LMFDB - Embedded newform 165.2.k.c.122.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(23,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("165.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} + 19 x^{12} - 80 x^{11} + 168 x^{10} + 28 x^{9} + 119 x^{8} - 432 x^{7} + \cdots + 16 $ x^16 - 4x^15 + 8x^14 + 19x^12 - 80x^11 + 168x^10 + 28x^9 + 119x^8 - 432x^7 + 784x^6 + 84x^5 + 169x^4 - 420x^3 + 392x^2 - 112x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			122.7
Root			$-1.14633 - 1.14633i$ of defining polynomial
Character	$\chi$	$=$	165.122
Dual form			165.2.k.c.23.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.14633 - 1.14633i) q^{2} +(-0.582649 - 1.63111i) q^{3} -0.628149i q^{4} +(-0.515221 - 2.17590i) q^{5} +(-2.53770 - 1.20188i) q^{6} +(-0.201884 - 0.201884i) q^{7} +(1.57260 + 1.57260i) q^{8} +(-2.32104 + 1.90073i) q^{9} +(-3.08492 - 1.90369i) q^{10} +1.00000i q^{11} +(-1.02458 + 0.365990i) q^{12} +(1.02066 - 1.02066i) q^{13} -0.462851 q^{14} +(-3.24894 + 2.10817i) q^{15} +4.86173 q^{16} +(2.87911 - 2.87911i) q^{17} +(-0.481818 + 4.83954i) q^{18} -0.281435i q^{19} +(-1.36679 + 0.323635i) q^{20} +(-0.211667 + 0.446922i) q^{21} +(1.14633 + 1.14633i) q^{22} +(5.22177 + 5.22177i) q^{23} +(1.64881 - 3.48135i) q^{24} +(-4.46910 + 2.24214i) q^{25} -2.34002i q^{26} +(4.45265 + 2.67842i) q^{27} +(-0.126813 + 0.126813i) q^{28} -9.71095 q^{29} +(-1.30771 + 6.14102i) q^{30} +4.46829 q^{31} +(2.42796 - 2.42796i) q^{32} +(1.63111 - 0.582649i) q^{33} -6.60083i q^{34} +(-0.335265 + 0.543294i) q^{35} +(1.19394 + 1.45796i) q^{36} +(2.37906 + 2.37906i) q^{37} +(-0.322618 - 0.322618i) q^{38} +(-2.25949 - 1.07012i) q^{39} +(2.61158 - 4.23205i) q^{40} +9.00173i q^{41} +(0.269680 + 0.754962i) q^{42} +(1.84728 - 1.84728i) q^{43} +0.628149 q^{44} +(5.33165 + 4.07106i) q^{45} +11.9718 q^{46} +(-3.98588 + 3.98588i) q^{47} +(-2.83268 - 7.93001i) q^{48} -6.91849i q^{49} +(-2.55283 + 7.69329i) q^{50} +(-6.37366 - 3.01864i) q^{51} +(-0.641125 - 0.641125i) q^{52} +(-4.75830 - 4.75830i) q^{53} +(8.17456 - 2.03386i) q^{54} +(2.17590 - 0.515221i) q^{55} -0.634963i q^{56} +(-0.459052 + 0.163978i) q^{57} +(-11.1320 + 11.1320i) q^{58} -2.68228 q^{59} +(1.32424 + 2.04082i) q^{60} -9.46983 q^{61} +(5.12214 - 5.12214i) q^{62} +(0.852307 + 0.0848544i) q^{63} +4.15697i q^{64} +(-2.74671 - 1.69499i) q^{65} +(1.20188 - 2.53770i) q^{66} +(-6.27596 - 6.27596i) q^{67} +(-1.80851 - 1.80851i) q^{68} +(5.47482 - 11.5597i) q^{69} +(0.238471 + 1.00712i) q^{70} +0.679177i q^{71} +(-6.63914 - 0.660982i) q^{72} +(-5.74145 + 5.74145i) q^{73} +5.45437 q^{74} +(6.26109 + 5.98321i) q^{75} -0.176783 q^{76} +(0.201884 - 0.201884i) q^{77} +(-3.81683 + 1.36341i) q^{78} +12.5134i q^{79} +(-2.50486 - 10.5786i) q^{80} +(1.77446 - 8.82334i) q^{81} +(10.3190 + 10.3190i) q^{82} +(4.93065 + 4.93065i) q^{83} +(0.280734 + 0.132959i) q^{84} +(-7.74804 - 4.78128i) q^{85} -4.23518i q^{86} +(5.65807 + 15.8396i) q^{87} +(-1.57260 + 1.57260i) q^{88} +2.97979 q^{89} +(10.7786 - 1.44504i) q^{90} -0.412109 q^{91} +(3.28005 - 3.28005i) q^{92} +(-2.60345 - 7.28828i) q^{93} +9.13826i q^{94} +(-0.612375 + 0.145001i) q^{95} +(-5.37491 - 2.54562i) q^{96} +(-11.4137 - 11.4137i) q^{97} +(-7.93087 - 7.93087i) q^{98} +(-1.90073 - 2.32104i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 2 q^{3} - 8 q^{5} - 4 q^{6} + 8 q^{7} + 16 q^{8} + 6 q^{9} - 4 q^{10} - 4 q^{12} - 24 q^{14} + 8 q^{15} - 4 q^{16} + 8 q^{17} - 32 q^{18} - 20 q^{20} - 8 q^{21} - 4 q^{22} + 14 q^{23} + 12 q^{24}+ \cdots - 4 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 2 * q^3 - 8 * q^5 - 4 * q^6 + 8 * q^7 + 16 * q^8 + 6 * q^9 - 4 * q^10 - 4 * q^12 - 24 * q^14 + 8 * q^15 - 4 * q^16 + 8 * q^17 - 32 * q^18 - 20 * q^20 - 8 * q^21 - 4 * q^22 + 14 * q^23 + 12 * q^24 - 18 * q^25 - 20 * q^27 + 8 * q^28 - 16 * q^29 + 20 * q^30 + 8 * q^31 + 28 * q^32 + 4 * q^33 + 44 * q^36 - 6 * q^37 + 24 * q^38 + 24 * q^39 + 16 * q^40 - 60 * q^42 + 16 * q^43 + 12 * q^44 + 24 * q^45 - 32 * q^46 + 48 * q^47 - 48 * q^48 - 12 * q^50 - 8 * q^51 + 36 * q^52 - 4 * q^53 + 4 * q^54 + 2 * q^55 - 8 * q^57 - 12 * q^58 - 68 * q^59 - 28 * q^60 - 8 * q^61 + 48 * q^62 - 12 * q^63 - 48 * q^65 + 8 * q^66 + 6 * q^67 + 24 * q^68 + 12 * q^69 - 4 * q^70 - 8 * q^72 + 8 * q^74 + 8 * q^75 + 16 * q^76 - 8 * q^77 - 48 * q^78 - 24 * q^80 + 2 * q^81 + 12 * q^82 - 8 * q^83 + 52 * q^84 - 4 * q^85 - 36 * q^87 - 16 * q^88 + 32 * q^89 + 44 * q^90 - 56 * q^91 + 20 * q^92 + 28 * q^93 - 48 * q^95 + 80 * q^96 + 18 * q^97 + 16 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.14633	−	1.14633i	0.810578	−	0.810578i	−0.174142	−	0.984721i	$-0.555715\pi$
$2$	1.14633	−	1.14633i	0.810578	−	0.810578i	0.984721	+	0.174142i	$0.0557153\pi$
$3$	−0.582649	−	1.63111i	−0.336392	−	0.941722i
$3$	−0.582649	−	1.63111i	−0.336392	−	0.941722i
$4$		−	0.628149i		−	0.314074i
$5$	−0.515221	−	2.17590i	−0.230414	−	0.973093i
$5$	−0.515221	−	2.17590i	−0.230414	−	0.973093i
$6$	−2.53770	−	1.20188i	−1.03601	−	0.490667i
$7$	−0.201884	−	0.201884i	−0.0763049	−	0.0763049i	0.667924	−	0.744229i	$-0.267183\pi$
$7$	−0.201884	−	0.201884i	−0.0763049	−	0.0763049i	−0.744229	+	0.667924i	$0.767183\pi$
$8$	1.57260	+	1.57260i	0.555996	+	0.555996i
$9$	−2.32104	+	1.90073i	−0.773680	+	0.633576i
$10$	−3.08492	−	1.90369i	−0.975536	−	0.602000i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	−1.02458	+	0.365990i	−0.295771	+	0.105652i
$13$	1.02066	−	1.02066i	0.283079	−	0.283079i	−0.551256	−	0.834336i	$-0.685851\pi$
$13$	1.02066	−	1.02066i	0.283079	−	0.283079i	0.834336	+	0.551256i	$0.185851\pi$
$14$	−0.462851			−0.123702
$15$	−3.24894	+	2.10817i	−0.838873	+	0.544327i
$16$	4.86173			1.21543
$17$	2.87911	−	2.87911i	0.698287	−	0.698287i	−0.265754	−	0.964041i	$-0.585621\pi$
$17$	2.87911	−	2.87911i	0.698287	−	0.698287i	0.964041	+	0.265754i	$0.0856209\pi$
$18$	−0.481818	+	4.83954i	−0.113566	+	1.14069i
$19$		−	0.281435i		−	0.0645657i	−0.999479	−	0.0322828i	$-0.989722\pi$
$19$		−	0.281435i		−	0.0645657i	0.999479	−	0.0322828i	$-0.0102777\pi$
$20$	−1.36679	+	0.323635i	−0.305623	+	0.0723670i
$21$	−0.211667	+	0.446922i	−0.0461896	+	0.0975264i
$22$	1.14633	+	1.14633i	0.244399	+	0.244399i
$23$	5.22177	+	5.22177i	1.08881	+	1.08881i	0.995651	+	0.0931634i	$0.0296979\pi$
$23$	5.22177	+	5.22177i	1.08881	+	1.08881i	0.0931634	+	0.995651i	$0.470302\pi$
$24$	1.64881	−	3.48135i	0.336561	−	0.710627i
$25$	−4.46910	+	2.24214i	−0.893819	+	0.448428i
$26$		−	2.34002i		−	0.458916i
$27$	4.45265	+	2.67842i	0.856913	+	0.515462i
$28$	−0.126813	+	0.126813i	−0.0239654	+	0.0239654i
$29$	−9.71095			−1.80328			−0.901639	−	0.432490i	$-0.857635\pi$
$29$	−9.71095			−1.80328			−0.901639	+	0.432490i	$0.857635\pi$
$30$	−1.30771	+	6.14102i	−0.238753	+	1.12119i
$31$	4.46829			0.802529			0.401265	−	0.915962i	$-0.368571\pi$
$31$	4.46829			0.802529			0.401265	+	0.915962i	$0.368571\pi$
$32$	2.42796	−	2.42796i	0.429206	−	0.429206i
$33$	1.63111	−	0.582649i	0.283940	−	0.101426i
$34$		−	6.60083i		−	1.13203i
$35$	−0.335265	+	0.543294i	−0.0566701	+	0.0918335i
$36$	1.19394	+	1.45796i	0.198990	+	0.242993i
$37$	2.37906	+	2.37906i	0.391114	+	0.391114i	0.875085	−	0.483970i	$-0.160806\pi$
$37$	2.37906	+	2.37906i	0.391114	+	0.391114i	−0.483970	+	0.875085i	$0.660806\pi$
$38$	−0.322618	−	0.322618i	−0.0523355	−	0.0523355i
$39$	−2.25949	−	1.07012i	−0.361808	−	0.171356i
$40$	2.61158	−	4.23205i	0.412927	−	0.669145i
$41$			9.00173i			1.40583i	0.711272	+	0.702917i	$0.248119\pi$
$41$			9.00173i			1.40583i	−0.711272	+	0.702917i	$0.751881\pi$
$42$	0.269680	+	0.754962i	0.0416125	+	0.116493i
$43$	1.84728	−	1.84728i	0.281707	−	0.281707i	−0.552083	−	0.833789i	$-0.686167\pi$
$43$	1.84728	−	1.84728i	0.281707	−	0.281707i	0.833789	+	0.552083i	$0.186167\pi$
$44$	0.628149			0.0946970
$45$	5.33165	+	4.07106i	0.794795	+	0.606878i
$46$	11.9718			1.76514
$47$	−3.98588	+	3.98588i	−0.581400	+	0.581400i	−0.935288	−	0.353888i	$-0.884859\pi$
$47$	−3.98588	+	3.98588i	−0.581400	+	0.581400i	0.353888	+	0.935288i	$0.384859\pi$
$48$	−2.83268	−	7.93001i	−0.408862	−	1.14460i
$49$		−	6.91849i		−	0.988355i
$50$	−2.55283	+	7.69329i	−0.361025	+	1.08800i
$51$	−6.37366	−	3.01864i	−0.892490	−	0.422694i
$52$	−0.641125	−	0.641125i	−0.0889080	−	0.0889080i
$53$	−4.75830	−	4.75830i	−0.653603	−	0.653603i	0.300256	−	0.953859i	$-0.402928\pi$
$53$	−4.75830	−	4.75830i	−0.653603	−	0.653603i	−0.953859	+	0.300256i	$0.902928\pi$
$54$	8.17456	−	2.03386i	1.11242	−	0.276773i
$55$	2.17590	−	0.515221i	0.293399	−	0.0694723i
$56$		−	0.634963i		−	0.0848505i
$57$	−0.459052	+	0.163978i	−0.0608029	+	0.0217194i
$58$	−11.1320	+	11.1320i	−1.46170	+	1.46170i
$59$	−2.68228			−0.349203			−0.174602	−	0.984639i	$-0.555864\pi$
$59$	−2.68228			−0.349203			−0.174602	+	0.984639i	$0.555864\pi$
$60$	1.32424	+	2.04082i	0.170959	+	0.263469i
$61$	−9.46983			−1.21249			−0.606244	−	0.795279i	$-0.707324\pi$
$61$	−9.46983			−1.21249			−0.606244	+	0.795279i	$0.707324\pi$
$62$	5.12214	−	5.12214i	0.650513	−	0.650513i
$63$	0.852307	+	0.0848544i	0.107381	+	0.0106907i
$64$			4.15697i			0.519622i
$65$	−2.74671	−	1.69499i	−0.340688	−	0.210237i
$66$	1.20188	−	2.53770i	0.147942	−	0.312369i
$67$	−6.27596	−	6.27596i	−0.766731	−	0.766731i	0.210799	−	0.977529i	$-0.432393\pi$
$67$	−6.27596	−	6.27596i	−0.766731	−	0.766731i	−0.977529	+	0.210799i	$0.932393\pi$
$68$	−1.80851	−	1.80851i	−0.219314	−	0.219314i
$69$	5.47482	−	11.5597i	0.659091	−	1.39163i
$70$	0.238471	+	1.00712i	0.0285027	+	0.120374i
$71$			0.679177i			0.0806035i	0.999188	+	0.0403017i	$0.0128319\pi$
$71$			0.679177i			0.0806035i	−0.999188	+	0.0403017i	$0.987168\pi$
$72$	−6.63914	−	0.660982i	−0.782430	−	0.0778975i
$73$	−5.74145	+	5.74145i	−0.671986	+	0.671986i	−0.958174	−	0.286188i	$-0.907612\pi$
$73$	−5.74145	+	5.74145i	−0.671986	+	0.671986i	0.286188	+	0.958174i	$0.407612\pi$
$74$	5.45437			0.634058
$75$	6.26109	+	5.98321i	0.722968	+	0.690881i
$76$	−0.176783			−0.0202784
$77$	0.201884	−	0.201884i	0.0230068	−	0.0230068i
$78$	−3.81683	+	1.36341i	−0.432171	+	0.154376i
$79$			12.5134i			1.40786i	0.710267	+	0.703932i	$0.248574\pi$
$79$			12.5134i			1.40786i	−0.710267	+	0.703932i	$0.751426\pi$
$80$	−2.50486	−	10.5786i	−0.280052	−	1.18273i
$81$	1.77446	−	8.82334i	0.197163	−	0.980371i
$82$	10.3190	+	10.3190i	1.13954	+	1.13954i
$83$	4.93065	+	4.93065i	0.541209	+	0.541209i	0.923883	−	0.382674i	$-0.124997\pi$
$83$	4.93065	+	4.93065i	0.541209	+	0.541209i	−0.382674	+	0.923883i	$0.624997\pi$
$84$	0.280734	+	0.132959i	0.0306305	+	0.0145070i
$85$	−7.74804	−	4.78128i	−0.840393	−	0.518603i
$86$		−	4.23518i		−	0.456691i
$87$	5.65807	+	15.8396i	0.606609	+	1.69819i
$88$	−1.57260	+	1.57260i	−0.167639	+	0.167639i
$89$	2.97979			0.315857			0.157928	−	0.987451i	$-0.449519\pi$
$89$	2.97979			0.315857			0.157928	+	0.987451i	$0.449519\pi$
$90$	10.7786	−	1.44504i	1.13617	−	0.152321i
$91$	−0.412109			−0.0432007
$92$	3.28005	−	3.28005i	0.341969	−	0.341969i
$93$	−2.60345	−	7.28828i	−0.269965	−	0.755759i
$94$			9.13826i			0.942540i
$95$	−0.612375	+	0.145001i	−0.0628284	+	0.0148768i
$96$	−5.37491	−	2.54562i	−0.548574	−	0.259811i
$97$	−11.4137	−	11.4137i	−1.15889	−	1.15889i	−0.984715	−	0.174172i	$-0.944275\pi$
$97$	−11.4137	−	11.4137i	−1.15889	−	1.15889i	−0.174172	−	0.984715i	$-0.555725\pi$
$98$	−7.93087	−	7.93087i	−0.801139	−	0.801139i
$99$	−1.90073	−	2.32104i	−0.191030	−	0.233273i
$100$	1.40840	+	2.80726i	0.140840	+	0.280726i
$101$		−	16.8528i		−	1.67692i	−0.544965	−	0.838458i	$-0.683457\pi$
$101$		−	16.8528i		−	1.67692i	0.544965	−	0.838458i	$-0.316543\pi$
$102$	−10.7667	+	3.84596i	−1.06606	+	0.380807i
$103$	4.78866	−	4.78866i	0.471841	−	0.471841i	−0.430669	−	0.902510i	$-0.641722\pi$
$103$	4.78866	−	4.78866i	0.471841	−	0.471841i	0.902510	+	0.430669i	$0.141722\pi$
$104$	3.21016			0.314782
$105$	1.08151	+	0.230304i	0.105545	+	0.0224754i
$106$	−10.9092			−1.05959
$107$	0.547413	−	0.547413i	0.0529204	−	0.0529204i	−0.680151	−	0.733072i	$-0.738086\pi$
$107$	0.547413	−	0.547413i	0.0529204	−	0.0529204i	0.733072	+	0.680151i	$0.238086\pi$
$108$	1.68244	−	2.79692i	0.161893	−	0.269134i
$109$			0.251236i			0.0240641i	0.999928	+	0.0120320i	$0.00383001\pi$
$109$			0.251236i			0.0240641i	−0.999928	+	0.0120320i	$0.996170\pi$
$110$	1.90369	−	3.08492i	0.181510	−	0.294135i
$111$	2.49435	−	5.26666i	0.236753	−	0.499889i
$112$	−0.981504	−	0.981504i	−0.0927434	−	0.0927434i
$113$	2.40152	+	2.40152i	0.225916	+	0.225916i	0.810984	−	0.585068i	$-0.198932\pi$
$113$	2.40152	+	2.40152i	0.225916	+	0.225916i	−0.585068	+	0.810984i	$0.698932\pi$
$114$	−0.338252	+	0.714198i	−0.0316802	+	0.0668908i
$115$	8.67169	−	14.0524i	0.808640	−	1.31039i
$116$			6.09992i			0.566363i
$117$	−0.428996	+	4.30898i	−0.0396607	+	0.398365i
$118$	−3.07478	+	3.07478i	−0.283057	+	0.283057i
$119$	−1.16249			−0.106565
$120$	−8.42457	−	1.79398i	−0.769054	−	0.163767i
$121$	−1.00000			−0.0909091
$122$	−10.8556	+	10.8556i	−0.982816	+	0.982816i
$123$	14.6828	−	5.24485i	1.32390	−	0.472912i
$124$		−	2.80675i		−	0.252054i
$125$	7.18124	+	8.56912i	0.642310	+	0.766445i
$126$	1.07430	−	0.879755i	0.0957060	−	0.0783748i
$127$	2.88720	+	2.88720i	0.256198	+	0.256198i	0.823506	−	0.567308i	$-0.192015\pi$
$127$	2.88720	+	2.88720i	0.256198	+	0.256198i	−0.567308	+	0.823506i	$0.692015\pi$
$128$	9.62118	+	9.62118i	0.850400	+	0.850400i
$129$	−4.08942	−	1.93680i	−0.360054	−	0.170525i
$130$	−5.09166	+	1.20563i	−0.446568	+	0.105741i
$131$			17.2568i			1.50774i	0.657026	+	0.753868i	$0.271814\pi$
$131$			17.2568i			1.50774i	−0.657026	+	0.753868i	$0.728186\pi$
$132$	−0.365990	−	1.02458i	−0.0318553	−	0.0891782i
$133$	−0.0568172	+	0.0568172i	−0.00492668	+	0.00492668i
$134$	−14.3887			−1.24299
$135$	3.53388	−	11.0685i	0.304148	−	0.952625i
$136$	9.05535			0.776490
$137$	14.3666	−	14.3666i	1.22742	−	1.22742i	0.262485	−	0.964936i	$-0.415458\pi$
$137$	14.3666	−	14.3666i	1.22742	−	1.22742i	0.964936	−	0.262485i	$-0.0845421\pi$
$138$	−6.97532	−	19.5272i	−0.593779	−	1.66227i
$139$		−	3.60234i		−	0.305547i	−0.988261	−	0.152773i	$-0.951180\pi$
$139$		−	3.60234i		−	0.305547i	0.988261	−	0.152773i	$-0.0488205\pi$
$140$	0.341269	+	0.210596i	0.0288425	+	0.0177986i
$141$	8.82377	+	4.17904i	0.743095	+	0.351938i
$142$	0.778561	+	0.778561i	0.0653354	+	0.0653354i
$143$	1.02066	+	1.02066i	0.0853517	+	0.0853517i
$144$	−11.2843	+	9.24082i	−0.940356	+	0.770068i
$145$	5.00328	+	21.1301i	0.415500	+	1.75476i
$146$			13.1632i			1.08939i
$147$	−11.2848	+	4.03105i	−0.930756	+	0.332475i
$148$	1.49440	−	1.49440i	0.122839	−	0.122839i
$149$	11.6538			0.954716			0.477358	−	0.878709i	$-0.341594\pi$
$149$	11.6538			0.954716			0.477358	+	0.878709i	$0.341594\pi$
$150$	14.0360	−	0.318541i	1.14604	−	0.0260087i
$151$	−16.7356			−1.36192			−0.680961	−	0.732319i	$-0.738438\pi$
$151$	−16.7356			−1.36192			−0.680961	+	0.732319i	$0.738438\pi$
$152$	0.442584	−	0.442584i	0.0358983	−	0.0358983i
$153$	−1.21013	+	12.1549i	−0.0978330	+	0.982669i
$154$		−	0.462851i		−	0.0372976i
$155$	−2.30216	−	9.72257i	−0.184914	−	0.780935i
$156$	−0.672195	+	1.41930i	−0.0538186	+	0.113635i
$157$	8.98141	+	8.98141i	0.716794	+	0.716794i	0.967947	−	0.251153i	$-0.0808097\pi$
$157$	8.98141	+	8.98141i	0.716794	+	0.716794i	−0.251153	+	0.967947i	$0.580810\pi$
$158$	14.3445	+	14.3445i	1.14118	+	1.14118i
$159$	−4.98890	+	10.5337i	−0.395645	+	0.835379i
$160$	−6.53393	−	4.03206i	−0.516552	−	0.318762i
$161$		−	2.10838i		−	0.166164i
$162$	−8.08034	−	12.1486i	−0.634851	−	0.954483i
$163$	12.8794	−	12.8794i	1.00879	−	1.00879i	0.00882847	−	0.999961i	$-0.497190\pi$
$163$	12.8794	−	12.8794i	1.00879	−	1.00879i	0.999961	−	0.00882847i	$-0.00281023\pi$
$164$	5.65442			0.441536
$165$	−2.10817	−	3.24894i	−0.164121	−	0.252930i
$166$	11.3043			0.877385
$167$	−1.49091	+	1.49091i	−0.115370	+	0.115370i	−0.762435	−	0.647065i	$-0.775996\pi$
$167$	−1.49091	+	1.49091i	−0.115370	+	0.115370i	0.647065	+	0.762435i	$0.275996\pi$
$168$	−1.03570	+	0.369961i	−0.0799056	+	0.0285431i
$169$			10.9165i			0.839732i
$170$	−14.3627	+	3.40088i	−1.10157	+	0.260836i
$171$	0.534932	+	0.653223i	0.0409073	+	0.0499532i
$172$	−1.16036	−	1.16036i	−0.0884769	−	0.0884769i
$173$	−12.3165	−	12.3165i	−0.936404	−	0.936404i	0.0616917	−	0.998095i	$-0.480350\pi$
$173$	−12.3165	−	12.3165i	−0.936404	−	0.936404i	−0.998095	+	0.0616917i	$0.980350\pi$
$174$	24.6435	+	11.6714i	1.86822	+	0.884809i
$175$	1.35489	+	0.449587i	0.102420	+	0.0339856i
$176$			4.86173i			0.366466i
$177$	1.56283	+	4.37510i	0.117469	+	0.328852i
$178$	3.41582	−	3.41582i	0.256027	−	0.256027i
$179$	20.3135			1.51830			0.759151	−	0.650915i	$-0.225615\pi$
$179$	20.3135			1.51830			0.759151	+	0.650915i	$0.225615\pi$
$180$	2.55723	−	3.34907i	0.190605	−	0.249625i
$181$	−14.0192			−1.04204			−0.521020	−	0.853544i	$-0.674448\pi$
$181$	−14.0192			−1.04204			−0.521020	+	0.853544i	$0.674448\pi$
$182$	−0.472413	+	0.472413i	−0.0350176	+	0.0350176i
$183$	5.51758	+	15.4463i	0.407871	+	1.14183i
$184$			16.4235i			1.21075i
$185$	3.95085	−	6.40233i	0.290473	−	0.470709i
$186$	−11.3392	−	5.37037i	−0.831430	−	0.393775i
$187$	2.87911	+	2.87911i	0.210541	+	0.210541i
$188$	2.50372	+	2.50372i	0.182603	+	0.182603i
$189$	−0.358189	−	1.43965i	−0.0260544	−	0.104719i
$190$	−0.535765	+	0.868204i	−0.0388685	+	0.0629861i
$191$			18.9839i			1.37363i	0.726832	+	0.686815i	$0.240992\pi$
$191$			18.9839i			1.37363i	−0.726832	+	0.686815i	$0.759008\pi$
$192$	6.78048	−	2.42205i	0.489339	−	0.174797i
$193$	−0.749286	+	0.749286i	−0.0539348	+	0.0539348i	−0.733560	−	0.679625i	$-0.762143\pi$
$193$	−0.749286	+	0.749286i	−0.0539348	+	0.0539348i	0.679625	+	0.733560i	$0.262143\pi$
$194$	−26.1678			−1.87874
$195$	−1.16434	+	5.46777i	−0.0833802	+	0.391555i
$196$	−4.34584			−0.310417
$197$	0.218136	−	0.218136i	0.0155416	−	0.0155416i	−0.699293	−	0.714835i	$-0.746502\pi$
$197$	0.218136	−	0.218136i	0.0155416	−	0.0155416i	0.714835	+	0.699293i	$0.246502\pi$
$198$	−4.83954	−	0.481818i	−0.343931	−	0.0342413i
$199$			2.62375i			0.185993i	0.995666	+	0.0929964i	$0.0296445\pi$
$199$			2.62375i			0.185993i	−0.995666	+	0.0929964i	$0.970355\pi$
$200$	−10.5541	−	3.50210i	−0.746284	−	0.247636i
$201$	−6.58010	+	13.8935i	−0.464125	+	0.979969i
$202$	−19.3189	−	19.3189i	−1.35927	−	1.35927i
$203$	1.96048	+	1.96048i	0.137599	+	0.137599i
$204$	−1.89615	+	4.00360i	−0.132757	+	0.280308i
$205$	19.5869	−	4.63788i	1.36801	−	0.323923i
$206$		−	10.9788i		−	0.764928i
$207$	−22.0451	−	2.19478i	−1.53224	−	0.152548i
$208$	4.96216	−	4.96216i	0.344064	−	0.344064i
$209$	0.281435			0.0194673
$210$	1.50378	−	0.975768i	0.103771	−	0.0673344i
$211$	−10.1379			−0.697919			−0.348959	−	0.937138i	$-0.613465\pi$
$211$	−10.1379			−0.697919			−0.348959	+	0.937138i	$0.613465\pi$
$212$	−2.98892	+	2.98892i	−0.205280	+	0.205280i
$213$	1.10781	−	0.395721i	0.0759060	−	0.0271144i
$214$		−	1.25503i		−	0.0857923i
$215$	−4.97124	−	3.06774i	−0.339036	−	0.209218i
$216$	2.79015	+	11.2143i	0.189846	+	0.763035i
$217$	−0.902076	−	0.902076i	−0.0612369	−	0.0612369i
$218$	0.288000	+	0.288000i	0.0195058	+	0.0195058i
$219$	12.7102	+	6.01969i	0.858875	+	0.406773i
$220$	−0.323635	−	1.36679i	−0.0218195	−	0.0921489i
$221$		−	5.87717i		−	0.395341i
$222$	−3.17798	−	8.89668i	−0.213292	−	0.597106i
$223$	15.2100	−	15.2100i	1.01854	−	1.01854i	0.0187139	−	0.999825i	$-0.494043\pi$
$223$	15.2100	−	15.2100i	1.01854	−	1.01854i	0.999825	−	0.0187139i	$-0.00595715\pi$
$224$	−0.980330			−0.0655011
$225$	6.11126	−	13.6986i	0.407417	−	0.913242i
$226$	5.50587			0.366245
$227$	9.77054	−	9.77054i	0.648494	−	0.648494i	−0.304135	−	0.952629i	$-0.598367\pi$
$227$	9.77054	−	9.77054i	0.648494	−	0.648494i	0.952629	+	0.304135i	$0.0983675\pi$
$228$	0.103002	+	0.288353i	0.00682150	+	0.0190966i
$229$		−	19.5023i		−	1.28875i	−0.764711	−	0.644373i	$-0.777118\pi$
$229$		−	19.5023i		−	1.28875i	0.764711	−	0.644373i	$-0.222882\pi$
$230$	−6.16809	−	26.0494i	−0.406712	−	1.71764i
$231$	−0.446922	−	0.211667i	−0.0294053	−	0.0139267i
$232$	−15.2714	−	15.2714i	−1.00262	−	1.00262i
$233$	−10.3725	−	10.3725i	−0.679522	−	0.679522i	0.280370	−	0.959892i	$-0.409543\pi$
$233$	−10.3725	−	10.3725i	−0.679522	−	0.679522i	−0.959892	+	0.280370i	$0.909543\pi$
$234$	4.44775	+	5.43129i	0.290758	+	0.355054i
$235$	10.7265	+	6.61927i	0.699718	+	0.431793i
$236$			1.68487i			0.109676i
$237$	20.4107	−	7.29090i	1.32582	−	0.473595i
$238$	−1.33260	+	1.33260i	−0.0863796	+	0.0863796i
$239$	−26.0494			−1.68499			−0.842497	−	0.538701i	$-0.818915\pi$
$239$	−26.0494			−1.68499			−0.842497	+	0.538701i	$0.818915\pi$
$240$	−15.7955	+	10.2493i	−1.01959	+	0.661592i
$241$	2.19788			0.141578			0.0707890	−	0.997491i	$-0.477448\pi$
$241$	2.19788			0.141578			0.0707890	+	0.997491i	$0.477448\pi$
$242$	−1.14633	+	1.14633i	−0.0736889	+	0.0736889i
$243$	−15.4257	+	2.24656i	−0.989561	+	0.144117i
$244$			5.94846i			0.380811i
$245$	−15.0539	+	3.56455i	−0.961761	+	0.227730i
$246$	10.8190	−	22.8437i	0.689796	−	1.45646i
$247$	−0.287249	−	0.287249i	−0.0182772	−	0.0182772i
$248$	7.02682	+	7.02682i	0.446203	+	0.446203i
$249$	5.16960	−	10.9153i	0.327610	−	0.691727i
$250$	18.0551	+	1.59096i	1.14191	+	0.100621i
$251$			3.44023i			0.217145i	0.994089	+	0.108573i	$0.0346280\pi$
$251$			3.44023i			0.217145i	−0.994089	+	0.108573i	$0.965372\pi$
$252$	0.0533012	−	0.535376i	0.00335766	−	0.0337255i
$253$	−5.22177	+	5.22177i	−0.328290	+	0.328290i
$254$	6.61938			0.415337
$255$	−3.28442	+	15.4237i	−0.205678	+	0.965870i
$256$	13.7442			0.859010
$257$	11.6741	−	11.6741i	0.728213	−	0.728213i	−0.242051	−	0.970264i	$-0.577820\pi$
$257$	11.6741	−	11.6741i	0.728213	−	0.728213i	0.970264	+	0.242051i	$0.0778200\pi$
$258$	−6.90804	+	2.46762i	−0.430076	+	0.153627i
$259$		−	0.960586i		−	0.0596879i
$260$	−1.06470	+	1.72534i	−0.0660301	+	0.107001i
$261$	22.5395	−	18.4579i	1.39516	−	1.14251i
$262$	19.7820	+	19.7820i	1.22214	+	1.22214i
$263$	−15.9766	−	15.9766i	−0.985158	−	0.985158i	0.0147331	−	0.999891i	$-0.495310\pi$
$263$	−15.9766	−	15.9766i	−0.985158	−	0.985158i	−0.999891	+	0.0147331i	$0.995310\pi$
$264$	3.48135	+	1.64881i	0.214262	+	0.101477i
$265$	−7.90202	+	12.8052i	−0.485417	+	0.786615i
$266$			0.130263i			0.00798692i
$267$	−1.73617	−	4.86036i	−0.106252	−	0.297449i
$268$	−3.94224	+	3.94224i	−0.240810	+	0.240810i
$269$	1.98520			0.121040			0.0605200	−	0.998167i	$-0.480724\pi$
$269$	1.98520			0.121040			0.0605200	+	0.998167i	$0.480724\pi$
$270$	−8.63717	−	16.7392i	−0.525642	−	1.01871i
$271$	−16.7391			−1.01683			−0.508413	−	0.861113i	$-0.669768\pi$
$271$	−16.7391			−1.01683			−0.508413	+	0.861113i	$0.669768\pi$
$272$	13.9974	−	13.9974i	0.848720	−	0.848720i
$273$	0.240114	+	0.672195i	0.0145324	+	0.0406831i
$274$		−	32.9377i		−	1.98984i
$275$	−2.24214	−	4.46910i	−0.135206	−	0.269497i
$276$	−7.26123	−	3.43900i	−0.437075	−	0.207004i
$277$	−15.6387	−	15.6387i	−0.939637	−	0.939637i	0.0586420	−	0.998279i	$-0.481323\pi$
$277$	−15.6387	−	15.6387i	−0.939637	−	0.939637i	−0.998279	+	0.0586420i	$0.981323\pi$
$278$	−4.12948	−	4.12948i	−0.247670	−	0.247670i
$279$	−10.3711	+	8.49301i	−0.620901	+	0.508463i
$280$	−1.38162	+	0.327146i	−0.0825675	+	0.0195507i
$281$			11.1500i			0.665153i	0.943076	+	0.332577i	$0.107918\pi$
$281$			11.1500i			0.665153i	−0.943076	+	0.332577i	$0.892082\pi$
$282$	14.9055	−	5.32440i	0.887610	−	0.317063i
$283$	9.74142	−	9.74142i	0.579068	−	0.579068i	−0.355579	−	0.934646i	$-0.615716\pi$
$283$	9.74142	−	9.74142i	0.579068	−	0.579068i	0.934646	+	0.355579i	$0.115716\pi$
$284$	0.426624			0.0253155
$285$	0.593312	+	0.914367i	0.0351448	+	0.0541624i
$286$	2.34002			0.138368
$287$	1.81730	−	1.81730i	0.107272	−	0.107272i
$288$	−1.02050	+	10.2503i	−0.0601336	+	0.604003i
$289$			0.421449i			0.0247911i
$290$	29.9575	+	18.4866i	1.75916	+	1.08557i
$291$	−11.9668	+	25.2672i	−0.701509	+	1.48119i
$292$	3.60648	+	3.60648i	0.211053	+	0.211053i
$293$	3.70667	+	3.70667i	0.216546	+	0.216546i	0.807041	−	0.590495i	$-0.201068\pi$
$293$	3.70667	+	3.70667i	0.216546	+	0.216546i	−0.590495	+	0.807041i	$0.701068\pi$
$294$	−8.31522	+	17.5570i	−0.484953	+	1.02395i
$295$	1.38197	+	5.83638i	0.0804612	+	0.339807i
$296$			7.48259i			0.434916i
$297$	−2.67842	+	4.45265i	−0.155418	+	0.258369i
$298$	13.3591	−	13.3591i	0.773872	−	0.773872i
$299$	10.6593			0.616442
$300$	3.75834	−	3.93289i	0.216988	−	0.227066i
$301$	−0.745870			−0.0429912
$302$	−19.1845	+	19.1845i	−1.10395	+	1.10395i
$303$	−27.4888	+	9.81926i	−1.57919	+	0.564102i
$304$		−	1.36826i		−	0.0784751i
$305$	4.87905	+	20.6054i	0.279374	+	1.17986i
$306$	12.5464	+	15.3208i	0.717229	+	0.875831i
$307$	5.20688	+	5.20688i	0.297172	+	0.297172i	0.839905	−	0.542733i	$-0.182610\pi$
$307$	5.20688	+	5.20688i	0.297172	+	0.297172i	−0.542733	+	0.839905i	$0.682610\pi$
$308$	−0.126813	−	0.126813i	−0.00722585	−	0.00722585i
$309$	−10.6009	−	5.02073i	−0.603067	−	0.285619i
$310$	−13.7843	−	8.50625i	−0.782896	−	0.483122i
$311$		−	22.2889i		−	1.26389i	−0.775013	−	0.631945i	$-0.782257\pi$
$311$		−	22.2889i		−	1.26389i	0.775013	−	0.631945i	$-0.217743\pi$
$312$	−1.87040	−	5.23613i	−0.105890	−	0.296437i
$313$	−8.76264	+	8.76264i	−0.495293	+	0.495293i	−0.909969	−	0.414676i	$-0.863895\pi$
$313$	−8.76264	+	8.76264i	−0.495293	+	0.495293i	0.414676	+	0.909969i	$0.363895\pi$
$314$	20.5913			1.16204
$315$	−0.254491	−	1.89826i	−0.0143390	−	0.106955i
$316$	7.86026			0.442174
$317$	−18.4371	+	18.4371i	−1.03553	+	1.03553i	−0.0361858	+	0.999345i	$0.511521\pi$
$317$	−18.4371	+	18.4371i	−1.03553	+	1.03553i	−0.999345	+	0.0361858i	$0.988479\pi$
$318$	6.35622	+	17.7941i	0.356439	+	0.997842i
$319$		−	9.71095i		−	0.543709i
$320$	9.04516	−	2.14176i	0.505640	−	0.119728i
$321$	−1.21184	−	0.573942i	−0.0676384	−	0.0320343i
$322$	−2.41690	−	2.41690i	−0.134689	−	0.134689i
$323$	−0.810283	−	0.810283i	−0.0450853	−	0.0450853i
$324$	−5.54237	−	1.11463i	−0.307909	−	0.0619238i
$325$	−2.27296	+	6.84987i	−0.126081	+	0.379962i
$326$		−	29.5280i		−	1.63541i
$327$	0.409794	−	0.146382i	0.0226617	−	0.00809496i
$328$	−14.1561	+	14.1561i	−0.781639	+	0.781639i
$329$	1.60937			0.0887273
$330$	−6.14102	−	1.30771i	−0.338052	−	0.0719868i
$331$	−0.848055			−0.0466133			−0.0233067	−	0.999728i	$-0.507419\pi$
$331$	−0.848055			−0.0466133			−0.0233067	+	0.999728i	$0.507419\pi$
$332$	3.09718	−	3.09718i	0.169980	−	0.169980i
$333$	−10.0438	−	0.999948i	−0.550398	−	0.0547968i
$334$			3.41815i			0.187033i
$335$	−10.4224	+	16.8894i	−0.569435	+	0.922765i
$336$	−1.02907	+	2.17281i	−0.0561403	+	0.118537i
$337$	24.8680	+	24.8680i	1.35465	+	1.35465i	0.880383	+	0.474264i	$0.157286\pi$
$337$	24.8680	+	24.8680i	1.35465	+	1.35465i	0.474264	+	0.880383i	$0.342714\pi$
$338$	12.5139	+	12.5139i	0.680669	+	0.680669i
$339$	2.51790	−	5.31639i	0.136754	−	0.288747i
$340$	−3.00336	+	4.86692i	−0.162880	+	0.263946i
$341$			4.46829i			0.241972i
$342$	1.36202	+	0.135600i	0.0736495	+	0.00733243i
$343$	−2.80992	+	2.80992i	−0.151721	+	0.151721i
$344$	5.81003			0.313256
$345$	−27.9736	−	5.95687i	−1.50605	−	0.320707i
$346$	−28.2375			−1.51806
$347$	−7.84495	+	7.84495i	−0.421139	+	0.421139i	−0.885596	−	0.464457i	$-0.846250\pi$
$347$	−7.84495	+	7.84495i	−0.421139	+	0.421139i	0.464457	+	0.885596i	$0.346250\pi$
$348$	9.94964	−	3.55411i	0.533357	−	0.190520i
$349$		−	3.21032i		−	0.171845i	−0.996302	−	0.0859223i	$-0.972616\pi$
$349$		−	3.21032i		−	0.171845i	0.996302	−	0.0859223i	$-0.0273837\pi$
$350$	2.06853	−	1.03778i	0.110567	−	0.0554715i
$351$	7.27838	−	1.81088i	0.388491	−	0.0966577i
$352$	2.42796	+	2.42796i	0.129410	+	0.129410i
$353$	2.32761	+	2.32761i	0.123886	+	0.123886i	0.766331	−	0.642445i	$-0.222080\pi$
$353$	2.32761	+	2.32761i	0.123886	+	0.123886i	−0.642445	+	0.766331i	$0.722080\pi$
$354$	6.80683	+	3.22379i	0.361779	+	0.171343i
$355$	1.47782	−	0.349926i	0.0784346	−	0.0185721i
$356$		−	1.87175i		−	0.0992024i
$357$	0.677324	+	1.89615i	0.0358478	+	0.100355i
$358$	23.2860	−	23.2860i	1.23070	−	1.23070i
$359$	−11.6869			−0.616811			−0.308406	−	0.951255i	$-0.599795\pi$
$359$	−11.6869			−0.616811			−0.308406	+	0.951255i	$0.599795\pi$
$360$	1.98239	+	14.7867i	0.104481	+	0.779325i
$361$	18.9208			0.995831
$362$	−16.0707	+	16.0707i	−0.844655	+	0.844655i
$363$	0.582649	+	1.63111i	0.0305811	+	0.0856111i
$364$			0.258865i			0.0135682i
$365$	15.4509	+	9.53472i	0.808739	+	0.499070i
$366$	24.0316	+	11.3816i	1.25615	+	0.594927i
$367$	−6.60685	−	6.60685i	−0.344875	−	0.344875i	0.513321	−	0.858196i	$-0.328415\pi$
$367$	−6.60685	−	6.60685i	−0.344875	−	0.344875i	−0.858196	+	0.513321i	$0.828415\pi$
$368$	25.3868	+	25.3868i	1.32338	+	1.32338i
$369$	−17.1098	−	20.8934i	−0.890703	−	1.08767i
$370$	−2.81020	−	11.8682i	−0.146096	−	0.616997i
$371$			1.92125i			0.0997463i
$372$	−4.57812	+	1.63535i	−0.237365	+	0.0847890i
$373$	−12.6827	+	12.6827i	−0.656683	+	0.656683i	−0.954594	−	0.297911i	$-0.903710\pi$
$373$	−12.6827	+	12.6827i	−0.656683	+	0.656683i	0.297911	+	0.954594i	$0.403710\pi$
$374$	6.60083			0.341321
$375$	9.79303	−	16.7062i	0.505710	−	0.862704i
$376$	−12.5363			−0.646512
$377$	−9.91155	+	9.91155i	−0.510471	+	0.510471i
$378$	−2.06091	−	1.23971i	−0.106002	−	0.0637638i
$379$			6.12762i			0.314755i	0.987539	+	0.157377i	$0.0503039\pi$
$379$			6.12762i			0.314755i	−0.987539	+	0.157377i	$0.949696\pi$
$380$	0.0910823	+	0.384663i	0.00467242	+	0.0197328i
$381$	3.02712	−	6.39157i	0.155084	−	0.327450i
$382$	21.7619	+	21.7619i	1.11343	+	1.11343i
$383$	−20.8849	−	20.8849i	−1.06717	−	1.06717i	−0.997576	−	0.0695907i	$-0.977831\pi$
$383$	−20.8849	−	20.8849i	−1.06717	−	1.06717i	−0.0695907	−	0.997576i	$-0.522169\pi$
$384$	10.0874	−	21.2990i	0.514772	−	1.08691i
$385$	−0.543294	−	0.335265i	−0.0276888	−	0.0170867i
$386$			1.71786i			0.0874367i
$387$	−0.776434	+	7.79877i	−0.0394684	+	0.396434i
$388$	−7.16951	+	7.16951i	−0.363977	+	0.363977i
$389$	−17.8685			−0.905968			−0.452984	−	0.891519i	$-0.649640\pi$
$389$	−17.8685			−0.905968			−0.452984	+	0.891519i	$0.649640\pi$
$390$	4.93316	+	7.60260i	0.249800	+	0.384973i
$391$	30.0681			1.52061
$392$	10.8800	−	10.8800i	0.549522	−	0.549522i
$393$	28.1478	−	10.0547i	1.41987	−	0.507191i
$394$		−	0.500113i		−	0.0251953i
$395$	27.2279	−	6.44715i	1.36998	−	0.324391i
$396$	−1.45796	+	1.19394i	−0.0732652	+	0.0599977i
$397$	10.2866	+	10.2866i	0.516271	+	0.516271i	0.916441	−	0.400170i	$-0.131049\pi$
$397$	10.2866	+	10.2866i	0.516271	+	0.516271i	−0.400170	+	0.916441i	$0.631049\pi$
$398$	3.00769	+	3.00769i	0.150762	+	0.150762i
$399$	0.125780	+	0.0595707i	0.00629686	+	0.00298226i
$400$	−21.7275	+	10.9007i	−1.08638	+	0.545033i
$401$		−	23.5884i		−	1.17795i	−0.808151	−	0.588975i	$-0.799532\pi$
$401$		−	23.5884i		−	1.17795i	0.808151	−	0.588975i	$-0.200468\pi$
$402$	8.38353	+	23.4695i	0.418132	+	1.17055i
$403$	4.56060	−	4.56060i	0.227180	−	0.227180i
$404$	−10.5861			−0.526677
$405$	−20.1130	+	0.684904i	−0.999421	+	0.0340331i
$406$	4.49473			0.223069
$407$	−2.37906	+	2.37906i	−0.117925	+	0.117925i
$408$	−5.27609	−	14.7703i	−0.261205	−	0.731238i
$409$		−	12.6076i		−	0.623405i	−0.950180	−	0.311703i	$-0.899101\pi$
$409$		−	12.6076i		−	0.623405i	0.950180	−	0.311703i	$-0.100899\pi$
$410$	17.1365	−	27.7696i	0.846311	−	1.37144i
$411$	−31.8042	−	15.0628i	−1.56878	−	0.742994i
$412$	−3.00799	−	3.00799i	−0.148193	−	0.148193i
$413$	0.541509	+	0.541509i	0.0266459	+	0.0266459i
$414$	−27.7869	+	22.7550i	−1.36565	+	1.11835i
$415$	8.18824	−	13.2690i	0.401945	−	0.651349i
$416$		−	4.95622i		−	0.242999i
$417$	−5.87582	+	2.09890i	−0.287740	+	0.102784i
$418$	0.322618	−	0.322618i	0.0157798	−	0.0157798i
$419$	33.5948			1.64121			0.820606	−	0.571495i	$-0.193636\pi$
$419$	33.5948			1.64121			0.820606	+	0.571495i	$0.193636\pi$
$420$	0.144665	−	0.679352i	0.00705894	−	0.0331490i
$421$	−11.1669			−0.544240			−0.272120	−	0.962263i	$-0.587725\pi$
$421$	−11.1669			−0.544240			−0.272120	+	0.962263i	$0.587725\pi$
$422$	−11.6213	+	11.6213i	−0.565718	+	0.565718i
$423$	1.67532	−	16.8274i	0.0814566	−	0.818178i
$424$		−	14.9658i		−	0.726802i
$425$	−6.41165	+	19.3224i	−0.311011	+	0.937273i
$426$	0.816292	−	1.72355i	0.0395495	−	0.0835061i
$427$	1.91181	+	1.91181i	0.0925187	+	0.0925187i
$428$	−0.343857	−	0.343857i	−0.0166209	−	0.0166209i
$429$	1.07012	−	2.25949i	0.0516659	−	0.109089i
$430$	−9.21533	+	2.18205i	−0.444403	+	0.105228i
$431$		−	3.65334i		−	0.175975i	−0.996122	−	0.0879875i	$-0.971956\pi$
$431$		−	3.65334i		−	0.175975i	0.996122	−	0.0879875i	$-0.0280436\pi$
$432$	21.6476	+	13.0217i	1.04152	+	0.626508i
$433$	3.56615	−	3.56615i	0.171378	−	0.171378i	−0.616207	−	0.787585i	$-0.711331\pi$
$433$	3.56615	−	3.56615i	0.171378	−	0.171378i	0.787585	+	0.616207i	$0.211331\pi$
$434$	−2.06816			−0.0992747
$435$	31.5503	−	20.4723i	1.51272	−	0.981572i
$436$	0.157814			0.00755790
$437$	1.46959	−	1.46959i	0.0703000	−	0.0703000i
$438$	21.4706	−	7.66952i	1.02591	−	0.366464i
$439$			34.7868i			1.66028i	0.557552	+	0.830142i	$0.311741\pi$
$439$			34.7868i			1.66028i	−0.557552	+	0.830142i	$0.688259\pi$
$440$	4.23205	+	2.61158i	0.201755	+	0.124502i
$441$	13.1502	+	16.0581i	0.626198	+	0.764671i
$442$	−6.73718	−	6.73718i	−0.320455	−	0.320455i
$443$	−10.4616	−	10.4616i	−0.497045	−	0.497045i	0.413472	−	0.910517i	$-0.364316\pi$
$443$	−10.4616	−	10.4616i	−0.497045	−	0.497045i	−0.910517	+	0.413472i	$0.864316\pi$
$444$	−3.30824	−	1.56682i	−0.157002	−	0.0743581i
$445$	−1.53525	−	6.48372i	−0.0727777	−	0.307358i
$446$		−	34.8714i		−	1.65121i
$447$	−6.79007	−	19.0086i	−0.321159	−	0.899077i
$448$	0.839226	−	0.839226i	0.0396497	−	0.0396497i
$449$	18.1102			0.854671			0.427335	−	0.904093i	$-0.359452\pi$
$449$	18.1102			0.854671			0.427335	+	0.904093i	$0.359452\pi$
$450$	−8.69764	−	22.7087i	−0.410011	−	1.07050i
$451$	−9.00173			−0.423875
$452$	1.50851	−	1.50851i	0.0709544	−	0.0709544i
$453$	9.75097	+	27.2976i	0.458140	+	1.28255i
$454$		−	22.4005i		−	1.05131i
$455$	0.212327	+	0.896708i	0.00995403	+	0.0420383i
$456$	−0.979774	−	0.464032i	−0.0458821	−	0.0217303i
$457$	−4.07759	−	4.07759i	−0.190742	−	0.190742i	0.605275	−	0.796016i	$-0.293063\pi$
$457$	−4.07759	−	4.07759i	−0.190742	−	0.190742i	−0.796016	+	0.605275i	$0.793063\pi$
$458$	−22.3561	−	22.3561i	−1.04463	−	1.04463i
$459$	20.5311	−	5.10821i	0.958311	−	0.238431i
$460$	−8.82701	−	5.44711i	−0.411561	−	0.253973i
$461$			22.5889i			1.05207i	0.850462	+	0.526036i	$0.176322\pi$
$461$			22.5889i			1.05207i	−0.850462	+	0.526036i	$0.823678\pi$
$462$	−0.754962	+	0.269680i	−0.0351240	+	0.0125466i
$463$	−4.81057	+	4.81057i	−0.223566	+	0.223566i	−0.809998	−	0.586432i	$-0.800532\pi$
$463$	−4.81057	+	4.81057i	−0.223566	+	0.223566i	0.586432	+	0.809998i	$0.300532\pi$
$464$	−47.2120			−2.19176
$465$	−14.5172	+	9.41991i	−0.673220	+	0.436838i
$466$	−23.7805			−1.10161
$467$	4.10549	−	4.10549i	0.189979	−	0.189979i	−0.605708	−	0.795687i	$-0.707110\pi$
$467$	4.10549	−	4.10549i	0.189979	−	0.189979i	0.795687	+	0.605708i	$0.207110\pi$
$468$	2.70668	+	0.269473i	0.125116	+	0.0124564i
$469$			2.53403i			0.117011i
$470$	19.8840	−	4.70822i	0.917179	−	0.217174i
$471$	9.41666	−	19.8827i	0.433897	−	0.916145i
$472$	−4.21814	−	4.21814i	−0.194156	−	0.194156i
$473$	1.84728	+	1.84728i	0.0849378	+	0.0849378i
$474$	15.0396	−	31.7552i	0.690793	−	1.45856i
$475$	0.631017	+	1.25776i	0.0289530	+	0.0577100i
$476$			0.730218i			0.0334695i
$477$	20.0885	+	1.99998i	0.919787	+	0.0915726i
$478$	−29.8612	+	29.8612i	−1.36582	+	1.36582i
$479$	−5.74056			−0.262293			−0.131146	−	0.991363i	$-0.541866\pi$
$479$	−5.74056			−0.262293			−0.131146	+	0.991363i	$0.541866\pi$
$480$	−2.76975	+	13.0068i	−0.126421	+	0.593678i
$481$	4.85640			0.221433
$482$	2.51950	−	2.51950i	0.114760	−	0.114760i
$483$	−3.43900	+	1.22845i	−0.156480	+	0.0558962i
$484$			0.628149i			0.0285522i
$485$	−18.9545	+	30.7157i	−0.860682	+	1.39473i
$486$	−15.1077	+	20.2583i	−0.685299	+	0.918934i
$487$	15.2791	+	15.2791i	0.692361	+	0.692361i	0.962751	−	0.270390i	$-0.0871527\pi$
$487$	15.2791	+	15.2791i	0.692361	+	0.692361i	−0.270390	+	0.962751i	$0.587153\pi$
$488$	−14.8922	−	14.8922i	−0.674139	−	0.674139i
$489$	−28.5118	−	13.5035i	−1.28935	−	0.610650i
$490$	−13.1707	+	21.3429i	−0.594989	+	0.964176i
$491$		−	9.79503i		−	0.442043i	−0.975269	−	0.221022i	$-0.929061\pi$
$491$		−	9.79503i		−	0.442043i	0.975269	−	0.221022i	$-0.0709392\pi$
$492$	−3.29454	−	9.22299i	−0.148529	−	0.415804i
$493$	−27.9589	+	27.9589i	−1.25920	+	1.25920i
$494$	−0.658565			−0.0296302
$495$	−4.07106	+	5.33165i	−0.182981	+	0.239640i
$496$	21.7236			0.975419
$497$	0.137115	−	0.137115i	0.00615044	−	0.00615044i
$498$	−6.58644	−	18.4386i	−0.295146	−	0.826253i
$499$			0.929617i			0.0416154i	0.999783	+	0.0208077i	$0.00662377\pi$
$499$			0.929617i			0.0416154i	−0.999783	+	0.0208077i	$0.993376\pi$
$500$	5.38268	−	4.51089i	0.240721	−	0.201733i
$501$	3.30051	+	1.56316i	0.147456	+	0.0698368i
$502$	3.94364	+	3.94364i	0.176013	+	0.176013i
$503$	6.49027	+	6.49027i	0.289387	+	0.289387i	0.836838	−	0.547451i	$-0.184402\pi$
$503$	6.49027	+	6.49027i	0.289387	+	0.289387i	−0.547451	+	0.836838i	$0.684402\pi$
$504$	1.20689	+	1.47378i	0.0537593	+	0.0656472i
$505$	−36.6700	+	8.68291i	−1.63180	+	0.386385i
$506$			11.9718i			0.532209i
$507$	17.8060	−	6.36049i	0.790794	−	0.282479i
$508$	1.81359	−	1.81359i	0.0804651	−	0.0804651i
$509$	13.0970			0.580515			0.290257	−	0.956949i	$-0.406259\pi$
$509$	13.0970			0.580515			0.290257	+	0.956949i	$0.406259\pi$
$510$	13.9156	+	21.4457i	0.616195	+	0.949632i
$511$	2.31821			0.102552
$512$	−3.48700	+	3.48700i	−0.154105	+	0.154105i
$513$	0.753801	−	1.25313i	0.0332811	−	0.0553271i
$514$		−	26.7649i		−	1.18055i
$515$	−12.8869	−	7.95244i	−0.567863	−	0.350426i
$516$	−1.21660	+	2.56876i	−0.0535577	+	0.113084i
$517$	−3.98588	−	3.98588i	−0.175299	−	0.175299i
$518$	−1.10115	−	1.10115i	−0.0483817	−	0.0483817i
$519$	−12.9133	+	27.2657i	−0.566833	+	1.19683i
$520$	−1.65394	−	6.98500i	−0.0725301	−	0.306312i
$521$			3.26098i			0.142866i	0.997445	+	0.0714330i	$0.0227572\pi$
$521$			3.26098i			0.142866i	−0.997445	+	0.0714330i	$0.977243\pi$
$522$	4.67891	−	46.9966i	0.204790	−	2.05698i
$523$	−17.8320	+	17.8320i	−0.779737	+	0.779737i	−0.979786	−	0.200049i	$-0.935890\pi$
$523$	−17.8320	+	17.8320i	−0.779737	+	0.779737i	0.200049	+	0.979786i	$0.435890\pi$
$524$	10.8399			0.473541
$525$	−0.0560992	−	2.47193i	−0.00244837	−	0.107884i
$526$	−36.6289			−1.59710
$527$	12.8647	−	12.8647i	0.560396	−	0.560396i
$528$	7.93001	−	2.83268i	0.345109	−	0.123276i
$529$			31.5338i			1.37103i
$530$	5.62063	+	23.7373i	0.244145	+	1.03108i
$531$	6.22569	−	5.09829i	0.270172	−	0.221247i
$532$	0.0356897	+	0.0356897i	0.00154734	+	0.00154734i
$533$	9.18768	+	9.18768i	0.397963	+	0.397963i
$534$	−7.56180	−	3.58136i	−0.327231	−	0.154980i
$535$	−1.47316	−	0.909079i	−0.0636901	−	0.0393029i
$536$		−	19.7391i		−	0.852599i
$537$	−11.8356	−	33.1335i	−0.510745	−	1.42982i
$538$	2.27570	−	2.27570i	0.0981124	−	0.0981124i
$539$	6.91849			0.298000
$540$	−6.95266	−	2.21980i	−0.299195	−	0.0955250i
$541$	29.4057			1.26425			0.632125	−	0.774866i	$-0.282183\pi$
$541$	29.4057			1.26425			0.632125	+	0.774866i	$0.282183\pi$
$542$	−19.1885	+	19.1885i	−0.824218	+	0.824218i
$543$	8.16828	+	22.8669i	0.350534	+	0.981312i
$544$		−	13.9807i		−	0.599418i
$545$	0.546665	−	0.129442i	0.0234166	−	0.00554469i
$546$	1.04581	+	0.495307i	0.0447564	+	0.0211972i
$547$	−6.91991	−	6.91991i	−0.295874	−	0.295874i	0.543521	−	0.839395i	$-0.317091\pi$
$547$	−6.91991	−	6.91991i	−0.295874	−	0.295874i	−0.839395	+	0.543521i	$0.817091\pi$
$548$	−9.02436	−	9.02436i	−0.385501	−	0.385501i
$549$	21.9799	−	17.9996i	0.938078	−	0.768203i
$550$	−7.69329	−	2.55283i	−0.328043	−	0.108853i
$551$			2.73300i			0.116430i
$552$	26.7885	−	9.56911i	1.14019	−	0.407288i
$553$	2.52625	−	2.52625i	0.107427	−	0.107427i
$554$	−35.8542			−1.52330
$555$	−12.7449	−	2.71397i	−0.540989	−	0.115202i
$556$	−2.26281			−0.0959644
$557$	−3.53461	+	3.53461i	−0.149766	+	0.149766i	−0.778014	−	0.628247i	$-0.783773\pi$
$557$	−3.53461	+	3.53461i	−0.149766	+	0.149766i	0.628247	+	0.778014i	$0.283773\pi$
$558$	−2.15290	+	21.6245i	−0.0911397	+	0.915438i
$559$		−	3.77087i		−	0.159491i
$560$	−1.62997	+	2.64135i	−0.0688786	+	0.111617i
$561$	3.01864	−	6.37366i	0.127447	−	0.269096i
$562$	12.7816	+	12.7816i	0.539159	+	0.539159i
$563$	11.1629	+	11.1629i	0.470458	+	0.470458i	0.902063	−	0.431605i	$-0.142052\pi$
$563$	11.1629	+	11.1629i	0.470458	+	0.470458i	−0.431605	+	0.902063i	$0.642052\pi$
$564$	2.62506	−	5.54264i	0.110535	−	0.233387i
$565$	3.98816	−	6.46279i	0.167783	−	0.271891i
$566$		−	22.3338i		−	0.938759i
$567$	−2.13953	+	1.42305i	−0.0898516	+	0.0597626i
$568$	−1.06807	+	1.06807i	−0.0448152	+	0.0448152i
$569$	11.5279			0.483275			0.241637	−	0.970367i	$-0.422316\pi$
$569$	11.5279			0.483275			0.241637	+	0.970367i	$0.422316\pi$
$570$	1.72830	+	0.368034i	0.0723905	+	0.0154153i
$571$	37.5721			1.57234			0.786172	−	0.618008i	$-0.212060\pi$
$571$	37.5721			1.57234			0.786172	+	0.618008i	$0.212060\pi$
$572$	0.641125	−	0.641125i	0.0268068	−	0.0268068i
$573$	30.9649	−	11.0610i	1.29358	−	0.462079i
$574$		−	4.16646i		−	0.173905i
$575$	−35.0445	−	11.6287i	−1.46146	−	0.484948i
$576$	−7.90127	−	9.64850i	−0.329220	−	0.402021i
$577$	−9.80937	−	9.80937i	−0.408369	−	0.408369i	0.472800	−	0.881170i	$-0.343243\pi$
$577$	−9.80937	−	9.80937i	−0.408369	−	0.408369i	−0.881170	+	0.472800i	$0.843243\pi$
$578$	0.483120	+	0.483120i	0.0200951	+	0.0200951i
$579$	1.65874	+	0.785598i	0.0689348	+	0.0326483i
$580$	13.2728	−	3.14280i	0.551124	−	0.130498i
$581$		−	1.99084i		−	0.0825939i
$582$	15.2466	+	42.6826i	0.631993	+	1.76925i
$583$	4.75830	−	4.75830i	0.197069	−	0.197069i
$584$	−18.0580			−0.747243
$585$	9.59695	−	1.28662i	0.396785	−	0.0531953i
$586$	8.49813			0.351055
$587$	28.3158	−	28.3158i	1.16872	−	1.16872i	0.186209	−	0.982510i	$-0.440380\pi$
$587$	28.3158	−	28.3158i	1.16872	−	1.16872i	0.982510	−	0.186209i	$-0.0596202\pi$
$588$	2.53210	+	7.08854i	0.104422	+	0.292326i
$589$		−	1.25754i		−	0.0518158i
$590$	8.27461	+	5.10623i	0.340660	+	0.210220i
$591$	−0.482901	−	0.228708i	−0.0198639	−	0.00940778i
$592$	11.5663	+	11.5663i	0.475373	+	0.475373i
$593$	−22.0674	−	22.0674i	−0.906199	−	0.906199i	0.0897641	−	0.995963i	$-0.471389\pi$
$593$	−22.0674	−	22.0674i	−0.906199	−	0.906199i	−0.995963	+	0.0897641i	$0.971389\pi$
$594$	2.03386	+	8.17456i	0.0834501	+	0.335406i
$595$	0.598940	+	2.52947i	0.0245541	+	0.103698i
$596$		−	7.32031i		−	0.299852i
$597$	4.27963	−	1.52873i	0.175154	−	0.0625666i
$598$	12.2191	−	12.2191i	0.499674	−	0.499674i
$599$	13.7723			0.562721			0.281361	−	0.959602i	$-0.409214\pi$
$599$	13.7723			0.562721			0.281361	+	0.959602i	$0.409214\pi$
$600$	0.436991	+	19.2553i	0.0178401	+	0.786095i
$601$	47.6415			1.94334			0.971669	−	0.236346i	$-0.0759500\pi$
$601$	47.6415			1.94334			0.971669	+	0.236346i	$0.0759500\pi$
$602$	−0.855014	+	0.855014i	−0.0348478	+	0.0348478i
$603$	26.4957	+	2.63787i	1.07899	+	0.107422i
$604$			10.5124i			0.427745i
$605$	0.515221	+	2.17590i	0.0209467	+	0.0884630i
$606$	−20.2551	+	42.7674i	−0.822808	+	1.73731i
$607$	−24.2606	−	24.2606i	−0.984709	−	0.984709i	0.0151761	−	0.999885i	$-0.495169\pi$
$607$	−24.2606	−	24.2606i	−0.984709	−	0.984709i	−0.999885	+	0.0151761i	$0.995169\pi$
$608$	−0.683312	−	0.683312i	−0.0277120	−	0.0277120i
$609$	2.05549	−	4.34004i	0.0832927	−	0.175867i
$610$	29.2136	+	18.0276i	1.18283	+	0.729917i
$611$			8.13643i			0.329165i
$612$	7.63511	+	0.760140i	0.308631	+	0.0307268i
$613$	2.32722	−	2.32722i	0.0939954	−	0.0939954i	−0.658546	−	0.752541i	$-0.728828\pi$
$613$	2.32722	−	2.32722i	0.0939954	−	0.0939954i	0.752541	+	0.658546i	$0.228828\pi$
$614$	11.9376			0.481763
$615$	−18.9772	−	29.2461i	−0.765233	−	1.17932i
$616$	0.634963			0.0255834
$617$	−14.3887	+	14.3887i	−0.579267	+	0.579267i	−0.934701	−	0.355434i	$-0.884333\pi$
$617$	−14.3887	+	14.3887i	−0.579267	+	0.579267i	0.355434	+	0.934701i	$0.384333\pi$
$618$	−17.9076	+	6.39677i	−0.720349	+	0.257316i
$619$			0.383560i			0.0154166i	0.999970	+	0.00770829i	$0.00245365\pi$
$619$			0.383560i			0.0154166i	−0.999970	+	0.00770829i	$0.997546\pi$
$620$	−6.10722	+	1.44610i	−0.245272	+	0.0580766i
$621$	9.26463	+	37.2368i	0.371777	+	1.49426i
$622$	−25.5505	−	25.5505i	−1.02448	−	1.02448i
$623$	−0.601571	−	0.601571i	−0.0241014	−	0.0241014i
$624$	−10.9850	−	5.20263i	−0.439753	−	0.208272i
$625$	14.9456	−	20.0407i	0.597825	−	0.801626i
$626$			20.0898i			0.802948i
$627$	−0.163978	−	0.459052i	−0.00654864	−	0.0183328i
$628$	5.64166	−	5.64166i	0.225127	−	0.225127i
$629$	13.6991			0.546220
$630$	−2.46776	−	1.88430i	−0.0983179	−	0.0750722i
$631$	15.5344			0.618416			0.309208	−	0.950994i	$-0.399936\pi$
$631$	15.5344			0.618416			0.309208	+	0.950994i	$0.399936\pi$
$632$	−19.6785	+	19.6785i	−0.782768	+	0.782768i
$633$	5.90681	+	16.5360i	0.234774	+	0.657245i
$634$			42.2700i			1.67876i
$635$	4.79472	−	7.76981i	0.190273	−	0.308336i
$636$	6.61675	+	3.13377i	0.262371	+	0.124262i
$637$	−7.06140	−	7.06140i	−0.279783	−	0.279783i
$638$	−11.1320	−	11.1320i	−0.440718	−	0.440718i
$639$	−1.29093	−	1.57640i	−0.0510684	−	0.0623613i
$640$	15.9777	−	25.8918i	0.631574	−	1.02346i
$641$			30.7396i			1.21414i	0.794648	+	0.607071i	$0.207656\pi$
$641$			30.7396i			1.21414i	−0.794648	+	0.607071i	$0.792344\pi$
$642$	−2.04710	+	0.731243i	−0.0807925	+	0.0288599i
$643$	5.50784	−	5.50784i	0.217208	−	0.217208i	−0.590113	−	0.807321i	$-0.700917\pi$
$643$	5.50784	−	5.50784i	0.217208	−	0.217208i	0.807321	+	0.590113i	$0.200917\pi$
$644$	−1.32438			−0.0521878
$645$	−2.10733	+	9.89606i	−0.0829759	+	0.389657i
$646$	−1.85770			−0.0730904
$647$	−1.83127	+	1.83127i	−0.0719945	+	0.0719945i	−0.742187	−	0.670193i	$-0.766211\pi$
$647$	−1.83127	+	1.83127i	−0.0719945	+	0.0719945i	0.670193	+	0.742187i	$0.266211\pi$
$648$	16.6661	−	11.0850i	0.654704	−	0.435461i
$649$		−	2.68228i		−	0.105289i
$650$	5.24665	+	10.4578i	0.205791	+	0.410188i
$651$	−0.945793	+	1.99698i	−0.0370685	+	0.0782678i
$652$	−8.09015	−	8.09015i	−0.316835	−	0.316835i
$653$	2.26241	+	2.26241i	0.0885350	+	0.0885350i	0.749987	−	0.661452i	$-0.230060\pi$
$653$	2.26241	+	2.26241i	0.0885350	+	0.0885350i	−0.661452	+	0.749987i	$0.730060\pi$
$654$	0.301957	−	0.637562i	0.0118074	−	0.0249306i
$655$	37.5492	−	8.89108i	1.46717	−	0.347403i
$656$			43.7639i			1.70870i
$657$	2.41321	−	24.2391i	0.0941481	−	0.945656i
$658$	1.84487	−	1.84487i	0.0719204	−	0.0719204i
$659$	−21.4513			−0.835624			−0.417812	−	0.908534i	$-0.637203\pi$
$659$	−21.4513			−0.835624			−0.417812	+	0.908534i	$0.637203\pi$
$660$	−2.04082	+	1.32424i	−0.0794388	+	0.0515461i
$661$	−23.6158			−0.918548			−0.459274	−	0.888295i	$-0.651890\pi$
$661$	−23.6158			−0.918548			−0.459274	+	0.888295i	$0.651890\pi$
$662$	−0.972152	+	0.972152i	−0.0377837	+	0.0377837i
$663$	−9.58631	+	3.42433i	−0.372302	+	0.132990i
$664$			15.5078i			0.601821i
$665$	0.152902	+	0.0943553i	0.00592929	+	0.00365894i
$666$	−12.6598	+	10.3673i	−0.490558	+	0.401724i
$667$	−50.7083	−	50.7083i	−1.96343	−	1.96343i
$668$	0.936511	+	0.936511i	0.0362347	+	0.0362347i
$669$	−33.6713	−	15.9471i	−1.30181	−	0.616552i
$670$	7.41333	+	31.3083i	0.286402	+	1.20954i
$671$		−	9.46983i		−	0.365579i
$672$	0.571188	+	1.59903i	0.0220341	+	0.0616838i
$673$	5.74356	−	5.74356i	0.221398	−	0.221398i	−0.587689	−	0.809087i	$-0.699962\pi$
$673$	5.74356	−	5.74356i	0.221398	−	0.221398i	0.809087	+	0.587689i	$0.199962\pi$
$674$	57.0139			2.19609
$675$	−25.9047	−	1.98665i	−0.997072	−	0.0764662i
$676$	6.85719			0.263738
$677$	−1.13494	+	1.13494i	−0.0436194	+	0.0436194i	−0.728580	−	0.684961i	$-0.759819\pi$
$677$	−1.13494	+	1.13494i	−0.0436194	+	0.0436194i	0.684961	+	0.728580i	$0.259819\pi$
$678$	−3.20799	−	8.98069i	−0.123202	−	0.344901i
$679$			4.60849i			0.176858i
$680$	−4.66550	−	19.7036i	−0.178914	−	0.755597i
$681$	−21.6296	−	10.2440i	−0.828849	−	0.392552i
$682$	5.12214	+	5.12214i	0.196137	+	0.196137i
$683$	1.61763	+	1.61763i	0.0618968	+	0.0618968i	0.737378	−	0.675481i	$-0.236064\pi$
$683$	1.61763	+	1.61763i	0.0618968	+	0.0618968i	−0.675481	+	0.737378i	$0.736064\pi$
$684$	0.410321	−	0.336017i	0.0156890	−	0.0128479i
$685$	−38.6623	−	23.8583i	−1.47721	−	0.911580i
$686$			6.44219i			0.245964i
$687$	−31.8104	+	11.3630i	−1.21364	+	0.433524i
$688$	8.98095	−	8.98095i	0.342395	−	0.342395i
$689$	−9.71319			−0.370043
$690$	−38.8955	+	25.2385i	−1.48073	+	0.960812i
$691$	−26.3783			−1.00348			−0.501739	−	0.865019i	$-0.667306\pi$
$691$	−26.3783			−1.00348			−0.501739	+	0.865019i	$0.667306\pi$
$692$	−7.73657	+	7.73657i	−0.294100	+	0.294100i
$693$	−0.0848544	+	0.852307i	−0.00322335	+	0.0323765i
$694$			17.9858i			0.682732i
$695$	−7.83835	+	1.85600i	−0.297325	+	0.0704022i
$696$	−16.0115	+	33.8072i	−0.606913	+	1.28146i
$697$	25.9170	+	25.9170i	0.981675	+	0.981675i
$698$	−3.68009	−	3.68009i	−0.139293	−	0.139293i
$699$	−10.8751	+	22.9621i	−0.411335	+	0.868507i
$700$	0.282407	−	0.851072i	0.0106740	−	0.0321675i
$701$			11.2314i			0.424205i	0.977247	+	0.212102i	$0.0680310\pi$
$701$			11.2314i			0.424205i	−0.977247	+	0.212102i	$0.931969\pi$
$702$	6.26756	−	10.4193i	0.236554	−	0.393251i
$703$	0.669550	−	0.669550i	0.0252526	−	0.0252526i
$704$	−4.15697			−0.156672
$705$	4.54699	−	21.3528i	0.171249	−	0.804192i
$706$	5.33641			0.200839
$707$	−3.40231	+	3.40231i	−0.127957	+	0.127957i
$708$	2.74821	−	0.981688i	0.103284	−	0.0368941i
$709$			13.2746i			0.498538i	0.968434	+	0.249269i	$0.0801903\pi$
$709$			13.2746i			0.498538i	−0.968434	+	0.249269i	$0.919810\pi$
$710$	1.29294	−	2.09520i	0.0485232	−	0.0786316i
$711$	−23.7845	−	29.0441i	−0.891989	−	1.08924i
$712$	4.68600	+	4.68600i	0.175615	+	0.175615i
$713$	23.3324	+	23.3324i	0.873805	+	0.873805i
$714$	2.95006	+	1.39718i	0.110403	+	0.0522882i
$715$	1.69499	−	2.74671i	0.0633889	−	0.102721i
$716$		−	12.7599i		−	0.476859i
$717$	15.1776	+	42.4894i	0.566819	+	1.58680i
$718$	−13.3971	+	13.3971i	−0.499974	+	0.499974i
$719$	45.9916			1.71520			0.857600	−	0.514318i	$-0.171955\pi$
$719$	45.9916			1.71520			0.857600	+	0.514318i	$0.171955\pi$
$720$	25.9210	+	19.7924i	0.966019	+	0.737619i
$721$	−1.93351			−0.0720076
$722$	21.6895	−	21.6895i	0.807199	−	0.807199i
$723$	−1.28059	−	3.58499i	−0.0476257	−	0.133327i
$724$			8.80615i			0.327278i
$725$	43.3991	−	21.7733i	1.61180	−	0.808640i
$726$	2.53770	+	1.20188i	0.0941829	+	0.0446061i
$727$	−5.64032	−	5.64032i	−0.209188	−	0.209188i	0.594734	−	0.803922i	$-0.297257\pi$
$727$	−5.64032	−	5.64032i	−0.209188	−	0.209188i	−0.803922	+	0.594734i	$0.797257\pi$
$728$	−0.648080	−	0.648080i	−0.0240194	−	0.0240194i
$729$	12.6522	+	23.8521i	0.468598	+	0.883411i
$730$	28.6418	−	6.78195i	1.06008	−	0.251011i
$731$		−	10.6370i		−	0.393424i
$732$	9.70259	−	3.46586i	0.358618	−	0.128102i
$733$	33.8431	−	33.8431i	1.25002	−	1.25002i	0.294313	−	0.955709i	$-0.404909\pi$
$733$	33.8431	−	33.8431i	1.25002	−	1.25002i	0.955709	−	0.294313i	$-0.0950907\pi$
$734$	−15.1473			−0.559096
$735$	14.5853	+	22.4778i	0.537988	+	0.829105i
$736$	25.3565			0.934651
$737$	6.27596	−	6.27596i	0.231178	−	0.231178i
$738$	−43.5643	−	4.33719i	−1.60362	−	0.159654i
$739$			5.33288i			0.196173i	0.995178	+	0.0980866i	$0.0312722\pi$
$739$			5.33288i			0.196173i	−0.995178	+	0.0980866i	$0.968728\pi$
$740$	−4.02161	−	2.48172i	−0.147838	−	0.0912299i
$741$	−0.301169	+	0.635900i	−0.0110637	+	0.0233604i
$742$	2.20239	+	2.20239i	0.0808522	+	0.0808522i
$743$	28.7768	+	28.7768i	1.05572	+	1.05572i	0.998353	+	0.0573664i	$0.0182703\pi$
$743$	28.7768	+	28.7768i	1.05572	+	1.05572i	0.0573664	+	0.998353i	$0.481730\pi$
$744$	7.36735	−	15.5557i	0.270100	−	0.570299i
$745$	−6.00427	−	25.3575i	−0.219980	−	0.929027i
$746$			29.0770i			1.06459i
$747$	−20.8161	−	2.07242i	−0.761620	−	0.0758258i
$748$	1.80851	−	1.80851i	0.0661256	−	0.0661256i
$749$	−0.221028			−0.00807618
$750$	−7.92476	−	30.3769i	−0.289371	−	1.10921i
$751$	14.4158			0.526040			0.263020	−	0.964790i	$-0.415281\pi$
$751$	14.4158			0.526040			0.263020	+	0.964790i	$0.415281\pi$
$752$	−19.3782	+	19.3782i	−0.706652	+	0.706652i
$753$	5.61140	−	2.00445i	0.204491	−	0.0730461i
$754$			22.7238i			0.827553i
$755$	8.62252	+	36.4150i	0.313806	+	1.32528i
$756$	−0.904312	+	0.224996i	−0.0328895	+	0.00818301i
$757$	28.9382	+	28.9382i	1.05178	+	1.05178i	0.998584	+	0.0531933i	$0.0169400\pi$
$757$	28.9382	+	28.9382i	1.05178	+	1.05178i	0.0531933	+	0.998584i	$0.483060\pi$
$758$	7.02428	+	7.02428i	0.255133	+	0.255133i
$759$	11.5597	+	5.47482i	0.419592	+	0.198724i
$760$	−1.19105	−	0.734990i	−0.0432038	−	0.0266609i
$761$		−	18.7778i		−	0.680696i	−0.940299	−	0.340348i	$-0.889455\pi$
$761$		−	18.7778i		−	0.680696i	0.940299	−	0.340348i	$-0.110545\pi$
$762$	−3.85677	−	10.7969i	−0.139716	−	0.391132i
$763$	0.0507205	−	0.0507205i	0.00183621	−	0.00183621i
$764$	11.9247			0.431422
$765$	27.0714	−	3.62936i	0.978770	−	0.131220i
$766$	−47.8819			−1.73004
$767$	−2.73769	+	2.73769i	−0.0988523	+	0.0988523i
$768$	−8.00801	−	22.4182i	−0.288964	−	0.808948i
$769$			0.107567i			0.00387895i	0.999998	+	0.00193948i	$0.000617355\pi$
$769$			0.107567i			0.00387895i	−0.999998	+	0.00193948i	$0.999383\pi$
$770$	−1.00712	+	0.238471i	−0.0362941	+	0.00859388i
$771$	−25.8437	−	12.2399i	−0.930740	−	0.440809i
$772$	0.470663	+	0.470663i	0.0169395	+	0.0169395i
$773$	−4.72647	−	4.72647i	−0.169999	−	0.169999i	0.616980	−	0.786979i	$-0.288356\pi$
$773$	−4.72647	−	4.72647i	−0.169999	−	0.169999i	−0.786979	+	0.616980i	$0.788356\pi$
$774$	8.04992	+	9.83002i	0.289348	+	0.353333i
$775$	−19.9692	+	10.0185i	−0.717316	+	0.359876i
$776$		−	35.8983i		−	1.28867i
$777$	−1.56682	+	0.559684i	−0.0562094	+	0.0200786i
$778$	−20.4832	+	20.4832i	−0.734358	+	0.734358i
$779$	2.53340			0.0907686
$780$	3.43458	+	0.731379i	0.122978	+	0.0261876i
$781$	−0.679177			−0.0243029
$782$	34.4680	−	34.4680i	1.23257	−	1.23257i
$783$	−43.2394	−	26.0100i	−1.54525	−	0.929521i
$784$		−	33.6358i		−	1.20128i
$785$	14.9153	−	24.1701i	0.532348	−	0.862667i
$786$	20.7407	−	43.7927i	0.739797	−	1.56203i
$787$	−20.3978	−	20.3978i	−0.727103	−	0.727103i	0.242939	−	0.970042i	$-0.421889\pi$
$787$	−20.3978	−	20.3978i	−0.727103	−	0.727103i	−0.970042	+	0.242939i	$0.921889\pi$
$788$	−0.137022	−	0.137022i	−0.00488121	−	0.00488121i
$789$	−16.7508	+	35.3683i	−0.596346	+	1.25914i
$790$	23.8216	−	38.6027i	0.847534	−	1.37342i
$791$		−	0.969657i		−	0.0344770i
$792$	0.660982	−	6.63914i	0.0234870	−	0.235911i
$793$	−9.66545	+	9.66545i	−0.343230	+	0.343230i
$794$	23.5838			0.836957
$795$	25.4907	+	5.42815i	0.904064	+	0.192517i
$796$	1.64811			0.0584156
$797$	−15.7865	+	15.7865i	−0.559186	+	0.559186i	−0.929076	−	0.369889i	$-0.879396\pi$
$797$	−15.7865	+	15.7865i	−0.559186	+	0.559186i	0.369889	+	0.929076i	$0.379396\pi$
$798$	0.212473	−	0.0758974i	0.00752145	−	0.00268674i
$799$			22.9515i			0.811967i
$800$	−5.40695	+	16.2946i	−0.191165	+	0.576100i
$801$	−6.91620	+	5.66376i	−0.244372	+	0.200119i
$802$	−27.0401	−	27.0401i	−0.954821	−	0.954821i
$803$	−5.74145	−	5.74145i	−0.202611	−	0.202611i
$804$	8.72716	+	4.13328i	0.307783	+	0.145770i
$805$	−4.58763	+	1.08628i	−0.161693	+	0.0382864i
$806$		−	10.4559i		−	0.368294i
$807$	−1.15668	−	3.23808i	−0.0407169	−	0.113986i
$808$	26.5026	−	26.5026i	0.932360	−	0.932360i
$809$	−47.1778			−1.65868			−0.829341	−	0.558742i	$-0.811284\pi$
$809$	−47.1778			−1.65868			−0.829341	+	0.558742i	$0.811284\pi$
$810$	−22.2710	+	23.8412i	−0.782522	+	0.837695i
$811$	−42.0723			−1.47736			−0.738680	−	0.674057i	$-0.764550\pi$
$811$	−42.0723			−1.47736			−0.738680	+	0.674057i	$0.764550\pi$
$812$	1.23148	−	1.23148i	0.0432163	−	0.0432163i
$813$	9.75300	+	27.3033i	0.342053	+	0.957568i
$814$			5.45437i			0.191176i
$815$	−34.6599	−	21.3885i	−1.21408	−	0.749207i
$816$	−30.9870	−	14.6758i	−1.08476	−	0.513755i
$817$	−0.519888	−	0.519888i	−0.0181886	−	0.0181886i
$818$	−14.4525	−	14.4525i	−0.505319	−	0.505319i
$819$	0.956521	−	0.783306i	0.0334235	−	0.0273709i
$820$	−2.91328	−	12.3035i	−0.101736	−	0.429656i
$821$		−	44.0134i		−	1.53608i	−0.640403	−	0.768039i	$-0.721233\pi$
$821$		−	44.0134i		−	1.53608i	0.640403	−	0.768039i	$-0.278767\pi$
$822$	−53.7251	+	19.1911i	−1.87388	+	0.669368i
$823$	−12.1320	+	12.1320i	−0.422896	+	0.422896i	−0.886200	−	0.463303i	$-0.846664\pi$
$823$	−12.1320	+	12.1320i	−0.422896	+	0.422896i	0.463303	+	0.886200i	$0.346664\pi$
$824$	15.0613			0.524684
$825$	−5.98321	+	6.26109i	−0.208309	+	0.217983i
$826$	1.24150			0.0431972
$827$	14.5719	−	14.5719i	0.506716	−	0.506716i	−0.406801	−	0.913517i	$-0.633356\pi$
$827$	14.5719	−	14.5719i	0.506716	−	0.506716i	0.913517	+	0.406801i	$0.133356\pi$
$828$	−1.37865	+	13.8476i	−0.0479113	+	0.481237i
$829$		−	34.3317i		−	1.19239i	−0.802840	−	0.596195i	$-0.796679\pi$
$829$		−	34.3317i		−	1.19239i	0.802840	−	0.596195i	$-0.203321\pi$
$830$	−5.82422	−	24.5971i	−0.202161	−	0.853777i
$831$	−16.3966	+	34.6203i	−0.568790	+	1.20096i
$832$	4.24284	+	4.24284i	0.147094	+	0.147094i
$833$	−19.9191	−	19.9191i	−0.690155	−	0.690155i
$834$	−4.32960	+	9.14167i	−0.149922	+	0.316550i
$835$	4.01221	+	2.47592i	0.138848	+	0.0856828i
$836$		−	0.176783i		−	0.00611417i
$837$	19.8957	+	11.9680i	0.687697	+	0.413673i
$838$	38.5107	−	38.5107i	1.33033	−	1.33033i
$839$	7.37612			0.254652			0.127326	−	0.991861i	$-0.459361\pi$
$839$	7.37612			0.254652			0.127326	+	0.991861i	$0.459361\pi$
$840$	1.33861	+	2.06296i	0.0461864	+	0.0711789i
$841$	65.3025			2.25181
$842$	−12.8009	+	12.8009i	−0.441149	+	0.441149i
$843$	18.1869	−	6.49653i	0.626389	−	0.223752i
$844$			6.36808i			0.219198i
$845$	23.7533	−	5.62441i	0.817137	−	0.193486i
$846$	−17.3694	−	21.2103i	−0.597171	−	0.729225i
$847$	0.201884	+	0.201884i	0.00693681	+	0.00693681i
$848$	−23.1336	−	23.1336i	−0.794410	−	0.794410i
$849$	−21.5652	−	10.2135i	−0.740115	−	0.350527i
$850$	14.8000	+	29.4997i	0.507635	+	1.01183i
$851$			24.8458i			0.851702i
$852$	−0.248572	−	0.695871i	−0.00851593	−	0.0238401i
$853$	−22.1377	+	22.1377i	−0.757980	+	0.757980i	−0.975955	−	0.217974i	$-0.930055\pi$
$853$	−22.1377	+	22.1377i	−0.757980	+	0.757980i	0.217974	+	0.975955i	$0.430055\pi$
$854$	4.38312			0.149987
$855$	1.14574	−	1.50051i	0.0391835	−	0.0513164i
$856$	1.72172			0.0588471
$857$	−8.67169	+	8.67169i	−0.296219	+	0.296219i	−0.839531	−	0.543312i	$-0.817170\pi$
$857$	−8.67169	+	8.67169i	−0.296219	+	0.296219i	0.543312	+	0.839531i	$0.317170\pi$
$858$	−1.36341	−	3.81683i	−0.0465461	−	0.130305i
$859$		−	15.3607i		−	0.524101i	−0.965054	−	0.262050i	$-0.915601\pi$
$859$		−	15.3607i		−	0.524101i	0.965054	−	0.262050i	$-0.0843987\pi$
$860$	−1.92699	+	3.12268i	−0.0657099	+	0.106482i
$861$	−4.02307	−	1.90537i	−0.137106	−	0.0649350i
$862$	−4.18793	−	4.18793i	−0.142642	−	0.142642i
$863$	−25.8970	−	25.8970i	−0.881543	−	0.881543i	0.112149	−	0.993691i	$-0.464227\pi$
$863$	−25.8970	−	25.8970i	−0.881543	−	0.881543i	−0.993691	+	0.112149i	$0.964227\pi$
$864$	17.3139	−	4.30775i	0.589031	−	0.146553i
$865$	−20.4537	+	33.1451i	−0.695447	+	1.12697i
$866$		−	8.17597i		−	0.277831i
$867$	0.687429	−	0.245556i	0.0233463	−	0.00833953i
$868$	−0.566638	+	0.566638i	−0.0192329	+	0.0192329i
$869$	−12.5134			−0.424487
$870$	12.6991	−	59.6351i	0.430539	−	2.02182i
$871$	−12.8112			−0.434091
$872$	−0.395093	+	0.395093i	−0.0133795	+	0.0133795i
$873$	48.1861	+	4.79733i	1.63085	+	0.162365i
$874$		−	3.36927i		−	0.113967i
$875$	0.280189	−	3.17974i	0.00947213	−	0.107495i
$876$	3.78126	−	7.98388i	0.127757	−	0.269750i
$877$	11.3433	+	11.3433i	0.383037	+	0.383037i	0.872195	−	0.489158i	$-0.162696\pi$
$877$	11.3433	+	11.3433i	0.383037	+	0.383037i	−0.489158	+	0.872195i	$0.662696\pi$
$878$	39.8772	+	39.8772i	1.34579	+	1.34579i
$879$	3.88630	−	8.20566i	0.131082	−	0.276770i
$880$	10.5786	−	2.50486i	0.356606	−	0.0844389i
$881$		−	45.7437i		−	1.54115i	−0.637352	−	0.770573i	$-0.719970\pi$
$881$		−	45.7437i		−	1.54115i	0.637352	−	0.770573i	$-0.280030\pi$
$882$	33.4823	+	3.33345i	1.12741	+	0.112243i
$883$	33.5492	−	33.5492i	1.12902	−	1.12902i	0.138685	−	0.990337i	$-0.455713\pi$
$883$	33.5492	−	33.5492i	1.12902	−	1.12902i	0.990337	−	0.138685i	$-0.0442875\pi$
$884$	−3.69174			−0.124167
$885$	8.71458	−	5.65470i	0.292937	−	0.190081i
$886$	−23.9849			−0.805788
$887$	−41.1834	+	41.1834i	−1.38280	+	1.38280i	−0.543204	+	0.839601i	$0.682789\pi$
$887$	−41.1834	+	41.1834i	−1.38280	+	1.38280i	−0.839601	+	0.543204i	$0.817211\pi$
$888$	12.2049	−	4.35972i	0.409570	−	0.146303i
$889$		−	1.16576i		−	0.0390983i
$890$	−9.19239	−	5.67259i	−0.308130	−	0.190146i
$891$	8.82334	+	1.77446i	0.295593	+	0.0594468i
$892$	−9.55416	−	9.55416i	−0.319897	−	0.319897i
$893$	1.12177	+	1.12177i	0.0375384	+	0.0375384i
$894$	−29.5738	−	14.0065i	−0.989097	−	0.468448i
$895$	−10.4659	−	44.2001i	−0.349837	−	1.47745i
$896$		−	3.88472i		−	0.129779i
$897$	−6.21061	−	17.3865i	−0.207366	−	0.580517i
$898$	20.7602	−	20.7602i	0.692778	−	0.692778i
$899$	−43.3914			−1.44718
$900$	−8.60478	−	3.83878i	−0.286826	−	0.127959i
$901$	−27.3994			−0.912805
$902$	−10.3190	+	10.3190i	−0.343584	+	0.343584i
$903$	0.434580	+	1.21660i	0.0144619	+	0.0404858i
$904$			7.55324i			0.251217i
$905$	7.22299	+	30.5044i	0.240100	+	1.01400i
$906$	42.4699	+	20.1142i	1.41097	+	0.668251i
$907$	40.3742	+	40.3742i	1.34060	+	1.34060i	0.895459	+	0.445143i	$0.146847\pi$
$907$	40.3742	+	40.3742i	1.34060	+	1.34060i	0.445143	+	0.895459i	$0.353153\pi$
$908$	−6.13735	−	6.13735i	−0.203675	−	0.203675i
$909$	32.0326	+	39.1161i	1.06245	+	1.29740i
$910$	1.27132	+	0.784527i	0.0421439	+	0.0260068i
$911$		−	3.96308i		−	0.131303i	−0.997843	−	0.0656514i	$-0.979087\pi$
$911$		−	3.96308i		−	0.131303i	0.997843	−	0.0656514i	$-0.0209125\pi$
$912$	−2.23178	+	0.797215i	−0.0739018	+	0.0263984i
$913$	−4.93065	+	4.93065i	−0.163181	+	0.163181i
$914$	−9.34853			−0.309222
$915$	30.7669	−	19.9640i	1.01712	−	0.659989i
$916$	−12.2503			−0.404762
$917$	3.48388	−	3.48388i	0.115048	−	0.115048i
$918$	17.6798	−	29.3912i	0.583519	−	0.970053i
$919$		−	7.06389i		−	0.233016i	−0.993190	−	0.116508i	$-0.962830\pi$
$919$		−	7.06389i		−	0.233016i	0.993190	−	0.116508i	$-0.0371701\pi$
$920$	35.7358	−	8.46171i	1.17818	−	0.278974i
$921$	5.45921	−	11.5268i	0.179887	−	0.379820i
$922$	25.8944	+	25.8944i	0.852787	+	0.852787i
$923$	0.693207	+	0.693207i	0.0228172	+	0.0228172i
$924$	−0.132959	+	0.280734i	−0.00437402	+	0.00923546i
$925$	−15.9664	−	5.29806i	−0.524972	−	0.174199i
$926$			11.0290i			0.362436i
$927$	−2.01274	+	20.2166i	−0.0661070	+	0.664001i
$928$	−23.5778	+	23.5778i	−0.773978	+	0.773978i
$929$	5.42663			0.178042			0.0890210	−	0.996030i	$-0.471626\pi$
$929$	5.42663			0.178042			0.0890210	+	0.996030i	$0.471626\pi$
$930$	−5.84321	+	27.4399i	−0.191607	+	0.899789i
$931$	−1.94711			−0.0638138
$932$	−6.51545	+	6.51545i	−0.213421	+	0.213421i
$933$	−36.3557	+	12.9866i	−1.19023	+	0.425163i
$934$		−	9.41249i		−	0.307986i
$935$	4.78128	−	7.74804i	0.156365	−	0.253388i
$936$	−7.45092	+	6.10165i	−0.243541	+	0.199439i
$937$	29.0081	+	29.0081i	0.947653	+	0.947653i	0.998696	−	0.0510439i	$-0.0162548\pi$
$937$	29.0081	+	29.0081i	0.947653	+	0.947653i	−0.0510439	+	0.998696i	$0.516255\pi$
$938$	2.90484	+	2.90484i	0.0948463	+	0.0948463i
$939$	19.3984	+	9.18729i	0.633042	+	0.299816i
$940$	4.15788	−	6.73782i	0.135615	−	0.219763i
$941$		−	17.7369i		−	0.578208i	−0.957298	−	0.289104i	$-0.906643\pi$
$941$		−	17.7369i		−	0.578208i	0.957298	−	0.289104i	$-0.0933573\pi$
$942$	−11.9975	−	33.5867i	−0.390900	−	1.09431i
$943$	−47.0050	+	47.0050i	−1.53069	+	1.53069i
$944$	−13.0405			−0.424433
$945$	−2.94798	+	1.52112i	−0.0958979	+	0.0494820i
$946$	4.23518			0.137697
$947$	−14.6533	+	14.6533i	−0.476169	+	0.476169i	−0.903904	−	0.427735i	$-0.859312\pi$
$947$	−14.6533	+	14.6533i	−0.476169	+	0.476169i	0.427735	+	0.903904i	$0.359312\pi$
$948$	−4.57977	−	12.8209i	−0.148744	−	0.416405i
$949$			11.7201i			0.380451i
$950$	2.16516	+	0.718456i	0.0702472	+	0.0233098i
$951$	40.8153	+	19.3306i	1.32353	+	0.626838i
$952$	−1.82813	−	1.82813i	−0.0592500	−	0.0592500i
$953$	11.7199	+	11.7199i	0.379646	+	0.379646i	0.870975	−	0.491328i	$-0.163488\pi$
$953$	11.7199	+	11.7199i	0.379646	+	0.379646i	−0.491328	+	0.870975i	$0.663488\pi$
$954$	25.3206	−	20.7354i	0.819786	−	0.671333i
$955$	41.3072	−	9.78092i	1.33667	−	0.316503i
$956$			16.3629i			0.529213i
$957$	−15.8396	+	5.65807i	−0.512022	+	0.182899i
$958$	−6.58058	+	6.58058i	−0.212609	+	0.212609i
$959$	−5.80077			−0.187317
$960$	−8.76359	−	13.5058i	−0.282844	−	0.435897i
$961$	−11.0344			−0.355947
$962$	5.56704	−	5.56704i	0.179489	−	0.179489i
$963$	−0.230085	+	2.31105i	−0.00741438	+	0.0744726i
$964$		−	1.38060i		−	0.0444660i
$965$	2.01642	+	1.24433i	0.0649109	+	0.0400562i
$966$	−2.53403	+	5.35044i	−0.0815311	+	0.172148i
$967$	−21.1658	−	21.1658i	−0.680647	−	0.680647i	0.279499	−	0.960146i	$-0.409832\pi$
$967$	−21.1658	−	21.1658i	−0.680647	−	0.680647i	−0.960146	+	0.279499i	$0.909832\pi$
$968$	−1.57260	−	1.57260i	−0.0505451	−	0.0505451i
$969$	−0.849551	+	1.79377i	−0.0272915	+	0.0576242i
$970$	13.4822	+	56.9385i	0.432887	+	1.82819i
$971$			15.3244i			0.491783i	0.969297	+	0.245891i	$0.0790807\pi$
$971$			15.3244i			0.491783i	−0.969297	+	0.245891i	$0.920919\pi$
$972$	1.41117	+	9.68965i	0.0452634	+	0.310796i
$973$	−0.727255	+	0.727255i	−0.0233147	+	0.0233147i
$974$	35.0297			1.12243
$975$	12.4972	−	0.283619i	0.400232	−	0.00908307i
$976$	−46.0397			−1.47370
$977$	−9.31965	+	9.31965i	−0.298162	+	0.298162i	−0.840294	−	0.542132i	$-0.817617\pi$
$977$	−9.31965	+	9.31965i	−0.298162	+	0.298162i	0.542132	+	0.840294i	$0.317617\pi$
$978$	−48.1635	+	17.2045i	−1.54010	+	0.550138i
$979$			2.97979i			0.0952344i
$980$	2.23906	+	9.45611i	0.0715243	+	0.302064i
$981$	−0.477532	−	0.583129i	−0.0152464	−	0.0186179i
$982$	−11.2283	−	11.2283i	−0.358311	−	0.358311i
$983$	−22.0174	−	22.0174i	−0.702247	−	0.702247i	0.262645	−	0.964892i	$-0.415405\pi$
$983$	−22.0174	−	22.0174i	−0.702247	−	0.702247i	−0.964892	+	0.262645i	$0.915405\pi$
$984$	31.3381	+	14.8421i	0.999024	+	0.473149i
$985$	−0.587032	−	0.362255i	−0.0187044	−	0.0115424i
$986$			64.1003i			2.04137i
$987$	−0.937696	−	2.62506i	−0.0298472	−	0.0835565i
$988$	−0.180435	+	0.180435i	−0.00574040	+	0.00574040i
$989$	19.2921			0.613453
$990$	1.44504	+	10.7786i	0.0459265	+	0.342567i
$991$	−1.02170			−0.0324553			−0.0162276	−	0.999868i	$-0.505166\pi$
$991$	−1.02170			−0.0324553			−0.0162276	+	0.999868i	$0.505166\pi$
$992$	10.8488	−	10.8488i	0.344450	−	0.344450i
$993$	0.494118	+	1.38327i	0.0156804	+	0.0438968i
$994$		−	0.314358i		−	0.00997083i
$995$	5.70903	−	1.35181i	0.180988	−	0.0428553i
$996$	−6.85641	−	3.24728i	−0.217254	−	0.102894i
$997$	−23.8372	−	23.8372i	−0.754932	−	0.754932i	0.220464	−	0.975395i	$-0.429243\pi$
$997$	−23.8372	−	23.8372i	−0.754932	−	0.754932i	−0.975395	+	0.220464i	$0.929243\pi$
$998$	1.06565	+	1.06565i	0.0337325	+	0.0337325i
$999$	4.22100	+	16.9652i	0.133546	+	0.536755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.k.c.122.7	yes	16
3.2	odd	2		165.2.k.d.122.2	yes	16
5.2	odd	4		825.2.k.i.518.7		16
5.3	odd	4		165.2.k.d.23.2	yes	16
5.4	even	2		825.2.k.j.782.2		16
15.2	even	4		825.2.k.j.518.2		16
15.8	even	4	inner	165.2.k.c.23.7	✓	16
15.14	odd	2		825.2.k.i.782.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.k.c.23.7	✓	16	15.8	even	4	inner
165.2.k.c.122.7	yes	16	1.1	even	1	trivial
165.2.k.d.23.2	yes	16	5.3	odd	4
165.2.k.d.122.2	yes	16	3.2	odd	2
825.2.k.i.518.7		16	5.2	odd	4
825.2.k.i.782.7		16	15.14	odd	2
825.2.k.j.518.2		16	15.2	even	4
825.2.k.j.782.2		16	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14633 - 1.14633i) q^{2} +(-0.582649 - 1.63111i) q^{3} -0.628149i q^{4} +(-0.515221 - 2.17590i) q^{5} +(-2.53770 - 1.20188i) q^{6} +(-0.201884 - 0.201884i) q^{7} +(1.57260 + 1.57260i) q^{8} +(-2.32104 + 1.90073i) q^{9} +(-3.08492 - 1.90369i) q^{10} +1.00000i q^{11} +(-1.02458 + 0.365990i) q^{12} +(1.02066 - 1.02066i) q^{13} -0.462851 q^{14} +(-3.24894 + 2.10817i) q^{15} +4.86173 q^{16} +(2.87911 - 2.87911i) q^{17} +(-0.481818 + 4.83954i) q^{18} -0.281435i q^{19} +(-1.36679 + 0.323635i) q^{20} +(-0.211667 + 0.446922i) q^{21} +(1.14633 + 1.14633i) q^{22} +(5.22177 + 5.22177i) q^{23} +(1.64881 - 3.48135i) q^{24} +(-4.46910 + 2.24214i) q^{25} -2.34002i q^{26} +(4.45265 + 2.67842i) q^{27} +(-0.126813 + 0.126813i) q^{28} -9.71095 q^{29} +(-1.30771 + 6.14102i) q^{30} +4.46829 q^{31} +(2.42796 - 2.42796i) q^{32} +(1.63111 - 0.582649i) q^{33} -6.60083i q^{34} +(-0.335265 + 0.543294i) q^{35} +(1.19394 + 1.45796i) q^{36} +(2.37906 + 2.37906i) q^{37} +(-0.322618 - 0.322618i) q^{38} +(-2.25949 - 1.07012i) q^{39} +(2.61158 - 4.23205i) q^{40} +9.00173i q^{41} +(0.269680 + 0.754962i) q^{42} +(1.84728 - 1.84728i) q^{43} +0.628149 q^{44} +(5.33165 + 4.07106i) q^{45} +11.9718 q^{46} +(-3.98588 + 3.98588i) q^{47} +(-2.83268 - 7.93001i) q^{48} -6.91849i q^{49} +(-2.55283 + 7.69329i) q^{50} +(-6.37366 - 3.01864i) q^{51} +(-0.641125 - 0.641125i) q^{52} +(-4.75830 - 4.75830i) q^{53} +(8.17456 - 2.03386i) q^{54} +(2.17590 - 0.515221i) q^{55} -0.634963i q^{56} +(-0.459052 + 0.163978i) q^{57} +(-11.1320 + 11.1320i) q^{58} -2.68228 q^{59} +(1.32424 + 2.04082i) q^{60} -9.46983 q^{61} +(5.12214 - 5.12214i) q^{62} +(0.852307 + 0.0848544i) q^{63} +4.15697i q^{64} +(-2.74671 - 1.69499i) q^{65} +(1.20188 - 2.53770i) q^{66} +(-6.27596 - 6.27596i) q^{67} +(-1.80851 - 1.80851i) q^{68} +(5.47482 - 11.5597i) q^{69} +(0.238471 + 1.00712i) q^{70} +0.679177i q^{71} +(-6.63914 - 0.660982i) q^{72} +(-5.74145 + 5.74145i) q^{73} +5.45437 q^{74} +(6.26109 + 5.98321i) q^{75} -0.176783 q^{76} +(0.201884 - 0.201884i) q^{77} +(-3.81683 + 1.36341i) q^{78} +12.5134i q^{79} +(-2.50486 - 10.5786i) q^{80} +(1.77446 - 8.82334i) q^{81} +(10.3190 + 10.3190i) q^{82} +(4.93065 + 4.93065i) q^{83} +(0.280734 + 0.132959i) q^{84} +(-7.74804 - 4.78128i) q^{85} -4.23518i q^{86} +(5.65807 + 15.8396i) q^{87} +(-1.57260 + 1.57260i) q^{88} +2.97979 q^{89} +(10.7786 - 1.44504i) q^{90} -0.412109 q^{91} +(3.28005 - 3.28005i) q^{92} +(-2.60345 - 7.28828i) q^{93} +9.13826i q^{94} +(-0.612375 + 0.145001i) q^{95} +(-5.37491 - 2.54562i) q^{96} +(-11.4137 - 11.4137i) q^{97} +(-7.93087 - 7.93087i) q^{98} +(-1.90073 - 2.32104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 2 q^{3} - 8 q^{5} - 4 q^{6} + 8 q^{7} + 16 q^{8} + 6 q^{9} - 4 q^{10} - 4 q^{12} - 24 q^{14} + 8 q^{15} - 4 q^{16} + 8 q^{17} - 32 q^{18} - 20 q^{20} - 8 q^{21} - 4 q^{22} + 14 q^{23} + 12 q^{24}+ \cdots - 4 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 8 * q^5 - 4 * q^6 + 8 * q^7 + 16 * q^8 + 6 * q^9 - 4 * q^10 - 4 * q^12 - 24 * q^14 + 8 * q^15 - 4 * q^16 + 8 * q^17 - 32 * q^18 - 20 * q^20 - 8 * q^21 - 4 * q^22 + 14 * q^23 + 12 * q^24 - 18 * q^25 - 20 * q^27 + 8 * q^28 - 16 * q^29 + 20 * q^30 + 8 * q^31 + 28 * q^32 + 4 * q^33 + 44 * q^36 - 6 * q^37 + 24 * q^38 + 24 * q^39 + 16 * q^40 - 60 * q^42 + 16 * q^43 + 12 * q^44 + 24 * q^45 - 32 * q^46 + 48 * q^47 - 48 * q^48 - 12 * q^50 - 8 * q^51 + 36 * q^52 - 4 * q^53 + 4 * q^54 + 2 * q^55 - 8 * q^57 - 12 * q^58 - 68 * q^59 - 28 * q^60 - 8 * q^61 + 48 * q^62 - 12 * q^63 - 48 * q^65 + 8 * q^66 + 6 * q^67 + 24 * q^68 + 12 * q^69 - 4 * q^70 - 8 * q^72 + 8 * q^74 + 8 * q^75 + 16 * q^76 - 8 * q^77 - 48 * q^78 - 24 * q^80 + 2 * q^81 + 12 * q^82 - 8 * q^83 + 52 * q^84 - 4 * q^85 - 36 * q^87 - 16 * q^88 + 32 * q^89 + 44 * q^90 - 56 * q^91 + 20 * q^92 + 28 * q^93 - 48 * q^95 + 80 * q^96 + 18 * q^97 + 16 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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