LMFDB - Embedded newform 855.2.be.d.334.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(64,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("855.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.be (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6x^{10} + 29x^{8} - 40x^{6} + 43x^{4} - 7x^{2} + 1 $ x^12 - 6x^10 + 29x^8 - 40x^6 + 43x^4 - 7*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			334.2
Root			$-1.00376 - 0.579521i$ of defining polynomial
Character	$\chi$	$=$	855.334
Dual form			855.2.be.d.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.747190 - 0.431391i) q^{2} +(-0.627804 - 1.08739i) q^{4} +(-1.95987 + 1.07652i) q^{5} -0.566520i q^{7} +2.80888i q^{8} +O(q^{10})$	\(q+(-0.747190 - 0.431391i) q^{2} +(-0.627804 - 1.08739i) q^{4} +(-1.95987 + 1.07652i) q^{5} -0.566520i q^{7} +2.80888i q^{8} +(1.92880 + 0.0411078i) q^{10} +1.91223 q^{11} +(0.168469 - 0.0972656i) q^{13} +(-0.244391 + 0.423298i) q^{14} +(-0.0438854 + 0.0760118i) q^{16} +(-4.58603 - 2.64775i) q^{17} +(2.36834 + 3.65936i) q^{19} +(2.40101 + 1.45530i) q^{20} +(-1.42880 - 0.824918i) q^{22} +(-2.92318 + 1.68770i) q^{23} +(2.68222 - 4.21968i) q^{25} -0.167838 q^{26} +(-0.616027 + 0.355664i) q^{28} +(4.36834 + 7.56619i) q^{29} +5.65662 q^{31} +(4.93070 - 2.84674i) q^{32} +(2.28442 + 3.95674i) q^{34} +(0.609869 + 1.11031i) q^{35} -0.955582i q^{37} +(-0.190988 - 3.75592i) q^{38} +(-3.02381 - 5.50505i) q^{40} +(5.02496 - 8.70349i) q^{41} +(4.27161 + 2.46622i) q^{43} +(-1.20051 - 2.07934i) q^{44} +2.91223 q^{46} +(7.65516 - 4.41971i) q^{47} +6.67906 q^{49} +(-3.82446 + 1.99582i) q^{50} +(-0.211531 - 0.122128i) q^{52} +(7.10669 - 4.10305i) q^{53} +(-3.74773 + 2.05855i) q^{55} +1.59128 q^{56} -7.53785i q^{58} +(-1.85713 + 3.21664i) q^{59} +(1.75561 + 3.04080i) q^{61} +(-4.22657 - 2.44021i) q^{62} -4.73669 q^{64} +(-0.225470 + 0.371988i) q^{65} +(-3.50190 + 2.02182i) q^{67} +6.64906i q^{68} +(0.0232884 - 1.09270i) q^{70} +(2.59767 - 4.49929i) q^{71} +(-7.45136 - 4.30205i) q^{73} +(-0.412229 + 0.714002i) q^{74} +(2.49230 - 4.87268i) q^{76} -1.08332i q^{77} +(3.31324 - 5.73870i) q^{79} +(0.00418190 - 0.196217i) q^{80} +(-7.50921 + 4.33544i) q^{82} +4.51737i q^{83} +(11.8384 + 0.252307i) q^{85} +(-2.12780 - 3.68547i) q^{86} +5.37122i q^{88} +(-1.68676 - 2.92155i) q^{89} +(-0.0551029 - 0.0954410i) q^{91} +(3.67037 + 2.11909i) q^{92} -7.62648 q^{94} +(-8.58103 - 4.62233i) q^{95} +(13.1568 + 7.59611i) q^{97} +(-4.99053 - 2.88128i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{4} + 2 q^{5}+O(q^{10}) $ 12 * q + 2 * q^4 + 2 * q^5	$ 12 q + 2 q^{4} + 2 q^{5} + 6 q^{10} - 4 q^{11} - 22 q^{14} - 14 q^{16} - 12 q^{19} + 40 q^{20} - 6 q^{25} + 44 q^{26} + 12 q^{29} + 60 q^{31} + 10 q^{34} + 10 q^{40} + 12 q^{41} - 20 q^{44} + 8 q^{46} - 4 q^{49} + 8 q^{50} - 18 q^{55} - 92 q^{56} - 20 q^{59} + 2 q^{61} + 24 q^{64} + 40 q^{65} + 46 q^{70} - 2 q^{71} + 22 q^{74} - 70 q^{76} + 24 q^{79} + 22 q^{80} + 2 q^{85} - 16 q^{86} - 36 q^{89} + 24 q^{91} - 60 q^{94} - 46 q^{95}+O(q^{100}) $ 12 * q + 2 * q^4 + 2 * q^5 + 6 * q^10 - 4 * q^11 - 22 * q^14 - 14 * q^16 - 12 * q^19 + 40 * q^20 - 6 * q^25 + 44 * q^26 + 12 * q^29 + 60 * q^31 + 10 * q^34 + 10 * q^40 + 12 * q^41 - 20 * q^44 + 8 * q^46 - 4 * q^49 + 8 * q^50 - 18 * q^55 - 92 * q^56 - 20 * q^59 + 2 * q^61 + 24 * q^64 + 40 * q^65 + 46 * q^70 - 2 * q^71 + 22 * q^74 - 70 * q^76 + 24 * q^79 + 22 * q^80 + 2 * q^85 - 16 * q^86 - 36 * q^89 + 24 * q^91 - 60 * q^94 - 46 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.747190	−	0.431391i	−0.528343	−	0.305039i	0.211998	−	0.977270i	$-0.432003\pi$
$2$	−0.747190	−	0.431391i	−0.528343	−	0.305039i	−0.740342	+	0.672231i	$0.765336\pi$
$3$		0			0
$3$		0			0
$4$	−0.627804	−	1.08739i	−0.313902	−	0.543695i
$5$	−1.95987	+	1.07652i	−0.876483	+	0.481433i
$5$	−1.95987	+	1.07652i	−0.876483	+	0.481433i
$6$		0			0
$7$		−	0.566520i		−	0.214124i	−0.994252	−	0.107062i	$-0.965856\pi$
$7$		−	0.566520i		−	0.214124i	0.994252	−	0.107062i	$-0.0341444\pi$
$8$			2.80888i			0.993088i
$9$		0			0
$10$	1.92880	+	0.0411078i	0.609940	+	0.0129994i
$11$	1.91223			0.576559			0.288279	−	0.957546i	$-0.406917\pi$
$11$	1.91223			0.576559			0.288279	+	0.957546i	$0.406917\pi$
$12$		0			0
$13$	0.168469	−	0.0972656i	0.0467249	−	0.0269766i	−0.476456	−	0.879199i	$-0.658079\pi$
$13$	0.168469	−	0.0972656i	0.0467249	−	0.0269766i	0.523180	+	0.852222i	$0.324745\pi$
$14$	−0.244391	+	0.423298i	−0.0653163	+	0.113131i
$15$		0			0
$16$	−0.0438854	+	0.0760118i	−0.0109714	+	0.0190029i
$17$	−4.58603	−	2.64775i	−1.11228	−	0.642173i	−0.172858	−	0.984947i	$-0.555300\pi$
$17$	−4.58603	−	2.64775i	−1.11228	−	0.642173i	−0.939418	+	0.342774i	$0.888633\pi$
$18$		0			0
$19$	2.36834	+	3.65936i	0.543335	+	0.839516i
$19$	2.36834	+	3.65936i	0.543335	+	0.839516i
$20$	2.40101	+	1.45530i	0.536883	+	0.325416i
$21$		0			0
$22$	−1.42880	−	0.824918i	−0.304621	−	0.175873i
$23$	−2.92318	+	1.68770i	−0.609525	+	0.351910i	−0.772780	−	0.634674i	$-0.781134\pi$
$23$	−2.92318	+	1.68770i	−0.609525	+	0.351910i	0.163254	+	0.986584i	$0.447801\pi$
$24$		0			0
$25$	2.68222	−	4.21968i	0.536444	−	0.843936i
$26$	−0.167838			−0.0329157
$27$		0			0
$28$	−0.616027	+	0.355664i	−0.116418	+	0.0672141i
$29$	4.36834	+	7.56619i	0.811181	+	1.40501i	0.912038	+	0.410106i	$0.134508\pi$
$29$	4.36834	+	7.56619i	0.811181	+	1.40501i	−0.100857	+	0.994901i	$0.532158\pi$
$30$		0			0
$31$	5.65662			1.01596			0.507980	−	0.861369i	$-0.330393\pi$
$31$	5.65662			1.01596			0.507980	+	0.861369i	$0.330393\pi$
$32$	4.93070	−	2.84674i	0.871633	−	0.503238i
$33$		0			0
$34$	2.28442	+	3.95674i	0.391776	+	0.678575i
$35$	0.609869	+	1.11031i	0.103087	+	0.187676i
$36$		0			0
$37$		−	0.955582i		−	0.157097i	−0.996910	−	0.0785484i	$-0.974971\pi$
$37$		−	0.955582i		−	0.157097i	0.996910	−	0.0785484i	$-0.0250285\pi$
$38$	−0.190988	−	3.75592i	−0.0309824	−	0.609291i
$39$		0			0
$40$	−3.02381	−	5.50505i	−0.478106	−	0.870425i
$41$	5.02496	−	8.70349i	0.784768	−	1.35926i	−0.144370	−	0.989524i	$-0.546116\pi$
$41$	5.02496	−	8.70349i	0.784768	−	1.35926i	0.929138	−	0.369734i	$-0.120551\pi$
$42$		0			0
$43$	4.27161	+	2.46622i	0.651415	+	0.376094i	0.788998	−	0.614396i	$-0.210600\pi$
$43$	4.27161	+	2.46622i	0.651415	+	0.376094i	−0.137583	+	0.990490i	$0.543934\pi$
$44$	−1.20051	−	2.07934i	−0.180983	−	0.313472i
$45$		0			0
$46$	2.91223			0.429385
$47$	7.65516	−	4.41971i	1.11662	−	0.644681i	0.176084	−	0.984375i	$-0.443657\pi$
$47$	7.65516	−	4.41971i	1.11662	−	0.644681i	0.940536	+	0.339694i	$0.110324\pi$
$48$		0			0
$49$	6.67906			0.954151
$50$	−3.82446	+	1.99582i	−0.540860	+	0.282252i
$51$		0			0
$52$	−0.211531	−	0.122128i	−0.0293341	−	0.0169361i
$53$	7.10669	−	4.10305i	0.976179	−	0.563597i	0.0750646	−	0.997179i	$-0.476084\pi$
$53$	7.10669	−	4.10305i	0.976179	−	0.563597i	0.901114	+	0.433581i	$0.142750\pi$
$54$		0			0
$55$	−3.74773	+	2.05855i	−0.505344	+	0.277575i
$56$	1.59128			0.212644
$57$		0			0
$58$		−	7.53785i		−	0.989768i
$59$	−1.85713	+	3.21664i	−0.241777	+	0.418770i	−0.961221	−	0.275781i	$-0.911064\pi$
$59$	−1.85713	+	3.21664i	−0.241777	+	0.418770i	0.719443	+	0.694551i	$0.244397\pi$
$60$		0			0
$61$	1.75561	+	3.04080i	0.224783	+	0.389335i	0.956254	−	0.292537i	$-0.0944995\pi$
$61$	1.75561	+	3.04080i	0.224783	+	0.389335i	−0.731472	+	0.681872i	$0.761166\pi$
$62$	−4.22657	−	2.44021i	−0.536775	−	0.309907i
$63$		0			0
$64$	−4.73669			−0.592086
$65$	−0.225470	+	0.371988i	−0.0279661	+	0.0461395i
$66$		0			0
$67$	−3.50190	+	2.02182i	−0.427825	+	0.247005i	−0.698420	−	0.715688i	$-0.746113\pi$
$67$	−3.50190	+	2.02182i	−0.427825	+	0.247005i	0.270594	+	0.962693i	$0.412780\pi$
$68$			6.64906i			0.806318i
$69$		0			0
$70$	0.0232884	−	1.09270i	0.00278349	−	0.130603i
$71$	2.59767	−	4.49929i	0.308286	−	0.533967i	−0.669701	−	0.742631i	$-0.733578\pi$
$71$	2.59767	−	4.49929i	0.308286	−	0.533967i	0.977988	+	0.208663i	$0.0669112\pi$
$72$		0			0
$73$	−7.45136	−	4.30205i	−0.872116	−	0.503516i	−0.00406505	−	0.999992i	$-0.501294\pi$
$73$	−7.45136	−	4.30205i	−0.872116	−	0.503516i	−0.868051	+	0.496475i	$0.834627\pi$
$74$	−0.412229	+	0.714002i	−0.0479207	+	0.0830010i
$75$		0			0
$76$	2.49230	−	4.87268i	0.285886	−	0.558934i
$77$		−	1.08332i		−	0.123455i
$78$		0			0
$79$	3.31324	−	5.73870i	0.372769	−	0.645654i	−0.617222	−	0.786789i	$-0.711742\pi$
$79$	3.31324	−	5.73870i	0.372769	−	0.645654i	0.989990	+	0.141135i	$0.0450751\pi$
$80$	0.00418190	−	0.196217i	0.000467551	−	0.0219377i
$81$		0			0
$82$	−7.50921	+	4.33544i	−0.829253	+	0.478770i
$83$			4.51737i			0.495845i	0.968780	+	0.247923i	$0.0797479\pi$
$83$			4.51737i			0.495845i	−0.968780	+	0.247923i	$0.920252\pi$
$84$		0			0
$85$	11.8384	+	0.252307i	1.28405	+	0.0273666i
$86$	−2.12780	−	3.68547i	−0.229447	−	0.397414i
$87$		0			0
$88$			5.37122i			0.572574i
$89$	−1.68676	−	2.92155i	−0.178796	−	0.309684i	0.762672	−	0.646785i	$-0.223887\pi$
$89$	−1.68676	−	2.92155i	−0.178796	−	0.309684i	−0.941468	+	0.337101i	$0.890554\pi$
$90$		0			0
$91$	−0.0551029	−	0.0954410i	−0.00577635	−	0.0100049i
$92$	3.67037	+	2.11909i	0.382663	+	0.220930i
$93$		0			0
$94$	−7.62648			−0.786612
$95$	−8.58103	−	4.62233i	−0.880395	−	0.474241i
$96$		0			0
$97$	13.1568	+	7.59611i	1.33588	+	0.771268i	0.986193	−	0.165600i	$-0.0529561\pi$
$97$	13.1568	+	7.59611i	1.33588	+	0.771268i	0.349683	+	0.936868i	$0.386289\pi$
$98$	−4.99053	−	2.88128i	−0.504119	−	0.291053i
$99$		0			0
$100$	−6.27234	−	0.267482i	−0.627234	−	0.0267482i
$101$	1.77068	+	3.06690i	0.176189	+	0.305168i	0.940572	−	0.339594i	$-0.110290\pi$
$101$	1.77068	+	3.06690i	0.176189	+	0.305168i	−0.764383	+	0.644762i	$0.776956\pi$
$102$		0			0
$103$			15.6919i			1.54617i	0.634301	+	0.773086i	$0.281288\pi$
$103$			15.6919i			1.54617i	−0.634301	+	0.773086i	$0.718712\pi$
$104$	0.273207	+	0.473209i	0.0267902	+	0.0464020i
$105$		0			0
$106$	−7.08007			−0.687677
$107$			1.05731i			0.102214i	0.998693	+	0.0511071i	$0.0162750\pi$
$107$			1.05731i			0.102214i	−0.998693	+	0.0511071i	$0.983725\pi$
$108$		0			0
$109$	−3.37220	+	5.84081i	−0.322998	+	0.559449i	−0.981105	−	0.193476i	$-0.938024\pi$
$109$	−3.37220	+	5.84081i	−0.322998	+	0.559449i	0.658107	+	0.752924i	$0.271357\pi$
$110$	3.68831	+	0.0786075i	0.351666	+	0.00749493i
$111$		0			0
$112$	0.0430622	+	0.0248620i	0.00406899	+	0.00234923i
$113$			7.90091i			0.743255i	0.928382	+	0.371627i	$0.121200\pi$
$113$			7.90091i			0.743255i	−0.928382	+	0.371627i	$0.878800\pi$
$114$		0			0
$115$	3.91223	−	6.45453i	0.364817	−	0.601888i
$116$	5.48493	−	9.50018i	0.509263	−	0.882069i
$117$		0			0
$118$	2.77525	−	1.60229i	0.255483	−	0.147503i
$119$	−1.50000	+	2.59808i	−0.137505	+	0.238165i
$120$		0			0
$121$	−7.34338			−0.667580
$122$		−	3.02941i		−	0.274270i
$123$		0			0
$124$	−3.55125	−	6.15095i	−0.318912	−	0.552371i
$125$	−0.714253	+	11.1575i	−0.0638847	+	0.997957i
$126$		0			0
$127$	7.34074	−	4.23818i	0.651385	−	0.376078i	−0.137601	−	0.990488i	$-0.543939\pi$
$127$	7.34074	−	4.23818i	0.651385	−	0.376078i	0.788987	+	0.614410i	$0.210606\pi$
$128$	−6.32219	−	3.65012i	−0.558808	−	0.322628i
$129$		0			0
$130$	0.328941	−	0.180681i	0.0288501	−	0.0158467i
$131$	0.937193	−	1.62327i	0.0818830	−	0.141825i	−0.822176	−	0.569234i	$-0.807240\pi$
$131$	0.937193	−	1.62327i	0.0818830	−	0.141825i	0.904059	+	0.427408i	$0.140573\pi$
$132$		0			0
$133$	2.07310	−	1.34171i	0.179761	−	0.116341i
$134$	3.48878			0.301385
$135$		0			0
$136$	7.43719	−	12.8816i	0.637734	−	1.10459i
$137$	10.7918	−	6.23068i	0.922010	−	0.532323i	0.0377341	−	0.999288i	$-0.487986\pi$
$137$	10.7918	−	6.23068i	0.922010	−	0.532323i	0.884276	+	0.466965i	$0.154653\pi$
$138$		0			0
$139$	−0.156620	−	0.271275i	−0.0132844	−	0.0230092i	0.859307	−	0.511460i	$-0.170895\pi$
$139$	−0.156620	−	0.271275i	−0.0132844	−	0.0230092i	−0.872591	+	0.488451i	$0.837562\pi$
$140$	0.824458	−	1.36022i	0.0696794	−	0.114960i
$141$		0			0
$142$	−3.88190	+	2.24122i	−0.325762	+	0.188079i
$143$	0.322151	−	0.185994i	0.0269397	−	0.0155536i
$144$		0			0
$145$	−16.7065	−	10.1262i	−1.38740	−	0.840935i
$146$	3.71172	+	6.42889i	0.307184	+	0.532059i
$147$		0			0
$148$	−1.03909	+	0.599919i	−0.0854127	+	0.0493130i
$149$	−2.18291	+	3.78091i	−0.178831	+	0.309744i	−0.941480	−	0.337068i	$-0.890565\pi$
$149$	−2.18291	+	3.78091i	−0.178831	+	0.309744i	0.762650	+	0.646812i	$0.223898\pi$
$150$		0			0
$151$	0.197977			0.0161111			0.00805555	−	0.999968i	$-0.497436\pi$
$151$	0.197977			0.0161111			0.00805555	+	0.999968i	$0.497436\pi$
$152$	−10.2787	+	6.65239i	−0.833713	+	0.539580i
$153$		0			0
$154$	−0.467332	+	0.809443i	−0.0376587	+	0.0652268i
$155$	−11.0863	+	6.08945i	−0.890470	+	0.489117i
$156$		0			0
$157$	13.6572	+	7.88498i	1.08996	+	0.629290i	0.933566	−	0.358405i	$-0.116679\pi$
$157$	13.6572	+	7.88498i	1.08996	+	0.629290i	0.156395	+	0.987695i	$0.450013\pi$
$158$	−4.95124	+	2.85860i	−0.393900	+	0.227418i
$159$		0			0
$160$	−6.59899	+	10.8872i	−0.521696	+	0.860712i
$161$	0.956115	+	1.65604i	0.0753524	+	0.130514i
$162$		0			0
$163$			9.18768i			0.719635i	0.933023	+	0.359817i	$0.117161\pi$
$163$			9.18768i			0.719635i	−0.933023	+	0.359817i	$0.882839\pi$
$164$	−12.6188			−0.985361
$165$		0			0
$166$	1.94875	−	3.37533i	0.151252	−	0.261977i
$167$	−2.65888	+	1.53510i	−0.205750	+	0.118790i	−0.599335	−	0.800498i	$-0.704568\pi$
$167$	−2.65888	+	1.53510i	−0.205750	+	0.118790i	0.393585	+	0.919288i	$0.371235\pi$
$168$		0			0
$169$	−6.48108	+	11.2256i	−0.498545	+	0.863504i
$170$	−8.73669	−	5.29549i	−0.670073	−	0.406146i
$171$		0			0
$172$		−	6.19320i		−	0.472227i
$173$	9.01838	+	5.20676i	0.685655	+	0.395863i	0.801982	−	0.597348i	$-0.203779\pi$
$173$	9.01838	+	5.20676i	0.685655	+	0.395863i	−0.116328	+	0.993211i	$0.537112\pi$
$174$		0			0
$175$	−2.39053	−	1.51953i	−0.180707	−	0.114866i
$176$	−0.0839190	+	0.145352i	−0.00632563	+	0.0109563i
$177$		0			0
$178$			2.91061i			0.218159i
$179$	−13.4432			−1.00479			−0.502397	−	0.864637i	$-0.667549\pi$
$179$	−13.4432			−1.00479			−0.502397	+	0.864637i	$0.667549\pi$
$180$		0			0
$181$	−3.98108	−	6.89543i	−0.295911	−	0.512533i	0.679285	−	0.733874i	$-0.262290\pi$
$181$	−3.98108	−	6.89543i	−0.295911	−	0.512533i	−0.975196	+	0.221341i	$0.928957\pi$
$182$			0.0950835i			0.00704806i
$183$		0			0
$184$	−4.74054	−	8.21086i	−0.349477	−	0.605312i
$185$	1.02870	+	1.87282i	0.0756316	+	0.137693i
$186$		0			0
$187$	−8.76954	−	5.06310i	−0.641292	−	0.370250i
$188$	−9.61189	−	5.54942i	−0.701019	−	0.404733i
$189$		0			0
$190$	4.41763	+	7.15554i	0.320489	+	0.519117i
$191$	14.0999			1.02023			0.510115	−	0.860106i	$-0.329603\pi$
$191$	14.0999			1.02023			0.510115	+	0.860106i	$0.329603\pi$
$192$		0			0
$193$	−3.44405	−	1.98842i	−0.247908	−	0.143130i	0.370898	−	0.928674i	$-0.379050\pi$
$193$	−3.44405	−	1.98842i	−0.247908	−	0.143130i	−0.618806	+	0.785544i	$0.712383\pi$
$194$	−6.55378	−	11.3515i	−0.470534	−	0.814989i
$195$		0			0
$196$	−4.19314	−	7.26273i	−0.299510	−	0.518767i
$197$			18.3494i			1.30734i	0.756781	+	0.653669i	$0.226771\pi$
$197$			18.3494i			1.30734i	−0.756781	+	0.653669i	$0.773229\pi$
$198$		0			0
$199$	−0.803346	−	1.39144i	−0.0569477	−	0.0986363i	0.836146	−	0.548507i	$-0.184803\pi$
$199$	−0.803346	−	1.39144i	−0.0569477	−	0.0986363i	−0.893094	+	0.449870i	$0.851470\pi$
$200$	11.8526	+	7.53403i	0.838103	+	0.532736i
$201$		0			0
$202$		−	3.05542i		−	0.214978i
$203$	4.28640	−	2.47475i	0.300846	−	0.173694i
$204$		0			0
$205$	−0.478836	+	22.4672i	−0.0334433	+	1.56918i
$206$	6.76936	−	11.7249i	0.471643	−	0.816910i
$207$		0			0
$208$			0.0170742i			0.00118388i
$209$	4.52882	+	6.99754i	0.313265	+	0.484030i
$210$		0			0
$211$	3.04993	−	5.28263i	0.209966	−	0.363671i	−0.741738	−	0.670690i	$-0.765998\pi$
$211$	3.04993	−	5.28263i	0.209966	−	0.363671i	0.951703	+	0.307019i	$0.0993314\pi$
$212$	−8.92322	−	5.15182i	−0.612849	−	0.353829i
$213$		0			0
$214$	0.456115	−	0.790014i	0.0311794	−	0.0540042i
$215$	−11.0267	−	0.235009i	−0.752018	−	0.0160275i
$216$		0			0
$217$		−	3.20459i		−	0.217542i
$218$	5.03934	−	2.90947i	0.341307	−	0.197054i
$219$		0			0
$220$	4.59128	+	2.78287i	0.309544	+	0.187621i
$221$	−1.03014			−0.0692946
$222$		0			0
$223$	−14.9175	−	8.61263i	−0.998950	−	0.576744i	−0.0910127	−	0.995850i	$-0.529010\pi$
$223$	−14.9175	−	8.61263i	−0.998950	−	0.576744i	−0.907938	+	0.419106i	$0.862344\pi$
$224$	−1.61274	−	2.79334i	−0.107755	−	0.186638i
$225$		0			0
$226$	3.40838	−	5.90348i	0.226722	−	0.392694i
$227$			1.18505i			0.0786542i	0.999226	+	0.0393271i	$0.0125214\pi$
$227$			1.18505i			0.0786542i	−0.999226	+	0.0393271i	$0.987479\pi$
$228$		0			0
$229$	−6.24791			−0.412873			−0.206437	−	0.978460i	$-0.566187\pi$
$229$	−6.24791			−0.412873			−0.206437	+	0.978460i	$0.566187\pi$
$230$	−5.70760	+	3.13507i	−0.376348	+	0.206720i
$231$		0			0
$232$	−21.2525	+	12.2701i	−1.39530	+	0.805574i
$233$	−2.38752	−	1.37844i	−0.156412	−	0.0903043i	0.419751	−	0.907639i	$-0.362117\pi$
$233$	−2.38752	−	1.37844i	−0.156412	−	0.0903043i	−0.576163	+	0.817335i	$0.695451\pi$
$234$		0			0
$235$	−10.2453	+	16.9030i	−0.668327	+	1.10263i
$236$	4.66365			0.303578
$237$		0			0
$238$	2.24157	−	1.29417i	0.145299	−	0.0838887i
$239$	17.3055			1.11940			0.559701	−	0.828695i	$-0.310916\pi$
$239$	17.3055			1.11940			0.559701	+	0.828695i	$0.310916\pi$
$240$		0			0
$241$	2.39331	+	4.14533i	0.154167	+	0.267024i	0.932755	−	0.360510i	$-0.117397\pi$
$241$	2.39331	+	4.14533i	0.154167	+	0.267024i	−0.778589	+	0.627535i	$0.784064\pi$
$242$	5.48690	+	3.16786i	0.352711	+	0.203638i
$243$		0			0
$244$	2.20436	−	3.81806i	0.141120	−	0.244426i
$245$	−13.0901	+	7.19012i	−0.836297	+	0.459360i
$246$		0			0
$247$	0.754923	+	0.386131i	0.0480346	+	0.0245689i
$248$			15.8888i			1.00894i
$249$		0			0
$250$	5.34692	−	8.02866i	0.338169	−	0.507777i
$251$	−13.1240	−	22.7314i	−0.828377	−	1.43479i	−0.899311	−	0.437309i	$-0.855932\pi$
$251$	−13.1240	−	22.7314i	−0.828377	−	1.43479i	0.0709346	−	0.997481i	$-0.477402\pi$
$252$		0			0
$253$	−5.58979	+	3.22727i	−0.351427	+	0.202897i
$254$	−7.31324			−0.458874
$255$		0			0
$256$	7.88594	+	13.6589i	0.492871	+	0.853678i
$257$	−19.2695	+	11.1252i	−1.20200	+	0.693974i	−0.960999	−	0.276552i	$-0.910808\pi$
$257$	−19.2695	+	11.1252i	−1.20200	+	0.693974i	−0.240999	+	0.970525i	$0.577475\pi$
$258$		0			0
$259$	−0.541356			−0.0336382
$260$	0.546047	+	0.0116377i	0.0338644	+	0.000721740i
$261$		0			0
$262$	−1.40052	+	0.808593i	−0.0865246	+	0.0499550i
$263$	7.63264	+	4.40671i	0.470649	+	0.271729i	0.716511	−	0.697576i	$-0.245738\pi$
$263$	7.63264	+	4.40671i	0.470649	+	0.271729i	−0.245863	+	0.969305i	$0.579071\pi$
$264$		0			0
$265$	−9.51122	+	15.6919i	−0.584269	+	0.963948i
$266$	−2.12780	+	0.108199i	−0.130464	+	0.00663409i
$267$		0			0
$268$	4.39702	+	2.53862i	0.268591	+	0.155071i
$269$	2.38209	−	4.12590i	0.145239	−	0.251561i	−0.784223	−	0.620479i	$-0.786938\pi$
$269$	2.38209	−	4.12590i	0.145239	−	0.251561i	0.929462	+	0.368918i	$0.120272\pi$
$270$		0			0
$271$	−1.75946	+	3.04748i	−0.106880	+	0.185121i	−0.914505	−	0.404576i	$-0.867419\pi$
$271$	−1.75946	+	3.04748i	−0.106880	+	0.185121i	0.807625	+	0.589696i	$0.200753\pi$
$272$	0.402520	−	0.232395i	0.0244063	−	0.0140910i
$273$		0			0
$274$	−10.7514			−0.649517
$275$	5.12902	−	8.06900i	0.309291	−	0.486579i
$276$		0			0
$277$		−	32.7724i		−	1.96910i	−0.175098	−	0.984551i	$-0.556024\pi$
$277$		−	32.7724i		−	1.96910i	0.175098	−	0.984551i	$-0.443976\pi$
$278$			0.270258i			0.0162090i
$279$		0			0
$280$	−3.11872	+	1.71305i	−0.186379	+	0.102374i
$281$	4.95997	+	8.59091i	0.295887	+	0.512491i	0.975191	−	0.221366i	$-0.0710516\pi$
$281$	4.95997	+	8.59091i	0.295887	+	0.512491i	−0.679304	+	0.733857i	$0.737718\pi$
$282$		0			0
$283$	2.14066	+	1.23591i	0.127249	+	0.0734673i	0.562273	−	0.826951i	$-0.309927\pi$
$283$	2.14066	+	1.23591i	0.127249	+	0.0734673i	−0.435024	+	0.900419i	$0.643260\pi$
$284$	−6.52330			−0.387087
$285$		0			0
$286$	−0.320945			−0.0189779
$287$	−4.93070	−	2.84674i	−0.291050	−	0.168038i
$288$		0			0
$289$	5.52111	+	9.56285i	0.324771	+	0.562520i
$290$	8.11463	+	14.7732i	0.476507	+	0.867515i
$291$		0			0
$292$			10.8034i			0.632219i
$293$		−	17.0284i		−	0.994812i	−0.867518	−	0.497406i	$-0.834286\pi$
$293$		−	17.0284i		−	0.994812i	0.867518	−	0.497406i	$-0.165714\pi$
$294$		0			0
$295$	0.176968	−	8.30344i	0.0103035	−	0.483445i
$296$	2.68411			0.156011
$297$		0			0
$298$	3.26209	−	1.88337i	0.188968	−	0.109101i
$299$	−0.328310	+	0.568650i	−0.0189867	+	0.0328859i
$300$		0			0
$301$	1.39716	−	2.41995i	0.0805310	−	0.139484i
$302$	−0.147926	−	0.0854052i	−0.00851220	−	0.00491452i
$303$		0			0
$304$	−0.382090	+	0.0194293i	−0.0219144	+	0.00111435i
$305$	−6.71425	−	4.06965i	−0.384457	−	0.233028i
$306$		0			0
$307$	−18.1686	−	10.4896i	−1.03694	−	0.598676i	−0.117972	−	0.993017i	$-0.537639\pi$
$307$	−18.1686	−	10.4896i	−1.03694	−	0.598676i	−0.918964	+	0.394341i	$0.870973\pi$
$308$	−1.17799	+	0.680110i	−0.0671220	+	0.0387529i
$309$		0			0
$310$	10.9105	+	0.232531i	0.619674	+	0.0132069i
$311$	3.14805			0.178509			0.0892547	−	0.996009i	$-0.471551\pi$
$311$	3.14805			0.178509			0.0892547	+	0.996009i	$0.471551\pi$
$312$		0			0
$313$	−10.6459	+	6.14641i	−0.601742	+	0.347416i	−0.769726	−	0.638374i	$-0.779607\pi$
$313$	−10.6459	+	6.14641i	−0.601742	+	0.347416i	0.167985	+	0.985790i	$0.446274\pi$
$314$	−6.80301	−	11.7832i	−0.383916	−	0.664962i
$315$		0			0
$316$	−8.32027			−0.468052
$317$	9.92630	−	5.73095i	0.557517	−	0.321882i	−0.194631	−	0.980876i	$-0.562351\pi$
$317$	9.92630	−	5.73095i	0.557517	−	0.321882i	0.752148	+	0.658994i	$0.229018\pi$
$318$		0			0
$319$	8.35327	+	14.4683i	0.467694	+	0.810069i
$320$	9.28331	−	5.09913i	0.518953	−	0.285050i
$321$		0			0
$322$		−	1.64984i		−	0.0919417i
$323$	−1.17223	−	23.0527i	−0.0652246	−	1.28269i
$324$		0			0
$325$	0.0414409	−	0.971773i	0.00229873	−	0.0539043i
$326$	3.96348	−	6.86495i	0.219517	−	0.380214i
$327$		0			0
$328$	24.4470	+	14.1145i	1.34986	+	0.779343i
$329$	−2.50385	−	4.33680i	−0.138042	−	0.239095i
$330$		0			0
$331$	5.85724			0.321943			0.160972	−	0.986959i	$-0.448537\pi$
$331$	5.85724			0.321943			0.160972	+	0.986959i	$0.448537\pi$
$332$	4.91213	−	2.83602i	0.269588	−	0.155647i
$333$		0			0
$334$	2.64892			0.144942
$335$	4.68676	−	7.73238i	0.256065	−	0.422465i
$336$		0			0
$337$	7.45644	+	4.30498i	0.406178	+	0.234507i	0.689146	−	0.724622i	$-0.257986\pi$
$337$	7.45644	+	4.30498i	0.406178	+	0.234507i	−0.282968	+	0.959129i	$0.591319\pi$
$338$	9.68520	−	5.59175i	0.526805	−	0.304151i
$339$		0			0
$340$	−7.15784	−	13.0313i	−0.388188	−	0.706723i
$341$	10.8168			0.585760
$342$		0			0
$343$		−	7.74945i		−	0.418431i
$344$	−6.92730	+	11.9984i	−0.373495	+	0.646912i
$345$		0			0
$346$	−4.49230	−	7.78089i	−0.241507	−	0.418303i
$347$	10.4704	+	6.04507i	0.562079	+	0.324517i	0.753980	−	0.656898i	$-0.228132\pi$
$347$	10.4704	+	6.04507i	0.562079	+	0.324517i	−0.191900	+	0.981414i	$0.561465\pi$
$348$		0			0
$349$	−18.9819			−1.01608			−0.508040	−	0.861333i	$-0.669630\pi$
$349$	−18.9819			−1.01608			−0.508040	+	0.861333i	$0.669630\pi$
$350$	1.13067	+	2.16663i	0.0604369	+	0.115811i
$351$		0			0
$352$	9.42863	−	5.44362i	0.502548	−	0.290146i
$353$			7.71759i			0.410766i	0.978682	+	0.205383i	$0.0658440\pi$
$353$			7.71759i			0.410766i	−0.978682	+	0.205383i	$0.934156\pi$
$354$		0			0
$355$	−0.247535	+	11.6145i	−0.0131378	+	0.616432i
$356$	−2.11791	+	3.66833i	−0.112249	+	0.194421i
$357$		0			0
$358$	10.0447	+	5.79929i	0.530877	+	0.306502i
$359$	3.51507	−	6.08828i	0.185518	−	0.321327i	−0.758233	−	0.651984i	$-0.773937\pi$
$359$	3.51507	−	6.08828i	0.185518	−	0.321327i	0.943751	+	0.330657i	$0.107270\pi$
$360$		0			0
$361$	−7.78190	+	17.3333i	−0.409573	+	0.912277i
$362$			6.86960i			0.361058i
$363$		0			0
$364$	−0.0691877	+	0.119837i	−0.00362642	+	0.00628114i
$365$	19.2350	+	0.409948i	1.00680	+	0.0214576i
$366$		0			0
$367$	29.1945	−	16.8554i	1.52394	−	0.879847i	0.524342	−	0.851508i	$-0.324311\pi$
$367$	29.1945	−	16.8554i	1.52394	−	0.879847i	0.999598	−	0.0283394i	$-0.00902191\pi$
$368$		−	0.296261i		−	0.0154437i
$369$		0			0
$370$	0.0392819	−	1.84313i	0.00204217	−	0.0958196i
$371$	−2.32446	−	4.02608i	−0.120680	−	0.209024i
$372$		0			0
$373$			10.0097i			0.518281i	0.965840	+	0.259141i	$0.0834393\pi$
$373$			10.0097i			0.518281i	−0.965840	+	0.259141i	$0.916561\pi$
$374$	4.36834	+	7.56619i	0.225882	+	0.391239i
$375$		0			0
$376$	12.4144	+	21.5024i	0.640225	+	1.10890i
$377$	1.47186	+	0.849780i	0.0758047	+	0.0437659i
$378$		0			0
$379$	35.8064			1.83925			0.919626	−	0.392796i	$-0.128492\pi$
$379$	35.8064			1.83925			0.919626	+	0.392796i	$0.128492\pi$
$380$	0.360934	+	12.2328i	0.0185155	+	0.627531i
$381$		0			0
$382$	−10.5353	−	6.08255i	−0.539032	−	0.311210i
$383$	−14.0725	−	8.12477i	−0.719072	−	0.415156i	0.0953393	−	0.995445i	$-0.469606\pi$
$383$	−14.0725	−	8.12477i	−0.719072	−	0.415156i	−0.814411	+	0.580289i	$0.802940\pi$
$384$		0			0
$385$	1.16621	+	2.12316i	0.0594355	+	0.108206i
$386$	1.71558	+	2.97146i	0.0873205	+	0.151244i
$387$		0			0
$388$		−	19.0755i		−	0.968411i
$389$	9.69280	+	16.7884i	0.491445	+	0.851207i	0.999951	−	0.00985094i	$-0.00313570\pi$
$389$	9.69280	+	16.7884i	0.491445	+	0.851207i	−0.508507	+	0.861058i	$0.669802\pi$
$390$		0			0
$391$	17.8744			0.903947
$392$			18.7607i			0.947556i
$393$		0			0
$394$	7.91574	−	13.7105i	0.398789	−	0.690723i
$395$	−0.315723	+	14.8139i	−0.0158858	+	0.745368i
$396$		0			0
$397$	4.63682	+	2.67707i	0.232716	+	0.134358i	0.611824	−	0.790994i	$-0.290436\pi$
$397$	4.63682	+	2.67707i	0.232716	+	0.134358i	−0.379109	+	0.925352i	$0.623769\pi$
$398$			1.38622i			0.0694851i
$399$		0			0
$400$	0.203035	+	0.389063i	0.0101518	+	0.0194531i
$401$	4.16916	−	7.22120i	0.208198	−	0.360609i	−0.742949	−	0.669348i	$-0.766574\pi$
$401$	4.16916	−	7.22120i	0.208198	−	0.360609i	0.951147	+	0.308739i	$0.0999068\pi$
$402$		0			0
$403$	0.952965	−	0.550195i	0.0474706	−	0.0274072i
$404$	2.22328	−	3.85083i	0.110612	−	0.191586i
$405$		0			0
$406$	−4.27034			−0.211933
$407$		−	1.82729i		−	0.0905755i
$408$		0			0
$409$	−17.6613	−	30.5903i	−0.873297	−	1.51259i	−0.858566	−	0.512703i	$-0.828644\pi$
$409$	−17.6613	−	30.5903i	−0.873297	−	1.51259i	−0.0147313	−	0.999891i	$-0.504689\pi$
$410$	10.0499	−	16.5807i	0.496331	−	0.818864i
$411$		0			0
$412$	17.0632	−	9.85147i	0.840646	−	0.485347i
$413$	1.82229	+	1.05210i	0.0896689	+	0.0517704i
$414$		0			0
$415$	−4.86302	−	8.85347i	−0.238716	−	0.434600i
$416$	0.553780	−	0.959176i	0.0271513	−	0.0470274i
$417$		0			0
$418$	−0.365214	−	7.18219i	−0.0178632	−	0.351292i
$419$	21.2453			1.03790			0.518949	−	0.854805i	$-0.326323\pi$
$419$	21.2453			1.03790			0.518949	+	0.854805i	$0.326323\pi$
$420$		0			0
$421$	7.43719	−	12.8816i	0.362467	−	0.627811i	−0.625900	−	0.779904i	$-0.715268\pi$
$421$	7.43719	−	12.8816i	0.362467	−	0.627811i	0.988366	+	0.152093i	$0.0486013\pi$
$422$	−4.55775	+	2.63142i	−0.221868	+	0.128096i
$423$		0			0
$424$	11.5250	+	19.9618i	0.559702	+	0.969432i
$425$	−23.4734	+	12.2497i	−1.13863	+	0.594200i
$426$		0			0
$427$	1.72268	−	0.994587i	0.0833661	−	0.0481314i
$428$	1.14971	−	0.663785i	0.0555733	−	0.0320853i
$429$		0			0
$430$	8.13770	+	4.93243i	0.392435	+	0.237863i
$431$	−8.47590	−	14.6807i	−0.408270	−	0.707144i	0.586426	−	0.810003i	$-0.300534\pi$
$431$	−8.47590	−	14.6807i	−0.408270	−	0.707144i	−0.994696	+	0.102858i	$0.967201\pi$
$432$		0			0
$433$	20.0450	−	11.5730i	0.963299	−	0.556161i	0.0661122	−	0.997812i	$-0.478940\pi$
$433$	20.0450	−	11.5730i	0.963299	−	0.556161i	0.897187	+	0.441651i	$0.145607\pi$
$434$	−1.38243	+	2.39444i	−0.0663587	+	0.114937i
$435$		0			0
$436$	8.46832			0.405559
$437$	−13.0990	−	6.69993i	−0.626610	−	0.320501i
$438$		0			0
$439$	16.7729	−	29.0515i	0.800525	−	1.38655i	−0.118745	−	0.992925i	$-0.537887\pi$
$439$	16.7729	−	29.0515i	0.800525	−	1.38655i	0.919271	−	0.393626i	$-0.128779\pi$
$440$	−5.78221	−	10.5269i	−0.275656	−	0.501851i
$441$		0			0
$442$	0.769710	+	0.444392i	0.0366114	+	0.0211376i
$443$	27.1567	−	15.6789i	1.29025	−	0.744929i	0.311555	−	0.950228i	$-0.399150\pi$
$443$	27.1567	−	15.6789i	1.29025	−	0.744929i	0.978699	+	0.205299i	$0.0658167\pi$
$444$		0			0
$445$	6.45094	+	3.91005i	0.305804	+	0.185354i
$446$	7.43081	+	12.8705i	0.351859	+	0.609438i
$447$		0			0
$448$			2.68343i			0.126780i
$449$	−16.0301			−0.756509			−0.378255	−	0.925702i	$-0.623476\pi$
$449$	−16.0301			−0.756509			−0.378255	+	0.925702i	$0.623476\pi$
$450$		0			0
$451$	9.60888	−	16.6431i	0.452465	−	0.783692i
$452$	8.59136	−	4.96022i	0.404104	−	0.233309i
$453$		0			0
$454$	0.511217	−	0.885455i	0.0239926	−	0.0415564i
$455$	0.210739	+	0.127733i	0.00987959	+	0.00598823i
$456$		0			0
$457$			15.3980i			0.720286i	0.932897	+	0.360143i	$0.117272\pi$
$457$			15.3980i			0.720286i	−0.932897	+	0.360143i	$0.882728\pi$
$458$	4.66837	+	2.69529i	0.218139	+	0.125943i
$459$		0			0
$460$	−9.47470	−	0.201931i	−0.441760	−	0.00941508i
$461$	−2.90705	+	5.03517i	−0.135395	+	0.234511i	−0.925748	−	0.378140i	$-0.876564\pi$
$461$	−2.90705	+	5.03517i	−0.135395	+	0.234511i	0.790353	+	0.612651i	$0.209897\pi$
$462$		0			0
$463$		−	32.6788i		−	1.51871i	−0.650675	−	0.759356i	$-0.725514\pi$
$463$		−	32.6788i		−	1.51871i	0.650675	−	0.759356i	$-0.274486\pi$
$464$	−0.766826			−0.0355990
$465$		0			0
$466$	1.18929	+	2.05991i	0.0550927	+	0.0954234i
$467$			6.59041i			0.304968i	0.988306	+	0.152484i	$0.0487272\pi$
$467$			6.59041i			0.304968i	−0.988306	+	0.152484i	$0.951273\pi$
$468$		0			0
$469$	1.14540	+	1.98390i	0.0528898	+	0.0916078i
$470$	14.9469	−	8.21004i	0.689451	−	0.378701i
$471$		0			0
$472$	−9.03514	−	5.21644i	−0.415876	−	0.240106i
$473$	8.16830	+	4.71597i	0.375579	+	0.216841i
$474$		0			0
$475$	21.7938	−	0.178437i	0.999966	−	0.00818726i
$476$	3.76683			0.172652
$477$		0			0
$478$	−12.9305	−	7.46545i	−0.591429	−	0.341462i
$479$	18.4032	+	31.8753i	0.840864	+	1.45642i	0.889165	+	0.457586i	$0.151286\pi$
$479$	18.4032	+	31.8753i	0.840864	+	1.45642i	−0.0483016	+	0.998833i	$0.515381\pi$
$480$		0			0
$481$	−0.0929453	−	0.160986i	−0.00423794	−	0.00734033i
$482$		−	4.12980i		−	0.188107i
$483$		0			0
$484$	4.61021	+	7.98511i	0.209555	+	0.362960i
$485$	−33.9631	−	0.723844i	−1.54219	−	0.0328680i
$486$		0			0
$487$			2.45475i			0.111235i	0.998452	+	0.0556176i	$0.0177128\pi$
$487$			2.45475i			0.111235i	−0.998452	+	0.0556176i	$0.982287\pi$
$488$	−8.54125	+	4.93129i	−0.386644	+	0.223229i
$489$		0			0
$490$	12.8826	+	0.274561i	0.581975	+	0.0124034i
$491$	8.89716	−	15.4103i	0.401523	−	0.695459i	−0.592387	−	0.805654i	$-0.701814\pi$
$491$	8.89716	−	15.4103i	0.401523	−	0.695459i	0.993910	+	0.110195i	$0.0351476\pi$
$492$		0			0
$493$		−	46.2651i		−	2.08367i
$494$	−0.397498	−	0.614180i	−0.0178843	−	0.0276333i
$495$		0			0
$496$	−0.248243	+	0.429970i	−0.0111464	+	0.0193062i
$497$	−2.54894	−	1.47163i	−0.114335	−	0.0660116i
$498$		0			0
$499$	−14.6399	+	25.3570i	−0.655371	+	1.13514i	0.326429	+	0.945222i	$0.394155\pi$
$499$	−14.6399	+	25.3570i	−0.655371	+	1.13514i	−0.981801	+	0.189915i	$0.939179\pi$
$500$	12.5810	−	6.22806i	0.562637	−	0.278527i
$501$		0			0
$502$			22.6462i			1.01075i
$503$	−25.4939	+	14.7189i	−1.13672	+	0.656283i	−0.945615	−	0.325287i	$-0.894539\pi$
$503$	−25.4939	+	14.7189i	−1.13672	+	0.656283i	−0.191100	+	0.981571i	$0.561206\pi$
$504$		0			0
$505$	−6.77188	−	4.10458i	−0.301345	−	0.182652i
$506$	5.56885			0.247566
$507$		0			0
$508$	−9.21710	−	5.32149i	−0.408943	−	0.236103i
$509$	−3.34723	−	5.79757i	−0.148363	−	0.256973i	0.782259	−	0.622953i	$-0.214067\pi$
$509$	−3.34723	−	5.79757i	−0.148363	−	0.256973i	−0.930623	+	0.365980i	$0.880734\pi$
$510$		0			0
$511$	−2.43719	+	4.22134i	−0.107815	+	0.186741i
$512$			0.992797i			0.0438758i
$513$		0			0
$514$	19.1973			0.846757
$515$	−16.8927	−	30.7542i	−0.744379	−	1.35519i
$516$		0			0
$517$	14.6384	−	8.45150i	0.643797	−	0.371696i
$518$	0.404496	+	0.233536i	0.0177725	+	0.0102610i
$519$		0			0
$520$	−1.04487	−	0.633318i	−0.0458206	−	0.0277728i
$521$	−20.0801			−0.879724			−0.439862	−	0.898065i	$-0.644973\pi$
$521$	−20.0801			−0.879724			−0.439862	+	0.898065i	$0.644973\pi$
$522$		0			0
$523$	−31.5615	+	18.2220i	−1.38009	+	0.796793i	−0.992169	−	0.124901i	$-0.960139\pi$
$523$	−31.5615	+	18.2220i	−1.38009	+	0.796793i	−0.387918	+	0.921694i	$0.626805\pi$
$524$	−2.35350			−0.102813
$525$		0			0
$526$	−3.80202	−	6.58530i	−0.165776	−	0.287133i
$527$	−25.9414	−	14.9773i	−1.13003	−	0.652421i
$528$		0			0
$529$	−5.80335	+	10.0517i	−0.252319	+	0.437030i
$530$	13.8760	−	7.62182i	0.602737	−	0.331071i
$531$		0			0
$532$	−2.76047	−	1.41193i	−0.119681	−	0.0612151i
$533$		−	1.95503i		−	0.0846816i
$534$		0			0
$535$	−1.13822	−	2.07220i	−0.0492094	−	0.0895890i
$536$	−5.67906	−	9.83641i	−0.245298	−	0.424868i
$537$		0			0
$538$	−3.55975	+	2.05522i	−0.153472	+	0.0886069i
$539$	12.7719			0.550124
$540$		0			0
$541$	7.31456	+	12.6692i	0.314478	+	0.544691i	0.979326	−	0.202287i	$-0.0648373\pi$
$541$	7.31456	+	12.6692i	0.314478	+	0.544691i	−0.664849	+	0.746978i	$0.731504\pi$
$542$	2.62930	−	1.51803i	0.112938	−	0.0652049i
$543$		0			0
$544$	−30.1498			−1.29266
$545$	0.321341	−	15.0775i	0.0137647	−	0.645849i
$546$		0			0
$547$	−17.6831	+	10.2093i	−0.756073	+	0.436519i	−0.827884	−	0.560899i	$-0.810455\pi$
$547$	−17.6831	+	10.2093i	−0.756073	+	0.436519i	0.0718112	+	0.997418i	$0.477122\pi$
$548$	−13.5503	−	7.82329i	−0.578842	−	0.334194i
$549$		0			0
$550$	−7.31324	+	3.81647i	−0.311838	+	0.162735i
$551$	−17.3417	+	33.9047i	−0.738782	+	1.44439i
$552$		0			0
$553$	−3.25109	−	1.87702i	−0.138250	−	0.0798188i
$554$	−14.1377	+	24.4872i	−0.600653	+	1.04036i
$555$		0			0
$556$	−0.196654	+	0.340615i	−0.00833999	+	0.0144453i
$557$	31.0728	−	17.9399i	1.31660	−	0.760138i	0.333418	−	0.942779i	$-0.391798\pi$
$557$	31.0728	−	17.9399i	1.31660	−	0.760138i	0.983180	+	0.182641i	$0.0584645\pi$
$558$		0			0
$559$	0.959512			0.0405830
$560$	−0.111161	−	0.00236913i	−0.00469740	−	0.000100114i
$561$		0			0
$562$		−	8.55873i		−	0.361028i
$563$		−	37.7708i		−	1.59185i	−0.605395	−	0.795925i	$-0.706985\pi$
$563$		−	37.7708i		−	1.59185i	0.605395	−	0.795925i	$-0.293015\pi$
$564$		0			0
$565$	−8.50547	−	15.4848i	−0.357828	−	0.651450i
$566$	−1.06632	−	1.84692i	−0.0448208	−	0.0776319i
$567$		0			0
$568$	12.6380	+	7.29653i	0.530277	+	0.306155i
$569$	28.0844			1.17736			0.588681	−	0.808366i	$-0.299648\pi$
$569$	28.0844			1.17736			0.588681	+	0.808366i	$0.299648\pi$
$570$		0			0
$571$	20.6040			0.862253			0.431126	−	0.902292i	$-0.358116\pi$
$571$	20.6040			0.862253			0.431126	+	0.902292i	$0.358116\pi$
$572$	−0.404496	−	0.233536i	−0.0169128	−	0.00976463i
$573$		0			0
$574$	2.45611	+	4.25412i	0.102516	+	0.177563i
$575$	−0.719059	+	16.8617i	−0.0299869	+	0.703180i
$576$		0			0
$577$			43.8371i			1.82496i	0.409119	+	0.912481i	$0.365836\pi$
$577$			43.8371i			1.82496i	−0.409119	+	0.912481i	$0.634164\pi$
$578$		−	9.52702i		−	0.396272i
$579$		0			0
$580$	−0.522666	+	24.5238i	−0.0217025	+	1.01829i
$581$	2.55918			0.106173
$582$		0			0
$583$	13.5896	−	7.84597i	0.562825	−	0.324947i
$584$	12.0839	−	20.9300i	0.500036	−	0.866088i
$585$		0			0
$586$	−7.34591	+	12.7235i	−0.303457	+	0.525602i
$587$	32.8925	+	18.9905i	1.35762	+	0.783821i	0.989302	−	0.145880i	$-0.0466015\pi$
$587$	32.8925	+	18.9905i	1.35762	+	0.783821i	0.368315	+	0.929701i	$0.379935\pi$
$588$		0			0
$589$	13.3968	+	20.6996i	0.552006	+	0.852914i
$590$	−3.71425	+	6.12790i	−0.152913	+	0.252282i
$591$		0			0
$592$	0.0726355	+	0.0419361i	0.00298530	+	0.00172356i
$593$	−4.65934	+	2.69007i	−0.191336	+	0.110468i	−0.592608	−	0.805491i	$-0.701902\pi$
$593$	−4.65934	+	2.69007i	−0.191336	+	0.110468i	0.401272	+	0.915959i	$0.368568\pi$
$594$		0			0
$595$	0.142937	−	6.70668i	0.00585985	−	0.274947i
$596$	5.48175			0.224541
$597$		0			0
$598$	0.490620	−	0.283260i	0.0200630	−	0.0115834i
$599$	−11.2143	−	19.4237i	−0.458202	−	0.793629i	0.540664	−	0.841239i	$-0.318173\pi$
$599$	−11.2143	−	19.4237i	−0.458202	−	0.793629i	−0.998866	+	0.0476095i	$0.984840\pi$
$600$		0			0
$601$	−29.5732			−1.20632			−0.603159	−	0.797621i	$-0.706091\pi$
$601$	−29.5732			−1.20632			−0.603159	+	0.797621i	$0.706091\pi$
$602$	−2.08789	+	1.20544i	−0.0850960	+	0.0491302i
$603$		0			0
$604$	−0.124291	−	0.215278i	−0.00505731	−	0.00875952i
$605$	14.3921	−	7.90528i	0.585122	−	0.321395i
$606$		0			0
$607$			24.5915i			0.998139i	0.866562	+	0.499069i	$0.166325\pi$
$607$			24.5915i			0.998139i	−0.866562	+	0.499069i	$0.833675\pi$
$608$	22.0949	+	11.3012i	0.896065	+	0.458323i
$609$		0			0
$610$	3.26122	+	5.93727i	0.132043	+	0.240393i
$611$	0.859772	−	1.48917i	0.0347826	−	0.0602453i
$612$		0			0
$613$	25.8856	+	14.9450i	1.04551	+	0.603624i	0.921388	−	0.388643i	$-0.127056\pi$
$613$	25.8856	+	14.9450i	1.04551	+	0.603624i	0.124119	+	0.992267i	$0.460389\pi$
$614$	9.05027	+	15.6755i	0.365239	+	0.632613i
$615$		0			0
$616$	3.04290			0.122602
$617$	−35.2594	+	20.3570i	−1.41949	+	0.819544i	−0.996254	−	0.0864749i	$-0.972440\pi$
$617$	−35.2594	+	20.3570i	−1.41949	+	0.819544i	−0.423238	+	0.906019i	$0.639106\pi$
$618$		0			0
$619$	28.4784			1.14464			0.572322	−	0.820029i	$-0.306043\pi$
$619$	28.4784			1.14464			0.572322	+	0.820029i	$0.306043\pi$
$620$	13.5816	+	8.23210i	0.545451	+	0.330609i
$621$		0			0
$622$	−2.35219	−	1.35804i	−0.0943143	−	0.0544524i
$623$	−1.65512	+	0.955582i	−0.0663109	+	0.0382846i
$624$		0			0
$625$	−10.6114	−	22.6362i	−0.424456	−	0.905449i
$626$	10.6060			0.423902
$627$		0			0
$628$		−	19.8009i		−	0.790141i
$629$	−2.53014	+	4.38233i	−0.100883	+	0.174735i
$630$		0			0
$631$	−21.2101	−	36.7369i	−0.844359	−	1.46247i	−0.886176	−	0.463348i	$-0.846648\pi$
$631$	−21.2101	−	36.7369i	−0.844359	−	1.46247i	0.0418172	−	0.999125i	$-0.486685\pi$
$632$	16.1193	+	9.30649i	0.641192	+	0.370192i
$633$		0			0
$634$	−9.88912			−0.392747
$635$	−9.82446	+	16.2087i	−0.389872	+	0.643224i
$636$		0			0
$637$	1.12521	−	0.649643i	0.0445826	−	0.0257398i
$638$		−	14.4141i		−	0.570659i
$639$		0			0
$640$	16.3201	+	0.347825i	0.645110	+	0.0137490i
$641$	−14.7630	+	25.5702i	−0.583102	+	1.00996i	0.412007	+	0.911181i	$0.364828\pi$
$641$	−14.7630	+	25.5702i	−0.583102	+	1.00996i	−0.995109	+	0.0987822i	$0.968505\pi$
$642$		0			0
$643$	−18.7036	−	10.7985i	−0.737597	−	0.425852i	0.0835979	−	0.996500i	$-0.473359\pi$
$643$	−18.7036	−	10.7985i	−0.737597	−	0.425852i	−0.821195	+	0.570648i	$0.806692\pi$
$644$	1.20051	−	2.07934i	0.0473066	−	0.0819374i
$645$		0			0
$646$	−9.06885	+	17.7305i	−0.356809	+	0.697596i
$647$		−	12.6128i		−	0.495861i	−0.968778	−	0.247930i	$-0.920250\pi$
$647$		−	12.6128i		−	0.495861i	0.968778	−	0.247930i	$-0.0797504\pi$
$648$		0			0
$649$	−3.55125	+	6.15095i	−0.139399	+	0.241446i
$650$	−0.450178	+	0.708222i	−0.0176574	+	0.0277788i
$651$		0			0
$652$	9.99059	−	5.76807i	0.391262	−	0.225895i
$653$			26.6312i			1.04216i	0.853508	+	0.521080i	$0.174471\pi$
$653$			26.6312i			1.04216i	−0.853508	+	0.521080i	$0.825529\pi$
$654$		0			0
$655$	−0.0893064	+	4.19030i	−0.00348949	+	0.163729i
$656$	0.441045	+	0.763913i	0.0172199	+	0.0298258i
$657$		0			0
$658$			4.32055i			0.168433i
$659$	−19.9772	−	34.6016i	−0.778202	−	1.34789i	−0.932977	−	0.359936i	$-0.882798\pi$
$659$	−19.9772	−	34.6016i	−0.778202	−	1.34789i	0.154775	−	0.987950i	$-0.450535\pi$
$660$		0			0
$661$	6.76165	+	11.7115i	0.262998	+	0.455526i	0.967037	−	0.254635i	$-0.0819555\pi$
$661$	6.76165	+	11.7115i	0.262998	+	0.455526i	−0.704039	+	0.710161i	$0.748622\pi$
$662$	−4.37648	−	2.52676i	−0.170097	−	0.0982053i
$663$		0			0
$664$	−12.6887			−0.492418
$665$	−2.61864	+	4.86132i	−0.101547	+	0.188514i
$666$		0			0
$667$	−25.5389	−	14.7449i	−0.988871	−	0.570925i
$668$	3.33851	+	1.92749i	0.129171	+	0.0745768i
$669$		0			0
$670$	−6.83758	+	3.75574i	−0.264159	+	0.145097i
$671$	3.35713	+	5.81471i	0.129600	+	0.224475i
$672$		0			0
$673$			34.4110i			1.32645i	0.748421	+	0.663224i	$0.230812\pi$
$673$			34.4110i			1.32645i	−0.748421	+	0.663224i	$0.769188\pi$
$674$	−3.71425	−	6.43327i	−0.143068	−	0.247800i
$675$		0			0
$676$	16.2754			0.625977
$677$		−	29.6650i		−	1.14012i	−0.821604	−	0.570059i	$-0.806920\pi$
$677$		−	29.6650i		−	1.14012i	0.821604	−	0.570059i	$-0.193080\pi$
$678$		0			0
$679$	4.30335	−	7.45361i	0.165147	−	0.286043i
$680$	−0.708700	+	33.2526i	−0.0271774	+	1.27518i
$681$		0			0
$682$	−8.08217	−	4.66625i	−0.309482	−	0.178680i
$683$			27.8978i			1.06748i	0.845648	+	0.533740i	$0.179214\pi$
$683$			27.8978i			1.06748i	−0.845648	+	0.533740i	$0.820786\pi$
$684$		0			0
$685$	−14.4432	+	23.8290i	−0.551848	+	0.910458i
$686$	−3.34304	+	5.79032i	−0.127638	+	0.221075i
$687$		0			0
$688$	−0.374923	+	0.216462i	−0.0142938	+	0.00825253i
$689$	0.798172	−	1.38247i	0.0304079	−	0.0526680i
$690$		0			0
$691$	−49.6386			−1.88834			−0.944170	−	0.329459i	$-0.893134\pi$
$691$	−49.6386			−1.88834			−0.944170	+	0.329459i	$0.893134\pi$
$692$		−	13.0753i		−	0.497049i
$693$		0			0
$694$	−5.21558	−	9.03364i	−0.197981	−	0.342912i
$695$	0.598988	+	0.363059i	0.0227209	+	0.0137716i
$696$		0			0
$697$	−46.0893	+	26.6097i	−1.74576	+	1.00791i
$698$	14.1831	+	8.18863i	0.536839	+	0.309944i
$699$		0			0
$700$	−0.151534	+	3.55341i	−0.00572744	+	0.134306i
$701$	−24.9906	+	43.2851i	−0.943883	+	1.63485i	−0.185911	+	0.982567i	$0.559524\pi$
$701$	−24.9906	+	43.2851i	−0.943883	+	1.63485i	−0.757972	+	0.652287i	$0.773810\pi$
$702$		0			0
$703$	3.49682	−	2.26315i	0.131885	−	0.0853562i
$704$	−9.05763			−0.341372
$705$		0			0
$706$	3.32929	−	5.76651i	0.125300	−	0.217025i
$707$	1.73746	−	1.00312i	0.0653440	−	0.0377264i
$708$		0			0
$709$	12.5938	+	21.8131i	0.472971	+	0.819209i	0.999521	−	0.0309345i	$-0.00984834\pi$
$709$	12.5938	+	21.8131i	0.472971	+	0.819209i	−0.526551	+	0.850144i	$0.676515\pi$
$710$	5.19533	−	8.57144i	0.194977	−	0.321680i
$711$		0			0
$712$	8.20628	−	4.73790i	0.307543	−	0.177560i
$713$	−16.5353	+	9.54667i	−0.619253	+	0.357526i
$714$		0			0
$715$	−0.431150	+	0.711327i	−0.0161241	+	0.0266021i
$716$	8.43972	+	14.6180i	0.315407	+	0.546301i
$717$		0			0
$718$	−5.25285	+	3.03274i	−0.196035	+	0.113181i
$719$	−8.58777	+	14.8745i	−0.320270	+	0.554724i	−0.980544	−	0.196301i	$-0.937107\pi$
$719$	−8.58777	+	14.8745i	−0.320270	+	0.554724i	0.660274	+	0.751025i	$0.270440\pi$
$720$		0			0
$721$	8.88979			0.331073
$722$	13.2920	−	9.59421i	0.494676	−	0.357060i
$723$		0			0
$724$	−4.99868	+	8.65796i	−0.185774	+	0.321771i
$725$	43.6438	+	1.86117i	1.62089	+	0.0691222i
$726$		0			0
$727$	−0.914981	−	0.528264i	−0.0339348	−	0.0195922i	0.482937	−	0.875655i	$-0.339570\pi$
$727$	−0.914981	−	0.528264i	−0.0339348	−	0.0195922i	−0.516871	+	0.856063i	$0.672903\pi$
$728$	0.268082	−	0.154777i	0.00993579	−	0.00573643i
$729$		0			0
$730$	−14.1953	−	8.60409i	−0.525393	−	0.318452i
$731$	−13.0598	−	22.6203i	−0.483035	−	0.836641i
$732$		0			0
$733$			20.5025i			0.757277i	0.925545	+	0.378639i	$0.123608\pi$
$733$			20.5025i			0.757277i	−0.925545	+	0.378639i	$0.876392\pi$
$734$	−29.0851			−1.07355
$735$		0			0
$736$	−9.60888	+	16.6431i	−0.354188	+	0.613472i
$737$	−6.69644	+	3.86619i	−0.246666	+	0.142413i
$738$		0			0
$739$	12.4548	−	21.5723i	0.458157	−	0.793551i	−0.540707	−	0.841211i	$-0.681843\pi$
$739$	12.4548	−	21.5723i	0.458157	−	0.793551i	0.998864	+	0.0476601i	$0.0151764\pi$
$740$	1.39066	−	2.29436i	0.0511218	−	0.0843425i
$741$		0			0
$742$			4.01100i			0.147248i
$743$	11.4812	+	6.62867i	0.421204	+	0.243182i	0.695592	−	0.718437i	$-0.255142\pi$
$743$	11.4812	+	6.62867i	0.421204	+	0.243182i	−0.274388	+	0.961619i	$0.588475\pi$
$744$		0			0
$745$	0.208012	−	9.76004i	0.00762098	−	0.357580i
$746$	4.31808	−	7.47913i	0.158096	−	0.273830i
$747$		0			0
$748$			12.7145i			0.464889i
$749$	0.598988			0.0218866
$750$		0			0
$751$	−12.4183	−	21.5091i	−0.453149	−	0.784877i	0.545430	−	0.838156i	$-0.316366\pi$
$751$	−12.4183	−	21.5091i	−0.453149	−	0.784877i	−0.998580	+	0.0532786i	$0.983033\pi$
$752$			0.775843i			0.0282921i
$753$		0			0
$754$	−0.733174	−	1.26989i	−0.0267006	−	0.0462468i
$755$	−0.388009	+	0.213125i	−0.0141211	+	0.00775643i
$756$		0			0
$757$	41.9726	+	24.2329i	1.52552	+	0.880760i	0.999542	+	0.0302631i	$0.00963450\pi$
$757$	41.9726	+	24.2329i	1.52552	+	0.880760i	0.525980	+	0.850497i	$0.323699\pi$
$758$	−26.7542	−	15.4465i	−0.971756	−	0.561044i
$759$		0			0
$760$	12.9836	−	24.1031i	0.470963	−	0.874310i
$761$	−40.3726			−1.46351			−0.731753	−	0.681570i	$-0.761298\pi$
$761$	−40.3726			−1.46351			−0.731753	+	0.681570i	$0.761298\pi$
$762$		0			0
$763$	3.30894	+	1.91042i	0.119792	+	0.0691617i
$764$	−8.85195	−	15.3320i	−0.320252	−	0.554693i
$765$		0			0
$766$	7.00989	+	12.1415i	0.253278	+	0.438690i
$767$			0.722538i			0.0260893i
$768$		0			0
$769$	−22.4772	−	38.9317i	−0.810550	−	1.40391i	−0.912480	−	0.409121i	$-0.865835\pi$
$769$	−22.4772	−	38.9317i	−0.810550	−	1.40391i	0.101930	−	0.994792i	$-0.467498\pi$
$770$	0.0445327	−	2.08950i	0.00160485	−	0.0753003i
$771$		0			0
$772$			4.99337i			0.179715i
$773$	−3.19256	+	1.84323i	−0.114828	+	0.0662962i	−0.556314	−	0.830972i	$-0.687785\pi$
$773$	−3.19256	+	1.84323i	−0.114828	+	0.0662962i	0.441486	+	0.897268i	$0.354452\pi$
$774$		0			0
$775$	15.1723	−	23.8691i	0.545005	−	0.857404i
$776$	−21.3365	+	36.9560i	−0.765937	+	1.32664i
$777$		0			0
$778$		−	16.7255i		−	0.599639i
$779$	43.7501	−	2.22469i	1.56751	−	0.0797078i
$780$		0			0
$781$	4.96733	−	8.60367i	0.177745	−	0.307864i
$782$	−13.3556	−	7.71084i	−0.477594	−	0.275739i
$783$		0			0
$784$	−0.293113	+	0.507687i	−0.0104683	+	0.0181317i
$785$	−35.2547	−	0.751370i	−1.25829	−	0.0268175i
$786$		0			0
$787$		−	45.7141i		−	1.62953i	−0.579790	−	0.814766i	$-0.696865\pi$
$787$		−	45.7141i		−	1.62953i	0.579790	−	0.814766i	$-0.303135\pi$
$788$	19.9529	−	11.5198i	0.710793	−	0.410376i
$789$		0			0
$790$	6.62648	−	10.9326i	0.235760	−	0.388965i
$791$	4.47602			0.159149
$792$		0			0
$793$	0.591531	+	0.341521i	0.0210059	+	0.0121278i
$794$	−2.30973	−	4.00056i	−0.0819691	−	0.141975i
$795$		0			0
$796$	−1.00869	+	1.74710i	−0.0357520	+	0.0619243i
$797$		−	30.3378i		−	1.07462i	−0.843385	−	0.537310i	$-0.819441\pi$
$797$		−	30.3378i		−	1.07462i	0.843385	−	0.537310i	$-0.180559\pi$
$798$		0			0
$799$	−46.8091			−1.65599
$800$	1.21288	−	28.4416i	0.0428818	−	1.00556i
$801$		0			0
$802$	−6.23031	+	3.59707i	−0.220000	+	0.127017i
$803$	−14.2487	−	8.22650i	−0.502826	−	0.290307i
$804$		0			0
$805$	−3.65662	−	2.21635i	−0.128879	−	0.0781162i
$806$	−0.949395			−0.0334410
$807$		0			0
$808$	−8.61456	+	4.97362i	−0.303059	+	0.174971i
$809$	34.5585			1.21501			0.607506	−	0.794315i	$-0.292170\pi$
$809$	34.5585			1.21501			0.607506	+	0.794315i	$0.292170\pi$
$810$		0			0
$811$	−16.6377	−	28.8173i	−0.584229	−	1.01191i	−0.994971	−	0.100162i	$-0.968064\pi$
$811$	−16.6377	−	28.8173i	−0.584229	−	1.01191i	0.410742	−	0.911751i	$-0.365270\pi$
$812$	−5.38204	−	3.10732i	−0.188873	−	0.109046i
$813$		0			0
$814$	−0.788277	+	1.36534i	−0.0276291	+	0.0478550i
$815$	−9.89071	−	18.0067i	−0.346456	−	0.630748i
$816$		0			0
$817$	1.09186	+	21.4722i	0.0381994	+	0.751218i
$818$			30.4757i			1.06556i
$819$		0			0
$820$	24.7312	−	13.5843i	0.863652	−	0.474386i
$821$	6.35063	+	10.9996i	0.221638	+	0.383889i	0.955306	−	0.295620i	$-0.0955262\pi$
$821$	6.35063	+	10.9996i	0.221638	+	0.383889i	−0.733667	+	0.679509i	$0.762193\pi$
$822$		0			0
$823$	−10.4002	+	6.00454i	−0.362527	+	0.209305i	−0.670189	−	0.742191i	$-0.733787\pi$
$823$	−10.4002	+	6.00454i	−0.362527	+	0.209305i	0.307662	+	0.951496i	$0.400453\pi$
$824$	−44.0767			−1.53549
$825$		0			0
$826$	−0.907731	−	1.57224i	−0.0315840	−	0.0547051i
$827$	7.40057	−	4.27272i	0.257343	−	0.148577i	−0.365779	−	0.930702i	$-0.619197\pi$
$827$	7.40057	−	4.27272i	0.257343	−	0.148577i	0.623122	+	0.782125i	$0.285864\pi$
$828$		0			0
$829$	27.1042			0.941369			0.470685	−	0.882302i	$-0.344007\pi$
$829$	27.1042			0.941369			0.470685	+	0.882302i	$0.344007\pi$
$830$	−0.185699	+	8.71309i	−0.00644570	+	0.302436i
$831$		0			0
$832$	−0.797985	+	0.460717i	−0.0276652	+	0.0159725i
$833$	−30.6303	−	17.6844i	−1.06128	−	0.612729i
$834$		0			0
$835$	3.55850	−	5.87094i	0.123147	−	0.203172i
$836$	4.76584	−	9.31767i	0.164830	−	0.322258i
$837$		0			0
$838$	−15.8743	−	9.16500i	−0.548367	−	0.316600i
$839$	18.2190	−	31.5562i	0.628989	−	1.08944i	−0.358766	−	0.933427i	$-0.616802\pi$
$839$	18.2190	−	31.5562i	0.628989	−	1.08944i	0.987755	−	0.156013i	$-0.0498642\pi$
$840$		0			0
$841$	−23.6649	+	40.9887i	−0.816029	+	1.41340i
$842$	−11.1140	+	6.41667i	−0.383014	+	0.221133i
$843$		0			0
$844$	−7.65903			−0.263635
$845$	0.617591	−	28.9777i	0.0212458	−	0.996863i
$846$		0			0
$847$			4.16017i			0.142945i
$848$			0.720256i			0.0247337i
$849$		0			0
$850$	22.8235	+	0.973300i	0.782840	+	0.0333839i
$851$	1.61274	+	2.79334i	0.0552838	+	0.0957544i
$852$		0			0
$853$	15.8890	+	9.17354i	0.544030	+	0.314096i	0.746711	−	0.665149i	$-0.231632\pi$
$853$	15.8890	+	9.17354i	0.544030	+	0.314096i	−0.202680	+	0.979245i	$0.564965\pi$
$854$	−1.71622			−0.0587279
$855$		0			0
$856$	−2.96986			−0.101508
$857$	6.80508	+	3.92892i	0.232457	+	0.134209i	0.611705	−	0.791086i	$-0.290484\pi$
$857$	6.80508	+	3.92892i	0.232457	+	0.134209i	−0.379248	+	0.925295i	$0.623817\pi$
$858$		0			0
$859$	−17.1511	−	29.7066i	−0.585188	−	1.01358i	−0.994852	−	0.101339i	$-0.967687\pi$
$859$	−17.1511	−	29.7066i	−0.585188	−	1.01358i	0.409664	−	0.912237i	$-0.365646\pi$
$860$	6.66709	+	12.1379i	0.227346	+	0.413899i
$861$		0			0
$862$			14.6257i			0.498153i
$863$			35.9451i			1.22359i	0.791018	+	0.611793i	$0.209551\pi$
$863$			35.9451i			1.22359i	−0.791018	+	0.611793i	$0.790449\pi$
$864$		0			0
$865$	−23.2801	−	0.496159i	−0.791546	−	0.0168699i
$866$	−19.9699			−0.678604
$867$		0			0
$868$	−3.48463	+	2.01185i	−0.118276	+	0.0682868i
$869$	6.33568	−	10.9737i	0.214923	−	0.372258i
$870$		0			0
$871$	−0.393308	+	0.681229i	−0.0133267	+	0.0230826i
$872$	−16.4061	−	9.47209i	−0.555582	−	0.320765i
$873$		0			0
$874$	6.89716	+	10.6569i	0.233300	+	0.360475i
$875$	6.32094	+	0.404638i	0.213687	+	0.0136793i
$876$		0			0
$877$	−21.8685	−	12.6258i	−0.738448	−	0.426343i	0.0830567	−	0.996545i	$-0.473532\pi$
$877$	−21.8685	−	12.6258i	−0.738448	−	0.426343i	−0.821505	+	0.570202i	$0.806865\pi$
$878$	−25.0651	+	14.4713i	−0.845905	+	0.488383i
$879$		0			0
$880$	0.00799675	−	0.375212i	0.000269570	−	0.0126484i
$881$	−17.7796			−0.599010			−0.299505	−	0.954095i	$-0.596821\pi$
$881$	−17.7796			−0.599010			−0.299505	+	0.954095i	$0.596821\pi$
$882$		0			0
$883$	6.54146	−	3.77671i	0.220138	−	0.127096i	−0.385876	−	0.922550i	$-0.626101\pi$
$883$	6.54146	−	3.77671i	0.220138	−	0.127096i	0.606014	+	0.795454i	$0.292768\pi$
$884$	0.646726	+	1.12016i	0.0217517	+	0.0376751i
$885$		0			0
$886$	−27.0550			−0.908930
$887$	−14.0648	+	8.12030i	−0.472249	+	0.272653i	−0.717181	−	0.696887i	$-0.754568\pi$
$887$	−14.0648	+	8.12030i	−0.472249	+	0.272653i	0.244932	+	0.969540i	$0.421234\pi$
$888$		0			0
$889$	−2.40101	−	4.15867i	−0.0805273	−	0.139477i
$890$	−3.13332	−	5.70443i	−0.105029	−	0.191213i
$891$		0			0
$892$			21.6282i			0.724165i
$893$	34.3034	+	17.5456i	1.14792	+	0.587142i
$894$		0			0
$895$	26.3471	−	14.4719i	0.880685	−	0.483742i
$896$	−2.06787	+	3.58165i	−0.0690825	+	0.119654i
$897$		0			0
$898$	11.9776	+	6.91525i	0.399697	+	0.230765i
$899$	24.7101	+	42.7991i	0.824127	+	1.42743i
$900$		0			0
$901$	−43.4553			−1.44771
$902$	−14.3593	+	8.29036i	−0.478113	+	0.276039i
$903$		0			0
$904$	−22.1927			−0.738118
$905$	15.2255	+	9.22848i	0.506112	+	0.306765i
$906$		0			0
$907$	−15.8080	−	9.12675i	−0.524896	−	0.303049i	0.214040	−	0.976825i	$-0.431338\pi$
$907$	−15.8080	−	9.12675i	−0.524896	−	0.303049i	−0.738935	+	0.673776i	$0.764671\pi$
$908$	1.28861	−	0.743977i	0.0427639	−	0.0246897i
$909$		0			0
$910$	−0.102359	−	0.186352i	−0.00339317	−	0.00617750i
$911$	−15.9019			−0.526853			−0.263426	−	0.964679i	$-0.584853\pi$
$911$	−15.9019			−0.526853			−0.263426	+	0.964679i	$0.584853\pi$
$912$		0			0
$913$			8.63824i			0.285884i
$914$	6.64254	−	11.5052i	0.219716	−	0.380558i
$915$		0			0
$916$	3.92246	+	6.79390i	0.129602	+	0.224477i
$917$	−0.919612	−	0.530939i	−0.0303683	−	0.0175331i
$918$		0			0
$919$	30.0748			0.992075			0.496038	−	0.868301i	$-0.334788\pi$
$919$	30.0748			0.992075			0.496038	+	0.868301i	$0.334788\pi$
$920$	18.1300	+	10.9890i	0.597728	+	0.362296i
$921$		0			0
$922$	4.34425	−	2.50815i	0.143070	−	0.0826016i
$923$		−	1.01065i		−	0.0332661i
$924$		0			0
$925$	−4.03225	−	2.56308i	−0.132580	−	0.0842736i
$926$	−14.0973	+	24.4173i	−0.463267	+	0.802402i
$927$		0			0
$928$	43.0780	+	24.8711i	1.41410	+	0.816433i
$929$	18.4221	−	31.9081i	0.604410	−	1.04687i	−0.387734	−	0.921771i	$-0.626742\pi$
$929$	18.4221	−	31.9081i	0.604410	−	1.04687i	0.992144	−	0.125098i	$-0.0399245\pi$
$930$		0			0
$931$	15.8183	+	24.4411i	0.518424	+	0.801025i
$932$			3.46155i			0.113387i
$933$		0			0
$934$	2.84304	−	4.92429i	0.0930272	−	0.161128i
$935$	22.6377	+	0.482469i	0.740332	+	0.0157784i
$936$		0			0
$937$	37.4401	−	21.6160i	1.22311	−	0.706165i	0.257533	−	0.966270i	$-0.417090\pi$
$937$	37.4401	−	21.6160i	1.22311	−	0.706165i	0.965580	+	0.260105i	$0.0837571\pi$
$938$		−	1.97646i		−	0.0645338i
$939$		0			0
$940$	24.8121	+	0.528812i	0.809283	+	0.0172480i
$941$	−10.1601	−	17.5979i	−0.331211	−	0.573674i	0.651539	−	0.758615i	$-0.274124\pi$
$941$	−10.1601	−	17.5979i	−0.331211	−	0.573674i	−0.982750	+	0.184941i	$0.940790\pi$
$942$		0			0
$943$			33.9225i			1.10467i
$944$	−0.163001	−	0.282327i	−0.00530525	−	0.00918896i
$945$		0			0
$946$	−4.06885	−	7.04745i	−0.132290	−	0.229133i
$947$	18.6239	+	10.7525i	0.605195	+	0.349409i	0.771083	−	0.636735i	$-0.219716\pi$
$947$	18.6239	+	10.7525i	0.605195	+	0.349409i	−0.165888	+	0.986145i	$0.553049\pi$
$948$		0			0
$949$	−1.67376			−0.0543327
$950$	−16.3611	−	9.26830i	−0.530823	−	0.300703i
$951$		0			0
$952$	−7.29768	−	4.21332i	−0.236519	−	0.136554i
$953$	15.3547	+	8.86503i	0.497387	+	0.287166i	0.727634	−	0.685966i	$-0.240620\pi$
$953$	15.3547	+	8.86503i	0.497387	+	0.287166i	−0.230247	+	0.973132i	$0.573953\pi$
$954$		0			0
$955$	−27.6340	+	15.1787i	−0.894214	+	0.491173i
$956$	−10.8645	−	18.8179i	−0.351383	−	0.608613i
$957$		0			0
$958$		−	31.7559i		−	1.02599i
$959$	−3.52980	−	6.11379i	−0.113983	−	0.197425i
$960$		0			0
$961$	0.997355			0.0321727
$962$			0.160383i			0.00517095i
$963$		0			0
$964$	3.00506	−	5.20491i	0.0967864	−	0.167639i
$965$	8.89049	+	0.189480i	0.286195	+	0.00609957i
$966$		0			0
$967$	−11.8239	−	6.82652i	−0.380230	−	0.219526i	0.297688	−	0.954663i	$-0.403784\pi$
$967$	−11.8239	−	6.82652i	−0.380230	−	0.219526i	−0.677919	+	0.735137i	$0.737118\pi$
$968$		−	20.6267i		−	0.662966i
$969$		0			0
$970$	25.0647	+	15.1922i	0.804778	+	0.487793i
$971$	13.9798	−	24.2136i	0.448632	−	0.777053i	−0.549666	−	0.835385i	$-0.685245\pi$
$971$	13.9798	−	24.2136i	0.448632	−	0.777053i	0.998297	+	0.0583319i	$0.0185782\pi$
$972$		0			0
$973$	−0.153682	+	0.0887286i	−0.00492683	+	0.00284451i
$974$	1.05895	−	1.83416i	0.0339311	−	0.0587704i
$975$		0			0
$976$	−0.308182			−0.00986468
$977$			17.8540i			0.571200i	0.958349	+	0.285600i	$0.0921929\pi$
$977$			17.8540i			0.571200i	−0.958349	+	0.285600i	$0.907807\pi$
$978$		0			0
$979$	−3.22547	−	5.58668i	−0.103086	−	0.178551i
$980$	16.0365	+	9.72006i	0.512267	+	0.310496i
$981$		0			0
$982$	−13.2957	+	7.67630i	−0.424284	+	0.244961i
$983$	−42.4736	−	24.5222i	−1.35470	−	0.782136i	−0.365795	−	0.930695i	$-0.619203\pi$
$983$	−42.4736	−	24.5222i	−1.35470	−	0.782136i	−0.988903	+	0.148559i	$0.952536\pi$
$984$		0			0
$985$	−19.7534	−	35.9625i	−0.629396	−	1.14586i
$986$	−19.9583	+	34.5688i	−0.635602	+	1.10089i
$987$		0			0
$988$	−0.0540692	−	1.06331i	−0.00172017	−	0.0338284i
$989$	−16.6489			−0.529405
$990$		0			0
$991$	12.5337	−	21.7089i	0.398145	−	0.689607i	−0.595352	−	0.803465i	$-0.702988\pi$
$991$	12.5337	−	21.7089i	0.398145	−	0.689607i	0.993497	+	0.113858i	$0.0363209\pi$
$992$	27.8911	−	16.1029i	0.885543	−	0.511269i
$993$		0			0
$994$	1.26969	+	2.19917i	0.0402722	+	0.0697536i
$995$	3.07236	+	1.86222i	0.0974005	+	0.0590365i
$996$		0			0
$997$	−26.0000	+	15.0111i	−0.823427	+	0.475406i	−0.851597	−	0.524197i	$-0.824365\pi$
$997$	−26.0000	+	15.0111i	−0.823427	+	0.475406i	0.0281699	+	0.999603i	$0.491032\pi$
$998$	21.8776	−	12.6310i	0.692522	−	0.399828i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.be.d.334.2		12
3.2	odd	2		95.2.i.b.49.5	yes	12
5.4	even	2	inner	855.2.be.d.334.5		12
15.2	even	4		475.2.e.g.201.2		12
15.8	even	4		475.2.e.g.201.5		12
15.14	odd	2		95.2.i.b.49.2	✓	12
19.7	even	3	inner	855.2.be.d.64.5		12
57.8	even	6		1805.2.b.g.1084.5		6
57.11	odd	6		1805.2.b.f.1084.2		6
57.26	odd	6		95.2.i.b.64.2	yes	12
95.64	even	6	inner	855.2.be.d.64.2		12
285.8	odd	12		9025.2.a.bt.1.5		6
285.68	even	12		9025.2.a.bu.1.2		6
285.83	even	12		475.2.e.g.26.5		12
285.122	odd	12		9025.2.a.bt.1.2		6
285.179	even	6		1805.2.b.g.1084.2		6
285.182	even	12		9025.2.a.bu.1.5		6
285.197	even	12		475.2.e.g.26.2		12
285.239	odd	6		1805.2.b.f.1084.5		6
285.254	odd	6		95.2.i.b.64.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.i.b.49.2	✓	12	15.14	odd	2
95.2.i.b.49.5	yes	12	3.2	odd	2
95.2.i.b.64.2	yes	12	57.26	odd	6
95.2.i.b.64.5	yes	12	285.254	odd	6
475.2.e.g.26.2		12	285.197	even	12
475.2.e.g.26.5		12	285.83	even	12
475.2.e.g.201.2		12	15.2	even	4
475.2.e.g.201.5		12	15.8	even	4
855.2.be.d.64.2		12	95.64	even	6	inner
855.2.be.d.64.5		12	19.7	even	3	inner
855.2.be.d.334.2		12	1.1	even	1	trivial
855.2.be.d.334.5		12	5.4	even	2	inner
1805.2.b.f.1084.2		6	57.11	odd	6
1805.2.b.f.1084.5		6	285.239	odd	6
1805.2.b.g.1084.2		6	285.179	even	6
1805.2.b.g.1084.5		6	57.8	even	6
9025.2.a.bt.1.2		6	285.122	odd	12
9025.2.a.bt.1.5		6	285.8	odd	12
9025.2.a.bu.1.2		6	285.68	even	12
9025.2.a.bu.1.5		6	285.182	even	12

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.747190 - 0.431391i) q^{2} +(-0.627804 - 1.08739i) q^{4} +(-1.95987 + 1.07652i) q^{5} -0.566520i q^{7} +2.80888i q^{8} +O(q^{10})\)	\(q+(-0.747190 - 0.431391i) q^{2} +(-0.627804 - 1.08739i) q^{4} +(-1.95987 + 1.07652i) q^{5} -0.566520i q^{7} +2.80888i q^{8} +(1.92880 + 0.0411078i) q^{10} +1.91223 q^{11} +(0.168469 - 0.0972656i) q^{13} +(-0.244391 + 0.423298i) q^{14} +(-0.0438854 + 0.0760118i) q^{16} +(-4.58603 - 2.64775i) q^{17} +(2.36834 + 3.65936i) q^{19} +(2.40101 + 1.45530i) q^{20} +(-1.42880 - 0.824918i) q^{22} +(-2.92318 + 1.68770i) q^{23} +(2.68222 - 4.21968i) q^{25} -0.167838 q^{26} +(-0.616027 + 0.355664i) q^{28} +(4.36834 + 7.56619i) q^{29} +5.65662 q^{31} +(4.93070 - 2.84674i) q^{32} +(2.28442 + 3.95674i) q^{34} +(0.609869 + 1.11031i) q^{35} -0.955582i q^{37} +(-0.190988 - 3.75592i) q^{38} +(-3.02381 - 5.50505i) q^{40} +(5.02496 - 8.70349i) q^{41} +(4.27161 + 2.46622i) q^{43} +(-1.20051 - 2.07934i) q^{44} +2.91223 q^{46} +(7.65516 - 4.41971i) q^{47} +6.67906 q^{49} +(-3.82446 + 1.99582i) q^{50} +(-0.211531 - 0.122128i) q^{52} +(7.10669 - 4.10305i) q^{53} +(-3.74773 + 2.05855i) q^{55} +1.59128 q^{56} -7.53785i q^{58} +(-1.85713 + 3.21664i) q^{59} +(1.75561 + 3.04080i) q^{61} +(-4.22657 - 2.44021i) q^{62} -4.73669 q^{64} +(-0.225470 + 0.371988i) q^{65} +(-3.50190 + 2.02182i) q^{67} +6.64906i q^{68} +(0.0232884 - 1.09270i) q^{70} +(2.59767 - 4.49929i) q^{71} +(-7.45136 - 4.30205i) q^{73} +(-0.412229 + 0.714002i) q^{74} +(2.49230 - 4.87268i) q^{76} -1.08332i q^{77} +(3.31324 - 5.73870i) q^{79} +(0.00418190 - 0.196217i) q^{80} +(-7.50921 + 4.33544i) q^{82} +4.51737i q^{83} +(11.8384 + 0.252307i) q^{85} +(-2.12780 - 3.68547i) q^{86} +5.37122i q^{88} +(-1.68676 - 2.92155i) q^{89} +(-0.0551029 - 0.0954410i) q^{91} +(3.67037 + 2.11909i) q^{92} -7.62648 q^{94} +(-8.58103 - 4.62233i) q^{95} +(13.1568 + 7.59611i) q^{97} +(-4.99053 - 2.88128i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{4} + 2 q^{5}+O(q^{10}) \) 12 * q + 2 * q^4 + 2 * q^5	\( 12 q + 2 q^{4} + 2 q^{5} + 6 q^{10} - 4 q^{11} - 22 q^{14} - 14 q^{16} - 12 q^{19} + 40 q^{20} - 6 q^{25} + 44 q^{26} + 12 q^{29} + 60 q^{31} + 10 q^{34} + 10 q^{40} + 12 q^{41} - 20 q^{44} + 8 q^{46} - 4 q^{49} + 8 q^{50} - 18 q^{55} - 92 q^{56} - 20 q^{59} + 2 q^{61} + 24 q^{64} + 40 q^{65} + 46 q^{70} - 2 q^{71} + 22 q^{74} - 70 q^{76} + 24 q^{79} + 22 q^{80} + 2 q^{85} - 16 q^{86} - 36 q^{89} + 24 q^{91} - 60 q^{94} - 46 q^{95}+O(q^{100}) \) 12 * q + 2 * q^4 + 2 * q^5 + 6 * q^10 - 4 * q^11 - 22 * q^14 - 14 * q^16 - 12 * q^19 + 40 * q^20 - 6 * q^25 + 44 * q^26 + 12 * q^29 + 60 * q^31 + 10 * q^34 + 10 * q^40 + 12 * q^41 - 20 * q^44 + 8 * q^46 - 4 * q^49 + 8 * q^50 - 18 * q^55 - 92 * q^56 - 20 * q^59 + 2 * q^61 + 24 * q^64 + 40 * q^65 + 46 * q^70 - 2 * q^71 + 22 * q^74 - 70 * q^76 + 24 * q^79 + 22 * q^80 + 2 * q^85 - 16 * q^86 - 36 * q^89 + 24 * q^91 - 60 * q^94 - 46 * q^95

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