LMFDB - Embedded newform 115.3.k.a.108.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [115,3,Mod(2,115)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(115, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("115.2"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	115.k (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.13352304014$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			108.11
Character	$\chi$	$=$	115.108
Dual form			115.3.k.a.82.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0193071 - 0.269949i) q^{2} +(-3.09539 - 0.673360i) q^{3} +(3.88679 - 0.558835i) q^{4} +(-2.00317 - 4.58119i) q^{5} +(-0.122010 + 0.848597i) q^{6} +(-2.03958 + 3.73521i) q^{7} +(-0.456013 - 2.09626i) q^{8} +(0.941319 + 0.429886i) q^{9} +(-1.19801 + 0.629204i) q^{10} +(-8.70369 - 10.0446i) q^{11} +(-12.4074 - 0.887395i) q^{12} +(-8.41778 - 15.4160i) q^{13} +(1.04770 + 0.478466i) q^{14} +(3.11580 + 15.5294i) q^{15} +(14.5137 - 4.26161i) q^{16} +(-3.32966 - 4.44791i) q^{17} +(0.0978731 - 0.262408i) q^{18} +(18.3678 - 2.64089i) q^{19} +(-10.3460 - 16.6867i) q^{20} +(8.82844 - 10.1886i) q^{21} +(-2.54348 + 2.54348i) q^{22} +(-21.7193 + 7.56769i) q^{23} +6.79579i q^{24} +(-16.9746 + 18.3538i) q^{25} +(-3.99902 + 2.57001i) q^{26} +(20.1992 + 15.1209i) q^{27} +(-5.84004 + 15.6578i) q^{28} +(27.0477 + 3.88887i) q^{29} +(4.13199 - 1.14094i) q^{30} +(28.2105 + 18.1298i) q^{31} +(-4.42944 - 11.8758i) q^{32} +(20.1777 + 36.9526i) q^{33} +(-1.13642 + 0.984716i) q^{34} +(21.1974 + 1.86143i) q^{35} +(3.89894 + 1.14483i) q^{36} +(-1.80893 - 4.84992i) q^{37} +(-1.06754 - 4.90738i) q^{38} +(15.6758 + 53.3867i) q^{39} +(-8.68989 + 6.28825i) q^{40} +(-23.0003 - 50.3637i) q^{41} +(-2.92084 - 2.18652i) q^{42} +(21.4280 + 4.66139i) q^{43} +(-39.4427 - 34.1773i) q^{44} +(0.0837661 - 5.17350i) q^{45} +(2.46223 + 5.71701i) q^{46} +(51.5322 - 51.5322i) q^{47} +(-47.7951 + 3.41837i) q^{48} +(16.6995 + 25.9849i) q^{49} +(5.28233 + 4.22792i) q^{50} +(7.31155 + 16.0101i) q^{51} +(-41.3331 - 55.2146i) q^{52} +(50.7985 + 27.7381i) q^{53} +(3.69189 - 5.74469i) q^{54} +(-28.5812 + 59.9943i) q^{55} +(8.76005 + 2.57218i) q^{56} +(-58.6338 - 4.19357i) q^{57} +(0.527584 - 7.37659i) q^{58} +(9.54592 - 32.5104i) q^{59} +(20.7888 + 58.6183i) q^{60} +(-95.0350 - 61.0753i) q^{61} +(4.34946 - 7.96544i) q^{62} +(-3.52561 + 2.63924i) q^{63} +(51.9176 - 23.7100i) q^{64} +(-53.7615 + 69.4444i) q^{65} +(9.58575 - 6.16039i) q^{66} +(0.325035 + 4.54459i) q^{67} +(-15.4273 - 15.4273i) q^{68} +(72.3256 - 8.79997i) q^{69} +(0.0932323 - 5.75814i) q^{70} +(-41.0454 + 47.3689i) q^{71} +(0.471899 - 2.16928i) q^{72} +(13.5742 - 18.1330i) q^{73} +(-1.27431 + 0.581956i) q^{74} +(64.9017 - 45.3822i) q^{75} +(69.9159 - 20.5292i) q^{76} +(55.2706 - 12.0234i) q^{77} +(14.1090 - 5.26240i) q^{78} +(-30.2793 + 103.122i) q^{79} +(-48.5966 - 57.9533i) q^{80} +(-58.4415 - 67.4451i) q^{81} +(-13.1516 + 7.18130i) q^{82} +(1.81373 - 0.676485i) q^{83} +(28.6205 - 44.5344i) q^{84} +(-13.7068 + 24.1638i) q^{85} +(0.844622 - 5.87448i) q^{86} +(-81.1045 - 30.2504i) q^{87} +(-17.0871 + 22.8257i) q^{88} +(-40.6141 - 63.1968i) q^{89} +(-1.39820 + 0.0772728i) q^{90} +74.7509 q^{91} +(-80.1894 + 41.5515i) q^{92} +(-75.1146 - 75.1146i) q^{93} +(-14.9060 - 12.9161i) q^{94} +(-48.8923 - 78.8563i) q^{95} +(5.71414 + 39.7427i) q^{96} +(-18.6466 - 6.95480i) q^{97} +(6.69218 - 5.00970i) q^{98} +(-3.87492 - 13.1968i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 18 q^{2} - 22 q^{3} - 14 q^{5} - 44 q^{6} - 6 q^{7} - 34 q^{8} - 18 q^{10} - 20 q^{11} - 70 q^{12} - 26 q^{13} - 82 q^{15} + 180 q^{16} - 46 q^{17} - 286 q^{18} + 34 q^{20} - 52 q^{21} + 4 q^{22}+ \cdots + 606 q^{98}+O(q^{100}) $ 440 * q - 18 * q^2 - 22 * q^3 - 14 * q^5 - 44 * q^6 - 6 * q^7 - 34 * q^8 - 18 * q^10 - 20 * q^11 - 70 * q^12 - 26 * q^13 - 82 * q^15 + 180 * q^16 - 46 * q^17 - 286 * q^18 + 34 * q^20 - 52 * q^21 + 4 * q^22 + 22 * q^23 - 106 * q^25 - 100 * q^26 + 110 * q^27 + 302 * q^28 + 178 * q^30 - 144 * q^31 - 206 * q^32 + 288 * q^33 + 26 * q^35 - 596 * q^36 - 678 * q^37 + 30 * q^38 - 222 * q^40 + 88 * q^41 - 434 * q^42 - 150 * q^43 - 248 * q^45 - 44 * q^46 - 20 * q^47 + 566 * q^48 + 206 * q^50 + 220 * q^51 + 1238 * q^52 - 346 * q^53 + 134 * q^55 - 1316 * q^56 + 714 * q^57 - 386 * q^58 - 522 * q^60 - 692 * q^61 + 22 * q^62 + 198 * q^63 + 174 * q^65 + 156 * q^66 + 330 * q^67 + 572 * q^68 - 232 * q^70 + 508 * q^71 + 368 * q^72 - 190 * q^73 - 962 * q^75 + 900 * q^76 + 270 * q^77 - 618 * q^78 - 1884 * q^80 + 1432 * q^81 + 798 * q^82 + 122 * q^83 - 818 * q^85 + 212 * q^86 - 558 * q^87 + 462 * q^88 - 700 * q^90 - 400 * q^91 - 22 * q^92 + 372 * q^93 + 796 * q^95 + 1796 * q^96 + 480 * q^97 + 606 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−0.0193071	−	0.269949i	−0.00965357	−	0.134974i	0.990340	−	0.138663i	$-0.0442805\pi$
$2$	−0.0193071	−	0.269949i	−0.00965357	−	0.134974i	−0.999993	+	0.00368846i	$0.998826\pi$
$3$	−3.09539	−	0.673360i	−1.03180	−	0.224453i	−0.335373	−	0.942085i	$-0.608862\pi$
$3$	−3.09539	−	0.673360i	−1.03180	−	0.224453i	−0.696423	+	0.717632i	$0.745226\pi$
$4$	3.88679	−	0.558835i	0.971697	−	0.139709i
$5$	−2.00317	−	4.58119i	−0.400634	−	0.916238i
$5$	−2.00317	−	4.58119i	−0.400634	−	0.916238i
$6$	−0.122010	+	0.848597i	−0.0203350	+	0.141433i
$7$	−2.03958	+	3.73521i	−0.291369	+	0.533602i	−0.981829	−	0.189769i	$-0.939226\pi$
$7$	−2.03958	+	3.73521i	−0.291369	+	0.533602i	0.690460	+	0.723370i	$0.257408\pi$
$8$	−0.456013	−	2.09626i	−0.0570017	−	0.262032i
$9$	0.941319	+	0.429886i	0.104591	+	0.0477651i
$10$	−1.19801	+	0.629204i	−0.119801	+	0.0629204i
$11$	−8.70369	−	10.0446i	−0.791244	−	0.913145i	0.206623	−	0.978421i	$-0.433753\pi$
$11$	−8.70369	−	10.0446i	−0.791244	−	0.913145i	−0.997867	+	0.0652759i	$0.979207\pi$
$12$	−12.4074	−	0.887395i	−1.03395	−	0.0739496i
$13$	−8.41778	−	15.4160i	−0.647522	−	1.18585i	−0.970879	−	0.239571i	$-0.922993\pi$
$13$	−8.41778	−	15.4160i	−0.647522	−	1.18585i	0.323357	−	0.946277i	$-0.395188\pi$
$14$	1.04770	+	0.478466i	0.0748354	+	0.0341762i
$15$	3.11580	+	15.5294i	0.207720	+	1.03529i
$16$	14.5137	−	4.26161i	0.907106	−	0.266350i
$17$	−3.32966	−	4.44791i	−0.195863	−	0.261642i	0.691849	−	0.722043i	$-0.256797\pi$
$17$	−3.32966	−	4.44791i	−0.195863	−	0.261642i	−0.887711	+	0.460401i	$0.847706\pi$
$18$	0.0978731	−	0.262408i	0.00543740	−	0.0145782i
$19$	18.3678	−	2.64089i	0.966727	−	0.138994i	0.359171	−	0.933272i	$-0.383059\pi$
$19$	18.3678	−	2.64089i	0.966727	−	0.138994i	0.607556	+	0.794277i	$0.292150\pi$
$20$	−10.3460	−	16.6867i	−0.517302	−	0.834333i
$21$	8.82844	−	10.1886i	0.420402	−	0.485169i
$22$	−2.54348	+	2.54348i	−0.115613	+	0.115613i
$23$	−21.7193	+	7.56769i	−0.944320	+	0.329030i
$23$	−21.7193	+	7.56769i	−0.944320	+	0.329030i
$24$			6.79579i			0.283158i
$25$	−16.9746	+	18.3538i	−0.678984	+	0.734153i
$26$	−3.99902	+	2.57001i	−0.153808	+	0.0988466i
$27$	20.1992	+	15.1209i	0.748118	+	0.560034i
$28$	−5.84004	+	15.6578i	−0.208573	+	0.559206i
$29$	27.0477	+	3.88887i	0.932680	+	0.134099i	0.591870	−	0.806033i	$-0.298390\pi$
$29$	27.0477	+	3.88887i	0.932680	+	0.134099i	0.340810	+	0.940132i	$0.389299\pi$
$30$	4.13199	−	1.14094i	0.137733	−	0.0380312i
$31$	28.2105	+	18.1298i	0.910017	+	0.584832i	0.909745	−	0.415168i	$-0.136277\pi$
$31$	28.2105	+	18.1298i	0.910017	+	0.584832i	0.000272077		1.00000i	$0.499913\pi$
$32$	−4.42944	−	11.8758i	−0.138420	−	0.371118i
$33$	20.1777	+	36.9526i	0.611444	+	1.11978i
$34$	−1.13642	+	0.984716i	−0.0334242	+	0.0289622i
$35$	21.1974	+	1.86143i	0.605639	+	0.0531838i
$36$	3.89894	+	1.14483i	0.108304	+	0.0318009i
$37$	−1.80893	−	4.84992i	−0.0488899	−	0.131079i	0.910210	−	0.414148i	$-0.135920\pi$
$37$	−1.80893	−	4.84992i	−0.0488899	−	0.131079i	−0.959100	+	0.283069i	$0.908648\pi$
$38$	−1.06754	−	4.90738i	−0.0280931	−	0.129142i
$39$	15.6758	+	53.3867i	0.401943	+	1.36889i
$40$	−8.68989	+	6.28825i	−0.217247	+	0.157206i
$41$	−23.0003	−	50.3637i	−0.560984	−	1.22838i	−0.951461	−	0.307771i	$-0.900417\pi$
$41$	−23.0003	−	50.3637i	−0.560984	−	1.22838i	0.390477	−	0.920613i	$-0.372310\pi$
$42$	−2.92084	−	2.18652i	−0.0695439	−	0.0520599i
$43$	21.4280	+	4.66139i	0.498327	+	0.108404i	0.454702	−	0.890644i	$-0.349746\pi$
$43$	21.4280	+	4.66139i	0.498327	+	0.108404i	0.0436247	+	0.999048i	$0.486109\pi$
$44$	−39.4427	−	34.1773i	−0.896424	−	0.776756i
$45$	0.0837661	−	5.17350i	0.00186147	−	0.114967i
$46$	2.46223	+	5.71701i	0.0535267	+	0.124283i
$47$	51.5322	−	51.5322i	1.09643	−	1.09643i	0.101606	−	0.994825i	$-0.467602\pi$
$47$	51.5322	−	51.5322i	1.09643	−	1.09643i	0.994825	−	0.101606i	$-0.0323980\pi$
$48$	−47.7951	+	3.41837i	−0.995731	+	0.0712161i
$49$	16.6995	+	25.9849i	0.340806	+	0.530304i
$50$	5.28233	+	4.22792i	0.105647	+	0.0845584i
$51$	7.31155	+	16.0101i	0.143364	+	0.313923i
$52$	−41.3331	−	55.2146i	−0.794868	−	1.06182i
$53$	50.7985	+	27.7381i	0.958462	+	0.523360i	0.880732	−	0.473615i	$-0.157051\pi$
$53$	50.7985	+	27.7381i	0.958462	+	0.523360i	0.0777296	+	0.996974i	$0.475233\pi$
$54$	3.69189	−	5.74469i	0.0683683	−	0.106383i
$55$	−28.5812	+	59.9943i	−0.519658	+	1.09081i
$56$	8.76005	+	2.57218i	0.156429	+	0.0459318i
$57$	−58.6338	−	4.19357i	−1.02866	−	0.0735714i
$58$	0.527584	−	7.37659i	0.00909628	−	0.127183i
$59$	9.54592	−	32.5104i	0.161795	−	0.551024i	−0.838189	−	0.545380i	$-0.816385\pi$
$59$	9.54592	−	32.5104i	0.161795	−	0.551024i	0.999984	−	0.00564376i	$-0.00179647\pi$
$60$	20.7888	+	58.6183i	0.346481	+	0.976971i
$61$	−95.0350	−	61.0753i	−1.55795	−	1.00123i	−0.983120	−	0.182962i	$-0.941431\pi$
$61$	−95.0350	−	61.0753i	−1.55795	−	1.00123i	−0.574831	−	0.818272i	$-0.694932\pi$
$62$	4.34946	−	7.96544i	0.0701526	−	0.128475i
$63$	−3.52561	+	2.63924i	−0.0559621	+	0.0418927i
$64$	51.9176	−	23.7100i	0.811212	−	0.370468i
$65$	−53.7615	+	69.4444i	−0.827099	+	1.06838i
$66$	9.58575	−	6.16039i	0.145239	−	0.0933392i
$67$	0.325035	+	4.54459i	0.00485127	+	0.0678296i	0.999301	−	0.0373831i	$-0.0119022\pi$
$67$	0.325035	+	4.54459i	0.00485127	+	0.0678296i	−0.994450	+	0.105213i	$0.966448\pi$
$68$	−15.4273	−	15.4273i	−0.226873	−	0.226873i
$69$	72.3256	−	8.79997i	1.04820	−	0.127536i
$70$	0.0932323	−	5.75814i	0.00133189	−	0.0822592i
$71$	−41.0454	+	47.3689i	−0.578104	+	0.667168i	−0.967196	−	0.254031i	$-0.918243\pi$
$71$	−41.0454	+	47.3689i	−0.578104	+	0.667168i	0.389092	+	0.921199i	$0.372789\pi$
$72$	0.471899	−	2.16928i	0.00655415	−	0.0301289i
$73$	13.5742	−	18.1330i	0.185948	−	0.248398i	−0.697874	−	0.716220i	$-0.745871\pi$
$73$	13.5742	−	18.1330i	0.185948	−	0.248398i	0.883822	+	0.467823i	$0.154961\pi$
$74$	−1.27431	+	0.581956i	−0.0172203	+	0.00786427i
$75$	64.9017	−	45.3822i	0.865356	−	0.605095i
$76$	69.9159	−	20.5292i	0.919947	−	0.270121i
$77$	55.2706	−	12.0234i	0.717800	−	0.156148i
$78$	14.1090	−	5.26240i	0.180885	−	0.0674667i
$79$	−30.2793	+	103.122i	−0.383282	+	1.30534i	0.511672	+	0.859181i	$0.329026\pi$
$79$	−30.2793	+	103.122i	−0.383282	+	1.30534i	−0.894954	+	0.446158i	$0.852792\pi$
$80$	−48.5966	−	57.9533i	−0.607458	−	0.724416i
$81$	−58.4415	−	67.4451i	−0.721500	−	0.832655i
$82$	−13.1516	+	7.18130i	−0.160385	+	0.0875768i
$83$	1.81373	−	0.676485i	0.0218521	−	0.00815043i	−0.338514	−	0.940961i	$-0.609924\pi$
$83$	1.81373	−	0.676485i	0.0218521	−	0.00815043i	0.360366	+	0.932811i	$0.382652\pi$
$84$	28.6205	−	44.5344i	0.340720	−	0.530171i
$85$	−13.7068	+	24.1638i	−0.161257	+	0.284279i
$86$	0.844622	−	5.87448i	0.00982119	−	0.0683079i
$87$	−81.1045	−	30.2504i	−0.932236	−	0.347706i
$88$	−17.0871	+	22.8257i	−0.194171	+	0.259382i
$89$	−40.6141	−	63.1968i	−0.456339	−	0.710077i	0.534494	−	0.845172i	$-0.320502\pi$
$89$	−40.6141	−	63.1968i	−0.456339	−	0.710077i	−0.990833	+	0.135095i	$0.956866\pi$
$90$	−1.39820	+	0.0772728i	−0.0155355	+	0.000858587i
$91$	74.7509			0.821438
$92$	−80.1894	+	41.5515i	−0.871624	+	0.451647i
$93$	−75.1146	−	75.1146i	−0.807684	−	0.807684i
$94$	−14.9060	−	12.9161i	−0.158575	−	0.137406i
$95$	−48.8923	−	78.8563i	−0.514656	−	0.830066i
$96$	5.71414	+	39.7427i	0.0595223	+	0.413987i
$97$	−18.6466	−	6.95480i	−0.192232	−	0.0716990i	0.251504	−	0.967856i	$-0.419075\pi$
$97$	−18.6466	−	6.95480i	−0.192232	−	0.0716990i	−0.443737	+	0.896157i	$0.646347\pi$
$98$	6.69218	−	5.00970i	0.0682875	−	0.0511194i
$99$	−3.87492	−	13.1968i	−0.0391406	−	0.133301i
$100$	−55.7199	+	80.8234i	−0.557199	+	0.808234i
$101$	−5.31147	+	11.6305i	−0.0525889	+	0.115154i	−0.934102	−	0.357005i	$-0.883798\pi$
$101$	−5.31147	+	11.6305i	−0.0525889	+	0.115154i	0.881514	+	0.472159i	$0.156525\pi$
$102$	4.18074	−	2.28286i	0.0409876	−	0.0223809i
$103$	12.5147	−	174.979i	0.121502	−	1.69882i	−0.462137	−	0.886809i	$-0.652917\pi$
$103$	12.5147	−	174.979i	0.121502	−	1.69882i	0.583639	−	0.812013i	$-0.301628\pi$
$104$	−28.4773	+	24.6758i	−0.273821	+	0.237267i
$105$	−64.3606	−	20.0353i	−0.612958	−	0.190813i
$106$	6.50709	−	14.2485i	0.0613876	−	0.134420i
$107$	90.9029	−	19.7747i	0.849560	−	0.184810i	0.233351	−	0.972393i	$-0.425031\pi$
$107$	90.9029	−	19.7747i	0.849560	−	0.184810i	0.616210	+	0.787582i	$0.288667\pi$
$108$	86.9600	+	47.4837i	0.805185	+	0.439664i
$109$	−14.0389	−	2.01849i	−0.128797	−	0.0185183i	0.0776146	−	0.996983i	$-0.475270\pi$
$109$	−14.0389	−	2.01849i	−0.128797	−	0.0185183i	−0.206412	+	0.978465i	$0.566179\pi$
$110$	16.7472	+	6.55715i	0.152247	+	0.0596105i
$111$	2.33358	+	16.2304i	0.0210233	+	0.146220i
$112$	−13.6838	+	62.9036i	−0.122177	+	0.561640i
$113$	−104.046	+	7.44153i	−0.920762	+	0.0658542i	−0.523667	−	0.851923i	$-0.675436\pi$
$113$	−104.046	+	7.44153i	−0.920762	+	0.0658542i	−0.397095	+	0.917777i	$0.629982\pi$
$114$			15.9091i			0.139553i
$115$	78.1766	+	84.3411i	0.679796	+	0.733401i
$116$	107.302			0.925017
$117$	−1.29669	−	18.1301i	−0.0110828	−	0.154958i
$118$	−8.96046	−	1.94923i	−0.0759361	−	0.0165189i
$119$	23.4050	−	3.36513i	0.196681	−	0.0282784i
$120$	31.1328	−	13.6131i	0.259440	−	0.113443i
$121$	−7.91954	+	55.0816i	−0.0654508	+	0.455220i
$122$	−14.6524	+	26.8338i	−0.120101	+	0.219949i
$123$	37.2820	+	171.383i	0.303106	+	1.39336i
$124$	119.780	+	54.7016i	0.965967	+	0.441142i
$125$	118.085	+	40.9981i	0.944683	+	0.327984i
$126$	0.780530	+	0.900779i	0.00619468	+	0.00714904i
$127$	176.488	+	12.6227i	1.38967	+	0.0993910i	0.746016	−	0.665928i	$-0.231964\pi$
$127$	176.488	+	12.6227i	1.38967	+	0.0993910i	0.643651	+	0.765319i	$0.277419\pi$
$128$	−31.7007	−	58.0554i	−0.247661	−	0.453558i
$129$	−63.1893	−	28.8576i	−0.489840	−	0.223702i
$130$	19.7844	+	13.1721i	0.152188	+	0.101324i
$131$	148.442	−	43.5866i	1.13315	−	0.332722i	0.339203	−	0.940713i	$-0.389843\pi$
$131$	148.442	−	43.5866i	1.13315	−	0.332722i	0.793944	+	0.607991i	$0.208024\pi$
$132$	99.0767	+	132.351i	0.750581	+	1.00266i
$133$	−27.5983	+	73.9940i	−0.207506	+	0.556346i
$134$	1.22053	−	0.175486i	0.00910844	−	0.00130960i
$135$	28.8094	−	122.826i	0.213403	−	0.909822i
$136$	−7.80560	+	9.00814i	−0.0573941	+	0.0662364i
$137$	−57.6287	+	57.6287i	−0.420648	+	0.420648i	−0.885427	−	0.464779i	$-0.846134\pi$
$137$	−57.6287	+	57.6287i	−0.420648	+	0.420648i	0.464779	+	0.885427i	$0.346134\pi$
$138$	−3.77194	−	19.3543i	−0.0273329	−	0.140249i
$139$			155.980i			1.12216i	0.827763	+	0.561078i	$0.189613\pi$
$139$			155.980i			1.12216i	−0.827763	+	0.561078i	$0.810387\pi$
$140$	83.4298	−	4.61083i	0.595927	−	0.0329345i
$141$	−194.212	+	124.812i	−1.37739	+	0.885195i
$142$	13.5797	+	10.1656i	0.0956314	+	0.0715888i
$143$	−81.5819	+	218.729i	−0.570503	+	1.52958i
$144$	15.4940	+	2.22770i	0.107597	+	0.0154702i
$145$	−36.3655	−	131.701i	−0.250797	−	0.908282i
$146$	−5.15707	−	3.31425i	−0.0353224	−	0.0227003i
$147$	−34.1941	−	91.6780i	−0.232613	−	0.623660i
$148$	−9.74121	−	17.8397i	−0.0658190	−	0.120539i
$149$	6.65456	−	5.76621i	0.0446615	−	0.0386994i	−0.632244	−	0.774769i	$-0.717866\pi$
$149$	6.65456	−	5.76621i	0.0446615	−	0.0386994i	0.676906	+	0.736070i	$0.263321\pi$
$150$	−13.5039	−	16.6440i	−0.0900262	−	0.110960i
$151$	−36.0982	−	10.5994i	−0.239061	−	0.0701946i	0.160007	−	0.987116i	$-0.448848\pi$
$151$	−36.0982	−	10.5994i	−0.239061	−	0.0701946i	−0.399068	+	0.916921i	$0.630666\pi$
$152$	−13.9120	−	37.2994i	−0.0915261	−	0.245391i
$153$	−1.22218	−	5.61828i	−0.00798812	−	0.0367208i
$154$	−4.31281	−	14.6881i	−0.0280053	−	0.0953773i
$155$	26.5456	−	165.555i	0.171262	−	1.06810i
$156$	90.7628	+	198.743i	0.581813	+	1.27399i
$157$	10.5891	+	7.92689i	0.0674464	+	0.0504897i	0.632469	−	0.774586i	$-0.282042\pi$
$157$	10.5891	+	7.92689i	0.0674464	+	0.0504897i	−0.565023	+	0.825075i	$0.691133\pi$
$158$	28.4222	+	6.18287i	0.179887	+	0.0391321i
$159$	−138.563	−	120.066i	−0.871467	−	0.755130i
$160$	−45.5323	+	44.0813i	−0.284577	+	0.275508i
$161$	16.0314	−	96.5613i	0.0995742	−	0.599760i
$162$	−17.0784	+	17.0784i	−0.105422	+	0.105422i
$163$	−37.5481	+	2.68549i	−0.230356	+	0.0164754i	−0.186040	−	0.982542i	$-0.559565\pi$
$163$	−37.5481	+	2.68549i	−0.230356	+	0.0164754i	−0.0443162	+	0.999018i	$0.514111\pi$
$164$	−117.542	−	182.900i	−0.716722	−	1.11524i
$165$	128.868	−	166.460i	0.781016	−	1.00885i
$166$	−0.217634	−	0.476553i	−0.00131105	−	0.00287080i
$167$	47.4176	+	63.3425i	0.283938	+	0.379297i	0.919722	−	0.392570i	$-0.128414\pi$
$167$	47.4176	+	63.3425i	0.283938	+	0.379297i	−0.635784	+	0.771867i	$0.719323\pi$
$168$	−25.3837	−	13.8606i	−0.151094	−	0.0825034i
$169$	−75.4263	+	117.366i	−0.446309	+	0.694471i
$170$	6.78762	+	3.23361i	0.0399272	+	0.0190213i
$171$	18.4253	+	5.41014i	0.107750	+	0.0316383i
$172$	85.8912	+	6.14306i	0.499367	+	0.0357155i
$173$	17.0141	−	237.888i	0.0983474	−	1.37508i	−0.673462	−	0.739222i	$-0.735193\pi$
$173$	17.0141	−	237.888i	0.0983474	−	1.37508i	0.771809	−	0.635854i	$-0.219352\pi$
$174$	−6.60018	+	22.4781i	−0.0379321	+	0.129185i
$175$	−33.9343	−	100.838i	−0.193911	−	0.576216i
$176$	−169.129	−	108.692i	−0.960959	−	0.617571i
$177$	−51.4395	+	94.2044i	−0.290619	+	0.532228i
$178$	−16.2758	+	12.1839i	−0.0914370	+	0.0684489i
$179$	−253.204	+	115.634i	−1.41455	+	0.646001i	−0.968501	−	0.249010i	$-0.919895\pi$
$179$	−253.204	+	115.634i	−1.41455	+	0.646001i	−0.446044	+	0.895011i	$0.647168\pi$
$180$	−2.56555	−	20.1551i	−0.0142531	−	0.111973i
$181$	−36.4838	+	23.4467i	−0.201568	+	0.129540i	−0.637531	−	0.770425i	$-0.720044\pi$
$181$	−36.4838	+	23.4467i	−0.201568	+	0.129540i	0.435963	+	0.899965i	$0.356408\pi$
$182$	−1.44322	−	20.1789i	−0.00792981	−	0.110873i
$183$	253.044	+	253.044i	1.38276	+	1.38276i
$184$	25.7681	+	42.0784i	0.140044	+	0.228687i
$185$	−18.5948	+	18.0022i	−0.100512	+	0.0973094i
$186$	−18.8269	+	21.7274i	−0.101220	+	0.116814i
$187$	−15.6971	+	72.1584i	−0.0839417	+	0.385874i
$188$	171.497	−	229.093i	0.912217	−	1.21858i
$189$	−97.6777	+	44.6079i	−0.516813	+	0.236021i
$190$	−20.3432	+	14.7209i	−0.107069	+	0.0774785i
$191$	−210.098	+	61.6905i	−1.09999	+	0.322987i	−0.780849	−	0.624720i	$-0.785213\pi$
$191$	−210.098	+	61.6905i	−1.09999	+	0.322987i	−0.319143	+	0.947707i	$0.603395\pi$
$192$	−176.670	+	38.4323i	−0.920158	+	0.200168i
$193$	340.091	−	126.847i	1.76213	−	0.657240i	0.762178	−	0.647368i	$-0.224130\pi$
$193$	340.091	−	126.847i	1.76213	−	0.657240i	0.999951	−	0.00987239i	$-0.00314253\pi$
$194$	−1.51743	+	5.16790i	−0.00782181	+	0.0266386i
$195$	213.174	−	178.756i	1.09320	−	0.916700i
$196$	79.4286	+	91.6654i	0.405248	+	0.467681i
$197$	184.811	−	100.915i	0.938129	−	0.512257i	0.0639995	−	0.997950i	$-0.479614\pi$
$197$	184.811	−	100.915i	0.938129	−	0.512257i	0.874130	+	0.485693i	$0.161433\pi$
$198$	−3.48764	+	1.30082i	−0.0176143	+	0.00656981i
$199$	121.178	−	188.557i	0.608936	−	0.947523i	−0.390699	−	0.920518i	$-0.627767\pi$
$199$	121.178	−	188.557i	0.608936	−	0.947523i	0.999635	−	0.0270044i	$-0.00859683\pi$
$200$	46.2150	+	27.2136i	0.231075	+	0.136068i
$201$	2.05403	−	14.2861i	0.0102191	−	0.0710752i
$202$	3.24219	+	1.20928i	0.0160505	+	0.00598651i
$203$	−69.6918	+	93.0973i	−0.343309	+	0.458607i
$204$	37.3654	+	58.1418i	0.183164	+	0.285009i
$205$	−184.652	+	206.256i	−0.900742	+	1.00613i
$206$	−47.4769			−0.230471
$207$	−23.6981	−	2.21324i	−0.114483	−	0.0106920i
$208$	−187.870	−	187.870i	−0.903222	−	0.903222i
$209$	−186.394	−	161.512i	−0.891839	−	0.772783i
$210$	−4.16589	+	17.7609i	−0.0198376	+	0.0845757i
$211$	−23.3640	−	162.500i	−0.110730	−	0.770143i	−0.967213	−	0.253968i	$-0.918264\pi$
$211$	−23.3640	−	162.500i	−0.110730	−	0.770143i	0.856483	−	0.516175i	$-0.172645\pi$
$212$	212.944	+	79.4239i	1.00445	+	0.374641i
$213$	158.948	−	118.987i	0.746233	−	0.558623i
$214$	−7.09324	−	24.1574i	−0.0331460	−	0.112885i
$215$	−21.5694	−	107.504i	−0.100323	−	0.500016i
$216$	22.4863	−	49.2380i	0.104103	−	0.227954i
$217$	−125.256	+	68.3951i	−0.577218	+	0.315185i
$218$	−0.273839	+	3.82877i	−0.00125614	+	0.0175631i
$219$	−54.2275	+	46.9884i	−0.247614	+	0.214559i
$220$	−77.5621	+	249.157i	−0.352555	+	1.13253i
$221$	−40.5407	+	88.7717i	−0.183442	+	0.401682i
$222$	4.33633	−	0.943312i	0.0195330	−	0.00424915i
$223$	−137.199	−	74.9164i	−0.615243	−	0.335948i	0.141227	−	0.989977i	$-0.454895\pi$
$223$	−137.199	−	74.9164i	−0.615243	−	0.335948i	−0.756469	+	0.654029i	$0.773077\pi$
$224$	53.3927	+	7.67672i	0.238360	+	0.0342711i
$225$	−23.8686	+	9.97966i	−0.106083	+	0.0443540i
$226$	4.01767	+	27.9435i	0.0177773	+	0.123644i
$227$	−81.8038	+	376.046i	−0.360369	+	1.65659i	0.338221	+	0.941067i	$0.390175\pi$
$227$	−81.8038	+	376.046i	−0.360369	+	1.65659i	−0.698590	+	0.715523i	$0.746189\pi$
$228$	−230.240	+	16.4671i	−1.00983	+	0.0722242i
$229$		−	388.570i		−	1.69681i	−0.529346	−	0.848406i	$-0.677563\pi$
$229$		−	388.570i		−	1.69681i	0.529346	−	0.848406i	$-0.322437\pi$
$230$	21.2584	−	22.7321i	0.0924280	−	0.0988351i
$231$	−179.180			−0.775670
$232$	−4.18203	−	58.4724i	−0.0180260	−	0.252036i
$233$	226.680	+	49.3111i	0.972874	+	0.211636i	0.670791	−	0.741646i	$-0.265955\pi$
$233$	226.680	+	49.3111i	0.972874	+	0.211636i	0.302083	+	0.953282i	$0.402318\pi$
$234$	−4.86916	+	0.700080i	−0.0208084	+	0.00299179i
$235$	−339.307	−	132.851i	−1.44386	−	0.565324i
$236$	18.9350	−	131.696i	0.0802329	−	0.558032i
$237$	163.164	−	298.813i	0.688456	−	1.26081i
$238$	−1.36030	−	6.25319i	−0.00571554	−	0.0262739i
$239$	182.123	+	83.1728i	0.762021	+	0.348003i	0.758228	−	0.651989i	$-0.226065\pi$
$239$	182.123	+	83.1728i	0.762021	+	0.348003i	0.00379312	+	0.999993i	$0.498793\pi$
$240$	111.402	+	212.111i	0.464175	+	0.883795i
$241$	198.439	+	229.010i	0.823397	+	0.950251i	0.999417	−	0.0341356i	$-0.0108678\pi$
$241$	198.439	+	229.010i	0.823397	+	0.950251i	−0.176020	+	0.984387i	$0.556322\pi$
$242$	15.0221	+	1.07440i	0.0620749	+	0.00443969i
$243$	26.6530	+	48.8113i	0.109683	+	0.200869i
$244$	−403.512	−	184.278i	−1.65374	−	0.755236i
$245$	85.5898	−	128.556i	0.349346	−	0.524717i
$246$	45.5448	−	13.3732i	0.185141	−	0.0543624i
$247$	−195.328	−	260.928i	−0.790803	−	1.05639i
$248$	25.1404	−	67.4040i	0.101373	−	0.271790i
$249$	−6.06971	+	0.872692i	−0.0243763	+	0.00350479i
$250$	8.78749	−	32.6686i	0.0351500	−	0.130674i
$251$	−146.644	+	169.236i	−0.584239	+	0.674248i	−0.968511	−	0.248972i	$-0.919907\pi$
$251$	−146.644	+	169.236i	−0.584239	+	0.674248i	0.384272	+	0.923220i	$0.374453\pi$
$252$	−12.2284	+	12.2284i	−0.0485254	+	0.0485254i
$253$	265.053	+	152.295i	1.04764	+	0.601957i
$254$		−	47.8864i		−	0.188529i
$255$	58.6989	−	65.5665i	0.230192	−	0.257124i
$256$	176.999	−	113.751i	0.691404	−	0.444338i
$257$	−88.7519	−	66.4388i	−0.345338	−	0.258517i	0.412503	−	0.910956i	$-0.364655\pi$
$257$	−88.7519	−	66.4388i	−0.345338	−	0.258517i	−0.757841	+	0.652439i	$0.773746\pi$
$258$	−6.57007	+	17.6150i	−0.0254654	+	0.0682754i
$259$	21.8049	+	3.13507i	0.0841889	+	0.0121045i
$260$	−170.151	+	299.959i	−0.654428	+	1.15369i
$261$	23.7888	+	15.2881i	0.0911447	+	0.0585751i
$262$	−14.6321	−	39.2303i	−0.0558479	−	0.149734i
$263$	87.9153	+	161.005i	0.334279	+	0.612186i	0.989713	−	0.143066i	$-0.0456962\pi$
$263$	87.9153	+	161.005i	0.334279	+	0.612186i	−0.655434	+	0.755252i	$0.727514\pi$
$264$	68.2610	−	59.1485i	0.258564	−	0.224047i
$265$	25.3153	−	288.282i	0.0955294	−	1.08785i
$266$	20.5075	+	6.02153i	0.0770957	+	0.0226373i
$267$	83.1623	+	222.967i	0.311469	+	0.835081i
$268$	3.80302	+	17.4822i	0.0141904	+	0.0652321i
$269$	90.6723	+	308.801i	0.337072	+	1.14796i	0.937414	+	0.348217i	$0.113213\pi$
$269$	90.6723	+	308.801i	0.337072	+	1.14796i	−0.600342	+	0.799743i	$0.704969\pi$
$270$	−33.7130	−	5.40564i	−0.124863	−	0.0200209i
$271$	174.933	+	383.050i	0.645510	+	1.41347i	0.895430	+	0.445202i	$0.146868\pi$
$271$	174.933	+	383.050i	0.645510	+	1.41347i	−0.249920	+	0.968266i	$0.580404\pi$
$272$	−67.2810	−	50.3659i	−0.247357	−	0.185169i
$273$	−231.383	−	50.3343i	−0.847556	−	0.184375i
$274$	16.6695	+	14.4442i	0.0608375	+	0.0527160i
$275$	332.098	+	10.7571i	1.20763	+	0.0391167i
$276$	276.196	−	74.6217i	1.00071	−	0.270368i
$277$	−220.277	+	220.277i	−0.795224	+	0.795224i	−0.982338	−	0.187114i	$-0.940087\pi$
$277$	−220.277	+	220.277i	−0.795224	+	0.795224i	0.187114	+	0.982338i	$0.440087\pi$
$278$	42.1065	−	3.01152i	0.151462	−	0.0108328i
$279$	18.7614	+	29.1932i	0.0672450	+	0.104635i
$280$	−5.76422	−	45.2840i	−0.0205865	−	0.161728i
$281$	−59.7608	−	130.858i	−0.212672	−	0.465686i	0.772990	−	0.634418i	$-0.218760\pi$
$281$	−59.7608	−	130.858i	−0.212672	−	0.465686i	−0.985662	+	0.168732i	$0.946033\pi$
$282$	37.4427	+	50.0175i	0.132775	+	0.177367i
$283$	−186.644	−	101.915i	−0.659519	−	0.360125i	0.114377	−	0.993437i	$-0.463513\pi$
$283$	−186.644	−	101.915i	−0.659519	−	0.360125i	−0.773896	+	0.633313i	$0.781695\pi$
$284$	−133.063	+	207.050i	−0.468533	+	0.729051i
$285$	98.2419	+	277.013i	0.344709	+	0.971975i
$286$	60.6209	+	17.7999i	0.211961	+	0.0622374i
$287$	235.030	+	16.8097i	0.818921	+	0.0585704i
$288$	0.935718	−	13.0830i	0.00324902	−	0.0454273i
$289$	72.7235	−	247.673i	0.251638	−	0.857001i
$290$	−34.8504	+	12.3596i	−0.120174	+	0.0426193i
$291$	53.0352	+	34.0837i	0.182252	+	0.117126i
$292$	42.6267	−	78.0650i	0.145982	−	0.267346i
$293$	−355.742	+	266.305i	−1.21414	+	0.908892i	−0.997725	−	0.0674102i	$-0.978526\pi$
$293$	−355.742	+	266.305i	−1.21414	+	0.908892i	−0.216412	+	0.976302i	$0.569435\pi$
$294$	−24.0882	+	11.0007i	−0.0819327	+	0.0374174i
$295$	−168.058	+	21.3923i	−0.569690	+	0.0725161i
$296$	−9.34179	+	6.00360i	−0.0315601	+	0.0202824i
$297$	−23.9239	−	334.500i	−0.0805519	−	1.12626i
$298$	−1.68506	−	1.68506i	−0.00565457	−	0.00565457i
$299$	299.492	+	271.123i	1.00165	+	0.906765i
$300$	226.898	−	212.660i	0.756326	−	0.708867i
$301$	−61.1155	+	70.5310i	−0.203042	+	0.234322i
$302$	−2.16434	+	9.94932i	−0.00716670	+	0.0329448i
$303$	24.2726	−	32.4244i	0.0801076	−	0.107011i
$304$	255.330	−	116.605i	0.839903	−	0.383571i
$305$	−89.4261	+	557.718i	−0.293200	+	1.82858i
$306$	−1.49305	+	0.438400i	−0.00487926	+	0.00143268i
$307$	341.136	−	74.2096i	1.11119	−	0.241725i	0.380735	−	0.924684i	$-0.375671\pi$
$307$	341.136	−	74.2096i	1.11119	−	0.241725i	0.730457	+	0.682959i	$0.239307\pi$
$308$	208.106	−	77.6194i	0.675668	−	0.252011i
$309$	−156.562	+	533.200i	−0.506672	+	1.72557i
$310$	−45.2039	−	3.96956i	−0.145819	−	0.0128050i
$311$	128.725	+	148.556i	0.413905	+	0.477672i	0.923971	−	0.382463i	$-0.124924\pi$
$311$	128.725	+	148.556i	0.413905	+	0.477672i	−0.510065	+	0.860136i	$0.670379\pi$
$312$	104.764	−	57.2055i	0.335782	−	0.183351i
$313$	114.011	−	42.5240i	0.364253	−	0.135860i	−0.160672	−	0.987008i	$-0.551366\pi$
$313$	114.011	−	42.5240i	0.364253	−	0.135860i	0.524925	+	0.851148i	$0.324093\pi$
$314$	1.93541	−	3.01156i	0.00616373	−	0.00959095i
$315$	19.1533	+	10.8646i	0.0608040	+	0.0344910i
$316$	−60.0610	+	417.733i	−0.190066	+	1.32194i
$317$	−19.6309	−	7.32196i	−0.0619272	−	0.0230977i	0.318310	−	0.947987i	$-0.396885\pi$
$317$	−19.6309	−	7.32196i	−0.0619272	−	0.0230977i	−0.380237	+	0.924889i	$0.624158\pi$
$318$	−29.7364	+	39.7231i	−0.0935106	+	0.124915i
$319$	−196.353	−	305.531i	−0.615526	−	0.957777i
$320$	−212.620	−	190.349i	−0.664436	−	0.594841i
$321$	−294.695			−0.918054
$322$	−26.3761	−	2.46335i	−0.0819135	−	0.00765016i
$323$	−72.9051	−	72.9051i	−0.225712	−	0.225712i
$324$	−264.840	−	229.485i	−0.817408	−	0.708288i
$325$	425.831	+	107.182i	1.31025	+	0.329792i
$326$	1.44989	+	10.0842i	0.00444752	+	0.0309332i
$327$	42.0967	+	15.7013i	0.128736	+	0.0480161i
$328$	−95.0869	+	71.1812i	−0.289899	+	0.217016i
$329$	87.3797	+	297.588i	0.265592	+	0.904523i
$330$	−47.4238	−	31.5738i	−0.143709	−	0.0956783i
$331$	272.280	−	596.210i	0.822598	−	1.80124i	0.283567	−	0.958952i	$-0.408482\pi$
$331$	272.280	−	596.210i	0.822598	−	1.80124i	0.539031	−	0.842286i	$-0.318791\pi$
$332$	6.67153	−	3.64293i	0.0200950	−	0.0109727i
$333$	0.382135	−	5.34295i	0.00114755	−	0.0160449i
$334$	16.1838	−	14.0233i	0.0484544	−	0.0419859i
$335$	20.1685	−	10.5926i	0.0602045	−	0.0316198i
$336$	84.7136	−	185.497i	0.252124	−	0.552074i
$337$	−92.5698	+	20.1373i	−0.274688	+	0.0597547i	−0.347799	−	0.937569i	$-0.613071\pi$
$337$	−92.5698	+	20.1373i	−0.274688	+	0.0597547i	0.0731111	+	0.997324i	$0.476707\pi$
$338$	33.1390	+	18.0953i	0.0980443	+	0.0535363i
$339$	327.074	+	47.0261i	0.964820	+	0.138720i
$340$	−39.7720	+	101.579i	−0.116976	+	0.298762i
$341$	−63.4292	−	441.159i	−0.186009	−	1.29372i
$342$	1.10472	−	5.07833i	0.00323019	−	0.0148489i
$343$	−339.121	+	24.2544i	−0.988691	+	0.0707126i
$344$		−	47.0444i		−	0.136757i
$345$	−185.195	−	313.709i	−0.536797	−	0.909302i
$346$	−64.5462			−0.186550
$347$	8.14318	+	113.857i	0.0234674	+	0.328117i	0.995601	+	0.0936908i	$0.0298665\pi$
$347$	8.14318	+	113.857i	0.0234674	+	0.328117i	−0.972134	+	0.234426i	$0.924679\pi$
$348$	−332.141	−	72.2529i	−0.954428	−	0.207623i
$349$	663.606	−	95.4122i	1.90145	−	0.273387i	0.911123	−	0.412134i	$-0.135216\pi$
$349$	663.606	−	95.4122i	1.90145	−	0.273387i	0.990328	+	0.138747i	$0.0443073\pi$
$350$	−26.5659	+	11.1074i	−0.0759026	+	0.0317355i
$351$	63.0720	−	438.675i	0.179692	−	1.24979i
$352$	−80.7349	+	147.855i	−0.229361	+	0.420042i
$353$	106.491	+	489.530i	0.301673	+	1.38677i	0.839337	+	0.543611i	$0.182943\pi$
$353$	106.491	+	489.530i	0.301673	+	1.38677i	−0.537664	+	0.843159i	$0.680693\pi$
$354$	26.4235	+	12.0672i	0.0746428	+	0.0340882i
$355$	299.227	+	93.1487i	0.842893	+	0.262391i
$356$	−193.175	−	222.936i	−0.542627	−	0.626225i
$357$	−74.7135	−	5.34362i	−0.209282	−	0.0149681i
$358$	36.1040	+	66.1195i	0.100849	+	0.184691i
$359$	99.2977	+	45.3477i	0.276595	+	0.126317i	0.548883	−	0.835899i	$-0.315053\pi$
$359$	99.2977	+	45.3477i	0.276595	+	0.126317i	−0.272288	+	0.962216i	$0.587780\pi$
$360$	−10.8832	+	2.18359i	−0.0302311	+	0.00606552i
$361$	−15.9747	+	4.69060i	−0.0442513	+	0.0129934i
$362$	7.03381	+	9.39607i	0.0194304	+	0.0259560i
$363$	61.6038	−	165.166i	0.169708	−	0.455003i
$364$	290.541	−	41.7734i	0.798189	−	0.114762i
$365$	−110.262	−	25.8625i	−0.302089	−	0.0708561i
$366$	63.4235	−	73.1947i	0.173288	−	0.199985i
$367$	−478.024	+	478.024i	−1.30252	+	1.30252i	−0.375829	+	0.926689i	$0.622642\pi$
$367$	−478.024	+	478.024i	−1.30252	+	1.30252i	−0.926689	+	0.375829i	$0.877358\pi$
$368$	−282.978	+	202.394i	−0.768961	+	0.549985i
$369$		−	57.2959i		−	0.155273i
$370$	5.21870	+	4.67208i	0.0141046	+	0.0126272i
$371$	−207.215	+	133.169i	−0.558531	+	0.358946i
$372$	−333.931	−	249.978i	−0.897664	−	0.671983i
$373$	134.901	−	361.683i	0.361664	−	0.969659i	−0.620926	−	0.783870i	$-0.713243\pi$
$373$	134.901	−	361.683i	0.361664	−	0.969659i	0.982590	−	0.185789i	$-0.0594842\pi$
$374$	19.7821	+	2.84424i	0.0528934	+	0.00760493i
$375$	−337.914	−	206.419i	−0.901103	−	0.550450i
$376$	−131.524	−	84.5255i	−0.349799	−	0.224802i
$377$	−167.731	−	449.704i	−0.444909	−	1.19285i
$378$	13.9277	+	25.5067i	0.0368459	+	0.0674781i
$379$	−377.547	+	327.147i	−0.996167	+	0.863184i	−0.990599	−	0.136801i	$-0.956318\pi$
$379$	−377.547	+	327.147i	−0.996167	+	0.863184i	−0.00556845	+	0.999984i	$0.501773\pi$
$380$	−234.102	−	279.175i	−0.616057	−	0.734670i
$381$	−537.798	−	157.912i	−1.41154	−	0.414467i
$382$	20.7097	+	55.5248i	0.0542138	+	0.145353i
$383$	57.7793	+	265.607i	0.150860	+	0.693492i	0.988985	+	0.148014i	$0.0472881\pi$
$383$	57.7793	+	265.607i	0.150860	+	0.693492i	−0.838125	+	0.545478i	$0.816348\pi$
$384$	59.0336	+	201.050i	0.153733	+	0.523568i
$385$	−165.798	−	229.120i	−0.430644	−	0.595117i
$386$	−40.8085	−	89.3581i	−0.105721	−	0.231498i
$387$	18.1668	+	13.5995i	0.0469425	+	0.0351407i
$388$	−76.3617	−	16.6115i	−0.196809	−	0.0428131i
$389$	566.023	+	490.461i	1.45507	+	1.26083i	0.904798	+	0.425842i	$0.140022\pi$
$389$	566.023	+	490.461i	1.45507	+	1.26083i	0.550273	+	0.834985i	$0.314523\pi$
$390$	−52.3709	−	54.0947i	−0.134284	−	0.138704i
$391$	105.979	+	71.4079i	0.271045	+	0.182629i
$392$	46.8559	−	46.8559i	0.119530	−	0.119530i
$393$	−488.836	+	34.9622i	−1.24386	+	0.0889624i
$394$	−30.8100	−	47.9413i	−0.0781980	−	0.121678i
$395$	533.075	−	67.8554i	1.34956	−	0.171786i
$396$	−22.4358	−	49.1275i	−0.0566561	−	0.124059i
$397$	96.9517	+	129.512i	0.244211	+	0.326227i	0.905853	−	0.423592i	$-0.139231\pi$
$397$	96.9517	+	129.512i	0.244211	+	0.326227i	−0.661642	+	0.749820i	$0.730140\pi$
$398$	−53.2404	−	29.0715i	−0.133770	−	0.0730438i
$399$	135.252	−	210.456i	0.338978	−	0.527460i
$400$	−168.148	+	338.721i	−0.420369	+	0.846802i
$401$	−25.3697	−	7.44922i	−0.0632661	−	0.0185766i	0.249946	−	0.968260i	$-0.419587\pi$
$401$	−25.3697	−	7.44922i	−0.0632661	−	0.0185766i	−0.313212	+	0.949683i	$0.601405\pi$
$402$	−3.89618	−	0.278660i	−0.00969199	−	0.000693185i
$403$	42.0193	−	587.507i	0.104266	−	1.45783i
$404$	−14.1450	+	48.1735i	−0.0350124	+	0.119241i
$405$	−191.910	+	402.836i	−0.473853	+	0.994656i
$406$	26.4771	+	17.0158i	0.0652145	+	0.0419108i
$407$	−32.9711	+	60.3821i	−0.0810101	+	0.148359i
$408$	30.2271	−	22.6277i	0.0740860	−	0.0554601i
$409$	−288.439	+	131.726i	−0.705229	+	0.322067i	−0.735548	−	0.677473i	$-0.763075\pi$
$409$	−288.439	+	131.726i	−0.705229	+	0.322067i	0.0303186	+	0.999540i	$0.490348\pi$
$410$	59.2437	+	45.8644i	0.144497	+	0.111865i
$411$	217.188	−	139.578i	0.528438	−	0.339607i
$412$	−49.1422	−	687.098i	−0.119277	−	1.66771i
$413$	101.964	+	101.964i	0.246885	+	0.246885i
$414$	−0.139919	+	6.44000i	−0.000337969	+	0.0155556i
$415$	−6.73232	−	6.95391i	−0.0162224	−	0.0167564i
$416$	−145.791	+	168.252i	−0.350460	+	0.404452i
$417$	105.030	−	482.817i	0.251872	−	1.15784i
$418$	−40.0012	+	53.4353i	−0.0956966	+	0.127836i
$419$	−128.565	+	58.7136i	−0.306837	+	0.140128i	−0.562882	−	0.826537i	$-0.690308\pi$
$419$	−128.565	+	58.7136i	−0.306837	+	0.140128i	0.256045	+	0.966665i	$0.417580\pi$
$420$	−261.352	−	41.9060i	−0.622267	−	0.0997762i
$421$	449.446	−	131.969i	1.06757	−	0.313466i	0.299673	−	0.954042i	$-0.403122\pi$
$421$	449.446	−	131.969i	1.06757	−	0.313466i	0.767895	+	0.640575i	$0.221304\pi$
$422$	−43.4157	+	9.44450i	−0.102881	+	0.0223803i
$423$	70.6613	−	26.3553i	0.167048	−	0.0623056i
$424$	34.9814	−	119.136i	0.0825033	−	0.280980i
$425$	138.156	+	14.3895i	0.325073	+	0.0338576i
$426$	−35.1892	−	40.6105i	−0.0826037	−	0.0953298i
$427$	421.961	−	230.408i	0.988198	−	0.539597i
$428$	342.269	−	127.660i	0.799695	−	0.298271i
$429$	399.811	−	622.118i	0.931961	−	1.45016i
$430$	−28.6040	+	7.89821i	−0.0665210	+	0.0183679i
$431$	14.4511	−	100.509i	0.0335292	−	0.233201i	−0.966165	−	0.257924i	$-0.916961\pi$
$431$	14.4511	−	100.509i	0.0335292	−	0.233201i	0.999694	+	0.0247236i	$0.00787058\pi$
$432$	357.604	+	133.379i	0.827787	+	0.308749i
$433$	−74.1616	+	99.0683i	−0.171274	+	0.228795i	−0.877962	−	0.478730i	$-0.841097\pi$
$433$	−74.1616	+	99.0683i	−0.171274	+	0.228795i	0.706688	+	0.707525i	$0.250188\pi$
$434$	20.8815	+	32.4923i	0.0481141	+	0.0748671i
$435$	23.8833	+	432.152i	0.0549042	+	0.993453i
$436$	−55.6943			−0.127739
$437$	−378.951	+	196.360i	−0.867166	+	0.449337i
$438$	13.7315	+	13.7315i	0.0313503	+	0.0313503i
$439$	−167.039	−	144.740i	−0.380498	−	0.329703i	0.443523	−	0.896263i	$-0.353729\pi$
$439$	−167.039	−	144.740i	−0.380498	−	0.329703i	−0.824021	+	0.566560i	$0.808274\pi$
$440$	138.797	+	32.5554i	0.315448	+	0.0739896i
$441$	4.54899	+	31.6389i	0.0103152	+	0.0717436i
$442$	24.7466	+	9.22999i	0.0559877	+	0.0208823i
$443$	298.310	−	223.312i	0.673386	−	0.504091i	−0.207004	−	0.978340i	$-0.566371\pi$
$443$	298.310	−	223.312i	0.673386	−	0.504091i	0.880391	+	0.474249i	$0.157280\pi$
$444$	18.1403	+	61.7801i	0.0408565	+	0.139144i
$445$	−208.160	+	312.655i	−0.467775	+	0.702596i
$446$	−17.5747	+	38.4832i	−0.0394051	+	0.0862851i
$447$	−24.4812	+	13.3677i	−0.0547677	+	0.0299054i
$448$	−17.3283	+	242.282i	−0.0386793	+	0.540807i
$449$	−188.902	+	163.684i	−0.420717	+	0.364553i	−0.839340	−	0.543607i	$-0.817058\pi$
$449$	−188.902	+	163.684i	−0.420717	+	0.364553i	0.418623	+	0.908160i	$0.362513\pi$
$450$	3.15483	+	6.25062i	0.00701074	+	0.0138903i
$451$	−305.695	+	669.379i	−0.677816	+	1.48421i
$452$	−400.247	+	87.0683i	−0.885501	+	0.192629i
$453$	104.601	+	57.1163i	0.230907	+	0.126085i
$454$	103.093	+	14.8225i	0.227076	+	0.0326486i
$455$	−149.739	−	342.448i	−0.329096	−	0.752633i
$456$	17.9470	+	124.824i	0.0393574	+	0.273737i
$457$	76.4414	−	351.395i	0.167268	−	0.768918i	−0.814702	−	0.579880i	$-0.803100\pi$
$457$	76.4414	−	351.395i	0.167268	−	0.768918i	0.981970	−	0.189038i	$-0.0605369\pi$
$458$	−104.894	+	7.50217i	−0.229026	+	0.0163803i
$459$		−	140.192i		−	0.305429i
$460$	350.988	+	284.128i	0.763018	+	0.617669i
$461$	707.529			1.53477			0.767385	−	0.641187i	$-0.221558\pi$
$461$	707.529			1.53477			0.767385	+	0.641187i	$0.221558\pi$
$462$	3.45945	+	48.3694i	0.00748799	+	0.104696i
$463$	−27.4523	−	5.97188i	−0.0592922	−	0.0128982i	0.182821	−	0.983146i	$-0.441477\pi$
$463$	−27.4523	−	5.97188i	−0.0592922	−	0.0128982i	−0.242114	+	0.970248i	$0.577841\pi$
$464$	409.135	−	58.8248i	0.881757	−	0.126778i
$465$	−193.647	+	494.582i	−0.416445	+	1.06362i
$466$	8.93496	−	62.1440i	0.0191737	−	0.133356i
$467$	−50.0357	+	91.6335i	−0.107143	+	0.196217i	−0.925750	−	0.378137i	$-0.876565\pi$
$467$	−50.0357	+	91.6335i	−0.107143	+	0.196217i	0.818607	+	0.574354i	$0.194747\pi$
$468$	−15.1717	−	69.7431i	−0.0324181	−	0.149024i
$469$	−17.6379	−	8.05497i	−0.0376075	−	0.0171748i
$470$	−29.3120	+	94.1605i	−0.0623659	+	0.200342i
$471$	−27.4397	−	31.6671i	−0.0582583	−	0.0672337i
$472$	−72.5033	−	5.18554i	−0.153609	−	0.0109863i
$473$	−139.681	−	255.807i	−0.295309	−	0.540819i
$474$	−83.8145	−	38.2768i	−0.176824	−	0.0807527i
$475$	−263.316	+	381.948i	−0.554349	+	0.804100i
$476$	89.0897	−	26.1591i	0.187163	−	0.0549561i
$477$	35.8934	+	47.9479i	0.0752482	+	0.100520i
$478$	18.9361	−	50.7698i	0.0396154	−	0.106213i
$479$	−156.283	+	22.4702i	−0.326270	+	0.0469105i	−0.303504	−	0.952830i	$-0.598156\pi$
$479$	−156.283	+	22.4702i	−0.326270	+	0.0469105i	−0.0227663	+	0.999741i	$0.507247\pi$
$480$	170.623	−	105.789i	0.355464	−	0.220394i
$481$	−59.5393	+	68.7120i	−0.123782	+	0.142852i
$482$	57.9899	−	57.9899i	0.120311	−	0.120311i
$483$	−114.644	+	288.100i	−0.237358	+	0.596480i
$484$			218.516i			0.451480i
$485$	5.49096	+	99.3551i	0.0113216	+	0.204856i
$486$	12.6620	−	8.13735i	0.0260534	−	0.0167435i
$487$	−4.93330	−	3.69302i	−0.0101300	−	0.00758320i	0.594201	−	0.804317i	$-0.297468\pi$
$487$	−4.93330	−	3.69302i	−0.0101300	−	0.00758320i	−0.604331	+	0.796734i	$0.706559\pi$
$488$	−84.6924	+	227.069i	−0.173550	+	0.465306i
$489$	118.034	+	16.9707i	0.241379	+	0.0347050i
$490$	−36.3560	−	20.6228i	−0.0741958	−	0.0420874i
$491$	−4.52898	−	2.91060i	−0.00922400	−	0.00592790i	0.536021	−	0.844205i	$-0.319927\pi$
$491$	−4.52898	−	2.91060i	−0.00922400	−	0.00592790i	−0.545245	+	0.838277i	$0.683563\pi$
$492$	240.682	+	645.293i	0.489191	+	1.31157i
$493$	−72.7625	−	133.254i	−0.147591	−	0.270293i
$494$	−66.6661	+	57.7665i	−0.134952	+	0.116936i
$495$	−52.6948	+	44.1871i	−0.106454	+	0.0892669i
$496$	486.701	+	142.908i	0.981252	+	0.288122i
$497$	−93.2176	−	249.926i	−0.187561	−	0.502869i
$498$	0.352771	+	1.62166i	0.000708375	+	0.00325635i
$499$	−70.5491	−	240.268i	−0.141381	−	0.481500i	0.858108	−	0.513470i	$-0.171640\pi$
$499$	−70.5491	−	240.268i	−0.141381	−	0.481500i	−0.999489	+	0.0319700i	$0.989822\pi$
$500$	481.884	+	93.3604i	0.963768	+	0.186721i
$501$	−104.124	−	227.999i	−0.207831	−	0.455087i
$502$	48.5164	+	36.3189i	0.0966462	+	0.0723485i
$503$	136.380	+	29.6676i	0.271133	+	0.0589813i	0.346076	−	0.938206i	$-0.387514\pi$
$503$	136.380	+	29.6676i	0.271133	+	0.0589813i	−0.0749433	+	0.997188i	$0.523878\pi$
$504$	7.14026	+	6.18707i	0.0141672	+	0.0122759i
$505$	63.9214	+	1.03497i	0.126577	+	0.00204946i
$506$	35.9945	−	74.4911i	0.0711354	−	0.147216i
$507$	312.503	−	312.503i	0.616376	−	0.616376i
$508$	693.024	−	49.5661i	1.36422	−	0.0975710i
$509$	−428.097	−	666.133i	−0.841056	−	1.30871i	−0.949232	−	0.314577i	$-0.898137\pi$
$509$	−428.097	−	666.133i	−0.841056	−	1.30871i	0.108176	−	0.994132i	$-0.465499\pi$
$510$	−18.8329	−	14.5798i	−0.0369273	−	0.0285878i
$511$	40.0450	+	87.6864i	0.0783660	+	0.171598i
$512$	−192.685	−	257.397i	−0.376337	−	0.502728i
$513$	410.947	+	224.394i	0.801067	+	0.437416i
$514$	−16.2216	+	25.2412i	−0.0315594	+	0.0491075i
$515$	−826.680	+	293.180i	−1.60520	+	0.569281i
$516$	−261.730	−	76.8508i	−0.507229	−	0.148936i
$517$	−966.141	−	69.0997i	−1.86874	−	0.133655i
$518$	0.425320	−	5.94675i	0.000821080	−	0.0114802i
$519$	−212.850	+	724.899i	−0.410115	+	1.39672i
$520$	170.089	+	81.0304i	0.327095	+	0.155828i
$521$	−235.950	−	151.636i	−0.452878	−	0.291047i	0.294248	−	0.955729i	$-0.404931\pi$
$521$	−235.950	−	151.636i	−0.452878	−	0.291047i	−0.747127	+	0.664682i	$0.768567\pi$
$522$	3.66772	−	6.71692i	0.00702628	−	0.0128677i
$523$	−214.979	+	160.931i	−0.411049	+	0.307708i	−0.784716	−	0.619855i	$-0.787191\pi$
$523$	−214.979	+	160.931i	−0.411049	+	0.307708i	0.373667	+	0.927563i	$0.378100\pi$
$524$	552.605	−	252.366i	1.05459	−	0.481615i
$525$	37.1397	+	334.982i	0.0707423	+	0.638061i
$526$	41.7657	−	26.8412i	0.0794025	−	0.0510289i
$527$	−13.2918	−	185.844i	−0.0252217	−	0.352645i
$528$	450.330	+	450.330i	0.852897	+	0.852897i
$529$	414.460	−	328.730i	0.783479	−	0.621419i
$530$	−78.3101	−	1.26795i	−0.147755	−	0.00239235i
$531$	22.9615	−	26.4990i	0.0432420	−	0.0499040i
$532$	−65.9184	+	303.022i	−0.123907	+	0.569590i
$533$	−582.796	+	778.525i	−1.09343	+	1.46065i
$534$	58.5840	−	26.7544i	0.109708	−	0.0501019i
$535$	−272.686	−	376.831i	−0.509693	−	0.704358i
$536$	9.37841	−	2.75375i	0.0174970	−	0.00513759i
$537$	861.627	−	187.435i	1.60452	−	0.349042i
$538$	81.6100	−	30.4390i	0.151691	−	0.0565780i
$539$	115.661	−	393.904i	0.214584	−	0.730805i
$540$	43.3363	−	493.498i	0.0802524	−	0.913886i
$541$	566.614	+	653.908i	1.04735	+	1.20870i	0.977454	+	0.211147i	$0.0677199\pi$
$541$	566.614	+	653.908i	1.04735	+	1.20870i	0.0698915	+	0.997555i	$0.477735\pi$
$542$	100.027	−	54.6186i	0.184551	−	0.100772i
$543$	128.720	−	48.0099i	0.237053	−	0.0884160i
$544$	−38.0739	+	59.2441i	−0.0699887	+	0.108905i
$545$	18.8753	+	68.3584i	0.0346335	+	0.125428i
$546$	−9.12034	+	63.4334i	−0.0167039	+	0.116178i
$547$	−634.511	−	236.660i	−1.15998	−	0.432651i	−0.305531	−	0.952182i	$-0.598834\pi$
$547$	−634.511	−	236.660i	−1.15998	−	0.432651i	−0.854452	+	0.519531i	$0.826107\pi$
$548$	−191.786	+	256.196i	−0.349974	+	0.467510i
$549$	−63.2029	−	98.3456i	−0.115124	−	0.179136i
$550$	−3.50800	−	89.8573i	−0.00637819	−	0.163377i
$551$	507.078			0.920286
$552$	−51.4284	−	147.600i	−0.0931675	−	0.267392i
$553$	−323.425	−	323.425i	−0.584855	−	0.584855i
$554$	63.7165	+	55.2106i	0.115012	+	0.0996582i
$555$	69.6801	−	43.2029i	0.125550	−	0.0778431i
$556$	87.1669	+	606.259i	0.156775	+	1.09039i
$557$	678.740	+	253.157i	1.21856	+	0.454500i	0.874767	−	0.484544i	$-0.161014\pi$
$557$	678.740	+	253.157i	1.21856	+	0.454500i	0.343796	+	0.939044i	$0.388287\pi$
$558$	7.51846	−	5.62825i	0.0134739	−	0.0100865i
$559$	−108.517	−	369.574i	−0.194126	−	0.661134i
$560$	315.585	−	63.3185i	0.563544	−	0.113069i
$561$	97.1771	−	212.788i	0.173221	−	0.379302i
$562$	−34.1711	+	18.6589i	−0.0608027	+	0.0332008i
$563$	68.0848	−	951.949i	0.120932	−	1.69085i	−0.468841	−	0.883282i	$-0.655328\pi$
$563$	68.0848	−	951.949i	0.120932	−	1.69085i	0.589773	−	0.807569i	$-0.299217\pi$
$564$	−685.111	+	593.652i	−1.21474	+	1.05257i
$565$	242.513	+	461.749i	0.429227	+	0.817254i
$566$	−23.9084	+	52.3520i	−0.0422409	+	0.0924947i
$567$	371.118	−	80.7318i	0.654529	−	0.142384i
$568$	118.015	+	64.4409i	0.207772	+	0.113452i
$569$	−622.305	−	89.4739i	−1.09368	−	0.157248i	−0.428216	−	0.903676i	$-0.640858\pi$
$569$	−622.305	−	89.4739i	−1.09368	−	0.157248i	−0.665466	+	0.746429i	$0.731767\pi$
$570$	72.8826	−	31.8686i	0.127864	−	0.0559099i
$571$	−16.0631	−	111.721i	−0.0281315	−	0.195659i	0.970909	−	0.239447i	$-0.0769663\pi$
$571$	−16.0631	−	111.721i	−0.0281315	−	0.195659i	−0.999041	+	0.0437886i	$0.986057\pi$
$572$	−194.857	+	895.745i	−0.340660	+	1.56599i
$573$	691.876	−	49.4839i	1.20746	−	0.0863594i
$574$		−	63.7707i		−	0.111099i
$575$	229.781	−	527.092i	0.399620	−	0.916681i
$576$	59.0636			0.102541
$577$	59.5487	+	832.600i	0.103204	+	1.44298i	0.740342	+	0.672231i	$0.234664\pi$
$577$	59.5487	+	832.600i	0.103204	+	1.44298i	−0.637138	+	0.770750i	$0.719882\pi$
$578$	−68.2633	−	14.8498i	−0.118103	−	0.0256916i
$579$	−1138.13	+	163.638i	−1.96568	+	0.282622i
$580$	−214.944	−	491.571i	−0.370593	−	0.847535i
$581$	−1.17243	+	8.15440i	−0.00201795	+	0.0140351i
$582$	8.17689	−	14.9749i	0.0140496	−	0.0257300i
$583$	−163.517	−	751.673i	−0.280474	−	1.28932i
$584$	−44.2015	−	20.1862i	−0.0756876	−	0.0345654i
$585$	−80.4599	+	42.2580i	−0.137538	+	0.0722360i
$586$	78.7572	+	90.8907i	0.134398	+	0.155104i
$587$	814.420	+	58.2485i	1.38743	+	0.0992308i	0.744974	−	0.667093i	$-0.232462\pi$
$587$	814.420	+	58.2485i	1.38743	+	0.0992308i	0.642454	+	0.766324i	$0.277916\pi$
$588$	−184.138	−	337.224i	−0.313160	−	0.573510i
$589$	566.045	+	258.504i	0.961026	+	0.438886i
$590$	9.01955	+	44.9542i	0.0152874	+	0.0761935i
$591$	−640.015	+	187.925i	−1.08294	+	0.317979i
$592$	−46.9226	−	62.6813i	−0.0792612	−	0.105881i
$593$	−130.444	+	349.733i	−0.219972	+	0.589769i	−0.999322	−	0.0368205i	$-0.988277\pi$
$593$	−130.444	+	349.733i	−0.219972	+	0.589769i	0.779349	+	0.626590i	$0.215550\pi$
$594$	−89.8361	+	12.9165i	−0.151239	+	0.0217449i
$595$	−62.3006	−	100.482i	−0.104707	−	0.168877i
$596$	22.6425	−	26.1308i	0.0379907	−	0.0438437i
$597$	−502.060	+	502.060i	−0.840972	+	0.840972i
$598$	67.4070	−	86.0823i	0.112721	−	0.143950i
$599$			493.340i			0.823606i	0.911273	+	0.411803i	$0.135101\pi$
$599$			493.340i			0.823606i	−0.911273	+	0.411803i	$0.864899\pi$
$600$	−124.729	−	115.356i	−0.207881	−	0.192260i
$601$	−415.039	+	266.729i	−0.690580	+	0.443809i	−0.838292	−	0.545221i	$-0.816446\pi$
$601$	−415.039	+	266.729i	−0.690580	+	0.443809i	0.147712	+	0.989030i	$0.452809\pi$
$602$	20.2197	+	15.1363i	0.0335876	+	0.0251434i
$603$	−1.64769	+	4.41763i	−0.00273249	+	0.00732609i
$604$	−146.229	−	21.0246i	−0.242102	−	0.0348089i
$605$	268.204	−	74.0570i	0.443312	−	0.122408i
$606$	−9.22156	−	5.92634i	−0.0152171	−	0.00977944i
$607$	60.5013	+	162.210i	0.0996727	+	0.267233i	0.977210	−	0.212276i	$-0.0680876\pi$
$607$	60.5013	+	162.210i	0.0996727	+	0.267233i	−0.877537	+	0.479509i	$0.840815\pi$
$608$	−112.722	−	206.434i	−0.185398	−	0.339530i
$609$	278.411	−	241.245i	0.457161	−	0.396132i
$610$	152.282	+	13.3726i	0.249642	+	0.0219222i
$611$	−1228.21	−	360.635i	−2.01016	−	0.590237i
$612$	−7.89005	−	21.1541i	−0.0128922	−	0.0345654i
$613$	−70.2508	−	322.938i	−0.114602	−	0.526815i	−0.998275	−	0.0587112i	$-0.981301\pi$
$613$	−70.2508	−	322.938i	−0.114602	−	0.526815i	0.883673	−	0.468104i	$-0.155063\pi$
$614$	−26.6192	−	90.6565i	−0.0433537	−	0.147649i
$615$	710.455	−	514.105i	1.15521	−	0.835943i
$616$	−50.4082	−	110.379i	−0.0818315	−	0.179186i
$617$	−601.799	−	450.501i	−0.975364	−	0.730148i	−0.0124402	−	0.999923i	$-0.503960\pi$
$617$	−601.799	−	450.501i	−0.975364	−	0.730148i	−0.962924	+	0.269774i	$0.913051\pi$
$618$	146.959	+	31.9691i	0.237799	+	0.0517299i
$619$	−135.339	−	117.272i	−0.218641	−	0.189454i	0.538653	−	0.842528i	$-0.318933\pi$
$619$	−135.339	−	117.272i	−0.218641	−	0.189454i	−0.757294	+	0.653074i	$0.773479\pi$
$620$	10.6590	−	658.311i	0.0171919	−	1.06179i
$621$	−553.143	−	175.555i	−0.890730	−	0.282698i
$622$	37.6173	−	37.6173i	0.0604779	−	0.0604779i
$623$	318.890	−	22.8074i	0.511861	−	0.0366090i
$624$	455.027	+	708.035i	0.729209	+	1.13467i
$625$	−48.7254	−	623.098i	−0.0779606	−	0.996956i
$626$	−13.6806	−	29.9562i	−0.0218539	−	0.0478534i
$627$	468.207	+	625.452i	0.746742	+	0.997531i
$628$	45.5873	+	24.8926i	0.0725913	+	0.0396378i
$629$	−15.5489	+	24.1945i	−0.0247200	+	0.0384651i
$630$	2.56311	−	5.38017i	0.00406842	−	0.00853995i
$631$	−355.523	−	104.391i	−0.563428	−	0.165437i	−0.0123985	−	0.999923i	$-0.503947\pi$
$631$	−355.523	−	104.391i	−0.563428	−	0.165437i	−0.551030	+	0.834486i	$0.685765\pi$
$632$	229.978	+	16.4483i	0.363889	+	0.0260258i
$633$	−37.1005	+	518.733i	−0.0586107	+	0.819484i
$634$	−1.59754	+	5.44071i	−0.00251978	+	0.00858157i
$635$	−295.708	−	833.809i	−0.465683	−	1.31309i
$636$	−605.663	−	389.236i	−0.952300	−	0.612006i
$637$	260.011	−	476.175i	0.408181	−	0.747527i
$638$	−78.6867	+	58.9042i	−0.123333	+	0.0923263i
$639$	−59.0001	+	26.9444i	−0.0923319	+	0.0421665i
$640$	−202.461	+	261.522i	−0.316345	+	0.408628i
$641$	878.819	−	564.783i	1.37101	−	0.881097i	0.372122	−	0.928184i	$-0.378630\pi$
$641$	878.819	−	564.783i	1.37101	−	0.881097i	0.998891	+	0.0470870i	$0.0149938\pi$
$642$	5.68972	+	79.5527i	0.00886249	+	0.123914i
$643$	−256.600	−	256.600i	−0.399067	−	0.399067i	0.478837	−	0.877904i	$-0.341059\pi$
$643$	−256.600	−	256.600i	−0.399067	−	0.399067i	−0.877904	+	0.478837i	$0.841059\pi$
$644$	8.34892	−	384.272i	0.0129642	−	0.596696i
$645$	−5.62309	+	347.289i	−0.00871796	+	0.538432i
$646$	−18.2731	+	21.0882i	−0.0282865	+	0.0326443i
$647$	−22.9673	+	105.579i	−0.0354981	+	0.163182i	−0.991484	−	0.130232i	$-0.958428\pi$
$647$	−22.9673	+	105.579i	−0.0354981	+	0.163182i	0.955985	+	0.293414i	$0.0947914\pi$
$648$	−114.732	+	153.264i	−0.177056	+	0.236519i
$649$	−409.638	+	187.076i	−0.631184	+	0.288252i
$650$	20.7122	−	117.022i	0.0318649	−	0.180034i
$651$	433.771	−	127.367i	0.666316	−	0.195648i
$652$	−144.441	+	31.4211i	−0.221535	+	0.0481919i
$653$	−604.882	+	225.609i	−0.926313	+	0.345497i	−0.766938	−	0.641721i	$-0.778221\pi$
$653$	−604.882	+	225.609i	−0.926313	+	0.345497i	−0.159375	+	0.987218i	$0.550948\pi$
$654$	3.42578	−	11.6671i	0.00523819	−	0.0178396i
$655$	−497.034	−	592.731i	−0.758830	−	0.904932i
$656$	−548.450	−	632.945i	−0.836052	−	0.964856i
$657$	20.5728	−	11.2336i	0.0313132	−	0.0170983i
$658$	78.6465	−	29.3336i	0.119524	−	0.0445800i
$659$	−273.159	+	425.044i	−0.414506	+	0.644984i	−0.984238	−	0.176846i	$-0.943410\pi$
$659$	−273.159	+	425.044i	−0.414506	+	0.644984i	0.569733	+	0.821830i	$0.307047\pi$
$660$	407.857	−	719.011i	0.617966	−	1.08941i
$661$	70.9678	−	493.592i	0.107364	−	0.746735i	−0.863020	−	0.505169i	$-0.831430\pi$
$661$	70.9678	−	493.592i	0.107364	−	0.746735i	0.970385	−	0.241565i	$-0.0776608\pi$
$662$	−166.203	−	61.9906i	−0.251062	−	0.0936414i
$663$	185.264	−	247.484i	0.279434	−	0.373280i
$664$	−2.24517	−	3.49356i	−0.00338128	−	0.00526138i
$665$	394.265	−	21.7895i	0.592879	−	0.0327661i
$666$	−1.44970			−0.00217673
$667$	−616.889	+	120.225i	−0.924871	+	0.180247i
$668$	219.700	+	219.700i	0.328893	+	0.328893i
$669$	374.239	+	324.280i	0.559400	+	0.484723i
$670$	−3.24887	−	5.23996i	−0.00484906	−	0.00782083i
$671$	213.679	+	1486.17i	0.318448	+	2.21486i
$672$	−160.102	−	59.7150i	−0.238247	−	0.0888616i
$673$	−335.147	+	250.888i	−0.497990	+	0.372791i	−0.818548	−	0.574438i	$-0.805221\pi$
$673$	−335.147	+	250.888i	−0.497990	+	0.372791i	0.320558	+	0.947229i	$0.396130\pi$
$674$	7.22331	+	24.6003i	0.0107171	+	0.0364990i
$675$	−620.400	+	114.060i	−0.919110	+	0.168978i
$676$	−227.578	+	498.326i	−0.336654	+	0.737168i
$677$	924.478	−	504.803i	1.36555	−	0.745647i	0.381640	−	0.924311i	$-0.375359\pi$
$677$	924.478	−	504.803i	1.36555	−	0.745647i	0.983910	+	0.178664i	$0.0571776\pi$
$678$	6.37980	−	89.2012i	0.00940973	−	0.131565i
$679$	64.0088	−	55.4640i	0.0942692	−	0.0816848i
$680$	56.9040	+	17.7141i	0.0836823	+	0.0260501i
$681$	506.429	−	1108.92i	0.743654	−	1.62838i
$682$	−117.866	+	25.6402i	−0.172824	+	0.0375955i
$683$	−511.380	−	279.235i	−0.748726	−	0.408835i	0.0591031	−	0.998252i	$-0.481176\pi$
$683$	−511.380	−	279.235i	−0.748726	−	0.408835i	−0.807829	+	0.589416i	$0.799358\pi$
$684$	74.6384	+	10.7314i	0.109120	+	0.0156892i
$685$	379.448	+	148.568i	0.553939	+	0.216888i
$686$	13.0949	+	91.0771i	0.0190888	+	0.132765i
$687$	−261.648	+	1202.77i	−0.380855	+	1.75076i
$688$	330.865	−	23.6639i	0.480909	−	0.0343953i
$689$		−	1016.60i		−	1.47548i
$690$	−81.1099	+	56.0500i	−0.117551	+	0.0812319i
$691$	−571.547			−0.827131			−0.413565	−	0.910474i	$-0.635717\pi$
$691$	−571.547			−0.827131			−0.413565	+	0.910474i	$0.635717\pi$
$692$	−66.8102	−	934.128i	−0.0965465	−	1.34990i
$693$	57.1959	+	12.4422i	0.0825338	+	0.0179541i
$694$	30.5782	−	4.39649i	0.0440609	−	0.00633500i
$695$	714.572	−	312.454i	1.02816	−	0.449574i
$696$	−26.4280	+	183.811i	−0.0379713	+	0.264096i
$697$	−147.430	+	269.998i	−0.211521	+	0.387371i
$698$	−38.5688	−	177.298i	−0.0552561	−	0.254008i
$699$	−668.457	−	305.274i	−0.956305	−	0.436730i
$700$	−188.247	−	372.972i	−0.268925	−	0.532816i
$701$	817.501	+	943.447i	1.16619	+	1.34586i	0.927078	+	0.374867i	$0.122312\pi$
$701$	817.501	+	943.447i	1.16619	+	1.34586i	0.239115	+	0.970991i	$0.423143\pi$
$702$	−119.638	−	8.55666i	−0.170424	−	0.0121890i
$703$	−46.0341	−	84.3052i	−0.0654824	−	0.119922i
$704$	−690.031	−	315.127i	−0.980158	−	0.447623i
$705$	960.829	+	639.701i	1.36288	+	0.907377i
$706$	130.092	−	38.1985i	0.184266	−	0.0541055i
$707$	−32.6092	−	43.5608i	−0.0461234	−	0.0616136i
$708$	−147.290	+	394.899i	−0.208036	+	0.557767i
$709$	1105.41	−	158.934i	1.55911	−	0.224167i	0.691860	−	0.722032i	$-0.256792\pi$
$709$	1105.41	−	158.934i	1.55911	−	0.224167i	0.867255	+	0.497865i	$0.165882\pi$
$710$	19.3682	−	82.5745i	0.0272791	−	0.116302i
$711$	−72.8331	+	84.0538i	−0.102437	+	0.118219i
$712$	−113.956	+	113.956i	−0.160051	+	0.160051i
$713$	−749.915	−	180.279i	−1.05177	−	0.252846i
$714$			20.2720i			0.0283922i
$715$	1165.46	−	64.4106i	1.63002	−	0.0900847i
$716$	−919.528	+	590.945i	−1.28426	+	0.825342i
$717$	−507.736	−	380.087i	−0.708140	−	0.530107i
$718$	10.3244	−	27.6808i	0.0143794	−	0.0385527i
$719$	−556.705	−	80.0420i	−0.774276	−	0.111324i	−0.256160	−	0.966634i	$-0.582457\pi$
$719$	−556.705	−	80.0420i	−0.774276	−	0.111324i	−0.518116	+	0.855310i	$0.673367\pi$
$720$	−20.8317	−	75.4435i	−0.0289328	−	0.104783i
$721$	628.058	+	403.628i	0.871093	+	0.559817i
$722$	1.57465	+	4.22180i	0.00218095	+	0.00584737i
$723$	−460.038	−	842.497i	−0.636291	−	1.16528i
$724$	−128.702	+	111.521i	−0.177765	+	0.154034i
$725$	−530.500	+	430.417i	−0.731724	+	0.593678i
$726$	−45.7759	−	13.4410i	−0.0630521	−	0.0185138i
$727$	332.710	+	892.029i	0.457647	+	1.22700i	0.936985	+	0.349370i	$0.113604\pi$
$727$	332.710	+	892.029i	0.457647	+	1.22700i	−0.479338	+	0.877631i	$0.659123\pi$
$728$	−34.0874	−	156.697i	−0.0468233	−	0.215243i
$729$	176.649	+	601.612i	0.242317	+	0.825257i
$730$	−4.85270	+	30.2645i	−0.00664754	+	0.0414583i
$731$	−50.6148	−	110.831i	−0.0692404	−	0.151615i
$732$	1124.94	+	842.119i	1.53680	+	1.15044i
$733$	1362.38	+	296.368i	1.85864	+	0.404321i	0.995007	−	0.0998068i	$-0.0318225\pi$
$733$	1362.38	+	296.368i	1.85864	+	0.404321i	0.863629	+	0.504128i	$0.168186\pi$
$734$	138.271	+	119.813i	0.188381	+	0.163233i
$735$	−351.498	+	340.297i	−0.478228	+	0.462989i
$736$	186.077	+	224.414i	0.252821	+	0.304910i
$737$	42.8195	−	42.8195i	0.0580997	−	0.0580997i
$738$	−15.4670	+	1.10622i	−0.0209579	+	0.00149894i
$739$	134.467	+	209.234i	0.181958	+	0.283132i	0.920236	−	0.391365i	$-0.127997\pi$
$739$	134.467	+	209.234i	0.181958	+	0.283132i	−0.738278	+	0.674497i	$0.764361\pi$
$740$	−62.2137	+	80.3623i	−0.0840726	+	0.108598i
$741$	428.918	+	939.200i	0.578837	+	1.26748i
$742$	39.9496	+	53.3664i	0.0538404	+	0.0719224i
$743$	775.549	+	423.482i	1.04381	+	0.569962i	0.907216	−	0.420665i	$-0.138203\pi$
$743$	775.549	+	423.482i	1.04381	+	0.569962i	0.136592	+	0.990627i	$0.456385\pi$
$744$	−123.206	+	191.713i	−0.165600	+	0.257679i
$745$	−39.7463	−	18.9351i	−0.0533508	−	0.0254162i
$746$	−100.240	−	29.4332i	−0.134371	−	0.0394548i
$747$	1.99811	+	0.142908i	0.00267484	+	0.000191309i
$748$	−20.6866	+	289.236i	−0.0276559	+	0.386679i
$749$	−111.541	+	379.874i	−0.148920	+	0.507175i
$750$	−49.1984	+	95.2048i	−0.0655979	+	0.126940i
$751$	671.218	+	431.365i	0.893765	+	0.574388i	0.904935	−	0.425550i	$-0.139919\pi$
$751$	671.218	+	431.365i	0.893765	+	0.574388i	−0.0111700	+	0.999938i	$0.503556\pi$
$752$	528.313	−	967.533i	0.702544	−	1.28661i
$753$	567.877	−	425.107i	0.754152	−	0.564551i
$754$	−118.159	+	53.9613i	−0.156709	+	0.0715667i
$755$	23.7531	+	186.605i	0.0314610	+	0.247159i
$756$	−354.724	+	227.967i	−0.469211	+	0.301544i
$757$	85.1384	+	1190.39i	0.112468	+	1.57251i	0.670003	+	0.742358i	$0.266293\pi$
$757$	85.1384	+	1190.39i	0.112468	+	1.57251i	−0.557535	+	0.830153i	$0.688253\pi$
$758$	95.6023	+	95.6023i	0.126124	+	0.126124i
$759$	−717.891	−	649.889i	−0.945838	−	0.856243i
$760$	−143.008	+	138.450i	−0.188168	+	0.182172i
$761$	−27.1480	+	31.3305i	−0.0356742	+	0.0411702i	−0.773306	−	0.634033i	$-0.781398\pi$
$761$	−27.1480	+	31.3305i	−0.0356742	+	0.0411702i	0.737632	+	0.675203i	$0.235944\pi$
$762$	−32.2448	+	148.227i	−0.0423160	+	0.194524i
$763$	36.1730	−	48.3215i	0.0474089	−	0.0633309i
$764$	−782.133	+	357.188i	−1.02373	+	0.467524i
$765$	−23.2902	+	16.8534i	−0.0304447	+	0.0220306i
$766$	70.5849	−	20.7256i	0.0921473	−	0.0270569i
$767$	−581.536	+	126.506i	−0.758196	+	0.164935i
$768$	−624.477	+	232.918i	−0.813121	+	0.303278i
$769$	140.704	−	479.193i	0.182970	−	0.623138i	−0.816012	−	0.578034i	$-0.803820\pi$
$769$	140.704	−	479.193i	0.182970	−	0.623138i	0.998982	−	0.0451039i	$-0.0143619\pi$
$770$	−58.6497	+	49.1806i	−0.0761684	+	0.0638709i
$771$	229.984	+	265.416i	0.298293	+	0.344249i
$772$	1250.97	−	683.083i	1.62043	−	0.884823i
$773$	255.923	−	95.4542i	0.331077	−	0.123485i	−0.178428	−	0.983953i	$-0.557101\pi$
$773$	255.923	−	95.4542i	0.331077	−	0.123485i	0.509505	+	0.860468i	$0.329828\pi$
$774$	3.32042	−	5.16667i	0.00428994	−	0.00667528i
$775$	−811.614	+	210.025i	−1.04724	+	0.271000i
$776$	−6.07600	+	42.2595i	−0.00782989	+	0.0544581i
$777$	−65.3836	−	24.3868i	−0.0841488	−	0.0313859i
$778$	121.471	−	162.267i	0.156133	−	0.208569i
$779$	−555.471	−	864.330i	−0.713057	−	1.10954i
$780$	728.665	−	813.917i	0.934186	−	1.04348i
$781$	833.048			1.06664
$782$	17.2303	−	29.9875i	0.0220337	−	0.0383472i
$783$	487.538	+	487.538i	0.622654	+	0.622654i
$784$	353.108	+	305.970i	0.450393	+	0.390268i
$785$	15.1028	−	64.3895i	0.0192393	−	0.0820249i
$786$	18.8760	+	131.286i	0.0240153	+	0.167030i
$787$	−527.928	−	196.907i	−0.670811	−	0.250200i	−0.00909996	−	0.999959i	$-0.502897\pi$
$787$	−527.928	−	196.907i	−0.670811	−	0.250200i	−0.661711	+	0.749759i	$0.730169\pi$
$788$	661.928	−	495.513i	0.840010	−	0.628824i
$789$	−163.718	−	557.571i	−0.207500	−	0.706681i
$790$	−28.6096	−	142.593i	−0.0362147	−	0.180497i
$791$	184.415	−	403.812i	0.233141	−	0.510508i
$792$	−25.8968	+	14.1407i	−0.0326980	+	0.0178545i
$793$	−141.554	+	1979.18i	−0.178504	+	2.49581i
$794$	33.0898	−	28.6725i	0.0416749	−	0.0361115i
$795$	−272.478	+	875.297i	−0.342740	+	1.10100i
$796$	365.622	−	800.600i	0.459324	−	1.00578i
$797$	467.333	−	101.662i	0.586365	−	0.127556i	0.0904107	−	0.995905i	$-0.471182\pi$
$797$	467.333	−	101.662i	0.586365	−	0.127556i	0.495954	+	0.868349i	$0.334818\pi$
$798$	−59.4238	−	32.4479i	−0.0744660	−	0.0406615i
$799$	−400.796	−	57.6257i	−0.501622	−	0.0721223i
$800$	293.154	+	120.290i	0.366442	+	0.150362i
$801$	−11.0634	−	76.9479i	−0.0138120	−	0.0960647i
$802$	−1.52109	+	6.99236i	−0.00189663	+	0.00871865i
$803$	−300.285	+	21.4768i	−0.373953	+	0.0267457i
$804$		−	56.6750i		−	0.0704912i
$805$	−474.479	+	119.986i	−0.589415	+	0.149051i
$806$	−159.408			−0.197777
$807$	−72.7312	−	1016.92i	−0.0901254	−	1.26012i
$808$	26.8027	+	5.83056i	0.0331716	+	0.00721604i
$809$	−54.0883	+	7.77673i	−0.0668582	+	0.00961276i	−0.175663	−	0.984450i	$-0.556207\pi$
$809$	−54.0883	+	7.77673i	−0.0668582	+	0.00961276i	0.108805	+	0.994063i	$0.465298\pi$
$810$	112.450	+	44.0284i	0.138828	+	0.0543561i
$811$	−40.8646	+	284.219i	−0.0503879	+	0.350456i	0.948994	+	0.315295i	$0.102103\pi$
$811$	−40.8646	+	284.219i	−0.0503879	+	0.350456i	−0.999382	+	0.0351607i	$0.988806\pi$
$812$	−218.851	+	400.796i	−0.269521	+	0.493591i
$813$	−283.555	−	1303.48i	−0.348776	−	1.60330i
$814$	16.9367	+	7.73471i	0.0208067	+	0.00950211i
$815$	87.5180	+	166.635i	0.107384	+	0.204461i
$816$	174.346	+	201.206i	0.213660	+	0.246576i
$817$	405.897	+	29.0303i	0.496813	+	0.0355328i
$818$	41.1281	+	75.3205i	0.0502789	+	0.0920788i
$819$	70.3644	+	32.1344i	0.0859150	+	0.0392361i
$820$	−602.440	+	904.863i	−0.734683	+	1.10349i
$821$	−427.246	+	125.451i	−0.520397	+	0.152802i	−0.531374	−	0.847137i	$-0.678324\pi$
$821$	−427.246	+	125.451i	−0.520397	+	0.152802i	0.0109770	+	0.999940i	$0.496506\pi$
$822$	−41.8723	−	55.9349i	−0.0509396	−	0.0680473i
$823$	374.632	−	1004.43i	0.455204	−	1.22045i	−0.483385	−	0.875408i	$-0.660593\pi$
$823$	374.632	−	1004.43i	0.455204	−	1.22045i	0.938588	−	0.345040i	$-0.112135\pi$
$824$	−372.507	+	53.5585i	−0.452072	+	0.0649982i
$825$	−1020.73	−	256.919i	−1.23725	−	0.311417i
$826$	25.5564	−	29.4936i	0.0309399	−	0.0357065i
$827$	−82.9943	+	82.9943i	−0.100356	+	0.100356i	−0.755502	−	0.655146i	$-0.772607\pi$
$827$	−82.9943	+	82.9943i	−0.100356	+	0.100356i	0.655146	+	0.755502i	$0.272607\pi$
$828$	−93.3462	+	4.64095i	−0.112737	+	0.00560501i
$829$			899.226i			1.08471i	0.840149	+	0.542356i	$0.182468\pi$
$829$			899.226i			1.08471i	−0.840149	+	0.542356i	$0.817532\pi$
$830$	−1.74722	+	1.95164i	−0.00210508	+	0.00235138i
$831$	830.168	−	533.517i	0.998999	−	0.642018i
$832$	−802.544	−	600.777i	−0.964596	−	0.722088i
$833$	59.9748	−	160.799i	0.0719986	−	0.193036i
$834$	−132.364	−	19.0311i	−0.158710	−	0.0228190i
$835$	195.199	−	344.115i	0.233771	−	0.412114i
$836$	−814.734	−	523.598i	−0.974562	−	0.626313i
$837$	295.690	+	792.776i	0.353274	+	0.947164i
$838$	18.3319	+	33.5723i	0.0218758	+	0.0400625i
$839$	220.198	−	190.802i	0.262453	−	0.227416i	−0.513687	−	0.857978i	$-0.671721\pi$
$839$	220.198	−	190.802i	0.262453	−	0.227416i	0.776139	+	0.630561i	$0.217175\pi$
$840$	−12.6499	+	144.053i	−0.0150594	+	0.171491i
$841$	−90.4779	−	26.5667i	−0.107584	−	0.0315894i
$842$	−44.3025	−	118.780i	−0.0526158	−	0.141068i
$843$	96.8683	+	445.296i	0.114909	+	0.528228i
$844$	−181.622	−	618.547i	−0.215192	−	0.732875i
$845$	688.766	+	110.439i	0.815108	+	0.130697i
$846$	−8.47885	−	18.5661i	−0.0100223	−	0.0219457i
$847$	−189.589	−	141.925i	−0.223836	−	0.167562i
$848$	855.482	+	186.099i	1.00882	+	0.219456i
$849$	509.109	+	441.146i	0.599658	+	0.519606i
$850$	1.21703	−	37.5729i	0.00143180	−	0.0442034i
$851$	75.9913	+	91.6477i	0.0892965	+	0.107694i
$852$	551.302	−	551.302i	0.647068	−	0.647068i
$853$	−940.223	+	67.2461i	−1.10225	+	0.0788348i	−0.610588	−	0.791949i	$-0.709067\pi$
$853$	−940.223	+	67.2461i	−1.10225	+	0.0788348i	−0.491667	+	0.870783i	$0.663612\pi$
$854$	−70.3453	−	109.459i	−0.0823715	−	0.128173i
$855$	−12.1241	−	95.2471i	−0.0141802	−	0.111400i
$856$	−82.9059	−	181.539i	−0.0968527	−	0.212078i
$857$	−147.184	−	196.614i	−0.171743	−	0.229422i	0.706409	−	0.707804i	$-0.250314\pi$
$857$	−147.184	−	196.614i	−0.171743	−	0.229422i	−0.878151	+	0.478383i	$0.841223\pi$
$858$	−175.659	−	95.9173i	−0.204731	−	0.111792i
$859$	497.068	−	773.453i	0.578659	−	0.900411i	−0.421320	−	0.906912i	$-0.638433\pi$
$859$	497.068	−	773.453i	0.578659	−	0.900411i	0.999979	+	0.00650127i	$0.00206943\pi$
$860$	−143.912	−	405.789i	−0.167340	−	0.471848i
$861$	−716.191	−	210.293i	−0.831813	−	0.244242i
$862$	−27.4114	−	1.96050i	−0.0317998	−	0.00227437i
$863$	−8.20504	+	114.722i	−0.00950758	+	0.132933i	−0.999989	−	0.00471393i	$-0.998500\pi$
$863$	−8.20504	+	114.722i	−0.00950758	+	0.132933i	0.990481	+	0.137647i	$0.0439541\pi$
$864$	90.1016	−	306.858i	0.104284	−	0.355160i
$865$	−1123.89	+	398.586i	−1.29930	+	0.460793i
$866$	28.1752	+	18.1071i	0.0325349	+	0.0209089i
$867$	−391.881	+	717.676i	−0.451996	+	0.827769i
$868$	−448.623	+	335.835i	−0.516847	+	0.386907i
$869$	1299.36	−	593.397i	1.49523	−	0.682850i
$870$	116.198	−	14.7909i	0.133561	−	0.0170010i
$871$	67.3234	−	43.2661i	0.0772943	−	0.0496740i
$872$	2.17065	+	30.3497i	0.00248928	+	0.0348047i
$873$	−14.5626	−	14.5626i	−0.0166811	−	0.0166811i
$874$	60.3237	+	98.5064i	0.0690203	+	0.112708i
$875$	−393.981	+	357.455i	−0.450264	+	0.408520i
$876$	−184.512	+	212.938i	−0.210630	+	0.243080i
$877$	44.4600	−	204.379i	0.0506955	−	0.233044i	−0.944827	−	0.327570i	$-0.893770\pi$
$877$	44.4600	−	204.379i	0.0506955	−	0.233044i	0.995522	+	0.0945267i	$0.0301338\pi$
$878$	−35.8473	+	47.8864i	−0.0408284	+	0.0545403i
$879$	1280.48	−	584.775i	1.45675	−	0.665273i
$880$	−159.147	+	992.541i	−0.180849	+	1.12789i
$881$	−461.737	+	135.578i	−0.524106	+	0.153891i	−0.533074	−	0.846068i	$-0.678963\pi$
$881$	−461.737	+	135.578i	−0.524106	+	0.153891i	0.00896845	+	0.999960i	$0.497145\pi$
$882$	8.45307	−	1.83885i	0.00958398	−	0.00208487i
$883$	−817.583	+	304.943i	−0.925915	+	0.345348i	−0.766781	−	0.641909i	$-0.778143\pi$
$883$	−817.583	+	304.943i	−0.925915	+	0.345348i	−0.159134	+	0.987257i	$0.550870\pi$
$884$	−107.964	+	367.692i	−0.122131	+	0.415941i
$885$	534.611	+	46.9466i	0.604080	+	0.0530470i
$886$	−66.0424	−	76.2170i	−0.0745400	−	0.0860237i
$887$	−604.979	+	330.344i	−0.682051	+	0.372428i	−0.782618	−	0.622502i	$-0.786116\pi$
$887$	−604.979	+	330.344i	−0.682051	+	0.372428i	0.100567	+	0.994930i	$0.467934\pi$
$888$	32.9590	−	12.2931i	0.0371160	−	0.0138436i
$889$	−407.109	+	633.474i	−0.457941	+	0.712570i
$890$	88.4199	+	50.1560i	0.0993482	+	0.0563551i
$891$	−168.802	+	1174.04i	−0.189452	+	1.31767i
$892$	−575.129	−	214.512i	−0.644764	−	0.240485i
$893$	810.443	−	1082.63i	0.907551	−	1.21235i
$894$	4.08127	+	6.35057i	0.00456518	+	0.00710355i
$895$	1036.95	+	928.339i	1.15861	+	1.03725i
$896$	281.505			0.314180
$897$	−744.482	−	1040.90i	−0.829968	−	1.16042i
$898$	47.8336	+	47.8336i	0.0532668	+	0.0532668i
$899$	692.526	+	600.077i	0.770329	+	0.667494i
$900$	−87.1951	+	52.1274i	−0.0968834	+	0.0579193i
$901$	−45.7654	−	318.306i	−0.0507940	−	0.353280i
$902$	186.600	+	69.5983i	0.206874	+	0.0771600i
$903$	236.669	−	177.168i	0.262092	−	0.196199i
$904$	63.0458	+	214.714i	0.0697409	+	0.237516i
$905$	180.497	+	120.171i	0.199444	+	0.132786i
$906$	13.3990	−	29.3396i	0.0147891	−	0.0323837i
$907$	1154.97	−	630.663i	1.27340	−	0.695328i	0.306837	−	0.951762i	$-0.400729\pi$
$907$	1154.97	−	630.663i	1.27340	−	0.695328i	0.966562	+	0.256434i	$0.0825476\pi$
$908$	−107.806	+	1507.32i	−0.118729	+	1.66005i
$909$	−9.99959	+	8.66469i	−0.0110006	+	0.00953211i
$910$	−89.5525	+	47.0335i	−0.0984093	+	0.0516852i
$911$	−19.0272	+	41.6638i	−0.0208861	+	0.0457342i	−0.919788	−	0.392417i	$-0.871639\pi$
$911$	−19.0272	+	41.6638i	−0.0208861	+	0.0457342i	0.898901	+	0.438151i	$0.144366\pi$
$912$	−868.864	+	189.010i	−0.952702	+	0.207248i
$913$	−22.5811	−	12.3302i	−0.0247329	−	0.0135052i
$914$	−96.3347	−	13.8508i	−0.105399	−	0.0151541i
$915$	652.353	−	1666.14i	0.712954	−	1.82091i
$916$	−217.147	−	1510.29i	−0.237060	−	1.64879i
$917$	−139.955	+	643.362i	−0.152622	+	0.701594i
$918$	−37.8446	+	2.70670i	−0.0412251	+	0.00294847i
$919$			79.2366i			0.0862204i	0.999070	+	0.0431102i	$0.0137267\pi$
$919$			79.2366i			0.0862204i	−0.999070	+	0.0431102i	$0.986273\pi$
$920$	141.151	−	202.339i	0.153425	−	0.219934i
$921$	−1105.92			−1.20078
$922$	−13.6604	−	190.997i	−0.0148160	−	0.207155i
$923$	1075.75	+	234.015i	1.16549	+	0.253538i
$924$	−696.434	+	100.132i	−0.753716	+	0.108368i
$925$	119.720	+	49.1247i	0.129427	+	0.0531078i
$926$	−1.08208	+	7.52602i	−0.00116855	+	0.00812745i
$927$	87.0012	−	159.331i	0.0938525	−	0.171878i
$928$	−73.6227	−	338.438i	−0.0793348	−	0.364696i
$929$	221.895	+	101.336i	0.238854	+	0.109081i	0.531246	−	0.847218i	$-0.321724\pi$
$929$	221.895	+	101.336i	0.238854	+	0.109081i	−0.292392	+	0.956299i	$0.594451\pi$
$930$	137.251	+	42.7258i	0.147581	+	0.0459417i
$931$	375.356	+	433.184i	0.403175	+	0.465289i
$932$	908.612	+	64.9852i	0.974906	+	0.0697266i
$933$	−298.421	−	546.516i	−0.319851	−	0.585763i
$934$	25.7024	+	11.7379i	0.0275186	+	0.0125673i
$935$	362.015	−	72.6342i	0.387182	−	0.0776836i
$936$	−37.4140	+	10.9858i	−0.0399723	+	0.0117369i
$937$	−884.136	−	1181.07i	−0.943581	−	1.26048i	−0.965416	−	0.260716i	$-0.916042\pi$
$937$	−884.136	−	1181.07i	−0.943581	−	1.26048i	0.0218343	−	0.999762i	$-0.493049\pi$
$938$	−1.83389	+	4.91686i	−0.00195511	+	0.00524186i
$939$	−381.543	+	54.8576i	−0.406329	+	0.0584213i
$940$	−1393.05	−	326.747i	−1.48197	−	0.347603i
$941$	340.231	−	392.647i	0.361563	−	0.417266i	−0.545600	−	0.838046i	$-0.683698\pi$
$941$	340.231	−	392.647i	0.361563	−	0.417266i	0.907163	+	0.420780i	$0.138244\pi$
$942$	−8.01871	+	8.01871i	−0.00851243	+	0.00851243i
$943$	880.689	+	919.808i	0.933923	+	0.975406i
$944$		−	512.527i		−	0.542931i
$945$	400.022	+	358.123i	0.423304	+	0.378966i
$946$	−66.3581	+	42.6457i	−0.0701459	+	0.0450801i
$947$	−641.879	−	480.504i	−0.677802	−	0.507397i	0.204027	−	0.978965i	$-0.434597\pi$
$947$	−641.879	−	480.504i	−0.677802	−	0.507397i	−0.881829	+	0.471569i	$0.843688\pi$
$948$	467.197	−	1252.60i	0.492824	−	1.32131i
$949$	−393.804	−	56.6205i	−0.414967	−	0.0596633i
$950$	108.190	+	63.7076i	0.113884	+	0.0670606i
$951$	55.8350	+	35.8830i	0.0587119	+	0.0377318i
$952$	−17.7272	−	47.5284i	−0.0186210	−	0.0499248i
$953$	−654.426	−	1198.49i	−0.686701	−	1.25760i	−0.955667	−	0.294450i	$-0.904864\pi$
$953$	−654.426	−	1198.49i	−0.686701	−	1.25760i	0.268966	−	0.963150i	$-0.413318\pi$
$954$	12.2505	−	10.6151i	0.0128412	−	0.0111270i
$955$	703.479	+	838.924i	0.736627	+	0.878455i
$956$	754.353	+	221.498i	0.789073	+	0.231693i
$957$	402.055	+	1077.95i	0.420121	+	1.12639i
$958$	9.08318	+	41.7547i	0.00948140	+	0.0435853i
$959$	−97.7172	−	332.794i	−0.101895	−	0.347022i
$960$	529.967	+	732.374i	0.552049	+	0.762890i
$961$	67.9302	+	148.746i	0.0706870	+	0.154783i
$962$	19.6983	+	14.7459i	0.0204764	+	0.0153284i
$963$	94.0696	+	20.4636i	0.0976839	+	0.0212498i
$964$	899.268	+	779.220i	0.932851	+	0.808320i
$965$	−1262.37	−	1303.92i	−1.30816	−	1.35122i
$966$	79.9857	+	25.3857i	0.0828009	+	0.0262792i
$967$	260.493	−	260.493i	0.269383	−	0.269383i	−0.559469	−	0.828852i	$-0.688995\pi$
$967$	260.493	−	260.493i	0.269383	−	0.269383i	0.828852	+	0.559469i	$0.188995\pi$
$968$	119.077	−	8.51654i	0.123013	−	0.00879808i
$969$	176.578	+	274.761i	0.182227	+	0.283551i
$970$	26.7148	−	3.40054i	0.0275410	−	0.00350571i
$971$	−737.614	−	1615.15i	−0.759643	−	1.66339i	−0.748219	−	0.663452i	$-0.769091\pi$
$971$	−737.614	−	1615.15i	−0.759643	−	1.66339i	−0.0114245	−	0.999935i	$-0.503637\pi$
$972$	130.872	+	174.824i	0.134642	+	0.179860i
$973$	−582.617	−	318.133i	−0.598784	−	0.326961i
$974$	−0.901679	+	1.40304i	−0.000925749	+	0.00144049i
$975$	−1245.94	−	618.509i	−1.27789	−	0.634368i
$976$	−1639.59	−	481.426i	−1.67991	−	0.493265i
$977$	−1543.78	−	110.413i	−1.58012	−	0.113013i	−0.746515	−	0.665369i	$-0.768274\pi$
$977$	−1543.78	−	110.413i	−1.58012	−	0.113013i	−0.833608	+	0.552357i	$0.813729\pi$
$978$	2.30234	−	32.1909i	0.00235413	−	0.0329150i
$979$	−281.294	+	957.998i	−0.287328	+	0.978548i
$980$	260.828	−	547.499i	0.266151	−	0.558672i
$981$	−12.3474	−	7.93519i	−0.0125865	−	0.00808887i
$982$	−0.698272	+	1.27879i	−0.000711071	+	0.00130223i
$983$	−674.108	+	504.631i	−0.685766	+	0.513358i	−0.884408	−	0.466714i	$-0.845438\pi$
$983$	−674.108	+	504.631i	−0.685766	+	0.513358i	0.198642	+	0.980072i	$0.436347\pi$
$984$	342.261	−	156.306i	0.347827	−	0.158847i
$985$	−832.518	−	644.507i	−0.845196	−	0.654322i
$986$	−34.5671	+	22.2149i	−0.0350579	+	0.0225303i
$987$	−70.0901	−	979.988i	−0.0710133	−	0.992896i
$988$	−905.015	−	905.015i	−0.916007	−	0.916007i
$989$	−500.679	+	60.9184i	−0.506248	+	0.0615960i
$990$	12.9457	+	13.3718i	0.0130764	+	0.0135068i
$991$	446.557	−	515.354i	0.450612	−	0.520034i	−0.484305	−	0.874899i	$-0.660928\pi$
$991$	446.557	−	515.354i	0.450612	−	0.520034i	0.934918	+	0.354865i	$0.115473\pi$
$992$	90.3488	−	415.327i	0.0910774	−	0.418676i
$993$	−1244.28	+	1662.16i	−1.25305	+	1.67388i
$994$	−65.6675	+	29.9893i	−0.0660639	+	0.0301704i
$995$	−1106.56	−	177.429i	−1.11212	−	0.178320i
$996$	−23.1040	+	6.78393i	−0.0231967	+	0.00681118i
$997$	−976.945	+	212.521i	−0.979885	+	0.213161i	−0.673857	−	0.738862i	$-0.735364\pi$
$997$	−976.945	+	212.521i	−0.979885	+	0.213161i	−0.306028	+	0.952023i	$0.599000\pi$
$998$	−63.4981	+	23.6836i	−0.0636253	+	0.0237310i
$999$	36.7964	−	125.317i	0.0368332	−	0.125442i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.3.k.a.108.11	yes	440
5.2	odd	4	inner	115.3.k.a.62.12	yes	440
23.13	even	11	inner	115.3.k.a.13.12	✓	440
115.82	odd	44	inner	115.3.k.a.82.11	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.k.a.13.12	✓	440	23.13	even	11	inner
115.3.k.a.62.12	yes	440	5.2	odd	4	inner
115.3.k.a.82.11	yes	440	115.82	odd	44	inner
115.3.k.a.108.11	yes	440	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	115.k (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0193071 - 0.269949i) q^{2} +(-3.09539 - 0.673360i) q^{3} +(3.88679 - 0.558835i) q^{4} +(-2.00317 - 4.58119i) q^{5} +(-0.122010 + 0.848597i) q^{6} +(-2.03958 + 3.73521i) q^{7} +(-0.456013 - 2.09626i) q^{8} +(0.941319 + 0.429886i) q^{9} +(-1.19801 + 0.629204i) q^{10} +(-8.70369 - 10.0446i) q^{11} +(-12.4074 - 0.887395i) q^{12} +(-8.41778 - 15.4160i) q^{13} +(1.04770 + 0.478466i) q^{14} +(3.11580 + 15.5294i) q^{15} +(14.5137 - 4.26161i) q^{16} +(-3.32966 - 4.44791i) q^{17} +(0.0978731 - 0.262408i) q^{18} +(18.3678 - 2.64089i) q^{19} +(-10.3460 - 16.6867i) q^{20} +(8.82844 - 10.1886i) q^{21} +(-2.54348 + 2.54348i) q^{22} +(-21.7193 + 7.56769i) q^{23} +6.79579i q^{24} +(-16.9746 + 18.3538i) q^{25} +(-3.99902 + 2.57001i) q^{26} +(20.1992 + 15.1209i) q^{27} +(-5.84004 + 15.6578i) q^{28} +(27.0477 + 3.88887i) q^{29} +(4.13199 - 1.14094i) q^{30} +(28.2105 + 18.1298i) q^{31} +(-4.42944 - 11.8758i) q^{32} +(20.1777 + 36.9526i) q^{33} +(-1.13642 + 0.984716i) q^{34} +(21.1974 + 1.86143i) q^{35} +(3.89894 + 1.14483i) q^{36} +(-1.80893 - 4.84992i) q^{37} +(-1.06754 - 4.90738i) q^{38} +(15.6758 + 53.3867i) q^{39} +(-8.68989 + 6.28825i) q^{40} +(-23.0003 - 50.3637i) q^{41} +(-2.92084 - 2.18652i) q^{42} +(21.4280 + 4.66139i) q^{43} +(-39.4427 - 34.1773i) q^{44} +(0.0837661 - 5.17350i) q^{45} +(2.46223 + 5.71701i) q^{46} +(51.5322 - 51.5322i) q^{47} +(-47.7951 + 3.41837i) q^{48} +(16.6995 + 25.9849i) q^{49} +(5.28233 + 4.22792i) q^{50} +(7.31155 + 16.0101i) q^{51} +(-41.3331 - 55.2146i) q^{52} +(50.7985 + 27.7381i) q^{53} +(3.69189 - 5.74469i) q^{54} +(-28.5812 + 59.9943i) q^{55} +(8.76005 + 2.57218i) q^{56} +(-58.6338 - 4.19357i) q^{57} +(0.527584 - 7.37659i) q^{58} +(9.54592 - 32.5104i) q^{59} +(20.7888 + 58.6183i) q^{60} +(-95.0350 - 61.0753i) q^{61} +(4.34946 - 7.96544i) q^{62} +(-3.52561 + 2.63924i) q^{63} +(51.9176 - 23.7100i) q^{64} +(-53.7615 + 69.4444i) q^{65} +(9.58575 - 6.16039i) q^{66} +(0.325035 + 4.54459i) q^{67} +(-15.4273 - 15.4273i) q^{68} +(72.3256 - 8.79997i) q^{69} +(0.0932323 - 5.75814i) q^{70} +(-41.0454 + 47.3689i) q^{71} +(0.471899 - 2.16928i) q^{72} +(13.5742 - 18.1330i) q^{73} +(-1.27431 + 0.581956i) q^{74} +(64.9017 - 45.3822i) q^{75} +(69.9159 - 20.5292i) q^{76} +(55.2706 - 12.0234i) q^{77} +(14.1090 - 5.26240i) q^{78} +(-30.2793 + 103.122i) q^{79} +(-48.5966 - 57.9533i) q^{80} +(-58.4415 - 67.4451i) q^{81} +(-13.1516 + 7.18130i) q^{82} +(1.81373 - 0.676485i) q^{83} +(28.6205 - 44.5344i) q^{84} +(-13.7068 + 24.1638i) q^{85} +(0.844622 - 5.87448i) q^{86} +(-81.1045 - 30.2504i) q^{87} +(-17.0871 + 22.8257i) q^{88} +(-40.6141 - 63.1968i) q^{89} +(-1.39820 + 0.0772728i) q^{90} +74.7509 q^{91} +(-80.1894 + 41.5515i) q^{92} +(-75.1146 - 75.1146i) q^{93} +(-14.9060 - 12.9161i) q^{94} +(-48.8923 - 78.8563i) q^{95} +(5.71414 + 39.7427i) q^{96} +(-18.6466 - 6.95480i) q^{97} +(6.69218 - 5.00970i) q^{98} +(-3.87492 - 13.1968i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 18 q^{2} - 22 q^{3} - 14 q^{5} - 44 q^{6} - 6 q^{7} - 34 q^{8} - 18 q^{10} - 20 q^{11} - 70 q^{12} - 26 q^{13} - 82 q^{15} + 180 q^{16} - 46 q^{17} - 286 q^{18} + 34 q^{20} - 52 q^{21} + 4 q^{22}+ \cdots + 606 q^{98}+O(q^{100}) \) 440 * q - 18 * q^2 - 22 * q^3 - 14 * q^5 - 44 * q^6 - 6 * q^7 - 34 * q^8 - 18 * q^10 - 20 * q^11 - 70 * q^12 - 26 * q^13 - 82 * q^15 + 180 * q^16 - 46 * q^17 - 286 * q^18 + 34 * q^20 - 52 * q^21 + 4 * q^22 + 22 * q^23 - 106 * q^25 - 100 * q^26 + 110 * q^27 + 302 * q^28 + 178 * q^30 - 144 * q^31 - 206 * q^32 + 288 * q^33 + 26 * q^35 - 596 * q^36 - 678 * q^37 + 30 * q^38 - 222 * q^40 + 88 * q^41 - 434 * q^42 - 150 * q^43 - 248 * q^45 - 44 * q^46 - 20 * q^47 + 566 * q^48 + 206 * q^50 + 220 * q^51 + 1238 * q^52 - 346 * q^53 + 134 * q^55 - 1316 * q^56 + 714 * q^57 - 386 * q^58 - 522 * q^60 - 692 * q^61 + 22 * q^62 + 198 * q^63 + 174 * q^65 + 156 * q^66 + 330 * q^67 + 572 * q^68 - 232 * q^70 + 508 * q^71 + 368 * q^72 - 190 * q^73 - 962 * q^75 + 900 * q^76 + 270 * q^77 - 618 * q^78 - 1884 * q^80 + 1432 * q^81 + 798 * q^82 + 122 * q^83 - 818 * q^85 + 212 * q^86 - 558 * q^87 + 462 * q^88 - 700 * q^90 - 400 * q^91 - 22 * q^92 + 372 * q^93 + 796 * q^95 + 1796 * q^96 + 480 * q^97 + 606 * q^98

Introduction

L-functions

Modular forms

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Database

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