LMFDB - Embedded newform 390.2.bj.a.89.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(59,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 11]))

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

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

chi := DirichletCharacter("390.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bj (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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			89.28
Character	$\chi$	$=$	390.89
Dual form			390.2.bj.a.149.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(1.70109 - 0.326014i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.00231 - 0.995366i) q^{5} +(0.125370 - 1.72751i) q^{6} +(0.991200 - 0.265591i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.78743 - 1.10916i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(1.70109 - 0.326014i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.00231 - 0.995366i) q^{5} +(0.125370 - 1.72751i) q^{6} +(0.991200 - 0.265591i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.78743 - 1.10916i) q^{9} +(-0.443213 - 2.19170i) q^{10} +(-1.65022 + 6.15872i) q^{11} +(-1.63620 - 0.568210i) q^{12} +(3.21121 - 1.63955i) q^{13} -1.02617i q^{14} +(3.08161 - 2.34599i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-5.23308 - 3.02132i) q^{17} +(-0.349925 - 2.97952i) q^{18} +(-6.34304 + 1.69961i) q^{19} +(-2.23173 - 0.139143i) q^{20} +(1.59954 - 0.774940i) q^{21} +(5.52176 + 3.18799i) q^{22} +(-1.26132 + 0.728222i) q^{23} +(-0.972327 + 1.43338i) q^{24} +(3.01849 - 3.98606i) q^{25} +(-0.752566 - 3.52614i) q^{26} +(4.38008 - 2.79552i) q^{27} +(-0.991200 - 0.265591i) q^{28} +(-4.41622 + 2.54971i) q^{29} +(-1.46847 - 3.58380i) q^{30} +(1.46390 + 1.46390i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.799357 + 11.0145i) q^{33} +(-4.27279 + 4.27279i) q^{34} +(1.72033 - 1.51840i) q^{35} +(-2.96856 - 0.433156i) q^{36} +(1.76092 - 6.57183i) q^{37} +6.56680i q^{38} +(4.92805 - 3.83593i) q^{39} +(-0.712018 + 2.11968i) q^{40} +(2.67788 + 0.717535i) q^{41} +(-0.334544 - 1.74560i) q^{42} +(-1.80849 + 3.13239i) q^{43} +(4.50850 - 4.50850i) q^{44} +(4.47728 - 4.99539i) q^{45} +(0.376955 + 1.40682i) q^{46} +(5.16205 - 5.16205i) q^{47} +(1.13288 + 1.31018i) q^{48} +(-5.15024 + 2.97349i) q^{49} +(-3.06900 - 3.94731i) q^{50} +(-9.88695 - 3.43349i) q^{51} +(-3.60077 - 0.185709i) q^{52} -8.98001 q^{53} +(-1.56662 - 4.95436i) q^{54} +(2.82592 + 13.9742i) q^{55} +(-0.513083 + 0.888685i) q^{56} +(-10.2360 + 4.95912i) q^{57} +(1.31982 + 4.92565i) q^{58} +(3.52134 - 0.943540i) q^{59} +(-3.84175 + 0.490880i) q^{60} +(-4.69068 + 8.12450i) q^{61} +(1.79290 - 1.03513i) q^{62} +(2.46832 - 1.83971i) q^{63} -1.00000i q^{64} +(4.79788 - 6.47922i) q^{65} +(10.4323 + 3.62289i) q^{66} +(-8.04942 - 2.15684i) q^{67} +(3.02132 + 5.23308i) q^{68} +(-1.90821 + 1.64998i) q^{69} +(-1.02141 - 2.05470i) q^{70} +(0.360402 + 1.34504i) q^{71} +(-1.18672 + 2.75530i) q^{72} +(8.65328 + 8.65328i) q^{73} +(-5.89214 - 3.40183i) q^{74} +(3.83523 - 7.76473i) q^{75} +(6.34304 + 1.69961i) q^{76} +6.54281i q^{77} +(-2.42975 - 5.75294i) q^{78} +6.23151 q^{79} +(1.86317 + 1.23637i) q^{80} +(6.53953 - 6.18340i) q^{81} +(1.38617 - 2.40092i) q^{82} +(5.68306 + 5.68306i) q^{83} +(-1.77271 - 0.128650i) q^{84} +(-13.4856 - 0.840794i) q^{85} +(2.55759 + 2.55759i) q^{86} +(-6.68116 + 5.77703i) q^{87} +(-3.18799 - 5.52176i) q^{88} +(2.95837 - 11.0408i) q^{89} +(-3.66637 - 5.61763i) q^{90} +(2.74750 - 2.47799i) q^{91} +1.45644 q^{92} +(2.96748 + 2.01297i) q^{93} +(-3.65012 - 6.32219i) q^{94} +(-11.0090 + 9.71680i) q^{95} +(1.55875 - 0.755180i) q^{96} +(1.09874 + 4.10057i) q^{97} +(1.53919 + 5.74435i) q^{98} +(2.23111 + 18.9974i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q+O(q^{10}) $ 112 * q	$ 112 q + 24 q^{10} - 8 q^{15} + 56 q^{16} - 32 q^{19} - 8 q^{21} - 24 q^{30} + 40 q^{31} + 24 q^{36} - 24 q^{39} - 48 q^{45} + 16 q^{46} - 48 q^{49} - 48 q^{54} - 8 q^{55} - 16 q^{60} - 32 q^{66} - 168 q^{69} - 32 q^{70} - 120 q^{75} + 32 q^{76} + 112 q^{79} - 88 q^{81} - 8 q^{84} + 24 q^{85} + 48 q^{91} + 32 q^{94} - 56 q^{99}+O(q^{100}) $ 112 * q + 24 * q^10 - 8 * q^15 + 56 * q^16 - 32 * q^19 - 8 * q^21 - 24 * q^30 + 40 * q^31 + 24 * q^36 - 24 * q^39 - 48 * q^45 + 16 * q^46 - 48 * q^49 - 48 * q^54 - 8 * q^55 - 16 * q^60 - 32 * q^66 - 168 * q^69 - 32 * q^70 - 120 * q^75 + 32 * q^76 + 112 * q^79 - 88 * q^81 - 8 * q^84 + 24 * q^85 + 48 * q^91 + 32 * q^94 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	1.70109	−	0.326014i	0.982126	−	0.188224i
$3$	1.70109	−	0.326014i	0.982126	−	0.188224i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	2.00231	−	0.995366i	0.895460	−	0.445141i
$5$	2.00231	−	0.995366i	0.895460	−	0.445141i
$6$	0.125370	−	1.72751i	0.0511821	−	0.705252i
$7$	0.991200	−	0.265591i	0.374638	−	0.100384i	−0.0665865	−	0.997781i	$-0.521211\pi$
$7$	0.991200	−	0.265591i	0.374638	−	0.100384i	0.441225	+	0.897397i	$0.354544\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.78743	−	1.10916i	0.929143	−	0.369720i
$10$	−0.443213	−	2.19170i	−0.140156	−	0.693077i
$11$	−1.65022	+	6.15872i	−0.497561	+	1.85692i	0.0176226	+	0.999845i	$0.494390\pi$
$11$	−1.65022	+	6.15872i	−0.497561	+	1.85692i	−0.515184	+	0.857080i	$0.672276\pi$
$12$	−1.63620	−	0.568210i	−0.472329	−	0.164028i
$13$	3.21121	−	1.63955i	0.890629	−	0.454730i
$13$	3.21121	−	1.63955i	0.890629	−	0.454730i
$14$		−	1.02617i		−	0.274254i
$15$	3.08161	−	2.34599i	0.795669	−	0.605732i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−5.23308	−	3.02132i	−1.26921	−	0.732778i	−0.294371	−	0.955691i	$-0.595110\pi$
$17$	−5.23308	−	3.02132i	−1.26921	−	0.732778i	−0.974838	+	0.222913i	$0.928443\pi$
$18$	−0.349925	−	2.97952i	−0.0824781	−	0.702280i
$19$	−6.34304	+	1.69961i	−1.45519	+	0.389918i	−0.897827	−	0.440349i	$-0.854855\pi$
$19$	−6.34304	+	1.69961i	−1.45519	+	0.389918i	−0.557367	+	0.830267i	$0.688188\pi$
$20$	−2.23173	−	0.139143i	−0.499031	−	0.0311134i
$21$	1.59954	−	0.774940i	0.349047	−	0.169106i
$22$	5.52176	+	3.18799i	1.17724	+	0.679681i
$23$	−1.26132	+	0.728222i	−0.263003	+	0.151845i	−0.625704	−	0.780061i	$-0.715188\pi$
$23$	−1.26132	+	0.728222i	−0.263003	+	0.151845i	0.362701	+	0.931906i	$0.381855\pi$
$24$	−0.972327	+	1.43338i	−0.198476	+	0.292588i
$25$	3.01849	−	3.98606i	0.603699	−	0.797212i
$26$	−0.752566	−	3.52614i	−0.147590	−	0.691532i
$27$	4.38008	−	2.79552i	0.842946	−	0.537998i
$28$	−0.991200	−	0.265591i	−0.187319	−	0.0501920i
$29$	−4.41622	+	2.54971i	−0.820071	+	0.473468i	−0.850441	−	0.526070i	$-0.823665\pi$
$29$	−4.41622	+	2.54971i	−0.820071	+	0.473468i	0.0303697	+	0.999539i	$0.490332\pi$
$30$	−1.46847	−	3.58380i	−0.268105	−	0.654309i
$31$	1.46390	+	1.46390i	0.262924	+	0.262924i	0.826241	−	0.563317i	$-0.190475\pi$
$31$	1.46390	+	1.46390i	0.262924	+	0.262924i	−0.563317	+	0.826241i	$0.690475\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−0.799357	+	11.0145i	−0.139150	+	1.91739i
$34$	−4.27279	+	4.27279i	−0.732778	+	0.732778i
$35$	1.72033	−	1.51840i	0.290789	−	0.256657i
$36$	−2.96856	−	0.433156i	−0.494761	−	0.0721926i
$37$	1.76092	−	6.57183i	0.289493	−	1.08040i	−0.656001	−	0.754760i	$-0.727753\pi$
$37$	1.76092	−	6.57183i	0.289493	−	1.08040i	0.945493	−	0.325641i	$-0.105580\pi$
$38$			6.56680i			1.06528i
$39$	4.92805	−	3.83593i	0.789119	−	0.614240i
$40$	−0.712018	+	2.11968i	−0.112580	+	0.335150i
$41$	2.67788	+	0.717535i	0.418214	+	0.112060i	0.461789	−	0.886990i	$-0.347208\pi$
$41$	2.67788	+	0.717535i	0.418214	+	0.112060i	−0.0435743	+	0.999050i	$0.513875\pi$
$42$	−0.334544	−	1.74560i	−0.0516213	−	0.269352i
$43$	−1.80849	+	3.13239i	−0.275792	+	0.477685i	−0.970335	−	0.241766i	$-0.922273\pi$
$43$	−1.80849	+	3.13239i	−0.275792	+	0.477685i	0.694543	+	0.719451i	$0.255607\pi$
$44$	4.50850	−	4.50850i	0.679681	−	0.679681i
$45$	4.47728	−	4.99539i	0.667434	−	0.744669i
$46$	0.376955	+	1.40682i	0.0555790	+	0.207424i
$47$	5.16205	−	5.16205i	0.752962	−	0.752962i	−0.222069	−	0.975031i	$-0.571281\pi$
$47$	5.16205	−	5.16205i	0.752962	−	0.752962i	0.975031	+	0.222069i	$0.0712811\pi$
$48$	1.13288	+	1.31018i	0.163517	+	0.189109i
$49$	−5.15024	+	2.97349i	−0.735748	+	0.424785i
$50$	−3.06900	−	3.94731i	−0.434022	−	0.558234i
$51$	−9.88695	−	3.43349i	−1.38445	−	0.480785i
$52$	−3.60077	−	0.185709i	−0.499336	−	0.0257532i
$53$	−8.98001			−1.23350			−0.616750	−	0.787159i	$-0.711551\pi$
$53$	−8.98001			−1.23350			−0.616750	+	0.787159i	$0.711551\pi$
$54$	−1.56662	−	4.95436i	−0.213190	−	0.674203i
$55$	2.82592	+	13.9742i	0.381047	+	1.88429i
$56$	−0.513083	+	0.888685i	−0.0685636	+	0.118756i
$57$	−10.2360	+	4.95912i	−1.35579	+	0.656851i
$58$	1.31982	+	4.92565i	0.173301	+	0.646770i
$59$	3.52134	−	0.943540i	0.458439	−	0.122838i	−0.0222062	−	0.999753i	$-0.507069\pi$
$59$	3.52134	−	0.943540i	0.458439	−	0.122838i	0.480646	+	0.876915i	$0.340402\pi$
$60$	−3.84175	+	0.490880i	−0.495968	+	0.0633724i
$61$	−4.69068	+	8.12450i	−0.600581	+	1.04024i	0.392153	+	0.919900i	$0.371730\pi$
$61$	−4.69068	+	8.12450i	−0.600581	+	1.04024i	−0.992733	+	0.120336i	$0.961603\pi$
$62$	1.79290	−	1.03513i	0.227699	−	0.131462i
$63$	2.46832	−	1.83971i	0.310979	−	0.231782i
$64$		−	1.00000i		−	0.125000i
$65$	4.79788	−	6.47922i	0.595104	−	0.803649i
$66$	10.4323	+	3.62289i	1.28413	+	0.445948i
$67$	−8.04942	−	2.15684i	−0.983393	−	0.263499i	−0.268920	−	0.963162i	$-0.586667\pi$
$67$	−8.04942	−	2.15684i	−0.983393	−	0.263499i	−0.714473	+	0.699663i	$0.753333\pi$
$68$	3.02132	+	5.23308i	0.366389	+	0.634604i
$69$	−1.90821	+	1.64998i	−0.229721	+	0.198634i
$70$	−1.02141	−	2.05470i	−0.122082	−	0.245584i
$71$	0.360402	+	1.34504i	0.0427719	+	0.159627i	0.984009	−	0.178121i	$-0.0570017\pi$
$71$	0.360402	+	1.34504i	0.0427719	+	0.159627i	−0.941237	+	0.337747i	$0.890335\pi$
$72$	−1.18672	+	2.75530i	−0.139856	+	0.324716i
$73$	8.65328	+	8.65328i	1.01279	+	1.01279i	0.999917	+	0.0128731i	$0.00409776\pi$
$73$	8.65328	+	8.65328i	1.01279	+	1.01279i	0.0128731	+	0.999917i	$0.495902\pi$
$74$	−5.89214	−	3.40183i	−0.684947	−	0.395454i
$75$	3.83523	−	7.76473i	0.442854	−	0.896594i
$76$	6.34304	+	1.69961i	0.727597	+	0.194959i
$77$			6.54281i			0.745622i
$78$	−2.42975	−	5.75294i	−0.275115	−	0.651392i
$79$	6.23151			0.701100			0.350550	−	0.936544i	$-0.385995\pi$
$79$	6.23151			0.701100			0.350550	+	0.936544i	$0.385995\pi$
$80$	1.86317	+	1.23637i	0.208308	+	0.138230i
$81$	6.53953	−	6.18340i	0.726615	−	0.687045i
$82$	1.38617	−	2.40092i	0.153077	−	0.265137i
$83$	5.68306	+	5.68306i	0.623797	+	0.623797i	0.946500	−	0.322703i	$-0.104592\pi$
$83$	5.68306	+	5.68306i	0.623797	+	0.623797i	−0.322703	+	0.946500i	$0.604592\pi$
$84$	−1.77271	−	0.128650i	−0.193418	−	0.0140369i
$85$	−13.4856	−	0.840794i	−1.46272	−	0.0911969i
$86$	2.55759	+	2.55759i	0.275792	+	0.275792i
$87$	−6.68116	+	5.77703i	−0.716295	+	0.619363i
$88$	−3.18799	−	5.52176i	−0.339841	−	0.588621i
$89$	2.95837	−	11.0408i	0.313587	−	1.17032i	−0.611712	−	0.791081i	$-0.709519\pi$
$89$	2.95837	−	11.0408i	0.313587	−	1.17032i	0.925298	−	0.379240i	$-0.123815\pi$
$90$	−3.66637	−	5.61763i	−0.386470	−	0.592150i
$91$	2.74750	−	2.47799i	0.288016	−	0.259764i
$92$	1.45644			0.151845
$93$	2.96748	+	2.01297i	0.307713	+	0.208736i
$94$	−3.65012	−	6.32219i	−0.376481	−	0.652084i
$95$	−11.0090	+	9.71680i	−1.12950	+	0.996922i
$96$	1.55875	−	0.755180i	0.159089	−	0.0770752i
$97$	1.09874	+	4.10057i	0.111560	+	0.416349i	0.999007	−	0.0445621i	$-0.0141892\pi$
$97$	1.09874	+	4.10057i	0.111560	+	0.416349i	−0.887446	+	0.460911i	$0.847523\pi$
$98$	1.53919	+	5.74435i	0.155482	+	0.580267i
$99$	2.23111	+	18.9974i	0.224235	+	1.90931i
$100$	−4.60712	+	1.94278i	−0.460712	+	0.194278i
$101$	−0.132789	−	0.229997i	−0.0132130	−	0.0228855i	0.859343	−	0.511399i	$-0.170873\pi$
$101$	−0.132789	−	0.229997i	−0.0132130	−	0.0228855i	−0.872556	+	0.488514i	$0.837539\pi$
$102$	−5.87543	+	8.66140i	−0.581754	+	0.857607i
$103$	2.07388			0.204346			0.102173	−	0.994767i	$-0.467421\pi$
$103$	2.07388			0.204346			0.102173	+	0.994767i	$0.467421\pi$
$104$	−1.11133	+	3.43001i	−0.108975	+	0.336340i
$105$	2.43142	−	3.14379i	0.237282	−	0.306803i
$106$	−2.32420	+	8.67403i	−0.225746	+	0.842496i
$107$	−1.55406	−	2.69171i	−0.150236	−	0.260217i	0.781078	−	0.624434i	$-0.214670\pi$
$107$	−1.55406	−	2.69171i	−0.150236	−	0.260217i	−0.931314	+	0.364217i	$0.881337\pi$
$108$	−5.19102	+	0.230955i	−0.499506	+	0.0222236i
$109$	14.2495	+	14.2495i	1.36485	+	1.36485i	0.867616	+	0.497236i	$0.165652\pi$
$109$	14.2495	+	14.2495i	1.36485	+	1.36485i	0.497236	+	0.867616i	$0.334348\pi$
$110$	14.2295	+	0.887175i	1.35673	+	0.0845888i
$111$	0.852975	−	11.7534i	0.0809608	−	1.11558i
$112$	0.725609	+	0.725609i	0.0685636	+	0.0685636i
$113$	−0.935400	+	1.62016i	−0.0879951	+	0.152412i	−0.906664	−	0.421854i	$-0.861379\pi$
$113$	−0.935400	+	1.62016i	−0.0879951	+	0.152412i	0.818668	+	0.574266i	$0.194713\pi$
$114$	2.14087	+	11.1707i	0.200510	+	1.04623i
$115$	−1.80070	+	2.71360i	−0.167916	+	0.253044i
$116$	5.09941			0.473468
$117$	7.13250	−	8.13188i	0.659399	−	0.751793i
$118$		−	3.64556i		−	0.335601i
$119$	−5.98947	−	1.60487i	−0.549053	−	0.147118i
$120$	−0.520164	+	3.83789i	−0.0474843	+	0.350350i
$121$	−25.6803	−	14.8265i	−2.33458	−	1.34787i
$122$	6.63363	+	6.63363i	0.600581	+	0.600581i
$123$	4.78924	+	0.347569i	0.431832	+	0.0313392i
$124$	−0.535824	−	1.99972i	−0.0481184	−	0.179580i
$125$	2.07637	−	10.9858i	0.185717	−	0.982603i
$126$	−1.13818	−	2.86036i	−0.101397	−	0.254822i
$127$	4.66763	+	8.08458i	0.414186	+	0.717390i	0.995343	−	0.0964011i	$-0.0307331\pi$
$127$	4.66763	+	8.08458i	0.414186	+	0.717390i	−0.581157	+	0.813791i	$0.697400\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	−2.05520	+	5.91808i	−0.180950	+	0.521058i
$130$	−5.01667	−	6.31134i	−0.439991	−	0.553542i
$131$		−	0.457960i		−	0.0400121i	−0.999800	−	0.0200061i	$-0.993631\pi$
$131$		−	0.457960i		−	0.0400121i	0.999800	−	0.0200061i	$-0.00636855\pi$
$132$	6.19954	−	9.13920i	0.539601	−	0.795465i
$133$	−5.83582	+	3.36931i	−0.506030	+	0.292156i
$134$	−4.16669	+	7.21691i	−0.359947	+	0.623446i
$135$	5.98771	−	9.95728i	0.515340	−	0.856986i
$136$	5.83674	−	1.56395i	0.500497	−	0.134108i
$137$	−0.246412	−	0.919621i	−0.0210524	−	0.0785685i	0.954600	−	0.297889i	$-0.0962826\pi$
$137$	−0.246412	−	0.919621i	−0.0210524	−	0.0785685i	−0.975653	+	0.219321i	$0.929616\pi$
$138$	1.09988	+	2.27023i	0.0936278	+	0.193255i
$139$	6.96065	−	12.0562i	0.590395	−	1.02259i	−0.403784	−	0.914854i	$-0.632305\pi$
$139$	6.96065	−	12.0562i	0.590395	−	1.02259i	0.994179	−	0.107740i	$-0.0343612\pi$
$140$	−2.24905	+	0.454810i	−0.190079	+	0.0384385i
$141$	7.09822	−	10.4640i	0.597778	−	0.881229i
$142$	1.39249			0.116855
$143$	4.79834	+	22.4826i	0.401257	+	1.88009i
$144$	2.35427	+	1.85941i	0.196190	+	0.154951i
$145$	−6.30475	+	9.50105i	−0.523581	+	0.789020i
$146$	10.5981	−	6.11880i	0.877102	−	0.506395i
$147$	−7.79163	+	6.73723i	−0.642643	+	0.555678i
$148$	−4.81091	+	4.81091i	−0.395454	+	0.395454i
$149$	−0.327629	−	1.22273i	−0.0268404	−	0.100170i	0.951206	−	0.308556i	$-0.0998457\pi$
$149$	−0.327629	−	1.22273i	−0.0268404	−	0.100170i	−0.978047	+	0.208386i	$0.933179\pi$
$150$	−6.50752	−	5.71421i	−0.531337	−	0.466563i
$151$	−4.89612	+	4.89612i	−0.398441	+	0.398441i	−0.877683	−	0.479242i	$-0.840912\pi$
$151$	−4.89612	+	4.89612i	−0.398441	+	0.398441i	0.479242	+	0.877683i	$0.340912\pi$
$152$	3.28340	−	5.68701i	0.266319	−	0.461278i
$153$	−17.9380	−	2.61740i	−1.45020	−	0.211605i
$154$	6.31987	+	1.69340i	0.509269	+	0.136458i
$155$	4.38829	+	1.47406i	0.352476	+	0.118400i
$156$	−6.18578	+	0.857990i	−0.495259	+	0.0686942i
$157$		−	0.752484i		−	0.0600547i	−0.999549	−	0.0300274i	$-0.990441\pi$
$157$		−	0.752484i		−	0.0600547i	0.999549	−	0.0300274i	$-0.00955944\pi$
$158$	1.61283	−	6.01918i	0.128310	−	0.478860i
$159$	−15.2758	+	2.92761i	−1.21145	+	0.232174i
$160$	1.67646	−	1.47969i	0.132536	−	0.116979i
$161$	−1.05681	+	1.05681i	−0.0832881	+	0.0832881i
$162$	−4.28015	−	7.91709i	−0.336281	−	0.622025i
$163$	2.95710	−	0.792352i	0.231618	−	0.0620618i	−0.141143	−	0.989989i	$-0.545078\pi$
$163$	2.95710	−	0.792352i	0.231618	−	0.0620618i	0.372761	+	0.927927i	$0.378411\pi$
$164$	−1.96034	−	1.96034i	−0.153077	−	0.153077i
$165$	9.36294	+	22.8502i	0.728904	+	1.77889i
$166$	6.96030	−	4.01853i	0.540224	−	0.311899i
$167$	−12.2225	−	3.27501i	−0.945806	−	0.253428i	−0.247224	−	0.968958i	$-0.579519\pi$
$167$	−12.2225	−	3.27501i	−0.945806	−	0.253428i	−0.698582	+	0.715530i	$0.746185\pi$
$168$	−0.583078	+	1.67901i	−0.0449854	+	0.129538i
$169$	7.62373	−	10.5299i	0.586440	−	0.809992i
$170$	−4.30247	+	12.8085i	−0.329984	+	0.982363i
$171$	−15.7956	+	11.7730i	−1.20792	+	0.900303i
$172$	3.13239	−	1.80849i	0.238843	−	0.137896i
$173$	−10.6379	−	6.14181i	−0.808787	−	0.466953i	0.0377477	−	0.999287i	$-0.487982\pi$
$173$	−10.6379	−	6.14181i	−0.808787	−	0.466953i	−0.846534	+	0.532334i	$0.821315\pi$
$174$	3.85097	+	7.94871i	0.291942	+	0.602590i
$175$	1.93327	−	4.75267i	0.146141	−	0.359268i
$176$	−6.15872	+	1.65022i	−0.464231	+	0.124390i
$177$	5.68252	−	2.75305i	0.427124	−	0.206932i
$178$	−9.89890	−	5.71513i	−0.741954	−	0.428367i
$179$	−8.88935	−	15.3968i	−0.664421	−	1.15081i	−0.979442	−	0.201726i	$-0.935345\pi$
$179$	−8.88935	−	15.3968i	−0.664421	−	1.15081i	0.315021	−	0.949085i	$-0.397989\pi$
$180$	−6.37514	+	2.08749i	−0.475175	+	0.155593i
$181$		−	22.3561i		−	1.66171i	−0.556487	−	0.830856i	$-0.687851\pi$
$181$		−	22.3561i		−	1.66171i	0.556487	−	0.830856i	$-0.312149\pi$
$182$	−1.68245	−	3.29523i	−0.124712	−	0.244259i
$183$	−5.33059	+	15.3498i	−0.394048	+	1.13469i
$184$	0.376955	−	1.40682i	0.0277895	−	0.103712i
$185$	−3.01547	−	14.9116i	−0.221702	−	1.09632i
$186$	2.71242	−	2.34537i	0.198885	−	0.171971i
$187$	27.2432	−	27.2432i	1.99222	−	1.99222i
$188$	−7.05148	+	1.88944i	−0.514282	+	0.137802i
$189$	3.59906	−	3.93423i	0.261793	−	0.286173i
$190$	6.53637	+	13.1488i	0.474198	+	0.953912i
$191$	14.1585	+	8.17439i	1.02447	+	0.591478i	0.915396	−	0.402555i	$-0.131878\pi$
$191$	14.1585	+	8.17439i	1.02447	+	0.591478i	0.109075	+	0.994034i	$0.465211\pi$
$192$	−0.326014	−	1.70109i	−0.0235280	−	0.122766i
$193$	6.04505	−	22.5604i	0.435132	−	1.62394i	−0.305617	−	0.952155i	$-0.598863\pi$
$193$	6.04505	−	22.5604i	0.435132	−	1.62394i	0.740749	−	0.671782i	$-0.234471\pi$
$194$	4.24522			0.304789
$195$	6.04932	−	12.5859i	0.433201	−	0.901297i
$196$	5.94698			0.424785
$197$	1.78041	−	6.64459i	0.126849	−	0.473408i	−0.873050	−	0.487631i	$-0.837861\pi$
$197$	1.78041	−	6.64459i	0.126849	−	0.473408i	0.999899	+	0.0142237i	$0.00452770\pi$
$198$	18.9275	+	2.76179i	1.34512	+	0.196272i
$199$	−3.15587	−	1.82204i	−0.223714	−	0.129161i	0.383955	−	0.923352i	$-0.374562\pi$
$199$	−3.15587	−	1.82204i	−0.223714	−	0.129161i	−0.607669	+	0.794191i	$0.707895\pi$
$200$	0.684173	+	4.95297i	0.0483784	+	0.350228i
$201$	−14.3960	−	1.04476i	−1.01541	−	0.0736914i
$202$	−0.256528	+	0.0687364i	−0.0180492	+	0.00483628i
$203$	−3.70018	+	3.70018i	−0.259701	+	0.259701i
$204$	6.84560	+	7.91696i	0.479288	+	0.554298i
$205$	6.07615	−	1.22874i	0.424377	−	0.0858189i
$206$	0.536760	−	2.00322i	0.0373979	−	0.139571i
$207$	−2.70812	+	3.42887i	−0.188227	+	0.238323i
$208$	3.02550	+	1.96121i	0.209781	+	0.135986i
$209$		−	41.8698i		−	2.89619i
$210$	−2.40737	−	3.16224i	−0.166125	−	0.218216i
$211$	−1.10154	−	1.90793i	−0.0758334	−	0.131347i	0.825615	−	0.564234i	$-0.190828\pi$
$211$	−1.10154	−	1.90793i	−0.0758334	−	0.131347i	−0.901448	+	0.432887i	$0.857495\pi$
$212$	7.77692	+	4.49001i	0.534121	+	0.308375i
$213$	1.05158	+	2.17054i	0.0720530	+	0.148723i
$214$	−3.00221	+	0.804439i	−0.205227	+	0.0549903i
$215$	−0.503278	+	8.07212i	−0.0343233	+	0.550514i
$216$	−1.12045	+	5.07391i	−0.0762369	+	0.345236i
$217$	1.83981	+	1.06222i	0.124895	+	0.0721080i
$218$	17.4520	−	10.0759i	1.18200	−	0.682426i
$219$	17.5411	+	11.8989i	1.18532	+	0.804056i
$220$	4.53981	−	13.5150i	0.306074	−	0.911182i
$221$	−21.7581	−	1.12217i	−1.46361	−	0.0754855i
$222$	−11.1321	−	3.86591i	−0.747139	−	0.259463i
$223$	6.80208	+	1.82261i	0.455501	+	0.122051i	0.479272	−	0.877666i	$-0.340901\pi$
$223$	6.80208	+	1.82261i	0.455501	+	0.122051i	−0.0237714	+	0.999717i	$0.507567\pi$
$224$	0.888685	−	0.513083i	0.0593778	−	0.0342818i
$225$	3.99267	−	14.4589i	0.266178	−	0.963924i
$226$	1.32286	+	1.32286i	0.0879951	+	0.0879951i
$227$	9.88478	−	2.64862i	0.656076	−	0.175795i	0.0846014	−	0.996415i	$-0.473038\pi$
$227$	9.88478	−	2.64862i	0.656076	−	0.175795i	0.571474	+	0.820620i	$0.306372\pi$
$228$	11.3442	+	0.823280i	0.751288	+	0.0545231i
$229$	−9.15867	+	9.15867i	−0.605222	+	0.605222i	−0.941694	−	0.336471i	$-0.890766\pi$
$229$	−9.15867	+	9.15867i	−0.605222	+	0.605222i	0.336471	+	0.941694i	$0.390766\pi$
$230$	2.15508	+	2.44168i	0.142102	+	0.160999i
$231$	2.13304	+	11.1299i	0.140344	+	0.732295i
$232$	1.31982	−	4.92565i	0.0866507	−	0.323385i
$233$		−	18.7699i		−	1.22966i	−0.788660	−	0.614830i	$-0.789225\pi$
$233$		−	18.7699i		−	1.22966i	0.788660	−	0.614830i	$-0.210775\pi$
$234$	−6.00877	−	8.99415i	−0.392806	−	0.587966i
$235$	5.19790	−	15.4741i	0.339073	−	1.00942i
$236$	−3.52134	−	0.943540i	−0.229220	−	0.0614192i
$237$	10.6004	−	2.03156i	0.688569	−	0.131964i
$238$	−3.10038	+	5.37001i	−0.200968	+	0.348086i
$239$	−10.1652	+	10.1652i	−0.657535	+	0.657535i	−0.954796	−	0.297261i	$-0.903927\pi$
$239$	−10.1652	+	10.1652i	−0.657535	+	0.657535i	0.297261	+	0.954796i	$0.403927\pi$
$240$	3.57249	+	1.49576i	0.230603	+	0.0965509i
$241$	0.254729	+	0.950660i	0.0164085	+	0.0612374i	0.973645	−	0.228070i	$-0.0732416\pi$
$241$	0.254729	+	0.950660i	0.0164085	+	0.0612374i	−0.957236	+	0.289308i	$0.906575\pi$
$242$	−20.9679	+	20.9679i	−1.34787	+	1.34787i
$243$	9.10848	−	12.6505i	0.584309	−	0.811531i
$244$	8.12450	−	4.69068i	0.520118	−	0.300290i
$245$	−7.35267	+	11.0802i	−0.469745	+	0.707890i
$246$	1.57527	−	4.53610i	0.100436	−	0.289211i
$247$	−17.5822	+	15.8576i	−1.11873	+	1.00899i
$248$	−2.07026			−0.131462
$249$	11.5202	+	7.81466i	0.730061	+	0.495234i
$250$	−10.0741	−	4.84897i	−0.637142	−	0.306676i
$251$	−4.44050	+	7.69117i	−0.280282	+	0.485462i	−0.971454	−	0.237228i	$-0.923761\pi$
$251$	−4.44050	+	7.69117i	−0.280282	+	0.485462i	0.691172	+	0.722690i	$0.257095\pi$
$252$	−3.05748	+	0.359081i	−0.192603	+	0.0226200i
$253$	−2.40346	−	8.96983i	−0.151104	−	0.563928i
$254$	9.01718	−	2.41614i	0.565788	−	0.151602i
$255$	−23.2143	+	2.96621i	−1.45374	+	0.185751i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.51243	−	3.18260i	0.343856	−	0.198525i	−0.318120	−	0.948050i	$-0.603051\pi$
$257$	5.51243	−	3.18260i	0.343856	−	0.198525i	0.661976	+	0.749525i	$0.269718\pi$
$258$	5.18450	+	3.51688i	0.322773	+	0.218952i
$259$		−	6.98168i		−	0.433820i
$260$	−7.39470	+	3.21223i	−0.458600	+	0.199214i
$261$	−9.48188	+	12.0054i	−0.586913	+	0.743116i
$262$	−0.442355	−	0.118529i	−0.0273288	−	0.00732273i
$263$	−11.1446	−	19.3031i	−0.687207	−	1.19028i	−0.972738	−	0.231908i	$-0.925503\pi$
$263$	−11.1446	−	19.3031i	−0.687207	−	1.19028i	0.285531	−	0.958370i	$-0.407830\pi$
$264$	−7.22323	−	8.35369i	−0.444559	−	0.514134i
$265$	−17.9808	+	8.93840i	−1.10455	+	0.549081i
$266$	1.74408	+	6.50901i	0.106937	+	0.399093i
$267$	1.43301	−	19.7459i	0.0876990	−	1.20843i
$268$	5.89258	+	5.89258i	0.359947	+	0.359947i
$269$	12.9508	+	7.47713i	0.789622	+	0.455888i	0.839829	−	0.542850i	$-0.182655\pi$
$269$	12.9508	+	7.47713i	0.789622	+	0.455888i	−0.0502075	+	0.998739i	$0.515988\pi$
$270$	−8.06826	−	8.36081i	−0.491019	−	0.508823i
$271$	1.29241	+	0.346301i	0.0785084	+	0.0210363i	0.297859	−	0.954610i	$-0.403727\pi$
$271$	1.29241	+	0.346301i	0.0785084	+	0.0210363i	−0.219351	+	0.975646i	$0.570394\pi$
$272$		−	6.04264i		−	0.366389i
$273$	3.86589	−	5.11102i	0.233974	−	0.309333i
$274$	−0.952061			−0.0575161
$275$	19.5679	+	25.1680i	1.17999	+	1.51769i
$276$	2.47755	−	0.474820i	0.149131	−	0.0285808i
$277$	−9.18624	+	15.9110i	−0.551948	+	0.956002i	0.446186	+	0.894940i	$0.352782\pi$
$277$	−9.18624	+	15.9110i	−0.551948	+	0.956002i	−0.998134	+	0.0610616i	$0.980551\pi$
$278$	−9.84385	−	9.84385i	−0.590395	−	0.590395i
$279$	5.70421	+	2.45682i	0.341502	+	0.147086i
$280$	−0.142784	+	2.29013i	−0.00853298	+	0.136861i
$281$	2.14505	+	2.14505i	0.127963	+	0.127963i	0.768188	−	0.640225i	$-0.221159\pi$
$281$	2.14505	+	2.14505i	0.127963	+	0.127963i	−0.640225	+	0.768188i	$0.721159\pi$
$282$	−8.27031	−	9.56464i	−0.492490	−	0.569566i
$283$	9.28235	+	16.0775i	0.551778	+	0.955708i	0.998146	+	0.0608586i	$0.0193839\pi$
$283$	9.28235	+	16.0775i	0.551778	+	0.955708i	−0.446368	+	0.894849i	$0.647283\pi$
$284$	0.360402	−	1.34504i	0.0213859	−	0.0798134i
$285$	−15.5595	+	20.1183i	−0.921666	+	1.19170i
$286$	22.9584	+	1.18408i	1.35756	+	0.0700159i
$287$	2.84488			0.167928
$288$	2.40538	−	1.79280i	0.141738	−	0.105642i
$289$	9.75676	+	16.8992i	0.573927	+	0.994071i
$290$	7.54552	+	8.54898i	0.443088	+	0.502013i
$291$	3.20590	+	6.61724i	0.187933	+	0.387909i
$292$	−3.16732	−	11.8206i	−0.185353	−	0.691749i
$293$	1.14072	+	4.25724i	0.0666418	+	0.248711i	0.991208	−	0.132310i	$-0.0422394\pi$
$293$	1.14072	+	4.25724i	0.0666418	+	0.248711i	−0.924567	+	0.381021i	$0.875573\pi$
$294$	4.49104	+	9.26986i	0.261923	+	0.540629i
$295$	6.11165	−	5.39428i	0.355834	−	0.314067i
$296$	3.40183	+	5.89214i	0.197727	+	0.342474i
$297$	9.98873	+	31.5889i	0.579605	+	1.83297i
$298$	−1.26586			−0.0733295
$299$	−2.85639	+	4.40647i	−0.165190	+	0.254833i
$300$	−7.20377	+	4.80684i	−0.415910	+	0.277523i
$301$	−0.960636	+	3.58514i	−0.0553702	+	0.206644i
$302$	3.46208	+	5.99650i	0.199220	+	0.345060i
$303$	−0.300868	−	0.347954i	−0.0172844	−	0.0199895i
$304$	−4.64343	−	4.64343i	−0.266319	−	0.266319i
$305$	−1.30536	+	20.9367i	−0.0747444	+	1.19883i
$306$	−7.17091	+	16.6493i	−0.409934	+	0.951778i
$307$	−12.4674	−	12.4674i	−0.711551	−	0.711551i	0.255309	−	0.966860i	$-0.417823\pi$
$307$	−12.4674	−	12.4674i	−0.711551	−	0.711551i	−0.966860	+	0.255309i	$0.917823\pi$
$308$	3.27140	−	5.66624i	0.186406	−	0.322864i
$309$	3.52786	−	0.676114i	0.200693	−	0.0384628i
$310$	2.55961	−	3.85725i	0.145376	−	0.219077i
$311$	12.1147			0.686963			0.343482	−	0.939159i	$-0.388394\pi$
$311$	12.1147			0.686963			0.343482	+	0.939159i	$0.388394\pi$
$312$	−0.772242	+	6.19707i	−0.0437196	+	0.350840i
$313$		−	3.94403i		−	0.222930i	−0.993768	−	0.111465i	$-0.964446\pi$
$313$		−	3.94403i		−	0.222930i	0.993768	−	0.111465i	$-0.0355543\pi$
$314$	−0.726843	−	0.194757i	−0.0410181	−	0.0109908i
$315$	3.11115	−	6.14056i	0.175293	−	0.345981i
$316$	−5.39665	−	3.11576i	−0.303585	−	0.175275i
$317$	−8.80930	−	8.80930i	−0.494779	−	0.494779i	0.415029	−	0.909808i	$-0.363771\pi$
$317$	−8.80930	−	8.80930i	−0.494779	−	0.494779i	−0.909808	+	0.415029i	$0.863771\pi$
$318$	−1.12583	+	15.5130i	−0.0631332	+	0.869928i
$319$	−8.41517	−	31.4058i	−0.471159	−	1.75839i
$320$	−0.995366	−	2.00231i	−0.0556426	−	0.111933i
$321$	−3.52113	−	4.07220i	−0.196530	−	0.227288i
$322$	0.747276	+	1.29432i	0.0416441	+	0.0721297i
$323$	38.3287	+	10.2702i	2.13267	+	0.571447i
$324$	−8.75511	+	2.08522i	−0.486395	+	0.115845i
$325$	3.15765	−	17.7491i	0.175155	−	0.984541i
$326$		−	3.06141i		−	0.169556i
$327$	28.8852	+	19.5941i	1.59735	+	1.08356i
$328$	−2.40092	+	1.38617i	−0.132569	+	0.0765385i
$329$	3.74562	−	6.48761i	0.206503	−	0.357674i
$330$	24.4949	−	3.12984i	1.34840	−	0.172292i
$331$	−4.24708	+	1.13800i	−0.233440	+	0.0625502i	−0.373643	−	0.927573i	$-0.621891\pi$
$331$	−4.24708	+	1.13800i	−0.233440	+	0.0625502i	0.140202	+	0.990123i	$0.455225\pi$
$332$	−2.08015	−	7.76321i	−0.114163	−	0.426061i
$333$	−2.38077	−	20.2716i	−0.130465	−	1.11088i
$334$	−6.32684	+	10.9584i	−0.346189	+	0.599617i
$335$	−18.2643	+	3.69346i	−0.997884	+	0.201795i
$336$	1.47089	+	0.997769i	0.0802434	+	0.0544328i
$337$	1.96895			0.107255			0.0536277	−	0.998561i	$-0.482922\pi$
$337$	1.96895			0.107255			0.0536277	+	0.998561i	$0.482922\pi$
$338$	−8.19794	−	10.0893i	−0.445909	−	0.548785i
$339$	−1.06301	+	3.06100i	−0.0577347	+	0.166251i
$340$	11.2585	+	7.47094i	0.610575	+	0.405168i
$341$	−11.4315	+	6.59998i	−0.619050	+	0.357409i
$342$	7.28362	+	18.3045i	0.393853	+	0.989794i
$343$	−9.39444	+	9.39444i	−0.507252	+	0.507252i
$344$	−0.936142	−	3.49373i	−0.0504734	−	0.188369i
$345$	−2.17849	+	5.20313i	−0.117286	+	0.280127i
$346$	−8.68583	+	8.68583i	−0.466953	+	0.466953i
$347$	−13.1149	+	22.7157i	−0.704045	+	1.21944i	0.262991	+	0.964798i	$0.415291\pi$
$347$	−13.1149	+	22.7157i	−0.704045	+	1.21944i	−0.967035	+	0.254643i	$0.918042\pi$
$348$	8.67457	−	1.66248i	0.465006	−	0.0891181i
$349$	10.3892	+	2.78377i	0.556120	+	0.149012i	0.525923	−	0.850532i	$-0.323720\pi$
$349$	10.3892	+	2.78377i	0.556120	+	0.149012i	0.0301969	+	0.999544i	$0.490387\pi$
$350$	−4.09036	−	3.09748i	−0.218639	−	0.165567i
$351$	9.48193	−	16.1584i	0.506108	−	0.862470i
$352$			6.37598i			0.339841i
$353$	1.74273	−	6.50394i	0.0927560	−	0.346170i	−0.903914	−	0.427715i	$-0.859319\pi$
$353$	1.74273	−	6.50394i	0.0927560	−	0.346170i	0.996670	+	0.0815449i	$0.0259854\pi$
$354$	−1.18850	−	6.20143i	−0.0631682	−	0.329602i
$355$	2.06044	+	2.33445i	0.109357	+	0.123900i
$356$	−8.08242	+	8.08242i	−0.428367	+	0.428367i
$357$	−10.7118	−	0.777389i	−0.566931	−	0.0411438i
$358$	−17.1729	+	4.60147i	−0.907616	+	0.243195i
$359$	10.3113	+	10.3113i	0.544211	+	0.544211i	0.924760	−	0.380550i	$-0.124265\pi$
$359$	10.3113	+	10.3113i	0.544211	+	0.544211i	−0.380550	+	0.924760i	$0.624265\pi$
$360$	0.366359	+	6.69819i	0.0193088	+	0.353026i
$361$	20.8910	−	12.0614i	1.09953	−	0.634812i
$362$	−21.5943	−	5.78617i	−1.13497	−	0.304114i
$363$	−48.5183	−	16.8492i	−2.54655	−	0.884353i
$364$	−3.61840	+	0.772257i	−0.189656	+	0.0404773i
$365$	25.9397	+	8.71338i	1.35775	+	0.456079i
$366$	13.4471	+	9.12176i	0.702890	+	0.476802i
$367$	−23.4982	+	13.5667i	−1.22660	+	0.708176i	−0.966317	−	0.257356i	$-0.917149\pi$
$367$	−23.4982	+	13.5667i	−1.22660	+	0.708176i	−0.260281	+	0.965533i	$0.583815\pi$
$368$	−1.26132	−	0.728222i	−0.0657507	−	0.0379612i
$369$	8.26026	−	0.970112i	0.430012	−	0.0505020i
$370$	−15.1840	−	0.946684i	−0.789376	−	0.0492157i
$371$	−8.90099	+	2.38501i	−0.462116	+	0.123824i
$372$	−1.56342	−	3.22703i	−0.0810597	−	0.167313i
$373$	−23.0745	−	13.3221i	−1.19475	−	0.689792i	−0.235373	−	0.971905i	$-0.575631\pi$
$373$	−23.0745	−	13.3221i	−1.19475	−	0.689792i	−0.959381	+	0.282113i	$0.908965\pi$
$374$	−19.2639	−	33.3660i	−0.996111	−	1.72532i
$375$	−0.0494277	−	19.3649i	−0.00255244	−	0.999997i
$376$			7.30023i			0.376481i
$377$	−10.0010	+	15.4283i	−0.515079	+	0.794596i
$378$	−2.86867	−	4.49468i	−0.147548	−	0.231182i
$379$	−4.26028	+	15.8996i	−0.218836	+	0.816707i	0.765945	+	0.642906i	$0.222271\pi$
$379$	−4.26028	+	15.8996i	−0.218836	+	0.816707i	−0.984781	+	0.173801i	$0.944395\pi$
$380$	14.3925	−	2.91049i	0.738318	−	0.149305i
$381$	10.5758	+	12.2309i	0.541813	+	0.626608i
$382$	11.5603	−	11.5603i	0.591478	−	0.591478i
$383$	−4.79215	+	1.28405i	−0.244867	+	0.0656120i	−0.379165	−	0.925329i	$-0.623789\pi$
$383$	−4.79215	+	1.28405i	−0.244867	+	0.0656120i	0.134298	+	0.990941i	$0.457122\pi$
$384$	−1.72751	−	0.125370i	−0.0881565	−	0.00639777i
$385$	6.51249	+	13.1007i	0.331907	+	0.667675i
$386$	−20.2271	−	11.6781i	−1.02953	−	0.594402i
$387$	−1.56671	+	10.7372i	−0.0796405	+	0.545804i
$388$	1.09874	−	4.10057i	0.0557802	−	0.208175i
$389$	−16.9673			−0.860276			−0.430138	−	0.902763i	$-0.641535\pi$
$389$	−16.9673			−0.860276			−0.430138	+	0.902763i	$0.641535\pi$
$390$	−10.5914	−	9.10068i	−0.536316	−	0.460831i
$391$	8.80077			0.445074
$392$	1.53919	−	5.74435i	0.0777410	−	0.290133i
$393$	−0.149301	−	0.779032i	−0.00753124	−	0.0392969i
$394$	−5.95738	−	3.43949i	−0.300128	−	0.173279i
$395$	12.4774	−	6.20263i	0.627807	−	0.312088i
$396$	7.56648	−	17.5678i	0.380230	−	0.882813i
$397$	20.6624	−	5.53646i	1.03701	−	0.277867i	0.300139	−	0.953896i	$-0.402967\pi$
$397$	20.6624	−	5.53646i	1.03701	−	0.277867i	0.736875	+	0.676029i	$0.236300\pi$
$398$	−2.57676	+	2.57676i	−0.129161	+	0.129161i
$399$	−8.82882	+	7.63407i	−0.441994	+	0.382181i
$400$	4.96128	+	0.621062i	0.248064	+	0.0310531i
$401$	5.14428	−	19.1987i	0.256893	−	0.958738i	−0.710134	−	0.704066i	$-0.751366\pi$
$401$	5.14428	−	19.1987i	0.256893	−	0.958738i	0.967027	−	0.254672i	$-0.0819676\pi$
$402$	−4.73511	+	13.6350i	−0.236166	+	0.680053i
$403$	7.10102	+	2.30074i	0.353727	+	0.114608i
$404$			0.265577i			0.0132130i
$405$	6.93943	−	18.8903i	0.344823	−	0.938668i
$406$	2.61642	+	4.53177i	0.129851	+	0.224908i
$407$	37.5681	+	21.6900i	1.86218	+	1.07513i
$408$	9.41897	−	4.56328i	0.466309	−	0.225916i
$409$	16.2635	−	4.35780i	0.804180	−	0.215479i	0.166761	−	0.985997i	$-0.446669\pi$
$409$	16.2635	−	4.35780i	0.804180	−	0.215479i	0.637418	+	0.770518i	$0.280002\pi$
$410$	0.385753	−	6.18713i	0.0190510	−	0.305561i
$411$	−0.718978	−	1.48403i	−0.0354646	−	0.0732016i
$412$	−1.79603	−	1.03694i	−0.0884843	−	0.0510864i
$413$	3.23975	−	1.87047i	0.159418	−	0.0920400i
$414$	2.61112	+	3.50330i	0.128330	+	0.172178i
$415$	17.0360	+	5.72253i	0.836263	+	0.280908i
$416$	2.67744	−	2.41481i	0.131272	−	0.118396i
$417$	7.91022	−	22.7780i	0.387365	−	1.11544i
$418$	−40.4431	−	10.8367i	−1.97814	−	0.530040i
$419$	−2.16612	+	1.25061i	−0.105822	+	0.0610962i	−0.551977	−	0.833859i	$-0.686126\pi$
$419$	−2.16612	+	1.25061i	−0.105822	+	0.0610962i	0.446155	+	0.894956i	$0.352793\pi$
$420$	−3.67757	+	1.50689i	−0.179447	+	0.0735289i
$421$	20.0753	+	20.0753i	0.978412	+	0.978412i	0.999772	−	0.0213603i	$-0.00679970\pi$
$421$	20.0753	+	20.0753i	0.978412	+	0.978412i	−0.0213603	+	0.999772i	$0.506800\pi$
$422$	−2.12802	+	0.570201i	−0.103590	+	0.0277570i
$423$	8.66331	−	20.1144i	0.421225	−	0.977994i
$424$	6.34983	−	6.34983i	0.308375	−	0.308375i
$425$	−27.8392	+	11.7395i	−1.35040	+	0.569452i
$426$	2.36875	−	0.453970i	0.114766	−	0.0219949i
$427$	−2.49161	+	9.29881i	−0.120577	+	0.450001i
$428$			3.10811i			0.150236i
$429$	15.4920	+	36.6806i	0.747963	+	1.77096i
$430$	7.66682	+	2.57535i	0.369727	+	0.124194i
$431$	−7.79159	−	2.08775i	−0.375308	−	0.100563i	0.0662340	−	0.997804i	$-0.478902\pi$
$431$	−7.79159	−	2.08775i	−0.375308	−	0.100563i	−0.441542	+	0.897241i	$0.645568\pi$
$432$	4.61103	+	2.39550i	0.221848	+	0.115253i
$433$	−9.61055	+	16.6460i	−0.461854	+	0.799954i	−0.999053	−	0.0435011i	$-0.986149\pi$
$433$	−9.61055	+	16.6460i	−0.461854	+	0.799954i	0.537200	+	0.843455i	$0.319482\pi$
$434$	1.50220	−	1.50220i	0.0721080	−	0.0721080i
$435$	−7.62749	+	18.2176i	−0.365710	+	0.873467i
$436$	−5.21567	−	19.4651i	−0.249785	−	0.932211i
$437$	6.76289	−	6.76289i	0.323513	−	0.323513i
$438$	16.0335	−	13.8638i	0.766109	−	0.662436i
$439$	−13.8805	+	8.01394i	−0.662482	+	0.382484i	−0.793222	−	0.608932i	$-0.791598\pi$
$439$	−13.8805	+	8.01394i	−0.662482	+	0.382484i	0.130740	+	0.991417i	$0.458265\pi$
$440$	−11.8795	−	7.88306i	−0.566333	−	0.375810i
$441$	−11.0579	+	14.0008i	−0.526565	+	0.666706i
$442$	−6.71536	+	20.7263i	−0.319417	+	0.985850i
$443$	0.826972			0.0392906			0.0196453	−	0.999807i	$-0.493746\pi$
$443$	0.826972			0.0392906			0.0196453	+	0.999807i	$0.493746\pi$
$444$	−6.61538	+	9.75223i	−0.313952	+	0.462820i
$445$	−5.06604	−	25.0517i	−0.240154	−	1.18757i
$446$	3.52101	−	6.09858i	0.166725	−	0.288776i
$447$	−0.955954	−	1.97316i	−0.0452151	−	0.0933275i
$448$	−0.265591	−	0.991200i	−0.0125480	−	0.0468298i
$449$	18.4012	−	4.93057i	0.868404	−	0.232688i	0.203007	−	0.979177i	$-0.434929\pi$
$449$	18.4012	−	4.93057i	0.868404	−	0.232688i	0.665398	+	0.746489i	$0.268262\pi$
$450$	−12.9328	−	7.59885i	−0.609658	−	0.358213i
$451$	−8.83820	+	15.3082i	−0.416175	+	0.720835i
$452$	1.62016	−	0.935400i	0.0762060	−	0.0439975i
$453$	−6.73256	+	9.92496i	−0.316323	+	0.466315i
$454$		−	10.2335i		−	0.480281i
$455$	3.03483	−	7.69648i	0.142275	−	0.360817i
$456$	3.73132	−	10.7446i	0.174735	−	0.503161i
$457$	−6.95921	−	1.86471i	−0.325538	−	0.0872277i	0.0923488	−	0.995727i	$-0.470563\pi$
$457$	−6.95921	−	1.86471i	−0.325538	−	0.0872277i	−0.417887	+	0.908499i	$0.637229\pi$
$458$	6.47616	+	11.2170i	0.302611	+	0.524138i
$459$	−31.3675	+	1.39558i	−1.46411	+	0.0651400i
$460$	2.91625	−	1.44969i	0.135971	−	0.0675923i
$461$	8.45238	+	31.5447i	0.393666	+	1.46918i	0.824040	+	0.566532i	$0.191715\pi$
$461$	8.45238	+	31.5447i	0.393666	+	1.46918i	−0.430373	+	0.902651i	$0.641618\pi$
$462$	11.3028	+	0.820273i	0.525852	+	0.0381625i
$463$	4.54794	+	4.54794i	0.211361	+	0.211361i	0.804845	−	0.593485i	$-0.202248\pi$
$463$	4.54794	+	4.54794i	0.211361	+	0.211361i	−0.593485	+	0.804845i	$0.702248\pi$
$464$	−4.41622	−	2.54971i	−0.205018	−	0.118367i
$465$	7.94545	+	1.07688i	0.368462	+	0.0499390i
$466$	−18.1304	−	4.85802i	−0.839873	−	0.225043i
$467$		−	9.72513i		−	0.450025i	−0.974356	−	0.225013i	$-0.927758\pi$
$467$		−	9.72513i		−	0.450025i	0.974356	−	0.225013i	$-0.0722424\pi$
$468$	−10.2429	+	3.47617i	−0.473477	+	0.160686i
$469$	−8.55142			−0.394868
$470$	−13.6016	−	9.02578i	−0.627393	−	0.416328i
$471$	−0.245320	−	1.28004i	−0.0113037	−	0.0589813i
$472$	−1.82278	+	3.15715i	−0.0839002	+	0.145319i
$473$	−16.3071	−	16.3071i	−0.749802	−	0.749802i
$474$	0.781246	−	10.7650i	0.0358838	−	0.494452i
$475$	−12.3717	+	30.4140i	−0.567651	+	1.39549i
$476$	4.38459	+	4.38459i	0.200968	+	0.200968i
$477$	−25.0312	+	9.96026i	−1.14610	+	0.456049i
$478$	7.18791	+	12.4498i	0.328767	+	0.569442i
$479$	−0.625661	+	2.33500i	−0.0285872	+	0.106689i	−0.978745	−	0.205080i	$-0.934255\pi$
$479$	−0.625661	+	2.33500i	−0.0285872	+	0.106689i	0.950158	+	0.311768i	$0.100921\pi$
$480$	2.36942	−	3.06363i	0.108149	−	0.139835i
$481$	−5.12020	−	23.9906i	−0.233461	−	1.09388i
$482$	0.984196			0.0448289
$483$	−1.45319	+	2.14226i	−0.0661226	+	0.0974763i
$484$	14.8265	+	25.6803i	0.673934	+	1.16729i
$485$	6.28159	+	7.11695i	0.285232	+	0.323164i
$486$	−9.86202	−	12.0723i	−0.447350	−	0.547611i
$487$	−7.14100	−	26.6506i	−0.323590	−	1.20765i	−0.915722	−	0.401812i	$-0.868380\pi$
$487$	−7.14100	−	26.6506i	−0.323590	−	1.20765i	0.592132	−	0.805841i	$-0.298286\pi$
$488$	−2.42808	−	9.06171i	−0.109914	−	0.410204i
$489$	4.77198	−	2.31192i	0.215796	−	0.104549i
$490$	8.79967	+	9.96990i	0.397528	+	0.450394i
$491$	8.24071	+	14.2733i	0.371898	+	0.644146i	0.989858	−	0.142064i	$-0.0453738\pi$
$491$	8.24071	+	14.2733i	0.371898	+	0.644146i	−0.617960	+	0.786210i	$0.712040\pi$
$492$	−3.97382	−	2.69563i	−0.179154	−	0.121528i
$493$	30.8139			1.38779
$494$	10.7666	+	21.0874i	0.484413	+	0.948765i
$495$	23.3767	+	35.8179i	1.05070	+	1.60989i
$496$	−0.535824	+	1.99972i	−0.0240592	+	0.0897902i
$497$	0.714461	+	1.23748i	0.0320480	+	0.0555087i
$498$	10.5300	−	9.10505i	0.471862	−	0.408007i
$499$	−25.1133	−	25.1133i	−1.12423	−	1.12423i	−0.991099	−	0.133128i	$-0.957498\pi$
$499$	−25.1133	−	25.1133i	−1.12423	−	1.12423i	−0.133128	−	0.991099i	$-0.542502\pi$
$500$	−7.29111	+	8.47583i	−0.326068	+	0.379051i
$501$	−21.8593	−	1.58639i	−0.976602	−	0.0708748i
$502$	6.27982	+	6.27982i	0.280282	+	0.280282i
$503$	17.1164	−	29.6465i	0.763183	−	1.32187i	−0.178019	−	0.984027i	$-0.556969\pi$
$503$	17.1164	−	29.6465i	0.763183	−	1.32187i	0.941202	−	0.337845i	$-0.109698\pi$
$504$	−0.444489	+	3.04624i	−0.0197991	+	0.135690i
$505$	−0.494815	−	0.328351i	−0.0220190	−	0.0146114i
$506$	−9.28625			−0.412824
$507$	9.53577	−	20.3978i	0.423498	−	0.905897i
$508$		−	9.33527i		−	0.414186i
$509$	−3.53811	−	0.948033i	−0.156824	−	0.0420208i	0.179553	−	0.983748i	$-0.442535\pi$
$509$	−3.53811	−	0.948033i	−0.156824	−	0.0420208i	−0.336377	+	0.941727i	$0.609202\pi$
$510$	−3.14317	+	23.1910i	−0.139182	+	1.02692i
$511$	10.8754	+	6.27890i	0.481098	+	0.277762i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−23.0317	+	25.1765i	−1.01687	+	1.11157i
$514$	−1.64744	−	6.14831i	−0.0726653	−	0.271191i
$515$	4.15256	−	2.06427i	0.182983	−	0.0909626i
$516$	4.73889	−	4.09760i	0.208618	−	0.180387i
$517$	23.2731	+	40.3101i	1.02355	+	1.77284i
$518$	−6.74378	−	1.80699i	−0.296305	−	0.0793946i
$519$	−20.0984	−	6.97968i	−0.882222	−	0.306374i
$520$	1.18889	+	7.97412i	0.0521362	+	0.349688i
$521$			16.5198i			0.723746i	0.932227	+	0.361873i	$0.117863\pi$
$521$			16.5198i			0.723746i	−0.932227	+	0.361873i	$0.882137\pi$
$522$	9.14225	+	12.2660i	0.400145	+	0.536869i
$523$	7.23105	−	4.17485i	0.316192	−	0.182553i	−0.333502	−	0.942749i	$-0.608230\pi$
$523$	7.23105	−	4.17485i	0.316192	−	0.182553i	0.649694	+	0.760196i	$0.274897\pi$
$524$	−0.228980	+	0.396605i	−0.0100030	+	0.0173258i
$525$	1.73923	−	8.71500i	0.0759064	−	0.380354i
$526$	−21.5298	+	5.76888i	−0.938742	+	0.251535i
$527$	−3.23779	−	12.0836i	−0.141040	−	0.526370i
$528$	−9.93856	+	4.81501i	−0.432520	+	0.209546i
$529$	−10.4394	+	18.0815i	−0.453886	+	0.786154i
$530$	3.98006	+	19.6815i	0.172883	+	0.854911i
$531$	8.76895	−	6.53577i	0.380540	−	0.283628i
$532$	6.73862			0.292156
$533$	9.77566	−	2.08637i	0.423431	−	0.0903707i
$534$	−18.7022	−	6.49479i	−0.809321	−	0.281057i
$535$	−5.79094	−	3.84278i	−0.250364	−	0.166138i
$536$	7.21691	−	4.16669i	0.311723	−	0.179973i
$537$	−20.1412	−	23.2933i	−0.869156	−	1.00518i
$538$	10.5743	−	10.5743i	0.455888	−	0.455888i
$539$	−9.81386	−	36.6258i	−0.422713	−	1.57759i
$540$	−10.1641	+	5.62940i	−0.437395	+	0.242251i
$541$	−24.6299	+	24.6299i	−1.05892	+	1.05892i	−0.0607697	+	0.998152i	$0.519356\pi$
$541$	−24.6299	+	24.6299i	−1.05892	+	1.05892i	−0.998152	+	0.0607697i	$0.980644\pi$
$542$	0.669002	−	1.15874i	0.0287361	−	0.0497723i
$543$	−7.28838	−	38.0297i	−0.312774	−	1.63201i
$544$	−5.83674	−	1.56395i	−0.250248	−	0.0670538i
$545$	42.7153	+	14.3484i	1.82972	+	0.614619i
$546$	−3.93630	−	5.05699i	−0.168458	−	0.216419i
$547$		−	22.9081i		−	0.979480i	−0.871869	−	0.489740i	$-0.837092\pi$
$547$		−	22.9081i		−	0.979480i	0.871869	−	0.489740i	$-0.162908\pi$
$548$	−0.246412	+	0.919621i	−0.0105262	+	0.0392842i
$549$	−4.06359	+	27.8492i	−0.173430	+	1.18857i
$550$	29.3749	−	12.3871i	1.25255	−	0.528190i
$551$	23.6787	−	23.6787i	1.00875	−	1.00875i
$552$	0.182595	−	2.51602i	0.00777174	−	0.107089i
$553$	6.17668	−	1.65504i	0.262659	−	0.0703793i
$554$	12.9913	+	12.9913i	0.551948	+	0.551948i
$555$	−9.99098	−	24.3829i	−0.424093	−	1.03500i
$556$	−12.0562	+	6.96065i	−0.511297	+	0.295197i
$557$	40.5897	+	10.8760i	1.71984	+	0.460830i	0.977803	−	0.209527i	$-0.0671924\pi$
$557$	40.5897	+	10.8760i	1.71984	+	0.460830i	0.742039	+	0.670357i	$0.233859\pi$
$558$	3.84946	−	4.87397i	0.162961	−	0.206332i
$559$	−0.671705	+	13.0239i	−0.0284101	+	0.550851i
$560$	2.17514	+	0.730648i	0.0919164	+	0.0308755i
$561$	37.4616	−	55.2249i	1.58163	−	2.33160i
$562$	2.62713	−	1.51678i	0.110819	−	0.0639813i
$563$	−15.8869	−	9.17233i	−0.669555	−	0.386568i	0.126353	−	0.991985i	$-0.459673\pi$
$563$	−15.8869	−	9.17233i	−0.669555	−	0.386568i	−0.795908	+	0.605418i	$0.793006\pi$
$564$	−11.3792	+	5.51299i	−0.479153	+	0.232139i
$565$	−0.260310	+	4.17513i	−0.0109513	+	0.175649i
$566$	17.9321	−	4.80490i	0.753743	−	0.201965i
$567$	4.83973	−	7.86583i	0.203249	−	0.330334i
$568$	−1.20593	−	0.696243i	−0.0505997	−	0.0292137i
$569$	12.2740	+	21.2592i	0.514554	+	0.891233i	0.999857	+	0.0168875i	$0.00537570\pi$
$569$	12.2740	+	21.2592i	0.514554	+	0.891233i	−0.485304	+	0.874346i	$0.661291\pi$
$570$	15.4056	+	20.2363i	0.645271	+	0.847607i
$571$		−	8.11844i		−	0.339746i	−0.985466	−	0.169873i	$-0.945664\pi$
$571$		−	8.11844i		−	0.339746i	0.985466	−	0.169873i	$-0.0543358\pi$
$572$	7.08580	−	21.8696i	0.296272	−	0.914416i
$573$	26.7498	+	9.28954i	1.11749	+	0.388076i
$574$	0.736310	−	2.74795i	0.0307330	−	0.114697i
$575$	−0.904542	+	7.22582i	−0.0377220	+	0.301338i
$576$	−1.10916	−	2.78743i	−0.0462149	−	0.116143i
$577$	−2.57971	+	2.57971i	−0.107395	+	0.107395i	−0.758762	−	0.651368i	$-0.774196\pi$
$577$	−2.57971	+	2.57971i	−0.107395	+	0.107395i	0.651368	+	0.758762i	$0.274196\pi$
$578$	18.8486	−	5.05047i	0.783999	−	0.210072i
$579$	2.92818	−	40.3482i	0.121691	−	1.67681i
$580$	10.2106	−	5.07578i	0.423972	−	0.210760i
$581$	7.14242	+	4.12368i	0.296318	+	0.171079i
$582$	7.22151	−	1.38400i	0.299341	−	0.0573686i
$583$	14.8190	−	55.3054i	0.613742	−	2.29052i
$584$	−12.2376			−0.506395
$585$	6.18727	−	23.3820i	0.255812	−	0.966726i
$586$	4.40742			0.182069
$587$	−9.51174	+	35.4983i	−0.392592	+	1.46517i	0.433252	+	0.901273i	$0.357366\pi$
$587$	−9.51174	+	35.4983i	−0.392592	+	1.46517i	−0.825844	+	0.563899i	$0.809301\pi$
$588$	10.1164	−	1.93880i	0.417192	−	0.0799547i
$589$	−11.7736	−	6.79750i	−0.485124	−	0.280086i
$590$	−3.62866	−	7.29954i	−0.149390	−	0.300517i
$591$	0.862420	−	11.8835i	0.0354752	−	0.488822i
$592$	6.57183	−	1.76092i	0.270100	−	0.0723732i
$593$	25.8979	−	25.8979i	1.06350	−	1.06350i	0.0656563	−	0.997842i	$-0.479086\pi$
$593$	25.8979	−	25.8979i	1.06350	−	1.06350i	0.997842	−	0.0656563i	$-0.0209141\pi$
$594$	33.0978	−	1.47256i	1.35802	−	0.0604200i
$595$	−13.5902	+	2.74825i	−0.557144	+	0.112667i
$596$	−0.327629	+	1.22273i	−0.0134202	+	0.0500849i
$597$	−5.96244	−	2.07061i	−0.244026	−	0.0847442i
$598$	3.51703	+	3.89954i	0.143822	+	0.159464i
$599$		−	32.6243i		−	1.33299i	−0.745508	−	0.666496i	$-0.767793\pi$
$599$		−	32.6243i		−	1.33299i	0.745508	−	0.666496i	$-0.232207\pi$
$600$	2.77858	+	8.20241i	0.113435	+	0.334862i
$601$	−0.650836	−	1.12728i	−0.0265481	−	0.0459827i	0.852446	−	0.522815i	$-0.175118\pi$
$601$	−0.650836	−	1.12728i	−0.0265481	−	0.0459827i	−0.878994	+	0.476832i	$0.841785\pi$
$602$	3.21435	+	1.85581i	0.131007	+	0.0756370i
$603$	−24.8295	+	2.91605i	−1.01113	+	0.118751i
$604$	6.68823	−	1.79211i	0.272140	−	0.0729197i
$605$	−66.1778	−	4.12603i	−2.69051	−	0.167747i
$606$	−0.413968	+	0.200559i	−0.0168163	+	0.00814713i
$607$	9.40438	+	5.42962i	0.381712	+	0.220382i	0.678563	−	0.734542i	$-0.262603\pi$
$607$	9.40438	+	5.42962i	0.381712	+	0.220382i	−0.296851	+	0.954924i	$0.595936\pi$
$608$	−5.68701	+	3.28340i	−0.230639	+	0.133159i
$609$	−5.08803	+	7.50065i	−0.206178	+	0.303942i
$610$	19.8855	+	6.67970i	0.805139	+	0.270453i
$611$	8.11295	−	25.0399i	0.328215	−	1.01300i
$612$	14.2260	+	11.2357i	0.575054	+	0.454177i
$613$	25.3350	+	6.78849i	1.02327	+	0.274185i	0.731164	−	0.682201i	$-0.238977\pi$
$613$	25.3350	+	6.78849i	1.02327	+	0.274185i	0.292106	+	0.956386i	$0.405644\pi$
$614$	−15.2694	+	8.81576i	−0.616221	+	0.355775i
$615$	9.93551	−	4.07111i	0.400638	−	0.164163i
$616$	−4.62646	−	4.62646i	−0.186406	−	0.186406i
$617$	−33.9205	+	9.08897i	−1.36559	+	0.365908i	−0.865865	−	0.500278i	$-0.833231\pi$
$617$	−33.9205	+	9.08897i	−1.36559	+	0.365908i	−0.499722	+	0.866186i	$0.666565\pi$
$618$	0.260003	−	3.58265i	0.0104588	−	0.144115i
$619$	27.0126	−	27.0126i	1.08573	−	1.08573i	0.0897654	−	0.995963i	$-0.471388\pi$
$619$	27.0126	−	27.0126i	1.08573	−	1.08573i	0.995963	−	0.0897654i	$-0.0286117\pi$
$620$	−3.06334	−	3.47072i	−0.123027	−	0.139388i
$621$	−3.48890	+	6.71571i	−0.140005	+	0.269492i
$622$	3.13552	−	11.7019i	0.125723	−	0.469204i
$623$		−	11.7293i		−	0.469926i
$624$	5.78604	+	2.34985i	0.231627	+	0.0940692i
$625$	−6.77738	−	24.0638i	−0.271095	−	0.962553i
$626$	−3.80964	−	1.02079i	−0.152264	−	0.0407990i
$627$	−13.6501	−	71.2243i	−0.545133	−	2.84443i
$628$	−0.376242	+	0.651670i	−0.0150137	+	0.0260045i
$629$	−29.0706	+	29.0706i	−1.15912	+	1.15912i
$630$	−5.12610	−	4.59443i	−0.204229	−	0.183047i
$631$	7.77905	+	29.0318i	0.309679	+	1.15574i	0.928842	+	0.370475i	$0.120805\pi$
$631$	7.77905	+	29.0318i	0.309679	+	1.15574i	−0.619163	+	0.785262i	$0.712528\pi$
$632$	−4.40635	+	4.40635i	−0.175275	+	0.175275i
$633$	−2.49584	−	2.88645i	−0.0992007	−	0.114726i
$634$	−10.7891	+	6.22911i	−0.428492	+	0.247390i
$635$	17.3932	+	11.5418i	0.690227	+	0.458024i
$636$	14.6931	+	5.10253i	0.582618	+	0.202329i
$637$	−11.6633	+	17.9926i	−0.462117	+	0.712893i
$638$	−32.5137			−1.28723
$639$	2.49646	+	3.34946i	0.0987583	+	0.132503i
$640$	−2.19170	+	0.443213i	−0.0866347	+	0.0175195i
$641$	14.0560	−	24.3458i	0.555180	−	0.961601i	−0.442709	−	0.896665i	$-0.645983\pi$
$641$	14.0560	−	24.3458i	0.555180	−	0.961601i	0.997889	−	0.0649353i	$-0.0206841\pi$
$642$	−4.84478	+	2.34719i	−0.191208	+	0.0926360i
$643$	4.85146	+	18.1059i	0.191323	+	0.714027i	0.993188	+	0.116522i	$0.0371745\pi$
$643$	4.85146	+	18.1059i	0.191323	+	0.714027i	−0.801865	+	0.597505i	$0.796159\pi$
$644$	1.44363	−	0.386819i	0.0568869	−	0.0152428i
$645$	1.77550	+	13.8955i	0.0699103	+	0.547135i
$646$	19.8404	−	34.3646i	0.780610	−	1.35206i
$647$	−18.2568	+	10.5406i	−0.717749	+	0.414392i	−0.813923	−	0.580972i	$-0.802673\pi$
$647$	−18.2568	+	10.5406i	−0.717749	+	0.414392i	0.0961748	+	0.995364i	$0.469339\pi$
$648$	−0.251822	+	8.99648i	−0.00989251	+	0.353415i
$649$			23.2440i			0.912407i
$650$	−16.3270	−	7.64385i	−0.640398	−	0.299817i
$651$	3.47599	+	1.20712i	0.136235	+	0.0473109i
$652$	−2.95710	−	0.792352i	−0.115809	−	0.0310309i
$653$	11.1059	+	19.2360i	0.434607	+	0.752761i	0.997263	−	0.0739297i	$-0.0235540\pi$
$653$	11.1059	+	19.2360i	0.434607	+	0.752761i	−0.562657	+	0.826691i	$0.690221\pi$
$654$	26.4025	−	22.8296i	1.03242	−	0.892708i
$655$	−0.455837	−	0.916977i	−0.0178110	−	0.0358293i
$656$	0.717535	+	2.67788i	0.0280150	+	0.104554i
$657$	33.7183	+	14.5226i	1.31548	+	0.566579i
$658$	−5.29711	−	5.29711i	−0.206503	−	0.206503i
$659$	29.0572	+	16.7762i	1.13191	+	0.653507i	0.944414	−	0.328759i	$-0.106630\pi$
$659$	29.0572	+	16.7762i	1.13191	+	0.653507i	0.187494	+	0.982266i	$0.439964\pi$
$660$	3.31655	−	24.4703i	0.129097	−	0.952506i
$661$	0.0849181	+	0.0227537i	0.00330293	+	0.000885018i	0.260470	−	0.965482i	$-0.416122\pi$
$661$	0.0849181	+	0.0227537i	0.00330293	+	0.000885018i	−0.257167	+	0.966367i	$0.582789\pi$
$662$			4.39690i			0.170890i
$663$	−37.3784	+	5.18453i	−1.45166	+	0.201350i
$664$	−8.03706			−0.311899
$665$	−8.33142	+	12.5552i	−0.323079	+	0.486869i
$666$	−20.1971	−	2.94704i	−0.782621	−	0.114196i
$667$	3.71350	−	6.43197i	0.143787	−	0.249047i
$668$	8.94750	+	8.94750i	0.346189	+	0.346189i
$669$	12.1652	+	0.882860i	0.470332	+	0.0341333i
$670$	−1.15953	+	18.5979i	−0.0447967	+	0.718498i
$671$	−42.2959	−	42.2959i	−1.63281	−	1.63281i
$672$	1.34446	−	1.16252i	0.0518638	−	0.0448454i
$673$	−14.6908	−	25.4452i	−0.566288	−	0.980840i	−0.996929	−	0.0783166i	$-0.975046\pi$
$673$	−14.6908	−	25.4452i	−0.566288	−	0.980840i	0.430640	−	0.902524i	$-0.358288\pi$
$674$	0.509601	−	1.90186i	0.0196291	−	0.0732568i
$675$	2.07811	−	25.8975i	0.0799866	−	0.996796i
$676$	−11.8673	+	5.30730i	−0.456434	+	0.204127i
$677$	−17.6086			−0.676752			−0.338376	−	0.941011i	$-0.609878\pi$
$677$	−17.6086			−0.676752			−0.338376	+	0.941011i	$0.609878\pi$
$678$	2.68157	+	1.81903i	0.102985	+	0.0698595i
$679$	2.17815	+	3.77266i	0.0835897	+	0.144782i
$680$	10.1303	−	8.94121i	0.388478	−	0.342880i
$681$	15.9514	−	7.72812i	0.611260	−	0.296142i
$682$	3.41640	+	12.7502i	0.130821	+	0.488230i
$683$	8.68055	+	32.3962i	0.332152	+	1.23961i	0.906924	+	0.421294i	$0.138424\pi$
$683$	8.68055	+	32.3962i	0.332152	+	1.23961i	−0.574772	+	0.818314i	$0.694909\pi$
$684$	19.5659	−	2.29789i	0.748122	−	0.0878619i
$685$	−1.40875	−	1.59610i	−0.0538256	−	0.0609837i
$686$	6.64287	+	11.5058i	0.253626	+	0.439293i
$687$	−12.5939	+	18.5656i	−0.480487	+	0.708322i
$688$	−3.61697			−0.137896
$689$	−28.8367	+	14.7232i	−1.09859	+	0.560910i
$690$	4.46201	+	3.45093i	0.169866	+	0.131375i
$691$	0.0923062	−	0.344492i	0.00351150	−	0.0131051i	−0.964148	−	0.265366i	$-0.914507\pi$
$691$	0.0923062	−	0.344492i	0.00351150	−	0.0131051i	0.967659	+	0.252261i	$0.0811740\pi$
$692$	6.14181	+	10.6379i	0.233477	+	0.404393i
$693$	7.25701	+	18.2376i	0.275671	+	0.692790i
$694$	18.5473	+	18.5473i	0.704045	+	0.704045i
$695$	1.93706	−	31.0687i	0.0734768	−	1.17850i
$696$	0.639314	−	8.80927i	0.0242331	−	0.333915i
$697$	−11.8456	−	11.8456i	−0.448686	−	0.448686i
$698$	5.37784	−	9.31469i	0.203554	−	0.352566i
$699$	−6.11926	−	31.9294i	−0.231452	−	1.20768i
$700$	−4.05059	+	3.14930i	−0.153098	+	0.119032i
$701$	−1.95412			−0.0738062			−0.0369031	−	0.999319i	$-0.511749\pi$
$701$	−1.95412			−0.0738062			−0.0369031	+	0.999319i	$0.511749\pi$
$702$	−13.1537	−	13.3409i	−0.496454	−	0.503521i
$703$			44.6782i			1.68507i
$704$	6.15872	+	1.65022i	0.232116	+	0.0621952i
$705$	3.79732	−	28.0175i	0.143015	−	1.05520i
$706$	−5.83128	−	3.36669i	−0.219463	−	0.126707i
$707$	−0.192705	−	0.192705i	−0.00724742	−	0.00724742i
$708$	−6.29773	−	0.457044i	−0.236683	−	0.0171768i
$709$	10.5960	+	39.5447i	0.397940	+	1.48513i	0.816714	+	0.577043i	$0.195793\pi$
$709$	10.5960	+	39.5447i	0.397940	+	1.48513i	−0.418774	+	0.908091i	$0.637540\pi$
$710$	2.78819	−	1.38603i	0.104639	−	0.0520169i
$711$	17.3699	−	6.91174i	0.651423	−	0.259210i
$712$	5.71513	+	9.89890i	0.214184	+	0.370977i
$713$	−2.91248	−	0.780397i	−0.109073	−	0.0292261i
$714$	−3.52333	+	10.1456i	−0.131857	+	0.379691i
$715$	31.9861	+	40.2410i	1.19621	+	1.50493i
$716$			17.7787i			0.664421i
$717$	−13.9780	+	20.6060i	−0.522018	+	0.769546i
$718$	12.6287	−	7.29120i	0.471300	−	0.272105i
$719$	7.18236	−	12.4402i	0.267857	−	0.463942i	−0.700451	−	0.713700i	$-0.747018\pi$
$719$	7.18236	−	12.4402i	0.267857	−	0.463942i	0.968308	+	0.249758i	$0.0803512\pi$
$720$	6.56478	+	1.37974i	0.244655	+	0.0514200i
$721$	2.05563	−	0.550805i	0.0765557	−	0.0205130i
$722$	−6.24345	−	23.3009i	−0.232357	−	0.867169i
$723$	0.743245	+	1.53412i	0.0276416	+	0.0570544i
$724$	−11.1780	+	19.3609i	−0.415428	+	0.719543i
$725$	−3.16705	+	25.2996i	−0.117621	+	0.939603i
$726$	−28.8325	+	42.5042i	−1.07007	+	1.57748i
$727$	−19.0475			−0.706431			−0.353216	−	0.935542i	$-0.614912\pi$
$727$	−19.0475			−0.706431			−0.353216	+	0.935542i	$0.614912\pi$
$728$	−0.190568	+	3.69498i	−0.00706293	+	0.136945i
$729$	11.3701	−	24.4892i	0.421116	−	0.907007i
$730$	15.1302	−	22.8007i	0.559993	−	0.843891i
$731$	18.9279	−	10.9280i	0.700074	−	0.404188i
$732$	12.2913	−	10.6280i	0.454300	−	0.392822i
$733$	7.21470	−	7.21470i	0.266481	−	0.266481i	−0.561199	−	0.827681i	$-0.689660\pi$
$733$	7.21470	−	7.21470i	0.266481	−	0.266481i	0.827681	+	0.561199i	$0.189660\pi$
$734$	7.02265	+	26.2089i	0.259211	+	0.967387i
$735$	−8.89526	+	21.2456i	−0.328107	+	0.783654i
$736$	−1.02986	+	1.02986i	−0.0379612	+	0.0379612i
$737$	26.5667	−	46.0149i	0.978597	−	1.69498i
$738$	1.20086	−	8.22988i	0.0442041	−	0.302946i
$739$	−49.2761	−	13.2035i	−1.81265	−	0.485699i	−0.816819	−	0.576894i	$-0.804264\pi$
$739$	−49.2761	−	13.2035i	−1.81265	−	0.485699i	−0.995833	+	0.0911958i	$0.970931\pi$
$740$	−4.84432	+	14.4216i	−0.178081	+	0.530147i
$741$	−24.7392	+	32.7072i	−0.908817	+	1.20153i
$742$			9.21498i			0.338293i
$743$	2.18816	−	8.16631i	0.0802757	−	0.299593i	−0.914102	−	0.405484i	$-0.867103\pi$
$743$	2.18816	−	8.16631i	0.0802757	−	0.299593i	0.994378	+	0.105891i	$0.0337696\pi$
$744$	−3.52171	+	0.674934i	−0.129112	+	0.0247443i
$745$	−1.87308	−	2.12217i	−0.0686243	−	0.0777504i
$746$	−18.8403	+	18.8403i	−0.689792	+	0.689792i
$747$	22.1446	+	9.53772i	0.810227	+	0.348967i
$748$	−37.2150	+	9.97172i	−1.36071	+	0.364602i
$749$	−2.25527	−	2.25527i	−0.0824059	−	0.0824059i
$750$	−18.7178	−	4.96425i	−0.683478	−	0.181269i
$751$	10.1598	−	5.86579i	0.370738	−	0.214046i	−0.303043	−	0.952977i	$-0.598003\pi$
$751$	10.1598	−	5.86579i	0.370738	−	0.214046i	0.673781	+	0.738931i	$0.264669\pi$
$752$	7.05148	+	1.88944i	0.257141	+	0.0689008i
$753$	−5.04627	+	14.5311i	−0.183896	+	0.529541i
$754$	12.3141	+	13.6534i	0.448453	+	0.497227i
$755$	−4.93013	+	14.6770i	−0.179426	+	0.534150i
$756$	−5.08400	+	1.60761i	−0.184903	+	0.0584682i
$757$	0.892625	−	0.515357i	0.0324430	−	0.0187310i	−0.483691	−	0.875239i	$-0.660704\pi$
$757$	0.892625	−	0.515357i	0.0324430	−	0.0187310i	0.516134	+	0.856508i	$0.327371\pi$
$758$	14.2552	+	8.23023i	0.517771	+	0.298935i
$759$	−7.01279	−	14.4750i	−0.254548	−	0.525407i
$760$	0.913727	−	14.6554i	0.0331443	−	0.531605i
$761$	−8.63105	+	2.31268i	−0.312875	+	0.0838347i	−0.411840	−	0.911256i	$-0.635114\pi$
$761$	−8.63105	+	2.31268i	−0.312875	+	0.0838347i	0.0989644	+	0.995091i	$0.468447\pi$
$762$	14.5514	−	7.04981i	0.527140	−	0.255388i
$763$	17.9086	+	10.3395i	0.648335	+	0.374316i
$764$	−8.17439	−	14.1585i	−0.295739	−	0.512235i
$765$	−38.5227	+	12.6140i	−1.39279	+	0.456060i
$766$			4.96120i			0.179255i
$767$	9.76077	−	8.80333i	0.352441	−	0.317870i
$768$	−0.568210	+	1.63620i	−0.0205035	+	0.0590411i
$769$	−0.331235	+	1.23619i	−0.0119447	+	0.0445780i	−0.971641	−	0.236461i	$-0.924012\pi$
$769$	−0.331235	+	1.23619i	−0.0119447	+	0.0445780i	0.959696	+	0.281039i	$0.0906791\pi$
$770$	14.3399	−	2.89986i	0.516774	−	0.104504i
$771$	8.33958	−	7.21103i	0.300343	−	0.259699i
$772$	−16.5154	+	16.5154i	−0.594402	+	0.594402i
$773$	−12.9339	+	3.46564i	−0.465201	+	0.124650i	−0.483804	−	0.875177i	$-0.660745\pi$
$773$	−12.9339	+	3.46564i	−0.465201	+	0.124650i	0.0186022	+	0.999827i	$0.494078\pi$
$774$	9.96586	+	4.29232i	0.358216	+	0.154284i
$775$	10.2540	−	1.41642i	0.368333	−	0.0508793i
$776$	−3.67647	−	2.12261i	−0.131977	−	0.0761972i
$777$	−2.27612	−	11.8765i	−0.0816554	−	0.426066i
$778$	−4.39146	+	16.3892i	−0.157441	+	0.587580i
$779$	−18.2054			−0.652277
$780$	−11.5318	+	7.87507i	−0.412906	+	0.281973i
$781$	−8.87846			−0.317696
$782$	2.27781	−	8.50089i	0.0814542	−	0.303991i
$783$	−12.2156	+	23.5135i	−0.436551	+	0.840305i
$784$	−5.15024	−	2.97349i	−0.183937	−	0.106196i
$785$	−0.748996	−	1.50671i	−0.0267328	−	0.0537766i
$786$	−0.791129	−	0.0574144i	−0.0282186	−	0.00204791i
$787$	−51.9593	+	13.9225i	−1.85215	+	0.496282i	−0.999650	−	0.0264472i	$-0.991581\pi$
$787$	−51.9593	+	13.9225i	−1.85215	+	0.496282i	−0.852499	+	0.522729i	$0.824914\pi$
$788$	−4.86418	+	4.86418i	−0.173279	+	0.173279i
$789$	−25.2511	−	29.2030i	−0.898963	−	1.03965i
$790$	−2.76189	−	13.6576i	−0.0982636	−	0.485917i
$791$	−0.496868	+	1.85434i	−0.0176666	+	0.0659326i
$792$	−15.0108	−	11.8555i	−0.533386	−	0.421268i
$793$	−1.74220	+	33.7801i	−0.0618675	+	1.19957i
$794$		−	21.3912i		−	0.759147i
$795$	−27.6729	+	21.0670i	−0.981457	+	0.747170i
$796$	1.82204	+	3.15587i	0.0645806	+	0.111857i
$797$	−9.20478	−	5.31438i	−0.326050	−	0.188245i	0.328036	−	0.944665i	$-0.393613\pi$
$797$	−9.20478	−	5.31438i	−0.326050	−	0.188245i	−0.654086	+	0.756420i	$0.726947\pi$
$798$	5.08887	+	10.5038i	0.180144	+	0.371832i
$799$	−42.6096	+	11.4172i	−1.50742	+	0.403912i
$800$	1.88397	−	4.63148i	0.0666085	−	0.163748i
$801$	−3.99973	−	34.0567i	−0.141324	−	1.20334i
$802$	−17.2131	−	9.93799i	−0.607816	−	0.350923i
$803$	−67.5730	+	39.0133i	−2.38460	+	1.37675i
$804$	11.9449	+	8.10277i	0.421264	+	0.285763i
$805$	−1.06415	+	3.16797i	−0.0375063	+	0.111656i
$806$	4.06023	−	6.26358i	0.143015	−	0.220625i
$807$	24.4681	+	8.49716i	0.861317	+	0.299114i
$808$	0.256528	+	0.0687364i	0.00902462	+	0.00241814i
$809$	18.7728	−	10.8385i	0.660016	−	0.381060i	−0.132267	−	0.991214i	$-0.542226\pi$
$809$	18.7728	−	10.8385i	0.660016	−	0.381060i	0.792283	+	0.610154i	$0.208892\pi$
$810$	−16.4506	−	11.5922i	−0.578015	−	0.407307i
$811$	2.44407	+	2.44407i	0.0858230	+	0.0858230i	0.748715	−	0.662892i	$-0.230671\pi$
$811$	2.44407	+	2.44407i	0.0858230	+	0.0858230i	−0.662892	+	0.748715i	$0.730671\pi$
$812$	5.05453	−	1.35436i	0.177379	−	0.0475287i
$813$	2.31141	+	0.167746i	0.0810647	+	0.00588309i
$814$	30.6743	−	30.6743i	1.07513	−	1.07513i
$815$	5.13235	−	4.52993i	0.179778	−	0.158676i
$816$	−1.96998	−	10.2791i	−0.0689632	−	0.359840i
$817$	6.14745	−	22.9426i	0.215072	−	0.802660i
$818$		−	16.8372i		−	0.588700i
$819$	4.90997	−	9.95465i	0.171568	−	0.347844i
$820$	−5.87647	−	1.97396i	−0.205215	−	0.0689336i
$821$	21.6615	+	5.80418i	0.755991	+	0.202567i	0.616174	−	0.787610i	$-0.288682\pi$
$821$	21.6615	+	5.80418i	0.755991	+	0.202567i	0.139817	+	0.990177i	$0.455348\pi$
$822$	−1.61954	+	0.310385i	−0.0564881	+	0.0108259i
$823$	23.7976	−	41.2187i	0.829533	−	1.43679i	−0.0688726	−	0.997625i	$-0.521940\pi$
$823$	23.7976	−	41.2187i	0.829533	−	1.43679i	0.898405	−	0.439167i	$-0.144726\pi$
$824$	−1.46646	+	1.46646i	−0.0510864	+	0.0510864i
$825$	41.4918	+	36.4336i	1.44456	+	1.26846i
$826$	−0.968228	−	3.61348i	−0.0336890	−	0.125729i
$827$	−21.2453	+	21.2453i	−0.738772	+	0.738772i	−0.972340	−	0.233568i	$-0.924960\pi$
$827$	−21.2453	+	21.2453i	−0.738772	+	0.738772i	0.233568	+	0.972340i	$0.424960\pi$
$828$	4.05974	−	1.61543i	0.141086	−	0.0561400i
$829$	21.9626	−	12.6801i	0.762793	−	0.440399i	−0.0675045	−	0.997719i	$-0.521504\pi$
$829$	21.9626	−	12.6801i	0.762793	−	0.440399i	0.830298	+	0.557320i	$0.188170\pi$
$830$	9.93678	−	14.9744i	0.344911	−	0.519769i
$831$	−10.4394	+	30.0610i	−0.362140	+	1.04280i
$832$	−1.63955	−	3.21121i	−0.0568413	−	0.111329i
$833$	35.9355			1.24509
$834$	−19.9545	−	13.5361i	−0.690969	−	0.468716i
$835$	−27.7331	+	5.60828i	−0.959743	+	0.194082i
$836$	−20.9349	+	36.2603i	−0.724048	+	1.25409i
$837$	10.5043	+	2.31963i	0.363083	+	0.0801780i
$838$	0.647363	+	2.41599i	0.0223628	+	0.0834590i
$839$	42.8732	−	11.4878i	1.48015	−	0.396604i	0.573750	−	0.819030i	$-0.305488\pi$
$839$	42.8732	−	11.4878i	1.48015	−	0.396604i	0.906398	+	0.422426i	$0.138821\pi$
$840$	0.503724	+	3.94227i	0.0173801	+	0.136021i
$841$	−1.49800	+	2.59462i	−0.0516553	+	0.0894697i
$842$	24.5872	−	14.1954i	0.847329	−	0.489206i
$843$	4.34823	+	2.94961i	0.149761	+	0.101590i
$844$			2.20309i			0.0758334i
$845$	4.78396	−	28.6725i	0.164573	−	0.986365i
$846$	−17.1868	−	13.5741i	−0.590893	−	0.466687i
$847$	−29.3921	−	7.87560i	−1.00993	−	0.270609i
$848$	−4.49001	−	7.77692i	−0.154187	−	0.267061i
$849$	21.0316	+	24.3231i	0.721803	+	0.834768i
$850$	4.13421	+	29.9290i	0.141802	+	1.02656i
$851$	2.56467	+	9.57150i	0.0879159	+	0.328107i
$852$	0.174576	−	2.40553i	0.00598088	−	0.0824122i
$853$	11.3355	+	11.3355i	0.388120	+	0.388120i	0.874016	−	0.485897i	$-0.161507\pi$
$853$	11.3355	+	11.3355i	0.388120	+	0.388120i	−0.485897	+	0.874016i	$0.661507\pi$
$854$	8.33708	+	4.81342i	0.285289	+	0.164712i
$855$	−19.9094	+	39.2956i	−0.680886	+	1.34388i
$856$	3.00221	+	0.804439i	0.102613	+	0.0274952i
$857$			4.96758i			0.169689i	0.996394	+	0.0848447i	$0.0270394\pi$
$857$			4.96758i			0.169689i	−0.996394	+	0.0848447i	$0.972961\pi$
$858$	39.4404	−	5.47053i	1.34647	−	0.186761i
$859$	−23.9617			−0.817561			−0.408781	−	0.912633i	$-0.634046\pi$
$859$	−23.9617			−0.817561			−0.408781	+	0.912633i	$0.634046\pi$
$860$	4.47191	−	6.73903i	0.152491	−	0.229799i
$861$	4.83941	−	0.927471i	0.164927	−	0.0316081i
$862$	−4.03322	+	6.98575i	−0.137372	+	0.237936i
$863$	20.9215	+	20.9215i	0.712177	+	0.712177i	0.966990	−	0.254813i	$-0.0820140\pi$
$863$	20.9215	+	20.9215i	0.712177	+	0.712177i	−0.254813	+	0.966990i	$0.582014\pi$
$864$	3.50729	−	3.83391i	0.119321	−	0.130432i
$865$	−27.4138	−	1.70918i	−0.932097	−	0.0581140i
$866$	13.5914	+	13.5914i	0.461854	+	0.461854i
$867$	22.1065	+	25.5663i	0.750777	+	0.868276i
$868$	−1.06222	−	1.83981i	−0.0360540	−	0.0624473i
$869$	−10.2834	+	38.3782i	−0.348840	+	1.30189i
$870$	15.6227	+	12.0827i	0.529660	+	0.409640i
$871$	−29.3846	+	6.27141i	−0.995660	+	0.212499i
$872$	−20.1518			−0.682426
$873$	7.61085	+	10.2114i	0.257588	+	0.345602i
$874$	−4.78209	−	8.28282i	−0.161756	−	0.280170i
$875$	−0.859640	−	11.4406i	−0.0290611	−	0.386764i
$876$	−9.24159	−	19.0754i	−0.312244	−	0.644496i
$877$	−8.29877	−	30.9714i	−0.280230	−	1.04583i	−0.952255	−	0.305303i	$-0.901242\pi$
$877$	−8.29877	−	30.9714i	−0.280230	−	1.04583i	0.672026	−	0.740528i	$-0.265424\pi$
$878$	4.14832	+	15.4817i	0.139999	+	0.522483i
$879$	3.32840	+	6.87007i	0.112264	+	0.231722i
$880$	−10.6891	+	9.43444i	−0.360329	+	0.318035i
$881$	−2.14328	−	3.71226i	−0.0722088	−	0.125069i	0.827660	−	0.561229i	$-0.189671\pi$
$881$	−2.14328	−	3.71226i	−0.0722088	−	0.125069i	−0.899869	+	0.436160i	$0.856338\pi$
$882$	10.6618	+	14.3048i	0.359001	+	0.481666i
$883$	23.6329			0.795312			0.397656	−	0.917535i	$-0.369824\pi$
$883$	23.6329			0.795312			0.397656	+	0.917535i	$0.369824\pi$
$884$	18.2820	+	11.8509i	0.614891	+	0.398589i
$885$	8.63787	−	11.1686i	0.290359	−	0.375430i
$886$	0.214036	−	0.798794i	0.00719069	−	0.0268360i
$887$	6.88369	+	11.9229i	0.231132	+	0.400332i	0.958141	−	0.286295i	$-0.0924238\pi$
$887$	6.88369	+	11.9229i	0.231132	+	0.400332i	−0.727010	+	0.686627i	$0.759090\pi$
$888$	7.70774	+	8.91403i	0.258655	+	0.299135i
$889$	6.77375	+	6.77375i	0.227184	+	0.227184i
$890$	−25.5093	−	1.59045i	−0.855074	−	0.0533119i
$891$	27.2902	+	50.4792i	0.914255	+	1.69112i
$892$	−4.97947	−	4.97947i	−0.166725	−	0.166725i
$893$	−23.9696	+	41.5165i	−0.802112	+	1.38930i
$894$	−2.15335	+	0.412688i	−0.0720188	+	0.0138024i
$895$	−33.1247	−	21.9810i	−1.10724	−	0.734745i
$896$	−1.02617			−0.0342818
$897$	−3.42242	+	8.42704i	−0.114271	+	0.281371i
$898$		−	19.0503i		−	0.635716i
$899$	−10.1974	−	2.73239i	−0.340102	−	0.0911302i
$900$	−10.6872	+	10.5254i	−0.356239	+	0.350847i
$901$	46.9932	+	27.1315i	1.56557	+	0.903882i
$902$	12.4991	+	12.4991i	0.416175	+	0.416175i
$903$	−0.465325	+	6.41184i	−0.0154851	+	0.213373i
$904$	−0.484199	−	1.80705i	−0.0161042	−	0.0601017i
$905$	−22.2524	−	44.7638i	−0.739696	−	1.48800i
$906$	7.84426	+	9.07192i	0.260608	+	0.301394i
$907$	14.9007	+	25.8088i	0.494771	+	0.856968i	0.999982	−	0.00602769i	$-0.00191869\pi$
$907$	14.9007	+	25.8088i	0.494771	+	0.856968i	−0.505211	+	0.862996i	$0.668585\pi$
$908$	−9.88478	−	2.64862i	−0.328038	−	0.0878975i
$909$	−0.625241	−	0.493816i	−0.0207380	−	0.0163788i
$910$	−6.64876	−	4.92342i	−0.220404	−	0.163210i
$911$			20.5335i			0.680304i	0.940370	+	0.340152i	$0.110479\pi$
$911$			20.5335i			0.680304i	−0.940370	+	0.340152i	$0.889521\pi$
$912$	−9.41272	−	6.38508i	−0.311686	−	0.211431i
$913$	−44.3787	+	25.6221i	−1.46872	+	0.847967i
$914$	−3.60235	+	6.23946i	−0.119155	+	0.206383i
$915$	4.60513	+	36.0409i	0.152241	+	1.19147i
$916$	12.5110	−	3.35231i	0.413374	−	0.110763i
$917$	−0.121630	−	0.453929i	−0.00401658	−	0.0149901i
$918$	−6.77047	+	30.6598i	−0.223459	+	1.01193i
$919$	27.4735	−	47.5856i	0.906268	−	1.56970i	0.0870627	−	0.996203i	$-0.472252\pi$
$919$	27.4735	−	47.5856i	0.906268	−	1.56970i	0.819206	−	0.573500i	$-0.194415\pi$
$920$	−0.645515	−	3.19209i	−0.0212820	−	0.105240i
$921$	−25.2727	−	17.1436i	−0.832763	−	0.564901i
$922$	32.6575			1.07552
$923$	3.36259	+	3.72830i	0.110681	+	0.122719i
$924$	3.71769	−	10.7053i	0.122303	−	0.352179i
$925$	−20.8804	−	26.8561i	−0.686543	−	0.883025i
$926$	5.57007	−	3.21588i	0.183044	−	0.105680i
$927$	5.78080	−	2.30026i	0.189866	−	0.0755506i
$928$	−3.60583	+	3.60583i	−0.118367	+	0.118367i
$929$	1.34151	+	5.00657i	0.0440134	+	0.164260i	0.984435	−	0.175752i	$-0.0562356\pi$
$929$	1.34151	+	5.00657i	0.0440134	+	0.164260i	−0.940421	+	0.340012i	$0.889569\pi$
$930$	3.09662	−	7.39600i	0.101542	−	0.242524i
$931$	27.6144	−	27.6144i	0.905025	−	0.905025i
$932$	−9.38497	+	16.2552i	−0.307415	+	0.532458i
$933$	20.6083	−	3.94957i	0.674684	−	0.129303i
$934$	−9.39376	−	2.51705i	−0.307373	−	0.0823604i
$935$	27.4324	−	81.6664i	0.897137	−	2.67078i
$936$	0.706673	+	10.7935i	0.0230983	+	0.352798i
$937$			17.7978i			0.581429i	0.956810	+	0.290714i	$0.0938929\pi$
$937$			17.7978i			0.581429i	−0.956810	+	0.290714i	$0.906107\pi$
$938$	−2.21327	+	8.26004i	−0.0722658	+	0.269700i
$939$	−1.28581	−	6.70916i	−0.0419607	−	0.218945i
$940$	−12.2386	+	10.8021i	−0.399178	+	0.352324i
$941$	−12.2790	+	12.2790i	−0.400283	+	0.400283i	−0.878333	−	0.478050i	$-0.841344\pi$
$941$	−12.2790	+	12.2790i	−0.400283	+	0.400283i	0.478050	+	0.878333i	$0.341344\pi$
$942$	−1.29992	−	0.0943389i	−0.0423537	−	0.00307373i
$943$	−3.90018	+	1.04505i	−0.127007	+	0.0340315i
$944$	2.57780	+	2.57780i	0.0839002	+	0.0839002i
$945$	3.29045	−	11.4599i	0.107038	−	0.372792i
$946$	−19.9721	+	11.5309i	−0.649347	+	0.374901i
$947$	−56.0904	−	15.0294i	−1.82269	−	0.488389i	−0.825576	−	0.564290i	$-0.809150\pi$
$947$	−56.0904	−	15.0294i	−1.82269	−	0.488389i	−0.997115	+	0.0759016i	$0.975817\pi$
$948$	−10.1960	−	3.54081i	−0.331150	−	0.115000i
$949$	41.9750	+	13.6000i	1.36257	+	0.441474i
$950$	26.1757	+	19.8218i	0.849251	+	0.643106i
$951$	−17.8574	−	12.1135i	−0.579065	−	0.392806i
$952$	5.37001	−	3.10038i	0.174043	−	0.100484i
$953$	−42.6568	−	24.6279i	−1.38179	−	0.797776i	−0.389418	−	0.921061i	$-0.627324\pi$
$953$	−42.6568	−	24.6279i	−1.38179	−	0.797776i	−0.992371	+	0.123285i	$0.960657\pi$
$954$	3.14233	+	26.7562i	0.101737	+	0.866262i
$955$	36.4861	+	2.27482i	1.18066	+	0.0736116i
$956$	13.8860	−	3.72074i	0.449105	−	0.120337i
$957$	−24.5537	−	50.6808i	−0.793709	−	1.63828i
$958$	2.09350	+	1.20868i	0.0676380	+	0.0390508i
$959$	−0.488486	−	0.846083i	−0.0157740	−	0.0273214i
$960$	−2.34599	−	3.08161i	−0.0757165	−	0.0994586i
$961$		−	26.7140i		−	0.861742i
$962$	−24.4984	−	1.26350i	−0.789859	−	0.0407369i
$963$	−7.31736	−	5.77925i	−0.235798	−	0.186234i
$964$	0.254729	−	0.950660i	0.00820425	−	0.0306187i
$965$	−10.3518	−	51.1901i	−0.333237	−	1.64787i
$966$	1.69315	+	1.95814i	0.0544763	+	0.0630020i
$967$	−23.6657	+	23.6657i	−0.761036	+	0.761036i	−0.976510	−	0.215473i	$-0.930871\pi$
$967$	−23.6657	+	23.6657i	−0.761036	+	0.761036i	0.215473	+	0.976510i	$0.430871\pi$
$968$	28.6427	−	7.67478i	0.920611	−	0.246677i
$969$	68.5489	+	4.97479i	2.20211	+	0.159813i
$970$	8.50024	−	4.22554i	0.272926	−	0.135674i
$971$	−27.5366	−	15.8983i	−0.883691	−	0.510199i	−0.0118174	−	0.999930i	$-0.503762\pi$
$971$	−27.5366	−	15.8983i	−0.883691	−	0.510199i	−0.871874	+	0.489731i	$0.837095\pi$
$972$	−14.2134	+	6.40143i	−0.455896	+	0.205326i
$973$	3.69738	−	13.7988i	0.118532	−	0.442369i
$974$	−27.5907			−0.884063
$975$	−0.414976	−	31.2222i	−0.0132899	−	0.999912i
$976$	−9.38137			−0.300290
$977$	8.55750	−	31.9370i	0.273779	−	1.02176i	−0.682877	−	0.730534i	$-0.739271\pi$
$977$	8.55750	−	31.9370i	0.273779	−	1.02176i	0.956655	−	0.291222i	$-0.0940620\pi$
$978$	−0.998062	−	5.20774i	−0.0319145	−	0.166525i
$979$	63.1152	+	36.4396i	2.01717	+	1.16461i
$980$	11.9077	−	5.91942i	0.380378	−	0.189089i
$981$	55.5243	+	23.9145i	1.77275	+	0.763530i
$982$	15.9198	−	4.26570i	0.508022	−	0.136124i
$983$	−9.06960	+	9.06960i	−0.289275	+	0.289275i	−0.836794	−	0.547518i	$-0.815573\pi$
$983$	−9.06960	+	9.06960i	−0.289275	+	0.289275i	0.547518	+	0.836794i	$0.315573\pi$
$984$	−3.63228	+	3.14074i	−0.115793	+	0.100123i
$985$	−3.04886	−	15.0767i	−0.0971447	−	0.480384i
$986$	7.97523	−	29.7640i	0.253983	−	0.947877i
$987$	4.25660	−	12.2572i	0.135489	−	0.390149i
$988$	23.1554	−	4.94195i	0.736673	−	0.157224i
$989$		−	5.26792i		−	0.167510i
$990$	40.6477	−	13.3098i	1.29187	−	0.423014i
$991$	11.2283	+	19.4479i	0.356678	+	0.617784i	0.987404	−	0.158222i	$-0.0505760\pi$
$991$	11.2283	+	19.4479i	0.356678	+	0.617784i	−0.630726	+	0.776006i	$0.717243\pi$
$992$	1.79290	+	1.03513i	0.0569247	+	0.0328655i
$993$	−6.85366	+	3.32045i	−0.217494	+	0.105371i
$994$	1.38023	−	0.369832i	0.0437783	−	0.0117304i
$995$	−8.13263	−	0.507050i	−0.257822	−	0.0160746i
$996$	−6.06943	−	12.5278i	−0.192317	−	0.396958i
$997$	−17.7299	−	10.2364i	−0.561511	−	0.324189i	0.192241	−	0.981348i	$-0.438425\pi$
$997$	−17.7299	−	10.2364i	−0.561511	−	0.324189i	−0.753752	+	0.657159i	$0.771758\pi$
$998$	−30.7574	+	17.7578i	−0.973609	+	0.562113i
$999$	−10.6587	−	33.7078i	−0.337228	−	1.06647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bj.a.89.28	yes	112
3.2	odd	2	inner	390.2.bj.a.89.11	yes	112
5.4	even	2	inner	390.2.bj.a.89.1	✓	112
13.6	odd	12	inner	390.2.bj.a.149.18	yes	112
15.14	odd	2	inner	390.2.bj.a.89.18	yes	112
39.32	even	12	inner	390.2.bj.a.149.1	yes	112
65.19	odd	12	inner	390.2.bj.a.149.11	yes	112
195.149	even	12	inner	390.2.bj.a.149.28	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bj.a.89.1	✓	112	5.4	even	2	inner
390.2.bj.a.89.11	yes	112	3.2	odd	2	inner
390.2.bj.a.89.18	yes	112	15.14	odd	2	inner
390.2.bj.a.89.28	yes	112	1.1	even	1	trivial
390.2.bj.a.149.1	yes	112	39.32	even	12	inner
390.2.bj.a.149.11	yes	112	65.19	odd	12	inner
390.2.bj.a.149.18	yes	112	13.6	odd	12	inner
390.2.bj.a.149.28	yes	112	195.149	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bj (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(1.70109 - 0.326014i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.00231 - 0.995366i) q^{5} +(0.125370 - 1.72751i) q^{6} +(0.991200 - 0.265591i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.78743 - 1.10916i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(1.70109 - 0.326014i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.00231 - 0.995366i) q^{5} +(0.125370 - 1.72751i) q^{6} +(0.991200 - 0.265591i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.78743 - 1.10916i) q^{9} +(-0.443213 - 2.19170i) q^{10} +(-1.65022 + 6.15872i) q^{11} +(-1.63620 - 0.568210i) q^{12} +(3.21121 - 1.63955i) q^{13} -1.02617i q^{14} +(3.08161 - 2.34599i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-5.23308 - 3.02132i) q^{17} +(-0.349925 - 2.97952i) q^{18} +(-6.34304 + 1.69961i) q^{19} +(-2.23173 - 0.139143i) q^{20} +(1.59954 - 0.774940i) q^{21} +(5.52176 + 3.18799i) q^{22} +(-1.26132 + 0.728222i) q^{23} +(-0.972327 + 1.43338i) q^{24} +(3.01849 - 3.98606i) q^{25} +(-0.752566 - 3.52614i) q^{26} +(4.38008 - 2.79552i) q^{27} +(-0.991200 - 0.265591i) q^{28} +(-4.41622 + 2.54971i) q^{29} +(-1.46847 - 3.58380i) q^{30} +(1.46390 + 1.46390i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.799357 + 11.0145i) q^{33} +(-4.27279 + 4.27279i) q^{34} +(1.72033 - 1.51840i) q^{35} +(-2.96856 - 0.433156i) q^{36} +(1.76092 - 6.57183i) q^{37} +6.56680i q^{38} +(4.92805 - 3.83593i) q^{39} +(-0.712018 + 2.11968i) q^{40} +(2.67788 + 0.717535i) q^{41} +(-0.334544 - 1.74560i) q^{42} +(-1.80849 + 3.13239i) q^{43} +(4.50850 - 4.50850i) q^{44} +(4.47728 - 4.99539i) q^{45} +(0.376955 + 1.40682i) q^{46} +(5.16205 - 5.16205i) q^{47} +(1.13288 + 1.31018i) q^{48} +(-5.15024 + 2.97349i) q^{49} +(-3.06900 - 3.94731i) q^{50} +(-9.88695 - 3.43349i) q^{51} +(-3.60077 - 0.185709i) q^{52} -8.98001 q^{53} +(-1.56662 - 4.95436i) q^{54} +(2.82592 + 13.9742i) q^{55} +(-0.513083 + 0.888685i) q^{56} +(-10.2360 + 4.95912i) q^{57} +(1.31982 + 4.92565i) q^{58} +(3.52134 - 0.943540i) q^{59} +(-3.84175 + 0.490880i) q^{60} +(-4.69068 + 8.12450i) q^{61} +(1.79290 - 1.03513i) q^{62} +(2.46832 - 1.83971i) q^{63} -1.00000i q^{64} +(4.79788 - 6.47922i) q^{65} +(10.4323 + 3.62289i) q^{66} +(-8.04942 - 2.15684i) q^{67} +(3.02132 + 5.23308i) q^{68} +(-1.90821 + 1.64998i) q^{69} +(-1.02141 - 2.05470i) q^{70} +(0.360402 + 1.34504i) q^{71} +(-1.18672 + 2.75530i) q^{72} +(8.65328 + 8.65328i) q^{73} +(-5.89214 - 3.40183i) q^{74} +(3.83523 - 7.76473i) q^{75} +(6.34304 + 1.69961i) q^{76} +6.54281i q^{77} +(-2.42975 - 5.75294i) q^{78} +6.23151 q^{79} +(1.86317 + 1.23637i) q^{80} +(6.53953 - 6.18340i) q^{81} +(1.38617 - 2.40092i) q^{82} +(5.68306 + 5.68306i) q^{83} +(-1.77271 - 0.128650i) q^{84} +(-13.4856 - 0.840794i) q^{85} +(2.55759 + 2.55759i) q^{86} +(-6.68116 + 5.77703i) q^{87} +(-3.18799 - 5.52176i) q^{88} +(2.95837 - 11.0408i) q^{89} +(-3.66637 - 5.61763i) q^{90} +(2.74750 - 2.47799i) q^{91} +1.45644 q^{92} +(2.96748 + 2.01297i) q^{93} +(-3.65012 - 6.32219i) q^{94} +(-11.0090 + 9.71680i) q^{95} +(1.55875 - 0.755180i) q^{96} +(1.09874 + 4.10057i) q^{97} +(1.53919 + 5.74435i) q^{98} +(2.23111 + 18.9974i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q+O(q^{10}) \) 112 * q	\( 112 q + 24 q^{10} - 8 q^{15} + 56 q^{16} - 32 q^{19} - 8 q^{21} - 24 q^{30} + 40 q^{31} + 24 q^{36} - 24 q^{39} - 48 q^{45} + 16 q^{46} - 48 q^{49} - 48 q^{54} - 8 q^{55} - 16 q^{60} - 32 q^{66} - 168 q^{69} - 32 q^{70} - 120 q^{75} + 32 q^{76} + 112 q^{79} - 88 q^{81} - 8 q^{84} + 24 q^{85} + 48 q^{91} + 32 q^{94} - 56 q^{99}+O(q^{100}) \) 112 * q + 24 * q^10 - 8 * q^15 + 56 * q^16 - 32 * q^19 - 8 * q^21 - 24 * q^30 + 40 * q^31 + 24 * q^36 - 24 * q^39 - 48 * q^45 + 16 * q^46 - 48 * q^49 - 48 * q^54 - 8 * q^55 - 16 * q^60 - 32 * q^66 - 168 * q^69 - 32 * q^70 - 120 * q^75 + 32 * q^76 + 112 * q^79 - 88 * q^81 - 8 * q^84 + 24 * q^85 + 48 * q^91 + 32 * q^94 - 56 * q^99

Introduction

L-functions

Modular forms

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