LMFDB - Embedded newform 403.2.f.b.94.17

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			94.17
Character	$\chi$	$=$	403.94
Dual form			403.2.f.b.373.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41028 + 2.44268i) q^{2} +(0.400852 + 0.694296i) q^{3} +(-2.97779 + 5.15768i) q^{4} -2.47906 q^{5} +(-1.13063 + 1.95831i) q^{6} +(0.397709 - 0.688852i) q^{7} -11.1570 q^{8} +(1.17864 - 2.04146i) q^{9} +O(q^{10})$	\(q+(1.41028 + 2.44268i) q^{2} +(0.400852 + 0.694296i) q^{3} +(-2.97779 + 5.15768i) q^{4} -2.47906 q^{5} +(-1.13063 + 1.95831i) q^{6} +(0.397709 - 0.688852i) q^{7} -11.1570 q^{8} +(1.17864 - 2.04146i) q^{9} +(-3.49618 - 6.05556i) q^{10} +(1.36943 + 2.37193i) q^{11} -4.77461 q^{12} +(2.72282 + 2.36353i) q^{13} +2.24353 q^{14} +(-0.993737 - 1.72120i) q^{15} +(-9.77888 - 16.9375i) q^{16} +(-1.66419 + 2.88246i) q^{17} +6.64883 q^{18} +(-0.350365 + 0.606849i) q^{19} +(7.38213 - 12.7862i) q^{20} +0.637690 q^{21} +(-3.86257 + 6.69017i) q^{22} +(3.59583 + 6.22817i) q^{23} +(-4.47229 - 7.74623i) q^{24} +1.14575 q^{25} +(-1.93339 + 9.98421i) q^{26} +4.29494 q^{27} +(2.36859 + 4.10251i) q^{28} +(0.340515 + 0.589789i) q^{29} +(2.80290 - 4.85476i) q^{30} -1.00000 q^{31} +(16.4250 - 28.4489i) q^{32} +(-1.09788 + 1.90158i) q^{33} -9.38789 q^{34} +(-0.985946 + 1.70771i) q^{35} +(7.01946 + 12.1581i) q^{36} +(-3.90751 - 6.76801i) q^{37} -1.97645 q^{38} +(-0.549538 + 2.83787i) q^{39} +27.6588 q^{40} +(1.18095 + 2.04546i) q^{41} +(0.899322 + 1.55767i) q^{42} +(-1.81596 + 3.14534i) q^{43} -16.3115 q^{44} +(-2.92191 + 5.06090i) q^{45} +(-10.1423 + 17.5669i) q^{46} +2.34284 q^{47} +(7.83976 - 13.5789i) q^{48} +(3.18365 + 5.51425i) q^{49} +(1.61583 + 2.79871i) q^{50} -2.66837 q^{51} +(-20.2983 + 7.00536i) q^{52} +3.27796 q^{53} +(6.05708 + 10.4912i) q^{54} +(-3.39491 - 5.88016i) q^{55} +(-4.43722 + 7.68550i) q^{56} -0.561777 q^{57} +(-0.960444 + 1.66354i) q^{58} +(5.41258 - 9.37487i) q^{59} +11.8366 q^{60} +(2.43957 - 4.22546i) q^{61} +(-1.41028 - 2.44268i) q^{62} +(-0.937508 - 1.62381i) q^{63} +53.5399 q^{64} +(-6.75004 - 5.85933i) q^{65} -6.19328 q^{66} +(-4.77340 - 8.26778i) q^{67} +(-9.91120 - 17.1667i) q^{68} +(-2.88279 + 4.99314i) q^{69} -5.56185 q^{70} +(-5.23211 + 9.06229i) q^{71} +(-13.1500 + 22.7764i) q^{72} +12.1046 q^{73} +(11.0214 - 19.0896i) q^{74} +(0.459277 + 0.795491i) q^{75} +(-2.08662 - 3.61414i) q^{76} +2.17854 q^{77} +(-7.70700 + 2.65985i) q^{78} +8.23000 q^{79} +(24.2424 + 41.9891i) q^{80} +(-1.81427 - 3.14241i) q^{81} +(-3.33093 + 5.76934i) q^{82} +13.8846 q^{83} +(-1.89891 + 3.28900i) q^{84} +(4.12563 - 7.14579i) q^{85} -10.2441 q^{86} +(-0.272992 + 0.472836i) q^{87} +(-15.2787 - 26.4635i) q^{88} +(-0.335874 - 0.581751i) q^{89} -16.4829 q^{90} +(2.71101 - 0.935626i) q^{91} -42.8305 q^{92} +(-0.400852 - 0.694296i) q^{93} +(3.30407 + 5.72282i) q^{94} +(0.868576 - 1.50442i) q^{95} +26.3359 q^{96} +(5.39254 - 9.34015i) q^{97} +(-8.97970 + 15.5533i) q^{98} +6.45625 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 $

$2$	1.41028	+	2.44268i	0.997220	+	1.72724i	0.563143	+	0.826359i	$0.309592\pi$
$2$	1.41028	+	2.44268i	0.997220	+	1.72724i	0.434076	+	0.900876i	$0.357075\pi$
$3$	0.400852	+	0.694296i	0.231432	+	0.400852i	0.958230	−	0.286000i	$-0.0923256\pi$
$3$	0.400852	+	0.694296i	0.231432	+	0.400852i	−0.726798	+	0.686851i	$0.758992\pi$
$4$	−2.97779	+	5.15768i	−1.48889	+	2.57884i
$5$	−2.47906			−1.10867			−0.554335	−	0.832293i	$-0.687027\pi$
$5$	−2.47906			−1.10867			−0.554335	+	0.832293i	$0.687027\pi$
$6$	−1.13063	+	1.95831i	−0.461577	+	0.799475i
$7$	0.397709	−	0.688852i	0.150320	−	0.260362i	−0.781025	−	0.624500i	$-0.785303\pi$
$7$	0.397709	−	0.688852i	0.150320	−	0.260362i	0.931345	+	0.364138i	$0.118636\pi$
$8$	−11.1570			−3.94458
$9$	1.17864	−	2.04146i	0.392879	−	0.680486i
$10$	−3.49618	−	6.05556i	−1.10559	−	1.91493i
$11$	1.36943	+	2.37193i	0.412900	+	0.715163i	0.995205	−	0.0978067i	$-0.0311827\pi$
$11$	1.36943	+	2.37193i	0.412900	+	0.715163i	−0.582306	+	0.812970i	$0.697849\pi$
$12$	−4.77461			−1.37831
$13$	2.72282	+	2.36353i	0.755174	+	0.655524i
$13$	2.72282	+	2.36353i	0.755174	+	0.655524i
$14$	2.24353			0.599608
$15$	−0.993737	−	1.72120i	−0.256582	−	0.444413i
$16$	−9.77888	−	16.9375i	−2.44472	−	4.23438i
$17$	−1.66419	+	2.88246i	−0.403625	+	0.699099i	−0.994160	−	0.107913i	$-0.965583\pi$
$17$	−1.66419	+	2.88246i	−0.403625	+	0.699099i	0.590536	+	0.807012i	$0.298917\pi$
$18$	6.64883			1.56714
$19$	−0.350365	+	0.606849i	−0.0803792	+	0.139221i	−0.903413	−	0.428772i	$-0.858946\pi$
$19$	−0.350365	+	0.606849i	−0.0803792	+	0.139221i	0.823034	+	0.567993i	$0.192280\pi$
$20$	7.38213	−	12.7862i	1.65069	−	2.85908i
$21$	0.637690			0.139155
$22$	−3.86257	+	6.69017i	−0.823503	+	1.42635i
$23$	3.59583	+	6.22817i	0.749783	+	1.29866i	0.947926	+	0.318490i	$0.103176\pi$
$23$	3.59583	+	6.22817i	0.749783	+	1.29866i	−0.198143	+	0.980173i	$0.563491\pi$
$24$	−4.47229	−	7.74623i	−0.912902	−	1.58119i
$25$	1.14575			0.229150
$26$	−1.93339	+	9.98421i	−0.379169	+	1.95807i
$27$	4.29494			0.826562
$28$	2.36859	+	4.10251i	0.447621	+	0.775302i
$29$	0.340515	+	0.589789i	0.0632321	+	0.109521i	0.895908	−	0.444239i	$-0.146526\pi$
$29$	0.340515	+	0.589789i	0.0632321	+	0.109521i	−0.832676	+	0.553760i	$0.813193\pi$
$30$	2.80290	−	4.85476i	0.511737	−	0.886354i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	16.4250	−	28.4489i	2.90355	−	5.02910i
$33$	−1.09788	+	1.90158i	−0.191116	+	0.331023i
$34$	−9.38789			−1.61001
$35$	−0.985946	+	1.70771i	−0.166655	+	0.288655i
$36$	7.01946	+	12.1581i	1.16991	+	2.02634i
$37$	−3.90751	−	6.76801i	−0.642391	−	1.11265i	−0.984898	−	0.173138i	$-0.944609\pi$
$37$	−3.90751	−	6.76801i	−0.642391	−	1.11265i	0.342507	−	0.939515i	$-0.388724\pi$
$38$	−1.97645			−0.320623
$39$	−0.549538	+	2.83787i	−0.0879965	+	0.454422i
$40$	27.6588			4.37324
$41$	1.18095	+	2.04546i	0.184433	+	0.319447i	0.943385	−	0.331699i	$-0.107622\pi$
$41$	1.18095	+	2.04546i	0.184433	+	0.319447i	−0.758952	+	0.651146i	$0.774289\pi$
$42$	0.899322	+	1.55767i	0.138768	+	0.240354i
$43$	−1.81596	+	3.14534i	−0.276932	+	0.479660i	−0.970621	−	0.240615i	$-0.922651\pi$
$43$	−1.81596	+	3.14534i	−0.276932	+	0.479660i	0.693689	+	0.720275i	$0.255984\pi$
$44$	−16.3115			−2.45906
$45$	−2.92191	+	5.06090i	−0.435573	+	0.754434i
$46$	−10.1423	+	17.5669i	−1.49540	+	2.59010i
$47$	2.34284			0.341739			0.170870	−	0.985294i	$-0.445342\pi$
$47$	2.34284			0.341739			0.170870	+	0.985294i	$0.445342\pi$
$48$	7.83976	−	13.5789i	1.13157	−	1.95994i
$49$	3.18365	+	5.51425i	0.454808	+	0.787750i
$50$	1.61583	+	2.79871i	0.228513	+	0.395797i
$51$	−2.66837			−0.373647
$52$	−20.2983	+	7.00536i	−2.81487	+	0.971469i
$53$	3.27796			0.450263			0.225132	−	0.974328i	$-0.427719\pi$
$53$	3.27796			0.450263			0.225132	+	0.974328i	$0.427719\pi$
$54$	6.05708	+	10.4912i	0.824264	+	1.42767i
$55$	−3.39491	−	5.88016i	−0.457770	−	0.792880i
$56$	−4.43722	+	7.68550i	−0.592949	+	1.02702i
$57$	−0.561777			−0.0744092
$58$	−0.960444	+	1.66354i	−0.126113	+	0.218433i
$59$	5.41258	−	9.37487i	0.704658	−	1.22050i	−0.262157	−	0.965025i	$-0.584434\pi$
$59$	5.41258	−	9.37487i	0.704658	−	1.22050i	0.966815	−	0.255478i	$-0.0822330\pi$
$60$	11.8366			1.52809
$61$	2.43957	−	4.22546i	0.312355	−	0.541014i	−0.666517	−	0.745490i	$-0.732216\pi$
$61$	2.43957	−	4.22546i	0.312355	−	0.541014i	0.978872	+	0.204476i	$0.0655489\pi$
$62$	−1.41028	−	2.44268i	−0.179106	−	0.310221i
$63$	−0.937508	−	1.62381i	−0.118115	−	0.204581i
$64$	53.5399			6.69249
$65$	−6.75004	−	5.85933i	−0.837240	−	0.726760i
$66$	−6.19328			−0.762340
$67$	−4.77340	−	8.26778i	−0.583164	−	1.01007i	−0.995102	−	0.0988579i	$-0.968481\pi$
$67$	−4.77340	−	8.26778i	−0.583164	−	1.01007i	0.411937	−	0.911212i	$-0.364852\pi$
$68$	−9.91120	−	17.1667i	−1.20191	−	2.08177i
$69$	−2.88279	+	4.99314i	−0.347048	+	0.601104i
$70$	−5.56185			−0.664768
$71$	−5.23211	+	9.06229i	−0.620938	+	1.07550i	0.368374	+	0.929678i	$0.379915\pi$
$71$	−5.23211	+	9.06229i	−0.620938	+	1.07550i	−0.989311	+	0.145818i	$0.953419\pi$
$72$	−13.1500	+	22.7764i	−1.54974	+	2.68423i
$73$	12.1046			1.41674			0.708371	−	0.705840i	$-0.249430\pi$
$73$	12.1046			1.41674			0.708371	+	0.705840i	$0.249430\pi$
$74$	11.0214	−	19.0896i	1.28121	−	2.21912i
$75$	0.459277	+	0.795491i	0.0530327	+	0.0918554i
$76$	−2.08662	−	3.61414i	−0.239352	−	0.414570i
$77$	2.17854			0.248268
$78$	−7.70700	+	2.65985i	−0.872646	+	0.301168i
$79$	8.23000			0.925947			0.462973	−	0.886372i	$-0.346783\pi$
$79$	8.23000			0.925947			0.462973	+	0.886372i	$0.346783\pi$
$80$	24.2424	+	41.9891i	2.71039	+	4.69453i
$81$	−1.81427	−	3.14241i	−0.201586	−	0.349157i
$82$	−3.33093	+	5.76934i	−0.367840	+	0.637118i
$83$	13.8846			1.52403			0.762015	−	0.647560i	$-0.224210\pi$
$83$	13.8846			1.52403			0.762015	+	0.647560i	$0.224210\pi$
$84$	−1.89891	+	3.28900i	−0.207188	+	0.358859i
$85$	4.12563	−	7.14579i	0.447487	−	0.775070i
$86$	−10.2441			−1.10465
$87$	−0.272992	+	0.472836i	−0.0292678	+	0.0506934i
$88$	−15.2787	−	26.4635i	−1.62872	−	2.82102i
$89$	−0.335874	−	0.581751i	−0.0356026	−	0.0616655i	0.847675	−	0.530516i	$-0.178002\pi$
$89$	−0.335874	−	0.581751i	−0.0356026	−	0.0616655i	−0.883278	+	0.468850i	$0.844668\pi$
$90$	−16.4829			−1.73745
$91$	2.71101	−	0.935626i	0.284191	−	0.0980802i
$92$	−42.8305			−4.46539
$93$	−0.400852	−	0.694296i	−0.0415664	−	0.0719951i
$94$	3.30407	+	5.72282i	0.340789	+	0.590264i
$95$	0.868576	−	1.50442i	0.0891140	−	0.154350i
$96$	26.3359			2.68790
$97$	5.39254	−	9.34015i	0.547529	−	0.948348i	−0.450914	−	0.892567i	$-0.648902\pi$
$97$	5.39254	−	9.34015i	0.547529	−	0.948348i	0.998443	−	0.0557807i	$-0.0177648\pi$
$98$	−8.97970	+	15.5533i	−0.907087	+	1.57112i
$99$	6.45625			0.648878
$100$	−3.41181	+	5.90942i	−0.341181	+	0.590942i
$101$	−4.26443	−	7.38621i	−0.424327	−	0.734956i	0.572030	−	0.820232i	$-0.306156\pi$
$101$	−4.26443	−	7.38621i	−0.424327	−	0.734956i	−0.996357	+	0.0852766i	$0.972823\pi$
$102$	−3.76315	−	6.51797i	−0.372608	−	0.645376i
$103$	0.634410			0.0625103			0.0312551	−	0.999511i	$-0.490050\pi$
$103$	0.634410			0.0625103			0.0312551	+	0.999511i	$0.490050\pi$
$104$	−30.3784	−	26.3697i	−2.97885	−	2.58577i
$105$	−1.58087			−0.154277
$106$	4.62285	+	8.00702i	0.449011	+	0.777710i
$107$	7.06132	+	12.2306i	0.682644	+	1.18237i	0.974171	+	0.225811i	$0.0725033\pi$
$107$	7.06132	+	12.2306i	0.682644	+	1.18237i	−0.291527	+	0.956563i	$0.594163\pi$
$108$	−12.7894	+	22.1520i	−1.23066	+	2.13157i
$109$	−19.4526			−1.86322			−0.931610	−	0.363459i	$-0.881596\pi$
$109$	−19.4526			−1.86322			−0.931610	+	0.363459i	$0.881596\pi$
$110$	9.57556	−	16.5854i	0.912994	−	1.58135i
$111$	3.13267	−	5.42594i	0.297340	−	0.515007i
$112$	−15.5566			−1.46996
$113$	−6.86157	+	11.8846i	−0.645482	+	1.11801i	0.338708	+	0.940892i	$0.390010\pi$
$113$	−6.86157	+	11.8846i	−0.645482	+	1.11801i	−0.984190	+	0.177116i	$0.943323\pi$
$114$	−0.792264	−	1.37224i	−0.0742023	−	0.128522i
$115$	−8.91430	−	15.4400i	−0.831263	−	1.43979i
$116$	−4.05593			−0.376583
$117$	8.03425	−	2.77278i	0.742766	−	0.256344i
$118$	30.5331			2.81080
$119$	1.32373	+	2.29276i	0.121346	+	0.210177i
$120$	11.0871	+	19.2034i	1.01211	+	1.75302i
$121$	1.74931	−	3.02989i	0.159028	−	0.275444i
$122$	13.7619			1.24595
$123$	−0.946769	+	1.63985i	−0.0853673	+	0.147860i
$124$	2.97779	−	5.15768i	0.267413	−	0.463173i
$125$	9.55492			0.854618
$126$	2.64430	−	4.58006i	0.235573	−	0.408025i
$127$	0.909435	+	1.57519i	0.0806993	+	0.139775i	0.903550	−	0.428482i	$-0.140951\pi$
$127$	0.909435	+	1.57519i	0.0806993	+	0.139775i	−0.822851	+	0.568257i	$0.807618\pi$
$128$	42.6564	+	73.8830i	3.77033	+	6.53040i
$129$	−2.91173			−0.256363
$130$	4.79300	−	24.7515i	0.420374	−	2.17085i
$131$	6.20618			0.542236			0.271118	−	0.962546i	$-0.412607\pi$
$131$	6.20618			0.542236			0.271118	+	0.962546i	$0.412607\pi$
$132$	−6.53851	−	11.3250i	−0.569104	−	0.985717i
$133$	0.278686	+	0.482699i	0.0241652	+	0.0418553i
$134$	13.4637	−	23.3198i	1.16309	−	2.01452i
$135$	−10.6474			−0.916385
$136$	18.5673	−	32.1595i	1.59213	−	2.75765i
$137$	−10.9750	+	19.0092i	−0.937656	+	1.62407i	−0.167829	+	0.985816i	$0.553676\pi$
$137$	−10.9750	+	19.0092i	−0.937656	+	1.62407i	−0.769827	+	0.638252i	$0.779658\pi$
$138$	−16.2622			−1.38433
$139$	1.40819	−	2.43905i	0.119441	−	0.206878i	−0.800105	−	0.599860i	$-0.795223\pi$
$139$	1.40819	−	2.43905i	0.119441	−	0.206878i	0.919546	+	0.392982i	$0.128556\pi$
$140$	−5.87188	−	10.1704i	−0.496264	−	0.859555i
$141$	0.939134	+	1.62663i	0.0790893	+	0.136987i
$142$	−29.5150			−2.47685
$143$	−1.87739	+	9.69502i	−0.156995	+	0.810738i
$144$	−46.1029			−3.84191
$145$	−0.844158	−	1.46212i	−0.0701035	−	0.121423i
$146$	17.0710	+	29.5678i	1.41280	+	2.44705i
$147$	−2.55235	+	4.42080i	−0.210514	+	0.364621i
$148$	46.5430			3.82581
$149$	1.71957	−	2.97838i	0.140873	−	0.243999i	−0.786953	−	0.617013i	$-0.788343\pi$
$149$	1.71957	−	2.97838i	0.140873	−	0.243999i	0.927825	+	0.373015i	$0.121676\pi$
$150$	−1.29542	+	2.24373i	−0.105771	+	0.183200i
$151$	−11.4025			−0.927919			−0.463959	−	0.885856i	$-0.653572\pi$
$151$	−11.4025			−0.927919			−0.463959	+	0.885856i	$0.653572\pi$
$152$	3.90900	−	6.77059i	0.317062	−	0.549168i
$153$	3.92294	+	6.79473i	0.317151	+	0.549322i
$154$	3.07236	+	5.32149i	0.247578	+	0.428817i
$155$	2.47906			0.199123
$156$	−13.0004	−	11.2849i	−1.04087	−	0.903516i
$157$	−10.8464			−0.865633			−0.432817	−	0.901482i	$-0.642480\pi$
$157$	−10.8464			−0.865633			−0.432817	+	0.901482i	$0.642480\pi$
$158$	11.6066	+	20.1032i	0.923373	+	1.59933i
$159$	1.31398	+	2.27588i	0.104205	+	0.180489i
$160$	−40.7186	+	70.5266i	−3.21908	+	5.57562i
$161$	5.72038			0.450829
$162$	5.11726	−	8.86336i	0.402050	−	0.696372i
$163$	5.68480	−	9.84637i	0.445268	−	0.771227i	−0.552803	−	0.833312i	$-0.686442\pi$
$163$	5.68480	−	9.84637i	0.445268	−	0.771227i	0.998071	+	0.0620852i	$0.0197750\pi$
$164$	−14.0664			−1.09840
$165$	2.72171	−	4.71414i	0.211885	−	0.366996i
$166$	19.5812	+	33.9156i	1.51979	+	2.63236i
$167$	−10.9081	−	18.8933i	−0.844090	−	1.46201i	−0.886409	−	0.462903i	$-0.846808\pi$
$167$	−10.9081	−	18.8933i	−0.844090	−	1.46201i	0.0423183	−	0.999104i	$-0.486526\pi$
$168$	−7.11468			−0.548909
$169$	1.82750	+	12.8709i	0.140577	+	0.990070i
$170$	23.2732			1.78497
$171$	0.825904	+	1.43051i	0.0631585	+	0.109394i
$172$	−10.8151	−	18.7323i	−0.824644	−	1.42833i
$173$	3.79182	−	6.56763i	0.288287	−	0.499328i	−0.685114	−	0.728436i	$-0.740248\pi$
$173$	3.79182	−	6.56763i	0.288287	−	0.499328i	0.973401	+	0.229108i	$0.0735810\pi$
$174$	−1.53998			−0.116746
$175$	0.455676	−	0.789254i	0.0344459	−	0.0596620i
$176$	26.7830	−	46.3896i	2.01885	−	3.49675i
$177$	8.67857			0.652322
$178$	0.947354	−	1.64087i	0.0710072	−	0.122988i
$179$	−7.02733	−	12.1717i	−0.525247	−	0.909755i	−0.999568	−	0.0294024i	$-0.990640\pi$
$179$	−7.02733	−	12.1717i	−0.525247	−	0.909755i	0.474321	−	0.880352i	$-0.342694\pi$
$180$	−17.4017	−	30.1406i	−1.29704	−	2.24655i
$181$	7.92725			0.589228			0.294614	−	0.955616i	$-0.404809\pi$
$181$	7.92725			0.589228			0.294614	+	0.955616i	$0.404809\pi$
$182$	6.10872	+	5.30263i	0.452809	+	0.393057i
$183$	3.91162			0.289155
$184$	−40.1186	−	69.4874i	−2.95758	−	5.12268i
$185$	9.68697	+	16.7783i	0.712200	+	1.23357i
$186$	1.13063	−	1.95831i	0.0829017	−	0.143590i
$187$	−9.11597			−0.666626
$188$	−6.97650	+	12.0836i	−0.508813	+	0.881291i
$189$	1.70814	−	2.95858i	0.124249	−	0.215205i
$190$	4.89975			0.355465
$191$	1.56214	−	2.70571i	0.113033	−	0.195779i	−0.803959	−	0.594685i	$-0.797277\pi$
$191$	1.56214	−	2.70571i	0.113033	−	0.195779i	0.916992	+	0.398906i	$0.130610\pi$
$192$	21.4616	+	37.1725i	1.54886	+	2.68270i
$193$	2.07043	+	3.58610i	0.149033	+	0.258133i	0.930870	−	0.365350i	$-0.119051\pi$
$193$	2.07043	+	3.58610i	0.149033	+	0.258133i	−0.781837	+	0.623483i	$0.785717\pi$
$194$	30.4200			2.18403
$195$	1.36234	−	7.03525i	0.0975591	−	0.503805i
$196$	−37.9210			−2.70864
$197$	−3.45327	−	5.98124i	−0.246035	−	0.426146i	0.716387	−	0.697703i	$-0.245795\pi$
$197$	−3.45327	−	5.98124i	−0.246035	−	0.426146i	−0.962422	+	0.271558i	$0.912461\pi$
$198$	9.10513	+	15.7706i	0.647074	+	1.12076i
$199$	−0.0504704	+	0.0874172i	−0.00357775	+	0.00619684i	−0.867809	−	0.496898i	$-0.834472\pi$
$199$	−0.0504704	+	0.0874172i	−0.00357775	+	0.00619684i	0.864231	+	0.503095i	$0.167806\pi$
$200$	−12.7831			−0.903902
$201$	3.82686	−	6.62831i	0.269926	−	0.467525i
$202$	12.0281	−	20.8333i	0.846294	−	1.46582i
$203$	0.541704			0.0380202
$204$	7.94584	−	13.7626i	0.556320	−	0.963575i
$205$	−2.92764	−	5.07082i	−0.204475	−	0.354161i
$206$	0.894697	+	1.54966i	0.0623365	+	0.107970i
$207$	16.9527			1.17829
$208$	13.4061	−	69.2304i	0.929546	−	4.80027i
$209$	−1.91920			−0.132754
$210$	−2.22948	−	3.86157i	−0.153848	−	0.266473i
$211$	−6.90990	−	11.9683i	−0.475697	−	0.823931i	0.523915	−	0.851770i	$-0.324471\pi$
$211$	−6.90990	−	11.9683i	−0.475697	−	0.823931i	−0.999612	+	0.0278388i	$0.991137\pi$
$212$	−9.76109	+	16.9067i	−0.670394	+	1.16116i
$213$	−8.38921			−0.574819
$214$	−19.9169	+	34.4971i	−1.36149	+	2.35817i
$215$	4.50188	−	7.79749i	0.307026	−	0.531784i
$216$	−47.9185			−3.26044
$217$	−0.397709	+	0.688852i	−0.0269983	+	0.0467623i
$218$	−27.4336	−	47.5164i	−1.85804	−	3.21822i
$219$	4.85217	+	8.40421i	0.327879	+	0.567904i
$220$	40.4373			2.72628
$221$	−11.3440	+	3.91506i	−0.763083	+	0.263356i
$222$	17.6718			1.18605
$223$	−12.2352	−	21.1919i	−0.819327	−	1.41912i	−0.906179	−	0.422895i	$-0.861014\pi$
$223$	−12.2352	−	21.1919i	−0.819327	−	1.41912i	0.0868520	−	0.996221i	$-0.472319\pi$
$224$	−13.0647	−	22.6288i	−0.872924	−	1.51195i
$225$	1.35042	−	2.33900i	0.0900283	−	0.155934i
$226$	−38.7070			−2.57475
$227$	7.62410	−	13.2053i	0.506029	−	0.876468i	−0.493946	−	0.869492i	$-0.664446\pi$
$227$	7.62410	−	13.2053i	0.506029	−	0.876468i	0.999976	−	0.00697596i	$-0.00222054\pi$
$228$	1.67285	−	2.89747i	0.110787	−	0.191890i
$229$	0.738993			0.0488340			0.0244170	−	0.999702i	$-0.492227\pi$
$229$	0.738993			0.0488340			0.0244170	+	0.999702i	$0.492227\pi$
$230$	25.1433	−	43.5495i	1.65790	−	2.87157i
$231$	0.873273	+	1.51255i	0.0574572	+	0.0995187i
$232$	−3.79911	−	6.58026i	−0.249424	−	0.432015i
$233$	2.13723			0.140014			0.0700072	−	0.997546i	$-0.477698\pi$
$233$	2.13723			0.140014			0.0700072	+	0.997546i	$0.477698\pi$
$234$	18.1036	+	15.7147i	1.18347	+	1.02730i
$235$	−5.80806			−0.378876
$236$	32.2351	+	55.8327i	2.09832	+	3.63440i
$237$	3.29901	+	5.71405i	0.214294	+	0.371168i
$238$	−3.73365	+	6.46687i	−0.242017	+	0.419185i
$239$	−10.4868			−0.678336			−0.339168	−	0.940726i	$-0.610145\pi$
$239$	−10.4868			−0.678336			−0.339168	+	0.940726i	$0.610145\pi$
$240$	−19.4353	+	33.6629i	−1.25454	+	2.17293i
$241$	0.872422	−	1.51108i	0.0561977	−	0.0973372i	−0.836558	−	0.547878i	$-0.815436\pi$
$241$	0.872422	−	1.51108i	0.0561977	−	0.0973372i	0.892756	+	0.450541i	$0.148769\pi$
$242$	9.86806			0.634343
$243$	7.89692	−	13.6779i	0.506588	−	0.877436i
$244$	14.5290	+	25.1650i	0.930126	+	1.61103i
$245$	−7.89248	−	13.6702i	−0.504232	−	0.873356i
$246$	−5.34084			−0.340520
$247$	−2.38828	+	0.824246i	−0.151963	+	0.0524455i
$248$	11.1570			0.708468
$249$	5.56566	+	9.64000i	0.352709	+	0.610910i
$250$	13.4751	+	23.3396i	0.852242	+	1.47613i
$251$	7.58800	−	13.1428i	0.478950	−	0.829566i	−0.520759	−	0.853704i	$-0.674351\pi$
$251$	7.58800	−	13.1428i	0.478950	−	0.829566i	0.999709	+	0.0241381i	$0.00768416\pi$
$252$	11.1668			0.703443
$253$	−9.84851	+	17.0581i	−0.619170	+	1.07243i
$254$	−2.56512	+	4.44291i	−0.160950	+	0.278773i
$255$	6.61506			0.414251
$256$	−66.7751	+	115.658i	−4.17344	+	7.22862i
$257$	8.24457	+	14.2800i	0.514282	+	0.890763i	0.999863	+	0.0165709i	$0.00527491\pi$
$257$	8.24457	+	14.2800i	0.514282	+	0.890763i	−0.485581	+	0.874192i	$0.661392\pi$
$258$	−4.10635	−	7.11242i	−0.255650	−	0.442800i
$259$	−6.21621			−0.386257
$260$	50.3207	−	17.3667i	3.12076	−	1.07704i
$261$	1.60537			0.0993701
$262$	8.75246	+	15.1597i	0.540729	+	0.936570i
$263$	−2.30996	−	4.00097i	−0.142438	−	0.246710i	0.785976	−	0.618257i	$-0.212161\pi$
$263$	−2.30996	−	4.00097i	−0.142438	−	0.246710i	−0.928414	+	0.371547i	$0.878828\pi$
$264$	12.2490	−	21.2159i	0.753874	−	1.30575i
$265$	−8.12628			−0.499193
$266$	−0.786053	+	1.36148i	−0.0481960	+	0.0834779i
$267$	0.269271	−	0.466392i	0.0164791	−	0.0285427i
$268$	56.8568			3.47308
$269$	−7.54558	+	13.0693i	−0.460062	+	0.796851i	−0.998964	−	0.0455180i	$-0.985506\pi$
$269$	−7.54558	+	13.0693i	−0.460062	+	0.796851i	0.538902	+	0.842369i	$0.318839\pi$
$270$	−15.0159	−	26.0083i	−0.913838	−	1.58281i
$271$	−10.8723	−	18.8314i	−0.660447	−	1.14393i	−0.980498	−	0.196528i	$-0.937033\pi$
$271$	−10.8723	−	18.8314i	−0.660447	−	1.14393i	0.320051	−	0.947400i	$-0.396300\pi$
$272$	65.0955			3.94700
$273$	1.73631	+	1.50720i	0.105087	+	0.0912196i
$274$	−61.9113			−3.74020
$275$	1.56903	+	2.71764i	0.0946161	+	0.163880i
$276$	−17.1687	−	29.7371i	−1.03343	−	1.78996i
$277$	5.13562	−	8.89516i	0.308570	−	0.534458i	−0.669480	−	0.742830i	$-0.733483\pi$
$277$	5.13562	−	8.89516i	0.308570	−	0.534458i	0.978050	+	0.208372i	$0.0668163\pi$
$278$	7.94377			0.476436
$279$	−1.17864	+	2.04146i	−0.0705631	+	0.122219i
$280$	11.0002	−	19.0528i	0.657385	−	1.13862i
$281$	−5.84620			−0.348755			−0.174378	−	0.984679i	$-0.555791\pi$
$281$	−5.84620			−0.348755			−0.174378	+	0.984679i	$0.555791\pi$
$282$	−2.64889	+	4.58801i	−0.157739	+	0.273212i
$283$	−11.3965	−	19.7393i	−0.677450	−	1.17338i	−0.975746	−	0.218904i	$-0.929752\pi$
$283$	−11.3965	−	19.7393i	−0.677450	−	1.17338i	0.298296	−	0.954473i	$-0.403582\pi$
$284$	−31.1603	−	53.9712i	−1.84902	−	3.20260i
$285$	1.39268			0.0824953
$286$	−26.3295	+	9.08685i	−1.55689	+	0.537317i
$287$	1.87869			0.110896
$288$	−38.7181	−	67.0618i	−2.28149	−	3.95165i
$289$	2.96096	+	5.12853i	0.174174	+	0.301678i
$290$	2.38100	−	4.12402i	0.139817	−	0.242171i
$291$	8.64643			0.506863
$292$	−36.0451	+	62.4319i	−2.10938	+	3.65355i
$293$	−10.1912	+	17.6517i	−0.595379	+	1.03123i	0.398115	+	0.917336i	$0.369665\pi$
$293$	−10.1912	+	17.6517i	−0.595379	+	1.03123i	−0.993493	+	0.113890i	$0.963669\pi$
$294$	−14.3981			−0.839715
$295$	−13.4181	+	23.2409i	−0.781234	+	1.35314i
$296$	43.5959	+	75.5104i	2.53396	+	4.38895i
$297$	5.88164	+	10.1873i	0.341287	+	0.591127i
$298$	9.70031			0.561924
$299$	−4.92962	+	25.4570i	−0.285087	+	1.47222i
$300$	−5.47052			−0.315840
$301$	1.44445	+	2.50186i	0.0832567	+	0.144205i
$302$	−16.0807	−	27.8526i	−0.925339	−	1.60273i
$303$	3.41881	−	5.92156i	0.196406	−	0.340184i
$304$	13.7047			0.786018
$305$	−6.04784	+	10.4752i	−0.346298	+	0.599806i
$306$	−11.0649	+	19.1650i	−0.632538	+	1.09559i
$307$	8.28427			0.472808			0.236404	−	0.971655i	$-0.424031\pi$
$307$	8.28427			0.472808			0.236404	+	0.971655i	$0.424031\pi$
$308$	−6.48724	+	11.2362i	−0.369645	+	0.640244i
$309$	0.254304	+	0.440468i	0.0144669	+	0.0250574i
$310$	3.49618	+	6.05556i	0.198569	+	0.343932i
$311$	3.33374			0.189039			0.0945194	−	0.995523i	$-0.469869\pi$
$311$	3.33374			0.189039			0.0945194	+	0.995523i	$0.469869\pi$
$312$	6.13117	−	31.6619i	0.347109	−	1.79250i
$313$	−7.51618			−0.424839			−0.212420	−	0.977179i	$-0.568134\pi$
$313$	−7.51618			−0.424839			−0.212420	+	0.977179i	$0.568134\pi$
$314$	−15.2964	−	26.4942i	−0.863227	−	1.49515i
$315$	2.32414	+	4.02553i	0.130951	+	0.226813i
$316$	−24.5072	+	42.4477i	−1.37864	+	2.38787i
$317$	−20.7761			−1.16690			−0.583450	−	0.812149i	$-0.698297\pi$
$317$	−20.7761			−1.16690			−0.583450	+	0.812149i	$0.698297\pi$
$318$	−3.70616	+	6.41926i	−0.207831	+	0.359974i
$319$	−0.932625	+	1.61535i	−0.0522170	+	0.0904425i
$320$	−132.729			−7.41976
$321$	−5.66109	+	9.80529i	−0.315971	+	0.547278i
$322$	8.06735	+	13.9731i	0.449576	+	0.778688i
$323$	−1.16614	−	2.01982i	−0.0648860	−	0.112386i
$324$	21.6101			1.20056
$325$	3.11968	+	2.70801i	0.173049	+	0.150214i
$326$	32.0687			1.77612
$327$	−7.79761	−	13.5059i	−0.431209	−	0.746875i
$328$	−13.1758	−	22.8211i	−0.727510	−	1.26008i
$329$	0.931771	−	1.61387i	0.0513702	−	0.0889758i
$330$	15.3535			0.845184
$331$	−0.741231	+	1.28385i	−0.0407417	+	0.0705668i	−0.885677	−	0.464301i	$-0.846305\pi$
$331$	−0.741231	+	1.28385i	−0.0407417	+	0.0705668i	0.844935	+	0.534868i	$0.179639\pi$
$332$	−41.3453	+	71.6122i	−2.26912	+	3.93023i
$333$	−18.4221			−1.00953
$334$	30.7669	−	53.2898i	1.68349	−	2.91589i
$335$	11.8336	+	20.4963i	0.646537	+	1.11983i
$336$	−6.23589	−	10.8009i	−0.340196	−	0.589236i
$337$	32.9100			1.79272			0.896361	−	0.443325i	$-0.146201\pi$
$337$	32.9100			1.79272			0.896361	+	0.443325i	$0.146201\pi$
$338$	−28.8622	+	22.6156i	−1.56990	+	1.23013i
$339$	−11.0019			−0.597541
$340$	24.5705	+	42.5573i	1.33252	+	2.30799i
$341$	−1.36943	−	2.37193i	−0.0741590	−	0.128447i
$342$	−2.32952	+	4.03484i	−0.125966	+	0.218179i
$343$	10.6326			0.574107
$344$	20.2606	−	35.0924i	1.09238	−	1.89206i
$345$	7.14663	−	12.3783i	0.384761	−	0.666426i
$346$	21.3901			1.14994
$347$	1.73880	−	3.01169i	0.0933436	−	0.161676i	−0.815572	−	0.578655i	$-0.803578\pi$
$347$	1.73880	−	3.01169i	0.0933436	−	0.161676i	0.908916	+	0.416979i	$0.136911\pi$
$348$	−1.62583	−	2.81601i	−0.0871534	−	0.150954i
$349$	3.89914	+	6.75350i	0.208716	+	0.361507i	0.951310	−	0.308235i	$-0.0997382\pi$
$349$	3.89914	+	6.75350i	0.208716	+	0.361507i	−0.742594	+	0.669742i	$0.766405\pi$
$350$	2.57053			0.137400
$351$	11.6944	+	10.1512i	0.624199	+	0.541831i
$352$	89.9716			4.79550
$353$	17.3659	+	30.0787i	0.924296	+	1.60093i	0.792689	+	0.609626i	$0.208680\pi$
$353$	17.3659	+	30.0787i	0.924296	+	1.60093i	0.131607	+	0.991302i	$0.457986\pi$
$354$	12.2392	+	21.1990i	0.650508	+	1.12671i
$355$	12.9707	−	22.4660i	0.688415	−	1.19237i
$356$	4.00065			0.212034
$357$	−1.06124	+	1.83811i	−0.0561665	+	0.0972833i
$358$	19.8210	−	34.3310i	1.04757	−	1.81445i
$359$	−6.67089			−0.352076			−0.176038	−	0.984383i	$-0.556328\pi$
$359$	−6.67089			−0.352076			−0.176038	+	0.984383i	$0.556328\pi$
$360$	32.5996	−	56.4642i	1.71815	−	2.97593i
$361$	9.25449	+	16.0292i	0.487078	+	0.843645i
$362$	11.1797	+	19.3637i	0.587590	+	1.01774i
$363$	2.80485			0.147216
$364$	−3.24716	+	16.7686i	−0.170197	+	0.878915i
$365$	−30.0082			−1.57070
$366$	5.51649	+	9.55484i	0.288351	+	0.499439i
$367$	3.79027	+	6.56494i	0.197851	+	0.342687i	0.947831	−	0.318773i	$-0.103271\pi$
$367$	3.79027	+	6.56494i	0.197851	+	0.342687i	−0.749981	+	0.661460i	$0.769937\pi$
$368$	70.3264	−	121.809i	3.66602	−	6.34973i
$369$	5.56762			0.289839
$370$	−27.3227	+	47.3243i	−1.42044	+	2.46027i
$371$	1.30368	−	2.25803i	0.0676835	−	0.117231i
$372$	4.77461			0.247552
$373$	−7.90082	+	13.6846i	−0.409089	+	0.708563i	−0.994788	−	0.101966i	$-0.967487\pi$
$373$	−7.90082	+	13.6846i	−0.409089	+	0.708563i	0.585699	+	0.810529i	$0.300820\pi$
$374$	−12.8561	−	22.2674i	−0.664773	−	1.15142i
$375$	3.83011	+	6.63394i	0.197786	+	0.342575i
$376$	−26.1390			−1.34802
$377$	−0.466821	+	2.41071i	−0.0240425	+	0.124158i
$378$	9.63583			0.495613
$379$	−8.93032	−	15.4678i	−0.458720	−	0.794525i	0.540174	−	0.841553i	$-0.318358\pi$
$379$	−8.93032	−	15.4678i	−0.458720	−	0.794525i	−0.998894	+	0.0470278i	$0.985025\pi$
$380$	5.17287	+	8.95968i	0.265363	+	0.459622i
$381$	−0.729097	+	1.26283i	−0.0373528	+	0.0646969i
$382$	8.81225			0.450874
$383$	4.93025	−	8.53944i	0.251924	−	0.436345i	−0.712132	−	0.702046i	$-0.752270\pi$
$383$	4.93025	−	8.53944i	0.251924	−	0.436345i	0.964055	+	0.265701i	$0.0856034\pi$
$384$	−34.1978	+	59.2323i	−1.74515	+	3.02268i
$385$	−5.40075			−0.275248
$386$	−5.83979	+	10.1148i	−0.297237	+	0.514830i
$387$	4.28071	+	7.41442i	0.217601	+	0.376896i
$388$	32.1157	+	55.6260i	1.63043	+	2.82398i
$389$	−15.6968			−0.795857			−0.397929	−	0.917416i	$-0.630271\pi$
$389$	−15.6968			−0.795857			−0.397929	+	0.917416i	$0.630271\pi$
$390$	19.1061	−	6.59392i	0.967477	−	0.333896i
$391$	−23.9366			−1.21052
$392$	−35.5199	−	61.5223i	−1.79403	−	3.10734i
$393$	2.48776	+	4.30892i	0.125491	+	0.217356i
$394$	9.74017	−	16.8705i	0.490702	−	0.849922i
$395$	−20.4027			−1.02657
$396$	−19.2254	+	33.2993i	−0.966110	+	1.67335i
$397$	10.8617	−	18.8129i	0.545131	−	0.944195i	−0.453468	−	0.891273i	$-0.649813\pi$
$397$	10.8617	−	18.8129i	0.545131	−	0.944195i	0.998599	−	0.0529218i	$-0.0168534\pi$
$398$	−0.284710			−0.0142712
$399$	−0.223424	+	0.386982i	−0.0111852	+	0.0193733i
$400$	−11.2042	−	19.4062i	−0.560208	−	0.970309i
$401$	−4.16302	−	7.21057i	−0.207891	−	0.360078i	0.743159	−	0.669115i	$-0.233327\pi$
$401$	−4.16302	−	7.21057i	−0.207891	−	0.360078i	−0.951050	+	0.309037i	$0.899993\pi$
$402$	21.5878			1.07670
$403$	−2.72282	−	2.36353i	−0.135633	−	0.117736i
$404$	50.7943			2.52711
$405$	4.49769	+	7.79023i	0.223492	+	0.387100i
$406$	0.763955	+	1.32321i	0.0379144	+	0.0656697i
$407$	10.7022	−	18.5367i	0.530486	−	0.918829i
$408$	29.7709			1.47388
$409$	−3.37755	+	5.85008i	−0.167009	+	0.289268i	−0.937367	−	0.348344i	$-0.886744\pi$
$409$	−3.37755	+	5.85008i	−0.167009	+	0.289268i	0.770358	+	0.637612i	$0.220078\pi$
$410$	8.25759	−	14.3026i	0.407813	−	0.706353i
$411$	−17.5974			−0.868014
$412$	−1.88914	+	3.27209i	−0.0930712	+	0.161204i
$413$	−4.30527	−	7.45694i	−0.211848	−	0.366932i
$414$	23.9081	+	41.4100i	1.17502	+	2.03519i
$415$	−34.4207			−1.68965
$416$	111.962	−	38.6404i	5.48939	−	1.89450i
$417$	2.25790			0.110570
$418$	−2.70662	−	4.68800i	−0.132385	−	0.229298i
$419$	12.8707	+	22.2928i	0.628777	+	1.08907i	0.987797	+	0.155744i	$0.0497776\pi$
$419$	12.8707	+	22.2928i	0.628777	+	1.08907i	−0.359020	+	0.933330i	$0.616889\pi$
$420$	4.70751	−	8.15364i	0.229703	−	0.397857i
$421$	−34.6397			−1.68824			−0.844118	−	0.536158i	$-0.819875\pi$
$421$	−34.6397			−1.68824			−0.844118	+	0.536158i	$0.819875\pi$
$422$	19.4898	−	33.7573i	0.948749	−	1.64328i
$423$	2.76136	−	4.78282i	0.134262	−	0.232549i
$424$	−36.5721			−1.77610
$425$	−1.90675	+	3.30258i	−0.0924908	+	0.160199i
$426$	−11.8312	−	20.4922i	−0.573221	−	0.992848i
$427$	−1.94048	−	3.36100i	−0.0939063	−	0.162650i
$428$	−84.1085			−4.06554
$429$	−7.48377	+	2.58280i	−0.361320	+	0.124699i
$430$	25.3957			1.22469
$431$	8.92773	+	15.4633i	0.430034	+	0.744840i	0.996876	−	0.0789863i	$-0.0251683\pi$
$431$	8.92773	+	15.4633i	0.430034	+	0.744840i	−0.566842	+	0.823827i	$0.691835\pi$
$432$	−41.9997	−	72.7457i	−2.02071	−	3.49998i
$433$	−13.9019	+	24.0788i	−0.668082	+	1.15715i	0.310357	+	0.950620i	$0.399551\pi$
$433$	−13.9019	+	24.0788i	−0.668082	+	1.15715i	−0.978440	+	0.206533i	$0.933782\pi$
$434$	−2.24353			−0.107693
$435$	0.676765	−	1.17219i	0.0324484	−	0.0562023i
$436$	57.9257	−	100.330i	2.77414	−	4.80495i
$437$	−5.03941			−0.241068
$438$	−13.6859	+	23.7046i	−0.653935	+	1.13265i
$439$	10.9636	+	18.9896i	0.523265	+	0.906322i	0.999633	+	0.0270761i	$0.00861966\pi$
$439$	10.9636	+	18.9896i	0.523265	+	0.906322i	−0.476368	+	0.879246i	$0.658047\pi$
$440$	37.8769	+	65.6047i	1.80571	+	3.12758i
$441$	15.0095			0.714737
$442$	−25.5615	−	22.1885i	−1.21584	−	1.05540i
$443$	28.9058			1.37336			0.686679	−	0.726961i	$-0.259068\pi$
$443$	28.9058			1.37336			0.686679	+	0.726961i	$0.259068\pi$
$444$	18.6568	+	32.3146i	0.885414	+	1.53358i
$445$	0.832653	+	1.44220i	0.0394715	+	0.0683667i
$446$	34.5100	−	59.7731i	1.63410	−	2.83034i
$447$	2.75717			0.130410
$448$	21.2933	−	36.8811i	1.00601	−	1.74247i
$449$	7.03172	−	12.1793i	0.331847	−	0.574777i	−0.651027	−	0.759055i	$-0.725661\pi$
$449$	7.03172	−	12.1793i	0.331847	−	0.574777i	0.982874	+	0.184278i	$0.0589947\pi$
$450$	7.61791			0.359112
$451$	−3.23445	+	5.60224i	−0.152304	+	0.263799i
$452$	−40.8646	−	70.7796i	−1.92211	−	3.32919i
$453$	−4.57070	−	7.91668i	−0.214750	−	0.371958i
$454$	43.0085			2.01849
$455$	−6.72076	+	2.31947i	−0.315074	+	0.108739i
$456$	6.26772			0.293513
$457$	2.26030	+	3.91495i	0.105732	+	0.183134i	0.914037	−	0.405630i	$-0.132948\pi$
$457$	2.26030	+	3.91495i	0.105732	+	0.183134i	−0.808305	+	0.588764i	$0.799615\pi$
$458$	1.04219	+	1.80512i	0.0486983	+	0.0843478i
$459$	−7.14759	+	12.3800i	−0.333621	+	0.577849i
$460$	106.180			4.95065
$461$	−10.3191	+	17.8732i	−0.480608	+	0.832437i	−0.999752	−	0.0222493i	$-0.992917\pi$
$461$	−10.3191	+	17.8732i	−0.480608	+	0.832437i	0.519145	+	0.854686i	$0.326251\pi$
$462$	−2.46312	+	4.26625i	−0.114595	+	0.198484i
$463$	20.6732			0.960764			0.480382	−	0.877059i	$-0.340498\pi$
$463$	20.6732			0.960764			0.480382	+	0.877059i	$0.340498\pi$
$464$	6.65971	−	11.5350i	0.309169	−	0.535497i
$465$	0.993737	+	1.72120i	0.0460834	+	0.0798189i
$466$	3.01409	+	5.22056i	0.139625	+	0.241838i
$467$	−13.3590			−0.618179			−0.309090	−	0.951033i	$-0.600024\pi$
$467$	−13.3590			−0.618179			−0.309090	+	0.951033i	$0.600024\pi$
$468$	−9.62315	+	49.6949i	−0.444830	+	2.29715i
$469$	−7.59371			−0.350645
$470$	−8.19100	−	14.1872i	−0.377823	−	0.654408i
$471$	−4.34778	−	7.53058i	−0.200335	−	0.346991i
$472$	−60.3879	+	104.595i	−2.77958	+	4.81437i
$473$	−9.94735			−0.457380
$474$	−9.30506	+	16.1168i	−0.427396	+	0.740271i
$475$	−0.401431	+	0.695299i	−0.0184189	+	0.0319025i
$476$	−15.7671			−0.722684
$477$	3.86353	−	6.69182i	0.176899	−	0.306398i
$478$	−14.7894	−	25.6159i	−0.676450	−	1.17165i
$479$	−8.44525	−	14.6276i	−0.385873	−	0.668352i	0.606017	−	0.795452i	$-0.292766\pi$
$479$	−8.44525	−	14.6276i	−0.385873	−	0.668352i	−0.991890	+	0.127100i	$0.959433\pi$
$480$	−65.2884			−2.98000
$481$	5.35691	−	27.6636i	0.244254	−	1.26135i
$482$	4.92144			0.224166
$483$	2.29303	+	3.97164i	0.104336	+	0.180716i
$484$	10.4181	+	18.0447i	0.473551	+	0.820215i
$485$	−13.3684	+	23.1548i	−0.607029	+	1.05141i
$486$	44.5475			2.02072
$487$	0.476375	−	0.825106i	0.0215866	−	0.0373891i	−0.855030	−	0.518578i	$-0.826462\pi$
$487$	0.476375	−	0.825106i	0.0215866	−	0.0373891i	0.876617	+	0.481189i	$0.159795\pi$
$488$	−27.2182	+	47.1432i	−1.23211	+	2.13407i
$489$	9.11505			0.412197
$490$	22.2612	−	38.5576i	1.00566	−	1.74185i
$491$	14.6343	+	25.3473i	0.660435	+	1.14391i	0.980501	+	0.196512i	$0.0629613\pi$
$491$	14.6343	+	25.3473i	0.660435	+	1.14391i	−0.320067	+	0.947395i	$0.603705\pi$
$492$	−5.63855	−	9.76626i	−0.254206	−	0.440297i
$493$	−2.26672			−0.102088
$494$	−5.38152	−	4.67139i	−0.242126	−	0.210176i
$495$	−16.0054			−0.719391
$496$	9.77888	+	16.9375i	0.439084	+	0.760517i
$497$	4.16172	+	7.20831i	0.186679	+	0.323337i
$498$	−15.6983	+	27.1902i	−0.703457	+	1.21842i
$499$	−0.0864706			−0.00387096			−0.00193548	−	0.999998i	$-0.500616\pi$
$499$	−0.0864706			−0.00387096			−0.00193548	+	0.999998i	$0.500616\pi$
$500$	−28.4525	+	49.2812i	−1.27244	+	2.20392i
$501$	8.74503	−	15.1468i	0.390699	−	0.676710i
$502$	42.8048			1.91047
$503$	6.13219	−	10.6213i	0.273421	−	0.473579i	−0.696315	−	0.717737i	$-0.745178\pi$
$503$	6.13219	−	10.6213i	0.273421	−	0.473579i	0.969736	+	0.244158i	$0.0785115\pi$
$504$	10.4597	+	18.1168i	0.465914	+	0.806986i
$505$	10.5718	+	18.3109i	0.470439	+	0.814824i
$506$	−55.5567			−2.46980
$507$	−8.20366	+	6.42815i	−0.364337	+	0.285484i
$508$	−10.8324			−0.480611
$509$	6.01374	+	10.4161i	0.266554	+	0.461686i	0.967970	−	0.251067i	$-0.0807815\pi$
$509$	6.01374	+	10.4161i	0.266554	+	0.461686i	−0.701415	+	0.712753i	$0.747448\pi$
$510$	9.32909	+	16.1585i	0.413099	+	0.715509i
$511$	4.81413	−	8.33832i	0.212965	−	0.368865i
$512$	−206.061			−9.10671
$513$	−1.50480	+	2.60638i	−0.0664384	+	0.115075i
$514$	−23.2543	+	40.2777i	−1.02570	+	1.77657i
$515$	−1.57274			−0.0693033
$516$	8.67051	−	15.0178i	0.381698	−	0.661120i
$517$	3.20837	+	5.55706i	0.141104	+	0.244399i
$518$	−8.76661	−	15.1842i	−0.385183	−	0.667156i
$519$	6.07984			0.266875
$520$	75.3099	+	65.3723i	3.30256	+	2.86676i
$521$	−29.5894			−1.29634			−0.648168	−	0.761497i	$-0.724465\pi$
$521$	−29.5894			−1.29634			−0.648168	+	0.761497i	$0.724465\pi$
$522$	2.26403	+	3.92141i	0.0990938	+	0.171636i
$523$	17.8409	+	30.9014i	0.780130	+	1.35122i	0.931866	+	0.362803i	$0.118180\pi$
$523$	17.8409	+	30.9014i	0.780130	+	1.35122i	−0.151736	+	0.988421i	$0.548486\pi$
$524$	−18.4807	+	32.0095i	−0.807333	+	1.39834i
$525$	0.730634			0.0318875
$526$	6.51539	−	11.2850i	0.284084	−	0.492049i
$527$	1.66419	−	2.88246i	0.0724931	−	0.125562i
$528$	42.9441			1.86890
$529$	−14.3600	+	24.8723i	−0.624350	+	1.08141i
$530$	−11.4603	−	19.8499i	−0.497806	−	0.862224i
$531$	−12.7589	−	22.0991i	−0.553690	−	0.959019i
$532$	−3.31948			−0.143918
$533$	−1.61899	+	8.36061i	−0.0701262	+	0.362138i
$534$	1.51899			0.0657333
$535$	−17.5055	−	30.3204i	−0.756827	−	1.31086i
$536$	53.2567	+	92.2433i	2.30034	+	3.98430i
$537$	5.63383	−	9.75809i	0.243118	−	0.421093i
$538$	−42.5656			−1.83513
$539$	−8.71960	+	15.1028i	−0.375580	+	0.650524i
$540$	31.7058	−	54.9161i	1.36440	−	2.36321i
$541$	31.6645			1.36136			0.680681	−	0.732580i	$-0.261684\pi$
$541$	31.6645			1.36136			0.680681	+	0.732580i	$0.261684\pi$
$542$	30.6661	−	53.1153i	1.31722	−	2.28150i
$543$	3.17765	+	5.50386i	0.136366	+	0.236193i
$544$	54.6685	+	94.6886i	2.34389	+	4.05974i
$545$	48.2242			2.06570
$546$	−1.23290	+	6.36683i	−0.0527634	+	0.272475i
$547$	−2.55247			−0.109136			−0.0545680	−	0.998510i	$-0.517378\pi$
$547$	−2.55247			−0.109136			−0.0545680	+	0.998510i	$0.517378\pi$
$548$	−65.3624	−	113.211i	−2.79214	−	4.83613i
$549$	−5.75072	−	9.96055i	−0.245435	−	0.425106i
$550$	−4.42555	+	7.66528i	−0.188706	+	0.326849i
$551$	−0.477218			−0.0203302
$552$	32.1632	−	55.7083i	1.36896	−	2.37110i
$553$	3.27314	−	5.66925i	0.139188	−	0.241081i
$554$	28.9707			1.23085
$555$	−7.76608	+	13.4512i	−0.329652	+	0.570973i
$556$	8.38658	+	14.5260i	0.355670	+	0.616039i
$557$	−3.29883	−	5.71374i	−0.139776	−	0.242099i	0.787636	−	0.616141i	$-0.211305\pi$
$557$	−3.29883	−	5.71374i	−0.139776	−	0.242099i	−0.927412	+	0.374042i	$0.877972\pi$
$558$	−6.64883			−0.281468
$559$	−12.3786	+	4.27212i	−0.523560	+	0.180691i
$560$	38.5658			1.62970
$561$	−3.65415	−	6.32918i	−0.154279	−	0.267218i
$562$	−8.24479	−	14.2804i	−0.347786	−	0.602382i
$563$	−11.8813	+	20.5791i	−0.500738	+	0.867304i	0.499261	+	0.866451i	$0.333605\pi$
$563$	−11.8813	+	20.5791i	−0.500738	+	0.867304i	−1.00000		0.000852604i	$0.999729\pi$
$564$	−11.1862			−0.471023
$565$	17.0103	−	29.4626i	0.715627	−	1.23950i
$566$	32.1445	−	55.6759i	1.35113	−	2.34023i
$567$	−2.88621			−0.121209
$568$	58.3745	−	101.108i	2.44934	−	4.24238i
$569$	−2.78463	−	4.82312i	−0.116738	−	0.202196i	0.801735	−	0.597679i	$-0.203910\pi$
$569$	−2.78463	−	4.82312i	−0.116738	−	0.202196i	−0.918473	+	0.395484i	$0.870577\pi$
$570$	1.96407	+	3.40187i	0.0822659	+	0.142489i
$571$	−6.26087			−0.262009			−0.131005	−	0.991382i	$-0.541820\pi$
$571$	−6.26087			−0.262009			−0.131005	+	0.991382i	$0.541820\pi$
$572$	−44.4134	−	38.5527i	−1.85702	−	1.61197i
$573$	2.50475			0.104638
$574$	2.64948	+	4.58904i	0.110587	+	0.191543i
$575$	4.11993	+	7.13594i	0.171813	+	0.297589i
$576$	63.1040	−	109.299i	2.62933	−	4.55414i
$577$	−16.8915			−0.703201			−0.351600	−	0.936150i	$-0.614362\pi$
$577$	−16.8915			−0.703201			−0.351600	+	0.936150i	$0.614362\pi$
$578$	−8.35158	+	14.4654i	−0.347380	+	0.601679i
$579$	−1.65987	+	2.87499i	−0.0689820	+	0.119480i
$580$	10.0549			0.417507
$581$	5.52202	−	9.56442i	0.229092	−	0.396799i
$582$	12.1939	+	21.1205i	0.505454	+	0.875471i
$583$	4.48895	+	7.77510i	0.185913	+	0.322012i
$584$	−135.051			−5.58845
$585$	−19.9174	+	6.87391i	−0.823483	+	0.284201i
$586$	−57.4901			−2.37489
$587$	−5.37245	−	9.30535i	−0.221745	−	0.384073i	0.733593	−	0.679589i	$-0.237842\pi$
$587$	−5.37245	−	9.30535i	−0.221745	−	0.384073i	−0.955338	+	0.295516i	$0.904508\pi$
$588$	−15.2007	−	26.3284i	−0.626867	−	1.08576i
$589$	0.350365	−	0.606849i	0.0144365	−	0.0250048i
$590$	−75.6934			−3.11625
$591$	2.76850	−	4.79518i	0.113881	−	0.197247i
$592$	−76.4221	+	132.367i	−3.14093	+	5.44025i
$593$	46.5732			1.91253			0.956266	−	0.292498i	$-0.0944865\pi$
$593$	46.5732			1.91253			0.956266	+	0.292498i	$0.0944865\pi$
$594$	−16.5895	+	28.7339i	−0.680677	+	1.17897i
$595$	−3.28160	−	5.68389i	−0.134532	−	0.233017i
$596$	10.2410	+	17.7380i	0.419489	+	0.726576i
$597$	−0.0809246			−0.00331202
$598$	−69.1355	+	23.8601i	−2.82716	+	0.975712i
$599$	3.98935			0.163000			0.0815002	−	0.996673i	$-0.474029\pi$
$599$	3.98935			0.163000			0.0815002	+	0.996673i	$0.474029\pi$
$600$	−5.12413	−	8.87526i	−0.209192	−	0.362331i
$601$	10.9578	+	18.9794i	0.446977	+	0.774186i	0.998188	−	0.0601797i	$-0.0191674\pi$
$601$	10.9578	+	18.9794i	0.446977	+	0.774186i	−0.551211	+	0.834366i	$0.685834\pi$
$602$	−4.07416	+	7.05665i	−0.166050	+	0.287608i
$603$	−22.5044			−0.916451
$604$	33.9541	−	58.8103i	1.38157	−	2.39296i
$605$	−4.33664	+	7.51128i	−0.176309	+	0.305377i
$606$	19.2860			0.783438
$607$	22.7760	−	39.4493i	0.924451	−	1.60120i	0.132009	−	0.991249i	$-0.457857\pi$
$607$	22.7760	−	39.4493i	0.924451	−	1.60120i	0.792442	−	0.609947i	$-0.208809\pi$
$608$	11.5095	+	19.9350i	0.466770	+	0.808470i
$609$	0.217143	+	0.376103i	0.00879908	+	0.0152404i
$610$	−34.1166			−1.38134
$611$	6.37915	+	5.53737i	0.258073	+	0.224018i
$612$	−46.7268			−1.88882
$613$	0.342845	+	0.593825i	0.0138474	+	0.0239844i	0.872866	−	0.487960i	$-0.162259\pi$
$613$	0.342845	+	0.593825i	0.0138474	+	0.0239844i	−0.859019	+	0.511944i	$0.828925\pi$
$614$	11.6831	+	20.2358i	0.471493	+	0.816651i
$615$	2.34710	−	4.06529i	0.0946442	−	0.163928i
$616$	−24.3059			−0.979314
$617$	10.6153	−	18.3862i	0.427354	−	0.740199i	−0.569283	−	0.822142i	$-0.692779\pi$
$617$	10.6153	−	18.3862i	0.427354	−	0.740199i	0.996637	+	0.0819429i	$0.0261125\pi$
$618$	−0.717282	+	1.24237i	−0.0288533	+	0.0499754i
$619$	−39.4648			−1.58622			−0.793112	−	0.609076i	$-0.791540\pi$
$619$	−39.4648			−1.58622			−0.793112	+	0.609076i	$0.791540\pi$
$620$	−7.38213	+	12.7862i	−0.296473	+	0.513507i
$621$	15.4439	+	26.7496i	0.619743	+	1.07343i
$622$	4.70151	+	8.14325i	0.188513	+	0.326515i
$623$	−0.534321			−0.0214071
$624$	53.4402	−	18.4433i	2.13932	−	0.738324i
$625$	−29.4160			−1.17664
$626$	−10.5999	−	18.3596i	−0.423658	−	0.733798i
$627$	−0.769316	−	1.33249i	−0.0307235	−	0.0532147i
$628$	32.2982	−	55.9420i	1.28884	−	2.23233i
$629$	26.0113			1.03714
$630$	−6.55539	+	11.3543i	−0.261173	+	0.452365i
$631$	−13.9614	+	24.1819i	−0.555795	+	0.962665i	0.442047	+	0.896992i	$0.354253\pi$
$631$	−13.9614	+	24.1819i	−0.555795	+	0.962665i	−0.997841	+	0.0656725i	$0.979081\pi$
$632$	−91.8217			−3.65247
$633$	5.53969	−	9.59503i	0.220183	−	0.381368i
$634$	−29.3001	−	50.7492i	−1.16366	−	2.01551i
$635$	−2.25455	−	3.90499i	−0.0894689	−	0.154965i
$636$	−15.6510			−0.620602
$637$	−4.36455	+	22.5390i	−0.172930	+	0.893026i
$638$	−5.26106			−0.208287
$639$	12.3335	+	21.3623i	0.487906	+	0.845078i
$640$	−105.748	−	183.161i	−4.18005	−	7.24006i
$641$	2.93692	−	5.08689i	0.116001	−	0.200920i	−0.802178	−	0.597085i	$-0.796326\pi$
$641$	2.93692	−	5.08689i	0.116001	−	0.200920i	0.918180	+	0.396165i	$0.129659\pi$
$642$	−31.9349			−1.26037
$643$	17.4930	−	30.2988i	0.689858	−	1.19487i	−0.282026	−	0.959407i	$-0.591006\pi$
$643$	17.4930	−	30.2988i	0.689858	−	1.19487i	0.971884	−	0.235462i	$-0.0756602\pi$
$644$	−17.0341	+	29.5039i	−0.671237	+	1.16262i
$645$	7.21835			0.284222
$646$	3.28919	−	5.69704i	0.129411	−	0.224147i
$647$	−1.81190	−	3.13830i	−0.0712332	−	0.123379i	0.828209	−	0.560420i	$-0.189360\pi$
$647$	−1.81190	−	3.13830i	−0.0712332	−	0.123379i	−0.899442	+	0.437040i	$0.856027\pi$
$648$	20.2417	+	35.0597i	0.795171	+	1.37728i
$649$	29.6487			1.16381
$650$	−2.21519	+	11.4394i	−0.0868868	+	0.448691i
$651$	−0.637690			−0.0249930
$652$	33.8563	+	58.6408i	1.32591	+	2.29655i
$653$	5.20884	+	9.02198i	0.203838	+	0.353057i	0.949762	−	0.312974i	$-0.101325\pi$
$653$	5.20884	+	9.02198i	0.203838	+	0.353057i	−0.745924	+	0.666031i	$0.767992\pi$
$654$	21.9936	−	38.0941i	0.860020	−	1.48960i
$655$	−15.3855			−0.601162
$656$	23.0966	−	40.0046i	0.901772	−	1.56192i
$657$	14.2670	−	24.7111i	0.556607	−	0.964072i
$658$	5.25624			0.204909
$659$	−3.18034	+	5.50851i	−0.123888	+	0.214581i	−0.921298	−	0.388858i	$-0.872870\pi$
$659$	−3.18034	+	5.50851i	−0.123888	+	0.214581i	0.797409	+	0.603439i	$0.206203\pi$
$660$	16.2094	+	28.0755i	0.630949	+	1.09284i
$661$	3.75790	+	6.50888i	0.146165	+	0.253166i	0.929807	−	0.368047i	$-0.119973\pi$
$661$	3.75790	+	6.50888i	0.146165	+	0.253166i	−0.783642	+	0.621213i	$0.786640\pi$
$662$	−4.18138			−0.162514
$663$	−7.26549	−	6.30676i	−0.282168	−	0.244934i
$664$	−154.910			−6.01166
$665$	−0.690881	−	1.19664i	−0.0267912	−	0.0464037i
$666$	−25.9804	−	44.9994i	−1.00672	−	1.74369i
$667$	−2.44887	+	4.24157i	−0.0948207	+	0.164234i
$668$	129.928			5.02705
$669$	9.80897	−	16.9896i	0.379237	−	0.656857i
$670$	−33.3773	+	57.8112i	−1.28948	+	2.23344i
$671$	13.3633			0.515885
$672$	10.4740	−	18.1416i	0.404045	−	0.699826i
$673$	−18.2772	−	31.6571i	−0.704535	−	1.22029i	−0.966859	−	0.255311i	$-0.917822\pi$
$673$	−18.2772	−	31.6571i	−0.704535	−	1.22029i	0.262324	−	0.964980i	$-0.415511\pi$
$674$	46.4124	+	80.3886i	1.78774	+	3.09645i
$675$	4.92094			0.189407
$676$	−71.8259	−	28.9012i	−2.76254	−	1.11158i
$677$	3.82456			0.146990			0.0734949	−	0.997296i	$-0.476585\pi$
$677$	3.82456			0.146990			0.0734949	+	0.997296i	$0.476585\pi$
$678$	−15.5158	−	26.8741i	−0.595879	−	1.03209i
$679$	−4.28932	−	7.42932i	−0.164609	−	0.285111i
$680$	−46.0294	+	79.7253i	−1.76515	+	3.05733i
$681$	12.2245			0.468445
$682$	3.86257	−	6.69017i	0.147906	−	0.256180i
$683$	7.50400	−	12.9973i	0.287132	−	0.497328i	−0.685992	−	0.727609i	$-0.740631\pi$
$683$	7.50400	−	12.9973i	0.287132	−	0.497328i	0.973124	+	0.230281i	$0.0739647\pi$
$684$	−9.83748			−0.376145
$685$	27.2077	−	47.1251i	1.03955	−	1.80056i
$686$	14.9950	+	25.9720i	0.572510	+	0.991617i
$687$	0.296227	+	0.513080i	0.0113018	+	0.0195752i
$688$	71.0323			2.70808
$689$	8.92531	+	7.74755i	0.340027	+	0.295158i
$690$	40.3150			1.53477
$691$	−0.833704	−	1.44402i	−0.0317156	−	0.0549330i	0.849732	−	0.527215i	$-0.176764\pi$
$691$	−0.833704	−	1.44402i	−0.0317156	−	0.0549330i	−0.881448	+	0.472282i	$0.843430\pi$
$692$	22.5825	+	39.1140i	0.858457	+	1.48689i
$693$	2.56771	−	4.44740i	0.0975392	−	0.168943i
$694$	9.80879			0.372337
$695$	−3.49099	+	6.04657i	−0.132421	+	0.229359i
$696$	3.04576	−	5.27542i	0.115449	−	0.199964i
$697$	−7.86126			−0.297766
$698$	−10.9978	+	19.0487i	−0.416272	+	0.721003i
$699$	0.856711	+	1.48387i	0.0324038	+	0.0561250i
$700$	2.71381	+	4.70046i	0.102573	+	0.177661i
$701$	−3.43921			−0.129897			−0.0649486	−	0.997889i	$-0.520688\pi$
$701$	−3.43921			−0.129897			−0.0649486	+	0.997889i	$0.520688\pi$
$702$	−8.30381	+	42.8816i	−0.313407	+	1.61846i
$703$	5.47621			0.206539
$704$	73.3193	+	126.993i	2.76333	+	4.78622i
$705$	−2.32817	−	4.03251i	−0.0876840	−	0.151873i
$706$	−48.9818	+	84.8389i	−1.84345	+	3.19295i
$707$	−6.78402			−0.255139
$708$	−25.8430	+	44.7613i	−0.971238	+	1.68223i
$709$	−9.42390	+	16.3227i	−0.353922	+	0.613011i	−0.986933	−	0.161132i	$-0.948486\pi$
$709$	−9.42390	+	16.3227i	−0.353922	+	0.613011i	0.633011	+	0.774143i	$0.281819\pi$
$710$	73.1696			2.74601
$711$	9.70017	−	16.8012i	0.363785	−	0.630094i
$712$	3.74733	+	6.49057i	0.140437	+	0.243244i
$713$	−3.59583	−	6.22817i	−0.134665	−	0.233247i
$714$	−5.98656			−0.224041
$715$	4.65417	−	24.0346i	0.174056	−	0.898842i
$716$	83.7036			3.12815
$717$	−4.20366	−	7.28095i	−0.156989	−	0.271912i
$718$	−9.40783	−	16.2948i	−0.351097	−	0.608118i
$719$	15.0093	−	25.9969i	0.559754	−	0.969522i	−0.437763	−	0.899091i	$-0.644229\pi$
$719$	15.0093	−	25.9969i	0.559754	−	0.969522i	0.997517	−	0.0704318i	$-0.0224377\pi$
$720$	114.292			4.25941
$721$	0.252311	−	0.437015i	0.00939654	−	0.0162753i
$722$	−26.1029	+	45.2115i	−0.971448	+	1.68260i
$723$	1.39885			0.0520237
$724$	−23.6057	+	40.8862i	−0.877298	+	1.51953i
$725$	0.390146	+	0.675752i	0.0144897	+	0.0250968i
$726$	3.95563	+	6.85135i	0.146807	+	0.254277i
$727$	−31.3969			−1.16445			−0.582224	−	0.813028i	$-0.697817\pi$
$727$	−31.3969			−1.16445			−0.582224	+	0.813028i	$0.697817\pi$
$728$	−30.2466	+	10.4387i	−1.12101	+	0.386885i
$729$	1.77636			0.0657912
$730$	−42.3200	−	73.3004i	−1.56633	−	2.71297i
$731$	−6.04420	−	10.4689i	−0.223553	−	0.387205i
$732$	−11.6480	+	20.1749i	−0.430522	+	0.745686i
$733$	−18.9999			−0.701779			−0.350889	−	0.936417i	$-0.614121\pi$
$733$	−18.9999			−0.701779			−0.350889	+	0.936417i	$0.614121\pi$
$734$	−10.6907	+	18.5168i	−0.394601	+	0.683469i
$735$	6.32743	−	10.9594i	0.233391	−	0.404245i
$736$	236.246			8.70814
$737$	13.0737	−	22.6443i	0.481577	−	0.834115i
$738$	7.85191	+	13.5999i	0.289033	+	0.500620i
$739$	1.34202	+	2.32445i	0.0493670	+	0.0855062i	0.889653	−	0.456637i	$-0.150946\pi$
$739$	1.34202	+	2.32445i	0.0493670	+	0.0855062i	−0.840286	+	0.542143i	$0.817613\pi$
$740$	−115.383			−4.24156
$741$	−1.52962	−	1.32777i	−0.0561919	−	0.0487770i
$742$	7.35420			0.269981
$743$	15.3223	+	26.5390i	0.562121	+	0.973622i	0.997311	+	0.0732835i	$0.0233478\pi$
$743$	15.3223	+	26.5390i	0.562121	+	0.973622i	−0.435190	+	0.900339i	$0.643319\pi$
$744$	4.47229	+	7.74623i	0.163962	+	0.283991i
$745$	−4.26292	+	7.38360i	−0.156181	+	0.270514i
$746$	−44.5695			−1.63181
$747$	16.3648	−	28.3447i	0.598758	−	1.03708i
$748$	27.1454	−	47.0173i	0.992536	−	1.71912i
$749$	11.2334			0.410460
$750$	−10.8031	+	18.7115i	−0.394472	+	0.683246i
$751$	8.55725	+	14.8216i	0.312259	+	0.540848i	0.978851	−	0.204575i	$-0.0655811\pi$
$751$	8.55725	+	14.8216i	0.312259	+	0.540848i	−0.666592	+	0.745422i	$0.732248\pi$
$752$	−22.9104	−	39.6820i	−0.835456	−	1.44705i
$753$	12.1666			0.443377
$754$	−6.54693	+	2.25948i	−0.238425	+	0.0822855i
$755$	28.2674			1.02876
$756$	10.1730	+	17.6201i	0.369987	+	0.640836i
$757$	−23.8404	−	41.2928i	−0.866494	−	1.50081i	−0.865556	−	0.500812i	$-0.833035\pi$
$757$	−23.8404	−	41.2928i	−0.866494	−	1.50081i	−0.000937977	−	1.00000i	$-0.500299\pi$
$758$	25.1885	−	43.6278i	0.914888	−	1.58463i
$759$	−15.7912			−0.573183
$760$	−9.69066	+	16.7847i	−0.351517	+	0.608846i
$761$	12.5669	−	21.7666i	0.455551	−	0.789038i	−0.543169	−	0.839624i	$-0.682776\pi$
$761$	12.5669	−	21.7666i	0.455551	−	0.789038i	0.998720	+	0.0505859i	$0.0161089\pi$
$762$	−4.11293			−0.148996
$763$	−7.73647	+	13.4000i	−0.280079	+	0.485111i
$764$	9.30347	+	16.1141i	0.336588	+	0.582987i
$765$	−9.72522	−	16.8446i	−0.351616	−	0.609017i
$766$	27.8121			1.00489
$767$	36.8952	−	12.7333i	1.33221	−	0.459773i
$768$	−107.068			−3.86347
$769$	12.3803	+	21.4433i	0.446446	+	0.773267i	0.998152	−	0.0607719i	$-0.0193562\pi$
$769$	12.3803	+	21.4433i	0.446446	+	0.773267i	−0.551706	+	0.834039i	$0.686023\pi$
$770$	−7.61658	−	13.1923i	−0.274482	−	0.475417i
$771$	−6.60970	+	11.4483i	−0.238043	+	0.412302i
$772$	−24.6613			−0.887578
$773$	−8.83144	+	15.2965i	−0.317645	+	0.550177i	−0.979996	−	0.199016i	$-0.936225\pi$
$773$	−8.83144	+	15.2965i	−0.317645	+	0.550177i	0.662351	+	0.749193i	$0.269559\pi$
$774$	−12.0740	+	20.9128i	−0.433992	+	0.751696i
$775$	−1.14575			−0.0411566
$776$	−60.1643	+	104.208i	−2.15977	+	3.74084i
$777$	−2.49178	−	4.31589i	−0.0893921	−	0.154832i
$778$	−22.1369	−	38.3422i	−0.793645	−	1.37463i
$779$	−1.65505			−0.0592982
$780$	32.2288	+	27.9760i	1.15398	+	1.00170i
$781$	−28.6601			−1.02554
$782$	−33.7573	−	58.4694i	−1.20716	−	2.09086i
$783$	1.46249	+	2.53311i	0.0522652	+	0.0905261i
$784$	62.2651	−	107.846i	2.22375	−	3.85166i
$785$	26.8888			0.959702
$786$	−7.01688	+	12.1536i	−0.250284	+	0.433504i
$787$	11.0961	−	19.2190i	0.395534	−	0.685085i	−0.597635	−	0.801768i	$-0.703893\pi$
$787$	11.0961	−	19.2190i	0.395534	−	0.685085i	0.993169	+	0.116683i	$0.0372263\pi$
$788$	41.1324			1.46528
$789$	1.85190	−	3.20759i	0.0659295	−	0.114193i
$790$	−28.7735	−	49.8372i	−1.02372	−	1.77313i
$791$	5.45782	+	9.45322i	0.194058	+	0.336118i
$792$	−72.0321			−2.55955
$793$	16.6295	−	5.73918i	0.590530	−	0.203804i
$794$	61.2720			2.17446
$795$	−3.25743	−	5.64204i	−0.115529	−	0.200103i
$796$	−0.300580	−	0.520620i	−0.0106538	−	0.0184529i
$797$	24.6742	−	42.7370i	0.874005	−	1.51382i	0.0161854	−	0.999869i	$-0.494848\pi$
$797$	24.6742	−	42.7370i	0.874005	−	1.51382i	0.857819	−	0.513952i	$-0.171819\pi$
$798$	−1.26036			−0.0446164
$799$	−3.89893	+	6.75315i	−0.137934	+	0.238909i
$800$	18.8190	−	32.5954i	0.665351	−	1.15242i
$801$	−1.58349			−0.0559500
$802$	11.7421	−	20.3379i	0.414627	−	0.718155i
$803$	16.5765	+	28.7113i	0.584972	+	1.01320i
$804$	22.7911	+	39.4754i	0.803782	+	1.39219i
$805$	−14.1812			−0.499821
$806$	1.93339	−	9.98421i	0.0681008	−	0.351679i
$807$	−12.0986			−0.425892
$808$	47.5781	+	82.4077i	1.67379	+	2.89909i
$809$	−18.0826	−	31.3199i	−0.635749	−	1.10115i	−0.986356	−	0.164626i	$-0.947358\pi$
$809$	−18.0826	−	31.3199i	−0.635749	−	1.10115i	0.350607	−	0.936523i	$-0.385975\pi$
$810$	−12.6860	+	21.9728i	−0.445741	+	0.772047i
$811$	−14.1704			−0.497592			−0.248796	−	0.968556i	$-0.580035\pi$
$811$	−14.1704			−0.497592			−0.248796	+	0.968556i	$0.580035\pi$
$812$	−1.61308	+	2.79394i	−0.0566080	+	0.0980479i
$813$	8.71639	−	15.0972i	0.305697	−	0.529483i
$814$	60.3722			2.11604
$815$	−14.0930	+	24.4098i	−0.493656	+	0.855037i
$816$	26.0937	+	45.1955i	0.913461	+	1.58216i
$817$	−1.27250	−	2.20403i	−0.0445191	−	0.0771093i
$818$	−19.0532			−0.666178
$819$	1.28525	−	6.63717i	0.0449104	−	0.231922i
$820$	34.8716			1.21777
$821$	13.5636	+	23.4928i	0.473372	+	0.819904i	0.999535	−	0.0304797i	$-0.00970348\pi$
$821$	13.5636	+	23.4928i	0.473372	+	0.819904i	−0.526164	+	0.850383i	$0.676370\pi$
$822$	−24.8173	−	42.9847i	−0.865601	−	1.49927i
$823$	6.42072	−	11.1210i	0.223812	−	0.387654i	−0.732150	−	0.681143i	$-0.761483\pi$
$823$	6.42072	−	11.1210i	0.223812	−	0.387654i	0.955962	+	0.293489i	$0.0948165\pi$
$824$	−7.07809			−0.246577
$825$	−1.25790	+	2.17874i	−0.0437944	+	0.0758541i
$826$	12.1433	−	21.0328i	0.422519	−	0.731824i
$827$	26.1988			0.911021			0.455511	−	0.890230i	$-0.349457\pi$
$827$	26.1988			0.911021			0.455511	+	0.890230i	$0.349457\pi$
$828$	−50.4816	+	87.4367i	−1.75436	+	3.03863i
$829$	−4.95242	−	8.57784i	−0.172005	−	0.297921i	0.767116	−	0.641508i	$-0.221691\pi$
$829$	−4.95242	−	8.57784i	−0.172005	−	0.297921i	−0.939121	+	0.343588i	$0.888358\pi$
$830$	−48.5429	−	84.0788i	−1.68495	−	2.91842i
$831$	8.23450			0.285652
$832$	145.779	+	126.543i	5.05399	+	4.38709i
$833$	−21.1928			−0.734287
$834$	3.18427	+	5.51533i	0.110262	+	0.190980i
$835$	27.0417	+	46.8377i	0.935818	+	1.62088i
$836$	5.71498	−	9.89864i	0.197657	−	0.342352i
$837$	−4.29494			−0.148455
$838$	−36.3028	+	62.8782i	−1.25406	+	2.17209i
$839$	−12.8328	+	22.2270i	−0.443037	+	0.767362i	−0.997913	−	0.0645708i	$-0.979432\pi$
$839$	−12.8328	+	22.2270i	−0.443037	+	0.767362i	0.554876	+	0.831933i	$0.312766\pi$
$840$	17.6377			0.608560
$841$	14.2681	−	24.7131i	0.492003	−	0.852175i
$842$	−48.8517	−	84.6137i	−1.68354	−	2.91598i
$843$	−2.34346	−	4.05899i	−0.0807131	−	0.139799i
$844$	82.3049			2.83305
$845$	−4.53048	−	31.9078i	−0.155853	−	1.09766i
$846$	15.5772			0.535555
$847$	−1.39143	−	2.41003i	−0.0478101	−	0.0828095i
$848$	−32.0548	−	55.5206i	−1.10077	−	1.90658i
$849$	9.13659	−	15.8250i	0.313567	−	0.543114i
$850$	−10.7562			−0.368935
$851$	28.1015	−	48.6733i	0.963308	−	1.66850i
$852$	24.9813	−	43.2689i	0.855845	−	1.48237i
$853$	−26.5737			−0.909867			−0.454933	−	0.890526i	$-0.650337\pi$
$853$	−26.5737			−0.909867			−0.454933	+	0.890526i	$0.650337\pi$
$854$	5.47324	−	9.47993i	0.187290	−	0.324396i
$855$	−2.04747	−	3.54632i	−0.0700220	−	0.121282i
$856$	−78.7829	−	136.456i	−2.69274	−	4.66397i
$857$	−23.5008			−0.802773			−0.401386	−	0.915909i	$-0.631472\pi$
$857$	−23.5008			−0.802773			−0.401386	+	0.915909i	$0.631472\pi$
$858$	−16.8632	−	14.6380i	−0.575700	−	0.499732i
$859$	42.2091			1.44016			0.720078	−	0.693893i	$-0.244106\pi$
$859$	42.2091			1.44016			0.720078	+	0.693893i	$0.244106\pi$
$860$	26.8113	+	46.4386i	0.914258	+	1.58354i
$861$	0.753077	+	1.30437i	0.0256648	+	0.0444527i
$862$	−25.1812	+	43.6152i	−0.857676	+	1.48554i
$863$	−26.8136			−0.912745			−0.456373	−	0.889789i	$-0.650852\pi$
$863$	−26.8136			−0.912745			−0.456373	+	0.889789i	$0.650852\pi$
$864$	70.5444	−	122.186i	2.39997	−	4.15687i
$865$	−9.40016	+	16.2816i	−0.319615	+	0.553590i
$866$	−78.4223			−2.66490
$867$	−2.37381	+	4.11156i	−0.0806189	+	0.139636i
$868$	−2.36859	−	4.10251i	−0.0803951	−	0.139248i
$869$	11.2704	+	19.5210i	0.382323	+	0.662203i
$870$	3.81772			0.129433
$871$	6.54398	−	33.7937i	0.221734	−	1.14506i
$872$	217.032			7.34962
$873$	−12.7117	−	22.0173i	−0.430225	−	0.745171i
$874$	−7.10699	−	12.3097i	−0.240398	−	0.416381i
$875$	3.80008	−	6.58193i	0.128466	−	0.222510i
$876$	−57.7950			−1.95271
$877$	5.88368	−	10.1908i	0.198678	−	0.344120i	−0.749422	−	0.662092i	$-0.769669\pi$
$877$	5.88368	−	10.1908i	0.198678	−	0.344120i	0.948100	+	0.317973i	$0.103002\pi$
$878$	−30.9236	+	53.5612i	−1.04362	+	1.80760i
$879$	−16.3407			−0.551158
$880$	−66.3968	+	115.003i	−2.23824	+	3.87674i
$881$	−21.1114	−	36.5660i	−0.711261	−	1.23194i	−0.964384	−	0.264506i	$-0.914791\pi$
$881$	−21.1114	−	36.5660i	−0.711261	−	1.23194i	0.253123	−	0.967434i	$-0.418542\pi$
$882$	21.1676	+	36.6633i	0.712750	+	1.23452i
$883$	48.0611			1.61738			0.808692	−	0.588232i	$-0.200176\pi$
$883$	48.0611			1.61738			0.808692	+	0.588232i	$0.200176\pi$
$884$	13.5875	−	70.1672i	0.456998	−	2.35998i
$885$	−21.5147			−0.723210
$886$	40.7654	+	70.6077i	1.36954	+	2.37211i
$887$	17.1921	+	29.7775i	0.577253	+	0.999832i	0.995793	+	0.0916336i	$0.0292088\pi$
$887$	17.1921	+	29.7775i	0.577253	+	0.999832i	−0.418539	+	0.908199i	$0.637458\pi$
$888$	−34.9510	+	60.5370i	−1.17288	+	2.03149i
$889$	1.44676			0.0485228
$890$	−2.34855	+	4.06781i	−0.0787236	+	0.136353i
$891$	4.96904	−	8.60664i	0.166469	−	0.288333i
$892$	145.735			4.87956
$893$	−0.820850	+	1.42175i	−0.0274687	+	0.0475772i
$894$	3.88839	+	6.73489i	0.130047	+	0.225248i
$895$	17.4212	+	30.1744i	0.582326	+	1.00862i
$896$	67.8593			2.26702
$897$	−19.6508	+	6.78188i	−0.656119	+	0.226440i
$898$	39.6668			1.32370
$899$	−0.340515	−	0.589789i	−0.0113568	−	0.0196706i
$900$	8.04256	+	13.9301i	0.268085	+	0.464337i
$901$	−5.45515	+	9.44859i	−0.181737	+	0.314778i
$902$	−18.2460			−0.607524
$903$	−1.15802	+	2.00575i	−0.0385365	+	0.0667472i
$904$	76.5542	−	132.596i	2.54616	−	4.41007i
$905$	−19.6522			−0.653260
$906$	12.8919	−	22.3295i	0.428306	−	0.741848i
$907$	−11.4342	−	19.8045i	−0.379665	−	0.657599i	0.611349	−	0.791361i	$-0.290627\pi$
$907$	−11.4342	−	19.8045i	−0.379665	−	0.657599i	−0.991013	+	0.133763i	$0.957294\pi$
$908$	45.4059	+	78.6453i	1.50685	+	2.60994i
$909$	−20.1049			−0.666836
$910$	−15.1439	−	13.1456i	−0.502016	−	0.435771i
$911$	−3.50913			−0.116263			−0.0581313	−	0.998309i	$-0.518514\pi$
$911$	−3.50913			−0.116263			−0.0581313	+	0.998309i	$0.518514\pi$
$912$	5.49355	+	9.51511i	0.181910	+	0.315077i
$913$	19.0140	+	32.9332i	0.629271	+	1.08993i
$914$	−6.37531	+	11.0424i	−0.210877	+	0.365249i
$915$	−9.69716			−0.320578
$916$	−2.20056	+	3.81149i	−0.0727087	+	0.125935i
$917$	2.46825	−	4.27514i	0.0815089	−	0.141178i
$918$	−40.3205			−1.33077
$919$	13.4318	−	23.2646i	0.443076	−	0.767430i	−0.554840	−	0.831957i	$-0.687221\pi$
$919$	13.4318	−	23.2646i	0.443076	−	0.767430i	0.997916	+	0.0645272i	$0.0205539\pi$
$920$	99.4564	+	172.264i	3.27898	+	5.67936i
$921$	3.32076	+	5.75173i	0.109423	+	0.189526i
$922$	−58.2113			−1.91709
$923$	−35.6651	+	12.3087i	−1.17393	+	0.405147i
$924$	−10.4017			−0.342191
$925$	−4.47704	−	7.75446i	−0.147204	−	0.254965i
$926$	29.1550	+	50.4979i	0.958092	+	1.65946i
$927$	0.747738	−	1.29512i	0.0245590	−	0.0425373i
$928$	22.3718			0.734391
$929$	−21.4165	+	37.0944i	−0.702652	+	1.21703i	0.264881	+	0.964281i	$0.414667\pi$
$929$	−21.4165	+	37.0944i	−0.702652	+	1.21703i	−0.967532	+	0.252747i	$0.918666\pi$
$930$	−2.80290	+	4.85476i	−0.0919106	+	0.159194i
$931$	−4.46176			−0.146228
$932$	−6.36421	+	11.0231i	−0.208467	+	0.361075i
$933$	1.33633	+	2.31460i	0.0437496	+	0.0757766i
$934$	−18.8399	−	32.6317i	−0.616460	−	1.06774i
$935$	22.5991			0.739069
$936$	−89.6378	+	30.9358i	−2.92990	+	1.01117i
$937$	−26.8951			−0.878625			−0.439313	−	0.898334i	$-0.644778\pi$
$937$	−26.8951			−0.878625			−0.439313	+	0.898334i	$0.644778\pi$
$938$	−10.7093	−	18.5490i	−0.349670	−	0.605646i
$939$	−3.01287	−	5.21845i	−0.0983214	−	0.170298i
$940$	17.2952	−	29.9561i	0.564106	−	0.977061i
$941$	11.6702			0.380437			0.190218	−	0.981742i	$-0.439080\pi$
$941$	11.6702			0.380437			0.190218	+	0.981742i	$0.439080\pi$
$942$	12.2632	−	21.2405i	0.399556	−	0.692052i
$943$	−8.49297	+	14.7103i	−0.276569	+	0.479032i
$944$	−211.716			−6.89076
$945$	−4.23458	+	7.33451i	−0.137751	+	0.238592i
$946$	−14.0286	−	24.2982i	−0.456108	−	0.790003i
$947$	−26.5221	−	45.9376i	−0.861852	−	1.49277i	−0.870139	−	0.492806i	$-0.835971\pi$
$947$	−26.5221	−	45.9376i	−0.861852	−	1.49277i	0.00828708	−	0.999966i	$-0.497362\pi$
$948$	−39.2950			−1.27624
$949$	32.9588	+	28.6096i	1.06989	+	0.928708i
$950$	−2.26452			−0.0734708
$951$	−8.32812	−	14.4247i	−0.270058	−	0.467754i
$952$	−14.7687	−	25.5802i	−0.478658	−	0.829060i
$953$	13.2972	−	23.0314i	0.430739	−	0.746062i	−0.566198	−	0.824269i	$-0.691586\pi$
$953$	13.2972	−	23.0314i	0.430739	−	0.746062i	0.996937	+	0.0782074i	$0.0249196\pi$
$954$	21.7946			0.705627
$955$	−3.87265	+	6.70763i	−0.125316	+	0.217054i
$956$	31.2275	−	54.0877i	1.00997	−	1.74932i
$957$	−1.49538			−0.0483387
$958$	23.8204	−	41.2581i	0.769601	−	1.33299i
$959$	8.72970	+	15.1203i	0.281897	+	0.488260i
$960$	−53.2046	−	92.1530i	−1.71717	−	2.97423i
$961$	1.00000			0.0322581
$962$	75.1280	−	25.9282i	2.42222	−	0.835959i
$963$	33.2909			1.07278
$964$	5.19578	+	8.99935i	0.167345	+	0.289850i
$965$	−5.13273	−	8.89016i	−0.165229	−	0.286184i
$966$	−6.46763	+	11.2023i	−0.208092	+	0.360427i
$967$	18.9521			0.609458			0.304729	−	0.952439i	$-0.401434\pi$
$967$	18.9521			0.609458			0.304729	+	0.952439i	$0.401434\pi$
$968$	−19.5169	+	33.8043i	−0.627298	+	1.08651i
$969$	0.934903	−	1.61930i	0.0300334	−	0.0520194i
$970$	−75.4130			−2.42137
$971$	−5.40143	+	9.35554i	−0.173340	+	0.300234i	−0.939586	−	0.342314i	$-0.888789\pi$
$971$	−5.40143	+	9.35554i	−0.173340	+	0.300234i	0.766246	+	0.642548i	$0.222123\pi$
$972$	47.0307	+	81.4596i	1.50851	+	2.61282i
$973$	−1.12010	−	1.94007i	−0.0359087	−	0.0621957i
$974$	2.68729			0.0861064
$975$	−0.629634	+	3.25149i	−0.0201644	+	0.104131i
$976$	−95.4249			−3.05448
$977$	−1.99478	−	3.45507i	−0.0638188	−	0.110537i	0.832351	−	0.554249i	$-0.186995\pi$
$977$	−1.99478	−	3.45507i	−0.0638188	−	0.110537i	−0.896169	+	0.443712i	$0.853661\pi$
$978$	12.8548	+	22.2652i	0.411051	+	0.711961i
$979$	0.919914	−	1.59334i	0.0294006	−	0.0509233i
$980$	94.0086			3.00299
$981$	−22.9275	+	39.7116i	−0.732019	+	1.26789i
$982$	−41.2769	+	71.4936i	−1.31720	+	2.28145i
$983$	9.57600			0.305427			0.152713	−	0.988271i	$-0.451199\pi$
$983$	9.57600			0.305427			0.152713	+	0.988271i	$0.451199\pi$
$984$	10.5631	−	18.2958i	0.336738	−	0.583247i
$985$	8.56087	+	14.8279i	0.272772	+	0.472455i
$986$	−3.19672	−	5.53688i	−0.101804	−	0.176330i
$987$	1.49401			0.0475548
$988$	2.86061	−	14.7724i	0.0910080	−	0.469974i
$989$	−26.1196			−0.830555
$990$	−22.5722	−	39.0962i	−0.717391	−	1.24256i
$991$	−8.39691	−	14.5439i	−0.266737	−	0.462002i	0.701280	−	0.712885i	$-0.252612\pi$
$991$	−8.39691	−	14.5439i	−0.266737	−	0.462002i	−0.968017	+	0.250884i	$0.919279\pi$
$992$	−16.4250	+	28.4489i	−0.521494	+	0.903253i
$993$	−1.18850			−0.0377158
$994$	−11.7384	+	20.3315i	−0.372319	+	0.644876i
$995$	0.125119	−	0.216713i	0.00396655	−	0.00687026i
$996$	−66.2934			−2.10059
$997$	8.52696	−	14.7691i	0.270052	−	0.467743i	−0.698823	−	0.715295i	$-0.746293\pi$
$997$	8.52696	−	14.7691i	0.270052	−	0.467743i	0.968875	+	0.247551i	$0.0796259\pi$
$998$	−0.121948	−	0.211220i	−0.00386020	−	0.00668605i
$999$	−16.7825	−	29.0682i	−0.530976	−	0.919678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.b.94.17	✓	34
13.3	even	3		5239.2.a.m.1.1		17
13.9	even	3	inner	403.2.f.b.373.17	yes	34
13.10	even	6		5239.2.a.n.1.17		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.b.94.17	✓	34	1.1	even	1	trivial
403.2.f.b.373.17	yes	34	13.9	even	3	inner
5239.2.a.m.1.1		17	13.3	even	3
5239.2.a.n.1.17		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)

\(f(q)\)	\(=\)	\(q+(1.41028 + 2.44268i) q^{2} +(0.400852 + 0.694296i) q^{3} +(-2.97779 + 5.15768i) q^{4} -2.47906 q^{5} +(-1.13063 + 1.95831i) q^{6} +(0.397709 - 0.688852i) q^{7} -11.1570 q^{8} +(1.17864 - 2.04146i) q^{9} +O(q^{10})\)	\(q+(1.41028 + 2.44268i) q^{2} +(0.400852 + 0.694296i) q^{3} +(-2.97779 + 5.15768i) q^{4} -2.47906 q^{5} +(-1.13063 + 1.95831i) q^{6} +(0.397709 - 0.688852i) q^{7} -11.1570 q^{8} +(1.17864 - 2.04146i) q^{9} +(-3.49618 - 6.05556i) q^{10} +(1.36943 + 2.37193i) q^{11} -4.77461 q^{12} +(2.72282 + 2.36353i) q^{13} +2.24353 q^{14} +(-0.993737 - 1.72120i) q^{15} +(-9.77888 - 16.9375i) q^{16} +(-1.66419 + 2.88246i) q^{17} +6.64883 q^{18} +(-0.350365 + 0.606849i) q^{19} +(7.38213 - 12.7862i) q^{20} +0.637690 q^{21} +(-3.86257 + 6.69017i) q^{22} +(3.59583 + 6.22817i) q^{23} +(-4.47229 - 7.74623i) q^{24} +1.14575 q^{25} +(-1.93339 + 9.98421i) q^{26} +4.29494 q^{27} +(2.36859 + 4.10251i) q^{28} +(0.340515 + 0.589789i) q^{29} +(2.80290 - 4.85476i) q^{30} -1.00000 q^{31} +(16.4250 - 28.4489i) q^{32} +(-1.09788 + 1.90158i) q^{33} -9.38789 q^{34} +(-0.985946 + 1.70771i) q^{35} +(7.01946 + 12.1581i) q^{36} +(-3.90751 - 6.76801i) q^{37} -1.97645 q^{38} +(-0.549538 + 2.83787i) q^{39} +27.6588 q^{40} +(1.18095 + 2.04546i) q^{41} +(0.899322 + 1.55767i) q^{42} +(-1.81596 + 3.14534i) q^{43} -16.3115 q^{44} +(-2.92191 + 5.06090i) q^{45} +(-10.1423 + 17.5669i) q^{46} +2.34284 q^{47} +(7.83976 - 13.5789i) q^{48} +(3.18365 + 5.51425i) q^{49} +(1.61583 + 2.79871i) q^{50} -2.66837 q^{51} +(-20.2983 + 7.00536i) q^{52} +3.27796 q^{53} +(6.05708 + 10.4912i) q^{54} +(-3.39491 - 5.88016i) q^{55} +(-4.43722 + 7.68550i) q^{56} -0.561777 q^{57} +(-0.960444 + 1.66354i) q^{58} +(5.41258 - 9.37487i) q^{59} +11.8366 q^{60} +(2.43957 - 4.22546i) q^{61} +(-1.41028 - 2.44268i) q^{62} +(-0.937508 - 1.62381i) q^{63} +53.5399 q^{64} +(-6.75004 - 5.85933i) q^{65} -6.19328 q^{66} +(-4.77340 - 8.26778i) q^{67} +(-9.91120 - 17.1667i) q^{68} +(-2.88279 + 4.99314i) q^{69} -5.56185 q^{70} +(-5.23211 + 9.06229i) q^{71} +(-13.1500 + 22.7764i) q^{72} +12.1046 q^{73} +(11.0214 - 19.0896i) q^{74} +(0.459277 + 0.795491i) q^{75} +(-2.08662 - 3.61414i) q^{76} +2.17854 q^{77} +(-7.70700 + 2.65985i) q^{78} +8.23000 q^{79} +(24.2424 + 41.9891i) q^{80} +(-1.81427 - 3.14241i) q^{81} +(-3.33093 + 5.76934i) q^{82} +13.8846 q^{83} +(-1.89891 + 3.28900i) q^{84} +(4.12563 - 7.14579i) q^{85} -10.2441 q^{86} +(-0.272992 + 0.472836i) q^{87} +(-15.2787 - 26.4635i) q^{88} +(-0.335874 - 0.581751i) q^{89} -16.4829 q^{90} +(2.71101 - 0.935626i) q^{91} -42.8305 q^{92} +(-0.400852 - 0.694296i) q^{93} +(3.30407 + 5.72282i) q^{94} +(0.868576 - 1.50442i) q^{95} +26.3359 q^{96} +(5.39254 - 9.34015i) q^{97} +(-8.97970 + 15.5533i) q^{98} +6.45625 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

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