LMFDB - Embedded newform 197.4.d.a.36.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,4,Mod(36,197)]

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([12]))

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

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

chi := DirichletCharacter("197.36");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	197.d (of order $7$, 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:	$294$
Relative dimension:	$49$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			36.5
Character	$\chi$	$=$	197.36
Dual form			197.4.d.a.104.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.23571 + 2.03981i) q^{2} +(5.41516 + 2.60780i) q^{3} +(8.79251 - 11.0255i) q^{4} +(-7.52587 - 9.43714i) q^{5} -28.2565 q^{6} +(15.8752 + 7.64508i) q^{7} +(-6.38361 + 27.9684i) q^{8} +(5.68910 + 7.13391i) q^{9} +(51.1274 + 24.6217i) q^{10} +(-15.4856 + 7.45746i) q^{11} +(76.3651 - 36.7755i) q^{12} +(-9.81465 - 43.0008i) q^{13} -82.8372 q^{14} +(-16.1436 - 70.7296i) q^{15} +(-4.90710 - 21.4994i) q^{16} +(-45.5664 - 57.1385i) q^{17} +(-38.6492 - 18.6125i) q^{18} -79.9476 q^{19} -170.220 q^{20} +(66.0297 + 82.7987i) q^{21} +(50.3806 - 63.1753i) q^{22} +(-145.384 + 70.0132i) q^{23} +(-107.504 + 134.806i) q^{24} +(-4.60582 + 20.1794i) q^{25} +(129.286 + 162.119i) q^{26} +(-23.9072 - 104.744i) q^{27} +(223.873 - 107.812i) q^{28} +(13.3778 - 6.44241i) q^{29} +(212.655 + 266.661i) q^{30} +(-41.7920 + 20.1260i) q^{31} +(-78.4521 - 98.3758i) q^{32} -103.304 q^{33} +(309.558 + 149.075i) q^{34} +(-47.3268 - 207.352i) q^{35} +128.676 q^{36} +(20.3115 - 88.9905i) q^{37} +(338.635 - 163.078i) q^{38} +(58.9897 - 258.451i) q^{39} +(311.984 - 150.244i) q^{40} +(-130.044 - 163.071i) q^{41} +(-448.577 - 216.023i) q^{42} +(380.937 - 183.450i) q^{43} +(-53.9352 + 236.305i) q^{44} +(24.5083 - 107.378i) q^{45} +(472.991 - 593.112i) q^{46} +(23.1199 - 101.295i) q^{47} +(29.4935 - 129.219i) q^{48} +(-20.2832 - 25.4343i) q^{49} +(-21.6533 - 94.8693i) q^{50} +(-97.7435 - 428.242i) q^{51} +(-560.399 - 269.874i) q^{52} +(-121.306 + 152.113i) q^{53} +(314.922 + 394.900i) q^{54} +(186.920 + 90.0157i) q^{55} +(-315.162 + 395.200i) q^{56} +(-432.929 - 208.488i) q^{57} +(-43.5232 + 54.5764i) q^{58} +(684.028 - 329.411i) q^{59} +(-921.769 - 443.901i) q^{60} +(254.657 - 122.636i) q^{61} +(135.966 - 170.496i) q^{62} +(35.7762 + 156.746i) q^{63} +(691.916 + 333.209i) q^{64} +(-331.941 + 416.241i) q^{65} +(437.568 - 210.722i) q^{66} +(-70.4808 + 308.796i) q^{67} -1030.62 q^{68} -969.858 q^{69} +(623.422 + 781.746i) q^{70} +(-256.628 - 321.801i) q^{71} +(-235.841 + 113.575i) q^{72} +(-244.066 + 1069.32i) q^{73} +(95.4902 + 418.370i) q^{74} +(-77.5653 + 97.2638i) q^{75} +(-702.940 + 881.459i) q^{76} -302.849 q^{77} +(277.328 + 1215.05i) q^{78} +(31.0049 - 38.8789i) q^{79} +(-165.963 + 208.111i) q^{80} +(198.512 - 869.739i) q^{81} +(883.464 + 425.454i) q^{82} -672.320 q^{83} +1493.46 q^{84} +(-196.297 + 860.033i) q^{85} +(-1239.34 + 1554.08i) q^{86} +89.2435 q^{87} +(-109.720 - 480.713i) q^{88} +(-280.934 - 135.291i) q^{89} +(115.220 + 504.813i) q^{90} +(172.935 - 757.679i) q^{91} +(-506.362 + 2218.52i) q^{92} -278.795 q^{93} +(108.693 + 476.217i) q^{94} +(601.675 + 754.477i) q^{95} +(-168.286 - 737.308i) q^{96} +(108.743 + 136.359i) q^{97} +(137.795 + 66.3585i) q^{98} +(-141.300 - 68.0464i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 294 q - 5 q^{2} - 5 q^{3} - 161 q^{4} - 5 q^{5} + 58 q^{6} + 15 q^{7} + 115 q^{8} - 446 q^{9} - 211 q^{10} + 93 q^{11} - 47 q^{12} + 23 q^{13} + 656 q^{14} + 343 q^{15} - 1505 q^{16} - 17 q^{17} + 132 q^{18}+ \cdots + 4526 q^{99}+O(q^{100}) $ 294 * q - 5 * q^2 - 5 * q^3 - 161 * q^4 - 5 * q^5 + 58 * q^6 + 15 * q^7 + 115 * q^8 - 446 * q^9 - 211 * q^10 + 93 * q^11 - 47 * q^12 + 23 * q^13 + 656 * q^14 + 343 * q^15 - 1505 * q^16 - 17 * q^17 + 132 * q^18 + 512 * q^19 + 148 * q^20 - 47 * q^21 - 845 * q^22 - 143 * q^23 + 775 * q^24 - 952 * q^25 + 39 * q^26 + 1159 * q^27 - 130 * q^28 - 169 * q^29 + 1048 * q^30 - 269 * q^31 - 39 * q^32 + 234 * q^33 + 761 * q^34 + 949 * q^35 + 15930 * q^36 + 715 * q^37 - 987 * q^38 - 417 * q^39 - 3303 * q^40 + 65 * q^41 - 2334 * q^42 + 581 * q^43 - 1751 * q^44 - 2497 * q^45 + 13 * q^46 - 361 * q^47 - 3995 * q^48 - 3728 * q^49 + 3671 * q^50 + 213 * q^51 + 4036 * q^52 - 47 * q^53 + 1358 * q^54 - 4339 * q^55 + 680 * q^56 - 2470 * q^57 + 1483 * q^58 - 3375 * q^59 + 1549 * q^60 + 805 * q^61 - 1149 * q^62 - 4839 * q^63 - 7061 * q^64 + 457 * q^65 + 1224 * q^66 + 2261 * q^67 + 1216 * q^68 - 4378 * q^69 + 1360 * q^70 - 1687 * q^71 + 936 * q^72 + 3075 * q^73 - 601 * q^74 + 3549 * q^75 - 5960 * q^76 - 4318 * q^77 - 11681 * q^78 + 2973 * q^79 - 1671 * q^80 - 4288 * q^81 + 2197 * q^82 + 9380 * q^83 - 7416 * q^84 - 5171 * q^85 - 3868 * q^86 + 1826 * q^87 - 3252 * q^88 - 79 * q^89 + 19791 * q^90 + 8303 * q^91 + 8077 * q^92 + 2118 * q^93 + 6319 * q^94 - 3280 * q^95 - 13752 * q^96 - 17 * q^97 - 4434 * q^98 + 4526 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

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 $

$2$	−4.23571	+	2.03981i	−1.49755	+	0.721182i	−0.990082	−	0.140488i	$-0.955133\pi$
$2$	−4.23571	+	2.03981i	−1.49755	+	0.721182i	−0.507468	+	0.861670i	$0.669419\pi$
$3$	5.41516	+	2.60780i	1.04215	+	0.501872i	0.875032	−	0.484065i	$-0.160840\pi$
$3$	5.41516	+	2.60780i	1.04215	+	0.501872i	0.167116	+	0.985937i	$0.446554\pi$
$4$	8.79251	−	11.0255i	1.09906	−	1.37818i
$5$	−7.52587	−	9.43714i	−0.673134	−	0.844084i	0.321567	−	0.946887i	$-0.395790\pi$
$5$	−7.52587	−	9.43714i	−0.673134	−	0.844084i	−0.994702	+	0.102803i	$0.967219\pi$
$6$	−28.2565			−1.92261
$7$	15.8752	+	7.64508i	0.857179	+	0.412796i	0.810237	−	0.586102i	$-0.199338\pi$
$7$	15.8752	+	7.64508i	0.857179	+	0.412796i	0.0469415	+	0.998898i	$0.485053\pi$
$8$	−6.38361	+	27.9684i	−0.282118	+	1.23604i
$9$	5.68910	+	7.13391i	0.210707	+	0.264219i
$10$	51.1274	+	24.6217i	1.61679	+	0.778605i
$11$	−15.4856	+	7.45746i	−0.424461	+	0.204410i	−0.633905	−	0.773411i	$-0.718549\pi$
$11$	−15.4856	+	7.45746i	−0.424461	+	0.204410i	0.209444	+	0.977821i	$0.432835\pi$
$12$	76.3651	−	36.7755i	1.83706	−	0.884681i
$13$	−9.81465	−	43.0008i	−0.209392	−	0.917405i	−0.964973	−	0.262350i	$-0.915502\pi$
$13$	−9.81465	−	43.0008i	−0.209392	−	0.917405i	0.755581	−	0.655055i	$-0.227355\pi$
$14$	−82.8372			−1.58137
$15$	−16.1436	−	70.7296i	−0.277884	−	1.21749i
$16$	−4.90710	−	21.4994i	−0.0766734	−	0.335928i
$17$	−45.5664	−	57.1385i	−0.650087	−	0.815183i	0.342137	−	0.939650i	$-0.388849\pi$
$17$	−45.5664	−	57.1385i	−0.650087	−	0.815183i	−0.992224	+	0.124467i	$0.960278\pi$
$18$	−38.6492	−	18.6125i	−0.506095	−	0.243723i
$19$	−79.9476			−0.965328			−0.482664	−	0.875806i	$-0.660331\pi$
$19$	−79.9476			−0.965328			−0.482664	+	0.875806i	$0.660331\pi$
$20$	−170.220			−1.90312
$21$	66.0297	+	82.7987i	0.686137	+	0.860388i
$22$	50.3806	−	63.1753i	0.488236	−	0.612228i
$23$	−145.384	+	70.0132i	−1.31803	+	0.634729i	−0.954877	−	0.297001i	$-0.904013\pi$
$23$	−145.384	+	70.0132i	−1.31803	+	0.634729i	−0.363151	+	0.931730i	$0.618299\pi$
$24$	−107.504	+	134.806i	−0.914344	+	1.14655i
$25$	−4.60582	+	20.1794i	−0.0368466	+	0.161435i
$26$	129.286	+	162.119i	0.975191	+	1.22285i
$27$	−23.9072	−	104.744i	−0.170405	−	0.746593i
$28$	223.873	−	107.812i	1.51100	−	0.727660i
$29$	13.3778	−	6.44241i	0.0856619	−	0.0412526i	−0.390562	−	0.920577i	$-0.627719\pi$
$29$	13.3778	−	6.44241i	0.0856619	−	0.0412526i	0.476224	+	0.879324i	$0.342005\pi$
$30$	212.655	+	266.661i	1.29418	+	1.62284i
$31$	−41.7920	+	20.1260i	−0.242131	+	0.116604i	−0.551014	−	0.834496i	$-0.685759\pi$
$31$	−41.7920	+	20.1260i	−0.242131	+	0.116604i	0.308883	+	0.951100i	$0.400045\pi$
$32$	−78.4521	−	98.3758i	−0.433391	−	0.543455i
$33$	−103.304			−0.544939
$34$	309.558	+	149.075i	1.56143	+	0.751947i
$35$	−47.3268	−	207.352i	−0.228562	−	1.00140i
$36$	128.676			0.595723
$37$	20.3115	−	88.9905i	0.0902484	−	0.395404i	−0.909548	−	0.415600i	$-0.863572\pi$
$37$	20.3115	−	88.9905i	0.0902484	−	0.395404i	0.999796	+	0.0201955i	$0.00642888\pi$
$38$	338.635	−	163.078i	1.44563	−	0.696178i
$39$	58.9897	−	258.451i	0.242203	−	1.06116i
$40$	311.984	−	150.244i	1.23323	−	0.593890i
$41$	−130.044	−	163.071i	−0.495354	−	0.621155i	0.469820	−	0.882762i	$-0.344319\pi$
$41$	−130.044	−	163.071i	−0.495354	−	0.621155i	−0.965174	+	0.261607i	$0.915747\pi$
$42$	−448.577	−	216.023i	−1.64802	−	0.793645i
$43$	380.937	−	183.450i	1.35099	−	0.650601i	0.388378	−	0.921500i	$-0.373035\pi$
$43$	380.937	−	183.450i	1.35099	−	0.650601i	0.962608	+	0.270899i	$0.0873211\pi$
$44$	−53.9352	+	236.305i	−0.184796	+	0.809645i
$45$	24.5083	−	107.378i	0.0811884	−	0.355709i
$46$	472.991	−	593.112i	1.51606	−	1.90108i
$47$	23.1199	−	101.295i	0.0717529	−	0.314370i	−0.926297	−	0.376795i	$-0.877026\pi$
$47$	23.1199	−	101.295i	0.0717529	−	0.314370i	0.998050	+	0.0624247i	$0.0198833\pi$
$48$	29.4935	−	129.219i	0.0886879	−	0.388567i
$49$	−20.2832	−	25.4343i	−0.0591346	−	0.0741524i
$50$	−21.6533	−	94.8693i	−0.0612447	−	0.268331i
$51$	−97.7435	−	428.242i	−0.268369	−	1.17580i
$52$	−560.399	−	269.874i	−1.49449	−	0.719707i
$53$	−121.306	+	152.113i	−0.314391	+	0.394234i	−0.913770	−	0.406231i	$-0.866843\pi$
$53$	−121.306	+	152.113i	−0.314391	+	0.394234i	0.599379	+	0.800465i	$0.295414\pi$
$54$	314.922	+	394.900i	0.793620	+	0.995168i
$55$	186.920	+	90.0157i	0.458259	+	0.220686i
$56$	−315.162	+	395.200i	−0.752058	+	0.943051i
$57$	−432.929	−	208.488i	−1.00602	−	0.484471i
$58$	−43.5232	+	54.5764i	−0.0985324	+	0.123556i
$59$	684.028	−	329.411i	1.50937	−	0.726875i	0.517687	−	0.855570i	$-0.326793\pi$
$59$	684.028	−	329.411i	1.50937	−	0.726875i	0.991684	+	0.128696i	$0.0410790\pi$
$60$	−921.769	−	443.901i	−1.98333	−	0.955122i
$61$	254.657	−	122.636i	0.534516	−	0.257409i	−0.147097	−	0.989122i	$-0.546993\pi$
$61$	254.657	−	122.636i	0.534516	−	0.257409i	0.681613	+	0.731713i	$0.261279\pi$
$62$	135.966	−	170.496i	0.278511	−	0.349241i
$63$	35.7762	+	156.746i	0.0715456	+	0.313462i
$64$	691.916	+	333.209i	1.35140	+	0.650799i
$65$	−331.941	+	416.241i	−0.633418	+	0.794281i
$66$	437.568	−	210.722i	0.816074	−	0.393001i
$67$	−70.4808	+	308.796i	−0.128516	+	0.563067i	0.869135	+	0.494574i	$0.164676\pi$
$67$	−70.4808	+	308.796i	−0.128516	+	0.563067i	−0.997652	+	0.0684925i	$0.978181\pi$
$68$	−1030.62			−1.83796
$69$	−969.858			−1.69213
$70$	623.422	+	781.746i	1.06447	+	1.33481i
$71$	−256.628	−	321.801i	−0.428959	−	0.537898i	0.519637	−	0.854387i	$-0.326067\pi$
$71$	−256.628	−	321.801i	−0.428959	−	0.537898i	−0.948596	+	0.316489i	$0.897496\pi$
$72$	−235.841	+	113.575i	−0.386030	+	0.185902i
$73$	−244.066	+	1069.32i	−0.391312	+	1.71445i	0.268726	+	0.963217i	$0.413397\pi$
$73$	−244.066	+	1069.32i	−0.391312	+	1.71445i	−0.660038	+	0.751232i	$0.729460\pi$
$74$	95.4902	+	418.370i	0.150007	+	0.657223i
$75$	−77.5653	+	97.2638i	−0.119420	+	0.149747i
$76$	−702.940	+	881.459i	−1.06096	+	1.33040i
$77$	−302.849			−0.448219
$78$	277.328	+	1215.05i	0.402579	+	1.76381i
$79$	31.0049	−	38.8789i	0.0441560	−	0.0553699i	−0.759263	−	0.650784i	$-0.774440\pi$
$79$	31.0049	−	38.8789i	0.0441560	−	0.0553699i	0.803419	+	0.595414i	$0.203012\pi$
$80$	−165.963	+	208.111i	−0.231940	+	0.290844i
$81$	198.512	−	869.739i	0.272308	−	1.19306i
$82$	883.464	+	425.454i	1.18978	+	0.572970i
$83$	−672.320			−0.889117			−0.444559	−	0.895750i	$-0.646639\pi$
$83$	−672.320			−0.889117			−0.444559	+	0.895750i	$0.646639\pi$
$84$	1493.46			1.93988
$85$	−196.297	+	860.033i	−0.250487	+	1.09746i
$86$	−1239.34	+	1554.08i	−1.55397	+	1.94861i
$87$	89.2435			0.109976
$88$	−109.720	−	480.713i	−0.132911	−	0.582320i
$89$	−280.934	−	135.291i	−0.334595	−	0.161132i	0.259041	−	0.965866i	$-0.416594\pi$
$89$	−280.934	−	135.291i	−0.334595	−	0.161132i	−0.593636	+	0.804734i	$0.702308\pi$
$90$	115.220	+	504.813i	0.134948	+	0.591245i
$91$	172.935	−	757.679i	0.199215	−	0.872816i
$92$	−506.362	+	2218.52i	−0.573825	+	2.51409i
$93$	−278.795			−0.310857
$94$	108.693	+	476.217i	0.119265	+	0.522532i
$95$	601.675	+	754.477i	0.649795	+	0.814818i
$96$	−168.286	−	737.308i	−0.178912	−	0.783867i
$97$	108.743	+	136.359i	0.113827	+	0.142734i	0.835481	−	0.549520i	$-0.185189\pi$
$97$	108.743	+	136.359i	0.113827	+	0.142734i	−0.721654	+	0.692254i	$0.756618\pi$
$98$	137.795	+	66.3585i	0.142034	+	0.0684002i
$99$	−141.300	−	68.0464i	−0.143446	−	0.0690800i
$100$	181.991	+	228.209i	0.181991	+	0.228209i
$101$	−111.032	−	486.463i	−0.109387	−	0.479256i	−0.999714	−	0.0239332i	$-0.992381\pi$
$101$	−111.032	−	486.463i	−0.109387	−	0.479256i	0.890327	−	0.455323i	$-0.150476\pi$
$102$	1287.55	+	1614.53i	1.24986	+	1.56728i
$103$	−407.709	−	1786.29i	−0.390027	−	1.70882i	−0.664555	−	0.747240i	$-0.731379\pi$
$103$	−407.709	−	1786.29i	−0.390027	−	1.70882i	0.274528	−	0.961579i	$-0.411478\pi$
$104$	1265.32			1.19302
$105$	284.452	−	1246.26i	0.264378	−	1.15831i
$106$	203.536	−	891.751i	0.186502	−	0.817118i
$107$	−193.554	−	848.015i	−0.174874	−	0.766175i	−0.983946	−	0.178465i	$-0.942887\pi$
$107$	−193.554	−	848.015i	−0.174874	−	0.766175i	0.809072	−	0.587710i	$-0.199970\pi$
$108$	−1365.06	−	657.376i	−1.21623	−	0.585704i
$109$	−59.0419	−	258.679i	−0.0518825	−	0.227312i	0.942339	−	0.334660i	$-0.108621\pi$
$109$	−59.0419	−	258.679i	−0.0518825	−	0.227312i	−0.994222	+	0.107348i	$0.965764\pi$
$110$	−975.353			−0.845420
$111$	342.060	−	428.930i	0.292495	−	0.366777i
$112$	86.4636	−	378.822i	0.0729468	−	0.319601i
$113$	−1010.62			−0.841338			−0.420669	−	0.907214i	$-0.638205\pi$
$113$	−1010.62			−0.841338			−0.420669	+	0.907214i	$0.638205\pi$
$114$	2259.04			1.85595
$115$	1754.87	+	845.099i	1.42297	+	0.685268i
$116$	46.5939	−	204.141i	0.0372943	−	0.163397i
$117$	250.927	−	314.653i	0.198275	−	0.248629i
$118$	−2225.41	+	2790.58i	−1.73615	+	2.17706i
$119$	−286.546	−	1255.44i	−0.220737	−	0.967110i
$120$	2081.25			1.58326
$121$	−645.676	+	809.652i	−0.485106	+	0.608303i
$122$	−828.498	+	1038.90i	−0.614825	+	0.770967i
$123$	−278.956	−	1222.18i	−0.204492	−	0.895940i
$124$	−145.558	+	637.733i	−0.105416	+	0.461856i
$125$	−1134.30	+	546.250i	−0.811640	+	0.390865i
$126$	−471.269	−	590.953i	−0.333206	−	0.417828i
$127$	145.868	+	182.913i	0.101919	+	0.127802i	0.830175	−	0.557503i	$-0.188240\pi$
$127$	145.868	+	182.913i	0.101919	+	0.127802i	−0.728256	+	0.685305i	$0.759669\pi$
$128$	−2603.82			−1.79803
$129$	2541.24			1.73445
$130$	556.953	−	2440.17i	0.375754	−	1.64629i
$131$	−657.128	+	316.456i	−0.438271	+	0.211060i	−0.639990	−	0.768383i	$-0.721062\pi$
$131$	−657.128	+	316.456i	−0.438271	+	0.211060i	0.201719	+	0.979443i	$0.435347\pi$
$132$	−908.306	+	1138.98i	−0.598923	+	0.751026i
$133$	−1269.18	−	611.206i	−0.827459	−	0.398483i
$134$	−331.350	−	1451.74i	−0.213614	−	0.935905i
$135$	−808.563	+	1013.91i	−0.515482	+	0.646393i
$136$	1888.95	−	909.671i	1.19100	−	0.573556i
$137$	2731.78	+	1315.55i	1.70359	+	0.820405i	0.993177	+	0.116617i	$0.0372051\pi$
$137$	2731.78	+	1315.55i	1.70359	+	0.820405i	0.710411	+	0.703787i	$0.248509\pi$
$138$	4108.04	−	1978.33i	2.53406	−	1.22034i
$139$	−1015.09	+	1272.89i	−0.619418	+	0.776726i	−0.988262	−	0.152765i	$-0.951182\pi$
$139$	−1015.09	+	1272.89i	−0.619418	+	0.776726i	0.368844	+	0.929491i	$0.379754\pi$
$140$	−2702.27	−	1301.35i	−1.63131	−	0.785599i
$141$	389.356	−	488.236i	0.232551	−	0.291609i
$142$	1743.42	+	839.584i	1.03031	+	0.496172i
$143$	472.662	+	592.699i	0.276406	+	0.346602i
$144$	125.458	−	157.319i	0.0726029	−	0.0910411i
$145$	−161.478	−	77.7635i	−0.0924826	−	0.0445373i
$146$	−1147.42	−	5027.19i	−0.650421	−	2.84968i
$147$	−43.5090	−	190.625i	−0.0244120	−	0.106956i
$148$	−802.572	−	1006.39i	−0.445750	−	0.558953i
$149$	−539.644	+	2364.34i	−0.296707	+	1.29996i	0.578290	+	0.815831i	$0.303720\pi$
$149$	−539.644	+	2364.34i	−0.296707	+	1.29996i	−0.874997	+	0.484128i	$0.839137\pi$
$150$	130.144	−	570.200i	0.0708416	−	0.310377i
$151$	1617.30	−	2028.03i	0.871614	−	1.09297i	−0.123312	−	0.992368i	$-0.539352\pi$
$151$	1617.30	−	2028.03i	0.871614	−	1.09297i	0.994927	−	0.100602i	$-0.0320768\pi$
$152$	510.354	−	2236.01i	0.272337	−	1.19319i
$153$	148.389	−	650.133i	0.0784085	−	0.343530i
$154$	1282.78	−	617.755i	0.671230	−	0.323248i
$155$	504.452	+	242.931i	0.261410	+	0.125889i
$156$	−2330.87	−	2922.82i	−1.19628	−	1.50008i
$157$	−398.936	+	192.117i	−0.202793	+	0.0976601i	−0.532524	−	0.846415i	$-0.678756\pi$
$157$	−398.936	+	192.117i	−0.202793	+	0.0976601i	0.329731	+	0.944075i	$0.393042\pi$
$158$	−52.0222	+	227.924i	−0.0261941	+	0.114764i
$159$	−1053.58	+	507.375i	−0.525497	+	0.253066i
$160$	−337.966	+	1480.73i	−0.166991	+	0.731636i
$161$	−2843.25			−1.39180
$162$	933.263	+	4088.89i	0.452618	+	1.98305i
$163$	2406.14	+	1158.74i	1.15622	+	0.556805i	0.910896	−	0.412636i	$-0.135392\pi$
$163$	2406.14	+	1158.74i	1.15622	+	0.556805i	0.245322	+	0.969442i	$0.421106\pi$
$164$	−2941.35			−1.40049
$165$	777.456	+	974.899i	0.366817	+	0.459974i
$166$	2847.75	−	1371.41i	1.33150	−	0.641216i
$167$	−365.981	−	458.925i	−0.169584	−	0.212651i	0.689776	−	0.724023i	$-0.257709\pi$
$167$	−365.981	−	458.925i	−0.169584	−	0.212651i	−0.859360	+	0.511372i	$0.829138\pi$
$168$	−2737.26	+	1318.19i	−1.25705	+	0.605362i
$169$	226.689	−	109.167i	0.103181	−	0.0496893i
$170$	−922.848	−	4043.26i	−0.416348	−	1.82414i
$171$	−454.830	−	570.339i	−0.203402	−	0.255058i
$172$	1326.78	−	5812.99i	0.588174	−	2.57696i
$173$	673.811	−	844.933i	0.296121	−	0.371324i	−0.611407	−	0.791317i	$-0.709396\pi$
$173$	673.811	−	844.933i	0.296121	−	0.371324i	0.907527	+	0.419993i	$0.137967\pi$
$174$	−378.010	+	182.040i	−0.164695	+	0.0793127i
$175$	−227.392	+	285.140i	−0.0982239	+	0.123169i
$176$	236.320	+	296.336i	0.101212	+	0.126916i
$177$	4563.16			1.93779
$178$	1465.92			0.617279
$179$	3415.22	+	1644.69i	1.42607	+	0.686757i	0.978262	−	0.207374i	$-0.0664918\pi$
$179$	3415.22	+	1644.69i	1.42607	+	0.686757i	0.447804	+	0.894132i	$0.352206\pi$
$180$	−968.400	−	1214.33i	−0.401001	−	0.502840i
$181$	23.6923	+	103.803i	0.00972948	+	0.0426277i	0.979560	−	0.201154i	$-0.0644691\pi$
$181$	23.6923	+	103.803i	0.00972948	+	0.0426277i	−0.969830	+	0.243782i	$0.921612\pi$
$182$	813.018	+	3562.06i	0.331126	+	1.45076i
$183$	1698.82			0.686231
$184$	−1030.09	−	4513.10i	−0.412711	−	1.80821i
$185$	−992.678	+	478.049i	−0.394503	+	0.189983i
$186$	1180.89	−	568.689i	0.465524	−	0.224184i
$187$	1131.73	+	545.012i	0.442568	+	0.213130i
$188$	−913.542	−	1145.55i	−0.354398	−	0.444401i
$189$	421.247	−	1845.60i	0.162123	−	0.710306i
$190$	−4087.51	−	1968.44i	−1.56073	−	0.751610i
$191$	1738.37			0.658557			0.329278	−	0.944233i	$-0.393195\pi$
$191$	1738.37			0.658557			0.329278	+	0.944233i	$0.393195\pi$
$192$	2877.89	+	3608.76i	1.08174	+	1.35646i
$193$	−1673.38	+	2098.35i	−0.624105	+	0.782603i	−0.988916	−	0.148479i	$-0.952562\pi$
$193$	−1673.38	+	2098.35i	−0.624105	+	0.782603i	0.364810	+	0.931082i	$0.381134\pi$
$194$	−738.752	−	355.764i	−0.273398	−	0.131662i
$195$	−2882.99	+	1388.37i	−1.05874	+	0.509864i
$196$	−458.764			−0.167188
$197$	−270.311	+	2751.78i	−0.0977607	+	0.995210i
$197$	−270.311	+	2751.78i	−0.0977607	+	0.995210i
$198$	737.307			0.264637
$199$	544.196	−	262.071i	0.193855	−	0.0933554i	−0.334438	−	0.942418i	$-0.608547\pi$
$199$	544.196	−	262.071i	0.193855	−	0.0933554i	0.528293	+	0.849062i	$0.322832\pi$
$200$	−534.985	−	257.635i	−0.189146	−	0.0910878i
$201$	−1186.95	+	1488.38i	−0.416521	+	0.522300i
$202$	1462.59	+	1834.03i	0.509443	+	0.638822i
$203$	261.628			0.0904564
$204$	−5580.98	−	2687.66i	−1.91542	−	0.922420i
$205$	−560.223	+	2454.50i	−0.190867	+	0.836241i
$206$	5370.63	+	6734.56i	1.81645	+	2.27776i
$207$	−1326.57	−	638.843i	−0.445426	−	0.214506i
$208$	−876.330	+	422.018i	−0.292128	+	0.140681i
$209$	1238.03	−	596.206i	0.409745	−	0.197323i
$210$	1337.29	+	5859.04i	0.439437	+	1.92530i
$211$	−2485.84			−0.811053			−0.405526	−	0.914083i	$-0.632912\pi$
$211$	−2485.84			−0.811053			−0.405526	+	0.914083i	$0.632912\pi$
$212$	610.533	+	2674.92i	0.197790	+	0.866576i
$213$	−550.487	−	2411.84i	−0.177083	−	0.775852i
$214$	2549.63	+	3197.13i	0.814435	+	1.02127i
$215$	−4598.13	−	2214.34i	−1.45856	−	0.702404i
$216$	3082.14			0.970895
$217$	−817.319			−0.255683
$218$	777.742	+	975.258i	0.241630	+	0.302994i
$219$	−4110.24	+	5154.08i	−1.26824	+	1.59032i
$220$	2635.96	−	1269.41i	0.807801	−	0.389016i
$221$	−2009.78	+	2520.18i	−0.611730	+	0.767086i
$222$	−573.932	+	2514.56i	−0.173513	+	0.760208i
$223$	−3968.70	−	4976.59i	−1.19177	−	1.49443i	−0.825953	−	0.563739i	$-0.809362\pi$
$223$	−3968.70	−	4976.59i	−1.19177	−	1.49443i	−0.365813	−	0.930688i	$-0.619209\pi$
$224$	−493.349	−	2161.50i	−0.147158	−	0.644739i
$225$	−170.161	+	81.9453i	−0.0504181	+	0.0242801i
$226$	4280.70	−	2061.47i	1.25995	−	0.606758i
$227$	3748.55	+	4700.54i	1.09604	+	1.37439i	0.920880	+	0.389846i	$0.127472\pi$
$227$	3748.55	+	4700.54i	1.09604	+	1.37439i	0.175156	+	0.984541i	$0.443957\pi$
$228$	−6105.21	+	2940.11i	−1.77336	+	0.854007i
$229$	−3777.29	−	4736.58i	−1.09000	−	1.36682i	−0.924753	−	0.380569i	$-0.875728\pi$
$229$	−3777.29	−	4736.58i	−1.09000	−	1.36682i	−0.165250	−	0.986252i	$-0.552843\pi$
$230$	−9156.95			−2.62518
$231$	−1639.98	−	789.771i	−0.467110	−	0.224949i
$232$	94.7854	+	415.282i	0.0268231	+	0.117520i
$233$	1885.65			0.530183			0.265092	−	0.964223i	$-0.414598\pi$
$233$	1885.65			0.530183			0.265092	+	0.964223i	$0.414598\pi$
$234$	−421.023	+	1844.62i	−0.117620	+	0.515328i
$235$	−1129.93	+	544.147i	−0.313654	+	0.151048i
$236$	2382.42	−	10438.1i	0.657129	−	2.87907i
$237$	269.285	−	129.681i	0.0738057	−	0.0355430i
$238$	3774.59	+	4733.19i	1.02803	+	1.28911i
$239$	−1127.78	−	543.109i	−0.305230	−	0.146991i	0.274999	−	0.961445i	$-0.411323\pi$
$239$	−1127.78	−	543.109i	−0.305230	−	0.146991i	−0.580229	+	0.814454i	$0.697037\pi$
$240$	−1441.43	+	694.155i	−0.387682	+	0.186698i
$241$	318.798	−	1396.75i	0.0852099	−	0.373329i	−0.914286	−	0.405069i	$-0.867248\pi$
$241$	318.798	−	1396.75i	0.0852099	−	0.373329i	0.999496	+	0.0317396i	$0.0101047\pi$
$242$	1083.36	−	4746.51i	0.287773	−	1.26081i
$243$	1534.45	−	1924.14i	0.405083	−	0.507958i
$244$	886.952	−	3885.99i	0.232710	−	1.01957i
$245$	−87.3785	+	382.830i	−0.0227853	+	0.0998290i
$246$	3674.60	+	4607.80i	0.952374	+	1.19424i
$247$	784.657	+	3437.81i	0.202132	+	0.885597i
$248$	−296.108	−	1297.33i	−0.0758179	−	0.332180i
$249$	−3640.72	−	1753.28i	−0.926592	−	0.446223i
$250$	3690.32	−	4627.52i	0.933586	−	1.17068i
$251$	−4448.84	−	5578.67i	−1.11876	−	1.40288i	−0.904695	−	0.426059i	$-0.859902\pi$
$251$	−4448.84	−	5578.67i	−1.11876	−	1.40288i	−0.214063	−	0.976820i	$-0.568670\pi$
$252$	2042.76	+	983.739i	0.510641	+	0.245912i
$253$	1729.23	−	2168.39i	0.429707	−	0.538836i
$254$	−990.962	−	477.222i	−0.244797	−	0.117888i
$255$	−3305.78	+	4145.31i	−0.811827	+	1.01800i
$256$	5493.72	−	2645.63i	1.34124	−	0.645907i
$257$	3444.03	+	1658.56i	0.835925	+	0.402560i	0.802334	−	0.596876i	$-0.203591\pi$
$257$	3444.03	+	1658.56i	0.835925	+	0.402560i	0.0335909	+	0.999436i	$0.489306\pi$
$258$	−10764.0	+	5183.65i	−2.59742	+	1.25085i
$259$	1002.79	−	1257.46i	0.240580	−	0.301678i
$260$	1670.65	+	7319.60i	0.398498	+	1.74593i
$261$	122.067	+	58.7845i	0.0289493	+	0.0139413i
$262$	2137.89	−	2680.83i	0.504120	−	0.632147i
$263$	2613.50	−	1258.60i	0.612758	−	0.295089i	−0.101648	−	0.994820i	$-0.532411\pi$
$263$	2613.50	−	1258.60i	0.612758	−	0.295089i	0.714406	+	0.699732i	$0.246697\pi$
$264$	659.456	−	2889.26i	0.153737	−	0.673568i
$265$	2348.45			0.544393
$266$	6622.63			1.52654
$267$	−1168.49	−	1465.24i	−0.267830	−	0.335848i
$268$	2784.92	+	3492.18i	0.634761	+	0.795966i
$269$	5237.12	−	2522.06i	1.18704	−	0.571647i	0.267083	−	0.963674i	$-0.413940\pi$
$269$	5237.12	−	2522.06i	1.18704	−	0.571647i	0.919954	+	0.392027i	$0.128226\pi$
$270$	1356.66	−	5943.93i	0.305792	−	1.33976i
$271$	598.523	+	2622.30i	0.134161	+	0.587799i	0.996654	+	0.0817303i	$0.0260446\pi$
$271$	598.523	+	2622.30i	0.134161	+	0.587799i	−0.862493	+	0.506069i	$0.831098\pi$
$272$	−1004.84	+	1260.03i	−0.223999	+	0.280885i
$273$	2912.35	−	3651.97i	0.645653	−	0.809624i
$274$	−14254.5			−3.14287
$275$	−79.1634	−	346.838i	−0.0173590	−	0.0760549i
$276$	−8527.49	+	10693.1i	−1.85976	+	2.33207i
$277$	1626.89	−	2040.05i	0.352889	−	0.442509i	−0.573427	−	0.819257i	$-0.694386\pi$
$277$	1626.89	−	2040.05i	0.352889	−	0.442509i	0.926316	+	0.376748i	$0.122958\pi$
$278$	1703.20	−	7462.19i	0.367449	−	1.60990i
$279$	−381.335	−	183.641i	−0.0818278	−	0.0394062i
$280$	6101.43			1.30225
$281$	1263.79			0.268297			0.134148	−	0.990961i	$-0.457170\pi$
$281$	1263.79			0.268297			0.134148	+	0.990961i	$0.457170\pi$
$282$	−653.288	+	2862.24i	−0.137953	+	0.604411i
$283$	−4008.74	+	5026.80i	−0.842031	+	1.05587i	0.155650	+	0.987812i	$0.450253\pi$
$283$	−4008.74	+	5026.80i	−0.842031	+	1.05587i	−0.997681	+	0.0680615i	$0.978319\pi$
$284$	−5804.41			−1.21278
$285$	1290.64	+	5654.66i	0.268249	+	1.17528i
$286$	−3211.06	−	1546.36i	−0.663894	−	0.319715i
$287$	−817.790	−	3582.97i	−0.168197	−	0.736921i
$288$	255.482	−	1119.34i	0.0522723	−	0.229020i
$289$	−95.2610	+	417.366i	−0.0193896	+	0.0849513i
$290$	842.595			0.170617
$291$	233.262	+	1021.99i	0.0469900	+	0.205876i
$292$	9643.82	+	12093.0i	1.93275	+	2.42359i
$293$	1887.87	+	8271.31i	0.376419	+	1.64920i	0.708325	+	0.705886i	$0.249451\pi$
$293$	1887.87	+	8271.31i	0.376419	+	1.64920i	−0.331906	+	0.943312i	$0.607692\pi$
$294$	573.131	+	718.683i	0.113693	+	0.142566i
$295$	−8256.60	−	3976.17i	−1.62955	−	0.784751i
$296$	2359.26	+	1136.16i	0.463275	+	0.223102i
$297$	1151.34	+	1443.74i	0.224941	+	0.282068i
$298$	−2537.02	−	11115.4i	−0.493174	−	2.16073i
$299$	4437.52	+	5564.47i	0.858288	+	1.07626i
$300$	390.384	+	1710.39i	0.0751295	+	0.329164i
$301$	7449.93			1.42660
$302$	−2713.61	+	11889.1i	−0.517056	+	2.26537i
$303$	667.343	−	2923.82i	0.126528	−	0.554354i
$304$	392.311	+	1718.83i	0.0740150	+	0.324281i
$305$	−3073.85	−	1480.29i	−0.577076	−	0.277905i
$306$	697.617	+	3056.46i	0.130327	+	0.571001i
$307$	−3987.57			−0.741312			−0.370656	−	0.928770i	$-0.620867\pi$
$307$	−3987.57			−0.741312			−0.370656	+	0.928770i	$0.620867\pi$
$308$	−2662.80	+	3339.05i	−0.492621	+	0.617727i
$309$	2450.48	−	10736.3i	0.451143	−	1.97659i
$310$	−2632.25			−0.482264
$311$	8915.63			1.62559			0.812796	−	0.582548i	$-0.197944\pi$
$311$	8915.63			1.62559			0.812796	+	0.582548i	$0.197944\pi$
$312$	6851.90	+	3299.70i	1.24331	+	0.598746i
$313$	1570.82	−	6882.23i	0.283669	−	1.24283i	−0.609382	−	0.792877i	$-0.708582\pi$
$313$	1570.82	−	6882.23i	0.283669	−	1.24283i	0.893050	−	0.449956i	$-0.148561\pi$
$314$	1297.89	−	1627.51i	0.233262	−	0.292502i
$315$	1209.98	−	1517.27i	0.216428	−	0.271392i
$316$	−156.047	−	683.687i	−0.0277795	−	0.121710i
$317$	−3217.65			−0.570098			−0.285049	−	0.958513i	$-0.592010\pi$
$317$	−3217.65			−0.570098			−0.285049	+	0.958513i	$0.592010\pi$
$318$	3427.69	−	4298.19i	0.604451	−	0.757958i
$319$	−159.119	+	199.529i	−0.0279277	+	0.0350203i
$320$	−2062.73	−	9037.40i	−0.360344	−	1.57877i
$321$	1163.33	−	5096.89i	0.202277	−	0.886232i
$322$	12043.2	−	5799.70i	2.08429	−	1.00374i
$323$	3642.92	+	4568.08i	0.627547	+	0.786919i
$324$	−7843.85	−	9835.88i	−1.34497	−	1.68654i
$325$	912.936			0.155817
$326$	−12555.3			−2.13305
$327$	354.864	−	1554.76i	0.0600123	−	0.262931i
$328$	5390.98	−	2596.16i	0.907522	−	0.437040i
$329$	1141.44	−	1431.32i	0.191276	−	0.239852i
$330$	−5281.69	−	2543.53i	−0.881053	−	0.424293i
$331$	565.085	+	2475.80i	0.0938366	+	0.411125i	0.999929	−	0.0119560i	$-0.00380580\pi$
$331$	565.085	+	2475.80i	0.0938366	+	0.411125i	−0.906092	+	0.423081i	$0.860949\pi$
$332$	−5911.38	+	7412.64i	−0.977197	+	1.22537i
$333$	750.404	−	361.376i	0.123489	−	0.0594693i
$334$	2486.31	+	1197.34i	0.407320	+	0.196155i
$335$	3444.58	−	1658.82i	0.561784	−	0.270541i
$336$	1456.11	−	1825.90i	0.236420	−	0.296462i
$337$	3465.09	+	1668.70i	0.560106	+	0.269733i	0.692444	−	0.721472i	$-0.256534\pi$
$337$	3465.09	+	1668.70i	0.560106	+	0.269733i	−0.132338	+	0.991205i	$0.542248\pi$
$338$	−737.507	+	924.804i	−0.118684	+	0.148825i
$339$	−5472.67	−	2635.50i	−0.876798	−	0.422244i
$340$	7756.32	+	9726.12i	1.23719	+	1.55139i
$341$	497.084	−	623.324i	0.0789402	−	0.0989879i
$342$	3089.91	+	1488.02i	0.488548	+	0.235272i
$343$	−1472.40	−	6451.01i	−0.231785	−	1.01552i
$344$	2699.05	+	11825.3i	0.423031	+	1.85342i
$345$	7299.03	+	9152.69i	1.13903	+	1.42830i
$346$	−1130.57	+	4953.34i	−0.175664	+	0.769633i
$347$	−1077.43	+	4720.52i	−0.166684	+	0.730290i	0.820623	+	0.571469i	$0.193626\pi$
$347$	−1077.43	+	4720.52i	−0.166684	+	0.730290i	−0.987307	+	0.158821i	$0.949231\pi$
$348$	784.674	−	983.951i	0.120871	−	0.151567i
$349$	−2471.85	+	10829.9i	−0.379126	+	1.66106i	0.321028	+	0.947070i	$0.395972\pi$
$349$	−2471.85	+	10829.9i	−0.379126	+	1.66106i	−0.700154	+	0.713992i	$0.746885\pi$
$350$	381.533	−	1671.61i	0.0582680	−	0.255289i
$351$	−4269.44	+	2056.05i	−0.649247	+	0.312661i
$352$	1948.51	+	938.352i	0.295045	+	0.142086i
$353$	2147.64	+	2693.05i	0.323816	+	0.406053i	0.916919	−	0.399074i	$-0.130668\pi$
$353$	2147.64	+	2693.05i	0.323816	+	0.406053i	−0.593102	+	0.805127i	$0.702097\pi$
$354$	−19328.2	+	9307.99i	−2.90193	+	1.39750i
$355$	−1105.54	+	4843.67i	−0.165284	+	0.724155i
$356$	−3961.76	+	1907.88i	−0.589811	+	0.284038i
$357$	1722.25	−	7545.67i	0.255325	−	1.11865i
$358$	−17820.8			−2.63088
$359$	1019.83	+	4468.15i	0.149929	+	0.656880i	0.992903	+	0.118926i	$0.0379453\pi$
$359$	1019.83	+	4468.15i	0.149929	+	0.656880i	−0.842975	+	0.537954i	$0.819198\pi$
$360$	2846.74	+	1370.92i	0.416767	+	0.200704i
$361$	−467.382			−0.0681415
$362$	−312.092	−	391.351i	−0.0453127	−	0.0568203i
$363$	−5607.85	+	2700.60i	−0.810842	+	0.390481i
$364$	−6833.22	−	8568.59i	−0.983951	−	1.23384i
$365$	11928.2	−	5744.30i	1.71054	−	0.823754i
$366$	−7195.71	+	3465.27i	−1.02767	+	0.494898i
$367$	−2409.16	−	10555.2i	−0.342663	−	1.50131i	−0.793429	−	0.608663i	$-0.791706\pi$
$367$	−2409.16	−	10555.2i	−0.342663	−	1.50131i	0.450766	−	0.892642i	$-0.351151\pi$
$368$	2218.66	+	2782.11i	0.314281	+	0.394096i
$369$	423.494	−	1855.45i	0.0597459	−	0.261764i
$370$	3229.57	−	4049.75i	0.453777	−	0.569018i
$371$	−3088.68	+	1487.43i	−0.432227	+	0.208150i
$372$	−2451.31	+	3073.84i	−0.341651	+	0.428417i
$373$	−1115.48	−	1398.76i	−0.154845	−	0.194169i	0.698358	−	0.715749i	$-0.253914\pi$
$373$	−1115.48	−	1398.76i	−0.154845	−	0.194169i	−0.853203	+	0.521579i	$0.825343\pi$
$374$	−5905.40			−0.816474
$375$	−7566.94			−1.04201
$376$	2685.47	+	1293.26i	0.368332	+	0.177379i
$377$	−408.327	−	512.026i	−0.0557823	−	0.0699487i
$378$	1980.40	+	8676.71i	0.269473	+	1.18064i
$379$	1574.68	+	6899.14i	0.213420	+	0.935052i	0.962224	+	0.272261i	$0.0877713\pi$
$379$	1574.68	+	6899.14i	0.213420	+	0.935052i	−0.748804	+	0.662792i	$0.769372\pi$
$380$	13608.7			1.83713
$381$	312.898	+	1370.90i	0.0420742	+	0.184339i
$382$	−7363.25	+	3545.96i	−0.986222	+	0.474939i
$383$	−7619.08	+	3669.15i	−1.01649	+	0.489517i	−0.866504	−	0.499171i	$-0.833638\pi$
$383$	−7619.08	+	3669.15i	−1.01649	+	0.489517i	−0.149989	+	0.988688i	$0.547924\pi$
$384$	−14100.1	−	6790.26i	−1.87381	−	0.902380i
$385$	2279.20	+	2858.03i	0.301711	+	0.378334i
$386$	2807.71	−	12301.4i	0.370229	−	1.62208i
$387$	3475.91	+	1673.91i	0.456564	+	0.219870i
$388$	2459.55			0.321816
$389$	−4077.56	−	5113.10i	−0.531466	−	0.666438i	0.441533	−	0.897245i	$-0.354435\pi$
$389$	−4077.56	−	5113.10i	−0.531466	−	0.666438i	−0.972999	+	0.230807i	$0.925863\pi$
$390$	9379.48	−	11761.5i	1.21782	−	1.52709i
$391$	10625.1	+	5116.76i	1.37425	+	0.661805i
$392$	840.837	−	404.926i	0.108338	−	0.0521730i
$393$	−4383.71			−0.562669
$394$	−4468.16	−	12207.1i	−0.571326	−	1.56088i
$395$	−600.245			−0.0764598
$396$	−1992.62	+	959.597i	−0.252861	+	0.121772i
$397$	3535.32	+	1702.52i	0.446934	+	0.215232i	0.643793	−	0.765200i	$-0.277360\pi$
$397$	3535.32	+	1702.52i	0.446934	+	0.215232i	−0.196859	+	0.980432i	$0.563074\pi$
$398$	−1770.48	+	2220.12i	−0.222981	+	0.279609i
$399$	−5278.92	−	6619.55i	−0.662347	−	0.830557i
$400$	456.447			0.0570558
$401$	−2003.40	−	964.788i	−0.249489	−	0.120148i	0.304960	−	0.952365i	$-0.401357\pi$
$401$	−2003.40	−	964.788i	−0.249489	−	0.120148i	−0.554449	+	0.832217i	$0.687071\pi$
$402$	1991.54	−	8725.50i	0.247087	−	1.08256i
$403$	1275.61	+	1599.56i	0.157674	+	0.197716i
$404$	−6339.72	−	3053.05i	−0.780725	−	0.375978i
$405$	−9701.83	+	4672.15i	−1.19034	+	0.573238i
$406$	−1108.18	+	533.671i	−0.135463	+	0.0652356i
$407$	349.108	+	1529.54i	0.0425175	+	0.186282i
$408$	12601.2			1.52905
$409$	−1464.55	−	6416.60i	−0.177059	−	0.775746i	−0.982978	−	0.183721i	$-0.941186\pi$
$409$	−1464.55	−	6416.60i	−0.177059	−	0.775746i	0.805919	−	0.592025i	$-0.201671\pi$
$410$	−2633.77	−	11539.3i	−0.317250	−	1.38996i
$411$	11362.3	+	14247.9i	1.36365	+	1.70997i
$412$	−23279.4	−	11210.8i	−2.78373	−	1.34057i
$413$	13377.4			1.59385
$414$	6922.10			0.821745
$415$	5059.79	+	6344.78i	0.598495	+	0.750489i
$416$	−3460.26	+	4339.02i	−0.407820	+	0.511390i
$417$	−8816.34	+	4245.72i	−1.03534	+	0.498595i
$418$	−4027.81	+	5050.71i	−0.471308	+	0.591001i
$419$	2112.32	−	9254.69i	0.246286	−	1.07905i	−0.688891	−	0.724865i	$-0.741902\pi$
$419$	2112.32	−	9254.69i	0.246286	−	1.07905i	0.935176	−	0.354183i	$-0.115241\pi$
$420$	−11239.6	−	14094.0i	−1.30580	−	1.63742i
$421$	1177.91	+	5160.75i	0.136360	+	0.597434i	0.996217	+	0.0868987i	$0.0276956\pi$
$421$	1177.91	+	5160.75i	0.136360	+	0.597434i	−0.859857	+	0.510535i	$0.829447\pi$
$422$	10529.3	−	5070.64i	1.21459	−	0.584917i
$423$	854.161	−	411.342i	0.0981813	−	0.0472816i
$424$	−3480.00	−	4363.78i	−0.398594	−	0.499821i
$425$	1362.89	−	656.334i	0.155553	−	0.0749103i
$426$	7251.40	+	9092.97i	0.824722	+	1.03417i
$427$	4980.28			0.564433
$428$	−11051.6	−	5322.16i	−1.24813	−	0.601066i
$429$	1013.90	+	4442.17i	0.114106	+	0.499930i
$430$	23993.2			2.69082
$431$	1017.84	−	4459.47i	0.113754	−	0.498387i	−0.885666	−	0.464323i	$-0.846298\pi$
$431$	1017.84	−	4459.47i	0.113754	−	0.498387i	0.999420	−	0.0340644i	$-0.0108451\pi$
$432$	−2134.62	+	1027.98i	−0.237736	+	0.114488i
$433$	−2376.15	+	10410.6i	−0.263719	+	1.15543i	0.653462	+	0.756960i	$0.273316\pi$
$433$	−2376.15	+	10410.6i	−0.263719	+	1.15543i	−0.917181	+	0.398471i	$0.869541\pi$
$434$	3461.93	−	1667.18i	0.382898	−	0.184394i
$435$	−671.635	−	842.203i	−0.0740286	−	0.0928289i
$436$	−3371.19	−	1623.48i	−0.370299	−	0.178327i
$437$	11623.1	−	5597.39i	1.27233	−	0.612722i
$438$	6896.45	−	30215.3i	0.752340	−	3.29622i
$439$	3097.80	−	13572.3i	0.336788	−	1.47556i	−0.468915	−	0.883243i	$-0.655355\pi$
$439$	3097.80	−	13572.3i	0.336788	−	1.47556i	0.805703	−	0.592320i	$-0.201788\pi$
$440$	−3710.82	+	4653.22i	−0.402060	+	0.504167i
$441$	66.0528	−	289.396i	0.00713236	−	0.0312489i
$442$	3372.15	−	14774.3i	0.362889	−	1.58992i
$443$	−6143.14	−	7703.26i	−0.658848	−	0.826169i	0.334370	−	0.942442i	$-0.391477\pi$
$443$	−6143.14	−	7703.26i	−0.658848	−	0.826169i	−0.993217	+	0.116273i	$0.962905\pi$
$444$	−1721.58	−	7542.74i	−0.184015	−	0.806222i
$445$	837.516	+	3669.40i	0.0892181	+	0.390890i
$446$	26961.6	+	12984.0i	2.86248	+	1.37850i
$447$	−9087.98	+	11396.0i	−0.961626	+	1.20584i
$448$	8436.87	+	10579.5i	0.889743	+	1.11570i
$449$	−6772.74	−	3261.58i	−0.711860	−	0.342814i	0.0426609	−	0.999090i	$-0.486416\pi$
$449$	−6772.74	−	3261.58i	−0.711860	−	0.342814i	−0.754521	+	0.656276i	$0.772131\pi$
$450$	553.601	−	694.193i	0.0579933	−	0.0727213i
$451$	3229.91	+	1555.44i	0.337229	+	0.162401i
$452$	−8885.89	+	11142.6i	−0.924684	+	1.15952i
$453$	14046.6	−	6764.50i	1.45688	−	0.701598i
$454$	−25466.0	−	12263.8i	−2.63255	−	1.26777i
$455$	−8451.81	+	4070.18i	−0.870828	+	0.419369i
$456$	8594.72	−	10777.4i	0.882642	−	1.10680i
$457$	−430.133	−	1884.54i	−0.0440280	−	0.192899i	0.948131	−	0.317879i	$-0.102971\pi$
$457$	−430.133	−	1884.54i	−0.0440280	−	0.192899i	−0.992159	+	0.124980i	$0.960113\pi$
$458$	25661.3	+	12357.8i	2.61806	+	1.26079i
$459$	−4895.55	+	6138.83i	−0.497832	+	0.624261i
$460$	24747.3	−	11917.7i	2.50836	−	1.20796i
$461$	4009.10	−	17565.0i	0.405037	−	1.77458i	−0.201457	−	0.979497i	$-0.564568\pi$
$461$	4009.10	−	17565.0i	0.405037	−	1.77458i	0.606495	−	0.795087i	$-0.292575\pi$
$462$	8557.45			0.861750
$463$	−1782.92			−0.178962			−0.0894810	−	0.995989i	$-0.528521\pi$
$463$	−1782.92			−0.178962			−0.0894810	+	0.995989i	$0.528521\pi$
$464$	−204.154	−	256.001i	−0.0204259	−	0.0256133i
$465$	2098.17	+	2631.03i	0.209248	+	0.262389i
$466$	−7987.05	+	3846.36i	−0.793977	+	0.382359i
$467$	4333.39	−	18985.8i	0.429390	−	1.88128i	−0.0415862	−	0.999135i	$-0.513241\pi$
$467$	4333.39	−	18985.8i	0.429390	−	1.88128i	0.470976	−	0.882146i	$-0.343902\pi$
$468$	−1262.91	−	5533.17i	−0.124739	−	0.546519i
$469$	−3479.67	+	4363.37i	−0.342593	+	0.429598i
$470$	3676.11	−	4609.70i	0.360780	−	0.452403i
$471$	−2661.31			−0.260354
$472$	4846.53	+	21234.0i	0.472626	+	2.07071i
$473$	−4530.96	+	5681.65i	−0.440452	+	0.552310i
$474$	−876.090	+	1098.58i	−0.0848949	+	0.106455i
$475$	368.224	−	1613.30i	0.0355690	−	0.155838i
$476$	−16361.3	−	7879.18i	−1.57546	−	0.758701i
$477$	−1775.29			−0.170408
$478$	5884.78			0.563104
$479$	2832.38	−	12409.5i	0.270177	−	1.18372i	−0.639628	−	0.768685i	$-0.720912\pi$
$479$	2832.38	−	12409.5i	0.270177	−	1.18372i	0.909805	−	0.415037i	$-0.136231\pi$
$480$	−5691.59	+	7137.02i	−0.541217	+	0.678665i
$481$	−4026.01			−0.381643
$482$	1498.76	+	6566.50i	0.141632	+	0.620531i
$483$	−15396.7	−	7414.64i	−1.45046	−	0.698505i
$484$	3249.67	+	14237.7i	0.305191	+	1.33713i
$485$	468.458	−	2052.45i	0.0438589	−	0.192158i
$486$	−2574.61	+	11280.1i	−0.240302	+	1.05283i
$487$	15203.3			1.41464			0.707319	−	0.706894i	$-0.249904\pi$
$487$	15203.3			1.41464			0.707319	+	0.706894i	$0.249904\pi$
$488$	1804.31	+	7905.21i	0.167372	+	0.733304i
$489$	10007.9	+	12549.5i	0.925505	+	1.16055i
$490$	−410.791	−	1799.79i	−0.0378728	−	0.165931i
$491$	−8202.65	−	10285.8i	−0.753931	−	0.945400i	0.245782	−	0.969325i	$-0.420955\pi$
$491$	−8202.65	−	10285.8i	−0.753931	−	0.945400i	−0.999714	+	0.0239250i	$0.992384\pi$
$492$	−15927.9	−	7670.45i	−1.45952	−	0.702867i
$493$	−977.687	−	470.829i	−0.0893161	−	0.0430124i
$494$	−10336.1	−	12961.0i	−0.941380	−	1.18045i
$495$	421.241	+	1845.58i	0.0382492	+	0.167581i
$496$	637.773	+	799.742i	0.0577356	+	0.0723982i
$497$	−1613.82	−	7070.59i	−0.145653	−	0.638147i
$498$	18997.4			1.70943
$499$	−872.792	+	3823.95i	−0.0782997	+	0.343053i	−0.998870	−	0.0475232i	$-0.984867\pi$
$499$	−872.792	+	3823.95i	−0.0782997	+	0.343053i	0.920570	+	0.390577i	$0.127724\pi$
$500$	−3950.69	+	17309.1i	−0.353360	+	1.54817i
$501$	−785.057	−	3439.56i	−0.0700075	−	0.306723i
$502$	30223.5	+	14554.8i	2.68713	+	1.29405i
$503$	3535.23	+	15488.9i	0.313376	+	1.37299i	0.848937	+	0.528493i	$0.177243\pi$
$503$	3535.23	+	15488.9i	0.313376	+	1.37299i	−0.535561	+	0.844496i	$0.679900\pi$
$504$	−4612.31			−0.407636
$505$	−3755.20	+	4708.88i	−0.330900	+	0.414935i
$506$	−2901.43	+	12712.0i	−0.254910	+	1.11683i
$507$	1512.24			0.132468
$508$	3299.24			0.288150
$509$	3618.34	+	1742.50i	0.315089	+	0.151739i	0.584743	−	0.811218i	$-0.301195\pi$
$509$	3618.34	+	1742.50i	0.315089	+	0.151739i	−0.269654	+	0.962957i	$0.586909\pi$
$510$	5546.66	−	24301.5i	0.481589	−	2.10998i
$511$	−12049.6	+	15109.8i	−1.04314	+	1.30806i
$512$	−4885.55	+	6126.29i	−0.421705	+	0.528801i
$513$	1911.32	+	8374.04i	0.164497	+	0.720707i
$514$	−17971.1			−1.54216
$515$	−13789.1	+	17291.0i	−1.17985	+	1.47948i
$516$	22343.9	−	28018.3i	1.90627	−	2.39038i
$517$	397.378	+	1741.03i	0.0338040	+	0.148105i
$518$	−1682.55	+	7371.73i	−0.142716	+	0.625280i
$519$	5852.21	−	2818.28i	0.494959	−	0.238360i
$520$	−9522.61	−	11941.0i	−0.803066	−	1.00701i
$521$	−11630.9	−	14584.7i	−0.978041	−	1.22643i	−0.974027	−	0.226433i	$-0.927293\pi$
$521$	−11630.9	−	14584.7i	−0.978041	−	1.22643i	−0.00401480	−	0.999992i	$-0.501278\pi$
$522$	−636.951			−0.0534073
$523$	−23803.8			−1.99018			−0.995092	−	0.0989544i	$-0.968450\pi$
$523$	−23803.8			−1.99018			−0.995092	+	0.0989544i	$0.968450\pi$
$524$	−2288.73	+	10027.6i	−0.190808	+	0.835987i
$525$	−1974.95	+	951.086i	−0.164179	+	0.0790644i
$526$	−8502.74	+	10662.1i	−0.704823	+	0.883820i
$527$	3054.28	+	1470.86i	0.252460	+	0.121578i
$528$	506.925	+	2220.98i	0.0417824	+	0.183060i
$529$	8648.64	−	10845.1i	0.710828	−	0.891350i
$530$	−9947.37	+	4790.40i	−0.815257	+	0.392607i
$531$	6241.49	+	3005.74i	0.510090	+	0.245646i
$532$	−17898.1	+	8619.28i	−1.45861	+	0.702431i
$533$	−5735.82	+	7192.49i	−0.466128	+	0.584506i
$534$	7938.21	+	3822.84i	0.643296	+	0.309795i
$535$	−6546.18	+	8208.65i	−0.529002	+	0.663347i
$536$	−8186.63	−	3942.47i	−0.659717	−	0.317703i
$537$	14205.0	+	17812.5i	1.14151	+	1.43141i
$538$	−17038.4	+	21365.5i	−1.36539	+	1.71214i
$539$	503.771	+	242.604i	0.0402578	+	0.0193872i
$540$	4069.48	+	17829.6i	0.324301	+	1.42086i
$541$	−4141.40	−	18144.6i	−0.329117	−	1.44196i	−0.820816	−	0.571192i	$-0.806481\pi$
$541$	−4141.40	−	18144.6i	−0.329117	−	1.44196i	0.491699	−	0.870765i	$-0.336376\pi$
$542$	−7884.18	−	9886.44i	−0.624824	−	0.783504i
$543$	−142.400	+	623.894i	−0.0112541	+	0.0493073i
$544$	−2046.26	+	8965.26i	−0.161273	+	0.706585i
$545$	−1996.85	+	2503.97i	−0.156946	+	0.196805i
$546$	−4886.54	+	21409.3i	−0.383012	+	1.67809i
$547$	2786.52	−	12208.5i	0.217811	−	0.954294i	−0.741280	−	0.671196i	$-0.765781\pi$
$547$	2786.52	−	12208.5i	0.217811	−	0.954294i	0.959091	−	0.283098i	$-0.0913621\pi$
$548$	38523.8	−	18552.1i	3.00302	−	1.44618i
$549$	2323.64	+	1119.01i	0.180639	+	0.0869911i
$550$	1042.80	+	1307.63i	0.0808455	+	0.101377i
$551$	−1069.52	+	515.055i	−0.0826918	+	0.0398223i
$552$	6191.20	−	27125.4i	0.477382	−	2.09155i
$553$	789.441	−	380.175i	0.0607061	−	0.0292345i
$554$	−2729.71	+	11959.6i	−0.209340	+	0.917177i
$555$	−6622.17			−0.506478
$556$	5108.95	+	22383.8i	0.389690	+	1.70734i
$557$	20698.1	+	9967.69i	1.57452	+	0.758249i	0.998257	−	0.0590156i	$-0.0187962\pi$
$557$	20698.1	+	9967.69i	1.57452	+	0.758249i	0.576263	+	0.817264i	$0.304510\pi$
$558$	1989.82			0.150960
$559$	−11627.2	−	14580.1i	−0.879750	−	1.10317i
$560$	−4225.71	+	2034.99i	−0.318873	+	0.153561i
$561$	4707.21	+	5902.66i	0.354258	+	0.444225i
$562$	−5353.05	+	2577.89i	−0.401788	+	0.193491i
$563$	2895.36	−	1394.33i	0.216741	−	0.104377i	−0.322363	−	0.946616i	$-0.604477\pi$
$563$	2895.36	−	1394.33i	0.216741	−	0.104377i	0.539104	+	0.842239i	$0.318763\pi$
$564$	−1959.62	−	8585.65i	−0.146303	−	0.640995i
$565$	7605.80	+	9537.37i	0.566333	+	0.710159i
$566$	6726.14	−	29469.2i	0.499507	−	2.18848i
$567$	9800.64	−	12289.6i	0.725905	−	0.910256i
$568$	10638.5	−	5123.22i	0.785882	−	0.378461i
$569$	13645.5	−	17110.9i	1.00536	−	1.26068i	0.0401490	−	0.999194i	$-0.487217\pi$
$569$	13645.5	−	17110.9i	1.00536	−	1.26068i	0.965208	−	0.261484i	$-0.0842118\pi$
$570$	−17001.2	−	21318.9i	−1.24930	−	1.56658i
$571$	−10983.2			−0.804964			−0.402482	−	0.915428i	$-0.631852\pi$
$571$	−10983.2			−0.804964			−0.402482	+	0.915428i	$0.631852\pi$
$572$	10690.7			0.781468
$573$	9413.57	+	4533.34i	0.686314	+	0.330511i
$574$	10772.5	+	13508.3i	0.783338	+	0.982275i
$575$	−743.214	−	3256.23i	−0.0539029	−	0.236164i
$576$	1559.30	+	6831.73i	0.112796	+	0.494193i
$577$	−6414.20			−0.462784			−0.231392	−	0.972861i	$-0.574328\pi$
$577$	−6414.20			−0.462784			−0.231392	+	0.972861i	$0.574328\pi$
$578$	−447.849	−	1962.16i	−0.0322285	−	0.141202i
$579$	−14533.7	+	6999.05i	−1.04318	+	0.502367i
$580$	−2277.17	+	1096.63i	−0.163025	+	0.0785086i
$581$	−10673.2	−	5139.94i	−0.762132	−	0.367024i
$582$	−3072.70	−	3853.04i	−0.218844	−	0.274422i
$583$	744.120	−	3260.20i	0.0528616	−	0.231602i
$584$	−28349.3	−	13652.3i	−2.00873	−	0.967355i
$585$	−4857.87			−0.343330
$586$	−24868.4	−	31184.0i	−1.75308	−	2.19829i
$587$	−100.979	+	126.624i	−0.00710028	+	0.00890346i	−0.785369	−	0.619028i	$-0.787527\pi$
$587$	−100.979	+	126.624i	−0.00710028	+	0.00890346i	0.778269	+	0.627931i	$0.216098\pi$
$588$	−2484.28	−	1196.37i	−0.174235	−	0.0839071i
$589$	3341.17	−	1609.02i	0.233736	−	0.112561i
$590$	43083.2			3.00629
$591$	−8639.89	+	14196.4i	−0.601349	+	0.988093i
$592$	−2012.91			−0.139747
$593$	−8988.77	+	4328.76i	−0.622470	+	0.299766i	−0.718408	−	0.695622i	$-0.755129\pi$
$593$	−8988.77	+	4328.76i	−0.622470	+	0.299766i	0.0959386	+	0.995387i	$0.469415\pi$
$594$	−7821.70	−	3766.73i	−0.540283	−	0.260187i
$595$	−9691.27	+	12152.5i	−0.667737	+	0.837315i
$596$	21323.1	+	26738.3i	1.46548	+	1.83765i
$597$	3630.34			0.248878
$598$	−30146.5	−	14517.8i	−2.06151	−	0.992770i
$599$	4447.89	−	19487.5i	0.303398	−	1.32928i	−0.561562	−	0.827435i	$-0.689799\pi$
$599$	4447.89	−	19487.5i	0.303398	−	1.32928i	0.864960	−	0.501841i	$-0.167344\pi$
$600$	−2225.17	−	2790.27i	−0.151404	−	0.189854i
$601$	13610.1	+	6554.28i	0.923739	+	0.444849i	0.834405	−	0.551152i	$-0.185812\pi$
$601$	13610.1	+	6554.28i	0.923739	+	0.444849i	0.0893346	+	0.996002i	$0.471526\pi$
$602$	−31555.8	+	15196.5i	−2.13641	+	1.02884i
$603$	−2603.90	+	1253.97i	−0.175852	+	0.0846860i
$604$	−8139.82	−	35662.9i	−0.548352	−	2.40249i
$605$	12500.1			0.840000
$606$	3137.37	+	13745.7i	0.210309	+	0.921422i
$607$	921.416	+	4036.99i	0.0616130	+	0.269944i	0.996346	−	0.0854060i	$-0.0272187\pi$
$607$	921.416	+	4036.99i	0.0616130	+	0.269944i	−0.934733	+	0.355350i	$0.884362\pi$
$608$	6272.05	+	7864.91i	0.418364	+	0.524612i
$609$	1416.76	+	682.274i	0.0942690	+	0.0453976i
$610$	16039.5			1.06462
$611$	−4582.68			−0.303429
$612$	−5863.31	−	7352.35i	−0.387271	−	0.485623i
$613$	−3048.60	+	3822.82i	−0.200867	+	0.251880i	−0.872055	−	0.489408i	$-0.837213\pi$
$613$	−3048.60	+	3822.82i	−0.200867	+	0.251880i	0.671188	+	0.741287i	$0.265784\pi$
$614$	16890.2	−	8133.90i	1.11015	−	0.534621i
$615$	−9434.54	+	11830.5i	−0.618597	+	0.775697i
$616$	1933.27	−	8470.21i	0.126451	−	0.554017i
$617$	11399.2	+	14294.1i	0.743782	+	0.932673i	0.999418	−	0.0341002i	$-0.0108565\pi$
$617$	11399.2	+	14294.1i	0.743782	+	0.932673i	−0.255637	+	0.966773i	$0.582285\pi$
$618$	11520.4	+	50474.3i	0.749870	+	3.28539i
$619$	−6910.85	+	3328.09i	−0.448741	+	0.216102i	−0.644585	−	0.764533i	$-0.722970\pi$
$619$	−6910.85	+	3328.09i	−0.448741	+	0.216102i	0.195844	+	0.980635i	$0.437255\pi$
$620$	7113.84	−	3425.84i	0.460804	−	0.221912i
$621$	10809.2	+	13554.3i	0.698483	+	0.875870i
$622$	−37764.1	+	18186.2i	−2.43441	+	1.17235i
$623$	−3425.57	−	4295.53i	−0.220293	−	0.276239i
$624$	−5846.01			−0.375044
$625$	16022.7	+	7716.13i	1.02545	+	0.493833i
$626$	7384.90	+	32355.3i	0.471501	+	2.06578i
$627$	8258.94			0.526045
$628$	−1389.47	+	6087.65i	−0.0882894	+	0.386821i
$629$	−6010.30	+	2894.41i	−0.380996	+	0.183478i
$630$	−2030.20	+	8894.87i	−0.128389	+	0.562508i
$631$	23198.9	−	11172.0i	1.46360	−	0.704834i	0.478707	−	0.877975i	$-0.341106\pi$
$631$	23198.9	−	11172.0i	1.46360	−	0.704834i	0.984897	+	0.173141i	$0.0553915\pi$
$632$	889.460	+	1115.35i	0.0559823	+	0.0701996i
$633$	−13461.2	−	6482.58i	−0.845237	−	0.407045i
$634$	13629.0	−	6563.40i	0.853751	−	0.411145i
$635$	628.389	−	2753.15i	0.0392707	−	0.172056i
$636$	−3669.53	+	16077.3i	−0.228784	+	1.00237i
$637$	−894.622	+	1121.82i	−0.0556455	+	0.0697773i
$638$	266.981	−	1169.72i	0.0165672	−	0.0725856i
$639$	835.718	−	3661.52i	0.0517378	−	0.226678i
$640$	19596.0	+	24572.6i	1.21031	+	1.51769i
$641$	4735.70	+	20748.4i	0.291808	+	1.27849i	0.882007	+	0.471236i	$0.156192\pi$
$641$	4735.70	+	20748.4i	0.291808	+	1.27849i	−0.590200	+	0.807257i	$0.700951\pi$
$642$	5469.15	+	23961.9i	0.336215	+	1.47306i
$643$	−8151.48	−	3925.55i	−0.499943	−	0.240760i	0.166878	−	0.985977i	$-0.446631\pi$
$643$	−8151.48	−	3925.55i	−0.499943	−	0.240760i	−0.666821	+	0.745218i	$0.732346\pi$
$644$	−24999.3	+	31348.2i	−1.52968	+	1.91815i
$645$	−19125.0	−	23982.0i	−1.16752	−	1.46402i
$646$	−24748.4	−	11918.2i	−1.50730	−	0.725875i
$647$	−11566.4	+	14503.8i	−0.702814	+	0.881301i	−0.997230	−	0.0743765i	$-0.976303\pi$
$647$	−11566.4	+	14503.8i	−0.702814	+	0.881301i	0.294416	+	0.955677i	$0.404875\pi$
$648$	23058.0	+	11104.2i	1.39785	+	0.673167i
$649$	−8136.00	+	10202.2i	−0.492089	+	0.617061i
$650$	−3866.93	+	1862.22i	−0.233344	+	0.112373i
$651$	−4425.92	−	2131.41i	−0.266460	−	0.128320i
$652$	33931.6	−	16340.6i	2.03814	−	0.981515i
$653$	11405.3	−	14301.8i	0.683497	−	0.857078i	−0.312174	−	0.950025i	$-0.601057\pi$
$653$	11405.3	−	14301.8i	0.683497	−	0.857078i	0.995671	+	0.0929466i	$0.0296286\pi$
$654$	1668.32	+	7309.38i	0.0997498	+	0.437032i
$655$	7931.90	+	3819.80i	0.473168	+	0.227866i
$656$	−2867.78	+	3596.08i	−0.170683	+	0.214030i
$657$	−9016.97	+	4342.34i	−0.535442	+	0.257855i
$658$	−1915.19	+	8390.99i	−0.113468	+	0.497135i
$659$	27426.7			1.62123			0.810615	−	0.585579i	$-0.199133\pi$
$659$	27426.7			1.62123			0.810615	+	0.585579i	$0.199133\pi$
$660$	17584.5			1.03708
$661$	−18271.5	−	22911.7i	−1.07516	−	1.34820i	−0.933617	−	0.358272i	$-0.883366\pi$
$661$	−18271.5	−	22911.7i	−1.07516	−	1.34820i	−0.141540	−	0.989932i	$-0.545206\pi$
$662$	−7443.71	−	9334.11i	−0.437021	−	0.548007i
$663$	−17455.4	+	8406.09i	−1.02249	+	0.492407i
$664$	4291.83	−	18803.7i	0.250836	−	1.09899i
$665$	3783.66	+	16577.3i	0.220638	+	0.966677i
$666$	−2441.36	+	3061.37i	−0.142043	+	0.178117i
$667$	−1493.86	+	1873.25i	−0.0867206	+	0.108744i
$668$	−8277.76			−0.479455
$669$	−8513.17	−	37298.6i	−0.491985	−	2.15553i
$670$	−11206.6	+	14052.6i	−0.646191	+	0.810298i
$671$	−3028.95	+	3798.19i	−0.174264	+	0.218521i
$672$	2965.22	−	12991.5i	0.170217	−	0.745768i
$673$	23623.6	+	11376.5i	1.35308	+	0.651609i	0.963082	−	0.269207i	$-0.0867617\pi$
$673$	23623.6	+	11376.5i	1.35308	+	0.651609i	0.389997	+	0.920816i	$0.372476\pi$
$674$	−18081.0			−1.03331
$675$	2223.79			0.126805
$676$	789.541	−	3459.20i	0.0449215	−	0.196814i
$677$	−12516.0	+	15694.6i	−0.710530	+	0.890976i	−0.997761	−	0.0668853i	$-0.978694\pi$
$677$	−12516.0	+	15694.6i	−0.710530	+	0.890976i	0.287231	+	0.957861i	$0.407265\pi$
$678$	28556.6			1.61756
$679$	683.835	+	2996.08i	0.0386498	+	0.169336i
$680$	−22800.7	−	10980.2i	−1.28583	−	0.619225i
$681$	8040.94	+	35229.7i	0.452466	+	1.98238i
$682$	−834.043	+	3654.18i	−0.0468287	+	0.205170i
$683$	172.613	−	756.267i	0.00967036	−	0.0423686i	−0.969863	−	0.243653i	$-0.921654\pi$
$683$	172.613	−	756.267i	0.00967036	−	0.0423686i	0.979533	+	0.201284i	$0.0645114\pi$
$684$	−10287.3			−0.575068
$685$	−8143.93	−	35680.9i	−0.454253	−	1.99021i
$686$	19395.5	+	24321.2i	1.07948	+	1.35363i
$687$	−8102.59	−	35499.8i	−0.449976	−	1.97147i
$688$	−5813.36	−	7289.72i	−0.322140	−	0.403950i
$689$	7731.57	+	3723.33i	0.427503	+	0.205875i
$690$	−49586.3	−	23879.5i	−2.73583	−	1.31750i
$691$	9849.32	+	12350.7i	0.542237	+	0.679944i	0.975164	−	0.221485i	$-0.0710905\pi$
$691$	9849.32	+	12350.7i	0.542237	+	0.679944i	−0.432927	+	0.901429i	$0.642519\pi$
$692$	−3391.28	−	14858.2i	−0.186296	−	0.816217i
$693$	−1722.94	−	2160.50i	−0.0944431	−	0.118428i
$694$	−5065.30	−	22192.5i	−0.277055	−	1.21386i
$695$	19651.9			1.07257
$696$	−569.696	+	2496.00i	−0.0310262	+	0.135935i
$697$	−3391.94	+	14861.1i	−0.184331	+	0.807609i
$698$	−11620.9	−	50914.4i	−0.630167	−	2.76094i
$699$	10211.1	+	4917.39i	0.552530	+	0.266084i
$700$	1144.46	+	5014.19i	0.0617949	+	0.270741i
$701$	−6366.83			−0.343041			−0.171521	−	0.985181i	$-0.554868\pi$
$701$	−6366.83			−0.343041			−0.171521	+	0.985181i	$0.554868\pi$
$702$	13890.2	−	17417.7i	0.746795	−	0.936451i
$703$	−1623.86	+	7114.58i	−0.0871193	+	0.381695i
$704$	−13199.6			−0.706646
$705$	−7537.80			−0.402681
$706$	−14590.1	−	7026.21i	−0.777769	−	0.374554i
$707$	1956.39	−	8571.53i	0.104070	−	0.455962i
$708$	40121.6	−	50311.0i	2.12975	−	2.67062i
$709$	14081.9	−	17658.2i	0.745920	−	0.935355i	−0.253569	−	0.967317i	$-0.581604\pi$
$709$	14081.9	−	17658.2i	0.745920	−	0.935355i	0.999489	+	0.0319627i	$0.0101758\pi$
$710$	−5197.44	−	22771.5i	−0.274727	−	1.20366i
$711$	453.749			0.0239338
$712$	5577.24	−	6993.64i	0.293562	−	0.368115i
$713$	4666.80	−	5851.98i	0.245123	−	0.307375i
$714$	8096.79	+	35474.4i	0.424391	+	1.85938i
$715$	2036.20	−	8921.16i	0.106503	−	0.466619i
$716$	48161.8	−	23193.5i	2.51381	−	1.21059i
$717$	−4690.78	−	5882.05i	−0.244324	−	0.306373i
$718$	−13433.9	−	16845.5i	−0.698256	−	0.875585i
$719$	1278.49			0.0663139			0.0331570	−	0.999450i	$-0.489444\pi$
$719$	1278.49			0.0663139			0.0331570	+	0.999450i	$0.489444\pi$
$720$	−2428.82			−0.125718
$721$	7183.88	−	31474.6i	0.371070	−	1.62576i
$722$	1979.70	−	953.372i	0.102045	−	0.0491424i
$723$	5368.78	−	6732.24i	0.276165	−	0.346300i
$724$	1352.79	+	651.469i	0.0694420	+	0.0334415i
$725$	68.3883	+	299.629i	0.00350328	+	0.0153489i
$726$	18244.5	−	22877.9i	0.932669	−	1.16953i
$727$	−18681.2	+	8996.37i	−0.953020	+	0.458950i	−0.844744	−	0.535170i	$-0.820247\pi$
$727$	−18681.2	+	8996.37i	−0.953020	+	0.458950i	−0.108276	+	0.994121i	$0.534533\pi$
$728$	20087.1	+	9673.45i	1.02264	+	0.492475i
$729$	−8374.42	+	4032.91i	−0.425464	+	0.204893i
$730$	−38807.0	+	48662.4i	−1.96755	+	2.46723i
$731$	−27840.0	−	13407.0i	−1.40862	−	0.678354i
$732$	14936.9	−	18730.3i	0.754212	−	0.945752i
$733$	−23363.8	−	11251.4i	−1.17730	−	0.566958i	−0.260177	−	0.965561i	$-0.583781\pi$
$733$	−23363.8	−	11251.4i	−1.17730	−	0.566958i	−0.917124	+	0.398603i	$0.869495\pi$
$734$	31735.2	+	39794.7i	1.59587	+	2.00116i
$735$	−1471.51	+	1845.22i	−0.0738471	+	0.0926013i
$736$	18293.3	+	8809.58i	0.916167	+	0.441203i
$737$	−1211.40	−	5307.50i	−0.0605462	−	0.265270i
$738$	1990.97	+	8723.00i	0.0993070	+	0.435092i
$739$	1910.74	+	2395.99i	0.0951119	+	0.119267i	0.827110	−	0.562040i	$-0.189983\pi$
$739$	1910.74	+	2395.99i	0.0951119	+	0.119267i	−0.731998	+	0.681307i	$0.761412\pi$
$740$	−3457.43	+	15148.0i	−0.171753	+	0.752501i
$741$	−4716.09	+	20662.5i	−0.233805	+	1.02437i
$742$	10048.7	−	12600.6i	0.497168	−	0.623429i
$743$	−6054.71	+	26527.4i	−0.298958	+	1.30982i	0.572724	+	0.819748i	$0.305887\pi$
$743$	−6054.71	+	26527.4i	−0.298958	+	1.30982i	−0.871682	+	0.490072i	$0.836971\pi$
$744$	1779.72	−	7797.45i	0.0876984	−	0.384232i
$745$	26373.9	−	12701.0i	1.29700	−	0.624601i
$746$	7578.05	+	3649.40i	0.371920	+	0.179107i
$747$	−3824.90	−	4796.27i	−0.187344	−	0.234921i
$748$	15959.8	−	7685.81i	0.780142	−	0.375697i
$749$	3410.44	−	14942.1i	0.166375	−	0.728936i
$750$	32051.4	−	15435.1i	1.56047	−	0.751481i
$751$	3252.06	−	14248.2i	0.158015	−	0.692310i	−0.832398	−	0.554178i	$-0.813033\pi$
$751$	3252.06	−	14248.2i	0.158015	−	0.692310i	0.990414	−	0.138133i	$-0.0441100\pi$
$752$	−2291.23			−0.111107
$753$	−9543.11	−	41811.1i	−0.461846	−	2.02348i
$754$	2773.99	+	1335.88i	0.133983	+	0.0645226i
$755$	−31310.3			−1.50927
$756$	−16644.8	−	20871.9i	−0.800748	−	1.00411i
$757$	16996.3	−	8184.99i	0.816039	−	0.392983i	0.0211781	−	0.999776i	$-0.493258\pi$
$757$	16996.3	−	8184.99i	0.816039	−	0.392983i	0.794860	+	0.606792i	$0.207544\pi$
$758$	−20742.8	−	26010.7i	−0.993950	−	1.24637i
$759$	15018.8	−	7232.68i	0.718246	−	0.345889i
$760$	−24942.4	+	12011.6i	−1.19047	+	0.573299i
$761$	3302.76	+	14470.3i	0.157326	+	0.689289i	0.990641	+	0.136492i	$0.0435827\pi$
$761$	3302.76	+	14470.3i	0.157326	+	0.689289i	−0.833315	+	0.552798i	$0.813560\pi$
$762$	−4121.72	−	5168.47i	−0.195950	−	0.245714i
$763$	1040.32	−	4557.96i	0.0493608	−	0.216264i
$764$	15284.7	−	19166.4i	0.723796	−	0.907611i
$765$	−7252.15	+	3492.45i	−0.342748	+	0.165059i
$766$	24787.8	−	31083.0i	1.16922	−	1.46615i
$767$	−20878.4	−	26180.7i	−0.982889	−	1.23250i
$768$	36648.7			1.72193
$769$	7351.97			0.344758			0.172379	−	0.985031i	$-0.444855\pi$
$769$	7351.97			0.344758			0.172379	+	0.985031i	$0.444855\pi$
$770$	−15483.9	−	7456.65i	−0.724676	−	0.348986i
$771$	14324.8	+	17962.7i	0.669124	+	0.839055i
$772$	8422.07	+	36899.5i	0.392638	+	1.72026i
$773$	−5971.18	−	26161.4i	−0.277837	−	1.21729i	−0.900521	−	0.434812i	$-0.856815\pi$
$773$	−5971.18	−	26161.4i	−0.277837	−	1.21729i	0.622684	−	0.782473i	$-0.286042\pi$
$774$	−18137.4			−0.842293
$775$	−213.644	−	936.035i	−0.00990234	−	0.0433850i
$776$	−4507.93	+	2170.91i	−0.208538	+	0.100427i
$777$	8709.46	−	4194.26i	0.402124	−	0.193653i
$778$	27701.1	+	13340.2i	1.27652	+	0.614740i
$779$	10396.7	+	13037.1i	0.478180	+	0.599618i
$780$	−10041.2	+	43993.5i	−0.460941	+	2.01951i
$781$	6373.85	+	3069.48i	0.292028	+	0.140633i
$782$	−55442.0			−2.53530
$783$	−994.630	−	1247.23i	−0.0453961	−	0.0569249i
$784$	−447.290	+	560.884i	−0.0203758	+	0.0255505i
$785$	4815.38	+	2318.96i	0.218940	+	0.105436i
$786$	18568.1	−	8941.94i	0.842625	−	0.405787i
$787$	18164.2			0.822724			0.411362	−	0.911472i	$-0.365053\pi$
$787$	18164.2			0.822724			0.411362	+	0.911472i	$0.365053\pi$
$788$	27963.0	+	27175.4i	1.26414	+	1.22853i
$789$	17434.7			0.786681
$790$	2542.47	−	1224.39i	0.114502	−	0.0551414i
$791$	−16043.8	−	7726.27i	−0.721177	−	0.347300i
$792$	2805.15	−	3517.55i	0.125855	−	0.157817i
$793$	−7772.82	−	9746.81i	−0.348072	−	0.436468i
$794$	−18447.4			−0.824528
$795$	12717.2	+	6124.30i	0.567339	+	0.273216i
$796$	1895.40	−	8304.28i	0.0843977	−	0.369771i
$797$	−7720.98	−	9681.80i	−0.343151	−	0.430297i	0.580070	−	0.814566i	$-0.303025\pi$
$797$	−7720.98	−	9681.80i	−0.343151	−	0.430297i	−0.923221	+	0.384269i	$0.874454\pi$
$798$	35862.6	+	17270.5i	1.59088	+	0.766128i
$799$	−6841.33	+	3294.61i	−0.302915	+	0.145876i
$800$	2346.50	−	1130.02i	0.103702	−	0.0499401i
$801$	−633.111	−	2773.84i	−0.0279274	−	0.122358i
$802$	10453.8			0.460271
$803$	−4194.93	−	18379.2i	−0.184354	−	0.807706i
$804$	5973.87	+	26173.2i	0.262043	+	1.14808i
$805$	21397.9	+	26832.2i	0.936868	+	1.17479i
$806$	−8665.90	−	4173.28i	−0.378714	−	0.182379i
$807$	34936.9			1.52396
$808$	14314.4			0.623240
$809$	−19958.5	−	25027.1i	−0.867370	−	1.08765i	−0.995393	−	0.0958769i	$-0.969434\pi$
$809$	−19958.5	−	25027.1i	−0.867370	−	1.08765i	0.128023	−	0.991771i	$-0.459137\pi$
$810$	31563.8	−	39579.8i	1.36919	−	1.71690i
$811$	−29082.4	+	14005.3i	−1.25921	+	0.606404i	−0.939966	−	0.341268i	$-0.889144\pi$
$811$	−29082.4	+	14005.3i	−1.25921	+	0.606404i	−0.319245	+	0.947672i	$0.603429\pi$
$812$	2300.36	−	2884.56i	0.0994174	−	0.124666i
$813$	−3597.35	+	15761.0i	−0.155184	+	0.679905i
$814$	−4598.70	−	5766.59i	−0.198015	−	0.248303i
$815$	−7173.14	−	31427.6i	−0.308300	−	1.35075i
$816$	−8727.31	+	4202.85i	−0.374408	+	0.180305i
$817$	−30455.0	+	14666.4i	−1.30414	+	0.628043i
$818$	19292.0	+	24191.5i	0.824609	+	1.03403i
$819$	6389.06	−	3076.81i	0.272591	−	0.131273i
$820$	22136.2	+	27757.9i	0.942719	+	1.18213i
$821$	−10294.2			−0.437599			−0.218799	−	0.975770i	$-0.570214\pi$
$821$	−10294.2			−0.437599			−0.218799	+	0.975770i	$0.570214\pi$
$822$	−77190.5	−	37173.0i	−3.27534	−	1.57732i
$823$	−10320.2	−	45215.9i	−0.437109	−	1.91510i	−0.401805	−	0.915725i	$-0.631617\pi$
$823$	−10320.2	−	45215.9i	−0.437109	−	1.91510i	−0.0353045	−	0.999377i	$-0.511240\pi$
$824$	52562.4			2.22220
$825$	475.802	−	2084.62i	0.0200792	−	0.0879725i
$826$	−56663.0	+	27287.4i	−2.38687	+	1.14946i
$827$	1459.49	−	6394.46i	0.0613682	−	0.268872i	−0.934930	−	0.354831i	$-0.884538\pi$
$827$	1459.49	−	6394.46i	0.0613682	−	0.268872i	0.996299	+	0.0859593i	$0.0273955\pi$
$828$	−18707.4	+	9009.03i	−0.785179	+	0.378122i
$829$	2046.47	+	2566.19i	0.0857380	+	0.107512i	0.822850	−	0.568258i	$-0.192383\pi$
$829$	2046.47	+	2566.19i	0.0857380	+	0.107512i	−0.737112	+	0.675770i	$0.763811\pi$
$830$	−34374.0	−	16553.6i	−1.43752	−	0.692271i
$831$	14129.9	−	6804.62i	0.589846	−	0.284055i
$832$	7537.34	−	33023.3i	0.314075	−	1.37605i
$833$	−529.045	+	2317.90i	−0.0220052	+	0.0964110i
$834$	28683.0	−	35967.3i	1.19090	−	1.49334i
$835$	−1576.62	+	6907.63i	−0.0653428	+	0.286285i
$836$	4311.99	−	18892.0i	0.178389	−	0.781573i
$837$	3107.20	+	3896.31i	0.128316	+	0.160903i
$838$	9930.63	+	43508.9i	0.409365	+	1.79355i
$839$	8309.36	+	36405.7i	0.341920	+	1.49805i	0.795016	+	0.606589i	$0.207462\pi$
$839$	8309.36	+	36405.7i	0.341920	+	1.49805i	−0.453096	+	0.891462i	$0.649680\pi$
$840$	33040.2	+	15911.3i	1.35714	+	0.653563i
$841$	−15068.8	+	18895.7i	−0.617854	+	0.774764i
$842$	−15516.2	−	19456.8i	−0.635066	−	0.796347i
$843$	6843.62	+	3295.71i	0.279605	+	0.134651i
$844$	−21856.8	+	27407.5i	−0.891399	+	1.11778i
$845$	−2736.26	−	1317.71i	−0.111397	−	0.0536458i
$846$	−2778.92	+	3484.65i	−0.112933	+	0.141613i
$847$	−16440.1	+	7917.12i	−0.666927	+	0.321175i
$848$	3865.61	+	1861.58i	0.156540	+	0.0753855i
$849$	−34816.9	+	16766.9i	−1.40744	+	0.677785i
$850$	−4434.02	+	5560.09i	−0.178924	+	0.224364i
$851$	3277.55	+	14359.9i	0.132024	+	0.578437i
$852$	−31431.8	−	15136.8i	−1.26389	−	0.608658i
$853$	−4425.84	+	5549.83i	−0.177653	+	0.222770i	−0.862683	−	0.505745i	$-0.831218\pi$
$853$	−4425.84	+	5549.83i	−0.177653	+	0.222770i	0.685030	+	0.728515i	$0.259789\pi$
$854$	−21095.1	+	10158.8i	−0.845267	+	0.407059i
$855$	−1959.38	+	8584.59i	−0.0783734	+	0.343376i
$856$	24953.2			0.996359
$857$	23036.7			0.918226			0.459113	−	0.888378i	$-0.348167\pi$
$857$	23036.7			0.918226			0.459113	+	0.888378i	$0.348167\pi$
$858$	−13355.8	−	16747.6i	−0.531420	−	0.666380i
$859$	−13471.9	−	16893.2i	−0.535105	−	0.671001i	0.438634	−	0.898666i	$-0.355462\pi$
$859$	−13471.9	−	16893.2i	−0.535105	−	0.671001i	−0.973740	+	0.227665i	$0.926891\pi$
$860$	−64843.2	+	31226.8i	−2.57109	+	1.23817i
$861$	4915.23	−	21535.0i	0.194553	−	0.852394i
$862$	4785.18	+	20965.2i	0.189076	+	0.828397i
$863$	6613.93	−	8293.61i	0.260882	−	0.327135i	−0.634089	−	0.773260i	$-0.718625\pi$
$863$	6613.93	−	8293.61i	0.260882	−	0.327135i	0.894971	+	0.446125i	$0.147196\pi$
$864$	−8428.72	+	10569.3i	−0.331888	+	0.416174i
$865$	−13044.8			−0.512758
$866$	−11171.0	−	48943.2i	−0.438343	−	1.92050i
$867$	−1604.26	+	2011.68i	−0.0628415	+	0.0788007i
$868$	−7186.29	+	9011.32i	−0.281012	+	0.352378i
$869$	−190.191	+	833.281i	−0.00742438	+	0.0325283i
$870$	4562.79	+	2197.32i	0.177808	+	0.0856279i
$871$	13970.2			0.543471
$872$	7611.76			0.295604
$873$	−354.126	+	1551.53i	−0.0137289	+	0.0601503i
$874$	−37814.5	+	47417.9i	−1.46349	+	1.83516i
$875$	−22183.3			−0.857067
$876$	20686.8	+	90634.6i	0.797877	+	3.49573i
$877$	−44909.0	−	21627.1i	−1.72916	−	0.832718i	−0.986645	−	0.162885i	$-0.947920\pi$
$877$	−44909.0	−	21627.1i	−1.72916	−	0.832718i	−0.742512	−	0.669833i	$-0.766366\pi$
$878$	14563.6	+	63807.4i	0.559794	+	2.45262i
$879$	−11346.8	+	49713.7i	−0.435403	+	1.90762i
$880$	1018.05	−	4460.37i	0.0389983	−	0.170863i
$881$	−16109.9			−0.616068			−0.308034	−	0.951375i	$-0.599671\pi$
$881$	−16109.9			−0.616068			−0.308034	+	0.951375i	$0.599671\pi$
$882$	310.533	+	1360.54i	0.0118551	+	0.0519406i
$883$	10645.0	+	13348.4i	0.405698	+	0.508730i	0.942145	−	0.335204i	$-0.108805\pi$
$883$	10645.0	+	13348.4i	0.405698	+	0.508730i	−0.536447	+	0.843934i	$0.680234\pi$
$884$	10115.2	+	44317.5i	0.384853	+	1.68615i
$885$	−34341.8	−	43063.2i	−1.30439	−	1.63565i
$886$	41733.8	+	20097.9i	1.58248	+	0.762080i
$887$	9636.42	+	4640.65i	0.364779	+	0.175668i	0.607290	−	0.794480i	$-0.292257\pi$
$887$	9636.42	+	4640.65i	0.364779	+	0.175668i	−0.242511	+	0.970149i	$0.577971\pi$
$888$	9812.91	+	12305.0i	0.370833	+	0.465010i
$889$	917.297	+	4018.94i	0.0346065	+	0.151621i
$890$	−11032.4	−	13834.1i	−0.415511	−	0.521035i
$891$	3411.97	+	14948.8i	0.128289	+	0.562069i
$892$	−89764.1			−3.36942
$893$	−1848.38	+	8098.29i	−0.0692651	+	0.303470i
$894$	15248.5	−	66807.8i	0.570453	−	2.49932i
$895$	−10181.4	−	44607.6i	−0.380253	−	1.66600i
$896$	−41336.1	−	19906.4i	−1.54123	−	0.742218i
$897$	9518.82	+	41704.7i	0.354319	+	1.55237i
$898$	35340.4			1.31328
$899$	−429.425	+	538.482i	−0.0159312	+	0.0199771i
$900$	−592.659	+	2596.61i	−0.0219503	+	0.0961707i
$901$	14219.0			0.525754
$902$	−16853.8			−0.622138
$903$	40342.6	+	19428.0i	1.48673	+	0.715972i
$904$	6451.41	−	28265.5i	0.237357	−	1.03993i
$905$	801.297	−	1004.79i	0.0294321	−	0.0369066i
$906$	−45699.1	+	57304.9i	−1.67578	+	2.10136i
$907$	5043.51	+	22097.1i	0.184638	+	0.808954i	0.979383	+	0.202010i	$0.0647475\pi$
$907$	5043.51	+	22097.1i	0.184638	+	0.808954i	−0.794745	+	0.606944i	$0.792395\pi$
$908$	84784.8			3.09877
$909$	2838.71	−	3559.63i	0.103580	−	0.129885i
$910$	27497.0	−	34480.2i	1.00167	−	1.25605i
$911$	−9884.80	−	43308.1i	−0.359493	−	1.57504i	−0.754460	−	0.656346i	$-0.772101\pi$
$911$	−9884.80	−	43308.1i	−0.359493	−	1.57504i	0.394967	−	0.918695i	$-0.370756\pi$
$912$	−2357.93	+	10330.8i	−0.0856129	+	0.375095i
$913$	10411.3	−	5013.80i	0.377396	−	0.181744i
$914$	5666.02	+	7104.97i	0.205050	+	0.257124i
$915$	−12785.1	−	16032.0i	−0.461926	−	0.579237i
$916$	−85434.9			−3.08171
$917$	−12851.4			−0.462802
$918$	8214.10	−	35988.3i	0.295322	−	1.29389i
$919$	17947.3	−	8642.96i	0.644207	−	0.310234i	−0.0831047	−	0.996541i	$-0.526484\pi$
$919$	17947.3	−	8642.96i	0.644207	−	0.310234i	0.727312	+	0.686307i	$0.240769\pi$
$920$	−34838.5	+	43686.0i	−1.24847	+	1.56553i
$921$	−21593.3	−	10398.8i	−0.772557	−	0.372044i
$922$	18847.9	+	82578.1i	0.673235	+	2.94964i
$923$	−11319.0	+	14193.6i	−0.403650	+	0.506161i
$924$	−23127.1	+	11137.4i	−0.823404	+	0.396531i
$925$	1702.23	+	819.749i	0.0605069	+	0.0291386i
$926$	7551.95	−	3636.83i	0.268005	−	0.129064i
$927$	10423.7	−	13070.9i	0.369320	−	0.463113i
$928$	−1683.29	−	810.631i	−0.0595440	−	0.0286749i
$929$	27985.5	−	35092.7i	0.988346	−	1.23935i	0.0174497	−	0.999848i	$-0.494445\pi$
$929$	27985.5	−	35092.7i	0.988346	−	1.23935i	0.970897	−	0.239499i	$-0.0769833\pi$
$930$	−14254.1	−	6864.39i	−0.502590	−	0.242035i
$931$	1621.59	+	2033.41i	0.0570843	+	0.0715814i
$932$	16579.6	−	20790.1i	0.582706	−	0.730690i
$933$	48279.6	+	23250.2i	1.69411	+	0.815840i
$934$	20372.5	+	89257.7i	0.713713	+	3.12698i
$935$	−3373.89	−	14782.0i	−0.118009	−	0.517029i
$936$	7198.52	+	9026.66i	0.251379	+	0.315220i
$937$	1519.35	−	6656.70i	0.0529722	−	0.232086i	−0.941511	−	0.336982i	$-0.890594\pi$
$937$	1519.35	−	6656.70i	0.0529722	−	0.232086i	0.994483	+	0.104896i	$0.0334509\pi$
$938$	5838.43	−	25579.8i	0.203232	−	0.890417i
$939$	26453.8	−	33172.0i	0.919368	−	1.15285i
$940$	−3935.48	+	17242.4i	−0.136554	+	0.598284i
$941$	−269.339	+	1180.05i	−0.00933072	+	0.0408805i	−0.979379	−	0.202032i	$-0.935246\pi$
$941$	−269.339	+	1180.05i	−0.00933072	+	0.0408805i	0.970048	+	0.242912i	$0.0781027\pi$
$942$	11272.5	−	5428.56i	0.389893	−	0.187762i
$943$	30323.5	+	14603.0i	1.04716	+	0.504284i
$944$	−10438.7	−	13089.7i	−0.359906	−	0.451308i
$945$	−20587.5	+	9914.40i	−0.708688	+	0.341286i
$946$	7602.37	−	33308.2i	0.261284	−	1.14476i
$947$	−4589.47	+	2210.17i	−0.157484	+	0.0758404i	−0.510966	−	0.859601i	$-0.670712\pi$
$947$	−4589.47	+	2210.17i	−0.157484	+	0.0758404i	0.353481	+	0.935442i	$0.384998\pi$
$948$	937.902	−	4109.22i	0.0321325	−	0.140782i
$949$	48377.1			1.65478
$950$	1731.13	+	7584.57i	0.0591213	+	0.259027i
$951$	−17424.1	−	8391.00i	−0.594127	−	0.286116i
$952$	36941.9			1.25766
$953$	−3933.01	−	4931.84i	−0.133686	−	0.167637i	0.710483	−	0.703715i	$-0.248477\pi$
$953$	−3933.01	−	4931.84i	−0.133686	−	0.167637i	−0.844168	+	0.536078i	$0.819905\pi$
$954$	7519.61	−	3621.25i	0.255195	−	0.122896i
$955$	−13082.8	−	16405.3i	−0.443297	−	0.555877i
$956$	−15904.0	+	7658.98i	−0.538047	+	0.259110i
$957$	−1381.99	+	665.530i	−0.0466805	+	0.0224802i
$958$	13315.8	+	58340.4i	0.449076	+	1.96753i
$959$	33309.9	+	41769.3i	1.12162	+	1.40647i
$960$	12397.8	−	54318.2i	0.416808	−	1.82616i
$961$	−17232.9	+	21609.3i	−0.578459	+	0.725365i
$962$	17053.0	−	8212.31i	0.571530	−	0.275234i
$963$	4948.51	−	6205.24i	0.165590	−	0.207644i
$964$	−12596.7	−	15795.8i	−0.420864	−	0.527747i
$965$	32396.0			1.08069
$966$	80340.3			2.67589
$967$	8640.30	+	4160.95i	0.287335	+	0.138373i	0.572000	−	0.820254i	$-0.306168\pi$
$967$	8640.30	+	4160.95i	0.287335	+	0.138373i	−0.284664	+	0.958627i	$0.591882\pi$
$968$	−18522.9	−	23227.0i	−0.615031	−	0.771224i
$969$	7814.36	+	34236.9i	0.259064	+	1.13503i
$970$	2202.35	+	9649.14i	0.0729003	+	0.319397i
$971$	46501.0			1.53686			0.768428	−	0.639936i	$-0.221039\pi$
$971$	46501.0			1.53686			0.768428	+	0.639936i	$0.221039\pi$
$972$	−7722.87	−	33836.1i	−0.254847	−	1.11656i
$973$	−25846.1	+	12446.8i	−0.851581	+	0.410100i
$974$	−64397.0	+	31011.9i	−2.11849	+	1.02021i
$975$	4943.69	+	2380.76i	0.162385	+	0.0782003i
$976$	−3886.23	−	4873.18i	−0.127454	−	0.159822i
$977$	−5581.66	+	24454.9i	−0.182777	+	0.800799i	0.797524	+	0.603288i	$0.206143\pi$
$977$	−5581.66	+	24454.9i	−0.182777	+	0.800799i	−0.980301	+	0.197511i	$0.936714\pi$
$978$	−67989.1	−	32741.8i	−2.22296	−	1.07052i
$979$	5359.35			0.174960
$980$	3452.60	+	4329.43i	0.112540	+	0.141121i
$981$	1509.50	−	1892.85i	0.0491281	−	0.0616046i
$982$	55725.1	+	26835.8i	1.81086	+	0.872062i
$983$	−29515.7	+	14214.0i	−0.957686	+	0.461197i	−0.846375	−	0.532588i	$-0.821220\pi$
$983$	−29515.7	+	14214.0i	−0.957686	+	0.461197i	−0.111312	+	0.993786i	$0.535505\pi$
$984$	35963.3			1.16511
$985$	28003.3	−	18158.6i	0.905847	−	0.587392i
$986$	5101.61			0.164775
$987$	9913.69	−	4774.18i	0.319713	−	0.153965i
$988$	44802.5	+	21575.8i	1.44267	+	0.694754i
$989$	−42538.3	+	53341.3i	−1.36768	+	1.71502i
$990$	−5548.88	−	6958.08i	−0.178136	−	0.223376i
$991$	40539.2			1.29946			0.649732	−	0.760163i	$-0.274881\pi$
$991$	40539.2			1.29946			0.649732	+	0.760163i	$0.274881\pi$
$992$	5258.57	+	2532.40i	0.168306	+	0.0810521i
$993$	−3396.37	+	14880.5i	−0.108540	+	0.475547i
$994$	21258.3	+	26657.1i	0.678343	+	0.850615i
$995$	−6568.75	−	3163.35i	−0.209290	−	0.100789i
$996$	−51341.8	+	24724.9i	−1.63336	+	0.786585i
$997$	−4190.68	+	2018.12i	−0.133119	+	0.0641069i	−0.499258	−	0.866453i	$-0.666394\pi$
$997$	−4190.68	+	2018.12i	−0.133119	+	0.0641069i	0.366138	+	0.930560i	$0.380680\pi$
$998$	−4103.25	−	17977.5i	−0.130146	−	0.570208i
$999$	−9806.82			−0.310585

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.4.d.a.36.5	✓	294
197.104	even	7	inner	197.4.d.a.104.5	yes	294

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.4.d.a.36.5	✓	294	1.1	even	1	trivial
197.4.d.a.104.5	yes	294	197.104	even	7	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.d (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.23571 + 2.03981i) q^{2} +(5.41516 + 2.60780i) q^{3} +(8.79251 - 11.0255i) q^{4} +(-7.52587 - 9.43714i) q^{5} -28.2565 q^{6} +(15.8752 + 7.64508i) q^{7} +(-6.38361 + 27.9684i) q^{8} +(5.68910 + 7.13391i) q^{9} +(51.1274 + 24.6217i) q^{10} +(-15.4856 + 7.45746i) q^{11} +(76.3651 - 36.7755i) q^{12} +(-9.81465 - 43.0008i) q^{13} -82.8372 q^{14} +(-16.1436 - 70.7296i) q^{15} +(-4.90710 - 21.4994i) q^{16} +(-45.5664 - 57.1385i) q^{17} +(-38.6492 - 18.6125i) q^{18} -79.9476 q^{19} -170.220 q^{20} +(66.0297 + 82.7987i) q^{21} +(50.3806 - 63.1753i) q^{22} +(-145.384 + 70.0132i) q^{23} +(-107.504 + 134.806i) q^{24} +(-4.60582 + 20.1794i) q^{25} +(129.286 + 162.119i) q^{26} +(-23.9072 - 104.744i) q^{27} +(223.873 - 107.812i) q^{28} +(13.3778 - 6.44241i) q^{29} +(212.655 + 266.661i) q^{30} +(-41.7920 + 20.1260i) q^{31} +(-78.4521 - 98.3758i) q^{32} -103.304 q^{33} +(309.558 + 149.075i) q^{34} +(-47.3268 - 207.352i) q^{35} +128.676 q^{36} +(20.3115 - 88.9905i) q^{37} +(338.635 - 163.078i) q^{38} +(58.9897 - 258.451i) q^{39} +(311.984 - 150.244i) q^{40} +(-130.044 - 163.071i) q^{41} +(-448.577 - 216.023i) q^{42} +(380.937 - 183.450i) q^{43} +(-53.9352 + 236.305i) q^{44} +(24.5083 - 107.378i) q^{45} +(472.991 - 593.112i) q^{46} +(23.1199 - 101.295i) q^{47} +(29.4935 - 129.219i) q^{48} +(-20.2832 - 25.4343i) q^{49} +(-21.6533 - 94.8693i) q^{50} +(-97.7435 - 428.242i) q^{51} +(-560.399 - 269.874i) q^{52} +(-121.306 + 152.113i) q^{53} +(314.922 + 394.900i) q^{54} +(186.920 + 90.0157i) q^{55} +(-315.162 + 395.200i) q^{56} +(-432.929 - 208.488i) q^{57} +(-43.5232 + 54.5764i) q^{58} +(684.028 - 329.411i) q^{59} +(-921.769 - 443.901i) q^{60} +(254.657 - 122.636i) q^{61} +(135.966 - 170.496i) q^{62} +(35.7762 + 156.746i) q^{63} +(691.916 + 333.209i) q^{64} +(-331.941 + 416.241i) q^{65} +(437.568 - 210.722i) q^{66} +(-70.4808 + 308.796i) q^{67} -1030.62 q^{68} -969.858 q^{69} +(623.422 + 781.746i) q^{70} +(-256.628 - 321.801i) q^{71} +(-235.841 + 113.575i) q^{72} +(-244.066 + 1069.32i) q^{73} +(95.4902 + 418.370i) q^{74} +(-77.5653 + 97.2638i) q^{75} +(-702.940 + 881.459i) q^{76} -302.849 q^{77} +(277.328 + 1215.05i) q^{78} +(31.0049 - 38.8789i) q^{79} +(-165.963 + 208.111i) q^{80} +(198.512 - 869.739i) q^{81} +(883.464 + 425.454i) q^{82} -672.320 q^{83} +1493.46 q^{84} +(-196.297 + 860.033i) q^{85} +(-1239.34 + 1554.08i) q^{86} +89.2435 q^{87} +(-109.720 - 480.713i) q^{88} +(-280.934 - 135.291i) q^{89} +(115.220 + 504.813i) q^{90} +(172.935 - 757.679i) q^{91} +(-506.362 + 2218.52i) q^{92} -278.795 q^{93} +(108.693 + 476.217i) q^{94} +(601.675 + 754.477i) q^{95} +(-168.286 - 737.308i) q^{96} +(108.743 + 136.359i) q^{97} +(137.795 + 66.3585i) q^{98} +(-141.300 - 68.0464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 294 q - 5 q^{2} - 5 q^{3} - 161 q^{4} - 5 q^{5} + 58 q^{6} + 15 q^{7} + 115 q^{8} - 446 q^{9} - 211 q^{10} + 93 q^{11} - 47 q^{12} + 23 q^{13} + 656 q^{14} + 343 q^{15} - 1505 q^{16} - 17 q^{17} + 132 q^{18}+ \cdots + 4526 q^{99}+O(q^{100}) \) 294 * q - 5 * q^2 - 5 * q^3 - 161 * q^4 - 5 * q^5 + 58 * q^6 + 15 * q^7 + 115 * q^8 - 446 * q^9 - 211 * q^10 + 93 * q^11 - 47 * q^12 + 23 * q^13 + 656 * q^14 + 343 * q^15 - 1505 * q^16 - 17 * q^17 + 132 * q^18 + 512 * q^19 + 148 * q^20 - 47 * q^21 - 845 * q^22 - 143 * q^23 + 775 * q^24 - 952 * q^25 + 39 * q^26 + 1159 * q^27 - 130 * q^28 - 169 * q^29 + 1048 * q^30 - 269 * q^31 - 39 * q^32 + 234 * q^33 + 761 * q^34 + 949 * q^35 + 15930 * q^36 + 715 * q^37 - 987 * q^38 - 417 * q^39 - 3303 * q^40 + 65 * q^41 - 2334 * q^42 + 581 * q^43 - 1751 * q^44 - 2497 * q^45 + 13 * q^46 - 361 * q^47 - 3995 * q^48 - 3728 * q^49 + 3671 * q^50 + 213 * q^51 + 4036 * q^52 - 47 * q^53 + 1358 * q^54 - 4339 * q^55 + 680 * q^56 - 2470 * q^57 + 1483 * q^58 - 3375 * q^59 + 1549 * q^60 + 805 * q^61 - 1149 * q^62 - 4839 * q^63 - 7061 * q^64 + 457 * q^65 + 1224 * q^66 + 2261 * q^67 + 1216 * q^68 - 4378 * q^69 + 1360 * q^70 - 1687 * q^71 + 936 * q^72 + 3075 * q^73 - 601 * q^74 + 3549 * q^75 - 5960 * q^76 - 4318 * q^77 - 11681 * q^78 + 2973 * q^79 - 1671 * q^80 - 4288 * q^81 + 2197 * q^82 + 9380 * q^83 - 7416 * q^84 - 5171 * q^85 - 3868 * q^86 + 1826 * q^87 - 3252 * q^88 - 79 * q^89 + 19791 * q^90 + 8303 * q^91 + 8077 * q^92 + 2118 * q^93 + 6319 * q^94 - 3280 * q^95 - 13752 * q^96 - 17 * q^97 - 4434 * q^98 + 4526 * q^99

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