.239933	+	0.174322i
$817$	−2.82122	−	8.68282i	−0.0987020	−	0.303773i
$818$	−3.72326	+	11.4590i	−0.130181	+	0.400655i
$819$	9.09373	+	6.60698i	0.317761	+	0.230867i
$820$	25.0271	+	18.1833i	0.873986	+	0.634988i
$821$	8.81698	−	27.1359i	0.307715	−	0.947048i	−0.670936	−	0.741516i	$-0.734107\pi$
$821$	8.81698	−	27.1359i	0.307715	−	0.947048i	0.978650	−	0.205533i	$-0.0658927\pi$
$822$	−0.886251	−	2.72760i	−0.0309116	−	0.0951360i
$823$	−21.5665	+	15.6690i	−0.751761	+	0.546186i	−0.896372	−	0.443302i	$-0.853807\pi$
$823$	−21.5665	+	15.6690i	−0.751761	+	0.546186i	0.144611	+	0.989489i	$0.453807\pi$
$824$	27.1659			0.946370
$825$		0			0
$826$	15.2102			0.529229
$827$	−1.39122	+	1.01078i	−0.0483775	+	0.0351483i	−0.611711	−	0.791081i	$-0.709519\pi$
$827$	−1.39122	+	1.01078i	−0.0483775	+	0.0351483i	0.563334	+	0.826229i	$0.309519\pi$
$828$	−4.09921	−	12.6161i	−0.142458	−	0.438439i
$829$	8.64026	−	26.5920i	0.300089	−	0.923578i	−0.681376	−	0.731934i	$-0.738618\pi$
$829$	8.64026	−	26.5920i	0.300089	−	0.923578i	0.981464	−	0.191644i	$-0.0613819\pi$
$830$	−6.87562	−	4.99543i	−0.238656	−	0.173394i
$831$	−12.0385	−	8.74647i	−0.417610	−	0.303412i
$832$	0.605562	−	1.86373i	0.0209941	−	0.0646132i
$833$	−0.851514	−	2.62069i	−0.0295032	−	0.0908015i
$834$	0.889929	−	0.646571i	0.0308157	−	0.0223889i
$835$	37.2375			1.28866
$836$		0			0
$837$	0.696468			0.0240735
$838$	−41.3024	+	30.0080i	−1.42677	+	1.03661i
$839$	11.0821	+	34.1072i	0.382596	+	1.17751i	0.938209	+	0.346069i	$0.112484\pi$
$839$	11.0821	+	34.1072i	0.382596	+	1.17751i	−0.555612	+	0.831441i	$0.687516\pi$
$840$	−0.792530	+	2.43916i	−0.0273449	+	0.0841589i
$841$	−36.7649	−	26.7113i	−1.26776	−	0.921078i
$842$	−17.5806	−	12.7730i	−0.605866	−	0.440188i
$843$	2.94913	−	9.07648i	0.101573	−	0.312611i
$844$	−2.15820	−	6.64225i	−0.0742882	−	0.228636i
$845$	12.2102	−	8.87125i	0.420045	−	0.305180i
$846$	60.7076			2.08717
$847$		0			0
$848$	19.4014			0.666248
$849$	1.67866	−	1.21962i	0.0576115	−	0.0418572i
$850$	−4.10841	−	12.6444i	−0.140917	−	0.433699i
$851$	1.39835	−	4.30367i	0.0479347	−	0.147528i
$852$	1.16933	+	0.849571i	0.0400607	+	0.0291058i
$853$	12.2507	+	8.90068i	0.419457	+	0.304754i	0.777419	−	0.628983i	$-0.216528\pi$
$853$	12.2507	+	8.90068i	0.419457	+	0.304754i	−0.357962	+	0.933736i	$0.616528\pi$
$854$	0.543016	−	1.67123i	0.0185816	−	0.0571884i
$855$	4.35721	+	13.4101i	0.149013	+	0.458616i
$856$	3.92528	−	2.85188i	0.134163	−	0.0974753i
$857$	25.3267			0.865142			0.432571	−	0.901600i	$-0.357606\pi$
$857$	25.3267			0.865142			0.432571	+	0.901600i	$0.357606\pi$
$858$		0			0
$859$	41.5291			1.41696			0.708478	−	0.705733i	$-0.249382\pi$
$859$	41.5291			1.41696			0.708478	+	0.705733i	$0.249382\pi$
$860$	−12.2664	+	8.91205i	−0.418280	+	0.303898i
$861$	−1.83461	−	5.64636i	−0.0625235	−	0.192427i
$862$	2.02753	−	6.24008i	0.0690578	−	0.212538i
$863$	19.4572	+	14.1365i	0.662329	+	0.481210i	0.867449	−	0.497527i	$-0.165758\pi$
$863$	19.4572	+	14.1365i	0.662329	+	0.481210i	−0.205119	+	0.978737i	$0.565758\pi$
$864$	−16.4443	−	11.9475i	−0.559445	−	0.406461i
$865$	17.6654	−	54.3685i	0.600641	−	1.84858i
$866$	15.9700	+	49.1507i	0.542684	+	1.67021i
$867$	4.70345	−	3.41726i	0.159738	−	0.116056i
$868$	0.232572			0.00789399
$869$		0			0
$870$	−26.3260			−0.892534
$871$	−18.8175	+	13.6717i	−0.637606	+	0.463248i
$872$	−5.85939	−	18.0334i	−0.198424	−	0.610687i
$873$	−9.39772	+	28.9232i	−0.318065	+	0.978902i
$874$	−12.1858	−	8.85349i	−0.412190	−	0.299474i
$875$	5.13577	+	3.73136i	0.173621	+	0.126143i
$876$	−2.20795	+	6.79537i	−0.0745997	+	0.229594i
$877$	10.4464	+	32.1506i	0.352749	+	1.08565i	0.957303	+	0.289086i	$0.0933514\pi$
$877$	10.4464	+	32.1506i	0.352749	+	1.08565i	−0.604554	+	0.796564i	$0.706649\pi$
$878$	20.4223	−	14.8376i	0.689218	−	0.500746i
$879$	4.22553			0.142524
$880$		0			0
$881$	−36.8296			−1.24082			−0.620410	−	0.784278i	$-0.713034\pi$
$881$	−36.8296			−1.24082			−0.620410	+	0.784278i	$0.713034\pi$
$882$	3.76477	−	2.73527i	0.126766	−	0.0921012i
$883$	16.5047	+	50.7963i	0.555428	+	1.70943i	0.694812	+	0.719192i	$0.255488\pi$
$883$	16.5047	+	50.7963i	0.555428	+	1.70943i	−0.139384	+	0.990238i	$0.544512\pi$
$884$	4.23890	−	13.0460i	0.142570	−	0.438784i
$885$	−11.8836	−	8.63397i	−0.399464	−	0.290228i
$886$	−39.1652	−	28.4552i	−1.31578	−	0.955970i
$887$	3.54183	−	10.9006i	0.118923	−	0.366007i	−0.873822	−	0.486246i	$-0.838366\pi$
$887$	3.54183	−	10.9006i	0.118923	−	0.366007i	0.992745	+	0.120239i	$0.0383659\pi$
$888$	−0.295465	−	0.909347i	−0.00991515	−	0.0305157i
$889$	15.7834	−	11.4673i	0.529357	−	0.384600i
$890$	75.5525			2.53253
$891$		0			0
$892$	−5.36254			−0.179551
$893$	20.4653	−	14.8689i	0.684846	−	0.497570i
$894$	−5.05631	−	15.5617i	−0.169108	−	0.520462i
$895$	3.18872	−	9.81386i	0.106587	−	0.328041i
$896$	8.81579	+	6.40505i	0.294515	+	0.213978i
$897$	9.38145	+	6.81602i	0.313237	+	0.227580i
$898$	−23.0233	+	70.8583i	−0.768296	+	2.36457i
$899$	−0.534812	−	1.64598i	−0.0178370	−	0.0548966i
$900$	6.66595	−	4.84309i	0.222198	−	0.161436i
$901$	10.7470			0.358034
$902$		0			0
$903$	2.90983			0.0968331
$904$	−22.2986	+	16.2009i	−0.741640	+	0.538833i
$905$	−4.09561	−	12.6050i	−0.136143	−	0.419004i
$906$	5.36517	−	16.5123i	0.178246	−	0.548585i
$907$	−46.1610	−	33.5380i	−1.53275	−	1.11361i	−0.954684	−	0.297621i	$-0.903807\pi$
$907$	−46.1610	−	33.5380i	−1.53275	−	1.11361i	−0.578068	−	0.815989i	$-0.696193\pi$
$908$	−16.2280	−	11.7903i	−0.538544	−	0.391275i
$909$	−2.76020	+	8.49501i	−0.0915499	+	0.281762i
$910$	−6.55011	−	20.1592i	−0.217134	−	0.668270i
$911$	−5.40072	+	3.92386i	−0.178934	+	0.130003i	−0.673647	−	0.739053i	$-0.735273\pi$
$911$	−5.40072	+	3.92386i	−0.178934	+	0.130003i	0.494713	+	0.869056i	$0.335273\pi$
$912$	−5.96167			−0.197410
$913$		0			0
$914$	34.6568			1.14635
$915$	−1.37292	+	0.997487i	−0.0453874	+	0.0329759i
$916$	−1.58583	−	4.88069i	−0.0523974	−	0.161263i
$917$	2.13159	−	6.56035i	0.0703912	−	0.216642i
$918$	−13.7584	−	9.99610i	−0.454096	−	0.329920i
$919$	23.5698	+	17.1245i	0.777496	+	0.564884i	0.904227	−	0.427053i	$-0.140448\pi$
$919$	23.5698	+	17.1245i	0.777496	+	0.564884i	−0.126730	+	0.991937i	$0.540448\pi$
$920$	5.60395	−	17.2472i	0.184757	−	0.568622i
$921$	−2.25303	−	6.93413i	−0.0742400	−	0.228487i
$922$	−17.5799	+	12.7725i	−0.578962	+	0.420641i
$923$	8.66015			0.285052
$924$		0			0
$925$	2.81073			0.0924161
$926$	−19.9236	+	14.4754i	−0.654731	+	0.475690i
$927$	14.7100	+	45.2728i	0.483140	+	1.48695i
$928$	−15.6084	+	48.0376i	−0.512370	+	1.57691i
$929$	−1.89692	−	1.37819i	−0.0622358	−	0.0452169i	0.556232	−	0.831027i	$-0.312246\pi$
$929$	−1.89692	−	1.37819i	−0.0622358	−	0.0452169i	−0.618468	+	0.785810i	$0.712246\pi$
$930$	−0.495144	−	0.359743i	−0.0162364	−	0.0117965i
$931$	0.599213	−	1.84419i	0.0196384	−	0.0604409i
$932$	−3.77388	−	11.6148i	−0.123618	−	0.380456i
$933$	−12.6569	+	9.19581i	−0.414370	+	0.301057i
$934$	−29.1876			−0.955047
$935$		0			0
$936$	−16.7940			−0.548928
$937$	−7.10948	+	5.16534i	−0.232257	+	0.168744i	−0.697827	−	0.716267i	$-0.745849\pi$
$937$	−7.10948	+	5.16534i	−0.232257	+	0.168744i	0.465570	+	0.885011i	$0.345849\pi$
$938$	2.97566	+	9.15813i	0.0971586	+	0.299023i
$939$	−3.75364	+	11.5525i	−0.122496	+	0.377003i
$940$	−33.9878	−	24.6936i	−1.10856	−	0.805416i
$941$	−7.19112	−	5.22465i	−0.234424	−	0.170319i	0.464372	−	0.885640i	$-0.346280\pi$
$941$	−7.19112	−	5.22465i	−0.234424	−	0.170319i	−0.698795	+	0.715322i	$0.746280\pi$
$942$	1.55858	−	4.79682i	0.0507813	−	0.156289i
$943$	12.9725	+	39.9252i	0.422442	+	1.30014i
$944$	−34.4383	+	25.0209i	−1.12087	+	0.814361i
$945$	−9.64380			−0.313713
$946$		0			0
$947$	−7.86275			−0.255505			−0.127752	−	0.991806i	$-0.540776\pi$
$947$	−7.86275			−0.255505			−0.127752	+	0.991806i	$0.540776\pi$
$948$	−3.64849	+	2.65078i	−0.118497	+	0.0860933i
$949$	13.2292	+	40.7153i	0.429438	+	1.32167i
$950$	2.89111	−	8.89791i	0.0937999	−	0.288686i
$951$	−1.80528	−	1.31161i	−0.0585402	−	0.0425320i
$952$	3.33070	+	2.41990i	0.107949	+	0.0784294i
$953$	−5.39679	+	16.6096i	−0.174819	+	0.538039i	−0.999625	−	0.0273775i	$-0.991284\pi$
$953$	−5.39679	+	16.6096i	−0.174819	+	0.538039i	0.824806	+	0.565416i	$0.191284\pi$
$954$	5.60843	+	17.2610i	0.181580	+	0.558845i
$955$	−1.86315	+	1.35365i	−0.0602900	+	0.0438032i
$956$	−11.3121			−0.365860
$957$		0			0
$958$	−44.0663			−1.42372
$959$	−2.11210	+	1.53453i	−0.0682032	+	0.0495525i
$960$	0.242111	+	0.745140i	0.00781408	+	0.0240493i
$961$	−9.56709	+	29.4445i	−0.308616	+	0.949822i
$962$	6.39314	+	4.64489i	0.206123	+	0.149757i
$963$	6.87823	+	4.99733i	0.221648	+	0.161037i
$964$	4.49657	−	13.8390i	0.144825	−	0.445725i
$965$	5.78318	+	17.7988i	0.186167	+	0.572964i
$966$	3.88389	−	2.82181i	0.124962	−	0.0907902i
$967$	−45.6122			−1.46679			−0.733395	−	0.679802i	$-0.762066\pi$
$967$	−45.6122			−1.46679			−0.733395	+	0.679802i	$0.762066\pi$
$968$		0			0
$969$	−3.30233			−0.106086
$970$	46.3959	−	33.7086i	1.48968	−	1.08232i
$971$	0.736629	+	2.26711i	0.0236396	+	0.0727551i	0.962180	−	0.272413i	$-0.0878218\pi$
$971$	0.736629	+	2.26711i	0.0236396	+	0.0727551i	−0.938541	+	0.345168i	$0.887822\pi$
$972$	4.99609	−	15.3764i	0.160250	−	0.493198i
$973$	−0.810097	−	0.588570i	−0.0259705	−	0.0188687i
$974$	20.6128	+	14.9761i	0.660476	+	0.479864i
$975$	−2.22577	+	6.85022i	−0.0712817	+	0.219383i
$976$	1.51972	+	4.67721i	0.0486450	+	0.149714i
$977$	15.5867	−	11.3244i	0.498662	−	0.362299i	−0.309844	−	0.950787i	$-0.600277\pi$
$977$	15.5867	−	11.3244i	0.498662	−	0.362299i	0.808506	+	0.588488i	$0.200277\pi$
$978$	8.82972			0.282343
$979$		0			0
$980$	−3.22035			−0.102870
$981$	26.8803	−	19.5297i	0.858222	−	0.623535i
$982$	−12.0946	−	37.2234i	−0.385955	−	1.18785i
$983$	−5.01399	+	15.4315i	−0.159922	+	0.492188i	−0.998626	−	0.0523985i	$-0.983313\pi$
$983$	−5.01399	+	15.4315i	−0.159922	+	0.492188i	0.838705	+	0.544587i	$0.183313\pi$
$984$	7.17611	+	5.21375i	0.228766	+	0.166208i
$985$	−24.5411	−	17.8302i	−0.781945	−	0.568116i
$986$	−13.0591	+	40.1917i	−0.415885	+	1.27996i
$987$	2.49148	+	7.66797i	0.0793045	+	0.244074i
$988$	7.80941	−	5.67387i	0.248450	−	0.180510i
$989$	−20.5753			−0.654256
$990$		0			0
$991$	−50.5214			−1.60487			−0.802433	−	0.596743i	$-0.796461\pi$
$991$	−50.5214			−1.60487			−0.802433	+	0.596743i	$0.796461\pi$
$992$	−0.949997	+	0.690213i	−0.0301624	+	0.0219143i
$993$	−5.06744	−	15.5960i	−0.160810	−	0.494923i
$994$	1.10791	−	3.40980i	0.0351408	−	0.108152i
$995$	47.1305	+	34.2423i	1.49414	+	1.08556i
$996$	0.997973	+	0.725070i	0.0316220	+	0.0229747i
$997$	−13.9121	+	42.8172i	−0.440602	+	1.35603i	0.446634	+	0.894717i	$0.352623\pi$
$997$	−13.9121	+	42.8172i	−0.440602	+	1.35603i	−0.887236	+	0.461316i	$0.847377\pi$
$998$	−13.9030	−	42.7892i	−0.440093	−	1.35447i
$999$	2.90868	−	2.11328i	0.0920266	−	0.0668612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.p.729.1		8
11.2	odd	10		847.2.a.k.1.2		4
11.3	even	5		77.2.f.a.71.2	yes	8
11.4	even	5	inner	847.2.f.p.323.1		8
11.5	even	5		77.2.f.a.64.2	✓	8
11.6	odd	10		847.2.f.q.372.1		8
11.7	odd	10		847.2.f.s.323.2		8
11.8	odd	10		847.2.f.q.148.1		8
11.9	even	5		847.2.a.l.1.3		4
11.10	odd	2		847.2.f.s.729.2		8
33.2	even	10		7623.2.a.co.1.3		4
33.5	odd	10		693.2.m.g.64.1		8
33.14	odd	10		693.2.m.g.379.1		8
33.20	odd	10		7623.2.a.ch.1.2		4
77.3	odd	30		539.2.q.b.324.1		16
77.5	odd	30		539.2.q.b.361.1		16
77.13	even	10		5929.2.a.bb.1.2		4
77.16	even	15		539.2.q.c.361.1		16
77.20	odd	10		5929.2.a.bi.1.3		4
77.25	even	15		539.2.q.c.324.1		16
77.27	odd	10		539.2.f.d.295.2		8
77.38	odd	30		539.2.q.b.471.2		16
77.47	odd	30		539.2.q.b.214.2		16
77.58	even	15		539.2.q.c.214.2		16
77.60	even	15		539.2.q.c.471.2		16
77.69	odd	10		539.2.f.d.148.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.64.2	✓	8	11.5	even	5
77.2.f.a.71.2	yes	8	11.3	even	5
539.2.f.d.148.2		8	77.69	odd	10
539.2.f.d.295.2		8	77.27	odd	10
539.2.q.b.214.2		16	77.47	odd	30
539.2.q.b.324.1		16	77.3	odd	30
539.2.q.b.361.1		16	77.5	odd	30
539.2.q.b.471.2		16	77.38	odd	30
539.2.q.c.214.2		16	77.58	even	15
539.2.q.c.324.1		16	77.25	even	15
539.2.q.c.361.1		16	77.16	even	15
539.2.q.c.471.2		16	77.60	even	15
693.2.m.g.64.1		8	33.5	odd	10
693.2.m.g.379.1		8	33.14	odd	10
847.2.a.k.1.2		4	11.2	odd	10
847.2.a.l.1.3		4	11.9	even	5
847.2.f.p.323.1		8	11.4	even	5	inner
847.2.f.p.729.1		8	1.1	even	1	trivial
847.2.f.q.148.1		8	11.8	odd	10
847.2.f.q.372.1		8	11.6	odd	10
847.2.f.s.323.2		8	11.7	odd	10
847.2.f.s.729.2		8	11.10	odd	2
5929.2.a.bb.1.2		4	77.13	even	10
5929.2.a.bi.1.3		4	77.20	odd	10
7623.2.a.ch.1.2		4	33.20	odd	10
7623.2.a.co.1.3		4	33.2	even	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.43801 + 1.04478i) q^{2} +(0.190983 + 0.587785i) q^{3} +(0.358290 - 1.10270i) q^{4} +(2.24703 + 1.63256i) q^{5} +(-0.888742 - 0.645709i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.461691 - 1.42094i) q^{8} +(2.11803 - 1.53884i) q^{9} +O(q^{10})\)	\(q+(-1.43801 + 1.04478i) q^{2} +(0.190983 + 0.587785i) q^{3} +(0.358290 - 1.10270i) q^{4} +(2.24703 + 1.63256i) q^{5} +(-0.888742 - 0.645709i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.461691 - 1.42094i) q^{8} +(2.11803 - 1.53884i) q^{9} -4.93693 q^{10} +0.716580 q^{12} +(3.47350 - 2.52364i) q^{13} +(-0.549273 - 1.69049i) q^{14} +(-0.530452 + 1.63256i) q^{15} +(4.02452 + 2.92398i) q^{16} +(2.22929 + 1.61968i) q^{17} +(-1.43801 + 4.42575i) q^{18} +(0.599213 + 1.84419i) q^{19} +(2.60532 - 1.89288i) q^{20} -0.618034 q^{21} +4.37009 q^{23} +(0.747032 - 0.542750i) q^{24} +(0.838802 + 2.58157i) q^{25} +(-2.35829 + 7.25807i) q^{26} +(2.80902 + 2.04087i) q^{27} +(0.938015 + 0.681508i) q^{28} +(2.66623 - 8.20580i) q^{29} +(-0.942871 - 2.90186i) q^{30} +(0.162279 - 0.117903i) q^{31} -5.85410 q^{32} -4.89796 q^{34} +(-2.24703 + 1.63256i) q^{35} +(-0.938015 - 2.88691i) q^{36} +(0.319981 - 0.984800i) q^{37} +(-2.78845 - 2.02593i) q^{38} +(2.14674 + 1.55970i) q^{39} +(1.28234 - 3.94664i) q^{40} +(2.96847 + 9.13600i) q^{41} +(0.888742 - 0.645709i) q^{42} -4.70820 q^{43} +7.27155 q^{45} +(-6.28426 + 4.56578i) q^{46} +(-4.03129 - 12.4070i) q^{47} +(-0.950059 + 2.92398i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-3.90337 - 2.83597i) q^{50} +(-0.526264 + 1.61968i) q^{51} +(-1.53831 - 4.73443i) q^{52} +(3.15526 - 2.29243i) q^{53} -6.17167 q^{54} +1.49406 q^{56} +(-0.969548 + 0.704418i) q^{57} +(4.73918 + 14.5857i) q^{58} +(-2.64430 + 8.13831i) q^{59} +(1.61018 + 1.16986i) q^{60} +(0.799801 + 0.581090i) q^{61} +(-0.110177 + 0.339091i) q^{62} +(0.809017 + 2.48990i) q^{63} +(0.369254 - 0.268279i) q^{64} +11.9251 q^{65} -5.41745 q^{67} +(2.58475 - 1.87793i) q^{68} +(0.834614 + 2.56868i) q^{69} +(1.52560 - 4.69530i) q^{70} +(1.63183 + 1.18559i) q^{71} +(-3.16448 - 2.29913i) q^{72} +(-3.08123 + 9.48306i) q^{73} +(0.568761 + 1.75047i) q^{74} +(-1.35721 + 0.986070i) q^{75} +2.24828 q^{76} -4.71658 q^{78} +(-5.09153 + 3.69921i) q^{79} +(4.26963 + 13.1406i) q^{80} +(1.76393 - 5.42882i) q^{81} +(-13.8138 - 10.0363i) q^{82} +(1.39269 + 1.01185i) q^{83} +(-0.221435 + 0.681508i) q^{84} +(2.36507 + 7.27892i) q^{85} +(6.77047 - 4.91903i) q^{86} +5.33245 q^{87} -15.3035 q^{89} +(-10.4566 + 7.59716i) q^{90} +(1.32676 + 4.08334i) q^{91} +(1.56576 - 4.81891i) q^{92} +(0.100294 + 0.0728678i) q^{93} +(18.7597 + 13.6297i) q^{94} +(-1.66431 + 5.12221i) q^{95} +(-1.11803 - 3.44095i) q^{96} +(-9.39772 + 6.82784i) q^{97} +1.77748 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 6 q^{3} - 7 q^{4} + 3 q^{5} - 2 q^{6} + 2 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - q^2 + 6 * q^3 - 7 * q^4 + 3 * q^5 - 2 * q^6 + 2 * q^7 - 12 * q^8 + 8 * q^9	\( 8 q - q^{2} + 6 q^{3} - 7 q^{4} + 3 q^{5} - 2 q^{6} + 2 q^{7} - 12 q^{8} + 8 q^{9} - 28 q^{10} - 14 q^{12} - 5 q^{13} + q^{14} - 9 q^{15} + 7 q^{16} + 14 q^{17} - q^{18} + 6 q^{19} - 4 q^{20} + 4 q^{21} - 16 q^{23} - 9 q^{24} - 5 q^{25} - 9 q^{26} + 18 q^{27} - 3 q^{28} + 6 q^{29} - 26 q^{30} + 14 q^{31} - 20 q^{32} - 24 q^{34} - 3 q^{35} + 3 q^{36} + q^{37} - 15 q^{38} + 29 q^{40} + 18 q^{41} + 2 q^{42} + 16 q^{43} + 18 q^{45} - 26 q^{46} + 7 q^{47} - q^{48} - 2 q^{49} + q^{50} + 8 q^{51} - 4 q^{52} + 7 q^{53} + 4 q^{54} - 18 q^{56} - 3 q^{57} + 36 q^{58} + 17 q^{60} + 12 q^{61} - 5 q^{62} + 2 q^{63} - 4 q^{64} + 24 q^{65} - 30 q^{67} - 7 q^{68} - 22 q^{69} - 12 q^{70} + 21 q^{71} + 3 q^{72} + 8 q^{73} + q^{74} - 52 q^{76} - 18 q^{78} + q^{79} + 37 q^{80} + 32 q^{81} - 34 q^{82} - 22 q^{83} - 11 q^{84} - 5 q^{85} + 13 q^{86} + 12 q^{87} - 34 q^{89} - 18 q^{90} - 5 q^{91} + 51 q^{92} + 3 q^{93} + 50 q^{94} - 41 q^{95} - 15 q^{97} + 4 q^{98}+O(q^{100}) \) 8 * q - q^2 + 6 * q^3 - 7 * q^4 + 3 * q^5 - 2 * q^6 + 2 * q^7 - 12 * q^8 + 8 * q^9 - 28 * q^10 - 14 * q^12 - 5 * q^13 + q^14 - 9 * q^15 + 7 * q^16 + 14 * q^17 - q^18 + 6 * q^19 - 4 * q^20 + 4 * q^21 - 16 * q^23 - 9 * q^24 - 5 * q^25 - 9 * q^26 + 18 * q^27 - 3 * q^28 + 6 * q^29 - 26 * q^30 + 14 * q^31 - 20 * q^32 - 24 * q^34 - 3 * q^35 + 3 * q^36 + q^37 - 15 * q^38 + 29 * q^40 + 18 * q^41 + 2 * q^42 + 16 * q^43 + 18 * q^45 - 26 * q^46 + 7 * q^47 - q^48 - 2 * q^49 + q^50 + 8 * q^51 - 4 * q^52 + 7 * q^53 + 4 * q^54 - 18 * q^56 - 3 * q^57 + 36 * q^58 + 17 * q^60 + 12 * q^61 - 5 * q^62 + 2 * q^63 - 4 * q^64 + 24 * q^65 - 30 * q^67 - 7 * q^68 - 22 * q^69 - 12 * q^70 + 21 * q^71 + 3 * q^72 + 8 * q^73 + q^74 - 52 * q^76 - 18 * q^78 + q^79 + 37 * q^80 + 32 * q^81 - 34 * q^82 - 22 * q^83 - 11 * q^84 - 5 * q^85 + 13 * q^86 + 12 * q^87 - 34 * q^89 - 18 * q^90 - 5 * q^91 + 51 * q^92 + 3 * q^93 + 50 * q^94 - 41 * q^95 - 15 * q^97 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more