LMFDB - Embedded newform 798.2.bo.d.757.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(43,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 16])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.43"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bo (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,9,0,6,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 18x^{10} + 153x^{8} - 773x^{6} + 2448x^{4} - 4608x^{2} + 4096 $ x^12 - 18x^10 + 153x^8 - 773x^6 + 2448x^4 - 4608*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			757.1
Root			$-1.97054 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	798.757
Dual form			798.2.bo.d.253.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.445049 + 2.52400i) q^{5} +(0.939693 + 0.342020i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +(1.96332 - 1.64742i) q^{10} +(1.61870 - 2.80367i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.978745 + 0.356234i) q^{13} +(0.173648 - 0.984808i) q^{14} +(-0.445049 - 2.52400i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(2.18496 + 1.83340i) q^{17} -1.00000 q^{18} +(3.33675 + 2.80465i) q^{19} -2.56293 q^{20} +(-0.766044 - 0.642788i) q^{21} +(-3.04216 + 1.10725i) q^{22} +(-0.790485 - 4.48306i) q^{23} +(-0.173648 + 0.984808i) q^{24} +(-1.47403 - 0.536505i) q^{25} +(-0.520779 - 0.902016i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(-0.766044 + 0.642788i) q^{28} +(-5.24556 + 4.40154i) q^{29} +(-1.28147 + 2.21957i) q^{30} +(3.84254 + 6.65548i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.562168 + 3.18821i) q^{33} +(-0.495290 - 2.80893i) q^{34} +(-2.40837 + 0.876575i) q^{35} +(0.766044 + 0.642788i) q^{36} -4.63444 q^{37} +(-0.753306 - 4.29331i) q^{38} -1.04156 q^{39} +(1.96332 + 1.64742i) q^{40} +(-11.4218 + 4.15721i) q^{41} +(0.173648 + 0.984808i) q^{42} +(-1.84905 + 10.4865i) q^{43} +(3.04216 + 1.10725i) q^{44} +(1.28147 + 2.21957i) q^{45} +(-2.27611 + 3.94234i) q^{46} +(3.25325 - 2.72980i) q^{47} +(0.766044 - 0.642788i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.784317 + 1.35848i) q^{50} +(-2.68025 - 0.975530i) q^{51} +(-0.180865 + 1.02574i) q^{52} +(0.0500955 + 0.284105i) q^{53} +(0.939693 - 0.342020i) q^{54} +(6.35605 + 5.33336i) q^{55} +1.00000 q^{56} +(-4.09477 - 1.49427i) q^{57} +6.84759 q^{58} +(0.251567 + 0.211090i) q^{59} +(2.40837 - 0.876575i) q^{60} +(0.222796 + 1.26354i) q^{61} +(1.33450 - 7.56833i) q^{62} +(0.939693 + 0.342020i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.33472 + 2.31181i) q^{65} +(2.47999 - 2.08096i) q^{66} +(0.0419464 - 0.0351972i) q^{67} +(-1.42613 + 2.47013i) q^{68} +(2.27611 + 3.94234i) q^{69} +(2.40837 + 0.876575i) q^{70} +(-2.56814 + 14.5647i) q^{71} +(-0.173648 - 0.984808i) q^{72} +(13.8228 - 5.03110i) q^{73} +(3.55018 + 2.97896i) q^{74} +1.56863 q^{75} +(-2.18262 + 3.77308i) q^{76} +3.23739 q^{77} +(0.797880 + 0.669501i) q^{78} +(9.01160 - 3.27995i) q^{79} +(-0.445049 - 2.52400i) q^{80} +(0.173648 - 0.984808i) q^{81} +(11.4218 + 4.15721i) q^{82} +(-4.21663 - 7.30341i) q^{83} +(0.500000 - 0.866025i) q^{84} +(-5.59990 + 4.69888i) q^{85} +(8.15705 - 6.84458i) q^{86} +(3.42379 - 5.93019i) q^{87} +(-1.61870 - 2.80367i) q^{88} +(7.75125 + 2.82122i) q^{89} +(0.445049 - 2.52400i) q^{90} +(0.180865 + 1.02574i) q^{91} +(4.27769 - 1.55695i) q^{92} +(-5.88712 - 4.93988i) q^{93} -4.24681 q^{94} +(-8.56396 + 7.17375i) q^{95} -1.00000 q^{96} +(-0.638906 - 0.536106i) q^{97} +(0.939693 - 0.342020i) q^{98} +(-0.562168 - 3.18821i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 9 q^{5} + 6 q^{7} + 6 q^{8} + 9 q^{10} + 3 q^{11} - 6 q^{12} - 9 q^{13} + 9 q^{15} + 15 q^{17} - 12 q^{18} + 9 q^{19} - 15 q^{22} + 3 q^{23} + 3 q^{25} + 3 q^{26} - 6 q^{27} + 3 q^{29} + 6 q^{31}+ \cdots - 12 q^{99}+O(q^{100}) $ 12 * q + 9 * q^5 + 6 * q^7 + 6 * q^8 + 9 * q^10 + 3 * q^11 - 6 * q^12 - 9 * q^13 + 9 * q^15 + 15 * q^17 - 12 * q^18 + 9 * q^19 - 15 * q^22 + 3 * q^23 + 3 * q^25 + 3 * q^26 - 6 * q^27 + 3 * q^29 + 6 * q^31 - 12 * q^33 - 6 * q^34 - 9 * q^38 + 6 * q^39 + 9 * q^40 - 27 * q^41 + 6 * q^43 + 15 * q^44 - 15 * q^46 - 6 * q^47 - 6 * q^49 - 21 * q^51 + 9 * q^52 - 9 * q^53 - 9 * q^55 + 12 * q^56 - 18 * q^57 + 12 * q^58 - 24 * q^59 - 15 * q^61 - 24 * q^62 - 6 * q^64 - 24 * q^65 + 3 * q^66 + 33 * q^67 - 6 * q^68 + 15 * q^69 - 33 * q^71 + 33 * q^73 + 12 * q^74 + 9 * q^76 + 6 * q^77 + 33 * q^79 + 9 * q^80 + 27 * q^82 - 36 * q^83 + 6 * q^84 + 15 * q^85 - 6 * q^86 + 6 * q^87 - 3 * q^88 - 6 * q^89 - 9 * q^90 - 9 * q^91 + 3 * q^92 - 21 * q^93 - 18 * q^94 - 18 * q^95 - 12 * q^96 + 21 * q^97 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.445049	+	2.52400i	−0.199032	+	1.12877i	0.707527	+	0.706687i	$0.249811\pi$
$5$	−0.445049	+	2.52400i	−0.199032	+	1.12877i	−0.906559	+	0.422080i	$0.861300\pi$
$6$	0.939693	+	0.342020i	0.383628	+	0.139629i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$	1.96332	−	1.64742i	0.620857	−	0.520961i
$11$	1.61870	−	2.80367i	0.488056	−	0.845337i	−0.511850	−	0.859075i	$-0.671040\pi$
$11$	1.61870	−	2.80367i	0.488056	−	0.845337i	0.999906	+	0.0137378i	$0.00437301\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	0.978745	+	0.356234i	0.271455	+	0.0988015i	0.474161	−	0.880438i	$-0.342751\pi$
$13$	0.978745	+	0.356234i	0.271455	+	0.0988015i	−0.202706	+	0.979240i	$0.564974\pi$
$14$	0.173648	−	0.984808i	0.0464094	−	0.263201i
$15$	−0.445049	−	2.52400i	−0.114911	−	0.651694i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	2.18496	+	1.83340i	0.529930	+	0.444664i	0.868077	−	0.496429i	$-0.165356\pi$
$17$	2.18496	+	1.83340i	0.529930	+	0.444664i	−0.338147	+	0.941093i	$0.609800\pi$
$18$	−1.00000			−0.235702
$19$	3.33675	+	2.80465i	0.765504	+	0.643431i
$19$	3.33675	+	2.80465i	0.765504	+	0.643431i
$20$	−2.56293			−0.573090
$21$	−0.766044	−	0.642788i	−0.167165	−	0.140268i
$22$	−3.04216	+	1.10725i	−0.648590	+	0.236067i
$23$	−0.790485	−	4.48306i	−0.164828	−	0.934783i	−0.949242	−	0.314546i	$-0.898148\pi$
$23$	−0.790485	−	4.48306i	−0.164828	−	0.934783i	0.784415	−	0.620237i	$-0.212964\pi$
$24$	−0.173648	+	0.984808i	−0.0354458	+	0.201023i
$25$	−1.47403	−	0.536505i	−0.294807	−	0.107301i
$26$	−0.520779	−	0.902016i	−0.102133	−	0.176900i
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	−0.766044	+	0.642788i	−0.144769	+	0.121475i
$29$	−5.24556	+	4.40154i	−0.974075	+	0.817346i	−0.983185	−	0.182612i	$-0.941545\pi$
$29$	−5.24556	+	4.40154i	−0.974075	+	0.817346i	0.00910961	+	0.999959i	$0.497100\pi$
$30$	−1.28147	+	2.21957i	−0.233963	+	0.405236i
$31$	3.84254	+	6.65548i	0.690141	+	1.19536i	0.971791	+	0.235842i	$0.0757848\pi$
$31$	3.84254	+	6.65548i	0.690141	+	1.19536i	−0.281650	+	0.959517i	$0.590882\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	−0.562168	+	3.18821i	−0.0978608	+	0.554996i
$34$	−0.495290	−	2.80893i	−0.0849415	−	0.481727i
$35$	−2.40837	+	0.876575i	−0.407089	+	0.148168i
$36$	0.766044	+	0.642788i	0.127674	+	0.107131i
$37$	−4.63444			−0.761896			−0.380948	−	0.924596i	$-0.624402\pi$
$37$	−4.63444			−0.761896			−0.380948	+	0.924596i	$0.624402\pi$
$38$	−0.753306	−	4.29331i	−0.122202	−	0.696467i
$39$	−1.04156			−0.166783
$40$	1.96332	+	1.64742i	0.310428	+	0.260480i
$41$	−11.4218	+	4.15721i	−1.78379	+	0.649247i	−0.784204	+	0.620503i	$0.786928\pi$
$41$	−11.4218	+	4.15721i	−1.78379	+	0.649247i	−0.999587	+	0.0287431i	$0.990850\pi$
$42$	0.173648	+	0.984808i	0.0267945	+	0.151959i
$43$	−1.84905	+	10.4865i	−0.281978	+	1.59918i	0.433906	+	0.900958i	$0.357135\pi$
$43$	−1.84905	+	10.4865i	−0.281978	+	1.59918i	−0.715884	+	0.698219i	$0.753976\pi$
$44$	3.04216	+	1.10725i	0.458622	+	0.166925i
$45$	1.28147	+	2.21957i	0.191030	+	0.330873i
$46$	−2.27611	+	3.94234i	−0.335594	+	0.581266i
$47$	3.25325	−	2.72980i	0.474535	−	0.398182i	−0.373911	−	0.927465i	$-0.621983\pi$
$47$	3.25325	−	2.72980i	0.474535	−	0.398182i	0.848446	+	0.529283i	$0.177539\pi$
$48$	0.766044	−	0.642788i	0.110569	−	0.0927784i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	0.784317	+	1.35848i	0.110919	+	0.192118i
$51$	−2.68025	−	0.975530i	−0.375310	−	0.136602i
$52$	−0.180865	+	1.02574i	−0.0250814	+	0.142244i
$53$	0.0500955	+	0.284105i	0.00688114	+	0.0390249i	0.988055	−	0.154102i	$-0.0492483\pi$
$53$	0.0500955	+	0.284105i	0.00688114	+	0.0390249i	−0.981174	+	0.193127i	$0.938137\pi$
$54$	0.939693	−	0.342020i	0.127876	−	0.0465430i
$55$	6.35605	+	5.33336i	0.857049	+	0.719150i
$56$	1.00000			0.133631
$57$	−4.09477	−	1.49427i	−0.542366	−	0.197921i
$58$	6.84759			0.899132
$59$	0.251567	+	0.211090i	0.0327513	+	0.0274816i	0.659016	−	0.752129i	$-0.270973\pi$
$59$	0.251567	+	0.211090i	0.0327513	+	0.0274816i	−0.626265	+	0.779610i	$0.715417\pi$
$60$	2.40837	−	0.876575i	0.310919	−	0.113165i
$61$	0.222796	+	1.26354i	0.0285261	+	0.161780i	0.995743	−	0.0921717i	$-0.0293809\pi$
$61$	0.222796	+	1.26354i	0.0285261	+	0.161780i	−0.967217	+	0.253951i	$0.918270\pi$
$62$	1.33450	−	7.56833i	0.169482	−	0.961179i
$63$	0.939693	+	0.342020i	0.118390	+	0.0430905i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−1.33472	+	2.31181i	−0.165552	+	0.286745i
$66$	2.47999	−	2.08096i	0.305265	−	0.256148i
$67$	0.0419464	−	0.0351972i	0.00512457	−	0.00430003i	−0.640222	−	0.768190i	$-0.721158\pi$
$67$	0.0419464	−	0.0351972i	0.00512457	−	0.00430003i	0.645346	+	0.763890i	$0.276713\pi$
$68$	−1.42613	+	2.47013i	−0.172944	+	0.299547i
$69$	2.27611	+	3.94234i	0.274012	+	0.474602i
$70$	2.40837	+	0.876575i	0.287855	+	0.104771i
$71$	−2.56814	+	14.5647i	−0.304782	+	1.72851i	0.319745	+	0.947504i	$0.396403\pi$
$71$	−2.56814	+	14.5647i	−0.304782	+	1.72851i	−0.624528	+	0.781003i	$0.714708\pi$
$72$	−0.173648	−	0.984808i	−0.0204646	−	0.116061i
$73$	13.8228	−	5.03110i	1.61784	−	0.588845i	0.634870	−	0.772619i	$-0.281054\pi$
$73$	13.8228	−	5.03110i	1.61784	−	0.588845i	0.982969	+	0.183774i	$0.0588313\pi$
$74$	3.55018	+	2.97896i	0.412700	+	0.346297i
$75$	1.56863			0.181130
$76$	−2.18262	+	3.77308i	−0.250364	+	0.432802i
$77$	3.23739			0.368935
$78$	0.797880	+	0.669501i	0.0903421	+	0.0758061i
$79$	9.01160	−	3.27995i	1.01388	−	0.369024i	0.218961	−	0.975734i	$-0.429733\pi$
$79$	9.01160	−	3.27995i	1.01388	−	0.369024i	0.794923	+	0.606710i	$0.207511\pi$
$80$	−0.445049	−	2.52400i	−0.0497580	−	0.282192i
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$	11.4218	+	4.15721i	1.26133	+	0.459087i
$83$	−4.21663	−	7.30341i	−0.462835	−	0.801654i	0.536266	−	0.844049i	$-0.319834\pi$
$83$	−4.21663	−	7.30341i	−0.462835	−	0.801654i	−0.999101	+	0.0423953i	$0.986501\pi$
$84$	0.500000	−	0.866025i	0.0545545	−	0.0944911i
$85$	−5.59990	+	4.69888i	−0.607395	+	0.509665i
$86$	8.15705	−	6.84458i	0.879597	−	0.738070i
$87$	3.42379	−	5.93019i	0.367069	−	0.635783i
$88$	−1.61870	−	2.80367i	−0.172554	−	0.298872i
$89$	7.75125	+	2.82122i	0.821631	+	0.299049i	0.718419	−	0.695610i	$-0.244866\pi$
$89$	7.75125	+	2.82122i	0.821631	+	0.299049i	0.103211	+	0.994659i	$0.467088\pi$
$90$	0.445049	−	2.52400i	0.0469123	−	0.266053i
$91$	0.180865	+	1.02574i	0.0189598	+	0.107526i
$92$	4.27769	−	1.55695i	0.445980	−	0.162323i
$93$	−5.88712	−	4.93988i	−0.610465	−	0.512241i
$94$	−4.24681			−0.438026
$95$	−8.56396	+	7.17375i	−0.878643	+	0.736012i
$96$	−1.00000			−0.102062
$97$	−0.638906	−	0.536106i	−0.0648710	−	0.0544333i	0.609776	−	0.792574i	$-0.291260\pi$
$97$	−0.638906	−	0.536106i	−0.0648710	−	0.0544333i	−0.674647	+	0.738141i	$0.735704\pi$
$98$	0.939693	−	0.342020i	0.0949233	−	0.0345493i
$99$	−0.562168	−	3.18821i	−0.0565000	−	0.320427i
$100$	0.272391	−	1.54480i	0.0272391	−	0.154480i
$101$	−17.0526	−	6.20663i	−1.69679	−	0.617583i	−0.701341	−	0.712826i	$-0.747415\pi$
$101$	−17.0526	−	6.20663i	−1.69679	−	0.617583i	−0.995454	+	0.0952433i	$0.969637\pi$
$102$	1.42613	+	2.47013i	0.141208	+	0.244579i
$103$	−7.20969	+	12.4875i	−0.710392	+	1.23043i	0.254318	+	0.967121i	$0.418149\pi$
$103$	−7.20969	+	12.4875i	−0.710392	+	1.23043i	−0.964710	+	0.263314i	$0.915184\pi$
$104$	0.797880	−	0.669501i	0.0782386	−	0.0656500i
$105$	1.96332	−	1.64742i	0.191601	−	0.160772i
$106$	0.144244	−	0.249838i	0.0140102	−	0.0242664i
$107$	−2.83282	−	4.90659i	−0.273859	−	0.474338i	0.695988	−	0.718054i	$-0.254967\pi$
$107$	−2.83282	−	4.90659i	−0.273859	−	0.474338i	−0.969847	+	0.243716i	$0.921633\pi$
$108$	−0.939693	−	0.342020i	−0.0904220	−	0.0329109i
$109$	−0.321734	+	1.82464i	−0.0308165	+	0.174769i	−0.996331	−	0.0855786i	$-0.972726\pi$
$109$	−0.321734	+	1.82464i	−0.0308165	+	0.174769i	0.965515	+	0.260348i	$0.0838372\pi$
$110$	−1.44080	−	8.17118i	−0.137375	−	0.779091i
$111$	4.35494	−	1.58507i	0.413353	−	0.150448i
$112$	−0.766044	−	0.642788i	−0.0723844	−	0.0607377i
$113$	1.34627			0.126646			0.0633231	−	0.997993i	$-0.479830\pi$
$113$	1.34627			0.126646			0.0633231	+	0.997993i	$0.479830\pi$
$114$	2.17628	+	3.77675i	0.203827	+	0.353725i
$115$	11.6670			1.08796
$116$	−5.24556	−	4.40154i	−0.487038	−	0.408673i
$117$	0.978745	−	0.356234i	0.0904850	−	0.0329338i
$118$	−0.0570257	−	0.323409i	−0.00524964	−	0.0297722i
$119$	−0.495290	+	2.80893i	−0.0454031	+	0.257494i
$120$	−2.40837	−	0.876575i	−0.219853	−	0.0800200i
$121$	0.259639	+	0.449708i	0.0236036	+	0.0408826i
$122$	0.641515	−	1.11114i	0.0580801	−	0.100598i
$123$	9.31116	−	7.81299i	0.839559	−	0.704474i
$124$	−5.88712	+	4.93988i	−0.528679	+	0.443614i
$125$	−4.39718	+	7.61614i	−0.393296	+	0.681209i
$126$	−0.500000	−	0.866025i	−0.0445435	−	0.0771517i
$127$	−6.10598	−	2.22240i	−0.541819	−	0.197206i	0.0565892	−	0.998398i	$-0.481977\pi$
$127$	−6.10598	−	2.22240i	−0.541819	−	0.197206i	−0.598408	+	0.801192i	$0.704200\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	−1.84905	−	10.4865i	−0.162800	−	0.923285i
$130$	2.50846	−	0.913005i	0.220006	−	0.0800758i
$131$	14.3796	+	12.0660i	1.25636	+	1.05421i	0.996060	+	0.0886780i	$0.0282642\pi$
$131$	14.3796	+	12.0660i	1.25636	+	1.05421i	0.260295	+	0.965529i	$0.416180\pi$
$132$	−3.23739			−0.281779
$133$	−0.760523	+	4.29204i	−0.0659457	+	0.372167i
$134$	−0.0547572			−0.00473030
$135$	−1.96332	−	1.64742i	−0.168976	−	0.141788i
$136$	2.68025	−	0.975530i	0.229829	−	0.0836510i
$137$	−1.70121	−	9.64801i	−0.145344	−	0.824286i	−0.967091	−	0.254433i	$-0.918111\pi$
$137$	−1.70121	−	9.64801i	−0.145344	−	0.824286i	0.821747	−	0.569853i	$-0.193000\pi$
$138$	0.790485	−	4.48306i	0.0672906	−	0.381624i
$139$	9.73237	+	3.54229i	0.825489	+	0.300453i	0.720006	−	0.693968i	$-0.244139\pi$
$139$	9.73237	+	3.54229i	0.825489	+	0.300453i	0.105483	+	0.994421i	$0.466361\pi$
$140$	−1.28147	−	2.21957i	−0.108304	−	0.187588i
$141$	−2.12341	+	3.67785i	−0.178823	+	0.309731i
$142$	11.3293	−	9.50640i	0.950733	−	0.797760i
$143$	2.58305	−	2.16744i	0.216006	−	0.181250i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−8.77496	−	15.1987i	−0.728721	−	1.26218i
$146$	−13.8228	−	5.03110i	−1.14398	−	0.416376i
$147$	0.173648	−	0.984808i	0.0143223	−	0.0812256i
$148$	−0.804761	−	4.56403i	−0.0661510	−	0.375161i
$149$	4.37389	−	1.59197i	0.358323	−	0.130419i	−0.156585	−	0.987665i	$-0.550048\pi$
$149$	4.37389	−	1.59197i	0.358323	−	0.130419i	0.514908	+	0.857246i	$0.327826\pi$
$150$	−1.20164	−	1.00830i	−0.0981138	−	0.0823273i
$151$	−8.28201			−0.673981			−0.336990	−	0.941508i	$-0.609409\pi$
$151$	−8.28201			−0.673981			−0.336990	+	0.941508i	$0.609409\pi$
$152$	4.09728	−	1.48739i	0.332333	−	0.120643i
$153$	2.85226			0.230592
$154$	−2.47999	−	2.08096i	−0.199843	−	0.167688i
$155$	−18.5085	+	6.73656i	−1.48664	+	0.541093i
$156$	−0.180865	−	1.02574i	−0.0144808	−	0.0821245i
$157$	−1.36850	+	7.76114i	−0.109218	+	0.619407i	0.880233	+	0.474541i	$0.157386\pi$
$157$	−1.36850	+	7.76114i	−0.109218	+	0.619407i	−0.989451	+	0.144865i	$0.953725\pi$
$158$	−9.01160	−	3.27995i	−0.716924	−	0.260939i
$159$	−0.144244	−	0.249838i	−0.0114393	−	0.0198135i
$160$	−1.28147	+	2.21957i	−0.101309	+	0.175472i
$161$	3.48720	−	2.92611i	0.274830	−	0.230610i
$162$	−0.766044	+	0.642788i	−0.0601861	+	0.0505022i
$163$	2.77994	−	4.81500i	0.217742	−	0.377140i	−0.736375	−	0.676573i	$-0.763464\pi$
$163$	2.77994	−	4.81500i	0.217742	−	0.377140i	0.954117	+	0.299433i	$0.0967976\pi$
$164$	−6.07743	−	10.5264i	−0.474568	−	0.821975i
$165$	−7.79685	−	2.83782i	−0.606984	−	0.220924i
$166$	−1.46442	+	8.30514i	−0.113661	+	0.644604i
$167$	−2.68485	−	15.2266i	−0.207760	−	1.17827i	−0.893037	−	0.449983i	$-0.851430\pi$
$167$	−2.68485	−	15.2266i	−0.207760	−	1.17827i	0.685277	−	0.728283i	$-0.259681\pi$
$168$	−0.939693	+	0.342020i	−0.0724989	+	0.0263874i
$169$	−9.12754	−	7.65891i	−0.702118	−	0.589147i
$170$	7.31016			0.560663
$171$	4.35890	+	0.00366395i	0.333333	+	0.000280190i
$172$	−10.6483			−0.811923
$173$	−7.59421	−	6.37230i	−0.577377	−	0.484477i	0.306707	−	0.951804i	$-0.400773\pi$
$173$	−7.59421	−	6.37230i	−0.577377	−	0.484477i	−0.884085	+	0.467327i	$0.845217\pi$
$174$	−6.43463	+	2.34201i	−0.487808	+	0.177548i
$175$	−0.272391	−	1.54480i	−0.0205908	−	0.116776i
$176$	−0.562168	+	3.18821i	−0.0423750	+	0.240320i
$177$	−0.308593	−	0.112319i	−0.0231953	−	0.00844238i
$178$	−4.12435	−	7.14359i	−0.309133	−	0.535435i
$179$	−0.264660	+	0.458404i	−0.0197816	+	0.0342628i	−0.875747	−	0.482771i	$-0.839630\pi$
$179$	−0.264660	+	0.458404i	−0.0197816	+	0.0342628i	0.855965	+	0.517034i	$0.172964\pi$
$180$	−1.96332	+	1.64742i	−0.146337	+	0.122792i
$181$	−1.10116	+	0.923983i	−0.0818486	+	0.0686791i	−0.682794	−	0.730611i	$-0.739235\pi$
$181$	−1.10116	+	0.923983i	−0.0818486	+	0.0686791i	0.600945	+	0.799290i	$0.294791\pi$
$182$	0.520779	−	0.902016i	0.0386027	−	0.0668619i
$183$	−0.641515	−	1.11114i	−0.0474222	−	0.0821376i
$184$	−4.27769	−	1.55695i	−0.315355	−	0.114780i
$185$	2.06255	−	11.6973i	0.151642	−	0.860003i
$186$	1.33450	+	7.56833i	0.0978503	+	0.554937i
$187$	8.67702	−	3.15818i	0.634526	−	0.230949i
$188$	3.25325	+	2.72980i	0.237268	+	0.199091i
$189$	−1.00000			−0.0727393
$190$	11.1716	+	0.00939047i	0.810471	+	0.000681257i
$191$	25.7249			1.86139			0.930693	−	0.365801i	$-0.119205\pi$
$191$	25.7249			1.86139			0.930693	+	0.365801i	$0.119205\pi$
$192$	0.766044	+	0.642788i	0.0552845	+	0.0463892i
$193$	−9.09242	+	3.30937i	−0.654486	+	0.238214i	−0.647854	−	0.761764i	$-0.724333\pi$
$193$	−9.09242	+	3.30937i	−0.654486	+	0.238214i	−0.00663229	+	0.999978i	$0.502111\pi$
$194$	0.144828	+	0.821361i	0.0103981	+	0.0589703i
$195$	0.463545	−	2.62889i	0.0331951	−	0.188259i
$196$	−0.939693	−	0.342020i	−0.0671209	−	0.0244300i
$197$	2.61989	+	4.53778i	0.186659	+	0.323304i	0.944134	−	0.329560i	$-0.106901\pi$
$197$	2.61989	+	4.53778i	0.186659	+	0.323304i	−0.757475	+	0.652864i	$0.773567\pi$
$198$	−1.61870	+	2.80367i	−0.115036	+	0.199248i
$199$	10.0188	−	8.40674i	0.710211	−	0.595938i	−0.214447	−	0.976736i	$-0.568795\pi$
$199$	10.0188	−	8.40674i	0.710211	−	0.595938i	0.924658	+	0.380797i	$0.124350\pi$
$200$	−1.20164	+	1.00830i	−0.0849691	+	0.0712975i
$201$	−0.0273786	+	0.0474211i	−0.00193114	+	0.00334483i
$202$	9.07349	+	15.7157i	0.638408	+	1.10576i
$203$	−6.43463	−	2.34201i	−0.451622	−	0.164377i
$204$	0.495290	−	2.80893i	0.0346772	−	0.196664i
$205$	−5.40951	−	30.6788i	−0.377816	−	2.14270i
$206$	13.5498	−	4.93172i	0.944058	−	0.343609i
$207$	−3.48720	−	2.92611i	−0.242377	−	0.203379i
$208$	−1.04156			−0.0722191
$209$	13.2645	−	4.81526i	0.917525	−	0.333079i
$210$	−2.56293			−0.176859
$211$	5.71686	+	4.79702i	0.393565	+	0.330240i	0.818000	−	0.575218i	$-0.195083\pi$
$211$	5.71686	+	4.79702i	0.393565	+	0.330240i	−0.424435	+	0.905458i	$0.639527\pi$
$212$	−0.271090	+	0.0986688i	−0.0186186	+	0.00677660i
$213$	−2.56814	−	14.5647i	−0.175966	−	0.997954i
$214$	−0.983828	+	5.57956i	−0.0672531	+	0.381411i
$215$	−25.6450	−	9.33401i	−1.74897	−	0.636574i
$216$	0.500000	+	0.866025i	0.0340207	+	0.0589256i
$217$	−3.84254	+	6.65548i	−0.260849	+	0.451803i
$218$	1.41932	−	1.19095i	0.0961286	−	0.0806615i
$219$	−11.2685	+	9.45537i	−0.761452	+	0.638934i
$220$	−4.14862	+	7.18561i	−0.279700	+	0.484454i
$221$	1.48540	+	2.57278i	0.0999187	+	0.173064i
$222$	−4.35494	−	1.58507i	−0.292285	−	0.106383i
$223$	0.267145	−	1.51506i	0.0178894	−	0.101456i	−0.974556	−	0.224146i	$-0.928041\pi$
$223$	0.267145	−	1.51506i	0.0178894	−	0.101456i	0.992445	+	0.122690i	$0.0391520\pi$
$224$	0.173648	+	0.984808i	0.0116024	+	0.0658002i
$225$	−1.47403	+	0.536505i	−0.0982690	+	0.0357670i
$226$	−1.03130	−	0.865365i	−0.0686011	−	0.0575632i
$227$	23.4065			1.55354			0.776772	−	0.629782i	$-0.216856\pi$
$227$	23.4065			1.55354			0.776772	+	0.629782i	$0.216856\pi$
$228$	0.760523	−	4.29204i	0.0503669	−	0.284247i
$229$	−24.9237			−1.64701			−0.823503	−	0.567312i	$-0.807983\pi$
$229$	−24.9237			−1.64701			−0.823503	+	0.567312i	$0.807983\pi$
$230$	−8.93748	−	7.49943i	−0.589320	−	0.494498i
$231$	−3.04216	+	1.10725i	−0.200159	+	0.0728520i
$232$	1.18907	+	6.74356i	0.0780663	+	0.442736i
$233$	−2.79269	+	15.8381i	−0.182955	+	1.03759i	0.745599	+	0.666394i	$0.232163\pi$
$233$	−2.79269	+	15.8381i	−0.182955	+	1.03759i	−0.928555	+	0.371196i	$0.878948\pi$
$234$	−0.978745	−	0.356234i	−0.0639826	−	0.0232877i
$235$	5.44215	+	9.42609i	0.355007	+	0.614890i
$236$	−0.164199	+	0.284401i	−0.0106884	+	0.0185129i
$237$	−7.34632	+	6.16430i	−0.477195	+	0.400414i
$238$	2.18496	−	1.83340i	0.141630	−	0.118841i
$239$	5.78753	−	10.0243i	0.374364	−	0.648418i	−0.615868	−	0.787850i	$-0.711194\pi$
$239$	5.78753	−	10.0243i	0.374364	−	0.648418i	0.990232	+	0.139432i	$0.0445277\pi$
$240$	1.28147	+	2.21957i	0.0827184	+	0.143272i
$241$	0.103308	+	0.0376010i	0.00665465	+	0.00242209i	0.345345	−	0.938476i	$-0.387762\pi$
$241$	0.103308	+	0.0376010i	0.00665465	+	0.00242209i	−0.338691	+	0.940898i	$0.609984\pi$
$242$	0.0901717	−	0.511389i	0.00579646	−	0.0328733i
$243$	0.173648	+	0.984808i	0.0111395	+	0.0631754i
$244$	−1.20565	+	0.438822i	−0.0771841	+	0.0280927i
$245$	−1.96332	−	1.64742i	−0.125432	−	0.105250i
$246$	−12.1549			−0.774966
$247$	2.26672	+	3.93370i	0.144228	+	0.250296i
$248$	7.68508			0.488003
$249$	6.46025	+	5.42079i	0.409402	+	0.343529i
$250$	8.26400	−	3.00785i	0.522661	−	0.190233i
$251$	3.53024	+	20.0210i	0.222827	+	1.26371i	0.866796	+	0.498663i	$0.166175\pi$
$251$	3.53024	+	20.0210i	0.222827	+	1.26371i	−0.643969	+	0.765051i	$0.722714\pi$
$252$	−0.173648	+	0.984808i	−0.0109388	+	0.0620371i
$253$	−13.8486	−	5.04047i	−0.870652	−	0.316891i
$254$	3.24893	+	5.62731i	0.203856	+	0.353089i
$255$	3.65508	−	6.33078i	0.228890	−	0.396449i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	14.6246	−	12.2715i	0.912258	−	0.765475i	−0.0602891	−	0.998181i	$-0.519202\pi$
$257$	14.6246	−	12.2715i	0.912258	−	0.765475i	0.972547	+	0.232705i	$0.0747578\pi$
$258$	−5.32414	+	9.22168i	−0.331466	+	0.574116i
$259$	−2.31722	−	4.01354i	−0.143985	−	0.249389i
$260$	−2.50846	−	0.913005i	−0.155568	−	0.0566221i
$261$	−1.18907	+	6.74356i	−0.0736017	+	0.417416i
$262$	−3.25960	−	18.4861i	−0.201379	−	1.14208i
$263$	18.2807	−	6.65362i	1.12724	−	0.410280i	0.289947	−	0.957043i	$-0.406362\pi$
$263$	18.2807	−	6.65362i	1.12724	−	0.410280i	0.837288	+	0.546763i	$0.184140\pi$
$264$	2.47999	+	2.08096i	0.152633	+	0.128074i
$265$	−0.739377			−0.0454195
$266$	3.34146	−	2.79904i	0.204878	−	0.171620i
$267$	−8.24871			−0.504813
$268$	0.0419464	+	0.0351972i	0.00256229	+	0.00215001i
$269$	18.4840	−	6.72762i	1.12699	−	0.410190i	0.289790	−	0.957090i	$-0.406414\pi$
$269$	18.4840	−	6.72762i	1.12699	−	0.410190i	0.837198	+	0.546900i	$0.184192\pi$
$270$	0.445049	+	2.52400i	0.0270848	+	0.153606i
$271$	0.112587	−	0.638512i	0.00683917	−	0.0387868i	−0.981197	−	0.193008i	$-0.938176\pi$
$271$	0.112587	−	0.638512i	0.00683917	−	0.0387868i	0.988036	+	0.154221i	$0.0492868\pi$
$272$	−2.68025	−	0.975530i	−0.162514	−	0.0591502i
$273$	−0.520779	−	0.902016i	−0.0315190	−	0.0545925i
$274$	−4.89843	+	8.48432i	−0.295925	+	0.512557i
$275$	−3.89020	+	3.26426i	−0.234588	+	0.196842i
$276$	−3.48720	+	2.92611i	−0.209905	+	0.176131i
$277$	12.4861	−	21.6266i	0.750217	−	1.29941i	−0.197500	−	0.980303i	$-0.563282\pi$
$277$	12.4861	−	21.6266i	0.750217	−	1.29941i	0.947717	−	0.319111i	$-0.103384\pi$
$278$	−5.17848	−	8.96940i	−0.310585	−	0.537949i
$279$	7.22162	+	2.62845i	0.432347	+	0.157361i
$280$	−0.445049	+	2.52400i	−0.0265968	+	0.150838i
$281$	1.42562	+	8.08510i	0.0850455	+	0.482317i	0.997347	+	0.0727972i	$0.0231926\pi$
$281$	1.42562	+	8.08510i	0.0850455	+	0.482317i	−0.912301	+	0.409520i	$0.865696\pi$
$282$	3.99070	−	1.45250i	0.237643	−	0.0864949i
$283$	−9.05500	−	7.59804i	−0.538264	−	0.451657i	0.332680	−	0.943040i	$-0.392047\pi$
$283$	−9.05500	−	7.59804i	−0.538264	−	0.451657i	−0.870944	+	0.491383i	$0.836492\pi$
$284$	−14.7893			−0.877586
$285$	5.59392	−	9.67017i	0.331355	−	0.572811i
$286$	−3.37194			−0.199387
$287$	−9.31116	−	7.81299i	−0.549621	−	0.461186i
$288$	0.939693	−	0.342020i	0.0553719	−	0.0201537i
$289$	−1.53932	−	8.72994i	−0.0905485	−	0.513526i
$290$	−3.04751	+	17.2833i	−0.178956	+	1.01491i
$291$	0.783734	+	0.285256i	0.0459433	+	0.0167220i
$292$	7.35497	+	12.7392i	0.430417	+	0.745504i
$293$	−11.4008	+	19.7468i	−0.666042	+	1.15362i	0.312960	+	0.949766i	$0.398679\pi$
$293$	−11.4008	+	19.7468i	−0.666042	+	1.15362i	−0.979002	+	0.203852i	$0.934654\pi$
$294$	−0.766044	+	0.642788i	−0.0446766	+	0.0374881i
$295$	−0.644750	+	0.541010i	−0.0375388	+	0.0314988i
$296$	−2.31722	+	4.01354i	−0.134686	+	0.233282i
$297$	1.61870	+	2.80367i	0.0939263	+	0.162685i
$298$	−4.37389	−	1.59197i	−0.253373	−	0.0922202i
$299$	0.823337	−	4.66937i	0.0476148	−	0.270037i
$300$	0.272391	+	1.54480i	0.0157265	+	0.0891893i
$301$	−10.0061	+	3.64192i	−0.576742	+	0.209917i
$302$	6.34439	+	5.32357i	0.365079	+	0.306337i
$303$	18.1470			1.04252
$304$	−4.09477	−	1.49427i	−0.234851	−	0.0857025i
$305$	−3.28832			−0.188289
$306$	−2.18496	−	1.83340i	−0.124906	−	0.104808i
$307$	20.6365	−	7.51107i	1.17779	−	0.428679i	0.322367	−	0.946615i	$-0.395522\pi$
$307$	20.6365	−	7.51107i	1.17779	−	0.428679i	0.855420	+	0.517936i	$0.173299\pi$
$308$	0.562168	+	3.18821i	0.0320325	+	0.181665i
$309$	2.50390	−	14.2003i	0.142442	−	0.807828i
$310$	18.5085	+	6.73656i	1.05121	+	0.382611i
$311$	7.33475	+	12.7042i	0.415915	+	0.720387i	0.995524	−	0.0945083i	$-0.0301279\pi$
$311$	7.33475	+	12.7042i	0.415915	+	0.720387i	−0.579609	+	0.814895i	$0.696795\pi$
$312$	−0.520779	+	0.902016i	−0.0294833	+	0.0510666i
$313$	1.24336	−	1.04330i	0.0702789	−	0.0589710i	−0.606972	−	0.794724i	$-0.707616\pi$
$313$	1.24336	−	1.04330i	0.0702789	−	0.0589710i	0.677250	+	0.735753i	$0.263171\pi$
$314$	6.03710	−	5.06573i	0.340693	−	0.285875i
$315$	−1.28147	+	2.21957i	−0.0722025	+	0.125058i
$316$	4.79497	+	8.30514i	0.269738	+	0.467200i
$317$	−20.3599	−	7.41038i	−1.14352	−	0.416209i	−0.300339	−	0.953832i	$-0.597100\pi$
$317$	−20.3599	−	7.41038i	−1.14352	−	0.416209i	−0.843185	+	0.537624i	$0.819322\pi$
$318$	−0.0500955	+	0.284105i	−0.00280921	+	0.0159318i
$319$	3.84949	+	21.8316i	0.215530	+	1.22233i
$320$	2.40837	−	0.876575i	0.134632	−	0.0490021i
$321$	4.34013	+	3.64180i	0.242242	+	0.203266i
$322$	−4.55222			−0.253685
$323$	2.14863	+	12.2456i	0.119553	+	0.681366i
$324$	1.00000			0.0555556
$325$	−1.25158	−	1.05020i	−0.0694253	−	0.0582548i
$326$	−5.22458	+	1.90159i	−0.289363	+	0.105319i
$327$	−0.321734	−	1.82464i	−0.0177919	−	0.100903i
$328$	−2.11067	+	11.9702i	−0.116542	+	0.660944i
$329$	3.99070	+	1.45250i	0.220014	+	0.0800787i
$330$	4.14862	+	7.18561i	0.228374	+	0.395555i
$331$	0.739531	−	1.28090i	0.0406483	−	0.0704049i	−0.844986	−	0.534789i	$-0.820391\pi$
$331$	0.739531	−	1.28090i	0.0406483	−	0.0704049i	0.885634	+	0.464384i	$0.153724\pi$
$332$	6.46025	−	5.42079i	0.354552	−	0.297505i
$333$	−3.55018	+	2.97896i	−0.194549	+	0.163246i
$334$	−7.73072	+	13.3900i	−0.423006	+	0.732668i
$335$	0.0701696	+	0.121537i	0.00383377	+	0.00664029i
$336$	0.939693	+	0.342020i	0.0512644	+	0.0186587i
$337$	5.19807	−	29.4797i	0.283157	−	1.60586i	−0.428638	−	0.903476i	$-0.641007\pi$
$337$	5.19807	−	29.4797i	0.283157	−	1.60586i	0.711795	−	0.702387i	$-0.247882\pi$
$338$	2.06905	+	11.7341i	0.112541	+	0.638253i
$339$	−1.26508	+	0.460451i	−0.0687096	+	0.0250083i
$340$	−5.59990	−	4.69888i	−0.303697	−	0.254832i
$341$	24.8796			1.34731
$342$	−3.33675	−	2.80465i	−0.180431	−	0.151658i
$343$	−1.00000			−0.0539949
$344$	8.15705	+	6.84458i	0.439799	+	0.369035i
$345$	−10.9634	+	3.99037i	−0.590252	+	0.214834i
$346$	1.72147	+	9.76293i	0.0925467	+	0.524859i
$347$	−2.64462	+	14.9984i	−0.141971	+	0.805155i	0.827779	+	0.561054i	$0.189604\pi$
$347$	−2.64462	+	14.9984i	−0.141971	+	0.805155i	−0.969750	+	0.244101i	$0.921507\pi$
$348$	6.43463	+	2.34201i	0.344932	+	0.125545i
$349$	12.0664	+	20.8996i	0.645898	+	1.11873i	0.984093	+	0.177652i	$0.0568500\pi$
$349$	12.0664	+	20.8996i	0.645898	+	1.11873i	−0.338196	+	0.941076i	$0.609817\pi$
$350$	−0.784317	+	1.35848i	−0.0419235	+	0.0726137i
$351$	−0.797880	+	0.669501i	−0.0425877	+	0.0357353i
$352$	2.47999	−	2.08096i	0.132184	−	0.110915i
$353$	12.6803	−	21.9629i	0.674903	−	1.16897i	−0.301595	−	0.953436i	$-0.597519\pi$
$353$	12.6803	−	21.9629i	0.674903	−	1.16897i	0.976497	−	0.215529i	$-0.0691477\pi$
$354$	0.164199	+	0.284401i	0.00872707	+	0.0151157i
$355$	−35.6182	−	12.9640i	−1.89042	−	0.688056i
$356$	−1.43237	+	8.12339i	−0.0759156	+	0.430539i
$357$	−0.495290	−	2.80893i	−0.0262135	−	0.148664i
$358$	0.497398	−	0.181038i	0.0262883	−	0.00956816i
$359$	−6.59150	−	5.53093i	−0.347886	−	0.291911i	0.452054	−	0.891990i	$-0.350691\pi$
$359$	−6.59150	−	5.53093i	−0.347886	−	0.291911i	−0.799941	+	0.600079i	$0.795136\pi$
$360$	2.56293			0.135079
$361$	3.26785	+	18.7169i	0.171992	+	0.985098i
$362$	1.43746			0.0755514
$363$	−0.397790	−	0.333786i	−0.0208786	−	0.0175192i
$364$	−0.978745	+	0.356234i	−0.0513002	+	0.0186717i
$365$	6.54664	+	37.1279i	0.342667	+	1.94336i
$366$	−0.222796	+	1.26354i	−0.0116457	+	0.0660462i
$367$	−19.6478	−	7.15123i	−1.02561	−	0.373291i	−0.226201	−	0.974081i	$-0.572631\pi$
$367$	−19.6478	−	7.15123i	−1.02561	−	0.373291i	−0.799407	+	0.600790i	$0.794853\pi$
$368$	2.27611	+	3.94234i	0.118650	+	0.205509i
$369$	−6.07743	+	10.5264i	−0.316378	+	0.547983i
$370$	−9.09889	+	7.63487i	−0.473029	+	0.396918i
$371$	−0.220995	+	0.185437i	−0.0114735	+	0.00962739i
$372$	3.84254	−	6.65548i	0.199227	−	0.345070i
$373$	−0.542849	−	0.940242i	−0.0281076	−	0.0486839i	0.851629	−	0.524144i	$-0.175615\pi$
$373$	−0.542849	−	0.940242i	−0.0281076	−	0.0486839i	−0.879737	+	0.475461i	$0.842281\pi$
$374$	−8.67702	−	3.15818i	−0.448678	−	0.163305i
$375$	1.52713	−	8.66076i	0.0788604	−	0.447240i
$376$	−0.737452	−	4.18230i	−0.0380312	−	0.215685i
$377$	−6.70204	+	2.43934i	−0.345173	+	0.125633i
$378$	0.766044	+	0.642788i	0.0394011	+	0.0330614i
$379$	36.5137			1.87559			0.937793	−	0.347196i	$-0.112866\pi$
$379$	36.5137			1.87559			0.937793	+	0.347196i	$0.112866\pi$
$380$	−8.55188	−	7.18814i	−0.438702	−	0.368744i
$381$	6.49785			0.332895
$382$	−19.7064	−	16.5356i	−1.00827	−	0.846036i
$383$	0.681077	−	0.247892i	0.0348014	−	0.0126667i	−0.324561	−	0.945865i	$-0.605216\pi$
$383$	0.681077	−	0.247892i	0.0348014	−	0.0126667i	0.359362	+	0.933198i	$0.382994\pi$
$384$	−0.173648	−	0.984808i	−0.00886145	−	0.0502558i
$385$	−1.44080	+	8.17118i	−0.0734299	+	0.416442i
$386$	9.09242	+	3.30937i	0.462792	+	0.168442i
$387$	5.32414	+	9.22168i	0.270641	+	0.468764i
$388$	0.417016	−	0.722293i	0.0211708	−	0.0366689i
$389$	−13.9730	+	11.7247i	−0.708459	+	0.594468i	−0.924166	−	0.381990i	$-0.875239\pi$
$389$	−13.9730	+	11.7247i	−0.708459	+	0.594468i	0.215707	+	0.976458i	$0.430794\pi$
$390$	−2.04491	+	1.71589i	−0.103548	+	0.0868873i
$391$	6.49206	−	11.2446i	0.328318	−	0.568663i
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$	−17.6392	−	6.42016i	−0.889782	−	0.323854i
$394$	0.909879	−	5.16018i	0.0458390	−	0.259966i
$395$	4.26800	+	24.2050i	0.214746	+	1.21789i
$396$	3.04216	−	1.10725i	0.152874	−	0.0556416i
$397$	19.0761	+	16.0068i	0.957404	+	0.803358i	0.980529	−	0.196375i	$-0.0629170\pi$
$397$	19.0761	+	16.0068i	0.957404	+	0.803358i	−0.0231245	+	0.999733i	$0.507361\pi$
$398$	−13.0786			−0.655569
$399$	−0.753306	−	4.29331i	−0.0377125	−	0.214934i
$400$	1.56863			0.0784317
$401$	−1.53815	−	1.29066i	−0.0768113	−	0.0644524i	0.603574	−	0.797307i	$-0.293743\pi$
$401$	−1.53815	−	1.29066i	−0.0768113	−	0.0644524i	−0.680385	+	0.732855i	$0.738187\pi$
$402$	0.0514549	−	0.0187281i	0.00256634	−	0.000934071i
$403$	1.38996	+	7.88286i	0.0692389	+	0.392673i
$404$	3.15119	−	17.8713i	0.156778	−	0.889129i
$405$	2.40837	+	0.876575i	0.119673	+	0.0435574i
$406$	3.42379	+	5.93019i	0.169920	+	0.294310i
$407$	−7.50175	+	12.9934i	−0.371848	+	0.644059i
$408$	−2.18496	+	1.83340i	−0.108172	+	0.0907667i
$409$	27.2457	−	22.8619i	1.34721	−	1.13045i	0.367505	−	0.930022i	$-0.380212\pi$
$409$	27.2457	−	22.8619i	1.34721	−	1.13045i	0.979709	−	0.200425i	$-0.0642323\pi$
$410$	−15.5761	+	26.9785i	−0.769247	+	1.33237i
$411$	4.89843	+	8.48432i	0.241622	+	0.418501i
$412$	−13.5498	−	4.93172i	−0.667550	−	0.242968i
$413$	−0.0570257	+	0.323409i	−0.00280605	+	0.0159139i
$414$	0.790485	+	4.48306i	0.0388502	+	0.220331i
$415$	20.3104	−	7.39238i	0.996999	−	0.362878i
$416$	0.797880	+	0.669501i	0.0391193	+	0.0328250i
$417$	−10.3570			−0.507183
$418$	−13.2564	−	4.83755i	−0.648391	−	0.236612i
$419$	12.7827			0.624474			0.312237	−	0.950004i	$-0.398922\pi$
$419$	12.7827			0.624474			0.312237	+	0.950004i	$0.398922\pi$
$420$	1.96332	+	1.64742i	0.0958003	+	0.0803860i
$421$	−21.0571	+	7.66415i	−1.02626	+	0.373528i	−0.799655	−	0.600459i	$-0.794984\pi$
$421$	−21.0571	+	7.66415i	−1.02626	+	0.373528i	−0.226604	+	0.973987i	$0.572762\pi$
$422$	−1.29591	−	7.34945i	−0.0630838	−	0.357766i
$423$	0.737452	−	4.18230i	0.0358561	−	0.203350i
$424$	0.271090	+	0.0986688i	0.0131653	+	0.00479178i
$425$	−2.23708	−	3.87473i	−0.108514	−	0.187952i
$426$	−7.39467	+	12.8079i	−0.358273	+	0.620547i
$427$	−0.982858	+	0.824716i	−0.0475638	+	0.0399108i
$428$	4.34013	−	3.64180i	0.209788	−	0.176033i
$429$	−1.68597	+	2.92018i	−0.0813993	+	0.140988i
$430$	13.6454	+	23.6346i	0.658040	+	1.13976i
$431$	16.4998	+	6.00542i	0.794766	+	0.289271i	0.707316	−	0.706898i	$-0.249906\pi$
$431$	16.4998	+	6.00542i	0.794766	+	0.289271i	0.0874500	+	0.996169i	$0.472128\pi$
$432$	0.173648	−	0.984808i	0.00835465	−	0.0473816i
$433$	−5.39793	−	30.6132i	−0.259408	−	1.47118i	−0.784499	−	0.620130i	$-0.787080\pi$
$433$	−5.39793	−	30.6132i	−0.259408	−	1.47118i	0.525091	−	0.851046i	$-0.324031\pi$
$434$	7.22162	−	2.62845i	0.346649	−	0.126170i
$435$	13.4440	+	11.2809i	0.644591	+	0.540876i
$436$	−1.85279			−0.0887327
$437$	9.93578	−	17.1759i	0.475293	−	0.821635i
$438$	14.7099			0.702868
$439$	17.9988	+	15.1028i	0.859035	+	0.720816i	0.961760	−	0.273894i	$-0.0883116\pi$
$439$	17.9988	+	15.1028i	0.859035	+	0.720816i	−0.102725	+	0.994710i	$0.532756\pi$
$440$	7.79685	−	2.83782i	0.371700	−	0.135288i
$441$	0.173648	+	0.984808i	0.00826896	+	0.0468956i
$442$	0.515873	−	2.92566i	0.0245376	−	0.139160i
$443$	−18.4272	−	6.70695i	−0.875502	−	0.318657i	−0.135109	−	0.990831i	$-0.543138\pi$
$443$	−18.4272	−	6.70695i	−0.875502	−	0.318657i	−0.740393	+	0.672174i	$0.765361\pi$
$444$	2.31722	+	4.01354i	0.109970	+	0.190474i
$445$	−10.5704	+	18.3086i	−0.501087	+	0.867909i
$446$	−1.17851	+	0.988883i	−0.0558038	+	0.0468250i
$447$	−3.56563	+	2.99192i	−0.168649	+	0.141513i
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	−2.75380	−	4.76972i	−0.129960	−	0.225097i	0.793701	−	0.608308i	$-0.208152\pi$
$449$	−2.75380	−	4.76972i	−0.129960	−	0.225097i	−0.923661	+	0.383211i	$0.874818\pi$
$450$	1.47403	+	0.536505i	0.0694867	+	0.0252911i
$451$	−6.83307	+	38.7523i	−0.321757	+	1.82477i
$452$	0.233777	+	1.32582i	0.0109959	+	0.0623611i
$453$	7.78255	−	2.83261i	0.365656	−	0.133088i
$454$	−17.9304	−	15.0454i	−0.841517	−	0.706116i
$455$	−2.66945			−0.125146
$456$	−3.34146	+	2.79904i	−0.156478	+	0.131077i
$457$	21.7210			1.01606			0.508032	−	0.861338i	$-0.330373\pi$
$457$	21.7210			1.01606			0.508032	+	0.861338i	$0.330373\pi$
$458$	19.0927	+	16.0207i	0.892142	+	0.748596i
$459$	−2.68025	+	0.975530i	−0.125103	+	0.0455339i
$460$	2.02596	+	11.4898i	0.0944610	+	0.535715i
$461$	−1.40847	+	7.98784i	−0.0655991	+	0.372031i	0.934281	+	0.356538i	$0.116043\pi$
$461$	−1.40847	+	7.98784i	−0.0655991	+	0.372031i	−0.999880	+	0.0154930i	$0.995068\pi$
$462$	3.04216	+	1.10725i	0.141534	+	0.0515141i
$463$	−19.2341	−	33.3145i	−0.893885	−	1.54825i	−0.835179	−	0.549979i	$-0.814636\pi$
$463$	−19.2341	−	33.3145i	−0.893885	−	1.54825i	−0.0587064	−	0.998275i	$-0.518698\pi$
$464$	3.42379	−	5.93019i	0.158946	−	0.275302i
$465$	15.0883	−	12.6606i	0.699703	−	0.587120i
$466$	12.3199	−	10.3376i	0.570707	−	0.478880i
$467$	−8.96708	+	15.5314i	−0.414947	+	0.718710i	−0.995423	−	0.0955679i	$-0.969533\pi$
$467$	−8.96708	+	15.5314i	−0.414947	+	0.718710i	0.580476	+	0.814278i	$0.302867\pi$
$468$	0.520779	+	0.902016i	0.0240730	+	0.0416957i
$469$	0.0514549	+	0.0187281i	0.00237597	+	0.000864782i
$470$	1.89004	−	10.7190i	0.0871811	−	0.494428i
$471$	−1.36850	−	7.76114i	−0.0630571	−	0.357615i
$472$	0.308593	−	0.112319i	0.0142041	−	0.00516988i
$473$	26.4076	+	22.1586i	1.21422	+	1.01885i
$474$	9.58995			0.440481
$475$	−3.41378	−	5.92434i	−0.156635	−	0.271827i
$476$	−2.85226			−0.130733
$477$	0.220995	+	0.185437i	0.0101187	+	0.00849056i
$478$	−10.8770	+	3.95890i	−0.497502	+	0.181076i
$479$	4.46425	+	25.3180i	0.203977	+	1.15681i	0.899041	+	0.437863i	$0.144265\pi$
$479$	4.46425	+	25.3180i	0.203977	+	1.15681i	−0.695065	+	0.718947i	$0.744624\pi$
$480$	0.445049	−	2.52400i	0.0203136	−	0.115204i
$481$	−4.53593	−	1.65094i	−0.206821	−	0.0752765i
$482$	−0.0549690	−	0.0952091i	−0.00250377	−	0.00433665i
$483$	−2.27611	+	3.94234i	−0.103567	+	0.179383i
$484$	−0.397790	+	0.333786i	−0.0180814	+	0.0151721i
$485$	1.63747	−	1.37400i	0.0743539	−	0.0623903i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−9.41204	−	16.3021i	−0.426500	−	0.738720i	0.570059	−	0.821604i	$-0.306920\pi$
$487$	−9.41204	−	16.3021i	−0.426500	−	0.738720i	−0.996559	+	0.0828835i	$0.973587\pi$
$488$	1.20565	+	0.438822i	0.0545774	+	0.0198646i
$489$	−0.965464	+	5.47542i	−0.0436598	+	0.247607i
$490$	0.445049	+	2.52400i	0.0201053	+	0.114023i
$491$	−14.4658	+	5.26512i	−0.652833	+	0.237612i	−0.647139	−	0.762372i	$-0.724035\pi$
$491$	−14.4658	+	5.26512i	−0.652833	+	0.237612i	−0.00569373	+	0.999984i	$0.501812\pi$
$492$	9.31116	+	7.81299i	0.419780	+	0.352237i
$493$	−19.5311			−0.879636
$494$	0.792129	−	4.47041i	0.0356396	−	0.201133i
$495$	8.29723			0.372933
$496$	−5.88712	−	4.93988i	−0.264339	−	0.221807i
$497$	−13.8974	+	5.05825i	−0.623385	+	0.226894i
$498$	−1.46442	−	8.30514i	−0.0656222	−	0.372162i
$499$	4.56483	−	25.8885i	0.204350	−	1.15893i	−0.694109	−	0.719870i	$-0.744201\pi$
$499$	4.56483	−	25.8885i	0.204350	−	1.15893i	0.898459	−	0.439057i	$-0.144687\pi$
$500$	−8.26400	−	3.00785i	−0.369577	−	0.134515i
$501$	7.73072	+	13.3900i	0.345383	+	0.598221i
$502$	10.1649	−	17.6062i	0.453683	−	0.785802i
$503$	6.94135	−	5.82448i	0.309499	−	0.259701i	−0.474786	−	0.880101i	$-0.657474\pi$
$503$	6.94135	−	5.82448i	0.309499	−	0.259701i	0.784285	+	0.620401i	$0.213030\pi$
$504$	0.766044	−	0.642788i	0.0341223	−	0.0286320i
$505$	23.2548	−	40.2784i	1.03482	−	1.79237i
$506$	7.36867	+	12.7629i	0.327577	+	0.567381i
$507$	11.1966	+	4.07522i	0.497258	+	0.180987i
$508$	1.12834	−	6.39914i	0.0500620	−	0.283916i
$509$	−0.672098	−	3.81166i	−0.0297902	−	0.168949i	0.966283	−	0.257483i	$-0.0828930\pi$
$509$	−0.672098	−	3.81166i	−0.0297902	−	0.168949i	−0.996073	+	0.0885338i	$0.971782\pi$
$510$	−6.86930	+	2.50022i	−0.304178	+	0.110712i
$511$	11.2685	+	9.45537i	0.498488	+	0.418281i
$512$	−1.00000			−0.0441942
$513$	−4.09728	+	1.48739i	−0.180899	+	0.0656698i
$514$	−19.0911			−0.842071
$515$	−28.3099	−	23.7548i	−1.24748	−	1.04676i
$516$	10.0061	−	3.64192i	0.440494	−	0.160327i
$517$	−2.38742	−	13.5397i	−0.104999	−	0.595477i
$518$	−0.804761	+	4.56403i	−0.0353592	+	0.200532i
$519$	9.31568	+	3.39063i	0.408913	+	0.148832i
$520$	1.33472	+	2.31181i	0.0585315	+	0.101380i
$521$	0.654406	−	1.13347i	0.0286701	−	0.0496580i	−0.851334	−	0.524623i	$-0.824206\pi$
$521$	0.654406	−	1.13347i	0.0286701	−	0.0496580i	0.880004	+	0.474965i	$0.157539\pi$
$522$	5.24556	−	4.40154i	0.229592	−	0.192650i
$523$	6.23425	−	5.23115i	0.272605	−	0.228742i	−0.496228	−	0.868192i	$-0.665282\pi$
$523$	6.23425	−	5.23115i	0.272605	−	0.228742i	0.768833	+	0.639450i	$0.220838\pi$
$524$	−9.38565	+	16.2564i	−0.410014	+	0.710165i
$525$	0.784317	+	1.35848i	0.0342304	+	0.0592888i
$526$	−18.2807	−	6.65362i	−0.797076	−	0.290112i
$527$	−3.80634	+	21.5868i	−0.165807	+	0.940338i
$528$	−0.562168	−	3.18821i	−0.0244652	−	0.138749i
$529$	2.13994	−	0.778873i	0.0930407	−	0.0338641i
$530$	0.566395	+	0.475262i	0.0246026	+	0.0206441i
$531$	0.328398			0.0142512
$532$	−4.35890	−	0.00366395i	−0.188982	−	0.000158853i
$533$	−12.6600			−0.548365
$534$	6.31888	+	5.30217i	0.273444	+	0.229447i
$535$	13.6450	−	4.96636i	0.589923	−	0.214714i
$536$	−0.00950849	−	0.0539253i	−0.000410704	−	0.00232922i
$537$	0.0919154	−	0.521278i	0.00396644	−	0.0224948i
$538$	−18.4840	−	6.72762i	−0.796901	−	0.290048i
$539$	1.61870	+	2.80367i	0.0697222	+	0.120762i
$540$	1.28147	−	2.21957i	0.0551456	−	0.0955149i
$541$	−25.0232	+	20.9970i	−1.07583	+	0.902730i	−0.995568	−	0.0940438i	$-0.970021\pi$
$541$	−25.0232	+	20.9970i	−1.07583	+	0.902730i	−0.0802635	+	0.996774i	$0.525576\pi$
$542$	−0.496674	+	0.416759i	−0.0213340	+	0.0179013i
$543$	0.718732	−	1.24488i	0.0308437	−	0.0534229i
$544$	1.42613	+	2.47013i	0.0611448	+	0.105906i
$545$	−4.46221	−	1.62411i	−0.191140	−	0.0695693i
$546$	−0.180865	+	1.02574i	−0.00774030	+	0.0438974i
$547$	−3.24307	−	18.3924i	−0.138664	−	0.786402i	−0.972238	−	0.233994i	$-0.924820\pi$
$547$	−3.24307	−	18.3924i	−0.138664	−	0.786402i	0.833574	−	0.552408i	$-0.186291\pi$
$548$	9.20603	−	3.35072i	0.393262	−	0.143136i
$549$	0.982858	+	0.824716i	0.0419474	+	0.0351980i
$550$	5.07829			0.216539
$551$	−29.8479	−	0.0250892i	−1.27156	−	0.00106884i
$552$	4.55222			0.193755
$553$	7.34632	+	6.16430i	0.312397	+	0.262133i
$554$	−23.4662	+	8.54099i	−0.996983	+	0.362872i
$555$	2.06255	+	11.6973i	0.0875504	+	0.496523i
$556$	−1.79847	+	10.1996i	−0.0762721	+	0.432560i
$557$	23.0959	+	8.40622i	0.978605	+	0.356183i	0.781298	−	0.624159i	$-0.214558\pi$
$557$	23.0959	+	8.40622i	0.978605	+	0.356183i	0.197307	+	0.980342i	$0.436780\pi$
$558$	−3.84254	−	6.65548i	−0.162668	−	0.281749i
$559$	−5.54540	+	9.60492i	−0.234545	+	0.406245i
$560$	1.96332	−	1.64742i	0.0829655	−	0.0696163i
$561$	−7.07357	+	5.93543i	−0.298646	+	0.250594i
$562$	4.10491	−	7.10992i	0.173155	−	0.299914i
$563$	−17.5090	−	30.3266i	−0.737918	−	1.27811i	−0.953431	−	0.301611i	$-0.902476\pi$
$563$	−17.5090	−	30.3266i	−0.737918	−	1.27811i	0.215513	−	0.976501i	$-0.430858\pi$
$564$	−3.99070	−	1.45250i	−0.168039	−	0.0611611i
$565$	−0.599155	+	3.39798i	−0.0252067	+	0.142954i
$566$	2.05260	+	11.6409i	0.0862773	+	0.489303i
$567$	0.939693	−	0.342020i	0.0394634	−	0.0143635i
$568$	11.3293	+	9.50640i	0.475366	+	0.398880i
$569$	−18.4491			−0.773427			−0.386713	−	0.922200i	$-0.626390\pi$
$569$	−18.4491			−0.773427			−0.386713	+	0.922200i	$0.626390\pi$
$570$	−10.5011	+	3.81208i	−0.439841	+	0.159670i
$571$	1.89926			0.0794817			0.0397408	−	0.999210i	$-0.487347\pi$
$571$	1.89926			0.0794817			0.0397408	+	0.999210i	$0.487347\pi$
$572$	2.58305	+	2.16744i	0.108003	+	0.0906252i
$573$	−24.1735	+	8.79842i	−1.00986	+	0.367559i
$574$	2.11067	+	11.9702i	0.0880976	+	0.499627i
$575$	−1.23998	+	7.03229i	−0.0517108	+	0.293267i
$576$	−0.939693	−	0.342020i	−0.0391539	−	0.0142508i
$577$	17.2292	+	29.8418i	0.717261	+	1.24233i	0.962081	+	0.272763i	$0.0879376\pi$
$577$	17.2292	+	29.8418i	0.717261	+	1.24233i	−0.244820	+	0.969568i	$0.578729\pi$
$578$	−4.43231	+	7.67698i	−0.184360	+	0.319320i
$579$	7.41221	−	6.21958i	0.308041	−	0.258477i
$580$	13.4440	−	11.2809i	0.558233	−	0.468413i
$581$	4.21663	−	7.30341i	0.174935	−	0.302997i
$582$	−0.417016	−	0.722293i	−0.0172859	−	0.0299400i
$583$	0.877626	+	0.319430i	0.0363476	+	0.0132294i
$584$	2.55435	−	14.4865i	0.105700	−	0.599454i
$585$	0.463545	+	2.62889i	0.0191652	+	0.108691i
$586$	21.4265	−	7.79860i	0.885120	−	0.322157i
$587$	−4.83063	−	4.05338i	−0.199381	−	0.167301i	0.537631	−	0.843180i	$-0.319319\pi$
$587$	−4.83063	−	4.05338i	−0.199381	−	0.167301i	−0.737012	+	0.675880i	$0.763764\pi$
$588$	1.00000			0.0412393
$589$	−5.84468	+	32.9847i	−0.240826	+	1.35911i
$590$	0.841662			0.0346507
$591$	−4.01391	−	3.36807i	−0.165110	−	0.138544i
$592$	4.35494	−	1.58507i	0.178987	−	0.0651460i
$593$	−0.397208	−	2.25268i	−0.0163114	−	0.0925064i	0.975565	−	0.219710i	$-0.0705110\pi$
$593$	−0.397208	−	2.25268i	−0.0163114	−	0.0925064i	−0.991877	+	0.127203i	$0.959400\pi$
$594$	0.562168	−	3.18821i	0.0230660	−	0.130814i
$595$	−6.86930	−	2.50022i	−0.281614	−	0.102499i
$596$	2.32730	+	4.03100i	0.0953299	+	0.165116i
$597$	−6.53928	+	11.3264i	−0.267635	+	0.463558i
$598$	−3.63213	+	3.04772i	−0.148529	+	0.124630i
$599$	33.6604	−	28.2444i	1.37533	−	1.15404i	0.404420	−	0.914574i	$-0.367474\pi$
$599$	33.6604	−	28.2444i	1.37533	−	1.15404i	0.970906	−	0.239462i	$-0.0769709\pi$
$600$	0.784317	−	1.35848i	0.0320196	−	0.0554596i
$601$	−10.9282	−	18.9281i	−0.445769	−	0.772094i	0.552337	−	0.833621i	$-0.313736\pi$
$601$	−10.9282	−	18.9281i	−0.445769	−	0.772094i	−0.998105	+	0.0615270i	$0.980403\pi$
$602$	10.0061	+	3.64192i	0.407818	+	0.148434i
$603$	0.00950849	−	0.0539253i	0.000387216	−	0.00219601i
$604$	−1.43816	−	8.15619i	−0.0585177	−	0.331871i
$605$	−1.25061	+	0.455187i	−0.0508447	+	0.0185060i
$606$	−13.9014	−	11.6646i	−0.564705	−	0.473844i
$607$	−9.43458			−0.382938			−0.191469	−	0.981499i	$-0.561325\pi$
$607$	−9.43458			−0.382938			−0.191469	+	0.981499i	$0.561325\pi$
$608$	2.17628	+	3.77675i	0.0882596	+	0.153167i
$609$	6.84759			0.277478
$610$	2.51900	+	2.11369i	0.101991	+	0.0855810i
$611$	4.15655	−	1.51286i	0.168156	−	0.0612038i
$612$	0.495290	+	2.80893i	0.0200209	+	0.113544i
$613$	−0.266001	+	1.50857i	−0.0107437	+	0.0609304i	−0.989708	−	0.143100i	$-0.954293\pi$
$613$	−0.266001	+	1.50857i	−0.0107437	+	0.0609304i	0.978965	+	0.204030i	$0.0654041\pi$
$614$	−20.6365	−	7.51107i	−0.832821	−	0.303122i
$615$	15.5761	+	26.9785i	0.628087	+	1.08788i
$616$	1.61870	−	2.80367i	0.0652192	−	0.112963i
$617$	12.3111	−	10.3303i	0.495628	−	0.415881i	−0.360410	−	0.932794i	$-0.617363\pi$
$617$	12.3111	−	10.3303i	0.495628	−	0.415881i	0.856038	+	0.516913i	$0.172919\pi$
$618$	−11.0459	+	9.26860i	−0.444331	+	0.372838i
$619$	−11.9018	+	20.6145i	−0.478373	+	0.828566i	−0.999693	−	0.0247951i	$-0.992107\pi$
$619$	−11.9018	+	20.6145i	−0.478373	+	0.828566i	0.521319	+	0.853362i	$0.325440\pi$
$620$	−9.84818	−	17.0576i	−0.395513	−	0.685048i
$621$	4.27769	+	1.55695i	0.171658	+	0.0624783i
$622$	2.54733	−	14.4466i	0.102139	−	0.579257i
$623$	1.43237	+	8.12339i	0.0573868	+	0.325457i
$624$	0.978745	−	0.356234i	0.0391812	−	0.0142608i
$625$	−23.2744	−	19.5295i	−0.930976	−	0.781181i
$626$	−1.62309			−0.0648718
$627$	−10.8176	+	9.06159i	−0.432015	+	0.361885i
$628$	−7.88087			−0.314481
$629$	−10.1260	−	8.49676i	−0.403752	−	0.338788i
$630$	2.40837	−	0.876575i	0.0959518	−	0.0349236i
$631$	−5.81608	−	32.9846i	−0.231534	−	1.31310i	−0.849791	−	0.527120i	$-0.823272\pi$
$631$	−5.81608	−	32.9846i	−0.231534	−	1.31310i	0.618256	−	0.785977i	$-0.287839\pi$
$632$	1.66528	−	9.44425i	0.0662411	−	0.375672i
$633$	−7.01277	−	2.55244i	−0.278733	−	0.101450i
$634$	10.8333	+	18.7638i	0.430244	+	0.745204i
$635$	8.32679	−	14.4224i	0.330438	−	0.572336i
$636$	0.220995	−	0.185437i	0.00876301	−	0.00735304i
$637$	−0.797880	+	0.669501i	−0.0316132	+	0.0265266i
$638$	11.0842	−	19.1983i	0.438827	−	0.760070i
$639$	7.39467	+	12.8079i	0.292529	+	0.506674i
$640$	−2.40837	−	0.876575i	−0.0951992	−	0.0346497i
$641$	−1.53218	+	8.68942i	−0.0605175	+	0.343212i	0.939482	+	0.342597i	$0.111307\pi$
$641$	−1.53218	+	8.68942i	−0.0605175	+	0.343212i	−1.00000		0.000614268i	$0.999804\pi$
$642$	−0.983828	−	5.57956i	−0.0388286	−	0.220208i
$643$	11.6757	−	4.24960i	0.460444	−	0.167588i	−0.101375	−	0.994848i	$-0.532324\pi$
$643$	11.6757	−	4.24960i	0.460444	−	0.167588i	0.561819	+	0.827260i	$0.310102\pi$
$644$	3.48720	+	2.92611i	0.137415	+	0.115305i
$645$	27.2908			1.07458
$646$	6.22540	−	10.7618i	0.244935	−	0.423418i
$647$	−14.1726			−0.557183			−0.278592	−	0.960410i	$-0.589868\pi$
$647$	−14.1726			−0.557183			−0.278592	+	0.960410i	$0.589868\pi$
$648$	−0.766044	−	0.642788i	−0.0300931	−	0.0252511i
$649$	0.999037	−	0.363620i	0.0392156	−	0.0142733i
$650$	0.283711	+	1.60900i	0.0111281	+	0.0631103i
$651$	1.33450	−	7.56833i	0.0523032	−	0.296626i
$652$	5.22458	+	1.90159i	0.204610	+	0.0744721i
$653$	−3.30337	−	5.72161i	−0.129271	−	0.223904i	0.794123	−	0.607757i	$-0.207930\pi$
$653$	−3.30337	−	5.72161i	−0.129271	−	0.223904i	−0.923394	+	0.383853i	$0.874597\pi$
$654$	−0.926396	+	1.60457i	−0.0362250	+	0.0627435i
$655$	−36.8541	+	30.9243i	−1.44001	+	1.20831i
$656$	9.31116	−	7.81299i	0.363540	−	0.305046i
$657$	7.35497	−	12.7392i	0.286945	−	0.497003i
$658$	−2.12341	−	3.67785i	−0.0827790	−	0.143378i
$659$	−43.5657	−	15.8566i	−1.69708	−	0.617686i	−0.701591	−	0.712580i	$-0.747527\pi$
$659$	−43.5657	−	15.8566i	−1.69708	−	0.617686i	−0.995487	+	0.0948937i	$0.969749\pi$
$660$	1.44080	−	8.17118i	0.0560830	−	0.318063i
$661$	−3.72542	−	21.1279i	−0.144902	−	0.821781i	−0.967446	−	0.253079i	$-0.918557\pi$
$661$	−3.72542	−	21.1279i	−0.144902	−	0.821781i	0.822543	−	0.568702i	$-0.192554\pi$
$662$	−1.38986	+	0.505869i	−0.0540186	+	0.0196612i
$663$	−2.27576	−	1.90959i	−0.0883833	−	0.0741624i
$664$	−8.43326			−0.327274
$665$	−10.4946	−	3.82973i	−0.406964	−	0.148510i
$666$	4.63444			0.179581
$667$	23.8789	+	20.0368i	0.924596	+	0.775828i
$668$	14.5290	−	5.28813i	0.562144	−	0.204604i
$669$	0.267145	+	1.51506i	0.0103284	+	0.0585755i
$670$	0.0243696	−	0.138207i	0.000941481	−	0.00533940i
$671$	3.90318	+	1.42064i	0.150681	+	0.0548432i
$672$	−0.500000	−	0.866025i	−0.0192879	−	0.0334077i
$673$	−24.3510	+	42.1771i	−0.938661	+	1.62581i	−0.170689	+	0.985325i	$0.554599\pi$
$673$	−24.3510	+	42.1771i	−0.938661	+	1.62581i	−0.767972	+	0.640483i	$0.778734\pi$
$674$	−22.9312	+	19.2415i	−0.883275	+	0.741156i
$675$	1.20164	−	1.00830i	0.0462513	−	0.0388095i
$676$	5.95758	−	10.3188i	0.229138	−	0.396878i
$677$	−1.97396	−	3.41901i	−0.0758656	−	0.131403i	0.825597	−	0.564261i	$-0.190839\pi$
$677$	−1.97396	−	3.41901i	−0.0758656	−	0.131403i	−0.901462	+	0.432858i	$0.857505\pi$
$678$	1.26508	+	0.460451i	0.0485850	+	0.0176835i
$679$	0.144828	−	0.821361i	0.00555799	−	0.0315210i
$680$	1.26940	+	7.19910i	0.0486791	+	0.276073i
$681$	−21.9949	+	8.00550i	−0.842847	+	0.306771i
$682$	−19.0589	−	15.9923i	−0.729804	−	0.612378i
$683$	37.9567			1.45237			0.726186	−	0.687498i	$-0.241291\pi$
$683$	37.9567			1.45237			0.726186	+	0.687498i	$0.241291\pi$
$684$	0.753306	+	4.29331i	0.0288034	+	0.164159i
$685$	25.1087			0.959354
$686$	0.766044	+	0.642788i	0.0292477	+	0.0245417i
$687$	23.4206	−	8.52442i	0.893553	−	0.325227i
$688$	−1.84905	−	10.4865i	−0.0704945	−	0.399794i
$689$	−0.0521774	+	0.295912i	−0.00198780	+	0.0112734i
$690$	10.9634	+	3.99037i	0.417371	+	0.151911i
$691$	−11.9111	−	20.6306i	−0.453120	−	0.784826i	0.545458	−	0.838138i	$-0.316356\pi$
$691$	−11.9111	−	20.6306i	−0.453120	−	0.784826i	−0.998578	+	0.0533117i	$0.983022\pi$
$692$	4.95677	−	8.58538i	0.188428	−	0.326367i
$693$	2.47999	−	2.08096i	0.0942070	−	0.0790490i
$694$	11.6667	−	9.78949i	0.442861	−	0.371604i
$695$	−13.2721	+	22.9880i	−0.503440	+	0.871984i
$696$	−3.42379	−	5.93019i	−0.129779	−	0.224783i
$697$	−32.5780	−	11.8574i	−1.23398	−	0.449132i
$698$	4.19060	−	23.7661i	0.158617	−	0.899560i
$699$	−2.79269	−	15.8381i	−0.105629	−	0.599053i
$700$	1.47403	−	0.536505i	0.0557133	−	0.0202780i
$701$	16.5082	+	13.8520i	0.623507	+	0.523184i	0.898904	−	0.438146i	$-0.144365\pi$
$701$	16.5082	+	13.8520i	0.623507	+	0.523184i	−0.275397	+	0.961331i	$0.588809\pi$
$702$	1.04156			0.0393111
$703$	−15.4640	−	12.9980i	−0.583235	−	0.490228i
$704$	−3.23739			−0.122014
$705$	−8.33786	−	6.99630i	−0.314022	−	0.263496i
$706$	−23.8311	+	8.67381i	−0.896896	+	0.326443i
$707$	−3.15119	−	17.8713i	−0.118513	−	0.672119i
$708$	0.0570257	−	0.323409i	0.00214316	−	0.0121544i
$709$	−34.9324	−	12.7143i	−1.31191	−	0.477497i	−0.411054	−	0.911611i	$-0.634839\pi$
$709$	−34.9324	−	12.7143i	−1.31191	−	0.477497i	−0.900858	+	0.434114i	$0.857062\pi$
$710$	18.9521	+	32.8259i	0.711258	+	1.23193i
$711$	4.79497	−	8.30514i	0.179826	−	0.311467i
$712$	6.31888	−	5.30217i	0.236810	−	0.198707i
$713$	26.7995	−	22.4874i	1.00365	−	0.842160i
$714$	−1.42613	+	2.47013i	−0.0533716	+	0.0924423i
$715$	4.32103	+	7.48424i	0.161597	+	0.279895i
$716$	−0.497398	−	0.181038i	−0.0185886	−	0.00676571i
$717$	−2.00999	+	11.3992i	−0.0750644	+	0.425711i
$718$	1.49417	+	8.47387i	0.0557620	+	0.316242i
$719$	30.3388	−	11.0424i	1.13145	−	0.411813i	0.292629	−	0.956226i	$-0.405470\pi$
$719$	30.3388	−	11.0424i	1.13145	−	0.411813i	0.838817	+	0.544414i	$0.183248\pi$
$720$	−1.96332	−	1.64742i	−0.0731687	−	0.0613958i
$721$	−14.4194			−0.537006
$722$	9.52765	−	16.4385i	0.354582	−	0.611777i
$723$	−0.109938			−0.00408864
$724$	−1.10116	−	0.923983i	−0.0409243	−	0.0343396i
$725$	10.0936	−	3.67376i	0.374866	−	0.136440i
$726$	0.0901717	+	0.511389i	0.00334659	+	0.0189794i
$727$	8.01516	−	45.4562i	0.297266	−	1.68588i	−0.360583	−	0.932727i	$-0.617422\pi$
$727$	8.01516	−	45.4562i	0.297266	−	1.68588i	0.657848	−	0.753150i	$-0.271467\pi$
$728$	0.978745	+	0.356234i	0.0362747	+	0.0132029i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	18.8503	−	32.6497i	0.697681	−	1.20842i
$731$	−23.2660	+	19.5225i	−0.860525	+	0.722066i
$732$	0.982858	−	0.824716i	0.0363275	−	0.0304824i
$733$	−13.8212	+	23.9390i	−0.510498	+	0.884208i	0.489428	+	0.872044i	$0.337205\pi$
$733$	−13.8212	+	23.9390i	−0.510498	+	0.884208i	−0.999926	+	0.0121644i	$0.996128\pi$
$734$	10.4544	+	18.1075i	0.385879	+	0.668361i
$735$	2.40837	+	0.876575i	0.0888341	+	0.0323330i
$736$	0.790485	−	4.48306i	0.0291377	−	0.165248i
$737$	−0.0307827	−	0.174577i	−0.00113390	−	0.00643064i
$738$	11.4218	−	4.15721i	0.420443	−	0.153029i
$739$	−37.4903	−	31.4581i	−1.37910	−	1.15720i	−0.969543	−	0.244920i	$-0.921238\pi$
$739$	−37.4903	−	31.4581i	−1.37910	−	1.15720i	−0.409558	−	0.912284i	$-0.634317\pi$
$740$	11.8778			0.436635
$741$	−3.47542	−	2.92121i	−0.127673	−	0.107313i
$742$	0.288488			0.0105907
$743$	−22.0427	−	18.4960i	−0.808668	−	0.678553i	0.141621	−	0.989921i	$-0.454769\pi$
$743$	−22.0427	−	18.4960i	−0.808668	−	0.678553i	−0.950290	+	0.311368i	$0.899213\pi$
$744$	−7.22162	+	2.62845i	−0.264757	+	0.0963638i
$745$	2.07152	+	11.7482i	0.0758948	+	0.430421i
$746$	−0.188529	+	1.06920i	−0.00690255	+	0.0391463i
$747$	−7.92467	−	2.88434i	−0.289948	−	0.105533i
$748$	4.61694	+	7.99678i	0.168812	+	0.292391i
$749$	2.83282	−	4.90659i	0.103509	−	0.179283i
$750$	−6.73687	+	5.65291i	−0.245996	+	0.206415i
$751$	36.6935	−	30.7895i	1.33897	−	1.12353i	0.357076	−	0.934075i	$-0.383774\pi$
$751$	36.6935	−	30.7895i	1.33897	−	1.12353i	0.981890	−	0.189450i	$-0.0606706\pi$
$752$	−2.12341	+	3.67785i	−0.0774327	+	0.134117i
$753$	−10.1649	−	17.6062i	−0.370431	−	0.641604i
$754$	6.70204	+	2.43934i	0.244074	+	0.0888357i
$755$	3.68590	−	20.9038i	0.134144	−	0.760766i
$756$	−0.173648	−	0.984808i	−0.00631552	−	0.0358171i
$757$	−10.5695	+	3.84699i	−0.384155	+	0.139821i	−0.526877	−	0.849942i	$-0.676637\pi$
$757$	−10.5695	+	3.84699i	−0.384155	+	0.139821i	0.142721	+	0.989763i	$0.454415\pi$
$758$	−27.9712	−	23.4706i	−1.01596	−	0.852490i
$759$	14.7373			0.534931
$760$	1.93067	+	11.0035i	0.0700329	+	0.399138i
$761$	10.0069			0.362748			0.181374	−	0.983414i	$-0.441946\pi$
$761$	10.0069			0.362748			0.181374	+	0.983414i	$0.441946\pi$
$762$	−4.97764	−	4.17674i	−0.180321	−	0.151307i
$763$	−1.74106	+	0.633692i	−0.0630304	+	0.0229412i
$764$	4.46708	+	25.3340i	0.161613	+	0.916554i
$765$	−1.26940	+	7.19910i	−0.0458951	+	0.260284i
$766$	−0.681077	−	0.247892i	−0.0246083	−	0.00895669i
$767$	0.171023	+	0.296220i	0.00617527	+	0.0106959i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−8.74563	+	7.33846i	−0.315376	+	0.264632i	−0.786710	−	0.617323i	$-0.788217\pi$
$769$	−8.74563	+	7.33846i	−0.315376	+	0.264632i	0.471334	+	0.881955i	$0.343773\pi$
$770$	6.35605	−	5.33336i	0.229056	−	0.192201i
$771$	−9.54554	+	16.5334i	−0.343774	+	0.595434i
$772$	−4.83797	−	8.37962i	−0.174122	−	0.301589i
$773$	1.21802	+	0.443324i	0.0438092	+	0.0159453i	0.363832	−	0.931465i	$-0.381468\pi$
$773$	1.21802	+	0.443324i	0.0438092	+	0.0159453i	−0.320023	+	0.947410i	$0.603691\pi$
$774$	1.84905	−	10.4865i	0.0664629	−	0.376930i
$775$	−2.09334	−	11.8719i	−0.0751952	−	0.426453i
$776$	−0.783734	+	0.285256i	−0.0281344	+	0.0102401i
$777$	3.55018	+	2.97896i	0.127362	+	0.106870i
$778$	18.2405			0.653952
$779$	−49.7714	−	18.1627i	−1.78324	−	0.650746i
$780$	2.66945			0.0955815
$781$	36.6774	+	30.7760i	1.31242	+	1.10125i
$782$	−12.2011	+	4.44083i	−0.436310	+	0.158804i
$783$	−1.18907	−	6.74356i	−0.0424939	−	0.240995i
$784$	0.173648	−	0.984808i	0.00620172	−	0.0351717i
$785$	−18.9801	−	6.90818i	−0.677427	−	0.246563i
$786$	9.38565	+	16.2564i	0.334775	+	0.579847i
$787$	−4.75793	+	8.24098i	−0.169602	+	0.293759i	−0.938280	−	0.345877i	$-0.887582\pi$
$787$	−4.75793	+	8.24098i	−0.169602	+	0.293759i	0.768678	+	0.639636i	$0.220915\pi$
$788$	−4.01391	+	3.36807i	−0.142989	+	0.119982i
$789$	−14.9025	+	12.5047i	−0.530545	+	0.445180i
$790$	12.2892	−	21.2855i	0.437230	−	0.757305i
$791$	0.673134	+	1.16590i	0.0239339	+	0.0414547i
$792$	−3.04216	−	1.10725i	−0.108098	−	0.0393446i
$793$	−0.232055	+	1.31605i	−0.00824051	+	0.0467343i
$794$	−4.32421	−	24.5238i	−0.153461	−	0.870318i
$795$	0.694787	−	0.252882i	0.0246415	−	0.00896879i
$796$	10.0188	+	8.40674i	0.355106	+	0.297969i
$797$	30.5897			1.08354			0.541770	−	0.840526i	$-0.317754\pi$
$797$	30.5897			1.08354			0.541770	+	0.840526i	$0.317754\pi$
$798$	−2.18262	+	3.77308i	−0.0772640	+	0.133566i
$799$	12.1130			0.428528
$800$	−1.20164	−	1.00830i	−0.0424845	−	0.0356488i
$801$	7.75125	−	2.82122i	0.273877	−	0.0996830i
$802$	0.348669	+	1.97740i	0.0123119	+	0.0698245i
$803$	8.26945	−	46.8984i	0.291823	−	1.65501i
$804$	−0.0514549	−	0.0187281i	−0.00181468	−	0.000660488i
$805$	5.83352	+	10.1040i	0.205605	+	0.356118i
$806$	4.00223	−	6.93207i	0.140973	−	0.244172i
$807$	−15.0683	+	12.6438i	−0.530429	+	0.445082i
$808$	−13.9014	+	11.6646i	−0.489049	+	0.410361i
$809$	26.4934	−	45.8879i	0.931458	−	1.61333i	0.150628	−	0.988591i	$-0.451870\pi$
$809$	26.4934	−	45.8879i	0.931458	−	1.61333i	0.780831	−	0.624743i	$-0.214796\pi$
$810$	−1.28147	−	2.21957i	−0.0450262	−	0.0779876i
$811$	−5.24116	−	1.90763i	−0.184042	−	0.0669858i	0.248355	−	0.968669i	$-0.420110\pi$
$811$	−5.24116	−	1.90763i	−0.184042	−	0.0669858i	−0.432397	+	0.901683i	$0.642332\pi$
$812$	1.18907	−	6.74356i	0.0417282	−	0.236652i
$813$	0.112587	+	0.638512i	0.00394860	+	0.0223936i
$814$	14.0987	−	5.13150i	0.494158	−	0.179859i
$815$	10.9158	+	9.15948i	0.382365	+	0.320843i
$816$	2.85226			0.0998491
$817$	−35.5808	+	29.8049i	−1.24482	+	1.04274i
$818$	−35.5668			−1.24356
$819$	0.797880	+	0.669501i	0.0278802	+	0.0233943i
$820$	29.2734	−	10.6547i	1.02227	−	0.372077i
$821$	7.18295	+	40.7365i	0.250687	+	1.42171i	0.806907	+	0.590679i	$0.201140\pi$
$821$	7.18295	+	40.7365i	0.250687	+	1.42171i	−0.556220	+	0.831035i	$0.687749\pi$
$822$	1.70121	−	9.64801i	0.0593363	−	0.336513i
$823$	21.7256	+	7.90749i	0.757308	+	0.275638i	0.691678	−	0.722206i	$-0.256872\pi$
$823$	21.7256	+	7.90749i	0.757308	+	0.275638i	0.0656307	+	0.997844i	$0.479094\pi$
$824$	7.20969	+	12.4875i	0.251161	+	0.435024i
$825$	2.53914	−	4.39793i	0.0884017	−	0.153116i
$826$	0.251567	−	0.211090i	0.00875314	−	0.00734476i
$827$	6.71745	−	5.63661i	0.233588	−	0.196004i	−0.518479	−	0.855091i	$-0.673501\pi$
$827$	6.71745	−	5.63661i	0.233588	−	0.196004i	0.752067	+	0.659087i	$0.229057\pi$
$828$	2.27611	−	3.94234i	0.0791003	−	0.137006i
$829$	−17.0616	−	29.5515i	−0.592573	−	1.02637i	−0.993885	−	0.110424i	$-0.964779\pi$
$829$	−17.0616	−	29.5515i	−0.592573	−	1.02637i	0.401312	−	0.915941i	$-0.368554\pi$
$830$	−20.3104	−	7.39238i	−0.704985	−	0.256593i
$831$	−4.33638	+	24.5928i	−0.150427	+	0.853115i
$832$	−0.180865	−	1.02574i	−0.00627036	−	0.0355610i
$833$	−2.68025	+	0.975530i	−0.0928651	+	0.0338001i
$834$	7.93390	+	6.65733i	0.274728	+	0.230525i
$835$	39.6267			1.37134
$836$	7.04546	+	12.2268i	0.243672	+	0.422873i
$837$	−7.68508			−0.265635
$838$	−9.79210	−	8.21654i	−0.338262	−	0.283836i
$839$	5.13345	−	1.86842i	0.177226	−	0.0645051i	−0.251883	−	0.967758i	$-0.581050\pi$
$839$	5.13345	−	1.86842i	0.177226	−	0.0645051i	0.429109	+	0.903253i	$0.358828\pi$
$840$	−0.445049	−	2.52400i	−0.0153556	−	0.0870862i
$841$	3.10647	−	17.6177i	0.107120	−	0.607506i
$842$	21.0571	+	7.66415i	0.725674	+	0.264124i
$843$	−4.10491	−	7.10992i	−0.141381	−	0.244879i
$844$	−3.73142	+	6.46300i	−0.128441	+	0.222466i
$845$	23.3933	−	19.6293i	0.804754	−	0.675268i
$846$	−3.25325	+	2.72980i	−0.111849	+	0.0938525i
$847$	−0.259639	+	0.449708i	−0.00892131	+	0.0154522i
$848$	−0.144244	−	0.249838i	−0.00495336	−	0.00857948i
$849$	11.1076	+	4.04283i	0.381212	+	0.138750i
$850$	−0.776929	+	4.40618i	−0.0266484	+	0.151131i
$851$	3.66345	+	20.7765i	0.125582	+	0.712208i
$852$	13.8974	−	5.05825i	0.476118	−	0.173293i
$853$	42.0375	+	35.2736i	1.43934	+	1.20775i	0.939925	+	0.341380i	$0.110894\pi$
$853$	42.0375	+	35.2736i	1.43934	+	1.20775i	0.499410	+	0.866366i	$0.333550\pi$
$854$	1.28303			0.0439044
$855$	−1.94917	+	11.0002i	−0.0666602	+	0.376200i
$856$	−5.66564			−0.193648
$857$	2.79285	+	2.34348i	0.0954021	+	0.0800518i	0.689241	−	0.724532i	$-0.257944\pi$
$857$	2.79285	+	2.34348i	0.0954021	+	0.0800518i	−0.593839	+	0.804584i	$0.702388\pi$
$858$	3.16858	−	1.15327i	0.108174	−	0.0393720i
$859$	−1.68345	−	9.54735i	−0.0574387	−	0.325751i	0.942526	−	0.334132i	$-0.108443\pi$
$859$	−1.68345	−	9.54735i	−0.0574387	−	0.325751i	−0.999965	+	0.00838118i	$0.997332\pi$
$860$	4.73900	−	26.8762i	0.161599	−	0.916472i
$861$	11.4218	+	4.15721i	0.389255	+	0.141677i
$862$	−8.77934	−	15.2063i	−0.299026	−	0.517927i
$863$	−11.7773	+	20.3989i	−0.400904	+	0.694386i	−0.993835	−	0.110867i	$-0.964637\pi$
$863$	−11.7773	+	20.3989i	−0.400904	+	0.694386i	0.592931	+	0.805253i	$0.297971\pi$
$864$	−0.766044	+	0.642788i	−0.0260614	+	0.0218681i
$865$	19.4635	−	16.3318i	0.661778	−	0.555298i
$866$	−15.5427	+	26.9208i	−0.528163	+	0.914806i
$867$	4.43231	+	7.67698i	0.150529	+	0.260724i
$868$	−7.22162	−	2.62845i	−0.245118	−	0.0892155i
$869$	5.39116	−	30.5748i	0.182882	−	1.03718i
$870$	−3.04751	−	17.2833i	−0.103320	−	0.585959i
$871$	0.0535933	−	0.0195064i	0.00181594	−	0.000660948i
$872$	1.41932	+	1.19095i	0.0480643	+	0.0403307i
$873$	−0.834032			−0.0282277
$874$	−18.6517	+	6.77092i	−0.630904	+	0.229030i
$875$	−8.79437			−0.297304
$876$	−11.2685	−	9.45537i	−0.380726	−	0.319467i
$877$	27.1118	−	9.86788i	0.915500	−	0.333215i	0.159053	−	0.987270i	$-0.449156\pi$
$877$	27.1118	−	9.86788i	0.915500	−	0.333215i	0.756447	+	0.654055i	$0.226934\pi$
$878$	−4.07999	−	23.1388i	−0.137693	−	0.780897i
$879$	3.95946	−	22.4552i	0.133549	−	0.757395i
$880$	−7.79685	−	2.83782i	−0.262832	−	0.0956629i
$881$	9.05570	+	15.6849i	0.305094	+	0.528439i	0.977282	−	0.211942i	$-0.0679787\pi$
$881$	9.05570	+	15.6849i	0.305094	+	0.528439i	−0.672188	+	0.740381i	$0.734645\pi$
$882$	0.500000	−	0.866025i	0.0168359	−	0.0291606i
$883$	30.3304	−	25.4503i	1.02070	−	0.856469i	0.0309851	−	0.999520i	$-0.490136\pi$
$883$	30.3304	−	25.4503i	1.02070	−	0.856469i	0.989715	+	0.143050i	$0.0456911\pi$
$884$	−2.27576	+	1.90959i	−0.0765421	+	0.0642265i
$885$	0.420831	−	0.728901i	0.0141461	−	0.0245017i
$886$	9.80490	+	16.9826i	0.329402	+	0.570541i
$887$	7.60712	+	2.76876i	0.255422	+	0.0929660i	0.466558	−	0.884491i	$-0.345494\pi$
$887$	7.60712	+	2.76876i	0.255422	+	0.0929660i	−0.211136	+	0.977457i	$0.567716\pi$
$888$	0.804761	−	4.56403i	0.0270060	−	0.153159i
$889$	−1.12834	−	6.39914i	−0.0378433	−	0.214620i
$890$	19.8659	−	7.23061i	0.665908	−	0.242371i
$891$	−2.47999	−	2.08096i	−0.0830827	−	0.0697147i
$892$	1.53843			0.0515104
$893$	18.5114	+	0.0155601i	0.619461	+	0.000520700i
$894$	4.65460			0.155673
$895$	−1.03923	−	0.872014i	−0.0347375	−	0.0291482i
$896$	−0.939693	+	0.342020i	−0.0313929	+	0.0114261i
$897$	0.823337	+	4.66937i	0.0274904	+	0.155906i
$898$	−0.956384	+	5.42393i	−0.0319150	+	0.180999i
$899$	−49.4507	−	17.9986i	−1.64927	−	0.600286i
$900$	−0.784317	−	1.35848i	−0.0261439	−	0.0452826i
$901$	−0.411422	+	0.712603i	−0.0137064	+	0.0237403i
$902$	30.1439	−	25.2937i	1.00368	−	0.842189i
$903$	8.15705	−	6.84458i	0.271450	−	0.227773i
$904$	0.673134	−	1.16590i	0.0223881	−	0.0387773i
$905$	−1.84206	−	3.19055i	−0.0612322	−	0.106057i
$906$	−7.78255	−	2.83261i	−0.258558	−	0.0941073i
$907$	−8.16513	+	46.3068i	−0.271119	+	1.53759i	0.479908	+	0.877319i	$0.340670\pi$
$907$	−8.16513	+	46.3068i	−0.271119	+	1.53759i	−0.751026	+	0.660272i	$0.770441\pi$
$908$	4.06450	+	23.0509i	0.134885	+	0.764971i
$909$	−17.0526	+	6.20663i	−0.565598	+	0.205861i
$910$	2.04491	+	1.71589i	0.0677883	+	0.0568811i
$911$	8.85879			0.293505			0.146752	−	0.989173i	$-0.453118\pi$
$911$	8.85879			0.293505			0.146752	+	0.989173i	$0.453118\pi$
$912$	4.35890	+	0.00366395i	0.144338	+	0.000121326i
$913$	−27.3018			−0.903557
$914$	−16.6392	−	13.9620i	−0.550377	−	0.461821i
$915$	3.09001	−	1.12467i	0.102153	−	0.0371805i
$916$	−4.32796	−	24.5451i	−0.143000	−	0.810992i
$917$	−3.25960	+	18.4861i	−0.107641	+	0.610465i
$918$	2.68025	+	0.975530i	0.0884613	+	0.0321973i
$919$	3.55597	+	6.15911i	0.117300	+	0.203170i	0.918697	−	0.394963i	$-0.129243\pi$
$919$	3.55597	+	6.15911i	0.117300	+	0.203170i	−0.801397	+	0.598133i	$0.795909\pi$
$920$	5.83352	−	10.1040i	0.192326	−	0.333118i
$921$	−16.8230	+	14.1162i	−0.554337	+	0.465144i
$922$	6.21344	−	5.21369i	0.204629	−	0.171704i
$923$	−7.70198	+	13.3402i	−0.253514	+	0.439099i
$924$	−1.61870	−	2.80367i	−0.0532512	−	0.0922338i
$925$	6.83132	+	2.48640i	0.224612	+	0.0817522i
$926$	−6.67994	+	37.8838i	−0.219516	+	1.24494i
$927$	2.50390	+	14.2003i	0.0822388	+	0.466400i
$928$	−6.43463	+	2.34201i	−0.211227	+	0.0768803i
$929$	−24.0718	−	20.1987i	−0.789771	−	0.662696i	0.155918	−	0.987770i	$-0.450166\pi$
$929$	−24.0718	−	20.1987i	−0.789771	−	0.662696i	−0.945689	+	0.325074i	$0.894611\pi$
$930$	−19.6964			−0.645869
$931$	−4.09728	+	1.48739i	−0.134283	+	0.0487472i
$932$	−16.0825			−0.526798
$933$	−11.2375	−	9.42937i	−0.367899	−	0.308704i
$934$	16.8526	−	6.13385i	0.551434	−	0.200706i
$935$	4.10953	+	23.3063i	0.134396	+	0.762198i
$936$	0.180865	−	1.02574i	0.00591175	−	0.0335272i
$937$	22.0857	+	8.03855i	0.721510	+	0.262608i	0.676567	−	0.736381i	$-0.263467\pi$
$937$	22.0857	+	8.03855i	0.721510	+	0.262608i	0.0449433	+	0.998990i	$0.485689\pi$
$938$	−0.0273786	−	0.0474211i	−0.000893943	−	0.00154835i
$939$	−0.811546	+	1.40564i	−0.0264838	+	0.0458713i
$940$	−8.33786	+	6.99630i	−0.271951	+	0.228194i
$941$	−41.0878	+	34.4767i	−1.33942	+	1.12391i	−0.357649	+	0.933856i	$0.616422\pi$
$941$	−41.0878	+	34.4767i	−1.33942	+	1.12391i	−0.981774	+	0.190053i	$0.939134\pi$
$942$	−3.94043	+	6.82503i	−0.128386	+	0.222372i
$943$	27.6658	+	47.9186i	0.900923	+	1.56044i
$944$	−0.308593	−	0.112319i	−0.0100438	−	0.00365566i
$945$	0.445049	−	2.52400i	0.0144774	−	0.0821057i
$946$	−5.98611	−	33.9489i	−0.194625	−	1.10378i
$947$	−2.79451	+	1.01712i	−0.0908094	+	0.0330519i	−0.387025	−	0.922069i	$-0.626497\pi$
$947$	−2.79451	+	1.01712i	−0.0908094	+	0.0330519i	0.296216	+	0.955121i	$0.404275\pi$
$948$	−7.34632	−	6.16430i	−0.238598	−	0.200207i
$949$	15.3213			0.497349
$950$	−1.19298	+	6.73264i	−0.0387055	+	0.218436i
$951$	21.6665			0.702585
$952$	2.18496	+	1.83340i	0.0708149	+	0.0594207i
$953$	18.2204	−	6.63168i	0.590216	−	0.214821i	−0.0296084	−	0.999562i	$-0.509426\pi$
$953$	18.2204	−	6.63168i	0.590216	−	0.214821i	0.619824	+	0.784740i	$0.287204\pi$
$954$	−0.0500955	−	0.284105i	−0.00162190	−	0.00919825i
$955$	−11.4488	+	64.9295i	−0.370475	+	2.10107i
$956$	10.8770	+	3.95890i	0.351787	+	0.128040i
$957$	−11.0842	−	19.1983i	−0.358300	−	0.620594i
$958$	12.8543	−	22.2643i	0.415304	−	0.719327i
$959$	7.50482	−	6.29729i	0.242343	−	0.203350i
$960$	−1.96332	+	1.64742i	−0.0633659	+	0.0531703i
$961$	−14.0303	+	24.3011i	−0.452589	+	0.783907i
$962$	2.41352	+	4.18034i	0.0778149	+	0.134779i
$963$	−5.32396	−	1.93776i	−0.171562	−	0.0624435i
$964$	−0.0190905	+	0.108268i	−0.000614864	+	0.00348707i
$965$	−4.30627	−	24.4221i	−0.138624	−	0.786174i
$966$	4.27769	−	1.55695i	0.137632	−	0.0500941i
$967$	−29.8393	−	25.0382i	−0.959568	−	0.805173i	0.0213149	−	0.999773i	$-0.493215\pi$
$967$	−29.8393	−	25.0382i	−0.959568	−	0.805173i	−0.980883	+	0.194600i	$0.937659\pi$
$968$	0.519278			0.0166902
$969$	−6.20730	−	10.7723i	−0.199407	−	0.346055i
$970$	−2.13757			−0.0686332
$971$	−15.4194	−	12.9384i	−0.494832	−	0.415214i	0.360922	−	0.932596i	$-0.382462\pi$
$971$	−15.4194	−	12.9384i	−0.494832	−	0.415214i	−0.855754	+	0.517382i	$0.826907\pi$
$972$	−0.939693	+	0.342020i	−0.0301407	+	0.0109703i
$973$	1.79847	+	10.1996i	0.0576563	+	0.326985i
$974$	−3.26877	+	18.5381i	−0.104738	+	0.593999i
$975$	1.53529	+	0.558801i	0.0491687	+	0.0178960i
$976$	−0.641515	−	1.11114i	−0.0205344	−	0.0355666i
$977$	−9.22689	+	15.9814i	−0.295194	+	0.511292i	−0.975030	−	0.222073i	$-0.928718\pi$
$977$	−9.22689	+	15.9814i	−0.295194	+	0.511292i	0.679836	+	0.733364i	$0.262051\pi$
$978$	4.25912	−	3.57383i	0.136192	−	0.114278i
$979$	20.4567	−	17.1652i	0.653799	−	0.548602i
$980$	1.28147	−	2.21957i	0.0409350	−	0.0709015i
$981$	0.926396	+	1.60457i	0.0295776	+	0.0512298i
$982$	14.4658	+	5.26512i	0.461622	+	0.168017i
$983$	−5.58500	+	31.6741i	−0.178134	+	1.01025i	0.756330	+	0.654190i	$0.226990\pi$
$983$	−5.58500	+	31.6741i	−0.178134	+	1.01025i	−0.934464	+	0.356058i	$0.884121\pi$
$984$	−2.11067	−	11.9702i	−0.0672857	−	0.381596i
$985$	−12.6193	+	4.59306i	−0.402086	+	0.146347i
$986$	14.9617	+	12.5543i	0.476477	+	0.399812i
$987$	−4.24681			−0.135178
$988$	−3.48033	+	2.91536i	−0.110724	+	0.0927500i
$989$	48.4733			1.54136
$990$	−6.35605	−	5.33336i	−0.202008	−	0.169505i
$991$	−40.3477	+	14.6853i	−1.28169	+	0.466495i	−0.890989	−	0.454024i	$-0.849988\pi$
$991$	−40.3477	+	14.6853i	−1.28169	+	0.466495i	−0.390696	+	0.920520i	$0.627766\pi$
$992$	1.33450	+	7.56833i	0.0423704	+	0.240295i
$993$	−0.256836	+	1.45659i	−0.00815045	+	0.0462235i
$994$	13.8974	+	5.05825i	0.440800	+	0.160438i
$995$	16.7598	+	29.0288i	0.531320	+	0.920273i
$996$	−4.21663	+	7.30341i	−0.133609	+	0.231418i
$997$	8.09766	−	6.79474i	0.256455	−	0.215192i	−0.505491	−	0.862832i	$-0.668689\pi$
$997$	8.09766	−	6.79474i	0.256455	−	0.215192i	0.761946	+	0.647640i	$0.224244\pi$
$998$	−20.1377	+	16.8975i	−0.637446	+	0.534881i
$999$	2.31722	−	4.01354i	0.0733135	−	0.126983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bo.d.757.1	yes	12
19.6	even	9	inner	798.2.bo.d.253.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bo.d.253.1	✓	12	19.6	even	9	inner
798.2.bo.d.757.1	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.445049 + 2.52400i) q^{5} +(0.939693 + 0.342020i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +(1.96332 - 1.64742i) q^{10} +(1.61870 - 2.80367i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.978745 + 0.356234i) q^{13} +(0.173648 - 0.984808i) q^{14} +(-0.445049 - 2.52400i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(2.18496 + 1.83340i) q^{17} -1.00000 q^{18} +(3.33675 + 2.80465i) q^{19} -2.56293 q^{20} +(-0.766044 - 0.642788i) q^{21} +(-3.04216 + 1.10725i) q^{22} +(-0.790485 - 4.48306i) q^{23} +(-0.173648 + 0.984808i) q^{24} +(-1.47403 - 0.536505i) q^{25} +(-0.520779 - 0.902016i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(-0.766044 + 0.642788i) q^{28} +(-5.24556 + 4.40154i) q^{29} +(-1.28147 + 2.21957i) q^{30} +(3.84254 + 6.65548i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.562168 + 3.18821i) q^{33} +(-0.495290 - 2.80893i) q^{34} +(-2.40837 + 0.876575i) q^{35} +(0.766044 + 0.642788i) q^{36} -4.63444 q^{37} +(-0.753306 - 4.29331i) q^{38} -1.04156 q^{39} +(1.96332 + 1.64742i) q^{40} +(-11.4218 + 4.15721i) q^{41} +(0.173648 + 0.984808i) q^{42} +(-1.84905 + 10.4865i) q^{43} +(3.04216 + 1.10725i) q^{44} +(1.28147 + 2.21957i) q^{45} +(-2.27611 + 3.94234i) q^{46} +(3.25325 - 2.72980i) q^{47} +(0.766044 - 0.642788i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.784317 + 1.35848i) q^{50} +(-2.68025 - 0.975530i) q^{51} +(-0.180865 + 1.02574i) q^{52} +(0.0500955 + 0.284105i) q^{53} +(0.939693 - 0.342020i) q^{54} +(6.35605 + 5.33336i) q^{55} +1.00000 q^{56} +(-4.09477 - 1.49427i) q^{57} +6.84759 q^{58} +(0.251567 + 0.211090i) q^{59} +(2.40837 - 0.876575i) q^{60} +(0.222796 + 1.26354i) q^{61} +(1.33450 - 7.56833i) q^{62} +(0.939693 + 0.342020i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.33472 + 2.31181i) q^{65} +(2.47999 - 2.08096i) q^{66} +(0.0419464 - 0.0351972i) q^{67} +(-1.42613 + 2.47013i) q^{68} +(2.27611 + 3.94234i) q^{69} +(2.40837 + 0.876575i) q^{70} +(-2.56814 + 14.5647i) q^{71} +(-0.173648 - 0.984808i) q^{72} +(13.8228 - 5.03110i) q^{73} +(3.55018 + 2.97896i) q^{74} +1.56863 q^{75} +(-2.18262 + 3.77308i) q^{76} +3.23739 q^{77} +(0.797880 + 0.669501i) q^{78} +(9.01160 - 3.27995i) q^{79} +(-0.445049 - 2.52400i) q^{80} +(0.173648 - 0.984808i) q^{81} +(11.4218 + 4.15721i) q^{82} +(-4.21663 - 7.30341i) q^{83} +(0.500000 - 0.866025i) q^{84} +(-5.59990 + 4.69888i) q^{85} +(8.15705 - 6.84458i) q^{86} +(3.42379 - 5.93019i) q^{87} +(-1.61870 - 2.80367i) q^{88} +(7.75125 + 2.82122i) q^{89} +(0.445049 - 2.52400i) q^{90} +(0.180865 + 1.02574i) q^{91} +(4.27769 - 1.55695i) q^{92} +(-5.88712 - 4.93988i) q^{93} -4.24681 q^{94} +(-8.56396 + 7.17375i) q^{95} -1.00000 q^{96} +(-0.638906 - 0.536106i) q^{97} +(0.939693 - 0.342020i) q^{98} +(-0.562168 - 3.18821i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 9 q^{5} + 6 q^{7} + 6 q^{8} + 9 q^{10} + 3 q^{11} - 6 q^{12} - 9 q^{13} + 9 q^{15} + 15 q^{17} - 12 q^{18} + 9 q^{19} - 15 q^{22} + 3 q^{23} + 3 q^{25} + 3 q^{26} - 6 q^{27} + 3 q^{29} + 6 q^{31}+ \cdots - 12 q^{99}+O(q^{100}) \) 12 * q + 9 * q^5 + 6 * q^7 + 6 * q^8 + 9 * q^10 + 3 * q^11 - 6 * q^12 - 9 * q^13 + 9 * q^15 + 15 * q^17 - 12 * q^18 + 9 * q^19 - 15 * q^22 + 3 * q^23 + 3 * q^25 + 3 * q^26 - 6 * q^27 + 3 * q^29 + 6 * q^31 - 12 * q^33 - 6 * q^34 - 9 * q^38 + 6 * q^39 + 9 * q^40 - 27 * q^41 + 6 * q^43 + 15 * q^44 - 15 * q^46 - 6 * q^47 - 6 * q^49 - 21 * q^51 + 9 * q^52 - 9 * q^53 - 9 * q^55 + 12 * q^56 - 18 * q^57 + 12 * q^58 - 24 * q^59 - 15 * q^61 - 24 * q^62 - 6 * q^64 - 24 * q^65 + 3 * q^66 + 33 * q^67 - 6 * q^68 + 15 * q^69 - 33 * q^71 + 33 * q^73 + 12 * q^74 + 9 * q^76 + 6 * q^77 + 33 * q^79 + 9 * q^80 + 27 * q^82 - 36 * q^83 + 6 * q^84 + 15 * q^85 - 6 * q^86 + 6 * q^87 - 3 * q^88 - 6 * q^89 - 9 * q^90 - 9 * q^91 + 3 * q^92 - 21 * q^93 - 18 * q^94 - 18 * q^95 - 12 * q^96 + 21 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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