LMFDB - Embedded newform 197.4.e.a.6.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,4,Mod(6,197)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([13]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("197.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	197.e (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.6233762711$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$48$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			6.19
Character	$\chi$	$=$	197.6
Dual form			197.4.e.a.33.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.69384 + 0.386608i) q^{2} +(8.91279 + 2.03429i) q^{3} +(-4.48812 + 2.16137i) q^{4} +(8.48300 - 17.6151i) q^{5} -15.8833 q^{6} +(0.935927 - 4.10056i) q^{7} +(17.6334 - 14.0622i) q^{8} +(50.9733 + 24.5474i) q^{9} +(-7.55869 + 33.1168i) q^{10} +(-3.07930 + 0.702831i) q^{11} +(-44.3985 + 10.1337i) q^{12} +(-48.7737 - 38.8958i) q^{13} +7.30753i q^{14} +(111.441 - 139.743i) q^{15} +(0.415436 - 0.520940i) q^{16} +(45.9395 - 95.3943i) q^{17} +(-95.8308 - 21.8727i) q^{18} -72.3042 q^{19} +97.3938i q^{20} +(16.6834 - 34.6435i) q^{21} +(4.94413 - 2.38097i) q^{22} +(15.3178 + 67.1116i) q^{23} +(185.769 - 89.4617i) q^{24} +(-160.395 - 201.129i) q^{25} +(97.6523 + 47.0269i) q^{26} +(211.395 + 168.582i) q^{27} +(4.66226 + 20.4267i) q^{28} +(40.8656 + 179.044i) q^{29} +(-134.738 + 279.786i) q^{30} +(265.933 - 60.6974i) q^{31} +(-78.7886 + 163.606i) q^{32} -28.8749 q^{33} +(-40.9339 + 179.343i) q^{34} +(-64.2925 - 51.2715i) q^{35} -281.830 q^{36} +(-110.750 - 138.876i) q^{37} +(122.472 - 27.9534i) q^{38} +(-355.585 - 445.889i) q^{39} +(-98.1227 - 429.904i) q^{40} +(403.719 + 194.421i) q^{41} +(-14.8656 + 65.1305i) q^{42} +(79.8688 + 349.928i) q^{43} +(12.3012 - 9.80990i) q^{44} +(864.812 - 689.665i) q^{45} +(-51.8917 - 107.754i) q^{46} +(-82.9105 - 103.966i) q^{47} +(4.76243 - 3.79791i) q^{48} +(293.094 + 141.146i) q^{49} +(349.442 + 278.671i) q^{50} +(603.508 - 756.775i) q^{51} +(302.971 + 69.1511i) q^{52} +(52.0533 - 25.0675i) q^{53} +(-423.244 - 203.824i) q^{54} +(-13.7413 + 60.2045i) q^{55} +(-41.1592 - 85.4680i) q^{56} +(-644.432 - 147.087i) q^{57} +(-138.439 - 287.472i) q^{58} +(-93.2902 - 408.731i) q^{59} +(-198.127 + 868.050i) q^{60} +(40.3358 + 176.723i) q^{61} +(-426.981 + 205.623i) q^{62} +(148.366 - 186.044i) q^{63} +(69.0177 - 302.386i) q^{64} +(-1098.90 + 529.203i) q^{65} +(48.9095 - 11.1633i) q^{66} +(-516.652 + 412.017i) q^{67} +527.434i q^{68} +629.312i q^{69} +(128.723 + 61.9898i) q^{70} +(137.660 - 285.853i) q^{71} +(1244.02 - 283.940i) q^{72} +(-611.686 + 487.804i) q^{73} +(241.282 + 192.416i) q^{74} +(-1020.41 - 2118.91i) q^{75} +(324.510 - 156.276i) q^{76} +13.2847i q^{77} +(774.688 + 617.793i) q^{78} +(379.972 + 789.019i) q^{79} +(-5.65228 - 11.7371i) q^{80} +(588.759 + 738.281i) q^{81} +(-758.999 - 173.237i) q^{82} +746.624 q^{83} +191.543i q^{84} +(-1290.68 - 1618.46i) q^{85} +(-270.570 - 561.844i) q^{86} +1678.91i q^{87} +(-44.4153 + 55.6950i) q^{88} +(-713.957 - 162.956i) q^{89} +(-1198.22 + 1502.52i) q^{90} +(-205.143 + 163.596i) q^{91} +(-213.801 - 268.098i) q^{92} +2493.68 q^{93} +(180.631 + 144.049i) q^{94} +(-613.357 + 1273.65i) q^{95} +(-1035.05 + 1297.91i) q^{96} +(-1347.35 - 648.849i) q^{97} +(-551.022 - 125.767i) q^{98} +(-174.215 - 39.7634i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 7 q^{2} - 7 q^{3} + 159 q^{4} - 7 q^{5} + 26 q^{6} - 53 q^{7} + 49 q^{8} + 391 q^{9} + 149 q^{10} + 91 q^{11} - 63 q^{12} - 7 q^{13} - 473 q^{15} - 1113 q^{16} - 7 q^{17} - 196 q^{18} + 464 q^{19}+ \cdots + 2464 q^{99}+O(q^{100}) $ 288 * q - 7 * q^2 - 7 * q^3 + 159 * q^4 - 7 * q^5 + 26 * q^6 - 53 * q^7 + 49 * q^8 + 391 * q^9 + 149 * q^10 + 91 * q^11 - 63 * q^12 - 7 * q^13 - 473 * q^15 - 1113 * q^16 - 7 * q^17 - 196 * q^18 + 464 * q^19 - 7 * q^21 + 807 * q^22 + 413 * q^23 - 1425 * q^24 + 1195 * q^25 - 543 * q^26 + 455 * q^27 + 174 * q^28 - 906 * q^29 + 798 * q^30 + 917 * q^31 + 945 * q^32 + 894 * q^33 - 219 * q^34 - 7 * q^35 + 3250 * q^36 + 1734 * q^37 - 63 * q^38 - 825 * q^39 + 141 * q^40 + 563 * q^41 + 432 * q^42 - 423 * q^43 + 2149 * q^44 - 3808 * q^45 - 2569 * q^46 - 289 * q^47 - 3703 * q^48 - 3747 * q^49 - 4963 * q^50 - 87 * q^51 + 3654 * q^52 - 1573 * q^53 - 1228 * q^54 + 2825 * q^55 + 98 * q^56 - 518 * q^57 - 5103 * q^58 + 2045 * q^59 + 3375 * q^60 + 287 * q^61 - 2547 * q^62 + 1453 * q^63 + 6475 * q^64 + 1268 * q^65 + 4634 * q^66 - 3577 * q^67 - 814 * q^70 - 273 * q^71 - 1008 * q^72 - 679 * q^73 - 315 * q^74 - 1281 * q^75 + 6078 * q^76 + 4739 * q^78 + 1463 * q^79 + 441 * q^80 - 4427 * q^81 - 7 * q^82 + 4900 * q^83 - 3351 * q^85 + 3472 * q^86 + 3738 * q^88 + 147 * q^89 + 7133 * q^90 - 14133 * q^91 - 803 * q^92 - 4894 * q^93 - 7833 * q^94 - 7700 * q^95 - 16450 * q^96 + 1233 * q^97 - 2030 * q^98 + 2464 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{14}\right)$

Coefficient data

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

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

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

$2$	−1.69384	+	0.386608i	−0.598863	+	0.136686i	−0.511197	−	0.859463i	$-0.670798\pi$
$2$	−1.69384	+	0.386608i	−0.598863	+	0.136686i	−0.0876655	+	0.996150i	$0.527941\pi$
$3$	8.91279	+	2.03429i	1.71527	+	0.391498i	0.963453	−	0.267878i	$-0.0863223\pi$
$3$	8.91279	+	2.03429i	1.71527	+	0.391498i	0.751813	+	0.659376i	$0.229179\pi$
$4$	−4.48812	+	2.16137i	−0.561016	+	0.270171i
$5$	8.48300	−	17.6151i	0.758742	−	1.57555i	−0.0578465	−	0.998325i	$-0.518423\pi$
$5$	8.48300	−	17.6151i	0.758742	−	1.57555i	0.816589	−	0.577220i	$-0.195862\pi$
$6$	−15.8833			−1.08072
$7$	0.935927	−	4.10056i	0.0505353	−	0.221410i	−0.943355	−	0.331786i	$-0.892349\pi$
$7$	0.935927	−	4.10056i	0.0505353	−	0.221410i	0.993890	+	0.110377i	$0.0352058\pi$
$8$	17.6334	−	14.0622i	0.779293	−	0.621466i
$9$	50.9733	+	24.5474i	1.88790	+	0.909164i
$10$	−7.55869	+	33.1168i	−0.239027	+	1.04724i
$11$	−3.07930	+	0.702831i	−0.0844041	+	0.0192647i	−0.264514	−	0.964382i	$-0.585212\pi$
$11$	−3.07930	+	0.702831i	−0.0844041	+	0.0192647i	0.180110	+	0.983646i	$0.442355\pi$
$12$	−44.3985	+	10.1337i	−1.06806	+	0.243778i
$13$	−48.7737	−	38.8958i	−1.04057	−	0.829826i	−0.0548959	−	0.998492i	$-0.517483\pi$
$13$	−48.7737	−	38.8958i	−1.04057	−	0.829826i	−0.985673	+	0.168666i	$0.946054\pi$
$14$			7.30753i			0.139501i
$15$	111.441	−	139.743i	1.91827	−	2.40543i
$16$	0.415436	−	0.520940i	0.00649118	−	0.00813969i
$17$	45.9395	−	95.3943i	0.655409	−	1.36097i	−0.262790	−	0.964853i	$-0.584643\pi$
$17$	45.9395	−	95.3943i	0.655409	−	1.36097i	0.918199	−	0.396118i	$-0.129643\pi$
$18$	−95.8308	−	21.8727i	−1.25486	−	0.286414i
$19$	−72.3042			−0.873038			−0.436519	−	0.899695i	$-0.643789\pi$
$19$	−72.3042			−0.873038			−0.436519	+	0.899695i	$0.643789\pi$
$20$			97.3938i			1.08890i
$21$	16.6834	−	34.6435i	0.173363	−	0.359992i
$22$	4.94413	−	2.38097i	0.0479132	−	0.0230738i
$23$	15.3178	+	67.1116i	0.138869	+	0.608423i	0.995685	+	0.0928010i	$0.0295820\pi$
$23$	15.3178	+	67.1116i	0.138869	+	0.608423i	−0.856816	+	0.515622i	$0.827561\pi$
$24$	185.769	−	89.4617i	1.58000	−	0.760887i
$25$	−160.395	−	201.129i	−1.28316	−	1.60903i
$26$	97.6523	+	47.0269i	0.736584	+	0.354720i
$27$	211.395	+	168.582i	1.50678	+	1.20161i
$28$	4.66226	+	20.4267i	0.0314673	+	0.137867i
$29$	40.8656	+	179.044i	0.261674	+	1.14647i	0.919435	+	0.393242i	$0.128646\pi$
$29$	40.8656	+	179.044i	0.261674	+	1.14647i	−0.657761	+	0.753227i	$0.728496\pi$
$30$	−134.738	+	279.786i	−0.819989	+	1.70273i
$31$	265.933	−	60.6974i	1.54074	−	0.351664i	0.633993	−	0.773339i	$-0.281415\pi$
$31$	265.933	−	60.6974i	1.54074	−	0.351664i	0.906747	+	0.421675i	$0.138558\pi$
$32$	−78.7886	+	163.606i	−0.435250	+	0.903806i
$33$	−28.8749			−0.152318
$34$	−40.9339	+	179.343i	−0.206474	+	0.904621i
$35$	−64.2925	−	51.2715i	−0.310497	−	0.247613i
$36$	−281.830			−1.30477
$37$	−110.750	−	138.876i	−0.492084	−	0.617054i	0.472339	−	0.881417i	$-0.343410\pi$
$37$	−110.750	−	138.876i	−0.492084	−	0.617054i	−0.964423	+	0.264363i	$0.914838\pi$
$38$	122.472	−	27.9534i	0.522830	−	0.119333i
$39$	−355.585	−	445.889i	−1.45998	−	1.83075i
$40$	−98.1227	−	429.904i	−0.387864	−	1.69934i
$41$	403.719	+	194.421i	1.53781	+	0.740571i	0.995056	−	0.0993192i	$-0.0316665\pi$
$41$	403.719	+	194.421i	1.53781	+	0.740571i	0.542756	+	0.839890i	$0.317381\pi$
$42$	−14.8656	+	65.1305i	−0.0546146	+	0.239282i
$43$	79.8688	+	349.928i	0.283253	+	1.24101i	0.893595	+	0.448874i	$0.148175\pi$
$43$	79.8688	+	349.928i	0.283253	+	1.24101i	−0.610342	+	0.792138i	$0.708968\pi$
$44$	12.3012	−	9.80990i	0.0421473	−	0.0336113i
$45$	864.812	−	689.665i	2.86486	−	2.28465i
$46$	−51.8917	−	107.754i	−0.166326	−	0.345380i
$47$	−82.9105	−	103.966i	−0.257313	−	0.322661i	0.636348	−	0.771402i	$-0.280444\pi$
$47$	−82.9105	−	103.966i	−0.257313	−	0.322661i	−0.893662	+	0.448741i	$0.851873\pi$
$48$	4.76243	−	3.79791i	0.0143208	−	0.0114204i
$49$	293.094	+	141.146i	0.854500	+	0.411506i
$50$	349.442	+	278.671i	0.988371	+	0.788200i
$51$	603.508	−	756.775i	1.65702	−	2.07784i
$52$	302.971	+	69.1511i	0.807970	+	0.184414i
$53$	52.0533	−	25.0675i	0.134907	−	0.0649678i	−0.365213	−	0.930924i	$-0.619004\pi$
$53$	52.0533	−	25.0675i	0.134907	−	0.0649678i	0.500120	+	0.865956i	$0.333289\pi$
$54$	−423.244	−	203.824i	−1.06660	−	0.513646i
$55$	−13.7413	+	60.2045i	−0.0336886	+	0.147599i
$56$	−41.1592	−	85.4680i	−0.0982166	−	0.203949i
$57$	−644.432	−	147.087i	−1.49749	−	0.341793i
$58$	−138.439	−	287.472i	−0.313414	−	0.650810i
$59$	−93.2902	−	408.731i	−0.205853	−	0.901903i	−0.967292	−	0.253666i	$-0.918364\pi$
$59$	−93.2902	−	408.731i	−0.205853	−	0.901903i	0.761439	−	0.648237i	$-0.224493\pi$
$60$	−198.127	+	868.050i	−0.426301	+	1.86775i
$61$	40.3358	+	176.723i	0.0846634	+	0.370934i	0.999456	−	0.0329901i	$-0.0105030\pi$
$61$	40.3358	+	176.723i	0.0846634	+	0.370934i	−0.914792	+	0.403925i	$0.867646\pi$
$62$	−426.981	+	205.623i	−0.874624	+	0.421197i
$63$	148.366	−	186.044i	0.296703	−	0.372054i
$64$	69.0177	−	302.386i	0.134800	−	0.590598i
$65$	−1098.90	+	529.203i	−2.09695	+	1.00984i
$66$	48.9095	−	11.1633i	0.0912173	−	0.0208198i
$67$	−516.652	+	412.017i	−0.942077	+	0.751281i	−0.968666	−	0.248365i	$-0.920107\pi$
$67$	−516.652	+	412.017i	−0.942077	+	0.751281i	0.0265897	+	0.999646i	$0.491535\pi$
$68$			527.434i			0.940599i
$69$			629.312i			1.09797i
$70$	128.723	+	61.9898i	0.219791	+	0.105846i
$71$	137.660	−	285.853i	0.230101	−	0.477810i	−0.753666	−	0.657257i	$-0.771717\pi$
$71$	137.660	−	285.853i	0.230101	−	0.477810i	0.983768	+	0.179447i	$0.0574308\pi$
$72$	1244.02	−	283.940i	2.03624	−	0.464759i
$73$	−611.686	+	487.804i	−0.980719	+	0.782097i	−0.975973	−	0.217892i	$-0.930082\pi$
$73$	−611.686	+	487.804i	−0.980719	+	0.782097i	−0.00474592	+	0.999989i	$0.501511\pi$
$74$	241.282	+	192.416i	0.379034	+	0.302269i
$75$	−1020.41	−	2118.91i	−1.57103	−	3.26228i
$76$	324.510	−	156.276i	0.489788	−	0.235869i
$77$			13.2847i			0.0196614i
$78$	774.688	+	617.793i	1.12457	+	0.896811i
$79$	379.972	+	789.019i	0.541141	+	1.12369i	0.974896	+	0.222660i	$0.0714740\pi$
$79$	379.972	+	789.019i	0.541141	+	1.12369i	−0.433755	+	0.901031i	$0.642812\pi$
$80$	−5.65228	−	11.7371i	−0.00789931	−	0.0164031i
$81$	588.759	+	738.281i	0.807626	+	1.01273i
$82$	−758.999	−	173.237i	−1.02216	−	0.233302i
$83$	746.624			0.987382			0.493691	−	0.869638i	$-0.335647\pi$
$83$	746.624			0.987382			0.493691	+	0.869638i	$0.335647\pi$
$84$			191.543i			0.248799i
$85$	−1290.68	−	1618.46i	−1.64699	−	2.06525i
$86$	−270.570	−	561.844i	−0.339259	−	0.704479i
$87$			1678.91i			2.06894i
$88$	−44.4153	+	55.6950i	−0.0538032	+	0.0674671i
$89$	−713.957	−	162.956i	−0.850329	−	0.194082i	−0.224918	−	0.974378i	$-0.572212\pi$
$89$	−713.957	−	162.956i	−0.850329	−	0.194082i	−0.625411	+	0.780295i	$0.715069\pi$
$90$	−1198.22	+	1502.52i	−1.40338	+	1.75978i
$91$	−205.143	+	163.596i	−0.236317	+	0.188456i
$92$	−213.801	−	268.098i	−0.242286	−	0.303817i
$93$	2493.68			2.78046
$94$	180.631	+	144.049i	0.198199	+	0.158058i
$95$	−613.357	+	1273.65i	−0.662411	+	1.37551i
$96$	−1035.05	+	1297.91i	−1.10041	+	1.37987i
$97$	−1347.35	−	648.849i	−1.41034	−	0.679182i	−0.435106	−	0.900379i	$-0.643289\pi$
$97$	−1347.35	−	648.849i	−1.41034	−	0.679182i	−0.975229	+	0.221198i	$0.929003\pi$
$98$	−551.022	−	125.767i	−0.567976	−	0.129637i
$99$	−174.215	−	39.7634i	−0.176861	−	0.0403674i
$100$	1154.59	+	556.020i	1.15459	+	0.556020i
$101$	−152.063	+	190.680i	−0.149810	+	0.187856i	−0.851074	−	0.525046i	$-0.824048\pi$
$101$	−152.063	+	190.680i	−0.149810	+	0.187856i	0.701264	+	0.712902i	$0.252619\pi$
$102$	−729.670	+	1515.18i	−0.708315	+	1.47083i
$103$	1058.30	+	843.963i	1.01240	+	0.807361i	0.981364	−	0.192158i	$-0.0615485\pi$
$103$	1058.30	+	843.963i	1.01240	+	0.807361i	0.0310342	+	0.999518i	$0.490120\pi$
$104$	−1407.00			−1.32662
$105$	−468.724	−	587.761i	−0.435646	−	0.546282i
$106$	−78.4786	+	62.5846i	−0.0719105	+	0.0573467i
$107$	−481.310	+	603.544i	−0.434860	+	0.545297i	−0.950180	−	0.311701i	$-0.899101\pi$
$107$	−481.310	+	603.544i	−0.434860	+	0.545297i	0.515321	+	0.856997i	$0.327673\pi$
$108$	−1313.13	−	299.714i	−1.16997	−	0.267037i
$109$	409.097	−	512.991i	0.359490	−	0.450786i	−0.568893	−	0.822412i	$-0.692628\pi$
$109$	409.097	−	512.991i	0.359490	−	0.450786i	0.928383	+	0.371626i	$0.121200\pi$
$110$		−	107.289i		−	0.0929966i
$111$	−704.574	−	1463.06i	−0.602480	−	1.25106i
$112$	−1.74733	−	2.19108i	−0.00147417	−	0.00184855i
$113$			888.192i			0.739416i	0.929148	+	0.369708i	$0.120542\pi$
$113$			888.192i			0.739416i	−0.929148	+	0.369708i	$0.879458\pi$
$114$	1148.43			0.943511
$115$	1312.12	+	299.483i	1.06396	+	0.242843i
$116$	−570.389	−	715.245i	−0.456546	−	0.572490i
$117$	−1531.37	−	3179.91i	−1.21004	−	2.51268i
$118$	316.037	+	656.258i	0.246556	+	0.511978i
$119$	−348.174	−	277.660i	−0.268211	−	0.213891i
$120$		−	4031.25i		−	3.06668i
$121$	−1190.20	+	573.171i	−0.894216	+	0.430632i
$122$	−136.645	−	283.745i	−0.101403	−	0.210566i
$123$	3202.75	+	2554.11i	2.34782	+	1.87233i
$124$	−1062.35	+	847.196i	−0.769370	+	0.613552i
$125$	−2520.91	+	575.381i	−1.80382	+	0.411709i
$126$	−179.381	+	372.489i	−0.126830	+	0.263365i
$127$	1191.09	+	573.600i	0.832223	+	0.400778i	0.800949	−	0.598733i	$-0.204329\pi$
$127$	1191.09	+	573.600i	0.832223	+	0.400778i	0.0312748	+	0.999511i	$0.490043\pi$
$128$		−	913.838i		−	0.631036i
$129$			3281.31i			2.23956i
$130$	1656.77	−	1321.23i	1.11776	−	0.891380i
$131$	−988.597	+	225.641i	−0.659344	+	0.150491i	−0.539085	−	0.842251i	$-0.681230\pi$
$131$	−988.597	+	225.641i	−0.659344	+	0.150491i	−0.120260	+	0.992742i	$0.538373\pi$
$132$	129.594	−	62.4093i	0.0854526	−	0.0411518i
$133$	−67.6714	+	296.488i	−0.0441192	+	0.193299i
$134$	715.837	−	897.632i	0.461485	−	0.578683i
$135$	4762.85	−	2293.67i	3.03645	−	1.46228i
$136$	−531.381	−	2328.13i	−0.335041	−	1.46791i
$137$	185.758	−	813.859i	0.115842	−	0.507538i	−0.883400	−	0.468619i	$-0.844752\pi$
$137$	185.758	−	813.859i	0.115842	−	0.507538i	0.999242	−	0.0389183i	$-0.0123912\pi$
$138$	−243.297	−	1065.95i	−0.150078	−	0.657536i
$139$	−1144.40	−	2376.37i	−0.698321	−	1.45008i	−0.884009	−	0.467470i	$-0.845166\pi$
$139$	−1144.40	−	2376.37i	−0.698321	−	1.45008i	0.185688	−	0.982609i	$-0.440549\pi$
$140$	399.369	+	91.1534i	0.241092	+	0.0550276i
$141$	−527.466	−	1095.29i	−0.315040	−	0.654187i
$142$	−122.660	+	537.410i	−0.0724889	+	0.317595i
$143$	177.526	+	85.4922i	0.103815	+	0.0499945i
$144$	33.9639	−	16.3561i	0.0196550	−	0.00946535i
$145$	3500.54	+	798.976i	2.00486	+	0.457595i
$146$	847.510	−	1062.74i	0.480414	−	0.602420i
$147$	2325.15	+	1854.24i	1.30459	+	1.04038i
$148$	797.219	+	383.920i	0.442777	+	0.213230i
$149$	−641.804	+	511.822i	−0.352877	+	0.281410i	−0.783844	−	0.620958i	$-0.786744\pi$
$149$	−641.804	+	511.822i	−0.352877	+	0.281410i	0.430967	+	0.902368i	$0.358172\pi$
$150$	2547.61	+	3194.60i	1.38674	+	1.73892i
$151$	987.509	+	2050.58i	0.532201	+	1.10513i	0.977731	+	0.209860i	$0.0673007\pi$
$151$	987.509	+	2050.58i	0.532201	+	1.10513i	−0.445531	+	0.895267i	$0.646985\pi$
$152$	−1274.97	+	1016.75i	−0.680353	+	0.542563i
$153$	4683.37	−	3734.86i	2.47469	−	1.97350i
$154$	−5.13596	−	22.5021i	−0.00268745	−	0.0117745i
$155$	1186.72	−	5199.34i	0.614963	−	2.69433i
$156$	2559.64	+	1232.66i	1.31369	+	0.632638i
$157$	−184.139	−	806.765i	−0.0936044	−	0.410108i	0.906318	−	0.422597i	$-0.138881\pi$
$157$	−184.139	−	806.765i	−0.0936044	−	0.410108i	−0.999922	+	0.0124896i	$0.996024\pi$
$158$	−948.652	−	1189.57i	−0.477663	−	0.598970i
$159$	514.934	−	117.530i	0.256836	−	0.0586212i
$160$	2213.58	+	2775.74i	1.09374	+	1.37151i
$161$	289.532			0.141728
$162$	−1282.69	−	1022.91i	−0.622084	−	0.496095i
$163$	56.4854	−	247.479i	0.0271428	−	0.118920i	−0.959542	−	0.281567i	$-0.909146\pi$
$163$	56.4854	−	247.479i	0.0271428	−	0.118920i	0.986684	+	0.162646i	$0.0520030\pi$
$164$	−2232.15			−1.06282
$165$	−244.946	+	508.636i	−0.115570	+	0.239983i
$166$	−1264.66	+	288.651i	−0.591306	+	0.134962i
$167$	−665.511	+	1381.95i	−0.308376	+	0.640349i	−0.996348	−	0.0853884i	$-0.972787\pi$
$167$	−665.511	+	1381.95i	−0.308376	+	0.640349i	0.687972	+	0.725737i	$0.258501\pi$
$168$	−192.977	−	845.487i	−0.0886220	−	0.388278i
$169$	377.119	+	1652.27i	0.171652	+	0.752055i
$170$	2811.91	+	2242.42i	1.26861	+	1.01168i
$171$	−3685.58	−	1774.88i	−1.64821	−	0.793735i
$172$	−1114.78	−	1397.90i	−0.494195	−	0.619701i
$173$	−2029.82	+	977.510i	−0.892049	+	0.429588i	−0.823011	−	0.568026i	$-0.807707\pi$
$173$	−2029.82	+	977.510i	−0.892049	+	0.429588i	−0.0690381	+	0.997614i	$0.521993\pi$
$174$	−649.080	−	2843.80i	−0.282797	−	1.23901i
$175$	−974.861	+	469.469i	−0.421101	+	0.202791i
$176$	−0.913120	+	1.89611i	−0.000391074	+	0.000812074i
$177$		−	3832.71i		−	1.62759i
$178$	1272.33			0.535759
$179$	−293.274	−	66.9379i	−0.122460	−	0.0279507i	0.160852	−	0.986979i	$-0.448576\pi$
$179$	−293.274	−	66.9379i	−0.122460	−	0.0279507i	−0.283312	+	0.959028i	$0.591433\pi$
$180$	−2390.77	+	4964.48i	−0.989985	+	2.05572i
$181$	985.396	−	1235.65i	0.404663	−	0.507431i	−0.537188	−	0.843462i	$-0.680513\pi$
$181$	985.396	−	1235.65i	0.404663	−	0.507431i	0.941851	+	0.336032i	$0.109085\pi$
$182$	284.232	−	356.416i	0.115762	−	0.145161i
$183$			1657.14i			0.669397i
$184$	1213.84	+	968.004i	0.486333	+	0.387838i
$185$	−3385.80	+	772.786i	−1.34556	+	0.307116i
$186$	−4223.89	+	964.076i	−1.66511	+	0.380051i
$187$	−74.4155	+	326.036i	−0.0291006	+	0.127498i
$188$	596.822	+	287.414i	0.231530	+	0.111499i
$189$	889.130	−	709.058i	0.342194	−	0.272891i
$190$	546.525	−	2394.48i	0.208680	−	0.914285i
$191$	60.8549			0.0230540			0.0115270	−	0.999934i	$-0.496331\pi$
$191$	60.8549			0.0230540			0.0115270	+	0.999934i	$0.496331\pi$
$192$	1230.28	−	2554.70i	0.462436	−	0.960259i
$193$	570.461	−	274.719i	0.212760	−	0.102460i	−0.324469	−	0.945896i	$-0.605186\pi$
$193$	570.461	−	274.719i	0.212760	−	0.102460i	0.537229	+	0.843437i	$0.319471\pi$
$194$	2533.04	+	578.150i	0.937432	+	0.213963i
$195$	−10870.8	+	2481.19i	−3.99218	+	0.911190i
$196$	−1620.51			−0.590565
$197$	2617.03	−	892.486i	0.946475	−	0.322777i
$197$	2617.03	−	892.486i	0.946475	−	0.322777i
$198$	310.465			0.111433
$199$	2765.05	−	631.105i	0.984971	−	0.224813i	0.300443	−	0.953800i	$-0.402865\pi$
$199$	2765.05	−	631.105i	0.984971	−	0.224813i	0.684528	+	0.728987i	$0.260008\pi$
$200$	−5656.62	−	1291.09i	−1.99992	−	0.456468i
$201$	−5442.97	+	2621.20i	−1.91004	+	0.919826i
$202$	183.851	−	381.771i	0.0640382	−	0.132977i
$203$	772.427			0.267063
$204$	−1072.95	+	4700.90i	−0.368243	+	1.61338i
$205$	6849.49	−	5462.29i	2.33361	−	1.86099i
$206$	−2118.87	−	1020.39i	−0.716643	−	0.345117i
$207$	−866.620	+	3796.91i	−0.290987	+	1.27490i
$208$	−40.5247	+	9.24950i	−0.0135091	+	0.00308335i
$209$	222.647	−	50.8177i	0.0736880	−	0.0168188i
$210$	1021.18	+	814.361i	0.335561	+	0.267601i
$211$			2559.52i			0.835094i	0.908655	+	0.417547i	$0.137110\pi$
$211$			2559.52i			0.835094i	−0.908655	+	0.417547i	$0.862890\pi$
$212$	−179.442	+	225.013i	−0.0581325	+	0.0728959i
$213$	1808.44	−	2267.71i	0.581747	−	0.729488i
$214$	581.927	−	1208.38i	0.185887	−	0.385997i
$215$	6841.56	+	1561.54i	2.17019	+	0.495331i
$216$	6098.23			1.92098
$217$		−	1147.28i		−	0.358906i
$218$	−494.618	+	1027.09i	−0.153669	+	0.319096i
$219$	−6444.16	+	3103.34i	−1.98838	+	0.957555i
$220$	−68.4514	−	299.905i	−0.0209772	−	0.0919072i
$221$	−5951.07	+	2865.89i	−1.81137	+	0.872309i
$222$	1759.07	+	2205.80i	0.531806	+	0.666864i
$223$	3767.89	+	1814.52i	1.13146	+	0.544884i	0.903416	−	0.428765i	$-0.141051\pi$
$223$	3767.89	+	1814.52i	1.13146	+	0.544884i	0.228048	+	0.973650i	$0.426766\pi$
$224$	597.137	+	476.201i	0.178116	+	0.142043i
$225$	−3238.66	−	14189.5i	−0.959604	−	4.20430i
$226$	−343.382	−	1504.45i	−0.101068	−	0.442809i
$227$	−2119.83	+	4401.87i	−0.619815	+	1.28706i	0.320659	+	0.947195i	$0.396096\pi$
$227$	−2119.83	+	4401.87i	−0.619815	+	1.28706i	−0.940474	+	0.339865i	$0.889619\pi$
$228$	3210.20	−	732.707i	0.932459	−	0.212828i
$229$	2414.75	−	5014.28i	0.696818	−	1.44696i	−0.188549	−	0.982064i	$-0.560379\pi$
$229$	2414.75	−	5014.28i	0.696818	−	1.44696i	0.885367	−	0.464893i	$-0.153907\pi$
$230$	−2338.30			−0.670361
$231$	−27.0248	+	118.403i	−0.00769741	+	0.0337246i
$232$	3238.34	+	2582.49i	0.916411	+	0.730814i
$233$	−4153.10			−1.16772			−0.583859	−	0.811855i	$-0.698458\pi$
$233$	−4153.10			−1.16772			−0.583859	+	0.811855i	$0.698458\pi$
$234$	3823.27	+	4794.22i	1.06810	+	1.33935i
$235$	−2534.71	+	578.531i	−0.703601	+	0.160592i
$236$	1302.12	+	1632.80i	0.359155	+	0.450366i
$237$	1781.52	+	7805.33i	0.488278	+	2.13929i
$238$	697.097	+	335.704i	0.189857	+	0.0914305i
$239$	759.163	−	3326.11i	0.205465	−	0.900201i	−0.762076	−	0.647488i	$-0.775820\pi$
$239$	759.163	−	3326.11i	0.205465	−	0.900201i	0.967541	−	0.252714i	$-0.0813231\pi$
$240$	−26.5010	−	116.108i	−0.00712764	−	0.0312282i
$241$	−2797.66	+	2231.06i	−0.747772	+	0.596329i	−0.921460	−	0.388472i	$-0.873003\pi$
$241$	−2797.66	+	2231.06i	−0.747772	+	0.596329i	0.173688	+	0.984801i	$0.444432\pi$
$242$	1794.42	−	1431.00i	0.476651	−	0.380116i
$243$	578.099	+	1200.43i	0.152613	+	0.316905i
$244$	−562.994	−	705.972i	−0.147713	−	0.185226i
$245$	4972.63	−	3965.54i	1.29669	−	1.03408i
$246$	−6412.39	−	3088.04i	−1.66195	−	0.800351i
$247$	3526.55	+	2812.33i	0.908457	+	0.724470i
$248$	3835.76	−	4809.89i	0.982141	−	1.23157i
$249$	6654.50	+	1518.85i	1.69362	+	0.386558i
$250$	4047.57	−	1949.21i	1.02396	−	0.493115i
$251$	1542.22	+	742.695i	0.387826	+	0.186767i	0.617628	−	0.786470i	$-0.288094\pi$
$251$	1542.22	+	742.695i	0.387826	+	0.186767i	−0.229802	+	0.973237i	$0.573808\pi$
$252$	−263.773	+	1155.66i	−0.0659369	+	0.288889i
$253$	−94.3362	−	195.891i	−0.0234422	−	0.0486782i
$254$	−2239.28	−	511.100i	−0.553168	−	0.126257i
$255$	−8211.13	−	17050.6i	−2.01647	−	4.18725i
$256$	905.438	+	3966.98i	0.221054	+	0.968502i
$257$	−767.507	+	3362.67i	−0.186287	+	0.816177i	0.792265	+	0.610177i	$0.208902\pi$
$257$	−767.507	+	3362.67i	−0.186287	+	0.816177i	−0.978552	+	0.206000i	$0.933955\pi$
$258$	−1268.58	−	5558.01i	−0.306118	−	1.34119i
$259$	−673.121	+	324.158i	−0.161489	+	0.0777691i
$260$	3788.20	−	4750.26i	0.903594	−	1.13307i
$261$	−2312.01	+	10129.6i	−0.548314	+	2.40232i
$262$	1587.29	−	764.399i	0.374287	−	0.180247i
$263$	1262.86	−	288.239i	0.296088	−	0.0675801i	−0.0718965	−	0.997412i	$-0.522905\pi$
$263$	1262.86	−	288.239i	0.296088	−	0.0675801i	0.367984	+	0.929832i	$0.380048\pi$
$264$	−509.163	+	406.044i	−0.118700	+	0.0946602i
$265$		−	1129.57i		−	0.261846i
$266$		−	528.365i		−	0.121790i
$267$	−6031.85	−	2904.79i	−1.38256	−	0.665805i
$268$	1428.28	−	2965.86i	0.325545	−	0.676002i
$269$	5215.86	−	1190.49i	1.18222	−	0.269834i	0.414155	−	0.910207i	$-0.364077\pi$
$269$	5215.86	−	1190.49i	1.18222	−	0.269834i	0.768064	+	0.640373i	$0.221220\pi$
$270$	−7180.75	+	5726.46i	−1.61854	+	1.29075i
$271$	875.930	+	698.531i	0.196343	+	0.156578i	0.716727	−	0.697354i	$-0.245640\pi$
$271$	875.930	+	698.531i	0.196343	+	0.156578i	−0.520384	+	0.853933i	$0.674211\pi$
$272$	−30.6098	−	63.5619i	−0.00682350	−	0.0141691i
$273$	−2161.20	+	1040.78i	−0.479127	+	0.230735i
$274$			1450.36i			0.319779i
$275$	635.266	+	506.608i	0.139302	+	0.111089i
$276$	−1360.17	−	2824.43i	−0.296641	−	0.615981i
$277$	1110.68	+	2306.36i	0.240919	+	0.500274i	0.986009	−	0.166690i	$-0.0533079\pi$
$277$	1110.68	+	2306.36i	0.240919	+	0.500274i	−0.745090	+	0.666964i	$0.767594\pi$
$278$	2857.15	+	3582.75i	0.616405	+	0.772947i
$279$	15045.4	+	3434.02i	3.22848	+	0.736880i
$280$	−1854.68			−0.395852
$281$		−	3917.49i		−	0.831666i	−0.909441	−	0.415833i	$-0.863490\pi$
$281$		−	3917.49i		−	0.831666i	0.909441	−	0.415833i	$-0.136510\pi$
$282$	1316.89	+	1651.33i	0.278084	+	0.348707i
$283$	1085.33	+	2253.71i	0.227973	+	0.473390i	0.983308	−	0.181948i	$-0.0582403\pi$
$283$	1085.33	+	2253.71i	0.227973	+	0.473390i	−0.755335	+	0.655338i	$0.772526\pi$
$284$			1580.48i			0.330226i
$285$	−8057.68	+	10104.0i	−1.67472	+	2.10003i
$286$	−333.753	−	76.1769i	−0.0690043	−	0.0157498i
$287$	1175.09	−	1473.51i	0.241683	−	0.303061i
$288$	−8032.23	+	6405.49i	−1.64342	+	1.31058i
$289$	−3926.43	−	4923.59i	−0.799192	−	1.00216i
$290$	−6238.24			−1.26318
$291$	−10688.7	−	8523.94i	−2.15320	−	1.71712i
$292$	1691.00	−	3511.40i	0.338899	−	0.703730i
$293$	−4413.56	+	5534.43i	−0.880010	+	1.10350i	0.113920	+	0.993490i	$0.463659\pi$
$293$	−4413.56	+	5534.43i	−0.880010	+	1.10350i	−0.993931	+	0.110008i	$0.964912\pi$
$294$	−4655.29	−	2241.87i	−0.923477	−	0.444723i
$295$	−7991.23	−	1823.95i	−1.57718	−	0.359981i
$296$	−3905.78	−	891.469i	−0.766956	−	0.175053i
$297$	−769.433	−	370.540i	−0.150327	−	0.0723936i
$298$	889.239	−	1115.07i	0.172860	−	0.216759i
$299$	1863.25	−	3869.08i	0.360383	−	0.748343i
$300$	9159.49	+	7304.45i	1.76275	+	1.40574i
$301$	1509.65			0.289086
$302$	−2465.45	−	3091.58i	−0.469771	−	0.589074i
$303$	−1743.20	+	1390.16i	−0.330509	+	0.263572i
$304$	−30.0378	+	37.6662i	−0.00566705	+	0.00710626i
$305$	3455.16	+	788.617i	0.648662	+	0.148053i
$306$	−6488.95	+	8136.89i	−1.21225	+	1.52011i
$307$		−	7140.76i		−	1.32751i	−0.747951	−	0.663754i	$-0.768962\pi$
$307$		−	7140.76i		−	1.32751i	0.747951	−	0.663754i	$-0.231038\pi$
$308$	−28.7131	−	59.6233i	−0.00531194	−	0.0110304i
$309$	7715.50	+	9674.94i	1.42045	+	1.78119i
$310$			9265.64i			1.69759i
$311$	6048.41			1.10281			0.551405	−	0.834238i	$-0.314092\pi$
$311$	6048.41			1.10281			0.551405	+	0.834238i	$0.314092\pi$
$312$	−12540.3	−	2862.25i	−2.27550	−	0.519368i
$313$	3896.37	+	4885.89i	0.703629	+	0.882323i	0.997289	−	0.0735870i	$-0.0234447\pi$
$313$	3896.37	+	4885.89i	0.703629	+	0.882323i	−0.293660	+	0.955910i	$0.594873\pi$
$314$	623.804	+	1295.34i	0.112112	+	0.232804i
$315$	−2018.61	−	4191.69i	−0.361066	−	0.749762i
$316$	−3410.72	−	2719.96i	−0.607177	−	0.484208i
$317$			1775.70i			0.314615i	0.987550	+	0.157308i	$0.0502814\pi$
$317$			1775.70i			0.314615i	−0.987550	+	0.157308i	$0.949719\pi$
$318$	−826.778	+	398.155i	−0.145797	+	0.0702121i
$319$	−251.675	−	522.609i	−0.0441727	−	0.0917256i
$320$	−4741.10	−	3780.90i	−0.828235	−	0.660496i
$321$	−5517.59	+	4400.13i	−0.959383	+	0.765082i
$322$	−490.420	+	111.935i	−0.0848759	+	0.0193724i
$323$	−3321.62	+	6897.41i	−0.572197	+	1.18818i
$324$	−4238.12	−	2040.97i	−0.726701	−	0.349961i
$325$			16048.5i			2.73911i
$326$			441.027i			0.0749271i
$327$	4689.76	−	3739.96i	0.793103	−	0.632478i
$328$	9852.91	−	2248.86i	1.65865	−	0.378575i
$329$	−503.919	+	242.675i	−0.0844436	+	0.0406659i
$330$	218.257	−	956.245i	0.0364080	−	0.159514i
$331$	7095.75	−	8897.78i	1.17830	−	1.47754i	0.333264	−	0.942834i	$-0.391850\pi$
$331$	7095.75	−	8897.78i	1.17830	−	1.47754i	0.845037	−	0.534709i	$-0.179579\pi$
$332$	−3350.94	+	1613.73i	−0.553936	+	0.266762i
$333$	−2236.23	−	9797.56i	−0.368002	−	1.61232i
$334$	592.997	−	2598.09i	0.0971477	−	0.425632i
$335$	2874.96	+	12596.0i	0.468884	+	2.05431i
$336$	−11.1163	−	23.0832i	−0.00180489	−	0.00374789i
$337$	−5385.17	−	1229.13i	−0.870471	−	0.198679i	−0.236119	−	0.971724i	$-0.575876\pi$
$337$	−5385.17	−	1229.13i	−0.870471	−	0.198679i	−0.634351	+	0.773045i	$0.718733\pi$
$338$	−1277.56	−	2652.88i	−0.205592	−	0.426915i
$339$	−1806.84	+	7916.26i	−0.289480	+	1.26830i
$340$	9290.81	+	4474.22i	1.48196	+	0.713672i
$341$	−776.228	+	373.812i	−0.123270	+	0.0593638i
$342$	6928.97	+	1581.49i	1.09554	+	0.250051i
$343$	1752.58	−	2197.67i	0.275890	−	0.345956i
$344$	6329.10	+	5047.29i	0.991984	+	0.791081i
$345$	11085.4	+	5338.45i	1.72991	+	0.833080i
$346$	3060.28	−	2440.49i	0.475496	−	0.379195i
$347$	−1144.39	−	1435.02i	−0.177043	−	0.222005i	0.685390	−	0.728176i	$-0.259632\pi$
$347$	−1144.39	−	1435.02i	−0.177043	−	0.222005i	−0.862433	+	0.506171i	$0.831060\pi$
$348$	−3628.74	−	7535.16i	−0.558968	−	1.16071i
$349$	9087.15	−	7246.76i	1.39376	−	1.11149i	0.414240	−	0.910168i	$-0.364047\pi$
$349$	9087.15	−	7246.76i	1.39376	−	1.11149i	0.979525	−	0.201323i	$-0.0645239\pi$
$350$	1469.76	−	1172.09i	0.224463	−	0.179003i
$351$	−3753.40	−	16444.7i	−0.570774	−	2.50072i
$352$	127.627	−	559.169i	0.0193253	−	0.0846699i
$353$	6027.41	+	2902.65i	0.908801	+	0.437655i	0.829060	−	0.559160i	$-0.188876\pi$
$353$	6027.41	+	2902.65i	0.908801	+	0.437655i	0.0797412	+	0.996816i	$0.474591\pi$
$354$	1481.76	+	6492.00i	0.222470	+	0.974706i
$355$	−3867.57	−	4849.78i	−0.578224	−	0.725070i
$356$	3556.54	−	811.756i	0.529483	−	0.120851i
$357$	−2538.36	−	3183.01i	−0.376315	−	0.471884i
$358$	522.638			0.0771572
$359$	−657.206	−	524.105i	−0.0966185	−	0.0770506i	0.573989	−	0.818863i	$-0.305395\pi$
$359$	−657.206	−	524.105i	−0.0966185	−	0.0770506i	−0.670608	+	0.741812i	$0.733967\pi$
$360$	5551.40	−	24322.3i	0.812734	−	3.56082i
$361$	−1631.10			−0.237804
$362$	−1191.39	+	2473.95i	−0.172978	+	0.359193i
$363$	−11774.0	+	2687.34i	−1.70241	+	0.388564i
$364$	567.116	−	1177.63i	0.0816620	−	0.169573i
$365$	3403.79	+	14913.0i	0.488116	+	2.13858i
$366$	−640.665	−	2806.94i	−0.0914975	−	0.400877i
$367$	−9714.69	−	7747.21i	−1.38175	−	1.10191i	−0.982746	−	0.184962i	$-0.940784\pi$
$367$	−9714.69	−	7747.21i	−1.38175	−	1.10191i	−0.399006	−	0.916948i	$-0.630645\pi$
$368$	41.3247	+	19.9009i	0.00585380	+	0.00281904i
$369$	15806.3	+	19820.5i	2.22993	+	2.79625i
$370$	5436.23	−	2617.95i	0.763828	−	0.367840i
$371$	−54.0730	−	236.909i	−0.00756693	−	0.0331529i
$372$	−11191.9	+	5389.75i	−1.55988	+	0.751198i
$373$	−3725.40	+	7735.87i	−0.517141	+	1.07386i	0.464930	+	0.885347i	$0.346079\pi$
$373$	−3725.40	+	7735.87i	−0.517141	+	1.07386i	−0.982072	+	0.188508i	$0.939635\pi$
$374$		−	581.022i		−	0.0803314i
$375$	−23638.8			−3.25521
$376$	−2923.98	−	667.380i	−0.401045	−	0.0915360i
$377$	4970.87	−	10322.1i	0.679080	−	1.41012i
$378$	−1231.92	+	1544.77i	−0.167627	+	0.210197i
$379$	179.075	−	224.554i	0.0242704	−	0.0304341i	−0.769548	−	0.638589i	$-0.779519\pi$
$379$	179.075	−	224.554i	0.0242704	−	0.0304341i	0.793819	+	0.608155i	$0.208090\pi$
$380$		−	7041.98i		−	0.950647i
$381$	9449.08	+	7535.39i	1.27058	+	1.01325i
$382$	−103.078	+	23.5270i	−0.0138062	+	0.00315116i
$383$	4954.53	−	1130.84i	0.661004	−	0.150870i	0.121158	−	0.992633i	$-0.461339\pi$
$383$	4954.53	−	1130.84i	0.661004	−	0.150870i	0.539847	+	0.841763i	$0.318482\pi$
$384$	1859.01	−	8144.84i	0.247050	−	1.08239i
$385$	234.011	+	112.694i	0.0309775	+	0.0149180i
$386$	−860.060	+	685.875i	−0.113409	+	0.0904407i
$387$	−4518.66	+	19797.6i	−0.593531	+	2.60043i
$388$	7449.47			0.974715
$389$	−176.814	+	367.158i	−0.0230458	+	0.0478551i	−0.912174	−	0.409803i	$-0.865597\pi$
$389$	−176.814	+	367.158i	−0.0230458	+	0.0478551i	0.889128	+	0.457658i	$0.151312\pi$
$390$	17454.2	−	8405.49i	2.26622	−	1.09135i
$391$	7105.75	+	1621.84i	0.919062	+	0.209770i
$392$	7153.06	−	1632.64i	0.921643	−	0.210359i
$393$	−9270.17			−1.18987
$394$	−4087.78	+	2523.49i	−0.522689	+	0.322669i
$395$	17122.0			2.18101
$396$	867.841	−	198.079i	0.110128	−	0.0251360i
$397$	−15148.9	−	3457.64i	−1.91512	−	0.437113i	−0.999375	−	0.0353428i	$-0.988748\pi$
$397$	−15148.9	−	3457.64i	−1.91512	−	0.437113i	−0.915741	−	0.401770i	$-0.868395\pi$
$398$	−4439.56	+	2137.98i	−0.559133	+	0.269265i
$399$	−1206.28	+	2504.87i	−0.151352	+	0.314287i
$400$	−171.410			−0.0214263
$401$	−965.107	+	4228.41i	−0.120187	+	0.526576i	0.878610	+	0.477541i	$0.158472\pi$
$401$	−965.107	+	4228.41i	−0.120187	+	0.526576i	−0.998797	+	0.0490349i	$0.984385\pi$
$402$	8206.14	−	6544.18i	1.01812	−	0.811926i
$403$	−15331.4	−	7383.22i	−1.89507	−	0.912616i
$404$	270.345	−	1184.46i	0.0332925	−	0.145864i
$405$	17999.4	−	4108.24i	2.20838	−	0.504049i
$406$	−1308.37	+	298.626i	−0.159934	+	0.0365039i
$407$	438.638	+	349.802i	0.0534213	+	0.0426020i
$408$		−	21831.1i		−	2.64902i
$409$	−7404.80	+	9285.33i	−0.895217	+	1.12257i	0.0966534	+	0.995318i	$0.469186\pi$
$409$	−7404.80	+	9285.33i	−0.895217	+	1.12257i	−0.991871	+	0.127249i	$0.959385\pi$
$410$	−9490.18	+	11900.3i	−1.14314	+	1.43345i
$411$	3311.24	−	6875.86i	0.397400	−	0.825210i
$412$	−6573.88	−	1500.44i	−0.786096	−	0.179421i
$413$	−1763.34			−0.210093
$414$		−	6766.40i		−	0.803261i
$415$	6333.61	−	13151.9i	0.749168	−	1.55566i
$416$	10206.4	−	4915.15i	1.20291	−	0.579290i
$417$	−5365.57	−	23508.1i	−0.630103	−	2.76066i
$418$	−357.481	+	172.154i	−0.0418301	+	0.0201443i
$419$	−1811.53	−	2271.59i	−0.211215	−	0.264855i	0.664927	−	0.746908i	$-0.268463\pi$
$419$	−1811.53	−	2271.59i	−0.211215	−	0.264855i	−0.876142	+	0.482053i	$0.839891\pi$
$420$	3374.06	+	1624.86i	0.391993	+	0.188774i
$421$	7714.84	+	6152.38i	0.893107	+	0.712229i	0.958337	−	0.285641i	$-0.0922064\pi$
$421$	7714.84	+	6152.38i	0.893107	+	0.712229i	−0.0652293	+	0.997870i	$0.520778\pi$
$422$	−989.532	−	4335.42i	−0.114146	−	0.500107i
$423$	−1674.11	−	7334.75i	−0.192430	−	0.843091i
$424$	565.372	−	1174.01i	0.0647569	−	0.134469i
$425$	−26555.1	+	6061.02i	−3.03085	+	0.691771i
$426$	−2186.49	+	4540.29i	−0.248675	+	0.516380i
$427$	762.413			0.0864069
$428$	855.700	−	3749.07i	0.0966397	−	0.423406i
$429$	1408.34	+	1123.11i	0.158497	+	0.126397i
$430$	−12192.2			−1.36735
$431$	−8394.83	−	10526.8i	−0.938201	−	1.17647i	−0.984117	−	0.177522i	$-0.943192\pi$
$431$	−8394.83	−	10526.8i	−0.938201	−	1.17647i	0.0459155	−	0.998945i	$-0.485380\pi$
$432$	175.642	−	40.0891i	0.0195615	−	0.00446479i
$433$	−6996.90	−	8773.83i	−0.776558	−	0.973773i	0.223442	−	0.974717i	$-0.428271\pi$
$433$	−6996.90	−	8773.83i	−0.776558	−	0.973773i	−1.00000		0.000944634i	$0.999699\pi$
$434$	443.548	+	1943.31i	0.0490576	+	0.214935i
$435$	29574.2	+	14242.2i	3.25971	+	1.56980i
$436$	−727.316	+	3186.58i	−0.0798901	+	0.350022i
$437$	−1107.54	−	4852.45i	−0.121238	−	0.531177i
$438$	9715.60	−	7747.93i	1.05988	−	0.845229i
$439$	−2466.46	+	1966.93i	−0.268149	+	0.213842i	−0.748328	−	0.663329i	$-0.769143\pi$
$439$	−2466.46	+	1966.93i	−0.268149	+	0.213842i	0.480179	+	0.877171i	$0.340572\pi$
$440$	604.299	+	1254.84i	0.0654747	+	0.135960i
$441$	11475.2	+	14389.4i	1.23908	+	1.55376i
$442$	8972.19	−	7155.08i	0.965528	−	0.769983i
$443$	8560.03	+	4122.29i	0.918057	+	0.442113i	0.832377	−	0.554210i	$-0.186979\pi$
$443$	8560.03	+	4122.29i	0.918057	+	0.442113i	0.0856802	+	0.996323i	$0.472694\pi$
$444$	6324.44	+	5043.57i	0.676001	+	0.539093i
$445$	−8926.99	+	11194.1i	−0.950966	+	1.19247i
$446$	−7083.71	−	1616.81i	−0.752070	−	0.171655i
$447$	−6761.46	+	3256.15i	−0.715449	+	0.344542i
$448$	−1175.36	−	566.023i	−0.123952	−	0.0596921i
$449$	2314.54	−	10140.7i	0.243274	−	1.06585i	−0.694742	−	0.719259i	$-0.744481\pi$
$449$	2314.54	−	10140.7i	0.243274	−	1.06585i	0.938016	−	0.346593i	$-0.112661\pi$
$450$	10971.5	+	22782.7i	1.14934	+	2.38663i
$451$	−1379.82	−	314.934i	−0.144065	−	0.0328818i
$452$	−1919.71	−	3986.32i	−0.199769	−	0.414824i
$453$	4629.98	+	20285.3i	0.480211	+	2.10394i
$454$	1888.85	−	8275.61i	0.195260	−	0.855492i
$455$	1141.54	+	5001.41i	0.117618	+	0.515318i
$456$	−13431.9	+	6468.46i	−1.37940	+	0.664283i
$457$	−2026.03	+	2540.56i	−0.207382	+	0.260049i	−0.874635	−	0.484782i	$-0.838899\pi$
$457$	−2026.03	+	2540.56i	−0.207382	+	0.260049i	0.667253	+	0.744832i	$0.267470\pi$
$458$	−2151.64	+	9426.95i	−0.219519	+	0.961774i
$459$	25793.1	−	12421.3i	2.62292	−	1.26313i
$460$	−6536.25	+	1491.86i	−0.662509	+	0.151213i
$461$	2850.51	−	2273.20i	0.287985	−	0.229661i	−0.468831	−	0.883288i	$-0.655325\pi$
$461$	2850.51	−	2273.20i	0.287985	−	0.229661i	0.756817	+	0.653627i	$0.226753\pi$
$462$		−	211.005i		−	0.0212485i
$463$		−	9477.68i		−	0.951328i	−0.879627	−	0.475664i	$-0.842208\pi$
$463$		−	9477.68i		−	0.951328i	0.879627	−	0.475664i	$-0.157792\pi$
$464$	110.248	+	53.0927i	0.0110305	+	0.00531199i
$465$	21153.9	−	43926.5i	2.10965	−	4.38073i
$466$	7034.68	−	1605.62i	0.699303	−	0.159611i
$467$	−11726.8	+	9351.82i	−1.16200	+	0.926661i	−0.998208	−	0.0598348i	$-0.980943\pi$
$467$	−11726.8	+	9351.82i	−1.16200	+	0.926661i	−0.163788	+	0.986496i	$0.552371\pi$
$468$	13745.9	+	10962.0i	1.35770	+	1.08273i
$469$	1205.95	+	2504.18i	0.118733	+	0.246551i
$470$	4069.73	−	1959.88i	0.399410	−	0.192346i
$471$		−	7565.12i		−	0.740090i
$472$	−7392.66	−	5895.45i	−0.720922	−	0.574916i
$473$	−491.881	−	1021.40i	−0.0478154	−	0.0992898i
$474$	−6035.20	−	12532.2i	−0.584823	−	1.21440i
$475$	11597.3	+	14542.5i	1.12025	+	1.40475i
$476$	2162.77	+	493.639i	0.208258	+	0.0475334i
$477$	3268.67			0.313757
$478$			5927.39i			0.567181i
$479$	−1502.72	−	1884.35i	−0.143342	−	0.179745i	0.704978	−	0.709229i	$-0.250957\pi$
$479$	−1502.72	−	1884.35i	−0.143342	−	0.179745i	−0.848320	+	0.529484i	$0.822386\pi$
$480$	14082.5	+	29242.7i	1.33912	+	2.78071i
$481$			11081.2i			1.05043i
$482$	3876.24	−	4860.65i	0.366303	−	0.459329i
$483$	2580.53	+	588.990i	0.243102	+	0.0554865i
$484$	4102.94	−	5144.92i	0.385325	−	0.483182i
$485$	−22859.1	+	18229.5i	−2.14016	+	1.70672i
$486$	−1443.30	−	1809.85i	−0.134711	−	0.168922i
$487$	−16372.9			−1.52346			−0.761731	−	0.647894i	$-0.775650\pi$
$487$	−16372.9			−1.52346			−0.761731	+	0.647894i	$0.775650\pi$
$488$	3196.36	+	2549.01i	0.296501	+	0.236451i
$489$	1006.88	−	2090.82i	0.0931143	−	0.193354i
$490$	−6889.72	+	8639.44i	−0.635196	+	0.796510i
$491$	−15095.4	−	7269.56i	−1.38747	−	0.668169i	−0.416889	−	0.908957i	$-0.636880\pi$
$491$	−15095.4	−	7269.56i	−1.38747	−	0.668169i	−0.970578	+	0.240789i	$0.922594\pi$
$492$	−19894.7	−	4540.84i	−1.82301	−	0.416091i
$493$	18957.1	+	4326.83i	1.73181	+	0.395275i
$494$	−7060.67	−	3400.24i	−0.643066	−	0.309684i
$495$	−2178.30	+	2731.50i	−0.197793	+	0.248024i
$496$	78.8583	−	163.751i	0.00713879	−	0.0148239i
$497$	−1043.32	−	832.020i	−0.0941635	−	0.0750929i
$498$	−11858.9			−1.06708
$499$	8874.56	+	11128.4i	0.796152	+	0.998344i	0.999814	+	0.0193022i	$0.00614446\pi$
$499$	8874.56	+	11128.4i	0.796152	+	0.998344i	−0.203661	+	0.979041i	$0.565284\pi$
$500$	10070.6	−	8031.00i	0.900737	−	0.718314i
$501$	−8742.83	+	10963.2i	−0.779642	+	0.977640i
$502$	−2899.41	−	661.771i	−0.257783	−	0.0588373i
$503$	−6316.58	+	7920.74i	−0.559925	+	0.702124i	−0.978544	−	0.206038i	$-0.933943\pi$
$503$	−6316.58	+	7920.74i	−0.559925	+	0.702124i	0.418619	+	0.908162i	$0.362514\pi$
$504$		−	5366.93i		−	0.474330i
$505$	2068.91	+	4296.14i	0.182308	+	0.378566i
$506$	235.523	+	295.337i	0.0206923	+	0.0259473i
$507$			15493.5i			1.35718i
$508$	−6585.53			−0.575169
$509$	−12213.1	−	2787.57i	−1.06353	−	0.242744i	−0.345261	−	0.938507i	$-0.612210\pi$
$509$	−12213.1	−	2787.57i	−1.06353	−	0.242744i	−0.718272	+	0.695762i	$0.755067\pi$
$510$	20500.2	+	25706.5i	1.77993	+	2.23196i
$511$	1427.78	+	2964.81i	0.123603	+	0.256664i
$512$	104.660	+	217.329i	0.00903393	+	0.0187591i
$513$	−15284.7	−	12189.2i	−1.31547	−	1.04905i
$514$		−	5992.54i		−	0.514241i
$515$	23844.0	−	11482.7i	2.04018	−	0.982500i
$516$	−7092.11	−	14726.9i	−0.605064	−	1.25643i
$517$	328.377	+	261.872i	0.0279343	+	0.0222768i
$518$	1014.84	−	809.306i	0.0860799	−	0.0686464i
$519$	−20079.9	+	4583.10i	−1.69828	+	0.387622i
$520$	−11935.6	+	24784.6i	−1.00656	+	2.09014i
$521$	10403.1	+	5009.86i	0.874793	+	0.421278i	0.816720	−	0.577034i	$-0.195790\pi$
$521$	10403.1	+	5009.86i	0.874793	+	0.421278i	0.0580732	+	0.998312i	$0.481504\pi$
$522$		−	18051.7i		−	1.51361i
$523$		−	7320.62i		−	0.612062i	−0.952022	−	0.306031i	$-0.900999\pi$
$523$		−	7320.62i		−	0.612062i	0.952022	−	0.306031i	$-0.0990010\pi$
$524$	3949.25	−	3149.42i	0.329244	−	0.262563i
$525$	−9643.76	+	2201.13i	−0.801692	+	0.182981i
$526$	−2027.64	+	976.461i	−0.168079	+	0.0809424i
$527$	6426.63	−	28156.9i	0.531211	−	2.32739i
$528$	−11.9957	+	15.0421i	−0.000988722	+	0.00123982i
$529$	6692.76	−	3223.06i	0.550075	−	0.264902i
$530$	436.702	+	1913.32i	0.0357908	+	0.156810i
$531$	5277.99	−	23124.4i	0.431347	−	1.88986i
$532$	−337.101	−	1476.94i	−0.0274722	−	0.120363i
$533$	−12128.7	−	25185.6i	−0.985654	−	2.04673i
$534$	11340.0	+	2588.28i	0.918969	+	0.209749i
$535$	6548.55	+	13598.2i	0.529193	+	1.09888i
$536$	−3316.49	+	14530.5i	−0.267259	+	1.17094i
$537$	−2477.72	−	1193.21i	−0.199109	−	0.0958858i
$538$	−8374.58	+	4032.99i	−0.671104	+	0.323187i
$539$	−1001.73	−	228.638i	−0.0800509	−	0.0182711i
$540$	−16418.8	+	20588.5i	−1.30843	+	1.64072i
$541$	−3244.46	−	2587.37i	−0.257838	−	0.205619i	0.486036	−	0.873939i	$-0.338442\pi$
$541$	−3244.46	−	2587.37i	−0.257838	−	0.205619i	−0.743874	+	0.668320i	$0.767014\pi$
$542$	−1753.74	−	844.558i	−0.138985	−	0.0669315i
$543$	11296.3	−	9008.49i	0.892763	−	0.711954i
$544$	11987.6	+	15032.0i	0.944787	+	1.18473i
$545$	−5566.04	−	11558.0i	−0.437473	−	0.908423i
$546$	3258.35	−	2598.45i	0.255393	−	0.203669i
$547$	−7073.37	+	5640.82i	−0.552898	+	0.440922i	−0.859661	−	0.510864i	$-0.829325\pi$
$547$	−7073.37	+	5640.82i	−0.552898	+	0.440922i	0.306763	+	0.951786i	$0.400754\pi$
$548$	925.342	+	4054.19i	0.0721326	+	0.316034i
$549$	−2282.04	+	9998.26i	−0.177404	+	0.777260i
$550$	−1271.90	−	612.513i	−0.0986070	−	0.0474866i
$551$	−2954.75	−	12945.6i	−0.228451	−	1.00091i
$552$	8849.48	+	11096.9i	0.682353	+	0.855644i
$553$	3591.05	−	819.633i	0.276143	−	0.0630278i
$554$	−2772.98	−	3477.21i	−0.212658	−	0.266665i
$555$	−31749.0			−2.42823
$556$	10272.4	+	8191.97i	0.783538	+	0.624851i
$557$	−3910.95	+	17135.0i	−0.297508	+	1.30347i	0.576316	+	0.817227i	$0.304490\pi$
$557$	−3910.95	+	17135.0i	−0.297508	+	1.30347i	−0.873824	+	0.486242i	$0.838367\pi$
$558$	−26812.2			−2.03414
$559$	9715.22	−	20173.9i	0.735080	−	1.52641i
$560$	−53.4188	+	12.1925i	−0.00403099	+	0.000920048i
$561$	−1326.50	+	2754.50i	−0.0998304	+	0.207300i
$562$	1514.53	+	6635.61i	0.113678	+	0.498054i
$563$	−839.460	−	3677.91i	−0.0628401	−	0.275321i	0.933740	−	0.357952i	$-0.116525\pi$
$563$	−839.460	−	3677.91i	−0.0628401	−	0.275321i	−0.996580	+	0.0826312i	$0.973668\pi$
$564$	4734.66	+	3775.77i	0.353485	+	0.281895i
$565$	15645.6	+	7534.53i	1.16498	+	0.561027i
$566$	−2709.68	−	3397.83i	−0.201230	−	0.252335i
$567$	3578.40	−	1723.27i	0.265042	−	0.127637i
$568$	−1592.31	−	6976.35i	−0.117626	−	0.515354i
$569$	9576.36	−	4611.73i	0.705557	−	0.339778i	−0.0464619	−	0.998920i	$-0.514795\pi$
$569$	9576.36	−	4611.73i	0.705557	−	0.339778i	0.752019	+	0.659142i	$0.229080\pi$
$570$	9742.13	−	20229.7i	0.715882	−	1.48654i
$571$		−	11578.9i		−	0.848620i	−0.905517	−	0.424310i	$-0.860517\pi$
$571$		−	11578.9i		−	0.848620i	0.905517	−	0.424310i	$-0.139483\pi$
$572$	−981.540			−0.0717487
$573$	542.387	+	123.796i	0.0395437	+	0.00902558i
$574$	−1420.74	+	2950.19i	−0.103311	+	0.214527i
$575$	11041.2	−	13845.2i	0.800783	−	1.00415i
$576$	10940.9	−	13719.4i	0.791440	−	0.992434i
$577$			16369.1i			1.18103i	0.807025	+	0.590517i	$0.201076\pi$
$577$			16369.1i			1.18103i	−0.807025	+	0.590517i	$0.798924\pi$
$578$	8554.24	+	6821.78i	0.615588	+	0.490915i
$579$	5643.25	−	1288.03i	0.405053	−	0.0924506i
$580$	−17437.7	+	3980.05i	−1.24838	+	0.284936i
$581$	698.786	−	3061.58i	0.0498976	−	0.218616i
$582$	21400.3	+	10305.9i	1.52418	+	0.734006i
$583$	−142.670	+	113.775i	−0.0101351	+	0.00808249i
$584$	−3926.53	+	17203.3i	−0.278221	+	1.21897i
$585$	−69005.2			−4.87694
$586$	5336.21	−	11080.8i	0.376172	−	0.781129i
$587$	1873.65	−	902.301i	0.131744	−	0.0634446i	−0.366851	−	0.930280i	$-0.619564\pi$
$587$	1873.65	−	902.301i	0.131744	−	0.0634446i	0.498595	+	0.866835i	$0.333850\pi$
$588$	−14443.3	−	3296.58i	−1.01298	−	0.231205i
$589$	−19228.1	+	4388.68i	−1.34513	+	0.307016i
$590$	14241.0			0.993717
$591$	25140.6	−	2630.76i	1.74982	−	0.183105i
$592$	−118.355			−0.00821683
$593$	−16524.5	+	3771.60i	−1.14431	+	0.261182i	−0.752328	−	0.658789i	$-0.771069\pi$
$593$	−16524.5	+	3771.60i	−1.14431	+	0.261182i	−0.391986	+	0.919971i	$0.628212\pi$
$594$	1446.55	+	330.166i	0.0999203	+	0.0228062i
$595$	−7844.57	+	3777.75i	−0.540498	+	0.260290i
$596$	1774.26	−	3684.30i	0.121941	−	0.253212i
$597$	25928.2			1.77750
$598$	−1660.23	+	7273.95i	−0.113532	+	0.497414i
$599$	−10975.8	+	8752.91i	−0.748680	+	0.597052i	−0.921717	−	0.387863i	$-0.873213\pi$
$599$	−10975.8	+	8752.91i	−0.748680	+	0.597052i	0.173037	+	0.984915i	$0.444642\pi$
$600$	−47789.8	−	23014.4i	−3.25169	−	1.56593i
$601$	3765.23	−	16496.5i	0.255552	−	1.11965i	−0.670398	−	0.742002i	$-0.733877\pi$
$601$	3765.23	−	16496.5i	0.255552	−	1.11965i	0.925950	−	0.377645i	$-0.123266\pi$
$602$	−2557.11	+	583.644i	−0.173123	+	0.0395142i
$603$	−36449.4	+	8319.34i	−2.46158	+	0.561840i
$604$	−8864.12	−	7068.90i	−0.597146	−	0.476208i
$605$			25827.8i			1.73562i
$606$	2415.26	−	3028.63i	0.161903	−	0.203020i
$607$	−1323.50	+	1659.61i	−0.0884994	+	0.110975i	−0.824110	−	0.566430i	$-0.808324\pi$
$607$	−1323.50	+	1659.61i	−0.0884994	+	0.110975i	0.735610	+	0.677405i	$0.236895\pi$
$608$	5696.75	−	11829.4i	0.379990	−	0.789057i
$609$	6884.48	+	1571.34i	0.458084	+	0.104555i
$610$	−6157.37			−0.408696
$611$			8295.70i			0.549276i
$612$	−12947.1	+	26885.0i	−0.855159	+	1.77576i
$613$	25672.2	−	12363.1i	1.69150	−	0.814583i	0.696187	−	0.717860i	$-0.254878\pi$
$613$	25672.2	−	12363.1i	1.69150	−	0.814583i	0.995311	−	0.0967222i	$-0.0308358\pi$
$614$	2760.68	+	12095.3i	0.181452	+	0.794995i
$615$	72159.9	−	34750.4i	4.73133	−	2.27849i
$616$	186.811	+	234.254i	0.0122189	+	0.0153220i
$617$	18141.1	+	8736.31i	1.18369	+	0.570033i	0.918983	−	0.394297i	$-0.129012\pi$
$617$	18141.1	+	8736.31i	1.18369	+	0.570033i	0.264703	+	0.964330i	$0.414726\pi$
$618$	−16809.2	−	13404.9i	−1.09412	−	0.872532i
$619$	261.232	+	1144.53i	0.0169625	+	0.0743176i	0.982701	−	0.185200i	$-0.0592934\pi$
$619$	261.232	+	1144.53i	0.0169625	+	0.0743176i	−0.965738	+	0.259518i	$0.916436\pi$
$620$	5911.55	+	25900.2i	0.382925	+	1.67771i
$621$	−8075.69	+	16769.3i	−0.521846	+	1.08362i
$622$	−10245.0	+	2338.36i	−0.660432	+	0.150739i
$623$	−1336.42	+	2775.11i	−0.0859433	+	0.178463i
$624$	−380.004			−0.0243787
$625$	−4093.91	+	17936.6i	−0.262011	+	1.14794i
$626$	−8488.75	−	6769.55i	−0.541979	−	0.432214i
$627$	2087.78			0.132979
$628$	2570.15	+	3222.87i	0.163313	+	0.204788i
$629$	−18335.7	+	4185.01i	−1.16231	+	0.265290i
$630$	5039.75	+	6319.64i	0.318712	+	0.399652i
$631$	1056.22	+	4627.60i	0.0666361	+	0.291952i	0.997256	−	0.0740364i	$-0.0235881\pi$
$631$	1056.22	+	4627.60i	0.0666361	+	0.291952i	−0.930619	+	0.365988i	$0.880731\pi$
$632$	17795.5	+	8569.86i	1.12004	+	0.539384i
$633$	−5206.80	+	22812.5i	−0.326938	+	1.43241i
$634$	−686.498	−	3007.74i	−0.0430037	−	0.188411i
$635$	20208.1	−	16115.4i	1.26289	−	1.00712i
$636$	−2057.06	+	1640.45i	−0.128251	+	0.102277i
$637$	−8805.27	−	18284.3i	−0.547689	−	1.13729i
$638$	628.342	+	787.915i	0.0389910	+	0.0488932i
$639$	14033.9	−	11191.7i	0.868816	−	0.692858i
$640$	−16097.4	−	7752.08i	−0.994226	−	0.478794i
$641$	11619.9	+	9266.59i	0.716006	+	0.570996i	0.912287	−	0.409552i	$-0.134315\pi$
$641$	11619.9	+	9266.59i	0.716006	+	0.570996i	−0.196281	+	0.980548i	$0.562886\pi$
$642$	7644.79	−	9586.26i	0.469962	−	0.589314i
$643$	19066.4	+	4351.78i	1.16937	+	0.266901i	0.762748	−	0.646695i	$-0.223850\pi$
$643$	19066.4	+	4351.78i	1.16937	+	0.266901i	0.406622	+	0.913597i	$0.366707\pi$
$644$	−1299.45	+	625.784i	−0.0795119	+	0.0382909i
$645$	57800.7	+	27835.3i	3.52853	+	1.69925i
$646$	2959.69	−	12967.3i	0.180259	−	0.789768i
$647$	5371.41	+	11153.8i	0.326386	+	0.677748i	0.998004	−	0.0631499i	$-0.0201146\pi$
$647$	5371.41	+	11153.8i	0.326386	+	0.677748i	−0.671618	+	0.740898i	$0.734400\pi$
$648$	20763.6	+	4739.17i	1.25875	+	0.287303i
$649$	574.538	+	1193.04i	0.0347497	+	0.0721586i
$650$	−6204.48	−	27183.6i	−0.374400	−	1.64035i
$651$	2333.90	−	10225.5i	0.140511	−	0.615620i
$652$	281.379	+	1232.80i	0.0169013	+	0.0740494i
$653$	−23687.6	+	11407.4i	−1.41955	+	0.683621i	−0.977023	−	0.213133i	$-0.931633\pi$
$653$	−23687.6	+	11407.4i	−1.41955	+	0.683621i	−0.442530	+	0.896754i	$0.645919\pi$
$654$	−6497.81	+	8148.00i	−0.388508	+	0.487174i
$655$	−4411.58	+	19328.4i	−0.263167	+	1.15301i
$656$	269.001	−	129.544i	0.0160102	−	0.00771012i
$657$	−43154.0	+	9849.61i	−2.56255	+	0.584886i
$658$	759.738	−	605.871i	0.0450116	−	0.0358956i
$659$		−	14147.1i		−	0.836256i	−0.908388	−	0.418128i	$-0.862686\pi$
$659$		−	14147.1i		−	0.836256i	0.908388	−	0.418128i	$-0.137314\pi$
$660$		−	2812.24i		−	0.165858i
$661$	−2226.97	−	1072.45i	−0.131043	−	0.0631068i	0.367214	−	0.930137i	$-0.380312\pi$
$661$	−2226.97	−	1072.45i	−0.131043	−	0.0631068i	−0.498256	+	0.867030i	$0.666026\pi$
$662$	−8579.10	+	17814.7i	−0.503680	+	1.04590i
$663$	−58870.7	+	13436.8i	−3.44849	+	0.787095i
$664$	13165.5	−	10499.2i	0.769460	−	0.613624i
$665$	4648.62	+	3707.15i	0.271076	+	0.216176i
$666$	7575.62	+	15730.9i	0.440765	+	0.915258i
$667$	−11389.9	+	5485.11i	−0.661200	+	0.318417i
$668$		−	7640.76i		−	0.442560i
$669$	29891.1	+	23837.4i	1.72744	+	1.37759i
$670$	−9739.45	−	20224.2i	−0.561594	−	1.16616i
$671$	−248.412	−	515.833i	−0.0142919	−	0.0296774i
$672$	4353.43	+	5459.03i	0.249906	+	0.313373i
$673$	2810.80	+	641.547i	0.160993	+	0.0367457i	0.302258	−	0.953226i	$-0.402260\pi$
$673$	2810.80	+	641.547i	0.160993	+	0.0367457i	−0.141265	+	0.989972i	$0.545117\pi$
$674$	9596.80			0.548449
$675$		−	69557.4i		−	3.96632i
$676$	−5263.71	−	6600.48i	−0.299483	−	0.375539i
$677$	1947.45	+	4043.93i	0.110556	+	0.229573i	0.948905	−	0.315562i	$-0.102193\pi$
$677$	1947.45	+	4043.93i	0.110556	+	0.229573i	−0.838349	+	0.545134i	$0.816479\pi$
$678$		−	14107.4i		−	0.799103i
$679$	−3921.66	+	4917.61i	−0.221649	+	0.277939i
$680$	−45518.1	−	10389.2i	−2.56697	−	0.585894i
$681$	−27848.2	+	34920.6i	−1.56703	+	1.96499i
$682$	1170.29	−	933.273i	0.0657077	−	0.0524001i
$683$	−16143.0	−	20242.7i	−0.904385	−	1.13406i	−0.990464	−	0.137774i	$-0.956005\pi$
$683$	−16143.0	−	20242.7i	−0.904385	−	1.13406i	0.0860788	−	0.996288i	$-0.472566\pi$
$684$	20377.5			1.13911
$685$	−12760.4	−	10176.1i	−0.711754	−	0.567605i
$686$	−2118.95	+	4400.05i	−0.117933	+	0.244890i
$687$	31722.6	−	39778.9i	1.76171	−	2.20911i
$688$	215.472	+	103.766i	0.0119401	+	0.00575005i
$689$	−3513.86	−	802.014i	−0.194292	−	0.0443459i
$690$	−20840.8	−	4756.77i	−1.14985	−	0.262445i
$691$	746.602	+	359.545i	0.0411029	+	0.0197941i	0.454322	−	0.890837i	$-0.349881\pi$
$691$	746.602	+	359.545i	0.0411029	+	0.0197941i	−0.413219	+	0.910631i	$0.635596\pi$
$692$	6997.33	−	8774.38i	0.384391	−	0.482011i
$693$	−326.105	+	677.163i	−0.0178755	+	0.0371188i
$694$	2493.20	+	1988.26i	0.136370	+	0.108751i
$695$	−51568.0			−2.81451
$696$	23609.1	+	29604.9i	1.28578	+	1.61231i
$697$	37093.3	−	29580.9i	2.01579	−	1.60754i
$698$	−12590.5	+	15788.0i	−0.682748	+	0.856139i
$699$	−37015.7	−	8448.58i	−2.00295	−	0.457160i
$700$	3360.61	−	4214.07i	0.181456	−	0.227538i
$701$		−	16732.2i		−	0.901519i	−0.892645	−	0.450760i	$-0.851153\pi$
$701$		−	16732.2i		−	0.901519i	0.892645	−	0.450760i	$-0.148847\pi$
$702$	12715.3	+	26403.6i	0.683631	+	1.41957i
$703$	8007.66	+	10041.3i	0.429608	+	0.538712i
$704$			979.647i			0.0524458i
$705$	−23768.2			−1.26974
$706$	−11331.7	−	2586.38i	−0.604068	−	0.137875i
$707$	639.578	+	802.005i	0.0340223	+	0.0426627i
$708$	8283.89	+	17201.7i	0.439729	+	0.913106i
$709$	756.212	+	1570.29i	0.0400566	+	0.0831784i	0.920037	−	0.391832i	$-0.128159\pi$
$709$	756.212	+	1570.29i	0.0400566	+	0.0831784i	−0.879980	+	0.475010i	$0.842444\pi$
$710$	8426.01	+	6719.52i	0.445384	+	0.355182i
$711$			49546.2i			2.61340i
$712$	−14881.0	+	7166.31i	−0.783271	+	0.377204i
$713$	8147.00	+	16917.4i	0.427921	+	0.888587i
$714$	5530.16	+	4410.15i	0.289861	+	0.231157i
$715$	3011.91	−	2401.92i	0.157537	−	0.125632i
$716$	1460.93	−	333.447i	0.0762534	−	0.0174043i
$717$	13532.5	−	28100.5i	0.704855	−	1.46365i
$718$	1315.82	+	633.668i	0.0683930	+	0.0329363i
$719$			16715.9i			0.867034i	0.901145	+	0.433517i	$0.142728\pi$
$719$			16715.9i			0.867034i	−0.901145	+	0.433517i	$0.857272\pi$
$720$		−	737.027i		−	0.0381491i
$721$	4451.21	−	3549.72i	0.229919	−	0.183354i
$722$	2762.82	−	630.596i	0.142412	−	0.0325046i
$723$	−29473.6	+	14193.7i	−1.51609	+	0.730111i
$724$	−1751.89	+	7675.55i	−0.0899290	+	0.394005i
$725$	29456.3	−	36937.0i	1.50894	−	1.89215i
$726$	18904.3	−	9103.84i	0.966398	−	0.465393i
$727$	−3039.54	−	13317.1i	−0.155062	−	0.679373i	−0.991368	−	0.131109i	$-0.958146\pi$
$727$	−3039.54	−	13317.1i	−0.155062	−	0.679373i	0.836306	−	0.548264i	$-0.184711\pi$
$728$	−1316.85	+	5769.51i	−0.0670410	+	0.293726i
$729$	−2962.95	−	12981.5i	−0.150533	−	0.659530i
$730$	−11530.9	−	23944.3i	−0.584629	−	1.21400i
$731$	37050.3	+	8456.48i	1.87463	+	0.427872i
$732$	−3581.70	−	7437.47i	−0.180852	−	0.375542i
$733$	1900.50	−	8326.65i	0.0957664	−	0.419580i	−0.904205	−	0.427098i	$-0.859536\pi$
$733$	1900.50	−	8326.65i	0.0957664	−	0.419580i	0.999972	+	0.00751810i	$0.00239311\pi$
$734$	19450.3	+	9366.75i	0.978096	+	0.471026i
$735$	52387.0	−	25228.2i	2.62901	−	1.26606i
$736$	−12186.7	−	2781.54i	−0.610339	−	0.139306i
$737$	1301.35	−	1631.84i	0.0650420	−	0.0815600i
$738$	−34436.2	−	27461.9i	−1.71763	−	1.36977i
$739$	14718.1	+	7087.88i	0.732632	+	0.352817i	0.762719	−	0.646730i	$-0.223864\pi$
$739$	14718.1	+	7087.88i	0.732632	+	0.352817i	−0.0300865	+	0.999547i	$0.509578\pi$
$740$	13525.6	−	10786.3i	0.671907	−	0.535828i
$741$	25710.3	+	32239.7i	1.27462	+	1.59832i
$742$	183.182	+	380.381i	0.00906310	+	0.0188197i
$743$	14060.1	−	11212.6i	0.694233	−	0.553632i	−0.211554	−	0.977366i	$-0.567852\pi$
$743$	14060.1	−	11212.6i	0.694233	−	0.553632i	0.905787	+	0.423734i	$0.139281\pi$
$744$	43972.0	−	35066.5i	2.16679	−	1.72796i
$745$	3571.38	+	15647.3i	0.175631	+	0.769491i
$746$	3319.48	−	14543.6i	0.162915	−	0.713778i
$747$	38057.9	+	18327.7i	1.86408	+	0.897692i
$748$	−370.697	−	1624.13i	−0.0181203	−	0.0793904i
$749$	2024.40	+	2538.51i	0.0987582	+	0.123839i
$750$	40040.4	−	9138.95i	1.94942	−	0.444943i
$751$	−6301.97	−	7902.42i	−0.306208	−	0.383973i	0.604789	−	0.796386i	$-0.293257\pi$
$751$	−6301.97	−	7902.42i	−0.306208	−	0.383973i	−0.910997	+	0.412413i	$0.864686\pi$
$752$	−88.6042			−0.00429663
$753$	12234.6	+	9756.81i	0.592105	+	0.472188i
$754$	−4429.25	+	19405.8i	−0.213931	+	0.937291i
$755$	44498.3			2.14498
$756$	−2457.99	+	5104.07i	−0.118249	+	0.245547i
$757$	17646.5	−	4027.69i	0.847255	−	0.193380i	0.223212	−	0.974770i	$-0.428346\pi$
$757$	17646.5	−	4027.69i	0.847255	−	0.193380i	0.624044	+	0.781390i	$0.285489\pi$
$758$	−216.511	+	449.590i	−0.0103747	+	0.0215433i
$759$	−442.300	−	1937.84i	−0.0211521	−	0.0926736i
$760$	7094.69	+	31083.9i	0.338620	+	1.48359i
$761$	7513.17	+	5991.56i	0.357887	+	0.285406i	0.785883	−	0.618375i	$-0.212209\pi$
$761$	7513.17	+	5991.56i	0.357887	+	0.285406i	−0.427996	+	0.903781i	$0.640780\pi$
$762$	−18918.5	−	9110.66i	−0.899402	−	0.433129i
$763$	−1720.67	−	2157.65i	−0.0816414	−	0.102375i
$764$	−273.124	+	131.530i	−0.0129336	+	0.00622851i
$765$	−26061.1	−	114181.i	−1.23169	−	5.39637i
$766$	−7954.99	+	3830.92i	−0.375229	+	0.180701i
$767$	−11347.8	+	23563.9i	−0.534218	+	1.10931i
$768$			37198.8i			1.74778i
$769$	19415.3			0.910446			0.455223	−	0.890377i	$-0.349560\pi$
$769$	19415.3			0.910446			0.455223	+	0.890377i	$0.349560\pi$
$770$	−439.946	−	100.415i	−0.0205903	−	0.00469961i
$771$	−13681.3	+	28409.4i	−0.639064	+	1.32703i
$772$	−1966.53	+	2465.95i	−0.0916799	+	0.114963i
$773$	5158.28	−	6468.28i	0.240013	−	0.300967i	−0.647206	−	0.762315i	$-0.724063\pi$
$773$	5158.28	−	6468.28i	0.240013	−	0.300967i	0.887219	+	0.461348i	$0.152634\pi$
$774$		−	35280.8i		−	1.63843i
$775$	−54862.4	−	43751.3i	−2.54286	−	2.02786i
$776$	−32882.5	+	7505.22i	−1.52115	+	0.347193i
$777$	−6658.82	+	1519.83i	−0.307444	+	0.0701720i
$778$	157.548	−	690.264i	0.00726013	−	0.0318087i
$779$	−29190.6	−	14057.4i	−1.34257	−	0.646547i
$780$	43426.8	−	34631.7i	1.99350	−	1.58976i
$781$	−222.989	+	976.981i	−0.0102166	+	0.0447620i
$782$	−12663.0			−0.579065
$783$	−21544.7	+	44738.1i	−0.983328	+	2.04190i
$784$	195.290	−	94.0469i	0.00889625	−	0.00428421i
$785$	−15773.3	−	3600.16i	−0.717165	−	0.163688i
$786$	15702.2	−	3583.92i	0.712568	−	0.162639i
$787$	20304.0			0.919643			0.459822	−	0.888011i	$-0.347913\pi$
$787$	20304.0			0.919643			0.459822	+	0.888011i	$0.347913\pi$
$788$	−9816.56	+	9661.95i	−0.443782	+	0.436793i
$789$	11841.9			0.534327
$790$	−29001.9	+	6619.49i	−1.30613	+	0.298115i
$791$	3642.09	+	831.282i	0.163714	+	0.0373666i
$792$	−3631.16	+	1748.67i	−0.162914	+	0.0784551i
$793$	4906.43	−	10188.3i	0.219713	−	0.456239i
$794$	26996.5			1.20664
$795$	2297.87	−	10067.6i	0.102512	−	0.449135i
$796$	−11045.8	+	8808.77i	−0.491846	+	0.392234i
$797$	5781.66	+	2784.30i	0.256960	+	0.123745i	0.557929	−	0.829888i	$-0.311596\pi$
$797$	5781.66	+	2784.30i	0.256960	+	0.123745i	−0.300970	+	0.953634i	$0.597310\pi$
$798$	1074.85	−	4709.21i	0.0476806	−	0.208902i
$799$	−13726.7	+	3133.02i	−0.607778	+	0.138721i
$800$	45543.3	−	10395.0i	2.01275	−	0.459397i
$801$	−32392.6	−	25832.2i	−1.42888	−	1.13950i
$802$		−	7535.37i		−	0.331774i
$803$	1540.73	−	1932.01i	0.0677099	−	0.0849055i
$804$	18763.4	−	23528.5i	0.823051	−	1.03207i
$805$	2456.10	−	5100.14i	0.107535	−	0.223300i
$806$	28823.4	+	6578.74i	1.25963	+	0.287502i
$807$	48909.7			2.13346
$808$			5500.67i			0.239496i
$809$	3388.49	−	7036.27i	0.147259	−	0.305787i	−0.814271	−	0.580484i	$-0.802863\pi$
$809$	3388.49	−	7036.27i	0.147259	−	0.305787i	0.961531	+	0.274697i	$0.0885775\pi$
$810$	−28899.7	+	13917.4i	−1.25362	+	0.603712i
$811$	−4695.87	−	20574.0i	−0.203322	−	0.890813i	−0.968897	−	0.247466i	$-0.920402\pi$
$811$	−4695.87	−	20574.0i	−0.203322	−	0.890813i	0.765574	−	0.643348i	$-0.222455\pi$
$812$	−3466.75	+	1669.50i	−0.149826	+	0.0721526i
$813$	6385.96	+	8007.75i	0.275480	+	0.345441i
$814$	−878.218	−	422.927i	−0.0378151	−	0.0182108i
$815$	−3880.20	−	3094.36i	−0.166770	−	0.132995i
$816$	−143.516	−	628.783i	−0.00615692	−	0.0269752i
$817$	−5774.85	−	25301.3i	−0.247291	−	1.08345i
$818$	8952.77	−	18590.6i	0.382673	−	0.794628i
$819$	−14472.7	+	3303.29i	−0.617480	+	0.140936i
$820$	−18935.4	+	39319.7i	−0.806404	+	1.67452i
$821$	−31389.5			−1.33435			−0.667176	−	0.744900i	$-0.732497\pi$
$821$	−31389.5			−1.33435			−0.667176	+	0.744900i	$0.732497\pi$
$822$	−2950.45	+	12926.8i	−0.125193	+	0.548507i
$823$	−25975.1	−	20714.5i	−1.10016	−	0.877352i	−0.107022	−	0.994257i	$-0.534131\pi$
$823$	−25975.1	−	20714.5i	−1.10016	−	0.877352i	−0.993143	+	0.116905i	$0.962703\pi$
$824$	30529.3			1.29070
$825$	4631.40	+	5807.60i	0.195448	+	0.245084i
$826$	2986.81	−	681.721i	0.125817	−	0.0287168i
$827$	−6941.27	−	8704.07i	−0.291864	−	0.365986i	0.614182	−	0.789164i	$-0.289486\pi$
$827$	−6941.27	−	8704.07i	−0.291864	−	0.365986i	−0.906047	+	0.423178i	$0.860914\pi$
$828$	−4317.02	−	18914.1i	−0.181192	−	0.793852i
$829$	−15069.0	−	7256.85i	−0.631325	−	0.304030i	0.0907198	−	0.995876i	$-0.471083\pi$
$829$	−15069.0	−	7256.85i	−0.631325	−	0.304030i	−0.722045	+	0.691846i	$0.756798\pi$
$830$	−5643.50	+	24725.8i	−0.236011	+	1.03403i
$831$	5207.50	+	22815.6i	0.217384	+	0.952422i
$832$	−15127.8	+	12064.0i	−0.630363	+	0.502698i
$833$	26929.1	−	21475.3i	1.12010	−	0.893246i
$834$	18176.8	+	37744.6i	0.754691	+	1.56713i
$835$	18697.6	+	23446.1i	0.774921	+	0.971720i
$836$	−889.431	+	709.297i	−0.0367962	+	0.0293440i
$837$	66449.3	+	32000.3i	2.74411	+	1.32150i
$838$	3946.66	+	3147.36i	0.162691	+	0.129742i
$839$	−22166.1	+	27795.4i	−0.912109	+	1.14375i	0.0770686	+	0.997026i	$0.475444\pi$
$839$	−22166.1	+	27795.4i	−0.912109	+	1.14375i	−0.989178	+	0.146723i	$0.953127\pi$
$840$	−16530.4	−	3772.95i	−0.678991	−	0.154975i
$841$	−8412.93	+	4051.45i	−0.344948	+	0.166118i
$842$	−15446.3	−	7438.52i	−0.632201	−	0.304452i
$843$	7969.30	−	34915.8i	0.325596	−	1.42653i
$844$	−5532.07	−	11487.5i	−0.225618	−	0.468501i
$845$	32304.0	+	7373.17i	1.31514	+	0.300171i
$846$	5671.34	+	11776.7i	0.230478	+	0.478593i
$847$	1236.38	+	5416.94i	0.0501565	+	0.219750i
$848$	8.56611	−	37.5306i	0.000346889	−	0.00151982i
$849$	5088.63	+	22294.8i	0.205702	+	0.901241i
$850$	42636.8	−	20532.8i	1.72051	−	0.828552i
$851$	7623.72	−	9559.84i	0.307095	−	0.385085i
$852$	−3215.14	+	14086.5i	−0.129283	+	0.566425i
$853$	−18072.1	+	8703.05i	−0.725411	+	0.349340i	−0.759877	−	0.650066i	$-0.774741\pi$
$853$	−18072.1	+	8703.05i	−0.725411	+	0.349340i	0.0344665	+	0.999406i	$0.489027\pi$
$854$	−1291.41	+	294.755i	−0.0517459	+	0.0118107i
$855$	−62529.6	+	49865.7i	−2.50113	+	1.99458i
$856$			17410.8i			0.695196i
$857$			17030.5i			0.678823i	0.940638	+	0.339411i	$0.110228\pi$
$857$			17030.5i			0.678823i	−0.940638	+	0.339411i	$0.889772\pi$
$858$	−2819.70	−	1357.90i	−0.112195	−	0.0540301i
$859$	−4062.17	+	8435.19i	−0.161350	+	0.335046i	−0.965932	−	0.258794i	$-0.916675\pi$
$859$	−4062.17	+	8435.19i	−0.161350	+	0.335046i	0.804583	+	0.593841i	$0.202389\pi$
$860$	−34080.8	+	7778.72i	−1.35133	+	0.308433i
$861$	13470.8	−	10742.6i	0.533199	−	0.425212i
$862$	18289.2	+	14585.2i	0.722661	+	0.576303i
$863$	−1016.60	−	2110.99i	−0.0400990	−	0.0832663i	0.879957	−	0.475053i	$-0.157571\pi$
$863$	−1016.60	−	2110.99i	−0.0400990	−	0.0832663i	−0.920056	+	0.391787i	$0.871857\pi$
$864$	−44236.5	+	21303.2i	−1.74185	+	0.838830i
$865$			44047.8i			1.73141i
$866$	15243.7	+	12156.4i	0.598153	+	0.477011i
$867$	−24979.5	−	51870.4i	−0.978485	−	2.03185i
$868$	2479.70	+	5149.15i	0.0969660	+	0.201352i
$869$	−1724.60	−	2162.57i	−0.0673221	−	0.0844192i
$870$	−55600.1	−	12690.4i	−2.16669	−	0.494533i
$871$	41224.8			1.60373
$872$		−	14798.6i		−	0.574705i
$873$	−52751.2	−	66147.9i	−2.04508	−	2.56445i
$874$	3751.99	+	7791.09i	0.145209	+	0.301530i
$875$			10875.7i			0.420188i
$876$	22214.7	−	27856.4i	0.856811	−	1.07441i
$877$	−25366.2	−	5789.67i	−0.976689	−	0.222923i	−0.295752	−	0.955265i	$-0.595570\pi$
$877$	−25366.2	−	5789.67i	−0.976689	−	0.222923i	−0.680937	+	0.732342i	$0.738427\pi$
$878$	3417.35	−	4285.22i	0.131355	−	0.164714i
$879$	−50595.7	+	40348.8i	−1.94147	+	1.54827i
$880$	25.6543	+	32.1695i	0.000982734	+	0.00123231i
$881$	40098.5			1.53343			0.766716	−	0.641987i	$-0.221890\pi$
$881$	40098.5			1.53343			0.766716	+	0.641987i	$0.221890\pi$
$882$	−25000.1	−	19936.9i	−0.954420	−	0.761124i
$883$	−14051.7	+	29178.6i	−0.535534	+	1.11205i	0.441163	+	0.897427i	$0.354566\pi$
$883$	−14051.7	+	29178.6i	−0.535534	+	1.11205i	−0.976697	+	0.214621i	$0.931148\pi$
$884$	20514.9	−	25724.9i	0.780534	−	0.978758i
$885$	−67513.7	−	32512.9i	−2.56435	−	1.23492i
$886$	−16093.0	−	3673.13i	−0.610221	−	0.139279i
$887$	10165.1	+	2320.11i	0.384791	+	0.0878260i	0.410540	−	0.911842i	$-0.365340\pi$
$887$	10165.1	+	2320.11i	0.384791	+	0.0878260i	−0.0257496	+	0.999668i	$0.508197\pi$
$888$	−32997.9	−	15890.9i	−1.24700	−	0.600524i
$889$	3466.86	−	4347.30i	0.130793	−	0.164009i
$890$	10793.2	−	22412.2i	0.406503	−	0.844112i
$891$	−2331.86	−	1859.59i	−0.0876769	−	0.0699200i
$892$	−20832.6			−0.781981
$893$	5994.78	+	7517.21i	0.224644	+	0.281695i
$894$	10194.0	−	8129.42i	0.381362	−	0.304126i
$895$	−3666.96	+	4598.23i	−0.136953	+	0.171734i
$896$	−3747.25	−	855.285i	−0.139717	−	0.0318896i
$897$	24477.6	−	30693.9i	0.911128	−	1.14252i
$898$			18071.5i			0.671551i
$899$	21735.0	+	45133.2i	0.806343	+	1.67439i
$900$	45204.3	+	56684.3i	1.67423	+	2.09942i
$901$		−	6117.18i		−	0.226185i
$902$	2458.95			0.0907694
$903$	13455.2	+	3071.07i	0.495860	+	0.113177i
$904$	12489.9	+	15661.8i	0.459522	+	0.576222i
$905$	−13407.0	−	27839.9i	−0.492445	−	1.02257i
$906$	−15684.9	−	32570.0i	−0.575161	−	1.19433i
$907$	−37384.4	−	29813.0i	−1.36861	−	1.09143i	−0.985859	−	0.167576i	$-0.946406\pi$
$907$	−37384.4	−	29813.0i	−1.36861	−	1.09143i	−0.382749	−	0.923852i	$-0.625023\pi$
$908$		−	24337.9i		−	0.889516i
$909$	−12431.8	+	5986.86i	−0.453617	+	0.218451i
$910$	−3867.17	−	8030.25i	−0.140874	−	0.292528i
$911$	7575.85	+	6041.54i	0.275521	+	0.219720i	0.751495	−	0.659739i	$-0.229333\pi$
$911$	7575.85	+	6041.54i	0.275521	+	0.219720i	−0.475974	+	0.879459i	$0.657905\pi$
$912$	−344.344	+	274.605i	−0.0125026	+	0.00997048i
$913$	−2299.08	+	524.751i	−0.0833391	+	0.0190216i
$914$	2449.57	−	5086.58i	0.0886483	−	0.184080i
$915$	29190.8	+	14057.6i	1.05467	+	0.507900i
$916$			27723.9i			1.00002i
$917$			4264.99i			0.153590i
$918$	−38887.2	+	31011.5i	−1.39811	+	1.11496i
$919$	26835.0	−	6124.90i	0.963225	−	0.219850i	0.288139	−	0.957589i	$-0.406964\pi$
$919$	26835.0	−	6124.90i	0.963225	−	0.219850i	0.675086	+	0.737739i	$0.264106\pi$
$920$	27348.5	−	13170.3i	0.980058	−	0.471971i
$921$	14526.4	−	63644.1i	0.519717	−	2.27703i
$922$	−3949.46	+	4952.47i	−0.141072	+	0.176899i
$923$	−17832.7	+	8587.75i	−0.635936	+	0.306251i
$924$	−134.623	−	589.820i	−0.00479303	−	0.0209996i
$925$	−10168.2	+	44550.0i	−0.361437	+	1.58356i
$926$	3664.14	+	16053.7i	0.130034	+	0.569715i
$927$	33227.7	+	68998.0i	1.17728	+	2.44465i
$928$	−32512.4	−	7420.75i	−1.15008	−	0.262498i
$929$	−2394.59	−	4972.42i	−0.0845683	−	0.175608i	0.854396	−	0.519622i	$-0.173927\pi$
$929$	−2394.59	−	4972.42i	−0.0845683	−	0.175608i	−0.938964	+	0.344014i	$0.888213\pi$
$930$	−18848.9	+	82582.6i	−0.664604	+	2.91182i
$931$	−21191.9	−	10205.5i	−0.746012	−	0.359260i
$932$	18639.6	−	8976.37i	0.655108	−	0.315484i
$933$	53908.2	+	12304.2i	1.89161	+	0.431748i
$934$	16247.8	−	20374.2i	0.569214	−	0.713772i
$935$	5111.90	+	4076.60i	0.178799	+	0.142587i
$936$	−71719.6	−	34538.3i	−2.50452	−	1.20611i
$937$	23848.0	−	19018.1i	0.831461	−	0.663068i	−0.112308	−	0.993673i	$-0.535824\pi$
$937$	23848.0	−	19018.1i	0.831461	−	0.663068i	0.943769	+	0.330605i	$0.107253\pi$
$938$	−3010.82	−	3775.45i	−0.104805	−	0.131421i
$939$	24788.2	+	51473.3i	0.861483	+	1.78889i
$940$	10125.7	−	8074.96i	0.351344	−	0.280187i
$941$	−30364.6	+	24215.0i	−1.05192	+	0.838879i	−0.987274	−	0.159030i	$-0.949163\pi$
$941$	−30364.6	+	24215.0i	−1.05192	+	0.838879i	−0.0646468	+	0.997908i	$0.520592\pi$
$942$	2924.73	+	12814.1i	0.101160	+	0.443212i
$943$	−6863.81	+	30072.3i	−0.237027	+	1.03848i
$944$	−251.680	−	121.203i	−0.00867744	−	0.00417883i
$945$	−4947.65	−	21677.1i	−0.170314	−	0.746196i
$946$	1228.05	+	1539.92i	0.0422065	+	0.0529252i
$947$	−49265.4	+	11244.5i	−1.69051	+	0.385847i	−0.956141	−	0.292907i	$-0.905377\pi$
$947$	−49265.4	+	11244.5i	−1.69051	+	0.385847i	−0.734366	+	0.678754i	$0.762520\pi$
$948$	−24865.8	−	31180.8i	−0.851904	−	1.06825i
$949$	48807.7			1.66951
$950$	−25266.1	−	20149.1i	−0.862886	−	0.688128i
$951$	−3612.27	+	15826.4i	−0.123171	+	0.539649i
$952$	−10044.0			−0.341941
$953$	−13525.8	+	28086.6i	−0.459752	+	0.954685i	0.534250	+	0.845326i	$0.320594\pi$
$953$	−13525.8	+	28086.6i	−0.459752	+	0.954685i	−0.994002	+	0.109359i	$0.965120\pi$
$954$	−5536.60	+	1263.69i	−0.187897	+	0.0428864i
$955$	516.232	−	1071.97i	0.0174920	−	0.0363225i
$956$	3781.73	+	16568.8i	0.127939	+	0.560538i
$957$	−1179.99	−	5169.88i	−0.0398576	−	0.174627i
$958$	3273.86	+	2610.82i	0.110411	+	0.0880498i
$959$	−3163.42	−	1523.42i	−0.106520	−	0.0512971i
$960$	−34564.9	−	43343.1i	−1.16206	−	1.45718i
$961$	40195.4	−	19357.1i	1.34924	−	0.649762i
$962$	−4284.06	−	18769.7i	−0.143580	−	0.629064i
$963$	−39349.4	+	18949.7i	−1.31674	+	0.634106i
$964$	7734.11	−	16060.0i	0.258401	−	0.536576i
$965$		−	12379.2i		−	0.412953i
$966$	−4598.72			−0.153169
$967$	8122.45	+	1853.90i	0.270114	+	0.0616518i	0.355433	−	0.934702i	$-0.384334\pi$
$967$	8122.45	+	1853.90i	0.270114	+	0.0616518i	−0.0853184	+	0.996354i	$0.527191\pi$
$968$	−12927.3	+	26843.7i	−0.429234	+	0.891313i
$969$	−43636.2	+	54718.0i	−1.44664	+	1.81403i
$970$	31672.0	−	39715.4i	1.04838	−	1.31462i
$971$			6624.25i			0.218931i	0.993991	+	0.109466i	$0.0349140\pi$
$971$			6624.25i			0.218931i	−0.993991	+	0.109466i	$0.965086\pi$
$972$	−5189.16	−	4138.22i	−0.171237	−	0.136557i
$973$	−10815.5	+	2468.57i	−0.356351	+	0.0813348i
$974$	27733.0	−	6329.88i	0.912344	−	0.208237i
$975$	−32647.3	+	143037.i	−1.07236	+	4.69831i
$976$	108.819	+	52.4043i	0.00356886	+	0.00171867i
$977$	−31407.3	+	25046.5i	−1.02846	+	0.820173i	−0.983879	−	0.178833i	$-0.942768\pi$
$977$	−31407.3	+	25046.5i	−1.02846	+	0.820173i	−0.0445845	+	0.999006i	$0.514196\pi$
$978$	−897.174	+	3930.78i	−0.0293338	+	0.128520i
$979$	2313.02			0.0755102
$980$	−13746.8	+	28545.5i	−0.448087	+	0.930462i
$981$	33445.6	−	16106.6i	1.08852	−	0.524203i
$982$	28379.7	+	6477.47i	0.922231	+	0.210493i
$983$	43700.8	−	9974.42i	1.41794	−	0.323636i	0.556229	−	0.831029i	$-0.312248\pi$
$983$	43700.8	−	9974.42i	1.41794	−	0.323636i	0.861715	+	0.507393i	$0.169391\pi$
$984$	92391.7			2.99323
$985$	6478.99	−	53670.3i	0.209582	−	1.73612i
$986$	−33783.1			−1.09115
$987$	−4984.99	+	1137.79i	−0.160764	+	0.0366933i
$988$	−21906.1	−	4999.91i	−0.705389	−	0.161000i
$989$	−22260.8	+	10720.2i	−0.715726	+	0.344675i
$990$	2633.67	−	5468.88i	0.0845491	−	0.175568i
$991$	−15617.5			−0.500612			−0.250306	−	0.968167i	$-0.580531\pi$
$991$	−15617.5			−0.500612			−0.250306	+	0.968167i	$0.580531\pi$
$992$	−11022.0	+	48290.6i	−0.352771	+	1.54559i
$993$	81343.5	−	64869.3i	2.59955	−	2.07308i
$994$	2088.88	+	1005.95i	0.0666552	+	0.0320995i
$995$	12338.9	−	54060.4i	0.393136	−	1.72244i
$996$	−33149.0	+	7566.05i	−1.05459	+	0.240702i
$997$	−1844.58	+	421.012i	−0.0585941	+	0.0133737i	−0.251717	−	0.967801i	$-0.580995\pi$
$997$	−1844.58	+	421.012i	−0.0585941	+	0.0133737i	0.193123	+	0.981174i	$0.438138\pi$
$998$	−19334.4	−	15418.7i	−0.613246	−	0.489047i
$999$		−	48027.9i		−	1.52106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.4.e.a.6.19	✓	288
197.33	even	14	inner	197.4.e.a.33.19	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.4.e.a.6.19	✓	288	1.1	even	1	trivial
197.4.e.a.33.19	yes	288	197.33	even	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	197.e (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69384 + 0.386608i) q^{2} +(8.91279 + 2.03429i) q^{3} +(-4.48812 + 2.16137i) q^{4} +(8.48300 - 17.6151i) q^{5} -15.8833 q^{6} +(0.935927 - 4.10056i) q^{7} +(17.6334 - 14.0622i) q^{8} +(50.9733 + 24.5474i) q^{9} +(-7.55869 + 33.1168i) q^{10} +(-3.07930 + 0.702831i) q^{11} +(-44.3985 + 10.1337i) q^{12} +(-48.7737 - 38.8958i) q^{13} +7.30753i q^{14} +(111.441 - 139.743i) q^{15} +(0.415436 - 0.520940i) q^{16} +(45.9395 - 95.3943i) q^{17} +(-95.8308 - 21.8727i) q^{18} -72.3042 q^{19} +97.3938i q^{20} +(16.6834 - 34.6435i) q^{21} +(4.94413 - 2.38097i) q^{22} +(15.3178 + 67.1116i) q^{23} +(185.769 - 89.4617i) q^{24} +(-160.395 - 201.129i) q^{25} +(97.6523 + 47.0269i) q^{26} +(211.395 + 168.582i) q^{27} +(4.66226 + 20.4267i) q^{28} +(40.8656 + 179.044i) q^{29} +(-134.738 + 279.786i) q^{30} +(265.933 - 60.6974i) q^{31} +(-78.7886 + 163.606i) q^{32} -28.8749 q^{33} +(-40.9339 + 179.343i) q^{34} +(-64.2925 - 51.2715i) q^{35} -281.830 q^{36} +(-110.750 - 138.876i) q^{37} +(122.472 - 27.9534i) q^{38} +(-355.585 - 445.889i) q^{39} +(-98.1227 - 429.904i) q^{40} +(403.719 + 194.421i) q^{41} +(-14.8656 + 65.1305i) q^{42} +(79.8688 + 349.928i) q^{43} +(12.3012 - 9.80990i) q^{44} +(864.812 - 689.665i) q^{45} +(-51.8917 - 107.754i) q^{46} +(-82.9105 - 103.966i) q^{47} +(4.76243 - 3.79791i) q^{48} +(293.094 + 141.146i) q^{49} +(349.442 + 278.671i) q^{50} +(603.508 - 756.775i) q^{51} +(302.971 + 69.1511i) q^{52} +(52.0533 - 25.0675i) q^{53} +(-423.244 - 203.824i) q^{54} +(-13.7413 + 60.2045i) q^{55} +(-41.1592 - 85.4680i) q^{56} +(-644.432 - 147.087i) q^{57} +(-138.439 - 287.472i) q^{58} +(-93.2902 - 408.731i) q^{59} +(-198.127 + 868.050i) q^{60} +(40.3358 + 176.723i) q^{61} +(-426.981 + 205.623i) q^{62} +(148.366 - 186.044i) q^{63} +(69.0177 - 302.386i) q^{64} +(-1098.90 + 529.203i) q^{65} +(48.9095 - 11.1633i) q^{66} +(-516.652 + 412.017i) q^{67} +527.434i q^{68} +629.312i q^{69} +(128.723 + 61.9898i) q^{70} +(137.660 - 285.853i) q^{71} +(1244.02 - 283.940i) q^{72} +(-611.686 + 487.804i) q^{73} +(241.282 + 192.416i) q^{74} +(-1020.41 - 2118.91i) q^{75} +(324.510 - 156.276i) q^{76} +13.2847i q^{77} +(774.688 + 617.793i) q^{78} +(379.972 + 789.019i) q^{79} +(-5.65228 - 11.7371i) q^{80} +(588.759 + 738.281i) q^{81} +(-758.999 - 173.237i) q^{82} +746.624 q^{83} +191.543i q^{84} +(-1290.68 - 1618.46i) q^{85} +(-270.570 - 561.844i) q^{86} +1678.91i q^{87} +(-44.4153 + 55.6950i) q^{88} +(-713.957 - 162.956i) q^{89} +(-1198.22 + 1502.52i) q^{90} +(-205.143 + 163.596i) q^{91} +(-213.801 - 268.098i) q^{92} +2493.68 q^{93} +(180.631 + 144.049i) q^{94} +(-613.357 + 1273.65i) q^{95} +(-1035.05 + 1297.91i) q^{96} +(-1347.35 - 648.849i) q^{97} +(-551.022 - 125.767i) q^{98} +(-174.215 - 39.7634i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 7 q^{2} - 7 q^{3} + 159 q^{4} - 7 q^{5} + 26 q^{6} - 53 q^{7} + 49 q^{8} + 391 q^{9} + 149 q^{10} + 91 q^{11} - 63 q^{12} - 7 q^{13} - 473 q^{15} - 1113 q^{16} - 7 q^{17} - 196 q^{18} + 464 q^{19}+ \cdots + 2464 q^{99}+O(q^{100}) \) 288 * q - 7 * q^2 - 7 * q^3 + 159 * q^4 - 7 * q^5 + 26 * q^6 - 53 * q^7 + 49 * q^8 + 391 * q^9 + 149 * q^10 + 91 * q^11 - 63 * q^12 - 7 * q^13 - 473 * q^15 - 1113 * q^16 - 7 * q^17 - 196 * q^18 + 464 * q^19 - 7 * q^21 + 807 * q^22 + 413 * q^23 - 1425 * q^24 + 1195 * q^25 - 543 * q^26 + 455 * q^27 + 174 * q^28 - 906 * q^29 + 798 * q^30 + 917 * q^31 + 945 * q^32 + 894 * q^33 - 219 * q^34 - 7 * q^35 + 3250 * q^36 + 1734 * q^37 - 63 * q^38 - 825 * q^39 + 141 * q^40 + 563 * q^41 + 432 * q^42 - 423 * q^43 + 2149 * q^44 - 3808 * q^45 - 2569 * q^46 - 289 * q^47 - 3703 * q^48 - 3747 * q^49 - 4963 * q^50 - 87 * q^51 + 3654 * q^52 - 1573 * q^53 - 1228 * q^54 + 2825 * q^55 + 98 * q^56 - 518 * q^57 - 5103 * q^58 + 2045 * q^59 + 3375 * q^60 + 287 * q^61 - 2547 * q^62 + 1453 * q^63 + 6475 * q^64 + 1268 * q^65 + 4634 * q^66 - 3577 * q^67 - 814 * q^70 - 273 * q^71 - 1008 * q^72 - 679 * q^73 - 315 * q^74 - 1281 * q^75 + 6078 * q^76 + 4739 * q^78 + 1463 * q^79 + 441 * q^80 - 4427 * q^81 - 7 * q^82 + 4900 * q^83 - 3351 * q^85 + 3472 * q^86 + 3738 * q^88 + 147 * q^89 + 7133 * q^90 - 14133 * q^91 - 803 * q^92 - 4894 * q^93 - 7833 * q^94 - 7700 * q^95 - 16450 * q^96 + 1233 * q^97 - 2030 * q^98 + 2464 * q^99

Introduction

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