LMFDB - Embedded newform 429.2.be.a.89.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(89,429)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("429.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.be (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			89.4
Character	$\chi$	$=$	429.89
Dual form			429.2.be.a.188.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.43755 - 0.653139i) q^{2} +(0.235409 + 1.71598i) q^{3} +(3.78299 + 2.18411i) q^{4} +(1.30401 - 1.30401i) q^{5} +(0.546952 - 4.33653i) q^{6} +(-1.18861 - 4.43596i) q^{7} +(-4.22588 - 4.22588i) q^{8} +(-2.88917 + 0.807913i) q^{9} +O(q^{10})$	\(q+(-2.43755 - 0.653139i) q^{2} +(0.235409 + 1.71598i) q^{3} +(3.78299 + 2.18411i) q^{4} +(1.30401 - 1.30401i) q^{5} +(0.546952 - 4.33653i) q^{6} +(-1.18861 - 4.43596i) q^{7} +(-4.22588 - 4.22588i) q^{8} +(-2.88917 + 0.807913i) q^{9} +(-4.03028 + 2.32688i) q^{10} +(-0.258819 + 0.965926i) q^{11} +(-2.85734 + 7.00570i) q^{12} +(-2.90196 - 2.13977i) q^{13} +11.5892i q^{14} +(2.54462 + 1.93067i) q^{15} +(3.17247 + 5.49488i) q^{16} +(-1.66010 + 2.87538i) q^{17} +(7.57016 - 0.0822994i) q^{18} +(-5.99153 + 1.60543i) q^{19} +(7.78115 - 2.08495i) q^{20} +(7.33220 - 3.08389i) q^{21} +(1.26177 - 2.18544i) q^{22} +(-2.18587 - 3.78604i) q^{23} +(6.25671 - 8.24633i) q^{24} +1.59913i q^{25} +(5.67611 + 7.11117i) q^{26} +(-2.06650 - 4.76756i) q^{27} +(5.19212 - 19.3773i) q^{28} +(-4.39536 + 2.53766i) q^{29} +(-4.94164 - 6.36810i) q^{30} +(1.35056 + 1.35056i) q^{31} +(-1.05057 - 3.92077i) q^{32} +(-1.71844 - 0.216741i) q^{33} +(5.92459 - 5.92459i) q^{34} +(-7.33448 - 4.23456i) q^{35} +(-12.6943 - 3.25393i) q^{36} +(-5.73842 - 1.53761i) q^{37} +15.6532 q^{38} +(2.98865 - 5.48343i) q^{39} -11.0212 q^{40} +(-0.919061 - 0.246262i) q^{41} +(-19.8868 + 2.72819i) q^{42} +(4.13239 + 2.38584i) q^{43} +(-3.08880 + 3.08880i) q^{44} +(-2.71397 + 4.82102i) q^{45} +(2.85535 + 10.6563i) q^{46} +(1.59108 + 1.59108i) q^{47} +(-8.68227 + 6.73744i) q^{48} +(-12.2027 + 7.04525i) q^{49} +(1.04445 - 3.89795i) q^{50} +(-5.32489 - 2.17181i) q^{51} +(-6.30462 - 14.4329i) q^{52} -5.48763i q^{53} +(1.92330 + 12.9709i) q^{54} +(0.922073 + 1.59708i) q^{55} +(-13.7229 + 23.7688i) q^{56} +(-4.16534 - 9.90341i) q^{57} +(12.3714 - 3.31489i) q^{58} +(-9.16543 + 2.45587i) q^{59} +(5.40949 + 12.8615i) q^{60} +(4.41207 - 7.64192i) q^{61} +(-2.40996 - 4.17417i) q^{62} +(7.01796 + 11.8559i) q^{63} -2.44665i q^{64} +(-6.57446 + 0.993910i) q^{65} +(4.04721 + 1.65069i) q^{66} +(1.89531 - 7.07341i) q^{67} +(-12.5603 + 7.25169i) q^{68} +(5.98219 - 4.64218i) q^{69} +(15.1124 + 15.1124i) q^{70} +(-3.41333 - 12.7387i) q^{71} +(15.6234 + 8.79513i) q^{72} +(-6.53518 + 6.53518i) q^{73} +(12.9834 + 7.49597i) q^{74} +(-2.74407 + 0.376448i) q^{75} +(-26.1724 - 7.01286i) q^{76} +4.59244 q^{77} +(-10.8664 + 11.4141i) q^{78} +10.2486 q^{79} +(11.3023 + 3.02844i) q^{80} +(7.69455 - 4.66839i) q^{81} +(2.07941 + 1.20055i) q^{82} +(12.1133 - 12.1133i) q^{83} +(34.4732 + 4.34799i) q^{84} +(1.58473 + 5.91430i) q^{85} +(-8.51462 - 8.51462i) q^{86} +(-5.38928 - 6.94496i) q^{87} +(5.17563 - 2.98815i) q^{88} +(-0.752302 + 2.80763i) q^{89} +(9.76422 - 9.97886i) q^{90} +(-6.04261 + 15.4163i) q^{91} -19.0968i q^{92} +(-1.99960 + 2.63547i) q^{93} +(-2.83913 - 4.91752i) q^{94} +(-5.71952 + 9.90649i) q^{95} +(6.48065 - 2.72574i) q^{96} +(4.38783 - 1.17571i) q^{97} +(34.3463 - 9.20306i) q^{98} +(-0.0326127 - 2.99982i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 12 q^{6} + 12 q^{7}+O(q^{10}) $ 184 * q - 12 * q^6 + 12 * q^7	$ 184 q - 12 q^{6} + 12 q^{7} - 48 q^{10} - 16 q^{13} + 16 q^{15} + 80 q^{16} - 8 q^{18} - 4 q^{19} - 24 q^{24} - 48 q^{27} - 40 q^{28} + 48 q^{30} - 20 q^{31} + 16 q^{34} - 36 q^{36} + 44 q^{37} + 48 q^{39} - 80 q^{40} + 20 q^{42} - 84 q^{43} - 4 q^{45} - 64 q^{46} + 44 q^{48} - 60 q^{49} - 200 q^{52} - 4 q^{54} - 64 q^{57} - 48 q^{58} - 148 q^{60} - 48 q^{61} + 40 q^{66} + 48 q^{67} - 12 q^{69} + 24 q^{70} - 128 q^{72} + 108 q^{73} - 60 q^{75} - 24 q^{76} + 148 q^{78} + 32 q^{79} + 16 q^{81} - 48 q^{82} + 116 q^{84} + 104 q^{85} - 24 q^{87} + 72 q^{88} + 60 q^{91} + 36 q^{93} + 16 q^{94} - 72 q^{96} + 4 q^{97}+O(q^{100}) $ 184 * q - 12 * q^6 + 12 * q^7 - 48 * q^10 - 16 * q^13 + 16 * q^15 + 80 * q^16 - 8 * q^18 - 4 * q^19 - 24 * q^24 - 48 * q^27 - 40 * q^28 + 48 * q^30 - 20 * q^31 + 16 * q^34 - 36 * q^36 + 44 * q^37 + 48 * q^39 - 80 * q^40 + 20 * q^42 - 84 * q^43 - 4 * q^45 - 64 * q^46 + 44 * q^48 - 60 * q^49 - 200 * q^52 - 4 * q^54 - 64 * q^57 - 48 * q^58 - 148 * q^60 - 48 * q^61 + 40 * q^66 + 48 * q^67 - 12 * q^69 + 24 * q^70 - 128 * q^72 + 108 * q^73 - 60 * q^75 - 24 * q^76 + 148 * q^78 + 32 * q^79 + 16 * q^81 - 48 * q^82 + 116 * q^84 + 104 * q^85 - 24 * q^87 + 72 * q^88 + 60 * q^91 + 36 * q^93 + 16 * q^94 - 72 * q^96 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$

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 $

$2$	−2.43755	−	0.653139i	−1.72361	−	0.461839i	−0.744912	−	0.667163i	$-0.767509\pi$
$2$	−2.43755	−	0.653139i	−1.72361	−	0.461839i	−0.978694	+	0.205324i	$0.934175\pi$
$3$	0.235409	+	1.71598i	0.135913	+	0.990721i
$3$	0.235409	+	1.71598i	0.135913	+	0.990721i
$4$	3.78299	+	2.18411i	1.89150	+	1.09206i
$5$	1.30401	−	1.30401i	0.583170	−	0.583170i	−0.352603	−	0.935773i	$-0.614703\pi$
$5$	1.30401	−	1.30401i	0.583170	−	0.583170i	0.935773	+	0.352603i	$0.114703\pi$
$6$	0.546952	−	4.33653i	0.223292	−	1.77038i
$7$	−1.18861	−	4.43596i	−0.449253	−	1.67663i	−0.704457	−	0.709747i	$-0.748809\pi$
$7$	−1.18861	−	4.43596i	−0.449253	−	1.67663i	0.255204	−	0.966887i	$-0.417857\pi$
$8$	−4.22588	−	4.22588i	−1.49407	−	1.49407i
$9$	−2.88917	+	0.807913i	−0.963055	+	0.269304i
$10$	−4.03028	+	2.32688i	−1.27449	+	0.735825i
$11$	−0.258819	+	0.965926i	−0.0780369	+	0.291238i
$11$	−0.258819	+	0.965926i	−0.0780369	+	0.291238i
$12$	−2.85734	+	7.00570i	−0.824843	+	2.02237i
$13$	−2.90196	−	2.13977i	−0.804860	−	0.593465i
$13$	−2.90196	−	2.13977i	−0.804860	−	0.593465i
$14$			11.5892i			3.09734i
$15$	2.54462	+	1.93067i	0.657019	+	0.498498i
$16$	3.17247	+	5.49488i	0.793118	+	1.37372i
$17$	−1.66010	+	2.87538i	−0.402633	+	0.697381i	−0.994043	−	0.108990i	$-0.965238\pi$
$17$	−1.66010	+	2.87538i	−0.402633	+	0.697381i	0.591410	+	0.806371i	$0.298572\pi$
$18$	7.57016	−	0.0822994i	1.78430	−	0.0193982i
$19$	−5.99153	+	1.60543i	−1.37455	+	0.368310i	−0.869139	−	0.494568i	$-0.835326\pi$
$19$	−5.99153	+	1.60543i	−1.37455	+	0.368310i	−0.505412	+	0.862878i	$0.668660\pi$
$20$	7.78115	−	2.08495i	1.73992	−	0.466210i
$21$	7.33220	−	3.08389i	1.60002	−	0.672961i
$22$	1.26177	−	2.18544i	0.269010	−	0.465938i
$23$	−2.18587	−	3.78604i	−0.455786	−	0.789444i	0.542947	−	0.839767i	$-0.317308\pi$
$23$	−2.18587	−	3.78604i	−0.455786	−	0.789444i	−0.998733	+	0.0503228i	$0.983975\pi$
$24$	6.25671	−	8.24633i	1.27715	−	1.68328i
$25$			1.59913i			0.319825i
$26$	5.67611	+	7.11117i	1.11318	+	1.39461i
$27$	−2.06650	−	4.76756i	−0.397697	−	0.917517i
$28$	5.19212	−	19.3773i	0.981219	−	3.66196i
$29$	−4.39536	+	2.53766i	−0.816198	+	0.471232i	−0.849104	−	0.528226i	$-0.822857\pi$
$29$	−4.39536	+	2.53766i	−0.816198	+	0.471232i	0.0329053	+	0.999458i	$0.489524\pi$
$30$	−4.94164	−	6.36810i	−0.902217	−	1.16265i
$31$	1.35056	+	1.35056i	0.242568	+	0.242568i	0.817912	−	0.575343i	$-0.195132\pi$
$31$	1.35056	+	1.35056i	0.242568	+	0.242568i	−0.575343	+	0.817912i	$0.695132\pi$
$32$	−1.05057	−	3.92077i	−0.185716	−	0.693101i
$33$	−1.71844	−	0.216741i	−0.299141	−	0.0377297i
$34$	5.92459	−	5.92459i	1.01606	−	1.01606i
$35$	−7.33448	−	4.23456i	−1.23975	−	0.715772i
$36$	−12.6943	−	3.25393i	−2.11571	−	0.542322i
$37$	−5.73842	−	1.53761i	−0.943391	−	0.252781i	−0.245835	−	0.969312i	$-0.579062\pi$
$37$	−5.73842	−	1.53761i	−0.943391	−	0.252781i	−0.697555	+	0.716531i	$0.745729\pi$
$38$	15.6532			2.53928
$39$	2.98865	−	5.48343i	0.478567	−	0.878051i
$40$	−11.0212			−1.74260
$41$	−0.919061	−	0.246262i	−0.143533	−	0.0384596i	0.186337	−	0.982486i	$-0.440338\pi$
$41$	−0.919061	−	0.246262i	−0.143533	−	0.0384596i	−0.329870	+	0.944026i	$0.607005\pi$
$42$	−19.8868	+	2.72819i	−3.06860	+	0.420970i
$43$	4.13239	+	2.38584i	0.630184	+	0.363837i	0.780823	−	0.624752i	$-0.214800\pi$
$43$	4.13239	+	2.38584i	0.630184	+	0.363837i	−0.150639	+	0.988589i	$0.548133\pi$
$44$	−3.08880	+	3.08880i	−0.465654	+	0.465654i
$45$	−2.71397	+	4.82102i	−0.404575	+	0.718675i
$46$	2.85535	+	10.6563i	0.420999	+	1.57119i
$47$	1.59108	+	1.59108i	0.232082	+	0.232082i	0.813561	−	0.581479i	$-0.197526\pi$
$47$	1.59108	+	1.59108i	0.232082	+	0.232082i	−0.581479	+	0.813561i	$0.697526\pi$
$48$	−8.68227	+	6.73744i	−1.25318	+	0.972465i
$49$	−12.2027	+	7.04525i	−1.74325	+	1.00646i
$50$	1.04445	−	3.89795i	0.147708	−	0.551253i
$51$	−5.32489	−	2.17181i	−0.745633	−	0.304114i
$52$	−6.30462	−	14.4329i	−0.874293	−	2.00149i
$53$		−	5.48763i		−	0.753784i	−0.926257	−	0.376892i	$-0.876993\pi$
$53$		−	5.48763i		−	0.753784i	0.926257	−	0.376892i	$-0.123007\pi$
$54$	1.92330	+	12.9709i	0.261729	+	1.76511i
$55$	0.922073	+	1.59708i	0.124332	+	0.215350i
$56$	−13.7229	+	23.7688i	−1.83380	+	3.17623i
$57$	−4.16534	−	9.90341i	−0.551712	−	1.31174i
$58$	12.3714	−	3.31489i	1.62444	−	0.435267i
$59$	−9.16543	+	2.45587i	−1.19324	+	0.319727i	−0.800165	−	0.599780i	$-0.795255\pi$
$59$	−9.16543	+	2.45587i	−1.19324	+	0.319727i	−0.393073	+	0.919507i	$0.628588\pi$
$60$	5.40949	+	12.8615i	0.698362	+	1.66041i
$61$	4.41207	−	7.64192i	0.564907	−	0.978448i	−0.432151	−	0.901801i	$-0.642245\pi$
$61$	4.41207	−	7.64192i	0.564907	−	0.978448i	0.997058	−	0.0766469i	$-0.0244214\pi$
$62$	−2.40996	−	4.17417i	−0.306065	−	0.530120i
$63$	7.01796	+	11.8559i	0.884180	+	1.49371i
$64$		−	2.44665i		−	0.305831i
$65$	−6.57446	+	0.993910i	−0.815461	+	0.123279i
$66$	4.04721	+	1.65069i	0.498177	+	0.203186i
$67$	1.89531	−	7.07341i	0.231549	−	0.864154i	−0.748125	−	0.663558i	$-0.769046\pi$
$67$	1.89531	−	7.07341i	0.231549	−	0.864154i	0.979674	−	0.200596i	$-0.0642878\pi$
$68$	−12.5603	+	7.25169i	−1.52316	+	0.879396i
$69$	5.98219	−	4.64218i	0.720171	−	0.558852i
$70$	15.1124	+	15.1124i	1.80628	+	1.80628i
$71$	−3.41333	−	12.7387i	−0.405088	−	1.51181i	−0.803894	−	0.594773i	$-0.797242\pi$
$71$	−3.41333	−	12.7387i	−0.405088	−	1.51181i	0.398806	−	0.917035i	$-0.369425\pi$
$72$	15.6234	+	8.79513i	1.84124	+	1.03652i
$73$	−6.53518	+	6.53518i	−0.764885	+	0.764885i	−0.977201	−	0.212316i	$-0.931899\pi$
$73$	−6.53518	+	6.53518i	−0.764885	+	0.764885i	0.212316	+	0.977201i	$0.431899\pi$
$74$	12.9834	+	7.49597i	1.50929	+	0.871389i
$75$	−2.74407	+	0.376448i	−0.316858	+	0.0434685i
$76$	−26.1724	−	7.01286i	−3.00218	−	0.804430i
$77$	4.59244			0.523357
$78$	−10.8664	+	11.4141i	−1.23038	+	1.29239i
$79$	10.2486			1.15305			0.576527	−	0.817078i	$-0.304407\pi$
$79$	10.2486			1.15305			0.576527	+	0.817078i	$0.304407\pi$
$80$	11.3023	+	3.02844i	1.26364	+	0.338590i
$81$	7.69455	−	4.66839i	0.854950	−	0.518710i
$82$	2.07941	+	1.20055i	0.229632	+	0.132578i
$83$	12.1133	−	12.1133i	1.32960	−	1.32960i	0.423888	−	0.905715i	$-0.360665\pi$
$83$	12.1133	−	12.1133i	1.32960	−	1.32960i	0.905715	−	0.423888i	$-0.139335\pi$
$84$	34.4732	+	4.34799i	3.76134	+	0.474405i
$85$	1.58473	+	5.91430i	0.171888	+	0.641495i
$86$	−8.51462	−	8.51462i	−0.918155	−	0.918155i
$87$	−5.38928	−	6.94496i	−0.577792	−	0.744578i
$88$	5.17563	−	2.98815i	0.551724	−	0.318538i
$89$	−0.752302	+	2.80763i	−0.0797438	+	0.297608i	−0.994267	−	0.106925i	$-0.965899\pi$
$89$	−0.752302	+	2.80763i	−0.0797438	+	0.297608i	0.914523	+	0.404533i	$0.132566\pi$
$90$	9.76422	−	9.97886i	1.02924	−	1.05186i
$91$	−6.04261	+	15.4163i	−0.633438	+	1.61607i
$92$		−	19.0968i		−	1.99097i
$93$	−1.99960	+	2.63547i	−0.207349	+	0.273286i
$94$	−2.83913	−	4.91752i	−0.292834	−	0.507203i
$95$	−5.71952	+	9.90649i	−0.586810	+	1.01638i
$96$	6.48065	−	2.72574i	0.661429	−	0.278194i
$97$	4.38783	−	1.17571i	0.445516	−	0.119376i	−0.0290844	−	0.999577i	$-0.509259\pi$
$97$	4.38783	−	1.17571i	0.445516	−	0.119376i	0.474601	+	0.880201i	$0.342592\pi$
$98$	34.3463	−	9.20306i	3.46950	−	0.929649i
$99$	−0.0326127	−	2.99982i	−0.00327770	−	0.301494i
$100$	−3.49267	+	6.04949i	−0.349267	+	0.604949i
$101$	4.00232	+	6.93222i	0.398245	+	0.689781i	0.993510	−	0.113749i	$-0.0362859\pi$
$101$	4.00232	+	6.93222i	0.398245	+	0.689781i	−0.595264	+	0.803530i	$0.702953\pi$
$102$	11.5612	+	8.77177i	1.14473	+	0.868534i
$103$		−	9.73794i		−	0.959507i	−0.877403	−	0.479754i	$-0.840726\pi$
$103$		−	9.73794i		−	0.959507i	0.877403	−	0.479754i	$-0.159274\pi$
$104$	3.22095	+	21.3058i	0.315840	+	2.08920i
$105$	5.53982	−	13.5827i	0.540631	−	1.32553i
$106$	−3.58418	+	13.3764i	−0.348127	+	1.29923i
$107$	12.6424	−	7.29907i	1.22218	−	0.705628i	0.256800	−	0.966464i	$-0.417332\pi$
$107$	12.6424	−	7.29907i	1.22218	−	0.705628i	0.965383	+	0.260837i	$0.0839984\pi$
$108$	2.59534	−	22.5491i	0.249737	−	2.16979i
$109$	−4.79132	−	4.79132i	−0.458925	−	0.458925i	0.439377	−	0.898303i	$-0.355199\pi$
$109$	−4.79132	−	4.79132i	−0.458925	−	0.458925i	−0.898303	+	0.439377i	$0.855199\pi$
$110$	−1.20448	−	4.49519i	−0.114843	−	0.428600i
$111$	1.28762	−	10.2090i	0.122216	−	0.968993i
$112$	20.6042	−	20.6042i	1.94692	−	1.94692i
$113$	−8.79969	−	5.08050i	−0.827805	−	0.477933i	0.0252956	−	0.999680i	$-0.491947\pi$
$113$	−8.79969	−	5.08050i	−0.827805	−	0.477933i	−0.853100	+	0.521747i	$0.825281\pi$
$114$	3.68490	+	26.8606i	0.345123	+	2.51572i
$115$	−7.78742	−	2.08663i	−0.726181	−	0.194580i
$116$	−22.1702			−2.05845
$117$	10.1130	+	3.83761i	0.934947	+	0.354787i
$118$	23.9452			2.20433
$119$	14.7283	+	3.94642i	1.35014	+	0.361768i
$120$	−2.59448	−	18.9121i	−0.236842	−	1.72643i
$121$	−0.866025	−	0.500000i	−0.0787296	−	0.0454545i
$122$	−15.7459	+	15.7459i	−1.42556	+	1.42556i
$123$	0.206225	−	1.63506i	0.0185947	−	0.147428i
$124$	2.15939	+	8.05896i	0.193919	+	0.723716i
$125$	8.60531	+	8.60531i	0.769683	+	0.769683i
$126$	−9.36305	−	33.4831i	−0.834126	−	2.98291i
$127$	−13.0115	+	7.51221i	−1.15459	+	0.666601i	−0.950001	−	0.312248i	$-0.898918\pi$
$127$	−13.0115	+	7.51221i	−1.15459	+	0.666601i	−0.204586	+	0.978849i	$0.565585\pi$
$128$	−3.69914	+	13.8054i	−0.326961	+	1.22023i
$129$	−3.12125	+	7.65275i	−0.274810	+	0.673787i
$130$	16.6747	+	1.87133i	1.46247	+	0.164126i
$131$			2.48858i			0.217428i	0.994073	+	0.108714i	$0.0346733\pi$
$131$			2.48858i			0.217428i	−0.994073	+	0.108714i	$0.965327\pi$
$132$	−6.02745	−	4.57319i	−0.524622	−	0.398045i
$133$	14.2432	+	24.6699i	1.23504	+	2.13916i
$134$	−9.23983	+	16.0039i	−0.798200	+	1.38252i
$135$	−8.91166	−	3.52220i	−0.766993	−	0.303143i
$136$	19.1664	−	5.13562i	1.64350	−	0.440375i
$137$	−0.762329	+	0.204265i	−0.0651302	+	0.0174516i	−0.291237	−	0.956651i	$-0.594067\pi$
$137$	−0.762329	+	0.204265i	−0.0651302	+	0.0174516i	0.226107	+	0.974103i	$0.427400\pi$
$138$	−17.6139	+	7.40832i	−1.49939	+	0.630638i
$139$	−0.758546	+	1.31384i	−0.0643391	+	0.111439i	−0.896401	−	0.443245i	$-0.853827\pi$
$139$	−0.758546	+	1.31384i	−0.0643391	+	0.111439i	0.832062	+	0.554683i	$0.187161\pi$
$140$	−18.4975	−	32.0387i	−1.56333	−	2.70776i
$141$	−2.35570	+	3.10481i	−0.198386	+	0.261472i
$142$			33.2806i			2.79285i
$143$	2.81794	−	2.24927i	0.235648	−	0.188093i
$144$	−13.6052	−	13.3125i	−1.13376	−	1.10938i
$145$	−2.42245	+	9.04072i	−0.201174	+	0.750791i
$146$	20.1982	−	11.6614i	1.67161	−	0.965107i
$147$	−14.9621	−	19.2811i	−1.23406	−	1.59028i
$148$	−18.3501	−	18.3501i	−1.50837	−	1.50837i
$149$	5.67693	+	21.1866i	0.465072	+	1.73567i	0.656649	+	0.754196i	$0.271973\pi$
$149$	5.67693	+	21.1866i	0.465072	+	1.73567i	−0.191577	+	0.981478i	$0.561360\pi$
$150$	6.93467	+	0.874646i	0.566213	+	0.0714145i
$151$	7.37749	−	7.37749i	0.600371	−	0.600371i	−0.340040	−	0.940411i	$-0.610440\pi$
$151$	7.37749	−	7.37749i	0.600371	−	0.600371i	0.940411	+	0.340040i	$0.110440\pi$
$152$	32.1038	+	18.5352i	2.60396	+	1.50340i
$153$	2.47325	−	9.64865i	0.199950	−	0.780047i
$154$	−11.1943	−	2.99950i	−0.902061	−	0.241707i
$155$	3.52229			0.282917
$156$	23.2825	−	14.2162i	1.86409	−	1.13821i
$157$	4.85407			0.387397			0.193698	−	0.981061i	$-0.437952\pi$
$157$	4.85407			0.387397			0.193698	+	0.981061i	$0.437952\pi$
$158$	−24.9814	−	6.69374i	−1.98741	−	0.532525i
$159$	9.41666	−	1.29184i	0.746790	−	0.102449i
$160$	−6.48267	−	3.74277i	−0.512500	−	0.295892i
$161$	−14.1966	+	14.1966i	−1.11885	+	1.11885i
$162$	−21.8049	+	6.35380i	−1.71316	+	0.499202i
$163$	3.48235	+	12.9963i	0.272759	+	1.01795i	0.957328	+	0.289002i	$0.0933235\pi$
$163$	3.48235	+	12.9963i	0.272759	+	1.01795i	−0.684570	+	0.728947i	$0.740010\pi$
$164$	−2.93894	−	2.93894i	−0.229493	−	0.229493i
$165$	−2.52349	+	1.95822i	−0.196453	+	0.152447i
$166$	−37.4383	+	21.6150i	−2.90577	+	1.67765i
$167$	4.71272	−	17.5881i	0.364681	−	1.36101i	−0.503171	−	0.864187i	$-0.667833\pi$
$167$	4.71272	−	17.5881i	0.364681	−	1.36101i	0.867852	−	0.496822i	$-0.165500\pi$
$168$	−44.0172	−	17.9528i	−3.39600	−	1.38509i
$169$	3.84279	+	12.4191i	0.295599	+	0.955312i
$170$		−	15.4514i		−	1.18507i
$171$	16.0135	−	9.47897i	1.22458	−	0.724875i
$172$	10.4219	+	18.0512i	0.794661	+	1.37639i
$173$	−2.90455	+	5.03083i	−0.220829	+	0.382487i	−0.955060	−	0.296413i	$-0.904210\pi$
$173$	−2.90455	+	5.03083i	−0.220829	+	0.382487i	0.734231	+	0.678900i	$0.237543\pi$
$174$	8.60061	+	20.4486i	0.652011	+	1.55021i
$175$	7.09366	−	1.90074i	0.536230	−	0.143682i
$176$	−6.12874	+	1.64219i	−0.461971	+	0.123785i
$177$	−6.37184	−	15.1496i	−0.478937	−	1.13871i
$178$	3.66754	−	6.35237i	0.274894	−	0.476130i
$179$	2.24944	+	3.89615i	0.168131	+	0.291212i	0.937763	−	0.347276i	$-0.112893\pi$
$179$	2.24944	+	3.89615i	0.168131	+	0.291212i	−0.769632	+	0.638488i	$0.779560\pi$
$180$	−20.7966	+	12.3103i	−1.55009	+	0.917553i
$181$		−	9.93162i		−	0.738212i	−0.929387	−	0.369106i	$-0.879664\pi$
$181$		−	9.93162i		−	0.738212i	0.929387	−	0.369106i	$-0.120336\pi$
$182$	24.7982	−	33.6314i	1.83816	−	2.49292i
$183$	14.1520	+	5.77204i	1.04615	+	0.426681i
$184$	−6.76212	+	25.2366i	−0.498510	+	1.86047i
$185$	−9.48800	+	5.47790i	−0.697571	+	0.402743i
$186$	6.59546	−	5.11807i	0.483603	−	0.375275i
$187$	−2.34773	−	2.34773i	−0.171683	−	0.171683i
$188$	2.54394	+	9.49413i	0.185536	+	0.692430i
$189$	−18.6924	+	14.8337i	−1.35967	+	1.07899i
$190$	20.4119	−	20.4119i	1.48083	−	1.48083i
$191$	−10.0408	−	5.79706i	−0.726526	−	0.419460i	0.0906237	−	0.995885i	$-0.471114\pi$
$191$	−10.0408	−	5.79706i	−0.726526	−	0.419460i	−0.817150	+	0.576425i	$0.804447\pi$
$192$	4.19840	−	0.575962i	0.302993	−	0.0415665i
$193$	−16.7900	−	4.49887i	−1.20857	−	0.323836i	−0.402371	−	0.915477i	$-0.631814\pi$
$193$	−16.7900	−	4.49887i	−1.20857	−	0.323836i	−0.806202	+	0.591641i	$0.798480\pi$
$194$	−11.4634			−0.823027
$195$	−3.25321	−	11.0477i	−0.232967	−	0.791139i
$196$	−61.5505			−4.39646
$197$	−14.2840	−	3.82737i	−1.01769	−	0.272689i	−0.288851	−	0.957374i	$-0.593273\pi$
$197$	−14.2840	−	3.82737i	−1.01769	−	0.272689i	−0.728839	+	0.684685i	$0.759940\pi$
$198$	−1.87981	+	7.33351i	−0.133592	+	0.521170i
$199$	0.916390	+	0.529078i	0.0649612	+	0.0375053i	0.532129	−	0.846663i	$-0.321392\pi$
$199$	0.916390	+	0.529078i	0.0649612	+	0.0375053i	−0.467168	+	0.884169i	$0.654726\pi$
$200$	6.75772	−	6.75772i	0.477843	−	0.477843i
$201$	12.5840	+	1.58718i	0.887606	+	0.111951i
$202$	−5.22814	−	19.5117i	−0.367850	−	1.37284i
$203$	16.4813	+	16.4813i	1.15676	+	1.15676i
$204$	−15.4005	−	19.8461i	−1.07825	−	1.38950i
$205$	−1.51959	+	0.877335i	−0.106133	+	0.0612758i
$206$	−6.36022	+	23.7367i	−0.443138	+	1.65381i
$207$	9.37413	+	9.17250i	0.651547	+	0.637533i
$208$	2.55137	−	22.7343i	0.176906	−	1.57634i
$209$		−	6.20289i		−	0.429063i
$210$	−22.3749	+	29.4901i	−1.54402	+	2.03501i
$211$	−7.04377	−	12.2002i	−0.484913	−	0.839894i	0.514937	−	0.857228i	$-0.327815\pi$
$211$	−7.04377	−	12.2002i	−0.484913	−	0.839894i	−0.999850	+	0.0173341i	$0.994482\pi$
$212$	11.9856	−	20.7597i	0.823175	−	1.42578i
$213$	21.0558	−	8.85601i	1.44272	−	0.606804i
$214$	−35.5837	+	9.53461i	−2.43245	+	0.651773i
$215$	8.49983	−	2.27752i	0.579683	−	0.155326i
$216$	−11.4144	+	28.8799i	−0.776649	+	1.96503i
$217$	4.38575	−	7.59634i	0.297724	−	0.515673i
$218$	8.54967	+	14.8085i	0.579057	+	1.00296i
$219$	−12.7527	−	9.67579i	−0.861746	−	0.653830i
$220$			8.05564i			0.543111i
$221$	10.9702	−	4.79201i	0.737934	−	0.322346i
$222$	−9.80652	+	24.0439i	−0.658171	+	1.61372i
$223$	0.528782	−	1.97344i	0.0354099	−	0.132151i	−0.945958	−	0.324289i	$-0.894875\pi$
$223$	0.528782	−	1.97344i	0.0354099	−	0.132151i	0.981368	+	0.192137i	$0.0615418\pi$
$224$	−16.1437	+	9.32055i	−1.07864	+	0.622755i
$225$	−1.29195	−	4.62014i	−0.0861303	−	0.308009i
$226$	18.1314	+	18.1314i	1.20608	+	1.20608i
$227$	−5.70606	−	21.2953i	−0.378725	−	1.41342i	−0.847826	−	0.530275i	$-0.822089\pi$
$227$	−5.70606	−	21.2953i	−0.378725	−	1.41342i	0.469101	−	0.883144i	$-0.344578\pi$
$228$	5.87272	−	46.5621i	0.388930	−	3.08365i
$229$	6.20652	−	6.20652i	0.410138	−	0.410138i	−0.471649	−	0.881787i	$-0.656341\pi$
$229$	6.20652	−	6.20652i	0.410138	−	0.410138i	0.881787	+	0.471649i	$0.156341\pi$
$230$	17.6193	+	10.1725i	1.16179	+	0.670757i
$231$	1.08110	+	7.88053i	0.0711312	+	0.518501i
$232$	29.2981	+	7.85042i	1.92352	+	0.515405i
$233$	−13.9665			−0.914976			−0.457488	−	0.889216i	$-0.651251\pi$
$233$	−13.9665			−0.914976			−0.457488	+	0.889216i	$0.651251\pi$
$234$	−22.1444	−	15.9595i	−1.44763	−	1.04331i
$235$	4.14955			0.270687
$236$	−40.0367	−	10.7278i	−2.60617	−	0.698320i
$237$	2.41260	+	17.5863i	0.156715	+	1.14235i
$238$	−33.3233	−	19.2392i	−2.16003	−	1.24709i
$239$	2.09074	−	2.09074i	0.135239	−	0.135239i	−0.636247	−	0.771485i	$-0.719514\pi$
$239$	2.09074	−	2.09074i	0.135239	−	0.135239i	0.771485	+	0.636247i	$0.219514\pi$
$240$	−2.53608	+	20.1074i	−0.163703	+	1.29793i
$241$	1.16466	+	4.34657i	0.0750224	+	0.279987i	0.993238	−	0.116093i	$-0.0370369\pi$
$241$	1.16466	+	4.34657i	0.0750224	+	0.279987i	−0.918216	+	0.396080i	$0.870370\pi$
$242$	1.78441	+	1.78441i	0.114706	+	0.114706i
$243$	9.82222	+	12.1047i	0.630096	+	0.776518i
$244$	33.3816	−	19.2729i	2.13704	−	1.23382i
$245$	−6.72540	+	25.0995i	−0.429670	+	1.60355i
$246$	−1.57060	+	3.85084i	−0.100138	+	0.245521i
$247$	20.8224	+	8.16159i	1.32490	+	0.519310i
$248$		−	11.4146i		−	0.724831i
$249$	23.6377	+	17.9345i	1.49798	+	1.13655i
$250$	−15.3554	−	26.5963i	−0.971160	−	1.68210i
$251$	−10.0368	+	17.3842i	−0.633516	+	1.09728i	0.353312	+	0.935506i	$0.385056\pi$
$251$	−10.0368	+	17.3842i	−0.633516	+	1.09728i	−0.986828	+	0.161776i	$0.948278\pi$
$252$	0.654238	+	60.1789i	0.0412131	+	3.79091i
$253$	4.22278	−	1.13149i	0.265484	−	0.0711362i
$254$	36.6227	−	9.81303i	2.29791	−	0.615724i
$255$	−9.77575	+	4.11164i	−0.612181	+	0.257481i
$256$	15.5870	−	26.9975i	0.974187	−	1.68734i
$257$	−5.57681	−	9.65931i	−0.347872	−	0.602531i	0.638000	−	0.770037i	$-0.279762\pi$
$257$	−5.57681	−	9.65931i	−0.347872	−	0.602531i	−0.985871	+	0.167505i	$0.946429\pi$
$258$	12.6065	−	16.6153i	0.784846	−	1.03442i
$259$			27.2830i			1.69528i
$260$	−27.0419	−	10.5994i	−1.67707	−	0.657347i
$261$	10.6487	−	10.8828i	0.659139	−	0.673629i
$262$	1.62539	−	6.06604i	0.100417	−	0.374761i
$263$	2.36204	−	1.36372i	0.145650	−	0.0840908i	−0.425404	−	0.905003i	$-0.639868\pi$
$263$	2.36204	−	1.36372i	0.145650	−	0.0840908i	0.571054	+	0.820913i	$0.306535\pi$
$264$	6.34599	+	8.17783i	0.390569	+	0.503310i
$265$	−7.15591	−	7.15591i	−0.439584	−	0.439584i
$266$	−18.6056	−	69.4369i	−1.14078	−	4.25745i
$267$	−4.99493	−	0.629993i	−0.305685	−	0.0385550i
$268$	22.6191	−	22.6191i	1.38168	−	1.38168i
$269$	9.72820	+	5.61658i	0.593139	+	0.342449i	0.766338	−	0.642438i	$-0.222077\pi$
$269$	9.72820	+	5.61658i	0.593139	+	0.342449i	−0.173199	+	0.984887i	$0.555410\pi$
$270$	19.4221	+	14.4061i	1.18199	+	0.876727i
$271$	−0.175149	−	0.0469310i	−0.0106395	−	0.00285086i	0.253495	−	0.967337i	$-0.418420\pi$
$271$	−0.175149	−	0.0469310i	−0.0106395	−	0.00285086i	−0.264135	+	0.964486i	$0.585086\pi$
$272$	−21.0665			−1.27734
$273$	−27.8766	−	6.73985i	−1.68717	−	0.407914i
$274$	1.99163			0.120319
$275$	−1.54464	−	0.413884i	−0.0931452	−	0.0249582i
$276$	32.7696	−	4.49554i	1.97250	−	0.270600i
$277$	6.30495	+	3.64016i	0.378827	+	0.218716i	0.677308	−	0.735700i	$-0.263146\pi$
$277$	6.30495	+	3.64016i	0.378827	+	0.218716i	−0.298481	+	0.954416i	$0.596480\pi$
$278$	2.70711	−	2.70711i	0.162362	−	0.162362i
$279$	−4.99314	−	2.81087i	−0.298932	−	0.168282i
$280$	13.0999	+	48.8894i	0.782867	+	2.92170i
$281$	−3.70817	−	3.70817i	−0.221211	−	0.221211i	0.587798	−	0.809008i	$-0.299995\pi$
$281$	−3.70817	−	3.70817i	−0.221211	−	0.221211i	−0.809008	+	0.587798i	$0.799995\pi$
$282$	7.77000	−	6.02952i	0.462697	−	0.359052i
$283$	−6.24361	+	3.60475i	−0.371144	+	0.214280i	−0.673958	−	0.738769i	$-0.735407\pi$
$283$	−6.24361	+	3.60475i	−0.371144	+	0.214280i	0.302814	+	0.953050i	$0.402074\pi$
$284$	14.9102	−	55.6456i	0.884757	−	3.30196i
$285$	−18.3458	−	7.48249i	−1.08671	−	0.443225i
$286$	−8.33795	+	3.64219i	−0.493033	+	0.215367i
$287$			4.36962i			0.257931i
$288$	6.20291	+	10.4790i	0.365510	+	0.617481i
$289$	2.98814	+	5.17561i	0.175773	+	0.304448i
$290$	11.8097	−	20.4550i	0.693489	−	1.20116i
$291$	3.05043	+	7.25264i	0.178820	+	0.425157i
$292$	−38.9961	+	10.4490i	−2.28208	+	0.611480i
$293$	−6.56902	+	1.76016i	−0.383766	+	0.102830i	−0.445544	−	0.895260i	$-0.646990\pi$
$293$	−6.56902	+	1.76016i	−0.383766	+	0.102830i	0.0617778	+	0.998090i	$0.480323\pi$
$294$	23.8777	+	56.7710i	1.39257	+	3.31095i
$295$	−8.74932	+	15.1543i	−0.509405	+	0.882316i
$296$	17.7521	+	30.7476i	1.03182	+	1.78717i
$297$	5.13995	−	0.762147i	0.298250	−	0.0442243i
$298$		−	55.3512i		−	3.20641i
$299$	−1.75793	+	15.6642i	−0.101663	+	0.905885i
$300$	−11.2030	−	4.56925i	−0.646805	−	0.263806i
$301$	5.67167	−	21.1670i	0.326909	−	1.22004i
$302$	−22.8015	+	13.1645i	−1.31208	+	0.757529i
$303$	−10.9534	+	8.49979i	−0.629254	+	0.488300i
$304$	−27.8296	−	27.8296i	−1.59614	−	1.59614i
$305$	−4.21176	−	15.7185i	−0.241165	−	0.900039i
$306$	−12.3306	+	21.9037i	−0.704892	+	1.25215i
$307$	−9.62932	+	9.62932i	−0.549574	+	0.549574i	−0.926318	−	0.376743i	$-0.877044\pi$
$307$	−9.62932	+	9.62932i	−0.549574	+	0.549574i	0.376743	+	0.926318i	$0.377044\pi$
$308$	17.3732	+	10.0304i	0.989928	+	0.571535i
$309$	16.7101	−	2.29240i	0.950604	−	0.130410i
$310$	−8.58575	−	2.30055i	−0.487638	−	0.130662i
$311$	−10.8946			−0.617777			−0.308888	−	0.951098i	$-0.599957\pi$
$311$	−10.8946			−0.617777			−0.308888	+	0.951098i	$0.599957\pi$
$312$	−35.8020	+	10.5426i	−2.02689	+	0.596860i
$313$	−13.6872			−0.773644			−0.386822	−	0.922154i	$-0.626427\pi$
$313$	−13.6872			−0.773644			−0.386822	+	0.922154i	$0.626427\pi$
$314$	−11.8320	−	3.17038i	−0.667719	−	0.178915i
$315$	24.6117	+	6.30874i	1.38671	+	0.355457i
$316$	38.7703	+	22.3840i	2.18100	+	1.25920i
$317$	−20.8914	+	20.8914i	−1.17338	+	1.17338i	−0.191981	+	0.981399i	$0.561491\pi$
$317$	−20.8914	+	20.8914i	−1.17338	+	1.17338i	−0.981399	+	0.191981i	$0.938509\pi$
$318$	−23.7973	−	3.00147i	−1.33449	−	0.168314i
$319$	−1.31359	−	4.90239i	−0.0735470	−	0.274481i
$320$	−3.19045	−	3.19045i	−0.178351	−	0.178351i
$321$	15.5012	+	19.9758i	0.865191	+	1.11494i
$322$	43.8771	−	25.3325i	2.44518	−	1.41172i
$323$	5.33033	−	19.8931i	0.296588	−	1.10688i
$324$	39.3047	−	0.854709i	2.18360	−	0.0474838i
$325$	3.42176	−	4.64061i	0.189805	−	0.257415i
$326$		−	33.9536i		−	1.88051i
$327$	7.09388	−	9.34972i	0.392293	−	0.517041i
$328$	2.84317	+	4.92451i	0.156988	+	0.271911i
$329$	5.16678	−	8.94912i	0.284854	−	0.493381i
$330$	7.43011	−	3.12507i	0.409014	−	0.172030i
$331$	29.1362	−	7.80703i	1.60147	−	0.429113i	0.655985	−	0.754774i	$-0.272253\pi$
$331$	29.1362	−	7.80703i	1.60147	−	0.429113i	0.945487	+	0.325660i	$0.105587\pi$
$332$	72.2811	−	19.3677i	3.96694	−	1.06294i
$333$	17.8215	−	0.193747i	0.976612	−	0.0106173i
$334$	−22.9750	+	39.7938i	−1.25713	+	2.17742i
$335$	−6.75227	−	11.6953i	−0.368916	−	0.638981i
$336$	40.2068	+	30.5060i	2.19346	+	1.66424i
$337$			22.8436i			1.24437i	0.782870	+	0.622186i	$0.213755\pi$
$337$			22.8436i			1.24437i	−0.782870	+	0.622186i	$0.786245\pi$
$338$	−1.25562	−	32.7819i	−0.0682965	−	1.78310i
$339$	6.64651	−	16.2961i	0.360989	−	0.885081i
$340$	−6.92246	+	25.8350i	−0.375423	+	1.40110i
$341$	−1.65410	+	0.954993i	−0.0895743	+	0.0517158i
$342$	−45.2247	+	12.6464i	−2.44547	+	0.683840i
$343$	23.0253	+	23.0253i	1.24325	+	1.24325i
$344$	−7.38073	−	27.5453i	−0.397942	−	1.48514i
$345$	1.74739	−	13.8543i	0.0940764	−	0.745888i
$346$	10.3658	−	10.3658i	0.557269	−	0.557269i
$347$	29.3897	+	16.9681i	1.57772	+	0.910898i	0.995177	+	0.0980985i	$0.0312760\pi$
$347$	29.3897	+	16.9681i	1.57772	+	0.910898i	0.582544	+	0.812799i	$0.302057\pi$
$348$	−5.21905	−	38.0436i	−0.279771	−	2.03935i
$349$	12.8275	+	3.43711i	0.686638	+	0.183984i	0.585238	−	0.810862i	$-0.301001\pi$
$349$	12.8275	+	3.43711i	0.686638	+	0.183984i	0.101400	+	0.994846i	$0.467668\pi$
$350$	−18.5326			−0.990607
$351$	−4.20457	+	18.2571i	−0.224423	+	0.974492i
$352$	4.05908			0.216350
$353$	−15.8310	−	4.24190i	−0.842598	−	0.225773i	−0.188396	−	0.982093i	$-0.560329\pi$
$353$	−15.8310	−	4.24190i	−0.842598	−	0.225773i	−0.654202	+	0.756320i	$0.726995\pi$
$354$	5.63691	+	41.0894i	0.299598	+	2.18388i
$355$	−21.0624	−	12.1604i	−1.11788	−	0.645406i
$356$	−8.97813	+	8.97813i	−0.475840	+	0.475840i
$357$	−3.30482	+	26.2024i	−0.174910	+	1.38678i
$358$	−2.93840	−	10.9662i	−0.155299	−	0.579584i
$359$	−26.7768	−	26.7768i	−1.41322	−	1.41322i	−0.733066	−	0.680158i	$-0.761911\pi$
$359$	−26.7768	−	26.7768i	−1.41322	−	1.41322i	−0.680158	−	0.733066i	$-0.738089\pi$
$360$	31.8420	−	8.90414i	1.67822	−	0.469289i
$361$	16.8666	−	9.73792i	0.887714	−	0.512522i
$362$	−6.48673	+	24.2088i	−0.340935	+	1.27239i
$363$	0.654119	−	1.60379i	0.0343324	−	0.0841769i
$364$	−56.5302	+	45.1222i	−2.96299	+	2.36504i
$365$			17.0439i			0.892116i
$366$	−30.7263	−	23.3128i	−1.60609	−	1.21858i
$367$	−13.2888	−	23.0170i	−0.693672	−	1.20148i	−0.970626	−	0.240592i	$-0.922658\pi$
$367$	−13.2888	−	23.0170i	−0.693672	−	1.20148i	0.276954	−	0.960883i	$-0.410675\pi$
$368$	13.8692	−	24.0222i	0.722984	−	1.25224i
$369$	2.85428	−	0.0310304i	0.148588	−	0.00161538i
$370$	26.7053	−	7.15565i	1.38834	−	0.372005i
$371$	−24.3429	+	6.52266i	−1.26382	+	0.338640i
$372$	−13.3207	+	5.60262i	−0.690644	+	0.290482i
$373$	8.30214	−	14.3797i	0.429869	−	0.744554i	−0.566993	−	0.823723i	$-0.691893\pi$
$373$	8.30214	−	14.3797i	0.429869	−	0.744554i	0.996861	+	0.0791687i	$0.0252266\pi$
$374$	4.18932	+	7.25611i	0.216624	+	0.375205i
$375$	−12.7408	+	16.7923i	−0.657930	+	0.867151i
$376$		−	13.4474i		−	0.693497i
$377$	18.1852	+	2.04085i	0.936585	+	0.105109i
$378$	55.2521	−	23.9490i	2.84186	−	1.23180i
$379$	8.33055	−	31.0900i	0.427912	−	1.59699i	−0.329569	−	0.944131i	$-0.606904\pi$
$379$	8.33055	−	31.0900i	0.427912	−	1.59699i	0.757481	−	0.652857i	$-0.226430\pi$
$380$	−43.2738	+	24.9841i	−2.21990	+	1.28166i
$381$	−15.9538	−	20.5591i	−0.817339	−	1.05327i
$382$	20.6886	+	20.6886i	1.05852	+	1.05852i
$383$	7.45412	+	27.8192i	0.380888	+	1.42149i	0.844548	+	0.535480i	$0.179869\pi$
$383$	7.45412	+	27.8192i	0.380888	+	1.42149i	−0.463660	+	0.886013i	$0.653464\pi$
$384$	−24.5605	−	3.09774i	−1.25335	−	0.158081i
$385$	5.98858	−	5.98858i	0.305206	−	0.305206i
$386$	37.9881	+	21.9324i	1.93354	+	1.11633i
$387$	−13.8667	−	3.55447i	−0.704885	−	0.180684i
$388$	19.1670	+	5.13579i	0.973058	+	0.260730i
$389$	10.0690			0.510517			0.255258	−	0.966873i	$-0.417839\pi$
$389$	10.0690			0.510517			0.255258	+	0.966873i	$0.417839\pi$
$390$	0.714211	+	29.0540i	0.0361655	+	1.47121i
$391$	14.5151			0.734058
$392$	81.3397	+	21.7949i	4.10828	+	1.10081i
$393$	−4.27035	+	0.585834i	−0.215411	+	0.0295514i
$394$	32.3180	+	18.6588i	1.62816	+	0.940017i
$395$	13.3642	−	13.3642i	0.672427	−	0.672427i
$396$	6.42858	−	11.4195i	0.323048	−	0.573854i
$397$	−1.56584	−	5.84378i	−0.0785870	−	0.293291i	0.915436	−	0.402464i	$-0.131846\pi$
$397$	−1.56584	−	5.84378i	−0.0785870	−	0.293291i	−0.994023	+	0.109174i	$0.965180\pi$
$398$	−1.88818	−	1.88818i	−0.0946460	−	0.0946460i
$399$	−38.9801	+	30.2485i	−1.95145	+	1.51432i
$400$	−8.78701	+	5.07318i	−0.439351	+	0.253659i
$401$	−2.25815	+	8.42752i	−0.112767	+	0.420850i	−0.999110	−	0.0421777i	$-0.986570\pi$
$401$	−2.25815	+	8.42752i	−0.112767	+	0.420850i	0.886344	+	0.463028i	$0.153237\pi$
$402$	−29.6374	−	12.0879i	−1.47818	−	0.602890i
$403$	−1.02940	−	6.80918i	−0.0512778	−	0.339190i
$404$			34.9660i			1.73963i
$405$	3.94615	−	16.1214i	0.196086	−	0.801077i
$406$	−29.4094	−	50.9387i	−1.45957	−	2.52804i
$407$	2.97043	−	5.14493i	0.147239	−	0.255025i
$408$	13.3245	+	31.6801i	0.659663	+	1.56840i
$409$	1.05361	−	0.282313i	0.0520975	−	0.0139595i	−0.232676	−	0.972554i	$-0.574748\pi$
$409$	1.05361	−	0.282313i	0.0520975	−	0.0139595i	0.284774	+	0.958595i	$0.408082\pi$
$410$	4.27709	−	1.14604i	0.211231	−	0.0565991i
$411$	−0.529974	−	1.26005i	−0.0261417	−	0.0621539i
$412$	21.2687	−	36.8386i	1.04784	−	1.81491i
$413$	21.7883	+	37.7384i	1.07213	+	1.85698i
$414$	−16.8590	−	28.4810i	−0.828573	−	1.39977i
$415$		−	31.5916i		−	1.55077i
$416$	−5.34083	+	13.6259i	−0.261856	+	0.668066i
$417$	−2.43309	−	0.992360i	−0.119149	−	0.0485961i
$418$	−4.05135	+	15.1198i	−0.198158	+	0.739535i
$419$	25.4466	−	14.6916i	1.24315	−	0.717731i	0.273413	−	0.961897i	$-0.411848\pi$
$419$	25.4466	−	14.6916i	1.24315	−	0.717731i	0.969733	+	0.244166i	$0.0785142\pi$
$420$	50.6232	−	39.2836i	2.47016	−	1.91684i
$421$	−9.24525	−	9.24525i	−0.450586	−	0.450586i	0.444963	−	0.895549i	$-0.353217\pi$
$421$	−9.24525	−	9.24525i	−0.450586	−	0.450586i	−0.895549	+	0.444963i	$0.853217\pi$
$422$	9.20112	+	34.3390i	0.447903	+	1.67160i
$423$	−5.88234	−	3.31143i	−0.286009	−	0.161007i
$424$	−23.1901	+	23.1901i	−1.12621	+	1.12621i
$425$	−4.59809	−	2.65471i	−0.223040	−	0.128772i
$426$	−57.1088	+	7.83454i	−2.76693	+	0.379585i
$427$	−39.1435	−	10.4885i	−1.89429	−	0.507572i
$428$	63.7680			3.08234
$429$	4.52307	+	4.30603i	0.218376	+	0.207897i
$430$	−22.2063			−1.07088
$431$	−15.8196	−	4.23885i	−0.762004	−	0.204178i	−0.143168	−	0.989698i	$-0.545729\pi$
$431$	−15.8196	−	4.23885i	−0.762004	−	0.204178i	−0.618836	+	0.785520i	$0.712395\pi$
$432$	19.6413	−	26.4801i	0.944991	−	1.27402i
$433$	−1.59881	−	0.923072i	−0.0768338	−	0.0443600i	0.461091	−	0.887353i	$-0.347458\pi$
$433$	−1.59881	−	0.923072i	−0.0768338	−	0.0443600i	−0.537925	+	0.842993i	$0.680792\pi$
$434$	−15.6519	+	15.6519i	−0.751317	+	0.751317i
$435$	−16.0840	−	2.02861i	−0.771167	−	0.0972646i
$436$	−7.66075	−	28.5903i	−0.366884	−	1.36923i
$437$	19.1749	+	19.1749i	0.917261	+	0.917261i
$438$	24.7656	+	31.9145i	1.18335	+	1.52493i
$439$	−30.1963	+	17.4338i	−1.44119	+	0.832071i	−0.997929	−	0.0643219i	$-0.979512\pi$
$439$	−30.1963	+	17.4338i	−1.44119	+	0.832071i	−0.443260	+	0.896393i	$0.646178\pi$
$440$	2.85249	−	10.6456i	0.135987	−	0.507510i
$441$	29.5638	−	30.2136i	1.40780	−	1.43875i
$442$	−29.8702	+	4.51570i	−1.42078	+	0.214790i
$443$		−	2.00024i		−	0.0950340i	−0.998870	−	0.0475170i	$-0.984869\pi$
$443$		−	2.00024i		−	0.0950340i	0.998870	−	0.0475170i	$-0.0151308\pi$
$444$	27.1686	−	35.8082i	1.28937	−	1.69938i
$445$	2.68016	+	4.64218i	0.127052	+	0.220060i
$446$	−2.57786	+	4.46499i	−0.122065	+	0.211423i
$447$	−35.0193	+	14.7290i	−1.65636	+	0.696658i
$448$	−10.8532	+	2.90811i	−0.512767	+	0.137395i
$449$	8.39243	−	2.24874i	0.396063	−	0.106125i	−0.0552897	−	0.998470i	$-0.517608\pi$
$449$	8.39243	−	2.24874i	0.396063	−	0.106125i	0.451353	+	0.892346i	$0.350942\pi$
$450$	0.131607	+	12.1056i	0.00620402	+	0.570665i
$451$	0.475741	−	0.824007i	0.0224018	−	0.0388010i
$452$	−22.1928	−	38.4390i	−1.04386	−	1.80802i
$453$	14.3963	+	10.9229i	0.676399	+	0.513202i
$454$			55.6352i			2.61109i
$455$	12.2234	+	27.9826i	0.573043	+	1.31185i
$456$	−24.2484	+	59.4528i	−1.13554	+	2.78413i
$457$	9.88679	−	36.8980i	0.462484	−	1.72602i	−0.202613	−	0.979259i	$-0.564943\pi$
$457$	9.88679	−	36.8980i	0.462484	−	1.72602i	0.665097	−	0.746757i	$-0.268390\pi$
$458$	−19.1824	+	11.0750i	−0.896334	+	0.517499i
$459$	17.1391	+	1.97266i	0.799985	+	0.0920761i
$460$	−24.9023	−	24.9023i	−1.16108	−	1.16108i
$461$	8.09779	+	30.2214i	0.377152	+	1.40755i	0.850175	+	0.526500i	$0.176496\pi$
$461$	8.09779	+	30.2214i	0.377152	+	1.40755i	−0.473023	+	0.881050i	$0.656837\pi$
$462$	2.51185	−	19.9153i	0.116862	−	0.926542i
$463$	−25.8083	+	25.8083i	−1.19941	+	1.19941i	−0.225071	+	0.974342i	$0.572262\pi$
$463$	−25.8083	+	25.8083i	−1.19941	+	1.19941i	−0.974342	+	0.225071i	$0.927738\pi$
$464$	−27.8883	−	16.1013i	−1.29468	−	0.747486i
$465$	0.829179	+	6.04418i	0.0384522	+	0.280292i
$466$	34.0440	+	9.12206i	1.57706	+	0.422571i
$467$	−0.771377			−0.0356950			−0.0178475	−	0.999841i	$-0.505681\pi$
$467$	−0.771377			−0.0356950			−0.0178475	+	0.999841i	$0.505681\pi$
$468$	29.8756	+	36.6056i	1.38100	+	1.69209i
$469$	−33.6301			−1.55289
$470$	−10.1147	−	2.71024i	−0.466558	−	0.125014i
$471$	1.14269	+	8.32947i	0.0526523	+	0.383802i
$472$	49.1102	+	28.3538i	2.26048	+	1.30509i
$473$	−3.37408	+	3.37408i	−0.155141	+	0.155141i
$474$	5.60548	−	44.4433i	0.257468	−	2.04135i
$475$	−2.56728	−	9.58122i	−0.117795	−	0.439616i
$476$	47.0975	+	47.0975i	2.15871	+	2.15871i
$477$	4.43353	+	15.8547i	0.202997	+	0.725936i
$478$	−6.46181	+	3.73073i	−0.295556	+	0.170640i
$479$	6.81853	−	25.4471i	0.311546	−	1.16271i	−0.615616	−	0.788047i	$-0.711093\pi$
$479$	6.81853	−	25.4471i	0.311546	−	1.16271i	0.927162	−	0.374661i	$-0.122241\pi$
$480$	4.89644	−	12.0052i	0.223491	−	0.547960i
$481$	13.3626	+	16.7410i	0.609281	+	0.763322i
$482$		−	11.3557i		−	0.517236i
$483$	−27.7030	−	21.0190i	−1.26053	−	0.956398i
$484$	−2.18411	−	3.78299i	−0.0992779	−	0.171954i
$485$	4.18862	−	7.25490i	0.190195	−	0.329428i
$486$	−16.0361	−	35.9211i	−0.727411	−	1.62941i
$487$	−22.8416	+	6.12038i	−1.03505	+	0.277341i	−0.736061	−	0.676916i	$-0.763316\pi$
$487$	−22.8416	+	6.12038i	−1.03505	+	0.277341i	−0.298989	+	0.954256i	$0.596650\pi$
$488$	−50.9387	+	13.6490i	−2.30589	+	0.617861i
$489$	−21.4816	+	9.03508i	−0.971432	+	0.408581i
$490$	32.7870	−	56.7887i	1.48116	−	2.56545i
$491$	6.00725	+	10.4049i	0.271104	+	0.469565i	0.969145	−	0.246493i	$-0.0792781\pi$
$491$	6.00725	+	10.4049i	0.271104	+	0.469565i	−0.698041	+	0.716058i	$0.745945\pi$
$492$	4.35130	−	5.73501i	0.196172	−	0.258554i
$493$		−	16.8511i		−	0.758935i
$494$	−45.4250	−	33.4942i	−2.04377	−	1.50698i
$495$	−3.95432	−	3.86927i	−0.177733	−	0.173911i
$496$	−3.13656	+	11.7058i	−0.140836	+	0.525607i
$497$	−52.4513	+	30.2828i	−2.35276	+	1.35837i
$498$	−45.9042	−	59.1549i	−2.05701	−	2.65079i
$499$	−10.2778	−	10.2778i	−0.460096	−	0.460096i	0.438591	−	0.898687i	$-0.355478\pi$
$499$	−10.2778	−	10.2778i	−0.460096	−	0.460096i	−0.898687	+	0.438591i	$0.855478\pi$
$500$	13.7589	+	51.3488i	0.615316	+	2.29639i
$501$	31.2902	+	3.94653i	1.39795	+	0.176318i
$502$	35.8194	−	35.8194i	1.59870	−	1.59870i
$503$	−28.1875	−	16.2741i	−1.25682	−	0.725626i	−0.284365	−	0.958716i	$-0.591783\pi$
$503$	−28.1875	−	16.2741i	−1.25682	−	0.725626i	−0.972455	+	0.233090i	$0.925116\pi$
$504$	20.4446	−	79.7588i	0.910677	−	3.55274i
$505$	14.2587	+	3.82061i	0.634505	+	0.170015i
$506$	−11.0322			−0.490443
$507$	−20.4062	+	9.51770i	−0.906272	+	0.422696i
$508$	−65.6300			−2.91186
$509$	6.56229	+	1.75836i	0.290868	+	0.0779379i	0.401303	−	0.915946i	$-0.368558\pi$
$509$	6.56229	+	1.75836i	0.290868	+	0.0779379i	−0.110434	+	0.993883i	$0.535224\pi$
$510$	26.5143	−	3.63740i	1.17407	−	0.161067i
$511$	36.7576	+	21.2220i	1.62606	+	0.938806i
$512$	−35.4147	+	35.4147i	−1.56512	+	1.56512i
$513$	20.0354	+	25.2474i	0.884586	+	1.11470i
$514$	7.28486	+	27.1875i	0.321321	+	1.19919i
$515$	−12.6983	−	12.6983i	−0.559556	−	0.559556i
$516$	−28.5221	+	22.1331i	−1.25562	+	0.974357i
$517$	−1.94866	+	1.12506i	−0.0857021	+	0.0494801i
$518$	17.8196	−	66.5036i	0.782948	−	2.92200i
$519$	−9.31655	−	3.79985i	−0.408951	−	0.166795i
$520$	31.9830	+	23.5827i	1.40255	+	1.03417i
$521$			15.3797i			0.673797i	0.941541	+	0.336898i	$0.109378\pi$
$521$			15.3797i			0.673797i	−0.941541	+	0.336898i	$0.890622\pi$
$522$	−33.0647	+	19.5722i	−1.44720	+	0.856654i
$523$	−9.05112	−	15.6770i	−0.395778	−	0.685507i	0.597422	−	0.801927i	$-0.296192\pi$
$523$	−9.05112	−	15.6770i	−0.395778	−	0.685507i	−0.993200	+	0.116420i	$0.962858\pi$
$524$	−5.43534	+	9.41429i	−0.237444	+	0.411265i
$525$	4.93154	+	11.7251i	0.215230	+	0.511726i
$526$	−6.64828	+	1.78140i	−0.289879	+	0.0776728i
$527$	−6.12545	+	1.64131i	−0.266829	+	0.0714966i
$528$	−4.26073	−	10.1302i	−0.185424	−	0.440861i
$529$	1.94393	−	3.36699i	0.0845188	−	0.146391i
$530$	12.7691	+	22.1167i	0.554653	+	0.960687i
$531$	24.4963	−	14.5003i	1.06305	−	0.629259i
$532$			124.435i			5.39494i
$533$	2.14014	+	2.68122i	0.0926997	+	0.116136i
$534$	11.7639	+	4.79802i	0.509074	+	0.207631i
$535$	6.96769	−	26.0038i	0.301240	−	1.12424i
$536$	−37.9007	+	21.8820i	−1.63706	+	0.945159i
$537$	−6.15617	+	4.77718i	−0.265658	+	0.206151i
$538$	−20.0445	−	20.0445i	−0.864181	−	0.864181i
$539$	−3.64689	−	13.6104i	−0.157083	−	0.586241i
$540$	−26.0199	−	32.7885i	−1.11972	−	1.41099i
$541$	15.8035	−	15.8035i	0.679445	−	0.679445i	−0.280430	−	0.959875i	$-0.590477\pi$
$541$	15.8035	−	15.8035i	0.679445	−	0.679445i	0.959875	+	0.280430i	$0.0904770\pi$
$542$	0.396281	+	0.228793i	0.0170217	+	0.00982751i
$543$	17.0425	−	2.33799i	0.731362	−	0.100333i
$544$	13.0177	+	3.48809i	0.558131	+	0.149551i
$545$	−12.4958			−0.535263
$546$	63.5484	+	34.6360i	2.71962	+	1.48228i
$547$	−6.57234			−0.281013			−0.140507	−	0.990080i	$-0.544873\pi$
$547$	−6.57234			−0.281013			−0.140507	+	0.990080i	$0.544873\pi$
$548$	−3.33002	−	0.892277i	−0.142252	−	0.0381162i
$549$	−6.57318	+	25.6433i	−0.280537	+	1.09443i
$550$	3.49480	+	2.01773i	0.149019	+	0.0860361i
$551$	22.2609	−	22.2609i	0.948347	−	0.948347i
$552$	−44.8973	−	5.66275i	−1.91096	−	0.241022i
$553$	−12.1816	−	45.4622i	−0.518013	−	1.93325i
$554$	−12.9911	−	12.9911i	−0.551938	−	0.551938i
$555$	−11.6335	−	14.9917i	−0.493815	−	0.636360i
$556$	−5.73915	+	3.31350i	−0.243394	+	0.140524i
$557$	4.67168	−	17.4349i	0.197945	−	0.738742i	−0.793539	−	0.608519i	$-0.791764\pi$
$557$	4.67168	−	17.4349i	0.197945	−	0.738742i	0.991485	−	0.130223i	$-0.0415693\pi$
$558$	10.3351	+	10.1128i	0.437521	+	0.428110i
$559$	−6.88692	−	15.7660i	−0.291286	−	0.666830i
$560$		−	53.7361i		−	2.27077i
$561$	3.47599	−	4.58134i	0.146756	−	0.193424i
$562$	6.61688	+	11.4608i	0.279116	+	0.483444i
$563$	0.961203	−	1.66485i	0.0405099	−	0.0701651i	−0.845060	−	0.534672i	$-0.820435\pi$
$563$	0.961203	−	1.66485i	0.0405099	−	0.0701651i	0.885569	+	0.464507i	$0.153768\pi$
$564$	−15.6929	+	6.60035i	−0.660788	+	0.277925i
$565$	−18.0999	+	4.84985i	−0.761467	+	0.204035i
$566$	17.5735	−	4.70880i	0.738669	−	0.197926i
$567$	−29.8546	−	28.5838i	−1.25378	−	1.20041i
$568$	−39.4080	+	68.2566i	−1.65352	+	2.86398i
$569$	2.16631	+	3.75217i	0.0908166	+	0.157299i	0.907855	−	0.419284i	$-0.137719\pi$
$569$	2.16631	+	3.75217i	0.0908166	+	0.157299i	−0.817038	+	0.576583i	$0.804386\pi$
$570$	39.8315	+	30.2212i	1.66836	+	1.26583i
$571$			9.90225i			0.414396i	0.978299	+	0.207198i	$0.0664345\pi$
$571$			9.90225i			0.414396i	−0.978299	+	0.207198i	$0.933566\pi$
$572$	15.5729	−	2.35427i	0.651136	−	0.0984371i
$573$	7.58393	−	18.5945i	0.316823	−	0.776795i
$574$	2.85397	−	10.6512i	0.119122	−	0.444571i
$575$	6.05436	−	3.49549i	0.252484	−	0.145772i
$576$	1.97668	+	7.06877i	0.0823616	+	0.294532i
$577$	19.9280	+	19.9280i	0.829616	+	0.829616i	0.987463	−	0.157848i	$-0.0504556\pi$
$577$	19.9280	+	19.9280i	0.829616	+	0.829616i	−0.157848	+	0.987463i	$0.550456\pi$
$578$	−3.90334	−	14.5675i	−0.162358	−	0.605927i
$579$	3.76745	−	29.8704i	0.156570	−	1.24137i
$580$	−28.9101	+	28.9101i	−1.20043	+	1.20043i
$581$	−68.1318	−	39.3359i	−2.82658	−	1.63193i
$582$	−2.69859	−	19.6710i	−0.111860	−	0.815390i
$583$	5.30064	+	1.42030i	0.219530	+	0.0588230i
$584$	55.2338			2.28559
$585$	18.1917	−	8.18316i	0.752134	−	0.338332i
$586$	17.1619			0.708952
$587$	19.3434	+	5.18305i	0.798389	+	0.213928i	0.634876	−	0.772614i	$-0.281051\pi$
$587$	19.3434	+	5.18305i	0.798389	+	0.213928i	0.163512	+	0.986541i	$0.447718\pi$
$588$	−14.4895	−	105.619i	−0.597538	−	4.35567i
$589$	−10.2602	−	5.92372i	−0.422763	−	0.244082i
$590$	31.2247	−	31.2247i	1.28550	−	1.28550i
$591$	3.20512	−	25.4120i	0.131841	−	1.04531i
$592$	−9.75602	−	36.4100i	−0.400970	−	1.49644i
$593$	5.90204	+	5.90204i	0.242368	+	0.242368i	0.817829	−	0.575461i	$-0.195177\pi$
$593$	5.90204	+	5.90204i	0.242368	+	0.242368i	−0.575461	+	0.817829i	$0.695177\pi$
$594$	−13.0267	−	1.49933i	−0.534491	−	0.0615184i
$595$	24.3519	−	14.0596i	0.998332	−	0.576387i
$596$	−24.7981	+	92.5478i	−1.01577	+	3.79091i
$597$	−0.692160	+	1.69706i	−0.0283282	+	0.0694558i
$598$	14.5159	−	37.0341i	0.593600	−	1.51444i
$599$		−	10.8532i		−	0.443449i	−0.975109	−	0.221725i	$-0.928831\pi$
$599$		−	10.8532i		−	0.443449i	0.975109	−	0.221725i	$-0.0711686\pi$
$600$	13.1869	+	10.0053i	0.538354	+	0.408464i
$601$	17.9121	+	31.0247i	0.730650	+	1.26552i	0.956606	+	0.291385i	$0.0941161\pi$
$601$	17.9121	+	31.0247i	0.730650	+	1.26552i	−0.225956	+	0.974138i	$0.572551\pi$
$602$	−27.6499	+	47.8911i	−1.12693	+	1.95189i
$603$	0.238821	+	21.9675i	0.00972554	+	0.894585i
$604$	44.0223	−	11.7957i	1.79124	−	0.479961i
$605$	−1.78131	+	0.477300i	−0.0724205	+	0.0194050i
$606$	32.2509	−	13.5646i	1.31010	−	0.551024i
$607$	7.04883	−	12.2089i	0.286103	−	0.495545i	−0.686773	−	0.726872i	$-0.740973\pi$
$607$	7.04883	−	12.2089i	0.286103	−	0.495545i	0.972876	+	0.231327i	$0.0743067\pi$
$608$	12.5890	+	21.8048i	0.510552	+	0.884303i
$609$	−24.4018	+	32.1615i	−0.988810	+	1.30325i
$610$			41.0654i			1.66269i
$611$	−1.21271	−	8.02178i	−0.0490611	−	0.324527i
$612$	30.4300	−	31.0989i	1.23006	−	1.25710i
$613$	1.83980	−	6.86625i	0.0743090	−	0.277325i	−0.918767	−	0.394801i	$-0.870814\pi$
$613$	1.83980	−	6.86625i	0.0743090	−	0.277325i	0.993076	+	0.117476i	$0.0374803\pi$
$614$	29.7612	−	17.1826i	1.20106	−	0.693435i
$615$	−1.86321	−	2.40105i	−0.0751320	−	0.0968197i
$616$	−19.4071	−	19.4071i	−0.781935	−	0.781935i
$617$	3.21245	+	11.9890i	0.129328	+	0.482660i	0.999957	−	0.00928080i	$-0.00295421\pi$
$617$	3.21245	+	11.9890i	0.129328	+	0.482660i	−0.870629	+	0.491941i	$0.836288\pi$
$618$	−42.2289	−	5.32619i	−1.69869	−	0.214251i
$619$	−19.7322	+	19.7322i	−0.793105	+	0.793105i	−0.981998	−	0.188893i	$-0.939510\pi$
$619$	−19.7322	+	19.7322i	−0.793105	+	0.793105i	0.188893	+	0.981998i	$0.439510\pi$
$620$	13.3248	+	7.69308i	0.535137	+	0.308962i
$621$	−13.5331	+	18.2451i	−0.543063	+	0.732151i
$622$	26.5561	+	7.11569i	1.06480	+	0.285313i
$623$	13.3487			0.534805
$624$	39.6122	−	0.973755i	1.58576	−	0.0389814i
$625$	14.4472			0.577886
$626$	33.3631	+	8.93961i	1.33346	+	0.357299i
$627$	10.6440	−	1.46021i	0.425081	−	0.0583153i
$628$	18.3629	+	10.6018i	0.732759	+	0.423059i
$629$	13.9475	−	13.9475i	0.556125	−	0.556125i
$630$	−55.8717	−	31.4527i	−2.22598	−	1.25311i
$631$	5.39854	+	20.1476i	0.214913	+	0.802065i	0.986197	+	0.165574i	$0.0529478\pi$
$631$	5.39854	+	20.1476i	0.214913	+	0.802065i	−0.771285	+	0.636490i	$0.780386\pi$
$632$	−43.3092	−	43.3092i	−1.72275	−	1.72275i
$633$	19.2771	−	14.9590i	0.766194	−	0.594566i
$634$	64.5688	−	37.2788i	2.56436	−	1.48053i
$635$	−7.17115	+	26.7631i	−0.284579	+	1.06206i
$636$	38.4447	+	15.6800i	1.52443	+	0.621754i
$637$	50.4871	+	5.66595i	2.00037	+	0.224493i
$638$			12.8078i			0.507064i
$639$	20.1534	+	34.0466i	0.797258	+	1.34686i
$640$	13.1786	+	22.8260i	0.520930	+	0.902277i
$641$	8.19394	−	14.1923i	0.323641	−	0.560563i	−0.657595	−	0.753371i	$-0.728426\pi$
$641$	8.19394	−	14.1923i	0.323641	−	0.560563i	0.981236	+	0.192809i	$0.0617596\pi$
$642$	−24.7379	−	58.8163i	−0.976327	−	2.32129i
$643$	−0.0796534	+	0.0213431i	−0.00314122	+	0.000841688i	−0.260389	−	0.965504i	$-0.583851\pi$
$643$	−0.0796534	+	0.0213431i	−0.00314122	+	0.000841688i	0.257248	+	0.966345i	$0.417184\pi$
$644$	−84.7124	+	22.6986i	−3.33814	+	0.894451i
$645$	5.90911	+	14.0494i	0.232671	+	0.553193i
$646$	−25.9859	+	45.0088i	−1.02240	+	1.77085i
$647$	14.0944	+	24.4123i	0.554110	+	0.959746i	0.997972	+	0.0636514i	$0.0202746\pi$
$647$	14.0944	+	24.4123i	0.554110	+	0.959746i	−0.443862	+	0.896095i	$0.646392\pi$
$648$	−52.2443	−	12.7882i	−2.05235	−	0.502369i
$649$		−	9.48875i		−	0.372466i
$650$	−11.3717	+	9.07682i	−0.446033	+	0.356022i
$651$	14.0676	+	5.73761i	0.551353	+	0.224875i
$652$	−15.2117	+	56.7708i	−0.595736	+	2.22332i
$653$	10.2130	−	5.89647i	0.399665	−	0.230747i	−0.286675	−	0.958028i	$-0.592550\pi$
$653$	10.2130	−	5.89647i	0.399665	−	0.230747i	0.686339	+	0.727281i	$0.259217\pi$
$654$	−23.3983	+	18.1571i	−0.914948	+	0.709999i
$655$	3.24513	+	3.24513i	0.126798	+	0.126798i
$656$	−1.56252	−	5.83139i	−0.0610060	−	0.227677i
$657$	13.6014	−	24.1611i	0.530640	−	0.942613i
$658$	−18.4393	+	18.4393i	−0.718838	+	0.718838i
$659$	20.0800	+	11.5932i	0.782206	+	0.451607i	0.837212	−	0.546879i	$-0.184184\pi$
$659$	20.0800	+	11.5932i	0.782206	+	0.451607i	−0.0550054	+	0.998486i	$0.517518\pi$
$660$	−13.8233	+	1.89637i	−0.538072	+	0.0738161i
$661$	−1.67451	−	0.448684i	−0.0651310	−	0.0174518i	0.226106	−	0.974103i	$-0.427400\pi$
$661$	−1.67451	−	0.448684i	−0.0651310	−	0.0174518i	−0.291237	+	0.956651i	$0.594067\pi$
$662$	−76.1200			−2.95849
$663$	10.8055	+	17.6965i	0.419650	+	0.687276i
$664$	−102.378			−3.97305
$665$	50.7430	+	13.5966i	1.96773	+	0.527252i
$666$	−43.5673	−	11.1676i	−1.68820	−	0.432737i
$667$	19.2154	+	11.0940i	0.744023	+	0.429562i
$668$	56.2426	−	56.2426i	2.17609	−	2.17609i
$669$	3.51086	+	0.442814i	0.135738	+	0.0171202i
$670$	8.82034	+	32.9180i	0.340760	+	1.27173i
$671$	6.23961	+	6.23961i	0.240877	+	0.240877i
$672$	−19.7942	−	25.5080i	−0.763579	−	0.983994i
$673$	−3.30738	+	1.90952i	−0.127490	+	0.0736065i	−0.562389	−	0.826873i	$-0.690118\pi$
$673$	−3.30738	+	1.90952i	−0.127490	+	0.0736065i	0.434899	+	0.900479i	$0.356784\pi$
$674$	14.9201	−	55.6824i	0.574699	−	2.14481i
$675$	7.62393	−	3.30459i	0.293445	−	0.127194i
$676$	−12.5874	+	55.3743i	−0.484129	+	2.12978i
$677$		−	37.3248i		−	1.43451i	−0.696811	−	0.717255i	$-0.745398\pi$
$677$		−	37.3248i		−	1.43451i	0.696811	−	0.717255i	$-0.254602\pi$
$678$	−26.8448	+	35.3813i	−1.03097	+	1.35881i
$679$	−10.4308	−	18.0667i	−0.400299	−	0.693338i
$680$	18.2962	−	31.6900i	0.701628	−	1.21526i
$681$	35.1990	−	14.8046i	1.34883	−	0.567313i
$682$	4.65568	−	1.24749i	0.178275	−	0.0477687i
$683$	−44.7361	+	11.9870i	−1.71178	+	0.458669i	−0.975859	−	0.218401i	$-0.929916\pi$
$683$	−44.7361	+	11.9870i	−1.71178	+	0.458669i	−0.735919	+	0.677070i	$0.763249\pi$
$684$	81.2820	−	0.883663i	3.10790	−	0.0337877i
$685$	−0.727719	+	1.26045i	−0.0278047	+	0.0481592i
$686$	−41.0866	−	71.1640i	−1.56869	−	2.71706i
$687$	12.1113	+	9.18918i	0.462076	+	0.350589i
$688$			30.2760i			1.15426i
$689$	−11.7423	+	15.9249i	−0.447344	+	0.606691i
$690$	−13.3081	+	32.6291i	−0.506631	+	1.24217i
$691$	−1.74904	+	6.52751i	−0.0665367	+	0.248318i	−0.991181	−	0.132513i	$-0.957695\pi$
$691$	−1.74904	+	6.52751i	−0.0665367	+	0.248318i	0.924645	+	0.380831i	$0.124362\pi$
$692$	−21.9758	+	12.6877i	−0.835394	+	0.482315i
$693$	−13.2683	+	3.71029i	−0.504022	+	0.140942i
$694$	−60.5562	−	60.5562i	−2.29868	−	2.29868i
$695$	0.724108	+	2.70241i	0.0274670	+	0.102508i
$696$	−6.57410	+	52.1231i	−0.249191	+	1.97572i
$697$	2.23383	−	2.23383i	0.0846122	−	0.0846122i
$698$	−29.0226	−	16.7562i	−1.09852	−	0.634232i
$699$	−3.28784	−	23.9662i	−0.124357	−	0.906486i
$700$	30.9867	+	8.30286i	1.17119	+	0.313819i
$701$	31.6077			1.19381			0.596903	−	0.802313i	$-0.296398\pi$
$701$	31.6077			1.19381			0.596903	+	0.802313i	$0.296398\pi$
$702$	22.1732	−	41.7564i	0.836875	−	1.57599i
$703$	36.8504			1.38984
$704$	2.36328	+	0.633239i	0.0890695	+	0.0238661i
$705$	0.976841	+	7.12055i	0.0367900	+	0.268175i
$706$	35.8182	+	20.6796i	1.34804	+	0.778289i
$707$	25.9938	−	25.9938i	0.977598	−	0.977598i
$708$	8.98368	−	71.2275i	0.337627	−	2.67689i
$709$	−1.41646	−	5.28629i	−0.0531961	−	0.198531i	0.934214	−	0.356714i	$-0.116103\pi$
$709$	−1.41646	−	5.28629i	−0.0531961	−	0.198531i	−0.987410	+	0.158183i	$0.949436\pi$
$710$	43.3982	+	43.3982i	1.62870	+	1.62870i
$711$	−29.6098	+	8.27995i	−1.11046	+	0.310522i
$712$	15.0438	−	8.68556i	0.563792	−	0.325505i
$713$	2.16113	−	8.06545i	0.0809350	−	0.302053i
$714$	25.1695	−	61.7111i	0.941943	−	2.30948i
$715$	0.741551	−	6.60768i	0.0277324	−	0.247113i
$716$			19.6522i			0.734435i
$717$	4.07984	+	3.09548i	0.152364	+	0.115603i
$718$	47.7807	+	82.7586i	1.78316	+	3.08852i
$719$	16.4867	−	28.5558i	0.614849	−	1.06495i	−0.375561	−	0.926797i	$-0.622550\pi$
$719$	16.4867	−	28.5558i	0.614849	−	1.06495i	0.990411	−	0.138153i	$-0.0441166\pi$
$720$	−35.1009	+	0.381602i	−1.30813	+	0.0142215i
$721$	−43.1971	+	11.5746i	−1.60874	+	0.431061i
$722$	−47.4733	+	12.7204i	−1.76677	+	0.473405i
$723$	−7.18446	+	3.02175i	−0.267193	+	0.112380i
$724$	21.6918	−	37.5713i	0.806169	−	1.39633i
$725$	−4.05805	−	7.02874i	−0.150712	−	0.261041i
$726$	−2.64194	+	3.48207i	−0.0980516	+	0.129232i
$727$			2.54065i			0.0942276i	0.998890	+	0.0471138i	$0.0150023\pi$
$727$			2.54065i			0.0942276i	−0.998890	+	0.0471138i	$0.984998\pi$
$728$	90.6830	−	39.6123i	3.36093	−	1.46813i
$729$	−18.4592	+	19.7043i	−0.683674	+	0.729788i
$730$	11.1320	−	41.5452i	0.412014	−	1.53766i
$731$	−13.7204	+	7.92146i	−0.507466	+	0.292986i
$732$	40.9302	+	52.7452i	1.51282	+	1.94952i
$733$	−15.4579	−	15.4579i	−0.570950	−	0.570950i	0.361444	−	0.932394i	$-0.382284\pi$
$733$	−15.4579	−	15.4579i	−0.570950	−	0.570950i	−0.932394	+	0.361444i	$0.882284\pi$
$734$	17.3589	+	64.7844i	0.640730	+	2.39124i
$735$	−44.6535	−	5.63199i	−1.64707	−	0.207739i
$736$	−12.5478	+	12.5478i	−0.462518	+	0.462518i
$737$	6.34184	+	3.66146i	0.233605	+	0.134872i
$738$	−6.97770	−	1.78860i	−0.256853	−	0.0658393i
$739$	1.40367	+	0.376113i	0.0516349	+	0.0138355i	0.284544	−	0.958663i	$-0.408158\pi$
$739$	1.40367	+	0.376113i	0.0516349	+	0.0138355i	−0.232909	+	0.972499i	$0.574824\pi$
$740$	−47.8574			−1.75927
$741$	−9.10334	+	37.6522i	−0.334419	+	1.38319i
$742$	63.5971			2.33472
$743$	6.32082	+	1.69366i	0.231888	+	0.0621343i	0.372892	−	0.927875i	$-0.378366\pi$
$743$	6.32082	+	1.69366i	0.231888	+	0.0621343i	−0.141004	+	0.990009i	$0.545033\pi$
$744$	19.5873	−	2.68711i	0.718105	−	0.0985141i
$745$	35.0303	+	20.2247i	1.28341	+	0.740977i
$746$	−29.6288	+	29.6288i	−1.08479	+	1.08479i
$747$	−25.2107	+	44.7837i	−0.922413	+	1.63855i
$748$	−3.75375	−	14.0092i	−0.137251	−	0.512226i
$749$	−47.4052	−	47.4052i	−1.73215	−	1.73215i
$750$	42.0239	−	32.6105i	1.53450	−	1.19077i
$751$	−6.62590	+	3.82547i	−0.241783	+	0.139593i	−0.615996	−	0.787749i	$-0.711246\pi$
$751$	−6.62590	+	3.82547i	−0.241783	+	0.139593i	0.374213	+	0.927343i	$0.377913\pi$
$752$	−3.69513	+	13.7904i	−0.134748	+	0.502885i
$753$	−32.1937	−	13.1305i	−1.17320	−	0.478502i
$754$	−42.9943	−	16.8521i	−1.56576	−	0.613718i
$755$		−	19.2406i		−	0.700237i
$756$	−103.112	+	15.2893i	−3.75014	+	0.556066i
$757$	1.20308	+	2.08379i	0.0437266	+	0.0757367i	0.887060	−	0.461653i	$-0.152744\pi$
$757$	1.20308	+	2.08379i	0.0437266	+	0.0757367i	−0.843334	+	0.537390i	$0.819410\pi$
$758$	−40.6122	+	70.3424i	−1.47510	+	2.55495i
$759$	2.93569	+	6.97984i	0.106559	+	0.253352i
$760$	66.0336	−	17.6937i	2.39529	−	0.641817i
$761$	9.51768	−	2.55026i	0.345016	−	0.0924467i	−0.0821501	−	0.996620i	$-0.526179\pi$
$761$	9.51768	−	2.55026i	0.345016	−	0.0924467i	0.427166	+	0.904173i	$0.359512\pi$
$762$	25.4603	+	60.5337i	0.922328	+	2.19291i
$763$	−15.5591	+	26.9491i	−0.563276	+	0.975623i
$764$	−25.3228	−	43.8605i	−0.916148	−	1.58682i
$765$	−9.35678	−	15.8071i	−0.338295	−	0.571505i
$766$		−	72.6791i		−	2.62600i
$767$	31.8527	+	12.4850i	1.15014	+	0.450809i
$768$	49.9964	+	20.3915i	1.80409	+	0.735815i
$769$	−1.61333	+	6.02104i	−0.0581783	+	0.217124i	−0.988895	−	0.148617i	$-0.952518\pi$
$769$	−1.61333	+	6.02104i	−0.0581783	+	0.217124i	0.930717	+	0.365741i	$0.119185\pi$
$770$	−18.5088	+	10.6861i	−0.667011	+	0.385099i
$771$	15.2623	−	11.8436i	0.549660	−	0.426536i
$772$	−53.6905	−	53.6905i	−1.93236	−	1.93236i
$773$	−2.79085	−	10.4156i	−0.100380	−	0.374622i	0.897400	−	0.441217i	$-0.145453\pi$
$773$	−2.79085	−	10.4156i	−0.100380	−	0.374622i	−0.997780	+	0.0665949i	$0.978786\pi$
$774$	31.4792	+	17.7211i	1.13150	+	0.636971i
$775$	−2.15972	+	2.15972i	−0.0775795	+	0.0775795i
$776$	−23.5109	−	13.5740i	−0.843991	−	0.487278i
$777$	−46.8171	+	6.42266i	−1.67955	+	0.230412i
$778$	−24.5436	−	6.57643i	−0.879930	−	0.235777i
$779$	5.90193			0.211459
$780$	11.8224	−	48.8986i	0.423311	−	1.75085i
$781$	13.1881			0.471907
$782$	−35.3811	−	9.48034i	−1.26523	−	0.339016i
$783$	21.1815	+	15.7111i	0.756964	+	0.561468i
$784$	−77.4257	−	44.7017i	−2.76520	−	1.59649i
$785$	6.32974	−	6.32974i	0.225918	−	0.225918i
$786$	10.7918	+	1.36114i	0.384931	+	0.0485501i
$787$	10.2810	+	38.3691i	0.366477	+	1.36771i	0.865408	+	0.501069i	$0.167060\pi$
$787$	10.2810	+	38.3691i	0.366477	+	1.36771i	−0.498931	+	0.866642i	$0.666274\pi$
$788$	−45.6767	−	45.6767i	−1.62717	−	1.62717i
$789$	2.89617	+	3.73218i	0.103106	+	0.132869i
$790$	−41.3046	+	23.8472i	−1.46955	+	0.848446i
$791$	−12.0775	+	45.0738i	−0.429426	+	1.60264i
$792$	−12.5391	+	12.8147i	−0.445557	+	0.455351i
$793$	−29.1556	+	12.7358i	−1.03535	+	0.452261i
$794$			15.2672i			0.541812i
$795$	10.5948	−	13.9640i	0.375760	−	0.495251i
$796$	2.31113	+	4.00300i	0.0819159	+	0.141882i
$797$	10.3274	−	17.8876i	0.365816	−	0.633612i	−0.623091	−	0.782149i	$-0.714123\pi$
$797$	10.3274	−	17.8876i	0.365816	−	0.633612i	0.988907	+	0.148538i	$0.0474567\pi$
$798$	114.772	−	48.2728i	4.06290	−	1.70884i
$799$	−7.21629	+	1.93360i	−0.255294	+	0.0684058i
$800$	6.26981	−	1.67999i	0.221671	−	0.0593967i
$801$	−0.0947945	−	8.71950i	−0.00334940	−	0.308088i
$802$	11.0087	−	19.0676i	0.388730	−	0.673300i
$803$	−4.62107	−	8.00393i	−0.163074	−	0.282453i
$804$	44.1386	+	33.4891i	1.55665	+	1.18107i
$805$			37.0249i			1.30495i
$806$	−1.93814	+	17.2700i	−0.0682681	+	0.608311i
$807$	−7.34782	+	18.0156i	−0.258656	+	0.634178i
$808$	12.3814	−	46.2080i	0.435576	−	1.62559i
$809$	−30.9284	+	17.8565i	−1.08739	+	0.627803i	−0.932879	−	0.360189i	$-0.882712\pi$
$809$	−30.9284	+	17.8565i	−1.08739	+	0.627803i	−0.154507	+	0.987992i	$0.549379\pi$
$810$	−20.1484	+	36.7192i	−0.707943	+	1.29018i
$811$	−4.28159	−	4.28159i	−0.150347	−	0.150347i	0.627926	−	0.778273i	$-0.283904\pi$
$811$	−4.28159	−	4.28159i	−0.150347	−	0.150347i	−0.778273	+	0.627926i	$0.783904\pi$
$812$	26.3517	+	98.3460i	0.924764	+	3.45127i
$813$	0.0393010	−	0.311600i	0.00137835	−	0.0109283i
$814$	−10.6009	+	10.6009i	−0.371562	+	0.371562i
$815$	21.4883	+	12.4063i	0.752702	+	0.434573i
$816$	−4.95923	−	36.1496i	−0.173608	−	1.26549i
$817$	−28.5896	−	7.66057i	−1.00023	−	0.268010i
$818$	−2.75260			−0.0962426
$819$	5.00304	−	49.4223i	0.174820	−	1.72695i
$820$	−7.66480			−0.267666
$821$	−37.3613	−	10.0109i	−1.30392	−	0.349384i	−0.460989	−	0.887406i	$-0.652505\pi$
$821$	−37.3613	−	10.0109i	−1.30392	−	0.349384i	−0.842931	+	0.538022i	$0.819172\pi$
$822$	0.468846	+	3.41759i	0.0163529	+	0.119202i
$823$	−28.8314	−	16.6458i	−1.00500	−	0.580236i	−0.0952750	−	0.995451i	$-0.530373\pi$
$823$	−28.8314	−	16.6458i	−1.00500	−	0.580236i	−0.909723	+	0.415215i	$0.863706\pi$
$824$	−41.1514	+	41.1514i	−1.43358	+	1.43358i
$825$	0.346596	−	2.74800i	0.0120669	−	0.0956730i
$826$	−28.4615	−	106.220i	−0.990303	−	3.69586i
$827$	−6.54887	−	6.54887i	−0.227727	−	0.227727i	0.584016	−	0.811742i	$-0.301481\pi$
$827$	−6.54887	−	6.54887i	−0.227727	−	0.227727i	−0.811742	+	0.584016i	$0.801481\pi$
$828$	15.4285	+	55.1737i	0.536178	+	1.91742i
$829$	−10.6780	+	6.16494i	−0.370862	+	0.214117i	−0.673835	−	0.738882i	$-0.735354\pi$
$829$	−10.6780	+	6.16494i	−0.370862	+	0.214117i	0.302973	+	0.952999i	$0.402021\pi$
$830$	−20.6337	+	77.0059i	−0.716205	+	2.67291i
$831$	−4.76220	+	11.6761i	−0.165199	+	0.405039i
$832$	−5.23526	+	7.10008i	−0.181500	+	0.246151i
$833$		−	46.7833i		−	1.62094i
$834$	5.28263	+	4.00807i	0.182922	+	0.138788i
$835$	−16.7896	−	29.0805i	−0.581029	−	1.00637i
$836$	13.5478	−	23.4655i	0.468561	−	0.811571i
$837$	3.64796	−	9.22983i	0.126092	−	0.319029i
$838$	−71.6228	+	19.1913i	−2.47417	+	0.662952i
$839$	−24.3645	+	6.52845i	−0.841156	+	0.225387i	−0.653575	−	0.756862i	$-0.726731\pi$
$839$	−24.3645	+	6.52845i	−0.841156	+	0.225387i	−0.187581	+	0.982249i	$0.560065\pi$
$840$	−80.8094	+	33.9881i	−2.78819	+	1.17270i
$841$	−1.62052	+	2.80682i	−0.0558800	+	0.0967870i
$842$	16.4973	+	28.5742i	0.568534	+	0.984730i
$843$	5.49020	−	7.23607i	0.189092	−	0.249223i
$844$		−	61.5375i		−	2.11821i
$845$	21.2056	+	11.1835i	0.729494	+	0.384725i
$846$	12.1756	+	11.9138i	0.418607	+	0.409603i
$847$	−1.18861	+	4.43596i	−0.0408412	+	0.152421i
$848$	30.1539	−	17.4094i	1.03549	−	0.597840i
$849$	−7.65548	−	9.86531i	−0.262735	−	0.338577i
$850$	9.47417	+	9.47417i	0.324961	+	0.324961i
$851$	6.72202	+	25.0869i	0.230428	+	0.859968i
$852$	98.9966	+	12.4861i	3.39157	+	0.427767i
$853$	−24.2680	+	24.2680i	−0.830920	+	0.830920i	−0.987643	−	0.156722i	$-0.949907\pi$
$853$	−24.2680	+	24.2680i	−0.830920	+	0.830920i	0.156722	+	0.987643i	$0.449907\pi$
$854$	88.5636	+	51.1322i	3.03059	+	1.74971i
$855$	8.52105	−	33.2424i	0.291414	−	1.13686i
$856$	−84.2701	−	22.5801i	−2.88029	−	0.771772i
$857$	−25.6235			−0.875283			−0.437641	−	0.899150i	$-0.644186\pi$
$857$	−25.6235			−0.875283			−0.437641	+	0.899150i	$0.644186\pi$
$858$	−8.21275	−	13.4503i	−0.280379	−	0.459187i
$859$	38.5288			1.31459			0.657293	−	0.753635i	$-0.271702\pi$
$859$	38.5288			1.31459			0.657293	+	0.753635i	$0.271702\pi$
$860$	37.1292	+	9.94873i	1.26609	+	0.339249i
$861$	−7.49818	+	1.02865i	−0.255537	+	0.0350562i
$862$	35.7925	+	20.6648i	1.21910	+	0.703846i
$863$	−29.0223	+	29.0223i	−0.987931	+	0.987931i	−0.999928	−	0.0119967i	$-0.996181\pi$
$863$	−29.0223	+	29.0223i	−0.987931	+	0.987931i	0.0119967	+	0.999928i	$0.496181\pi$
$864$	−16.5215	+	13.1109i	−0.562073	+	0.446042i
$865$	2.77268	+	10.3478i	0.0942741	+	0.351836i
$866$	3.29428	+	3.29428i	0.111944	+	0.111944i
$867$	−8.17781	+	6.34597i	−0.277733	+	0.215521i
$868$	33.1825	−	19.1579i	1.12629	−	0.650263i
$869$	−2.65253	+	9.89936i	−0.0899808	+	0.335813i
$870$	37.8804	+	15.4499i	1.28427	+	0.523801i
$871$	−20.6356	+	16.4712i	−0.699210	+	0.558107i
$872$			40.4951i			1.37134i
$873$	−11.7273	+	6.94181i	−0.396908	+	0.234945i
$874$	−34.2159	−	59.2637i	−1.15737	−	2.00462i
$875$	27.9444	−	48.4012i	0.944694	−	1.63626i
$876$	−27.1103	−	64.4567i	−0.915971	−	2.17779i
$877$	−45.1156	+	12.0887i	−1.52344	+	0.408206i	−0.920874	−	0.389860i	$-0.872523\pi$
$877$	−45.1156	+	12.0887i	−1.52344	+	0.408206i	−0.602570	+	0.798066i	$0.705857\pi$
$878$	84.9915	−	22.7734i	2.86833	−	0.768566i
$879$	−4.56680	−	10.8579i	−0.154035	−	0.366229i
$880$	−5.85050	+	10.1334i	−0.197220	+	0.341596i
$881$	−11.8344	−	20.4977i	−0.398710	−	0.690586i	0.594857	−	0.803831i	$-0.297209\pi$
$881$	−11.8344	−	20.4977i	−0.398710	−	0.690586i	−0.993567	+	0.113246i	$0.963875\pi$
$882$	−91.7968	+	54.3379i	−3.09096	+	1.82965i
$883$		−	0.297430i		−	0.0100093i	−0.999987	−	0.00500466i	$-0.998407\pi$
$883$		−	0.297430i		−	0.0100093i	0.999987	−	0.00500466i	$-0.00159304\pi$
$884$	51.9664	+	5.83197i	1.74782	+	0.196150i
$885$	−28.0641	−	11.4462i	−0.943363	−	0.384760i
$886$	−1.30643	+	4.87567i	−0.0438904	+	0.163801i
$887$	17.9615	−	10.3701i	0.603090	−	0.348194i	−0.167166	−	0.985929i	$-0.553462\pi$
$887$	17.9615	−	10.3701i	0.603090	−	0.348194i	0.770256	+	0.637735i	$0.220128\pi$
$888$	−48.5833	+	37.7006i	−1.63035	+	1.26515i
$889$	48.7895	+	48.7895i	1.63635	+	1.63635i
$890$	−3.50104	−	13.0660i	−0.117355	−	0.437975i
$891$	2.51782	+	8.64064i	0.0843501	+	0.289472i
$892$	6.31060	−	6.31060i	0.211295	−	0.211295i
$893$	−12.0873	−	6.97863i	−0.404488	−	0.233531i
$894$	94.9814	−	13.0301i	3.17665	−	0.435793i
$895$	8.01390	+	2.14732i	0.267875	+	0.0717770i
$896$	65.6368			2.19277
$897$	−27.2933	+	0.670929i	−0.911296	+	0.0224017i
$898$	−21.9257			−0.731669
$899$	−9.36350	−	2.50894i	−0.312290	−	0.0836779i
$900$	5.20345	−	20.2997i	0.173448	−	0.676658i
$901$	15.7790	+	9.11001i	0.525675	+	0.303498i
$902$	−1.69783	+	1.69783i	−0.0565316	+	0.0565316i
$903$	37.6572	+	4.74957i	1.25315	+	0.158056i
$904$	15.7168	+	58.6560i	0.522734	+	1.95087i
$905$	−12.9509	−	12.9509i	−0.430503	−	0.430503i
$906$	−27.9576	−	36.0279i	−0.928829	−	1.19695i
$907$	34.1083	−	19.6925i	1.13255	−	0.653878i	0.187974	−	0.982174i	$-0.439808\pi$
$907$	34.1083	−	19.6925i	1.13255	−	0.653878i	0.944575	+	0.328296i	$0.106474\pi$
$908$	24.9254	−	93.0227i	0.827177	−	3.08707i
$909$	−17.1640	−	16.7948i	−0.569293	−	0.557048i
$910$	−11.5186	−	76.1926i	−0.381838	−	2.52576i
$911$		−	0.235330i		−	0.00779684i	−0.999992	−	0.00389842i	$-0.998759\pi$
$911$		−	0.235330i		−	0.00779684i	0.999992	−	0.00389842i	$-0.00124091\pi$
$912$	41.2036	−	54.3063i	1.36439	−	1.79826i
$913$	8.56537	+	14.8356i	0.283472	+	0.490988i
$914$	−48.1990	+	83.4832i	−1.59428	+	2.76138i
$915$	25.9811	−	10.9276i	0.858910	−	0.361254i
$916$	37.0349	−	9.92348i	1.22367	−	0.327881i
$917$	11.0392	−	2.95796i	0.364548	−	0.0976803i
$918$	−40.4890	−	16.0027i	−1.33633	−	0.528167i
$919$	16.5743	−	28.7075i	0.546735	−	0.946973i	−0.451760	−	0.892139i	$-0.649204\pi$
$919$	16.5743	−	28.7075i	0.546735	−	0.946973i	0.998496	−	0.0548337i	$-0.0174629\pi$
$920$	24.0908	+	41.7266i	0.794252	+	1.37568i
$921$	−18.7905	−	14.2569i	−0.619169	−	0.469780i
$922$		−	78.9550i		−	2.60024i
$923$	−17.3525	+	44.2710i	−0.571166	+	1.45720i
$924$	−13.1222	+	32.1732i	−0.431688	+	1.05842i
$925$	2.45883	−	9.17646i	0.0808457	−	0.301720i
$926$	79.7654	−	46.0526i	2.62125	−	1.51338i
$927$	7.86740	+	28.1345i	0.258399	+	0.924058i
$928$	14.5672	+	14.5672i	0.478193	+	0.478193i
$929$	5.94690	+	22.1941i	0.195112	+	0.728166i	0.992238	+	0.124354i	$0.0396858\pi$
$929$	5.94690	+	22.1941i	0.195112	+	0.728166i	−0.797126	+	0.603812i	$0.793648\pi$
$930$	1.92653	−	15.2745i	0.0631733	−	0.500872i
$931$	61.8024	−	61.8024i	2.02549	−	2.02549i
$932$	−52.8352	−	30.5044i	−1.73067	−	0.999205i
$933$	−2.56469	−	18.6949i	−0.0839641	−	0.612044i
$934$	1.88027	+	0.503816i	0.0615242	+	0.0164854i
$935$	−6.12293			−0.200241
$936$	−26.5191	−	58.9536i	−0.866802	−	1.92696i
$937$	40.9903			1.33909			0.669547	−	0.742770i	$-0.266488\pi$
$937$	40.9903			1.33909			0.669547	+	0.742770i	$0.266488\pi$
$938$	81.9750	+	21.9651i	2.67658	+	0.717187i
$939$	−3.22208	−	23.4869i	−0.105149	−	0.766465i
$940$	15.6977	+	9.06310i	0.512004	+	0.295606i
$941$	11.3962	−	11.3962i	0.371504	−	0.371504i	−0.496521	−	0.868025i	$-0.665389\pi$
$941$	11.3962	−	11.3962i	0.371504	−	0.371504i	0.868025	+	0.496521i	$0.165389\pi$
$942$	2.65494	−	21.0498i	0.0865027	−	0.685840i
$943$	1.07659	+	4.01790i	0.0350587	+	0.130841i
$944$	−42.5718	−	42.5718i	−1.38559	−	1.38559i
$945$	−5.03185	+	43.7183i	−0.163686	+	1.42216i
$946$	10.4282	−	6.02074i	0.339051	−	0.195751i
$947$	6.07785	−	22.6828i	0.197504	−	0.737094i	−0.794101	−	0.607786i	$-0.792058\pi$
$947$	6.07785	−	22.6828i	0.197504	−	0.737094i	0.991605	−	0.129308i	$-0.0412755\pi$
$948$	−29.2837	+	71.7984i	−0.951089	+	2.33190i
$949$	32.9486	−	4.98109i	1.06956	−	0.161693i
$950$			25.0315i			0.812128i
$951$	−40.7673	−	30.9312i	−1.32197	−	1.00301i
$952$	−45.5627	−	78.9170i	−1.47670	−	2.55771i
$953$	9.43282	−	16.3381i	0.305559	−	0.529244i	−0.671827	−	0.740708i	$-0.734490\pi$
$953$	9.43282	−	16.3381i	0.305559	−	0.529244i	0.977386	+	0.211465i	$0.0678234\pi$
$954$	−0.451629	−	41.5422i	−0.0146220	−	1.34498i
$955$	−20.6527	+	5.53387i	−0.668305	+	0.179072i
$956$	12.4756	−	3.34284i	0.403491	−	0.108115i
$957$	8.10317	−	3.40816i	0.261938	−	0.110170i
$958$	−33.2410	+	57.5750i	−1.07397	+	1.86016i
$959$	1.81223	+	3.13887i	0.0585198	+	0.101359i
$960$	4.72368	−	6.22580i	0.152456	−	0.200937i
$961$		−	27.3520i		−	0.882321i
$962$	−21.6377	−	49.5345i	−0.697629	−	1.59706i
$963$	−30.6289	+	31.3022i	−0.987001	+	1.00870i
$964$	−5.08750	+	18.9868i	−0.163857	+	0.611524i
$965$	−27.7609	+	16.0278i	−0.893655	+	0.515952i
$966$	53.7990	+	69.3287i	1.73095	+	2.23061i
$967$	7.92522	+	7.92522i	0.254858	+	0.254858i	0.822959	−	0.568101i	$-0.192322\pi$
$967$	7.92522	+	7.92522i	0.254858	+	0.254858i	−0.568101	+	0.822959i	$0.692322\pi$
$968$	1.54678	+	5.77266i	0.0497154	+	0.185540i
$969$	35.3909	+	4.46373i	1.13692	+	0.143396i
$970$	−14.9484	+	14.9484i	−0.479965	+	0.479965i
$971$	−2.04669	−	1.18166i	−0.0656815	−	0.0379212i	0.466800	−	0.884363i	$-0.345407\pi$
$971$	−2.04669	−	1.18166i	−0.0656815	−	0.0379212i	−0.532481	+	0.846442i	$0.678740\pi$
$972$	10.7193	+	67.2449i	0.343823	+	2.15688i
$973$	6.72976	+	1.80323i	0.215746	+	0.0578090i
$974$	59.6748			1.91211
$975$	8.76870	+	4.77923i	0.280823	+	0.153058i
$976$	55.9886			1.79215
$977$	16.6427	+	4.45939i	0.532447	+	0.142669i	0.515018	−	0.857179i	$-0.327785\pi$
$977$	16.6427	+	4.45939i	0.532447	+	0.142669i	0.0174289	+	0.999848i	$0.494452\pi$
$978$	58.2636	−	7.99297i	1.86306	−	0.255587i
$979$	−2.51725	−	1.45334i	−0.0804517	−	0.0464488i
$980$	−80.2624	+	80.2624i	−2.56389	+	2.56389i
$981$	17.7139	+	9.97195i	0.565561	+	0.318380i
$982$	−7.84714	−	29.2859i	−0.250412	−	0.934551i
$983$	29.7812	+	29.7812i	0.949872	+	0.949872i	0.998802	−	0.0489300i	$-0.0155811\pi$
$983$	29.7812	+	29.7812i	0.949872	+	0.949872i	−0.0489300	+	0.998802i	$0.515581\pi$
$984$	−7.78105	+	6.03809i	−0.248051	+	0.192487i
$985$	−23.6173	+	13.6355i	−0.752510	+	0.434462i
$986$	−11.0061	+	41.0753i	−0.350506	+	1.30811i
$987$	16.5728	+	6.75938i	0.527518	+	0.215153i
$988$	60.9453	+	76.3538i	1.93893	+	2.42914i
$989$		−	20.8605i		−	0.663327i
$990$	7.11167	+	12.0142i	0.226024	+	0.381837i
$991$	5.61966	+	9.73354i	0.178514	+	0.309196i	0.941372	−	0.337371i	$-0.109538\pi$
$991$	5.61966	+	9.73354i	0.178514	+	0.309196i	−0.762857	+	0.646567i	$0.776204\pi$
$992$	3.87640	−	6.71412i	0.123076	−	0.213173i
$993$	20.2556	+	48.1593i	0.642793	+	1.52829i
$994$	147.631	−	39.5577i	4.68258	−	1.25469i
$995$	1.88490	−	0.505058i	0.0597554	−	0.0160114i
$996$	50.2501	+	119.473i	1.59224	+	3.78566i
$997$	−23.3812	+	40.4974i	−0.740490	+	1.28257i	0.211782	+	0.977317i	$0.432073\pi$
$997$	−23.3812	+	40.4974i	−0.740490	+	1.28257i	−0.952272	+	0.305250i	$0.901260\pi$
$998$	18.3397	+	31.7653i	0.580534	+	1.00551i
$999$	4.52780	+	30.5357i	0.143253	+	0.966107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.be.a.89.4	✓	184
3.2	odd	2	inner	429.2.be.a.89.43	yes	184
13.6	odd	12	inner	429.2.be.a.188.43	yes	184
39.32	even	12	inner	429.2.be.a.188.4	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.be.a.89.4	✓	184	1.1	even	1	trivial
429.2.be.a.89.43	yes	184	3.2	odd	2	inner
429.2.be.a.188.4	yes	184	39.32	even	12	inner
429.2.be.a.188.43	yes	184	13.6	odd	12	inner

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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.43755 - 0.653139i) q^{2} +(0.235409 + 1.71598i) q^{3} +(3.78299 + 2.18411i) q^{4} +(1.30401 - 1.30401i) q^{5} +(0.546952 - 4.33653i) q^{6} +(-1.18861 - 4.43596i) q^{7} +(-4.22588 - 4.22588i) q^{8} +(-2.88917 + 0.807913i) q^{9} +O(q^{10})\)	\(q+(-2.43755 - 0.653139i) q^{2} +(0.235409 + 1.71598i) q^{3} +(3.78299 + 2.18411i) q^{4} +(1.30401 - 1.30401i) q^{5} +(0.546952 - 4.33653i) q^{6} +(-1.18861 - 4.43596i) q^{7} +(-4.22588 - 4.22588i) q^{8} +(-2.88917 + 0.807913i) q^{9} +(-4.03028 + 2.32688i) q^{10} +(-0.258819 + 0.965926i) q^{11} +(-2.85734 + 7.00570i) q^{12} +(-2.90196 - 2.13977i) q^{13} +11.5892i q^{14} +(2.54462 + 1.93067i) q^{15} +(3.17247 + 5.49488i) q^{16} +(-1.66010 + 2.87538i) q^{17} +(7.57016 - 0.0822994i) q^{18} +(-5.99153 + 1.60543i) q^{19} +(7.78115 - 2.08495i) q^{20} +(7.33220 - 3.08389i) q^{21} +(1.26177 - 2.18544i) q^{22} +(-2.18587 - 3.78604i) q^{23} +(6.25671 - 8.24633i) q^{24} +1.59913i q^{25} +(5.67611 + 7.11117i) q^{26} +(-2.06650 - 4.76756i) q^{27} +(5.19212 - 19.3773i) q^{28} +(-4.39536 + 2.53766i) q^{29} +(-4.94164 - 6.36810i) q^{30} +(1.35056 + 1.35056i) q^{31} +(-1.05057 - 3.92077i) q^{32} +(-1.71844 - 0.216741i) q^{33} +(5.92459 - 5.92459i) q^{34} +(-7.33448 - 4.23456i) q^{35} +(-12.6943 - 3.25393i) q^{36} +(-5.73842 - 1.53761i) q^{37} +15.6532 q^{38} +(2.98865 - 5.48343i) q^{39} -11.0212 q^{40} +(-0.919061 - 0.246262i) q^{41} +(-19.8868 + 2.72819i) q^{42} +(4.13239 + 2.38584i) q^{43} +(-3.08880 + 3.08880i) q^{44} +(-2.71397 + 4.82102i) q^{45} +(2.85535 + 10.6563i) q^{46} +(1.59108 + 1.59108i) q^{47} +(-8.68227 + 6.73744i) q^{48} +(-12.2027 + 7.04525i) q^{49} +(1.04445 - 3.89795i) q^{50} +(-5.32489 - 2.17181i) q^{51} +(-6.30462 - 14.4329i) q^{52} -5.48763i q^{53} +(1.92330 + 12.9709i) q^{54} +(0.922073 + 1.59708i) q^{55} +(-13.7229 + 23.7688i) q^{56} +(-4.16534 - 9.90341i) q^{57} +(12.3714 - 3.31489i) q^{58} +(-9.16543 + 2.45587i) q^{59} +(5.40949 + 12.8615i) q^{60} +(4.41207 - 7.64192i) q^{61} +(-2.40996 - 4.17417i) q^{62} +(7.01796 + 11.8559i) q^{63} -2.44665i q^{64} +(-6.57446 + 0.993910i) q^{65} +(4.04721 + 1.65069i) q^{66} +(1.89531 - 7.07341i) q^{67} +(-12.5603 + 7.25169i) q^{68} +(5.98219 - 4.64218i) q^{69} +(15.1124 + 15.1124i) q^{70} +(-3.41333 - 12.7387i) q^{71} +(15.6234 + 8.79513i) q^{72} +(-6.53518 + 6.53518i) q^{73} +(12.9834 + 7.49597i) q^{74} +(-2.74407 + 0.376448i) q^{75} +(-26.1724 - 7.01286i) q^{76} +4.59244 q^{77} +(-10.8664 + 11.4141i) q^{78} +10.2486 q^{79} +(11.3023 + 3.02844i) q^{80} +(7.69455 - 4.66839i) q^{81} +(2.07941 + 1.20055i) q^{82} +(12.1133 - 12.1133i) q^{83} +(34.4732 + 4.34799i) q^{84} +(1.58473 + 5.91430i) q^{85} +(-8.51462 - 8.51462i) q^{86} +(-5.38928 - 6.94496i) q^{87} +(5.17563 - 2.98815i) q^{88} +(-0.752302 + 2.80763i) q^{89} +(9.76422 - 9.97886i) q^{90} +(-6.04261 + 15.4163i) q^{91} -19.0968i q^{92} +(-1.99960 + 2.63547i) q^{93} +(-2.83913 - 4.91752i) q^{94} +(-5.71952 + 9.90649i) q^{95} +(6.48065 - 2.72574i) q^{96} +(4.38783 - 1.17571i) q^{97} +(34.3463 - 9.20306i) q^{98} +(-0.0326127 - 2.99982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 12 q^{6} + 12 q^{7}+O(q^{10}) \) 184 * q - 12 * q^6 + 12 * q^7	\( 184 q - 12 q^{6} + 12 q^{7} - 48 q^{10} - 16 q^{13} + 16 q^{15} + 80 q^{16} - 8 q^{18} - 4 q^{19} - 24 q^{24} - 48 q^{27} - 40 q^{28} + 48 q^{30} - 20 q^{31} + 16 q^{34} - 36 q^{36} + 44 q^{37} + 48 q^{39} - 80 q^{40} + 20 q^{42} - 84 q^{43} - 4 q^{45} - 64 q^{46} + 44 q^{48} - 60 q^{49} - 200 q^{52} - 4 q^{54} - 64 q^{57} - 48 q^{58} - 148 q^{60} - 48 q^{61} + 40 q^{66} + 48 q^{67} - 12 q^{69} + 24 q^{70} - 128 q^{72} + 108 q^{73} - 60 q^{75} - 24 q^{76} + 148 q^{78} + 32 q^{79} + 16 q^{81} - 48 q^{82} + 116 q^{84} + 104 q^{85} - 24 q^{87} + 72 q^{88} + 60 q^{91} + 36 q^{93} + 16 q^{94} - 72 q^{96} + 4 q^{97}+O(q^{100}) \) 184 * q - 12 * q^6 + 12 * q^7 - 48 * q^10 - 16 * q^13 + 16 * q^15 + 80 * q^16 - 8 * q^18 - 4 * q^19 - 24 * q^24 - 48 * q^27 - 40 * q^28 + 48 * q^30 - 20 * q^31 + 16 * q^34 - 36 * q^36 + 44 * q^37 + 48 * q^39 - 80 * q^40 + 20 * q^42 - 84 * q^43 - 4 * q^45 - 64 * q^46 + 44 * q^48 - 60 * q^49 - 200 * q^52 - 4 * q^54 - 64 * q^57 - 48 * q^58 - 148 * q^60 - 48 * q^61 + 40 * q^66 + 48 * q^67 - 12 * q^69 + 24 * q^70 - 128 * q^72 + 108 * q^73 - 60 * q^75 - 24 * q^76 + 148 * q^78 + 32 * q^79 + 16 * q^81 - 48 * q^82 + 116 * q^84 + 104 * q^85 - 24 * q^87 + 72 * q^88 + 60 * q^91 + 36 * q^93 + 16 * q^94 - 72 * q^96 + 4 * q^97

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