LMFDB - Embedded newform 112.3.x.a.101.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [112,3,Mod(5,112)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(112, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 3, 10])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("112.5"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	112.x (of order $12$, degree $4$, 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:	$3.05177896084$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$30$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			101.11
Character	$\chi$	$=$	112.101
Dual form			112.3.x.a.61.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.04241 - 1.70686i) q^{2} +(0.387260 - 0.103766i) q^{3} +(-1.82674 + 3.55851i) q^{4} +(-2.83046 - 0.758420i) q^{5} +(-0.580800 - 0.552832i) q^{6} +(-6.87124 + 1.33643i) q^{7} +(7.97811 - 0.591454i) q^{8} +(-7.65503 + 4.41963i) q^{9} +(1.65600 + 5.62179i) q^{10} +(-8.31644 + 2.22838i) q^{11} +(-0.338172 + 1.56762i) q^{12} +(-4.40585 - 4.40585i) q^{13} +(9.44378 + 10.3351i) q^{14} -1.17482 q^{15} +(-9.32603 - 13.0010i) q^{16} +(15.8018 + 9.12315i) q^{17} +(15.5234 + 8.45897i) q^{18} +(-4.21386 + 15.7263i) q^{19} +(7.86937 - 8.68679i) q^{20} +(-2.52228 + 1.23055i) q^{21} +(12.4727 + 11.8721i) q^{22} +(-6.34669 + 3.66426i) q^{23} +(3.02823 - 1.05690i) q^{24} +(-14.2143 - 8.20665i) q^{25} +(-2.92745 + 12.1129i) q^{26} +(-5.05733 + 5.05733i) q^{27} +(7.79629 - 26.8927i) q^{28} +(29.7739 - 29.7739i) q^{29} +(1.22465 + 2.00526i) q^{30} +(-42.9245 - 24.7825i) q^{31} +(-12.4692 + 29.4706i) q^{32} +(-2.98940 + 1.72593i) q^{33} +(-0.900051 - 36.4815i) q^{34} +(20.4624 + 1.42858i) q^{35} +(-1.74356 - 35.3140i) q^{36} +(9.34970 - 34.8935i) q^{37} +(31.2352 - 9.20089i) q^{38} +(-2.16339 - 1.24903i) q^{39} +(-23.0303 - 4.37666i) q^{40} -9.03499 q^{41} +(4.72964 + 3.02244i) q^{42} +(0.640499 + 0.640499i) q^{43} +(7.26226 - 33.6649i) q^{44} +(25.0192 - 6.70387i) q^{45} +(12.8703 + 7.01323i) q^{46} +(-65.6497 + 37.9028i) q^{47} +(-4.96066 - 4.06703i) q^{48} +(45.4279 - 18.3658i) q^{49} +(0.809633 + 32.8166i) q^{50} +(7.06607 + 1.89335i) q^{51} +(23.7266 - 7.62993i) q^{52} +(47.0432 - 12.6052i) q^{53} +(13.9040 + 3.36032i) q^{54} +25.2294 q^{55} +(-54.0291 + 14.7262i) q^{56} +6.52744i q^{57} +(-81.8566 - 19.7831i) q^{58} +(2.01838 + 7.53268i) q^{59} +(2.14610 - 4.18062i) q^{60} +(-15.1533 + 56.5528i) q^{61} +(2.44493 + 99.0997i) q^{62} +(46.6930 - 40.5987i) q^{63} +(63.3004 - 9.43737i) q^{64} +(9.12911 + 15.8121i) q^{65} +(6.06211 + 3.30335i) q^{66} +(-0.662730 - 2.47334i) q^{67} +(-61.3306 + 39.5651i) q^{68} +(-2.07760 + 2.07760i) q^{69} +(-18.8919 - 36.4155i) q^{70} +98.9570i q^{71} +(-58.4586 + 39.7879i) q^{72} +(-52.5670 + 91.0487i) q^{73} +(-69.3047 + 20.4149i) q^{74} +(-6.35622 - 1.70314i) q^{75} +(-48.2647 - 43.7230i) q^{76} +(54.1662 - 26.4261i) q^{77} +(0.123224 + 4.99462i) q^{78} +(-48.3594 - 83.7610i) q^{79} +(16.5368 + 43.8718i) q^{80} +(38.3430 - 66.4119i) q^{81} +(9.41821 + 15.4215i) q^{82} +(93.2835 + 93.2835i) q^{83} +(0.228642 - 11.2235i) q^{84} +(-37.8071 - 37.8071i) q^{85} +(0.425576 - 1.76091i) q^{86} +(8.44073 - 14.6198i) q^{87} +(-65.0315 + 22.6971i) q^{88} +(17.6754 + 30.6147i) q^{89} +(-37.5229 - 35.7160i) q^{90} +(36.1618 + 24.3856i) q^{91} +(-1.44556 - 29.2785i) q^{92} +(-19.1945 - 5.14316i) q^{93} +(133.129 + 72.5443i) q^{94} +(23.8543 - 41.3169i) q^{95} +(-1.77079 + 12.7067i) q^{96} +131.836i q^{97} +(-78.7027 - 58.3943i) q^{98} +(53.8140 - 53.8140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - 6 q^{5} + 4 q^{8} - 60 q^{10} - 18 q^{11} - 6 q^{12} - 28 q^{14} - 16 q^{15} + 8 q^{16} - 12 q^{17} + 2 q^{18} - 6 q^{19} + 14 q^{21} - 20 q^{22} - 6 q^{24} - 6 q^{26}+ \cdots - 848 q^{99}+O(q^{100}) $ 120 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 - 6 * q^5 + 4 * q^8 - 60 * q^10 - 18 * q^11 - 6 * q^12 - 28 * q^14 - 16 * q^15 + 8 * q^16 - 12 * q^17 + 2 * q^18 - 6 * q^19 + 14 * q^21 - 20 * q^22 - 6 * q^24 - 6 * q^26 - 6 * q^28 + 24 * q^29 + 10 * q^30 - 12 * q^31 - 92 * q^32 - 12 * q^33 + 94 * q^35 + 128 * q^36 + 46 * q^37 - 6 * q^38 - 66 * q^40 - 78 * q^42 + 88 * q^43 - 182 * q^44 - 60 * q^45 - 108 * q^46 - 12 * q^47 - 8 * q^49 - 8 * q^50 - 118 * q^51 - 564 * q^52 - 82 * q^53 - 306 * q^54 + 400 * q^56 + 346 * q^58 - 198 * q^59 - 186 * q^60 - 6 * q^61 - 204 * q^63 + 16 * q^64 - 4 * q^65 + 870 * q^66 + 222 * q^67 + 384 * q^68 + 556 * q^70 - 52 * q^72 + 126 * q^74 - 156 * q^75 - 102 * q^77 - 28 * q^78 - 4 * q^79 + 300 * q^80 + 248 * q^81 - 810 * q^82 - 288 * q^84 - 108 * q^85 - 196 * q^86 + 366 * q^88 + 88 * q^91 + 172 * q^92 - 38 * q^93 + 606 * q^94 - 388 * q^95 + 996 * q^96 - 848 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.04241	−	1.70686i	−0.521207	−	0.853430i
$2$	−1.04241	−	1.70686i	−0.521207	−	0.853430i
$3$	0.387260	−	0.103766i	0.129087	−	0.0345887i	−0.193697	−	0.981061i	$-0.562048\pi$
$3$	0.387260	−	0.103766i	0.129087	−	0.0345887i	0.322784	+	0.946473i	$0.395381\pi$
$4$	−1.82674	+	3.55851i	−0.456685	+	0.889628i
$5$	−2.83046	−	0.758420i	−0.566092	−	0.151684i	−0.0355884	−	0.999367i	$-0.511331\pi$
$5$	−2.83046	−	0.758420i	−0.566092	−	0.151684i	−0.530504	+	0.847683i	$0.677997\pi$
$6$	−0.580800	−	0.552832i	−0.0968000	−	0.0921386i
$7$	−6.87124	+	1.33643i	−0.981606	+	0.190918i
$7$	−6.87124	+	1.33643i	−0.981606	+	0.190918i
$8$	7.97811	−	0.591454i	0.997263	−	0.0739318i
$9$	−7.65503	+	4.41963i	−0.850558	+	0.491070i
$10$	1.65600	+	5.62179i	0.165600	+	0.562179i
$11$	−8.31644	+	2.22838i	−0.756040	+	0.202580i	−0.616196	−	0.787593i	$-0.711327\pi$
$11$	−8.31644	+	2.22838i	−0.756040	+	0.202580i	−0.139845	+	0.990173i	$0.544660\pi$
$12$	−0.338172	+	1.56762i	−0.0281810	+	0.130635i
$13$	−4.40585	−	4.40585i	−0.338912	−	0.338912i	0.517046	−	0.855958i	$-0.327032\pi$
$13$	−4.40585	−	4.40585i	−0.338912	−	0.338912i	−0.855958	+	0.517046i	$0.827032\pi$
$14$	9.44378	+	10.3351i	0.674556	+	0.738224i
$15$	−1.17482			−0.0783216
$16$	−9.32603	−	13.0010i	−0.582877	−	0.812561i
$17$	15.8018	+	9.12315i	0.929516	+	0.536656i	0.886658	−	0.462425i	$-0.153021\pi$
$17$	15.8018	+	9.12315i	0.929516	+	0.536656i	0.0428573	+	0.999081i	$0.486354\pi$
$18$	15.5234	+	8.45897i	0.862411	+	0.469943i
$19$	−4.21386	+	15.7263i	−0.221782	+	0.827701i	0.761886	+	0.647711i	$0.224273\pi$
$19$	−4.21386	+	15.7263i	−0.221782	+	0.827701i	−0.983668	+	0.179991i	$0.942393\pi$
$20$	7.86937	−	8.68679i	0.393468	−	0.434340i
$21$	−2.52228	+	1.23055i	−0.120109	+	0.0585975i
$22$	12.4727	+	11.8721i	0.566942	+	0.539641i
$23$	−6.34669	+	3.66426i	−0.275943	+	0.159316i	−0.631585	−	0.775306i	$-0.717595\pi$
$23$	−6.34669	+	3.66426i	−0.275943	+	0.159316i	0.355642	+	0.934622i	$0.384262\pi$
$24$	3.02823	−	1.05690i	0.126176	−	0.0440377i
$25$	−14.2143	−	8.20665i	−0.568573	−	0.328266i
$26$	−2.92745	+	12.1129i	−0.112594	+	0.465881i
$27$	−5.05733	+	5.05733i	−0.187308	+	0.187308i
$28$	7.79629	−	26.8927i	0.278439	−	0.960454i
$29$	29.7739	−	29.7739i	1.02669	−	1.02669i	0.0270519	−	0.999634i	$-0.491388\pi$
$29$	29.7739	−	29.7739i	1.02669	−	1.02669i	0.999634	−	0.0270519i	$-0.00861193\pi$
$30$	1.22465	+	2.00526i	0.0408218	+	0.0668420i
$31$	−42.9245	−	24.7825i	−1.38466	−	0.799434i	−0.391953	−	0.919985i	$-0.628201\pi$
$31$	−42.9245	−	24.7825i	−1.38466	−	0.799434i	−0.992707	+	0.120551i	$0.961534\pi$
$32$	−12.4692	+	29.4706i	−0.389664	+	0.920957i
$33$	−2.98940	+	1.72593i	−0.0905878	+	0.0523009i
$34$	−0.900051	−	36.4815i	−0.0264721	−	1.07299i
$35$	20.4624	+	1.42858i	0.584639	+	0.0408165i
$36$	−1.74356	−	35.3140i	−0.0484321	−	0.980945i
$37$	9.34970	−	34.8935i	0.252695	−	0.943069i	−0.716664	−	0.697419i	$-0.754332\pi$
$37$	9.34970	−	34.8935i	0.252695	−	0.943069i	0.969359	−	0.245650i	$-0.0790015\pi$
$38$	31.2352	−	9.20089i	0.821980	−	0.242129i
$39$	−2.16339	−	1.24903i	−0.0554716	−	0.0320265i
$40$	−23.0303	−	4.37666i	−0.575757	−	0.109417i
$41$	−9.03499			−0.220366			−0.110183	−	0.993911i	$-0.535144\pi$
$41$	−9.03499			−0.220366			−0.110183	+	0.993911i	$0.535144\pi$
$42$	4.72964	+	3.02244i	0.112610	+	0.0719629i
$43$	0.640499	+	0.640499i	0.0148953	+	0.0148953i	0.714515	−	0.699620i	$-0.246647\pi$
$43$	0.640499	+	0.640499i	0.0148953	+	0.0148953i	−0.699620	+	0.714515i	$0.746647\pi$
$44$	7.26226	−	33.6649i	0.165051	−	0.765110i
$45$	25.0192	−	6.70387i	0.555982	−	0.148975i
$46$	12.8703	+	7.01323i	0.279789	+	0.152462i
$47$	−65.6497	+	37.9028i	−1.39680	+	0.806443i	−0.994056	−	0.108869i	$-0.965277\pi$
$47$	−65.6497	+	37.9028i	−1.39680	+	0.806443i	−0.402745	+	0.915312i	$0.631944\pi$
$48$	−4.96066	−	4.06703i	−0.103347	−	0.0847299i
$49$	45.4279	−	18.3658i	0.927100	−	0.374813i
$50$	0.809633	+	32.8166i	0.0161927	+	0.656332i
$51$	7.06607	+	1.89335i	0.138550	+	0.0371245i
$52$	23.7266	−	7.62993i	0.456282	−	0.146729i
$53$	47.0432	−	12.6052i	0.887607	−	0.237834i	0.213921	−	0.976851i	$-0.431377\pi$
$53$	47.0432	−	12.6052i	0.887607	−	0.237834i	0.673686	+	0.739017i	$0.264710\pi$
$54$	13.9040	+	3.36032i	0.257481	+	0.0622281i
$55$	25.2294			0.458717
$56$	−54.0291	+	14.7262i	−0.964805	+	0.262968i
$57$			6.52744i			0.114516i
$58$	−81.8566	−	19.7831i	−1.41132	−	0.341088i
$59$	2.01838	+	7.53268i	0.0342098	+	0.127673i	0.980919	−	0.194417i	$-0.0622815\pi$
$59$	2.01838	+	7.53268i	0.0342098	+	0.127673i	−0.946709	+	0.322089i	$0.895615\pi$
$60$	2.14610	−	4.18062i	0.0357683	−	0.0696771i
$61$	−15.1533	+	56.5528i	−0.248415	+	0.927096i	0.723222	+	0.690616i	$0.242660\pi$
$61$	−15.1533	+	56.5528i	−0.248415	+	0.927096i	−0.971636	+	0.236480i	$0.924006\pi$
$62$	2.44493	+	99.0997i	0.0394344	+	1.59838i
$63$	46.6930	−	40.5987i	0.741159	−	0.644424i
$64$	63.3004	−	9.43737i	0.989068	−	0.147459i
$65$	9.12911	+	15.8121i	0.140448	+	0.243263i
$66$	6.06211	+	3.30335i	0.0918502	+	0.0500507i
$67$	−0.662730	−	2.47334i	−0.00989150	−	0.0369156i	0.960804	−	0.277230i	$-0.0894163\pi$
$67$	−0.662730	−	2.47334i	−0.00989150	−	0.0369156i	−0.970695	+	0.240314i	$0.922750\pi$
$68$	−61.3306	+	39.5651i	−0.901921	+	0.581840i
$69$	−2.07760	+	2.07760i	−0.0301101	+	0.0301101i
$70$	−18.8919	−	36.4155i	−0.269884	−	0.520222i
$71$			98.9570i			1.39376i	0.717188	+	0.696880i	$0.245429\pi$
$71$			98.9570i			1.39376i	−0.717188	+	0.696880i	$0.754571\pi$
$72$	−58.4586	+	39.7879i	−0.811925	+	0.552610i
$73$	−52.5670	+	91.0487i	−0.720096	+	1.24724i	0.240865	+	0.970559i	$0.422569\pi$
$73$	−52.5670	+	91.0487i	−0.720096	+	1.24724i	−0.960961	+	0.276684i	$0.910765\pi$
$74$	−69.3047	+	20.4149i	−0.936550	+	0.275877i
$75$	−6.35622	−	1.70314i	−0.0847496	−	0.0227086i
$76$	−48.2647	−	43.7230i	−0.635062	−	0.575303i
$77$	54.1662	−	26.4261i	0.703457	−	0.343196i
$78$	0.123224	+	4.99462i	0.00157980	+	0.0640336i
$79$	−48.3594	−	83.7610i	−0.612145	−	1.06027i	−0.990878	−	0.134760i	$-0.956974\pi$
$79$	−48.3594	−	83.7610i	−0.612145	−	1.06027i	0.378734	−	0.925506i	$-0.376360\pi$
$80$	16.5368	+	43.8718i	0.206710	+	0.548397i
$81$	38.3430	−	66.4119i	0.473370	−	0.819901i
$82$	9.41821	+	15.4215i	0.114856	+	0.188067i
$83$	93.2835	+	93.2835i	1.12390	+	1.12390i	0.991150	+	0.132747i	$0.0423799\pi$
$83$	93.2835	+	93.2835i	1.12390	+	1.12390i	0.132747	+	0.991150i	$0.457620\pi$
$84$	0.228642	−	11.2235i	0.00272193	−	0.133613i
$85$	−37.8071	−	37.8071i	−0.444789	−	0.444789i
$86$	0.425576	−	1.76091i	0.00494856	−	0.0204757i
$87$	8.44073	−	14.6198i	0.0970199	−	0.168043i
$88$	−65.0315	+	22.6971i	−0.738994	+	0.257921i
$89$	17.6754	+	30.6147i	0.198600	+	0.343986i	0.948075	−	0.318047i	$-0.103027\pi$
$89$	17.6754	+	30.6147i	0.198600	+	0.343986i	−0.749475	+	0.662033i	$0.769694\pi$
$90$	−37.5229	−	35.7160i	−0.416922	−	0.396845i
$91$	36.1618	+	24.3856i	0.397382	+	0.267973i
$92$	−1.44556	−	29.2785i	−0.0157126	−	0.318244i
$93$	−19.1945	−	5.14316i	−0.206393	−	0.0553028i
$94$	133.129	+	72.5443i	1.41627	+	0.771748i
$95$	23.8543	−	41.3169i	0.251098	−	0.434914i
$96$	−1.77079	+	12.7067i	−0.0184457	+	0.132361i
$97$			131.836i			1.35914i	0.733612	+	0.679569i	$0.237833\pi$
$97$			131.836i			1.35914i	−0.733612	+	0.679569i	$0.762167\pi$
$98$	−78.7027	−	58.3943i	−0.803088	−	0.595860i
$99$	53.8140	−	53.8140i	0.543575	−	0.543575i
$100$	55.1694	−	35.5904i	0.551694	−	0.355904i
$101$	−33.3218	−	124.359i	−0.329919	−	1.23127i	−0.909274	−	0.416199i	$-0.863362\pi$
$101$	−33.3218	−	124.359i	−0.329919	−	1.23127i	0.579355	−	0.815075i	$-0.303305\pi$
$102$	−4.13410	−	14.0344i	−0.0405304	−	0.137593i
$103$	−19.4928	−	33.7624i	−0.189250	−	0.327791i	0.755750	−	0.654860i	$-0.227272\pi$
$103$	−19.4928	−	33.7624i	−0.189250	−	0.327791i	−0.945000	+	0.327069i	$0.893939\pi$
$104$	−37.7562	−	32.5445i	−0.363041	−	0.312928i
$105$	8.07250	−	1.57007i	0.0768809	−	0.0149530i
$106$	−70.5538	−	67.1563i	−0.665602	−	0.633550i
$107$	−15.0462	+	56.1533i	−0.140619	+	0.524798i	0.859292	+	0.511485i	$0.170904\pi$
$107$	−15.0462	+	56.1533i	−0.140619	+	0.524798i	−0.999911	+	0.0133127i	$0.995762\pi$
$108$	−8.75813	−	27.2350i	−0.0810938	−	0.252176i
$109$	−10.4550	−	39.0185i	−0.0959173	−	0.357968i	0.901240	−	0.433321i	$-0.142658\pi$
$109$	−10.4550	−	39.0185i	−0.0959173	−	0.357968i	−0.997157	+	0.0753529i	$0.975992\pi$
$110$	−26.2995	−	43.0631i	−0.239087	−	0.391483i
$111$		−	14.4831i		−	0.130478i
$112$	81.4562	+	76.8692i	0.727288	+	0.686332i
$113$	−132.819			−1.17539			−0.587695	−	0.809083i	$-0.699964\pi$
$113$	−132.819			−1.17539			−0.587695	+	0.809083i	$0.699964\pi$
$114$	11.1414	−	6.80430i	0.0977318	−	0.0596868i
$115$	20.7431	−	5.55810i	0.180375	−	0.0483313i
$116$	51.5616	+	160.340i	0.444496	+	1.38224i
$117$	53.1992	+	14.2547i	0.454694	+	0.121835i
$118$	10.7532	−	11.2973i	0.0911292	−	0.0957395i
$119$	−120.770	−	41.5695i	−1.01488	−	0.349323i
$120$	−9.37287	+	0.694855i	−0.0781072	+	0.00579045i
$121$	−40.5915	+	23.4355i	−0.335467	+	0.193682i
$122$	112.324	−	33.0870i	0.920687	−	0.271205i
$123$	−3.49889	+	0.937525i	−0.0284463	+	0.00762216i
$124$	166.601	−	107.476i	1.34355	−	0.866743i
$125$	85.8100	+	85.8100i	0.686480	+	0.686480i
$126$	−117.970	−	37.3777i	−0.936269	−	0.296648i
$127$	−39.1377			−0.308171			−0.154085	−	0.988058i	$-0.549243\pi$
$127$	−39.1377			−0.308171			−0.154085	+	0.988058i	$0.549243\pi$
$128$	−82.0935	−	98.2072i	−0.641356	−	0.767244i
$129$	0.314502	+	0.181578i	0.00243800	+	0.00140758i
$130$	17.4727	−	32.0649i	0.134405	−	0.246653i
$131$	35.2645	−	131.609i	0.269195	−	1.00465i	−0.690438	−	0.723391i	$-0.742582\pi$
$131$	35.2645	−	131.609i	0.269195	−	1.00465i	0.959633	−	0.281256i	$-0.0907511\pi$
$132$	−0.680884	−	13.7906i	−0.00515822	−	0.104475i
$133$	7.93732	−	113.691i	0.0596791	−	0.854819i
$134$	−3.53081	+	3.70944i	−0.0263493	+	0.0276824i
$135$	18.1501	−	10.4790i	0.134446	−	0.0776222i
$136$	131.464	+	63.4395i	0.966648	+	0.466467i
$137$	−3.69605	−	2.13391i	−0.0269785	−	0.0155760i	0.486450	−	0.873708i	$-0.338292\pi$
$137$	−3.69605	−	2.13391i	−0.0269785	−	0.0155760i	−0.513429	+	0.858132i	$0.671625\pi$
$138$	5.71188	+	1.38045i	0.0413905	+	0.0100032i
$139$	26.0488	−	26.0488i	0.187402	−	0.187402i	−0.607170	−	0.794572i	$-0.707695\pi$
$139$	26.0488	−	26.0488i	0.187402	−	0.187402i	0.794572	+	0.607170i	$0.207695\pi$
$140$	−42.4631	+	70.2059i	−0.303308	+	0.501471i
$141$	−21.4905	+	21.4905i	−0.152415	+	0.152415i
$142$	168.906	−	103.154i	1.18948	−	0.726438i
$143$	46.4590	+	26.8231i	0.324888	+	0.187574i
$144$	128.850	+	58.3052i	0.894795	+	0.404897i
$145$	−106.855	+	61.6927i	−0.736931	+	0.425467i
$146$	210.204	−	5.18603i	1.43975	−	0.0355208i
$147$	15.6867	−	11.8262i	0.106712	−	0.0804506i
$148$	107.090	+	97.0125i	0.723579	+	0.655490i
$149$	−22.4954	+	83.9538i	−0.150976	+	0.563448i	0.848441	+	0.529290i	$0.177542\pi$
$149$	−22.4954	+	83.9538i	−0.150976	+	0.563448i	−0.999416	+	0.0341582i	$0.989125\pi$
$150$	3.71879	+	12.6246i	0.0247919	+	0.0841637i
$151$	−43.8563	−	25.3204i	−0.290439	−	0.167685i	0.347701	−	0.937606i	$-0.386963\pi$
$151$	−43.8563	−	25.3204i	−0.290439	−	0.167685i	−0.638140	+	0.769920i	$0.720296\pi$
$152$	−24.3172	+	127.959i	−0.159982	+	0.841833i
$153$	−161.284			−1.05414
$154$	−101.569	−	64.9072i	−0.659541	−	0.421475i
$155$	102.701	+	102.701i	0.662584	+	0.662584i
$156$	8.39666	−	5.41679i	0.0538248	−	0.0347230i
$157$	−217.225	+	58.2053i	−1.38360	+	0.370734i	−0.872427	−	0.488744i	$-0.837455\pi$
$157$	−217.225	+	58.2053i	−1.38360	+	0.370734i	−0.511172	+	0.859478i	$0.670789\pi$
$158$	−92.5577	+	169.856i	−0.585808	+	1.07504i
$159$	16.9100	−	9.76297i	0.106352	−	0.0614024i
$160$	57.6448	−	73.9585i	0.360280	−	0.462241i
$161$	38.7126	−	33.6599i	0.240451	−	0.209068i
$162$	−153.325	+	3.78275i	−0.946452	+	0.0233503i
$163$	146.489	+	39.2515i	0.898703	+	0.240807i	0.678459	−	0.734638i	$-0.262648\pi$
$163$	146.489	+	39.2515i	0.898703	+	0.240807i	0.220244	+	0.975445i	$0.429315\pi$
$164$	16.5046	−	32.1511i	0.100638	−	0.196043i
$165$	9.77035	−	2.61796i	0.0592143	−	0.0158664i
$166$	61.9817	−	256.462i	0.373384	−	1.54495i
$167$	48.1800			0.288503			0.144251	−	0.989541i	$-0.453923\pi$
$167$	48.1800			0.288503			0.144251	+	0.989541i	$0.453923\pi$
$168$	−19.3952	+	11.3093i	−0.115448	+	0.0673170i
$169$		−	130.177i		−	0.770277i
$170$	−25.1207	+	103.942i	−0.147769	+	0.611424i
$171$	−37.2474	−	139.009i	−0.217821	−	0.812919i
$172$	−3.44925	+	1.10920i	−0.0200538	+	0.00644882i
$173$	−22.5528	+	84.1682i	−0.130363	+	0.486521i	−0.999974	−	0.00721627i	$-0.997703\pi$
$173$	−22.5528	+	84.1682i	−0.130363	+	0.486521i	0.869611	+	0.493738i	$0.164370\pi$
$174$	−33.7526	+	0.832726i	−0.193981	+	0.00478578i
$175$	108.638	+	37.3934i	0.620787	+	0.213677i
$176$	106.531	+	87.3399i	0.605287	+	0.496249i
$177$	1.56327	+	2.70767i	0.00883206	+	0.0152976i
$178$	33.8299	−	62.0827i	0.190056	−	0.348779i
$179$	−79.2899	−	295.914i	−0.442960	−	1.65315i	−0.721266	−	0.692658i	$-0.756440\pi$
$179$	−79.2899	−	295.914i	−0.442960	−	1.65315i	0.278306	−	0.960492i	$-0.410227\pi$
$180$	−21.8478	+	101.277i	−0.121377	+	0.562652i
$181$	−206.279	+	206.279i	−1.13966	+	1.13966i	−0.151153	+	0.988510i	$0.548299\pi$
$181$	−206.279	+	206.279i	−1.13966	+	1.13966i	−0.988510	+	0.151153i	$0.951701\pi$
$182$	3.92718	−	87.1430i	0.0215779	−	0.478808i
$183$			23.4731i			0.128268i
$184$	−48.4673	+	32.9877i	−0.263409	+	0.179281i
$185$	−52.9279	+	91.6738i	−0.286097	+	0.495534i
$186$	11.2300	+	38.1237i	0.0603764	+	0.204966i
$187$	−151.744	−	40.6598i	−0.811467	−	0.217432i
$188$	−14.9528	−	302.854i	−0.0795361	−	1.61092i
$189$	27.9914	−	41.5089i	0.148102	−	0.219624i
$190$	−95.3882	+	2.35336i	−0.502043	+	0.0123861i
$191$	30.1507	+	52.2226i	0.157857	+	0.273417i	0.934096	−	0.357023i	$-0.116208\pi$
$191$	30.1507	+	52.2226i	0.157857	+	0.273417i	−0.776238	+	0.630439i	$0.782875\pi$
$192$	23.5344	−	10.2232i	0.122575	−	0.0532456i
$193$	−32.5963	+	56.4585i	−0.168893	+	0.292531i	−0.938031	−	0.346552i	$-0.887353\pi$
$193$	−32.5963	+	56.4585i	−0.168893	+	0.292531i	0.769138	+	0.639083i	$0.220686\pi$
$194$	225.026	−	137.428i	1.15993	−	0.708393i
$195$	5.17610	+	5.17610i	0.0265441	+	0.0265441i
$196$	−17.6300	+	195.205i	−0.0899491	+	0.995946i
$197$	−102.673	−	102.673i	−0.521185	−	0.521185i	0.396744	−	0.917929i	$-0.370140\pi$
$197$	−102.673	−	102.673i	−0.521185	−	0.521185i	−0.917929	+	0.396744i	$0.870140\pi$
$198$	−147.949	−	35.7564i	−0.747219	−	0.180588i
$199$	17.1526	−	29.7092i	0.0861939	−	0.149292i	−0.819705	−	0.572785i	$-0.805863\pi$
$199$	17.1526	−	29.7092i	0.0861939	−	0.149292i	0.905899	+	0.423493i	$0.139196\pi$
$200$	−118.257	−	57.0664i	−0.591286	−	0.285332i
$201$	−0.513298	−	0.889059i	−0.00255372	−	0.00442318i
$202$	−177.528	+	186.509i	−0.878850	+	0.923312i
$203$	−164.793	+	244.374i	−0.811788	+	1.20381i
$204$	−19.6454	+	21.6860i	−0.0963009	+	0.106304i
$205$	25.5732	+	6.85231i	0.124747	+	0.0334259i
$206$	−37.3082	+	68.4659i	−0.181108	+	0.332359i
$207$	32.3894	−	56.1001i	0.156471	−	0.271015i
$208$	−16.1913	+	98.3695i	−0.0778426	+	0.472930i
$209$		−	140.177i		−	0.670704i
$210$	−11.0948	−	12.1420i	−0.0528323	−	0.0578189i
$211$	−253.482	+	253.482i	−1.20134	+	1.20134i	−0.227575	+	0.973761i	$0.573080\pi$
$211$	−253.482	+	253.482i	−1.20134	+	1.20134i	−0.973761	+	0.227575i	$0.926920\pi$
$212$	−41.0800	+	190.430i	−0.193774	+	0.898255i
$213$	10.2684	+	38.3221i	0.0482084	+	0.179916i
$214$	111.530	−	32.8533i	0.521170	−	0.153520i
$215$	−1.32714	−	2.29867i	−0.00617274	−	0.0106915i
$216$	−37.3567	+	43.3391i	−0.172948	+	0.200644i
$217$	328.064	+	112.921i	1.51182	+	0.520372i
$218$	−55.7007	+	58.5187i	−0.255508	+	0.268434i
$219$	−10.9093	+	40.7142i	−0.0498143	+	0.185910i
$220$	−46.0876	+	89.7792i	−0.209489	+	0.408087i
$221$	−29.4250	−	109.816i	−0.133145	−	0.496903i
$222$	−24.7206	+	15.0974i	−0.111354	+	0.0680062i
$223$			164.601i			0.738121i	0.929405	+	0.369061i	$0.120321\pi$
$223$			164.601i			0.738121i	−0.929405	+	0.369061i	$0.879679\pi$
$224$	46.2938	−	219.164i	0.206669	−	0.978411i
$225$	145.081			0.644806
$226$	138.452	+	226.703i	0.612622	+	1.00311i
$227$	−391.348	+	104.861i	−1.72400	+	0.461945i	−0.978787	−	0.204880i	$-0.934320\pi$
$227$	−391.348	+	104.861i	−1.72400	+	0.461945i	−0.745215	+	0.666825i	$0.767653\pi$
$228$	−23.2280	−	11.9239i	−0.101877	−	0.0522980i
$229$	382.866	+	102.589i	1.67190	+	0.447985i	0.965623	−	0.259947i	$-0.0837051\pi$
$229$	382.866	+	102.589i	1.67190	+	0.447985i	0.706280	+	0.707932i	$0.250372\pi$
$230$	−31.1098	−	29.6117i	−0.135260	−	0.128747i
$231$	18.2343	−	15.8544i	0.0789364	−	0.0686338i
$232$	219.929	−	255.149i	0.947971	−	1.09978i
$233$	361.218	−	208.549i	1.55029	−	0.895061i	0.552174	−	0.833729i	$-0.313798\pi$
$233$	361.218	−	208.549i	1.55029	−	0.895061i	0.998117	−	0.0613326i	$-0.0195350\pi$
$234$	−31.1249	−	105.663i	−0.133012	−	0.451551i
$235$	214.565	−	57.4925i	0.913043	−	0.244649i
$236$	−30.4922	−	6.57785i	−0.129204	−	0.0278722i
$237$	−27.4192	−	27.4192i	−0.115693	−	0.115693i
$238$	54.9394	+	249.470i	0.230838	+	1.04820i
$239$	273.051			1.14247			0.571237	−	0.820785i	$-0.306464\pi$
$239$	273.051			1.14247			0.571237	+	0.820785i	$0.306464\pi$
$240$	10.9564	+	15.2738i	0.0456518	+	0.0636410i
$241$	−202.680	−	117.018i	−0.840997	−	0.485550i	0.0166058	−	0.999862i	$-0.494714\pi$
$241$	−202.680	−	117.018i	−0.840997	−	0.485550i	−0.857603	+	0.514312i	$0.828047\pi$
$242$	82.3144	+	44.8545i	0.340142	+	0.185349i
$243$	24.6174	−	91.8734i	0.101306	−	0.378080i
$244$	−173.563	−	157.231i	−0.711323	−	0.644388i
$245$	−142.511	+	17.5304i	−0.581677	+	0.0715525i
$246$	5.24752	+	4.99483i	0.0213314	+	0.0203042i
$247$	87.8535	−	50.7223i	0.355682	−	0.205353i
$248$	−357.114	−	172.329i	−1.43997	−	0.694876i
$249$	45.8047	+	26.4453i	0.183954	+	0.106206i
$250$	57.0161	−	235.915i	0.228064	−	0.943662i
$251$	306.285	−	306.285i	1.22026	−	1.22026i	0.252720	−	0.967539i	$-0.418675\pi$
$251$	306.285	−	306.285i	1.22026	−	1.22026i	0.967539	−	0.252720i	$-0.0813253\pi$
$252$	59.1751	+	240.321i	0.234822	+	0.953655i
$253$	44.6165	−	44.6165i	0.176350	−	0.176350i
$254$	40.7977	+	66.8026i	0.160621	+	0.263002i
$255$	−18.5643	−	10.7181i	−0.0728011	−	0.0420317i
$256$	−82.0504	+	242.495i	−0.320509	+	0.947245i
$257$	130.052	−	75.0853i	0.506037	−	0.292161i	−0.225166	−	0.974320i	$-0.572292\pi$
$257$	130.052	−	75.0853i	0.506037	−	0.292161i	0.731203	+	0.682160i	$0.238959\pi$
$258$	−0.0179137	−	0.726090i	−6.94329e−5	−	0.00281430i
$259$	−17.6113	+	252.257i	−0.0679974	+	0.973966i
$260$	−72.9440	+	3.60146i	−0.280554	+	0.0138518i
$261$	−96.3303	+	359.510i	−0.369082	+	1.37743i
$262$	−261.398	+	76.9995i	−0.997703	+	0.293891i
$263$	13.7860	+	7.95932i	0.0524181	+	0.0302636i	0.525980	−	0.850497i	$-0.323699\pi$
$263$	13.7860	+	7.95932i	0.0524181	+	0.0302636i	−0.473562	+	0.880761i	$0.657032\pi$
$264$	−22.8289	+	15.5377i	−0.0864732	+	0.0588551i
$265$	−142.714			−0.538543
$266$	−202.328	+	104.965i	−0.760633	+	0.394606i
$267$	10.0218	+	10.0218i	0.0375347	+	0.0375347i
$268$	10.0121	+	2.15983i	0.0373584	+	0.00805905i
$269$	149.853	−	40.1531i	0.557076	−	0.149268i	0.0307134	−	0.999528i	$-0.490222\pi$
$269$	149.853	−	40.1531i	0.557076	−	0.149268i	0.526363	+	0.850260i	$0.323555\pi$
$270$	−36.8062	−	20.0563i	−0.136319	−	0.0742826i
$271$	−308.387	+	178.047i	−1.13796	+	0.657001i	−0.945924	−	0.324387i	$-0.894842\pi$
$271$	−308.387	+	178.047i	−1.13796	+	0.657001i	−0.192035	+	0.981388i	$0.561509\pi$
$272$	−28.7579	−	290.521i	−0.105727	−	1.06809i
$273$	16.5344	+	5.69120i	0.0605657	+	0.0208469i
$274$	0.210523	+	8.53306i	0.000768332	+	0.0311426i
$275$	136.500	+	36.5751i	0.496364	+	0.133000i
$276$	−3.59792	−	11.1884i	−0.0130359	−	0.0405376i
$277$	158.849	−	42.5634i	0.573461	−	0.153659i	0.0395778	−	0.999216i	$-0.487399\pi$
$277$	158.849	−	42.5634i	0.573461	−	0.153659i	0.533884	+	0.845558i	$0.320732\pi$
$278$	−71.6154	−	17.3080i	−0.257609	−	0.0622591i
$279$	438.117			1.57031
$280$	164.096	−	0.705200i	0.586056	−	0.00251857i
$281$		−	222.264i		−	0.790977i	−0.918471	−	0.395488i	$-0.870575\pi$
$281$		−	222.264i		−	0.790977i	0.918471	−	0.395488i	$-0.129425\pi$
$282$	59.0832	+	14.2792i	0.209515	+	0.0506356i
$283$	−105.385	−	393.304i	−0.372387	−	1.38977i	−0.857126	−	0.515107i	$-0.827752\pi$
$283$	−105.385	−	393.304i	−0.372387	−	1.38977i	0.484739	−	0.874659i	$-0.338915\pi$
$284$	−352.140	−	180.769i	−1.23993	−	0.636510i
$285$	4.95054	−	18.4757i	0.0173703	−	0.0648269i
$286$	−2.64625	−	107.260i	−0.00925263	−	0.375034i
$287$	62.0816	−	12.0746i	0.216312	−	0.0420718i
$288$	−34.7969	−	280.708i	−0.120823	−	0.974680i
$289$	21.9639	+	38.0425i	0.0759995	+	0.131635i
$290$	216.688	+	118.077i	0.747200	+	0.407162i
$291$	13.6801	+	51.0550i	0.0470108	+	0.175447i
$292$	−227.972	−	353.383i	−0.780725	−	1.21021i
$293$	124.881	−	124.881i	0.426215	−	0.426215i	−0.461122	−	0.887337i	$-0.652553\pi$
$293$	124.881	−	124.881i	0.426215	−	0.426215i	0.887337	+	0.461122i	$0.152553\pi$
$294$	−36.5378	−	14.4471i	−0.124278	−	0.0491399i
$295$		−	22.8517i		−	0.0774635i
$296$	53.9549	−	283.914i	0.182280	−	0.959170i
$297$	30.7893	−	53.3287i	0.103668	−	0.179558i
$298$	166.747	−	49.1183i	0.559553	−	0.164826i
$299$	44.1068	+	11.8184i	0.147514	+	0.0395264i
$300$	17.6718	−	19.5075i	0.0589061	−	0.0650249i
$301$	−5.25700	−	3.54504i	−0.0174651	−	0.0117775i
$302$	2.49801	+	101.251i	0.00827155	+	0.335268i
$303$	−25.8084	−	44.7015i	−0.0851763	−	0.147530i
$304$	243.756	−	91.8799i	0.801829	−	0.302237i
$305$	85.7816	−	148.578i	0.281251	−	0.487141i
$306$	168.125	+	275.289i	0.549427	+	0.899637i
$307$	−217.234	−	217.234i	−0.707603	−	0.707603i	0.258427	−	0.966031i	$-0.416796\pi$
$307$	−217.234	−	217.234i	−0.707603	−	0.707603i	−0.966031	+	0.258427i	$0.916796\pi$
$308$	−4.91011	+	241.025i	−0.0159419	+	0.782548i
$309$	−11.0522	−	11.0522i	−0.0357675	−	0.0357675i
$310$	68.2389	−	282.352i	0.220125	−	0.910813i
$311$	2.15426	−	3.73130i	0.00692690	−	0.0119977i	−0.862541	−	0.505987i	$-0.831128\pi$
$311$	2.15426	−	3.73130i	0.00692690	−	0.0119977i	0.869468	+	0.493989i	$0.164462\pi$
$312$	−17.9985	−	8.68538i	−0.0576875	−	0.0278378i
$313$	−94.5176	−	163.709i	−0.301973	−	0.523033i	0.674610	−	0.738175i	$-0.264312\pi$
$313$	−94.5176	−	163.709i	−0.301973	−	0.523033i	−0.976583	+	0.215142i	$0.930979\pi$
$314$	325.787	+	310.099i	1.03754	+	0.987576i
$315$	−162.954	+	79.5002i	−0.517313	+	0.252382i
$316$	386.405	−	19.0779i	1.22280	−	0.0603732i
$317$	−198.200	−	53.1075i	−0.625237	−	0.167532i	−0.0677294	−	0.997704i	$-0.521575\pi$
$317$	−198.200	−	53.1075i	−0.625237	−	0.167532i	−0.557507	+	0.830172i	$0.688242\pi$
$318$	−34.2912	−	18.6859i	−0.107834	−	0.0587606i
$319$	−181.265	+	313.961i	−0.568230	+	0.984202i
$320$	−186.327	−	21.2961i	−0.582271	−	0.0665504i
$321$			23.3073i			0.0726083i
$322$	−97.8074	−	30.9894i	−0.303750	−	0.0962404i
$323$	−210.060	+	210.060i	−0.650341	+	0.650341i
$324$	166.285	+	257.761i	0.513226	+	0.795560i
$325$	26.4690	+	98.7835i	0.0814430	+	0.303949i
$326$	−85.7051	−	290.952i	−0.262899	−	0.892490i
$327$	−8.09760	−	14.0255i	−0.0247633	−	0.0428913i
$328$	−72.0821	+	5.34378i	−0.219762	+	0.0162920i
$329$	400.440	−	348.176i	1.21714	−	1.05828i
$330$	−14.6533	−	13.9476i	−0.0444038	−	0.0422655i
$331$	64.9467	−	242.384i	0.196213	−	0.732279i	−0.795736	−	0.605644i	$-0.792916\pi$
$331$	64.9467	−	242.384i	0.196213	−	0.732279i	0.991949	−	0.126635i	$-0.0404177\pi$
$332$	−502.355	+	161.546i	−1.51312	+	0.486583i
$333$	82.6444	+	308.433i	0.248181	+	0.926226i
$334$	−50.2235	−	82.2365i	−0.150370	−	0.246217i
$335$			7.50333i			0.0223980i
$336$	39.5212	+	21.3160i	0.117623	+	0.0634405i
$337$	−62.8095			−0.186378			−0.0931892	−	0.995648i	$-0.529706\pi$
$337$	−62.8095			−0.186378			−0.0931892	+	0.995648i	$0.529706\pi$
$338$	−222.194	+	135.698i	−0.657378	+	0.401474i
$339$	−51.4355	+	13.7821i	−0.151727	+	0.0406552i
$340$	203.601	−	65.4732i	0.598826	−	0.192568i
$341$	412.204	+	110.450i	1.20881	+	0.323899i
$342$	−198.442	+	208.481i	−0.580239	+	0.609594i
$343$	−287.602	+	186.907i	−0.838489	+	0.544919i
$344$	5.48879	+	4.73114i	0.0159558	+	0.0137533i
$345$	7.45624	−	4.30486i	0.0216123	−	0.0124779i
$346$	167.173	−	49.2437i	0.483158	−	0.142323i
$347$	−523.845	+	140.364i	−1.50964	+	0.404507i	−0.916316	−	0.400457i	$-0.868851\pi$
$347$	−523.845	+	140.364i	−1.50964	+	0.404507i	−0.593324	+	0.804964i	$0.702185\pi$
$348$	36.6056	+	56.7430i	0.105189	+	0.163055i
$349$	−349.173	−	349.173i	−1.00049	−	1.00049i	−1.00000		0.000495101i	$-0.999842\pi$
$349$	−349.173	−	349.173i	−1.00049	−	1.00049i	−0.000495101	−	1.00000i	$-0.500158\pi$
$350$	−49.4202	−	224.409i	−0.141201	−	0.641168i
$351$	44.5637			0.126962
$352$	38.0279	−	272.877i	0.108034	−	0.775219i
$353$	412.307	+	238.046i	1.16801	+	0.674350i	0.953210	−	0.302308i	$-0.0977571\pi$
$353$	412.307	+	238.046i	1.16801	+	0.674350i	0.214799	+	0.976658i	$0.431090\pi$
$354$	2.99203	−	5.49081i	0.00845207	−	0.0155108i
$355$	75.0509	−	280.094i	0.211411	−	0.788997i
$356$	−141.231	+	6.97301i	−0.396717	+	0.0195871i
$357$	−51.0830	−	3.56636i	−0.143090	−	0.00998980i
$358$	−422.431	+	443.802i	−1.17997	+	1.23967i
$359$	−237.926	+	137.367i	−0.662746	+	0.382637i	−0.793322	−	0.608802i	$-0.791651\pi$
$359$	−237.926	+	137.367i	−0.662746	+	0.382637i	0.130577	+	0.991438i	$0.458317\pi$
$360$	195.641	−	68.2819i	0.543446	−	0.189672i
$361$	83.0744	+	47.9631i	0.230123	+	0.132862i
$362$	567.118	+	137.061i	1.56662	+	0.378622i
$363$	−13.2877	+	13.2877i	−0.0366052	+	0.0366052i
$364$	−152.835	+	84.1360i	−0.419876	+	0.231143i
$365$	217.842	−	217.842i	0.596827	−	0.596827i
$366$	40.0652	−	24.4687i	0.109468	−	0.0668543i
$367$	368.371	+	212.679i	1.00374	+	0.579507i	0.909352	−	0.416028i	$-0.136578\pi$
$367$	368.371	+	212.679i	1.00374	+	0.579507i	0.0943847	+	0.995536i	$0.469912\pi$
$368$	106.828	+	48.3401i	0.290295	+	0.131359i
$369$	69.1631	−	39.9313i	0.187434	−	0.108215i
$370$	211.647	−	5.22164i	0.572020	−	0.0141125i
$371$	−306.399	+	149.483i	−0.825874	+	0.402919i
$372$	53.3654	−	58.9087i	0.143455	−	0.158357i
$373$	−190.799	+	712.073i	−0.511527	+	1.90904i	−0.107775	+	0.994175i	$0.534373\pi$
$373$	−190.799	+	712.073i	−0.511527	+	1.90904i	−0.403751	+	0.914869i	$0.632294\pi$
$374$	88.7801	+	301.391i	0.237380	+	0.805858i
$375$	42.1350	+	24.3267i	0.112360	+	0.0648711i
$376$	−501.342	+	341.222i	−1.33336	+	0.907505i
$377$	−262.359			−0.695912
$378$	−100.028	−	4.50787i	−0.264626	−	0.0119256i
$379$	161.112	+	161.112i	0.425097	+	0.425097i	0.886954	−	0.461857i	$-0.152817\pi$
$379$	161.112	+	161.112i	0.425097	+	0.425097i	−0.461857	+	0.886954i	$0.652817\pi$
$380$	103.451	+	160.361i	0.272239	+	0.422003i
$381$	−15.1565	+	4.06117i	−0.0397808	+	0.0106592i
$382$	57.7071	−	105.901i	0.151066	−	0.277227i
$383$	−177.117	+	102.259i	−0.462447	+	0.266994i	−0.713073	−	0.701090i	$-0.752697\pi$
$383$	−177.117	+	102.259i	−0.462447	+	0.266994i	0.250626	+	0.968084i	$0.419364\pi$
$384$	−41.9821	−	29.5132i	−0.109329	−	0.0768574i
$385$	−173.357	+	33.7173i	−0.450279	+	0.0875774i
$386$	130.346	−	3.21581i	0.337683	−	0.00833113i
$387$	−7.73380	−	2.07227i	−0.0199840	−	0.00535469i
$388$	−469.141	−	240.831i	−1.20913	−	0.620698i
$389$	−163.761	+	43.8795i	−0.420979	+	0.112801i	−0.463088	−	0.886312i	$-0.653259\pi$
$389$	−163.761	+	43.8795i	−0.420979	+	0.112801i	0.0421098	+	0.999113i	$0.486592\pi$
$390$	3.43923	−	14.2305i	0.00881855	−	0.0364885i
$391$	−133.719			−0.341991
$392$	351.566	−	173.393i	0.896853	−	0.442329i
$393$		−	54.6262i		−	0.138998i
$394$	−68.2209	+	282.278i	−0.173149	+	0.716441i
$395$	73.3535	+	273.759i	0.185705	+	0.693060i
$396$	93.1934	+	289.802i	0.235337	+	0.731823i
$397$	10.0250	−	37.4139i	0.0252520	−	0.0942416i	−0.952150	−	0.305632i	$-0.901132\pi$
$397$	10.0250	−	37.4139i	0.0252520	−	0.0942416i	0.977402	+	0.211390i	$0.0677990\pi$
$398$	−68.5895	+	1.69220i	−0.172335	+	0.00425176i
$399$	−8.72345	−	44.8516i	−0.0218633	−	0.112410i
$400$	25.8689	+	261.335i	0.0646721	+	0.653339i
$401$	−300.814	−	521.026i	−0.750160	−	1.29932i	−0.947745	−	0.319030i	$-0.896643\pi$
$401$	−300.814	−	521.026i	−0.750160	−	1.29932i	0.197584	−	0.980286i	$-0.436690\pi$
$402$	−0.982429	+	1.80290i	−0.00244385	+	0.00448482i
$403$	79.9311	+	298.307i	0.198340	+	0.740216i
$404$	503.402	+	108.595i	1.24605	+	0.268800i
$405$	−158.896	+	158.896i	−0.392337	+	0.392337i
$406$	588.895	+	26.5391i	1.45048	+	0.0653672i
$407$			311.025i			0.764189i
$408$	57.4937	+	10.9261i	0.140916	+	0.0267796i
$409$	−303.498	+	525.673i	−0.742048	+	1.28526i	0.209513	+	0.977806i	$0.432812\pi$
$409$	−303.498	+	525.673i	−0.742048	+	1.28526i	−0.951561	+	0.307459i	$0.900521\pi$
$410$	−14.9619	−	50.7928i	−0.0364925	−	0.123885i
$411$	−1.65276	−	0.442856i	−0.00402132	−	0.00107751i
$412$	155.752	−	7.68995i	0.378040	−	0.0186649i
$413$	−23.9356	−	49.0615i	−0.0579555	−	0.118793i
$414$	−129.518	+	3.19540i	−0.312846	+	0.00771836i
$415$	−193.287	−	334.783i	−0.465752	−	0.806707i
$416$	184.781	−	74.9056i	0.444185	−	0.180062i
$417$	7.38470	−	12.7907i	0.0177091	−	0.0306731i
$418$	−239.263	+	146.123i	−0.572399	+	0.349576i
$419$	−176.831	−	176.831i	−0.422032	−	0.422032i	0.463871	−	0.885903i	$-0.346460\pi$
$419$	−176.831	−	176.831i	−0.422032	−	0.422032i	−0.885903	+	0.463871i	$0.846460\pi$
$420$	−9.15926	+	31.5942i	−0.0218078	+	0.0752243i
$421$	−488.135	−	488.135i	−1.15947	−	1.15947i	−0.984590	−	0.174876i	$-0.944047\pi$
$421$	−488.135	−	488.135i	−1.15947	−	1.15947i	−0.174876	−	0.984590i	$-0.555953\pi$
$422$	696.891	+	168.425i	1.65140	+	0.399111i
$423$	335.033	−	580.294i	0.792041	−	1.37185i
$424$	367.860	−	128.389i	0.867594	−	0.302805i
$425$	−149.741	−	259.359i	−0.352332	−	0.610256i
$426$	54.7066	−	57.4742i	0.128419	−	0.134916i
$427$	28.5431	−	408.840i	0.0668457	−	0.957470i
$428$	−172.337	−	156.120i	−0.402656	−	0.364766i
$429$	20.7750	+	5.56666i	0.0484267	+	0.0129759i
$430$	−2.54008	+	4.66141i	−0.00590717	+	0.0108405i
$431$	−7.11802	+	12.3288i	−0.0165151	+	0.0286050i	−0.874165	−	0.485629i	$-0.838591\pi$
$431$	−7.11802	+	12.3288i	−0.0165151	+	0.0286050i	0.857650	+	0.514234i	$0.171924\pi$
$432$	112.915	+	18.5854i	0.261377	+	0.0430217i
$433$			572.228i			1.32154i	0.750588	+	0.660771i	$0.229771\pi$
$433$			572.228i			1.32154i	−0.750588	+	0.660771i	$0.770229\pi$
$434$	−149.239	−	677.670i	−0.343869	−	1.56145i
$435$	−34.9791	+	34.9791i	−0.0804117	+	0.0804117i
$436$	157.946	+	34.0726i	0.362263	+	0.0781481i
$437$	−30.8814	−	115.251i	−0.0706668	−	0.263732i
$438$	80.8655	−	23.8204i	0.184624	−	0.0543845i
$439$	−217.711	−	377.086i	−0.495924	−	0.858966i	0.504065	−	0.863666i	$-0.331837\pi$
$439$	−217.711	−	377.086i	−0.495924	−	0.858966i	−0.999989	+	0.00470013i	$0.998504\pi$
$440$	201.283	−	14.9220i	0.457461	−	0.0339137i
$441$	−266.582	+	341.366i	−0.604494	+	0.774072i
$442$	−156.767	+	164.698i	−0.354676	+	0.372619i
$443$	−115.864	+	432.409i	−0.261543	+	0.976092i	0.702789	+	0.711398i	$0.251938\pi$
$443$	−115.864	+	432.409i	−0.261543	+	0.976092i	−0.964332	+	0.264694i	$0.914729\pi$
$444$	51.5382	+	26.4568i	0.116077	+	0.0595875i
$445$	−26.8108	−	100.059i	−0.0602489	−	0.224852i
$446$	280.951	−	171.583i	0.629935	−	0.384714i
$447$			34.8462i			0.0779558i
$448$	−422.340	+	149.443i	−0.942723	+	0.333578i
$449$	−122.744			−0.273371			−0.136685	−	0.990614i	$-0.543645\pi$
$449$	−122.744			−0.273371			−0.136685	+	0.990614i	$0.543645\pi$
$450$	−151.235	−	247.634i	−0.336078	−	0.550297i
$451$	75.1390	−	20.1334i	0.166605	−	0.0446417i
$452$	242.626	−	472.638i	0.536783	−	1.04566i
$453$	−19.6112	−	5.25481i	−0.0432919	−	0.0116000i
$454$	586.931	+	558.668i	1.29280	+	1.23055i
$455$	−83.8600	−	96.4483i	−0.184308	−	0.211974i
$456$	3.86068	+	52.0766i	0.00846641	+	0.114203i
$457$	559.539	−	323.050i	1.22437	−	0.706893i	0.258527	−	0.966004i	$-0.416763\pi$
$457$	559.539	−	323.050i	1.22437	−	0.706893i	0.965848	+	0.259111i	$0.0834296\pi$
$458$	−224.001	−	760.438i	−0.489085	−	1.66035i
$459$	−126.054	+	33.7759i	−0.274626	+	0.0735859i
$460$	−18.1137	+	83.9679i	−0.0393777	+	0.182539i
$461$	150.310	+	150.310i	0.326053	+	0.326053i	0.851083	−	0.525031i	$-0.175946\pi$
$461$	150.310	+	150.310i	0.326053	+	0.326053i	−0.525031	+	0.851083i	$0.675946\pi$
$462$	−46.0689	−	14.5965i	−0.0997163	−	0.0315942i
$463$	342.009			0.738679			0.369340	−	0.929294i	$-0.379584\pi$
$463$	342.009			0.738679			0.369340	+	0.929294i	$0.379584\pi$
$464$	−664.762	−	109.417i	−1.43268	−	0.235813i
$465$	50.4287	+	29.1150i	0.108449	+	0.0626129i
$466$	−732.503	−	399.154i	−1.57190	−	0.856553i
$467$	176.312	−	658.007i	0.377543	−	1.40901i	−0.472052	−	0.881571i	$-0.656486\pi$
$467$	176.312	−	658.007i	0.377543	−	1.40901i	0.849594	−	0.527437i	$-0.176847\pi$
$468$	−147.907	+	163.270i	−0.316040	+	0.348868i
$469$	7.85923	+	16.1093i	0.0167574	+	0.0343481i
$470$	−321.797	−	306.301i	−0.684676	−	0.651705i
$471$	−78.0829	+	45.0812i	−0.165781	+	0.0957138i
$472$	20.5581	+	58.9028i	0.0435552	+	0.124794i
$473$	−6.75395	−	3.89940i	−0.0142790	−	0.00824397i
$474$	−18.2186	+	75.3830i	−0.0384358	+	0.159036i
$475$	188.958	−	188.958i	0.397805	−	0.397805i
$476$	368.541	−	353.826i	0.774247	−	0.743331i
$477$	−304.406	+	304.406i	−0.638169	+	0.638169i
$478$	−284.633	−	466.060i	−0.595466	−	0.975021i
$479$	511.061	+	295.061i	1.06693	+	0.615994i	0.927342	−	0.374215i	$-0.122088\pi$
$479$	511.061	+	295.061i	1.06693	+	0.615994i	0.139592	+	0.990209i	$0.455421\pi$
$480$	14.6492	−	34.6228i	0.0305191	−	0.0721308i
$481$	−194.929	+	112.542i	−0.405258	+	0.233976i
$482$	11.5445	+	467.928i	0.0239511	+	0.970805i
$483$	11.4991	−	17.0522i	0.0238077	−	0.0353048i
$484$	−9.24539	−	187.256i	−0.0191020	−	0.386893i
$485$	99.9873	−	373.158i	0.206159	−	0.769397i
$486$	−182.477	+	53.7517i	−0.375466	+	0.110600i
$487$	−127.746	−	73.7540i	−0.262311	−	0.151446i	0.363077	−	0.931759i	$-0.381726\pi$
$487$	−127.746	−	73.7540i	−0.262311	−	0.151446i	−0.625388	+	0.780314i	$0.715059\pi$
$488$	−87.4461	+	460.147i	−0.179193	+	0.942924i
$489$	60.8022			0.124340
$490$	178.477	+	224.972i	0.364240	+	0.459127i
$491$	−40.8114	−	40.8114i	−0.0831190	−	0.0831190i	0.664325	−	0.747444i	$-0.268719\pi$
$491$	−40.8114	−	40.8114i	−0.0831190	−	0.0831190i	−0.747444	+	0.664325i	$0.768719\pi$
$492$	3.05538	−	14.1635i	0.00621012	−	0.0287875i
$493$	742.112	−	198.848i	1.50530	−	0.403343i
$494$	−178.156	−	97.0800i	−0.360639	−	0.196518i
$495$	−193.132	+	111.505i	−0.390165	+	0.225262i
$496$	78.1189	+	789.182i	0.157498	+	1.59109i
$497$	−132.249	−	679.957i	−0.266094	−	1.36812i
$498$	−2.60898	−	105.749i	−0.00523892	−	0.212348i
$499$	787.318	+	210.961i	1.57779	+	0.422768i	0.938241	−	0.345981i	$-0.112454\pi$
$499$	787.318	+	210.961i	1.57779	+	0.422768i	0.639550	+	0.768749i	$0.279121\pi$
$500$	−462.109	+	148.603i	−0.924218	+	0.297207i
$501$	18.6582	−	4.99945i	0.0372419	−	0.00997894i
$502$	−842.062	−	203.510i	−1.67741	−	0.405398i
$503$	574.999			1.14314			0.571570	−	0.820553i	$-0.306335\pi$
$503$	574.999			1.14314			0.571570	+	0.820553i	$0.306335\pi$
$504$	348.510	−	351.518i	0.691487	−	0.697456i
$505$			377.264i			0.747058i
$506$	−122.663	−	29.6452i	−0.242417	−	0.0585874i
$507$	−13.5079	−	50.4124i	−0.0266429	−	0.0994326i
$508$	71.4945	−	139.272i	0.140737	−	0.274157i
$509$	−250.625	+	935.346i	−0.492387	+	1.83761i	0.0518102	+	0.998657i	$0.483501\pi$
$509$	−250.625	+	935.346i	−0.492387	+	1.83761i	−0.544197	+	0.838957i	$0.683166\pi$
$510$	1.05740	+	42.8593i	0.00207334	+	0.0840379i
$511$	239.520	−	695.869i	0.468729	−	1.36178i
$512$	499.435	−	112.732i	0.975459	−	0.220179i
$513$	−58.2223	−	100.844i	−0.113494	−	0.196577i
$514$	−263.728	−	143.710i	−0.513089	−	0.279591i
$515$	29.5674	+	110.347i	0.0574124	+	0.214266i
$516$	−1.22066	+	0.787463i	−0.00236562	+	0.00152609i
$517$	461.510	−	461.510i	0.892668	−	0.892668i
$518$	448.926	−	232.897i	0.866653	−	0.449607i
$519$			34.9352i			0.0673126i
$520$	82.1851	+	120.751i	0.158048	+	0.232214i
$521$	−115.973	+	200.871i	−0.222597	+	0.385549i	−0.955596	−	0.294681i	$-0.904787\pi$
$521$	−115.973	+	200.871i	−0.222597	+	0.385549i	0.732999	+	0.680230i	$0.238120\pi$
$522$	714.049	−	210.336i	1.36791	−	0.402942i
$523$	652.661	+	174.880i	1.24792	+	0.334379i	0.821532	−	0.570162i	$-0.193120\pi$
$523$	652.661	+	174.880i	1.24792	+	0.334379i	0.426387	+	0.904541i	$0.359786\pi$
$524$	403.913	+	365.905i	0.770826	+	0.698291i
$525$	45.9512	+	3.20808i	0.0875262	+	0.00611063i
$526$	−0.785233	−	31.8276i	−0.00149284	−	0.0605088i
$527$	−452.188	−	783.213i	−0.858042	−	1.48617i
$528$	50.3180	+	22.7690i	0.0952992	+	0.0431231i
$529$	−237.646	+	411.616i	−0.449237	+	0.778101i
$530$	148.767	+	243.593i	0.280693	+	0.459609i
$531$	−48.7424	−	48.7424i	−0.0917936	−	0.0917936i
$532$	390.071	+	235.929i	0.733216	+	0.443476i
$533$	39.8068	+	39.8068i	0.0746845	+	0.0746845i
$534$	6.65891	−	27.5526i	0.0124699	−	0.0515966i
$535$	85.1756	−	147.528i	0.159207	−	0.275754i
$536$	−6.75020	−	19.3406i	−0.0125937	−	0.0360833i
$537$	−61.4117	−	106.368i	−0.114361	−	0.198078i
$538$	−224.745	−	213.923i	−0.417742	−	0.397626i
$539$	−336.873	+	253.969i	−0.624996	+	0.471186i
$540$	4.13399	+	83.7300i	0.00765554	+	0.155055i
$541$	−1028.42	−	275.564i	−1.90096	−	0.509361i	−0.996580	−	0.0826390i	$-0.973665\pi$
$541$	−1028.42	−	275.564i	−1.90096	−	0.509361i	−0.904383	−	0.426722i	$-0.859668\pi$
$542$	625.369	+	340.774i	1.15382	+	0.628735i
$543$	−58.4789	+	101.288i	−0.107696	+	0.186535i
$544$	−465.901	+	351.929i	−0.856436	+	0.646929i
$545$			118.370i			0.217192i
$546$	−7.52165	−	34.1545i	−0.0137759	−	0.0625541i
$547$	510.527	−	510.527i	0.933322	−	0.933322i	−0.0645896	−	0.997912i	$-0.520574\pi$
$547$	510.527	−	510.527i	0.933322	−	0.933322i	0.997912	+	0.0645896i	$0.0205738\pi$
$548$	14.3453	−	9.25432i	0.0261775	−	0.0168875i
$549$	−133.944	−	499.885i	−0.243978	−	0.910538i
$550$	−79.8613	−	271.113i	−0.145202	−	0.492933i
$551$	342.771	+	593.697i	0.622089	+	1.07749i
$552$	−15.3465	+	17.8041i	−0.0278016	+	0.0322538i
$553$	444.230	+	510.913i	0.803309	+	0.923893i
$554$	−238.236	−	226.764i	−0.430029	−	0.409321i
$555$	−10.9842	+	40.9938i	−0.0197914	+	0.0738626i
$556$	45.1106	+	140.280i	0.0811342	+	0.252302i
$557$	222.747	+	831.304i	0.399905	+	1.49247i	0.813262	+	0.581897i	$0.197689\pi$
$557$	222.747	+	831.304i	0.399905	+	1.49247i	−0.413357	+	0.910569i	$0.635644\pi$
$558$	−456.700	−	747.805i	−0.818459	−	1.34015i
$559$		−	5.64389i		−	0.0100964i
$560$	−172.260	−	279.353i	−0.307606	−	0.498845i
$561$	−62.9837			−0.112270
$562$	−379.374	+	231.692i	−0.675043	+	0.412263i
$563$	331.233	−	88.7537i	0.588336	−	0.157644i	0.0476437	−	0.998864i	$-0.484829\pi$
$563$	331.233	−	88.7537i	0.588336	−	0.157644i	0.540693	+	0.841220i	$0.318162\pi$
$564$	−37.2166	−	115.732i	−0.0659869	−	0.205198i
$565$	375.939	+	100.733i	0.665379	+	0.178288i
$566$	−561.459	+	589.864i	−0.991977	+	1.04216i
$567$	−174.709	+	507.575i	−0.308129	+	0.895194i
$568$	58.5285	+	789.489i	0.103043	+	1.38995i
$569$	−157.351	+	90.8468i	−0.276540	+	0.159660i	−0.631856	−	0.775086i	$-0.717707\pi$
$569$	−157.351	+	90.8468i	−0.276540	+	0.159660i	0.355316	+	0.934746i	$0.384373\pi$
$570$	−36.6959	+	10.8094i	−0.0643787	+	0.0189639i
$571$	839.309	−	224.892i	1.46989	−	0.393857i	0.566999	−	0.823719i	$-0.308104\pi$
$571$	839.309	−	224.892i	1.46989	−	0.393857i	0.902895	+	0.429862i	$0.141438\pi$
$572$	−180.319	+	116.326i	−0.315243	+	0.203367i
$573$	17.0951	+	17.0951i	0.0298344	+	0.0298344i
$574$	−85.3244	−	93.3778i	−0.148649	−	0.162679i
$575$	120.285			0.209192
$576$	−442.856	+	352.008i	−0.768848	+	0.611124i
$577$	869.810	+	502.185i	1.50747	+	0.870338i	0.999962	+	0.00869059i	$0.00276634\pi$
$577$	869.810	+	502.185i	1.50747	+	0.870338i	0.507507	+	0.861647i	$0.330567\pi$
$578$	42.0378	−	77.1453i	0.0727297	−	0.133469i
$579$	−6.76479	+	25.2465i	−0.0116836	+	0.0436037i
$580$	−24.3380	−	492.941i	−0.0419620	−	0.849899i
$581$	−765.640	−	516.307i	−1.31780	−	0.888652i
$582$	72.8833	−	76.5706i	0.125229	−	0.131565i
$583$	−363.143	+	209.661i	−0.622886	+	0.359624i
$584$	−365.534	+	757.487i	−0.625914	+	1.29707i
$585$	−139.767	−	80.6946i	−0.238918	−	0.137940i
$586$	−343.332	−	82.9766i	−0.585891	−	0.141598i
$587$	−348.480	+	348.480i	−0.593663	+	0.593663i	−0.938619	−	0.344956i	$-0.887894\pi$
$587$	−348.480	+	348.480i	−0.593663	+	0.593663i	0.344956	+	0.938619i	$0.387894\pi$
$588$	13.4283	+	77.4247i	0.0228373	+	0.131675i
$589$	570.615	−	570.615i	0.968785	−	0.968785i
$590$	−39.0047	+	23.8210i	−0.0661097	+	0.0403746i
$591$	−50.4154	−	29.1073i	−0.0853052	−	0.0492510i
$592$	−540.846	+	203.863i	−0.913590	+	0.344363i
$593$	−314.345	+	181.487i	−0.530092	+	0.306049i	−0.741054	−	0.671445i	$-0.765674\pi$
$593$	−314.345	+	181.487i	−0.530092	+	0.306049i	0.210962	+	0.977494i	$0.432340\pi$
$594$	−123.120	+	3.03754i	−0.207272	+	0.00511371i
$595$	310.308	+	209.255i	0.521526	+	0.351689i
$596$	−257.657	−	233.412i	−0.432311	−	0.391631i
$597$	3.55971	−	13.2850i	0.00596267	−	0.0222530i
$598$	−25.8053	−	87.6038i	−0.0431526	−	0.146495i
$599$	−256.643	−	148.173i	−0.428453	−	0.247367i	0.270234	−	0.962795i	$-0.412899\pi$
$599$	−256.643	−	148.173i	−0.428453	−	0.247367i	−0.698687	+	0.715427i	$0.746232\pi$
$600$	−51.7179	−	9.82845i	−0.0861965	−	0.0163807i
$601$	−1076.94			−1.79191			−0.895953	−	0.444148i	$-0.853506\pi$
$601$	−1076.94			−1.79191			−0.895953	+	0.444148i	$0.853506\pi$
$602$	−0.570911	+	12.6684i	−0.000948358	+	0.0210438i
$603$	16.0045	+	16.0045i	0.0265414	+	0.0265414i
$604$	170.217	−	109.809i	0.281817	−	0.181803i
$605$	132.667	−	35.5479i	0.219284	−	0.0587569i
$606$	−49.3961	+	90.6489i	−0.0815118	+	0.149586i
$607$	−203.596	+	117.546i	−0.335413	+	0.193651i	−0.658242	−	0.752807i	$-0.728700\pi$
$607$	−203.596	+	117.546i	−0.335413	+	0.193651i	0.322829	+	0.946457i	$0.395366\pi$
$608$	−410.921	−	320.280i	−0.675857	−	0.526777i
$609$	−38.4600	+	111.736i	−0.0631527	+	0.183475i
$610$	−343.022	+	8.46285i	−0.562331	+	0.0138735i
$611$	456.237	+	122.248i	0.746706	+	0.200079i
$612$	294.624	−	573.931i	0.481412	−	0.937795i
$613$	483.385	−	129.523i	0.788556	−	0.211293i	0.158003	−	0.987439i	$-0.449495\pi$
$613$	483.385	−	129.523i	0.788556	−	0.211293i	0.630554	+	0.776146i	$0.282828\pi$
$614$	−144.340	+	597.237i	−0.235082	+	0.972698i
$615$	10.6145			0.0172594
$616$	416.514	−	242.867i	0.676159	−	0.394265i
$617$			344.961i			0.559093i	0.960132	+	0.279547i	$0.0901842\pi$
$617$			344.961i			0.559093i	−0.960132	+	0.279547i	$0.909816\pi$
$618$	−7.34356	+	30.3854i	−0.0118828	+	0.0491674i
$619$	34.3876	+	128.336i	0.0555535	+	0.207329i	0.988124	−	0.153660i	$-0.0491060\pi$
$619$	34.3876	+	128.336i	0.0555535	+	0.207329i	−0.932570	+	0.360989i	$0.882439\pi$
$620$	−553.069	+	177.854i	−0.892046	+	0.286861i
$621$	13.5659	−	50.6287i	0.0218453	−	0.0815277i
$622$	−8.61444	+	0.212531i	−0.0138496	+	0.000341689i
$623$	−162.366	−	186.739i	−0.260620	−	0.299742i
$624$	3.93719	+	39.7747i	0.00630959	+	0.0637415i
$625$	27.3642	+	47.3962i	0.0437827	+	0.0758339i
$626$	−180.902	+	331.981i	−0.288981	+	0.530322i
$627$	−14.5456	−	54.2851i	−0.0231988	−	0.0865791i
$628$	189.690	−	879.324i	0.302054	−	1.40020i
$629$	466.081	−	466.081i	0.740987	−	0.740987i
$630$	305.561	+	195.267i	0.485018	+	0.309947i
$631$		−	470.715i		−	0.745982i	−0.927835	−	0.372991i	$-0.878332\pi$
$631$		−	470.715i		−	0.745982i	0.927835	−	0.372991i	$-0.121668\pi$
$632$	−435.357	−	639.652i	−0.688857	−	1.01211i
$633$	−71.8606	+	124.466i	−0.113524	+	0.196629i
$634$	115.960	+	393.660i	0.182901	+	0.620914i
$635$	110.778	+	29.6828i	0.174453	+	0.0467446i
$636$	3.85152	+	78.0088i	0.00605585	+	0.122655i
$637$	−281.066	−	119.232i	−0.441234	−	0.187177i
$638$	724.840	−	17.8829i	1.13611	−	0.0280296i
$639$	−437.353	−	757.518i	−0.684434	−	1.18547i
$640$	157.880	+	340.233i	0.246688	+	0.531614i
$641$	−332.772	+	576.377i	−0.519144	+	0.899184i	0.480608	+	0.876935i	$0.340416\pi$
$641$	−332.772	+	576.377i	−0.519144	+	0.899184i	−0.999752	+	0.0222489i	$0.992917\pi$
$642$	39.7822	−	24.2958i	0.0619661	−	0.0378440i
$643$	−56.7122	−	56.7122i	−0.0881993	−	0.0881993i	0.661631	−	0.749830i	$-0.269865\pi$
$643$	−56.7122	−	56.7122i	−0.0881993	−	0.0881993i	−0.749830	+	0.661631i	$0.769865\pi$
$644$	49.0614	+	199.247i	0.0761822	+	0.309390i
$645$	−0.752473	−	0.752473i	−0.00116663	−	0.00116663i
$646$	577.513	+	139.573i	0.893983	+	0.216058i
$647$	−333.619	+	577.844i	−0.515639	+	0.893113i	0.484196	+	0.874960i	$0.339112\pi$
$647$	−333.619	+	577.844i	−0.515639	+	0.893113i	−0.999835	+	0.0181538i	$0.994221\pi$
$648$	266.625	−	552.520i	0.411458	−	0.852654i
$649$	−33.5714	−	58.1474i	−0.0517279	−	0.0895954i
$650$	141.018	−	148.152i	0.216951	−	0.227927i
$651$	138.764	+	9.68778i	0.213155	+	0.0148814i
$652$	−407.274	+	449.579i	−0.624653	+	0.689538i
$653$	559.385	+	149.887i	0.856639	+	0.229536i	0.660301	−	0.751001i	$-0.270429\pi$
$653$	559.385	+	149.887i	0.856639	+	0.229536i	0.196338	+	0.980536i	$0.437095\pi$
$654$	−15.4984	+	28.4418i	−0.0236979	+	0.0434890i
$655$	−199.630	+	345.768i	−0.304778	+	0.527891i
$656$	84.2605	+	117.464i	0.128446	+	0.179060i
$657$		−	929.307i		−	1.41447i
$658$	−1011.71	−	320.552i	−1.53756	−	0.487161i
$659$	−302.209	+	302.209i	−0.458588	+	0.458588i	−0.898192	−	0.439604i	$-0.855119\pi$
$659$	−302.209	+	302.209i	−0.458588	+	0.458588i	0.439604	+	0.898192i	$0.355119\pi$
$660$	−8.53188	+	39.5503i	−0.0129271	+	0.0599246i
$661$	−46.4410	−	173.320i	−0.0702587	−	0.262209i	0.921858	−	0.387529i	$-0.126671\pi$
$661$	−46.4410	−	173.320i	−0.0702587	−	0.262209i	−0.992116	+	0.125319i	$0.960004\pi$
$662$	−481.417	+	141.810i	−0.727216	+	0.214215i
$663$	−22.7903	−	39.4739i	−0.0343745	−	0.0595383i
$664$	799.398	+	689.053i	1.20391	+	1.03773i
$665$	−108.692	+	315.778i	−0.163446	+	0.474854i
$666$	440.303	−	462.578i	0.661115	−	0.694561i
$667$	−79.8663	+	298.065i	−0.119740	+	0.446874i
$668$	−88.0124	+	171.449i	−0.131755	+	0.256660i
$669$	17.0800	+	63.7435i	0.0255307	+	0.0952817i
$670$	12.8071	−	7.82158i	0.0191151	−	0.0116740i
$671$		−	504.086i		−	0.751246i
$672$	−4.81404	−	89.6773i	−0.00716375	−	0.133448i
$673$	733.774			1.09030			0.545152	−	0.838337i	$-0.316472\pi$
$673$	733.774			1.09030			0.545152	+	0.838337i	$0.316472\pi$
$674$	65.4736	+	107.207i	0.0971418	+	0.159061i
$675$	113.390	−	30.3828i	0.167986	−	0.0450116i
$676$	463.236	+	237.800i	0.685261	+	0.351775i
$677$	108.639	+	29.1098i	0.160471	+	0.0429982i	0.338160	−	0.941089i	$-0.390195\pi$
$677$	108.639	+	29.1098i	0.160471	+	0.0429982i	−0.177689	+	0.984087i	$0.556862\pi$
$678$	77.1413	+	73.4266i	0.113778	+	0.108299i
$679$	−176.190	−	905.879i	−0.259484	−	1.33414i
$680$	−323.990	−	279.268i	−0.476456	−	0.410688i
$681$	−140.673	+	81.2174i	−0.206568	+	0.119262i
$682$	−241.165	−	818.709i	−0.353615	−	1.20045i
$683$	−499.584	+	133.863i	−0.731456	+	0.195993i	−0.605278	−	0.796015i	$-0.706938\pi$
$683$	−499.584	+	133.863i	−0.731456	+	0.195993i	−0.126178	+	0.992008i	$0.540271\pi$
$684$	562.707	+	121.389i	0.822671	+	0.177469i
$685$	8.84312	+	8.84312i	0.0129097	+	0.0129097i
$686$	618.825	+	296.061i	0.902077	+	0.431575i
$687$	158.914			0.231316
$688$	2.35380	−	14.3004i	0.00342122	−	0.0207855i
$689$	−262.802	−	151.729i	−0.381425	−	0.220216i
$690$	−15.1203	−	8.23931i	−0.0219135	−	0.0119410i
$691$	−8.06759	+	30.1086i	−0.0116752	+	0.0435726i	−0.971518	−	0.236967i	$-0.923847\pi$
$691$	−8.06759	+	30.1086i	−0.0116752	+	0.0435726i	0.959842	+	0.280539i	$0.0905134\pi$
$692$	−258.315	−	234.008i	−0.373288	−	0.338162i
$693$	−297.850	+	441.687i	−0.429798	+	0.637355i
$694$	785.645	+	747.813i	1.13205	+	1.07754i
$695$	−93.4862	+	53.9743i	−0.134512	+	0.0776608i
$696$	58.6941	−	121.630i	0.0843306	−	0.174756i
$697$	−142.769	−	82.4276i	−0.204833	−	0.118261i
$698$	−232.006	+	959.972i	−0.332387	+	1.37532i
$699$	118.245	−	118.245i	0.169163	−	0.169163i
$700$	−331.518	+	318.280i	−0.473597	+	0.454686i
$701$	−108.069	+	108.069i	−0.154165	+	0.154165i	−0.779975	−	0.625811i	$-0.784768\pi$
$701$	−108.069	+	108.069i	−0.154165	+	0.154165i	0.625811	+	0.779975i	$0.284768\pi$
$702$	−46.4539	−	76.0640i	−0.0661736	−	0.108353i
$703$	509.349	+	294.073i	0.724536	+	0.418311i
$704$	−505.404	+	219.543i	−0.717903	+	0.311851i
$705$	77.1268	−	44.5292i	0.109400	−	0.0631619i
$706$	−23.4846	−	951.893i	−0.0332643	−	1.34829i
$707$	395.159	+	809.966i	0.558923	+	1.14564i
$708$	−12.4910	+	0.616716i	−0.0176426	+	0.000871068i
$709$	35.6955	−	133.218i	0.0503463	−	0.187895i	−0.936173	−	0.351539i	$-0.885658\pi$
$709$	35.6955	−	133.218i	0.0503463	−	0.187895i	0.986519	+	0.163644i	$0.0523250\pi$
$710$	−556.315	+	163.873i	−0.783542	+	0.230806i
$711$	740.385	+	427.462i	1.04133	+	0.601212i
$712$	159.124	+	233.793i	0.223488	+	0.328361i
$713$	363.238			0.509450
$714$	47.1624	+	90.9092i	0.0660538	+	0.127324i
$715$	−111.157	−	111.157i	−0.155465	−	0.155465i
$716$	1197.86	+	258.404i	1.67298	+	0.360900i
$717$	105.742	−	28.3335i	0.147478	−	0.0395167i
$718$	482.483	+	262.913i	0.671982	+	0.366174i
$719$	−658.837	+	380.380i	−0.916324	+	0.529040i	−0.882460	−	0.470387i	$-0.844114\pi$
$719$	−658.837	+	380.380i	−0.916324	+	0.529040i	−0.0338633	+	0.999426i	$0.510781\pi$
$720$	−320.486	−	262.753i	−0.445120	−	0.364935i
$721$	179.060	+	205.939i	0.248350	+	0.285630i
$722$	−4.73183	−	191.794i	−0.00655378	−	0.265642i
$723$	−90.6325	−	24.2849i	−0.125356	−	0.0335891i
$724$	−357.228	−	1110.87i	−0.493409	−	1.53434i
$725$	−667.560	+	178.872i	−0.920772	+	0.246720i
$726$	36.5315	+	8.82893i	0.0503188	+	0.0121611i
$727$	−1266.35			−1.74189			−0.870943	−	0.491385i	$-0.836491\pi$
$727$	−1266.35			−1.74189			−0.870943	+	0.491385i	$0.836491\pi$
$728$	302.926	+	173.163i	0.416107	+	0.237861i
$729$			652.040i			0.894430i
$730$	−598.907	−	144.744i	−0.820421	−	0.198279i
$731$	4.27764	+	15.9644i	0.00585177	+	0.0218391i
$732$	−83.5292	−	42.8792i	−0.114111	−	0.0585782i
$733$	266.619	−	995.036i	0.363737	−	1.35748i	−0.505389	−	0.862892i	$-0.668651\pi$
$733$	266.619	−	995.036i	0.363737	−	1.35748i	0.869125	−	0.494592i	$-0.164682\pi$
$734$	−20.9820	−	850.458i	−0.0285859	−	1.15866i
$735$	−53.3698	+	21.5766i	−0.0726120	+	0.0293559i
$736$	−28.8497	−	232.732i	−0.0391980	−	0.316211i
$737$	11.0231	+	19.0926i	0.0149567	+	0.0259058i
$738$	−140.254	−	76.4267i	−0.190046	−	0.103559i
$739$	−40.5646	−	151.389i	−0.0548912	−	0.204857i	0.933034	−	0.359788i	$-0.117151\pi$
$739$	−40.5646	−	151.389i	−0.0548912	−	0.204857i	−0.987925	+	0.154931i	$0.950484\pi$
$740$	−229.537	−	355.809i	−0.310185	−	0.480823i
$741$	28.7589	−	28.7589i	0.0388110	−	0.0388110i
$742$	574.542	+	367.157i	0.774315	+	0.494821i
$743$		−	232.439i		−	0.312839i	−0.987691	−	0.156419i	$-0.950005\pi$
$743$		−	232.439i		−	0.312839i	0.987691	−	0.156419i	$-0.0499951\pi$
$744$	−156.178	−	29.6800i	−0.209917	−	0.0398924i
$745$	127.344	−	220.567i	0.170932	−	0.296063i
$746$	1414.30	−	416.608i	1.89585	−	0.558456i
$747$	−1126.37	−	301.809i	−1.50785	−	0.404028i
$748$	421.886	−	465.709i	0.564019	−	0.622606i
$749$	28.3415	−	405.951i	0.0378391	−	0.541991i
$750$	−2.39996	−	97.2770i	−0.00319995	−	0.129703i
$751$	−195.841	−	339.206i	−0.260773	−	0.451672i	0.705674	−	0.708536i	$-0.250644\pi$
$751$	−195.841	−	339.206i	−0.260773	−	0.451672i	−0.966448	+	0.256864i	$0.917311\pi$
$752$	1105.02	+	500.026i	1.46945	+	0.664928i
$753$	86.8301	−	150.394i	0.115312	−	0.199727i
$754$	273.487	+	447.810i	0.362715	+	0.593912i
$755$	104.930	+	104.930i	0.138980	+	0.138980i
$756$	96.5769	+	175.434i	0.127747	+	0.232055i
$757$	61.4264	+	61.4264i	0.0811445	+	0.0811445i	0.746514	−	0.665370i	$-0.231726\pi$
$757$	61.4264	+	61.4264i	0.0811445	+	0.0811445i	−0.665370	+	0.746514i	$0.731726\pi$
$758$	107.050	−	442.940i	0.141227	−	0.584354i
$759$	12.6485	−	21.9079i	0.0166647	−	0.0288642i
$760$	165.875	−	343.739i	0.218257	−	0.452288i
$761$	−441.268	−	764.298i	−0.579852	−	1.00433i	−0.995496	−	0.0948062i	$-0.969777\pi$
$761$	−441.268	−	764.298i	−0.579852	−	1.00433i	0.415643	−	0.909528i	$-0.363556\pi$
$762$	22.7312	+	21.6366i	0.0298310	+	0.0283944i
$763$	123.984	+	254.133i	0.162496	+	0.333071i
$764$	−240.913	+	11.8946i	−0.315331	+	0.0155688i
$765$	456.508	+	122.321i	0.596742	+	0.159897i
$766$	359.171	+	195.718i	0.468891	+	0.255507i
$767$	24.2952	−	42.0806i	0.0316757	−	0.0548638i
$768$	−6.61214	+	102.423i	−0.00860955	+	0.133363i
$769$			151.443i			0.196935i	0.995140	+	0.0984677i	$0.0313941\pi$
$769$			151.443i			0.196935i	−0.995140	+	0.0984677i	$0.968606\pi$
$770$	238.261	+	260.749i	0.309430	+	0.338636i
$771$	42.5725	−	42.5725i	0.0552173	−	0.0552173i
$772$	−141.363	−	219.130i	−0.183113	−	0.283847i
$773$	−172.355	−	643.237i	−0.222969	−	0.832131i	−0.983208	−	0.182488i	$-0.941585\pi$
$773$	−172.355	−	643.237i	−0.222969	−	0.832131i	0.760239	−	0.649643i	$-0.225082\pi$
$774$	4.52476	+	15.3607i	0.00584595	+	0.0198458i
$775$	406.762	+	704.532i	0.524854	+	0.909073i
$776$	77.9752	+	1051.80i	0.100483	+	1.35542i
$777$	19.3556	+	99.5167i	0.0249107	+	0.128078i
$778$	245.603	+	233.776i	0.315685	+	0.300483i
$779$	38.0721	−	142.087i	0.0488731	−	0.182397i
$780$	−27.8746	+	8.96382i	−0.0357367	+	0.0114921i
$781$	−220.514	−	822.970i	−0.282348	−	1.05374i
$782$	139.390	+	228.239i	0.178248	+	0.291866i
$783$			301.153i			0.384614i
$784$	−662.436	−	419.327i	−0.844944	−	0.534856i
$785$	658.991			0.839479
$786$	−93.2392	+	56.9431i	−0.118625	+	0.0724467i
$787$	−767.124	+	205.550i	−0.974744	+	0.261182i	−0.710830	−	0.703364i	$-0.751680\pi$
$787$	−767.124	+	205.550i	−0.974744	+	0.261182i	−0.263914	+	0.964546i	$0.585014\pi$
$788$	552.923	−	177.807i	0.701679	−	0.225643i
$789$	6.16466	+	1.65182i	0.00781326	+	0.00209356i
$790$	390.803	−	410.574i	0.494688	−	0.519715i
$791$	912.631	−	177.503i	1.15377	−	0.224403i
$792$	397.505	−	461.162i	0.501900	−	0.582275i
$793$	315.927	−	182.400i	0.398394	−	0.230013i
$794$	−74.3105	+	21.8895i	−0.0935901	+	0.0275686i
$795$	−55.2674	+	14.8089i	−0.0695188	+	0.0186275i
$796$	74.3871	+	115.309i	0.0934511	+	0.144860i
$797$	417.744	+	417.744i	0.524145	+	0.524145i	0.918821	−	0.394675i	$-0.129143\pi$
$797$	417.744	+	417.744i	0.524145	+	0.524145i	−0.394675	+	0.918821i	$0.629143\pi$
$798$	−67.4620	+	61.6437i	−0.0845388	+	0.0772477i
$799$	−1383.17			−1.73113
$800$	419.097	−	316.574i	0.523871	−	0.395718i
$801$	−270.612	−	156.238i	−0.337842	−	0.195053i
$802$	−575.745	+	1056.57i	−0.717886	+	1.31742i
$803$	234.279	−	874.341i	0.291755	−	1.08884i
$804$	4.10139	−	0.202498i	0.00510123	−	0.000251863i
$805$	−135.103	+	65.9127i	−0.167830	+	0.0818792i
$806$	425.847	−	447.391i	0.528346	−	0.555075i
$807$	53.8658	−	31.0994i	0.0667482	−	0.0385371i
$808$	−339.397	−	972.438i	−0.420046	−	1.20351i
$809$	−392.626	−	226.683i	−0.485323	−	0.280201i	0.237309	−	0.971434i	$-0.423735\pi$
$809$	−392.626	−	226.683i	−0.485323	−	0.280201i	−0.722632	+	0.691233i	$0.757068\pi$
$810$	436.850	+	105.578i	0.539321	+	0.130343i
$811$	−246.101	+	246.101i	−0.303453	+	0.303453i	−0.842363	−	0.538910i	$-0.818836\pi$
$811$	−246.101	+	246.101i	−0.303453	+	0.303453i	0.538910	+	0.842363i	$0.318836\pi$
$812$	−568.575	−	1032.83i	−0.700215	−	1.27195i
$813$	−100.951	+	100.951i	−0.124171	+	0.124171i
$814$	530.876	−	324.217i	0.652182	−	0.398301i
$815$	−384.861	−	222.200i	−0.472222	−	0.272638i
$816$	−41.2830	−	109.523i	−0.0505919	−	0.134220i
$817$	−12.7717	+	7.37372i	−0.0156324	+	0.00902537i
$818$	1213.62	−	29.9418i	1.48364	−	0.0366036i
$819$	−384.595	−	26.8505i	−0.469591	−	0.0327844i
$820$	−71.0996	+	78.4851i	−0.0867069	+	0.0957135i
$821$	−297.927	+	1111.88i	−0.362884	+	1.35430i	0.507384	+	0.861720i	$0.330613\pi$
$821$	−297.927	+	1111.88i	−0.362884	+	1.35430i	−0.870267	+	0.492580i	$0.836054\pi$
$822$	0.966970	+	3.28267i	0.00117636	+	0.00399352i
$823$	−60.0703	−	34.6816i	−0.0729895	−	0.0421405i	0.463061	−	0.886326i	$-0.346751\pi$
$823$	−60.0703	−	34.6816i	−0.0729895	−	0.0421405i	−0.536051	+	0.844186i	$0.680084\pi$
$824$	−175.484	−	257.831i	−0.212966	−	0.312902i
$825$	56.6564			0.0686744
$826$	−58.7902	+	91.9972i	−0.0711745	+	0.111377i
$827$	−594.269	−	594.269i	−0.718584	−	0.718584i	0.249731	−	0.968315i	$-0.419658\pi$
$827$	−594.269	−	594.269i	−0.718584	−	0.718584i	−0.968315	+	0.249731i	$0.919658\pi$
$828$	140.466	+	217.738i	0.169645	+	0.262969i
$829$	−258.095	+	69.1565i	−0.311334	+	0.0834216i	−0.411103	−	0.911589i	$-0.634856\pi$
$829$	−258.095	+	69.1565i	−0.311334	+	0.0834216i	0.0997692	+	0.995011i	$0.468190\pi$
$830$	−369.943	+	678.897i	−0.445714	+	0.817949i
$831$	57.0992	−	32.9662i	0.0687115	−	0.0396706i
$832$	−320.472	−	237.313i	−0.385183	−	0.285231i
$833$	885.396	+	124.233i	1.06290	+	0.149140i
$834$	−29.5298	+	0.728543i	−0.0354074	+	0.000873552i
$835$	−136.372	−	36.5406i	−0.163319	−	0.0437613i
$836$	498.822	+	256.068i	0.596677	+	0.306301i
$837$	342.416	−	91.7501i	0.409099	−	0.109618i
$838$	−117.495	+	486.158i	−0.140208	+	0.580141i
$839$	−390.110			−0.464970			−0.232485	−	0.972600i	$-0.574686\pi$
$839$	−390.110			−0.464970			−0.232485	+	0.972600i	$0.574686\pi$
$840$	63.4746	−	17.3007i	0.0755650	−	0.0205960i
$841$		−	931.969i		−	1.10817i
$842$	−324.339	+	1342.02i	−0.385201	+	1.59385i
$843$	−23.0635	−	86.0742i	−0.0273589	−	0.102105i
$844$	−438.972	−	1365.06i	−0.520109	−	1.61737i
$845$	−98.7287	+	368.461i	−0.116839	+	0.436048i
$846$	−1339.73	+	33.0529i	−1.58360	+	0.0390697i
$847$	247.594	−	215.279i	0.292319	−	0.254166i
$848$	−602.606	−	494.051i	−0.710620	−	0.582607i
$849$	−81.6232	−	141.376i	−0.0961404	−	0.166520i
$850$	−286.597	+	525.947i	−0.337173	+	0.618761i
$851$	68.5195	+	255.718i	0.0805165	+	0.300492i
$852$	−155.127	−	33.4645i	−0.182074	−	0.0392775i
$853$	−119.575	+	119.575i	−0.140182	+	0.140182i	−0.773715	−	0.633534i	$-0.781604\pi$
$853$	−119.575	+	119.575i	−0.140182	+	0.140182i	0.633534	+	0.773715i	$0.281604\pi$
$854$	−727.586	+	377.461i	−0.851974	+	0.441992i
$855$			421.709i			0.493227i
$856$	−86.8284	+	456.896i	−0.101435	+	0.533758i
$857$	−304.160	+	526.820i	−0.354912	+	0.614726i	−0.987103	−	0.160087i	$-0.948823\pi$
$857$	−304.160	+	526.820i	−0.354912	+	0.614726i	0.632191	+	0.774813i	$0.282156\pi$
$858$	−12.1547	−	41.2629i	−0.0141663	−	0.0480919i
$859$	1076.07	+	288.332i	1.25270	+	0.335660i	0.823379	−	0.567492i	$-0.192086\pi$
$859$	1076.07	+	288.332i	1.25270	+	0.335660i	0.429322	+	0.903152i	$0.358753\pi$
$860$	10.6042	−	0.523561i	0.0123305	−	0.000608791i
$861$	22.7888	−	11.1180i	0.0264678	−	0.0129129i
$862$	28.4634	−	0.702234i	0.0330202	−	0.000814656i
$863$	648.491	+	1123.22i	0.751439	+	1.30153i	0.947126	+	0.320863i	$0.103973\pi$
$863$	648.491	+	1123.22i	0.751439	+	1.30153i	−0.195687	+	0.980666i	$0.562694\pi$
$864$	−85.9816	−	212.104i	−0.0995157	−	0.245490i
$865$	127.670	−	221.130i	0.147595	−	0.255642i
$866$	976.713	−	596.499i	1.12784	−	0.688798i
$867$	12.4533	+	12.4533i	0.0143636	+	0.0143636i
$868$	−1001.12	+	961.144i	−1.15336	+	1.10731i
$869$	588.830	+	588.830i	0.677595	+	0.677595i
$870$	96.1671	+	23.2417i	0.110537	+	0.0267146i
$871$	−7.97730	+	13.8171i	−0.00915878	+	0.0158635i
$872$	−106.489	−	305.110i	−0.122120	−	0.349897i
$873$	−582.668	−	1009.21i	−0.667432	−	1.15603i
$874$	−164.526	+	172.849i	−0.188245	+	0.197768i
$875$	−704.300	−	474.943i	−0.804915	−	0.542792i
$876$	−124.954	−	113.195i	−0.142641	−	0.129218i
$877$	−369.917	−	99.1189i	−0.421798	−	0.113020i	0.0416755	−	0.999131i	$-0.486730\pi$
$877$	−369.917	−	99.1189i	−0.421798	−	0.113020i	−0.463474	+	0.886111i	$0.653397\pi$
$878$	−416.688	+	764.682i	−0.474588	+	0.870936i
$879$	35.4031	−	61.3199i	0.0402765	−	0.0697610i
$880$	−235.290	−	328.007i	−0.267375	−	0.372735i
$881$		−	219.960i		−	0.249670i	−0.992177	−	0.124835i	$-0.960160\pi$
$881$		−	219.960i		−	0.249670i	0.992177	−	0.124835i	$-0.0398402\pi$
$882$	860.552	+	99.1730i	0.975683	+	0.112441i
$883$	62.7491	−	62.7491i	0.0710635	−	0.0710635i	−0.670682	−	0.741745i	$-0.733998\pi$
$883$	62.7491	−	62.7491i	0.0710635	−	0.0710635i	0.741745	+	0.670682i	$0.233998\pi$
$884$	444.532	+	95.8955i	0.502864	+	0.108479i
$885$	−2.37124	−	8.84957i	−0.00267936	−	0.00999952i
$886$	858.839	−	252.986i	0.969344	−	0.285538i
$887$	93.0792	+	161.218i	0.104937	+	0.181756i	0.913712	−	0.406361i	$-0.133203\pi$
$887$	93.0792	+	161.218i	0.104937	+	0.181756i	−0.808775	+	0.588118i	$0.799869\pi$
$888$	−8.56607	−	115.547i	−0.00964648	−	0.130121i
$889$	268.925	−	52.3047i	0.302502	−	0.0588354i
$890$	−142.839	+	150.065i	−0.160493	+	0.168613i
$891$	−170.886	+	637.754i	−0.191791	+	0.715773i
$892$	−585.735	−	300.684i	−0.656653	−	0.337089i
$893$	−319.434	−	1192.14i	−0.357709	−	1.33499i
$894$	59.4776	−	36.3242i	0.0665298	−	0.0406311i
$895$			897.708i			1.00303i
$896$	695.331	+	565.093i	0.776039	+	0.630685i
$897$	18.3072			0.0204093
$898$	127.950	+	209.506i	0.142483	+	0.233303i
$899$	−2015.90	+	540.158i	−2.24238	+	0.600844i
$900$	−265.026	+	516.274i	−0.294474	+	0.573638i
$901$	858.364	+	229.998i	0.952679	+	0.255270i
$902$	−112.691	−	107.264i	−0.124934	−	0.118918i
$903$	−2.40368	−	0.827356i	−0.00266189	−	0.000916230i
$904$	−1059.64	+	78.5564i	−1.17217	+	0.0868986i
$905$	740.311	−	427.419i	0.818023	−	0.472286i
$906$	11.4738	+	38.9513i	0.0126642	+	0.0429926i
$907$	790.750	−	211.881i	0.871830	−	0.233606i	0.204951	−	0.978772i	$-0.434296\pi$
$907$	790.750	−	211.881i	0.871830	−	0.233606i	0.666879	+	0.745166i	$0.267630\pi$
$908$	341.742	−	1584.17i	0.376367	−	1.74468i
$909$	804.699	+	804.699i	0.885257	+	0.885257i
$910$	−77.2067	+	243.676i	−0.0848425	+	0.267776i
$911$	−22.3401			−0.0245226			−0.0122613	−	0.999925i	$-0.503903\pi$
$911$	−22.3401			−0.0245226			−0.0122613	+	0.999925i	$0.503903\pi$
$912$	84.8630	−	60.8751i	0.0930516	−	0.0667490i
$913$	−983.658	−	567.915i	−1.07739	−	0.622032i
$914$	−1134.67	−	618.303i	−1.24144	−	0.676480i
$915$	17.8024	−	66.4396i	0.0194562	−	0.0726116i
$916$	−1064.46	+	1175.03i	−1.16207	+	1.28278i
$917$	−66.4251	+	951.445i	−0.0724374	+	1.03756i
$918$	189.051	+	179.947i	0.205938	+	0.196021i
$919$	−480.864	+	277.627i	−0.523247	+	0.302097i	−0.738262	−	0.674514i	$-0.764353\pi$
$919$	−480.864	+	277.627i	−0.523247	+	0.302097i	0.215015	+	0.976611i	$0.431020\pi$
$920$	162.203	−	56.6117i	0.176308	−	0.0615345i
$921$	−106.668	−	61.5847i	−0.115817	−	0.0668672i
$922$	99.8729	−	413.244i	0.108322	−	0.448204i
$923$	435.990	−	435.990i	0.472362	−	0.472362i
$924$	23.1087	+	93.8489i	0.0250094	+	0.101568i
$925$	−419.259	+	419.259i	−0.453253	+	0.453253i
$926$	−356.515	−	583.761i	−0.385005	−	0.630411i
$927$	298.435	+	172.302i	0.321936	+	0.185870i
$928$	506.197	+	1248.71i	0.545471	+	1.34560i
$929$	−164.094	+	94.7395i	−0.176635	+	0.101980i	−0.585711	−	0.810520i	$-0.699184\pi$
$929$	−164.094	+	94.7395i	−0.176635	+	0.101980i	0.409076	+	0.912500i	$0.365851\pi$
$930$	−2.87236	−	116.425i	−0.00308856	−	0.125188i
$931$	97.4004	+	791.805i	0.104619	+	0.850489i
$932$	82.2733	+	1666.36i	0.0882761	+	1.78794i
$933$	0.447079	−	1.66852i	0.000479185	−	0.00178834i
$934$	−1306.92	+	384.976i	−1.39927	+	0.412179i
$935$	398.669	+	230.172i	0.426384	+	0.246173i
$936$	432.860	+	82.2604i	0.462457	+	0.0878851i
$937$	1196.60			1.27705			0.638526	−	0.769600i	$-0.279545\pi$
$937$	1196.60			1.27705			0.638526	+	0.769600i	$0.279545\pi$
$938$	19.3037	−	30.2071i	0.0205796	−	0.0322038i
$939$	−53.5904	−	53.5904i	−0.0570718	−	0.0570718i
$940$	−187.367	+	868.556i	−0.199327	+	0.923996i
$941$	261.923	−	70.1820i	0.278345	−	0.0745823i	−0.116946	−	0.993138i	$-0.537310\pi$
$941$	261.923	−	70.1820i	0.278345	−	0.0745823i	0.395291	+	0.918556i	$0.370644\pi$
$942$	158.342	+	86.2833i	0.168091	+	0.0915959i
$943$	57.3423	−	33.1066i	0.0608084	−	0.0351077i
$944$	79.1087	−	96.4908i	0.0838016	−	0.102215i
$945$	−110.710	+	96.2601i	−0.117153	+	0.101862i
$946$	0.384698	+	15.5928i	0.000406657	+	0.0164829i
$947$	592.263	+	158.696i	0.625409	+	0.167578i	0.557586	−	0.830119i	$-0.311728\pi$
$947$	592.263	+	158.696i	0.625409	+	0.167578i	0.0678236	+	0.997697i	$0.478394\pi$
$948$	147.660	−	47.4838i	0.155759	−	0.0500884i
$949$	632.750	−	169.545i	0.666754	−	0.178656i
$950$	−519.496	−	125.552i	−0.546838	−	0.132160i
$951$	−82.2658			−0.0865045
$952$	−988.104	−	260.216i	−1.03792	−	0.273336i
$953$			1536.95i			1.61275i	0.591407	+	0.806373i	$0.298573\pi$
$953$			1536.95i			1.61275i	−0.591407	+	0.806373i	$0.701427\pi$
$954$	836.897	+	202.261i	0.877251	+	0.212014i
$955$	−45.7338	−	170.681i	−0.0478888	−	0.178724i
$956$	−498.794	+	971.656i	−0.521751	+	1.01638i
$957$	−37.6184	+	140.394i	−0.0393086	+	0.146702i
$958$	−29.1095	−	1179.89i	−0.0303857	−	1.23161i
$959$	28.2483	+	9.72314i	0.0294560	+	0.0101388i
$960$	−74.3668	+	11.0872i	−0.0774654	+	0.0115492i
$961$	747.840	+	1295.30i	0.778190	+	1.34786i
$962$	395.291	+	215.401i	0.410906	+	0.223910i
$963$	−132.998	−	496.354i	−0.138108	−	0.515425i
$964$	786.653	−	507.480i	0.816030	−	0.526431i
$965$	135.082	−	135.082i	0.139981	−	0.139981i
$966$	−41.0926	−	1.85187i	−0.0425389	−	0.00191705i
$967$		−	959.130i		−	0.991861i	−0.868362	−	0.495931i	$-0.834827\pi$
$967$		−	959.130i		−	0.991861i	0.868362	−	0.495931i	$-0.165173\pi$
$968$	−309.983	+	210.979i	−0.320230	+	0.217954i
$969$	−59.5508	+	103.145i	−0.0614560	+	0.106445i
$970$	−741.156	+	218.321i	−0.764078	+	0.225073i
$971$	1631.38	+	437.127i	1.68010	+	0.450183i	0.967807	−	0.251694i	$-0.0809877\pi$
$971$	1631.38	+	437.127i	1.68010	+	0.450183i	0.712298	+	0.701877i	$0.247654\pi$
$972$	281.963	+	255.430i	0.290085	+	0.262788i
$973$	−144.175	+	213.800i	−0.148176	+	0.219733i
$974$	7.27625	+	294.926i	0.00747049	+	0.302799i
$975$	20.5008	+	35.5084i	0.0210264	+	0.0364188i
$976$	876.562	−	330.406i	0.898117	−	0.338531i
$977$	378.101	−	654.890i	0.387002	−	0.670307i	−0.605043	−	0.796193i	$-0.706844\pi$
$977$	378.101	−	654.890i	0.387002	−	0.670307i	0.992045	+	0.125886i	$0.0401773\pi$
$978$	−63.3811	−	103.781i	−0.0648069	−	0.106115i
$979$	−215.218	−	215.218i	−0.219835	−	0.219835i
$980$	197.949	−	539.151i	0.201989	−	0.550154i
$981$	252.481	+	252.481i	0.257371	+	0.257371i
$982$	−27.1169	+	112.202i	−0.0276140	+	0.114258i
$983$	191.523	−	331.728i	0.194835	−	0.337465i	−0.752011	−	0.659150i	$-0.770916\pi$
$983$	191.523	−	331.728i	0.194835	−	0.337465i	0.946847	+	0.321686i	$0.104249\pi$
$984$	−27.3600	+	9.54911i	−0.0278049	+	0.00970438i
$985$	212.744	+	368.483i	0.215983	+	0.374094i
$986$	−1112.99	−	1059.40i	−1.12880	−	1.07444i
$987$	118.946	−	176.387i	0.120512	−	0.178710i
$988$	20.0101	+	405.284i	0.0202531	+	0.410207i
$989$	−6.41201	−	1.71809i	−0.00648332	−	0.00173720i
$990$	391.646	+	213.415i	0.395602	+	0.215571i
$991$	620.552	−	1074.83i	0.626188	−	1.08459i	−0.362122	−	0.932131i	$-0.617948\pi$
$991$	620.552	−	1074.83i	0.626188	−	1.08459i	0.988310	−	0.152458i	$-0.0487189\pi$
$992$	1265.59	−	955.993i	1.27580	−	0.963702i
$993$		−	100.605i		−	0.101314i
$994$	−1022.73	+	934.528i	−1.02891	+	0.940169i
$995$	−71.0817	+	71.0817i	−0.0714389	+	0.0714389i
$996$	−177.779	+	114.688i	−0.178493	+	0.115148i
$997$	−331.514	−	1237.23i	−0.332511	−	1.24095i	−0.906542	−	0.422115i	$-0.861288\pi$
$997$	−331.514	−	1237.23i	−0.332511	−	1.24095i	0.574031	−	0.818833i	$-0.305379\pi$
$998$	−460.631	−	1563.75i	−0.461554	−	1.56688i
$999$	129.184	+	223.753i	0.129313	+	0.223977i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.3.x.a.101.11	yes	120
7.5	odd	6	inner	112.3.x.a.5.10	✓	120
16.13	even	4	inner	112.3.x.a.45.10	yes	120
112.61	odd	12	inner	112.3.x.a.61.11	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.3.x.a.5.10	✓	120	7.5	odd	6	inner
112.3.x.a.45.10	yes	120	16.13	even	4	inner
112.3.x.a.61.11	yes	120	112.61	odd	12	inner
112.3.x.a.101.11	yes	120	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	112.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04241 - 1.70686i) q^{2} +(0.387260 - 0.103766i) q^{3} +(-1.82674 + 3.55851i) q^{4} +(-2.83046 - 0.758420i) q^{5} +(-0.580800 - 0.552832i) q^{6} +(-6.87124 + 1.33643i) q^{7} +(7.97811 - 0.591454i) q^{8} +(-7.65503 + 4.41963i) q^{9} +(1.65600 + 5.62179i) q^{10} +(-8.31644 + 2.22838i) q^{11} +(-0.338172 + 1.56762i) q^{12} +(-4.40585 - 4.40585i) q^{13} +(9.44378 + 10.3351i) q^{14} -1.17482 q^{15} +(-9.32603 - 13.0010i) q^{16} +(15.8018 + 9.12315i) q^{17} +(15.5234 + 8.45897i) q^{18} +(-4.21386 + 15.7263i) q^{19} +(7.86937 - 8.68679i) q^{20} +(-2.52228 + 1.23055i) q^{21} +(12.4727 + 11.8721i) q^{22} +(-6.34669 + 3.66426i) q^{23} +(3.02823 - 1.05690i) q^{24} +(-14.2143 - 8.20665i) q^{25} +(-2.92745 + 12.1129i) q^{26} +(-5.05733 + 5.05733i) q^{27} +(7.79629 - 26.8927i) q^{28} +(29.7739 - 29.7739i) q^{29} +(1.22465 + 2.00526i) q^{30} +(-42.9245 - 24.7825i) q^{31} +(-12.4692 + 29.4706i) q^{32} +(-2.98940 + 1.72593i) q^{33} +(-0.900051 - 36.4815i) q^{34} +(20.4624 + 1.42858i) q^{35} +(-1.74356 - 35.3140i) q^{36} +(9.34970 - 34.8935i) q^{37} +(31.2352 - 9.20089i) q^{38} +(-2.16339 - 1.24903i) q^{39} +(-23.0303 - 4.37666i) q^{40} -9.03499 q^{41} +(4.72964 + 3.02244i) q^{42} +(0.640499 + 0.640499i) q^{43} +(7.26226 - 33.6649i) q^{44} +(25.0192 - 6.70387i) q^{45} +(12.8703 + 7.01323i) q^{46} +(-65.6497 + 37.9028i) q^{47} +(-4.96066 - 4.06703i) q^{48} +(45.4279 - 18.3658i) q^{49} +(0.809633 + 32.8166i) q^{50} +(7.06607 + 1.89335i) q^{51} +(23.7266 - 7.62993i) q^{52} +(47.0432 - 12.6052i) q^{53} +(13.9040 + 3.36032i) q^{54} +25.2294 q^{55} +(-54.0291 + 14.7262i) q^{56} +6.52744i q^{57} +(-81.8566 - 19.7831i) q^{58} +(2.01838 + 7.53268i) q^{59} +(2.14610 - 4.18062i) q^{60} +(-15.1533 + 56.5528i) q^{61} +(2.44493 + 99.0997i) q^{62} +(46.6930 - 40.5987i) q^{63} +(63.3004 - 9.43737i) q^{64} +(9.12911 + 15.8121i) q^{65} +(6.06211 + 3.30335i) q^{66} +(-0.662730 - 2.47334i) q^{67} +(-61.3306 + 39.5651i) q^{68} +(-2.07760 + 2.07760i) q^{69} +(-18.8919 - 36.4155i) q^{70} +98.9570i q^{71} +(-58.4586 + 39.7879i) q^{72} +(-52.5670 + 91.0487i) q^{73} +(-69.3047 + 20.4149i) q^{74} +(-6.35622 - 1.70314i) q^{75} +(-48.2647 - 43.7230i) q^{76} +(54.1662 - 26.4261i) q^{77} +(0.123224 + 4.99462i) q^{78} +(-48.3594 - 83.7610i) q^{79} +(16.5368 + 43.8718i) q^{80} +(38.3430 - 66.4119i) q^{81} +(9.41821 + 15.4215i) q^{82} +(93.2835 + 93.2835i) q^{83} +(0.228642 - 11.2235i) q^{84} +(-37.8071 - 37.8071i) q^{85} +(0.425576 - 1.76091i) q^{86} +(8.44073 - 14.6198i) q^{87} +(-65.0315 + 22.6971i) q^{88} +(17.6754 + 30.6147i) q^{89} +(-37.5229 - 35.7160i) q^{90} +(36.1618 + 24.3856i) q^{91} +(-1.44556 - 29.2785i) q^{92} +(-19.1945 - 5.14316i) q^{93} +(133.129 + 72.5443i) q^{94} +(23.8543 - 41.3169i) q^{95} +(-1.77079 + 12.7067i) q^{96} +131.836i q^{97} +(-78.7027 - 58.3943i) q^{98} +(53.8140 - 53.8140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - 6 q^{5} + 4 q^{8} - 60 q^{10} - 18 q^{11} - 6 q^{12} - 28 q^{14} - 16 q^{15} + 8 q^{16} - 12 q^{17} + 2 q^{18} - 6 q^{19} + 14 q^{21} - 20 q^{22} - 6 q^{24} - 6 q^{26}+ \cdots - 848 q^{99}+O(q^{100}) \) 120 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 - 6 * q^5 + 4 * q^8 - 60 * q^10 - 18 * q^11 - 6 * q^12 - 28 * q^14 - 16 * q^15 + 8 * q^16 - 12 * q^17 + 2 * q^18 - 6 * q^19 + 14 * q^21 - 20 * q^22 - 6 * q^24 - 6 * q^26 - 6 * q^28 + 24 * q^29 + 10 * q^30 - 12 * q^31 - 92 * q^32 - 12 * q^33 + 94 * q^35 + 128 * q^36 + 46 * q^37 - 6 * q^38 - 66 * q^40 - 78 * q^42 + 88 * q^43 - 182 * q^44 - 60 * q^45 - 108 * q^46 - 12 * q^47 - 8 * q^49 - 8 * q^50 - 118 * q^51 - 564 * q^52 - 82 * q^53 - 306 * q^54 + 400 * q^56 + 346 * q^58 - 198 * q^59 - 186 * q^60 - 6 * q^61 - 204 * q^63 + 16 * q^64 - 4 * q^65 + 870 * q^66 + 222 * q^67 + 384 * q^68 + 556 * q^70 - 52 * q^72 + 126 * q^74 - 156 * q^75 - 102 * q^77 - 28 * q^78 - 4 * q^79 + 300 * q^80 + 248 * q^81 - 810 * q^82 - 288 * q^84 - 108 * q^85 - 196 * q^86 + 366 * q^88 + 88 * q^91 + 172 * q^92 - 38 * q^93 + 606 * q^94 - 388 * q^95 + 996 * q^96 - 848 * q^99

Introduction

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