LMFDB - Embedded newform 273.2.cg.a.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.8
Character	$\chi$	$=$	273.19
Dual form			273.2.cg.a.115.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.02536 + 0.542694i) q^{2} -1.00000i q^{3} +(2.07553 + 1.19831i) q^{4} +(1.89270 - 0.507149i) q^{5} +(0.542694 - 2.02536i) q^{6} +(-1.04247 + 2.43172i) q^{7} +(0.588043 + 0.588043i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(2.02536 + 0.542694i) q^{2} -1.00000i q^{3} +(2.07553 + 1.19831i) q^{4} +(1.89270 - 0.507149i) q^{5} +(0.542694 - 2.02536i) q^{6} +(-1.04247 + 2.43172i) q^{7} +(0.588043 + 0.588043i) q^{8} -1.00000 q^{9} +4.10864 q^{10} +(1.77246 + 1.77246i) q^{11} +(1.19831 - 2.07553i) q^{12} +(-3.33753 - 1.36415i) q^{13} +(-3.43106 + 4.35937i) q^{14} +(-0.507149 - 1.89270i) q^{15} +(-1.52474 - 2.64092i) q^{16} +(3.66044 - 6.34007i) q^{17} +(-2.02536 - 0.542694i) q^{18} +(0.681492 + 0.681492i) q^{19} +(4.53608 + 1.21544i) q^{20} +(2.43172 + 1.04247i) q^{21} +(2.62798 + 4.55179i) q^{22} +(-5.74884 + 3.31909i) q^{23} +(0.588043 - 0.588043i) q^{24} +(-1.00500 + 0.580235i) q^{25} +(-6.01939 - 4.57415i) q^{26} +1.00000i q^{27} +(-5.07762 + 3.79790i) q^{28} +(-5.21743 + 9.03685i) q^{29} -4.10864i q^{30} +(-0.782577 + 2.92062i) q^{31} +(-2.08541 - 7.78286i) q^{32} +(1.77246 - 1.77246i) q^{33} +(10.8544 - 10.8544i) q^{34} +(-0.739848 + 5.13121i) q^{35} +(-2.07553 - 1.19831i) q^{36} +(-0.356539 + 1.33062i) q^{37} +(1.01043 + 1.75011i) q^{38} +(-1.36415 + 3.33753i) q^{39} +(1.41122 + 0.814767i) q^{40} +(-0.710011 + 0.190247i) q^{41} +(4.35937 + 3.43106i) q^{42} +(10.1261 - 5.84633i) q^{43} +(1.55484 + 5.80275i) q^{44} +(-1.89270 + 0.507149i) q^{45} +(-13.4447 + 3.60251i) q^{46} +(-0.971849 - 3.62699i) q^{47} +(-2.64092 + 1.52474i) q^{48} +(-4.82651 - 5.06999i) q^{49} +(-2.35037 + 0.629781i) q^{50} +(-6.34007 - 3.66044i) q^{51} +(-5.29246 - 6.83071i) q^{52} +(-1.15862 - 2.00679i) q^{53} +(-0.542694 + 2.02536i) q^{54} +(4.25365 + 2.45585i) q^{55} +(-2.04297 + 0.816937i) q^{56} +(0.681492 - 0.681492i) q^{57} +(-15.4714 + 15.4714i) q^{58} +(1.22948 + 4.58848i) q^{59} +(1.21544 - 4.53608i) q^{60} -9.45408i q^{61} +(-3.17000 + 5.49061i) q^{62} +(1.04247 - 2.43172i) q^{63} -10.7959i q^{64} +(-7.00878 - 0.889307i) q^{65} +(4.55179 - 2.62798i) q^{66} +(4.43646 - 4.43646i) q^{67} +(15.1947 - 8.77265i) q^{68} +(3.31909 + 5.74884i) q^{69} +(-4.28314 + 9.99105i) q^{70} +(8.32895 + 2.23174i) q^{71} +(-0.588043 - 0.588043i) q^{72} +(7.50661 + 2.01139i) q^{73} +(-1.44424 + 2.50150i) q^{74} +(0.580235 + 1.00500i) q^{75} +(0.597819 + 2.23109i) q^{76} +(-6.15788 + 2.46239i) q^{77} +(-4.57415 + 6.01939i) q^{78} +(-2.31642 + 4.01217i) q^{79} +(-4.22522 - 4.22522i) q^{80} +1.00000 q^{81} -1.54128 q^{82} +(10.1090 + 10.1090i) q^{83} +(3.79790 + 5.07762i) q^{84} +(3.71277 - 13.8563i) q^{85} +(23.6819 - 6.34554i) q^{86} +(9.03685 + 5.21743i) q^{87} +2.08457i q^{88} +(-3.95954 - 1.06096i) q^{89} -4.10864 q^{90} +(6.79650 - 6.69384i) q^{91} -15.9091 q^{92} +(2.92062 + 0.782577i) q^{93} -7.87339i q^{94} +(1.63548 + 0.944245i) q^{95} +(-7.78286 + 2.08541i) q^{96} +(2.63968 - 9.85141i) q^{97} +(-7.02397 - 12.8879i) q^{98} +(-1.77246 - 1.77246i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^7 - 36 * q^9	$ 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) $ 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.02536	+	0.542694i	1.43215	+	0.383743i	0.889777	−	0.456396i	$-0.150860\pi$
$2$	2.02536	+	0.542694i	1.43215	+	0.383743i	0.542371	+	0.840139i	$0.317527\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	2.07553	+	1.19831i	1.03776	+	0.599153i
$5$	1.89270	−	0.507149i	0.846443	−	0.226804i	0.190569	−	0.981674i	$-0.438967\pi$
$5$	1.89270	−	0.507149i	0.846443	−	0.226804i	0.655874	+	0.754870i	$0.272300\pi$
$6$	0.542694	−	2.02536i	0.221554	−	0.826851i
$7$	−1.04247	+	2.43172i	−0.394017	+	0.919103i
$7$	−1.04247	+	2.43172i	−0.394017	+	0.919103i
$8$	0.588043	+	0.588043i	0.207905	+	0.207905i
$9$	−1.00000			−0.333333
$10$	4.10864			1.29927
$11$	1.77246	+	1.77246i	0.534418	+	0.534418i	0.921884	−	0.387466i	$-0.126650\pi$
$11$	1.77246	+	1.77246i	0.534418	+	0.534418i	−0.387466	+	0.921884i	$0.626650\pi$
$12$	1.19831	−	2.07553i	0.345921	−	0.599153i
$13$	−3.33753	−	1.36415i	−0.925664	−	0.378347i
$13$	−3.33753	−	1.36415i	−0.925664	−	0.378347i
$14$	−3.43106	+	4.35937i	−0.916990	+	1.16509i
$15$	−0.507149	−	1.89270i	−0.130945	−	0.488694i
$16$	−1.52474	−	2.64092i	−0.381185	−	0.660231i
$17$	3.66044	−	6.34007i	0.887787	−	1.53769i	0.0453018	−	0.998973i	$-0.485575\pi$
$17$	3.66044	−	6.34007i	0.887787	−	1.53769i	0.842485	−	0.538719i	$-0.181092\pi$
$18$	−2.02536	−	0.542694i	−0.477383	−	0.127914i
$19$	0.681492	+	0.681492i	0.156345	+	0.156345i	0.780945	−	0.624600i	$-0.214738\pi$
$19$	0.681492	+	0.681492i	0.156345	+	0.156345i	−0.624600	+	0.780945i	$0.714738\pi$
$20$	4.53608	+	1.21544i	1.01430	+	0.271780i
$21$	2.43172	+	1.04247i	0.530644	+	0.227486i
$22$	2.62798	+	4.55179i	0.560287	+	0.970445i
$23$	−5.74884	+	3.31909i	−1.19872	+	0.692079i	−0.960269	−	0.279077i	$-0.909972\pi$
$23$	−5.74884	+	3.31909i	−1.19872	+	0.692079i	−0.238447	+	0.971156i	$0.576638\pi$
$24$	0.588043	−	0.588043i	0.120034	−	0.120034i
$25$	−1.00500	+	0.580235i	−0.200999	+	0.116047i
$26$	−6.01939	−	4.57415i	−1.18050	−	0.897065i
$27$			1.00000i			0.192450i
$28$	−5.07762	+	3.79790i	−0.959580	+	0.717735i
$29$	−5.21743	+	9.03685i	−0.968852	+	1.67810i	−0.269965	+	0.962870i	$0.587012\pi$
$29$	−5.21743	+	9.03685i	−0.968852	+	1.67810i	−0.698888	+	0.715232i	$0.746321\pi$
$30$		−	4.10864i		−	0.750132i
$31$	−0.782577	+	2.92062i	−0.140555	+	0.524558i	0.859358	+	0.511374i	$0.170863\pi$
$31$	−0.782577	+	2.92062i	−0.140555	+	0.524558i	−0.999913	+	0.0131839i	$0.995803\pi$
$32$	−2.08541	−	7.78286i	−0.368652	−	1.37583i
$33$	1.77246	−	1.77246i	0.308546	−	0.308546i
$34$	10.8544	−	10.8544i	1.86152	−	1.86152i
$35$	−0.739848	+	5.13121i	−0.125057	+	0.867333i
$36$	−2.07553	−	1.19831i	−0.345921	−	0.199718i
$37$	−0.356539	+	1.33062i	−0.0586147	+	0.218753i	−0.989021	−	0.147778i	$-0.952788\pi$
$37$	−0.356539	+	1.33062i	−0.0586147	+	0.218753i	0.930406	+	0.366531i	$0.119455\pi$
$38$	1.01043	+	1.75011i	0.163913	+	0.283905i
$39$	−1.36415	+	3.33753i	−0.218439	+	0.534432i
$40$	1.41122	+	0.814767i	0.223133	+	0.128826i
$41$	−0.710011	+	0.190247i	−0.110885	+	0.0297116i	−0.313835	−	0.949478i	$-0.601614\pi$
$41$	−0.710011	+	0.190247i	−0.110885	+	0.0297116i	0.202950	+	0.979189i	$0.434947\pi$
$42$	4.35937	+	3.43106i	0.672665	+	0.529424i
$43$	10.1261	−	5.84633i	1.54422	−	0.891556i	0.545656	−	0.838009i	$-0.316281\pi$
$43$	10.1261	−	5.84633i	1.54422	−	0.891556i	0.998565	−	0.0535470i	$-0.0170527\pi$
$44$	1.55484	+	5.80275i	0.234401	+	0.874798i
$45$	−1.89270	+	0.507149i	−0.282148	+	0.0756012i
$46$	−13.4447	+	3.60251i	−1.98232	+	0.531160i
$47$	−0.971849	−	3.62699i	−0.141759	−	0.529051i	−0.999878	−	0.0156008i	$-0.995034\pi$
$47$	−0.971849	−	3.62699i	−0.141759	−	0.529051i	0.858120	−	0.513450i	$-0.171633\pi$
$48$	−2.64092	+	1.52474i	−0.381185	+	0.220077i
$49$	−4.82651	−	5.06999i	−0.689501	−	0.724285i
$50$	−2.35037	+	0.629781i	−0.332393	+	0.0890645i
$51$	−6.34007	−	3.66044i	−0.887787	−	0.512564i
$52$	−5.29246	−	6.83071i	−0.733932	−	0.947249i
$53$	−1.15862	−	2.00679i	−0.159149	−	0.275654i	0.775413	−	0.631454i	$-0.217542\pi$
$53$	−1.15862	−	2.00679i	−0.159149	−	0.275654i	−0.934562	+	0.355800i	$0.884208\pi$
$54$	−0.542694	+	2.02536i	−0.0738513	+	0.275617i
$55$	4.25365	+	2.45585i	0.573563	+	0.331147i
$56$	−2.04297	+	0.816937i	−0.273004	+	0.109168i
$57$	0.681492	−	0.681492i	0.0902658	−	0.0902658i
$58$	−15.4714	+	15.4714i	−2.03150	+	2.03150i
$59$	1.22948	+	4.58848i	0.160065	+	0.597369i	0.998618	+	0.0525503i	$0.0167350\pi$
$59$	1.22948	+	4.58848i	0.160065	+	0.597369i	−0.838554	+	0.544819i	$0.816598\pi$
$60$	1.21544	−	4.53608i	0.156912	−	0.585605i
$61$		−	9.45408i		−	1.21047i	−0.796046	−	0.605236i	$-0.793079\pi$
$61$		−	9.45408i		−	1.21047i	0.796046	−	0.605236i	$-0.206921\pi$
$62$	−3.17000	+	5.49061i	−0.402591	+	0.697308i
$63$	1.04247	−	2.43172i	0.131339	−	0.306368i
$64$		−	10.7959i		−	1.34949i
$65$	−7.00878	−	0.889307i	−0.869332	−	0.110305i
$66$	4.55179	−	2.62798i	0.560287	−	0.323482i
$67$	4.43646	−	4.43646i	0.542000	−	0.542000i	−0.382115	−	0.924115i	$-0.624804\pi$
$67$	4.43646	−	4.43646i	0.542000	−	0.542000i	0.924115	+	0.382115i	$0.124804\pi$
$68$	15.1947	−	8.77265i	1.84263	−	1.06384i
$69$	3.31909	+	5.74884i	0.399572	+	0.692079i
$70$	−4.28314	+	9.99105i	−0.511933	+	1.19416i
$71$	8.32895	+	2.23174i	0.988465	+	0.264858i	0.716606	−	0.697479i	$-0.245695\pi$
$71$	8.32895	+	2.23174i	0.988465	+	0.264858i	0.271859	+	0.962337i	$0.412361\pi$
$72$	−0.588043	−	0.588043i	−0.0693016	−	0.0693016i
$73$	7.50661	+	2.01139i	0.878583	+	0.235415i	0.669795	−	0.742546i	$-0.266382\pi$
$73$	7.50661	+	2.01139i	0.878583	+	0.235415i	0.208787	+	0.977961i	$0.433048\pi$
$74$	−1.44424	+	2.50150i	−0.167890	+	0.290794i
$75$	0.580235	+	1.00500i	0.0669998	+	0.116047i
$76$	0.597819	+	2.23109i	0.0685745	+	0.255923i
$77$	−6.15788	+	2.46239i	−0.701755	+	0.280615i
$78$	−4.57415	+	6.01939i	−0.517921	+	0.681562i
$79$	−2.31642	+	4.01217i	−0.260618	+	0.451404i	−0.966406	−	0.257019i	$-0.917260\pi$
$79$	−2.31642	+	4.01217i	−0.260618	+	0.451404i	0.705788	+	0.708423i	$0.250593\pi$
$80$	−4.22522	−	4.22522i	−0.472394	−	0.472394i
$81$	1.00000			0.111111
$82$	−1.54128			−0.170206
$83$	10.1090	+	10.1090i	1.10961	+	1.10961i	0.993202	+	0.116405i	$0.0371372\pi$
$83$	10.1090	+	10.1090i	1.10961	+	1.10961i	0.116405	+	0.993202i	$0.462863\pi$
$84$	3.79790	+	5.07762i	0.414384	+	0.554014i
$85$	3.71277	−	13.8563i	0.402707	−	1.50292i
$86$	23.6819	−	6.34554i	2.55368	−	0.684257i
$87$	9.03685	+	5.21743i	0.968852	+	0.559367i
$88$			2.08457i			0.222216i
$89$	−3.95954	−	1.06096i	−0.419711	−	0.112461i	0.0427815	−	0.999084i	$-0.486378\pi$
$89$	−3.95954	−	1.06096i	−0.419711	−	0.112461i	−0.462492	+	0.886623i	$0.653045\pi$
$90$	−4.10864			−0.433089
$91$	6.79650	−	6.69384i	0.712467	−	0.701705i
$92$	−15.9091			−1.65864
$93$	2.92062	+	0.782577i	0.302854	+	0.0811494i
$94$		−	7.87339i		−	0.812078i
$95$	1.63548	+	0.944245i	0.167797	+	0.0968775i
$96$	−7.78286	+	2.08541i	−0.794335	+	0.212841i
$97$	2.63968	−	9.85141i	0.268019	−	1.00026i	−0.692358	−	0.721554i	$-0.743428\pi$
$97$	2.63968	−	9.85141i	0.268019	−	1.00026i	0.960377	−	0.278705i	$-0.0899052\pi$
$98$	−7.02397	−	12.8879i	−0.709528	−	1.30187i
$99$	−1.77246	−	1.77246i	−0.178139	−	0.178139i
$100$	−2.78120			−0.278120
$101$	−3.80563			−0.378675			−0.189337	−	0.981912i	$-0.560634\pi$
$101$	−3.80563			−0.378675			−0.189337	+	0.981912i	$0.560634\pi$
$102$	−10.8544	−	10.8544i	−1.07475	−	1.07475i
$103$	4.75097	−	8.22892i	0.468127	−	0.810819i	−0.531210	−	0.847240i	$-0.678262\pi$
$103$	4.75097	−	8.22892i	0.468127	−	0.810819i	0.999337	+	0.0364211i	$0.0115958\pi$
$104$	−1.16043	−	2.76479i	−0.113790	−	0.271110i
$105$	5.13121	+	0.739848i	0.500755	+	0.0722018i
$106$	−1.25755	−	4.69325i	−0.122144	−	0.455849i
$107$	4.87752	+	8.44811i	0.471527	+	0.816709i	0.999469	−	0.0325711i	$-0.0103695\pi$
$107$	4.87752	+	8.44811i	0.471527	+	0.816709i	−0.527942	+	0.849280i	$0.677036\pi$
$108$	−1.19831	+	2.07553i	−0.115307	+	0.199718i
$109$	−5.75506	−	1.54206i	−0.551235	−	0.147703i	−0.0275585	−	0.999620i	$-0.508773\pi$
$109$	−5.75506	−	1.54206i	−0.551235	−	0.147703i	−0.523676	+	0.851917i	$0.675440\pi$
$110$	7.28242	+	7.28242i	0.694351	+	0.694351i
$111$	1.33062	+	0.356539i	0.126297	+	0.0338412i
$112$	8.01148	−	0.954645i	0.757014	−	0.0902055i
$113$	5.65861	+	9.80099i	0.532317	+	0.922000i	0.999288	+	0.0377273i	$0.0120118\pi$
$113$	5.65861	+	9.80099i	0.532317	+	0.922000i	−0.466971	+	0.884273i	$0.654655\pi$
$114$	1.75011	−	1.01043i	0.163913	−	0.0946351i
$115$	−9.19757	+	9.19757i	−0.857678	+	0.857678i
$116$	−21.6578	+	12.5042i	−2.01088	+	1.16098i
$117$	3.33753	+	1.36415i	0.308555	+	0.126116i
$118$			9.96057i			0.916945i
$119$	11.6014	+	15.5105i	1.06349	+	1.42185i
$120$	0.814767	−	1.41122i	0.0743777	−	0.128826i
$121$		−	4.71674i		−	0.428795i
$122$	5.13068	−	19.1479i	0.464510	−	1.73357i
$123$	0.190247	+	0.710011i	0.0171540	+	0.0640196i
$124$	−5.12405	+	5.12405i	−0.460153	+	0.460153i
$125$	−8.53568	+	8.53568i	−0.763454	+	0.763454i
$126$	3.43106	−	4.35937i	0.305663	−	0.388363i
$127$	9.81199	+	5.66496i	0.870673	+	0.502684i	0.867572	−	0.497312i	$-0.165679\pi$
$127$	9.81199	+	5.66496i	0.870673	+	0.502684i	0.00310144	+	0.999995i	$0.499013\pi$
$128$	1.68805	−	6.29990i	0.149204	−	0.556838i
$129$	−5.84633	−	10.1261i	−0.514740	−	0.891556i
$130$	−13.7127	−	5.60479i	−1.20268	−	0.491573i
$131$	−12.3925	−	7.15480i	−1.08274	−	0.625118i	−0.151102	−	0.988518i	$-0.548282\pi$
$131$	−12.3925	−	7.15480i	−1.08274	−	0.625118i	−0.931633	+	0.363401i	$0.881616\pi$
$132$	5.80275	−	1.55484i	0.505065	−	0.135332i
$133$	−2.36763	+	0.946760i	−0.205300	+	0.0820945i
$134$	11.3931	−	6.57780i	0.984213	−	0.568235i
$135$	0.507149	+	1.89270i	0.0436484	+	0.162898i
$136$	5.88073	−	1.57574i	0.504269	−	0.135118i
$137$	5.50160	−	1.47415i	0.470034	−	0.125945i	−0.0160245	−	0.999872i	$-0.505101\pi$
$137$	5.50160	−	1.47415i	0.470034	−	0.125945i	0.486058	+	0.873926i	$0.338434\pi$
$138$	3.60251	+	13.4447i	0.306666	+	1.14449i
$139$	−9.38055	+	5.41586i	−0.795648	+	0.459368i	−0.841947	−	0.539560i	$-0.818591\pi$
$139$	−9.38055	+	5.41586i	−0.795648	+	0.459368i	0.0462992	+	0.998928i	$0.485257\pi$
$140$	−7.68433	+	9.76340i	−0.649445	+	0.825158i
$141$	−3.62699	+	0.971849i	−0.305448	+	0.0818444i
$142$	15.6580	+	9.04015i	1.31399	+	0.758633i
$143$	−3.49775	−	8.33356i	−0.292496	−	0.696887i
$144$	1.52474	+	2.64092i	0.127062	+	0.220077i
$145$	−5.29202	+	19.7501i	−0.439479	+	1.64016i
$146$	14.1120	+	8.14759i	1.16792	+	0.674300i
$147$	−5.06999	+	4.82651i	−0.418166	+	0.398084i
$148$	−2.33450	+	2.33450i	−0.191895	+	0.191895i
$149$	6.30814	−	6.30814i	0.516783	−	0.516783i	−0.399813	−	0.916597i	$-0.630925\pi$
$149$	6.30814	−	6.30814i	0.516783	−	0.516783i	0.916597	+	0.399813i	$0.130925\pi$
$150$	0.629781	+	2.35037i	0.0514214	+	0.191907i
$151$	3.32882	−	12.4233i	0.270896	−	1.01100i	−0.687647	−	0.726046i	$-0.741356\pi$
$151$	3.32882	−	12.4233i	0.270896	−	1.01100i	0.958542	−	0.284951i	$-0.0919772\pi$
$152$			0.801493i			0.0650097i
$153$	−3.66044	+	6.34007i	−0.295929	+	0.512564i
$154$	−13.8083	+	1.64539i	−1.11270	+	0.132589i
$155$			5.92474i			0.475887i
$156$	−6.83071	+	5.29246i	−0.546894	+	0.423736i
$157$	−3.95550	+	2.28371i	−0.315683	+	0.182260i	−0.649467	−	0.760390i	$-0.725008\pi$
$157$	−3.95550	+	2.28371i	−0.315683	+	0.182260i	0.333784	+	0.942650i	$0.391675\pi$
$158$	−6.86898	+	6.86898i	−0.546467	+	0.546467i
$159$	−2.00679	+	1.15862i	−0.159149	+	0.0918846i
$160$	−7.89413	−	13.6730i	−0.624086	−	1.08095i
$161$	−2.07810	−	17.4396i	−0.163777	−	1.37443i
$162$	2.02536	+	0.542694i	0.159128	+	0.0426381i
$163$	−1.81401	−	1.81401i	−0.142084	−	0.142084i	0.632487	−	0.774571i	$-0.282034\pi$
$163$	−1.81401	−	1.81401i	−0.142084	−	0.142084i	−0.774571	+	0.632487i	$0.782034\pi$
$164$	−1.70162	−	0.455948i	−0.132874	−	0.0356036i
$165$	2.45585	−	4.25365i	0.191188	−	0.331147i
$166$	14.9883	+	25.9605i	1.16332	+	2.01493i
$167$	−1.90396	−	7.10569i	−0.147333	−	0.549855i	−0.999640	−	0.0268134i	$-0.991464\pi$
$167$	−1.90396	−	7.10569i	−0.147333	−	0.549855i	0.852307	−	0.523041i	$-0.175203\pi$
$168$	0.816937	+	2.04297i	0.0630281	+	0.157619i
$169$	9.27820	+	9.10577i	0.713708	+	0.700444i
$170$	15.0394	−	26.0491i	1.15347	−	1.99787i
$171$	−0.681492	−	0.681492i	−0.0521150	−	0.0521150i
$172$	28.0227			2.13671
$173$	−18.3415			−1.39448			−0.697241	−	0.716837i	$-0.745589\pi$
$173$	−18.3415			−1.39448			−0.697241	+	0.716837i	$0.745589\pi$
$174$	15.4714	+	15.4714i	1.17289	+	1.17289i
$175$	−0.363288	−	3.04875i	−0.0274620	−	0.230464i
$176$	1.97840	−	7.38349i	0.149127	−	0.556551i
$177$	4.58848	−	1.22948i	0.344891	−	0.0924134i
$178$	−7.44374	−	4.29764i	−0.557932	−	0.322122i
$179$		−	1.90952i		−	0.142724i	−0.997450	−	0.0713620i	$-0.977265\pi$
$179$		−	1.90952i		−	0.142724i	0.997450	−	0.0713620i	$-0.0227345\pi$
$180$	−4.53608	−	1.21544i	−0.338099	−	0.0905934i
$181$	18.9344			1.40738			0.703691	−	0.710506i	$-0.251534\pi$
$181$	18.9344			1.40738			0.703691	+	0.710506i	$0.251534\pi$
$182$	17.3981	−	9.86904i	1.28963	−	0.731542i
$183$	−9.45408			−0.698866
$184$	−5.33234	−	1.42879i	−0.393105	−	0.105332i
$185$			2.69929i			0.198456i
$186$	5.49061	+	3.17000i	0.402591	+	0.232436i
$187$	17.7255	−	4.74955i	1.29622	−	0.347321i
$188$	2.32914	−	8.69248i	0.169870	−	0.633965i
$189$	−2.43172	−	1.04247i	−0.176881	−	0.0758286i
$190$	2.80000	+	2.80000i	0.203134	+	0.203134i
$191$	10.7890			0.780663			0.390331	−	0.920674i	$-0.372360\pi$
$191$	10.7890			0.780663			0.390331	+	0.920674i	$0.372360\pi$
$192$	−10.7959			−0.779127
$193$	13.8977	+	13.8977i	1.00038	+	1.00038i	1.00000		0.000375974i	$0.000119676\pi$
$193$	13.8977	+	13.8977i	1.00038	+	1.00038i	0.000375974		1.00000i	$0.499880\pi$
$194$	10.6926	−	18.5201i	0.767685	−	1.32967i
$195$	−0.889307	+	7.00878i	−0.0636846	+	0.501909i
$196$	−3.94214	−	16.3065i	−0.281581	−	1.16475i
$197$	−2.96842	−	11.0783i	−0.211491	−	0.789295i	−0.987372	−	0.158417i	$-0.949361\pi$
$197$	−2.96842	−	11.0783i	−0.211491	−	0.789295i	0.775881	−	0.630879i	$-0.217306\pi$
$198$	−2.62798	−	4.55179i	−0.186762	−	0.323482i
$199$	−2.77736	+	4.81053i	−0.196882	+	0.341009i	−0.947516	−	0.319709i	$-0.896415\pi$
$199$	−2.77736	+	4.81053i	−0.196882	+	0.341009i	0.750634	+	0.660718i	$0.229748\pi$
$200$	−0.932185	−	0.249778i	−0.0659155	−	0.0176620i
$201$	−4.43646	−	4.43646i	−0.312924	−	0.312924i
$202$	−7.70779	−	2.06530i	−0.542318	−	0.145314i
$203$	−16.5361	−	22.1080i	−1.16060	−	1.55168i
$204$	−8.77265	−	15.1947i	−0.614209	−	1.06384i
$205$	−1.24736	+	0.720162i	−0.0871193	+	0.0502983i
$206$	14.0882	−	14.0882i	0.981573	−	0.981573i
$207$	5.74884	−	3.31909i	0.399572	−	0.230693i
$208$	1.48625	+	10.8941i	0.103053	+	0.755372i
$209$			2.41584i			0.167107i
$210$	9.99105	+	4.28314i	0.689448	+	0.295565i
$211$	−8.06339	+	13.9662i	−0.555106	+	0.961473i	0.442789	+	0.896626i	$0.353989\pi$
$211$	−8.06339	+	13.9662i	−0.555106	+	0.961473i	−0.997895	+	0.0648467i	$0.979344\pi$
$212$		−	5.55353i		−	0.381418i
$213$	2.23174	−	8.32895i	0.152916	−	0.570690i
$214$	5.29400	+	19.7575i	0.361890	+	1.35059i
$215$	16.2008	−	16.2008i	1.10489	−	1.10489i
$216$	−0.588043	+	0.588043i	−0.0400113	+	0.0400113i
$217$	−6.28630	−	4.94766i	−0.426742	−	0.335869i
$218$	−10.8192	−	6.24648i	−0.732770	−	0.423065i
$219$	2.01139	−	7.50661i	0.135917	−	0.507250i
$220$	5.88571	+	10.1944i	0.396815	+	0.687303i
$221$	−20.8656	+	16.1668i	−1.40357	+	1.08750i
$222$	2.50150	+	1.44424i	0.167890	+	0.0969313i
$223$	−25.6580	+	6.87505i	−1.71819	+	0.460387i	−0.977408	−	0.211359i	$-0.932211\pi$
$223$	−25.6580	+	6.87505i	−1.71819	+	0.460387i	−0.740781	+	0.671747i	$0.765544\pi$
$224$	21.0997	+	3.04228i	1.40978	+	0.203271i
$225$	1.00500	−	0.580235i	0.0669998	−	0.0386824i
$226$	6.14179	+	22.9215i	0.408546	+	1.52471i
$227$	1.71699	−	0.460067i	0.113961	−	0.0305357i	−0.201388	−	0.979512i	$-0.564545\pi$
$227$	1.71699	−	0.460067i	0.113961	−	0.0305357i	0.315349	+	0.948976i	$0.397878\pi$
$228$	2.23109	−	0.597819i	0.147757	−	0.0395915i
$229$	−2.32685	−	8.68390i	−0.153762	−	0.573849i	−0.999208	−	0.0397875i	$-0.987332\pi$
$229$	−2.32685	−	8.68390i	−0.153762	−	0.573849i	0.845446	−	0.534061i	$-0.179335\pi$
$230$	−23.6199	+	13.6370i	−1.55745	+	0.899194i
$231$	2.46239	+	6.15788i	0.162013	+	0.405159i
$232$	−8.38214	+	2.24599i	−0.550314	+	0.147456i
$233$	−0.891738	−	0.514845i	−0.0584197	−	0.0337286i	0.470506	−	0.882397i	$-0.344072\pi$
$233$	−0.891738	−	0.514845i	−0.0584197	−	0.0337286i	−0.528925	+	0.848668i	$0.677405\pi$
$234$	6.01939	+	4.57415i	0.393500	+	0.299022i
$235$	−3.67884	−	6.37195i	−0.239981	−	0.415660i
$236$	−2.94659	+	10.9968i	−0.191806	+	0.715831i
$237$	4.01217	+	2.31642i	0.260618	+	0.150468i
$238$	15.0795	+	37.7104i	0.977458	+	2.44440i
$239$	−13.2347	+	13.2347i	−0.856079	+	0.856079i	−0.990874	−	0.134795i	$-0.956962\pi$
$239$	−13.2347	+	13.2347i	−0.856079	+	0.856079i	0.134795	+	0.990874i	$0.456962\pi$
$240$	−4.22522	+	4.22522i	−0.272737	+	0.272737i
$241$	−0.760109	−	2.83676i	−0.0489629	−	0.182732i	0.937114	−	0.349025i	$-0.113487\pi$
$241$	−0.760109	−	2.83676i	−0.0489629	−	0.182732i	−0.986076	+	0.166293i	$0.946820\pi$
$242$	2.55975	−	9.55311i	0.164547	−	0.614097i
$243$		−	1.00000i		−	0.0641500i
$244$	11.3289	−	19.6222i	0.725257	−	1.25618i
$245$	−11.7064	−	7.14824i	−0.747894	−	0.456685i
$246$			1.54128i			0.0982682i
$247$	−1.34484	−	3.20415i	−0.0855703	−	0.203875i
$248$	−2.17764	+	1.25726i	−0.138280	+	0.0798361i
$249$	10.1090	−	10.1090i	0.640632	−	0.640632i
$250$	−21.9201	+	12.6556i	−1.38635	+	0.800409i
$251$	−0.244838	−	0.424072i	−0.0154540	−	0.0267672i	0.858195	−	0.513324i	$-0.171586\pi$
$251$	−0.244838	−	0.424072i	−0.0154540	−	0.0267672i	−0.873649	+	0.486557i	$0.838253\pi$
$252$	5.07762	−	3.79790i	0.319860	−	0.239245i
$253$	−16.0726	−	4.30664i	−1.01047	−	0.270756i
$254$	16.7985	+	16.7985i	1.05403	+	1.05403i
$255$	−13.8563	−	3.71277i	−0.867713	−	0.232503i
$256$	−3.95806	+	6.85557i	−0.247379	+	0.428473i
$257$	9.35585	+	16.2048i	0.583602	+	1.01083i	0.995048	+	0.0993941i	$0.0316904\pi$
$257$	9.35585	+	16.2048i	0.583602	+	1.01083i	−0.411446	+	0.911434i	$0.634976\pi$
$258$	−6.34554	−	23.6819i	−0.395056	−	1.47437i
$259$	−2.86402	−	2.25414i	−0.177961	−	0.140065i
$260$	−13.4812	−	10.2444i	−0.836072	−	0.635333i
$261$	5.21743	−	9.03685i	0.322951	−	0.559367i
$262$	−21.2164	−	21.2164i	−1.31075	−	1.31075i
$263$	−3.44239			−0.212267			−0.106133	−	0.994352i	$-0.533847\pi$
$263$	−3.44239			−0.212267			−0.106133	+	0.994352i	$0.533847\pi$
$264$	2.08457			0.128297
$265$	−3.21067	−	3.21067i	−0.197230	−	0.197230i
$266$	−5.30911	+	0.632632i	−0.325523	+	0.0387892i
$267$	−1.06096	+	3.95954i	−0.0649295	+	0.242320i
$268$	14.5242	−	3.89176i	0.887208	−	0.237727i
$269$	−7.83469	−	4.52336i	−0.477689	−	0.275794i	0.241764	−	0.970335i	$-0.422274\pi$
$269$	−7.83469	−	4.52336i	−0.477689	−	0.275794i	−0.719453	+	0.694541i	$0.755607\pi$
$270$			4.10864i			0.250044i
$271$	−7.55815	−	2.02520i	−0.459125	−	0.123022i	0.0218411	−	0.999761i	$-0.493047\pi$
$271$	−7.55815	−	2.02520i	−0.459125	−	0.123022i	−0.480966	+	0.876739i	$0.659714\pi$
$272$	−22.3249			−1.35364
$273$	−6.69384	−	6.79650i	−0.405130	−	0.411343i
$274$	11.9428			0.721488
$275$	−2.80977	−	0.752875i	−0.169435	−	0.0454001i
$276$			15.9091i			0.957618i
$277$	1.34157	+	0.774557i	0.0806072	+	0.0465386i	0.539762	−	0.841818i	$-0.318514\pi$
$277$	1.34157	+	0.774557i	0.0806072	+	0.0465386i	−0.459155	+	0.888356i	$0.651848\pi$
$278$	−21.9382	+	5.87832i	−1.31576	+	0.352558i
$279$	0.782577	−	2.92062i	0.0468516	−	0.174853i
$280$	−3.45244	+	2.58231i	−0.206323	+	0.154323i
$281$	4.20181	+	4.20181i	0.250659	+	0.250659i	0.821241	−	0.570582i	$-0.193282\pi$
$281$	4.20181	+	4.20181i	0.250659	+	0.250659i	−0.570582	+	0.821241i	$0.693282\pi$
$282$	−7.87339			−0.468853
$283$	−4.65614			−0.276779			−0.138389	−	0.990378i	$-0.544193\pi$
$283$	−4.65614			−0.276779			−0.138389	+	0.990378i	$0.544193\pi$
$284$	14.6127	+	14.6127i	0.867102	+	0.867102i
$285$	0.944245	−	1.63548i	0.0559322	−	0.0968775i
$286$	−2.56163	−	18.7767i	−0.151473	−	1.11029i
$287$	0.277540	−	1.92487i	0.0163826	−	0.113622i
$288$	2.08541	+	7.78286i	0.122884	+	0.458609i
$289$	−18.2976	−	31.6925i	−1.07633	−	1.86426i
$290$	−21.4365	+	37.1292i	−1.25880	+	2.18030i
$291$	−9.85141	−	2.63968i	−0.577500	−	0.154741i
$292$	13.1699	+	13.1699i	0.770711	+	0.770711i
$293$	−10.8009	−	2.89410i	−0.630997	−	0.169075i	−0.0708751	−	0.997485i	$-0.522579\pi$
$293$	−10.8009	−	2.89410i	−0.630997	−	0.169075i	−0.560122	+	0.828410i	$0.689246\pi$
$294$	−12.8879	+	7.02397i	−0.751637	+	0.409646i
$295$	4.65408	+	8.06111i	0.270971	+	0.469336i
$296$	−0.992125	+	0.572804i	−0.0576661	+	0.0332935i
$297$	−1.77246	+	1.77246i	−0.102849	+	0.102849i
$298$	16.1997	−	9.35289i	0.938422	−	0.541798i
$299$	23.7146	−	3.23530i	1.37145	−	0.187102i
$300$			2.78120i			0.160573i
$301$	3.66041	+	30.7185i	0.210983	+	1.77059i
$302$	13.4841	−	23.3552i	0.775925	−	1.34394i
$303$			3.80563i			0.218628i
$304$	0.760671	−	2.83886i	0.0436275	−	0.162820i
$305$	−4.79463	−	17.8938i	−0.274539	−	1.02460i
$306$	−10.8544	+	10.8544i	−0.620507	+	0.620507i
$307$	−2.63969	+	2.63969i	−0.150655	+	0.150655i	−0.778411	−	0.627756i	$-0.783974\pi$
$307$	−2.63969	+	2.63969i	−0.150655	+	0.150655i	0.627756	+	0.778411i	$0.283974\pi$
$308$	−15.7315	−	2.26826i	−0.896387	−	0.129246i
$309$	−8.22892	−	4.75097i	−0.468127	−	0.270273i
$310$	−3.21533	+	11.9998i	−0.182618	+	0.681540i
$311$	16.2833	+	28.2035i	0.923341	+	1.59927i	0.794208	+	0.607646i	$0.207886\pi$
$311$	16.2833	+	28.2035i	0.923341	+	1.59927i	0.129133	+	0.991627i	$0.458780\pi$
$312$	−2.76479	+	1.16043i	−0.156525	+	0.0656966i
$313$	−12.7123	−	7.33945i	−0.718541	−	0.414850i	0.0956743	−	0.995413i	$-0.469499\pi$
$313$	−12.7123	−	7.33945i	−0.718541	−	0.414850i	−0.814216	+	0.580563i	$0.802833\pi$
$314$	−9.25067	+	2.47871i	−0.522046	+	0.139882i
$315$	0.739848	−	5.13121i	0.0416857	−	0.289111i
$316$	−9.61560	+	5.55157i	−0.540920	+	0.312300i
$317$	−2.65822	−	9.92063i	−0.149301	−	0.557198i	−0.999526	−	0.0307793i	$-0.990201\pi$
$317$	−2.65822	−	9.92063i	−0.149301	−	0.557198i	0.850225	−	0.526419i	$-0.176466\pi$
$318$	−4.69325	+	1.25755i	−0.263185	+	0.0705201i
$319$	−25.2652	+	6.76979i	−1.41458	+	0.379036i
$320$	−5.47513	−	20.4335i	−0.306069	−	1.14226i
$321$	8.44811	−	4.87752i	0.471527	−	0.272236i
$322$	5.25547	−	36.4493i	0.292876	−	2.03124i
$323$	6.81526	−	1.82614i	0.379211	−	0.101609i
$324$	2.07553	+	1.19831i	0.115307	+	0.0665725i
$325$	4.14573	−	0.565587i	0.229964	−	0.0313731i
$326$	−2.68957	−	4.65848i	−0.148962	−	0.258009i
$327$	−1.54206	+	5.75506i	−0.0852763	+	0.318256i
$328$	−0.529391	−	0.305644i	−0.0292307	−	0.0168764i
$329$	9.83294	+	1.41777i	0.542108	+	0.0781642i
$330$	7.28242	−	7.28242i	0.400884	−	0.400884i
$331$	−17.8973	+	17.8973i	−0.983723	+	0.983723i	−0.999870	−	0.0161469i	$-0.994860\pi$
$331$	−17.8973	+	17.8973i	−0.983723	+	0.983723i	0.0161469	+	0.999870i	$0.494860\pi$
$332$	8.86783	+	33.0952i	0.486685	+	1.81633i
$333$	0.356539	−	1.33062i	0.0195382	−	0.0729177i
$334$		−	15.4249i		−	0.844011i
$335$	6.14696	−	10.6469i	0.335845	−	0.581700i
$336$	−0.954645	−	8.01148i	−0.0520802	−	0.437062i
$337$		−	0.741618i		−	0.0403985i	−0.999796	−	0.0201993i	$-0.993570\pi$
$337$		−	0.741618i		−	0.0403985i	0.999796	−	0.0201993i	$-0.00643006\pi$
$338$	13.8501	+	23.4777i	0.753344	+	1.27702i
$339$	9.80099	−	5.65861i	0.532317	−	0.307333i
$340$	24.3100	−	24.3100i	1.31839	−	1.31839i
$341$	−6.56378	+	3.78960i	−0.355448	+	0.205218i
$342$	−1.01043	−	1.75011i	−0.0546376	−	0.0946351i
$343$	17.3603	−	6.45138i	0.937368	−	0.348342i
$344$	9.39250	+	2.51671i	0.506410	+	0.135692i
$345$	9.19757	+	9.19757i	0.495181	+	0.495181i
$346$	−37.1483	−	9.95385i	−1.99710	−	0.535122i
$347$	−17.0886	+	29.5983i	−0.917364	+	1.58892i	−0.113962	+	0.993485i	$0.536354\pi$
$347$	−17.0886	+	29.5983i	−0.917364	+	1.58892i	−0.803402	+	0.595437i	$0.796979\pi$
$348$	12.5042	+	21.6578i	0.670293	+	1.16098i
$349$	−7.26033	−	27.0959i	−0.388636	−	1.45041i	−0.832354	−	0.554244i	$-0.813007\pi$
$349$	−7.26033	−	27.0959i	−0.388636	−	1.45041i	0.443718	−	0.896167i	$-0.353659\pi$
$350$	0.918749	−	6.37198i	0.0491092	−	0.340596i
$351$	1.36415	−	3.33753i	0.0728129	−	0.178144i
$352$	10.0985	−	17.4912i	0.538253	−	0.932282i
$353$	6.82751	+	6.82751i	0.363391	+	0.363391i	0.865060	−	0.501668i	$-0.167280\pi$
$353$	6.82751	+	6.82751i	0.363391	+	0.363391i	−0.501668	+	0.865060i	$0.667280\pi$
$354$	9.96057			0.529398
$355$	16.8961			0.896750
$356$	−6.94679	−	6.94679i	−0.368179	−	0.368179i
$357$	15.5105	−	11.6014i	0.820903	−	0.614009i
$358$	1.03628	−	3.86746i	0.0547693	−	0.204402i
$359$	−33.0271	+	8.84959i	−1.74311	+	0.467064i	−0.983133	−	0.182891i	$-0.941454\pi$
$359$	−33.0271	+	8.84959i	−1.74311	+	0.467064i	−0.759973	+	0.649955i	$0.774788\pi$
$360$	−1.41122	−	0.814767i	−0.0743777	−	0.0429420i
$361$		−	18.0711i		−	0.951113i
$362$	38.3490	+	10.2756i	2.01558	+	0.540073i
$363$	−4.71674			−0.247565
$364$	22.1276	−	5.74896i	1.15980	−	0.301327i
$365$	15.2279			0.797063
$366$	−19.1479	−	5.13068i	−1.00088	−	0.268185i
$367$			26.7853i			1.39818i	0.715033	+	0.699090i	$0.246412\pi$
$367$			26.7853i			1.39818i	−0.715033	+	0.699090i	$0.753588\pi$
$368$	17.5309	+	10.1215i	0.913863	+	0.527619i
$369$	0.710011	−	0.190247i	0.0369617	−	0.00990386i
$370$	−1.46489	+	5.46705i	−0.0761561	+	0.284218i
$371$	6.08777	−	0.725417i	0.316062	−	0.0376618i
$372$	5.12405	+	5.12405i	0.265670	+	0.265670i
$373$	3.66467			0.189749			0.0948747	−	0.995489i	$-0.469755\pi$
$373$	3.66467			0.189749			0.0948747	+	0.995489i	$0.469755\pi$
$374$	38.4782			1.98966
$375$	8.53568	+	8.53568i	0.440780	+	0.440780i
$376$	1.56134	−	2.70432i	0.0805198	−	0.139464i
$377$	29.7409	−	23.0434i	1.53174	−	1.18680i
$378$	−4.35937	−	3.43106i	−0.224222	−	0.176475i
$379$	−6.16351	−	23.0025i	−0.316598	−	1.18156i	−0.922492	−	0.386016i	$-0.873851\pi$
$379$	−6.16351	−	23.0025i	−0.316598	−	1.18156i	0.605894	−	0.795545i	$-0.292816\pi$
$380$	2.26299	+	3.91961i	0.116089	+	0.201072i
$381$	5.66496	−	9.81199i	0.290224	−	0.502684i
$382$	21.8516	+	5.85511i	1.11802	+	0.299574i
$383$	−21.6378	−	21.6378i	−1.10564	−	1.10564i	−0.993717	−	0.111923i	$-0.964299\pi$
$383$	−21.6378	−	21.6378i	−1.10564	−	1.10564i	−0.111923	−	0.993717i	$-0.535701\pi$
$384$	−6.29990	−	1.68805i	−0.321490	−	0.0861431i
$385$	−10.4062	+	7.78354i	−0.530351	+	0.396686i
$386$	20.6056	+	35.6900i	1.04880	+	1.81657i
$387$	−10.1261	+	5.84633i	−0.514740	+	0.297185i
$388$	17.2837	−	17.2837i	0.877448	−	0.877448i
$389$	1.02102	−	0.589484i	0.0517676	−	0.0298880i	−0.473893	−	0.880583i	$-0.657152\pi$
$389$	1.02102	−	0.589484i	0.0517676	−	0.0298880i	0.525660	+	0.850694i	$0.323818\pi$
$390$	−5.60479	+	13.7127i	−0.283810	+	0.694370i
$391$			48.5974i			2.45767i
$392$	0.143181	−	5.81957i	0.00723174	−	0.293933i
$393$	−7.15480	+	12.3925i	−0.360912	+	0.625118i
$394$		−	24.0485i		−	1.21155i
$395$	−2.34954	+	8.76861i	−0.118218	+	0.441197i
$396$	−1.55484	−	5.80275i	−0.0781338	−	0.291599i
$397$	8.59230	−	8.59230i	0.431235	−	0.431235i	−0.457813	−	0.889048i	$-0.651367\pi$
$397$	8.59230	−	8.59230i	0.431235	−	0.431235i	0.889048	+	0.457813i	$0.151367\pi$
$398$	−8.23581	+	8.23581i	−0.412824	+	0.412824i
$399$	0.946760	+	2.36763i	0.0473973	+	0.118530i
$400$	3.06471	+	1.76941i	0.153236	+	0.0884707i
$401$	−0.558206	+	2.08325i	−0.0278755	+	0.104033i	−0.978462	−	0.206427i	$-0.933816\pi$
$401$	−0.558206	+	2.08325i	−0.0278755	+	0.104033i	0.950586	+	0.310460i	$0.100483\pi$
$402$	−6.57780	−	11.3931i	−0.328071	−	0.568235i
$403$	6.59603	−	8.68009i	0.328571	−	0.432386i
$404$	−7.89869	−	4.56031i	−0.392975	−	0.226884i
$405$	1.89270	−	0.507149i	0.0940492	−	0.0252004i
$406$	−21.4936	−	53.7507i	−1.06671	−	2.66760i
$407$	−2.99044	+	1.72653i	−0.148230	+	0.0855809i
$408$	−1.57574	−	5.88073i	−0.0780106	−	0.291140i
$409$	−4.63911	+	1.24305i	−0.229389	+	0.0614647i	−0.371683	−	0.928360i	$-0.621219\pi$
$409$	−4.63911	+	1.24305i	−0.229389	+	0.0614647i	0.142293	+	0.989825i	$0.454552\pi$
$410$	−2.91718	+	0.781656i	−0.144069	+	0.0386032i
$411$	−1.47415	−	5.50160i	−0.0727145	−	0.271374i
$412$	19.7215	−	11.3862i	0.971609	−	0.560959i
$413$	−12.4396	−	1.79361i	−0.612112	−	0.0882579i
$414$	13.4447	−	3.60251i	0.660773	−	0.177053i
$415$	24.2601	+	14.0066i	1.19088	+	0.687556i
$416$	−3.65686	+	28.8203i	−0.179292	+	1.41303i
$417$	5.41586	+	9.38055i	0.265216	+	0.459368i
$418$	−1.31106	+	4.89295i	−0.0641262	+	0.239322i
$419$	18.2738	+	10.5504i	0.892733	+	0.515420i	0.874836	−	0.484420i	$-0.160969\pi$
$419$	18.2738	+	10.5504i	0.892733	+	0.515420i	0.0178978	+	0.999840i	$0.494303\pi$
$420$	9.76340	+	7.68433i	0.476405	+	0.374957i
$421$	24.4128	−	24.4128i	1.18981	−	1.18981i	0.212688	−	0.977120i	$-0.431778\pi$
$421$	24.4128	−	24.4128i	1.18981	−	1.18981i	0.977120	−	0.212688i	$-0.0682218\pi$
$422$	−23.9107	+	23.9107i	−1.16395	+	1.16395i
$423$	0.971849	+	3.62699i	0.0472529	+	0.176350i
$424$	0.498760	−	1.86140i	0.0242219	−	0.0903975i
$425$			8.49567i			0.412100i
$426$	9.04015	−	15.6580i	0.437997	−	0.758633i
$427$	22.9897	+	9.85561i	1.11255	+	0.476947i
$428$			23.3790i			1.13007i
$429$	−8.33356	+	3.49775i	−0.402348	+	0.168873i
$430$	41.6046	−	24.0204i	2.00635	−	1.15837i
$431$	5.82798	−	5.82798i	0.280724	−	0.280724i	−0.552674	−	0.833398i	$-0.686392\pi$
$431$	5.82798	−	5.82798i	0.280724	−	0.280724i	0.833398	+	0.552674i	$0.186392\pi$
$432$	2.64092	−	1.52474i	0.127062	−	0.0733590i
$433$	13.2942	+	23.0262i	0.638878	+	1.10657i	0.985679	+	0.168631i	$0.0539346\pi$
$433$	13.2942	+	23.0262i	0.638878	+	1.10657i	−0.346801	+	0.937939i	$0.612732\pi$
$434$	−10.0470	−	13.4324i	−0.482270	−	0.644774i
$435$	19.7501	+	5.29202i	0.946945	+	0.253733i
$436$	−10.0969	−	10.0969i	−0.483555	−	0.483555i
$437$	−6.17972	−	1.65585i	−0.295616	−	0.0792101i
$438$	8.14759	−	14.1120i	0.389307	−	0.674300i
$439$	−8.93996	−	15.4845i	−0.426681	−	0.739033i	0.569895	−	0.821718i	$-0.306984\pi$
$439$	−8.93996	−	15.4845i	−0.426681	−	0.739033i	−0.996576	+	0.0826847i	$0.973651\pi$
$440$	1.05719	+	3.94548i	0.0503994	+	0.188093i
$441$	4.82651	+	5.06999i	0.229834	+	0.241428i
$442$	−51.0341	+	21.4199i	−2.42744	+	1.01884i
$443$	10.8928	−	18.8669i	0.517532	−	0.896392i	−0.482261	−	0.876028i	$-0.660184\pi$
$443$	10.8928	−	18.8669i	0.517532	−	0.896392i	0.999793	−	0.0203640i	$-0.00648252\pi$
$444$	2.33450	+	2.33450i	0.110790	+	0.110790i
$445$	−8.03231			−0.380768
$446$	−55.6979			−2.63737
$447$	−6.30814	−	6.30814i	−0.298365	−	0.298365i
$448$	26.2526	+	11.2544i	1.24032	+	0.531721i
$449$	−0.850694	+	3.17483i	−0.0401467	+	0.149830i	−0.983090	−	0.183125i	$-0.941379\pi$
$449$	−0.850694	+	3.17483i	−0.0401467	+	0.149830i	0.942943	+	0.332954i	$0.108045\pi$
$450$	2.35037	−	0.629781i	0.110798	−	0.0296882i
$451$	−1.59568	−	0.921264i	−0.0751374	−	0.0433806i
$452$			27.1230i			1.27576i
$453$	−12.4233	−	3.32882i	−0.583699	−	0.156402i
$454$	3.72721			0.174927
$455$	9.46900	−	16.1163i	0.443913	−	0.755544i
$456$	0.801493			0.0375334
$457$	−34.9035	−	9.35236i	−1.63272	−	0.437485i	−0.678014	−	0.735049i	$-0.737159\pi$
$457$	−34.9035	−	9.35236i	−1.63272	−	0.437485i	−0.954702	+	0.297564i	$0.903826\pi$
$458$		−	18.8508i		−	0.880841i
$459$	6.34007	+	3.66044i	0.295929	+	0.170855i
$460$	−30.1113	+	8.06830i	−1.40395	+	0.376187i
$461$	−3.32485	+	12.4085i	−0.154854	+	0.577922i	0.844264	+	0.535927i	$0.180038\pi$
$461$	−3.32485	+	12.4085i	−0.154854	+	0.577922i	−0.999118	+	0.0419948i	$0.986629\pi$
$462$	1.64539	+	13.8083i	0.0765504	+	0.642418i
$463$	22.2200	+	22.2200i	1.03265	+	1.03265i	0.999449	+	0.0332014i	$0.0105703\pi$
$463$	22.2200	+	22.2200i	1.03265	+	1.03265i	0.0332014	+	0.999449i	$0.489430\pi$
$464$	31.8209			1.47725
$465$	5.92474			0.274753
$466$	−1.52669	−	1.52669i	−0.0707225	−	0.0707225i
$467$	17.1486	−	29.7023i	0.793543	−	1.37446i	−0.130217	−	0.991486i	$-0.541567\pi$
$467$	17.1486	−	29.7023i	0.793543	−	1.37446i	0.923760	−	0.382972i	$-0.125099\pi$
$468$	5.29246	+	6.83071i	0.244644	+	0.315750i
$469$	6.16334	+	15.4131i	0.284597	+	0.711711i
$470$	−3.99298	−	14.9020i	−0.184182	−	0.687378i
$471$	2.28371	+	3.95550i	0.105228	+	0.182260i
$472$	−1.97524	+	3.42121i	−0.0909177	+	0.157474i
$473$	28.3106	+	7.58581i	1.30172	+	0.348796i
$474$	6.86898	+	6.86898i	0.315503	+	0.315503i
$475$	−1.08032	−	0.289472i	−0.0495686	−	0.0132819i
$476$	5.49260	+	46.0944i	0.251753	+	2.11273i
$477$	1.15862	+	2.00679i	0.0530496	+	0.0918846i
$478$	−33.9873	+	19.6226i	−1.55455	+	0.897517i
$479$	1.69038	−	1.69038i	0.0772354	−	0.0772354i	−0.667434	−	0.744669i	$-0.732607\pi$
$479$	1.69038	−	1.69038i	0.0772354	−	0.0772354i	0.744669	+	0.667434i	$0.232607\pi$
$480$	−13.6730	+	7.89413i	−0.624086	+	0.360316i
$481$	3.00513	−	3.95462i	0.137022	−	0.180315i
$482$		−	6.15798i		−	0.280489i
$483$	−17.4396	+	2.07810i	−0.793530	+	0.0945568i
$484$	5.65210	−	9.78972i	0.256913	−	0.444987i
$485$		−	19.9845i		−	0.907450i
$486$	0.542694	−	2.02536i	0.0246171	−	0.0918723i
$487$	−2.17213	−	8.10651i	−0.0984288	−	0.367341i	0.899088	−	0.437768i	$-0.144231\pi$
$487$	−2.17213	−	8.10651i	−0.0984288	−	0.367341i	−0.997517	+	0.0704263i	$0.977564\pi$
$488$	5.55941	−	5.55941i	0.251663	−	0.251663i
$489$	−1.81401	+	1.81401i	−0.0820323	+	0.0820323i
$490$	−19.8304	−	20.8308i	−0.895845	−	0.941039i
$491$	−5.46870	−	3.15735i	−0.246799	−	0.142489i	0.371499	−	0.928433i	$-0.378844\pi$
$491$	−5.46870	−	3.15735i	−0.246799	−	0.142489i	−0.618298	+	0.785944i	$0.712177\pi$
$492$	−0.455948	+	1.70162i	−0.0205557	+	0.0767150i
$493$	38.1962	+	66.1577i	1.72027	+	2.97959i
$494$	−0.984917	−	7.21941i	−0.0443135	−	0.324817i
$495$	−4.25365	−	2.45585i	−0.191188	−	0.110382i
$496$	8.90635	−	2.38645i	0.399907	−	0.107155i
$497$	−14.1096	+	17.9271i	−0.632904	+	0.804142i
$498$	25.9605	−	14.9883i	1.16332	−	0.671642i
$499$	−9.09774	−	33.9532i	−0.407271	−	1.51996i	−0.799829	−	0.600228i	$-0.795077\pi$
$499$	−9.09774	−	33.9532i	−0.407271	−	1.51996i	0.392558	−	0.919727i	$-0.371590\pi$
$500$	−27.9444	+	7.48767i	−1.24971	+	0.334859i
$501$	−7.10569	+	1.90396i	−0.317459	+	0.0850628i
$502$	−0.265744	−	0.991772i	−0.0118608	−	0.0442649i
$503$	8.32980	−	4.80921i	0.371408	−	0.214432i	−0.302666	−	0.953097i	$-0.597877\pi$
$503$	8.32980	−	4.80921i	0.371408	−	0.214432i	0.674073	+	0.738665i	$0.264543\pi$
$504$	2.04297	−	0.816937i	0.0910013	−	0.0363893i
$505$	−7.20294	+	1.93002i	−0.320527	+	0.0858849i
$506$	−30.2156	−	17.4450i	−1.34325	−	0.775525i
$507$	9.10577	−	9.27820i	0.404401	−	0.412059i
$508$	13.5767	+	23.5155i	0.602369	+	1.04333i
$509$	3.33616	−	12.4507i	0.147873	−	0.551868i	−0.851738	−	0.523968i	$-0.824451\pi$
$509$	3.33616	−	12.4507i	0.147873	−	0.551868i	0.999611	−	0.0279003i	$-0.00888209\pi$
$510$	−26.0491	−	15.0394i	−1.15347	−	0.665957i
$511$	−12.7166	+	16.1571i	−0.562548	+	0.714750i
$512$	−20.9607	+	20.9607i	−0.926340	+	0.926340i
$513$	−0.681492	+	0.681492i	−0.0300886	+	0.0300886i
$514$	10.1547	+	37.8980i	0.447906	+	1.67161i
$515$	4.81889	−	17.9844i	0.212346	−	0.792485i
$516$		−	28.0227i		−	1.23363i
$517$	4.70614	−	8.15128i	0.206976	−	0.358493i
$518$	−4.57737	−	6.11974i	−0.201118	−	0.268886i
$519$			18.3415i			0.805104i
$520$	−3.59852	−	4.64442i	−0.157805	−	0.203671i
$521$	−9.09809	+	5.25278i	−0.398594	+	0.230129i	−0.685877	−	0.727717i	$-0.740581\pi$
$521$	−9.09809	+	5.25278i	−0.398594	+	0.230129i	0.287283	+	0.957846i	$0.407248\pi$
$522$	15.4714	−	15.4714i	0.677166	−	0.677166i
$523$	−0.494684	+	0.285606i	−0.0216310	+	0.0124887i	−0.510777	−	0.859714i	$-0.670642\pi$
$523$	−0.494684	+	0.285606i	−0.0216310	+	0.0124887i	0.489146	+	0.872202i	$0.337309\pi$
$524$	−17.1473	−	29.6999i	−0.749082	−	1.29745i
$525$	−3.04875	+	0.363288i	−0.133058	+	0.0158552i
$526$	−6.97208	−	1.86816i	−0.303997	−	0.0814558i
$527$	15.6523	+	15.6523i	0.681826	+	0.681826i
$528$	−7.38349	−	1.97840i	−0.321325	−	0.0860988i
$529$	10.5327	−	18.2433i	0.457946	−	0.793185i
$530$	−4.76035	−	8.24517i	−0.206777	−	0.358147i
$531$	−1.22948	−	4.58848i	−0.0533549	−	0.199123i
$532$	−6.04859	−	0.872121i	−0.262240	−	0.0378112i
$533$	2.62921	+	0.333606i	0.113884	+	0.0144501i
$534$	−4.29764	+	7.44374i	−0.185977	+	0.322122i
$535$	13.5161	+	13.5161i	0.584354	+	0.584354i
$536$	5.21766			0.225369
$537$	−1.90952			−0.0824017
$538$	−13.4133	−	13.4133i	−0.578288	−	0.578288i
$539$	0.431573	−	17.5412i	0.0185892	−	0.755553i
$540$	−1.21544	+	4.53608i	−0.0523041	+	0.195202i
$541$	11.9041	−	3.18970i	0.511798	−	0.137136i	0.00632795	−	0.999980i	$-0.497986\pi$
$541$	11.9041	−	3.18970i	0.511798	−	0.137136i	0.505470	+	0.862844i	$0.331319\pi$
$542$	−14.2089	−	8.20352i	−0.610325	−	0.352372i
$543$		−	18.9344i		−	0.812552i
$544$	−56.9774	−	15.2670i	−2.44289	−	0.654569i
$545$	−11.6747			−0.500089
$546$	−9.86904	−	17.3981i	−0.422356	−	0.744570i
$547$	−16.2110			−0.693132			−0.346566	−	0.938026i	$-0.612652\pi$
$547$	−16.2110			−0.693132			−0.346566	+	0.938026i	$0.612652\pi$
$548$	13.1852	+	3.53296i	0.563244	+	0.150921i
$549$			9.45408i			0.403490i
$550$	−5.28222	−	3.04969i	−0.225235	−	0.130039i
$551$	−9.71418	+	2.60291i	−0.413838	+	0.110887i
$552$	−1.42879	+	5.33234i	−0.0608135	+	0.226959i
$553$	−7.34165	−	9.81546i	−0.312199	−	0.417396i
$554$	2.29682	+	2.29682i	0.0975826	+	0.0975826i
$555$	2.69929			0.114579
$556$	−25.9594			−1.10093
$557$	23.6805	+	23.6805i	1.00337	+	1.00337i	0.999994	+	0.00338004i	$0.00107590\pi$
$557$	23.6805	+	23.6805i	1.00337	+	1.00337i	0.00338004	+	0.999994i	$0.498924\pi$
$558$	3.17000	−	5.49061i	0.134197	−	0.232436i
$559$	−41.7715	+	5.69873i	−1.76675	+	0.241031i
$560$	14.6792	−	5.86987i	0.620310	−	0.248047i
$561$	−4.74955	−	17.7255i	−0.200526	−	0.748373i
$562$	6.22989	+	10.7905i	0.262792	+	0.455170i
$563$	−0.0785071	+	0.135978i	−0.00330868	+	0.00573080i	−0.867675	−	0.497132i	$-0.834387\pi$
$563$	−0.0785071	+	0.135978i	−0.00330868	+	0.00573080i	0.864366	+	0.502863i	$0.167720\pi$
$564$	−8.69248	−	2.32914i	−0.366020	−	0.0980747i
$565$	15.6806	+	15.6806i	0.659689	+	0.659689i
$566$	−9.43036	−	2.52686i	−0.396388	−	0.106212i
$567$	−1.04247	+	2.43172i	−0.0437797	+	0.102123i
$568$	3.58543	+	6.21014i	0.150441	+	0.260572i
$569$	−36.5944	+	21.1278i	−1.53412	+	0.885724i	−0.534953	+	0.844882i	$0.679671\pi$
$569$	−36.5944	+	21.1278i	−1.53412	+	0.885724i	−0.999166	+	0.0408418i	$0.986996\pi$
$570$	2.80000	−	2.80000i	0.117279	−	0.117279i
$571$	−28.4747	+	16.4399i	−1.19163	+	0.687987i	−0.958676	−	0.284502i	$-0.908172\pi$
$571$	−28.4747	+	16.4399i	−1.19163	+	0.687987i	−0.232952	+	0.972488i	$0.574839\pi$
$572$	2.72648	−	21.4879i	0.114000	−	0.898454i
$573$		−	10.7890i		−	0.450716i
$574$	1.60674	−	3.74795i	0.0670639	−	0.156436i
$575$	3.85171	−	6.67136i	0.160627	−	0.278215i
$576$			10.7959i			0.449829i
$577$	11.1497	−	41.6112i	0.464167	−	1.73230i	−0.195467	−	0.980710i	$-0.562622\pi$
$577$	11.1497	−	41.6112i	0.464167	−	1.73230i	0.659635	−	0.751586i	$-0.270711\pi$
$578$	−19.8601	−	74.1187i	−0.826070	−	3.08293i
$579$	13.8977	−	13.8977i	0.577567	−	0.577567i
$580$	−34.6504	+	34.6504i	−1.43878	+	1.43878i
$581$	−35.1206	+	14.0439i	−1.45705	+	0.582639i
$582$	−18.5201	−	10.6926i	−0.767685	−	0.443223i
$583$	1.50335	−	5.61058i	0.0622624	−	0.232366i
$584$	3.23143	+	5.59700i	0.133717	+	0.231605i
$585$	7.00878	+	0.889307i	0.289777	+	0.0367683i
$586$	−20.3052	−	11.7232i	−0.838800	−	0.484281i
$587$	15.3441	−	4.11144i	0.633318	−	0.169697i	0.0721432	−	0.997394i	$-0.477016\pi$
$587$	15.3441	−	4.11144i	0.633318	−	0.169697i	0.561175	+	0.827697i	$0.310349\pi$
$588$	−16.3065	+	3.94214i	−0.672470	+	0.162571i
$589$	−2.52369	+	1.45706i	−0.103987	+	0.0600369i
$590$	5.05149	+	18.8524i	0.207967	+	0.776142i
$591$	−11.0783	+	2.96842i	−0.455700	+	0.122104i
$592$	4.05770	−	1.08726i	0.166771	−	0.0446861i
$593$	5.02665	+	18.7597i	0.206420	+	0.770369i	0.989012	+	0.147834i	$0.0472302\pi$
$593$	5.02665	+	18.7597i	0.206420	+	0.770369i	−0.782592	+	0.622534i	$0.786103\pi$
$594$	−4.55179	+	2.62798i	−0.186762	+	0.107827i
$595$	29.8241	+	23.4732i	1.22267	+	0.962307i
$596$	20.6518	−	5.53363i	0.845931	−	0.226666i
$597$	4.81053	+	2.77736i	0.196882	+	0.113670i
$598$	49.7865	+	6.31715i	2.03592	+	0.258327i
$599$	22.3885	+	38.7780i	0.914770	+	1.58443i	0.807238	+	0.590226i	$0.200961\pi$
$599$	22.3885	+	38.7780i	0.914770	+	1.58443i	0.107531	+	0.994202i	$0.465705\pi$
$600$	−0.249778	+	0.932185i	−0.0101972	+	0.0380563i
$601$	33.7722	+	19.4984i	1.37760	+	0.795355i	0.991870	−	0.127258i	$-0.0406176\pi$
$601$	33.7722	+	19.4984i	1.37760	+	0.795355i	0.385726	+	0.922613i	$0.373951\pi$
$602$	−9.25711	+	64.2027i	−0.377292	+	2.61671i
$603$	−4.43646	+	4.43646i	−0.180667	+	0.180667i
$604$	21.7960	−	21.7960i	0.886867	−	0.886867i
$605$	−2.39209	−	8.92739i	−0.0972522	−	0.362950i
$606$	−2.06530	+	7.70779i	−0.0838969	+	0.313108i
$607$			31.9789i			1.29798i	0.760795	+	0.648992i	$0.224809\pi$
$607$			31.9789i			1.29798i	−0.760795	+	0.648992i	$0.775191\pi$
$608$	3.88276	−	6.72514i	0.157467	−	0.272741i
$609$	−22.1080	+	16.5361i	−0.895861	+	0.670075i
$610$		−	38.8434i		−	1.57272i
$611$	−1.70418	+	13.4309i	−0.0689437	+	0.543357i
$612$	−15.1947	+	8.77265i	−0.614209	+	0.354613i
$613$	15.6835	−	15.6835i	0.633452	−	0.633452i	−0.315480	−	0.948932i	$-0.602166\pi$
$613$	15.6835	−	15.6835i	0.633452	−	0.633452i	0.948932	+	0.315480i	$0.102166\pi$
$614$	−6.77887	+	3.91378i	−0.273573	+	0.157947i
$615$	0.720162	+	1.24736i	0.0290398	+	0.0502983i
$616$	−5.06909	−	2.17311i	−0.204239	−	0.0875570i
$617$	19.7363	+	5.28833i	0.794554	+	0.212900i	0.633192	−	0.773995i	$-0.281744\pi$
$617$	19.7363	+	5.28833i	0.794554	+	0.212900i	0.161363	+	0.986895i	$0.448411\pi$
$618$	−14.0882	−	14.0882i	−0.566711	−	0.566711i
$619$	−27.8712	−	7.46806i	−1.12024	−	0.300167i	−0.349258	−	0.937027i	$-0.613566\pi$
$619$	−27.8712	−	7.46806i	−1.12024	−	0.300167i	−0.770980	+	0.636860i	$0.780233\pi$
$620$	−7.09966	+	12.2970i	−0.285129	+	0.493858i
$621$	−3.31909	−	5.74884i	−0.133191	−	0.230693i
$622$	17.6737	+	65.9592i	0.708651	+	2.64472i
$623$	6.70766	−	8.52248i	0.268737	−	0.341446i
$624$	10.8941	−	1.48625i	0.436114	−	0.0594974i
$625$	−8.92548	+	15.4594i	−0.357019	+	0.618375i
$626$	−21.7639	−	21.7639i	−0.869862	−	0.869862i
$627$	2.41584			0.0964793
$628$	−10.9463			−0.436806
$629$	7.13115	+	7.13115i	0.284338	+	0.284338i
$630$	4.28314	−	9.99105i	0.170644	−	0.398053i
$631$	−0.897330	+	3.34888i	−0.0357221	+	0.133317i	−0.981484	−	0.191544i	$-0.938651\pi$
$631$	−0.897330	+	3.34888i	−0.0357221	+	0.133317i	0.945762	+	0.324860i	$0.105317\pi$
$632$	−3.72148	+	0.997169i	−0.148033	+	0.0396652i
$633$	13.9662	+	8.06339i	0.555106	+	0.320491i
$634$		−	21.5355i		−	0.855283i
$635$	21.4442	+	5.74595i	0.850986	+	0.228021i
$636$	−5.55353			−0.220212
$637$	9.19238	+	23.5053i	0.364215	+	0.931315i
$638$	−54.8451			−2.17134
$639$	−8.32895	−	2.23174i	−0.329488	−	0.0882861i
$640$		−	12.7799i		−	0.505172i
$641$	5.79715	+	3.34699i	0.228974	+	0.132198i	0.610098	−	0.792326i	$-0.291130\pi$
$641$	5.79715	+	3.34699i	0.228974	+	0.132198i	−0.381125	+	0.924524i	$0.624463\pi$
$642$	19.7575	−	5.29400i	0.779766	−	0.208938i
$643$	11.3176	−	42.2380i	0.446324	−	1.66570i	−0.266092	−	0.963948i	$-0.585732\pi$
$643$	11.3176	−	42.2380i	0.446324	−	1.66570i	0.712416	−	0.701757i	$-0.247601\pi$
$644$	16.5848	−	38.6866i	0.653534	−	1.52446i
$645$	−16.2008	−	16.2008i	−0.637907	−	0.637907i
$646$	14.7944			0.582079
$647$	2.42484			0.0953303			0.0476652	−	0.998863i	$-0.484822\pi$
$647$	2.42484			0.0953303			0.0476652	+	0.998863i	$0.484822\pi$
$648$	0.588043	+	0.588043i	0.0231005	+	0.0231005i
$649$	−5.95371	+	10.3121i	−0.233704	+	0.404787i
$650$	8.70356	+	1.10435i	0.341382	+	0.0433161i
$651$	−4.94766	+	6.28630i	−0.193914	+	0.246380i
$652$	−1.59129	−	5.93876i	−0.0623196	−	0.232580i
$653$	−9.48737	−	16.4326i	−0.371269	−	0.643058i	0.618492	−	0.785791i	$-0.287744\pi$
$653$	−9.48737	−	16.4326i	−0.371269	−	0.643058i	−0.989761	+	0.142734i	$0.954411\pi$
$654$	−6.24648	+	10.8192i	−0.244257	+	0.423065i
$655$	−27.0838	−	7.25709i	−1.05825	−	0.283558i
$656$	1.58501	+	1.58501i	0.0618842	+	0.0618842i
$657$	−7.50661	−	2.01139i	−0.292861	−	0.0784718i
$658$	19.1459	+	8.20778i	0.746383	+	0.319973i
$659$	−1.16446	−	2.01691i	−0.0453610	−	0.0785676i	0.842453	−	0.538769i	$-0.181110\pi$
$659$	−1.16446	−	2.01691i	−0.0453610	−	0.0785676i	−0.887814	+	0.460202i	$0.847777\pi$
$660$	10.1944	−	5.88571i	0.396815	−	0.229101i
$661$	−18.1901	+	18.1901i	−0.707514	+	0.707514i	−0.966012	−	0.258498i	$-0.916773\pi$
$661$	−18.1901	+	18.1901i	−0.707514	+	0.707514i	0.258498	+	0.966012i	$0.416773\pi$
$662$	−45.9612	+	26.5357i	−1.78633	+	1.03134i
$663$	16.1668	+	20.8656i	0.627866	+	0.810354i
$664$			11.8891i			0.461385i
$665$	−4.00108	+	2.99268i	−0.155155	+	0.116051i
$666$	1.44424	−	2.50150i	0.0559633	−	0.0969313i
$667$		−	69.2685i		−	2.68209i
$668$	4.56306	−	17.0296i	0.176550	−	0.658894i
$669$	6.87505	+	25.6580i	0.265805	+	0.991997i
$670$	18.2278	−	18.2278i	0.704202	−	0.704202i
$671$	16.7570	−	16.7570i	0.646898	−	0.646898i
$672$	3.04228	−	21.0997i	0.117358	−	0.813939i
$673$	−24.9952	−	14.4310i	−0.963493	−	0.556273i	−0.0662467	−	0.997803i	$-0.521102\pi$
$673$	−24.9952	−	14.4310i	−0.963493	−	0.556273i	−0.897246	+	0.441530i	$0.854436\pi$
$674$	0.402472	−	1.50205i	0.0155026	−	0.0578566i
$675$	−0.580235	−	1.00500i	−0.0223333	−	0.0386824i
$676$	8.34565	+	30.0174i	0.320987	+	1.15451i
$677$	13.4814	+	7.78352i	0.518134	+	0.299145i	0.736171	−	0.676796i	$-0.236632\pi$
$677$	13.4814	+	7.78352i	0.518134	+	0.299145i	−0.218037	+	0.975941i	$0.569965\pi$
$678$	22.9215	−	6.14179i	0.880293	−	0.235874i
$679$	21.2041	+	16.6888i	0.813737	+	0.640456i
$680$	10.3314	−	5.96481i	0.396189	−	0.228740i
$681$	−0.460067	−	1.71699i	−0.0176298	−	0.0657954i
$682$	−15.3506	+	4.11319i	−0.587806	+	0.157502i
$683$	40.6350	−	10.8881i	1.55486	−	0.416622i	0.623825	−	0.781564i	$-0.285578\pi$
$683$	40.6350	−	10.8881i	1.55486	−	0.416622i	0.931031	+	0.364941i	$0.118911\pi$
$684$	−0.597819	−	2.23109i	−0.0228582	−	0.0853078i
$685$	9.66529	−	5.58026i	0.369292	−	0.213211i
$686$	38.6620	−	3.64505i	1.47612	−	0.139169i
$687$	−8.68390	+	2.32685i	−0.331312	+	0.0887747i
$688$	−30.8794	−	17.8282i	−1.17727	−	0.679695i
$689$	1.12937	+	8.27825i	0.0430256	+	0.315376i
$690$	13.6370	+	23.6199i	0.519150	+	0.899194i
$691$	−5.66969	+	21.1596i	−0.215685	+	0.804948i	0.770239	+	0.637755i	$0.220137\pi$
$691$	−5.66969	+	21.1596i	−0.215685	+	0.804948i	−0.985924	+	0.167193i	$0.946530\pi$
$692$	−38.0684	−	21.9788i	−1.44714	−	0.835508i
$693$	6.15788	−	2.46239i	0.233918	−	0.0935385i
$694$	−50.6735	+	50.6735i	−1.92354	+	1.92354i
$695$	−15.0080	+	15.0080i	−0.569284	+	0.569284i
$696$	2.24599	+	8.38214i	0.0851339	+	0.317724i
$697$	−1.39278	+	5.19791i	−0.0527551	+	0.196885i
$698$		−	58.8192i		−	2.22634i
$699$	−0.514845	+	0.891738i	−0.0194732	+	0.0337286i
$700$	2.89932	−	6.76309i	0.109584	−	0.255621i
$701$		−	15.8478i		−	0.598564i	−0.954165	−	0.299282i	$-0.903253\pi$
$701$		−	15.8478i		−	0.598564i	0.954165	−	0.299282i	$-0.0967471\pi$
$702$	4.57415	−	6.01939i	0.172640	−	0.227187i
$703$	−1.14979	+	0.663830i	−0.0433650	+	0.0250368i
$704$	19.1354	−	19.1354i	0.721191	−	0.721191i
$705$	−6.37195	+	3.67884i	−0.239981	+	0.138553i
$706$	10.1229	+	17.5334i	0.380981	+	0.659879i
$707$	3.96727	−	9.25423i	0.149204	−	0.348041i
$708$	10.9968	+	2.94659i	0.413285	+	0.110739i
$709$	34.1644	+	34.1644i	1.28307	+	1.28307i	0.938911	+	0.344160i	$0.111836\pi$
$709$	34.1644	+	34.1644i	1.28307	+	1.28307i	0.344160	+	0.938911i	$0.388164\pi$
$710$	34.2207	+	9.16940i	1.28428	+	0.344121i
$711$	2.31642	−	4.01217i	0.0868727	−	0.150468i
$712$	−1.70449	−	2.95227i	−0.0638786	−	0.110641i
$713$	−5.19489	−	19.3876i	−0.194550	−	0.726071i
$714$	37.7104	−	15.0795i	1.41128	−	0.564336i
$715$	−10.8466	−	13.9991i	−0.405638	−	0.523536i
$716$	2.28818	−	3.96325i	0.0855134	−	0.148114i
$717$	13.2347	+	13.2347i	0.494257	+	0.494257i
$718$	−71.6946			−2.67562
$719$	10.6433			0.396927			0.198463	−	0.980108i	$-0.436405\pi$
$719$	10.6433			0.396927			0.198463	+	0.980108i	$0.436405\pi$
$720$	4.22522	+	4.22522i	0.157465	+	0.157465i
$721$	15.0577	+	20.1314i	0.560776	+	0.749733i
$722$	9.80710	−	36.6006i	0.364983	−	1.36213i
$723$	−2.83676	+	0.760109i	−0.105500	+	0.0282688i
$724$	39.2988	+	22.6892i	1.46053	+	0.843237i
$725$		−	12.1093i		−	0.449730i
$726$	−9.55311	−	2.55975i	−0.354549	−	0.0950012i
$727$	−5.89296			−0.218558			−0.109279	−	0.994011i	$-0.534854\pi$
$727$	−5.89296			−0.218558			−0.109279	+	0.994011i	$0.534854\pi$
$728$	7.93291	+	0.0603683i	0.294013	+	0.00223740i
$729$	−1.00000			−0.0370370
$730$	30.8420	+	8.26408i	1.14151	+	0.305867i
$731$		−	85.6005i		−	3.16605i
$732$	−19.6222	−	11.3289i	−0.725257	−	0.418728i
$733$	37.0791	−	9.93532i	1.36955	−	0.366970i	0.502235	−	0.864731i	$-0.332511\pi$
$733$	37.0791	−	9.93532i	1.36955	−	0.366970i	0.867314	+	0.497762i	$0.165845\pi$
$734$	−14.5362	+	54.2499i	−0.536542	+	2.00240i
$735$	−7.14824	+	11.7064i	−0.263667	+	0.431797i
$736$	37.8207	+	37.8207i	1.39409	+	1.39409i
$737$	15.7269			0.579309
$738$	1.54128			0.0567352
$739$	−14.6029	−	14.6029i	−0.537176	−	0.537176i	0.385522	−	0.922699i	$-0.374021\pi$
$739$	−14.6029	−	14.6029i	−0.537176	−	0.537176i	−0.922699	+	0.385522i	$0.874021\pi$
$740$	−3.23458	+	5.60246i	−0.118906	+	0.205950i
$741$	−3.20415	+	1.34484i	−0.117708	+	0.0494040i
$742$	12.7236	+	1.83457i	0.467099	+	0.0673491i
$743$	8.72671	+	32.5685i	0.320152	+	1.19482i	0.919097	+	0.394033i	$0.128920\pi$
$743$	8.72671	+	32.5685i	0.320152	+	1.19482i	−0.598945	+	0.800790i	$0.704413\pi$
$744$	1.25726	+	2.17764i	0.0460934	+	0.0798361i
$745$	8.74028	−	15.1386i	0.320219	−	0.554636i
$746$	7.42228	+	1.98879i	0.271749	+	0.0728150i
$747$	−10.1090	−	10.1090i	−0.369869	−	0.369869i
$748$	42.4812	+	11.3828i	1.55327	+	0.416197i
$749$	−25.6281	+	3.05384i	−0.936430	+	0.111585i
$750$	12.6556	+	21.9201i	0.462116	+	0.800409i
$751$	27.5178	−	15.8874i	1.00414	−	0.579741i	0.0946696	−	0.995509i	$-0.469821\pi$
$751$	27.5178	−	15.8874i	1.00414	−	0.579741i	0.909471	+	0.415768i	$0.136487\pi$
$752$	−8.09679	+	8.09679i	−0.295259	+	0.295259i
$753$	−0.424072	+	0.244838i	−0.0154540	+	0.00892240i
$754$	72.7417	−	30.5310i	2.64910	−	1.11187i
$755$		−	25.2019i		−	0.917191i
$756$	−3.79790	−	5.07762i	−0.138128	−	0.184671i
$757$	−13.6215	+	23.5930i	−0.495080	+	0.857504i	−0.999984	−	0.00567171i	$-0.998195\pi$
$757$	−13.6215	+	23.5930i	−0.495080	+	0.857504i	0.504904	+	0.863176i	$0.331528\pi$
$758$		−	49.9334i		−	1.81366i
$759$	−4.30664	+	16.0726i	−0.156321	+	0.583398i
$760$	0.406476	+	1.51699i	0.0147444	+	0.0550270i
$761$	−20.1667	+	20.1667i	−0.731042	+	0.731042i	−0.970826	−	0.239784i	$-0.922923\pi$
$761$	−20.1667	+	20.1667i	−0.731042	+	0.731042i	0.239784	+	0.970826i	$0.422923\pi$
$762$	16.7985	−	16.7985i	0.608546	−	0.608546i
$763$	9.74935	−	12.3871i	0.352950	−	0.448444i
$764$	22.3928	+	12.9285i	0.810143	+	0.467736i
$765$	−3.71277	+	13.8563i	−0.134236	+	0.500974i
$766$	−32.0817	−	55.5671i	−1.15916	−	2.00772i
$767$	2.15595	−	16.9914i	0.0778467	−	0.613523i
$768$	6.85557	+	3.95806i	0.247379	+	0.142824i
$769$	27.2629	−	7.30506i	0.983124	−	0.263427i	0.268764	−	0.963206i	$-0.413385\pi$
$769$	27.2629	−	7.30506i	0.983124	−	0.263427i	0.714360	+	0.699779i	$0.246718\pi$
$770$	−25.3005	+	10.1171i	−0.911767	+	0.364594i
$771$	16.2048	−	9.35585i	0.583602	−	0.336943i
$772$	12.1913	+	45.4986i	0.438775	+	1.63753i
$773$	11.7186	−	3.13999i	0.421488	−	0.112937i	−0.0418396	−	0.999124i	$-0.513322\pi$
$773$	11.7186	−	3.13999i	0.421488	−	0.112937i	0.463328	+	0.886187i	$0.346655\pi$
$774$	−23.6819	+	6.34554i	−0.851227	+	0.228086i
$775$	−0.908157	−	3.38929i	−0.0326220	−	0.121747i
$776$	7.34530	−	4.24081i	0.263681	−	0.152236i
$777$	−2.25414	+	2.86402i	−0.0808668	+	0.102746i
$778$	2.38784	−	0.639819i	0.0856082	−	0.0229386i
$779$	−0.613518	−	0.354215i	−0.0219816	−	0.0126911i
$780$	−10.2444	+	13.4812i	−0.366810	+	0.482706i
$781$	10.8071	+	18.7184i	0.386708	+	0.669799i
$782$	−26.3735	+	98.4273i	−0.943115	+	3.51975i
$783$	−9.03685	−	5.21743i	−0.322951	−	0.186456i
$784$	−6.03031	+	20.4768i	−0.215368	+	0.731316i
$785$	−6.32841	+	6.32841i	−0.225871	+	0.225871i
$786$	−21.2164	+	21.2164i	−0.756763	+	0.756763i
$787$	−4.81648	−	17.9754i	−0.171689	−	0.640753i	−0.997092	−	0.0762083i	$-0.975719\pi$
$787$	−4.81648	−	17.9754i	−0.171689	−	0.640753i	0.825403	−	0.564544i	$-0.190948\pi$
$788$	7.11415	−	26.5504i	0.253431	−	0.945817i
$789$			3.44239i			0.122552i
$790$	−9.51735	+	16.4845i	−0.338612	+	0.586494i
$791$	−29.7322	+	3.54288i	−1.05715	+	0.125970i
$792$		−	2.08457i		−	0.0740720i
$793$	−12.8968	+	31.5533i	−0.457978	+	1.12049i
$794$	22.0655	−	12.7395i	0.783076	−	0.452109i
$795$	−3.21067	+	3.21067i	−0.113871	+	0.113871i
$796$	−11.5290	+	6.65625i	−0.408634	+	0.235925i
$797$	−16.8639	−	29.2091i	−0.597350	−	1.03464i	−0.993211	−	0.116330i	$-0.962887\pi$
$797$	−16.8639	−	29.2091i	−0.597350	−	1.03464i	0.395861	−	0.918311i	$-0.370446\pi$
$798$	0.632632	+	5.30911i	0.0223949	+	0.187941i
$799$	−26.5528	−	7.11479i	−0.939369	−	0.251703i
$800$	6.61172	+	6.61172i	0.233760	+	0.233760i
$801$	3.95954	+	1.06096i	0.139904	+	0.0374871i
$802$	−2.26114	+	3.91641i	−0.0798437	+	0.138293i
$803$	9.74009	+	16.8703i	0.343720	+	0.595341i
$804$	−3.89176	−	14.5242i	−0.137252	−	0.512230i
$805$	−12.7777	−	31.9541i	−0.450355	−	1.12623i
$806$	18.0700	−	14.0007i	0.636488	−	0.493154i
$807$	−4.52336	+	7.83469i	−0.159230	+	0.275794i
$808$	−2.23788	−	2.23788i	−0.0787283	−	0.0787283i
$809$	−45.3592			−1.59475			−0.797373	−	0.603487i	$-0.793778\pi$
$809$	−45.3592			−1.59475			−0.797373	+	0.603487i	$0.793778\pi$
$810$	4.10864			0.144363
$811$	−11.6911	−	11.6911i	−0.410531	−	0.410531i	0.471392	−	0.881924i	$-0.343752\pi$
$811$	−11.6911	−	11.6911i	−0.410531	−	0.410531i	−0.881924	+	0.471392i	$0.843752\pi$
$812$	−7.82891	−	65.7010i	−0.274741	−	2.30565i
$813$	−2.02520	+	7.55815i	−0.0710268	+	0.265076i
$814$	−6.99369	+	1.87395i	−0.245129	+	0.0656821i
$815$	−4.35335	−	2.51341i	−0.152491	−	0.0880409i
$816$			22.3249i			0.781526i
$817$	10.8851	+	2.91665i	0.380821	+	0.102041i
$818$	−10.0705			−0.352106
$819$	−6.79650	+	6.69384i	−0.237489	+	0.233902i
$820$	−3.45190			−0.120546
$821$	−17.3943	−	4.66078i	−0.607064	−	0.162662i	−0.0578239	−	0.998327i	$-0.518416\pi$
$821$	−17.3943	−	4.66078i	−0.607064	−	0.162662i	−0.549240	+	0.835664i	$0.685083\pi$
$822$		−	11.9428i		−	0.416551i
$823$	−19.4125	−	11.2078i	−0.676676	−	0.390679i	0.121925	−	0.992539i	$-0.461093\pi$
$823$	−19.4125	−	11.2078i	−0.676676	−	0.390679i	−0.798602	+	0.601860i	$0.794426\pi$
$824$	7.63273	−	2.04518i	0.265899	−	0.0712474i
$825$	−0.752875	+	2.80977i	−0.0262117	+	0.0978236i
$826$	−24.2213	−	10.3836i	−0.842767	−	0.361292i
$827$	21.3413	+	21.3413i	0.742110	+	0.742110i	0.972984	−	0.230873i	$-0.0741584\pi$
$827$	21.3413	+	21.3413i	0.742110	+	0.742110i	−0.230873	+	0.972984i	$0.574158\pi$
$828$	15.9091			0.552881
$829$	−2.33268			−0.0810172			−0.0405086	−	0.999179i	$-0.512898\pi$
$829$	−2.33268			−0.0810172			−0.0405086	+	0.999179i	$0.512898\pi$
$830$	41.5343	+	41.5343i	1.44167	+	1.44167i
$831$	0.774557	−	1.34157i	0.0268691	−	0.0465386i
$832$	−14.7272	+	36.0316i	−0.510574	+	1.24917i
$833$	−49.8112	+	12.0420i	−1.72586	+	0.417230i
$834$	5.87832	+	21.9382i	0.203549	+	0.759657i
$835$	−7.20728	−	12.4834i	−0.249418	−	0.432005i
$836$	−2.89491	+	5.01414i	−0.100123	+	0.173418i
$837$	−2.92062	−	0.782577i	−0.100951	−	0.0270498i
$838$	31.2854	+	31.2854i	1.08074	+	1.08074i
$839$	−32.4718	−	8.70079i	−1.12105	−	0.300385i	−0.349742	−	0.936846i	$-0.613731\pi$
$839$	−32.4718	−	8.70079i	−1.12105	−	0.300385i	−0.771308	+	0.636462i	$0.780397\pi$
$840$	2.58231	+	3.45244i	0.0890982	+	0.119120i
$841$	−39.9432	−	69.1836i	−1.37735	−	2.38564i
$842$	62.6935	−	36.1961i	2.16056	−	1.24740i
$843$	4.20181	−	4.20181i	0.144718	−	0.144718i
$844$	−33.4715	+	19.3248i	−1.15214	+	0.665187i
$845$	22.1789	+	12.5291i	0.762976	+	0.431014i
$846$			7.87339i			0.270693i
$847$	11.4698	+	4.91707i	0.394106	+	0.168952i
$848$	−3.53319	+	6.11966i	−0.121330	+	0.210150i
$849$			4.65614i			0.159798i
$850$	−4.61055	+	17.2068i	−0.158141	+	0.590189i
$851$	−2.36677	−	8.83292i	−0.0811320	−	0.302789i
$852$	14.6127	−	14.6127i	0.500621	−	0.500621i
$853$	−4.02453	+	4.02453i	−0.137797	+	0.137797i	−0.772641	−	0.634844i	$-0.781065\pi$
$853$	−4.02453	+	4.02453i	−0.137797	+	0.137797i	0.634844	+	0.772641i	$0.281065\pi$
$854$	41.2138	+	32.4376i	1.41031	+	1.10999i
$855$	−1.63548	−	0.944245i	−0.0559322	−	0.0322925i
$856$	−2.09966	+	7.83604i	−0.0717650	+	0.267830i
$857$	−7.66605	−	13.2780i	−0.261867	−	0.453567i	0.704871	−	0.709336i	$-0.251005\pi$
$857$	−7.66605	−	13.2780i	−0.261867	−	0.453567i	−0.966738	+	0.255768i	$0.917672\pi$
$858$	−18.7767	+	2.56163i	−0.641025	+	0.0874527i
$859$	−27.5049	−	15.8800i	−0.938455	−	0.541817i	−0.0489791	−	0.998800i	$-0.515597\pi$
$859$	−27.5049	−	15.8800i	−0.938455	−	0.541817i	−0.889476	+	0.456983i	$0.848930\pi$
$860$	53.0388	−	14.2117i	1.80861	−	0.484615i
$861$	−1.92487	−	0.277540i	−0.0655995	−	0.00945852i
$862$	14.9666	−	8.64096i	0.509764	−	0.294312i
$863$	0.350876	+	1.30949i	0.0119439	+	0.0445754i	0.971641	−	0.236462i	$-0.0759880\pi$
$863$	0.350876	+	1.30949i	0.0119439	+	0.0445754i	−0.959697	+	0.281038i	$0.909321\pi$
$864$	7.78286	−	2.08541i	0.264778	−	0.0709471i
$865$	−34.7151	+	9.30189i	−1.18035	+	0.316274i
$866$	14.4294	+	53.8511i	0.490330	+	1.82994i
$867$	−31.6925	+	18.2976i	−1.07633	+	0.621421i
$868$	−7.11857	−	17.8019i	−0.241620	−	0.604236i
$869$	−11.2172	+	3.00564i	−0.380517	+	0.101959i
$870$	37.1292	+	21.4365i	1.25880	+	0.726767i
$871$	−20.8588	+	8.75483i	−0.706774	+	0.296646i
$872$	−2.47742	−	4.29103i	−0.0838962	−	0.145312i
$873$	−2.63968	+	9.85141i	−0.0893396	+	0.333420i
$874$	−11.6175	−	6.70740i	−0.392969	−	0.226881i
$875$	−11.8582	−	29.6546i	−0.400879	−	1.00251i
$876$	13.1699	−	13.1699i	0.444970	−	0.444970i
$877$	33.1880	−	33.1880i	1.12068	−	1.12068i	0.129039	−	0.991640i	$-0.458811\pi$
$877$	33.1880	−	33.1880i	1.12068	−	1.12068i	0.991640	−	0.129039i	$-0.0411893\pi$
$878$	−9.70333	−	36.2133i	−0.327471	−	1.22214i
$879$	−2.89410	+	10.8009i	−0.0976156	+	0.364306i
$880$		−	14.9781i		−	0.504912i
$881$	−3.74445	+	6.48558i	−0.126154	+	0.218505i	−0.922183	−	0.386753i	$-0.873597\pi$
$881$	−3.74445	+	6.48558i	−0.126154	+	0.218505i	0.796030	+	0.605258i	$0.206930\pi$
$882$	7.02397	+	12.8879i	0.236509	+	0.433958i
$883$		−	21.6436i		−	0.728364i	−0.931328	−	0.364182i	$-0.881349\pi$
$883$		−	21.6436i		−	0.728364i	0.931328	−	0.364182i	$-0.118651\pi$
$884$	−62.6799	+	8.55118i	−2.10815	+	0.287607i
$885$	8.06111	−	4.65408i	0.270971	−	0.156445i
$886$	32.3008	−	32.3008i	1.08517	−	1.08517i
$887$	8.60156	−	4.96611i	0.288812	−	0.166746i	−0.348594	−	0.937274i	$-0.613341\pi$
$887$	8.60156	−	4.96611i	0.288812	−	0.166746i	0.637406	+	0.770528i	$0.280007\pi$
$888$	0.572804	+	0.992125i	0.0192220	+	0.0332935i
$889$	−24.0043	+	17.9544i	−0.805078	+	0.602173i
$890$	−16.2683	−	4.35909i	−0.545316	−	0.146117i
$891$	1.77246	+	1.77246i	0.0593798	+	0.0593798i
$892$	−61.4923	−	16.4768i	−2.05892	−	0.551685i
$893$	1.80946	−	3.13407i	0.0605511	−	0.104878i
$894$	−9.35289	−	16.1997i	−0.312807	−	0.541798i
$895$	−0.968408	−	3.61415i	−0.0323703	−	0.120808i
$896$	13.5598	+	10.6723i	0.453002	+	0.356538i
$897$	−3.23530	−	23.7146i	−0.108024	−	0.791809i
$898$	−3.44593	+	5.96852i	−0.114992	+	0.199172i
$899$	−22.3101	−	22.3101i	−0.744085	−	0.744085i
$900$	2.78120			0.0927066
$901$	−16.9642			−0.565161
$902$	−2.73186	−	2.73186i	−0.0909609	−	0.0909609i
$903$	30.7185	−	3.66041i	1.02225	−	0.121811i
$904$	−2.43590	+	9.09091i	−0.0810169	+	0.302359i
$905$	35.8372	−	9.60255i	1.19127	−	0.319199i
$906$	−23.3552	−	13.4841i	−0.775925	−	0.447981i
$907$			40.1732i			1.33393i	0.745089	+	0.666965i	$0.232407\pi$
$907$			40.1732i			1.33393i	−0.745089	+	0.666965i	$0.767593\pi$
$908$	4.11497	+	1.10260i	0.136560	+	0.0365912i
$909$	3.80563			0.126225
$910$	27.9244	−	27.5026i	0.925684	−	0.911702i
$911$	15.0163			0.497513			0.248757	−	0.968566i	$-0.419978\pi$
$911$	15.0163			0.497513			0.248757	+	0.968566i	$0.419978\pi$
$912$	−2.83886	−	0.760671i	−0.0940042	−	0.0251883i
$913$			35.8357i			1.18599i
$914$	−65.6167	−	37.8838i	−2.17041	−	1.25309i
$915$	−17.8938	+	4.79463i	−0.591550	+	0.158505i
$916$	5.57654	−	20.8119i	0.184254	−	0.687646i
$917$	30.3173	−	22.6763i	1.00116	−	0.748838i
$918$	10.8544	+	10.8544i	0.358250	+	0.358250i
$919$	18.8754			0.622643			0.311321	−	0.950305i	$-0.399228\pi$
$919$	18.8754			0.622643			0.311321	+	0.950305i	$0.399228\pi$
$920$	−10.8171			−0.356631
$921$	2.63969	+	2.63969i	0.0869807	+	0.0869807i
$922$	−13.4681	+	23.3274i	−0.443547	+	0.768246i
$923$	−24.7537	−	18.8104i	−0.814778	−	0.619152i
$924$	−2.26826	+	15.7315i	−0.0746204	+	0.517529i
$925$	−0.413754	−	1.54415i	−0.0136041	−	0.0507713i
$926$	32.9449	+	57.0622i	1.08264	+	1.87518i
$927$	−4.75097	+	8.22892i	−0.156042	+	0.270273i
$928$	81.2131	+	21.7610i	2.66595	+	0.714339i
$929$	33.1445	+	33.1445i	1.08744	+	1.08744i	0.995792	+	0.0916445i	$0.0292124\pi$
$929$	33.1445	+	33.1445i	1.08744	+	1.08744i	0.0916445	+	0.995792i	$0.470788\pi$
$930$	11.9998	+	3.21533i	0.393488	+	0.105435i
$931$	0.165935	−	6.74438i	0.00543829	−	0.221038i
$932$	−1.23388	−	2.13715i	−0.0404172	−	0.0700046i
$933$	28.2035	−	16.2833i	0.923341	−	0.533091i
$934$	50.8514	−	50.8514i	1.66391	−	1.66391i
$935$	31.1405	−	17.9790i	1.01840	−	0.587975i
$936$	1.16043	+	2.76479i	0.0379299	+	0.0903700i
$937$		−	17.9722i		−	0.587126i	−0.955940	−	0.293563i	$-0.905159\pi$
$937$		−	17.9722i		−	0.587126i	0.955940	−	0.293563i	$-0.0948411\pi$
$938$	4.11839	+	34.5619i	0.134470	+	1.12849i
$939$	−7.33945	+	12.7123i	−0.239514	+	0.414850i
$940$		−	17.6335i		−	0.575142i
$941$	−9.15389	+	34.1628i	−0.298408	+	1.11367i	0.640065	+	0.768321i	$0.278908\pi$
$941$	−9.15389	+	34.1628i	−0.298408	+	1.11367i	−0.938473	+	0.345353i	$0.887759\pi$
$942$	2.47871	+	9.25067i	0.0807608	+	0.301403i
$943$	3.45029	−	3.45029i	0.112357	−	0.112357i
$944$	10.2432	−	10.2432i	0.333388	−	0.333388i
$945$	−5.13121	−	0.739848i	−0.166918	−	0.0240673i
$946$	53.2225	+	30.7280i	1.73041	+	0.999054i
$947$	−0.0341422	+	0.127421i	−0.00110947	+	0.00414061i	−0.966478	−	0.256748i	$-0.917349\pi$
$947$	−0.0341422	+	0.127421i	−0.00110947	+	0.00414061i	0.965369	+	0.260889i	$0.0840156\pi$
$948$	5.55157	+	9.61560i	0.180307	+	0.312300i
$949$	−22.3097	−	16.9532i	−0.724204	−	0.550324i
$950$	−2.03095	−	1.17257i	−0.0658927	−	0.0380432i
$951$	−9.92063	+	2.65822i	−0.321698	+	0.0861988i
$952$	−2.29875	+	15.9429i	−0.0745028	+	0.516714i
$953$	30.3290	−	17.5105i	0.982454	−	0.567220i	0.0794437	−	0.996839i	$-0.474686\pi$
$953$	30.3290	−	17.5105i	0.982454	−	0.567220i	0.903010	+	0.429619i	$0.141352\pi$
$954$	1.25755	+	4.69325i	0.0407148	+	0.151950i
$955$	20.4203	−	5.47161i	0.660787	−	0.177057i
$956$	−43.3280	+	11.6097i	−1.40133	+	0.375485i
$957$	6.76979	+	25.2652i	0.218836	+	0.816708i
$958$	4.34099	−	2.50627i	0.140251	−	0.0809740i
$959$	−2.15055	+	14.9151i	−0.0694448	+	0.481634i
$960$	−20.4335	+	5.47513i	−0.659487	+	0.176709i
$961$	18.9292	+	10.9288i	0.610620	+	0.352542i
$962$	8.23263	−	6.37868i	0.265430	−	0.205657i
$963$	−4.87752	−	8.44811i	−0.157176	−	0.272236i
$964$	1.82169	−	6.79862i	0.0586725	−	0.218969i
$965$	33.3524	+	19.2560i	1.07365	+	0.619872i
$966$	−36.4493	−	5.25547i	−1.17274	−	0.169092i
$967$	−13.6207	+	13.6207i	−0.438014	+	0.438014i	−0.891343	−	0.453329i	$-0.850236\pi$
$967$	−13.6207	+	13.6207i	−0.438014	+	0.438014i	0.453329	+	0.891343i	$0.350236\pi$
$968$	2.77365	−	2.77365i	0.0891484	−	0.0891484i
$969$	−1.82614	−	6.81526i	−0.0586642	−	0.218938i
$970$	10.8455	−	40.4759i	0.348228	−	1.29960i
$971$			3.40717i			0.109341i	0.998504	+	0.0546707i	$0.0174109\pi$
$971$			3.40717i			0.109341i	−0.998504	+	0.0546707i	$0.982589\pi$
$972$	1.19831	−	2.07553i	0.0384357	−	0.0665725i
$973$	−3.39090	−	28.4567i	−0.108707	−	0.912281i
$974$		−	17.5974i		−	0.563858i
$975$	−0.565587	−	4.14573i	−0.0181133	−	0.132770i
$976$	−24.9675	+	14.4150i	−0.799191	+	0.461413i
$977$	8.46644	−	8.46644i	0.270865	−	0.270865i	−0.558583	−	0.829449i	$-0.688655\pi$
$977$	8.46644	−	8.46644i	0.270865	−	0.270865i	0.829449	+	0.558583i	$0.188655\pi$
$978$	−4.65848	+	2.68957i	−0.148962	+	0.0860031i
$979$	−5.13764	−	8.89866i	−0.164200	−	0.284402i
$980$	−15.7311	−	28.8642i	−0.502513	−	0.922033i
$981$	5.75506	+	1.54206i	0.183745	+	0.0492343i
$982$	−9.36262	−	9.36262i	−0.298773	−	0.298773i
$983$	−10.9991	−	2.94720i	−0.350817	−	0.0940010i	0.0791074	−	0.996866i	$-0.474793\pi$
$983$	−10.9991	−	2.94720i	−0.350817	−	0.0940010i	−0.429924	+	0.902865i	$0.641460\pi$
$984$	−0.305644	+	0.529391i	−0.00974357	+	0.0168764i
$985$	−11.2367	−	19.4625i	−0.358030	−	0.620127i
$986$	41.4577	+	154.722i	1.32028	+	4.92736i
$987$	1.41777	−	9.83294i	0.0451281	−	0.312986i
$988$	1.04830	−	8.26184i	0.0333509	−	0.262844i
$989$	−38.8090	+	67.2192i	−1.23405	+	2.13744i
$990$	−7.28242	−	7.28242i	−0.231450	−	0.231450i
$991$	33.8862			1.07643			0.538216	−	0.842807i	$-0.319099\pi$
$991$	33.8862			1.07643			0.538216	+	0.842807i	$0.319099\pi$
$992$	24.3627			0.773518
$993$	17.8973	+	17.8973i	0.567953	+	0.567953i
$994$	−38.3061	+	28.6517i	−1.21500	+	0.908778i
$995$	−2.81707	+	10.5134i	−0.0893071	+	0.333299i
$996$	33.0952	−	8.86783i	1.04866	−	0.280988i
$997$	−31.6123	−	18.2514i	−1.00117	−	0.578026i	−0.0925764	−	0.995706i	$-0.529510\pi$
$997$	−31.6123	−	18.2514i	−1.00117	−	0.578026i	−0.908595	+	0.417679i	$0.862844\pi$
$998$		−	73.7049i		−	2.33309i
$999$	−1.33062	−	0.356539i	−0.0420991	−	0.0112804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.a.19.8	yes	36
3.2	odd	2		819.2.gh.c.19.2		36
7.3	odd	6		273.2.bt.a.136.2	✓	36
13.11	odd	12		273.2.bt.a.271.2	yes	36
21.17	even	6		819.2.et.c.136.8		36
39.11	even	12		819.2.et.c.271.8		36
91.24	even	12	inner	273.2.cg.a.115.8	yes	36
273.206	odd	12		819.2.gh.c.388.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.2	✓	36	7.3	odd	6
273.2.bt.a.271.2	yes	36	13.11	odd	12
273.2.cg.a.19.8	yes	36	1.1	even	1	trivial
273.2.cg.a.115.8	yes	36	91.24	even	12	inner
819.2.et.c.136.8		36	21.17	even	6
819.2.et.c.271.8		36	39.11	even	12
819.2.gh.c.19.2		36	3.2	odd	2
819.2.gh.c.388.2		36	273.206	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.02536 + 0.542694i) q^{2} -1.00000i q^{3} +(2.07553 + 1.19831i) q^{4} +(1.89270 - 0.507149i) q^{5} +(0.542694 - 2.02536i) q^{6} +(-1.04247 + 2.43172i) q^{7} +(0.588043 + 0.588043i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(2.02536 + 0.542694i) q^{2} -1.00000i q^{3} +(2.07553 + 1.19831i) q^{4} +(1.89270 - 0.507149i) q^{5} +(0.542694 - 2.02536i) q^{6} +(-1.04247 + 2.43172i) q^{7} +(0.588043 + 0.588043i) q^{8} -1.00000 q^{9} +4.10864 q^{10} +(1.77246 + 1.77246i) q^{11} +(1.19831 - 2.07553i) q^{12} +(-3.33753 - 1.36415i) q^{13} +(-3.43106 + 4.35937i) q^{14} +(-0.507149 - 1.89270i) q^{15} +(-1.52474 - 2.64092i) q^{16} +(3.66044 - 6.34007i) q^{17} +(-2.02536 - 0.542694i) q^{18} +(0.681492 + 0.681492i) q^{19} +(4.53608 + 1.21544i) q^{20} +(2.43172 + 1.04247i) q^{21} +(2.62798 + 4.55179i) q^{22} +(-5.74884 + 3.31909i) q^{23} +(0.588043 - 0.588043i) q^{24} +(-1.00500 + 0.580235i) q^{25} +(-6.01939 - 4.57415i) q^{26} +1.00000i q^{27} +(-5.07762 + 3.79790i) q^{28} +(-5.21743 + 9.03685i) q^{29} -4.10864i q^{30} +(-0.782577 + 2.92062i) q^{31} +(-2.08541 - 7.78286i) q^{32} +(1.77246 - 1.77246i) q^{33} +(10.8544 - 10.8544i) q^{34} +(-0.739848 + 5.13121i) q^{35} +(-2.07553 - 1.19831i) q^{36} +(-0.356539 + 1.33062i) q^{37} +(1.01043 + 1.75011i) q^{38} +(-1.36415 + 3.33753i) q^{39} +(1.41122 + 0.814767i) q^{40} +(-0.710011 + 0.190247i) q^{41} +(4.35937 + 3.43106i) q^{42} +(10.1261 - 5.84633i) q^{43} +(1.55484 + 5.80275i) q^{44} +(-1.89270 + 0.507149i) q^{45} +(-13.4447 + 3.60251i) q^{46} +(-0.971849 - 3.62699i) q^{47} +(-2.64092 + 1.52474i) q^{48} +(-4.82651 - 5.06999i) q^{49} +(-2.35037 + 0.629781i) q^{50} +(-6.34007 - 3.66044i) q^{51} +(-5.29246 - 6.83071i) q^{52} +(-1.15862 - 2.00679i) q^{53} +(-0.542694 + 2.02536i) q^{54} +(4.25365 + 2.45585i) q^{55} +(-2.04297 + 0.816937i) q^{56} +(0.681492 - 0.681492i) q^{57} +(-15.4714 + 15.4714i) q^{58} +(1.22948 + 4.58848i) q^{59} +(1.21544 - 4.53608i) q^{60} -9.45408i q^{61} +(-3.17000 + 5.49061i) q^{62} +(1.04247 - 2.43172i) q^{63} -10.7959i q^{64} +(-7.00878 - 0.889307i) q^{65} +(4.55179 - 2.62798i) q^{66} +(4.43646 - 4.43646i) q^{67} +(15.1947 - 8.77265i) q^{68} +(3.31909 + 5.74884i) q^{69} +(-4.28314 + 9.99105i) q^{70} +(8.32895 + 2.23174i) q^{71} +(-0.588043 - 0.588043i) q^{72} +(7.50661 + 2.01139i) q^{73} +(-1.44424 + 2.50150i) q^{74} +(0.580235 + 1.00500i) q^{75} +(0.597819 + 2.23109i) q^{76} +(-6.15788 + 2.46239i) q^{77} +(-4.57415 + 6.01939i) q^{78} +(-2.31642 + 4.01217i) q^{79} +(-4.22522 - 4.22522i) q^{80} +1.00000 q^{81} -1.54128 q^{82} +(10.1090 + 10.1090i) q^{83} +(3.79790 + 5.07762i) q^{84} +(3.71277 - 13.8563i) q^{85} +(23.6819 - 6.34554i) q^{86} +(9.03685 + 5.21743i) q^{87} +2.08457i q^{88} +(-3.95954 - 1.06096i) q^{89} -4.10864 q^{90} +(6.79650 - 6.69384i) q^{91} -15.9091 q^{92} +(2.92062 + 0.782577i) q^{93} -7.87339i q^{94} +(1.63548 + 0.944245i) q^{95} +(-7.78286 + 2.08541i) q^{96} +(2.63968 - 9.85141i) q^{97} +(-7.02397 - 12.8879i) q^{98} +(-1.77246 - 1.77246i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^7 - 36 * q^9	\( 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

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