LMFDB - Embedded newform 546.2.bv.a.317.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(317,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("546.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bv (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			317.6
Character	$\chi$	$=$	546.317
Dual form			546.2.bv.a.515.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(-0.977016 - 1.43019i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.28039 - 0.343079i) q^{5} +(1.31389 + 1.12859i) q^{6} +(-2.62526 + 0.328643i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.09088 + 2.79463i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.977016 - 1.43019i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.28039 - 0.343079i) q^{5} +(1.31389 + 1.12859i) q^{6} +(-2.62526 + 0.328643i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.09088 + 2.79463i) q^{9} +(-1.14797 + 0.662779i) q^{10} +(4.65127 + 1.24631i) q^{11} +(-1.56122 - 0.750071i) q^{12} +(1.95662 + 3.02847i) q^{13} +(2.45075 - 0.996912i) q^{14} +(-1.74163 - 1.49600i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.65499 + 6.33063i) q^{17} +(0.330403 - 2.98175i) q^{18} +(-1.57446 - 5.87595i) q^{19} +(0.937311 - 0.937311i) q^{20} +(3.03494 + 3.43353i) q^{21} -4.81535 q^{22} +(2.18890 - 3.79129i) q^{23} +(1.70215 + 0.320441i) q^{24} +(-2.80843 + 1.62145i) q^{25} +(-2.67377 - 2.41887i) q^{26} +(5.06266 - 1.17024i) q^{27} +(-2.10922 + 1.59724i) q^{28} -5.80299i q^{29} +(2.06948 + 0.994263i) q^{30} +(4.27281 + 1.14490i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-2.76192 - 7.86986i) q^{33} +(-5.16894 - 5.16894i) q^{34} +(-3.24861 + 1.32146i) q^{35} +(0.452589 + 2.96566i) q^{36} +(2.77431 - 0.743375i) q^{37} +(3.04162 + 5.26823i) q^{38} +(2.41964 - 5.75720i) q^{39} +(-0.662779 + 1.14797i) q^{40} +(-0.0540235 - 0.0540235i) q^{41} +(-3.82019 - 2.53103i) q^{42} -5.41380i q^{43} +(4.65127 - 1.24631i) q^{44} +(-0.437968 + 3.95248i) q^{45} +(-1.13306 + 4.22863i) q^{46} +(2.68147 + 10.0074i) q^{47} +(-1.72709 + 0.131027i) q^{48} +(6.78399 - 1.72554i) q^{49} +(2.29307 - 2.29307i) q^{50} +(5.48301 - 11.4125i) q^{51} +(3.20872 + 1.64442i) q^{52} +(0.697985 - 0.402982i) q^{53} +(-4.58727 + 2.44068i) q^{54} +6.38303 q^{55} +(1.62395 - 2.08873i) q^{56} +(-6.86545 + 7.99267i) q^{57} +(1.50192 + 5.60525i) q^{58} +(11.2251 + 3.00777i) q^{59} +(-2.25630 - 0.424763i) q^{60} +(5.51133 - 9.54591i) q^{61} -4.42354 q^{62} +(1.94540 - 7.69515i) q^{63} -1.00000i q^{64} +(3.54424 + 3.20635i) q^{65} +(4.70468 + 6.88686i) q^{66} +(1.64304 + 0.440252i) q^{67} +(6.33063 + 3.65499i) q^{68} +(-7.56085 + 0.573609i) q^{69} +(2.79589 - 2.11724i) q^{70} +(-0.953731 - 0.953731i) q^{71} +(-1.20474 - 2.74747i) q^{72} +(-0.966231 + 3.60603i) q^{73} +(-2.48738 + 1.43609i) q^{74} +(5.06286 + 2.43240i) q^{75} +(-4.30150 - 4.30150i) q^{76} +(-12.6204 - 1.74327i) q^{77} +(-0.847118 + 6.18728i) q^{78} +(-2.52485 + 4.37317i) q^{79} +(0.343079 - 1.28039i) q^{80} +(-6.61997 - 6.09721i) q^{81} +(0.0661650 + 0.0382004i) q^{82} +(7.21896 + 7.21896i) q^{83} +(4.34510 + 1.45605i) q^{84} +(6.85173 + 6.85173i) q^{85} +(1.40120 + 5.22933i) q^{86} +(-8.29936 + 5.66961i) q^{87} +(-4.17022 + 2.40768i) q^{88} +(1.07628 + 4.01675i) q^{89} +(-0.599933 - 3.93116i) q^{90} +(-6.13192 - 7.30750i) q^{91} -4.37780i q^{92} +(-2.53719 - 7.22951i) q^{93} +(-5.18020 - 8.97237i) q^{94} +(-4.03184 - 6.98335i) q^{95} +(1.63433 - 0.573565i) q^{96} +(-10.1999 + 10.1999i) q^{97} +(-6.10623 + 3.42257i) q^{98} +(-8.55694 + 11.6390i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7}+O(q^{10}) $ 144 * q - 16 * q^7	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) $ 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	−0.977016	−	1.43019i	−0.564081	−	0.825720i
$3$	−0.977016	−	1.43019i	−0.564081	−	0.825720i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	1.28039	−	0.343079i	0.572608	−	0.153430i	0.0391155	−	0.999235i	$-0.487546\pi$
$5$	1.28039	−	0.343079i	0.572608	−	0.153430i	0.533492	+	0.845805i	$0.320879\pi$
$6$	1.31389	+	1.12859i	0.536391	+	0.460743i
$7$	−2.62526	+	0.328643i	−0.992255	+	0.124215i
$7$	−2.62526	+	0.328643i	−0.992255	+	0.124215i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.09088	+	2.79463i	−0.363626	+	0.931545i
$10$	−1.14797	+	0.662779i	−0.363019	+	0.209589i
$11$	4.65127	+	1.24631i	1.40241	+	0.375775i	0.879210	−	0.476434i	$-0.158071\pi$
$11$	4.65127	+	1.24631i	1.40241	+	0.375775i	0.523202	+	0.852209i	$0.324737\pi$
$12$	−1.56122	−	0.750071i	−0.450684	−	0.216527i
$13$	1.95662	+	3.02847i	0.542668	+	0.839947i
$13$	1.95662	+	3.02847i	0.542668	+	0.839947i
$14$	2.45075	−	0.996912i	0.654990	−	0.266436i
$15$	−1.74163	−	1.49600i	−0.449687	−	0.386267i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	3.65499	+	6.33063i	0.886466	+	1.53540i	0.844024	+	0.536305i	$0.180180\pi$
$17$	3.65499	+	6.33063i	0.886466	+	1.53540i	0.0424416	+	0.999099i	$0.486486\pi$
$18$	0.330403	−	2.98175i	0.0778767	−	0.702805i
$19$	−1.57446	−	5.87595i	−0.361205	−	1.34804i	−0.872493	−	0.488626i	$-0.837498\pi$
$19$	−1.57446	−	5.87595i	−0.361205	−	1.34804i	0.511288	−	0.859409i	$-0.329169\pi$
$20$	0.937311	−	0.937311i	0.209589	−	0.209589i
$21$	3.03494	+	3.43353i	0.662279	+	0.749257i
$22$	−4.81535			−1.02664
$23$	2.18890	−	3.79129i	0.456418	−	0.790538i	−0.542351	−	0.840152i	$-0.682466\pi$
$23$	2.18890	−	3.79129i	0.456418	−	0.790538i	0.998768	+	0.0496137i	$0.0157990\pi$
$24$	1.70215	+	0.320441i	0.347450	+	0.0654098i
$25$	−2.80843	+	1.62145i	−0.561686	+	0.324290i
$26$	−2.67377	−	2.41887i	−0.524370	−	0.474379i
$27$	5.06266	−	1.17024i	0.974309	−	0.225213i
$28$	−2.10922	+	1.59724i	−0.398605	+	0.301851i
$29$		−	5.80299i		−	1.07759i	−0.842438	−	0.538794i	$-0.818880\pi$
$29$		−	5.80299i		−	1.07759i	0.842438	−	0.538794i	$-0.181120\pi$
$30$	2.06948	+	0.994263i	0.377834	+	0.181527i
$31$	4.27281	+	1.14490i	0.767419	+	0.205629i	0.621231	−	0.783627i	$-0.286633\pi$
$31$	4.27281	+	1.14490i	0.767419	+	0.205629i	0.146188	+	0.989257i	$0.453299\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−2.76192	−	7.86986i	−0.480788	−	1.36997i
$34$	−5.16894	−	5.16894i	−0.886466	−	0.886466i
$35$	−3.24861	+	1.32146i	−0.549115	+	0.223368i
$36$	0.452589	+	2.96566i	0.0754315	+	0.494277i
$37$	2.77431	−	0.743375i	0.456095	−	0.122210i	−0.0234551	−	0.999725i	$-0.507467\pi$
$37$	2.77431	−	0.743375i	0.456095	−	0.122210i	0.479550	+	0.877515i	$0.340800\pi$
$38$	3.04162	+	5.26823i	0.493415	+	0.854620i
$39$	2.41964	−	5.75720i	0.387452	−	0.921890i
$40$	−0.662779	+	1.14797i	−0.104795	+	0.181509i
$41$	−0.0540235	−	0.0540235i	−0.00843705	−	0.00843705i	0.702876	−	0.711313i	$-0.251899\pi$
$41$	−0.0540235	−	0.0540235i	−0.00843705	−	0.00843705i	−0.711313	+	0.702876i	$0.751899\pi$
$42$	−3.82019	−	2.53103i	−0.589469	−	0.390547i
$43$		−	5.41380i		−	0.825597i	−0.910822	−	0.412799i	$-0.864551\pi$
$43$		−	5.41380i		−	0.825597i	0.910822	−	0.412799i	$-0.135449\pi$
$44$	4.65127	−	1.24631i	0.701206	−	0.187888i
$45$	−0.437968	+	3.95248i	−0.0652884	+	0.589201i
$46$	−1.13306	+	4.22863i	−0.167060	+	0.623478i
$47$	2.68147	+	10.0074i	0.391132	+	1.45973i	0.828269	+	0.560330i	$0.189326\pi$
$47$	2.68147	+	10.0074i	0.391132	+	1.45973i	−0.437137	+	0.899395i	$0.644007\pi$
$48$	−1.72709	+	0.131027i	−0.249284	+	0.0189121i
$49$	6.78399	−	1.72554i	0.969141	−	0.246506i
$50$	2.29307	−	2.29307i	0.324290	−	0.324290i
$51$	5.48301	−	11.4125i	0.767775	−	1.59806i
$52$	3.20872	+	1.64442i	0.444969	+	0.228041i
$53$	0.697985	−	0.402982i	0.0958756	−	0.0553538i	−0.451296	−	0.892375i	$-0.649038\pi$
$53$	0.697985	−	0.402982i	0.0958756	−	0.0553538i	0.547171	+	0.837021i	$0.315705\pi$
$54$	−4.58727	+	2.44068i	−0.624249	+	0.332135i
$55$	6.38303			0.860687
$56$	1.62395	−	2.08873i	0.217010	−	0.279118i
$57$	−6.86545	+	7.99267i	−0.909351	+	1.05865i
$58$	1.50192	+	5.60525i	0.197212	+	0.736006i
$59$	11.2251	+	3.00777i	1.46139	+	0.391578i	0.899969	−	0.435954i	$-0.143589\pi$
$59$	11.2251	+	3.00777i	1.46139	+	0.391578i	0.561419	+	0.827532i	$0.310256\pi$
$60$	−2.25630	−	0.424763i	−0.291287	−	0.0548367i
$61$	5.51133	−	9.54591i	0.705654	−	1.22223i	−0.260801	−	0.965392i	$-0.583987\pi$
$61$	5.51133	−	9.54591i	0.705654	−	1.22223i	0.966455	−	0.256836i	$-0.0826799\pi$
$62$	−4.42354			−0.561790
$63$	1.94540	−	7.69515i	0.245098	−	0.969498i
$64$		−	1.00000i		−	0.125000i
$65$	3.54424	+	3.20635i	0.439609	+	0.397699i
$66$	4.70468	+	6.88686i	0.579106	+	0.847714i
$67$	1.64304	+	0.440252i	0.200730	+	0.0537854i	0.357783	−	0.933805i	$-0.383533\pi$
$67$	1.64304	+	0.440252i	0.200730	+	0.0537854i	−0.157053	+	0.987590i	$0.550199\pi$
$68$	6.33063	+	3.65499i	0.767702	+	0.443233i
$69$	−7.56085	+	0.573609i	−0.910219	+	0.0690544i
$70$	2.79589	−	2.11724i	0.334173	−	0.253058i
$71$	−0.953731	−	0.953731i	−0.113187	−	0.113187i	0.648245	−	0.761432i	$-0.275503\pi$
$71$	−0.953731	−	0.953731i	−0.113187	−	0.113187i	−0.761432	+	0.648245i	$0.775503\pi$
$72$	−1.20474	−	2.74747i	−0.141980	−	0.323793i
$73$	−0.966231	+	3.60603i	−0.113089	+	0.422053i	−0.999137	−	0.0415402i	$-0.986774\pi$
$73$	−0.966231	+	3.60603i	−0.113089	+	0.422053i	0.886048	+	0.463594i	$0.153440\pi$
$74$	−2.48738	+	1.43609i	−0.289152	+	0.166942i
$75$	5.06286	+	2.43240i	0.584609	+	0.280870i
$76$	−4.30150	−	4.30150i	−0.493415	−	0.493415i
$77$	−12.6204	−	1.74327i	−1.43823	−	0.198664i
$78$	−0.847118	+	6.18728i	−0.0959172	+	0.700571i
$79$	−2.52485	+	4.37317i	−0.284068	+	0.492020i	−0.972383	−	0.233392i	$-0.925017\pi$
$79$	−2.52485	+	4.37317i	−0.284068	+	0.492020i	0.688315	+	0.725412i	$0.258351\pi$
$80$	0.343079	−	1.28039i	0.0383575	−	0.143152i
$81$	−6.61997	−	6.09721i	−0.735552	−	0.677468i
$82$	0.0661650	+	0.0382004i	0.00730670	+	0.00421853i
$83$	7.21896	+	7.21896i	0.792383	+	0.792383i	0.981881	−	0.189498i	$-0.0606860\pi$
$83$	7.21896	+	7.21896i	0.792383	+	0.792383i	−0.189498	+	0.981881i	$0.560686\pi$
$84$	4.34510	+	1.45605i	0.474090	+	0.158868i
$85$	6.85173	+	6.85173i	0.743174	+	0.743174i
$86$	1.40120	+	5.22933i	0.151095	+	0.563893i
$87$	−8.29936	+	5.66961i	−0.889785	+	0.607846i
$88$	−4.17022	+	2.40768i	−0.444547	+	0.256659i
$89$	1.07628	+	4.01675i	0.114086	+	0.425775i	0.999217	−	0.0395675i	$-0.0125980\pi$
$89$	1.07628	+	4.01675i	0.114086	+	0.425775i	−0.885131	+	0.465342i	$0.845931\pi$
$90$	−0.599933	−	3.93116i	−0.0632385	−	0.414380i
$91$	−6.13192	−	7.30750i	−0.642800	−	0.766034i
$92$		−	4.37780i		−	0.456418i
$93$	−2.53719	−	7.22951i	−0.263094	−	0.749665i
$94$	−5.18020	−	8.97237i	−0.534297	−	0.925429i
$95$	−4.03184	−	6.98335i	−0.413658	−	0.716476i
$96$	1.63433	−	0.573565i	0.166803	−	0.0585393i
$97$	−10.1999	+	10.1999i	−1.03564	+	1.03564i	−0.0362990	+	0.999341i	$0.511557\pi$
$97$	−10.1999	+	10.1999i	−1.03564	+	1.03564i	−0.999341	+	0.0362990i	$0.988443\pi$
$98$	−6.10623	+	3.42257i	−0.616822	+	0.345732i
$99$	−8.55694	+	11.6390i	−0.860005	+	1.16977i
$100$	−1.62145	+	2.80843i	−0.162145	+	0.280843i
$101$	−0.706767	−	1.22416i	−0.0703259	−	0.121808i	0.828718	−	0.559666i	$-0.189071\pi$
$101$	−0.706767	−	1.22416i	−0.0703259	−	0.121808i	−0.899044	+	0.437858i	$0.855737\pi$
$102$	−2.34242	+	12.4427i	−0.231934	+	1.23201i
$103$	−7.02742	−	4.05729i	−0.692433	−	0.399776i	0.112090	−	0.993698i	$-0.464246\pi$
$103$	−7.02742	−	4.05729i	−0.692433	−	0.399776i	−0.804523	+	0.593922i	$0.797579\pi$
$104$	−3.52499	−	0.757915i	−0.345654	−	0.0743197i
$105$	5.06388	+	3.35503i	0.494185	+	0.327417i
$106$	−0.569902	+	0.569902i	−0.0553538	+	0.0553538i
$107$	−11.4051	−	6.58474i	−1.10257	−	0.636571i	−0.165677	−	0.986180i	$-0.552981\pi$
$107$	−11.4051	−	6.58474i	−1.10257	−	0.636571i	−0.936896	+	0.349609i	$0.886314\pi$
$108$	3.79927	−	3.54479i	0.365585	−	0.341098i
$109$	1.86273	+	0.499116i	0.178417	+	0.0478067i	0.346921	−	0.937894i	$-0.387227\pi$
$109$	1.86273	+	0.499116i	0.178417	+	0.0478067i	−0.168504	+	0.985701i	$0.553894\pi$
$110$	−6.16553	+	1.65205i	−0.587860	+	0.157517i
$111$	−3.77372	−	3.24150i	−0.358185	−	0.307670i
$112$	−1.02802	+	2.43786i	−0.0971385	+	0.230356i
$113$			14.8220i			1.39434i	0.716906	+	0.697169i	$0.245557\pi$
$113$			14.8220i			1.39434i	−0.716906	+	0.697169i	$0.754443\pi$
$114$	4.56286	−	9.49724i	0.427351	−	0.889498i
$115$	1.50193	−	5.60530i	0.140056	−	0.522696i
$116$	−2.90149	−	5.02553i	−0.269397	−	0.466609i
$117$	−10.5979	+	2.16434i	−0.979777	+	0.200093i
$118$	−11.6211			−1.06981
$119$	−11.6758	−	15.4184i	−1.07032	−	1.41340i
$120$	2.28935	−	0.173683i	0.208988	−	0.0158551i
$121$	10.5548	+	6.09381i	0.959527	+	0.553983i
$122$	−2.85288	+	10.6471i	−0.258287	+	0.963941i
$123$	−0.0244819	+	0.130046i	−0.00220746	+	0.0117258i
$124$	4.27281	−	1.14490i	0.383710	−	0.102815i
$125$	−7.72616	+	7.72616i	−0.691048	+	0.691048i
$126$	0.112537	+	7.93646i	0.0100256	+	0.707036i
$127$		−	10.5146i		−	0.933017i	−0.884517	−	0.466508i	$-0.845512\pi$
$127$		−	10.5146i		−	0.933017i	0.884517	−	0.466508i	$-0.154488\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−7.74276	+	5.28937i	−0.681712	+	0.465703i
$130$	−4.25334	−	2.17978i	−0.373043	−	0.191179i
$131$	−8.91736	−	5.14844i	−0.779113	−	0.449821i	0.0570029	−	0.998374i	$-0.481846\pi$
$131$	−8.91736	−	5.14844i	−0.779113	−	0.449821i	−0.836116	+	0.548553i	$0.815179\pi$
$132$	−6.32682	−	5.43454i	−0.550679	−	0.473016i
$133$	6.06445	+	14.9085i	0.525854	+	1.29273i
$134$	−1.70100			−0.146944
$135$	6.08069	−	3.23526i	0.523343	−	0.278447i
$136$	−7.06090	−	1.89196i	−0.605467	−	0.162235i
$137$	1.11456	+	0.298645i	0.0952233	+	0.0255150i	0.306116	−	0.951994i	$-0.400970\pi$
$137$	1.11456	+	0.298645i	0.0952233	+	0.0255150i	−0.210893	+	0.977509i	$0.567637\pi$
$138$	7.15476	−	2.51096i	0.609054	−	0.213747i
$139$	14.4535			1.22593			0.612965	−	0.790110i	$-0.289977\pi$
$139$	14.4535			1.22593			0.612965	+	0.790110i	$0.289977\pi$
$140$	−2.15264	+	2.76872i	−0.181932	+	0.234000i
$141$	11.6926	−	13.6124i	0.984694	−	1.14637i
$142$	1.16808	+	0.674390i	0.0980229	+	0.0565935i
$143$	5.32637	+	16.5248i	0.445413	+	1.38187i
$144$	1.87479	+	2.34205i	0.156232	+	0.195170i
$145$	−1.99089	−	7.43009i	−0.165334	−	0.617035i
$146$		−	3.73323i		−	0.308964i
$147$	−9.09592	−	8.01650i	−0.750219	−	0.661189i
$148$	2.03094	−	2.03094i	0.166942	−	0.166942i
$149$	12.3476	−	3.30854i	1.01156	−	0.271046i	0.285277	−	0.958445i	$-0.407914\pi$
$149$	12.3476	−	3.30854i	1.01156	−	0.271046i	0.726280	+	0.687399i	$0.241248\pi$
$150$	−5.51990	−	1.03916i	−0.450698	−	0.0848469i
$151$	3.01874	−	11.2661i	0.245662	−	0.916822i	−0.727388	−	0.686227i	$-0.759266\pi$
$151$	3.01874	−	11.2661i	0.245662	−	0.916822i	0.973050	−	0.230596i	$-0.0740675\pi$
$152$	5.26823	+	3.04162i	0.427310	+	0.246708i
$153$	−21.6790	+	3.30842i	−1.75264	+	0.267470i
$154$	12.6416	−	1.58253i	1.01869	−	0.127524i
$155$	5.86365			0.470980
$156$	−0.783132	−	6.19570i	−0.0627008	−	0.496053i
$157$	3.41094	+	5.90792i	0.272222	+	0.471503i	0.969431	−	0.245366i	$-0.0789080\pi$
$157$	3.41094	+	5.90792i	0.272222	+	0.471503i	−0.697208	+	0.716869i	$0.745575\pi$
$158$	1.30696	−	4.87763i	0.103976	−	0.388044i
$159$	−1.25828	−	0.604530i	−0.0997883	−	0.0479424i
$160$			1.32556i			0.104795i
$161$	−4.50046	+	10.6725i	−0.354686	+	0.841110i
$162$	7.97247	+	4.17608i	0.626377	+	0.328104i
$163$	−10.9294	+	2.92852i	−0.856055	+	0.229379i	−0.660048	−	0.751223i	$-0.729464\pi$
$163$	−10.9294	+	2.92852i	−0.856055	+	0.229379i	−0.196007	+	0.980603i	$0.562797\pi$
$164$	−0.0737975	−	0.0197740i	−0.00576261	−	0.00154409i
$165$	−6.23632	−	9.12893i	−0.485497	−	0.710686i
$166$	−8.84138	−	5.10457i	−0.686224	−	0.396192i
$167$	−1.97273	+	1.97273i	−0.152655	+	0.152655i	−0.779302	−	0.626648i	$-0.784426\pi$
$167$	−1.97273	+	1.97273i	−0.152655	+	0.152655i	0.626648	+	0.779302i	$0.284426\pi$
$168$	−4.57390	−	0.281842i	−0.352884	−	0.0217446i
$169$	−5.34329	+	11.8511i	−0.411022	+	0.911625i
$170$	−8.39162	−	4.84490i	−0.643608	−	0.371587i
$171$	18.1387	+	2.00992i	1.38710	+	0.153702i
$172$	−2.70690	−	4.68849i	−0.206399	−	0.357494i
$173$	11.3917	−	19.7311i	0.866099	−	1.50013i	0.000146630	−	1.00000i	$-0.499953\pi$
$173$	11.3917	−	19.7311i	0.866099	−	1.50013i	0.865952	−	0.500127i	$-0.166713\pi$
$174$	6.54917	−	7.62446i	0.496491	−	0.578009i
$175$	6.83999	−	5.17970i	0.517055	−	0.391548i
$176$	3.40497	−	3.40497i	0.256659	−	0.256659i
$177$	−6.66547	−	18.9927i	−0.501007	−	1.42758i
$178$	−2.07922	−	3.60132i	−0.155844	−	0.269930i
$179$	−12.8156	−	22.1972i	−0.957881	−	1.65910i	−0.727634	−	0.685965i	$-0.759380\pi$
$179$	−12.8156	−	22.1972i	−0.957881	−	1.65910i	−0.230246	−	0.973132i	$-0.573953\pi$
$180$	1.59695	+	3.64193i	0.119030	+	0.271454i
$181$			23.9594i			1.78089i	0.455095	+	0.890443i	$0.349605\pi$
$181$			23.9594i			1.78089i	−0.455095	+	0.890443i	$0.650395\pi$
$182$	7.81430	+	5.47145i	0.579234	+	0.405571i
$183$	−19.0371	+	1.44426i	−1.40726	+	0.106763i
$184$	1.13306	+	4.22863i	0.0835302	+	0.311739i
$185$	3.29717	−	1.90362i	0.242413	−	0.139957i
$186$	4.32187	+	6.32649i	0.316895	+	0.463881i
$187$	9.11047	+	34.0007i	0.666224	+	2.48638i
$188$	7.32591	+	7.32591i	0.534297	+	0.534297i
$189$	−12.9062	+	4.73600i	−0.938789	+	0.344493i
$190$	5.70188	+	5.70188i	0.413658	+	0.413658i
$191$	12.6850	+	7.32367i	0.917852	+	0.529922i	0.882949	−	0.469468i	$-0.155554\pi$
$191$	12.6850	+	7.32367i	0.917852	+	0.529922i	0.0349030	+	0.999391i	$0.488888\pi$
$192$	−1.43019	+	0.977016i	−0.103215	+	0.0705101i
$193$	2.02294	−	7.54971i	0.145614	−	0.543440i	−0.854113	−	0.520088i	$-0.825899\pi$
$193$	2.02294	−	7.54971i	0.145614	−	0.543440i	0.999727	−	0.0233527i	$-0.00743406\pi$
$194$	7.21240	−	12.4922i	0.517820	−	0.896891i
$195$	1.12290	−	8.20159i	0.0804127	−	0.587328i
$196$	5.01233	−	4.88636i	0.358024	−	0.349026i
$197$	1.74763	+	1.74763i	0.124513	+	0.124513i	0.766618	−	0.642104i	$-0.221938\pi$
$197$	1.74763	+	1.74763i	0.124513	+	0.124513i	−0.642104	+	0.766618i	$0.721938\pi$
$198$	5.25296	−	13.4572i	0.373312	−	0.956358i
$199$	−18.5493	+	10.7094i	−1.31492	+	0.759172i	−0.982907	−	0.184101i	$-0.941063\pi$
$199$	−18.5493	+	10.7094i	−1.31492	+	0.759172i	−0.332017	+	0.943273i	$0.607729\pi$
$200$	0.839324	−	3.13240i	0.0593491	−	0.221494i
$201$	−0.975637	−	2.78000i	−0.0688161	−	0.196086i
$202$	0.999519	+	0.999519i	0.0703259	+	0.0703259i
$203$	1.90711	+	15.2344i	0.133853	+	1.06924i
$204$	−0.957803	−	12.6250i	−0.0670596	−	0.883926i
$205$	−0.0877055	−	0.0506368i	−0.00612562	−	0.00353663i
$206$	7.83807	+	2.10021i	0.546104	+	0.146328i
$207$	8.20744	+	10.2530i	0.570457	+	0.712634i
$208$	3.60104	−	0.180245i	0.249687	−	0.0124978i
$209$		−	29.2929i		−	2.02623i
$210$	−5.75968	−	1.93008i	−0.397456	−	0.133188i
$211$	−11.4688			−0.789542			−0.394771	−	0.918780i	$-0.629176\pi$
$211$	−11.4688			−0.789542			−0.394771	+	0.918780i	$0.629176\pi$
$212$	0.402982	−	0.697985i	0.0276769	−	0.0479378i
$213$	−0.432205	+	2.29583i	−0.0296142	+	0.157307i
$214$	12.7207	+	3.40851i	0.869572	+	0.233001i
$215$	−1.85736	−	6.93178i	−0.126671	−	0.472743i
$216$	−2.75236	+	4.40733i	−0.187274	+	0.299881i
$217$	−11.5935	−	1.60142i	−0.787018	−	0.108712i
$218$	−1.92844			−0.130610
$219$	6.10132	−	2.14125i	0.412289	−	0.144692i
$220$	5.52786	−	3.19151i	0.372688	−	0.215172i
$221$	−12.0207	+	23.4557i	−0.808601	+	1.57780i
$222$	4.48409	+	2.15434i	0.300953	+	0.144590i
$223$	2.41289	−	2.41289i	0.161579	−	0.161579i	−0.621687	−	0.783266i	$-0.713552\pi$
$223$	2.41289	−	2.41289i	0.161579	−	0.161579i	0.783266	+	0.621687i	$0.213552\pi$
$224$	0.362023	−	2.62087i	0.0241887	−	0.175114i
$225$	−1.46770	−	9.61735i	−0.0978467	−	0.641156i
$226$	−3.83622	−	14.3170i	−0.255182	−	0.952351i
$227$	−4.69557	+	17.5241i	−0.311656	+	1.16312i	0.615406	+	0.788210i	$0.288992\pi$
$227$	−4.69557	+	17.5241i	−0.311656	+	1.16312i	−0.927063	+	0.374907i	$0.877675\pi$
$228$	−1.94932	+	10.3546i	−0.129097	+	0.685749i
$229$	−16.9730	+	4.54789i	−1.12160	+	0.300533i	−0.771533	−	0.636190i	$-0.780510\pi$
$229$	−16.9730	+	4.54789i	−1.12160	+	0.300533i	−0.350072	+	0.936723i	$0.613843\pi$
$230$			5.80303i			0.382640i
$231$	9.83713	+	19.7527i	0.647236	+	1.29964i
$232$	4.10333	+	4.10333i	0.269397	+	0.269397i
$233$	−1.72719	+	2.99159i	−0.113152	+	0.195985i	−0.917040	−	0.398796i	$-0.869428\pi$
$233$	−1.72719	+	2.99159i	−0.113152	+	0.195985i	0.803887	+	0.594782i	$0.202761\pi$
$234$	9.67662	−	4.83353i	0.632580	−	0.315978i
$235$	6.86665	+	11.8934i	0.447931	+	0.775839i
$236$	11.2251	−	3.00777i	0.730694	−	0.195789i
$237$	8.72127	−	0.661645i	0.566508	−	0.0429785i
$238$	15.2685	+	11.8711i	0.989713	+	0.769488i
$239$	14.0018	+	14.0018i	0.905701	+	0.905701i	0.995922	−	0.0902211i	$-0.0287574\pi$
$239$	14.0018	+	14.0018i	0.905701	+	0.905701i	−0.0902211	+	0.995922i	$0.528757\pi$
$240$	−2.16639	+	0.760294i	−0.139840	+	0.0490767i
$241$	1.00883	−	3.76499i	0.0649842	−	0.242524i	−0.925792	−	0.378034i	$-0.876600\pi$
$241$	1.00883	−	3.76499i	0.0649842	−	0.242524i	0.990776	+	0.135509i	$0.0432670\pi$
$242$	−11.7723	−	3.15439i	−0.756755	−	0.202772i
$243$	−2.25235	+	15.4249i	−0.144488	+	0.989507i
$244$		−	11.0227i		−	0.705654i
$245$	8.09415	−	4.53682i	0.517116	−	0.289847i
$246$	−0.0100105	−	0.131951i	−0.000638249	−	0.00841288i
$247$	14.7145	−	16.2652i	0.936264	−	1.03493i
$248$	−3.83090	+	2.21177i	−0.243262	+	0.140447i
$249$	3.27143	−	17.3775i	0.207318	−	1.10125i
$250$	5.46322	−	9.46257i	0.345524	−	0.598465i
$251$	−22.7689			−1.43716			−0.718579	−	0.695445i	$-0.755207\pi$
$251$	−22.7689			−1.43716			−0.718579	+	0.695445i	$0.755207\pi$
$252$	−2.16281	−	7.63690i	−0.136244	−	0.481080i
$253$	14.9063	−	14.9063i	0.937150	−	0.937150i
$254$	2.72137	+	10.1563i	0.170754	+	0.637262i
$255$	3.10501	−	16.4935i	0.194443	−	1.03286i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.496381	+	0.859757i	−0.0309634	+	0.0536302i	−0.881092	−	0.472945i	$-0.843191\pi$
$257$	−0.496381	+	0.859757i	−0.0309634	+	0.0536302i	0.850128	+	0.526575i	$0.176524\pi$
$258$	6.10994	−	7.11312i	0.380388	−	0.442843i
$259$	−7.03900	+	2.86331i	−0.437382	+	0.177918i
$260$	4.67258	+	1.00466i	0.289781	+	0.0623063i
$261$	16.2172	+	6.33035i	1.00382	+	0.391839i
$262$	9.94602	+	2.66503i	0.614467	+	0.164646i
$263$	6.80686	−	3.92994i	0.419729	−	0.242330i	−0.275233	−	0.961378i	$-0.588755\pi$
$263$	6.80686	−	3.92994i	0.419729	−	0.242330i	0.694961	+	0.719047i	$0.255422\pi$
$264$	7.51780	+	3.61186i	0.462689	+	0.222295i
$265$	0.755438	−	0.755438i	0.0464062	−	0.0464062i
$266$	−9.71640	−	12.8309i	−0.595751	−	0.786712i
$267$	4.69316	−	5.46372i	0.287217	−	0.334374i
$268$	1.64304	−	0.440252i	0.100365	−	0.0268927i
$269$	6.97939	−	4.02955i	0.425541	−	0.245686i	−0.271904	−	0.962324i	$-0.587653\pi$
$269$	6.97939	−	4.02955i	0.425541	−	0.245686i	0.697445	+	0.716638i	$0.254320\pi$
$270$	−5.03615	+	4.69882i	−0.306490	+	0.285961i
$271$	2.00147	−	0.536293i	0.121581	−	0.0325775i	−0.197516	−	0.980300i	$-0.563287\pi$
$271$	2.00147	−	0.536293i	0.121581	−	0.0325775i	0.319096	+	0.947722i	$0.396621\pi$
$272$	7.30998			0.443233
$273$	−4.46012	+	15.9093i	−0.269939	+	0.962878i
$274$	−1.15388			−0.0697083
$275$	−15.0836	+	4.04164i	−0.909576	+	0.243720i
$276$	−6.26108	+	4.27718i	−0.376873	+	0.257456i
$277$	1.27049	−	0.733518i	0.0763364	−	0.0440728i	−0.461346	−	0.887220i	$-0.652633\pi$
$277$	1.27049	−	0.733518i	0.0763364	−	0.0440728i	0.537682	+	0.843147i	$0.319300\pi$
$278$	−13.9610	+	3.74084i	−0.837325	+	0.224361i
$279$	−7.86068	+	10.6920i	−0.470607	+	0.640113i
$280$	1.36270	−	3.23153i	0.0814367	−	0.193121i
$281$	14.4645	−	14.4645i	0.862879	−	0.862879i	−0.128793	−	0.991672i	$-0.541110\pi$
$281$	14.4645	−	14.4645i	0.862879	−	0.862879i	0.991672	+	0.128793i	$0.0411102\pi$
$282$	−7.77104	+	16.1748i	−0.462758	+	0.963196i
$283$	3.71114	−	2.14263i	0.220604	−	0.127366i	−0.385626	−	0.922655i	$-0.626014\pi$
$283$	3.71114	−	2.14263i	0.220604	−	0.127366i	0.606230	+	0.795289i	$0.292681\pi$
$284$	−1.30282	−	0.349090i	−0.0773082	−	0.0207147i
$285$	−6.04833	+	12.5891i	−0.358272	+	0.745716i
$286$	−9.42181	−	14.5832i	−0.557123	−	0.862321i
$287$	0.159580	+	0.124071i	0.00941972	+	0.00732370i
$288$	−2.41707	−	1.77701i	−0.142427	−	0.104711i
$289$	−18.2179	+	31.5544i	−1.07164	+	1.85614i
$290$	3.84610	+	6.66163i	0.225851	+	0.391185i
$291$	24.5532	+	4.62230i	1.43933	+	0.270964i
$292$	0.966231	+	3.60603i	0.0565444	+	0.211027i
$293$	6.29141	−	6.29141i	0.367548	−	0.367548i	−0.499034	−	0.866582i	$-0.666312\pi$
$293$	6.29141	−	6.29141i	0.367548	−	0.367548i	0.866582	+	0.499034i	$0.166312\pi$
$294$	10.8608	+	5.38914i	0.633415	+	0.314301i
$295$	15.4045			0.896882
$296$	−1.43609	+	2.48738i	−0.0834711	+	0.144576i
$297$	25.0063	+	0.866502i	1.45101	+	0.0502796i
$298$	−11.0706	+	6.39160i	−0.641301	+	0.370255i
$299$	15.7647	−	0.789079i	0.911694	−	0.0456336i
$300$	5.60077	−	0.424906i	0.323361	−	0.0245320i
$301$	1.77921	+	14.2126i	0.102552	+	0.819203i
$302$			11.6635i			0.671161i
$303$	−1.06025	+	2.20683i	−0.0609098	+	0.126779i
$304$	−5.87595	−	1.57446i	−0.337009	−	0.0903013i
$305$	3.78165	−	14.1133i	0.216537	−	0.808126i
$306$	20.0840	−	8.80662i	1.14812	−	0.503441i
$307$	−11.5755	−	11.5755i	−0.660650	−	0.660650i	0.294883	−	0.955533i	$-0.404719\pi$
$307$	−11.5755	−	11.5755i	−0.660650	−	0.660650i	−0.955533	+	0.294883i	$0.904719\pi$
$308$	−11.8012	+	4.80048i	−0.672437	+	0.273533i
$309$	1.06323	+	14.0146i	0.0604848	+	0.797261i
$310$	−5.66386	+	1.51763i	−0.321685	+	0.0861953i
$311$	−9.47591	−	16.4128i	−0.537330	−	0.930682i	−0.999047	−	0.0436550i	$-0.986100\pi$
$311$	−9.47591	−	16.4128i	−0.537330	−	0.930682i	0.461717	−	0.887027i	$-0.347234\pi$
$312$	2.36001	+	5.78190i	0.133609	+	0.327335i
$313$	10.3836	−	17.9850i	0.586919	−	1.01657i	−0.407715	−	0.913109i	$-0.633674\pi$
$313$	10.3836	−	17.9850i	0.586919	−	1.01657i	0.994633	−	0.103463i	$-0.0329925\pi$
$314$	−4.82379	−	4.82379i	−0.272222	−	0.272222i
$315$	−0.149174	−	10.5202i	−0.00840498	−	0.592748i
$316$			5.04970i			0.284068i
$317$	−21.5441	+	5.77271i	−1.21003	+	0.324228i	−0.806776	−	0.590858i	$-0.798789\pi$
$317$	−21.5441	+	5.77271i	−1.21003	+	0.324228i	−0.403259	+	0.915086i	$0.632123\pi$
$318$	1.37187	+	0.258264i	0.0769307	+	0.0144827i
$319$	7.23229	−	26.9913i	0.404931	−	1.51122i
$320$	−0.343079	−	1.28039i	−0.0191787	−	0.0715760i
$321$	1.72555	+	22.7448i	0.0963110	+	1.26949i
$322$	1.58487	−	11.4736i	0.0883211	−	0.639401i
$323$	31.4439	−	31.4439i	1.74958	−	1.74958i
$324$	−8.78167	−	1.97036i	−0.487870	−	0.109464i
$325$	−10.4055	−	5.33270i	−0.577196	−	0.295805i
$326$	9.79901	−	5.65746i	0.542717	−	0.313338i
$327$	−1.10608	−	3.15170i	−0.0611666	−	0.174289i
$328$	0.0764008			0.00421853
$329$	−10.3284	−	25.3907i	−0.569423	−	1.39984i
$330$	8.38657	+	7.20379i	0.461665	+	0.396556i
$331$	−0.343693	−	1.28268i	−0.0188911	−	0.0705025i	0.955837	−	0.293898i	$-0.0949526\pi$
$331$	−0.343693	−	1.28268i	−0.0188911	−	0.0705025i	−0.974728	+	0.223395i	$0.928286\pi$
$332$	9.86128	+	2.64232i	0.541208	+	0.145016i
$333$	−0.948977	+	8.56413i	−0.0520036	+	0.469311i
$334$	1.39493	−	2.41609i	0.0763273	−	0.132203i
$335$	2.25478			0.123192
$336$	4.49099	−	0.911574i	0.245004	−	0.0497304i
$337$		−	24.5514i		−	1.33740i	−0.743532	−	0.668700i	$-0.766851\pi$
$337$		−	24.5514i		−	1.33740i	0.743532	−	0.668700i	$-0.233149\pi$
$338$	2.09392	−	12.8303i	0.113894	−	0.697874i
$339$	21.1983	−	14.4814i	1.15133	−	0.786519i
$340$	9.35963	+	2.50791i	0.507597	+	0.136010i
$341$	18.4471	+	10.6505i	0.998968	+	0.576754i
$342$	−18.0408	+	2.75321i	−0.975536	+	0.148876i
$343$	−17.2427	+	6.75951i	−0.931016	+	0.364979i
$344$	3.82814	+	3.82814i	0.206399	+	0.206399i
$345$	−9.48404	+	3.32842i	−0.510604	+	0.179196i
$346$	−5.89680	+	22.0072i	−0.317014	+	1.18311i
$347$	−22.4856	+	12.9821i	−1.20709	+	0.696915i	−0.962123	−	0.272616i	$-0.912111\pi$
$347$	−22.4856	+	12.9821i	−1.20709	+	0.696915i	−0.244969	+	0.969531i	$0.578778\pi$
$348$	−4.35265	+	9.05971i	−0.233327	+	0.485651i
$349$	4.54021	+	4.54021i	0.243032	+	0.243032i	0.818103	−	0.575071i	$-0.195026\pi$
$349$	4.54021	+	4.54021i	0.243032	+	0.243032i	−0.575071	+	0.818103i	$0.695026\pi$
$350$	−5.26632	+	6.77352i	−0.281497	+	0.362060i
$351$	13.4497	+	13.0424i	0.717894	+	0.696152i
$352$	−2.40768	+	4.17022i	−0.128330	+	0.222273i
$353$	−3.49020	+	13.0256i	−0.185765	+	0.693283i	0.808701	+	0.588220i	$0.200171\pi$
$353$	−3.49020	+	13.0256i	−0.185765	+	0.693283i	−0.994466	+	0.105063i	$0.966496\pi$
$354$	11.3540	+	16.6204i	0.603459	+	0.883364i
$355$	−1.54835	−	0.893942i	−0.0821781	−	0.0474455i
$356$	2.94046	+	2.94046i	0.155844	+	0.155844i
$357$	−10.6437	+	31.7626i	−0.563325	+	1.68106i
$358$	18.1239	+	18.1239i	0.957881	+	0.957881i
$359$	−4.33446	−	16.1764i	−0.228764	−	0.853760i	−0.980861	−	0.194707i	$-0.937624\pi$
$359$	−4.33446	−	16.1764i	−0.228764	−	0.853760i	0.752097	−	0.659052i	$-0.229042\pi$
$360$	−2.48514	−	3.10452i	−0.130978	−	0.163622i
$361$	−15.5934	+	9.00286i	−0.820706	+	0.473835i
$362$	−6.20114	−	23.1430i	−0.325925	−	1.21637i
$363$	−1.59690	−	21.0491i	−0.0838158	−	1.10479i
$364$	−8.96415	−	3.26252i	−0.469849	−	0.171003i
$365$			4.94861i			0.259022i
$366$	18.0146	−	6.32222i	0.941640	−	0.330468i
$367$	−12.2472	−	21.2129i	−0.639301	−	1.10730i	−0.985586	−	0.169173i	$-0.945890\pi$
$367$	−12.2472	−	21.2129i	−0.639301	−	1.10730i	0.346285	−	0.938129i	$-0.387443\pi$
$368$	−2.18890	−	3.79129i	−0.114104	−	0.197635i
$369$	0.209909	−	0.0920429i	0.0109274	−	0.00479156i
$370$	−2.69213	+	2.69213i	−0.139957	+	0.139957i
$371$	−1.69996	+	1.28732i	−0.0882573	+	0.0668343i
$372$	−5.81202	−	4.99234i	−0.301339	−	0.258841i
$373$	10.3616	−	17.9468i	0.536503	−	0.929250i	−0.462586	−	0.886574i	$-0.653079\pi$
$373$	10.3616	−	17.9468i	0.536503	−	0.929250i	0.999089	−	0.0426754i	$-0.0135881\pi$
$374$	−17.6001	−	30.4842i	−0.910079	−	1.57630i
$375$	18.5984	+	3.50128i	0.960419	+	0.180805i
$376$	−8.97237	−	5.18020i	−0.462714	−	0.267148i
$377$	17.5742	−	11.3542i	0.905117	−	0.584773i
$378$	11.2407	−	7.91500i	0.578158	−	0.407103i
$379$	−13.1529	+	13.1529i	−0.675620	+	0.675620i	−0.959006	−	0.283386i	$-0.908542\pi$
$379$	−13.1529	+	13.1529i	−0.675620	+	0.675620i	0.283386	+	0.959006i	$0.408542\pi$
$380$	−6.98335	−	4.03184i	−0.358238	−	0.206829i
$381$	−15.0378	+	10.2729i	−0.770410	+	0.526297i
$382$	−14.1482	−	3.79101i	−0.723887	−	0.193965i
$383$	−11.7556	+	3.14991i	−0.600685	+	0.160953i	−0.546332	−	0.837569i	$-0.683976\pi$
$383$	−11.7556	+	3.14991i	−0.600685	+	0.160953i	−0.0543529	+	0.998522i	$0.517310\pi$
$384$	1.12859	−	1.31389i	0.0575929	−	0.0670489i
$385$	−16.7571	+	2.09773i	−0.854021	+	0.106910i
$386$			7.81604i			0.397826i
$387$	15.1296	+	5.90580i	0.769081	+	0.300209i
$388$	−3.73341	+	13.9333i	−0.189535	+	0.707355i
$389$	1.45477	+	2.51973i	0.0737597	+	0.127756i	0.900546	−	0.434760i	$-0.143167\pi$
$389$	1.45477	+	2.51973i	0.0737597	+	0.127756i	−0.826787	+	0.562516i	$0.809834\pi$
$390$	1.03809	+	8.21276i	0.0525656	+	0.415869i
$391$	32.0017			1.61839
$392$	−3.57686	+	6.01715i	−0.180659	+	0.303912i
$393$	1.34917	+	17.7836i	0.0680564	+	0.897064i
$394$	−2.14040	−	1.23576i	−0.107832	−	0.0622567i
$395$	−1.73245	+	6.46558i	−0.0871689	+	0.325319i
$396$	−1.59101	+	14.3582i	−0.0799511	+	0.721526i
$397$	−10.7155	+	2.87121i	−0.537795	+	0.144102i	−0.517486	−	0.855692i	$-0.673132\pi$
$397$	−10.7155	+	2.87121i	−0.537795	+	0.144102i	−0.0203097	+	0.999794i	$0.506465\pi$
$398$	15.1454	−	15.1454i	0.759172	−	0.759172i
$399$	15.3969	−	23.2391i	0.770807	−	1.16341i
$400$			3.24290i			0.162145i
$401$	1.89431	+	7.06965i	0.0945972	+	0.353042i	0.996958	−	0.0779397i	$-0.0248342\pi$
$401$	1.89431	+	7.06965i	0.0945972	+	0.353042i	−0.902361	+	0.430981i	$0.858167\pi$
$402$	1.66191	+	2.43276i	0.0828885	+	0.121335i
$403$	4.89297	+	15.1802i	0.243736	+	0.756180i
$404$	−1.22416	−	0.706767i	−0.0609040	−	0.0351630i
$405$	−10.5680	−	5.53564i	−0.525127	−	0.275068i
$406$	−5.78507	−	14.2217i	−0.287108	−	0.705809i
$407$	13.8306			0.685556
$408$	4.19275	+	11.9469i	0.207572	+	0.591460i
$409$	−5.21620	−	1.39768i	−0.257924	−	0.0691107i	0.127540	−	0.991833i	$-0.459292\pi$
$409$	−5.21620	−	1.39768i	−0.257924	−	0.0691107i	−0.385464	+	0.922723i	$0.625959\pi$
$410$	0.0978228	+	0.0262115i	0.00483112	+	0.00129450i
$411$	−0.661824	−	1.88581i	−0.0326454	−	0.0930202i
$412$	−8.11457			−0.399776
$413$	−30.4574	−	4.20711i	−1.49871	−	0.207019i
$414$	−10.5815	−	7.77941i	−0.520050	−	0.382337i
$415$	11.7198	+	6.76640i	0.575300	+	0.332150i
$416$	−3.43169	+	1.10612i	−0.168252	+	0.0542321i
$417$	−14.1213	−	20.6712i	−0.691523	−	1.01227i
$418$	7.58156	+	28.2948i	0.370826	+	1.38394i
$419$			12.1715i			0.594619i	0.954781	+	0.297310i	$0.0960893\pi$
$419$			12.1715i			0.594619i	−0.954781	+	0.297310i	$0.903911\pi$
$420$	6.06297	+	0.373598i	0.295843	+	0.0182297i
$421$	16.5862	−	16.5862i	0.808364	−	0.808364i	−0.176022	−	0.984386i	$-0.556323\pi$
$421$	16.5862	−	16.5862i	0.808364	−	0.808364i	0.984386	+	0.176022i	$0.0563230\pi$
$422$	11.0780	−	2.96833i	0.539267	−	0.144496i
$423$	−30.8921	−	3.42310i	−1.50203	−	0.166437i
$424$	−0.208599	+	0.778501i	−0.0101304	+	0.0378073i
$425$	−20.5296	−	11.8528i	−0.995832	−	0.574944i
$426$	−0.176726	−	2.32946i	−0.00856241	−	0.112863i
$427$	−11.3315	+	26.8718i	−0.548369	+	1.30042i
$428$	−13.1695			−0.636571
$429$	18.4296	−	23.7627i	0.889791	−	1.14727i
$430$	3.58815	+	6.21486i	0.173036	+	0.299707i
$431$	9.09962	−	33.9602i	0.438313	−	1.63581i	−0.294698	−	0.955590i	$-0.595219\pi$
$431$	9.09962	−	33.9602i	0.438313	−	1.63581i	0.733011	−	0.680216i	$-0.238114\pi$
$432$	1.51787	−	4.96951i	0.0730286	−	0.239096i
$433$		−	25.4681i		−	1.22392i	−0.790889	−	0.611960i	$-0.790381\pi$
$433$		−	25.4681i		−	1.22392i	0.790889	−	0.611960i	$-0.209619\pi$
$434$	11.6129	−	1.45376i	0.557439	−	0.0697829i
$435$	−8.68130	+	10.1067i	−0.416236	+	0.484577i
$436$	1.86273	−	0.499116i	0.0892085	−	0.0239033i
$437$	−25.7238	−	6.89266i	−1.23053	−	0.329721i
$438$	−5.33923	+	3.64743i	−0.255118	+	0.174281i
$439$	−9.12459	−	5.26808i	−0.435493	−	0.251432i	0.266191	−	0.963920i	$-0.414235\pi$
$439$	−9.12459	−	5.26808i	−0.435493	−	0.251432i	−0.701684	+	0.712488i	$0.747568\pi$
$440$	−4.51348	+	4.51348i	−0.215172	+	0.215172i
$441$	−2.57824	+	20.8411i	−0.122773	+	0.992435i
$442$	5.54035	−	25.7676i	0.263527	−	1.22564i
$443$	−0.0277916	−	0.0160455i	−0.00132042	−	0.000762345i	0.499340	−	0.866406i	$-0.333576\pi$
$443$	−0.0277916	−	0.0160455i	−0.00132042	−	0.000762345i	−0.500660	+	0.865644i	$0.666909\pi$
$444$	−4.88889	−	0.920365i	−0.232016	−	0.0436786i
$445$	2.75613	+	4.77375i	0.130653	+	0.226298i
$446$	−1.70617	+	2.95518i	−0.0807895	+	0.139932i
$447$	−16.7957	−	14.4269i	−0.794407	−	0.682371i
$448$	0.328643	+	2.62526i	0.0155269	+	0.124032i
$449$	−17.7664	+	17.7664i	−0.838446	+	0.838446i	−0.988654	−	0.150208i	$-0.952006\pi$
$449$	−17.7664	+	17.7664i	−0.838446	+	0.838446i	0.150208	+	0.988654i	$0.452006\pi$
$450$	3.90684	+	8.90977i	0.184170	+	0.420011i
$451$	−0.183948	−	0.318608i	−0.00866179	−	0.0150027i
$452$	7.41101	+	12.8362i	0.348585	+	0.603766i
$453$	−19.0620	+	6.68979i	−0.895611	+	0.314314i
$454$		−	18.1423i		−	0.851460i
$455$	−10.3583	−	7.25272i	−0.485605	−	0.340013i
$456$	−0.797066	−	10.5063i	−0.0373260	−	0.492001i
$457$	−4.75108	−	17.7313i	−0.222246	−	0.829434i	−0.983489	−	0.180967i	$-0.942077\pi$
$457$	−4.75108	−	17.7313i	−0.222246	−	0.829434i	0.761243	−	0.648467i	$-0.224590\pi$
$458$	15.2175	−	8.78585i	0.711069	−	0.410536i
$459$	25.9124	+	27.7726i	1.20949	+	1.29631i
$460$	−1.50193	−	5.60530i	−0.0700281	−	0.261348i
$461$	21.5427	+	21.5427i	1.00334	+	1.00334i	0.999994	+	0.00334897i	$0.00106601\pi$
$461$	21.5427	+	21.5427i	1.00334	+	1.00334i	0.00334897	+	0.999994i	$0.498934\pi$
$462$	−14.6143	−	16.5337i	−0.679920	−	0.769215i
$463$	−13.9505	−	13.9505i	−0.648337	−	0.648337i	0.304254	−	0.952591i	$-0.401593\pi$
$463$	−13.9505	−	13.9505i	−0.648337	−	0.648337i	−0.952591	+	0.304254i	$0.901593\pi$
$464$	−5.02553	−	2.90149i	−0.233305	−	0.134698i
$465$	−5.72889	−	8.38613i	−0.265671	−	0.388898i
$466$	0.894061	−	3.33668i	0.0414166	−	0.154569i
$467$	10.1766	−	17.6264i	0.470918	−	0.815654i	−0.528528	−	0.848916i	$-0.677256\pi$
$467$	10.1766	−	17.6264i	0.470918	−	0.815654i	0.999447	+	0.0332612i	$0.0105893\pi$
$468$	−8.09589	+	7.17333i	−0.374232	+	0.331587i
$469$	−4.45810	−	0.615803i	−0.205856	−	0.0284351i
$470$	−9.71091	−	9.71091i	−0.447931	−	0.447931i
$471$	5.11689	−	10.6504i	0.235774	−	0.490745i
$472$	−10.0642	+	5.81056i	−0.463242	+	0.267453i
$473$	6.74725	−	25.1811i	0.310239	−	1.15783i
$474$	−8.25286	+	2.89633i	−0.379066	+	0.133033i
$475$	13.9493	+	13.9493i	0.640038	+	0.640038i
$476$	−17.8207	−	7.51479i	−0.816813	−	0.344440i
$477$	0.364770	+	2.39022i	0.0167017	+	0.109441i
$478$	−17.1486	−	9.90076i	−0.784360	−	0.452850i
$479$	8.12965	+	2.17833i	0.371453	+	0.0995306i	0.439716	−	0.898137i	$-0.355079\pi$
$479$	8.12965	+	2.17833i	0.371453	+	0.0995306i	−0.0682629	+	0.997667i	$0.521746\pi$
$480$	1.89580	−	1.29509i	0.0865309	−	0.0591126i
$481$	7.67957	+	6.94743i	0.350158	+	0.316776i
$482$			3.89781i			0.177540i
$483$	19.6607	−	3.99069i	0.894592	−	0.181583i
$484$	12.1876			0.553983
$485$	−9.56045	+	16.5592i	−0.434118	+	0.751914i
$486$	−1.81665	−	15.4822i	−0.0824051	−	0.702289i
$487$	−3.02437	−	0.810378i	−0.137047	−	0.0367217i	0.189643	−	0.981853i	$-0.439267\pi$
$487$	−3.02437	−	0.810378i	−0.137047	−	0.0367217i	−0.326691	+	0.945131i	$0.605934\pi$
$488$	2.85288	+	10.6471i	0.129144	+	0.481970i
$489$	14.8665	+	12.7699i	0.672287	+	0.577473i
$490$	−6.64414	+	6.47715i	−0.300151	+	0.292608i
$491$	−42.7727			−1.93031			−0.965153	−	0.261688i	$-0.915721\pi$
$491$	−42.7727			−1.93031			−0.965153	+	0.261688i	$0.915721\pi$
$492$	0.0438208	+	0.124864i	0.00197560	+	0.00562929i
$493$	36.7366	−	21.2099i	1.65453	−	0.955245i
$494$	−10.0034	+	19.5194i	−0.450075	+	0.878218i
$495$	−6.96311	+	17.8382i	−0.312968	+	0.801769i
$496$	3.12791	−	3.12791i	0.140447	−	0.140447i
$497$	2.81723	+	2.19036i	0.126370	+	0.0982509i
$498$	1.33767	+	17.6321i	0.0599425	+	0.790113i
$499$	3.89664	+	14.5424i	0.174437	+	0.651009i	0.996647	+	0.0818241i	$0.0260746\pi$
$499$	3.89664	+	14.5424i	0.174437	+	0.651009i	−0.822209	+	0.569185i	$0.807259\pi$
$500$	−2.82797	+	10.5541i	−0.126471	+	0.471995i
$501$	4.74877	+	0.893987i	0.212159	+	0.0399404i
$502$	21.9930	−	5.89302i	0.981597	−	0.263018i
$503$			33.7834i			1.50633i	0.657834	+	0.753163i	$0.271473\pi$
$503$			33.7834i			1.50633i	−0.657834	+	0.753163i	$0.728527\pi$
$504$	4.06569	+	6.81690i	0.181100	+	0.303649i
$505$	−1.32492	−	1.32492i	−0.0589581	−	0.0589581i
$506$	−10.5403	+	18.2564i	−0.468575	+	0.811596i
$507$	22.1698	−	3.93684i	0.984597	−	0.174841i
$508$	−5.25728	−	9.10588i	−0.233254	−	0.404008i
$509$	2.21830	−	0.594393i	0.0983246	−	0.0263460i	−0.209321	−	0.977847i	$-0.567125\pi$
$509$	2.21830	−	0.594393i	0.0983246	−	0.0263460i	0.307646	+	0.951501i	$0.400459\pi$
$510$	1.26962	+	16.7351i	0.0562198	+	0.741045i
$511$	1.35152	−	9.78430i	0.0597876	−	0.432832i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−14.8472	−	27.9055i	−0.655521	−	1.23206i
$514$	0.256946	−	0.958934i	0.0113334	−	0.0422968i
$515$	−10.3898	−	2.78394i	−0.457830	−	0.122675i
$516$	−4.06074	+	8.45211i	−0.178764	+	0.372083i
$517$			49.8890i			2.19411i
$518$	6.05807	−	4.58757i	0.266176	−	0.201566i
$519$	−39.3491	+	2.98525i	−1.72723	+	0.131038i
$520$	−4.77339	+	0.238926i	−0.209327	+	0.0104776i
$521$	−13.7549	+	7.94142i	−0.602615	+	0.347920i	−0.770070	−	0.637960i	$-0.779779\pi$
$521$	−13.7549	+	7.94142i	−0.602615	+	0.347920i	0.167455	+	0.985880i	$0.446445\pi$
$522$	−17.3031	−	1.91732i	−0.757334	−	0.0839189i
$523$	−7.41978	+	12.8514i	−0.324444	+	0.561954i	−0.981400	−	0.191975i	$-0.938511\pi$
$523$	−7.41978	+	12.8514i	−0.324444	+	0.561954i	0.656955	+	0.753929i	$0.271844\pi$
$524$	−10.2969			−0.449821
$525$	−14.0907	−	4.72183i	−0.614970	−	0.206077i
$526$	−5.55777	+	5.55777i	−0.242330	+	0.242330i
$527$	8.36917	+	31.2342i	0.364567	+	1.36058i
$528$	−8.19646	−	1.54304i	−0.356705	−	0.0671521i
$529$	1.91742	+	3.32107i	0.0833661	+	0.144394i
$530$	−0.534175	+	0.925219i	−0.0232031	+	0.0401889i
$531$	−20.6509	+	28.0891i	−0.896171	+	1.21896i
$532$	12.7062	+	9.87889i	0.550884	+	0.428304i
$533$	0.0579053	−	0.269312i	0.00250816	−	0.0116652i
$534$	−3.11913	+	6.49223i	−0.134978	+	0.280946i
$535$	−16.8621	−	4.51818i	−0.729011	−	0.195338i
$536$	−1.47311	+	0.850502i	−0.0636288	+	0.0367361i
$537$	−19.2252	+	40.0157i	−0.829628	+	1.72681i
$538$	−5.69864	+	5.69864i	−0.245686	+	0.245686i
$539$	33.7047	+	0.428938i	1.45177	+	0.0184757i
$540$	3.64840	−	5.84217i	0.157002	−	0.251407i
$541$	43.2517	−	11.5893i	1.85953	−	0.498261i	0.859615	−	0.510942i	$-0.170703\pi$
$541$	43.2517	−	11.5893i	1.85953	−	0.498261i	0.999920	+	0.0126809i	$0.00403657\pi$
$542$	−1.79447	+	1.03604i	−0.0770791	+	0.0445016i
$543$	34.2664	−	23.4087i	1.47051	−	1.00456i
$544$	−7.06090	+	1.89196i	−0.302734	+	0.0811173i
$545$	2.55625			0.109498
$546$	0.190502	−	16.5216i	0.00815274	−	0.707060i
$547$	−16.4459			−0.703176			−0.351588	−	0.936155i	$-0.614358\pi$
$547$	−16.4459			−0.703176			−0.351588	+	0.936155i	$0.614358\pi$
$548$	1.11456	−	0.298645i	0.0476116	−	0.0127575i
$549$	20.6651	+	25.8156i	0.881966	+	1.10178i
$550$	13.5236	−	7.80785i	0.576648	−	0.332928i
$551$	−34.0981	+	9.13655i	−1.45263	+	0.389230i
$552$	4.94073	−	5.75193i	0.210291	−	0.244818i
$553$	5.19118	−	12.3105i	0.220751	−	0.523495i
$554$	−1.03735	+	1.03735i	−0.0440728	+	0.0440728i
$555$	−5.94392	−	2.85570i	−0.252306	−	0.121218i
$556$	12.5171	−	7.22675i	0.530843	−	0.306482i
$557$	−22.1265	−	5.92877i	−0.937529	−	0.251210i	−0.242467	−	0.970160i	$-0.577956\pi$
$557$	−22.1265	−	5.92877i	−0.937529	−	0.251210i	−0.695062	+	0.718950i	$0.744623\pi$
$558$	4.82554	−	12.3622i	0.204281	−	0.523333i
$559$	16.3956	−	10.5927i	0.693458	−	0.448025i
$560$	−0.479882	+	3.47411i	−0.0202787	+	0.146808i
$561$	39.7264	−	46.2490i	1.67725	−	1.95263i
$562$	−10.2279	+	17.7153i	−0.431439	+	0.747275i
$563$	−3.59034	−	6.21865i	−0.151315	−	0.262085i	0.780396	−	0.625285i	$-0.215017\pi$
$563$	−3.59034	−	6.21865i	−0.151315	−	0.262085i	−0.931711	+	0.363200i	$0.881684\pi$
$564$	3.31990	−	17.6350i	0.139793	−	0.742566i
$565$	5.08513	+	18.9780i	0.213933	+	0.798409i
$566$	−3.03013	+	3.03013i	−0.127366	+	0.127366i
$567$	19.3829	+	13.8312i	0.814007	+	0.580855i
$568$	1.34878			0.0565935
$569$	1.47774	−	2.55952i	0.0619500	−	0.107301i	−0.833387	−	0.552690i	$-0.813601\pi$
$569$	1.47774	−	2.55952i	0.0619500	−	0.107301i	0.895337	+	0.445389i	$0.146935\pi$
$570$	2.58393	−	13.7256i	0.108229	−	0.574902i
$571$	−30.4608	+	17.5866i	−1.27475	+	0.735974i	−0.975877	−	0.218320i	$-0.929942\pi$
$571$	−30.4608	+	17.5866i	−1.27475	+	0.735974i	−0.298868	+	0.954295i	$0.596609\pi$
$572$	12.8752	+	11.6477i	0.538338	+	0.487015i
$573$	−1.91919	−	25.2972i	−0.0801754	−	1.05681i
$574$	−0.186255	−	0.0785413i	−0.00777412	−	0.00327825i
$575$			14.1968i			0.592046i
$576$	2.79463	+	1.09088i	0.116443	+	0.0454533i
$577$	−15.1844	−	4.06864i	−0.632133	−	0.169380i	−0.0714958	−	0.997441i	$-0.522777\pi$
$577$	−15.1844	−	4.06864i	−0.632133	−	0.169380i	−0.560638	+	0.828061i	$0.689444\pi$
$578$	9.43030	−	35.1944i	0.392249	−	1.46389i
$579$	−12.7740	+	4.48301i	−0.530868	+	0.186307i
$580$	−5.43920	−	5.43920i	−0.225851	−	0.225851i
$581$	−21.3241	−	16.5792i	−0.884673	−	0.687821i
$582$	−24.9129	+	1.89003i	−1.03267	+	0.0783444i
$583$	3.74876	−	1.00448i	0.155258	−	0.0416012i
$584$	−1.86662	−	3.23307i	−0.0772411	−	0.133786i
$585$	−12.8269	+	6.40712i	−0.530328	+	0.264902i
$586$	−4.44870	+	7.70537i	−0.183774	+	0.318306i
$587$	18.7144	+	18.7144i	0.772427	+	0.772427i	0.978530	−	0.206103i	$-0.0660783\pi$
$587$	18.7144	+	18.7144i	0.772427	+	0.772427i	−0.206103	+	0.978530i	$0.566078\pi$
$588$	−11.8855	−	2.39453i	−0.490152	−	0.0987487i
$589$		−	26.9094i		−	1.10878i
$590$	−14.8796	+	3.98697i	−0.612582	+	0.164141i
$591$	0.791977	−	4.20690i	0.0325776	−	0.173049i
$592$	0.743375	−	2.77431i	0.0305525	−	0.114024i
$593$	1.77839	+	6.63703i	0.0730296	+	0.272550i	0.992779	−	0.119955i	$-0.0382751\pi$
$593$	1.77839	+	6.63703i	0.0730296	+	0.272550i	−0.919750	+	0.392505i	$0.871608\pi$
$594$	−24.3785	+	5.63513i	−1.00026	+	0.231212i
$595$	−20.2393	−	15.7358i	−0.829732	−	0.645105i
$596$	9.03909	−	9.03909i	0.370255	−	0.370255i
$597$	33.4395	+	16.0657i	1.36859	+	0.657525i
$598$	−15.0233	+	4.84239i	−0.614347	+	0.198020i
$599$	0.177150	−	0.102277i	0.00723814	−	0.00417894i	−0.496377	−	0.868107i	$-0.665336\pi$
$599$	0.177150	−	0.102277i	0.00723814	−	0.00417894i	0.503615	+	0.863928i	$0.332003\pi$
$600$	−5.29995	+	1.86001i	−0.216370	+	0.0759347i
$601$	−27.8036			−1.13413			−0.567066	−	0.823673i	$-0.691921\pi$
$601$	−27.8036			−1.13413			−0.567066	+	0.823673i	$0.691921\pi$
$602$	−5.39708	−	13.2679i	−0.219969	−	0.540758i
$603$	−3.02271	+	4.11145i	−0.123094	+	0.167431i
$604$	−3.01874	−	11.2661i	−0.122831	−	0.458411i
$605$	15.6049	+	4.18133i	0.634430	+	0.169995i
$606$	0.452954	−	2.40605i	0.0184000	−	0.0977390i
$607$	10.3426	−	17.9138i	0.419792	−	0.727100i	−0.576127	−	0.817360i	$-0.695436\pi$
$607$	10.3426	−	17.9138i	0.419792	−	0.727100i	0.995918	+	0.0902601i	$0.0287698\pi$
$608$	6.08323			0.246708
$609$	19.9247	−	17.6117i	0.807390	−	0.713664i
$610$			14.6112i			0.591589i
$611$	−25.0604	+	27.7014i	−1.01384	+	1.12068i
$612$	−17.1203	+	13.7047i	−0.692048	+	0.553978i
$613$	2.66032	+	0.712832i	0.107450	+	0.0287910i	0.312143	−	0.950035i	$-0.398953\pi$
$613$	2.66032	+	0.712832i	0.107450	+	0.0287910i	−0.204694	+	0.978826i	$0.565620\pi$
$614$	14.1771	+	8.18513i	0.572140	+	0.330325i
$615$	0.0132695	+	0.174908i	0.000535080	+	0.00705299i
$616$	10.1566	−	7.69129i	0.409223	−	0.309891i
$617$	−14.1114	−	14.1114i	−0.568102	−	0.568102i	0.363494	−	0.931596i	$-0.381584\pi$
$617$	−14.1114	−	14.1114i	−0.568102	−	0.568102i	−0.931596	+	0.363494i	$0.881584\pi$
$618$	−4.65424	−	13.2619i	−0.187221	−	0.533470i
$619$	−2.14141	+	7.99186i	−0.0860706	+	0.321220i	−0.995515	−	0.0946061i	$-0.969841\pi$
$619$	−2.14141	+	7.99186i	−0.0860706	+	0.321220i	0.909444	+	0.415826i	$0.136508\pi$
$620$	5.07807	−	2.93183i	0.203940	−	0.117745i
$621$	6.64494	−	21.7556i	0.266652	−	0.873020i
$622$	13.4010	+	13.4010i	0.537330	+	0.537330i
$623$	−4.14560	−	10.1913i	−0.166090	−	0.408306i
$624$	−3.77606	−	4.97407i	−0.151163	−	0.199122i
$625$	0.865437	−	1.49898i	0.0346175	−	0.0599592i
$626$	−5.37497	+	20.0597i	−0.214827	+	0.801746i
$627$	−41.8944	+	28.6197i	−1.67310	+	1.14296i
$628$	5.90792	+	3.41094i	0.235752	+	0.136111i
$629$	14.8461	+	14.8461i	0.591954	+	0.591954i
$630$	2.86693	+	10.1232i	0.114221	+	0.403316i
$631$	−8.41152	−	8.41152i	−0.334857	−	0.334857i	0.519570	−	0.854428i	$-0.326092\pi$
$631$	−8.41152	−	8.41152i	−0.334857	−	0.334857i	−0.854428	+	0.519570i	$0.826092\pi$
$632$	−1.30696	−	4.87763i	−0.0519880	−	0.194022i
$633$	11.2052	+	16.4025i	0.445365	+	0.651940i
$634$	19.3159	−	11.1520i	0.767131	−	0.442903i
$635$	−3.60733	−	13.4627i	−0.143153	−	0.534253i
$636$	−1.39197	+	0.105603i	−0.0551952	+	0.00418742i
$637$	18.4994	+	17.1689i	0.732975	+	0.680256i
$638$			27.9434i			1.10629i
$639$	3.70574	−	1.62493i	0.146597	−	0.0642811i
$640$	0.662779	+	1.14797i	0.0261986	+	0.0453774i
$641$	−1.21297	−	2.10092i	−0.0479094	−	0.0829815i	0.841076	−	0.540917i	$-0.181923\pi$
$641$	−1.21297	−	2.10092i	−0.0479094	−	0.0829815i	−0.888986	+	0.457935i	$0.848589\pi$
$642$	−7.55356	−	21.5232i	−0.298115	−	0.849454i
$643$	4.61228	−	4.61228i	0.181890	−	0.181890i	−0.610289	−	0.792179i	$-0.708947\pi$
$643$	4.61228	−	4.61228i	0.181890	−	0.181890i	0.792179	+	0.610289i	$0.208947\pi$
$644$	1.43873	+	11.4929i	0.0566940	+	0.452883i
$645$	−8.09908	+	9.42884i	−0.318901	+	0.371260i
$646$	−22.2342	+	38.5107i	−0.874792	+	1.51518i
$647$	0.631130	+	1.09315i	0.0248123	+	0.0429761i	0.878165	−	0.478358i	$-0.158768\pi$
$647$	0.631130	+	1.09315i	0.0248123	+	0.0429761i	−0.853353	+	0.521334i	$0.825435\pi$
$648$	8.99241	−	0.369644i	0.353255	−	0.0145210i
$649$	48.4626	+	27.9799i	1.90232	+	1.09831i
$650$	11.4312	+	2.45784i	0.448368	+	0.0964044i
$651$	9.03670	+	18.1455i	0.354176	+	0.711179i
$652$	−8.00086	+	8.00086i	−0.313338	+	0.313338i
$653$	6.79930	+	3.92558i	0.266077	+	0.153620i	0.627104	−	0.778936i	$-0.284240\pi$
$653$	6.79930	+	3.92558i	0.266077	+	0.153620i	−0.361026	+	0.932556i	$0.617574\pi$
$654$	1.88412	+	2.75803i	0.0736747	+	0.107847i
$655$	−13.1840	−	3.53265i	−0.515142	−	0.138032i
$656$	−0.0737975	+	0.0197740i	−0.00288131	+	0.000772044i
$657$	−9.02348	−	6.63400i	−0.352040	−	0.258817i
$658$	16.5481	+	21.8524i	0.645111	+	0.851894i
$659$		−	20.6367i		−	0.803890i	−0.915664	−	0.401945i	$-0.868334\pi$
$659$		−	20.6367i		−	0.803890i	0.915664	−	0.401945i	$-0.131666\pi$
$660$	−9.96528	−	4.78773i	−0.387898	−	0.186362i
$661$	11.6943	−	43.6437i	0.454855	−	1.69754i	−0.233657	−	0.972319i	$-0.575069\pi$
$661$	11.6943	−	43.6437i	0.454855	−	1.69754i	0.688512	−	0.725225i	$-0.258264\pi$
$662$	0.663964	+	1.15002i	0.0258057	+	0.0446968i
$663$	45.2905	−	5.72469i	1.75894	−	0.222328i
$664$	−10.2091			−0.396192
$665$	12.8796	+	17.0081i	0.499451	+	0.659545i
$666$	−1.29992	−	8.51793i	−0.0503708	−	0.330063i
$667$	−22.0008	−	12.7022i	−0.851874	−	0.491830i
$668$	−0.722070	+	2.69480i	−0.0279377	+	0.104265i
$669$	−5.80832	−	1.09345i	−0.224563	−	0.0422754i
$670$	−2.17795	+	0.583580i	−0.0841415	+	0.0225456i
$671$	37.5318	−	37.5318i	1.44890	−	1.44890i
$672$	−4.10204	+	2.04287i	−0.158239	+	0.0788053i
$673$		−	2.11909i		−	0.0816848i	−0.999166	−	0.0408424i	$-0.986996\pi$
$673$		−	2.11909i		−	0.0816848i	0.999166	−	0.0408424i	$-0.0130042\pi$
$674$	6.35437	+	23.7148i	0.244761	+	0.913461i
$675$	−12.3206	+	11.4954i	−0.474222	+	0.442458i
$676$	1.29814	+	12.9350i	0.0499286	+	0.497501i
$677$	−18.3091	−	10.5708i	−0.703676	−	0.406267i	0.105039	−	0.994468i	$-0.466503\pi$
$677$	−18.3091	−	10.5708i	−0.703676	−	0.406267i	−0.808715	+	0.588201i	$0.799837\pi$
$678$	−16.7279	+	19.4744i	−0.642432	+	0.747911i
$679$	23.4252	−	30.1294i	0.898977	−	1.15626i
$680$	−9.68980			−0.371587
$681$	29.6504	−	10.4058i	1.13621	−	0.398751i
$682$	−20.5751	−	5.51308i	−0.787861	−	0.211107i
$683$	46.4033	+	12.4337i	1.77557	+	0.475764i	0.989765	−	0.142705i	$-0.0455800\pi$
$683$	46.4033	+	12.4337i	1.77557	+	0.475764i	0.785809	+	0.618469i	$0.212247\pi$
$684$	16.7135	−	7.32870i	0.639057	−	0.280220i
$685$	1.52953			0.0584403
$686$	14.9056	−	10.9919i	0.569100	−	0.419673i
$687$	23.0872	+	19.8312i	0.880832	+	0.756606i
$688$	−4.68849	−	2.70690i	−0.178747	−	0.103200i
$689$	2.58611	+	1.32535i	0.0985229	+	0.0504917i
$690$	8.29943	−	5.66965i	0.315954	−	0.215840i
$691$	−6.10773	−	22.7944i	−0.232349	−	0.867139i	−0.979326	−	0.202289i	$-0.935162\pi$
$691$	−6.10773	−	22.7944i	−0.232349	−	0.867139i	0.746977	−	0.664850i	$-0.231505\pi$
$692$		−	22.7835i		−	0.866099i
$693$	18.6391	−	33.3677i	0.708042	−	1.26753i
$694$	18.3594	−	18.3594i	0.696915	−	0.696915i
$695$	18.5061	−	4.95870i	0.701977	−	0.188094i
$696$	1.85952	−	9.87756i	0.0704848	−	0.374408i
$697$	0.144547	−	0.539458i	0.00547512	−	0.0204334i
$698$	−5.56060	−	3.21041i	−0.210472	−	0.121516i
$699$	5.96603	−	0.452617i	0.225656	−	0.0171195i
$700$	3.33376	−	7.90574i	0.126004	−	0.298809i
$701$	−31.4037			−1.18610			−0.593051	−	0.805165i	$-0.702077\pi$
$701$	−31.4037			−1.18610			−0.593051	+	0.805165i	$0.702077\pi$
$702$	−16.3671	−	9.11695i	−0.617736	−	0.344097i
$703$	−8.73608	−	15.1313i	−0.329487	−	0.570689i
$704$	1.24631	−	4.65127i	0.0469719	−	0.175301i
$705$	10.3010	−	21.4406i	0.387956	−	0.807501i
$706$		−	13.4851i		−	0.507519i
$707$	2.25776	+	2.98145i	0.0849117	+	0.112129i
$708$	−15.2688	−	13.1154i	−0.573837	−	0.492908i
$709$	−2.72739	+	0.730801i	−0.102429	+	0.0274458i	−0.309670	−	0.950844i	$-0.600218\pi$
$709$	−2.72739	+	0.730801i	−0.102429	+	0.0274458i	0.207240	+	0.978290i	$0.433552\pi$
$710$	1.72696	+	0.462739i	0.0648118	+	0.0173663i
$711$	−9.46710	−	11.8266i	−0.355044	−	0.443533i
$712$	−3.60132	−	2.07922i	−0.134965	−	0.0779222i
$713$	13.6934	−	13.6934i	0.512822	−	0.512822i
$714$	2.06026	−	33.4351i	0.0771034	−	1.25128i
$715$	12.4891	+	19.3308i	0.467068	+	0.722932i
$716$	−22.1972	−	12.8156i	−0.829549	−	0.478940i
$717$	6.34522	−	33.7052i	0.236967	−	1.25874i
$718$	8.37354	+	14.5034i	0.312498	+	0.541262i
$719$	7.49673	−	12.9847i	0.279581	−	0.484248i	−0.691700	−	0.722185i	$-0.743138\pi$
$719$	7.49673	−	12.9847i	0.279581	−	0.484248i	0.971281	+	0.237937i	$0.0764711\pi$
$720$	3.20396	+	2.35553i	0.119405	+	0.0877855i
$721$	19.7822	+	8.34192i	0.736728	+	0.310669i
$722$	12.7320	−	12.7320i	0.473835	−	0.473835i
$723$	−6.37029	+	2.23565i	−0.236913	+	0.0831446i
$724$	11.9797	+	20.7494i	0.445221	+	0.771146i
$725$	9.40925	+	16.2973i	0.349451	+	0.605266i
$726$	6.99040	+	19.9186i	0.259438	+	0.739247i
$727$		−	14.1425i		−	0.524516i	−0.964998	−	0.262258i	$-0.915533\pi$
$727$		−	14.1425i		−	0.524516i	0.964998	−	0.262258i	$-0.0844671\pi$
$728$	9.50310	+	0.831262i	0.352209	+	0.0308086i
$729$	24.2611	−	11.8491i	0.898558	−	0.438855i
$730$	−1.28080	−	4.77999i	−0.0474044	−	0.176915i
$731$	34.2728	−	19.7874i	1.26763	−	0.731864i
$732$	−15.7645	+	10.7693i	−0.582672	+	0.398046i
$733$	−3.09236	−	11.5408i	−0.114219	−	0.426270i	0.885009	−	0.465575i	$-0.154152\pi$
$733$	−3.09236	−	11.5408i	−0.114219	−	0.426270i	−0.999227	+	0.0393047i	$0.987486\pi$
$734$	17.3202	+	17.3202i	0.639301	+	0.639301i
$735$	−14.3966	−	7.14362i	−0.531027	−	0.263496i
$736$	3.09557	+	3.09557i	0.114104	+	0.114104i
$737$	7.09356	+	4.09547i	0.261295	+	0.150858i
$738$	−0.178934	+	0.143235i	−0.00658665	+	0.00527256i
$739$	−9.62061	+	35.9046i	−0.353900	+	1.32077i	0.527963	+	0.849267i	$0.322956\pi$
$739$	−9.62061	+	35.9046i	−0.353900	+	1.32077i	−0.881863	+	0.471505i	$0.843711\pi$
$740$	1.90362	−	3.29717i	0.0699785	−	0.121206i
$741$	−37.6386	−	5.15321i	−1.38269	−	0.189308i
$742$	1.30885	−	1.68344i	0.0480493	−	0.0618009i
$743$	−9.53481	−	9.53481i	−0.349798	−	0.349798i	0.510236	−	0.860034i	$-0.329558\pi$
$743$	−9.53481	−	9.53481i	−0.349798	−	0.349798i	−0.860034	+	0.510236i	$0.829558\pi$
$744$	6.90610	+	3.31797i	0.253190	+	0.121643i
$745$	14.6747	−	8.47243i	0.537639	−	0.310406i
$746$	−5.36355	+	20.0170i	−0.196374	+	0.732876i
$747$	−28.0494	+	12.2993i	−1.02627	+	0.450010i
$748$	24.8903	+	24.8903i	0.910079	+	0.910079i
$749$	32.1054	+	13.5385i	1.17311	+	0.494684i
$750$	−18.8709	+	1.43165i	−0.689068	+	0.0522766i
$751$	0.261657	+	0.151068i	0.00954800	+	0.00551254i	0.504766	−	0.863256i	$-0.331579\pi$
$751$	0.261657	+	0.151068i	0.00954800	+	0.00551254i	−0.495218	+	0.868769i	$0.664912\pi$
$752$	10.0074	+	2.68147i	0.364931	+	0.0977831i
$753$	22.2456	+	32.5638i	0.810673	+	1.18669i
$754$	−14.0367	+	15.5159i	−0.511185	+	0.565055i
$755$		−	15.4607i		−	0.562672i
$756$	−8.80911	+	10.5546i	−0.320384	+	0.383867i
$757$	−9.43744			−0.343010			−0.171505	−	0.985183i	$-0.554863\pi$
$757$	−9.43744			−0.343010			−0.171505	+	0.985183i	$0.554863\pi$
$758$	9.30051	−	16.1090i	0.337810	−	0.585104i
$759$	−35.8825	−	6.75511i	−1.30245	−	0.245195i
$760$	7.78891	+	2.08703i	0.282533	+	0.0757046i
$761$	1.52018	+	5.67340i	0.0551066	+	0.205661i	0.987990	−	0.154518i	$-0.0493824\pi$
$761$	1.52018	+	5.67340i	0.0551066	+	0.205661i	−0.932883	+	0.360179i	$0.882716\pi$
$762$	11.8666	−	13.8149i	0.429881	−	0.500462i
$763$	−5.05418	−	0.698139i	−0.182974	−	0.0252743i
$764$	14.6473			0.529922
$765$	−26.6225	+	11.6737i	−0.962538	+	0.422063i
$766$	10.5398	−	6.08516i	0.380819	−	0.219866i
$767$	12.8544	+	39.8801i	0.464145	+	1.43999i
$768$	−0.750071	+	1.56122i	−0.0270659	+	0.0563355i
$769$	3.10866	−	3.10866i	0.112101	−	0.112101i	−0.648831	−	0.760932i	$-0.724742\pi$
$769$	3.10866	−	3.10866i	0.112101	−	0.112101i	0.760932	+	0.648831i	$0.224742\pi$
$770$	15.6432	−	6.36332i	0.563742	−	0.229318i
$771$	1.71459	−	0.130078i	0.0617493	−	0.00468466i
$772$	−2.02294	−	7.54971i	−0.0728072	−	0.271720i
$773$	4.77049	−	17.8037i	0.171583	−	0.640355i	−0.825526	−	0.564364i	$-0.809121\pi$
$773$	4.77049	−	17.8037i	0.171583	−	0.640355i	0.997109	−	0.0759910i	$-0.0242120\pi$
$774$	−16.1426	−	1.78874i	−0.580234	−	0.0642948i
$775$	−13.8563	+	3.71278i	−0.497733	+	0.133367i
$776$		−	14.4248i		−	0.517820i
$777$	10.9723	+	7.26959i	0.393629	+	0.260795i
$778$	−2.05735	−	2.05735i	−0.0737597	−	0.0737597i
$779$	−0.232382	+	0.402497i	−0.00832594	+	0.0144210i
$780$	−3.12833	−	7.66424i	−0.112012	−	0.274424i
$781$	−3.24743	−	5.62471i	−0.116202	−	0.201268i
$782$	−30.9112	+	8.28264i	−1.10538	+	0.296187i
$783$	−6.79090	−	29.3786i	−0.242687	−	1.04990i
$784$	1.89763	−	6.73788i	0.0677724	−	0.240639i
$785$	6.39422	+	6.39422i	0.228219	+	0.228219i
$786$	−5.90593	−	16.8285i	−0.210658	−	0.600251i
$787$	−11.1598	+	41.6490i	−0.397805	+	1.48463i	0.419146	+	0.907919i	$0.362330\pi$
$787$	−11.1598	+	41.6490i	−0.397805	+	1.48463i	−0.816950	+	0.576708i	$0.804337\pi$
$788$	2.38731	+	0.639677i	0.0850443	+	0.0227876i
$789$	−12.2710	−	5.89547i	−0.436858	−	0.209884i
$790$		−	6.69367i		−	0.238150i
$791$	−4.87115	−	38.9117i	−0.173198	−	1.38354i
$792$	−2.17938	−	14.2807i	−0.0774408	−	0.507443i
$793$	39.6931	−	1.98678i	1.40954	−	0.0705528i
$794$	9.60725	−	5.54675i	0.340949	−	0.196847i
$795$	−1.81849	−	0.342344i	−0.0644953	−	0.0121417i
$796$	−10.7094	+	18.5493i	−0.379586	+	0.657462i
$797$	−4.58340			−0.162352			−0.0811762	−	0.996700i	$-0.525868\pi$
$797$	−4.58340			−0.162352			−0.0811762	+	0.996700i	$0.525868\pi$
$798$	−8.85750	+	26.4323i	−0.313552	+	0.935692i
$799$	−53.5523	+	53.5523i	−1.89454	+	1.89454i
$800$	−0.839324	−	3.13240i	−0.0296746	−	0.110747i
$801$	−12.3994	−	1.37396i	−0.438113	−	0.0485465i
$802$	−3.65952	−	6.33848i	−0.129222	−	0.223819i
$803$	−8.98842	+	15.5684i	−0.317194	+	0.549397i
$804$	−2.23492	−	1.91973i	−0.0788197	−	0.0677036i
$805$	−2.10083	+	15.2090i	−0.0740446	+	0.536045i
$806$	−8.65518	−	13.3966i	−0.304866	−	0.471874i
$807$	−12.5820	−	6.04490i	−0.442907	−	0.212791i
$808$	1.36537	+	0.365849i	0.0480335	+	0.0128705i
$809$	−14.4682	+	8.35324i	−0.508676	+	0.293684i	−0.732289	−	0.680994i	$-0.761548\pi$
$809$	−14.4682	+	8.35324i	−0.508676	+	0.293684i	0.223613	+	0.974678i	$0.428215\pi$
$810$	11.6406	+	2.61182i	0.409009	+	0.0917700i
$811$	−22.0459	+	22.0459i	−0.774137	+	0.774137i	−0.978827	−	0.204690i	$-0.934381\pi$
$811$	−22.0459	+	22.0459i	−0.774137	+	0.774137i	0.204690	+	0.978827i	$0.434381\pi$
$812$	9.26878	+	12.2398i	0.325270	+	0.429532i
$813$	−2.72247	−	2.33851i	−0.0954812	−	0.0820153i
$814$	−13.3593	+	3.57962i	−0.468243	+	0.125465i
$815$	−12.9892	+	7.49929i	−0.454990	+	0.262689i
$816$	−7.14197	−	10.4547i	−0.250019	−	0.365986i
$817$	−31.8112	+	8.52380i	−1.11293	+	0.298210i
$818$	5.40021			0.188814
$819$	27.1110	−	9.16488i	0.947334	−	0.320247i
$820$	−0.101274			−0.00353663
$821$	−40.9521	+	10.9731i	−1.42924	+	0.382964i	−0.888752	−	0.458389i	$-0.848427\pi$
$821$	−40.9521	+	10.9731i	−1.42924	+	0.382964i	−0.540487	+	0.841352i	$0.681760\pi$
$822$	1.12736	+	1.65026i	0.0393211	+	0.0575595i
$823$	−26.4559	+	15.2743i	−0.922195	+	0.532429i	−0.884335	−	0.466854i	$-0.845388\pi$
$823$	−26.4559	+	15.2743i	−0.922195	+	0.532429i	−0.0378602	+	0.999283i	$0.512054\pi$
$824$	7.83807	−	2.10021i	0.273052	−	0.0731641i
$825$	20.5172	+	17.6237i	0.714319	+	0.613577i
$826$	30.5085	−	3.81919i	1.06153	−	0.132887i
$827$	−14.3134	+	14.3134i	−0.497727	+	0.497727i	−0.910730	−	0.413003i	$-0.864480\pi$
$827$	−14.3134	+	14.3134i	−0.497727	+	0.497727i	0.413003	+	0.910730i	$0.364480\pi$
$828$	12.2344	+	4.77565i	0.425173	+	0.165965i
$829$	9.11828	−	5.26444i	0.316691	−	0.182842i	−0.333226	−	0.942847i	$-0.608137\pi$
$829$	9.11828	−	5.26444i	0.316691	−	0.182842i	0.649917	+	0.760005i	$0.274804\pi$
$830$	−13.0717	−	3.50255i	−0.453725	−	0.121575i
$831$	−2.29036	−	1.10038i	−0.0794516	−	0.0381718i
$832$	3.02847	−	1.95662i	0.104993	−	0.0678335i
$833$	35.7192	+	36.6401i	1.23760	+	1.26950i
$834$	18.9902	+	16.3120i	0.657578	+	0.564839i
$835$	−1.84906	+	3.20267i	−0.0639894	+	0.110833i
$836$	−14.6465	−	25.3684i	−0.506558	−	0.877385i
$837$	22.9716	+	0.795997i	0.794014	+	0.0275137i
$838$	−3.15023	−	11.7568i	−0.108823	−	0.406132i
$839$	15.6619	−	15.6619i	0.540709	−	0.540709i	−0.383028	−	0.923737i	$-0.625119\pi$
$839$	15.6619	−	15.6619i	0.540709	−	0.540709i	0.923737	+	0.383028i	$0.125119\pi$
$840$	−5.95307	+	1.20834i	−0.205400	+	0.0416918i
$841$	−4.67466			−0.161195
$842$	−11.7282	+	20.3139i	−0.404182	+	0.700064i
$843$	−34.8190	−	6.55490i	−1.19923	−	0.225763i
$844$	−9.93223	+	5.73438i	−0.341882	+	0.197385i
$845$	−2.77561	+	17.0072i	−0.0954840	+	0.585067i
$846$	30.7255	−	4.68900i	1.05636	−	0.161211i
$847$	−29.7118	−	12.5291i	−1.02091	−	0.430505i
$848$		−	0.805963i		−	0.0276769i
$849$	−6.69020	−	3.21425i	−0.229607	−	0.110313i
$850$	22.8978	+	6.13544i	0.785388	+	0.210444i
$851$	3.25435	−	12.1454i	0.111558	−	0.416339i
$852$	0.773613	+	2.20435i	0.0265036	+	0.0755197i
$853$	−10.4427	−	10.4427i	−0.357550	−	0.357550i	0.505359	−	0.862909i	$-0.331360\pi$
$853$	−10.4427	−	10.4427i	−0.357550	−	0.357550i	−0.862909	+	0.505359i	$0.831360\pi$
$854$	3.99046	−	28.8889i	0.136551	−	0.988559i
$855$	23.9141	−	3.64953i	0.817847	−	0.124811i
$856$	12.7207	−	3.40851i	0.434786	−	0.116501i
$857$	4.79452	+	8.30436i	0.163778	+	0.283672i	0.936221	−	0.351413i	$-0.114299\pi$
$857$	4.79452	+	8.30436i	0.163778	+	0.283672i	−0.772443	+	0.635084i	$0.780965\pi$
$858$	−11.6514	+	27.7230i	−0.397773	+	0.946446i
$859$	23.0343	−	39.8966i	0.785921	−	1.36126i	−0.142526	−	0.989791i	$-0.545522\pi$
$859$	23.0343	−	39.8966i	0.785921	−	1.36126i	0.928447	−	0.371465i	$-0.121144\pi$
$860$	−5.07441	−	5.07441i	−0.173036	−	0.173036i
$861$	0.0215330	−	0.349449i	0.000733842	−	0.0119092i
$862$			35.1582i			1.19749i
$863$	−38.4629	+	10.3061i	−1.30929	+	0.350824i	−0.844956	−	0.534836i	$-0.820373\pi$
$863$	−38.4629	+	10.3061i	−1.30929	+	0.350824i	−0.464335	+	0.885660i	$0.653707\pi$
$864$	−0.179946	+	5.19304i	−0.00612188	+	0.176671i
$865$	7.81655	−	29.1718i	0.265771	−	0.991870i
$866$	6.59164	+	24.6003i	0.223993	+	0.835953i
$867$	62.9280	−	4.77407i	2.13715	−	0.162136i
$868$	−10.8410	+	4.40988i	−0.367967	+	0.149681i
$869$	−17.1941	+	17.1941i	−0.583269	+	0.583269i
$870$	5.76969	−	12.0092i	0.195611	−	0.407149i
$871$	1.88152	+	5.83732i	0.0637528	+	0.197790i
$872$	−1.67008	+	0.964219i	−0.0565559	+	0.0326526i
$873$	−17.3781	−	39.6317i	−0.588160	−	1.34133i
$874$	26.6312			0.900814
$875$	17.7440	−	22.8223i	0.599858	−	0.771535i
$876$	4.21327	−	4.90504i	0.142353	−	0.165726i
$877$	−9.55898	−	35.6746i	−0.322784	−	1.20465i	−0.916521	−	0.399986i	$-0.869015\pi$
$877$	−9.55898	−	35.6746i	−0.322784	−	1.20465i	0.593737	−	0.804659i	$-0.297652\pi$
$878$	10.1772	+	2.72696i	0.343462	+	0.0920305i
$879$	−15.1447	−	2.85109i	−0.510819	−	0.0961650i
$880$	3.19151	−	5.52786i	0.107586	−	0.186344i
$881$	32.7833			1.10450			0.552249	−	0.833679i	$-0.313770\pi$
$881$	32.7833			1.10450			0.552249	+	0.833679i	$0.313770\pi$
$882$	−2.90369	−	20.7983i	−0.0977725	−	0.700315i
$883$		−	12.5343i		−	0.421812i	−0.977506	−	0.210906i	$-0.932359\pi$
$883$		−	12.5343i		−	0.421812i	0.977506	−	0.210906i	$-0.0676413\pi$
$884$	1.31759	+	26.3236i	0.0443154	+	0.885358i
$885$	−15.0504	−	22.0313i	−0.505914	−	0.740573i
$886$	0.0309976	+	0.00830577i	0.00104138	+	0.000279038i
$887$	26.8558	+	15.5052i	0.901729	+	0.520613i	0.877761	−	0.479099i	$-0.159037\pi$
$887$	26.8558	+	15.5052i	0.901729	+	0.520613i	0.0239682	+	0.999713i	$0.492370\pi$
$888$	4.96051	−	0.376333i	0.166464	−	0.0126289i
$889$	3.45553	+	27.6035i	0.115895	+	0.925791i
$890$	−3.89775	−	3.89775i	−0.130653	−	0.130653i
$891$	−23.1923	−	36.6103i	−0.776971	−	1.22649i
$892$	0.883179	−	3.29607i	0.0295710	−	0.110361i
$893$	54.5810	−	31.5123i	1.82648	−	1.05452i
$894$	19.9573	+	9.58831i	0.667473	+	0.320681i
$895$	−24.0243	−	24.0243i	−0.803045	−	0.803045i
$896$	−0.996912	−	2.45075i	−0.0333045	−	0.0818738i
$897$	−16.5309	−	21.7755i	−0.551949	−	0.727062i
$898$	12.5627	−	21.7593i	0.419223	−	0.726116i
$899$	6.64382	−	24.7951i	0.221584	−	0.826962i
$900$	−6.07974	−	7.59501i	−0.202658	−	0.253167i
$901$	5.10226	+	2.94579i	0.169981	+	0.0981385i
$902$	0.260142	+	0.260142i	0.00866179	+	0.00866179i
$903$	18.5884	−	16.4306i	0.618585	−	0.546776i
$904$	−10.4808	−	10.4808i	−0.348585	−	0.348585i
$905$	8.21997	+	30.6773i	0.273241	+	1.01975i
$906$	16.6810	−	11.3955i	0.554190	−	0.378589i
$907$	33.1954	−	19.1654i	1.10224	−	0.636377i	0.165429	−	0.986222i	$-0.447099\pi$
$907$	33.1954	−	19.1654i	1.10224	−	0.636377i	0.936808	+	0.349845i	$0.113766\pi$
$908$	4.69557	+	17.5241i	0.155828	+	0.581558i
$909$	4.19206	−	0.639750i	0.139042	−	0.0212192i
$910$	11.8825	+	4.32466i	0.393901	+	0.143361i
$911$			11.3113i			0.374759i	0.982288	+	0.187379i	$0.0599994\pi$
$911$			11.3113i			0.374759i	−0.982288	+	0.187379i	$0.940001\pi$
$912$	3.48913	+	9.94199i	0.115537	+	0.329212i
$913$	24.5803	+	42.5744i	0.813490	+	1.40901i
$914$	9.17839	+	15.8974i	0.303594	+	0.525840i
$915$	−23.8794	+	8.38046i	−0.789429	+	0.277050i
$916$	−12.4251	+	12.4251i	−0.410536	+	0.410536i
$917$	25.1024	+	10.5854i	0.828954	+	0.349560i
$918$	−32.2175	−	20.1197i	−1.06334	−	0.664048i
$919$	−2.71176	+	4.69690i	−0.0894526	+	0.154936i	−0.907280	−	0.420527i	$-0.861845\pi$
$919$	−2.71176	+	4.69690i	−0.0894526	+	0.154936i	0.817827	+	0.575464i	$0.195178\pi$
$920$	2.90151	+	5.02557i	0.0956601	+	0.165688i
$921$	−5.24571	+	27.8647i	−0.172852	+	0.918172i
$922$	−26.3843	−	15.2330i	−0.868921	−	0.501672i
$923$	1.02226	−	4.75444i	0.0336481	−	0.156494i
$924$	18.3956	+	12.1878i	0.605170	+	0.400950i
$925$	−6.58613	+	6.58613i	−0.216551	+	0.216551i
$926$	17.0859	+	9.86452i	0.561476	+	0.324168i
$927$	19.0047	−	15.2131i	0.624196	−	0.499663i
$928$	5.60525	+	1.50192i	0.184002	+	0.0493031i
$929$	11.5930	−	3.10632i	0.380353	−	0.101915i	−0.0635768	−	0.997977i	$-0.520251\pi$
$929$	11.5930	−	3.10632i	0.380353	−	0.101915i	0.443929	+	0.896062i	$0.353584\pi$
$930$	7.70417	+	6.61764i	0.252630	+	0.217001i
$931$	−20.8203	−	37.1456i	−0.682358	−	1.21740i
$932$			3.45439i			0.113152i
$933$	−14.2152	+	29.5879i	−0.465385	+	0.968664i
$934$	−5.26781	+	19.6597i	−0.172368	+	0.643286i
$935$	23.3299	+	40.4086i	0.762970	+	1.32150i
$936$	5.96343	−	9.02427i	0.194921	−	0.294968i
$937$	−18.6777			−0.610172			−0.305086	−	0.952325i	$-0.598685\pi$
$937$	−18.6777			−0.610172			−0.305086	+	0.952325i	$0.598685\pi$
$938$	4.46558	−	0.559022i	0.145806	−	0.0182527i
$939$	−35.8669	+	2.72107i	−1.17047	+	0.0887988i
$940$	11.8934	+	6.86665i	0.387919	+	0.223965i
$941$	9.16020	−	34.1863i	0.298614	−	1.11444i	−0.639691	−	0.768633i	$-0.720938\pi$
$941$	9.16020	−	34.1863i	0.298614	−	1.11444i	0.938305	−	0.345810i	$-0.112396\pi$
$942$	−2.18601	+	11.6119i	−0.0712240	+	0.378335i
$943$	−0.323071	+	0.0865666i	−0.0105206	+	0.00281899i
$944$	8.21737	−	8.21737i	0.267453	−	0.267453i
$945$	−14.9002	+	10.4918i	−0.484702	+	0.341298i
$946$			26.0694i			0.847588i
$947$	10.4550	+	39.0187i	0.339743	+	1.26794i	0.898635	+	0.438697i	$0.144560\pi$
$947$	10.4550	+	39.0187i	0.339743	+	1.26794i	−0.558892	+	0.829240i	$0.688773\pi$
$948$	7.22202	−	4.93364i	0.234560	−	0.160237i
$949$	−12.8113	+	4.12941i	−0.415872	+	0.134046i
$950$	−17.0843	−	9.86365i	−0.554289	−	0.320019i
$951$	29.3050	+	25.1720i	0.950279	+	0.816259i
$952$	19.1585	+	2.64638i	0.620930	+	0.0857698i
$953$	7.35013			0.238094			0.119047	−	0.992889i	$-0.462016\pi$
$953$	7.35013			0.238094			0.119047	+	0.992889i	$0.462016\pi$
$954$	−0.970975	−	2.21436i	−0.0314365	−	0.0716926i
$955$	18.7543	+	5.02520i	0.606875	+	0.162612i
$956$	19.1268	+	5.12501i	0.618605	+	0.165755i
$957$	−45.6687	+	16.0274i	−1.47626	+	0.518092i
$958$	−8.41644			−0.271923
$959$	−3.02416	−	0.417730i	−0.0976551	−	0.0134892i
$960$	−1.49600	+	1.74163i	−0.0482834	+	0.0562109i
$961$	−9.90067	−	5.71615i	−0.319376	−	0.184392i
$962$	−9.21602	−	4.72309i	−0.297136	−	0.152278i
$963$	30.8435	−	24.6900i	0.993919	−	0.795623i
$964$	−1.00883	−	3.76499i	−0.0324921	−	0.121262i
$965$		−	10.3606i		−	0.333520i
$966$	−17.9579	+	8.94327i	−0.577786	+	0.287745i
$967$	−18.8737	+	18.8737i	−0.606939	+	0.606939i	−0.942145	−	0.335206i	$-0.891194\pi$
$967$	−18.8737	+	18.8737i	−0.606939	+	0.606939i	0.335206	+	0.942145i	$0.391194\pi$
$968$	−11.7723	+	3.15439i	−0.378378	+	0.101386i
$969$	−75.6918	−	14.2495i	−2.43157	−	0.457759i
$970$	4.94885	−	18.4694i	0.158898	−	0.593016i
$971$	44.4767	+	25.6786i	1.42733	+	0.824067i	0.996909	−	0.0785637i	$-0.0250334\pi$
$971$	44.4767	+	25.6786i	1.42733	+	0.824067i	0.430416	+	0.902630i	$0.358367\pi$
$972$	5.76185	+	14.4845i	0.184811	+	0.464591i
$973$	−37.9442	+	4.75003i	−1.21644	+	0.152279i
$974$	3.13106			0.100326
$975$	2.53962	+	20.0920i	0.0813329	+	0.643460i
$976$	−5.51133	−	9.54591i	−0.176413	−	0.305557i
$977$	−7.62077	+	28.4411i	−0.243810	+	0.909911i	0.730168	+	0.683268i	$0.239442\pi$
$977$	−7.62077	+	28.4411i	−0.243810	+	0.909911i	−0.973978	+	0.226643i	$0.927225\pi$
$978$	−17.6650	−	8.48700i	−0.564866	−	0.271384i
$979$			20.0244i			0.639982i
$980$	4.74133	−	7.97608i	0.151456	−	0.254786i
$981$	−3.42686	+	4.66117i	−0.109411	+	0.148820i
$982$	41.3153	−	11.0704i	1.31842	−	0.353270i
$983$	14.6586	+	3.92777i	0.467538	+	0.125276i	0.484894	−	0.874573i	$-0.338858\pi$
$983$	14.6586	+	3.92777i	0.467538	+	0.125276i	−0.0173559	+	0.999849i	$0.505525\pi$
$984$	−0.0746448	−	0.109267i	−0.00237959	−	0.00348332i
$985$	2.83722	+	1.63807i	0.0904015	+	0.0521933i
$986$	−29.9953	+	29.9953i	−0.955245	+	0.955245i
$987$	−26.2225	+	39.5787i	−0.834671	+	1.25980i
$988$	4.61057	−	21.4433i	0.146682	−	0.682204i
$989$	−20.5253	−	11.8503i	−0.652666	−	0.376817i
$990$	2.10897	−	19.0326i	0.0670275	−	0.604895i
$991$	−10.1600	−	17.5976i	−0.322742	−	0.559006i	0.658311	−	0.752746i	$-0.271271\pi$
$991$	−10.1600	−	17.5976i	−0.322742	−	0.559006i	−0.981053	+	0.193741i	$0.937938\pi$
$992$	−2.21177	+	3.83090i	−0.0702237	+	0.121631i
$993$	−1.49868	+	1.74474i	−0.0475592	+	0.0553678i
$994$	−3.28814	−	1.38657i	−0.104294	−	0.0439793i
$995$	−20.0761	+	20.0761i	−0.636457	+	0.636457i
$996$	−5.85561	−	16.6851i	−0.185542	−	0.528687i
$997$	5.75201	+	9.96277i	0.182168	+	0.315524i	0.942619	−	0.333872i	$-0.108355\pi$
$997$	5.75201	+	9.96277i	0.182168	+	0.315524i	−0.760451	+	0.649396i	$0.775022\pi$
$998$	−7.52772	−	13.0384i	−0.238286	−	0.412723i
$999$	13.1755	−	7.01008i	0.416854	−	0.221789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.317.6	✓	144
3.2	odd	2	inner	546.2.bv.a.317.26	yes	144
7.4	even	3	inner	546.2.bv.a.473.26	yes	144
13.8	odd	4	inner	546.2.bv.a.359.6	yes	144
21.11	odd	6	inner	546.2.bv.a.473.6	yes	144
39.8	even	4	inner	546.2.bv.a.359.26	yes	144
91.60	odd	12	inner	546.2.bv.a.515.26	yes	144
273.242	even	12	inner	546.2.bv.a.515.6	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.6	✓	144	1.1	even	1	trivial
546.2.bv.a.317.26	yes	144	3.2	odd	2	inner
546.2.bv.a.359.6	yes	144	13.8	odd	4	inner
546.2.bv.a.359.26	yes	144	39.8	even	4	inner
546.2.bv.a.473.6	yes	144	21.11	odd	6	inner
546.2.bv.a.473.26	yes	144	7.4	even	3	inner
546.2.bv.a.515.6	yes	144	273.242	even	12	inner
546.2.bv.a.515.26	yes	144	91.60	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.977016 - 1.43019i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.28039 - 0.343079i) q^{5} +(1.31389 + 1.12859i) q^{6} +(-2.62526 + 0.328643i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.09088 + 2.79463i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.977016 - 1.43019i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.28039 - 0.343079i) q^{5} +(1.31389 + 1.12859i) q^{6} +(-2.62526 + 0.328643i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.09088 + 2.79463i) q^{9} +(-1.14797 + 0.662779i) q^{10} +(4.65127 + 1.24631i) q^{11} +(-1.56122 - 0.750071i) q^{12} +(1.95662 + 3.02847i) q^{13} +(2.45075 - 0.996912i) q^{14} +(-1.74163 - 1.49600i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.65499 + 6.33063i) q^{17} +(0.330403 - 2.98175i) q^{18} +(-1.57446 - 5.87595i) q^{19} +(0.937311 - 0.937311i) q^{20} +(3.03494 + 3.43353i) q^{21} -4.81535 q^{22} +(2.18890 - 3.79129i) q^{23} +(1.70215 + 0.320441i) q^{24} +(-2.80843 + 1.62145i) q^{25} +(-2.67377 - 2.41887i) q^{26} +(5.06266 - 1.17024i) q^{27} +(-2.10922 + 1.59724i) q^{28} -5.80299i q^{29} +(2.06948 + 0.994263i) q^{30} +(4.27281 + 1.14490i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-2.76192 - 7.86986i) q^{33} +(-5.16894 - 5.16894i) q^{34} +(-3.24861 + 1.32146i) q^{35} +(0.452589 + 2.96566i) q^{36} +(2.77431 - 0.743375i) q^{37} +(3.04162 + 5.26823i) q^{38} +(2.41964 - 5.75720i) q^{39} +(-0.662779 + 1.14797i) q^{40} +(-0.0540235 - 0.0540235i) q^{41} +(-3.82019 - 2.53103i) q^{42} -5.41380i q^{43} +(4.65127 - 1.24631i) q^{44} +(-0.437968 + 3.95248i) q^{45} +(-1.13306 + 4.22863i) q^{46} +(2.68147 + 10.0074i) q^{47} +(-1.72709 + 0.131027i) q^{48} +(6.78399 - 1.72554i) q^{49} +(2.29307 - 2.29307i) q^{50} +(5.48301 - 11.4125i) q^{51} +(3.20872 + 1.64442i) q^{52} +(0.697985 - 0.402982i) q^{53} +(-4.58727 + 2.44068i) q^{54} +6.38303 q^{55} +(1.62395 - 2.08873i) q^{56} +(-6.86545 + 7.99267i) q^{57} +(1.50192 + 5.60525i) q^{58} +(11.2251 + 3.00777i) q^{59} +(-2.25630 - 0.424763i) q^{60} +(5.51133 - 9.54591i) q^{61} -4.42354 q^{62} +(1.94540 - 7.69515i) q^{63} -1.00000i q^{64} +(3.54424 + 3.20635i) q^{65} +(4.70468 + 6.88686i) q^{66} +(1.64304 + 0.440252i) q^{67} +(6.33063 + 3.65499i) q^{68} +(-7.56085 + 0.573609i) q^{69} +(2.79589 - 2.11724i) q^{70} +(-0.953731 - 0.953731i) q^{71} +(-1.20474 - 2.74747i) q^{72} +(-0.966231 + 3.60603i) q^{73} +(-2.48738 + 1.43609i) q^{74} +(5.06286 + 2.43240i) q^{75} +(-4.30150 - 4.30150i) q^{76} +(-12.6204 - 1.74327i) q^{77} +(-0.847118 + 6.18728i) q^{78} +(-2.52485 + 4.37317i) q^{79} +(0.343079 - 1.28039i) q^{80} +(-6.61997 - 6.09721i) q^{81} +(0.0661650 + 0.0382004i) q^{82} +(7.21896 + 7.21896i) q^{83} +(4.34510 + 1.45605i) q^{84} +(6.85173 + 6.85173i) q^{85} +(1.40120 + 5.22933i) q^{86} +(-8.29936 + 5.66961i) q^{87} +(-4.17022 + 2.40768i) q^{88} +(1.07628 + 4.01675i) q^{89} +(-0.599933 - 3.93116i) q^{90} +(-6.13192 - 7.30750i) q^{91} -4.37780i q^{92} +(-2.53719 - 7.22951i) q^{93} +(-5.18020 - 8.97237i) q^{94} +(-4.03184 - 6.98335i) q^{95} +(1.63433 - 0.573565i) q^{96} +(-10.1999 + 10.1999i) q^{97} +(-6.10623 + 3.42257i) q^{98} +(-8.55694 + 11.6390i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7}+O(q^{10}) \) 144 * q - 16 * q^7	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Introduction

L-functions

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