LMFDB - Embedded newform 85.3.q.a.46.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [85,3,Mod(6,85)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(85, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 15])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("85.6"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	85.q (of order $16$, degree $8$, 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:	$2.31608224706$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			46.6
Character	$\chi$	$=$	85.46
Dual form			85.3.q.a.61.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.369527 - 0.892116i) q^{2} +(2.03052 - 1.35675i) q^{3} +(2.16911 - 2.16911i) q^{4} +(-2.19310 - 0.436235i) q^{5} +(-1.96072 - 1.31011i) q^{6} +(3.61453 - 0.718974i) q^{7} +(-6.30510 - 2.61166i) q^{8} +(-1.16190 + 2.80507i) q^{9} +(0.421237 + 2.11770i) q^{10} +(2.67188 - 3.99876i) q^{11} +(1.46148 - 7.34736i) q^{12} +(1.64069 + 1.64069i) q^{13} +(-1.97707 - 2.95890i) q^{14} +(-5.04501 + 2.08971i) q^{15} -5.68035i q^{16} +(-2.30902 - 16.8425i) q^{17} +2.93181 q^{18} +(13.1725 + 31.8012i) q^{19} +(-5.70331 + 3.81083i) q^{20} +(6.36391 - 6.36391i) q^{21} +(-4.55469 - 0.905984i) q^{22} +(2.03220 + 1.35787i) q^{23} +(-16.3460 + 3.25143i) q^{24} +(4.61940 + 1.91342i) q^{25} +(0.857405 - 2.06996i) q^{26} +(5.73438 + 28.8287i) q^{27} +(6.28076 - 9.39982i) q^{28} +(-10.1660 + 51.1081i) q^{29} +(3.72853 + 3.72853i) q^{30} +(8.78233 + 13.1437i) q^{31} +(-30.2879 + 12.5457i) q^{32} -11.7447i q^{33} +(-14.1722 + 8.28365i) q^{34} -8.24067 q^{35} +(3.56422 + 8.60478i) q^{36} +(6.16017 - 4.11609i) q^{37} +(23.5028 - 23.5028i) q^{38} +(5.55746 + 1.10545i) q^{39} +(12.6884 + 8.47814i) q^{40} +(13.6935 - 2.72380i) q^{41} +(-8.02899 - 3.32572i) q^{42} +(18.3147 - 44.2156i) q^{43} +(-2.87813 - 14.4693i) q^{44} +(3.77184 - 5.64495i) q^{45} +(0.460427 - 2.31472i) q^{46} +(-23.0835 - 23.0835i) q^{47} +(-7.70683 - 11.5341i) q^{48} +(-32.7222 + 13.5540i) q^{49} -4.82810i q^{50} +(-27.5396 - 31.0663i) q^{51} +7.11764 q^{52} +(-4.77734 - 11.5335i) q^{53} +(23.5995 - 15.7687i) q^{54} +(-7.60411 + 7.60411i) q^{55} +(-24.6677 - 4.90671i) q^{56} +(69.8934 + 46.7013i) q^{57} +(49.3510 - 9.81653i) q^{58} +(-25.1448 - 10.4153i) q^{59} +(-6.41036 + 15.4760i) q^{60} +(-13.3880 - 67.3061i) q^{61} +(8.48040 - 12.6918i) q^{62} +(-2.18294 + 10.9744i) q^{63} +(6.31796 + 6.31796i) q^{64} +(-2.88247 - 4.31392i) q^{65} +(-10.4776 + 4.33997i) q^{66} -63.2487i q^{67} +(-41.5416 - 31.5246i) q^{68} +5.96872 q^{69} +(3.04515 + 7.35164i) q^{70} +(-34.6942 + 23.1819i) q^{71} +(14.6518 - 14.6518i) q^{72} +(52.0944 + 10.3622i) q^{73} +(-5.94838 - 3.97458i) q^{74} +(11.9758 - 2.38214i) q^{75} +(97.5527 + 40.4076i) q^{76} +(6.78259 - 16.3746i) q^{77} +(-1.06744 - 5.36639i) q^{78} +(-36.8708 + 55.1810i) q^{79} +(-2.47797 + 12.4576i) q^{80} +(31.4350 + 31.4350i) q^{81} +(-7.49005 - 11.2097i) q^{82} +(-109.522 + 45.3657i) q^{83} -27.6080i q^{84} +(-2.28335 + 37.9445i) q^{85} -46.2132 q^{86} +(48.6987 + 117.569i) q^{87} +(-27.2899 + 18.2345i) q^{88} +(69.2116 - 69.2116i) q^{89} +(-6.42975 - 1.27896i) q^{90} +(7.10991 + 4.75069i) q^{91} +(7.35341 - 1.46268i) q^{92} +(35.6655 + 14.7731i) q^{93} +(-12.0632 + 29.1231i) q^{94} +(-15.0158 - 75.4896i) q^{95} +(-44.4790 + 66.5676i) q^{96} +(-7.05322 + 35.4589i) q^{97} +(24.1835 + 24.1835i) q^{98} +(8.11235 + 12.1410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 192 q^{12} - 48 q^{13} - 64 q^{14} + 16 q^{17} + 128 q^{18} + 48 q^{19} + 192 q^{22} + 112 q^{23} + 240 q^{24} - 224 q^{26} - 288 q^{27} - 480 q^{28} - 64 q^{31} - 80 q^{32} + 64 q^{34} + 192 q^{36}+ \cdots - 592 q^{99}+O(q^{100}) $ 96 * q - 192 * q^12 - 48 * q^13 - 64 * q^14 + 16 * q^17 + 128 * q^18 + 48 * q^19 + 192 * q^22 + 112 * q^23 + 240 * q^24 - 224 * q^26 - 288 * q^27 - 480 * q^28 - 64 * q^31 - 80 * q^32 + 64 * q^34 + 192 * q^36 + 256 * q^37 + 208 * q^38 + 16 * q^39 - 320 * q^40 - 432 * q^41 + 864 * q^42 + 256 * q^43 - 32 * q^44 - 160 * q^45 - 48 * q^46 - 320 * q^48 - 32 * q^49 + 64 * q^51 + 192 * q^53 - 976 * q^54 + 160 * q^55 + 80 * q^56 - 1120 * q^57 + 512 * q^58 - 224 * q^59 + 640 * q^60 - 224 * q^61 - 560 * q^62 + 624 * q^63 + 160 * q^64 + 240 * q^65 + 48 * q^66 + 384 * q^69 + 48 * q^71 + 1040 * q^72 + 672 * q^74 + 496 * q^76 + 960 * q^77 + 768 * q^79 + 1424 * q^81 + 1200 * q^82 - 288 * q^83 + 64 * q^86 - 1344 * q^87 - 1664 * q^88 - 1152 * q^89 + 336 * q^91 - 2016 * q^92 - 1024 * q^93 - 1344 * q^94 + 768 * q^96 - 256 * q^97 - 816 * q^98 - 592 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{13}{16}\right)$

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 $

$2$	−0.369527	−	0.892116i	−0.184763	−	0.446058i	0.804174	−	0.594394i	$-0.202608\pi$
$2$	−0.369527	−	0.892116i	−0.184763	−	0.446058i	−0.988937	+	0.148336i	$0.952608\pi$
$3$	2.03052	−	1.35675i	0.676842	−	0.452251i	−0.169049	−	0.985608i	$-0.554070\pi$
$3$	2.03052	−	1.35675i	0.676842	−	0.452251i	0.845891	+	0.533357i	$0.179070\pi$
$4$	2.16911	−	2.16911i	0.542276	−	0.542276i
$5$	−2.19310	−	0.436235i	−0.438621	−	0.0872470i
$5$	−2.19310	−	0.436235i	−0.438621	−	0.0872470i
$6$	−1.96072	−	1.31011i	−0.326786	−	0.218351i
$7$	3.61453	−	0.718974i	0.516361	−	0.102711i	0.0699708	−	0.997549i	$-0.477709\pi$
$7$	3.61453	−	0.718974i	0.516361	−	0.102711i	0.446390	+	0.894838i	$0.352709\pi$
$8$	−6.30510	−	2.61166i	−0.788138	−	0.326457i
$9$	−1.16190	+	2.80507i	−0.129100	+	0.311675i
$10$	0.421237	+	2.11770i	0.0421237	+	0.211770i
$11$	2.67188	−	3.99876i	0.242898	−	0.363523i	−0.689910	−	0.723895i	$-0.742350\pi$
$11$	2.67188	−	3.99876i	0.242898	−	0.363523i	0.932809	+	0.360372i	$0.117350\pi$
$12$	1.46148	−	7.34736i	0.121790	−	0.612280i
$13$	1.64069	+	1.64069i	0.126207	+	0.126207i	0.767389	−	0.641182i	$-0.221556\pi$
$13$	1.64069	+	1.64069i	0.126207	+	0.126207i	−0.641182	+	0.767389i	$0.721556\pi$
$14$	−1.97707	−	2.95890i	−0.141219	−	0.211350i
$15$	−5.04501	+	2.08971i	−0.336334	+	0.139314i
$16$		−	5.68035i		−	0.355022i
$17$	−2.30902	−	16.8425i	−0.135825	−	0.990733i
$17$	−2.30902	−	16.8425i	−0.135825	−	0.990733i
$18$	2.93181			0.162878
$19$	13.1725	+	31.8012i	0.693289	+	1.67375i	0.738047	+	0.674749i	$0.235748\pi$
$19$	13.1725	+	31.8012i	0.693289	+	1.67375i	−0.0447581	+	0.998998i	$0.514252\pi$
$20$	−5.70331	+	3.81083i	−0.285166	+	0.190542i
$21$	6.36391	−	6.36391i	0.303044	−	0.303044i
$22$	−4.55469	−	0.905984i	−0.207031	−	0.0411811i
$23$	2.03220	+	1.35787i	0.0883563	+	0.0590378i	0.598964	−	0.800776i	$-0.295579\pi$
$23$	2.03220	+	1.35787i	0.0883563	+	0.0590378i	−0.510607	+	0.859814i	$0.670579\pi$
$24$	−16.3460	+	3.25143i	−0.681085	+	0.135476i
$25$	4.61940	+	1.91342i	0.184776	+	0.0765367i
$26$	0.857405	−	2.06996i	0.0329771	−	0.0796138i
$27$	5.73438	+	28.8287i	0.212385	+	1.06773i
$28$	6.28076	−	9.39982i	0.224313	−	0.335708i
$29$	−10.1660	+	51.1081i	−0.350553	+	1.76235i	0.255387	+	0.966839i	$0.417797\pi$
$29$	−10.1660	+	51.1081i	−0.350553	+	1.76235i	−0.605940	+	0.795510i	$0.707203\pi$
$30$	3.72853	+	3.72853i	0.124284	+	0.124284i
$31$	8.78233	+	13.1437i	0.283301	+	0.423990i	0.945640	−	0.325214i	$-0.105436\pi$
$31$	8.78233	+	13.1437i	0.283301	+	0.423990i	−0.662339	+	0.749204i	$0.730436\pi$
$32$	−30.2879	+	12.5457i	−0.946498	+	0.392052i
$33$		−	11.7447i		−	0.355899i
$34$	−14.1722	+	8.28365i	−0.416829	+	0.243637i
$35$	−8.24067			−0.235448
$36$	3.56422	+	8.60478i	0.0990061	+	0.239022i
$37$	6.16017	−	4.11609i	0.166491	−	0.111246i	−0.469533	−	0.882915i	$-0.655578\pi$
$37$	6.16017	−	4.11609i	0.166491	−	0.111246i	0.636024	+	0.771669i	$0.280578\pi$
$38$	23.5028	−	23.5028i	0.618494	−	0.618494i
$39$	5.55746	+	1.10545i	0.142499	+	0.0283448i
$40$	12.6884	+	8.47814i	0.317211	+	0.211954i
$41$	13.6935	−	2.72380i	0.333987	−	0.0664342i	−0.0252481	−	0.999681i	$-0.508038\pi$
$41$	13.6935	−	2.72380i	0.333987	−	0.0664342i	0.359235	+	0.933247i	$0.383038\pi$
$42$	−8.02899	−	3.32572i	−0.191166	−	0.0791837i
$43$	18.3147	−	44.2156i	0.425923	−	1.02827i	−0.554645	−	0.832087i	$-0.687146\pi$
$43$	18.3147	−	44.2156i	0.425923	−	1.02827i	0.980568	−	0.196182i	$-0.0628543\pi$
$44$	−2.87813	−	14.4693i	−0.0654120	−	0.328848i
$45$	3.77184	−	5.64495i	0.0838186	−	0.125443i
$46$	0.460427	−	2.31472i	0.0100093	−	0.0503201i
$47$	−23.0835	−	23.0835i	−0.491138	−	0.491138i	0.417527	−	0.908665i	$-0.362897\pi$
$47$	−23.0835	−	23.0835i	−0.491138	−	0.491138i	−0.908665	+	0.417527i	$0.862897\pi$
$48$	−7.70683	−	11.5341i	−0.160559	−	0.240293i
$49$	−32.7222	+	13.5540i	−0.667800	+	0.276612i
$50$		−	4.82810i		−	0.0965620i
$51$	−27.5396	−	31.0663i	−0.539992	−	0.609142i
$52$	7.11764			0.136878
$53$	−4.77734	−	11.5335i	−0.0901386	−	0.217614i	0.872381	−	0.488827i	$-0.162575\pi$
$53$	−4.77734	−	11.5335i	−0.0901386	−	0.217614i	−0.962519	+	0.271213i	$0.912575\pi$
$54$	23.5995	−	15.7687i	0.437029	−	0.292013i
$55$	−7.60411	+	7.60411i	−0.138257	+	0.138257i
$56$	−24.6677	−	4.90671i	−0.440494	−	0.0876197i
$57$	69.8934	+	46.7013i	1.22620	+	0.819321i
$58$	49.3510	−	9.81653i	0.850880	−	0.169250i
$59$	−25.1448	−	10.4153i	−0.426183	−	0.176531i	0.159274	−	0.987234i	$-0.449085\pi$
$59$	−25.1448	−	10.4153i	−0.426183	−	0.176531i	−0.585457	+	0.810704i	$0.699085\pi$
$60$	−6.41036	+	15.4760i	−0.106839	+	0.257933i
$61$	−13.3880	−	67.3061i	−0.219476	−	1.10338i	−0.920650	−	0.390389i	$-0.872340\pi$
$61$	−13.3880	−	67.3061i	−0.219476	−	1.10338i	0.701174	−	0.712990i	$-0.252660\pi$
$62$	8.48040	−	12.6918i	0.136781	−	0.204707i
$63$	−2.18294	+	10.9744i	−0.0346499	+	0.174197i
$64$	6.31796	+	6.31796i	0.0987181	+	0.0987181i
$65$	−2.88247	−	4.31392i	−0.0443456	−	0.0663679i
$66$	−10.4776	+	4.33997i	−0.158752	+	0.0657571i
$67$		−	63.2487i		−	0.944011i	−0.881596	−	0.472005i	$-0.843530\pi$
$67$		−	63.2487i		−	0.944011i	0.881596	−	0.472005i	$-0.156470\pi$
$68$	−41.5416	−	31.5246i	−0.610906	−	0.463596i
$69$	5.96872			0.0865031
$70$	3.04515	+	7.35164i	0.0435021	+	0.105023i
$71$	−34.6942	+	23.1819i	−0.488651	+	0.326506i	−0.775369	−	0.631509i	$-0.782436\pi$
$71$	−34.6942	+	23.1819i	−0.488651	+	0.326506i	0.286717	+	0.958015i	$0.407436\pi$
$72$	14.6518	−	14.6518i	0.203497	−	0.203497i
$73$	52.0944	+	10.3622i	0.713622	+	0.141948i	0.538533	−	0.842604i	$-0.318979\pi$
$73$	52.0944	+	10.3622i	0.713622	+	0.141948i	0.175089	+	0.984553i	$0.443979\pi$
$74$	−5.94838	−	3.97458i	−0.0803835	−	0.0537105i
$75$	11.9758	−	2.38214i	0.159678	−	0.0317619i
$76$	97.5527	+	40.4076i	1.28359	+	0.531679i
$77$	6.78259	−	16.3746i	0.0880856	−	0.212657i
$78$	−1.06744	−	5.36639i	−0.0136852	−	0.0687999i
$79$	−36.8708	+	55.1810i	−0.466718	+	0.698494i	−0.987924	−	0.154937i	$-0.950482\pi$
$79$	−36.8708	+	55.1810i	−0.466718	+	0.698494i	0.521206	+	0.853431i	$0.325482\pi$
$80$	−2.47797	+	12.4576i	−0.0309746	+	0.155720i
$81$	31.4350	+	31.4350i	0.388087	+	0.388087i
$82$	−7.49005	−	11.2097i	−0.0913421	−	0.136703i
$83$	−109.522	+	45.3657i	−1.31955	+	0.546574i	−0.927655	−	0.373437i	$-0.878179\pi$
$83$	−109.522	+	45.3657i	−1.31955	+	0.546574i	−0.391891	+	0.920012i	$0.628179\pi$
$84$		−	27.6080i		−	0.328667i
$85$	−2.28335	+	37.9445i	−0.0268630	+	0.446406i
$86$	−46.2132			−0.537363
$87$	48.6987	+	117.569i	0.559755	+	1.35137i
$88$	−27.2899	+	18.2345i	−0.310112	+	0.207210i
$89$	69.2116	−	69.2116i	0.777658	−	0.777658i	−0.201774	−	0.979432i	$-0.564671\pi$
$89$	69.2116	−	69.2116i	0.777658	−	0.777658i	0.979432	+	0.201774i	$0.0646707\pi$
$90$	−6.42975	−	1.27896i	−0.0714417	−	0.0142106i
$91$	7.10991	+	4.75069i	0.0781309	+	0.0522054i
$92$	7.35341	−	1.46268i	0.0799283	−	0.0158987i
$93$	35.6655	+	14.7731i	0.383500	+	0.158851i
$94$	−12.0632	+	29.1231i	−0.128332	+	0.309820i
$95$	−15.0158	−	75.4896i	−0.158061	−	0.794627i
$96$	−44.4790	+	66.5676i	−0.463323	+	0.693412i
$97$	−7.05322	+	35.4589i	−0.0727136	+	0.365556i	−0.999960	−	0.00889462i	$-0.997169\pi$
$97$	−7.05322	+	35.4589i	−0.0727136	+	0.365556i	0.927247	+	0.374451i	$0.122169\pi$
$98$	24.1835	+	24.1835i	0.246770	+	0.246770i
$99$	8.11235	+	12.1410i	0.0819429	+	0.122636i
$100$	14.1704	−	5.86956i	0.141704	−	0.0586956i
$101$		−	124.397i		−	1.23166i	−0.787880	−	0.615829i	$-0.788821\pi$
$101$		−	124.397i		−	1.23166i	0.787880	−	0.615829i	$-0.211179\pi$
$102$	−17.5381	+	36.0483i	−0.171942	+	0.353415i
$103$	−163.755			−1.58985			−0.794925	−	0.606707i	$-0.792490\pi$
$103$	−163.755			−1.58985			−0.794925	+	0.606707i	$0.792490\pi$
$104$	−6.05978	−	14.6296i	−0.0582671	−	0.140669i
$105$	−16.7329	+	11.1806i	−0.159361	+	0.106481i
$106$	−8.52390	+	8.52390i	−0.0804141	+	0.0804141i
$107$	−4.64598	−	0.924143i	−0.0434204	−	0.00863685i	0.173332	−	0.984863i	$-0.444547\pi$
$107$	−4.64598	−	0.924143i	−0.0434204	−	0.00863685i	−0.216753	+	0.976227i	$0.569547\pi$
$108$	74.9709	+	50.0940i	0.694175	+	0.463833i
$109$	39.3336	−	7.82394i	0.360859	−	0.0717792i	−0.0113314	−	0.999936i	$-0.503607\pi$
$109$	39.3336	−	7.82394i	0.360859	−	0.0717792i	0.372190	+	0.928157i	$0.378607\pi$
$110$	9.59368	+	3.97383i	0.0872152	+	0.0361257i
$111$	6.92385	−	16.7156i	0.0623770	−	0.150591i
$112$	−4.08402	−	20.5318i	−0.0364645	−	0.183319i
$113$	−64.0781	+	95.8997i	−0.567063	+	0.848670i	−0.998571	−	0.0534391i	$-0.982982\pi$
$113$	−64.0781	+	95.8997i	−0.567063	+	0.848670i	0.431508	+	0.902109i	$0.357982\pi$
$114$	15.8355	−	79.6105i	0.138908	−	0.698337i
$115$	−3.86446	−	3.86446i	−0.0336040	−	0.0336040i
$116$	88.8077	+	132.910i	0.765583	+	1.14578i
$117$	−6.50856	+	2.69593i	−0.0556287	+	0.0230422i
$118$			26.2808i			0.222719i
$119$	−20.4553	−	59.2174i	−0.171893	−	0.497625i
$120$	37.2669			0.310558
$121$	37.4536	+	90.4210i	0.309534	+	0.747281i
$122$	−55.0977	+	36.8151i	−0.451620	+	0.301763i
$123$	24.1094	−	24.1094i	0.196011	−	0.196011i
$124$	47.5599	+	9.46024i	0.383547	+	0.0762923i
$125$	−9.29611	−	6.21146i	−0.0743689	−	0.0496917i
$126$	10.5971	−	2.10789i	0.0841039	−	0.0167293i
$127$	−221.668	−	91.8180i	−1.74542	−	0.722976i	−0.998300	−	0.0582871i	$-0.981436\pi$
$127$	−221.668	−	91.8180i	−1.74542	−	0.722976i	−0.747120	−	0.664689i	$-0.768564\pi$
$128$	−46.8810	+	113.181i	−0.366258	+	0.884225i
$129$	−22.8012	−	114.629i	−0.176753	−	0.888599i
$130$	−2.78337	+	4.16560i	−0.0214105	+	0.0320431i
$131$	42.5779	−	214.053i	0.325022	−	1.63400i	−0.380126	−	0.924935i	$-0.624119\pi$
$131$	42.5779	−	214.053i	0.325022	−	1.63400i	0.705147	−	0.709061i	$-0.250881\pi$
$132$	−25.4754	−	25.4754i	−0.192995	−	0.192995i
$133$	70.4765	+	105.476i	0.529899	+	0.793049i
$134$	−56.4252	+	23.3721i	−0.421084	+	0.174419i
$135$		−	65.7258i		−	0.486858i
$136$	−29.4281	+	112.224i	−0.216383	+	0.825175i
$137$	153.897			1.12334			0.561668	−	0.827362i	$-0.310160\pi$
$137$	153.897			1.12334			0.561668	+	0.827362i	$0.310160\pi$
$138$	−2.20560	−	5.32479i	−0.0159826	−	0.0385854i
$139$	152.360	−	101.804i	1.09611	−	0.732401i	0.130259	−	0.991480i	$-0.458419\pi$
$139$	152.360	−	101.804i	1.09611	−	0.732401i	0.965856	+	0.259079i	$0.0834191\pi$
$140$	−17.8749	+	17.8749i	−0.127678	+	0.127678i
$141$	−78.1901	−	15.5530i	−0.554540	−	0.110305i
$142$	33.5014	+	22.3849i	0.235926	+	0.157640i
$143$	10.9444	−	2.17698i	0.0765344	−	0.0152236i
$144$	15.9338	+	6.60000i	0.110651	+	0.0458333i
$145$	44.5903	−	107.651i	0.307519	−	0.742418i
$146$	−10.0060	−	50.3034i	−0.0685341	−	0.344544i
$147$	−48.0539	+	71.9177i	−0.326897	+	0.489236i
$148$	4.43381	−	22.2903i	0.0299582	−	0.150610i
$149$	40.3951	+	40.3951i	0.271108	+	0.271108i	0.829546	−	0.558438i	$-0.188599\pi$
$149$	40.3951	+	40.3951i	0.271108	+	0.271108i	−0.558438	+	0.829546i	$0.688599\pi$
$150$	−6.55054	−	9.80358i	−0.0436703	−	0.0653572i
$151$	−54.5664	+	22.6021i	−0.361367	+	0.149683i	−0.555977	−	0.831198i	$-0.687656\pi$
$151$	−54.5664	+	22.6021i	−0.361367	+	0.149683i	0.194610	+	0.980881i	$0.437656\pi$
$152$		−	234.912i		−	1.54547i
$153$	49.9272	+	13.0923i	0.326322	+	0.0855704i
$154$	−17.1144			−0.111133
$155$	−13.5268	−	32.6566i	−0.0872698	−	0.210688i
$156$	14.4525	−	9.65688i	0.0926445	−	0.0619031i
$157$	3.65977	−	3.65977i	0.0233107	−	0.0233107i	−0.695355	−	0.718666i	$-0.744753\pi$
$157$	3.65977	−	3.65977i	0.0233107	−	0.0233107i	0.718666	+	0.695355i	$0.244753\pi$
$158$	62.8526	+	12.5022i	0.397801	+	0.0791276i
$159$	−25.3487	−	16.9374i	−0.159426	−	0.106525i
$160$	71.8974	−	14.3013i	0.449359	−	0.0893831i
$161$	8.32169	+	3.44696i	0.0516875	+	0.0214097i
$162$	16.4276	−	39.6598i	0.101405	−	0.244813i
$163$	−21.4707	−	107.940i	−0.131722	−	0.662211i	−0.989067	−	0.147469i	$-0.952887\pi$
$163$	−21.4707	−	107.940i	−0.131722	−	0.662211i	0.857345	−	0.514743i	$-0.172113\pi$
$164$	23.7944	−	35.6108i	0.145088	−	0.217139i
$165$	−5.12343	+	25.7572i	−0.0310511	+	0.156104i
$166$	80.9429	+	80.9429i	0.487608	+	0.487608i
$167$	118.557	+	177.433i	0.709923	+	1.06247i	0.994593	+	0.103849i	$0.0331158\pi$
$167$	118.557	+	177.433i	0.709923	+	1.06247i	−0.284671	+	0.958625i	$0.591884\pi$
$168$	−56.7455	+	23.5048i	−0.337771	+	0.139909i
$169$		−	163.616i		−	0.968144i
$170$	34.6947	−	11.9845i	0.204086	−	0.0704970i
$171$	−104.510			−0.611169
$172$	−56.1817	−	135.635i	−0.326638	−	0.788574i
$173$	150.906	−	100.832i	0.872287	−	0.582844i	−0.0368589	−	0.999320i	$-0.511735\pi$
$173$	150.906	−	100.832i	0.872287	−	0.582844i	0.909146	+	0.416477i	$0.136735\pi$
$174$	86.8898	−	86.8898i	0.499367	−	0.499367i
$175$	18.0726	+	3.59487i	0.103272	+	0.0205421i
$176$	−22.7143	−	15.1772i	−0.129059	−	0.0862343i
$177$	−65.1881	+	12.9667i	−0.368295	+	0.0732583i
$178$	−87.3203	−	36.1693i	−0.490564	−	0.203198i
$179$	−13.9147	+	33.5930i	−0.0777356	+	0.187670i	−0.957970	−	0.286869i	$-0.907385\pi$
$179$	−13.9147	+	33.5930i	−0.0777356	+	0.187670i	0.880234	+	0.474540i	$0.157385\pi$
$180$	−4.06299	−	20.4260i	−0.0225721	−	0.113478i
$181$	−115.240	+	172.469i	−0.636686	+	0.952868i	0.363091	+	0.931754i	$0.381721\pi$
$181$	−115.240	+	172.469i	−0.636686	+	0.952868i	−0.999777	+	0.0211143i	$0.993279\pi$
$182$	1.61087	−	8.09838i	0.00885092	−	0.0444966i
$183$	−118.503	−	118.503i	−0.647555	−	0.647555i
$184$	−9.26691	−	13.8689i	−0.0503636	−	0.0753745i
$185$	−15.3055	+	6.33973i	−0.0827322	+	0.0342688i
$186$		−	37.2768i		−	0.200413i
$187$	−73.5183	−	35.7679i	−0.393146	−	0.191272i
$188$	−100.141			−0.532665
$189$	41.4541	+	100.079i	0.219334	+	0.529519i
$190$	−61.7968	+	41.2913i	−0.325246	+	0.217323i
$191$	−131.649	+	131.649i	−0.689260	+	0.689260i	−0.962068	−	0.272808i	$-0.912048\pi$
$191$	−131.649	+	131.649i	−0.689260	+	0.689260i	0.272808	+	0.962068i	$0.412048\pi$
$192$	21.4007	+	4.25686i	0.111462	+	0.0221712i
$193$	224.053	+	149.707i	1.16089	+	0.775685i	0.978237	−	0.207492i	$-0.0665301\pi$
$193$	224.053	+	149.707i	1.16089	+	0.775685i	0.182657	+	0.983177i	$0.441530\pi$
$194$	34.2399	−	6.81073i	0.176494	−	0.0351069i
$195$	−11.7058	−	4.84872i	−0.0600299	−	0.0248652i
$196$	−41.5779	+	100.378i	−0.212132	+	0.512133i
$197$	42.9951	+	216.151i	0.218249	+	1.09721i	0.922126	+	0.386890i	$0.126451\pi$
$197$	42.9951	+	216.151i	0.218249	+	1.09721i	−0.703877	+	0.710322i	$0.748549\pi$
$198$	7.83344	−	11.7236i	0.0395628	−	0.0592100i
$199$	−48.6247	+	244.453i	−0.244345	+	1.22841i	0.642480	+	0.766302i	$0.277905\pi$
$199$	−48.6247	+	244.453i	−0.244345	+	1.22841i	−0.886826	+	0.462104i	$0.847095\pi$
$200$	−24.1286	−	24.1286i	−0.120643	−	0.120643i
$201$	−85.8129	−	128.428i	−0.426930	−	0.638946i
$202$	−110.977	+	45.9682i	−0.549391	+	0.227565i
$203$			192.041i			0.946013i
$204$	−127.122	−	7.64973i	−0.623148	−	0.0374987i
$205$	−31.2194			−0.152290
$206$	60.5117	+	146.088i	0.293746	+	0.709166i
$207$	−6.17013	+	4.12275i	−0.0298074	+	0.0199167i
$208$	9.31967	−	9.31967i	0.0448061	−	0.0448061i
$209$	162.361	+	32.2955i	0.776845	+	0.154524i
$210$	16.1576	+	10.7962i	0.0769410	+	0.0514103i
$211$	9.91358	−	1.97193i	0.0469838	−	0.00934565i	−0.171542	−	0.985177i	$-0.554875\pi$
$211$	9.91358	−	1.97193i	0.0469838	−	0.00934565i	0.218526	+	0.975831i	$0.429875\pi$
$212$	−35.3800	−	14.6549i	−0.166887	−	0.0691268i
$213$	−38.9953	+	94.1430i	−0.183077	+	0.441986i
$214$	0.892371	+	4.48625i	0.00416996	+	0.0209638i
$215$	−59.4544	+	88.9798i	−0.276532	+	0.413859i
$216$	39.1348	−	196.744i	0.181180	−	0.910852i
$217$	41.1939	+	41.1939i	0.189834	+	0.189834i
$218$	−21.5147	−	32.1990i	−0.0986912	−	0.147702i
$219$	119.838	−	49.6385i	0.547206	−	0.226660i
$220$			32.9882i			0.149947i
$221$	23.8448	−	31.4216i	0.107895	−	0.142179i
$222$	−17.4709			−0.0786975
$223$	−93.5097	−	225.752i	−0.419326	−	1.01234i	−0.982543	−	0.186034i	$-0.940437\pi$
$223$	−93.5097	−	225.752i	−0.419326	−	1.01234i	0.563217	−	0.826309i	$-0.309563\pi$
$224$	−100.457	+	67.1229i	−0.448467	+	0.299656i
$225$	−10.7346	+	10.7346i	−0.0477091	+	0.0477091i
$226$	109.232	+	21.7277i	0.483329	+	0.0961401i
$227$	329.953	+	220.468i	1.45354	+	0.971223i	0.996657	+	0.0816943i	$0.0260331\pi$
$227$	329.953	+	220.468i	1.45354	+	0.971223i	0.456880	+	0.889528i	$0.348967\pi$
$228$	252.906	−	50.3062i	1.10924	−	0.220641i
$229$	−387.156	−	160.365i	−1.69064	−	0.700286i	−0.690896	−	0.722954i	$-0.742784\pi$
$229$	−387.156	−	160.365i	−1.69064	−	0.700286i	−0.999743	+	0.0226689i	$0.992784\pi$
$230$	−2.01953	+	4.87557i	−0.00878056	+	0.0211981i
$231$	−8.44410	−	42.4514i	−0.0365546	−	0.183772i
$232$	197.575	−	295.692i	0.851616	−	1.27453i
$233$	−49.9022	+	250.875i	−0.214172	+	1.07672i	0.712737	+	0.701432i	$0.247455\pi$
$233$	−49.9022	+	250.875i	−0.214172	+	1.07672i	−0.926909	+	0.375286i	$0.877545\pi$
$234$	4.81017	+	4.81017i	0.0205563	+	0.0205563i
$235$	40.5546	+	60.6942i	0.172573	+	0.258273i
$236$	−77.1336	+	31.9498i	−0.326837	+	0.135380i
$237$			162.071i			0.683843i
$238$	−45.2700	+	40.1309i	−0.190210	+	0.168617i
$239$	226.338			0.947021			0.473511	−	0.880788i	$-0.342987\pi$
$239$	226.338			0.947021			0.473511	+	0.880788i	$0.342987\pi$
$240$	11.8703	+	28.6574i	0.0494596	+	0.119406i
$241$	380.956	−	254.547i	1.58073	−	1.05621i	0.617846	−	0.786299i	$-0.288006\pi$
$241$	380.956	−	254.547i	1.58073	−	1.05621i	0.962885	−	0.269911i	$-0.0869943\pi$
$242$	66.8260	−	66.8260i	0.276140	−	0.276140i
$243$	−152.979	−	30.4294i	−0.629543	−	0.125224i
$244$	−175.034	−	116.954i	−0.717353	−	0.479320i
$245$	77.6759	−	15.4507i	0.317045	−	0.0630641i
$246$	−30.4175	−	12.5993i	−0.123648	−	0.0512168i
$247$	−30.5639	+	73.7877i	−0.123740	+	0.298736i
$248$	−21.0467	−	105.809i	−0.0848656	−	0.426648i
$249$	−160.838	+	240.711i	−0.645935	+	0.966710i
$250$	−2.10619	+	10.5885i	−0.00842475	+	0.0423541i
$251$	74.4069	+	74.4069i	0.296442	+	0.296442i	0.839618	−	0.543177i	$-0.182779\pi$
$251$	74.4069	+	74.4069i	0.296442	+	0.296442i	−0.543177	+	0.839618i	$0.682779\pi$
$252$	19.0696	+	28.5396i	0.0756729	+	0.113253i
$253$	10.8596	−	4.49818i	0.0429232	−	0.0177794i
$254$			231.683i			0.912138i
$255$	46.8449	+	80.1452i	0.183706	+	0.314295i
$256$	154.034			0.601695
$257$	−31.6976	−	76.5248i	−0.123337	−	0.297762i	0.850136	−	0.526563i	$-0.176519\pi$
$257$	−31.6976	−	76.5248i	−0.123337	−	0.297762i	−0.973473	+	0.228801i	$0.926519\pi$
$258$	−93.8371	+	62.6999i	−0.363710	+	0.243023i
$259$	19.3067	−	19.3067i	0.0745433	−	0.0745433i
$260$	−15.6097	−	3.10497i	−0.0600374	−	0.0119422i
$261$	−131.550	−	87.8990i	−0.504023	−	0.336778i
$262$	−206.694	+	41.1140i	−0.788909	+	0.156924i
$263$	−2.23755	−	0.926824i	−0.00850780	−	0.00352405i	0.378425	−	0.925632i	$-0.376466\pi$
$263$	−2.23755	−	0.926824i	−0.00850780	−	0.00352405i	−0.386933	+	0.922108i	$0.626466\pi$
$264$	−30.6730	+	74.0513i	−0.116186	+	0.280497i
$265$	5.44588	+	27.3783i	0.0205505	+	0.103314i
$266$	68.0535	−	101.849i	0.255840	−	0.382892i
$267$	46.6328	−	234.439i	0.174655	−	0.878048i
$268$	−137.193	−	137.193i	−0.511915	−	0.511915i
$269$	79.6966	+	119.274i	0.296270	+	0.443399i	0.949503	−	0.313757i	$-0.101588\pi$
$269$	79.6966	+	119.274i	0.296270	+	0.443399i	−0.653233	+	0.757157i	$0.726588\pi$
$270$	−58.6351	+	24.2874i	−0.217167	+	0.0899535i
$271$			51.5741i			0.190310i	0.995462	+	0.0951551i	$0.0303347\pi$
$271$			51.5741i			0.190310i	−0.995462	+	0.0951551i	$0.969665\pi$
$272$	−95.6710	+	13.1160i	−0.351732	+	0.0482207i
$273$	20.8824			0.0764922
$274$	−56.8691	−	137.294i	−0.207552	−	0.501074i
$275$	19.9938	−	13.3594i	0.0727047	−	0.0485797i
$276$	12.9468	−	12.9468i	0.0469086	−	0.0469086i
$277$	−350.729	−	69.7643i	−1.26617	−	0.251857i	−0.484080	−	0.875024i	$-0.660846\pi$
$277$	−350.729	−	69.7643i	−1.26617	−	0.251857i	−0.782089	+	0.623167i	$0.785846\pi$
$278$	−147.122	−	98.3037i	−0.529215	−	0.353610i
$279$	−47.0732	+	9.36344i	−0.168721	+	0.0335607i
$280$	51.9583	+	21.5218i	0.185565	+	0.0768636i
$281$	182.827	−	441.383i	0.650630	−	1.57076i	−0.161236	−	0.986916i	$-0.551548\pi$
$281$	182.827	−	441.383i	0.650630	−	1.57076i	0.811866	−	0.583844i	$-0.198452\pi$
$282$	15.0183	+	75.5019i	0.0532563	+	0.267737i
$283$	122.046	−	182.654i	0.431257	−	0.645422i	−0.550661	−	0.834729i	$-0.685624\pi$
$283$	122.046	−	182.654i	0.431257	−	0.645422i	0.981918	+	0.189307i	$0.0606242\pi$
$284$	−24.9714	+	125.540i	−0.0879273	+	0.442041i
$285$	−132.911	−	132.911i	−0.466353	−	0.466353i
$286$	−5.98638	−	8.95925i	−0.0209314	−	0.0313260i
$287$	47.5371	−	19.6905i	0.165634	−	0.0686080i
$288$		−	99.5367i		−	0.345614i
$289$	−278.337	+	77.7792i	−0.963103	+	0.269132i
$290$	−112.514			−0.387980
$291$	33.7873	+	81.5697i	0.116108	+	0.280308i
$292$	135.475	−	90.5216i	0.463956	−	0.310005i
$293$	352.092	−	352.092i	1.20168	−	1.20168i	0.228023	−	0.973656i	$-0.426774\pi$
$293$	352.092	−	352.092i	1.20168	−	1.20168i	0.973656	−	0.228023i	$-0.0732262\pi$
$294$	81.9161	+	16.2941i	0.278626	+	0.0554222i
$295$	50.6016	+	33.8109i	0.171531	+	0.114613i
$296$	−49.5903	+	9.86412i	−0.167535	+	0.0333247i
$297$	130.600	+	54.0965i	0.439732	+	0.182143i
$298$	21.1101	−	50.9642i	0.0708392	−	0.171021i
$299$	1.10636	+	5.56203i	0.00370019	+	0.0186021i
$300$	20.8097	−	31.1440i	0.0693658	−	0.103813i
$301$	34.4091	−	172.986i	0.114316	−	0.574705i
$302$	40.3275	+	40.3275i	0.133535	+	0.133535i
$303$	−168.777	−	252.592i	−0.557019	−	0.833637i
$304$	180.642	−	74.8243i	0.594217	−	0.246133i
$305$			153.450i			0.503113i
$306$	−6.76960	−	49.3788i	−0.0221229	−	0.161369i
$307$	153.821			0.501046			0.250523	−	0.968111i	$-0.419397\pi$
$307$	153.821			0.501046			0.250523	+	0.968111i	$0.419397\pi$
$308$	−20.8061	−	50.2304i	−0.0675524	−	0.163086i
$309$	−332.508	+	222.175i	−1.07608	+	0.719012i
$310$	−24.1350	+	24.1350i	−0.0778548	+	0.0778548i
$311$	−301.680	−	60.0079i	−0.970032	−	0.192951i	−0.315450	−	0.948942i	$-0.602155\pi$
$311$	−301.680	−	60.0079i	−0.970032	−	0.192951i	−0.654582	+	0.755991i	$0.727155\pi$
$312$	−32.1533	−	21.4841i	−0.103055	−	0.0688594i
$313$	234.843	−	46.7133i	0.750299	−	0.149244i	0.194894	−	0.980824i	$-0.437564\pi$
$313$	234.843	−	46.7133i	0.750299	−	0.149244i	0.555404	+	0.831581i	$0.312564\pi$
$314$	−4.61733	−	1.91256i	−0.0147049	−	0.00609095i
$315$	9.57483	−	23.1157i	0.0303963	−	0.0733831i
$316$	39.7168	+	199.670i	0.125686	+	0.631867i
$317$	163.783	−	245.119i	0.516666	−	0.773245i	−0.477782	−	0.878479i	$-0.658559\pi$
$317$	163.783	−	245.119i	0.516666	−	0.773245i	0.994448	+	0.105233i	$0.0335590\pi$
$318$	−5.74316	+	28.8728i	−0.0180602	+	0.0907950i
$319$	177.206	+	177.206i	0.555506	+	0.555506i
$320$	−11.0998	−	16.6121i	−0.0346869	−	0.0519127i
$321$	−10.6876	+	4.42695i	−0.0332947	+	0.0137911i
$322$		−	8.69766i		−	0.0270114i
$323$	505.195	−	295.287i	1.56407	−	0.914200i
$324$	136.372			0.420900
$325$	4.43966	+	10.7183i	0.0136605	+	0.0329794i
$326$	−88.3614	+	59.0412i	−0.271047	+	0.181108i
$327$	69.2527	−	69.2527i	0.211782	−	0.211782i
$328$	−93.4524	−	18.5888i	−0.284916	−	0.0566733i
$329$	−100.032	−	66.8394i	−0.304049	−	0.203159i
$330$	24.8717	−	4.94729i	0.0753688	−	0.0149918i
$331$	325.328	+	134.755i	0.982865	+	0.407116i	0.815486	−	0.578777i	$-0.196470\pi$
$331$	325.328	+	134.755i	0.982865	+	0.407116i	0.167379	+	0.985893i	$0.446470\pi$
$332$	−139.163	+	335.968i	−0.419165	+	1.01195i
$333$	4.38845	+	22.0622i	0.0131785	+	0.0662529i
$334$	114.481	−	171.333i	0.342758	−	0.512973i
$335$	−27.5913	+	138.711i	−0.0823622	+	0.414063i
$336$	−36.1492	−	36.1492i	−0.107587	−	0.107587i
$337$	−104.502	−	156.398i	−0.310095	−	0.464090i	0.643386	−	0.765542i	$-0.277529\pi$
$337$	−104.502	−	156.398i	−0.310095	−	0.464090i	−0.953482	+	0.301451i	$0.902529\pi$
$338$	−145.965	+	60.4606i	−0.431849	+	0.178878i
$339$			281.665i			0.830870i
$340$	77.3528	+	87.2585i	0.227508	+	0.256643i
$341$	76.0238			0.222944
$342$	38.6192	+	93.2349i	0.112922	+	0.272617i
$343$	−258.678	+	172.843i	−0.754165	+	0.503917i
$344$	−230.952	+	230.952i	−0.671372	+	0.671372i
$345$	−13.0900	−	2.60376i	−0.0379420	−	0.00754714i
$346$	−145.718	−	97.3654i	−0.421149	−	0.281403i
$347$	−355.397	+	70.6929i	−1.02420	+	0.203726i	−0.678485	−	0.734614i	$-0.737363\pi$
$347$	−355.397	+	70.6929i	−1.02420	+	0.203726i	−0.345714	+	0.938340i	$0.612363\pi$
$348$	360.652	+	149.387i	1.03636	+	0.429273i
$349$	121.253	−	292.730i	0.347429	−	0.838767i	−0.649493	−	0.760367i	$-0.725019\pi$
$349$	121.253	−	292.730i	0.347429	−	0.838767i	0.996922	−	0.0783995i	$-0.0249810\pi$
$350$	−3.47128	−	17.4513i	−0.00991794	−	0.0498608i
$351$	−37.8905	+	56.7071i	−0.107950	+	0.161559i
$352$	−30.7588	+	154.635i	−0.0873828	+	0.439303i
$353$	−77.6740	−	77.6740i	−0.220040	−	0.220040i	0.588475	−	0.808515i	$-0.299728\pi$
$353$	−77.6740	−	77.6740i	−0.220040	−	0.220040i	−0.808515	+	0.588475i	$0.799728\pi$
$354$	35.6566	+	53.3639i	0.100725	+	0.150745i
$355$	86.2008	−	35.7055i	0.242819	−	0.100579i
$356$		−	300.254i		−	0.843411i
$357$	−121.878	−	92.4896i	−0.341396	−	0.259074i
$358$	35.1107			0.0980746
$359$	181.912	+	439.175i	0.506719	+	1.22333i	0.945761	+	0.324862i	$0.105318\pi$
$359$	181.912	+	439.175i	0.506719	+	1.22333i	−0.439042	+	0.898467i	$0.644682\pi$
$360$	−38.5245	+	25.7413i	−0.107013	+	0.0715035i
$361$	−582.536	+	582.536i	−1.61367	+	1.61367i
$362$	196.447	+	39.0757i	0.542671	+	0.107944i
$363$	198.729	+	132.787i	0.547464	+	0.365804i
$364$	25.7269	−	5.11740i	0.0706783	−	0.0140588i
$365$	−109.728	−	45.4509i	−0.300625	−	0.124523i
$366$	−61.9282	+	149.508i	−0.169203	+	0.408492i
$367$	−25.3166	−	127.275i	−0.0689824	−	0.346798i	0.930844	−	0.365416i	$-0.119073\pi$
$367$	−25.3166	−	127.275i	−0.0689824	−	0.346798i	−0.999827	+	0.0186181i	$0.994073\pi$
$368$	7.71317	−	11.5436i	0.0209597	−	0.0313684i
$369$	−8.26998	+	41.5760i	−0.0224119	+	0.112672i
$370$	11.3116	+	11.3116i	0.0305718	+	0.0305718i
$371$	−25.5601	−	38.2535i	−0.0688953	−	0.103109i
$372$	109.407	−	45.3177i	0.294104	−	0.121822i
$373$			602.500i			1.61528i	0.589676	+	0.807640i	$0.299256\pi$
$373$			602.500i			1.61528i	−0.589676	+	0.807640i	$0.700744\pi$
$374$	−4.74213	+	78.8041i	−0.0126795	+	0.210706i
$375$	−27.3034			−0.0728091
$376$	85.2575	+	205.830i	0.226749	+	0.547420i
$377$	−100.532	+	67.1731i	−0.266662	+	0.178178i
$378$	73.9639	−	73.9639i	0.195672	−	0.195672i
$379$	−345.346	−	68.6936i	−0.911203	−	0.181250i	−0.282838	−	0.959168i	$-0.591276\pi$
$379$	−345.346	−	68.6936i	−0.911203	−	0.181250i	−0.628365	+	0.777918i	$0.716276\pi$
$380$	−196.316	−	131.174i	−0.516620	−	0.345195i
$381$	−574.677	+	114.310i	−1.50834	+	0.300027i
$382$	166.094	+	68.7983i	0.434800	+	0.180100i
$383$	−94.9085	+	229.129i	−0.247803	+	0.598249i	−0.998017	−	0.0629459i	$-0.979950\pi$
$383$	−94.9085	+	229.129i	−0.247803	+	0.598249i	0.750214	+	0.661195i	$0.229950\pi$
$384$	58.3653	+	293.422i	0.151993	+	0.764121i
$385$	−22.0181	+	32.9524i	−0.0571899	+	0.0855907i
$386$	50.7628	−	255.202i	0.131510	−	0.661144i
$387$	102.748	+	102.748i	0.265499	+	0.265499i
$388$	61.6150	+	92.2134i	0.158802	+	0.237663i
$389$	343.713	−	142.371i	0.883581	−	0.365991i	0.105697	−	0.994398i	$-0.466293\pi$
$389$	343.713	−	142.371i	0.883581	−	0.365991i	0.777885	+	0.628407i	$0.216293\pi$
$390$			12.2347i			0.0313710i
$391$	18.1775	−	37.3625i	0.0464897	−	0.0955563i
$392$	241.715			0.616621
$393$	−203.962	−	492.408i	−0.518988	−	1.25295i
$394$	176.944	−	118.230i	0.449096	−	0.300077i
$395$	104.933	−	104.933i	0.265654	−	0.265654i
$396$	43.9316	+	8.73854i	0.110938	+	0.0220670i
$397$	−629.967	−	420.930i	−1.58682	−	1.06028i	−0.959575	−	0.281454i	$-0.909183\pi$
$397$	−629.967	−	420.930i	−1.58682	−	1.06028i	−0.627243	−	0.778824i	$-0.715817\pi$
$398$	236.049	−	46.9530i	0.593087	−	0.117972i
$399$	286.209	+	118.552i	0.717315	+	0.297122i
$400$	10.8689	−	26.2398i	0.0271722	−	0.0655995i
$401$	78.7581	+	395.944i	0.196404	+	0.987391i	0.945672	+	0.325123i	$0.105406\pi$
$401$	78.7581	+	395.944i	0.196404	+	0.987391i	−0.749267	+	0.662268i	$0.769594\pi$
$402$	−82.8627	+	124.013i	−0.206126	+	0.308489i
$403$	−7.15562	+	35.9737i	−0.0177559	+	0.0892648i
$404$	−269.831	−	269.831i	−0.667899	−	0.667899i
$405$	−55.2272	−	82.6533i	−0.136363	−	0.204082i
$406$	171.323	−	70.9642i	0.421977	−	0.174789i
$407$		−	35.6307i		−	0.0875448i
$408$	92.5054	+	267.800i	0.226729	+	0.656372i
$409$	−439.976			−1.07574			−0.537868	−	0.843029i	$-0.680770\pi$
$409$	−439.976			−1.07574			−0.537868	+	0.843029i	$0.680770\pi$
$410$	11.5364	+	27.8513i	0.0281376	+	0.0679301i
$411$	312.492	−	208.800i	0.760321	−	0.508030i
$412$	−355.201	+	355.201i	−0.862138	+	0.862138i
$413$	−98.3749	−	19.5680i	−0.238196	−	0.0473801i
$414$	5.95800	+	3.98101i	0.0143913	+	0.00961596i
$415$	259.984	−	51.7140i	0.626467	−	0.124612i
$416$	−70.2765	−	29.1095i	−0.168934	−	0.0699747i
$417$	171.248	−	413.430i	0.410667	−	0.991438i
$418$	−31.1852	−	156.779i	−0.0746058	−	0.375068i
$419$	353.408	−	528.913i	0.843457	−	1.26232i	−0.119546	−	0.992829i	$-0.538144\pi$
$419$	353.408	−	528.913i	0.843457	−	1.26232i	0.963002	−	0.269493i	$-0.0868562\pi$
$420$	−12.0436	+	60.5472i	−0.0286752	+	0.144160i
$421$	466.115	+	466.115i	1.10716	+	1.10716i	0.993522	+	0.113640i	$0.0362510\pi$
$421$	466.115	+	466.115i	1.10716	+	1.10716i	0.113640	+	0.993522i	$0.463749\pi$
$422$	−5.42253	−	8.11538i	−0.0128496	−	0.0192308i
$423$	91.5715	−	37.9302i	0.216481	−	0.0896694i
$424$			85.1969i			0.200936i
$425$	21.5604	−	82.2201i	0.0507303	−	0.193459i
$426$	98.3964			0.230977
$427$	−96.7827	−	233.654i	−0.226657	−	0.547199i
$428$	−12.0822	+	8.07306i	−0.0282294	+	0.0188623i
$429$	19.2693	−	19.2693i	0.0449168	−	0.0449168i
$430$	101.350	+	20.1598i	0.235698	+	0.0468833i
$431$	−30.0089	−	20.0513i	−0.0696262	−	0.0465227i	0.520270	−	0.854002i	$-0.325831\pi$
$431$	−30.0089	−	20.0513i	−0.0696262	−	0.0465227i	−0.589896	+	0.807479i	$0.700831\pi$
$432$	163.757	−	32.5733i	0.379067	−	0.0754011i
$433$	−29.5441	−	12.2376i	−0.0682312	−	0.0282623i	0.348307	−	0.937381i	$-0.386757\pi$
$433$	−29.5441	−	12.2376i	−0.0682312	−	0.0282623i	−0.416538	+	0.909118i	$0.636757\pi$
$434$	21.5275	−	51.9721i	0.0496026	−	0.119751i
$435$	−55.5135	−	279.085i	−0.127617	−	0.641575i
$436$	68.3478	−	102.290i	0.156761	−	0.234609i
$437$	−16.4128	+	82.5128i	−0.0375579	+	0.188816i
$438$	−88.5667	−	88.5667i	−0.202207	−	0.202207i
$439$	−135.063	−	202.136i	−0.307661	−	0.460447i	0.645131	−	0.764072i	$-0.276803\pi$
$439$	−135.063	−	202.136i	−0.307661	−	0.460447i	−0.952792	+	0.303625i	$0.901803\pi$
$440$	67.8041	−	28.0854i	0.154100	−	0.0638304i
$441$		−	107.537i		−	0.243847i
$442$	−36.8430	−	9.66124i	−0.0833552	−	0.0218580i
$443$	−674.566			−1.52272			−0.761361	−	0.648328i	$-0.775469\pi$
$443$	−674.566			−1.52272			−0.761361	+	0.648328i	$0.775469\pi$
$444$	−21.2394	−	51.2766i	−0.0478366	−	0.115488i
$445$	−181.981	+	121.596i	−0.408945	+	0.273248i
$446$	−166.843	+	166.843i	−0.374088	+	0.374088i
$447$	136.830	+	27.2171i	0.306106	+	0.0608883i
$448$	27.3789	+	18.2940i	0.0611136	+	0.0408348i
$449$	−514.273	+	102.295i	−1.14538	+	0.227829i	−0.731066	−	0.682307i	$-0.760977\pi$
$449$	−514.273	+	102.295i	−1.14538	+	0.227829i	−0.414309	+	0.910136i	$0.635977\pi$
$450$	13.5432	+	5.60977i	0.0300959	+	0.0124662i
$451$	25.6955	−	62.0345i	0.0569746	−	0.137549i
$452$	69.0243	+	347.009i	0.152709	+	0.767719i
$453$	−80.1328	+	119.927i	−0.176894	+	0.264740i
$454$	74.7563	−	375.825i	0.164661	−	0.827809i
$455$	−13.5203	−	13.5203i	−0.0297150	−	0.0297150i
$456$	−318.717	−	476.994i	−0.698942	−	1.04604i
$457$	509.027	−	210.846i	1.11384	−	0.461369i	0.251584	−	0.967835i	$-0.419048\pi$
$457$	509.027	−	210.846i	1.11384	−	0.461369i	0.862260	+	0.506466i	$0.169048\pi$
$458$			404.648i			0.883510i
$459$	472.305	−	163.147i	1.02899	−	0.355440i
$460$	−16.7648			−0.0364453
$461$	−93.3130	−	225.278i	−0.202414	−	0.488672i	0.789777	−	0.613394i	$-0.210196\pi$
$461$	−93.3130	−	225.278i	−0.202414	−	0.488672i	−0.992192	+	0.124722i	$0.960196\pi$
$462$	−34.7512	+	23.2200i	−0.0752192	+	0.0502598i
$463$	−260.222	+	260.222i	−0.562035	+	0.562035i	−0.929885	−	0.367850i	$-0.880094\pi$
$463$	−260.222	+	260.222i	−0.562035	+	0.562035i	0.367850	+	0.929885i	$0.380094\pi$
$464$	290.312	+	57.7466i	0.625672	+	0.124454i
$465$	−71.7735	−	47.9575i	−0.154352	−	0.103134i
$466$	242.250	−	48.1865i	0.519850	−	0.103405i
$467$	38.9983	+	16.1536i	0.0835081	+	0.0345902i	0.424046	−	0.905640i	$-0.360609\pi$
$467$	38.9983	+	16.1536i	0.0835081	+	0.0345902i	−0.340538	+	0.940231i	$0.610609\pi$
$468$	−8.26998	+	19.9655i	−0.0176709	+	0.0426613i
$469$	−45.4742	−	228.614i	−0.0969599	−	0.487450i
$470$	39.1603	−	58.6076i	0.0833198	−	0.124697i
$471$	2.46585	−	12.3967i	0.00523535	−	0.0263199i
$472$	131.339	+	131.339i	0.278261	+	0.278261i
$473$	−127.873	−	191.375i	−0.270344	−	0.404598i
$474$	144.586	−	59.8895i	0.305034	−	0.126349i
$475$			172.107i			0.362330i
$476$	−172.818	−	84.0790i	−0.363064	−	0.176637i
$477$	37.9032			0.0794616
$478$	−83.6380	−	201.920i	−0.174975	−	0.422427i
$479$	49.4214	−	33.0224i	0.103176	−	0.0689402i	−0.502912	−	0.864338i	$-0.667738\pi$
$479$	49.4214	−	33.0224i	0.103176	−	0.0689402i	0.606088	+	0.795398i	$0.292738\pi$
$480$	126.586	−	126.586i	0.263721	−	0.263721i
$481$	16.8601	+	3.35368i	0.0350522	+	0.00697231i
$482$	−367.859	−	245.795i	−0.763193	−	0.509949i
$483$	21.5741	−	4.29135i	0.0446668	−	0.00888478i
$484$	277.373	+	114.892i	0.573086	+	0.237380i
$485$	30.9369	−	74.6882i	0.0637874	−	0.153996i
$486$	29.3833	+	147.720i	0.0604594	+	0.303950i
$487$	−314.829	+	471.175i	−0.646466	+	0.967504i	0.353026	+	0.935614i	$0.385153\pi$
$487$	−314.829	+	471.175i	−0.646466	+	0.967504i	−0.999491	+	0.0318907i	$0.989847\pi$
$488$	−91.3678	+	459.337i	−0.187229	+	0.941265i
$489$	−190.045	−	190.045i	−0.388641	−	0.388641i
$490$	−42.4872	−	63.5865i	−0.0867085	−	0.129768i
$491$	457.623	−	189.554i	0.932022	−	0.386056i	0.135577	−	0.990767i	$-0.456711\pi$
$491$	457.623	−	189.554i	0.932022	−	0.386056i	0.796445	+	0.604711i	$0.206711\pi$
$492$		−	104.592i		−	0.212585i
$493$	884.260	+	53.2114i	1.79363	+	0.107934i
$494$	77.1214			0.156116
$495$	−12.4949	−	30.1653i	−0.0252422	−	0.0609400i
$496$	74.6607	−	49.8867i	0.150526	−	0.100578i
$497$	−108.736	+	108.736i	−0.218785	+	0.218785i
$498$	274.176	+	54.5370i	0.550554	+	0.109512i
$499$	199.361	+	133.209i	0.399522	+	0.266952i	0.739059	−	0.673641i	$-0.235270\pi$
$499$	199.361	+	133.209i	0.399522	+	0.266952i	−0.339537	+	0.940593i	$0.610270\pi$
$500$	−33.6376	+	6.69093i	−0.0672751	+	0.0133819i
$501$	481.466	+	199.430i	0.961010	+	0.398063i
$502$	38.8843	−	93.8749i	0.0774587	−	0.187002i
$503$	39.5565	+	198.864i	0.0786411	+	0.395355i	0.999978	+	0.00659103i	$0.00209801\pi$
$503$	39.5565	+	198.864i	0.0786411	+	0.395355i	−0.921337	+	0.388764i	$0.872902\pi$
$504$	42.4250	−	63.4935i	0.0841767	−	0.125979i
$505$	−54.2666	+	272.816i	−0.107459	+	0.540230i
$506$	−8.02581	−	8.02581i	−0.0158613	−	0.0158613i
$507$	−221.987	−	332.227i	−0.437844	−	0.655280i
$508$	−679.985	+	281.659i	−1.33855	+	0.554447i
$509$		−	979.909i		−	1.92516i	−0.270990	−	0.962582i	$-0.587351\pi$
$509$		−	979.909i		−	1.92516i	0.270990	−	0.962582i	$-0.412649\pi$
$510$	54.1884	−	71.4069i	0.106252	−	0.140014i
$511$	195.747			0.383066
$512$	130.604	+	315.307i	0.255087	+	0.615834i
$513$	−841.251	+	562.106i	−1.63986	+	1.09572i
$514$	−56.5559	+	56.5559i	−0.110031	+	0.110031i
$515$	359.131	+	71.4355i	0.697341	+	0.138710i
$516$	−298.101	−	199.185i	−0.577716	−	0.386017i
$517$	−153.981	+	30.6288i	−0.297837	+	0.0592434i
$518$	−24.3582	−	10.0895i	−0.0470235	−	0.0194778i
$519$	169.614	−	409.484i	0.326809	−	0.788986i
$520$	6.90777	+	34.7277i	0.0132842	+	0.0667841i
$521$	171.777	−	257.082i	0.329706	−	0.493439i	−0.629169	−	0.777268i	$-0.716605\pi$
$521$	171.777	−	257.082i	0.329706	−	0.493439i	0.958875	+	0.283829i	$0.0916048\pi$
$522$	−29.8048	+	149.839i	−0.0570974	+	0.287048i
$523$	−333.555	−	333.555i	−0.637772	−	0.637772i	0.312233	−	0.950005i	$-0.398923\pi$
$523$	−333.555	−	333.555i	−0.637772	−	0.637772i	−0.950005	+	0.312233i	$0.898923\pi$
$524$	−371.949	−	556.660i	−0.709825	−	1.06233i
$525$	41.5743	−	17.2206i	0.0791891	−	0.0328012i
$526$			2.33864i			0.00444609i
$527$	201.093	−	178.265i	0.381582	−	0.338264i
$528$	−66.7138			−0.126352
$529$	−200.154	−	483.213i	−0.378362	−	0.913447i
$530$	22.4122	−	14.9754i	0.0422872	−	0.0282554i
$531$	58.4315	−	58.4315i	0.110040	−	0.110040i
$532$	381.659	+	75.9166i	0.717403	+	0.142700i
$533$	26.9356	+	17.9978i	0.0505358	+	0.0337669i
$534$	−226.379	+	45.0295i	−0.423930	+	0.0843250i
$535$	9.78597	+	4.05348i	0.0182915	+	0.00757660i
$536$	−165.184	+	398.790i	−0.308179	+	0.744011i
$537$	17.3233	+	87.0902i	0.0322594	+	0.162179i
$538$	76.9567	−	115.174i	0.143042	−	0.214078i
$539$	−33.2309	+	167.063i	−0.0616528	+	0.309950i
$540$	−142.566	−	142.566i	−0.264011	−	0.264011i
$541$	512.263	+	766.656i	0.946882	+	1.41711i	0.908518	+	0.417846i	$0.137215\pi$
$541$	512.263	+	766.656i	0.946882	+	1.41711i	0.0383645	+	0.999264i	$0.487785\pi$
$542$	46.0101	−	19.0580i	0.0848895	−	0.0351624i
$543$			506.555i			0.932883i
$544$	281.236	+	481.155i	0.516977	+	0.884477i
$545$	−89.6757			−0.164543
$546$	−7.71659	−	18.6295i	−0.0141330	−	0.0341200i
$547$	487.252	−	325.572i	0.890772	−	0.595195i	−0.0237557	−	0.999718i	$-0.507562\pi$
$547$	487.252	−	325.572i	0.890772	−	0.595195i	0.914528	+	0.404523i	$0.132562\pi$
$548$	333.819	−	333.819i	0.609159	−	0.609159i
$549$	204.354	+	40.6486i	0.372230	+	0.0740411i
$550$	−19.3064	−	12.9001i	−0.0351025	−	0.0234548i
$551$	−1759.21	+	349.929i	−3.19276	+	0.635080i
$552$	−37.6334	−	15.5883i	−0.0681764	−	0.0282396i
$553$	−93.5966	+	225.962i	−0.169252	+	0.408612i
$554$	67.3658	+	338.671i	0.121599	+	0.611319i
$555$	−22.4767	+	33.6387i	−0.0404985	+	0.0606103i
$556$	109.662	−	551.308i	0.197234	−	0.991561i
$557$	195.753	+	195.753i	0.351442	+	0.351442i	0.860646	−	0.509204i	$-0.170060\pi$
$557$	195.753	+	195.753i	0.351442	+	0.351442i	−0.509204	+	0.860646i	$0.670060\pi$
$558$	25.7481	+	38.5347i	0.0461435	+	0.0690587i
$559$	102.592	−	42.4952i	0.183529	−	0.0760200i
$560$			46.8099i			0.0835890i
$561$	−197.809	+	27.1187i	−0.352601	+	0.0483399i
$562$	−461.325			−0.820863
$563$	−96.5883	−	233.185i	−0.171560	−	0.414183i	0.814590	−	0.580037i	$-0.196962\pi$
$563$	−96.5883	−	233.185i	−0.171560	−	0.414183i	−0.986150	+	0.165854i	$0.946962\pi$
$564$	−203.339	+	135.867i	−0.360530	+	0.240898i
$565$	182.365	−	182.365i	0.322770	−	0.322770i
$566$	−208.048	−	41.3834i	−0.367576	−	0.0731155i
$567$	136.224	+	91.0217i	0.240253	+	0.160532i
$568$	279.294	−	55.5550i	0.491715	−	0.0978082i
$569$	−434.022	−	179.778i	−0.762781	−	0.315954i	−0.0328365	−	0.999461i	$-0.510454\pi$
$569$	−434.022	−	179.778i	−0.762781	−	0.315954i	−0.729944	+	0.683507i	$0.760454\pi$
$570$	−69.4578	+	167.686i	−0.121856	+	0.294186i
$571$	158.498	+	796.824i	0.277580	+	1.39549i	0.828059	+	0.560640i	$0.189445\pi$
$571$	158.498	+	796.824i	0.277580	+	1.39549i	−0.550479	+	0.834849i	$0.685555\pi$
$572$	19.0175	−	28.4617i	0.0332474	−	0.0497582i
$573$	−88.7012	+	445.931i	−0.154801	+	0.778239i
$574$	−35.1324	−	35.1324i	−0.0612063	−	0.0612063i
$575$	6.78935	+	10.1610i	0.0118076	+	0.0176713i
$576$	−25.0632	+	10.3815i	−0.0435125	+	0.0180235i
$577$			834.634i			1.44651i	0.690583	+	0.723253i	$0.257354\pi$
$577$			834.634i			1.44651i	−0.690583	+	0.723253i	$0.742646\pi$
$578$	172.241	+	219.567i	0.297995	+	0.379874i
$579$	658.060			1.13655
$580$	−136.784	−	330.226i	−0.235835	−	0.569356i
$581$	−363.255	+	242.719i	−0.625223	+	0.417761i
$582$	60.2844	−	60.2844i	0.103581	−	0.103581i
$583$	−58.8843	−	11.7128i	−0.101002	−	0.0200906i
$584$	−301.398	−	201.388i	−0.516093	−	0.344842i
$585$	15.4500	−	3.07319i	0.0264102	−	0.00525332i
$586$	−444.214	−	184.000i	−0.758045	−	0.313993i
$587$	−205.403	+	495.886i	−0.349920	+	0.844781i	0.646709	+	0.762737i	$0.276145\pi$
$587$	−205.403	+	495.886i	−0.349920	+	0.844781i	−0.996629	+	0.0820440i	$0.973855\pi$
$588$	51.7632	+	260.231i	0.0880326	+	0.442570i
$589$	−302.300	+	452.424i	−0.513243	+	0.768122i
$590$	11.4646	−	57.6365i	0.0194316	−	0.0976891i
$591$	380.566	+	380.566i	0.643936	+	0.643936i
$592$	−23.3808	−	34.9919i	−0.0394946	−	0.0591079i
$593$	484.571	−	200.716i	0.817152	−	0.338475i	0.0653481	−	0.997863i	$-0.479184\pi$
$593$	484.571	−	200.716i	0.817152	−	0.338475i	0.751803	+	0.659387i	$0.229184\pi$
$594$		−	136.501i		−	0.229800i
$595$	19.0279	+	138.793i	0.0319796	+	0.233266i
$596$	175.243			0.294031
$597$	232.929	+	562.339i	0.390165	+	0.941942i
$598$	4.55315	−	3.04232i	0.00761396	−	0.00508749i
$599$	−164.659	+	164.659i	−0.274890	+	0.274890i	−0.831065	−	0.556175i	$-0.812268\pi$
$599$	−164.659	+	164.659i	−0.274890	+	0.274890i	0.556175	+	0.831065i	$0.312268\pi$
$600$	−81.7302	−	16.2572i	−0.136217	−	0.0270953i
$601$	127.119	+	84.9381i	0.211512	+	0.141328i	0.656814	−	0.754053i	$-0.271904\pi$
$601$	127.119	+	84.9381i	0.211512	+	0.141328i	−0.445302	+	0.895380i	$0.646904\pi$
$602$	−167.039	+	33.2261i	−0.277473	+	0.0551928i
$603$	177.417	+	73.4887i	0.294225	+	0.121872i
$604$	−69.3338	+	167.387i	−0.114791	+	0.277130i
$605$	−42.6948	−	214.641i	−0.0705699	−	0.354779i
$606$	−162.974	+	243.908i	−0.268934	+	0.402488i
$607$	217.351	−	1092.70i	0.358074	−	1.80016i	−0.210576	−	0.977578i	$-0.567534\pi$
$607$	217.351	−	1092.70i	0.358074	−	1.80016i	0.568649	−	0.822580i	$-0.307466\pi$
$608$	−797.935	−	797.935i	−1.31239	−	1.31239i
$609$	260.552	+	389.943i	0.427836	+	0.640301i
$610$	136.895	−	56.7037i	0.224418	−	0.0929569i
$611$		−	75.7454i		−	0.123970i
$612$	136.696	−	79.8988i	0.223359	−	0.130554i
$613$	130.322			0.212597			0.106298	−	0.994334i	$-0.466100\pi$
$613$	130.322			0.212597			0.106298	+	0.994334i	$0.466100\pi$
$614$	−56.8410	−	137.226i	−0.0925750	−	0.223496i
$615$	−63.3918	+	42.3570i	−0.103076	+	0.0688732i
$616$	−85.5299	+	85.5299i	−0.138847	+	0.138847i
$617$	−98.2934	−	19.5518i	−0.159309	−	0.0316885i	0.114792	−	0.993390i	$-0.463380\pi$
$617$	−98.2934	−	19.5518i	−0.159309	−	0.0316885i	−0.274100	+	0.961701i	$0.588380\pi$
$618$	321.076	+	214.536i	0.519541	+	0.347146i
$619$	426.866	−	84.9089i	0.689606	−	0.137171i	0.162166	−	0.986763i	$-0.448152\pi$
$619$	426.866	−	84.9089i	0.689606	−	0.137171i	0.527440	+	0.849592i	$0.323152\pi$
$620$	−100.177	−	41.4946i	−0.161575	−	0.0669267i
$621$	−27.4922	+	66.3721i	−0.0442709	+	0.106879i
$622$	57.9448	+	291.308i	0.0931589	+	0.468341i
$623$	200.406	−	299.928i	0.321678	−	0.481426i
$624$	6.27932	−	31.5683i	0.0100630	−	0.0505902i
$625$	17.6777	+	17.6777i	0.0282843	+	0.0282843i
$626$	−128.455	−	192.246i	−0.205199	−	0.307102i
$627$	373.494	−	154.706i	0.595685	−	0.246741i
$628$		−	15.8769i		−	0.0252816i
$629$	−83.5490	−	94.2482i	−0.132828	−	0.149838i
$630$	−24.1600			−0.0383493
$631$	46.4257	+	112.082i	0.0735748	+	0.177625i	0.956388	−	0.292099i	$-0.0943535\pi$
$631$	46.4257	+	112.082i	0.0735748	+	0.177625i	−0.882813	+	0.469724i	$0.844354\pi$
$632$	376.588	−	251.628i	0.595867	−	0.398145i
$633$	17.4543	−	17.4543i	0.0275740	−	0.0275740i
$634$	−279.197	−	55.5357i	−0.440373	−	0.0875957i
$635$	446.087	+	298.066i	0.702499	+	0.469395i
$636$	−91.7230	+	18.2448i	−0.144219	+	0.0286869i
$637$	−75.9247	−	31.4490i	−0.119191	−	0.0493706i
$638$	92.6063	−	223.571i	0.145151	−	0.350425i
$639$	−24.7159	−	124.255i	−0.0386790	−	0.194452i
$640$	152.188	−	227.766i	0.237794	−	0.355884i
$641$	−47.9641	+	241.132i	−0.0748270	+	0.376181i	−0.999994	−	0.00337889i	$-0.998924\pi$
$641$	−47.9641	+	241.132i	−0.0748270	+	0.376181i	0.925167	+	0.379560i	$0.123924\pi$
$642$	7.89872	+	7.89872i	0.0123033	+	0.0123033i
$643$	−63.5318	−	95.0820i	−0.0988052	−	0.147872i	0.778773	−	0.627306i	$-0.215842\pi$
$643$	−63.5318	−	95.0820i	−0.0988052	−	0.147872i	−0.877578	+	0.479433i	$0.840842\pi$
$644$	25.5274	−	10.5738i	0.0396389	−	0.0164190i
$645$			261.341i			0.405179i
$646$	−450.113	−	341.576i	−0.696770	−	0.528756i
$647$	−534.514			−0.826143			−0.413071	−	0.910699i	$-0.635544\pi$
$647$	−534.514			−0.826143			−0.413071	+	0.910699i	$0.635544\pi$
$648$	−116.103	−	280.299i	−0.179172	−	0.432560i
$649$	−108.832	+	72.7194i	−0.167692	+	0.112048i
$650$	7.92139	−	7.92139i	0.0121868	−	0.0121868i
$651$	139.535	+	27.7553i	0.214340	+	0.0426349i
$652$	−280.706	−	187.562i	−0.430531	−	0.287672i
$653$	788.185	−	156.780i	1.20702	−	0.240092i	0.449728	−	0.893166i	$-0.351521\pi$
$653$	788.185	−	156.780i	1.20702	−	0.240092i	0.757294	+	0.653074i	$0.226521\pi$
$654$	−87.3722	−	36.1907i	−0.133597	−	0.0553375i
$655$	−186.755	+	450.867i	−0.285123	+	0.688347i
$656$	−15.4721	−	77.7837i	−0.0235856	−	0.118573i
$657$	−89.5953	+	134.089i	−0.136370	+	0.204093i
$658$	−22.6639	+	113.939i	−0.0344437	+	0.173160i
$659$	382.598	+	382.598i	0.580574	+	0.580574i	0.935061	−	0.354487i	$-0.115344\pi$
$659$	382.598	+	382.598i	0.580574	+	0.580574i	−0.354487	+	0.935061i	$0.615344\pi$
$660$	44.7569	+	66.9834i	0.0678135	+	0.101490i
$661$	555.991	−	230.299i	0.841136	−	0.348410i	0.0798346	−	0.996808i	$-0.474561\pi$
$661$	555.991	−	230.299i	0.841136	−	0.348410i	0.761301	+	0.648398i	$0.224561\pi$
$662$		−	340.027i		−	0.513635i
$663$	5.78616	−	96.1538i	0.00872724	−	0.145028i
$664$	809.029			1.21842
$665$	−108.550	−	262.063i	−0.163233	−	0.394080i
$666$	18.0604	−	12.0676i	0.0271177	−	0.0181195i
$667$	−90.0575	+	90.0575i	−0.135019	+	0.135019i
$668$	642.034	+	127.709i	0.961129	+	0.191180i
$669$	−496.164	−	331.526i	−0.741650	−	0.495555i
$670$	133.942	−	26.6427i	0.199914	−	0.0397653i
$671$	−304.912	−	126.299i	−0.454414	−	0.188225i
$672$	−112.910	+	272.589i	−0.168021	+	0.405639i
$673$	−212.613	−	1068.88i	−0.315918	−	1.58823i	−0.733566	−	0.679618i	$-0.762146\pi$
$673$	−212.613	−	1068.88i	−0.315918	−	1.58823i	0.417648	−	0.908609i	$-0.362854\pi$
$674$	−100.909	+	151.021i	−0.149717	+	0.224067i
$675$	−28.6719	+	144.143i	−0.0424769	+	0.213546i
$676$	−354.901	−	354.901i	−0.525001	−	0.525001i
$677$	−239.398	−	358.284i	−0.353616	−	0.529223i	0.611432	−	0.791297i	$-0.290594\pi$
$677$	−239.398	−	358.284i	−0.353616	−	0.529223i	−0.965048	+	0.262074i	$0.915594\pi$
$678$	251.278	−	104.083i	0.370616	−	0.153514i
$679$			133.238i			0.196227i
$680$	113.495	−	233.281i	0.166904	−	0.343060i
$681$	969.098			1.42305
$682$	−28.0928	−	67.8221i	−0.0411918	−	0.0994458i
$683$	−448.957	+	299.984i	−0.657331	+	0.439215i	−0.838990	−	0.544147i	$-0.816853\pi$
$683$	−448.957	+	299.984i	−0.657331	+	0.439215i	0.181659	+	0.983362i	$0.441853\pi$
$684$	−226.693	+	226.693i	−0.331422	+	0.331422i
$685$	−337.512	−	67.1354i	−0.492719	−	0.0980078i
$686$	249.785	+	166.901i	0.364118	+	0.243296i
$687$	−1003.71	+	199.650i	−1.46100	+	0.290611i
$688$	−251.160	−	104.034i	−0.365058	−	0.151212i
$689$	11.0848	−	26.7610i	0.0160882	−	0.0388404i
$690$	2.51425	+	12.6400i	0.00364384	+	0.0183188i
$691$	595.542	−	891.292i	0.861855	−	1.28986i	−0.0938662	−	0.995585i	$-0.529923\pi$
$691$	595.542	−	891.292i	0.861855	−	1.28986i	0.955721	−	0.294273i	$-0.0950774\pi$
$692$	108.615	−	546.046i	0.156958	−	0.789083i
$693$	38.0513	+	38.0513i	0.0549081	+	0.0549081i
$694$	194.395	+	290.933i	0.280108	+	0.419211i
$695$	−378.551	+	156.801i	−0.544678	+	0.225613i
$696$		−	868.470i		−	1.24780i
$697$	−77.4940	−	224.342i	−0.111182	−	0.321869i
$698$	−305.955			−0.438331
$699$	239.048	+	577.113i	0.341986	+	0.825627i
$700$	46.9991	−	31.4038i	0.0671416	−	0.0448626i
$701$	747.664	−	747.664i	1.06657	−	1.06657i	0.0689480	−	0.997620i	$-0.478036\pi$
$701$	747.664	−	747.664i	1.06657	−	1.06657i	0.997620	−	0.0689480i	$-0.0219642\pi$
$702$	64.5909	+	12.8479i	0.0920099	+	0.0183019i
$703$	212.041	+	141.681i	0.301624	+	0.201538i
$704$	42.1448	−	8.38313i	0.0598648	−	0.0119079i
$705$	164.694	+	68.2186i	0.233609	+	0.0967639i
$706$	−40.5916	+	97.9969i	−0.0574952	+	0.138806i
$707$	−89.4385	−	449.638i	−0.126504	−	0.635980i
$708$	−113.274	+	169.526i	−0.159991	+	0.239444i
$709$	−26.7092	+	134.276i	−0.0376716	+	0.189388i	−0.995039	−	0.0994848i	$-0.968281\pi$
$709$	−26.7092	+	134.276i	−0.0376716	+	0.189388i	0.957367	+	0.288873i	$0.0932805\pi$
$710$	−63.7070	−	63.7070i	−0.0897282	−	0.0897282i
$711$	−111.947	−	167.540i	−0.157450	−	0.235640i
$712$	−617.143	+	255.629i	−0.866774	+	0.359030i
$713$			38.6358i			0.0541877i
$714$	−37.4741	+	142.907i	−0.0524848	+	0.200150i
$715$	−24.9519			−0.0348978
$716$	42.6843	+	103.049i	0.0596150	+	0.143923i
$717$	459.585	−	307.085i	0.640983	−	0.428291i
$718$	324.574	−	324.574i	0.452053	−	0.452053i
$719$	−178.522	−	35.5103i	−0.248292	−	0.0493884i	0.0693750	−	0.997591i	$-0.477900\pi$
$719$	−178.522	−	35.5103i	−0.248292	−	0.0493884i	−0.317667	+	0.948202i	$0.602900\pi$
$720$	−32.0653	−	21.4253i	−0.0445351	−	0.0297574i
$721$	−591.895	+	117.735i	−0.820937	+	0.163294i
$722$	734.953	+	304.427i	1.01794	+	0.421645i
$723$	428.184	−	1033.73i	0.592232	−	1.42977i
$724$	124.136	+	624.072i	0.171458	+	0.861977i
$725$	−144.752	+	216.637i	−0.199658	+	0.298809i
$726$	45.0254	−	226.358i	0.0620185	−	0.311788i
$727$	235.573	+	235.573i	0.324035	+	0.324035i	0.850313	−	0.526278i	$-0.176413\pi$
$727$	235.573	+	235.573i	0.324035	+	0.324035i	−0.526278	+	0.850313i	$0.676413\pi$
$728$	−32.4215	−	48.5223i	−0.0445351	−	0.0666514i
$729$	−721.559	+	298.880i	−0.989793	+	0.409986i
$730$			114.686i			0.157103i
$731$	−786.988	−	206.370i	−1.07659	−	0.282312i
$732$	−514.089			−0.702307
$733$	−258.816	−	624.836i	−0.353091	−	0.852437i	−0.996235	−	0.0866918i	$-0.972370\pi$
$733$	−258.816	−	624.836i	−0.353091	−	0.852437i	0.643144	−	0.765745i	$-0.277630\pi$
$734$	−104.189	+	69.6168i	−0.141947	+	0.0948458i
$735$	136.760	−	136.760i	0.186068	−	0.186068i
$736$	−78.5864	−	15.6318i	−0.106775	−	0.0212389i
$737$	−252.916	−	168.993i	−0.343170	−	0.229299i
$738$	40.1466	−	7.98566i	0.0543992	−	0.0108207i
$739$	−398.638	−	165.121i	−0.539429	−	0.223439i	0.0962982	−	0.995353i	$-0.469300\pi$
$739$	−398.638	−	165.121i	−0.539429	−	0.223439i	−0.635727	+	0.771914i	$0.719300\pi$
$740$	−19.4476	+	46.9507i	−0.0262806	+	0.0634469i
$741$	38.0510	+	191.295i	0.0513509	+	0.258158i
$742$	−24.6814	+	36.9383i	−0.0332633	+	0.0497821i
$743$	−181.893	+	914.439i	−0.244809	+	1.23074i	0.641310	+	0.767282i	$0.278391\pi$
$743$	−181.893	+	914.439i	−0.244809	+	1.23074i	−0.886119	+	0.463457i	$0.846609\pi$
$744$	−186.292	−	186.292i	−0.250393	−	0.250393i
$745$	−70.9689	−	106.212i	−0.0952602	−	0.142567i
$746$	537.500	−	222.640i	0.720509	−	0.298445i
$747$		−	359.929i		−	0.481832i
$748$	−237.053	+	81.8847i	−0.316916	+	0.109472i
$749$	−17.4574			−0.0233077
$750$	10.0893	+	24.3578i	0.0134525	+	0.0324771i
$751$	277.138	−	185.177i	0.369025	−	0.246574i	−0.357206	−	0.934026i	$-0.616271\pi$
$751$	277.138	−	185.177i	0.369025	−	0.246574i	0.726231	+	0.687451i	$0.241271\pi$
$752$	−131.122	+	131.122i	−0.174365	+	0.174365i
$753$	252.037	+	50.1332i	0.334710	+	0.0665780i
$754$	97.0753	+	64.8637i	0.128747	+	0.0860261i
$755$	129.529	−	25.7650i	0.171562	−	0.0341258i
$756$	307.001	+	127.164i	0.406086	+	0.168206i
$757$	160.378	−	387.187i	0.211860	−	0.511475i	−0.781849	−	0.623468i	$-0.785723\pi$
$757$	160.378	−	387.187i	0.211860	−	0.511475i	0.993709	+	0.111993i	$0.0357233\pi$
$758$	66.3319	+	333.473i	0.0875091	+	0.439938i
$759$	15.9477	−	23.8674i	0.0210115	−	0.0314459i
$760$	−102.477	+	515.186i	−0.134838	+	0.677876i
$761$	947.231	+	947.231i	1.24472	+	1.24472i	0.958021	+	0.286698i	$0.0925575\pi$
$761$	947.231	+	947.231i	1.24472	+	1.24472i	0.286698	+	0.958021i	$0.407442\pi$
$762$	314.337	+	470.438i	0.412516	+	0.617373i
$763$	136.547	−	56.5596i	0.178961	−	0.0741280i
$764$			571.120i			0.747539i
$765$	−103.784	−	50.4927i	−0.135666	−	0.0660035i
$766$	239.481			0.312639
$767$	−24.1664	−	58.3430i	−0.0315077	−	0.0760664i
$768$	312.770	−	208.986i	0.407252	−	0.272117i
$769$	−420.026	+	420.026i	−0.546198	+	0.546198i	−0.925339	−	0.379141i	$-0.876219\pi$
$769$	−420.026	+	420.026i	−0.546198	+	0.546198i	0.379141	+	0.925339i	$0.376219\pi$
$770$	37.5337	+	7.46591i	0.0487450	+	0.00969599i
$771$	−168.188	−	112.380i	−0.218143	−	0.145758i
$772$	810.724	−	161.263i	1.05016	−	0.208890i
$773$	−272.733	−	112.970i	−0.352825	−	0.146145i	0.199230	−	0.979953i	$-0.436156\pi$
$773$	−272.733	−	112.970i	−0.352825	−	0.146145i	−0.552054	+	0.833808i	$0.686156\pi$
$774$	53.6951	−	129.631i	0.0693735	−	0.167483i
$775$	15.4197	+	77.5202i	0.0198964	+	0.100026i
$776$	137.078	−	205.152i	0.176647	−	0.264371i
$777$	13.0083	−	65.3972i	0.0167417	−	0.0841663i
$778$	−254.022	−	254.022i	−0.326507	−	0.326507i
$779$	266.997	+	399.590i	0.342744	+	0.512952i
$780$	−35.9086	+	14.8738i	−0.0460366	+	0.0190690i
$781$			200.673i			0.256944i
$782$	−40.0488	−	2.40998i	−0.0512133	−	0.00308182i
$783$	−1531.68			−1.95616
$784$	76.9914	+	185.874i	0.0982033	+	0.237084i
$785$	−9.62278	+	6.42973i	−0.0122583	+	0.00819074i
$786$	−363.916	+	363.916i	−0.462998	+	0.462998i
$787$	−816.561	−	162.424i	−1.03756	−	0.206384i	−0.353216	−	0.935542i	$-0.614912\pi$
$787$	−816.561	−	162.424i	−1.03756	−	0.206384i	−0.684346	+	0.729158i	$0.739912\pi$
$788$	562.115	+	375.593i	0.713344	+	0.476641i
$789$	−5.80087	+	1.15387i	−0.00735218	+	0.00146244i
$790$	−132.388	−	54.8370i	−0.167580	−	0.0694140i
$791$	−162.663	+	392.703i	−0.205642	+	0.496463i
$792$	−19.4411	−	97.7368i	−0.0245468	−	0.123405i
$793$	88.4627	−	132.394i	0.111554	−	0.166953i
$794$	−142.729	+	717.548i	−0.179760	+	0.903713i
$795$	48.2035	+	48.2035i	0.0606334	+	0.0606334i
$796$	424.772	+	635.716i	0.533633	+	0.798638i
$797$	−807.124	+	334.322i	−1.01270	+	0.419475i	−0.826440	−	0.563025i	$-0.809637\pi$
$797$	−807.124	+	334.322i	−1.01270	+	0.419475i	−0.186263	+	0.982500i	$0.559637\pi$
$798$		−	299.139i		−	0.374861i
$799$	−335.482	+	442.083i	−0.419878	+	0.553295i
$800$	−163.917			−0.204896
$801$	113.727	+	274.560i	0.141981	+	0.342772i
$802$	324.125	−	216.573i	0.404146	−	0.270041i
$803$	180.626	−	180.626i	0.224939	−	0.224939i
$804$	−464.711	−	92.4368i	−0.577999	−	0.114971i
$805$	−16.7466	−	11.1897i	−0.0208033	−	0.0139003i
$806$	34.7369	−	6.90960i	0.0430979	−	0.00857271i
$807$	323.652	+	134.061i	0.401056	+	0.166123i
$808$	−324.884	+	784.339i	−0.402084	+	0.970716i
$809$	−136.966	−	688.576i	−0.169303	−	0.851145i	−0.968296	−	0.249805i	$-0.919634\pi$
$809$	−136.966	−	688.576i	−0.169303	−	0.851145i	0.798993	−	0.601340i	$-0.205366\pi$
$810$	−53.3285	+	79.8117i	−0.0658376	+	0.0985329i
$811$	234.186	−	1177.33i	0.288762	−	1.45171i	−0.515222	−	0.857056i	$-0.672291\pi$
$811$	234.186	−	1177.33i	0.288762	−	1.45171i	0.803985	−	0.594650i	$-0.202709\pi$
$812$	416.557	+	416.557i	0.513001	+	0.513001i
$813$	69.9733	+	104.722i	0.0860680	+	0.128810i
$814$	−31.7867	+	13.1665i	−0.0390501	+	0.0161751i
$815$			246.091i			0.301952i
$816$	−176.467	+	156.434i	−0.216259	+	0.191709i
$817$	1647.36			2.01635
$818$	162.583	+	392.510i	0.198757	+	0.479841i
$819$	−21.5870	+	14.4240i	−0.0263578	+	0.0176117i
$820$	−67.7182	+	67.7182i	−0.0825832	+	0.0825832i
$821$	−52.7387	−	10.4904i	−0.0642371	−	0.0127776i	0.162867	−	0.986648i	$-0.447926\pi$
$821$	−52.7387	−	10.4904i	−0.0642371	−	0.0127776i	−0.227104	+	0.973870i	$0.572926\pi$
$822$	−301.748	−	201.622i	−0.367091	−	0.245282i
$823$	1145.72	−	227.898i	1.39213	−	0.276911i	0.558621	−	0.829423i	$-0.311331\pi$
$823$	1145.72	−	227.898i	1.39213	−	0.276911i	0.833505	+	0.552512i	$0.186331\pi$
$824$	1032.49	+	427.671i	1.25302	+	0.519019i
$825$	22.4724	−	54.2533i	0.0272393	−	0.0657615i
$826$	18.8952	+	94.9927i	0.0228756	+	0.115003i
$827$	−328.920	+	492.264i	−0.397727	+	0.595241i	−0.975242	−	0.221139i	$-0.929022\pi$
$827$	−328.920	+	492.264i	−0.397727	+	0.595241i	0.577515	+	0.816380i	$0.304022\pi$
$828$	−4.44099	+	22.3263i	−0.00536351	+	0.0269642i
$829$	565.240	+	565.240i	0.681833	+	0.681833i	0.960413	−	0.278580i	$-0.0898637\pi$
$829$	565.240	+	565.240i	0.681833	+	0.681833i	−0.278580	+	0.960413i	$0.589864\pi$
$830$	−142.206	−	212.826i	−0.171332	−	0.256417i
$831$	−806.817	+	334.194i	−0.970898	+	0.402159i
$832$			20.7316i			0.0249178i
$833$	303.839	+	519.826i	0.364752	+	0.624041i
$834$	−432.108			−0.518115
$835$	−182.605	−	440.848i	−0.218689	−	0.527962i
$836$	422.230	−	282.125i	0.505059	−	0.337470i
$837$	−328.554	+	328.554i	−0.392538	+	0.392538i
$838$	−602.446	−	119.834i	−0.718909	−	0.143000i
$839$	1264.66	+	845.022i	1.50735	+	1.00718i	0.988315	+	0.152423i	$0.0487077\pi$
$839$	1264.66	+	845.022i	1.50735	+	1.00718i	0.519033	+	0.854754i	$0.326292\pi$
$840$	134.702	−	26.7940i	0.160360	−	0.0318976i
$841$	−1731.71	−	717.297i	−2.05911	−	0.852910i
$842$	243.587	−	588.071i	0.289296	−	0.698422i
$843$	−227.614	−	1144.29i	−0.270004	−	1.35740i
$844$	17.2263	−	25.7809i	0.0204103	−	0.0305461i
$845$	−71.3752	+	358.827i	−0.0844677	+	0.424648i
$846$	−67.6762	−	67.6762i	−0.0799956	−	0.0799956i
$847$	200.387	+	299.901i	0.236585	+	0.354074i
$848$	−65.5145	+	27.1370i	−0.0772576	+	0.0320012i
$849$		−	536.470i		−	0.631885i
$850$	−81.3171	+	11.1482i	−0.0956671	+	0.0131155i
$851$	18.1078			0.0212782
$852$	119.621	+	288.791i	0.140400	+	0.338957i
$853$	216.944	−	144.957i	0.254330	−	0.169938i	−0.421869	−	0.906657i	$-0.638626\pi$
$853$	216.944	−	144.957i	0.254330	−	0.169938i	0.676199	+	0.736719i	$0.263626\pi$
$854$	−172.683	+	172.683i	−0.202205	+	0.202205i
$855$	229.201	+	45.5909i	0.268071	+	0.0533227i
$856$	26.8798	+	17.9605i	0.0314017	+	0.0209819i
$857$	1194.09	−	237.520i	1.39334	−	0.277153i	0.559350	−	0.828932i	$-0.311051\pi$
$857$	1194.09	−	237.520i	1.39334	−	0.277153i	0.833990	+	0.551779i	$0.186051\pi$
$858$	−24.3110	−	10.0699i	−0.0283345	−	0.0117365i
$859$	−137.942	+	333.021i	−0.160584	+	0.387685i	−0.983607	−	0.180323i	$-0.942286\pi$
$859$	−137.942	+	333.021i	−0.160584	+	0.387685i	0.823023	+	0.568008i	$0.192286\pi$
$860$	64.0437	+	321.969i	0.0744694	+	0.374383i
$861$	69.8100	−	104.478i	0.0810802	−	0.121345i
$862$	−6.79900	+	34.1809i	−0.00788747	+	0.0396530i
$863$	−503.780	−	503.780i	−0.583754	−	0.583754i	0.352178	−	0.935933i	$-0.385441\pi$
$863$	−503.780	−	503.780i	−0.583754	−	0.583754i	−0.935933	+	0.352178i	$0.885441\pi$
$864$	−535.358	−	801.220i	−0.619627	−	0.927338i
$865$	−374.938	+	155.304i	−0.433455	+	0.179543i
$866$			30.8789i			0.0356569i
$867$	−459.643	+	535.567i	−0.530153	+	0.617724i
$868$	178.708			0.205885
$869$	122.141	+	294.874i	0.140553	+	0.339326i
$870$	−228.463	+	152.654i	−0.262601	+	0.175464i
$871$	103.771	−	103.771i	0.119140	−	0.119140i
$872$	−268.436	−	53.3952i	−0.307839	−	0.0612330i
$873$	−91.2698	−	60.9845i	−0.104547	−	0.0698563i
$874$	79.6760	−	15.8485i	0.0911624	−	0.0181333i
$875$	−38.0669	−	15.7678i	−0.0435051	−	0.0180204i
$876$	152.270	−	367.613i	0.173824	−	0.419649i
$877$	−142.612	−	716.957i	−0.162613	−	0.817511i	−0.972855	−	0.231415i	$-0.925664\pi$
$877$	−142.612	−	716.957i	−0.162613	−	0.817511i	0.810242	−	0.586095i	$-0.199336\pi$
$878$	−130.420	+	195.187i	−0.148542	+	0.222309i
$879$	237.229	−	1192.63i	0.269886	−	1.35681i
$880$	43.1940	+	43.1940i	0.0490841	+	0.0490841i
$881$	206.168	+	308.553i	0.234016	+	0.350230i	0.929828	−	0.367994i	$-0.119955\pi$
$881$	206.168	+	308.553i	0.234016	+	0.350230i	−0.695812	+	0.718224i	$0.744955\pi$
$882$	−95.9352	+	39.7377i	−0.108770	+	0.0450540i
$883$			1572.78i			1.78118i	0.454805	+	0.890591i	$0.349709\pi$
$883$			1572.78i			1.78118i	−0.454805	+	0.890591i	$0.650291\pi$
$884$	−16.4348	−	119.879i	−0.0185914	−	0.135609i
$885$	148.621			0.167933
$886$	249.270	+	601.791i	0.281343	+	0.679223i
$887$	−792.790	+	529.725i	−0.893788	+	0.597210i	−0.915395	−	0.402557i	$-0.868122\pi$
$887$	−792.790	+	529.725i	−0.893788	+	0.597210i	0.0216074	+	0.999767i	$0.493122\pi$
$888$	−87.3112	+	87.3112i	−0.0983234	+	0.0983234i
$889$	−867.241	−	172.505i	−0.975524	−	0.194044i
$890$	175.724	+	117.415i	0.197443	+	0.131927i
$891$	209.692	−	41.7103i	0.235344	−	0.0468129i
$892$	−692.513	−	286.848i	−0.776360	−	0.321579i
$893$	430.015	−	1038.15i	0.481540	−	1.16254i
$894$	−26.2814	−	132.125i	−0.0293975	−	0.147791i
$895$	45.1707	−	67.6028i	0.0504701	−	0.0755339i
$896$	−88.0786	+	442.801i	−0.0983020	+	0.494198i
$897$	9.79279	+	9.79279i	0.0109173	+	0.0109173i
$898$	281.297	+	420.991i	0.313249	+	0.468810i
$899$	−761.031	+	315.229i	−0.846530	+	0.350644i
$900$			46.5688i			0.0517431i
$901$	−183.222	+	107.093i	−0.203354	+	0.118861i
$902$	−64.8372			−0.0718816
$903$	−164.831	−	397.937i	−0.182537	−	0.440684i
$904$	654.477	−	437.307i	0.723979	−	0.483747i
$905$	327.971	−	327.971i	0.362398	−	0.362398i
$906$	136.600	+	27.1715i	0.150773	+	0.0299906i
$907$	17.0762	+	11.4100i	0.0188271	+	0.0125799i	0.564948	−	0.825126i	$-0.308896\pi$
$907$	17.0762	+	11.4100i	0.0188271	+	0.0125799i	−0.546121	+	0.837706i	$0.683896\pi$
$908$	1193.92	−	237.485i	1.31489	−	0.261548i
$909$	348.944	+	144.537i	0.383877	+	0.159007i
$910$	−7.06559	+	17.0579i	−0.00776439	+	0.0187449i
$911$	12.6018	+	63.3533i	0.0138329	+	0.0695426i	0.987085	−	0.160196i	$-0.0512128\pi$
$911$	12.6018	+	63.3533i	0.0138329	+	0.0695426i	−0.973252	+	0.229739i	$0.926213\pi$
$912$	265.280	−	397.019i	0.290877	−	0.435328i
$913$	−111.225	+	559.165i	−0.121823	+	0.612448i
$914$	−376.198	−	376.198i	−0.411595	−	0.411595i
$915$	208.193	+	311.583i	0.227534	+	0.340528i
$916$	−1187.63	+	491.933i	−1.29654	+	0.537045i
$917$		−	804.314i		−	0.877115i
$918$	−320.076	−	361.064i	−0.348666	−	0.393316i
$919$	−1708.90			−1.85952			−0.929760	−	0.368167i	$-0.879986\pi$
$919$	−1708.90			−1.85952			−0.929760	+	0.368167i	$0.879986\pi$
$920$	14.2732	+	34.4585i	0.0155143	+	0.0374549i
$921$	312.338	−	208.697i	0.339129	−	0.226599i
$922$	−166.492	+	166.492i	−0.180577	+	0.180577i
$923$	−94.9566	−	18.8880i	−0.102878	−	0.0204638i
$924$	−110.398	−	73.7654i	−0.119478	−	0.0798326i
$925$	36.3321	−	7.22689i	0.0392779	−	0.00781286i
$926$	328.307	+	135.989i	0.354544	+	0.146857i
$927$	190.266	−	459.344i	0.205250	−	0.495517i
$928$	−333.278	−	1675.50i	−0.359135	−	1.80550i
$929$	−71.3897	+	106.842i	−0.0768458	+	0.115008i	−0.867902	−	0.496736i	$-0.834532\pi$
$929$	−71.3897	+	106.842i	−0.0768458	+	0.115008i	0.791056	+	0.611744i	$0.209532\pi$
$930$	−16.2615	+	81.7519i	−0.0174854	+	0.0879053i
$931$	−862.066	−	862.066i	−0.925957	−	0.925957i
$932$	435.931	+	652.418i	0.467738	+	0.700019i
$933$	−693.985	+	287.458i	−0.743821	+	0.308101i
$934$		−	40.7602i		−	0.0436405i
$935$	145.630	+	110.514i	0.155754	+	0.118197i
$936$	48.0780			0.0513654
$937$	479.379	+	1157.32i	0.511610	+	1.23514i	0.942946	+	0.332945i	$0.108042\pi$
$937$	479.379	+	1157.32i	0.511610	+	1.23514i	−0.431336	+	0.902191i	$0.641958\pi$
$938$	−187.147	+	125.047i	−0.199517	+	0.133313i
$939$	413.477	−	413.477i	0.440338	−	0.440338i
$940$	219.619	+	43.6850i	0.233638	+	0.0464734i
$941$	−251.481	−	168.034i	−0.267249	−	0.178570i	0.414725	−	0.909947i	$-0.363878\pi$
$941$	−251.481	−	168.034i	−0.267249	−	0.178570i	−0.681973	+	0.731377i	$0.738878\pi$
$942$	−11.9705	+	2.38107i	−0.0127075	+	0.00252768i
$943$	31.5264	+	13.0587i	0.0334320	+	0.0138480i
$944$	−59.1626	+	142.831i	−0.0626723	+	0.151304i
$945$	−47.2551	−	237.568i	−0.0500054	−	0.251394i
$946$	−123.476	+	184.795i	−0.130525	+	0.195344i
$947$	64.3908	−	323.715i	0.0679946	−	0.341832i	−0.931781	−	0.363021i	$-0.881745\pi$
$947$	64.3908	−	323.715i	0.0679946	−	0.341832i	0.999775	+	0.0211894i	$0.00674530\pi$
$948$	351.549	+	351.549i	0.370832	+	0.370832i
$949$	68.4694	+	102.472i	0.0721490	+	0.107979i
$950$	153.539	−	63.5981i	0.161620	−	0.0669454i
$951$		−	719.933i		−	0.757027i
$952$	−25.6828	+	426.794i	−0.0269777	+	0.448313i
$953$	519.872			0.545511			0.272755	−	0.962083i	$-0.412065\pi$
$953$	519.872			0.545511			0.272755	+	0.962083i	$0.412065\pi$
$954$	−14.0062	−	33.8141i	−0.0146816	−	0.0354445i
$955$	346.149	−	231.289i	0.362460	−	0.242188i
$956$	490.951	−	490.951i	0.513547	−	0.513547i
$957$	600.247	+	119.397i	0.627218	+	0.124761i
$958$	−47.7223	−	31.8870i	−0.0498145	−	0.0332850i
$959$	556.265	−	110.648i	0.580047	−	0.115379i
$960$	−45.0769	−	18.6715i	−0.0469551	−	0.0194494i
$961$	272.132	−	656.984i	0.283175	−	0.683646i
$962$	−3.23838	−	16.2805i	−0.00336630	−	0.0169235i
$963$	7.99045	−	11.9586i	0.00829746	−	0.0124180i
$964$	274.195	−	1378.47i	0.284435	−	1.42995i
$965$	−426.063	−	426.063i	−0.441516	−	0.441516i
$966$	−11.8006	−	17.6608i	−0.0122159	−	0.0182824i
$967$	1113.70	−	461.309i	1.15171	−	0.477052i	0.276600	−	0.960985i	$-0.410792\pi$
$967$	1113.70	−	461.309i	1.15171	−	0.477052i	0.875105	+	0.483933i	$0.160792\pi$
$968$		−	667.930i		−	0.690010i
$969$	625.179	−	1285.01i	0.645180	−	1.32612i
$970$	−78.0626			−0.0804769
$971$	445.904	+	1076.51i	0.459222	+	1.10866i	0.968713	+	0.248184i	$0.0798336\pi$
$971$	445.904	+	1076.51i	0.459222	+	1.10866i	−0.509491	+	0.860476i	$0.670166\pi$
$972$	−397.832	+	265.823i	−0.409292	+	0.273480i
$973$	477.515	−	477.515i	0.490766	−	0.490766i
$974$	536.680	+	106.752i	0.551006	+	0.109602i
$975$	23.5569	+	15.7402i	0.0241610	+	0.0161438i
$976$	−382.322	+	76.0486i	−0.391724	+	0.0779187i
$977$	496.049	+	205.470i	0.507727	+	0.210307i	0.621816	−	0.783163i	$-0.286395\pi$
$977$	496.049	+	205.470i	0.507727	+	0.210307i	−0.114090	+	0.993470i	$0.536395\pi$
$978$	−99.3157	+	239.769i	−0.101550	+	0.245163i
$979$	−91.8349	−	461.685i	−0.0938048	−	0.471589i
$980$	134.973	−	202.001i	0.137728	−	0.206124i
$981$	−23.7550	+	119.424i	−0.0242150	+	0.121737i
$982$	−338.208	−	338.208i	−0.344407	−	0.344407i
$983$	−247.073	−	369.770i	−0.251345	−	0.376165i	0.684245	−	0.729252i	$-0.260132\pi$
$983$	−247.073	−	369.770i	−0.251345	−	0.376165i	−0.935590	+	0.353087i	$0.885132\pi$
$984$	−214.978	+	89.0467i	−0.218473	+	0.0904947i
$985$		−	492.797i		−	0.500302i
$986$	−279.287	−	808.526i	−0.283252	−	0.820006i
$987$	−293.802			−0.297672
$988$	93.7570	+	226.349i	0.0948958	+	0.229099i
$989$	97.2580	−	64.9857i	0.0983397	−	0.0657085i
$990$	−22.2938	+	22.2938i	−0.0225190	+	0.0225190i
$991$	−1092.29	−	217.270i	−1.10221	−	0.219243i	−0.389725	−	0.920931i	$-0.627430\pi$
$991$	−1092.29	−	217.270i	−1.10221	−	0.219243i	−0.712484	+	0.701688i	$0.752430\pi$
$992$	−430.895	−	287.915i	−0.434370	−	0.290237i
$993$	843.417	−	167.766i	0.849363	−	0.168949i
$994$	137.186	+	56.8243i	0.138014	+	0.0571673i
$995$	213.278	−	514.898i	0.214350	−	0.517486i
$996$	173.253	+	871.002i	0.173949	+	0.874500i
$997$	−906.023	+	1355.96i	−0.908750	+	1.36004i	0.0240755	+	0.999710i	$0.492336\pi$
$997$	−906.023	+	1355.96i	−0.908750	+	1.36004i	−0.932825	+	0.360330i	$0.882664\pi$
$998$	45.1686	−	227.078i	0.0452591	−	0.227533i
$999$	153.986	+	153.986i	0.154140	+	0.154140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.3.q.a.46.6	✓	96
5.2	odd	4		425.3.t.e.199.7		96
5.3	odd	4		425.3.t.h.199.6		96
5.4	even	2		425.3.u.e.301.7		96
17.10	odd	16	inner	85.3.q.a.61.6	yes	96
85.27	even	16		425.3.t.h.299.6		96
85.44	odd	16		425.3.u.e.401.7		96
85.78	even	16		425.3.t.e.299.7		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.3.q.a.46.6	✓	96	1.1	even	1	trivial
85.3.q.a.61.6	yes	96	17.10	odd	16	inner
425.3.t.e.199.7		96	5.2	odd	4
425.3.t.e.299.7		96	85.78	even	16
425.3.t.h.199.6		96	5.3	odd	4
425.3.t.h.299.6		96	85.27	even	16
425.3.u.e.301.7		96	5.4	even	2
425.3.u.e.401.7		96	85.44	odd	16

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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	85.q (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.369527 - 0.892116i) q^{2} +(2.03052 - 1.35675i) q^{3} +(2.16911 - 2.16911i) q^{4} +(-2.19310 - 0.436235i) q^{5} +(-1.96072 - 1.31011i) q^{6} +(3.61453 - 0.718974i) q^{7} +(-6.30510 - 2.61166i) q^{8} +(-1.16190 + 2.80507i) q^{9} +(0.421237 + 2.11770i) q^{10} +(2.67188 - 3.99876i) q^{11} +(1.46148 - 7.34736i) q^{12} +(1.64069 + 1.64069i) q^{13} +(-1.97707 - 2.95890i) q^{14} +(-5.04501 + 2.08971i) q^{15} -5.68035i q^{16} +(-2.30902 - 16.8425i) q^{17} +2.93181 q^{18} +(13.1725 + 31.8012i) q^{19} +(-5.70331 + 3.81083i) q^{20} +(6.36391 - 6.36391i) q^{21} +(-4.55469 - 0.905984i) q^{22} +(2.03220 + 1.35787i) q^{23} +(-16.3460 + 3.25143i) q^{24} +(4.61940 + 1.91342i) q^{25} +(0.857405 - 2.06996i) q^{26} +(5.73438 + 28.8287i) q^{27} +(6.28076 - 9.39982i) q^{28} +(-10.1660 + 51.1081i) q^{29} +(3.72853 + 3.72853i) q^{30} +(8.78233 + 13.1437i) q^{31} +(-30.2879 + 12.5457i) q^{32} -11.7447i q^{33} +(-14.1722 + 8.28365i) q^{34} -8.24067 q^{35} +(3.56422 + 8.60478i) q^{36} +(6.16017 - 4.11609i) q^{37} +(23.5028 - 23.5028i) q^{38} +(5.55746 + 1.10545i) q^{39} +(12.6884 + 8.47814i) q^{40} +(13.6935 - 2.72380i) q^{41} +(-8.02899 - 3.32572i) q^{42} +(18.3147 - 44.2156i) q^{43} +(-2.87813 - 14.4693i) q^{44} +(3.77184 - 5.64495i) q^{45} +(0.460427 - 2.31472i) q^{46} +(-23.0835 - 23.0835i) q^{47} +(-7.70683 - 11.5341i) q^{48} +(-32.7222 + 13.5540i) q^{49} -4.82810i q^{50} +(-27.5396 - 31.0663i) q^{51} +7.11764 q^{52} +(-4.77734 - 11.5335i) q^{53} +(23.5995 - 15.7687i) q^{54} +(-7.60411 + 7.60411i) q^{55} +(-24.6677 - 4.90671i) q^{56} +(69.8934 + 46.7013i) q^{57} +(49.3510 - 9.81653i) q^{58} +(-25.1448 - 10.4153i) q^{59} +(-6.41036 + 15.4760i) q^{60} +(-13.3880 - 67.3061i) q^{61} +(8.48040 - 12.6918i) q^{62} +(-2.18294 + 10.9744i) q^{63} +(6.31796 + 6.31796i) q^{64} +(-2.88247 - 4.31392i) q^{65} +(-10.4776 + 4.33997i) q^{66} -63.2487i q^{67} +(-41.5416 - 31.5246i) q^{68} +5.96872 q^{69} +(3.04515 + 7.35164i) q^{70} +(-34.6942 + 23.1819i) q^{71} +(14.6518 - 14.6518i) q^{72} +(52.0944 + 10.3622i) q^{73} +(-5.94838 - 3.97458i) q^{74} +(11.9758 - 2.38214i) q^{75} +(97.5527 + 40.4076i) q^{76} +(6.78259 - 16.3746i) q^{77} +(-1.06744 - 5.36639i) q^{78} +(-36.8708 + 55.1810i) q^{79} +(-2.47797 + 12.4576i) q^{80} +(31.4350 + 31.4350i) q^{81} +(-7.49005 - 11.2097i) q^{82} +(-109.522 + 45.3657i) q^{83} -27.6080i q^{84} +(-2.28335 + 37.9445i) q^{85} -46.2132 q^{86} +(48.6987 + 117.569i) q^{87} +(-27.2899 + 18.2345i) q^{88} +(69.2116 - 69.2116i) q^{89} +(-6.42975 - 1.27896i) q^{90} +(7.10991 + 4.75069i) q^{91} +(7.35341 - 1.46268i) q^{92} +(35.6655 + 14.7731i) q^{93} +(-12.0632 + 29.1231i) q^{94} +(-15.0158 - 75.4896i) q^{95} +(-44.4790 + 66.5676i) q^{96} +(-7.05322 + 35.4589i) q^{97} +(24.1835 + 24.1835i) q^{98} +(8.11235 + 12.1410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 192 q^{12} - 48 q^{13} - 64 q^{14} + 16 q^{17} + 128 q^{18} + 48 q^{19} + 192 q^{22} + 112 q^{23} + 240 q^{24} - 224 q^{26} - 288 q^{27} - 480 q^{28} - 64 q^{31} - 80 q^{32} + 64 q^{34} + 192 q^{36}+ \cdots - 592 q^{99}+O(q^{100}) \) 96 * q - 192 * q^12 - 48 * q^13 - 64 * q^14 + 16 * q^17 + 128 * q^18 + 48 * q^19 + 192 * q^22 + 112 * q^23 + 240 * q^24 - 224 * q^26 - 288 * q^27 - 480 * q^28 - 64 * q^31 - 80 * q^32 + 64 * q^34 + 192 * q^36 + 256 * q^37 + 208 * q^38 + 16 * q^39 - 320 * q^40 - 432 * q^41 + 864 * q^42 + 256 * q^43 - 32 * q^44 - 160 * q^45 - 48 * q^46 - 320 * q^48 - 32 * q^49 + 64 * q^51 + 192 * q^53 - 976 * q^54 + 160 * q^55 + 80 * q^56 - 1120 * q^57 + 512 * q^58 - 224 * q^59 + 640 * q^60 - 224 * q^61 - 560 * q^62 + 624 * q^63 + 160 * q^64 + 240 * q^65 + 48 * q^66 + 384 * q^69 + 48 * q^71 + 1040 * q^72 + 672 * q^74 + 496 * q^76 + 960 * q^77 + 768 * q^79 + 1424 * q^81 + 1200 * q^82 - 288 * q^83 + 64 * q^86 - 1344 * q^87 - 1664 * q^88 - 1152 * q^89 + 336 * q^91 - 2016 * q^92 - 1024 * q^93 - 1344 * q^94 + 768 * q^96 - 256 * q^97 - 816 * q^98 - 592 * q^99

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