LMFDB - Embedded newform 950.2.bb.a.357.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			357.2
Character	$\chi$	$=$	950.357
Dual form			950.2.bb.a.793.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.906308 - 0.422618i) q^{2} +(1.85075 - 2.64314i) q^{3} +(0.642788 - 0.766044i) q^{4} +(0.560307 - 3.17766i) q^{6} +(-3.57554 + 0.958062i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-2.53487 - 6.96451i) q^{9} +O(q^{10})$	\(q+(0.906308 - 0.422618i) q^{2} +(1.85075 - 2.64314i) q^{3} +(0.642788 - 0.766044i) q^{4} +(0.560307 - 3.17766i) q^{6} +(-3.57554 + 0.958062i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-2.53487 - 6.96451i) q^{9} +(-1.03209 - 1.78763i) q^{11} +(-0.835127 - 3.11674i) q^{12} +(1.78968 - 1.25315i) q^{13} +(-2.83564 + 2.37939i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(-0.543308 - 1.16513i) q^{17} +(-5.24070 - 5.24070i) q^{18} +(1.10359 + 4.21688i) q^{19} +(-4.08512 + 11.2238i) q^{21} +(-1.69088 - 1.18396i) q^{22} +(-3.68758 + 0.322621i) q^{23} +(-2.07407 - 2.47178i) q^{24} +(1.09240 - 1.89209i) q^{26} +(-13.7494 - 3.68414i) q^{27} +(-1.56439 + 3.35485i) q^{28} +(7.40333 - 2.69459i) q^{29} +(7.91147 + 4.56769i) q^{31} +(-0.573576 - 0.819152i) q^{32} +(-6.63510 - 0.580496i) q^{33} +(-0.984808 - 0.826352i) q^{34} +(-6.96451 - 2.53487i) q^{36} +(4.90984 - 4.90984i) q^{37} +(2.78232 + 3.35540i) q^{38} -7.04963i q^{39} +(-7.67752 + 1.35375i) q^{41} +(1.04100 + 11.8986i) q^{42} +(0.866836 - 9.90798i) q^{43} +(-2.03282 - 0.358441i) q^{44} +(-3.20574 + 1.85083i) q^{46} +(8.82464 + 4.11500i) q^{47} +(-2.92437 - 1.36365i) q^{48} +(5.80439 - 3.35117i) q^{49} +(-4.08512 - 0.720317i) q^{51} +(0.190417 - 2.17648i) q^{52} +(-0.791938 - 9.05189i) q^{53} +(-14.0182 + 2.47178i) q^{54} +3.70167i q^{56} +(13.1883 + 4.88744i) q^{57} +(5.57091 - 5.57091i) q^{58} +(1.99654 + 0.726682i) q^{59} +(8.62108 + 7.23395i) q^{61} +(9.10062 + 0.796201i) q^{62} +(15.7360 + 22.4733i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-6.25877 + 2.27801i) q^{66} +(-1.07953 + 2.31505i) q^{67} +(-1.24177 - 0.332731i) q^{68} +(-5.97205 + 10.3439i) q^{69} +(-2.53209 - 3.01763i) q^{71} +(-7.38327 + 0.645953i) q^{72} +(-4.33934 - 3.03844i) q^{73} +(2.37484 - 6.52481i) q^{74} +(3.93969 + 1.86516i) q^{76} +(5.40293 + 5.40293i) q^{77} +(-2.97930 - 6.38913i) q^{78} +(-0.385920 - 2.18866i) q^{79} +(-18.1518 + 15.2312i) q^{81} +(-6.38607 + 4.47158i) q^{82} +(3.67656 + 13.7211i) q^{83} +(5.97205 + 10.3439i) q^{84} +(-3.40167 - 9.34602i) q^{86} +(6.57951 - 24.5551i) q^{87} +(-1.99384 + 0.534249i) q^{88} +(-0.335316 + 1.90167i) q^{89} +(-5.19846 + 6.19529i) q^{91} +(-2.12319 + 3.03223i) q^{92} +(26.7152 - 12.4575i) q^{93} +9.73692 q^{94} -3.22668 q^{96} +(-4.66105 + 2.17348i) q^{97} +(3.84430 - 5.49023i) q^{98} +(-9.83375 + 11.7194i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 36 q^{6}+O(q^{10}) $ 24 * q + 36 * q^6	$ 24 q + 36 q^{6} + 12 q^{11} - 12 q^{21} + 12 q^{26} + 108 q^{31} - 36 q^{36} - 84 q^{41} - 36 q^{46} - 12 q^{51} - 12 q^{61} - 60 q^{66} - 24 q^{71} + 72 q^{76} - 216 q^{81} + 12 q^{86} - 12 q^{91} - 24 q^{96}+O(q^{100}) $ 24 * q + 36 * q^6 + 12 * q^11 - 12 * q^21 + 12 * q^26 + 108 * q^31 - 36 * q^36 - 84 * q^41 - 36 * q^46 - 12 * q^51 - 12 * q^61 - 60 * q^66 - 24 * q^71 + 72 * q^76 - 216 * q^81 + 12 * q^86 - 12 * q^91 - 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.906308	−	0.422618i	0.640856	−	0.298836i
$2$	0.906308	−	0.422618i	0.640856	−	0.298836i
$3$	1.85075	−	2.64314i	1.06853	−	1.52602i	0.236227	−	0.971698i	$-0.424089\pi$
$3$	1.85075	−	2.64314i	1.06853	−	1.52602i	0.832303	−	0.554321i	$-0.187022\pi$
$4$	0.642788	−	0.766044i	0.321394	−	0.383022i
$5$		0			0
$5$		0			0
$6$	0.560307	−	3.17766i	0.228745	−	1.29727i
$7$	−3.57554	+	0.958062i	−1.35143	+	0.362113i	−0.860661	−	0.509179i	$-0.829949\pi$
$7$	−3.57554	+	0.958062i	−1.35143	+	0.362113i	−0.490765	+	0.871292i	$0.663282\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$	−2.53487	−	6.96451i	−0.844958	−	2.32150i
$10$		0			0
$11$	−1.03209	−	1.78763i	−0.311187	−	0.538991i	0.667433	−	0.744670i	$-0.267393\pi$
$11$	−1.03209	−	1.78763i	−0.311187	−	0.538991i	−0.978620	+	0.205679i	$0.934060\pi$
$12$	−0.835127	−	3.11674i	−0.241080	−	0.899724i
$13$	1.78968	−	1.25315i	0.496367	−	0.347560i	−0.298434	−	0.954430i	$-0.596464\pi$
$13$	1.78968	−	1.25315i	0.496367	−	0.347560i	0.794801	+	0.606870i	$0.207575\pi$
$14$	−2.83564	+	2.37939i	−0.757857	+	0.635917i
$15$		0			0
$16$	−0.173648	−	0.984808i	−0.0434120	−	0.246202i
$17$	−0.543308	−	1.16513i	−0.131771	−	0.282585i	0.829341	−	0.558743i	$-0.188716\pi$
$17$	−0.543308	−	1.16513i	−0.131771	−	0.282585i	−0.961112	+	0.276159i	$0.910939\pi$
$18$	−5.24070	−	5.24070i	−1.23525	−	1.23525i
$19$	1.10359	+	4.21688i	0.253181	+	0.967419i
$19$	1.10359	+	4.21688i	0.253181	+	0.967419i
$20$		0			0
$21$	−4.08512	+	11.2238i	−0.891447	+	2.44923i
$22$	−1.69088	−	1.18396i	−0.360496	−	0.252422i
$23$	−3.68758	+	0.322621i	−0.768914	+	0.0672712i	−0.464861	−	0.885384i	$-0.653896\pi$
$23$	−3.68758	+	0.322621i	−0.768914	+	0.0672712i	−0.304053	+	0.952655i	$0.598340\pi$
$24$	−2.07407	−	2.47178i	−0.423368	−	0.504550i
$25$		0			0
$26$	1.09240	−	1.89209i	0.214237	−	0.371069i
$27$	−13.7494	−	3.68414i	−2.64607	−	0.709013i
$28$	−1.56439	+	3.35485i	−0.295642	+	0.634007i
$29$	7.40333	−	2.69459i	1.37476	−	0.500373i	0.454178	−	0.890911i	$-0.349933\pi$
$29$	7.40333	−	2.69459i	1.37476	−	0.500373i	0.920587	+	0.390538i	$0.127711\pi$
$30$		0			0
$31$	7.91147	+	4.56769i	1.42094	+	0.820382i	0.996380	−	0.0850167i	$-0.0270944\pi$
$31$	7.91147	+	4.56769i	1.42094	+	0.820382i	0.424563	+	0.905398i	$0.360428\pi$
$32$	−0.573576	−	0.819152i	−0.101395	−	0.144807i
$33$	−6.63510	−	0.580496i	−1.15502	−	0.101051i
$34$	−0.984808	−	0.826352i	−0.168893	−	0.141718i
$35$		0			0
$36$	−6.96451	−	2.53487i	−1.16075	−	0.422479i
$37$	4.90984	−	4.90984i	0.807173	−	0.807173i	−0.177032	−	0.984205i	$-0.556650\pi$
$37$	4.90984	−	4.90984i	0.807173	−	0.807173i	0.984205	+	0.177032i	$0.0566497\pi$
$38$	2.78232	+	3.35540i	0.451352	+	0.544317i
$39$		−	7.04963i		−	1.12884i
$40$		0			0
$41$	−7.67752	+	1.35375i	−1.19903	+	0.211421i	−0.737278	−	0.675590i	$-0.763889\pi$
$41$	−7.67752	+	1.35375i	−1.19903	+	0.211421i	−0.461749	+	0.887011i	$0.652778\pi$
$42$	1.04100	+	11.8986i	0.160629	+	1.83600i
$43$	0.866836	−	9.90798i	0.132191	−	1.51095i	−0.583257	−	0.812288i	$-0.698222\pi$
$43$	0.866836	−	9.90798i	0.132191	−	1.51095i	0.715448	−	0.698666i	$-0.246222\pi$
$44$	−2.03282	−	0.358441i	−0.306459	−	0.0540370i
$45$		0			0
$46$	−3.20574	+	1.85083i	−0.472660	+	0.272890i
$47$	8.82464	+	4.11500i	1.28721	+	0.600234i	0.941153	−	0.337980i	$-0.109744\pi$
$47$	8.82464	+	4.11500i	1.28721	+	0.600234i	0.346054	+	0.938215i	$0.387522\pi$
$48$	−2.92437	−	1.36365i	−0.422096	−	0.196827i
$49$	5.80439	−	3.35117i	0.829199	−	0.478738i
$50$		0			0
$51$	−4.08512	−	0.720317i	−0.572032	−	0.100865i
$52$	0.190417	−	2.17648i	0.0264061	−	0.301823i
$53$	−0.791938	−	9.05189i	−0.108781	−	1.24337i	−0.832793	−	0.553585i	$-0.813259\pi$
$53$	−0.791938	−	9.05189i	−0.108781	−	1.24337i	0.724012	−	0.689788i	$-0.242296\pi$
$54$	−14.0182	+	2.47178i	−1.90763	+	0.336367i
$55$		0			0
$56$			3.70167i			0.494656i
$57$	13.1883	+	4.88744i	1.74683	+	0.647357i
$58$	5.57091	−	5.57091i	0.731497	−	0.731497i
$59$	1.99654	+	0.726682i	0.259928	+	0.0946059i	0.468697	−	0.883359i	$-0.344724\pi$
$59$	1.99654	+	0.726682i	0.259928	+	0.0946059i	−0.208769	+	0.977965i	$0.566946\pi$
$60$		0			0
$61$	8.62108	+	7.23395i	1.10382	+	0.926212i	0.997676	−	0.0681392i	$-0.0217062\pi$
$61$	8.62108	+	7.23395i	1.10382	+	0.926212i	0.106141	+	0.994351i	$0.466151\pi$
$62$	9.10062	+	0.796201i	1.15578	+	0.101118i
$63$	15.7360	+	22.4733i	1.98254	+	2.83137i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$		0			0
$66$	−6.25877	+	2.27801i	−0.770401	+	0.280403i
$67$	−1.07953	+	2.31505i	−0.131885	+	0.282829i	−0.961150	−	0.276028i	$-0.910982\pi$
$67$	−1.07953	+	2.31505i	−0.131885	+	0.282829i	0.829265	+	0.558856i	$0.188760\pi$
$68$	−1.24177	−	0.332731i	−0.150587	−	0.0403496i
$69$	−5.97205	+	10.3439i	−0.718950	+	1.24526i
$70$		0			0
$71$	−2.53209	−	3.01763i	−0.300504	−	0.358126i	0.594571	−	0.804043i	$-0.297322\pi$
$71$	−2.53209	−	3.01763i	−0.300504	−	0.358126i	−0.895074	+	0.445917i	$0.852878\pi$
$72$	−7.38327	+	0.645953i	−0.870127	+	0.0761262i
$73$	−4.33934	−	3.03844i	−0.507882	−	0.355623i	0.291378	−	0.956608i	$-0.405886\pi$
$73$	−4.33934	−	3.03844i	−0.507882	−	0.355623i	−0.799260	+	0.600985i	$0.794775\pi$
$74$	2.37484	−	6.52481i	0.276069	−	0.758494i
$75$		0			0
$76$	3.93969	+	1.86516i	0.451914	+	0.213949i
$77$	5.40293	+	5.40293i	0.615721	+	0.615721i
$78$	−2.97930	−	6.38913i	−0.337340	−	0.723427i
$79$	−0.385920	−	2.18866i	−0.0434194	−	0.246244i	0.955371	−	0.295408i	$-0.0954555\pi$
$79$	−0.385920	−	2.18866i	−0.0434194	−	0.246244i	−0.998791	+	0.0491638i	$0.984344\pi$
$80$		0			0
$81$	−18.1518	+	15.2312i	−2.01687	+	1.69235i
$82$	−6.38607	+	4.47158i	−0.705224	+	0.493803i
$83$	3.67656	+	13.7211i	0.403555	+	1.50609i	0.806706	+	0.590953i	$0.201248\pi$
$83$	3.67656	+	13.7211i	0.403555	+	1.50609i	−0.403151	+	0.915133i	$0.632085\pi$
$84$	5.97205	+	10.3439i	0.651604	+	1.12861i
$85$		0			0
$86$	−3.40167	−	9.34602i	−0.366812	−	1.00781i
$87$	6.57951	−	24.5551i	0.705398	−	2.63258i
$88$	−1.99384	+	0.534249i	−0.212544	+	0.0569511i
$89$	−0.335316	+	1.90167i	−0.0355435	+	0.201577i	−0.997408	−	0.0719479i	$-0.977078\pi$
$89$	−0.335316	+	1.90167i	−0.0355435	+	0.201577i	0.961865	+	0.273525i	$0.0881896\pi$
$90$		0			0
$91$	−5.19846	+	6.19529i	−0.544947	+	0.649443i
$92$	−2.12319	+	3.03223i	−0.221358	+	0.316132i
$93$	26.7152	−	12.4575i	2.77024	−	1.29178i
$94$	9.73692			1.00429
$95$		0			0
$96$	−3.22668			−0.329322
$97$	−4.66105	+	2.17348i	−0.473258	+	0.220684i	−0.644589	−	0.764530i	$-0.722971\pi$
$97$	−4.66105	+	2.17348i	−0.473258	+	0.220684i	0.171330	+	0.985214i	$0.445193\pi$
$98$	3.84430	−	5.49023i	0.388333	−	0.554597i
$99$	−9.83375	+	11.7194i	−0.988329	+	1.17784i
$100$		0			0
$101$	−1.00727	+	5.71253i	−0.100228	+	0.568418i	0.892792	+	0.450469i	$0.148743\pi$
$101$	−1.00727	+	5.71253i	−0.100228	+	0.568418i	−0.993020	+	0.117949i	$0.962368\pi$
$102$	−4.00680	+	1.07362i	−0.396732	+	0.106304i
$103$	0.530483	−	1.97979i	0.0522701	−	0.195075i	−0.934854	−	0.355033i	$-0.884469\pi$
$103$	0.530483	−	1.97979i	0.0522701	−	0.195075i	0.987124	+	0.159959i	$0.0511362\pi$
$104$	−0.747243	−	2.05303i	−0.0732732	−	0.201316i
$105$		0			0
$106$	−4.54323	−	7.86911i	−0.441278	−	0.764316i
$107$	3.86768	+	14.4344i	0.373903	+	1.39542i	0.854942	+	0.518724i	$0.173593\pi$
$107$	3.86768	+	14.4344i	0.373903	+	1.39542i	−0.481039	+	0.876699i	$0.659740\pi$
$108$	−11.6602	+	8.16453i	−1.12200	+	0.785632i
$109$	−7.50016	+	6.29339i	−0.718386	+	0.602797i	−0.926938	−	0.375214i	$-0.877569\pi$
$109$	−7.50016	+	6.29339i	−0.718386	+	0.602797i	0.208553	+	0.978011i	$0.433125\pi$
$110$		0			0
$111$	−3.89053	−	22.0643i	−0.369273	−	2.09425i
$112$	1.56439	+	3.35485i	0.147821	+	0.317003i
$113$	−7.12192	−	7.12192i	−0.669974	−	0.669974i	0.287736	−	0.957710i	$-0.407098\pi$
$113$	−7.12192	−	7.12192i	−0.669974	−	0.669974i	−0.957710	+	0.287736i	$0.907098\pi$
$114$	14.0182	−	1.14409i	1.31292	−	0.107153i
$115$		0			0
$116$	2.69459	−	7.40333i	0.250187	−	0.687382i
$117$	−13.2641	−	9.28766i	−1.22627	−	0.858644i
$118$	2.11659	−	0.185178i	0.194848	−	0.0170470i
$119$	3.05888	+	3.64543i	0.280407	+	0.334176i
$120$		0			0
$121$	3.36959	−	5.83629i	0.306326	−	0.530572i
$122$	10.8706	+	2.91276i	0.984173	+	0.263708i
$123$	−10.6310	+	22.7982i	−0.958564	+	2.05565i
$124$	8.58445	−	3.12449i	0.770907	−	0.280587i
$125$		0			0
$126$	23.7592	+	13.7174i	2.11664	+	1.22204i
$127$	1.91549	+	2.73560i	0.169972	+	0.242746i	0.895096	−	0.445873i	$-0.147107\pi$
$127$	1.91549	+	2.73560i	0.169972	+	0.242746i	−0.725124	+	0.688618i	$0.758218\pi$
$128$	−0.996195	−	0.0871557i	−0.0880520	−	0.00770355i
$129$	−24.5839	−	20.6284i	−2.16449	−	1.81623i
$130$		0			0
$131$	16.7738	+	6.10516i	1.46553	+	0.533410i	0.946883	−	0.321577i	$-0.104213\pi$
$131$	16.7738	+	6.10516i	1.46553	+	0.533410i	0.518649	+	0.854987i	$0.326435\pi$
$132$	−4.70965	+	4.70965i	−0.409922	+	0.409922i
$133$	−7.98596	−	14.0203i	−0.692470	−	1.21571i
$134$			2.55438i			0.220665i
$135$		0			0
$136$	−1.26604	+	0.223238i	−0.108562	+	0.0191425i
$137$	−1.31925	−	15.0791i	−0.112711	−	1.28829i	−0.816276	−	0.577662i	$-0.803965\pi$
$137$	−1.31925	−	15.0791i	−0.112711	−	1.28829i	0.703565	−	0.710631i	$-0.251590\pi$
$138$	−1.04100	+	11.8986i	−0.0886155	+	1.01288i
$139$	21.7702	+	3.83868i	1.84653	+	0.325592i	0.983687	−	0.179886i	$-0.0575730\pi$
$139$	21.7702	+	3.83868i	1.84653	+	0.325592i	0.862839	+	0.505479i	$0.168684\pi$
$140$		0			0
$141$	27.2087	−	15.7090i	2.29139	−	1.32293i
$142$	−3.57016	−	1.66479i	−0.299601	−	0.139706i
$143$	−4.08727	−	1.90592i	−0.341794	−	0.159381i
$144$	−6.41852	+	3.70574i	−0.534877	+	0.308811i
$145$		0			0
$146$	−5.21688	−	0.919877i	−0.431752	−	0.0761296i
$147$	1.88486	−	21.5440i	0.155460	−	1.77692i
$148$	−0.605171	−	6.91714i	−0.0497448	−	0.568585i
$149$	−15.1025	+	2.66297i	−1.23724	+	0.218159i	−0.753733	−	0.657181i	$-0.771749\pi$
$149$	−15.1025	+	2.66297i	−1.23724	+	0.218159i	−0.483508	+	0.875340i	$0.660638\pi$
$150$		0			0
$151$			6.33012i			0.515138i	0.966260	+	0.257569i	$0.0829215\pi$
$151$			6.33012i			0.515138i	−0.966260	+	0.257569i	$0.917078\pi$
$152$	4.35882	+	0.0254230i	0.353547	+	0.00206208i
$153$	−6.73732	+	6.73732i	−0.544680	+	0.544680i
$154$	7.18009	+	2.61334i	0.578589	+	0.210589i
$155$		0			0
$156$	−5.40033	−	4.53141i	−0.432372	−	0.362804i
$157$	3.49465	+	0.305743i	0.278904	+	0.0244009i	0.225749	−	0.974185i	$-0.427517\pi$
$157$	3.49465	+	0.305743i	0.278904	+	0.0244009i	0.0531542	+	0.998586i	$0.483073\pi$
$158$	−1.27473	−	1.82051i	−0.101412	−	0.144832i
$159$	−25.3911	−	14.6596i	−2.01365	−	1.16258i
$160$		0			0
$161$	12.8760	−	4.68647i	1.01477	−	0.369346i
$162$	−10.0142	+	21.4754i	−0.786787	+	1.68727i
$163$	13.6561	+	3.65915i	1.06963	+	0.286607i	0.750341	−	0.661050i	$-0.229889\pi$
$163$	13.6561	+	3.65915i	1.06963	+	0.286607i	0.319290	+	0.947657i	$0.396556\pi$
$164$	−3.89798	+	6.75150i	−0.304381	+	0.527203i
$165$		0			0
$166$	9.13088	+	10.8818i	0.708694	+	0.844588i
$167$	−4.38698	+	0.383811i	−0.339474	+	0.0297002i	−0.255618	−	0.966778i	$-0.582279\pi$
$167$	−4.38698	+	0.383811i	−0.339474	+	0.0297002i	−0.0838559	+	0.996478i	$0.526724\pi$
$168$	9.78403	+	6.85085i	0.754855	+	0.528555i
$169$	−2.81369	+	7.73055i	−0.216438	+	0.594658i
$170$		0			0
$171$	26.5710	−	18.3752i	2.03194	−	1.40519i
$172$	−7.03276	−	7.03276i	−0.536243	−	0.536243i
$173$	−9.59154	−	20.5691i	−0.729232	−	1.56384i	−0.822866	−	0.568236i	$-0.807626\pi$
$173$	−9.59154	−	20.5691i	−0.729232	−	1.56384i	0.0936344	−	0.995607i	$-0.470152\pi$
$174$	−4.41436	−	25.0351i	−0.334652	−	1.89790i
$175$		0			0
$176$	−1.58125	+	1.32683i	−0.119191	+	0.100013i
$177$	5.61582	−	3.93224i	0.422111	−	0.295565i
$178$	0.499782	+	1.86521i	0.0374603	+	0.139804i
$179$	4.85586	+	8.41060i	0.362944	+	0.628638i	0.988444	−	0.151587i	$-0.0484383\pi$
$179$	4.85586	+	8.41060i	0.362944	+	0.628638i	−0.625500	+	0.780224i	$0.715105\pi$
$180$		0			0
$181$	−3.32501	−	9.13538i	−0.247146	−	0.679028i	−0.999788	−	0.0205977i	$-0.993443\pi$
$181$	−3.32501	−	9.13538i	−0.247146	−	0.679028i	0.752642	−	0.658430i	$-0.228779\pi$
$182$	−2.09317	+	7.81180i	−0.155156	+	0.579049i
$183$	35.0758	−	9.39853i	2.59288	−	0.694760i
$184$	−0.642788	+	3.64543i	−0.0473869	+	0.268745i
$185$		0			0
$186$	18.9474	−	22.5807i	1.38929	−	1.65570i
$187$	−1.52207	+	2.17375i	−0.111305	+	0.158960i
$188$	8.82464	−	4.11500i	0.643603	−	0.300117i
$189$	52.6911			3.83271
$190$		0			0
$191$	−15.7469			−1.13941			−0.569703	−	0.821850i	$-0.692942\pi$
$191$	−15.7469			−1.13941			−0.569703	+	0.821850i	$0.692942\pi$
$192$	−2.92437	+	1.36365i	−0.211048	+	0.0984133i
$193$	−5.51698	+	7.87906i	−0.397121	+	0.567147i	−0.967063	−	0.254538i	$-0.918077\pi$
$193$	−5.51698	+	7.87906i	−0.397121	+	0.567147i	0.569942	+	0.821685i	$0.306966\pi$
$194$	−3.30579	+	3.93969i	−0.237342	+	0.282853i
$195$		0			0
$196$	1.16385	−	6.60051i	0.0831320	−	0.471465i
$197$	1.09199	−	0.292599i	0.0778014	−	0.0208468i	−0.219708	−	0.975566i	$-0.570511\pi$
$197$	1.09199	−	0.292599i	0.0778014	−	0.0208468i	0.297510	+	0.954719i	$0.403844\pi$
$198$	−3.95957	+	14.7773i	−0.281394	+	1.05018i
$199$	1.33883	+	3.67840i	0.0949069	+	0.260755i	0.978058	−	0.208335i	$-0.0668044\pi$
$199$	1.33883	+	3.67840i	0.0949069	+	0.260755i	−0.883151	+	0.469089i	$0.844582\pi$
$200$		0			0
$201$	4.12108	+	7.13792i	0.290679	+	0.503470i
$202$	1.50132	+	5.60301i	0.105633	+	0.394226i
$203$	−23.8893	+	16.7275i	−1.67670	+	1.17404i
$204$	−3.17766	+	2.66637i	−0.222481	+	0.186684i
$205$		0			0
$206$	−0.355914	−	2.01849i	−0.0247977	−	0.140635i
$207$	11.5944	+	24.8644i	0.805870	+	1.72819i
$208$	−1.54488	−	1.54488i	−0.107118	−	0.107118i
$209$	6.39922	−	6.32501i	0.442643	−	0.437510i
$210$		0			0
$211$	−3.33022	+	9.14971i	−0.229262	+	0.629892i	−0.999973	−	0.00729228i	$-0.997679\pi$
$211$	−3.33022	+	9.14971i	−0.229262	+	0.629892i	0.770711	+	0.637184i	$0.219901\pi$
$212$	−7.44320	−	5.21178i	−0.511201	−	0.357947i
$213$	−12.6623	+	1.10781i	−0.867605	+	0.0759056i
$214$	9.60554	+	11.4474i	0.656621	+	0.782530i
$215$		0			0
$216$	−7.11721	+	12.3274i	−0.484265	+	0.838771i
$217$	−32.6639	−	8.75226i	−2.21737	−	0.594142i
$218$	−4.13776	+	8.87345i	−0.280244	+	0.600986i
$219$	−16.0621	+	5.84611i	−1.08537	+	0.395044i
$220$		0			0
$221$	−2.43242	−	1.40436i	−0.163622	−	0.0944673i
$222$	−12.8508	−	18.3528i	−0.862488	−	1.23176i
$223$	−3.13866	−	0.274597i	−0.210180	−	0.0183884i	−0.0184205	−	0.999830i	$-0.505864\pi$
$223$	−3.13866	−	0.274597i	−0.210180	−	0.0183884i	−0.191759	+	0.981442i	$0.561419\pi$
$224$	2.83564	+	2.37939i	0.189464	+	0.158979i
$225$		0			0
$226$	−9.46451	−	3.44480i	−0.629570	−	0.229145i
$227$	−0.863822	+	0.863822i	−0.0573339	+	0.0573339i	−0.735192	−	0.677858i	$-0.762908\pi$
$227$	−0.863822	+	0.863822i	−0.0573339	+	0.0573339i	0.677858	+	0.735192i	$0.262908\pi$
$228$	12.2213	−	6.96123i	0.809373	−	0.461019i
$229$			23.2344i			1.53537i	0.640825	+	0.767687i	$0.278592\pi$
$229$			23.2344i			1.53537i	−0.640825	+	0.767687i	$0.721408\pi$
$230$		0			0
$231$	24.2802	−	4.28125i	1.59752	−	0.281686i
$232$	−0.686653	−	7.84848i	−0.0450810	−	0.515278i
$233$	0.367557	−	4.20119i	0.0240794	−	0.275229i	−0.974604	−	0.223935i	$-0.928110\pi$
$233$	0.367557	−	4.20119i	0.0240794	−	0.275229i	0.998684	−	0.0512945i	$-0.0163347\pi$
$234$	−15.9465	−	2.81180i	−1.04246	−	0.183813i
$235$		0			0
$236$	1.84002	−	1.06234i	0.119775	−	0.0691523i
$237$	−6.49919	−	3.03062i	−0.422168	−	0.196860i
$238$	4.31291	+	2.01114i	0.279564	+	0.130363i
$239$	22.1552	−	12.7913i	1.43310	−	0.827402i	0.435746	−	0.900070i	$-0.356485\pi$
$239$	22.1552	−	12.7913i	1.43310	−	0.827402i	0.997356	+	0.0726674i	$0.0231512\pi$
$240$		0			0
$241$	−17.5103	−	3.08753i	−1.12794	−	0.198885i	−0.421613	−	0.906776i	$-0.638536\pi$
$241$	−17.5103	−	3.08753i	−1.12794	−	0.198885i	−0.706322	+	0.707890i	$0.749647\pi$
$242$	0.587357	−	6.71353i	0.0377568	−	0.431562i
$243$	2.94191	+	33.6262i	0.188724	+	2.15712i
$244$	11.0830	−	1.95424i	0.709519	−	0.125107i
$245$		0			0
$246$			25.1551i			1.60383i
$247$	7.25944	+	6.16390i	0.461907	+	0.392199i
$248$	6.45969	−	6.45969i	0.410191	−	0.410191i
$249$	43.0712	+	15.6766i	2.72953	+	0.993467i
$250$		0			0
$251$	−10.0719	−	8.45134i	−0.635734	−	0.533444i	0.266971	−	0.963705i	$-0.413977\pi$
$251$	−10.0719	−	8.45134i	−0.635734	−	0.533444i	−0.902705	+	0.430261i	$0.858422\pi$
$252$	27.3304	+	2.39110i	1.72165	+	0.150625i
$253$	4.38264	+	6.25906i	0.275534	+	0.393504i
$254$	2.89214	+	1.66978i	0.181469	+	0.104771i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	5.51174	−	11.8200i	0.343813	−	0.737309i	−0.656035	−	0.754730i	$-0.727768\pi$
$257$	5.51174	−	11.8200i	0.343813	−	0.737309i	0.999848	+	0.0174210i	$0.00554556\pi$
$258$	−30.9985	−	8.30603i	−1.92988	−	0.517111i
$259$	−12.8514	+	22.2592i	−0.798546	+	1.38312i
$260$		0			0
$261$	−37.5330	−	44.7301i	−2.32324	−	2.76872i
$262$	17.7824	−	1.55576i	1.09860	−	0.0961149i
$263$	5.17817	+	3.62579i	0.319299	+	0.223576i	0.722227	−	0.691656i	$-0.243119\pi$
$263$	5.17817	+	3.62579i	0.319299	+	0.223576i	−0.402928	+	0.915232i	$0.632007\pi$
$264$	−2.27801	+	6.25877i	−0.140202	+	0.385201i
$265$		0			0
$266$	−13.1630	−	9.33170i	−0.807074	−	0.572163i
$267$	4.40581	+	4.40581i	0.269631	+	0.269631i
$268$	1.07953	+	2.31505i	0.0659426	+	0.141414i
$269$	0.753138	+	4.27126i	0.0459196	+	0.260423i	0.999121	−	0.0419120i	$-0.0133449\pi$
$269$	0.753138	+	4.27126i	0.0459196	+	0.260423i	−0.953202	+	0.302335i	$0.902234\pi$
$270$		0			0
$271$	9.70755	−	8.14560i	0.589692	−	0.494810i	−0.298422	−	0.954434i	$-0.596460\pi$
$271$	9.70755	−	8.14560i	0.589692	−	0.494810i	0.888114	+	0.459624i	$0.152016\pi$
$272$	−1.05308	+	0.737376i	−0.0638524	+	0.0447100i
$273$	6.75398	+	25.2062i	0.408770	+	1.52555i
$274$	−7.56834	−	13.1088i	−0.457220	−	0.791929i
$275$		0			0
$276$	4.08512	+	11.2238i	0.245895	+	0.675592i
$277$	−0.578676	+	2.15965i	−0.0347693	+	0.129761i	−0.981129	−	0.193354i	$-0.938063\pi$
$277$	−0.578676	+	2.15965i	−0.0347693	+	0.129761i	0.946360	+	0.323115i	$0.104730\pi$
$278$	21.3528	−	5.72147i	1.28066	−	0.343151i
$279$	11.7571	−	66.6780i	0.703881	−	3.99191i
$280$		0			0
$281$	−6.12449	+	7.29888i	−0.365356	+	0.435415i	−0.917135	−	0.398576i	$-0.869505\pi$
$281$	−6.12449	+	7.29888i	−0.365356	+	0.435415i	0.551779	+	0.833990i	$0.313949\pi$
$282$	18.0206	−	25.7361i	1.07311	−	1.53256i
$283$	−24.1389	+	11.2561i	−1.43491	+	0.669108i	−0.975678	−	0.219209i	$-0.929652\pi$
$283$	−24.1389	+	11.2561i	−1.43491	+	0.669108i	−0.459230	+	0.888318i	$0.651875\pi$
$284$	−3.93923			−0.233750
$285$		0			0
$286$	−4.50980			−0.266670
$287$	26.1543	−	12.1959i	1.54384	−	0.719903i
$288$	−4.25105	+	6.07112i	−0.250495	+	0.357744i
$289$	9.86505	−	11.7567i	0.580297	−	0.691571i
$290$		0			0
$291$	−2.88161	+	16.3424i	−0.168923	+	0.958009i
$292$	−5.11686	+	1.37106i	−0.299441	+	0.0802351i
$293$	1.64034	−	6.12185i	0.0958299	−	0.357642i	−0.901314	−	0.433166i	$-0.857396\pi$
$293$	1.64034	−	6.12185i	0.0958299	−	0.357642i	0.997144	+	0.0755241i	$0.0240630\pi$
$294$	−7.39663	−	20.3221i	−0.431380	−	1.18521i
$295$		0			0
$296$	−3.47178	−	6.01330i	−0.201793	−	0.349516i
$297$	7.60472	+	28.3812i	0.441271	+	1.64684i
$298$	−12.5621	+	8.79605i	−0.727700	+	0.509541i
$299$	−6.19529	+	5.19846i	−0.358283	+	0.300635i
$300$		0			0
$301$	6.39306	+	36.2568i	0.368490	+	2.08981i
$302$	2.67523	+	5.73704i	0.153942	+	0.330130i
$303$	13.2348	+	13.2348i	0.760321	+	0.760321i
$304$	3.96118	−	1.81908i	0.227189	−	0.104331i
$305$		0			0
$306$	−3.25877	+	8.95340i	−0.186292	+	0.511832i
$307$	−7.36823	−	5.15929i	−0.420527	−	0.294456i	0.344095	−	0.938935i	$-0.388186\pi$
$307$	−7.36823	−	5.15929i	−0.420527	−	0.294456i	−0.764622	+	0.644478i	$0.777075\pi$
$308$	7.61182	−	0.665948i	0.433724	−	0.0379459i
$309$	−4.25108	−	5.06624i	−0.241835	−	0.288208i
$310$		0			0
$311$	4.97952	−	8.62479i	0.282363	−	0.489067i	−0.689603	−	0.724187i	$-0.742215\pi$
$311$	4.97952	−	8.62479i	0.282363	−	0.489067i	0.971966	+	0.235120i	$0.0755485\pi$
$312$	−6.80942	−	1.82458i	−0.385507	−	0.103296i
$313$	−9.31017	+	19.9657i	−0.526242	+	1.12853i	0.446103	+	0.894981i	$0.352811\pi$
$313$	−9.31017	+	19.9657i	−0.526242	+	1.12853i	−0.972345	+	0.233548i	$0.924966\pi$
$314$	3.29644	−	1.19981i	0.186029	−	0.0677090i
$315$		0			0
$316$	−1.92468	−	1.11121i	−0.108272	−	0.0625106i
$317$	15.2579	+	21.7905i	0.856968	+	1.22388i	0.973040	+	0.230637i	$0.0740810\pi$
$317$	15.2579	+	21.7905i	0.856968	+	1.22388i	−0.116071	+	0.993241i	$0.537030\pi$
$318$	−29.2076	−	2.55533i	−1.63788	−	0.143296i
$319$	−12.4578	−	10.4534i	−0.697505	−	0.585276i
$320$		0			0
$321$	45.3102	+	16.4916i	2.52897	+	0.920470i
$322$	9.68901	−	9.68901i	0.539948	−	0.539948i
$323$	4.31361	−	3.57689i	0.240016	−	0.199023i
$324$			23.6955i			1.31642i
$325$		0			0
$326$	13.9231	−	2.45502i	0.771128	−	0.135971i
$327$	2.75340	+	31.4715i	0.152263	+	1.74038i
$328$	−0.679462	+	7.76629i	−0.0375170	+	0.428822i
$329$	−35.4953	−	6.25877i	−1.95692	−	0.345057i
$330$		0			0
$331$	−22.7001	+	13.1059i	−1.24771	+	0.720366i	−0.970652	−	0.240487i	$-0.922693\pi$
$331$	−22.7001	+	13.1059i	−1.24771	+	0.720366i	−0.277059	+	0.960853i	$0.589360\pi$
$332$	12.8742	+	6.00335i	0.706565	+	0.329476i
$333$	−46.6404	−	21.7488i	−2.55588	−	1.19183i
$334$	−3.81374	+	2.20187i	−0.208679	+	0.120481i
$335$		0			0
$336$	11.7626	+	2.07407i	0.641705	+	0.113150i
$337$	−2.08234	+	23.8013i	−0.113432	+	1.29654i	0.699691	+	0.714446i	$0.253321\pi$
$337$	−2.08234	+	23.8013i	−0.113432	+	1.29654i	−0.813123	+	0.582092i	$0.802234\pi$
$338$	0.717003	+	8.19538i	0.0389998	+	0.445770i
$339$	−32.0051	+	5.64337i	−1.73828	+	0.306506i
$340$		0			0
$341$		−	18.8571i		−	1.02117i
$342$	16.3158	−	27.8830i	0.882259	−	1.50774i
$343$	0.779134	−	0.779134i	0.0420693	−	0.0420693i
$344$	−9.34602	−	3.40167i	−0.503904	−	0.183406i
$345$		0			0
$346$	−17.3858	−	14.5884i	−0.934665	−	0.784277i
$347$	−11.8602	−	1.03763i	−0.636688	−	0.0557030i	−0.235758	−	0.971812i	$-0.575757\pi$
$347$	−11.8602	−	1.03763i	−0.636688	−	0.0557030i	−0.400930	+	0.916109i	$0.631313\pi$
$348$	−14.5811	−	20.8239i	−0.781626	−	1.11628i
$349$	13.6519	+	7.88191i	0.730768	+	0.421909i	0.818703	−	0.574217i	$-0.194693\pi$
$349$	13.6519	+	7.88191i	0.730768	+	0.421909i	−0.0879351	+	0.996126i	$0.528027\pi$
$350$		0			0
$351$	−29.2237	+	10.6366i	−1.55985	+	0.567738i
$352$	−0.872359	+	1.87078i	−0.0464969	+	0.0997129i
$353$	−12.1278	−	3.24962i	−0.645496	−	0.172960i	−0.0788042	−	0.996890i	$-0.525110\pi$
$353$	−12.1278	−	3.24962i	−0.645496	−	0.172960i	−0.566692	+	0.823930i	$0.691777\pi$
$354$	3.42782	−	5.93717i	0.182187	−	0.315557i
$355$		0			0
$356$	1.24123	+	1.47924i	0.0657850	+	0.0783995i
$357$	15.2966	−	1.33828i	0.809582	−	0.0708293i
$358$	7.95538	+	5.57041i	0.420455	+	0.294406i
$359$	−5.60575	+	15.4017i	−0.295860	+	0.812869i	0.699320	+	0.714809i	$0.253486\pi$
$359$	−5.60575	+	15.4017i	−0.295860	+	0.812869i	−0.995180	+	0.0980607i	$0.968736\pi$
$360$		0			0
$361$	−16.5642	+	9.30742i	−0.871799	+	0.489864i
$362$	−6.87426	−	6.87426i	−0.361303	−	0.361303i
$363$	−9.18990	−	19.7078i	−0.482345	−	1.03439i
$364$	1.40436	+	7.96451i	0.0736083	+	0.417454i
$365$		0			0
$366$	27.8175	−	23.3416i	1.45404	−	1.22009i
$367$	−16.7223	+	11.7091i	−0.872896	+	0.611209i	−0.921830	−	0.387593i	$-0.873306\pi$
$367$	−16.7223	+	11.7091i	−0.872896	+	0.611209i	0.0489341	+	0.998802i	$0.484418\pi$
$368$	0.958062	+	3.57554i	0.0499424	+	0.186388i
$369$	28.8898	+	50.0385i	1.50394	+	2.60490i
$370$		0			0
$371$	11.5039	+	31.6066i	0.597251	+	1.64093i
$372$	7.62920	−	28.4726i	0.395556	−	1.47623i
$373$	33.0754	−	8.86252i	1.71258	−	0.458884i	0.736524	−	0.676411i	$-0.236466\pi$
$373$	33.0754	−	8.86252i	1.71258	−	0.458884i	0.976054	+	0.217527i	$0.0697990\pi$
$374$	−0.460802	+	2.61334i	−0.0238275	+	0.135133i
$375$		0			0
$376$	6.25877	−	7.45891i	0.322771	−	0.384664i
$377$	9.87286	−	14.0999i	0.508478	−	0.726182i
$378$	47.7543	−	22.2682i	2.45622	−	1.14535i
$379$	33.0656			1.69847			0.849234	−	0.528017i	$-0.177064\pi$
$379$	33.0656			1.69847			0.849234	+	0.528017i	$0.177064\pi$
$380$		0			0
$381$	10.7757			0.552055
$382$	−14.2715	+	6.65493i	−0.730196	+	0.340496i
$383$	−8.90050	+	12.7112i	−0.454794	+	0.649513i	−0.979423	−	0.201818i	$-0.935315\pi$
$383$	−8.90050	+	12.7112i	−0.454794	+	0.649513i	0.524629	+	0.851331i	$0.324204\pi$
$384$	−2.07407	+	2.47178i	−0.105842	+	0.126138i
$385$		0			0
$386$	−1.67024	+	9.47243i	−0.0850132	+	0.482134i
$387$	−71.2015	+	19.0784i	−3.61938	+	0.969809i
$388$	−1.33108	+	4.96766i	−0.0675754	+	0.252195i
$389$	−4.15312	−	11.4106i	−0.210571	−	0.578540i	0.788775	−	0.614682i	$-0.210716\pi$
$389$	−4.15312	−	11.4106i	−0.210571	−	0.578540i	−0.999347	+	0.0361415i	$0.988493\pi$
$390$		0			0
$391$	2.37939	+	4.12122i	0.120331	+	0.208419i
$392$	−1.73469	−	6.47396i	−0.0876152	−	0.326984i
$393$	47.1809	−	33.0364i	2.37996	−	1.66647i
$394$	0.866025	−	0.726682i	0.0436297	−	0.0366097i
$395$		0			0
$396$	2.65657	+	15.0662i	0.133498	+	0.757104i
$397$	5.65663	+	12.1307i	0.283898	+	0.608822i	0.995605	−	0.0936552i	$-0.0298551\pi$
$397$	5.65663	+	12.1307i	0.283898	+	0.608822i	−0.711706	+	0.702477i	$0.752077\pi$
$398$	2.76795	+	2.76795i	0.138745	+	0.138745i
$399$	−51.8377	−	4.84002i	−2.59513	−	0.242304i
$400$		0			0
$401$	5.46522	−	15.0156i	0.272920	−	0.749842i	−0.725199	−	0.688539i	$-0.758252\pi$
$401$	5.46522	−	15.0156i	0.272920	−	0.749842i	0.998119	−	0.0613028i	$-0.0195255\pi$
$402$	6.75158	+	4.72751i	0.336738	+	0.235787i
$403$	19.8830	−	1.73953i	0.990441	−	0.0866524i
$404$	3.72859	+	4.44356i	0.185504	+	0.221076i
$405$		0			0
$406$	−14.5817	+	25.2563i	−0.723679	+	1.25345i
$407$	−13.8444	−	3.70959i	−0.686240	−	0.183877i
$408$	−1.75308	+	3.75949i	−0.0867904	+	0.186123i
$409$	9.39052	−	3.41787i	0.464331	−	0.169003i	−0.0992514	−	0.995062i	$-0.531645\pi$
$409$	9.39052	−	3.41787i	0.464331	−	0.169003i	0.563583	+	0.826060i	$0.309423\pi$
$410$		0			0
$411$	−42.2978	−	24.4206i	−2.08640	−	1.20458i
$412$	−1.17562	−	1.67896i	−0.0579186	−	0.0827163i
$413$	−7.83491	−	0.685466i	−0.385531	−	0.0337296i
$414$	21.0163	+	17.6348i	1.03289	+	0.866701i
$415$		0			0
$416$	−2.05303	−	0.747243i	−0.100658	−	0.0366366i
$417$	50.4374	−	50.4374i	2.46993	−	2.46993i
$418$	3.12660	−	8.43683i	0.152927	−	0.412659i
$419$		−	21.6304i		−	1.05671i	−0.849022	−	0.528357i	$-0.822808\pi$
$419$		−	21.6304i		−	1.05671i	0.849022	−	0.528357i	$-0.177192\pi$
$420$		0			0
$421$	15.8892	−	2.80169i	0.774392	−	0.136546i	0.227532	−	0.973771i	$-0.426934\pi$
$421$	15.8892	−	2.80169i	0.774392	−	0.136546i	0.546859	+	0.837224i	$0.315823\pi$
$422$	0.848628	+	9.69987i	0.0413106	+	0.472182i
$423$	6.28959	−	71.8903i	0.305810	−	3.49543i
$424$	−8.94842	−	1.57785i	−0.434574	−	0.0766271i
$425$		0			0
$426$	−11.0077	+	6.35532i	−0.533327	+	0.307916i
$427$	−37.7555	−	17.6057i	−1.82712	−	0.852000i
$428$	13.5435	+	6.31542i	0.654648	+	0.305267i
$429$	−12.6021	+	7.27584i	−0.608437	+	0.351281i
$430$		0			0
$431$	−0.309993	−	0.0546601i	−0.0149318	−	0.00263288i	0.166177	−	0.986096i	$-0.446858\pi$
$431$	−0.309993	−	0.0546601i	−0.0149318	−	0.00263288i	−0.181109	+	0.983463i	$0.557969\pi$
$432$	−1.24061	+	14.1803i	−0.0596890	+	0.682248i
$433$	0.581970	+	6.65195i	0.0279677	+	0.319672i	0.997272	+	0.0738095i	$0.0235157\pi$
$433$	0.581970	+	6.65195i	0.0279677	+	0.319672i	−0.969305	+	0.245863i	$0.920929\pi$
$434$	−33.3024	+	5.87211i	−1.59857	+	0.281870i
$435$		0			0
$436$			9.79077i			0.468893i
$437$	−5.43003	−	15.1940i	−0.259754	−	0.726830i
$438$	−12.0865	+	12.0865i	−0.577515	+	0.577515i
$439$	15.8102	+	5.75443i	0.754579	+	0.274644i	0.690531	−	0.723303i	$-0.257377\pi$
$439$	15.8102	+	5.75443i	0.754579	+	0.274644i	0.0640474	+	0.997947i	$0.479599\pi$
$440$		0			0
$441$	−38.0526	−	31.9299i	−1.81203	−	1.52047i
$442$	−2.79803	−	0.244796i	−0.133089	−	0.0116437i
$443$	−18.8721	−	26.9521i	−0.896640	−	1.28053i	−0.959268	−	0.282497i	$-0.908837\pi$
$443$	−18.8721	−	26.9521i	−0.896640	−	1.28053i	0.0626285	−	0.998037i	$-0.480052\pi$
$444$	−19.4030	−	11.2023i	−0.920826	−	0.531639i
$445$		0			0
$446$	−2.96064	+	1.07758i	−0.140190	+	0.0510251i
$447$	−20.9122	+	44.8464i	−0.989115	+	2.12116i
$448$	3.57554	+	0.958062i	0.168928	+	0.0452642i
$449$	4.17680	−	7.23442i	0.197115	−	0.341414i	−0.750477	−	0.660897i	$-0.770176\pi$
$449$	4.17680	−	7.23442i	0.197115	−	0.341414i	0.947592	+	0.319483i	$0.103509\pi$
$450$		0			0
$451$	10.3439	+	12.3274i	0.487075	+	0.580473i
$452$	−10.0336	+	0.877826i	−0.471940	+	0.0412894i
$453$	16.7314	+	11.7155i	0.786111	+	0.550441i
$454$	−0.417822	+	1.14796i	−0.0196093	+	0.0538762i
$455$		0			0
$456$	8.13429	−	11.4739i	0.380923	−	0.537317i
$457$	7.96206	+	7.96206i	0.372450	+	0.372450i	0.868369	−	0.495919i	$-0.165169\pi$
$457$	7.96206	+	7.96206i	0.372450	+	0.372450i	−0.495919	+	0.868369i	$0.665169\pi$
$458$	9.81929	+	21.0575i	0.458825	+	0.983954i
$459$	3.17766	+	18.0214i	0.148321	+	0.841167i
$460$		0			0
$461$	6.97384	−	5.85175i	0.324804	−	0.272543i	−0.465775	−	0.884903i	$-0.654224\pi$
$461$	6.97384	−	5.85175i	0.324804	−	0.272543i	0.790579	+	0.612360i	$0.209780\pi$
$462$	20.1960	−	14.1414i	0.939602	−	0.657917i
$463$	−1.39015	−	5.18810i	−0.0646056	−	0.241111i	0.926070	−	0.377351i	$-0.123165\pi$
$463$	−1.39015	−	5.18810i	−0.0646056	−	0.241111i	−0.990676	+	0.136240i	$0.956498\pi$
$464$	−3.93923	−	6.82295i	−0.182874	−	0.316747i
$465$		0			0
$466$	−1.44238	−	3.96291i	−0.0668170	−	0.183578i
$467$	2.39939	−	8.95465i	0.111031	−	0.414372i	−0.887929	−	0.459981i	$-0.847856\pi$
$467$	2.39939	−	8.95465i	0.111031	−	0.414372i	0.998959	+	0.0456091i	$0.0145229\pi$
$468$	−15.6408	+	4.19094i	−0.722996	+	0.193726i
$469$	1.64192	−	9.31180i	0.0758169	−	0.429979i
$470$		0			0
$471$	7.27584	−	8.67101i	0.335253	−	0.399539i
$472$	1.21866	−	1.74043i	0.0560935	−	0.0801099i
$473$	−18.6065	+	8.67634i	−0.855526	+	0.398938i
$474$	−7.17106			−0.329378
$475$		0			0
$476$	4.75877			0.218118
$477$	−61.0345	+	28.4609i	−2.79458	+	1.30313i
$478$	14.6736	−	20.9561i	0.671155	−	0.958509i
$479$	−9.08040	+	10.8216i	−0.414894	+	0.494452i	−0.932501	−	0.361167i	$-0.882379\pi$
$479$	−9.08040	+	10.8216i	−0.414894	+	0.494452i	0.517607	+	0.855618i	$0.326823\pi$
$480$		0			0
$481$	2.63429	−	14.9398i	0.120113	−	0.681195i
$482$	−17.1745	+	4.60190i	−0.782279	+	0.209611i
$483$	11.4432	−	42.7065i	0.520683	−	1.94322i
$484$	−2.30493	−	6.33275i	−0.104770	−	0.287852i
$485$		0			0
$486$	16.8773	+	29.2324i	0.765571	+	1.32601i
$487$	1.05258	+	3.92829i	0.0476971	+	0.178008i	0.985665	−	0.168714i	$-0.0539614\pi$
$487$	1.05258	+	3.92829i	0.0476971	+	0.178008i	−0.937968	+	0.346722i	$0.887295\pi$
$488$	9.21876	−	6.45504i	0.417313	−	0.292206i
$489$	34.9457	−	29.3229i	1.58030	−	1.32603i
$490$		0			0
$491$	−0.489322	−	2.77509i	−0.0220828	−	0.125238i	0.971774	−	0.235916i	$-0.0758089\pi$
$491$	−0.489322	−	2.77509i	−0.0220828	−	0.125238i	−0.993856	+	0.110678i	$0.964698\pi$
$492$	10.6310	+	22.7982i	0.479282	+	1.02782i
$493$	−7.16183	−	7.16183i	−0.322553	−	0.322553i
$494$	9.18426	+	2.51842i	0.413219	+	0.113309i
$495$		0			0
$496$	3.12449	−	8.58445i	0.140294	−	0.385453i
$497$	11.9446	+	8.36373i	0.535791	+	0.375165i
$498$	45.6610	−	3.99482i	2.04612	−	0.179012i
$499$	1.67382	+	1.99479i	0.0749306	+	0.0892989i	0.802207	−	0.597045i	$-0.203659\pi$
$499$	1.67382	+	1.99479i	0.0749306	+	0.0892989i	−0.727277	+	0.686344i	$0.759214\pi$
$500$		0			0
$501$	−7.10472	+	12.3057i	−0.317416	+	0.549780i
$502$	−12.7000	−	3.40294i	−0.566827	−	0.151881i
$503$	−3.62237	+	7.76819i	−0.161513	+	0.346367i	−0.970364	−	0.241647i	$-0.922312\pi$
$503$	−3.62237	+	7.76819i	−0.161513	+	0.346367i	0.808851	+	0.588014i	$0.200090\pi$
$504$	25.7803	−	9.38326i	1.14835	−	0.417963i
$505$		0			0
$506$	6.61721	+	3.82045i	0.294171	+	0.169840i
$507$	15.2255	+	21.7443i	0.676189	+	0.965698i
$508$	3.32685	+	0.291061i	0.147605	+	0.0129138i
$509$	−16.4526	−	13.8054i	−0.729251	−	0.611914i	0.200677	−	0.979658i	$-0.435686\pi$
$509$	−16.4526	−	13.8054i	−0.729251	−	0.611914i	−0.929927	+	0.367744i	$0.880130\pi$
$510$		0			0
$511$	18.4265	+	6.70669i	0.815140	+	0.296687i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	0.361882	−	62.0454i	0.0159775	−	2.73937i
$514$		−	13.0419i		−	0.575253i
$515$		0			0
$516$	−31.6045	+	5.57272i	−1.39131	+	0.245325i
$517$	−1.75172	−	20.0222i	−0.0770405	−	0.880577i
$518$	−2.24014	+	25.6049i	−0.0984262	+	1.12502i
$519$	−72.1187	−	12.7165i	−3.16566	−	0.558191i
$520$		0			0
$521$	−24.1783	+	13.9593i	−1.05927	+	0.611570i	−0.925230	−	0.379406i	$-0.876128\pi$
$521$	−24.1783	+	13.9593i	−1.05927	+	0.611570i	−0.134040	+	0.990976i	$0.542795\pi$
$522$	−52.9202	−	24.6771i	−2.31626	−	1.08009i
$523$	19.1582	+	8.93364i	0.837732	+	0.390641i	0.793641	−	0.608387i	$-0.208183\pi$
$523$	19.1582	+	8.93364i	0.837732	+	0.390641i	0.0440910	+	0.999028i	$0.485961\pi$
$524$	15.4588	−	8.92514i	0.675321	−	0.389897i
$525$		0			0
$526$	6.22534	+	1.09769i	0.271438	+	0.0478618i
$527$	1.02358	−	11.6995i	0.0445877	−	0.509640i
$528$	0.580496	+	6.63510i	0.0252628	+	0.288756i
$529$	−9.15641	+	1.61452i	−0.398105	+	0.0701966i
$530$		0			0
$531$		−	15.7470i		−	0.683360i
$532$	−15.8734	−	2.89448i	−0.688201	−	0.125491i
$533$	−12.0438	+	12.0438i	−0.521676	+	0.521676i
$534$	5.85499	+	2.13104i	0.253370	+	0.0922193i
$535$		0			0
$536$	1.95677	+	1.64192i	0.0845195	+	0.0709202i
$537$	31.2174	+	2.73117i	1.34713	+	0.117859i
$538$	2.48769	+	3.55279i	0.107252	+	0.153171i
$539$	−11.9813	−	6.91740i	−0.516071	−	0.297954i
$540$		0			0
$541$	14.3020	−	5.20550i	0.614891	−	0.223802i	−0.0157509	−	0.999876i	$-0.505014\pi$
$541$	14.3020	−	5.20550i	0.614891	−	0.223802i	0.630642	+	0.776074i	$0.282792\pi$
$542$	5.35555	−	11.4850i	0.230040	−	0.493323i
$543$	−30.2999	−	8.11883i	−1.30029	−	0.348412i
$544$	−0.642788	+	1.11334i	−0.0275593	+	0.0477341i
$545$		0			0
$546$	16.7738	+	19.9902i	0.717852	+	0.855502i
$547$	−39.2080	+	3.43025i	−1.67641	+	0.146667i	−0.885305	−	0.465011i	$-0.846050\pi$
$547$	−39.2080	+	3.43025i	−1.67641	+	0.146667i	−0.791107	+	0.611678i	$0.790495\pi$
$548$	−12.3992	−	8.68205i	−0.529670	−	0.370879i
$549$	28.5275	−	78.3787i	1.21753	−	3.34512i
$550$		0			0
$551$	19.5330	+	28.2452i	0.832135	+	1.20329i
$552$	8.44575	+	8.44575i	0.359475	+	0.359475i
$553$	3.47675	+	7.45591i	0.147846	+	0.317057i
$554$	0.388249	+	2.20187i	0.0164951	+	0.0935484i
$555$		0			0
$556$	16.9342	−	14.2095i	0.718171	−	0.602617i
$557$	−8.14183	+	5.70097i	−0.344980	+	0.241558i	−0.733206	−	0.680007i	$-0.761977\pi$
$557$	−8.14183	+	5.70097i	−0.344980	+	0.241558i	0.388226	+	0.921564i	$0.373088\pi$
$558$	−17.5238	−	65.3996i	−0.741840	−	2.76859i
$559$	−10.8648	−	18.8184i	−0.459532	−	0.795932i
$560$		0			0
$561$	2.92855	+	8.04612i	0.123643	+	0.339707i
$562$	−2.46603	+	9.20335i	−0.104023	+	0.388220i
$563$	15.4508	−	4.14004i	0.651175	−	0.174482i	0.0819150	−	0.996639i	$-0.473896\pi$
$563$	15.4508	−	4.14004i	0.651175	−	0.174482i	0.569260	+	0.822157i	$0.307230\pi$
$564$	5.45567	−	30.9406i	0.229725	−	1.30284i
$565$		0			0
$566$	−17.1202	+	20.4031i	−0.719616	+	0.857605i
$567$	50.3101	−	71.8502i	2.11282	−	3.01743i
$568$	−3.57016	+	1.66479i	−0.149800	+	0.0698531i
$569$	−11.5163			−0.482789			−0.241395	−	0.970427i	$-0.577605\pi$
$569$	−11.5163			−0.482789			−0.241395	+	0.970427i	$0.577605\pi$
$570$		0			0
$571$	−44.4593			−1.86057			−0.930283	−	0.366843i	$-0.880439\pi$
$571$	−44.4593			−1.86057			−0.930283	+	0.366843i	$0.880439\pi$
$572$	−4.08727	+	1.90592i	−0.170897	+	0.0796907i
$573$	−29.1436	+	41.6213i	−1.21749	+	1.73876i
$574$	18.5496	−	22.1065i	0.774245	−	0.922709i
$575$		0			0
$576$	−1.28699	+	7.29888i	−0.0536245	+	0.304120i
$577$	14.9109	−	3.99535i	0.620747	−	0.166329i	0.0652797	−	0.997867i	$-0.479206\pi$
$577$	14.9109	−	3.99535i	0.620747	−	0.166329i	0.555467	+	0.831538i	$0.312539\pi$
$578$	3.97217	−	14.8243i	0.165221	−	0.616612i
$579$	10.6149	+	29.1643i	0.441142	+	1.21203i
$580$		0			0
$581$	−26.2913	−	45.5379i	−1.09075	−	1.88923i
$582$	4.29498	+	16.0291i	0.178032	+	0.664426i
$583$	−15.3641	+	10.7580i	−0.636315	+	0.445553i
$584$	−4.05801	+	3.40508i	−0.167922	+	0.140903i
$585$		0			0
$586$	−1.10055	−	6.24152i	−0.0454632	−	0.257835i
$587$	−1.14200	−	2.44904i	−0.0471356	−	0.101083i	0.881330	−	0.472502i	$-0.156649\pi$
$587$	−1.14200	−	2.44904i	−0.0471356	−	0.101083i	−0.928465	+	0.371419i	$0.878871\pi$
$588$	−15.2921	−	15.2921i	−0.630636	−	0.630636i
$589$	−10.5304	+	38.4026i	−0.433897	+	1.58235i
$590$		0			0
$591$	1.24763	−	3.42782i	0.0513205	−	0.141002i
$592$	−5.68783	−	3.98266i	−0.233769	−	0.163686i
$593$	−8.26288	+	0.722909i	−0.339316	+	0.0296863i	−0.255540	−	0.966798i	$-0.582253\pi$
$593$	−8.26288	+	0.722909i	−0.339316	+	0.0296863i	−0.0837754	+	0.996485i	$0.526698\pi$
$594$	18.8866	+	22.5082i	0.774928	+	0.923523i
$595$		0			0
$596$	−7.66772	+	13.2809i	−0.314082	+	0.544006i
$597$	12.2004	+	3.26908i	0.499327	+	0.133794i
$598$	−3.41787	+	7.32965i	−0.139767	+	0.299732i
$599$	−0.193064	+	0.0702697i	−0.00788840	+	0.00287114i	−0.345961	−	0.938249i	$-0.612447\pi$
$599$	−0.193064	+	0.0702697i	−0.00788840	+	0.00287114i	0.338073	+	0.941120i	$0.390225\pi$
$600$		0			0
$601$	−1.44175	−	0.832396i	−0.0588103	−	0.0339541i	0.470307	−	0.882503i	$-0.344143\pi$
$601$	−1.44175	−	0.832396i	−0.0588103	−	0.0339541i	−0.529117	+	0.848549i	$0.677477\pi$
$602$	21.1169	+	30.1580i	0.860659	+	1.22915i
$603$	18.8597	+	1.65001i	0.768025	+	0.0671935i
$604$	4.84916	+	4.06893i	0.197309	+	0.165562i
$605$		0			0
$606$	17.5881	+	6.40155i	0.714468	+	0.260045i
$607$	−14.3272	+	14.3272i	−0.581524	+	0.581524i	−0.935322	−	0.353798i	$-0.884890\pi$
$607$	−14.3272	+	14.3272i	−0.581524	+	0.581524i	0.353798	+	0.935322i	$0.384890\pi$
$608$	2.82127	−	3.32271i	0.114418	−	0.134754i
$609$			94.1011i			3.81317i
$610$		0			0
$611$	20.9500	−	3.69404i	0.847545	−	0.149445i
$612$	0.830421	+	9.49175i	0.0335678	+	0.383681i
$613$	−2.18465	+	24.9707i	−0.0882373	+	1.00856i	0.815013	+	0.579443i	$0.196730\pi$
$613$	−2.18465	+	24.9707i	−0.0882373	+	1.00856i	−0.903250	+	0.429114i	$0.858826\pi$
$614$	−8.85829	−	1.56196i	−0.357492	−	0.0630354i
$615$		0			0
$616$	6.61721	−	3.82045i	0.266615	−	0.153930i
$617$	5.24969	+	2.44797i	0.211345	+	0.0985516i	0.525408	−	0.850850i	$-0.323913\pi$
$617$	5.24969	+	2.44797i	0.211345	+	0.0985516i	−0.314063	+	0.949402i	$0.601690\pi$
$618$	−5.99387	−	2.79499i	−0.241109	−	0.112431i
$619$	−26.0474	+	15.0385i	−1.04693	+	0.604448i	−0.921790	−	0.387691i	$-0.873273\pi$
$619$	−26.0474	+	15.0385i	−1.04693	+	0.604448i	−0.125145	+	0.992138i	$0.539940\pi$
$620$		0			0
$621$	51.8906	+	9.14971i	2.08230	+	0.367165i
$622$	0.867988	−	9.92115i	0.0348031	−	0.397802i
$623$	−0.622985	−	7.12076i	−0.0249594	−	0.285287i
$624$	−6.94253	+	1.22416i	−0.277924	+	0.0490054i
$625$		0			0
$626$			22.0297i			0.880486i
$627$	−4.87455	−	28.6201i	−0.194671	−	1.14297i
$628$	2.48053	−	2.48053i	0.0989840	−	0.0989840i
$629$	−8.38814	−	3.05303i	−0.334457	−	0.121732i
$630$		0			0
$631$	−7.77584	−	6.52471i	−0.309551	−	0.259745i	0.474755	−	0.880118i	$-0.342537\pi$
$631$	−7.77584	−	6.52471i	−0.309551	−	0.259745i	−0.784307	+	0.620373i	$0.786981\pi$
$632$	−2.21397	−	0.193697i	−0.0880670	−	0.00770486i
$633$	18.0206	+	25.7361i	0.716254	+	1.02292i
$634$	23.0374	+	13.3007i	0.914933	+	0.528237i
$635$		0			0
$636$	−27.5510	+	10.0277i	−1.09247	+	0.397626i
$637$	6.18849	−	13.2713i	0.245197	−	0.525826i
$638$	−15.7084	−	4.20906i	−0.621902	−	0.166638i
$639$	−14.5978	+	25.2841i	−0.577478	+	1.00022i
$640$		0			0
$641$	−11.5903	−	13.8128i	−0.457791	−	0.545574i	0.486934	−	0.873439i	$-0.338115\pi$
$641$	−11.5903	−	13.8128i	−0.457791	−	0.545574i	−0.944725	+	0.327865i	$0.893671\pi$
$642$	48.0346	−	4.20249i	1.89578	−	0.165859i
$643$	−16.3163	−	11.4248i	−0.643450	−	0.450549i	0.205761	−	0.978602i	$-0.434033\pi$
$643$	−16.3163	−	11.4248i	−0.643450	−	0.450549i	−0.849211	+	0.528054i	$0.822922\pi$
$644$	4.68647	−	12.8760i	0.184673	−	0.507385i
$645$		0			0
$646$	2.39780	−	5.06477i	0.0943403	−	0.199271i
$647$	2.68415	+	2.68415i	0.105525	+	0.105525i	0.757898	−	0.652373i	$-0.226226\pi$
$647$	2.68415	+	2.68415i	0.105525	+	0.105525i	−0.652373	+	0.757898i	$0.726226\pi$
$648$	10.0142	+	21.4754i	0.393393	+	0.843635i
$649$	−0.761570	−	4.31908i	−0.0298942	−	0.169539i
$650$		0			0
$651$	−83.5861	+	70.1371i	−3.27600	+	2.74889i
$652$	11.5811	−	8.10915i	0.453550	−	0.317579i
$653$	6.33751	+	23.6519i	0.248006	+	0.925571i	0.971849	+	0.235606i	$0.0757075\pi$
$653$	6.33751	+	23.6519i	0.248006	+	0.925571i	−0.723843	+	0.689965i	$0.757626\pi$
$654$	15.7958	+	27.3592i	0.617667	+	1.06983i
$655$		0			0
$656$	2.66637	+	7.32580i	0.104104	+	0.286025i
$657$	−10.1616	+	37.9235i	−0.396440	+	1.47953i
$658$	−34.8147	+	9.32857i	−1.35722	+	0.363665i
$659$	2.20718	−	12.5175i	0.0859795	−	0.487614i	−0.911161	−	0.412050i	$-0.864813\pi$
$659$	2.20718	−	12.5175i	0.0859795	−	0.487614i	0.997141	−	0.0755645i	$-0.0240759\pi$
$660$		0			0
$661$	9.46229	−	11.2767i	0.368040	−	0.438613i	−0.549961	−	0.835190i	$-0.685358\pi$
$661$	9.46229	−	11.2767i	0.368040	−	0.438613i	0.918002	+	0.396577i	$0.129802\pi$
$662$	−15.0345	+	21.4715i	−0.584332	+	0.834513i
$663$	−8.21371	+	3.83012i	−0.318994	+	0.148749i
$664$	14.2051			0.551266
$665$		0			0
$666$	−51.4620			−1.99411
$667$	−26.4311	+	12.3250i	−1.02341	+	0.477226i
$668$	−2.52588	+	3.60733i	−0.0977291	+	0.139572i
$669$	−6.53466	+	7.78770i	−0.252645	+	0.301090i
$670$		0			0
$671$	4.03390	−	22.8774i	0.155727	−	0.883172i
$672$	11.5371	−	3.09136i	0.445054	−	0.119252i
$673$	−5.05413	+	18.8623i	−0.194822	+	0.727087i	0.797491	+	0.603331i	$0.206160\pi$
$673$	−5.05413	+	18.8623i	−0.194822	+	0.727087i	−0.992313	+	0.123755i	$0.960506\pi$
$674$	8.17161	+	22.4513i	0.314759	+	0.864792i
$675$		0			0
$676$	4.11334	+	7.12452i	0.158205	+	0.274020i
$677$	−0.0241410	−	0.0900954i	−0.000927814	−	0.00346265i	0.965460	−	0.260550i	$-0.0839039\pi$
$677$	−0.0241410	−	0.0900954i	−0.000927814	−	0.00346265i	−0.966388	+	0.257087i	$0.917237\pi$
$678$	−26.6215	+	18.6406i	−1.02239	+	0.715887i
$679$	14.5834	−	12.2369i	0.559661	−	0.469611i
$680$		0			0
$681$	0.684488	+	3.88192i	0.0262296	+	0.148756i
$682$	−7.96934	−	17.0903i	−0.305162	−	0.654421i
$683$	16.0864	+	16.0864i	0.615529	+	0.615529i	0.944381	−	0.328852i	$-0.106662\pi$
$683$	16.0864	+	16.0864i	0.615529	+	0.615529i	−0.328852	+	0.944381i	$0.606662\pi$
$684$	3.00330	−	32.1660i	0.114834	−	1.22990i
$685$		0			0
$686$	0.376859	−	1.03541i	0.0143885	−	0.0395322i
$687$	61.4119	+	43.0011i	2.34301	+	1.64059i
$688$	−9.90798	+	0.866836i	−0.377738	+	0.0330478i
$689$	−12.7606	−	15.2075i	−0.486142	−	0.579361i
$690$		0			0
$691$	−5.42989	+	9.40485i	−0.206563	+	0.357777i	−0.950630	−	0.310328i	$-0.899561\pi$
$691$	−5.42989	+	9.40485i	−0.206563	+	0.357777i	0.744067	+	0.668105i	$0.232894\pi$
$692$	−21.9222	−	5.87403i	−0.833357	−	0.223297i
$693$	23.9330	−	51.3245i	0.909140	−	1.94966i
$694$	−11.1875	+	4.07192i	−0.424672	+	0.154568i
$695$		0			0
$696$	−22.0155	−	12.7106i	−0.834495	−	0.481796i
$697$	5.74855	+	8.20978i	0.217742	+	0.310968i
$698$	15.7038	+	1.37391i	0.594399	+	0.0520032i
$699$	−10.4241	−	8.74685i	−0.394275	−	0.330836i
$700$		0			0
$701$	20.1386	+	7.32986i	0.760625	+	0.276845i	0.693070	−	0.720871i	$-0.256258\pi$
$701$	20.1386	+	7.32986i	0.760625	+	0.276845i	0.0675556	+	0.997716i	$0.478480\pi$
$702$	−21.9905	+	21.9905i	−0.829978	+	0.829978i
$703$	26.1227	+	15.2858i	0.985235	+	0.576513i
$704$			2.06418i			0.0777966i
$705$		0			0
$706$	−12.3648	+	2.18025i	−0.465357	+	0.0820550i
$707$	−1.87142	−	21.3904i	−0.0703819	−	0.804469i
$708$	0.597509	−	6.82956i	0.0224558	−	0.256671i
$709$	−6.98551	−	1.23173i	−0.262346	−	0.0462587i	0.0409277	−	0.999162i	$-0.486969\pi$
$709$	−6.98551	−	1.23173i	−0.262346	−	0.0462587i	−0.303274	+	0.952903i	$0.598080\pi$
$710$		0			0
$711$	−14.2647	+	8.23573i	−0.534968	+	0.308864i
$712$	1.75009	+	0.816080i	0.0655874	+	0.0305839i
$713$	−30.6478	−	14.2913i	−1.14777	−	0.535214i
$714$	13.2979	−	7.67752i	0.497660	−	0.287324i
$715$		0			0
$716$	9.56418	+	1.68642i	0.357430	+	0.0630246i
$717$	7.19445	−	82.2330i	0.268682	−	3.07105i
$718$	1.42849	+	16.3277i	0.0533109	+	0.609346i
$719$	29.8553	−	5.26429i	1.11341	−	0.196325i	0.413466	−	0.910519i	$-0.364318\pi$
$719$	29.8553	−	5.26429i	1.11341	−	0.196325i	0.699947	+	0.714194i	$0.253207\pi$
$720$		0			0
$721$			7.58705i			0.282556i
$722$	−11.0788	+	15.4357i	−0.412309	+	0.574458i
$723$	−40.5679	+	40.5679i	−1.50874	+	1.50874i
$724$	−9.13538	−	3.32501i	−0.339514	−	0.123573i
$725$		0			0
$726$	−16.6578	−	13.9775i	−0.618227	−	0.518754i
$727$	−29.1194	−	2.54762i	−1.07998	−	0.0944860i	−0.466749	−	0.884390i	$-0.654575\pi$
$727$	−29.1194	−	2.54762i	−1.07998	−	0.0944860i	−0.613231	+	0.789904i	$0.710130\pi$
$728$	4.63873	+	6.62479i	0.171923	+	0.245531i
$729$	32.7608	+	18.9145i	1.21336	+	0.700536i
$730$		0			0
$731$	−12.0150	+	4.37311i	−0.444391	+	0.161745i
$732$	15.3466	−	32.9109i	0.567227	−	1.21642i
$733$	47.5677	+	12.7457i	1.75695	+	0.470774i	0.986088	−	0.166225i	$-0.0531579\pi$
$733$	47.5677	+	12.7457i	1.75695	+	0.470774i	0.770864	+	0.636999i	$0.219825\pi$
$734$	−10.2071	+	17.6792i	−0.376750	+	0.652550i
$735$		0			0
$736$	2.37939	+	2.83564i	0.0877053	+	0.104523i
$737$	5.25263	−	0.459545i	0.193483	−	0.0169276i
$738$	47.3302	+	33.1410i	1.74225	+	1.21994i
$739$	8.11338	−	22.2913i	0.298455	−	0.820000i	−0.696303	−	0.717748i	$-0.745173\pi$
$739$	8.11338	−	22.2913i	0.298455	−	0.820000i	0.994759	−	0.102252i	$-0.0326047\pi$
$740$		0			0
$741$	29.7275	−	7.77990i	1.09207	−	0.285802i
$742$	23.7836	+	23.7836i	0.873123	+	0.873123i
$743$	13.1579	+	28.2173i	0.482718	+	1.03519i	0.985327	+	0.170678i	$0.0545959\pi$
$743$	13.1579	+	28.2173i	0.482718	+	1.03519i	−0.502609	+	0.864514i	$0.667626\pi$
$744$	−5.11862	−	29.0292i	−0.187658	−	1.06426i
$745$		0			0
$746$	26.2310	−	22.0104i	0.960386	−	0.805859i
$747$	86.2411	−	60.3867i	3.15540	−	2.20943i
$748$	0.686817	+	2.56323i	0.0251125	+	0.0937211i
$749$	−27.6580	−	47.9051i	−1.01060	−	1.75042i
$750$		0			0
$751$	1.79339	+	4.92729i	0.0654416	+	0.179799i	0.968103	−	0.250552i	$-0.0806120\pi$
$751$	1.79339	+	4.92729i	0.0654416	+	0.179799i	−0.902662	+	0.430351i	$0.858390\pi$
$752$	2.52010	−	9.40514i	0.0918986	−	0.342970i
$753$	−40.9787	+	10.9802i	−1.49335	+	0.400141i
$754$	2.98897	−	16.9513i	0.108852	−	0.617330i
$755$		0			0
$756$	33.8692	−	40.3637i	1.23181	−	1.46801i
$757$	−13.6281	+	19.4630i	−0.495323	+	0.707395i	−0.986518	−	0.163655i	$-0.947672\pi$
$757$	−13.6281	+	19.4630i	−0.495323	+	0.707395i	0.491194	+	0.871050i	$0.336561\pi$
$758$	29.9676	−	13.9741i	1.08847	−	0.507564i
$759$	24.6547			0.894910
$760$		0			0
$761$	−31.7347			−1.15038			−0.575191	−	0.818019i	$-0.695072\pi$
$761$	−31.7347			−1.15038			−0.575191	+	0.818019i	$0.695072\pi$
$762$	9.76608	−	4.55400i	0.353788	−	0.164974i
$763$	20.7877	−	29.6878i	0.752563	−	1.07477i
$764$	−10.1219	+	12.0628i	−0.366198	+	0.436418i
$765$		0			0
$766$	−2.69459	+	15.2818i	−0.0973596	+	0.552154i
$767$	4.48380	−	1.20143i	0.161901	−	0.0433812i
$768$	−0.835127	+	3.11674i	−0.0301350	+	0.112465i
$769$	8.86948	+	24.3687i	0.319842	+	0.878758i	0.990564	+	0.137050i	$0.0437620\pi$
$769$	8.86948	+	24.3687i	0.319842	+	0.878758i	−0.670722	+	0.741708i	$0.734016\pi$
$770$		0			0
$771$	−21.0410	−	36.4441i	−0.757774	−	1.31250i
$772$	2.48947	+	9.29081i	0.0895978	+	0.334384i
$773$	24.6447	−	17.2564i	0.886409	−	0.620670i	−0.0391668	−	0.999233i	$-0.512470\pi$
$773$	24.6447	−	17.2564i	0.886409	−	0.620670i	0.925576	+	0.378562i	$0.123581\pi$
$774$	−56.4676	+	47.3820i	−2.02969	+	1.70311i
$775$		0			0
$776$	0.893056	+	5.06477i	0.0320588	+	0.181815i
$777$	35.0497	+	75.1643i	1.25740	+	2.69650i
$778$	−8.58633	−	8.58633i	−0.307835	−	0.307835i
$779$	−14.1815	−	30.8812i	−0.508103	−	1.10643i
$780$		0			0
$781$	−2.78106	+	7.64090i	−0.0995141	+	0.273413i
$782$	3.89816	+	2.72952i	0.139398	+	0.0976074i
$783$	−111.719	+	9.77411i	−3.99250	+	0.349298i
$784$	−4.30818	−	5.13429i	−0.153863	−	0.183367i
$785$		0			0
$786$	28.7986	−	49.8806i	1.02721	−	1.77918i
$787$	24.0457	+	6.44302i	0.857136	+	0.229669i	0.660517	−	0.750811i	$-0.270337\pi$
$787$	24.0457	+	6.44302i	0.857136	+	0.229669i	0.196619	+	0.980480i	$0.437004\pi$
$788$	0.477777	−	1.02460i	0.0170201	−	0.0364997i
$789$	19.1670	−	6.97620i	0.682362	−	0.248359i
$790$		0			0
$791$	32.2879	+	18.6414i	1.14803	+	0.662813i
$792$	8.77492	+	12.5319i	0.311803	+	0.445301i
$793$	24.4941	+	2.14296i	0.869812	+	0.0760987i
$794$	10.2533	+	8.60354i	0.363876	+	0.305328i
$795$		0			0
$796$	3.67840	+	1.33883i	0.130377	+	0.0474535i
$797$	9.13482	−	9.13482i	0.323572	−	0.323572i	−0.526564	−	0.850136i	$-0.676520\pi$
$797$	9.13482	−	9.13482i	0.323572	−	0.323572i	0.850136	+	0.526564i	$0.176520\pi$
$798$	−49.0264	+	17.5210i	−1.73551	+	0.620236i
$799$		−	12.5175i		−	0.442839i
$800$		0			0
$801$	14.0942	−	2.48519i	0.497994	−	0.0878098i
$802$	−1.39268	−	15.9184i	−0.0491773	−	0.562100i
$803$	−0.953021	+	10.8931i	−0.0336314	+	0.384409i
$804$	8.11695	+	1.43124i	0.286263	+	0.0504758i
$805$		0			0
$806$	17.2849	−	9.97946i	0.608836	−	0.351511i
$807$	12.6834	+	5.91437i	0.446477	+	0.208196i
$808$	5.25718	+	2.45146i	0.184947	+	0.0862422i
$809$	38.0948	−	21.9941i	1.33934	−	0.773270i	0.352634	−	0.935762i	$-0.385286\pi$
$809$	38.0948	−	21.9941i	1.33934	−	0.773270i	0.986710	+	0.162491i	$0.0519529\pi$
$810$		0			0
$811$	−6.36025	−	1.12148i	−0.223339	−	0.0393806i	0.0608589	−	0.998146i	$-0.480616\pi$
$811$	−6.36025	−	1.12148i	−0.223339	−	0.0393806i	−0.284198	+	0.958766i	$0.591727\pi$
$812$	−2.54176	+	29.0525i	−0.0891983	+	1.01954i
$813$	−3.56375	−	40.7339i	−0.124986	−	1.42860i
$814$	−14.1150	+	2.48886i	−0.494731	+	0.0872343i
$815$		0			0
$816$			4.14814i			0.145214i
$817$	42.7374	−	7.27901i	1.49519	−	0.254660i
$818$	7.06625	−	7.06625i	0.247066	−	0.247066i
$819$	56.3246	+	20.5005i	1.96814	+	0.716344i
$820$		0			0
$821$	19.2690	+	16.1686i	0.672494	+	0.564290i	0.913802	−	0.406159i	$-0.133132\pi$
$821$	19.2690	+	16.1686i	0.672494	+	0.564290i	−0.241308	+	0.970448i	$0.577577\pi$
$822$	−48.6554	−	4.25680i	−1.69705	−	0.148473i
$823$	−24.9100	−	35.5752i	−0.868309	−	1.24007i	−0.969472	−	0.245203i	$-0.921145\pi$
$823$	−24.9100	−	35.5752i	−0.868309	−	1.24007i	0.101163	−	0.994870i	$-0.467744\pi$
$824$	−1.77503	−	1.02481i	−0.0618362	−	0.0357011i
$825$		0			0
$826$	−7.39053	+	2.68993i	−0.257149	+	0.0935947i
$827$	−6.55512	+	14.0575i	−0.227944	+	0.488827i	−0.986701	−	0.162547i	$-0.948029\pi$
$827$	−6.55512	+	14.0575i	−0.227944	+	0.488827i	0.758757	+	0.651374i	$0.225807\pi$
$828$	26.5000	+	7.10065i	0.920938	+	0.246765i
$829$	22.3718	−	38.7490i	0.777003	−	1.34581i	−0.156658	−	0.987653i	$-0.550072\pi$
$829$	22.3718	−	38.7490i	0.777003	−	1.34581i	0.933662	−	0.358156i	$-0.116595\pi$
$830$		0			0
$831$	4.63728	+	5.52649i	0.160865	+	0.191712i
$832$	−2.17648	+	0.190417i	−0.0754558	+	0.00660153i
$833$	−7.05810	−	4.94214i	−0.244549	−	0.171235i
$834$	24.3960	−	67.0276i	0.844766	−	2.32097i
$835$		0			0
$836$	−0.731896	−	8.96773i	−0.0253132	−	0.310155i
$837$	−91.9500	−	91.9500i	−3.17826	−	3.17826i
$838$	−9.14141	−	19.6038i	−0.315785	−	0.677203i
$839$	−9.72552	−	55.1562i	−0.335762	−	1.90420i	−0.419575	−	0.907721i	$-0.637821\pi$
$839$	−9.72552	−	55.1562i	−0.335762	−	1.90420i	0.0838127	−	0.996482i	$-0.473290\pi$
$840$		0			0
$841$	25.3332	−	21.2571i	0.873559	−	0.733003i
$842$	13.2164	−	9.25426i	0.455469	−	0.318923i
$843$	7.95709	+	29.6963i	0.274057	+	1.02279i
$844$	4.86846	+	8.43242i	0.167579	+	0.290256i
$845$		0			0
$846$	−24.6819	−	67.8128i	−0.848580	−	2.33145i
$847$	−6.45654	+	24.0961i	−0.221849	+	0.827953i
$848$	−8.77685	+	2.35175i	−0.301398	+	0.0807594i
$849$	−14.9234	+	84.6348i	−0.512170	+	2.90466i
$850$		0			0
$851$	−16.5214	+	19.6895i	−0.566347	+	0.674946i
$852$	−7.29053	+	10.4120i	−0.249769	+	0.356708i
$853$	−0.171300	+	0.0798783i	−0.00586519	+	0.00273498i	−0.425549	−	0.904936i	$-0.639919\pi$
$853$	−0.171300	+	0.0798783i	−0.00586519	+	0.00273498i	0.419683	+	0.907671i	$0.362141\pi$
$854$	−41.6586			−1.42553
$855$		0			0
$856$	14.9436			0.510760
$857$	−22.1305	+	10.3196i	−0.755963	+	0.352511i	−0.762091	−	0.647470i	$-0.775827\pi$
$857$	−22.1305	+	10.3196i	−0.755963	+	0.352511i	0.00612819	+	0.999981i	$0.498049\pi$
$858$	−8.34651	+	11.9200i	−0.284945	+	0.406944i
$859$	−21.5057	+	25.6295i	−0.733766	+	0.874469i	−0.995890	−	0.0905656i	$-0.971133\pi$
$859$	−21.5057	+	25.6295i	−0.733766	+	0.874469i	0.262124	+	0.965034i	$0.415577\pi$
$860$		0			0
$861$	16.1694	−	91.7010i	0.551051	−	3.12516i
$862$	−0.304049	+	0.0814698i	−0.0103560	+	0.00277487i
$863$	−2.26824	+	8.46520i	−0.0772119	+	0.288159i	−0.993726	−	0.111844i	$-0.964324\pi$
$863$	−2.26824	+	8.46520i	−0.0772119	+	0.288159i	0.916514	+	0.400003i	$0.130991\pi$
$864$	4.86846	+	13.3760i	0.165628	+	0.455060i
$865$		0			0
$866$	3.33868	+	5.78276i	0.113453	+	0.196506i
$867$	−12.8169	−	47.8335i	−0.435286	−	1.62451i
$868$	−27.7006	+	19.3961i	−0.940218	+	0.658348i
$869$	−3.51422	+	2.94878i	−0.119212	+	0.100030i
$870$		0			0
$871$	0.969093	+	5.49600i	0.0328365	+	0.186225i
$872$	4.13776	+	8.87345i	0.140122	+	0.300493i
$873$	26.9524	+	26.9524i	0.912202	+	0.912202i
$874$	−11.3426	−	11.4757i	−0.383668	−	0.388170i
$875$		0			0
$876$	−5.84611	+	16.0621i	−0.197522	+	0.542687i
$877$	−21.0549	−	14.7428i	−0.710973	−	0.497829i	0.161265	−	0.986911i	$-0.448443\pi$
$877$	−21.0549	−	14.7428i	−0.710973	−	0.497829i	−0.872237	+	0.489083i	$0.837332\pi$
$878$	16.7608	−	1.46638i	0.565650	−	0.0494880i
$879$	−13.1450	−	15.6657i	−0.443371	−	0.528390i
$880$		0			0
$881$	18.8097	−	32.5794i	0.633716	−	1.09763i	−0.353069	−	0.935597i	$-0.614862\pi$
$881$	18.8097	−	32.5794i	0.633716	−	1.09763i	0.986786	−	0.162032i	$-0.0518047\pi$
$882$	−47.9816	−	12.8566i	−1.61562	−	0.432905i
$883$	−19.7033	+	42.2538i	−0.663067	+	1.42195i	0.230522	+	0.973067i	$0.425957\pi$
$883$	−19.7033	+	42.2538i	−0.663067	+	1.42195i	−0.893589	+	0.448886i	$0.851821\pi$
$884$	−2.63933	+	0.960637i	−0.0887702	+	0.0323097i
$885$		0			0
$886$	−28.4944	−	16.4512i	−0.957287	−	0.552690i
$887$	−9.61244	−	13.7280i	−0.322754	−	0.460940i	0.624685	−	0.780877i	$-0.285227\pi$
$887$	−9.61244	−	13.7280i	−0.322754	−	0.460940i	−0.947439	+	0.319936i	$0.896338\pi$
$888$	−22.3194	−	1.95270i	−0.748990	−	0.0655282i
$889$	−9.46978	−	7.94609i	−0.317606	−	0.266503i
$890$		0			0
$891$	45.9620	+	16.7288i	1.53979	+	0.560436i
$892$	−2.22784	+	2.22784i	−0.0745937	+	0.0745937i
$893$	−7.61367	+	41.7538i	−0.254782	+	1.39724i
$894$			49.4826i			1.65494i
$895$		0			0
$896$	3.64543	−	0.642788i	0.121785	−	0.0214740i
$897$	2.27436	+	25.9961i	0.0759387	+	0.867984i
$898$	0.728063	−	8.32180i	0.0242958	−	0.277702i
$899$	70.8793	+	12.4979i	2.36396	+	0.416830i
$900$		0			0
$901$	−10.1163	+	5.84067i	−0.337024	+	0.194581i
$902$	14.5845	+	6.80087i	0.485611	+	0.226444i
$903$	107.664	+	50.2045i	3.58283	+	1.67070i
$904$	−8.72254	+	5.03596i	−0.290107	+	0.167494i
$905$		0			0
$906$	20.1150	+	3.54682i	0.668276	+	0.117835i
$907$	−3.62075	+	41.3854i	−0.120225	+	1.37418i	0.661214	+	0.750197i	$0.270041\pi$
$907$	−3.62075	+	41.3854i	−0.120225	+	1.37418i	−0.781439	+	0.623981i	$0.785514\pi$
$908$	0.106472	+	1.21698i	0.00353340	+	0.0403869i
$909$	42.3383	−	7.46538i	1.40427	−	0.247611i
$910$		0			0
$911$			23.1584i			0.767273i	0.923484	+	0.383636i	$0.125328\pi$
$911$			23.1584i			0.767273i	−0.923484	+	0.383636i	$0.874672\pi$
$912$	2.52307	−	13.8366i	0.0835471	−	0.458176i
$913$	20.7337	−	20.7337i	0.686186	−	0.686186i
$914$	10.5810	+	3.85117i	0.349988	+	0.127385i
$915$		0			0
$916$	17.7986	+	14.9348i	0.588082	+	0.493460i
$917$	−65.8244	−	5.75889i	−2.17371	−	0.190175i
$918$	10.4961	+	14.9900i	0.346423	+	0.494744i
$919$	22.4279	+	12.9488i	0.739829	+	0.427141i	0.822007	−	0.569477i	$-0.192854\pi$
$919$	22.4279	+	12.9488i	0.739829	+	0.427141i	−0.0821778	+	0.996618i	$0.526188\pi$
$920$		0			0
$921$	−27.2735	+	9.92674i	−0.898692	+	0.327097i
$922$	3.84739	−	8.25076i	0.126707	−	0.271724i
$923$	−8.31315	−	2.22750i	−0.273631	−	0.0733191i
$924$	12.3274	−	21.3516i	0.405541	−	0.702417i
$925$		0			0
$926$	−3.45249	−	4.11451i	−0.113456	−	0.135211i
$927$	−15.1330	+	1.32396i	−0.497032	+	0.0434847i
$928$	−6.45366	−	4.51890i	−0.211852	−	0.148340i
$929$	−8.24476	+	22.6523i	−0.270502	+	0.743198i	0.727846	+	0.685740i	$0.240521\pi$
$929$	−8.24476	+	22.6523i	−0.270502	+	0.743198i	−0.998348	+	0.0574572i	$0.981701\pi$
$930$		0			0
$931$	20.5371	+	20.7781i	0.673078	+	0.680975i
$932$	−2.98204	−	2.98204i	−0.0976799	−	0.0976799i
$933$	−13.5807	−	29.1239i	−0.444612	−	0.953474i
$934$	−1.60981	−	9.12970i	−0.0526747	−	0.298733i
$935$		0			0
$936$	−12.4042	+	10.4084i	−0.405444	+	0.340208i
$937$	6.30034	−	4.41154i	0.205823	−	0.144119i	−0.466120	−	0.884721i	$-0.654349\pi$
$937$	6.30034	−	4.41154i	0.205823	−	0.144119i	0.671943	+	0.740602i	$0.265460\pi$
$938$	−2.44725	−	9.13327i	−0.0799056	−	0.298212i
$939$	35.5415	+	61.5596i	1.15985	+	2.00892i
$940$		0			0
$941$	5.80706	+	15.9548i	0.189305	+	0.520110i	0.997644	−	0.0686069i	$-0.0218554\pi$
$941$	5.80706	+	15.9548i	0.189305	+	0.520110i	−0.808339	+	0.588717i	$0.799633\pi$
$942$	2.92963	−	10.9335i	0.0954524	−	0.356233i
$943$	27.8747	−	7.46901i	0.907726	−	0.243224i
$944$	0.368946	−	2.09240i	0.0120082	−	0.0681017i
$945$		0			0
$946$	−13.1964	+	15.7269i	−0.429052	+	0.511324i
$947$	17.3490	−	24.7769i	0.563765	−	0.805140i	−0.431523	−	0.902102i	$-0.642024\pi$
$947$	17.3490	−	24.7769i	0.563765	−	0.805140i	0.995288	+	0.0969618i	$0.0309125\pi$
$948$	−6.49919	+	3.03062i	−0.211084	+	0.0984300i
$949$	−11.5736			−0.375696
$950$		0			0
$951$	85.8340			2.78336
$952$	4.31291	−	2.01114i	0.139782	−	0.0651815i
$953$	30.1701	−	43.0873i	0.977304	−	1.39573i	0.0597101	−	0.998216i	$-0.480982\pi$
$953$	30.1701	−	43.0873i	0.977304	−	1.39573i	0.917594	−	0.397519i	$-0.130129\pi$
$954$	−43.2880	+	51.5886i	−1.40150	+	1.67024i
$955$		0			0
$956$	4.44238	−	25.1940i	0.143677	−	0.814832i
$957$	−50.6860	+	13.5813i	−1.63845	+	0.439021i
$958$	−3.65623	+	13.6452i	−0.118128	+	0.440858i
$959$	19.1637	+	52.6519i	0.618829	+	1.70022i
$960$		0			0
$961$	26.2276	+	45.4276i	0.846052	+	1.46541i
$962$	−3.92635	−	14.6533i	−0.126591	−	0.472442i
$963$	90.7242	−	63.5258i	2.92355	−	2.04709i
$964$	−13.6206	+	11.4290i	−0.438689	+	0.368104i
$965$		0			0
$966$	−7.67752	−	43.5414i	−0.247020	−	1.40092i
$967$	−1.38978	−	2.98039i	−0.0446923	−	0.0958430i	0.882694	−	0.469949i	$-0.155728\pi$
$967$	−1.38978	−	2.98039i	−0.0446923	−	0.0958430i	−0.927386	+	0.374106i	$0.877950\pi$
$968$	−4.76531	−	4.76531i	−0.153163	−	0.153163i
$969$	−1.47081	−	18.0214i	−0.0472492	−	0.578931i
$970$		0			0
$971$	11.7426	−	32.2626i	0.376839	−	1.03536i	−0.595820	−	0.803118i	$-0.703173\pi$
$971$	11.7426	−	32.2626i	0.376839	−	1.03536i	0.972659	−	0.232238i	$-0.0746050\pi$
$972$	27.6502	+	19.3609i	0.886880	+	0.621000i
$973$	−81.5179	+	7.13189i	−2.61334	+	0.228638i
$974$	2.61413	+	3.11540i	0.0837622	+	0.0998239i
$975$		0			0
$976$	5.62701	−	9.74627i	0.180116	−	0.311970i
$977$	−15.4183	−	4.13133i	−0.493276	−	0.132173i	0.00360160	−	0.999994i	$-0.498854\pi$
$977$	−15.4183	−	4.13133i	−0.493276	−	0.132173i	−0.496878	+	0.867821i	$0.665520\pi$
$978$	19.2792	−	41.3443i	0.616480	−	1.32205i
$979$	3.74557	−	1.36327i	0.119709	−	0.0435704i
$980$		0			0
$981$	62.8423	+	36.2820i	2.00640	+	1.15840i
$982$	−1.61628	−	2.30829i	−0.0515775	−	0.0736603i
$983$	−30.3910	−	2.65887i	−0.969323	−	0.0848048i	−0.408516	−	0.912751i	$-0.633954\pi$
$983$	−30.3910	−	2.65887i	−0.969323	−	0.0848048i	−0.560807	+	0.827946i	$0.689509\pi$
$984$	19.2699	+	16.1694i	0.614302	+	0.515461i
$985$		0			0
$986$	−9.51754	−	3.46410i	−0.303100	−	0.110319i
$987$	−82.2356	+	82.2356i	−2.61759	+	2.61759i
$988$	9.38810	−	1.59897i	0.298675	−	0.0508701i
$989$			36.8161i			1.17069i
$990$		0			0
$991$	−16.3307	+	2.87954i	−0.518761	+	0.0914716i	−0.426898	−	0.904300i	$-0.640394\pi$
$991$	−16.3307	+	2.87954i	−0.518761	+	0.0914716i	−0.0918638	+	0.995772i	$0.529282\pi$
$992$	−0.796201	−	9.10062i	−0.0252794	−	0.288945i
$993$	−7.37139	+	84.2554i	−0.233924	+	2.67376i
$994$	14.3602	+	2.53209i	0.455478	+	0.0803130i
$995$		0			0
$996$	39.6946	−	22.9177i	1.25777	−	0.726176i
$997$	27.3622	+	12.7592i	0.866570	+	0.404088i	0.804478	−	0.593982i	$-0.202445\pi$
$997$	27.3622	+	12.7592i	0.866570	+	0.404088i	0.0620919	+	0.998070i	$0.480223\pi$
$998$	2.36003	+	1.10050i	0.0747055	+	0.0348358i
$999$	−85.5959	+	49.4188i	−2.70813	+	1.56354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.a.357.2	yes	24
5.2	odd	4	inner	950.2.bb.a.243.2	yes	24
5.3	odd	4	inner	950.2.bb.a.243.1	✓	24
5.4	even	2	inner	950.2.bb.a.357.1	yes	24
19.14	odd	18	inner	950.2.bb.a.907.1	yes	24
95.14	odd	18	inner	950.2.bb.a.907.2	yes	24
95.33	even	36	inner	950.2.bb.a.793.2	yes	24
95.52	even	36	inner	950.2.bb.a.793.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.a.243.1	✓	24	5.3	odd	4	inner
950.2.bb.a.243.2	yes	24	5.2	odd	4	inner
950.2.bb.a.357.1	yes	24	5.4	even	2	inner
950.2.bb.a.357.2	yes	24	1.1	even	1	trivial
950.2.bb.a.793.1	yes	24	95.52	even	36	inner
950.2.bb.a.793.2	yes	24	95.33	even	36	inner
950.2.bb.a.907.1	yes	24	19.14	odd	18	inner
950.2.bb.a.907.2	yes	24	95.14	odd	18	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.906308 - 0.422618i) q^{2} +(1.85075 - 2.64314i) q^{3} +(0.642788 - 0.766044i) q^{4} +(0.560307 - 3.17766i) q^{6} +(-3.57554 + 0.958062i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-2.53487 - 6.96451i) q^{9} +O(q^{10})\)	\(q+(0.906308 - 0.422618i) q^{2} +(1.85075 - 2.64314i) q^{3} +(0.642788 - 0.766044i) q^{4} +(0.560307 - 3.17766i) q^{6} +(-3.57554 + 0.958062i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-2.53487 - 6.96451i) q^{9} +(-1.03209 - 1.78763i) q^{11} +(-0.835127 - 3.11674i) q^{12} +(1.78968 - 1.25315i) q^{13} +(-2.83564 + 2.37939i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(-0.543308 - 1.16513i) q^{17} +(-5.24070 - 5.24070i) q^{18} +(1.10359 + 4.21688i) q^{19} +(-4.08512 + 11.2238i) q^{21} +(-1.69088 - 1.18396i) q^{22} +(-3.68758 + 0.322621i) q^{23} +(-2.07407 - 2.47178i) q^{24} +(1.09240 - 1.89209i) q^{26} +(-13.7494 - 3.68414i) q^{27} +(-1.56439 + 3.35485i) q^{28} +(7.40333 - 2.69459i) q^{29} +(7.91147 + 4.56769i) q^{31} +(-0.573576 - 0.819152i) q^{32} +(-6.63510 - 0.580496i) q^{33} +(-0.984808 - 0.826352i) q^{34} +(-6.96451 - 2.53487i) q^{36} +(4.90984 - 4.90984i) q^{37} +(2.78232 + 3.35540i) q^{38} -7.04963i q^{39} +(-7.67752 + 1.35375i) q^{41} +(1.04100 + 11.8986i) q^{42} +(0.866836 - 9.90798i) q^{43} +(-2.03282 - 0.358441i) q^{44} +(-3.20574 + 1.85083i) q^{46} +(8.82464 + 4.11500i) q^{47} +(-2.92437 - 1.36365i) q^{48} +(5.80439 - 3.35117i) q^{49} +(-4.08512 - 0.720317i) q^{51} +(0.190417 - 2.17648i) q^{52} +(-0.791938 - 9.05189i) q^{53} +(-14.0182 + 2.47178i) q^{54} +3.70167i q^{56} +(13.1883 + 4.88744i) q^{57} +(5.57091 - 5.57091i) q^{58} +(1.99654 + 0.726682i) q^{59} +(8.62108 + 7.23395i) q^{61} +(9.10062 + 0.796201i) q^{62} +(15.7360 + 22.4733i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-6.25877 + 2.27801i) q^{66} +(-1.07953 + 2.31505i) q^{67} +(-1.24177 - 0.332731i) q^{68} +(-5.97205 + 10.3439i) q^{69} +(-2.53209 - 3.01763i) q^{71} +(-7.38327 + 0.645953i) q^{72} +(-4.33934 - 3.03844i) q^{73} +(2.37484 - 6.52481i) q^{74} +(3.93969 + 1.86516i) q^{76} +(5.40293 + 5.40293i) q^{77} +(-2.97930 - 6.38913i) q^{78} +(-0.385920 - 2.18866i) q^{79} +(-18.1518 + 15.2312i) q^{81} +(-6.38607 + 4.47158i) q^{82} +(3.67656 + 13.7211i) q^{83} +(5.97205 + 10.3439i) q^{84} +(-3.40167 - 9.34602i) q^{86} +(6.57951 - 24.5551i) q^{87} +(-1.99384 + 0.534249i) q^{88} +(-0.335316 + 1.90167i) q^{89} +(-5.19846 + 6.19529i) q^{91} +(-2.12319 + 3.03223i) q^{92} +(26.7152 - 12.4575i) q^{93} +9.73692 q^{94} -3.22668 q^{96} +(-4.66105 + 2.17348i) q^{97} +(3.84430 - 5.49023i) q^{98} +(-9.83375 + 11.7194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 36 q^{6}+O(q^{10}) \) 24 * q + 36 * q^6	\( 24 q + 36 q^{6} + 12 q^{11} - 12 q^{21} + 12 q^{26} + 108 q^{31} - 36 q^{36} - 84 q^{41} - 36 q^{46} - 12 q^{51} - 12 q^{61} - 60 q^{66} - 24 q^{71} + 72 q^{76} - 216 q^{81} + 12 q^{86} - 12 q^{91} - 24 q^{96}+O(q^{100}) \) 24 * q + 36 * q^6 + 12 * q^11 - 12 * q^21 + 12 * q^26 + 108 * q^31 - 36 * q^36 - 84 * q^41 - 36 * q^46 - 12 * q^51 - 12 * q^61 - 60 * q^66 - 24 * q^71 + 72 * q^76 - 216 * q^81 + 12 * q^86 - 12 * q^91 - 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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