LMFDB - Embedded newform 684.2.o.a.11.54

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(11,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 4]))

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

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

chi := DirichletCharacter("684.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.o (of order $6$, degree $2$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$232$
Relative dimension:	$116$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.54
Character	$\chi$	$=$	684.11
Dual form			684.2.o.a.311.54

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.181298 + 1.40254i) q^{2} +(-1.25014 + 1.19881i) q^{3} +(-1.93426 - 0.508558i) q^{4} +1.79274i q^{5} +(-1.45474 - 1.97072i) q^{6} +(2.43772 + 1.40742i) q^{7} +(1.06395 - 2.62069i) q^{8} +(0.125699 - 2.99737i) q^{9} +(-2.51439 - 0.325021i) q^{10} +(-2.00035 + 3.46471i) q^{11} +(3.02776 - 1.68305i) q^{12} +(-2.05352 + 3.55679i) q^{13} +(-2.41592 + 3.16385i) q^{14} +(-2.14916 - 2.24117i) q^{15} +(3.48274 + 1.96737i) q^{16} +(-6.65138 - 3.84018i) q^{17} +(4.18115 + 0.719717i) q^{18} +(-2.29881 + 3.70344i) q^{19} +(0.911712 - 3.46762i) q^{20} +(-4.73472 + 1.16290i) q^{21} +(-4.49675 - 3.43373i) q^{22} +(-0.417491 + 0.723116i) q^{23} +(1.81162 + 4.55171i) q^{24} +1.78609 q^{25} +(-4.61626 - 3.52499i) q^{26} +(3.43614 + 3.89782i) q^{27} +(-3.99943 - 3.96204i) q^{28} -6.45469i q^{29} +(3.53298 - 2.60796i) q^{30} +(3.07334 - 1.77440i) q^{31} +(-3.39074 + 4.52801i) q^{32} +(-1.65282 - 6.72941i) q^{33} +(6.59190 - 8.63264i) q^{34} +(-2.52313 + 4.37019i) q^{35} +(-1.76747 + 5.73376i) q^{36} +4.43303 q^{37} +(-4.77747 - 3.89561i) q^{38} +(-1.69675 - 6.90827i) q^{39} +(4.69820 + 1.90739i) q^{40} -7.35803i q^{41} +(-0.772619 - 6.85149i) q^{42} +(-2.11621 + 1.22179i) q^{43} +(5.63121 - 5.68436i) q^{44} +(5.37349 + 0.225346i) q^{45} +(-0.938512 - 0.716650i) q^{46} +4.37304 q^{47} +(-6.71241 + 1.71566i) q^{48} +(0.461654 + 0.799607i) q^{49} +(-0.323816 + 2.50507i) q^{50} +(12.9188 - 3.17300i) q^{51} +(5.78087 - 5.83544i) q^{52} +(-2.21477 + 1.27870i) q^{53} +(-6.08983 + 4.11267i) q^{54} +(-6.21131 - 3.58610i) q^{55} +(6.28203 - 4.89107i) q^{56} +(-1.56590 - 7.38566i) q^{57} +(9.05299 + 1.17023i) q^{58} -6.16527 q^{59} +(3.01726 + 5.42799i) q^{60} -0.777566 q^{61} +(1.93148 + 4.63220i) q^{62} +(4.52497 - 7.12983i) q^{63} +(-5.73600 - 5.57658i) q^{64} +(-6.37640 - 3.68142i) q^{65} +(9.73795 - 1.09812i) q^{66} +(-0.683087 - 0.394381i) q^{67} +(10.9126 + 10.8105i) q^{68} +(-0.344958 - 1.40449i) q^{69} +(-5.67195 - 4.33111i) q^{70} +(-3.39181 + 5.87479i) q^{71} +(-7.72142 - 3.51848i) q^{72} +(-5.70240 + 9.87685i) q^{73} +(-0.803701 + 6.21752i) q^{74} +(-2.23286 + 2.14119i) q^{75} +(6.32991 - 5.99435i) q^{76} +(-9.75259 + 5.63066i) q^{77} +(9.99677 - 1.12730i) q^{78} +(-1.34514 + 0.776617i) q^{79} +(-3.52698 + 6.24363i) q^{80} +(-8.96840 - 0.753534i) q^{81} +(10.3200 + 1.33400i) q^{82} +(-1.25828 + 2.17940i) q^{83} +(9.74959 + 0.158532i) q^{84} +(6.88443 - 11.9242i) q^{85} +(-1.32995 - 3.18958i) q^{86} +(7.73796 + 8.06927i) q^{87} +(6.95163 + 8.92858i) q^{88} +(-14.2251 + 8.21288i) q^{89} +(-1.29026 + 7.49570i) q^{90} +(-10.0118 + 5.78031i) q^{91} +(1.17528 - 1.18638i) q^{92} +(-1.71494 + 5.90260i) q^{93} +(-0.792825 + 6.13338i) q^{94} +(-6.63930 - 4.12116i) q^{95} +(-1.18934 - 9.72551i) q^{96} +(3.35880 + 5.81762i) q^{97} +(-1.20518 + 0.502522i) q^{98} +(10.1336 + 6.43129i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 232 q - 3 q^{2} + q^{4} + 3 q^{6} + 2 q^{10} - q^{12} + 2 q^{13} + q^{16} - 12 q^{17} - 16 q^{18} - 27 q^{20} - 14 q^{21} + 6 q^{22} - 10 q^{24} - 204 q^{25} - 6 q^{28} - 9 q^{30} - 3 q^{32} - 12 q^{33}+ \cdots - 162 q^{98}+O(q^{100}) $ 232 * q - 3 * q^2 + q^4 + 3 * q^6 + 2 * q^10 - q^12 + 2 * q^13 + q^16 - 12 * q^17 - 16 * q^18 - 27 * q^20 - 14 * q^21 + 6 * q^22 - 10 * q^24 - 204 * q^25 - 6 * q^28 - 9 * q^30 - 3 * q^32 - 12 * q^33 + 2 * q^34 + 13 * q^36 - 16 * q^37 - 3 * q^38 - 16 * q^40 - 43 * q^42 + 21 * q^44 + 2 * q^45 - 24 * q^46 + 58 * q^48 + 88 * q^49 + 9 * q^50 + 17 * q^52 + 41 * q^54 - 48 * q^56 - 12 * q^57 + 2 * q^58 + 16 * q^60 - 4 * q^61 + 6 * q^62 + 16 * q^64 + 12 * q^65 - 27 * q^66 - 18 * q^68 - 14 * q^69 + 60 * q^70 + 15 * q^72 + 2 * q^73 - 30 * q^74 + 3 * q^76 - 12 * q^77 - 64 * q^78 + 54 * q^80 + 4 * q^81 + 2 * q^82 - 10 * q^84 + 22 * q^85 + 51 * q^86 - 18 * q^88 + 14 * q^90 + 57 * q^92 + 4 * q^93 - 6 * q^94 - 17 * q^96 - 4 * q^97 - 162 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.181298	+	1.40254i	−0.128197	+	0.991749i
$2$	−0.181298	+	1.40254i	−0.128197	+	0.991749i
$3$	−1.25014	+	1.19881i	−0.721769	+	0.692134i
$3$	−1.25014	+	1.19881i	−0.721769	+	0.692134i
$4$	−1.93426	−	0.508558i	−0.967131	−	0.254279i
$5$			1.79274i			0.801737i	0.916136	+	0.400868i	$0.131292\pi$
$5$			1.79274i			0.801737i	−0.916136	+	0.400868i	$0.868708\pi$
$6$	−1.45474	−	1.97072i	−0.593895	−	0.804543i
$7$	2.43772	+	1.40742i	0.921372	+	0.531954i	0.884072	−	0.467350i	$-0.154791\pi$
$7$	2.43772	+	1.40742i	0.921372	+	0.531954i	0.0372993	+	0.999304i	$0.488125\pi$
$8$	1.06395	−	2.62069i	0.376165	−	0.926553i
$9$	0.125699	−	2.99737i	0.0418998	−	0.999122i
$10$	−2.51439	−	0.325021i	−0.795121	−	0.102781i
$11$	−2.00035	+	3.46471i	−0.603128	+	1.04465i	0.389216	+	0.921146i	$0.372746\pi$
$11$	−2.00035	+	3.46471i	−0.603128	+	1.04465i	−0.992344	+	0.123502i	$0.960587\pi$
$12$	3.02776	−	1.68305i	0.874040	−	0.485854i
$13$	−2.05352	+	3.55679i	−0.569543	+	0.986477i	0.427068	+	0.904219i	$0.359546\pi$
$13$	−2.05352	+	3.55679i	−0.569543	+	0.986477i	−0.996611	+	0.0822577i	$0.973787\pi$
$14$	−2.41592	+	3.16385i	−0.645682	+	0.845574i
$15$	−2.14916	−	2.24117i	−0.554910	−	0.578668i
$16$	3.48274	+	1.96737i	0.870684	+	0.491842i
$17$	−6.65138	−	3.84018i	−1.61320	−	0.931380i	−0.988623	−	0.150414i	$-0.951939\pi$
$17$	−6.65138	−	3.84018i	−1.61320	−	0.931380i	−0.624574	−	0.780966i	$-0.714727\pi$
$18$	4.18115	+	0.719717i	0.985506	+	0.169639i
$19$	−2.29881	+	3.70344i	−0.527382	+	0.849628i
$19$	−2.29881	+	3.70344i	−0.527382	+	0.849628i
$20$	0.911712	−	3.46762i	0.203865	−	0.775384i
$21$	−4.73472	+	1.16290i	−1.03320	+	0.253765i
$22$	−4.49675	−	3.43373i	−0.958709	−	0.732073i
$23$	−0.417491	+	0.723116i	−0.0870530	+	0.150780i	−0.906264	−	0.422712i	$-0.861078\pi$
$23$	−0.417491	+	0.723116i	−0.0870530	+	0.150780i	0.819211	+	0.573492i	$0.194412\pi$
$24$	1.81162	+	4.55171i	0.369795	+	0.929113i
$25$	1.78609			0.357218
$26$	−4.61626	−	3.52499i	−0.905323	−	0.691307i
$27$	3.43614	+	3.89782i	0.661285	+	0.750135i
$28$	−3.99943	−	3.96204i	−0.755822	−	0.748755i
$29$		−	6.45469i		−	1.19861i	−0.800522	−	0.599303i	$-0.795444\pi$
$29$		−	6.45469i		−	1.19861i	0.800522	−	0.599303i	$-0.204556\pi$
$30$	3.53298	−	2.60796i	0.645032	−	0.476147i
$31$	3.07334	−	1.77440i	0.551989	−	0.318691i	−0.197935	−	0.980215i	$-0.563423\pi$
$31$	3.07334	−	1.77440i	0.551989	−	0.318691i	0.749924	+	0.661524i	$0.230090\pi$
$32$	−3.39074	+	4.52801i	−0.599403	+	0.800447i
$33$	−1.65282	−	6.72941i	−0.287718	−	1.17144i
$34$	6.59190	−	8.63264i	1.13050	−	1.48049i
$35$	−2.52313	+	4.37019i	−0.426487	+	0.738697i
$36$	−1.76747	+	5.73376i	−0.294578	+	0.955627i
$37$	4.43303			0.728785			0.364392	−	0.931245i	$-0.381277\pi$
$37$	4.43303			0.728785			0.364392	+	0.931245i	$0.381277\pi$
$38$	−4.77747	−	3.89561i	−0.775008	−	0.631951i
$39$	−1.69675	−	6.90827i	−0.271697	−	1.10621i
$40$	4.69820	+	1.90739i	0.742851	+	0.301585i
$41$		−	7.35803i		−	1.14913i	−0.818459	−	0.574566i	$-0.805171\pi$
$41$		−	7.35803i		−	1.14913i	0.818459	−	0.574566i	$-0.194829\pi$
$42$	−0.772619	−	6.85149i	−0.119218	−	1.05721i
$43$	−2.11621	+	1.22179i	−0.322718	+	0.186322i	−0.652604	−	0.757700i	$-0.726323\pi$
$43$	−2.11621	+	1.22179i	−0.322718	+	0.186322i	0.329885	+	0.944021i	$0.392990\pi$
$44$	5.63121	−	5.68436i	0.848936	−	0.856949i
$45$	5.37349	+	0.225346i	0.801033	+	0.0335926i
$46$	−0.938512	−	0.716650i	−0.138376	−	0.105664i
$47$	4.37304			0.637873			0.318937	−	0.947776i	$-0.396674\pi$
$47$	4.37304			0.637873			0.318937	+	0.947776i	$0.396674\pi$
$48$	−6.71241	+	1.71566i	−0.968854	+	0.247634i
$49$	0.461654	+	0.799607i	0.0659505	+	0.114230i
$50$	−0.323816	+	2.50507i	−0.0457944	+	0.354271i
$51$	12.9188	−	3.17300i	1.80899	−	0.444309i
$52$	5.78087	−	5.83544i	0.801663	−	0.809230i
$53$	−2.21477	+	1.27870i	−0.304222	+	0.175643i	−0.644338	−	0.764741i	$-0.722867\pi$
$53$	−2.21477	+	1.27870i	−0.304222	+	0.175643i	0.340116	+	0.940383i	$0.389534\pi$
$54$	−6.08983	+	4.11267i	−0.828720	+	0.559663i
$55$	−6.21131	−	3.58610i	−0.837533	−	0.483550i
$56$	6.28203	−	4.89107i	0.839471	−	0.653597i
$57$	−1.56590	−	7.38566i	−0.207409	−	0.978254i
$58$	9.05299	+	1.17023i	1.18872	+	0.153658i
$59$	−6.16527			−0.802650			−0.401325	−	0.915936i	$-0.631450\pi$
$59$	−6.16527			−0.802650			−0.401325	+	0.915936i	$0.631450\pi$
$60$	3.01726	+	5.42799i	0.389527	+	0.700750i
$61$	−0.777566			−0.0995571			−0.0497786	−	0.998760i	$-0.515852\pi$
$61$	−0.777566			−0.0995571			−0.0497786	+	0.998760i	$0.515852\pi$
$62$	1.93148	+	4.63220i	0.245298	+	0.588289i
$63$	4.52497	−	7.12983i	0.570092	−	0.898274i
$64$	−5.73600	−	5.57658i	−0.717000	−	0.697073i
$65$	−6.37640	−	3.68142i	−0.790895	−	0.456623i
$66$	9.73795	−	1.09812i	1.19866	−	0.135169i
$67$	−0.683087	−	0.394381i	−0.0834524	−	0.0481812i	0.457693	−	0.889110i	$-0.348676\pi$
$67$	−0.683087	−	0.394381i	−0.0834524	−	0.0481812i	−0.541145	+	0.840929i	$0.682009\pi$
$68$	10.9126	+	10.8105i	1.32334	+	1.31097i
$69$	−0.344958	−	1.40449i	−0.0415280	−	0.169081i
$70$	−5.67195	−	4.33111i	−0.677928	−	0.517667i
$71$	−3.39181	+	5.87479i	−0.402534	+	0.697209i	−0.994031	−	0.109098i	$-0.965204\pi$
$71$	−3.39181	+	5.87479i	−0.402534	+	0.697209i	0.591497	+	0.806307i	$0.298537\pi$
$72$	−7.72142	−	3.51848i	−0.909978	−	0.414657i
$73$	−5.70240	+	9.87685i	−0.667416	+	1.15600i	0.311209	+	0.950342i	$0.399266\pi$
$73$	−5.70240	+	9.87685i	−0.667416	+	1.15600i	−0.978624	+	0.205656i	$0.934067\pi$
$74$	−0.803701	+	6.21752i	−0.0934283	+	0.722772i
$75$	−2.23286	+	2.14119i	−0.257829	+	0.247243i
$76$	6.32991	−	5.99435i	0.726090	−	0.687599i
$77$	−9.75259	+	5.63066i	−1.11141	+	0.641673i
$78$	9.99677	−	1.12730i	1.13191	−	0.127642i
$79$	−1.34514	+	0.776617i	−0.151340	+	0.0873763i	−0.573758	−	0.819025i	$-0.694515\pi$
$79$	−1.34514	+	0.776617i	−0.151340	+	0.0873763i	0.422418	+	0.906401i	$0.361182\pi$
$80$	−3.52698	+	6.24363i	−0.394328	+	0.698059i
$81$	−8.96840	−	0.753534i	−0.996489	−	0.0837260i
$82$	10.3200	+	1.33400i	1.13965	+	0.147316i
$83$	−1.25828	+	2.17940i	−0.138114	+	0.239220i	−0.926783	−	0.375598i	$-0.877437\pi$
$83$	−1.25828	+	2.17940i	−0.138114	+	0.239220i	0.788669	+	0.614818i	$0.210771\pi$
$84$	9.74959	+	0.158532i	1.06377	+	0.0172972i
$85$	6.88443	−	11.9242i	0.746721	−	1.29336i
$86$	−1.32995	−	3.18958i	−0.143412	−	0.343941i
$87$	7.73796	+	8.06927i	0.829597	+	0.865116i
$88$	6.95163	+	8.92858i	0.741047	+	0.951790i
$89$	−14.2251	+	8.21288i	−1.50786	+	0.870563i	−0.507902	+	0.861415i	$0.669579\pi$
$89$	−14.2251	+	8.21288i	−1.50786	+	0.870563i	−0.999958	+	0.00914830i	$0.997088\pi$
$90$	−1.29026	+	7.49570i	−0.136006	+	0.790117i
$91$	−10.0118	+	5.78031i	−1.04952	+	0.605941i
$92$	1.17528	−	1.18638i	0.122532	−	0.123688i
$93$	−1.71494	+	5.90260i	−0.177831	+	0.612071i
$94$	−0.792825	+	6.13338i	−0.0817737	+	0.632610i
$95$	−6.63930	−	4.12116i	−0.681178	−	0.422822i
$96$	−1.18934	−	9.72551i	−0.121386	−	0.992605i
$97$	3.35880	+	5.81762i	0.341035	+	0.590689i	0.984625	−	0.174681i	$-0.0558893\pi$
$97$	3.35880	+	5.81762i	0.341035	+	0.590689i	−0.643590	+	0.765370i	$0.722556\pi$
$98$	−1.20518	+	0.502522i	−0.121742	+	0.0507624i
$99$	10.1336	+	6.43129i	1.01846	+	0.646369i
$100$	−3.45477	−	0.908332i	−0.345477	−	0.0908332i
$101$			8.68436i			0.864126i	0.901843	+	0.432063i	$0.142214\pi$
$101$			8.68436i			0.864126i	−0.901843	+	0.432063i	$0.857786\pi$
$102$	2.10811	+	18.6945i	0.208734	+	1.85103i
$103$	2.06089	−	1.18985i	0.203065	−	0.117240i	−0.395019	−	0.918673i	$-0.629262\pi$
$103$	2.06089	−	1.18985i	0.203065	−	0.117240i	0.598084	+	0.801433i	$0.295929\pi$
$104$	7.13640	+	9.16589i	0.699781	+	0.898789i
$105$	−2.08477	−	8.48811i	−0.203453	−	0.828355i
$106$	−1.39190	−	3.33814i	−0.135193	−	0.324229i
$107$	−0.151752			−0.0146704			−0.00733522	−	0.999973i	$-0.502335\pi$
$107$	−0.151752			−0.0146704			−0.00733522	+	0.999973i	$0.502335\pi$
$108$	−4.66412	−	9.28687i	−0.448805	−	0.893630i
$109$	9.30823	−	16.1223i	0.891567	−	1.54424i	0.0535700	−	0.998564i	$-0.482940\pi$
$109$	9.30823	−	16.1223i	0.891567	−	1.54424i	0.837997	−	0.545675i	$-0.183727\pi$
$110$	6.15577	−	8.06149i	0.586930	−	0.768633i
$111$	−5.54190	+	5.31436i	−0.526014	+	0.504417i
$112$	5.72103	+	9.69757i	0.540586	+	0.916334i
$113$	12.3814	−	7.14841i	1.16474	−	0.672466i	0.212308	−	0.977203i	$-0.431902\pi$
$113$	12.3814	−	7.14841i	1.16474	−	0.672466i	0.952436	+	0.304737i	$0.0985687\pi$
$114$	10.6426	−	0.857239i	0.996772	−	0.0802878i
$115$	−1.29636	−	0.748452i	−0.120886	−	0.0697936i
$116$	−3.28259	+	12.4851i	−0.304781	+	1.15921i
$117$	10.4029	+	6.60222i	0.961747	+	0.610376i
$118$	1.11775	−	8.64707i	0.102898	−	0.796027i
$119$	−10.8095	−	18.7226i	−0.990903	−	1.71629i
$120$	−8.16002	+	3.24776i	−0.744904	+	0.296478i
$121$	−2.50280	−	4.33498i	−0.227527	−	0.394089i
$122$	0.140972	−	1.09057i	0.0127630	−	0.0987357i
$123$	8.82090	+	9.19857i	0.795353	+	0.829407i
$124$	−6.84703	+	1.86917i	−0.614882	+	0.167857i
$125$			12.1657i			1.08813i
$126$	9.17953	+	7.63909i	0.817777	+	0.680545i
$127$	2.59683	−	1.49928i	0.230431	−	0.133040i	−0.380340	−	0.924847i	$-0.624193\pi$
$127$	2.59683	−	1.49928i	0.230431	−	0.133040i	0.610771	+	0.791807i	$0.290860\pi$
$128$	8.86133	−	7.03397i	0.783239	−	0.621721i
$129$	1.18085	−	4.06434i	0.103968	−	0.357845i
$130$	6.31938	−	8.27575i	0.554246	−	0.725831i
$131$	8.28796			0.724123			0.362061	−	0.932154i	$-0.382073\pi$
$131$	8.28796			0.724123			0.362061	+	0.932154i	$0.382073\pi$
$132$	−0.225320	+	13.8570i	−0.0196116	+	1.20610i
$133$	−10.8161	+	5.79258i	−0.937878	+	0.502280i
$134$	0.676979	−	0.886559i	0.0584821	−	0.0765871i
$135$	−6.98776	+	6.16009i	−0.601411	+	0.530176i
$136$	−17.1407	+	13.3454i	−1.46980	+	1.14436i
$137$			14.4636i			1.23571i	0.786293	+	0.617854i	$0.211998\pi$
$137$			14.4636i			1.23571i	−0.786293	+	0.617854i	$0.788002\pi$
$138$	2.03240	−	0.229187i	0.173009	−	0.0195097i
$139$	−17.9404	−	10.3579i	−1.52169	−	0.878546i	−0.999672	−	0.0256085i	$-0.991848\pi$
$139$	−17.9404	−	10.3579i	−1.52169	−	0.878546i	−0.522014	−	0.852937i	$-0.674819\pi$
$140$	7.10290	−	7.16994i	0.600304	−	0.605970i
$141$	−5.46691	+	5.24245i	−0.460397	+	0.441494i
$142$	−7.62472	−	5.82225i	−0.639852	−	0.488593i
$143$	−8.21550	−	14.2297i	−0.687015	−	1.18994i
$144$	6.33470	−	10.1917i	0.527892	−	0.849312i
$145$	11.5716			0.960967
$146$	−12.8189	−	9.78853i	−1.06090	−	0.810105i
$147$	−1.53571	−	0.446185i	−0.126663	−	0.0368007i
$148$	−8.57463	−	2.25445i	−0.704830	−	0.185315i
$149$			9.49001i			0.777452i	0.921354	+	0.388726i	$0.127085\pi$
$149$			9.49001i			0.777452i	−0.921354	+	0.388726i	$0.872915\pi$
$150$	−2.59830	−	3.51989i	−0.212150	−	0.287397i
$151$	15.1692	+	8.75796i	1.23446	+	0.712713i	0.967955	−	0.251122i	$-0.0807995\pi$
$151$	15.1692	+	8.75796i	1.23446	+	0.712713i	0.266500	+	0.963835i	$0.414133\pi$
$152$	7.25974	+	9.96475i	0.588843	+	0.808248i
$153$	−12.3465	+	19.4539i	−0.998154	+	1.57276i
$154$	−6.12912	−	14.6993i	−0.493899	−	1.18450i
$155$	3.18103	+	5.50970i	0.255506	+	0.442550i
$156$	−0.231308	+	14.2253i	−0.0185195	+	1.13894i
$157$	−18.2677			−1.45792			−0.728961	−	0.684555i	$-0.759996\pi$
$157$	−18.2677			−1.45792			−0.728961	+	0.684555i	$0.759996\pi$
$158$	−0.845368	−	2.02742i	−0.0672539	−	0.161293i
$159$	1.23585	−	4.25364i	0.0980096	−	0.337336i
$160$	−8.11754	−	6.07870i	−0.641748	−	0.480564i
$161$	−2.03545	+	1.17517i	−0.160416	+	0.0926164i
$162$	2.68282	−	12.4420i	0.210782	−	0.977533i
$163$		−	5.04086i		−	0.394831i	−0.980320	−	0.197415i	$-0.936745\pi$
$163$		−	5.04086i		−	0.394831i	0.980320	−	0.197415i	$-0.0632547\pi$
$164$	−3.74199	+	14.2324i	−0.292200	+	1.11136i
$165$	12.0641	−	2.96307i	0.939187	−	0.230674i
$166$	−2.82858	−	2.15991i	−0.219541	−	0.167642i
$167$	−6.07102	+	10.5153i	−0.469790	+	0.813699i	−0.999403	−	0.0345395i	$-0.989004\pi$
$167$	−6.07102	+	10.5153i	−0.469790	+	0.813699i	0.529614	+	0.848239i	$0.322337\pi$
$168$	−1.98993	+	13.6455i	−0.153527	+	1.05277i
$169$	−1.93385	−	3.34953i	−0.148758	−	0.257656i
$170$	15.4761	+	11.8176i	1.18696	+	0.906365i
$171$	10.8116	+	7.35588i	0.826785	+	0.562518i
$172$	4.71465	−	1.28705i	0.359489	−	0.0981367i
$173$	20.6152	−	11.9022i	1.56735	−	0.904908i	0.570870	−	0.821040i	$-0.306606\pi$
$173$	20.6152	−	11.9022i	1.56735	−	0.904908i	0.996477	−	0.0838681i	$-0.0267274\pi$
$174$	−12.7204	+	9.38989i	−0.964330	+	0.711846i
$175$	4.35399	+	2.51378i	0.329131	+	0.190024i
$176$	−13.7831	+	8.13124i	−1.03894	+	0.612915i
$177$	7.70745	−	7.39100i	0.579328	−	0.555542i
$178$	−8.93993	−	21.4403i	−0.670076	−	1.60702i
$179$	−24.6916			−1.84553			−0.922767	−	0.385359i	$-0.874078\pi$
$179$	−24.6916			−1.84553			−0.922767	+	0.385359i	$0.874078\pi$
$180$	−10.2791	−	3.16861i	−0.766161	−	0.236174i
$181$	3.56559	+	6.17578i	0.265028	+	0.459042i	0.967571	−	0.252599i	$-0.0812855\pi$
$181$	3.56559	+	6.17578i	0.265028	+	0.459042i	−0.702543	+	0.711641i	$0.747952\pi$
$182$	−6.29202	−	15.0899i	−0.466396	−	1.11854i
$183$	0.972066	−	0.932156i	0.0718572	−	0.0689069i
$184$	1.45087	+	1.86348i	0.106960	+	0.137377i
$185$			7.94725i			0.584294i
$186$	−7.96775	−	3.47542i	−0.584224	−	0.254830i
$187$	26.6102	−	15.3634i	1.94593	−	1.12348i
$188$	−8.45860	−	2.22394i	−0.616907	−	0.162198i
$189$	2.89048	+	14.3379i	0.210252	+	1.04293i
$190$	6.98380	−	8.56476i	0.506658	−	0.621353i
$191$	−11.7234	+	20.3056i	−0.848277	+	1.46926i	0.0344679	+	0.999406i	$0.489026\pi$
$191$	−11.7234	+	20.3056i	−0.848277	+	1.46926i	−0.882745	+	0.469853i	$0.844307\pi$
$192$	13.8561	+	0.0951193i	0.999976	+	0.00686464i
$193$	3.14592			0.226449			0.113224	−	0.993569i	$-0.463882\pi$
$193$	3.14592			0.226449			0.113224	+	0.993569i	$0.463882\pi$
$194$	−8.76841	+	3.65614i	−0.629535	+	0.262496i
$195$	12.3847	−	3.04182i	0.886888	−	0.217829i
$196$	−0.486312	−	1.78143i	−0.0347366	−	0.127245i
$197$			19.5577i			1.39343i	0.717349	+	0.696714i	$0.245355\pi$
$197$			19.5577i			1.39343i	−0.717349	+	0.696714i	$0.754645\pi$
$198$	−10.8574	+	13.0468i	−0.771600	+	0.927194i
$199$	−19.6330	+	11.3351i	−1.39174	+	0.803523i	−0.993508	−	0.113760i	$-0.963711\pi$
$199$	−19.6330	+	11.3351i	−1.39174	+	0.803523i	−0.398235	+	0.917283i	$0.630377\pi$
$200$	1.90032	−	4.68079i	0.134373	−	0.330982i
$201$	1.32674	−	0.325862i	0.0935812	−	0.0229845i
$202$	−12.1802	−	1.57446i	−0.856996	−	0.110779i
$203$	9.08445	−	15.7347i	0.637604	−	1.10436i
$204$	−26.6020	−	0.432558i	−1.86251	−	0.0302851i
$205$	13.1910			0.921301
$206$	1.29519	+	3.10620i	0.0902399	+	0.216419i
$207$	2.11497	+	1.34227i	0.147000	+	0.0932942i
$208$	−14.1494	+	8.34735i	−0.981083	+	0.578785i
$209$	−8.23293	−	15.3729i	−0.569484	−	1.06336i
$210$	12.2829	−	1.38510i	0.847602	−	0.0955812i
$211$			27.7223i			1.90848i	0.299040	+	0.954240i	$0.403333\pi$
$211$			27.7223i			1.90848i	−0.299040	+	0.954240i	$0.596667\pi$
$212$	4.93424	−	1.34700i	0.338885	−	0.0925121i
$213$	−2.80253	−	11.4104i	−0.192026	−	0.781831i
$214$	0.0275125	−	0.212839i	0.00188071	−	0.0145494i
$215$	−2.19035	−	3.79380i	−0.149381	−	0.258735i
$216$	13.8708	−	4.85794i	0.943792	−	0.330541i
$217$	9.98927			0.678116
$218$	20.9247	+	15.9782i	1.41720	+	1.08218i
$219$	−4.71169	−	19.1836i	−0.318386	−	1.29630i
$220$	10.1906	+	10.0953i	0.687047	+	0.680623i
$221$	27.3174	−	15.7717i	1.83757	−	1.06092i
$222$	−6.44889	−	8.73625i	−0.432821	−	0.586339i
$223$	−9.98765	+	5.76637i	−0.668822	+	0.386145i	−0.795630	−	0.605782i	$-0.792860\pi$
$223$	−9.98765	+	5.76637i	−0.668822	+	0.386145i	0.126808	+	0.991927i	$0.459527\pi$
$224$	−14.6385	+	6.26584i	−0.978075	+	0.418654i
$225$	0.224511	−	5.35357i	0.0149674	−	0.356905i
$226$	7.78123	+	18.6615i	0.517600	+	1.24134i
$227$	8.12056	−	14.0652i	0.538981	−	0.933542i	−0.459979	−	0.887930i	$-0.652143\pi$
$227$	8.12056	−	14.0652i	0.538981	−	0.933542i	0.998959	−	0.0456119i	$-0.0145238\pi$
$228$	−0.727173	+	15.0821i	−0.0481582	+	0.998840i
$229$	1.91127	+	3.31041i	0.126300	+	0.218758i	0.922240	−	0.386617i	$-0.126356\pi$
$229$	1.91127	+	3.31041i	0.126300	+	0.218758i	−0.795940	+	0.605375i	$0.793023\pi$
$230$	1.28477	−	1.68251i	0.0847149	−	0.110941i
$231$	5.44200	−	18.7306i	0.358057	−	1.23238i
$232$	−16.9157	−	6.86750i	−1.11057	−	0.450873i
$233$	16.8430	+	9.72434i	1.10342	+	0.637063i	0.937118	−	0.349012i	$-0.113483\pi$
$233$	16.8430	+	9.72434i	1.10342	+	0.637063i	0.166306	+	0.986074i	$0.446816\pi$
$234$	−11.1459	+	13.3935i	−0.728633	+	0.875563i
$235$			7.83971i			0.511406i
$236$	11.9253	+	3.13540i	0.776268	+	0.204097i
$237$	0.750596	−	2.58345i	0.0487564	−	0.167813i
$238$	28.2190	−	11.7664i	1.82916	−	0.762702i
$239$	−8.39290	−	14.5369i	−0.542892	−	0.940316i	−0.998736	−	0.0502564i	$-0.983996\pi$
$239$	−8.39290	−	14.5369i	−0.542892	−	0.940316i	0.455845	−	0.890059i	$-0.349337\pi$
$240$	−3.07573	−	12.0336i	−0.198537	−	0.776765i
$241$	12.3210			0.793665			0.396833	−	0.917891i	$-0.370109\pi$
$241$	12.3210			0.793665			0.396833	+	0.917891i	$0.370109\pi$
$242$	6.53375	−	2.72436i	0.420005	−	0.175129i
$243$	12.1151	−	9.80940i	0.777184	−	0.629273i
$244$	1.50402	+	0.395438i	0.0962848	+	0.0253153i
$245$	−1.43349	+	0.827624i	−0.0915821	+	0.0528749i
$246$	−14.5006	+	10.7040i	−0.924525	+	0.682463i
$247$	−8.45175	−	15.7815i	−0.537772	−	1.00415i
$248$	−1.38024	−	9.94215i	−0.0876453	−	0.631327i
$249$	−1.03967	−	4.23300i	−0.0658864	−	0.268255i
$250$	−17.0629	−	2.20562i	−1.07915	−	0.139496i
$251$	6.35327	+	11.0042i	0.401015	+	0.694578i	0.993849	−	0.110747i	$-0.0353243\pi$
$251$	6.35327	+	11.0042i	0.401015	+	0.694578i	−0.592834	+	0.805325i	$0.701991\pi$
$252$	−12.3784	+	11.4897i	−0.779766	+	0.723786i
$253$	−1.67026	−	2.89297i	−0.105008	−	0.181880i
$254$	1.63201	+	3.91399i	0.102401	+	0.245585i
$255$	5.68835	+	23.1600i	0.356218	+	1.45034i
$256$	8.25891	+	13.7037i	0.516182	+	0.856479i
$257$	1.83140	+	1.05736i	0.114240	+	0.0659562i	0.556031	−	0.831162i	$-0.312324\pi$
$257$	1.83140	+	1.05736i	0.114240	+	0.0659562i	−0.441791	+	0.897118i	$0.645657\pi$
$258$	5.48633	+	2.39306i	0.341564	+	0.148985i
$259$	10.8065	+	6.23912i	0.671482	+	0.387680i
$260$	10.4614	+	10.3636i	0.648789	+	0.642723i
$261$	−19.3471	−	0.811351i	−1.19755	−	0.0502214i
$262$	−1.50259	+	11.6242i	−0.0928306	+	0.718148i
$263$	−0.980055	−	1.69750i	−0.0604328	−	0.104673i	0.834226	−	0.551422i	$-0.185915\pi$
$263$	−0.980055	−	1.69750i	−0.0604328	−	0.104673i	−0.894659	+	0.446750i	$0.852581\pi$
$264$	−19.3942	−	2.82827i	−1.19363	−	0.174068i
$265$	−2.29237	−	3.97050i	−0.140819	−	0.243906i
$266$	−6.16339	−	16.2203i	−0.377902	−	0.994531i
$267$	7.93769	−	27.3205i	0.485779	−	1.67199i
$268$	1.12070	+	1.11022i	0.0684579	+	0.0678178i
$269$	−21.4693	−	12.3953i	−1.30901	−	0.755757i	−0.327078	−	0.944997i	$-0.606064\pi$
$269$	−21.4693	−	12.3953i	−1.30901	−	0.755757i	−0.981931	+	0.189241i	$0.939397\pi$
$270$	−7.37293	−	10.9175i	−0.448702	−	0.664416i
$271$	−1.11291	−	0.642537i	−0.0676042	−	0.0390313i	0.465817	−	0.884881i	$-0.345761\pi$
$271$	−1.11291	−	0.642537i	−0.0676042	−	0.0390313i	−0.533421	+	0.845850i	$0.679094\pi$
$272$	−15.6100	−	26.4600i	−0.946493	−	1.60438i
$273$	5.58664	−	19.2285i	0.338119	−	1.16376i
$274$	−20.2858	−	2.62223i	−1.22551	−	0.158415i
$275$	−3.57281	+	6.18829i	−0.215448	+	0.373168i
$276$	−0.0470263	+	2.89208i	−0.00283065	+	0.174083i
$277$	2.99077	−	5.18016i	0.179698	−	0.311246i	−0.762079	−	0.647484i	$-0.775821\pi$
$277$	2.99077	−	5.18016i	0.179698	−	0.311246i	0.941777	+	0.336238i	$0.109155\pi$
$278$	17.7800	−	23.2843i	1.06637	−	1.39650i
$279$	−4.93219	−	9.43497i	−0.295283	−	0.564857i
$280$	8.76841	+	11.2620i	0.524013	+	0.673035i
$281$		−	9.01630i		−	0.537867i	−0.963159	−	0.268934i	$-0.913329\pi$
$281$		−	9.01630i		−	0.537867i	0.963159	−	0.268934i	$-0.0866712\pi$
$282$	−6.36163	−	8.61803i	−0.378829	−	0.513196i
$283$			31.9615i			1.89991i	0.312383	+	0.949956i	$0.398873\pi$
$283$			31.9615i			1.89991i	−0.312383	+	0.949956i	$0.601127\pi$
$284$	9.54832	−	9.63844i	0.566589	−	0.571936i
$285$	13.2405	−	2.80725i	0.784302	−	0.166287i
$286$	21.4472	−	8.94279i	1.26820	−	0.528798i
$287$	10.3558	−	17.9368i	0.611285	−	1.05878i
$288$	13.1459	+	10.7324i	0.774629	+	0.632416i
$289$	20.9939	+	36.3625i	1.23494	+	2.13897i
$290$	−2.09791	+	16.2296i	−0.123193	+	0.953037i
$291$	−11.1732	−	3.24626i	−0.654985	−	0.190299i
$292$	16.0529	−	16.2044i	0.939424	−	0.948291i
$293$	−12.7570	+	7.36523i	−0.745270	+	0.430282i	−0.823982	−	0.566616i	$-0.808252\pi$
$293$	−12.7570	+	7.36523i	−0.745270	+	0.430282i	0.0787126	+	0.996897i	$0.474919\pi$
$294$	0.904217	−	2.07301i	0.0527350	−	0.120900i
$295$		−	11.0527i		−	0.643514i
$296$	4.71654	−	11.6176i	0.274143	−	0.675258i
$297$	−20.3783	+	4.10821i	−1.18247	+	0.238383i
$298$	−13.3102	−	1.72052i	−0.771036	−	0.0996672i
$299$	−1.71465	−	2.96986i	−0.0991608	−	0.171751i
$300$	5.40786	−	3.00608i	0.312223	−	0.173556i
$301$	−6.87829			−0.396458
$302$	−15.0336	+	19.6877i	−0.865086	+	1.13290i
$303$	−10.4109	−	10.8567i	−0.598091	−	0.623699i
$304$	−15.2922	+	8.37552i	−0.877067	+	0.480369i
$305$		−	1.39397i		−	0.0798186i
$306$	−25.0466	−	20.8435i	−1.43182	−	1.19154i
$307$	−4.99607	−	2.88448i	−0.285141	−	0.164626i	0.350608	−	0.936522i	$-0.385975\pi$
$307$	−4.99607	−	2.88448i	−0.285141	−	0.164626i	−0.635748	+	0.771896i	$0.719308\pi$
$308$	21.7276	−	5.93141i	1.23804	−	0.337973i
$309$	−1.14999	+	3.95810i	−0.0654204	+	0.225168i
$310$	−8.30431	+	3.46263i	−0.471653	+	0.196664i
$311$	2.57758	+	4.46449i	0.146161	+	0.253158i	0.929805	−	0.368051i	$-0.119975\pi$
$311$	2.57758	+	4.46449i	0.146161	+	0.253158i	−0.783645	+	0.621210i	$0.786642\pi$
$312$	−19.9097	−	2.90344i	−1.12716	−	0.164375i
$313$	16.2255			0.917121			0.458560	−	0.888663i	$-0.348365\pi$
$313$	16.2255			0.917121			0.458560	+	0.888663i	$0.348365\pi$
$314$	3.31191	−	25.6213i	0.186902	−	1.44589i
$315$	12.7819	+	8.11208i	0.720179	+	0.457064i
$316$	2.99681	−	0.818099i	0.168584	−	0.0460216i
$317$		−	0.108879i		−	0.00611525i	−0.999995	−	0.00305762i	$-0.999027\pi$
$317$		−	0.108879i		−	0.00611525i	0.999995	−	0.00305762i	$-0.000973273\pi$
$318$	5.74187	+	2.50452i	0.321988	+	0.140446i
$319$	22.3636	+	12.9116i	1.25212	+	0.722913i
$320$	9.99735	−	10.2831i	0.558869	−	0.574845i
$321$	0.189712	−	0.181922i	0.0105887	−	0.0101539i
$322$	−1.27920	−	3.06787i	−0.0712872	−	0.170966i
$323$	29.5121	−	15.8052i	1.64210	−	0.879424i
$324$	16.9640	+	6.01849i	0.942445	+	0.334360i
$325$	−3.66777	+	6.35276i	−0.203451	+	0.352388i
$326$	7.07003	+	0.913900i	0.391573	+	0.0506162i
$327$	7.69105	+	31.3140i	0.425316	+	1.73167i
$328$	−19.2831	−	7.82861i	−1.06473	−	0.432263i
$329$	10.6602	+	6.15469i	0.587718	+	0.339319i
$330$	1.96863	+	17.4576i	0.108370	+	0.961009i
$331$	−2.75516	−	1.59069i	−0.151437	−	0.0874325i	0.422366	−	0.906425i	$-0.361200\pi$
$331$	−2.75516	−	1.59069i	−0.151437	−	0.0874325i	−0.573804	+	0.818993i	$0.694533\pi$
$332$	3.54219	−	3.57563i	0.194403	−	0.196238i
$333$	0.557229	−	13.2874i	0.0305359	−	0.728145i
$334$	−13.6475	−	10.4213i	−0.746760	−	0.570227i
$335$	0.707021	−	1.22460i	0.0386287	−	0.0669068i
$336$	−18.7776	−	5.26488i	−1.02440	−	0.287223i
$337$	21.4509			1.16851			0.584253	−	0.811571i	$-0.301387\pi$
$337$	21.4509			1.16851			0.584253	+	0.811571i	$0.301387\pi$
$338$	5.04847	−	2.10505i	0.274601	−	0.114500i
$339$	−6.90889	+	23.7795i	−0.375239	+	1.29152i
$340$	−19.3804	+	19.5634i	−1.05105	+	1.06097i
$341$			14.1976i			0.768846i
$342$	−12.2771	+	13.8302i	−0.663869	+	0.747849i
$343$		−	17.1049i		−	0.923578i
$344$	0.950388	+	6.84584i	0.0512415	+	0.369103i
$345$	2.51788	−	0.618419i	0.135558	−	0.0332946i
$346$	12.9559	+	31.0716i	0.696512	+	1.67042i
$347$	27.2356			1.46208			0.731042	−	0.682333i	$-0.239035\pi$
$347$	27.2356			1.46208			0.731042	+	0.682333i	$0.239035\pi$
$348$	−10.8636	−	19.5433i	−0.582348	−	1.04763i
$349$	−7.95134	+	13.7721i	−0.425626	+	0.737205i	−0.996479	−	0.0838470i	$-0.973279\pi$
$349$	−7.95134	+	13.7721i	−0.425626	+	0.737205i	0.570853	+	0.821052i	$0.306613\pi$
$350$	−4.31506	+	5.65092i	−0.230650	+	0.302055i
$351$	−20.9199	+	4.21740i	−1.11662	+	0.225108i
$352$	−8.90558	−	20.8055i	−0.474669	−	1.10894i
$353$	−20.1971	−	11.6608i	−1.07498	−	0.620642i	−0.145445	−	0.989366i	$-0.546461\pi$
$353$	−20.1971	−	11.6608i	−1.07498	−	0.620642i	−0.929539	+	0.368724i	$0.879795\pi$
$354$	8.96886	+	12.1500i	0.476690	+	0.645767i
$355$	−10.5320	−	6.08063i	−0.558978	−	0.322726i
$356$	31.6918	−	8.65155i	1.67966	−	0.458531i
$357$	35.9582	+	10.4473i	1.90311	+	0.552929i
$358$	4.47654	−	34.6310i	0.236593	−	1.83031i
$359$	3.75437	−	6.50276i	0.198148	−	0.343203i	−0.749780	−	0.661687i	$-0.769841\pi$
$359$	3.75437	−	6.50276i	0.198148	−	0.343203i	0.947928	+	0.318485i	$0.103174\pi$
$360$	6.30771	−	13.8425i	0.332445	−	0.729563i
$361$	−8.43098	−	17.0270i	−0.443736	−	0.896158i
$362$	−9.30824	+	3.88124i	−0.489230	+	0.203993i
$363$	8.32567	+	2.41894i	0.436984	+	0.126961i
$364$	22.3051	−	6.08906i	1.16910	−	0.319153i
$365$	−17.7066	−	10.2229i	−0.926806	−	0.535092i
$366$	1.13116	+	1.53236i	0.0591264	+	0.0800980i
$367$			21.2697i			1.11027i	0.831761	+	0.555134i	$0.187333\pi$
$367$			21.2697i			1.11027i	−0.831761	+	0.555134i	$0.812667\pi$
$368$	−2.87665	+	1.69706i	−0.149956	+	0.0884656i
$369$	−22.0547	−	0.924900i	−1.14812	−	0.0481484i
$370$	−11.1464	−	1.44082i	−0.579472	−	0.0749049i
$371$	−7.19865			−0.373735
$372$	6.31897	−	10.5450i	0.327623	−	0.546734i
$373$	−3.99784	−	6.92447i	−0.207000	−	0.358535i	0.743768	−	0.668438i	$-0.233037\pi$
$373$	−3.99784	−	6.92447i	−0.207000	−	0.358535i	−0.950768	+	0.309903i	$0.899703\pi$
$374$	16.7235	+	40.1073i	0.864749	+	2.07390i
$375$	−14.5844	−	15.2088i	−0.753133	−	0.785379i
$376$	4.65271	−	11.4604i	0.239945	−	0.591023i
$377$	22.9580	+	13.2548i	1.18240	+	0.682658i
$378$	−20.6335	+	1.45459i	−1.06127	+	0.0748162i
$379$		−	26.4444i		−	1.35836i	−0.733972	−	0.679180i	$-0.762336\pi$
$379$		−	26.4444i		−	1.35836i	0.733972	−	0.679180i	$-0.237664\pi$
$380$	10.7463	+	11.3479i	0.551273	+	0.582133i
$381$	−1.44904	+	4.98742i	−0.0742368	+	0.255513i
$382$	−26.3540	−	20.1240i	−1.34839	−	1.02963i
$383$	20.3853			1.04164			0.520819	−	0.853667i	$-0.325627\pi$
$383$	20.3853			1.04164			0.520819	+	0.853667i	$0.325627\pi$
$384$	−2.64549	+	19.4165i	−0.135002	+	0.990845i
$385$	−10.0943	−	17.4838i	−0.514453	−	0.891059i
$386$	−0.570351	+	4.41230i	−0.0290301	+	0.224580i
$387$	3.39615	+	6.49662i	0.172636	+	0.330242i
$388$	−3.53821	−	12.9609i	−0.179625	−	0.657992i
$389$			0.341040i			0.0172914i	0.999963	+	0.00864570i	$0.00275204\pi$
$389$			0.341040i			0.0172914i	−0.999963	+	0.00864570i	$0.997248\pi$
$390$	2.02096	+	17.9216i	0.102335	+	0.907495i
$391$	5.55379	−	3.20648i	0.280867	−	0.162159i
$392$	2.58670	−	0.359104i	0.130648	−	0.0181375i
$393$	−10.3611	+	9.93571i	−0.522649	+	0.501190i
$394$	−27.4305	−	3.54578i	−1.38193	−	0.178634i
$395$	−1.39227	−	2.41148i	−0.0700527	−	0.121335i
$396$	−16.3303	−	17.5933i	−0.820626	−	0.884097i
$397$	−6.00936	+	10.4085i	−0.301601	+	0.522389i	−0.976499	−	0.215523i	$-0.930855\pi$
$397$	−6.00936	+	10.4085i	−0.301601	+	0.522389i	0.674897	+	0.737912i	$0.264188\pi$
$398$	−12.3385	−	29.5911i	−0.618475	−	1.48327i
$399$	6.57748	−	20.2080i	0.329286	−	1.01167i
$400$	6.22049	+	3.51390i	0.311024	+	0.175695i
$401$			5.16485i			0.257920i	0.991650	+	0.128960i	$0.0411639\pi$
$401$			5.16485i			0.257920i	−0.991650	+	0.128960i	$0.958836\pi$
$402$	0.216500	+	1.91989i	0.0107980	+	0.0957556i
$403$			14.5750i			0.726032i
$404$	4.41650	−	16.7978i	0.219729	−	0.835723i
$405$	1.35089	−	16.0780i	0.0671262	−	0.798922i
$406$	20.4217	+	15.5940i	1.01351	+	0.773919i
$407$	−8.86760	+	15.3591i	−0.439551	+	0.761324i
$408$	5.42958	−	37.2321i	0.268804	−	1.84326i
$409$	3.69305	−	6.39656i	0.182610	−	0.316289i	−0.760159	−	0.649737i	$-0.774879\pi$
$409$	3.69305	−	6.39656i	0.182610	−	0.316289i	0.942768	+	0.333448i	$0.108212\pi$
$410$	−2.39151	+	18.5010i	−0.118108	+	0.913699i
$411$	−17.3391	−	18.0815i	−0.855277	−	0.891896i
$412$	−4.59140	+	1.25341i	−0.226202	+	0.0617509i
$413$	−15.0292	−	8.67712i	−0.739539	−	0.426973i
$414$	−2.26603	+	2.72298i	−0.111369	+	0.133827i
$415$	−3.90710	−	2.25576i	−0.191792	−	0.110731i
$416$	−9.14227	−	21.3585i	−0.448237	−	1.04719i
$417$	34.8452	−	8.55835i	1.70638	−	0.419104i
$418$	23.0538	−	8.75997i	1.12760	−	0.428464i
$419$	1.79225	+	3.10427i	0.0875573	+	0.151654i	0.906478	−	0.422253i	$-0.138761\pi$
$419$	1.79225	+	3.10427i	0.0875573	+	0.151654i	−0.818921	+	0.573907i	$0.805427\pi$
$420$	−0.284206	+	17.4785i	−0.0138678	+	0.852862i
$421$	−3.28516	−	5.69006i	−0.160109	−	0.277317i	0.774799	−	0.632208i	$-0.217851\pi$
$421$	−3.28516	−	5.69006i	−0.160109	−	0.277317i	−0.934908	+	0.354891i	$0.884518\pi$
$422$	−38.8817	−	5.02601i	−1.89273	−	0.244662i
$423$	0.549688	−	13.1076i	0.0267267	−	0.637313i
$424$	0.994653	+	7.16469i	0.0483046	+	0.347948i
$425$	−11.8800	−	6.85891i	−0.576263	−	0.332706i
$426$	16.5118	−	1.86197i	0.799997	−	0.0902130i
$427$	−1.89549	−	1.09436i	−0.0917291	−	0.0529598i
$428$	0.293529	+	0.0771749i	0.0141882	+	0.00373039i
$429$	27.3292	+	7.94023i	1.31947	+	0.383358i
$430$	5.71808	−	2.38426i	0.275750	−	0.114979i
$431$	−10.2172	−	17.6968i	−0.492147	−	0.852423i	0.507812	−	0.861468i	$-0.330454\pi$
$431$	−10.2172	−	17.6968i	−0.492147	−	0.852423i	−0.999959	+	0.00904469i	$0.997121\pi$
$432$	4.29871	+	20.3352i	0.206822	+	0.978379i
$433$	−12.8544	−	22.2645i	−0.617743	−	1.06996i	−0.989897	−	0.141791i	$-0.954714\pi$
$433$	−12.8544	−	22.2645i	−0.617743	−	1.06996i	0.372154	−	0.928171i	$-0.378619\pi$
$434$	−1.81104	+	14.0104i	−0.0869327	+	0.672520i
$435$	−14.4661	+	13.8721i	−0.693596	+	0.665118i
$436$	−26.2037	+	26.4510i	−1.25493	+	1.26677i
$437$	−1.71829	−	3.20846i	−0.0821969	−	0.153481i
$438$	27.7600	−	3.13040i	1.32642	−	0.149576i
$439$	29.6483	−	17.1175i	1.41504	−	0.816972i	0.419179	−	0.907904i	$-0.362318\pi$
$439$	29.6483	−	17.1175i	1.41504	−	0.816972i	0.995857	+	0.0909320i	$0.0289846\pi$
$440$	−16.0066	+	12.4625i	−0.763085	+	0.594124i
$441$	2.45475	−	1.28323i	0.116893	−	0.0611064i
$442$	17.1679	+	41.1733i	0.816596	+	1.95841i
$443$	20.9145			0.993677			0.496839	−	0.867843i	$-0.334494\pi$
$443$	20.9145			0.993677			0.496839	+	0.867843i	$0.334494\pi$
$444$	13.4222	−	7.46099i	0.636987	−	0.354083i
$445$	−14.7235	−	25.5019i	−0.697963	−	1.20891i
$446$	−6.27685	−	15.0536i	−0.297217	−	0.712807i
$447$	−11.3767	−	11.8638i	−0.538101	−	0.561140i
$448$	−6.13418	−	21.6671i	−0.289813	−	1.02367i
$449$			10.7359i			0.506659i	0.967380	+	0.253329i	$0.0815257\pi$
$449$			10.7359i			0.506659i	−0.967380	+	0.253329i	$0.918474\pi$
$450$	7.46792	+	1.28548i	0.352041	+	0.0605981i
$451$	25.4934	+	14.7186i	1.20044	+	0.693073i
$452$	−27.5843	+	7.53022i	−1.29745	+	0.354192i
$453$	−29.4628	+	7.23639i	−1.38428	+	0.339995i
$454$	18.2549	+	13.9395i	0.856743	+	0.654211i
$455$	−10.3626	−	17.9485i	−0.485805	−	0.841440i
$456$	−21.0215	−	3.75426i	−0.984424	−	0.175809i
$457$	5.37257	−	9.30557i	0.251318	−	0.435296i	−0.712571	−	0.701600i	$-0.752469\pi$
$457$	5.37257	−	9.30557i	0.251318	−	0.435296i	0.963889	+	0.266304i	$0.0858026\pi$
$458$	−4.98951	+	2.08046i	−0.233144	+	0.0972136i
$459$	−7.88675	−	39.1212i	−0.368122	−	1.82602i
$460$	2.12686	+	2.10698i	0.0991655	+	0.0982383i
$461$	−5.64696	+	3.26027i	−0.263005	+	0.151846i	−0.625705	−	0.780060i	$-0.715188\pi$
$461$	−5.64696	+	3.26027i	−0.263005	+	0.151846i	0.362700	+	0.931906i	$0.381855\pi$
$462$	25.2839	+	11.0285i	1.17631	+	0.513091i
$463$	−33.3422	+	19.2501i	−1.54954	+	0.894629i	−0.551366	+	0.834264i	$0.685893\pi$
$463$	−33.3422	+	19.2501i	−1.54954	+	0.894629i	−0.998176	+	0.0603651i	$0.980773\pi$
$464$	12.6988	−	22.4800i	0.589525	−	1.04361i
$465$	−10.5818	−	3.07444i	−0.490720	−	0.142574i
$466$	−16.6924	+	21.8601i	−0.773262	+	1.01265i
$467$	−20.5044			−0.948828			−0.474414	−	0.880302i	$-0.657340\pi$
$467$	−20.5044			−0.948828			−0.474414	+	0.880302i	$0.657340\pi$
$468$	−16.7643	−	18.0609i	−0.774929	−	0.834866i
$469$	−1.11012	−	1.92278i	−0.0512604	−	0.0887857i
$470$	−10.9955	−	1.42133i	−0.507186	−	0.0655609i
$471$	22.8372	−	21.8995i	1.05228	−	1.00908i
$472$	−6.55957	+	16.1573i	−0.301929	+	0.743698i
$473$		−	9.77604i		−	0.449503i
$474$	3.48732	+	1.52112i	0.160178	+	0.0698673i
$475$	−4.10588	+	6.61469i	−0.188391	+	0.303503i
$476$	11.3868	+	41.7116i	0.521915	+	1.91185i
$477$	3.55433	+	6.79921i	0.162742	+	0.311314i
$478$	21.9103	−	9.13589i	1.00215	−	0.417866i
$479$	22.8821			1.04551			0.522756	−	0.852483i	$-0.324904\pi$
$479$	22.8821			1.04551			0.522756	+	0.852483i	$0.324904\pi$
$480$	17.4353	−	2.13217i	0.795808	−	0.0973199i
$481$	−9.10329	+	15.7674i	−0.415074	+	0.718930i
$482$	−2.23378	+	17.2808i	−0.101746	+	0.787117i
$483$	1.13579	−	3.90925i	0.0516804	−	0.177877i
$484$	2.63648	+	9.65780i	0.119840	+	0.438991i
$485$	−10.4295	+	6.02145i	−0.473577	+	0.273420i
$486$	11.5617	+	18.7704i	0.524448	+	0.851442i
$487$		−	6.02934i		−	0.273215i	−0.990625	−	0.136608i	$-0.956380\pi$
$487$		−	6.02934i		−	0.273215i	0.990625	−	0.136608i	$-0.0436200\pi$
$488$	−0.827295	+	2.03776i	−0.0374499	+	0.0922449i
$489$	6.04304	+	6.30178i	0.273276	+	0.284976i
$490$	−0.900890	−	2.16058i	−0.0406981	−	0.0976048i
$491$	4.50019			0.203091			0.101545	−	0.994831i	$-0.467621\pi$
$491$	4.50019			0.203091			0.101545	+	0.994831i	$0.467621\pi$
$492$	−12.3839	−	22.2784i	−0.558310	−	1.00439i
$493$	−24.7872	+	42.9326i	−1.11636	+	1.93359i
$494$	23.6665	−	8.99280i	1.06481	−	0.404605i
$495$	−11.5296	+	18.1668i	−0.518218	+	0.816537i
$496$	14.1945	−	0.133351i	0.637354	−	0.00598762i
$497$	−16.5366	+	9.54739i	−0.741766	+	0.428259i
$498$	6.12545	−	0.690747i	0.274488	−	0.0309531i
$499$		−	10.6457i		−	0.476566i	−0.971196	−	0.238283i	$-0.923415\pi$
$499$		−	10.6457i		−	0.476566i	0.971196	−	0.238283i	$-0.0765846\pi$
$500$	6.18696	−	23.5316i	0.276689	−	1.05237i
$501$	−5.01626	−	20.4236i	−0.224110	−	0.912460i
$502$	−16.5857	+	6.91570i	−0.740255	+	0.308663i
$503$	−9.46733	−	16.3979i	−0.422127	−	0.731146i	0.574020	−	0.818841i	$-0.305383\pi$
$503$	−9.46733	−	16.3979i	−0.422127	−	0.731146i	−0.996147	+	0.0876952i	$0.972050\pi$
$504$	−13.8707	−	19.4443i	−0.617850	−	0.866119i
$505$	−15.5688			−0.692801
$506$	4.36034	−	1.81812i	0.193841	−	0.0808253i
$507$	6.43305	+	1.86906i	0.285702	+	0.0830078i
$508$	−5.78542	+	1.57936i	−0.256686	+	0.0700728i
$509$	33.8244	+	19.5285i	1.49924	+	0.865586i	1.00000		0.000877837i	$-0.000279424\pi$
$509$	33.8244	+	19.5285i	1.49924	+	0.865586i	0.499240	+	0.866464i	$0.333613\pi$
$510$	−33.5143	+	3.77929i	−1.48404	+	0.167350i
$511$	−27.8017	+	16.0513i	−1.22988	+	0.710069i
$512$	−20.7173	+	9.09904i	−0.915585	+	0.402125i
$513$	−22.3344	+	3.76521i	−0.986086	+	0.166238i
$514$	−1.81502	+	2.37692i	−0.0800572	+	0.104842i
$515$	2.13309	+	3.69463i	0.0939954	+	0.162805i
$516$	−4.35104	+	7.26097i	−0.191544	+	0.319646i
$517$	−8.74760	+	15.1513i	−0.384719	+	0.666353i
$518$	−10.7098	+	14.0254i	−0.470564	+	0.616242i
$519$	−11.5034	+	39.5932i	−0.504944	+	1.73795i
$520$	−16.4320	+	12.7937i	−0.720592	+	0.561040i
$521$		−	22.1149i		−	0.968871i	−0.874827	−	0.484435i	$-0.839025\pi$
$521$		−	22.1149i		−	0.968871i	0.874827	−	0.484435i	$-0.160975\pi$
$522$	4.64555	−	26.9880i	0.203330	−	1.18123i
$523$	10.2374	−	5.91056i	0.447650	−	0.258451i	−0.259187	−	0.965827i	$-0.583455\pi$
$523$	10.2374	−	5.91056i	0.447650	−	0.258451i	0.706837	+	0.707376i	$0.250121\pi$
$524$	−16.0311	−	4.21491i	−0.700321	−	0.184129i
$525$	−8.45665	+	2.07704i	−0.369078	+	0.0906496i
$526$	2.55851	−	1.06682i	0.111556	−	0.0465154i
$527$	−27.2560			−1.18729
$528$	7.48292	−	26.6885i	0.325652	−	1.16147i
$529$	11.1514	+	19.3148i	0.484844	+	0.839774i
$530$	5.98441	−	2.49530i	0.259946	−	0.108389i
$531$	−0.774971	+	18.4796i	−0.0336309	+	0.801945i
$532$	23.8671	−	5.70372i	1.03477	−	0.247288i
$533$	26.1710	+	15.1098i	1.13359	+	0.654479i
$534$	36.8791	+	16.0861i	1.59592	+	0.696115i
$535$		−	0.272052i		−	0.0117618i
$536$	−1.76032	+	1.37055i	−0.0760343	+	0.0591990i
$537$	30.8679	−	29.6005i	1.33205	−	1.27736i
$538$	21.2774	−	27.8645i	0.917332	−	1.20132i
$539$	−3.69387			−0.159106
$540$	16.6489	−	8.36154i	0.716456	−	0.359824i
$541$	3.39836	+	5.88613i	0.146107	+	0.253064i	0.929785	−	0.368102i	$-0.119992\pi$
$541$	3.39836	+	5.88613i	0.146107	+	0.253064i	−0.783679	+	0.621167i	$0.786659\pi$
$542$	1.10295	−	1.44441i	0.0473760	−	0.0620427i
$543$	−11.8611	−	3.44612i	−0.509008	−	0.147887i
$544$	39.9415	−	17.0965i	1.71248	−	0.733006i
$545$	28.9031	+	16.6872i	1.23807	+	0.714802i
$546$	25.9559	+	11.3216i	1.11081	+	0.484520i
$547$			43.3641i			1.85411i	0.374921	+	0.927057i	$0.377670\pi$
$547$			43.3641i			1.85411i	−0.374921	+	0.927057i	$0.622330\pi$
$548$	7.35558	−	27.9764i	0.314215	−	1.19509i
$549$	−0.0977396	+	2.33065i	−0.00417142	+	0.0994697i
$550$	−8.03160	−	6.13295i	−0.342469	−	0.261510i
$551$	23.9046	+	14.8381i	1.01837	+	0.632124i
$552$	−4.04775	−	0.590287i	−0.172284	−	0.0251243i
$553$	−4.37210			−0.185921
$554$	6.72319	+	5.13384i	0.285641	+	0.218116i
$555$	−9.52726	−	9.93518i	−0.404410	−	0.421725i
$556$	29.4339	+	29.1586i	1.24827	+	1.23660i
$557$	19.8699	−	11.4719i	0.841913	−	0.486079i	−0.0160009	−	0.999872i	$-0.505093\pi$
$557$	19.8699	−	11.4719i	0.841913	−	0.486079i	0.857914	+	0.513793i	$0.171760\pi$
$558$	14.1272	−	5.20708i	0.598051	−	0.220433i
$559$		−	10.0359i		−	0.424472i
$560$	−17.3852	+	10.2563i	−0.734658	+	0.433408i
$561$	−14.8486	+	51.1070i	−0.626909	+	2.15774i
$562$	12.6458	+	1.63464i	0.533429	+	0.0689532i
$563$	12.8515	+	22.2595i	0.541627	+	0.938125i	0.998811	+	0.0487529i	$0.0155247\pi$
$563$	12.8515	+	22.2595i	0.541627	+	0.938125i	−0.457184	+	0.889372i	$0.651142\pi$
$564$	13.2405	−	7.36003i	0.557527	−	0.309913i
$565$	12.8152	+	22.1966i	0.539140	+	0.933818i
$566$	−44.8274	−	5.79457i	−1.88424	−	0.243564i
$567$	−20.8019	−	14.4592i	−0.873598	−	0.607229i
$568$	11.7872	+	15.1394i	0.494582	+	0.635234i
$569$	9.75621	+	5.63275i	0.409002	+	0.236137i	0.690361	−	0.723465i	$-0.257452\pi$
$569$	9.75621	+	5.63275i	0.409002	+	0.236137i	−0.281359	+	0.959603i	$0.590785\pi$
$570$	1.53681	+	19.0794i	0.0643697	+	0.799148i
$571$	17.0698	−	9.85524i	0.714348	−	0.412429i	−0.0983209	−	0.995155i	$-0.531347\pi$
$571$	17.0698	−	9.85524i	0.714348	−	0.412429i	0.812669	+	0.582726i	$0.198014\pi$
$572$	8.65431	+	31.7020i	0.361855	+	1.32553i
$573$	−9.68663	−	39.4390i	−0.404665	−	1.64759i
$574$	23.2797	+	17.7764i	0.971676	+	0.741974i
$575$	−0.745678	+	1.29155i	−0.0310969	+	0.0538614i
$576$	−17.4361	+	16.4919i	−0.726503	+	0.687163i
$577$	37.4911			1.56078			0.780388	−	0.625295i	$-0.215021\pi$
$577$	37.4911			1.56078			0.780388	+	0.625295i	$0.215021\pi$
$578$	−54.8062	+	22.8524i	−2.27964	+	0.950535i
$579$	−3.93285	+	3.77137i	−0.163443	+	0.156733i
$580$	−22.3824	−	5.88482i	−0.929381	−	0.244354i
$581$	−6.13466	+	3.54185i	−0.254509	+	0.146941i
$582$	6.57871	−	15.0824i	0.272696	−	0.625184i
$583$		−	10.2314i		−	0.423740i
$584$	19.8170	+	25.4527i	0.820035	+	1.05324i
$585$	−11.8361	+	18.6496i	−0.489361	+	0.771068i
$586$	−8.01725	−	19.2275i	−0.331190	−	0.794281i
$587$	3.14952	+	5.45513i	0.129995	+	0.225157i	0.923674	−	0.383179i	$-0.125171\pi$
$587$	3.14952	+	5.45513i	0.129995	+	0.225157i	−0.793680	+	0.608336i	$0.791837\pi$
$588$	2.74355	+	1.64404i	0.113142	+	0.0677990i
$589$	−0.493649	+	15.4609i	−0.0203404	+	0.637057i
$590$	15.5019	+	2.00384i	0.638204	+	0.0824968i
$591$	−23.4460	−	24.4499i	−0.964440	−	1.00573i
$592$	15.4391	+	8.72140i	0.634542	+	0.358447i
$593$	30.8163	−	17.7918i	1.26547	−	0.730621i	0.291345	−	0.956618i	$-0.405897\pi$
$593$	30.8163	−	17.7918i	1.26547	−	0.730621i	0.974128	+	0.225997i	$0.0725641\pi$
$594$	−2.06740	−	29.3262i	−0.0848264	−	1.20327i
$595$	33.5646	−	19.3785i	1.37602	−	0.794443i
$596$	4.82622	−	18.3562i	0.197690	−	0.751897i
$597$	10.9553	−	37.7067i	0.448370	−	1.54323i
$598$	4.47623	−	1.86644i	0.183046	−	0.0763245i
$599$	−1.96321	+	3.40038i	−0.0802147	+	0.138936i	−0.903342	−	0.428921i	$-0.858894\pi$
$599$	−1.96321	+	3.40038i	−0.0802147	+	0.138936i	0.823127	+	0.567857i	$0.192227\pi$
$600$	3.23572	+	8.12976i	0.132098	+	0.331896i
$601$	−17.9063	+	31.0147i	−0.730415	+	1.26512i	0.226291	+	0.974060i	$0.427340\pi$
$601$	−17.9063	+	31.0147i	−0.730415	+	1.26512i	−0.956706	+	0.291056i	$0.905993\pi$
$602$	1.24702	−	9.64711i	0.0508249	−	0.393187i
$603$	−1.26797	+	1.99789i	−0.0516356	+	0.0813603i
$604$	−24.8873	−	24.6546i	−1.01265	−	1.00318i
$605$	7.77147	−	4.48686i	0.315955	−	0.182417i
$606$	17.1144	−	12.6335i	0.695226	−	0.513200i
$607$	−18.5677	+	10.7201i	−0.753641	+	0.435115i	−0.827008	−	0.562190i	$-0.809959\pi$
$607$	−18.5677	+	10.7201i	−0.753641	+	0.435115i	0.0733673	+	0.997305i	$0.476625\pi$
$608$	−8.97458	−	22.9664i	−0.363967	−	0.931412i
$609$	7.50615	+	30.5612i	0.304165	+	1.23840i
$610$	1.95511	+	0.252725i	0.0791600	+	0.0102325i
$611$	−8.98010	+	15.5540i	−0.363296	+	0.629247i
$612$	33.7748	−	31.3500i	1.36526	−	1.26725i
$613$	21.6932	−	37.5738i	0.876182	−	1.51759i	0.0206840	−	0.999786i	$-0.493416\pi$
$613$	21.6932	−	37.5738i	0.876182	−	1.51759i	0.855498	−	0.517806i	$-0.173251\pi$
$614$	4.95139	−	6.48425i	0.199822	−	0.261683i
$615$	−16.4906	+	15.8136i	−0.664966	+	0.637664i
$616$	4.37989	+	31.5492i	0.176471	+	1.27116i
$617$	−36.0362	−	20.8055i	−1.45076	−	0.837599i	−0.452239	−	0.891897i	$-0.649375\pi$
$617$	−36.0362	−	20.8055i	−1.45076	−	0.837599i	−0.998525	+	0.0542976i	$0.982708\pi$
$618$	−5.34292	−	2.33050i	−0.214924	−	0.0937466i
$619$	−12.7039	−	7.33463i	−0.510615	−	0.294804i	0.222472	−	0.974939i	$-0.428588\pi$
$619$	−12.7039	−	7.33463i	−0.510615	−	0.294804i	−0.733086	+	0.680136i	$0.761921\pi$
$620$	−3.35093	−	12.2749i	−0.134577	−	0.492973i
$621$	−4.25313	+	0.857421i	−0.170672	+	0.0344071i
$622$	−6.72896	+	2.80576i	−0.269807	+	0.112501i
$623$	−46.2358			−1.85240
$624$	7.68180	−	27.3978i	0.307518	−	1.09679i
$625$	−12.8794			−0.515177
$626$	−2.94166	+	22.7570i	−0.117572	+	0.909553i
$627$	28.7215	+	9.34851i	1.14703	+	0.373343i
$628$	35.3345	+	9.29019i	1.41000	+	0.370719i
$629$	−29.4857	−	17.0236i	−1.17567	−	0.678775i
$630$	−13.6949	+	16.4565i	−0.545618	+	0.655642i
$631$	−7.23451	+	4.17685i	−0.288001	+	0.166278i	−0.637040	−	0.770831i	$-0.719841\pi$
$631$	−7.23451	+	4.17685i	−0.288001	+	0.166278i	0.349039	+	0.937108i	$0.386508\pi$
$632$	0.604103	+	4.35148i	0.0240299	+	0.173092i
$633$	−33.2338	−	34.6567i	−1.32093	−	1.37748i
$634$	0.152707	+	0.0197396i	0.00606479	+	0.000783958i
$635$	2.68782	+	4.65543i	0.106663	+	0.184745i
$636$	−4.55369	+	7.59916i	−0.180566	+	0.301326i
$637$	−3.79205			−0.150247
$638$	−22.1636	+	29.0251i	−0.877467	+	1.14912i
$639$	17.1825	+	10.9050i	0.679731	+	0.431393i
$640$	12.6101	+	15.8860i	0.498457	+	0.627951i
$641$	5.96935	−	3.44640i	0.235775	−	0.136125i	−0.377458	−	0.926027i	$-0.623202\pi$
$641$	5.96935	−	3.44640i	0.235775	−	0.136125i	0.613233	+	0.789902i	$0.289869\pi$
$642$	0.220760	+	0.299061i	0.00871270	+	0.0118030i
$643$			16.8686i			0.665234i	0.943062	+	0.332617i	$0.107932\pi$
$643$			16.8686i			0.665234i	−0.943062	+	0.332617i	$0.892068\pi$
$644$	4.53474	−	1.23794i	0.178694	−	0.0487816i
$645$	7.28630	+	2.11696i	0.286898	+	0.0833553i
$646$	16.8170	+	44.2575i	0.661655	+	1.74129i
$647$	15.5815			0.612572			0.306286	−	0.951939i	$-0.400914\pi$
$647$	15.5815			0.612572			0.306286	+	0.951939i	$0.400914\pi$
$648$	−11.5167	+	22.7016i	−0.452420	+	0.891805i
$649$	12.3327	−	21.3609i	0.484101	−	0.838488i
$650$	−8.24507	−	6.29595i	−0.323398	−	0.246948i
$651$	−12.4880	+	11.9753i	−0.489443	+	0.469347i
$652$	−2.56357	+	9.75034i	−0.100397	+	0.381853i
$653$	−32.7006	+	18.8797i	−1.27967	+	0.738819i	−0.976788	−	0.214208i	$-0.931283\pi$
$653$	−32.7006	+	18.8797i	−1.27967	+	0.738819i	−0.302885	+	0.953027i	$0.597950\pi$
$654$	−45.3136	+	5.10986i	−1.77190	+	0.199812i
$655$			14.8581i			0.580556i
$656$	14.4760	−	25.6261i	0.565191	−	1.00053i
$657$	28.8877	+	18.3337i	1.12702	+	0.715266i
$658$	−10.5649	+	13.8356i	−0.411863	+	0.539369i
$659$	2.48029			0.0966185			0.0483092	−	0.998832i	$-0.484617\pi$
$659$	2.48029			0.0966185			0.0483092	+	0.998832i	$0.484617\pi$
$660$	−24.8420	−	0.403939i	−0.966972	−	0.0157233i
$661$	20.2831	−	35.1314i	0.788922	−	1.36645i	−0.137706	−	0.990473i	$-0.543973\pi$
$661$	20.2831	−	35.1314i	0.788922	−	1.36645i	0.926628	−	0.375980i	$-0.122694\pi$
$662$	2.73053	−	3.57585i	0.106125	−	0.138979i
$663$	−15.2433	+	52.4653i	−0.592000	+	2.03758i
$664$	4.37278	+	5.61634i	0.169697	+	0.217956i
$665$	−10.3846	−	19.3905i	−0.402696	−	0.751931i
$666$	18.5351	+	3.19052i	0.718222	+	0.123630i
$667$	4.66749	+	2.69478i	0.180726	+	0.104342i
$668$	17.0906	−	17.2519i	0.661255	−	0.667496i
$669$	5.57316	−	19.1821i	0.215471	−	0.741622i
$670$	1.58937	+	1.21365i	0.0614027	+	0.0468872i
$671$	1.55540	−	2.69404i	0.0600457	−	0.104002i
$672$	10.7886	−	25.3820i	0.416179	−	0.979130i
$673$	3.10684	−	5.38120i	0.119760	−	0.207430i	−0.799913	−	0.600117i	$-0.795121\pi$
$673$	3.10684	−	5.38120i	0.119760	−	0.207430i	0.919672	+	0.392686i	$0.128454\pi$
$674$	−3.88902	+	30.0859i	−0.149800	+	1.15887i
$675$	6.13725	+	6.96186i	0.236223	+	0.267962i
$676$	2.03715	+	7.46235i	0.0783518	+	0.287014i
$677$	12.2111	+	7.05007i	0.469310	+	0.270956i	0.715951	−	0.698151i	$-0.245993\pi$
$677$	12.2111	+	7.05007i	0.469310	+	0.270956i	−0.246641	+	0.969107i	$0.579327\pi$
$678$	−32.0992	−	14.0012i	−1.23276	−	0.537713i
$679$			18.9090i			0.725659i
$680$	−23.9248	−	30.7287i	−0.917475	−	1.17839i
$681$	6.70973	+	27.3185i	0.257117	+	1.04685i
$682$	−19.9128	−	2.57401i	−0.762502	−	0.0985640i
$683$	30.2520			1.15756			0.578780	−	0.815483i	$-0.303529\pi$
$683$	30.2520			1.15756			0.578780	+	0.815483i	$0.303529\pi$
$684$	−17.1716	−	19.7265i	−0.656572	−	0.754263i
$685$	−25.9294			−0.990713
$686$	23.9904	+	3.10109i	0.915957	+	0.118400i
$687$	−6.35791	−	1.84723i	−0.242569	−	0.0704761i
$688$	−9.77390	+	0.0918209i	−0.372627	+	0.00350064i
$689$		−	10.5033i		−	0.400144i
$690$	0.410872	+	3.64356i	0.0156416	+	0.138708i
$691$	−27.2410	−	15.7276i	−1.03630	−	0.598306i	−0.117514	−	0.993071i	$-0.537492\pi$
$691$	−27.2410	−	15.7276i	−1.03630	−	0.598306i	−0.918782	+	0.394766i	$0.870826\pi$
$692$	−45.9282	+	12.5379i	−1.74593	+	0.476621i
$693$	15.6512	+	29.9398i	0.594542	+	1.13732i
$694$	−4.93777	+	38.1991i	−0.187435	+	1.45002i
$695$	18.5690	−	32.1624i	0.704362	−	1.21999i
$696$	29.3799	−	11.6934i	1.11364	−	0.443239i
$697$	−28.2561	+	48.9411i	−1.07028	+	1.85377i
$698$	−17.8745	−	13.6490i	−0.676558	−	0.516621i
$699$	−32.7138	+	8.03487i	−1.23735	+	0.303907i
$700$	−7.14336	−	7.07656i	−0.269994	−	0.267469i
$701$	−12.2607	−	7.07872i	−0.463080	−	0.267359i	0.250258	−	0.968179i	$-0.419484\pi$
$701$	−12.2607	−	7.07872i	−0.463080	−	0.267359i	−0.713339	+	0.700820i	$0.752818\pi$
$702$	−2.12235	−	30.1057i	−0.0801029	−	1.13627i
$703$	−10.1907	+	16.4175i	−0.384348	+	0.619196i
$704$	30.7952	−	8.71846i	1.16064	−	0.328589i
$705$	−9.39834	−	9.80073i	−0.353962	−	0.369117i
$706$	20.0165	−	26.2133i	0.753332	−	0.986550i
$707$	−12.2225	+	21.1700i	−0.459675	+	0.796181i
$708$	−18.6670	+	10.3764i	−0.701549	+	0.389971i
$709$	−33.3208			−1.25139			−0.625694	−	0.780069i	$-0.715184\pi$
$709$	−33.3208			−1.25139			−0.625694	+	0.780069i	$0.715184\pi$
$710$	10.4378	−	13.6691i	0.391723	−	0.512993i
$711$	2.15872	+	4.12950i	0.0809584	+	0.154868i
$712$	6.38850	+	46.0177i	0.239419	+	1.72459i
$713$			2.96318i			0.110972i
$714$	−21.1719	+	48.5389i	−0.792340	+	1.81652i
$715$	25.5101	−	14.7282i	0.954022	−	0.550805i
$716$	47.7599	+	12.5571i	1.78487	+	0.469281i
$717$	27.9193	+	8.11168i	1.04267	+	0.302936i
$718$	8.43975	+	6.44462i	0.314969	+	0.240511i
$719$	−26.6582	+	46.1734i	−0.994184	+	1.72198i	−0.403827	+	0.914835i	$0.632320\pi$
$719$	−26.6582	+	46.1734i	−0.994184	+	1.72198i	−0.590357	+	0.807142i	$0.701013\pi$
$720$	18.2711	+	11.3565i	0.680924	+	0.423230i
$721$	6.69849			0.249465
$722$	25.4096	−	8.73785i	0.945649	−	0.325189i
$723$	−15.4030	+	14.7706i	−0.572843	+	0.549323i
$724$	−3.75604	−	13.7589i	−0.139592	−	0.511345i
$725$		−	11.5287i		−	0.428164i
$726$	−4.90210	+	11.2386i	−0.181934	+	0.417103i
$727$	21.0858	−	12.1739i	0.782028	−	0.451504i	−0.0551207	−	0.998480i	$-0.517554\pi$
$727$	21.0858	−	12.1739i	0.782028	−	0.451504i	0.837148	+	0.546976i	$0.184221\pi$
$728$	4.49630	+	32.3878i	0.166644	+	1.20037i
$729$	−3.38594	+	26.7869i	−0.125405	+	0.992106i
$730$	17.5483	−	22.9809i	0.649491	−	0.850561i
$731$	18.7676			0.694144
$732$	−2.35429	+	1.30868i	−0.0870169	+	0.0483702i
$733$	−16.2281	−	28.1079i	−0.599399	−	1.03819i	−0.992910	−	0.118870i	$-0.962073\pi$
$733$	−16.2281	−	28.1079i	−0.599399	−	1.03819i	0.393511	−	0.919320i	$-0.371260\pi$
$734$	−29.8317	−	3.85616i	−1.10111	−	0.142334i
$735$	0.799893	−	2.75313i	0.0295045	−	0.101551i
$736$	−1.85868	−	4.34230i	−0.0685117	−	0.160059i
$737$	2.73283	−	1.57780i	0.100665	−	0.0581189i
$738$	5.29570	−	30.7650i	0.194937	−	1.13248i
$739$	28.6574	+	16.5454i	1.05418	+	0.608632i	0.923817	−	0.382834i	$-0.125052\pi$
$739$	28.6574	+	16.5454i	1.05418	+	0.608632i	0.130364	+	0.991466i	$0.458385\pi$
$740$	4.04164	−	15.3721i	0.148574	−	0.565088i
$741$	29.4849	+	9.59697i	1.08315	+	0.352554i
$742$	1.30510	−	10.0964i	0.0479119	−	0.370652i
$743$	−23.2405			−0.852610			−0.426305	−	0.904580i	$-0.640185\pi$
$743$	−23.2405			−0.852610			−0.426305	+	0.904580i	$0.640185\pi$
$744$	13.6443	+	10.7744i	0.500223	+	0.395010i
$745$	−17.0131			−0.623311
$746$	10.4367	−	4.35176i	0.382114	−	0.159329i
$747$	6.37430	+	4.04547i	0.233223	+	0.148016i
$748$	−59.2842	+	16.1840i	−2.16765	+	0.591746i
$749$	−0.369930	−	0.213579i	−0.0135169	−	0.00780401i
$750$	23.9751	−	17.6979i	0.875449	−	0.646236i
$751$	−37.6530	−	21.7389i	−1.37398	−	0.793265i	−0.382550	−	0.923935i	$-0.624954\pi$
$751$	−37.6530	−	21.7389i	−1.37398	−	0.793265i	−0.991426	+	0.130670i	$0.958287\pi$
$752$	15.2301	+	8.60338i	0.555386	+	0.313733i
$753$	−21.1344	−	6.14039i	−0.770181	−	0.223768i
$754$	−22.7527	+	29.7966i	−0.828605	+	1.08513i
$755$	−15.7007	+	27.1945i	−0.571408	+	0.989708i
$756$	1.70070	−	29.2032i	0.0618537	−	1.06211i
$757$	21.6050	−	37.4210i	0.785248	−	1.36009i	−0.143603	−	0.989635i	$-0.545869\pi$
$757$	21.6050	−	37.4210i	0.785248	−	1.36009i	0.928851	−	0.370454i	$-0.120798\pi$
$758$	37.0895	+	4.79434i	1.34715	+	0.174138i
$759$	5.55618	+	1.61429i	0.201677	+	0.0585951i
$760$	−17.8642	+	13.0148i	−0.648002	+	0.472097i
$761$	−21.3438	+	12.3229i	−0.773712	+	0.446703i	−0.834197	−	0.551466i	$-0.814069\pi$
$761$	−21.3438	+	12.3229i	−0.773712	+	0.446703i	0.0604849	+	0.998169i	$0.480735\pi$
$762$	−6.73237	−	2.93656i	−0.243888	−	0.106380i
$763$	45.3817	−	26.2012i	1.64293	−	0.948545i
$764$	33.0027	−	33.3142i	1.19400	−	1.20527i
$765$	−34.8758	−	22.1340i	−1.26094	−	0.800257i
$766$	−3.69582	+	28.5912i	−0.133535	+	1.03304i
$767$	12.6605	−	21.9286i	0.457144	−	0.791796i
$768$	−26.7529	−	7.23061i	−0.965363	−	0.260912i
$769$	4.91758	−	8.51750i	0.177333	−	0.307149i	−0.763633	−	0.645650i	$-0.776586\pi$
$769$	4.91758	−	8.51750i	0.177333	−	0.307149i	0.940966	+	0.338501i	$0.109920\pi$
$770$	26.3519	−	10.9879i	0.949658	−	0.395977i
$771$	−3.55708	+	0.873657i	−0.128105	+	0.0314640i
$772$	−6.08504	−	1.59989i	−0.219005	−	0.0575812i
$773$	24.8976	−	14.3746i	0.895505	−	0.517020i	0.0197660	−	0.999805i	$-0.493708\pi$
$773$	24.8976	−	14.3746i	0.895505	−	0.517020i	0.875739	+	0.482784i	$0.160375\pi$
$774$	−9.72751	+	3.58543i	−0.349648	+	0.128875i
$775$	5.48927	−	3.16923i	0.197180	−	0.113842i
$776$	18.8198	−	2.61269i	0.675590	−	0.0937902i
$777$	−20.9891	+	5.15516i	−0.752981	+	0.184940i
$778$	−0.478323	−	0.0618300i	−0.0171487	−	0.00221671i
$779$	27.2500	+	16.9147i	0.976334	+	0.606032i
$780$	−25.5022	−	0.414675i	−0.913126	−	0.0148477i
$781$	−13.5696	−	23.5033i	−0.485559	−	0.841013i
$782$	3.49034	+	8.37076i	0.124814	+	0.299338i
$783$	25.1592	−	22.1792i	0.899117	−	0.792620i
$784$	0.0346945	+	3.69307i	0.00123909	+	0.131895i
$785$		−	32.7492i		−	1.16887i
$786$	−12.0568	−	16.3332i	−0.430052	−	0.582588i
$787$	8.15443	−	4.70796i	0.290674	−	0.167821i	−0.347572	−	0.937653i	$-0.612994\pi$
$787$	8.15443	−	4.70796i	0.290674	−	0.167821i	0.638246	+	0.769833i	$0.279660\pi$
$788$	9.94623	−	37.8297i	0.354320	−	1.34763i
$789$	3.26019	+	0.947217i	0.116066	+	0.0337218i
$790$	3.63463	−	1.51552i	0.129314	−	0.0539199i
$791$	40.2432			1.43088
$792$	27.6360	−	19.7143i	0.982004	−	0.700516i
$793$	1.59674	−	2.76564i	0.0567021	−	0.0982108i
$794$	−13.5089	−	10.3155i	−0.479414	−	0.366082i
$795$	7.62567	+	2.21556i	0.270455	+	0.0785779i
$796$	43.7398	−	11.9405i	1.55032	−	0.423221i
$797$	10.9915	−	6.34592i	0.389338	−	0.224784i	−0.292536	−	0.956255i	$-0.594499\pi$
$797$	10.9915	−	6.34592i	0.389338	−	0.224784i	0.681873	+	0.731471i	$0.261166\pi$
$798$	27.1502	+	12.8889i	0.961107	+	0.456262i
$799$	−29.0867	−	16.7932i	−1.02901	−	0.594102i
$800$	−6.05617	+	8.08744i	−0.214118	+	0.285934i
$801$	22.8289	+	43.6702i	0.806620	+	1.54301i
$802$	−7.24393	−	0.936379i	−0.255792	−	0.0330647i
$803$	−22.8136	−	39.5143i	−0.805074	−	1.39443i
$804$	−2.73199	−	0.0444231i	−0.0963498	−	0.00156668i
$805$	−2.10677	−	3.64904i	−0.0742539	−	0.128612i
$806$	−20.4421	−	2.64242i	−0.720042	−	0.0930754i
$807$	41.6993	−	10.2418i	1.46789	−	0.360529i
$808$	22.7590	+	9.23976i	0.800658	+	0.325054i
$809$			7.68181i			0.270078i	0.990840	+	0.135039i	$0.0431160\pi$
$809$			7.68181i			0.270078i	−0.990840	+	0.135039i	$0.956884\pi$
$810$	22.3052	+	4.80960i	0.783724	+	0.168992i
$811$	−8.25992	+	4.76887i	−0.290045	+	0.167458i	−0.637962	−	0.770068i	$-0.720222\pi$
$811$	−8.25992	+	4.76887i	−0.290045	+	0.167458i	0.347917	+	0.937525i	$0.386889\pi$
$812$	−25.5737	+	25.8151i	−0.897462	+	0.905933i
$813$	2.16157	−	0.530905i	0.0758095	−	0.0186196i
$814$	−19.9342	−	15.2218i	−0.698693	−	0.533524i
$815$	9.03694			0.316550
$816$	51.2353	+	14.3654i	1.79359	+	0.502888i
$817$	0.339911	−	10.6459i	0.0118920	−	0.372453i
$818$	8.30191	+	6.33936i	0.290269	+	0.221650i
$819$	16.0672	+	30.7356i	0.561435	+	1.07399i
$820$	−25.5149	−	6.70840i	−0.891018	−	0.234268i
$821$			31.8166i			1.11041i	0.831715	+	0.555203i	$0.187359\pi$
$821$			31.8166i			1.11041i	−0.831715	+	0.555203i	$0.812641\pi$
$822$	28.5037	−	21.0408i	0.994181	−	0.733881i
$823$	−15.0649	−	8.69770i	−0.525128	−	0.303183i	0.213902	−	0.976855i	$-0.431383\pi$
$823$	−15.0649	−	8.69770i	−0.525128	−	0.303183i	−0.739030	+	0.673672i	$0.764716\pi$
$824$	−0.925544	−	6.66689i	−0.0322429	−	0.232252i
$825$	−2.95208	−	12.0193i	−0.102778	−	0.418460i
$826$	14.8948	−	19.5060i	0.518257	−	0.678700i
$827$	9.71682	+	16.8300i	0.337887	+	0.585237i	0.984035	−	0.177975i	$-0.0569545\pi$
$827$	9.71682	+	16.8300i	0.337887	+	0.585237i	−0.646148	+	0.763212i	$0.723621\pi$
$828$	−3.40827	−	3.67188i	−0.118446	−	0.127607i
$829$	−32.3396			−1.12320			−0.561600	−	0.827409i	$-0.689814\pi$
$829$	−32.3396			−1.12320			−0.561600	+	0.827409i	$0.689814\pi$
$830$	3.87216	−	5.07091i	0.134405	−	0.176014i
$831$	2.47116	+	10.0613i	0.0857237	+	0.349023i
$832$	31.6137	−	8.95018i	1.09601	−	0.310292i
$833$		−	7.09132i		−	0.245700i
$834$	5.68609	+	50.4236i	0.196893	+	1.74602i
$835$	−18.8512	−	10.8837i	−0.652373	−	0.376648i
$836$	8.10664	+	33.9221i	0.280374	+	1.17322i
$837$	17.4767	+	5.88226i	0.604083	+	0.203321i
$838$	−4.67881	+	1.95091i	−0.161627	+	0.0673932i
$839$	19.0029	+	32.9139i	0.656052	+	1.13631i	0.981629	+	0.190799i	$0.0611080\pi$
$839$	19.0029	+	32.9139i	0.656052	+	1.13631i	−0.325577	+	0.945515i	$0.605559\pi$
$840$	−24.4628	−	3.56743i	−0.844047	−	0.123088i
$841$	−12.6631			−0.436657
$842$	8.57616	−	3.57598i	0.295554	−	0.123236i
$843$	10.8088	+	11.2716i	0.372276	+	0.388216i
$844$	14.0984	−	53.6222i	0.485287	−	1.84575i
$845$	6.00484	−	3.46689i	0.206573	−	0.119265i
$846$	18.2843	+	3.14735i	0.628628	+	0.108208i
$847$		−	14.0899i		−	0.484136i
$848$	−10.2291	+	0.0960976i	−0.351270	+	0.00330000i
$849$	−38.3158	−	39.9563i	−1.31499	−	1.37130i
$850$	11.7737	−	15.4187i	0.403836	−	0.528856i
$851$	−1.85075	+	3.20559i	−0.0634429	+	0.109886i
$852$	−0.382054	+	23.4960i	−0.0130890	+	0.804961i
$853$	13.0648	+	22.6289i	0.447331	+	0.774800i	0.998211	−	0.0597840i	$-0.0190412\pi$
$853$	13.0648	+	22.6289i	0.447331	+	0.774800i	−0.550880	+	0.834584i	$0.685708\pi$
$854$	1.87854	−	2.46010i	0.0642823	−	0.0841829i
$855$	−13.1872	+	19.3824i	−0.450992	+	0.662864i
$856$	−0.161458	+	0.397695i	−0.00551850	+	0.0135929i
$857$	−7.80328	+	4.50523i	−0.266555	+	0.153896i	−0.627321	−	0.778761i	$-0.715849\pi$
$857$	−7.80328	+	4.50523i	−0.266555	+	0.153896i	0.360766	+	0.932656i	$0.382515\pi$
$858$	−16.0913	+	36.8909i	−0.549347	+	1.25943i
$859$	24.8568	+	14.3511i	0.848104	+	0.489653i	0.860011	−	0.510276i	$-0.170457\pi$
$859$	24.8568	+	14.3511i	0.848104	+	0.489653i	−0.0119065	+	0.999929i	$0.503790\pi$
$860$	2.30735	+	8.45213i	0.0786798	+	0.288215i
$861$	8.55664	+	34.8382i	0.291610	+	1.18728i
$862$	26.6729	−	11.1217i	0.908481	−	0.378807i
$863$	52.3373			1.78158			0.890792	−	0.454412i	$-0.150151\pi$
$863$	52.3373			1.78158			0.890792	+	0.454412i	$0.150151\pi$
$864$	−29.3004	+	2.34239i	−0.996820	+	0.0796898i
$865$	21.3375	+	36.9577i	0.725498	+	1.25660i
$866$	33.5574	−	13.9923i	1.14033	−	0.475479i
$867$	−69.8371	−	20.2905i	−2.37179	−	0.689101i
$868$	−19.3219	−	5.08013i	−0.655827	−	0.172431i
$869$		−	6.21402i		−	0.210796i
$870$	−16.8336	−	22.8043i	−0.570713	−	0.773139i
$871$	2.80546	−	1.61973i	0.0950594	−	0.0548826i
$872$	−32.3480	−	41.5474i	−1.09544	−	1.40697i
$873$	17.8597	−	9.33629i	0.604460	−	0.315985i
$874$	4.81153	−	1.82829i	0.162752	−	0.0618427i
$875$	−17.1222	+	29.6565i	−0.578836	+	1.00257i
$876$	−0.642319	+	39.5022i	−0.0217020	+	1.33465i
$877$	−3.60999			−0.121901			−0.0609503	−	0.998141i	$-0.519413\pi$
$877$	−3.60999			−0.121901			−0.0609503	+	0.998141i	$0.519413\pi$
$878$	18.6328	+	44.6864i	0.628827	+	1.50809i
$879$	7.11845	−	24.5008i	0.240099	−	0.826390i
$880$	−14.5772	−	24.7094i	−0.491397	−	0.832954i
$881$		−	2.96110i		−	0.0997620i	−0.998755	−	0.0498810i	$-0.984116\pi$
$881$		−	2.96110i		−	0.0997620i	0.998755	−	0.0498810i	$-0.0158842\pi$
$882$	1.35475	+	3.67554i	0.0456169	+	0.123762i
$883$	20.9235	−	12.0802i	0.704133	−	0.406531i	−0.104752	−	0.994498i	$-0.533405\pi$
$883$	20.9235	−	12.0802i	0.704133	−	0.406531i	0.808885	+	0.587967i	$0.200071\pi$
$884$	−60.8599	+	16.6141i	−2.04694	+	0.558794i
$885$	13.2501	+	13.8174i	0.445398	+	0.464468i
$886$	−3.79176	+	29.3335i	−0.127387	+	0.985478i
$887$	−25.8310	+	44.7405i	−0.867319	+	1.50224i	−0.00259288	+	0.999997i	$0.500825\pi$
$887$	−25.8310	+	44.7405i	−0.867319	+	1.50224i	−0.864726	+	0.502244i	$0.832508\pi$
$888$	8.03096	+	20.1778i	0.269501	+	0.677124i
$889$	8.44046			0.283084
$890$	38.4369	−	16.0270i	1.28841	−	0.537225i
$891$	20.5507	−	29.5656i	0.688475	−	0.990483i
$892$	22.2513	−	6.07437i	0.745027	−	0.203385i
$893$	−10.0528	+	16.1953i	−0.336403	+	0.541955i
$894$	18.7021	−	13.8055i	0.625493	−	0.461724i
$895$		−	44.2655i		−	1.47963i
$896$	31.5012	−	4.67525i	1.05238	−	0.156189i
$897$	5.70386	+	1.65720i	0.190446	+	0.0553322i
$898$	−15.0576	−	1.94640i	−0.502478	−	0.0649523i
$899$	−11.4532	−	19.8375i	−0.381985	−	0.661617i
$900$	−3.15686	+	10.2410i	−0.105229	+	0.341368i
$901$	19.6417			0.654360
$902$	−25.2655	+	33.0872i	−0.841248	+	1.10168i
$903$	8.59882	−	8.24578i	0.286151	−	0.274402i
$904$	−5.56049	−	40.0534i	−0.184939	−	1.33215i
$905$	−11.0715	+	6.39216i	−0.368031	+	0.212483i
$906$	−4.80779	−	42.6349i	−0.159728	−	1.41645i
$907$	−32.3448	+	18.6743i	−1.07399	+	0.620070i	−0.929269	−	0.369403i	$-0.879562\pi$
$907$	−32.3448	+	18.6743i	−1.07399	+	0.620070i	−0.144723	+	0.989472i	$0.546229\pi$
$908$	−22.8603	+	23.0761i	−0.758645	+	0.765806i
$909$	26.0302	+	1.09162i	0.863367	+	0.0362067i
$910$	27.0523	−	11.2799i	0.896776	−	0.373927i
$911$	2.46360	−	4.26707i	0.0816226	−	0.141374i	−0.822324	−	0.569019i	$-0.807323\pi$
$911$	2.46360	−	4.26707i	0.0816226	−	0.141374i	0.903947	+	0.427644i	$0.140656\pi$
$912$	9.07669	−	28.8030i	0.300559	−	0.953763i
$913$	−5.03399	−	8.71913i	−0.166601	−	0.288561i
$914$	12.0774	+	9.22236i	0.399486	+	0.305048i
$915$	1.67111	+	1.74266i	0.0552452	+	0.0576106i
$916$	−2.01335	−	7.37519i	−0.0665230	−	0.243683i
$917$	20.2037	+	11.6646i	0.667186	+	0.385200i
$918$	56.2991	−	3.96890i	1.85815	−	0.130993i
$919$		−	57.3260i		−	1.89101i	−0.325606	−	0.945506i	$-0.605568\pi$
$919$		−	57.3260i		−	1.89101i	0.325606	−	0.945506i	$-0.394432\pi$
$920$	−3.34073	+	2.60103i	−0.110140	+	0.0857534i
$921$	9.70373	−	2.38334i	0.319749	−	0.0785337i
$922$	−3.54889	−	8.51119i	−0.116877	−	0.280301i
$923$	−13.9303	−	24.1279i	−0.458520	−	0.794181i
$924$	−20.0519	+	33.4624i	−0.659658	+	1.10083i
$925$	7.91779			0.260335
$926$	−20.9543	−	50.2539i	−0.688600	−	1.65145i
$927$	−3.30737	−	6.32679i	−0.108628	−	0.207799i
$928$	29.2269	+	21.8862i	0.959421	+	0.718449i
$929$	−10.1343	+	5.85103i	−0.332495	+	0.191966i	−0.656948	−	0.753936i	$-0.728153\pi$
$929$	−10.1343	+	5.85103i	−0.332495	+	0.191966i	0.324453	+	0.945902i	$0.394820\pi$
$930$	6.23051	−	14.2841i	0.204306	−	0.468393i
$931$	−4.02255	−	0.128435i	−0.131834	−	0.00420929i
$932$	−27.6335	−	27.3751i	−0.905164	−	0.896701i
$933$	−8.57442	−	2.49121i	−0.280714	−	0.0815586i
$934$	3.71741	−	28.7583i	0.121637	−	0.940999i
$935$	27.5425	+	47.7051i	0.900737	+	1.56012i
$936$	28.3706	−	20.2382i	0.927321	−	0.661508i
$937$	3.22655	+	5.58855i	0.105407	+	0.182570i	0.913904	−	0.405930i	$-0.133052\pi$
$937$	3.22655	+	5.58855i	0.105407	+	0.182570i	−0.808498	+	0.588500i	$0.799719\pi$
$938$	2.89805	−	1.20839i	0.0946245	−	0.0394554i
$939$	−20.2842	+	19.4513i	−0.661949	+	0.634771i
$940$	3.98695	−	15.1640i	0.130040	−	0.494597i
$941$	−16.3924	−	9.46418i	−0.534378	−	0.308524i	0.208419	−	0.978040i	$-0.433168\pi$
$941$	−16.3924	−	9.46418i	−0.534378	−	0.308524i	−0.742798	+	0.669516i	$0.766502\pi$
$942$	26.5747	+	36.0005i	0.865852	+	1.17296i
$943$	5.32071	+	3.07191i	0.173266	+	0.100035i
$944$	−21.4720	−	12.1294i	−0.698855	−	0.394777i
$945$	−25.7040	+	5.18187i	−0.836152	+	0.168566i
$946$	13.7113	+	1.77238i	0.445794	+	0.0576251i
$947$	3.37692	+	5.84899i	0.109735	+	0.190067i	0.915663	−	0.401947i	$-0.131666\pi$
$947$	3.37692	+	5.84899i	0.109735	+	0.190067i	−0.805928	+	0.592014i	$0.798333\pi$
$948$	−2.76568	+	4.61535i	−0.0898252	+	0.149900i
$949$	−23.4199	−	40.5645i	−0.760244	−	1.31678i
$950$	−8.53300	−	6.95791i	−0.276847	−	0.225744i
$951$	0.130525	+	0.136114i	0.00423257	+	0.00441379i
$952$	−60.5667	+	8.40830i	−1.96298	+	0.272515i
$953$	−4.85581	−	2.80350i	−0.157295	−	0.0908143i	0.419286	−	0.907854i	$-0.362280\pi$
$953$	−4.85581	−	2.80350i	−0.157295	−	0.0908143i	−0.576581	+	0.817040i	$0.695614\pi$
$954$	−10.1806	+	3.75242i	−0.329609	+	0.121489i
$955$	−36.4025	−	21.0170i	−1.17796	−	0.680095i
$956$	8.84119	+	32.3865i	0.285944	+	1.04745i
$957$	−43.4363	+	10.6684i	−1.40410	+	0.344861i
$958$	−4.14850	+	32.0932i	−0.134032	+	1.03688i
$959$	−20.3563	+	35.2582i	−0.657340	+	1.13855i
$960$	−0.170524	+	24.8403i	−0.00550364	+	0.801718i
$961$	−9.20304	+	15.9401i	−0.296872	+	0.514198i
$962$	−20.4640	−	15.6264i	−0.659786	−	0.503814i
$963$	−0.0190752	+	0.454857i	−0.000614689	+	0.0146576i
$964$	−23.8320	−	6.26595i	−0.767578	−	0.201813i
$965$			5.63982i			0.181552i
$966$	5.27698	+	2.30174i	0.169784	+	0.0740574i
$967$		−	4.66646i		−	0.150063i	−0.997181	−	0.0750315i	$-0.976094\pi$
$967$		−	4.66646i		−	0.150063i	0.997181	−	0.0750315i	$-0.0239057\pi$
$968$	−14.0235	+	1.94684i	−0.450732	+	0.0625738i
$969$	−17.9468	+	55.1382i	−0.576535	+	1.77129i
$970$	−6.55451	−	15.7195i	−0.210453	−	0.504721i
$971$	−26.9215	+	46.6295i	−0.863953	+	1.49641i	0.00412986	+	0.999991i	$0.498685\pi$
$971$	−26.9215	+	46.6295i	−0.863953	+	1.49641i	−0.868083	+	0.496419i	$0.834648\pi$
$972$	−28.4224	+	12.8127i	−0.911650	+	0.410968i
$973$	−29.1558	−	50.4993i	−0.934692	−	1.61893i
$974$	8.45641	+	1.09311i	0.270961	+	0.0350255i
$975$	−3.03054	−	12.3388i	−0.0970550	−	0.395158i
$976$	−2.70806	−	1.52976i	−0.0866828	−	0.0489664i
$977$	35.8836	−	20.7174i	1.14802	−	0.662808i	0.199614	−	0.979875i	$-0.436031\pi$
$977$	35.8836	−	20.7174i	1.14802	−	0.662808i	0.948403	+	0.317067i	$0.102698\pi$
$978$	−9.93412	+	7.33313i	−0.317658	+	0.234488i
$979$		−	65.7145i		−	2.10025i
$980$	3.19363	−	0.871830i	0.102017	−	0.0278496i
$981$	−47.1545	−	29.9267i	−1.50553	−	0.955487i
$982$	−0.815877	+	6.31171i	−0.0260357	+	0.201415i
$983$	−22.5154	−	38.9978i	−0.718130	−	1.24384i	−0.961740	−	0.273964i	$-0.911665\pi$
$983$	−22.5154	−	38.9978i	−0.718130	−	1.24384i	0.243610	−	0.969873i	$-0.421668\pi$
$984$	33.4916	−	13.3300i	1.06767	−	0.424943i
$985$	−35.0618			−1.11716
$986$	−55.7210	−	42.5487i	−1.77452	−	1.35503i
$987$	−20.7051	+	5.08540i	−0.659051	+	0.161870i
$988$	8.32210	+	34.8237i	0.264761	+	1.10789i
$989$		−	2.04035i		−	0.0648794i
$990$	−23.3894	−	19.4644i	−0.743365	−	0.618620i
$991$	−7.73322	−	4.46477i	−0.245654	−	0.141828i	0.372119	−	0.928185i	$-0.378631\pi$
$991$	−7.73322	−	4.46477i	−0.245654	−	0.141828i	−0.617772	+	0.786357i	$0.711965\pi$
$992$	−2.38642	+	19.9326i	−0.0757688	+	0.632862i
$993$	5.35128	−	1.31433i	0.169818	−	0.0417091i
$994$	−10.3926	−	24.9242i	−0.329633	−	0.790548i
$995$	−20.3208	−	35.1967i	−0.644214	−	1.11581i
$996$	−0.141733	+	8.71645i	−0.00449097	+	0.276191i
$997$	−32.7263			−1.03645			−0.518226	−	0.855244i	$-0.673407\pi$
$997$	−32.7263			−1.03645			−0.518226	+	0.855244i	$0.673407\pi$
$998$	14.9311	+	1.93005i	0.472634	+	0.0610946i
$999$	15.2325	+	17.2791i	0.481934	+	0.546687i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.o.a.11.54	yes	232
4.3	odd	2	inner	684.2.o.a.11.15	✓	232
9.5	odd	6		684.2.bi.a.239.92	yes	232
19.7	even	3		684.2.bi.a.83.25	yes	232
36.23	even	6		684.2.bi.a.239.25	yes	232
76.7	odd	6		684.2.bi.a.83.92	yes	232
171.140	odd	6	inner	684.2.o.a.311.15	yes	232
684.311	even	6	inner	684.2.o.a.311.54	yes	232

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.o.a.11.15	✓	232	4.3	odd	2	inner
684.2.o.a.11.54	yes	232	1.1	even	1	trivial
684.2.o.a.311.15	yes	232	171.140	odd	6	inner
684.2.o.a.311.54	yes	232	684.311	even	6	inner
684.2.bi.a.83.25	yes	232	19.7	even	3
684.2.bi.a.83.92	yes	232	76.7	odd	6
684.2.bi.a.239.25	yes	232	36.23	even	6
684.2.bi.a.239.92	yes	232	9.5	odd	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.181298 + 1.40254i) q^{2} +(-1.25014 + 1.19881i) q^{3} +(-1.93426 - 0.508558i) q^{4} +1.79274i q^{5} +(-1.45474 - 1.97072i) q^{6} +(2.43772 + 1.40742i) q^{7} +(1.06395 - 2.62069i) q^{8} +(0.125699 - 2.99737i) q^{9} +(-2.51439 - 0.325021i) q^{10} +(-2.00035 + 3.46471i) q^{11} +(3.02776 - 1.68305i) q^{12} +(-2.05352 + 3.55679i) q^{13} +(-2.41592 + 3.16385i) q^{14} +(-2.14916 - 2.24117i) q^{15} +(3.48274 + 1.96737i) q^{16} +(-6.65138 - 3.84018i) q^{17} +(4.18115 + 0.719717i) q^{18} +(-2.29881 + 3.70344i) q^{19} +(0.911712 - 3.46762i) q^{20} +(-4.73472 + 1.16290i) q^{21} +(-4.49675 - 3.43373i) q^{22} +(-0.417491 + 0.723116i) q^{23} +(1.81162 + 4.55171i) q^{24} +1.78609 q^{25} +(-4.61626 - 3.52499i) q^{26} +(3.43614 + 3.89782i) q^{27} +(-3.99943 - 3.96204i) q^{28} -6.45469i q^{29} +(3.53298 - 2.60796i) q^{30} +(3.07334 - 1.77440i) q^{31} +(-3.39074 + 4.52801i) q^{32} +(-1.65282 - 6.72941i) q^{33} +(6.59190 - 8.63264i) q^{34} +(-2.52313 + 4.37019i) q^{35} +(-1.76747 + 5.73376i) q^{36} +4.43303 q^{37} +(-4.77747 - 3.89561i) q^{38} +(-1.69675 - 6.90827i) q^{39} +(4.69820 + 1.90739i) q^{40} -7.35803i q^{41} +(-0.772619 - 6.85149i) q^{42} +(-2.11621 + 1.22179i) q^{43} +(5.63121 - 5.68436i) q^{44} +(5.37349 + 0.225346i) q^{45} +(-0.938512 - 0.716650i) q^{46} +4.37304 q^{47} +(-6.71241 + 1.71566i) q^{48} +(0.461654 + 0.799607i) q^{49} +(-0.323816 + 2.50507i) q^{50} +(12.9188 - 3.17300i) q^{51} +(5.78087 - 5.83544i) q^{52} +(-2.21477 + 1.27870i) q^{53} +(-6.08983 + 4.11267i) q^{54} +(-6.21131 - 3.58610i) q^{55} +(6.28203 - 4.89107i) q^{56} +(-1.56590 - 7.38566i) q^{57} +(9.05299 + 1.17023i) q^{58} -6.16527 q^{59} +(3.01726 + 5.42799i) q^{60} -0.777566 q^{61} +(1.93148 + 4.63220i) q^{62} +(4.52497 - 7.12983i) q^{63} +(-5.73600 - 5.57658i) q^{64} +(-6.37640 - 3.68142i) q^{65} +(9.73795 - 1.09812i) q^{66} +(-0.683087 - 0.394381i) q^{67} +(10.9126 + 10.8105i) q^{68} +(-0.344958 - 1.40449i) q^{69} +(-5.67195 - 4.33111i) q^{70} +(-3.39181 + 5.87479i) q^{71} +(-7.72142 - 3.51848i) q^{72} +(-5.70240 + 9.87685i) q^{73} +(-0.803701 + 6.21752i) q^{74} +(-2.23286 + 2.14119i) q^{75} +(6.32991 - 5.99435i) q^{76} +(-9.75259 + 5.63066i) q^{77} +(9.99677 - 1.12730i) q^{78} +(-1.34514 + 0.776617i) q^{79} +(-3.52698 + 6.24363i) q^{80} +(-8.96840 - 0.753534i) q^{81} +(10.3200 + 1.33400i) q^{82} +(-1.25828 + 2.17940i) q^{83} +(9.74959 + 0.158532i) q^{84} +(6.88443 - 11.9242i) q^{85} +(-1.32995 - 3.18958i) q^{86} +(7.73796 + 8.06927i) q^{87} +(6.95163 + 8.92858i) q^{88} +(-14.2251 + 8.21288i) q^{89} +(-1.29026 + 7.49570i) q^{90} +(-10.0118 + 5.78031i) q^{91} +(1.17528 - 1.18638i) q^{92} +(-1.71494 + 5.90260i) q^{93} +(-0.792825 + 6.13338i) q^{94} +(-6.63930 - 4.12116i) q^{95} +(-1.18934 - 9.72551i) q^{96} +(3.35880 + 5.81762i) q^{97} +(-1.20518 + 0.502522i) q^{98} +(10.1336 + 6.43129i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 232 q - 3 q^{2} + q^{4} + 3 q^{6} + 2 q^{10} - q^{12} + 2 q^{13} + q^{16} - 12 q^{17} - 16 q^{18} - 27 q^{20} - 14 q^{21} + 6 q^{22} - 10 q^{24} - 204 q^{25} - 6 q^{28} - 9 q^{30} - 3 q^{32} - 12 q^{33}+ \cdots - 162 q^{98}+O(q^{100}) \) 232 * q - 3 * q^2 + q^4 + 3 * q^6 + 2 * q^10 - q^12 + 2 * q^13 + q^16 - 12 * q^17 - 16 * q^18 - 27 * q^20 - 14 * q^21 + 6 * q^22 - 10 * q^24 - 204 * q^25 - 6 * q^28 - 9 * q^30 - 3 * q^32 - 12 * q^33 + 2 * q^34 + 13 * q^36 - 16 * q^37 - 3 * q^38 - 16 * q^40 - 43 * q^42 + 21 * q^44 + 2 * q^45 - 24 * q^46 + 58 * q^48 + 88 * q^49 + 9 * q^50 + 17 * q^52 + 41 * q^54 - 48 * q^56 - 12 * q^57 + 2 * q^58 + 16 * q^60 - 4 * q^61 + 6 * q^62 + 16 * q^64 + 12 * q^65 - 27 * q^66 - 18 * q^68 - 14 * q^69 + 60 * q^70 + 15 * q^72 + 2 * q^73 - 30 * q^74 + 3 * q^76 - 12 * q^77 - 64 * q^78 + 54 * q^80 + 4 * q^81 + 2 * q^82 - 10 * q^84 + 22 * q^85 + 51 * q^86 - 18 * q^88 + 14 * q^90 + 57 * q^92 + 4 * q^93 - 6 * q^94 - 17 * q^96 - 4 * q^97 - 162 * q^98

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