LMFDB - Embedded newform 174.4.f.a.17.19

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)

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);

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")

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			17.19
Character	$\chi$	$=$	174.17
Dual form			174.4.f.a.41.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41421 + 1.41421i) q^{2} +(-3.92999 - 3.39930i) q^{3} +4.00000i q^{4} -1.42088 q^{5} +(-0.750511 - 10.3652i) q^{6} +6.13369 q^{7} +(-5.65685 + 5.65685i) q^{8} +(3.88959 + 26.7184i) q^{9} +(-2.00943 - 2.00943i) q^{10} +(-25.3324 - 25.3324i) q^{11} +(13.5972 - 15.7199i) q^{12} -63.0706i q^{13} +(8.67435 + 8.67435i) q^{14} +(5.58405 + 4.83000i) q^{15} -16.0000 q^{16} +(-71.2790 - 71.2790i) q^{17} +(-32.2848 + 43.2862i) q^{18} +(-82.3877 + 82.3877i) q^{19} -5.68353i q^{20} +(-24.1053 - 20.8502i) q^{21} -71.6509i q^{22} -134.812i q^{23} +(41.4607 - 3.00204i) q^{24} -122.981 q^{25} +(89.1953 - 89.1953i) q^{26} +(75.5376 - 118.225i) q^{27} +24.5348i q^{28} +(-143.612 - 61.3560i) q^{29} +(1.06639 + 14.7277i) q^{30} +(142.561 - 142.561i) q^{31} +(-22.6274 - 22.6274i) q^{32} +(13.4437 + 185.668i) q^{33} -201.607i q^{34} -8.71526 q^{35} +(-106.873 + 15.5583i) q^{36} +(312.323 + 312.323i) q^{37} -233.028 q^{38} +(-214.396 + 247.867i) q^{39} +(8.03772 - 8.03772i) q^{40} +(-225.390 + 225.390i) q^{41} +(-4.60340 - 63.5768i) q^{42} +(79.9118 - 79.9118i) q^{43} +(101.330 - 101.330i) q^{44} +(-5.52664 - 37.9636i) q^{45} +(190.653 - 190.653i) q^{46} +(361.724 - 361.724i) q^{47} +(62.8798 + 54.3887i) q^{48} -305.378 q^{49} +(-173.922 - 173.922i) q^{50} +(37.8271 + 522.424i) q^{51} +252.282 q^{52} +331.628i q^{53} +(274.021 - 60.3686i) q^{54} +(35.9944 + 35.9944i) q^{55} +(-34.6974 + 34.6974i) q^{56} +(603.843 - 43.7225i) q^{57} +(-116.328 - 289.869i) q^{58} +215.986i q^{59} +(-19.3200 + 22.3362i) q^{60} +(341.341 - 341.341i) q^{61} +403.222 q^{62} +(23.8575 + 163.882i) q^{63} -64.0000i q^{64} +89.6159i q^{65} +(-243.562 + 281.587i) q^{66} +392.396i q^{67} +(285.116 - 285.116i) q^{68} +(-458.265 + 529.809i) q^{69} +(-12.3252 - 12.3252i) q^{70} -59.9611 q^{71} +(-173.145 - 129.139i) q^{72} +(-745.932 - 745.932i) q^{73} +883.383i q^{74} +(483.314 + 418.049i) q^{75} +(-329.551 - 329.551i) q^{76} +(-155.381 - 155.381i) q^{77} +(-653.738 + 47.3352i) q^{78} +(76.1582 - 76.1582i) q^{79} +22.7341 q^{80} +(-698.742 + 207.847i) q^{81} -637.498 q^{82} +751.267i q^{83} +(83.4009 - 96.4213i) q^{84} +(101.279 + 101.279i) q^{85} +226.025 q^{86} +(355.827 + 729.308i) q^{87} +286.603 q^{88} +(19.0121 + 19.0121i) q^{89} +(45.8729 - 61.5046i) q^{90} -386.856i q^{91} +539.247 q^{92} +(-1044.87 + 75.6557i) q^{93} +1023.11 q^{94} +(117.063 - 117.063i) q^{95} +(12.0082 + 165.843i) q^{96} +(-291.810 - 291.810i) q^{97} +(-431.869 - 431.869i) q^{98} +(578.308 - 775.373i) 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
$3$	−3.92999	−	3.39930i	−0.756326	−	0.654195i
$3$	−3.92999	−	3.39930i	−0.756326	−	0.654195i
$4$			4.00000i			0.500000i
$5$	−1.42088			−0.127088			−0.0635438	−	0.997979i	$-0.520240\pi$
$5$	−1.42088			−0.127088			−0.0635438	+	0.997979i	$0.520240\pi$
$6$	−0.750511	−	10.3652i	−0.0510658	−	0.705260i
$7$	6.13369			0.331188			0.165594	−	0.986194i	$-0.447046\pi$
$7$	6.13369			0.331188			0.165594	+	0.986194i	$0.447046\pi$
$8$	−5.65685	+	5.65685i	−0.250000	+	0.250000i
$9$	3.88959	+	26.7184i	0.144059	+	0.989569i
$10$	−2.00943	−	2.00943i	−0.0635438	−	0.0635438i
$11$	−25.3324	−	25.3324i	−0.694364	−	0.694364i	0.268825	−	0.963189i	$-0.413365\pi$
$11$	−25.3324	−	25.3324i	−0.694364	−	0.694364i	−0.963189	+	0.268825i	$0.913365\pi$
$12$	13.5972	−	15.7199i	0.327097	−	0.378163i
$13$		−	63.0706i		−	1.34559i	−0.739830	−	0.672794i	$-0.765094\pi$
$13$		−	63.0706i		−	1.34559i	0.739830	−	0.672794i	$-0.234906\pi$
$14$	8.67435	+	8.67435i	0.165594	+	0.165594i
$15$	5.58405	+	4.83000i	0.0961196	+	0.0831400i
$16$	−16.0000			−0.250000
$17$	−71.2790	−	71.2790i	−1.01692	−	1.01692i	−0.999854	−	0.0170690i	$-0.994567\pi$
$17$	−71.2790	−	71.2790i	−1.01692	−	1.01692i	−0.0170690	−	0.999854i	$-0.505433\pi$
$18$	−32.2848	+	43.2862i	−0.422755	+	0.566814i
$19$	−82.3877	+	82.3877i	−0.994792	+	0.994792i	−0.999987	−	0.00519488i	$-0.998346\pi$
$19$	−82.3877	+	82.3877i	−0.994792	+	0.994792i	0.00519488	+	0.999987i	$0.498346\pi$
$20$		−	5.68353i		−	0.0635438i
$21$	−24.1053	−	20.8502i	−0.250486	−	0.216662i
$22$		−	71.6509i		−	0.694364i
$23$		−	134.812i		−	1.22218i	−0.791560	−	0.611092i	$-0.790731\pi$
$23$		−	134.812i		−	1.22218i	0.791560	−	0.611092i	$-0.209269\pi$
$24$	41.4607	−	3.00204i	0.352630	−	0.0255329i
$25$	−122.981			−0.983849
$26$	89.1953	−	89.1953i	0.672794	−	0.672794i
$27$	75.5376	−	118.225i	0.538415	−	0.842680i
$28$			24.5348i			0.165594i
$29$	−143.612	−	61.3560i	−0.919590	−	0.392880i
$29$	−143.612	−	61.3560i	−0.919590	−	0.392880i
$30$	1.06639	+	14.7277i	0.00648983	+	0.0896298i
$31$	142.561	−	142.561i	0.825956	−	0.825956i	−0.160998	−	0.986955i	$-0.551471\pi$
$31$	142.561	−	142.561i	0.825956	−	0.825956i	0.986955	+	0.160998i	$0.0514713\pi$
$32$	−22.6274	−	22.6274i	−0.125000	−	0.125000i
$33$	13.4437	+	185.668i	0.0709165	+	0.979415i
$34$		−	201.607i		−	1.01692i
$35$	−8.71526			−0.0420899
$36$	−106.873	+	15.5583i	−0.494785	+	0.0720294i
$37$	312.323	+	312.323i	1.38772	+	1.38772i	0.830092	+	0.557627i	$0.188288\pi$
$37$	312.323	+	312.323i	1.38772	+	1.38772i	0.557627	+	0.830092i	$0.311712\pi$
$38$	−233.028			−0.994792
$39$	−214.396	+	247.867i	−0.880276	+	1.01770i
$40$	8.03772	−	8.03772i	0.0317719	−	0.0317719i
$41$	−225.390	+	225.390i	−0.858535	+	0.858535i	−0.991166	−	0.132631i	$-0.957658\pi$
$41$	−225.390	+	225.390i	−0.858535	+	0.858535i	0.132631	+	0.991166i	$0.457658\pi$
$42$	−4.60340	−	63.5768i	−0.0169124	−	0.233574i
$43$	79.9118	−	79.9118i	0.283406	−	0.283406i	−0.551060	−	0.834466i	$-0.685776\pi$
$43$	79.9118	−	79.9118i	0.283406	−	0.283406i	0.834466	+	0.551060i	$0.185776\pi$
$44$	101.330	−	101.330i	0.347182	−	0.347182i
$45$	−5.52664	−	37.9636i	−0.0183081	−	0.125762i
$46$	190.653	−	190.653i	0.611092	−	0.611092i
$47$	361.724	−	361.724i	1.12261	−	1.12261i	0.131268	−	0.991347i	$-0.458095\pi$
$47$	361.724	−	361.724i	1.12261	−	1.12261i	0.991347	−	0.131268i	$-0.0419047\pi$
$48$	62.8798	+	54.3887i	0.189082	+	0.163549i
$49$	−305.378			−0.890314
$50$	−173.922	−	173.922i	−0.491924	−	0.491924i
$51$	37.8271	+	522.424i	0.103860	+	1.43439i
$52$	252.282			0.672794
$53$			331.628i			0.859483i	0.902952	+	0.429741i	$0.141395\pi$
$53$			331.628i			0.859483i	−0.902952	+	0.429741i	$0.858605\pi$
$54$	274.021	−	60.3686i	0.690547	−	0.152132i
$55$	35.9944	+	35.9944i	0.0882451	+	0.0882451i
$56$	−34.6974	+	34.6974i	−0.0827971	+	0.0827971i
$57$	603.843	−	43.7225i	1.40317	−	0.101600i
$58$	−116.328	−	289.869i	−0.263355	−	0.656235i
$59$			215.986i			0.476594i	0.971192	+	0.238297i	$0.0765891\pi$
$59$			215.986i			0.476594i	−0.971192	+	0.238297i	$0.923411\pi$
$60$	−19.3200	+	22.3362i	−0.0415700	+	0.0480598i
$61$	341.341	−	341.341i	0.716463	−	0.716463i	−0.251416	−	0.967879i	$-0.580896\pi$
$61$	341.341	−	341.341i	0.716463	−	0.716463i	0.967879	+	0.251416i	$0.0808962\pi$
$62$	403.222			0.825956
$63$	23.8575	+	163.882i	0.0477106	+	0.327734i
$64$		−	64.0000i		−	0.125000i
$65$			89.6159i			0.171007i
$66$	−243.562	+	281.587i	−0.454249	+	0.525166i
$67$			392.396i			0.715505i	0.933816	+	0.357753i	$0.116457\pi$
$67$			392.396i			0.715505i	−0.933816	+	0.357753i	$0.883543\pi$
$68$	285.116	−	285.116i	0.508462	−	0.508462i
$69$	−458.265	+	529.809i	−0.799546	+	0.924369i
$70$	−12.3252	−	12.3252i	−0.0210450	−	0.0210450i
$71$	−59.9611			−0.100226			−0.0501132	−	0.998744i	$-0.515958\pi$
$71$	−59.9611			−0.100226			−0.0501132	+	0.998744i	$0.515958\pi$
$72$	−173.145	−	129.139i	−0.283407	−	0.211378i
$73$	−745.932	−	745.932i	−1.19595	−	1.19595i	−0.975367	−	0.220587i	$-0.929203\pi$
$73$	−745.932	−	745.932i	−1.19595	−	1.19595i	−0.220587	−	0.975367i	$-0.570797\pi$
$74$			883.383i			1.38772i
$75$	483.314	+	418.049i	0.744111	+	0.643629i
$76$	−329.551	−	329.551i	−0.497396	−	0.497396i
$77$	−155.381	−	155.381i	−0.229965	−	0.229965i
$78$	−653.738	+	47.3352i	−0.948990	+	0.0687135i
$79$	76.1582	−	76.1582i	0.108462	−	0.108462i	−0.650793	−	0.759255i	$-0.725564\pi$
$79$	76.1582	−	76.1582i	0.108462	−	0.108462i	0.759255	+	0.650793i	$0.225564\pi$
$80$	22.7341			0.0317719
$81$	−698.742	+	207.847i	−0.958494	+	0.285112i
$82$	−637.498			−0.858535
$83$			751.267i			0.993521i	0.867888	+	0.496760i	$0.165477\pi$
$83$			751.267i			0.993521i	−0.867888	+	0.496760i	$0.834523\pi$
$84$	83.4009	−	96.4213i	0.108331	−	0.125243i
$85$	101.279	+	101.279i	0.129238	+	0.129238i
$86$	226.025			0.283406
$87$	355.827	+	729.308i	0.438490	+	0.898736i
$88$	286.603			0.347182
$89$	19.0121	+	19.0121i	0.0226436	+	0.0226436i	0.718338	−	0.695694i	$-0.244903\pi$
$89$	19.0121	+	19.0121i	0.0226436	+	0.0226436i	−0.695694	+	0.718338i	$0.744903\pi$
$90$	45.8729	−	61.5046i	0.0537269	−	0.0720350i
$91$		−	386.856i		−	0.445643i
$92$	539.247			0.611092
$93$	−1044.87	+	75.6557i	−1.16503	+	0.0843563i
$94$	1023.11			1.12261
$95$	117.063	−	117.063i	0.126426	−	0.126426i
$96$	12.0082	+	165.843i	0.0127664	+	0.176315i
$97$	−291.810	−	291.810i	−0.305451	−	0.305451i	0.537691	−	0.843142i	$-0.319297\pi$
$97$	−291.810	−	291.810i	−0.305451	−	0.305451i	−0.843142	+	0.537691i	$0.819297\pi$
$98$	−431.869	−	431.869i	−0.445157	−	0.445157i
$99$	578.308	−	775.373i	0.587092	−	0.787151i
$100$		−	491.924i		−	0.491924i
$101$	665.309	+	665.309i	0.655453	+	0.655453i	0.954301	−	0.298848i	$-0.0966024\pi$
$101$	665.309	+	665.309i	0.655453	+	0.655453i	−0.298848	+	0.954301i	$0.596602\pi$
$102$	−685.323	+	792.315i	−0.665266	+	0.769126i
$103$	−25.2560			−0.0241607			−0.0120803	−	0.999927i	$-0.503845\pi$
$103$	−25.2560			−0.0241607			−0.0120803	+	0.999927i	$0.503845\pi$
$104$	356.781	+	356.781i	0.336397	+	0.336397i
$105$	34.2508	+	29.6257i	0.0318337	+	0.0275350i
$106$	−468.992	+	468.992i	−0.429741	+	0.429741i
$107$			904.322i			0.817048i	0.912748	+	0.408524i	$0.133956\pi$
$107$			904.322i			0.817048i	−0.912748	+	0.408524i	$0.866044\pi$
$108$	472.899	+	302.150i	0.421340	+	0.269208i
$109$		−	411.342i		−	0.361463i	−0.983533	−	0.180731i	$-0.942154\pi$
$109$		−	411.342i		−	0.361463i	0.983533	−	0.180731i	$-0.0578465\pi$
$110$			101.807i			0.0882451i
$111$	−165.747	−	2289.10i	−0.141730	−	1.95741i
$112$	−98.1391			−0.0827971
$113$	−778.950	+	778.950i	−0.648473	+	0.648473i	−0.952624	−	0.304151i	$-0.901627\pi$
$113$	−778.950	+	778.950i	−0.648473	+	0.648473i	0.304151	+	0.952624i	$0.401627\pi$
$114$	915.796	+	792.130i	0.752387	+	0.650787i
$115$			191.552i			0.155324i
$116$	245.424	−	574.449i	0.196440	−	0.459795i
$117$	1685.14	−	245.319i	1.33155	−	0.193844i
$118$	−305.451	+	305.451i	−0.238297	+	0.238297i
$119$	−437.204	−	437.204i	−0.336793	−	0.336793i
$120$	−58.9107	+	4.26555i	−0.0448149	+	0.00324491i
$121$		−	47.5385i		−	0.0357164i
$122$	965.459			0.716463
$123$	1651.94	−	119.612i	1.21098	−	0.0876835i
$124$	570.243	+	570.243i	0.412978	+	0.412978i
$125$	352.352			0.252122
$126$	−198.025	+	265.504i	−0.140012	+	0.187722i
$127$	1409.05	−	1409.05i	0.984509	−	0.984509i	−0.0153730	−	0.999882i	$-0.504894\pi$
$127$	1409.05	−	1409.05i	0.984509	−	0.984509i	0.999882	+	0.0153730i	$0.00489359\pi$
$128$	90.5097	−	90.5097i	0.0625000	−	0.0625000i
$129$	−585.696	+	42.4085i	−0.399750	+	0.0289447i
$130$	−126.736	+	126.736i	−0.0855037	+	0.0855037i
$131$	1173.07	−	1173.07i	0.782380	−	0.782380i	−0.197852	−	0.980232i	$-0.563396\pi$
$131$	1173.07	−	1173.07i	0.782380	−	0.782380i	0.980232	+	0.197852i	$0.0633965\pi$
$132$	−742.673	+	53.7748i	−0.489708	+	0.0354583i
$133$	−505.341	+	505.341i	−0.329463	+	0.329463i
$134$	−554.932	+	554.932i	−0.357753	+	0.357753i
$135$	−107.330	+	167.983i	−0.0684259	+	0.107094i
$136$	806.430			0.508462
$137$	−1777.52	−	1777.52i	−1.10849	−	1.10849i	−0.993349	−	0.115145i	$-0.963267\pi$
$137$	−1777.52	−	1777.52i	−1.10849	−	1.10849i	−0.115145	−	0.993349i	$-0.536733\pi$
$138$	−1397.35	+	101.178i	−0.861958	+	0.0624118i
$139$	3132.55			1.91151			0.955753	−	0.294169i	$-0.0950430\pi$
$139$	3132.55			1.91151			0.955753	+	0.294169i	$0.0950430\pi$
$140$		−	34.8610i		−	0.0210450i
$141$	−2651.18	+	191.964i	−1.58347	+	0.114654i
$142$	−84.7978	−	84.7978i	−0.0501132	−	0.0501132i
$143$	−1597.73	+	1597.73i	−0.934328	+	0.934328i
$144$	−62.2334	−	427.494i	−0.0360147	−	0.247392i
$145$	204.056	+	87.1796i	0.116868	+	0.0499301i
$146$		−	2109.81i		−	1.19595i
$147$	1200.13	+	1038.07i	0.673368	+	0.582439i
$148$	−1249.29	+	1249.29i	−0.693859	+	0.693859i
$149$	−1185.56			−0.651843			−0.325922	−	0.945397i	$-0.605675\pi$
$149$	−1185.56			−0.651843			−0.325922	+	0.945397i	$0.605675\pi$
$150$	92.2986	+	1274.72i	0.0502410	+	0.693870i
$151$		−	258.273i		−	0.139192i	−0.997575	−	0.0695958i	$-0.977829\pi$
$151$		−	258.273i		−	0.139192i	0.997575	−	0.0695958i	$-0.0221710\pi$
$152$		−	932.111i		−	0.497396i
$153$	1627.21	−	2181.70i	0.859819	−	1.15281i
$154$		−	439.484i		−	0.229965i
$155$	−202.562	+	202.562i	−0.104969	+	0.104969i
$156$	−991.467	−	857.582i	−0.508852	−	0.440138i
$157$	−1161.71	−	1161.71i	−0.590536	−	0.590536i	0.347240	−	0.937776i	$-0.387119\pi$
$157$	−1161.71	−	1161.71i	−0.590536	−	0.590536i	−0.937776	+	0.347240i	$0.887119\pi$
$158$	215.408			0.108462
$159$	1127.30	−	1303.29i	0.562269	−	0.650049i
$160$	32.1509	+	32.1509i	0.0158859	+	0.0158859i
$161$		−	826.895i		−	0.404773i
$162$	−1282.11	−	694.231i	−0.621803	−	0.336691i
$163$	−1339.89	−	1339.89i	−0.643853	−	0.643853i	0.307647	−	0.951500i	$-0.400458\pi$
$163$	−1339.89	−	1339.89i	−0.643853	−	0.643853i	−0.951500	+	0.307647i	$0.900458\pi$
$164$	−901.558	−	901.558i	−0.429267	−	0.429267i
$165$	−19.1019	−	263.813i	−0.00901261	−	0.124471i
$166$	−1062.45	+	1062.45i	−0.496760	+	0.496760i
$167$	−1520.24			−0.704430			−0.352215	−	0.935919i	$-0.614571\pi$
$167$	−1520.24			−0.704430			−0.352215	+	0.935919i	$0.614571\pi$
$168$	254.307	−	18.4136i	0.116787	−	0.00845620i
$169$	−1780.90			−0.810606
$170$			286.460i			0.129238i
$171$	−2521.72	−	1880.81i	−1.12772	−	0.841107i
$172$	319.647	+	319.647i	0.141703	+	0.141703i
$173$	4360.21			1.91619			0.958095	−	0.286450i	$-0.0924753\pi$
$173$	4360.21			1.91619			0.958095	+	0.286450i	$0.0924753\pi$
$174$	−528.182	+	1534.61i	−0.230123	+	0.668613i
$175$	−754.328			−0.325839
$176$	405.318	+	405.318i	0.173591	+	0.173591i
$177$	734.201	−	848.823i	0.311785	−	0.360460i
$178$			53.7744i			0.0226436i
$179$	−3491.79			−1.45804			−0.729019	−	0.684493i	$-0.760024\pi$
$179$	−3491.79			−1.45804			−0.729019	+	0.684493i	$0.760024\pi$
$180$	151.855	−	22.1066i	0.0628810	−	0.00915404i
$181$	−2503.71			−1.02817			−0.514086	−	0.857739i	$-0.671869\pi$
$181$	−2503.71			−1.02817			−0.514086	+	0.857739i	$0.671869\pi$
$182$	547.097	−	547.097i	0.222821	−	0.222821i
$183$	−2501.79	+	181.147i	−1.01059	+	0.0731735i
$184$	762.611	+	762.611i	0.305546	+	0.305546i
$185$	−443.774	−	443.774i	−0.176362	−	0.176362i
$186$	−1584.66	−	1370.67i	−0.624693	−	0.540336i
$187$			3611.34i			1.41223i
$188$	1446.90	+	1446.90i	0.561307	+	0.561307i
$189$	463.324	−	725.154i	0.178317	−	0.279086i
$190$	331.105			0.126426
$191$	648.681	+	648.681i	0.245743	+	0.245743i	0.819221	−	0.573478i	$-0.194406\pi$
$191$	648.681	+	648.681i	0.245743	+	0.245743i	−0.573478	+	0.819221i	$0.694406\pi$
$192$	−217.555	+	251.519i	−0.0817743	+	0.0945408i
$193$	385.438	−	385.438i	0.143754	−	0.143754i	−0.631567	−	0.775321i	$-0.717588\pi$
$193$	385.438	−	385.438i	0.143754	−	0.143754i	0.775321	+	0.631567i	$0.217588\pi$
$194$		−	825.362i		−	0.305451i
$195$	304.631	−	352.189i	0.111872	−	0.129337i
$196$		−	1221.51i		−	0.445157i
$197$		−	220.753i		−	0.0798375i	−0.999203	−	0.0399187i	$-0.987290\pi$
$197$		−	220.753i		−	0.0798375i	0.999203	−	0.0399187i	$-0.0127099\pi$
$198$	1914.39	−	278.692i	0.687122	−	0.100029i
$199$	1698.15			0.604918			0.302459	−	0.953162i	$-0.402192\pi$
$199$	1698.15			0.604918			0.302459	+	0.953162i	$0.402192\pi$
$200$	695.686	−	695.686i	0.245962	−	0.245962i
$201$	1333.87	−	1542.11i	0.468080	−	0.541155i
$202$			1881.78i			0.655453i
$203$	−880.873	−	376.339i	−0.304557	−	0.130117i
$204$	−2089.70	+	151.309i	−0.717196	+	0.0519300i
$205$	320.252	−	320.252i	0.109109	−	0.109109i
$206$	−35.7174	−	35.7174i	−0.0120803	−	0.0120803i
$207$	3601.95	−	524.362i	1.20943	−	0.176066i
$208$			1009.13i			0.336397i
$209$	4174.16			1.38150
$210$	6.54089	+	90.3351i	0.00214935	+	0.0296844i
$211$	1959.38	+	1959.38i	0.639287	+	0.639287i	0.950380	−	0.311093i	$-0.100695\pi$
$211$	1959.38	+	1959.38i	0.639287	+	0.639287i	−0.311093	+	0.950380i	$0.600695\pi$
$212$	−1326.51			−0.429741
$213$	235.646	+	203.825i	0.0758038	+	0.0655675i
$214$	−1278.90	+	1278.90i	−0.408524	+	0.408524i
$215$	−113.545	+	113.545i	−0.0360173	+	0.0360173i
$216$	241.475	+	1096.08i	0.0760660	+	0.345274i
$217$	874.423	−	874.423i	0.273547	−	0.273547i
$218$	581.726	−	581.726i	0.180731	−	0.180731i
$219$	395.859	+	5467.14i	0.122145	+	1.68692i
$220$	−143.977	+	143.977i	−0.0441225	+	0.0441225i
$221$	−4495.61	+	4495.61i	−1.36836	+	1.36836i
$222$	3002.88	−	3471.68i	0.907838	−	1.04957i
$223$	2134.67			0.641021			0.320511	−	0.947245i	$-0.396145\pi$
$223$	2134.67			0.641021			0.320511	+	0.947245i	$0.396145\pi$
$224$	−138.790	−	138.790i	−0.0413985	−	0.0413985i
$225$	−478.346	−	3285.85i	−0.141732	−	0.973586i
$226$	−2203.20			−0.648473
$227$		−	2388.99i		−	0.698513i	−0.937027	−	0.349257i	$-0.886434\pi$
$227$		−	2388.99i		−	0.698513i	0.937027	−	0.349257i	$-0.113566\pi$
$228$	174.890	+	2415.37i	0.0507998	+	0.701587i
$229$	−1280.94	−	1280.94i	−0.369638	−	0.369638i	0.497707	−	0.867345i	$-0.334175\pi$
$229$	−1280.94	−	1280.94i	−0.369638	−	0.369638i	−0.867345	+	0.497707i	$0.834175\pi$
$230$	−270.895	+	270.895i	−0.0776621	+	0.0776621i
$231$	82.4595	+	1138.83i	0.0234867	+	0.324371i
$232$	1159.47	−	465.311i	0.328117	−	0.131677i
$233$			410.947i			0.115545i	0.998330	+	0.0577726i	$0.0183998\pi$
$233$			410.947i			0.115545i	−0.998330	+	0.0577726i	$0.981600\pi$
$234$	2730.09	+	2036.22i	0.762698	+	0.568854i
$235$	−513.967	+	513.967i	−0.142670	+	0.142670i
$236$	−863.945			−0.238297
$237$	−558.185	+	40.4165i	−0.152987	+	0.0110774i
$238$		−	1236.60i		−	0.336793i
$239$		−	1411.18i		−	0.381932i	−0.981597	−	0.190966i	$-0.938838\pi$
$239$		−	1411.18i		−	0.381932i	0.981597	−	0.190966i	$-0.0611620\pi$
$240$	−89.3448	−	77.2800i	−0.0240299	−	0.0207850i
$241$			3471.71i			0.927935i	0.885852	+	0.463967i	$0.153575\pi$
$241$			3471.71i			0.927935i	−0.885852	+	0.463967i	$0.846425\pi$
$242$	67.2296	−	67.2296i	0.0178582	−	0.0178582i
$243$	3452.58	+	1558.40i	0.911453	+	0.411404i
$244$	1365.36	+	1365.36i	0.358232	+	0.358232i
$245$	433.906			0.113148
$246$	2505.36	+	2167.04i	0.649332	+	0.561649i
$247$	5196.24	+	5196.24i	1.33858	+	1.33858i
$248$			1612.89i			0.412978i
$249$	2553.78	−	2952.47i	0.649956	−	0.751426i
$250$	498.301	+	498.301i	0.126061	+	0.126061i
$251$	−1662.17	−	1662.17i	−0.417988	−	0.417988i	0.466522	−	0.884510i	$-0.345507\pi$
$251$	−1662.17	−	1662.17i	−0.417988	−	0.417988i	−0.884510	+	0.466522i	$0.845507\pi$
$252$	−655.529	+	95.4301i	−0.163867	+	0.0238553i
$253$	−3415.11	+	3415.11i	−0.848640	+	0.848640i
$254$	3985.38			0.984509
$255$	−53.7479	−	742.303i	−0.0131993	−	0.182293i
$256$	256.000			0.0625000
$257$			7905.98i			1.91892i	0.281850	+	0.959459i	$0.409052\pi$
$257$			7905.98i			1.91892i	−0.281850	+	0.959459i	$0.590948\pi$
$258$	−888.274	−	768.325i	−0.214347	−	0.185402i
$259$	1915.69	+	1915.69i	0.459596	+	0.459596i
$260$	−358.464			−0.0855037
$261$	1080.74	−	4075.73i	0.256307	−	0.966595i
$262$	3317.95			0.782380
$263$	634.797	+	634.797i	0.148834	+	0.148834i	0.777597	−	0.628763i	$-0.216439\pi$
$263$	634.797	+	634.797i	0.148834	+	0.148834i	−0.628763	+	0.777597i	$0.716439\pi$
$264$	−1126.35	−	974.250i	−0.262583	−	0.227125i
$265$		−	471.204i		−	0.109230i
$266$	−1429.32			−0.329463
$267$	−10.0896	−	139.345i	−0.00231263	−	0.0319393i
$268$	−1569.59			−0.357753
$269$	5120.20	−	5120.20i	1.16054	−	1.16054i	0.176177	−	0.984358i	$-0.443627\pi$
$269$	5120.20	−	5120.20i	1.16054	−	1.16054i	0.984358	−	0.176177i	$-0.0563731\pi$
$270$	−389.352	+	85.7767i	−0.0877600	+	0.0193341i
$271$	−4552.80	−	4552.80i	−1.02053	−	1.02053i	−0.999785	−	0.0207425i	$-0.993397\pi$
$271$	−4552.80	−	4552.80i	−1.02053	−	1.02053i	−0.0207425	−	0.999785i	$-0.506603\pi$
$272$	1140.46	+	1140.46i	0.254231	+	0.254231i
$273$	−1315.04	+	1520.34i	−0.291537	+	0.337051i
$274$		−	5027.58i		−	1.10849i
$275$	3115.41	+	3115.41i	0.683149	+	0.683149i
$276$	−2119.24	−	1833.06i	−0.462185	−	0.399773i
$277$	−8054.07			−1.74701			−0.873505	−	0.486814i	$-0.838159\pi$
$277$	−8054.07			−1.74701			−0.873505	+	0.486814i	$0.838159\pi$
$278$	4430.09	+	4430.09i	0.955753	+	0.955753i
$279$	4363.49	+	3254.49i	0.936327	+	0.698355i
$280$	49.3009	−	49.3009i	0.0105225	−	0.0105225i
$281$			1010.91i			0.214612i	0.994226	+	0.107306i	$0.0342225\pi$
$281$			1010.91i			0.214612i	−0.994226	+	0.107306i	$0.965778\pi$
$282$	−4020.81	−	3477.85i	−0.849063	−	0.734408i
$283$			868.704i			0.182470i	0.995829	+	0.0912351i	$0.0290815\pi$
$283$			868.704i			0.182470i	−0.995829	+	0.0912351i	$0.970919\pi$
$284$		−	239.844i		−	0.0501132i
$285$	−857.989	+	62.1244i	−0.178326	+	0.0129121i
$286$	−4519.06			−0.934328
$287$	−1382.47	+	1382.47i	−0.284337	+	0.284337i
$288$	516.556	−	692.579i	0.105689	−	0.141703i
$289$			5248.39i			1.06827i
$290$	165.288	+	411.869i	0.0334691	+	0.0833993i
$291$	154.861	+	2138.75i	0.0311962	+	0.430845i
$292$	2983.73	−	2983.73i	0.597977	−	0.597977i
$293$	−3062.66	−	3062.66i	−0.610656	−	0.610656i	0.332461	−	0.943117i	$-0.392121\pi$
$293$	−3062.66	−	3062.66i	−0.610656	−	0.610656i	−0.943117	+	0.332461i	$0.892121\pi$
$294$	229.189	+	3165.29i	0.0454646	+	0.627903i
$295$		−	306.891i		−	0.0605691i
$296$	−3533.53			−0.693859
$297$	−4908.46	+	1081.37i	−0.958983	+	0.211270i
$298$	−1676.63	−	1676.63i	−0.325922	−	0.325922i
$299$	−8502.67			−1.64455
$300$	−1672.20	+	1933.26i	−0.321814	+	0.372055i
$301$	490.155	−	490.155i	0.0938606	−	0.0938606i
$302$	365.253	−	365.253i	0.0695958	−	0.0695958i
$303$	−353.074	−	4876.24i	−0.0669424	−	0.924530i
$304$	1318.20	−	1318.20i	0.248698	−	0.248698i
$305$	−485.006	+	485.006i	−0.0910536	+	0.0910536i
$306$	5386.62	−	784.170i	1.00632	−	0.146497i
$307$	−796.337	+	796.337i	−0.148043	+	0.148043i	−0.777243	−	0.629200i	$-0.783383\pi$
$307$	−796.337	+	796.337i	−0.148043	+	0.148043i	0.629200	+	0.777243i	$0.283383\pi$
$308$	621.525	−	621.525i	0.114983	−	0.114983i
$309$	99.2557	+	85.8526i	0.0182733	+	0.0158058i
$310$	−572.932			−0.104969
$311$	−2167.29	−	2167.29i	−0.395163	−	0.395163i	0.481360	−	0.876523i	$-0.340143\pi$
$311$	−2167.29	−	2167.29i	−0.395163	−	0.395163i	−0.876523	+	0.481360i	$0.840143\pi$
$312$	−189.341	−	2614.95i	−0.0343568	−	0.474495i
$313$	−2254.32			−0.407097			−0.203549	−	0.979065i	$-0.565248\pi$
$313$	−2254.32			−0.407097			−0.203549	+	0.979065i	$0.565248\pi$
$314$		−	3285.80i		−	0.590536i
$315$	−33.8987	−	232.857i	−0.00606342	−	0.0416509i
$316$	304.633	+	304.633i	0.0542308	+	0.0542308i
$317$	891.183	−	891.183i	0.157899	−	0.157899i	−0.623736	−	0.781635i	$-0.714386\pi$
$317$	891.183	−	891.183i	0.157899	−	0.157899i	0.781635	+	0.623736i	$0.214386\pi$
$318$	3437.38	−	248.890i	0.606159	−	0.0438902i
$319$	2083.75	+	5192.33i	0.365729	+	0.911332i
$320$			90.9364i			0.0158859i
$321$	3074.06	−	3553.97i	0.534508	−	0.617955i
$322$	1169.41	−	1169.41i	0.202386	−	0.202386i
$323$	11745.0			2.02325
$324$	−831.387	−	2794.97i	−0.142556	−	0.479247i
$325$			7756.49i			1.32385i
$326$		−	3789.77i		−	0.643853i
$327$	−1398.27	+	1616.57i	−0.236467	+	0.273384i
$328$		−	2549.99i		−	0.429267i
$329$	2218.70	−	2218.70i	0.371797	−	0.371797i
$330$	346.073	−	400.102i	0.0577294	−	0.0667421i
$331$	−3113.59	−	3113.59i	−0.517035	−	0.517035i	0.399638	−	0.916673i	$-0.369136\pi$
$331$	−3113.59	−	3113.59i	−0.517035	−	0.517035i	−0.916673	+	0.399638i	$0.869136\pi$
$332$	−3005.07			−0.496760
$333$	−7129.95	+	9559.57i	−1.17333	+	1.57316i
$334$	−2149.95	−	2149.95i	−0.352215	−	0.352215i
$335$		−	557.549i		−	0.0909318i
$336$	385.685	+	333.604i	0.0626216	+	0.0541654i
$337$	−663.556	−	663.556i	−0.107259	−	0.107259i	0.651441	−	0.758700i	$-0.274165\pi$
$337$	−663.556	−	663.556i	−0.107259	−	0.107259i	−0.758700	+	0.651441i	$0.774165\pi$
$338$	−2518.58	−	2518.58i	−0.405303	−	0.405303i
$339$	5709.15	−	413.382i	0.914685	−	0.0662296i
$340$	−405.116	+	405.116i	−0.0646191	+	0.0646191i
$341$	−7222.81			−1.14703
$342$	−906.381	−	6226.12i	−0.143308	−	0.984415i
$343$	−3976.95			−0.626050
$344$			904.099i			0.141703i
$345$	651.141	−	752.796i	0.101612	−	0.117476i
$346$	6166.27	+	6166.27i	0.958095	+	0.958095i
$347$	9981.33			1.54417			0.772083	−	0.635522i	$-0.219215\pi$
$347$	9981.33			1.54417			0.772083	+	0.635522i	$0.219215\pi$
$348$	−2917.23	+	1423.31i	−0.449368	+	0.219245i
$349$	7528.08			1.15464			0.577319	−	0.816519i	$-0.304099\pi$
$349$	7528.08			1.15464			0.577319	+	0.816519i	$0.304099\pi$
$350$	−1066.78	−	1066.78i	−0.162920	−	0.162920i
$351$	−7456.50	−	4764.20i	−1.13390	−	0.724485i
$352$			1146.41i			0.173591i
$353$	4915.57			0.741159			0.370580	−	0.928801i	$-0.379159\pi$
$353$	4915.57			0.741159			0.370580	+	0.928801i	$0.379159\pi$
$354$	2238.74	−	162.100i	0.336123	−	0.0243376i
$355$	85.1976			0.0127375
$356$	−76.0485	+	76.0485i	−0.0113218	+	0.0113218i
$357$	232.020	+	3204.39i	0.0343972	+	0.475054i
$358$	−4938.14	−	4938.14i	−0.729019	−	0.729019i
$359$	−6160.03	−	6160.03i	−0.905609	−	0.905609i	0.0903048	−	0.995914i	$-0.471216\pi$
$359$	−6160.03	−	6160.03i	−0.905609	−	0.905609i	−0.995914	+	0.0903048i	$0.971216\pi$
$360$	246.018	+	183.491i	0.0360175	+	0.0268635i
$361$		−	6716.48i		−	0.979221i
$362$	−3540.78	−	3540.78i	−0.514086	−	0.514086i
$363$	−161.597	+	186.826i	−0.0233655	+	0.0270132i
$364$	1547.42			0.222821
$365$	1059.88	+	1059.88i	0.151991	+	0.151991i
$366$	−3794.24	−	3281.88i	−0.541880	−	0.468707i
$367$	8962.75	−	8962.75i	1.27480	−	1.27480i	0.331261	−	0.943539i	$-0.392526\pi$
$367$	8962.75	−	8962.75i	1.27480	−	1.27480i	0.943539	−	0.331261i	$-0.107474\pi$
$368$			2156.99i			0.305546i
$369$	−6898.71	−	5145.37i	−0.973259	−	0.725900i
$370$		−	1255.18i		−	0.176362i
$371$			2034.10i			0.284651i
$372$	−302.623	−	4179.47i	−0.0421781	−	0.582514i
$373$	12809.0			1.77809			0.889043	−	0.457824i	$-0.151371\pi$
$373$	12809.0			1.77809			0.889043	+	0.457824i	$0.151371\pi$
$374$	−5107.20	+	5107.20i	−0.706115	+	0.706115i
$375$	−1384.74	−	1197.75i	−0.190687	−	0.164937i
$376$			4092.44i			0.561307i
$377$	−3869.76	+	9057.71i	−0.528654	+	1.23739i
$378$	1680.76	−	370.283i	0.228701	−	0.0503844i
$379$	−675.716	+	675.716i	−0.0915810	+	0.0915810i	−0.751413	−	0.659832i	$-0.770627\pi$
$379$	−675.716	+	675.716i	−0.0915810	+	0.0915810i	0.659832	+	0.751413i	$0.270627\pi$
$380$	468.253	+	468.253i	0.0632128	+	0.0632128i
$381$	−10327.3	+	747.768i	−1.38867	+	0.100549i
$382$			1834.75i			0.245743i
$383$	−2103.90			−0.280691			−0.140345	−	0.990103i	$-0.544821\pi$
$383$	−2103.90			−0.280691			−0.140345	+	0.990103i	$0.544821\pi$
$384$	−663.371	+	48.0327i	−0.0881576	+	0.00638322i
$385$	220.778	+	220.778i	0.0292257	+	0.0292257i
$386$	1090.18			0.143754
$387$	2445.94	+	1824.29i	0.321276	+	0.239622i
$388$	1167.24	−	1167.24i	0.152726	−	0.152726i
$389$	−5167.02	+	5167.02i	−0.673467	+	0.673467i	−0.958514	−	0.285047i	$-0.907991\pi$
$389$	−5167.02	+	5167.02i	−0.673467	+	0.673467i	0.285047	+	0.958514i	$0.407991\pi$
$390$	928.884	−	67.2577i	0.120605	−	0.00873263i
$391$	−9609.25	+	9609.25i	−1.24287	+	1.24287i
$392$	1727.48	−	1727.48i	0.222579	−	0.222579i
$393$	−8597.78	+	622.539i	−1.10356	+	0.0799057i
$394$	312.192	−	312.192i	0.0399187	−	0.0399187i
$395$	−108.212	+	108.212i	−0.0137841	+	0.0137841i
$396$	3101.49	+	2313.23i	0.393575	+	0.293546i
$397$	3298.37			0.416978			0.208489	−	0.978025i	$-0.433145\pi$
$397$	3298.37			0.416978			0.208489	+	0.978025i	$0.433145\pi$
$398$	2401.55	+	2401.55i	0.302459	+	0.302459i
$399$	3703.79	−	268.180i	0.464715	−	0.0336486i
$400$	1967.70			0.245962
$401$		−	14040.0i		−	1.74844i	−0.485532	−	0.874219i	$-0.661374\pi$
$401$		−	14040.0i		−	1.74844i	0.485532	−	0.874219i	$-0.338626\pi$
$402$	4067.25	−	294.498i	0.504617	−	0.0365378i
$403$	−8991.39	−	8991.39i	−1.11140	−	1.11140i
$404$	−2661.24	+	2661.24i	−0.327726	+	0.327726i
$405$	992.830	−	295.326i	0.121813	−	0.0362342i
$406$	−713.519	−	1777.97i	−0.0872201	−	0.217337i
$407$		−	15823.8i		−	1.92716i
$408$	−3169.26	−	2741.29i	−0.384563	−	0.332633i
$409$	6800.96	−	6800.96i	0.822215	−	0.822215i	−0.164210	−	0.986425i	$-0.552508\pi$
$409$	6800.96	−	6800.96i	0.822215	−	0.822215i	0.986425	+	0.164210i	$0.0525076\pi$
$410$	905.809			0.109109
$411$	943.314	+	13027.9i	0.113212	+	1.56355i
$412$		−	101.024i		−	0.0120803i
$413$			1324.79i			0.157842i
$414$	5835.49	+	4352.37i	0.692751	+	0.516684i
$415$		−	1067.46i		−	0.126264i
$416$	−1427.13	+	1427.13i	−0.168198	+	0.168198i
$417$	−12310.9	−	10648.5i	−1.44572	−	1.25050i
$418$	5903.15	+	5903.15i	0.690748	+	0.690748i
$419$	−4492.52			−0.523804			−0.261902	−	0.965094i	$-0.584350\pi$
$419$	−4492.52			−0.523804			−0.261902	+	0.965094i	$0.584350\pi$
$420$	−118.503	+	137.003i	−0.0137675	+	0.0159169i
$421$	−8808.67	−	8808.67i	−1.01973	−	1.01973i	−0.999801	−	0.0199336i	$-0.993655\pi$
$421$	−8808.67	−	8808.67i	−1.01973	−	1.01973i	−0.0199336	−	0.999801i	$-0.506345\pi$
$422$			5541.97i			0.639287i
$423$	11071.6	+	8257.72i	1.27263	+	0.949182i
$424$	−1875.97	−	1875.97i	−0.214871	−	0.214871i
$425$	8765.97	+	8765.97i	1.00050	+	1.00050i
$426$	45.0014	+	621.507i	0.00511814	+	0.0706857i
$427$	2093.68	−	2093.68i	0.237284	−	0.237284i
$428$	−3617.29			−0.408524
$429$	11710.2	−	847.902i	1.31789	−	0.0954244i
$430$	−321.155			−0.0360173
$431$		−	8396.61i		−	0.938400i	−0.883092	−	0.469200i	$-0.844542\pi$
$431$		−	8396.61i		−	0.938400i	0.883092	−	0.469200i	$-0.155458\pi$
$432$	−1208.60	+	1891.59i	−0.134604	+	0.210670i
$433$	−8643.79	−	8643.79i	−0.959339	−	0.959339i	0.0398657	−	0.999205i	$-0.487307\pi$
$433$	−8643.79	−	8643.79i	−0.959339	−	0.959339i	−0.999205	+	0.0398657i	$0.987307\pi$
$434$	2473.24			0.273547
$435$	−505.588	−	1036.26i	−0.0557266	−	0.114218i
$436$	1645.37			0.180731
$437$	11106.8	+	11106.8i	1.21582	+	1.21582i
$438$	−7171.88	+	8291.54i	−0.782387	+	0.904532i
$439$			10338.4i			1.12398i	0.827144	+	0.561990i	$0.189964\pi$
$439$			10338.4i			1.12398i	−0.827144	+	0.561990i	$0.810036\pi$
$440$	−407.230			−0.0441225
$441$	−1187.79	−	8159.20i	−0.128258	−	0.881028i
$442$	−12715.5			−1.36836
$443$	−1799.97	+	1799.97i	−0.193045	+	0.193045i	−0.797011	−	0.603965i	$-0.793587\pi$
$443$	−1799.97	+	1799.97i	−0.193045	+	0.193045i	0.603965	+	0.797011i	$0.293587\pi$
$444$	9156.41	−	662.988i	0.978703	−	0.0708650i
$445$	−27.0140	−	27.0140i	−0.00287772	−	0.00287772i
$446$	3018.87	+	3018.87i	0.320511	+	0.320511i
$447$	4659.22	+	4030.06i	0.493006	+	0.426432i
$448$		−	392.556i		−	0.0413985i
$449$	2156.21	+	2156.21i	0.226632	+	0.226632i	0.811284	−	0.584652i	$-0.198769\pi$
$449$	2156.21	+	2156.21i	0.226632	+	0.226632i	−0.584652	+	0.811284i	$0.698769\pi$
$450$	3970.42	−	5323.38i	0.415927	−	0.557659i
$451$	11419.3			1.19227
$452$	−3115.80	−	3115.80i	−0.324237	−	0.324237i
$453$	−877.945	+	1015.01i	−0.0910584	+	0.105274i
$454$	3378.54	−	3378.54i	0.349257	−	0.349257i
$455$			549.676i			0.0566357i
$456$	−3168.52	+	3663.18i	−0.325394	+	0.376194i
$457$			6071.96i			0.621519i	0.950489	+	0.310760i	$0.100583\pi$
$457$			6071.96i			0.621519i	−0.950489	+	0.310760i	$0.899417\pi$
$458$		−	3623.05i		−	0.369638i
$459$	−13811.2	+	3042.69i	−1.40447	+	0.309413i
$460$	−766.207			−0.0776621
$461$	6594.67	−	6594.67i	0.666257	−	0.666257i	−0.290590	−	0.956848i	$-0.593852\pi$
$461$	6594.67	−	6594.67i	0.666257	−	0.666257i	0.956848	+	0.290590i	$0.0938517\pi$
$462$	−1493.94	+	1727.17i	−0.150442	+	0.173929i
$463$		−	2566.46i		−	0.257611i	−0.991670	−	0.128805i	$-0.958886\pi$
$463$		−	2566.46i		−	0.257611i	0.991670	−	0.128805i	$-0.0411142\pi$
$464$	2297.79	+	981.695i	0.229897	+	0.0982200i
$465$	1484.63	−	107.498i	0.148061	−	0.0107206i
$466$	−581.167	+	581.167i	−0.0577726	+	0.0577726i
$467$	4478.43	+	4478.43i	0.443763	+	0.443763i	0.893274	−	0.449512i	$-0.148402\pi$
$467$	4478.43	+	4478.43i	0.443763	+	0.443763i	−0.449512	+	0.893274i	$0.648402\pi$
$468$	981.274	+	6740.58i	0.0969218	+	0.665776i
$469$			2406.84i			0.236967i
$470$	−1453.72			−0.142670
$471$	616.507	+	8514.47i	0.0603124	+	0.832964i
$472$	−1221.80	−	1221.80i	−0.119148	−	0.119148i
$473$	−4048.72			−0.393573
$474$	−846.551	−	732.235i	−0.0820324	−	0.0709550i
$475$	10132.1	−	10132.1i	0.978725	−	0.978725i
$476$	1748.81	−	1748.81i	0.168397	−	0.168397i
$477$	−8860.55	+	1289.89i	−0.850517	+	0.123816i
$478$	1995.71	−	1995.71i	0.190966	−	0.190966i
$479$	3918.19	−	3918.19i	0.373751	−	0.373751i	−0.495090	−	0.868841i	$-0.664865\pi$
$479$	3918.19	−	3918.19i	0.373751	−	0.373751i	0.868841	+	0.495090i	$0.164865\pi$
$480$	−17.0622	−	235.643i	−0.00162246	−	0.0224075i
$481$	19698.4	−	19698.4i	1.86730	−	1.86730i
$482$	−4909.73	+	4909.73i	−0.463967	+	0.463967i
$483$	−2810.86	+	3249.68i	−0.264800	+	0.306140i
$484$	190.154			0.0178582
$485$	414.627	+	414.627i	0.0388191	+	0.0388191i
$486$	2678.78	+	7086.59i	0.250025	+	0.661429i
$487$	−7563.62			−0.703779			−0.351890	−	0.936042i	$-0.614461\pi$
$487$	−7563.62			−0.703779			−0.351890	+	0.936042i	$0.614461\pi$
$488$			3861.84i			0.358232i
$489$	711.066	+	9820.41i	0.0657577	+	0.908168i
$490$	613.635	+	613.635i	0.0565739	+	0.0565739i
$491$	8506.19	−	8506.19i	0.781831	−	0.781831i	−0.198308	−	0.980140i	$-0.563545\pi$
$491$	8506.19	−	8506.19i	0.781831	−	0.781831i	0.980140	+	0.198308i	$0.0635448\pi$
$492$	478.449	+	6607.77i	0.0438418	+	0.605491i
$493$	5863.14	+	14609.9i	0.535624	+	1.33468i
$494$			14697.2i			1.33858i
$495$	−821.707	+	1101.71i	−0.0746121	+	0.100037i
$496$	−2280.97	+	2280.97i	−0.206489	+	0.206489i
$497$	−367.783			−0.0331938
$498$	7787.01	−	563.834i	0.700691	−	0.0507349i
$499$		−	16856.8i		−	1.51225i	−0.654428	−	0.756124i	$-0.727091\pi$
$499$		−	16856.8i		−	1.51225i	0.654428	−	0.756124i	$-0.272909\pi$
$500$			1409.41i			0.126061i
$501$	5974.53	+	5167.75i	0.532779	+	0.460834i
$502$		−	4701.32i		−	0.417988i
$503$	352.664	−	352.664i	0.0312614	−	0.0312614i	−0.691303	−	0.722565i	$-0.742963\pi$
$503$	352.664	−	352.664i	0.0312614	−	0.0312614i	0.722565	+	0.691303i	$0.242963\pi$
$504$	−1062.02	−	792.100i	−0.0938611	−	0.0700058i
$505$	−945.325	−	945.325i	−0.0832999	−	0.0832999i
$506$	−9659.39			−0.848640
$507$	6998.92	+	6053.81i	0.613083	+	0.530294i
$508$	5636.18	+	5636.18i	0.492254	+	0.492254i
$509$		−	1000.64i		−	0.0871369i	−0.999050	−	0.0435685i	$-0.986127\pi$
$509$		−	1000.64i		−	0.0871369i	0.999050	−	0.0435685i	$-0.0138727\pi$
$510$	973.763	−	1125.79i	0.0845470	−	0.0977463i
$511$	−4575.32	−	4575.32i	−0.396086	−	0.396086i
$512$	362.039	+	362.039i	0.0312500	+	0.0312500i
$513$	3516.89	+	15963.6i	0.302679	+	1.37390i
$514$	−11180.7	+	11180.7i	−0.959459	+	0.959459i
$515$	35.8858			0.00307052
$516$	−169.634	−	2342.79i	−0.0144723	−	0.199875i
$517$	−18326.7			−1.55901
$518$			5418.40i			0.459596i
$519$	−17135.6	−	14821.7i	−1.44927	−	1.25356i
$520$	−506.944	−	506.944i	−0.0427519	−	0.0427519i
$521$	−10766.0			−0.905313			−0.452657	−	0.891685i	$-0.649524\pi$
$521$	−10766.0			−0.905313			−0.452657	+	0.891685i	$0.649524\pi$
$522$	7292.35	−	4235.56i	0.611451	−	0.355144i
$523$	−449.958			−0.0376200			−0.0188100	−	0.999823i	$-0.505988\pi$
$523$	−449.958			−0.0376200			−0.0188100	+	0.999823i	$0.505988\pi$
$524$	4692.29	+	4692.29i	0.391190	+	0.391190i
$525$	2964.50	+	2564.18i	0.246441	+	0.213162i
$526$			1795.48i			0.148834i
$527$	−20323.2			−1.67987
$528$	−215.099	−	2970.69i	−0.0177291	−	0.244854i
$529$	−6007.24			−0.493732
$530$	666.383	−	666.383i	0.0546148	−	0.0546148i
$531$	−5770.80	+	840.098i	−0.471622	+	0.0686575i
$532$	−2021.36	−	2021.36i	−0.164732	−	0.164732i
$533$	14215.5	+	14215.5i	1.15523	+	1.15523i
$534$	182.795	−	211.333i	0.0148133	−	0.0171260i
$535$		−	1284.93i		−	0.103837i
$536$	−2219.73	−	2219.73i	−0.178876	−	0.178876i
$537$	13722.7	+	11869.6i	1.10275	+	0.953841i
$538$	14482.1			1.16054
$539$	7735.95	+	7735.95i	0.618202	+	0.618202i
$540$	−671.933	−	429.320i	−0.0535470	−	0.0342129i
$541$	5928.01	−	5928.01i	0.471100	−	0.471100i	−0.431170	−	0.902271i	$-0.641899\pi$
$541$	5928.01	−	5928.01i	0.471100	−	0.471100i	0.902271	+	0.431170i	$0.141899\pi$
$542$		−	12877.3i		−	1.02053i
$543$	9839.54	+	8510.84i	0.777633	+	0.672624i
$544$			3225.72i			0.254231i
$545$			584.469i			0.0459374i
$546$	−4009.83	+	290.340i	−0.314294	+	0.0227571i
$547$	−23842.3			−1.86366			−0.931831	−	0.362893i	$-0.881789\pi$
$547$	−23842.3			−1.86366			−0.931831	+	0.362893i	$0.881789\pi$
$548$	7110.07	−	7110.07i	0.554247	−	0.554247i
$549$	10447.8	+	7792.40i	0.812203	+	0.605777i
$550$			8811.70i			0.683149i
$551$	16886.9	−	6776.90i	1.30563	−	0.523967i
$552$	−404.711	−	5589.39i	−0.0312059	−	0.430979i
$553$	467.131	−	467.131i	0.0359212	−	0.0359212i
$554$	−11390.2	−	11390.2i	−0.873505	−	0.873505i
$555$	235.507	+	3252.55i	0.0180121	+	0.248762i
$556$			12530.2i			0.955753i
$557$	2844.28			0.216366			0.108183	−	0.994131i	$-0.465497\pi$
$557$	2844.28			0.216366			0.108183	+	0.994131i	$0.465497\pi$
$558$	1568.37	+	10773.4i	0.118986	+	0.817341i
$559$	−5040.09	−	5040.09i	−0.381347	−	0.381347i
$560$	139.444			0.0105225
$561$	12276.0	−	14192.5i	0.923874	−	1.06811i
$562$	−1429.65	+	1429.65i	−0.107306	+	0.107306i
$563$	−9464.30	+	9464.30i	−0.708477	+	0.708477i	−0.966215	−	0.257738i	$-0.917023\pi$
$563$	−9464.30	+	9464.30i	−0.708477	+	0.708477i	0.257738	+	0.966215i	$0.417023\pi$
$564$	−767.855	−	10604.7i	−0.0573272	−	0.791736i
$565$	1106.80	−	1106.80i	0.0824129	−	0.0824129i
$566$	−1228.53	+	1228.53i	−0.0912351	+	0.0912351i
$567$	−4285.87	+	1274.87i	−0.317442	+	0.0944258i
$568$	339.191	−	339.191i	0.0250566	−	0.0250566i
$569$	4873.74	−	4873.74i	0.359083	−	0.359083i	−0.504392	−	0.863475i	$-0.668283\pi$
$569$	4873.74	−	4873.74i	0.359083	−	0.359083i	0.863475	+	0.504392i	$0.168283\pi$
$570$	−1301.24	−	1125.52i	−0.0956190	−	0.0827070i
$571$	17381.0			1.27385			0.636927	−	0.770924i	$-0.280205\pi$
$571$	17381.0			1.27385			0.636927	+	0.770924i	$0.280205\pi$
$572$	−6390.92	−	6390.92i	−0.467164	−	0.467164i
$573$	−344.249	−	4754.37i	−0.0250981	−	0.346626i
$574$	−3910.22			−0.284337
$575$			16579.3i			1.20244i
$576$	1709.98	−	248.934i	0.123696	−	0.0180073i
$577$	−12774.4	−	12774.4i	−0.921672	−	0.921672i	0.0754757	−	0.997148i	$-0.475952\pi$
$577$	−12774.4	−	12774.4i	−0.921672	−	0.921672i	−0.997148	+	0.0754757i	$0.975952\pi$
$578$	−7422.35	+	7422.35i	−0.534133	+	0.534133i
$579$	−2824.98	+	204.549i	−0.202767	+	0.0146818i
$580$	−348.718	+	816.224i	−0.0249651	+	0.0584342i
$581$			4608.04i			0.329043i
$582$	−2805.65	+	3243.66i	−0.199825	+	0.231021i
$583$	8400.93	−	8400.93i	0.596794	−	0.596794i
$584$	8439.25			0.597977
$585$	−2394.39	+	348.569i	−0.169224	+	0.0246351i
$586$		−	8662.50i		−	0.610656i
$587$		−	14576.7i		−	1.02495i	−0.858702	−	0.512476i	$-0.828728\pi$
$587$		−	14576.7i		−	1.02495i	0.858702	−	0.512476i	$-0.171272\pi$
$588$	−4152.28	+	4800.52i	−0.291219	+	0.336684i
$589$			23490.5i			1.64331i
$590$	434.010	−	434.010i	0.0302846	−	0.0302846i
$591$	−750.404	+	867.556i	−0.0522293	+	0.0603832i
$592$	−4997.17	−	4997.17i	−0.346930	−	0.346930i
$593$	7784.36			0.539065			0.269532	−	0.962991i	$-0.413131\pi$
$593$	7784.36			0.539065			0.269532	+	0.962991i	$0.413131\pi$
$594$	−8470.90	−	5412.33i	−0.585127	−	0.373856i
$595$	621.215	+	621.215i	0.0428022	+	0.0428022i
$596$		−	4742.23i		−	0.325922i
$597$	−6673.71	−	5772.52i	−0.457516	−	0.395734i
$598$	−12024.6	−	12024.6i	−0.822277	−	0.822277i
$599$	2297.69	+	2297.69i	0.156729	+	0.156729i	0.781116	−	0.624386i	$-0.214651\pi$
$599$	2297.69	+	2297.69i	0.156729	+	0.156729i	−0.624386	+	0.781116i	$0.714651\pi$
$600$	−5098.88	+	369.195i	−0.346935	+	0.0251205i
$601$	6532.72	−	6532.72i	0.443386	−	0.443386i	−0.449762	−	0.893148i	$-0.648491\pi$
$601$	6532.72	−	6532.72i	0.443386	−	0.443386i	0.893148	+	0.449762i	$0.148491\pi$
$602$	1386.37			0.0938606
$603$	−10484.2	+	1526.26i	−0.708042	+	0.103075i
$604$	1033.09			0.0695958
$605$			67.5466i			0.00453911i
$606$	6396.72	−	7395.36i	0.428794	−	0.495736i
$607$	6176.70	+	6176.70i	0.413022	+	0.413022i	0.882790	−	0.469768i	$-0.155662\pi$
$607$	6176.70	+	6176.70i	0.413022	+	0.413022i	−0.469768	+	0.882790i	$0.655662\pi$
$608$	3728.44			0.248698
$609$	2182.53	+	4473.35i	0.145223	+	0.297651i
$610$	−1371.80			−0.0910536
$611$	−22814.2	−	22814.2i	−1.51058	−	1.51058i
$612$	8726.82	+	6508.85i	0.576406	+	0.429910i
$613$			8648.38i			0.569828i	0.958553	+	0.284914i	$0.0919651\pi$
$613$			8648.38i			0.569828i	−0.958553	+	0.284914i	$0.908035\pi$
$614$	−2252.38			−0.148043
$615$	−2347.22	+	169.955i	−0.153901	+	0.0111435i
$616$	1757.94			0.114983
$617$	−3726.44	+	3726.44i	−0.243146	+	0.243146i	−0.818150	−	0.575005i	$-0.805000\pi$
$617$	−3726.44	+	3726.44i	−0.243146	+	0.243146i	0.575005	+	0.818150i	$0.305000\pi$
$618$	18.9549	+	261.783i	0.00123378	+	0.0170396i
$619$	−4610.35	−	4610.35i	−0.299363	−	0.299363i	0.541402	−	0.840764i	$-0.317894\pi$
$619$	−4610.35	−	4610.35i	−0.299363	−	0.299363i	−0.840764	+	0.541402i	$0.817894\pi$
$620$	−810.248	−	810.248i	−0.0524844	−	0.0524844i
$621$	−15938.1	−	10183.4i	−1.02991	−	0.658042i
$622$		−	6130.02i		−	0.395163i
$623$	116.615	+	116.615i	0.00749930	+	0.00749930i
$624$	3430.33	−	3965.87i	0.220069	−	0.254426i
$625$	14872.0			0.951807
$626$	−3188.09	−	3188.09i	−0.203549	−	0.203549i
$627$	−16404.4	−	14189.2i	−1.04486	−	0.903767i
$628$	4646.82	−	4646.82i	0.295268	−	0.295268i
$629$		−	44524.1i		−	2.82241i
$630$	281.370	−	377.250i	0.0177937	−	0.0238571i
$631$			3251.45i			0.205132i	0.994726	+	0.102566i	$0.0327053\pi$
$631$			3251.45i			0.205132i	−0.994726	+	0.102566i	$0.967295\pi$
$632$			861.632i			0.0542308i
$633$	−1039.83	−	14360.9i	−0.0652914	−	0.901727i
$634$	2520.65			0.157899
$635$	−2002.09	+	2002.09i	−0.125119	+	0.125119i
$636$	5213.17	+	4509.20i	0.325025	+	0.281134i
$637$			19260.4i			1.19800i
$638$	−4396.21	+	10289.9i	−0.272802	+	0.638530i
$639$	−233.224	−	1602.06i	−0.0144385	−	0.0991809i
$640$	−128.604	+	128.604i	−0.00794297	+	0.00794297i
$641$	14704.8	+	14704.8i	0.906090	+	0.906090i	0.995954	−	0.0898638i	$-0.0286432\pi$
$641$	14704.8	+	14704.8i	0.906090	+	0.906090i	−0.0898638	+	0.995954i	$0.528643\pi$
$642$	9373.45	−	678.703i	0.576231	−	0.0417232i
$643$			29890.9i			1.83325i	0.399743	+	0.916627i	$0.369100\pi$
$643$			29890.9i			1.83325i	−0.399743	+	0.916627i	$0.630900\pi$
$644$	3307.58			0.202386
$645$	832.205	−	60.2575i	0.0508032	−	0.00367851i
$646$	16610.0	+	16610.0i	1.01163	+	1.01163i
$647$	−2745.64			−0.166835			−0.0834176	−	0.996515i	$-0.526584\pi$
$647$	−2745.64			−0.166835			−0.0834176	+	0.996515i	$0.526584\pi$
$648$	2776.92	−	5128.44i	0.168345	−	0.310902i
$649$	5471.45	−	5471.45i	0.330930	−	0.330930i
$650$	−10969.3	+	10969.3i	−0.661927	+	0.661927i
$651$	−6408.90	+	464.049i	−0.385844	+	0.0279378i
$652$	5359.55	−	5359.55i	0.321926	−	0.321926i
$653$	−9003.78	+	9003.78i	−0.539579	+	0.539579i	−0.923405	−	0.383826i	$-0.874606\pi$
$653$	−9003.78	+	9003.78i	−0.539579	+	0.539579i	0.383826	+	0.923405i	$0.374606\pi$
$654$	−4263.63	+	308.717i	−0.254925	+	0.0184584i
$655$	−1666.80	+	1666.80i	−0.0994308	+	0.0994308i
$656$	3606.23	−	3606.23i	0.214634	−	0.214634i
$657$	17028.7	−	22831.4i	1.01119	−	1.35577i
$658$	6275.45			0.371797
$659$	−5595.61	−	5595.61i	−0.330765	−	0.330765i	0.522112	−	0.852877i	$-0.325144\pi$
$659$	−5595.61	−	5595.61i	−0.330765	−	0.330765i	−0.852877	+	0.522112i	$0.825144\pi$
$660$	1055.25	−	76.4076i	0.0622357	−	0.00450630i
$661$	22949.6			1.35043			0.675216	−	0.737620i	$-0.264050\pi$
$661$	22949.6			1.35043			0.675216	+	0.737620i	$0.264050\pi$
$662$		−	8806.58i		−	0.517035i
$663$	32949.6	−	2385.78i	1.93010	−	0.139753i
$664$	−4249.81	−	4249.81i	−0.248380	−	0.248380i
$665$	718.030	−	718.030i	0.0418707	−	0.0418707i
$666$	−23602.5	+	3435.99i	−1.37324	+	0.199913i
$667$	−8271.51	+	19360.6i	−0.480171	+	1.12391i
$668$		−	6080.96i		−	0.352215i
$669$	−8389.21	−	7256.36i	−0.484821	−	0.419353i
$670$	788.493	−	788.493i	0.0454659	−	0.0454659i
$671$	−17294.0			−0.994973
$672$	73.6545	+	1017.23i	0.00422810	+	0.0583935i
$673$		−	12568.7i		−	0.719893i	−0.932973	−	0.359947i	$-0.882795\pi$
$673$		−	12568.7i		−	0.719893i	0.932973	−	0.359947i	$-0.117205\pi$
$674$		−	1876.82i		−	0.107259i
$675$	−9289.70	+	14539.4i	−0.529719	+	0.829069i
$676$		−	7123.61i		−	0.405303i
$677$	−2461.65	+	2461.65i	−0.139747	+	0.139747i	−0.773520	−	0.633772i	$-0.781506\pi$
$677$	−2461.65	+	2461.65i	−0.139747	+	0.139747i	0.633772	+	0.773520i	$0.281506\pi$
$678$	8658.56	+	7489.34i	0.490457	+	0.424228i
$679$	−1789.87	−	1789.87i	−0.101162	−	0.101162i
$680$	−1145.84			−0.0646191
$681$	−8120.87	+	9388.68i	−0.456964	+	0.528304i
$682$	−10214.6	−	10214.6i	−0.573515	−	0.573515i
$683$		−	20945.3i		−	1.17342i	−0.809796	−	0.586712i	$-0.800422\pi$
$683$		−	20945.3i		−	1.17342i	0.809796	−	0.586712i	$-0.199578\pi$
$684$	7523.25	−	10086.9i	0.420553	−	0.563862i
$685$	2525.64	+	2525.64i	0.140876	+	0.140876i
$686$	−5624.26	−	5624.26i	−0.313025	−	0.313025i
$687$	679.785	+	9388.39i	0.0377517	+	0.521382i
$688$	−1278.59	+	1278.59i	−0.0708514	+	0.0708514i
$689$	20916.0			1.15651
$690$	1985.47	−	143.762i	0.109544	−	0.00793176i
$691$	−32418.4			−1.78474			−0.892369	−	0.451307i	$-0.850958\pi$
$691$	−32418.4			−1.78474			−0.892369	+	0.451307i	$0.850958\pi$
$692$			17440.9i			0.958095i
$693$	3547.16	−	4755.90i	0.194438	−	0.260695i
$694$	14115.7	+	14115.7i	0.772083	+	0.772083i
$695$	−4450.98			−0.242929
$696$	−6138.45	−	2112.73i	−0.334307	−	0.115062i
$697$	32131.1			1.74613
$698$	10646.3	+	10646.3i	0.577319	+	0.577319i
$699$	1396.93	−	1615.02i	0.0755891	−	0.0873899i
$700$		−	3017.31i		−	0.162920i
$701$	−27238.0			−1.46757			−0.733784	−	0.679383i	$-0.762248\pi$
$701$	−27238.0			−1.46757			−0.733784	+	0.679383i	$0.762248\pi$
$702$	−3807.49	−	17282.7i	−0.204707	−	0.929192i
$703$	−51463.2			−2.76098
$704$	−1621.27	+	1621.27i	−0.0867955	+	0.0867955i
$705$	3767.01	−	272.758i	0.201239	−	0.0145711i
$706$	6951.66	+	6951.66i	0.370580	+	0.370580i
$707$	4080.80	+	4080.80i	0.217078	+	0.217078i
$708$	3395.29	+	2936.81i	0.180230	+	0.155893i
$709$			26869.4i			1.42327i	0.702548	+	0.711637i	$0.252046\pi$
$709$			26869.4i			1.42327i	−0.702548	+	0.711637i	$0.747954\pi$
$710$	120.488	+	120.488i	0.00636876	+	0.00636876i
$711$	2331.05	+	1738.60i	0.122955	+	0.0917055i
$712$	−215.098			−0.0113218
$713$	−19218.9	−	19218.9i	−1.00947	−	1.00947i
$714$	−4203.56	+	4859.81i	−0.220328	+	0.254725i
$715$	2270.19	−	2270.19i	0.118741	−	0.118741i
$716$		−	13967.2i		−	0.729019i
$717$	−4797.02	+	5545.92i	−0.249858	+	0.288865i
$718$		−	17423.2i		−	0.905609i
$719$			2081.45i			0.107963i	0.998542	+	0.0539813i	$0.0171911\pi$
$719$			2081.45i			0.107963i	−0.998542	+	0.0539813i	$0.982809\pi$
$720$	88.4263	+	607.418i	0.00457702	+	0.0314405i
$721$	−154.913			−0.00800173
$722$	9498.53	−	9498.53i	0.489610	−	0.489610i
$723$	11801.4	−	13643.8i	0.607050	−	0.701821i
$724$		−	10014.8i		−	0.514086i
$725$	17661.6	+	7545.62i	0.904737	+	0.386534i
$726$	−492.745	+	35.6782i	−0.0251893	+	0.00182389i
$727$	22321.5	−	22321.5i	1.13873	−	1.13873i	0.150054	−	0.988678i	$-0.452055\pi$
$727$	22321.5	−	22321.5i	1.13873	−	1.13873i	0.988678	−	0.150054i	$-0.0479447\pi$
$728$	2188.39	+	2188.39i	0.111411	+	0.111411i
$729$	−8271.14	−	17860.8i	−0.420218	−	0.907423i
$730$			2997.80i			0.151991i
$731$	−11392.1			−0.576403
$732$	−724.587	−	10007.1i	−0.0365868	−	0.505293i
$733$	22642.3	+	22642.3i	1.14095	+	1.14095i	0.988278	+	0.152668i	$0.0487864\pi$
$733$	22642.3	+	22642.3i	1.14095	+	1.14095i	0.152668	+	0.988278i	$0.451214\pi$
$734$	25350.5			1.27480
$735$	−1705.24	−	1474.97i	−0.0855767	−	0.0740207i
$736$	−3050.44	+	3050.44i	−0.152773	+	0.152773i
$737$	9940.34	−	9940.34i	0.496821	−	0.496821i
$738$	−2479.60	−	17032.9i	−0.123679	−	0.849580i
$739$	−8110.79	+	8110.79i	−0.403735	+	0.403735i	−0.879547	−	0.475812i	$-0.842154\pi$
$739$	−8110.79	+	8110.79i	−0.403735	+	0.403735i	0.475812	+	0.879547i	$0.342154\pi$
$740$	1775.10	−	1775.10i	0.0881809	−	0.0881809i
$741$	−2757.60	−	38084.7i	−0.136711	−	1.88809i
$742$	−2876.66	+	2876.66i	−0.142325	+	0.142325i
$743$	−3721.91	+	3721.91i	−0.183774	+	0.183774i	−0.792998	−	0.609224i	$-0.791481\pi$
$743$	−3721.91	+	3721.91i	−0.183774	+	0.183774i	0.609224	+	0.792998i	$0.291481\pi$
$744$	5482.69	−	6338.63i	0.270168	−	0.312346i
$745$	1684.54			0.0828411
$746$	18114.7	+	18114.7i	0.889043	+	0.889043i
$747$	−20072.6	+	2922.12i	−0.983158	+	0.143125i
$748$	−14445.3			−0.706115
$749$			5546.83i			0.270597i
$750$	−264.444	−	3652.19i	−0.0128748	−	0.177812i
$751$	16096.2	+	16096.2i	0.782101	+	0.782101i	0.980185	−	0.198084i	$-0.0634718\pi$
$751$	16096.2	+	16096.2i	0.782101	+	0.782101i	−0.198084	+	0.980185i	$0.563472\pi$
$752$	−5787.59	+	5787.59i	−0.280654	+	0.280654i
$753$	882.097	+	12182.5i	0.0426898	+	0.589581i
$754$	−18282.2	+	7336.87i	−0.883022	+	0.354367i
$755$			366.975i			0.0176895i
$756$	2900.62	+	1853.30i	0.139543	+	0.0891585i
$757$	−23437.4	+	23437.4i	−1.12529	+	1.12529i	−0.134360	+	0.990933i	$0.542898\pi$
$757$	−23437.4	+	23437.4i	−1.12529	+	1.12529i	−0.990933	+	0.134360i	$0.957102\pi$
$758$	−1911.21			−0.0915810
$759$	25030.3	−	1812.37i	1.19703	−	0.0866730i
$760$			1324.42i			0.0632128i
$761$			32161.6i			1.53201i	0.642836	+	0.766004i	$0.277758\pi$
$761$			32161.6i			1.53201i	−0.642836	+	0.766004i	$0.722242\pi$
$762$	−15662.5	−	13547.5i	−0.744610	−	0.644060i
$763$		−	2523.05i		−	0.119712i
$764$	−2594.72	+	2594.72i	−0.122872	+	0.122872i
$765$	−2312.08	+	3099.94i	−0.109272	+	0.146508i
$766$	−2975.37	−	2975.37i	−0.140345	−	0.140345i
$767$	13622.4			0.641299
$768$	−1006.08	−	870.220i	−0.0472704	−	0.0408872i
$769$	−11854.0	−	11854.0i	−0.555872	−	0.555872i	0.372257	−	0.928130i	$-0.378584\pi$
$769$	−11854.0	−	11854.0i	−0.555872	−	0.555872i	−0.928130	+	0.372257i	$0.878584\pi$
$770$			624.456i			0.0292257i
$771$	26874.8	−	31070.4i	1.25535	−	1.45133i
$772$	1541.75	+	1541.75i	0.0718768	+	0.0718768i
$773$	24640.9	+	24640.9i	1.14653	+	1.14653i	0.987229	+	0.159305i	$0.0509253\pi$
$773$	24640.9	+	24640.9i	1.14653	+	1.14653i	0.159305	+	0.987229i	$0.449075\pi$
$774$	879.143	+	6039.01i	0.0408271	+	0.280449i
$775$	−17532.3	+	17532.3i	−0.812616	+	0.812616i
$776$	3301.45			0.152726
$777$	−1016.64	−	14040.7i	−0.0469393	−	0.648270i
$778$	−14614.6			−0.673467
$779$		−	37138.7i		−	1.70813i
$780$	1408.76	+	1218.52i	0.0646687	+	0.0559361i
$781$	1518.96	+	1518.96i	0.0695936	+	0.0695936i
$782$	−27179.1			−1.24287
$783$	−18101.9	+	12343.8i	−0.826193	+	0.563387i
$784$	4886.04			0.222579
$785$	1650.65	+	1650.65i	0.0750498	+	0.0750498i
$786$	−13039.5	−	11278.7i	−0.591735	−	0.511829i
$787$		−	1562.42i		−	0.0707680i	−0.999374	−	0.0353840i	$-0.988735\pi$
$787$		−	1562.42i		−	0.0707680i	0.999374	−	0.0353840i	$-0.0112654\pi$
$788$	883.011			0.0399187
$789$	−336.881	−	4652.61i	−0.0152006	−	0.209933i
$790$	−306.069			−0.0137841
$791$	−4777.84	+	4777.84i	−0.214767	+	0.214767i
$792$	1114.77	+	7657.58i	0.0500146	+	0.343561i
$793$	−21528.6	−	21528.6i	−0.964064	−	0.964064i
$794$	4664.59	+	4664.59i	0.208489	+	0.208489i
$795$	−1601.76	+	1851.83i	−0.0714574	+	0.0826132i
$796$			6792.61i			0.302459i
$797$	−1755.70	−	1755.70i	−0.0780304	−	0.0780304i	0.667014	−	0.745045i	$-0.267572\pi$
$797$	−1755.70	−	1755.70i	−0.0780304	−	0.0780304i	−0.745045	+	0.667014i	$0.767572\pi$
$798$	5617.21	+	4858.68i	0.249182	+	0.215533i
$799$	−51566.7			−2.28323
$800$	2782.74	+	2782.74i	0.122981	+	0.122981i
$801$	−434.024	+	581.923i	−0.0191454	+	0.0256694i
$802$	19855.5	−	19855.5i	0.874219	−	0.874219i
$803$			37792.5i			1.66086i
$804$	6168.45	+	5335.48i	0.270578	+	0.234040i
$805$			1174.92i			0.0514416i
$806$		−	25431.5i		−	1.11140i
$807$	−37527.4	+	2717.25i	−1.63696	+	0.118527i
$808$	−7527.11			−0.327726
$809$	−26541.4	+	26541.4i	−1.15346	+	1.15346i	−0.167603	+	0.985855i	$0.553603\pi$
$809$	−26541.4	+	26541.4i	−1.15346	+	1.15346i	−0.985855	+	0.167603i	$0.946397\pi$
$810$	1821.73	+	986.420i	0.0790234	+	0.0427892i
$811$			25121.8i			1.08773i	0.839174	+	0.543864i	$0.183039\pi$
$811$			25121.8i			1.08773i	−0.839174	+	0.543864i	$0.816961\pi$
$812$	1505.35	−	3523.49i	0.0650586	−	0.152279i
$813$	2416.13	+	33368.8i	0.104228	+	1.43948i
$814$	22378.2	−	22378.2i	0.963582	−	0.963582i
$815$	1903.82	+	1903.82i	0.0818257	+	0.0818257i
$816$	−605.234	−	8358.78i	−0.0259650	−	0.358598i
$817$			13167.5i			0.563859i
$818$	19236.0			0.822215
$819$	10336.2	−	1504.71i	0.440995	−	0.0641988i
$820$	1281.01	+	1281.01i	0.0545545	+	0.0545545i
$821$	241.457			0.0102642			0.00513211	−	0.999987i	$-0.498366\pi$
$821$	241.457			0.0102642			0.00513211	+	0.999987i	$0.498366\pi$
$822$	−17090.2	+	19758.3i	−0.725171	+	0.838383i
$823$	15558.1	−	15558.1i	0.658958	−	0.658958i	−0.296175	−	0.955134i	$-0.595711\pi$
$823$	15558.1	−	15558.1i	0.658958	−	0.658958i	0.955134	+	0.296175i	$0.0957113\pi$
$824$	142.870	−	142.870i	0.00604016	−	0.00604016i
$825$	−1653.32	−	22833.7i	−0.0697711	−	0.963597i
$826$	−1873.54	+	1873.54i	−0.0789211	+	0.0789211i
$827$	696.475	−	696.475i	0.0292851	−	0.0292851i	−0.692313	−	0.721598i	$-0.743408\pi$
$827$	696.475	−	696.475i	0.0292851	−	0.0292851i	0.721598	+	0.692313i	$0.243408\pi$
$828$	2097.45	+	14407.8i	0.0880331	+	0.604717i
$829$	−4813.99	+	4813.99i	−0.201685	+	0.201685i	−0.800722	−	0.599037i	$-0.795550\pi$
$829$	−4813.99	+	4813.99i	−0.201685	+	0.201685i	0.599037	+	0.800722i	$0.295550\pi$
$830$	1509.62	−	1509.62i	0.0631321	−	0.0631321i
$831$	31652.4	+	27378.2i	1.32131	+	1.14289i
$832$	−4036.52			−0.168198
$833$	21767.0	+	21767.0i	0.905381	+	0.905381i
$834$	−2351.01	−	32469.4i	−0.0976126	−	1.34811i
$835$	2160.08			0.0895243
$836$			16696.6i			0.690748i
$837$	−6085.50	−	27622.9i	−0.251309	−	1.14072i
$838$	−6353.39	−	6353.39i	−0.261902	−	0.261902i
$839$	−26714.5	+	26714.5i	−1.09927	+	1.09927i	−0.104772	+	0.994496i	$0.533411\pi$
$839$	−26714.5	+	26714.5i	−1.09927	+	1.09927i	−0.994496	+	0.104772i	$0.966589\pi$
$840$	−361.340	+	26.1636i	−0.0148422	+	0.00107468i
$841$	16859.9	+	17622.9i	0.691291	+	0.722577i
$842$		−	24914.7i		−	1.01973i
$843$	3436.39	−	3972.87i	0.140398	−	0.162317i
$844$	−7837.53	+	7837.53i	−0.319643	+	0.319643i
$845$	2530.45			0.103018
$846$	3979.48	+	27335.8i	0.161722	+	1.11090i
$847$		−	291.587i		−	0.0118288i
$848$		−	5306.04i		−	0.214871i
$849$	2952.98	−	3413.99i	0.119371	−	0.138007i
$850$			24793.9i			1.00050i
$851$	42104.8	−	42104.8i	1.69605	−	1.69605i
$852$	−815.302	+	942.585i	−0.0327838	+	0.0379019i
$853$	11764.5	+	11764.5i	0.472224	+	0.472224i	0.902634	−	0.430409i	$-0.141631\pi$
$853$	11764.5	+	11764.5i	0.472224	+	0.472224i	−0.430409	+	0.902634i	$0.641631\pi$
$854$	5921.83			0.237284
$855$	3583.07	+	2672.41i	0.143320	+	0.106894i
$856$	−5115.62	−	5115.62i	−0.204262	−	0.204262i
$857$			9236.09i			0.368143i	0.982913	+	0.184072i	$0.0589278\pi$
$857$			9236.09i			0.368143i	−0.982913	+	0.184072i	$0.941072\pi$
$858$	17759.9	+	15361.6i	0.706657	+	0.611232i
$859$	4869.86	+	4869.86i	0.193431	+	0.193431i	0.797177	−	0.603746i	$-0.206326\pi$
$859$	4869.86	+	4869.86i	0.193431	+	0.193431i	−0.603746	+	0.797177i	$0.706326\pi$
$860$	−454.181	−	454.181i	−0.0180087	−	0.0180087i
$861$	10132.5	−	733.665i	0.401063	−	0.0290398i
$862$	11874.6	−	11874.6i	0.469200	−	0.469200i
$863$	25981.3			1.02482			0.512408	−	0.858742i	$-0.328754\pi$
$863$	25981.3			1.02482			0.512408	+	0.858742i	$0.328754\pi$
$864$	−4384.34	+	965.898i	−0.172637	+	0.0380330i
$865$	−6195.35			−0.243524
$866$		−	24448.3i		−	0.959339i
$867$	17840.8	−	20626.1i	0.698854	−	0.807958i
$868$	3497.69	+	3497.69i	0.136774	+	0.136774i
$869$	−3858.54			−0.150624
$870$	750.485	−	2180.50i	0.0292458	−	0.0849724i
$871$	24748.7			0.962775
$872$	2326.90	+	2326.90i	0.0903657	+	0.0903657i
$873$	6661.66	−	8931.70i	0.258262	−	0.346268i
$874$			31414.9i			1.21582i
$875$	2161.22			0.0835000
$876$	−21868.6	+	1583.44i	−0.843459	+	0.0610724i
$877$	−21870.8			−0.842102			−0.421051	−	0.907037i	$-0.638339\pi$
$877$	−21870.8			−0.842102			−0.421051	+	0.907037i	$0.638339\pi$
$878$	−14620.8	+	14620.8i	−0.561990	+	0.561990i
$879$	1625.32	+	22447.1i	0.0623673	+	0.861343i
$880$	−575.910	−	575.910i	−0.0220613	−	0.0220613i
$881$	−15430.2	−	15430.2i	−0.590075	−	0.590075i	0.347576	−	0.937652i	$-0.387005\pi$
$881$	−15430.2	−	15430.2i	−0.590075	−	0.590075i	−0.937652	+	0.347576i	$0.887005\pi$
$882$	9859.05	−	13218.6i	0.376385	−	0.504643i
$883$		−	26637.6i		−	1.01520i	−0.861591	−	0.507602i	$-0.830532\pi$
$883$		−	26637.6i		−	1.01520i	0.861591	−	0.507602i	$-0.169468\pi$
$884$	−17982.4	−	17982.4i	−0.684180	−	0.684180i
$885$	−1043.21	+	1206.08i	−0.0396240	+	0.0458100i
$886$	−5091.08			−0.193045
$887$	15323.0	+	15323.0i	0.580040	+	0.580040i	0.934914	−	0.354874i	$-0.115476\pi$
$887$	15323.0	+	15323.0i	0.580040	+	0.580040i	−0.354874	+	0.934914i	$0.615476\pi$
$888$	13886.7	+	12011.5i	0.524784	+	0.453919i
$889$	8642.66	−	8642.66i	0.326058	−	0.326058i
$890$		−	76.4071i		−	0.00287772i
$891$	22966.1	+	12435.6i	0.863516	+	0.467572i
$892$			8538.66i			0.320511i
$893$			59603.3i			2.23354i
$894$	889.773	+	12288.5i	0.0332869	+	0.459719i
$895$	4961.43			0.185299
$896$	555.159	−	555.159i	0.0206993	−	0.0206993i
$897$	33415.4	+	28903.1i	1.24382	+	1.07586i
$898$			6098.67i			0.226632i
$899$	−29220.4	+	11726.5i	−1.08404	+	0.435040i
$900$	13143.4	−	1913.38i	0.486793	−	0.0708660i
$901$	23638.1	−	23638.1i	0.874028	−	0.874028i
$902$	16149.4	+	16149.4i	0.596136	+	0.596136i
$903$	−3592.48	+	260.121i	−0.132392	+	0.00958614i
$904$		−	8812.82i		−	0.324237i
$905$	3557.47			0.130668
$906$	−2677.04	+	193.836i	−0.0981664	+	0.00710793i
$907$	15942.1	+	15942.1i	0.583626	+	0.583626i	0.935898	−	0.352272i	$-0.114591\pi$
$907$	15942.1	+	15942.1i	0.583626	+	0.583626i	−0.352272	+	0.935898i	$0.614591\pi$
$908$	9555.94			0.349257
$909$	−15188.2	+	20363.7i	−0.554192	+	0.743039i
$910$	−777.360	+	777.360i	−0.0283178	+	0.0283178i
$911$	−17809.7	+	17809.7i	−0.647708	+	0.647708i	−0.952438	−	0.304731i	$-0.901433\pi$
$911$	−17809.7	+	17809.7i	−0.647708	+	0.647708i	0.304731	+	0.952438i	$0.401433\pi$
$912$	−9661.49	+	699.559i	−0.350794	+	0.0253999i
$913$	19031.4	−	19031.4i	0.689865	−	0.689865i
$914$	−8587.05	+	8587.05i	−0.310760	+	0.310760i
$915$	3554.74	−	257.388i	0.128433	−	0.00929945i
$916$	5123.77	−	5123.77i	0.184819	−	0.184819i
$917$	7195.27	−	7195.27i	0.259115	−	0.259115i
$918$	−23835.0	−	15228.9i	−0.856940	−	0.547527i
$919$	20514.0			0.736339			0.368170	−	0.929759i	$-0.379985\pi$
$919$	20514.0			0.736339			0.368170	+	0.929759i	$0.379985\pi$
$920$	−1083.58	−	1083.58i	−0.0388311	−	0.0388311i
$921$	5836.57	−	422.609i	0.208818	−	0.0151199i
$922$	18652.6			0.666257
$923$			3781.78i			0.134863i
$924$	−4555.33	+	329.838i	−0.162185	+	0.0117434i
$925$	−38409.8	−	38409.8i	−1.36531	−	1.36531i
$926$	3629.53	−	3629.53i	0.128805	−	0.128805i
$927$	−98.2354	−	674.799i	−0.00348055	−	0.0239086i
$928$	1861.24	+	4637.90i	0.0658387	+	0.164059i
$929$		−	6321.31i		−	0.223246i	−0.993751	−	0.111623i	$-0.964395\pi$
$929$		−	6321.31i		−	0.223246i	0.993751	−	0.111623i	$-0.0356049\pi$
$930$	2251.61	+	1947.56i	0.0793906	+	0.0686700i
$931$	25159.4	−	25159.4i	0.885677	−	0.885677i
$932$	−1643.79			−0.0577726
$933$	1150.16	+	15884.7i	0.0403586	+	0.557386i
$934$			12666.9i			0.443763i
$935$		−	5131.28i		−	0.179477i
$936$	−8144.88	+	10920.3i	−0.284427	+	0.381349i
$937$		−	15310.0i		−	0.533783i	−0.963727	−	0.266892i	$-0.914003\pi$
$937$		−	15310.0i		−	0.533783i	0.963727	−	0.266892i	$-0.0859966\pi$
$938$	−3403.78	+	3403.78i	−0.118483	+	0.118483i
$939$	8859.43	+	7663.09i	0.307898	+	0.266321i
$940$	−2055.87	−	2055.87i	−0.0713352	−	0.0713352i
$941$	−9434.57			−0.326842			−0.163421	−	0.986556i	$-0.552253\pi$
$941$	−9434.57			−0.326842			−0.163421	+	0.986556i	$0.552253\pi$
$942$	−11169.4	+	12913.1i	−0.386326	+	0.446638i
$943$	30385.2	+	30385.2i	1.04929	+	1.04929i
$944$		−	3455.78i		−	0.119148i
$945$	−658.329	+	1030.36i	−0.0226619	+	0.0354683i
$946$	−5725.75	−	5725.75i	−0.196787	−	0.196787i
$947$	−3523.55	−	3523.55i	−0.120908	−	0.120908i	0.644064	−	0.764972i	$-0.277247\pi$
$947$	−3523.55	−	3523.55i	−0.120908	−	0.120908i	−0.764972	+	0.644064i	$0.777247\pi$
$948$	−161.666	−	2232.74i	−0.00553868	−	0.0764937i
$949$	−47046.4	+	47046.4i	−1.60926	+	1.60926i
$950$	28658.0			0.978725
$951$	−6531.73	+	472.943i	−0.222719	+	0.0161264i
$952$	4946.39			0.168397
$953$		−	30017.4i		−	1.02031i	−0.860082	−	0.510157i	$-0.829587\pi$
$953$		−	30017.4i		−	1.02031i	0.860082	−	0.510157i	$-0.170413\pi$
$954$	−14354.9	−	10706.5i	−0.487167	−	0.363351i
$955$	−921.699	−	921.699i	−0.0312309	−	0.0312309i
$956$	5644.72			0.190966
$957$	9461.18	−	27489.1i	0.319578	−	0.928522i
$958$	11082.3			0.373751
$959$	−10902.8	−	10902.8i	−0.367120	−	0.367120i
$960$	309.120	−	357.379i	0.0103925	−	0.0120150i
$961$		−	10856.1i		−	0.364408i
$962$	55715.5			1.86730
$963$	−24162.0	+	3517.44i	−0.808525	+	0.117703i
$964$	−13886.8			−0.463967
$965$	−547.662	+	547.662i	−0.0182693	+	0.0182693i
$966$	−8570.90	+	620.593i	−0.285470	+	0.0206700i
$967$	−10532.8	−	10532.8i	−0.350271	−	0.350271i	0.509939	−	0.860210i	$-0.329668\pi$
$967$	−10532.8	−	10532.8i	−0.350271	−	0.350271i	−0.860210	+	0.509939i	$0.829668\pi$
$968$	268.918	+	268.918i	0.00892909	+	0.00892909i
$969$	−46157.8	−	39924.8i	−1.53024	−	1.32360i
$970$			1172.74i			0.0388191i
$971$	−37462.1	−	37462.1i	−1.23812	−	1.23812i	−0.960767	−	0.277355i	$-0.910542\pi$
$971$	−37462.1	−	37462.1i	−1.23812	−	1.23812i	−0.277355	−	0.960767i	$-0.589458\pi$
$972$	−6233.58	+	13810.3i	−0.205702	+	0.455727i
$973$	19214.1			0.633069
$974$	−10696.6	−	10696.6i	−0.351890	−	0.351890i
$975$	26366.6	−	30482.9i	0.866059	−	1.00127i
$976$	−5461.46	+	5461.46i	−0.179116	+	0.179116i
$977$			7270.94i			0.238094i	0.992889	+	0.119047i	$0.0379839\pi$
$977$			7270.94i			0.238094i	−0.992889	+	0.119047i	$0.962016\pi$
$978$	−12882.6	+	14893.8i	−0.421205	+	0.486963i
$979$		−	963.246i		−	0.0314458i
$980$			1735.62i			0.0565739i
$981$	10990.4	−	1599.95i	0.357692	−	0.0520719i
$982$	24059.1			0.781831
$983$	−1201.77	+	1201.77i	−0.0389933	+	0.0389933i	−0.726335	−	0.687341i	$-0.758778\pi$
$983$	−1201.77	+	1201.77i	−0.0389933	+	0.0389933i	0.687341	+	0.726335i	$0.258778\pi$
$984$	−8668.17	+	10021.4i	−0.280824	+	0.324666i
$985$			313.664i			0.0101464i
$986$	−12369.8	+	28953.3i	−0.399529	+	0.935152i
$987$	−16261.5	+	1177.45i	−0.524427	+	0.0379722i
$988$	−20785.0	+	20785.0i	−0.669290	+	0.669290i
$989$	−10773.1	−	10773.1i	−0.346374	−	0.346374i
$990$	−2720.13	+	395.989i	−0.0873246	+	0.0127125i
$991$		−	29098.7i		−	0.932745i	−0.884588	−	0.466373i	$-0.845561\pi$
$991$		−	29098.7i		−	0.932745i	0.884588	−	0.466373i	$-0.154439\pi$
$992$	−6451.56			−0.206489
$993$	1652.36	+	22820.4i	0.0528056	+	0.729289i
$994$	−520.124	−	520.124i	−0.0165969	−	0.0165969i
$995$	−2412.87			−0.0768776
$996$	11809.9	+	10215.1i	0.375713	+	0.324978i
$997$	580.851	−	580.851i	0.0184511	−	0.0184511i	−0.697821	−	0.716272i	$-0.745847\pi$
$997$	580.851	−	580.851i	0.0184511	−	0.0184511i	0.716272	+	0.697821i	$0.245847\pi$
$998$	23839.1	−	23839.1i	0.756124	−	0.756124i
$999$	60516.4	−	13332.2i	1.91657	−	0.422233i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	174.4.f.a.17.19	yes	60
3.2	odd	2	inner	174.4.f.a.17.11	✓	60
29.12	odd	4	inner	174.4.f.a.41.11	yes	60
87.41	even	4	inner	174.4.f.a.41.19	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
174.4.f.a.17.11	✓	60	3.2	odd	2	inner
174.4.f.a.17.19	yes	60	1.1	even	1	trivial
174.4.f.a.41.11	yes	60	29.12	odd	4	inner
174.4.f.a.41.19	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} +(-3.92999 - 3.39930i) q^{3} +4.00000i q^{4} -1.42088 q^{5} +(-0.750511 - 10.3652i) q^{6} +6.13369 q^{7} +(-5.65685 + 5.65685i) q^{8} +(3.88959 + 26.7184i) q^{9} +(-2.00943 - 2.00943i) q^{10} +(-25.3324 - 25.3324i) q^{11} +(13.5972 - 15.7199i) q^{12} -63.0706i q^{13} +(8.67435 + 8.67435i) q^{14} +(5.58405 + 4.83000i) q^{15} -16.0000 q^{16} +(-71.2790 - 71.2790i) q^{17} +(-32.2848 + 43.2862i) q^{18} +(-82.3877 + 82.3877i) q^{19} -5.68353i q^{20} +(-24.1053 - 20.8502i) q^{21} -71.6509i q^{22} -134.812i q^{23} +(41.4607 - 3.00204i) q^{24} -122.981 q^{25} +(89.1953 - 89.1953i) q^{26} +(75.5376 - 118.225i) q^{27} +24.5348i q^{28} +(-143.612 - 61.3560i) q^{29} +(1.06639 + 14.7277i) q^{30} +(142.561 - 142.561i) q^{31} +(-22.6274 - 22.6274i) q^{32} +(13.4437 + 185.668i) q^{33} -201.607i q^{34} -8.71526 q^{35} +(-106.873 + 15.5583i) q^{36} +(312.323 + 312.323i) q^{37} -233.028 q^{38} +(-214.396 + 247.867i) q^{39} +(8.03772 - 8.03772i) q^{40} +(-225.390 + 225.390i) q^{41} +(-4.60340 - 63.5768i) q^{42} +(79.9118 - 79.9118i) q^{43} +(101.330 - 101.330i) q^{44} +(-5.52664 - 37.9636i) q^{45} +(190.653 - 190.653i) q^{46} +(361.724 - 361.724i) q^{47} +(62.8798 + 54.3887i) q^{48} -305.378 q^{49} +(-173.922 - 173.922i) q^{50} +(37.8271 + 522.424i) q^{51} +252.282 q^{52} +331.628i q^{53} +(274.021 - 60.3686i) q^{54} +(35.9944 + 35.9944i) q^{55} +(-34.6974 + 34.6974i) q^{56} +(603.843 - 43.7225i) q^{57} +(-116.328 - 289.869i) q^{58} +215.986i q^{59} +(-19.3200 + 22.3362i) q^{60} +(341.341 - 341.341i) q^{61} +403.222 q^{62} +(23.8575 + 163.882i) q^{63} -64.0000i q^{64} +89.6159i q^{65} +(-243.562 + 281.587i) q^{66} +392.396i q^{67} +(285.116 - 285.116i) q^{68} +(-458.265 + 529.809i) q^{69} +(-12.3252 - 12.3252i) q^{70} -59.9611 q^{71} +(-173.145 - 129.139i) q^{72} +(-745.932 - 745.932i) q^{73} +883.383i q^{74} +(483.314 + 418.049i) q^{75} +(-329.551 - 329.551i) q^{76} +(-155.381 - 155.381i) q^{77} +(-653.738 + 47.3352i) q^{78} +(76.1582 - 76.1582i) q^{79} +22.7341 q^{80} +(-698.742 + 207.847i) q^{81} -637.498 q^{82} +751.267i q^{83} +(83.4009 - 96.4213i) q^{84} +(101.279 + 101.279i) q^{85} +226.025 q^{86} +(355.827 + 729.308i) q^{87} +286.603 q^{88} +(19.0121 + 19.0121i) q^{89} +(45.8729 - 61.5046i) q^{90} -386.856i q^{91} +539.247 q^{92} +(-1044.87 + 75.6557i) q^{93} +1023.11 q^{94} +(117.063 - 117.063i) q^{95} +(12.0082 + 165.843i) q^{96} +(-291.810 - 291.810i) q^{97} +(-431.869 - 431.869i) q^{98} +(578.308 - 775.373i) 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

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Database

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