LMFDB - Embedded newform 950.2.bb.a.243.1

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			243.1
Character	$\chi$	$=$	950.243
Dual form			950.2.bb.a.907.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.422618 - 0.906308i) q^{2} +(2.64314 + 1.85075i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(0.560307 - 3.17766i) q^{6} +(0.958062 + 3.57554i) q^{7} +(0.965926 + 0.258819i) q^{8} +(2.53487 + 6.96451i) q^{9} +O(q^{10})$	\(q+(-0.422618 - 0.906308i) q^{2} +(2.64314 + 1.85075i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(0.560307 - 3.17766i) q^{6} +(0.958062 + 3.57554i) q^{7} +(0.965926 + 0.258819i) q^{8} +(2.53487 + 6.96451i) q^{9} +(-1.03209 - 1.78763i) q^{11} +(-3.11674 + 0.835127i) q^{12} +(1.25315 + 1.78968i) q^{13} +(2.83564 - 2.37939i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(-1.16513 + 0.543308i) q^{17} +(5.24070 - 5.24070i) q^{18} +(-1.10359 - 4.21688i) q^{19} +(-4.08512 + 11.2238i) q^{21} +(-1.18396 + 1.69088i) q^{22} +(-0.322621 - 3.68758i) q^{23} +(2.07407 + 2.47178i) q^{24} +(1.09240 - 1.89209i) q^{26} +(-3.68414 + 13.7494i) q^{27} +(-3.35485 - 1.56439i) q^{28} +(-7.40333 + 2.69459i) q^{29} +(7.91147 + 4.56769i) q^{31} +(-0.819152 + 0.573576i) q^{32} +(0.580496 - 6.63510i) q^{33} +(0.984808 + 0.826352i) q^{34} +(-6.96451 - 2.53487i) q^{36} +(-4.90984 - 4.90984i) q^{37} +(-3.35540 + 2.78232i) q^{38} +7.04963i q^{39} +(-7.67752 + 1.35375i) q^{41} +(11.8986 - 1.04100i) q^{42} +(9.90798 + 0.866836i) q^{43} +(2.03282 + 0.358441i) q^{44} +(-3.20574 + 1.85083i) q^{46} +(4.11500 - 8.82464i) q^{47} +(1.36365 - 2.92437i) q^{48} +(-5.80439 + 3.35117i) q^{49} +(-4.08512 - 0.720317i) q^{51} +(-2.17648 - 0.190417i) q^{52} +(9.05189 - 0.791938i) q^{53} +(14.0182 - 2.47178i) q^{54} +3.70167i q^{56} +(4.88744 - 13.1883i) q^{57} +(5.57091 + 5.57091i) q^{58} +(-1.99654 - 0.726682i) q^{59} +(8.62108 + 7.23395i) q^{61} +(0.796201 - 9.10062i) q^{62} +(-22.4733 + 15.7360i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-6.25877 + 2.27801i) q^{66} +(2.31505 + 1.07953i) q^{67} +(0.332731 - 1.24177i) q^{68} +(5.97205 - 10.3439i) q^{69} +(-2.53209 - 3.01763i) q^{71} +(0.645953 + 7.38327i) q^{72} +(3.03844 - 4.33934i) q^{73} +(-2.37484 + 6.52481i) q^{74} +(3.93969 + 1.86516i) q^{76} +(5.40293 - 5.40293i) q^{77} +(6.38913 - 2.97930i) q^{78} +(0.385920 + 2.18866i) q^{79} +(-18.1518 + 15.2312i) q^{81} +(4.47158 + 6.38607i) q^{82} +(-13.7211 + 3.67656i) q^{83} +(-5.97205 - 10.3439i) q^{84} +(-3.40167 - 9.34602i) q^{86} +(-24.5551 - 6.57951i) q^{87} +(-0.534249 - 1.99384i) q^{88} +(0.335316 - 1.90167i) q^{89} +(-5.19846 + 6.19529i) q^{91} +(3.03223 + 2.12319i) q^{92} +(12.4575 + 26.7152i) q^{93} -9.73692 q^{94} -3.22668 q^{96} +(2.17348 + 4.66105i) q^{97} +(5.49023 + 3.84430i) 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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.422618	−	0.906308i	−0.298836	−	0.640856i
$2$	−0.422618	−	0.906308i	−0.298836	−	0.640856i
$3$	2.64314	+	1.85075i	1.52602	+	1.06853i	0.971698	+	0.236227i	$0.0759111\pi$
$3$	2.64314	+	1.85075i	1.52602	+	1.06853i	0.554321	+	0.832303i	$0.312978\pi$
$4$	−0.642788	+	0.766044i	−0.321394	+	0.383022i
$5$		0			0
$5$		0			0
$6$	0.560307	−	3.17766i	0.228745	−	1.29727i
$7$	0.958062	+	3.57554i	0.362113	+	1.35143i	0.871292	+	0.490765i	$0.163282\pi$
$7$	0.958062	+	3.57554i	0.362113	+	1.35143i	−0.509179	+	0.860661i	$0.670051\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$	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	$0.934060\pi$
$12$	−3.11674	+	0.835127i	−0.899724	+	0.241080i
$13$	1.25315	+	1.78968i	0.347560	+	0.496367i	0.954430	−	0.298434i	$-0.0964642\pi$
$13$	1.25315	+	1.78968i	0.347560	+	0.496367i	−0.606870	+	0.794801i	$0.707575\pi$
$14$	2.83564	−	2.37939i	0.757857	−	0.635917i
$15$		0			0
$16$	−0.173648	−	0.984808i	−0.0434120	−	0.246202i
$17$	−1.16513	+	0.543308i	−0.282585	+	0.131771i	−0.558743	−	0.829341i	$-0.688716\pi$
$17$	−1.16513	+	0.543308i	−0.282585	+	0.131771i	0.276159	+	0.961112i	$0.410939\pi$
$18$	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
$22$	−1.18396	+	1.69088i	−0.252422	+	0.360496i
$23$	−0.322621	−	3.68758i	−0.0672712	−	0.768914i	−0.952655	−	0.304053i	$-0.901660\pi$
$23$	−0.322621	−	3.68758i	−0.0672712	−	0.768914i	0.885384	−	0.464861i	$-0.153896\pi$
$24$	2.07407	+	2.47178i	0.423368	+	0.504550i
$25$		0			0
$26$	1.09240	−	1.89209i	0.214237	−	0.371069i
$27$	−3.68414	+	13.7494i	−0.709013	+	2.64607i
$28$	−3.35485	−	1.56439i	−0.634007	−	0.295642i
$29$	−7.40333	+	2.69459i	−1.37476	+	0.500373i	−0.920587	−	0.390538i	$-0.872289\pi$
$29$	−7.40333	+	2.69459i	−1.37476	+	0.500373i	−0.454178	+	0.890911i	$0.650067\pi$
$30$		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	$0.360428\pi$
$32$	−0.819152	+	0.573576i	−0.144807	+	0.101395i
$33$	0.580496	−	6.63510i	0.101051	−	1.15502i
$34$	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	$-0.443350\pi$
$37$	−4.90984	−	4.90984i	−0.807173	−	0.807173i	−0.984205	+	0.177032i	$0.943350\pi$
$38$	−3.35540	+	2.78232i	−0.544317	+	0.451352i
$39$			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	$0.652778\pi$
$42$	11.8986	−	1.04100i	1.83600	−	0.160629i
$43$	9.90798	+	0.866836i	1.51095	+	0.132191i	0.812288	−	0.583257i	$-0.198222\pi$
$43$	9.90798	+	0.866836i	1.51095	+	0.132191i	0.698666	+	0.715448i	$0.253778\pi$
$44$	2.03282	+	0.358441i	0.306459	+	0.0540370i
$45$		0			0
$46$	−3.20574	+	1.85083i	−0.472660	+	0.272890i
$47$	4.11500	−	8.82464i	0.600234	−	1.28721i	−0.337980	−	0.941153i	$-0.609744\pi$
$47$	4.11500	−	8.82464i	0.600234	−	1.28721i	0.938215	−	0.346054i	$-0.112478\pi$
$48$	1.36365	−	2.92437i	0.196827	−	0.422096i
$49$	−5.80439	+	3.35117i	−0.829199	+	0.478738i
$50$		0			0
$51$	−4.08512	−	0.720317i	−0.572032	−	0.100865i
$52$	−2.17648	−	0.190417i	−0.301823	−	0.0264061i
$53$	9.05189	−	0.791938i	1.24337	−	0.108781i	0.553585	−	0.832793i	$-0.313259\pi$
$53$	9.05189	−	0.791938i	1.24337	−	0.108781i	0.689788	+	0.724012i	$0.257704\pi$
$54$	14.0182	−	2.47178i	1.90763	−	0.336367i
$55$		0			0
$56$			3.70167i			0.494656i
$57$	4.88744	−	13.1883i	0.647357	−	1.74683i
$58$	5.57091	+	5.57091i	0.731497	+	0.731497i
$59$	−1.99654	−	0.726682i	−0.259928	−	0.0946059i	0.208769	−	0.977965i	$-0.433054\pi$
$59$	−1.99654	−	0.726682i	−0.259928	−	0.0946059i	−0.468697	+	0.883359i	$0.655276\pi$
$60$		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	$0.466151\pi$
$62$	0.796201	−	9.10062i	0.101118	−	1.15578i
$63$	−22.4733	+	15.7360i	−2.83137	+	1.98254i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$		0			0
$66$	−6.25877	+	2.27801i	−0.770401	+	0.280403i
$67$	2.31505	+	1.07953i	0.282829	+	0.131885i	0.558856	−	0.829265i	$-0.311240\pi$
$67$	2.31505	+	1.07953i	0.282829	+	0.131885i	−0.276028	+	0.961150i	$0.589018\pi$
$68$	0.332731	−	1.24177i	0.0403496	−	0.150587i
$69$	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	$0.852878\pi$
$72$	0.645953	+	7.38327i	0.0761262	+	0.870127i
$73$	3.03844	−	4.33934i	0.355623	−	0.507882i	−0.600985	−	0.799260i	$-0.705225\pi$
$73$	3.03844	−	4.33934i	0.355623	−	0.507882i	0.956608	+	0.291378i	$0.0941139\pi$
$74$	−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
$78$	6.38913	−	2.97930i	0.723427	−	0.337340i
$79$	0.385920	+	2.18866i	0.0434194	+	0.246244i	0.998791	−	0.0491638i	$-0.0156556\pi$
$79$	0.385920	+	2.18866i	0.0434194	+	0.246244i	−0.955371	+	0.295408i	$0.904545\pi$
$80$		0			0
$81$	−18.1518	+	15.2312i	−2.01687	+	1.69235i
$82$	4.47158	+	6.38607i	0.493803	+	0.705224i
$83$	−13.7211	+	3.67656i	−1.50609	+	0.403555i	−0.915133	−	0.403151i	$-0.867915\pi$
$83$	−13.7211	+	3.67656i	−1.50609	+	0.403555i	−0.590953	+	0.806706i	$0.701248\pi$
$84$	−5.97205	−	10.3439i	−0.651604	−	1.12861i
$85$		0			0
$86$	−3.40167	−	9.34602i	−0.366812	−	1.00781i
$87$	−24.5551	−	6.57951i	−2.63258	−	0.705398i
$88$	−0.534249	−	1.99384i	−0.0569511	−	0.212544i
$89$	0.335316	−	1.90167i	0.0355435	−	0.201577i	−0.961865	−	0.273525i	$-0.911810\pi$
$89$	0.335316	−	1.90167i	0.0355435	−	0.201577i	0.997408	+	0.0719479i	$0.0229215\pi$
$90$		0			0
$91$	−5.19846	+	6.19529i	−0.544947	+	0.649443i
$92$	3.03223	+	2.12319i	0.316132	+	0.221358i
$93$	12.4575	+	26.7152i	1.29178	+	2.77024i
$94$	−9.73692			−1.00429
$95$		0			0
$96$	−3.22668			−0.329322
$97$	2.17348	+	4.66105i	0.220684	+	0.473258i	0.985214	−	0.171330i	$-0.0548065\pi$
$97$	2.17348	+	4.66105i	0.220684	+	0.473258i	−0.764530	+	0.644589i	$0.777029\pi$
$98$	5.49023	+	3.84430i	0.554597	+	0.388333i
$99$	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	$0.962368\pi$
$102$	1.07362	+	4.00680i	0.106304	+	0.396732i
$103$	1.97979	+	0.530483i	0.195075	+	0.0522701i	0.355033	−	0.934854i	$-0.384469\pi$
$103$	1.97979	+	0.530483i	0.195075	+	0.0522701i	−0.159959	+	0.987124i	$0.551136\pi$
$104$	0.747243	+	2.05303i	0.0732732	+	0.201316i
$105$		0			0
$106$	−4.54323	−	7.86911i	−0.441278	−	0.764316i
$107$	14.4344	−	3.86768i	1.39542	−	0.373903i	0.518724	−	0.854942i	$-0.326407\pi$
$107$	14.4344	−	3.86768i	1.39542	−	0.373903i	0.876699	+	0.481039i	$0.159740\pi$
$108$	−8.16453	−	11.6602i	−0.785632	−	1.12200i
$109$	7.50016	−	6.29339i	0.718386	−	0.602797i	−0.208553	−	0.978011i	$-0.566875\pi$
$109$	7.50016	−	6.29339i	0.718386	−	0.602797i	0.926938	+	0.375214i	$0.122431\pi$
$110$		0			0
$111$	−3.89053	−	22.0643i	−0.369273	−	2.09425i
$112$	3.35485	−	1.56439i	0.317003	−	0.147821i
$113$	7.12192	−	7.12192i	0.669974	−	0.669974i	−0.287736	−	0.957710i	$-0.592902\pi$
$113$	7.12192	−	7.12192i	0.669974	−	0.669974i	0.957710	+	0.287736i	$0.0929025\pi$
$114$	−14.0182	+	1.14409i	−1.31292	+	0.107153i
$115$		0			0
$116$	2.69459	−	7.40333i	0.250187	−	0.687382i
$117$	−9.28766	+	13.2641i	−0.858644	+	1.22627i
$118$	0.185178	+	2.11659i	0.0170470	+	0.194848i
$119$	−3.05888	−	3.64543i	−0.280407	−	0.334176i
$120$		0			0
$121$	3.36959	−	5.83629i	0.306326	−	0.530572i
$122$	2.91276	−	10.8706i	0.263708	−	0.984173i
$123$	−22.7982	−	10.6310i	−2.05565	−	0.958564i
$124$	−8.58445	+	3.12449i	−0.770907	+	0.280587i
$125$		0			0
$126$	23.7592	+	13.7174i	2.11664	+	1.22204i
$127$	2.73560	−	1.91549i	0.242746	−	0.169972i	−0.445873	−	0.895096i	$-0.647107\pi$
$127$	2.73560	−	1.91549i	0.242746	−	0.169972i	0.688618	+	0.725124i	$0.258218\pi$
$128$	0.0871557	−	0.996195i	0.00770355	−	0.0880520i
$129$	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
$133$	14.0203	−	7.98596i	1.21571	−	0.692470i
$134$		−	2.55438i		−	0.220665i
$135$		0			0
$136$	−1.26604	+	0.223238i	−0.108562	+	0.0191425i
$137$	−15.0791	+	1.31925i	−1.28829	+	0.112711i	−0.710631	−	0.703565i	$-0.751590\pi$
$137$	−15.0791	+	1.31925i	−1.28829	+	0.112711i	−0.577662	+	0.816276i	$0.696035\pi$
$138$	−11.8986	−	1.04100i	−1.01288	−	0.0886155i
$139$	−21.7702	−	3.83868i	−1.84653	−	0.325592i	−0.862839	−	0.505479i	$-0.831316\pi$
$139$	−21.7702	−	3.83868i	−1.84653	−	0.325592i	−0.983687	+	0.179886i	$0.942427\pi$
$140$		0			0
$141$	27.2087	−	15.7090i	2.29139	−	1.32293i
$142$	−1.66479	+	3.57016i	−0.139706	+	0.299601i
$143$	1.90592	−	4.08727i	0.159381	−	0.341794i
$144$	6.41852	−	3.70574i	0.534877	−	0.308811i
$145$		0			0
$146$	−5.21688	−	0.919877i	−0.431752	−	0.0761296i
$147$	−21.5440	−	1.88486i	−1.77692	−	0.155460i
$148$	6.91714	−	0.605171i	0.568585	−	0.0497448i
$149$	15.1025	−	2.66297i	1.23724	−	0.218159i	0.483508	−	0.875340i	$-0.339362\pi$
$149$	15.1025	−	2.66297i	1.23724	−	0.218159i	0.753733	+	0.657181i	$0.228251\pi$
$150$		0			0
$151$			6.33012i			0.515138i	0.966260	+	0.257569i	$0.0829215\pi$
$151$			6.33012i			0.515138i	−0.966260	+	0.257569i	$0.917078\pi$
$152$	0.0254230	−	4.35882i	0.00206208	−	0.353547i
$153$	−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
$157$	0.305743	−	3.49465i	0.0244009	−	0.278904i	−0.974185	−	0.225749i	$-0.927517\pi$
$157$	0.305743	−	3.49465i	0.0244009	−	0.278904i	0.998586	−	0.0531542i	$-0.0169275\pi$
$158$	1.82051	−	1.27473i	0.144832	−	0.101412i
$159$	25.3911	+	14.6596i	2.01365	+	1.16258i
$160$		0			0
$161$	12.8760	−	4.68647i	1.01477	−	0.369346i
$162$	21.4754	+	10.0142i	1.68727	+	0.786787i
$163$	−3.65915	+	13.6561i	−0.286607	+	1.06963i	0.661050	+	0.750341i	$0.270111\pi$
$163$	−3.65915	+	13.6561i	−0.286607	+	1.06963i	−0.947657	+	0.319290i	$0.896556\pi$
$164$	3.89798	−	6.75150i	0.304381	−	0.527203i
$165$		0			0
$166$	9.13088	+	10.8818i	0.708694	+	0.844588i
$167$	0.383811	+	4.38698i	0.0297002	+	0.339474i	0.996478	+	0.0838559i	$0.0267235\pi$
$167$	0.383811	+	4.38698i	0.0297002	+	0.339474i	−0.966778	+	0.255618i	$0.917721\pi$
$168$	−6.85085	+	9.78403i	−0.528555	+	0.754855i
$169$	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
$173$	20.5691	−	9.59154i	1.56384	−	0.729232i	0.568236	−	0.822866i	$-0.307626\pi$
$173$	20.5691	−	9.59154i	1.56384	−	0.729232i	0.995607	+	0.0936344i	$0.0298485\pi$
$174$	4.41436	+	25.0351i	0.334652	+	1.89790i
$175$		0			0
$176$	−1.58125	+	1.32683i	−0.119191	+	0.100013i
$177$	−3.93224	−	5.61582i	−0.295565	−	0.422111i
$178$	−1.86521	+	0.499782i	−0.139804	+	0.0374603i
$179$	−4.85586	−	8.41060i	−0.362944	−	0.628638i	0.625500	−	0.780224i	$-0.284895\pi$
$179$	−4.85586	−	8.41060i	−0.362944	−	0.628638i	−0.988444	+	0.151587i	$0.951562\pi$
$180$		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	$-0.228779\pi$
$182$	7.81180	+	2.09317i	0.579049	+	0.155156i
$183$	9.39853	+	35.0758i	0.694760	+	2.59288i
$184$	0.642788	−	3.64543i	0.0473869	−	0.268745i
$185$		0			0
$186$	18.9474	−	22.5807i	1.38929	−	1.65570i
$187$	2.17375	+	1.52207i	0.158960	+	0.111305i
$188$	4.11500	+	8.82464i	0.300117	+	0.643603i
$189$	−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	$0.692942\pi$
$192$	1.36365	+	2.92437i	0.0984133	+	0.211048i
$193$	−7.87906	−	5.51698i	−0.567147	−	0.397121i	0.254538	−	0.967063i	$-0.418077\pi$
$193$	−7.87906	−	5.51698i	−0.567147	−	0.397121i	−0.821685	+	0.569942i	$0.806966\pi$
$194$	3.30579	−	3.93969i	0.237342	−	0.282853i
$195$		0			0
$196$	1.16385	−	6.60051i	0.0831320	−	0.471465i
$197$	−0.292599	−	1.09199i	−0.0208468	−	0.0778014i	0.954719	−	0.297510i	$-0.0961561\pi$
$197$	−0.292599	−	1.09199i	−0.0208468	−	0.0778014i	−0.975566	+	0.219708i	$0.929489\pi$
$198$	−14.7773	−	3.95957i	−1.05018	−	0.281394i
$199$	−1.33883	−	3.67840i	−0.0949069	−	0.260755i	0.883151	−	0.469089i	$-0.155418\pi$
$199$	−1.33883	−	3.67840i	−0.0949069	−	0.260755i	−0.978058	+	0.208335i	$0.933196\pi$
$200$		0			0
$201$	4.12108	+	7.13792i	0.290679	+	0.503470i
$202$	5.60301	−	1.50132i	0.394226	−	0.105633i
$203$	−16.7275	−	23.8893i	−1.17404	−	1.67670i
$204$	3.17766	−	2.66637i	0.222481	−	0.186684i
$205$		0			0
$206$	−0.355914	−	2.01849i	−0.0247977	−	0.140635i
$207$	24.8644	−	11.5944i	1.72819	−	0.805870i
$208$	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	$0.219901\pi$
$212$	−5.21178	+	7.44320i	−0.357947	+	0.511201i
$213$	−1.10781	−	12.6623i	−0.0759056	−	0.867605i
$214$	−9.60554	−	11.4474i	−0.656621	−	0.782530i
$215$		0			0
$216$	−7.11721	+	12.3274i	−0.484265	+	0.838771i
$217$	−8.75226	+	32.6639i	−0.594142	+	2.21737i
$218$	−8.87345	−	4.13776i	−0.600986	−	0.280244i
$219$	16.0621	−	5.84611i	1.08537	−	0.395044i
$220$		0			0
$221$	−2.43242	−	1.40436i	−0.163622	−	0.0944673i
$222$	−18.3528	+	12.8508i	−1.23176	+	0.862488i
$223$	0.274597	−	3.13866i	0.0183884	−	0.210180i	−0.981442	−	0.191759i	$-0.938581\pi$
$223$	0.274597	−	3.13866i	0.0183884	−	0.210180i	0.999830	−	0.0184205i	$-0.00586376\pi$
$224$	−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	$-0.237092\pi$
$227$	0.863822	+	0.863822i	0.0573339	+	0.0573339i	−0.677858	+	0.735192i	$0.737092\pi$
$228$	6.96123	+	12.2213i	0.461019	+	0.809373i
$229$		−	23.2344i		−	1.53537i	−0.640825	−	0.767687i	$-0.721408\pi$
$229$		−	23.2344i		−	1.53537i	0.640825	−	0.767687i	$-0.278592\pi$
$230$		0			0
$231$	24.2802	−	4.28125i	1.59752	−	0.281686i
$232$	−7.84848	+	0.686653i	−0.515278	+	0.0450810i
$233$	4.20119	+	0.367557i	0.275229	+	0.0240794i	0.223935	−	0.974604i	$-0.428110\pi$
$233$	4.20119	+	0.367557i	0.275229	+	0.0240794i	0.0512945	+	0.998684i	$0.483665\pi$
$234$	15.9465	+	2.81180i	1.04246	+	0.183813i
$235$		0			0
$236$	1.84002	−	1.06234i	0.119775	−	0.0691523i
$237$	−3.03062	+	6.49919i	−0.196860	+	0.422168i
$238$	−2.01114	+	4.31291i	−0.130363	+	0.279564i
$239$	−22.1552	+	12.7913i	−1.43310	+	0.827402i	−0.997356	−	0.0726674i	$-0.976849\pi$
$239$	−22.1552	+	12.7913i	−1.43310	+	0.827402i	−0.435746	+	0.900070i	$0.643515\pi$
$240$		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	$0.749647\pi$
$242$	−6.71353	−	0.587357i	−0.431562	−	0.0377568i
$243$	−33.6262	+	2.94191i	−2.15712	+	0.188724i
$244$	−11.0830	+	1.95424i	−0.709519	+	0.125107i
$245$		0			0
$246$			25.1551i			1.60383i
$247$	6.16390	−	7.25944i	0.392199	−	0.461907i
$248$	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	$0.858422\pi$
$252$	2.39110	−	27.3304i	0.150625	−	1.72165i
$253$	−6.25906	+	4.38264i	−0.393504	+	0.275534i
$254$	−2.89214	−	1.66978i	−0.181469	−	0.104771i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−11.8200	−	5.51174i	−0.737309	−	0.343813i	0.0174210	−	0.999848i	$-0.494454\pi$
$257$	−11.8200	−	5.51174i	−0.737309	−	0.343813i	−0.754730	+	0.656035i	$0.772232\pi$
$258$	8.30603	−	30.9985i	0.517111	−	1.92988i
$259$	12.8514	−	22.2592i	0.798546	−	1.38312i
$260$		0			0
$261$	−37.5330	−	44.7301i	−2.32324	−	2.76872i
$262$	−1.55576	−	17.7824i	−0.0961149	−	1.09860i
$263$	−3.62579	+	5.17817i	−0.223576	+	0.319299i	−0.915232	−	0.402928i	$-0.867993\pi$
$263$	−3.62579	+	5.17817i	−0.223576	+	0.319299i	0.691656	+	0.722227i	$0.256881\pi$
$264$	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
$268$	−2.31505	+	1.07953i	−0.141414	+	0.0659426i
$269$	−0.753138	−	4.27126i	−0.0459196	−	0.260423i	0.953202	−	0.302335i	$-0.0977662\pi$
$269$	−0.753138	−	4.27126i	−0.0459196	−	0.260423i	−0.999121	+	0.0419120i	$0.986655\pi$
$270$		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	$0.152016\pi$
$272$	0.737376	+	1.05308i	0.0447100	+	0.0638524i
$273$	−25.2062	+	6.75398i	−1.52555	+	0.408770i
$274$	7.56834	+	13.1088i	0.457220	+	0.791929i
$275$		0			0
$276$	4.08512	+	11.2238i	0.245895	+	0.675592i
$277$	2.15965	+	0.578676i	0.129761	+	0.0347693i	0.323115	−	0.946360i	$-0.395270\pi$
$277$	2.15965	+	0.578676i	0.129761	+	0.0347693i	−0.193354	+	0.981129i	$0.561937\pi$
$278$	5.72147	+	21.3528i	0.343151	+	1.28066i
$279$	−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	$0.313949\pi$
$282$	−25.7361	−	18.0206i	−1.53256	−	1.07311i
$283$	−11.2561	−	24.1389i	−0.669108	−	1.43491i	−0.888318	−	0.459230i	$-0.848125\pi$
$283$	−11.2561	−	24.1389i	−0.669108	−	1.43491i	0.219209	−	0.975678i	$-0.429652\pi$
$284$	3.93923			0.233750
$285$		0			0
$286$	−4.50980			−0.266670
$287$	−12.1959	−	26.1543i	−0.719903	−	1.54384i
$288$	−6.07112	−	4.25105i	−0.357744	−	0.250495i
$289$	−9.86505	+	11.7567i	−0.580297	+	0.691571i
$290$		0			0
$291$	−2.88161	+	16.3424i	−0.168923	+	0.958009i
$292$	1.37106	+	5.11686i	0.0802351	+	0.299441i
$293$	6.12185	+	1.64034i	0.357642	+	0.0958299i	0.433166	−	0.901314i	$-0.357396\pi$
$293$	6.12185	+	1.64034i	0.357642	+	0.0958299i	−0.0755241	+	0.997144i	$0.524063\pi$
$294$	7.39663	+	20.3221i	0.431380	+	1.18521i
$295$		0			0
$296$	−3.47178	−	6.01330i	−0.201793	−	0.349516i
$297$	28.3812	−	7.60472i	1.64684	−	0.441271i
$298$	−8.79605	−	12.5621i	−0.509541	−	0.727700i
$299$	6.19529	−	5.19846i	0.358283	−	0.300635i
$300$		0			0
$301$	6.39306	+	36.2568i	0.368490	+	2.08981i
$302$	5.73704	−	2.67523i	0.330130	−	0.153942i
$303$	−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
$307$	−5.15929	+	7.36823i	−0.294456	+	0.420527i	−0.938935	−	0.344095i	$-0.888186\pi$
$307$	−5.15929	+	7.36823i	−0.294456	+	0.420527i	0.644478	+	0.764622i	$0.277075\pi$
$308$	0.665948	+	7.61182i	0.0379459	+	0.433724i
$309$	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	$0.0755485\pi$
$312$	−1.82458	+	6.80942i	−0.103296	+	0.385507i
$313$	−19.9657	−	9.31017i	−1.12853	−	0.526242i	−0.233548	−	0.972345i	$-0.575034\pi$
$313$	−19.9657	−	9.31017i	−1.12853	−	0.526242i	−0.894981	+	0.446103i	$0.852811\pi$
$314$	−3.29644	+	1.19981i	−0.186029	+	0.0677090i
$315$		0			0
$316$	−1.92468	−	1.11121i	−0.108272	−	0.0625106i
$317$	21.7905	−	15.2579i	1.22388	−	0.856968i	0.230637	−	0.973040i	$-0.425919\pi$
$317$	21.7905	−	15.2579i	1.22388	−	0.856968i	0.993241	+	0.116071i	$0.0370301\pi$
$318$	2.55533	−	29.2076i	0.143296	−	1.63788i
$319$	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
$323$	3.57689	+	4.31361i	0.199023	+	0.240016i
$324$		−	23.6955i		−	1.31642i
$325$		0			0
$326$	13.9231	−	2.45502i	0.771128	−	0.135971i
$327$	31.4715	−	2.75340i	1.74038	−	0.152263i
$328$	−7.76629	−	0.679462i	−0.428822	−	0.0375170i
$329$	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	$0.589360\pi$
$332$	6.00335	−	12.8742i	0.329476	−	0.706565i
$333$	21.7488	−	46.6404i	1.19183	−	2.55588i
$334$	3.81374	−	2.20187i	0.208679	−	0.120481i
$335$		0			0
$336$	11.7626	+	2.07407i	0.641705	+	0.113150i
$337$	23.8013	+	2.08234i	1.29654	+	0.113432i	0.714446	−	0.699691i	$-0.246679\pi$
$337$	23.8013	+	2.08234i	1.29654	+	0.113432i	0.582092	+	0.813123i	$0.302234\pi$
$338$	−8.19538	+	0.717003i	−0.445770	+	0.0389998i
$339$	32.0051	−	5.64337i	1.73828	−	0.306506i
$340$		0			0
$341$		−	18.8571i		−	1.02117i
$342$	−27.8830	−	16.3158i	−1.50774	−	0.882259i
$343$	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
$347$	−1.03763	+	11.8602i	−0.0557030	+	0.636688i	0.916109	+	0.400930i	$0.131313\pi$
$347$	−1.03763	+	11.8602i	−0.0557030	+	0.636688i	−0.971812	+	0.235758i	$0.924243\pi$
$348$	20.8239	−	14.5811i	1.11628	−	0.781626i
$349$	−13.6519	−	7.88191i	−0.730768	−	0.421909i	0.0879351	−	0.996126i	$-0.471973\pi$
$349$	−13.6519	−	7.88191i	−0.730768	−	0.421909i	−0.818703	+	0.574217i	$0.805307\pi$
$350$		0			0
$351$	−29.2237	+	10.6366i	−1.55985	+	0.567738i
$352$	1.87078	+	0.872359i	0.0997129	+	0.0464969i
$353$	3.24962	−	12.1278i	0.172960	−	0.645496i	−0.823930	−	0.566692i	$-0.808223\pi$
$353$	3.24962	−	12.1278i	0.172960	−	0.645496i	0.996890	−	0.0788042i	$-0.0251102\pi$
$354$	−3.42782	+	5.93717i	−0.182187	+	0.315557i
$355$		0			0
$356$	1.24123	+	1.47924i	0.0657850	+	0.0783995i
$357$	−1.33828	−	15.2966i	−0.0708293	−	0.809582i
$358$	−5.57041	+	7.95538i	−0.294406	+	0.420455i
$359$	5.60575	−	15.4017i	0.295860	−	0.812869i	−0.699320	−	0.714809i	$-0.746514\pi$
$359$	5.60575	−	15.4017i	0.295860	−	0.812869i	0.995180	−	0.0980607i	$-0.0312639\pi$
$360$		0			0
$361$	−16.5642	+	9.30742i	−0.871799	+	0.489864i
$362$	−6.87426	+	6.87426i	−0.361303	+	0.361303i
$363$	19.7078	−	9.18990i	1.03439	−	0.482345i
$364$	−1.40436	−	7.96451i	−0.0736083	−	0.417454i
$365$		0			0
$366$	27.8175	−	23.3416i	1.45404	−	1.22009i
$367$	11.7091	+	16.7223i	0.611209	+	0.872896i	0.998802	−	0.0489341i	$-0.0155824\pi$
$367$	11.7091	+	16.7223i	0.611209	+	0.872896i	−0.387593	+	0.921830i	$0.626694\pi$
$368$	−3.57554	+	0.958062i	−0.186388	+	0.0499424i
$369$	−28.8898	−	50.0385i	−1.50394	−	2.60490i
$370$		0			0
$371$	11.5039	+	31.6066i	0.597251	+	1.64093i
$372$	−28.4726	−	7.62920i	−1.47623	−	0.395556i
$373$	8.86252	+	33.0754i	0.458884	+	1.71258i	0.676411	+	0.736524i	$0.263534\pi$
$373$	8.86252	+	33.0754i	0.458884	+	1.71258i	−0.217527	+	0.976054i	$0.569799\pi$
$374$	0.460802	−	2.61334i	0.0238275	−	0.135133i
$375$		0			0
$376$	6.25877	−	7.45891i	0.322771	−	0.384664i
$377$	−14.0999	−	9.87286i	−0.726182	−	0.508478i
$378$	22.2682	+	47.7543i	1.14535	+	2.45622i
$379$	−33.0656			−1.69847			−0.849234	−	0.528017i	$-0.822936\pi$
$379$	−33.0656			−1.69847			−0.849234	+	0.528017i	$0.822936\pi$
$380$		0			0
$381$	10.7757			0.552055
$382$	6.65493	+	14.2715i	0.340496	+	0.730196i
$383$	−12.7112	−	8.90050i	−0.649513	−	0.454794i	0.201818	−	0.979423i	$-0.435315\pi$
$383$	−12.7112	−	8.90050i	−0.649513	−	0.454794i	−0.851331	+	0.524629i	$0.824204\pi$
$384$	2.07407	−	2.47178i	0.105842	−	0.126138i
$385$		0			0
$386$	−1.67024	+	9.47243i	−0.0850132	+	0.482134i
$387$	19.0784	+	71.2015i	0.969809	+	3.61938i
$388$	−4.96766	−	1.33108i	−0.252195	−	0.0675754i
$389$	4.15312	+	11.4106i	0.210571	+	0.578540i	0.999347	−	0.0361415i	$-0.0115067\pi$
$389$	4.15312	+	11.4106i	0.210571	+	0.578540i	−0.788775	+	0.614682i	$0.789284\pi$
$390$		0			0
$391$	2.37939	+	4.12122i	0.120331	+	0.208419i
$392$	−6.47396	+	1.73469i	−0.326984	+	0.0876152i
$393$	33.0364	+	47.1809i	1.66647	+	2.37996i
$394$	−0.866025	+	0.726682i	−0.0436297	+	0.0366097i
$395$		0			0
$396$	2.65657	+	15.0662i	0.133498	+	0.757104i
$397$	12.1307	−	5.65663i	0.608822	−	0.283898i	−0.0936552	−	0.995605i	$-0.529855\pi$
$397$	12.1307	−	5.65663i	0.608822	−	0.283898i	0.702477	+	0.711706i	$0.252077\pi$
$398$	−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	$-0.0195255\pi$
$402$	4.72751	−	6.75158i	0.235787	−	0.336738i
$403$	1.73953	+	19.8830i	0.0866524	+	0.990441i
$404$	−3.72859	−	4.44356i	−0.185504	−	0.221076i
$405$		0			0
$406$	−14.5817	+	25.2563i	−0.723679	+	1.25345i
$407$	−3.70959	+	13.8444i	−0.183877	+	0.686240i
$408$	−3.75949	−	1.75308i	−0.186123	−	0.0867904i
$409$	−9.39052	+	3.41787i	−0.464331	+	0.169003i	−0.563583	−	0.826060i	$-0.690577\pi$
$409$	−9.39052	+	3.41787i	−0.464331	+	0.169003i	0.0992514	+	0.995062i	$0.468355\pi$
$410$		0			0
$411$	−42.2978	−	24.4206i	−2.08640	−	1.20458i
$412$	−1.67896	+	1.17562i	−0.0827163	+	0.0579186i
$413$	0.685466	−	7.83491i	0.0337296	−	0.385531i
$414$	−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
$418$	8.43683	+	3.12660i	0.412659	+	0.152927i
$419$			21.6304i			1.05671i	0.849022	+	0.528357i	$0.177192\pi$
$419$			21.6304i			1.05671i	−0.849022	+	0.528357i	$0.822808\pi$
$420$		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	$0.315823\pi$
$422$	9.69987	−	0.848628i	0.472182	−	0.0413106i
$423$	71.8903	+	6.28959i	3.49543	+	0.305810i
$424$	8.94842	+	1.57785i	0.434574	+	0.0766271i
$425$		0			0
$426$	−11.0077	+	6.35532i	−0.533327	+	0.307916i
$427$	−17.6057	+	37.7555i	−0.852000	+	1.82712i
$428$	−6.31542	+	13.5435i	−0.305267	+	0.654648i
$429$	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	$0.557969\pi$
$432$	14.1803	+	1.24061i	0.682248	+	0.0596890i
$433$	−6.65195	+	0.581970i	−0.319672	+	0.0279677i	−0.245863	−	0.969305i	$-0.579071\pi$
$433$	−6.65195	+	0.581970i	−0.319672	+	0.0279677i	−0.0738095	+	0.997272i	$0.523516\pi$
$434$	33.3024	−	5.87211i	1.59857	−	0.281870i
$435$		0			0
$436$			9.79077i			0.468893i
$437$	−15.1940	+	5.43003i	−0.726830	+	0.259754i
$438$	−12.0865	−	12.0865i	−0.577515	−	0.577515i
$439$	−15.8102	−	5.75443i	−0.754579	−	0.274644i	−0.0640474	−	0.997947i	$-0.520401\pi$
$439$	−15.8102	−	5.75443i	−0.754579	−	0.274644i	−0.690531	+	0.723303i	$0.742623\pi$
$440$		0			0
$441$	−38.0526	−	31.9299i	−1.81203	−	1.52047i
$442$	−0.244796	+	2.79803i	−0.0116437	+	0.133089i
$443$	26.9521	−	18.8721i	1.28053	−	0.896640i	0.282497	−	0.959268i	$-0.408837\pi$
$443$	26.9521	−	18.8721i	1.28053	−	0.896640i	0.998037	+	0.0626285i	$0.0199483\pi$
$444$	19.4030	+	11.2023i	0.920826	+	0.531639i
$445$		0			0
$446$	−2.96064	+	1.07758i	−0.140190	+	0.0510251i
$447$	44.8464	+	20.9122i	2.12116	+	0.989115i
$448$	−0.958062	+	3.57554i	−0.0452642	+	0.168928i
$449$	−4.17680	+	7.23442i	−0.197115	+	0.341414i	−0.947592	−	0.319483i	$-0.896491\pi$
$449$	−4.17680	+	7.23442i	−0.197115	+	0.341414i	0.750477	+	0.660897i	$0.229824\pi$
$450$		0			0
$451$	10.3439	+	12.3274i	0.487075	+	0.580473i
$452$	0.877826	+	10.0336i	0.0412894	+	0.471940i
$453$	−11.7155	+	16.7314i	−0.550441	+	0.786111i
$454$	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	−0.495919	−	0.868369i	$-0.665169\pi$
$457$	7.96206	−	7.96206i	0.372450	−	0.372450i	0.868369	+	0.495919i	$0.165169\pi$
$458$	−21.0575	+	9.81929i	−0.983954	+	0.458825i
$459$	−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	$0.209780\pi$
$462$	−14.1414	−	20.1960i	−0.657917	−	0.939602i
$463$	5.18810	−	1.39015i	0.241111	−	0.0646056i	−0.136240	−	0.990676i	$-0.543502\pi$
$463$	5.18810	−	1.39015i	0.241111	−	0.0646056i	0.377351	+	0.926070i	$0.376835\pi$
$464$	3.93923	+	6.82295i	0.182874	+	0.316747i
$465$		0			0
$466$	−1.44238	−	3.96291i	−0.0668170	−	0.183578i
$467$	−8.95465	−	2.39939i	−0.414372	−	0.111031i	0.0456091	−	0.998959i	$-0.485477\pi$
$467$	−8.95465	−	2.39939i	−0.414372	−	0.111031i	−0.459981	+	0.887929i	$0.652144\pi$
$468$	−4.19094	−	15.6408i	−0.193726	−	0.722996i
$469$	−1.64192	+	9.31180i	−0.0758169	+	0.429979i
$470$		0			0
$471$	7.27584	−	8.67101i	0.335253	−	0.399539i
$472$	−1.74043	−	1.21866i	−0.0801099	−	0.0560935i
$473$	−8.67634	−	18.6065i	−0.398938	−	0.855526i
$474$	7.17106			0.329378
$475$		0			0
$476$	4.75877			0.218118
$477$	28.4609	+	61.0345i	1.30313	+	2.79458i
$478$	20.9561	+	14.6736i	0.958509	+	0.671155i
$479$	9.08040	−	10.8216i	0.414894	−	0.494452i	−0.517607	−	0.855618i	$-0.673177\pi$
$479$	9.08040	−	10.8216i	0.414894	−	0.494452i	0.932501	+	0.361167i	$0.117621\pi$
$480$		0			0
$481$	2.63429	−	14.9398i	0.120113	−	0.681195i
$482$	4.60190	+	17.1745i	0.209611	+	0.782279i
$483$	42.7065	+	11.4432i	1.94322	+	0.520683i
$484$	2.30493	+	6.33275i	0.104770	+	0.287852i
$485$		0			0
$486$	16.8773	+	29.2324i	0.765571	+	1.32601i
$487$	3.92829	−	1.05258i	0.178008	−	0.0476971i	−0.168714	−	0.985665i	$-0.553961\pi$
$487$	3.92829	−	1.05258i	0.178008	−	0.0476971i	0.346722	+	0.937968i	$0.387295\pi$
$488$	6.45504	+	9.21876i	0.292206	+	0.417313i
$489$	−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	$0.964698\pi$
$492$	22.7982	−	10.6310i	1.02782	−	0.479282i
$493$	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
$497$	8.36373	−	11.9446i	0.375165	−	0.535791i
$498$	3.99482	+	45.6610i	0.179012	+	2.04612i
$499$	−1.67382	−	1.99479i	−0.0749306	−	0.0892989i	0.727277	−	0.686344i	$-0.240786\pi$
$499$	−1.67382	−	1.99479i	−0.0749306	−	0.0892989i	−0.802207	+	0.597045i	$0.796341\pi$
$500$		0			0
$501$	−7.10472	+	12.3057i	−0.317416	+	0.549780i
$502$	−3.40294	+	12.7000i	−0.151881	+	0.566827i
$503$	−7.76819	−	3.62237i	−0.346367	−	0.161513i	0.241647	−	0.970364i	$-0.422312\pi$
$503$	−7.76819	−	3.62237i	−0.346367	−	0.161513i	−0.588014	+	0.808851i	$0.700090\pi$
$504$	−25.7803	+	9.38326i	−1.14835	+	0.417963i
$505$		0			0
$506$	6.61721	+	3.82045i	0.294171	+	0.169840i
$507$	21.7443	−	15.2255i	0.965698	−	0.676189i
$508$	−0.291061	+	3.32685i	−0.0129138	+	0.147605i
$509$	16.4526	+	13.8054i	0.729251	+	0.611914i	0.929927	−	0.367744i	$-0.119870\pi$
$509$	16.4526	+	13.8054i	0.729251	+	0.611914i	−0.200677	+	0.979658i	$0.564314\pi$
$510$		0			0
$511$	18.4265	+	6.70669i	0.815140	+	0.296687i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	62.0454	+	0.361882i	2.73937	+	0.0159775i
$514$			13.0419i			0.575253i
$515$		0			0
$516$	−31.6045	+	5.57272i	−1.39131	+	0.245325i
$517$	−20.0222	+	1.75172i	−0.880577	+	0.0770405i
$518$	−25.6049	−	2.24014i	−1.12502	−	0.0984262i
$519$	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	$0.542795\pi$
$522$	−24.6771	+	52.9202i	−1.08009	+	2.31626i
$523$	−8.93364	+	19.1582i	−0.390641	+	0.837732i	0.608387	+	0.793641i	$0.291817\pi$
$523$	−8.93364	+	19.1582i	−0.390641	+	0.837732i	−0.999028	+	0.0440910i	$0.985961\pi$
$524$	−15.4588	+	8.92514i	−0.675321	+	0.389897i
$525$		0			0
$526$	6.22534	+	1.09769i	0.271438	+	0.0478618i
$527$	−11.6995	−	1.02358i	−0.509640	−	0.0445877i
$528$	−6.63510	+	0.580496i	−0.288756	+	0.0252628i
$529$	9.15641	−	1.61452i	0.398105	−	0.0701966i
$530$		0			0
$531$		−	15.7470i		−	0.683360i
$532$	−2.89448	+	15.8734i	−0.125491	+	0.688201i
$533$	−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
$537$	2.73117	−	31.2174i	0.117859	−	1.34713i
$538$	−3.55279	+	2.48769i	−0.153171	+	0.107252i
$539$	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	$0.282792\pi$
$542$	−11.4850	−	5.35555i	−0.493323	−	0.230040i
$543$	8.11883	−	30.2999i	0.348412	−	1.30029i
$544$	0.642788	−	1.11334i	0.0275593	−	0.0477341i
$545$		0			0
$546$	16.7738	+	19.9902i	0.717852	+	0.855502i
$547$	3.43025	+	39.2080i	0.146667	+	1.67641i	0.611678	+	0.791107i	$0.290495\pi$
$547$	3.43025	+	39.2080i	0.146667	+	1.67641i	−0.465011	+	0.885305i	$0.653950\pi$
$548$	8.68205	−	12.3992i	0.370879	−	0.529670i
$549$	−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
$553$	−7.45591	+	3.47675i	−0.317057	+	0.147846i
$554$	−0.388249	−	2.20187i	−0.0164951	−	0.0935484i
$555$		0			0
$556$	16.9342	−	14.2095i	0.718171	−	0.602617i
$557$	5.70097	+	8.14183i	0.241558	+	0.344980i	0.921564	−	0.388226i	$-0.126912\pi$
$557$	5.70097	+	8.14183i	0.241558	+	0.344980i	−0.680007	+	0.733206i	$0.738023\pi$
$558$	65.3996	−	17.5238i	2.76859	−	0.741840i
$559$	10.8648	+	18.8184i	0.459532	+	0.795932i
$560$		0			0
$561$	2.92855	+	8.04612i	0.123643	+	0.339707i
$562$	9.20335	+	2.46603i	0.388220	+	0.104023i
$563$	4.14004	+	15.4508i	0.174482	+	0.651175i	0.996639	+	0.0819150i	$0.0261036\pi$
$563$	4.14004	+	15.4508i	0.174482	+	0.651175i	−0.822157	+	0.569260i	$0.807230\pi$
$564$	−5.45567	+	30.9406i	−0.229725	+	1.30284i
$565$		0			0
$566$	−17.1202	+	20.4031i	−0.719616	+	0.857605i
$567$	−71.8502	−	50.3101i	−3.01743	−	2.11282i
$568$	−1.66479	−	3.57016i	−0.0698531	−	0.149800i
$569$	11.5163			0.482789			0.241395	−	0.970427i	$-0.422395\pi$
$569$	11.5163			0.482789			0.241395	+	0.970427i	$0.422395\pi$
$570$		0			0
$571$	−44.4593			−1.86057			−0.930283	−	0.366843i	$-0.880439\pi$
$571$	−44.4593			−1.86057			−0.930283	+	0.366843i	$0.880439\pi$
$572$	1.90592	+	4.08727i	0.0796907	+	0.170897i
$573$	−41.6213	−	29.1436i	−1.73876	−	1.21749i
$574$	−18.5496	+	22.1065i	−0.774245	+	0.922709i
$575$		0			0
$576$	−1.28699	+	7.29888i	−0.0536245	+	0.304120i
$577$	−3.99535	−	14.9109i	−0.166329	−	0.620747i	−0.997867	−	0.0652797i	$-0.979206\pi$
$577$	−3.99535	−	14.9109i	−0.166329	−	0.620747i	0.831538	−	0.555467i	$-0.187461\pi$
$578$	14.8243	+	3.97217i	0.616612	+	0.165221i
$579$	−10.6149	−	29.1643i	−0.441142	−	1.21203i
$580$		0			0
$581$	−26.2913	−	45.5379i	−1.09075	−	1.88923i
$582$	16.0291	−	4.29498i	0.664426	−	0.178032i
$583$	−10.7580	−	15.3641i	−0.445553	−	0.636315i
$584$	4.05801	−	3.40508i	0.167922	−	0.140903i
$585$		0			0
$586$	−1.10055	−	6.24152i	−0.0454632	−	0.257835i
$587$	−2.44904	+	1.14200i	−0.101083	+	0.0471356i	−0.472502	−	0.881330i	$-0.656649\pi$
$587$	−2.44904	+	1.14200i	−0.101083	+	0.0471356i	0.371419	+	0.928465i	$0.378871\pi$
$588$	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
$592$	−3.98266	+	5.68783i	−0.163686	+	0.233769i
$593$	−0.722909	−	8.26288i	−0.0296863	−	0.339316i	−0.996485	−	0.0837754i	$-0.973302\pi$
$593$	−0.722909	−	8.26288i	−0.0296863	−	0.339316i	0.966798	−	0.255540i	$-0.0822534\pi$
$594$	−18.8866	−	22.5082i	−0.774928	−	0.923523i
$595$		0			0
$596$	−7.66772	+	13.2809i	−0.314082	+	0.544006i
$597$	3.26908	−	12.2004i	0.133794	−	0.499327i
$598$	−7.32965	−	3.41787i	−0.299732	−	0.139767i
$599$	0.193064	−	0.0702697i	0.00788840	−	0.00287114i	−0.338073	−	0.941120i	$-0.609775\pi$
$599$	0.193064	−	0.0702697i	0.00788840	−	0.00287114i	0.345961	+	0.938249i	$0.387553\pi$
$600$		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	$0.677477\pi$
$602$	30.1580	−	21.1169i	1.22915	−	0.860659i
$603$	−1.65001	+	18.8597i	−0.0671935	+	0.768025i
$604$	−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	$-0.115110\pi$
$607$	14.3272	+	14.3272i	0.581524	+	0.581524i	−0.353798	+	0.935322i	$0.615110\pi$
$608$	3.32271	+	2.82127i	0.134754	+	0.114418i
$609$		−	94.1011i		−	3.81317i
$610$		0			0
$611$	20.9500	−	3.69404i	0.847545	−	0.149445i
$612$	9.49175	−	0.830421i	0.383681	−	0.0335678i
$613$	−24.9707	−	2.18465i	−1.00856	−	0.0882373i	−0.429114	−	0.903250i	$-0.641174\pi$
$613$	−24.9707	−	2.18465i	−1.00856	−	0.0882373i	−0.579443	+	0.815013i	$0.696730\pi$
$614$	8.85829	+	1.56196i	0.357492	+	0.0630354i
$615$		0			0
$616$	6.61721	−	3.82045i	0.266615	−	0.153930i
$617$	2.44797	−	5.24969i	0.0985516	−	0.211345i	−0.850850	−	0.525408i	$-0.823913\pi$
$617$	2.44797	−	5.24969i	0.0985516	−	0.211345i	0.949402	+	0.314063i	$0.101690\pi$
$618$	2.79499	−	5.99387i	0.112431	−	0.241109i
$619$	26.0474	−	15.0385i	1.04693	−	0.604448i	0.125145	−	0.992138i	$-0.460060\pi$
$619$	26.0474	−	15.0385i	1.04693	−	0.604448i	0.921790	+	0.387691i	$0.126727\pi$
$620$		0			0
$621$	51.8906	+	9.14971i	2.08230	+	0.367165i
$622$	−9.92115	−	0.867988i	−0.397802	−	0.0348031i
$623$	7.12076	−	0.622985i	0.285287	−	0.0249594i
$624$	6.94253	−	1.22416i	0.277924	−	0.0490054i
$625$		0			0
$626$			22.0297i			0.880486i
$627$	−28.6201	+	4.87455i	−1.14297	+	0.194671i
$628$	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	$0.786981\pi$
$632$	−0.193697	+	2.21397i	−0.00770486	+	0.0880670i
$633$	−25.7361	+	18.0206i	−1.02292	+	0.716254i
$634$	−23.0374	−	13.3007i	−0.914933	−	0.528237i
$635$		0			0
$636$	−27.5510	+	10.0277i	−1.09247	+	0.397626i
$637$	−13.2713	−	6.18849i	−0.525826	−	0.245197i
$638$	4.20906	−	15.7084i	0.166638	−	0.621902i
$639$	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	$0.893671\pi$
$642$	−4.20249	−	48.0346i	−0.165859	−	1.89578i
$643$	11.4248	−	16.3163i	0.450549	−	0.643450i	−0.528054	−	0.849211i	$-0.677078\pi$
$643$	11.4248	−	16.3163i	0.450549	−	0.643450i	0.978602	+	0.205761i	$0.0659668\pi$
$644$	−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	−0.652373	−	0.757898i	$-0.726226\pi$
$647$	2.68415	−	2.68415i	0.105525	−	0.105525i	0.757898	+	0.652373i	$0.226226\pi$
$648$	−21.4754	+	10.0142i	−0.843635	+	0.393393i
$649$	0.761570	+	4.31908i	0.0298942	+	0.169539i
$650$		0			0
$651$	−83.5861	+	70.1371i	−3.27600	+	2.74889i
$652$	−8.10915	−	11.5811i	−0.317579	−	0.453550i
$653$	−23.6519	+	6.33751i	−0.925571	+	0.248006i	−0.689965	−	0.723843i	$-0.742374\pi$
$653$	−23.6519	+	6.33751i	−0.925571	+	0.248006i	−0.235606	+	0.971849i	$0.575708\pi$
$654$	−15.7958	−	27.3592i	−0.617667	−	1.06983i
$655$		0			0
$656$	2.66637	+	7.32580i	0.104104	+	0.286025i
$657$	37.9235	+	10.1616i	1.47953	+	0.396440i
$658$	−9.32857	−	34.8147i	−0.363665	−	1.35722i
$659$	−2.20718	+	12.5175i	−0.0859795	+	0.487614i	0.911161	+	0.412050i	$0.135187\pi$
$659$	−2.20718	+	12.5175i	−0.0859795	+	0.487614i	−0.997141	+	0.0755645i	$0.975924\pi$
$660$		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	$0.129802\pi$
$662$	21.4715	+	15.0345i	0.834513	+	0.584332i
$663$	−3.83012	−	8.21371i	−0.148749	−	0.318994i
$664$	−14.2051			−0.551266
$665$		0			0
$666$	−51.4620			−1.99411
$667$	12.3250	+	26.4311i	0.477226	+	1.02341i
$668$	−3.60733	−	2.52588i	−0.139572	−	0.0977291i
$669$	6.53466	−	7.78770i	0.252645	−	0.301090i
$670$		0			0
$671$	4.03390	−	22.8774i	0.155727	−	0.883172i
$672$	−3.09136	−	11.5371i	−0.119252	−	0.445054i
$673$	−18.8623	−	5.05413i	−0.727087	−	0.194822i	−0.123755	−	0.992313i	$-0.539494\pi$
$673$	−18.8623	−	5.05413i	−0.727087	−	0.194822i	−0.603331	+	0.797491i	$0.706160\pi$
$674$	−8.17161	−	22.4513i	−0.314759	−	0.864792i
$675$		0			0
$676$	4.11334	+	7.12452i	0.158205	+	0.274020i
$677$	−0.0900954	+	0.0241410i	−0.00346265	+	0.000927814i	−0.260550	−	0.965460i	$-0.583904\pi$
$677$	−0.0900954	+	0.0241410i	−0.00346265	+	0.000927814i	0.257087	+	0.966388i	$0.417237\pi$
$678$	−18.6406	−	26.6215i	−0.715887	−	1.02239i
$679$	−14.5834	+	12.2369i	−0.559661	+	0.469611i
$680$		0			0
$681$	0.684488	+	3.88192i	0.0262296	+	0.148756i
$682$	−17.0903	+	7.96934i	−0.654421	+	0.305162i
$683$	−16.0864	+	16.0864i	−0.615529	+	0.615529i	−0.944381	−	0.328852i	$-0.893338\pi$
$683$	−16.0864	+	16.0864i	−0.615529	+	0.615529i	0.328852	+	0.944381i	$0.393338\pi$
$684$	−3.00330	+	32.1660i	−0.114834	+	1.22990i
$685$		0			0
$686$	0.376859	−	1.03541i	0.0143885	−	0.0395322i
$687$	43.0011	−	61.4119i	1.64059	−	2.34301i
$688$	−0.866836	−	9.90798i	−0.0330478	−	0.377738i
$689$	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	$0.232894\pi$
$692$	−5.87403	+	21.9222i	−0.223297	+	0.833357i
$693$	51.3245	+	23.9330i	1.94966	+	0.909140i
$694$	11.1875	−	4.07192i	0.424672	−	0.154568i
$695$		0			0
$696$	−22.0155	−	12.7106i	−0.834495	−	0.481796i
$697$	8.20978	−	5.74855i	0.310968	−	0.217742i
$698$	−1.37391	+	15.7038i	−0.0520032	+	0.594399i
$699$	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
$703$	−15.2858	+	26.1227i	−0.576513	+	0.985235i
$704$		−	2.06418i		−	0.0777966i
$705$		0			0
$706$	−12.3648	+	2.18025i	−0.465357	+	0.0820550i
$707$	−21.3904	+	1.87142i	−0.804469	+	0.0703819i
$708$	6.82956	+	0.597509i	0.256671	+	0.0224558i
$709$	6.98551	+	1.23173i	0.262346	+	0.0462587i	0.303274	−	0.952903i	$-0.401920\pi$
$709$	6.98551	+	1.23173i	0.262346	+	0.0462587i	−0.0409277	+	0.999162i	$0.513031\pi$
$710$		0			0
$711$	−14.2647	+	8.23573i	−0.534968	+	0.308864i
$712$	0.816080	−	1.75009i	0.0305839	−	0.0655874i
$713$	14.2913	−	30.6478i	0.535214	−	1.14777i
$714$	−13.2979	+	7.67752i	−0.497660	+	0.287324i
$715$		0			0
$716$	9.56418	+	1.68642i	0.357430	+	0.0630246i
$717$	−82.2330	−	7.19445i	−3.07105	−	0.268682i
$718$	−16.3277	+	1.42849i	−0.609346	+	0.0533109i
$719$	−29.8553	+	5.26429i	−1.11341	+	0.196325i	−0.699947	−	0.714194i	$-0.746793\pi$
$719$	−29.8553	+	5.26429i	−1.11341	+	0.196325i	−0.413466	+	0.910519i	$0.635682\pi$
$720$		0			0
$721$			7.58705i			0.282556i
$722$	15.4357	+	11.0788i	0.574458	+	0.412309i
$723$	−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
$727$	−2.54762	+	29.1194i	−0.0944860	+	1.07998i	0.789904	+	0.613231i	$0.210130\pi$
$727$	−2.54762	+	29.1194i	−0.0944860	+	1.07998i	−0.884390	+	0.466749i	$0.845425\pi$
$728$	−6.62479	+	4.63873i	−0.245531	+	0.171923i
$729$	−32.7608	−	18.9145i	−1.21336	−	0.700536i
$730$		0			0
$731$	−12.0150	+	4.37311i	−0.444391	+	0.161745i
$732$	−32.9109	−	15.3466i	−1.21642	−	0.567227i
$733$	−12.7457	+	47.5677i	−0.470774	+	1.75695i	0.166225	+	0.986088i	$0.446842\pi$
$733$	−12.7457	+	47.5677i	−0.470774	+	1.75695i	−0.636999	+	0.770864i	$0.719825\pi$
$734$	10.2071	−	17.6792i	0.376750	−	0.652550i
$735$		0			0
$736$	2.37939	+	2.83564i	0.0877053	+	0.104523i
$737$	−0.459545	−	5.25263i	−0.0169276	−	0.193483i
$738$	−33.1410	+	47.3302i	−1.21994	+	1.74225i
$739$	−8.11338	+	22.2913i	−0.298455	+	0.820000i	0.696303	+	0.717748i	$0.254827\pi$
$739$	−8.11338	+	22.2913i	−0.298455	+	0.820000i	−0.994759	+	0.102252i	$0.967395\pi$
$740$		0			0
$741$	29.7275	−	7.77990i	1.09207	−	0.285802i
$742$	23.7836	−	23.7836i	0.873123	−	0.873123i
$743$	−28.2173	+	13.1579i	−1.03519	+	0.482718i	−0.864514	−	0.502609i	$-0.832374\pi$
$743$	−28.2173	+	13.1579i	−1.03519	+	0.482718i	−0.170678	+	0.985327i	$0.554596\pi$
$744$	5.11862	+	29.0292i	0.187658	+	1.06426i
$745$		0			0
$746$	26.2310	−	22.0104i	0.960386	−	0.805859i
$747$	−60.3867	−	86.2411i	−2.20943	−	3.15540i
$748$	−2.56323	+	0.686817i	−0.0937211	+	0.0251125i
$749$	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	$0.858390\pi$
$752$	−9.40514	−	2.52010i	−0.342970	−	0.0918986i
$753$	−10.9802	−	40.9787i	−0.400141	−	1.49335i
$754$	−2.98897	+	16.9513i	−0.108852	+	0.617330i
$755$		0			0
$756$	33.8692	−	40.3637i	1.23181	−	1.46801i
$757$	19.4630	+	13.6281i	0.707395	+	0.495323i	0.871050	−	0.491194i	$-0.163439\pi$
$757$	19.4630	+	13.6281i	0.707395	+	0.495323i	−0.163655	+	0.986518i	$0.552328\pi$
$758$	13.9741	+	29.9676i	0.507564	+	1.08847i
$759$	−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	$0.695072\pi$
$762$	−4.55400	−	9.76608i	−0.164974	−	0.353788i
$763$	29.6878	+	20.7877i	1.07477	+	0.752563i
$764$	10.1219	−	12.0628i	0.366198	−	0.436418i
$765$		0			0
$766$	−2.69459	+	15.2818i	−0.0973596	+	0.552154i
$767$	−1.20143	−	4.48380i	−0.0433812	−	0.161901i
$768$	−3.11674	−	0.835127i	−0.112465	−	0.0301350i
$769$	−8.86948	−	24.3687i	−0.319842	−	0.878758i	−0.990564	−	0.137050i	$-0.956238\pi$
$769$	−8.86948	−	24.3687i	−0.319842	−	0.878758i	0.670722	−	0.741708i	$-0.265984\pi$
$770$		0			0
$771$	−21.0410	−	36.4441i	−0.757774	−	1.31250i
$772$	9.29081	−	2.48947i	0.334384	−	0.0895978i
$773$	17.2564	+	24.6447i	0.620670	+	0.886409i	0.999233	−	0.0391668i	$-0.0124704\pi$
$773$	17.2564	+	24.6447i	0.620670	+	0.886409i	−0.378562	+	0.925576i	$0.623581\pi$
$774$	56.4676	−	47.3820i	2.02969	−	1.70311i
$775$		0			0
$776$	0.893056	+	5.06477i	0.0320588	+	0.181815i
$777$	75.1643	−	35.0497i	2.69650	−	1.25740i
$778$	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
$782$	2.72952	−	3.89816i	0.0976074	−	0.139398i
$783$	−9.77411	−	111.719i	−0.349298	−	3.99250i
$784$	4.30818	+	5.13429i	0.153863	+	0.183367i
$785$		0			0
$786$	28.7986	−	49.8806i	1.02721	−	1.77918i
$787$	6.44302	−	24.0457i	0.229669	−	0.857136i	−0.750811	−	0.660517i	$-0.770337\pi$
$787$	6.44302	−	24.0457i	0.229669	−	0.857136i	0.980480	−	0.196619i	$-0.0629963\pi$
$788$	1.02460	+	0.477777i	0.0364997	+	0.0170201i
$789$	−19.1670	+	6.97620i	−0.682362	+	0.248359i
$790$		0			0
$791$	32.2879	+	18.6414i	1.14803	+	0.662813i
$792$	12.5319	−	8.77492i	0.445301	−	0.311803i
$793$	−2.14296	+	24.4941i	−0.0760987	+	0.869812i
$794$	−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	$-0.323480\pi$
$797$	−9.13482	−	9.13482i	−0.323572	−	0.323572i	−0.850136	+	0.526564i	$0.823480\pi$
$798$	−17.5210	−	49.0264i	−0.620236	−	1.73551i
$799$			12.5175i			0.442839i
$800$		0			0
$801$	14.0942	−	2.48519i	0.497994	−	0.0878098i
$802$	−15.9184	+	1.39268i	−0.562100	+	0.0491773i
$803$	−10.8931	−	0.953021i	−0.384409	−	0.0336314i
$804$	−8.11695	−	1.43124i	−0.286263	−	0.0504758i
$805$		0			0
$806$	17.2849	−	9.97946i	0.608836	−	0.351511i
$807$	5.91437	−	12.6834i	0.208196	−	0.446477i
$808$	−2.45146	+	5.25718i	−0.0862422	+	0.184947i
$809$	−38.0948	+	21.9941i	−1.33934	+	0.773270i	−0.986710	−	0.162491i	$-0.948047\pi$
$809$	−38.0948	+	21.9941i	−1.33934	+	0.773270i	−0.352634	+	0.935762i	$0.614714\pi$
$810$		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	$0.591727\pi$
$812$	29.0525	+	2.54176i	1.01954	+	0.0891983i
$813$	40.7339	−	3.56375i	1.42860	−	0.124986i
$814$	14.1150	−	2.48886i	0.494731	−	0.0872343i
$815$		0			0
$816$			4.14814i			0.145214i
$817$	−7.27901	−	42.7374i	−0.254660	−	1.49519i
$818$	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	$0.577577\pi$
$822$	−4.25680	+	48.6554i	−0.148473	+	1.69705i
$823$	35.5752	−	24.9100i	1.24007	−	0.868309i	0.245203	−	0.969472i	$-0.421145\pi$
$823$	35.5752	−	24.9100i	1.24007	−	0.868309i	0.994870	+	0.101163i	$0.0322564\pi$
$824$	1.77503	+	1.02481i	0.0618362	+	0.0357011i
$825$		0			0
$826$	−7.39053	+	2.68993i	−0.257149	+	0.0935947i
$827$	14.0575	+	6.55512i	0.488827	+	0.227944i	0.651374	−	0.758757i	$-0.274193\pi$
$827$	14.0575	+	6.55512i	0.488827	+	0.227944i	−0.162547	+	0.986701i	$0.551971\pi$
$828$	−7.10065	+	26.5000i	−0.246765	+	0.920938i
$829$	−22.3718	+	38.7490i	−0.777003	+	1.34581i	0.156658	+	0.987653i	$0.449928\pi$
$829$	−22.3718	+	38.7490i	−0.777003	+	1.34581i	−0.933662	+	0.358156i	$0.883405\pi$
$830$		0			0
$831$	4.63728	+	5.52649i	0.160865	+	0.191712i
$832$	0.190417	+	2.17648i	0.00660153	+	0.0754558i
$833$	4.94214	−	7.05810i	0.171235	−	0.244549i
$834$	−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
$838$	19.6038	−	9.14141i	0.677203	−	0.315785i
$839$	9.72552	+	55.1562i	0.335762	+	1.90420i	0.419575	+	0.907721i	$0.362179\pi$
$839$	9.72552	+	55.1562i	0.335762	+	1.90420i	−0.0838127	+	0.996482i	$0.526710\pi$
$840$		0			0
$841$	25.3332	−	21.2571i	0.873559	−	0.733003i
$842$	−9.25426	−	13.2164i	−0.318923	−	0.455469i
$843$	−29.6963	+	7.95709i	−1.02279	+	0.274057i
$844$	−4.86846	−	8.43242i	−0.167579	−	0.290256i
$845$		0			0
$846$	−24.6819	−	67.8128i	−0.848580	−	2.33145i
$847$	24.0961	+	6.45654i	0.827953	+	0.221849i
$848$	−2.35175	−	8.77685i	−0.0807594	−	0.301398i
$849$	14.9234	−	84.6348i	0.512170	−	2.90466i
$850$		0			0
$851$	−16.5214	+	19.6895i	−0.566347	+	0.674946i
$852$	10.4120	+	7.29053i	0.356708	+	0.249769i
$853$	−0.0798783	−	0.171300i	−0.00273498	−	0.00586519i	0.904936	−	0.425549i	$-0.139919\pi$
$853$	−0.0798783	−	0.171300i	−0.00273498	−	0.00586519i	−0.907671	+	0.419683i	$0.862141\pi$
$854$	41.6586			1.42553
$855$		0			0
$856$	14.9436			0.510760
$857$	10.3196	+	22.1305i	0.352511	+	0.755963i	0.999981	−	0.00612819i	$-0.00195068\pi$
$857$	10.3196	+	22.1305i	0.352511	+	0.755963i	−0.647470	+	0.762091i	$0.724173\pi$
$858$	−11.9200	−	8.34651i	−0.406944	−	0.284945i
$859$	21.5057	−	25.6295i	0.733766	−	0.874469i	−0.262124	−	0.965034i	$-0.584423\pi$
$859$	21.5057	−	25.6295i	0.733766	−	0.874469i	0.995890	+	0.0905656i	$0.0288675\pi$
$860$		0			0
$861$	16.1694	−	91.7010i	0.551051	−	3.12516i
$862$	0.0814698	+	0.304049i	0.00277487	+	0.0103560i
$863$	−8.46520	−	2.26824i	−0.288159	−	0.0772119i	0.111844	−	0.993726i	$-0.464324\pi$
$863$	−8.46520	−	2.26824i	−0.288159	−	0.0772119i	−0.400003	+	0.916514i	$0.630991\pi$
$864$	−4.86846	−	13.3760i	−0.165628	−	0.455060i
$865$		0			0
$866$	3.33868	+	5.78276i	0.113453	+	0.196506i
$867$	−47.8335	+	12.8169i	−1.62451	+	0.435286i
$868$	−19.3961	−	27.7006i	−0.658348	−	0.940218i
$869$	3.51422	−	2.94878i	0.119212	−	0.100030i
$870$		0			0
$871$	0.969093	+	5.49600i	0.0328365	+	0.186225i
$872$	8.87345	−	4.13776i	0.300493	−	0.140122i
$873$	−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
$877$	−14.7428	+	21.0549i	−0.497829	+	0.710973i	−0.986911	−	0.161265i	$-0.948443\pi$
$877$	−14.7428	+	21.0549i	−0.497829	+	0.710973i	0.489083	+	0.872237i	$0.337332\pi$
$878$	1.46638	+	16.7608i	0.0494880	+	0.565650i
$879$	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	$-0.0518047\pi$
$882$	−12.8566	+	47.9816i	−0.432905	+	1.61562i
$883$	−42.2538	−	19.7033i	−1.42195	−	0.663067i	−0.448886	−	0.893589i	$-0.648179\pi$
$883$	−42.2538	−	19.7033i	−1.42195	−	0.663067i	−0.973067	+	0.230522i	$0.925957\pi$
$884$	2.63933	−	0.960637i	0.0887702	−	0.0323097i
$885$		0			0
$886$	−28.4944	−	16.4512i	−0.957287	−	0.552690i
$887$	−13.7280	+	9.61244i	−0.460940	+	0.322754i	−0.780877	−	0.624685i	$-0.785227\pi$
$887$	−13.7280	+	9.61244i	−0.460940	+	0.322754i	0.319936	+	0.947439i	$0.396338\pi$
$888$	1.95270	−	22.3194i	0.0655282	−	0.748990i
$889$	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
$893$	−41.7538	−	7.61367i	−1.39724	−	0.254782i
$894$		−	49.4826i		−	1.65494i
$895$		0			0
$896$	3.64543	−	0.642788i	0.121785	−	0.0214740i
$897$	25.9961	−	2.27436i	0.867984	−	0.0759387i
$898$	8.32180	+	0.728063i	0.277702	+	0.0242958i
$899$	−70.8793	−	12.4979i	−2.36396	−	0.416830i
$900$		0			0
$901$	−10.1163	+	5.84067i	−0.337024	+	0.194581i
$902$	6.80087	−	14.5845i	0.226444	−	0.485611i
$903$	−50.2045	+	107.664i	−1.67070	+	3.58283i
$904$	8.72254	−	5.03596i	0.290107	−	0.167494i
$905$		0			0
$906$	20.1150	+	3.54682i	0.668276	+	0.117835i
$907$	41.3854	+	3.62075i	1.37418	+	0.120225i	0.750197	−	0.661214i	$-0.229959\pi$
$907$	41.3854	+	3.62075i	1.37418	+	0.120225i	0.623981	+	0.781439i	$0.285514\pi$
$908$	−1.21698	+	0.106472i	−0.0403869	+	0.00353340i
$909$	−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	$0.874672\pi$
$912$	−13.8366	−	2.52307i	−0.458176	−	0.0835471i
$913$	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
$917$	−5.75889	+	65.8244i	−0.190175	+	2.17371i
$918$	−14.9900	+	10.4961i	−0.494744	+	0.346423i
$919$	−22.4279	−	12.9488i	−0.739829	−	0.427141i	0.0821778	−	0.996618i	$-0.473812\pi$
$919$	−22.4279	−	12.9488i	−0.739829	−	0.427141i	−0.822007	+	0.569477i	$0.807146\pi$
$920$		0			0
$921$	−27.2735	+	9.92674i	−0.898692	+	0.327097i
$922$	−8.25076	−	3.84739i	−0.271724	−	0.126707i
$923$	2.22750	−	8.31315i	0.0733191	−	0.273631i
$924$	−12.3274	+	21.3516i	−0.405541	+	0.702417i
$925$		0			0
$926$	−3.45249	−	4.11451i	−0.113456	−	0.135211i
$927$	1.32396	+	15.1330i	0.0434847	+	0.497032i
$928$	4.51890	−	6.45366i	0.148340	−	0.211852i
$929$	8.24476	−	22.6523i	0.270502	−	0.743198i	−0.727846	−	0.685740i	$-0.759479\pi$
$929$	8.24476	−	22.6523i	0.270502	−	0.743198i	0.998348	−	0.0574572i	$-0.0182993\pi$
$930$		0			0
$931$	20.5371	+	20.7781i	0.673078	+	0.680975i
$932$	−2.98204	+	2.98204i	−0.0976799	+	0.0976799i
$933$	29.1239	−	13.5807i	0.953474	−	0.444612i
$934$	1.60981	+	9.12970i	0.0526747	+	0.298733i
$935$		0			0
$936$	−12.4042	+	10.4084i	−0.405444	+	0.340208i
$937$	−4.41154	−	6.30034i	−0.144119	−	0.205823i	0.740602	−	0.671943i	$-0.234540\pi$
$937$	−4.41154	−	6.30034i	−0.144119	−	0.205823i	−0.884721	+	0.466120i	$0.845651\pi$
$938$	9.13327	−	2.44725i	0.298212	−	0.0799056i
$939$	−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	$0.799633\pi$
$942$	−10.9335	−	2.92963i	−0.356233	−	0.0954524i
$943$	7.46901	+	27.8747i	0.243224	+	0.907726i
$944$	−0.368946	+	2.09240i	−0.0120082	+	0.0681017i
$945$		0			0
$946$	−13.1964	+	15.7269i	−0.429052	+	0.511324i
$947$	−24.7769	−	17.3490i	−0.805140	−	0.563765i	0.0969618	−	0.995288i	$-0.469088\pi$
$947$	−24.7769	−	17.3490i	−0.805140	−	0.563765i	−0.902102	+	0.431523i	$0.857976\pi$
$948$	−3.03062	−	6.49919i	−0.0984300	−	0.211084i
$949$	11.5736			0.375696
$950$		0			0
$951$	85.8340			2.78336
$952$	−2.01114	−	4.31291i	−0.0651815	−	0.139782i
$953$	43.0873	+	30.1701i	1.39573	+	0.977304i	0.998216	+	0.0597101i	$0.0190176\pi$
$953$	43.0873	+	30.1701i	1.39573	+	0.977304i	0.397519	+	0.917594i	$0.369871\pi$
$954$	43.2880	−	51.5886i	1.40150	−	1.67024i
$955$		0			0
$956$	4.44238	−	25.1940i	0.143677	−	0.814832i
$957$	13.5813	+	50.6860i	0.439021	+	1.63845i
$958$	−13.6452	−	3.65623i	−0.440858	−	0.118128i
$959$	−19.1637	−	52.6519i	−0.618829	−	1.70022i
$960$		0			0
$961$	26.2276	+	45.4276i	0.846052	+	1.46541i
$962$	−14.6533	+	3.92635i	−0.472442	+	0.126591i
$963$	63.5258	+	90.7242i	2.04709	+	2.92355i
$964$	13.6206	−	11.4290i	0.438689	−	0.368104i
$965$		0			0
$966$	−7.67752	−	43.5414i	−0.247020	−	1.40092i
$967$	−2.98039	+	1.38978i	−0.0958430	+	0.0446923i	−0.469949	−	0.882694i	$-0.655728\pi$
$967$	−2.98039	+	1.38978i	−0.0958430	+	0.0446923i	0.374106	+	0.927386i	$0.377950\pi$
$968$	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	$-0.0746050\pi$
$972$	19.3609	−	27.6502i	0.621000	−	0.886880i
$973$	−7.13189	−	81.5179i	−0.228638	−	2.61334i
$974$	−2.61413	−	3.11540i	−0.0837622	−	0.0998239i
$975$		0			0
$976$	5.62701	−	9.74627i	0.180116	−	0.311970i
$977$	−4.13133	+	15.4183i	−0.132173	+	0.493276i	−0.999994	−	0.00360160i	$-0.998854\pi$
$977$	−4.13133	+	15.4183i	−0.132173	+	0.493276i	0.867821	+	0.496878i	$0.165520\pi$
$978$	41.3443	+	19.2792i	1.32205	+	0.616480i
$979$	−3.74557	+	1.36327i	−0.119709	+	0.0435704i
$980$		0			0
$981$	62.8423	+	36.2820i	2.00640	+	1.15840i
$982$	−2.30829	+	1.61628i	−0.0736603	+	0.0515775i
$983$	2.65887	−	30.3910i	0.0848048	−	0.969323i	−0.827946	−	0.560807i	$-0.810491\pi$
$983$	2.65887	−	30.3910i	0.0848048	−	0.969323i	0.912751	−	0.408516i	$-0.133954\pi$
$984$	−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
$988$	1.59897	+	9.38810i	0.0508701	+	0.298675i
$989$		−	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	$0.529282\pi$
$992$	−9.10062	+	0.796201i	−0.288945	+	0.0252794i
$993$	−84.2554	−	7.37139i	−2.67376	−	0.233924i
$994$	−14.3602	−	2.53209i	−0.455478	−	0.0803130i
$995$		0			0
$996$	39.6946	−	22.9177i	1.25777	−	0.726176i
$997$	12.7592	−	27.3622i	0.404088	−	0.866570i	−0.593982	−	0.804478i	$-0.702445\pi$
$997$	12.7592	−	27.3622i	0.404088	−	0.866570i	0.998070	−	0.0620919i	$-0.0197772\pi$
$998$	−1.10050	+	2.36003i	−0.0348358	+	0.0747055i
$999$	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.243.1	✓	24
5.2	odd	4	inner	950.2.bb.a.357.2	yes	24
5.3	odd	4	inner	950.2.bb.a.357.1	yes	24
5.4	even	2	inner	950.2.bb.a.243.2	yes	24
19.14	odd	18	inner	950.2.bb.a.793.2	yes	24
95.14	odd	18	inner	950.2.bb.a.793.1	yes	24
95.33	even	36	inner	950.2.bb.a.907.2	yes	24
95.52	even	36	inner	950.2.bb.a.907.1	yes	24

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

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

Related objects

Downloads

Learn more