LMFDB - Embedded newform 1638.2.bj.i.1135.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.bj (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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} + 18 x^{13} + 143 x^{12} - 148 x^{11} + 172 x^{10} + 1612 x^{9} + \cdots + 97344 $ x^16 - 2x^15 + 2x^14 + 18x^13 + 143x^12 - 148x^11 + 172x^10 + 1612x^9 + 6655x^8 + 478x^7 + 1106x^6 + 11266x^5 + 55249x^4 + 8856x^3 + 288x^2 + 7488*x + 97344
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1135.1
Root			$-0.977855 - 0.977855i$ of defining polynomial
Character	$\chi$	$=$	1638.1135
Dual form			1638.2.bj.i.127.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -4.11786i q^{5} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -4.11786i q^{5} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-2.05893 + 3.56617i) q^{10} +(5.41244 + 3.12488i) q^{11} +(1.33817 + 3.34803i) q^{13} +1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.23358 + 3.86867i) q^{17} +(-2.94624 + 1.70101i) q^{19} +(3.56617 - 2.05893i) q^{20} +(-3.12488 - 5.41244i) q^{22} +(-1.49377 + 2.58729i) q^{23} -11.9568 q^{25} +(0.515130 - 3.56856i) q^{26} +(-0.866025 - 0.500000i) q^{28} +(-2.51441 + 4.35509i) q^{29} +10.7341i q^{31} +(0.866025 - 0.500000i) q^{32} -4.46716i q^{34} +(2.05893 + 3.56617i) q^{35} +(3.52191 + 2.03338i) q^{37} +3.40202 q^{38} -4.11786 q^{40} +(-5.96376 - 3.44318i) q^{41} +(-1.83425 - 3.17701i) q^{43} +6.24975i q^{44} +(2.58729 - 1.49377i) q^{46} +9.29971i q^{47} +(0.500000 - 0.866025i) q^{49} +(10.3549 + 5.97839i) q^{50} +(-2.23040 + 2.83290i) q^{52} +1.32672 q^{53} +(12.8678 - 22.2877i) q^{55} +(0.500000 + 0.866025i) q^{56} +(4.35509 - 2.51441i) q^{58} +(2.81300 - 1.62409i) q^{59} +(-0.550788 - 0.953993i) q^{61} +(5.36704 - 9.29599i) q^{62} -1.00000 q^{64} +(13.7867 - 5.51038i) q^{65} +(0.360328 + 0.208035i) q^{67} +(-2.23358 + 3.86867i) q^{68} -4.11786i q^{70} +(13.1880 - 7.61410i) q^{71} +11.7075i q^{73} +(-2.03338 - 3.52191i) q^{74} +(-2.94624 - 1.70101i) q^{76} -6.24975 q^{77} +1.31198 q^{79} +(3.56617 + 2.05893i) q^{80} +(3.44318 + 5.96376i) q^{82} +8.04856i q^{83} +(15.9306 - 9.19756i) q^{85} +3.66850i q^{86} +(3.12488 - 5.41244i) q^{88} +(-8.60309 - 4.96700i) q^{89} +(-2.83290 - 2.23040i) q^{91} -2.98755 q^{92} +(4.64986 - 8.05379i) q^{94} +(7.00452 + 12.1322i) q^{95} +(-10.5248 + 6.07652i) q^{97} +(-0.866025 + 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} + 2 q^{10} + 12 q^{11} + 10 q^{13} + 16 q^{14} - 8 q^{16} + 6 q^{17} - 4 q^{22} + 12 q^{23} - 20 q^{25} + 2 q^{26} - 16 q^{29} - 2 q^{35} - 6 q^{37} + 4 q^{40} - 12 q^{41} - 6 q^{43} + 6 q^{46} + 8 q^{49} + 24 q^{50} - 4 q^{52} + 40 q^{53} + 20 q^{55} + 8 q^{56} + 6 q^{58} - 6 q^{59} - 2 q^{61} + 14 q^{62} - 16 q^{64} + 52 q^{65} - 30 q^{67} - 6 q^{68} - 12 q^{71} - 24 q^{74} - 8 q^{77} - 16 q^{79} + 2 q^{82} + 6 q^{85} + 4 q^{88} - 30 q^{89} + 4 q^{91} + 24 q^{92} - 8 q^{94} + 40 q^{95} - 24 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^10 + 12 * q^11 + 10 * q^13 + 16 * q^14 - 8 * q^16 + 6 * q^17 - 4 * q^22 + 12 * q^23 - 20 * q^25 + 2 * q^26 - 16 * q^29 - 2 * q^35 - 6 * q^37 + 4 * q^40 - 12 * q^41 - 6 * q^43 + 6 * q^46 + 8 * q^49 + 24 * q^50 - 4 * q^52 + 40 * q^53 + 20 * q^55 + 8 * q^56 + 6 * q^58 - 6 * q^59 - 2 * q^61 + 14 * q^62 - 16 * q^64 + 52 * q^65 - 30 * q^67 - 6 * q^68 - 12 * q^71 - 24 * q^74 - 8 * q^77 - 16 * q^79 + 2 * q^82 + 6 * q^85 + 4 * q^88 - 30 * q^89 + 4 * q^91 + 24 * q^92 - 8 * q^94 + 40 * q^95 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	4.11786i		−	1.84156i	−0.390078	−	0.920782i	$-0.627552\pi$
$5$		−	4.11786i		−	1.84156i	0.390078	−	0.920782i	$-0.372448\pi$
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−2.05893	+	3.56617i	−0.651091	+	1.12772i
$11$	5.41244	+	3.12488i	1.63191	+	0.942185i	0.983503	+	0.180894i	$0.0578993\pi$
$11$	5.41244	+	3.12488i	1.63191	+	0.942185i	0.648410	+	0.761291i	$0.275434\pi$
$12$		0			0
$13$	1.33817	+	3.34803i	0.371140	+	0.928577i
$13$	1.33817	+	3.34803i	0.371140	+	0.928577i
$14$	1.00000			0.267261
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.23358	+	3.86867i	0.541722	+	0.938290i	0.998805	+	0.0488663i	$0.0155608\pi$
$17$	2.23358	+	3.86867i	0.541722	+	0.938290i	−0.457083	+	0.889424i	$0.651106\pi$
$18$		0			0
$19$	−2.94624	+	1.70101i	−0.675913	+	0.390239i	−0.798313	−	0.602242i	$-0.794274\pi$
$19$	−2.94624	+	1.70101i	−0.675913	+	0.390239i	0.122400	+	0.992481i	$0.460941\pi$
$20$	3.56617	−	2.05893i	0.797420	−	0.460391i
$21$		0			0
$22$	−3.12488	−	5.41244i	−0.666226	−	1.15394i
$23$	−1.49377	+	2.58729i	−0.311474	+	0.539488i	−0.978682	−	0.205383i	$-0.934156\pi$
$23$	−1.49377	+	2.58729i	−0.311474	+	0.539488i	0.667208	+	0.744871i	$0.267489\pi$
$24$		0			0
$25$	−11.9568			−2.39136
$26$	0.515130	−	3.56856i	0.101025	−	0.699853i
$27$		0			0
$28$	−0.866025	−	0.500000i	−0.163663	−	0.0944911i
$29$	−2.51441	+	4.35509i	−0.466915	+	0.808720i	−0.999286	−	0.0377911i	$-0.987968\pi$
$29$	−2.51441	+	4.35509i	−0.466915	+	0.808720i	0.532371	+	0.846511i	$0.321301\pi$
$30$		0			0
$31$			10.7341i			1.92790i	0.266087	+	0.963949i	$0.414269\pi$
$31$			10.7341i			1.92790i	−0.266087	+	0.963949i	$0.585731\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$		−	4.46716i		−	0.766111i
$35$	2.05893	+	3.56617i	0.348023	+	0.602793i
$36$		0			0
$37$	3.52191	+	2.03338i	0.578999	+	0.334285i	0.760736	−	0.649062i	$-0.224838\pi$
$37$	3.52191	+	2.03338i	0.578999	+	0.334285i	−0.181736	+	0.983347i	$0.558172\pi$
$38$	3.40202			0.551881
$39$		0			0
$40$	−4.11786			−0.651091
$41$	−5.96376	−	3.44318i	−0.931382	−	0.537734i	−0.0441339	−	0.999026i	$-0.514053\pi$
$41$	−5.96376	−	3.44318i	−0.931382	−	0.537734i	−0.887249	+	0.461292i	$0.847386\pi$
$42$		0			0
$43$	−1.83425	−	3.17701i	−0.279720	−	0.484490i	0.691595	−	0.722286i	$-0.256908\pi$
$43$	−1.83425	−	3.17701i	−0.279720	−	0.484490i	−0.971315	+	0.237796i	$0.923575\pi$
$44$			6.24975i			0.942185i
$45$		0			0
$46$	2.58729	−	1.49377i	0.381476	−	0.220245i
$47$			9.29971i			1.35650i	0.734830	+	0.678251i	$0.237262\pi$
$47$			9.29971i			1.35650i	−0.734830	+	0.678251i	$0.762738\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	10.3549	+	5.97839i	1.46440	+	0.845472i
$51$		0			0
$52$	−2.23040	+	2.83290i	−0.309300	+	0.392853i
$53$	1.32672			0.182239			0.0911197	−	0.995840i	$-0.470955\pi$
$53$	1.32672			0.182239			0.0911197	+	0.995840i	$0.470955\pi$
$54$		0			0
$55$	12.8678	−	22.2877i	1.73509	−	3.00527i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$		0			0
$58$	4.35509	−	2.51441i	0.571852	−	0.330159i
$59$	2.81300	−	1.62409i	0.366221	−	0.211438i	−0.305585	−	0.952165i	$-0.598852\pi$
$59$	2.81300	−	1.62409i	0.366221	−	0.211438i	0.671806	+	0.740727i	$0.265519\pi$
$60$		0			0
$61$	−0.550788	−	0.953993i	−0.0705212	−	0.122146i	0.828609	−	0.559828i	$-0.189133\pi$
$61$	−0.550788	−	0.953993i	−0.0705212	−	0.122146i	−0.899130	+	0.437682i	$0.855800\pi$
$62$	5.36704	−	9.29599i	0.681615	−	1.18059i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	13.7867	−	5.51038i	1.71003	−	0.683478i
$66$		0			0
$67$	0.360328	+	0.208035i	0.0440210	+	0.0254156i	0.521849	−	0.853038i	$-0.325242\pi$
$67$	0.360328	+	0.208035i	0.0440210	+	0.0254156i	−0.477828	+	0.878453i	$0.658576\pi$
$68$	−2.23358	+	3.86867i	−0.270861	+	0.469145i
$69$		0			0
$70$		−	4.11786i		−	0.492178i
$71$	13.1880	−	7.61410i	1.56513	−	0.903627i	0.568404	−	0.822750i	$-0.307561\pi$
$71$	13.1880	−	7.61410i	1.56513	−	0.903627i	0.996724	−	0.0808772i	$-0.0257722\pi$
$72$		0			0
$73$			11.7075i			1.37026i	0.728422	+	0.685128i	$0.240254\pi$
$73$			11.7075i			1.37026i	−0.728422	+	0.685128i	$0.759746\pi$
$74$	−2.03338	−	3.52191i	−0.236375	−	0.409414i
$75$		0			0
$76$	−2.94624	−	1.70101i	−0.337957	−	0.195119i
$77$	−6.24975			−0.712225
$78$		0			0
$79$	1.31198			0.147609			0.0738047	−	0.997273i	$-0.476486\pi$
$79$	1.31198			0.147609			0.0738047	+	0.997273i	$0.476486\pi$
$80$	3.56617	+	2.05893i	0.398710	+	0.230195i
$81$		0			0
$82$	3.44318	+	5.96376i	0.380235	+	0.658587i
$83$			8.04856i			0.883444i	0.897152	+	0.441722i	$0.145632\pi$
$83$			8.04856i			0.883444i	−0.897152	+	0.441722i	$0.854368\pi$
$84$		0			0
$85$	15.9306	−	9.19756i	1.72792	−	0.997616i
$86$			3.66850i			0.395584i
$87$		0			0
$88$	3.12488	−	5.41244i	0.333113	−	0.576968i
$89$	−8.60309	−	4.96700i	−0.911926	−	0.526500i	−0.0308754	−	0.999523i	$-0.509829\pi$
$89$	−8.60309	−	4.96700i	−0.911926	−	0.526500i	−0.881050	+	0.473023i	$0.843163\pi$
$90$		0			0
$91$	−2.83290	−	2.23040i	−0.296969	−	0.233809i
$92$	−2.98755			−0.311474
$93$		0			0
$94$	4.64986	−	8.05379i	0.479596	−	0.830685i
$95$	7.00452	+	12.1322i	0.718649	+	1.24474i
$96$		0			0
$97$	−10.5248	+	6.07652i	−1.06864	+	0.616978i	−0.927809	−	0.373057i	$-0.878310\pi$
$97$	−10.5248	+	6.07652i	−1.06864	+	0.616978i	−0.140828	+	0.990034i	$0.544976\pi$
$98$	−0.866025	+	0.500000i	−0.0874818	+	0.0505076i
$99$		0			0
$100$	−5.97839	−	10.3549i	−0.597839	−	1.03549i
$101$	0.760904	−	1.31792i	0.0757128	−	0.131138i	−0.825683	−	0.564134i	$-0.809210\pi$
$101$	0.760904	−	1.31792i	0.0757128	−	0.131138i	0.901396	+	0.432996i	$0.142543\pi$
$102$		0			0
$103$	−7.82331			−0.770853			−0.385427	−	0.922738i	$-0.625946\pi$
$103$	−7.82331			−0.770853			−0.385427	+	0.922738i	$0.625946\pi$
$104$	3.34803	−	1.33817i	0.328301	−	0.131218i
$105$		0			0
$106$	−1.14898	−	0.663361i	−0.111598	−	0.0644314i
$107$	5.52507	−	9.56970i	0.534129	−	0.925138i	−0.465076	−	0.885271i	$-0.653973\pi$
$107$	5.52507	−	9.56970i	0.534129	−	0.925138i	0.999205	−	0.0398672i	$-0.0126935\pi$
$108$		0			0
$109$			5.49373i			0.526204i	0.964768	+	0.263102i	$0.0847455\pi$
$109$			5.49373i			0.526204i	−0.964768	+	0.263102i	$0.915254\pi$
$110$	−22.2877	+	12.8678i	−2.12505	+	1.22690i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$	−9.46724	−	16.3977i	−0.890603	−	1.54257i	−0.839154	−	0.543894i	$-0.816949\pi$
$113$	−9.46724	−	16.3977i	−0.890603	−	1.54257i	−0.0514489	−	0.998676i	$-0.516384\pi$
$114$		0			0
$115$	10.6541	+	6.15116i	0.993501	+	0.573598i
$116$	−5.02883			−0.466915
$117$		0			0
$118$	−3.24817			−0.299018
$119$	−3.86867	−	2.23358i	−0.354640	−	0.204752i
$120$		0			0
$121$	14.0297	+	24.3001i	1.27543	+	2.20910i
$122$			1.10158i			0.0997320i
$123$		0			0
$124$	−9.29599	+	5.36704i	−0.834804	+	0.481975i
$125$			28.6470i			2.56227i
$126$		0			0
$127$	0.430100	−	0.744955i	0.0381652	−	0.0661041i	−0.846312	−	0.532688i	$-0.821182\pi$
$127$	0.430100	−	0.744955i	0.0381652	−	0.0661041i	0.884477	+	0.466584i	$0.154515\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−14.6948	−	2.12124i	−1.28882	−	0.186045i
$131$	18.7409			1.63740			0.818700	−	0.574222i	$-0.194695\pi$
$131$	18.7409			1.63740			0.818700	+	0.574222i	$0.194695\pi$
$132$		0			0
$133$	1.70101	−	2.94624i	0.147496	−	0.255471i
$134$	−0.208035	−	0.360328i	−0.0179715	−	0.0311276i
$135$		0			0
$136$	3.86867	−	2.23358i	0.331736	−	0.191528i
$137$	7.13797	−	4.12111i	0.609838	−	0.352090i	−0.163064	−	0.986616i	$-0.552138\pi$
$137$	7.13797	−	4.12111i	0.609838	−	0.352090i	0.772902	+	0.634525i	$0.218804\pi$
$138$		0			0
$139$	0.790446	+	1.36909i	0.0670448	+	0.116125i	0.897599	−	0.440813i	$-0.145310\pi$
$139$	0.790446	+	1.36909i	0.0670448	+	0.116125i	−0.830554	+	0.556937i	$0.811976\pi$
$140$	−2.05893	+	3.56617i	−0.174011	+	0.301397i
$141$		0			0
$142$	−15.2282			−1.27792
$143$	−3.21944	+	22.3026i	−0.269223	+	1.86504i
$144$		0			0
$145$	17.9337	+	10.3540i	1.48931	+	0.859853i
$146$	5.85374	−	10.1390i	0.484459	−	0.839107i
$147$		0			0
$148$			4.06676i			0.334285i
$149$	7.21451	−	4.16530i	0.591036	−	0.341235i	−0.174471	−	0.984662i	$-0.555822\pi$
$149$	7.21451	−	4.16530i	0.591036	−	0.341235i	0.765507	+	0.643428i	$0.222488\pi$
$150$		0			0
$151$		−	2.17427i		−	0.176940i	−0.996079	−	0.0884699i	$-0.971802\pi$
$151$		−	2.17427i		−	0.176940i	0.996079	−	0.0884699i	$-0.0281977\pi$
$152$	1.70101	+	2.94624i	0.137970	+	0.238971i
$153$		0			0
$154$	5.41244	+	3.12488i	0.436147	+	0.251810i
$155$	44.2015			3.55035
$156$		0			0
$157$	−13.3590			−1.06616			−0.533080	−	0.846065i	$-0.678966\pi$
$157$	−13.3590			−1.06616			−0.533080	+	0.846065i	$0.678966\pi$
$158$	−1.13621	−	0.655990i	−0.0903919	−	0.0521878i
$159$		0			0
$160$	−2.05893	−	3.56617i	−0.162773	−	0.281931i
$161$		−	2.98755i		−	0.235452i
$162$		0			0
$163$	3.27411	−	1.89031i	0.256448	−	0.148060i	−0.366265	−	0.930510i	$-0.619364\pi$
$163$	3.27411	−	1.89031i	0.256448	−	0.148060i	0.622713	+	0.782450i	$0.286030\pi$
$164$		−	6.88635i		−	0.537734i
$165$		0			0
$166$	4.02428	−	6.97026i	0.312345	−	0.540997i
$167$	−16.7994	−	9.69912i	−1.29997	−	0.750540i	−0.319574	−	0.947561i	$-0.603540\pi$
$167$	−16.7994	−	9.69912i	−1.29997	−	0.750540i	−0.980399	+	0.197021i	$0.936873\pi$
$168$		0			0
$169$	−9.41863	+	8.96044i	−0.724510	+	0.689265i
$170$	−18.3951			−1.41084
$171$		0			0
$172$	1.83425	−	3.17701i	0.139860	−	0.242245i
$173$	−5.62116	−	9.73613i	−0.427369	−	0.740224i	0.569270	−	0.822151i	$-0.307226\pi$
$173$	−5.62116	−	9.73613i	−0.427369	−	0.740224i	−0.996638	+	0.0819265i	$0.973893\pi$
$174$		0			0
$175$	10.3549	−	5.97839i	0.782755	−	0.451924i
$176$	−5.41244	+	3.12488i	−0.407978	+	0.235546i
$177$		0			0
$178$	4.96700	+	8.60309i	0.372292	+	0.644829i
$179$	1.21435	−	2.10332i	0.0907648	−	0.157209i	−0.817068	−	0.576541i	$-0.804402\pi$
$179$	1.21435	−	2.10332i	0.0907648	−	0.157209i	0.907833	+	0.419332i	$0.137736\pi$
$180$		0			0
$181$	10.1851			0.757054			0.378527	−	0.925590i	$-0.376431\pi$
$181$	10.1851			0.757054			0.378527	+	0.925590i	$0.376431\pi$
$182$	1.33817	+	3.34803i	0.0991914	+	0.248173i
$183$		0			0
$184$	2.58729	+	1.49377i	0.190738	+	0.110123i
$185$	8.37317	−	14.5028i	0.615608	−	1.06626i
$186$		0			0
$187$			27.9186i			2.04161i
$188$	−8.05379	+	4.64986i	−0.587383	+	0.339126i
$189$		0			0
$190$		−	14.0090i		−	1.01632i
$191$	−1.90530	−	3.30008i	−0.137863	−	0.238785i	0.788825	−	0.614618i	$-0.210690\pi$
$191$	−1.90530	−	3.30008i	−0.137863	−	0.238785i	−0.926687	+	0.375833i	$0.877357\pi$
$192$		0			0
$193$	−18.6462	−	10.7654i	−1.34218	−	0.774909i	−0.355055	−	0.934846i	$-0.615538\pi$
$193$	−18.6462	−	10.7654i	−1.34218	−	0.774909i	−0.987127	+	0.159936i	$0.948871\pi$
$194$	12.1530			0.872538
$195$		0			0
$196$	1.00000			0.0714286
$197$	6.21480	+	3.58811i	0.442786	+	0.255643i	0.704779	−	0.709427i	$-0.251046\pi$
$197$	6.21480	+	3.58811i	0.442786	+	0.255643i	−0.261993	+	0.965070i	$0.584380\pi$
$198$		0			0
$199$	5.40006	+	9.35318i	0.382800	+	0.663029i	0.991461	−	0.130401i	$-0.0416265\pi$
$199$	5.40006	+	9.35318i	0.382800	+	0.663029i	−0.608661	+	0.793430i	$0.708293\pi$
$200$			11.9568i			0.845472i
$201$		0			0
$202$	−1.31792	+	0.760904i	−0.0927289	+	0.0535370i
$203$		−	5.02883i		−	0.352954i
$204$		0			0
$205$	−14.1785	+	24.5579i	−0.990271	+	1.71520i
$206$	6.77518	+	3.91165i	0.472049	+	0.272538i
$207$		0			0
$208$	−3.56856	−	0.515130i	−0.247435	−	0.0357179i
$209$	−21.2618			−1.47071
$210$		0			0
$211$	10.7105	−	18.5512i	0.737344	−	1.27712i	−0.216343	−	0.976317i	$-0.569413\pi$
$211$	10.7105	−	18.5512i	0.737344	−	1.27712i	0.953687	−	0.300800i	$-0.0972538\pi$
$212$	0.663361	+	1.14898i	0.0455598	+	0.0789120i
$213$		0			0
$214$	−9.56970	+	5.52507i	−0.654171	+	0.377686i
$215$	−13.0825	+	7.55318i	−0.892218	+	0.515122i
$216$		0			0
$217$	−5.36704	−	9.29599i	−0.364339	−	0.631053i
$218$	2.74686	−	4.75771i	0.186041	−	0.322233i
$219$		0			0
$220$	25.7356			1.73509
$221$	−9.96353	+	12.6550i	−0.670220	+	0.851268i
$222$		0			0
$223$	9.03542	+	5.21660i	0.605056	+	0.349329i	0.771028	−	0.636801i	$-0.219743\pi$
$223$	9.03542	+	5.21660i	0.605056	+	0.349329i	−0.165972	+	0.986130i	$0.553076\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$		0			0
$226$			18.9345i			1.25950i
$227$	5.80625	−	3.35224i	0.385375	−	0.222496i	−0.294779	−	0.955565i	$-0.595246\pi$
$227$	5.80625	−	3.35224i	0.385375	−	0.222496i	0.680154	+	0.733069i	$0.261913\pi$
$228$		0			0
$229$		−	13.1866i		−	0.871396i	−0.900093	−	0.435698i	$-0.856502\pi$
$229$		−	13.1866i		−	0.871396i	0.900093	−	0.435698i	$-0.143498\pi$
$230$	−6.15116	−	10.6541i	−0.405595	−	0.702511i
$231$		0			0
$232$	4.35509	+	2.51441i	0.285926	+	0.165079i
$233$	−10.6067			−0.694868			−0.347434	−	0.937704i	$-0.612947\pi$
$233$	−10.6067			−0.694868			−0.347434	+	0.937704i	$0.612947\pi$
$234$		0			0
$235$	38.2949			2.49808
$236$	2.81300	+	1.62409i	0.183111	+	0.105719i
$237$		0			0
$238$	2.23358	+	3.86867i	0.144781	+	0.250769i
$239$		−	11.1145i		−	0.718937i	−0.933157	−	0.359468i	$-0.882958\pi$
$239$		−	11.1145i		−	0.718937i	0.933157	−	0.359468i	$-0.117042\pi$
$240$		0			0
$241$	24.8768	−	14.3626i	1.60246	−	0.925179i	0.611463	−	0.791273i	$-0.290581\pi$
$241$	24.8768	−	14.3626i	1.60246	−	0.925179i	0.990994	−	0.133906i	$-0.0427519\pi$
$242$		−	28.0594i		−	1.80373i
$243$		0			0
$244$	0.550788	−	0.953993i	0.0352606	−	0.0610731i
$245$	−3.56617	−	2.05893i	−0.227834	−	0.131540i
$246$		0			0
$247$	−9.63759	−	7.58786i	−0.613225	−	0.482804i
$248$	10.7341			0.681615
$249$		0			0
$250$	14.3235	−	24.8091i	0.905899	−	1.56906i
$251$	6.36546	+	11.0253i	0.401784	+	0.695911i	0.993941	−	0.109912i	$-0.0350568\pi$
$251$	6.36546	+	11.0253i	0.401784	+	0.695911i	−0.592157	+	0.805823i	$0.701723\pi$
$252$		0			0
$253$	−16.1699	+	9.33572i	−1.01660	+	0.586932i
$254$	−0.744955	+	0.430100i	−0.0467427	+	0.0269869i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.51414	−	16.4790i	0.593476	−	1.02793i	−0.400284	−	0.916391i	$-0.631089\pi$
$257$	9.51414	−	16.4790i	0.593476	−	1.02793i	0.993760	−	0.111539i	$-0.0355781\pi$
$258$		0			0
$259$	−4.06676			−0.252696
$260$	11.6655	+	9.18447i	0.723463	+	0.569596i
$261$		0			0
$262$	−16.2301	−	9.37045i	−1.00270	−	0.578908i
$263$	4.05345	−	7.02078i	0.249946	−	0.432920i	−0.713564	−	0.700590i	$-0.752920\pi$
$263$	4.05345	−	7.02078i	0.249946	−	0.432920i	0.963511	+	0.267670i	$0.0862537\pi$
$264$		0			0
$265$		−	5.46326i		−	0.335605i
$266$	−2.94624	+	1.70101i	−0.180645	+	0.104296i
$267$		0			0
$268$			0.416071i			0.0254156i
$269$	5.28375	+	9.15173i	0.322156	+	0.557991i	0.980933	−	0.194348i	$-0.0622591\pi$
$269$	5.28375	+	9.15173i	0.322156	+	0.557991i	−0.658777	+	0.752339i	$0.728926\pi$
$270$		0			0
$271$	2.63603	+	1.52191i	0.160127	+	0.0924496i	0.577922	−	0.816092i	$-0.303864\pi$
$271$	2.63603	+	1.52191i	0.160127	+	0.0924496i	−0.417795	+	0.908541i	$0.637197\pi$
$272$	−4.46716			−0.270861
$273$		0			0
$274$	−8.24222			−0.497931
$275$	−64.7154	−	37.3634i	−3.90248	−	2.25310i
$276$		0			0
$277$	4.37810	+	7.58309i	0.263054	+	0.455624i	0.967052	−	0.254579i	$-0.0819368\pi$
$277$	4.37810	+	7.58309i	0.263054	+	0.455624i	−0.703998	+	0.710202i	$0.748603\pi$
$278$		−	1.58089i		−	0.0948156i
$279$		0			0
$280$	3.56617	−	2.05893i	0.213120	−	0.123045i
$281$			10.5427i			0.628926i	0.949270	+	0.314463i	$0.101824\pi$
$281$			10.5427i			0.628926i	−0.949270	+	0.314463i	$0.898176\pi$
$282$		0			0
$283$	6.82738	−	11.8254i	0.405846	−	0.702945i	−0.588574	−	0.808443i	$-0.700310\pi$
$283$	6.82738	−	11.8254i	0.405846	−	0.702945i	0.994419	+	0.105498i	$0.0336437\pi$
$284$	13.1880	+	7.61410i	0.782564	+	0.451813i
$285$		0			0
$286$	13.9394	−	17.7049i	0.824256	−	1.04691i
$287$	6.88635			0.406489
$288$		0			0
$289$	−1.47774	+	2.55952i	−0.0869258	+	0.150560i
$290$	−10.3540	−	17.9337i	−0.608008	−	1.05310i
$291$		0			0
$292$	−10.1390	+	5.85374i	−0.593339	+	0.342564i
$293$	−10.0829	+	5.82134i	−0.589047	+	0.340086i	−0.764721	−	0.644362i	$-0.777123\pi$
$293$	−10.0829	+	5.82134i	−0.589047	+	0.340086i	0.175674	+	0.984448i	$0.443790\pi$
$294$		0			0
$295$	−6.68776	−	11.5835i	−0.389376	−	0.674420i
$296$	2.03338	−	3.52191i	0.118188	−	0.204707i
$297$		0			0
$298$	−8.33060			−0.482579
$299$	−10.6613	−	1.53898i	−0.616556	−	0.0890014i
$300$		0			0
$301$	3.17701	+	1.83425i	0.183120	+	0.105724i
$302$	−1.08714	+	1.88298i	−0.0625577	+	0.108353i
$303$		0			0
$304$		−	3.40202i		−	0.195119i
$305$	−3.92841	+	2.26807i	−0.224940	+	0.129869i
$306$		0			0
$307$			14.7772i			0.843382i	0.906740	+	0.421691i	$0.138563\pi$
$307$			14.7772i			0.843382i	−0.906740	+	0.421691i	$0.861437\pi$
$308$	−3.12488	−	5.41244i	−0.178056	−	0.308403i
$309$		0			0
$310$	−38.2796	−	22.1007i	−2.17413	−	1.25524i
$311$	−21.4453			−1.21605			−0.608026	−	0.793917i	$-0.708039\pi$
$311$	−21.4453			−1.21605			−0.608026	+	0.793917i	$0.708039\pi$
$312$		0			0
$313$	−9.74579			−0.550865			−0.275432	−	0.961320i	$-0.588821\pi$
$313$	−9.74579			−0.550865			−0.275432	+	0.961320i	$0.588821\pi$
$314$	11.5692	+	6.67948i	0.652887	+	0.376945i
$315$		0			0
$316$	0.655990	+	1.13621i	0.0369023	+	0.0639167i
$317$			19.5132i			1.09597i	0.836488	+	0.547986i	$0.184605\pi$
$317$			19.5132i			1.09597i	−0.836488	+	0.547986i	$0.815395\pi$
$318$		0			0
$319$	−27.2182	+	15.7145i	−1.52393	+	0.879841i
$320$			4.11786i			0.230195i
$321$		0			0
$322$	−1.49377	+	2.58729i	−0.0832448	+	0.144184i
$323$	−13.1613	−	7.59868i	−0.732314	−	0.422802i
$324$		0			0
$325$	−16.0001	−	40.0317i	−0.887528	−	2.22056i
$326$	−3.78061			−0.209389
$327$		0			0
$328$	−3.44318	+	5.96376i	−0.190118	+	0.329293i
$329$	−4.64986	−	8.05379i	−0.256355	−	0.444020i
$330$		0			0
$331$	5.12322	−	2.95789i	0.281598	−	0.162580i	−0.352549	−	0.935793i	$-0.614685\pi$
$331$	5.12322	−	2.95789i	0.281598	−	0.162580i	0.634146	+	0.773213i	$0.281352\pi$
$332$	−6.97026	+	4.02428i	−0.382542	+	0.220861i
$333$		0			0
$334$	9.69912	+	16.7994i	0.530712	+	0.919220i
$335$	0.856660	−	1.48378i	0.0468044	−	0.0810675i
$336$		0			0
$337$	30.5181			1.66243			0.831214	−	0.555953i	$-0.187647\pi$
$337$	30.5181			1.66243			0.831214	+	0.555953i	$0.187647\pi$
$338$	12.6370	−	3.05065i	0.687362	−	0.165934i
$339$		0			0
$340$	15.9306	+	9.19756i	0.863960	+	0.498808i
$341$	−33.5427	+	58.0976i	−1.81644	+	3.14616i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−3.17701	+	1.83425i	−0.171293	+	0.0988960i
$345$		0			0
$346$			11.2423i			0.604391i
$347$	−9.72992	−	16.8527i	−0.522329	−	0.904701i	−0.999662	−	0.0259786i	$-0.991730\pi$
$347$	−9.72992	−	16.8527i	−0.522329	−	0.904701i	0.477333	−	0.878722i	$-0.341604\pi$
$348$		0			0
$349$	25.5323	+	14.7411i	1.36671	+	0.789073i	0.990507	−	0.137463i	$-0.0438947\pi$
$349$	25.5323	+	14.7411i	1.36671	+	0.789073i	0.376207	+	0.926536i	$0.377228\pi$
$350$	−11.9568			−0.639117
$351$		0			0
$352$	6.24975			0.333113
$353$	−2.60497	−	1.50398i	−0.138649	−	0.0800489i	0.429071	−	0.903271i	$-0.358841\pi$
$353$	−2.60497	−	1.50398i	−0.138649	−	0.0800489i	−0.567720	+	0.823222i	$0.692174\pi$
$354$		0			0
$355$	−31.3538	−	54.3064i	−1.66409	−	2.88228i
$356$		−	9.93399i		−	0.526500i
$357$		0			0
$358$	−2.10332	+	1.21435i	−0.111164	+	0.0641804i
$359$		−	16.7899i		−	0.886139i	−0.896487	−	0.443069i	$-0.853890\pi$
$359$		−	16.7899i		−	0.886139i	0.896487	−	0.443069i	$-0.146110\pi$
$360$		0			0
$361$	−3.71313	+	6.43132i	−0.195428	+	0.338491i
$362$	−8.82058	−	5.09256i	−0.463599	−	0.267659i
$363$		0			0
$364$	0.515130	−	3.56856i	0.0270002	−	0.187044i
$365$	48.2098			2.52341
$366$		0			0
$367$	3.87653	−	6.71435i	0.202353	−	0.350486i	−0.746933	−	0.664899i	$-0.768474\pi$
$367$	3.87653	−	6.71435i	0.202353	−	0.350486i	0.949286	+	0.314413i	$0.101808\pi$
$368$	−1.49377	−	2.58729i	−0.0778684	−	0.134872i
$369$		0			0
$370$	−14.5028	+	8.37317i	−0.753962	+	0.435300i
$371$	−1.14898	+	0.663361i	−0.0596518	+	0.0344400i
$372$		0			0
$373$	−11.0737	−	19.1802i	−0.573373	−	0.993111i	−0.996216	−	0.0869082i	$-0.972301\pi$
$373$	−11.0737	−	19.1802i	−0.573373	−	0.993111i	0.422843	−	0.906203i	$-0.361032\pi$
$374$	13.9593	−	24.1782i	0.721818	−	1.25023i
$375$		0			0
$376$	9.29971			0.479596
$377$	−17.9457	−	2.59050i	−0.924250	−	0.133418i
$378$		0			0
$379$	3.82614	+	2.20902i	0.196536	+	0.113470i	0.595039	−	0.803697i	$-0.297137\pi$
$379$	3.82614	+	2.20902i	0.196536	+	0.113470i	−0.398503	+	0.917167i	$0.630470\pi$
$380$	−7.00452	+	12.1322i	−0.359325	+	0.622368i
$381$		0			0
$382$			3.81060i			0.194967i
$383$	−21.7299	+	12.5458i	−1.11035	+	0.641060i	−0.938919	−	0.344137i	$-0.888172\pi$
$383$	−21.7299	+	12.5458i	−1.11035	+	0.641060i	−0.171428	+	0.985197i	$0.554838\pi$
$384$		0			0
$385$			25.7356i			1.31161i
$386$	10.7654	+	18.6462i	0.547944	+	0.949066i
$387$		0			0
$388$	−10.5248	−	6.07652i	−0.534318	−	0.308489i
$389$	−36.4404			−1.84760			−0.923801	−	0.382872i	$-0.874935\pi$
$389$	−36.4404			−1.84760			−0.923801	+	0.382872i	$0.874935\pi$
$390$		0			0
$391$	−13.3458			−0.674928
$392$	−0.866025	−	0.500000i	−0.0437409	−	0.0252538i
$393$		0			0
$394$	−3.58811	−	6.21480i	−0.180767	−	0.313097i
$395$		−	5.40255i		−	0.271832i
$396$		0			0
$397$	−28.6158	+	16.5213i	−1.43619	+	0.829182i	−0.997582	−	0.0694990i	$-0.977860\pi$
$397$	−28.6158	+	16.5213i	−1.43619	+	0.829182i	−0.438603	+	0.898681i	$0.644527\pi$
$398$		−	10.8001i		−	0.541361i
$399$		0			0
$400$	5.97839	−	10.3549i	0.298919	−	0.517744i
$401$	16.9804	+	9.80364i	0.847960	+	0.489570i	0.859962	−	0.510358i	$-0.170487\pi$
$401$	16.9804	+	9.80364i	0.847960	+	0.489570i	−0.0120017	+	0.999928i	$0.503820\pi$
$402$		0			0
$403$	−35.9380	+	14.3640i	−1.79020	+	0.715521i
$404$	1.52181			0.0757128
$405$		0			0
$406$	−2.51441	+	4.35509i	−0.124788	+	0.216140i
$407$	12.7081	+	22.0111i	0.629917	+	1.09105i
$408$		0			0
$409$	3.32420	−	1.91923i	0.164371	−	0.0948997i	−0.415558	−	0.909567i	$-0.636414\pi$
$409$	3.32420	−	1.91923i	0.164371	−	0.0948997i	0.579929	+	0.814667i	$0.303080\pi$
$410$	24.5579	−	14.1785i	1.21283	−	0.700227i
$411$		0			0
$412$	−3.91165	−	6.77518i	−0.192713	−	0.333789i
$413$	−1.62409	+	2.81300i	−0.0799161	+	0.138419i
$414$		0			0
$415$	33.1428			1.62692
$416$	2.83290	+	2.23040i	0.138894	+	0.109354i
$417$		0			0
$418$	18.4132	+	10.6309i	0.900621	+	0.519974i
$419$	−6.76587	+	11.7188i	−0.330535	+	0.572503i	−0.982617	−	0.185646i	$-0.940562\pi$
$419$	−6.76587	+	11.7188i	−0.330535	+	0.572503i	0.652082	+	0.758148i	$0.273896\pi$
$420$		0			0
$421$			36.5436i			1.78103i	0.454956	+	0.890514i	$0.349655\pi$
$421$			36.5436i			1.78103i	−0.454956	+	0.890514i	$0.650345\pi$
$422$	−18.5512	+	10.7105i	−0.903059	+	0.521381i
$423$		0			0
$424$		−	1.32672i		−	0.0644314i
$425$	−26.7064	−	46.2568i	−1.29545	−	2.24379i
$426$		0			0
$427$	0.953993	+	0.550788i	0.0461669	+	0.0266545i
$428$	11.0501			0.534129
$429$		0			0
$430$	15.1064			0.728493
$431$	1.88366	+	1.08753i	0.0907329	+	0.0523847i	0.544680	−	0.838644i	$-0.316651\pi$
$431$	1.88366	+	1.08753i	0.0907329	+	0.0523847i	−0.453947	+	0.891029i	$0.649984\pi$
$432$		0			0
$433$	−1.90065	−	3.29203i	−0.0913396	−	0.158205i	0.816735	−	0.577012i	$-0.195782\pi$
$433$	−1.90065	−	3.29203i	−0.0913396	−	0.158205i	−0.908075	+	0.418808i	$0.862448\pi$
$434$			10.7341i			0.515252i
$435$		0			0
$436$	−4.75771	+	2.74686i	−0.227853	+	0.131551i
$437$		−	10.1637i		−	0.486196i
$438$		0			0
$439$	15.1976	−	26.3230i	0.725341	−	1.25633i	−0.233492	−	0.972359i	$-0.575015\pi$
$439$	15.1976	−	26.3230i	0.725341	−	1.25633i	0.958833	−	0.283970i	$-0.0916515\pi$
$440$	−22.2877	−	12.8678i	−1.06252	−	0.613448i
$441$		0			0
$442$	14.9562	−	5.97779i	0.711393	−	0.284335i
$443$	−2.12575			−0.100997			−0.0504987	−	0.998724i	$-0.516081\pi$
$443$	−2.12575			−0.100997			−0.0504987	+	0.998724i	$0.516081\pi$
$444$		0			0
$445$	−20.4534	+	35.4263i	−0.969584	+	1.67937i
$446$	−5.21660	−	9.03542i	−0.247013	−	0.427839i
$447$		0			0
$448$	0.866025	−	0.500000i	0.0409159	−	0.0236228i
$449$	20.3406	−	11.7437i	0.959935	−	0.554218i	0.0637817	−	0.997964i	$-0.479684\pi$
$449$	20.3406	−	11.7437i	0.959935	−	0.554218i	0.896153	+	0.443745i	$0.146351\pi$
$450$		0			0
$451$	−21.5190	−	37.2720i	−1.01329	−	1.75507i
$452$	9.46724	−	16.3977i	0.445301	−	0.771285i
$453$		0			0
$454$	−6.70448			−0.314657
$455$	−9.18447	+	11.6655i	−0.430574	+	0.546887i
$456$		0			0
$457$	26.8155	+	15.4820i	1.25438	+	0.724215i	0.971976	−	0.235081i	$-0.0755354\pi$
$457$	26.8155	+	15.4820i	1.25438	+	0.724215i	0.282402	+	0.959296i	$0.408869\pi$
$458$	−6.59331	+	11.4199i	−0.308085	+	0.533619i
$459$		0			0
$460$			12.3023i			0.573598i
$461$	4.95610	−	2.86140i	0.230828	−	0.133269i	−0.380126	−	0.924935i	$-0.624119\pi$
$461$	4.95610	−	2.86140i	0.230828	−	0.133269i	0.610954	+	0.791666i	$0.290786\pi$
$462$		0			0
$463$			37.6710i			1.75072i	0.483470	+	0.875361i	$0.339376\pi$
$463$			37.6710i			1.75072i	−0.483470	+	0.875361i	$0.660624\pi$
$464$	−2.51441	−	4.35509i	−0.116729	−	0.202180i
$465$		0			0
$466$	9.18567	+	5.30335i	0.425518	+	0.245673i
$467$	−9.44884			−0.437240			−0.218620	−	0.975810i	$-0.570156\pi$
$467$	−9.44884			−0.437240			−0.218620	+	0.975810i	$0.570156\pi$
$468$		0			0
$469$	−0.416071			−0.0192124
$470$	−33.1644	−	19.1475i	−1.52976	−	0.883206i
$471$		0			0
$472$	−1.62409	−	2.81300i	−0.0747546	−	0.129479i
$473$		−	22.9272i		−	1.05419i
$474$		0			0
$475$	35.2275	−	20.3386i	1.61635	−	0.933199i
$476$		−	4.46716i		−	0.204752i
$477$		0			0
$478$	−5.55724	+	9.62543i	−0.254182	+	0.440257i
$479$	−8.65853	−	4.99900i	−0.395618	−	0.228410i	0.288973	−	0.957337i	$-0.406686\pi$
$479$	−8.65853	−	4.99900i	−0.395618	−	0.228410i	−0.684592	+	0.728927i	$0.740019\pi$
$480$		0			0
$481$	−2.09491	+	14.5125i	−0.0955197	+	0.661712i
$482$	−28.7253			−1.30840
$483$		0			0
$484$	−14.0297	+	24.3001i	−0.637713	+	1.10455i
$485$	25.0223	+	43.3399i	1.13620	+	1.96796i
$486$		0			0
$487$	4.63049	−	2.67341i	0.209827	−	0.121144i	−0.391404	−	0.920219i	$-0.628010\pi$
$487$	4.63049	−	2.67341i	0.209827	−	0.121144i	0.601231	+	0.799075i	$0.294677\pi$
$488$	−0.953993	+	0.550788i	−0.0431852	+	0.0249330i
$489$		0			0
$490$	2.05893	+	3.56617i	0.0930130	+	0.161103i
$491$	17.8164	−	30.8588i	0.804041	−	1.39264i	−0.112895	−	0.993607i	$-0.536012\pi$
$491$	17.8164	−	30.8588i	0.804041	−	1.39264i	0.916936	−	0.399033i	$-0.130654\pi$
$492$		0			0
$493$	−22.4645			−1.01175
$494$	4.55247	+	11.3901i	0.204825	+	0.512464i
$495$		0			0
$496$	−9.29599	−	5.36704i	−0.417402	−	0.240987i
$497$	−7.61410	+	13.1880i	−0.341539	+	0.591563i
$498$		0			0
$499$		−	42.5633i		−	1.90540i	−0.303920	−	0.952698i	$-0.598295\pi$
$499$		−	42.5633i		−	1.90540i	0.303920	−	0.952698i	$-0.401705\pi$
$500$	−24.8091	+	14.3235i	−1.10949	+	0.640567i
$501$		0			0
$502$		−	12.7309i		−	0.568209i
$503$	−12.0972	−	20.9529i	−0.539386	−	0.934244i	−0.998937	−	0.0460924i	$-0.985323\pi$
$503$	−12.0972	−	20.9529i	−0.539386	−	0.934244i	0.459551	−	0.888151i	$-0.348010\pi$
$504$		0			0
$505$	−5.42703	−	3.13330i	−0.241500	−	0.139430i
$506$	18.6714			0.830047
$507$		0			0
$508$	0.860200			0.0381652
$509$	−10.7639	−	6.21457i	−0.477104	−	0.275456i	0.242105	−	0.970250i	$-0.422162\pi$
$509$	−10.7639	−	6.21457i	−0.477104	−	0.275456i	−0.719209	+	0.694794i	$0.755495\pi$
$510$		0			0
$511$	−5.85374	−	10.1390i	−0.258954	−	0.448522i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−16.4790	+	9.51414i	−0.726857	+	0.419651i
$515$			32.2153i			1.41958i
$516$		0			0
$517$	−29.0604	+	50.3342i	−1.27808	+	2.21369i
$518$	3.52191	+	2.03338i	0.154744	+	0.0893415i
$519$		0			0
$520$	−5.51038	−	13.7867i	−0.241646	−	0.604588i
$521$	43.6478			1.91224			0.956122	−	0.292970i	$-0.0946437\pi$
$521$	43.6478			1.91224			0.956122	+	0.292970i	$0.0946437\pi$
$522$		0			0
$523$	−6.58284	+	11.4018i	−0.287847	+	0.498566i	−0.973296	−	0.229555i	$-0.926273\pi$
$523$	−6.58284	+	11.4018i	−0.287847	+	0.498566i	0.685448	+	0.728121i	$0.259606\pi$
$524$	9.37045	+	16.2301i	0.409350	+	0.709015i
$525$		0			0
$526$	−7.02078	+	4.05345i	−0.306120	+	0.176739i
$527$	−41.5266	+	23.9754i	−1.80893	+	1.04439i
$528$		0			0
$529$	7.03728	+	12.1889i	0.305968	+	0.529953i
$530$	−2.73163	+	4.73132i	−0.118654	+	0.205515i
$531$		0			0
$532$	3.40202			0.147496
$533$	3.54737	−	24.5744i	0.153654	−	1.06443i
$534$		0			0
$535$	−39.4067	−	22.7515i	−1.70370	−	0.983631i
$536$	0.208035	−	0.360328i	0.00898576	−	0.0155638i
$537$		0			0
$538$		−	10.5675i		−	0.455597i
$539$	5.41244	−	3.12488i	0.233130	−	0.134598i
$540$		0			0
$541$		−	24.9321i		−	1.07192i	−0.844245	−	0.535958i	$-0.819950\pi$
$541$		−	24.9321i		−	1.07192i	0.844245	−	0.535958i	$-0.180050\pi$
$542$	−1.52191	−	2.63603i	−0.0653717	−	0.113227i
$543$		0			0
$544$	3.86867	+	2.23358i	0.165868	+	0.0957639i
$545$	22.6224			0.969038
$546$		0			0
$547$	24.8755			1.06360			0.531799	−	0.846870i	$-0.321516\pi$
$547$	24.8755			1.06360			0.531799	+	0.846870i	$0.321516\pi$
$548$	7.13797	+	4.12111i	0.304919	+	0.176045i
$549$		0			0
$550$	37.3634	+	64.7154i	1.59318	+	2.75947i
$551$		−	17.1082i		−	0.728833i
$552$		0			0
$553$	−1.13621	+	0.655990i	−0.0483165	+	0.0278956i
$554$		−	8.75619i		−	0.372015i
$555$		0			0
$556$	−0.790446	+	1.36909i	−0.0335224	+	0.0580625i
$557$	12.8488	+	7.41825i	0.544421	+	0.314321i	0.746869	−	0.664972i	$-0.231556\pi$
$557$	12.8488	+	7.41825i	0.544421	+	0.314321i	−0.202448	+	0.979293i	$0.564890\pi$
$558$		0			0
$559$	8.18220	−	10.3925i	0.346070	−	0.439555i
$560$	−4.11786			−0.174011
$561$		0			0
$562$	5.27136	−	9.13027i	0.222359	−	0.385137i
$563$	16.7341	+	28.9843i	0.705258	+	1.22154i	0.966598	+	0.256296i	$0.0825022\pi$
$563$	16.7341	+	28.9843i	0.705258	+	1.22154i	−0.261340	+	0.965247i	$0.584164\pi$
$564$		0			0
$565$	−67.5236	+	38.9848i	−2.84074	+	1.64010i
$566$	−11.8254	+	6.82738i	−0.497057	+	0.286976i
$567$		0			0
$568$	−7.61410	−	13.1880i	−0.319480	−	0.553356i
$569$	8.41931	−	14.5827i	0.352956	−	0.611337i	−0.633810	−	0.773489i	$-0.718510\pi$
$569$	8.41931	−	14.5827i	0.352956	−	0.611337i	0.986766	+	0.162151i	$0.0518433\pi$
$570$		0			0
$571$	−34.2607			−1.43376			−0.716882	−	0.697194i	$-0.754432\pi$
$571$	−34.2607			−1.43376			−0.716882	+	0.697194i	$0.754432\pi$
$572$	−20.9244	+	8.36320i	−0.874892	+	0.349683i
$573$		0			0
$574$	−5.96376	−	3.44318i	−0.248922	−	0.143715i
$575$	17.8607	−	30.9357i	0.744844	−	1.29011i
$576$		0			0
$577$			1.82396i			0.0759324i	0.999279	+	0.0379662i	$0.0120879\pi$
$577$			1.82396i			0.0759324i	−0.999279	+	0.0379662i	$0.987912\pi$
$578$	2.55952	−	1.47774i	0.106462	−	0.0614658i
$579$		0			0
$580$			20.7080i			0.859853i
$581$	−4.02428	−	6.97026i	−0.166955	−	0.289175i
$582$		0			0
$583$	7.18081	+	4.14584i	0.297399	+	0.171703i
$584$	11.7075			0.484459
$585$		0			0
$586$	11.6427			0.480955
$587$	−18.6111	−	10.7451i	−0.768160	−	0.443498i	0.0640577	−	0.997946i	$-0.479596\pi$
$587$	−18.6111	−	10.7451i	−0.768160	−	0.443498i	−0.832218	+	0.554449i	$0.812929\pi$
$588$		0			0
$589$	−18.2588	−	31.6252i	−0.752340	−	1.30309i
$590$			13.3755i			0.550661i
$591$		0			0
$592$	−3.52191	+	2.03338i	−0.144750	+	0.0835713i
$593$		−	11.7130i		−	0.480993i	−0.970650	−	0.240497i	$-0.922690\pi$
$593$		−	11.7130i		−	0.480993i	0.970650	−	0.240497i	$-0.0773103\pi$
$594$		0			0
$595$	−9.19756	+	15.9306i	−0.377063	+	0.653093i
$596$	7.21451	+	4.16530i	0.295518	+	0.170617i
$597$		0			0
$598$	8.46343	+	6.66342i	0.346095	+	0.272488i
$599$	19.8644			0.811639			0.405819	−	0.913953i	$-0.366986\pi$
$599$	19.8644			0.811639			0.405819	+	0.913953i	$0.366986\pi$
$600$		0			0
$601$	12.7552	−	22.0927i	0.520297	−	0.901181i	−0.479424	−	0.877583i	$-0.659154\pi$
$601$	12.7552	−	22.0927i	0.520297	−	0.901181i	0.999722	−	0.0235981i	$-0.00751221\pi$
$602$	−1.83425	−	3.17701i	−0.0747584	−	0.129485i
$603$		0			0
$604$	1.88298	−	1.08714i	0.0766172	−	0.0442350i
$605$	100.065	−	57.7723i	4.06820	−	2.34878i
$606$		0			0
$607$	14.0326	+	24.3051i	0.569564	+	0.986514i	0.996609	+	0.0822837i	$0.0262214\pi$
$607$	14.0326	+	24.3051i	0.569564	+	0.986514i	−0.427045	+	0.904231i	$0.640445\pi$
$608$	−1.70101	+	2.94624i	−0.0689851	+	0.119486i
$609$		0			0
$610$	4.53614			0.183663
$611$	−31.1357	+	12.4446i	−1.25962	+	0.503453i
$612$		0			0
$613$	−16.1584	−	9.32906i	−0.652632	−	0.376797i	0.136832	−	0.990594i	$-0.456308\pi$
$613$	−16.1584	−	9.32906i	−0.652632	−	0.376797i	−0.789464	+	0.613797i	$0.789641\pi$
$614$	7.38862	−	12.7975i	0.298180	−	0.516464i
$615$		0			0
$616$			6.24975i			0.251810i
$617$	−30.2029	+	17.4377i	−1.21592	+	0.702014i	−0.964044	−	0.265744i	$-0.914382\pi$
$617$	−30.2029	+	17.4377i	−1.21592	+	0.702014i	−0.251880	+	0.967758i	$0.581049\pi$
$618$		0			0
$619$		−	2.81567i		−	0.113171i	−0.998398	−	0.0565857i	$-0.981979\pi$
$619$		−	2.81567i		−	0.113171i	0.998398	−	0.0565857i	$-0.0180214\pi$
$620$	22.1007	+	38.2796i	0.887587	+	1.53735i
$621$		0			0
$622$	18.5722	+	10.7227i	0.744677	+	0.429940i
$623$	9.93399			0.397997
$624$		0			0
$625$	58.1806			2.32722
$626$	8.44010	+	4.87290i	0.337334	+	0.194760i
$627$		0			0
$628$	−6.67948	−	11.5692i	−0.266540	−	0.461661i
$629$			18.1668i			0.724359i
$630$		0			0
$631$	−38.0787	+	21.9848i	−1.51589	+	0.875200i	−0.516064	+	0.856550i	$0.672603\pi$
$631$	−38.0787	+	21.9848i	−1.51589	+	0.875200i	−0.999826	+	0.0186497i	$0.994063\pi$
$632$		−	1.31198i		−	0.0521878i
$633$		0			0
$634$	9.75660	−	16.8989i	0.387484	−	0.671142i
$635$	−3.06762	−	1.77109i	−0.121735	−	0.0702837i
$636$		0			0
$637$	3.56856	+	0.515130i	0.141392	+	0.0204102i
$638$	31.4289			1.24428
$639$		0			0
$640$	2.05893	−	3.56617i	0.0813864	−	0.140965i
$641$	6.55815	+	11.3590i	0.259031	+	0.448655i	0.965983	−	0.258607i	$-0.0832634\pi$
$641$	6.55815	+	11.3590i	0.259031	+	0.448655i	−0.706951	+	0.707262i	$0.749930\pi$
$642$		0			0
$643$	8.39536	−	4.84706i	0.331081	−	0.191150i	−0.325240	−	0.945631i	$-0.605445\pi$
$643$	8.39536	−	4.84706i	0.331081	−	0.191150i	0.656321	+	0.754482i	$0.272112\pi$
$644$	2.58729	−	1.49377i	0.101954	−	0.0588630i
$645$		0			0
$646$	7.59868	+	13.1613i	0.298966	+	0.517824i
$647$	−6.63337	+	11.4893i	−0.260785	+	0.451693i	−0.966451	−	0.256852i	$-0.917315\pi$
$647$	−6.63337	+	11.4893i	−0.260785	+	0.451693i	0.705666	+	0.708545i	$0.250648\pi$
$648$		0			0
$649$	20.3003			0.796855
$650$	−6.15930	+	42.6685i	−0.241588	+	1.67360i
$651$		0			0
$652$	3.27411	+	1.89031i	0.128224	+	0.0740301i
$653$	−13.6158	+	23.5832i	−0.532826	+	0.922882i	0.466439	+	0.884553i	$0.345537\pi$
$653$	−13.6158	+	23.5832i	−0.532826	+	0.922882i	−0.999265	+	0.0383287i	$0.987797\pi$
$654$		0			0
$655$		−	77.1724i		−	3.01538i
$656$	5.96376	−	3.44318i	0.232846	−	0.134433i
$657$		0			0
$658$			9.29971i			0.362540i
$659$	17.5897	+	30.4663i	0.685199	+	1.18680i	0.973374	+	0.229222i	$0.0736182\pi$
$659$	17.5897	+	30.4663i	0.685199	+	1.18680i	−0.288175	+	0.957578i	$0.593048\pi$
$660$		0			0
$661$	4.94408	+	2.85447i	0.192303	+	0.111026i	0.593060	−	0.805158i	$-0.297920\pi$
$661$	4.94408	+	2.85447i	0.192303	+	0.111026i	−0.400757	+	0.916184i	$0.631253\pi$
$662$	−5.91578			−0.229923
$663$		0			0
$664$	8.04856			0.312345
$665$	−12.1322	−	7.00452i	−0.470466	−	0.271624i
$666$		0			0
$667$	−7.51193	−	13.0110i	−0.290863	−	0.503790i
$668$		−	19.3982i		−	0.750540i
$669$		0			0
$670$	−1.48378	+	0.856660i	−0.0573234	+	0.0330957i
$671$		−	6.88457i		−	0.265776i
$672$		0			0
$673$	−0.929842	+	1.61053i	−0.0358428	+	0.0620815i	−0.883390	−	0.468638i	$-0.844745\pi$
$673$	−0.929842	+	1.61053i	−0.0358428	+	0.0620815i	0.847548	+	0.530719i	$0.178078\pi$
$674$	−26.4295	−	15.2591i	−1.01802	−	0.587757i
$675$		0			0
$676$	−12.4693	−	3.67655i	−0.479588	−	0.141406i
$677$	8.40742			0.323123			0.161562	−	0.986863i	$-0.448347\pi$
$677$	8.40742			0.323123			0.161562	+	0.986863i	$0.448347\pi$
$678$		0			0
$679$	6.07652	−	10.5248i	0.233196	−	0.403907i
$680$	−9.19756	−	15.9306i	−0.352710	−	0.610912i
$681$		0			0
$682$	58.0976	−	33.5427i	2.22467	−	1.28442i
$683$	20.2259	−	11.6775i	0.773924	−	0.446825i	−0.0603486	−	0.998177i	$-0.519221\pi$
$683$	20.2259	−	11.6775i	0.773924	−	0.446825i	0.834273	+	0.551352i	$0.185888\pi$
$684$		0			0
$685$	−16.9702	−	29.3932i	−0.648397	−	1.12306i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$		0			0
$688$	3.66850			0.139860
$689$	1.77537	+	4.44191i	0.0676364	+	0.169223i
$690$		0			0
$691$	−3.60505	−	2.08138i	−0.137143	−	0.0791794i	0.429859	−	0.902896i	$-0.358563\pi$
$691$	−3.60505	−	2.08138i	−0.137143	−	0.0791794i	−0.567002	+	0.823717i	$0.691897\pi$
$692$	5.62116	−	9.73613i	0.213684	−	0.370112i
$693$		0			0
$694$			19.4598i			0.738685i
$695$	5.63773	−	3.25495i	0.213851	−	0.123467i
$696$		0			0
$697$		−	30.7624i		−	1.16521i
$698$	−14.7411	−	25.5323i	−0.557959	−	0.966413i
$699$		0			0
$700$	10.3549	+	5.97839i	0.391377	+	0.225962i
$701$	0.243866			0.00921069			0.00460534	−	0.999989i	$-0.498534\pi$
$701$	0.243866			0.00921069			0.00460534	+	0.999989i	$0.498534\pi$
$702$		0			0
$703$	−13.8352			−0.521804
$704$	−5.41244	−	3.12488i	−0.203989	−	0.117773i
$705$		0			0
$706$	1.50398	+	2.60497i	0.0566031	+	0.0980394i
$707$			1.52181i			0.0572335i
$708$		0			0
$709$	15.4216	−	8.90364i	0.579169	−	0.334383i	−0.181634	−	0.983366i	$-0.558139\pi$
$709$	15.4216	−	8.90364i	0.579169	−	0.334383i	0.760803	+	0.648983i	$0.224805\pi$
$710$			62.7076i			2.35337i
$711$		0			0
$712$	−4.96700	+	8.60309i	−0.186146	+	0.322414i
$713$	−27.7722	−	16.0343i	−1.04008	−	0.600489i
$714$		0			0
$715$	91.8391	+	13.2572i	3.43459	+	0.495791i
$716$	2.42870			0.0907648
$717$		0			0
$718$	−8.39497	+	14.5405i	−0.313297	+	0.542647i
$719$	−11.1683	−	19.3440i	−0.416506	−	0.721409i	0.579079	−	0.815271i	$-0.303412\pi$
$719$	−11.1683	−	19.3440i	−0.416506	−	0.721409i	−0.995585	+	0.0938618i	$0.970079\pi$
$720$		0			0
$721$	6.77518	−	3.91165i	0.252321	−	0.145678i
$722$	6.43132	−	3.71313i	0.239349	−	0.138188i
$723$		0			0
$724$	5.09256	+	8.82058i	0.189264	+	0.327814i
$725$	30.0643	−	52.0729i	1.11656	−	1.93394i
$726$		0			0
$727$	38.1281			1.41409			0.707047	−	0.707167i	$-0.250027\pi$
$727$	38.1281			1.41409			0.707047	+	0.707167i	$0.250027\pi$
$728$	−2.23040	+	2.83290i	−0.0826640	+	0.104994i
$729$		0			0
$730$	−41.7509	−	24.1049i	−1.54527	−	0.892162i
$731$	8.19387	−	14.1922i	0.303061	−	0.524917i
$732$		0			0
$733$		−	15.8673i		−	0.586074i	−0.956101	−	0.293037i	$-0.905334\pi$
$733$		−	15.8673i		−	0.586074i	0.956101	−	0.293037i	$-0.0946659\pi$
$734$	−6.71435	+	3.87653i	−0.247831	+	0.143085i
$735$		0			0
$736$			2.98755i			0.110123i
$737$	1.30017	+	2.25196i	0.0478923	+	0.0829520i
$738$		0			0
$739$	18.0203	+	10.4040i	0.662889	+	0.382719i	0.793377	−	0.608731i	$-0.208321\pi$
$739$	18.0203	+	10.4040i	0.662889	+	0.382719i	−0.130488	+	0.991450i	$0.541654\pi$
$740$	16.7463			0.615608
$741$		0			0
$742$	1.32672			0.0487055
$743$	18.4871	+	10.6736i	0.678227	+	0.391575i	0.799187	−	0.601083i	$-0.205264\pi$
$743$	18.4871	+	10.6736i	0.678227	+	0.391575i	−0.120959	+	0.992657i	$0.538597\pi$
$744$		0			0
$745$	−17.1521	−	29.7083i	−0.628405	−	1.08843i
$746$			22.1473i			0.810872i
$747$		0			0
$748$	−24.1782	+	13.9593i	−0.884043	+	0.510403i
$749$			11.0501i			0.403763i
$750$		0			0
$751$	−0.0492560	+	0.0853139i	−0.00179738	+	0.00311315i	−0.866923	−	0.498443i	$-0.833905\pi$
$751$	−0.0492560	+	0.0853139i	−0.00179738	+	0.00311315i	0.865125	+	0.501556i	$0.167239\pi$
$752$	−8.05379	−	4.64986i	−0.293691	−	0.169563i
$753$		0			0
$754$	14.2462	+	11.2163i	0.518815	+	0.408473i
$755$	−8.95335			−0.325846
$756$		0			0
$757$	20.6664	−	35.7953i	0.751134	−	1.30100i	−0.196140	−	0.980576i	$-0.562841\pi$
$757$	20.6664	−	35.7953i	0.751134	−	1.30100i	0.947274	−	0.320426i	$-0.103826\pi$
$758$	−2.20902	−	3.82614i	−0.0802354	−	0.138972i
$759$		0			0
$760$	12.1322	−	7.00452i	0.440081	−	0.254081i
$761$	28.7617	−	16.6056i	1.04261	−	0.601951i	0.122038	−	0.992525i	$-0.461057\pi$
$761$	28.7617	−	16.6056i	1.04261	−	0.601951i	0.920571	+	0.390574i	$0.127724\pi$
$762$		0			0
$763$	−2.74686	−	4.75771i	−0.0994432	−	0.172241i
$764$	1.90530	−	3.30008i	0.0689314	−	0.119393i
$765$		0			0
$766$	25.0916			0.906595
$767$	9.20175	+	7.24472i	0.332256	+	0.261591i
$768$		0			0
$769$	−21.7530	−	12.5591i	−0.784432	−	0.452892i	0.0535666	−	0.998564i	$-0.482941\pi$
$769$	−21.7530	−	12.5591i	−0.784432	−	0.452892i	−0.837999	+	0.545672i	$0.816274\pi$
$770$	12.8678	−	22.2877i	0.463723	−	0.803192i
$771$		0			0
$772$		−	21.5308i		−	0.774909i
$773$	4.47908	−	2.58600i	0.161101	−	0.0930118i	−0.417282	−	0.908777i	$-0.637017\pi$
$773$	4.47908	−	2.58600i	0.161101	−	0.0930118i	0.578383	+	0.815765i	$0.303684\pi$
$774$		0			0
$775$		−	128.345i		−	4.61029i
$776$	6.07652	+	10.5248i	0.218134	+	0.377820i
$777$		0			0
$778$	31.5583	+	18.2202i	1.13142	+	0.653226i
$779$	23.4275			0.839378
$780$		0			0
$781$	95.1724			3.40554
$782$	11.5578	+	6.67292i	0.413308	+	0.238623i
$783$		0			0
$784$	0.500000	+	0.866025i	0.0178571	+	0.0309295i
$785$			55.0103i			1.96340i
$786$		0			0
$787$	31.4431	−	18.1537i	1.12082	−	0.647108i	0.179213	−	0.983810i	$-0.442645\pi$
$787$	31.4431	−	18.1537i	1.12082	−	0.647108i	0.941611	+	0.336702i	$0.109312\pi$
$788$			7.17623i			0.255643i
$789$		0			0
$790$	−2.70128	+	4.67875i	−0.0961071	+	0.166462i
$791$	16.3977	+	9.46724i	0.583036	+	0.336616i
$792$		0			0
$793$	2.45695	−	3.12066i	0.0872489	−	0.110818i
$794$	33.0427			1.17264
$795$		0			0
$796$	−5.40006	+	9.35318i	−0.191400	+	0.331515i
$797$	−4.26260	−	7.38303i	−0.150989	−	0.261520i	0.780602	−	0.625028i	$-0.214912\pi$
$797$	−4.26260	−	7.38303i	−0.150989	−	0.261520i	−0.931591	+	0.363508i	$0.881579\pi$
$798$		0			0
$799$	−35.9775	+	20.7716i	−1.27279	+	0.734847i
$800$	−10.3549	+	5.97839i	−0.366100	+	0.211368i
$801$		0			0
$802$	−9.80364	−	16.9804i	−0.346178	−	0.599599i
$803$	−36.5844	+	63.3661i	−1.29104	+	2.23614i
$804$		0			0
$805$	−12.3023			−0.433599
$806$	38.3052	+	5.52945i	1.34924	+	0.194767i
$807$		0			0
$808$	−1.31792	−	0.760904i	−0.0463644	−	0.0267685i
$809$	−20.5252	+	35.5507i	−0.721628	+	1.24990i	0.238719	+	0.971089i	$0.423273\pi$
$809$	−20.5252	+	35.5507i	−0.721628	+	1.24990i	−0.960347	+	0.278808i	$0.910061\pi$
$810$		0			0
$811$			26.5943i			0.933852i	0.884296	+	0.466926i	$0.154639\pi$
$811$			26.5943i			0.933852i	−0.884296	+	0.466926i	$0.845361\pi$
$812$	4.35509	−	2.51441i	0.152834	−	0.0882386i
$813$		0			0
$814$		−	25.4162i		−	0.890838i
$815$	−7.78401	−	13.4823i	−0.272662	−	0.472265i
$816$		0			0
$817$	10.8083	+	6.24015i	0.378133	+	0.218315i
$818$	−3.83845			−0.134208
$819$		0			0
$820$	−28.3570			−0.990271
$821$	9.12143	+	5.26626i	0.318340	+	0.183794i	0.650652	−	0.759376i	$-0.274495\pi$
$821$	9.12143	+	5.26626i	0.318340	+	0.183794i	−0.332312	+	0.943169i	$0.607829\pi$
$822$		0			0
$823$	10.9573	+	18.9787i	0.381949	+	0.661555i	0.991341	−	0.131314i	$-0.0419196\pi$
$823$	10.9573	+	18.9787i	0.381949	+	0.661555i	−0.609392	+	0.792869i	$0.708586\pi$
$824$			7.82331i			0.272538i
$825$		0			0
$826$	2.81300	−	1.62409i	0.0978768	−	0.0565092i
$827$			16.9832i			0.590563i	0.955410	+	0.295282i	$0.0954135\pi$
$827$			16.9832i			0.590563i	−0.955410	+	0.295282i	$0.904587\pi$
$828$		0			0
$829$	−22.2937	+	38.6137i	−0.774291	+	1.34111i	0.160902	+	0.986970i	$0.448560\pi$
$829$	−22.2937	+	38.6137i	−0.774291	+	1.34111i	−0.935192	+	0.354140i	$0.884774\pi$
$830$	−28.7025	−	16.5714i	−0.996280	−	0.575202i
$831$		0			0
$832$	−1.33817	−	3.34803i	−0.0463925	−	0.116072i
$833$	4.46716			0.154778
$834$		0			0
$835$	−39.9396	+	69.1774i	−1.38217	+	2.39398i
$836$	−10.6309	−	18.4132i	−0.367677	−	0.636835i
$837$		0			0
$838$	11.7188	−	6.76587i	0.404821	−	0.233723i
$839$	17.0996	−	9.87247i	0.590344	−	0.340835i	−0.174889	−	0.984588i	$-0.555957\pi$
$839$	17.0996	−	9.87247i	0.590344	−	0.340835i	0.765234	+	0.643753i	$0.222623\pi$
$840$		0			0
$841$	1.85545	+	3.21374i	0.0639811	+	0.110819i
$842$	18.2718	−	31.6477i	0.629689	−	1.09065i
$843$		0			0
$844$	21.4211			0.737344
$845$	36.8978	+	38.7846i	1.26932	+	1.33423i
$846$		0			0
$847$	−24.3001	−	14.0297i	−0.834963	−	0.482066i
$848$	−0.663361	+	1.14898i	−0.0227799	+	0.0394560i
$849$		0			0
$850$			53.4128i			1.83204i
$851$	−10.5219	+	6.07482i	−0.360686	+	0.208242i
$852$		0			0
$853$			40.7924i			1.39671i	0.715753	+	0.698353i	$0.246083\pi$
$853$			40.7924i			1.39671i	−0.715753	+	0.698353i	$0.753917\pi$
$854$	−0.550788	−	0.953993i	−0.0188476	−	0.0326450i
$855$		0			0
$856$	−9.56970	−	5.52507i	−0.327086	−	0.188843i
$857$	−16.4711			−0.562641			−0.281320	−	0.959614i	$-0.590772\pi$
$857$	−16.4711			−0.562641			−0.281320	+	0.959614i	$0.590772\pi$
$858$		0			0
$859$	15.6600			0.534313			0.267156	−	0.963653i	$-0.413916\pi$
$859$	15.6600			0.534313			0.267156	+	0.963653i	$0.413916\pi$
$860$	−13.0825	−	7.55318i	−0.446109	−	0.257561i
$861$		0			0
$862$	−1.08753	−	1.88366i	−0.0370416	−	0.0641578i
$863$			50.6267i			1.72335i	0.507457	+	0.861677i	$0.330586\pi$
$863$			50.6267i			1.72335i	−0.507457	+	0.861677i	$0.669414\pi$
$864$		0			0
$865$	−40.0920	+	23.1471i	−1.36317	+	0.787027i
$866$			3.80131i			0.129174i
$867$		0			0
$868$	5.36704	−	9.29599i	0.182169	−	0.315526i
$869$	7.10102	+	4.09978i	0.240886	+	0.139075i
$870$		0			0
$871$	−0.214331	+	1.48477i	−0.00726232	+	0.0503097i
$872$	5.49373			0.186041
$873$		0			0
$874$	−5.08185	+	8.80203i	−0.171896	+	0.297733i
$875$	−14.3235	−	24.8091i	−0.484223	−	0.838699i
$876$		0			0
$877$	23.7967	−	13.7390i	0.803556	−	0.463933i	−0.0411570	−	0.999153i	$-0.513104\pi$
$877$	23.7967	−	13.7390i	0.803556	−	0.463933i	0.844713	+	0.535219i	$0.179771\pi$
$878$	−26.3230	+	15.1976i	−0.888358	+	0.512894i
$879$		0			0
$880$	12.8678	+	22.2877i	0.433774	+	0.751318i
$881$	25.0473	−	43.3833i	0.843866	−	1.46162i	−0.0427356	−	0.999086i	$-0.513607\pi$
$881$	25.0473	−	43.3833i	0.843866	−	1.46162i	0.886602	−	0.462533i	$-0.153059\pi$
$882$		0			0
$883$	−33.7157			−1.13462			−0.567311	−	0.823503i	$-0.692016\pi$
$883$	−33.7157			−1.13462			−0.567311	+	0.823503i	$0.692016\pi$
$884$	−15.9413	−	2.30117i	−0.536165	−	0.0773966i
$885$		0			0
$886$	1.84095	+	1.06288i	0.0618481	+	0.0357080i
$887$	16.7954	−	29.0906i	0.563936	−	0.976766i	−0.433212	−	0.901292i	$-0.642620\pi$
$887$	16.7954	−	29.0906i	0.563936	−	0.976766i	0.997148	−	0.0754735i	$-0.0240468\pi$
$888$		0			0
$889$			0.860200i			0.0288502i
$890$	35.4263	−	20.4534i	1.18749	−	0.685599i
$891$		0			0
$892$			10.4332i			0.349329i
$893$	−15.8189	−	27.3991i	−0.529360	−	0.916878i
$894$		0			0
$895$	−8.66117	−	5.00053i	−0.289511	−	0.167149i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	−23.4874			−0.783783
$899$	−46.7479	−	26.9899i	−1.55913	−	0.900164i
$900$		0			0
$901$	2.96334	+	5.13265i	0.0987231	+	0.170993i
$902$			43.0380i			1.43301i
$903$		0			0
$904$	−16.3977	+	9.46724i	−0.545381	+	0.314876i
$905$		−	41.9409i		−	1.39416i
$906$		0			0
$907$	5.57940	−	9.66381i	0.185261	−	0.320882i	−0.758403	−	0.651785i	$-0.774020\pi$
$907$	5.57940	−	9.66381i	0.185261	−	0.320882i	0.943664	+	0.330904i	$0.107354\pi$
$908$	5.80625	+	3.35224i	0.192687	+	0.111248i
$909$		0			0
$910$	13.7867	−	5.51038i	0.457026	−	0.182667i
$911$	20.9736			0.694887			0.347444	−	0.937701i	$-0.387050\pi$
$911$	20.9736			0.694887			0.347444	+	0.937701i	$0.387050\pi$
$912$		0			0
$913$	−25.1507	+	43.5624i	−0.832368	+	1.44170i
$914$	−15.4820	−	26.8155i	−0.512098	−	0.886979i
$915$		0			0
$916$	11.4199	−	6.59331i	0.377326	−	0.217849i
$917$	−16.2301	+	9.37045i	−0.535965	+	0.309439i
$918$		0			0
$919$	24.3219	+	42.1268i	0.802307	+	1.38964i	0.918094	+	0.396362i	$0.129728\pi$
$919$	24.3219	+	42.1268i	0.802307	+	1.38964i	−0.115787	+	0.993274i	$0.536939\pi$
$920$	6.15116	−	10.6541i	0.202798	−	0.351256i
$921$		0			0
$922$	−5.72281			−0.188471
$923$	43.1400	+	33.9649i	1.41997	+	1.11797i
$924$		0			0
$925$	−42.1107	−	24.3126i	−1.38459	−	0.799395i
$926$	18.8355	−	32.6241i	0.618974	−	1.07209i
$927$		0			0
$928$			5.02883i			0.165079i
$929$	−9.70741	+	5.60458i	−0.318490	+	0.183880i	−0.650719	−	0.759318i	$-0.725533\pi$
$929$	−9.70741	+	5.60458i	−0.318490	+	0.183880i	0.332229	+	0.943199i	$0.392199\pi$
$930$		0			0
$931$			3.40202i			0.111497i
$932$	−5.30335	−	9.18567i	−0.173717	−	0.300887i
$933$		0			0
$934$	8.18293	+	4.72442i	0.267754	+	0.154588i
$935$	114.965			3.75976
$936$		0			0
$937$	−12.8992			−0.421398			−0.210699	−	0.977551i	$-0.567574\pi$
$937$	−12.8992			−0.421398			−0.210699	+	0.977551i	$0.567574\pi$
$938$	0.360328	+	0.208035i	0.0117651	+	0.00679259i
$939$		0			0
$940$	19.1475	+	33.1644i	0.624521	+	1.08170i
$941$			39.5017i			1.28772i	0.765144	+	0.643859i	$0.222668\pi$
$941$			39.5017i			1.28772i	−0.765144	+	0.643859i	$0.777332\pi$
$942$		0			0
$943$	17.8170	−	10.2867i	0.580202	−	0.334980i
$944$			3.24817i			0.105719i
$945$		0			0
$946$	−11.4636	+	19.8555i	−0.372714	+	0.645559i
$947$	−18.4382	−	10.6453i	−0.599162	−	0.345926i	0.169550	−	0.985522i	$-0.445769\pi$
$947$	−18.4382	−	10.6453i	−0.599162	−	0.345926i	−0.768712	+	0.639595i	$0.779102\pi$
$948$		0			0
$949$	−39.1970	+	15.6665i	−1.27239	+	0.508558i
$950$	−40.6772			−1.31974
$951$		0			0
$952$	−2.23358	+	3.86867i	−0.0723907	+	0.125384i
$953$	17.1134	+	29.6413i	0.554358	+	0.960176i	0.997953	+	0.0639491i	$0.0203695\pi$
$953$	17.1134	+	29.6413i	0.554358	+	0.960176i	−0.443595	+	0.896227i	$0.646297\pi$
$954$		0			0
$955$	−13.5893	+	7.84576i	−0.439738	+	0.253883i
$956$	9.62543	−	5.55724i	0.311309	−	0.179734i
$957$		0			0
$958$	4.99900	+	8.65853i	0.161510	+	0.279744i
$959$	−4.12111	+	7.13797i	−0.133078	+	0.230497i
$960$		0			0
$961$	−84.2205			−2.71679
$962$	9.07048	−	11.5207i	0.292444	−	0.371443i
$963$		0			0
$964$	24.8768	+	14.3626i	0.801228	+	0.462589i
$965$	−44.3303	+	76.7824i	−1.42704	+	2.47171i
$966$		0			0
$967$		−	28.3149i		−	0.910546i	−0.890352	−	0.455273i	$-0.849542\pi$
$967$		−	28.3149i		−	0.910546i	0.890352	−	0.455273i	$-0.150458\pi$
$968$	24.3001	−	14.0297i	0.781036	−	0.450931i
$969$		0			0
$970$		−	50.0446i		−	1.60683i
$971$	22.2729	+	38.5777i	0.714771	+	1.23802i	0.963048	+	0.269330i	$0.0868022\pi$
$971$	22.2729	+	38.5777i	0.714771	+	1.23802i	−0.248277	+	0.968689i	$0.579864\pi$
$972$		0			0
$973$	−1.36909	−	0.790446i	−0.0438911	−	0.0253405i
$974$	−5.34683			−0.171323
$975$		0			0
$976$	1.10158			0.0352606
$977$	−9.94891	−	5.74400i	−0.318294	−	0.183767i	0.332338	−	0.943160i	$-0.392163\pi$
$977$	−9.94891	−	5.74400i	−0.318294	−	0.183767i	−0.650632	+	0.759393i	$0.725496\pi$
$978$		0			0
$979$	−31.0425	−	53.7672i	−0.992122	−	1.71841i
$980$		−	4.11786i		−	0.131540i
$981$		0			0
$982$	−30.8588	+	17.8164i	−0.984745	+	0.568543i
$983$			20.2880i			0.647088i	0.946213	+	0.323544i	$0.104874\pi$
$983$			20.2880i			0.647088i	−0.946213	+	0.323544i	$0.895126\pi$
$984$		0			0
$985$	14.7754	−	25.5917i	0.470782	−	0.815418i
$986$	19.4549	+	11.2323i	0.619569	+	0.357708i
$987$		0			0
$988$	1.75248	−	12.1403i	0.0557540	−	0.386235i
$989$	10.9598			0.348502
$990$		0			0
$991$	15.8149	−	27.3922i	0.502376	−	0.870141i	−0.497620	−	0.867395i	$-0.665793\pi$
$991$	15.8149	−	27.3922i	0.502376	−	0.870141i	0.999996	−	0.00274582i	$-0.000874024\pi$
$992$	5.36704	+	9.29599i	0.170404	+	0.295148i
$993$		0			0
$994$	13.1880	−	7.61410i	0.418298	−	0.241504i
$995$	38.5151	−	22.2367i	1.22101	−	0.704950i
$996$		0			0
$997$	23.7092	+	41.0655i	0.750877	+	1.30056i	0.947398	+	0.320058i	$0.103702\pi$
$997$	23.7092	+	41.0655i	0.750877	+	1.30056i	−0.196521	+	0.980500i	$0.562964\pi$
$998$	−21.2817	+	36.8609i	−0.673659	+	1.16681i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.bj.i.1135.1	yes	16
3.2	odd	2		1638.2.bj.h.1135.8	yes	16
13.10	even	6	inner	1638.2.bj.i.127.4	yes	16
39.23	odd	6		1638.2.bj.h.127.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.bj.h.127.5	✓	16	39.23	odd	6
1638.2.bj.h.1135.8	yes	16	3.2	odd	2
1638.2.bj.i.127.4	yes	16	13.10	even	6	inner
1638.2.bj.i.1135.1	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -4.11786i q^{5} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -4.11786i q^{5} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-2.05893 + 3.56617i) q^{10} +(5.41244 + 3.12488i) q^{11} +(1.33817 + 3.34803i) q^{13} +1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.23358 + 3.86867i) q^{17} +(-2.94624 + 1.70101i) q^{19} +(3.56617 - 2.05893i) q^{20} +(-3.12488 - 5.41244i) q^{22} +(-1.49377 + 2.58729i) q^{23} -11.9568 q^{25} +(0.515130 - 3.56856i) q^{26} +(-0.866025 - 0.500000i) q^{28} +(-2.51441 + 4.35509i) q^{29} +10.7341i q^{31} +(0.866025 - 0.500000i) q^{32} -4.46716i q^{34} +(2.05893 + 3.56617i) q^{35} +(3.52191 + 2.03338i) q^{37} +3.40202 q^{38} -4.11786 q^{40} +(-5.96376 - 3.44318i) q^{41} +(-1.83425 - 3.17701i) q^{43} +6.24975i q^{44} +(2.58729 - 1.49377i) q^{46} +9.29971i q^{47} +(0.500000 - 0.866025i) q^{49} +(10.3549 + 5.97839i) q^{50} +(-2.23040 + 2.83290i) q^{52} +1.32672 q^{53} +(12.8678 - 22.2877i) q^{55} +(0.500000 + 0.866025i) q^{56} +(4.35509 - 2.51441i) q^{58} +(2.81300 - 1.62409i) q^{59} +(-0.550788 - 0.953993i) q^{61} +(5.36704 - 9.29599i) q^{62} -1.00000 q^{64} +(13.7867 - 5.51038i) q^{65} +(0.360328 + 0.208035i) q^{67} +(-2.23358 + 3.86867i) q^{68} -4.11786i q^{70} +(13.1880 - 7.61410i) q^{71} +11.7075i q^{73} +(-2.03338 - 3.52191i) q^{74} +(-2.94624 - 1.70101i) q^{76} -6.24975 q^{77} +1.31198 q^{79} +(3.56617 + 2.05893i) q^{80} +(3.44318 + 5.96376i) q^{82} +8.04856i q^{83} +(15.9306 - 9.19756i) q^{85} +3.66850i q^{86} +(3.12488 - 5.41244i) q^{88} +(-8.60309 - 4.96700i) q^{89} +(-2.83290 - 2.23040i) q^{91} -2.98755 q^{92} +(4.64986 - 8.05379i) q^{94} +(7.00452 + 12.1322i) q^{95} +(-10.5248 + 6.07652i) q^{97} +(-0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} + 2 q^{10} + 12 q^{11} + 10 q^{13} + 16 q^{14} - 8 q^{16} + 6 q^{17} - 4 q^{22} + 12 q^{23} - 20 q^{25} + 2 q^{26} - 16 q^{29} - 2 q^{35} - 6 q^{37} + 4 q^{40} - 12 q^{41} - 6 q^{43} + 6 q^{46} + 8 q^{49} + 24 q^{50} - 4 q^{52} + 40 q^{53} + 20 q^{55} + 8 q^{56} + 6 q^{58} - 6 q^{59} - 2 q^{61} + 14 q^{62} - 16 q^{64} + 52 q^{65} - 30 q^{67} - 6 q^{68} - 12 q^{71} - 24 q^{74} - 8 q^{77} - 16 q^{79} + 2 q^{82} + 6 q^{85} + 4 q^{88} - 30 q^{89} + 4 q^{91} + 24 q^{92} - 8 q^{94} + 40 q^{95} - 24 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^10 + 12 * q^11 + 10 * q^13 + 16 * q^14 - 8 * q^16 + 6 * q^17 - 4 * q^22 + 12 * q^23 - 20 * q^25 + 2 * q^26 - 16 * q^29 - 2 * q^35 - 6 * q^37 + 4 * q^40 - 12 * q^41 - 6 * q^43 + 6 * q^46 + 8 * q^49 + 24 * q^50 - 4 * q^52 + 40 * q^53 + 20 * q^55 + 8 * q^56 + 6 * q^58 - 6 * q^59 - 2 * q^61 + 14 * q^62 - 16 * q^64 + 52 * q^65 - 30 * q^67 - 6 * q^68 - 12 * q^71 - 24 * q^74 - 8 * q^77 - 16 * q^79 + 2 * q^82 + 6 * q^85 + 4 * q^88 - 30 * q^89 + 4 * q^91 + 24 * q^92 - 8 * q^94 + 40 * q^95 - 24 * q^97

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