LMFDB - Embedded newform 546.2.bv.a.473.26

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			473.26
Character	$\chi$	$=$	546.473
Dual form			546.2.bv.a.359.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.750071 + 1.56122i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.343079 + 1.28039i) q^{5} +(1.31389 + 1.12859i) q^{6} +(0.328643 - 2.62526i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.87479 - 2.34205i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.750071 + 1.56122i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.343079 + 1.28039i) q^{5} +(1.31389 + 1.12859i) q^{6} +(0.328643 - 2.62526i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.87479 - 2.34205i) q^{9} +(1.14797 + 0.662779i) q^{10} +(-1.24631 - 4.65127i) q^{11} +(1.43019 - 0.977016i) 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} +(-2.74747 + 1.20474i) q^{18} +(5.87595 + 1.57446i) q^{19} +(0.937311 - 0.937311i) q^{20} +(3.85209 + 2.48221i) q^{21} -4.81535 q^{22} +(2.18890 + 3.79129i) q^{23} +(-0.573565 - 1.63433i) q^{24} +(2.80843 + 1.62145i) q^{25} +(3.43169 - 1.10612i) q^{26} +(5.06266 - 1.17024i) q^{27} +(-1.59724 + 2.10922i) q^{28} -5.80299i q^{29} +(-1.89580 + 1.29509i) q^{30} +(-1.14490 - 4.27281i) q^{31} +(0.965926 - 0.258819i) q^{32} +(8.19646 + 1.54304i) q^{33} +(-5.16894 - 5.16894i) q^{34} +(3.24861 + 1.32146i) q^{35} +(0.452589 + 2.96566i) q^{36} +(-0.743375 + 2.77431i) q^{37} +(3.04162 - 5.26823i) q^{38} +(-6.19570 + 0.783132i) q^{39} +(-0.662779 - 1.14797i) q^{40} +(-0.0540235 - 0.0540235i) q^{41} +(3.39463 - 3.07839i) q^{42} -5.41380i q^{43} +(-1.24631 + 4.65127i) q^{44} +(3.64193 - 1.59695i) q^{45} +(4.22863 - 1.13306i) q^{46} +(-10.0074 - 2.68147i) q^{47} +(-1.72709 + 0.131027i) q^{48} +(-6.78399 - 1.72554i) q^{49} +(2.29307 - 2.29307i) q^{50} +(7.14197 + 10.4547i) q^{51} +(-0.180245 - 3.60104i) q^{52} +(-0.697985 - 0.402982i) q^{53} +(0.179946 - 5.19304i) q^{54} +6.38303 q^{55} +(1.62395 + 2.08873i) q^{56} +(-6.86545 + 7.99267i) q^{57} +(-5.60525 - 1.50192i) q^{58} +(-3.00777 - 11.2251i) q^{59} +(0.760294 + 2.16639i) q^{60} +(5.51133 + 9.54591i) q^{61} -4.42354 q^{62} +(-6.76462 + 4.15211i) q^{63} -1.00000i q^{64} +(-4.54890 + 1.46623i) q^{65} +(3.61186 - 7.51780i) q^{66} +(-0.440252 - 1.64304i) q^{67} +(-6.33063 + 3.65499i) q^{68} +(-7.56085 + 0.573609i) q^{69} +(2.11724 - 2.79589i) q^{70} +(-0.953731 - 0.953731i) q^{71} +(2.98175 + 0.330403i) q^{72} +(3.60603 - 0.966231i) q^{73} +(2.48738 + 1.43609i) q^{74} +(-4.63796 + 3.16836i) 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} +(-1.28039 + 0.343079i) q^{80} +(-1.97036 + 8.78167i) q^{81} +(-0.0661650 + 0.0382004i) q^{82} +(7.21896 + 7.21896i) q^{83} +(-2.09490 - 4.07571i) q^{84} +(6.85173 + 6.85173i) q^{85} +(-5.22933 - 1.40120i) q^{86} +(9.05971 + 4.35265i) q^{87} +(4.17022 + 2.40768i) q^{88} +(-4.01675 - 1.07628i) q^{89} +(-0.599933 - 3.93116i) q^{90} +(8.59356 - 4.14135i) q^{91} -4.37780i q^{92} +(7.52953 + 1.41748i) q^{93} +(-5.18020 + 8.97237i) q^{94} +(-4.03184 + 6.98335i) q^{95} +(-0.320441 + 1.70215i) q^{96} +(-10.1999 + 10.1999i) q^{97} +(-3.42257 + 6.10623i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	−0.750071	+	1.56122i	−0.433054	+	0.901368i
$3$	−0.750071	+	1.56122i	−0.433054	+	0.901368i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.343079	+	1.28039i	−0.153430	+	0.572608i	0.845805	+	0.533492i	$0.179121\pi$
$5$	−0.343079	+	1.28039i	−0.153430	+	0.572608i	−0.999235	+	0.0391155i	$0.987546\pi$
$6$	1.31389	+	1.12859i	0.536391	+	0.460743i
$7$	0.328643	−	2.62526i	0.124215	−	0.992255i
$7$	0.328643	−	2.62526i	0.124215	−	0.992255i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.87479	−	2.34205i	−0.624929	−	0.780682i
$10$	1.14797	+	0.662779i	0.363019	+	0.209589i
$11$	−1.24631	−	4.65127i	−0.375775	−	1.40241i	−0.852209	−	0.523202i	$-0.824737\pi$
$11$	−1.24631	−	4.65127i	−0.375775	−	1.40241i	0.476434	−	0.879210i	$-0.341929\pi$
$12$	1.43019	−	0.977016i	0.412860	−	0.282040i
$13$	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	0.0424416	−	0.999099i	$-0.486486\pi$
$17$	3.65499	−	6.33063i	0.886466	−	1.53540i	0.844024	−	0.536305i	$-0.180180\pi$
$18$	−2.74747	+	1.20474i	−0.647586	+	0.283959i
$19$	5.87595	+	1.57446i	1.34804	+	0.361205i	0.859409	−	0.511288i	$-0.170831\pi$
$19$	5.87595	+	1.57446i	1.34804	+	0.361205i	0.488626	+	0.872493i	$0.337498\pi$
$20$	0.937311	−	0.937311i	0.209589	−	0.209589i
$21$	3.85209	+	2.48221i	0.840595	+	0.541664i
$22$	−4.81535			−1.02664
$23$	2.18890	+	3.79129i	0.456418	+	0.790538i	0.998768	−	0.0496137i	$-0.0157990\pi$
$23$	2.18890	+	3.79129i	0.456418	+	0.790538i	−0.542351	+	0.840152i	$0.682466\pi$
$24$	−0.573565	−	1.63433i	−0.117079	−	0.333605i
$25$	2.80843	+	1.62145i	0.561686	+	0.324290i
$26$	3.43169	−	1.10612i	0.673010	−	0.216928i
$27$	5.06266	−	1.17024i	0.974309	−	0.225213i
$28$	−1.59724	+	2.10922i	−0.301851	+	0.398605i
$29$		−	5.80299i		−	1.07759i	−0.842438	−	0.538794i	$-0.818880\pi$
$29$		−	5.80299i		−	1.07759i	0.842438	−	0.538794i	$-0.181120\pi$
$30$	−1.89580	+	1.29509i	−0.346124	+	0.236450i
$31$	−1.14490	−	4.27281i	−0.205629	−	0.767419i	−0.989257	−	0.146188i	$-0.953299\pi$
$31$	−1.14490	−	4.27281i	−0.205629	−	0.767419i	0.783627	−	0.621231i	$-0.213367\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	8.19646	+	1.54304i	1.42682	+	0.268608i
$34$	−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
$37$	−0.743375	+	2.77431i	−0.122210	+	0.456095i	−0.999725	−	0.0234551i	$-0.992533\pi$
$37$	−0.743375	+	2.77431i	−0.122210	+	0.456095i	0.877515	+	0.479550i	$0.159200\pi$
$38$	3.04162	−	5.26823i	0.493415	−	0.854620i
$39$	−6.19570	+	0.783132i	−0.992106	+	0.125402i
$40$	−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	$0.751899\pi$
$42$	3.39463	−	3.07839i	0.523803	−	0.475006i
$43$		−	5.41380i		−	0.825597i	−0.910822	−	0.412799i	$-0.864551\pi$
$43$		−	5.41380i		−	0.825597i	0.910822	−	0.412799i	$-0.135449\pi$
$44$	−1.24631	+	4.65127i	−0.187888	+	0.701206i
$45$	3.64193	−	1.59695i	0.542907	−	0.238059i
$46$	4.22863	−	1.13306i	0.623478	−	0.167060i
$47$	−10.0074	−	2.68147i	−1.45973	−	0.391132i	−0.560330	−	0.828269i	$-0.689326\pi$
$47$	−10.0074	−	2.68147i	−1.45973	−	0.391132i	−0.899395	+	0.437137i	$0.855993\pi$
$48$	−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
$51$	7.14197	+	10.4547i	1.00008	+	1.46394i
$52$	−0.180245	−	3.60104i	−0.0249955	−	0.499375i
$53$	−0.697985	−	0.402982i	−0.0958756	−	0.0553538i	0.451296	−	0.892375i	$-0.350962\pi$
$53$	−0.697985	−	0.402982i	−0.0958756	−	0.0553538i	−0.547171	+	0.837021i	$0.684295\pi$
$54$	0.179946	−	5.19304i	0.0244875	−	0.706683i
$55$	6.38303			0.860687
$56$	1.62395	+	2.08873i	0.217010	+	0.279118i
$57$	−6.86545	+	7.99267i	−0.909351	+	1.05865i
$58$	−5.60525	−	1.50192i	−0.736006	−	0.197212i
$59$	−3.00777	−	11.2251i	−0.391578	−	1.46139i	−0.827532	−	0.561419i	$-0.810256\pi$
$59$	−3.00777	−	11.2251i	−0.391578	−	1.46139i	0.435954	−	0.899969i	$-0.356411\pi$
$60$	0.760294	+	2.16639i	0.0981535	+	0.279680i
$61$	5.51133	+	9.54591i	0.705654	+	1.22223i	0.966455	+	0.256836i	$0.0826799\pi$
$61$	5.51133	+	9.54591i	0.705654	+	1.22223i	−0.260801	+	0.965392i	$0.583987\pi$
$62$	−4.42354			−0.561790
$63$	−6.76462	+	4.15211i	−0.852261	+	0.523116i
$64$		−	1.00000i		−	0.125000i
$65$	−4.54890	+	1.46623i	−0.564222	+	0.181863i
$66$	3.61186	−	7.51780i	0.444589	−	0.925378i
$67$	−0.440252	−	1.64304i	−0.0537854	−	0.200730i	0.933805	−	0.357783i	$-0.116467\pi$
$67$	−0.440252	−	1.64304i	−0.0537854	−	0.200730i	−0.987590	+	0.157053i	$0.949801\pi$
$68$	−6.33063	+	3.65499i	−0.767702	+	0.443233i
$69$	−7.56085	+	0.573609i	−0.910219	+	0.0690544i
$70$	2.11724	−	2.79589i	0.253058	−	0.334173i
$71$	−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	$0.775503\pi$
$72$	2.98175	+	0.330403i	0.351403	+	0.0389383i
$73$	3.60603	−	0.966231i	0.422053	−	0.113089i	−0.0415402	−	0.999137i	$-0.513226\pi$
$73$	3.60603	−	0.966231i	0.422053	−	0.113089i	0.463594	+	0.886048i	$0.346560\pi$
$74$	2.48738	+	1.43609i	0.289152	+	0.166942i
$75$	−4.63796	+	3.16836i	−0.535545	+	0.365851i
$76$	−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	0.688315	−	0.725412i	$-0.258351\pi$
$79$	−2.52485	−	4.37317i	−0.284068	−	0.492020i	−0.972383	+	0.233392i	$0.925017\pi$
$80$	−1.28039	+	0.343079i	−0.143152	+	0.0383575i
$81$	−1.97036	+	8.78167i	−0.218929	+	0.975741i
$82$	−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	$0.560686\pi$
$84$	−2.09490	−	4.07571i	−0.228573	−	0.444696i
$85$	6.85173	+	6.85173i	0.743174	+	0.743174i
$86$	−5.22933	−	1.40120i	−0.563893	−	0.151095i
$87$	9.05971	+	4.35265i	0.971303	+	0.466654i
$88$	4.17022	+	2.40768i	0.444547	+	0.256659i
$89$	−4.01675	−	1.07628i	−0.425775	−	0.114086i	0.0395675	−	0.999217i	$-0.487402\pi$
$89$	−4.01675	−	1.07628i	−0.425775	−	0.114086i	−0.465342	+	0.885131i	$0.654069\pi$
$90$	−0.599933	−	3.93116i	−0.0632385	−	0.414380i
$91$	8.59356	−	4.14135i	0.900850	−	0.434131i
$92$		−	4.37780i		−	0.456418i
$93$	7.52953	+	1.41748i	0.780776	+	0.146986i
$94$	−5.18020	+	8.97237i	−0.534297	+	0.925429i
$95$	−4.03184	+	6.98335i	−0.413658	+	0.716476i
$96$	−0.320441	+	1.70215i	−0.0327049	+	0.173725i
$97$	−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	$0.988443\pi$
$98$	−3.42257	+	6.10623i	−0.345732	+	0.616822i
$99$	−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	−0.899044	−	0.437858i	$-0.855737\pi$
$101$	−0.706767	+	1.22416i	−0.0703259	+	0.121808i	0.828718	+	0.559666i	$0.189071\pi$
$102$	11.9469	−	4.19275i	1.18292	−	0.415144i
$103$	7.02742	−	4.05729i	0.692433	−	0.399776i	−0.112090	−	0.993698i	$-0.535754\pi$
$103$	7.02742	−	4.05729i	0.692433	−	0.399776i	0.804523	+	0.593922i	$0.202421\pi$
$104$	−3.52499	−	0.757915i	−0.345654	−	0.0743197i
$105$	−4.49978	+	4.08058i	−0.439133	+	0.398224i
$106$	−0.569902	+	0.569902i	−0.0553538	+	0.0553538i
$107$	11.4051	−	6.58474i	1.10257	−	0.636571i	0.165677	−	0.986180i	$-0.447019\pi$
$107$	11.4051	−	6.58474i	1.10257	−	0.636571i	0.936896	+	0.349609i	$0.113686\pi$
$108$	−4.96951	−	1.51787i	−0.478192	−	0.146057i
$109$	−0.499116	−	1.86273i	−0.0478067	−	0.178417i	0.937894	−	0.346921i	$-0.112773\pi$
$109$	−0.499116	−	1.86273i	−0.0478067	−	0.178417i	−0.985701	+	0.168504i	$0.946106\pi$
$110$	1.65205	−	6.16553i	0.157517	−	0.587860i
$111$	−3.77372	−	3.24150i	−0.358185	−	0.307670i
$112$	2.43786	−	1.02802i	0.230356	−	0.0971385i
$113$			14.8220i			1.39434i	0.716906	+	0.697169i	$0.245557\pi$
$113$			14.8220i			1.39434i	−0.716906	+	0.697169i	$0.754443\pi$
$114$	5.94342	+	8.70017i	0.556652	+	0.814846i
$115$	−5.60530	+	1.50193i	−0.522696	+	0.140056i
$116$	−2.90149	+	5.02553i	−0.269397	+	0.466609i
$117$	3.42458	−	10.2602i	0.316603	−	0.948558i
$118$	−11.6211			−1.06981
$119$	−15.4184	−	11.6758i	−1.41340	−	1.07032i
$120$	2.28935	−	0.173683i	0.208988	−	0.0158551i
$121$	−10.5548	+	6.09381i	−0.959527	+	0.553983i
$122$	10.6471	−	2.85288i	0.963941	−	0.258287i
$123$	0.124864	−	0.0438208i	0.0112586	−	0.00395119i
$124$	−1.14490	+	4.27281i	−0.102815	+	0.383710i
$125$	−7.72616	+	7.72616i	−0.691048	+	0.691048i
$126$	2.25981	+	7.60876i	0.201320	+	0.677842i
$127$		−	10.5146i		−	0.933017i	−0.884517	−	0.466508i	$-0.845512\pi$
$127$		−	10.5146i		−	0.933017i	0.884517	−	0.466508i	$-0.154488\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	8.45211	+	4.06074i	0.744167	+	0.357528i
$130$	0.238926	+	4.77339i	0.0209552	+	0.418654i
$131$	8.91736	−	5.14844i	0.779113	−	0.449821i	−0.0570029	−	0.998374i	$-0.518154\pi$
$131$	8.91736	−	5.14844i	0.779113	−	0.449821i	0.836116	+	0.548553i	$0.184821\pi$
$132$	−6.32682	−	5.43454i	−0.550679	−	0.473016i
$133$	6.06445	−	14.9085i	0.525854	−	1.29273i
$134$	−1.70100			−0.146944
$135$	−0.238528	+	6.88367i	−0.0205293	+	0.592452i
$136$	1.89196	+	7.06090i	0.162235	+	0.605467i
$137$	−0.298645	−	1.11456i	−0.0255150	−	0.0952233i	0.951994	−	0.306116i	$-0.0990296\pi$
$137$	−0.298645	−	1.11456i	−0.0255150	−	0.0952233i	−0.977509	+	0.210893i	$0.932363\pi$
$138$	−1.40283	+	7.45168i	−0.119417	+	0.634329i
$139$	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
$143$	11.6477	−	12.8752i	0.974030	−	1.07668i
$144$	1.09088	−	2.79463i	0.0909065	−	0.232886i
$145$	7.43009	+	1.99089i	0.617035	+	0.165334i
$146$		−	3.73323i		−	0.308964i
$147$	7.78242	−	9.29698i	0.641883	−	0.766802i
$148$	2.03094	−	2.03094i	0.166942	−	0.166942i
$149$	−3.30854	+	12.3476i	−0.271046	+	1.01156i	0.687399	+	0.726280i	$0.258752\pi$
$149$	−3.30854	+	12.3476i	−0.271046	+	1.01156i	−0.958445	+	0.285277i	$0.907914\pi$
$150$	1.86001	+	5.29995i	0.151869	+	0.432739i
$151$	−11.2661	+	3.01874i	−0.916822	+	0.245662i	−0.686227	−	0.727388i	$-0.740734\pi$
$151$	−11.2661	+	3.01874i	−0.916822	+	0.245662i	−0.230596	+	0.973050i	$0.574067\pi$
$152$	−5.26823	+	3.04162i	−0.427310	+	0.246708i
$153$	−21.6790	+	3.30842i	−1.75264	+	0.267470i
$154$	−1.58253	+	12.6416i	−0.127524	+	1.01869i
$155$	5.86365			0.470980
$156$	5.75720	+	2.41964i	0.460945	+	0.193726i
$157$	3.41094	−	5.90792i	0.272222	−	0.471503i	−0.697208	−	0.716869i	$-0.745575\pi$
$157$	3.41094	−	5.90792i	0.272222	−	0.471503i	0.969431	+	0.245366i	$0.0789080\pi$
$158$	−4.87763	+	1.30696i	−0.388044	+	0.103976i
$159$	1.15268	−	0.787439i	0.0914134	−	0.0624480i
$160$			1.32556i			0.104795i
$161$	10.6725	−	4.50046i	0.841110	−	0.354686i
$162$	7.97247	+	4.17608i	0.626377	+	0.328104i
$163$	2.92852	−	10.9294i	0.229379	−	0.856055i	−0.751223	−	0.660048i	$-0.770536\pi$
$163$	2.92852	−	10.9294i	0.229379	−	0.856055i	0.980603	−	0.196007i	$-0.0627975\pi$
$164$	0.0197740	+	0.0737975i	0.00154409	+	0.00576261i
$165$	−4.78773	+	9.96528i	−0.372724	+	0.775796i
$166$	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	$0.284426\pi$
$168$	−4.47903	+	0.968649i	−0.345565	+	0.0747329i
$169$	−5.34329	+	11.8511i	−0.411022	+	0.911625i
$170$	8.39162	−	4.84490i	0.643608	−	0.371587i
$171$	−7.32870	−	16.7135i	−0.560440	−	1.27811i
$172$	−2.70690	+	4.68849i	−0.206399	+	0.357494i
$173$	11.3917	+	19.7311i	0.866099	+	1.50013i	0.865952	+	0.500127i	$0.166713\pi$
$173$	11.3917	+	19.7311i	0.866099	+	1.50013i	0.000146630		1.00000i	$0.499953\pi$
$174$	6.54917	−	7.62446i	0.496491	−	0.578009i
$175$	5.17970	−	6.83999i	0.391548	−	0.517055i
$176$	3.40497	−	3.40497i	0.256659	−	0.256659i
$177$	19.7809	+	3.72388i	1.48682	+	0.279904i
$178$	−2.07922	+	3.60132i	−0.155844	+	0.269930i
$179$	−12.8156	+	22.1972i	−0.957881	+	1.65910i	−0.230246	+	0.973132i	$0.573953\pi$
$179$	−12.8156	+	22.1972i	−0.957881	+	1.65910i	−0.727634	+	0.685965i	$0.759380\pi$
$180$	−3.95248	−	0.437968i	−0.294601	−	0.0326442i
$181$			23.9594i			1.78089i	0.455095	+	0.890443i	$0.349605\pi$
$181$			23.9594i			1.78089i	−0.455095	+	0.890443i	$0.650395\pi$
$182$	−1.77606	−	9.37260i	−0.131650	−	0.694743i
$183$	−19.0371	+	1.44426i	−1.40726	+	0.106763i
$184$	−4.22863	−	1.13306i	−0.311739	−	0.0835302i
$185$	−3.29717	−	1.90362i	−0.242413	−	0.139957i
$186$	3.31797	−	6.90610i	0.243285	−	0.506380i
$187$	−34.0007	−	9.11047i	−2.48638	−	0.666224i
$188$	7.32591	+	7.32591i	0.534297	+	0.534297i
$189$	−1.40839	−	13.6754i	−0.102445	−	0.994739i
$190$	5.70188	+	5.70188i	0.413658	+	0.413658i
$191$	−12.6850	+	7.32367i	−0.917852	+	0.529922i	−0.882949	−	0.469468i	$-0.844446\pi$
$191$	−12.6850	+	7.32367i	−0.917852	+	0.529922i	−0.0349030	+	0.999391i	$0.511112\pi$
$192$	1.56122	+	0.750071i	0.112671	+	0.0541317i
$193$	−7.54971	+	2.02294i	−0.543440	+	0.145614i	−0.520088	−	0.854113i	$-0.674101\pi$
$193$	−7.54971	+	2.02294i	−0.543440	+	0.145614i	−0.0233527	+	0.999727i	$0.507434\pi$
$194$	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	$0.721938\pi$
$198$	9.02776	+	11.2778i	0.641575	+	0.801477i
$199$	18.5493	+	10.7094i	1.31492	+	0.759172i	0.982907	−	0.184101i	$-0.0589374\pi$
$199$	18.5493	+	10.7094i	1.31492	+	0.759172i	0.332017	+	0.943273i	$0.392271\pi$
$200$	−3.13240	+	0.839324i	−0.221494	+	0.0593491i
$201$	2.89537	+	0.545072i	0.204223	+	0.0384464i
$202$	0.999519	+	0.999519i	0.0703259	+	0.0703259i
$203$	−15.2344	−	1.90711i	−1.06924	−	0.133853i
$204$	−0.957803	−	12.6250i	−0.0670596	−	0.883926i
$205$	0.0877055	−	0.0506368i	0.00612562	−	0.00353663i
$206$	−2.10021	−	7.83807i	−0.146328	−	0.546104i
$207$	4.77565	−	12.2344i	0.331931	−	0.850347i
$208$	−1.64442	+	3.20872i	−0.114020	+	0.222485i
$209$		−	29.2929i		−	2.02623i
$210$	2.77691	+	5.40258i	0.191625	+	0.372814i
$211$	−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
$213$	2.20435	−	0.773613i	0.151039	−	0.0530071i
$214$	−3.40851	−	12.7207i	−0.233001	−	0.869572i
$215$	6.93178	+	1.85736i	0.472743	+	0.126671i
$216$	−2.75236	+	4.40733i	−0.187274	+	0.299881i
$217$	−11.5935	+	1.60142i	−0.787018	+	0.108712i
$218$	−1.92844			−0.130610
$219$	−1.19628	+	6.35452i	−0.0808372	+	0.429399i
$220$	−5.52786	−	3.19151i	−0.372688	−	0.215172i
$221$	26.3236	−	1.31759i	1.77072	−	0.0886308i
$222$	−4.10776	+	2.80617i	−0.275695	+	0.188338i
$223$	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
$226$	14.3170	+	3.83622i	0.952351	+	0.255182i
$227$	17.5241	−	4.69557i	1.16312	−	0.311656i	0.374907	−	0.927063i	$-0.377675\pi$
$227$	17.5241	−	4.69557i	1.16312	−	0.311656i	0.788210	+	0.615406i	$0.211008\pi$
$228$	9.94199	−	3.48913i	0.658424	−	0.231073i
$229$	4.54789	−	16.9730i	0.300533	−	1.12160i	−0.636190	−	0.771533i	$-0.719490\pi$
$229$	4.54789	−	16.9730i	0.300533	−	1.12160i	0.936723	−	0.350072i	$-0.113843\pi$
$230$			5.80303i			0.382640i
$231$	6.74458	−	21.0107i	0.443761	−	1.38240i
$232$	4.10333	+	4.10333i	0.269397	+	0.269397i
$233$	−1.72719	−	2.99159i	−0.113152	−	0.195985i	0.803887	−	0.594782i	$-0.202761\pi$
$233$	−1.72719	−	2.99159i	−0.113152	−	0.195985i	−0.917040	+	0.398796i	$0.869428\pi$
$234$	−9.02427	−	5.96343i	−0.589935	−	0.389842i
$235$	6.86665	−	11.8934i	0.447931	−	0.775839i
$236$	−3.00777	+	11.2251i	−0.195789	+	0.730694i
$237$	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	$0.528757\pi$
$240$	0.424763	−	2.25630i	0.0274183	−	0.145643i
$241$	−3.76499	+	1.00883i	−0.242524	+	0.0649842i	−0.378034	−	0.925792i	$-0.623400\pi$
$241$	−3.76499	+	1.00883i	−0.242524	+	0.0649842i	0.135509	+	0.990776i	$0.456733\pi$
$242$	3.15439	+	11.7723i	0.202772	+	0.756755i
$243$	−12.2322	−	9.66303i	−0.784694	−	0.619884i
$244$		−	11.0227i		−	0.705654i
$245$	4.53682	−	8.09415i	0.289847	−	0.517116i
$246$	−0.0100105	−	0.131951i	−0.000638249	−	0.00841288i
$247$	6.72880	+	20.8758i	0.428143	+	1.32829i
$248$	3.83090	+	2.21177i	0.243262	+	0.140447i
$249$	−16.6851	+	5.85561i	−1.05737	+	0.371084i
$250$	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	$0.755207\pi$
$252$	7.93438	−	0.213521i	0.499819	−	0.0134506i
$253$	14.9063	−	14.9063i	0.937150	−	0.937150i
$254$	−10.1563	−	2.72137i	−0.637262	−	0.170754i
$255$	−15.8363	+	5.55774i	−0.991708	+	0.348039i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.496381	−	0.859757i	−0.0309634	−	0.0536302i	0.850128	−	0.526575i	$-0.176524\pi$
$257$	−0.496381	−	0.859757i	−0.0309634	−	0.0536302i	−0.881092	+	0.472945i	$0.843191\pi$
$258$	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
$261$	−13.5909	+	10.8794i	−0.841253	+	0.673415i
$262$	−2.66503	−	9.94602i	−0.164646	−	0.614467i
$263$	−6.80686	−	3.92994i	−0.419729	−	0.242330i	0.275233	−	0.961378i	$-0.411245\pi$
$263$	−6.80686	−	3.92994i	−0.419729	−	0.242330i	−0.694961	+	0.719047i	$0.744578\pi$
$264$	−6.88686	+	4.70468i	−0.423857	+	0.289553i
$265$	0.755438	−	0.755438i	0.0464062	−	0.0464062i
$266$	−12.8309	−	9.71640i	−0.786712	−	0.595751i
$267$	4.69316	−	5.46372i	0.287217	−	0.334374i
$268$	−0.440252	+	1.64304i	−0.0268927	+	0.100365i
$269$	−6.97939	−	4.02955i	−0.425541	−	0.245686i	0.271904	−	0.962324i	$-0.412347\pi$
$269$	−6.97939	−	4.02955i	−0.425541	−	0.245686i	−0.697445	+	0.716638i	$0.745680\pi$
$270$	6.58738	+	2.01202i	0.400895	+	0.122448i
$271$	−0.536293	+	2.00147i	−0.0325775	+	0.121581i	−0.980300	−	0.197516i	$-0.936713\pi$
$271$	−0.536293	+	2.00147i	−0.0325775	+	0.121581i	0.947722	+	0.319096i	$0.103379\pi$
$272$	7.30998			0.443233
$273$	0.0197559	+	16.5227i	0.00119568	+	0.999999i
$274$	−1.15388			−0.0697083
$275$	4.04164	−	15.0836i	0.243720	−	0.909576i
$276$	6.83469	+	3.28366i	0.411400	+	0.197653i
$277$	−1.27049	−	0.733518i	−0.0763364	−	0.0440728i	0.461346	−	0.887220i	$-0.347367\pi$
$277$	−1.27049	−	0.733518i	−0.0763364	−	0.0440728i	−0.537682	+	0.843147i	$0.680700\pi$
$278$	3.74084	−	13.9610i	0.224361	−	0.837325i
$279$	−7.86068	+	10.6920i	−0.470607	+	0.640113i
$280$	−3.23153	+	1.36270i	−0.193121	+	0.0814367i
$281$	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	$0.0411102\pi$
$282$	−10.1223	−	14.8173i	−0.602773	−	0.882358i
$283$	−3.71114	−	2.14263i	−0.220604	−	0.127366i	0.385626	−	0.922655i	$-0.373986\pi$
$283$	−3.71114	−	2.14263i	−0.220604	−	0.127366i	−0.606230	+	0.795289i	$0.707319\pi$
$284$	0.349090	+	1.30282i	0.0207147	+	0.0773082i
$285$	−7.87834	−	11.5326i	−0.466673	−	0.683131i
$286$	−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
$291$	−8.27356	−	23.5748i	−0.485005	−	1.38198i
$292$	−3.60603	−	0.966231i	−0.211027	−	0.0565444i
$293$	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	$0.166312\pi$
$294$	−6.96596	−	9.92348i	−0.406263	−	0.578749i
$295$	15.4045			0.896882
$296$	−1.43609	−	2.48738i	−0.0834711	−	0.144576i
$297$	−11.7527	−	22.0893i	−0.681963	−	1.28175i
$298$	11.0706	+	6.39160i	0.641301	+	0.370255i
$299$	−7.19897	+	14.0471i	−0.416327	+	0.812367i
$300$	5.60077	−	0.424906i	0.323361	−	0.0245320i
$301$	−14.2126	−	1.77921i	−0.819203	−	0.102552i
$302$			11.6635i			0.671161i
$303$	−1.38104	−	2.02162i	−0.0793390	−	0.116139i
$304$	1.57446	+	5.87595i	0.0903013	+	0.337009i
$305$	−14.1133	+	3.78165i	−0.808126	+	0.216537i
$306$	−2.41524	+	21.7965i	−0.138070	+	1.24603i
$307$	−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
$310$	1.51763	−	5.66386i	0.0861953	−	0.321685i
$311$	−9.47591	+	16.4128i	−0.537330	+	0.930682i	0.461717	+	0.887027i	$0.347234\pi$
$311$	−9.47591	+	16.4128i	−0.537330	+	0.930682i	−0.999047	+	0.0436550i	$0.986100\pi$
$312$	3.82726	−	4.93478i	0.216676	−	0.279377i
$313$	10.3836	+	17.9850i	0.586919	+	1.01657i	0.994633	+	0.103463i	$0.0329925\pi$
$313$	10.3836	+	17.9850i	0.586919	+	1.01657i	−0.407715	+	0.913109i	$0.633674\pi$
$314$	−4.82379	−	4.82379i	−0.272222	−	0.272222i
$315$	−2.99551	−	10.0858i	−0.168778	−	0.568273i
$316$			5.04970i			0.284068i
$317$	5.77271	−	21.5441i	0.324228	−	1.21003i	−0.590858	−	0.806776i	$-0.701211\pi$
$317$	5.77271	−	21.5441i	0.324228	−	1.21003i	0.915086	−	0.403259i	$-0.132123\pi$
$318$	−0.462273	−	1.31721i	−0.0259230	−	0.0738653i
$319$	−26.9913	+	7.23229i	−1.51122	+	0.404931i
$320$	1.28039	+	0.343079i	0.0715760	+	0.0191787i
$321$	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
$324$	6.09721	−	6.61997i	0.338734	−	0.367776i
$325$	0.584517	+	11.6778i	0.0324232	+	0.647769i
$326$	−9.79901	−	5.65746i	−0.542717	−	0.313338i
$327$	3.28249	+	0.617951i	0.181522	+	0.0341728i
$328$	0.0764008			0.00421853
$329$	−10.3284	+	25.3907i	−0.569423	+	1.39984i
$330$	8.38657	+	7.20379i	0.461665	+	0.396556i
$331$	1.28268	+	0.343693i	0.0705025	+	0.0188911i	0.293898	−	0.955837i	$-0.405047\pi$
$331$	1.28268	+	0.343693i	0.0705025	+	0.0188911i	−0.223395	+	0.974728i	$0.571714\pi$
$332$	−2.64232	−	9.86128i	−0.145016	−	0.541208i
$333$	7.89124	−	3.46023i	0.432437	−	0.189619i
$334$	1.39493	+	2.41609i	0.0763273	+	0.132203i
$335$	2.25478			0.123192
$336$	−0.223615	+	4.57712i	−0.0121992	+	0.249702i
$337$		−	24.5514i		−	1.33740i	−0.743532	−	0.668700i	$-0.766851\pi$
$337$		−	24.5514i		−	1.33740i	0.743532	−	0.668700i	$-0.233149\pi$
$338$	10.0644	+	8.22852i	0.547429	+	0.447572i
$339$	−23.1404	−	11.1176i	−1.25681	−	0.603824i
$340$	−2.50791	−	9.35963i	−0.136010	−	0.507597i
$341$	−18.4471	+	10.6505i	−0.998968	+	0.576754i
$342$	−18.0408	+	2.75321i	−0.975536	+	0.148876i
$343$	−6.75951	+	17.2427i	−0.364979	+	0.931016i
$344$	3.82814	+	3.82814i	0.206399	+	0.206399i
$345$	1.85953	−	9.87763i	0.100114	−	0.531794i
$346$	22.0072	−	5.89680i	1.18311	−	0.317014i
$347$	22.4856	+	12.9821i	1.20709	+	0.696915i	0.962123	−	0.272616i	$-0.0878890\pi$
$347$	22.4856	+	12.9821i	1.20709	+	0.696915i	0.244969	+	0.969531i	$0.421222\pi$
$348$	−5.66961	−	8.29936i	−0.303923	−	0.444893i
$349$	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
$353$	13.0256	−	3.49020i	0.693283	−	0.185765i	0.105063	−	0.994466i	$-0.466496\pi$
$353$	13.0256	−	3.49020i	0.693283	−	0.185765i	0.588220	+	0.808701i	$0.299829\pi$
$354$	8.71667	−	18.1431i	0.463286	−	0.964293i
$355$	1.54835	−	0.893942i	0.0821781	−	0.0474455i
$356$	2.94046	+	2.94046i	0.155844	+	0.155844i
$357$	29.7934	−	15.3137i	1.57683	−	0.810487i
$358$	18.1239	+	18.1239i	0.957881	+	0.957881i
$359$	16.1764	+	4.33446i	0.853760	+	0.228764i	0.659052	−	0.752097i	$-0.270958\pi$
$359$	16.1764	+	4.33446i	0.853760	+	0.228764i	0.194707	+	0.980861i	$0.437624\pi$
$360$	−1.44602	+	3.70445i	−0.0762120	+	0.195242i
$361$	15.5934	+	9.00286i	0.820706	+	0.473835i
$362$	23.1430	+	6.20114i	1.21637	+	0.325925i
$363$	−1.59690	−	21.0491i	−0.0838158	−	1.10479i
$364$	−9.51291	−	0.710265i	−0.498612	−	0.0372280i
$365$			4.94861i			0.259022i
$366$	−3.53211	+	18.7622i	−0.184627	+	0.980718i
$367$	−12.2472	+	21.2129i	−0.639301	+	1.10730i	0.346285	+	0.938129i	$0.387443\pi$
$367$	−12.2472	+	21.2129i	−0.639301	+	1.10730i	−0.985586	+	0.169173i	$0.945890\pi$
$368$	−2.18890	+	3.79129i	−0.114104	+	0.197635i
$369$	−0.0252430	+	0.227808i	−0.00131410	+	0.0118592i
$370$	−2.69213	+	2.69213i	−0.139957	+	0.139957i
$371$	−1.28732	+	1.69996i	−0.0668343	+	0.0882573i
$372$	−5.81202	−	4.99234i	−0.301339	−	0.258841i
$373$	10.3616	+	17.9468i	0.536503	+	0.929250i	0.999089	+	0.0426754i	$0.0135881\pi$
$373$	10.3616	+	17.9468i	0.536503	+	0.929250i	−0.462586	+	0.886574i	$0.653079\pi$
$374$	−17.6001	+	30.4842i	−0.910079	+	1.57630i
$375$	−6.26702	−	17.8574i	−0.323628	−	0.922150i
$376$	8.97237	−	5.18020i	0.462714	−	0.267148i
$377$	17.5742	−	11.3542i	0.905117	−	0.584773i
$378$	−13.5739	−	2.17906i	−0.698168	−	0.112079i
$379$	−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
$381$	16.4155	+	7.88668i	0.840992	+	0.404047i
$382$	3.79101	+	14.1482i	0.193965	+	0.723887i
$383$	3.14991	−	11.7556i	0.160953	−	0.600685i	−0.837569	−	0.546332i	$-0.816024\pi$
$383$	3.14991	−	11.7556i	0.160953	−	0.600685i	0.998522	−	0.0543529i	$-0.0173096\pi$
$384$	1.12859	−	1.31389i	0.0575929	−	0.0670489i
$385$	2.09773	−	16.7571i	0.106910	−	0.854021i
$386$			7.81604i			0.397826i
$387$	−12.6794	+	10.1497i	−0.644529	+	0.515939i
$388$	13.9333	−	3.73341i	0.707355	−	0.189535i
$389$	1.45477	−	2.51973i	0.0737597	−	0.127756i	−0.826787	−	0.562516i	$-0.809834\pi$
$389$	1.45477	−	2.51973i	0.0737597	−	0.127756i	0.900546	+	0.434760i	$0.143167\pi$
$390$	−7.63150	−	3.20737i	−0.386436	−	0.162411i
$391$	32.0017			1.61839
$392$	6.01715	−	3.57686i	0.303912	−	0.180659i
$393$	1.34917	+	17.7836i	0.0680564	+	0.897064i
$394$	2.14040	−	1.23576i	0.107832	−	0.0622567i
$395$	6.46558	−	1.73245i	0.325319	−	0.0871689i
$396$	13.2301	−	5.80124i	0.664835	−	0.291523i
$397$	2.87121	−	10.7155i	0.144102	−	0.537795i	−0.855692	−	0.517486i	$-0.826868\pi$
$397$	2.87121	−	10.7155i	0.144102	−	0.537795i	0.999794	−	0.0203097i	$-0.00646522\pi$
$398$	15.1454	−	15.1454i	0.759172	−	0.759172i
$399$	18.7266	+	20.6503i	0.937501	+	1.03381i
$400$			3.24290i			0.162145i
$401$	−7.06965	−	1.89431i	−0.353042	−	0.0945972i	0.0779397	−	0.996958i	$-0.475166\pi$
$401$	−7.06965	−	1.89431i	−0.353042	−	0.0945972i	−0.430981	+	0.902361i	$0.641833\pi$
$402$	1.27587	−	2.65563i	0.0636348	−	0.132451i
$403$	10.7000	−	11.8275i	0.533003	−	0.589172i
$404$	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
$408$	−12.4427	−	2.34242i	−0.616005	−	0.115967i
$409$	1.39768	+	5.21620i	0.0691107	+	0.257924i	0.991833	−	0.127540i	$-0.0407080\pi$
$409$	1.39768	+	5.21620i	0.0691107	+	0.257924i	−0.922723	+	0.385464i	$0.874041\pi$
$410$	−0.0262115	−	0.0978228i	−0.00129450	−	0.00483112i
$411$	1.96407	+	0.369750i	0.0968806	+	0.0182384i
$412$	−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
$416$	2.67377	+	2.41887i	0.131093	+	0.118595i
$417$	−10.8412	+	22.5650i	−0.530894	+	1.10501i
$418$	−28.2948	−	7.58156i	−1.38394	−	0.370826i
$419$			12.1715i			0.594619i	0.954781	+	0.297310i	$0.0960893\pi$
$419$			12.1715i			0.594619i	−0.954781	+	0.297310i	$0.903911\pi$
$420$	5.93721	−	1.28400i	0.289706	−	0.0626528i
$421$	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	$0.0563230\pi$
$422$	−2.96833	+	11.0780i	−0.144496	+	0.539267i
$423$	12.4816	+	28.4649i	0.606874	+	1.38401i
$424$	0.778501	−	0.208599i	0.0378073	−	0.0101304i
$425$	20.5296	−	11.8528i	0.995832	−	0.574944i
$426$	−0.176726	−	2.32946i	−0.00856241	−	0.112863i
$427$	26.8718	−	11.3315i	1.30042	−	0.548369i
$428$	−13.1695			−0.636571
$429$	11.3643	+	27.8419i	0.548673	+	1.34422i
$430$	3.58815	−	6.21486i	0.173036	−	0.299707i
$431$	−33.9602	+	9.09962i	−1.63581	+	0.438313i	−0.955590	−	0.294698i	$-0.904781\pi$
$431$	−33.9602	+	9.09962i	−1.63581	+	0.438313i	−0.680216	+	0.733011i	$0.738114\pi$
$432$	3.54479	+	3.79927i	0.170549	+	0.182793i
$433$		−	25.4681i		−	1.22392i	−0.790889	−	0.611960i	$-0.790381\pi$
$433$		−	25.4681i		−	1.22392i	0.790889	−	0.611960i	$-0.209619\pi$
$434$	−1.45376	+	11.6129i	−0.0697829	+	0.557439i
$435$	−8.68130	+	10.1067i	−0.416236	+	0.484577i
$436$	−0.499116	+	1.86273i	−0.0239033	+	0.0892085i
$437$	6.89266	+	25.7238i	0.329721	+	1.23053i
$438$	5.82838	+	2.80019i	0.278491	+	0.133798i
$439$	9.12459	−	5.26808i	0.435493	−	0.251432i	−0.266191	−	0.963920i	$-0.585765\pi$
$439$	9.12459	−	5.26808i	0.435493	−	0.251432i	0.701684	+	0.712488i	$0.252432\pi$
$440$	−4.51348	+	4.51348i	−0.215172	+	0.215172i
$441$	8.67722	+	19.1234i	0.413201	+	0.910640i
$442$	5.54035	−	25.7676i	0.263527	−	1.22564i
$443$	0.0277916	−	0.0160455i	0.00132042	−	0.000762345i	−0.499340	−	0.866406i	$-0.666424\pi$
$443$	0.0277916	−	0.0160455i	0.00132042	−	0.000762345i	0.500660	+	0.865644i	$0.333091\pi$
$444$	1.64738	+	4.69408i	0.0781814	+	0.222771i
$445$	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
$448$	−2.62526	−	0.328643i	−0.124032	−	0.0155269i
$449$	−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	$0.452006\pi$
$450$	−9.66951	−	1.07146i	−0.455825	−	0.0505092i
$451$	−0.183948	+	0.318608i	−0.00866179	+	0.0150027i
$452$	7.41101	−	12.8362i	0.348585	−	0.603766i
$453$	3.73747	−	19.8531i	0.175602	−	0.932779i
$454$		−	18.1423i		−	0.851460i
$455$	2.35427	+	12.4239i	0.110370	+	0.582442i
$456$	−0.797066	−	10.5063i	−0.0373260	−	0.492001i
$457$	17.7313	+	4.75108i	0.829434	+	0.222246i	0.648467	−	0.761243i	$-0.275410\pi$
$457$	17.7313	+	4.75108i	0.829434	+	0.222246i	0.180967	+	0.983489i	$0.442077\pi$
$458$	−15.2175	−	8.78585i	−0.711069	−	0.410536i
$459$	11.0956	−	36.3271i	0.517899	−	1.69560i
$460$	5.60530	+	1.50193i	0.261348	+	0.0700281i
$461$	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	$0.498934\pi$
$462$	−18.5492	−	11.9527i	−0.862986	−	0.556092i
$463$	−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
$465$	−4.39816	+	9.15443i	−0.203960	+	0.424526i
$466$	−3.33668	+	0.894061i	−0.154569	+	0.0414166i
$467$	10.1766	+	17.6264i	0.470918	+	0.815654i	0.999447	−	0.0332612i	$-0.0105893\pi$
$467$	10.1766	+	17.6264i	0.470918	+	0.815654i	−0.528528	+	0.848916i	$0.677256\pi$
$468$	−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
$471$	6.66508	+	9.75657i	0.307111	+	0.449559i
$472$	10.0642	+	5.81056i	0.463242	+	0.267453i
$473$	−25.1811	+	6.74725i	−1.15783	+	0.310239i
$474$	1.61813	−	8.59535i	0.0743232	−	0.394797i
$475$	13.9493	+	13.9493i	0.640038	+	0.640038i
$476$	7.51479	+	17.8207i	0.344440	+	0.816813i
$477$	0.364770	+	2.39022i	0.0167017	+	0.109441i
$478$	17.1486	−	9.90076i	0.784360	−	0.452850i
$479$	−2.17833	−	8.12965i	−0.0995306	−	0.371453i	0.898137	−	0.439716i	$-0.144921\pi$
$479$	−2.17833	−	8.12965i	−0.0995306	−	0.371453i	−0.997667	+	0.0682629i	$0.978254\pi$
$480$	−2.06948	−	0.994263i	−0.0944584	−	0.0453817i
$481$	−9.85644	+	3.17698i	−0.449415	+	0.144858i
$482$			3.89781i			0.177540i
$483$	−0.978944	+	20.0377i	−0.0445435	+	0.911748i
$484$	12.1876			0.553983
$485$	−9.56045	−	16.5592i	−0.434118	−	0.751914i
$486$	−12.4997	+	9.31439i	−0.566997	+	0.422509i
$487$	0.810378	+	3.02437i	0.0367217	+	0.137047i	0.981853	−	0.189643i	$-0.0607331\pi$
$487$	0.810378	+	3.02437i	0.0367217	+	0.137047i	−0.945131	+	0.326691i	$0.894066\pi$
$488$	−10.6471	−	2.85288i	−0.481970	−	0.129144i
$489$	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	$0.915721\pi$
$492$	−0.130046	−	0.0244819i	−0.00586291	−	0.00110373i
$493$	−36.7366	−	21.2099i	−1.65453	−	0.955245i
$494$	21.9060	−	1.09647i	0.985597	−	0.0493327i
$495$	−11.9668	−	14.9493i	−0.537868	−	0.671923i
$496$	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
$499$	−14.5424	−	3.89664i	−0.651009	−	0.174437i	−0.0818241	−	0.996647i	$-0.526075\pi$
$499$	−14.5424	−	3.89664i	−0.651009	−	0.174437i	−0.569185	+	0.822209i	$0.692741\pi$
$500$	10.5541	−	2.82797i	0.471995	−	0.126471i
$501$	−1.60017	−	4.55955i	−0.0714903	−	0.203706i
$502$	−5.89302	+	21.9930i	−0.263018	+	0.981597i
$503$			33.7834i			1.50633i	0.657834	+	0.753163i	$0.271473\pi$
$503$			33.7834i			1.50633i	−0.657834	+	0.753163i	$0.728527\pi$
$504$	1.84732	−	7.71929i	0.0822863	−	0.343844i
$505$	−1.32492	−	1.32492i	−0.0589581	−	0.0589581i
$506$	−10.5403	−	18.2564i	−0.468575	−	0.811596i
$507$	−14.4943	−	17.2312i	−0.643715	−	0.765265i
$508$	−5.25728	+	9.10588i	−0.233254	+	0.404008i
$509$	−0.594393	+	2.21830i	−0.0263460	+	0.0983246i	−0.977847	−	0.209321i	$-0.932875\pi$
$509$	−0.594393	+	2.21830i	−0.0263460	+	0.0983246i	0.951501	+	0.307646i	$0.0995412\pi$
$510$	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
$513$	31.5904	+	1.09465i	1.39475	+	0.0483300i
$514$	−0.958934	+	0.256946i	−0.0422968	+	0.0113334i
$515$	2.78394	+	10.3898i	0.122675	+	0.457830i
$516$	−5.28937	−	7.74276i	−0.232852	−	0.340856i
$517$			49.8890i			2.19411i
$518$	4.58757	−	6.05807i	0.201566	−	0.266176i
$519$	−39.3491	+	2.98525i	−1.72723	+	0.131038i
$520$	2.17978	−	4.25334i	0.0955896	−	0.186521i
$521$	13.7549	+	7.94142i	0.602615	+	0.347920i	0.770070	−	0.637960i	$-0.220221\pi$
$521$	13.7549	+	7.94142i	0.602615	+	0.347920i	−0.167455	+	0.985880i	$0.553555\pi$
$522$	6.99108	+	15.9435i	0.305991	+	0.697830i
$523$	−7.41978	−	12.8514i	−0.324444	−	0.561954i	0.656955	−	0.753929i	$-0.271844\pi$
$523$	−7.41978	−	12.8514i	−0.324444	−	0.561954i	−0.981400	+	0.191975i	$0.938511\pi$
$524$	−10.2969			−0.449821
$525$	6.79355	+	13.2171i	0.296495	+	0.576842i
$526$	−5.55777	+	5.55777i	−0.242330	+	0.242330i
$527$	−31.2342	−	8.36917i	−1.36058	−	0.364567i
$528$	2.76192	+	7.86986i	0.120197	+	0.342492i
$529$	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
$534$	−4.06287	−	5.94736i	−0.175818	−	0.257367i
$535$	4.51818	+	16.8621i	0.195338	+	0.729011i
$536$	1.47311	+	0.850502i	0.0636288	+	0.0367361i
$537$	−25.0420	−	36.6574i	−1.08064	−	1.58188i
$538$	−5.69864	+	5.69864i	−0.245686	+	0.245686i
$539$	0.428938	+	33.7047i	0.0184757	+	1.45177i
$540$	3.64840	−	5.84217i	0.157002	−	0.251407i
$541$	−11.5893	+	43.2517i	−0.498261	+	1.85953i	0.0126809	+	0.999920i	$0.495963\pi$
$541$	−11.5893	+	43.2517i	−0.498261	+	1.85953i	−0.510942	+	0.859615i	$0.670703\pi$
$542$	1.79447	+	1.03604i	0.0770791	+	0.0445016i
$543$	−37.4057	−	17.9712i	−1.60523	−	0.771219i
$544$	1.89196	−	7.06090i	0.0811173	−	0.302734i
$545$	2.55625			0.109498
$546$	15.9648	+	4.25731i	0.683231	+	0.182196i
$547$	−16.4459			−0.703176			−0.351588	−	0.936155i	$-0.614358\pi$
$547$	−16.4459			−0.703176			−0.351588	+	0.936155i	$0.614358\pi$
$548$	−0.298645	+	1.11456i	−0.0127575	+	0.0476116i
$549$	12.0244	−	30.8043i	0.513188	−	1.31470i
$550$	−13.5236	−	7.80785i	−0.576648	−	0.332928i
$551$	9.13655	−	34.0981i	0.389230	−	1.45263i
$552$	4.94073	−	5.75193i	0.210291	−	0.244818i
$553$	−12.3105	+	5.19118i	−0.523495	+	0.220751i
$554$	−1.03735	+	1.03735i	−0.0440728	+	0.0440728i
$555$	5.44507	−	3.71974i	0.231131	−	0.157894i
$556$	−12.5171	−	7.22675i	−0.530843	−	0.306482i
$557$	5.92877	+	22.1265i	0.251210	+	0.937529i	0.970160	+	0.242467i	$0.0779565\pi$
$557$	5.92877	+	22.1265i	0.251210	+	0.937529i	−0.718950	+	0.695062i	$0.755377\pi$
$558$	8.29319	+	10.3601i	0.351079	+	0.438579i
$559$	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	−0.931711	−	0.363200i	$-0.881684\pi$
$563$	−3.59034	+	6.21865i	−0.151315	+	0.262085i	0.780396	+	0.625285i	$0.215017\pi$
$564$	−16.9323	+	5.94236i	−0.712977	+	0.250219i
$565$	−18.9780	−	5.08513i	−0.798409	−	0.213933i
$566$	−3.03013	+	3.03013i	−0.127366	+	0.127366i
$567$	22.4066	+	8.05873i	0.940990	+	0.338435i
$568$	1.34878			0.0565935
$569$	1.47774	+	2.55952i	0.0619500	+	0.107301i	0.895337	−	0.445389i	$-0.146935\pi$
$569$	1.47774	+	2.55952i	0.0619500	+	0.107301i	−0.833387	+	0.552690i	$0.813601\pi$
$570$	−13.1787	+	4.62504i	−0.551994	+	0.193722i
$571$	30.4608	+	17.5866i	1.27475	+	0.735974i	0.975877	−	0.218320i	$-0.0700577\pi$
$571$	30.4608	+	17.5866i	1.27475	+	0.735974i	0.298868	+	0.954295i	$0.403391\pi$
$572$	−16.5248	+	5.32637i	−0.690937	+	0.222707i
$573$	−1.91919	−	25.2972i	−0.0801754	−	1.05681i
$574$	0.0785413	+	0.186255i	0.00327825	+	0.00777412i
$575$			14.1968i			0.592046i
$576$	−2.34205	+	1.87479i	−0.0975852	+	0.0781161i
$577$	4.06864	+	15.1844i	0.169380	+	0.632133i	0.997441	+	0.0714958i	$0.0227773\pi$
$577$	4.06864	+	15.1844i	0.169380	+	0.632133i	−0.828061	+	0.560638i	$0.810556\pi$
$578$	−35.1944	+	9.43030i	−1.46389	+	0.392249i
$579$	2.50458	−	13.3041i	0.104087	−	0.552899i
$580$	−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
$583$	−1.00448	+	3.74876i	−0.0416012	+	0.155258i
$584$	−1.86662	+	3.23307i	−0.0772411	+	0.133786i
$585$	11.9622	+	7.90487i	0.494576	+	0.326826i
$586$	−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	$0.566078\pi$
$588$	−11.3883	+	4.16021i	−0.469644	+	0.171564i
$589$		−	26.9094i		−	1.10878i
$590$	3.98697	−	14.8796i	0.164141	−	0.612582i
$591$	−4.03927	+	1.41758i	−0.166154	+	0.0583114i
$592$	−2.77431	+	0.743375i	−0.114024	+	0.0305525i
$593$	−6.63703	−	1.77839i	−0.272550	−	0.0730296i	0.119955	−	0.992779i	$-0.461725\pi$
$593$	−6.63703	−	1.77839i	−0.272550	−	0.0730296i	−0.392505	+	0.919750i	$0.628392\pi$
$594$	−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
$597$	−30.6330	+	20.9266i	−1.25373	+	0.856469i
$598$	11.7053	+	10.5893i	0.478664	+	0.433030i
$599$	−0.177150	−	0.102277i	−0.00723814	−	0.00417894i	0.496377	−	0.868107i	$-0.334664\pi$
$599$	−0.177150	−	0.102277i	−0.00723814	−	0.00417894i	−0.503615	+	0.863928i	$0.667997\pi$
$600$	1.03916	−	5.51990i	0.0424234	−	0.225349i
$601$	−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
$604$	11.2661	+	3.01874i	0.458411	+	0.122831i
$605$	−4.18133	−	15.6049i	−0.169995	−	0.634430i
$606$	−2.31017	+	0.810754i	−0.0938444	+	0.0329346i
$607$	10.3426	+	17.9138i	0.419792	+	0.727100i	0.995918	−	0.0902601i	$-0.0287698\pi$
$607$	10.3426	+	17.9138i	0.419792	+	0.727100i	−0.576127	+	0.817360i	$0.695436\pi$
$608$	6.08323			0.246708
$609$	14.4043	−	22.3536i	0.583690	−	0.905815i
$610$			14.6112i			0.591589i
$611$	−11.4599	−	35.5537i	−0.463616	−	1.43835i
$612$	20.4287	+	7.97430i	0.825783	+	0.322342i
$613$	−0.712832	−	2.66032i	−0.0287910	−	0.107450i	0.950035	−	0.312143i	$-0.101047\pi$
$613$	−0.712832	−	2.66032i	−0.0287910	−	0.107450i	−0.978826	+	0.204694i	$0.934380\pi$
$614$	−14.1771	+	8.18513i	−0.572140	+	0.330325i
$615$	0.0132695	+	0.174908i	0.000535080	+	0.00705299i
$616$	7.69129	−	10.1566i	0.309891	−	0.409223i
$617$	−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	$0.881584\pi$
$618$	13.8122	+	2.60024i	0.555609	+	0.104597i
$619$	7.99186	−	2.14141i	0.321220	−	0.0860706i	−0.0946061	−	0.995515i	$-0.530159\pi$
$619$	7.99186	−	2.14141i	0.321220	−	0.0860706i	0.415826	+	0.909444i	$0.363492\pi$
$620$	−5.07807	−	2.93183i	−0.203940	−	0.117745i
$621$	15.5184	+	16.6325i	0.622732	+	0.667438i
$622$	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
$626$	20.0597	−	5.37497i	0.801746	−	0.214827i
$627$	45.7325	+	21.9718i	1.82638	+	0.877468i
$628$	−5.90792	+	3.41094i	−0.235752	+	0.136111i
$629$	14.8461	+	14.8461i	0.591954	+	0.591954i
$630$	−10.5175	+	0.283035i	−0.419026	+	0.0112764i
$631$	−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	$0.826092\pi$
$632$	4.87763	+	1.30696i	0.194022	+	0.0519880i
$633$	8.60239	−	17.9052i	0.341914	−	0.711668i
$634$	−19.3159	−	11.1520i	−0.767131	−	0.442903i
$635$	13.4627	+	3.60733i	0.534253	+	0.143153i
$636$	−1.39197	+	0.105603i	−0.0551952	+	0.00418742i
$637$	−8.04791	−	23.9214i	−0.318870	−	0.947798i
$638$			27.9434i			1.10629i
$639$	−0.445641	+	4.02172i	−0.0176293	+	0.159097i
$640$	0.662779	−	1.14797i	0.0261986	−	0.0453774i
$641$	−1.21297	+	2.10092i	−0.0479094	+	0.0829815i	−0.888986	−	0.457935i	$-0.848589\pi$
$641$	−1.21297	+	2.10092i	−0.0479094	+	0.0829815i	0.841076	+	0.540917i	$0.181923\pi$
$642$	22.4164	+	4.22004i	0.884706	+	0.166552i
$643$	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	$0.208947\pi$
$644$	−11.4929	−	1.43873i	−0.452883	−	0.0566940i
$645$	−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	−0.853353	−	0.521334i	$-0.825435\pi$
$647$	0.631130	−	1.09315i	0.0248123	−	0.0429761i	0.878165	+	0.478358i	$0.158768\pi$
$648$	−4.81632	−	7.60283i	−0.189203	−	0.298667i
$649$	−48.4626	+	27.9799i	−1.90232	+	1.09831i
$650$	11.4312	+	2.45784i	0.448368	+	0.0964044i
$651$	6.19579	−	19.3011i	0.242832	−	0.756471i
$652$	−8.00086	+	8.00086i	−0.313338	+	0.313338i
$653$	−6.79930	+	3.92558i	−0.266077	+	0.153620i	−0.627104	−	0.778936i	$-0.715760\pi$
$653$	−6.79930	+	3.92558i	−0.266077	+	0.153620i	0.361026	+	0.932556i	$0.382426\pi$
$654$	1.44647	−	3.01071i	0.0565613	−	0.117728i
$655$	3.53265	+	13.1840i	0.138032	+	0.515142i
$656$	0.0197740	−	0.0737975i	0.000772044	−	0.00288131i
$657$	−9.02348	−	6.63400i	−0.352040	−	0.258817i
$658$	21.8524	+	16.5481i	0.851894	+	0.645111i
$659$		−	20.6367i		−	0.803890i	−0.915664	−	0.401945i	$-0.868334\pi$
$659$		−	20.6367i		−	0.803890i	0.915664	−	0.401945i	$-0.131666\pi$
$660$	9.12893	−	6.23632i	0.355343	−	0.242748i
$661$	−43.6437	+	11.6943i	−1.69754	+	0.454855i	−0.972319	−	0.233657i	$-0.924931\pi$
$661$	−43.6437	+	11.6943i	−1.69754	+	0.454855i	−0.725225	+	0.688512i	$0.758264\pi$
$662$	0.663964	−	1.15002i	0.0258057	−	0.0446968i
$663$	−17.6875	+	42.0850i	−0.686926	+	1.63445i
$664$	−10.2091			−0.396192
$665$	17.0081	+	12.8796i	0.659545	+	0.499451i
$666$	−1.29992	−	8.51793i	−0.0503708	−	0.330063i
$667$	22.0008	−	12.7022i	0.851874	−	0.491830i
$668$	2.69480	−	0.722070i	0.104265	−	0.0279377i
$669$	1.95720	+	5.57688i	0.0756698	+	0.215615i
$670$	0.583580	−	2.17795i	0.0225456	−	0.0841415i
$671$	37.5318	−	37.5318i	1.44890	−	1.44890i
$672$	4.36328	+	1.40064i	0.168317	+	0.0540309i
$673$		−	2.11909i		−	0.0816848i	−0.999166	−	0.0408424i	$-0.986996\pi$
$673$		−	2.11909i		−	0.0816848i	0.999166	−	0.0408424i	$-0.0130042\pi$
$674$	−23.7148	−	6.35437i	−0.913461	−	0.244761i
$675$	16.1156	+	4.92230i	0.620291	+	0.189459i
$676$	10.5530	−	7.59174i	0.405884	−	0.291990i
$677$	18.3091	−	10.5708i	0.703676	−	0.406267i	−0.105039	−	0.994468i	$-0.533497\pi$
$677$	18.3091	−	10.5708i	0.703676	−	0.406267i	0.808715	+	0.588201i	$0.200163\pi$
$678$	−16.7279	+	19.4744i	−0.642432	+	0.747911i
$679$	23.4252	+	30.1294i	0.898977	+	1.15626i
$680$	−9.68980			−0.371587
$681$	−5.81354	+	30.8809i	−0.222775	+	1.18336i
$682$	5.51308	+	20.5751i	0.211107	+	0.787861i
$683$	−12.4337	−	46.4033i	−0.475764	−	1.77557i	−0.618469	−	0.785809i	$-0.712247\pi$
$683$	−12.4337	−	46.4033i	−0.475764	−	1.77557i	0.142705	−	0.989765i	$-0.454420\pi$
$684$	−2.00992	+	18.1387i	−0.0768511	+	0.693550i
$685$	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
$689$	−0.145271	−	2.90231i	−0.00553439	−	0.110569i
$690$	−9.05978	−	4.35269i	−0.344900	−	0.165704i
$691$	22.7944	+	6.10773i	0.867139	+	0.232349i	0.664850	−	0.746977i	$-0.268495\pi$
$691$	22.7944	+	6.10773i	0.867139	+	0.232349i	0.202289	+	0.979326i	$0.435162\pi$
$692$		−	22.7835i		−	0.866099i
$693$	27.7434	+	26.2893i	1.05388	+	0.998648i
$694$	18.3594	−	18.3594i	0.696915	−	0.696915i
$695$	−4.95870	+	18.5061i	−0.188094	+	0.701977i
$696$	−9.48397	+	3.32839i	−0.359489	+	0.126162i
$697$	−0.539458	+	0.144547i	−0.0204334	+	0.00547512i
$698$	5.56060	−	3.21041i	0.210472	−	0.121516i
$699$	5.96603	−	0.452617i	0.225656	−	0.0171195i
$700$	−7.90574	+	3.33376i	−0.298809	+	0.126004i
$701$	−31.4037			−1.18610			−0.593051	−	0.805165i	$-0.702077\pi$
$701$	−31.4037			−1.18610			−0.593051	+	0.805165i	$0.702077\pi$
$702$	16.0790	−	9.61583i	0.606865	−	0.362926i
$703$	−8.73608	+	15.1313i	−0.329487	+	0.570689i
$704$	−4.65127	+	1.24631i	−0.175301	+	0.0469719i
$705$	13.4177	+	19.6412i	0.505338	+	0.739731i
$706$		−	13.4851i		−	0.507519i
$707$	2.98145	+	2.25776i	0.112129	+	0.0849117i
$708$	−15.2688	−	13.1154i	−0.573837	−	0.492908i
$709$	0.730801	−	2.72739i	0.0274458	−	0.102429i	−0.950844	−	0.309670i	$-0.899782\pi$
$709$	0.730801	−	2.72739i	0.0274458	−	0.102429i	0.978290	+	0.207240i	$0.0664482\pi$
$710$	−0.462739	−	1.72696i	−0.0173663	−	0.0648118i
$711$	−5.50861	+	14.1121i	−0.206589	+	0.529244i
$712$	3.60132	−	2.07922i	0.134965	−	0.0779222i
$713$	13.6934	−	13.6934i	0.512822	−	0.512822i
$714$	−7.08081	−	32.7416i	−0.264993	−	1.22533i
$715$	12.4891	+	19.3308i	0.467068	+	0.722932i
$716$	22.1972	−	12.8156i	0.829549	−	0.478940i
$717$	−32.3622	+	11.3575i	−1.20859	+	0.424152i
$718$	8.37354	−	14.5034i	0.312498	−	0.541262i
$719$	7.49673	+	12.9847i	0.279581	+	0.484248i	0.971281	−	0.237937i	$-0.0764711\pi$
$719$	7.49673	+	12.9847i	0.279581	+	0.484248i	−0.691700	+	0.722185i	$0.743138\pi$
$720$	3.20396	+	2.35553i	0.119405	+	0.0877855i
$721$	−8.34192	−	19.7822i	−0.310669	−	0.736728i
$722$	12.7320	−	12.7320i	0.473835	−	0.473835i
$723$	1.24902	−	6.63465i	0.0464514	−	0.246745i
$724$	11.9797	−	20.7494i	0.445221	−	0.771146i
$725$	9.40925	−	16.2973i	0.349451	−	0.605266i
$726$	−20.7452	−	3.90542i	−0.769926	−	0.144944i
$727$		−	14.1425i		−	0.524516i	−0.964998	−	0.262258i	$-0.915533\pi$
$727$		−	14.1425i		−	0.524516i	0.964998	−	0.262258i	$-0.0844671\pi$
$728$	−3.14819	+	9.00494i	−0.116680	+	0.333745i
$729$	24.2611	−	11.8491i	0.898558	−	0.438855i
$730$	4.77999	+	1.28080i	0.176915	+	0.0474044i
$731$	−34.2728	−	19.7874i	−1.26763	−	0.731864i
$732$	17.2088	+	8.26779i	0.636054	+	0.305586i
$733$	11.5408	+	3.09236i	0.426270	+	0.114219i	0.465575	−	0.885009i	$-0.345848\pi$
$733$	11.5408	+	3.09236i	0.426270	+	0.114219i	−0.0393047	+	0.999227i	$0.512514\pi$
$734$	17.3202	+	17.3202i	0.639301	+	0.639301i
$735$	9.23378	+	13.1541i	0.340593	+	0.485198i
$736$	3.09557	+	3.09557i	0.114104	+	0.114104i
$737$	−7.09356	+	4.09547i	−0.261295	+	0.150858i
$738$	0.213512	+	0.0833439i	0.00785949	+	0.00306793i
$739$	35.9046	−	9.62061i	1.32077	−	0.353900i	0.471505	−	0.881863i	$-0.343711\pi$
$739$	35.9046	−	9.62061i	1.32077	−	0.353900i	0.849267	+	0.527963i	$0.177044\pi$
$740$	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	$0.829558\pi$
$744$	−6.32649	+	4.32187i	−0.231941	+	0.158447i
$745$	−14.6747	−	8.47243i	−0.537639	−	0.310406i
$746$	20.0170	−	5.36355i	0.732876	−	0.196374i
$747$	3.37313	−	30.4411i	0.123416	−	1.11378i
$748$	24.8903	+	24.8903i	0.910079	+	0.910079i
$749$	−13.5385	−	32.1054i	−0.494684	−	1.17311i
$750$	−18.8709	+	1.43165i	−0.689068	+	0.0522766i
$751$	−0.261657	+	0.151068i	−0.00954800	+	0.00551254i	−0.504766	−	0.863256i	$-0.668421\pi$
$751$	−0.261657	+	0.151068i	−0.00954800	+	0.00551254i	0.495218	+	0.868769i	$0.335088\pi$
$752$	−2.68147	−	10.0074i	−0.0977831	−	0.364931i
$753$	17.0783	−	35.5471i	0.622367	−	1.29541i
$754$	−6.41881	−	19.9140i	−0.233759	−	0.725227i
$755$		−	15.4607i		−	0.562672i
$756$	−5.61800	+	12.5474i	−0.204325	+	0.456346i
$757$	−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
$759$	12.0911	+	34.4527i	0.438881	+	1.25055i
$760$	−2.08703	−	7.78891i	−0.0757046	−	0.282533i
$761$	−5.67340	−	1.52018i	−0.205661	−	0.0551066i	0.154518	−	0.987990i	$-0.450618\pi$
$761$	−5.67340	−	1.52018i	−0.205661	−	0.0551066i	−0.360179	+	0.932883i	$0.617284\pi$
$762$	11.8666	−	13.8149i	0.429881	−	0.500462i
$763$	−5.05418	+	0.698139i	−0.182974	+	0.0252743i
$764$	14.6473			0.529922
$765$	3.20154	−	28.8926i	0.115752	−	1.04461i
$766$	−10.5398	−	6.08516i	−0.380819	−	0.219866i
$767$	28.1100	−	31.0722i	1.01499	−	1.12195i
$768$	−0.977016	−	1.43019i	−0.0352550	−	0.0516075i
$769$	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
$772$	7.54971	+	2.02294i	0.271720	+	0.0728072i
$773$	−17.8037	+	4.77049i	−0.640355	+	0.171583i	−0.564364	−	0.825526i	$-0.690879\pi$
$773$	−17.8037	+	4.77049i	−0.640355	+	0.171583i	−0.0759910	+	0.997109i	$0.524212\pi$
$774$	6.52221	+	14.8743i	0.234436	+	0.534645i
$775$	3.71278	−	13.8563i	0.133367	−	0.497733i
$776$		−	14.4248i		−	0.517820i
$777$	−9.75000	+	8.84170i	−0.349779	+	0.317194i
$778$	−2.05735	−	2.05735i	−0.0737597	−	0.0737597i
$779$	−0.232382	−	0.402497i	−0.00832594	−	0.0144210i
$780$	−5.07326	+	6.54133i	−0.181652	+	0.234217i
$781$	−3.24743	+	5.62471i	−0.116202	+	0.201268i
$782$	8.28264	−	30.9112i	0.296187	−	1.10538i
$783$	−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
$786$	17.5268	+	3.29954i	0.625161	+	0.117691i
$787$	41.6490	−	11.1598i	1.48463	−	0.397805i	0.576708	−	0.816950i	$-0.304337\pi$
$787$	41.6490	−	11.1598i	1.48463	−	0.397805i	0.907919	+	0.419146i	$0.137670\pi$
$788$	−0.639677	−	2.38731i	−0.0227876	−	0.0850443i
$789$	11.2411	−	7.67923i	0.400194	−	0.273388i
$790$		−	6.69367i		−	0.238150i
$791$	38.9117	+	4.87115i	1.38354	+	0.173198i
$792$	−2.17938	−	14.2807i	−0.0774408	−	0.507443i
$793$	−18.1259	+	35.3686i	−0.643671	+	1.25598i
$794$	−9.60725	−	5.54675i	−0.340949	−	0.196847i
$795$	0.612769	+	1.74603i	0.0217327	+	0.0619254i
$796$	−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	$0.525868\pi$
$798$	24.7935	−	12.7438i	0.877679	−	0.451125i
$799$	−53.5523	+	53.5523i	−1.89454	+	1.89454i
$800$	3.13240	+	0.839324i	0.110747	+	0.0296746i
$801$	5.00984	+	11.4252i	0.177014	+	0.403690i
$802$	−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
$807$	11.5260	−	7.87387i	0.405736	−	0.277173i
$808$	−0.365849	−	1.36537i	−0.0128705	−	0.0480335i
$809$	14.4682	+	8.35324i	0.508676	+	0.293684i	0.732289	−	0.680994i	$-0.238452\pi$
$809$	14.4682	+	8.35324i	0.508676	+	0.293684i	−0.223613	+	0.974678i	$0.571785\pi$
$810$	−8.08221	+	8.77515i	−0.283980	+	0.308327i
$811$	−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	$0.434381\pi$
$812$	12.2398	+	9.26878i	0.429532	+	0.325270i
$813$	−2.72247	−	2.33851i	−0.0954812	−	0.0820153i
$814$	3.57962	−	13.3593i	0.125465	−	0.468243i
$815$	12.9892	+	7.49929i	0.454990	+	0.262689i
$816$	−5.48301	+	11.4125i	−0.191944	+	0.399516i
$817$	8.52380	−	31.8112i	0.298210	−	1.11293i
$818$	5.40021			0.188814
$819$	−25.8103	−	12.3624i	−0.901885	−	0.431976i
$820$	−0.101274			−0.00353663
$821$	10.9731	−	40.9521i	0.382964	−	1.42924i	−0.458389	−	0.888752i	$-0.651573\pi$
$821$	10.9731	−	40.9521i	0.382964	−	1.42924i	0.841352	−	0.540487i	$-0.181760\pi$
$822$	0.865490	−	1.80145i	0.0301874	−	0.0628328i
$823$	26.4559	+	15.2743i	0.922195	+	0.532429i	0.884335	−	0.466854i	$-0.154612\pi$
$823$	26.4559	+	15.2743i	0.922195	+	0.532429i	0.0378602	+	0.999283i	$0.487946\pi$
$824$	−2.10021	+	7.83807i	−0.0731641	+	0.273052i
$825$	20.5172	+	17.6237i	0.714319	+	0.613577i
$826$	−3.81919	+	30.5085i	−0.132887	+	1.06153i
$827$	−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	$0.364480\pi$
$828$	−10.2530	+	8.20744i	−0.356317	+	0.285228i
$829$	−9.11828	−	5.26444i	−0.316691	−	0.182842i	0.333226	−	0.942847i	$-0.391863\pi$
$829$	−9.11828	−	5.26444i	−0.316691	−	0.182842i	−0.649917	+	0.760005i	$0.725196\pi$
$830$	3.50255	+	13.0717i	0.121575	+	0.453725i
$831$	2.09814	−	1.43332i	0.0727836	−	0.0497212i
$832$	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
$837$	−10.7964	−	20.2920i	−0.373180	−	0.701394i
$838$	11.7568	+	3.15023i	0.406132	+	0.108823i
$839$	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	$0.125119\pi$
$840$	0.296415	−	6.06723i	0.0102273	−	0.209339i
$841$	−4.67466			−0.161195
$842$	−11.7282	−	20.3139i	−0.404182	−	0.700064i
$843$	11.7328	+	33.4316i	0.404098	+	1.15144i
$844$	9.93223	+	5.73438i	0.341882	+	0.197385i
$845$	−13.3409	−	10.9074i	−0.458941	−	0.375225i
$846$	30.7255	−	4.68900i	1.05636	−	0.161211i
$847$	12.5291	+	29.7118i	0.430505	+	1.02091i
$848$		−	0.805963i		−	0.0276769i
$849$	6.12872	−	4.18676i	0.210337	−	0.143689i
$850$	−6.13544	−	22.8978i	−0.210444	−	0.785388i
$851$	−12.1454	+	3.25435i	−0.416339	+	0.111558i
$852$	−2.29583	−	0.432205i	−0.0786537	−	0.0148071i
$853$	−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
$856$	−3.40851	+	12.7207i	−0.116501	+	0.434786i
$857$	4.79452	−	8.30436i	0.163778	−	0.283672i	−0.772443	−	0.635084i	$-0.780965\pi$
$857$	4.79452	−	8.30436i	0.163778	−	0.283672i	0.936221	+	0.351413i	$0.114299\pi$
$858$	29.8345	−	3.77106i	1.01853	−	0.128742i
$859$	23.0343	+	39.8966i	0.785921	+	1.36126i	0.928447	+	0.371465i	$0.121144\pi$
$859$	23.0343	+	39.8966i	0.785921	+	1.36126i	−0.142526	+	0.989791i	$0.545522\pi$
$860$	−5.07441	−	5.07441i	−0.173036	−	0.173036i
$861$	−0.0740055	−	0.342201i	−0.00252210	−	0.0116622i
$862$			35.1582i			1.19749i
$863$	10.3061	−	38.4629i	0.350824	−	1.30929i	−0.534836	−	0.844956i	$-0.679627\pi$
$863$	10.3061	−	38.4629i	0.350824	−	1.30929i	0.885660	−	0.464335i	$-0.153707\pi$
$864$	4.58727	−	2.44068i	0.156062	−	0.0830336i
$865$	−29.1718	+	7.81655i	−0.991870	+	0.265771i
$866$	−24.6003	−	6.59164i	−0.835953	−	0.223993i
$867$	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
$870$	7.51540	+	11.0013i	0.254796	+	0.372978i
$871$	4.11451	−	4.54810i	0.139415	−	0.154107i
$872$	1.67008	+	0.964219i	0.0565559	+	0.0326526i
$873$	43.0111	+	4.76599i	1.45571	+	0.161304i
$874$	26.6312			0.900814
$875$	17.7440	+	22.8223i	0.599858	+	0.771535i
$876$	4.21327	−	4.90504i	0.142353	−	0.165726i
$877$	35.6746	+	9.55898i	1.20465	+	0.322784i	0.804659	−	0.593737i	$-0.202348\pi$
$877$	35.6746	+	9.55898i	1.20465	+	0.322784i	0.399986	+	0.916521i	$0.369015\pi$
$878$	−2.72696	−	10.1772i	−0.0920305	−	0.343462i
$879$	5.10324	+	14.5413i	0.172128	+	0.490464i
$880$	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	$0.313770\pi$
$882$	20.7177	−	3.43204i	0.697600	−	0.115563i
$883$		−	12.5343i		−	0.421812i	−0.977506	−	0.210906i	$-0.932359\pi$
$883$		−	12.5343i		−	0.421812i	0.977506	−	0.210906i	$-0.0676413\pi$
$884$	−23.4557	−	12.0207i	−0.788900	−	0.404301i
$885$	−11.5544	+	24.0497i	−0.388398	+	0.808421i
$886$	−0.00830577	−	0.0309976i	−0.000279038	−	0.00104138i
$887$	−26.8558	+	15.5052i	−0.901729	+	0.520613i	−0.877761	−	0.479099i	$-0.840963\pi$
$887$	−26.8558	+	15.5052i	−0.901729	+	0.520613i	−0.0239682	+	0.999713i	$0.507630\pi$
$888$	4.96051	−	0.376333i	0.166464	−	0.0126289i
$889$	−27.6035	−	3.45553i	−0.925791	−	0.115895i
$890$	−3.89775	−	3.89775i	−0.130653	−	0.130653i
$891$	43.3016	−	1.77997i	1.45066	−	0.0596312i
$892$	−3.29607	+	0.883179i	−0.110361	+	0.0295710i
$893$	−54.5810	−	31.5123i	−1.82648	−	1.05452i
$894$	−18.2824	+	12.4894i	−0.611454	+	0.417708i
$895$	−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
$899$	−24.7951	+	6.64382i	−0.826962	+	0.221584i
$900$	−3.53761	+	9.06272i	−0.117920	+	0.302091i
$901$	−5.10226	+	2.94579i	−0.169981	+	0.0981385i
$902$	0.260142	+	0.260142i	0.00866179	+	0.00866179i
$903$	13.4382	−	20.8545i	0.447196	−	0.693993i
$904$	−10.4808	−	10.4808i	−0.348585	−	0.348585i
$905$	−30.6773	−	8.21997i	−1.01975	−	0.273241i
$906$	−18.2093	−	8.74848i	−0.604963	−	0.290649i
$907$	−33.1954	−	19.1654i	−1.10224	−	0.636377i	−0.165429	−	0.986222i	$-0.552901\pi$
$907$	−33.1954	−	19.1654i	−1.10224	−	0.636377i	−0.936808	+	0.349845i	$0.886234\pi$
$908$	−17.5241	−	4.69557i	−0.581558	−	0.155828i
$909$	4.19206	−	0.639750i	0.139042	−	0.0212192i
$910$	12.6099	+	0.941497i	0.418015	+	0.0312103i
$911$			11.3113i			0.374759i	0.982288	+	0.187379i	$0.0599994\pi$
$911$			11.3113i			0.374759i	−0.982288	+	0.187379i	$0.940001\pi$
$912$	−10.3546	−	1.94932i	−0.342874	−	0.0645484i
$913$	24.5803	−	42.5744i	0.813490	−	1.40901i
$914$	9.17839	−	15.8974i	0.303594	−	0.525840i
$915$	4.68202	−	24.8704i	0.154783	−	0.822191i
$916$	−12.4251	+	12.4251i	−0.410536	+	0.410536i
$917$	−10.5854	−	25.1024i	−0.349560	−	0.828954i
$918$	−32.2175	−	20.1197i	−1.06334	−	0.664048i
$919$	−2.71176	−	4.69690i	−0.0894526	−	0.154936i	0.817827	−	0.575464i	$-0.195178\pi$
$919$	−2.71176	−	4.69690i	−0.0894526	−	0.154936i	−0.907280	+	0.420527i	$0.861845\pi$
$920$	2.90151	−	5.02557i	0.0956601	−	0.165688i
$921$	26.7544	−	9.38941i	0.881586	−	0.309392i
$922$	26.3843	−	15.2330i	0.868921	−	0.501672i
$923$	1.02226	−	4.75444i	0.0336481	−	0.156494i
$924$	−16.3463	+	14.8235i	−0.537755	+	0.487659i
$925$	−6.58613	+	6.58613i	−0.216551	+	0.216551i
$926$	−17.0859	+	9.86452i	−0.561476	+	0.324168i
$927$	−22.6773	−	8.85201i	−0.744819	−	0.290738i
$928$	−1.50192	−	5.60525i	−0.0493031	−	0.184002i
$929$	−3.10632	+	11.5930i	−0.101915	+	0.380353i	−0.997977	−	0.0635768i	$-0.979749\pi$
$929$	−3.10632	+	11.5930i	−0.101915	+	0.380353i	0.896062	+	0.443929i	$0.146416\pi$
$930$	7.70417	+	6.61764i	0.252630	+	0.217001i
$931$	−37.1456	−	20.8203i	−1.21740	−	0.682358i
$932$			3.45439i			0.113152i
$933$	−18.5162	−	27.1047i	−0.606194	−	0.887367i
$934$	19.6597	−	5.26781i	0.643286	−	0.172368i
$935$	23.3299	−	40.4086i	0.762970	−	1.32150i
$936$	4.83353	+	9.67662i	0.157989	+	0.316290i
$937$	−18.6777			−0.610172			−0.305086	−	0.952325i	$-0.598685\pi$
$937$	−18.6777			−0.610172			−0.305086	+	0.952325i	$0.598685\pi$
$938$	−0.559022	+	4.46558i	−0.0182527	+	0.145806i
$939$	−35.8669	+	2.72107i	−1.17047	+	0.0887988i
$940$	−11.8934	+	6.86665i	−0.387919	+	0.223965i
$941$	−34.1863	+	9.16020i	−1.11444	+	0.298614i	−0.768633	−	0.639691i	$-0.779062\pi$
$941$	−34.1863	+	9.16020i	−1.11444	+	0.298614i	−0.345810	+	0.938305i	$0.612396\pi$
$942$	11.1492	−	3.91279i	0.363260	−	0.127486i
$943$	0.0865666	−	0.323071i	0.00281899	−	0.0105206i
$944$	8.21737	−	8.21737i	0.267453	−	0.267453i
$945$	17.9930	+	2.88846i	0.585313	+	0.0939618i
$946$			26.0694i			0.847588i
$947$	−39.0187	−	10.4550i	−1.26794	−	0.339743i	−0.438697	−	0.898635i	$-0.644560\pi$
$947$	−39.0187	−	10.4550i	−1.26794	−	0.339743i	−0.829240	+	0.558892i	$0.811227\pi$
$948$	−7.88367	−	3.78763i	−0.256050	−	0.123017i
$949$	9.98182	+	9.03020i	0.324024	+	0.293133i
$950$	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	$0.462016\pi$
$954$	2.40318	+	0.266293i	0.0778059	+	0.00862154i
$955$	−5.02520	−	18.7543i	−0.162612	−	0.606875i
$956$	−5.12501	−	19.1268i	−0.165755	−	0.618605i
$957$	8.95423	−	47.5639i	0.289449	−	1.53752i
$958$	−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
$962$	0.517698	+	10.3429i	0.0166912	+	0.333467i
$963$	−36.8039	−	14.3663i	−1.18599	−	0.462948i
$964$	3.76499	+	1.00883i	0.121262	+	0.0324921i
$965$		−	10.3606i		−	0.333520i
$966$	19.1016	+	6.13173i	0.614583	+	0.197285i
$967$	−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	$0.391194\pi$
$968$	3.15439	−	11.7723i	0.101386	−	0.378378i
$969$	25.5055	+	72.6758i	0.819355	+	2.33468i
$970$	−18.4694	+	4.94885i	−0.593016	+	0.158898i
$971$	−44.4767	+	25.6786i	−1.42733	+	0.824067i	−0.996909	−	0.0785637i	$-0.974967\pi$
$971$	−44.4767	+	25.6786i	−1.42733	+	0.824067i	−0.430416	+	0.902630i	$0.641633\pi$
$972$	5.76185	+	14.4845i	0.184811	+	0.464591i
$973$	4.75003	−	37.9442i	0.152279	−	1.21644i
$974$	3.13106			0.100326
$975$	−18.6700	−	7.84664i	−0.597919	−	0.251294i
$976$	−5.51133	+	9.54591i	−0.176413	+	0.305557i
$977$	28.4411	−	7.62077i	0.909911	−	0.243810i	0.226643	−	0.973978i	$-0.427225\pi$
$977$	28.4411	−	7.62077i	0.909911	−	0.243810i	0.683268	+	0.730168i	$0.260558\pi$
$978$	16.1825	−	11.0549i	0.517459	−	0.353496i
$979$			20.0244i			0.639982i
$980$	−7.97608	+	4.74133i	−0.254786	+	0.151456i
$981$	−3.42686	+	4.66117i	−0.109411	+	0.148820i
$982$	−11.0704	+	41.3153i	−0.353270	+	1.31842i
$983$	−3.92777	−	14.6586i	−0.125276	−	0.467538i	0.874573	−	0.484894i	$-0.161142\pi$
$983$	−3.92777	−	14.6586i	−0.125276	−	0.467538i	−0.999849	+	0.0173559i	$0.994475\pi$
$984$	−0.0573060	+	0.119278i	−0.00182685	+	0.00380244i
$985$	−2.83722	+	1.63807i	−0.0904015	+	0.0521933i
$986$	−29.9953	+	29.9953i	−0.955245	+	0.955245i
$987$	−31.8933	−	35.1697i	−1.01518	−	1.11946i
$988$	4.61057	−	21.4433i	0.146682	−	0.682204i
$989$	20.5253	−	11.8503i	0.652666	−	0.376817i
$990$	−17.5372	+	7.68987i	−0.557369	+	0.244400i
$991$	−10.1600	+	17.5976i	−0.322742	+	0.559006i	−0.981053	−	0.193741i	$-0.937938\pi$
$991$	−10.1600	+	17.5976i	−0.322742	+	0.559006i	0.658311	+	0.752746i	$0.271271\pi$
$992$	−2.21177	−	3.83090i	−0.0702237	−	0.121631i
$993$	−1.49868	+	1.74474i	−0.0475592	+	0.0553678i
$994$	1.38657	+	3.28814i	0.0439793	+	0.104294i
$995$	−20.0761	+	20.0761i	−0.636457	+	0.636457i
$996$	17.3775	+	3.27143i	0.550627	+	0.103659i
$997$	5.75201	−	9.96277i	0.182168	−	0.315524i	−0.760451	−	0.649396i	$-0.775022\pi$
$997$	5.75201	−	9.96277i	0.182168	−	0.315524i	0.942619	+	0.333872i	$0.108355\pi$
$998$	−7.52772	+	13.0384i	−0.238286	+	0.412723i
$999$	−0.516837	+	14.9153i	−0.0163520	+	0.471901i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.6	✓	144	7.2	even	3	inner
546.2.bv.a.317.26	yes	144	21.2	odd	6	inner
546.2.bv.a.359.6	yes	144	91.86	odd	12	inner
546.2.bv.a.359.26	yes	144	273.86	even	12	inner
546.2.bv.a.473.6	yes	144	3.2	odd	2	inner
546.2.bv.a.473.26	yes	144	1.1	even	1	trivial
546.2.bv.a.515.6	yes	144	39.8	even	4	inner
546.2.bv.a.515.26	yes	144	13.8	odd	4	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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.750071 + 1.56122i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.343079 + 1.28039i) q^{5} +(1.31389 + 1.12859i) q^{6} +(0.328643 - 2.62526i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.87479 - 2.34205i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.750071 + 1.56122i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.343079 + 1.28039i) q^{5} +(1.31389 + 1.12859i) q^{6} +(0.328643 - 2.62526i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.87479 - 2.34205i) q^{9} +(1.14797 + 0.662779i) q^{10} +(-1.24631 - 4.65127i) q^{11} +(1.43019 - 0.977016i) 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} +(-2.74747 + 1.20474i) q^{18} +(5.87595 + 1.57446i) q^{19} +(0.937311 - 0.937311i) q^{20} +(3.85209 + 2.48221i) q^{21} -4.81535 q^{22} +(2.18890 + 3.79129i) q^{23} +(-0.573565 - 1.63433i) q^{24} +(2.80843 + 1.62145i) q^{25} +(3.43169 - 1.10612i) q^{26} +(5.06266 - 1.17024i) q^{27} +(-1.59724 + 2.10922i) q^{28} -5.80299i q^{29} +(-1.89580 + 1.29509i) q^{30} +(-1.14490 - 4.27281i) q^{31} +(0.965926 - 0.258819i) q^{32} +(8.19646 + 1.54304i) q^{33} +(-5.16894 - 5.16894i) q^{34} +(3.24861 + 1.32146i) q^{35} +(0.452589 + 2.96566i) q^{36} +(-0.743375 + 2.77431i) q^{37} +(3.04162 - 5.26823i) q^{38} +(-6.19570 + 0.783132i) q^{39} +(-0.662779 - 1.14797i) q^{40} +(-0.0540235 - 0.0540235i) q^{41} +(3.39463 - 3.07839i) q^{42} -5.41380i q^{43} +(-1.24631 + 4.65127i) q^{44} +(3.64193 - 1.59695i) q^{45} +(4.22863 - 1.13306i) q^{46} +(-10.0074 - 2.68147i) q^{47} +(-1.72709 + 0.131027i) q^{48} +(-6.78399 - 1.72554i) q^{49} +(2.29307 - 2.29307i) q^{50} +(7.14197 + 10.4547i) q^{51} +(-0.180245 - 3.60104i) q^{52} +(-0.697985 - 0.402982i) q^{53} +(0.179946 - 5.19304i) q^{54} +6.38303 q^{55} +(1.62395 + 2.08873i) q^{56} +(-6.86545 + 7.99267i) q^{57} +(-5.60525 - 1.50192i) q^{58} +(-3.00777 - 11.2251i) q^{59} +(0.760294 + 2.16639i) q^{60} +(5.51133 + 9.54591i) q^{61} -4.42354 q^{62} +(-6.76462 + 4.15211i) q^{63} -1.00000i q^{64} +(-4.54890 + 1.46623i) q^{65} +(3.61186 - 7.51780i) q^{66} +(-0.440252 - 1.64304i) q^{67} +(-6.33063 + 3.65499i) q^{68} +(-7.56085 + 0.573609i) q^{69} +(2.11724 - 2.79589i) q^{70} +(-0.953731 - 0.953731i) q^{71} +(2.98175 + 0.330403i) q^{72} +(3.60603 - 0.966231i) q^{73} +(2.48738 + 1.43609i) q^{74} +(-4.63796 + 3.16836i) 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} +(-1.28039 + 0.343079i) q^{80} +(-1.97036 + 8.78167i) q^{81} +(-0.0661650 + 0.0382004i) q^{82} +(7.21896 + 7.21896i) q^{83} +(-2.09490 - 4.07571i) q^{84} +(6.85173 + 6.85173i) q^{85} +(-5.22933 - 1.40120i) q^{86} +(9.05971 + 4.35265i) q^{87} +(4.17022 + 2.40768i) q^{88} +(-4.01675 - 1.07628i) q^{89} +(-0.599933 - 3.93116i) q^{90} +(8.59356 - 4.14135i) q^{91} -4.37780i q^{92} +(7.52953 + 1.41748i) q^{93} +(-5.18020 + 8.97237i) q^{94} +(-4.03184 + 6.98335i) q^{95} +(-0.320441 + 1.70215i) q^{96} +(-10.1999 + 10.1999i) q^{97} +(-3.42257 + 6.10623i) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more