LMFDB - Embedded newform 403.2.f.b.94.1

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			94.1
Character	$\chi$	$=$	403.94
Dual form			403.2.f.b.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36162 - 2.35840i) q^{2} +(1.42643 + 2.47066i) q^{3} +(-2.70804 + 4.69046i) q^{4} -1.48160 q^{5} +(3.88453 - 6.72821i) q^{6} +(1.05061 - 1.81970i) q^{7} +9.30282 q^{8} +(-2.56943 + 4.45038i) q^{9} +O(q^{10})$	\(q+(-1.36162 - 2.35840i) q^{2} +(1.42643 + 2.47066i) q^{3} +(-2.70804 + 4.69046i) q^{4} -1.48160 q^{5} +(3.88453 - 6.72821i) q^{6} +(1.05061 - 1.81970i) q^{7} +9.30282 q^{8} +(-2.56943 + 4.45038i) q^{9} +(2.01739 + 3.49422i) q^{10} +(1.86378 + 3.22816i) q^{11} -15.4514 q^{12} +(-3.34298 - 1.35074i) q^{13} -5.72212 q^{14} +(-2.11341 - 3.66053i) q^{15} +(-7.25086 - 12.5589i) q^{16} +(-1.96505 + 3.40356i) q^{17} +13.9944 q^{18} +(-2.97816 + 5.15833i) q^{19} +(4.01224 - 6.94940i) q^{20} +5.99448 q^{21} +(5.07553 - 8.79107i) q^{22} +(0.947992 + 1.64197i) q^{23} +(13.2699 + 22.9841i) q^{24} -2.80485 q^{25} +(1.36630 + 9.72328i) q^{26} -6.10188 q^{27} +(5.69016 + 9.85564i) q^{28} +(3.39418 + 5.87889i) q^{29} +(-5.75534 + 9.96854i) q^{30} -1.00000 q^{31} +(-10.4431 + 18.0879i) q^{32} +(-5.31711 + 9.20951i) q^{33} +10.7026 q^{34} +(-1.55658 + 2.69608i) q^{35} +(-13.9162 - 24.1036i) q^{36} +(-1.06541 - 1.84534i) q^{37} +16.2206 q^{38} +(-1.43133 - 10.1861i) q^{39} -13.7831 q^{40} +(3.41168 + 5.90920i) q^{41} +(-8.16222 - 14.1374i) q^{42} +(2.41305 - 4.17952i) q^{43} -20.1887 q^{44} +(3.80687 - 6.59370i) q^{45} +(2.58162 - 4.47149i) q^{46} +8.45973 q^{47} +(20.6858 - 35.8288i) q^{48} +(1.29246 + 2.23860i) q^{49} +(3.81915 + 6.61497i) q^{50} -11.2121 q^{51} +(15.3885 - 12.0223i) q^{52} -11.1099 q^{53} +(8.30846 + 14.3907i) q^{54} +(-2.76138 - 4.78285i) q^{55} +(9.77359 - 16.9284i) q^{56} -16.9926 q^{57} +(9.24319 - 16.0097i) q^{58} +(-0.852126 + 1.47593i) q^{59} +22.8928 q^{60} +(-2.28984 + 3.96612i) q^{61} +(1.36162 + 2.35840i) q^{62} +(5.39891 + 9.35119i) q^{63} +27.8747 q^{64} +(4.95297 + 2.00126i) q^{65} +28.9596 q^{66} +(-4.31372 - 7.47159i) q^{67} +(-10.6429 - 18.4340i) q^{68} +(-2.70450 + 4.68433i) q^{69} +8.47791 q^{70} +(8.13031 - 14.0821i) q^{71} +(-23.9029 + 41.4011i) q^{72} -2.72582 q^{73} +(-2.90137 + 5.02532i) q^{74} +(-4.00094 - 6.92982i) q^{75} +(-16.1300 - 27.9379i) q^{76} +7.83238 q^{77} +(-22.0740 + 17.2453i) q^{78} +7.19465 q^{79} +(10.7429 + 18.6073i) q^{80} +(-0.995641 - 1.72450i) q^{81} +(9.29084 - 16.0922i) q^{82} -11.4569 q^{83} +(-16.2333 + 28.1169i) q^{84} +(2.91142 - 5.04273i) q^{85} -13.1427 q^{86} +(-9.68315 + 16.7717i) q^{87} +(17.3384 + 30.0310i) q^{88} +(7.10595 + 12.3079i) q^{89} -20.7341 q^{90} +(-5.97009 + 4.66413i) q^{91} -10.2688 q^{92} +(-1.42643 - 2.47066i) q^{93} +(-11.5190 - 19.9514i) q^{94} +(4.41246 - 7.64260i) q^{95} -59.5854 q^{96} +(9.13350 - 15.8197i) q^{97} +(3.51968 - 6.09626i) q^{98} -19.1554 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 $

$2$	−1.36162	−	2.35840i	−0.962813	−	1.66764i	−0.715379	−	0.698737i	$-0.753746\pi$
$2$	−1.36162	−	2.35840i	−0.962813	−	1.66764i	−0.247435	−	0.968905i	$-0.579588\pi$
$3$	1.42643	+	2.47066i	0.823552	+	1.42643i	0.903021	+	0.429597i	$0.141344\pi$
$3$	1.42643	+	2.47066i	0.823552	+	1.42643i	−0.0794687	+	0.996837i	$0.525322\pi$
$4$	−2.70804	+	4.69046i	−1.35402	+	2.34523i
$5$	−1.48160			−0.662593			−0.331297	−	0.943527i	$-0.607486\pi$
$5$	−1.48160			−0.662593			−0.331297	+	0.943527i	$0.607486\pi$
$6$	3.88453	−	6.72821i	1.58585	−	2.74678i
$7$	1.05061	−	1.81970i	0.397092	−	0.687783i	−0.596274	−	0.802781i	$-0.703353\pi$
$7$	1.05061	−	1.81970i	0.397092	−	0.687783i	0.993366	+	0.114998i	$0.0366862\pi$
$8$	9.30282			3.28904
$9$	−2.56943	+	4.45038i	−0.856476	+	1.48346i
$10$	2.01739	+	3.49422i	0.637954	+	1.10497i
$11$	1.86378	+	3.22816i	0.561950	+	0.973326i	0.997326	+	0.0730776i	$0.0232821\pi$
$11$	1.86378	+	3.22816i	0.561950	+	0.973326i	−0.435376	+	0.900249i	$0.643385\pi$
$12$	−15.4514			−4.46042
$13$	−3.34298	−	1.35074i	−0.927175	−	0.374627i
$13$	−3.34298	−	1.35074i	−0.927175	−	0.374627i
$14$	−5.72212			−1.52930
$15$	−2.11341	−	3.66053i	−0.545680	−	0.945146i
$16$	−7.25086	−	12.5589i	−1.81272	−	3.13972i
$17$	−1.96505	+	3.40356i	−0.476594	+	0.825486i	−0.999640	−	0.0268189i	$-0.991462\pi$
$17$	−1.96505	+	3.40356i	−0.476594	+	0.825486i	0.523046	+	0.852304i	$0.324796\pi$
$18$	13.9944			3.29851
$19$	−2.97816	+	5.15833i	−0.683238	+	1.18340i	0.290750	+	0.956799i	$0.406095\pi$
$19$	−2.97816	+	5.15833i	−0.683238	+	1.18340i	−0.973987	+	0.226603i	$0.927238\pi$
$20$	4.01224	−	6.94940i	0.897164	−	1.55393i
$21$	5.99448			1.30810
$22$	5.07553	−	8.79107i	1.08211	−	1.87426i
$23$	0.947992	+	1.64197i	0.197670	+	0.342375i	0.947773	−	0.318947i	$-0.103329\pi$
$23$	0.947992	+	1.64197i	0.197670	+	0.342375i	−0.750103	+	0.661322i	$0.769996\pi$
$24$	13.2699	+	22.9841i	2.70870	+	4.69160i
$25$	−2.80485			−0.560970
$26$	1.36630	+	9.72328i	0.267953	+	1.90689i
$27$	−6.10188			−1.17431
$28$	5.69016	+	9.85564i	1.07534	+	1.86254i
$29$	3.39418	+	5.87889i	0.630284	+	1.09168i	0.987494	+	0.157659i	$0.0503947\pi$
$29$	3.39418	+	5.87889i	0.630284	+	1.09168i	−0.357210	+	0.934024i	$0.616272\pi$
$30$	−5.75534	+	9.96854i	−1.05078	+	1.82000i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	−10.4431	+	18.0879i	−1.84609	+	3.19752i
$33$	−5.31711	+	9.20951i	−0.925590	+	1.60317i
$34$	10.7026			1.83549
$35$	−1.55658	+	2.69608i	−0.263110	+	0.455720i
$36$	−13.9162	−	24.1036i	−2.31937	−	4.01727i
$37$	−1.06541	−	1.84534i	−0.175152	−	0.303372i	0.765062	−	0.643957i	$-0.222708\pi$
$37$	−1.06541	−	1.84534i	−0.175152	−	0.303372i	−0.940214	+	0.340585i	$0.889375\pi$
$38$	16.2206			2.63132
$39$	−1.43133	−	10.1861i	−0.229196	−	1.63108i
$40$	−13.7831			−2.17930
$41$	3.41168	+	5.90920i	0.532814	+	0.922862i	0.999266	+	0.0383148i	$0.0121990\pi$
$41$	3.41168	+	5.90920i	0.532814	+	0.922862i	−0.466451	+	0.884547i	$0.654468\pi$
$42$	−8.16222	−	14.1374i	−1.25946	−	2.18145i
$43$	2.41305	−	4.17952i	0.367987	−	0.637371i	−0.621264	−	0.783601i	$-0.713381\pi$
$43$	2.41305	−	4.17952i	0.367987	−	0.637371i	0.989251	+	0.146230i	$0.0467139\pi$
$44$	−20.1887			−3.04356
$45$	3.80687	−	6.59370i	0.567495	−	0.982931i
$46$	2.58162	−	4.47149i	0.380639	−	0.659286i
$47$	8.45973			1.23398			0.616989	−	0.786972i	$-0.288352\pi$
$47$	8.45973			1.23398			0.616989	+	0.786972i	$0.288352\pi$
$48$	20.6858	−	35.8288i	2.98573	−	5.17144i
$49$	1.29246	+	2.23860i	0.184637	+	0.319800i
$50$	3.81915	+	6.61497i	0.540110	+	0.935497i
$51$	−11.2121			−1.57000
$52$	15.3885	−	12.0223i	2.13400	−	1.66719i
$53$	−11.1099			−1.52607			−0.763034	−	0.646359i	$-0.776291\pi$
$53$	−11.1099			−1.52607			−0.763034	+	0.646359i	$0.776291\pi$
$54$	8.30846	+	14.3907i	1.13064	+	1.95832i
$55$	−2.76138	−	4.78285i	−0.372344	−	0.644919i
$56$	9.77359	−	16.9284i	1.30605	−	2.26215i
$57$	−16.9926			−2.25073
$58$	9.24319	−	16.0097i	1.21369	−	2.10217i
$59$	−0.852126	+	1.47593i	−0.110937	+	0.192149i	−0.916148	−	0.400839i	$-0.868719\pi$
$59$	−0.852126	+	1.47593i	−0.110937	+	0.192149i	0.805211	+	0.592988i	$0.202052\pi$
$60$	22.8928			2.95544
$61$	−2.28984	+	3.96612i	−0.293184	+	0.507809i	−0.974561	−	0.224123i	$-0.928048\pi$
$61$	−2.28984	+	3.96612i	−0.293184	+	0.507809i	0.681377	+	0.731933i	$0.261381\pi$
$62$	1.36162	+	2.35840i	0.172926	+	0.299517i
$63$	5.39891	+	9.35119i	0.680199	+	1.17814i
$64$	27.8747			3.48434
$65$	4.95297	+	2.00126i	0.614340	+	0.248226i
$66$	28.9596			3.56468
$67$	−4.31372	−	7.47159i	−0.527005	−	0.912800i	−0.999505	−	0.0314689i	$-0.989981\pi$
$67$	−4.31372	−	7.47159i	−0.527005	−	0.912800i	0.472499	−	0.881331i	$-0.343352\pi$
$68$	−10.6429	−	18.4340i	−1.29064	−	2.23545i
$69$	−2.70450	+	4.68433i	−0.325583	+	0.563927i
$70$	8.47791			1.01330
$71$	8.13031	−	14.0821i	0.964890	−	1.67124i	0.254979	−	0.966947i	$-0.417931\pi$
$71$	8.13031	−	14.0821i	0.964890	−	1.67124i	0.709911	−	0.704292i	$-0.248735\pi$
$72$	−23.9029	+	41.4011i	−2.81699	+	4.87916i
$73$	−2.72582			−0.319034			−0.159517	−	0.987195i	$-0.550994\pi$
$73$	−2.72582			−0.319034			−0.159517	+	0.987195i	$0.550994\pi$
$74$	−2.90137	+	5.02532i	−0.337277	+	0.584182i
$75$	−4.00094	−	6.92982i	−0.461988	−	0.800187i
$76$	−16.1300	−	27.9379i	−1.85023	−	3.20470i
$77$	7.83238			0.892583
$78$	−22.0740	+	17.2453i	−2.49938	+	1.95264i
$79$	7.19465			0.809462			0.404731	−	0.914436i	$-0.367365\pi$
$79$	7.19465			0.809462			0.404731	+	0.914436i	$0.367365\pi$
$80$	10.7429	+	18.6073i	1.20109	+	2.08035i
$81$	−0.995641	−	1.72450i	−0.110627	−	0.191611i
$82$	9.29084	−	16.0922i	1.02600	−	1.77709i
$83$	−11.4569			−1.25756			−0.628779	−	0.777584i	$-0.716445\pi$
$83$	−11.4569			−1.25756			−0.628779	+	0.777584i	$0.716445\pi$
$84$	−16.2333	+	28.1169i	−1.77120	+	3.06780i
$85$	2.91142	−	5.04273i	0.315788	−	0.546961i
$86$	−13.1427			−1.41721
$87$	−9.68315	+	16.7717i	−1.03814	+	1.79812i
$88$	17.3384	+	30.0310i	1.84828	+	3.20131i
$89$	7.10595	+	12.3079i	0.753229	+	1.30463i	0.946250	+	0.323436i	$0.104838\pi$
$89$	7.10595	+	12.3079i	0.753229	+	1.30463i	−0.193021	+	0.981195i	$0.561829\pi$
$90$	−20.7341			−2.18557
$91$	−5.97009	+	4.66413i	−0.625836	+	0.488934i
$92$	−10.2688			−1.07060
$93$	−1.42643	−	2.47066i	−0.147914	−	0.256195i
$94$	−11.5190	−	19.9514i	−1.18809	−	2.05783i
$95$	4.41246	−	7.64260i	0.452709	−	0.784114i
$96$	−59.5854			−6.08141
$97$	9.13350	−	15.8197i	0.927366	−	1.60625i	0.139655	−	0.990200i	$-0.455401\pi$
$97$	9.13350	−	15.8197i	0.927366	−	1.60625i	0.787711	−	0.616045i	$-0.211266\pi$
$98$	3.51968	−	6.09626i	0.355541	−	0.615815i
$99$	−19.1554			−1.92519
$100$	7.59564	−	13.1560i	0.759564	−	1.31560i
$101$	−3.93056	−	6.80793i	−0.391105	−	0.677414i	0.601490	−	0.798880i	$-0.294574\pi$
$101$	−3.93056	−	6.80793i	−0.391105	−	0.677414i	−0.992596	+	0.121466i	$0.961241\pi$
$102$	15.2666	+	26.4425i	1.51162	+	2.61820i
$103$	1.97209			0.194316			0.0971580	−	0.995269i	$-0.469025\pi$
$103$	1.97209			0.194316			0.0971580	+	0.995269i	$0.469025\pi$
$104$	−31.0991	−	12.5657i	−3.04952	−	1.23217i
$105$	−8.88144			−0.866740
$106$	15.1276	+	26.2017i	1.46932	+	2.54493i
$107$	6.28717	+	10.8897i	0.607804	+	1.05275i	0.991602	+	0.129330i	$0.0412825\pi$
$107$	6.28717	+	10.8897i	0.607804	+	1.05275i	−0.383798	+	0.923417i	$0.625384\pi$
$108$	16.5241	−	28.6206i	1.59003	−	2.75402i
$109$	−3.40791			−0.326418			−0.163209	−	0.986592i	$-0.552185\pi$
$109$	−3.40791			−0.326418			−0.163209	+	0.986592i	$0.552185\pi$
$110$	−7.51992	+	13.0249i	−0.716996	+	1.24187i
$111$	3.03947	−	5.26451i	0.288494	−	0.499686i
$112$	−30.4712			−2.87926
$113$	0.770934	−	1.33530i	0.0725233	−	0.125614i	−0.827483	−	0.561490i	$-0.810228\pi$
$113$	0.770934	−	1.33530i	0.0725233	−	0.125614i	0.900007	+	0.435876i	$0.143561\pi$
$114$	23.1375	+	40.0754i	2.16703	+	3.75341i
$115$	−1.40455	−	2.43275i	−0.130975	−	0.226855i
$116$	−36.7663			−3.41366
$117$	14.6008	−	11.4069i	1.34985	−	1.05457i
$118$	4.64110			0.427248
$119$	4.12898	+	7.15161i	0.378503	+	0.655587i
$120$	−19.6607	−	34.0533i	−1.79477	−	3.10862i
$121$	−1.44734	+	2.50686i	−0.131576	+	0.227896i
$122$	12.4716			1.12913
$123$	−9.73306	+	16.8582i	−0.877601	+	1.52005i
$124$	2.70804	−	4.69046i	0.243189	−	0.421216i
$125$	11.5637			1.03429
$126$	14.7026	−	25.4656i	1.30981	−	2.26866i
$127$	6.31532	+	10.9384i	0.560394	+	0.970630i	0.997462	+	0.0712019i	$0.0226835\pi$
$127$	6.31532	+	10.9384i	0.560394	+	0.970630i	−0.437068	+	0.899428i	$0.643983\pi$
$128$	−17.0687	−	29.5638i	−1.50867	−	2.61310i
$129$	13.7682			1.21222
$130$	−2.02431	−	14.4060i	−0.177544	−	1.26349i
$131$	9.79673			0.855945			0.427972	−	0.903792i	$-0.359228\pi$
$131$	9.79673			0.855945			0.427972	+	0.903792i	$0.359228\pi$
$132$	−28.7979	−	49.8794i	−2.50653	−	4.34144i
$133$	6.25775	+	10.8387i	0.542616	+	0.939838i
$134$	−11.7473	+	20.3470i	−1.01482	+	1.75771i
$135$	9.04056			0.778088
$136$	−18.2805	+	31.6627i	−1.56754	+	2.71506i
$137$	9.69354	−	16.7897i	0.828175	−	1.43444i	−0.0712927	−	0.997455i	$-0.522712\pi$
$137$	9.69354	−	16.7897i	0.828175	−	1.43444i	0.899468	−	0.436986i	$-0.143954\pi$
$138$	14.7300			1.25390
$139$	2.39541	−	4.14897i	0.203176	−	0.351911i	−0.746374	−	0.665526i	$-0.768207\pi$
$139$	2.39541	−	4.14897i	0.203176	−	0.351911i	0.949550	+	0.313616i	$0.101540\pi$
$140$	−8.43056	−	14.6022i	−0.712512	−	1.23411i
$141$	12.0672	+	20.9011i	1.01625	+	1.76019i
$142$	−44.2817			−3.71604
$143$	−1.87017	−	13.3091i	−0.156392	−	1.11297i
$144$	74.5223			6.21019
$145$	−5.02883	−	8.71019i	−0.417622	−	0.723342i
$146$	3.71155	+	6.42859i	0.307170	+	0.532034i
$147$	−3.68721	+	6.38643i	−0.304116	+	0.526744i
$148$	11.5407			0.948637
$149$	8.77847	−	15.2047i	0.719160	−	1.24562i	−0.242173	−	0.970233i	$-0.577860\pi$
$149$	8.77847	−	15.2047i	0.719160	−	1.24562i	0.961333	−	0.275388i	$-0.0888065\pi$
$150$	−10.8955	+	18.8716i	−0.889617	+	1.54086i
$151$	3.58365			0.291633			0.145817	−	0.989312i	$-0.453419\pi$
$151$	3.58365			0.291633			0.145817	+	0.989312i	$0.453419\pi$
$152$	−27.7053	+	47.9870i	−2.24720	+	3.89226i
$153$	−10.0981	−	17.4904i	−0.816383	−	1.41402i
$154$	−10.6648	−	18.4719i	−0.859390	−	1.48851i
$155$	1.48160			0.119005
$156$	51.6535	+	20.8707i	4.13559	+	1.67100i
$157$	10.6833			0.852619			0.426309	−	0.904577i	$-0.359813\pi$
$157$	10.6833			0.852619			0.426309	+	0.904577i	$0.359813\pi$
$158$	−9.79641	−	16.9679i	−0.779360	−	1.34989i
$159$	−15.8476	−	27.4488i	−1.25680	−	2.17684i
$160$	15.4725	−	26.7991i	1.22321	−	2.11866i
$161$	3.98386			0.313972
$162$	−2.71138	+	4.69624i	−0.213026	+	0.368971i
$163$	−2.39960	+	4.15624i	−0.187952	+	0.325542i	−0.944567	−	0.328318i	$-0.893518\pi$
$163$	−2.39960	+	4.15624i	−0.187952	+	0.325542i	0.756616	+	0.653860i	$0.226851\pi$
$164$	−36.9558			−2.88576
$165$	7.87785	−	13.6448i	0.613290	−	1.06225i
$166$	15.6000	+	27.0200i	1.21079	+	2.09716i
$167$	0.805412	+	1.39501i	0.0623247	+	0.107949i	0.895504	−	0.445053i	$-0.146815\pi$
$167$	0.805412	+	1.39501i	0.0623247	+	0.107949i	−0.833179	+	0.553003i	$0.813482\pi$
$168$	55.7655			4.30240
$169$	9.35101	+	9.03098i	0.719309	+	0.694691i
$170$	−15.8570			−1.21618
$171$	−15.3044	−	26.5079i	−1.17035	−	2.02711i
$172$	13.0693	+	22.6366i	0.996521	+	1.72603i
$173$	0.901450	−	1.56136i	0.0685360	−	0.118708i	−0.829721	−	0.558178i	$-0.811501\pi$
$173$	0.901450	−	1.56136i	0.0685360	−	0.118708i	0.898257	+	0.439470i	$0.144834\pi$
$174$	52.7392			3.99815
$175$	−2.94679	+	5.10399i	−0.222757	+	0.385826i
$176$	27.0280	−	46.8139i	2.03731	−	3.52873i
$177$	−4.86201			−0.365451
$178$	19.3512	−	33.5173i	1.45044	−	2.51223i
$179$	−4.78108	−	8.28107i	−0.357355	−	0.618956i	0.630163	−	0.776463i	$-0.282988\pi$
$179$	−4.78108	−	8.28107i	−0.357355	−	0.618956i	−0.987518	+	0.157506i	$0.949655\pi$
$180$	20.6183	+	35.7120i	1.53680	+	2.66181i
$181$	−10.8096			−0.803468			−0.401734	−	0.915756i	$-0.631592\pi$
$181$	−10.8096			−0.803468			−0.401734	+	0.915756i	$0.631592\pi$
$182$	19.1289	+	7.72908i	1.41793	+	0.572918i
$183$	−13.0652			−0.965809
$184$	8.81900	+	15.2750i	0.650145	+	1.12608i
$185$	1.57851	+	2.73406i	0.116055	+	0.201012i
$186$	−3.88453	+	6.72821i	−0.284828	+	0.493336i
$187$	−14.6497			−1.07129
$188$	−22.9093	+	39.6800i	−1.67083	+	2.89396i
$189$	−6.41067	+	11.1036i	−0.466307	+	0.807668i
$190$	−24.0324			−1.74350
$191$	−6.88656	+	11.9279i	−0.498294	+	0.863071i	−0.999998	−	0.00196862i	$-0.999373\pi$
$191$	−6.88656	+	11.9279i	−0.498294	+	0.863071i	0.501704	+	0.865039i	$0.332707\pi$
$192$	39.7614	+	68.8688i	2.86953	+	4.97018i
$193$	−7.63322	−	13.2211i	−0.549451	−	0.951678i	−0.998312	−	0.0580759i	$-0.981503\pi$
$193$	−7.63322	−	13.2211i	−0.549451	−	0.951678i	0.448861	−	0.893602i	$-0.351830\pi$
$194$	−49.7455			−3.57152
$195$	2.12066	+	15.0917i	0.151864	+	1.08074i
$196$	−14.0001			−1.00001
$197$	5.31402	+	9.20415i	0.378608	+	0.655769i	0.990860	−	0.134894i	$-0.0430694\pi$
$197$	5.31402	+	9.20415i	0.378608	+	0.655769i	−0.612252	+	0.790663i	$0.709736\pi$
$198$	26.0824	+	45.1761i	1.85360	+	3.21052i
$199$	−2.69833	+	4.67364i	−0.191279	+	0.331306i	−0.945674	−	0.325115i	$-0.894597\pi$
$199$	−2.69833	+	4.67364i	−0.191279	+	0.331306i	0.754395	+	0.656421i	$0.227930\pi$
$200$	−26.0930			−1.84506
$201$	12.3065	−	21.3155i	0.868033	−	1.50348i
$202$	−10.7039	+	18.5397i	−0.753123	+	1.30445i
$203$	14.2638			1.00112
$204$	30.3627	−	52.5897i	2.12581	−	3.68201i
$205$	−5.05475	−	8.75509i	−0.353039	−	0.611482i
$206$	−2.68525	−	4.65098i	−0.187090	−	0.324049i
$207$	−9.74319			−0.677199
$208$	7.27574	+	51.7780i	0.504482	+	3.59016i
$209$	−22.2025			−1.53578
$210$	12.0932	+	20.9460i	0.834509	+	1.44541i
$211$	−0.719162	−	1.24563i	−0.0495092	−	0.0857524i	0.840209	−	0.542263i	$-0.182432\pi$
$211$	−0.719162	−	1.24563i	−0.0495092	−	0.0857524i	−0.889718	+	0.456511i	$0.849099\pi$
$212$	30.0861	−	52.1107i	2.06632	−	3.57898i
$213$	46.3894			3.17855
$214$	17.1215	−	29.6553i	1.17040	−	2.02720i
$215$	−3.57518	+	6.19240i	−0.243825	+	0.422318i
$216$	−56.7647			−3.86235
$217$	−1.05061	+	1.81970i	−0.0713197	+	0.123529i
$218$	4.64029	+	8.03721i	0.314280	+	0.544349i
$219$	−3.88821	−	6.73458i	−0.262741	−	0.455080i
$220$	29.9117			2.01665
$221$	11.1664	−	8.72378i	0.751136	−	0.586825i
$222$	−16.5545			−1.11106
$223$	5.75335	+	9.96510i	0.385273	+	0.667312i	0.991807	−	0.127745i	$-0.0407740\pi$
$223$	5.75335	+	9.96510i	0.385273	+	0.667312i	−0.606534	+	0.795057i	$0.707441\pi$
$224$	21.9431	+	38.0066i	1.46613	+	2.53942i
$225$	7.20687	−	12.4827i	0.480458	−	0.832177i
$226$	−4.19889			−0.279306
$227$	−0.345815	+	0.598969i	−0.0229525	+	0.0397549i	−0.877274	−	0.479991i	$-0.840640\pi$
$227$	−0.345815	+	0.598969i	−0.0229525	+	0.0397549i	0.854321	+	0.519746i	$0.173973\pi$
$228$	46.0166	−	79.7032i	3.04753	−	5.27847i
$229$	−19.1306			−1.26419			−0.632093	−	0.774893i	$-0.717804\pi$
$229$	−19.1306			−1.26419			−0.632093	+	0.774893i	$0.717804\pi$
$230$	−3.82493	+	6.62498i	−0.252209	+	0.436838i
$231$	11.1724	+	19.3511i	0.735088	+	1.27321i
$232$	31.5754	+	54.6903i	2.07303	+	3.59059i
$233$	24.4339			1.60072			0.800358	−	0.599522i	$-0.204643\pi$
$233$	24.4339			1.60072			0.800358	+	0.599522i	$0.204643\pi$
$234$	−46.7829	−	18.9027i	−3.05829	−	1.23571i
$235$	−12.5340			−0.817626
$236$	−4.61518	−	7.99372i	−0.300422	−	0.520347i
$237$	10.2627	+	17.7755i	0.666634	+	1.15464i
$238$	11.2442	−	19.4756i	0.728856	−	1.26242i
$239$	11.7124			0.757613			0.378807	−	0.925476i	$-0.376335\pi$
$239$	11.7124			0.757613			0.378807	+	0.925476i	$0.376335\pi$
$240$	−30.6481	+	53.0840i	−1.97833	+	3.42656i
$241$	−11.7386	+	20.3319i	−0.756152	+	1.30969i	0.188648	+	0.982045i	$0.439590\pi$
$241$	−11.7386	+	20.3319i	−0.756152	+	1.30969i	−0.944800	+	0.327649i	$0.893744\pi$
$242$	7.88291			0.506732
$243$	−6.31238	+	10.9334i	−0.404940	+	0.701376i
$244$	−12.4019	−	21.4808i	−0.793953	−	1.37517i
$245$	−1.91491	−	3.31672i	−0.122339	−	0.211897i
$246$	53.0111			3.37986
$247$	16.9235	−	13.2215i	1.07682	−	0.841262i
$248$	−9.30282			−0.590730
$249$	−16.3425	−	28.3061i	−1.03567	−	1.79382i
$250$	−15.7454	−	27.2718i	−0.995827	−	1.72482i
$251$	1.64519	−	2.84955i	0.103843	−	0.179862i	−0.809422	−	0.587228i	$-0.800219\pi$
$251$	1.64519	−	2.84955i	0.103843	−	0.179862i	0.913265	+	0.407366i	$0.133553\pi$
$252$	−58.4818			−3.68401
$253$	−3.53369	+	6.12054i	−0.222161	+	0.384795i
$254$	17.1982	−	29.7881i	1.07911	−	1.86907i
$255$	16.6118			1.04027
$256$	−18.6076	+	32.2293i	−1.16297	+	2.01433i
$257$	1.15360	+	1.99809i	0.0719596	+	0.124638i	0.899760	−	0.436385i	$-0.143741\pi$
$257$	1.15360	+	1.99809i	0.0719596	+	0.124638i	−0.827800	+	0.561023i	$0.810408\pi$
$258$	−18.7471	−	32.4710i	−1.16715	−	2.02156i
$259$	−4.47729			−0.278206
$260$	−22.7996	+	17.8122i	−1.41397	+	1.10467i
$261$	−34.8844			−2.15929
$262$	−13.3395	−	23.1046i	−0.824115	−	1.42741i
$263$	−1.15564	−	2.00163i	−0.0712598	−	0.123426i	0.828194	−	0.560442i	$-0.189369\pi$
$263$	−1.15564	−	2.00163i	−0.0712598	−	0.123426i	−0.899454	+	0.437016i	$0.856035\pi$
$264$	−49.4641	+	85.6744i	−3.04431	+	5.27289i
$265$	16.4605			1.01116
$266$	17.0414	−	29.5166i	1.04488	−	1.80978i
$267$	−20.2723	+	35.1127i	−1.24065	+	2.14886i
$268$	46.7269			2.85430
$269$	−1.93890	+	3.35827i	−0.118217	+	0.204758i	−0.919061	−	0.394115i	$-0.871051\pi$
$269$	−1.93890	+	3.35827i	−0.118217	+	0.204758i	0.800844	+	0.598873i	$0.204384\pi$
$270$	−12.3098	−	21.3213i	−0.749153	−	1.29757i
$271$	1.23416	+	2.13762i	0.0749696	+	0.129851i	0.901073	−	0.433667i	$-0.142781\pi$
$271$	1.23416	+	2.13762i	0.0749696	+	0.129851i	−0.826103	+	0.563518i	$0.809447\pi$
$272$	56.9932			3.45572
$273$	−20.0394	−	8.09697i	−1.21284	−	0.490051i
$274$	−52.7958			−3.18951
$275$	−5.22762	−	9.05450i	−0.315237	−	0.546007i
$276$	−14.6478	−	25.3707i	−0.881691	−	1.52713i
$277$	3.82483	−	6.62479i	0.229811	−	0.398045i	−0.727941	−	0.685640i	$-0.759522\pi$
$277$	3.82483	−	6.62479i	0.229811	−	0.398045i	0.957752	+	0.287595i	$0.0928557\pi$
$278$	−13.0466			−0.782481
$279$	2.56943	−	4.45038i	0.153828	−	0.266437i
$280$	−14.4806	+	25.0811i	−0.865381	+	1.49888i
$281$	−22.4921			−1.34177			−0.670884	−	0.741563i	$-0.734085\pi$
$281$	−22.4921			−1.34177			−0.670884	+	0.741563i	$0.734085\pi$
$282$	32.8621	−	56.9188i	1.95691	−	3.38947i
$283$	2.43300	+	4.21408i	0.144627	+	0.250501i	0.929234	−	0.369493i	$-0.120469\pi$
$283$	2.43300	+	4.21408i	0.144627	+	0.250501i	−0.784607	+	0.619994i	$0.787135\pi$
$284$	44.0344	+	76.2697i	2.61296	+	4.52578i
$285$	25.1763			1.49132
$286$	−28.8418	+	22.5327i	−1.70545	+	1.33238i
$287$	14.3373			0.846304
$288$	−53.6655	−	92.9513i	−3.16227	−	5.47721i
$289$	0.777166	+	1.34609i	0.0457157	+	0.0791818i
$290$	−13.6947	+	23.7200i	−0.804183	+	1.39289i
$291$	52.1133			3.05494
$292$	7.38164	−	12.7854i	0.431978	−	0.748207i
$293$	−1.48135	+	2.56578i	−0.0865416	+	0.149894i	−0.906047	−	0.423177i	$-0.860915\pi$
$293$	−1.48135	+	2.56578i	−0.0865416	+	0.149894i	0.819505	+	0.573071i	$0.194248\pi$
$294$	20.0824			1.17123
$295$	1.26251	−	2.18674i	0.0735063	−	0.127317i
$296$	−9.91130	−	17.1669i	−0.576083	−	0.997804i
$297$	−11.3725	−	19.6978i	−0.659902	−	1.14298i
$298$	−47.8119			−2.76967
$299$	−0.951245	−	6.76956i	−0.0550119	−	0.391494i
$300$	43.3387			2.50216
$301$	−5.07032	−	8.78206i	−0.292249	−	0.506190i
$302$	−4.87958	−	8.45168i	−0.280788	−	0.486339i
$303$	11.2134	−	19.4221i	0.644191	−	1.11577i
$304$	86.3770			4.95406
$305$	3.39263	−	5.87621i	0.194262	−	0.336471i
$306$	−27.4996	+	47.6308i	−1.57205	+	2.72287i
$307$	8.33149			0.475503			0.237752	−	0.971326i	$-0.423590\pi$
$307$	8.33149			0.475503			0.237752	+	0.971326i	$0.423590\pi$
$308$	−21.2104	+	36.7375i	−1.20857	+	2.09331i
$309$	2.81306	+	4.87236i	0.160029	+	0.277179i
$310$	−2.01739	−	3.49422i	−0.114580	−	0.198458i
$311$	−10.8995			−0.618053			−0.309026	−	0.951053i	$-0.600003\pi$
$311$	−10.8995			−0.618053			−0.309026	+	0.951053i	$0.600003\pi$
$312$	−13.3154	−	94.7594i	−0.753835	−	5.36469i
$313$	13.6878			0.773680			0.386840	−	0.922147i	$-0.373567\pi$
$313$	13.6878			0.773680			0.386840	+	0.922147i	$0.373567\pi$
$314$	−14.5466	−	25.1955i	−0.820913	−	1.42186i
$315$	−7.99905	−	13.8548i	−0.450695	−	0.780627i
$316$	−19.4834	+	33.7462i	−1.09603	+	1.89837i
$317$	−12.7083			−0.713771			−0.356885	−	0.934148i	$-0.616161\pi$
$317$	−12.7083			−0.713771			−0.356885	+	0.934148i	$0.616161\pi$
$318$	−43.1569	+	74.7500i	−2.42012	+	4.19177i
$319$	−12.6520	+	21.9139i	−0.708376	+	1.22694i
$320$	−41.2992			−2.30870
$321$	−17.9365	+	31.0669i	−1.00112	+	1.73398i
$322$	−5.42452	−	9.39555i	−0.302297	−	0.523593i
$323$	−11.7045	−	20.2727i	−0.651254	−	1.12801i
$324$	10.7849			0.599163
$325$	9.37656	+	3.78862i	0.520118	+	0.210155i
$326$	13.0694			0.723849
$327$	−4.86115	−	8.41976i	−0.268822	−	0.465614i
$328$	31.7382	+	54.9722i	1.75245	+	3.03533i
$329$	8.88784	−	15.3942i	0.490002	−	0.848709i
$330$	−42.9067			−2.36193
$331$	−7.75539	+	13.4327i	−0.426275	+	0.738330i	−0.996539	−	0.0831321i	$-0.973508\pi$
$331$	−7.75539	+	13.4327i	−0.426275	+	0.738330i	0.570264	+	0.821462i	$0.306841\pi$
$332$	31.0257	−	53.7381i	1.70276	−	2.94926i
$333$	10.9500			0.600054
$334$	2.19334	−	3.79897i	0.120014	−	0.207870i
$335$	6.39123	+	11.0699i	0.349190	+	0.604815i
$336$	−43.4651	−	75.2838i	−2.37122	−	4.10707i
$337$	−1.13512			−0.0618337			−0.0309168	−	0.999522i	$-0.509843\pi$
$337$	−1.13512			−0.0618337			−0.0309168	+	0.999522i	$0.509843\pi$
$338$	8.56611	−	34.3502i	0.465935	−	1.86841i
$339$	4.39874			0.238907
$340$	15.7685	+	27.3118i	0.855166	+	1.48119i
$341$	−1.86378	−	3.22816i	−0.100929	−	0.174815i
$342$	−41.6775	+	72.1876i	−2.25366	+	3.90346i
$343$	20.1399			1.08745
$344$	22.4482	−	38.8813i	1.21032	−	2.09634i
$345$	4.00699	−	6.94031i	0.215729	−	0.373654i
$346$	−4.90974			−0.263949
$347$	−15.6861	+	27.1692i	−0.842076	+	1.45852i	0.0460599	+	0.998939i	$0.485333\pi$
$347$	−15.6861	+	27.1692i	−0.842076	+	1.45852i	−0.888136	+	0.459580i	$0.848000\pi$
$348$	−52.4447	−	90.8368i	−2.81133	−	4.86937i
$349$	1.77508	+	3.07452i	0.0950177	+	0.164575i	0.909616	−	0.415450i	$-0.136376\pi$
$349$	1.77508	+	3.07452i	0.0950177	+	0.164575i	−0.814598	+	0.580026i	$0.803043\pi$
$350$	16.0497			0.857892
$351$	20.3984	+	8.24204i	1.08879	+	0.439928i
$352$	−77.8543			−4.14965
$353$	12.7914	+	22.1554i	0.680818	+	1.17921i	0.974732	+	0.223379i	$0.0717088\pi$
$353$	12.7914	+	22.1554i	0.680818	+	1.17921i	−0.293914	+	0.955832i	$0.594958\pi$
$354$	6.62022	+	11.4666i	0.351861	+	0.609441i
$355$	−12.0459	+	20.8641i	−0.639329	+	1.10735i
$356$	−76.9727			−4.07954
$357$	−11.7794	+	20.4026i	−0.623434	+	1.07982i
$358$	−13.0201	+	22.5514i	−0.688132	+	1.19188i
$359$	−27.6723			−1.46049			−0.730243	−	0.683187i	$-0.760593\pi$
$359$	−27.6723			−1.46049			−0.730243	+	0.683187i	$0.760593\pi$
$360$	35.4147	−	61.3400i	1.86652	−	3.23290i
$361$	−8.23891	−	14.2702i	−0.433627	−	0.751064i
$362$	14.7185	+	25.4933i	0.773589	+	1.33990i
$363$	−8.25812			−0.433439
$364$	−5.70968	−	40.6331i	−0.299269	−	2.12975i
$365$	4.03859			0.211390
$366$	17.7899	+	30.8130i	0.929894	+	1.61062i
$367$	−1.03156	−	1.78672i	−0.0538472	−	0.0932661i	0.837845	−	0.545908i	$-0.183815\pi$
$367$	−1.03156	−	1.78672i	−0.0538472	−	0.0932661i	−0.891693	+	0.452642i	$0.850482\pi$
$368$	13.7475	−	23.8114i	0.716639	−	1.24126i
$369$	−35.0642			−1.82537
$370$	4.29868	−	7.44553i	0.223478	−	0.387075i
$371$	−11.6722	+	20.2168i	−0.605989	+	1.04960i
$372$	15.4514			0.801115
$373$	−4.09554	+	7.09369i	−0.212059	+	0.367297i	−0.952359	−	0.304980i	$-0.901350\pi$
$373$	−4.09554	+	7.09369i	−0.212059	+	0.367297i	0.740300	+	0.672277i	$0.234684\pi$
$374$	19.9473	+	34.5498i	1.03145	+	1.78653i
$375$	16.4948	+	28.5699i	0.851790	+	1.47534i
$376$	78.6993			4.05861
$377$	−3.40583	−	24.2377i	−0.175409	−	1.24830i
$378$	34.9157			1.79587
$379$	−0.489696	−	0.848179i	−0.0251540	−	0.0435680i	0.853174	−	0.521626i	$-0.174674\pi$
$379$	−0.489696	−	0.848179i	−0.0251540	−	0.0435680i	−0.878328	+	0.478058i	$0.841341\pi$
$380$	23.8982	+	41.3929i	1.22595	+	2.12341i
$381$	−18.0168	+	31.2059i	−0.923027	+	1.59873i
$382$	37.5076			1.91906
$383$	−2.81158	+	4.86981i	−0.143665	+	0.248835i	−0.928874	−	0.370395i	$-0.879222\pi$
$383$	−2.81158	+	4.86981i	−0.143665	+	0.248835i	0.785209	+	0.619231i	$0.212556\pi$
$384$	48.6947	−	84.3417i	2.48494	−	4.30405i
$385$	−11.6045			−0.591419
$386$	−20.7872	+	36.0044i	−1.05804	+	1.83258i
$387$	12.4003	+	21.4780i	0.630343	+	1.09179i
$388$	49.4677	+	85.6806i	2.51134	+	4.34977i
$389$	15.6021			0.791057			0.395528	−	0.918454i	$-0.370562\pi$
$389$	15.6021			0.791057			0.395528	+	0.918454i	$0.370562\pi$
$390$	32.7049	−	25.5506i	1.65607	−	1.29381i
$391$	−7.45140			−0.376834
$392$	12.0235	+	20.8253i	0.607278	+	1.05184i
$393$	13.9744	+	24.2044i	0.704915	+	1.22095i
$394$	14.4714	−	25.0652i	0.729058	−	1.26277i
$395$	−10.6596			−0.536344
$396$	51.8735	−	89.8475i	2.60674	−	4.51501i
$397$	18.3527	−	31.7877i	0.921093	−	1.59538i	0.123367	−	0.992361i	$-0.460631\pi$
$397$	18.3527	−	31.7877i	0.921093	−	1.59538i	0.797727	−	0.603019i	$-0.206036\pi$
$398$	14.6964			0.736665
$399$	−17.8525	+	30.9215i	−0.893745	+	1.54801i
$400$	20.3376	+	35.2257i	1.01688	+	1.76129i
$401$	0.559483	+	0.969053i	0.0279392	+	0.0483922i	0.879657	−	0.475609i	$-0.157772\pi$
$401$	0.559483	+	0.969053i	0.0279392	+	0.0483922i	−0.851718	+	0.524001i	$0.824439\pi$
$402$	−67.0272			−3.34301
$403$	3.34298	+	1.35074i	0.166526	+	0.0672851i
$404$	42.5764			2.11826
$405$	1.47514	+	2.55503i	0.0733005	+	0.126960i
$406$	−19.4219	−	33.6397i	−0.963893	−	1.66951i
$407$	3.97137	−	6.87861i	0.196853	−	0.340960i
$408$	−104.304			−5.16380
$409$	7.35907	−	12.7463i	0.363883	−	0.630264i	−0.624713	−	0.780854i	$-0.714784\pi$
$409$	7.35907	−	12.7463i	0.363883	−	0.630264i	0.988596	+	0.150591i	$0.0481175\pi$
$410$	−13.7653	+	23.8423i	−0.679822	+	1.17749i
$411$	55.3088			2.72818
$412$	−5.34050	+	9.25002i	−0.263108	+	0.455716i
$413$	1.79050	+	3.10123i	0.0881045	+	0.152602i
$414$	13.2666	+	22.9784i	0.652016	+	1.12932i
$415$	16.9746			0.833250
$416$	59.3430	−	46.3617i	2.90953	−	2.27307i
$417$	13.6676			0.669303
$418$	30.2315	+	52.3625i	1.47867	+	2.56113i
$419$	−5.99948	−	10.3914i	−0.293094	−	0.507653i	0.681446	−	0.731869i	$-0.261352\pi$
$419$	−5.99948	−	10.3914i	−0.293094	−	0.507653i	−0.974540	+	0.224215i	$0.928018\pi$
$420$	24.0513	−	41.6580i	1.17358	−	2.03270i
$421$	12.2208			0.595606			0.297803	−	0.954627i	$-0.403746\pi$
$421$	12.2208			0.595606			0.297803	+	0.954627i	$0.403746\pi$
$422$	−1.95846	+	3.39215i	−0.0953362	+	0.165127i
$423$	−21.7367	+	37.6490i	−1.05687	+	1.83056i
$424$	−103.354			−5.01930
$425$	5.51167	−	9.54649i	0.267355	−	0.463073i
$426$	−63.1649	−	109.405i	−3.06035	−	5.30068i
$427$	4.81144	+	8.33365i	0.232842	+	0.403294i
$428$	−68.1036			−3.29191
$429$	30.2146	−	23.6052i	1.45878	−	1.13967i
$430$	19.4722			0.939033
$431$	10.3802	+	17.9791i	0.499998	+	0.866022i	1.00000		2.09028e-6i	$-6.65357e-7\pi$
$431$	10.3802	+	17.9791i	0.499998	+	0.866022i	−0.500002	+	0.866024i	$0.666667\pi$
$432$	44.2439	+	76.6326i	2.12868	+	3.68699i
$433$	−4.74696	+	8.22198i	−0.228125	+	0.395123i	−0.957252	−	0.289254i	$-0.906593\pi$
$433$	−4.74696	+	8.22198i	−0.228125	+	0.395123i	0.729128	+	0.684378i	$0.239926\pi$
$434$	5.72212			0.274670
$435$	14.3466	−	24.8490i	0.687866	−	1.19142i
$436$	9.22874	−	15.9846i	0.441976	−	0.765526i
$437$	−11.2931			−0.540222
$438$	−10.5886	+	18.3399i	−0.505941	+	0.876315i
$439$	−18.6807	−	32.3559i	−0.891581	−	1.54426i	−0.837979	−	0.545702i	$-0.816263\pi$
$439$	−18.6807	−	32.3559i	−0.891581	−	1.54426i	−0.0536019	−	0.998562i	$-0.517070\pi$
$440$	−25.6886	−	44.4940i	−1.22466	−	2.12117i
$441$	−13.2835			−0.632547
$442$	−35.7787	−	14.4565i	−1.70182	−	0.687623i
$443$	4.91644			0.233587			0.116794	−	0.993156i	$-0.462738\pi$
$443$	4.91644			0.233587			0.116794	+	0.993156i	$0.462738\pi$
$444$	16.4620	+	28.5130i	0.781252	+	1.35317i
$445$	−10.5282	−	18.2354i	−0.499084	−	0.864439i
$446$	15.6678	−	27.1374i	0.741892	−	1.28499i
$447$	50.0876			2.36906
$448$	29.2853	−	50.7236i	1.38360	−	2.39647i
$449$	11.6310	−	20.1455i	0.548902	−	0.950726i	−0.449448	−	0.893306i	$-0.648379\pi$
$449$	11.6310	−	20.1455i	0.548902	−	0.950726i	0.998350	−	0.0574198i	$-0.0182873\pi$
$450$	−39.2522			−1.85036
$451$	−12.7172	+	22.0269i	−0.598830	+	1.03720i
$452$	4.17543	+	7.23206i	0.196396	+	0.340168i
$453$	5.11184	+	8.85396i	0.240175	+	0.415995i
$454$	1.88348			0.0883960
$455$	8.84531	−	6.91039i	0.414675	−	0.323964i
$456$	−158.079			−7.40274
$457$	−6.30081	−	10.9133i	−0.294740	−	0.510504i	0.680185	−	0.733041i	$-0.261900\pi$
$457$	−6.30081	−	10.9133i	−0.294740	−	0.510504i	−0.974924	+	0.222537i	$0.928566\pi$
$458$	26.0487	+	45.1176i	1.21717	+	2.10821i
$459$	11.9905	−	20.7681i	0.559668	−	0.969373i
$460$	15.2143			0.709370
$461$	−17.4086	+	30.1526i	−0.810801	+	1.40435i	0.101504	+	0.994835i	$0.467635\pi$
$461$	−17.4086	+	30.1526i	−0.810801	+	1.40435i	−0.912304	+	0.409513i	$0.865699\pi$
$462$	30.4251	−	52.6979i	1.41551	−	2.45173i
$463$	2.50847			0.116579			0.0582893	−	0.998300i	$-0.481435\pi$
$463$	2.50847			0.116579			0.0582893	+	0.998300i	$0.481435\pi$
$464$	49.2215	−	85.2541i	2.28505	−	3.95782i
$465$	2.11341	+	3.66053i	0.0980070	+	0.169753i
$466$	−33.2697	−	57.6249i	−1.54119	−	2.66942i
$467$	−3.17663			−0.146997			−0.0734984	−	0.997295i	$-0.523416\pi$
$467$	−3.17663			−0.146997			−0.0734984	+	0.997295i	$0.523416\pi$
$468$	13.9640	+	99.3750i	0.645485	+	4.59361i
$469$	−18.1281			−0.837077
$470$	17.0665	+	29.5601i	0.787221	+	1.36351i
$471$	15.2390	+	26.3947i	0.702176	+	1.21620i
$472$	−7.92717	+	13.7303i	−0.364878	+	0.631987i
$473$	17.9895			0.827160
$474$	27.9479	−	48.4071i	1.28369	−	2.22341i
$475$	8.35331	−	14.4683i	0.383276	−	0.663853i
$476$	−44.7258			−2.05000
$477$	28.5462	−	49.4435i	1.30704	−	2.26386i
$478$	−15.9479	−	27.6226i	−0.729440	−	1.26343i
$479$	−3.08650	−	5.34597i	−0.141026	−	0.244264i	0.786857	−	0.617135i	$-0.211707\pi$
$479$	−3.08650	−	5.34597i	−0.141026	−	0.244264i	−0.927883	+	0.372871i	$0.878373\pi$
$480$	88.2820			4.02950
$481$	1.06906	+	7.60802i	0.0487451	+	0.346896i
$482$	63.9344			2.91213
$483$	5.68272	+	9.84276i	0.258573	+	0.447861i
$484$	−7.83888	−	13.5773i	−0.356313	−	0.617152i
$485$	−13.5322	+	23.4385i	−0.614466	+	1.06429i
$486$	34.3804			1.55953
$487$	5.47993	−	9.49152i	0.248319	−	0.430102i	−0.714740	−	0.699390i	$-0.753455\pi$
$487$	5.47993	−	9.49152i	0.248319	−	0.430102i	0.963060	+	0.269288i	$0.0867884\pi$
$488$	−21.3020	+	36.8961i	−0.964295	+	1.67021i
$489$	−13.6915			−0.619151
$490$	−5.21477	+	9.03224i	−0.235579	+	0.408035i
$491$	8.56142	+	14.8288i	0.386372	+	0.669215i	0.991958	−	0.126564i	$-0.0403949\pi$
$491$	8.56142	+	14.8288i	0.386372	+	0.669215i	−0.605587	+	0.795779i	$0.707062\pi$
$492$	−52.7150	−	91.3051i	−2.37658	−	4.11635i
$493$	−26.6789			−1.20156
$494$	−54.2250	−	21.9097i	−2.43970	−	0.985765i
$495$	28.3807			1.27562
$496$	7.25086	+	12.5589i	0.325573	+	0.563910i
$497$	−17.0835	−	29.5895i	−0.766299	−	1.32727i
$498$	−44.5047	+	77.0844i	−1.99430	+	3.45424i
$499$	−11.6532			−0.521669			−0.260835	−	0.965383i	$-0.583998\pi$
$499$	−11.6532			−0.521669			−0.260835	+	0.965383i	$0.583998\pi$
$500$	−31.3149	+	54.2390i	−1.40045	+	2.42564i
$501$	−2.29774	+	3.97979i	−0.102655	+	0.177804i
$502$	−8.96052			−0.399927
$503$	−3.48612	+	6.03814i	−0.155438	+	0.269227i	−0.933219	−	0.359309i	$-0.883012\pi$
$503$	−3.48612	+	6.03814i	−0.155438	+	0.269227i	0.777780	+	0.628536i	$0.216346\pi$
$504$	50.2251	+	86.9924i	2.23720	+	3.87495i
$505$	5.82353	+	10.0867i	0.259144	+	0.448850i
$506$	19.2462			0.855600
$507$	−8.97384	+	35.9852i	−0.398542	+	1.59816i
$508$	−68.4085			−3.03513
$509$	−1.09457	−	1.89584i	−0.0485158	−	0.0840317i	0.840748	−	0.541427i	$-0.182116\pi$
$509$	−1.09457	−	1.89584i	−0.0485158	−	0.0840317i	−0.889263	+	0.457395i	$0.848782\pi$
$510$	−22.6190	−	39.1773i	−1.00159	−	1.73480i
$511$	−2.86377	+	4.96019i	−0.126686	+	0.219426i
$512$	33.0713			1.46156
$513$	18.1724	−	31.4755i	0.802331	−	1.38968i
$514$	3.14154	−	5.44130i	0.138567	−	0.240006i
$515$	−2.92186			−0.128752
$516$	−37.2849	+	64.5793i	−1.64137	+	2.84294i
$517$	15.7671	+	27.3093i	0.693434	+	1.20106i
$518$	6.09639	+	10.5593i	0.267860	+	0.463947i
$519$	5.14344			0.225772
$520$	46.0766	+	18.6173i	2.02059	+	0.816425i
$521$	41.7337			1.82839			0.914193	−	0.405279i	$-0.132826\pi$
$521$	41.7337			1.82839			0.914193	+	0.405279i	$0.132826\pi$
$522$	47.4994	+	82.2715i	2.07899	+	3.60092i
$523$	16.1224	+	27.9248i	0.704983	+	1.22107i	0.966698	+	0.255921i	$0.0823786\pi$
$523$	16.1224	+	27.9248i	0.704983	+	1.22107i	−0.261715	+	0.965145i	$0.584288\pi$
$524$	−26.5299	+	45.9512i	−1.15897	+	2.00739i
$525$	−16.8136			−0.733807
$526$	−3.14709	+	5.45092i	−0.137220	+	0.237672i
$527$	1.96505	−	3.40356i	0.0855989	−	0.148262i
$528$	154.215			6.71133
$529$	9.70262	−	16.8054i	0.421853	−	0.730671i
$530$	−22.4130	−	38.8205i	−0.973560	−	1.68626i
$531$	−4.37895	−	7.58457i	−0.190030	−	0.329142i
$532$	−67.7849			−2.93885
$533$	−3.42338	−	24.3626i	−0.148283	−	1.05526i
$534$	110.413			4.77804
$535$	−9.31509	−	16.1342i	−0.402726	−	0.697543i
$536$	−40.1298	−	69.5068i	−1.73334	−	3.00224i
$537$	13.6398	−	23.6248i	0.588600	−	1.01949i
$538$	10.5602			0.455283
$539$	−4.81770	+	8.34451i	−0.207513	+	0.359423i
$540$	−24.4822	+	42.4044i	−1.05355	+	1.82479i
$541$	−42.1436			−1.81189			−0.905947	−	0.423390i	$-0.860840\pi$
$541$	−42.1436			−1.81189			−0.905947	+	0.423390i	$0.860840\pi$
$542$	3.36091	−	5.82127i	0.144363	−	0.250045i
$543$	−15.4191	−	26.7067i	−0.661697	−	1.14609i
$544$	−41.0423	−	71.0873i	−1.75967	−	3.04784i
$545$	5.04917			0.216282
$546$	8.19023	+	58.2860i	0.350509	+	2.49441i
$547$	32.5367			1.39117			0.695585	−	0.718444i	$-0.255145\pi$
$547$	32.5367			1.39117			0.695585	+	0.718444i	$0.255145\pi$
$548$	52.5010	+	90.9343i	2.24273	+	3.88452i
$549$	−11.7672	−	20.3813i	−0.502210	−	0.869853i
$550$	−14.2361	+	24.6577i	−0.607029	+	1.05141i
$551$	−40.4337			−1.72253
$552$	−25.1594	+	43.5774i	−1.07086	+	1.85478i
$553$	7.55874	−	13.0921i	0.321430	−	0.556734i
$554$	−20.8319			−0.885062
$555$	−4.50329	+	7.79992i	−0.191154	+	0.331088i
$556$	12.9737	+	22.4711i	0.550208	+	0.952987i
$557$	7.32011	+	12.6788i	0.310163	+	0.537218i	0.978397	−	0.206733i	$-0.0662831\pi$
$557$	7.32011	+	12.6788i	0.310163	+	0.537218i	−0.668235	+	0.743951i	$0.732950\pi$
$558$	−13.9944			−0.592429
$559$	−13.7122	+	10.7127i	−0.579965	+	0.453097i
$560$	45.1462			1.90778
$561$	−20.8968	−	36.1943i	−0.882262	−	1.52812i
$562$	30.6258	+	53.0454i	1.29187	+	2.23759i
$563$	−10.1452	+	17.5720i	−0.427569	+	0.740571i	−0.996656	−	0.0817062i	$-0.973963\pi$
$563$	−10.1452	+	17.5720i	−0.427569	+	0.740571i	0.569088	+	0.822277i	$0.307296\pi$
$564$	−130.714			−5.50406
$565$	−1.14222	+	1.97838i	−0.0480535	+	0.0832310i
$566$	6.62566	−	11.4760i	0.278497	−	0.482371i
$567$	−4.18410			−0.175716
$568$	75.6348	−	131.003i	3.17356	−	5.49677i
$569$	16.7022	+	28.9290i	0.700192	+	1.21277i	0.968399	+	0.249406i	$0.0802354\pi$
$569$	16.7022	+	28.9290i	0.700192	+	1.21277i	−0.268207	+	0.963361i	$0.586431\pi$
$570$	−34.2807	−	59.3759i	−1.43586	−	2.48698i
$571$	−5.79670			−0.242584			−0.121292	−	0.992617i	$-0.538704\pi$
$571$	−5.79670			−0.242584			−0.121292	+	0.992617i	$0.538704\pi$
$572$	67.4905	+	27.2697i	2.82192	+	1.14020i
$573$	−39.2929			−1.64148
$574$	−19.5220	−	33.8131i	−0.814833	−	1.41133i
$575$	−2.65898	−	4.60548i	−0.110887	−	0.192062i
$576$	−71.6220	+	124.053i	−2.98425	+	5.16887i
$577$	−36.9609			−1.53870			−0.769352	−	0.638825i	$-0.779421\pi$
$577$	−36.9609			−1.53870			−0.769352	+	0.638825i	$0.779421\pi$
$578$	2.11642	−	3.66574i	0.0880313	−	0.152475i
$579$	21.7766	−	37.7181i	0.905004	−	1.56751i
$580$	54.4730			2.26187
$581$	−12.0367	+	20.8482i	−0.499366	+	0.864927i
$582$	−70.9587	−	122.904i	−2.94133	−	5.09454i
$583$	−20.7065	−	35.8646i	−0.857574	−	1.48536i
$584$	−25.3579			−1.04932
$585$	−21.6327	+	16.9005i	−0.894400	+	0.698750i
$586$	8.06818			0.333294
$587$	−13.1132	−	22.7128i	−0.541242	−	0.937458i	−0.998833	−	0.0482954i	$-0.984621\pi$
$587$	−13.1132	−	22.7128i	−0.541242	−	0.937458i	0.457591	−	0.889163i	$-0.348712\pi$
$588$	−19.9702	−	34.5894i	−0.823557	−	1.42644i
$589$	2.97816	−	5.15833i	0.122713	−	0.212545i
$590$	−6.87627			−0.283091
$591$	−15.1602	+	26.2582i	−0.623607	+	1.08012i
$592$	−15.4503	+	26.7606i	−0.635002	+	1.09986i
$593$	26.8828			1.10394			0.551972	−	0.833862i	$-0.313875\pi$
$593$	26.8828			1.10394			0.551972	+	0.833862i	$0.313875\pi$
$594$	−30.9702	+	53.6420i	−1.27072	+	2.20096i
$595$	−6.11751	−	10.5958i	−0.250794	−	0.434387i
$596$	47.5448	+	82.3501i	1.94751	+	3.37319i
$597$	−15.3959			−0.630114
$598$	−14.6701	+	11.4610i	−0.599905	+	0.468676i
$599$	−13.5483			−0.553567			−0.276784	−	0.960932i	$-0.589269\pi$
$599$	−13.5483			−0.553567			−0.276784	+	0.960932i	$0.589269\pi$
$600$	−37.2200	−	64.4669i	−1.51950	−	2.63185i
$601$	−22.7270	−	39.3642i	−0.927052	−	1.60570i	−0.788228	−	0.615384i	$-0.789001\pi$
$601$	−22.7270	−	39.3642i	−0.927052	−	1.60570i	−0.138824	−	0.990317i	$-0.544332\pi$
$602$	−13.8077	+	23.9157i	−0.562762	+	0.974732i
$603$	44.3352			1.80547
$604$	−9.70465	+	16.8090i	−0.394877	+	0.683947i
$605$	2.14438	−	3.71417i	0.0871813	−	0.151003i
$606$	−61.0736			−2.48094
$607$	−4.92037	+	8.52234i	−0.199712	+	0.345911i	−0.948435	−	0.316972i	$-0.897334\pi$
$607$	−4.92037	+	8.52234i	−0.199712	+	0.345911i	0.748723	+	0.662883i	$0.230667\pi$
$608$	−62.2023	−	107.738i	−2.52264	−	4.36934i
$609$	20.3463	+	35.2409i	0.824475	+	1.42803i
$610$	−18.4780			−0.748151
$611$	−28.2807	−	11.4269i	−1.14411	−	0.462282i
$612$	109.384			4.42159
$613$	−8.84674	−	15.3230i	−0.357316	−	0.618890i	0.630195	−	0.776437i	$-0.282975\pi$
$613$	−8.84674	−	15.3230i	−0.357316	−	0.618890i	−0.987512	+	0.157547i	$0.949642\pi$
$614$	−11.3443	−	19.6490i	−0.457821	−	0.792969i
$615$	14.4205	−	24.9771i	0.581492	−	1.00717i
$616$	72.8632			2.93574
$617$	4.83822	−	8.38004i	0.194779	−	0.337368i	−0.752049	−	0.659107i	$-0.770934\pi$
$617$	4.83822	−	8.38004i	0.194779	−	0.337368i	0.946828	+	0.321740i	$0.104268\pi$
$618$	7.66066	−	13.2686i	0.308157	−	0.533743i
$619$	20.0237			0.804820			0.402410	−	0.915460i	$-0.368173\pi$
$619$	20.0237			0.804820			0.402410	+	0.915460i	$0.368173\pi$
$620$	−4.01224	+	6.94940i	−0.161135	+	0.279095i
$621$	−5.78453	−	10.0191i	−0.232125	−	0.402053i
$622$	14.8410	+	25.7053i	0.595069	+	1.03069i
$623$	29.8622			1.19640
$624$	−117.547	+	91.8338i	−4.70566	+	3.67629i
$625$	−3.10855			−0.124342
$626$	−18.6376	−	32.2813i	−0.744909	−	1.29022i
$627$	−31.6705	−	54.8548i	−1.26480	−	2.19069i
$628$	−28.9307	+	50.1095i	−1.15446	+	1.99959i
$629$	8.37432			0.333906
$630$	−21.7834	+	37.7299i	−0.867871	+	1.50320i
$631$	11.7990	−	20.4365i	0.469711	−	0.813564i	−0.529689	−	0.848192i	$-0.677691\pi$
$631$	11.7990	−	20.4365i	0.469711	−	0.813564i	0.999400	+	0.0346282i	$0.0110247\pi$
$632$	66.9305			2.66235
$633$	2.05167	−	3.55360i	0.0815467	−	0.141243i
$634$	17.3040	+	29.9713i	0.687228	+	1.19031i
$635$	−9.35679	−	16.2064i	−0.371313	−	0.643133i
$636$	171.664			6.80690
$637$	−1.29689	−	9.22936i	−0.0513847	−	0.365681i
$638$	68.9090			2.72813
$639$	41.7805	+	72.3659i	1.65281	+	2.86275i
$640$	25.2890	+	43.8019i	0.999636	+	1.73142i
$641$	3.83536	−	6.64303i	0.151487	−	0.262384i	−0.780287	−	0.625422i	$-0.784927\pi$
$641$	3.83536	−	6.64303i	0.151487	−	0.262384i	0.931774	+	0.363038i	$0.118260\pi$
$642$	97.6909			3.85555
$643$	1.90940	−	3.30718i	0.0752994	−	0.130422i	−0.825917	−	0.563792i	$-0.809342\pi$
$643$	1.90940	−	3.30718i	0.0752994	−	0.130422i	0.901216	+	0.433369i	$0.142675\pi$
$644$	−10.7885	+	18.6861i	−0.425125	+	0.736337i
$645$	−20.3990			−0.803212
$646$	−31.8742	+	55.2077i	−1.25407	+	2.17212i
$647$	24.6814	+	42.7494i	0.970325	+	1.68065i	0.694571	+	0.719424i	$0.255594\pi$
$647$	24.6814	+	42.7494i	0.970325	+	1.68065i	0.275754	+	0.961228i	$0.411073\pi$
$648$	−9.26226	−	16.0427i	−0.363856	−	0.630217i
$649$	−6.35269			−0.249365
$650$	−3.83226	−	27.2724i	−0.150313	−	1.06971i
$651$	−5.99448			−0.234942
$652$	−12.9964	−	22.5105i	−0.508980	−	0.881579i
$653$	−9.94200	−	17.2200i	−0.389060	−	0.673872i	0.603263	−	0.797542i	$-0.293867\pi$
$653$	−9.94200	−	17.2200i	−0.389060	−	0.673872i	−0.992323	+	0.123670i	$0.960534\pi$
$654$	−13.2381	+	22.9291i	−0.517652	+	0.896599i
$655$	−14.5149			−0.567143
$656$	49.4752	−	85.6936i	1.93168	−	3.34577i
$657$	7.00381	−	12.1310i	0.273245	−	0.473274i
$658$	−48.4076			−1.88712
$659$	−1.83821	+	3.18387i	−0.0716065	+	0.124026i	−0.899606	−	0.436703i	$-0.856146\pi$
$659$	−1.83821	+	3.18387i	−0.0716065	+	0.124026i	0.827999	+	0.560730i	$0.189479\pi$
$660$	42.6670	+	73.9015i	1.66081	+	2.87661i
$661$	−1.60745	−	2.78419i	−0.0625226	−	0.108292i	0.833070	−	0.553168i	$-0.186581\pi$
$661$	−1.60745	−	2.78419i	−0.0625226	−	0.108292i	−0.895592	+	0.444876i	$0.853248\pi$
$662$	42.2397			1.64169
$663$	37.4816	+	15.1445i	1.45567	+	0.588165i
$664$	−106.582			−4.13617
$665$	−9.27150	−	16.0587i	−0.359533	−	0.622730i
$666$	−14.9097	−	25.8244i	−0.577740	−	1.00068i
$667$	−6.43531	+	11.1463i	−0.249176	+	0.431586i
$668$	−8.72435			−0.337555
$669$	−16.4136	+	28.4291i	−0.634585	+	1.09913i
$670$	17.4049	−	30.1462i	0.672410	−	1.16465i
$671$	−17.0710			−0.659019
$672$	−62.6008	+	108.428i	−2.41488	+	4.18269i
$673$	−4.96414	−	8.59814i	−0.191353	−	0.331434i	0.754346	−	0.656478i	$-0.227954\pi$
$673$	−4.96414	−	8.59814i	−0.191353	−	0.331434i	−0.945699	+	0.325044i	$0.894621\pi$
$674$	1.54560	+	2.67706i	0.0595343	+	0.103116i
$675$	17.1149			0.658751
$676$	−67.6823	+	19.4043i	−2.60317	+	0.746319i
$677$	20.3472			0.782006			0.391003	−	0.920389i	$-0.372128\pi$
$677$	20.3472			0.782006			0.391003	+	0.920389i	$0.372128\pi$
$678$	−5.98943	−	10.3740i	−0.230023	−	0.398411i
$679$	−19.1914	−	33.2405i	−0.736498	−	1.27565i
$680$	27.0844	−	46.9116i	1.03864	−	1.79898i
$681$	−1.97313			−0.0756104
$682$	−5.07553	+	8.79107i	−0.194352	+	0.336628i
$683$	−8.31406	+	14.4004i	−0.318129	+	0.551015i	−0.980098	−	0.198516i	$-0.936388\pi$
$683$	−8.31406	+	14.4004i	−0.318129	+	0.551015i	0.661969	+	0.749531i	$0.269721\pi$
$684$	165.779			6.33872
$685$	−14.3620	+	24.8757i	−0.548743	+	0.950451i
$686$	−27.4230	−	47.4980i	−1.04701	−	1.81348i
$687$	−27.2885	−	47.2651i	−1.04112	−	1.80328i
$688$	−69.9867			−2.66822
$689$	37.1403	+	15.0066i	1.41493	+	0.571707i
$690$	−21.8241			−0.830828
$691$	−9.90330	−	17.1530i	−0.376739	−	0.652532i	0.613846	−	0.789425i	$-0.289621\pi$
$691$	−9.90330	−	17.1530i	−0.376739	−	0.652532i	−0.990586	+	0.136894i	$0.956288\pi$
$692$	4.88232	+	8.45643i	0.185598	+	0.321465i
$693$	−20.1247	+	34.8571i	−0.764476	+	1.32411i
$694$	85.4345			3.24305
$695$	−3.54904	+	6.14712i	−0.134623	+	0.233174i
$696$	−90.0806	+	156.024i	−3.41450	+	5.91408i
$697$	−26.8164			−1.01575
$698$	4.83397	−	8.37269i	0.182969	−	0.316911i
$699$	34.8533	+	60.3677i	1.31827	+	2.28332i
$700$	−15.9600	−	27.6436i	−0.603233	−	1.04483i
$701$	40.8641			1.54342			0.771709	−	0.635976i	$-0.219402\pi$
$701$	40.8641			1.54342			0.771709	+	0.635976i	$0.219402\pi$
$702$	−8.33697	−	59.3303i	−0.314659	−	2.23928i
$703$	12.6918			0.478682
$704$	51.9522	+	89.9839i	1.95802	+	3.39140i
$705$	−17.8789	−	30.9671i	−0.673357	−	1.16629i
$706$	34.8342	−	60.3345i	1.31100	−	2.27072i
$707$	−16.5179			−0.621218
$708$	13.1665	−	22.8050i	0.494827	−	0.857066i
$709$	4.09621	−	7.09485i	0.153836	−	0.266453i	−0.778798	−	0.627274i	$-0.784170\pi$
$709$	4.09621	−	7.09485i	0.153836	−	0.266453i	0.932635	+	0.360822i	$0.117504\pi$
$710$	65.6079			2.46222
$711$	−18.4861	+	32.0189i	−0.693285	+	1.20080i
$712$	66.1053	+	114.498i	2.47740	+	4.29099i
$713$	−0.947992	−	1.64197i	−0.0355026	−	0.0614923i
$714$	64.1567			2.40100
$715$	2.77085	+	19.7189i	0.103624	+	0.737444i
$716$	51.7894			1.93546
$717$	16.7070	+	28.9374i	0.623934	+	1.08069i
$718$	37.6792	+	65.2623i	1.40618	+	2.43557i
$719$	19.1731	−	33.2088i	0.715036	−	1.23848i	−0.247909	−	0.968783i	$-0.579743\pi$
$719$	19.1731	−	33.2088i	0.715036	−	1.23848i	0.962945	−	0.269696i	$-0.0869233\pi$
$720$	−110.412			−4.11483
$721$	2.07189	−	3.58862i	0.0771612	−	0.133647i
$722$	−22.4366	+	38.8613i	−0.835004	+	1.44627i
$723$	−66.9775			−2.49092
$724$	29.2727	−	50.7018i	1.08791	−	1.88432i
$725$	−9.52017	−	16.4894i	−0.353570	−	0.612402i
$726$	11.2444	+	19.4760i	0.417321	+	0.722820i
$727$	−11.3527			−0.421047			−0.210524	−	0.977589i	$-0.567517\pi$
$727$	−11.3527			−0.421047			−0.210524	+	0.977589i	$0.567517\pi$
$728$	−55.5387	+	43.3896i	−2.05840	+	1.60812i
$729$	−41.9906			−1.55521
$730$	−5.49904	−	9.52462i	−0.203529	−	0.352522i
$731$	9.48352	+	16.4259i	0.350761	+	0.607535i
$732$	35.3811	−	61.2819i	1.30772	−	2.26504i
$733$	16.1295			0.595756			0.297878	−	0.954604i	$-0.403721\pi$
$733$	16.1295			0.595756			0.297878	+	0.954604i	$0.403721\pi$
$734$	−2.80920	+	4.86569i	−0.103690	+	0.179596i
$735$	5.46298	−	9.46216i	0.201505	−	0.349017i
$736$	−39.5998			−1.45967
$737$	16.0796	−	27.8508i	0.592301	−	1.02590i
$738$	47.7443	+	82.6956i	1.75749	+	3.04407i
$739$	−3.38951	−	5.87081i	−0.124685	−	0.215961i	0.796925	−	0.604079i	$-0.206459\pi$
$739$	−3.38951	−	5.87081i	−0.124685	−	0.215961i	−0.921610	+	0.388118i	$0.873125\pi$
$740$	−17.0987			−0.628560
$741$	56.8059	+	22.9526i	2.08682	+	0.843184i
$742$	63.5724			2.33382
$743$	−21.0377	−	36.4384i	−0.771799	−	1.33680i	−0.936576	−	0.350464i	$-0.886024\pi$
$743$	−21.0377	−	36.4384i	−0.771799	−	1.33680i	0.164777	−	0.986331i	$-0.447310\pi$
$744$	−13.2699	−	22.9841i	−0.486497	−	0.842637i
$745$	−13.0062	+	22.5274i	−0.476510	+	0.825340i
$746$	22.3064			0.816694
$747$	29.4377	−	50.9876i	1.07707	−	1.86554i
$748$	39.6718	−	68.7136i	1.45055	−	2.51242i
$749$	26.4213			0.965415
$750$	44.9196	−	77.8029i	1.64023	−	2.84096i
$751$	−3.24907	−	5.62755i	−0.118560	−	0.205352i	0.800637	−	0.599150i	$-0.204495\pi$
$751$	−3.24907	−	5.62755i	−0.118560	−	0.205352i	−0.919197	+	0.393797i	$0.871161\pi$
$752$	−61.3403	−	106.245i	−2.23685	−	3.87434i
$753$	9.38702			0.342082
$754$	−52.5247	+	41.0349i	−1.91284	+	1.49440i
$755$	−5.30954			−0.193234
$756$	−34.7207	−	60.1379i	−1.26278	−	2.18720i
$757$	−21.0894	−	36.5280i	−0.766508	−	1.32763i	−0.939445	−	0.342698i	$-0.888659\pi$
$757$	−21.0894	−	36.5280i	−0.766508	−	1.32763i	0.172937	−	0.984933i	$-0.444674\pi$
$758$	−1.33356	+	2.30980i	−0.0484372	+	0.0838957i
$759$	−20.1623			−0.731846
$760$	41.0483	−	71.0977i	1.48898	−	2.57899i
$761$	−1.88043	+	3.25700i	−0.0681655	+	0.118066i	−0.898094	−	0.439804i	$-0.855048\pi$
$761$	−1.88043	+	3.25700i	−0.0681655	+	0.118066i	0.829928	+	0.557870i	$0.188381\pi$
$762$	98.1282			3.55481
$763$	−3.58036	+	6.20137i	−0.129618	+	0.224505i
$764$	−37.2981	−	64.6023i	−1.34940	−	2.33723i
$765$	14.9614	+	25.9139i	0.540930	+	0.936918i
$766$	15.3133			0.553291
$767$	4.84223	−	3.78299i	0.174843	−	0.136596i
$768$	−106.170			−3.83108
$769$	25.4457	+	44.0732i	0.917594	+	1.58932i	0.803058	+	0.595901i	$0.203205\pi$
$769$	25.4457	+	44.0732i	0.917594	+	1.58932i	0.114536	+	0.993419i	$0.463462\pi$
$770$	15.8009	+	27.3680i	0.569426	+	0.986275i
$771$	−3.29107	+	5.70030i	−0.118525	+	0.205291i
$772$	82.6842			2.97587
$773$	1.96101	−	3.39657i	0.0705326	−	0.122166i	−0.828602	−	0.559838i	$-0.810863\pi$
$773$	1.96101	−	3.39657i	0.0705326	−	0.122166i	0.899135	+	0.437672i	$0.144197\pi$
$774$	33.7691	−	58.4898i	1.21381	−	2.10237i
$775$	2.80485			0.100753
$776$	84.9673	−	147.168i	3.05015	−	5.28301i
$777$	−6.38657	−	11.0619i	−0.229117	−	0.396842i
$778$	−21.2442	−	36.7960i	−0.761640	−	1.31920i
$779$	−40.6421			−1.45616
$780$	−76.5301	−	30.9221i	−2.74022	−	1.10719i
$781$	60.6123			2.16888
$782$	10.1460	+	17.5734i	0.362820	+	0.628424i
$783$	−20.7109	−	35.8723i	−0.740146	−	1.28197i
$784$	18.7428	−	32.4636i	0.669387	−	1.15941i
$785$	−15.8284			−0.564939
$786$	38.0557	−	65.9145i	1.35740	−	2.35109i
$787$	−10.1688	+	17.6129i	−0.362479	+	0.627832i	−0.988368	−	0.152080i	$-0.951403\pi$
$787$	−10.1688	+	17.6129i	−0.362479	+	0.627832i	0.625889	+	0.779912i	$0.284736\pi$
$788$	−57.5623			−2.05057
$789$	3.29689	−	5.71038i	0.117372	−	0.203295i
$790$	14.5144	+	25.1397i	0.516399	+	0.894429i
$791$	−1.61989	−	2.80574i	−0.0575968	−	0.0997606i
$792$	−178.199			−6.33203
$793$	13.0121	−	10.1657i	0.462072	−	0.360994i
$794$	−99.9576			−3.54736
$795$	23.4799	+	40.6683i	0.832745	+	1.44236i
$796$	−14.6143	−	25.3128i	−0.517992	−	0.897188i
$797$	−27.3191	+	47.3181i	−0.967693	+	1.67609i	−0.265496	+	0.964112i	$0.585536\pi$
$797$	−27.3191	+	47.3181i	−0.967693	+	1.67609i	−0.702198	+	0.711982i	$0.747798\pi$
$798$	97.2337			3.44204
$799$	−16.6238	+	28.7932i	−0.588107	+	1.01863i
$800$	29.2913	−	50.7340i	1.03560	−	1.79372i
$801$	−73.0329			−2.58049
$802$	1.52361	−	2.63897i	0.0538005	−	0.0931853i
$803$	−5.08033	−	8.79939i	−0.179281	−	0.310524i
$804$	66.6529	+	115.446i	2.35067	+	4.07147i
$805$	−5.90251			−0.208036
$806$	−1.36630	−	9.72328i	−0.0481257	−	0.342488i
$807$	−11.0629			−0.389431
$808$	−36.5653	−	63.3329i	−1.28636	−	2.22804i
$809$	1.62909	+	2.82167i	0.0572758	+	0.0992045i	0.893242	−	0.449577i	$-0.148425\pi$
$809$	1.62909	+	2.82167i	0.0572758	+	0.0992045i	−0.835966	+	0.548781i	$0.815092\pi$
$810$	4.01718	−	6.95797i	0.141149	−	0.244478i
$811$	7.90675			0.277644			0.138822	−	0.990317i	$-0.455668\pi$
$811$	7.90675			0.277644			0.138822	+	0.990317i	$0.455668\pi$
$812$	−38.6269	+	66.9037i	−1.35554	+	2.34786i
$813$	−3.52088	+	6.09835i	−0.123483	+	0.213878i
$814$	−21.6300			−0.758132
$815$	3.55526	−	6.15789i	0.124535	−	0.215702i
$816$	81.2970	+	140.811i	2.84597	+	4.92936i
$817$	14.3729	+	24.8946i	0.502844	+	0.870952i
$818$	−40.0812			−1.40140
$819$	−5.41744	−	38.5533i	−0.189301	−	1.34716i
$820$	54.7538			1.91209
$821$	−4.00911	−	6.94397i	−0.139919	−	0.242346i	0.787547	−	0.616255i	$-0.211351\pi$
$821$	−4.00911	−	6.94397i	−0.139919	−	0.242346i	−0.927466	+	0.373908i	$0.878017\pi$
$822$	−75.3098	−	130.440i	−2.62673	−	4.54963i
$823$	26.1716	−	45.3305i	0.912284	−	1.58012i	0.101454	−	0.994840i	$-0.467650\pi$
$823$	26.1716	−	45.3305i	0.912284	−	1.58012i	0.810830	−	0.585282i	$-0.199016\pi$
$824$	18.3460			0.639114
$825$	14.9137	−	25.8313i	0.519229	−	0.899331i
$826$	4.87596	−	8.44542i	0.169656	−	0.293854i
$827$	−33.0105			−1.14789			−0.573944	−	0.818895i	$-0.694587\pi$
$827$	−33.0105			−1.14789			−0.573944	+	0.818895i	$0.694587\pi$
$828$	26.3849	−	45.7000i	0.916940	−	1.58819i
$829$	27.1119	+	46.9592i	0.941634	+	1.63096i	0.762353	+	0.647161i	$0.224044\pi$
$829$	27.1119	+	46.9592i	0.941634	+	1.63096i	0.179281	+	0.983798i	$0.442623\pi$
$830$	−23.1130	−	40.0329i	−0.802264	−	1.38956i
$831$	21.8234			0.757047
$832$	−93.1845	−	37.6514i	−3.23059	−	1.30533i
$833$	−10.1590			−0.351987
$834$	−18.6101	−	32.2336i	−0.644414	−	1.11616i
$835$	−1.19330	−	2.06686i	−0.0412959	−	0.0715266i
$836$	60.1253	−	104.140i	2.07948	−	3.60176i
$837$	6.10188			0.210912
$838$	−16.3381	+	28.2984i	−0.564389	+	0.977551i
$839$	4.03759	−	6.99332i	0.139393	−	0.241436i	−0.787874	−	0.615837i	$-0.788818\pi$
$839$	4.03759	−	6.99332i	0.139393	−	0.241436i	0.927267	+	0.374401i	$0.122151\pi$
$840$	−82.6224			−2.85074
$841$	−8.54093	+	14.7933i	−0.294515	+	0.510114i
$842$	−16.6401	−	28.8216i	−0.573457	−	0.993257i
$843$	−32.0835	−	55.5703i	−1.10502	−	1.91394i
$844$	7.79007			0.268145
$845$	−13.8545	−	13.3803i	−0.476609	−	0.460297i
$846$	118.389			4.07029
$847$	3.04116	+	5.26744i	0.104495	+	0.180991i
$848$	80.5566	+	139.528i	2.76633	+	4.79142i
$849$	−6.94102	+	12.0222i	−0.238215	+	0.412601i
$850$	−30.0193			−1.02965
$851$	2.02000	−	3.49874i	0.0692446	−	0.119935i
$852$	−125.624	+	217.588i	−4.30381	+	7.45443i
$853$	46.7327			1.60010			0.800048	−	0.599936i	$-0.204807\pi$
$853$	46.7327			1.60010			0.800048	+	0.599936i	$0.204807\pi$
$854$	13.1027	−	22.6946i	0.448366	−	0.776593i
$855$	22.6750	+	39.2742i	0.775468	+	1.34315i
$856$	58.4884	+	101.305i	1.99909	+	3.46253i
$857$	−32.8329			−1.12155			−0.560775	−	0.827969i	$-0.689497\pi$
$857$	−32.8329			−1.12155			−0.560775	+	0.827969i	$0.689497\pi$
$858$	−96.8114	−	39.1169i	−3.30509	−	1.33543i
$859$	26.8471			0.916013			0.458006	−	0.888949i	$-0.348564\pi$
$859$	26.8471			0.916013			0.458006	+	0.888949i	$0.348564\pi$
$860$	−19.3635	−	33.5385i	−0.660288	−	1.14365i
$861$	20.4512	+	35.4226i	0.696976	+	1.20720i
$862$	28.2679	−	48.9615i	0.962810	−	1.66764i
$863$	28.8717			0.982805			0.491402	−	0.870933i	$-0.336484\pi$
$863$	28.8717			0.982805			0.491402	+	0.870933i	$0.336484\pi$
$864$	63.7223	−	110.370i	2.16788	−	3.75488i
$865$	−1.33559	+	2.31331i	−0.0454115	+	0.0786550i
$866$	25.8543			0.878565
$867$	−2.21715	+	3.84022i	−0.0752985	+	0.130421i
$868$	−5.69016	−	9.85564i	−0.193137	−	0.334522i
$869$	13.4092	+	23.2255i	0.454877	+	0.787870i
$870$	−78.1386			−2.64915
$871$	4.32852	+	30.8041i	0.146666	+	1.04376i
$872$	−31.7031			−1.07360
$873$	46.9357	+	81.2951i	1.58853	+	2.75142i
$874$	15.3770	+	26.6337i	0.520133	+	0.900897i
$875$	12.1489	−	21.0425i	0.410707	−	0.711366i
$876$	42.1177			1.42302
$877$	−18.6893	+	32.3708i	−0.631093	+	1.09309i	0.356235	+	0.934396i	$0.384060\pi$
$877$	−18.6893	+	32.3708i	−0.631093	+	1.09309i	−0.987329	+	0.158689i	$0.949273\pi$
$878$	−50.8722	+	88.1132i	−1.71685	+	2.97368i
$879$	−8.45221			−0.285086
$880$	−40.0448	+	69.3596i	−1.34991	+	2.33811i
$881$	−2.44268	−	4.23085i	−0.0822961	−	0.142541i	0.821940	−	0.569574i	$-0.192892\pi$
$881$	−2.44268	−	4.23085i	−0.0822961	−	0.142541i	−0.904236	+	0.427033i	$0.859559\pi$
$882$	18.0871	+	31.3278i	0.609025	+	1.05486i
$883$	6.40509			0.215548			0.107774	−	0.994175i	$-0.465628\pi$
$883$	6.40509			0.215548			0.107774	+	0.994175i	$0.465628\pi$
$884$	10.6794	+	76.0001i	0.359186	+	2.55616i
$885$	7.20356			0.242145
$886$	−6.69434	−	11.5949i	−0.224901	−	0.389539i
$887$	8.15671	+	14.1278i	0.273875	+	0.474366i	0.969851	−	0.243699i	$-0.0783611\pi$
$887$	8.15671	+	14.1278i	0.273875	+	0.474366i	−0.695975	+	0.718066i	$0.745028\pi$
$888$	28.2756	−	48.9748i	0.948868	−	1.64349i
$889$	26.5396			0.890110
$890$	−28.6709	+	49.6594i	−0.961050	+	1.66459i
$891$	3.71131	−	6.42817i	0.124333	−	0.215352i
$892$	−62.3212			−2.08667
$893$	−25.1945	+	43.6381i	−0.843100	+	1.46029i
$894$	−68.2005	−	118.127i	−2.28097	−	3.95075i
$895$	7.08366	+	12.2693i	0.236781	+	0.410116i
$896$	−71.7298			−2.39633
$897$	15.3684	−	12.0065i	0.513135	−	0.400886i
$898$	−63.3483			−2.11396
$899$	−3.39418	−	5.87889i	−0.113202	−	0.196072i
$900$	39.0329	+	67.6070i	1.30110	+	2.25357i
$901$	21.8316	−	37.8134i	0.727315	−	1.25975i
$902$	69.2642			2.30625
$903$	14.4650	−	25.0541i	0.481364	−	0.833747i
$904$	7.17186	−	12.4220i	0.238532	−	0.413150i
$905$	16.0155			0.532372
$906$	13.9208	−	24.1115i	0.462487	−	0.801052i
$907$	−22.0645	−	38.2169i	−0.732641	−	1.26897i	−0.955751	−	0.294178i	$-0.904954\pi$
$907$	−22.0645	−	38.2169i	−0.732641	−	1.26897i	0.223110	−	0.974793i	$-0.428379\pi$
$908$	−1.87296	−	3.24406i	−0.0621563	−	0.107658i
$909$	40.3972			1.33989
$910$	−28.3415	−	11.4514i	−0.939510	−	0.379611i
$911$	−21.0194			−0.696404			−0.348202	−	0.937420i	$-0.613208\pi$
$911$	−21.0194			−0.696404			−0.348202	+	0.937420i	$0.613208\pi$
$912$	123.211	+	213.408i	4.07993	+	7.06664i
$913$	−21.3531	−	36.9847i	−0.706685	−	1.22401i
$914$	−17.1587	+	29.7197i	−0.567558	+	0.983040i
$915$	19.3575			0.639938
$916$	51.8064	−	89.7313i	1.71173	−	2.96480i
$917$	10.2925	−	17.8271i	0.339888	−	0.588704i
$918$	−65.3061			−2.15542
$919$	−5.15371	+	8.92650i	−0.170005	+	0.294458i	−0.938421	−	0.345493i	$-0.887712\pi$
$919$	−5.15371	+	8.92650i	−0.170005	+	0.294458i	0.768416	+	0.639951i	$0.221045\pi$
$920$	−13.0663	−	22.6314i	−0.430782	−	0.746136i
$921$	11.8843	+	20.5842i	0.391602	+	0.678274i
$922$	94.8160			3.12260
$923$	−46.2007	+	36.0943i	−1.52071	+	1.18806i
$924$	−121.021			−3.98129
$925$	2.98831	+	5.17591i	0.0982551	+	0.170183i
$926$	−3.41559	−	5.91598i	−0.112243	−	0.194411i
$927$	−5.06715	+	8.77656i	−0.166427	+	0.288260i
$928$	−141.783			−4.65424
$929$	−21.6193	+	37.4457i	−0.709306	+	1.22855i	0.255809	+	0.966727i	$0.417658\pi$
$929$	−21.6193	+	37.4457i	−0.709306	+	1.22855i	−0.965115	+	0.261827i	$0.915675\pi$
$930$	5.75534	−	9.96854i	0.188725	−	0.326881i
$931$	−15.3966			−0.504603
$932$	−66.1679	+	114.606i	−2.16740	+	3.75405i
$933$	−15.5474	−	26.9289i	−0.508999	−	0.881611i
$934$	4.32537	+	7.49176i	0.141530	+	0.245138i
$935$	21.7050			0.709829
$936$	135.829	−	106.116i	4.43971	−	3.46852i
$937$	−9.89909			−0.323389			−0.161695	−	0.986841i	$-0.551696\pi$
$937$	−9.89909			−0.323389			−0.161695	+	0.986841i	$0.551696\pi$
$938$	24.6836	+	42.7533i	0.805949	+	1.39594i
$939$	19.5247	+	33.8178i	0.637166	+	1.10360i
$940$	33.9424	−	58.7900i	1.10708	−	1.91752i
$941$	38.5248			1.25587			0.627937	−	0.778264i	$-0.283900\pi$
$941$	38.5248			1.25587			0.627937	+	0.778264i	$0.283900\pi$
$942$	41.4996	−	71.8794i	1.35213	−	2.34196i
$943$	−6.46849	+	11.2037i	−0.210643	+	0.364844i
$944$	24.7146			0.804391
$945$	9.49806	−	16.4511i	0.308972	−	0.535155i
$946$	−24.4950	−	42.4266i	−0.796401	−	1.37941i
$947$	−29.8378	−	51.6806i	−0.969599	−	1.67940i	−0.696714	−	0.717349i	$-0.745356\pi$
$947$	−29.8378	−	51.6806i	−0.969599	−	1.67940i	−0.272885	−	0.962047i	$-0.587978\pi$
$948$	−111.167			−3.61054
$949$	9.11237	+	3.68188i	0.295800	+	0.119519i
$950$	−45.4962			−1.47609
$951$	−18.1276	−	31.3979i	−0.587828	−	1.01815i
$952$	38.4112	+	66.5301i	1.24491	+	2.15625i
$953$	−19.7324	+	34.1776i	−0.639196	+	1.10712i	0.346414	+	0.938082i	$0.387399\pi$
$953$	−19.7324	+	34.1776i	−0.639196	+	1.10712i	−0.985610	+	0.169038i	$0.945934\pi$
$954$	−155.477			−5.03374
$955$	10.2032	−	17.6724i	0.330166	−	0.571865i
$956$	−31.7177	+	54.9366i	−1.02582	+	1.77678i
$957$	−72.1890			−2.33354
$958$	−8.40530	+	14.5584i	−0.271563	+	0.470361i
$959$	−20.3682	−	35.2787i	−0.657723	−	1.13921i
$960$	−58.9106	−	102.036i	−1.90133	−	3.29320i
$961$	1.00000			0.0322581
$962$	16.4871	−	12.8805i	0.531566	−	0.415285i
$963$	−64.6177			−2.08228
$964$	−63.5773	−	110.119i	−2.04769	−	3.54670i
$965$	11.3094	+	19.5885i	0.364063	+	0.630575i
$966$	15.4754	−	26.8043i	0.497914	−	0.862413i
$967$	−26.7494			−0.860203			−0.430102	−	0.902781i	$-0.641522\pi$
$967$	−26.7494			−0.860203			−0.430102	+	0.902781i	$0.641522\pi$
$968$	−13.4643	+	23.3209i	−0.432759	+	0.749561i
$969$	33.3913	−	57.8355i	1.07268	−	1.85794i
$970$	73.7032			2.36647
$971$	19.9352	−	34.5288i	0.639751	−	1.10808i	−0.345736	−	0.938332i	$-0.612371\pi$
$971$	19.9352	−	34.5288i	0.639751	−	1.10808i	0.985487	−	0.169750i	$-0.0542959\pi$
$972$	−34.1884	−	59.2160i	−1.09659	−	1.89935i
$973$	−5.03325	−	8.71785i	−0.161359	−	0.279481i
$974$	−29.8464			−0.956340
$975$	4.01466	+	28.5705i	0.128572	+	0.914987i
$976$	66.4132			2.12584
$977$	21.8226	+	37.7978i	0.698166	+	1.20926i	0.969102	+	0.246662i	$0.0793338\pi$
$977$	21.8226	+	37.7978i	0.698166	+	1.20926i	−0.270935	+	0.962598i	$0.587333\pi$
$978$	18.6427	+	32.2901i	0.596127	+	1.03252i
$979$	−26.4878	+	45.8782i	−0.846554	+	1.46627i
$980$	20.7426			0.662597
$981$	8.75637	−	15.1665i	0.279569	−	0.484228i
$982$	23.3149	−	40.3825i	0.744007	−	1.28866i
$983$	12.2883			0.391937			0.195969	−	0.980610i	$-0.437215\pi$
$983$	12.2883			0.391937			0.195969	+	0.980610i	$0.437215\pi$
$984$	−90.5449	+	156.828i	−2.88647	+	4.99951i
$985$	−7.87327	−	13.6369i	−0.250863	−	0.434508i
$986$	36.3267	+	62.9196i	1.15688	+	2.00377i
$987$	50.7117			1.61417
$988$	16.1853	+	115.183i	0.514923	+	3.66447i
$989$	9.15021			0.290960
$990$	−38.6438	−	66.9330i	−1.22818	−	2.12727i
$991$	17.7089	+	30.6727i	0.562541	+	0.974349i	0.997274	+	0.0737897i	$0.0235094\pi$
$991$	17.7089	+	30.6727i	0.562541	+	0.974349i	−0.434733	+	0.900559i	$0.643157\pi$
$992$	10.4431	−	18.0879i	0.331568	−	0.574292i
$993$	−44.2502			−1.40424
$994$	−46.5226	+	80.5794i	−1.47561	+	2.55582i
$995$	3.99785	−	6.92448i	0.126740	−	0.219521i
$996$	177.025			5.60924
$997$	−11.7059	+	20.2753i	−0.370731	+	0.642125i	−0.989678	−	0.143308i	$-0.954226\pi$
$997$	−11.7059	+	20.2753i	−0.370731	+	0.642125i	0.618947	+	0.785432i	$0.287559\pi$
$998$	15.8673	+	27.4830i	0.502270	+	0.869958i
$999$	6.50099	+	11.2600i	0.205682	+	0.356252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.b.94.1	✓	34
13.3	even	3		5239.2.a.m.1.17		17
13.9	even	3	inner	403.2.f.b.373.1	yes	34
13.10	even	6		5239.2.a.n.1.1		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.b.94.1	✓	34	1.1	even	1	trivial
403.2.f.b.373.1	yes	34	13.9	even	3	inner
5239.2.a.m.1.17		17	13.3	even	3
5239.2.a.n.1.1		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)

\(f(q)\)	\(=\)	\(q+(-1.36162 - 2.35840i) q^{2} +(1.42643 + 2.47066i) q^{3} +(-2.70804 + 4.69046i) q^{4} -1.48160 q^{5} +(3.88453 - 6.72821i) q^{6} +(1.05061 - 1.81970i) q^{7} +9.30282 q^{8} +(-2.56943 + 4.45038i) q^{9} +O(q^{10})\)	\(q+(-1.36162 - 2.35840i) q^{2} +(1.42643 + 2.47066i) q^{3} +(-2.70804 + 4.69046i) q^{4} -1.48160 q^{5} +(3.88453 - 6.72821i) q^{6} +(1.05061 - 1.81970i) q^{7} +9.30282 q^{8} +(-2.56943 + 4.45038i) q^{9} +(2.01739 + 3.49422i) q^{10} +(1.86378 + 3.22816i) q^{11} -15.4514 q^{12} +(-3.34298 - 1.35074i) q^{13} -5.72212 q^{14} +(-2.11341 - 3.66053i) q^{15} +(-7.25086 - 12.5589i) q^{16} +(-1.96505 + 3.40356i) q^{17} +13.9944 q^{18} +(-2.97816 + 5.15833i) q^{19} +(4.01224 - 6.94940i) q^{20} +5.99448 q^{21} +(5.07553 - 8.79107i) q^{22} +(0.947992 + 1.64197i) q^{23} +(13.2699 + 22.9841i) q^{24} -2.80485 q^{25} +(1.36630 + 9.72328i) q^{26} -6.10188 q^{27} +(5.69016 + 9.85564i) q^{28} +(3.39418 + 5.87889i) q^{29} +(-5.75534 + 9.96854i) q^{30} -1.00000 q^{31} +(-10.4431 + 18.0879i) q^{32} +(-5.31711 + 9.20951i) q^{33} +10.7026 q^{34} +(-1.55658 + 2.69608i) q^{35} +(-13.9162 - 24.1036i) q^{36} +(-1.06541 - 1.84534i) q^{37} +16.2206 q^{38} +(-1.43133 - 10.1861i) q^{39} -13.7831 q^{40} +(3.41168 + 5.90920i) q^{41} +(-8.16222 - 14.1374i) q^{42} +(2.41305 - 4.17952i) q^{43} -20.1887 q^{44} +(3.80687 - 6.59370i) q^{45} +(2.58162 - 4.47149i) q^{46} +8.45973 q^{47} +(20.6858 - 35.8288i) q^{48} +(1.29246 + 2.23860i) q^{49} +(3.81915 + 6.61497i) q^{50} -11.2121 q^{51} +(15.3885 - 12.0223i) q^{52} -11.1099 q^{53} +(8.30846 + 14.3907i) q^{54} +(-2.76138 - 4.78285i) q^{55} +(9.77359 - 16.9284i) q^{56} -16.9926 q^{57} +(9.24319 - 16.0097i) q^{58} +(-0.852126 + 1.47593i) q^{59} +22.8928 q^{60} +(-2.28984 + 3.96612i) q^{61} +(1.36162 + 2.35840i) q^{62} +(5.39891 + 9.35119i) q^{63} +27.8747 q^{64} +(4.95297 + 2.00126i) q^{65} +28.9596 q^{66} +(-4.31372 - 7.47159i) q^{67} +(-10.6429 - 18.4340i) q^{68} +(-2.70450 + 4.68433i) q^{69} +8.47791 q^{70} +(8.13031 - 14.0821i) q^{71} +(-23.9029 + 41.4011i) q^{72} -2.72582 q^{73} +(-2.90137 + 5.02532i) q^{74} +(-4.00094 - 6.92982i) q^{75} +(-16.1300 - 27.9379i) q^{76} +7.83238 q^{77} +(-22.0740 + 17.2453i) q^{78} +7.19465 q^{79} +(10.7429 + 18.6073i) q^{80} +(-0.995641 - 1.72450i) q^{81} +(9.29084 - 16.0922i) q^{82} -11.4569 q^{83} +(-16.2333 + 28.1169i) q^{84} +(2.91142 - 5.04273i) q^{85} -13.1427 q^{86} +(-9.68315 + 16.7717i) q^{87} +(17.3384 + 30.0310i) q^{88} +(7.10595 + 12.3079i) q^{89} -20.7341 q^{90} +(-5.97009 + 4.66413i) q^{91} -10.2688 q^{92} +(-1.42643 - 2.47066i) q^{93} +(-11.5190 - 19.9514i) q^{94} +(4.41246 - 7.64260i) q^{95} -59.5854 q^{96} +(9.13350 - 15.8197i) q^{97} +(3.51968 - 6.09626i) q^{98} -19.1554 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

Related objects

Downloads

Learn more