LMFDB - Embedded newform 273.2.t.d.4.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(4,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 1]))

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

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

chi := DirichletCharacter("273.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + \cdots + 576 $ x^20 + 33x^18 + 455x^16 + 3403x^14 + 15006x^12 + 39799x^10 + 62505x^8 + 55993x^6 + 27166x^4 + 6435*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.5
Root			$-0.560998i$ of defining polynomial
Character	$\chi$	$=$	273.4
Dual form			273.2.t.d.205.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.560998i q^{2} +(0.500000 + 0.866025i) q^{3} +1.68528 q^{4} +(0.449963 - 0.259786i) q^{5} +(0.485838 - 0.280499i) q^{6} +(0.680125 + 2.55684i) q^{7} -2.06743i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-0.560998i q^{2} +(0.500000 + 0.866025i) q^{3} +1.68528 q^{4} +(0.449963 - 0.259786i) q^{5} +(0.485838 - 0.280499i) q^{6} +(0.680125 + 2.55684i) q^{7} -2.06743i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.145740 - 0.252428i) q^{10} +(-1.87712 + 1.08375i) q^{11} +(0.842641 + 1.45950i) q^{12} +(3.29920 - 1.45439i) q^{13} +(1.43438 - 0.381548i) q^{14} +(0.449963 + 0.259786i) q^{15} +2.21074 q^{16} -4.96102 q^{17} +(0.485838 + 0.280499i) q^{18} +(-4.78119 - 2.76042i) q^{19} +(0.758315 - 0.437813i) q^{20} +(-1.87423 + 1.86743i) q^{21} +(0.607984 + 1.05306i) q^{22} +6.79504 q^{23} +(1.79045 - 1.03372i) q^{24} +(-2.36502 + 4.09634i) q^{25} +(-0.815910 - 1.85085i) q^{26} -1.00000 q^{27} +(1.14620 + 4.30900i) q^{28} +(3.81357 - 6.60529i) q^{29} +(0.145740 - 0.252428i) q^{30} +(5.15974 + 2.97898i) q^{31} -5.37509i q^{32} +(-1.87712 - 1.08375i) q^{33} +2.78312i q^{34} +(0.970263 + 0.973797i) q^{35} +(-0.842641 + 1.45950i) q^{36} -5.84715i q^{37} +(-1.54859 + 2.68224i) q^{38} +(2.90914 + 2.13000i) q^{39} +(-0.537091 - 0.930269i) q^{40} +(-9.23279 - 5.33055i) q^{41} +(1.04762 + 1.05144i) q^{42} +(-2.11946 - 3.67102i) q^{43} +(-3.16347 + 1.82643i) q^{44} +0.519573i q^{45} -3.81200i q^{46} +(-9.69377 + 5.59670i) q^{47} +(1.10537 + 1.91455i) q^{48} +(-6.07486 + 3.47794i) q^{49} +(2.29804 + 1.32677i) q^{50} +(-2.48051 - 4.29637i) q^{51} +(5.56009 - 2.45106i) q^{52} +(1.04639 - 1.81239i) q^{53} +0.560998i q^{54} +(-0.563089 + 0.975299i) q^{55} +(5.28610 - 1.40611i) q^{56} -5.52084i q^{57} +(-3.70555 - 2.13940i) q^{58} +3.04831i q^{59} +(0.758315 + 0.437813i) q^{60} +(-3.12454 + 5.41186i) q^{61} +(1.67120 - 2.89460i) q^{62} +(-2.55435 - 0.689415i) q^{63} +1.40606 q^{64} +(1.10669 - 1.51151i) q^{65} +(-0.607984 + 1.05306i) q^{66} +(-1.71581 + 0.990626i) q^{67} -8.36071 q^{68} +(3.39752 + 5.88468i) q^{69} +(0.546298 - 0.544315i) q^{70} +(-8.61474 + 4.97372i) q^{71} +(1.79045 + 1.03372i) q^{72} +(-2.47088 - 1.42656i) q^{73} -3.28024 q^{74} -4.73004 q^{75} +(-8.05765 - 4.65209i) q^{76} +(-4.04766 - 4.06240i) q^{77} +(1.19492 - 1.63202i) q^{78} +(2.48141 + 4.29793i) q^{79} +(0.994750 - 0.574319i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.99043 + 5.17957i) q^{82} -3.65923i q^{83} +(-3.15860 + 3.14714i) q^{84} +(-2.23228 + 1.28880i) q^{85} +(-2.05943 + 1.18901i) q^{86} +7.62713 q^{87} +(2.24059 + 3.88082i) q^{88} -2.53038i q^{89} +0.291479 q^{90} +(5.96251 + 7.44637i) q^{91} +11.4516 q^{92} +5.95796i q^{93} +(3.13974 + 5.43818i) q^{94} -2.86848 q^{95} +(4.65496 - 2.68754i) q^{96} +(8.01957 - 4.63010i) q^{97} +(1.95112 + 3.40798i) q^{98} -2.16751i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9}+O(q^{10}) $ 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9	$ 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9} + 2 q^{10} - 12 q^{11} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} + 42 q^{16} + 16 q^{17} + 3 q^{18} - 9 q^{19} - 5 q^{21} - 9 q^{22} - 36 q^{23} + 3 q^{24} + 12 q^{25} - 16 q^{26} - 20 q^{27} - 2 q^{28} - 3 q^{29} - 2 q^{30} - 18 q^{31} - 12 q^{33} + 18 q^{35} + 13 q^{36} + 9 q^{38} + 7 q^{39} + 5 q^{40} + 21 q^{41} + 16 q^{42} + 16 q^{43} - 6 q^{44} + 21 q^{47} + 21 q^{48} - 24 q^{49} - 54 q^{50} + 8 q^{51} - 41 q^{52} - 26 q^{53} + 17 q^{55} - 6 q^{56} + 42 q^{58} + 4 q^{62} - 7 q^{63} - 46 q^{64} - 50 q^{65} + 9 q^{66} - 3 q^{67} + 6 q^{68} - 18 q^{69} + 15 q^{71} + 3 q^{72} - 9 q^{73} + 12 q^{74} + 24 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} - 24 q^{80} - 10 q^{81} + 15 q^{82} + 41 q^{84} - 78 q^{85} + 3 q^{86} - 6 q^{87} - 22 q^{88} - 4 q^{90} + 4 q^{91} + 142 q^{92} + 36 q^{94} - 84 q^{95} - 24 q^{96} - 15 q^{97} + 81 q^{98}+O(q^{100}) $ 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9 + 2 * q^10 - 12 * q^11 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 + 42 * q^16 + 16 * q^17 + 3 * q^18 - 9 * q^19 - 5 * q^21 - 9 * q^22 - 36 * q^23 + 3 * q^24 + 12 * q^25 - 16 * q^26 - 20 * q^27 - 2 * q^28 - 3 * q^29 - 2 * q^30 - 18 * q^31 - 12 * q^33 + 18 * q^35 + 13 * q^36 + 9 * q^38 + 7 * q^39 + 5 * q^40 + 21 * q^41 + 16 * q^42 + 16 * q^43 - 6 * q^44 + 21 * q^47 + 21 * q^48 - 24 * q^49 - 54 * q^50 + 8 * q^51 - 41 * q^52 - 26 * q^53 + 17 * q^55 - 6 * q^56 + 42 * q^58 + 4 * q^62 - 7 * q^63 - 46 * q^64 - 50 * q^65 + 9 * q^66 - 3 * q^67 + 6 * q^68 - 18 * q^69 + 15 * q^71 + 3 * q^72 - 9 * q^73 + 12 * q^74 + 24 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 - 24 * q^80 - 10 * q^81 + 15 * q^82 + 41 * q^84 - 78 * q^85 + 3 * q^86 - 6 * q^87 - 22 * q^88 - 4 * q^90 + 4 * q^91 + 142 * q^92 + 36 * q^94 - 84 * q^95 - 24 * q^96 - 15 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	0.560998i		−	0.396685i	−0.980133	−	0.198343i	$-0.936444\pi$
$2$		−	0.560998i		−	0.396685i	0.980133	−	0.198343i	$-0.0635559\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.68528			0.842641
$5$	0.449963	−	0.259786i	0.201230	−	0.116180i	−0.395999	−	0.918251i	$-0.629602\pi$
$5$	0.449963	−	0.259786i	0.201230	−	0.116180i	0.597229	+	0.802071i	$0.296268\pi$
$6$	0.485838	−	0.280499i	0.198343	−	0.114513i
$7$	0.680125	+	2.55684i	0.257063	+	0.966395i
$7$	0.680125	+	2.55684i	0.257063	+	0.966395i
$8$		−	2.06743i		−	0.730948i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.145740	−	0.252428i	−0.0460869	−	0.0798248i
$11$	−1.87712	+	1.08375i	−0.565972	+	0.326764i	−0.755539	−	0.655104i	$-0.772625\pi$
$11$	−1.87712	+	1.08375i	−0.565972	+	0.326764i	0.189567	+	0.981868i	$0.439292\pi$
$12$	0.842641	+	1.45950i	0.243249	+	0.421320i
$13$	3.29920	−	1.45439i	0.915035	−	0.403375i
$13$	3.29920	−	1.45439i	0.915035	−	0.403375i
$14$	1.43438	−	0.381548i	0.383355	−	0.101973i
$15$	0.449963	+	0.259786i	0.116180	+	0.0670766i
$16$	2.21074			0.552684
$17$	−4.96102			−1.20322			−0.601612	−	0.798789i	$-0.705475\pi$
$17$	−4.96102			−1.20322			−0.601612	+	0.798789i	$0.705475\pi$
$18$	0.485838	+	0.280499i	0.114513	+	0.0661142i
$19$	−4.78119	−	2.76042i	−1.09688	−	0.633284i	−0.161481	−	0.986876i	$-0.551627\pi$
$19$	−4.78119	−	2.76042i	−1.09688	−	0.633284i	−0.935400	+	0.353592i	$0.884960\pi$
$20$	0.758315	−	0.437813i	0.169564	−	0.0978980i
$21$	−1.87423	+	1.86743i	−0.408990	+	0.407506i
$22$	0.607984	+	1.05306i	0.129623	+	0.224513i
$23$	6.79504			1.41686			0.708432	−	0.705779i	$-0.249403\pi$
$23$	6.79504			1.41686			0.708432	+	0.705779i	$0.249403\pi$
$24$	1.79045	−	1.03372i	0.365474	−	0.211007i
$25$	−2.36502	+	4.09634i	−0.473004	+	0.819268i
$26$	−0.815910	−	1.85085i	−0.160013	−	0.362981i
$27$	−1.00000			−0.192450
$28$	1.14620	+	4.30900i	0.216612	+	0.814324i
$29$	3.81357	−	6.60529i	0.708161	−	1.22657i	−0.257377	−	0.966311i	$-0.582858\pi$
$29$	3.81357	−	6.60529i	0.708161	−	1.22657i	0.965538	−	0.260260i	$-0.0838084\pi$
$30$	0.145740	−	0.252428i	0.0266083	−	0.0460869i
$31$	5.15974	+	2.97898i	0.926717	+	0.535040i	0.885772	−	0.464121i	$-0.153630\pi$
$31$	5.15974	+	2.97898i	0.926717	+	0.535040i	0.0409451	+	0.999161i	$0.486963\pi$
$32$		−	5.37509i		−	0.950190i
$33$	−1.87712	−	1.08375i	−0.326764	−	0.188657i
$34$			2.78312i			0.477301i
$35$	0.970263	+	0.973797i	0.164004	+	0.164602i
$36$	−0.842641	+	1.45950i	−0.140440	+	0.243249i
$37$		−	5.84715i		−	0.961266i	−0.876922	−	0.480633i	$-0.840407\pi$
$37$		−	5.84715i		−	0.961266i	0.876922	−	0.480633i	$-0.159593\pi$
$38$	−1.54859	+	2.68224i	−0.251215	+	0.435116i
$39$	2.90914	+	2.13000i	0.465835	+	0.341073i
$40$	−0.537091	−	0.930269i	−0.0849216	−	0.147089i
$41$	−9.23279	−	5.33055i	−1.44192	−	0.832492i	−0.443941	−	0.896056i	$-0.646420\pi$
$41$	−9.23279	−	5.33055i	−1.44192	−	0.832492i	−0.997978	+	0.0635633i	$0.979754\pi$
$42$	1.04762	+	1.05144i	0.161651	+	0.162240i
$43$	−2.11946	−	3.67102i	−0.323215	−	0.559825i	0.657934	−	0.753075i	$-0.271430\pi$
$43$	−2.11946	−	3.67102i	−0.323215	−	0.559825i	−0.981150	+	0.193250i	$0.938097\pi$
$44$	−3.16347	+	1.82643i	−0.476911	+	0.275345i
$45$			0.519573i			0.0774533i
$46$		−	3.81200i		−	0.562049i
$47$	−9.69377	+	5.59670i	−1.41398	+	0.816363i	−0.995761	−	0.0919829i	$-0.970679\pi$
$47$	−9.69377	+	5.59670i	−1.41398	+	0.816363i	−0.418221	+	0.908345i	$0.637346\pi$
$48$	1.10537	+	1.91455i	0.159546	+	0.276342i
$49$	−6.07486	+	3.47794i	−0.867837	+	0.496848i
$50$	2.29804	+	1.32677i	0.324991	+	0.187634i
$51$	−2.48051	−	4.29637i	−0.347341	−	0.601612i
$52$	5.56009	−	2.45106i	0.771045	−	0.339901i
$53$	1.04639	−	1.81239i	0.143732	−	0.248951i	−0.785167	−	0.619284i	$-0.787423\pi$
$53$	1.04639	−	1.81239i	0.143732	−	0.248951i	0.928899	+	0.370333i	$0.120756\pi$
$54$			0.560998i			0.0763421i
$55$	−0.563089	+	0.975299i	−0.0759269	+	0.131509i
$56$	5.28610	−	1.40611i	0.706385	−	0.187900i
$57$		−	5.52084i		−	0.731254i
$58$	−3.70555	−	2.13940i	−0.486563	−	0.280917i
$59$			3.04831i			0.396856i	0.980115	+	0.198428i	$0.0635837\pi$
$59$			3.04831i			0.396856i	−0.980115	+	0.198428i	$0.936416\pi$
$60$	0.758315	+	0.437813i	0.0978980	+	0.0565214i
$61$	−3.12454	+	5.41186i	−0.400056	+	0.692917i	−0.993732	−	0.111787i	$-0.964343\pi$
$61$	−3.12454	+	5.41186i	−0.400056	+	0.692917i	0.593676	+	0.804704i	$0.297676\pi$
$62$	1.67120	−	2.89460i	0.212243	−	0.367615i
$63$	−2.55435	−	0.689415i	−0.321818	−	0.0868581i
$64$	1.40606			0.175758
$65$	1.10669	−	1.51151i	0.137268	−	0.187480i
$66$	−0.607984	+	1.05306i	−0.0748376	+	0.129623i
$67$	−1.71581	+	0.990626i	−0.209620	+	0.121024i	−0.601135	−	0.799148i	$-0.705285\pi$
$67$	−1.71581	+	0.990626i	−0.209620	+	0.121024i	0.391515	+	0.920172i	$0.371951\pi$
$68$	−8.36071			−1.01389
$69$	3.39752	+	5.88468i	0.409014	+	0.708432i
$70$	0.546298	−	0.544315i	0.0652951	−	0.0650581i
$71$	−8.61474	+	4.97372i	−1.02238	+	0.590272i	−0.914793	−	0.403923i	$-0.867646\pi$
$71$	−8.61474	+	4.97372i	−1.02238	+	0.590272i	−0.107589	+	0.994195i	$0.534313\pi$
$72$	1.79045	+	1.03372i	0.211007	+	0.121825i
$73$	−2.47088	−	1.42656i	−0.289195	−	0.166967i	0.348384	−	0.937352i	$-0.386731\pi$
$73$	−2.47088	−	1.42656i	−0.289195	−	0.166967i	−0.637579	+	0.770385i	$0.720064\pi$
$74$	−3.28024			−0.381320
$75$	−4.73004			−0.546178
$76$	−8.05765	−	4.65209i	−0.924276	−	0.533631i
$77$	−4.04766	−	4.06240i	−0.461274	−	0.462953i
$78$	1.19492	−	1.63202i	0.135299	−	0.184790i
$79$	2.48141	+	4.29793i	0.279181	+	0.483555i	0.971181	−	0.238342i	$-0.0766039\pi$
$79$	2.48141	+	4.29793i	0.279181	+	0.483555i	−0.692001	+	0.721897i	$0.743271\pi$
$80$	0.994750	−	0.574319i	0.111216	−	0.0642109i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.99043	+	5.17957i	−0.330238	+	0.571988i
$83$		−	3.65923i		−	0.401653i	−0.979627	−	0.200826i	$-0.935637\pi$
$83$		−	3.65923i		−	0.401653i	0.979627	−	0.200826i	$-0.0643627\pi$
$84$	−3.15860	+	3.14714i	−0.344631	+	0.343381i
$85$	−2.23228	+	1.28880i	−0.242124	+	0.139791i
$86$	−2.05943	+	1.18901i	−0.222074	+	0.128215i
$87$	7.62713			0.817714
$88$	2.24059	+	3.88082i	0.238848	+	0.413696i
$89$		−	2.53038i		−	0.268220i	−0.990966	−	0.134110i	$-0.957182\pi$
$89$		−	2.53038i		−	0.268220i	0.990966	−	0.134110i	$-0.0428176\pi$
$90$	0.291479			0.0307246
$91$	5.96251	+	7.44637i	0.625041	+	0.780592i
$92$	11.4516			1.19391
$93$			5.95796i			0.617811i
$94$	3.13974	+	5.43818i	0.323839	+	0.560906i
$95$	−2.86848			−0.294300
$96$	4.65496	−	2.68754i	0.475095	−	0.274296i
$97$	8.01957	−	4.63010i	0.814264	−	0.470116i	−0.0341702	−	0.999416i	$-0.510879\pi$
$97$	8.01957	−	4.63010i	0.814264	−	0.470116i	0.848435	+	0.529300i	$0.177545\pi$
$98$	1.95112	+	3.40798i	0.197092	+	0.344258i
$99$		−	2.16751i		−	0.217843i
$100$	−3.98573	+	6.90348i	−0.398573	+	0.690348i
$101$	4.52199	+	7.83231i	0.449955	+	0.779344i	0.998383	−	0.0568535i	$-0.0181068\pi$
$101$	4.52199	+	7.83231i	0.449955	+	0.779344i	−0.548428	+	0.836198i	$0.684773\pi$
$102$	−2.41025	+	1.39156i	−0.238651	+	0.137785i
$103$	−8.82890	−	15.2921i	−0.869937	−	1.50678i	−0.862060	−	0.506806i	$-0.830826\pi$
$103$	−8.82890	−	15.2921i	−0.869937	−	1.50678i	−0.00787730	−	0.999969i	$-0.502507\pi$
$104$	−3.00686	−	6.82089i	−0.294847	−	0.668843i
$105$	−0.358201	+	1.32717i	−0.0349569	+	0.129519i
$106$	−1.01675	−	0.587020i	−0.0987553	−	0.0570164i
$107$	19.4601			1.88128			0.940639	−	0.339408i	$-0.110227\pi$
$107$	19.4601			1.88128			0.940639	+	0.339408i	$0.110227\pi$
$108$	−1.68528			−0.162166
$109$	−14.1408	−	8.16420i	−1.35444	−	0.781989i	−0.365576	−	0.930782i	$-0.619128\pi$
$109$	−14.1408	−	8.16420i	−1.35444	−	0.781989i	−0.988868	+	0.148793i	$0.952461\pi$
$110$	0.547140	+	0.315892i	0.0521678	+	0.0301191i
$111$	5.06378	−	2.92358i	0.480633	−	0.277494i
$112$	1.50358	+	5.65250i	0.142075	+	0.534111i
$113$	6.19998	+	10.7387i	0.583245	+	1.01021i	0.995092	+	0.0989565i	$0.0315505\pi$
$113$	6.19998	+	10.7387i	0.583245	+	1.01021i	−0.411847	+	0.911253i	$0.635116\pi$
$114$	−3.09718			−0.290078
$115$	3.05752	−	1.76526i	0.285115	−	0.164611i
$116$	6.42693	−	11.1318i	0.596726	−	1.03356i
$117$	−0.390063	+	3.58439i	−0.0360613	+	0.331377i
$118$	1.71010			0.157427
$119$	−3.37411	−	12.6845i	−0.309304	−	1.16279i
$120$	0.537091	−	0.930269i	0.0490295	−	0.0849216i
$121$	−3.15095	+	5.45761i	−0.286450	+	0.496147i
$122$	3.03604	+	1.75286i	0.274870	+	0.158696i
$123$		−	10.6611i		−	0.961280i
$124$	8.69562	+	5.02042i	0.780889	+	0.450847i
$125$			5.05547i			0.452175i
$126$	−0.386760	+	1.43298i	−0.0344553	+	0.127660i
$127$	10.1675	−	17.6107i	0.902223	−	1.56270i	0.0776210	−	0.996983i	$-0.475268\pi$
$127$	10.1675	−	17.6107i	0.902223	−	1.56270i	0.824602	−	0.565713i	$-0.191399\pi$
$128$		−	11.5390i		−	1.01991i
$129$	2.11946	−	3.67102i	0.186608	−	0.323215i
$130$	−0.847954	−	0.620850i	−0.0743705	−	0.0544522i
$131$	6.88948	+	11.9329i	0.601937	+	1.04258i	0.992528	+	0.122020i	$0.0389374\pi$
$131$	6.88948	+	11.9329i	0.601937	+	1.04258i	−0.390591	+	0.920564i	$0.627729\pi$
$132$	−3.16347	−	1.82643i	−0.275345	−	0.158970i
$133$	3.80615	−	14.1022i	0.330035	−	1.22281i
$134$	0.555739	+	0.962568i	0.0480085	+	0.0831532i
$135$	−0.449963	+	0.259786i	−0.0387267	+	0.0223589i
$136$			10.2566i			0.879494i
$137$			1.62129i			0.138516i	0.997599	+	0.0692579i	$0.0220631\pi$
$137$			1.62129i			0.138516i	−0.997599	+	0.0692579i	$0.977937\pi$
$138$	3.30129	−	1.90600i	0.281025	−	0.162250i
$139$	3.66875	+	6.35446i	0.311179	+	0.538979i	0.978618	−	0.205686i	$-0.0659426\pi$
$139$	3.66875	+	6.35446i	0.311179	+	0.538979i	−0.667439	+	0.744665i	$0.732609\pi$
$140$	1.63517	+	1.64112i	0.138197	+	0.138700i
$141$	−9.69377	−	5.59670i	−0.816363	−	0.471327i
$142$	2.79025	+	4.83285i	0.234152	+	0.405564i
$143$	−4.61679	+	6.30559i	−0.386075	+	0.527300i
$144$	−1.10537	+	1.91455i	−0.0921140	+	0.159546i
$145$		−	3.96285i		−	0.329097i
$146$	−0.800299	+	1.38616i	−0.0662332	+	0.114719i
$147$	−6.04941	−	3.52201i	−0.498947	−	0.290491i
$148$		−	9.85410i		−	0.810002i
$149$	−0.930883	−	0.537446i	−0.0762609	−	0.0440293i	0.461385	−	0.887200i	$-0.347353\pi$
$149$	−0.930883	−	0.537446i	−0.0762609	−	0.0440293i	−0.537646	+	0.843171i	$0.680686\pi$
$150$			2.65354i			0.216661i
$151$	10.8708	+	6.27625i	0.884652	+	0.510754i	0.872189	−	0.489168i	$-0.162700\pi$
$151$	10.8708	+	6.27625i	0.884652	+	0.510754i	0.0124624	+	0.999922i	$0.496033\pi$
$152$	−5.70699	+	9.88480i	−0.462898	+	0.801763i
$153$	2.48051	−	4.29637i	0.200537	−	0.347341i
$154$	−2.27900	+	2.27073i	−0.183647	+	0.182980i
$155$	3.09559			0.248644
$156$	4.90272	+	3.58965i	0.392532	+	0.287402i
$157$	0.346108	−	0.599476i	0.0276224	−	0.0478434i	−0.851884	−	0.523731i	$-0.824540\pi$
$157$	0.346108	−	0.599476i	0.0276224	−	0.0478434i	0.879506	+	0.475888i	$0.157873\pi$
$158$	2.41113	−	1.39207i	0.191819	−	0.110747i
$159$	2.09277			0.165968
$160$	−1.39637	−	2.41859i	−0.110393	−	0.191206i
$161$	4.62148	+	17.3738i	0.364223	+	1.36925i
$162$	−0.485838	+	0.280499i	−0.0381711	+	0.0220381i
$163$	9.00438	+	5.19868i	0.705277	+	0.407192i	0.809310	−	0.587382i	$-0.199841\pi$
$163$	9.00438	+	5.19868i	0.705277	+	0.407192i	−0.104033	+	0.994574i	$0.533175\pi$
$164$	−15.5598	−	8.98348i	−1.21502	−	0.701492i
$165$	−1.12618			−0.0876729
$166$	−2.05282			−0.159330
$167$	20.9105	+	12.0727i	1.61810	+	0.934213i	0.987410	+	0.158181i	$0.0505629\pi$
$167$	20.9105	+	12.0727i	1.61810	+	0.934213i	0.630694	+	0.776032i	$0.282770\pi$
$168$	3.86078	+	3.87484i	0.297866	+	0.298950i
$169$	8.76949	−	9.59666i	0.674577	−	0.738205i
$170$	0.723017	+	1.25230i	0.0554528	+	0.0960471i
$171$	4.78119	−	2.76042i	0.365627	−	0.211095i
$172$	−3.57189	−	6.18670i	−0.272354	−	0.471731i
$173$	−1.86929	+	3.23770i	−0.142119	+	0.246158i	−0.928295	−	0.371846i	$-0.878725\pi$
$173$	−1.86929	+	3.23770i	−0.142119	+	0.246158i	0.786175	+	0.618004i	$0.212058\pi$
$174$		−	4.27880i		−	0.324375i
$175$	−12.0822	−	3.26096i	−0.913328	−	0.246506i
$176$	−4.14981	+	2.39590i	−0.312804	+	0.180597i
$177$	−2.63992	+	1.52416i	−0.198428	+	0.114563i
$178$	−1.41954			−0.106399
$179$	2.83905	+	4.91738i	0.212200	+	0.367542i	0.952403	−	0.304842i	$-0.0986037\pi$
$179$	2.83905	+	4.91738i	0.212200	+	0.367542i	−0.740202	+	0.672384i	$0.765270\pi$
$180$			0.875626i			0.0652653i
$181$	−9.94903			−0.739506			−0.369753	−	0.929130i	$-0.620558\pi$
$181$	−9.94903			−0.739506			−0.369753	+	0.929130i	$0.620558\pi$
$182$	4.17740	−	3.34496i	0.309649	−	0.247945i
$183$	−6.24908			−0.461945
$184$		−	14.0483i		−	1.03565i
$185$	−1.51901	−	2.63100i	−0.111680	−	0.193435i
$186$	3.34240			0.245077
$187$	9.31241	−	5.37652i	0.680991	−	0.393170i
$188$	−16.3367	+	9.43201i	−1.19148	+	0.687900i
$189$	−0.680125	−	2.55684i	−0.0494718	−	0.185983i
$190$			1.60921i			0.116744i
$191$	−4.75437	+	8.23481i	−0.344014	+	0.595850i	−0.985174	−	0.171557i	$-0.945120\pi$
$191$	−4.75437	+	8.23481i	−0.344014	+	0.595850i	0.641160	+	0.767407i	$0.278454\pi$
$192$	0.703031	+	1.21769i	0.0507369	+	0.0878789i
$193$	−2.69504	+	1.55598i	−0.193993	+	0.112002i	−0.593851	−	0.804575i	$-0.702393\pi$
$193$	−2.69504	+	1.55598i	−0.193993	+	0.112002i	0.399857	+	0.916577i	$0.369060\pi$
$194$	−2.59748	−	4.49896i	−0.186488	−	0.323007i
$195$	1.86235	+	0.202666i	0.133366	+	0.0145132i
$196$	−10.2379	+	5.86131i	−0.731275	+	0.418665i
$197$	4.41349	+	2.54813i	0.314448	+	0.181547i	0.648915	−	0.760861i	$-0.275223\pi$
$197$	4.41349	+	2.54813i	0.314448	+	0.181547i	−0.334467	+	0.942407i	$0.608556\pi$
$198$	−1.21597			−0.0864150
$199$	13.9107			0.986105			0.493053	−	0.869999i	$-0.335881\pi$
$199$	13.9107			0.986105			0.493053	+	0.869999i	$0.335881\pi$
$200$	8.46891	+	4.88953i	0.598842	+	0.345742i
$201$	−1.71581	−	0.990626i	−0.121024	−	0.0698734i
$202$	4.39391	−	2.53683i	0.309154	−	0.178490i
$203$	19.4824	+	5.25826i	1.36739	+	0.369057i
$204$	−4.18036	−	7.24059i	−0.292683	−	0.506943i
$205$	−5.53922			−0.386876
$206$	−8.57883	+	4.95299i	−0.597716	+	0.345091i
$207$	−3.39752	+	5.88468i	−0.236144	+	0.409014i
$208$	7.29367	−	3.21528i	0.505725	−	0.222939i
$209$	11.9665			0.827738
$210$	0.744540	+	0.200950i	0.0513781	+	0.0138669i
$211$	−6.30791	+	10.9256i	−0.434255	+	0.752151i	−0.997234	−	0.0743195i	$-0.976322\pi$
$211$	−6.30791	+	10.9256i	−0.434255	+	0.752151i	0.562980	+	0.826471i	$0.309655\pi$
$212$	1.76345	−	3.05439i	0.121115	−	0.209777i
$213$	−8.61474	−	4.97372i	−0.590272	−	0.340794i
$214$		−	10.9171i		−	0.746275i
$215$	−1.90736	−	1.10122i	−0.130081	−	0.0751023i
$216$			2.06743i			0.140671i
$217$	−4.10750	+	15.2187i	−0.278835	+	1.03311i
$218$	−4.58010	+	7.93296i	−0.310203	+	0.537288i
$219$		−	2.85313i		−	0.192796i
$220$	−0.948964	+	1.64365i	−0.0639791	+	0.110815i
$221$	−16.3674	+	7.21526i	−1.10099	+	0.485351i
$222$	−1.64012	−	2.84077i	−0.110078	−	0.190660i
$223$	0.659526	+	0.380777i	0.0441651	+	0.0254987i	0.521920	−	0.852994i	$-0.325216\pi$
$223$	0.659526	+	0.380777i	0.0441651	+	0.0254987i	−0.477755	+	0.878493i	$0.658549\pi$
$224$	13.7432	−	3.65573i	0.918259	−	0.244259i
$225$	−2.36502	−	4.09634i	−0.157668	−	0.273089i
$226$	6.02437	−	3.47817i	0.400735	−	0.231365i
$227$		−	1.54056i		−	0.102250i	−0.998692	−	0.0511252i	$-0.983719\pi$
$227$		−	1.54056i		−	0.102250i	0.998692	−	0.0511252i	$-0.0162808\pi$
$228$		−	9.30418i		−	0.616184i
$229$	−4.86535	+	2.80901i	−0.321512	+	0.185625i	−0.652066	−	0.758162i	$-0.726098\pi$
$229$	−4.86535	+	2.80901i	−0.321512	+	0.185625i	0.330555	+	0.943787i	$0.392764\pi$
$230$	−0.990307	−	1.71526i	−0.0652989	−	0.113101i
$231$	1.49431	−	5.53658i	0.0983185	−	0.364280i
$232$	−13.6560	−	7.88430i	−0.896560	−	0.517629i
$233$	−8.57478	−	14.8520i	−0.561753	−	0.972984i	−0.997344	−	0.0728395i	$-0.976794\pi$
$233$	−8.57478	−	14.8520i	−0.561753	−	0.972984i	0.435591	−	0.900145i	$-0.356539\pi$
$234$	2.01083	+	0.218824i	0.131452	+	0.0143050i
$235$	−2.90789	+	5.03662i	−0.189690	+	0.328553i
$236$			5.13726i			0.334407i
$237$	−2.48141	+	4.29793i	−0.161185	+	0.279181i
$238$	−7.11599	+	1.89287i	−0.461261	+	0.122696i
$239$			25.6658i			1.66018i	0.557628	+	0.830091i	$0.311711\pi$
$239$			25.6658i			1.66018i	−0.557628	+	0.830091i	$0.688289\pi$
$240$	0.994750	+	0.574319i	0.0642109	+	0.0370722i
$241$		−	4.71718i		−	0.303861i	−0.988391	−	0.151930i	$-0.951451\pi$
$241$		−	4.71718i		−	0.303861i	0.988391	−	0.151930i	$-0.0485489\pi$
$242$	3.06171	+	1.76768i	0.196814	+	0.113631i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−5.26573	+	9.12050i	−0.337104	+	0.583880i
$245$	−1.82994	+	3.14311i	−0.116911	+	0.200806i
$246$	−5.98086			−0.381325
$247$	−19.7889	−	2.15347i	−1.25913	−	0.137022i
$248$	6.15884	−	10.6674i	0.391087	−	0.677382i
$249$	3.16899	−	1.82961i	0.200826	−	0.115947i
$250$	2.83610			0.179371
$251$	−0.0982527	−	0.170179i	−0.00620165	−	0.0107416i	0.862908	−	0.505361i	$-0.168641\pi$
$251$	−0.0982527	−	0.170179i	−0.00620165	−	0.0107416i	−0.869110	+	0.494620i	$0.835307\pi$
$252$	−4.30480	−	1.16186i	−0.271177	−	0.0731902i
$253$	−12.7551	+	7.36416i	−0.801906	+	0.462981i
$254$	−9.87956	−	5.70397i	−0.619899	−	0.357899i
$255$	−2.23228	−	1.28880i	−0.139791	−	0.0807081i
$256$	−3.66121			−0.228826
$257$	−1.50601			−0.0939422			−0.0469711	−	0.998896i	$-0.514957\pi$
$257$	−1.50601			−0.0939422			−0.0469711	+	0.998896i	$0.514957\pi$
$258$	−2.05943	−	1.18901i	−0.128215	−	0.0740248i
$259$	14.9502	−	3.97679i	0.928962	−	0.247106i
$260$	1.86508	−	2.54732i	0.115668	−	0.157978i
$261$	3.81357	+	6.60529i	0.236054	+	0.408857i
$262$	6.69435	−	3.86498i	0.413578	−	0.238779i
$263$	−3.44299	−	5.96344i	−0.212304	−	0.367721i	0.740131	−	0.672463i	$-0.234763\pi$
$263$	−3.44299	−	5.96344i	−0.212304	−	0.367721i	−0.952435	+	0.304741i	$0.901430\pi$
$264$	−2.24059	+	3.88082i	−0.137899	+	0.238848i
$265$		−	1.08735i		−	0.0667952i
$266$	−7.91129	−	2.13524i	−0.485072	−	0.130920i
$267$	2.19138	−	1.26519i	0.134110	−	0.0774285i
$268$	−2.89163	+	1.66948i	−0.176634	+	0.101980i
$269$	−11.8710			−0.723785			−0.361893	−	0.932220i	$-0.617869\pi$
$269$	−11.8710			−0.723785			−0.361893	+	0.932220i	$0.617869\pi$
$270$	0.145740	+	0.252428i	0.00886943	+	0.0153623i
$271$		−	13.7433i		−	0.834843i	−0.908713	−	0.417422i	$-0.862934\pi$
$271$		−	13.7433i		−	0.834843i	0.908713	−	0.417422i	$-0.137066\pi$
$272$	−10.9675			−0.665003
$273$	−3.46749	+	8.88687i	−0.209862	+	0.537858i
$274$	0.909537			0.0549472
$275$		−	10.2524i		−	0.618244i
$276$	5.72578	+	9.91734i	0.344652	+	0.596954i
$277$	11.2160			0.673905			0.336952	−	0.941522i	$-0.390604\pi$
$277$	11.2160			0.673905			0.336952	+	0.941522i	$0.390604\pi$
$278$	3.56484	−	2.05816i	0.213805	−	0.123440i
$279$	−5.15974	+	2.97898i	−0.308906	+	0.178347i
$280$	2.01326	−	2.00596i	0.120315	−	0.119879i
$281$		−	1.81616i		−	0.108343i	−0.998532	−	0.0541714i	$-0.982748\pi$
$281$		−	1.81616i		−	0.108343i	0.998532	−	0.0541714i	$-0.0172517\pi$
$282$	−3.13974	+	5.43818i	−0.186969	+	0.323839i
$283$	−15.4189	−	26.7063i	−0.916556	−	1.58752i	−0.804606	−	0.593809i	$-0.797624\pi$
$283$	−15.4189	−	26.7063i	−0.916556	−	1.58752i	−0.111950	−	0.993714i	$-0.535710\pi$
$284$	−14.5183	+	8.38212i	−0.861500	+	0.497387i
$285$	−1.43424	−	2.48418i	−0.0849571	−	0.147150i
$286$	3.53742	+	2.59001i	0.209172	+	0.153150i
$287$	7.34992	−	27.2322i	0.433852	−	1.60747i
$288$	4.65496	+	2.68754i	0.274296	+	0.158365i
$289$	7.61170			0.447747
$290$	−2.22315			−0.130548
$291$	8.01957	+	4.63010i	0.470116	+	0.271421i
$292$	−4.16413	−	2.40416i	−0.243687	−	0.140693i
$293$	−0.948761	+	0.547767i	−0.0554272	+	0.0320009i	−0.527458	−	0.849581i	$-0.676855\pi$
$293$	−0.948761	+	0.547767i	−0.0554272	+	0.0320009i	0.472030	+	0.881582i	$0.343521\pi$
$294$	−1.97584	+	3.39371i	−0.115233	+	0.197925i
$295$	0.791910	+	1.37163i	0.0461068	+	0.0798593i
$296$	−12.0886			−0.702636
$297$	1.87712	−	1.08375i	0.108921	−	0.0628858i
$298$	−0.301506	+	0.522223i	−0.0174658	+	0.0302516i
$299$	22.4182	−	9.88265i	1.29648	−	0.571528i
$300$	−7.97146			−0.460232
$301$	7.94471	−	7.91588i	0.457925	−	0.456264i
$302$	3.52096	−	6.09848i	0.202609	−	0.350928i
$303$	−4.52199	+	7.83231i	−0.259781	+	0.449955i
$304$	−10.5700	−	6.10257i	−0.606229	−	0.350006i
$305$			3.24685i			0.185914i
$306$	−2.41025	−	1.39156i	−0.137785	−	0.0795502i
$307$		−	4.90247i		−	0.279799i	−0.990166	−	0.139899i	$-0.955322\pi$
$307$		−	4.90247i		−	0.279799i	0.990166	−	0.139899i	$-0.0446779\pi$
$308$	−6.82145	−	6.84629i	−0.388688	−	0.390104i
$309$	8.82890	−	15.2921i	0.502258	−	0.869937i
$310$		−	1.73662i		−	0.0986334i
$311$	−5.78751	+	10.0243i	−0.328179	+	0.568423i	−0.982151	−	0.188096i	$-0.939768\pi$
$311$	−5.78751	+	10.0243i	−0.328179	+	0.568423i	0.653971	+	0.756519i	$0.273102\pi$
$312$	4.40363	−	6.01446i	0.249307	−	0.340502i
$313$	2.53480	+	4.39041i	0.143275	+	0.248160i	0.928728	−	0.370761i	$-0.120903\pi$
$313$	2.53480	+	4.39041i	0.143275	+	0.248160i	−0.785453	+	0.618922i	$0.787570\pi$
$314$	−0.336305	−	0.194166i	−0.0189788	−	0.0109574i
$315$	−1.32846	+	0.353374i	−0.0748505	+	0.0199104i
$316$	4.18188	+	7.24322i	0.235249	+	0.407463i
$317$	14.8929	−	8.59841i	0.836468	−	0.482935i	−0.0195943	−	0.999808i	$-0.506237\pi$
$317$	14.8929	−	8.59841i	0.836468	−	0.482935i	0.856062	+	0.516873i	$0.172904\pi$
$318$		−	1.17404i		−	0.0658369i
$319$			16.5319i			0.925607i
$320$	0.632676	−	0.365276i	0.0353677	−	0.0204195i
$321$	9.73005	+	16.8529i	0.543078	+	0.940639i
$322$	9.74668	−	2.59264i	0.543161	−	0.144482i
$323$	23.7196	+	13.6945i	1.31979	+	0.761983i
$324$	−0.842641	−	1.45950i	−0.0468134	−	0.0810831i
$325$	−1.84501	+	16.9543i	−0.102343	+	0.940457i
$326$	2.91645	−	5.05143i	0.161527	−	0.279773i
$327$		−	16.3284i		−	0.902963i
$328$	−11.0206	+	19.0882i	−0.608509	+	1.05397i
$329$	−20.9028	−	20.9790i	−1.15241	−	1.15661i
$330$			0.631783i			0.0347785i
$331$	17.6853	+	10.2106i	0.972075	+	0.561228i	0.899868	−	0.436162i	$-0.143663\pi$
$331$	17.6853	+	10.2106i	0.972075	+	0.561228i	0.0722066	+	0.997390i	$0.476996\pi$
$332$		−	6.16683i		−	0.338449i
$333$	5.06378	+	2.92358i	0.277494	+	0.160211i
$334$	6.77275	−	11.7307i	0.370588	−	0.641878i
$335$	−0.514702	+	0.891491i	−0.0281212	+	0.0487073i
$336$	−4.14342	+	4.12839i	−0.226042	+	0.225222i
$337$	−13.1872			−0.718353			−0.359176	−	0.933270i	$-0.616942\pi$
$337$	−13.1872			−0.718353			−0.359176	+	0.933270i	$0.616942\pi$
$338$	−5.38371	−	4.91967i	−0.292835	−	0.267595i
$339$	−6.19998	+	10.7387i	−0.336736	+	0.583245i
$340$	−3.76201	+	2.17200i	−0.204024	+	0.117793i
$341$	−12.9139			−0.699328
$342$	−1.54859	−	2.68224i	−0.0837382	−	0.145039i
$343$	−13.0242	−	13.1670i	−0.703240	−	0.710952i
$344$	−7.58959	+	4.38185i	−0.409203	+	0.236254i
$345$	3.05752	+	1.76526i	0.164611	+	0.0950384i
$346$	1.81634	+	1.04867i	0.0976473	+	0.0563767i
$347$	−8.68752			−0.466371			−0.233185	−	0.972432i	$-0.574915\pi$
$347$	−8.68752			−0.466371			−0.233185	+	0.972432i	$0.574915\pi$
$348$	12.8539			0.689039
$349$	30.2239	+	17.4498i	1.61785	+	0.934064i	0.987476	+	0.157770i	$0.0504303\pi$
$349$	30.2239	+	17.4498i	1.61785	+	0.934064i	0.630370	+	0.776294i	$0.282903\pi$
$350$	−1.82939	+	6.77808i	−0.0977851	+	0.362304i
$351$	−3.29920	+	1.45439i	−0.176098	+	0.0776296i
$352$	5.82527	+	10.0897i	0.310488	+	0.537781i
$353$	−12.5698	+	7.25715i	−0.669021	+	0.386259i	−0.795706	−	0.605684i	$-0.792900\pi$
$353$	−12.5698	+	7.25715i	−0.669021	+	0.386259i	0.126685	+	0.991943i	$0.459566\pi$
$354$	0.855048	+	1.48099i	0.0454453	+	0.0787136i
$355$	−2.58421	+	4.47598i	−0.137156	+	0.237561i
$356$		−	4.26441i		−	0.226013i
$357$	9.29807	−	9.26433i	0.492106	−	0.490320i
$358$	2.75864	−	1.59270i	0.145798	−	0.0841768i
$359$	0.460772	−	0.266027i	0.0243186	−	0.0140404i	−0.487791	−	0.872960i	$-0.662197\pi$
$359$	0.460772	−	0.266027i	0.0243186	−	0.0140404i	0.512110	+	0.858920i	$0.328864\pi$
$360$	1.07418			0.0566144
$361$	5.73986	+	9.94173i	0.302098	+	0.523249i
$362$			5.58138i			0.293351i
$363$	−6.30191			−0.330764
$364$	10.0485	+	12.5492i	0.526685	+	0.657758i
$365$	−1.48241			−0.0775927
$366$			3.50572i			0.183247i
$367$	−2.92633	−	5.06855i	−0.152753	−	0.264576i	0.779485	−	0.626420i	$-0.215481\pi$
$367$	−2.92633	−	5.06855i	−0.152753	−	0.264576i	−0.932239	+	0.361844i	$0.882147\pi$
$368$	15.0221			0.783079
$369$	9.23279	−	5.33055i	0.480640	−	0.277497i
$370$	−1.47599	+	0.852161i	−0.0767329	+	0.0443018i
$371$	5.34567	+	1.44279i	0.277533	+	0.0749058i
$372$			10.0408i			0.520593i
$373$	−12.1259	+	21.0026i	−0.627853	+	1.08747i	0.360128	+	0.932903i	$0.382733\pi$
$373$	−12.1259	+	21.0026i	−0.627853	+	1.08747i	−0.987982	+	0.154571i	$0.950600\pi$
$374$	−3.01622	−	5.22424i	−0.155965	−	0.270139i
$375$	−4.37816	+	2.52773i	−0.226087	+	0.130532i
$376$	11.5708	+	20.0412i	0.596719	+	1.03355i
$377$	2.97506	−	27.3386i	0.153223	−	1.40801i
$378$	−1.43438	+	0.381548i	−0.0737766	+	0.0196247i
$379$	−1.19932	−	0.692428i	−0.0616050	−	0.0355677i	0.468881	−	0.883261i	$-0.344657\pi$
$379$	−1.19932	−	0.692428i	−0.0616050	−	0.0355677i	−0.530486	+	0.847694i	$0.677991\pi$
$380$	−4.83420			−0.247989
$381$	20.3351			1.04180
$382$	4.61971	+	2.66719i	0.236365	+	0.136465i
$383$	17.0939	+	9.86915i	0.873456	+	0.504290i	0.868495	−	0.495698i	$-0.165088\pi$
$383$	17.0939	+	9.86915i	0.873456	+	0.504290i	0.00496051	+	0.999988i	$0.498421\pi$
$384$	9.99304	−	5.76949i	0.509955	−	0.294423i
$385$	−2.87665	−	0.776404i	−0.146608	−	0.0395692i
$386$	0.872902	+	1.51191i	0.0444295	+	0.0769542i
$387$	4.23893			0.215477
$388$	13.5152	−	7.80303i	0.686132	−	0.396139i
$389$	2.48623	−	4.30628i	0.126057	−	0.218337i	−0.796089	−	0.605180i	$-0.793101\pi$
$389$	2.48623	−	4.30628i	0.126057	−	0.218337i	0.922146	+	0.386843i	$0.126434\pi$
$390$	0.113695	−	1.04477i	0.00575718	−	0.0529042i
$391$	−33.7103			−1.70480
$392$	7.19041	+	12.5594i	0.363171	+	0.634344i
$393$	−6.88948	+	11.9329i	−0.347528	+	0.601937i
$394$	1.42950	−	2.47596i	0.0720170	−	0.124737i
$395$	2.23309	+	1.28927i	0.112359	+	0.0648704i
$396$		−	3.65286i		−	0.183563i
$397$	8.50970	+	4.91308i	0.427090	+	0.246580i	0.698106	−	0.715994i	$-0.254026\pi$
$397$	8.50970	+	4.91308i	0.427090	+	0.246580i	−0.271016	+	0.962575i	$0.587360\pi$
$398$		−	7.80389i		−	0.391173i
$399$	14.1159	−	3.75486i	0.706680	−	0.187978i
$400$	−5.22844	+	9.05593i	−0.261422	+	0.452796i
$401$		−	29.2596i		−	1.46115i	−0.682830	−	0.730577i	$-0.739251\pi$
$401$		−	29.2596i		−	1.46115i	0.682830	−	0.730577i	$-0.260749\pi$
$402$	−0.555739	+	0.962568i	−0.0277177	+	0.0480085i
$403$	21.3556	+	2.32398i	1.06380	+	0.115765i
$404$	7.62082	+	13.1997i	0.379150	+	0.656707i
$405$	−0.449963	−	0.259786i	−0.0223589	−	0.0129089i
$406$	2.94987	−	10.9296i	0.146400	−	0.542425i
$407$	6.33688	+	10.9758i	0.314107	+	0.544050i
$408$	−8.88246	+	5.12829i	−0.439747	+	0.253888i
$409$		−	12.8399i		−	0.634892i	−0.948276	−	0.317446i	$-0.897175\pi$
$409$		−	12.8399i		−	0.634892i	0.948276	−	0.317446i	$-0.102825\pi$
$410$			3.10749i			0.153468i
$411$	−1.40407	+	0.810643i	−0.0692579	+	0.0399861i
$412$	−14.8792	−	25.7715i	−0.733045	−	1.26967i
$413$	−7.79405	+	2.07323i	−0.383520	+	0.102017i
$414$	3.30129	+	1.90600i	0.162250	+	0.0936749i
$415$	−0.950618	−	1.64652i	−0.0466640	−	0.0808244i
$416$	−7.81748	−	17.7335i	−0.383283	−	0.869457i
$417$	−3.66875	+	6.35446i	−0.179660	+	0.311179i
$418$		−	6.71317i		−	0.328352i
$419$	13.1853	−	22.8376i	0.644144	−	1.11569i	−0.340354	−	0.940297i	$-0.610547\pi$
$419$	13.1853	−	22.8376i	0.644144	−	1.11569i	0.984498	−	0.175393i	$-0.0561197\pi$
$420$	−0.603670	+	2.23666i	−0.0294561	+	0.109138i
$421$		−	2.71377i		−	0.132261i	−0.997811	−	0.0661306i	$-0.978935\pi$
$421$		−	2.71377i		−	0.132261i	0.997811	−	0.0661306i	$-0.0210654\pi$
$422$	6.12925	+	3.53873i	0.298367	+	0.172262i
$423$		−	11.1934i		−	0.544242i
$424$	−3.74700	−	2.16333i	−0.181971	−	0.105061i
$425$	11.7329	−	20.3220i	0.569130	−	0.985762i
$426$	−2.79025	+	4.83285i	−0.135188	+	0.234152i
$427$	−15.9623	−	4.30821i	−0.772471	−	0.208489i
$428$	32.7957			1.58524
$429$	−7.76919	−	0.845464i	−0.375100	−	0.0408194i
$430$	−0.617779	+	1.07003i	−0.0297920	+	0.0516012i
$431$	−32.1180	+	18.5433i	−1.54707	+	0.893200i	−0.548704	+	0.836016i	$0.684879\pi$
$431$	−32.1180	+	18.5433i	−1.54707	+	0.893200i	−0.998364	+	0.0571837i	$0.981788\pi$
$432$	−2.21074			−0.106364
$433$	7.21536	+	12.4974i	0.346748	+	0.600585i	0.985670	−	0.168686i	$-0.0539525\pi$
$433$	7.21536	+	12.4974i	0.346748	+	0.600585i	−0.638922	+	0.769272i	$0.720619\pi$
$434$	8.53766	+	2.30430i	0.409821	+	0.110610i
$435$	3.43193	−	1.98142i	0.164548	−	0.0950020i
$436$	−23.8312	−	13.7590i	−1.14131	−	0.658936i
$437$	−32.4884	−	18.7572i	−1.55413	−	0.897278i
$438$	−1.60060			−0.0764795
$439$	14.6300			0.698254			0.349127	−	0.937075i	$-0.386478\pi$
$439$	14.6300			0.698254			0.349127	+	0.937075i	$0.386478\pi$
$440$	2.01637	+	1.16415i	0.0961265	+	0.0554987i
$441$	0.0254470	−	6.99995i	0.00121176	−	0.333331i
$442$	4.04774	+	9.18208i	0.192532	+	0.436747i
$443$	18.3045	+	31.7043i	0.869672	+	1.50632i	0.862332	+	0.506343i	$0.169003\pi$
$443$	18.3045	+	31.7043i	0.869672	+	1.50632i	0.00733990	+	0.999973i	$0.497664\pi$
$444$	8.53390	−	4.92705i	0.405001	−	0.233827i
$445$	−0.657359	−	1.13858i	−0.0311618	−	0.0539738i
$446$	0.213615	−	0.369993i	0.0101150	−	0.0175197i
$447$		−	1.07489i		−	0.0508406i
$448$	0.956298	+	3.59508i	0.0451808	+	0.169851i
$449$	−5.59341	+	3.22935i	−0.263969	+	0.152403i	−0.626144	−	0.779708i	$-0.715368\pi$
$449$	−5.59341	+	3.22935i	−0.263969	+	0.152403i	0.362175	+	0.932110i	$0.382034\pi$
$450$	−2.29804	+	1.32677i	−0.108330	+	0.0625446i
$451$	23.1080			1.08811
$452$	10.4487	+	18.0977i	0.491466	+	0.851244i
$453$			12.5525i			0.589768i
$454$	−0.864250			−0.0405613
$455$	4.61738	+	1.80161i	0.216466	+	0.0844609i
$456$	−11.4140			−0.534509
$457$			19.1940i			0.897855i	0.893568	+	0.448928i	$0.148194\pi$
$457$			19.1940i			0.897855i	−0.893568	+	0.448928i	$0.851806\pi$
$458$	1.57585	+	2.72945i	0.0736346	+	0.127539i
$459$	4.96102			0.231560
$460$	5.15278	−	2.97496i	0.240250	−	0.138708i
$461$	−5.50203	+	3.17660i	−0.256255	+	0.147949i	−0.622625	−	0.782520i	$-0.713934\pi$
$461$	−5.50203	+	3.17660i	−0.256255	+	0.147949i	0.366370	+	0.930469i	$0.380600\pi$
$462$	−3.10601	−	0.838306i	−0.144504	−	0.0390015i
$463$			10.8299i			0.503307i	0.967817	+	0.251653i	$0.0809743\pi$
$463$			10.8299i			0.503307i	−0.967817	+	0.251653i	$0.919026\pi$
$464$	8.43079	−	14.6026i	0.391390	−	0.677907i
$465$	1.54780	+	2.68086i	0.0717773	+	0.124322i
$466$	−8.33191	+	4.81043i	−0.385968	+	0.222839i
$467$	5.84012	+	10.1154i	0.270248	+	0.468084i	0.968925	−	0.247353i	$-0.0795609\pi$
$467$	5.84012	+	10.1154i	0.270248	+	0.468084i	−0.698677	+	0.715437i	$0.746228\pi$
$468$	−0.657365	+	6.04071i	−0.0303867	+	0.279232i
$469$	−3.69984	−	3.71331i	−0.170843	−	0.171465i
$470$	2.82553	+	1.63132i	0.130332	+	0.0752472i
$471$	0.692215			0.0318956
$472$	6.30219			0.290082
$473$	7.95696	+	4.59395i	0.365862	+	0.211230i
$474$	2.41113	+	1.39207i	0.110747	+	0.0639397i
$475$	22.6152	−	13.0569i	1.03766	−	0.599093i
$476$	−5.68633	−	21.3770i	−0.260632	−	0.979813i
$477$	1.04639	+	1.81239i	0.0479107	+	0.0829838i
$478$	14.3984			0.658570
$479$	20.8050	−	12.0118i	0.950606	−	0.548833i	0.0573371	−	0.998355i	$-0.481739\pi$
$479$	20.8050	−	12.0118i	0.950606	−	0.548833i	0.893269	+	0.449522i	$0.148406\pi$
$480$	1.39637	−	2.41859i	0.0637355	−	0.110393i
$481$	−8.50405	−	19.2909i	−0.387751	−	0.879592i
$482$	−2.64633			−0.120537
$483$	−12.7354	+	12.6892i	−0.579483	+	0.577380i
$484$	−5.31024	+	9.19761i	−0.241375	+	0.418073i
$485$	2.40568	−	4.16675i	0.109236	−	0.189202i
$486$	−0.485838	−	0.280499i	−0.0220381	−	0.0127237i
$487$		−	6.04028i		−	0.273711i	−0.990591	−	0.136856i	$-0.956300\pi$
$487$		−	6.04028i		−	0.273711i	0.990591	−	0.136856i	$-0.0436996\pi$
$488$	11.1887	+	6.45978i	0.506487	+	0.292420i
$489$			10.3974i			0.470185i
$490$	1.76328	+	1.02659i	0.0796568	+	0.0463768i
$491$	−7.05626	+	12.2218i	−0.318444	+	0.551562i	−0.980164	−	0.198190i	$-0.936494\pi$
$491$	−7.05626	+	12.2218i	−0.318444	+	0.551562i	0.661719	+	0.749752i	$0.269827\pi$
$492$		−	17.9670i		−	0.810013i
$493$	−18.9192	+	32.7690i	−0.852076	+	1.47584i
$494$	−1.20809	+	11.1015i	−0.0543547	+	0.499480i
$495$	−0.563089	−	0.975299i	−0.0253090	−	0.0438364i
$496$	11.4068	+	6.58574i	0.512182	+	0.295708i
$497$	−18.5761	−	18.6438i	−0.833252	−	0.836287i
$498$	−1.02641	−	1.77779i	−0.0459945	−	0.0796648i
$499$	−28.4481	+	16.4245i	−1.27351	+	0.735263i	−0.975647	−	0.219345i	$-0.929608\pi$
$499$	−28.4481	+	16.4245i	−1.27351	+	0.735263i	−0.297865	+	0.954608i	$0.596274\pi$
$500$			8.51988i			0.381021i
$501$			24.1454i			1.07874i
$502$	−0.0954698	+	0.0551195i	−0.00426103	+	0.00246010i
$503$	−19.5590	−	33.8772i	−0.872093	−	1.51051i	−0.859828	−	0.510584i	$-0.829429\pi$
$503$	−19.5590	−	33.8772i	−0.872093	−	1.51051i	−0.0122649	−	0.999925i	$-0.503904\pi$
$504$	−1.42532	+	5.28095i	−0.0634888	+	0.235232i
$505$	4.06946	+	2.34950i	0.181088	+	0.104551i
$506$	4.13127	+	7.15558i	0.183658	+	0.318104i
$507$	12.6957	+	2.79627i	0.563836	+	0.124187i
$508$	17.1352	−	29.6790i	0.760250	−	1.31679i
$509$			1.10833i			0.0491260i	0.999698	+	0.0245630i	$0.00781944\pi$
$509$			1.10833i			0.0491260i	−0.999698	+	0.0245630i	$0.992181\pi$
$510$	−0.723017	+	1.25230i	−0.0320157	+	0.0554528i
$511$	1.96699	−	7.28789i	0.0870144	−	0.322397i
$512$		−	21.0240i		−	0.929139i
$513$	4.78119	+	2.76042i	0.211095	+	0.121876i
$514$			0.844867i			0.0372655i
$515$	−7.94536	−	4.58726i	−0.350114	−	0.202139i
$516$	3.57189	−	6.18670i	0.157244	−	0.272354i
$517$	12.1309	−	21.0113i	0.533516	−	0.924077i
$518$	−2.23097	−	8.38705i	−0.0980232	−	0.368506i
$519$	−3.73858			−0.164105
$520$	−3.12495	−	2.28801i	−0.137038	−	0.100336i
$521$	6.87363	−	11.9055i	0.301139	−	0.521589i	−0.675255	−	0.737584i	$-0.735966\pi$
$521$	6.87363	−	11.9055i	0.301139	−	0.521589i	0.976394	+	0.215996i	$0.0692997\pi$
$522$	3.70555	−	2.13940i	0.162188	−	0.0936391i
$523$	−2.41355			−0.105537			−0.0527686	−	0.998607i	$-0.516805\pi$
$523$	−2.41355			−0.105537			−0.0527686	+	0.998607i	$0.516805\pi$
$524$	11.6107	+	20.1103i	0.507216	+	0.878524i
$525$	−3.21702	−	12.0940i	−0.140402	−	0.527824i
$526$	−3.34548	+	1.93151i	−0.145870	+	0.0842179i
$527$	−25.5976	−	14.7788i	−1.11505	−	0.643773i
$528$	−4.14981	−	2.39590i	−0.180597	−	0.104268i
$529$	23.1726			1.00751
$530$	−0.609999			−0.0264967
$531$	−2.63992	−	1.52416i	−0.114563	−	0.0661427i
$532$	6.41444	−	23.7661i	0.278101	−	1.03039i
$533$	−38.2136	−	4.15850i	−1.65521	−	0.180125i
$534$	−0.709770	−	1.22936i	−0.0307147	−	0.0531995i
$535$	8.75633	−	5.05547i	0.378569	−	0.218567i
$536$	2.04805	+	3.54733i	0.0884625	+	0.153222i
$537$	−2.83905	+	4.91738i	−0.122514	+	0.212200i
$538$			6.65958i			0.287115i
$539$	7.63400	−	13.1122i	0.328819	−	0.564780i
$540$	−0.758315	+	0.437813i	−0.0326327	+	0.0188405i
$541$	7.81869	−	4.51412i	0.336152	−	0.194077i	−0.322417	−	0.946598i	$-0.604495\pi$
$541$	7.81869	−	4.51412i	0.336152	−	0.194077i	0.658569	+	0.752520i	$0.271162\pi$
$542$	−7.70993			−0.331170
$543$	−4.97451	−	8.61611i	−0.213477	−	0.369753i
$544$			26.6659i			1.14329i
$545$	−8.48379			−0.363406
$546$	4.98552	+	1.94525i	0.213360	+	0.0832491i
$547$	−24.3206			−1.03987			−0.519936	−	0.854205i	$-0.674044\pi$
$547$	−24.3206			−1.03987			−0.519936	+	0.854205i	$0.674044\pi$
$548$			2.73232i			0.116719i
$549$	−3.12454	−	5.41186i	−0.133352	−	0.230972i
$550$	−5.75158			−0.245248
$551$	−36.4668	+	21.0541i	−1.55354	+	0.896935i
$552$	12.1662	−	7.02415i	0.517827	−	0.298968i
$553$	−9.30145	+	9.26770i	−0.395538	+	0.394103i
$554$		−	6.29216i		−	0.267328i
$555$	1.51901	−	2.63100i	0.0644784	−	0.111680i
$556$	6.18288	+	10.7091i	0.262212	+	0.454165i
$557$	23.8965	−	13.7966i	1.01253	−	0.584582i	0.100596	−	0.994927i	$-0.467925\pi$
$557$	23.8965	−	13.7966i	1.01253	−	0.584582i	0.911930	+	0.410345i	$0.134592\pi$
$558$	1.67120	+	2.89460i	0.0707475	+	0.122538i
$559$	−12.3316	−	9.02891i	−0.521573	−	0.381882i
$560$	2.14500	+	2.15281i	0.0906427	+	0.0909728i
$561$	9.31241	+	5.37652i	0.393170	+	0.226997i
$562$	−1.01886			−0.0429780
$563$	−7.70429			−0.324697			−0.162349	−	0.986733i	$-0.551907\pi$
$563$	−7.70429			−0.324697			−0.162349	+	0.986733i	$0.551907\pi$
$564$	−16.3367	−	9.43201i	−0.687900	−	0.397159i
$565$	5.57952	+	3.22134i	0.234732	+	0.135523i
$566$	−14.9822	+	8.64995i	−0.629747	+	0.363584i
$567$	1.87423	−	1.86743i	0.0787101	−	0.0784245i
$568$	10.2828	+	17.8104i	0.431459	+	0.747308i
$569$	−23.2480			−0.974605			−0.487302	−	0.873233i	$-0.662019\pi$
$569$	−23.2480			−0.974605			−0.487302	+	0.873233i	$0.662019\pi$
$570$	−1.39362	+	0.804605i	−0.0583722	+	0.0337012i
$571$	−2.06269	+	3.57268i	−0.0863209	+	0.149512i	−0.905953	−	0.423378i	$-0.860844\pi$
$571$	−2.06269	+	3.57268i	−0.0863209	+	0.149512i	0.819632	+	0.572890i	$0.194178\pi$
$572$	−7.78059	+	10.6267i	−0.325323	+	0.444324i
$573$	−9.50875			−0.397234
$574$	−15.2772	−	4.12329i	−0.637658	−	0.172103i
$575$	−16.0704	+	27.8348i	−0.670183	+	1.16079i
$576$	−0.703031	+	1.21769i	−0.0292930	+	0.0507369i
$577$	−6.14307	−	3.54670i	−0.255739	−	0.147651i	0.366650	−	0.930359i	$-0.380505\pi$
$577$	−6.14307	−	3.54670i	−0.255739	−	0.147651i	−0.622389	+	0.782708i	$0.713838\pi$
$578$		−	4.27015i		−	0.177615i
$579$	−2.69504	−	1.55598i	−0.112002	−	0.0646644i
$580$		−	6.67852i		−	0.277310i
$581$	9.35606	−	2.48873i	0.388155	−	0.103250i
$582$	2.59748	−	4.49896i	0.107669	−	0.186488i
$583$			4.53610i			0.187866i
$584$	−2.94933	+	5.10838i	−0.122044	+	0.211386i
$585$	0.755662	+	1.71418i	0.0312428	+	0.0708725i
$586$	0.307296	+	0.532253i	0.0126943	+	0.0219871i
$587$	−1.42269	−	0.821391i	−0.0587208	−	0.0339025i	0.470352	−	0.882479i	$-0.344127\pi$
$587$	−1.42269	−	0.821391i	−0.0587208	−	0.0339025i	−0.529073	+	0.848576i	$0.677460\pi$
$588$	−10.1950	−	5.93559i	−0.420433	−	0.244779i
$589$	−16.4465	−	28.4861i	−0.677665	−	1.17375i
$590$	0.769480	−	0.444260i	0.0316790	−	0.0182899i
$591$			5.09626i			0.209632i
$592$		−	12.9265i		−	0.531277i
$593$	37.1597	−	21.4542i	1.52597	−	0.881016i	0.526440	−	0.850212i	$-0.323527\pi$
$593$	37.1597	−	21.4542i	1.52597	−	0.881016i	0.999525	−	0.0308039i	$-0.00980675\pi$
$594$	−0.607984	−	1.05306i	−0.0249459	−	0.0432075i
$595$	−4.81349	−	4.83102i	−0.197334	−	0.198053i
$596$	−1.56880	−	0.905747i	−0.0642606	−	0.0371009i
$597$	6.95536	+	12.0470i	0.284664	+	0.493053i
$598$	−5.54414	−	12.5766i	−0.226717	−	0.514295i
$599$	15.5990	−	27.0183i	0.637358	−	1.10394i	−0.348653	−	0.937252i	$-0.613361\pi$
$599$	15.5990	−	27.0183i	0.637358	−	1.10394i	0.986010	−	0.166684i	$-0.0533060\pi$
$600$			9.77906i			0.399228i
$601$	−17.5568	+	30.4093i	−0.716157	+	1.24042i	0.246354	+	0.969180i	$0.420767\pi$
$601$	−17.5568	+	30.4093i	−0.716157	+	1.24042i	−0.962511	+	0.271241i	$0.912566\pi$
$602$	−4.44079	−	4.45696i	−0.180993	−	0.181652i
$603$		−	1.98125i		−	0.0806828i
$604$	18.3203	+	10.5772i	0.745444	+	0.430382i
$605$			3.27430i			0.133119i
$606$	4.39391	+	2.53683i	0.178490	+	0.103051i
$607$	1.15886	−	2.00720i	0.0470365	−	0.0814696i	−0.841549	−	0.540181i	$-0.818356\pi$
$607$	1.15886	−	2.00720i	0.0470365	−	0.0814696i	0.888585	+	0.458712i	$0.151689\pi$
$608$	−14.8375	+	25.6993i	−0.601741	+	1.04225i
$609$	5.18740	+	19.5014i	0.210204	+	0.790235i
$610$	1.82148			0.0737494
$611$	−23.8419	+	32.5632i	−0.964541	+	1.31737i
$612$	4.18036	−	7.24059i	0.168981	−	0.292683i
$613$	−14.7745	+	8.53004i	−0.596735	+	0.344525i	−0.767756	−	0.640742i	$-0.778627\pi$
$613$	−14.7745	+	8.53004i	−0.596735	+	0.344525i	0.171021	+	0.985267i	$0.445293\pi$
$614$	−2.75027			−0.110992
$615$	−2.76961	−	4.79711i	−0.111681	−	0.193438i
$616$	−8.39875	+	8.36827i	−0.338395	+	0.337167i
$617$	−20.5147	+	11.8442i	−0.825890	+	0.476828i	−0.852443	−	0.522820i	$-0.824880\pi$
$617$	−20.5147	+	11.8442i	−0.825890	+	0.476828i	0.0265537	+	0.999647i	$0.491547\pi$
$618$	−8.57883	−	4.95299i	−0.345091	−	0.199239i
$619$	−13.5416	−	7.81825i	−0.544283	−	0.314242i	0.202530	−	0.979276i	$-0.435084\pi$
$619$	−13.5416	−	7.81825i	−0.544283	−	0.314242i	−0.746813	+	0.665034i	$0.768417\pi$
$620$	5.21694			0.209517
$621$	−6.79504			−0.272676
$622$	5.62359	+	3.24678i	0.225485	+	0.130184i
$623$	6.46979	−	1.72098i	0.259206	−	0.0689494i
$624$	6.43135	+	4.70887i	0.257460	+	0.188506i
$625$	−10.5118	−	18.2069i	−0.420471	−	0.728277i
$626$	2.46301	−	1.42202i	0.0984416	−	0.0568353i
$627$	5.98324	+	10.3633i	0.238948	+	0.413869i
$628$	0.583289	−	1.01029i	0.0232758	−	0.0403148i
$629$			29.0078i			1.15662i
$630$	0.198242	+	0.745265i	0.00789815	+	0.0296921i
$631$	−19.8241	+	11.4455i	−0.789186	+	0.455637i	−0.839676	−	0.543088i	$-0.817255\pi$
$631$	−19.8241	+	11.4455i	−0.789186	+	0.455637i	0.0504898	+	0.998725i	$0.483922\pi$
$632$	8.88569	−	5.13015i	0.353454	−	0.204067i
$633$	−12.6158			−0.501434
$634$	−4.82369	−	8.35487i	−0.191573	−	0.331814i
$635$		−	10.5656i		−	0.419281i
$636$	3.52691			0.139851
$637$	−14.9839	+	20.3097i	−0.593685	+	0.804698i
$638$	9.27434			0.367175
$639$		−	9.94745i		−	0.393515i
$640$	−2.99767	−	5.19211i	−0.118493	−	0.205236i
$641$	−46.2048			−1.82498			−0.912490	−	0.409100i	$-0.865843\pi$
$641$	−46.2048			−1.82498			−0.912490	+	0.409100i	$0.865843\pi$
$642$	9.45446	−	5.45853i	0.373138	−	0.215431i
$643$	8.19662	−	4.73232i	0.323243	−	0.186625i	−0.329594	−	0.944123i	$-0.606912\pi$
$643$	8.19662	−	4.73232i	0.323243	−	0.186625i	0.652837	+	0.757498i	$0.273579\pi$
$644$	7.78849	+	29.2798i	0.306909	+	1.15379i
$645$		−	2.20243i		−	0.0867206i
$646$	7.68259	−	13.3066i	0.302267	−	0.523542i
$647$	−2.85296	−	4.94148i	−0.112162	−	0.194270i	0.804480	−	0.593980i	$-0.202444\pi$
$647$	−2.85296	−	4.94148i	−0.112162	−	0.194270i	−0.916642	+	0.399710i	$0.869111\pi$
$648$	−1.79045	+	1.03372i	−0.0703355	+	0.0406082i
$649$	−3.30362	−	5.72204i	−0.129678	−	0.224610i
$650$	9.51134	+	1.03505i	0.373065	+	0.0405979i
$651$	−15.2335	+	4.05215i	−0.597049	+	0.158816i
$652$	15.1749	+	8.76124i	0.594295	+	0.343117i
$653$	33.0133			1.29191			0.645956	−	0.763375i	$-0.276459\pi$
$653$	33.0133			1.29191			0.645956	+	0.763375i	$0.276459\pi$
$654$	−9.16020			−0.358192
$655$	6.20002	+	3.57959i	0.242255	+	0.139866i
$656$	−20.4113	−	11.7845i	−0.796926	−	0.460106i
$657$	2.47088	−	1.42656i	0.0963982	−	0.0556555i
$658$	−11.7691	+	11.7264i	−0.458809	+	0.457144i
$659$	−11.4177	−	19.7760i	−0.444770	−	0.770363i	0.553267	−	0.833004i	$-0.313381\pi$
$659$	−11.4177	−	19.7760i	−0.444770	−	0.770363i	−0.998036	+	0.0626408i	$0.980048\pi$
$660$	−1.89793			−0.0738767
$661$	−1.58812	+	0.916900i	−0.0617706	+	0.0356633i	−0.530567	−	0.847643i	$-0.678021\pi$
$661$	−1.58812	+	0.916900i	−0.0617706	+	0.0356633i	0.468797	+	0.883306i	$0.344688\pi$
$662$	5.72815	−	9.92144i	0.222631	−	0.385608i
$663$	−14.4323	−	10.5670i	−0.560504	−	0.410387i
$664$	−7.56522			−0.293587
$665$	−1.95092	−	7.33425i	−0.0756536	−	0.284410i
$666$	1.64012	−	2.84077i	0.0635533	−	0.110078i
$667$	25.9133	−	44.8832i	1.00337	−	1.73789i
$668$	35.2401	+	20.3459i	1.36348	+	0.787206i
$669$			0.761555i			0.0294434i
$670$	0.500124	+	0.288747i	0.0193215	+	0.0111553i
$671$		−	13.5449i		−	0.522896i
$672$	10.0376	+	10.0741i	0.387208	+	0.388618i
$673$	14.8231	−	25.6743i	0.571387	−	0.989672i	−0.425037	−	0.905176i	$-0.639739\pi$
$673$	14.8231	−	25.6743i	0.571387	−	0.989672i	0.996424	−	0.0844955i	$-0.0269278\pi$
$674$			7.39799i			0.284960i
$675$	2.36502	−	4.09634i	0.0910297	−	0.157668i
$676$	14.7791	−	16.1731i	0.568426	−	0.622042i
$677$	−21.1048	−	36.5546i	−0.811124	−	1.40491i	−0.912078	−	0.410017i	$-0.865523\pi$
$677$	−21.1048	−	36.5546i	−0.811124	−	1.40491i	0.100954	−	0.994891i	$-0.467811\pi$
$678$	6.02437	+	3.47817i	0.231365	+	0.133578i
$679$	17.2927	+	17.3557i	0.663635	+	0.666051i
$680$	2.66452	+	4.61508i	0.102180	+	0.176980i
$681$	1.33416	−	0.770280i	0.0511252	−	0.0295172i
$682$			7.24468i			0.277413i
$683$		−	24.8889i		−	0.952347i	−0.879351	−	0.476173i	$-0.842023\pi$
$683$		−	24.8889i		−	0.952347i	0.879351	−	0.476173i	$-0.157977\pi$
$684$	8.05765	−	4.65209i	0.308092	−	0.177877i
$685$	0.421188	+	0.729519i	0.0160928	+	0.0278735i
$686$	−7.38667	+	7.30654i	−0.282024	+	0.278965i
$687$	−4.86535	−	2.80901i	−0.185625	−	0.107171i
$688$	−4.68558	−	8.11566i	−0.178636	−	0.309407i
$689$	0.816312	−	7.50131i	0.0310990	−	0.285777i
$690$	0.990307	−	1.71526i	0.0377003	−	0.0652989i
$691$			37.5585i			1.42879i	0.699741	+	0.714396i	$0.253299\pi$
$691$			37.5585i			1.42879i	−0.699741	+	0.714396i	$0.746701\pi$
$692$	−3.15028	+	5.45644i	−0.119756	+	0.207423i
$693$	5.54197	−	1.47418i	0.210522	−	0.0559993i
$694$			4.87368i			0.185002i
$695$	3.30161	+	1.90618i	0.125237	+	0.0723057i
$696$		−	15.7686i		−	0.597707i
$697$	45.8040	+	26.4450i	1.73495	+	1.00167i
$698$	9.78927	−	16.9555i	0.370529	−	0.641776i
$699$	8.57478	−	14.8520i	0.324328	−	0.561753i
$700$	−20.3619	−	5.49564i	−0.769607	−	0.207716i
$701$	36.1312			1.36466			0.682328	−	0.731046i	$-0.260968\pi$
$701$	36.1312			1.36466			0.682328	+	0.731046i	$0.260968\pi$
$702$	0.815910	+	1.85085i	0.0307945	+	0.0698557i
$703$	−16.1406	+	27.9564i	−0.608755	+	1.05439i
$704$	−2.63934	+	1.52383i	−0.0994740	+	0.0574314i
$705$	−5.81579			−0.219035
$706$	4.07125	+	7.05161i	0.153223	+	0.265391i
$707$	−16.9505	+	16.8890i	−0.637488	+	0.635174i
$708$	−4.44900	+	2.56863i	−0.167204	+	0.0965351i
$709$	−21.6643	−	12.5079i	−0.813619	−	0.469743i	0.0345923	−	0.999402i	$-0.488987\pi$
$709$	−21.6643	−	12.5079i	−0.813619	−	0.469743i	−0.848211	+	0.529659i	$0.822320\pi$
$710$	2.51102	+	1.44974i	0.0942368	+	0.0544076i
$711$	−4.96282			−0.186120
$712$	−5.23140			−0.196055
$713$	35.0607	+	20.2423i	1.31303	+	0.758079i
$714$	−5.19727	−	5.21620i	−0.194503	−	0.195211i
$715$	−0.439280	+	4.03666i	−0.0164281	+	0.150963i
$716$	4.78460	+	8.28716i	0.178809	+	0.309706i
$717$	−22.2272	+	12.8329i	−0.830091	+	0.479253i
$718$	−0.149240	−	0.258492i	−0.00556960	−	0.00964684i
$719$	3.31824	−	5.74736i	0.123749	−	0.214340i	−0.797494	−	0.603327i	$-0.793841\pi$
$719$	3.31824	−	5.74736i	0.123749	−	0.214340i	0.921243	+	0.388987i	$0.127175\pi$
$720$			1.14864i			0.0428072i
$721$	33.0947	−	32.9746i	1.23251	−	1.22804i
$722$	5.57729	−	3.22005i	0.207565	−	0.119838i
$723$	4.08520	−	2.35859i	0.151930	−	0.0877170i
$724$	−16.7669			−0.623138
$725$	18.0383	+	31.2433i	0.669927	+	1.16035i
$726$			3.53536i			0.131209i
$727$	18.2640			0.677375			0.338688	−	0.940899i	$-0.390017\pi$
$727$	18.2640			0.677375			0.338688	+	0.940899i	$0.390017\pi$
$728$	15.3949	−	12.3271i	0.570572	−	0.456873i
$729$	1.00000			0.0370370
$730$			0.831627i			0.0307799i
$731$	10.5147	+	18.2120i	0.388900	+	0.673595i
$732$	−10.5315			−0.389254
$733$	26.5047	−	15.3025i	0.978972	−	0.565210i	0.0770123	−	0.997030i	$-0.475462\pi$
$733$	26.5047	−	15.3025i	0.978972	−	0.565210i	0.901960	+	0.431820i	$0.142129\pi$
$734$	−2.84345	+	1.64166i	−0.104953	+	0.0605949i
$735$	−3.63699	−	0.0132216i	−0.134152	−	0.000487686i
$736$		−	36.5240i		−	1.34629i
$737$	2.14719	−	3.71904i	0.0790928	−	0.136993i
$738$	−2.99043	−	5.17957i	−0.110079	−	0.190663i
$739$	−30.3042	+	17.4962i	−1.11476	+	0.643607i	−0.940058	−	0.341014i	$-0.889229\pi$
$739$	−30.3042	+	17.4962i	−1.11476	+	0.643607i	−0.174702	+	0.984621i	$0.555896\pi$
$740$	−2.55996	−	4.43398i	−0.0941060	−	0.162996i
$741$	−8.02947	−	18.2144i	−0.294970	−	0.669122i
$742$	0.809400	−	2.99891i	0.0297140	−	0.110093i
$743$	6.87469	+	3.96910i	0.252208	+	0.145612i	0.620775	−	0.783989i	$-0.286818\pi$
$743$	6.87469	+	3.96910i	0.252208	+	0.145612i	−0.368567	+	0.929601i	$0.620151\pi$
$744$	12.3177			0.451588
$745$	−0.558484			−0.0204613
$746$	11.7824	+	6.80258i	0.431385	+	0.249060i
$747$	3.16899	+	1.82961i	0.115947	+	0.0669421i
$748$	15.6940	−	9.06096i	0.573831	−	0.331301i
$749$	13.2353	+	49.7563i	0.483607	+	1.81806i
$750$	1.41805	+	2.45614i	0.0517800	+	0.0896855i
$751$	−30.8388			−1.12532			−0.562662	−	0.826687i	$-0.690223\pi$
$751$	−30.8388			−1.12532			−0.562662	+	0.826687i	$0.690223\pi$
$752$	−21.4304	+	12.3728i	−0.781485	+	0.451191i
$753$	0.0982527	−	0.170179i	0.00358053	−	0.00620165i
$754$	−15.3369	−	1.66900i	−0.558537	−	0.0607814i
$755$	6.52194			0.237358
$756$	−1.14620	−	4.30900i	−0.0416869	−	0.156717i
$757$	3.83594	−	6.64405i	0.139420	−	0.241482i	−0.787857	−	0.615858i	$-0.788810\pi$
$757$	3.83594	−	6.64405i	0.139420	−	0.241482i	0.927277	+	0.374376i	$0.122143\pi$
$758$	−0.388451	+	0.672816i	−0.0141092	+	0.0244378i
$759$	−12.7551	−	7.36416i	−0.462981	−	0.267302i
$760$			5.93040i			0.215118i
$761$	24.5371	+	14.1665i	0.889470	+	0.513535i	0.873769	−	0.486341i	$-0.161669\pi$
$761$	24.5371	+	14.1665i	0.889470	+	0.513535i	0.0157006	+	0.999877i	$0.495002\pi$
$762$		−	11.4079i		−	0.413266i
$763$	11.2570	−	41.7085i	0.407532	−	1.50995i
$764$	−8.01246	+	13.8780i	−0.289881	+	0.502088i
$765$		−	2.57761i		−	0.0931937i
$766$	5.53657	−	9.58962i	0.200044	−	0.346487i
$767$	4.43344	+	10.0570i	0.160082	+	0.363137i
$768$	−1.83061	−	3.17070i	−0.0660563	−	0.114413i
$769$	8.61926	+	4.97633i	0.310819	+	0.179451i	0.647293	−	0.762242i	$-0.275901\pi$
$769$	8.61926	+	4.97633i	0.310819	+	0.179451i	−0.336474	+	0.941693i	$0.609234\pi$
$770$	−0.435561	+	1.61380i	−0.0156965	+	0.0581572i
$771$	−0.753004	−	1.30424i	−0.0271188	−	0.0469711i
$772$	−4.54190	+	2.62227i	−0.163466	+	0.0943774i
$773$			36.8023i			1.32369i	0.749641	+	0.661844i	$0.230226\pi$
$773$			36.8023i			1.32369i	−0.749641	+	0.661844i	$0.769774\pi$
$774$		−	2.37803i		−	0.0854765i
$775$	−24.4058	+	14.0907i	−0.876682	+	0.506153i
$776$	−9.57244	−	16.5799i	−0.343630	−	0.595185i
$777$	10.9191	+	10.9589i	0.391721	+	0.393148i
$778$	−2.41581	−	1.39477i	−0.0866111	−	0.0500050i
$779$	29.4292	+	50.9728i	1.05441	+	1.82629i
$780$	3.13859	+	0.341549i	0.112379	+	0.0122294i
$781$	10.7806	−	18.6725i	0.385760	−	0.668155i
$782$			18.9114i			0.676271i
$783$	−3.81357	+	6.60529i	−0.136286	+	0.236054i
$784$	−13.4299	+	7.68881i	−0.479640	+	0.274600i
$785$		−	0.359656i		−	0.0128367i
$786$	6.69435	+	3.86498i	0.238779	+	0.137859i
$787$			14.3887i			0.512903i	0.966557	+	0.256451i	$0.0825534\pi$
$787$			14.3887i			0.512903i	−0.966557	+	0.256451i	$0.917447\pi$
$788$	7.43798	+	4.29432i	0.264967	+	0.152979i
$789$	3.44299	−	5.96344i	0.122574	−	0.212304i
$790$	0.723279	−	1.25276i	0.0257331	−	0.0445711i
$791$	−23.2403	+	23.1560i	−0.826330	+	0.823332i
$792$	−4.48118			−0.159232
$793$	−2.43753	+	22.3991i	−0.0865592	+	0.795416i
$794$	2.75623	−	4.77392i	0.0978148	−	0.169420i
$795$	0.941670	−	0.543673i	0.0333976	−	0.0192821i
$796$	23.4435			0.830933
$797$	15.6589	+	27.1221i	0.554668	+	0.960712i	0.997929	+	0.0643202i	$0.0204879\pi$
$797$	15.6589	+	27.1221i	0.554668	+	0.960712i	−0.443262	+	0.896392i	$0.646179\pi$
$798$	−2.10647	−	7.91900i	−0.0745682	−	0.280329i
$799$	48.0910	−	27.7653i	1.70134	−	0.982267i
$800$	22.0182	+	12.7122i	0.778460	+	0.449444i
$801$	2.19138	+	1.26519i	0.0774285	+	0.0447034i
$802$	−16.4146			−0.579618
$803$	6.18417			0.218235
$804$	−2.89163	−	1.66948i	−0.101980	−	0.0588782i
$805$	6.59298	+	6.61699i	0.232372	+	0.233218i
$806$	1.30374	−	11.9805i	0.0459225	−	0.421994i
$807$	−5.93548	−	10.2806i	−0.208939	−	0.361893i
$808$	16.1928	−	9.34892i	0.569661	−	0.328894i
$809$	−27.7311	−	48.0316i	−0.974973	−	1.68870i	−0.680026	−	0.733188i	$-0.738031\pi$
$809$	−27.7311	−	48.0316i	−0.974973	−	1.68870i	−0.294947	−	0.955514i	$-0.595302\pi$
$810$	−0.145740	+	0.252428i	−0.00512077	+	0.00886943i
$811$		−	8.46874i		−	0.297378i	−0.988884	−	0.148689i	$-0.952495\pi$
$811$		−	8.46874i		−	0.297378i	0.988884	−	0.148689i	$-0.0475053\pi$
$812$	32.8333	+	8.86164i	1.15222	+	0.310983i
$813$	11.9020	−	6.87163i	0.417422	−	0.240998i
$814$	6.15739	−	3.55497i	0.215817	−	0.124602i
$815$	5.40218			0.189230
$816$	−5.48375	−	9.49814i	−0.191970	−	0.332501i
$817$			23.4025i			0.818748i
$818$	−7.20315			−0.251852
$819$	−9.43000	+	1.44050i	−0.329511	+	0.0503353i
$820$	−9.33515			−0.325997
$821$		−	26.5861i		−	0.927862i	−0.885871	−	0.463931i	$-0.846439\pi$
$821$		−	26.5861i		−	0.927862i	0.885871	−	0.463931i	$-0.153561\pi$
$822$	0.454769	+	0.787682i	0.0158619	+	0.0274736i
$823$	−48.9627			−1.70673			−0.853366	−	0.521312i	$-0.825443\pi$
$823$	−48.9627			−1.70673			−0.853366	+	0.521312i	$0.825443\pi$
$824$	−31.6154	+	18.2532i	−1.10138	+	0.635879i
$825$	8.87885	−	5.12620i	0.309122	−	0.178472i
$826$	1.16308	+	4.37244i	0.0404687	+	0.152137i
$827$		−	16.8817i		−	0.587034i	−0.955954	−	0.293517i	$-0.905174\pi$
$827$		−	16.8817i		−	0.587034i	0.955954	−	0.293517i	$-0.0948257\pi$
$828$	−5.72578	+	9.91734i	−0.198985	+	0.344652i
$829$	−4.72080	−	8.17666i	−0.163960	−	0.283987i	0.772325	−	0.635227i	$-0.219093\pi$
$829$	−4.72080	−	8.17666i	−0.163960	−	0.283987i	−0.936286	+	0.351240i	$0.885760\pi$
$830$	−0.923693	+	0.533294i	−0.0320619	+	0.0185109i
$831$	5.60801	+	9.71335i	0.194540	+	0.336952i
$832$	4.63889	−	2.04496i	0.160824	−	0.0708964i
$833$	30.1375	−	17.2541i	1.04420	−	0.597820i
$834$	3.56484	+	2.05816i	0.123440	+	0.0712683i
$835$	12.5453			0.434147
$836$	20.1669			0.697486
$837$	−5.15974	−	2.97898i	−0.178347	−	0.102969i
$838$	−12.8119	−	7.39693i	−0.442578	−	0.255523i
$839$	−32.5016	+	18.7648i	−1.12208	+	0.647833i	−0.941931	−	0.335806i	$-0.890991\pi$
$839$	−32.5016	+	18.7648i	−1.12208	+	0.647833i	−0.180149	+	0.983639i	$0.557658\pi$
$840$	2.74384	+	0.740558i	0.0946714	+	0.0255517i
$841$	−14.5866	−	25.2647i	−0.502985	−	0.871195i
$842$	−1.52242			−0.0524661
$843$	1.57284	−	0.908078i	0.0541714	−	0.0312759i
$844$	−10.6306	+	18.4128i	−0.365921	+	0.633793i
$845$	1.45287	−	6.59634i	0.0499802	−	0.226921i
$846$	−6.27947			−0.215893
$847$	−16.0973	−	4.34463i	−0.553109	−	0.149283i
$848$	2.31328	−	4.00672i	0.0794385	−	0.137591i
$849$	15.4189	−	26.7063i	0.529174	−	0.916556i
$850$	−11.4006	−	6.58214i	−0.391037	−	0.225766i
$851$		−	39.7317i		−	1.36198i
$852$	−14.5183	−	8.38212i	−0.497387	−	0.287167i
$853$		−	35.3664i		−	1.21092i	−0.795875	−	0.605461i	$-0.792989\pi$
$853$		−	35.3664i		−	1.21092i	0.795875	−	0.605461i	$-0.207011\pi$
$854$	−2.41689	+	8.95483i	−0.0827044	+	0.306428i
$855$	1.43424	−	2.48418i	0.0490500	−	0.0849571i
$856$		−	40.2325i		−	1.37512i
$857$	−2.53098	+	4.38379i	−0.0864568	+	0.149748i	−0.906011	−	0.423254i	$-0.860888\pi$
$857$	−2.53098	+	4.38379i	−0.0864568	+	0.149748i	0.819554	+	0.573002i	$0.194221\pi$
$858$	−0.474303	+	4.35850i	−0.0161924	+	0.148797i
$859$	2.61058	+	4.52166i	0.0890719	+	0.154277i	0.907119	−	0.420874i	$-0.138277\pi$
$859$	2.61058	+	4.52166i	0.0890719	+	0.154277i	−0.818047	+	0.575151i	$0.804943\pi$
$860$	−3.21444	−	1.85586i	−0.109612	−	0.0632842i
$861$	27.2587	−	7.25088i	0.928975	−	0.247109i
$862$	10.4028	+	18.0181i	0.354319	+	0.613699i
$863$	−1.53116	+	0.884017i	−0.0521214	+	0.0300923i	−0.525834	−	0.850587i	$-0.676247\pi$
$863$	−1.53116	+	0.884017i	−0.0521214	+	0.0300923i	0.473713	+	0.880679i	$0.342913\pi$
$864$			5.37509i			0.182864i
$865$			1.94246i			0.0660458i
$866$	7.01100	−	4.04780i	0.238243	−	0.137550i
$867$	3.80585	+	6.59193i	0.129253	+	0.223874i
$868$	−6.92230	+	25.6478i	−0.234958	+	0.870543i
$869$	−9.31580	−	5.37848i	−0.316017	−	0.182452i
$870$	−1.11157	−	1.92530i	−0.0376859	−	0.0652739i
$871$	−4.22007	+	5.76374i	−0.142991	+	0.195297i
$872$	−16.8790	+	29.2352i	−0.571593	+	0.990029i
$873$			9.26021i			0.313411i
$874$	−10.5227	+	18.2259i	−0.355937	+	0.616501i
$875$	−12.9260	+	3.43835i	−0.436979	+	0.116237i
$876$		−	4.80832i		−	0.162458i
$877$	49.2185	+	28.4163i	1.66199	+	0.959550i	0.971763	+	0.235957i	$0.0758225\pi$
$877$	49.2185	+	28.4163i	1.66199	+	0.959550i	0.690227	+	0.723593i	$0.257511\pi$
$878$		−	8.20742i		−	0.276987i
$879$	−0.948761	−	0.547767i	−0.0320009	−	0.0184757i
$880$	−1.24484	+	2.15613i	−0.0419636	+	0.0726831i
$881$	20.9164	−	36.2283i	0.704693	−	1.22056i	−0.262110	−	0.965038i	$-0.584418\pi$
$881$	20.9164	−	36.2283i	0.704693	−	1.22056i	0.966802	−	0.255525i	$-0.0822484\pi$
$882$	−3.92696	−	0.0142757i	−0.132228	−	0.000480689i
$883$	−8.23784			−0.277225			−0.138613	−	0.990347i	$-0.544264\pi$
$883$	−8.23784			−0.277225			−0.138613	+	0.990347i	$0.544264\pi$
$884$	−27.5837	+	12.1597i	−0.927740	+	0.408976i
$885$	−0.791910	+	1.37163i	−0.0266198	+	0.0461068i
$886$	17.7860	−	10.2688i	0.597533	−	0.344986i
$887$	−54.7544			−1.83847			−0.919236	−	0.393706i	$-0.871193\pi$
$887$	−54.7544			−1.83847			−0.919236	+	0.393706i	$0.871193\pi$
$888$	−6.04430	−	10.4690i	−0.202834	−	0.351318i
$889$	51.9429	+	14.0193i	1.74211	+	0.470192i
$890$	−0.638741	+	0.368777i	−0.0214106	+	0.0123614i
$891$	1.87712	+	1.08375i	0.0628858	+	0.0363071i
$892$	1.11149	+	0.641717i	0.0372153	+	0.0214863i
$893$	61.7970			2.06796
$894$	−0.603012			−0.0201677
$895$	2.55493	+	1.47509i	0.0854020	+	0.0493069i
$896$	29.5033	−	7.84794i	0.985636	−	0.262181i
$897$	19.7677	+	14.4734i	0.660026	+	0.483254i
$898$	1.81166	+	3.13789i	0.0604559	+	0.104713i
$899$	39.3540	−	22.7211i	1.31253	−	0.757789i
$900$	−3.98573	−	6.90348i	−0.132858	−	0.230116i
$901$	−5.19114	+	8.99131i	−0.172942	+	0.299544i
$902$		−	12.9636i		−	0.431639i
$903$	10.8277	+	2.92238i	0.360323	+	0.0972507i
$904$	22.2015	−	12.8180i	0.738411	−	0.426322i
$905$	−4.47670	+	2.58462i	−0.148810	+	0.0859158i
$906$	7.04192			0.233952
$907$	−5.77857	−	10.0088i	−0.191874	−	0.332336i	0.753997	−	0.656878i	$-0.228123\pi$
$907$	−5.77857	−	10.0088i	−0.191874	−	0.332336i	−0.945871	+	0.324542i	$0.894790\pi$
$908$		−	2.59628i		−	0.0861604i
$909$	−9.04398			−0.299970
$910$	1.01070	−	2.59034i	0.0335044	−	0.0858689i
$911$	23.9338			0.792961			0.396481	−	0.918043i	$-0.370231\pi$
$911$	23.9338			0.792961			0.396481	+	0.918043i	$0.370231\pi$
$912$		−	12.2051i		−	0.404152i
$913$	3.96570	+	6.86880i	0.131246	+	0.227324i
$914$	10.7678			0.356166
$915$	−2.81185	+	1.62342i	−0.0929570	+	0.0536688i
$916$	−8.19949	+	4.73398i	−0.270919	+	0.156415i
$917$	−25.8249	+	25.7312i	−0.852813	+	0.849718i
$918$		−	2.78312i		−	0.0918566i
$919$	−1.56904	+	2.71766i	−0.0517580	+	0.0896474i	−0.890744	−	0.454506i	$-0.849816\pi$
$919$	−1.56904	+	2.71766i	−0.0517580	+	0.0896474i	0.838986	+	0.544154i	$0.183149\pi$
$920$	−3.64956	−	6.32122i	−0.120322	−	0.208405i
$921$	4.24566	−	2.45124i	0.139899	−	0.0807709i
$922$	1.78206	+	3.08662i	0.0586891	+	0.101653i
$923$	−21.1880	+	28.9385i	−0.697413	+	0.952523i
$924$	2.51834	−	9.33069i	0.0828472	−	0.306957i
$925$	23.9519	+	13.8286i	0.787534	+	0.454683i
$926$	6.07553			0.199654
$927$	17.6578			0.579958
$928$	−35.5040	−	20.4982i	−1.16548	−	0.672888i
$929$	18.3572	+	10.5986i	0.602282	+	0.347728i	0.769939	−	0.638118i	$-0.220287\pi$
$929$	18.3572	+	10.5986i	0.602282	+	0.347728i	−0.167657	+	0.985845i	$0.553620\pi$
$930$	1.50396	−	0.868310i	0.0493167	−	0.0284730i
$931$	38.6457	+	0.140489i	1.26656	+	0.00460435i
$932$	−14.4509	−	25.0297i	−0.473356	−	0.819876i
$933$	−11.5750			−0.378949
$934$	5.67470	−	3.27629i	0.185682	−	0.107204i
$935$	2.79350	−	4.83848i	0.0913571	−	0.158235i
$936$	7.41049	+	0.806429i	0.242219	+	0.0263590i
$937$	−26.0293			−0.850339			−0.425169	−	0.905114i	$-0.639786\pi$
$937$	−26.0293			−0.850339			−0.425169	+	0.905114i	$0.639786\pi$
$938$	−2.08316	+	2.07560i	−0.0680176	+	0.0677708i
$939$	−2.53480	+	4.39041i	−0.0827201	+	0.143275i
$940$	−4.90062	+	8.48812i	−0.159841	+	0.276852i
$941$	14.2589	+	8.23240i	0.464828	+	0.268369i	0.714072	−	0.700072i	$-0.246849\pi$
$941$	14.2589	+	8.23240i	0.464828	+	0.268369i	−0.249244	+	0.968441i	$0.580182\pi$
$942$		−	0.388331i		−	0.0126525i
$943$	−62.7372	−	36.2213i	−2.04300	−	1.17953i
$944$			6.73902i			0.219336i
$945$	−0.970263	−	0.973797i	−0.0315627	−	0.0316776i
$946$	2.57720	−	4.46384i	0.0837919	−	0.145132i
$947$			14.2330i			0.462511i	0.972893	+	0.231255i	$0.0742833\pi$
$947$			14.2330i			0.462511i	−0.972893	+	0.231255i	$0.925717\pi$
$948$	−4.18188	+	7.24322i	−0.135821	+	0.235249i
$949$	−10.2267	−	1.11290i	−0.331973	−	0.0361262i
$950$	−7.32490	−	12.6871i	−0.237651	−	0.411624i
$951$	14.8929	+	8.59841i	0.482935	+	0.278823i
$952$	−26.2244	+	6.97575i	−0.849939	+	0.226085i
$953$	−22.2750	−	38.5815i	−0.721559	−	1.24978i	−0.960375	−	0.278712i	$-0.910092\pi$
$953$	−22.2750	−	38.5815i	−0.721559	−	1.24978i	0.238815	−	0.971065i	$-0.423241\pi$
$954$	1.01675	−	0.587020i	0.0329184	−	0.0190055i
$955$			4.94049i			0.159870i
$956$			43.2541i			1.39894i
$957$	−14.3170	+	8.26593i	−0.462803	+	0.267200i
$958$	−6.73859	−	11.6716i	−0.217714	−	0.377092i
$959$	−4.14537	+	1.10268i	−0.133861	+	0.0356073i
$960$	0.632676	+	0.365276i	0.0204195	+	0.0117892i
$961$	2.24861	+	3.89472i	0.0725360	+	0.125636i
$962$	−10.8222	+	4.77075i	−0.348921	+	0.153815i
$963$	−9.73005	+	16.8529i	−0.313546	+	0.543078i
$964$		−	7.94978i		−	0.256045i
$965$	−0.808445	+	1.40027i	−0.0260248	+	0.0450762i
$966$	7.11863	+	7.14456i	0.229038	+	0.229872i
$967$			17.7030i			0.569289i	0.958633	+	0.284645i	$0.0918756\pi$
$967$			17.7030i			0.569289i	−0.958633	+	0.284645i	$0.908124\pi$
$968$	11.2833	+	6.51439i	0.362658	+	0.209380i
$969$			27.3890i			0.879862i
$970$	−2.33754	−	1.34958i	−0.0750538	−	0.0433324i
$971$	−3.16344	+	5.47924i	−0.101520	+	0.175837i	−0.912311	−	0.409498i	$-0.865704\pi$
$971$	−3.16344	+	5.47924i	−0.101520	+	0.175837i	0.810791	+	0.585335i	$0.199037\pi$
$972$	0.842641	−	1.45950i	0.0270277	−	0.0468134i
$973$	−13.7521	+	13.7022i	−0.440873	+	0.439274i
$974$	−3.38858			−0.108577
$975$	−15.6054	+	6.87933i	−0.499772	+	0.220315i
$976$	−6.90753	+	11.9642i	−0.221105	+	0.382965i
$977$	−7.94569	+	4.58744i	−0.254205	+	0.146765i	−0.621688	−	0.783265i	$-0.713553\pi$
$977$	−7.94569	+	4.58744i	−0.254205	+	0.146765i	0.367483	+	0.930030i	$0.380220\pi$
$978$	5.83289			0.186515
$979$	2.74231	+	4.74983i	0.0876447	+	0.151805i
$980$	−3.08397	+	5.29703i	−0.0985138	+	0.169207i
$981$	14.1408	−	8.16420i	0.451481	−	0.260663i
$982$	6.85640	+	3.95854i	0.218796	+	0.126322i
$983$	42.7704	+	24.6935i	1.36416	+	0.787601i	0.990175	−	0.139832i	$-0.0446562\pi$
$983$	42.7704	+	24.6935i	1.36416	+	0.787601i	0.373990	+	0.927433i	$0.377990\pi$
$984$	−22.0411			−0.702646
$985$	2.64788			0.0843685
$986$	18.3833	+	10.6136i	0.585444	+	0.338006i
$987$	7.71690	−	28.5919i	0.245632	−	0.910089i
$988$	−33.3498	−	3.62921i	−1.06100	−	0.115461i
$989$	−14.4018	−	24.9447i	−0.457952	−	0.793196i
$990$	−0.547140	+	0.315892i	−0.0173893	+	0.0100397i
$991$	−17.9465	−	31.0842i	−0.570088	−	0.987421i	−0.996556	−	0.0829187i	$-0.973576\pi$
$991$	−17.9465	−	31.0842i	−0.570088	−	0.987421i	0.426468	−	0.904502i	$-0.359758\pi$
$992$	16.0123	−	27.7341i	0.508390	−	0.880557i
$993$			20.4213i			0.648050i
$994$	−10.4591	+	10.4212i	−0.331743	+	0.330539i
$995$	6.25932	−	3.61382i	0.198434	−	0.114566i
$996$	5.34063	−	3.08342i	0.169224	−	0.0977018i
$997$	42.2451			1.33791			0.668957	−	0.743301i	$-0.266741\pi$
$997$	42.2451			1.33791			0.668957	+	0.743301i	$0.266741\pi$
$998$	9.21412	+	15.9593i	0.291668	+	0.505184i
$999$			5.84715i			0.184996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.t.d.4.5	✓	20
3.2	odd	2		819.2.bm.g.550.6		20
7.2	even	3		273.2.bl.d.121.5	yes	20
13.10	even	6		273.2.bl.d.88.5	yes	20
21.2	odd	6		819.2.do.g.667.6		20
39.23	odd	6		819.2.do.g.361.6		20
91.23	even	6	inner	273.2.t.d.205.6	yes	20
273.23	odd	6		819.2.bm.g.478.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.d.4.5	✓	20	1.1	even	1	trivial
273.2.t.d.205.6	yes	20	91.23	even	6	inner
273.2.bl.d.88.5	yes	20	13.10	even	6
273.2.bl.d.121.5	yes	20	7.2	even	3
819.2.bm.g.478.5		20	273.23	odd	6
819.2.bm.g.550.6		20	3.2	odd	2
819.2.do.g.361.6		20	39.23	odd	6
819.2.do.g.667.6		20	21.2	odd	6

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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.560998i q^{2} +(0.500000 + 0.866025i) q^{3} +1.68528 q^{4} +(0.449963 - 0.259786i) q^{5} +(0.485838 - 0.280499i) q^{6} +(0.680125 + 2.55684i) q^{7} -2.06743i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-0.560998i q^{2} +(0.500000 + 0.866025i) q^{3} +1.68528 q^{4} +(0.449963 - 0.259786i) q^{5} +(0.485838 - 0.280499i) q^{6} +(0.680125 + 2.55684i) q^{7} -2.06743i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.145740 - 0.252428i) q^{10} +(-1.87712 + 1.08375i) q^{11} +(0.842641 + 1.45950i) q^{12} +(3.29920 - 1.45439i) q^{13} +(1.43438 - 0.381548i) q^{14} +(0.449963 + 0.259786i) q^{15} +2.21074 q^{16} -4.96102 q^{17} +(0.485838 + 0.280499i) q^{18} +(-4.78119 - 2.76042i) q^{19} +(0.758315 - 0.437813i) q^{20} +(-1.87423 + 1.86743i) q^{21} +(0.607984 + 1.05306i) q^{22} +6.79504 q^{23} +(1.79045 - 1.03372i) q^{24} +(-2.36502 + 4.09634i) q^{25} +(-0.815910 - 1.85085i) q^{26} -1.00000 q^{27} +(1.14620 + 4.30900i) q^{28} +(3.81357 - 6.60529i) q^{29} +(0.145740 - 0.252428i) q^{30} +(5.15974 + 2.97898i) q^{31} -5.37509i q^{32} +(-1.87712 - 1.08375i) q^{33} +2.78312i q^{34} +(0.970263 + 0.973797i) q^{35} +(-0.842641 + 1.45950i) q^{36} -5.84715i q^{37} +(-1.54859 + 2.68224i) q^{38} +(2.90914 + 2.13000i) q^{39} +(-0.537091 - 0.930269i) q^{40} +(-9.23279 - 5.33055i) q^{41} +(1.04762 + 1.05144i) q^{42} +(-2.11946 - 3.67102i) q^{43} +(-3.16347 + 1.82643i) q^{44} +0.519573i q^{45} -3.81200i q^{46} +(-9.69377 + 5.59670i) q^{47} +(1.10537 + 1.91455i) q^{48} +(-6.07486 + 3.47794i) q^{49} +(2.29804 + 1.32677i) q^{50} +(-2.48051 - 4.29637i) q^{51} +(5.56009 - 2.45106i) q^{52} +(1.04639 - 1.81239i) q^{53} +0.560998i q^{54} +(-0.563089 + 0.975299i) q^{55} +(5.28610 - 1.40611i) q^{56} -5.52084i q^{57} +(-3.70555 - 2.13940i) q^{58} +3.04831i q^{59} +(0.758315 + 0.437813i) q^{60} +(-3.12454 + 5.41186i) q^{61} +(1.67120 - 2.89460i) q^{62} +(-2.55435 - 0.689415i) q^{63} +1.40606 q^{64} +(1.10669 - 1.51151i) q^{65} +(-0.607984 + 1.05306i) q^{66} +(-1.71581 + 0.990626i) q^{67} -8.36071 q^{68} +(3.39752 + 5.88468i) q^{69} +(0.546298 - 0.544315i) q^{70} +(-8.61474 + 4.97372i) q^{71} +(1.79045 + 1.03372i) q^{72} +(-2.47088 - 1.42656i) q^{73} -3.28024 q^{74} -4.73004 q^{75} +(-8.05765 - 4.65209i) q^{76} +(-4.04766 - 4.06240i) q^{77} +(1.19492 - 1.63202i) q^{78} +(2.48141 + 4.29793i) q^{79} +(0.994750 - 0.574319i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.99043 + 5.17957i) q^{82} -3.65923i q^{83} +(-3.15860 + 3.14714i) q^{84} +(-2.23228 + 1.28880i) q^{85} +(-2.05943 + 1.18901i) q^{86} +7.62713 q^{87} +(2.24059 + 3.88082i) q^{88} -2.53038i q^{89} +0.291479 q^{90} +(5.96251 + 7.44637i) q^{91} +11.4516 q^{92} +5.95796i q^{93} +(3.13974 + 5.43818i) q^{94} -2.86848 q^{95} +(4.65496 - 2.68754i) q^{96} +(8.01957 - 4.63010i) q^{97} +(1.95112 + 3.40798i) q^{98} -2.16751i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9}+O(q^{10}) \) 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9	\( 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9} + 2 q^{10} - 12 q^{11} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} + 42 q^{16} + 16 q^{17} + 3 q^{18} - 9 q^{19} - 5 q^{21} - 9 q^{22} - 36 q^{23} + 3 q^{24} + 12 q^{25} - 16 q^{26} - 20 q^{27} - 2 q^{28} - 3 q^{29} - 2 q^{30} - 18 q^{31} - 12 q^{33} + 18 q^{35} + 13 q^{36} + 9 q^{38} + 7 q^{39} + 5 q^{40} + 21 q^{41} + 16 q^{42} + 16 q^{43} - 6 q^{44} + 21 q^{47} + 21 q^{48} - 24 q^{49} - 54 q^{50} + 8 q^{51} - 41 q^{52} - 26 q^{53} + 17 q^{55} - 6 q^{56} + 42 q^{58} + 4 q^{62} - 7 q^{63} - 46 q^{64} - 50 q^{65} + 9 q^{66} - 3 q^{67} + 6 q^{68} - 18 q^{69} + 15 q^{71} + 3 q^{72} - 9 q^{73} + 12 q^{74} + 24 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} - 24 q^{80} - 10 q^{81} + 15 q^{82} + 41 q^{84} - 78 q^{85} + 3 q^{86} - 6 q^{87} - 22 q^{88} - 4 q^{90} + 4 q^{91} + 142 q^{92} + 36 q^{94} - 84 q^{95} - 24 q^{96} - 15 q^{97} + 81 q^{98}+O(q^{100}) \) 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9 + 2 * q^10 - 12 * q^11 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 + 42 * q^16 + 16 * q^17 + 3 * q^18 - 9 * q^19 - 5 * q^21 - 9 * q^22 - 36 * q^23 + 3 * q^24 + 12 * q^25 - 16 * q^26 - 20 * q^27 - 2 * q^28 - 3 * q^29 - 2 * q^30 - 18 * q^31 - 12 * q^33 + 18 * q^35 + 13 * q^36 + 9 * q^38 + 7 * q^39 + 5 * q^40 + 21 * q^41 + 16 * q^42 + 16 * q^43 - 6 * q^44 + 21 * q^47 + 21 * q^48 - 24 * q^49 - 54 * q^50 + 8 * q^51 - 41 * q^52 - 26 * q^53 + 17 * q^55 - 6 * q^56 + 42 * q^58 + 4 * q^62 - 7 * q^63 - 46 * q^64 - 50 * q^65 + 9 * q^66 - 3 * q^67 + 6 * q^68 - 18 * q^69 + 15 * q^71 + 3 * q^72 - 9 * q^73 + 12 * q^74 + 24 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 - 24 * q^80 - 10 * q^81 + 15 * q^82 + 41 * q^84 - 78 * q^85 + 3 * q^86 - 6 * q^87 - 22 * q^88 - 4 * q^90 + 4 * q^91 + 142 * q^92 + 36 * q^94 - 84 * q^95 - 24 * q^96 - 15 * q^97 + 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more