LMFDB - Embedded newform 210.2.j.b.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(113,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("210.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.j (of order $4$, 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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} + 86x^{8} + 196x^{6} + 185x^{4} + 60x^{2} + 4 $ x^12 + 16x^10 + 86x^8 + 196x^6 + 185x^4 + 60*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			113.2
Root			$-1.69093i$ of defining polynomial
Character	$\chi$	$=$	210.113
Dual form			210.2.j.b.197.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.27508 + 1.17225i) q^{3} +1.00000i q^{4} +(-1.37462 + 1.76364i) q^{5} +(-0.0727133 - 1.73052i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.251664 + 2.98943i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.27508 + 1.17225i) q^{3} +1.00000i q^{4} +(-1.37462 + 1.76364i) q^{5} +(-0.0727133 - 1.73052i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.251664 + 2.98943i) q^{9} +(2.21908 - 0.275081i) q^{10} +2.48992i q^{11} +(-1.17225 + 1.27508i) q^{12} +(-1.31138 - 1.31138i) q^{13} +1.00000 q^{14} +(-3.82017 + 0.637391i) q^{15} -1.00000 q^{16} +(2.15197 + 2.15197i) q^{17} +(1.93589 - 2.29180i) q^{18} +1.26198i q^{19} +(-1.76364 - 1.37462i) q^{20} +(-1.73052 + 0.0727133i) q^{21} +(1.76064 - 1.76064i) q^{22} +(3.83635 - 3.83635i) q^{23} +(1.73052 - 0.0727133i) q^{24} +(-1.22086 - 4.84866i) q^{25} +1.85457i q^{26} +(-3.18346 + 4.10677i) q^{27} +(-0.707107 - 0.707107i) q^{28} +2.68900 q^{29} +(3.15197 + 2.25057i) q^{30} +10.1010 q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.91881 + 3.17486i) q^{33} -3.04335i q^{34} +(-0.275081 - 2.21908i) q^{35} +(-2.98943 + 0.251664i) q^{36} +(3.73101 - 3.73101i) q^{37} +(0.892352 - 0.892352i) q^{38} +(-0.134852 - 3.20938i) q^{39} +(0.275081 + 2.21908i) q^{40} +9.92875i q^{41} +(1.27508 + 1.17225i) q^{42} +(-7.18740 - 7.18740i) q^{43} -2.48992 q^{44} +(-5.61821 - 3.66547i) q^{45} -5.42542 q^{46} +(-9.47825 - 9.47825i) q^{47} +(-1.27508 - 1.17225i) q^{48} -1.00000i q^{49} +(-2.56525 + 4.29180i) q^{50} +(0.221292 + 5.26659i) q^{51} +(1.31138 - 1.31138i) q^{52} +(6.59040 - 6.59040i) q^{53} +(5.15497 - 0.652882i) q^{54} +(-4.39133 - 3.42269i) q^{55} +1.00000i q^{56} +(-1.47935 + 1.60912i) q^{57} +(-1.90141 - 1.90141i) q^{58} -1.66786 q^{59} +(-0.637391 - 3.82017i) q^{60} -1.70551 q^{61} +(-7.14250 - 7.14250i) q^{62} +(-2.29180 - 1.93589i) q^{63} -1.00000i q^{64} +(4.11545 - 0.510158i) q^{65} +(4.30887 - 0.181051i) q^{66} +(-4.58359 + 4.58359i) q^{67} +(-2.15197 + 2.15197i) q^{68} +(9.38883 - 0.394500i) q^{69} +(-1.37462 + 1.76364i) q^{70} -2.61784i q^{71} +(2.29180 + 1.93589i) q^{72} +(8.49621 + 8.49621i) q^{73} -5.27645 q^{74} +(4.12715 - 7.61358i) q^{75} -1.26198 q^{76} +(-1.76064 - 1.76064i) q^{77} +(-2.17402 + 2.36473i) q^{78} -3.26305i q^{79} +(1.37462 - 1.76364i) q^{80} +(-8.87333 + 1.50466i) q^{81} +(7.02069 - 7.02069i) q^{82} +(-1.42445 + 1.42445i) q^{83} +(-0.0727133 - 1.73052i) q^{84} +(-6.75345 + 0.837169i) q^{85} +10.1645i q^{86} +(3.42869 + 3.15217i) q^{87} +(1.76064 + 1.76064i) q^{88} +11.6683 q^{89} +(1.38080 + 6.56456i) q^{90} +1.85457 q^{91} +(3.83635 + 3.83635i) q^{92} +(12.8796 + 11.8409i) q^{93} +13.4043i q^{94} +(-2.22567 - 1.73473i) q^{95} +(0.0727133 + 1.73052i) q^{96} +(-0.983930 + 0.983930i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(-7.44344 + 0.626625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} + 4 q^{5}+O(q^{10}) $ 12 * q + 4 * q^3 + 4 * q^5	$ 12 q + 4 q^{3} + 4 q^{5} - 4 q^{12} + 12 q^{14} - 12 q^{15} - 12 q^{16} - 28 q^{17} - 8 q^{18} - 4 q^{21} + 4 q^{22} + 24 q^{23} + 4 q^{24} + 20 q^{25} + 28 q^{27} - 8 q^{29} - 16 q^{30} - 8 q^{31} - 36 q^{33} + 8 q^{35} + 4 q^{36} - 20 q^{37} + 4 q^{38} + 40 q^{39} - 8 q^{40} + 4 q^{42} + 8 q^{43} - 8 q^{44} - 48 q^{45} + 8 q^{46} - 16 q^{47} - 4 q^{48} + 16 q^{50} + 8 q^{51} + 24 q^{53} + 4 q^{54} - 16 q^{55} + 44 q^{57} - 8 q^{58} - 32 q^{59} + 4 q^{60} - 28 q^{62} - 8 q^{66} + 28 q^{68} + 32 q^{69} + 4 q^{70} - 24 q^{73} - 8 q^{74} - 4 q^{75} - 4 q^{77} - 8 q^{78} - 4 q^{80} - 36 q^{81} + 32 q^{82} + 24 q^{83} - 36 q^{85} - 16 q^{87} + 4 q^{88} - 48 q^{89} - 8 q^{90} + 24 q^{91} + 24 q^{92} - 20 q^{93} + 8 q^{97} + 40 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 + 4 * q^5 - 4 * q^12 + 12 * q^14 - 12 * q^15 - 12 * q^16 - 28 * q^17 - 8 * q^18 - 4 * q^21 + 4 * q^22 + 24 * q^23 + 4 * q^24 + 20 * q^25 + 28 * q^27 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 36 * q^33 + 8 * q^35 + 4 * q^36 - 20 * q^37 + 4 * q^38 + 40 * q^39 - 8 * q^40 + 4 * q^42 + 8 * q^43 - 8 * q^44 - 48 * q^45 + 8 * q^46 - 16 * q^47 - 4 * q^48 + 16 * q^50 + 8 * q^51 + 24 * q^53 + 4 * q^54 - 16 * q^55 + 44 * q^57 - 8 * q^58 - 32 * q^59 + 4 * q^60 - 28 * q^62 - 8 * q^66 + 28 * q^68 + 32 * q^69 + 4 * q^70 - 24 * q^73 - 8 * q^74 - 4 * q^75 - 4 * q^77 - 8 * q^78 - 4 * q^80 - 36 * q^81 + 32 * q^82 + 24 * q^83 - 36 * q^85 - 16 * q^87 + 4 * q^88 - 48 * q^89 - 8 * q^90 + 24 * q^91 + 24 * q^92 - 20 * q^93 + 8 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	1.27508	+	1.17225i	0.736168	+	0.676798i
$3$	1.27508	+	1.17225i	0.736168	+	0.676798i
$4$			1.00000i			0.500000i
$5$	−1.37462	+	1.76364i	−0.614747	+	0.788724i
$5$	−1.37462	+	1.76364i	−0.614747	+	0.788724i
$6$	−0.0727133	−	1.73052i	−0.0296851	−	0.706483i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.251664	+	2.98943i	0.0838880	+	0.996475i
$10$	2.21908	−	0.275081i	0.701736	−	0.0869883i
$11$			2.48992i			0.750741i	0.926875	+	0.375370i	$0.122484\pi$
$11$			2.48992i			0.750741i	−0.926875	+	0.375370i	$0.877516\pi$
$12$	−1.17225	+	1.27508i	−0.338399	+	0.368084i
$13$	−1.31138	−	1.31138i	−0.363712	−	0.363712i	0.501466	−	0.865178i	$-0.332794\pi$
$13$	−1.31138	−	1.31138i	−0.363712	−	0.363712i	−0.865178	+	0.501466i	$0.832794\pi$
$14$	1.00000			0.267261
$15$	−3.82017	+	0.637391i	−0.986365	+	0.164574i
$16$	−1.00000			−0.250000
$17$	2.15197	+	2.15197i	0.521931	+	0.521931i	0.918154	−	0.396223i	$-0.129679\pi$
$17$	2.15197	+	2.15197i	0.521931	+	0.521931i	−0.396223	+	0.918154i	$0.629679\pi$
$18$	1.93589	−	2.29180i	0.456294	−	0.540182i
$19$			1.26198i			0.289517i	0.989467	+	0.144759i	$0.0462406\pi$
$19$			1.26198i			0.289517i	−0.989467	+	0.144759i	$0.953759\pi$
$20$	−1.76364	−	1.37462i	−0.394362	−	0.307374i
$21$	−1.73052	+	0.0727133i	−0.377631	+	0.0158673i
$22$	1.76064	−	1.76064i	0.375370	−	0.375370i
$23$	3.83635	−	3.83635i	0.799935	−	0.799935i	−0.183150	−	0.983085i	$-0.558629\pi$
$23$	3.83635	−	3.83635i	0.799935	−	0.799935i	0.983085	+	0.183150i	$0.0586294\pi$
$24$	1.73052	−	0.0727133i	0.353242	−	0.0148425i
$25$	−1.22086	−	4.84866i	−0.244171	−	0.969732i
$26$			1.85457i			0.363712i
$27$	−3.18346	+	4.10677i	−0.612657	+	0.790349i
$28$	−0.707107	−	0.707107i	−0.133631	−	0.133631i
$29$	2.68900			0.499334			0.249667	−	0.968332i	$-0.419679\pi$
$29$	2.68900			0.499334			0.249667	+	0.968332i	$0.419679\pi$
$30$	3.15197	+	2.25057i	0.575469	+	0.410896i
$31$	10.1010			1.81420			0.907098	−	0.420919i	$-0.138292\pi$
$31$	10.1010			1.81420			0.907098	+	0.420919i	$0.138292\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−2.91881	+	3.17486i	−0.508100	+	0.552672i
$34$		−	3.04335i		−	0.521931i
$35$	−0.275081	−	2.21908i	−0.0464972	−	0.375094i
$36$	−2.98943	+	0.251664i	−0.498238	+	0.0419440i
$37$	3.73101	−	3.73101i	0.613375	−	0.613375i	−0.330449	−	0.943824i	$-0.607200\pi$
$37$	3.73101	−	3.73101i	0.613375	−	0.613375i	0.943824	+	0.330449i	$0.107200\pi$
$38$	0.892352	−	0.892352i	0.144759	−	0.144759i
$39$	−0.134852	−	3.20938i	−0.0215936	−	0.513913i
$40$	0.275081	+	2.21908i	0.0434942	+	0.350868i
$41$			9.92875i			1.55061i	0.631587	+	0.775305i	$0.282404\pi$
$41$			9.92875i			1.55061i	−0.631587	+	0.775305i	$0.717596\pi$
$42$	1.27508	+	1.17225i	0.196749	+	0.180882i
$43$	−7.18740	−	7.18740i	−1.09607	−	1.09607i	−0.994866	−	0.101202i	$-0.967731\pi$
$43$	−7.18740	−	7.18740i	−1.09607	−	1.09607i	−0.101202	−	0.994866i	$-0.532269\pi$
$44$	−2.48992			−0.375370
$45$	−5.61821	−	3.66547i	−0.837514	−	0.546416i
$46$	−5.42542			−0.799935
$47$	−9.47825	−	9.47825i	−1.38255	−	1.38255i	−0.840075	−	0.542471i	$-0.817489\pi$
$47$	−9.47825	−	9.47825i	−1.38255	−	1.38255i	−0.542471	−	0.840075i	$-0.682511\pi$
$48$	−1.27508	−	1.17225i	−0.184042	−	0.169200i
$49$		−	1.00000i		−	0.142857i
$50$	−2.56525	+	4.29180i	−0.362780	+	0.606952i
$51$	0.221292	+	5.26659i	0.0309871	+	0.737471i
$52$	1.31138	−	1.31138i	0.181856	−	0.181856i
$53$	6.59040	−	6.59040i	0.905262	−	0.905262i	−0.0906236	−	0.995885i	$-0.528886\pi$
$53$	6.59040	−	6.59040i	0.905262	−	0.905262i	0.995885	+	0.0906236i	$0.0288860\pi$
$54$	5.15497	−	0.652882i	0.701503	−	0.0888460i
$55$	−4.39133	−	3.42269i	−0.592127	−	0.461516i
$56$			1.00000i			0.133631i
$57$	−1.47935	+	1.60912i	−0.195945	+	0.213133i
$58$	−1.90141	−	1.90141i	−0.249667	−	0.249667i
$59$	−1.66786			−0.217137			−0.108569	−	0.994089i	$-0.534627\pi$
$59$	−1.66786			−0.217137			−0.108569	+	0.994089i	$0.534627\pi$
$60$	−0.637391	−	3.82017i	−0.0822869	−	0.493182i
$61$	−1.70551			−0.218368			−0.109184	−	0.994022i	$-0.534824\pi$
$61$	−1.70551			−0.218368			−0.109184	+	0.994022i	$0.534824\pi$
$62$	−7.14250	−	7.14250i	−0.907098	−	0.907098i
$63$	−2.29180	−	1.93589i	−0.288739	−	0.243899i
$64$		−	1.00000i		−	0.125000i
$65$	4.11545	−	0.510158i	0.510459	−	0.0632773i
$66$	4.30887	−	0.181051i	0.530386	−	0.0222858i
$67$	−4.58359	+	4.58359i	−0.559975	+	0.559975i	−0.929300	−	0.369325i	$-0.879589\pi$
$67$	−4.58359	+	4.58359i	−0.559975	+	0.559975i	0.369325	+	0.929300i	$0.379589\pi$
$68$	−2.15197	+	2.15197i	−0.260965	+	0.260965i
$69$	9.38883	−	0.394500i	1.13028	−	0.0474923i
$70$	−1.37462	+	1.76364i	−0.164298	+	0.210795i
$71$		−	2.61784i		−	0.310680i	−0.987861	−	0.155340i	$-0.950353\pi$
$71$		−	2.61784i		−	0.310680i	0.987861	−	0.155340i	$-0.0496474\pi$
$72$	2.29180	+	1.93589i	0.270091	+	0.228147i
$73$	8.49621	+	8.49621i	0.994406	+	0.994406i	0.999984	−	0.00557820i	$-0.00177561\pi$
$73$	8.49621	+	8.49621i	0.994406	+	0.994406i	−0.00557820	+	0.999984i	$0.501776\pi$
$74$	−5.27645			−0.613375
$75$	4.12715	−	7.61358i	0.476562	−	0.879141i
$76$	−1.26198			−0.144759
$77$	−1.76064	−	1.76064i	−0.200644	−	0.200644i
$78$	−2.17402	+	2.36473i	−0.246160	+	0.267753i
$79$		−	3.26305i		−	0.367122i	−0.983008	−	0.183561i	$-0.941238\pi$
$79$		−	3.26305i		−	0.367122i	0.983008	−	0.183561i	$-0.0587624\pi$
$80$	1.37462	−	1.76364i	0.153687	−	0.197181i
$81$	−8.87333	+	1.50466i	−0.985926	+	0.167185i
$82$	7.02069	−	7.02069i	0.775305	−	0.775305i
$83$	−1.42445	+	1.42445i	−0.156354	+	0.156354i	−0.780949	−	0.624595i	$-0.785264\pi$
$83$	−1.42445	+	1.42445i	−0.156354	+	0.156354i	0.624595	+	0.780949i	$0.285264\pi$
$84$	−0.0727133	−	1.73052i	−0.00793367	−	0.188816i
$85$	−6.75345	+	0.837169i	−0.732515	+	0.0908037i
$86$			10.1645i			1.09607i
$87$	3.42869	+	3.15217i	0.367594	+	0.337948i
$88$	1.76064	+	1.76064i	0.187685	+	0.187685i
$89$	11.6683			1.23684			0.618420	−	0.785848i	$-0.287773\pi$
$89$	11.6683			1.23684			0.618420	+	0.785848i	$0.287773\pi$
$90$	1.38080	+	6.56456i	0.145549	+	0.691965i
$91$	1.85457			0.194412
$92$	3.83635	+	3.83635i	0.399968	+	0.399968i
$93$	12.8796	+	11.8409i	1.33555	+	1.22784i
$94$			13.4043i			1.38255i
$95$	−2.22567	−	1.73473i	−0.228349	−	0.177980i
$96$	0.0727133	+	1.73052i	0.00742127	+	0.176621i
$97$	−0.983930	+	0.983930i	−0.0999029	+	0.0999029i	−0.755292	−	0.655389i	$-0.772505\pi$
$97$	−0.983930	+	0.983930i	−0.0999029	+	0.0999029i	0.655389	+	0.755292i	$0.272505\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$	−7.44344	+	0.626625i	−0.748094	+	0.0629782i
$100$	4.84866	−	1.22086i	0.484866	−	0.122086i
$101$			2.56790i			0.255516i	0.991805	+	0.127758i	$0.0407781\pi$
$101$			2.56790i			0.255516i	−0.991805	+	0.127758i	$0.959222\pi$
$102$	3.56757	−	3.88052i	0.353242	−	0.384229i
$103$	10.5580	+	10.5580i	1.04032	+	1.04032i	0.999152	+	0.0411626i	$0.0131062\pi$
$103$	10.5580	+	10.5580i	1.04032	+	1.04032i	0.0411626	+	0.999152i	$0.486894\pi$
$104$	−1.85457			−0.181856
$105$	2.25057	−	3.15197i	0.219633	−	0.307601i
$106$	−9.32024			−0.905262
$107$	−6.91089	−	6.91089i	−0.668100	−	0.668100i	0.289176	−	0.957276i	$-0.406619\pi$
$107$	−6.91089	−	6.91089i	−0.668100	−	0.668100i	−0.957276	+	0.289176i	$0.906619\pi$
$108$	−4.10677	−	3.18346i	−0.395174	−	0.306329i
$109$			9.17118i			0.878439i	0.898380	+	0.439220i	$0.144745\pi$
$109$			9.17118i			0.878439i	−0.898380	+	0.439220i	$0.855255\pi$
$110$	0.684931	+	5.52535i	0.0653057	+	0.526821i
$111$	9.13102	−	0.383668i	0.866679	−	0.0364162i
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$	12.5488	−	12.5488i	1.18049	−	1.18049i	0.200873	−	0.979617i	$-0.435622\pi$
$113$	12.5488	−	12.5488i	1.18049	−	1.18049i	0.979617	−	0.200873i	$-0.0643779\pi$
$114$	2.18388	−	0.0917624i	0.204539	−	0.00859434i
$115$	1.49243	+	12.0395i	0.139170	+	1.12269i
$116$			2.68900i			0.249667i
$117$	3.59025	−	4.25030i	0.331919	−	0.392941i
$118$	1.17936	+	1.17936i	0.108569	+	0.108569i
$119$	−3.04335			−0.278984
$120$	−2.25057	+	3.15197i	−0.205448	+	0.287735i
$121$	4.80027			0.436389
$122$	1.20598	+	1.20598i	0.109184	+	0.109184i
$123$	−11.6390	+	12.6600i	−1.04945	+	1.14151i
$124$			10.1010i			0.907098i
$125$	10.2295	+	4.51190i	0.914955	+	0.403557i
$126$	0.251664	+	2.98943i	0.0224200	+	0.266319i
$127$	−8.13842	+	8.13842i	−0.722168	+	0.722168i	−0.969046	−	0.246879i	$-0.920595\pi$
$127$	−8.13842	+	8.13842i	−0.722168	+	0.722168i	0.246879	+	0.969046i	$0.420595\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−0.739096	−	17.5899i	−0.0650737	−	1.54871i
$130$	−3.27080	−	2.54933i	−0.286868	−	0.223591i
$131$		−	9.18103i		−	0.802151i	−0.916045	−	0.401075i	$-0.868637\pi$
$131$		−	9.18103i		−	0.802151i	0.916045	−	0.401075i	$-0.131363\pi$
$132$	−3.17486	−	2.91881i	−0.276336	−	0.254050i
$133$	−0.892352	−	0.892352i	−0.0773767	−	0.0773767i
$134$	6.48218			0.559975
$135$	−2.86684	−	11.2597i	−0.246738	−	0.969082i
$136$	3.04335			0.260965
$137$	10.3214	+	10.3214i	0.881813	+	0.881813i	0.993719	−	0.111906i	$-0.0356955\pi$
$137$	10.3214	+	10.3214i	0.881813	+	0.881813i	−0.111906	+	0.993719i	$0.535696\pi$
$138$	−6.91786	−	6.35995i	−0.588887	−	0.541395i
$139$		−	6.42231i		−	0.544733i	−0.962194	−	0.272367i	$-0.912194\pi$
$139$		−	6.42231i		−	0.544733i	0.962194	−	0.272367i	$-0.0878064\pi$
$140$	2.21908	−	0.275081i	0.187547	−	0.0232486i
$141$	−0.974669	−	23.1964i	−0.0820819	−	1.95349i
$142$	−1.85109	+	1.85109i	−0.155340	+	0.155340i
$143$	3.26524	−	3.26524i	0.273053	−	0.273053i
$144$	−0.251664	−	2.98943i	−0.0209720	−	0.249119i
$145$	−3.69634	+	4.74242i	−0.306964	+	0.393837i
$146$		−	12.0155i		−	0.994406i
$147$	1.17225	−	1.27508i	0.0966855	−	0.105167i
$148$	3.73101	+	3.73101i	0.306687	+	0.306687i
$149$	−17.9577			−1.47115			−0.735576	−	0.677442i	$-0.763088\pi$
$149$	−17.9577			−1.47115			−0.735576	+	0.677442i	$0.763088\pi$
$150$	−8.30195	+	2.46528i	−0.677851	+	0.201289i
$151$	−6.24908			−0.508543			−0.254271	−	0.967133i	$-0.581836\pi$
$151$	−6.24908			−0.508543			−0.254271	+	0.967133i	$0.581836\pi$
$152$	0.892352	+	0.892352i	0.0723793	+	0.0723793i
$153$	−5.89159	+	6.97474i	−0.476307	+	0.563875i
$154$			2.48992i			0.200644i
$155$	−13.8850	+	17.8146i	−1.11527	+	1.43090i
$156$	3.20938	−	0.134852i	0.256956	−	0.0107968i
$157$	−2.01956	+	2.01956i	−0.161178	+	0.161178i	−0.783089	−	0.621910i	$-0.786357\pi$
$157$	−2.01956	+	2.01956i	−0.161178	+	0.161178i	0.621910	+	0.783089i	$0.286357\pi$
$158$	−2.30732	+	2.30732i	−0.183561	+	0.183561i
$159$	16.1289	−	0.677705i	1.27910	−	0.0537455i
$160$	−2.21908	+	0.275081i	−0.175434	+	0.0217471i
$161$			5.42542i			0.427583i
$162$	7.33835	+	5.21044i	0.576555	+	0.409370i
$163$	−10.4716	−	10.4716i	−0.820199	−	0.820199i	0.165937	−	0.986136i	$-0.446935\pi$
$163$	−10.4716	−	10.4716i	−0.820199	−	0.820199i	−0.986136	+	0.165937i	$0.946935\pi$
$164$	−9.92875			−0.775305
$165$	−1.58706	−	9.51195i	−0.123552	−	0.740504i
$166$	2.01448			0.156354
$167$	−4.80821	−	4.80821i	−0.372071	−	0.372071i	0.496160	−	0.868231i	$-0.334743\pi$
$167$	−4.80821	−	4.80821i	−0.372071	−	0.372071i	−0.868231	+	0.496160i	$0.834743\pi$
$168$	−1.17225	+	1.27508i	−0.0904410	+	0.0983747i
$169$		−	9.56056i		−	0.735427i
$170$	5.36738	+	4.18344i	0.411659	+	0.320855i
$171$	−3.77258	+	0.317594i	−0.288497	+	0.0242870i
$172$	7.18740	−	7.18740i	0.548034	−	0.548034i
$173$	−9.17963	+	9.17963i	−0.697915	+	0.697915i	−0.963960	−	0.266046i	$-0.914283\pi$
$173$	−9.17963	+	9.17963i	−0.697915	+	0.697915i	0.266046	+	0.963960i	$0.414283\pi$
$174$	−0.195526	−	4.65337i	−0.0148228	−	0.352771i
$175$	4.29180	+	2.56525i	0.324429	+	0.193914i
$176$		−	2.48992i		−	0.187685i
$177$	−2.12666	−	1.95515i	−0.159850	−	0.146958i
$178$	−8.25075	−	8.25075i	−0.618420	−	0.618420i
$179$	−10.4187			−0.778728			−0.389364	−	0.921084i	$-0.627305\pi$
$179$	−10.4187			−0.778728			−0.389364	+	0.921084i	$0.627305\pi$
$180$	3.66547	−	5.61821i	0.273208	−	0.418757i
$181$	3.47436			0.258247			0.129124	−	0.991629i	$-0.458784\pi$
$181$	3.47436			0.258247			0.129124	+	0.991629i	$0.458784\pi$
$182$	−1.31138	−	1.31138i	−0.0972061	−	0.0972061i
$183$	−2.17466	−	1.99928i	−0.160756	−	0.147791i
$184$		−	5.42542i		−	0.399968i
$185$	1.45145	+	11.7089i	0.106713	+	0.860854i
$186$	−0.734478	−	17.4800i	−0.0538545	−	1.28170i
$187$	−5.35826	+	5.35826i	−0.391834	+	0.391834i
$188$	9.47825	−	9.47825i	0.691273	−	0.691273i
$189$	−0.652882	−	5.15497i	−0.0474902	−	0.374969i
$190$	0.347146	+	2.80043i	0.0251846	+	0.203165i
$191$		−	9.02930i		−	0.653337i	−0.945139	−	0.326668i	$-0.894074\pi$
$191$		−	9.02930i		−	0.653337i	0.945139	−	0.326668i	$-0.105926\pi$
$192$	1.17225	−	1.27508i	0.0845998	−	0.0920211i
$193$	4.88918	+	4.88918i	0.351931	+	0.351931i	0.860828	−	0.508897i	$-0.169946\pi$
$193$	4.88918	+	4.88918i	0.351931	+	0.351931i	−0.508897	+	0.860828i	$0.669946\pi$
$194$	1.39149			0.0999029
$195$	5.84557	+	4.17384i	0.418610	+	0.298895i
$196$	1.00000			0.0714286
$197$	9.74560	+	9.74560i	0.694345	+	0.694345i	0.963185	−	0.268840i	$-0.0866402\pi$
$197$	9.74560	+	9.74560i	0.694345	+	0.694345i	−0.268840	+	0.963185i	$0.586640\pi$
$198$	5.70640	+	4.82022i	0.405536	+	0.342558i
$199$		−	6.73634i		−	0.477526i	−0.971078	−	0.238763i	$-0.923258\pi$
$199$		−	6.73634i		−	0.477526i	0.971078	−	0.238763i	$-0.0767419\pi$
$200$	−4.29180	−	2.56525i	−0.303476	−	0.181390i
$201$	−11.2176	+	0.471341i	−0.791226	+	0.0332458i
$202$	1.81578	−	1.81578i	0.127758	−	0.127758i
$203$	−1.90141	+	1.90141i	−0.133453	+	0.133453i
$204$	−5.26659	+	0.221292i	−0.368735	+	0.0154935i
$205$	−17.5107	−	13.6482i	−1.22300	−	0.953234i
$206$		−	14.9313i		−	1.04032i
$207$	12.4340	+	10.5030i	0.864220	+	0.730010i
$208$	1.31138	+	1.31138i	0.0909279	+	0.0909279i
$209$	−3.14223			−0.217352
$210$	−3.82017	+	0.637391i	−0.263617	+	0.0439842i
$211$	24.0503			1.65569			0.827846	−	0.560956i	$-0.189566\pi$
$211$	24.0503			1.65569			0.827846	+	0.560956i	$0.189566\pi$
$212$	6.59040	+	6.59040i	0.452631	+	0.452631i
$213$	3.06876	−	3.33796i	0.210268	−	0.228713i
$214$			9.77347i			0.668100i
$215$	22.5559	−	2.79607i	1.53830	−	0.190690i
$216$	0.652882	+	5.15497i	0.0444230	+	0.350751i
$217$	−7.14250	+	7.14250i	−0.484864	+	0.484864i
$218$	6.48500	−	6.48500i	0.439220	−	0.439220i
$219$	0.873683	+	20.7930i	0.0590380	+	1.40506i
$220$	3.42269	−	4.39133i	0.230758	−	0.296064i
$221$		−	5.64412i		−	0.379665i
$222$	−6.72790	−	6.18532i	−0.451547	−	0.415131i
$223$	−15.0658	−	15.0658i	−1.00888	−	1.00888i	−0.999960	−	0.00891851i	$-0.997161\pi$
$223$	−15.0658	−	15.0658i	−1.00888	−	1.00888i	−0.00891851	−	0.999960i	$-0.502839\pi$
$224$	−1.00000			−0.0668153
$225$	14.1875	−	4.86989i	0.945831	−	0.324660i
$226$	−17.7467			−1.18049
$227$	18.5051	+	18.5051i	1.22822	+	1.22822i	0.964635	+	0.263589i	$0.0849062\pi$
$227$	18.5051	+	18.5051i	1.22822	+	1.22822i	0.263589	+	0.964635i	$0.415094\pi$
$228$	−1.60912	−	1.47935i	−0.106567	−	0.0979724i
$229$		−	8.01695i		−	0.529775i	−0.964279	−	0.264887i	$-0.914665\pi$
$229$		−	8.01695i		−	0.529775i	0.964279	−	0.264887i	$-0.0853348\pi$
$230$	7.45788	−	9.56850i	0.491758	−	0.630928i
$231$	−0.181051	−	4.30887i	−0.0119123	−	0.283503i
$232$	1.90141	−	1.90141i	0.124834	−	0.124834i
$233$	−14.9849	+	14.9849i	−0.981691	+	0.981691i	−0.999835	−	0.0181442i	$-0.994224\pi$
$233$	−14.9849	+	14.9849i	−0.981691	+	0.981691i	0.0181442	+	0.999835i	$0.494224\pi$
$234$	−5.54411	+	0.466730i	−0.362430	+	0.0305111i
$235$	29.7452	−	3.68726i	1.94036	−	0.240531i
$236$		−	1.66786i		−	0.108569i
$237$	3.82510	−	4.16065i	0.248467	−	0.270263i
$238$	2.15197	+	2.15197i	0.139492	+	0.139492i
$239$	−16.0367			−1.03733			−0.518664	−	0.854978i	$-0.673570\pi$
$239$	−16.0367			−1.03733			−0.518664	+	0.854978i	$0.673570\pi$
$240$	3.82017	−	0.637391i	0.246591	−	0.0411434i
$241$	−16.0247			−1.03224			−0.516121	−	0.856516i	$-0.672624\pi$
$241$	−16.0247			−1.03224			−0.516121	+	0.856516i	$0.672624\pi$
$242$	−3.39431	−	3.39431i	−0.218194	−	0.218194i
$243$	−13.0781	−	8.48319i	−0.838958	−	0.544197i
$244$		−	1.70551i		−	0.109184i
$245$	1.76364	+	1.37462i	0.112675	+	0.0878211i
$246$	17.1819	−	0.721952i	1.09548	−	0.0460300i
$247$	1.65493	−	1.65493i	0.105301	−	0.105301i
$248$	7.14250	−	7.14250i	0.453549	−	0.453549i
$249$	−3.48610	+	0.146479i	−0.220922	+	0.00928274i
$250$	−4.04296	−	10.4237i	−0.255699	−	0.659256i
$251$			23.4966i			1.48309i	0.670903	+	0.741545i	$0.265907\pi$
$251$			23.4966i			1.48309i	−0.670903	+	0.741545i	$0.734093\pi$
$252$	1.93589	−	2.29180i	0.121950	−	0.144370i
$253$	9.55223	+	9.55223i	0.600544	+	0.600544i
$254$	11.5095			0.722168
$255$	−9.59257	−	6.84927i	−0.600710	−	0.428918i
$256$	1.00000			0.0625000
$257$	−14.3897	−	14.3897i	−0.897604	−	0.897604i	0.0976195	−	0.995224i	$-0.468877\pi$
$257$	−14.3897	−	14.3897i	−0.897604	−	0.897604i	−0.995224	+	0.0976195i	$0.968877\pi$
$258$	−11.9153	+	12.9606i	−0.741817	+	0.806891i
$259$			5.27645i			0.327863i
$260$	0.510158	+	4.11545i	0.0316387	+	0.255230i
$261$	0.676724	+	8.03855i	0.0418882	+	0.497574i
$262$	−6.49197	+	6.49197i	−0.401075	+	0.401075i
$263$	10.1237	−	10.1237i	0.624257	−	0.624257i	−0.322360	−	0.946617i	$-0.604476\pi$
$263$	10.1237	−	10.1237i	0.624257	−	0.624257i	0.946617	+	0.322360i	$0.104476\pi$
$264$	0.181051	+	4.30887i	0.0111429	+	0.265193i
$265$	2.56382	+	20.6824i	0.157494	+	1.27051i
$266$			1.26198i			0.0773767i
$267$	14.8781	+	13.6782i	0.910522	+	0.837091i
$268$	−4.58359	−	4.58359i	−0.279988	−	0.279988i
$269$	−26.0829			−1.59030			−0.795151	−	0.606412i	$-0.792608\pi$
$269$	−26.0829			−1.59030			−0.795151	+	0.606412i	$0.792608\pi$
$270$	−5.93466	+	9.98898i	−0.361172	+	0.607910i
$271$	−3.44082			−0.209015			−0.104508	−	0.994524i	$-0.533327\pi$
$271$	−3.44082			−0.209015			−0.104508	+	0.994524i	$0.533327\pi$
$272$	−2.15197	−	2.15197i	−0.130483	−	0.130483i
$273$	2.36473	+	2.17402i	0.143120	+	0.131578i
$274$		−	14.5966i		−	0.881813i
$275$	12.0728	−	3.03984i	0.728017	−	0.183309i
$276$	0.394500	+	9.38883i	0.0237461	+	0.565141i
$277$	4.51869	−	4.51869i	0.271502	−	0.271502i	−0.558203	−	0.829705i	$-0.688509\pi$
$277$	4.51869	−	4.51869i	0.271502	−	0.271502i	0.829705	+	0.558203i	$0.188509\pi$
$278$	−4.54126	+	4.54126i	−0.272367	+	0.272367i
$279$	2.54206	+	30.1962i	0.152189	+	1.80780i
$280$	−1.76364	−	1.37462i	−0.105398	−	0.0821491i
$281$		−	19.0774i		−	1.13806i	−0.822316	−	0.569031i	$-0.807319\pi$
$281$		−	19.0774i		−	1.13806i	0.822316	−	0.569031i	$-0.192681\pi$
$282$	−15.7131	+	17.0915i	−0.935704	+	1.01779i
$283$	−10.8604	−	10.8604i	−0.645583	−	0.645583i	0.306340	−	0.951922i	$-0.400896\pi$
$283$	−10.8604	−	10.8604i	−0.645583	−	0.645583i	−0.951922	+	0.306340i	$0.900896\pi$
$284$	2.61784			0.155340
$285$	−0.804373	−	4.82097i	−0.0476469	−	0.285570i
$286$	−4.61775			−0.273053
$287$	−7.02069	−	7.02069i	−0.414418	−	0.414418i
$288$	−1.93589	+	2.29180i	−0.114073	+	0.135045i
$289$		−	7.73801i		−	0.455177i
$290$	5.96711	−	0.739692i	0.350401	−	0.0434362i
$291$	−2.40800	+	0.101180i	−0.141160	+	0.00593125i
$292$	−8.49621	+	8.49621i	−0.497203	+	0.497203i
$293$	−6.91427	+	6.91427i	−0.403936	+	0.403936i	−0.879617	−	0.475682i	$-0.842201\pi$
$293$	−6.91427	+	6.91427i	−0.403936	+	0.403936i	0.475682	+	0.879617i	$0.342201\pi$
$294$	−1.73052	+	0.0727133i	−0.100926	+	0.00424072i
$295$	2.29268	−	2.94151i	0.133485	−	0.171262i
$296$		−	5.27645i		−	0.306687i
$297$	−10.2256	−	7.92657i	−0.593347	−	0.459946i
$298$	12.6980	+	12.6980i	0.735576	+	0.735576i
$299$	−10.0618			−0.581892
$300$	7.61358	+	4.12715i	0.439570	+	0.238281i
$301$	10.1645			0.585873
$302$	4.41877	+	4.41877i	0.254271	+	0.254271i
$303$	−3.01022	+	3.27428i	−0.172933	+	0.188103i
$304$		−	1.26198i		−	0.0723793i
$305$	2.34442	−	3.00791i	0.134241	−	0.172232i
$306$	9.09787	−	0.765903i	0.520091	−	0.0437837i
$307$	6.57653	−	6.57653i	0.375343	−	0.375343i	−0.494076	−	0.869419i	$-0.664494\pi$
$307$	6.57653	−	6.57653i	0.375343	−	0.375343i	0.869419	+	0.494076i	$0.164494\pi$
$308$	1.76064	−	1.76064i	0.100322	−	0.100322i
$309$	1.08571	+	25.8390i	0.0617637	+	1.46993i
$310$	22.4150	−	2.77860i	1.27309	−	0.157814i
$311$		−	31.7244i		−	1.79893i	−0.436996	−	0.899464i	$-0.643958\pi$
$311$		−	31.7244i		−	1.79893i	0.436996	−	0.899464i	$-0.356042\pi$
$312$	−2.36473	−	2.17402i	−0.133877	−	0.123080i
$313$	7.97460	+	7.97460i	0.450751	+	0.450751i	0.895604	−	0.444853i	$-0.146744\pi$
$313$	7.97460	+	7.97460i	0.450751	+	0.450751i	−0.444853	+	0.895604i	$0.646744\pi$
$314$	2.85609			0.161178
$315$	6.56456	−	1.38080i	0.369871	−	0.0777992i
$316$	3.26305			0.183561
$317$	−7.61016	−	7.61016i	−0.427429	−	0.427429i	0.460323	−	0.887752i	$-0.347734\pi$
$317$	−7.61016	−	7.61016i	−0.427429	−	0.427429i	−0.887752	+	0.460323i	$0.847734\pi$
$318$	−11.8841	−	10.9256i	−0.666425	−	0.612680i
$319$			6.69540i			0.374870i
$320$	1.76364	+	1.37462i	0.0985905	+	0.0768434i
$321$	−0.710661	−	16.9132i	−0.0396652	−	0.944004i
$322$	3.83635	−	3.83635i	0.213792	−	0.213792i
$323$	−2.71574	+	2.71574i	−0.151108	+	0.151108i
$324$	−1.50466	−	8.87333i	−0.0835924	−	0.492963i
$325$	−4.75744	+	7.95945i	−0.263895	+	0.441511i
$326$			14.8091i			0.820199i
$327$	−10.7509	+	11.6940i	−0.594526	+	0.646679i
$328$	7.02069	+	7.02069i	0.387653	+	0.387653i
$329$	13.4043			0.739002
$330$	−5.60374	+	7.84818i	−0.308476	+	0.432028i
$331$	−4.84463			−0.266285			−0.133142	−	0.991097i	$-0.542507\pi$
$331$	−4.84463			−0.266285			−0.133142	+	0.991097i	$0.542507\pi$
$332$	−1.42445	−	1.42445i	−0.0781768	−	0.0781768i
$333$	12.0926	+	10.2146i	0.662668	+	0.559758i
$334$			6.79984i			0.372071i
$335$	−1.78313	−	14.3845i	−0.0974226	−	0.785909i
$336$	1.73052	−	0.0727133i	0.0944078	−	0.00396683i
$337$	16.7280	−	16.7280i	0.911234	−	0.911234i	−0.0851350	−	0.996369i	$-0.527132\pi$
$337$	16.7280	−	16.7280i	0.911234	−	0.911234i	0.996369	+	0.0851350i	$0.0271321\pi$
$338$	−6.76033	+	6.76033i	−0.367714	+	0.367714i
$339$	30.7110	−	1.29042i	1.66799	−	0.0700859i
$340$	−0.837169	−	6.75345i	−0.0454019	−	0.366257i
$341$			25.1508i			1.36199i
$342$	2.89219	+	2.44305i	0.156392	+	0.132105i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−10.1645			−0.548034
$345$	−12.2103	+	17.1008i	−0.657379	+	0.920676i
$346$	12.9820			0.697915
$347$	−12.6747	−	12.6747i	−0.680411	−	0.680411i	0.279682	−	0.960093i	$-0.409771\pi$
$347$	−12.6747	−	12.6747i	−0.680411	−	0.680411i	−0.960093	+	0.279682i	$0.909771\pi$
$348$	−3.15217	+	3.42869i	−0.168974	+	0.183797i
$349$			3.51880i			0.188357i	0.995555	+	0.0941786i	$0.0300225\pi$
$349$			3.51880i			0.188357i	−0.995555	+	0.0941786i	$0.969978\pi$
$350$	−1.22086	−	4.84866i	−0.0652575	−	0.259172i
$351$	9.56028	−	1.21082i	0.510290	−	0.0646286i
$352$	−1.76064	+	1.76064i	−0.0938426	+	0.0938426i
$353$	−15.9979	+	15.9979i	−0.851482	+	0.851482i	−0.990316	−	0.138834i	$-0.955665\pi$
$353$	−15.9979	+	15.9979i	−0.851482	+	0.851482i	0.138834	+	0.990316i	$0.455665\pi$
$354$	0.121276	+	2.88628i	0.00644574	+	0.153404i
$355$	4.61693	+	3.59853i	0.245041	+	0.190990i
$356$			11.6683i			0.618420i
$357$	−3.88052	−	3.56757i	−0.205379	−	0.188816i
$358$	7.36712	+	7.36712i	0.389364	+	0.389364i
$359$	32.9263			1.73778			0.868891	−	0.495004i	$-0.164833\pi$
$359$	32.9263			1.73778			0.868891	+	0.495004i	$0.164833\pi$
$360$	−6.56456	+	1.38080i	−0.345982	+	0.0727745i
$361$	17.4074			0.916180
$362$	−2.45674	−	2.45674i	−0.129124	−	0.129124i
$363$	6.12074	+	5.62712i	0.321256	+	0.295347i
$364$			1.85457i			0.0972061i
$365$	−26.6633	+	3.30523i	−1.39562	+	0.173003i
$366$	0.124013	+	2.95143i	0.00648228	+	0.154274i
$367$	−11.4381	+	11.4381i	−0.597062	+	0.597062i	−0.939530	−	0.342467i	$-0.888737\pi$
$367$	−11.4381	+	11.4381i	−0.597062	+	0.597062i	0.342467	+	0.939530i	$0.388737\pi$
$368$	−3.83635	+	3.83635i	−0.199984	+	0.199984i
$369$	−29.6813	+	2.49871i	−1.54514	+	0.130078i
$370$	7.25310	−	9.30576i	0.377071	−	0.483784i
$371$			9.32024i			0.483883i
$372$	−11.8409	+	12.8796i	−0.613922	+	0.667777i
$373$	−19.1458	−	19.1458i	−0.991330	−	0.991330i	0.00863259	−	0.999963i	$-0.497252\pi$
$373$	−19.1458	−	19.1458i	−0.991330	−	0.991330i	−0.999963	+	0.00863259i	$0.997252\pi$
$374$	7.57772			0.391834
$375$	7.75438	+	17.7446i	0.400434	+	0.916325i
$376$	−13.4043			−0.691273
$377$	−3.52630	−	3.52630i	−0.181614	−	0.181614i
$378$	−3.18346	+	4.10677i	−0.163739	+	0.211230i
$379$			9.89995i			0.508526i	0.967135	+	0.254263i	$0.0818329\pi$
$379$			9.89995i			0.508526i	−0.967135	+	0.254263i	$0.918167\pi$
$380$	1.73473	−	2.22567i	0.0889900	−	0.114175i
$381$	−19.9174	+	0.836891i	−1.02040	+	0.0428752i
$382$	−6.38468	+	6.38468i	−0.326668	+	0.326668i
$383$	3.91121	−	3.91121i	0.199853	−	0.199853i	−0.600084	−	0.799937i	$-0.704866\pi$
$383$	3.91121	−	3.91121i	0.199853	−	0.199853i	0.799937	+	0.600084i	$0.204866\pi$
$384$	−1.73052	+	0.0727133i	−0.0883104	+	0.00371063i
$385$	5.52535	−	0.684931i	0.281598	−	0.0349073i
$386$		−	6.91435i		−	0.351931i
$387$	19.6774	−	23.2950i	1.00026	−	1.18415i
$388$	−0.983930	−	0.983930i	−0.0499515	−	0.0499515i
$389$	18.4682			0.936373			0.468186	−	0.883630i	$-0.344908\pi$
$389$	18.4682			0.936373			0.468186	+	0.883630i	$0.344908\pi$
$390$	−1.18209	−	7.08479i	−0.0598574	−	0.358752i
$391$	16.5115			0.835021
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$	10.7625	−	11.7066i	0.542894	−	0.590518i
$394$		−	13.7824i		−	0.694345i
$395$	5.75484	+	4.48544i	0.289558	+	0.225687i
$396$	−0.626625	−	7.44344i	−0.0314891	−	0.374047i
$397$	15.6934	−	15.6934i	0.787628	−	0.787628i	−0.193477	−	0.981105i	$-0.561977\pi$
$397$	15.6934	−	15.6934i	0.787628	−	0.787628i	0.981105	+	0.193477i	$0.0619765\pi$
$398$	−4.76331	+	4.76331i	−0.238763	+	0.238763i
$399$	−0.0917624	−	2.18388i	−0.00459387	−	0.109331i
$400$	1.22086	+	4.84866i	0.0610428	+	0.242433i
$401$		−	3.34286i		−	0.166934i	−0.996511	−	0.0834672i	$-0.973401\pi$
$401$		−	3.34286i		−	0.166934i	0.996511	−	0.0834672i	$-0.0265994\pi$
$402$	8.26531	+	7.59873i	0.412236	+	0.378990i
$403$	−13.2463	−	13.2463i	−0.659844	−	0.659844i
$404$	−2.56790			−0.127758
$405$	9.54375	−	17.7177i	0.474233	−	0.880400i
$406$	2.68900			0.133453
$407$	9.28995	+	9.28995i	0.460485	+	0.460485i
$408$	3.88052	+	3.56757i	0.192114	+	0.176621i
$409$		−	15.4069i		−	0.761824i	−0.924611	−	0.380912i	$-0.875610\pi$
$409$		−	15.4069i		−	0.761824i	0.924611	−	0.380912i	$-0.124390\pi$
$410$	2.73121	+	22.0327i	0.134885	+	1.08812i
$411$	1.06137	+	25.2598i	0.0523534	+	1.24597i
$412$	−10.5580	+	10.5580i	−0.520158	+	0.520158i
$413$	1.17936	−	1.17936i	0.0580324	−	0.0580324i
$414$	−1.36538	−	16.2189i	−0.0671050	−	0.797115i
$415$	−0.554144	−	4.47029i	−0.0272019	−	0.219438i
$416$		−	1.85457i		−	0.0909279i
$417$	7.52855	−	8.18897i	0.368675	−	0.401016i
$418$	2.22189	+	2.22189i	0.108676	+	0.108676i
$419$	12.4526			0.608350			0.304175	−	0.952616i	$-0.401619\pi$
$419$	12.4526			0.608350			0.304175	+	0.952616i	$0.401619\pi$
$420$	3.15197	+	2.25057i	0.153801	+	0.109816i
$421$	−24.7648			−1.20696			−0.603482	−	0.797377i	$-0.706220\pi$
$421$	−24.7648			−1.20696			−0.603482	+	0.797377i	$0.706220\pi$
$422$	−17.0061	−	17.0061i	−0.827846	−	0.827846i
$423$	25.9492	−	30.7199i	1.26169	−	1.49365i
$424$		−	9.32024i		−	0.452631i
$425$	7.80694	−	13.0614i	0.378692	−	0.633573i
$426$	−4.53023	+	0.190352i	−0.219490	+	0.00922257i
$427$	1.20598	−	1.20598i	0.0583614	−	0.0583614i
$428$	6.91089	−	6.91089i	0.334050	−	0.334050i
$429$	7.99112	−	0.335772i	0.385815	−	0.0162112i
$430$	−17.9266	−	13.9723i	−0.864495	−	0.673805i
$431$		−	3.97434i		−	0.191437i	−0.995408	−	0.0957185i	$-0.969485\pi$
$431$		−	3.97434i		−	0.191437i	0.995408	−	0.0957185i	$-0.0305149\pi$
$432$	3.18346	−	4.10677i	0.153164	−	0.197587i
$433$	−4.89906	−	4.89906i	−0.235434	−	0.235434i	0.579522	−	0.814956i	$-0.303239\pi$
$433$	−4.89906	−	4.89906i	−0.235434	−	0.235434i	−0.814956	+	0.579522i	$0.803239\pi$
$434$	10.1010			0.484864
$435$	−10.2724	+	1.71394i	−0.492526	+	0.0821773i
$436$	−9.17118			−0.439220
$437$	4.84139	+	4.84139i	0.231595	+	0.231595i
$438$	14.0851	−	15.3207i	0.673012	−	0.732051i
$439$		−	31.2830i		−	1.49306i	−0.665353	−	0.746528i	$-0.731719\pi$
$439$		−	31.2830i		−	1.49306i	0.665353	−	0.746528i	$-0.268281\pi$
$440$	−5.52535	+	0.684931i	−0.263411	+	0.0326528i
$441$	2.98943	−	0.251664i	0.142354	−	0.0119840i
$442$	−3.99100	+	3.99100i	−0.189832	+	0.189832i
$443$	11.5755	−	11.5755i	0.549971	−	0.549971i	−0.376462	−	0.926432i	$-0.622859\pi$
$443$	11.5755	−	11.5755i	0.549971	−	0.549971i	0.926432	+	0.376462i	$0.122859\pi$
$444$	0.383668	+	9.13102i	0.0182081	+	0.433339i
$445$	−16.0395	+	20.5787i	−0.760344	+	0.975525i
$446$			21.3062i			1.00888i
$447$	−22.8975	−	21.0509i	−1.08302	−	0.995673i
$448$	0.707107	+	0.707107i	0.0334077	+	0.0334077i
$449$	−0.439882			−0.0207593			−0.0103796	−	0.999946i	$-0.503304\pi$
$449$	−0.439882			−0.0207593			−0.0103796	+	0.999946i	$0.503304\pi$
$450$	−13.4756	−	6.58852i	−0.635245	−	0.310586i
$451$	−24.7218			−1.16411
$452$	12.5488	+	12.5488i	0.590245	+	0.590245i
$453$	−7.96808	−	7.32548i	−0.374373	−	0.344181i
$454$		−	26.1701i		−	1.22822i
$455$	−2.54933	+	3.27080i	−0.119514	+	0.153338i
$456$	0.0917624	+	2.18388i	0.00429717	+	0.102270i
$457$	−2.59356	+	2.59356i	−0.121322	+	0.121322i	−0.765161	−	0.643839i	$-0.777341\pi$
$457$	−2.59356	+	2.59356i	−0.121322	+	0.121322i	0.643839	+	0.765161i	$0.277341\pi$
$458$	−5.66884	+	5.66884i	−0.264887	+	0.264887i
$459$	−15.6884	+	1.98695i	−0.732272	+	0.0927428i
$460$	−12.0395	+	1.49243i	−0.561343	+	0.0695850i
$461$			11.2097i			0.522086i	0.965327	+	0.261043i	$0.0840664\pi$
$461$			11.2097i			0.522086i	−0.965327	+	0.261043i	$0.915934\pi$
$462$	−2.91881	+	3.17486i	−0.135795	+	0.147708i
$463$	−1.38982	−	1.38982i	−0.0645903	−	0.0645903i	0.674074	−	0.738664i	$-0.264543\pi$
$463$	−1.38982	−	1.38982i	−0.0645903	−	0.0645903i	−0.738664	+	0.674074i	$0.764543\pi$
$464$	−2.68900			−0.124834
$465$	−38.5876	+	6.43830i	−1.78946	+	0.298569i
$466$	21.1918			0.981691
$467$	3.70297	+	3.70297i	0.171353	+	0.171353i	0.787574	−	0.616221i	$-0.211337\pi$
$467$	3.70297	+	3.70297i	0.171353	+	0.171353i	−0.616221	+	0.787574i	$0.711337\pi$
$468$	4.25030	+	3.59025i	0.196470	+	0.165959i
$469$		−	6.48218i		−	0.299319i
$470$	−23.6403	−	18.4257i	−1.09045	−	0.849916i
$471$	−4.94253	+	0.207675i	−0.227740	+	0.00956918i
$472$	−1.17936	+	1.17936i	−0.0542844	+	0.0542844i
$473$	17.8961	−	17.8961i	0.822863	−	0.822863i
$474$	−5.64678	+	0.237267i	−0.259365	+	0.0108980i
$475$	6.11889	−	1.54069i	0.280754	−	0.0706918i
$476$		−	3.04335i		−	0.139492i
$477$	21.3601	+	18.0430i	0.978011	+	0.826130i
$478$	11.3397	+	11.3397i	0.518664	+	0.518664i
$479$	−6.21338			−0.283897			−0.141948	−	0.989874i	$-0.545337\pi$
$479$	−6.21338			−0.283897			−0.141948	+	0.989874i	$0.545337\pi$
$480$	−3.15197	−	2.25057i	−0.143867	−	0.102724i
$481$	−9.78557			−0.446183
$482$	11.3312	+	11.3312i	0.516121	+	0.516121i
$483$	−6.35995	+	6.91786i	−0.289388	+	0.314773i
$484$			4.80027i			0.218194i
$485$	−0.382772	−	3.08782i	−0.0173808	−	0.140211i
$486$	3.24906	+	15.2461i	0.147380	+	0.691577i
$487$	−8.76055	+	8.76055i	−0.396979	+	0.396979i	−0.877166	−	0.480187i	$-0.840569\pi$
$487$	−8.76055	+	8.76055i	−0.396979	+	0.396979i	0.480187	+	0.877166i	$0.340569\pi$
$488$	−1.20598	+	1.20598i	−0.0545921	+	0.0545921i
$489$	−1.07682	−	25.6275i	−0.0486953	−	1.15891i
$490$	−0.275081	−	2.21908i	−0.0124269	−	0.100248i
$491$			15.4882i			0.698972i	0.936942	+	0.349486i	$0.113644\pi$
$491$			15.4882i			0.698972i	−0.936942	+	0.349486i	$0.886356\pi$
$492$	−12.6600	−	11.6390i	−0.570755	−	0.524725i
$493$	5.78665	+	5.78665i	0.260618	+	0.260618i
$494$	−2.34043			−0.105301
$495$	9.12674	−	13.9889i	0.410217	−	0.628756i
$496$	−10.1010			−0.453549
$497$	1.85109	+	1.85109i	0.0830328	+	0.0830328i
$498$	2.56862	+	2.36147i	0.115103	+	0.105820i
$499$			33.2574i			1.48880i	0.667732	+	0.744402i	$0.267265\pi$
$499$			33.2574i			1.48880i	−0.667732	+	0.744402i	$0.732735\pi$
$500$	−4.51190	+	10.2295i	−0.201778	+	0.457477i
$501$	−0.494439	−	11.7673i	−0.0220899	−	0.525724i
$502$	16.6146	−	16.6146i	0.741545	−	0.741545i
$503$	−14.7389	+	14.7389i	−0.657174	+	0.657174i	−0.954710	−	0.297536i	$-0.903835\pi$
$503$	−14.7389	+	14.7389i	−0.657174	+	0.657174i	0.297536	+	0.954710i	$0.403835\pi$
$504$	−2.98943	+	0.251664i	−0.133160	+	0.0112100i
$505$	−4.52886	−	3.52988i	−0.201532	−	0.157078i
$506$		−	13.5089i		−	0.600544i
$507$	11.2074	−	12.1905i	0.497736	−	0.541399i
$508$	−8.13842	−	8.13842i	−0.361084	−	0.361084i
$509$	2.69010			0.119236			0.0596182	−	0.998221i	$-0.481012\pi$
$509$	2.69010			0.119236			0.0596182	+	0.998221i	$0.481012\pi$
$510$	1.93981	+	11.6261i	0.0858961	+	0.514814i
$511$	−12.0155			−0.531532
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−5.18265	−	4.01745i	−0.228820	−	0.177375i
$514$			20.3501i			0.897604i
$515$	−33.1339	+	4.10733i	−1.46005	+	0.180991i
$516$	17.5899	−	0.739096i	0.774354	−	0.0325369i
$517$	23.6001	−	23.6001i	1.03793	−	1.03793i
$518$	3.73101	−	3.73101i	0.163931	−	0.163931i
$519$	−22.4656	+	0.943961i	−0.986130	+	0.0414353i
$520$	2.54933	−	3.27080i	0.111795	−	0.143434i
$521$		−	7.42366i		−	0.325237i	−0.986689	−	0.162618i	$-0.948006\pi$
$521$		−	7.42366i		−	0.325237i	0.986689	−	0.162618i	$-0.0519939\pi$
$522$	5.20560	−	6.16263i	0.227843	−	0.269731i
$523$	12.4973	+	12.4973i	0.546470	+	0.546470i	0.925418	−	0.378948i	$-0.123714\pi$
$523$	12.4973	+	12.4973i	0.546470	+	0.546470i	−0.378948	+	0.925418i	$0.623714\pi$
$524$	9.18103			0.401075
$525$	2.46528	+	8.30195i	0.107594	+	0.362327i
$526$	−14.3171			−0.624257
$527$	21.7371	+	21.7371i	0.946884	+	0.946884i
$528$	2.91881	−	3.17486i	0.127025	−	0.138168i
$529$		−	6.43522i		−	0.279792i
$530$	12.8118	−	16.4376i	0.556507	−	0.714002i
$531$	−0.419742	−	4.98596i	−0.0182152	−	0.216372i
$532$	0.892352	−	0.892352i	0.0386884	−	0.0386884i
$533$	13.0204	−	13.0204i	0.563975	−	0.563975i
$534$	−0.848442	−	20.1923i	−0.0367157	−	0.873807i
$535$	21.6881	−	2.68850i	0.937660	−	0.116234i
$536$			6.48218i			0.279988i
$537$	−13.2847	−	12.2133i	−0.573275	−	0.527042i
$538$	18.4434	+	18.4434i	0.795151	+	0.795151i
$539$	2.48992			0.107249
$540$	11.2597	−	2.86684i	0.484541	−	0.123369i
$541$	26.2804			1.12988			0.564941	−	0.825131i	$-0.308899\pi$
$541$	26.2804			1.12988			0.564941	+	0.825131i	$0.308899\pi$
$542$	2.43303	+	2.43303i	0.104508	+	0.104508i
$543$	4.43009	+	4.07282i	0.190113	+	0.174781i
$544$			3.04335i			0.130483i
$545$	−16.1747	−	12.6069i	−0.692846	−	0.540018i
$546$	−0.134852	−	3.20938i	−0.00577114	−	0.137349i
$547$	−9.03049	+	9.03049i	−0.386116	+	0.386116i	−0.873299	−	0.487184i	$-0.838024\pi$
$547$	−9.03049	+	9.03049i	−0.386116	+	0.386116i	0.487184	+	0.873299i	$0.338024\pi$
$548$	−10.3214	+	10.3214i	−0.440906	+	0.440906i
$549$	−0.429216	−	5.09850i	−0.0183185	−	0.217599i
$550$	−10.6863	−	6.38727i	−0.455663	−	0.272354i
$551$			3.39345i			0.144566i
$552$	6.35995	−	6.91786i	0.270697	−	0.294443i
$553$	2.30732	+	2.30732i	0.0981174	+	0.0981174i
$554$	−6.39040			−0.271502
$555$	−11.8750	+	16.6312i	−0.504066	+	0.705957i
$556$	6.42231			0.272367
$557$	−22.4290	−	22.4290i	−0.950345	−	0.950345i	0.0484790	−	0.998824i	$-0.484563\pi$
$557$	−22.4290	−	22.4290i	−0.950345	−	0.950345i	−0.998824	+	0.0484790i	$0.984563\pi$
$558$	19.5545	−	23.1495i	0.827806	−	0.979995i
$559$			18.8508i			0.797306i
$560$	0.275081	+	2.21908i	0.0116243	+	0.0937734i
$561$	−13.1134	+	0.551001i	−0.553649	+	0.0232633i
$562$	−13.4897	+	13.4897i	−0.569031	+	0.569031i
$563$	4.13454	−	4.13454i	0.174250	−	0.174250i	−0.614594	−	0.788844i	$-0.710680\pi$
$563$	4.13454	−	4.13454i	0.174250	−	0.174250i	0.788844	+	0.614594i	$0.210680\pi$
$564$	23.1964	−	0.974669i	0.976745	−	0.0410410i
$565$	4.88177	+	39.3813i	0.205378	+	1.65678i
$566$			15.3589i			0.645583i
$567$	5.21044	−	7.33835i	0.218818	−	0.308182i
$568$	−1.85109	−	1.85109i	−0.0776701	−	0.0776701i
$569$	18.9758			0.795507			0.397754	−	0.917492i	$-0.369790\pi$
$569$	18.9758			0.795507			0.397754	+	0.917492i	$0.369790\pi$
$570$	−2.84016	+	3.97772i	−0.118961	+	0.166608i
$571$	−23.1460			−0.968629			−0.484315	−	0.874894i	$-0.660931\pi$
$571$	−23.1460			−0.968629			−0.484315	+	0.874894i	$0.660931\pi$
$572$	3.26524	+	3.26524i	0.136527	+	0.136527i
$573$	10.5846	−	11.5131i	0.442177	−	0.480966i
$574$			9.92875i			0.414418i
$575$	−23.2848	−	13.9175i	−0.971044	−	0.580402i
$576$	2.98943	−	0.251664i	0.124559	−	0.0104860i
$577$	1.79499	−	1.79499i	0.0747263	−	0.0747263i	−0.668756	−	0.743482i	$-0.733173\pi$
$577$	1.79499	−	1.79499i	0.0747263	−	0.0747263i	0.743482	+	0.668756i	$0.233173\pi$
$578$	−5.47160	+	5.47160i	−0.227588	+	0.227588i
$579$	0.502765	+	11.9654i	0.0208942	+	0.497267i
$580$	−4.74242	−	3.69634i	−0.196918	−	0.153482i
$581$		−	2.01448i		−	0.0835745i
$582$	1.77426	+	1.63117i	0.0735454	+	0.0676141i
$583$	16.4096	+	16.4096i	0.679617	+	0.679617i
$584$	12.0155			0.497203
$585$	2.56079	+	12.1745i	0.105876	+	0.503352i
$586$	9.77825			0.403936
$587$	4.68454	+	4.68454i	0.193352	+	0.193352i	0.797143	−	0.603791i	$-0.206344\pi$
$587$	4.68454	+	4.68454i	0.193352	+	0.193352i	−0.603791	+	0.797143i	$0.706344\pi$
$588$	1.27508	+	1.17225i	0.0525835	+	0.0483427i
$589$			12.7472i			0.525241i
$590$	−3.70113	+	0.458798i	−0.152373	+	0.0188884i
$591$	1.00216	+	23.8507i	0.0412234	+	0.981087i
$592$	−3.73101	+	3.73101i	−0.153344	+	0.153344i
$593$	8.39604	−	8.39604i	0.344784	−	0.344784i	−0.513378	−	0.858162i	$-0.671606\pi$
$593$	8.39604	−	8.39604i	0.344784	−	0.344784i	0.858162	+	0.513378i	$0.171606\pi$
$594$	1.62563	+	12.8355i	0.0667003	+	0.526647i
$595$	4.18344	−	5.36738i	0.171504	−	0.220041i
$596$		−	17.9577i		−	0.735576i
$597$	7.89666	−	8.58938i	0.323189	−	0.351540i
$598$	7.11480	+	7.11480i	0.290946	+	0.290946i
$599$	16.7879			0.685935			0.342968	−	0.939347i	$-0.388568\pi$
$599$	16.7879			0.685935			0.342968	+	0.939347i	$0.388568\pi$
$600$	−2.46528	−	8.30195i	−0.100645	−	0.338926i
$601$	−11.3458			−0.462807			−0.231403	−	0.972858i	$-0.574332\pi$
$601$	−11.3458			−0.462807			−0.231403	+	0.972858i	$0.574332\pi$
$602$	−7.18740	−	7.18740i	−0.292937	−	0.292937i
$603$	−14.8558	−	12.5488i	−0.604976	−	0.511026i
$604$		−	6.24908i		−	0.254271i
$605$	−6.59854	+	8.46596i	−0.268269	+	0.344190i
$606$	4.44382	−	0.186721i	0.180518	−	0.00758501i
$607$	−22.2601	+	22.2601i	−0.903509	+	0.903509i	−0.995738	−	0.0922293i	$-0.970601\pi$
$607$	−22.2601	+	22.2601i	−0.903509	+	0.903509i	0.0922293	+	0.995738i	$0.470601\pi$
$608$	−0.892352	+	0.892352i	−0.0361896	+	0.0361896i
$609$	−4.65337	+	0.195526i	−0.188564	+	0.00792310i
$610$	−3.78467	+	0.469154i	−0.153237	+	0.0189955i
$611$			24.8592i			1.00570i
$612$	−6.97474	−	5.89159i	−0.281937	−	0.238154i
$613$	−4.97308	−	4.97308i	−0.200861	−	0.200861i	0.599508	−	0.800369i	$-0.295363\pi$
$613$	−4.97308	−	4.97308i	−0.200861	−	0.200861i	−0.800369	+	0.599508i	$0.795363\pi$
$614$	−9.30062			−0.375343
$615$	−6.32850	−	37.9296i	−0.255190	−	1.52947i
$616$	−2.48992			−0.100322
$617$	17.9613	+	17.9613i	0.723094	+	0.723094i	0.969234	−	0.246140i	$-0.0791624\pi$
$617$	17.9613	+	17.9613i	0.723094	+	0.723094i	−0.246140	+	0.969234i	$0.579162\pi$
$618$	17.5032	−	19.0387i	0.704084	−	0.765847i
$619$			2.56903i			0.103258i	0.998666	+	0.0516291i	$0.0164414\pi$
$619$			2.56903i			0.103258i	−0.998666	+	0.0516291i	$0.983559\pi$
$620$	−17.8146	−	13.8850i	−0.715450	−	0.557636i
$621$	3.54216	+	27.9679i	0.142142	+	1.12231i
$622$	−22.4326	+	22.4326i	−0.899464	+	0.899464i
$623$	−8.25075	+	8.25075i	−0.330559	+	0.330559i
$624$	0.134852	+	3.20938i	0.00539841	+	0.128478i
$625$	−22.0190	+	11.8390i	−0.880761	+	0.473561i
$626$		−	11.2778i		−	0.450751i
$627$	−4.00659	−	3.68347i	−0.160008	−	0.147104i
$628$	−2.01956	−	2.01956i	−0.0805892	−	0.0805892i
$629$	16.0581			0.640278
$630$	−5.61821	−	3.66547i	−0.223835	−	0.146036i
$631$	8.43901			0.335952			0.167976	−	0.985791i	$-0.446277\pi$
$631$	8.43901			0.335952			0.167976	+	0.985791i	$0.446277\pi$
$632$	−2.30732	−	2.30732i	−0.0917804	−	0.0917804i
$633$	30.6661	+	28.1929i	1.21887	+	1.12057i
$634$			10.7624i			0.427429i
$635$	−3.16604	−	25.5404i	−0.125640	−	1.01354i
$636$	0.677705	+	16.1289i	0.0268728	+	0.639552i
$637$	−1.31138	+	1.31138i	−0.0519588	+	0.0519588i
$638$	4.73436	−	4.73436i	0.187435	−	0.187435i
$639$	7.82583	−	0.658816i	0.309585	−	0.0260624i
$640$	−0.275081	−	2.21908i	−0.0108735	−	0.0877170i
$641$		−	5.98170i		−	0.236263i	−0.992998	−	0.118131i	$-0.962310\pi$
$641$		−	5.98170i		−	0.236263i	0.992998	−	0.118131i	$-0.0376904\pi$
$642$	−11.4569	+	12.4620i	−0.452169	+	0.491835i
$643$	10.3036	+	10.3036i	0.406335	+	0.406335i	0.880458	−	0.474123i	$-0.157235\pi$
$643$	10.3036	+	10.3036i	0.406335	+	0.406335i	−0.474123	+	0.880458i	$0.657235\pi$
$644$	−5.42542			−0.213792
$645$	32.0383	+	22.8759i	1.26151	+	0.900739i
$646$	3.84064			0.151108
$647$	−14.4071	−	14.4071i	−0.566401	−	0.566401i	0.364717	−	0.931118i	$-0.381166\pi$
$647$	−14.4071	−	14.4071i	−0.566401	−	0.566401i	−0.931118	+	0.364717i	$0.881166\pi$
$648$	−5.21044	+	7.33835i	−0.204685	+	0.288278i
$649$		−	4.15286i		−	0.163014i
$650$	8.99220	−	2.26417i	0.352703	−	0.0888080i
$651$	−17.4800	+	0.734478i	−0.685097	+	0.0287865i
$652$	10.4716	−	10.4716i	0.410099	−	0.410099i
$653$	−29.3549	+	29.3549i	−1.14874	+	1.14874i	−0.161945	+	0.986800i	$0.551777\pi$
$653$	−29.3549	+	29.3549i	−1.14874	+	1.14874i	−0.986800	+	0.161945i	$0.948223\pi$
$654$	15.8709	−	0.666866i	0.620603	−	0.0260765i
$655$	16.1920	+	12.6204i	0.632675	+	0.493120i
$656$		−	9.92875i		−	0.387653i
$657$	−23.2606	+	27.5370i	−0.907482	+	1.07432i
$658$	−9.47825	−	9.47825i	−0.369501	−	0.369501i
$659$	14.4888			0.564403			0.282202	−	0.959355i	$-0.408935\pi$
$659$	14.4888			0.564403			0.282202	+	0.959355i	$0.408935\pi$
$660$	9.51195	−	1.58706i	0.370252	−	0.0617761i
$661$	43.2493			1.68220			0.841101	−	0.540878i	$-0.181908\pi$
$661$	43.2493			1.68220			0.841101	+	0.540878i	$0.181908\pi$
$662$	3.42567	+	3.42567i	0.133142	+	0.133142i
$663$	6.61631	−	7.19671i	0.256956	−	0.279497i
$664$			2.01448i			0.0781768i
$665$	2.80043	−	0.347146i	0.108596	−	0.0134617i
$666$	−1.32789	−	15.7736i	−0.0514548	−	0.611213i
$667$	10.3159	−	10.3159i	0.399435	−	0.399435i
$668$	4.80821	−	4.80821i	0.186035	−	0.186035i
$669$	−1.54925	−	36.8709i	−0.0598973	−	1.42551i
$670$	−8.91051	+	11.4322i	−0.344243	+	0.441666i
$671$		−	4.24659i		−	0.163938i
$672$	−1.27508	−	1.17225i	−0.0491873	−	0.0452205i
$673$	2.40134	+	2.40134i	0.0925647	+	0.0925647i	0.751873	−	0.659308i	$-0.229151\pi$
$673$	2.40134	+	2.40134i	0.0925647	+	0.0925647i	−0.659308	+	0.751873i	$0.729151\pi$
$674$	−23.6570			−0.911234
$675$	23.7989	+	10.4217i	0.916020	+	0.401133i
$676$	9.56056			0.367714
$677$	32.4655	+	32.4655i	1.24775	+	1.24775i	0.956711	+	0.291038i	$0.0940006\pi$
$677$	32.4655	+	32.4655i	1.24775	+	1.24775i	0.291038	+	0.956711i	$0.405999\pi$
$678$	−22.6284	−	20.8035i	−0.869040	−	0.798954i
$679$		−	1.39149i		−	0.0534004i
$680$	−4.18344	+	5.36738i	−0.160428	+	0.205830i
$681$	1.90291	+	45.2880i	0.0729198	+	1.73544i
$682$	17.7843	−	17.7843i	0.680995	−	0.680995i
$683$	−20.2970	+	20.2970i	−0.776643	+	0.776643i	−0.979258	−	0.202616i	$-0.935056\pi$
$683$	−20.2970	+	20.2970i	−0.776643	+	0.776643i	0.202616	+	0.979258i	$0.435056\pi$
$684$	−0.317594	−	3.77258i	−0.0121435	−	0.144248i
$685$	−32.3911	+	4.01525i	−1.23760	+	0.153415i
$686$		−	1.00000i		−	0.0381802i
$687$	9.39786	−	10.2223i	0.358551	−	0.390004i
$688$	7.18740	+	7.18740i	0.274017	+	0.274017i
$689$	−17.2851			−0.658509
$690$	20.7261	−	3.45812i	0.789028	−	0.131648i
$691$	−11.5734			−0.440273			−0.220137	−	0.975469i	$-0.570650\pi$
$691$	−11.5734			−0.440273			−0.220137	+	0.975469i	$0.570650\pi$
$692$	−9.17963	−	9.17963i	−0.348957	−	0.348957i
$693$	4.82022	−	5.70640i	0.183105	−	0.216768i
$694$			17.9247i			0.680411i
$695$	11.3267	+	8.82822i	0.429644	+	0.334873i
$696$	4.65337	−	0.195526i	0.176386	−	0.00741138i
$697$	−21.3664	+	21.3664i	−0.809311	+	0.809311i
$698$	2.48817	−	2.48817i	0.0941786	−	0.0941786i
$699$	−36.6729	+	1.54093i	−1.38710	+	0.0582831i
$700$	−2.56525	+	4.29180i	−0.0969572	+	0.162215i
$701$			40.8136i			1.54151i	0.637134	+	0.770753i	$0.280120\pi$
$701$			40.8136i			1.54151i	−0.637134	+	0.770753i	$0.719880\pi$
$702$	−7.61631	−	5.90396i	−0.287459	−	0.222831i
$703$	4.70845	+	4.70845i	0.177583	+	0.177583i
$704$	2.48992			0.0938426
$705$	42.2499	+	30.1672i	1.59122	+	1.13616i
$706$	22.6244			0.851482
$707$	−1.81578	−	1.81578i	−0.0682895	−	0.0682895i
$708$	1.95515	−	2.12666i	0.0734791	−	0.0799249i
$709$			39.7104i			1.49136i	0.666307	+	0.745678i	$0.267874\pi$
$709$			39.7104i			1.49136i	−0.666307	+	0.745678i	$0.732126\pi$
$710$	−0.720118	−	5.80920i	−0.0270256	−	0.218015i
$711$	9.75464	−	0.821192i	0.365828	−	0.0307971i
$712$	8.25075	−	8.25075i	0.309210	−	0.309210i
$713$	38.7511	−	38.7511i	1.45124	−	1.45124i
$714$	0.221292	+	5.26659i	0.00828165	+	0.197097i
$715$	1.27026	+	10.2472i	0.0475049	+	0.383222i
$716$		−	10.4187i		−	0.389364i
$717$	−20.4481	−	18.7990i	−0.763648	−	0.702062i
$718$	−23.2824	−	23.2824i	−0.868891	−	0.868891i
$719$	11.2595			0.419907			0.209954	−	0.977711i	$-0.432669\pi$
$719$	11.2595			0.419907			0.209954	+	0.977711i	$0.432669\pi$
$720$	5.61821	+	3.66547i	0.209378	+	0.136604i
$721$	−14.9313			−0.556072
$722$	−12.3089	−	12.3089i	−0.458090	−	0.458090i
$723$	−20.4328	−	18.7849i	−0.759903	−	0.698619i
$724$			3.47436i			0.129124i
$725$	−3.28288	−	13.0380i	−0.121923	−	0.484220i
$726$	−0.349044	−	8.30699i	−0.0129542	−	0.308301i
$727$	−6.31002	+	6.31002i	−0.234026	+	0.234026i	−0.814371	−	0.580345i	$-0.802918\pi$
$727$	−6.31002	+	6.31002i	−0.234026	+	0.234026i	0.580345	+	0.814371i	$0.302918\pi$
$728$	1.31138	−	1.31138i	0.0486030	−	0.0486030i
$729$	−6.73118	−	26.1475i	−0.249303	−	0.968426i
$730$	21.1909	+	16.5167i	0.784312	+	0.611309i
$731$		−	30.9342i		−	1.14414i
$732$	1.99928	−	2.17466i	0.0738956	−	0.0803779i
$733$	−26.3661	−	26.3661i	−0.973855	−	0.973855i	0.0258120	−	0.999667i	$-0.491783\pi$
$733$	−26.3661	−	26.3661i	−0.973855	−	0.973855i	−0.999667	+	0.0258120i	$0.991783\pi$
$734$	16.1759			0.597062
$735$	0.637391	+	3.82017i	0.0235105	+	0.140909i
$736$	5.42542			0.199984
$737$	−11.4128	−	11.4128i	−0.420396	−	0.420396i
$738$	22.7547	+	19.2210i	0.837611	+	0.707534i
$739$		−	29.8538i		−	1.09819i	−0.835761	−	0.549094i	$-0.814973\pi$
$739$		−	29.8538i		−	1.09819i	0.835761	−	0.549094i	$-0.185027\pi$
$740$	−11.7089	+	1.45145i	−0.430427	+	0.0533565i
$741$	4.05017	−	0.170180i	0.148787	−	0.00625172i
$742$	6.59040	−	6.59040i	0.241941	−	0.241941i
$743$	13.9580	−	13.9580i	0.512068	−	0.512068i	−0.403092	−	0.915160i	$-0.632064\pi$
$743$	13.9580	−	13.9580i	0.512068	−	0.512068i	0.915160	+	0.403092i	$0.132064\pi$
$744$	17.4800	−	0.734478i	0.640850	−	0.0269273i
$745$	24.6850	−	31.6709i	0.904387	−	1.16033i
$746$			27.0762i			0.991330i
$747$	−4.61677	−	3.89980i	−0.168919	−	0.142686i
$748$	−5.35826	−	5.35826i	−0.195917	−	0.195917i
$749$	9.77347			0.357115
$750$	7.06413	−	18.0305i	0.257946	−	0.658380i
$751$	23.8662			0.870892			0.435446	−	0.900215i	$-0.356591\pi$
$751$	23.8662			0.870892			0.435446	+	0.900215i	$0.356591\pi$
$752$	9.47825	+	9.47825i	0.345636	+	0.345636i
$753$	−27.5438	+	29.9600i	−1.00375	+	1.09180i
$754$			4.98694i			0.181614i
$755$	8.59009	−	11.0211i	0.312625	−	0.401100i
$756$	5.15497	−	0.652882i	0.187485	−	0.0237451i
$757$	10.9223	−	10.9223i	0.396979	−	0.396979i	−0.480187	−	0.877166i	$-0.659431\pi$
$757$	10.9223	−	10.9223i	0.396979	−	0.396979i	0.877166	+	0.480187i	$0.159431\pi$
$758$	7.00032	−	7.00032i	0.254263	−	0.254263i
$759$	0.982276	+	23.3775i	0.0356544	+	0.848548i
$760$	−2.80043	+	0.347146i	−0.101582	+	0.0125923i
$761$		−	26.9407i		−	0.976601i	−0.872675	−	0.488301i	$-0.837617\pi$
$761$		−	26.9407i		−	0.976601i	0.872675	−	0.488301i	$-0.162383\pi$
$762$	14.6755	+	13.4920i	0.531637	+	0.488762i
$763$	−6.48500	−	6.48500i	−0.234773	−	0.234773i
$764$	9.02930			0.326668
$765$	−4.20226	−	19.9783i	−0.151933	−	0.722315i
$766$	−5.53128			−0.199853
$767$	2.18721	+	2.18721i	0.0789755	+	0.0789755i
$768$	1.27508	+	1.17225i	0.0460105	+	0.0422999i
$769$			19.3890i			0.699185i	0.936902	+	0.349592i	$0.113680\pi$
$769$			19.3890i			0.699185i	−0.936902	+	0.349592i	$0.886320\pi$
$770$	−4.39133	−	3.42269i	−0.158253	−	0.123345i
$771$	−1.47972	−	35.2163i	−0.0532909	−	1.26829i
$772$	−4.88918	+	4.88918i	−0.175966	+	0.175966i
$773$	−33.6535	+	33.6535i	−1.21043	+	1.21043i	−0.239546	+	0.970885i	$0.576998\pi$
$773$	−33.6535	+	33.6535i	−1.21043	+	1.21043i	−0.970885	+	0.239546i	$0.923002\pi$
$774$	−30.3861	+	2.55804i	−1.09220	+	0.0919470i
$775$	−12.3319	−	48.9764i	−0.442974	−	1.75928i
$776$			1.39149i			0.0499515i
$777$	−6.18532	+	6.72790i	−0.221897	+	0.241362i
$778$	−13.0590	−	13.0590i	−0.468186	−	0.468186i
$779$	−12.5298			−0.448928
$780$	−4.17384	+	5.84557i	−0.149448	+	0.209305i
$781$	6.51822			0.233240
$782$	−11.6754	−	11.6754i	−0.417511	−	0.417511i
$783$	−8.56031	+	11.0431i	−0.305921	+	0.394648i
$784$			1.00000i			0.0357143i
$785$	−0.785656	−	6.33790i	−0.0280413	−	0.226209i
$786$	−15.8880	+	0.667583i	−0.566706	+	0.0238119i
$787$	9.30807	−	9.30807i	0.331797	−	0.331797i	−0.521472	−	0.853269i	$-0.674617\pi$
$787$	9.30807	−	9.30807i	0.331797	−	0.331797i	0.853269	+	0.521472i	$0.174617\pi$
$788$	−9.74560	+	9.74560i	−0.347173	+	0.347173i
$789$	24.7761	−	1.04105i	0.882054	−	0.0370622i
$790$	−0.897603	−	7.24097i	−0.0319353	−	0.257622i
$791$			17.7467i			0.630999i
$792$	−4.82022	+	5.70640i	−0.171279	+	0.202768i
$793$	2.23657	+	2.23657i	0.0794231	+	0.0794231i
$794$	−22.1938			−0.787628
$795$	−20.9758	+	29.3772i	−0.743936	+	1.04190i
$796$	6.73634			0.238763
$797$	−30.9837	−	30.9837i	−1.09750	−	1.09750i	−0.994703	−	0.102795i	$-0.967221\pi$
$797$	−30.9837	−	30.9837i	−1.09750	−	1.09750i	−0.102795	−	0.994703i	$-0.532779\pi$
$798$	−1.47935	+	1.60912i	−0.0523684	+	0.0569623i
$799$		−	40.7939i		−	1.44319i
$800$	2.56525	−	4.29180i	0.0906951	−	0.151738i
$801$	2.93650	+	34.8816i	0.103756	+	1.23248i
$802$	−2.36376	+	2.36376i	−0.0834672	+	0.0834672i
$803$	−21.1549	+	21.1549i	−0.746541	+	0.746541i
$804$	−0.471341	−	11.2176i	−0.0166229	−	0.395613i
$805$	−9.56850	−	7.45788i	−0.337245	−	0.262856i
$806$			18.7331i			0.659844i
$807$	−33.2578	−	30.5756i	−1.17073	−	1.07631i
$808$	1.81578	+	1.81578i	0.0638790	+	0.0638790i
$809$	37.5965			1.32182			0.660911	−	0.750464i	$-0.270170\pi$
$809$	37.5965			1.32182			0.660911	+	0.750464i	$0.270170\pi$
$810$	−19.2768	+	5.77986i	−0.677316	+	0.203083i
$811$	−55.3927			−1.94510			−0.972551	−	0.232690i	$-0.925247\pi$
$811$	−55.3927			−1.94510			−0.972551	+	0.232690i	$0.925247\pi$
$812$	−1.90141	−	1.90141i	−0.0667263	−	0.0667263i
$813$	−4.38733	−	4.03350i	−0.153870	−	0.141461i
$814$		−	13.1380i		−	0.460485i
$815$	32.8626	−	4.07370i	1.15113	−	0.142695i
$816$	−0.221292	−	5.26659i	−0.00774677	−	0.184368i
$817$	9.07033	−	9.07033i	0.317331	−	0.317331i
$818$	−10.8944	+	10.8944i	−0.380912	+	0.380912i
$819$	0.466730	+	5.54411i	0.0163089	+	0.193727i
$820$	13.6482	−	17.5107i	0.476617	−	0.611502i
$821$		−	50.0649i		−	1.74728i	−0.486576	−	0.873638i	$-0.661754\pi$
$821$		−	50.0649i		−	1.74728i	0.486576	−	0.873638i	$-0.338246\pi$
$822$	17.1109	−	18.6118i	0.596809	−	0.649163i
$823$	−33.3463	−	33.3463i	−1.16238	−	1.16238i	−0.983953	−	0.178425i	$-0.942900\pi$
$823$	−33.3463	−	33.3463i	−1.16238	−	1.16238i	−0.178425	−	0.983953i	$-0.557100\pi$
$824$	14.9313			0.520158
$825$	18.9573	+	10.2763i	0.660007	+	0.357774i
$826$	−1.66786			−0.0580324
$827$	−11.0886	−	11.0886i	−0.385588	−	0.385588i	0.487522	−	0.873110i	$-0.337901\pi$
$827$	−11.0886	−	11.0886i	−0.385588	−	0.385588i	−0.873110	+	0.487522i	$0.837901\pi$
$828$	−10.5030	+	12.4340i	−0.365005	+	0.432110i
$829$			22.1675i			0.769909i	0.922936	+	0.384954i	$0.125783\pi$
$829$			22.1675i			0.769909i	−0.922936	+	0.384954i	$0.874217\pi$
$830$	−2.76913	+	3.55281i	−0.0961180	+	0.123320i
$831$	11.0587	−	0.464667i	0.383623	−	0.0161191i
$832$	−1.31138	+	1.31138i	−0.0454640	+	0.0454640i
$833$	2.15197	−	2.15197i	0.0745615	−	0.0745615i
$834$	−11.1140	+	0.466987i	−0.384845	+	0.0161705i
$835$	15.0894	−	1.87051i	0.522191	−	0.0647316i
$836$		−	3.14223i		−	0.108676i
$837$	−32.1562	+	41.4826i	−1.11148	+	1.43385i
$838$	−8.80532	−	8.80532i	−0.304175	−	0.304175i
$839$	−32.9972			−1.13919			−0.569595	−	0.821925i	$-0.692900\pi$
$839$	−32.9972			−1.13919			−0.569595	+	0.821925i	$0.692900\pi$
$840$	−0.637391	−	3.82017i	−0.0219921	−	0.131809i
$841$	−21.7693			−0.750665
$842$	17.5114	+	17.5114i	0.603482	+	0.603482i
$843$	22.3634	−	24.3252i	0.770238	−	0.837805i
$844$			24.0503i			0.827846i
$845$	16.8614	+	13.1421i	0.580049	+	0.452102i
$846$	−40.0711	+	3.37338i	−1.37767	+	0.115979i
$847$	−3.39431	+	3.39431i	−0.116630	+	0.116630i
$848$	−6.59040	+	6.59040i	−0.226315	+	0.226315i
$849$	−1.11680	−	26.5789i	−0.0383283	−	0.912187i
$850$	−14.7562	+	3.71550i	−0.506133	+	0.127440i
$851$		−	28.6270i		−	0.981320i
$852$	3.33796	+	3.06876i	0.114357	+	0.105134i
$853$	3.03563	+	3.03563i	0.103938	+	0.103938i	0.757163	−	0.653225i	$-0.226585\pi$
$853$	3.03563	+	3.03563i	0.103938	+	0.103938i	−0.653225	+	0.757163i	$0.726585\pi$
$854$	−1.70551			−0.0583614
$855$	4.62574	−	7.09005i	0.158197	−	0.242475i
$856$	−9.77347			−0.334050
$857$	33.3587	+	33.3587i	1.13951	+	1.13951i	0.988538	+	0.150972i	$0.0482405\pi$
$857$	33.3587	+	33.3587i	1.13951	+	1.13951i	0.150972	+	0.988538i	$0.451760\pi$
$858$	−5.88800	−	5.41315i	−0.201013	−	0.184802i
$859$		−	10.1819i		−	0.347402i	−0.984798	−	0.173701i	$-0.944427\pi$
$859$		−	10.1819i		−	0.347402i	0.984798	−	0.173701i	$-0.0555726\pi$
$860$	2.79607	+	22.5559i	0.0953451	+	0.769150i
$861$	−0.721952	−	17.1819i	−0.0246041	−	0.585559i
$862$	−2.81028	+	2.81028i	−0.0957185	+	0.0957185i
$863$	−5.73988	+	5.73988i	−0.195388	+	0.195388i	−0.798019	−	0.602632i	$-0.794119\pi$
$863$	−5.73988	+	5.73988i	−0.195388	+	0.195388i	0.602632	+	0.798019i	$0.294119\pi$
$864$	−5.15497	+	0.652882i	−0.175376	+	0.0222115i
$865$	−3.57109	−	28.8081i	−0.121421	−	0.979503i
$866$			6.92832i			0.235434i
$867$	9.07087	−	9.86659i	0.308063	−	0.335087i
$868$	−7.14250	−	7.14250i	−0.242432	−	0.242432i
$869$	8.12474			0.275613
$870$	8.47565	+	6.05177i	0.287351	+	0.205174i
$871$	12.0217			0.407339
$872$	6.48500	+	6.48500i	0.219610	+	0.219610i
$873$	−3.18900	−	2.69376i	−0.107931	−	0.0911701i
$874$		−	6.84675i		−	0.231595i
$875$	−10.4237	+	4.04296i	−0.352387	+	0.136677i
$876$	−20.7930	+	0.873683i	−0.702532	+	0.0295190i
$877$	−0.864549	+	0.864549i	−0.0291937	+	0.0291937i	−0.721553	−	0.692359i	$-0.756571\pi$
$877$	−0.864549	+	0.864549i	−0.0291937	+	0.0291937i	0.692359	+	0.721553i	$0.256571\pi$
$878$	−22.1204	+	22.1204i	−0.746528	+	0.746528i
$879$	−16.9215	+	0.711009i	−0.570748	+	0.0239817i
$880$	4.39133	+	3.42269i	0.148032	+	0.115379i
$881$		−	23.3062i		−	0.785206i	−0.919708	−	0.392603i	$-0.871575\pi$
$881$		−	23.3062i		−	0.785206i	0.919708	−	0.392603i	$-0.128425\pi$
$882$	−2.29180	−	1.93589i	−0.0771688	−	0.0651848i
$883$	−2.59691	−	2.59691i	−0.0873928	−	0.0873928i	0.662059	−	0.749452i	$-0.269683\pi$
$883$	−2.59691	−	2.59691i	−0.0873928	−	0.0873928i	−0.749452	+	0.662059i	$0.769683\pi$
$884$	5.64412			0.189832
$885$	6.37153	−	1.06308i	0.214177	−	0.0357351i
$886$	−16.3703			−0.549971
$887$	11.5313	+	11.5313i	0.387183	+	0.387183i	0.873681	−	0.486499i	$-0.161726\pi$
$887$	11.5313	+	11.5313i	0.387183	+	0.387183i	−0.486499	+	0.873681i	$0.661726\pi$
$888$	6.18532	−	6.72790i	0.207566	−	0.225774i
$889$		−	11.5095i		−	0.386015i
$890$	25.8930	−	3.20974i	0.867934	−	0.107591i
$891$	−3.74650	−	22.0939i	−0.125512	−	0.740174i
$892$	15.0658	−	15.0658i	0.504439	−	0.504439i
$893$	11.9613	−	11.9613i	0.400271	−	0.400271i
$894$	1.30576	+	31.0762i	0.0436713	+	1.03934i
$895$	14.3217	−	18.3748i	0.478721	−	0.614202i
$896$		−	1.00000i		−	0.0334077i
$897$	−12.8297	−	11.7950i	−0.428370	−	0.393823i
$898$	0.311043	+	0.311043i	0.0103796	+	0.0103796i
$899$	27.1616			0.905890
$900$	4.86989	+	14.1875i	0.162330	+	0.472915i
$901$	28.3648			0.944967
$902$	17.4810	+	17.4810i	0.582053	+	0.582053i
$903$	12.9606	+	11.9153i	0.431301	+	0.396518i
$904$		−	17.7467i		−	0.590245i
$905$	−4.77592	+	6.12752i	−0.158757	+	0.203686i
$906$	0.454391	+	10.8142i	0.0150961	+	0.359277i
$907$	32.3018	−	32.3018i	1.07256	−	1.07256i	0.0754116	−	0.997152i	$-0.475973\pi$
$907$	32.3018	−	32.3018i	1.07256	−	1.07256i	0.997152	−	0.0754116i	$-0.0240271\pi$
$908$	−18.5051	+	18.5051i	−0.614112	+	0.614112i
$909$	−7.67655	+	0.646249i	−0.254615	+	0.0214347i
$910$	4.11545	−	0.510158i	0.136426	−	0.0169116i
$911$			4.28831i			0.142078i	0.997474	+	0.0710391i	$0.0226315\pi$
$911$			4.28831i			0.142078i	−0.997474	+	0.0710391i	$0.977368\pi$
$912$	1.47935	−	1.60912i	0.0489862	−	0.0532834i
$913$	−3.54677	−	3.54677i	−0.117381	−	0.117381i
$914$	3.66785			0.121322
$915$	6.51535	−	1.08708i	0.215391	−	0.0359377i
$916$	8.01695			0.264887
$917$	6.49197	+	6.49197i	0.214384	+	0.214384i
$918$	12.4984	+	9.68839i	0.412507	+	0.319764i
$919$			32.7595i			1.08064i	0.841461	+	0.540319i	$0.181696\pi$
$919$			32.7595i			1.08064i	−0.841461	+	0.540319i	$0.818304\pi$
$920$	9.56850	+	7.45788i	0.315464	+	0.245879i
$921$	16.0949	−	0.676279i	0.530347	−	0.0222841i
$922$	7.92642	−	7.92642i	0.261043	−	0.261043i
$923$	−3.43299	+	3.43299i	−0.112998	+	0.112998i
$924$	4.30887	−	0.181051i	0.141752	−	0.00595613i
$925$	−22.6455	−	13.5354i	−0.744578	−	0.445041i
$926$			1.96550i			0.0645903i
$927$	−28.9054	+	34.2196i	−0.949378	+	1.12392i
$928$	1.90141	+	1.90141i	0.0624168	+	0.0624168i
$929$	−14.4962			−0.475605			−0.237802	−	0.971314i	$-0.576427\pi$
$929$	−14.4962			−0.475605			−0.237802	+	0.971314i	$0.576427\pi$
$930$	31.8382	+	22.7330i	1.04401	+	0.745445i
$931$	1.26198			0.0413596
$932$	−14.9849	−	14.9849i	−0.490846	−	0.490846i
$933$	37.1889	−	40.4512i	1.21751	−	1.32431i
$934$		−	5.23679i		−	0.171353i
$935$	−2.08449	−	16.8156i	−0.0681700	−	0.549928i
$936$	−0.466730	−	5.54411i	−0.0152555	−	0.181215i
$937$	18.6626	−	18.6626i	0.609680	−	0.609680i	−0.333183	−	0.942862i	$-0.608123\pi$
$937$	18.6626	−	18.6626i	0.609680	−	0.609680i	0.942862	+	0.333183i	$0.108123\pi$
$938$	−4.58359	+	4.58359i	−0.149660	+	0.149660i
$939$	0.820045	+	19.5165i	0.0267612	+	0.636897i
$940$	3.68726	+	29.7452i	0.120265	+	0.970181i
$941$		−	27.3919i		−	0.892951i	−0.894796	−	0.446475i	$-0.852679\pi$
$941$		−	27.3919i		−	0.892951i	0.894796	−	0.446475i	$-0.147321\pi$
$942$	3.64174	+	3.34805i	0.118654	+	0.109085i
$943$	38.0902	+	38.0902i	1.24039	+	1.24039i
$944$	1.66786			0.0542844
$945$	9.98898	+	5.93466i	0.324942	+	0.193055i
$946$	−25.3089			−0.822863
$947$	18.4757	+	18.4757i	0.600380	+	0.600380i	0.940413	−	0.340033i	$-0.110438\pi$
$947$	18.4757	+	18.4757i	0.600380	+	0.600380i	−0.340033	+	0.940413i	$0.610438\pi$
$948$	4.16065	+	3.82510i	0.135132	+	0.124234i
$949$		−	22.2835i		−	0.723355i
$950$	−5.41614	−	3.23728i	−0.175723	−	0.105031i
$951$	−0.782569	−	18.6246i	−0.0253765	−	0.603943i
$952$	−2.15197	+	2.15197i	−0.0697459	+	0.0697459i
$953$	−21.0733	+	21.0733i	−0.682631	+	0.682631i	−0.960592	−	0.277961i	$-0.910341\pi$
$953$	−21.0733	+	21.0733i	−0.682631	+	0.682631i	0.277961	+	0.960592i	$0.410341\pi$
$954$	−2.34557	−	27.8622i	−0.0759406	−	0.902071i
$955$	15.9244	+	12.4118i	0.515302	+	0.401637i
$956$		−	16.0367i		−	0.518664i
$957$	−7.84867	+	8.53718i	−0.253712	+	0.275968i
$958$	4.39353	+	4.39353i	0.141948	+	0.141948i
$959$	−14.5966			−0.471349
$960$	0.637391	+	3.82017i	0.0205717	+	0.123296i
$961$	71.0305			2.29131
$962$	6.91944	+	6.91944i	0.223092	+	0.223092i
$963$	18.9204	−	22.3988i	0.609700	−	0.721791i
$964$		−	16.0247i		−	0.516121i
$965$	−15.3435	+	1.90201i	−0.493925	+	0.0612278i
$966$	9.38883	−	0.394500i	0.302080	−	0.0126928i
$967$	−31.6125	+	31.6125i	−1.01659	+	1.01659i	−0.0167296	+	0.999860i	$0.505325\pi$
$967$	−31.6125	+	31.6125i	−1.01659	+	1.01659i	−0.999860	+	0.0167296i	$0.994675\pi$
$968$	3.39431	−	3.39431i	0.109097	−	0.109097i
$969$	−6.64632	+	0.279265i	−0.213510	+	0.00897130i
$970$	−1.91276	+	2.45408i	−0.0614151	+	0.0787958i
$971$		−	16.3784i		−	0.525607i	−0.964849	−	0.262803i	$-0.915353\pi$
$971$		−	16.3784i		−	0.525607i	0.964849	−	0.262803i	$-0.0846470\pi$
$972$	8.48319	−	13.0781i	0.272098	−	0.419479i
$973$	4.54126	+	4.54126i	0.145586	+	0.145586i
$974$	12.3893			0.396979
$975$	−15.3966	+	4.57205i	−0.493085	+	0.146423i
$976$	1.70551			0.0545921
$977$	28.0270	+	28.0270i	0.896663	+	0.896663i	0.995139	−	0.0984762i	$-0.0313968\pi$
$977$	28.0270	+	28.0270i	0.896663	+	0.896663i	−0.0984762	+	0.995139i	$0.531397\pi$
$978$	−17.3599	+	18.8828i	−0.555109	+	0.603804i
$979$			29.0532i			0.928546i
$980$	−1.37462	+	1.76364i	−0.0439105	+	0.0563374i
$981$	−27.4165	+	2.30806i	−0.875343	+	0.0736906i
$982$	10.9518	−	10.9518i	0.349486	−	0.349486i
$983$	−20.6447	+	20.6447i	−0.658463	+	0.658463i	−0.955016	−	0.296553i	$-0.904163\pi$
$983$	−20.6447	+	20.6447i	−0.658463	+	0.658463i	0.296553	+	0.955016i	$0.404163\pi$
$984$	0.721952	+	17.1819i	0.0230150	+	0.547740i
$985$	−30.5842	+	3.79127i	−0.974494	+	0.120800i
$986$		−	8.18356i		−	0.260618i
$987$	17.0915	+	15.7131i	0.544030	+	0.500155i
$988$	1.65493	+	1.65493i	0.0526504	+	0.0526504i
$989$	−55.1468			−1.75357
$990$	−16.3453	+	3.43808i	−0.519486	+	0.109269i
$991$	32.5844			1.03508			0.517538	−	0.855660i	$-0.326848\pi$
$991$	32.5844			1.03508			0.517538	+	0.855660i	$0.326848\pi$
$992$	7.14250	+	7.14250i	0.226775	+	0.226775i
$993$	−6.17729	−	5.67911i	−0.196030	−	0.180221i
$994$		−	2.61784i		−	0.0830328i
$995$	11.8805	+	9.25988i	0.376636	+	0.293558i
$996$	−0.146479	−	3.48610i	−0.00464137	−	0.110461i
$997$	−20.4115	+	20.4115i	−0.646438	+	0.646438i	−0.952130	−	0.305692i	$-0.901112\pi$
$997$	−20.4115	+	20.4115i	−0.646438	+	0.646438i	0.305692	+	0.952130i	$0.401112\pi$
$998$	23.5165	−	23.5165i	0.744402	−	0.744402i
$999$	3.44490	+	27.2000i	0.108992	+	0.860569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.j.b.113.2	yes	12
3.2	odd	2		210.2.j.a.113.5	✓	12
5.2	odd	4		210.2.j.a.197.5	yes	12
5.3	odd	4		1050.2.j.c.407.2		12
5.4	even	2		1050.2.j.d.743.5		12
15.2	even	4	inner	210.2.j.b.197.2	yes	12
15.8	even	4		1050.2.j.d.407.5		12
15.14	odd	2		1050.2.j.c.743.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.j.a.113.5	✓	12	3.2	odd	2
210.2.j.a.197.5	yes	12	5.2	odd	4
210.2.j.b.113.2	yes	12	1.1	even	1	trivial
210.2.j.b.197.2	yes	12	15.2	even	4	inner
1050.2.j.c.407.2		12	5.3	odd	4
1050.2.j.c.743.2		12	15.14	odd	2
1050.2.j.d.407.5		12	15.8	even	4
1050.2.j.d.743.5		12	5.4	even	2

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.27508 + 1.17225i) q^{3} +1.00000i q^{4} +(-1.37462 + 1.76364i) q^{5} +(-0.0727133 - 1.73052i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.251664 + 2.98943i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.27508 + 1.17225i) q^{3} +1.00000i q^{4} +(-1.37462 + 1.76364i) q^{5} +(-0.0727133 - 1.73052i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.251664 + 2.98943i) q^{9} +(2.21908 - 0.275081i) q^{10} +2.48992i q^{11} +(-1.17225 + 1.27508i) q^{12} +(-1.31138 - 1.31138i) q^{13} +1.00000 q^{14} +(-3.82017 + 0.637391i) q^{15} -1.00000 q^{16} +(2.15197 + 2.15197i) q^{17} +(1.93589 - 2.29180i) q^{18} +1.26198i q^{19} +(-1.76364 - 1.37462i) q^{20} +(-1.73052 + 0.0727133i) q^{21} +(1.76064 - 1.76064i) q^{22} +(3.83635 - 3.83635i) q^{23} +(1.73052 - 0.0727133i) q^{24} +(-1.22086 - 4.84866i) q^{25} +1.85457i q^{26} +(-3.18346 + 4.10677i) q^{27} +(-0.707107 - 0.707107i) q^{28} +2.68900 q^{29} +(3.15197 + 2.25057i) q^{30} +10.1010 q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.91881 + 3.17486i) q^{33} -3.04335i q^{34} +(-0.275081 - 2.21908i) q^{35} +(-2.98943 + 0.251664i) q^{36} +(3.73101 - 3.73101i) q^{37} +(0.892352 - 0.892352i) q^{38} +(-0.134852 - 3.20938i) q^{39} +(0.275081 + 2.21908i) q^{40} +9.92875i q^{41} +(1.27508 + 1.17225i) q^{42} +(-7.18740 - 7.18740i) q^{43} -2.48992 q^{44} +(-5.61821 - 3.66547i) q^{45} -5.42542 q^{46} +(-9.47825 - 9.47825i) q^{47} +(-1.27508 - 1.17225i) q^{48} -1.00000i q^{49} +(-2.56525 + 4.29180i) q^{50} +(0.221292 + 5.26659i) q^{51} +(1.31138 - 1.31138i) q^{52} +(6.59040 - 6.59040i) q^{53} +(5.15497 - 0.652882i) q^{54} +(-4.39133 - 3.42269i) q^{55} +1.00000i q^{56} +(-1.47935 + 1.60912i) q^{57} +(-1.90141 - 1.90141i) q^{58} -1.66786 q^{59} +(-0.637391 - 3.82017i) q^{60} -1.70551 q^{61} +(-7.14250 - 7.14250i) q^{62} +(-2.29180 - 1.93589i) q^{63} -1.00000i q^{64} +(4.11545 - 0.510158i) q^{65} +(4.30887 - 0.181051i) q^{66} +(-4.58359 + 4.58359i) q^{67} +(-2.15197 + 2.15197i) q^{68} +(9.38883 - 0.394500i) q^{69} +(-1.37462 + 1.76364i) q^{70} -2.61784i q^{71} +(2.29180 + 1.93589i) q^{72} +(8.49621 + 8.49621i) q^{73} -5.27645 q^{74} +(4.12715 - 7.61358i) q^{75} -1.26198 q^{76} +(-1.76064 - 1.76064i) q^{77} +(-2.17402 + 2.36473i) q^{78} -3.26305i q^{79} +(1.37462 - 1.76364i) q^{80} +(-8.87333 + 1.50466i) q^{81} +(7.02069 - 7.02069i) q^{82} +(-1.42445 + 1.42445i) q^{83} +(-0.0727133 - 1.73052i) q^{84} +(-6.75345 + 0.837169i) q^{85} +10.1645i q^{86} +(3.42869 + 3.15217i) q^{87} +(1.76064 + 1.76064i) q^{88} +11.6683 q^{89} +(1.38080 + 6.56456i) q^{90} +1.85457 q^{91} +(3.83635 + 3.83635i) q^{92} +(12.8796 + 11.8409i) q^{93} +13.4043i q^{94} +(-2.22567 - 1.73473i) q^{95} +(0.0727133 + 1.73052i) q^{96} +(-0.983930 + 0.983930i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(-7.44344 + 0.626625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) 12 * q + 4 * q^3 + 4 * q^5	\( 12 q + 4 q^{3} + 4 q^{5} - 4 q^{12} + 12 q^{14} - 12 q^{15} - 12 q^{16} - 28 q^{17} - 8 q^{18} - 4 q^{21} + 4 q^{22} + 24 q^{23} + 4 q^{24} + 20 q^{25} + 28 q^{27} - 8 q^{29} - 16 q^{30} - 8 q^{31} - 36 q^{33} + 8 q^{35} + 4 q^{36} - 20 q^{37} + 4 q^{38} + 40 q^{39} - 8 q^{40} + 4 q^{42} + 8 q^{43} - 8 q^{44} - 48 q^{45} + 8 q^{46} - 16 q^{47} - 4 q^{48} + 16 q^{50} + 8 q^{51} + 24 q^{53} + 4 q^{54} - 16 q^{55} + 44 q^{57} - 8 q^{58} - 32 q^{59} + 4 q^{60} - 28 q^{62} - 8 q^{66} + 28 q^{68} + 32 q^{69} + 4 q^{70} - 24 q^{73} - 8 q^{74} - 4 q^{75} - 4 q^{77} - 8 q^{78} - 4 q^{80} - 36 q^{81} + 32 q^{82} + 24 q^{83} - 36 q^{85} - 16 q^{87} + 4 q^{88} - 48 q^{89} - 8 q^{90} + 24 q^{91} + 24 q^{92} - 20 q^{93} + 8 q^{97} + 40 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 + 4 * q^5 - 4 * q^12 + 12 * q^14 - 12 * q^15 - 12 * q^16 - 28 * q^17 - 8 * q^18 - 4 * q^21 + 4 * q^22 + 24 * q^23 + 4 * q^24 + 20 * q^25 + 28 * q^27 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 36 * q^33 + 8 * q^35 + 4 * q^36 - 20 * q^37 + 4 * q^38 + 40 * q^39 - 8 * q^40 + 4 * q^42 + 8 * q^43 - 8 * q^44 - 48 * q^45 + 8 * q^46 - 16 * q^47 - 4 * q^48 + 16 * q^50 + 8 * q^51 + 24 * q^53 + 4 * q^54 - 16 * q^55 + 44 * q^57 - 8 * q^58 - 32 * q^59 + 4 * q^60 - 28 * q^62 - 8 * q^66 + 28 * q^68 + 32 * q^69 + 4 * q^70 - 24 * q^73 - 8 * q^74 - 4 * q^75 - 4 * q^77 - 8 * q^78 - 4 * q^80 - 36 * q^81 + 32 * q^82 + 24 * q^83 - 36 * q^85 - 16 * q^87 + 4 * q^88 - 48 * q^89 - 8 * q^90 + 24 * q^91 + 24 * q^92 - 20 * q^93 + 8 * q^97 + 40 * q^99

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