LMFDB - Embedded newform 174.4.f.a.17.21

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			17.21
Character	$\chi$	$=$	174.17
Dual form			174.4.f.a.41.21

$q$-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} +(-1.17009 - 5.06270i) 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} +(20.2508 - 4.68035i) q^{12} +63.8874i q^{13} +(22.3862 + 22.3862i) q^{14} +(18.4359 + 79.7680i) q^{15} -16.0000 q^{16} +(-29.1612 - 29.1612i) q^{17} +(-51.0664 - 17.5563i) q^{18} +(-42.1853 + 42.1853i) q^{19} -63.0241i q^{20} +(-18.5218 - 80.1395i) 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} +(88.3692 + 108.967i) 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} +(323.442 - 74.7538i) 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} +(18.7214 + 81.0031i) 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} +(-319.072 + 73.7438i) 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} +(494.688 - 114.332i) q^{66} +440.734i q^{67} +(116.645 - 116.645i) q^{68} +(1030.25 - 238.111i) q^{69} +(-352.717 - 352.717i) q^{70} +1001.10 q^{71} +(70.2253 - 204.266i) q^{72} +(-444.626 - 444.626i) q^{73} -271.485i q^{74} +(-144.216 - 623.991i) 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} +(320.558 - 74.0872i) q^{84} +(459.466 + 459.466i) q^{85} +895.143 q^{86} +(-763.191 - 275.757i) q^{87} -390.849 q^{88} +(1113.51 + 1113.51i) q^{89} +(804.604 + 276.618i) 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} +(-1247.45 - 428.867i) 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
$3$	−1.17009	−	5.06270i	−0.225183	−	0.974316i
$3$	−1.17009	−	5.06270i	−0.225183	−	0.974316i
$4$			4.00000i			0.500000i
$5$	−15.7560			−1.40926			−0.704631	−	0.709574i	$-0.748888\pi$
$5$	−15.7560			−1.40926			−0.704631	+	0.709574i	$0.748888\pi$
$6$	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	0.998661	−	0.0517362i	$-0.0164755\pi$
$11$	34.5465	+	34.5465i	0.946925	+	0.946925i	−0.0517362	+	0.998661i	$0.516475\pi$
$12$	20.2508	−	4.68035i	0.487158	−	0.112592i
$13$			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
$15$	18.4359	+	79.7680i	0.317343	+	1.37307i
$16$	−16.0000			−0.250000
$17$	−29.1612	−	29.1612i	−0.416038	−	0.416038i	0.467798	−	0.883836i	$-0.345048\pi$
$17$	−29.1612	−	29.1612i	−0.416038	−	0.416038i	−0.883836	+	0.467798i	$0.845048\pi$
$18$	−51.0664	−	17.5563i	−0.668692	−	0.229892i
$19$	−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
$21$	−18.5218	−	80.1395i	−0.192466	−	0.832756i
$22$			97.7123i			0.946925i
$23$			203.498i			1.84488i	0.386139	+	0.922441i	$0.373809\pi$
$23$			203.498i			1.84488i	−0.386139	+	0.922441i	$0.626191\pi$
$24$	35.2580	+	22.0199i	0.299875	+	0.187283i
$25$	123.253			0.986021
$26$	−90.3504	+	90.3504i	−0.681506	+	0.681506i
$27$	88.3692	+	108.967i	0.629876	+	0.776695i
$28$			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
$39$	323.442	−	74.7538i	1.32801	−	0.306928i
$40$	89.1296	−	89.1296i	0.352316	−	0.352316i
$41$	−256.367	+	256.367i	−0.976530	+	0.976530i	−0.999731	−	0.0232006i	$-0.992614\pi$
$41$	−256.367	+	256.367i	−0.976530	+	0.976530i	0.0232006	+	0.999731i	$0.492614\pi$
$42$	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	−0.955684	−	0.294396i	$-0.904882\pi$
$47$	−213.077	+	213.077i	−0.661288	+	0.661288i	0.294396	+	0.955684i	$0.404882\pi$
$48$	18.7214	+	81.0031i	0.0562959	+	0.243579i
$49$	−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	$0.0247142\pi$
$53$			59.8555i			0.155128i	−0.996987	+	0.0775640i	$0.975286\pi$
$54$	−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	$-0.706666\pi$
$59$		−	721.957i		−	1.59306i	0.604597	−	0.796532i	$-0.293334\pi$
$60$	−319.072	+	73.7438i	−0.686534	+	0.158671i
$61$	−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
$66$	494.688	−	114.332i	0.922604	−	0.213232i
$67$			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
$69$	1030.25	−	238.111i	1.79750	−	0.415437i
$70$	−352.717	−	352.717i	−0.602254	−	0.602254i
$71$	1001.10			1.67336			0.836682	−	0.547689i	$-0.184492\pi$
$71$	1001.10			1.67336			0.836682	+	0.547689i	$0.184492\pi$
$72$	70.2253	−	204.266i	0.114946	−	0.334346i
$73$	−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
$75$	−144.216	−	623.991i	−0.222036	−	0.960696i
$76$	−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	$-0.959755\pi$
$83$		−	190.699i		−	0.252192i	0.992018	−	0.126096i	$-0.0402447\pi$
$84$	320.558	−	74.0872i	0.416378	−	0.0962330i
$85$	459.466	+	459.466i	0.586306	+	0.586306i
$86$	895.143			1.12239
$87$	−763.191	−	275.757i	−0.940491	−	0.339819i
$88$	−390.849			−0.473462
$89$	1113.51	+	1113.51i	1.32620	+	1.32620i	0.908658	+	0.417542i	$0.137108\pi$
$89$	1113.51	+	1113.51i	1.32620	+	1.32620i	0.417542	+	0.908658i	$0.362892\pi$
$90$	804.604	+	276.618i	0.942363	+	0.323979i
$91$			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
$99$	−1247.45	−	428.867i	−1.26640	−	0.435382i
$100$			493.010i			0.493010i
$101$	−1.66851	−	1.66851i	−0.00164379	−	0.00164379i	0.706284	−	0.707928i	$-0.250370\pi$
$101$	−1.66851	−	1.66851i	−0.00164379	−	0.00164379i	−0.707928	+	0.706284i	$0.750370\pi$
$102$	−417.574	+	96.5094i	−0.405352	+	0.0936848i
$103$	−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
$105$	291.830	+	1262.68i	0.271235	+	1.17357i
$106$	−84.6484	+	84.6484i	−0.0775640	+	0.0775640i
$107$			156.630i			0.141514i	0.997494	+	0.0707572i	$0.0225415\pi$
$107$			156.630i			0.141514i	−0.997494	+	0.0707572i	$0.977458\pi$
$108$	−435.869	+	353.477i	−0.388348	+	0.314938i
$109$		−	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	−0.758238	−	0.651978i	$-0.773940\pi$
$113$	−127.641	+	127.641i	−0.106261	+	0.106261i	0.651978	+	0.758238i	$0.273940\pi$
$114$	139.613	+	604.071i	0.114701	+	0.496284i
$115$		−	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
$126$	−808.351	−	277.906i	−0.571536	−	0.196491i
$127$	−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	−0.969191	−	0.246312i	$-0.920781\pi$
$131$	−1083.86	+	1083.86i	−0.722879	+	0.722879i	0.246312	+	0.969191i	$0.420781\pi$
$132$	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
$135$	−1392.35	−	1716.89i	−0.887661	−	1.09457i
$136$	329.922			0.208019
$137$	292.426	+	292.426i	0.182362	+	0.182362i	0.792384	−	0.610022i	$-0.208839\pi$
$137$	292.426	+	292.426i	0.182362	+	0.182362i	−0.610022	+	0.792384i	$0.708839\pi$
$138$	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
$147$	108.151	+	467.944i	0.0606813	+	0.262554i
$148$	383.938	−	383.938i	0.213240	−	0.213240i
$149$	8.44638			0.00464399			0.00232199	−	0.999997i	$-0.499261\pi$
$149$	8.44638			0.00464399			0.00232199	+	0.999997i	$0.499261\pi$
$150$	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
$153$	1052.99	+	362.013i	0.556402	+	0.191288i
$154$			1546.73i			0.809344i
$155$	442.838	−	442.838i	0.229481	−	0.229481i
$156$	299.015	+	1293.77i	0.153464	+	0.664003i
$157$	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
$159$	303.030	−	70.0361i	0.151144	−	0.0349322i
$160$	356.518	+	356.518i	0.176158	+	0.176158i
$161$			3221.25i			1.57683i
$162$	1446.96	−	179.066i	0.701754	−	0.0868443i
$163$	−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	$-0.743831\pi$
$167$	−2992.32			−1.38654			−0.693271	+	0.720677i	$0.743831\pi$
$168$	558.112	+	348.562i	0.256305	+	0.160072i
$169$	−1884.59			−0.857803
$170$			1299.56i			0.586306i
$171$	523.696	−	1523.28i	0.234199	−	0.681219i
$172$	1265.92	+	1265.92i	0.561196	+	0.561196i
$173$	3448.21			1.51539			0.757696	−	0.652608i	$-0.226325\pi$
$173$	3448.21			1.51539			0.757696	+	0.652608i	$0.226325\pi$
$174$	−689.336	−	1469.30i	−0.300336	−	0.640155i
$175$	1951.02			0.842760
$176$	−552.744	−	552.744i	−0.236731	−	0.236731i
$177$	−3655.05	+	844.753i	−1.55215	+	0.358732i
$178$			3149.48i			1.32620i
$179$	3489.39			1.45703			0.728516	−	0.685028i	$-0.240210\pi$
$179$	3489.39			1.45703			0.728516	+	0.685028i	$0.240210\pi$
$180$	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
$186$	93.0169	+	402.462i	0.0366684	+	0.158656i
$187$		−	2014.84i		−	0.787913i
$188$	−852.310	−	852.310i	−0.330644	−	0.330644i
$189$	1398.83	+	1724.89i	0.538360	+	0.663848i
$190$	1879.98			0.717832
$191$	1105.13	+	1105.13i	0.418663	+	0.418663i	0.884743	−	0.466080i	$-0.154334\pi$
$191$	1105.13	+	1105.13i	0.418663	+	0.418663i	−0.466080	+	0.884743i	$0.654334\pi$
$192$	−324.013	+	74.8856i	−0.121790	+	0.0281479i
$193$	−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
$195$	−5096.17	+	1177.82i	−1.87151	+	0.432542i
$196$		−	369.719i		−	0.134737i
$197$		−	3567.87i		−	1.29036i	−0.764031	−	0.645179i	$-0.776783\pi$
$197$		−	3567.87i		−	1.29036i	0.764031	−	0.645179i	$-0.223217\pi$
$198$	−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
$201$	2231.30	−	515.697i	0.783004	−	0.180967i
$202$		−	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
$213$	−1171.38	−	5068.27i	−0.376814	−	1.63039i
$214$	−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
$222$	−1374.45	+	317.661i	−0.415526	+	0.0960361i
$223$	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	$-0.870370\pi$
$227$		−	2709.27i		−	0.792162i	0.918216	−	0.396081i	$-0.129630\pi$
$228$	−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	$0.0232478\pi$
$233$			519.051i			0.145941i	−0.997334	+	0.0729703i	$0.976752\pi$
$234$	1121.63	−	3262.50i	0.313346	−	0.911436i
$235$	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	$0.119334\pi$
$239$			2705.94i			0.732354i	−0.930545	+	0.366177i	$0.880666\pi$
$240$	−294.975	−	1276.29i	−0.0793357	−	0.343267i
$241$			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
$243$	−3435.00	−	1596.78i	−0.906811	−	0.421537i
$244$	−2165.78	−	2165.78i	−0.568237	−	0.568237i
$245$	1456.33			0.379761
$246$	848.447	+	3671.03i	0.219898	+	0.951449i
$247$	−2695.11	−	2695.11i	−0.694273	−	0.694273i
$248$		−	317.983i		−	0.0814190i
$249$	−965.450	+	223.134i	−0.245714	+	0.0567894i
$250$	38.9362	+	38.9362i	0.00985017	+	0.00985017i
$251$	51.1710	+	51.1710i	0.0128681	+	0.0128681i	0.713512	−	0.700643i	$-0.247104\pi$
$251$	51.1710	+	51.1710i	0.0128681	+	0.0128681i	−0.700643	+	0.713512i	$0.747104\pi$
$252$	−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	$-0.973292\pi$
$257$		−	690.565i		−	0.167612i	0.996482	−	0.0838060i	$-0.0267076\pi$
$258$	−1047.40	−	4531.83i	−0.252744	−	1.09356i
$259$	−1519.38	−	1519.38i	−0.364515	−	0.364515i
$260$	4026.45			0.960421
$261$	−503.075	+	4186.47i	−0.119309	+	0.992857i
$262$	−3065.61			−0.722879
$263$	827.368	+	827.368i	0.193984	+	0.193984i	0.797415	−	0.603431i	$-0.206200\pi$
$263$	827.368	+	827.368i	0.193984	+	0.193984i	−0.603431	+	0.797415i	$0.706200\pi$
$264$	457.328	+	1978.75i	0.106616	+	0.461302i
$265$		−	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	−0.191515	−	0.981490i	$-0.561340\pi$
$269$	3485.31	−	3485.31i	0.789974	−	0.789974i	0.981490	+	0.191515i	$0.0613401\pi$
$270$	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
$273$	5119.90	−	1183.31i	1.13506	−	0.262334i
$274$			827.106i			0.182362i
$275$	4257.95	+	4257.95i	0.933687	+	0.933687i
$276$	952.442	+	4121.00i	0.207718	+	0.898749i
$277$	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
$279$	348.913	−	1014.89i	0.0748704	−	0.217777i
$280$	1410.87	−	1410.87i	0.301127	−	0.301127i
$281$		−	6674.92i		−	1.41706i	−0.705683	−	0.708528i	$-0.749360\pi$
$281$		−	6674.92i		−	1.41706i	0.705683	−	0.708528i	$-0.250640\pi$
$282$	705.182	+	3051.16i	0.148911	+	0.644304i
$283$		−	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
$288$	817.062	+	280.901i	0.167173	+	0.0574731i
$289$		−	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	0.543889	−	0.839157i	$-0.316951\pi$
$293$	−1480.87	−	1480.87i	−0.295268	−	0.295268i	−0.839157	+	0.543889i	$0.816951\pi$
$294$	−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
$300$	2495.96	−	576.865i	0.480348	−	0.111018i
$301$	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
$309$	842.281	+	3644.35i	0.155067	+	0.670939i
$310$	1252.54			0.229481
$311$	2206.75	+	2206.75i	0.402358	+	0.402358i	0.879063	−	0.476705i	$-0.158169\pi$
$311$	2206.75	+	2206.75i	0.402358	+	0.402358i	−0.476705	+	0.879063i	$0.658169\pi$
$312$	−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	−0.760315	−	0.649554i	$-0.774955\pi$
$317$	−625.136	+	625.136i	−0.110761	+	0.110761i	0.649554	+	0.760315i	$0.274955\pi$
$318$	527.595	+	329.503i	0.0930379	+	0.0581057i
$319$	7459.78	−	1602.02i	1.30930	−	0.281179i
$320$			1008.39i			0.176158i
$321$	792.972	−	183.271i	0.137880	−	0.0318667i
$322$	−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
$327$	−1447.68	+	334.587i	−0.244822	+	0.0565832i
$328$		−	2900.46i		−	0.488265i
$329$	−3372.89	+	3372.89i	−0.565208	+	0.565208i
$330$	−7794.32	+	1801.42i	−1.30019	+	0.300500i
$331$	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
$333$	3465.94	+	1191.57i	0.570367	+	0.196089i
$334$	−4231.78	−	4231.78i	−0.693271	−	0.693271i
$335$		−	6944.21i		−	1.13255i
$336$	296.349	+	1282.23i	0.0481165	+	0.208189i
$337$	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
$345$	−16232.6	+	3751.68i	−2.53315	+	0.585460i
$346$	4876.51	+	4876.51i	0.757696	+	0.757696i
$347$	4046.09			0.625952			0.312976	−	0.949761i	$-0.398674\pi$
$347$	4046.09			0.625952			0.312976	+	0.949761i	$0.398674\pi$
$348$	1103.03	−	3052.77i	0.169910	−	0.470245i
$349$	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
$351$	−6961.64	+	5645.67i	−1.05865	+	0.858529i
$352$		−	1563.40i		−	0.236731i
$353$	−6741.35			−1.01645			−0.508224	−	0.861225i	$-0.669698\pi$
$353$	−6741.35			−1.01645			−0.508224	+	0.861225i	$0.669698\pi$
$354$	−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	$-0.966824\pi$
$359$	−7472.84	−	7472.84i	−1.09861	−	1.09861i	−0.104038	−	0.994573i	$-0.533176\pi$
$360$	−1106.47	+	3218.41i	−0.161989	+	0.471182i
$361$			3299.80i			0.481091i
$362$	1177.05	+	1177.05i	0.170896	+	0.170896i
$363$	5345.83	−	1235.53i	0.772957	−	0.178645i
$364$	−4045.20			−0.582489
$365$	7005.54	+	7005.54i	1.00462	+	1.00462i
$366$	1791.92	+	7753.21i	0.255915	+	1.10729i
$367$	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
$369$	3182.58	−	9257.24i	0.448994	−	1.30600i
$370$			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
$375$	−32.2149	−	139.386i	−0.00443619	−	0.0191944i
$376$		−	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	$-0.364785\pi$
$383$	6178.22			0.824262			0.412131	+	0.911125i	$0.364785\pi$
$384$	−564.127	−	352.319i	−0.0749687	−	0.0468208i
$385$	−8616.20	−	8616.20i	−1.14058	−	1.14058i
$386$	−4286.65			−0.565245
$387$	−3928.85	+	11427.9i	−0.516059	+	1.50107i
$388$	−1541.05	+	1541.05i	−0.201636	+	0.201636i
$389$	305.839	−	305.839i	0.0398628	−	0.0398628i	−0.686894	−	0.726757i	$-0.741027\pi$
$389$	305.839	−	305.839i	0.0398628	−	0.0398628i	0.726757	+	0.686894i	$0.241027\pi$
$390$	−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
$396$	1715.47	−	4989.82i	0.217691	−	0.633201i
$397$	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	$0.256134\pi$
$401$			11572.9i			1.44120i	−0.693350	+	0.720601i	$0.743866\pi$
$402$	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
$408$	−386.037	−	1670.29i	−0.0468424	−	0.202676i
$409$	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
$414$	3572.68	−	10391.9i	0.424124	−	1.23366i
$415$			3004.66i			0.355404i
$416$	1445.61	−	1445.61i	0.170377	−	0.170377i
$417$	610.000	+	2639.33i	0.0716351	+	0.309948i
$418$	−4122.02	−	4122.02i	−0.482332	−	0.482332i
$419$	−14877.8			−1.73467			−0.867337	−	0.497721i	$-0.834170\pi$
$419$	−14877.8			−1.73467			−0.867337	+	0.497721i	$0.834170\pi$
$420$	−5050.72	+	1167.32i	−0.586786	+	0.135618i
$421$	−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
$423$	2645.18	−	7694.10i	0.304050	−	0.884397i
$424$	−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	$0.186485\pi$
$431$			9894.77i			1.10583i	−0.833236	+	0.552917i	$0.813515\pi$
$432$	−1413.91	−	1743.48i	−0.157469	−	0.194174i
$433$	−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
$435$	12024.9	+	4344.84i	1.32540	+	0.478895i
$436$	1143.80			0.125638
$437$	−8584.62	−	8584.62i	−0.939721	−	0.939721i
$438$	−6366.80	+	1471.49i	−0.694561	+	0.160526i
$439$			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	−0.300211	−	0.953873i	$-0.597057\pi$
$443$	6094.79	−	6094.79i	0.653662	−	0.653662i	0.953873	+	0.300211i	$0.0970571\pi$
$444$	−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
$447$	−9.88300	−	42.7615i	−0.00104575	−	0.00452471i
$448$		−	1013.08i		−	0.106838i
$449$	3305.30	+	3305.30i	0.347410	+	0.347410i	0.859144	−	0.511734i	$-0.170997\pi$
$449$	3305.30	+	3305.30i	0.347410	+	0.347410i	−0.511734	+	0.859144i	$0.670997\pi$
$450$	−6294.06	−	2163.86i	−0.659345	−	0.226679i
$451$	−17713.2			−1.84940
$452$	−510.564	−	510.564i	−0.0531304	−	0.0531304i
$453$	2057.00	−	475.412i	0.213347	−	0.0493087i
$454$	3831.49	−	3831.49i	0.396081	−	0.396081i
$455$		−	15934.1i		−	1.64176i
$456$	−2416.28	+	558.450i	−0.248142	+	0.0573505i
$457$			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	$0.539330\pi$
$461$	−11042.5	+	11042.5i	−1.11562	+	1.11562i	−0.992376	+	0.123246i	$0.960670\pi$
$462$	7830.62	−	1809.81i	0.788557	−	0.182251i
$463$			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	0.461108	−	0.887344i	$-0.347452\pi$
$467$	−4301.55	−	4301.55i	−0.426236	−	0.426236i	−0.887344	+	0.461108i	$0.847452\pi$
$468$	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
$474$	−1028.94	−	4451.98i	−0.0997062	−	0.431405i
$475$	−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	−0.924016	−	0.382355i	$-0.875113\pi$
$479$	−5678.46	+	5678.46i	−0.541661	+	0.541661i	0.382355	+	0.924016i	$0.375113\pi$
$480$	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
$483$	16308.2	−	3769.15i	1.53634	−	0.355077i
$484$	−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	$0.510188\pi$
$491$	−11222.4	+	11222.4i	−1.03149	+	1.03149i	−0.999488	+	0.0320000i	$0.989812\pi$
$492$	−3991.74	+	6391.51i	−0.365775	+	0.585674i
$493$	−6296.91	+	1352.29i	−0.575250	+	0.123538i
$494$		−	7622.91i		−	0.694273i
$495$	19654.9	+	6757.25i	1.78469	+	0.613567i
$496$	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
$501$	3501.28	+	15149.2i	0.312226	+	1.35093i
$502$			144.733i			0.0128681i
$503$	9744.83	−	9744.83i	0.863819	−	0.863819i	−0.127961	−	0.991779i	$-0.540843\pi$
$503$	9744.83	−	9744.83i	0.863819	−	0.863819i	0.991779	+	0.127961i	$0.0408431\pi$
$504$	1111.62	−	3233.40i	0.0982454	−	0.285768i
$505$	26.2891	+	26.2891i	0.00231654	+	0.00231654i
$506$	−19884.3			−1.74696
$507$	2205.14	+	9541.13i	0.193163	+	0.835772i
$508$	−967.673	−	967.673i	−0.0845149	−	0.0845149i
$509$		−	3483.49i		−	0.303345i	−0.988431	−	0.151673i	$-0.951534\pi$
$509$		−	3483.49i		−	0.303345i	0.988431	−	0.151673i	$-0.0484660\pi$
$510$	6579.30	−	1520.60i	0.571248	−	0.132026i
$511$	−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
$519$	−4034.71	−	17457.2i	−0.341241	−	1.47647i
$520$	5694.25	+	5694.25i	0.480211	+	0.480211i
$521$	−2368.28			−0.199148			−0.0995742	−	0.995030i	$-0.531748\pi$
$521$	−2368.28			−0.199148			−0.0995742	+	0.995030i	$0.531748\pi$
$522$	−6632.01	+	5209.10i	−0.556083	+	0.436774i
$523$	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
$525$	−2282.86	−	9877.40i	−0.189776	−	0.821114i
$526$			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
$534$	15944.9	−	3685.17i	1.29214	−	0.298638i
$535$		−	2467.87i		−	0.199431i
$536$	−2493.17	−	2493.17i	−0.200911	−	0.200911i
$537$	−4082.89	−	17665.7i	−0.328100	−	1.41961i
$538$	9857.95			0.789974
$539$	−3193.13	−	3193.13i	−0.255172	−	0.255172i
$540$	6867.57	−	5569.39i	0.547284	−	0.443831i
$541$	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
$543$	−973.864	−	4213.68i	−0.0769660	−	0.333014i
$544$			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
$549$	6721.60	−	19551.3i	0.522534	−	1.51990i
$550$			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	$-0.537798\pi$
$557$	−3114.66			−0.236934			−0.118467	+	0.992958i	$0.537798\pi$
$558$	1928.71	−	941.832i	0.146324	−	0.0714533i
$559$	20219.1	+	20219.1i	1.52983	+	1.52983i
$560$	3990.54			0.301127
$561$	−10200.5	+	2357.54i	−0.767676	+	0.177425i
$562$	9439.77	−	9439.77i	0.708528	−	0.708528i
$563$	3327.41	−	3327.41i	0.249083	−	0.249083i	−0.571511	−	0.820594i	$-0.693643\pi$
$563$	3327.41	−	3327.41i	0.249083	−	0.249083i	0.820594	+	0.571511i	$0.193643\pi$
$564$	−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	−0.947911	−	0.318534i	$-0.896809\pi$
$569$	−8542.39	+	8542.39i	−0.629377	+	0.629377i	0.318534	+	0.947911i	$0.396809\pi$
$570$	−2199.74	−	9517.76i	−0.161644	−	0.699395i
$571$	−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
$582$	5516.75	−	1275.03i	0.392915	−	0.0908103i
$583$	−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	$0.249044\pi$
$587$			20052.3i			1.40996i	−0.709227	+	0.704980i	$0.750956\pi$
$588$	−1871.78	+	432.604i	−0.131277	+	0.0303406i
$589$		−	2371.32i		−	0.165889i
$590$	−16086.9	+	16086.9i	−1.12252	+	1.12252i
$591$	−18063.1	+	4174.73i	−1.25722	+	0.290567i
$592$	1535.75	+	1535.75i	0.106620	+	0.106620i
$593$	−11309.6			−0.783185			−0.391592	−	0.920139i	$-0.628076\pi$
$593$	−11309.6			−0.783185			−0.391592	+	0.920139i	$0.628076\pi$
$594$	−10647.5	+	8634.76i	−0.735472	+	0.596445i
$595$	7273.07	+	7273.07i	0.501121	+	0.501121i
$596$			33.7855i			0.00232199i
$597$	−3255.84	−	14087.3i	−0.223204	−	0.965751i
$598$	−18386.1	−	18386.1i	−1.25730	−	1.25730i
$599$	272.130	+	272.130i	0.0185625	+	0.0185625i	0.716327	−	0.697765i	$-0.245822\pi$
$599$	272.130	+	272.130i	0.0185625	+	0.0185625i	−0.697765	+	0.716327i	$0.745822\pi$
$600$	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
$606$	−23.8922	+	5.52195i	−0.00160158	+	0.000370155i
$607$	−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
$609$	−12080.9	−	4365.08i	−0.803845	−	0.290446i
$610$	24129.4			1.60159
$611$	−13613.0	−	13613.0i	−0.901344	−	0.901344i
$612$	−1448.05	+	4211.98i	−0.0956439	+	0.278201i
$613$			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	−0.208847	−	0.977948i	$-0.566971\pi$
$617$	11787.2	−	11787.2i	0.769101	−	0.769101i	0.977948	+	0.208847i	$0.0669712\pi$
$618$	−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
$621$	−22174.6	+	17983.0i	−1.43291	+	1.16205i
$622$			6241.63i			0.402358i
$623$	17626.2	+	17626.2i	1.13351	+	1.13351i
$624$	−5175.08	+	1196.06i	−0.332001	+	0.0767320i
$625$	−15840.4			−1.01378
$626$	−6828.03	−	6828.03i	−0.435947	−	0.435947i
$627$	3410.47	+	14756.3i	0.217226	+	0.939888i
$628$	−549.416	+	549.416i	−0.0349110	+	0.0349110i
$629$			5598.05i			0.354863i
$630$	12736.4	+	4378.70i	0.805445	+	0.276907i
$631$			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
$636$	280.145	+	1212.12i	0.0174661	+	0.0755718i
$637$		−	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	0.550807	−	0.834633i	$-0.314320\pi$
$641$	−4606.16	−	4606.16i	−0.283826	−	0.283826i	−0.834633	+	0.550807i	$0.814320\pi$
$642$	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	$-0.546211\pi$
$647$	−4761.60			−0.289332			−0.144666	+	0.989481i	$0.546211\pi$
$648$	716.265	+	5787.85i	0.0434221	+	0.350877i
$649$	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	−0.745904	−	0.666053i	$-0.767982\pi$
$653$	−1332.45	+	1332.45i	−0.0798512	+	0.0798512i	0.666053	+	0.745904i	$0.267982\pi$
$654$	−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
$657$	16055.2	+	5519.67i	0.953381	+	0.327767i
$658$	−9539.97			−0.565208
$659$	6743.81	+	6743.81i	0.398636	+	0.398636i	0.877752	−	0.479115i	$-0.159042\pi$
$659$	6743.81	+	6743.81i	0.398636	+	0.398636i	−0.479115	+	0.877752i	$0.659042\pi$
$660$	−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
$669$	−6013.93	−	26020.9i	−0.347552	−	1.50378i
$670$	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
$675$	10891.7	+	13430.5i	0.621071	+	0.765838i
$676$		−	7538.38i		−	0.428902i
$677$	16837.8	−	16837.8i	0.955876	−	0.955876i	−0.0431909	−	0.999067i	$-0.513752\pi$
$677$	16837.8	−	16837.8i	0.955876	−	0.955876i	0.999067	+	0.0431909i	$0.0137524\pi$
$678$	422.429	+	1827.75i	0.0239282	+	0.103532i
$679$	6098.47	+	6098.47i	0.344680	+	0.344680i
$680$	−5198.26			−0.293153
$681$	−13716.2	+	3170.09i	−0.771816	+	0.178382i
$682$	−2746.30	−	2746.30i	−0.154195	−	0.154195i
$683$			27769.5i			1.55574i	0.628424	+	0.777871i	$0.283700\pi$
$683$			27769.5i			1.55574i	−0.628424	+	0.777871i	$0.716300\pi$
$684$	6093.14	+	2094.79i	0.340610	+	0.117100i
$685$	−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
$693$	−19746.5	−	6788.72i	−1.08240	−	0.372124i
$694$	5722.03	+	5722.03i	0.312976	+	0.312976i
$695$	8214.07			0.448313
$696$	5877.18	−	2757.34i	0.320078	−	0.150168i
$697$	14951.9			0.812547
$698$	16114.8	+	16114.8i	0.873858	+	0.873858i
$699$	2627.80	−	607.335i	0.142192	−	0.0328634i
$700$			7804.06i			0.421380i
$701$	−27473.0			−1.48023			−0.740114	−	0.672481i	$-0.765229\pi$
$701$	−27473.0			−1.48023			−0.740114	+	0.672481i	$0.765229\pi$
$702$	−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
$708$	−3379.01	−	14620.2i	−0.179366	−	0.776074i
$709$			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
$711$	−3859.62	+	11226.5i	−0.203582	+	0.592164i
$712$	−12597.9			−0.663100
$713$	−5719.51	−	5719.51i	−0.300417	−	0.300417i
$714$	−6609.94	+	1527.69i	−0.346458	+	0.0800731i
$715$	34774.9	−	34774.9i	1.81889	−	1.81889i
$716$			13957.5i			0.728516i
$717$	13699.3	−	3166.19i	0.713545	−	0.164914i
$718$		−	21136.4i		−	1.09861i
$719$			9112.14i			0.472636i	0.971676	+	0.236318i	$0.0759407\pi$
$719$			9112.14i			0.472636i	−0.971676	+	0.236318i	$0.924059\pi$
$720$	−6116.31	+	2986.74i	−0.316585	+	0.154596i
$721$	−11394.7			−0.588573
$722$	−4666.63	+	4666.63i	−0.240545	+	0.240545i
$723$	32715.4	−	7561.17i	1.68285	−	0.388939i
$724$			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
$735$	−1704.03	−	7372.95i	−0.0855158	−	0.370007i
$736$	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	$-0.401163\pi$
$743$	25472.2	−	25472.2i	1.25772	−	1.25772i	0.952179	−	0.305541i	$-0.0988372\pi$
$744$	−1609.85	+	372.067i	−0.0793279	+	0.0183342i
$745$	−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
$756$	−6899.55	+	5595.33i	−0.331924	+	0.269180i
$757$	−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	$0.148504\pi$
$761$			18885.3i			0.899594i	−0.893131	+	0.449797i	$0.851496\pi$
$762$	800.631	+	3464.14i	0.0380627	+	0.164688i
$763$		−	4526.42i		−	0.214767i
$764$	−4420.53	+	4420.53i	−0.209331	+	0.209331i
$765$	−16591.0	−	5703.89i	−0.784117	−	0.269575i
$766$	8737.33	+	8737.33i	0.412131	+	0.412131i
$767$	46123.9			2.17137
$768$	−299.542	−	1296.05i	−0.0140740	−	0.0608948i
$769$	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
$771$	−3496.12	+	808.022i	−0.163307	+	0.0377435i
$772$	−6062.24	−	6062.24i	−0.282623	−	0.282623i
$773$	4598.80	+	4598.80i	0.213981	+	0.213981i	0.805956	−	0.591975i	$-0.201652\pi$
$773$	4598.80	+	4598.80i	0.213981	+	0.213981i	−0.591975	+	0.805956i	$0.701652\pi$
$774$	−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
$780$	−4711.29	−	20384.7i	−0.216271	−	0.935754i
$781$	34584.6	+	34584.6i	1.58455	+	1.58455i
$782$	16784.6			0.767540
$783$	21783.4	−	2351.62i	0.994223	−	0.107331i
$784$	1478.88			0.0673687
$785$	−2164.15	−	2164.15i	−0.0983974	−	0.0983974i
$786$	3587.04	+	15520.3i	0.162780	+	0.704313i
$787$		−	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
$795$	−4774.55	+	1103.49i	−0.213001	+	0.0492287i
$796$			11130.2i			0.495604i
$797$	−9321.29	−	9321.29i	−0.414275	−	0.414275i	0.468950	−	0.883225i	$-0.344632\pi$
$797$	−9321.29	−	9321.29i	−0.414275	−	0.414275i	−0.883225	+	0.468950i	$0.844632\pi$
$798$	2209.98	+	9562.09i	0.0980358	+	0.424178i
$799$	12427.2			0.550242
$800$	−2788.89	−	2788.89i	−0.123253	−	0.123253i
$801$	−40208.1	−	13823.3i	−1.77364	−	0.609767i
$802$	−16366.5	+	16366.5i	−0.720601	+	0.720601i
$803$		−	30720.5i		−	1.35007i
$804$	2062.79	+	8925.20i	0.0904837	+	0.391502i
$805$		−	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	−0.749444	−	0.662068i	$-0.769679\pi$
$809$	−2010.56	+	2010.56i	−0.0873766	+	0.0873766i	0.662068	+	0.749444i	$0.269679\pi$
$810$	−22798.4	+	2821.37i	−0.988955	+	0.122386i
$811$			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	$-0.257298\pi$
$821$	32496.9			1.38142			0.690711	+	0.723131i	$0.257298\pi$
$822$	4187.39	−	967.787i	0.177679	−	0.0410650i
$823$	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	−0.956861	−	0.290546i	$-0.906163\pi$
$827$	−15846.7	+	15846.7i	−0.666315	+	0.666315i	0.290546	+	0.956861i	$0.406163\pi$
$828$	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
$831$	−10571.1	−	45738.5i	−0.441283	−	1.90933i
$832$	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	−0.633041	−	0.774118i	$-0.718193\pi$
$839$	3428.47	−	3428.47i	0.141078	−	0.141078i	0.774118	+	0.633041i	$0.218193\pi$
$840$	−8793.64	−	5491.96i	−0.361202	−	0.225584i
$841$	−10013.5	−	22238.6i	−0.410574	−	0.911827i
$842$		−	2629.97i		−	0.107642i
$843$	−33793.1	+	7810.25i	−1.38066	+	0.319097i
$844$	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
$849$	−38102.1	+	8806.13i	−1.54024	+	0.355978i
$850$		−	10165.9i		−	0.410222i
$851$	19532.6	−	19532.6i	0.786804	−	0.786804i
$852$	20273.1	−	4685.50i	0.815193	−	0.188407i
$853$	−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
$855$	−8251.38	+	24000.9i	−0.330048	+	0.960017i
$856$	−886.035	−	886.035i	−0.0353786	−	0.0353786i
$857$		−	13072.3i		−	0.521051i	−0.965467	−	0.260526i	$-0.916104\pi$
$857$		−	13072.3i		−	0.521051i	0.965467	−	0.260526i	$-0.0838959\pi$
$858$	7304.37	+	31604.3i	0.290638	+	1.25752i
$859$	−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	$-0.674673\pi$
$863$	−26448.5			−1.04324			−0.521621	+	0.853177i	$0.674673\pi$
$864$	466.083	−	4465.22i	0.0183524	−	0.175821i
$865$	−54330.1			−2.13558
$866$		−	21526.3i		−	0.844679i
$867$	−16262.6	+	3758.61i	−0.637033	+	0.147231i
$868$	−1779.60	−	1779.60i	−0.0695894	−	0.0695894i
$869$	21481.3			0.838554
$870$	10861.2	+	23150.3i	0.423252	+	0.902147i
$871$	−28157.3			−1.09538
$872$	1617.58	+	1617.58i	0.0628190	+	0.0628190i
$873$	−13911.6	−	4782.72i	−0.539331	−	0.185419i
$874$		−	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	$0.187330\pi$
$881$	36266.6	+	36266.6i	1.38689	+	1.38689i	0.555127	+	0.831765i	$0.312670\pi$
$882$	4720.06	+	1622.73i	0.180196	+	0.0619502i
$883$		−	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
$885$	57589.1	−	13310.0i	2.18738	−	0.505547i
$886$	17238.7			0.653662
$887$	−27396.7	−	27396.7i	−1.03708	−	1.03708i	−0.999285	−	0.0377971i	$-0.987966\pi$
$887$	−27396.7	−	27396.7i	−1.03708	−	1.03708i	−0.0377971	−	0.999285i	$-0.512034\pi$
$888$	−1270.64	−	5497.78i	−0.0480181	−	0.207763i
$889$	−3829.42	+	3829.42i	−0.144471	+	0.144471i
$890$		−	49623.3i		−	1.86896i
$891$	35346.5	−	4374.24i	1.32902	−	0.164470i
$892$			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
$897$	15212.3	+	65819.9i	0.566246	+	2.45001i
$898$			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
$909$	60.2490	+	20.7132i	0.00219838	+	0.000755792i
$910$	22534.2	−	22534.2i	0.820879	−	0.820879i
$911$	−14589.7	+	14589.7i	−0.530600	+	0.530600i	−0.920751	−	0.390151i	$-0.872423\pi$
$911$	−14589.7	+	14589.7i	−0.530600	+	0.530600i	0.390151	+	0.920751i	$0.372423\pi$
$912$	−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
$918$	8987.68	−	7288.73i	0.323135	−	0.262052i
$919$	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	$-0.906237\pi$
$929$		−	16441.3i		−	0.580647i	0.956929	−	0.290323i	$-0.0937628\pi$
$930$	−1465.58	−	6341.21i	−0.0516754	−	0.223588i
$931$	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
$936$	13050.0	+	4486.51i	0.455718	+	0.156673i
$937$			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
$939$	5649.35	+	24443.4i	0.196336	+	0.849501i
$940$	13429.0	+	13429.0i	0.465964	+	0.465964i
$941$	47721.4			1.65321			0.826607	−	0.562780i	$-0.190268\pi$
$941$	47721.4			1.65321			0.826607	+	0.562780i	$0.190268\pi$
$942$	1966.84	−	454.574i	0.0680287	−	0.0157227i
$943$	−52170.1	−	52170.1i	−1.80158	−	1.80158i
$944$			11551.3i			0.398266i
$945$	−22040.0	−	27177.4i	−0.758691	−	0.935535i
$946$	30924.1	+	30924.1i	1.06282	+	1.06282i
$947$	−12280.8	−	12280.8i	−0.421408	−	0.421408i	0.464280	−	0.885688i	$-0.346313\pi$
$947$	−12280.8	−	12280.8i	−0.421408	−	0.421408i	−0.885688	+	0.464280i	$0.846313\pi$
$948$	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	$-0.970053\pi$
$953$		−	5527.47i		−	0.187883i	0.995578	−	0.0939414i	$-0.0299466\pi$
$954$	1050.84	−	3056.60i	0.0356627	−	0.103733i
$955$	−17412.5	−	17412.5i	−0.590006	−	0.590006i
$956$	−10823.8			−0.366177
$957$	−16839.2	−	35892.1i	−0.568790	−	1.21236i
$958$	−16061.1			−0.541661
$959$	4628.93	+	4628.93i	0.155867	+	0.155867i
$960$	5105.15	−	1179.90i	0.171633	−	0.0396678i
$961$			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
$969$	−2878.83	−	12456.0i	−0.0954399	−	0.412946i
$970$		−	17169.1i		−	0.568317i
$971$	−2685.79	−	2685.79i	−0.0887652	−	0.0887652i	0.661330	−	0.750095i	$-0.269992\pi$
$971$	−2685.79	−	2685.79i	−0.0887652	−	0.0887652i	−0.750095	+	0.661330i	$0.769992\pi$
$972$	6387.12	−	13740.0i	0.210769	−	0.453406i
$973$	−8252.32			−0.271898
$974$	−13646.4	−	13646.4i	−0.448932	−	0.448932i
$975$	39865.1	−	9213.60i	1.30944	−	0.302637i
$976$	8663.12	−	8663.12i	0.284119	−	0.284119i
$977$		−	30679.8i		−	1.00464i	−0.864682	−	0.502320i	$-0.832480\pi$
$977$		−	30679.8i		−	1.00464i	0.864682	−	0.502320i	$-0.167520\pi$
$978$	−11059.2	+	2555.99i	−0.361589	+	0.0835701i
$979$			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	−0.935408	−	0.353571i	$-0.884967\pi$
$983$	−17932.1	+	17932.1i	−0.581836	+	0.581836i	0.353571	+	0.935408i	$0.384967\pi$
$984$	−14684.1	+	3393.79i	−0.475725	+	0.109949i
$985$			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
$996$	−892.537	−	3861.80i	−0.0283947	−	0.122857i
$997$	−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.17.21	yes	60
3.2	odd	2	inner	174.4.f.a.17.13	✓	60
29.12	odd	4	inner	174.4.f.a.41.13	yes	60
87.41	even	4	inner	174.4.f.a.41.21	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
174.4.f.a.17.13	✓	60	3.2	odd	2	inner
174.4.f.a.17.21	yes	60	1.1	even	1	trivial
174.4.f.a.41.13	yes	60	29.12	odd	4	inner
174.4.f.a.41.21	yes	60	87.41	even	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} +(-1.17009 - 5.06270i) 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} +(20.2508 - 4.68035i) q^{12} +63.8874i q^{13} +(22.3862 + 22.3862i) q^{14} +(18.4359 + 79.7680i) q^{15} -16.0000 q^{16} +(-29.1612 - 29.1612i) q^{17} +(-51.0664 - 17.5563i) q^{18} +(-42.1853 + 42.1853i) q^{19} -63.0241i q^{20} +(-18.5218 - 80.1395i) 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} +(88.3692 + 108.967i) 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} +(323.442 - 74.7538i) 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} +(18.7214 + 81.0031i) 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} +(-319.072 + 73.7438i) 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} +(494.688 - 114.332i) q^{66} +440.734i q^{67} +(116.645 - 116.645i) q^{68} +(1030.25 - 238.111i) q^{69} +(-352.717 - 352.717i) q^{70} +1001.10 q^{71} +(70.2253 - 204.266i) q^{72} +(-444.626 - 444.626i) q^{73} -271.485i q^{74} +(-144.216 - 623.991i) 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} +(320.558 - 74.0872i) q^{84} +(459.466 + 459.466i) q^{85} +895.143 q^{86} +(-763.191 - 275.757i) q^{87} -390.849 q^{88} +(1113.51 + 1113.51i) q^{89} +(804.604 + 276.618i) 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} +(-1247.45 - 428.867i) 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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