LMFDB - Embedded newform 725.2.l.a.576.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(226,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("725.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.l (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			576.1
Root			$0.900969 + 0.433884i$ of defining polynomial
Character	$\chi$	$=$	725.576
Dual form			725.2.l.a.326.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.178448 - 0.781831i) q^{2} +(-1.22252 + 0.588735i) q^{3} +(1.22252 + 0.588735i) q^{4} +(0.242135 + 1.06086i) q^{6} +(4.27144 - 2.05702i) q^{7} +(1.67845 - 2.10471i) q^{8} +(-0.722521 + 0.906013i) q^{9} +O(q^{10})$	\(q+(0.178448 - 0.781831i) q^{2} +(-1.22252 + 0.588735i) q^{3} +(1.22252 + 0.588735i) q^{4} +(0.242135 + 1.06086i) q^{6} +(4.27144 - 2.05702i) q^{7} +(1.67845 - 2.10471i) q^{8} +(-0.722521 + 0.906013i) q^{9} +(-0.568532 - 0.712916i) q^{11} -1.84117 q^{12} +(-3.71648 - 4.66032i) q^{13} +(-0.846011 - 3.70662i) q^{14} +(0.346011 + 0.433884i) q^{16} +5.74094 q^{17} +(0.579417 + 0.726566i) q^{18} +(-1.98039 - 0.953703i) q^{19} +(-4.01089 + 5.02949i) q^{21} +(-0.658834 + 0.317278i) q^{22} +(1.01961 + 4.46722i) q^{23} +(-0.812823 + 3.56121i) q^{24} +(-4.30678 + 2.07404i) q^{26} +(1.25571 - 5.50162i) q^{27} +6.43296 q^{28} +(5.36443 - 0.472129i) q^{29} +(-0.548917 + 2.40496i) q^{31} +(5.25182 - 2.52915i) q^{32} +(1.11476 + 0.536840i) q^{33} +(1.02446 - 4.48845i) q^{34} +(-1.41670 + 0.682246i) q^{36} +(-4.94989 + 6.20696i) q^{37} +(-1.09903 + 1.37814i) q^{38} +(7.28717 + 3.50932i) q^{39} +5.31767 q^{41} +(3.21648 + 4.03334i) q^{42} +(-2.06584 - 9.05105i) q^{43} +(-0.275323 - 1.20627i) q^{44} +3.67456 q^{46} +(-5.01842 - 6.29290i) q^{47} +(-0.678448 - 0.326723i) q^{48} +(9.64944 - 12.1000i) q^{49} +(-7.01842 + 3.37989i) q^{51} +(-1.79978 - 7.88536i) q^{52} +(-1.39612 + 6.11682i) q^{53} +(-4.07726 - 1.96351i) q^{54} +(2.83997 - 12.4427i) q^{56} +2.98254 q^{57} +(0.588146 - 4.27833i) q^{58} +4.84548 q^{59} +(3.79105 - 1.82567i) q^{61} +(1.78232 + 0.858322i) q^{62} +(-1.22252 + 5.35621i) q^{63} +(-0.793209 - 3.47527i) q^{64} +(0.618645 - 0.775757i) q^{66} +(3.67845 - 4.61263i) q^{67} +(7.01842 + 3.37989i) q^{68} +(-3.87651 - 4.86099i) q^{69} +(6.91185 + 8.66719i) q^{71} +(0.694177 + 3.04139i) q^{72} +(-0.519614 - 2.27658i) q^{73} +(3.96950 + 4.97760i) q^{74} +(-1.85958 - 2.33184i) q^{76} +(-3.89493 - 1.87570i) q^{77} +(4.04407 - 5.07111i) q^{78} +(-5.66487 + 7.10353i) q^{79} +(0.930272 + 4.07579i) q^{81} +(0.948927 - 4.15752i) q^{82} +(7.88620 + 3.79779i) q^{83} +(-7.86443 + 3.78731i) q^{84} -7.44504 q^{86} +(-6.28017 + 3.73541i) q^{87} -2.45473 q^{88} +(-2.00000 + 8.76257i) q^{89} +(-25.4611 - 12.2614i) q^{91} +(-1.38351 + 6.06156i) q^{92} +(-0.744824 - 3.26329i) q^{93} +(-5.81551 + 2.80060i) q^{94} +(-4.93147 + 6.18387i) q^{96} +(-9.39493 - 4.52436i) q^{97} +(-7.73825 - 9.70346i) q^{98} +1.05669 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 7 q^{3} + 7 q^{4} + 14 q^{6} + 7 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 7 * q^3 + 7 * q^4 + 14 * q^6 + 7 * q^7 + 6 * q^8 - 4 * q^9	$ 6 q - 3 q^{2} - 7 q^{3} + 7 q^{4} + 14 q^{6} + 7 q^{7} + 6 q^{8} - 4 q^{9} + 2 q^{11} - 28 q^{12} - 3 q^{13} - 3 q^{16} + 6 q^{17} - 5 q^{18} + q^{19} - 21 q^{21} + 13 q^{22} + 19 q^{23} + 7 q^{24} + 5 q^{26} + 14 q^{27} - q^{29} + 15 q^{31} - 14 q^{33} - 3 q^{34} + 21 q^{36} - 7 q^{37} - 11 q^{38} - 2 q^{41} - 10 q^{43} - 21 q^{44} - 20 q^{46} - 2 q^{47} - 14 q^{51} - 21 q^{52} - 26 q^{53} - 35 q^{54} - 7 q^{56} - 14 q^{57} + 11 q^{58} + 8 q^{59} + 17 q^{61} - 11 q^{62} - 7 q^{63} + 20 q^{64} + 21 q^{66} + 18 q^{67} + 14 q^{68} - 28 q^{69} + 34 q^{71} - 25 q^{72} - 16 q^{73} + 14 q^{74} + 28 q^{78} - 36 q^{79} - 30 q^{81} + 43 q^{82} + 8 q^{83} - 14 q^{84} - 44 q^{86} - 35 q^{87} + 30 q^{88} - 12 q^{89} - 42 q^{91} + 28 q^{92} - 14 q^{93} - 20 q^{94} - 35 q^{96} - 33 q^{97} - 21 q^{98} + 64 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 7 * q^3 + 7 * q^4 + 14 * q^6 + 7 * q^7 + 6 * q^8 - 4 * q^9 + 2 * q^11 - 28 * q^12 - 3 * q^13 - 3 * q^16 + 6 * q^17 - 5 * q^18 + q^19 - 21 * q^21 + 13 * q^22 + 19 * q^23 + 7 * q^24 + 5 * q^26 + 14 * q^27 - q^29 + 15 * q^31 - 14 * q^33 - 3 * q^34 + 21 * q^36 - 7 * q^37 - 11 * q^38 - 2 * q^41 - 10 * q^43 - 21 * q^44 - 20 * q^46 - 2 * q^47 - 14 * q^51 - 21 * q^52 - 26 * q^53 - 35 * q^54 - 7 * q^56 - 14 * q^57 + 11 * q^58 + 8 * q^59 + 17 * q^61 - 11 * q^62 - 7 * q^63 + 20 * q^64 + 21 * q^66 + 18 * q^67 + 14 * q^68 - 28 * q^69 + 34 * q^71 - 25 * q^72 - 16 * q^73 + 14 * q^74 + 28 * q^78 - 36 * q^79 - 30 * q^81 + 43 * q^82 + 8 * q^83 - 14 * q^84 - 44 * q^86 - 35 * q^87 + 30 * q^88 - 12 * q^89 - 42 * q^91 + 28 * q^92 - 14 * q^93 - 20 * q^94 - 35 * q^96 - 33 * q^97 - 21 * q^98 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	0.178448	−	0.781831i	0.126182	−	0.552838i	−0.871830	−	0.489809i	$-0.837067\pi$
$2$	0.178448	−	0.781831i	0.126182	−	0.552838i	0.998012	−	0.0630296i	$-0.0200763\pi$
$3$	−1.22252	+	0.588735i	−0.705823	+	0.339906i	−0.752124	−	0.659021i	$-0.770971\pi$
$3$	−1.22252	+	0.588735i	−0.705823	+	0.339906i	0.0463016	+	0.998928i	$0.485256\pi$
$4$	1.22252	+	0.588735i	0.611260	+	0.294368i
$5$		0			0
$5$		0			0
$6$	0.242135	+	1.06086i	0.0988513	+	0.433096i
$7$	4.27144	−	2.05702i	1.61445	−	0.777479i	0.614517	−	0.788903i	$-0.289351\pi$
$7$	4.27144	−	2.05702i	1.61445	−	0.777479i	0.999935	+	0.0114244i	$0.00363657\pi$
$8$	1.67845	−	2.10471i	0.593421	−	0.744126i
$9$	−0.722521	+	0.906013i	−0.240840	+	0.302004i
$10$		0			0
$11$	−0.568532	−	0.712916i	−0.171419	−	0.214952i	0.688700	−	0.725047i	$-0.258182\pi$
$11$	−0.568532	−	0.712916i	−0.171419	−	0.214952i	−0.860118	+	0.510094i	$0.829610\pi$
$12$	−1.84117			−0.531499
$13$	−3.71648	−	4.66032i	−1.03077	−	1.29254i	−0.955378	−	0.295386i	$-0.904552\pi$
$13$	−3.71648	−	4.66032i	−1.03077	−	1.29254i	−0.0753880	−	0.997154i	$-0.524020\pi$
$14$	−0.846011	−	3.70662i	−0.226106	−	0.990635i
$15$		0			0
$16$	0.346011	+	0.433884i	0.0865027	+	0.108471i
$17$	5.74094			1.39238			0.696191	−	0.717857i	$-0.254877\pi$
$17$	5.74094			1.39238			0.696191	+	0.717857i	$0.254877\pi$
$18$	0.579417	+	0.726566i	0.136570	+	0.171253i
$19$	−1.98039	−	0.953703i	−0.454332	−	0.218795i	0.192700	−	0.981258i	$-0.438276\pi$
$19$	−1.98039	−	0.953703i	−0.454332	−	0.218795i	−0.647032	+	0.762463i	$0.723990\pi$
$20$		0			0
$21$	−4.01089	+	5.02949i	−0.875247	+	1.09752i
$22$	−0.658834	+	0.317278i	−0.140464	+	0.0676438i
$23$	1.01961	+	4.46722i	0.212604	+	0.931480i	0.962789	+	0.270252i	$0.0871072\pi$
$23$	1.01961	+	4.46722i	0.212604	+	0.931480i	−0.750185	+	0.661228i	$0.770036\pi$
$24$	−0.812823	+	3.56121i	−0.165917	+	0.726929i
$25$		0			0
$26$	−4.30678	+	2.07404i	−0.844629	+	0.406752i
$27$	1.25571	−	5.50162i	0.241661	−	1.05879i
$28$	6.43296			1.21572
$29$	5.36443	−	0.472129i	0.996149	−	0.0876721i
$29$	5.36443	−	0.472129i	0.996149	−	0.0876721i
$30$		0			0
$31$	−0.548917	+	2.40496i	−0.0985885	+	0.431944i	−0.999999	−	0.00102013i	$-0.999675\pi$
$31$	−0.548917	+	2.40496i	−0.0985885	+	0.431944i	0.901411	+	0.432964i	$0.142532\pi$
$32$	5.25182	−	2.52915i	0.928400	−	0.447094i
$33$	1.11476	+	0.536840i	0.194055	+	0.0934519i
$34$	1.02446	−	4.48845i	0.175693	−	0.769762i
$35$		0			0
$36$	−1.41670	+	0.682246i	−0.236116	+	0.113708i
$37$	−4.94989	+	6.20696i	−0.813756	+	1.02042i	0.185530	+	0.982639i	$0.440600\pi$
$37$	−4.94989	+	6.20696i	−0.813756	+	1.02042i	−0.999286	+	0.0377795i	$0.987972\pi$
$38$	−1.09903	+	1.37814i	−0.178286	+	0.223564i
$39$	7.28717	+	3.50932i	1.16688	+	0.561940i
$40$		0			0
$41$	5.31767			0.830480			0.415240	−	0.909712i	$-0.363698\pi$
$41$	5.31767			0.830480			0.415240	+	0.909712i	$0.363698\pi$
$42$	3.21648	+	4.03334i	0.496314	+	0.622358i
$43$	−2.06584	−	9.05105i	−0.315038	−	1.38027i	−0.846138	−	0.532963i	$-0.821078\pi$
$43$	−2.06584	−	9.05105i	−0.315038	−	1.38027i	0.531100	−	0.847309i	$-0.321779\pi$
$44$	−0.275323	−	1.20627i	−0.0415065	−	0.181852i
$45$		0			0
$46$	3.67456			0.541785
$47$	−5.01842	−	6.29290i	−0.732011	−	0.917913i	0.266939	−	0.963713i	$-0.413988\pi$
$47$	−5.01842	−	6.29290i	−0.732011	−	0.917913i	−0.998951	+	0.0458000i	$0.985416\pi$
$48$	−0.678448	−	0.326723i	−0.0979255	−	0.0471584i
$49$	9.64944	−	12.1000i	1.37849	−	1.72857i
$50$		0			0
$51$	−7.01842	+	3.37989i	−0.982775	+	0.473280i
$52$	−1.79978	−	7.88536i	−0.249585	−	1.09350i
$53$	−1.39612	+	6.11682i	−0.191772	+	0.840210i	0.783884	+	0.620907i	$0.213236\pi$
$53$	−1.39612	+	6.11682i	−0.191772	+	0.840210i	−0.975657	+	0.219303i	$0.929622\pi$
$54$	−4.07726	−	1.96351i	−0.554845	−	0.267199i
$55$		0			0
$56$	2.83997	−	12.4427i	0.379507	−	1.66273i
$57$	2.98254			0.395047
$58$	0.588146	−	4.27833i	0.0772274	−	0.561772i
$59$	4.84548			0.630828			0.315414	−	0.948954i	$-0.397857\pi$
$59$	4.84548			0.630828			0.315414	+	0.948954i	$0.397857\pi$
$60$		0			0
$61$	3.79105	−	1.82567i	0.485395	−	0.233754i	−0.175148	−	0.984542i	$-0.556040\pi$
$61$	3.79105	−	1.82567i	0.485395	−	0.233754i	0.660543	+	0.750788i	$0.270326\pi$
$62$	1.78232	+	0.858322i	0.226355	+	0.109007i
$63$	−1.22252	+	5.35621i	−0.154023	+	0.674820i
$64$	−0.793209	−	3.47527i	−0.0991511	−	0.434409i
$65$		0			0
$66$	0.618645	−	0.775757i	0.0761500	−	0.0954891i
$67$	3.67845	−	4.61263i	0.449394	−	0.563522i	−0.504598	−	0.863354i	$-0.668359\pi$
$67$	3.67845	−	4.61263i	0.449394	−	0.563522i	0.953992	+	0.299832i	$0.0969307\pi$
$68$	7.01842	+	3.37989i	0.851108	+	0.409872i
$69$	−3.87651	−	4.86099i	−0.466677	−	0.585194i
$70$		0			0
$71$	6.91185	+	8.66719i	0.820286	+	1.02861i	0.999000	+	0.0447053i	$0.0142349\pi$
$71$	6.91185	+	8.66719i	0.820286	+	1.02861i	−0.178714	+	0.983901i	$0.557194\pi$
$72$	0.694177	+	3.04139i	0.0818096	+	0.358431i
$73$	−0.519614	−	2.27658i	−0.0608163	−	0.266453i	0.935374	−	0.353660i	$-0.115063\pi$
$73$	−0.519614	−	2.27658i	−0.0608163	−	0.266453i	−0.996190	+	0.0872067i	$0.972206\pi$
$74$	3.96950	+	4.97760i	0.461445	+	0.578634i
$75$		0			0
$76$	−1.85958	−	2.33184i	−0.213309	−	0.267481i
$77$	−3.89493	−	1.87570i	−0.443868	−	0.213756i
$78$	4.04407	−	5.07111i	0.457901	−	0.574190i
$79$	−5.66487	+	7.10353i	−0.637348	+	0.799209i	−0.990669	−	0.136293i	$-0.956481\pi$
$79$	−5.66487	+	7.10353i	−0.637348	+	0.799209i	0.353320	+	0.935502i	$0.385053\pi$
$80$		0			0
$81$	0.930272	+	4.07579i	0.103364	+	0.452865i
$82$	0.948927	−	4.15752i	0.104791	−	0.459121i
$83$	7.88620	+	3.79779i	0.865623	+	0.416862i	0.813353	−	0.581771i	$-0.197640\pi$
$83$	7.88620	+	3.79779i	0.865623	+	0.416862i	0.0522702	+	0.998633i	$0.483354\pi$
$84$	−7.86443	+	3.78731i	−0.858080	+	0.413229i
$85$		0			0
$86$	−7.44504			−0.802820
$87$	−6.28017	+	3.73541i	−0.673305	+	0.400478i
$88$	−2.45473			−0.261675
$89$	−2.00000	+	8.76257i	−0.212000	+	0.928831i	0.751207	+	0.660067i	$0.229472\pi$
$89$	−2.00000	+	8.76257i	−0.212000	+	0.928831i	−0.963206	+	0.268764i	$0.913385\pi$
$90$		0			0
$91$	−25.4611	−	12.2614i	−2.66905	−	1.28534i
$92$	−1.38351	+	6.06156i	−0.144241	+	0.631961i
$93$	−0.744824	−	3.26329i	−0.0772346	−	0.338387i
$94$	−5.81551	+	2.80060i	−0.599824	+	0.288860i
$95$		0			0
$96$	−4.93147	+	6.18387i	−0.503316	+	0.631138i
$97$	−9.39493	−	4.52436i	−0.953910	−	0.459379i	−0.108855	−	0.994058i	$-0.534718\pi$
$97$	−9.39493	−	4.52436i	−0.953910	−	0.459379i	−0.845055	+	0.534679i	$0.820433\pi$
$98$	−7.73825	−	9.70346i	−0.781681	−	0.980197i
$99$	1.05669			0.106201
$100$		0			0
$101$	0.109916	+	0.481575i	0.0109371	+	0.0479185i	0.980102	−	0.198494i	$-0.0636052\pi$
$101$	0.109916	+	0.481575i	0.0109371	+	0.0479185i	−0.969165	+	0.246413i	$0.920748\pi$
$102$	1.39008	+	6.09035i	0.137639	+	0.603035i
$103$	8.15130	+	10.2214i	0.803172	+	1.00715i	0.999645	+	0.0266362i	$0.00847955\pi$
$103$	8.15130	+	10.2214i	0.803172	+	1.00715i	−0.196474	+	0.980509i	$0.562949\pi$
$104$	−16.0465			−1.57349
$105$		0			0
$106$	4.53319	+	2.18307i	0.440302	+	0.212038i
$107$	−9.29321	+	11.6533i	−0.898408	+	1.12657i	0.0929870	+	0.995667i	$0.470358\pi$
$107$	−9.29321	+	11.6533i	−0.898408	+	1.12657i	−0.991395	+	0.130901i	$0.958213\pi$
$108$	4.77413	−	5.98657i	0.459391	−	0.576058i
$109$	−13.6223	+	6.56015i	−1.30478	+	0.628348i	−0.951638	−	0.307222i	$-0.900601\pi$
$109$	−13.6223	+	6.56015i	−1.30478	+	0.628348i	−0.353141	+	0.935570i	$0.614886\pi$
$110$		0			0
$111$	2.39708	−	10.5023i	0.227521	−	0.996835i
$112$	2.37047	+	1.14156i	0.223988	+	0.107867i
$113$	−13.9133	+	6.70031i	−1.30886	+	0.630313i	−0.952643	−	0.304092i	$-0.901647\pi$
$113$	−13.9133	+	6.70031i	−1.30886	+	0.630313i	−0.356215	+	0.934404i	$0.615933\pi$
$114$	0.532228	−	2.33184i	0.0498478	−	0.218397i
$115$		0			0
$116$	6.83609	+	2.58104i	0.634715	+	0.239644i
$117$	6.90754			0.638602
$118$	0.864666	−	3.78835i	0.0795989	−	0.348746i
$119$	24.5221	−	11.8092i	2.24793	−	1.08255i
$120$		0			0
$121$	2.26271	−	9.91358i	0.205701	−	0.901234i
$122$	−0.750864	−	3.28975i	−0.0679801	−	0.297840i
$123$	−6.50096	+	3.13070i	−0.586172	+	0.282285i
$124$	−2.08695	+	2.61695i	−0.187414	+	0.235009i
$125$		0			0
$126$	3.96950	+	1.91161i	0.353631	+	0.170300i
$127$	−0.408502	−	0.512245i	−0.0362487	−	0.0454544i	0.763377	−	0.645954i	$-0.223540\pi$
$127$	−0.408502	−	0.512245i	−0.0362487	−	0.0454544i	−0.799625	+	0.600499i	$0.794969\pi$
$128$	8.79954			0.777777
$129$	7.85421	+	9.84886i	0.691524	+	0.867144i
$130$		0			0
$131$	−1.57606	−	6.90519i	−0.137701	−	0.603309i	−0.995937	−	0.0900532i	$-0.971296\pi$
$131$	−1.57606	−	6.90519i	−0.137701	−	0.603309i	0.858236	−	0.513256i	$-0.171561\pi$
$132$	1.04676	+	1.31260i	0.0911089	+	0.114247i
$133$	−10.4209			−0.903605
$134$	−2.94989	−	3.69904i	−0.254831	−	0.319548i
$135$		0			0
$136$	9.63587	−	12.0830i	0.826269	−	1.03611i
$137$	−1.03199	+	1.29408i	−0.0881690	+	0.110560i	−0.823959	−	0.566649i	$-0.808240\pi$
$137$	−1.03199	+	1.29408i	−0.0881690	+	0.110560i	0.735790	+	0.677210i	$0.236811\pi$
$138$	−4.49223	+	2.16334i	−0.382404	+	0.184156i
$139$	2.69202	+	11.7945i	0.228334	+	1.00040i	0.950998	+	0.309198i	$0.100061\pi$
$139$	2.69202	+	11.7945i	0.228334	+	1.00040i	−0.722663	+	0.691200i	$0.757082\pi$
$140$		0			0
$141$	9.83997	+	4.73868i	0.828675	+	0.399069i
$142$	8.00969	−	3.85726i	0.672158	−	0.323694i
$143$	−1.20948	+	5.29908i	−0.101142	+	0.443131i
$144$	−0.643104			−0.0535920
$145$		0			0
$146$	−1.87263			−0.154980
$147$	−4.67294	+	20.4735i	−0.385418	+	1.68862i
$148$	−9.70560	+	4.67397i	−0.797795	+	0.384198i
$149$	−18.6739	−	8.99288i	−1.52983	−	0.736725i	−0.535644	−	0.844444i	$-0.679931\pi$
$149$	−18.6739	−	8.99288i	−1.52983	−	0.736725i	−0.994181	+	0.107719i	$0.965645\pi$
$150$		0			0
$151$	0.656145	+	2.87476i	0.0533963	+	0.233945i	0.994583	−	0.103941i	$-0.0331454\pi$
$151$	0.656145	+	2.87476i	0.0533963	+	0.233945i	−0.941187	+	0.337886i	$0.890288\pi$
$152$	−5.33124	+	2.56739i	−0.432421	+	0.208243i
$153$	−4.14795	+	5.20136i	−0.335342	+	0.420505i
$154$	−2.16152	+	2.71046i	−0.174180	+	0.218415i
$155$		0			0
$156$	6.84266	+	8.58042i	0.547851	+	0.686984i
$157$	−9.69202			−0.773508			−0.386754	−	0.922183i	$-0.626404\pi$
$157$	−9.69202			−0.773508			−0.386754	+	0.922183i	$0.626404\pi$
$158$	4.54288	+	5.69659i	0.361412	+	0.453196i
$159$	−1.89440	−	8.29989i	−0.150235	−	0.658224i
$160$		0			0
$161$	13.5444	+	16.9841i	1.06745	+	1.33853i
$162$	3.35258			0.263404
$163$	−4.59299	−	5.75943i	−0.359751	−	0.451113i	0.568713	−	0.822536i	$-0.307441\pi$
$163$	−4.59299	−	5.75943i	−0.359751	−	0.451113i	−0.928464	+	0.371423i	$0.878870\pi$
$164$	6.50096	+	3.13070i	0.507640	+	0.244466i
$165$		0			0
$166$	4.37651	−	5.48797i	0.339683	−	0.425949i
$167$	7.80678	−	3.75955i	0.604107	−	0.290923i	−0.106720	−	0.994289i	$-0.534035\pi$
$167$	7.80678	−	3.75955i	0.604107	−	0.290923i	0.710827	+	0.703366i	$0.248321\pi$
$168$	3.85354	+	16.8835i	0.297307	+	1.30259i
$169$	−5.01357	+	21.9659i	−0.385660	+	1.68968i
$170$		0			0
$171$	2.29494	−	1.10518i	0.175498	−	0.0845155i
$172$	2.80313	−	12.2813i	0.213737	−	0.936443i
$173$	−7.64310			−0.581094			−0.290547	−	0.956861i	$-0.593837\pi$
$173$	−7.64310			−0.581094			−0.290547	+	0.956861i	$0.593837\pi$
$174$	1.79978	+	5.57661i	0.136441	+	0.422762i
$175$		0			0
$176$	0.112605	−	0.493353i	0.00848790	−	0.0371879i
$177$	−5.92370	+	2.85270i	−0.445252	+	0.214422i
$178$	6.49396	+	3.12733i	0.486743	+	0.234403i
$179$	0.635571	−	2.78462i	0.0475048	−	0.208132i	−0.945605	−	0.325316i	$-0.894529\pi$
$179$	0.635571	−	2.78462i	0.0475048	−	0.208132i	0.993110	+	0.117183i	$0.0373866\pi$
$180$		0			0
$181$	−0.306782	+	0.147738i	−0.0228029	+	0.0109813i	−0.445250	−	0.895406i	$-0.646885\pi$
$181$	−0.306782	+	0.147738i	−0.0228029	+	0.0109813i	0.422448	+	0.906387i	$0.361171\pi$
$182$	−14.1298	+	17.7182i	−1.04737	+	1.31336i
$183$	−3.55980	+	4.46385i	−0.263148	+	0.329977i
$184$	11.1136	+	5.35201i	0.819303	+	0.394555i
$185$		0			0
$186$	−2.68425			−0.196819
$187$	−3.26391	−	4.09281i	−0.238680	−	0.299296i
$188$	−2.43027	−	10.6477i	−0.177246	−	0.776565i
$189$	−5.95324	−	26.0828i	−0.433034	−	1.89725i
$190$		0			0
$191$	−6.06531			−0.438870			−0.219435	−	0.975627i	$-0.570421\pi$
$191$	−6.06531			−0.438870			−0.219435	+	0.975627i	$0.570421\pi$
$192$	3.01573	+	3.78161i	0.217642	+	0.272914i
$193$	−14.3910	−	6.93036i	−1.03589	−	0.498858i	−0.162924	−	0.986639i	$-0.552092\pi$
$193$	−14.3910	−	6.93036i	−1.03589	−	0.498858i	−0.872966	+	0.487780i	$0.837807\pi$
$194$	−5.21379	+	6.53789i	−0.374328	+	0.469393i
$195$		0			0
$196$	18.9203	−	9.11156i	1.35145	−	0.650826i
$197$	3.89762	+	17.0766i	0.277694	+	1.21666i	0.900701	+	0.434440i	$0.143054\pi$
$197$	3.89762	+	17.0766i	0.277694	+	1.21666i	−0.623007	+	0.782216i	$0.714089\pi$
$198$	0.188564	−	0.826151i	0.0134006	−	0.0587120i
$199$	−2.52930	−	1.21805i	−0.179298	−	0.0863451i	0.342082	−	0.939670i	$-0.388868\pi$
$199$	−2.52930	−	1.21805i	−0.179298	−	0.0863451i	−0.521379	+	0.853325i	$0.674582\pi$
$200$		0			0
$201$	−1.78136	+	7.80467i	−0.125648	+	0.550499i
$202$	0.396125			0.0278712
$203$	21.9426	−	13.0514i	1.54007	−	0.916028i
$204$	−10.5700			−0.740050
$205$		0			0
$206$	9.44600	−	4.54895i	0.658134	−	0.316941i
$207$	−4.78405	−	2.30388i	−0.332515	−	0.160131i
$208$	0.736094	−	3.22504i	0.0510390	−	0.223616i
$209$	0.446001	+	1.95406i	0.0308506	+	0.135165i
$210$		0			0
$211$	−11.3312	+	14.2089i	−0.780075	+	0.978183i	0.219922	+	0.975518i	$0.429420\pi$
$211$	−11.3312	+	14.2089i	−0.780075	+	0.978183i	−0.999996	+	0.00266530i	$0.999152\pi$
$212$	−5.30798	+	6.65599i	−0.364553	+	0.457136i
$213$	−13.5526	−	6.52657i	−0.928606	−	0.447193i
$214$	7.45257	+	9.34523i	0.509448	+	0.638827i
$215$		0			0
$216$	−9.47166	−	11.8771i	−0.644465	−	0.808133i
$217$	2.60238	+	11.4018i	0.176661	+	0.774004i
$218$	2.69806	+	11.8210i	0.182736	+	0.800618i
$219$	1.97554	+	2.47725i	0.133495	+	0.167397i
$220$		0			0
$221$	−21.3361	−	26.7546i	−1.43522	−	1.79971i
$222$	−7.78328	−	3.74823i	−0.522380	−	0.251565i
$223$	−1.21313	+	1.52121i	−0.0812370	+	0.101868i	−0.820789	−	0.571231i	$-0.806466\pi$
$223$	−1.21313	+	1.52121i	−0.0812370	+	0.101868i	0.739552	+	0.673099i	$0.235037\pi$
$224$	17.2303	−	21.6062i	1.15125	−	1.44362i
$225$		0			0
$226$	2.75571	+	12.0735i	0.183307	+	0.803121i
$227$	−1.42758	+	6.25465i	−0.0947520	+	0.415136i	−0.999951	−	0.00985122i	$-0.996864\pi$
$227$	−1.42758	+	6.25465i	−0.0947520	+	0.415136i	0.905199	+	0.424987i	$0.139721\pi$
$228$	3.64622	+	1.75593i	0.241477	+	0.116289i
$229$	−5.91454	+	2.84829i	−0.390844	+	0.188221i	−0.618976	−	0.785410i	$-0.712452\pi$
$229$	−5.91454	+	2.84829i	−0.390844	+	0.188221i	0.228132	+	0.973630i	$0.426738\pi$
$230$		0			0
$231$	5.86592			0.385949
$232$	8.01022	−	12.0830i	0.525897	−	0.793287i
$233$	3.37435			0.221061			0.110531	−	0.993873i	$-0.464745\pi$
$233$	3.37435			0.221061			0.110531	+	0.993873i	$0.464745\pi$
$234$	1.23264	−	5.40053i	0.0805800	−	0.353044i
$235$		0			0
$236$	5.92370	+	2.85270i	0.385600	+	0.185695i
$237$	2.74333	−	12.0193i	0.178199	−	0.780739i
$238$	−4.85690	−	21.2795i	−0.314826	−	1.37934i
$239$	10.0271	−	4.82882i	0.648602	−	0.312350i	−0.0805006	−	0.996755i	$-0.525652\pi$
$239$	10.0271	−	4.82882i	0.648602	−	0.312350i	0.729103	+	0.684404i	$0.239938\pi$
$240$		0			0
$241$	−3.34266	+	4.19156i	−0.215320	+	0.270002i	−0.877748	−	0.479123i	$-0.840955\pi$
$241$	−3.34266	+	4.19156i	−0.215320	+	0.270002i	0.662428	+	0.749126i	$0.269526\pi$
$242$	−7.34697	−	3.53811i	−0.472281	−	0.227439i
$243$	7.01842	+	8.80082i	0.450232	+	0.564573i
$244$	5.70948			0.365512
$245$		0			0
$246$	1.28759	+	5.64132i	0.0820940	+	0.359678i
$247$	2.91550	+	12.7736i	0.185509	+	0.812768i
$248$	4.14042	+	5.19192i	0.262917	+	0.329687i
$249$	−11.8769			−0.752670
$250$		0			0
$251$	−1.60776	−	0.774257i	−0.101481	−	0.0488706i	0.382455	−	0.923974i	$-0.375079\pi$
$251$	−1.60776	−	0.774257i	−0.101481	−	0.0488706i	−0.483936	+	0.875104i	$0.660793\pi$
$252$	−4.64795	+	5.82834i	−0.292793	+	0.367151i
$253$	2.60507	−	3.26666i	0.163779	−	0.205373i
$254$	−0.473385	+	0.227970i	−0.0297028	+	0.0143041i
$255$		0			0
$256$	3.15668	−	13.8303i	0.197292	−	0.864394i
$257$	−13.9378	−	6.71209i	−0.869416	−	0.418689i	−0.0546687	−	0.998505i	$-0.517410\pi$
$257$	−13.9378	−	6.71209i	−0.869416	−	0.418689i	−0.814748	+	0.579816i	$0.803125\pi$
$258$	9.10172	−	4.38316i	0.566648	−	0.272883i
$259$	−8.37531	+	36.6946i	−0.520417	+	2.28009i
$260$		0			0
$261$	−3.44816	+	5.20136i	−0.213436	+	0.321956i
$262$	−5.67994			−0.350908
$263$	2.33124	−	10.2138i	0.143750	−	0.629812i	−0.850794	−	0.525499i	$-0.823879\pi$
$263$	2.33124	−	10.2138i	0.143750	−	0.629812i	0.994545	−	0.104313i	$-0.0332643\pi$
$264$	3.00096	−	1.44519i	0.184696	−	0.0889450i
$265$		0			0
$266$	−1.85958	+	8.14737i	−0.114018	+	0.499547i
$267$	−2.71379	−	11.8899i	−0.166081	−	0.727650i
$268$	7.21260	−	3.47340i	0.440579	−	0.212172i
$269$	9.12983	−	11.4484i	0.556655	−	0.698024i	−0.421280	−	0.906931i	$-0.638419\pi$
$269$	9.12983	−	11.4484i	0.556655	−	0.698024i	0.977936	+	0.208907i	$0.0669905\pi$
$270$		0			0
$271$	13.3046	+	6.40717i	0.808198	+	0.389208i	0.791894	−	0.610659i	$-0.209095\pi$
$271$	13.3046	+	6.40717i	0.808198	+	0.389208i	0.0163050	+	0.999867i	$0.494810\pi$
$272$	1.98643	+	2.49090i	0.120445	+	0.151033i
$273$	38.3454			2.32077
$274$	0.827593	+	1.03777i	0.0499967	+	0.0626939i
$275$		0			0
$276$	−1.87728	−	8.22490i	−0.112999	−	0.495081i
$277$	1.57942	+	1.98053i	0.0948980	+	0.118998i	0.827013	−	0.562183i	$-0.190038\pi$
$277$	1.57942	+	1.98053i	0.0948980	+	0.118998i	−0.732115	+	0.681181i	$0.761467\pi$
$278$	9.70171			0.581870
$279$	−1.78232	−	2.23496i	−0.106705	−	0.133804i
$280$		0			0
$281$	−9.27628	+	11.6321i	−0.553377	+	0.693912i	−0.977318	−	0.211777i	$-0.932075\pi$
$281$	−9.27628	+	11.6321i	−0.553377	+	0.693912i	0.423941	+	0.905690i	$0.360646\pi$
$282$	5.46077	−	6.84759i	0.325184	−	0.407768i
$283$	−21.2838	+	10.2497i	−1.26519	+	0.609284i	−0.941543	−	0.336893i	$-0.890624\pi$
$283$	−21.2838	+	10.2497i	−1.26519	+	0.609284i	−0.323649	+	0.946177i	$0.604910\pi$
$284$	3.34721	+	14.6651i	0.198620	+	0.870212i
$285$		0			0
$286$	3.92716	+	1.89122i	0.232218	+	0.111830i
$287$	22.7141	−	10.9385i	1.34077	−	0.645681i
$288$	−1.50312	+	6.58558i	−0.0885719	+	0.388059i
$289$	15.9584			0.938728
$290$		0			0
$291$	14.1491			0.829438
$292$	0.705063	−	3.08908i	0.0412607	−	0.180775i
$293$	−19.1603	+	9.22713i	−1.11936	+	0.539054i	−0.899694	−	0.436521i	$-0.856210\pi$
$293$	−19.1603	+	9.22713i	−1.11936	+	0.539054i	−0.219664	+	0.975576i	$0.570496\pi$
$294$	15.1729	+	7.30690i	0.884904	+	0.426147i
$295$		0			0
$296$	4.75571	+	20.8361i	0.276420	+	1.21107i
$297$	−4.63610	+	2.23263i	−0.269014	+	0.129550i
$298$	−10.3632	+	12.9951i	−0.600326	+	0.752785i
$299$	17.0293	−	21.3541i	0.984830	−	1.23494i
$300$		0			0
$301$	−27.4423	−	34.4115i	−1.58175	−	1.98345i
$302$	2.36467			0.136071
$303$	−0.417895	−	0.524023i	−0.0240074	−	0.0301044i
$304$	−0.271438	−	1.18925i	−0.0155681	−	0.0682081i
$305$		0			0
$306$	3.32640	+	4.17117i	0.190157	+	0.238450i
$307$	9.22952			0.526757			0.263378	−	0.964693i	$-0.415163\pi$
$307$	9.22952			0.526757			0.263378	+	0.964693i	$0.415163\pi$
$308$	−3.65734	−	4.58616i	−0.208396	−	0.261321i
$309$	−15.9828	−	7.69693i	−0.909232	−	0.437863i
$310$		0			0
$311$	15.8162	−	19.8329i	0.896853	−	1.12462i	−0.0947760	−	0.995499i	$-0.530213\pi$
$311$	15.8162	−	19.8329i	0.896853	−	1.12462i	0.991629	−	0.129119i	$-0.0412151\pi$
$312$	19.6172	−	9.44715i	1.11061	−	0.534840i
$313$	−2.19806	−	9.63034i	−0.124242	−	0.544339i	−0.998288	−	0.0584955i	$-0.981370\pi$
$313$	−2.19806	−	9.63034i	−0.124242	−	0.544339i	0.874046	−	0.485843i	$-0.161487\pi$
$314$	−1.72952	+	7.57753i	−0.0976025	+	0.427625i
$315$		0			0
$316$	−11.1075	+	5.34910i	−0.624847	+	0.300910i
$317$	3.60872	−	15.8108i	0.202686	−	0.888025i	−0.766607	−	0.642116i	$-0.778057\pi$
$317$	3.60872	−	15.8108i	0.202686	−	0.888025i	0.969293	−	0.245909i	$-0.0790863\pi$
$318$	−6.82717			−0.382848
$319$	−3.38644	−	3.55597i	−0.189604	−	0.199096i
$320$		0			0
$321$	4.50043	−	19.7177i	0.251189	−	1.10053i
$322$	15.6957	−	7.55864i	0.874685	−	0.421226i
$323$	−11.3693	−	5.47515i	−0.632603	−	0.304646i
$324$	−1.26228	+	5.53042i	−0.0701268	+	0.307246i
$325$		0			0
$326$	−5.32251	+	2.56319i	−0.294787	+	0.141962i
$327$	12.7913	−	16.0398i	0.707363	−	0.887005i
$328$	8.92543	−	11.1921i	0.492824	−	0.617982i
$329$	−34.3805	−	16.5568i	−1.89546	−	0.912803i
$330$		0			0
$331$	−5.14377			−0.282727			−0.141364	−	0.989958i	$-0.545149\pi$
$331$	−5.14377			−0.282727			−0.141364	+	0.989958i	$0.545149\pi$
$332$	7.40515	+	9.28576i	0.406410	+	0.509622i
$333$	−2.04719	−	8.96932i	−0.112185	−	0.491516i
$334$	−1.54623	−	6.77447i	−0.0846059	−	0.370683i
$335$		0			0
$336$	−3.57002			−0.194761
$337$	−16.9303	−	21.2299i	−0.922251	−	1.15647i	−0.987345	−	0.158587i	$-0.949306\pi$
$337$	−16.9303	−	21.2299i	−0.922251	−	1.15647i	0.0650944	−	0.997879i	$-0.479265\pi$
$338$	16.2790	+	7.83954i	0.885459	+	0.426415i
$339$	13.0646	−	16.3825i	0.709574	−	0.889778i
$340$		0			0
$341$	2.02661	−	0.975966i	0.109747	−	0.0528515i
$342$	−0.454541	−	1.99147i	−0.0245787	−	0.107686i
$343$	8.94235	−	39.1790i	0.482842	−	2.11547i
$344$	−22.5172	−	10.8437i	−1.21405	−	0.584654i
$345$		0			0
$346$	−1.36390	+	5.97562i	−0.0733235	+	0.321251i
$347$	25.8756			1.38908			0.694538	−	0.719456i	$-0.255609\pi$
$347$	25.8756			1.38908			0.694538	+	0.719456i	$0.255609\pi$
$348$	−9.87681	+	0.869268i	−0.529452	+	0.0465976i
$349$	16.4101			0.878414			0.439207	−	0.898386i	$-0.355259\pi$
$349$	16.4101			0.878414			0.439207	+	0.898386i	$0.355259\pi$
$350$		0			0
$351$	−30.3061	+	14.5947i	−1.61762	+	0.779005i
$352$	−4.78890	−	2.30621i	−0.255249	−	0.122921i
$353$	−5.00580	+	21.9319i	−0.266432	+	1.16732i	0.647699	+	0.761896i	$0.275731\pi$
$353$	−5.00580	+	21.9319i	−0.266432	+	1.16732i	−0.914131	+	0.405419i	$0.867126\pi$
$354$	1.17326	+	5.14039i	0.0623581	+	0.273209i
$355$		0			0
$356$	−7.60388	+	9.53496i	−0.403005	+	0.505352i
$357$	−23.0262	+	28.8740i	−1.21868	+	1.52817i
$358$	−2.06369	−	0.993819i	−0.109069	−	0.0525250i
$359$	7.24764	+	9.08826i	0.382516	+	0.479660i	0.935396	−	0.353601i	$-0.115043\pi$
$359$	7.24764	+	9.08826i	0.382516	+	0.479660i	−0.552880	+	0.833261i	$0.686471\pi$
$360$		0			0
$361$	−8.83393	−	11.0774i	−0.464944	−	0.583021i
$362$	0.0607620	+	0.266216i	0.00319358	+	0.0139920i
$363$	3.07026	+	13.4517i	0.161147	+	0.706031i
$364$	−23.9080	−	29.9796i	−1.25312	−	1.57136i
$365$		0			0
$366$	2.85474	+	3.57973i	0.149220	+	0.187116i
$367$	17.4731	+	8.41462i	0.912091	+	0.439240i	0.830241	−	0.557405i	$-0.188203\pi$
$367$	17.4731	+	8.41462i	0.912091	+	0.439240i	0.0818501	+	0.996645i	$0.473917\pi$
$368$	−1.58546	+	1.98810i	−0.0826477	+	0.103637i
$369$	−3.84213	+	4.81787i	−0.200013	+	0.250808i
$370$		0			0
$371$	6.61894	+	28.9995i	0.343638	+	1.50558i
$372$	1.01065	−	4.42794i	0.0523997	−	0.229578i
$373$	24.9496	+	12.0151i	1.29184	+	0.622119i	0.948407	−	0.317056i	$-0.102694\pi$
$373$	24.9496	+	12.0151i	1.29184	+	0.622119i	0.343437	+	0.939176i	$0.388409\pi$
$374$	−3.78232	+	1.82147i	−0.195579	+	0.0941860i
$375$		0			0
$376$	−21.6679			−1.11743
$377$	−22.1371	−	23.2453i	−1.14012	−	1.19719i
$378$	−21.4547			−1.10351
$379$	0.603875	−	2.64575i	0.0310190	−	0.135903i	−0.957047	−	0.289931i	$-0.906368\pi$
$379$	0.603875	−	2.64575i	0.0310190	−	0.135903i	0.988066	+	0.154028i	$0.0492247\pi$
$380$		0			0
$381$	0.800978	+	0.385731i	0.0410354	+	0.0197616i
$382$	−1.08234	+	4.74205i	−0.0553774	+	0.242624i
$383$	4.74482	+	20.7884i	0.242449	+	1.06224i	0.938780	+	0.344518i	$0.111958\pi$
$383$	4.74482	+	20.7884i	0.242449	+	1.06224i	−0.696331	+	0.717721i	$0.745185\pi$
$384$	−10.7576	+	5.18060i	−0.548973	+	0.264371i
$385$		0			0
$386$	−7.98643	+	10.0147i	−0.406498	+	0.509733i
$387$	9.69298	+	4.66789i	0.492722	+	0.237282i
$388$	−8.82185	−	11.0622i	−0.447861	−	0.561601i
$389$	−9.23251			−0.468107			−0.234053	−	0.972224i	$-0.575199\pi$
$389$	−9.23251			−0.468107			−0.234053	+	0.972224i	$0.575199\pi$
$390$		0			0
$391$	5.85354	+	25.6460i	0.296026	+	1.29698i
$392$	−9.27091	−	40.6185i	−0.468251	−	2.05154i
$393$	5.99210	+	7.51385i	0.302261	+	0.379024i
$394$	14.0465			0.707654
$395$		0			0
$396$	1.29182	+	0.622109i	0.0649165	+	0.0312621i
$397$	3.63251	−	4.55503i	0.182311	−	0.228610i	−0.682275	−	0.731095i	$-0.739009\pi$
$397$	3.63251	−	4.55503i	0.182311	−	0.228610i	0.864586	+	0.502485i	$0.167581\pi$
$398$	−1.40366	+	1.76013i	−0.0703590	+	0.0882274i
$399$	12.7397	−	6.13514i	0.637785	−	0.307141i
$400$		0			0
$401$	−8.63079	+	37.8139i	−0.431001	+	1.88834i	0.0274588	+	0.999623i	$0.491259\pi$
$401$	−8.63079	+	37.8139i	−0.431001	+	1.88834i	−0.458460	+	0.888715i	$0.651599\pi$
$402$	5.78405	+	2.78545i	0.288482	+	0.138926i
$403$	13.2479	−	6.37987i	0.659927	−	0.317804i
$404$	−0.149145	+	0.653447i	−0.00742024	+	0.0325102i
$405$		0			0
$406$	−6.28836	−	19.4844i	−0.312086	−	0.966997i
$407$	7.23921			0.358834
$408$	−4.66637	+	20.4447i	−0.231020	+	1.01216i
$409$	4.18210	−	2.01399i	0.206791	−	0.0995855i	−0.327621	−	0.944809i	$-0.606247\pi$
$409$	4.18210	−	2.01399i	0.206791	−	0.0995855i	0.534413	+	0.845224i	$0.320533\pi$
$410$		0			0
$411$	0.499763	−	2.18960i	0.0246515	−	0.108005i
$412$	3.94743	+	17.2948i	0.194476	+	0.852056i
$413$	20.6972	−	9.96723i	1.01844	−	0.490455i
$414$	−2.65495	+	3.32920i	−0.130484	+	0.163621i
$415$		0			0
$416$	−31.3049	−	15.0757i	−1.53485	−	0.739145i
$417$	−10.2349	−	12.8342i	−0.501205	−	0.628491i
$418$	1.60733			0.0786172
$419$	8.79404	+	11.0274i	0.429617	+	0.538722i	0.948774	−	0.315957i	$-0.102325\pi$
$419$	8.79404	+	11.0274i	0.429617	+	0.538722i	−0.519157	+	0.854679i	$0.673754\pi$
$420$		0			0
$421$	−3.18880	−	13.9710i	−0.155413	−	0.680907i	−0.991258	−	0.131942i	$-0.957879\pi$
$421$	−3.18880	−	13.9710i	−0.155413	−	0.680907i	0.835845	−	0.548966i	$-0.184978\pi$
$422$	9.08695	+	11.3947i	0.442346	+	0.554684i
$423$	9.32736			0.453512
$424$	10.5308	+	13.2052i	0.511421	+	0.641301i
$425$		0			0
$426$	−7.52111	+	9.43117i	−0.364399	+	0.456942i
$427$	12.4378	−	15.5965i	0.601908	−	0.754768i
$428$	−18.2219	+	8.77518i	−0.880787	+	0.424165i
$429$	−1.64114	−	7.19030i	−0.0792349	−	0.347151i
$430$		0			0
$431$	−3.73341	−	1.79791i	−0.179832	−	0.0866025i	0.341802	−	0.939772i	$-0.388963\pi$
$431$	−3.73341	−	1.79791i	−0.179832	−	0.0866025i	−0.521634	+	0.853170i	$0.674677\pi$
$432$	2.82155	−	1.35879i	0.135752	−	0.0653747i
$433$	7.75882	−	33.9936i	0.372865	−	1.63363i	−0.345825	−	0.938299i	$-0.612401\pi$
$433$	7.75882	−	33.9936i	0.372865	−	1.63363i	0.718690	−	0.695331i	$-0.244742\pi$
$434$	9.37867			0.450190
$435$		0			0
$436$	−20.5157			−0.982525
$437$	2.24118	−	9.81923i	0.107210	−	0.469718i
$438$	2.28932	−	1.10248i	0.109388	−	0.0526785i
$439$	−4.76875	−	2.29651i	−0.227600	−	0.109606i	0.316609	−	0.948556i	$-0.397456\pi$
$439$	−4.76875	−	2.29651i	−0.227600	−	0.109606i	−0.544209	+	0.838950i	$0.683170\pi$
$440$		0			0
$441$	3.99084	+	17.4850i	0.190040	+	0.832620i
$442$	−24.7250	+	11.9069i	−1.17605	+	0.566354i
$443$	−5.45675	+	6.84255i	−0.259258	+	0.325100i	−0.894376	−	0.447316i	$-0.852380\pi$
$443$	−5.45675	+	6.84255i	−0.259258	+	0.325100i	0.635118	+	0.772415i	$0.280951\pi$
$444$	9.11356	−	11.4280i	0.432511	−	0.542351i
$445$		0			0
$446$	0.972853	+	1.21992i	0.0460659	+	0.0577648i
$447$	28.1237			1.33020
$448$	−10.5368	−	13.2128i	−0.497819	−	0.624245i
$449$	6.77509	+	29.6836i	0.319736	+	1.40086i	0.838017	+	0.545645i	$0.183715\pi$
$449$	6.77509	+	29.6836i	0.319736	+	1.40086i	−0.518281	+	0.855211i	$0.673428\pi$
$450$		0			0
$451$	−3.02326	−	3.79105i	−0.142360	−	0.178514i
$452$	−20.9541			−0.985596
$453$	−2.49462	−	3.12816i	−0.117208	−	0.146974i
$454$	4.63533	+	2.23226i	0.217547	+	0.104765i
$455$		0			0
$456$	5.00604	−	6.27738i	0.234429	−	0.293965i
$457$	−9.13802	+	4.40064i	−0.427459	+	0.205853i	−0.635228	−	0.772325i	$-0.719094\pi$
$457$	−9.13802	+	4.40064i	−0.427459	+	0.205853i	0.207769	+	0.978178i	$0.433380\pi$
$458$	1.17145	+	5.13245i	0.0547382	+	0.239824i
$459$	7.20895	−	31.5845i	0.336485	−	1.47424i
$460$		0			0
$461$	21.5378	−	10.3721i	1.00312	−	0.483075i	0.141121	−	0.989992i	$-0.454929\pi$
$461$	21.5378	−	10.3721i	1.00312	−	0.483075i	0.861995	+	0.506918i	$0.169215\pi$
$462$	1.04676	−	4.58616i	0.0486997	−	0.213368i
$463$	36.7144			1.70626			0.853131	−	0.521697i	$-0.174701\pi$
$463$	36.7144			1.70626			0.853131	+	0.521697i	$0.174701\pi$
$464$	2.06100	+	2.16418i	0.0956795	+	0.100469i
$465$		0			0
$466$	0.602147	−	2.63818i	0.0278939	−	0.122211i
$467$	−10.4889	+	5.05118i	−0.485367	+	0.233741i	−0.660531	−	0.750799i	$-0.729669\pi$
$467$	−10.4889	+	5.05118i	−0.485367	+	0.233741i	0.175164	+	0.984539i	$0.443955\pi$
$468$	8.44461	+	4.06671i	0.390352	+	0.187984i
$469$	6.22401	−	27.2692i	0.287398	−	1.25917i
$470$		0			0
$471$	11.8487	−	5.70603i	0.545959	−	0.262920i
$472$	8.13288	−	10.1983i	0.374346	−	0.469415i
$473$	−5.27814	+	6.61858i	−0.242689	+	0.304323i
$474$	−8.90754	−	4.28965i	−0.409137	−	0.197030i
$475$		0			0
$476$	36.9312			1.69274
$477$	−4.53319	−	5.68444i	−0.207560	−	0.260273i
$478$	−1.98600	−	8.70123i	−0.0908375	−	0.397985i
$479$	5.70679	+	25.0031i	0.260750	+	1.14242i	0.920440	+	0.390883i	$0.127830\pi$
$479$	5.70679	+	25.0031i	0.260750	+	1.14242i	−0.659690	+	0.751537i	$0.729313\pi$
$480$		0			0
$481$	47.3226			2.15772
$482$	2.68060	+	3.36137i	0.122098	+	0.153106i
$483$	−26.5574	−	12.7894i	−1.20840	−	0.581937i
$484$	8.60268	−	10.7874i	0.391031	−	0.490337i
$485$		0			0
$486$	8.13318	−	3.91673i	0.368928	−	0.177667i
$487$	8.29978	+	36.3637i	0.376099	+	1.64780i	0.709274	+	0.704933i	$0.249023\pi$
$487$	8.29978	+	36.3637i	0.376099	+	1.64780i	−0.333175	+	0.942865i	$0.608120\pi$
$488$	2.52057	−	11.0434i	0.114101	−	0.499909i
$489$	9.00580	+	4.33697i	0.407257	+	0.196124i
$490$		0			0
$491$	3.01118	−	13.1928i	0.135893	−	0.595385i	−0.860420	−	0.509586i	$-0.829799\pi$
$491$	3.01118	−	13.1928i	0.135893	−	0.595385i	0.996312	−	0.0857989i	$-0.0273442\pi$
$492$	−9.79071			−0.441399
$493$	30.7969	−	2.71046i	1.38702	−	0.122073i
$494$	10.5071			0.472737
$495$		0			0
$496$	−1.23341	+	0.593977i	−0.0553816	+	0.0266704i
$497$	47.3521	+	22.8036i	2.12403	+	1.02288i
$498$	−2.11941	+	9.28576i	−0.0949733	+	0.416105i
$499$	6.38069	+	27.9556i	0.285639	+	1.25147i	0.890444	+	0.455093i	$0.150394\pi$
$499$	6.38069	+	27.9556i	0.285639	+	1.25147i	−0.604805	+	0.796373i	$0.706749\pi$
$500$		0			0
$501$	−7.33058	+	9.19225i	−0.327506	+	0.410680i
$502$	−0.892240	+	1.11883i	−0.0398226	+	0.0499360i
$503$	−37.7962	−	18.2017i	−1.68525	−	0.811573i	−0.996223	−	0.0868368i	$-0.972324\pi$
$503$	−37.7962	−	18.2017i	−1.68525	−	0.811573i	−0.689026	−	0.724736i	$-0.741962\pi$
$504$	9.22132	+	11.5632i	0.410750	+	0.515065i
$505$		0			0
$506$	−2.08911	−	2.61966i	−0.0928721	−	0.116458i
$507$	−6.80290	−	29.8054i	−0.302127	−	1.32371i
$508$	−0.197825	−	0.866729i	−0.00877708	−	0.0384549i
$509$	−27.5296	−	34.5210i	−1.22023	−	1.53012i	−0.771190	−	0.636605i	$-0.780338\pi$
$509$	−27.5296	−	34.5210i	−1.22023	−	1.53012i	−0.449038	−	0.893513i	$-0.648233\pi$
$510$		0			0
$511$	−6.90246	−	8.65541i	−0.305347	−	0.382893i
$512$	5.60656	+	2.69998i	0.247777	+	0.119323i
$513$	−7.73370	+	9.69776i	−0.341451	+	0.428166i
$514$	−7.73490	+	9.69926i	−0.341172	+	0.427816i
$515$		0			0
$516$	3.80356	+	16.6645i	0.167442	+	0.733613i
$517$	−1.63318	+	7.15542i	−0.0718271	+	0.314695i
$518$	27.1945	+	13.0962i	1.19486	+	0.575413i
$519$	9.34385	−	4.49976i	0.410150	−	0.197518i
$520$		0			0
$521$	27.1159			1.18797			0.593984	−	0.804477i	$-0.297554\pi$
$521$	27.1159			1.18797			0.593984	+	0.804477i	$0.297554\pi$
$522$	3.45127	+	3.62405i	0.151058	+	0.158620i
$523$	−24.1438			−1.05573			−0.527867	−	0.849327i	$-0.677008\pi$
$523$	−24.1438			−1.05573			−0.527867	+	0.849327i	$0.677008\pi$
$524$	2.13856	−	9.36962i	0.0934232	−	0.409314i
$525$		0			0
$526$	−7.56949	−	3.64527i	−0.330045	−	0.158942i
$527$	−3.15130	+	13.8068i	−0.137273	+	0.601432i
$528$	0.152793	+	0.669429i	0.00664945	+	0.0291332i
$529$	1.80582	−	0.869638i	0.0785140	−	0.0378104i
$530$		0			0
$531$	−3.50096	+	4.39006i	−0.151929	+	0.190513i
$532$	−12.7397	−	6.13514i	−0.552338	−	0.265992i
$533$	−19.7630	−	24.7820i	−0.856031	−	1.07343i
$534$	−9.78017			−0.423229
$535$		0			0
$536$	−3.53415	−	15.4841i	−0.152652	−	0.668812i
$537$	0.862404	+	3.77844i	0.0372155	+	0.163052i
$538$	−7.32155	−	9.18094i	−0.315655	−	0.395818i
$539$	−14.1123			−0.607860
$540$		0			0
$541$	7.70171	+	3.70895i	0.331122	+	0.159460i	0.592056	−	0.805896i	$-0.298316\pi$
$541$	7.70171	+	3.70895i	0.331122	+	0.159460i	−0.260934	+	0.965357i	$0.584031\pi$
$542$	7.38351	−	9.25863i	0.317149	−	0.397692i
$543$	0.288069	−	0.361227i	0.0123622	−	0.0155017i
$544$	30.1504	−	14.5197i	1.29269	−	0.622526i
$545$		0			0
$546$	6.84266	−	29.9796i	0.292839	−	1.28301i
$547$	11.9330	+	5.74661i	0.510217	+	0.245707i	0.671236	−	0.741244i	$-0.265764\pi$
$547$	11.9330	+	5.74661i	0.510217	+	0.245707i	−0.161019	+	0.986951i	$0.551478\pi$
$548$	−2.02350	+	0.974466i	−0.0864396	+	0.0416271i
$549$	−1.08503	+	4.75383i	−0.0463080	+	0.202889i
$550$		0			0
$551$	−11.0739	−	4.18108i	−0.471764	−	0.178120i
$552$	−16.7375			−0.712394
$553$	−9.58509	+	41.9950i	−0.407599	+	1.78581i
$554$	1.83028	−	0.881417i	0.0777612	−	0.0374478i
$555$		0			0
$556$	−3.65279	+	16.0039i	−0.154913	+	0.678718i
$557$	−5.91939	−	25.9345i	−0.250812	−	1.09888i	−0.930763	−	0.365623i	$-0.880856\pi$
$557$	−5.91939	−	25.9345i	−0.250812	−	1.09888i	0.679950	−	0.733258i	$-0.262001\pi$
$558$	−2.06542	+	0.994652i	−0.0874360	+	0.0421070i
$559$	−34.5031	+	43.2655i	−1.45933	+	1.82994i
$560$		0			0
$561$	6.39977	+	3.08197i	0.270199	+	0.130121i
$562$	7.43900	+	9.32821i	0.313795	+	0.393487i
$563$	33.8079			1.42483			0.712417	−	0.701757i	$-0.247601\pi$
$563$	33.8079			1.42483			0.712417	+	0.701757i	$0.247601\pi$
$564$	9.23974	+	11.5863i	0.389063	+	0.487870i
$565$		0			0
$566$	4.21552	+	18.4694i	0.177192	+	0.776327i
$567$	12.3576	+	15.4959i	0.518969	+	0.650766i
$568$	29.8431			1.25219
$569$	9.47501	+	11.8813i	0.397213	+	0.498089i	0.939712	−	0.341967i	$-0.111093\pi$
$569$	9.47501	+	11.8813i	0.397213	+	0.498089i	−0.542499	+	0.840057i	$0.682522\pi$
$570$		0			0
$571$	16.8076	−	21.0761i	0.703377	−	0.882006i	−0.293894	−	0.955838i	$-0.594951\pi$
$571$	16.8076	−	21.0761i	0.703377	−	0.882006i	0.997271	+	0.0738316i	$0.0235227\pi$
$572$	−4.59837	+	5.76617i	−0.192267	+	0.241096i
$573$	7.41497	−	3.57086i	0.309765	−	0.149175i
$574$	−4.49880	−	19.7105i	−0.187776	−	0.822702i
$575$		0			0
$576$	3.72175	+	1.79230i	0.155073	+	0.0746792i
$577$	−16.2289	+	7.81541i	−0.675616	+	0.325360i	−0.740040	−	0.672563i	$-0.765193\pi$
$577$	−16.2289	+	7.81541i	−0.675616	+	0.325360i	0.0644237	+	0.997923i	$0.479479\pi$
$578$	2.84774	−	12.4768i	0.118450	−	0.518965i
$579$	21.6735			0.900720
$580$		0			0
$581$	41.4975			1.72161
$582$	2.52489	−	11.0622i	0.104660	−	0.458545i
$583$	5.15452	−	2.48229i	0.213478	−	0.102806i
$584$	−5.66368	−	2.72748i	−0.234365	−	0.112864i
$585$		0			0
$586$	3.79494	+	16.6267i	0.156767	+	0.686843i
$587$	22.0172	−	10.6029i	0.908748	−	0.437630i	0.0797073	−	0.996818i	$-0.474601\pi$
$587$	22.0172	−	10.6029i	0.908748	−	0.437630i	0.829041	+	0.559188i	$0.188887\pi$
$588$	−17.7662	+	22.2781i	−0.732667	+	0.918735i
$589$	3.38069	−	4.23925i	0.139299	−	0.174675i
$590$		0			0
$591$	−14.8185	−	18.5818i	−0.609551	−	0.764353i
$592$	−4.40581			−0.181078
$593$	−27.4678	−	34.4435i	−1.12797	−	1.41442i	−0.897316	−	0.441388i	$-0.854486\pi$
$593$	−27.4678	−	34.4435i	−1.12797	−	1.41442i	−0.230650	−	0.973037i	$-0.574085\pi$
$594$	0.918237	+	4.02306i	0.0376757	+	0.165068i
$595$		0			0
$596$	−17.5348	−	21.9880i	−0.718254	−	0.900662i
$597$	3.80923			0.155902
$598$	−13.6564	−	17.1246i	−0.558453	−	0.700278i
$599$	−34.0318	−	16.3888i	−1.39050	−	0.669629i	−0.419289	−	0.907853i	$-0.637721\pi$
$599$	−34.0318	−	16.3888i	−1.39050	−	0.669629i	−0.971210	+	0.238223i	$0.923435\pi$
$600$		0			0
$601$	5.64257	−	7.07556i	0.230165	−	0.288618i	−0.653315	−	0.757086i	$-0.726622\pi$
$601$	5.64257	−	7.07556i	0.230165	−	0.288618i	0.883481	+	0.468468i	$0.155194\pi$
$602$	−31.8010	+	15.3146i	−1.29611	+	0.624175i
$603$	1.52134	+	6.66544i	0.0619539	+	0.271438i
$604$	−0.890321	+	3.90075i	−0.0362266	+	0.158719i
$605$		0			0
$606$	−0.484271	+	0.233212i	−0.0196721	+	0.00947361i
$607$	2.02470	−	8.87077i	0.0821799	−	0.360053i	−0.917072	−	0.398721i	$-0.869454\pi$
$607$	2.02470	−	8.87077i	0.0821799	−	0.360053i	0.999252	+	0.0386675i	$0.0123113\pi$
$608$	−12.8127			−0.519623
$609$	−19.1415	+	28.8740i	−0.775654	+	1.17003i
$610$		0			0
$611$	−10.6761	+	46.7749i	−0.431907	+	1.89231i
$612$	−8.13318	+	3.91673i	−0.328764	+	0.158325i
$613$	−16.5770	−	7.98307i	−0.669540	−	0.322433i	0.0680506	−	0.997682i	$-0.478322\pi$
$613$	−16.5770	−	7.98307i	−0.669540	−	0.322433i	−0.737590	+	0.675249i	$0.764036\pi$
$614$	1.64699	−	7.21593i	0.0664671	−	0.291211i
$615$		0			0
$616$	−10.4852	+	5.04942i	−0.422462	+	0.203447i
$617$	−19.9291	+	24.9903i	−0.802314	+	1.00607i	0.197354	+	0.980332i	$0.436765\pi$
$617$	−19.9291	+	24.9903i	−0.802314	+	1.00607i	−0.999669	+	0.0257382i	$0.991806\pi$
$618$	−8.86981	+	11.1224i	−0.356796	+	0.447408i
$619$	23.2700	+	11.2062i	0.935300	+	0.450417i	0.838509	−	0.544888i	$-0.183428\pi$
$619$	23.2700	+	11.2062i	0.935300	+	0.450417i	0.0967914	+	0.995305i	$0.469142\pi$
$620$		0			0
$621$	25.8573			1.03762
$622$	−12.6836	−	15.9047i	−0.508566	−	0.637721i
$623$	9.48188	+	41.5428i	0.379883	+	1.66438i
$624$	0.998804	+	4.37604i	0.0399841	+	0.175182i
$625$		0			0
$626$	−7.92154			−0.316609
$627$	−1.69567	−	2.12630i	−0.0677185	−	0.0849163i
$628$	−11.8487	−	5.70603i	−0.472815	−	0.227695i
$629$	−28.4170	+	35.6338i	−1.13306	+	1.42081i
$630$		0			0
$631$	−4.65495	+	2.24171i	−0.185311	+	0.0892409i	−0.524239	−	0.851571i	$-0.675650\pi$
$631$	−4.65495	+	2.24171i	−0.185311	+	0.0892409i	0.338928	+	0.940812i	$0.389936\pi$
$632$	5.44265	+	23.8458i	0.216497	+	0.948535i
$633$	5.48739	−	24.0418i	0.218104	−	0.955576i
$634$	−11.7174	−	5.64282i	−0.465359	−	0.224105i
$635$		0			0
$636$	2.57050	−	11.2621i	0.101927	−	0.446571i
$637$	−92.2519			−3.65515
$638$	−3.38447	+	2.01307i	−0.133992	+	0.0796981i
$639$	−12.8465			−0.508201
$640$		0			0
$641$	−16.4731	+	7.93305i	−0.650650	+	0.313337i	−0.729936	−	0.683515i	$-0.760450\pi$
$641$	−16.4731	+	7.93305i	−0.650650	+	0.313337i	0.0792860	+	0.996852i	$0.474736\pi$
$642$	−14.6128	−	7.03715i	−0.576721	−	0.277734i
$643$	9.75816	−	42.7533i	0.384824	−	1.68603i	−0.297296	−	0.954785i	$-0.596085\pi$
$643$	9.75816	−	42.7533i	0.384824	−	1.68603i	0.682120	−	0.731240i	$-0.261058\pi$
$644$	6.55914	+	28.7375i	0.258466	+	1.13241i
$645$		0			0
$646$	−6.30947	+	7.91183i	−0.248243	+	0.311287i
$647$	−8.44116	+	10.5849i	−0.331856	+	0.416134i	−0.919565	−	0.392938i	$-0.871459\pi$
$647$	−8.44116	+	10.5849i	−0.331856	+	0.416134i	0.587709	+	0.809073i	$0.300030\pi$
$648$	10.1398	+	4.88305i	0.398327	+	0.191824i
$649$	−2.75481	−	3.45442i	−0.108136	−	0.135598i
$650$		0			0
$651$	−9.89410	−	12.4068i	−0.387780	−	0.486261i
$652$	−2.22425	−	9.74508i	−0.0871083	−	0.381647i
$653$	3.28962	+	14.4128i	0.128733	+	0.564015i	0.997617	+	0.0689992i	$0.0219806\pi$
$653$	3.28962	+	14.4128i	0.128733	+	0.564015i	−0.868884	+	0.495016i	$0.835162\pi$
$654$	−10.2579	−	12.8630i	−0.401114	−	0.502981i
$655$		0			0
$656$	1.83997	+	2.30725i	0.0718388	+	0.0900830i
$657$	2.43804	+	1.17410i	0.0951171	+	0.0458060i
$658$	−19.0797	+	23.9252i	−0.743805	+	0.932701i
$659$	4.23795	−	5.31423i	0.165087	−	0.207013i	−0.692406	−	0.721508i	$-0.743449\pi$
$659$	4.23795	−	5.31423i	0.165087	−	0.207013i	0.857493	+	0.514495i	$0.172021\pi$
$660$		0			0
$661$	−5.93751	−	26.0139i	−0.230942	−	1.01182i	−0.948860	−	0.315697i	$-0.897762\pi$
$661$	−5.93751	−	26.0139i	−0.230942	−	1.01182i	0.717918	−	0.696128i	$-0.245095\pi$
$662$	−0.917895	+	4.02156i	−0.0356750	+	0.156302i
$663$	41.8352	+	20.1468i	1.62474	+	0.782435i
$664$	21.2298	−	10.2237i	0.823877	−	0.396758i
$665$		0			0
$666$	−7.37781			−0.285884
$667$	7.57875	+	23.4827i	0.293450	+	0.909254i
$668$	11.7573			0.454905
$669$	0.587482	−	2.57393i	0.0227134	−	0.0995138i
$670$		0			0
$671$	−3.45689	−	1.66475i	−0.133452	−	0.0642669i
$672$	−8.34415	+	36.5581i	−0.321883	+	1.41026i
$673$	9.69859	+	42.4923i	0.373853	+	1.63796i	0.715848	+	0.698257i	$0.246041\pi$
$673$	9.69859	+	42.4923i	0.373853	+	1.63796i	−0.341994	+	0.939702i	$0.611102\pi$
$674$	−19.6194	+	9.44819i	−0.755710	+	0.363931i
$675$		0			0
$676$	−19.0613	+	23.9021i	−0.733127	+	0.919312i
$677$	31.8533	+	15.3397i	1.22422	+	0.589554i	0.930484	−	0.366332i	$-0.119386\pi$
$677$	31.8533	+	15.3397i	1.22422	+	0.589554i	0.293738	+	0.955886i	$0.405101\pi$
$678$	−10.4770	−	13.1378i	−0.402368	−	0.504554i
$679$	−49.4365			−1.89720
$680$		0			0
$681$	−1.93708	−	8.48691i	−0.0742291	−	0.325219i
$682$	−0.401396	−	1.75863i	−0.0153702	−	0.0673414i
$683$	0.0296715	+	0.0372069i	0.00113535	+	0.00142368i	0.782399	−	0.622778i	$-0.213996\pi$
$683$	0.0296715	+	0.0372069i	0.00113535	+	0.00142368i	−0.781263	+	0.624201i	$0.785424\pi$
$684$	3.45627			0.132154
$685$		0			0
$686$	−29.0356	−	13.9828i	−1.10859	−	0.533867i
$687$	5.55376	−	6.96420i	0.211889	−	0.265701i
$688$	3.21230	−	4.02810i	0.122468	−	0.153570i
$689$	33.6950	−	16.2267i	1.28368	−	0.618186i
$690$		0			0
$691$	7.88955	−	34.5664i	0.300133	−	1.31497i	−0.569795	−	0.821787i	$-0.692977\pi$
$691$	7.88955	−	34.5664i	0.300133	−	1.31497i	0.869927	−	0.493180i	$-0.164166\pi$
$692$	−9.34385	−	4.49976i	−0.355200	−	0.171055i
$693$	4.51357	−	2.17362i	0.171456	−	0.0825691i
$694$	4.61745	−	20.2304i	0.175276	−	0.767934i
$695$		0			0
$696$	−2.67898	+	19.4876i	−0.101546	+	0.738676i
$697$	30.5284			1.15635
$698$	2.92835	−	12.8300i	0.110840	−	0.485621i
$699$	−4.12522	+	1.98660i	−0.156030	+	0.0751401i
$700$		0			0
$701$	−4.81282	+	21.0864i	−0.181778	+	0.796421i	0.799006	+	0.601323i	$0.205360\pi$
$701$	−4.81282	+	21.0864i	−0.181778	+	0.796421i	−0.980784	+	0.195098i	$0.937498\pi$
$702$	6.00250	+	26.2987i	0.226550	+	0.992579i
$703$	15.7223	−	7.57145i	0.592977	−	0.285563i
$704$	−2.02661	+	2.54129i	−0.0763809	+	0.0957786i
$705$		0			0
$706$	16.2537	+	7.82739i	0.611718	+	0.294588i
$707$	1.46011	+	1.83092i	0.0549130	+	0.0688587i
$708$	−8.92133			−0.335284
$709$	−6.09986	−	7.64898i	−0.229085	−	0.287264i	0.653982	−	0.756510i	$-0.273097\pi$
$709$	−6.09986	−	7.64898i	−0.229085	−	0.287264i	−0.883067	+	0.469246i	$0.844526\pi$
$710$		0			0
$711$	−2.34290	−	10.2649i	−0.0878654	−	0.384964i
$712$	15.0858	+	18.9169i	0.565362	+	0.708942i
$713$	−11.3032			−0.423308
$714$	18.4656	+	23.1551i	0.691058	+	0.866560i
$715$		0			0
$716$	2.41640	−	3.03007i	0.0903052	−	0.113239i
$717$	−9.41550	+	11.8067i	−0.351628	+	0.440928i
$718$	8.39881	−	4.04466i	0.313441	−	0.150945i
$719$	−8.44653	−	37.0067i	−0.315003	−	1.38012i	−0.846199	−	0.532867i	$-0.821114\pi$
$719$	−8.44653	−	37.0067i	−0.315003	−	1.38012i	0.531196	−	0.847249i	$-0.321743\pi$
$720$		0			0
$721$	55.8434	+	26.8928i	2.07972	+	1.00154i
$722$	−10.2371	+	4.92991i	−0.380984	+	0.183472i
$723$	1.61875	−	7.09221i	0.0602020	−	0.263762i
$724$	−0.462026			−0.0171711
$725$		0			0
$726$	11.0648			0.410655
$727$	2.50239	−	10.9637i	0.0928086	−	0.406621i	−0.907089	−	0.420939i	$-0.861701\pi$
$727$	2.50239	−	10.9637i	0.0928086	−	0.406621i	0.999897	+	0.0143180i	$0.00455773\pi$
$728$	−68.5417	+	33.0080i	−2.54033	+	1.22336i
$729$	−25.0613	−	12.0689i	−0.928196	−	0.446996i
$730$		0			0
$731$	−11.8599	−	51.9615i	−0.438653	−	1.92187i
$732$	−6.97996	+	3.36137i	−0.257987	+	0.124240i
$733$	−30.3593	+	38.0694i	−1.12135	+	1.40613i	−0.218676	+	0.975798i	$0.570174\pi$
$733$	−30.3593	+	38.0694i	−1.12135	+	1.40613i	−0.902672	+	0.430328i	$0.858398\pi$
$734$	9.69687	−	12.1595i	0.357918	−	0.448815i
$735$		0			0
$736$	16.6531	+	20.8823i	0.613841	+	0.769732i
$737$	−5.37973			−0.198165
$738$	3.08115	+	3.86363i	0.113419	+	0.142222i
$739$	3.06853	+	13.4441i	0.112878	+	0.494550i	0.999487	+	0.0320303i	$0.0101973\pi$
$739$	3.06853	+	13.4441i	0.112878	+	0.494550i	−0.886609	+	0.462519i	$0.846946\pi$
$740$		0			0
$741$	−11.0846	−	13.8996i	−0.407201	−	0.510614i
$742$	23.8538			0.875702
$743$	18.8173	+	23.5961i	0.690340	+	0.865659i	0.996261	−	0.0863983i	$-0.0275358\pi$
$743$	18.8173	+	23.5961i	0.690340	+	0.865659i	−0.305921	+	0.952057i	$0.598964\pi$
$744$	−8.11841	−	3.90962i	−0.297635	−	0.143334i
$745$		0			0
$746$	13.8460	−	17.3623i	0.506938	−	0.635681i
$747$	−9.13879	+	4.40101i	−0.334371	+	0.161025i
$748$	−1.58061	−	6.92512i	−0.0577929	−	0.253207i
$749$	−15.7243	+	68.8927i	−0.574554	+	2.51728i
$750$		0			0
$751$	34.6030	−	16.6639i	1.26268	−	0.608075i	0.321798	−	0.946808i	$-0.395713\pi$
$751$	34.6030	−	16.6639i	1.26268	−	0.608075i	0.940882	+	0.338733i	$0.109998\pi$
$752$	0.993959	−	4.35482i	0.0362460	−	0.158804i
$753$	2.42135			0.0882390
$754$	−22.1242	+	13.1594i	−0.805716	+	0.479236i
$755$		0			0
$756$	8.07792	−	35.3917i	0.293791	−	1.28718i
$757$	9.83513	−	4.73635i	0.357464	−	0.172145i	−0.246529	−	0.969135i	$-0.579290\pi$
$757$	9.83513	−	4.73635i	0.357464	−	0.172145i	0.603992	+	0.796990i	$0.293576\pi$
$758$	−1.96077	−	0.944258i	−0.0712184	−	0.0342970i
$759$	−1.26156	+	5.52725i	−0.0457917	+	0.200627i
$760$		0			0
$761$	−0.210676	+	0.101456i	−0.00763701	+	0.00367779i	−0.437698	−	0.899122i	$-0.644206\pi$
$761$	−0.210676	+	0.101456i	−0.00763701	+	0.00367779i	0.430061	+	0.902800i	$0.358492\pi$
$762$	0.444509	−	0.557397i	0.0161029	−	0.0201924i
$763$	−44.6924	+	56.0426i	−1.61798	+	2.02888i
$764$	−7.41497	−	3.57086i	−0.268264	−	0.129189i
$765$		0			0
$766$	17.0998			0.617839
$767$	−18.0081	−	22.5815i	−0.650236	−	0.815370i
$768$	4.28328	+	18.7663i	0.154560	+	0.677170i
$769$	7.81043	+	34.2197i	0.281651	+	1.23400i	0.895676	+	0.444708i	$0.146693\pi$
$769$	7.81043	+	34.2197i	0.281651	+	1.23400i	−0.614024	+	0.789287i	$0.710450\pi$
$770$		0			0
$771$	20.9909			0.755969
$772$	−13.5132	−	16.9450i	−0.486351	−	0.609865i
$773$	33.8521	+	16.3023i	1.21758	+	0.586354i	0.928635	−	0.370994i	$-0.120983\pi$
$773$	33.8521	+	16.3023i	1.21758	+	0.586354i	0.288940	+	0.957347i	$0.406697\pi$
$774$	5.37920	−	6.74530i	0.193351	−	0.242455i
$775$		0			0
$776$	−25.2913	+	12.1797i	−0.907906	+	0.437225i
$777$	−11.3644	−	49.7908i	−0.407697	−	1.78624i
$778$	−1.64752	+	7.21826i	−0.0590665	+	0.258787i
$779$	−10.5310	−	5.07148i	−0.377313	−	0.181705i
$780$		0			0
$781$	2.24937	−	9.85514i	0.0804889	−	0.352645i
$782$	21.0954			0.754371
$783$	4.13869	−	30.1059i	0.147905	−	1.07590i
$784$	8.58881			0.306743
$785$		0			0
$786$	6.94385	−	3.34398i	0.247679	−	0.119276i
$787$	−32.0797	−	15.4488i	−1.14352	−	0.550689i	−0.236438	−	0.971647i	$-0.575980\pi$
$787$	−32.0797	−	15.4488i	−1.14352	−	0.550689i	−0.907080	+	0.420957i	$0.861694\pi$
$788$	−5.28866	+	23.1711i	−0.188401	+	0.825437i
$789$	3.16325	+	13.8591i	0.112615	+	0.493397i
$790$		0			0
$791$	−45.6473	+	57.2400i	−1.62303	+	2.03522i
$792$	1.77359	−	2.22402i	0.0630219	−	0.0790270i
$793$	−22.5976	−	10.8824i	−0.802464	−	0.386446i
$794$	−2.91305	−	3.65285i	−0.103380	−	0.129635i
$795$		0			0
$796$	−2.37502	−	2.97818i	−0.0841803	−	0.105559i
$797$	−3.32855	−	14.5833i	−0.117903	−	0.516568i	−0.999044	−	0.0437143i	$-0.986081\pi$
$797$	−3.32855	−	14.5833i	−0.117903	−	0.516568i	0.881141	−	0.472854i	$-0.156776\pi$
$798$	−2.52326	−	11.0551i	−0.0893225	−	0.391348i
$799$	−28.8104	−	36.1271i	−1.01924	−	1.27809i
$800$		0			0
$801$	−6.49396	−	8.14317i	−0.229453	−	0.287725i
$802$	28.0240	+	13.4956i	0.989561	+	0.476548i
$803$	−1.32759	+	1.66475i	−0.0468497	+	0.0587477i
$804$	−6.77263	+	8.49262i	−0.238852	+	0.299511i
$805$		0			0
$806$	−2.62392	−	11.4961i	−0.0924235	−	0.404934i
$807$	−4.42131	+	19.3710i	−0.155637	+	0.681892i
$808$	1.19806	+	0.576956i	0.0421477	+	0.0202973i
$809$	−23.9693	+	11.5430i	−0.842714	+	0.405830i	−0.804868	−	0.593454i	$-0.797764\pi$
$809$	−23.9693	+	11.5430i	−0.842714	+	0.405830i	−0.0378463	+	0.999284i	$0.512050\pi$
$810$		0			0
$811$	−33.6752			−1.18249			−0.591247	−	0.806490i	$-0.701364\pi$
$811$	−33.6752			−1.18249			−0.591247	+	0.806490i	$0.701364\pi$
$812$	34.5092	−	3.03719i	1.21103	−	0.106584i
$813$	−20.0373			−0.702739
$814$	1.29182	−	5.65984i	0.0452783	−	0.198377i
$815$		0			0
$816$	−3.89493	−	1.87570i	−0.136350	−	0.0656626i
$817$	−4.54085	+	19.8948i	−0.158864	+	0.696030i
$818$	−0.828315	−	3.62909i	−0.0289614	−	0.126888i
$819$	29.5051	−	14.2089i	1.03099	−	0.496500i
$820$		0			0
$821$	12.7515	−	15.9898i	0.445029	−	0.558049i	−0.507832	−	0.861456i	$-0.669553\pi$
$821$	12.7515	−	15.9898i	0.445029	−	0.558049i	0.952861	+	0.303408i	$0.0981244\pi$
$822$	−1.62272	−	0.781461i	−0.0565989	−	0.0272566i
$823$	−29.9562	−	37.5639i	−1.04421	−	1.30940i	−0.949458	−	0.313895i	$-0.898366\pi$
$823$	−29.9562	−	37.5639i	−1.04421	−	1.30940i	−0.0947505	−	0.995501i	$-0.530205\pi$
$824$	35.1946			1.22606
$825$		0			0
$826$	−4.09933	−	17.9603i	−0.142634	−	0.624920i
$827$	4.76845	+	20.8920i	0.165815	+	0.726485i	0.987639	+	0.156743i	$0.0500995\pi$
$827$	4.76845	+	20.8920i	0.165815	+	0.726485i	−0.821824	+	0.569741i	$0.807043\pi$
$828$	−4.49223	−	5.63308i	−0.156116	−	0.195763i
$829$	18.4222			0.639830			0.319915	−	0.947446i	$-0.396346\pi$
$829$	18.4222			0.639830			0.319915	+	0.947446i	$0.396346\pi$
$830$		0			0
$831$	−3.09688	−	1.49138i	−0.107429	−	0.0517353i
$832$	−13.2479	+	16.6124i	−0.459290	+	0.575931i
$833$	55.3968	−	69.4654i	1.91939	−	2.40684i
$834$	−11.8605	+	5.71174i	−0.410697	+	0.197781i
$835$		0			0
$836$	−0.605177	+	2.65146i	−0.0209305	+	0.0917025i
$837$	12.5419	+	6.03987i	0.433512	+	0.208768i
$838$	10.1908	−	4.90764i	0.352036	−	0.169532i
$839$	−8.46346	+	37.0808i	−0.292191	+	1.28017i	0.589278	+	0.807931i	$0.299412\pi$
$839$	−8.46346	+	37.0808i	−0.292191	+	1.28017i	−0.881469	+	0.472242i	$0.843445\pi$
$840$		0			0
$841$	28.5542	−	5.06540i	0.984627	−	0.174669i
$842$	−11.4920			−0.396042
$843$	4.49223	−	19.6817i	0.154721	−	0.677875i
$844$	−22.2180	+	10.6996i	−0.764774	+	0.368296i
$845$		0			0
$846$	1.66445	−	7.29242i	0.0572249	−	0.250719i
$847$	−10.7274	−	46.9997i	−0.368597	−	1.61493i
$848$	−3.13706	+	1.51073i	−0.107727	+	0.0518787i
$849$	19.9855	−	25.0611i	0.685901	−	0.860093i
$850$		0			0
$851$	−32.7748	−	15.7835i	−1.12351	−	0.541053i
$852$	−12.7259	−	15.9577i	−0.435981	−	0.546703i
$853$	13.7990			0.472467			0.236234	−	0.971696i	$-0.424087\pi$
$853$	13.7990			0.472467			0.236234	+	0.971696i	$0.424087\pi$
$854$	−9.97434	−	12.5074i	−0.341315	−	0.427996i
$855$		0			0
$856$	8.92865	+	39.1190i	0.305175	+	1.33706i
$857$	4.19687	+	5.26270i	0.143362	+	0.179771i	0.848328	−	0.529470i	$-0.177609\pi$
$857$	4.19687	+	5.26270i	0.143362	+	0.179771i	−0.704966	+	0.709241i	$0.749038\pi$
$858$	−5.91446			−0.201916
$859$	14.3448	+	17.9878i	0.489439	+	0.613737i	0.963811	−	0.266588i	$-0.0858962\pi$
$859$	14.3448	+	17.9878i	0.489439	+	0.613737i	−0.474372	+	0.880325i	$0.657325\pi$
$860$		0			0
$861$	−21.3286	+	26.7452i	−0.726875	+	0.911473i
$862$	−2.07188	+	2.59806i	−0.0705687	+	0.0884903i
$863$	28.9252	−	13.9296i	0.984625	−	0.474170i	0.128932	−	0.991653i	$-0.458845\pi$
$863$	28.9252	−	13.9296i	0.984625	−	0.474170i	0.855693	+	0.517483i	$0.173131\pi$
$864$	−7.31963	−	32.0694i	−0.249019	−	1.09102i
$865$		0			0
$866$	−25.1927	−	12.1322i	−0.856084	−	0.412268i
$867$	−19.5095	+	9.39526i	−0.662576	+	0.319080i
$868$	−3.53116	+	15.4710i	−0.119855	+	0.525121i
$869$	8.28488			0.281045
$870$		0			0
$871$	−35.1672			−1.19159
$872$	−9.05711	+	39.6818i	−0.306713	+	1.34380i
$873$	10.8872	−	5.24298i	0.368474	−	0.177448i
$874$	−7.27705	−	3.50444i	−0.246150	−	0.118540i
$875$		0			0
$876$	0.956696	+	4.19156i	0.0323238	+	0.141620i
$877$	17.6398	−	8.49486i	0.595652	−	0.286851i	−0.111667	−	0.993746i	$-0.535619\pi$
$877$	17.6398	−	8.49486i	0.595652	−	0.286851i	0.707319	+	0.706895i	$0.249905\pi$
$878$	−2.64646	+	3.31855i	−0.0893136	+	0.111996i
$879$	17.9916	−	22.5607i	0.606840	−	0.760954i
$880$		0			0
$881$	−10.9336	−	13.7103i	−0.368363	−	0.461913i	0.562759	−	0.826621i	$-0.309740\pi$
$881$	−10.9336	−	13.7103i	−0.368363	−	0.461913i	−0.931122	+	0.364709i	$0.881169\pi$
$882$	14.3825			0.484284
$883$	11.8946	+	14.9153i	0.400284	+	0.501940i	0.940598	−	0.339524i	$-0.110266\pi$
$883$	11.8946	+	14.9153i	0.400284	+	0.501940i	−0.540314	+	0.841464i	$0.681694\pi$
$884$	−10.3324	−	45.2694i	−0.347517	−	1.52257i
$885$		0			0
$886$	4.37598	+	5.48730i	0.147014	+	0.184350i
$887$	−17.6840			−0.593770			−0.296885	−	0.954913i	$-0.595948\pi$
$887$	−17.6840			−0.593770			−0.296885	+	0.954913i	$0.595948\pi$
$888$	−18.0809	−	22.6727i	−0.606756	−	0.760847i
$889$	−2.79859	−	1.34773i	−0.0938615	−	0.0452013i
$890$		0			0
$891$	2.37681	−	2.98042i	0.0796260	−	0.0998478i
$892$	−2.37867	+	1.14551i	−0.0796436	+	0.0383544i
$893$	3.93685	+	17.2484i	0.131741	+	0.577197i
$894$	5.01861	−	21.9880i	0.167847	−	0.735387i
$895$		0			0
$896$	37.5867	−	18.1008i	1.25568	−	0.604706i
$897$	−8.24679	+	36.1315i	−0.275352	+	1.20640i
$898$	24.4166			0.814791
$899$	−1.80917	+	13.1604i	−0.0603394	+	0.438924i
$900$		0			0
$901$	−8.01507	+	35.1163i	−0.267021	+	1.16989i
$902$	−3.50346	+	1.68718i	−0.116652	+	0.0561768i
$903$	53.8080	+	25.9126i	1.79062	+	0.862317i
$904$	−9.25063	+	40.5296i	−0.307671	+	1.34800i
$905$		0			0
$906$	−2.89085	+	1.39216i	−0.0960422	+	0.0462515i
$907$	5.29321	−	6.63747i	0.175758	−	0.220394i	−0.686148	−	0.727462i	$-0.740700\pi$
$907$	5.29321	−	6.63747i	0.175758	−	0.220394i	0.861906	+	0.507069i	$0.169271\pi$
$908$	−5.42758	+	6.80597i	−0.180121	+	0.225864i
$909$	−0.515729	−	0.248362i	−0.0171057	−	0.00823765i
$910$		0			0
$911$	21.6907			0.718645			0.359322	−	0.933213i	$-0.383008\pi$
$911$	21.6907			0.718645			0.359322	+	0.933213i	$0.383008\pi$
$912$	1.03199	+	1.29408i	0.0341727	+	0.0428511i
$913$	−1.77605	−	7.78136i	−0.0587785	−	0.257526i
$914$	1.80990	+	7.92968i	0.0598661	+	0.262290i
$915$		0			0
$916$	−8.90754			−0.294313
$917$	−20.9361	−	26.2531i	−0.691373	−	0.866954i
$918$	−23.4073	−	11.2724i	−0.772556	−	0.372043i
$919$	37.5658	−	47.1060i	1.23918	−	1.55388i	0.532284	−	0.846566i	$-0.321334\pi$
$919$	37.5658	−	47.1060i	1.23918	−	1.55388i	0.706896	−	0.707318i	$-0.250095\pi$
$920$		0			0
$921$	−11.2833	+	5.43374i	−0.371797	+	0.179048i
$922$	−4.26582	−	18.6898i	−0.140487	−	0.615516i
$923$	14.7041	−	64.4229i	0.483991	−	2.12051i
$924$	7.17121	+	3.45347i	0.235916	+	0.113611i
$925$		0			0
$926$	6.55161	−	28.7045i	0.215299	−	0.943287i
$927$	−15.1502			−0.497598
$928$	26.9790	−	16.0470i	0.885627	−	0.526767i
$929$	−16.2145			−0.531979			−0.265990	−	0.963976i	$-0.585699\pi$
$929$	−16.2145			−0.531979			−0.265990	+	0.963976i	$0.585699\pi$
$930$		0			0
$931$	−30.6494	+	14.7600i	−1.00449	+	0.483739i
$932$	4.12522	+	1.98660i	0.135126	+	0.0650733i
$933$	−7.65931	+	33.5576i	−0.250754	+	1.09863i
$934$	2.07745	+	9.10191i	0.0679763	+	0.297823i
$935$		0			0
$936$	11.5939	−	14.5384i	0.378960	−	0.475201i
$937$	−16.5925	+	20.8063i	−0.542052	+	0.679712i	−0.975127	−	0.221646i	$-0.928857\pi$
$937$	−16.5925	+	20.8063i	−0.542052	+	0.679712i	0.433075	+	0.901358i	$0.357428\pi$
$938$	−20.2092	−	9.73226i	−0.659855	−	0.317770i
$939$	8.35690	+	10.4792i	0.272717	+	0.341976i
$940$		0			0
$941$	35.1933	+	44.1310i	1.14727	+	1.43863i	0.879979	+	0.475012i	$0.157556\pi$
$941$	35.1933	+	44.1310i	1.14727	+	1.43863i	0.267289	+	0.963616i	$0.413872\pi$
$942$	−2.34678	−	10.2819i	−0.0764622	−	0.335003i
$943$	5.42197	+	23.7552i	0.176564	+	0.773576i
$944$	1.67659	+	2.10237i	0.0545683	+	0.0684265i
$945$		0			0
$946$	4.23274	+	5.30769i	0.137618	+	0.172568i
$947$	−24.1875	−	11.6481i	−0.785987	−	0.378512i	−0.00256135	−	0.999997i	$-0.500815\pi$
$947$	−24.1875	−	11.6481i	−0.785987	−	0.378512i	−0.783426	+	0.621485i	$0.786530\pi$
$948$	10.4300	−	13.0788i	0.338750	−	0.424779i
$949$	−8.67845	+	10.8824i	−0.281714	+	0.353259i
$950$		0			0
$951$	4.89666	+	21.4537i	0.158785	+	0.695682i
$952$	16.3041	−	71.4329i	0.528419	−	2.31515i
$953$	3.08546	+	1.48588i	0.0999478	+	0.0481323i	0.483190	−	0.875516i	$-0.339478\pi$
$953$	3.08546	+	1.48588i	0.0999478	+	0.0481323i	−0.383242	+	0.923648i	$0.625192\pi$
$954$	−5.25321	+	2.52981i	−0.170079	+	0.0819057i
$955$		0			0
$956$	15.1013			0.488411
$957$	6.23351	+	2.35353i	0.201501	+	0.0760789i
$958$	20.5666			0.664476
$959$	−1.74615	+	7.65039i	−0.0563862	+	0.247044i
$960$		0			0
$961$	22.4475	+	10.8101i	0.724113	+	0.348714i
$962$	8.44461	−	36.9983i	0.272265	−	1.19287i
$963$	−3.84351	−	16.8395i	−0.123855	−	0.542646i
$964$	−6.55419	+	3.15633i	−0.211096	+	0.101659i
$965$		0			0
$966$	−14.7383	+	18.4812i	−0.474195	+	0.594622i
$967$	16.5211	+	7.95615i	0.531283	+	0.255852i	0.680238	−	0.732992i	$-0.261877\pi$
$967$	16.5211	+	7.95615i	0.531283	+	0.255852i	−0.148955	+	0.988844i	$0.547591\pi$
$968$	−17.0673	−	21.4018i	−0.548565	−	0.687879i
$969$	17.1226			0.550057
$970$		0			0
$971$	−11.7252	−	51.3715i	−0.376280	−	1.64859i	−0.708738	−	0.705472i	$-0.750735\pi$
$971$	−11.7252	−	51.3715i	−0.376280	−	1.64859i	0.332458	−	0.943118i	$-0.392122\pi$
$972$	3.39881	+	14.8912i	0.109017	+	0.477635i
$973$	35.7603	+	44.8420i	1.14642	+	1.43757i
$974$	29.9114			0.958422
$975$		0			0
$976$	2.10388	+	1.01317i	0.0673434	+	0.0324309i
$977$	−1.93110	+	2.42152i	−0.0617814	+	0.0774714i	−0.811762	−	0.583988i	$-0.801491\pi$
$977$	−1.93110	+	2.42152i	−0.0617814	+	0.0774714i	0.749981	+	0.661460i	$0.230063\pi$
$978$	4.99784	−	6.26710i	0.159813	−	0.200400i
$979$	7.38404	−	3.55597i	0.235995	−	0.113649i
$980$		0			0
$981$	3.89881	−	17.0818i	0.124480	−	0.545380i
$982$	−9.77724	−	4.70847i	−0.312004	−	0.150253i
$983$	16.5429	−	7.96663i	0.527636	−	0.254096i	−0.151048	−	0.988526i	$-0.548265\pi$
$983$	16.5429	−	7.96663i	0.527636	−	0.254096i	0.678684	+	0.734430i	$0.262551\pi$
$984$	−4.32232	+	18.9373i	−0.137791	+	0.603700i
$985$		0			0
$986$	3.37651	−	24.5616i	0.107530	−	0.782202i
$987$	51.7784			1.64812
$988$	−3.95603	+	17.3325i	−0.125858	+	0.551421i
$989$	38.3267	−	18.4572i	1.21872	−	0.586904i
$990$		0			0
$991$	3.96173	−	17.3575i	0.125849	−	0.551378i	−0.872212	−	0.489128i	$-0.837315\pi$
$991$	3.96173	−	17.3575i	0.125849	−	0.551378i	0.998061	−	0.0622505i	$-0.0198278\pi$
$992$	3.19969	+	14.0187i	0.101590	+	0.445095i
$993$	6.28836	−	3.02832i	0.199555	−	0.0961007i
$994$	26.2784	−	32.9521i	0.833501	−	1.04518i
$995$		0			0
$996$	−14.5198	−	6.99237i	−0.460078	−	0.221562i
$997$	−10.3415	−	12.9678i	−0.327517	−	0.410694i	0.590624	−	0.806947i	$-0.298882\pi$
$997$	−10.3415	−	12.9678i	−0.327517	−	0.410694i	−0.918141	+	0.396253i	$0.870310\pi$
$998$	22.9952			0.727901
$999$	27.9327	+	35.0265i	0.883752	+	1.10819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.l.a.576.1	yes	6
5.2	odd	4		725.2.r.a.199.2		12
5.3	odd	4		725.2.r.a.199.1		12
5.4	even	2		725.2.l.c.576.1	yes	6
29.7	even	7	inner	725.2.l.a.326.1	✓	6
145.7	odd	28		725.2.r.a.674.1		12
145.94	even	14		725.2.l.c.326.1	yes	6
145.123	odd	28		725.2.r.a.674.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
725.2.l.a.326.1	✓	6	29.7	even	7	inner
725.2.l.a.576.1	yes	6	1.1	even	1	trivial
725.2.l.c.326.1	yes	6	145.94	even	14
725.2.l.c.576.1	yes	6	5.4	even	2
725.2.r.a.199.1		12	5.3	odd	4
725.2.r.a.199.2		12	5.2	odd	4
725.2.r.a.674.1		12	145.7	odd	28
725.2.r.a.674.2		12	145.123	odd	28

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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.l (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.178448 - 0.781831i) q^{2} +(-1.22252 + 0.588735i) q^{3} +(1.22252 + 0.588735i) q^{4} +(0.242135 + 1.06086i) q^{6} +(4.27144 - 2.05702i) q^{7} +(1.67845 - 2.10471i) q^{8} +(-0.722521 + 0.906013i) q^{9} +O(q^{10})\)	\(q+(0.178448 - 0.781831i) q^{2} +(-1.22252 + 0.588735i) q^{3} +(1.22252 + 0.588735i) q^{4} +(0.242135 + 1.06086i) q^{6} +(4.27144 - 2.05702i) q^{7} +(1.67845 - 2.10471i) q^{8} +(-0.722521 + 0.906013i) q^{9} +(-0.568532 - 0.712916i) q^{11} -1.84117 q^{12} +(-3.71648 - 4.66032i) q^{13} +(-0.846011 - 3.70662i) q^{14} +(0.346011 + 0.433884i) q^{16} +5.74094 q^{17} +(0.579417 + 0.726566i) q^{18} +(-1.98039 - 0.953703i) q^{19} +(-4.01089 + 5.02949i) q^{21} +(-0.658834 + 0.317278i) q^{22} +(1.01961 + 4.46722i) q^{23} +(-0.812823 + 3.56121i) q^{24} +(-4.30678 + 2.07404i) q^{26} +(1.25571 - 5.50162i) q^{27} +6.43296 q^{28} +(5.36443 - 0.472129i) q^{29} +(-0.548917 + 2.40496i) q^{31} +(5.25182 - 2.52915i) q^{32} +(1.11476 + 0.536840i) q^{33} +(1.02446 - 4.48845i) q^{34} +(-1.41670 + 0.682246i) q^{36} +(-4.94989 + 6.20696i) q^{37} +(-1.09903 + 1.37814i) q^{38} +(7.28717 + 3.50932i) q^{39} +5.31767 q^{41} +(3.21648 + 4.03334i) q^{42} +(-2.06584 - 9.05105i) q^{43} +(-0.275323 - 1.20627i) q^{44} +3.67456 q^{46} +(-5.01842 - 6.29290i) q^{47} +(-0.678448 - 0.326723i) q^{48} +(9.64944 - 12.1000i) q^{49} +(-7.01842 + 3.37989i) q^{51} +(-1.79978 - 7.88536i) q^{52} +(-1.39612 + 6.11682i) q^{53} +(-4.07726 - 1.96351i) q^{54} +(2.83997 - 12.4427i) q^{56} +2.98254 q^{57} +(0.588146 - 4.27833i) q^{58} +4.84548 q^{59} +(3.79105 - 1.82567i) q^{61} +(1.78232 + 0.858322i) q^{62} +(-1.22252 + 5.35621i) q^{63} +(-0.793209 - 3.47527i) q^{64} +(0.618645 - 0.775757i) q^{66} +(3.67845 - 4.61263i) q^{67} +(7.01842 + 3.37989i) q^{68} +(-3.87651 - 4.86099i) q^{69} +(6.91185 + 8.66719i) q^{71} +(0.694177 + 3.04139i) q^{72} +(-0.519614 - 2.27658i) q^{73} +(3.96950 + 4.97760i) q^{74} +(-1.85958 - 2.33184i) q^{76} +(-3.89493 - 1.87570i) q^{77} +(4.04407 - 5.07111i) q^{78} +(-5.66487 + 7.10353i) q^{79} +(0.930272 + 4.07579i) q^{81} +(0.948927 - 4.15752i) q^{82} +(7.88620 + 3.79779i) q^{83} +(-7.86443 + 3.78731i) q^{84} -7.44504 q^{86} +(-6.28017 + 3.73541i) q^{87} -2.45473 q^{88} +(-2.00000 + 8.76257i) q^{89} +(-25.4611 - 12.2614i) q^{91} +(-1.38351 + 6.06156i) q^{92} +(-0.744824 - 3.26329i) q^{93} +(-5.81551 + 2.80060i) q^{94} +(-4.93147 + 6.18387i) q^{96} +(-9.39493 - 4.52436i) q^{97} +(-7.73825 - 9.70346i) q^{98} +1.05669 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 7 q^{3} + 7 q^{4} + 14 q^{6} + 7 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 7 * q^3 + 7 * q^4 + 14 * q^6 + 7 * q^7 + 6 * q^8 - 4 * q^9	\( 6 q - 3 q^{2} - 7 q^{3} + 7 q^{4} + 14 q^{6} + 7 q^{7} + 6 q^{8} - 4 q^{9} + 2 q^{11} - 28 q^{12} - 3 q^{13} - 3 q^{16} + 6 q^{17} - 5 q^{18} + q^{19} - 21 q^{21} + 13 q^{22} + 19 q^{23} + 7 q^{24} + 5 q^{26} + 14 q^{27} - q^{29} + 15 q^{31} - 14 q^{33} - 3 q^{34} + 21 q^{36} - 7 q^{37} - 11 q^{38} - 2 q^{41} - 10 q^{43} - 21 q^{44} - 20 q^{46} - 2 q^{47} - 14 q^{51} - 21 q^{52} - 26 q^{53} - 35 q^{54} - 7 q^{56} - 14 q^{57} + 11 q^{58} + 8 q^{59} + 17 q^{61} - 11 q^{62} - 7 q^{63} + 20 q^{64} + 21 q^{66} + 18 q^{67} + 14 q^{68} - 28 q^{69} + 34 q^{71} - 25 q^{72} - 16 q^{73} + 14 q^{74} + 28 q^{78} - 36 q^{79} - 30 q^{81} + 43 q^{82} + 8 q^{83} - 14 q^{84} - 44 q^{86} - 35 q^{87} + 30 q^{88} - 12 q^{89} - 42 q^{91} + 28 q^{92} - 14 q^{93} - 20 q^{94} - 35 q^{96} - 33 q^{97} - 21 q^{98} + 64 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 7 * q^3 + 7 * q^4 + 14 * q^6 + 7 * q^7 + 6 * q^8 - 4 * q^9 + 2 * q^11 - 28 * q^12 - 3 * q^13 - 3 * q^16 + 6 * q^17 - 5 * q^18 + q^19 - 21 * q^21 + 13 * q^22 + 19 * q^23 + 7 * q^24 + 5 * q^26 + 14 * q^27 - q^29 + 15 * q^31 - 14 * q^33 - 3 * q^34 + 21 * q^36 - 7 * q^37 - 11 * q^38 - 2 * q^41 - 10 * q^43 - 21 * q^44 - 20 * q^46 - 2 * q^47 - 14 * q^51 - 21 * q^52 - 26 * q^53 - 35 * q^54 - 7 * q^56 - 14 * q^57 + 11 * q^58 + 8 * q^59 + 17 * q^61 - 11 * q^62 - 7 * q^63 + 20 * q^64 + 21 * q^66 + 18 * q^67 + 14 * q^68 - 28 * q^69 + 34 * q^71 - 25 * q^72 - 16 * q^73 + 14 * q^74 + 28 * q^78 - 36 * q^79 - 30 * q^81 + 43 * q^82 + 8 * q^83 - 14 * q^84 - 44 * q^86 - 35 * q^87 + 30 * q^88 - 12 * q^89 - 42 * q^91 + 28 * q^92 - 14 * q^93 - 20 * q^94 - 35 * q^96 - 33 * q^97 - 21 * q^98 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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