LMFDB - Embedded newform 950.2.bb.a.357.1

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			357.1
Character	$\chi$	$=$	950.357
Dual form			950.2.bb.a.793.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.906308 + 0.422618i) q^{2} +(-1.85075 + 2.64314i) q^{3} +(0.642788 - 0.766044i) q^{4} +(0.560307 - 3.17766i) q^{6} +(3.57554 - 0.958062i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-2.53487 - 6.96451i) q^{9} +O(q^{10})$	\(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	$0.575911\pi$
$3$	−1.85075	+	2.64314i	−1.06853	+	1.52602i	−0.832303	+	0.554321i	$0.812978\pi$
$4$	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	0.490765	−	0.871292i	$-0.336718\pi$
$7$	3.57554	−	0.958062i	1.35143	−	0.362113i	0.860661	+	0.509179i	$0.170051\pi$
$8$	−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	−0.794801	−	0.606870i	$-0.792425\pi$
$13$	−1.78968	+	1.25315i	−0.496367	+	0.347560i	0.298434	+	0.954430i	$0.403536\pi$
$14$	−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	0.961112	−	0.276159i	$-0.0890615\pi$
$17$	0.543308	+	1.16513i	0.131771	+	0.282585i	−0.829341	+	0.558743i	$0.811284\pi$
$18$	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	0.304053	−	0.952655i	$-0.401660\pi$
$23$	3.68758	−	0.322621i	0.768914	−	0.0672712i	0.464861	+	0.885384i	$0.346104\pi$
$24$	−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	−0.984205	−	0.177032i	$-0.943350\pi$
$37$	−4.90984	+	4.90984i	−0.807173	+	0.807173i	0.177032	+	0.984205i	$0.443350\pi$
$38$	−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	$0.301778\pi$
$43$	−0.866836	+	9.90798i	−0.132191	+	1.51095i	−0.715448	+	0.698666i	$0.753778\pi$
$44$	−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	−0.346054	−	0.938215i	$-0.612478\pi$
$47$	−8.82464	−	4.11500i	−1.28721	−	0.600234i	−0.941153	+	0.337980i	$0.890256\pi$
$48$	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	$0.186741\pi$
$53$	0.791938	+	9.05189i	0.108781	+	1.24337i	−0.724012	+	0.689788i	$0.757704\pi$
$54$	−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	−0.829265	−	0.558856i	$-0.811240\pi$
$67$	1.07953	−	2.31505i	0.131885	−	0.282829i	0.961150	+	0.276028i	$0.0890181\pi$
$68$	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	0.799260	−	0.600985i	$-0.205225\pi$
$73$	4.33934	+	3.03844i	0.507882	+	0.355623i	−0.291378	+	0.956608i	$0.594114\pi$
$74$	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	$-0.798752\pi$
$83$	−3.67656	−	13.7211i	−0.403555	−	1.50609i	0.403151	−	0.915133i	$-0.367915\pi$
$84$	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	−0.171330	−	0.985214i	$-0.554807\pi$
$97$	4.66105	−	2.17348i	0.473258	−	0.220684i	0.644589	+	0.764530i	$0.277029\pi$
$98$	−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	−0.987124	−	0.159959i	$-0.948864\pi$
$103$	−0.530483	+	1.97979i	−0.0522701	+	0.195075i	0.934854	+	0.355033i	$0.115531\pi$
$104$	−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	$-0.826407\pi$
$107$	−3.86768	−	14.4344i	−0.373903	−	1.39542i	0.481039	−	0.876699i	$-0.340260\pi$
$108$	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	0.957710	−	0.287736i	$-0.0929025\pi$
$113$	7.12192	+	7.12192i	0.669974	+	0.669974i	−0.287736	+	0.957710i	$0.592902\pi$
$114$	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	0.725124	−	0.688618i	$-0.241782\pi$
$127$	−1.91549	−	2.73560i	−0.169972	−	0.242746i	−0.895096	+	0.445873i	$0.852893\pi$
$128$	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	$0.196035\pi$
$137$	1.31925	+	15.0791i	0.112711	+	1.28829i	−0.703565	+	0.710631i	$0.748410\pi$
$138$	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	−0.0531542	−	0.998586i	$-0.516927\pi$
$157$	−3.49465	−	0.305743i	−0.278904	−	0.0244009i	−0.225749	+	0.974185i	$0.572483\pi$
$158$	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	−0.319290	−	0.947657i	$-0.603444\pi$
$163$	−13.6561	−	3.65915i	−1.06963	−	0.286607i	−0.750341	+	0.661050i	$0.770111\pi$
$164$	−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	0.0838559	−	0.996478i	$-0.473276\pi$
$167$	4.38698	−	0.383811i	0.339474	−	0.0297002i	0.255618	+	0.966778i	$0.417721\pi$
$168$	−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	$0.192374\pi$
$173$	9.59154	+	20.5691i	0.729232	+	1.56384i	−0.0936344	+	0.995607i	$0.529848\pi$
$174$	−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	−0.569942	−	0.821685i	$-0.693034\pi$
$193$	5.51698	−	7.87906i	0.397121	−	0.567147i	0.967063	+	0.254538i	$0.0819233\pi$
$194$	−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	−0.297510	−	0.954719i	$-0.596156\pi$
$197$	−1.09199	+	0.292599i	−0.0778014	+	0.0208468i	0.219708	+	0.975566i	$0.429489\pi$
$198$	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	0.191759	−	0.981442i	$-0.438581\pi$
$223$	3.13866	+	0.274597i	0.210180	+	0.0183884i	0.0184205	+	0.999830i	$0.494136\pi$
$224$	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	−0.677858	−	0.735192i	$-0.737092\pi$
$227$	0.863822	−	0.863822i	0.0573339	−	0.0573339i	0.735192	+	0.677858i	$0.237092\pi$
$228$	−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	$0.0718903\pi$
$233$	−0.367557	+	4.20119i	−0.0240794	+	0.275229i	−0.998684	+	0.0512945i	$0.983665\pi$
$234$	−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	−0.999848	−	0.0174210i	$-0.994454\pi$
$257$	−5.51174	+	11.8200i	−0.343813	+	0.737309i	0.656035	+	0.754730i	$0.272232\pi$
$258$	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	0.402928	−	0.915232i	$-0.367993\pi$
$263$	−5.17817	−	3.62579i	−0.319299	−	0.223576i	−0.722227	+	0.691656i	$0.756881\pi$
$264$	−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	−0.946360	−	0.323115i	$-0.895270\pi$
$277$	0.578676	−	2.15965i	0.0347693	−	0.129761i	0.981129	+	0.193354i	$0.0619366\pi$
$278$	−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	0.459230	−	0.888318i	$-0.348125\pi$
$283$	24.1389	−	11.2561i	1.43491	−	0.669108i	0.975678	+	0.219209i	$0.0703477\pi$
$284$	−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	−0.997144	−	0.0755241i	$-0.975937\pi$
$293$	−1.64034	+	6.12185i	−0.0958299	+	0.357642i	0.901314	+	0.433166i	$0.142604\pi$
$294$	−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	0.764622	−	0.644478i	$-0.222925\pi$
$307$	7.36823	+	5.15929i	0.420527	+	0.294456i	−0.344095	+	0.938935i	$0.611814\pi$
$308$	−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	$-0.647189\pi$
$313$	9.31017	−	19.9657i	0.526242	−	1.12853i	0.972345	−	0.233548i	$-0.0750336\pi$
$314$	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	$-0.925919\pi$
$317$	−15.2579	−	21.7905i	−0.856968	−	1.22388i	0.116071	−	0.993241i	$-0.462970\pi$
$318$	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	$-0.746679\pi$
$337$	2.08234	−	23.8013i	0.113432	−	1.29654i	0.813123	−	0.582092i	$-0.197766\pi$
$338$	−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	0.400930	−	0.916109i	$-0.368687\pi$
$347$	11.8602	+	1.03763i	0.636688	+	0.0557030i	0.235758	+	0.971812i	$0.424243\pi$
$348$	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	0.566692	−	0.823930i	$-0.308223\pi$
$353$	12.1278	+	3.24962i	0.645496	+	0.172960i	0.0788042	+	0.996890i	$0.474890\pi$
$354$	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	−0.0489341	−	0.998802i	$-0.515582\pi$
$367$	16.7223	−	11.7091i	0.872896	−	0.611209i	0.921830	+	0.387593i	$0.126694\pi$
$368$	−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	−0.976054	−	0.217527i	$-0.930201\pi$
$373$	−33.0754	+	8.86252i	−1.71258	+	0.458884i	−0.736524	+	0.676411i	$0.763534\pi$
$374$	−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	−0.524629	−	0.851331i	$-0.675796\pi$
$383$	8.90050	−	12.7112i	0.454794	−	0.649513i	0.979423	+	0.201818i	$0.0646848\pi$
$384$	−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	0.711706	−	0.702477i	$-0.247923\pi$
$397$	−5.65663	−	12.1307i	−0.283898	−	0.608822i	−0.995605	+	0.0936552i	$0.970145\pi$
$398$	−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	$-0.976484\pi$
$433$	−0.581970	−	6.65195i	−0.0279677	−	0.319672i	0.969305	−	0.245863i	$-0.0790712\pi$
$434$	−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	$0.0911628\pi$
$443$	18.8721	+	26.9521i	0.896640	+	1.28053i	−0.0626285	+	0.998037i	$0.519948\pi$
$444$	−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	0.495919	−	0.868369i	$-0.334831\pi$
$457$	−7.96206	−	7.96206i	−0.372450	−	0.372450i	−0.868369	+	0.495919i	$0.834831\pi$
$458$	−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	0.990676	−	0.136240i	$-0.0435017\pi$
$463$	1.39015	+	5.18810i	0.0646056	+	0.241111i	−0.926070	+	0.377351i	$0.876835\pi$
$464$	−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	−0.998959	−	0.0456091i	$-0.985477\pi$
$467$	−2.39939	+	8.95465i	−0.111031	+	0.414372i	0.887929	+	0.459981i	$0.152144\pi$
$468$	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	0.937968	−	0.346722i	$-0.112705\pi$
$487$	−1.05258	−	3.92829i	−0.0476971	−	0.178008i	−0.985665	+	0.168714i	$0.946039\pi$
$488$	−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	−0.808851	−	0.588014i	$-0.799910\pi$
$503$	3.62237	−	7.76819i	0.161513	−	0.346367i	0.970364	+	0.241647i	$0.0776877\pi$
$504$	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	−0.0440910	−	0.999028i	$-0.514039\pi$
$523$	−19.1582	−	8.93364i	−0.837732	−	0.390641i	−0.793641	+	0.608387i	$0.791817\pi$
$524$	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	0.791107	−	0.611678i	$-0.209505\pi$
$547$	39.2080	−	3.43025i	1.67641	−	0.146667i	0.885305	+	0.465011i	$0.153950\pi$
$548$	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	−0.388226	−	0.921564i	$-0.626912\pi$
$557$	8.14183	−	5.70097i	0.344980	−	0.241558i	0.733206	+	0.680007i	$0.238023\pi$
$558$	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	−0.569260	−	0.822157i	$-0.692770\pi$
$563$	−15.4508	+	4.14004i	−0.651175	+	0.174482i	−0.0819150	+	0.996639i	$0.526104\pi$
$564$	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	−0.555467	−	0.831538i	$-0.687461\pi$
$577$	−14.9109	+	3.99535i	−0.620747	+	0.166329i	−0.0652797	+	0.997867i	$0.520794\pi$
$578$	−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	0.928465	−	0.371419i	$-0.121129\pi$
$587$	1.14200	+	2.44904i	0.0471356	+	0.101083i	−0.881330	+	0.472502i	$0.843351\pi$
$588$	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	0.0837754	−	0.996485i	$-0.473302\pi$
$593$	8.26288	−	0.722909i	0.339316	−	0.0296863i	0.255540	+	0.966798i	$0.417747\pi$
$594$	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	−0.353798	−	0.935322i	$-0.615110\pi$
$607$	14.3272	−	14.3272i	0.581524	−	0.581524i	0.935322	+	0.353798i	$0.115110\pi$
$608$	−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	$-0.803270\pi$
$613$	2.18465	−	24.9707i	0.0882373	−	1.00856i	0.903250	−	0.429114i	$-0.141174\pi$
$614$	−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	0.314063	−	0.949402i	$-0.398310\pi$
$617$	−5.24969	−	2.44797i	−0.211345	−	0.0985516i	−0.525408	+	0.850850i	$0.676087\pi$
$618$	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	0.849211	−	0.528054i	$-0.177078\pi$
$643$	16.3163	+	11.4248i	0.643450	+	0.450549i	−0.205761	+	0.978602i	$0.565967\pi$
$644$	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	$-0.273774\pi$
$647$	−2.68415	−	2.68415i	−0.105525	−	0.105525i	−0.757898	+	0.652373i	$0.773774\pi$
$648$	−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	$-0.924292\pi$
$653$	−6.33751	−	23.6519i	−0.248006	−	0.925571i	0.723843	−	0.689965i	$-0.242374\pi$
$654$	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	$-0.793840\pi$
$673$	5.05413	−	18.8623i	0.194822	−	0.727087i	0.992313	−	0.123755i	$-0.0394937\pi$
$674$	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	0.966388	−	0.257087i	$-0.0827628\pi$
$677$	0.0241410	+	0.0900954i	0.000927814	+	0.00346265i	−0.965460	+	0.260550i	$0.916096\pi$
$678$	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	0.328852	−	0.944381i	$-0.393338\pi$
$683$	−16.0864	−	16.0864i	−0.615529	−	0.615529i	−0.944381	+	0.328852i	$0.893338\pi$
$684$	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	0.613231	−	0.789904i	$-0.289870\pi$
$727$	29.1194	+	2.54762i	1.07998	+	0.0944860i	0.466749	+	0.884390i	$0.345425\pi$
$728$	−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	−0.770864	−	0.636999i	$-0.780175\pi$
$733$	−47.5677	−	12.7457i	−1.75695	−	0.470774i	−0.986088	+	0.166225i	$0.946842\pi$
$734$	−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	$-0.945404\pi$
$743$	−13.1579	−	28.2173i	−0.482718	−	1.03519i	0.502609	−	0.864514i	$-0.332374\pi$
$744$	−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	−0.491194	−	0.871050i	$-0.663439\pi$
$757$	13.6281	−	19.4630i	0.495323	−	0.707395i	0.986518	+	0.163655i	$0.0523283\pi$
$758$	−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	−0.925576	−	0.378562i	$-0.876419\pi$
$773$	−24.6447	+	17.2564i	−0.886409	+	0.620670i	0.0391668	+	0.999233i	$0.487530\pi$
$774$	−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	−0.196619	−	0.980480i	$-0.562996\pi$
$787$	−24.0457	−	6.44302i	−0.857136	−	0.229669i	−0.660517	+	0.750811i	$0.729663\pi$
$788$	−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	−0.850136	−	0.526564i	$-0.823480\pi$
$797$	−9.13482	+	9.13482i	−0.323572	+	0.323572i	0.526564	+	0.850136i	$0.323480\pi$
$798$	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	$0.0788548\pi$
$823$	24.9100	+	35.5752i	0.868309	+	1.24007i	−0.101163	+	0.994870i	$0.532256\pi$
$824$	−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	−0.758757	−	0.651374i	$-0.774193\pi$
$827$	6.55512	−	14.0575i	0.227944	−	0.488827i	0.986701	+	0.162547i	$0.0519708\pi$
$828$	−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	−0.419683	−	0.907671i	$-0.637859\pi$
$853$	0.171300	−	0.0798783i	0.00586519	−	0.00273498i	0.425549	+	0.904936i	$0.360081\pi$
$854$	−41.6586			−1.42553
$855$		0			0
$856$	14.9436			0.510760
$857$	22.1305	−	10.3196i	0.755963	−	0.352511i	−0.00612819	−	0.999981i	$-0.501951\pi$
$857$	22.1305	−	10.3196i	0.755963	−	0.352511i	0.762091	+	0.647470i	$0.224173\pi$
$858$	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	−0.916514	−	0.400003i	$-0.869009\pi$
$863$	2.26824	−	8.46520i	0.0772119	−	0.288159i	0.993726	+	0.111844i	$0.0356757\pi$
$864$	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	0.872237	−	0.489083i	$-0.162668\pi$
$877$	21.0549	+	14.7428i	0.710973	+	0.497829i	−0.161265	+	0.986911i	$0.551557\pi$
$878$	−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	$-0.574043\pi$
$883$	19.7033	−	42.2538i	0.663067	−	1.42195i	0.893589	−	0.448886i	$-0.148179\pi$
$884$	−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	0.947439	−	0.319936i	$-0.103662\pi$
$887$	9.61244	+	13.7280i	0.322754	+	0.460940i	−0.624685	+	0.780877i	$0.714773\pi$
$888$	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	$-0.729959\pi$
$907$	3.62075	−	41.3854i	0.120225	−	1.37418i	0.781439	−	0.623981i	$-0.214486\pi$
$908$	−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	−0.671943	−	0.740602i	$-0.734540\pi$
$937$	−6.30034	+	4.41154i	−0.205823	+	0.144119i	0.466120	+	0.884721i	$0.345651\pi$
$938$	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	−0.995288	−	0.0969618i	$-0.969088\pi$
$947$	−17.3490	+	24.7769i	−0.563765	+	0.805140i	0.431523	+	0.902102i	$0.357976\pi$
$948$	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	$0.519018\pi$
$953$	−30.1701	+	43.0873i	−0.977304	+	1.39573i	−0.917594	+	0.397519i	$0.869871\pi$
$954$	−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	0.927386	−	0.374106i	$-0.122050\pi$
$967$	1.38978	+	2.98039i	0.0446923	+	0.0958430i	−0.882694	+	0.469949i	$0.844272\pi$
$968$	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	0.496878	−	0.867821i	$-0.334480\pi$
$977$	15.4183	+	4.13133i	0.493276	+	0.132173i	−0.00360160	+	0.999994i	$0.501146\pi$
$978$	−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	0.560807	−	0.827946i	$-0.310491\pi$
$983$	30.3910	+	2.65887i	0.969323	+	0.0848048i	0.408516	+	0.912751i	$0.366046\pi$
$984$	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	−0.0620919	−	0.998070i	$-0.519777\pi$
$997$	−27.3622	−	12.7592i	−0.866570	−	0.404088i	−0.804478	+	0.593982i	$0.797555\pi$
$998$	−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.357.1	yes	24
5.2	odd	4	inner	950.2.bb.a.243.1	✓	24
5.3	odd	4	inner	950.2.bb.a.243.2	yes	24
5.4	even	2	inner	950.2.bb.a.357.2	yes	24
19.14	odd	18	inner	950.2.bb.a.907.2	yes	24
95.14	odd	18	inner	950.2.bb.a.907.1	yes	24
95.33	even	36	inner	950.2.bb.a.793.1	yes	24
95.52	even	36	inner	950.2.bb.a.793.2	yes	24

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

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Database

Properties

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