LMFDB - Embedded newform 115.3.k.a.82.11

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)

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);

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")

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			82.11
Character	$\chi$	$=$	115.82
Dual form			115.3.k.a.108.11

$q$-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 $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{11}\right)$

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	−0.999993	−	0.00368846i	$-0.998826\pi$
$2$	−0.0193071	+	0.269949i	−0.00965357	+	0.134974i	0.990340	+	0.138663i	$0.0442805\pi$
$3$	−3.09539	+	0.673360i	−1.03180	+	0.224453i	−0.696423	−	0.717632i	$-0.745226\pi$
$3$	−3.09539	+	0.673360i	−1.03180	+	0.224453i	−0.335373	+	0.942085i	$0.608862\pi$
$4$	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	0.690460	−	0.723370i	$-0.257408\pi$
$7$	−2.03958	−	3.73521i	−0.291369	−	0.533602i	−0.981829	+	0.189769i	$0.939226\pi$
$8$	−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	−0.997867	−	0.0652759i	$-0.979207\pi$
$11$	−8.70369	+	10.0446i	−0.791244	+	0.913145i	0.206623	+	0.978421i	$0.433753\pi$
$12$	−12.4074	+	0.887395i	−1.03395	+	0.0739496i
$13$	−8.41778	+	15.4160i	−0.647522	+	1.18585i	0.323357	+	0.946277i	$0.395188\pi$
$13$	−8.41778	+	15.4160i	−0.647522	+	1.18585i	−0.970879	+	0.239571i	$0.922993\pi$
$14$	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	−0.887711	−	0.460401i	$-0.847706\pi$
$17$	−3.32966	+	4.44791i	−0.195863	+	0.261642i	0.691849	+	0.722043i	$0.256797\pi$
$18$	0.0978731	+	0.262408i	0.00543740	+	0.0145782i
$19$	18.3678	+	2.64089i	0.966727	+	0.138994i	0.607556	−	0.794277i	$-0.292150\pi$
$19$	18.3678	+	2.64089i	0.966727	+	0.138994i	0.359171	+	0.933272i	$0.383059\pi$
$20$	−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	0.340810	−	0.940132i	$-0.389299\pi$
$29$	27.0477	−	3.88887i	0.932680	−	0.134099i	0.591870	+	0.806033i	$0.298390\pi$
$30$	4.13199	+	1.14094i	0.137733	+	0.0380312i
$31$	28.2105	−	18.1298i	0.910017	−	0.584832i	0.000272077	−	1.00000i	$-0.499913\pi$
$31$	28.2105	−	18.1298i	0.910017	−	0.584832i	0.909745	+	0.415168i	$0.136277\pi$
$32$	−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	−0.959100	−	0.283069i	$-0.908648\pi$
$37$	−1.80893	+	4.84992i	−0.0488899	+	0.131079i	0.910210	+	0.414148i	$0.135920\pi$
$38$	−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	0.390477	+	0.920613i	$0.372310\pi$
$41$	−23.0003	+	50.3637i	−0.560984	+	1.22838i	−0.951461	+	0.307771i	$0.900417\pi$
$42$	−2.92084	+	2.18652i	−0.0695439	+	0.0520599i
$43$	21.4280	−	4.66139i	0.498327	−	0.108404i	0.0436247	−	0.999048i	$-0.486109\pi$
$43$	21.4280	−	4.66139i	0.498327	−	0.108404i	0.454702	+	0.890644i	$0.349746\pi$
$44$	−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	0.994825	+	0.101606i	$0.0323980\pi$
$47$	51.5322	+	51.5322i	1.09643	+	1.09643i	0.101606	+	0.994825i	$0.467602\pi$
$48$	−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	0.0777296	−	0.996974i	$-0.475233\pi$
$53$	50.7985	−	27.7381i	0.958462	−	0.523360i	0.880732	+	0.473615i	$0.157051\pi$
$54$	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	0.999984	+	0.00564376i	$0.00179647\pi$
$59$	9.54592	+	32.5104i	0.161795	+	0.551024i	−0.838189	+	0.545380i	$0.816385\pi$
$60$	20.7888	−	58.6183i	0.346481	−	0.976971i
$61$	−95.0350	+	61.0753i	−1.55795	+	1.00123i	−0.574831	+	0.818272i	$0.694932\pi$
$61$	−95.0350	+	61.0753i	−1.55795	+	1.00123i	−0.983120	+	0.182962i	$0.941431\pi$
$62$	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	−0.994450	−	0.105213i	$-0.966448\pi$
$67$	0.325035	−	4.54459i	0.00485127	−	0.0678296i	0.999301	+	0.0373831i	$0.0119022\pi$
$68$	−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	0.389092	−	0.921199i	$-0.372789\pi$
$71$	−41.0454	−	47.3689i	−0.578104	−	0.667168i	−0.967196	+	0.254031i	$0.918243\pi$
$72$	0.471899	+	2.16928i	0.00655415	+	0.0301289i
$73$	13.5742	+	18.1330i	0.185948	+	0.248398i	0.883822	−	0.467823i	$-0.154961\pi$
$73$	13.5742	+	18.1330i	0.185948	+	0.248398i	−0.697874	+	0.716220i	$0.745871\pi$
$74$	−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	−0.894954	−	0.446158i	$-0.852792\pi$
$79$	−30.2793	−	103.122i	−0.383282	−	1.30534i	0.511672	−	0.859181i	$-0.329026\pi$
$80$	−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	0.360366	−	0.932811i	$-0.382652\pi$
$83$	1.81373	+	0.676485i	0.0218521	+	0.00815043i	−0.338514	+	0.940961i	$0.609924\pi$
$84$	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	−0.990833	−	0.135095i	$-0.956866\pi$
$89$	−40.6141	+	63.1968i	−0.456339	+	0.710077i	0.534494	+	0.845172i	$0.320502\pi$
$90$	−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	−0.443737	−	0.896157i	$-0.646347\pi$
$97$	−18.6466	+	6.95480i	−0.192232	+	0.0716990i	0.251504	+	0.967856i	$0.419075\pi$
$98$	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	0.881514	−	0.472159i	$-0.156525\pi$
$101$	−5.31147	−	11.6305i	−0.0525889	−	0.115154i	−0.934102	+	0.357005i	$0.883798\pi$
$102$	4.18074	+	2.28286i	0.0409876	+	0.0223809i
$103$	12.5147	+	174.979i	0.121502	+	1.69882i	0.583639	+	0.812013i	$0.301628\pi$
$103$	12.5147	+	174.979i	0.121502	+	1.69882i	−0.462137	+	0.886809i	$0.652917\pi$
$104$	−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	0.616210	−	0.787582i	$-0.288667\pi$
$107$	90.9029	+	19.7747i	0.849560	+	0.184810i	0.233351	+	0.972393i	$0.425031\pi$
$108$	86.9600	−	47.4837i	0.805185	−	0.439664i
$109$	−14.0389	+	2.01849i	−0.128797	+	0.0185183i	−0.206412	−	0.978465i	$-0.566179\pi$
$109$	−14.0389	+	2.01849i	−0.128797	+	0.0185183i	0.0776146	+	0.996983i	$0.475270\pi$
$110$	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	−0.397095	−	0.917777i	$-0.629982\pi$
$113$	−104.046	−	7.44153i	−0.920762	−	0.0658542i	−0.523667	+	0.851923i	$0.675436\pi$
$114$		−	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	0.643651	−	0.765319i	$-0.277419\pi$
$127$	176.488	−	12.6227i	1.38967	−	0.0993910i	0.746016	+	0.665928i	$0.231964\pi$
$128$	−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	0.793944	−	0.607991i	$-0.208024\pi$
$131$	148.442	+	43.5866i	1.13315	+	0.332722i	0.339203	+	0.940713i	$0.389843\pi$
$132$	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	0.464779	−	0.885427i	$-0.346134\pi$
$137$	−57.6287	−	57.6287i	−0.420648	−	0.420648i	−0.885427	+	0.464779i	$0.846134\pi$
$138$	−3.77194	+	19.3543i	−0.0273329	+	0.140249i
$139$		−	155.980i		−	1.12216i	−0.827763	−	0.561078i	$-0.810387\pi$
$139$		−	155.980i		−	1.12216i	0.827763	−	0.561078i	$-0.189613\pi$
$140$	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	0.676906	−	0.736070i	$-0.263321\pi$
$149$	6.65456	+	5.76621i	0.0446615	+	0.0386994i	−0.632244	+	0.774769i	$0.717866\pi$
$150$	−13.5039	+	16.6440i	−0.0900262	+	0.110960i
$151$	−36.0982	+	10.5994i	−0.239061	+	0.0701946i	−0.399068	−	0.916921i	$-0.630666\pi$
$151$	−36.0982	+	10.5994i	−0.239061	+	0.0701946i	0.160007	+	0.987116i	$0.448848\pi$
$152$	−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	−0.565023	−	0.825075i	$-0.691133\pi$
$157$	10.5891	−	7.92689i	0.0674464	−	0.0504897i	0.632469	+	0.774586i	$0.282042\pi$
$158$	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	−0.0443162	−	0.999018i	$-0.514111\pi$
$163$	−37.5481	−	2.68549i	−0.230356	−	0.0164754i	−0.186040	+	0.982542i	$0.559565\pi$
$164$	−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	−0.635784	−	0.771867i	$-0.719323\pi$
$167$	47.4176	−	63.3425i	0.283938	−	0.379297i	0.919722	+	0.392570i	$0.128414\pi$
$168$	−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	0.771809	+	0.635854i	$0.219352\pi$
$173$	17.0141	+	237.888i	0.0983474	+	1.37508i	−0.673462	+	0.739222i	$0.735193\pi$
$174$	−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	−0.446044	−	0.895011i	$-0.647168\pi$
$179$	−253.204	−	115.634i	−1.41455	−	0.646001i	−0.968501	+	0.249010i	$0.919895\pi$
$180$	−2.56555	+	20.1551i	−0.0142531	+	0.111973i
$181$	−36.4838	−	23.4467i	−0.201568	−	0.129540i	0.435963	−	0.899965i	$-0.356408\pi$
$181$	−36.4838	−	23.4467i	−0.201568	−	0.129540i	−0.637531	+	0.770425i	$0.720044\pi$
$182$	−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	−0.319143	−	0.947707i	$-0.603395\pi$
$191$	−210.098	−	61.6905i	−1.09999	−	0.322987i	−0.780849	+	0.624720i	$0.785213\pi$
$192$	−176.670	−	38.4323i	−0.920158	−	0.200168i
$193$	340.091	+	126.847i	1.76213	+	0.657240i	0.999951	+	0.00987239i	$0.00314253\pi$
$193$	340.091	+	126.847i	1.76213	+	0.657240i	0.762178	+	0.647368i	$0.224130\pi$
$194$	−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	0.874130	−	0.485693i	$-0.161433\pi$
$197$	184.811	+	100.915i	0.938129	+	0.512257i	0.0639995	+	0.997950i	$0.479614\pi$
$198$	−3.48764	−	1.30082i	−0.0176143	−	0.00656981i
$199$	121.178	+	188.557i	0.608936	+	0.947523i	0.999635	+	0.0270044i	$0.00859683\pi$
$199$	121.178	+	188.557i	0.608936	+	0.947523i	−0.390699	+	0.920518i	$0.627767\pi$
$200$	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	0.856483	+	0.516175i	$0.172645\pi$
$211$	−23.3640	+	162.500i	−0.110730	+	0.770143i	−0.967213	+	0.253968i	$0.918264\pi$
$212$	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	−0.756469	−	0.654029i	$-0.773077\pi$
$223$	−137.199	+	74.9164i	−0.615243	+	0.335948i	0.141227	+	0.989977i	$0.454895\pi$
$224$	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	−0.698590	−	0.715523i	$-0.746189\pi$
$227$	−81.8038	−	376.046i	−0.360369	−	1.65659i	0.338221	−	0.941067i	$-0.390175\pi$
$228$	−230.240	−	16.4671i	−1.00983	−	0.0722242i
$229$			388.570i			1.69681i	0.529346	+	0.848406i	$0.322437\pi$
$229$			388.570i			1.69681i	−0.529346	+	0.848406i	$0.677563\pi$
$230$	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	0.302083	−	0.953282i	$-0.402318\pi$
$233$	226.680	−	49.3111i	0.972874	−	0.211636i	0.670791	+	0.741646i	$0.265955\pi$
$234$	−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	0.00379312	−	0.999993i	$-0.498793\pi$
$239$	182.123	−	83.1728i	0.762021	−	0.348003i	0.758228	+	0.651989i	$0.226065\pi$
$240$	111.402	−	212.111i	0.464175	−	0.883795i
$241$	198.439	−	229.010i	0.823397	−	0.950251i	−0.176020	−	0.984387i	$-0.556322\pi$
$241$	198.439	−	229.010i	0.823397	−	0.950251i	0.999417	+	0.0341356i	$0.0108678\pi$
$242$	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	0.384272	−	0.923220i	$-0.374453\pi$
$251$	−146.644	−	169.236i	−0.584239	−	0.674248i	−0.968511	+	0.248972i	$0.919907\pi$
$252$	−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	−0.757841	−	0.652439i	$-0.773746\pi$
$257$	−88.7519	+	66.4388i	−0.345338	+	0.258517i	0.412503	+	0.910956i	$0.364655\pi$
$258$	−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	−0.655434	−	0.755252i	$-0.727514\pi$
$263$	87.9153	−	161.005i	0.334279	−	0.612186i	0.989713	+	0.143066i	$0.0456962\pi$
$264$	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	−0.600342	−	0.799743i	$-0.704969\pi$
$269$	90.6723	−	308.801i	0.337072	−	1.14796i	0.937414	−	0.348217i	$-0.113213\pi$
$270$	−33.7130	+	5.40564i	−0.124863	+	0.0200209i
$271$	174.933	−	383.050i	0.645510	−	1.41347i	−0.249920	−	0.968266i	$-0.580404\pi$
$271$	174.933	−	383.050i	0.645510	−	1.41347i	0.895430	−	0.445202i	$-0.146868\pi$
$272$	−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	0.187114	−	0.982338i	$-0.440087\pi$
$277$	−220.277	−	220.277i	−0.795224	−	0.795224i	−0.982338	+	0.187114i	$0.940087\pi$
$278$	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	−0.985662	−	0.168732i	$-0.946033\pi$
$281$	−59.7608	+	130.858i	−0.212672	+	0.465686i	0.772990	+	0.634418i	$0.218760\pi$
$282$	37.4427	−	50.0175i	0.132775	−	0.177367i
$283$	−186.644	+	101.915i	−0.659519	+	0.360125i	−0.773896	−	0.633313i	$-0.781695\pi$
$283$	−186.644	+	101.915i	−0.659519	+	0.360125i	0.114377	+	0.993437i	$0.463513\pi$
$284$	−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	−0.216412	−	0.976302i	$-0.569435\pi$
$293$	−355.742	−	266.305i	−1.21414	−	0.908892i	−0.997725	+	0.0674102i	$0.978526\pi$
$294$	−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	0.730457	−	0.682959i	$-0.239307\pi$
$307$	341.136	+	74.2096i	1.11119	+	0.241725i	0.380735	+	0.924684i	$0.375671\pi$
$308$	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	−0.510065	−	0.860136i	$-0.670379\pi$
$311$	128.725	−	148.556i	0.413905	−	0.477672i	0.923971	+	0.382463i	$0.124924\pi$
$312$	104.764	+	57.2055i	0.335782	+	0.183351i
$313$	114.011	+	42.5240i	0.364253	+	0.135860i	0.524925	−	0.851148i	$-0.324093\pi$
$313$	114.011	+	42.5240i	0.364253	+	0.135860i	−0.160672	+	0.987008i	$0.551366\pi$
$314$	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	−0.380237	−	0.924889i	$-0.624158\pi$
$317$	−19.6309	+	7.32196i	−0.0619272	+	0.0230977i	0.318310	+	0.947987i	$0.396885\pi$
$318$	−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	0.539031	+	0.842286i	$0.318791\pi$
$331$	272.280	+	596.210i	0.822598	+	1.80124i	0.283567	+	0.958952i	$0.408482\pi$
$332$	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	0.0731111	−	0.997324i	$-0.476707\pi$
$337$	−92.5698	−	20.1373i	−0.274688	−	0.0597547i	−0.347799	+	0.937569i	$0.613071\pi$
$338$	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	−0.972134	−	0.234426i	$-0.924679\pi$
$347$	8.14318	−	113.857i	0.0234674	−	0.328117i	0.995601	−	0.0936908i	$-0.0298665\pi$
$348$	−332.141	+	72.2529i	−0.954428	+	0.207623i
$349$	663.606	+	95.4122i	1.90145	+	0.273387i	0.990328	−	0.138747i	$-0.0443073\pi$
$349$	663.606	+	95.4122i	1.90145	+	0.273387i	0.911123	+	0.412134i	$0.135216\pi$
$350$	−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	−0.537664	−	0.843159i	$-0.680693\pi$
$353$	106.491	−	489.530i	0.301673	−	1.38677i	0.839337	−	0.543611i	$-0.182943\pi$
$354$	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	−0.272288	−	0.962216i	$-0.587780\pi$
$359$	99.2977	−	45.3477i	0.276595	−	0.126317i	0.548883	+	0.835899i	$0.315053\pi$
$360$	−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	−0.926689	−	0.375829i	$-0.877358\pi$
$367$	−478.024	−	478.024i	−1.30252	−	1.30252i	−0.375829	−	0.926689i	$-0.622642\pi$
$368$	−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	0.982590	+	0.185789i	$0.0594842\pi$
$373$	134.901	+	361.683i	0.361664	+	0.969659i	−0.620926	+	0.783870i	$0.713243\pi$
$374$	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	−0.00556845	−	0.999984i	$-0.501773\pi$
$379$	−377.547	−	327.147i	−0.996167	−	0.863184i	−0.990599	+	0.136801i	$0.956318\pi$
$380$	−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	−0.838125	−	0.545478i	$-0.816348\pi$
$383$	57.7793	−	265.607i	0.150860	−	0.693492i	0.988985	−	0.148014i	$-0.0472881\pi$
$384$	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	0.550273	−	0.834985i	$-0.314523\pi$
$389$	566.023	−	490.461i	1.45507	−	1.26083i	0.904798	−	0.425842i	$-0.140022\pi$
$390$	−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	−0.661642	−	0.749820i	$-0.730140\pi$
$397$	96.9517	−	129.512i	0.244211	−	0.326227i	0.905853	+	0.423592i	$0.139231\pi$
$398$	−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	−0.313212	−	0.949683i	$-0.601405\pi$
$401$	−25.3697	+	7.44922i	−0.0632661	+	0.0185766i	0.249946	+	0.968260i	$0.419587\pi$
$402$	−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	0.0303186	−	0.999540i	$-0.490348\pi$
$409$	−288.439	−	131.726i	−0.705229	−	0.322067i	−0.735548	+	0.677473i	$0.763075\pi$
$410$	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	0.256045	−	0.966665i	$-0.417580\pi$
$419$	−128.565	−	58.7136i	−0.306837	−	0.140128i	−0.562882	+	0.826537i	$0.690308\pi$
$420$	−261.352	+	41.9060i	−0.622267	+	0.0997762i
$421$	449.446	+	131.969i	1.06757	+	0.313466i	0.767895	−	0.640575i	$-0.221304\pi$
$421$	449.446	+	131.969i	1.06757	+	0.313466i	0.299673	+	0.954042i	$0.403122\pi$
$422$	−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	0.999694	−	0.0247236i	$-0.00787058\pi$
$431$	14.4511	+	100.509i	0.0335292	+	0.233201i	−0.966165	+	0.257924i	$0.916961\pi$
$432$	357.604	−	133.379i	0.827787	−	0.308749i
$433$	−74.1616	−	99.0683i	−0.171274	−	0.228795i	0.706688	−	0.707525i	$-0.250188\pi$
$433$	−74.1616	−	99.0683i	−0.171274	−	0.228795i	−0.877962	+	0.478730i	$0.841097\pi$
$434$	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	−0.824021	−	0.566560i	$-0.808274\pi$
$439$	−167.039	+	144.740i	−0.380498	+	0.329703i	0.443523	+	0.896263i	$0.353729\pi$
$440$	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	0.880391	−	0.474249i	$-0.157280\pi$
$443$	298.310	+	223.312i	0.673386	+	0.504091i	−0.207004	+	0.978340i	$0.566371\pi$
$444$	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	0.418623	−	0.908160i	$-0.362513\pi$
$449$	−188.902	−	163.684i	−0.420717	−	0.364553i	−0.839340	+	0.543607i	$0.817058\pi$
$450$	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	0.981970	+	0.189038i	$0.0605369\pi$
$457$	76.4414	+	351.395i	0.167268	+	0.768918i	−0.814702	+	0.579880i	$0.803100\pi$
$458$	−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	−0.242114	−	0.970248i	$-0.577841\pi$
$463$	−27.4523	+	5.97188i	−0.0592922	+	0.0128982i	0.182821	+	0.983146i	$0.441477\pi$
$464$	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	0.818607	−	0.574354i	$-0.194747\pi$
$467$	−50.0357	−	91.6335i	−0.107143	−	0.196217i	−0.925750	+	0.378137i	$0.876565\pi$
$468$	−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	−0.0227663	−	0.999741i	$-0.507247\pi$
$479$	−156.283	−	22.4702i	−0.326270	−	0.0469105i	−0.303504	+	0.952830i	$0.598156\pi$
$480$	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	−0.604331	−	0.796734i	$-0.706559\pi$
$487$	−4.93330	+	3.69302i	−0.0101300	+	0.00758320i	0.594201	+	0.804317i	$0.297468\pi$
$488$	−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	−0.545245	−	0.838277i	$-0.683563\pi$
$491$	−4.52898	+	2.91060i	−0.00922400	+	0.00592790i	0.536021	+	0.844205i	$0.319927\pi$
$492$	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	−0.999489	−	0.0319700i	$-0.989822\pi$
$499$	−70.5491	+	240.268i	−0.141381	+	0.481500i	0.858108	+	0.513470i	$0.171640\pi$
$500$	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	−0.0749433	−	0.997188i	$-0.523878\pi$
$503$	136.380	−	29.6676i	0.271133	−	0.0589813i	0.346076	+	0.938206i	$0.387514\pi$
$504$	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	0.108176	+	0.994132i	$0.465499\pi$
$509$	−428.097	+	666.133i	−0.841056	+	1.30871i	−0.949232	+	0.314577i	$0.898137\pi$
$510$	−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	−0.747127	−	0.664682i	$-0.768567\pi$
$521$	−235.950	+	151.636i	−0.452878	+	0.291047i	0.294248	+	0.955729i	$0.404931\pi$
$522$	3.66772	+	6.71692i	0.00702628	+	0.0128677i
$523$	−214.979	−	160.931i	−0.411049	−	0.307708i	0.373667	−	0.927563i	$-0.378100\pi$
$523$	−214.979	−	160.931i	−0.411049	−	0.307708i	−0.784716	+	0.619855i	$0.787191\pi$
$524$	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	0.0698915	−	0.997555i	$-0.477735\pi$
$541$	566.614	−	653.908i	1.04735	−	1.20870i	0.977454	−	0.211147i	$-0.0677199\pi$
$542$	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	−0.854452	−	0.519531i	$-0.826107\pi$
$547$	−634.511	+	236.660i	−1.15998	+	0.432651i	−0.305531	+	0.952182i	$0.598834\pi$
$548$	−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	0.343796	−	0.939044i	$-0.388287\pi$
$557$	678.740	−	253.157i	1.21856	−	0.454500i	0.874767	+	0.484544i	$0.161014\pi$
$558$	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	0.589773	+	0.807569i	$0.299217\pi$
$563$	68.0848	+	951.949i	0.120932	+	1.69085i	−0.468841	+	0.883282i	$0.655328\pi$
$564$	−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	−0.665466	−	0.746429i	$-0.731767\pi$
$569$	−622.305	+	89.4739i	−1.09368	+	0.157248i	−0.428216	+	0.903676i	$0.640858\pi$
$570$	72.8826	+	31.8686i	0.127864	+	0.0559099i
$571$	−16.0631	+	111.721i	−0.0281315	+	0.195659i	−0.999041	−	0.0437886i	$-0.986057\pi$
$571$	−16.0631	+	111.721i	−0.0281315	+	0.195659i	0.970909	+	0.239447i	$0.0769663\pi$
$572$	−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	−0.637138	−	0.770750i	$-0.719882\pi$
$577$	59.5487	−	832.600i	0.103204	−	1.44298i	0.740342	−	0.672231i	$-0.234664\pi$
$578$	−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	0.642454	−	0.766324i	$-0.277916\pi$
$587$	814.420	−	58.2485i	1.38743	−	0.0992308i	0.744974	+	0.667093i	$0.232462\pi$
$588$	−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	0.779349	−	0.626590i	$-0.215550\pi$
$593$	−130.444	−	349.733i	−0.219972	−	0.589769i	−0.999322	+	0.0368205i	$0.988277\pi$
$594$	−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	$-0.864899\pi$
$599$		−	493.340i		−	0.823606i	0.911273	−	0.411803i	$-0.135101\pi$
$600$	−124.729	+	115.356i	−0.207881	+	0.192260i
$601$	−415.039	−	266.729i	−0.690580	−	0.443809i	0.147712	−	0.989030i	$-0.452809\pi$
$601$	−415.039	−	266.729i	−0.690580	−	0.443809i	−0.838292	+	0.545221i	$0.816446\pi$
$602$	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	−0.877537	−	0.479509i	$-0.840815\pi$
$607$	60.5013	−	162.210i	0.0996727	−	0.267233i	0.977210	+	0.212276i	$0.0680876\pi$
$608$	−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	0.883673	+	0.468104i	$0.155063\pi$
$613$	−70.2508	+	322.938i	−0.114602	+	0.526815i	−0.998275	+	0.0587112i	$0.981301\pi$
$614$	−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	−0.962924	−	0.269774i	$-0.913051\pi$
$617$	−601.799	+	450.501i	−0.975364	+	0.730148i	−0.0124402	+	0.999923i	$0.503960\pi$
$618$	146.959	−	31.9691i	0.237799	−	0.0517299i
$619$	−135.339	+	117.272i	−0.218641	+	0.189454i	−0.757294	−	0.653074i	$-0.773479\pi$
$619$	−135.339	+	117.272i	−0.218641	+	0.189454i	0.538653	+	0.842528i	$0.318933\pi$
$620$	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	−0.551030	−	0.834486i	$-0.685765\pi$
$631$	−355.523	+	104.391i	−0.563428	+	0.165437i	−0.0123985	+	0.999923i	$0.503947\pi$
$632$	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	0.998891	−	0.0470870i	$-0.0149938\pi$
$641$	878.819	+	564.783i	1.37101	+	0.881097i	0.372122	+	0.928184i	$0.378630\pi$
$642$	5.68972	−	79.5527i	0.00886249	−	0.123914i
$643$	−256.600	+	256.600i	−0.399067	+	0.399067i	−0.877904	−	0.478837i	$-0.841059\pi$
$643$	−256.600	+	256.600i	−0.399067	+	0.399067i	0.478837	+	0.877904i	$0.341059\pi$
$644$	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	0.955985	−	0.293414i	$-0.0947914\pi$
$647$	−22.9673	−	105.579i	−0.0354981	−	0.163182i	−0.991484	+	0.130232i	$0.958428\pi$
$648$	−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	−0.159375	−	0.987218i	$-0.550948\pi$
$653$	−604.882	−	225.609i	−0.926313	−	0.345497i	−0.766938	+	0.641721i	$0.778221\pi$
$654$	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	0.569733	−	0.821830i	$-0.307047\pi$
$659$	−273.159	−	425.044i	−0.414506	−	0.644984i	−0.984238	+	0.176846i	$0.943410\pi$
$660$	407.857	+	719.011i	0.617966	+	1.08941i
$661$	70.9678	+	493.592i	0.107364	+	0.746735i	0.970385	+	0.241565i	$0.0776608\pi$
$661$	70.9678	+	493.592i	0.107364	+	0.746735i	−0.863020	+	0.505169i	$0.831430\pi$
$662$	−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	0.320558	−	0.947229i	$-0.396130\pi$
$673$	−335.147	−	250.888i	−0.497990	−	0.372791i	−0.818548	+	0.574438i	$0.805221\pi$
$674$	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	0.983910	−	0.178664i	$-0.0571776\pi$
$677$	924.478	+	504.803i	1.36555	+	0.745647i	0.381640	+	0.924311i	$0.375359\pi$
$678$	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	−0.807829	−	0.589416i	$-0.799358\pi$
$683$	−511.380	+	279.235i	−0.748726	+	0.408835i	0.0591031	+	0.998252i	$0.481176\pi$
$684$	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	0.239115	−	0.970991i	$-0.423143\pi$
$701$	817.501	−	943.447i	1.16619	−	1.34586i	0.927078	−	0.374867i	$-0.122312\pi$
$702$	−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	0.867255	−	0.497865i	$-0.165882\pi$
$709$	1105.41	+	158.934i	1.55911	+	0.224167i	0.691860	+	0.722032i	$0.256792\pi$
$710$	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	−0.518116	−	0.855310i	$-0.673367\pi$
$719$	−556.705	+	80.0420i	−0.774276	+	0.111324i	−0.256160	+	0.966634i	$0.582457\pi$
$720$	−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	−0.479338	−	0.877631i	$-0.659123\pi$
$727$	332.710	−	892.029i	0.457647	−	1.22700i	0.936985	−	0.349370i	$-0.113604\pi$
$728$	−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	0.863629	−	0.504128i	$-0.168186\pi$
$733$	1362.38	−	296.368i	1.85864	−	0.404321i	0.995007	+	0.0998068i	$0.0318225\pi$
$734$	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	−0.738278	−	0.674497i	$-0.764361\pi$
$739$	134.467	−	209.234i	0.181958	−	0.283132i	0.920236	+	0.391365i	$0.127997\pi$
$740$	−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	0.136592	−	0.990627i	$-0.456385\pi$
$743$	775.549	−	423.482i	1.04381	−	0.569962i	0.907216	+	0.420665i	$0.138203\pi$
$744$	−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	−0.0111700	−	0.999938i	$-0.503556\pi$
$751$	671.218	−	431.365i	0.893765	−	0.574388i	0.904935	+	0.425550i	$0.139919\pi$
$752$	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	−0.557535	−	0.830153i	$-0.688253\pi$
$757$	85.1384	−	1190.39i	0.112468	−	1.57251i	0.670003	−	0.742358i	$-0.266293\pi$
$758$	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	0.737632	−	0.675203i	$-0.235944\pi$
$761$	−27.1480	−	31.3305i	−0.0356742	−	0.0411702i	−0.773306	+	0.634033i	$0.781398\pi$
$762$	−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	0.998982	+	0.0451039i	$0.0143619\pi$
$769$	140.704	+	479.193i	0.182970	+	0.623138i	−0.816012	+	0.578034i	$0.803820\pi$
$770$	−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	0.509505	−	0.860468i	$-0.329828\pi$
$773$	255.923	+	95.4542i	0.331077	+	0.123485i	−0.178428	+	0.983953i	$0.557101\pi$
$774$	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	−0.661711	−	0.749759i	$-0.730169\pi$
$787$	−527.928	+	196.907i	−0.670811	+	0.250200i	−0.00909996	+	0.999959i	$0.502897\pi$
$788$	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	0.495954	−	0.868349i	$-0.334818\pi$
$797$	467.333	+	101.662i	0.586365	+	0.127556i	0.0904107	+	0.995905i	$0.471182\pi$
$798$	−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	0.108805	−	0.994063i	$-0.465298\pi$
$809$	−54.0883	−	7.77673i	−0.0668582	−	0.00961276i	−0.175663	+	0.984450i	$0.556207\pi$
$810$	112.450	−	44.0284i	0.138828	−	0.0543561i
$811$	−40.8646	−	284.219i	−0.0503879	−	0.350456i	−0.999382	−	0.0351607i	$-0.988806\pi$
$811$	−40.8646	−	284.219i	−0.0503879	−	0.350456i	0.948994	−	0.315295i	$-0.102103\pi$
$812$	−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	0.0109770	−	0.999940i	$-0.496506\pi$
$821$	−427.246	−	125.451i	−0.520397	−	0.152802i	−0.531374	+	0.847137i	$0.678324\pi$
$822$	−41.8723	+	55.9349i	−0.0509396	+	0.0680473i
$823$	374.632	+	1004.43i	0.455204	+	1.22045i	0.938588	+	0.345040i	$0.112135\pi$
$823$	374.632	+	1004.43i	0.455204	+	1.22045i	−0.483385	+	0.875408i	$0.660593\pi$
$824$	−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	0.655146	−	0.755502i	$-0.272607\pi$
$827$	−82.9943	−	82.9943i	−0.100356	−	0.100356i	−0.755502	+	0.655146i	$0.772607\pi$
$828$	−93.3462	−	4.64095i	−0.112737	−	0.00560501i
$829$		−	899.226i		−	1.08471i	−0.840149	−	0.542356i	$-0.817532\pi$
$829$		−	899.226i		−	1.08471i	0.840149	−	0.542356i	$-0.182468\pi$
$830$	−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	0.776139	−	0.630561i	$-0.217175\pi$
$839$	220.198	+	190.802i	0.262453	+	0.227416i	−0.513687	+	0.857978i	$0.671721\pi$
$840$	−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	−0.491667	−	0.870783i	$-0.663612\pi$
$853$	−940.223	−	67.2461i	−1.10225	−	0.0788348i	−0.610588	+	0.791949i	$0.709067\pi$
$854$	−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	−0.878151	−	0.478383i	$-0.841223\pi$
$857$	−147.184	+	196.614i	−0.171743	+	0.229422i	0.706409	+	0.707804i	$0.250314\pi$
$858$	−175.659	+	95.9173i	−0.204731	+	0.111792i
$859$	497.068	+	773.453i	0.578659	+	0.900411i	0.999979	−	0.00650127i	$-0.00206943\pi$
$859$	497.068	+	773.453i	0.578659	+	0.900411i	−0.421320	+	0.906912i	$0.638433\pi$
$860$	−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	0.990481	−	0.137647i	$-0.0439541\pi$
$863$	−8.20504	−	114.722i	−0.00950758	−	0.132933i	−0.999989	+	0.00471393i	$0.998500\pi$
$864$	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	0.995522	−	0.0945267i	$-0.0301338\pi$
$877$	44.4600	+	204.379i	0.0506955	+	0.233044i	−0.944827	+	0.327570i	$0.893770\pi$
$878$	−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	0.00896845	−	0.999960i	$-0.497145\pi$
$881$	−461.737	−	135.578i	−0.524106	−	0.153891i	−0.533074	+	0.846068i	$0.678963\pi$
$882$	8.45307	+	1.83885i	0.00958398	+	0.00208487i
$883$	−817.583	−	304.943i	−0.925915	−	0.345348i	−0.159134	−	0.987257i	$-0.550870\pi$
$883$	−817.583	−	304.943i	−0.925915	−	0.345348i	−0.766781	+	0.641909i	$0.778143\pi$
$884$	−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	0.100567	−	0.994930i	$-0.467934\pi$
$887$	−604.979	−	330.344i	−0.682051	−	0.372428i	−0.782618	+	0.622502i	$0.786116\pi$
$888$	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	0.966562	−	0.256434i	$-0.0825476\pi$
$907$	1154.97	+	630.663i	1.27340	+	0.695328i	0.306837	+	0.951762i	$0.400729\pi$
$908$	−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	0.898901	−	0.438151i	$-0.144366\pi$
$911$	−19.0272	−	41.6638i	−0.0208861	−	0.0457342i	−0.919788	+	0.392417i	$0.871639\pi$
$912$	−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	$-0.986273\pi$
$919$		−	79.2366i		−	0.0862204i	0.999070	−	0.0431102i	$-0.0137267\pi$
$920$	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	−0.292392	−	0.956299i	$-0.594451\pi$
$929$	221.895	−	101.336i	0.238854	−	0.109081i	0.531246	+	0.847218i	$0.321724\pi$
$930$	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	0.0218343	+	0.999762i	$0.493049\pi$
$937$	−884.136	+	1181.07i	−0.943581	+	1.26048i	−0.965416	+	0.260716i	$0.916042\pi$
$938$	−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	0.907163	−	0.420780i	$-0.138244\pi$
$941$	340.231	+	392.647i	0.361563	+	0.417266i	−0.545600	+	0.838046i	$0.683698\pi$
$942$	−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	−0.881829	−	0.471569i	$-0.843688\pi$
$947$	−641.879	+	480.504i	−0.677802	+	0.507397i	0.204027	+	0.978965i	$0.434597\pi$
$948$	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	0.268966	+	0.963150i	$0.413318\pi$
$953$	−654.426	+	1198.49i	−0.686701	+	1.25760i	−0.955667	+	0.294450i	$0.904864\pi$
$954$	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	0.828852	−	0.559469i	$-0.188995\pi$
$967$	260.493	+	260.493i	0.269383	+	0.269383i	−0.559469	+	0.828852i	$0.688995\pi$
$968$	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	−0.0114245	+	0.999935i	$0.503637\pi$
$971$	−737.614	+	1615.15i	−0.759643	+	1.66339i	−0.748219	+	0.663452i	$0.769091\pi$
$972$	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	−0.833608	−	0.552357i	$-0.813729\pi$
$977$	−1543.78	+	110.413i	−1.58012	+	0.113013i	−0.746515	+	0.665369i	$0.768274\pi$
$978$	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	0.198642	−	0.980072i	$-0.436347\pi$
$983$	−674.108	−	504.631i	−0.685766	−	0.513358i	−0.884408	+	0.466714i	$0.845438\pi$
$984$	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	0.934918	−	0.354865i	$-0.115473\pi$
$991$	446.557	+	515.354i	0.450612	+	0.520034i	−0.484305	+	0.874899i	$0.660928\pi$
$992$	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	−0.306028	−	0.952023i	$-0.599000\pi$
$997$	−976.945	−	212.521i	−0.979885	−	0.213161i	−0.673857	+	0.738862i	$0.735364\pi$
$998$	−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.82.11	yes	440
5.3	odd	4	inner	115.3.k.a.13.12	✓	440
23.16	even	11	inner	115.3.k.a.62.12	yes	440
115.108	odd	44	inner	115.3.k.a.108.11	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.k.a.13.12	✓	440	5.3	odd	4	inner
115.3.k.a.62.12	yes	440	23.16	even	11	inner
115.3.k.a.82.11	yes	440	1.1	even	1	trivial
115.3.k.a.108.11	yes	440	115.108	odd	44	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 $\F_{q}$
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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Representations

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Database

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