LMFDB - Embedded newform 174.4.f.a.17.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [174,4,Mod(17,174)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(174, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("174.17"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 174 = 2 \cdot 3 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	174.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$10.2663323410$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.13
Character	$\chi$	$=$	174.17
Dual form			174.4.f.a.41.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41421 - 1.41421i) q^{2} +(5.06270 + 1.17009i) q^{3} +4.00000i q^{4} +15.7560 q^{5} +(-5.50498 - 8.81449i) q^{6} +15.8294 q^{7} +(5.65685 - 5.65685i) q^{8} +(24.2618 + 11.8476i) q^{9} +(-22.2824 - 22.2824i) q^{10} +(-34.5465 - 34.5465i) q^{11} +(-4.68035 + 20.2508i) q^{12} +63.8874i q^{13} +(-22.3862 - 22.3862i) q^{14} +(79.7680 + 18.4359i) q^{15} -16.0000 q^{16} +(29.1612 + 29.1612i) q^{17} +(-17.5563 - 51.0664i) q^{18} +(-42.1853 + 42.1853i) q^{19} +63.0241i q^{20} +(80.1395 + 18.5218i) q^{21} +97.7123i q^{22} -203.498i q^{23} +(35.2580 - 22.0199i) q^{24} +123.253 q^{25} +(90.3504 - 90.3504i) q^{26} +(108.967 + 88.3692i) q^{27} +63.3176i q^{28} +(-84.7806 + 131.154i) q^{29} +(-86.7367 - 138.881i) q^{30} +(-28.1059 + 28.1059i) q^{31} +(22.6274 + 22.6274i) q^{32} +(-134.476 - 215.321i) q^{33} -82.4805i q^{34} +249.409 q^{35} +(-47.3904 + 97.0472i) q^{36} +(-95.9844 - 95.9844i) q^{37} +119.318 q^{38} +(-74.7538 + 323.442i) q^{39} +(89.1296 - 89.1296i) q^{40} +(256.367 - 256.367i) q^{41} +(-87.1406 - 139.528i) q^{42} +(316.481 - 316.481i) q^{43} +(138.186 - 138.186i) q^{44} +(382.270 + 186.671i) q^{45} +(-287.790 + 287.790i) q^{46} +(213.077 - 213.077i) q^{47} +(-81.0031 - 18.7214i) q^{48} -92.4298 q^{49} +(-174.306 - 174.306i) q^{50} +(113.513 + 181.756i) q^{51} -255.549 q^{52} -59.8555i q^{53} +(-29.1302 - 279.076i) q^{54} +(-544.316 - 544.316i) q^{55} +(89.5447 - 89.5447i) q^{56} +(-262.932 + 164.211i) q^{57} +(305.377 - 65.5812i) q^{58} +721.957i q^{59} +(-73.7438 + 319.072i) q^{60} +(-541.445 + 541.445i) q^{61} +79.4956 q^{62} +(384.050 + 187.540i) q^{63} -64.0000i q^{64} +1006.61i q^{65} +(-114.332 + 494.688i) q^{66} +440.734i q^{67} +(-116.645 + 116.645i) q^{68} +(238.111 - 1030.25i) q^{69} +(-352.717 - 352.717i) q^{70} -1001.10 q^{71} +(204.266 - 70.2253i) q^{72} +(-444.626 - 444.626i) q^{73} +271.485i q^{74} +(623.991 + 144.216i) q^{75} +(-168.741 - 168.741i) q^{76} +(-546.851 - 546.851i) q^{77} +(563.134 - 351.699i) q^{78} +(310.904 - 310.904i) q^{79} -252.097 q^{80} +(448.269 + 574.888i) q^{81} -725.114 q^{82} +190.699i q^{83} +(-74.0872 + 320.558i) q^{84} +(459.466 + 459.466i) q^{85} -895.143 q^{86} +(-582.680 + 564.790i) q^{87} -390.849 q^{88} +(-1113.51 - 1113.51i) q^{89} +(-276.618 - 804.604i) q^{90} +1011.30i q^{91} +813.992 q^{92} +(-175.178 + 109.405i) q^{93} -602.674 q^{94} +(-664.673 + 664.673i) q^{95} +(88.0797 + 141.032i) q^{96} +(385.262 + 385.262i) q^{97} +(130.716 + 130.716i) q^{98} +(-428.867 - 1247.45i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 24 q^{10} + 88 q^{15} - 960 q^{16} + 48 q^{19} - 752 q^{21} + 64 q^{24} + 1500 q^{25} + 600 q^{27} + 312 q^{30} - 300 q^{31} - 224 q^{36} - 192 q^{37} - 172 q^{39} + 96 q^{40} + 888 q^{43} - 1532 q^{45}+ \cdots - 6000 q^{99}+O(q^{100}) $ 60 * q - 24 * q^10 + 88 * q^15 - 960 * q^16 + 48 * q^19 - 752 * q^21 + 64 * q^24 + 1500 * q^25 + 600 * q^27 + 312 * q^30 - 300 * q^31 - 224 * q^36 - 192 * q^37 - 172 * q^39 + 96 * q^40 + 888 * q^43 - 1532 * q^45 - 1104 * q^46 + 2292 * q^49 - 768 * q^52 - 1688 * q^54 + 2616 * q^55 - 1176 * q^58 - 352 * q^60 + 216 * q^61 + 192 * q^66 - 452 * q^69 + 192 * q^70 - 1668 * q^73 + 4840 * q^75 + 192 * q^76 - 1336 * q^78 + 3588 * q^79 - 280 * q^81 + 4224 * q^82 - 3008 * q^84 - 792 * q^85 - 4716 * q^87 - 800 * q^90 - 3072 * q^94 - 2916 * q^97 - 6000 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/174\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.41421	−	1.41421i	−0.500000	−	0.500000i
$2$	−1.41421	−	1.41421i	−0.500000	−	0.500000i
$3$	5.06270	+	1.17009i	0.974316	+	0.225183i
$3$	5.06270	+	1.17009i	0.974316	+	0.225183i
$4$			4.00000i			0.500000i
$5$	15.7560			1.40926			0.704631	−	0.709574i	$-0.251112\pi$
$5$	15.7560			1.40926			0.704631	+	0.709574i	$0.251112\pi$
$6$	−5.50498	−	8.81449i	−0.374566	−	0.599750i
$7$	15.8294			0.854708			0.427354	−	0.904084i	$-0.359446\pi$
$7$	15.8294			0.854708			0.427354	+	0.904084i	$0.359446\pi$
$8$	5.65685	−	5.65685i	0.250000	−	0.250000i
$9$	24.2618	+	11.8476i	0.898585	+	0.438800i
$10$	−22.2824	−	22.2824i	−0.704631	−	0.704631i
$11$	−34.5465	−	34.5465i	−0.946925	−	0.946925i	0.0517362	−	0.998661i	$-0.483525\pi$
$11$	−34.5465	−	34.5465i	−0.946925	−	0.946925i	−0.998661	+	0.0517362i	$0.983525\pi$
$12$	−4.68035	+	20.2508i	−0.112592	+	0.487158i
$13$			63.8874i			1.36301i	0.731812	+	0.681506i	$0.238675\pi$
$13$			63.8874i			1.36301i	−0.731812	+	0.681506i	$0.761325\pi$
$14$	−22.3862	−	22.3862i	−0.427354	−	0.427354i
$15$	79.7680	+	18.4359i	1.37307	+	0.317343i
$16$	−16.0000			−0.250000
$17$	29.1612	+	29.1612i	0.416038	+	0.416038i	0.883836	−	0.467798i	$-0.154952\pi$
$17$	29.1612	+	29.1612i	0.416038	+	0.416038i	−0.467798	+	0.883836i	$0.654952\pi$
$18$	−17.5563	−	51.0664i	−0.229892	−	0.668692i
$19$	−42.1853	+	42.1853i	−0.509367	+	0.509367i	−0.914332	−	0.404965i	$-0.867284\pi$
$19$	−42.1853	+	42.1853i	−0.509367	+	0.509367i	0.404965	+	0.914332i	$0.367284\pi$
$20$			63.0241i			0.704631i
$21$	80.1395	+	18.5218i	0.832756	+	0.192466i
$22$			97.7123i			0.946925i
$23$		−	203.498i		−	1.84488i	−0.386139	−	0.922441i	$-0.626191\pi$
$23$		−	203.498i		−	1.84488i	0.386139	−	0.922441i	$-0.373809\pi$
$24$	35.2580	−	22.0199i	0.299875	−	0.187283i
$25$	123.253			0.986021
$26$	90.3504	−	90.3504i	0.681506	−	0.681506i
$27$	108.967	+	88.3692i	0.776695	+	0.629876i
$28$			63.3176i			0.427354i
$29$	−84.7806	+	131.154i	−0.542875	+	0.839814i
$29$	−84.7806	+	131.154i	−0.542875	+	0.839814i
$30$	−86.7367	−	138.881i	−0.527862	−	0.845205i
$31$	−28.1059	+	28.1059i	−0.162838	+	0.162838i	−0.783823	−	0.620985i	$-0.786733\pi$
$31$	−28.1059	+	28.1059i	−0.162838	+	0.162838i	0.620985	+	0.783823i	$0.286733\pi$
$32$	22.6274	+	22.6274i	0.125000	+	0.125000i
$33$	−134.476	−	215.321i	−0.709372	−	1.13584i
$34$		−	82.4805i		−	0.416038i
$35$	249.409			1.20451
$36$	−47.3904	+	97.0472i	−0.219400	+	0.449292i
$37$	−95.9844	−	95.9844i	−0.426479	−	0.426479i	0.460948	−	0.887427i	$-0.347510\pi$
$37$	−95.9844	−	95.9844i	−0.426479	−	0.426479i	−0.887427	+	0.460948i	$0.847510\pi$
$38$	119.318			0.509367
$39$	−74.7538	+	323.442i	−0.306928	+	1.32801i
$40$	89.1296	−	89.1296i	0.352316	−	0.352316i
$41$	256.367	−	256.367i	0.976530	−	0.976530i	−0.0232006	−	0.999731i	$-0.507386\pi$
$41$	256.367	−	256.367i	0.976530	−	0.976530i	0.999731	+	0.0232006i	$0.00738565\pi$
$42$	−87.1406	−	139.528i	−0.320145	−	0.512611i
$43$	316.481	−	316.481i	1.12239	−	1.12239i	0.131011	−	0.991381i	$-0.458178\pi$
$43$	316.481	−	316.481i	1.12239	−	1.12239i	0.991381	−	0.131011i	$-0.0418223\pi$
$44$	138.186	−	138.186i	0.473462	−	0.473462i
$45$	382.270	+	186.671i	1.26634	+	0.618384i
$46$	−287.790	+	287.790i	−0.922441	+	0.922441i
$47$	213.077	−	213.077i	0.661288	−	0.661288i	−0.294396	−	0.955684i	$-0.595118\pi$
$47$	213.077	−	213.077i	0.661288	−	0.661288i	0.955684	+	0.294396i	$0.0951183\pi$
$48$	−81.0031	−	18.7214i	−0.243579	−	0.0562959i
$49$	−92.4298			−0.269475
$50$	−174.306	−	174.306i	−0.493010	−	0.493010i
$51$	113.513	+	181.756i	0.311668	+	0.499037i
$52$	−255.549			−0.681506
$53$		−	59.8555i		−	0.155128i	−0.996987	−	0.0775640i	$-0.975286\pi$
$53$		−	59.8555i		−	0.155128i	0.996987	−	0.0775640i	$-0.0247142\pi$
$54$	−29.1302	−	279.076i	−0.0734095	−	0.703286i
$55$	−544.316	−	544.316i	−1.33447	−	1.33447i
$56$	89.5447	−	89.5447i	0.213677	−	0.213677i
$57$	−262.932	+	164.211i	−0.610985	+	0.381583i
$58$	305.377	−	65.5812i	0.691344	−	0.148470i
$59$			721.957i			1.59306i	0.604597	+	0.796532i	$0.293334\pi$
$59$			721.957i			1.59306i	−0.604597	+	0.796532i	$0.706666\pi$
$60$	−73.7438	+	319.072i	−0.158671	+	0.686534i
$61$	−541.445	+	541.445i	−1.13647	+	1.13647i	−0.147397	+	0.989077i	$0.547090\pi$
$61$	−541.445	+	541.445i	−1.13647	+	1.13647i	−0.989077	+	0.147397i	$0.952910\pi$
$62$	79.4956			0.162838
$63$	384.050	+	187.540i	0.768027	+	0.375046i
$64$		−	64.0000i		−	0.125000i
$65$			1006.61i			1.92084i
$66$	−114.332	+	494.688i	−0.213232	+	0.922604i
$67$			440.734i			0.803644i	0.915718	+	0.401822i	$0.131623\pi$
$67$			440.734i			0.803644i	−0.915718	+	0.401822i	$0.868377\pi$
$68$	−116.645	+	116.645i	−0.208019	+	0.208019i
$69$	238.111	−	1030.25i	0.415437	−	1.79750i
$70$	−352.717	−	352.717i	−0.602254	−	0.602254i
$71$	−1001.10			−1.67336			−0.836682	−	0.547689i	$-0.815508\pi$
$71$	−1001.10			−1.67336			−0.836682	+	0.547689i	$0.815508\pi$
$72$	204.266	−	70.2253i	0.334346	−	0.114946i
$73$	−444.626	−	444.626i	−0.712870	−	0.712870i	0.254265	−	0.967135i	$-0.418167\pi$
$73$	−444.626	−	444.626i	−0.712870	−	0.712870i	−0.967135	+	0.254265i	$0.918167\pi$
$74$			271.485i			0.426479i
$75$	623.991	+	144.216i	0.960696	+	0.222036i
$76$	−168.741	−	168.741i	−0.254683	−	0.254683i
$77$	−546.851	−	546.851i	−0.809344	−	0.809344i
$78$	563.134	−	351.699i	0.817467	−	0.510539i
$79$	310.904	−	310.904i	0.442777	−	0.442777i	−0.450167	−	0.892944i	$-0.648636\pi$
$79$	310.904	−	310.904i	0.442777	−	0.442777i	0.892944	+	0.450167i	$0.148636\pi$
$80$	−252.097			−0.352316
$81$	448.269	+	574.888i	0.614909	+	0.788598i
$82$	−725.114			−0.976530
$83$			190.699i			0.252192i	0.992018	+	0.126096i	$0.0402447\pi$
$83$			190.699i			0.252192i	−0.992018	+	0.126096i	$0.959755\pi$
$84$	−74.0872	+	320.558i	−0.0962330	+	0.416378i
$85$	459.466	+	459.466i	0.586306	+	0.586306i
$86$	−895.143			−1.12239
$87$	−582.680	+	564.790i	−0.718044	+	0.695998i
$88$	−390.849			−0.473462
$89$	−1113.51	−	1113.51i	−1.32620	−	1.32620i	−0.908658	−	0.417542i	$-0.862892\pi$
$89$	−1113.51	−	1113.51i	−1.32620	−	1.32620i	−0.417542	−	0.908658i	$-0.637108\pi$
$90$	−276.618	−	804.604i	−0.323979	−	0.942363i
$91$			1011.30i			1.16498i
$92$	813.992			0.922441
$93$	−175.178	+	109.405i	−0.195324	+	0.121987i
$94$	−602.674			−0.661288
$95$	−664.673	+	664.673i	−0.717832	+	0.717832i
$96$	88.0797	+	141.032i	0.0936416	+	0.149937i
$97$	385.262	+	385.262i	0.403273	+	0.403273i	0.879385	−	0.476112i	$-0.157954\pi$
$97$	385.262	+	385.262i	0.403273	+	0.403273i	−0.476112	+	0.879385i	$0.657954\pi$
$98$	130.716	+	130.716i	0.134737	+	0.134737i
$99$	−428.867	−	1247.45i	−0.435382	−	1.26640i
$100$			493.010i			0.493010i
$101$	1.66851	+	1.66851i	0.00164379	+	0.00164379i	0.707928	−	0.706284i	$-0.249630\pi$
$101$	1.66851	+	1.66851i	0.00164379	+	0.00164379i	−0.706284	+	0.707928i	$0.749630\pi$
$102$	96.5094	−	417.574i	0.0936848	−	0.405352i
$103$	−719.844			−0.688625			−0.344313	−	0.938855i	$-0.611888\pi$
$103$	−719.844			−0.688625			−0.344313	+	0.938855i	$0.611888\pi$
$104$	361.401	+	361.401i	0.340753	+	0.340753i
$105$	1262.68	+	291.830i	1.17357	+	0.271235i
$106$	−84.6484	+	84.6484i	−0.0775640	+	0.0775640i
$107$		−	156.630i		−	0.141514i	−0.997494	−	0.0707572i	$-0.977458\pi$
$107$		−	156.630i		−	0.141514i	0.997494	−	0.0707572i	$-0.0225415\pi$
$108$	−353.477	+	435.869i	−0.314938	+	0.388348i
$109$		−	285.950i		−	0.251276i	−0.992076	−	0.125638i	$-0.959902\pi$
$109$		−	285.950i		−	0.251276i	0.992076	−	0.125638i	$-0.0400978\pi$
$110$			1539.56i			1.33447i
$111$	−373.630	−	598.250i	−0.319490	−	0.511562i
$112$	−253.271			−0.213677
$113$	127.641	−	127.641i	0.106261	−	0.106261i	−0.651978	−	0.758238i	$-0.726060\pi$
$113$	127.641	−	127.641i	0.106261	−	0.106261i	0.758238	+	0.651978i	$0.226060\pi$
$114$	604.071	+	139.613i	0.496284	+	0.114701i
$115$		−	3206.32i		−	2.59992i
$116$	−524.614	−	339.122i	−0.419907	−	0.271437i
$117$	−756.912	+	1550.02i	−0.598090	+	1.22478i
$118$	1021.00	−	1021.00i	0.796532	−	0.796532i
$119$	461.605	+	461.605i	0.355591	+	0.355591i
$120$	555.525	−	346.947i	0.422603	−	0.263931i
$121$			1055.93i			0.793332i
$122$	1531.44			1.13647
$123$	1597.88	−	997.935i	1.17135	−	0.731551i
$124$	−112.424	−	112.424i	−0.0814190	−	0.0814190i
$125$	−27.5321			−0.0197003
$126$	−277.906	−	808.351i	−0.196491	−	0.571536i
$127$	−241.918	+	241.918i	−0.169030	+	0.169030i	−0.786553	−	0.617523i	$-0.788136\pi$
$127$	−241.918	+	241.918i	−0.169030	+	0.169030i	0.617523	+	0.786553i	$0.288136\pi$
$128$	−90.5097	+	90.5097i	−0.0625000	+	0.0625000i
$129$	1972.56	−	1231.94i	1.34631	−	0.840821i
$130$	1423.56	−	1423.56i	0.960421	−	0.960421i
$131$	1083.86	−	1083.86i	0.722879	−	0.722879i	−0.246312	−	0.969191i	$-0.579219\pi$
$131$	1083.86	−	1083.86i	0.722879	−	0.722879i	0.969191	+	0.246312i	$0.0792188\pi$
$132$	861.284	−	537.905i	0.567918	−	0.354686i
$133$	−667.768	+	667.768i	−0.435360	+	0.435360i
$134$	623.291	−	623.291i	0.401822	−	0.401822i
$135$	1716.89	+	1392.35i	1.09457	+	0.887661i
$136$	329.922			0.208019
$137$	−292.426	−	292.426i	−0.182362	−	0.182362i	0.610022	−	0.792384i	$-0.291161\pi$
$137$	−292.426	−	292.426i	−0.182362	−	0.182362i	−0.792384	+	0.610022i	$0.791161\pi$
$138$	−1793.73	+	1120.25i	−1.10647	+	0.691031i
$139$	−521.328			−0.318119			−0.159059	−	0.987269i	$-0.550846\pi$
$139$	−521.328			−0.318119			−0.159059	+	0.987269i	$0.550846\pi$
$140$			997.635i			0.602254i
$141$	1328.07	−	829.427i	0.793215	−	0.495393i
$142$	1415.77	+	1415.77i	0.836682	+	0.836682i
$143$	2207.09	−	2207.09i	1.29067	−	1.29067i
$144$	−388.189	−	189.562i	−0.224646	−	0.109700i
$145$	−1335.81	+	2066.46i	−0.765053	+	1.18352i
$146$			1257.59i			0.712870i
$147$	−467.944	−	108.151i	−0.262554	−	0.0606813i
$148$	383.938	−	383.938i	0.213240	−	0.213240i
$149$	−8.44638			−0.00464399			−0.00232199	−	0.999997i	$-0.500739\pi$
$149$	−8.44638			−0.00464399			−0.00232199	+	0.999997i	$0.500739\pi$
$150$	−678.503	−	1086.41i	−0.369330	−	0.591366i
$151$			406.305i			0.218971i	0.993988	+	0.109486i	$0.0349203\pi$
$151$			406.305i			0.218971i	−0.993988	+	0.109486i	$0.965080\pi$
$152$			477.272i			0.254683i
$153$	362.013	+	1052.99i	0.191288	+	0.556402i
$154$			1546.73i			0.809344i
$155$	−442.838	+	442.838i	−0.229481	+	0.229481i
$156$	−1293.77	−	299.015i	−0.664003	−	0.153464i
$157$	137.354	+	137.354i	0.0698219	+	0.0698219i	0.741155	−	0.671333i	$-0.234278\pi$
$157$	137.354	+	137.354i	0.0698219	+	0.0698219i	−0.671333	+	0.741155i	$0.734278\pi$
$158$	−879.369			−0.442777
$159$	70.0361	−	303.030i	0.0349322	−	0.151144i
$160$	356.518	+	356.518i	0.176158	+	0.176158i
$161$		−	3221.25i		−	1.57683i
$162$	179.066	−	1446.96i	0.0868443	−	0.701754i
$163$	−772.318	−	772.318i	−0.371120	−	0.371120i	0.496765	−	0.867885i	$-0.334521\pi$
$163$	−772.318	−	772.318i	−0.371120	−	0.371120i	−0.867885	+	0.496765i	$0.834521\pi$
$164$	1025.47	+	1025.47i	0.488265	+	0.488265i
$165$	−2118.81	−	3392.61i	−0.999692	−	1.60069i
$166$	269.689	−	269.689i	0.126096	−	0.126096i
$167$	2992.32			1.38654			0.693271	−	0.720677i	$-0.256169\pi$
$167$	2992.32			1.38654			0.693271	+	0.720677i	$0.256169\pi$
$168$	558.112	−	348.562i	0.256305	−	0.160072i
$169$	−1884.59			−0.857803
$170$		−	1299.56i		−	0.586306i
$171$	−1523.28	+	523.696i	−0.681219	+	0.234199i
$172$	1265.92	+	1265.92i	0.561196	+	0.561196i
$173$	−3448.21			−1.51539			−0.757696	−	0.652608i	$-0.773675\pi$
$173$	−3448.21			−1.51539			−0.757696	+	0.652608i	$0.773675\pi$
$174$	1622.77	+	25.3000i	0.707021	+	0.0110229i
$175$	1951.02			0.842760
$176$	552.744	+	552.744i	0.236731	+	0.236731i
$177$	−844.753	+	3655.05i	−0.358732	+	1.55215i
$178$			3149.48i			1.32620i
$179$	−3489.39			−1.45703			−0.728516	−	0.685028i	$-0.759790\pi$
$179$	−3489.39			−1.45703			−0.728516	+	0.685028i	$0.759790\pi$
$180$	−746.685	+	1529.08i	−0.309192	+	0.633171i
$181$	832.300			0.341792			0.170896	−	0.985289i	$-0.445334\pi$
$181$	832.300			0.341792			0.170896	+	0.985289i	$0.445334\pi$
$182$	1430.19	−	1430.19i	0.582489	−	0.582489i
$183$	−3374.71	+	2107.63i	−1.36320	+	0.851371i
$184$	−1151.16	−	1151.16i	−0.461220	−	0.461220i
$185$	−1512.33	−	1512.33i	−0.601021	−	0.601021i
$186$	402.462	+	93.0169i	0.158656	+	0.0366684i
$187$		−	2014.84i		−	0.787913i
$188$	852.310	+	852.310i	0.330644	+	0.330644i
$189$	1724.89	+	1398.83i	0.663848	+	0.538360i
$190$	1879.98			0.717832
$191$	−1105.13	−	1105.13i	−0.418663	−	0.418663i	0.466080	−	0.884743i	$-0.345666\pi$
$191$	−1105.13	−	1105.13i	−0.418663	−	0.418663i	−0.884743	+	0.466080i	$0.845666\pi$
$192$	74.8856	−	324.013i	0.0281479	−	0.121790i
$193$	−1515.56	+	1515.56i	−0.565245	+	0.565245i	−0.930793	−	0.365547i	$-0.880882\pi$
$193$	−1515.56	+	1515.56i	−0.565245	+	0.565245i	0.365547	+	0.930793i	$0.380882\pi$
$194$		−	1089.69i		−	0.403273i
$195$	−1177.82	+	5096.17i	−0.432542	+	1.87151i
$196$		−	369.719i		−	0.134737i
$197$			3567.87i			1.29036i	0.764031	+	0.645179i	$0.223217\pi$
$197$			3567.87i			1.29036i	−0.764031	+	0.645179i	$0.776783\pi$
$198$	−1157.66	+	2370.68i	−0.415510	+	0.850892i
$199$	2782.56			0.991209			0.495604	−	0.868548i	$-0.334947\pi$
$199$	2782.56			0.991209			0.495604	+	0.868548i	$0.334947\pi$
$200$	697.222	−	697.222i	0.246505	−	0.246505i
$201$	−515.697	+	2231.30i	−0.180967	+	0.783004i
$202$		−	4.71927i		−	0.00164379i
$203$	−1342.03	+	2076.08i	−0.463999	+	0.717795i
$204$	−727.023	+	454.053i	−0.249519	+	0.155834i
$205$	4039.32	−	4039.32i	1.37619	−	1.37619i
$206$	1018.01	+	1018.01i	0.344313	+	0.344313i
$207$	2410.96	−	4937.23i	0.809534	−	1.65778i
$208$		−	1022.20i		−	0.340753i
$209$	2914.71			0.964664
$210$	−1372.99	−	2198.41i	−0.451168	−	0.722403i
$211$	−1730.56	−	1730.56i	−0.564629	−	0.564629i	0.365990	−	0.930619i	$-0.380730\pi$
$211$	−1730.56	−	1730.56i	−0.564629	−	0.564629i	−0.930619	+	0.365990i	$0.880730\pi$
$212$	239.422			0.0775640
$213$	−5068.27	−	1171.38i	−1.63039	−	0.376814i
$214$	−221.509	+	221.509i	−0.0707572	+	0.0707572i
$215$	4986.48	−	4986.48i	1.58174	−	1.58174i
$216$	1116.30	−	116.521i	0.351643	−	0.0367048i
$217$	−444.901	+	444.901i	−0.139179	+	0.139179i
$218$	−404.395	+	404.395i	−0.125638	+	0.125638i
$219$	−1730.75	−	2771.26i	−0.534034	−	0.855087i
$220$	2177.27	−	2177.27i	0.667233	−	0.667233i
$221$	−1863.03	+	1863.03i	−0.567065	+	0.567065i
$222$	−317.661	+	1374.45i	−0.0960361	+	0.415526i
$223$	5139.73			1.54342			0.771708	−	0.635977i	$-0.219403\pi$
$223$	5139.73			1.54342			0.771708	+	0.635977i	$0.219403\pi$
$224$	358.179	+	358.179i	0.106838	+	0.106838i
$225$	2990.33	+	1460.25i	0.886023	+	0.432666i
$226$	−361.023			−0.106261
$227$			2709.27i			0.792162i	0.918216	+	0.396081i	$0.129630\pi$
$227$			2709.27i			0.792162i	−0.918216	+	0.396081i	$0.870370\pi$
$228$	−656.843	−	1051.73i	−0.190792	−	0.305493i
$229$	−116.830	−	116.830i	−0.0337133	−	0.0337133i	0.690049	−	0.723762i	$-0.257589\pi$
$229$	−116.830	−	116.830i	−0.0337133	−	0.0337133i	−0.723762	+	0.690049i	$0.757589\pi$
$230$	−4534.42	+	4534.42i	−1.29996	+	1.29996i
$231$	−2128.68	−	3408.40i	−0.606306	−	0.970808i
$232$	262.325	+	1221.51i	0.0742348	+	0.345672i
$233$		−	519.051i		−	0.145941i	−0.997334	−	0.0729703i	$-0.976752\pi$
$233$		−	519.051i		−	0.145941i	0.997334	−	0.0729703i	$-0.0232478\pi$
$234$	3262.50	−	1121.63i	0.911436	−	0.313346i
$235$	3357.26	−	3357.26i	0.931929	−	0.931929i
$236$	−2887.83			−0.796532
$237$	1937.80	−	1210.23i	0.531111	−	0.331699i
$238$		−	1305.62i		−	0.355591i
$239$		−	2705.94i		−	0.732354i	−0.930545	−	0.366177i	$-0.880666\pi$
$239$		−	2705.94i		−	0.732354i	0.930545	−	0.366177i	$-0.119334\pi$
$240$	−1276.29	−	294.975i	−0.343267	−	0.0793357i
$241$			6462.05i			1.72721i	0.504170	+	0.863604i	$0.331798\pi$
$241$			6462.05i			1.72721i	−0.504170	+	0.863604i	$0.668202\pi$
$242$	1493.30	−	1493.30i	0.396666	−	0.396666i
$243$	1596.78	+	3435.00i	0.421537	+	0.906811i
$244$	−2165.78	−	2165.78i	−0.568237	−	0.568237i
$245$	−1456.33			−0.379761
$246$	−3671.03	−	848.447i	−0.951449	−	0.219898i
$247$	−2695.11	−	2695.11i	−0.694273	−	0.694273i
$248$			317.983i			0.0814190i
$249$	−223.134	+	965.450i	−0.0567894	+	0.245714i
$250$	38.9362	+	38.9362i	0.00985017	+	0.00985017i
$251$	−51.1710	−	51.1710i	−0.0128681	−	0.0128681i	0.700643	−	0.713512i	$-0.252896\pi$
$251$	−51.1710	−	51.1710i	−0.0128681	−	0.0128681i	−0.713512	+	0.700643i	$0.752896\pi$
$252$	−750.162	+	1536.20i	−0.187523	+	0.384014i
$253$	−7030.15	+	7030.15i	−1.74696	+	1.74696i
$254$	684.248			0.169030
$255$	1788.52	+	2863.75i	0.439221	+	0.703274i
$256$	256.000			0.0625000
$257$			690.565i			0.167612i	0.996482	+	0.0838060i	$0.0267076\pi$
$257$			690.565i			0.167612i	−0.996482	+	0.0838060i	$0.973292\pi$
$258$	−4531.83	−	1047.40i	−1.09356	−	0.252744i
$259$	−1519.38	−	1519.38i	−0.364515	−	0.364515i
$260$	−4026.45			−0.960421
$261$	−3610.78	+	2177.57i	−0.856329	+	0.516431i
$262$	−3065.61			−0.722879
$263$	−827.368	−	827.368i	−0.193984	−	0.193984i	0.603431	−	0.797415i	$-0.293800\pi$
$263$	−827.368	−	827.368i	−0.193984	−	0.193984i	−0.797415	+	0.603431i	$0.793800\pi$
$264$	−1978.75	−	457.328i	−0.461302	−	0.106616i
$265$		−	943.085i		−	0.218616i
$266$	1888.73			0.435360
$267$	−4334.46	−	6940.26i	−0.993500	−	1.59078i
$268$	−1762.93			−0.401822
$269$	−3485.31	+	3485.31i	−0.789974	+	0.789974i	−0.981490	−	0.191515i	$-0.938660\pi$
$269$	−3485.31	+	3485.31i	−0.789974	+	0.789974i	0.191515	+	0.981490i	$0.438660\pi$
$270$	−458.976	−	4397.13i	−0.103453	−	0.991114i
$271$	3916.95	+	3916.95i	0.877999	+	0.877999i	0.993327	−	0.115329i	$-0.0367922\pi$
$271$	3916.95	+	3916.95i	0.877999	+	0.877999i	−0.115329	+	0.993327i	$0.536792\pi$
$272$	−466.580	−	466.580i	−0.104009	−	0.104009i
$273$	−1183.31	+	5119.90i	−0.262334	+	1.13506i
$274$			827.106i			0.182362i
$275$	−4257.95	−	4257.95i	−0.933687	−	0.933687i
$276$	4121.00	+	952.442i	0.898749	+	0.207718i
$277$	9034.42			1.95966			0.979830	−	0.199835i	$-0.0640405\pi$
$277$	9034.42			1.95966			0.979830	+	0.199835i	$0.0640405\pi$
$278$	737.269	+	737.269i	0.159059	+	0.159059i
$279$	−1014.89	+	348.913i	−0.217777	+	0.0748704i
$280$	1410.87	−	1410.87i	0.301127	−	0.301127i
$281$			6674.92i			1.41706i	0.705683	+	0.708528i	$0.250640\pi$
$281$			6674.92i			1.41706i	−0.705683	+	0.708528i	$0.749360\pi$
$282$	−3051.16	−	705.182i	−0.644304	−	0.148911i
$283$		−	7526.04i		−	1.58084i	−0.612567	−	0.790418i	$-0.709863\pi$
$283$		−	7526.04i		−	1.58084i	0.612567	−	0.790418i	$-0.290137\pi$
$284$		−	4004.40i		−	0.836682i
$285$	−4142.76	+	2587.31i	−0.861039	+	0.537751i
$286$	−6242.58			−1.29067
$287$	4058.13	−	4058.13i	0.834648	−	0.834648i
$288$	280.901	+	817.062i	0.0574731	+	0.167173i
$289$		−	3212.24i		−	0.653825i
$290$	4811.53	−	1033.30i	0.974285	−	0.209233i
$291$	1499.67	+	2401.26i	0.302105	+	0.483725i
$292$	1778.50	−	1778.50i	0.356435	−	0.356435i
$293$	1480.87	+	1480.87i	0.295268	+	0.295268i	0.839157	−	0.543889i	$-0.183049\pi$
$293$	1480.87	+	1480.87i	0.295268	+	0.295268i	−0.543889	+	0.839157i	$0.683049\pi$
$294$	508.824	+	814.722i	0.100936	+	0.161617i
$295$			11375.2i			2.24504i
$296$	−1085.94			−0.213240
$297$	−711.594	−	6817.29i	−0.139027	−	1.33192i
$298$	11.9450	+	11.9450i	0.00232199	+	0.00232199i
$299$	13001.0			2.51460
$300$	−576.865	+	2495.96i	−0.111018	+	0.480348i
$301$	5009.70	−	5009.70i	0.959317	−	0.959317i
$302$	574.602	−	574.602i	0.109486	−	0.109486i
$303$	6.49487	+	10.3995i	0.00123142	+	0.00197173i
$304$	674.965	−	674.965i	0.127342	−	0.127342i
$305$	−8531.03	+	8531.03i	−1.60159	+	1.60159i
$306$	977.195	−	2001.12i	0.182557	−	0.373845i
$307$	3216.65	−	3216.65i	0.597994	−	0.597994i	−0.341784	−	0.939778i	$-0.611031\pi$
$307$	3216.65	−	3216.65i	0.597994	−	0.597994i	0.939778	+	0.341784i	$0.111031\pi$
$308$	2187.40	−	2187.40i	0.404672	−	0.404672i
$309$	−3644.35	−	842.281i	−0.670939	−	0.155067i
$310$	1252.54			0.229481
$311$	−2206.75	−	2206.75i	−0.402358	−	0.402358i	0.476705	−	0.879063i	$-0.341831\pi$
$311$	−2206.75	−	2206.75i	−0.402358	−	0.402358i	−0.879063	+	0.476705i	$0.841831\pi$
$312$	1406.79	+	2252.54i	0.255269	+	0.408733i
$313$	−4828.14			−0.871894			−0.435947	−	0.899972i	$-0.643586\pi$
$313$	−4828.14			−0.871894			−0.435947	+	0.899972i	$0.643586\pi$
$314$		−	388.496i		−	0.0698219i
$315$	6051.10	+	2954.89i	1.08235	+	0.528538i
$316$	1243.62	+	1243.62i	0.221389	+	0.221389i
$317$	625.136	−	625.136i	0.110761	−	0.110761i	−0.649554	−	0.760315i	$-0.725045\pi$
$317$	625.136	−	625.136i	0.110761	−	0.110761i	0.760315	+	0.649554i	$0.225045\pi$
$318$	−527.595	+	329.503i	−0.0930379	+	0.0581057i
$319$	7459.78	−	1602.02i	1.30930	−	0.281179i
$320$		−	1008.39i		−	0.176158i
$321$	183.271	−	792.972i	0.0318667	−	0.137880i
$322$	−4555.54	+	4555.54i	−0.788417	+	0.788417i
$323$	−2460.35			−0.423832
$324$	−2299.55	+	1793.08i	−0.394299	+	0.307455i
$325$			7874.28i			1.34396i
$326$			2184.44i			0.371120i
$327$	334.587	−	1447.68i	0.0565832	−	0.244822i
$328$		−	2900.46i		−	0.488265i
$329$	3372.89	−	3372.89i	0.565208	−	0.565208i
$330$	−1801.42	+	7794.32i	−0.300500	+	1.30019i
$331$	1065.41	+	1065.41i	0.176919	+	0.176919i	0.790011	−	0.613092i	$-0.210075\pi$
$331$	1065.41	+	1065.41i	0.176919	+	0.176919i	−0.613092	+	0.790011i	$0.710075\pi$
$332$	−762.795			−0.126096
$333$	−1191.57	−	3465.94i	−0.196089	−	0.570367i
$334$	−4231.78	−	4231.78i	−0.693271	−	0.693271i
$335$			6944.21i			1.13255i
$336$	−1282.23	−	296.349i	−0.208189	−	0.0481165i
$337$	1716.86	+	1716.86i	0.277517	+	0.277517i	0.832117	−	0.554600i	$-0.187129\pi$
$337$	1716.86	+	1716.86i	0.277517	+	0.277517i	−0.554600	+	0.832117i	$0.687129\pi$
$338$	2665.22	+	2665.22i	0.428902	+	0.428902i
$339$	795.559	−	496.857i	0.127460	−	0.0796034i
$340$	−1837.86	+	1837.86i	−0.293153	+	0.293153i
$341$	1941.93			0.308391
$342$	2894.87	+	1413.63i	0.457709	+	0.223510i
$343$	−6892.60			−1.08503
$344$		−	3580.57i		−	0.561196i
$345$	3751.68	−	16232.6i	0.585460	−	2.53315i
$346$	4876.51	+	4876.51i	0.757696	+	0.757696i
$347$	−4046.09			−0.625952			−0.312976	−	0.949761i	$-0.601326\pi$
$347$	−4046.09			−0.625952			−0.312976	+	0.949761i	$0.601326\pi$
$348$	−2259.16	−	2330.72i	−0.347999	−	0.359022i
$349$	11394.9			1.74772			0.873858	−	0.486182i	$-0.161611\pi$
$349$	11394.9			1.74772			0.873858	+	0.486182i	$0.161611\pi$
$350$	−2759.15	−	2759.15i	−0.421380	−	0.421380i
$351$	−5645.67	+	6961.64i	−0.858529	+	1.05865i
$352$		−	1563.40i		−	0.236731i
$353$	6741.35			1.01645			0.508224	−	0.861225i	$-0.330302\pi$
$353$	6741.35			1.01645			0.508224	+	0.861225i	$0.330302\pi$
$354$	6363.68	−	3974.36i	0.955440	−	0.596708i
$355$	−15773.4			−2.35821
$356$	4454.04	−	4454.04i	0.663100	−	0.663100i
$357$	1796.85	+	2877.09i	0.266385	+	0.426531i
$358$	4934.74	+	4934.74i	0.728516	+	0.728516i
$359$	7472.84	+	7472.84i	1.09861	+	1.09861i	0.994573	+	0.104038i	$0.0331763\pi$
$359$	7472.84	+	7472.84i	1.09861	+	1.09861i	0.104038	+	0.994573i	$0.466824\pi$
$360$	3218.41	−	1106.47i	0.471182	−	0.161989i
$361$			3299.80i			0.481091i
$362$	−1177.05	−	1177.05i	−0.170896	−	0.170896i
$363$	−1235.53	+	5345.83i	−0.178645	+	0.772957i
$364$	−4045.20			−0.582489
$365$	−7005.54	−	7005.54i	−1.00462	−	1.00462i
$366$	7753.21	+	1791.92i	1.10729	+	0.255915i
$367$	1472.34	−	1472.34i	0.209416	−	0.209416i	−0.594603	−	0.804019i	$-0.702691\pi$
$367$	1472.34	−	1472.34i	0.209416	−	0.209416i	0.804019	+	0.594603i	$0.202691\pi$
$368$			3255.97i			0.461220i
$369$	9257.24	−	3182.58i	1.30600	−	0.448994i
$370$			4277.53i			0.601021i
$371$		−	947.476i		−	0.132589i
$372$	−437.622	−	700.713i	−0.0609936	−	0.0976621i
$373$	4644.75			0.644762			0.322381	−	0.946610i	$-0.395517\pi$
$373$	4644.75			0.644762			0.322381	+	0.946610i	$0.395517\pi$
$374$	−2849.41	+	2849.41i	−0.393956	+	0.393956i
$375$	−139.386	−	32.2149i	−0.0191944	−	0.00443619i
$376$		−	2410.70i		−	0.330644i
$377$	−8379.05	−	5416.41i	−1.14468	−	0.739945i
$378$	−461.113	−	4417.61i	−0.0627437	−	0.601104i
$379$	−8048.30	+	8048.30i	−1.09080	+	1.09080i	−0.0953577	+	0.995443i	$0.530400\pi$
$379$	−8048.30	+	8048.30i	−1.09080	+	1.09080i	−0.995443	+	0.0953577i	$0.969600\pi$
$380$	−2658.69	−	2658.69i	−0.358916	−	0.358916i
$381$	−1507.82	+	941.694i	−0.202751	+	0.126626i
$382$			3125.79i			0.418663i
$383$	−6178.22			−0.824262			−0.412131	−	0.911125i	$-0.635215\pi$
$383$	−6178.22			−0.824262			−0.412131	+	0.911125i	$0.635215\pi$
$384$	−564.127	+	352.319i	−0.0749687	+	0.0468208i
$385$	−8616.20	−	8616.20i	−1.14058	−	1.14058i
$386$	4286.65			0.565245
$387$	11427.9	−	3928.85i	1.50107	−	0.516059i
$388$	−1541.05	+	1541.05i	−0.201636	+	0.201636i
$389$	−305.839	+	305.839i	−0.0398628	+	0.0398628i	−0.726757	−	0.686894i	$-0.758973\pi$
$389$	−305.839	+	305.839i	−0.0398628	+	0.0398628i	0.686894	+	0.726757i	$0.258973\pi$
$390$	8872.76	−	5541.38i	1.15203	−	0.719483i
$391$	5934.26	−	5934.26i	0.767540	−	0.767540i
$392$	−522.862	+	522.862i	−0.0673687	+	0.0673687i
$393$	6755.45	−	4219.04i	0.867093	−	0.541532i
$394$	5045.74	−	5045.74i	0.645179	−	0.645179i
$395$	4898.61	−	4898.61i	0.623990	−	0.623990i
$396$	4989.82	−	1715.47i	0.633201	−	0.217691i
$397$	11435.0			1.44561			0.722804	−	0.691053i	$-0.242853\pi$
$397$	11435.0			1.44561			0.722804	+	0.691053i	$0.242853\pi$
$398$	−3935.14	−	3935.14i	−0.495604	−	0.495604i
$399$	−4162.05	+	2599.36i	−0.522214	+	0.326142i
$400$	−1972.04			−0.246505
$401$		−	11572.9i		−	1.44120i	−0.693350	−	0.720601i	$-0.743866\pi$
$401$		−	11572.9i		−	1.44120i	0.693350	−	0.720601i	$-0.256134\pi$
$402$	3884.84	−	2426.23i	0.481986	−	0.301018i
$403$	−1795.61	−	1795.61i	−0.221950	−	0.221950i
$404$	−6.67405	+	6.67405i	−0.000821897	+	0.000821897i
$405$	7062.94	+	9057.95i	0.866569	+	1.11134i
$406$	4833.94	−	1038.11i	0.590897	−	0.126898i
$407$			6631.86i			0.807688i
$408$	1670.29	+	386.037i	0.202676	+	0.0468424i
$409$	7947.71	−	7947.71i	0.960853	−	0.960853i	−0.0384094	−	0.999262i	$-0.512229\pi$
$409$	7947.71	−	7947.71i	0.960853	−	0.960853i	0.999262	+	0.0384094i	$0.0122291\pi$
$410$	−11424.9			−1.37619
$411$	−1138.30	−	1822.63i	−0.136614	−	0.218744i
$412$		−	2879.38i		−	0.344313i
$413$			11428.1i			1.36160i
$414$	−10391.9	+	3572.68i	−1.23366	+	0.424124i
$415$			3004.66i			0.355404i
$416$	−1445.61	+	1445.61i	−0.170377	+	0.170377i
$417$	−2639.33	−	610.000i	−0.309948	−	0.0716351i
$418$	−4122.02	−	4122.02i	−0.482332	−	0.482332i
$419$	14877.8			1.73467			0.867337	−	0.497721i	$-0.165830\pi$
$419$	14877.8			1.73467			0.867337	+	0.497721i	$0.165830\pi$
$420$	−1167.32	+	5050.72i	−0.135618	+	0.586786i
$421$	−929.834	−	929.834i	−0.107642	−	0.107642i	0.651234	−	0.758877i	$-0.274251\pi$
$421$	−929.834	−	929.834i	−0.107642	−	0.107642i	−0.758877	+	0.651234i	$0.774251\pi$
$422$			4894.76i			0.564629i
$423$	7694.10	−	2645.18i	0.884397	−	0.304050i
$424$	−338.594	−	338.594i	−0.0387820	−	0.0387820i
$425$	3594.20	+	3594.20i	0.410222	+	0.410222i
$426$	5511.04	+	8824.19i	0.626786	+	1.00360i
$427$	−8570.76	+	8570.76i	−0.971354	+	0.971354i
$428$	626.522			0.0707572
$429$	13756.3	−	8591.32i	1.54816	−	0.966884i
$430$	−14103.9			−1.58174
$431$		−	9894.77i		−	1.10583i	−0.833236	−	0.552917i	$-0.813515\pi$
$431$		−	9894.77i		−	1.10583i	0.833236	−	0.552917i	$-0.186485\pi$
$432$	−1743.48	−	1413.91i	−0.194174	−	0.157469i
$433$	−7610.68	−	7610.68i	−0.844679	−	0.844679i	0.144784	−	0.989463i	$-0.453751\pi$
$433$	−7610.68	−	7610.68i	−0.844679	−	0.844679i	−0.989463	+	0.144784i	$0.953751\pi$
$434$	1258.37			0.139179
$435$	−9180.72	+	8898.85i	−1.01191	+	0.980844i
$436$	1143.80			0.125638
$437$	8584.62	+	8584.62i	0.939721	+	0.939721i
$438$	−1471.49	+	6366.80i	−0.160526	+	0.694561i
$439$			4406.25i			0.479041i	0.970891	+	0.239520i	$0.0769902\pi$
$439$			4406.25i			0.479041i	−0.970891	+	0.239520i	$0.923010\pi$
$440$	−6158.24			−0.667233
$441$	−2242.51	−	1095.07i	−0.242146	−	0.118245i
$442$	5269.46			0.567065
$443$	−6094.79	+	6094.79i	−0.653662	+	0.653662i	−0.953873	−	0.300211i	$-0.902943\pi$
$443$	−6094.79	+	6094.79i	−0.653662	+	0.653662i	0.300211	+	0.953873i	$0.402943\pi$
$444$	2393.00	−	1494.52i	0.255781	−	0.159745i
$445$	−17544.5	−	17544.5i	−1.86896	−	1.86896i
$446$	−7268.67	−	7268.67i	−0.771708	−	0.771708i
$447$	−42.7615	−	9.88300i	−0.00452471	−	0.00104575i
$448$		−	1013.08i		−	0.106838i
$449$	−3305.30	−	3305.30i	−0.347410	−	0.347410i	0.511734	−	0.859144i	$-0.329003\pi$
$449$	−3305.30	−	3305.30i	−0.347410	−	0.347410i	−0.859144	+	0.511734i	$0.829003\pi$
$450$	−2163.86	−	6294.06i	−0.226679	−	0.659345i
$451$	−17713.2			−1.84940
$452$	510.564	+	510.564i	0.0531304	+	0.0531304i
$453$	−475.412	+	2057.00i	−0.0493087	+	0.213347i
$454$	3831.49	−	3831.49i	0.396081	−	0.396081i
$455$			15934.1i			1.64176i
$456$	−558.450	+	2416.28i	−0.0573505	+	0.248142i
$457$			6262.39i			0.641011i	0.947247	+	0.320506i	$0.103853\pi$
$457$			6262.39i			0.641011i	−0.947247	+	0.320506i	$0.896147\pi$
$458$			330.445i			0.0337133i
$459$	600.667	+	5754.58i	0.0610823	+	0.585187i
$460$	12825.3			1.29996
$461$	11042.5	−	11042.5i	1.11562	−	1.11562i	0.123246	−	0.992376i	$-0.460670\pi$
$461$	11042.5	−	11042.5i	1.11562	−	1.11562i	0.992376	−	0.123246i	$-0.0393303\pi$
$462$	−1809.81	+	7830.62i	−0.182251	+	0.788557i
$463$			16393.4i			1.64550i	0.568407	+	0.822748i	$0.307560\pi$
$463$			16393.4i			1.64550i	−0.568407	+	0.822748i	$0.692440\pi$
$464$	1356.49	−	2098.46i	0.135719	−	0.209953i
$465$	−2760.12	+	1723.80i	−0.275263	+	0.171912i
$466$	−734.049	+	734.049i	−0.0729703	+	0.0729703i
$467$	4301.55	+	4301.55i	0.426236	+	0.426236i	0.887344	−	0.461108i	$-0.152548\pi$
$467$	4301.55	+	4301.55i	0.426236	+	0.426236i	−0.461108	+	0.887344i	$0.652548\pi$
$468$	−6200.09	−	3027.65i	−0.612391	−	0.299045i
$469$			6976.55i			0.686881i
$470$	−9495.75			−0.931929
$471$	534.665	+	856.098i	0.0523059	+	0.0837514i
$472$	4084.00	+	4084.00i	0.398266	+	0.398266i
$473$	−21866.6			−2.12564
$474$	−4451.98	−	1028.94i	−0.431405	−	0.0997062i
$475$	−5199.45	+	5199.45i	−0.502246	+	0.502246i
$476$	−1846.42	+	1846.42i	−0.177795	+	0.177795i
$477$	709.143	−	1452.20i	0.0680701	−	0.139396i
$478$	−3826.78	+	3826.78i	−0.366177	+	0.366177i
$479$	5678.46	−	5678.46i	0.541661	−	0.541661i	−0.382355	−	0.924016i	$-0.624887\pi$
$479$	5678.46	−	5678.46i	0.541661	−	0.541661i	0.924016	+	0.382355i	$0.124887\pi$
$480$	1387.79	+	2222.10i	0.131966	+	0.211301i
$481$	6132.19	−	6132.19i	0.581297	−	0.581297i
$482$	9138.72	−	9138.72i	0.863604	−	0.863604i
$483$	3769.15	−	16308.2i	0.355077	−	1.53634i
$484$	−4223.70			−0.396666
$485$	6070.20	+	6070.20i	0.568317	+	0.568317i
$486$	2599.63	−	7116.01i	0.242637	−	0.664174i
$487$	−9649.48			−0.897864			−0.448932	−	0.893566i	$-0.648195\pi$
$487$	−9649.48			−0.897864			−0.448932	+	0.893566i	$0.648195\pi$
$488$			6125.75i			0.568237i
$489$	−3006.33	−	4813.69i	−0.278018	−	0.445159i
$490$	2059.56	+	2059.56i	0.189880	+	0.189880i
$491$	11222.4	−	11222.4i	1.03149	−	1.03149i	0.0320000	−	0.999488i	$-0.489812\pi$
$491$	11222.4	−	11222.4i	1.03149	−	1.03149i	0.999488	−	0.0320000i	$-0.0101877\pi$
$492$	3991.74	+	6391.51i	0.365775	+	0.585674i
$493$	−6296.91	+	1352.29i	−0.575250	+	0.123538i
$494$			7622.91i			0.694273i
$495$	−6757.25	−	19654.9i	−0.613567	−	1.78469i
$496$	449.695	−	449.695i	0.0407095	−	0.0407095i
$497$	−15846.8			−1.43024
$498$	1680.91	−	1049.79i	0.151252	−	0.0944625i
$499$		−	13718.4i		−	1.23070i	−0.788253	−	0.615351i	$-0.789014\pi$
$499$		−	13718.4i		−	1.23070i	0.788253	−	0.615351i	$-0.210986\pi$
$500$		−	110.128i		−	0.00985017i
$501$	15149.2	+	3501.28i	1.35093	+	0.312226i
$502$			144.733i			0.0128681i
$503$	−9744.83	+	9744.83i	−0.863819	+	0.863819i	−0.991779	−	0.127961i	$-0.959157\pi$
$503$	−9744.83	+	9744.83i	−0.863819	+	0.863819i	0.127961	+	0.991779i	$0.459157\pi$
$504$	3233.40	−	1111.62i	0.285768	−	0.0982454i
$505$	26.2891	+	26.2891i	0.00231654	+	0.00231654i
$506$	19884.3			1.74696
$507$	−9541.13	−	2205.14i	−0.835772	−	0.193163i
$508$	−967.673	−	967.673i	−0.0845149	−	0.0845149i
$509$			3483.49i			0.303345i	0.988431	+	0.151673i	$0.0484660\pi$
$509$			3483.49i			0.303345i	−0.988431	+	0.151673i	$0.951534\pi$
$510$	1520.60	−	6579.30i	0.132026	−	0.571248i
$511$	−7038.16	−	7038.16i	−0.609295	−	0.609295i
$512$	−362.039	−	362.039i	−0.0312500	−	0.0312500i
$513$	−8324.70	+	868.939i	−0.716461	+	0.0747848i
$514$	976.607	−	976.607i	0.0838060	−	0.0838060i
$515$	−11341.9			−0.970453
$516$	4927.74	+	7890.22i	0.420410	+	0.673154i
$517$	−14722.2			−1.25238
$518$			4297.45i			0.364515i
$519$	−17457.2	−	4034.71i	−1.47647	−	0.341241i
$520$	5694.25	+	5694.25i	0.480211	+	0.480211i
$521$	2368.28			0.199148			0.0995742	−	0.995030i	$-0.468252\pi$
$521$	2368.28			0.199148			0.0995742	+	0.995030i	$0.468252\pi$
$522$	8185.97	+	2026.87i	0.686380	+	0.169949i
$523$	9106.60			0.761384			0.380692	−	0.924702i	$-0.375686\pi$
$523$	9106.60			0.761384			0.380692	+	0.924702i	$0.375686\pi$
$524$	4335.43	+	4335.43i	0.361439	+	0.361439i
$525$	9877.40	+	2282.86i	0.821114	+	0.189776i
$526$			2340.15i			0.193984i
$527$	−1639.21			−0.135493
$528$	2151.62	+	3445.14i	0.177343	+	0.283959i
$529$	−29244.5			−2.40359
$530$	−1333.72	+	1333.72i	−0.109308	+	0.109308i
$531$	−8553.45	+	17516.0i	−0.699036	+	1.43150i
$532$	−2671.07	−	2671.07i	−0.217680	−	0.217680i
$533$	16378.6	+	16378.6i	1.33102	+	1.33102i
$534$	−3685.17	+	15944.9i	−0.298638	+	1.29214i
$535$		−	2467.87i		−	0.199431i
$536$	2493.17	+	2493.17i	0.200911	+	0.200911i
$537$	−17665.7	−	4082.89i	−1.41961	−	0.328100i
$538$	9857.95			0.789974
$539$	3193.13	+	3193.13i	0.255172	+	0.255172i
$540$	−5569.39	+	6867.57i	−0.443831	+	0.547284i
$541$	14412.0	−	14412.0i	1.14532	−	1.14532i	0.157861	−	0.987461i	$-0.449540\pi$
$541$	14412.0	−	14412.0i	1.14532	−	1.14532i	0.987461	−	0.157861i	$-0.0504598\pi$
$542$		−	11078.8i		−	0.877999i
$543$	4213.68	+	973.864i	0.333014	+	0.0769660i
$544$			1319.69i			0.104009i
$545$		−	4505.44i		−	0.354114i
$546$	8914.08	−	5567.18i	0.698695	−	0.436361i
$547$	6306.06			0.492920			0.246460	−	0.969153i	$-0.420733\pi$
$547$	6306.06			0.492920			0.246460	+	0.969153i	$0.420733\pi$
$548$	1169.71	−	1169.71i	0.0911812	−	0.0911812i
$549$	−19551.3	+	6721.60i	−1.51990	+	0.522534i
$550$			12043.3i			0.933687i
$551$	−1956.26	−	9109.24i	−0.151251	−	0.704296i
$552$	−4481.01	−	7174.92i	−0.345515	−	0.553234i
$553$	4921.42	−	4921.42i	0.378445	−	0.378445i
$554$	−12776.6	−	12776.6i	−0.979830	−	0.979830i
$555$	−5886.92	−	9426.05i	−0.450245	−	0.720925i
$556$		−	2085.31i		−	0.159059i
$557$	3114.66			0.236934			0.118467	−	0.992958i	$-0.462202\pi$
$557$	3114.66			0.236934			0.118467	+	0.992958i	$0.462202\pi$
$558$	1928.71	+	941.832i	0.146324	+	0.0714533i
$559$	20219.1	+	20219.1i	1.52983	+	1.52983i
$560$	−3990.54			−0.301127
$561$	2357.54	−	10200.5i	0.177425	−	0.767676i
$562$	9439.77	−	9439.77i	0.708528	−	0.708528i
$563$	−3327.41	+	3327.41i	−0.249083	+	0.249083i	−0.820594	−	0.571511i	$-0.806357\pi$
$563$	−3327.41	+	3327.41i	−0.249083	+	0.249083i	0.571511	+	0.820594i	$0.306357\pi$
$564$	3317.71	+	5312.26i	0.247696	+	0.396608i
$565$	2011.12	−	2011.12i	0.149749	−	0.149749i
$566$	−10643.4	+	10643.4i	−0.790418	+	0.790418i
$567$	7095.83	+	9100.13i	0.525568	+	0.674021i
$568$	−5663.08	+	5663.08i	−0.418341	+	0.418341i
$569$	8542.39	−	8542.39i	0.629377	−	0.629377i	−0.318534	−	0.947911i	$-0.603191\pi$
$569$	8542.39	−	8542.39i	0.629377	−	0.629377i	0.947911	+	0.318534i	$0.103191\pi$
$570$	9517.76	+	2199.74i	0.699395	+	0.161644i
$571$	−367.898			−0.0269633			−0.0134817	−	0.999909i	$-0.504291\pi$
$571$	−367.898			−0.0269633			−0.0134817	+	0.999909i	$0.504291\pi$
$572$	8828.35	+	8828.35i	0.645335	+	0.645335i
$573$	−4301.85	−	6888.06i	−0.313634	−	0.502186i
$574$	−11478.1			−0.834648
$575$		−	25081.7i		−	1.81909i
$576$	758.246	−	1552.75i	0.0548500	−	0.112323i
$577$	1122.03	+	1122.03i	0.0809544	+	0.0809544i	0.746425	−	0.665470i	$-0.231769\pi$
$577$	1122.03	+	1122.03i	0.0809544	+	0.0809544i	−0.665470	+	0.746425i	$0.731769\pi$
$578$	−4542.80	+	4542.80i	−0.326913	+	0.326913i
$579$	−9446.15	+	5899.48i	−0.678012	+	0.423444i
$580$	−8265.84	−	5343.22i	−0.591759	−	0.382526i
$581$			3018.65i			0.215550i
$582$	1275.03	−	5516.75i	0.0908103	−	0.392915i
$583$	−2067.80	+	2067.80i	−0.146894	+	0.146894i
$584$	−5030.36			−0.356435
$585$	−11925.9	+	24422.2i	−0.842865	+	1.72604i
$586$		−	4188.54i		−	0.295268i
$587$		−	20052.3i		−	1.40996i	−0.709227	−	0.704980i	$-0.750956\pi$
$587$		−	20052.3i		−	1.40996i	0.709227	−	0.704980i	$-0.249044\pi$
$588$	432.604	−	1871.78i	0.0303406	−	0.131277i
$589$		−	2371.32i		−	0.165889i
$590$	16086.9	−	16086.9i	1.12252	−	1.12252i
$591$	−4174.73	+	18063.1i	−0.290567	+	1.25722i
$592$	1535.75	+	1535.75i	0.106620	+	0.106620i
$593$	11309.6			0.783185			0.391592	−	0.920139i	$-0.371924\pi$
$593$	11309.6			0.783185			0.391592	+	0.920139i	$0.371924\pi$
$594$	−8634.76	+	10647.5i	−0.596445	+	0.735472i
$595$	7273.07	+	7273.07i	0.501121	+	0.501121i
$596$		−	33.7855i		−	0.00232199i
$597$	14087.3	+	3255.84i	0.965751	+	0.223204i
$598$	−18386.1	−	18386.1i	−1.25730	−	1.25730i
$599$	−272.130	−	272.130i	−0.0185625	−	0.0185625i	0.697765	−	0.716327i	$-0.254178\pi$
$599$	−272.130	−	272.130i	−0.0185625	−	0.0185625i	−0.716327	+	0.697765i	$0.754178\pi$
$600$	4345.63	−	2714.01i	0.295683	−	0.184665i
$601$	−4879.02	+	4879.02i	−0.331147	+	0.331147i	−0.853022	−	0.521875i	$-0.825233\pi$
$601$	−4879.02	+	4879.02i	−0.331147	+	0.331147i	0.521875	+	0.853022i	$0.325233\pi$
$602$	−14169.6			−0.959317
$603$	−5221.63	+	10693.0i	−0.352639	+	0.722143i
$604$	−1625.22			−0.109486
$605$			16637.2i			1.11801i
$606$	5.52195	−	23.8922i	0.000370155	−	0.00160158i
$607$	−6436.61	−	6436.61i	−0.430402	−	0.430402i	0.458363	−	0.888765i	$-0.348436\pi$
$607$	−6436.61	−	6436.61i	−0.430402	−	0.430402i	−0.888765	+	0.458363i	$0.848436\pi$
$608$	−1909.09			−0.127342
$609$	−9223.47	+	8940.29i	−0.613718	+	0.594875i
$610$	24129.4			1.60159
$611$	13613.0	+	13613.0i	0.901344	+	0.901344i
$612$	−4211.98	+	1448.05i	−0.278201	+	0.0956439i
$613$			28676.9i			1.88948i	0.327827	+	0.944738i	$0.393684\pi$
$613$			28676.9i			1.88948i	−0.327827	+	0.944738i	$0.606316\pi$
$614$	−9098.07			−0.597994
$615$	25176.2	−	15723.5i	1.65074	−	1.03095i
$616$	−6186.91			−0.404672
$617$	−11787.2	+	11787.2i	−0.769101	+	0.769101i	−0.977948	−	0.208847i	$-0.933029\pi$
$617$	−11787.2	+	11787.2i	−0.769101	+	0.769101i	0.208847	+	0.977948i	$0.433029\pi$
$618$	3962.73	+	6345.06i	0.257936	+	0.413003i
$619$	8372.80	+	8372.80i	0.543670	+	0.543670i	0.924603	−	0.380933i	$-0.124397\pi$
$619$	8372.80	+	8372.80i	0.543670	+	0.543670i	−0.380933	+	0.924603i	$0.624397\pi$
$620$	−1771.35	−	1771.35i	−0.114741	−	0.114741i
$621$	17983.0	−	22174.6i	1.16205	−	1.43291i
$622$			6241.63i			0.402358i
$623$	−17626.2	−	17626.2i	−1.13351	−	1.13351i
$624$	1196.06	−	5175.08i	0.0767320	−	0.332001i
$625$	−15840.4			−1.01378
$626$	6828.03	+	6828.03i	0.435947	+	0.435947i
$627$	14756.3	+	3410.47i	0.939888	+	0.217226i
$628$	−549.416	+	549.416i	−0.0349110	+	0.0349110i
$629$		−	5598.05i		−	0.354863i
$630$	−4378.70	−	12736.4i	−0.276907	−	0.805445i
$631$			13809.1i			0.871208i	0.900139	+	0.435604i	$0.143465\pi$
$631$			13809.1i			0.871208i	−0.900139	+	0.435604i	$0.856535\pi$
$632$		−	3517.48i		−	0.221389i
$633$	−6736.39	−	10786.2i	−0.422982	−	0.677272i
$634$	−1768.15			−0.110761
$635$	−3811.67	+	3811.67i	−0.238207	+	0.238207i
$636$	1212.12	+	280.145i	0.0755718	+	0.0174661i
$637$		−	5905.10i		−	0.367298i
$638$	−12815.3	−	8284.11i	−0.795240	−	0.514061i
$639$	−24288.5	−	11860.6i	−1.50366	−	0.734272i
$640$	−1426.07	+	1426.07i	−0.0880789	+	0.0880789i
$641$	4606.16	+	4606.16i	0.283826	+	0.283826i	0.834633	−	0.550807i	$-0.185680\pi$
$641$	4606.16	+	4606.16i	0.283826	+	0.283826i	−0.550807	+	0.834633i	$0.685680\pi$
$642$	−1380.62	+	862.247i	−0.0848732	+	0.0530065i
$643$		−	18074.2i		−	1.10852i	−0.832345	−	0.554258i	$-0.813002\pi$
$643$		−	18074.2i		−	1.10852i	0.832345	−	0.554258i	$-0.186998\pi$
$644$	12885.0			0.788417
$645$	31079.7	−	19410.4i	1.89730	−	1.18494i
$646$	3479.46	+	3479.46i	0.211916	+	0.211916i
$647$	4761.60			0.289332			0.144666	−	0.989481i	$-0.453789\pi$
$647$	4761.60			0.289332			0.144666	+	0.989481i	$0.453789\pi$
$648$	5787.85	+	716.265i	0.350877	+	0.0434221i
$649$	24941.1	−	24941.1i	1.50851	−	1.50851i
$650$	11135.9	−	11135.9i	0.671979	−	0.671979i
$651$	−2772.97	+	1731.82i	−0.166945	+	0.104263i
$652$	3089.27	−	3089.27i	0.185560	−	0.185560i
$653$	1332.45	−	1332.45i	0.0798512	−	0.0798512i	−0.666053	−	0.745904i	$-0.732018\pi$
$653$	1332.45	−	1332.45i	0.0798512	−	0.0798512i	0.745904	+	0.666053i	$0.232018\pi$
$654$	−2520.51	+	1574.15i	−0.150703	+	0.0941195i
$655$	17077.3	−	17077.3i	1.01873	−	1.01873i
$656$	−4101.87	+	4101.87i	−0.244133	+	0.244133i
$657$	−5519.67	−	16055.2i	−0.327767	−	0.953381i
$658$	−9539.97			−0.565208
$659$	−6743.81	−	6743.81i	−0.398636	−	0.398636i	0.479115	−	0.877752i	$-0.340958\pi$
$659$	−6743.81	−	6743.81i	−0.398636	−	0.398636i	−0.877752	+	0.479115i	$0.840958\pi$
$660$	13570.4	−	8475.24i	0.800346	−	0.499846i
$661$	7758.25			0.456522			0.228261	−	0.973600i	$-0.426696\pi$
$661$	7758.25			0.456522			0.228261	+	0.973600i	$0.426696\pi$
$662$		−	3013.44i		−	0.176919i
$663$	−11611.9	+	7252.07i	−0.680194	+	0.424807i
$664$	1078.75	+	1078.75i	0.0630479	+	0.0630479i
$665$	−10521.4	+	10521.4i	−0.613536	+	0.613536i
$666$	−3216.44	+	6586.71i	−0.187139	+	0.383228i
$667$	26689.5	+	17252.7i	1.54936	+	1.00154i
$668$			11969.3i			0.693271i
$669$	26020.9	+	6013.93i	1.50378	+	0.347552i
$670$	9820.60	−	9820.60i	0.566273	−	0.566273i
$671$	37410.1			2.15231
$672$	1394.25	+	2232.45i	0.0800362	+	0.128153i
$673$			576.439i			0.0330165i	0.999864	+	0.0165082i	$0.00525498\pi$
$673$			576.439i			0.0330165i	−0.999864	+	0.0165082i	$0.994745\pi$
$674$		−	4856.00i		−	0.277517i
$675$	13430.5	+	10891.7i	0.765838	+	0.621071i
$676$		−	7538.38i		−	0.428902i
$677$	−16837.8	+	16837.8i	−0.955876	+	0.955876i	−0.999067	−	0.0431909i	$-0.986248\pi$
$677$	−16837.8	+	16837.8i	−0.955876	+	0.955876i	0.0431909	+	0.999067i	$0.486248\pi$
$678$	−1827.75	−	422.429i	−0.103532	−	0.0239282i
$679$	6098.47	+	6098.47i	0.344680	+	0.344680i
$680$	5198.26			0.293153
$681$	−3170.09	+	13716.2i	−0.178382	+	0.771816i
$682$	−2746.30	−	2746.30i	−0.154195	−	0.154195i
$683$		−	27769.5i		−	1.55574i	−0.628424	−	0.777871i	$-0.716300\pi$
$683$		−	27769.5i		−	1.55574i	0.628424	−	0.777871i	$-0.283700\pi$
$684$	−2094.79	−	6093.14i	−0.117100	−	0.340610i
$685$	−4607.48	−	4607.48i	−0.256997	−	0.256997i
$686$	9747.60	+	9747.60i	0.542515	+	0.542515i
$687$	−454.773	−	728.176i	−0.0252557	−	0.0404391i
$688$	−5063.69	+	5063.69i	−0.280598	+	0.280598i
$689$	3824.01			0.211441
$690$	−28262.1	+	17650.7i	−1.55930	+	0.973844i
$691$	−7657.03			−0.421544			−0.210772	−	0.977535i	$-0.567598\pi$
$691$	−7657.03			−0.421544			−0.210772	+	0.977535i	$0.567598\pi$
$692$		−	13792.8i		−	0.757696i
$693$	−6788.72	−	19746.5i	−0.372124	−	1.08240i
$694$	5722.03	+	5722.03i	0.312976	+	0.312976i
$695$	−8214.07			−0.448313
$696$	−101.200	+	6491.07i	−0.00551145	+	0.353510i
$697$	14951.9			0.812547
$698$	−16114.8	−	16114.8i	−0.873858	−	0.873858i
$699$	607.335	−	2627.80i	0.0328634	−	0.142192i
$700$			7804.06i			0.421380i
$701$	27473.0			1.48023			0.740114	−	0.672481i	$-0.234771\pi$
$701$	27473.0			1.48023			0.740114	+	0.672481i	$0.234771\pi$
$702$	17829.4	−	1861.05i	0.958588	−	0.100058i
$703$	8098.26			0.434469
$704$	−2210.98	+	2210.98i	−0.118366	+	0.118366i
$705$	20925.1	−	13068.5i	1.11785	−	0.698138i
$706$	−9533.71	−	9533.71i	−0.508224	−	0.508224i
$707$	26.4116	+	26.4116i	0.00140496	+	0.00140496i
$708$	−14620.2	−	3379.01i	−0.776074	−	0.179366i
$709$			20013.9i			1.06014i	0.847955	+	0.530068i	$0.177834\pi$
$709$			20013.9i			1.06014i	−0.847955	+	0.530068i	$0.822166\pi$
$710$	22306.9	+	22306.9i	1.17910	+	1.17910i
$711$	11226.5	−	3859.62i	0.592164	−	0.203582i
$712$	−12597.9			−0.663100
$713$	5719.51	+	5719.51i	0.300417	+	0.300417i
$714$	1527.69	−	6609.94i	0.0800731	−	0.346458i
$715$	34774.9	−	34774.9i	1.81889	−	1.81889i
$716$		−	13957.5i		−	0.728516i
$717$	3166.19	−	13699.3i	0.164914	−	0.713545i
$718$		−	21136.4i		−	1.09861i
$719$		−	9112.14i		−	0.472636i	−0.971676	−	0.236318i	$-0.924059\pi$
$719$		−	9112.14i		−	0.472636i	0.971676	−	0.236318i	$-0.0759407\pi$
$720$	−6116.31	−	2986.74i	−0.316585	−	0.154596i
$721$	−11394.7			−0.588573
$722$	4666.63	−	4666.63i	0.240545	−	0.240545i
$723$	−7561.17	+	32715.4i	−0.388939	+	1.68285i
$724$			3329.20i			0.170896i
$725$	−10449.4	+	16165.0i	−0.535286	+	0.828074i
$726$	9307.44	−	5812.85i	0.475801	−	0.297156i
$727$	−4344.61	+	4344.61i	−0.221640	+	0.221640i	−0.809189	−	0.587549i	$-0.800093\pi$
$727$	−4344.61	+	4344.61i	−0.221640	+	0.221640i	0.587549	+	0.809189i	$0.300093\pi$
$728$	5720.77	+	5720.77i	0.291244	+	0.291244i
$729$	4064.77	+	19258.7i	0.206512	+	0.978444i
$730$			19814.7i			1.00462i
$731$	18457.9			0.933915
$732$	−8430.54	−	13498.8i	−0.425685	−	0.681601i
$733$	12615.9	+	12615.9i	0.635716	+	0.635716i	0.949496	−	0.313780i	$-0.101595\pi$
$733$	12615.9	+	12615.9i	0.635716	+	0.635716i	−0.313780	+	0.949496i	$0.601595\pi$
$734$	−4164.42			−0.209416
$735$	−7372.95	−	1704.03i	−0.370007	−	0.0855158i
$736$	4604.64	−	4604.64i	0.230610	−	0.230610i
$737$	15225.8	−	15225.8i	0.760991	−	0.760991i
$738$	−17592.6	−	8590.86i	−0.877495	−	0.428501i
$739$	−22751.0	+	22751.0i	−1.13249	+	1.13249i	−0.142725	+	0.989762i	$0.545586\pi$
$739$	−22751.0	+	22751.0i	−1.13249	+	1.13249i	−0.989762	+	0.142725i	$0.954414\pi$
$740$	6049.33	−	6049.33i	0.300511	−	0.300511i
$741$	−10491.0	−	16798.0i	−0.520103	−	0.832781i
$742$	−1339.93	+	1339.93i	−0.0662945	+	0.0662945i
$743$	−25472.2	+	25472.2i	−1.25772	+	1.25772i	−0.305541	+	0.952179i	$0.598837\pi$
$743$	−25472.2	+	25472.2i	−1.25772	+	1.25772i	−0.952179	+	0.305541i	$0.901163\pi$
$744$	−372.067	+	1609.85i	−0.0183342	+	0.0793279i
$745$	−133.081			−0.00654460
$746$	−6568.67	−	6568.67i	−0.322381	−	0.322381i
$747$	−2259.32	+	4626.69i	−0.110662	+	0.226616i
$748$	8059.36			0.393956
$749$		−	2479.37i		−	0.120953i
$750$	151.563	+	242.681i	0.00737908	+	0.0118153i
$751$	−10634.2	−	10634.2i	−0.516707	−	0.516707i	0.399867	−	0.916573i	$-0.369056\pi$
$751$	−10634.2	−	10634.2i	−0.516707	−	0.516707i	−0.916573	+	0.399867i	$0.869056\pi$
$752$	−3409.24	+	3409.24i	−0.165322	+	0.165322i
$753$	−199.189	−	318.938i	−0.00963989	−	0.0154352i
$754$	4189.81	+	19509.7i	0.202366	+	0.942311i
$755$			6401.75i			0.308588i
$756$	−5595.33	+	6899.55i	−0.269180	+	0.331924i
$757$	−1529.77	+	1529.77i	−0.0734485	+	0.0734485i	−0.742877	−	0.669428i	$-0.766539\pi$
$757$	−1529.77	+	1529.77i	−0.0734485	+	0.0734485i	0.669428	+	0.742877i	$0.266539\pi$
$758$	22764.0			1.09080
$759$	−43817.4	+	27365.6i	−2.09548	+	1.30871i
$760$			7519.92i			0.358916i
$761$		−	18885.3i		−	0.899594i	−0.893131	−	0.449797i	$-0.851496\pi$
$761$		−	18885.3i		−	0.899594i	0.893131	−	0.449797i	$-0.148504\pi$
$762$	3464.14	+	800.631i	0.164688	+	0.0380627i
$763$		−	4526.42i		−	0.214767i
$764$	4420.53	−	4420.53i	0.209331	−	0.209331i
$765$	5703.89	+	16591.0i	0.269575	+	0.784117i
$766$	8737.33	+	8737.33i	0.412131	+	0.412131i
$767$	−46123.9			−2.17137
$768$	1296.05	+	299.542i	0.0608948	+	0.0140740i
$769$	26440.6	+	26440.6i	1.23989	+	1.23989i	0.960047	+	0.279840i	$0.0902814\pi$
$769$	26440.6	+	26440.6i	1.23989	+	1.23989i	0.279840	+	0.960047i	$0.409719\pi$
$770$			24370.3i			1.14058i
$771$	−808.022	+	3496.12i	−0.0377435	+	0.163307i
$772$	−6062.24	−	6062.24i	−0.282623	−	0.282623i
$773$	−4598.80	−	4598.80i	−0.213981	−	0.213981i	0.591975	−	0.805956i	$-0.298348\pi$
$773$	−4598.80	−	4598.80i	−0.213981	−	0.213981i	−0.805956	+	0.591975i	$0.798348\pi$
$774$	−21717.8	−	10605.3i	−1.00856	−	0.492505i
$775$	−3464.13	+	3464.13i	−0.160562	+	0.160562i
$776$	4358.74			0.201636
$777$	−5914.34	−	9469.94i	−0.273070	−	0.437236i
$778$	865.043			0.0398628
$779$			21629.8i			0.994824i
$780$	−20384.7	−	4711.29i	−0.935754	−	0.216271i
$781$	34584.6	+	34584.6i	1.58455	+	1.58455i
$782$	−16784.6			−0.767540
$783$	−20828.3	+	6799.46i	−0.950627	+	0.310336i
$784$	1478.88			0.0673687
$785$	2164.15	+	2164.15i	0.0983974	+	0.0983974i
$786$	−15520.3	−	3587.04i	−0.704313	−	0.162780i
$787$		−	3842.32i		−	0.174033i	−0.996207	−	0.0870164i	$-0.972267\pi$
$787$		−	3842.32i		−	0.174033i	0.996207	−	0.0870164i	$-0.0277333\pi$
$788$	−14271.5			−0.645179
$789$	−3220.62	−	5156.81i	−0.145320	−	0.232683i
$790$	−13855.4			−0.623990
$791$	2020.48	−	2020.48i	0.0908219	−	0.0908219i
$792$	−9482.71	−	4630.63i	−0.425446	−	0.207755i
$793$	−34591.5	−	34591.5i	−1.54903	−	1.54903i
$794$	−16171.5	−	16171.5i	−0.722804	−	0.722804i
$795$	1103.49	−	4774.55i	0.0492287	−	0.213001i
$796$			11130.2i			0.495604i
$797$	9321.29	+	9321.29i	0.414275	+	0.414275i	0.883225	−	0.468950i	$-0.155368\pi$
$797$	9321.29	+	9321.29i	0.414275	+	0.414275i	−0.468950	+	0.883225i	$0.655368\pi$
$798$	9562.09	+	2209.98i	0.424178	+	0.0980358i
$799$	12427.2			0.550242
$800$	2788.89	+	2788.89i	0.123253	+	0.123253i
$801$	−13823.3	−	40208.1i	−0.609767	−	1.77364i
$802$	−16366.5	+	16366.5i	−0.720601	+	0.720601i
$803$			30720.5i			1.35007i
$804$	−8925.20	−	2062.79i	−0.391502	−	0.0904837i
$805$		−	50754.2i		−	2.22217i
$806$			5078.77i			0.221950i
$807$	−21723.2	+	13567.0i	−0.947574	+	0.591796i
$808$	18.8771			0.000821897
$809$	2010.56	−	2010.56i	0.0873766	−	0.0873766i	−0.662068	−	0.749444i	$-0.730321\pi$
$809$	2010.56	−	2010.56i	0.0873766	−	0.0873766i	0.749444	+	0.662068i	$0.230321\pi$
$810$	2821.37	−	22798.4i	0.122386	−	0.988955i
$811$			40158.1i			1.73877i	0.494135	+	0.869385i	$0.335485\pi$
$811$			40158.1i			1.73877i	−0.494135	+	0.869385i	$0.664515\pi$
$812$	−8304.33	−	5368.11i	−0.358898	−	0.232000i
$813$	15247.1	+	24413.5i	0.657738	+	1.05316i
$814$	9378.86	−	9378.86i	0.403844	−	0.403844i
$815$	−12168.7	−	12168.7i	−0.523006	−	0.523006i
$816$	−1816.21	−	2908.09i	−0.0779169	−	0.124759i
$817$			26701.7i			1.14342i
$818$	−22479.5			−0.960853
$819$	−11981.5	+	24535.9i	−0.511192	+	1.04683i
$820$	16157.3	+	16157.3i	0.688094	+	0.688094i
$821$	−32496.9			−1.38142			−0.690711	−	0.723131i	$-0.742702\pi$
$821$	−32496.9			−1.38142			−0.690711	+	0.723131i	$0.742702\pi$
$822$	−967.787	+	4187.39i	−0.0410650	+	0.177679i
$823$	20109.0	−	20109.0i	0.851707	−	0.851707i	−0.138637	−	0.990343i	$-0.544272\pi$
$823$	20109.0	−	20109.0i	0.851707	−	0.851707i	0.990343	+	0.138637i	$0.0442720\pi$
$824$	−4072.05	+	4072.05i	−0.172156	+	0.172156i
$825$	−16574.5	−	26538.9i	−0.699456	−	1.11996i
$826$	16161.8	−	16161.8i	0.680802	−	0.680802i
$827$	15846.7	−	15846.7i	0.666315	−	0.666315i	−0.290546	−	0.956861i	$-0.593837\pi$
$827$	15846.7	−	15846.7i	0.666315	−	0.666315i	0.956861	+	0.290546i	$0.0938369\pi$
$828$	19748.9	+	9643.85i	0.828891	+	0.404767i
$829$	10339.2	−	10339.2i	0.433166	−	0.433166i	−0.456538	−	0.889704i	$-0.650911\pi$
$829$	10339.2	−	10339.2i	0.433166	−	0.433166i	0.889704	+	0.456538i	$0.150911\pi$
$830$	4249.22	−	4249.22i	0.177702	−	0.177702i
$831$	45738.5	+	10571.1i	1.90933	+	0.441283i
$832$	4088.79			0.170377
$833$	−2695.37	−	2695.37i	−0.112112	−	0.112112i
$834$	2869.90	+	4595.24i	0.119157	+	0.190792i
$835$	47147.1			1.95400
$836$			11658.8i			0.482332i
$837$	−5546.33	+	578.930i	−0.229043	+	0.0239077i
$838$	−21040.4	−	21040.4i	−0.867337	−	0.867337i
$839$	−3428.47	+	3428.47i	−0.141078	+	0.141078i	−0.774118	−	0.633041i	$-0.781807\pi$
$839$	−3428.47	+	3428.47i	−0.141078	+	0.141078i	0.633041	+	0.774118i	$0.281807\pi$
$840$	8793.64	−	5491.96i	0.361202	−	0.225584i
$841$	−10013.5	−	22238.6i	−0.410574	−	0.911827i
$842$			2629.97i			0.107642i
$843$	−7810.25	+	33793.1i	−0.319097	+	1.38066i
$844$	6922.24	−	6922.24i	0.282314	−	0.282314i
$845$	−29693.7			−1.20887
$846$	−14622.0	−	7140.24i	−0.594223	−	0.290173i
$847$			16714.7i			0.678067i
$848$			957.687i			0.0387820i
$849$	8806.13	−	38102.1i	0.355978	−	1.54024i
$850$		−	10165.9i		−	0.410222i
$851$	−19532.6	+	19532.6i	−0.786804	+	0.786804i
$852$	4685.50	−	20273.1i	0.188407	−	0.815193i
$853$	−6684.17	−	6684.17i	−0.268302	−	0.268302i	0.560114	−	0.828416i	$-0.310757\pi$
$853$	−6684.17	−	6684.17i	−0.268302	−	0.268302i	−0.828416	+	0.560114i	$0.810757\pi$
$854$	24241.8			0.971354
$855$	−24000.9	+	8251.38i	−0.960017	+	0.330048i
$856$	−886.035	−	886.035i	−0.0353786	−	0.0353786i
$857$			13072.3i			0.521051i	0.965467	+	0.260526i	$0.0838959\pi$
$857$			13072.3i			0.521051i	−0.965467	+	0.260526i	$0.916104\pi$
$858$	−31604.3	−	7304.37i	−1.25752	−	0.290638i
$859$	−20319.2	−	20319.2i	−0.807079	−	0.807079i	0.177112	−	0.984191i	$-0.443325\pi$
$859$	−20319.2	−	20319.2i	−0.807079	−	0.807079i	−0.984191	+	0.177112i	$0.943325\pi$
$860$	19945.9	+	19945.9i	0.790872	+	0.790872i
$861$	25293.5	−	15796.7i	1.00116	−	0.625262i
$862$	−13993.3	+	13993.3i	−0.552917	+	0.552917i
$863$	26448.5			1.04324			0.521621	−	0.853177i	$-0.325327\pi$
$863$	26448.5			1.04324			0.521621	+	0.853177i	$0.325327\pi$
$864$	466.083	+	4465.22i	0.0183524	+	0.175821i
$865$	−54330.1			−2.13558
$866$			21526.3i			0.844679i
$867$	3758.61	−	16262.6i	0.147231	−	0.637033i
$868$	−1779.60	−	1779.60i	−0.0695894	−	0.0695894i
$869$	−21481.3			−0.838554
$870$	25568.4	+	398.627i	0.996378	+	0.0155342i
$871$	−28157.3			−1.09538
$872$	−1617.58	−	1617.58i	−0.0628190	−	0.0628190i
$873$	4782.72	+	13911.6i	0.185419	+	0.539331i
$874$		−	24281.0i		−	0.939721i
$875$	−435.816			−0.0168380
$876$	11085.0	−	6923.01i	0.427544	−	0.267017i
$877$	14409.3			0.554809			0.277404	−	0.960753i	$-0.410526\pi$
$877$	14409.3			0.554809			0.277404	+	0.960753i	$0.410526\pi$
$878$	6231.38	−	6231.38i	0.239520	−	0.239520i
$879$	5764.46	+	9229.97i	0.221195	+	0.354174i
$880$	8709.06	+	8709.06i	0.333616	+	0.333616i
$881$	−36266.6	−	36266.6i	−1.38689	−	1.38689i	−0.831765	−	0.555127i	$-0.812670\pi$
$881$	−36266.6	−	36266.6i	−1.38689	−	1.38689i	−0.555127	−	0.831765i	$-0.687330\pi$
$882$	1622.73	+	4720.06i	0.0619502	+	0.180196i
$883$		−	42460.6i		−	1.61825i	−0.587638	−	0.809124i	$-0.699942\pi$
$883$		−	42460.6i		−	1.61825i	0.587638	−	0.809124i	$-0.300058\pi$
$884$	−7452.14	−	7452.14i	−0.283532	−	0.283532i
$885$	−13310.0	+	57589.1i	−0.505547	+	2.18738i
$886$	17238.7			0.653662
$887$	27396.7	+	27396.7i	1.03708	+	1.03708i	0.999285	+	0.0377971i	$0.0120340\pi$
$887$	27396.7	+	27396.7i	1.03708	+	1.03708i	0.0377971	+	0.999285i	$0.487966\pi$
$888$	−5497.78	−	1270.64i	−0.207763	−	0.0480181i
$889$	−3829.42	+	3829.42i	−0.144471	+	0.144471i
$890$			49623.3i			1.86896i
$891$	4374.24	−	35346.5i	0.164470	−	1.32902i
$892$			20558.9i			0.771708i
$893$			17977.5i			0.673676i
$894$	46.4972	+	74.4505i	0.00173948	+	0.00278523i
$895$	−54978.9			−2.05334
$896$	−1432.71	+	1432.71i	−0.0534192	+	0.0534192i
$897$	65819.9	+	15212.3i	2.45001	+	0.566246i
$898$			9348.81i			0.347410i
$899$	−1303.36	−	6069.03i	−0.0483530	−	0.225154i
$900$	−5840.99	+	11961.3i	−0.216333	+	0.443012i
$901$	1745.46	−	1745.46i	0.0645391	−	0.0645391i
$902$	25050.2	+	25050.2i	0.924701	+	0.924701i
$903$	31224.4	−	19500.8i	1.15070	−	0.718656i
$904$		−	1444.09i		−	0.0531304i
$905$	13113.8			0.481675
$906$	3581.37	−	2236.70i	0.131328	−	0.0820192i
$907$	6667.55	+	6667.55i	0.244093	+	0.244093i	0.818541	−	0.574448i	$-0.194783\pi$
$907$	6667.55	+	6667.55i	0.244093	+	0.244093i	−0.574448	+	0.818541i	$0.694783\pi$
$908$	−10837.1			−0.396081
$909$	20.7132	+	60.2490i	0.000755792	+	0.00219838i
$910$	22534.2	−	22534.2i	0.820879	−	0.820879i
$911$	14589.7	−	14589.7i	0.530600	−	0.530600i	−0.390151	−	0.920751i	$-0.627577\pi$
$911$	14589.7	−	14589.7i	0.530600	−	0.530600i	0.920751	+	0.390151i	$0.127577\pi$
$912$	4206.91	−	2627.37i	0.152746	−	0.0953959i
$913$	6587.98	−	6587.98i	0.238806	−	0.238806i
$914$	8856.36	−	8856.36i	0.320506	−	0.320506i
$915$	−53172.1	+	33208.0i	−1.92111	+	1.19980i
$916$	467.320	−	467.320i	0.0168566	−	0.0168566i
$917$	17156.8	−	17156.8i	0.617850	−	0.617850i
$918$	7288.73	−	8987.68i	0.262052	−	0.323135i
$919$	44892.2			1.61138			0.805689	−	0.592339i	$-0.201795\pi$
$919$	44892.2			1.61138			0.805689	+	0.592339i	$0.201795\pi$
$920$	−18137.7	−	18137.7i	−0.649981	−	0.649981i
$921$	20048.7	−	12521.2i	0.717294	−	0.447977i
$922$	−31233.0			−1.11562
$923$		−	63957.7i		−	2.28082i
$924$	13633.6	−	8514.71i	0.485404	−	0.303153i
$925$	−11830.3	−	11830.3i	−0.420518	−	0.420518i
$926$	23183.7	−	23183.7i	0.822748	−	0.822748i
$927$	−17464.7	−	8528.43i	−0.618788	−	0.302169i
$928$	−4886.03	+	1049.30i	−0.172836	+	0.0371174i
$929$			16441.3i			0.580647i	0.956929	+	0.290323i	$0.0937628\pi$
$929$			16441.3i			0.580647i	−0.956929	+	0.290323i	$0.906237\pi$
$930$	6341.21	+	1465.58i	0.223588	+	0.0516754i
$931$	3899.18	−	3899.18i	0.137262	−	0.137262i
$932$	2076.20			0.0729703
$933$	−8590.01	−	13754.2i	−0.301419	−	0.482628i
$934$		−	12166.6i		−	0.426236i
$935$		−	31745.9i		−	1.11038i
$936$	4486.51	+	13050.0i	0.156673	+	0.455718i
$937$			7348.83i			0.256218i	0.991760	+	0.128109i	$0.0408907\pi$
$937$			7348.83i			0.256218i	−0.991760	+	0.128109i	$0.959109\pi$
$938$	9866.33	−	9866.33i	0.343440	−	0.343440i
$939$	−24443.4	−	5649.35i	−0.849501	−	0.196336i
$940$	13429.0	+	13429.0i	0.465964	+	0.465964i
$941$	−47721.4			−1.65321			−0.826607	−	0.562780i	$-0.809732\pi$
$941$	−47721.4			−1.65321			−0.826607	+	0.562780i	$0.809732\pi$
$942$	454.574	−	1966.84i	0.0157227	−	0.0680287i
$943$	−52170.1	−	52170.1i	−1.80158	−	1.80158i
$944$		−	11551.3i		−	0.398266i
$945$	27177.4	+	22040.0i	0.935535	+	0.758691i
$946$	30924.1	+	30924.1i	1.06282	+	1.06282i
$947$	12280.8	+	12280.8i	0.421408	+	0.421408i	0.885688	−	0.464280i	$-0.153687\pi$
$947$	12280.8	+	12280.8i	0.421408	+	0.421408i	−0.464280	+	0.885688i	$0.653687\pi$
$948$	4840.91	+	7751.19i	0.165850	+	0.265556i
$949$	28406.0	−	28406.0i	0.971651	−	0.971651i
$950$	14706.3			0.502246
$951$	3896.34	−	2433.41i	0.132857	−	0.0829745i
$952$	5222.47			0.177795
$953$			5527.47i			0.187883i	0.995578	+	0.0939414i	$0.0299466\pi$
$953$			5527.47i			0.187883i	−0.995578	+	0.0939414i	$0.970053\pi$
$954$	−3056.60	+	1050.84i	−0.103733	+	0.0356627i
$955$	−17412.5	−	17412.5i	−0.590006	−	0.590006i
$956$	10823.8			0.366177
$957$	39641.1	+	618.030i	1.33899	+	0.0208757i
$958$	−16061.1			−0.541661
$959$	−4628.93	−	4628.93i	−0.155867	−	0.155867i
$960$	1179.90	−	5105.15i	0.0396678	−	0.171633i
$961$			28211.1i			0.946968i
$962$	−17344.5			−0.581297
$963$	1855.69	−	3800.13i	0.0620965	−	0.127163i
$964$	−25848.2			−0.863604
$965$	−23879.2	+	23879.2i	−0.796579	+	0.796579i
$966$	−28393.7	+	17732.9i	−0.945706	+	0.590629i
$967$	−27095.3	−	27095.3i	−0.901061	−	0.901061i	0.0944673	−	0.995528i	$-0.469885\pi$
$967$	−27095.3	−	27095.3i	−0.901061	−	0.901061i	−0.995528	+	0.0944673i	$0.969885\pi$
$968$	5973.22	+	5973.22i	0.198333	+	0.198333i
$969$	−12456.0	−	2878.83i	−0.412946	−	0.0954399i
$970$		−	17169.1i		−	0.568317i
$971$	2685.79	+	2685.79i	0.0887652	+	0.0887652i	0.750095	−	0.661330i	$-0.230008\pi$
$971$	2685.79	+	2685.79i	0.0887652	+	0.0887652i	−0.661330	+	0.750095i	$0.730008\pi$
$972$	−13740.0	+	6387.12i	−0.453406	+	0.210769i
$973$	−8252.32			−0.271898
$974$	13646.4	+	13646.4i	0.448932	+	0.448932i
$975$	−9213.60	+	39865.1i	−0.302637	+	1.30944i
$976$	8663.12	−	8663.12i	0.284119	−	0.284119i
$977$			30679.8i			1.00464i	0.864682	+	0.502320i	$0.167520\pi$
$977$			30679.8i			1.00464i	−0.864682	+	0.502320i	$0.832480\pi$
$978$	−2555.99	+	11059.2i	−0.0835701	+	0.361589i
$979$			76935.8i			2.51162i
$980$		−	5825.31i		−	0.189880i
$981$	3387.82	−	6937.67i	0.110260	−	0.225793i
$982$	−31741.8			−1.03149
$983$	17932.1	−	17932.1i	0.581836	−	0.581836i	−0.353571	−	0.935408i	$-0.615033\pi$
$983$	17932.1	−	17932.1i	0.581836	−	0.581836i	0.935408	+	0.353571i	$0.115033\pi$
$984$	3393.79	−	14684.1i	0.109949	−	0.475725i
$985$			56215.6i			1.81845i
$986$	10817.6	+	6992.74i	0.349394	+	0.225856i
$987$	21022.5	−	13129.3i	0.677967	−	0.423416i
$988$	10780.4	−	10780.4i	0.347137	−	0.347137i
$989$	−64403.2	−	64403.2i	−2.07068	−	2.07068i
$990$	−18240.1	+	37352.5i	−0.585563	+	1.19913i
$991$			28659.4i			0.918664i	0.888265	+	0.459332i	$0.151911\pi$
$991$			28659.4i			0.918664i	−0.888265	+	0.459332i	$0.848089\pi$
$992$	−1271.93			−0.0407095
$993$	4147.23	+	6640.48i	0.132536	+	0.212215i
$994$	22410.8	+	22410.8i	0.715118	+	0.715118i
$995$	43842.1			1.39687
$996$	−3861.80	−	892.537i	−0.122857	−	0.0283947i
$997$	−2279.88	+	2279.88i	−0.0724217	+	0.0724217i	−0.742390	−	0.669968i	$-0.766308\pi$
$997$	−2279.88	+	2279.88i	−0.0724217	+	0.0724217i	0.669968	+	0.742390i	$0.266308\pi$
$998$	−19400.8	+	19400.8i	−0.615351	+	0.615351i
$999$	−1977.10	−	18941.2i	−0.0626153	−	0.599874i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	174.4.f.a.17.13	✓	60
3.2	odd	2	inner	174.4.f.a.17.21	yes	60
29.12	odd	4	inner	174.4.f.a.41.21	yes	60
87.41	even	4	inner	174.4.f.a.41.13	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
174.4.f.a.17.13	✓	60	1.1	even	1	trivial
174.4.f.a.17.21	yes	60	3.2	odd	2	inner
174.4.f.a.41.13	yes	60	87.41	even	4	inner
174.4.f.a.41.21	yes	60	29.12	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 174 = 2 \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	174.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 1.41421i) q^{2} +(5.06270 + 1.17009i) q^{3} +4.00000i q^{4} +15.7560 q^{5} +(-5.50498 - 8.81449i) q^{6} +15.8294 q^{7} +(5.65685 - 5.65685i) q^{8} +(24.2618 + 11.8476i) q^{9} +(-22.2824 - 22.2824i) q^{10} +(-34.5465 - 34.5465i) q^{11} +(-4.68035 + 20.2508i) q^{12} +63.8874i q^{13} +(-22.3862 - 22.3862i) q^{14} +(79.7680 + 18.4359i) q^{15} -16.0000 q^{16} +(29.1612 + 29.1612i) q^{17} +(-17.5563 - 51.0664i) q^{18} +(-42.1853 + 42.1853i) q^{19} +63.0241i q^{20} +(80.1395 + 18.5218i) q^{21} +97.7123i q^{22} -203.498i q^{23} +(35.2580 - 22.0199i) q^{24} +123.253 q^{25} +(90.3504 - 90.3504i) q^{26} +(108.967 + 88.3692i) q^{27} +63.3176i q^{28} +(-84.7806 + 131.154i) q^{29} +(-86.7367 - 138.881i) q^{30} +(-28.1059 + 28.1059i) q^{31} +(22.6274 + 22.6274i) q^{32} +(-134.476 - 215.321i) q^{33} -82.4805i q^{34} +249.409 q^{35} +(-47.3904 + 97.0472i) q^{36} +(-95.9844 - 95.9844i) q^{37} +119.318 q^{38} +(-74.7538 + 323.442i) q^{39} +(89.1296 - 89.1296i) q^{40} +(256.367 - 256.367i) q^{41} +(-87.1406 - 139.528i) q^{42} +(316.481 - 316.481i) q^{43} +(138.186 - 138.186i) q^{44} +(382.270 + 186.671i) q^{45} +(-287.790 + 287.790i) q^{46} +(213.077 - 213.077i) q^{47} +(-81.0031 - 18.7214i) q^{48} -92.4298 q^{49} +(-174.306 - 174.306i) q^{50} +(113.513 + 181.756i) q^{51} -255.549 q^{52} -59.8555i q^{53} +(-29.1302 - 279.076i) q^{54} +(-544.316 - 544.316i) q^{55} +(89.5447 - 89.5447i) q^{56} +(-262.932 + 164.211i) q^{57} +(305.377 - 65.5812i) q^{58} +721.957i q^{59} +(-73.7438 + 319.072i) q^{60} +(-541.445 + 541.445i) q^{61} +79.4956 q^{62} +(384.050 + 187.540i) q^{63} -64.0000i q^{64} +1006.61i q^{65} +(-114.332 + 494.688i) q^{66} +440.734i q^{67} +(-116.645 + 116.645i) q^{68} +(238.111 - 1030.25i) q^{69} +(-352.717 - 352.717i) q^{70} -1001.10 q^{71} +(204.266 - 70.2253i) q^{72} +(-444.626 - 444.626i) q^{73} +271.485i q^{74} +(623.991 + 144.216i) q^{75} +(-168.741 - 168.741i) q^{76} +(-546.851 - 546.851i) q^{77} +(563.134 - 351.699i) q^{78} +(310.904 - 310.904i) q^{79} -252.097 q^{80} +(448.269 + 574.888i) q^{81} -725.114 q^{82} +190.699i q^{83} +(-74.0872 + 320.558i) q^{84} +(459.466 + 459.466i) q^{85} -895.143 q^{86} +(-582.680 + 564.790i) q^{87} -390.849 q^{88} +(-1113.51 - 1113.51i) q^{89} +(-276.618 - 804.604i) q^{90} +1011.30i q^{91} +813.992 q^{92} +(-175.178 + 109.405i) q^{93} -602.674 q^{94} +(-664.673 + 664.673i) q^{95} +(88.0797 + 141.032i) q^{96} +(385.262 + 385.262i) q^{97} +(130.716 + 130.716i) q^{98} +(-428.867 - 1247.45i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 24 q^{10} + 88 q^{15} - 960 q^{16} + 48 q^{19} - 752 q^{21} + 64 q^{24} + 1500 q^{25} + 600 q^{27} + 312 q^{30} - 300 q^{31} - 224 q^{36} - 192 q^{37} - 172 q^{39} + 96 q^{40} + 888 q^{43} - 1532 q^{45}+ \cdots - 6000 q^{99}+O(q^{100}) \) 60 * q - 24 * q^10 + 88 * q^15 - 960 * q^16 + 48 * q^19 - 752 * q^21 + 64 * q^24 + 1500 * q^25 + 600 * q^27 + 312 * q^30 - 300 * q^31 - 224 * q^36 - 192 * q^37 - 172 * q^39 + 96 * q^40 + 888 * q^43 - 1532 * q^45 - 1104 * q^46 + 2292 * q^49 - 768 * q^52 - 1688 * q^54 + 2616 * q^55 - 1176 * q^58 - 352 * q^60 + 216 * q^61 + 192 * q^66 - 452 * q^69 + 192 * q^70 - 1668 * q^73 + 4840 * q^75 + 192 * q^76 - 1336 * q^78 + 3588 * q^79 - 280 * q^81 + 4224 * q^82 - 3008 * q^84 - 792 * q^85 - 4716 * q^87 - 800 * q^90 - 3072 * q^94 - 2916 * q^97 - 6000 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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