LMFDB - Embedded newform 49.4.e.a.8.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,4,Mod(8,49)] 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("49.8"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([12])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	49.e (of order $7$, degree $6$, 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:	$2.89109359028$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			8.8
Character	$\chi$	$=$	49.8
Dual form			49.4.e.a.43.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.521845 + 0.654373i) q^{2} +(5.78023 - 2.78361i) q^{3} +(1.62429 - 7.11646i) q^{4} +(-1.28950 + 0.620991i) q^{5} +(4.83790 + 2.32981i) q^{6} +(-17.3557 - 6.46381i) q^{7} +(11.5371 - 5.55599i) q^{8} +(8.82835 - 11.0704i) q^{9} +(-1.07928 - 0.519753i) q^{10} +(33.8930 + 42.5005i) q^{11} +(-10.4207 - 45.6562i) q^{12} +(41.8811 + 52.5173i) q^{13} +(-4.82722 - 14.7302i) q^{14} +(-5.72501 + 7.17894i) q^{15} +(-42.9565 - 20.6868i) q^{16} +(-4.21013 - 18.4458i) q^{17} +11.8512 q^{18} -58.6213 q^{19} +(2.32474 + 10.1853i) q^{20} +(-118.313 + 10.9491i) q^{21} +(-10.1243 + 44.3573i) q^{22} +(-4.27322 + 18.7222i) q^{23} +(51.2216 - 64.2299i) q^{24} +(-76.6590 + 96.1274i) q^{25} +(-12.5104 + 54.8117i) q^{26} +(-18.3310 + 80.3133i) q^{27} +(-74.1900 + 113.012i) q^{28} +(-50.8862 - 222.947i) q^{29} -7.68527 q^{30} +165.221 q^{31} +(-31.6753 - 138.778i) q^{32} +(314.214 + 151.318i) q^{33} +(9.87339 - 12.3808i) q^{34} +(26.3941 - 2.44262i) q^{35} +(-64.4423 - 80.8081i) q^{36} +(-53.1486 - 232.859i) q^{37} +(-30.5912 - 38.3601i) q^{38} +(388.270 + 186.981i) q^{39} +(-11.4269 + 14.3289i) q^{40} +(-174.801 + 84.1798i) q^{41} +(-68.9056 - 71.7067i) q^{42} +(-206.174 - 99.2879i) q^{43} +(357.505 - 172.165i) q^{44} +(-4.50955 + 19.7576i) q^{45} +(-14.4812 + 6.97380i) q^{46} +(153.504 + 192.488i) q^{47} -305.882 q^{48} +(259.438 + 224.368i) q^{49} -102.907 q^{50} +(-75.6815 - 94.9016i) q^{51} +(441.764 - 212.742i) q^{52} +(118.302 - 518.313i) q^{53} +(-62.1207 + 29.9158i) q^{54} +(-70.0975 - 33.7572i) q^{55} +(-236.148 + 21.8540i) q^{56} +(-338.844 + 163.179i) q^{57} +(119.336 - 149.642i) q^{58} +(-150.933 - 72.6854i) q^{59} +(41.7896 + 52.4025i) q^{60} +(100.825 + 441.743i) q^{61} +(86.2197 + 108.116i) q^{62} +(-224.779 + 135.069i) q^{63} +(-163.531 + 205.062i) q^{64} +(-86.6185 - 41.7133i) q^{65} +(64.9530 + 284.578i) q^{66} +153.689 q^{67} -138.107 q^{68} +(27.4151 + 120.114i) q^{69} +(15.3720 + 15.9969i) q^{70} +(137.788 - 603.690i) q^{71} +(40.3468 - 176.771i) q^{72} +(-247.285 + 310.085i) q^{73} +(124.641 - 156.295i) q^{74} +(-175.526 + 769.028i) q^{75} +(-95.2177 + 417.176i) q^{76} +(-313.521 - 956.703i) q^{77} +(80.2615 + 351.649i) q^{78} -981.604 q^{79} +68.2387 q^{80} +(202.675 + 887.979i) q^{81} +(-146.304 - 70.4563i) q^{82} +(-258.066 + 323.604i) q^{83} +(-114.254 + 859.751i) q^{84} +(16.8836 + 21.1714i) q^{85} +(-42.6193 - 186.727i) q^{86} +(-914.732 - 1147.04i) q^{87} +(627.161 + 302.025i) q^{88} +(833.012 - 1044.56i) q^{89} +(-15.2821 + 7.35948i) q^{90} +(-387.413 - 1182.18i) q^{91} +(126.295 + 60.8204i) q^{92} +(955.016 - 459.911i) q^{93} +(-45.8536 + 200.898i) q^{94} +(75.5921 - 36.4033i) q^{95} +(-569.396 - 714.000i) q^{96} +1061.38 q^{97} +(-11.4335 + 286.854i) q^{98} +769.717 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + 9 q^{10} - 103 q^{11} + 364 q^{12} - 35 q^{13} + 161 q^{14} - 245 q^{15} - 205 q^{16} - 285 q^{17} + 16 q^{18} + 628 q^{19}+ \cdots + 10768 q^{99}+O(q^{100}) $ 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9 + 9 * q^10 - 103 * q^11 + 364 * q^12 - 35 * q^13 + 161 * q^14 - 245 * q^15 - 205 * q^16 - 285 * q^17 + 16 * q^18 + 628 * q^19 + 553 * q^20 - 21 * q^21 - 605 * q^22 + 149 * q^23 + 653 * q^24 - 370 * q^25 - 511 * q^26 - 65 * q^27 + 70 * q^28 - 187 * q^29 + 84 * q^30 + 1276 * q^31 + 1399 * q^32 - 23 * q^33 - 765 * q^34 - 805 * q^35 - 1691 * q^36 - 1531 * q^37 - 1041 * q^38 - 1351 * q^39 - 1759 * q^40 - 301 * q^41 + 3395 * q^42 - 257 * q^43 - 883 * q^44 + 3105 * q^45 + 1593 * q^46 + 733 * q^47 - 1948 * q^48 + 1288 * q^49 + 6148 * q^50 + 1197 * q^51 - 1099 * q^52 - 285 * q^53 + 660 * q^54 + 2641 * q^55 - 1988 * q^56 - 2352 * q^57 + 1173 * q^58 - 3603 * q^59 - 175 * q^60 - 2613 * q^61 - 1927 * q^62 - 3066 * q^63 + 1589 * q^64 - 371 * q^65 - 2175 * q^66 + 352 * q^67 + 6076 * q^68 + 5549 * q^69 - 6293 * q^70 - 2623 * q^71 + 6220 * q^72 + 2039 * q^73 - 2411 * q^74 - 3903 * q^75 + 4130 * q^76 + 1029 * q^77 - 3759 * q^78 + 44 * q^79 - 1608 * q^80 + 1394 * q^81 - 10920 * q^82 - 553 * q^83 - 7798 * q^84 + 497 * q^85 - 2985 * q^86 - 4273 * q^87 - 2197 * q^88 - 3957 * q^89 - 2958 * q^90 + 14119 * q^91 - 9136 * q^92 + 6272 * q^93 + 14912 * q^94 + 5866 * q^95 + 21882 * q^96 - 1540 * q^97 - 2303 * q^98 + 10768 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

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 $

$2$	0.521845	+	0.654373i	0.184500	+	0.231356i	0.865476	−	0.500950i	$-0.167016\pi$
$2$	0.521845	+	0.654373i	0.184500	+	0.231356i	−0.680976	+	0.732305i	$0.738444\pi$
$3$	5.78023	−	2.78361i	1.11241	−	0.535707i	0.214868	−	0.976643i	$-0.431068\pi$
$3$	5.78023	−	2.78361i	1.11241	−	0.535707i	0.897538	+	0.440937i	$0.145354\pi$
$4$	1.62429	−	7.11646i	0.203036	−	0.889558i
$5$	−1.28950	+	0.620991i	−0.115336	+	0.0555431i	−0.490662	−	0.871350i	$-0.663245\pi$
$5$	−1.28950	+	0.620991i	−0.115336	+	0.0555431i	0.375326	+	0.926893i	$0.377531\pi$
$6$	4.83790	+	2.32981i	0.329178	+	0.158524i
$7$	−17.3557	−	6.46381i	−0.937118	−	0.349013i
$7$	−17.3557	−	6.46381i	−0.937118	−	0.349013i
$8$	11.5371	−	5.55599i	0.509874	−	0.245543i
$9$	8.82835	−	11.0704i	0.326976	−	0.410015i
$10$	−1.07928	−	0.519753i	−0.0341298	−	0.0164360i
$11$	33.8930	+	42.5005i	0.929012	+	1.16494i	0.986029	+	0.166571i	$0.0532694\pi$
$11$	33.8930	+	42.5005i	0.929012	+	1.16494i	−0.0570176	+	0.998373i	$0.518159\pi$
$12$	−10.4207	−	45.6562i	−0.250684	−	1.09832i
$13$	41.8811	+	52.5173i	0.893518	+	1.12044i	0.992118	+	0.125309i	$0.0399923\pi$
$13$	41.8811	+	52.5173i	0.893518	+	1.12044i	−0.0985995	+	0.995127i	$0.531436\pi$
$14$	−4.82722	−	14.7302i	−0.0921520	−	0.281200i
$15$	−5.72501	+	7.17894i	−0.0985461	+	0.123573i
$16$	−42.9565	−	20.6868i	−0.671195	−	0.323231i
$17$	−4.21013	−	18.4458i	−0.0600651	−	0.263163i	0.935975	−	0.352066i	$-0.114521\pi$
$17$	−4.21013	−	18.4458i	−0.0600651	−	0.263163i	−0.996040	+	0.0889037i	$0.971664\pi$
$18$	11.8512			0.155186
$19$	−58.6213			−0.707823			−0.353912	−	0.935279i	$-0.615149\pi$
$19$	−58.6213			−0.707823			−0.353912	+	0.935279i	$0.615149\pi$
$20$	2.32474	+	10.1853i	0.0259914	+	0.113876i
$21$	−118.313	+	10.9491i	−1.22942	+	0.113776i
$22$	−10.1243	+	44.3573i	−0.0981137	+	0.429864i
$23$	−4.27322	+	18.7222i	−0.0387403	+	0.169732i	−0.990597	−	0.136810i	$-0.956315\pi$
$23$	−4.27322	+	18.7222i	−0.0387403	+	0.169732i	0.951857	+	0.306542i	$0.0991722\pi$
$24$	51.2216	−	64.2299i	0.435649	−	0.546286i
$25$	−76.6590	+	96.1274i	−0.613272	+	0.769019i
$26$	−12.5104	+	54.8117i	−0.0943652	+	0.413441i
$27$	−18.3310	+	80.3133i	−0.130659	+	0.572455i
$28$	−74.1900	+	113.012i	−0.500736	+	0.762758i
$29$	−50.8862	−	222.947i	−0.325839	−	1.42759i	−0.826981	−	0.562229i	$-0.809944\pi$
$29$	−50.8862	−	222.947i	−0.325839	−	1.42759i	0.501142	−	0.865365i	$-0.332913\pi$
$30$	−7.68527			−0.0467711
$31$	165.221			0.957244			0.478622	−	0.878021i	$-0.341136\pi$
$31$	165.221			0.957244			0.478622	+	0.878021i	$0.341136\pi$
$32$	−31.6753	−	138.778i	−0.174983	−	0.766650i
$33$	314.214	+	151.318i	1.65751	+	0.798213i
$34$	9.87339	−	12.3808i	0.0498021	−	0.0624499i
$35$	26.3941	−	2.44262i	0.127469	−	0.0117965i
$36$	−64.4423	−	80.8081i	−0.298344	−	0.374112i
$37$	−53.1486	−	232.859i	−0.236151	−	1.03464i	−0.944430	−	0.328711i	$-0.893386\pi$
$37$	−53.1486	−	232.859i	−0.236151	−	1.03464i	0.708280	−	0.705932i	$-0.249472\pi$
$38$	−30.5912	−	38.3601i	−0.130593	−	0.163759i
$39$	388.270	+	186.981i	1.59418	+	0.767717i
$40$	−11.4269	+	14.3289i	−0.0451689	+	0.0566400i
$41$	−174.801	+	84.1798i	−0.665838	+	0.320651i	−0.736095	−	0.676878i	$-0.763332\pi$
$41$	−174.801	+	84.1798i	−0.665838	+	0.320651i	0.0702570	+	0.997529i	$0.477618\pi$
$42$	−68.9056	−	71.7067i	−0.253151	−	0.263443i
$43$	−206.174	−	99.2879i	−0.731190	−	0.352123i	0.0309621	−	0.999521i	$-0.490143\pi$
$43$	−206.174	−	99.2879i	−0.731190	−	0.352123i	−0.762152	+	0.647398i	$0.775857\pi$
$44$	357.505	−	172.165i	1.22491	−	0.589884i
$45$	−4.50955	+	19.7576i	−0.0149387	+	0.0654509i
$46$	−14.4812	+	6.97380i	−0.0464161	+	0.0223528i
$47$	153.504	+	192.488i	0.476402	+	0.597389i	0.960726	−	0.277500i	$-0.0895059\pi$
$47$	153.504	+	192.488i	0.476402	+	0.597389i	−0.484324	+	0.874889i	$0.660934\pi$
$48$	−305.882			−0.919799
$49$	259.438	+	224.368i	0.756380	+	0.654133i
$50$	−102.907			−0.291066
$51$	−75.6815	−	94.9016i	−0.207795	−	0.260566i
$52$	441.764	−	212.742i	1.17811	−	0.567347i
$53$	118.302	−	518.313i	0.306603	−	1.34332i	−0.553352	−	0.832948i	$-0.686651\pi$
$53$	118.302	−	518.313i	0.306603	−	1.34332i	0.859955	−	0.510370i	$-0.170491\pi$
$54$	−62.1207	+	29.9158i	−0.156547	+	0.0753893i
$55$	−70.0975	−	33.7572i	−0.171854	−	0.0827603i
$56$	−236.148	+	21.8540i	−0.563510	+	0.0521495i
$57$	−338.844	+	163.179i	−0.787387	+	0.379185i
$58$	119.336	−	149.642i	0.270165	−	0.338776i
$59$	−150.933	−	72.6854i	−0.333047	−	0.160387i	0.259885	−	0.965640i	$-0.416315\pi$
$59$	−150.933	−	72.6854i	−0.333047	−	0.160387i	−0.592932	+	0.805253i	$0.702030\pi$
$60$	41.7896	+	52.4025i	0.0899169	+	0.112752i
$61$	100.825	+	441.743i	0.211628	+	0.927203i	0.963461	+	0.267849i	$0.0863129\pi$
$61$	100.825	+	441.743i	0.211628	+	0.927203i	−0.751833	+	0.659354i	$0.770830\pi$
$62$	86.2197	+	108.116i	0.176612	+	0.221464i
$63$	−224.779	+	135.069i	−0.449516	+	0.270113i
$64$	−163.531	+	205.062i	−0.319397	+	0.400511i
$65$	−86.6185	−	41.7133i	−0.165288	−	0.0795984i
$66$	64.9530	+	284.578i	0.121139	+	0.530744i
$67$	153.689			0.280239			0.140120	−	0.990135i	$-0.455251\pi$
$67$	153.689			0.280239			0.140120	+	0.990135i	$0.455251\pi$
$68$	−138.107			−0.246294
$69$	27.4151	+	120.114i	0.0478318	+	0.209565i
$70$	15.3720	+	15.9969i	0.0262472	+	0.0273142i
$71$	137.788	−	603.690i	0.230316	−	1.00908i	−0.719062	−	0.694946i	$-0.755428\pi$
$71$	137.788	−	603.690i	0.230316	−	1.00908i	0.949378	−	0.314135i	$-0.101715\pi$
$72$	40.3468	−	176.771i	0.0660406	−	0.289343i
$73$	−247.285	+	310.085i	−0.396473	+	0.497161i	−0.939498	−	0.342556i	$-0.888707\pi$
$73$	−247.285	+	310.085i	−0.396473	+	0.497161i	0.543025	+	0.839717i	$0.317279\pi$
$74$	124.641	−	156.295i	0.195801	−	0.245526i
$75$	−175.526	+	769.028i	−0.270239	+	1.18400i
$76$	−95.2177	+	417.176i	−0.143713	+	0.629650i
$77$	−313.521	−	956.703i	−0.464013	−	1.41593i
$78$	80.2615	+	351.649i	0.116511	+	0.510466i
$79$	−981.604			−1.39796			−0.698982	−	0.715139i	$-0.746363\pi$
$79$	−981.604			−1.39796			−0.698982	+	0.715139i	$0.746363\pi$
$80$	68.2387			0.0953665
$81$	202.675	+	887.979i	0.278018	+	1.21808i
$82$	−146.304	−	70.4563i	−0.197031	−	0.0948853i
$83$	−258.066	+	323.604i	−0.341282	+	0.427954i	−0.922621	−	0.385707i	$-0.873957\pi$
$83$	−258.066	+	323.604i	−0.341282	+	0.427954i	0.581339	+	0.813661i	$0.302529\pi$
$84$	−114.254	+	859.751i	−0.148407	+	1.11674i
$85$	16.8836	+	21.1714i	0.0215446	+	0.0270160i
$86$	−42.6193	−	186.727i	−0.0534390	−	0.234132i
$87$	−914.732	−	1147.04i	−1.12724	−	1.41351i
$88$	627.161	+	302.025i	0.759723	+	0.365863i
$89$	833.012	−	1044.56i	0.992125	−	1.24409i	0.0224347	−	0.999748i	$-0.492858\pi$
$89$	833.012	−	1044.56i	0.992125	−	1.24409i	0.969690	−	0.244337i	$-0.0785704\pi$
$90$	−15.2821	+	7.35948i	−0.0178986	+	0.00861953i
$91$	−387.413	−	1182.18i	−0.446285	−	1.36183i
$92$	126.295	+	60.8204i	0.143121	+	0.0689235i
$93$	955.016	−	459.911i	1.06484	−	0.512802i
$94$	−45.8536	+	200.898i	−0.0503132	+	0.220436i
$95$	75.5921	−	36.4033i	0.0816378	−	0.0393147i
$96$	−569.396	−	714.000i	−0.605352	−	0.759087i
$97$	1061.38			1.11100			0.555501	−	0.831516i	$-0.312527\pi$
$97$	1061.38			1.11100			0.555501	+	0.831516i	$0.312527\pi$
$98$	−11.4335	+	286.854i	−0.0117853	+	0.295680i
$99$	769.717			0.781409
$100$	559.571	+	701.680i	0.559571	+	0.701680i
$101$	1790.60	−	862.309i	1.76408	−	0.849534i	0.793561	−	0.608491i	$-0.208225\pi$
$101$	1790.60	−	862.309i	1.76408	−	0.849534i	0.970514	−	0.241043i	$-0.0774895\pi$
$102$	22.6070	−	99.0478i	0.0219454	−	0.0961490i
$103$	−842.671	+	405.809i	−0.806125	+	0.388209i	−0.791107	−	0.611678i	$-0.790495\pi$
$103$	−842.671	+	405.809i	−0.806125	+	0.388209i	−0.0150180	+	0.999887i	$0.504781\pi$
$104$	774.974	+	373.208i	0.730697	+	0.351885i
$105$	145.765	−	87.5899i	0.135478	−	0.0814085i
$106$	400.905	−	193.066i	0.367352	−	0.176908i
$107$	−790.337	+	991.051i	−0.714063	+	0.895406i	−0.997986	−	0.0634407i	$-0.979793\pi$
$107$	−790.337	+	991.051i	−0.714063	+	0.895406i	0.283923	+	0.958847i	$0.408364\pi$
$108$	541.772	+	260.903i	0.482704	+	0.232458i
$109$	−447.179	−	560.745i	−0.392954	−	0.492749i	0.545520	−	0.838098i	$-0.316332\pi$
$109$	−447.179	−	560.745i	−0.392954	−	0.492749i	−0.938474	+	0.345349i	$0.887761\pi$
$110$	−14.4902	−	63.4859i	−0.0125599	−	0.0550286i
$111$	−955.401	−	1198.03i	−0.816961	−	1.02444i
$112$	611.823	+	636.695i	0.516177	+	0.537161i
$113$	249.253	−	312.553i	0.207502	−	0.260200i	−0.667180	−	0.744897i	$-0.732499\pi$
$113$	249.253	−	312.553i	0.207502	−	0.260200i	0.874682	+	0.484697i	$0.161070\pi$
$114$	−283.604	−	136.576i	−0.233000	−	0.112207i
$115$	−6.11599	−	26.7959i	−0.00495930	−	0.0217281i
$116$	−1669.25			−1.33608
$117$	951.129			0.751555
$118$	−31.2001	−	136.697i	−0.0243407	−	0.106644i
$119$	−46.1606	+	347.353i	−0.0355591	+	0.267578i
$120$	−26.1641	+	114.633i	−0.0199037	+	0.0872040i
$121$	−361.381	+	1583.31i	−0.271511	+	1.18957i
$122$	−236.449	+	296.498i	−0.175468	+	0.220030i
$123$	−776.067	+	973.158i	−0.568908	+	0.713388i
$124$	268.366	−	1175.79i	0.194355	−	0.851524i
$125$	78.9677	−	345.980i	0.0565047	−	0.247563i
$126$	−205.685	−	76.6039i	−0.145428	−	0.0541621i
$127$	41.7539	+	182.936i	0.0291737	+	0.127818i	0.987418	−	0.158133i	$-0.0505475\pi$
$127$	41.7539	+	182.936i	0.0291737	+	0.127818i	−0.958244	+	0.285952i	$0.907690\pi$
$128$	−1358.30			−0.937955
$129$	−1468.11			−1.00201
$130$	−17.9054	−	78.4486i	−0.0120800	−	0.0529261i
$131$	−426.891	−	205.580i	−0.284715	−	0.137111i	0.286076	−	0.958207i	$-0.407649\pi$
$131$	−426.891	−	205.580i	−0.284715	−	0.137111i	−0.570791	+	0.821095i	$0.693363\pi$
$132$	1587.22	−	1990.31i	1.04659	−	1.31238i
$133$	1017.41	+	378.917i	0.663314	+	0.247040i
$134$	80.2016	+	100.570i	0.0517042	+	0.0648350i
$135$	−26.2360	−	114.947i	−0.0167262	−	0.0732822i
$136$	−151.058	−	189.420i	−0.0952433	−	0.119431i
$137$	−468.430	−	225.584i	−0.292122	−	0.140679i	0.282083	−	0.959390i	$-0.408975\pi$
$137$	−468.430	−	225.584i	−0.292122	−	0.140679i	−0.574205	+	0.818711i	$0.694689\pi$
$138$	−64.2926	+	80.6203i	−0.0396590	+	0.0497309i
$139$	−1733.93	+	835.018i	−1.05806	+	0.509535i	−0.880240	−	0.474528i	$-0.842619\pi$
$139$	−1733.93	+	835.018i	−1.05806	+	0.509535i	−0.177820	+	0.984063i	$0.556904\pi$
$140$	25.4888	−	191.800i	0.0153871	−	0.115786i
$141$	1423.10	+	685.329i	0.849977	+	0.409327i
$142$	466.942	−	224.867i	0.275950	−	0.132891i
$143$	−812.533	+	3559.94i	−0.475157	+	2.08180i
$144$	−608.246	+	292.916i	−0.351994	+	0.169511i
$145$	204.066	+	255.890i	0.116874	+	0.146555i
$146$	−331.956			−0.188170
$147$	2124.17	+	574.721i	1.19182	+	0.322464i
$148$	−1743.46			−0.968322
$149$	2044.84	+	2564.15i	1.12429	+	1.40982i	0.900322	+	0.435225i	$0.143331\pi$
$149$	2044.84	+	2564.15i	1.12429	+	1.40982i	0.223973	+	0.974595i	$0.428097\pi$
$150$	−594.828	+	286.454i	−0.323783	+	0.155926i
$151$	486.589	−	2131.89i	0.262239	−	1.14894i	−0.656578	−	0.754258i	$-0.727997\pi$
$151$	486.589	−	2131.89i	0.262239	−	1.14894i	0.918817	−	0.394685i	$-0.129146\pi$
$152$	−676.322	+	325.699i	−0.360901	+	0.173801i
$153$	−241.371	−	116.238i	−0.127540	−	0.0614202i
$154$	462.431	−	704.410i	0.241972	−	0.368591i
$155$	−213.053	+	102.601i	−0.110405	+	0.0531683i
$156$	1961.31	−	2459.40i	1.00660	−	1.26224i
$157$	−1798.65	−	866.185i	−0.914318	−	0.440313i	−0.0832791	−	0.996526i	$-0.526539\pi$
$157$	−1798.65	−	866.185i	−0.914318	−	0.440313i	−0.831039	+	0.556214i	$0.812254\pi$
$158$	−512.245	−	642.335i	−0.257924	−	0.323427i
$159$	−758.973	−	3325.28i	−0.378556	−	1.65856i
$160$	127.025	+	159.285i	0.0627640	+	0.0787036i
$161$	195.181	−	297.315i	0.0955431	−	0.145538i
$162$	−475.304	+	596.012i	−0.230515	+	0.289056i
$163$	−233.613	−	112.502i	−0.112258	−	0.0540604i	0.376912	−	0.926249i	$-0.376986\pi$
$163$	−233.613	−	112.502i	−0.112258	−	0.0540604i	−0.489170	+	0.872189i	$0.662700\pi$
$164$	315.135	+	1380.70i	0.150048	+	0.657405i
$165$	−499.147			−0.235506
$166$	−346.428			−0.161976
$167$	125.964	+	551.883i	0.0583674	+	0.255724i	0.995691	−	0.0927367i	$-0.0295615\pi$
$167$	125.964	+	551.883i	0.0583674	+	0.255724i	−0.937323	+	0.348461i	$0.886704\pi$
$168$	−1304.16	+	783.665i	−0.598915	+	0.359887i
$169$	−515.157	+	2257.05i	−0.234482	+	1.02733i
$170$	−5.04335	+	22.0964i	−0.00227534	+	0.00996891i
$171$	−517.529	+	648.961i	−0.231441	+	0.290218i
$172$	−1041.46	+	1305.95i	−0.461691	+	0.578942i
$173$	−751.152	+	3291.01i	−0.330110	+	1.44631i	0.488806	+	0.872393i	$0.337433\pi$
$173$	−751.152	+	3291.01i	−0.330110	+	1.44631i	−0.818916	+	0.573914i	$0.805424\pi$
$174$	273.242	−	1197.15i	0.119048	−	0.521585i
$175$	1951.82	−	1172.85i	0.843106	−	0.506621i
$176$	−576.728	−	2526.81i	−0.247003	−	1.08219i
$177$	−1074.75			−0.456404
$178$	1118.24			0.470873
$179$	−609.189	−	2669.03i	−0.254374	−	1.11449i	−0.927165	−	0.374653i	$-0.877762\pi$
$179$	−609.189	−	2669.03i	−0.254374	−	1.11449i	0.672791	−	0.739832i	$-0.265095\pi$
$180$	133.280	+	64.1840i	0.0551893	+	0.0265777i
$181$	2149.24	−	2695.06i	0.882607	−	1.10675i	−0.110996	−	0.993821i	$-0.535404\pi$
$181$	2149.24	−	2695.06i	0.882607	−	1.10675i	0.993603	−	0.112933i	$-0.0360246\pi$
$182$	571.420	−	870.429i	0.232728	−	0.354508i
$183$	1812.43	+	2272.72i	0.732125	+	0.918056i
$184$	54.7197	+	239.743i	0.0219238	+	0.0960546i
$185$	213.138	+	267.267i	0.0847041	+	0.106216i
$186$	799.323	+	384.934i	0.315103	+	0.151746i
$187$	641.262	−	804.117i	0.250768	−	0.314454i
$188$	1619.17	−	779.750i	0.628138	−	0.302495i
$189$	837.276	−	1275.40i	0.322238	−	0.490856i
$190$	63.2687	+	30.4686i	0.0241578	+	0.0116338i
$191$	1298.60	−	625.375i	0.491957	−	0.236914i	−0.171422	−	0.985198i	$-0.554836\pi$
$191$	1298.60	−	625.375i	0.491957	−	0.236914i	0.663379	+	0.748284i	$0.269122\pi$
$192$	−374.436	+	1640.51i	−0.140743	+	0.616634i
$193$	1570.65	−	756.386i	0.585792	−	0.282103i	−0.117420	−	0.993082i	$-0.537462\pi$
$193$	1570.65	−	756.386i	0.585792	−	0.282103i	0.703213	+	0.710980i	$0.251748\pi$
$194$	553.877	+	694.540i	0.204980	+	0.257036i
$195$	−616.789			−0.226508
$196$	2018.11	−	1481.84i	0.735461	−	0.540031i
$197$	2819.62			1.01974			0.509872	−	0.860250i	$-0.329693\pi$
$197$	2819.62			1.01974			0.509872	+	0.860250i	$0.329693\pi$
$198$	401.673	+	503.682i	0.144170	+	0.180783i
$199$	−768.184	+	369.938i	−0.273644	+	0.131780i	−0.565673	−	0.824629i	$-0.691384\pi$
$199$	−768.184	+	369.938i	−0.273644	+	0.131780i	0.292030	+	0.956409i	$0.405669\pi$
$200$	−350.343	+	1534.95i	−0.123865	+	0.542688i
$201$	888.355	−	427.809i	0.311740	−	0.150126i
$202$	1498.69	+	721.730i	0.522016	+	0.251390i
$203$	−557.924	+	4198.31i	−0.192900	+	1.45155i
$204$	−798.292	+	384.437i	−0.273979	+	0.131941i
$205$	173.131	−	217.100i	0.0589854	−	0.0739654i
$206$	−705.294	−	339.652i	−0.238544	−	0.114877i
$207$	169.537	+	212.592i	0.0569257	+	0.0713825i
$208$	−712.655	−	3122.34i	−0.237566	−	1.04084i
$209$	−1986.85	−	2491.43i	−0.657576	−	0.824574i
$210$	133.383	+	49.6762i	0.0438300	+	0.0163237i
$211$	584.828	−	733.351i	0.190811	−	0.239270i	−0.677218	−	0.735782i	$-0.736815\pi$
$211$	584.828	−	733.351i	0.190811	−	0.239270i	0.868030	+	0.496512i	$0.165386\pi$
$212$	−3496.40	−	1683.78i	−1.13271	−	0.545483i
$213$	−883.991	−	3873.02i	−0.284366	−	1.24589i
$214$	−1060.95			−0.338902
$215$	327.518			0.103891
$216$	234.733	+	1028.43i	0.0739424	+	0.323963i
$217$	−2867.52	−	1067.96i	−0.897051	−	0.334091i
$218$	133.578	−	585.244i	0.0415002	−	0.181824i
$219$	−566.206	+	2480.71i	−0.174706	+	0.765438i
$220$	−354.090	+	444.015i	−0.108512	+	0.136070i
$221$	792.398	−	993.636i	0.241188	−	0.302440i
$222$	285.390	−	1250.38i	0.0862799	−	0.378017i
$223$	−1103.05	+	4832.79i	−0.331237	+	1.45124i	0.485501	+	0.874236i	$0.338637\pi$
$223$	−1103.05	+	4832.79i	−0.331237	+	1.45124i	−0.816738	+	0.577008i	$0.804220\pi$
$224$	−347.293	+	2613.34i	−0.103591	+	0.779513i
$225$	387.396	+	1697.29i	0.114784	+	0.502902i
$226$	334.598			0.0984828
$227$	1929.91			0.564285			0.282143	−	0.959373i	$-0.408955\pi$
$227$	1929.91			0.564285			0.282143	+	0.959373i	$0.408955\pi$
$228$	610.876	+	2676.42i	0.177440	+	0.777414i
$229$	−4558.51	−	2195.26i	−1.31544	−	0.633481i	−0.361187	−	0.932493i	$-0.617628\pi$
$229$	−4558.51	−	2195.26i	−1.31544	−	0.633481i	−0.954249	+	0.299013i	$0.903343\pi$
$230$	14.3429	−	17.9854i	0.00411193	−	0.00515619i
$231$	−4475.31	−	4657.24i	−1.27469	−	1.32651i
$232$	−1825.77	−	2289.45i	−0.516672	−	0.647886i
$233$	1514.32	+	6634.65i	0.425777	+	1.86545i	0.496626	+	0.867965i	$0.334572\pi$
$233$	1514.32	+	6634.65i	0.425777	+	1.86545i	−0.0708490	+	0.997487i	$0.522571\pi$
$234$	496.342	+	622.393i	0.138662	+	0.173876i
$235$	−317.477	−	152.889i	−0.0881273	−	0.0424399i
$236$	−762.421	+	956.045i	−0.210294	+	0.263700i
$237$	−5673.90	+	2732.41i	−1.55510	+	0.748898i
$238$	−251.387	+	151.058i	−0.0684663	+	0.0411413i
$239$	2342.66	+	1128.17i	0.634034	+	0.305334i	0.723154	−	0.690686i	$-0.242691\pi$
$239$	2342.66	+	1128.17i	0.634034	+	0.305334i	−0.0891209	+	0.996021i	$0.528406\pi$
$240$	394.436	−	189.950i	0.106086	−	0.0510885i
$241$	1238.43	−	5425.91i	0.331013	−	1.45026i	−0.486160	−	0.873870i	$-0.661603\pi$
$241$	1238.43	−	5425.91i	0.331013	−	1.45026i	0.817173	−	0.576393i	$-0.195540\pi$
$242$	−1224.66	+	589.765i	−0.325306	+	0.156659i
$243$	2256.52	+	2829.59i	0.595703	+	0.746988i
$244$	3307.41			0.867769
$245$	−473.876	−	128.213i	−0.123571	−	0.0334337i
$246$	−1041.79			−0.270010
$247$	−2455.13	−	3078.63i	−0.632453	−	0.793071i
$248$	1906.18	−	917.967i	0.488074	−	0.235044i
$249$	−590.891	+	2588.86i	−0.150386	+	0.658885i
$250$	267.609	−	128.874i	0.0677003	−	0.0326027i
$251$	1018.98	+	490.713i	0.256244	+	0.123401i	0.557596	−	0.830112i	$-0.311724\pi$
$251$	1018.98	+	490.713i	0.256244	+	0.123401i	−0.301352	+	0.953513i	$0.597438\pi$
$252$	596.111	+	1819.02i	0.149014	+	0.454713i
$253$	−940.535	+	452.938i	−0.233719	+	0.112553i
$254$	−97.9192	+	122.787i	−0.0241890	+	0.0303320i
$255$	156.524	+	75.3782i	0.0384390	+	0.0185112i
$256$	599.427	+	751.657i	0.146344	+	0.183510i
$257$	1402.93	+	6146.65i	0.340516	+	1.49190i	0.797988	+	0.602673i	$0.205898\pi$
$257$	1402.93	+	6146.65i	0.340516	+	1.49190i	−0.457472	+	0.889224i	$0.651245\pi$
$258$	−766.125	−	960.691i	−0.184872	−	0.231822i
$259$	−582.729	+	4384.97i	−0.139803	+	1.05200i
$260$	−437.544	+	548.663i	−0.104367	+	0.130872i
$261$	−2917.36	−	1404.92i	−0.691876	−	0.333190i
$262$	−88.2450	−	386.627i	−0.0208084	−	0.0911675i
$263$	4800.80			1.12559			0.562794	−	0.826597i	$-0.309726\pi$
$263$	4800.80			1.12559			0.562794	+	0.826597i	$0.309726\pi$
$264$	4465.86			1.04112
$265$	169.318	+	741.829i	0.0392495	+	0.171963i
$266$	282.978	+	863.502i	0.0652274	+	0.199040i
$267$	1907.34	−	8356.61i	0.437181	−	1.91542i
$268$	249.634	−	1093.72i	0.0568986	−	0.249289i
$269$	4118.44	−	5164.36i	0.933478	−	1.17054i	−0.0516401	−	0.998666i	$-0.516445\pi$
$269$	4118.44	−	5164.36i	0.933478	−	1.17054i	0.985118	−	0.171879i	$-0.0549837\pi$
$270$	61.5273	−	77.1528i	0.0138683	−	0.0173903i
$271$	−366.708	+	1606.65i	−0.0821991	+	0.360138i	−0.999254	−	0.0386236i	$-0.987703\pi$
$271$	−366.708	+	1606.65i	−0.0821991	+	0.360138i	0.917055	+	0.398761i	$0.130560\pi$
$272$	−200.731	+	879.461i	−0.0447468	+	0.196048i
$273$	−5530.08	−	5754.89i	−1.22599	−	1.27583i
$274$	−96.8318	−	424.248i	−0.0213497	−	0.0935392i
$275$	−6683.67			−1.46560
$276$	899.314			0.196132
$277$	834.020	+	3654.08i	0.180908	+	0.792608i	0.981199	+	0.192997i	$0.0618209\pi$
$277$	834.020	+	3654.08i	0.180908	+	0.792608i	−0.800292	+	0.599611i	$0.795322\pi$
$278$	−1451.26	−	698.889i	−0.313096	−	0.150779i
$279$	1458.63	−	1829.06i	0.312996	−	0.392484i
$280$	290.941	−	174.826i	0.0620967	−	0.0373138i
$281$	−2808.44	−	3521.67i	−0.596219	−	0.747635i	0.388564	−	0.921422i	$-0.372971\pi$
$281$	−2808.44	−	3521.67i	−0.596219	−	0.747635i	−0.984783	+	0.173786i	$0.944400\pi$
$282$	294.177	+	1288.87i	0.0621205	+	0.272168i
$283$	2515.54	+	3154.38i	0.528386	+	0.662575i	0.972366	−	0.233462i	$-0.0750054\pi$
$283$	2515.54	+	3154.38i	0.528386	+	0.662575i	−0.443980	+	0.896037i	$0.646434\pi$
$284$	−4072.33	−	1961.13i	−0.850874	−	0.409759i
$285$	335.608	−	420.839i	0.0697532	−	0.0874678i
$286$	−2753.54	+	1326.04i	−0.569302	+	0.274161i
$287$	3577.91	−	331.114i	0.735880	−	0.0681013i
$288$	−1815.97	−	874.527i	−0.371553	−	0.178931i
$289$	4103.94	−	1976.35i	0.835322	−	0.402270i
$290$	−60.9570	+	267.070i	−0.0123432	+	0.0540790i
$291$	6135.04	−	2954.48i	1.23588	−	0.595171i
$292$	1805.05	+	2263.46i	0.361755	+	0.453627i
$293$	−2875.42			−0.573323			−0.286661	−	0.958032i	$-0.592545\pi$
$293$	−2875.42			−0.573323			−0.286661	+	0.958032i	$0.592545\pi$
$294$	732.403	+	1689.91i	0.145288	+	0.335230i
$295$	239.765			0.0473208
$296$	−1906.95	−	2391.24i	−0.374456	−	0.469553i
$297$	−4034.65	+	1942.98i	−0.788262	+	0.379607i
$298$	−610.819	+	2676.18i	−0.118738	+	0.520224i
$299$	−1162.21	+	559.689i	−0.224790	+	0.108253i
$300$	5187.65	+	2498.24i	0.998364	+	0.480787i
$301$	2936.50	+	3055.88i	0.562316	+	0.585175i
$302$	1648.97	−	794.103i	0.314198	−	0.151310i
$303$	7949.76	−	9968.69i	1.50727	−	1.89005i
$304$	2518.16	+	1212.68i	0.475088	+	0.228790i
$305$	−404.332	−	507.016i	−0.0759081	−	0.0951858i
$306$	−49.8951	−	218.605i	−0.00932129	−	0.0408392i
$307$	−1754.72	−	2200.35i	−0.326213	−	0.409058i	0.591499	−	0.806306i	$-0.298537\pi$
$307$	−1754.72	−	2200.35i	−0.326213	−	0.409058i	−0.917711	+	0.397248i	$0.869965\pi$
$308$	−7317.59	+	677.198i	−1.35376	+	0.125282i
$309$	−3741.22	+	4691.34i	−0.688772	+	0.863693i
$310$	−178.319	−	85.8741i	−0.0326705	−	0.0157333i
$311$	−269.070	−	1178.87i	−0.0490597	−	0.214944i	0.944456	−	0.328637i	$-0.106589\pi$
$311$	−269.070	−	1178.87i	−0.0490597	−	0.214944i	−0.993516	+	0.113693i	$0.963732\pi$
$312$	5518.40			1.00134
$313$	5256.27			0.949208			0.474604	−	0.880200i	$-0.342591\pi$
$313$	5256.27			0.949208			0.474604	+	0.880200i	$0.342591\pi$
$314$	−371.809	−	1629.00i	−0.0668229	−	0.292770i
$315$	205.976	−	313.758i	0.0368426	−	0.0561214i
$316$	−1594.41	+	6985.55i	−0.283837	+	1.24357i
$317$	1977.13	−	8662.36i	0.350304	−	1.53478i	−0.426175	−	0.904641i	$-0.640139\pi$
$317$	1977.13	−	8662.36i	0.350304	−	1.53478i	0.776479	−	0.630143i	$-0.217004\pi$
$318$	1779.90	−	2231.93i	0.313874	−	0.393586i
$319$	7750.67	−	9719.04i	1.36036	−	1.70584i
$320$	83.5323	−	365.979i	0.0145925	−	0.0639339i
$321$	−1809.63	+	7928.49i	−0.314653	+	1.37858i
$322$	296.409	−	27.4309i	0.0512988	−	0.00474740i
$323$	246.803	+	1081.32i	0.0425155	+	0.186273i
$324$	6648.47			1.14000
$325$	−8258.92			−1.40961
$326$	−48.2914	−	211.579i	−0.00820434	−	0.0359456i
$327$	−4145.70	−	1996.46i	−0.701094	−	0.337629i
$328$	−1549.00	+	1942.39i	−0.260760	+	0.326983i
$329$	−1419.96	−	4332.98i	−0.237948	−	0.726094i
$330$	−260.477	−	326.628i	−0.0434509	−	0.0544857i
$331$	2353.14	+	10309.8i	0.390756	+	1.71201i	0.662000	+	0.749504i	$0.269708\pi$
$331$	2353.14	+	10309.8i	0.390756	+	1.71201i	−0.271244	+	0.962511i	$0.587435\pi$
$332$	1883.74	+	2362.14i	0.311397	+	0.390480i
$333$	−3047.06	−	1467.39i	−0.501435	−	0.241478i
$334$	−295.404	+	370.424i	−0.0483945	+	0.0606848i
$335$	−198.181	+	95.4391i	−0.0323218	+	0.0155654i
$336$	5308.79	+	1977.17i	0.861960	+	0.321022i
$337$	−7446.34	−	3585.97i	−1.20364	−	0.579645i	−0.278932	−	0.960311i	$-0.589980\pi$
$337$	−7446.34	−	3585.97i	−1.20364	−	0.579645i	−0.924712	+	0.380666i	$0.875695\pi$
$338$	−1745.78	+	840.725i	−0.280941	+	0.135294i
$339$	570.712	−	2500.45i	0.0914361	−	0.400608i
$340$	178.089	−	85.7633i	0.0284066	−	0.0136799i
$341$	5599.84	+	7021.98i	0.889291	+	1.11514i
$342$	−694.732			−0.109844
$343$	−3052.45	−	5571.01i	−0.480516	−	0.876986i
$344$	−2930.30			−0.459276
$345$	−109.941	−	137.862i	−0.0171566	−	0.0215137i
$346$	−2545.53	+	1225.86i	−0.395516	+	0.190471i
$347$	−1371.57	+	6009.23i	−0.212189	+	0.929662i	0.750887	+	0.660431i	$0.229626\pi$
$347$	−1371.57	+	6009.23i	−0.212189	+	0.929662i	−0.963076	+	0.269230i	$0.913231\pi$
$348$	−9648.64	+	4646.54i	−1.48627	+	0.715749i
$349$	1390.53	+	669.642i	0.213276	+	0.102708i	0.537472	−	0.843282i	$-0.319379\pi$
$349$	1390.53	+	669.642i	0.213276	+	0.102708i	−0.324196	+	0.945990i	$0.605094\pi$
$350$	1786.02	+	665.173i	0.272763	+	0.101586i
$351$	−4985.56	+	2400.92i	−0.758146	+	0.365104i
$352$	4824.59	−	6049.84i	0.730543	−	0.916072i
$353$	8630.77	+	4156.36i	1.30133	+	0.626687i	0.950783	−	0.309858i	$-0.100281\pi$
$353$	8630.77	+	4156.36i	1.30133	+	0.626687i	0.350547	+	0.936545i	$0.385996\pi$
$354$	−560.855	−	703.290i	−0.0842065	−	0.105592i
$355$	197.208	+	864.023i	0.0294837	+	0.129176i
$356$	−6080.55	−	7624.77i	−0.905249	−	1.13515i
$357$	700.077	+	2136.27i	0.103787	+	0.316704i
$358$	1428.64	−	1791.46i	0.210910	−	0.264473i
$359$	−9744.76	−	4692.83i	−1.43262	−	0.689911i	−0.453133	−	0.891443i	$-0.649694\pi$
$359$	−9744.76	−	4692.83i	−1.43262	−	0.689911i	−0.979482	+	0.201532i	$0.935408\pi$
$360$	57.7459	+	253.001i	0.00845410	+	0.0370398i
$361$	−3422.55			−0.498986
$362$	2885.15			0.418895
$363$	2318.46	+	10157.9i	0.335228	+	1.46873i
$364$	−9042.24	+	836.805i	−1.30204	+	0.120496i
$365$	126.314	−	553.417i	0.0181139	−	0.0793621i
$366$	−541.396	+	2372.01i	−0.0773203	+	0.338763i
$367$	−6467.18	+	8109.59i	−0.919848	+	1.15345i	0.0679461	+	0.997689i	$0.478355\pi$
$367$	−6467.18	+	8109.59i	−0.919848	+	1.15345i	−0.987794	+	0.155764i	$0.950216\pi$
$368$	570.864	−	715.841i	0.0808651	−	0.101402i
$369$	−611.302	+	2678.29i	−0.0862415	+	0.377849i
$370$	−63.6671	+	278.944i	−0.00894567	+	0.0391935i
$371$	−5403.48	+	8230.99i	−0.756159	+	1.15184i
$372$	−1721.72	−	7543.36i	−0.239965	−	1.05136i
$373$	−1084.71			−0.150574			−0.0752871	−	0.997162i	$-0.523987\pi$
$373$	−1084.71			−0.150574			−0.0752871	+	0.997162i	$0.523987\pi$
$374$	860.831			0.119017
$375$	−506.623	−	2219.66i	−0.0697651	−	0.305661i
$376$	2840.46	+	1367.89i	0.389589	+	0.187616i
$377$	9577.40	−	12009.7i	1.30839	−	1.64066i
$378$	1271.52	−	117.671i	0.173015	−	0.0160115i
$379$	3423.62	+	4293.09i	0.464010	+	0.581850i	0.957693	−	0.287792i	$-0.0929212\pi$
$379$	3423.62	+	4293.09i	0.464010	+	0.581850i	−0.493683	+	0.869642i	$0.664350\pi$
$380$	−136.279	−	597.078i	−0.0183973	−	0.0806038i
$381$	750.570	+	941.186i	0.100926	+	0.126557i
$382$	1086.90	+	523.423i	0.145577	+	0.0701064i
$383$	2550.00	−	3197.59i	0.340205	−	0.426604i	−0.582069	−	0.813139i	$-0.697757\pi$
$383$	2550.00	−	3197.59i	0.340205	−	0.426604i	0.922275	+	0.386535i	$0.126328\pi$
$384$	−7851.31	+	3780.99i	−1.04339	+	0.502469i
$385$	998.388	+	1038.98i	0.132163	+	0.137535i
$386$	1314.59	+	633.075i	0.173345	+	0.0834784i
$387$	−2919.33	+	1405.88i	−0.383457	+	0.184663i
$388$	1723.99	−	7553.29i	0.225573	−	0.988299i
$389$	−7987.39	+	3846.53i	−1.04107	+	0.501354i	−0.874677	−	0.484706i	$-0.838927\pi$
$389$	−7987.39	+	3846.53i	−1.04107	+	0.501354i	−0.166394	+	0.986059i	$0.553212\pi$
$390$	−321.868	−	403.610i	−0.0417908	−	0.0524040i
$391$	363.337			0.0469942
$392$	4239.76	+	1147.12i	0.546276	+	0.147802i
$393$	−3039.79			−0.390170
$394$	1471.40	+	1845.08i	0.188143	+	0.235924i
$395$	1265.78	−	609.567i	0.161236	−	0.0776472i
$396$	1250.24	−	5477.66i	0.158654	−	0.695108i
$397$	2196.93	−	1057.98i	0.277734	−	0.133750i	−0.289832	−	0.957078i	$-0.593599\pi$
$397$	2196.93	−	1057.98i	0.277734	−	0.133750i	0.567566	+	0.823328i	$0.307885\pi$
$398$	−642.950	−	309.629i	−0.0809754	−	0.0389957i
$399$	6935.63	−	641.851i	0.870215	−	0.0805331i
$400$	5281.57	−	2543.47i	0.660196	−	0.317934i
$401$	459.549	−	576.257i	0.0572289	−	0.0717628i	−0.752393	−	0.658714i	$-0.771101\pi$
$401$	459.549	−	576.257i	0.0572289	−	0.0717628i	0.809622	+	0.586951i	$0.199672\pi$
$402$	743.530	+	358.065i	0.0922486	+	0.0444246i
$403$	6919.64	+	8676.96i	0.855315	+	1.07253i
$404$	−3228.14	−	14143.4i	−0.397539	−	1.74173i
$405$	−812.777	−	1019.19i	−0.0997215	−	0.125047i
$406$	−3038.41	+	1825.78i	−0.371413	+	0.223182i
$407$	8095.26	−	10151.1i	0.985915	−	1.23630i
$408$	−1400.42	−	674.407i	−0.169929	−	0.0818337i
$409$	−495.846	−	2172.44i	−0.0599463	−	0.262642i	0.936070	−	0.351814i	$-0.114435\pi$
$409$	−495.846	−	2172.44i	−0.0599463	−	0.262642i	−0.996016	+	0.0891722i	$0.971578\pi$
$410$	232.412			0.0279951
$411$	−3335.57			−0.400321
$412$	1519.19	+	6655.99i	0.181662	+	0.795915i
$413$	2149.71	+	2237.10i	0.256127	+	0.266539i
$414$	−50.6427	+	221.880i	−0.00601197	+	0.0263402i
$415$	131.821	−	577.544i	0.0155923	−	0.0683145i
$416$	5961.67	−	7475.70i	0.702632	−	0.881073i
$417$	−7698.17	+	9653.20i	−0.904031	+	1.13362i
$418$	593.498	−	2600.28i	0.0694472	−	0.304268i
$419$	2521.32	−	11046.6i	0.293972	−	1.28798i	−0.584973	−	0.811053i	$-0.698895\pi$
$419$	2521.32	−	11046.6i	0.293972	−	1.28798i	0.878945	−	0.476923i	$-0.158248\pi$
$420$	−386.566	−	1179.60i	−0.0449107	−	0.137044i
$421$	1411.48	+	6184.11i	0.163400	+	0.715903i	0.988538	+	0.150972i	$0.0482402\pi$
$421$	1411.48	+	6184.11i	0.163400	+	0.715903i	−0.825138	+	0.564931i	$0.808903\pi$
$422$	785.074			0.0905611
$423$	3486.11			0.400710
$424$	−1514.88	−	6637.14i	−0.173512	−	0.760207i
$425$	2095.89	+	1009.33i	0.239213	+	0.115199i
$426$	2073.09	−	2599.57i	0.235778	−	0.295657i
$427$	1105.46	−	8318.46i	0.125286	−	0.942759i
$428$	5769.04	+	7234.15i	0.651535	+	0.817000i
$429$	5212.86	+	22839.0i	0.586665	+	2.57035i
$430$	170.913	+	214.319i	0.0191679	+	0.0240357i
$431$	−1003.19	−	483.112i	−0.112116	−	0.0539923i	0.376985	−	0.926219i	$-0.376961\pi$
$431$	−1003.19	−	483.112i	−0.112116	−	0.0539923i	−0.489101	+	0.872227i	$0.662675\pi$
$432$	2448.86	−	3070.77i	0.272733	−	0.341996i
$433$	−4194.01	+	2019.73i	−0.465476	+	0.224162i	−0.651896	−	0.758309i	$-0.726026\pi$
$433$	−4194.01	+	2019.73i	−0.465476	+	0.224162i	0.186419	+	0.982470i	$0.440312\pi$
$434$	−797.558	−	2433.73i	−0.0882120	−	0.269177i
$435$	1891.85	+	911.066i	0.208522	+	0.100419i
$436$	−4716.87	+	2271.52i	−0.518112	+	0.249510i
$437$	250.501	−	1097.52i	0.0274213	−	0.120141i
$438$	−1918.78	+	924.036i	−0.209322	+	0.100804i
$439$	−2663.20	−	3339.55i	−0.289539	−	0.363071i	0.615694	−	0.787985i	$-0.288876\pi$
$439$	−2663.20	−	3339.55i	−0.289539	−	0.363071i	−0.905234	+	0.424914i	$0.860304\pi$
$440$	−996.279			−0.107945
$441$	4774.25	−	891.290i	0.515522	−	0.0962412i
$442$	1063.72			0.114470
$443$	−2025.57	−	2539.98i	−0.217240	−	0.272411i	0.661255	−	0.750161i	$-0.270024\pi$
$443$	−2025.57	−	2539.98i	−0.217240	−	0.272411i	−0.878496	+	0.477750i	$0.841453\pi$
$444$	−10077.6	+	4853.12i	−1.07717	+	0.518736i
$445$	−425.505	+	1864.26i	−0.0453278	+	0.198594i
$446$	−3738.07	+	1800.16i	−0.396867	+	0.191121i
$447$	18957.2	+	9129.33i	2.00592	+	0.966001i
$448$	4163.68	−	2501.95i	0.439096	−	0.263853i
$449$	6674.49	−	3214.27i	0.701534	−	0.337841i	−0.0488840	−	0.998804i	$-0.515566\pi$
$449$	6674.49	−	3214.27i	0.701534	−	0.337841i	0.750418	+	0.660963i	$0.229852\pi$
$450$	−908.501	+	1139.22i	−0.0951715	+	0.119341i
$451$	−9502.23	−	4576.03i	−0.992112	−	0.477776i
$452$	−1819.42	−	2281.48i	−0.189332	−	0.237415i
$453$	−3121.75	−	13677.3i	−0.323780	−	1.41857i
$454$	1007.11	+	1262.88i	0.104111	+	0.130551i
$455$	1233.69	+	1283.85i	0.127113	+	0.132281i
$456$	−3002.68	+	3765.24i	−0.308362	+	0.386674i
$457$	666.199	+	320.824i	0.0681914	+	0.0328392i	0.467669	−	0.883904i	$-0.345094\pi$
$457$	666.199	+	320.824i	0.0681914	+	0.0328392i	−0.399477	+	0.916743i	$0.630808\pi$
$458$	−942.315	−	4128.55i	−0.0961386	−	0.421211i
$459$	1558.62			0.158497
$460$	−200.626			−0.0203353
$461$	−602.522	−	2639.82i	−0.0608725	−	0.266700i	0.935329	−	0.353780i	$-0.115104\pi$
$461$	−602.522	−	2639.82i	−0.0608725	−	0.266700i	−0.996201	+	0.0870796i	$0.972247\pi$
$462$	712.155	−	5358.88i	0.0717152	−	0.539649i
$463$	276.058	−	1209.49i	0.0277095	−	0.121403i	−0.959182	−	0.282791i	$-0.908740\pi$
$463$	276.058	−	1209.49i	0.0277095	−	0.121403i	0.986891	+	0.161387i	$0.0515969\pi$
$464$	−2426.16	+	10629.7i	−0.242741	+	1.06352i
$465$	−945.892	+	1186.11i	−0.0943327	+	0.118289i
$466$	−3551.29	+	4453.18i	−0.353027	+	0.442682i
$467$	−2909.77	+	12748.5i	−0.288326	+	1.26324i	0.598496	+	0.801126i	$0.295765\pi$
$467$	−2909.77	+	12748.5i	−0.288326	+	1.26324i	−0.886822	+	0.462112i	$0.847092\pi$
$468$	1544.91	−	6768.67i	0.152592	−	0.668551i
$469$	−2667.37	−	993.414i	−0.262617	−	0.0978073i
$470$	−65.6274	−	287.532i	−0.00644078	−	0.0282189i
$471$	−12807.7			−1.25297
$472$	−2145.17			−0.209194
$473$	−2768.06	−	12127.6i	−0.269081	−	1.17892i
$474$	−4748.91	−	2286.95i	−0.460178	−	0.221610i
$475$	4493.85	−	5635.11i	0.434088	−	0.544330i
$476$	2396.94	+	892.700i	0.230806	+	0.0859597i
$477$	−4693.53	−	5885.50i	−0.450528	−	0.564944i
$478$	484.264	+	2121.70i	0.0463383	+	0.203021i
$479$	6873.82	+	8619.50i	0.655684	+	0.822202i	0.992866	−	0.119237i	$-0.0380450\pi$
$479$	6873.82	+	8619.50i	0.655684	+	0.822202i	−0.337181	+	0.941440i	$0.609474\pi$
$480$	1177.62	+	567.114i	0.111981	+	0.0539273i
$481$	10003.2	−	12543.6i	0.948247	−	1.18906i
$482$	4196.83	−	2021.09i	0.396598	−	0.190992i
$483$	300.584	−	2261.86i	0.0283168	−	0.213081i
$484$	10680.6	+	5143.50i	1.00306	+	0.483049i
$485$	−1368.65	+	659.109i	−0.128139	+	0.0617084i
$486$	−674.051	+	2953.21i	−0.0629127	+	0.275638i
$487$	−13591.8	+	6545.49i	−1.26469	+	0.609044i	−0.941412	−	0.337260i	$-0.890500\pi$
$487$	−13591.8	+	6545.49i	−1.26469	+	0.609044i	−0.323280	+	0.946303i	$0.604786\pi$
$488$	3617.55	+	4536.27i	0.335572	+	0.420793i
$489$	−1663.50			−0.153836
$490$	−163.390	−	376.999i	−0.0150637	−	0.0347573i
$491$	14530.5			1.33555			0.667774	−	0.744364i	$-0.267247\pi$
$491$	14530.5			1.33555			0.667774	+	0.744364i	$0.267247\pi$
$492$	5664.88	+	7103.54i	0.519091	+	0.650919i
$493$	−3898.20	+	1877.27i	−0.356118	+	0.171497i
$494$	733.377	−	3213.13i	0.0667939	−	0.292643i
$495$	−992.551	+	477.987i	−0.0901249	+	0.0434019i
$496$	−7097.32	−	3417.89i	−0.642498	−	0.309411i
$497$	−6293.54	+	9586.80i	−0.568016	+	0.865245i
$498$	−2002.43	+	964.321i	−0.180183	+	0.0867716i
$499$	6113.75	−	7666.40i	0.548475	−	0.687766i	−0.427906	−	0.903823i	$-0.640748\pi$
$499$	6113.75	−	7666.40i	0.548475	−	0.687766i	0.976381	+	0.216058i	$0.0693199\pi$
$500$	−2333.89	−	1123.94i	−0.208749	−	0.100528i
$501$	2264.33	+	2839.38i	0.201922	+	0.253202i
$502$	210.638	+	922.867i	0.0187276	+	0.0820509i
$503$	−13414.5	−	16821.2i	−1.18911	−	1.49110i	−0.829967	−	0.557813i	$-0.811641\pi$
$503$	−13414.5	−	16821.2i	−1.18911	−	1.49110i	−0.359143	−	0.933283i	$-0.616931\pi$
$504$	−1842.86	+	2807.19i	−0.162872	+	0.248099i
$505$	−1773.50	+	2223.89i	−0.156276	+	0.195964i
$506$	−787.203	−	379.097i	−0.0691610	−	0.0333062i
$507$	3305.03	+	14480.3i	0.289510	+	1.26843i
$508$	1369.68			0.119625
$509$	−5022.03			−0.437324			−0.218662	−	0.975801i	$-0.570169\pi$
$509$	−5022.03			−0.437324			−0.218662	+	0.975801i	$0.570169\pi$
$510$	32.3560	+	141.761i	0.00280931	+	0.0123084i
$511$	6296.13	−	3783.34i	0.545057	−	0.327524i
$512$	−2597.07	+	11378.5i	−0.224170	+	0.982154i
$513$	1074.59	−	4708.07i	0.0924836	−	0.405197i
$514$	−3290.09	+	4125.64i	−0.282334	+	0.354035i
$515$	834.621	−	1046.58i	0.0714132	−	0.0895493i
$516$	−2384.63	+	10447.7i	−0.203445	+	0.891350i
$517$	−2978.12	+	13048.0i	−0.253342	+	1.10996i
$518$	−3173.50	+	1906.95i	−0.269180	+	0.161750i
$519$	4819.07	+	21113.7i	0.407579	+	1.78572i
$520$	−1231.09			−0.103821
$521$	−9059.77			−0.761834			−0.380917	−	0.924609i	$-0.624392\pi$
$521$	−9059.77			−0.761834			−0.380917	+	0.924609i	$0.624392\pi$
$522$	−603.063	−	2642.19i	−0.0505658	−	0.221543i
$523$	−17635.6	−	8492.88i	−1.47448	−	0.710072i	−0.487831	−	0.872938i	$-0.662212\pi$
$523$	−17635.6	−	8492.88i	−1.47448	−	0.710072i	−0.986648	+	0.162866i	$0.947926\pi$
$524$	−2156.40	+	2704.03i	−0.179776	+	0.225432i
$525$	8017.22	−	12212.4i	0.666476	−	1.01523i
$526$	2505.27	+	3141.51i	0.207671	+	0.260411i
$527$	−695.602	−	3047.63i	−0.0574970	−	0.251911i
$528$	−10367.3	−	13000.2i	−0.854504	−	1.07151i
$529$	10629.8	+	5119.06i	0.873661	+	0.420733i
$530$	−397.075	+	497.917i	−0.0325431	+	0.0408078i
$531$	−2137.14	+	1029.19i	−0.174659	+	0.0841116i
$532$	4349.11	−	6624.90i	0.354432	−	0.539898i
$533$	−11741.8	−	5654.54i	−0.954207	−	0.459522i
$534$	6463.67	−	3112.74i	0.523802	−	0.252250i
$535$	403.706	−	1768.75i	0.0326238	−	0.142934i
$536$	1773.13	−	853.893i	0.142887	−	0.0688107i
$537$	−10950.8	−	13731.9i	−0.880004	−	1.10349i
$538$	5528.60			0.443039
$539$	−742.591	+	18630.8i	−0.0593426	+	1.48884i
$540$	−860.633			−0.0685847
$541$	4642.48	+	5821.49i	0.368939	+	0.462635i	0.931298	−	0.364258i	$-0.118678\pi$
$541$	4642.48	+	5821.49i	0.368939	+	0.462635i	−0.562359	+	0.826893i	$0.690106\pi$
$542$	−1242.72	+	598.460i	−0.0984856	+	0.0474282i
$543$	4921.10	−	21560.7i	0.388922	−	1.70398i
$544$	−2426.52	+	1168.55i	−0.191243	+	0.0920979i
$545$	924.855	+	445.387i	0.0726907	+	0.0350060i
$546$	880.000	−	6621.89i	0.0689753	−	0.519031i
$547$	−15117.9	+	7280.40i	−1.18171	+	0.569081i	−0.918409	−	0.395633i	$-0.870525\pi$
$547$	−15117.9	+	7280.40i	−1.18171	+	0.569081i	−0.263301	+	0.964714i	$0.584811\pi$
$548$	−2366.23	+	2967.15i	−0.184453	+	0.231297i
$549$	5780.39	+	2783.69i	0.449364	+	0.216402i
$550$	−3487.84	−	4373.61i	−0.270403	−	0.339075i
$551$	2983.01	+	13069.4i	0.230636	+	1.01048i
$552$	983.643	+	1233.45i	0.0758453	+	0.0951070i
$553$	17036.4	+	6344.91i	1.31006	+	0.487908i
$554$	−1955.90	+	2452.62i	−0.149997	+	0.188090i
$555$	1975.96	+	951.571i	0.151126	+	0.0727783i
$556$	3125.97	+	13695.8i	0.238437	+	1.04466i
$557$	−19923.1			−1.51557			−0.757783	−	0.652506i	$-0.773718\pi$
$557$	−19923.1			−1.51557			−0.757783	+	0.652506i	$0.773718\pi$
$558$	1958.07			0.148551
$559$	−3420.45	−	14986.0i	−0.258801	−	1.13388i
$560$	−1184.33	−	441.082i	−0.0893697	−	0.0332842i
$561$	1468.29	−	6433.00i	0.110501	−	0.484138i
$562$	838.917	−	3675.54i	0.0629672	−	0.275877i
$563$	−12713.0	+	15941.6i	−0.951666	+	1.19335i	0.0293786	+	0.999568i	$0.490647\pi$
$563$	−12713.0	+	15941.6i	−0.951666	+	1.19335i	−0.981044	+	0.193783i	$0.937924\pi$
$564$	7188.64	−	9014.27i	0.536696	−	0.672995i
$565$	−127.319	+	557.822i	−0.00948028	+	0.0415358i
$566$	−751.422	+	3292.20i	−0.0558032	+	0.244490i
$567$	2222.16	−	16721.5i	0.164589	−	1.23851i
$568$	−1764.41	−	7730.41i	−0.130340	−	0.571057i
$569$	826.351			0.0608830			0.0304415	−	0.999537i	$-0.490309\pi$
$569$	826.351			0.0608830			0.0304415	+	0.999537i	$0.490309\pi$
$570$	450.520			0.0331056
$571$	2876.66	+	12603.5i	0.210831	+	0.923710i	0.964004	+	0.265888i	$0.0856650\pi$
$571$	2876.66	+	12603.5i	0.210831	+	0.923710i	−0.753173	+	0.657822i	$0.771478\pi$
$572$	24014.4	+	11564.7i	1.75541	+	0.845359i
$573$	5765.43	−	7229.63i	0.420339	−	0.527089i
$574$	2083.79	+	2168.50i	0.151525	+	0.157685i
$575$	−1472.13	−	1846.00i	−0.106769	−	0.133884i
$576$	826.405	+	3620.72i	0.0597804	+	0.261915i
$577$	−10156.9	−	12736.4i	−0.732821	−	0.918928i	0.266166	−	0.963927i	$-0.414243\pi$
$577$	−10156.9	−	12736.4i	−0.732821	−	0.918928i	−0.998987	+	0.0449988i	$0.985672\pi$
$578$	3434.89	+	1654.16i	0.247184	+	0.119038i
$579$	6973.24	−	8744.17i	0.500515	−	0.627626i
$580$	2152.50	−	1036.59i	0.154099	−	0.0742103i
$581$	6570.62	−	3948.28i	0.469183	−	0.281931i
$582$	5134.87	+	2472.82i	0.365717	+	0.176120i
$583$	26038.2	−	12539.3i	1.84973	−	0.890782i
$584$	−1130.13	+	4951.41i	−0.0800771	+	0.350841i
$585$	−1226.48	+	590.642i	−0.0866816	+	0.0417437i
$586$	−1500.52	−	1881.59i	−0.105778	−	0.132641i
$587$	14432.0			1.01477			0.507386	−	0.861719i	$-0.330612\pi$
$587$	14432.0			1.01477			0.507386	+	0.861719i	$0.330612\pi$
$588$	7540.23	−	14183.0i	0.528833	−	0.994725i
$589$	−9685.46			−0.677560
$590$	125.120	+	156.896i	0.00873069	+	0.0109479i
$591$	16298.1	−	7848.73i	1.13437	−	0.546284i
$592$	−2534.02	+	11102.3i	−0.175925	+	0.770779i
$593$	9972.84	−	4802.67i	0.690616	−	0.332583i	−0.0554438	−	0.998462i	$-0.517657\pi$
$593$	9972.84	−	4802.67i	0.690616	−	0.332583i	0.746060	+	0.665878i	$0.231943\pi$
$594$	−3376.89	−	1626.23i	−0.233259	−	0.112331i
$595$	−156.179	−	476.577i	−0.0107608	−	0.0328365i
$596$	21569.1	−	10387.1i	1.48239	−	0.713881i
$597$	−3410.52	+	4276.66i	−0.233808	+	0.293186i
$598$	−972.736	−	468.445i	−0.0665186	−	0.0320337i
$599$	−11649.1	−	14607.5i	−0.794609	−	0.996408i	−0.999843	−	0.0176950i	$-0.994367\pi$
$599$	−11649.1	−	14607.5i	−0.794609	−	0.996408i	0.205235	−	0.978713i	$-0.434204\pi$
$600$	2247.65	+	9847.60i	0.152933	+	0.670044i
$601$	−1364.21	−	1710.66i	−0.0925909	−	0.116105i	0.733378	−	0.679821i	$-0.237943\pi$
$601$	−1364.21	−	1710.66i	−0.0925909	−	0.116105i	−0.825969	+	0.563716i	$0.809371\pi$
$602$	−467.284	+	3516.26i	−0.0316363	+	0.238060i
$603$	1356.82	−	1701.39i	0.0916316	−	0.114902i
$604$	−14381.1	−	6925.58i	−0.968807	−	0.466553i
$605$	−517.222	−	2266.10i	−0.0347571	−	0.152281i
$606$	10671.8			0.715365
$607$	6041.06			0.403953			0.201976	−	0.979390i	$-0.435264\pi$
$607$	6041.06			0.403953			0.201976	+	0.979390i	$0.435264\pi$
$608$	1856.85	+	8135.37i	0.123857	+	0.542653i
$609$	8461.55	+	25820.3i	0.563020	+	1.71805i
$610$	120.779	−	529.168i	0.00801672	−	0.0351236i
$611$	−3680.02	+	16123.2i	−0.243663	+	1.06756i
$612$	−1219.26	+	1528.90i	−0.0805321	+	0.100984i
$613$	276.479	−	346.693i	0.0182168	−	0.0228431i	−0.772640	−	0.634845i	$-0.781064\pi$
$613$	276.479	−	346.693i	0.0182168	−	0.0228431i	0.790856	+	0.612002i	$0.209635\pi$
$614$	524.157	−	2296.48i	0.0344516	−	0.150942i
$615$	396.417	−	1736.82i	0.0259920	−	0.113878i
$616$	−8932.57	−	9295.70i	−0.584259	−	0.608010i
$617$	−1632.86	−	7154.03i	−0.106542	−	0.466792i	−0.999850	−	0.0173455i	$-0.994478\pi$
$617$	−1632.86	−	7154.03i	−0.106542	−	0.466792i	0.893307	−	0.449446i	$-0.148379\pi$
$618$	−5022.22			−0.326899
$619$	17256.5			1.12051			0.560256	−	0.828319i	$-0.310703\pi$
$619$	17256.5			1.12051			0.560256	+	0.828319i	$0.310703\pi$
$620$	384.096	+	1682.83i	0.0248801	+	0.109007i
$621$	−1425.31	−	686.392i	−0.0921025	−	0.0443542i
$622$	631.009	−	791.260i	0.0406771	−	0.0510075i
$623$	−21209.4	+	12744.7i	−1.36394	+	0.819590i
$624$	−12810.7	−	16064.1i	−0.821857	−	1.03058i
$625$	−3306.89	−	14488.4i	−0.211641	−	0.927260i
$626$	2742.96	+	3439.56i	0.175129	+	0.219605i
$627$	−18419.6	−	8870.44i	−1.17322	−	0.564994i
$628$	−9085.69	+	11393.1i	−0.577323	+	0.723940i
$629$	−4071.51	+	1960.74i	−0.258095	+	0.124292i
$630$	312.802	−	28.9479i	0.0197815	−	0.00183065i
$631$	−4010.27	−	1931.24i	−0.253005	−	0.121841i	0.303083	−	0.952964i	$-0.401984\pi$
$631$	−4010.27	−	1931.24i	−0.253005	−	0.121841i	−0.556088	+	0.831123i	$0.687698\pi$
$632$	−11324.9	+	5453.79i	−0.712786	+	0.343260i
$633$	1339.07	−	5866.87i	0.0840813	−	0.368384i
$634$	6700.16	−	3226.63i	0.419712	−	0.202123i
$635$	−167.443	−	209.967i	−0.0104642	−	0.0131217i
$636$	−24897.0			−1.55225
$637$	−917.609	+	23021.8i	−0.0570753	+	1.43196i
$638$	10404.5			0.645641
$639$	−5466.65	−	6854.96i	−0.338431	−	0.424379i
$640$	1751.53	−	843.494i	0.108180	−	0.0520969i
$641$	−342.669	+	1501.33i	−0.0211148	+	0.0925101i	−0.984387	−	0.176015i	$-0.943679\pi$
$641$	−342.669	+	1501.33i	−0.0211148	+	0.0925101i	0.963273	+	0.268525i	$0.0865363\pi$
$642$	−6132.53	+	2953.27i	−0.376997	+	0.181552i
$643$	−1555.54	−	749.107i	−0.0954034	−	0.0459438i	0.385574	−	0.922677i	$-0.374004\pi$
$643$	−1555.54	−	749.107i	−0.0954034	−	0.0459438i	−0.480977	+	0.876733i	$0.659718\pi$
$644$	−1798.80	−	1871.92i	−0.110066	−	0.114541i
$645$	1893.13	−	911.683i	0.115569	−	0.0556550i
$646$	−578.791	+	725.780i	−0.0352511	+	0.0442035i
$647$	2900.27	+	1396.70i	0.176231	+	0.0848683i	0.519919	−	0.854216i	$-0.325962\pi$
$647$	2900.27	+	1396.70i	0.176231	+	0.0848683i	−0.343688	+	0.939084i	$0.611676\pi$
$648$	7271.90	+	9118.68i	0.440845	+	0.552802i
$649$	−2026.40	−	8878.25i	−0.122563	−	0.536983i
$650$	−4309.87	−	5404.41i	−0.260072	−	0.326121i
$651$	−19547.7	+	1809.02i	−1.17686	+	0.108911i
$652$	−1180.07	+	1479.76i	−0.0708821	+	0.0888834i
$653$	4967.66	+	2392.30i	0.297702	+	0.143366i	0.576772	−	0.816905i	$-0.304312\pi$
$653$	4967.66	+	2392.30i	0.297702	+	0.143366i	−0.279070	+	0.960271i	$0.590026\pi$
$654$	−856.980	−	3754.67i	−0.0512394	−	0.224494i
$655$	678.140			0.0404536
$656$	9250.26			0.550552
$657$	1249.65	+	5475.09i	0.0742064	+	0.325119i
$658$	2094.39	−	3190.32i	0.124085	−	0.189015i
$659$	−1123.04	+	4920.35i	−0.0663844	+	0.290849i	−0.997213	−	0.0746069i	$-0.976230\pi$
$659$	−1123.04	+	4920.35i	−0.0663844	+	0.290849i	0.930829	+	0.365456i	$0.119087\pi$
$660$	−810.757	+	3552.16i	−0.0478162	+	0.209496i
$661$	15497.5	−	19433.2i	0.911925	−	1.14352i	−0.0772839	−	0.997009i	$-0.524625\pi$
$661$	15497.5	−	19433.2i	0.911925	−	1.14352i	0.989209	−	0.146509i	$-0.0468038\pi$
$662$	−5518.46	+	6919.93i	−0.323990	+	0.406270i
$663$	1814.35	−	7949.17i	0.106280	−	0.465642i
$664$	−1179.40	+	5167.28i	−0.0689300	+	0.302002i
$665$	−1547.26	+	143.189i	−0.0902256	+	0.00834983i
$666$	−629.874	−	2759.66i	−0.0366473	−	0.160562i
$667$	4391.50			0.254932
$668$	4132.05			0.239332
$669$	7076.72	+	31005.1i	0.408971	+	1.79182i
$670$	−165.873	−	79.8801i	−0.00956451	−	0.00460603i
$671$	−15357.0	+	19257.1i	−0.883535	+	1.10792i
$672$	5267.08	+	16072.4i	0.302354	+	0.922629i
$673$	1677.84	+	2103.94i	0.0961010	+	0.120507i	0.827557	−	0.561382i	$-0.189730\pi$
$673$	1677.84	+	2103.94i	0.0961010	+	0.120507i	−0.731456	+	0.681889i	$0.761159\pi$
$674$	−1539.27	−	6744.00i	−0.0879683	−	0.385414i
$675$	−6315.07	−	7918.85i	−0.360100	−	0.451550i
$676$	15225.5	+	7332.19i	0.866264	+	0.417171i
$677$	−1177.99	+	1477.16i	−0.0668745	+	0.0838579i	−0.814144	−	0.580664i	$-0.802793\pi$
$677$	−1177.99	+	1477.16i	−0.0668745	+	0.0838579i	0.747269	+	0.664522i	$0.231365\pi$
$678$	1934.05	−	931.390i	0.109553	−	0.0527579i
$679$	−18421.0	−	6860.58i	−1.04114	−	0.387754i
$680$	312.417	+	150.452i	0.0176186	+	0.00848467i
$681$	11155.3	−	5372.13i	0.627714	−	0.302291i
$682$	−1672.74	+	7328.76i	−0.0939188	+	0.411485i
$683$	8673.07	−	4176.73i	0.485894	−	0.233994i	−0.174865	−	0.984592i	$-0.555949\pi$
$683$	8673.07	−	4176.73i	0.485894	−	0.233994i	0.660759	+	0.750598i	$0.270235\pi$
$684$	3777.69	+	4737.07i	0.211175	+	0.264805i
$685$	744.127			0.0415060
$686$	2052.61	−	4904.64i	0.114241	−	0.272974i
$687$	−32460.0			−1.80266
$688$	6802.55	+	8530.13i	0.376955	+	0.472686i
$689$	32175.0	−	15494.7i	1.77906	−	0.856749i
$690$	32.8408	−	143.885i	0.00181193	−	0.00793857i
$691$	−19468.2	+	9375.40i	−1.07179	+	0.516146i	−0.884683	−	0.466194i	$-0.845625\pi$
$691$	−19468.2	+	9375.40i	−1.07179	+	0.516146i	−0.187106	+	0.982340i	$0.559911\pi$
$692$	22200.3	+	10691.1i	1.21955	+	0.587304i
$693$	−13359.0	−	4975.31i	−0.732272	−	0.272722i
$694$	−4648.02	+	2238.37i	−0.254231	+	0.122431i
$695$	1717.37	−	2153.51i	0.0937317	−	0.117536i
$696$	−16926.3	−	8151.29i	−0.921826	−	0.443928i
$697$	2288.70	+	2869.94i	0.124377	+	0.155964i
$698$	287.443	+	1259.37i	0.0155872	+	0.0682921i
$699$	27221.4	+	34134.5i	1.47297	+	1.84705i
$700$	−5176.20	−	15795.1i	−0.279488	−	0.852854i
$701$	8988.48	−	11271.2i	0.484294	−	0.607286i	−0.478312	−	0.878190i	$-0.658751\pi$
$701$	8988.48	−	11271.2i	0.484294	−	0.607286i	0.962606	+	0.270904i	$0.0873226\pi$
$702$	−4172.78	−	2009.51i	−0.224347	−	0.108040i
$703$	3115.64	+	13650.5i	0.167153	+	0.732344i
$704$	−14257.8			−0.763297
$705$	−2260.67			−0.120769
$706$	1784.11	+	7816.71i	0.0951076	+	0.416694i
$707$	−36650.9	+	3391.82i	−1.94964	+	0.180428i
$708$	−1745.71	+	7648.45i	−0.0926663	+	0.405998i
$709$	−219.629	+	962.259i	−0.0116338	+	0.0509709i	−0.980412	−	0.196959i	$-0.936893\pi$
$709$	−219.629	+	962.259i	−0.0116338	+	0.0509709i	0.968778	+	0.247930i	$0.0797504\pi$
$710$	−462.481	+	579.933i	−0.0244459	+	0.0306542i
$711$	−8665.95	+	10866.8i	−0.457101	+	0.573186i
$712$	3806.99	−	16679.5i	0.200383	−	0.877936i
$713$	−706.025	+	3093.30i	−0.0370839	+	0.162475i
$714$	−1032.59	+	1572.91i	−0.0541227	+	0.0824437i
$715$	−1162.93	−	5095.12i	−0.0608266	−	0.266499i
$716$	−19983.6			−1.04305
$717$	16681.5			0.868873
$718$	−2014.39	−	8825.63i	−0.104703	−	0.458732i
$719$	−972.630	−	468.394i	−0.0504492	−	0.0242951i	0.408489	−	0.912763i	$-0.366056\pi$
$719$	−972.630	−	468.394i	−0.0504492	−	0.0242951i	−0.458938	+	0.888468i	$0.651770\pi$
$720$	602.435	−	755.430i	0.0311826	−	0.0391017i
$721$	17248.2	−	1596.22i	0.890924	−	0.0824496i
$722$	−1786.04	−	2239.62i	−0.0920630	−	0.115443i
$723$	−7945.22	−	34810.3i	−0.408694	−	1.79061i
$724$	−15688.3	−	19672.5i	−0.805321	−	1.00984i
$725$	25332.2	+	12199.3i	1.29768	+	0.624927i
$726$	−5437.14	+	6817.96i	−0.277949	+	0.348538i
$727$	15295.5	−	7365.92i	0.780300	−	0.375773i	−0.000942846	−	1.00000i	$-0.500300\pi$
$727$	15295.5	−	7365.92i	0.780300	−	0.375773i	0.781243	+	0.624227i	$0.214586\pi$
$728$	−11037.8	−	11486.6i	−0.561937	−	0.584781i
$729$	−1236.96	−	595.687i	−0.0628439	−	0.0302640i
$730$	428.057	−	206.141i	0.0217029	−	0.0104516i
$731$	−963.427	+	4221.05i	−0.0487464	+	0.213572i
$732$	19117.6	−	9206.56i	0.965311	−	0.464869i
$733$	5973.64	+	7490.71i	0.301012	+	0.377457i	0.909217	−	0.416323i	$-0.136682\pi$
$733$	5973.64	+	7490.71i	0.301012	+	0.377457i	−0.608205	+	0.793780i	$0.708110\pi$
$734$	−8681.56			−0.436570
$735$	−3096.01	+	577.984i	−0.155371	+	0.0290058i
$736$	2733.59			0.136904
$737$	5208.97	+	6531.84i	0.260346	+	0.326463i
$738$	−2071.60	+	997.632i	−0.103329	+	0.0497606i
$739$	−709.526	+	3108.64i	−0.0353185	+	0.154740i	−0.989512	−	0.144449i	$-0.953859\pi$
$739$	−709.526	+	3108.64i	−0.0353185	+	0.154740i	0.954194	+	0.299189i	$0.0967162\pi$
$740$	2248.19	−	1082.67i	0.111683	−	0.0537836i
$741$	−22760.9	−	10961.1i	−1.12840	−	0.543408i
$742$	−8205.92	+	759.408i	−0.405995	+	0.0375724i
$743$	−6526.63	+	3143.06i	−0.322260	+	0.155192i	−0.588018	−	0.808847i	$-0.700092\pi$
$743$	−6526.63	+	3143.06i	−0.322260	+	0.155192i	0.265759	+	0.964040i	$0.414377\pi$
$744$	8462.89	−	10612.1i	0.417022	−	0.522929i
$745$	−4229.14	−	2036.64i	−0.207978	−	0.100157i
$746$	−566.050	−	709.805i	−0.0277809	−	0.0348362i
$747$	1304.13	+	5713.78i	0.0638765	+	0.279861i
$748$	−4680.87	−	5869.63i	−0.228810	−	0.286918i
$749$	20122.8	−	12091.8i	0.981670	−	0.589884i
$750$	1188.11	−	1489.84i	0.0578447	−	0.0725349i
$751$	−466.852	−	224.824i	−0.0226840	−	0.0109240i	0.422507	−	0.906359i	$-0.361150\pi$
$751$	−466.852	−	224.824i	−0.0226840	−	0.0109240i	−0.445191	+	0.895435i	$0.646864\pi$
$752$	−2612.04	−	11444.1i	−0.126664	−	0.554952i
$753$	7255.88			0.351154
$754$	12856.7			0.620974
$755$	696.425	+	3051.24i	0.0335702	+	0.147081i
$756$	−7716.37	−	8030.06i	−0.371219	−	0.386310i
$757$	5596.74	−	24520.9i	0.268715	−	1.17732i	−0.642795	−	0.766038i	$-0.722225\pi$
$757$	5596.74	−	24520.9i	0.268715	−	1.17732i	0.911510	−	0.411278i	$-0.134918\pi$
$758$	−1022.68	+	4480.65i	−0.0490044	+	0.214703i
$759$	−4175.71	+	5236.17i	−0.199695	+	0.250410i
$760$	669.861	−	839.979i	0.0319716	−	0.0400911i
$761$	−1030.95	+	4516.90i	−0.0491090	+	0.215161i	−0.993529	−	0.113582i	$-0.963768\pi$
$761$	−1030.95	+	4516.90i	−0.0491090	+	0.215161i	0.944420	+	0.328742i	$0.106625\pi$
$762$	−224.205	+	982.306i	−0.0106589	+	0.0466997i
$763$	4136.54	+	12622.6i	0.196269	+	0.598910i
$764$	−2341.15	−	10257.3i	−0.110864	−	0.485726i
$765$	383.431			0.0181215
$766$	3423.12			0.161465
$767$	−2504.00	−	10970.7i	−0.117880	−	0.516467i
$768$	5557.15	+	2676.18i	0.261102	+	0.125740i
$769$	−17050.5	+	21380.6i	−0.799552	+	1.00261i	0.200187	+	0.979758i	$0.435845\pi$
$769$	−17050.5	+	21380.6i	−0.799552	+	1.00261i	−0.999739	+	0.0228489i	$0.992726\pi$
$770$	−158.873	+	1195.50i	−0.00743557	+	0.0559518i
$771$	25219.2	+	31623.9i	1.17801	+	1.47718i
$772$	−2831.60	−	12406.1i	−0.132010	−	0.578373i
$773$	17721.2	+	22221.7i	0.824563	+	1.03397i	0.998786	+	0.0492635i	$0.0156874\pi$
$773$	17721.2	+	22221.7i	0.824563	+	1.03397i	−0.174222	+	0.984706i	$0.555741\pi$
$774$	−2443.40	−	1176.68i	−0.113471	−	0.0546446i
$775$	−12665.7	+	15882.3i	−0.587051	+	0.736139i
$776$	12245.3	−	5897.04i	0.566471	−	0.272798i
$777$	8837.74	+	26968.2i	0.408047	+	1.24515i
$778$	−6685.24	−	3219.44i	−0.308069	−	0.148358i
$779$	10247.1	−	4934.73i	0.471296	−	0.226964i
$780$	−1001.84	+	4389.35i	−0.0459893	+	0.201492i
$781$	30327.2	−	14604.8i	1.38949	−	0.669143i
$782$	189.605	+	237.757i	0.00867042	+	0.0108724i
$783$	18838.4			0.859808
$784$	−6503.12	−	15005.0i	−0.296243	−	0.683536i
$785$	2857.25			0.129911
$786$	−1586.30	−	1989.15i	−0.0719864	−	0.0902681i
$787$	3465.15	−	1668.73i	0.156949	−	0.0755829i	−0.353760	−	0.935336i	$-0.615097\pi$
$787$	3465.15	−	1668.73i	0.156949	−	0.0755829i	0.510710	+	0.859753i	$0.329383\pi$
$788$	4579.87	−	20065.7i	0.207045	−	0.907122i
$789$	27749.7	−	13363.6i	1.25211	−	0.602985i
$790$	1059.42	+	510.192i	0.0477122	+	0.0229770i
$791$	−6346.24	+	3813.45i	−0.285267	+	0.171417i
$792$	8880.34	−	4276.55i	0.398421	−	0.191869i
$793$	−18976.5	+	23795.7i	−0.849779	+	1.06559i
$794$	1838.77	+	885.505i	0.0821858	+	0.0395786i
$795$	3043.66	+	3816.63i	0.135783	+	0.170267i
$796$	1384.90	+	6067.64i	0.0616664	+	0.270178i
$797$	−1324.75	−	1661.18i	−0.0588770	−	0.0738295i	0.751521	−	0.659709i	$-0.229321\pi$
$797$	−1324.75	−	1661.18i	−0.0588770	−	0.0738295i	−0.810398	+	0.585880i	$0.800749\pi$
$798$	4039.33	+	4203.54i	0.179186	+	0.186471i
$799$	2904.32	−	3641.91i	0.128595	−	0.161253i
$800$	15768.6	+	7593.76i	0.696881	+	0.335600i
$801$	−4209.62	−	18443.6i	−0.185693	−	0.813572i
$802$	616.900			0.0271615
$803$	−21560.0			−0.947493
$804$	−1601.55	−	7016.83i	−0.0702515	−	0.307792i
$805$	−67.0567	+	504.593i	−0.00293595	+	0.0220926i
$806$	−2066.98	+	9056.05i	−0.0903305	+	0.395764i
$807$	9429.95	−	41315.3i	0.411338	−	1.80219i
$808$	15867.5	−	19897.2i	0.690860	−	0.866311i
$809$	258.358	−	323.970i	0.0112279	−	0.0140793i	−0.776186	−	0.630504i	$-0.782848\pi$
$809$	258.358	−	323.970i	0.0112279	−	0.0140793i	0.787414	+	0.616425i	$0.211420\pi$
$810$	242.787	−	1063.72i	0.0105317	−	0.0461423i
$811$	3954.77	−	17327.0i	0.171234	−	0.750225i	−0.814258	−	0.580503i	$-0.802856\pi$
$811$	3954.77	−	17327.0i	0.171234	−	0.750225i	0.985492	−	0.169722i	$-0.0542870\pi$
$812$	28970.9	+	10789.7i	1.25207	+	0.466311i
$813$	2352.64	+	10307.6i	0.101489	+	0.444654i
$814$	10867.1			0.467926
$815$	371.107			0.0159501
$816$	1287.81	+	5642.25i	0.0552478	+	0.242057i
$817$	12086.2	+	5820.38i	0.517553	+	0.249240i
$818$	1162.83	−	1458.15i	0.0497036	−	0.0623263i
$819$	−16507.5	−	6147.92i	−0.704295	−	0.262302i
$820$	−1263.77	−	1584.71i	−0.0538203	−	0.0674886i
$821$	−4620.21	−	20242.5i	−0.196403	−	0.860496i	−0.973056	−	0.230568i	$-0.925942\pi$
$821$	−4620.21	−	20242.5i	−0.196403	−	0.860496i	0.776654	−	0.629928i	$-0.216916\pi$
$822$	−1740.65	−	2182.71i	−0.0738591	−	0.0926164i
$823$	−15079.9	−	7262.08i	−0.638701	−	0.307582i	0.0863629	−	0.996264i	$-0.472476\pi$
$823$	−15079.9	−	7262.08i	−0.638701	−	0.307582i	−0.725064	+	0.688682i	$0.758190\pi$
$824$	−7467.34	+	9363.75i	−0.315701	+	0.395876i
$825$	−38633.2	+	18604.7i	−1.63034	+	0.785132i
$826$	−342.083	+	2574.14i	−0.0144099	+	0.108433i
$827$	−30762.2	−	14814.3i	−1.29348	−	0.622905i	−0.344658	−	0.938728i	$-0.612005\pi$
$827$	−30762.2	−	14814.3i	−1.29348	−	0.622905i	−0.948818	+	0.315823i	$0.897720\pi$
$828$	1788.28	−	861.191i	0.0750568	−	0.0361455i
$829$	−9958.03	+	43629.0i	−0.417198	+	1.82786i	0.130834	+	0.991404i	$0.458235\pi$
$829$	−9958.03	+	43629.0i	−0.417198	+	1.82786i	−0.548031	+	0.836458i	$0.684623\pi$
$830$	446.719	−	215.128i	0.0186817	−	0.00899665i
$831$	14992.4	+	18799.9i	0.625848	+	0.784789i
$832$	−17618.2			−0.734135
$833$	3046.37	−	5730.16i	0.126711	−	0.238341i
$834$	−10334.0			−0.429063
$835$	−505.144	−	633.431i	−0.0209356	−	0.0262524i
$836$	−20957.4	+	10092.6i	−0.867018	+	0.417534i
$837$	−3028.66	+	13269.4i	−0.125073	+	0.547980i
$838$	8544.33	−	4114.73i	0.352218	−	0.169619i
$839$	−12069.3	−	5812.26i	−0.496636	−	0.239167i	0.168761	−	0.985657i	$-0.446023\pi$
$839$	−12069.3	−	5812.26i	−0.496636	−	0.239167i	−0.665397	+	0.746490i	$0.731738\pi$
$840$	1195.06	−	1820.40i	0.0490875	−	0.0747737i
$841$	−25142.3	+	12107.9i	−1.03088	+	0.496448i
$842$	−3310.14	+	4150.78i	−0.135481	+	0.169888i
$843$	−26036.4	−	12538.5i	−1.06375	−	0.512275i
$844$	−4268.93	−	5353.07i	−0.174103	−	0.218318i
$845$	−737.312	−	3230.38i	−0.0300169	−	0.131513i
$846$	1819.21	+	2281.21i	0.0739310	+	0.0927066i
$847$	16506.2	−	25143.5i	0.669612	−	1.02000i
$848$	−15804.1	+	19817.7i	−0.639992	+	0.802525i
$849$	23321.0	+	11230.8i	0.942725	+	0.453992i
$850$	433.253	+	1898.21i	0.0174829	+	0.0765976i
$851$	4586.75			0.184761
$852$	−28998.0			−1.16603
$853$	2002.20	+	8772.21i	0.0803681	+	0.352116i	0.999083	−	0.0428046i	$-0.0136293\pi$
$853$	2002.20	+	8772.21i	0.0803681	+	0.352116i	−0.918715	+	0.394920i	$0.870772\pi$
$854$	6020.25	−	3617.56i	0.241228	−	0.144954i
$855$	264.355	−	1158.22i	0.0105740	−	0.0463277i
$856$	−3611.95	+	15825.0i	−0.144222	+	0.631878i
$857$	−7557.13	+	9476.34i	−0.301221	+	0.377719i	−0.909289	−	0.416166i	$-0.863374\pi$
$857$	−7557.13	+	9476.34i	−0.301221	+	0.377719i	0.608068	+	0.793885i	$0.291945\pi$
$858$	−12224.9	+	15329.6i	−0.486425	+	0.609958i
$859$	−7084.09	+	31037.4i	−0.281381	+	1.23281i	0.614644	+	0.788805i	$0.289300\pi$
$859$	−7084.09	+	31037.4i	−0.281381	+	1.23281i	−0.896024	+	0.444005i	$0.853557\pi$
$860$	531.982	−	2330.77i	0.0210935	−	0.0924169i
$861$	19759.5	−	11873.4i	0.782115	−	0.469972i
$862$	−207.375	−	908.571i	−0.00819400	−	0.0359003i
$863$	14.1844			0.000559494			0.000279747	−	1.00000i	$-0.499911\pi$
$863$	14.1844			0.000559494			0.000279747		1.00000i	$0.499911\pi$
$864$	11726.4			0.461736
$865$	−1075.08	−	4710.22i	−0.0422586	−	0.185147i
$866$	−3510.28	−	1690.46i	−0.137741	−	0.0663328i
$867$	18220.3	−	22847.5i	0.713719	−	0.894975i
$868$	−12257.8	+	18671.9i	−0.479326	+	0.730146i
$869$	−33269.5	−	41718.7i	−1.29872	−	1.62855i
$870$	391.074	+	1713.41i	0.0152398	+	0.0667701i
$871$	6436.65	+	8071.30i	0.250399	+	0.313990i
$872$	−8274.67	−	3984.87i	−0.321348	−	0.154753i
$873$	9370.26	−	11749.9i	0.363271	−	0.455527i
$874$	848.909	−	408.813i	0.0328544	−	0.0158219i
$875$	−3606.89	+	5494.28i	−0.139354	+	0.212275i
$876$	16734.2	+	8058.77i	0.645430	+	0.310822i
$877$	−19595.0	+	9436.45i	−0.754477	+	0.363337i	−0.771258	−	0.636522i	$-0.780372\pi$
$877$	−19595.0	+	9436.45i	−0.754477	+	0.363337i	0.0167816	+	0.999859i	$0.494658\pi$
$878$	795.532	−	3485.45i	0.0305785	−	0.133973i
$879$	−16620.6	+	8004.04i	−0.637768	+	0.307133i
$880$	2312.82	+	2900.18i	0.0885966	+	0.111097i
$881$	−13047.2			−0.498944			−0.249472	−	0.968382i	$-0.580257\pi$
$881$	−13047.2			−0.498944			−0.249472	+	0.968382i	$0.580257\pi$
$882$	3074.65	+	2659.02i	0.117380	+	0.101512i
$883$	21340.2			0.813312			0.406656	−	0.913581i	$-0.366695\pi$
$883$	21340.2			0.813312			0.406656	+	0.913581i	$0.366695\pi$
$884$	−5784.09	−	7253.02i	−0.220068	−	0.275956i
$885$	1385.90	−	667.412i	0.0526400	−	0.0253501i
$886$	605.062	−	2650.95i	0.0229429	−	0.100520i
$887$	19905.9	−	9586.16i	0.753521	−	0.362877i	−0.0173653	−	0.999849i	$-0.505528\pi$
$887$	19905.9	−	9586.16i	0.753521	−	0.362877i	0.770887	+	0.636973i	$0.219814\pi$
$888$	−17678.9	−	8513.69i	−0.668090	−	0.321735i
$889$	457.797	−	3444.87i	0.0172711	−	0.129963i
$890$	−1441.97	+	694.415i	−0.0543088	+	0.0261538i
$891$	−30870.3	+	38710.1i	−1.16071	+	1.45548i
$892$	32600.7	+	15699.7i	1.22371	+	0.589309i
$893$	−8998.60	−	11283.9i	−0.337208	−	0.422846i
$894$	3918.76	+	17169.2i	0.146603	+	0.642309i
$895$	2442.99	+	3063.42i	0.0912405	+	0.114412i
$896$	23574.3	+	8779.83i	0.878975	+	0.327359i
$897$	−5159.86	+	6470.26i	−0.192066	+	0.240843i
$898$	5586.38	+	2690.26i	0.207594	+	0.0999722i
$899$	−8407.47	−	36835.5i	−0.311908	−	1.36656i
$900$	12708.0			0.470665
$901$	−10058.8			−0.371927
$902$	−1964.26	−	8605.97i	−0.0725084	−	0.317680i
$903$	25480.0	+	9489.59i	0.939006	+	0.349716i
$904$	1139.12	−	4990.82i	0.0419100	−	0.183620i
$905$	−1097.84	+	4809.94i	−0.0403242	+	0.176672i
$906$	7320.96	−	9180.20i	0.268458	−	0.336635i
$907$	16785.4	−	21048.2i	0.614498	−	0.770556i	−0.373061	−	0.927807i	$-0.621692\pi$
$907$	16785.4	−	21048.2i	0.614498	−	0.770556i	0.987559	+	0.157251i	$0.0502632\pi$
$908$	3134.73	−	13734.1i	0.114570	−	0.501964i
$909$	6261.96	−	27435.5i	0.228489	−	1.00107i
$910$	−196.317	+	1477.26i	−0.00715149	+	0.0538141i
$911$	7175.01	+	31435.8i	0.260943	+	1.14326i	0.920231	+	0.391375i	$0.128000\pi$
$911$	7175.01	+	31435.8i	0.260943	+	1.14326i	−0.659289	+	0.751890i	$0.729142\pi$
$912$	17931.2			0.651055
$913$	−22500.0			−0.815597
$914$	137.714	+	603.363i	0.00498376	+	0.0218353i
$915$	−3748.47	−	1805.17i	−0.135432	−	0.0652208i
$916$	−23026.8	+	28874.7i	−0.830598	+	1.04154i
$917$	6080.15	+	6327.32i	0.218958	+	0.227859i
$918$	813.357	+	1019.92i	0.0292427	+	0.0366691i
$919$	1595.08	+	6988.50i	0.0572544	+	0.250848i	0.995454	−	0.0952477i	$-0.0303643\pi$
$919$	1595.08	+	6988.50i	0.0572544	+	0.250848i	−0.938199	+	0.346096i	$0.887507\pi$
$920$	−219.439	−	275.168i	−0.00786379	−	0.00986088i
$921$	−16267.6	−	7834.07i	−0.582016	−	0.280284i
$922$	1413.00	−	1771.85i	0.0504716	−	0.0632893i
$923$	37474.9	−	18046.9i	1.33640	−	0.643578i
$924$	−40412.3	+	24283.7i	−1.43882	+	0.864583i
$925$	26458.5	+	12741.7i	0.940485	+	0.452914i
$926$	935.517	−	450.521i	0.0331998	−	0.0159882i
$927$	−2946.93	+	12911.3i	−0.104412	+	0.457458i
$928$	−29328.4	+	14123.8i	−1.03745	+	0.499609i
$929$	−8461.20	−	10610.0i	−0.298819	−	0.374708i	0.609642	−	0.792677i	$-0.291313\pi$
$929$	−8461.20	−	10610.0i	−0.298819	−	0.374708i	−0.908461	+	0.417970i	$0.862742\pi$
$930$	−1269.77			−0.0447713
$931$	−15208.6	−	13152.7i	−0.535383	−	0.463010i
$932$	49674.9			1.74587
$933$	−4836.81	−	6065.17i	−0.169721	−	0.212824i
$934$	−9860.75	+	4748.68i	−0.345453	+	0.166362i
$935$	−327.558	+	1435.13i	−0.0114570	+	0.0501964i
$936$	10973.3	−	5284.47i	0.383199	−	0.184539i
$937$	−21387.1	−	10299.5i	−0.745664	−	0.359093i	0.0221592	−	0.999754i	$-0.492946\pi$
$937$	−21387.1	−	10299.5i	−0.745664	−	0.359093i	−0.767824	+	0.640661i	$0.778660\pi$
$938$	−741.888	−	2263.86i	−0.0258246	−	0.0788035i
$939$	30382.5	−	14631.4i	1.05590	−	0.508497i
$940$	−1603.70	+	2010.98i	−0.0556457	+	0.0697775i
$941$	−24781.4	−	11934.1i	−0.858503	−	0.413433i	−0.0477760	−	0.998858i	$-0.515213\pi$
$941$	−24781.4	−	11934.1i	−0.858503	−	0.413433i	−0.810727	+	0.585425i	$0.800928\pi$
$942$	−6683.65	−	8381.04i	−0.231173	−	0.289882i
$943$	−829.067	−	3632.38i	−0.0286300	−	0.125436i
$944$	4979.92	+	6244.62i	0.171698	+	0.215302i
$945$	−287.655	+	2164.57i	−0.00990204	+	0.0745117i
$946$	6491.50	−	8140.09i	0.223105	−	0.279764i
$947$	26811.1	+	12911.5i	0.920002	+	0.443050i	0.833072	−	0.553165i	$-0.186580\pi$
$947$	26811.1	+	12911.5i	0.920002	+	0.443050i	0.0869303	+	0.996214i	$0.472294\pi$
$948$	10229.0	+	44816.3i	0.350447	+	1.53541i
$949$	−26641.4			−0.911293
$950$	6032.55			0.206023
$951$	−12684.4	−	55574.0i	−0.432513	−	1.89496i
$952$	1397.33	+	4263.92i	0.0475711	+	0.145162i
$953$	2358.75	−	10334.3i	0.0801756	−	0.351272i	−0.918889	−	0.394516i	$-0.870912\pi$
$953$	2358.75	−	10334.3i	0.0801756	−	0.351272i	0.999065	+	0.0432441i	$0.0137693\pi$
$954$	1402.02	−	6142.63i	0.0475807	−	0.208464i
$955$	−1286.20	+	1612.84i	−0.0435816	+	0.0546496i
$956$	11833.7	−	14839.0i	0.400344	−	0.502016i
$957$	17746.7	−	77753.2i	0.599444	−	2.62634i
$958$	−2053.30	+	8996.08i	−0.0692474	+	0.303393i
$959$	6671.79	+	6943.01i	0.224654	+	0.233787i
$960$	−535.907	−	2347.96i	−0.0180170	−	0.0789377i
$961$	−2493.02			−0.0836837
$962$	13428.3			0.450048
$963$	3993.96	+	17498.7i	0.133649	+	0.585553i
$964$	−36601.7	−	17626.4i	−1.22289	−	0.588910i
$965$	−1555.65	+	1950.72i	−0.0518943	+	0.0650735i
$966$	1636.96	−	983.644i	0.0545219	−	0.0327622i
$967$	29795.1	+	37361.8i	0.990842	+	1.24248i	0.970103	+	0.242692i	$0.0780304\pi$
$967$	29795.1	+	37361.8i	0.990842	+	1.24248i	0.0207388	+	0.999785i	$0.493398\pi$
$968$	4627.57	+	20274.7i	0.153653	+	0.673197i
$969$	4436.55	+	5563.25i	0.147082	+	0.184435i
$970$	−1145.53	−	551.657i	−0.0379182	−	0.0182605i
$971$	−19242.2	+	24129.0i	−0.635955	+	0.797463i	−0.990491	−	0.137580i	$-0.956068\pi$
$971$	−19242.2	+	24129.0i	−0.635955	+	0.797463i	0.354535	+	0.935043i	$0.384639\pi$
$972$	23801.9	−	11462.4i	0.785438	−	0.378247i
$973$	35491.0	−	3284.48i	1.16936	−	0.108217i
$974$	−11376.0	−	5478.40i	−0.374241	−	0.180225i
$975$	−47738.5	+	22989.6i	−1.56806	+	0.755136i
$976$	4807.14	−	21061.5i	0.157657	−	0.690739i
$977$	−13996.6	+	6740.39i	−0.458332	+	0.220721i	−0.648779	−	0.760976i	$-0.724720\pi$
$977$	−13996.6	+	6740.39i	−0.458332	+	0.220721i	0.190448	+	0.981697i	$0.439006\pi$
$978$	−868.088	−	1088.55i	−0.0283828	−	0.0355909i
$979$	72627.8			2.37099
$980$	−1682.14	+	3164.06i	−0.0548305	+	0.103135i
$981$	−10155.5			−0.330521
$982$	7582.69	+	9508.39i	0.246409	+	0.308987i
$983$	−9172.12	+	4417.06i	−0.297605	+	0.143319i	−0.576728	−	0.816937i	$-0.695671\pi$
$983$	−9172.12	+	4417.06i	−0.297605	+	0.143319i	0.279123	+	0.960255i	$0.409956\pi$
$984$	−3546.74	+	15539.3i	−0.114904	+	0.503429i
$985$	−3635.90	+	1750.96i	−0.117614	+	0.0566398i
$986$	−3262.69	−	1571.23i	−0.105381	−	0.0507486i
$987$	−20269.0	−	21093.0i	−0.653668	−	0.680241i
$988$	−25896.8	+	12471.2i	−0.833893	+	0.401582i
$989$	2739.91	−	3435.74i	0.0880931	−	0.110465i
$990$	−830.739	−	400.063i	−0.0266693	−	0.0128433i
$991$	−16545.9	−	20747.9i	−0.530372	−	0.665065i	0.442403	−	0.896816i	$-0.354126\pi$
$991$	−16545.9	−	20747.9i	−0.530372	−	0.665065i	−0.972775	+	0.231751i	$0.925555\pi$
$992$	−5233.42	−	22929.1i	−0.167501	−	0.733871i
$993$	42300.1	+	53042.7i	1.35182	+	1.69512i
$994$	−9557.59	+	884.497i	−0.304978	+	0.0282239i
$995$	760.846	−	954.071i	0.0242417	−	0.0303981i
$996$	17463.8	+	8410.10i	0.555583	+	0.267555i
$997$	−1841.16	−	8066.64i	−0.0584855	−	0.256242i	0.937230	−	0.348712i	$-0.113381\pi$
$997$	−1841.16	−	8066.64i	−0.0584855	−	0.256242i	−0.995715	+	0.0924702i	$0.970524\pi$
$998$	8207.11			0.260312
$999$	19675.9			0.623142

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.4.e.a.8.8	✓	78
49.22	even	7		2401.4.a.d.1.23		39
49.27	odd	14		2401.4.a.c.1.23		39
49.43	even	7	inner	49.4.e.a.43.8	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.8.8	✓	78	1.1	even	1	trivial
49.4.e.a.43.8	yes	78	49.43	even	7	inner
2401.4.a.c.1.23		39	49.27	odd	14
2401.4.a.d.1.23		39	49.22	even	7

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.521845 + 0.654373i) q^{2} +(5.78023 - 2.78361i) q^{3} +(1.62429 - 7.11646i) q^{4} +(-1.28950 + 0.620991i) q^{5} +(4.83790 + 2.32981i) q^{6} +(-17.3557 - 6.46381i) q^{7} +(11.5371 - 5.55599i) q^{8} +(8.82835 - 11.0704i) q^{9} +(-1.07928 - 0.519753i) q^{10} +(33.8930 + 42.5005i) q^{11} +(-10.4207 - 45.6562i) q^{12} +(41.8811 + 52.5173i) q^{13} +(-4.82722 - 14.7302i) q^{14} +(-5.72501 + 7.17894i) q^{15} +(-42.9565 - 20.6868i) q^{16} +(-4.21013 - 18.4458i) q^{17} +11.8512 q^{18} -58.6213 q^{19} +(2.32474 + 10.1853i) q^{20} +(-118.313 + 10.9491i) q^{21} +(-10.1243 + 44.3573i) q^{22} +(-4.27322 + 18.7222i) q^{23} +(51.2216 - 64.2299i) q^{24} +(-76.6590 + 96.1274i) q^{25} +(-12.5104 + 54.8117i) q^{26} +(-18.3310 + 80.3133i) q^{27} +(-74.1900 + 113.012i) q^{28} +(-50.8862 - 222.947i) q^{29} -7.68527 q^{30} +165.221 q^{31} +(-31.6753 - 138.778i) q^{32} +(314.214 + 151.318i) q^{33} +(9.87339 - 12.3808i) q^{34} +(26.3941 - 2.44262i) q^{35} +(-64.4423 - 80.8081i) q^{36} +(-53.1486 - 232.859i) q^{37} +(-30.5912 - 38.3601i) q^{38} +(388.270 + 186.981i) q^{39} +(-11.4269 + 14.3289i) q^{40} +(-174.801 + 84.1798i) q^{41} +(-68.9056 - 71.7067i) q^{42} +(-206.174 - 99.2879i) q^{43} +(357.505 - 172.165i) q^{44} +(-4.50955 + 19.7576i) q^{45} +(-14.4812 + 6.97380i) q^{46} +(153.504 + 192.488i) q^{47} -305.882 q^{48} +(259.438 + 224.368i) q^{49} -102.907 q^{50} +(-75.6815 - 94.9016i) q^{51} +(441.764 - 212.742i) q^{52} +(118.302 - 518.313i) q^{53} +(-62.1207 + 29.9158i) q^{54} +(-70.0975 - 33.7572i) q^{55} +(-236.148 + 21.8540i) q^{56} +(-338.844 + 163.179i) q^{57} +(119.336 - 149.642i) q^{58} +(-150.933 - 72.6854i) q^{59} +(41.7896 + 52.4025i) q^{60} +(100.825 + 441.743i) q^{61} +(86.2197 + 108.116i) q^{62} +(-224.779 + 135.069i) q^{63} +(-163.531 + 205.062i) q^{64} +(-86.6185 - 41.7133i) q^{65} +(64.9530 + 284.578i) q^{66} +153.689 q^{67} -138.107 q^{68} +(27.4151 + 120.114i) q^{69} +(15.3720 + 15.9969i) q^{70} +(137.788 - 603.690i) q^{71} +(40.3468 - 176.771i) q^{72} +(-247.285 + 310.085i) q^{73} +(124.641 - 156.295i) q^{74} +(-175.526 + 769.028i) q^{75} +(-95.2177 + 417.176i) q^{76} +(-313.521 - 956.703i) q^{77} +(80.2615 + 351.649i) q^{78} -981.604 q^{79} +68.2387 q^{80} +(202.675 + 887.979i) q^{81} +(-146.304 - 70.4563i) q^{82} +(-258.066 + 323.604i) q^{83} +(-114.254 + 859.751i) q^{84} +(16.8836 + 21.1714i) q^{85} +(-42.6193 - 186.727i) q^{86} +(-914.732 - 1147.04i) q^{87} +(627.161 + 302.025i) q^{88} +(833.012 - 1044.56i) q^{89} +(-15.2821 + 7.35948i) q^{90} +(-387.413 - 1182.18i) q^{91} +(126.295 + 60.8204i) q^{92} +(955.016 - 459.911i) q^{93} +(-45.8536 + 200.898i) q^{94} +(75.5921 - 36.4033i) q^{95} +(-569.396 - 714.000i) q^{96} +1061.38 q^{97} +(-11.4335 + 286.854i) q^{98} +769.717 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + 9 q^{10} - 103 q^{11} + 364 q^{12} - 35 q^{13} + 161 q^{14} - 245 q^{15} - 205 q^{16} - 285 q^{17} + 16 q^{18} + 628 q^{19}+ \cdots + 10768 q^{99}+O(q^{100}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9 + 9 * q^10 - 103 * q^11 + 364 * q^12 - 35 * q^13 + 161 * q^14 - 245 * q^15 - 205 * q^16 - 285 * q^17 + 16 * q^18 + 628 * q^19 + 553 * q^20 - 21 * q^21 - 605 * q^22 + 149 * q^23 + 653 * q^24 - 370 * q^25 - 511 * q^26 - 65 * q^27 + 70 * q^28 - 187 * q^29 + 84 * q^30 + 1276 * q^31 + 1399 * q^32 - 23 * q^33 - 765 * q^34 - 805 * q^35 - 1691 * q^36 - 1531 * q^37 - 1041 * q^38 - 1351 * q^39 - 1759 * q^40 - 301 * q^41 + 3395 * q^42 - 257 * q^43 - 883 * q^44 + 3105 * q^45 + 1593 * q^46 + 733 * q^47 - 1948 * q^48 + 1288 * q^49 + 6148 * q^50 + 1197 * q^51 - 1099 * q^52 - 285 * q^53 + 660 * q^54 + 2641 * q^55 - 1988 * q^56 - 2352 * q^57 + 1173 * q^58 - 3603 * q^59 - 175 * q^60 - 2613 * q^61 - 1927 * q^62 - 3066 * q^63 + 1589 * q^64 - 371 * q^65 - 2175 * q^66 + 352 * q^67 + 6076 * q^68 + 5549 * q^69 - 6293 * q^70 - 2623 * q^71 + 6220 * q^72 + 2039 * q^73 - 2411 * q^74 - 3903 * q^75 + 4130 * q^76 + 1029 * q^77 - 3759 * q^78 + 44 * q^79 - 1608 * q^80 + 1394 * q^81 - 10920 * q^82 - 553 * q^83 - 7798 * q^84 + 497 * q^85 - 2985 * q^86 - 4273 * q^87 - 2197 * q^88 - 3957 * q^89 - 2958 * q^90 + 14119 * q^91 - 9136 * q^92 + 6272 * q^93 + 14912 * q^94 + 5866 * q^95 + 21882 * q^96 - 1540 * q^97 - 2303 * q^98 + 10768 * q^99

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