LMFDB - Embedded newform 403.2.f.b.94.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(94,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("403.94");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.f (of order $3$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			94.14
Character	$\chi$	$=$	403.94
Dual form			403.2.f.b.373.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11298 + 1.92773i) q^{2} +(-0.337463 - 0.584504i) q^{3} +(-1.47744 + 2.55900i) q^{4} +1.70140 q^{5} +(0.751178 - 1.30108i) q^{6} +(2.45364 - 4.24983i) q^{7} -2.12551 q^{8} +(1.27224 - 2.20358i) q^{9} +O(q^{10})$	\(q+(1.11298 + 1.92773i) q^{2} +(-0.337463 - 0.584504i) q^{3} +(-1.47744 + 2.55900i) q^{4} +1.70140 q^{5} +(0.751178 - 1.30108i) q^{6} +(2.45364 - 4.24983i) q^{7} -2.12551 q^{8} +(1.27224 - 2.20358i) q^{9} +(1.89362 + 3.27984i) q^{10} +(1.43490 + 2.48531i) q^{11} +1.99432 q^{12} +(-3.48374 - 0.929285i) q^{13} +10.9234 q^{14} +(-0.574159 - 0.994473i) q^{15} +(0.589231 + 1.02058i) q^{16} +(-1.82786 + 3.16594i) q^{17} +5.66388 q^{18} +(-1.68231 + 2.91384i) q^{19} +(-2.51371 + 4.35387i) q^{20} -3.31205 q^{21} +(-3.19401 + 5.53219i) q^{22} +(-1.08754 - 1.88368i) q^{23} +(0.717282 + 1.24237i) q^{24} -2.10525 q^{25} +(-2.08591 - 7.74999i) q^{26} -3.74211 q^{27} +(7.25020 + 12.5577i) q^{28} +(-4.61421 - 7.99204i) q^{29} +(1.27805 - 2.21365i) q^{30} -1.00000 q^{31} +(-3.43711 + 5.95325i) q^{32} +(0.968449 - 1.67740i) q^{33} -8.13745 q^{34} +(4.17462 - 7.23065i) q^{35} +(3.75930 + 6.51130i) q^{36} +(4.66578 + 8.08136i) q^{37} -7.48947 q^{38} +(0.632463 + 2.34986i) q^{39} -3.61634 q^{40} +(3.86213 + 6.68940i) q^{41} +(-3.68624 - 6.38476i) q^{42} +(-6.18781 + 10.7176i) q^{43} -8.47988 q^{44} +(2.16458 - 3.74916i) q^{45} +(2.42082 - 4.19298i) q^{46} +10.9376 q^{47} +(0.397688 - 0.688816i) q^{48} +(-8.54069 - 14.7929i) q^{49} +(-2.34309 - 4.05835i) q^{50} +2.46734 q^{51} +(7.52504 - 7.54191i) q^{52} +6.20847 q^{53} +(-4.16489 - 7.21380i) q^{54} +(2.44133 + 4.22850i) q^{55} +(-5.21523 + 9.03305i) q^{56} +2.27087 q^{57} +(10.2710 - 17.7899i) q^{58} +(-4.08051 + 7.06765i) q^{59} +3.39314 q^{60} +(3.07647 - 5.32860i) q^{61} +(-1.11298 - 1.92773i) q^{62} +(-6.24322 - 10.8136i) q^{63} -12.9448 q^{64} +(-5.92722 - 1.58108i) q^{65} +4.31145 q^{66} +(-2.24813 - 3.89387i) q^{67} +(-5.40109 - 9.35496i) q^{68} +(-0.734011 + 1.27134i) q^{69} +18.5850 q^{70} +(1.99517 - 3.45574i) q^{71} +(-2.70415 + 4.68373i) q^{72} -6.02184 q^{73} +(-10.3858 + 17.9887i) q^{74} +(0.710443 + 1.23052i) q^{75} +(-4.97100 - 8.61003i) q^{76} +14.0829 q^{77} +(-3.82598 + 3.83456i) q^{78} +2.87249 q^{79} +(1.00252 + 1.73641i) q^{80} +(-2.55388 - 4.42346i) q^{81} +(-8.59692 + 14.8903i) q^{82} -2.83097 q^{83} +(4.89335 - 8.47553i) q^{84} +(-3.10991 + 5.38652i) q^{85} -27.5476 q^{86} +(-3.11425 + 5.39404i) q^{87} +(-3.04988 - 5.28255i) q^{88} +(-4.83416 - 8.37302i) q^{89} +9.63652 q^{90} +(-12.4971 + 12.5252i) q^{91} +6.42710 q^{92} +(0.337463 + 0.584504i) q^{93} +(12.1734 + 21.0849i) q^{94} +(-2.86227 + 4.95760i) q^{95} +4.63960 q^{96} +(3.81210 - 6.60276i) q^{97} +(19.0112 - 32.9284i) q^{98} +7.30211 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9}+O(q^{10}) $ 34 * q + 4 * q^2 - 20 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 - 12 * q^8 - 17 * q^9	\( 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9} - 6 q^{10} + 13 q^{11} + 8 q^{12} - 3 q^{13} + 4 q^{15} - 34 q^{16} + 6 q^{17} + 24 q^{18} + 4 q^{19} + 28 q^{20} - 36 q^{21} + 34 q^{22} + 8 q^{23} + 40 q^{24} + 16 q^{25} - 26 q^{26} - 6 q^{27} + 21 q^{28} + 6 q^{29} - 19 q^{30} - 34 q^{31} + 6 q^{32} + 7 q^{33} - 48 q^{34} + 9 q^{35} + 14 q^{37} + 22 q^{38} - 21 q^{39} - 20 q^{40} + 43 q^{41} - 33 q^{42} - 18 q^{43} - 56 q^{44} + 26 q^{45} + 7 q^{46} - 12 q^{47} + 95 q^{48} + q^{49} + 44 q^{50} + 52 q^{51} - 24 q^{52} - 10 q^{53} + 27 q^{54} - 39 q^{55} - 39 q^{56} - 92 q^{57} + 8 q^{58} - q^{59} - 42 q^{60} + 19 q^{61} - 4 q^{62} + 5 q^{63} + 84 q^{64} - 32 q^{65} + 52 q^{66} + 10 q^{67} - 34 q^{68} - 32 q^{69} + 48 q^{70} + 35 q^{71} - 26 q^{72} - 22 q^{73} + 68 q^{74} + 62 q^{75} + 2 q^{76} + 42 q^{77} - 81 q^{78} + 2 q^{79} + 49 q^{80} - 37 q^{81} - 35 q^{82} - 48 q^{83} - 34 q^{84} - 13 q^{85} - 152 q^{86} + 22 q^{87} + 37 q^{88} + 42 q^{89} + 30 q^{90} - 39 q^{91} + 30 q^{92} - 42 q^{94} - 34 q^{95} - 66 q^{96} - 38 q^{97} + 8 q^{98} - 34 q^{99}+O(q^{100}) \) 34 * q + 4 * q^2 - 20 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 - 12 * q^8 - 17 * q^9 - 6 * q^10 + 13 * q^11 + 8 * q^12 - 3 * q^13 + 4 * q^15 - 34 * q^16 + 6 * q^17 + 24 * q^18 + 4 * q^19 + 28 * q^20 - 36 * q^21 + 34 * q^22 + 8 * q^23 + 40 * q^24 + 16 * q^25 - 26 * q^26 - 6 * q^27 + 21 * q^28 + 6 * q^29 - 19 * q^30 - 34 * q^31 + 6 * q^32 + 7 * q^33 - 48 * q^34 + 9 * q^35 + 14 * q^37 + 22 * q^38 - 21 * q^39 - 20 * q^40 + 43 * q^41 - 33 * q^42 - 18 * q^43 - 56 * q^44 + 26 * q^45 + 7 * q^46 - 12 * q^47 + 95 * q^48 + q^49 + 44 * q^50 + 52 * q^51 - 24 * q^52 - 10 * q^53 + 27 * q^54 - 39 * q^55 - 39 * q^56 - 92 * q^57 + 8 * q^58 - q^59 - 42 * q^60 + 19 * q^61 - 4 * q^62 + 5 * q^63 + 84 * q^64 - 32 * q^65 + 52 * q^66 + 10 * q^67 - 34 * q^68 - 32 * q^69 + 48 * q^70 + 35 * q^71 - 26 * q^72 - 22 * q^73 + 68 * q^74 + 62 * q^75 + 2 * q^76 + 42 * q^77 - 81 * q^78 + 2 * q^79 + 49 * q^80 - 37 * q^81 - 35 * q^82 - 48 * q^83 - 34 * q^84 - 13 * q^85 - 152 * q^86 + 22 * q^87 + 37 * q^88 + 42 * q^89 + 30 * q^90 - 39 * q^91 + 30 * q^92 - 42 * q^94 - 34 * q^95 - 66 * q^96 - 38 * q^97 + 8 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.11298	+	1.92773i	0.786994	+	1.36311i	0.927801	+	0.373076i	$0.121697\pi$
$2$	1.11298	+	1.92773i	0.786994	+	1.36311i	−0.140807	+	0.990037i	$0.544970\pi$
$3$	−0.337463	−	0.584504i	−0.194835	−	0.337463i	0.752012	−	0.659150i	$-0.229084\pi$
$3$	−0.337463	−	0.584504i	−0.194835	−	0.337463i	−0.946846	+	0.321686i	$0.895750\pi$
$4$	−1.47744	+	2.55900i	−0.738719	+	1.27950i
$5$	1.70140			0.760888			0.380444	−	0.924804i	$-0.375771\pi$
$5$	1.70140			0.760888			0.380444	+	0.924804i	$0.375771\pi$
$6$	0.751178	−	1.30108i	0.306667	−	0.531163i
$7$	2.45364	−	4.24983i	0.927388	−	1.60628i	0.139714	−	0.990192i	$-0.455382\pi$
$7$	2.45364	−	4.24983i	0.927388	−	1.60628i	0.787674	−	0.616092i	$-0.211285\pi$
$8$	−2.12551			−0.751481
$9$	1.27224	−	2.20358i	0.424079	−	0.734526i
$10$	1.89362	+	3.27984i	0.598814	+	1.03718i
$11$	1.43490	+	2.48531i	0.432637	+	0.749350i	0.997099	−	0.0761091i	$-0.0242497\pi$
$11$	1.43490	+	2.48531i	0.432637	+	0.749350i	−0.564462	+	0.825459i	$0.690916\pi$
$12$	1.99432			0.575712
$13$	−3.48374	−	0.929285i	−0.966215	−	0.257737i
$13$	−3.48374	−	0.929285i	−0.966215	−	0.257737i
$14$	10.9234			2.91940
$15$	−0.574159	−	0.994473i	−0.148247	−	0.256772i
$16$	0.589231	+	1.02058i	0.147308	+	0.255145i
$17$	−1.82786	+	3.16594i	−0.443320	+	0.767853i	−0.997934	−	0.0642549i	$-0.979533\pi$
$17$	−1.82786	+	3.16594i	−0.443320	+	0.767853i	0.554613	+	0.832108i	$0.312866\pi$
$18$	5.66388			1.33499
$19$	−1.68231	+	2.91384i	−0.385947	+	0.668480i	−0.991900	−	0.127020i	$-0.959459\pi$
$19$	−1.68231	+	2.91384i	−0.385947	+	0.668480i	0.605953	+	0.795501i	$0.292792\pi$
$20$	−2.51371	+	4.35387i	−0.562083	+	0.973555i
$21$	−3.31205			−0.722749
$22$	−3.19401	+	5.53219i	−0.680966	+	1.17947i
$23$	−1.08754	−	1.88368i	−0.226768	−	0.392774i	0.730080	−	0.683361i	$-0.239483\pi$
$23$	−1.08754	−	1.88368i	−0.226768	−	0.392774i	−0.956848	+	0.290587i	$0.906149\pi$
$24$	0.717282	+	1.24237i	0.146414	+	0.253597i
$25$	−2.10525			−0.421049
$26$	−2.08591	−	7.74999i	−0.409080	−	1.51990i
$27$	−3.74211			−0.720170
$28$	7.25020	+	12.5577i	1.37016	+	2.37318i
$29$	−4.61421	−	7.99204i	−0.856837	−	1.48409i	−0.874930	−	0.484249i	$-0.839093\pi$
$29$	−4.61421	−	7.99204i	−0.856837	−	1.48409i	0.0180934	−	0.999836i	$-0.494240\pi$
$30$	1.27805	−	2.21365i	0.233339	−	0.404156i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	−3.43711	+	5.95325i	−0.607601	+	1.05240i
$33$	0.968449	−	1.67740i	0.168585	−	0.291998i
$34$	−8.13745			−1.39556
$35$	4.17462	−	7.23065i	0.705639	−	1.22220i
$36$	3.75930	+	6.51130i	0.626550	+	1.08522i
$37$	4.66578	+	8.08136i	0.767049	+	1.32857i	0.939157	+	0.343489i	$0.111609\pi$
$37$	4.66578	+	8.08136i	0.767049	+	1.32857i	−0.172108	+	0.985078i	$0.555058\pi$
$38$	−7.48947			−1.21495
$39$	0.632463	+	2.34986i	0.101275	+	0.376278i
$40$	−3.61634			−0.571793
$41$	3.86213	+	6.68940i	0.603163	+	1.04471i	0.992339	+	0.123545i	$0.0394264\pi$
$41$	3.86213	+	6.68940i	0.603163	+	1.04471i	−0.389176	+	0.921163i	$0.627240\pi$
$42$	−3.68624	−	6.38476i	−0.568799	−	0.985189i
$43$	−6.18781	+	10.7176i	−0.943632	+	1.63442i	−0.185165	+	0.982707i	$0.559282\pi$
$43$	−6.18781	+	10.7176i	−0.943632	+	1.63442i	−0.758467	+	0.651711i	$0.774051\pi$
$44$	−8.47988			−1.27839
$45$	2.16458	−	3.74916i	0.322677	−	0.558893i
$46$	2.42082	−	4.19298i	0.356930	−	0.618222i
$47$	10.9376			1.59542			0.797710	−	0.603042i	$-0.206045\pi$
$47$	10.9376			1.59542			0.797710	+	0.603042i	$0.206045\pi$
$48$	0.397688	−	0.688816i	0.0574013	−	0.0994220i
$49$	−8.54069	−	14.7929i	−1.22010	−	2.11327i
$50$	−2.34309	−	4.05835i	−0.331363	−	0.573938i
$51$	2.46734			0.345497
$52$	7.52504	−	7.54191i	1.04354	−	1.04588i
$53$	6.20847			0.852799			0.426400	−	0.904535i	$-0.359782\pi$
$53$	6.20847			0.852799			0.426400	+	0.904535i	$0.359782\pi$
$54$	−4.16489	−	7.21380i	−0.566769	−	0.981674i
$55$	2.44133	+	4.22850i	0.329189	+	0.570171i
$56$	−5.21523	+	9.03305i	−0.696915	+	1.20709i
$57$	2.27087			0.300783
$58$	10.2710	−	17.7899i	1.34865	−	2.33593i
$59$	−4.08051	+	7.06765i	−0.531237	+	0.920130i	0.468098	+	0.883677i	$0.344939\pi$
$59$	−4.08051	+	7.06765i	−0.531237	+	0.920130i	−0.999335	+	0.0364535i	$0.988394\pi$
$60$	3.39314			0.438052
$61$	3.07647	−	5.32860i	0.393901	−	0.682257i	−0.599059	−	0.800705i	$-0.704458\pi$
$61$	3.07647	−	5.32860i	0.393901	−	0.682257i	0.992960	+	0.118448i	$0.0377918\pi$
$62$	−1.11298	−	1.92773i	−0.141348	−	0.244822i
$63$	−6.24322	−	10.8136i	−0.786572	−	1.36238i
$64$	−12.9448			−1.61810
$65$	−5.92722	−	1.58108i	−0.735182	−	0.196109i
$66$	4.31145			0.530703
$67$	−2.24813	−	3.89387i	−0.274652	−	0.475712i	0.695395	−	0.718628i	$-0.255229\pi$
$67$	−2.24813	−	3.89387i	−0.274652	−	0.475712i	−0.970047	+	0.242916i	$0.921896\pi$
$68$	−5.40109	−	9.35496i	−0.654978	−	1.13446i
$69$	−0.734011	+	1.27134i	−0.0883646	+	0.153052i
$70$	18.5850			2.22133
$71$	1.99517	−	3.45574i	0.236784	−	0.410121i	−0.723006	−	0.690842i	$-0.757240\pi$
$71$	1.99517	−	3.45574i	0.236784	−	0.410121i	0.959790	+	0.280721i	$0.0905734\pi$
$72$	−2.70415	+	4.68373i	−0.318687	+	0.551983i
$73$	−6.02184			−0.704803			−0.352401	−	0.935849i	$-0.614635\pi$
$73$	−6.02184			−0.704803			−0.352401	+	0.935849i	$0.614635\pi$
$74$	−10.3858	+	17.9887i	−1.20733	+	2.09115i
$75$	0.710443	+	1.23052i	0.0820349	+	0.142089i
$76$	−4.97100	−	8.61003i	−0.570213	−	0.987638i
$77$	14.0829			1.60489
$78$	−3.82598	+	3.83456i	−0.433207	+	0.434178i
$79$	2.87249			0.323180			0.161590	−	0.986858i	$-0.448338\pi$
$79$	2.87249			0.323180			0.161590	+	0.986858i	$0.448338\pi$
$80$	1.00252	+	1.73641i	0.112085	+	0.194137i
$81$	−2.55388	−	4.42346i	−0.283765	−	0.491495i
$82$	−8.59692	+	14.8903i	−0.949371	+	1.64436i
$83$	−2.83097			−0.310739			−0.155369	−	0.987856i	$-0.549657\pi$
$83$	−2.83097			−0.310739			−0.155369	+	0.987856i	$0.549657\pi$
$84$	4.89335	−	8.47553i	0.533909	−	0.924757i
$85$	−3.10991	+	5.38652i	−0.337317	+	0.584251i
$86$	−27.5476			−2.97053
$87$	−3.11425	+	5.39404i	−0.333883	+	0.578302i
$88$	−3.04988	−	5.28255i	−0.325119	−	0.563122i
$89$	−4.83416	−	8.37302i	−0.512420	−	0.887538i	−0.999896	−	0.0144017i	$-0.995416\pi$
$89$	−4.83416	−	8.37302i	−0.512420	−	0.887538i	0.487476	−	0.873136i	$-0.337918\pi$
$90$	9.63652			1.01578
$91$	−12.4971	+	12.5252i	−1.31006	+	1.31299i
$92$	6.42710			0.670072
$93$	0.337463	+	0.584504i	0.0349933	+	0.0606102i
$94$	12.1734	+	21.0849i	1.25559	+	2.17474i
$95$	−2.86227	+	4.95760i	−0.293663	+	0.508639i
$96$	4.63960			0.473527
$97$	3.81210	−	6.60276i	0.387060	−	0.670408i	−0.604992	−	0.796231i	$-0.706824\pi$
$97$	3.81210	−	6.60276i	0.387060	−	0.670408i	0.992053	+	0.125823i	$0.0401571\pi$
$98$	19.0112	−	32.9284i	1.92042	−	3.32627i
$99$	7.30211			0.733890
$100$	3.11037	−	5.38732i	0.311037	−	0.538732i
$101$	−3.51830	−	6.09387i	−0.350084	−	0.606363i	0.636180	−	0.771541i	$-0.280514\pi$
$101$	−3.51830	−	6.09387i	−0.350084	−	0.606363i	−0.986264	+	0.165178i	$0.947180\pi$
$102$	2.74609	+	4.75637i	0.271904	+	0.470951i
$103$	−13.8012			−1.35987			−0.679936	−	0.733271i	$-0.737993\pi$
$103$	−13.8012			−1.35987			−0.679936	+	0.733271i	$0.737993\pi$
$104$	7.40472	+	1.97520i	0.726092	+	0.193685i
$105$	−5.63512			−0.549931
$106$	6.90989	+	11.9683i	0.671148	+	1.16246i
$107$	4.80349	+	8.31988i	0.464371	+	0.804314i	0.999173	−	0.0406637i	$-0.0129472\pi$
$107$	4.80349	+	8.31988i	0.464371	+	0.804314i	−0.534802	+	0.844977i	$0.679614\pi$
$108$	5.52874	−	9.57606i	0.532003	−	0.921457i
$109$	−1.27538			−0.122159			−0.0610796	−	0.998133i	$-0.519454\pi$
$109$	−1.27538			−0.122159			−0.0610796	+	0.998133i	$0.519454\pi$
$110$	−5.43429	+	9.41246i	−0.518139	+	0.897443i
$111$	3.14906	−	5.45433i	0.298895	−	0.517702i
$112$	5.78304			0.546446
$113$	4.47739	−	7.75506i	0.421197	−	0.729535i	−0.574860	−	0.818252i	$-0.694943\pi$
$113$	4.47739	−	7.75506i	0.421197	−	0.729535i	0.996057	+	0.0887171i	$0.0282767\pi$
$114$	2.52742	+	4.37762i	0.236715	+	0.410002i
$115$	−1.85034	−	3.20489i	−0.172545	−	0.298857i
$116$	27.2688			2.53185
$117$	−6.47989	+	6.49442i	−0.599066	+	0.600409i
$118$	−18.1661			−1.67232
$119$	8.96980	+	15.5362i	0.822260	+	1.42420i
$120$	1.22038	+	2.11376i	0.111405	+	0.192959i
$121$	1.38215	−	2.39395i	0.125650	−	0.217632i
$122$	13.6962			1.23999
$123$	2.60665	−	4.51485i	0.235034	−	0.407091i
$124$	1.47744	−	2.55900i	0.132678	−	0.229805i
$125$	−12.0888			−1.08126
$126$	13.8971	−	24.0705i	1.23805	−	2.14437i
$127$	5.98186	+	10.3609i	0.530805	+	0.919381i	0.999354	+	0.0359431i	$0.0114435\pi$
$127$	5.98186	+	10.3609i	0.530805	+	0.919381i	−0.468549	+	0.883437i	$0.655223\pi$
$128$	−7.53303	−	13.0476i	−0.665832	−	1.15326i
$129$	8.35263			0.735408
$130$	−3.54896	−	13.1858i	−0.311264	−	1.15647i
$131$	−18.0735			−1.57909			−0.789543	−	0.613695i	$-0.789682\pi$
$131$	−18.0735			−1.57909			−0.789543	+	0.613695i	$0.789682\pi$
$132$	2.86165	+	4.95652i	0.249074	+	0.431410i
$133$	8.25554	+	14.2990i	0.715846	+	1.23988i
$134$	5.00423	−	8.66758i	0.432300	−	0.748765i
$135$	−6.36682			−0.547969
$136$	3.88513	−	6.72924i	0.333147	−	0.577027i
$137$	1.98520	−	3.43847i	0.169607	−	0.293769i	−0.768675	−	0.639640i	$-0.779083\pi$
$137$	1.98520	−	3.43847i	0.169607	−	0.293769i	0.938282	+	0.345872i	$0.112417\pi$
$138$	−3.26775			−0.278169
$139$	−3.70409	+	6.41568i	−0.314177	+	0.544171i	−0.979262	−	0.202597i	$-0.935062\pi$
$139$	−3.70409	+	6.41568i	−0.314177	+	0.544171i	0.665085	+	0.746767i	$0.268395\pi$
$140$	12.3355	+	21.3657i	1.04254	+	1.80573i
$141$	−3.69105	−	6.39309i	−0.310843	−	0.538396i
$142$	8.88234			0.745389
$143$	−2.68924	−	9.99160i	−0.224885	−	0.835540i
$144$	2.99857			0.249881
$145$	−7.85060	−	13.5976i	−0.651957	−	1.12922i
$146$	−6.70217	−	11.6085i	−0.554676	−	0.960726i
$147$	−5.76434	+	9.98413i	−0.475435	+	0.823477i
$148$	−27.5736			−2.26653
$149$	8.66408	−	15.0066i	0.709789	−	1.22939i	−0.255146	−	0.966902i	$-0.582124\pi$
$149$	8.66408	−	15.0066i	0.709789	−	1.22939i	0.964935	−	0.262488i	$-0.0845430\pi$
$150$	−1.58141	+	2.73909i	−0.129122	+	0.223646i
$151$	17.0089			1.38417			0.692083	−	0.721818i	$-0.256693\pi$
$151$	17.0089			1.38417			0.692083	+	0.721818i	$0.256693\pi$
$152$	3.57576	−	6.19339i	0.290032	−	0.502350i
$153$	4.65093	+	8.05565i	0.376006	+	0.651261i
$154$	15.6739	+	27.1480i	1.26304	+	2.18765i
$155$	−1.70140			−0.136660
$156$	−6.94770	−	1.85330i	−0.556261	−	0.148382i
$157$	−12.9489			−1.03343			−0.516717	−	0.856156i	$-0.672846\pi$
$157$	−12.9489			−1.03343			−0.516717	+	0.856156i	$0.672846\pi$
$158$	3.19701	+	5.53739i	0.254341	+	0.440531i
$159$	−2.09513	−	3.62887i	−0.166155	−	0.287788i
$160$	−5.84789	+	10.1289i	−0.462317	+	0.800756i
$161$	−10.6737			−0.841209
$162$	5.68483	−	9.84642i	0.446643	−	0.773608i
$163$	1.15729	−	2.00448i	0.0906459	−	0.157003i	−0.817137	−	0.576443i	$-0.804440\pi$
$163$	1.15729	−	2.00448i	0.0906459	−	0.157003i	0.907783	+	0.419440i	$0.137774\pi$
$164$	−22.8242			−1.78227
$165$	1.64772	−	2.85393i	0.128275	−	0.222178i
$166$	−3.15080	−	5.45735i	−0.244550	−	0.423572i
$167$	4.00515	+	6.93711i	0.309927	+	0.536810i	0.978346	−	0.206975i	$-0.0663619\pi$
$167$	4.00515	+	6.93711i	0.309927	+	0.536810i	−0.668419	+	0.743785i	$0.733029\pi$
$168$	7.03980			0.543132
$169$	11.2729	+	6.47477i	0.867143	+	0.498059i
$170$	−13.8450			−1.06187
$171$	4.28058	+	7.41418i	0.327344	+	0.566977i
$172$	−18.2842	−	31.6692i	−1.39416	−	2.41475i
$173$	−1.49914	+	2.59658i	−0.113977	+	0.197414i	−0.917370	−	0.398034i	$-0.869692\pi$
$173$	−1.49914	+	2.59658i	−0.113977	+	0.197414i	0.803393	+	0.595449i	$0.203026\pi$
$174$	−13.8644			−1.05106
$175$	−5.16551	+	8.94693i	−0.390476	+	0.676324i
$176$	−1.69097	+	2.92885i	−0.127462	+	0.220770i
$177$	5.50809			0.414014
$178$	10.7606	−	18.6380i	0.806543	−	1.39697i
$179$	−0.0675428	−	0.116987i	−0.00504838	−	0.00874405i	0.863490	−	0.504366i	$-0.168274\pi$
$179$	−0.0675428	−	0.116987i	−0.00504838	−	0.00874405i	−0.868539	+	0.495622i	$0.834940\pi$
$180$	6.39607	+	11.0783i	0.476735	+	0.825729i
$181$	17.4249			1.29518			0.647590	−	0.761989i	$-0.275777\pi$
$181$	17.4249			1.29518			0.647590	+	0.761989i	$0.275777\pi$
$182$	−38.0542	−	10.1509i	−2.82076	−	0.752437i
$183$	−4.15278			−0.306982
$184$	2.31158	+	4.00378i	0.170412	+	0.295162i
$185$	7.93834	+	13.7496i	0.583639	+	1.01089i
$186$	−0.751178	+	1.30108i	−0.0550791	+	0.0953997i
$187$	−10.4911			−0.767188
$188$	−16.1597	+	27.9894i	−1.17857	+	2.04134i
$189$	−9.18180	+	15.9033i	−0.667877	+	1.15680i
$190$	−12.7426			−0.924443
$191$	7.16440	−	12.4091i	0.518398	−	0.897891i	−0.481374	−	0.876515i	$-0.659862\pi$
$191$	7.16440	−	12.4091i	0.518398	−	0.897891i	0.999772	−	0.0213759i	$-0.00680469\pi$
$192$	4.36839	+	7.56627i	0.315261	+	0.546049i
$193$	9.17970	+	15.8997i	0.660769	+	1.14449i	0.980414	+	0.196948i	$0.0631031\pi$
$193$	9.17970	+	15.8997i	0.660769	+	1.14449i	−0.319645	+	0.947537i	$0.603564\pi$
$194$	16.9711			1.21846
$195$	1.07607	+	3.99804i	0.0770591	+	0.286306i
$196$	50.4734			3.60524
$197$	−1.24876	−	2.16292i	−0.0889707	−	0.154102i	0.818106	−	0.575068i	$-0.195024\pi$
$197$	−1.24876	−	2.16292i	−0.0889707	−	0.154102i	−0.907076	+	0.420966i	$0.861691\pi$
$198$	8.12708	+	14.0765i	0.577567	+	1.00037i
$199$	3.80747	−	6.59473i	0.269904	−	0.467488i	−0.698933	−	0.715188i	$-0.746341\pi$
$199$	3.80747	−	6.59473i	0.269904	−	0.467488i	0.968837	+	0.247700i	$0.0796746\pi$
$200$	4.47472			0.316410
$201$	−1.51732	+	2.62808i	−0.107024	+	0.185370i
$202$	7.83158	−	13.5647i	0.551028	−	0.954408i
$203$	−45.2864			−3.17848
$204$	−3.64534	+	6.31391i	−0.255225	+	0.442062i
$205$	6.57101	+	11.3813i	0.458940	+	0.794907i
$206$	−15.3604	−	26.6050i	−1.07021	−	1.85366i
$207$	−5.53444			−0.384670
$208$	−1.10432	−	4.10299i	−0.0765707	−	0.284491i
$209$	−9.65573			−0.667901
$210$	−6.27176	−	10.8630i	−0.432793	−	0.749619i
$211$	10.1105	+	17.5119i	0.696037	+	1.20557i	0.969830	+	0.243783i	$0.0783884\pi$
$211$	10.1105	+	17.5119i	0.696037	+	1.20557i	−0.273793	+	0.961789i	$0.588278\pi$
$212$	−9.17263	+	15.8875i	−0.629979	+	1.09116i
$213$	−2.69319			−0.184535
$214$	−10.6923	+	18.5197i	−0.730914	+	1.26598i
$215$	−10.5279	+	18.2349i	−0.717999	+	1.24361i
$216$	7.95390			0.541194
$217$	−2.45364	+	4.24983i	−0.166564	+	0.288497i
$218$	−1.41947	−	2.45859i	−0.0961385	−	0.166517i
$219$	2.03215	+	3.51979i	0.137320	+	0.237845i
$220$	−14.4276			−0.972711
$221$	9.30983	−	9.33071i	0.626247	−	0.627651i
$222$	14.0193			0.940915
$223$	−7.14409	−	12.3739i	−0.478404	−	0.828620i	0.521290	−	0.853380i	$-0.325451\pi$
$223$	−7.14409	−	12.3739i	−0.478404	−	0.828620i	−0.999693	+	0.0247602i	$0.992118\pi$
$224$	16.8669	+	29.2143i	1.12696	+	1.95196i
$225$	−2.67837	+	4.63907i	−0.178558	+	0.309272i
$226$	19.9329			1.32592
$227$	−5.23723	+	9.07115i	−0.347607	+	0.602073i	−0.985824	−	0.167783i	$-0.946339\pi$
$227$	−5.23723	+	9.07115i	−0.347607	+	0.602073i	0.638217	+	0.769857i	$0.279672\pi$
$228$	−3.35506	+	5.81114i	−0.222194	+	0.384852i
$229$	−16.9367			−1.11921			−0.559606	−	0.828759i	$-0.689047\pi$
$229$	−16.9367			−1.11921			−0.559606	+	0.828759i	$0.689047\pi$
$230$	4.11878	−	7.13393i	0.271584	−	0.470398i
$231$	−4.75245	−	8.23149i	−0.312688	−	0.541592i
$232$	9.80754	+	16.9872i	0.643897	+	1.11526i
$233$	17.6448			1.15595			0.577974	−	0.816055i	$-0.303844\pi$
$233$	17.6448			1.15595			0.577974	+	0.816055i	$0.303844\pi$
$234$	−19.7315	−	5.26336i	−1.28989	−	0.344077i
$235$	18.6093			1.21394
$236$	−12.0574	−	20.8840i	−0.784870	−	1.35943i
$237$	−0.969359	−	1.67898i	−0.0629666	−	0.109061i
$238$	−19.9664	+	34.5828i	−1.29423	+	2.24167i
$239$	−14.9040			−0.964063			−0.482031	−	0.876154i	$-0.660101\pi$
$239$	−14.9040			−0.964063			−0.482031	+	0.876154i	$0.660101\pi$
$240$	0.676625	−	1.17195i	0.0436760	−	0.0756490i
$241$	10.4494	−	18.0990i	0.673107	−	1.16586i	−0.303911	−	0.952700i	$-0.598293\pi$
$241$	10.4494	−	18.0990i	0.673107	−	1.16586i	0.977018	−	0.213156i	$-0.0683741\pi$
$242$	6.15320			0.395543
$243$	−7.33686	+	12.7078i	−0.470659	+	0.815206i
$244$	9.09058	+	15.7453i	0.581965	+	1.00799i
$245$	−14.5311	−	25.1686i	−0.928359	−	1.60796i
$246$	11.6046			0.739881
$247$	8.56850	−	8.58771i	0.545200	−	0.546423i
$248$	2.12551			0.134970
$249$	0.955347	+	1.65471i	0.0605427	+	0.104863i
$250$	−13.4546	−	23.3041i	−0.850945	−	1.47388i
$251$	6.15520	−	10.6611i	0.388512	−	0.672923i	−0.603737	−	0.797183i	$-0.706322\pi$
$251$	6.15520	−	10.6611i	0.388512	−	0.672923i	0.992250	+	0.124260i	$0.0396557\pi$
$252$	36.8959			2.32422
$253$	3.12102	−	5.40576i	0.196217	−	0.339857i
$254$	−13.3154	+	23.0629i	−0.835480	+	1.44709i
$255$	4.19792			0.262884
$256$	3.82340	−	6.62233i	0.238963	−	0.413896i
$257$	−0.465849	−	0.806874i	−0.0290589	−	0.0503314i	0.851130	−	0.524955i	$-0.175918\pi$
$257$	−0.465849	−	0.806874i	−0.0290589	−	0.0503314i	−0.880189	+	0.474623i	$0.842584\pi$
$258$	9.29629	+	16.1017i	0.578762	+	1.00245i
$259$	45.7925			2.84541
$260$	12.8031	−	12.8318i	0.794014	−	0.795794i
$261$	−23.4815			−1.45347
$262$	−20.1154	−	34.8408i	−1.24273	−	2.15247i
$263$	−6.78349	−	11.7493i	−0.418288	−	0.724496i	0.577480	−	0.816405i	$-0.304036\pi$
$263$	−6.78349	−	11.7493i	−0.418288	−	0.724496i	−0.995767	+	0.0919094i	$0.970703\pi$
$264$	−2.05845	+	3.56534i	−0.126689	+	0.219431i
$265$	10.5631			0.648885
$266$	−18.3765	+	31.8290i	−1.12673	+	1.95156i
$267$	−3.26271	+	5.65117i	−0.199674	+	0.345846i
$268$	13.2859			0.811564
$269$	6.31235	−	10.9333i	0.384871	−	0.666616i	−0.606880	−	0.794793i	$-0.707579\pi$
$269$	6.31235	−	10.9333i	0.384871	−	0.666616i	0.991751	+	0.128177i	$0.0409126\pi$
$270$	−7.08613	−	12.2735i	−0.431248	−	0.746944i
$271$	1.22813	+	2.12719i	0.0746038	+	0.129218i	0.900914	−	0.433998i	$-0.142897\pi$
$271$	1.22813	+	2.12719i	0.0746038	+	0.129218i	−0.826310	+	0.563215i	$0.809564\pi$
$272$	−4.30812			−0.261218
$273$	11.5383	+	3.07784i	0.698331	+	0.186279i
$274$	8.83795			0.533920
$275$	−3.02081	−	5.23219i	−0.182162	−	0.315513i
$276$	−2.16891	−	3.75666i	−0.130553	−	0.226125i
$277$	1.79734	−	3.11309i	0.107992	−	0.187047i	−0.806965	−	0.590600i	$-0.798891\pi$
$277$	1.79734	−	3.11309i	0.107992	−	0.187047i	0.914957	+	0.403552i	$0.132225\pi$
$278$	−16.4903			−0.989022
$279$	−1.27224	+	2.20358i	−0.0761668	+	0.131925i
$280$	−8.87319	+	15.3688i	−0.530274	+	0.918462i
$281$	4.40394			0.262717			0.131358	−	0.991335i	$-0.458066\pi$
$281$	4.40394			0.262717			0.131358	+	0.991335i	$0.458066\pi$
$282$	8.21612	−	14.2307i	0.489263	−	0.847428i
$283$	2.78094	+	4.81673i	0.165310	+	0.286325i	0.936765	−	0.349958i	$-0.113804\pi$
$283$	2.78094	+	4.81673i	0.165310	+	0.286325i	−0.771455	+	0.636283i	$0.780471\pi$
$284$	5.89549	+	10.2113i	0.349833	+	0.605929i
$285$	3.86365			0.228863
$286$	16.2681	−	16.3046i	0.961952	−	0.964109i
$287$	37.9051			2.23747
$288$	8.74564	+	15.1479i	0.515342	+	0.892598i
$289$	1.81788	+	3.14866i	0.106934	+	0.185215i
$290$	17.4751	−	30.2677i	1.02617	−	1.77738i
$291$	−5.14578			−0.301651
$292$	8.89689	−	15.4099i	0.520651	−	0.901794i
$293$	3.40144	−	5.89146i	0.198714	−	0.344183i	−0.749398	−	0.662120i	$-0.769657\pi$
$293$	3.40144	−	5.89146i	0.198714	−	0.344183i	0.948112	+	0.317937i	$0.102990\pi$
$294$	−25.6623			−1.49666
$295$	−6.94257	+	12.0249i	−0.404212	+	0.700116i
$296$	−9.91715	−	17.1770i	−0.576423	−	0.998393i
$297$	−5.36954	−	9.30032i	−0.311572	−	0.539659i
$298$	38.5717			2.23440
$299$	2.03824	+	7.57288i	0.117874	+	0.437951i
$300$	−4.19854			−0.242403
$301$	30.3653	+	52.5942i	1.75023	+	3.03148i
$302$	18.9305	+	32.7887i	1.08933	+	1.88678i
$303$	−2.37459	+	4.11292i	−0.136417	+	0.236281i
$304$	−3.96507			−0.227412
$305$	5.23430	−	9.06607i	0.299715	−	0.519121i
$306$	−10.3528	+	17.9315i	−0.591828	+	1.02508i
$307$	25.1957			1.43799			0.718996	−	0.695014i	$-0.244602\pi$
$307$	25.1957			1.43799			0.718996	+	0.695014i	$0.244602\pi$
$308$	−20.8066	+	36.0380i	−1.18556	+	2.05346i
$309$	4.65740	+	8.06685i	0.264950	+	0.458907i
$310$	−1.89362	−	3.27984i	−0.107550	−	0.186282i
$311$	−8.18100			−0.463902			−0.231951	−	0.972728i	$-0.574511\pi$
$311$	−8.18100			−0.463902			−0.231951	+	0.972728i	$0.574511\pi$
$312$	−1.34431	−	4.99464i	−0.0761064	−	0.282766i
$313$	−13.9760			−0.789969			−0.394985	−	0.918688i	$-0.629250\pi$
$313$	−13.9760			−0.789969			−0.394985	+	0.918688i	$0.629250\pi$
$314$	−14.4118	−	24.9620i	−0.813306	−	1.40869i
$315$	−10.6222	−	18.3982i	−0.598493	−	1.03662i
$316$	−4.24392	+	7.35069i	−0.238739	+	0.413508i
$317$	14.3405			0.805443			0.402721	−	0.915323i	$-0.368064\pi$
$317$	14.3405			0.805443			0.402721	+	0.915323i	$0.368064\pi$
$318$	4.66367	−	8.07771i	0.261526	−	0.452976i
$319$	13.2418	−	22.9355i	0.741399	−	1.28414i
$320$	−22.0242			−1.23119
$321$	3.24200	−	5.61531i	0.180951	−	0.313416i
$322$	−11.8796	−	20.5761i	−0.662026	−	1.14666i
$323$	−6.15002	−	10.6522i	−0.342197	−	0.592702i
$324$	15.0928			0.838490
$325$	7.33412	+	1.95637i	0.406824	+	0.108520i
$326$	5.15215			0.285351
$327$	0.430394	+	0.745464i	0.0238008	+	0.0412243i
$328$	−8.20899	−	14.2184i	−0.453265	−	0.785079i
$329$	26.8370	−	46.4831i	1.47957	−	2.56270i
$330$	7.33549			0.403805
$331$	1.05338	−	1.82450i	0.0578988	−	0.100284i	−0.835623	−	0.549303i	$-0.814893\pi$
$331$	1.05338	−	1.82450i	0.0578988	−	0.100284i	0.893522	+	0.449019i	$0.148227\pi$
$332$	4.18258	−	7.24443i	0.229549	−	0.397590i
$333$	23.7439			1.30116
$334$	−8.91527	+	15.4417i	−0.487822	+	0.844933i
$335$	−3.82496	−	6.62502i	−0.208980	−	0.361964i
$336$	−1.95157	−	3.38021i	−0.106467	−	0.184406i
$337$	−16.9416			−0.922869			−0.461434	−	0.887174i	$-0.652665\pi$
$337$	−16.9416			−0.922869			−0.461434	+	0.887174i	$0.652665\pi$
$338$	0.0648056	+	28.9373i	0.00352496	+	1.57398i
$339$	−6.04382			−0.328255
$340$	−9.18940	−	15.9165i	−0.498365	−	0.863194i
$341$	−1.43490	−	2.48531i	−0.0777040	−	0.134587i
$342$	−9.52838	+	16.5036i	−0.515236	+	0.892415i
$343$	−49.4722			−2.67125
$344$	13.1522	−	22.7804i	0.709122	−	1.22823i
$345$	−1.24885	+	2.16306i	−0.0672356	+	0.116455i
$346$	−6.67402			−0.358798
$347$	5.18991	−	8.98918i	0.278609	−	0.482565i	−0.692430	−	0.721485i	$-0.743460\pi$
$347$	5.18991	−	8.98918i	0.278609	−	0.482565i	0.971039	+	0.238920i	$0.0767934\pi$
$348$	−9.20223	−	15.9387i	−0.493291	−	0.854405i
$349$	−5.19549	−	8.99885i	−0.278108	−	0.481697i	0.692806	−	0.721124i	$-0.256374\pi$
$349$	−5.19549	−	8.99885i	−0.278108	−	0.481697i	−0.970915	+	0.239426i	$0.923041\pi$
$350$	−22.9964			−1.22921
$351$	13.0365	+	3.47749i	0.695839	+	0.185615i
$352$	−19.7276			−1.05148
$353$	−8.64684	−	14.9768i	−0.460225	−	0.797133i	0.538747	−	0.842468i	$-0.318898\pi$
$353$	−8.64684	−	14.9768i	−0.460225	−	0.797133i	−0.998972	+	0.0453347i	$0.985565\pi$
$354$	6.13038	+	10.6181i	0.325826	+	0.564347i
$355$	3.39459	−	5.87959i	0.180166	−	0.312056i
$356$	28.5687			1.51414
$357$	6.05396	−	10.4858i	0.320409	−	0.554965i
$358$	0.150347	−	0.260409i	0.00794609	−	0.0137630i
$359$	−19.4810			−1.02817			−0.514083	−	0.857740i	$-0.671868\pi$
$359$	−19.4810			−1.02817			−0.514083	+	0.857740i	$0.671868\pi$
$360$	−4.60084	+	7.96889i	−0.242485	+	0.419997i
$361$	3.83970	+	6.65055i	0.202089	+	0.350029i
$362$	19.3935	+	33.5905i	1.01930	+	1.76548i
$363$	−1.86570			−0.0979238
$364$	−13.5881	−	50.4853i	−0.712210	−	2.64615i
$365$	−10.2455			−0.536276
$366$	−4.62195	−	8.00545i	−0.241593	−	0.418452i
$367$	−6.37216	−	11.0369i	−0.332624	−	0.576122i	0.650401	−	0.759591i	$-0.274601\pi$
$367$	−6.37216	−	11.0369i	−0.332624	−	0.576122i	−0.983026	+	0.183469i	$0.941267\pi$
$368$	1.28163	−	2.21984i	0.0668094	−	0.115717i
$369$	19.6542			1.02315
$370$	−17.6704	+	30.6060i	−0.918640	+	1.59113i
$371$	15.2333	−	26.3849i	0.790876	−	1.36984i
$372$	−1.99432			−0.103401
$373$	3.36061	−	5.82076i	0.174006	−	0.301387i	−0.765811	−	0.643066i	$-0.777662\pi$
$373$	3.36061	−	5.82076i	0.174006	−	0.301387i	0.939817	+	0.341679i	$0.110995\pi$
$374$	−11.6764	−	20.2241i	−0.603772	−	1.04576i
$375$	4.07954	+	7.06598i	0.210667	+	0.364885i
$376$	−23.2481			−1.19893
$377$	8.64781	+	32.1301i	0.445385	+	1.65478i
$378$	−40.8765			−2.10246
$379$	−15.2630	−	26.4362i	−0.784006	−	1.35794i	−0.929591	−	0.368593i	$-0.879840\pi$
$379$	−15.2630	−	26.4362i	−0.784006	−	1.35794i	0.145585	−	0.989346i	$-0.453494\pi$
$380$	−8.45765	−	14.6491i	−0.433868	−	0.751482i
$381$	4.03732	−	6.99284i	0.206838	−	0.358254i
$382$	31.8953			1.63190
$383$	−10.2503	+	17.7541i	−0.523767	+	0.907191i	0.475850	+	0.879526i	$0.342140\pi$
$383$	−10.2503	+	17.7541i	−0.523767	+	0.907191i	−0.999617	+	0.0276645i	$0.991193\pi$
$384$	−5.08424	+	8.80617i	−0.259454	+	0.449388i
$385$	23.9606			1.22114
$386$	−20.4336	+	35.3920i	−1.04004	+	1.80141i
$387$	15.7447	+	27.2707i	0.800349	+	1.38625i
$388$	11.2643	+	19.5103i	0.571858	+	0.990487i
$389$	−5.51210			−0.279475			−0.139737	−	0.990189i	$-0.544626\pi$
$389$	−5.51210			−0.279475			−0.139737	+	0.990189i	$0.544626\pi$
$390$	−6.50952	+	6.52411i	−0.329622	+	0.330361i
$391$	7.95148			0.402124
$392$	18.1533	+	31.4425i	0.916881	+	1.58808i
$393$	6.09913	+	10.5640i	0.307660	+	0.532884i
$394$	2.77969	−	4.81457i	0.140039	−	0.242554i
$395$	4.88724			0.245904
$396$	−10.7884	+	18.6861i	−0.542138	+	0.939011i
$397$	−15.0352	+	26.0417i	−0.754593	+	1.30699i	0.190983	+	0.981593i	$0.438832\pi$
$397$	−15.0352	+	26.0417i	−0.754593	+	1.30699i	−0.945576	+	0.325400i	$0.894501\pi$
$398$	16.9505			0.849652
$399$	5.57188	−	9.65079i	0.278943	−	0.483144i
$400$	−1.24048	−	2.14857i	−0.0620238	−	0.107428i
$401$	−1.89475	−	3.28181i	−0.0946194	−	0.163886i	0.814830	−	0.579700i	$-0.196830\pi$
$401$	−1.89475	−	3.28181i	−0.0946194	−	0.163886i	−0.909450	+	0.415814i	$0.863497\pi$
$402$	−6.75498			−0.336908
$403$	3.48374	+	0.929285i	0.173537	+	0.0462910i
$404$	20.7923			1.03445
$405$	−4.34517	−	7.52606i	−0.215913	−	0.373973i
$406$	−50.4028	−	87.3001i	−2.50145	−	4.33263i
$407$	−13.3898	+	23.1918i	−0.663708	+	1.14958i
$408$	−5.24435			−0.259634
$409$	−1.44653	+	2.50547i	−0.0715264	+	0.123887i	−0.899570	−	0.436776i	$-0.856120\pi$
$409$	−1.44653	+	2.50547i	−0.0715264	+	0.123887i	0.828044	+	0.560663i	$0.189454\pi$
$410$	−14.6268	+	25.3343i	−0.722365	+	1.25117i
$411$	−2.67973			−0.132181
$412$	20.3904	−	35.3172i	1.00456	−	1.73996i
$413$	20.0242	+	34.6829i	0.985327	+	1.70664i
$414$	−6.15971	−	10.6689i	−0.302733	−	0.524350i
$415$	−4.81660			−0.236438
$416$	17.5063	−	17.5455i	0.858315	−	0.860240i
$417$	4.99998			0.244850
$418$	−10.7466	−	18.6137i	−0.525634	−	0.910424i
$419$	10.6104	+	18.3778i	0.518353	+	0.897813i	0.999773	+	0.0213232i	$0.00678791\pi$
$419$	10.6104	+	18.3778i	0.518353	+	0.897813i	−0.481420	+	0.876490i	$0.659879\pi$
$420$	8.32554	−	14.4203i	0.406245	−	0.703637i
$421$	−19.2370			−0.937554			−0.468777	−	0.883316i	$-0.655305\pi$
$421$	−19.2370			−0.937554			−0.468777	+	0.883316i	$0.655305\pi$
$422$	−22.5056	+	38.9808i	−1.09555	+	1.89755i
$423$	13.9153	−	24.1020i	0.676584	−	1.17188i
$424$	−13.1962			−0.640862
$425$	3.84809	−	6.66508i	0.186660	−	0.323304i
$426$	−2.99746	−	5.19176i	−0.145228	−	0.251541i
$427$	−15.0971	−	26.1489i	−0.730599	−	1.26543i
$428$	−28.3874			−1.37216
$429$	−4.93261	+	4.94367i	−0.238149	+	0.238683i
$430$	−46.8694			−2.26024
$431$	5.14212	+	8.90641i	0.247687	+	0.429007i	0.962884	−	0.269917i	$-0.0869962\pi$
$431$	5.14212	+	8.90641i	0.247687	+	0.429007i	−0.715197	+	0.698923i	$0.753663\pi$
$432$	−2.20497	−	3.81912i	−0.106087	−	0.183747i
$433$	−3.68422	+	6.38126i	−0.177052	+	0.306664i	−0.940870	−	0.338769i	$-0.889990\pi$
$433$	−3.68422	+	6.38126i	−0.177052	+	0.306664i	0.763817	+	0.645433i	$0.223323\pi$
$434$	−10.9234			−0.524339
$435$	−5.29858	+	9.17741i	−0.254048	+	0.440023i
$436$	1.88429	−	3.26369i	0.0902413	−	0.156303i
$437$	7.31831			0.350082
$438$	−4.52347	+	7.83489i	−0.216140	+	0.374365i
$439$	−4.60987	−	7.98454i	−0.220017	−	0.381081i	0.734796	−	0.678289i	$-0.237278\pi$
$439$	−4.60987	−	7.98454i	−0.220017	−	0.381081i	−0.954813	+	0.297207i	$0.903945\pi$
$440$	−5.18907	−	8.98773i	−0.247379	−	0.428473i
$441$	−43.4631			−2.06967
$442$	28.3488	+	7.56201i	1.34841	+	0.359688i
$443$	32.8723			1.56181			0.780905	−	0.624650i	$-0.214758\pi$
$443$	32.8723			1.56181			0.780905	+	0.624650i	$0.214758\pi$
$444$	9.30507	+	16.1169i	0.441599	+	0.764872i
$445$	−8.22484	−	14.2458i	−0.389895	−	0.675317i
$446$	15.9024	−	27.5438i	0.753002	−	1.30424i
$447$	−11.6952			−0.553166
$448$	−31.7618	+	55.0131i	−1.50061	+	2.59913i
$449$	−2.44471	+	4.23436i	−0.115373	+	0.199832i	−0.917929	−	0.396745i	$-0.870140\pi$
$449$	−2.44471	+	4.23436i	−0.115373	+	0.199832i	0.802556	+	0.596577i	$0.203473\pi$
$450$	−11.9239			−0.562096
$451$	−11.0835	+	19.1972i	−0.521902	+	0.903960i
$452$	13.2301	+	22.9152i	0.622293	+	1.07784i
$453$	−5.73989	−	9.94178i	−0.269683	−	0.467105i
$454$	−23.3157			−1.09426
$455$	−21.2626	+	21.3103i	−0.996806	+	0.999041i
$456$	−4.82675			−0.226033
$457$	−3.18960	−	5.52455i	−0.149203	−	0.258428i	0.781730	−	0.623617i	$-0.214338\pi$
$457$	−3.18960	−	5.52455i	−0.149203	−	0.258428i	−0.930933	+	0.365189i	$0.881004\pi$
$458$	−18.8502	−	32.6495i	−0.880813	−	1.52561i
$459$	6.84005	−	11.8473i	0.319266	−	0.552985i
$460$	10.9351			0.509850
$461$	16.9303	−	29.3241i	0.788521	−	1.36576i	−0.138353	−	0.990383i	$-0.544181\pi$
$461$	16.9303	−	29.3241i	0.788521	−	1.36576i	0.926873	−	0.375375i	$-0.122486\pi$
$462$	10.5787	−	18.3229i	0.492168	−	0.852459i
$463$	20.9683			0.974480			0.487240	−	0.873268i	$-0.338004\pi$
$463$	20.9683			0.974480			0.487240	+	0.873268i	$0.338004\pi$
$464$	5.43767	−	9.41832i	0.252438	−	0.437235i
$465$	0.574159	+	0.994473i	0.0266260	+	0.0461176i
$466$	19.6382	+	34.0144i	0.909724	+	1.57569i
$467$	3.34971			0.155006			0.0775030	−	0.996992i	$-0.475305\pi$
$467$	3.34971			0.155006			0.0775030	+	0.996992i	$0.475305\pi$
$468$	−7.04557	−	26.1771i	−0.325681	−	1.21004i
$469$	−22.0644			−1.01884
$470$	20.7117	+	35.8737i	0.955360	+	1.65473i
$471$	4.36977	+	7.56867i	0.201349	+	0.348746i
$472$	8.67317	−	15.0224i	0.399215	−	0.691460i
$473$	−35.5154			−1.63300
$474$	2.15775	−	3.73733i	0.0991087	−	0.171661i
$475$	3.54166	−	6.13434i	0.162503	−	0.281463i
$476$	−53.0093			−2.42968
$477$	7.89865	−	13.6809i	0.361654	−	0.626403i
$478$	−16.5879	−	28.7310i	−0.758711	−	1.31413i
$479$	5.55093	+	9.61450i	0.253629	+	0.439298i	0.964522	−	0.264002i	$-0.0850426\pi$
$479$	5.55093	+	9.61450i	0.253629	+	0.439298i	−0.710894	+	0.703300i	$0.751709\pi$
$480$	7.89380			0.360301
$481$	−8.74445	−	32.4892i	−0.398713	−	1.48138i
$482$	46.5199			2.11893
$483$	3.60200	+	6.23884i	0.163897	+	0.283877i
$484$	4.08408	+	7.07383i	0.185640	+	0.321538i
$485$	6.48590	−	11.2339i	0.294510	−	0.510106i
$486$	−32.6630			−1.48162
$487$	−10.9569	+	18.9778i	−0.496503	+	0.859968i	−0.999992	−	0.00403372i	$-0.998716\pi$
$487$	−10.9569	+	18.9778i	−0.496503	+	0.859968i	0.503489	+	0.864001i	$0.332049\pi$
$488$	−6.53906	+	11.3260i	−0.296009	+	0.512703i
$489$	−1.56217			−0.0706438
$490$	32.3456	−	56.0242i	1.46123	−	2.53092i
$491$	10.5528	+	18.2779i	0.476239	+	0.824871i	0.999629	−	0.0272225i	$-0.00866627\pi$
$491$	10.5528	+	18.2779i	0.476239	+	0.824871i	−0.523390	+	0.852093i	$0.675333\pi$
$492$	7.70233	+	13.3408i	0.347248	+	0.601451i
$493$	33.7364			1.51941
$494$	26.0914	+	6.95985i	1.17391	+	0.313139i
$495$	12.4238			0.558408
$496$	−0.589231	−	1.02058i	−0.0264573	−	0.0458253i
$497$	−9.79087	−	16.9583i	−0.439181	−	0.760683i
$498$	−2.12656	+	3.68331i	−0.0952934	+	0.165053i
$499$	5.41255			0.242299			0.121150	−	0.992634i	$-0.461342\pi$
$499$	5.41255			0.242299			0.121150	+	0.992634i	$0.461342\pi$
$500$	17.8605	−	30.9353i	0.798747	−	1.38347i
$501$	2.70318	−	4.68204i	0.120769	−	0.209178i
$502$	27.4024			1.22303
$503$	−5.85636	+	10.1435i	−0.261122	+	0.452277i	−0.966540	−	0.256514i	$-0.917426\pi$
$503$	−5.85636	+	10.1435i	−0.261122	+	0.452277i	0.705418	+	0.708791i	$0.250759\pi$
$504$	13.2700	+	22.9844i	0.591094	+	1.02380i
$505$	−5.98603	−	10.3681i	−0.266375	−	0.461375i
$506$	13.8945			0.617686
$507$	−0.0196496	−	8.77403i	−0.000872667	−	0.389668i
$508$	−35.3513			−1.56846
$509$	2.69605	+	4.66969i	0.119500	+	0.206980i	0.919570	−	0.392927i	$-0.128537\pi$
$509$	2.69605	+	4.66969i	0.119500	+	0.206980i	−0.800070	+	0.599907i	$0.795204\pi$
$510$	4.67220	+	8.09248i	0.206888	+	0.358341i
$511$	−14.7754	+	25.5918i	−0.653626	+	1.13211i
$512$	−13.1107			−0.579416
$513$	6.29538	−	10.9039i	0.277948	−	0.481419i
$514$	1.03696	−	1.79606i	0.0457383	−	0.0792210i
$515$	−23.4813			−1.03471
$516$	−12.3405	+	21.3744i	−0.543260	+	0.940954i
$517$	15.6944	+	27.1835i	0.690238	+	1.19553i
$518$	50.9661	+	88.2758i	2.23932	+	3.87862i
$519$	2.02362			0.0888268
$520$	12.5984	+	3.36061i	0.552475	+	0.147372i
$521$	−26.0558			−1.14153			−0.570763	−	0.821115i	$-0.693352\pi$
$521$	−26.0558			−1.14153			−0.570763	+	0.821115i	$0.693352\pi$
$522$	−26.1343	−	45.2660i	−1.14387	−	1.98124i
$523$	10.5064	+	18.1977i	0.459415	+	0.795730i	0.998930	−	0.0462461i	$-0.0147258\pi$
$523$	10.5064	+	18.1977i	0.459415	+	0.795730i	−0.539515	+	0.841976i	$0.681393\pi$
$524$	26.7024	−	46.2499i	1.16650	−	2.02044i
$525$	6.97268			0.304313
$526$	15.0997	−	26.1535i	0.658380	−	1.14035i
$527$	1.82786	−	3.16594i	0.0796227	−	0.137911i
$528$	2.28256			0.0993358
$529$	9.13450	−	15.8214i	0.397152	−	0.687888i
$530$	11.7565	+	20.3628i	0.510668	+	0.884504i
$531$	10.3828	+	17.9835i	0.450573	+	0.780416i
$532$	−48.7882			−2.11524
$533$	−7.23828	−	26.8931i	−0.313525	−	1.16487i
$534$	−14.5253			−0.628570
$535$	8.17264	+	14.1554i	0.353334	+	0.611993i
$536$	4.77842	+	8.27646i	0.206396	+	0.357489i
$537$	−0.0455864	+	0.0789580i	−0.00196720	+	0.00340729i
$538$	28.1020			1.21156
$539$	24.5100	−	42.4526i	1.05572	−	1.82856i
$540$	9.40659	−	16.2927i	0.404795	−	0.701126i
$541$	4.81257			0.206908			0.103454	−	0.994634i	$-0.467010\pi$
$541$	4.81257			0.206908			0.103454	+	0.994634i	$0.467010\pi$
$542$	−2.73377	+	4.73503i	−0.117425	+	0.203387i
$543$	−5.88025	−	10.1849i	−0.252346	−	0.437076i
$544$	−12.5651	−	21.7634i	−0.538724	−	0.933097i
$545$	−2.16993			−0.0929495
$546$	6.90864	+	25.6684i	0.295662	+	1.09851i
$547$	−25.5414			−1.09207			−0.546035	−	0.837762i	$-0.683863\pi$
$547$	−25.5414			−1.09207			−0.546035	+	0.837762i	$0.683863\pi$
$548$	5.86603	+	10.1603i	0.250584	+	0.434025i
$549$	−7.82799	−	13.5585i	−0.334091	−	0.578662i
$550$	6.72418	−	11.6466i	0.286720	−	0.496614i
$551$	31.0500			1.32278
$552$	1.56015	−	2.70226i	0.0664043	−	0.115016i
$553$	7.04805	−	12.2076i	0.299713	−	0.519119i
$554$	8.00161			0.339956
$555$	5.35780	−	9.27998i	0.227426	−	0.393913i
$556$	−10.9451	−	18.9575i	−0.464177	−	0.803978i
$557$	−9.73307	−	16.8582i	−0.412403	−	0.714303i	0.582749	−	0.812652i	$-0.301977\pi$
$557$	−9.73307	−	16.8582i	−0.412403	−	0.714303i	−0.995152	+	0.0983490i	$0.968644\pi$
$558$	−5.66388			−0.239771
$559$	31.5164	−	31.5871i	1.33300	−	1.33599i
$560$	9.83926			0.415785
$561$	3.54037	+	6.13211i	0.149475	+	0.258898i
$562$	4.90148	+	8.48962i	0.206757	+	0.358113i
$563$	0.980438	−	1.69817i	0.0413205	−	0.0715693i	−0.844626	−	0.535358i	$-0.820177\pi$
$563$	0.980438	−	1.69817i	0.0413205	−	0.0715693i	0.885946	+	0.463788i	$0.153510\pi$
$564$	21.8132			0.918502
$565$	7.61782	−	13.1944i	0.320484	−	0.555095i
$566$	−6.19025	+	10.7218i	−0.260196	+	0.450672i
$567$	−25.0652			−1.05264
$568$	−4.24076	+	7.34521i	−0.177938	+	0.308198i
$569$	10.8163	+	18.7344i	0.453444	+	0.785388i	0.998597	−	0.0529486i	$-0.0168619\pi$
$569$	10.8163	+	18.7344i	0.453444	+	0.785388i	−0.545153	+	0.838336i	$0.683529\pi$
$570$	4.30015	+	7.44808i	0.180113	+	0.311966i
$571$	25.3974			1.06285			0.531424	−	0.847106i	$-0.321657\pi$
$571$	25.3974			1.06285			0.531424	+	0.847106i	$0.321657\pi$
$572$	29.5417	+	7.88022i	1.23520	+	0.329489i
$573$	−9.67089			−0.404007
$574$	42.1875	+	73.0709i	1.76087	+	3.04992i
$575$	2.28954	+	3.96560i	0.0954805	+	0.165377i
$576$	−16.4688	+	28.5249i	−0.686201	+	1.18854i
$577$	−12.9784			−0.540296			−0.270148	−	0.962819i	$-0.587073\pi$
$577$	−12.9784			−0.540296			−0.270148	+	0.962819i	$0.587073\pi$
$578$	−4.04652	+	7.00878i	−0.168313	+	0.291527i
$579$	6.19562	−	10.7311i	0.257481	−	0.445971i
$580$	46.3951			1.92645
$581$	−6.94617	+	12.0311i	−0.288176	+	0.499135i
$582$	−5.72714	−	9.91969i	−0.237397	−	0.411185i
$583$	8.90851	+	15.4300i	0.368953	+	0.639045i
$584$	12.7995			0.529646
$585$	−11.0249	+	11.0496i	−0.455823	+	0.456845i
$586$	15.1429			0.625547
$587$	1.53528	+	2.65919i	0.0633679	+	0.109756i	0.895969	−	0.444117i	$-0.146483\pi$
$587$	1.53528	+	2.65919i	0.0633679	+	0.109756i	−0.832601	+	0.553873i	$0.813149\pi$
$588$	−17.0329	−	29.5019i	−0.702425	−	1.21664i
$589$	1.68231	−	2.91384i	0.0693182	−	0.120063i
$590$	−30.9077			−1.27245
$591$	−0.842824	+	1.45981i	−0.0346691	+	0.0600487i
$592$	−5.49844	+	9.52358i	−0.225985	+	0.391417i
$593$	−6.15663			−0.252822			−0.126411	−	0.991978i	$-0.540346\pi$
$593$	−6.15663			−0.252822			−0.126411	+	0.991978i	$0.540346\pi$
$594$	11.9524	−	20.7021i	0.490411	−	0.849417i
$595$	15.2612	+	26.4332i	0.625648	+	1.08365i
$596$	25.6013	+	44.3427i	1.04867	+	1.81635i
$597$	−5.13953			−0.210347
$598$	−12.3300	+	12.3576i	−0.504210	+	0.505341i
$599$	16.7875			0.685919			0.342960	−	0.939350i	$-0.388571\pi$
$599$	16.7875			0.685919			0.342960	+	0.939350i	$0.388571\pi$
$600$	−1.51005	−	2.61549i	−0.0616477	−	0.106777i
$601$	12.8554	+	22.2661i	0.524381	+	0.908255i	0.999597	+	0.0283858i	$0.00903669\pi$
$601$	12.8554	+	22.2661i	0.524381	+	0.908255i	−0.475216	+	0.879869i	$0.657630\pi$
$602$	−67.5918	+	117.072i	−2.75484	+	4.77152i
$603$	−11.4406			−0.465897
$604$	−25.1296	+	43.5258i	−1.02251	+	1.77104i
$605$	2.35159	−	4.07307i	0.0956056	−	0.165594i
$606$	−10.5715			−0.429437
$607$	−5.68095	+	9.83970i	−0.230583	+	0.399381i	−0.957980	−	0.286836i	$-0.907397\pi$
$607$	−5.68095	+	9.83970i	−0.230583	+	0.399381i	0.727397	+	0.686217i	$0.240730\pi$
$608$	−11.5645	−	20.0304i	−0.469004	−	0.812339i
$609$	15.2825	+	26.4701i	0.619278	+	1.07262i
$610$	23.3026			0.943495
$611$	−38.1039	−	10.1642i	−1.54152	−	0.411199i
$612$	−27.4859			−1.11105
$613$	10.1449	+	17.5715i	0.409748	+	0.709704i	0.994861	−	0.101247i	$-0.0322833\pi$
$613$	10.1449	+	17.5715i	0.409748	+	0.709704i	−0.585113	+	0.810952i	$0.698950\pi$
$614$	28.0422	+	48.5705i	1.13169	+	1.96015i
$615$	4.43495	−	7.68156i	0.178835	−	0.309751i
$616$	−29.9333			−1.20605
$617$	−0.0888552	+	0.153902i	−0.00357718	+	0.00619585i	−0.867808	−	0.496899i	$-0.834472\pi$
$617$	−0.0888552	+	0.153902i	−0.00357718	+	0.00619585i	0.864231	+	0.503095i	$0.167805\pi$
$618$	−10.3672	+	17.9565i	−0.417028	+	0.722314i
$619$	46.8600			1.88346			0.941731	−	0.336367i	$-0.109198\pi$
$619$	46.8600			1.88346			0.941731	+	0.336367i	$0.109198\pi$
$620$	2.51371	−	4.35387i	0.100953	−	0.174856i
$621$	4.06971	+	7.04894i	0.163312	+	0.282864i
$622$	−9.10526	−	15.7708i	−0.365088	−	0.632351i
$623$	−47.4452			−1.90085
$624$	−2.02555	+	2.03009i	−0.0810867	+	0.0812685i
$625$	−10.0417			−0.401669
$626$	−15.5550	−	26.9420i	−0.621701	−	1.07682i
$627$	3.25845	+	5.64381i	0.130130	+	0.225392i
$628$	19.1312	−	33.1362i	0.763417	−	1.32228i
$629$	−34.1135			−1.36019
$630$	23.6445	−	40.9536i	0.942021	−	1.63163i
$631$	−0.391456	+	0.678022i	−0.0155836	+	0.0269916i	−0.873712	−	0.486443i	$-0.838294\pi$
$631$	−0.391456	+	0.678022i	−0.0155836	+	0.0269916i	0.858128	+	0.513435i	$0.171627\pi$
$632$	−6.10550			−0.242864
$633$	6.82386	−	11.8193i	0.271224	−	0.469774i
$634$	15.9607	+	27.6447i	0.633879	+	1.09791i
$635$	10.1775	+	17.6280i	0.403883	+	0.699546i
$636$	12.3817			0.490967
$637$	16.0067	+	59.4714i	0.634209	+	2.35634i
$638$	58.9514			2.33391
$639$	−5.07667	−	8.79305i	−0.200830	−	0.347848i
$640$	−12.8167	−	22.1992i	−0.506624	−	0.877498i
$641$	15.7395	−	27.2616i	0.621673	−	1.07677i	−0.367501	−	0.930023i	$-0.619787\pi$
$641$	15.7395	−	27.2616i	0.621673	−	1.07677i	0.989174	−	0.146746i	$-0.0468801\pi$
$642$	14.4331			0.569629
$643$	−18.3717	+	31.8207i	−0.724508	+	1.25488i	0.234668	+	0.972076i	$0.424600\pi$
$643$	−18.3717	+	31.8207i	−0.724508	+	1.25488i	−0.959176	+	0.282809i	$0.908734\pi$
$644$	15.7698	−	27.3141i	0.621417	−	1.07633i
$645$	14.2112			0.559564
$646$	13.6897	−	23.7112i	0.538613	−	0.932905i
$647$	6.02601	+	10.4374i	0.236907	+	0.410335i	0.959825	−	0.280599i	$-0.0905330\pi$
$647$	6.02601	+	10.4374i	0.236907	+	0.410335i	−0.722918	+	0.690934i	$0.757200\pi$
$648$	5.42831	+	9.40210i	0.213244	+	0.369349i
$649$	−23.4204			−0.919332
$650$	4.39135	+	16.3156i	0.172243	+	0.639952i
$651$	3.31205			0.129810
$652$	3.41965	+	5.92300i	0.133924	+	0.231963i
$653$	15.7610	+	27.2988i	0.616774	+	1.06828i	0.990070	+	0.140572i	$0.0448941\pi$
$653$	15.7610	+	27.2988i	0.616774	+	1.06828i	−0.373296	+	0.927712i	$0.621773\pi$
$654$	−0.958037	+	1.65937i	−0.0374622	+	0.0648865i
$655$	−30.7501			−1.20151
$656$	−4.55137	+	7.88321i	−0.177701	+	0.307787i
$657$	−7.66121	+	13.2696i	−0.298892	+	0.517696i
$658$	119.476			4.65766
$659$	−5.39399	+	9.34266i	−0.210120	+	0.363938i	−0.951752	−	0.306869i	$-0.900719\pi$
$659$	−5.39399	+	9.34266i	−0.210120	+	0.363938i	0.741632	+	0.670807i	$0.234052\pi$
$660$	4.86880	+	8.43301i	0.189518	+	0.328254i
$661$	6.11777	+	10.5963i	0.237953	+	0.412148i	0.960127	−	0.279565i	$-0.0901901\pi$
$661$	6.11777	+	10.5963i	0.237953	+	0.412148i	−0.722173	+	0.691712i	$0.756857\pi$
$662$	4.68954			0.182264
$663$	−8.59556	−	2.29286i	−0.333824	−	0.0890473i
$664$	6.01725			0.233514
$665$	14.0460	+	24.3283i	0.544679	+	0.943411i
$666$	26.4264	+	45.7719i	1.02400	+	1.77362i
$667$	−10.0363	+	17.3834i	−0.388607	+	0.673087i
$668$	−23.6694			−0.915797
$669$	−4.82174	+	8.35150i	−0.186419	+	0.322887i
$670$	8.51419	−	14.7470i	0.328932	−	0.569727i
$671$	17.6576			0.681666
$672$	11.3839	−	19.7175i	0.439143	−	0.760619i
$673$	−20.1411	−	34.8854i	−0.776383	−	1.34474i	−0.934014	−	0.357237i	$-0.883719\pi$
$673$	−20.1411	−	34.8854i	−0.776383	−	1.34474i	0.157630	−	0.987498i	$-0.449615\pi$
$674$	−18.8556	−	32.6589i	−0.726292	−	1.25797i
$675$	7.87807			0.303227
$676$	−33.2239	+	19.2811i	−1.27784	+	0.741582i
$677$	2.49485			0.0958847			0.0479423	−	0.998850i	$-0.484734\pi$
$677$	2.49485			0.0958847			0.0479423	+	0.998850i	$0.484734\pi$
$678$	−6.72663	−	11.6509i	−0.258335	−	0.447449i
$679$	−18.7071	−	32.4016i	−0.717911	−	1.24346i
$680$	6.61015	−	11.4491i	0.253488	−	0.439053i
$681$	7.06949			0.270904
$682$	3.19401	−	5.53219i	0.122305	−	0.211839i
$683$	21.7199	−	37.6200i	0.831090	−	1.43949i	−0.0660843	−	0.997814i	$-0.521051\pi$
$683$	21.7199	−	37.6200i	0.831090	−	1.43949i	0.897174	−	0.441676i	$-0.145616\pi$
$684$	−25.2972			−0.967261
$685$	3.37762	−	5.85021i	0.129052	−	0.223525i
$686$	−55.0614	−	95.3691i	−2.10225	−	3.64121i
$687$	5.71553	+	9.89959i	0.218061	+	0.377693i
$688$	−14.5842			−0.556017
$689$	−21.6287	−	5.76944i	−0.823987	−	0.219798i
$690$	−5.55975			−0.211656
$691$	−16.5791	−	28.7159i	−0.630700	−	1.09241i	−0.987409	−	0.158189i	$-0.949434\pi$
$691$	−16.5791	−	28.7159i	−0.630700	−	1.09241i	0.356708	−	0.934216i	$-0.383899\pi$
$692$	−4.42976	−	7.67257i	−0.168394	−	0.291668i
$693$	17.9167	−	31.0327i	0.680601	−	1.17884i
$694$	23.1050			0.877054
$695$	−6.30214	+	10.9156i	−0.239054	+	0.414053i
$696$	6.61937	−	11.4651i	0.250907	−	0.434583i
$697$	−28.2377			−1.06958
$698$	11.5649	−	20.0310i	0.437739	−	0.758186i
$699$	−5.95446	−	10.3134i	−0.225219	−	0.390090i
$700$	−15.2634	−	26.4371i	−0.576904	−	0.999227i
$701$	−38.7377			−1.46310			−0.731551	−	0.681787i	$-0.761203\pi$
$701$	−38.7377			−1.46310			−0.731551	+	0.681787i	$0.761203\pi$
$702$	7.80570	+	29.0013i	0.294607	+	1.09459i
$703$	−31.3970			−1.18416
$704$	−18.5744	−	32.1718i	−0.700050	−	1.21252i
$705$	−6.27995	−	10.8772i	−0.236517	−	0.409659i
$706$	19.2475	−	33.3376i	0.724388	−	1.25468i
$707$	−34.5306			−1.29866
$708$	−8.13786	+	14.0952i	−0.305840	+	0.529730i
$709$	−0.792320	+	1.37234i	−0.0297562	+	0.0515393i	−0.880520	−	0.474009i	$-0.842806\pi$
$709$	−0.792320	+	1.37234i	−0.0297562	+	0.0515393i	0.850764	+	0.525548i	$0.176140\pi$
$710$	15.1124			0.567158
$711$	3.65448	−	6.32975i	0.137054	−	0.237384i
$712$	10.2751	+	17.7969i	0.385074	+	0.666968i
$713$	1.08754	+	1.88368i	0.0407288	+	0.0705443i
$714$	26.9517			1.00864
$715$	−4.57546	−	16.9997i	−0.171113	−	0.635752i
$716$	0.399161			0.0149173
$717$	5.02957	+	8.71147i	0.187833	+	0.325336i
$718$	−21.6819	−	37.5541i	−0.809160	−	1.40151i
$719$	3.49085	−	6.04632i	0.130187	−	0.225490i	−0.793562	−	0.608490i	$-0.791776\pi$
$719$	3.49085	−	6.04632i	0.130187	−	0.225490i	0.923748	+	0.383000i	$0.125109\pi$
$720$	5.10176			0.190131
$721$	−33.8632	+	58.6527i	−1.26113	+	2.18434i
$722$	−8.54700	+	14.8038i	−0.318086	+	0.550942i
$723$	−14.1052			−0.524578
$724$	−25.7441	+	44.5902i	−0.956773	+	1.65718i
$725$	9.71404	+	16.8252i	0.360770	+	0.624873i
$726$	−2.07648	−	3.59657i	−0.0770654	−	0.133481i
$727$	−15.9515			−0.591609			−0.295805	−	0.955248i	$-0.595588\pi$
$727$	−15.9515			−0.591609			−0.295805	+	0.955248i	$0.595588\pi$
$728$	26.5628	−	26.6223i	0.984482	−	0.986690i
$729$	−5.41963			−0.200727
$730$	−11.4031	−	19.7507i	−0.422046	−	0.731005i
$731$	−22.6209	−	39.1805i	−0.836663	−	1.44914i
$732$	6.13547	−	10.6270i	0.226774	−	0.392784i
$733$	11.3960			0.420921			0.210461	−	0.977602i	$-0.432504\pi$
$733$	11.3960			0.420921			0.210461	+	0.977602i	$0.432504\pi$
$734$	14.1841	−	24.5677i	0.523546	−	0.906809i
$735$	−9.80744	+	16.9870i	−0.361753	+	0.626574i
$736$	14.9520			0.551139
$737$	6.45166	−	11.1746i	0.237650	−	0.411622i
$738$	21.8746	+	37.8880i	0.805217	+	1.39468i
$739$	−2.07286	−	3.59030i	−0.0762515	−	0.132071i	0.825378	−	0.564580i	$-0.190962\pi$
$739$	−2.07286	−	3.59030i	−0.0762515	−	0.132071i	−0.901630	+	0.432509i	$0.857629\pi$
$740$	−46.9136			−1.72458
$741$	−7.91110	−	2.11028i	−0.290621	−	0.0775231i
$742$	67.8175			2.48966
$743$	10.6541	+	18.4535i	0.390862	+	0.676993i	0.992563	−	0.121728i	$-0.0388436\pi$
$743$	10.6541	+	18.4535i	0.390862	+	0.676993i	−0.601701	+	0.798721i	$0.705510\pi$
$744$	−0.717282	−	1.24237i	−0.0262968	−	0.0455474i
$745$	14.7410	−	25.5322i	0.540070	−	0.935429i
$746$	14.9612			0.547767
$747$	−3.60166	+	6.23826i	−0.131778	+	0.228246i
$748$	15.5000	−	26.8468i	0.566736	−	0.981616i
$749$	47.1441			1.72261
$750$	−9.08088	+	15.7285i	−0.331587	+	0.574325i
$751$	16.4074	+	28.4185i	0.598715	+	1.03700i	0.993011	+	0.118021i	$0.0376551\pi$
$751$	16.4074	+	28.4185i	0.598715	+	1.03700i	−0.394296	+	0.918983i	$0.629012\pi$
$752$	6.44480	+	11.1627i	0.235018	+	0.407063i
$753$	−8.30861			−0.302783
$754$	−52.3135	+	52.4307i	−1.90514	+	1.90941i
$755$	28.9389			1.05320
$756$	−27.1311	−	46.9924i	−0.986747	−	1.70910i
$757$	2.29431	+	3.97386i	0.0833881	+	0.144432i	0.904703	−	0.426042i	$-0.140093\pi$
$757$	2.29431	+	3.97386i	0.0833881	+	0.144432i	−0.821315	+	0.570475i	$0.806759\pi$
$758$	33.9747	−	58.8459i	1.23402	−	2.13738i
$759$	−4.21292			−0.152919
$760$	6.08378	−	10.5374i	0.220682	−	0.382232i
$761$	23.9168	−	41.4250i	0.866982	−	1.50166i	0.00191542	−	0.999998i	$-0.499390\pi$
$761$	23.9168	−	41.4250i	0.866982	−	1.50166i	0.865066	−	0.501658i	$-0.167276\pi$
$762$	17.9738			0.651121
$763$	−3.12932	+	5.42014i	−0.113289	+	0.196222i
$764$	21.1699	+	36.6674i	0.765901	+	1.32658i
$765$	7.91309	+	13.7059i	0.286098	+	0.495537i
$766$	−45.6335			−1.64881
$767$	20.7833	−	20.8299i	0.750441	−	0.752124i
$768$	−5.16103			−0.186233
$769$	−8.28073	−	14.3426i	−0.298611	−	0.517209i	0.677208	−	0.735792i	$-0.263190\pi$
$769$	−8.28073	−	14.3426i	−0.298611	−	0.517209i	−0.975818	+	0.218583i	$0.929857\pi$
$770$	26.6676	+	46.1896i	0.961032	+	1.66456i
$771$	−0.314414	+	0.544581i	−0.0113233	+	0.0196126i
$772$	−54.2497			−1.95249
$773$	−3.09299	+	5.35722i	−0.111247	+	0.192686i	−0.916273	−	0.400553i	$-0.868818\pi$
$773$	−3.09299	+	5.35722i	−0.111247	+	0.192686i	0.805026	+	0.593239i	$0.202151\pi$
$774$	−35.0470	+	60.7032i	−1.25974	+	2.18193i
$775$	2.10525			0.0756226
$776$	−8.10266	+	14.0342i	−0.290869	+	0.503799i
$777$	−15.4533	−	26.7659i	−0.554384	−	0.960221i
$778$	−6.13485	−	10.6259i	−0.219945	−	0.380956i
$779$	−25.9891			−0.931156
$780$	−11.8208	−	3.15319i	−0.423253	−	0.112902i
$781$	11.4515			0.409766
$782$	8.84982	+	15.3283i	0.316469	+	0.548140i
$783$	17.2669	+	29.9071i	0.617068	+	1.06879i
$784$	10.0649	−	17.4329i	0.359460	−	0.622603i
$785$	−22.0312			−0.786327
$786$	−13.5764	+	23.5150i	−0.484254	+	0.838752i
$787$	−2.70146	+	4.67907i	−0.0962967	+	0.166791i	−0.910149	−	0.414281i	$-0.864033\pi$
$787$	−2.70146	+	4.67907i	−0.0962967	+	0.166791i	0.813852	+	0.581072i	$0.197366\pi$
$788$	7.37988			0.262897
$789$	−4.57836	+	7.92995i	−0.162994	+	0.282314i
$790$	5.43939	+	9.42130i	0.193525	+	0.335195i
$791$	−21.9718	−	38.0563i	−0.781227	−	1.35312i
$792$	−15.5207			−0.551504
$793$	−15.6694	+	15.7045i	−0.556437	+	0.557684i
$794$	−66.9352			−2.37544
$795$	−3.56465	−	6.17416i	−0.126425	−	0.218975i
$796$	11.2506	+	19.4866i	0.398767	+	0.690684i
$797$	1.05773	−	1.83205i	0.0374668	−	0.0648944i	−0.846684	−	0.532096i	$-0.821404\pi$
$797$	1.05773	−	1.83205i	0.0374668	−	0.0648944i	0.884151	+	0.467202i	$0.154738\pi$
$798$	24.8055			0.878106
$799$	−19.9924	+	34.6279i	−0.707282	+	1.22505i
$800$	7.23596	−	12.5331i	0.255830	−	0.443110i
$801$	−24.6008			−0.869227
$802$	4.21763	−	7.30515i	0.148930	−	0.257954i
$803$	−8.64071	−	14.9661i	−0.304924	−	0.528144i
$804$	−4.48350	−	7.76564i	−0.158121	−	0.273873i
$805$	−18.1603			−0.640066
$806$	2.08591	+	7.74999i	0.0734730	+	0.272982i
$807$	−8.52075			−0.299945
$808$	7.47818	+	12.9526i	0.263081	+	0.455670i
$809$	20.3888	+	35.3145i	0.716833	+	1.24159i	0.962248	+	0.272174i	$0.0877425\pi$
$809$	20.3888	+	35.3145i	0.716833	+	1.24159i	−0.245415	+	0.969418i	$0.578924\pi$
$810$	9.67216	−	16.7527i	0.339845	−	0.588629i
$811$	−23.8550			−0.837661			−0.418830	−	0.908064i	$-0.637560\pi$
$811$	−23.8550			−0.837661			−0.418830	+	0.908064i	$0.637560\pi$
$812$	66.9078	−	115.888i	2.34801	−	4.06686i
$813$	0.828900	−	1.43570i	0.0290708	−	0.0503521i
$814$	−59.6102			−2.08934
$815$	1.96901	−	3.41043i	0.0689714	−	0.119462i
$816$	1.45383	+	2.51811i	0.0508943	+	0.0881516i
$817$	−20.8196	−	36.0605i	−0.728384	−	1.26160i
$818$	−6.43983			−0.225163
$819$	11.7009	+	43.4734i	0.408861	+	1.51908i
$820$	−38.8331			−1.35611
$821$	−2.72382	−	4.71779i	−0.0950619	−	0.164652i	0.814573	−	0.580062i	$-0.196972\pi$
$821$	−2.72382	−	4.71779i	−0.0950619	−	0.164652i	−0.909634	+	0.415410i	$0.863638\pi$
$822$	−2.98248	−	5.16581i	−0.104026	−	0.180178i
$823$	−18.6518	+	32.3059i	−0.650161	+	1.12611i	0.332923	+	0.942954i	$0.391965\pi$
$823$	−18.6518	+	32.3059i	−0.650161	+	1.12611i	−0.983084	+	0.183158i	$0.941368\pi$
$824$	29.3346			1.02192
$825$	−2.03882	+	3.53135i	−0.0709827	+	0.122946i
$826$	−44.5730	+	77.2027i	−1.55089	+	2.68622i
$827$	−31.7429			−1.10381			−0.551905	−	0.833907i	$-0.686099\pi$
$827$	−31.7429			−1.10381			−0.551905	+	0.833907i	$0.686099\pi$
$828$	8.17680	−	14.1626i	0.284163	−	0.492185i
$829$	−16.6882	−	28.9047i	−0.579603	−	1.00390i	−0.995525	−	0.0945020i	$-0.969874\pi$
$829$	−16.6882	−	28.9047i	−0.579603	−	1.00390i	0.415921	−	0.909401i	$-0.363459\pi$
$830$	−5.36077	−	9.28512i	−0.186075	−	0.322291i
$831$	−2.42615			−0.0841622
$832$	45.0962	+	12.0294i	1.56343	+	0.417044i
$833$	62.4446			2.16358
$834$	5.56487	+	9.63863i	0.192696	+	0.333759i
$835$	6.81435	+	11.8028i	0.235820	+	0.408452i
$836$	14.2657	−	24.7090i	0.493391	−	0.854578i
$837$	3.74211			0.129346
$838$	−23.6183	+	40.9081i	−0.815881	+	1.41315i
$839$	19.1367	−	33.1457i	0.660671	−	1.14432i	−0.319768	−	0.947496i	$-0.603605\pi$
$839$	19.1367	−	33.1457i	0.660671	−	1.14432i	0.980440	−	0.196821i	$-0.0630616\pi$
$840$	11.9775			0.413263
$841$	−28.0818	+	48.6392i	−0.968339	+	1.67721i
$842$	−21.4104	−	37.0838i	−0.737850	−	1.27799i
$843$	−1.48617	−	2.57412i	−0.0511863	−	0.0886573i
$844$	−59.7507			−2.05670
$845$	19.1796	+	11.0162i	0.659799	+	0.378967i
$846$	61.9496			2.12987
$847$	−6.78259	−	11.7478i	−0.233053	−	0.403659i
$848$	3.65822	+	6.33623i	0.125624	+	0.217587i
$849$	1.87693	−	3.25094i	0.0644161	−	0.111572i
$850$	17.1313			0.587600
$851$	10.1485	−	17.5776i	0.347885	−	0.602554i
$852$	3.97902	−	6.89187i	0.136319	−	0.236112i
$853$	−12.2984			−0.421088			−0.210544	−	0.977584i	$-0.567523\pi$
$853$	−12.2984			−0.421088			−0.210544	+	0.977584i	$0.567523\pi$
$854$	33.6054	−	58.2063i	1.14995	−	1.99178i
$855$	7.28297	+	12.6145i	0.249072	+	0.431406i
$856$	−10.2099	−	17.6840i	−0.348966	−	0.604426i
$857$	36.4568			1.24534			0.622670	−	0.782485i	$-0.286048\pi$
$857$	36.4568			1.24534			0.622670	+	0.782485i	$0.286048\pi$
$858$	−15.0200	−	4.00656i	−0.512773	−	0.136782i
$859$	−15.6812			−0.535035			−0.267518	−	0.963553i	$-0.586203\pi$
$859$	−15.6812			−0.535035			−0.267518	+	0.963553i	$0.586203\pi$
$860$	−31.1087	−	53.8819i	−1.06080	−	1.83736i
$861$	−12.7916	−	22.1556i	−0.435936	−	0.755062i
$862$	−11.4461	+	19.8253i	−0.389856	+	0.675251i
$863$	−1.33775			−0.0455375			−0.0227688	−	0.999741i	$-0.507248\pi$
$863$	−1.33775			−0.0455375			−0.0227688	+	0.999741i	$0.507248\pi$
$864$	12.8621	−	22.2777i	0.437576	−	0.757904i
$865$	−2.55063	+	4.41782i	−0.0867240	+	0.150210i
$866$	−16.4018			−0.557356
$867$	1.22694	−	2.12511i	0.0416689	−	0.0721727i
$868$	−7.25020	−	12.5577i	−0.246088	−	0.426237i
$869$	4.12172	+	7.13903i	0.139820	+	0.242175i
$870$	−23.5888			−0.799736
$871$	4.21337	+	15.6544i	0.142765	+	0.530428i
$872$	2.71083			0.0918003
$873$	−9.69980	−	16.8005i	−0.328288	−	0.568612i
$874$	8.14511	+	14.1078i	0.275513	+	0.477202i
$875$	−29.6617	+	51.3755i	−1.00275	+	1.73681i
$876$	−12.0095			−0.405763
$877$	−2.27078	+	3.93311i	−0.0766788	+	0.132812i	−0.901815	−	0.432122i	$-0.857765\pi$
$877$	−2.27078	+	3.93311i	−0.0766788	+	0.132812i	0.825136	+	0.564934i	$0.191098\pi$
$878$	10.2614	−	17.7732i	0.346305	−	0.599817i
$879$	−4.59144			−0.154865
$880$	−2.87701	+	4.98313i	−0.0969841	+	0.167981i
$881$	−15.9627	−	27.6483i	−0.537798	−	0.931494i	−0.999022	−	0.0442103i	$-0.985923\pi$
$881$	−15.9627	−	27.6483i	−0.537798	−	0.931494i	0.461224	−	0.887284i	$-0.347410\pi$
$882$	−48.3735	−	83.7853i	−1.62882	−	2.82120i
$883$	43.3171			1.45774			0.728868	−	0.684655i	$-0.240047\pi$
$883$	43.3171			1.45774			0.728868	+	0.684655i	$0.240047\pi$
$884$	10.1226	+	37.6094i	0.340458	+	1.26494i
$885$	9.37146			0.315018
$886$	36.5861	+	63.3690i	1.22913	+	2.12892i
$887$	−0.930518	−	1.61170i	−0.0312437	−	0.0541158i	0.849981	−	0.526814i	$-0.176613\pi$
$887$	−0.930518	−	1.61170i	−0.0312437	−	0.0541158i	−0.881224	+	0.472698i	$0.843280\pi$
$888$	−6.69335	+	11.5932i	−0.224614	+	0.389043i
$889$	58.7093			1.96905
$890$	18.3081	−	31.7106i	0.613689	−	1.06294i
$891$	7.32912	−	12.6944i	0.245535	−	0.425278i
$892$	42.2198			1.41362
$893$	−18.4005	+	31.8705i	−0.615748	+	1.06651i
$894$	−13.0165	−	22.5453i	−0.435338	−	0.754027i
$895$	−0.114917	−	0.199042i	−0.00384126	−	0.00665325i
$896$	−73.9334			−2.46994
$897$	3.73854	−	3.74693i	0.124826	−	0.125106i
$898$	−10.8836			−0.363192
$899$	4.61421	+	7.99204i	0.153892	+	0.266550i
$900$	−7.91425	−	13.7079i	−0.263808	−	0.456930i
$901$	−11.3482	+	19.6557i	−0.378063	+	0.654825i
$902$	−49.3427			−1.64293
$903$	20.4944	−	35.4973i	0.682009	−	1.18127i
$904$	−9.51673	+	16.4835i	−0.316522	+	0.548232i
$905$	29.6466			0.985487
$906$	12.7767	−	22.1299i	0.424478	−	0.735218i
$907$	14.1225	+	24.4608i	0.468928	+	0.812208i	0.999369	−	0.0355141i	$-0.0113069\pi$
$907$	14.1225	+	24.4608i	0.468928	+	0.812208i	−0.530441	+	0.847722i	$0.677974\pi$
$908$	−15.4754	−	26.8041i	−0.513568	−	0.889526i
$909$	−17.9044			−0.593853
$910$	−64.7453	−	17.2708i	−2.14629	−	0.572521i
$911$	3.81575			0.126421			0.0632107	−	0.998000i	$-0.479866\pi$
$911$	3.81575			0.126421			0.0632107	+	0.998000i	$0.479866\pi$
$912$	1.33806	+	2.31760i	0.0443077	+	0.0767433i
$913$	−4.06214	−	7.03583i	−0.134437	−	0.232852i
$914$	7.09991	−	12.2974i	0.234844	−	0.406762i
$915$	−7.06553			−0.233579
$916$	25.0230	−	43.3411i	0.826783	−	1.43203i
$917$	−44.3458	+	76.8091i	−1.46443	+	2.53646i
$918$	30.4513			1.00504
$919$	12.3483	−	21.3878i	0.407332	−	0.705519i	−0.587258	−	0.809400i	$-0.699793\pi$
$919$	12.3483	−	21.3878i	0.407332	−	0.705519i	0.994590	+	0.103881i	$0.0331260\pi$
$920$	3.93292	+	6.81202i	0.129664	+	0.224586i
$921$	−8.50261	−	14.7270i	−0.280171	−	0.485270i
$922$	75.3720			2.48224
$923$	−10.1620	+	10.1848i	−0.334487	+	0.335237i
$924$	28.0858			0.923955
$925$	−9.82260	−	17.0132i	−0.322965	−	0.559392i
$926$	23.3373	+	40.4213i	0.766910	+	1.32833i
$927$	−17.5584	+	30.4120i	−0.576693	+	0.998862i
$928$	63.4382			2.08246
$929$	6.74225	−	11.6779i	0.221206	−	0.383140i	−0.733968	−	0.679184i	$-0.762334\pi$
$929$	6.74225	−	11.6779i	0.221206	−	0.383140i	0.955174	+	0.296043i	$0.0956673\pi$
$930$	−1.27805	+	2.21365i	−0.0419090	+	0.0725885i
$931$	57.4722			1.88358
$932$	−26.0691	+	45.1529i	−0.853920	+	1.47903i
$933$	2.76079	+	4.78182i	0.0903841	+	0.156550i
$934$	3.72815	+	6.45735i	0.121989	+	0.211291i
$935$	−17.8496			−0.583744
$936$	13.7731	−	13.8040i	0.450187	−	0.451196i
$937$	−29.1851			−0.953437			−0.476719	−	0.879056i	$-0.658174\pi$
$937$	−29.1851			−0.953437			−0.476719	+	0.879056i	$0.658174\pi$
$938$	−24.5572	−	42.5342i	−0.801819	−	1.38879i
$939$	4.71638	+	8.16901i	0.153913	+	0.266586i
$940$	−27.4941	+	47.6211i	−0.896757	+	1.55323i
$941$	16.6845			0.543899			0.271950	−	0.962311i	$-0.412332\pi$
$941$	16.6845			0.543899			0.271950	+	0.962311i	$0.412332\pi$
$942$	−9.72692	+	16.8475i	−0.316920	+	0.548922i
$943$	8.40045	−	14.5500i	0.273556	−	0.473813i
$944$	−9.61746			−0.313022
$945$	−15.6219	+	27.0579i	−0.508180	+	0.880194i
$946$	−39.5279	−	68.4643i	−1.28516	−	2.22597i
$947$	−20.3748	−	35.2902i	−0.662091	−	1.14678i	−0.980065	−	0.198676i	$-0.936336\pi$
$947$	−20.3748	−	35.2902i	−0.662091	−	1.14678i	0.317974	−	0.948100i	$-0.396998\pi$
$948$	5.72867			0.186059
$949$	20.9785	+	5.59600i	0.680991	+	0.181654i
$950$	15.7672			0.511555
$951$	−4.83939	−	8.38207i	−0.156928	−	0.271807i
$952$	−19.0654	−	33.0222i	−0.617913	−	1.07026i
$953$	−6.20171	+	10.7417i	−0.200893	+	0.347957i	−0.948816	−	0.315828i	$-0.897718\pi$
$953$	−6.20171	+	10.7417i	−0.200893	+	0.347957i	0.747923	+	0.663785i	$0.231051\pi$
$954$	35.1641			1.13848
$955$	12.1895	−	21.1128i	0.394443	−	0.683195i
$956$	22.0198	−	38.1394i	0.712171	−	1.23352i
$957$	−17.8745			−0.577801
$958$	−12.3561	+	21.4014i	−0.399208	+	0.691449i
$959$	−9.74194	−	16.8735i	−0.314584	−	0.544875i
$960$	7.43237	+	12.8732i	0.239879	+	0.415482i
$961$	1.00000			0.0322581
$962$	52.8981	−	53.0167i	1.70550	−	1.70933i
$963$	24.4447			0.787719
$964$	30.8768	+	53.4801i	0.994474	+	1.72248i
$965$	15.6183	+	27.0517i	0.502772	+	0.870826i
$966$	−8.01788	+	13.8874i	−0.257971	+	0.446819i
$967$	−36.6876			−1.17979			−0.589896	−	0.807479i	$-0.700831\pi$
$967$	−36.6876			−1.17979			−0.589896	+	0.807479i	$0.700831\pi$
$968$	−2.93777	+	5.08837i	−0.0944235	+	0.163546i
$969$	−4.15082	+	7.18942i	−0.133343	+	0.230958i
$970$	28.8747			0.927110
$971$	11.1272	−	19.2728i	0.357088	−	0.618494i	−0.630385	−	0.776283i	$-0.717103\pi$
$971$	11.1272	−	19.2728i	0.357088	−	0.618494i	0.987473	+	0.157788i	$0.0504364\pi$
$972$	−21.6795	−	37.5500i	−0.695370	−	1.20442i
$973$	18.1770	+	31.4835i	0.582728	+	1.00932i
$974$	−48.7789			−1.56298
$975$	−1.33149	−	4.94703i	−0.0426418	−	0.158432i
$976$	7.25100			0.232099
$977$	28.8074	+	49.8959i	0.921631	+	1.59631i	0.796892	+	0.604122i	$0.206476\pi$
$977$	28.8074	+	49.8959i	0.921631	+	1.59631i	0.124739	+	0.992190i	$0.460191\pi$
$978$	−1.73866	−	3.01145i	−0.0555963	−	0.0962956i
$979$	13.8730	−	24.0288i	0.443384	−	0.767964i
$980$	85.8753			2.74318
$981$	−1.62258	+	2.81040i	−0.0518051	+	0.0897291i
$982$	−23.4900	+	40.6858i	−0.749595	+	1.29834i
$983$	4.60055			0.146735			0.0733673	−	0.997305i	$-0.476625\pi$
$983$	4.60055			0.146735			0.0733673	+	0.997305i	$0.476625\pi$
$984$	−5.54046	+	9.59637i	−0.176624	+	0.305921i
$985$	−2.12464	−	3.67999i	−0.0676968	−	0.117254i
$986$	37.5479	+	65.0349i	1.19577	+	2.07113i
$987$	−36.2261			−1.15309
$988$	9.31650	+	34.6146i	0.296397	+	1.10124i
$989$	26.9180			0.855943
$990$	13.8274	+	23.9498i	0.439464	+	0.761173i
$991$	−16.3736	−	28.3598i	−0.520123	−	0.900880i	−0.999726	−	0.0233941i	$-0.992553\pi$
$991$	−16.3736	−	28.3598i	−0.520123	−	0.900880i	0.479603	−	0.877485i	$-0.340781\pi$
$992$	3.43711	−	5.95325i	0.109128	−	0.189016i
$993$	−1.42190			−0.0451227
$994$	21.7940	−	37.7484i	0.691265	−	1.19731i
$995$	6.47802	−	11.2203i	0.205367	−	0.355706i
$996$	−5.64586			−0.178896
$997$	14.8536	−	25.7271i	0.470417	−	0.814787i	−0.529010	−	0.848615i	$-0.677437\pi$
$997$	14.8536	−	25.7271i	0.470417	−	0.814787i	0.999428	+	0.0338285i	$0.0107700\pi$
$998$	6.02405	+	10.4340i	0.190688	+	0.330281i
$999$	−17.4599	−	30.2414i	−0.552406	−	0.956795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.b.94.14	✓	34
13.3	even	3		5239.2.a.m.1.4		17
13.9	even	3	inner	403.2.f.b.373.14	yes	34
13.10	even	6		5239.2.a.n.1.14		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.b.94.14	✓	34	1.1	even	1	trivial
403.2.f.b.373.14	yes	34	13.9	even	3	inner
5239.2.a.m.1.4		17	13.3	even	3
5239.2.a.n.1.14		17	13.10	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11298 + 1.92773i) q^{2} +(-0.337463 - 0.584504i) q^{3} +(-1.47744 + 2.55900i) q^{4} +1.70140 q^{5} +(0.751178 - 1.30108i) q^{6} +(2.45364 - 4.24983i) q^{7} -2.12551 q^{8} +(1.27224 - 2.20358i) q^{9} +O(q^{10})\)	\(q+(1.11298 + 1.92773i) q^{2} +(-0.337463 - 0.584504i) q^{3} +(-1.47744 + 2.55900i) q^{4} +1.70140 q^{5} +(0.751178 - 1.30108i) q^{6} +(2.45364 - 4.24983i) q^{7} -2.12551 q^{8} +(1.27224 - 2.20358i) q^{9} +(1.89362 + 3.27984i) q^{10} +(1.43490 + 2.48531i) q^{11} +1.99432 q^{12} +(-3.48374 - 0.929285i) q^{13} +10.9234 q^{14} +(-0.574159 - 0.994473i) q^{15} +(0.589231 + 1.02058i) q^{16} +(-1.82786 + 3.16594i) q^{17} +5.66388 q^{18} +(-1.68231 + 2.91384i) q^{19} +(-2.51371 + 4.35387i) q^{20} -3.31205 q^{21} +(-3.19401 + 5.53219i) q^{22} +(-1.08754 - 1.88368i) q^{23} +(0.717282 + 1.24237i) q^{24} -2.10525 q^{25} +(-2.08591 - 7.74999i) q^{26} -3.74211 q^{27} +(7.25020 + 12.5577i) q^{28} +(-4.61421 - 7.99204i) q^{29} +(1.27805 - 2.21365i) q^{30} -1.00000 q^{31} +(-3.43711 + 5.95325i) q^{32} +(0.968449 - 1.67740i) q^{33} -8.13745 q^{34} +(4.17462 - 7.23065i) q^{35} +(3.75930 + 6.51130i) q^{36} +(4.66578 + 8.08136i) q^{37} -7.48947 q^{38} +(0.632463 + 2.34986i) q^{39} -3.61634 q^{40} +(3.86213 + 6.68940i) q^{41} +(-3.68624 - 6.38476i) q^{42} +(-6.18781 + 10.7176i) q^{43} -8.47988 q^{44} +(2.16458 - 3.74916i) q^{45} +(2.42082 - 4.19298i) q^{46} +10.9376 q^{47} +(0.397688 - 0.688816i) q^{48} +(-8.54069 - 14.7929i) q^{49} +(-2.34309 - 4.05835i) q^{50} +2.46734 q^{51} +(7.52504 - 7.54191i) q^{52} +6.20847 q^{53} +(-4.16489 - 7.21380i) q^{54} +(2.44133 + 4.22850i) q^{55} +(-5.21523 + 9.03305i) q^{56} +2.27087 q^{57} +(10.2710 - 17.7899i) q^{58} +(-4.08051 + 7.06765i) q^{59} +3.39314 q^{60} +(3.07647 - 5.32860i) q^{61} +(-1.11298 - 1.92773i) q^{62} +(-6.24322 - 10.8136i) q^{63} -12.9448 q^{64} +(-5.92722 - 1.58108i) q^{65} +4.31145 q^{66} +(-2.24813 - 3.89387i) q^{67} +(-5.40109 - 9.35496i) q^{68} +(-0.734011 + 1.27134i) q^{69} +18.5850 q^{70} +(1.99517 - 3.45574i) q^{71} +(-2.70415 + 4.68373i) q^{72} -6.02184 q^{73} +(-10.3858 + 17.9887i) q^{74} +(0.710443 + 1.23052i) q^{75} +(-4.97100 - 8.61003i) q^{76} +14.0829 q^{77} +(-3.82598 + 3.83456i) q^{78} +2.87249 q^{79} +(1.00252 + 1.73641i) q^{80} +(-2.55388 - 4.42346i) q^{81} +(-8.59692 + 14.8903i) q^{82} -2.83097 q^{83} +(4.89335 - 8.47553i) q^{84} +(-3.10991 + 5.38652i) q^{85} -27.5476 q^{86} +(-3.11425 + 5.39404i) q^{87} +(-3.04988 - 5.28255i) q^{88} +(-4.83416 - 8.37302i) q^{89} +9.63652 q^{90} +(-12.4971 + 12.5252i) q^{91} +6.42710 q^{92} +(0.337463 + 0.584504i) q^{93} +(12.1734 + 21.0849i) q^{94} +(-2.86227 + 4.95760i) q^{95} +4.63960 q^{96} +(3.81210 - 6.60276i) q^{97} +(19.0112 - 32.9284i) q^{98} +7.30211 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9}+O(q^{10}) \) 34 * q + 4 * q^2 - 20 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 - 12 * q^8 - 17 * q^9	\( 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9} - 6 q^{10} + 13 q^{11} + 8 q^{12} - 3 q^{13} + 4 q^{15} - 34 q^{16} + 6 q^{17} + 24 q^{18} + 4 q^{19} + 28 q^{20} - 36 q^{21} + 34 q^{22} + 8 q^{23} + 40 q^{24} + 16 q^{25} - 26 q^{26} - 6 q^{27} + 21 q^{28} + 6 q^{29} - 19 q^{30} - 34 q^{31} + 6 q^{32} + 7 q^{33} - 48 q^{34} + 9 q^{35} + 14 q^{37} + 22 q^{38} - 21 q^{39} - 20 q^{40} + 43 q^{41} - 33 q^{42} - 18 q^{43} - 56 q^{44} + 26 q^{45} + 7 q^{46} - 12 q^{47} + 95 q^{48} + q^{49} + 44 q^{50} + 52 q^{51} - 24 q^{52} - 10 q^{53} + 27 q^{54} - 39 q^{55} - 39 q^{56} - 92 q^{57} + 8 q^{58} - q^{59} - 42 q^{60} + 19 q^{61} - 4 q^{62} + 5 q^{63} + 84 q^{64} - 32 q^{65} + 52 q^{66} + 10 q^{67} - 34 q^{68} - 32 q^{69} + 48 q^{70} + 35 q^{71} - 26 q^{72} - 22 q^{73} + 68 q^{74} + 62 q^{75} + 2 q^{76} + 42 q^{77} - 81 q^{78} + 2 q^{79} + 49 q^{80} - 37 q^{81} - 35 q^{82} - 48 q^{83} - 34 q^{84} - 13 q^{85} - 152 q^{86} + 22 q^{87} + 37 q^{88} + 42 q^{89} + 30 q^{90} - 39 q^{91} + 30 q^{92} - 42 q^{94} - 34 q^{95} - 66 q^{96} - 38 q^{97} + 8 q^{98} - 34 q^{99}+O(q^{100}) \) 34 * q + 4 * q^2 - 20 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 - 12 * q^8 - 17 * q^9 - 6 * q^10 + 13 * q^11 + 8 * q^12 - 3 * q^13 + 4 * q^15 - 34 * q^16 + 6 * q^17 + 24 * q^18 + 4 * q^19 + 28 * q^20 - 36 * q^21 + 34 * q^22 + 8 * q^23 + 40 * q^24 + 16 * q^25 - 26 * q^26 - 6 * q^27 + 21 * q^28 + 6 * q^29 - 19 * q^30 - 34 * q^31 + 6 * q^32 + 7 * q^33 - 48 * q^34 + 9 * q^35 + 14 * q^37 + 22 * q^38 - 21 * q^39 - 20 * q^40 + 43 * q^41 - 33 * q^42 - 18 * q^43 - 56 * q^44 + 26 * q^45 + 7 * q^46 - 12 * q^47 + 95 * q^48 + q^49 + 44 * q^50 + 52 * q^51 - 24 * q^52 - 10 * q^53 + 27 * q^54 - 39 * q^55 - 39 * q^56 - 92 * q^57 + 8 * q^58 - q^59 - 42 * q^60 + 19 * q^61 - 4 * q^62 + 5 * q^63 + 84 * q^64 - 32 * q^65 + 52 * q^66 + 10 * q^67 - 34 * q^68 - 32 * q^69 + 48 * q^70 + 35 * q^71 - 26 * q^72 - 22 * q^73 + 68 * q^74 + 62 * q^75 + 2 * q^76 + 42 * q^77 - 81 * q^78 + 2 * q^79 + 49 * q^80 - 37 * q^81 - 35 * q^82 - 48 * q^83 - 34 * q^84 - 13 * q^85 - 152 * q^86 + 22 * q^87 + 37 * q^88 + 42 * q^89 + 30 * q^90 - 39 * q^91 + 30 * q^92 - 42 * q^94 - 34 * q^95 - 66 * q^96 - 38 * q^97 + 8 * q^98 - 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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