LMFDB - Embedded newform 403.2.h.b.118.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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([0, 2]))

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

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

chi := DirichletCharacter("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (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			118.4
Character	$\chi$	$=$	403.118
Dual form			403.2.h.b.222.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.72349 q^{2} +(-1.49143 - 2.58324i) q^{3} +0.970414 q^{4} +(-1.96711 + 3.40713i) q^{5} +(2.57047 + 4.45218i) q^{6} +(0.142448 + 0.246727i) q^{7} +1.77448 q^{8} +(-2.94874 + 5.10737i) q^{9} +O(q^{10})$	\(q-1.72349 q^{2} +(-1.49143 - 2.58324i) q^{3} +0.970414 q^{4} +(-1.96711 + 3.40713i) q^{5} +(2.57047 + 4.45218i) q^{6} +(0.142448 + 0.246727i) q^{7} +1.77448 q^{8} +(-2.94874 + 5.10737i) q^{9} +(3.39029 - 5.87216i) q^{10} +(2.19472 - 3.80137i) q^{11} +(-1.44731 - 2.50681i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-0.245507 - 0.425231i) q^{14} +11.7352 q^{15} -4.99912 q^{16} +(2.72208 + 4.71478i) q^{17} +(5.08212 - 8.80250i) q^{18} +(-0.983819 - 1.70403i) q^{19} +(-1.90891 + 3.30633i) q^{20} +(0.424902 - 0.735952i) q^{21} +(-3.78258 + 6.55162i) q^{22} +0.503278 q^{23} +(-2.64652 - 4.58390i) q^{24} +(-5.23904 - 9.07428i) q^{25} +(0.861744 - 1.49259i) q^{26} +8.64280 q^{27} +(0.138233 + 0.239427i) q^{28} -1.05528 q^{29} -20.2256 q^{30} +(-3.07690 - 4.64033i) q^{31} +5.06698 q^{32} -13.0931 q^{33} +(-4.69148 - 8.12587i) q^{34} -1.12084 q^{35} +(-2.86150 + 4.95626i) q^{36} +(-2.36478 - 4.09593i) q^{37} +(1.69560 + 2.93687i) q^{38} +2.98286 q^{39} +(-3.49060 + 6.04589i) q^{40} +(2.42267 - 4.19619i) q^{41} +(-0.732314 + 1.26841i) q^{42} +(-2.52626 - 4.37561i) q^{43} +(2.12979 - 3.68890i) q^{44} +(-11.6010 - 20.0935i) q^{45} -0.867394 q^{46} +13.5233 q^{47} +(7.45586 + 12.9139i) q^{48} +(3.45942 - 5.99189i) q^{49} +(9.02942 + 15.6394i) q^{50} +(8.11960 - 14.0636i) q^{51} +(-0.485207 + 0.840403i) q^{52} +(-5.72403 + 9.91431i) q^{53} -14.8958 q^{54} +(8.63451 + 14.9554i) q^{55} +(0.252771 + 0.437812i) q^{56} +(-2.93460 + 5.08288i) q^{57} +1.81877 q^{58} +(-3.96529 - 6.86809i) q^{59} +11.3880 q^{60} +11.2007 q^{61} +(5.30301 + 7.99756i) q^{62} -1.68017 q^{63} +1.26537 q^{64} +(-1.96711 - 3.40713i) q^{65} +22.5658 q^{66} +(0.707197 - 1.22490i) q^{67} +(2.64154 + 4.57529i) q^{68} +(-0.750605 - 1.30009i) q^{69} +1.93176 q^{70} +(5.19624 - 9.00016i) q^{71} +(-5.23248 + 9.06293i) q^{72} +(4.53442 - 7.85385i) q^{73} +(4.07568 + 7.05928i) q^{74} +(-15.6273 + 27.0673i) q^{75} +(-0.954712 - 1.65361i) q^{76} +1.25053 q^{77} -5.14093 q^{78} +(-4.01900 - 6.96112i) q^{79} +(9.83382 - 17.0327i) q^{80} +(-4.04393 - 7.00429i) q^{81} +(-4.17544 + 7.23208i) q^{82} +(-0.505524 + 0.875594i) q^{83} +(0.412331 - 0.714178i) q^{84} -21.4185 q^{85} +(4.35398 + 7.54131i) q^{86} +(1.57388 + 2.72604i) q^{87} +(3.89449 - 6.74546i) q^{88} +14.0470 q^{89} +(19.9942 + 34.6309i) q^{90} -0.284895 q^{91} +0.488388 q^{92} +(-7.39808 + 14.8691i) q^{93} -23.3073 q^{94} +7.74112 q^{95} +(-7.55705 - 13.0892i) q^{96} -1.31688 q^{97} +(-5.96227 + 10.3269i) q^{98} +(12.9433 + 22.4185i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) $ 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.72349			−1.21869			−0.609345	−	0.792905i	$-0.708568\pi$
$2$	−1.72349			−1.21869			−0.609345	+	0.792905i	$0.708568\pi$
$3$	−1.49143	−	2.58324i	−0.861079	−	1.49143i	−0.870889	−	0.491481i	$-0.836456\pi$
$3$	−1.49143	−	2.58324i	−0.861079	−	1.49143i	0.00980961	−	0.999952i	$-0.496877\pi$
$4$	0.970414			0.485207
$5$	−1.96711	+	3.40713i	−0.879718	+	1.52372i	−0.0280673	+	0.999606i	$0.508935\pi$
$5$	−1.96711	+	3.40713i	−0.879718	+	1.52372i	−0.851651	+	0.524110i	$0.824398\pi$
$6$	2.57047	+	4.45218i	1.04939	+	1.81759i
$7$	0.142448	+	0.246727i	0.0538402	+	0.0932539i	0.891689	−	0.452648i	$-0.149521\pi$
$7$	0.142448	+	0.246727i	0.0538402	+	0.0932539i	−0.837849	+	0.545902i	$0.816187\pi$
$8$	1.77448			0.627374
$9$	−2.94874	+	5.10737i	−0.982914	+	1.70246i
$10$	3.39029	−	5.87216i	1.07210	−	1.85694i
$11$	2.19472	−	3.80137i	0.661734	−	1.14616i	−0.318426	−	0.947948i	$-0.603154\pi$
$11$	2.19472	−	3.80137i	0.661734	−	1.14616i	0.980160	−	0.198209i	$-0.0635123\pi$
$12$	−1.44731	−	2.50681i	−0.417801	−	0.723653i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	−0.245507	−	0.425231i	−0.0656145	−	0.113648i
$15$	11.7352			3.03003
$16$	−4.99912			−1.24978
$17$	2.72208	+	4.71478i	0.660201	+	1.14350i	0.980563	+	0.196207i	$0.0628624\pi$
$17$	2.72208	+	4.71478i	0.660201	+	1.14350i	−0.320361	+	0.947296i	$0.603804\pi$
$18$	5.08212	−	8.80250i	1.19787	−	2.07477i
$19$	−0.983819	−	1.70403i	−0.225704	−	0.390930i	0.730827	−	0.682563i	$-0.239135\pi$
$19$	−0.983819	−	1.70403i	−0.225704	−	0.390930i	−0.956530	+	0.291633i	$0.905801\pi$
$20$	−1.90891	+	3.30633i	−0.426845	+	0.739318i
$21$	0.424902	−	0.735952i	0.0927213	−	0.160598i
$22$	−3.78258	+	6.55162i	−0.806449	+	1.39681i
$23$	0.503278			0.104941			0.0524704	−	0.998622i	$-0.483290\pi$
$23$	0.503278			0.104941			0.0524704	+	0.998622i	$0.483290\pi$
$24$	−2.64652	−	4.58390i	−0.540218	−	0.935685i
$25$	−5.23904	−	9.07428i	−1.04781	−	1.81486i
$26$	0.861744	−	1.49259i	0.169002	−	0.292720i
$27$	8.64280			1.66331
$28$	0.138233	+	0.239427i	0.0261236	+	0.0452474i
$29$	−1.05528			−0.195961			−0.0979804	−	0.995188i	$-0.531238\pi$
$29$	−1.05528			−0.195961			−0.0979804	+	0.995188i	$0.531238\pi$
$30$	−20.2256			−3.69266
$31$	−3.07690	−	4.64033i	−0.552628	−	0.833428i
$31$	−3.07690	−	4.64033i	−0.552628	−	0.833428i
$32$	5.06698			0.895723
$33$	−13.0931			−2.27922
$34$	−4.69148	−	8.12587i	−0.804581	−	1.39358i
$35$	−1.12084			−0.189457
$36$	−2.86150	+	4.95626i	−0.476917	+	0.826044i
$37$	−2.36478	−	4.09593i	−0.388768	−	0.673366i	0.603516	−	0.797351i	$-0.293766\pi$
$37$	−2.36478	−	4.09593i	−0.388768	−	0.673366i	−0.992284	+	0.123985i	$0.960433\pi$
$38$	1.69560	+	2.93687i	0.275063	+	0.476423i
$39$	2.98286			0.477641
$40$	−3.49060	+	6.04589i	−0.551912	+	0.955939i
$41$	2.42267	−	4.19619i	0.378357	−	0.655334i	−0.612466	−	0.790497i	$-0.709822\pi$
$41$	2.42267	−	4.19619i	0.378357	−	0.655334i	0.990823	+	0.135163i	$0.0431557\pi$
$42$	−0.732314	+	1.26841i	−0.112999	+	0.195719i
$43$	−2.52626	−	4.37561i	−0.385251	−	0.667274i	0.606553	−	0.795043i	$-0.292552\pi$
$43$	−2.52626	−	4.37561i	−0.385251	−	0.667274i	−0.991804	+	0.127769i	$0.959218\pi$
$44$	2.12979	−	3.68890i	0.321078	−	0.556123i
$45$	−11.6010	−	20.0935i	−1.72937	−	2.99536i
$46$	−0.867394			−0.127890
$47$	13.5233			1.97258			0.986289	−	0.165027i	$-0.0527712\pi$
$47$	13.5233			1.97258			0.986289	+	0.165027i	$0.0527712\pi$
$48$	7.45586	+	12.9139i	1.07616	+	1.86396i
$49$	3.45942	−	5.99189i	0.494202	−	0.855984i
$50$	9.02942	+	15.6394i	1.27695	+	2.21175i
$51$	8.11960	−	14.0636i	1.13697	−	1.96929i
$52$	−0.485207	+	0.840403i	−0.0672861	+	0.116543i
$53$	−5.72403	+	9.91431i	−0.786256	+	1.36184i	0.141990	+	0.989868i	$0.454650\pi$
$53$	−5.72403	+	9.91431i	−0.786256	+	1.36184i	−0.928246	+	0.371967i	$0.878683\pi$
$54$	−14.8958			−2.02706
$55$	8.63451	+	14.9554i	1.16428	+	2.01659i
$56$	0.252771	+	0.437812i	0.0337779	+	0.0585050i
$57$	−2.93460	+	5.08288i	−0.388697	+	0.673244i
$58$	1.81877			0.238816
$59$	−3.96529	−	6.86809i	−0.516237	−	0.894149i	−0.999822	−	0.0188519i	$-0.993999\pi$
$59$	−3.96529	−	6.86809i	−0.516237	−	0.894149i	0.483585	−	0.875297i	$-0.339334\pi$
$60$	11.3880			1.47019
$61$	11.2007			1.43410			0.717049	−	0.697023i	$-0.245492\pi$
$61$	11.2007			1.43410			0.717049	+	0.697023i	$0.245492\pi$
$62$	5.30301	+	7.99756i	0.673483	+	1.01569i
$63$	−1.68017			−0.211681
$64$	1.26537			0.158172
$65$	−1.96711	−	3.40713i	−0.243990	−	0.422603i
$66$	22.5658			2.77766
$67$	0.707197	−	1.22490i	0.0863979	−	0.149646i	−0.819588	−	0.572953i	$-0.805798\pi$
$67$	0.707197	−	1.22490i	0.0863979	−	0.149646i	0.905986	+	0.423308i	$0.139131\pi$
$68$	2.64154	+	4.57529i	0.320334	+	0.554835i
$69$	−0.750605	−	1.30009i	−0.0903623	−	0.156512i
$70$	1.93176			0.230889
$71$	5.19624	−	9.00016i	0.616681	−	1.06812i	−0.373406	−	0.927668i	$-0.621810\pi$
$71$	5.19624	−	9.00016i	0.616681	−	1.06812i	0.990087	−	0.140454i	$-0.0448564\pi$
$72$	−5.23248	+	9.06293i	−0.616654	+	1.06808i
$73$	4.53442	−	7.85385i	0.530714	−	0.919224i	−0.468644	−	0.883387i	$-0.655257\pi$
$73$	4.53442	−	7.85385i	0.530714	−	0.919224i	0.999358	−	0.0358363i	$-0.0114095\pi$
$74$	4.07568	+	7.05928i	0.473788	+	0.820625i
$75$	−15.6273	+	27.0673i	−1.80449	+	3.12547i
$76$	−0.954712	−	1.65361i	−0.109513	−	0.189682i
$77$	1.25053			0.142511
$78$	−5.14093			−0.582096
$79$	−4.01900	−	6.96112i	−0.452173	−	0.783187i	0.546347	−	0.837559i	$-0.316018\pi$
$79$	−4.01900	−	6.96112i	−0.452173	−	0.783187i	−0.998521	+	0.0543715i	$0.982684\pi$
$80$	9.83382	−	17.0327i	1.09945	−	1.90431i
$81$	−4.04393	−	7.00429i	−0.449325	−	0.778254i
$82$	−4.17544	+	7.23208i	−0.461101	+	0.798650i
$83$	−0.505524	+	0.875594i	−0.0554885	+	0.0961089i	−0.892435	−	0.451175i	$-0.851005\pi$
$83$	−0.505524	+	0.875594i	−0.0554885	+	0.0961089i	0.836947	+	0.547284i	$0.184338\pi$
$84$	0.412331	−	0.714178i	0.0449890	−	0.0779232i
$85$	−21.4185			−2.32316
$86$	4.35398	+	7.54131i	0.469501	+	0.813200i
$87$	1.57388	+	2.72604i	0.168738	+	0.292262i
$88$	3.89449	−	6.74546i	0.415154	−	0.719068i
$89$	14.0470			1.48898			0.744488	−	0.667636i	$-0.232694\pi$
$89$	14.0470			1.48898			0.744488	+	0.667636i	$0.232694\pi$
$90$	19.9942	+	34.6309i	2.10757	+	3.65042i
$91$	−0.284895			−0.0298652
$92$	0.488388			0.0509180
$93$	−7.39808	+	14.8691i	−0.767145	+	1.54185i
$94$	−23.3073			−2.40396
$95$	7.74112			0.794222
$96$	−7.55705	−	13.0892i	−0.771288	−	1.33591i
$97$	−1.31688			−0.133709			−0.0668545	−	0.997763i	$-0.521296\pi$
$97$	−1.31688			−0.133709			−0.0668545	+	0.997763i	$0.521296\pi$
$98$	−5.96227	+	10.3269i	−0.602280	+	1.04318i
$99$	12.9433	+	22.4185i	1.30085	+	2.25315i
$100$	−5.08403	−	8.80580i	−0.508403	−	0.880580i
$101$	1.92367			0.191412			0.0957062	−	0.995410i	$-0.469489\pi$
$101$	1.92367			0.191412			0.0957062	+	0.995410i	$0.469489\pi$
$102$	−13.9940	+	24.2384i	−1.38562	+	2.39996i
$103$	−2.01665	+	3.49294i	−0.198706	+	0.344169i	−0.948109	−	0.317945i	$-0.897007\pi$
$103$	−2.01665	+	3.49294i	−0.198706	+	0.344169i	0.749403	+	0.662114i	$0.230341\pi$
$104$	−0.887240	+	1.53675i	−0.0870011	+	0.150690i
$105$	1.67166	+	2.89540i	0.163137	+	0.282562i
$106$	9.86530	−	17.0872i	0.958203	−	1.65966i
$107$	−7.57237	−	13.1157i	−0.732049	−	1.26795i	−0.956006	−	0.293347i	$-0.905231\pi$
$107$	−7.57237	−	13.1157i	−0.732049	−	1.26795i	0.223957	−	0.974599i	$-0.428102\pi$
$108$	8.38709			0.807048
$109$	5.43050			0.520147			0.260074	−	0.965589i	$-0.416253\pi$
$109$	5.43050			0.520147			0.260074	+	0.965589i	$0.416253\pi$
$110$	−14.8815	−	25.7755i	−1.41889	−	2.45760i
$111$	−7.05383	+	12.2176i	−0.669520	+	1.15964i
$112$	−0.712114	−	1.23342i	−0.0672884	−	0.116547i
$113$	−0.281428	+	0.487448i	−0.0264745	+	0.0458552i	−0.878959	−	0.476897i	$-0.841761\pi$
$113$	−0.281428	+	0.487448i	−0.0264745	+	0.0458552i	0.852485	+	0.522752i	$0.175095\pi$
$114$	5.05775	−	8.76028i	0.473702	−	0.820476i
$115$	−0.990003	+	1.71474i	−0.0923182	+	0.159900i
$116$	−1.02406			−0.0950815
$117$	−2.94874	−	5.10737i	−0.272611	−	0.472177i
$118$	6.83414	+	11.8371i	0.629134	+	1.08969i
$119$	−0.775508	+	1.34322i	−0.0710907	+	0.123133i
$120$	20.8240			1.90096
$121$	−4.13361	−	7.15962i	−0.375783	−	0.650875i
$122$	−19.3042			−1.74772
$123$	−14.4530			−1.30318
$124$	−2.98587	−	4.50304i	−0.268139	−	0.404385i
$125$	21.5519			1.92766
$126$	2.89575			0.257974
$127$	7.52902	+	13.0406i	0.668093	+	1.15717i	0.978437	+	0.206546i	$0.0662223\pi$
$127$	7.52902	+	13.0406i	0.668093	+	1.15717i	−0.310344	+	0.950624i	$0.600444\pi$
$128$	−12.3148			−1.08849
$129$	−7.53549	+	13.0518i	−0.663463	+	1.14915i
$130$	3.39029	+	5.87216i	0.297348	+	0.515022i
$131$	−1.80816	−	3.13182i	−0.157979	−	0.273628i	0.776161	−	0.630535i	$-0.217165\pi$
$131$	−1.80816	−	3.13182i	−0.157979	−	0.273628i	−0.934140	+	0.356907i	$0.883831\pi$
$132$	−12.7057			−1.10589
$133$	0.280286	−	0.485469i	0.0243039	−	0.0420955i
$134$	−1.21885	+	2.11110i	−0.105292	+	0.182372i
$135$	−17.0013	+	29.4472i	−1.46324	+	2.53441i
$136$	4.83028	+	8.36629i	0.414193	+	0.717403i
$137$	3.84892	−	6.66653i	0.328836	−	0.569560i	−0.653446	−	0.756974i	$-0.726677\pi$
$137$	3.84892	−	6.66653i	0.328836	−	0.569560i	0.982281	+	0.187414i	$0.0600105\pi$
$138$	1.29366	+	2.24068i	0.110124	+	0.190740i
$139$	−16.2622			−1.37935			−0.689673	−	0.724121i	$-0.742246\pi$
$139$	−16.2622			−1.37935			−0.689673	+	0.724121i	$0.742246\pi$
$140$	−1.08768			−0.0919257
$141$	−20.1691	−	34.9339i	−1.69855	−	2.94197i
$142$	−8.95567	+	15.5117i	−0.751543	+	1.30171i
$143$	2.19472	+	3.80137i	0.183532	+	0.317887i
$144$	14.7411	−	25.5324i	1.22843	−	2.12770i
$145$	2.07585	−	3.59548i	0.172390	−	0.298589i
$146$	−7.81503	+	13.5360i	−0.646776	+	1.12025i
$147$	−20.6379			−1.70219
$148$	−2.29482	−	3.97474i	−0.188633	−	0.326722i
$149$	0.882419	+	1.52839i	0.0722906	+	0.125211i	0.899905	−	0.436086i	$-0.143636\pi$
$149$	0.882419	+	1.52839i	0.0722906	+	0.125211i	−0.827614	+	0.561297i	$0.810302\pi$
$150$	26.9335	−	46.6503i	2.19911	−	3.80898i
$151$	−14.4398			−1.17509			−0.587546	−	0.809191i	$-0.699906\pi$
$151$	−14.4398			−1.17509			−0.587546	+	0.809191i	$0.699906\pi$
$152$	−1.74577	−	3.02376i	−0.141601	−	0.245259i
$153$	−32.1068			−2.59568
$154$	−2.15528			−0.173677
$155$	21.8628	−	1.35538i	1.75606	−	0.108867i
$156$	2.89461			0.231755
$157$	13.7892			1.10050			0.550249	−	0.835001i	$-0.314533\pi$
$157$	13.7892			1.10050			0.550249	+	0.835001i	$0.314533\pi$
$158$	6.92671	+	11.9974i	0.551059	+	0.954463i
$159$	34.1480			2.70811
$160$	−9.96729	+	17.2639i	−0.787984	+	1.36483i
$161$	0.0716908	+	0.124172i	0.00565003	+	0.00978614i
$162$	6.96967	+	12.0718i	0.547589	+	0.948451i
$163$	20.6972			1.62113			0.810564	−	0.585649i	$-0.199160\pi$
$163$	20.6972			1.62113			0.810564	+	0.585649i	$0.199160\pi$
$164$	2.35099	−	4.07204i	0.183582	−	0.317973i
$165$	25.7556	−	44.6100i	2.00507	−	3.47288i
$166$	0.871266	−	1.50908i	0.0676233	−	0.117127i
$167$	5.31886	+	9.21254i	0.411586	+	0.712888i	0.995063	−	0.0992417i	$-0.0316417\pi$
$167$	5.31886	+	9.21254i	0.411586	+	0.712888i	−0.583478	+	0.812129i	$0.698308\pi$
$168$	0.753981	−	1.30593i	0.0581709	−	0.100755i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	36.9146			2.83122
$171$	11.6041			0.887389
$172$	−2.45152	−	4.24615i	−0.186926	−	0.323766i
$173$	6.17766	−	10.7000i	0.469679	−	0.813507i	−0.529720	−	0.848172i	$-0.677703\pi$
$173$	6.17766	−	10.7000i	0.469679	−	0.813507i	0.999399	+	0.0346651i	$0.0110365\pi$
$174$	−2.71257	−	4.69830i	−0.205639	−	0.356177i
$175$	1.49258	−	2.58522i	0.112828	−	0.195424i
$176$	−10.9717	+	19.0035i	−0.827022	+	1.43244i
$177$	−11.8279	+	20.4866i	−0.889042	+	1.53987i
$178$	−24.2098			−1.81460
$179$	−9.17272	−	15.8876i	−0.685601	−	1.18750i	−0.973248	−	0.229759i	$-0.926206\pi$
$179$	−9.17272	−	15.8876i	−0.685601	−	1.18750i	0.287647	−	0.957737i	$-0.407127\pi$
$180$	−11.2578	−	19.4990i	−0.839104	−	1.45337i
$181$	8.45399	−	14.6427i	0.628380	−	1.08839i	−0.359497	−	0.933146i	$-0.617052\pi$
$181$	8.45399	−	14.6427i	0.628380	−	1.08839i	0.987877	−	0.155240i	$-0.0496150\pi$
$182$	0.491014			0.0363964
$183$	−16.7050	−	28.9340i	−1.23487	−	2.13886i
$184$	0.893057			0.0658370
$185$	18.6072			1.36802
$186$	12.7505	−	25.6267i	0.934913	−	1.87904i
$187$	23.8968			1.74751
$188$	13.1232			0.957109
$189$	1.23115	+	2.13241i	0.0895528	+	0.155110i
$190$	−13.3417			−0.967911
$191$	−8.99331	+	15.5769i	−0.650733	+	1.12710i	0.332212	+	0.943205i	$0.392205\pi$
$191$	−8.99331	+	15.5769i	−0.650733	+	1.12710i	−0.982945	+	0.183898i	$0.941128\pi$
$192$	−1.88722	−	3.26876i	−0.136198	−	0.235903i
$193$	6.36595	+	11.0262i	0.458231	+	0.793680i	0.998868	−	0.0475766i	$-0.0151498\pi$
$193$	6.36595	+	11.0262i	0.458231	+	0.793680i	−0.540636	+	0.841256i	$0.681816\pi$
$194$	2.26963			0.162950
$195$	−5.86762	+	10.1630i	−0.420189	+	0.727789i
$196$	3.35707	−	5.81461i	0.239790	−	0.415329i
$197$	−5.22317	+	9.04679i	−0.372135	+	0.644557i	−0.989894	−	0.141811i	$-0.954708\pi$
$197$	−5.22317	+	9.04679i	−0.372135	+	0.644557i	0.617759	+	0.786368i	$0.288041\pi$
$198$	−22.3077	−	38.6381i	−1.58534	−	2.74589i
$199$	1.64202	−	2.84406i	0.116400	−	0.201610i	−0.801939	−	0.597406i	$-0.796198\pi$
$199$	1.64202	−	2.84406i	0.116400	−	0.201610i	0.918338	+	0.395796i	$0.129531\pi$
$200$	−9.29656	−	16.1021i	−0.657366	−	1.13859i
$201$	−4.21895			−0.297582
$202$	−3.31543			−0.233273
$203$	−0.150322	−	0.260366i	−0.0105506	−	0.0182741i
$204$	7.87937	−	13.6475i	0.551666	−	0.955514i
$205$	9.53131	+	16.5087i	0.665695	+	1.15302i
$206$	3.47567	−	6.02004i	0.242161	−	0.419436i
$207$	−1.48404	+	2.57043i	−0.103148	+	0.178657i
$208$	2.49956	−	4.32937i	0.173313	−	0.300188i
$209$	−8.63684			−0.597423
$210$	−2.88108	−	4.99018i	−0.198814	−	0.344355i
$211$	−9.03055	−	15.6414i	−0.621689	−	1.07680i	−0.989171	−	0.146766i	$-0.953113\pi$
$211$	−9.03055	−	15.6414i	−0.621689	−	1.07680i	0.367482	−	0.930031i	$-0.380220\pi$
$212$	−5.55468	+	9.62098i	−0.381497	+	0.660772i
$213$	−30.9994			−2.12404
$214$	13.0509	+	22.6048i	0.892141	+	1.54523i
$215$	19.8777			1.35565
$216$	15.3365			1.04352
$217$	0.706596	−	1.42016i	0.0479668	−	0.0964066i
$218$	−9.35940			−0.633899
$219$	−27.0511			−1.82795
$220$	8.37905	+	14.5129i	0.564916	+	0.978463i
$221$	−5.44416			−0.366214
$222$	12.1572	−	21.0569i	0.815938	−	1.41325i
$223$	−1.83304	−	3.17492i	−0.122749	−	0.212608i	0.798102	−	0.602523i	$-0.205838\pi$
$223$	−1.83304	−	3.17492i	−0.122749	−	0.212608i	−0.920851	+	0.389915i	$0.872504\pi$
$224$	0.721779	+	1.25016i	0.0482259	+	0.0835297i
$225$	61.7942			4.11962
$226$	0.485038	−	0.840111i	0.0322643	−	0.0558833i
$227$	−2.13470	+	3.69741i	−0.141685	+	0.245405i	−0.928131	−	0.372253i	$-0.878585\pi$
$227$	−2.13470	+	3.69741i	−0.141685	+	0.245405i	0.786446	+	0.617659i	$0.211919\pi$
$228$	−2.84778	+	4.93249i	−0.188599	+	0.326662i
$229$	−10.8694	−	18.8264i	−0.718272	−	1.24408i	−0.961684	−	0.274161i	$-0.911600\pi$
$229$	−10.8694	−	18.8264i	−0.718272	−	1.24408i	0.243412	−	0.969923i	$-0.421733\pi$
$230$	1.70626	−	2.95533i	0.112507	−	0.194869i
$231$	−1.86508	−	3.23042i	−0.122714	−	0.212546i
$232$	−1.87258			−0.122941
$233$	−17.3895			−1.13923			−0.569613	−	0.821913i	$-0.692907\pi$
$233$	−17.3895			−1.13923			−0.569613	+	0.821913i	$0.692907\pi$
$234$	5.08212	+	8.80250i	0.332229	+	0.575437i
$235$	−26.6018	+	46.0757i	−1.73531	+	3.00565i
$236$	−3.84798	−	6.66489i	−0.250482	−	0.433847i
$237$	−11.9881	+	20.7641i	−0.778714	+	1.34877i
$238$	1.33658	−	2.31502i	0.0866376	−	0.150061i
$239$	−5.05622	+	8.75763i	−0.327060	+	0.566484i	−0.981927	−	0.189260i	$-0.939391\pi$
$239$	−5.05622	+	8.75763i	−0.327060	+	0.566484i	0.654867	+	0.755744i	$0.272724\pi$
$240$	−58.6659			−3.78687
$241$	5.39697	+	9.34783i	0.347650	+	0.602147i	0.985831	−	0.167739i	$-0.0536465\pi$
$241$	5.39697	+	9.34783i	0.347650	+	0.602147i	−0.638182	+	0.769886i	$0.720313\pi$
$242$	7.12423	+	12.3395i	0.457963	+	0.793215i
$243$	0.901708	−	1.56180i	0.0578446	−	0.100190i
$244$	10.8693			0.695834
$245$	13.6101	+	23.5734i	0.869517	+	1.50605i
$246$	24.9096			1.58818
$247$	1.96764			0.125198
$248$	−5.45990	−	8.23418i	−0.346704	−	0.522871i
$249$	3.01582			0.191120
$250$	−37.1445			−2.34922
$251$	11.7025	+	20.2693i	0.738655	+	1.27939i	0.953101	+	0.302651i	$0.0978718\pi$
$251$	11.7025	+	20.2693i	0.738655	+	1.27939i	−0.214447	+	0.976736i	$0.568795\pi$
$252$	−1.63046			−0.102709
$253$	1.10456	−	1.91315i	0.0694428	−	0.120278i
$254$	−12.9762	−	22.4754i	−0.814198	−	1.41023i
$255$	31.9443	+	55.3291i	2.00043	+	3.46484i
$256$	18.6937			1.16836
$257$	−2.05783	+	3.56426i	−0.128364	+	0.222333i	−0.923043	−	0.384697i	$-0.874306\pi$
$257$	−2.05783	+	3.56426i	−0.128364	+	0.222333i	0.794679	+	0.607030i	$0.207639\pi$
$258$	12.9873	−	22.4947i	0.808556	−	1.40046i
$259$	0.673716	−	1.16691i	0.0418627	−	0.0725083i
$260$	−1.90891	−	3.30633i	−0.118386	−	0.205050i
$261$	3.11175	−	5.38971i	0.192613	−	0.333615i
$262$	3.11634	+	5.39766i	0.192528	+	0.333468i
$263$	−8.74231			−0.539074			−0.269537	−	0.962990i	$-0.586871\pi$
$263$	−8.74231			−0.539074			−0.269537	+	0.962990i	$0.586871\pi$
$264$	−23.2335			−1.42992
$265$	−22.5196	−	39.0051i	−1.38337	−	2.39606i
$266$	−0.483069	+	0.836700i	−0.0296189	+	0.0513014i
$267$	−20.9501	−	36.2866i	−1.28213	−	2.22071i
$268$	0.686274	−	1.18866i	0.0419209	−	0.0726090i
$269$	−6.60006	+	11.4316i	−0.402413	+	0.696999i	−0.994017	−	0.109230i	$-0.965162\pi$
$269$	−6.60006	+	11.4316i	−0.402413	+	0.696999i	0.591604	+	0.806229i	$0.298495\pi$
$270$	29.3016	−	50.7519i	1.78324	−	3.08866i
$271$	10.2575			0.623100			0.311550	−	0.950230i	$-0.399152\pi$
$271$	10.2575			0.623100			0.311550	+	0.950230i	$0.399152\pi$
$272$	−13.6080	−	23.5698i	−0.825107	−	1.42913i
$273$	0.424902	+	0.735952i	0.0257163	+	0.0445419i
$274$	−6.63357	+	11.4897i	−0.400749	+	0.694117i
$275$	−45.9929			−2.77348
$276$	−0.728398	−	1.26162i	−0.0438444	−	0.0759407i
$277$	22.4898			1.35128			0.675642	−	0.737230i	$-0.263867\pi$
$277$	22.4898			1.35128			0.675642	+	0.737230i	$0.263867\pi$
$278$	28.0278			1.68100
$279$	32.7729	−	2.03174i	1.96206	−	0.121637i
$280$	−1.98891			−0.118860
$281$	10.3314			0.616318			0.308159	−	0.951335i	$-0.400287\pi$
$281$	10.3314			0.616318			0.308159	+	0.951335i	$0.400287\pi$
$282$	34.7612	+	60.2082i	2.07000	+	3.58535i
$283$	−16.6331			−0.988737			−0.494368	−	0.869252i	$-0.664601\pi$
$283$	−16.6331			−0.988737			−0.494368	+	0.869252i	$0.664601\pi$
$284$	5.04251	−	8.73388i	0.299218	−	0.518260i
$285$	−11.5454	−	19.9971i	−0.683888	−	1.18453i
$286$	−3.78258	−	6.55162i	−0.223669	−	0.387405i
$287$	1.38041			0.0814833
$288$	−14.9412	+	25.8789i	−0.880419	+	1.52493i
$289$	−6.31944	+	10.9456i	−0.371732	+	0.643859i
$290$	−3.57771	+	6.19678i	−0.210090	+	0.363887i
$291$	1.96404	+	3.40182i	0.115134	+	0.199418i
$292$	4.40027	−	7.62148i	0.257506	−	0.446014i
$293$	−6.40046	−	11.0859i	−0.373919	−	0.647647i	0.616246	−	0.787554i	$-0.288653\pi$
$293$	−6.40046	−	11.0859i	−0.373919	−	0.647647i	−0.990165	+	0.139907i	$0.955319\pi$
$294$	35.5693			2.07444
$295$	31.2007			1.81657
$296$	−4.19626	−	7.26814i	−0.243903	−	0.422452i
$297$	18.9685	−	32.8545i	1.10067	−	1.90641i
$298$	−1.52084	−	2.63417i	−0.0880999	−	0.152593i
$299$	−0.251639	+	0.435852i	−0.0145527	+	0.0252060i
$300$	−15.1650	+	26.2665i	−0.875551	+	1.51650i
$301$	0.719719	−	1.24659i	0.0414839	−	0.0718523i
$302$	24.8868			1.43207
$303$	−2.86903	−	4.96930i	−0.164821	−	0.285479i
$304$	4.91824	+	8.51863i	0.282080	+	0.488577i
$305$	−22.0329	+	38.1621i	−1.26160	+	2.18516i
$306$	55.3358			3.16334
$307$	−13.9160	−	24.1032i	−0.794229	−	1.37564i	−0.923328	−	0.384013i	$-0.874542\pi$
$307$	−13.9160	−	24.1032i	−0.794229	−	1.37564i	0.129099	−	0.991632i	$-0.458792\pi$
$308$	1.21353			0.0691475
$309$	12.0308			0.684407
$310$	−37.6803	+	2.33598i	−2.14010	+	0.132675i
$311$	12.4177			0.704142			0.352071	−	0.935973i	$-0.385478\pi$
$311$	12.4177			0.704142			0.352071	+	0.935973i	$0.385478\pi$
$312$	5.29304			0.299659
$313$	3.24239	+	5.61599i	0.183271	+	0.317435i	0.942993	−	0.332814i	$-0.107998\pi$
$313$	3.24239	+	5.61599i	0.183271	+	0.317435i	−0.759722	+	0.650249i	$0.774665\pi$
$314$	−23.7655			−1.34117
$315$	3.30507	−	5.72455i	0.186220	−	0.322542i
$316$	−3.90010	−	6.75517i	−0.219398	−	0.380008i
$317$	−14.1705	−	24.5439i	−0.795892	−	1.37852i	−0.922271	−	0.386543i	$-0.873669\pi$
$317$	−14.1705	−	24.5439i	−0.795892	−	1.37852i	0.126380	−	0.991982i	$-0.459664\pi$
$318$	−58.8537			−3.30035
$319$	−2.31605	+	4.01151i	−0.129674	+	0.224602i
$320$	−2.48913	+	4.31130i	−0.139147	+	0.241009i
$321$	−22.5874	+	39.1225i	−1.26070	+	2.18360i
$322$	−0.123558	−	0.214009i	−0.00688564	−	0.0119263i
$323$	5.35607	−	9.27699i	0.298020	−	0.516185i
$324$	−3.92428	−	6.79706i	−0.218016	−	0.377614i
$325$	10.4781			0.581219
$326$	−35.6714			−1.97565
$327$	−8.09922	−	14.0283i	−0.447888	−	0.775764i
$328$	4.29898	−	7.44605i	0.237371	−	0.411139i
$329$	1.92637	+	3.33656i	0.106204	+	0.183951i
$330$	−44.3895	+	76.8848i	−2.44356	+	4.23237i
$331$	2.59869	−	4.50106i	0.142837	−	0.247401i	−0.785727	−	0.618573i	$-0.787711\pi$
$331$	2.59869	−	4.50106i	0.142837	−	0.247401i	0.928564	+	0.371173i	$0.121044\pi$
$332$	−0.490568	+	0.849688i	−0.0269234	+	0.0466327i
$333$	27.8925			1.52850
$334$	−9.16700	−	15.8777i	−0.501596	−	0.868789i
$335$	2.78227	+	4.81903i	0.152012	+	0.263292i
$336$	−2.12414	+	3.67912i	−0.115881	+	0.200712i
$337$	−11.5640			−0.629930			−0.314965	−	0.949103i	$-0.601993\pi$
$337$	−11.5640			−0.629930			−0.314965	+	0.949103i	$0.601993\pi$
$338$	0.861744	+	1.49259i	0.0468727	+	0.0811859i
$339$	1.67892			0.0911866
$340$	−20.7848			−1.12722
$341$	−24.3926	+	1.51221i	−1.32093	+	0.0818907i
$342$	−19.9996			−1.08145
$343$	3.96541			0.214112
$344$	−4.48280	−	7.76443i	−0.241696	−	0.418630i
$345$	5.90609			0.317973
$346$	−10.6471	+	18.4414i	−0.572393	+	0.991414i
$347$	16.3466	+	28.3131i	0.877530	+	1.51993i	0.854043	+	0.520202i	$0.174144\pi$
$347$	16.3466	+	28.3131i	0.877530	+	1.51993i	0.0234871	+	0.999724i	$0.492523\pi$
$348$	1.52732	+	2.64539i	0.0818727	+	0.141808i
$349$	19.2350			1.02963			0.514813	−	0.857302i	$-0.327861\pi$
$349$	19.2350			1.02963			0.514813	+	0.857302i	$0.327861\pi$
$350$	−2.57244	+	4.45560i	−0.137503	+	0.238162i
$351$	−4.32140	+	7.48488i	−0.230659	+	0.399514i
$352$	11.1206	−	19.2614i	0.592730	−	1.02664i
$353$	11.8708	+	20.5608i	0.631819	+	1.09434i	0.987180	+	0.159614i	$0.0510248\pi$
$353$	11.8708	+	20.5608i	0.631819	+	1.09434i	−0.355360	+	0.934729i	$0.615642\pi$
$354$	20.3853	−	35.3084i	1.08347	−	1.87662i
$355$	20.4432	+	35.4086i	1.08501	+	1.87929i
$356$	13.6314			0.722461
$357$	4.62647			0.244859
$358$	15.8091	+	27.3821i	0.835535	+	1.44719i
$359$	11.1881	−	19.3783i	0.590484	−	1.02275i	−0.403683	−	0.914899i	$-0.632270\pi$
$359$	11.1881	−	19.3783i	0.590484	−	1.02275i	0.994167	−	0.107849i	$-0.0343964\pi$
$360$	−20.5857	−	35.6555i	−1.08496	−	1.87921i
$361$	7.56420	−	13.1016i	0.398116	−	0.689557i
$362$	−14.5704	+	25.2366i	−0.765801	+	1.32641i
$363$	−12.3300	+	21.3562i	−0.647157	+	1.12091i
$364$	−0.276466			−0.0144908
$365$	17.8394	+	30.8988i	0.933757	+	1.61731i
$366$	28.7909	+	49.8674i	1.50493	+	2.60661i
$367$	2.13405	−	3.69628i	0.111397	−	0.192944i	−0.804937	−	0.593360i	$-0.797801\pi$
$367$	2.13405	−	3.69628i	0.111397	−	0.192944i	0.916334	+	0.400416i	$0.131134\pi$
$368$	−2.51595			−0.131153
$369$	14.2877	+	24.7469i	0.743785	+	1.28827i
$370$	−32.0692			−1.66720
$371$	−3.26150			−0.169329
$372$	−7.17920	+	14.4292i	−0.372224	+	0.748119i
$373$	10.5071			0.544035			0.272017	−	0.962292i	$-0.412309\pi$
$373$	10.5071			0.544035			0.272017	+	0.962292i	$0.412309\pi$
$374$	−41.1859			−2.12967
$375$	−32.1432	−	55.6737i	−1.65987	−	2.87498i
$376$	23.9969			1.23754
$377$	0.527641	−	0.913900i	0.0271749	−	0.0470683i
$378$	−2.12187	−	3.67518i	−0.109137	−	0.189031i
$379$	5.11343	+	8.85671i	0.262659	+	0.454939i	0.966948	−	0.254975i	$-0.0820672\pi$
$379$	5.11343	+	8.85671i	0.262659	+	0.454939i	−0.704289	+	0.709914i	$0.748734\pi$
$380$	7.51209			0.385362
$381$	22.4581	−	38.8985i	1.15056	−	1.99283i
$382$	15.4999	−	26.8466i	0.793042	−	1.37359i
$383$	1.86447	−	3.22936i	0.0952700	−	0.165012i	−0.814451	−	0.580232i	$-0.802962\pi$
$383$	1.86447	−	3.22936i	0.0952700	−	0.165012i	0.909721	+	0.415219i	$0.136295\pi$
$384$	18.3667	+	31.8121i	0.937272	+	1.62340i
$385$	−2.45993	+	4.26073i	−0.125370	+	0.217147i
$386$	−10.9716	−	19.0035i	−0.558442	−	0.967250i
$387$	29.7971			1.51467
$388$	−1.27792			−0.0648766
$389$	1.14376	+	1.98105i	0.0579909	+	0.100443i	0.893563	−	0.448937i	$-0.148197\pi$
$389$	1.14376	+	1.98105i	0.0579909	+	0.100443i	−0.835573	+	0.549380i	$0.814864\pi$
$390$	10.1128	−	17.5158i	0.512080	−	0.886949i
$391$	1.36996	+	2.37285i	0.0692820	+	0.120000i
$392$	6.13867	−	10.6325i	0.310050	−	0.537022i
$393$	−5.39349	+	9.34179i	−0.272065	+	0.471231i
$394$	9.00207	−	15.5920i	0.453518	−	0.785515i
$395$	31.6233			1.59114
$396$	12.5604	+	21.7552i	0.631183	+	1.09324i
$397$	−10.2554	−	17.7629i	−0.514704	−	0.891494i	−0.999854	−	0.0170631i	$-0.994568\pi$
$397$	−10.2554	−	17.7629i	−0.514704	−	0.891494i	0.485150	−	0.874431i	$-0.338765\pi$
$398$	−2.83000	+	4.90170i	−0.141855	+	0.245700i
$399$	−1.67211			−0.0837101
$400$	26.1906	+	45.3634i	1.30953	+	2.26817i
$401$	1.49557			0.0746850			0.0373425	−	0.999303i	$-0.488111\pi$
$401$	1.49557			0.0746850			0.0373425	+	0.999303i	$0.488111\pi$
$402$	7.27131			0.362660
$403$	5.55710	−	0.344510i	0.276819	−	0.0171613i
$404$	1.86676			0.0928747
$405$	31.8194			1.58112
$406$	0.259079	+	0.448738i	0.0128579	+	0.0222705i
$407$	−20.7602			−1.02904
$408$	14.4081	−	24.9555i	0.713306	−	1.23548i
$409$	−9.99000	−	17.3032i	−0.493974	−	0.855587i	0.506002	−	0.862532i	$-0.331123\pi$
$409$	−9.99000	−	17.3032i	−0.493974	−	0.855587i	−0.999976	+	0.00694470i	$0.997789\pi$
$410$	−16.4271	−	28.4526i	−0.811277	−	1.40517i
$411$	−22.9616			−1.13261
$412$	−1.95698	+	3.38959i	−0.0964137	+	0.166993i
$413$	1.12969	−	1.95669i	0.0555886	−	0.0962823i
$414$	2.55772	−	4.43010i	0.125705	−	0.217728i
$415$	−1.98884	−	3.44478i	−0.0976285	−	0.169097i
$416$	−2.53349	+	4.38813i	−0.124214	+	0.215146i
$417$	24.2540	+	42.0092i	1.18773	+	2.05720i
$418$	14.8855			0.728074
$419$	−11.2655			−0.550358			−0.275179	−	0.961393i	$-0.588737\pi$
$419$	−11.2655			−0.550358			−0.275179	+	0.961393i	$0.588737\pi$
$420$	1.62220	+	2.80973i	0.0791553	+	0.137101i
$421$	10.7086	−	18.5479i	0.521907	−	0.903969i	−0.477769	−	0.878486i	$-0.658554\pi$
$421$	10.7086	−	18.5479i	0.521907	−	0.903969i	0.999675	−	0.0254832i	$-0.00811243\pi$
$422$	15.5641	+	26.9577i	0.757647	+	1.31228i
$423$	−39.8768	+	69.0686i	−1.93887	+	3.35823i
$424$	−10.1572	+	17.5927i	−0.493276	+	0.854379i
$425$	28.5221	−	49.4018i	1.38353	−	2.39634i
$426$	53.4271			2.58855
$427$	1.59551	+	2.76350i	0.0772121	+	0.133735i
$428$	−7.34833	−	12.7277i	−0.355195	−	0.615216i
$429$	6.54656	−	11.3390i	0.316071	−	0.547451i
$430$	−34.2590			−1.65212
$431$	−17.3927	−	30.1251i	−0.837779	−	1.45108i	−0.891747	−	0.452534i	$-0.850520\pi$
$431$	−17.3927	−	30.1251i	−0.837779	−	1.45108i	0.0539682	−	0.998543i	$-0.482813\pi$
$432$	−43.2064			−2.07877
$433$	0.0954850			0.00458872			0.00229436	−	0.999997i	$-0.499270\pi$
$433$	0.0954850			0.00458872			0.00229436	+	0.999997i	$0.499270\pi$
$434$	−1.21781	+	2.44763i	−0.0584567	+	0.117490i
$435$	−12.3840			−0.593766
$436$	5.26983			0.252379
$437$	−0.495135	−	0.857599i	−0.0236855	−	0.0410245i
$438$	46.6223			2.22770
$439$	−9.99694	+	17.3152i	−0.477128	+	0.826410i	−0.999656	−	0.0262118i	$-0.991656\pi$
$439$	−9.99694	+	17.3152i	−0.477128	+	0.826410i	0.522528	+	0.852622i	$0.324989\pi$
$440$	15.3218	+	26.5381i	0.730437	+	1.26515i
$441$	20.4019	+	35.3370i	0.971517	+	1.68272i
$442$	9.38295			0.446301
$443$	1.19664	−	2.07264i	0.0568539	−	0.0984739i	−0.836198	−	0.548428i	$-0.815226\pi$
$443$	1.19664	−	2.07264i	0.0568539	−	0.0984739i	0.893052	+	0.449954i	$0.148560\pi$
$444$	−6.84513	+	11.8561i	−0.324856	+	0.562667i
$445$	−27.6319	+	47.8599i	−1.30988	+	2.26878i
$446$	3.15922	+	5.47194i	0.149594	+	0.259104i
$447$	2.63214	−	4.55899i	0.124496	−	0.215633i
$448$	0.180250	+	0.312202i	0.00851600	+	0.0147501i
$449$	−7.00619			−0.330643			−0.165321	−	0.986240i	$-0.552866\pi$
$449$	−7.00619			−0.330643			−0.165321	+	0.986240i	$0.552866\pi$
$450$	−106.502			−5.02054
$451$	−10.6342	−	18.4189i	−0.500744	−	0.867313i
$452$	−0.273102	+	0.473026i	−0.0128456	+	0.0222493i
$453$	21.5359	+	37.3014i	1.01185	+	1.75257i
$454$	3.67913	−	6.37244i	0.172670	−	0.299073i
$455$	0.560420	−	0.970677i	0.0262729	−	0.0455060i
$456$	−5.20739	+	9.01947i	−0.243858	+	0.422375i
$457$	−33.2893			−1.55721			−0.778603	−	0.627516i	$-0.784072\pi$
$457$	−33.2893			−1.55721			−0.778603	+	0.627516i	$0.784072\pi$
$458$	18.7333	+	32.4471i	0.875352	+	1.51615i
$459$	23.5264	+	40.7489i	1.09812	+	1.90200i
$460$	−0.960713	+	1.66400i	−0.0447935	+	0.0775845i
$461$	27.5968			1.28531			0.642655	−	0.766156i	$-0.277833\pi$
$461$	27.5968			1.28531			0.642655	+	0.766156i	$0.277833\pi$
$462$	3.21445	+	5.56760i	0.149550	+	0.259028i
$463$	21.9218			1.01879			0.509396	−	0.860532i	$-0.329869\pi$
$463$	21.9218			1.01879			0.509396	+	0.860532i	$0.329869\pi$
$464$	5.27548			0.244908
$465$	−36.1082	−	54.4554i	−1.67448	−	2.52531i
$466$	29.9706			1.38836
$467$	−29.3072			−1.35617			−0.678087	−	0.734982i	$-0.737191\pi$
$467$	−29.3072			−1.35617			−0.678087	+	0.734982i	$0.737191\pi$
$468$	−2.86150	−	4.95626i	−0.132273	−	0.229103i
$469$	0.402954			0.0186067
$470$	45.8480	−	79.4110i	2.11481	−	3.66296i
$471$	−20.5657	−	35.6208i	−0.947615	−	1.64132i
$472$	−7.03634	−	12.1873i	−0.323874	−	0.560966i
$473$	−22.1777			−1.01973
$474$	20.6614	−	35.7867i	0.949011	−	1.64374i
$475$	−10.3085	+	17.8549i	−0.472988	+	0.819239i
$476$	−0.752564	+	1.30348i	−0.0344937	+	0.0597449i
$477$	−33.7574	−	58.4695i	−1.54564	−	2.67713i
$478$	8.71434	−	15.0937i	0.398585	−	0.690369i
$479$	5.65436	+	9.79363i	0.258354	+	0.447482i	0.965801	−	0.259284i	$-0.0834865\pi$
$479$	5.65436	+	9.79363i	0.258354	+	0.447482i	−0.707447	+	0.706766i	$0.750153\pi$
$480$	59.4622			2.71406
$481$	4.72957			0.215650
$482$	−9.30162	−	16.1109i	−0.423677	−	0.733831i
$483$	0.213844	−	0.370389i	0.00973024	−	0.0168533i
$484$	−4.01131	−	6.94780i	−0.182332	−	0.315809i
$485$	2.59045	−	4.48679i	0.117626	−	0.203735i
$486$	−1.55408	+	2.69175i	−0.0704947	+	0.122100i
$487$	−5.74161	+	9.94476i	−0.260177	+	0.450640i	−0.966289	−	0.257460i	$-0.917114\pi$
$487$	−5.74161	+	9.94476i	−0.260177	+	0.450640i	0.706112	+	0.708100i	$0.250448\pi$
$488$	19.8754			0.899715
$489$	−30.8685	−	53.4657i	−1.39592	−	2.41780i
$490$	−23.4569	−	40.6285i	−1.05967	−	1.83541i
$491$	−7.35221	+	12.7344i	−0.331801	+	0.574695i	−0.982865	−	0.184327i	$-0.940989\pi$
$491$	−7.35221	+	12.7344i	−0.331801	+	0.574695i	0.651064	+	0.759022i	$0.274323\pi$
$492$	−14.0254			−0.632313
$493$	−2.87256	−	4.97542i	−0.129374	−	0.224082i
$494$	−3.39120			−0.152577
$495$	−101.844			−4.57754
$496$	15.3818	+	23.1976i	0.690664	+	1.04160i
$497$	2.96077			0.132809
$498$	−5.19774			−0.232916
$499$	11.3715	+	19.6960i	0.509057	+	0.881712i	0.999945	+	0.0104898i	$0.00333906\pi$
$499$	11.3715	+	19.6960i	0.509057	+	0.881712i	−0.490888	+	0.871223i	$0.663328\pi$
$500$	20.9143			0.935315
$501$	15.8654	−	27.4798i	0.708816	−	1.22770i
$502$	−20.1691	−	34.9339i	−0.900191	−	1.55918i
$503$	0.814567	+	1.41087i	0.0363197	+	0.0629076i	0.883614	−	0.468216i	$-0.155103\pi$
$503$	0.814567	+	1.41087i	0.0363197	+	0.0629076i	−0.847294	+	0.531124i	$0.821770\pi$
$504$	−2.98142			−0.132803
$505$	−3.78407	+	6.55420i	−0.168389	+	0.291658i
$506$	−1.90369	+	3.29729i	−0.0846293	+	0.146582i
$507$	−1.49143	+	2.58324i	−0.0662368	+	0.114726i
$508$	7.30627	+	12.6548i	0.324163	+	0.561467i
$509$	−7.65500	+	13.2589i	−0.339302	+	0.587688i	−0.984302	−	0.176495i	$-0.943524\pi$
$509$	−7.65500	+	13.2589i	−0.339302	+	0.587688i	0.645000	+	0.764183i	$0.276858\pi$
$510$	−55.0556	−	95.3591i	−2.43790	−	4.22257i
$511$	2.58367			0.114295
$512$	−7.58874			−0.335378
$513$	−8.50296	−	14.7276i	−0.375415	−	0.650237i
$514$	3.54664	−	6.14297i	0.156436	−	0.270955i
$515$	−7.93393	−	13.7420i	−0.349611	−	0.605544i
$516$	−7.31254	+	12.6657i	−0.321917	+	0.557576i
$517$	29.6799	−	51.4071i	1.30532	−	2.26088i
$518$	−1.16114	+	2.01116i	−0.0510177	+	0.0883652i
$519$	−36.8542			−1.61772
$520$	−3.49060	−	6.04589i	−0.153073	−	0.265130i
$521$	9.46953	+	16.4017i	0.414868	+	0.718572i	0.995415	−	0.0956551i	$-0.0304946\pi$
$521$	9.46953	+	16.4017i	0.414868	+	0.718572i	−0.580547	+	0.814227i	$0.697161\pi$
$522$	−5.36307	+	9.28911i	−0.234735	+	0.406573i
$523$	29.5628			1.29269			0.646346	−	0.763044i	$-0.276296\pi$
$523$	29.5628			1.29269			0.646346	+	0.763044i	$0.276296\pi$
$524$	−1.75466	−	3.03916i	−0.0766527	−	0.132766i
$525$	−8.90431			−0.388616
$526$	15.0673			0.656964
$527$	13.5026	−	27.1383i	0.588181	−	1.18216i
$528$	65.4541			2.84853
$529$	−22.7467			−0.988987
$530$	38.8122	+	67.2248i	1.68590	+	2.92006i
$531$	46.7705			2.02967
$532$	0.271993	−	0.471106i	0.0117924	−	0.0204250i
$533$	2.42267	+	4.19619i	0.104937	+	0.181757i
$534$	36.1073	+	62.5396i	1.56251	+	2.70635i
$535$	59.5827			2.57599
$536$	1.25491	−	2.17356i	0.0542037	−	0.0938836i
$537$	−27.3610	+	47.3906i	−1.18071	+	2.04505i
$538$	11.3751	−	19.7023i	0.490416	−	0.849426i
$539$	−15.1849	−	26.3011i	−0.654061	−	1.13287i
$540$	−16.4983	+	28.5759i	−0.709975	+	1.22971i
$541$	−9.19666	−	15.9291i	−0.395395	−	0.684844i	0.597756	−	0.801678i	$-0.296059\pi$
$541$	−9.19666	−	15.9291i	−0.395395	−	0.684844i	−0.993152	+	0.116833i	$0.962726\pi$
$542$	−17.6787			−0.759366
$543$	−50.4342			−2.16434
$544$	13.7927	+	23.8897i	0.591358	+	1.02426i
$545$	−10.6824	+	18.5024i	−0.457583	+	0.792557i
$546$	−0.732314	−	1.26841i	−0.0313402	−	0.0542828i
$547$	12.0781	−	20.9198i	0.516421	−	0.894467i	−0.483397	−	0.875401i	$-0.660597\pi$
$547$	12.0781	−	20.9198i	0.516421	−	0.894467i	0.999818	−	0.0190660i	$-0.00606927\pi$
$548$	3.73505	−	6.46929i	0.159553	−	0.276354i
$549$	−33.0279	+	57.2059i	−1.40959	+	2.44149i
$550$	79.2683			3.38001
$551$	1.03821	+	1.79823i	0.0442291	+	0.0766070i
$552$	−1.33193	−	2.30698i	−0.0566909	−	0.0981915i
$553$	1.14500	−	1.98319i	0.0486902	−	0.0843339i
$554$	−38.7610			−1.64680
$555$	−27.7513	−	48.0667i	−1.17798	−	2.04032i
$556$	−15.7811			−0.669268
$557$	−34.7425			−1.47209			−0.736043	−	0.676935i	$-0.763308\pi$
$557$	−34.7425			−1.47209			−0.736043	+	0.676935i	$0.763308\pi$
$558$	−56.4837	+	3.50169i	−2.39115	+	0.148238i
$559$	5.05252			0.213699
$560$	5.60322			0.236779
$561$	−35.6405	−	61.7312i	−1.50474	−	2.60629i
$562$	−17.8060			−0.751101
$563$	5.75857	−	9.97414i	0.242695	−	0.420360i	−0.718786	−	0.695231i	$-0.755302\pi$
$563$	5.75857	−	9.97414i	0.242695	−	0.420360i	0.961481	+	0.274871i	$0.0886353\pi$
$564$	−19.5724	−	33.9004i	−0.824146	−	1.42746i
$565$	−1.10720	−	1.91773i	−0.0465802	−	0.0806793i
$566$	28.6670			1.20496
$567$	1.15210	−	1.99549i	0.0483835	−	0.0838027i
$568$	9.22063	−	15.9706i	0.386889	−	0.670112i
$569$	−12.8090	+	22.1859i	−0.536982	+	0.930079i	0.462083	+	0.886837i	$0.347102\pi$
$569$	−12.8090	+	22.1859i	−0.536982	+	0.930079i	−0.999065	+	0.0432427i	$0.986231\pi$
$570$	19.8983	+	34.4649i	0.833448	+	1.44357i
$571$	−13.8809	+	24.0424i	−0.580896	+	1.00614i	0.414477	+	0.910060i	$0.363964\pi$
$571$	−13.8809	+	24.0424i	−0.580896	+	1.00614i	−0.995373	+	0.0960819i	$0.969369\pi$
$572$	2.12979	+	3.68890i	0.0890509	+	0.154241i
$573$	53.6517			2.24133
$574$	−2.37913			−0.0993029
$575$	−2.63669	−	4.56688i	−0.109958	−	0.190452i
$576$	−3.73126	+	6.46274i	−0.155469	+	0.269281i
$577$	−9.97895	−	17.2840i	−0.415429	−	0.719544i	0.580044	−	0.814585i	$-0.303035\pi$
$577$	−9.97895	−	17.2840i	−0.415429	−	0.719544i	−0.995473	+	0.0950406i	$0.969702\pi$
$578$	10.8915	−	18.8646i	0.453026	−	0.784664i
$579$	18.9888	−	32.8895i	0.789147	−	1.36684i
$580$	2.01444	−	3.48911i	0.0836449	−	0.144877i
$581$	−0.288043			−0.0119500
$582$	−3.38500	−	5.86299i	−0.140313	−	0.243029i
$583$	25.1253	+	43.5183i	1.04058	+	1.80234i
$584$	8.04624	−	13.9365i	0.332956	−	0.576697i
$585$	23.2020			0.959284
$586$	11.0311	+	19.1065i	0.455691	+	0.789281i
$587$	16.8075			0.693719			0.346859	−	0.937917i	$-0.387248\pi$
$587$	16.8075			0.693719			0.346859	+	0.937917i	$0.387248\pi$
$588$	−20.0274			−0.825914
$589$	−4.88012	+	9.80837i	−0.201082	+	0.404147i
$590$	−53.7740			−2.21384
$591$	31.1600			1.28175
$592$	11.8218	+	20.4760i	0.485875	+	0.841560i
$593$	35.3173			1.45031			0.725154	−	0.688586i	$-0.241768\pi$
$593$	35.3173			1.45031			0.725154	+	0.688586i	$0.241768\pi$
$594$	−32.6921	+	56.6243i	−1.34137	+	2.32332i
$595$	−3.05102	−	5.28452i	−0.125080	−	0.216644i
$596$	0.856312	+	1.48318i	0.0350759	+	0.0607532i
$597$	−9.79583			−0.400917
$598$	0.433697	−	0.751185i	0.0177352	−	0.0307183i
$599$	3.45578	−	5.98559i	0.141200	−	0.244565i	−0.786749	−	0.617273i	$-0.788237\pi$
$599$	3.45578	−	5.98559i	0.141200	−	0.244565i	0.927949	+	0.372708i	$0.121571\pi$
$600$	−27.7304	+	48.0305i	−1.13209	+	1.96084i
$601$	14.3145	+	24.7935i	0.583901	+	1.01135i	0.995011	+	0.0997610i	$0.0318078\pi$
$601$	14.3145	+	24.7935i	0.583901	+	1.01135i	−0.411110	+	0.911586i	$0.634859\pi$
$602$	−1.24043	+	2.14848i	−0.0505561	+	0.0875657i
$603$	4.17068	+	7.22384i	0.169843	+	0.294177i
$604$	−14.0126			−0.570163
$605$	32.5250			1.32233
$606$	4.94474	+	8.56453i	0.200866	+	0.347910i
$607$	−9.12245	+	15.8006i	−0.370269	+	0.641325i	−0.989607	−	0.143800i	$-0.954068\pi$
$607$	−9.12245	+	15.8006i	−0.370269	+	0.641325i	0.619338	+	0.785125i	$0.287401\pi$
$608$	−4.98499	−	8.63425i	−0.202168	−	0.350165i
$609$	−0.448391	+	0.776637i	−0.0181697	+	0.0314709i
$610$	37.9735	−	65.7720i	1.53750	−	2.66303i
$611$	−6.76166	+	11.7115i	−0.273547	+	0.473798i
$612$	−31.1569			−1.25944
$613$	20.7489	+	35.9382i	0.838042	+	1.45153i	0.891529	+	0.452963i	$0.149633\pi$
$613$	20.7489	+	35.9382i	0.838042	+	1.45153i	−0.0534876	+	0.998569i	$0.517034\pi$
$614$	23.9841	+	41.5417i	0.967919	+	1.67649i
$615$	28.4306	−	49.2433i	1.14643	−	1.98568i
$616$	2.21905			0.0894079
$617$	−2.29891	−	3.98183i	−0.0925506	−	0.160302i	0.816033	−	0.578005i	$-0.196169\pi$
$617$	−2.29891	−	3.98183i	−0.0925506	−	0.160302i	−0.908584	+	0.417703i	$0.862835\pi$
$618$	−20.7349			−0.834081
$619$	−34.4649			−1.38526			−0.692630	−	0.721293i	$-0.743548\pi$
$619$	−34.4649			−1.38526			−0.692630	+	0.721293i	$0.743548\pi$
$620$	21.2160	−	1.31528i	0.852055	−	0.0528229i
$621$	4.34973			0.174549
$622$	−21.4017			−0.858131
$623$	2.00096	+	3.46576i	0.0801667	+	0.138853i
$624$	−14.9117			−0.596946
$625$	−16.1998	+	28.0589i	−0.647992	+	1.12236i
$626$	−5.58823	−	9.67910i	−0.223351	−	0.386855i
$627$	12.8813	+	22.3110i	0.514428	+	0.891016i
$628$	13.3812			0.533969
$629$	12.8743	−	22.2989i	0.513330	−	0.889114i
$630$	−5.69625	+	9.86620i	−0.226944	+	0.393079i
$631$	−1.75803	+	3.04501i	−0.0699863	+	0.121220i	−0.898895	−	0.438164i	$-0.855629\pi$
$631$	−1.75803	+	3.04501i	−0.0699863	+	0.121220i	0.828909	+	0.559384i	$0.188962\pi$
$632$	−7.13164	−	12.3524i	−0.283682	−	0.491351i
$633$	−26.9369	+	46.6561i	−1.07065	+	1.85441i
$634$	24.4226	+	42.3012i	0.969946	+	1.68000i
$635$	−59.2416			−2.35093
$636$	33.1377			1.31400
$637$	3.45942	+	5.99189i	0.137067	+	0.237407i
$638$	3.99168	−	6.91380i	0.158032	−	0.273720i
$639$	30.6448	+	53.0783i	1.21229	+	2.09974i
$640$	24.2246	−	41.9582i	0.957560	−	1.65854i
$641$	−5.51565	+	9.55339i	−0.217855	+	0.377336i	−0.954152	−	0.299322i	$-0.903239\pi$
$641$	−5.51565	+	9.55339i	−0.217855	+	0.377336i	0.736297	+	0.676659i	$0.236573\pi$
$642$	38.9291	−	67.4271i	1.53641	−	2.66114i
$643$	−27.8612			−1.09874			−0.549369	−	0.835580i	$-0.685132\pi$
$643$	−27.8612			−1.09874			−0.549369	+	0.835580i	$0.685132\pi$
$644$	0.0695698	+	0.120498i	0.00274143	+	0.00474830i
$645$	−29.6462	−	51.3488i	−1.16732	−	2.02186i
$646$	−9.23113	+	15.9888i	−0.363194	+	0.629070i
$647$	11.1755			0.439354			0.219677	−	0.975573i	$-0.429500\pi$
$647$	11.1755			0.439354			0.219677	+	0.975573i	$0.429500\pi$
$648$	−7.17587	−	12.4290i	−0.281895	−	0.488256i
$649$	−34.8109			−1.36645
$650$	−18.0588			−0.708326
$651$	−4.72245	+	0.292767i	−0.185087	+	0.0114744i
$652$	20.0848			0.786583
$653$	9.43311			0.369146			0.184573	−	0.982819i	$-0.440910\pi$
$653$	9.43311			0.369146			0.184573	+	0.982819i	$0.440910\pi$
$654$	13.9589	+	24.1775i	0.545837	+	0.945417i
$655$	14.2274			0.555909
$656$	−12.1112	+	20.9773i	−0.472864	+	0.819024i
$657$	26.7417	+	46.3179i	1.04329	+	1.80704i
$658$	−3.32007	−	5.75053i	−0.129430	−	0.224179i
$659$	−8.42384			−0.328146			−0.164073	−	0.986448i	$-0.552463\pi$
$659$	−8.42384			−0.328146			−0.164073	+	0.986448i	$0.552463\pi$
$660$	24.9936	−	43.2902i	0.972874	−	1.68507i
$661$	−16.5657	+	28.6926i	−0.644330	+	1.11601i	0.340126	+	0.940380i	$0.389530\pi$
$661$	−16.5657	+	28.6926i	−0.644330	+	1.11601i	−0.984456	+	0.175633i	$0.943803\pi$
$662$	−4.47881	+	7.75753i	−0.174074	+	0.301505i
$663$	8.11960	+	14.0636i	0.315339	+	0.546183i
$664$	−0.897043	+	1.55372i	−0.0348120	+	0.0602962i
$665$	1.10270	+	1.90994i	0.0427611	+	0.0740643i
$666$	−48.0725			−1.86277
$667$	−0.531100			−0.0205643
$668$	5.16150	+	8.93997i	0.199704	+	0.345898i
$669$	−5.46771	+	9.47036i	−0.211394	+	0.366145i
$670$	−4.79521	−	8.30554i	−0.185255	−	0.320871i
$671$	24.5823	−	42.5779i	0.948991	−	1.64370i
$672$	2.15297	−	3.72905i	0.0830526	−	0.143851i
$673$	3.76690	−	6.52447i	0.145203	−	0.251500i	−0.784245	−	0.620451i	$-0.786950\pi$
$673$	3.76690	−	6.52447i	0.145203	−	0.251500i	0.929449	+	0.368951i	$0.120283\pi$
$674$	19.9304			0.767690
$675$	−45.2799	−	78.4271i	−1.74283	−	3.01866i
$676$	−0.485207	−	0.840403i	−0.0186618	−	0.0323232i
$677$	13.5846	−	23.5293i	0.522100	−	0.904303i	−0.477570	−	0.878594i	$-0.658482\pi$
$677$	13.5846	−	23.5293i	0.522100	−	0.904303i	0.999669	−	0.0257096i	$-0.00818451\pi$
$678$	−2.89361			−0.111128
$679$	−0.187587	−	0.324910i	−0.00719892	−	0.0124689i
$680$	−38.0067			−1.45749
$681$	12.7350			0.488008
$682$	42.0403	−	2.60628i	1.60981	−	0.0997995i
$683$	−27.6752			−1.05896			−0.529481	−	0.848322i	$-0.677613\pi$
$683$	−27.6752			−1.05896			−0.529481	+	0.848322i	$0.677613\pi$
$684$	11.2608			0.430567
$685$	15.1425	+	26.2276i	0.578565	+	1.00210i
$686$	−6.83434			−0.260936
$687$	−32.4220	+	56.1566i	−1.23698	+	2.14251i
$688$	12.6291	+	21.8742i	0.481479	+	0.833946i
$689$	−5.72403	−	9.91431i	−0.218068	−	0.377705i
$690$	−10.1791			−0.387511
$691$	17.3549	−	30.0596i	0.660213	−	1.14352i	−0.320346	−	0.947301i	$-0.603799\pi$
$691$	17.3549	−	30.0596i	0.660213	−	1.14352i	0.980559	−	0.196222i	$-0.0628674\pi$
$692$	5.99488	−	10.3834i	0.227891	−	0.394719i
$693$	−3.68750	+	6.38693i	−0.140076	+	0.242620i
$694$	−28.1731	−	48.7973i	−1.06944	−	1.85232i
$695$	31.9896	−	55.4076i	1.21343	−	2.10173i
$696$	2.79282	+	4.83731i	0.105862	+	0.183358i
$697$	26.3788			0.999168
$698$	−33.1513			−1.25480
$699$	25.9353	+	44.9212i	0.980963	+	1.69908i
$700$	1.44842	−	2.50873i	0.0547450	−	0.0948212i
$701$	14.9666	+	25.9228i	0.565279	+	0.979092i	0.997024	+	0.0770964i	$0.0245649\pi$
$701$	14.9666	+	25.9228i	0.565279	+	0.979092i	−0.431744	+	0.901996i	$0.642102\pi$
$702$	7.44789	−	12.9001i	0.281102	−	0.486883i
$703$	−4.65304	+	8.05930i	−0.175493	+	0.303962i
$704$	2.77715	−	4.81016i	0.104668	−	0.181290i
$705$	158.699			5.97696
$706$	−20.4592	−	35.4364i	−0.769992	−	1.33367i
$707$	0.274023	+	0.474621i	0.0103057	+	0.0178500i
$708$	−11.4780	+	19.8805i	−0.431369	+	0.747154i
$709$	−23.2378			−0.872715			−0.436357	−	0.899773i	$-0.643732\pi$
$709$	−23.2378			−0.872715			−0.436357	+	0.899773i	$0.643732\pi$
$710$	−35.2336	−	61.0263i	−1.32229	−	2.29028i
$711$	47.4040			1.77779
$712$	24.9261			0.934144
$713$	−1.54854	−	2.33538i	−0.0579932	−	0.0874606i
$714$	−7.97367			−0.298407
$715$	−17.2690			−0.645825
$716$	−8.90133	−	15.4176i	−0.332658	−	0.576181i
$717$	30.1640			1.12650
$718$	−19.2825	+	33.3983i	−0.719617	+	1.24641i
$719$	−24.6681	−	42.7265i	−0.919966	−	1.59343i	−0.799463	−	0.600715i	$-0.794882\pi$
$719$	−24.6681	−	42.7265i	−0.919966	−	1.59343i	−0.120503	−	0.992713i	$-0.538451\pi$
$720$	57.9948	+	100.450i	2.16134	+	3.74355i
$721$	−1.14907			−0.0427935
$722$	−13.0368	+	22.5804i	−0.485180	+	0.840356i
$723$	16.0984	−	27.8833i	0.598708	−	1.03699i
$724$	8.20387	−	14.2095i	0.304894	−	0.528092i
$725$	5.52866	+	9.57591i	0.205329	+	0.355640i
$726$	21.2506	−	36.8071i	0.788684	−	1.36604i
$727$	−2.15207	−	3.72749i	−0.0798157	−	0.138245i	0.823355	−	0.567527i	$-0.192100\pi$
$727$	−2.15207	−	3.72749i	−0.0798157	−	0.138245i	−0.903170	+	0.429282i	$0.858767\pi$
$728$	−0.505541			−0.0187366
$729$	−29.6429			−1.09789
$730$	−30.7460	−	53.2537i	−1.13796	−	1.97101i
$731$	13.7534	−	23.8215i	0.508686	−	0.881070i
$732$	−16.2108	−	28.0779i	−0.599168	−	1.03779i
$733$	−19.3357	+	33.4904i	−0.714179	+	1.23699i	0.249096	+	0.968479i	$0.419866\pi$
$733$	−19.3357	+	33.4904i	−0.714179	+	1.23699i	−0.963275	+	0.268516i	$0.913467\pi$
$734$	−3.67801	+	6.37051i	−0.135758	+	0.235140i
$735$	40.5971	−	70.3162i	1.49745	−	2.59365i
$736$	2.55010			0.0939979
$737$	−3.10420	−	5.37664i	−0.114345	−	0.198051i
$738$	−24.6246	−	42.6511i	−0.906444	−	1.57001i
$739$	21.8031	−	37.7642i	0.802042	−	1.38918i	−0.116228	−	0.993223i	$-0.537080\pi$
$739$	21.8031	−	37.7642i	0.802042	−	1.38918i	0.918270	−	0.395955i	$-0.129586\pi$
$740$	18.0566			0.663775
$741$	−2.93460	−	5.08288i	−0.107805	−	0.186724i
$742$	5.62116			0.206359
$743$	16.5682			0.607830			0.303915	−	0.952699i	$-0.401706\pi$
$743$	16.5682			0.607830			0.303915	+	0.952699i	$0.401706\pi$
$744$	−13.1277	+	26.3849i	−0.481287	+	0.967319i
$745$	−6.94326			−0.254381
$746$	−18.1088			−0.663010
$747$	−2.98132	−	5.16380i	−0.109081	−	0.188934i
$748$	23.1898			0.847904
$749$	2.15733	−	3.73661i	0.0788273	−	0.136533i
$750$	55.3985	+	95.9530i	2.02287	+	3.50371i
$751$	−2.00080	−	3.46548i	−0.0730101	−	0.126457i	0.827209	−	0.561894i	$-0.189927\pi$
$751$	−2.00080	−	3.46548i	−0.0730101	−	0.126457i	−0.900219	+	0.435437i	$0.856594\pi$
$752$	−67.6047			−2.46529
$753$	34.9069	−	60.4606i	1.27208	−	2.20331i
$754$	−0.909383	+	1.57510i	−0.0331178	+	0.0573617i
$755$	28.4046	−	49.1982i	1.03375	−	1.79051i
$756$	1.19472	+	2.06932i	0.0434516	+	0.0752604i
$757$	10.4037	−	18.0198i	0.378129	−	0.654939i	−0.612661	−	0.790346i	$-0.709901\pi$
$757$	10.4037	−	18.0198i	0.378129	−	0.654939i	0.990790	+	0.135407i	$0.0432341\pi$
$758$	−8.81293	−	15.2644i	−0.320100	−	0.554430i
$759$	−6.58948			−0.239183
$760$	13.7365			0.498274
$761$	−3.57006	−	6.18352i	−0.129415	−	0.224153i	0.794035	−	0.607872i	$-0.207976\pi$
$761$	−3.57006	−	6.18352i	−0.129415	−	0.224153i	−0.923450	+	0.383719i	$0.874643\pi$
$762$	−38.7062	+	67.0411i	−1.40218	+	2.42864i
$763$	0.773562	+	1.33985i	0.0280048	+	0.0485058i
$764$	−8.72723	+	15.1160i	−0.315740	+	0.546878i
$765$	63.1577	−	109.392i	2.28347	−	3.95509i
$766$	−3.21339	+	5.56576i	−0.116105	+	0.201099i
$767$	7.93059			0.286357
$768$	−27.8804	−	48.2902i	−1.00605	−	1.74252i
$769$	−10.9620	−	18.9867i	−0.395299	−	0.684677i	0.597841	−	0.801615i	$-0.296026\pi$
$769$	−10.9620	−	18.9867i	−0.395299	−	0.684677i	−0.993139	+	0.116938i	$0.962692\pi$
$770$	4.23967	−	7.34332i	0.152787	−	0.264635i
$771$	12.2764			0.442126
$772$	6.17761	+	10.6999i	0.222337	+	0.385099i
$773$	−46.6454			−1.67772			−0.838859	−	0.544348i	$-0.816777\pi$
$773$	−46.6454			−1.67772			−0.838859	+	0.544348i	$0.816777\pi$
$774$	−51.3550			−1.84592
$775$	−25.9876	+	52.2315i	−0.933503	+	1.87621i
$776$	−2.33678			−0.0838855
$777$	−4.01921			−0.144188
$778$	−1.97126	−	3.41432i	−0.0706730	−	0.122409i
$779$	−9.53388			−0.341587
$780$	−5.69402	+	9.86233i	−0.203879	+	0.353128i
$781$	−22.8086	−	39.5057i	−0.816157	−	1.41362i
$782$	−2.36112	−	4.08957i	−0.0844334	−	0.146243i
$783$	−9.12059			−0.325943
$784$	−17.2941	+	29.9542i	−0.617645	+	1.06979i
$785$	−27.1248	+	46.9816i	−0.968127	+	1.67685i
$786$	9.29561	−	16.1005i	0.331564	−	0.574285i
$787$	11.2857	+	19.5475i	0.402293	+	0.696793i	0.994002	−	0.109359i	$-0.0348798\pi$
$787$	11.2857	+	19.5475i	0.402293	+	0.696793i	−0.591709	+	0.806152i	$0.701546\pi$
$788$	−5.06863	+	8.77913i	−0.180563	+	0.312743i
$789$	13.0386	+	22.5834i	0.464185	+	0.803992i
$790$	−54.5024			−1.93911
$791$	−0.160355			−0.00570157
$792$	22.9677	+	39.7812i	0.816122	+	1.41356i
$793$	−5.60033	+	9.70006i	−0.198874	+	0.344459i
$794$	17.6751	+	30.6141i	0.627265	+	1.08646i
$795$	−67.1729	+	116.347i	−2.38238	+	4.12640i
$796$	1.59344	−	2.75991i	0.0564778	−	0.0978225i
$797$	8.14355	−	14.1050i	0.288459	−	0.499626i	−0.684983	−	0.728559i	$-0.740190\pi$
$797$	8.14355	−	14.1050i	0.288459	−	0.499626i	0.973442	+	0.228933i	$0.0735237\pi$
$798$	2.88186			0.102017
$799$	36.8115	+	63.7595i	1.30230	+	2.25565i
$800$	−26.5461	−	45.9791i	−0.938545	−	1.62561i
$801$	−41.4209	+	71.7430i	−1.46353	+	2.53492i
$802$	−2.57759			−0.0910179
$803$	−19.9036	−	34.4740i	−0.702383	−	1.21656i
$804$	−4.09412			−0.144389
$805$	−0.564095			−0.0198817
$806$	−9.57759	+	0.593760i	−0.337356	+	0.0209143i
$807$	39.3742			1.38604
$808$	3.41352			0.120087
$809$	−14.5623	−	25.2227i	−0.511984	−	0.886783i	−0.999903	−	0.0138940i	$-0.995577\pi$
$809$	−14.5623	−	25.2227i	−0.511984	−	0.886783i	0.487919	−	0.872889i	$-0.337756\pi$
$810$	−54.8404			−1.92689
$811$	21.1350	−	36.6070i	0.742152	−	1.28544i	−0.209362	−	0.977838i	$-0.567139\pi$
$811$	21.1350	−	36.6070i	0.742152	−	1.28544i	0.951514	−	0.307606i	$-0.0995280\pi$
$812$	−0.145875	−	0.252663i	−0.00511921	−	0.00886673i
$813$	−15.2984	−	26.4976i	−0.536538	−	0.929312i
$814$	35.7799			1.25409
$815$	−40.7136	+	70.5181i	−1.42614	+	2.47014i
$816$	−40.5909	+	70.3055i	−1.42097	+	2.46118i
$817$	−4.97076	+	8.60962i	−0.173905	+	0.301212i
$818$	17.2177	+	29.8218i	0.602001	+	1.04270i
$819$	0.840083	−	1.45507i	0.0293549	−	0.0508441i
$820$	9.24931	+	16.0203i	0.323000	+	0.559452i
$821$	−10.9597			−0.382496			−0.191248	−	0.981542i	$-0.561253\pi$
$821$	−10.9597			−0.382496			−0.191248	+	0.981542i	$0.561253\pi$
$822$	39.5741			1.38031
$823$	14.0680	+	24.3665i	0.490380	+	0.849362i	0.999939	−	0.0110733i	$-0.00352481\pi$
$823$	14.0680	+	24.3665i	0.490380	+	0.849362i	−0.509559	+	0.860436i	$0.670191\pi$
$824$	−3.57850	+	6.19815i	−0.124663	+	0.215923i
$825$	68.5953	+	118.811i	2.38818	+	4.13645i
$826$	−1.94702	+	3.37233i	−0.0677453	+	0.117338i
$827$	−3.01037	+	5.21411i	−0.104681	+	0.181312i	−0.913608	−	0.406597i	$-0.866715\pi$
$827$	−3.01037	+	5.21411i	−0.104681	+	0.181312i	0.808927	+	0.587909i	$0.200049\pi$
$828$	−1.44013	+	2.49438i	−0.0500480	+	0.0866856i
$829$	−48.0842			−1.67003			−0.835017	−	0.550223i	$-0.814543\pi$
$829$	−48.0842			−1.67003			−0.835017	+	0.550223i	$0.814543\pi$
$830$	3.42775	+	5.93703i	0.118979	+	0.206077i
$831$	−33.5421	−	58.0966i	−1.16356	−	2.01535i
$832$	−0.632687	+	1.09585i	−0.0219345	+	0.0379916i
$833$	37.6672			1.30509
$834$	−41.8016	−	72.4024i	−1.44747	−	2.50709i
$835$	−41.8511			−1.44832
$836$	−8.38131			−0.289874
$837$	−26.5931	−	40.1055i	−0.919190	−	1.38625i
$838$	19.4160			0.670716
$839$	50.1176			1.73025			0.865126	−	0.501555i	$-0.167238\pi$
$839$	50.1176			1.73025			0.865126	+	0.501555i	$0.167238\pi$
$840$	2.96632	+	5.13782i	0.102348	+	0.177272i
$841$	−27.8864			−0.961599
$842$	−18.4562	+	31.9671i	−0.636043	+	1.10166i
$843$	−15.4085	−	26.6884i	−0.530698	−	0.919196i
$844$	−8.76337	−	15.1786i	−0.301648	−	0.522469i
$845$	3.93422			0.135341
$846$	68.7271	−	119.039i	2.36289	−	4.09264i
$847$	1.17765	−	2.03974i	0.0404644	−	0.0700864i
$848$	28.6151	−	49.5629i	0.982648	−	1.70200i
$849$	24.8072	+	42.9673i	0.851380	+	1.47463i
$850$	−49.1576	+	85.1435i	−1.68609	+	2.92040i
$851$	−1.19014	−	2.06139i	−0.0407976	−	0.0706635i
$852$	−30.0822			−1.03060
$853$	45.5975			1.56123			0.780614	−	0.625013i	$-0.214906\pi$
$853$	45.5975			1.56123			0.780614	+	0.625013i	$0.214906\pi$
$854$	−2.74984	−	4.76286i	−0.0940976	−	0.162982i
$855$	−22.8266	+	39.5368i	−0.780652	+	1.35213i
$856$	−13.4370	−	23.2736i	−0.459268	−	0.795476i
$857$	16.0100	−	27.7301i	0.546891	−	0.947243i	−0.451594	−	0.892224i	$-0.649144\pi$
$857$	16.0100	−	27.7301i	0.546891	−	0.947243i	0.998485	−	0.0550199i	$-0.0175222\pi$
$858$	−11.2829	+	19.5426i	−0.385193	+	0.667173i
$859$	13.6907	−	23.7129i	0.467120	−	0.809075i	−0.532175	−	0.846634i	$-0.678625\pi$
$859$	13.6907	−	23.7129i	0.467120	−	0.809075i	0.999294	+	0.0375597i	$0.0119584\pi$
$860$	19.2896			0.657770
$861$	−2.05880	−	3.56594i	−0.0701636	−	0.121527i
$862$	29.9762	+	51.9203i	1.02099	+	1.76841i
$863$	−2.93417	+	5.08214i	−0.0998804	+	0.172998i	−0.911635	−	0.411001i	$-0.865179\pi$
$863$	−2.93417	+	5.08214i	−0.0998804	+	0.172998i	0.811755	+	0.583999i	$0.198513\pi$
$864$	43.7929			1.48986
$865$	24.3043	+	42.0962i	0.826369	+	1.43131i
$866$	−0.164567			−0.00559223
$867$	37.7001			1.28036
$868$	0.685690	−	1.37814i	0.0232738	−	0.0467772i
$869$	−35.2824			−1.19687
$870$	21.3437			0.723618
$871$	0.707197	+	1.22490i	0.0239625	+	0.0415042i
$872$	9.63631			0.326327
$873$	3.88314	−	6.72580i	0.131425	−	0.227634i
$874$	0.853359	+	1.47806i	0.0288653	+	0.0499962i
$875$	3.07002	+	5.31743i	0.103786	+	0.179762i
$876$	−26.2508			−0.886932
$877$	−13.7817	+	23.8705i	−0.465373	+	0.806050i	−0.999218	−	0.0395321i	$-0.987413\pi$
$877$	−13.7817	+	23.8705i	−0.465373	+	0.806050i	0.533845	+	0.845582i	$0.320747\pi$
$878$	17.2296	−	29.8426i	0.581472	−	1.00714i
$879$	−19.0917	+	33.0678i	−0.643947	+	1.11535i
$880$	−43.1650	−	74.7640i	−1.45509	−	2.52029i
$881$	23.6528	−	40.9678i	0.796881	−	1.38024i	−0.124756	−	0.992187i	$-0.539815\pi$
$881$	23.6528	−	40.9678i	0.796881	−	1.38024i	0.921638	−	0.388052i	$-0.126852\pi$
$882$	−35.1624	−	60.9030i	−1.18398	−	2.05071i
$883$	−21.7793			−0.732933			−0.366466	−	0.930431i	$-0.619433\pi$
$883$	−21.7793			−0.732933			−0.366466	+	0.930431i	$0.619433\pi$
$884$	−5.28309			−0.177690
$885$	−46.5337	−	80.5987i	−1.56421	−	2.70930i
$886$	−2.06239	+	3.57216i	−0.0692873	+	0.120009i
$887$	14.8304	+	25.6870i	0.497956	+	0.862485i	0.999997	−	0.00235860i	$-0.000750766\pi$
$887$	14.8304	+	25.6870i	0.497956	+	0.862485i	−0.502041	+	0.864844i	$0.667417\pi$
$888$	−12.5169	+	21.6799i	−0.420039	+	0.727529i
$889$	−2.14498	+	3.71522i	−0.0719404	+	0.124604i
$890$	47.6233	−	82.4860i	1.59634	−	2.76494i
$891$	−35.5012			−1.18933
$892$	−1.77881	−	3.08099i	−0.0595589	−	0.103159i
$893$	−13.3045	−	23.0441i	−0.445218	−	0.771140i
$894$	−4.53646	+	7.85738i	−0.151722	+	0.262790i
$895$	72.1749			2.41254
$896$	−1.75422	−	3.03839i	−0.0586043	−	0.101506i
$897$	1.50121			0.0501240
$898$	12.0751			0.402951
$899$	3.24700	+	4.89685i	0.108293	+	0.163319i
$900$	59.9660			1.99887
$901$	−62.3251			−2.07635
$902$	18.3279	+	31.7448i	0.610251	+	1.05699i
$903$	−4.29365			−0.142884
$904$	−0.499389	+	0.864966i	−0.0166094	+	0.0287684i
$905$	33.2598	+	57.6077i	1.10559	+	1.91495i
$906$	−37.1170	−	64.2885i	−1.23313	−	2.13584i
$907$	−30.6804			−1.01873			−0.509363	−	0.860551i	$-0.670119\pi$
$907$	−30.6804			−1.01873			−0.509363	+	0.860551i	$0.670119\pi$
$908$	−2.07154	+	3.58801i	−0.0687465	+	0.119072i
$909$	−5.67241	+	9.82490i	−0.188142	+	0.325871i
$910$	−0.965878	+	1.67295i	−0.0320186	+	0.0554578i
$911$	20.4421	+	35.4067i	0.677276	+	1.17308i	0.975798	+	0.218674i	$0.0701730\pi$
$911$	20.4421	+	35.4067i	0.677276	+	1.17308i	−0.298522	+	0.954403i	$0.596494\pi$
$912$	14.6704	−	25.4099i	0.485787	−	0.841407i
$913$	2.21897	+	3.84337i	0.0734372	+	0.127197i
$914$	57.3737			1.89775
$915$	131.442			4.34535
$916$	−10.5478	−	18.2694i	−0.348511	−	0.603638i
$917$	0.515136	−	0.892241i	0.0170113	−	0.0294644i
$918$	−40.5475	−	70.2303i	−1.33827	−	2.31795i
$919$	1.51080	−	2.61678i	0.0498366	−	0.0863195i	−0.840031	−	0.542538i	$-0.817463\pi$
$919$	1.51080	−	2.61678i	0.0498366	−	0.0863195i	0.889868	+	0.456219i	$0.150797\pi$
$920$	−1.75674	+	3.04276i	−0.0579180	+	0.100317i
$921$	−41.5096	+	71.8967i	−1.36779	+	2.36908i
$922$	−47.5628			−1.56640
$923$	5.19624	+	9.00016i	0.171036	+	0.296244i
$924$	−1.80990	−	3.13485i	−0.0595415	−	0.103129i
$925$	−24.7784	+	42.9174i	−0.814708	+	1.41112i
$926$	−37.7819			−1.24159
$927$	−11.8931	−	20.5995i	−0.390622	−	0.676578i
$928$	−5.34708			−0.175527
$929$	−3.56041			−0.116813			−0.0584067	−	0.998293i	$-0.518602\pi$
$929$	−3.56041			−0.116813			−0.0584067	+	0.998293i	$0.518602\pi$
$930$	62.2321	+	93.8533i	2.04067	+	3.07757i
$931$	−13.6138			−0.446173
$932$	−16.8750			−0.552760
$933$	−18.5201	−	32.0778i	−0.606322	−	1.05018i
$934$	50.5106			1.65276
$935$	−47.0077	+	81.4197i	−1.53732	+	2.66271i
$936$	−5.23248	−	9.06293i	−0.171029	−	0.296231i
$937$	−0.252994	−	0.438199i	−0.00826497	−	0.0143153i	0.861863	−	0.507141i	$-0.169298\pi$
$937$	−0.252994	−	0.438199i	−0.00826497	−	0.0143153i	−0.870128	+	0.492825i	$0.835964\pi$
$938$	−0.694488			−0.0226758
$939$	9.67163	−	16.7517i	0.315622	−	0.546673i
$940$	−25.8148	+	44.7125i	−0.841985	+	1.45836i
$941$	2.15200	−	3.72737i	0.0701531	−	0.121509i	−0.828815	−	0.559522i	$-0.810985\pi$
$941$	2.15200	−	3.72737i	0.0701531	−	0.121509i	0.898968	+	0.438014i	$0.144318\pi$
$942$	35.4447	+	61.3920i	1.15485	+	2.00026i
$943$	1.21928	−	2.11185i	0.0397051	−	0.0687713i
$944$	19.8230	+	34.3344i	0.645184	+	1.11749i
$945$	−9.68720			−0.315125
$946$	38.2231			1.24274
$947$	9.73707	+	16.8651i	0.316412	+	0.548042i	0.979737	−	0.200290i	$-0.0641884\pi$
$947$	9.73707	+	16.8651i	0.316412	+	0.548042i	−0.663324	+	0.748332i	$0.730855\pi$
$948$	−11.6335	+	20.1497i	−0.377837	+	0.654433i
$949$	4.53442	+	7.85385i	0.147194	+	0.254947i
$950$	17.7666	−	30.7727i	0.576426	−	0.998399i
$951$	−42.2685	+	73.2113i	−1.37065	+	2.37404i
$952$	−1.37612	+	2.38352i	−0.0446004	+	0.0772502i
$953$	−27.7577			−0.899159			−0.449580	−	0.893240i	$-0.648426\pi$
$953$	−27.7577			−0.899159			−0.449580	+	0.893240i	$0.648426\pi$
$954$	58.1805	+	100.771i	1.88366	+	3.26260i
$955$	−35.3816	−	61.2828i	−1.14492	−	1.98306i
$956$	−4.90663	+	8.49852i	−0.158692	+	0.274862i
$957$	13.8169			0.446638
$958$	−9.74522	−	16.8792i	−0.314854	−	0.545343i
$959$	2.19308			0.0708183
$960$	14.8495			0.479265
$961$	−12.0653	+	28.5557i	−0.389205	+	0.921151i
$962$	−8.15136			−0.262810
$963$	89.3159			2.87816
$964$	5.23730	+	9.07127i	0.168682	+	0.292166i
$965$	−50.0901			−1.61246
$966$	−0.368558	+	0.638361i	−0.0118582	+	0.0205389i
$967$	−18.6328	−	32.2729i	−0.599189	−	1.03783i	−0.992941	−	0.118609i	$-0.962156\pi$
$967$	−18.6328	−	32.2729i	−0.599189	−	1.03783i	0.393752	−	0.919217i	$-0.371177\pi$
$968$	−7.33501	−	12.7046i	−0.235756	−	0.408342i
$969$	−31.9529			−1.02647
$970$	−4.46461	+	7.73293i	−0.143350	+	0.248290i
$971$	−14.4687	+	25.0606i	−0.464323	+	0.804232i	−0.999171	−	0.0407171i	$-0.987036\pi$
$971$	−14.4687	+	25.0606i	−0.464323	+	0.804232i	0.534847	+	0.844949i	$0.320369\pi$
$972$	0.875030	−	1.51560i	0.0280666	−	0.0486128i
$973$	−2.31652	−	4.01233i	−0.0742642	−	0.128629i
$974$	9.89560	−	17.1397i	0.317075	−	0.549191i
$975$	−15.6273	−	27.0673i	−0.500475	−	0.866849i
$976$	−55.9935			−1.79231
$977$	−8.08638			−0.258706			−0.129353	−	0.991599i	$-0.541290\pi$
$977$	−8.08638			−0.258706			−0.129353	+	0.991599i	$0.541290\pi$
$978$	53.2014	+	92.1476i	1.70119	+	2.94656i
$979$	30.8292	−	53.3977i	0.985305	−	1.70660i
$980$	13.2074	+	22.8759i	0.421896	+	0.730745i
$981$	−16.0131	+	27.7356i	−0.511260	+	0.885528i
$982$	12.6715	−	21.9476i	0.404362	−	0.700376i
$983$	−2.69271	+	4.66392i	−0.0858842	+	0.148756i	−0.905768	−	0.423775i	$-0.860705\pi$
$983$	−2.69271	+	4.66392i	−0.0858842	+	0.148756i	0.819883	+	0.572530i	$0.194038\pi$
$984$	−25.6465			−0.817582
$985$	−20.5491	−	35.5920i	−0.654748	−	1.13406i
$986$	4.95083	+	8.57508i	0.157666	+	0.273086i
$987$	5.74609	−	9.95251i	0.182900	−	0.316792i
$988$	1.90942			0.0607469
$989$	−1.27141	−	2.20215i	−0.0404285	−	0.0700242i
$990$	175.527			5.57860
$991$	39.4455			1.25303			0.626513	−	0.779411i	$-0.284482\pi$
$991$	39.4455			1.25303			0.626513	+	0.779411i	$0.284482\pi$
$992$	−15.5906	−	23.5124i	−0.495002	−	0.746521i
$993$	−15.5031			−0.491975
$994$	−5.10286			−0.161853
$995$	6.46005	+	11.1891i	0.204797	+	0.354720i
$996$	2.92660			0.0927327
$997$	28.3191	−	49.0501i	0.896874	−	1.55343i	0.0654063	−	0.997859i	$-0.479166\pi$
$997$	28.3191	−	49.0501i	0.896874	−	1.55343i	0.831468	−	0.555573i	$-0.187501\pi$
$998$	−19.5986	−	33.9458i	−0.620383	−	1.07453i
$999$	−20.4384	−	35.4003i	−0.646641	−	1.12001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.b.118.4	✓	34
31.5	even	3	inner	403.2.h.b.222.4	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.b.118.4	✓	34	1.1	even	1	trivial
403.2.h.b.222.4	yes	34	31.5	even	3	inner

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.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.72349 q^{2} +(-1.49143 - 2.58324i) q^{3} +0.970414 q^{4} +(-1.96711 + 3.40713i) q^{5} +(2.57047 + 4.45218i) q^{6} +(0.142448 + 0.246727i) q^{7} +1.77448 q^{8} +(-2.94874 + 5.10737i) q^{9} +O(q^{10})\)	\(q-1.72349 q^{2} +(-1.49143 - 2.58324i) q^{3} +0.970414 q^{4} +(-1.96711 + 3.40713i) q^{5} +(2.57047 + 4.45218i) q^{6} +(0.142448 + 0.246727i) q^{7} +1.77448 q^{8} +(-2.94874 + 5.10737i) q^{9} +(3.39029 - 5.87216i) q^{10} +(2.19472 - 3.80137i) q^{11} +(-1.44731 - 2.50681i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-0.245507 - 0.425231i) q^{14} +11.7352 q^{15} -4.99912 q^{16} +(2.72208 + 4.71478i) q^{17} +(5.08212 - 8.80250i) q^{18} +(-0.983819 - 1.70403i) q^{19} +(-1.90891 + 3.30633i) q^{20} +(0.424902 - 0.735952i) q^{21} +(-3.78258 + 6.55162i) q^{22} +0.503278 q^{23} +(-2.64652 - 4.58390i) q^{24} +(-5.23904 - 9.07428i) q^{25} +(0.861744 - 1.49259i) q^{26} +8.64280 q^{27} +(0.138233 + 0.239427i) q^{28} -1.05528 q^{29} -20.2256 q^{30} +(-3.07690 - 4.64033i) q^{31} +5.06698 q^{32} -13.0931 q^{33} +(-4.69148 - 8.12587i) q^{34} -1.12084 q^{35} +(-2.86150 + 4.95626i) q^{36} +(-2.36478 - 4.09593i) q^{37} +(1.69560 + 2.93687i) q^{38} +2.98286 q^{39} +(-3.49060 + 6.04589i) q^{40} +(2.42267 - 4.19619i) q^{41} +(-0.732314 + 1.26841i) q^{42} +(-2.52626 - 4.37561i) q^{43} +(2.12979 - 3.68890i) q^{44} +(-11.6010 - 20.0935i) q^{45} -0.867394 q^{46} +13.5233 q^{47} +(7.45586 + 12.9139i) q^{48} +(3.45942 - 5.99189i) q^{49} +(9.02942 + 15.6394i) q^{50} +(8.11960 - 14.0636i) q^{51} +(-0.485207 + 0.840403i) q^{52} +(-5.72403 + 9.91431i) q^{53} -14.8958 q^{54} +(8.63451 + 14.9554i) q^{55} +(0.252771 + 0.437812i) q^{56} +(-2.93460 + 5.08288i) q^{57} +1.81877 q^{58} +(-3.96529 - 6.86809i) q^{59} +11.3880 q^{60} +11.2007 q^{61} +(5.30301 + 7.99756i) q^{62} -1.68017 q^{63} +1.26537 q^{64} +(-1.96711 - 3.40713i) q^{65} +22.5658 q^{66} +(0.707197 - 1.22490i) q^{67} +(2.64154 + 4.57529i) q^{68} +(-0.750605 - 1.30009i) q^{69} +1.93176 q^{70} +(5.19624 - 9.00016i) q^{71} +(-5.23248 + 9.06293i) q^{72} +(4.53442 - 7.85385i) q^{73} +(4.07568 + 7.05928i) q^{74} +(-15.6273 + 27.0673i) q^{75} +(-0.954712 - 1.65361i) q^{76} +1.25053 q^{77} -5.14093 q^{78} +(-4.01900 - 6.96112i) q^{79} +(9.83382 - 17.0327i) q^{80} +(-4.04393 - 7.00429i) q^{81} +(-4.17544 + 7.23208i) q^{82} +(-0.505524 + 0.875594i) q^{83} +(0.412331 - 0.714178i) q^{84} -21.4185 q^{85} +(4.35398 + 7.54131i) q^{86} +(1.57388 + 2.72604i) q^{87} +(3.89449 - 6.74546i) q^{88} +14.0470 q^{89} +(19.9942 + 34.6309i) q^{90} -0.284895 q^{91} +0.488388 q^{92} +(-7.39808 + 14.8691i) q^{93} -23.3073 q^{94} +7.74112 q^{95} +(-7.55705 - 13.0892i) q^{96} -1.31688 q^{97} +(-5.96227 + 10.3269i) q^{98} +(12.9433 + 22.4185i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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