LMFDB - Embedded newform 210.2.j.a.197.5

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			197.5
Root			$-1.69093i$ of defining polynomial
Character	$\chi$	$=$	210.197
Dual form			210.2.j.a.113.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.17225 - 1.27508i) q^{3} -1.00000i q^{4} +(1.37462 + 1.76364i) q^{5} +(-0.0727133 - 1.73052i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.251664 - 2.98943i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.17225 - 1.27508i) 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} +(-1.27508 - 1.17225i) q^{12} +(-1.31138 + 1.31138i) q^{13} -1.00000 q^{14} +(3.86018 + 0.314678i) q^{15} -1.00000 q^{16} +(-2.15197 + 2.15197i) q^{17} +(-2.29180 - 1.93589i) 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} +(-4.10677 - 3.18346i) q^{27} +(-0.707107 + 0.707107i) q^{28} -2.68900 q^{29} +(2.95207 - 2.50705i) q^{30} +10.1010 q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.17486 + 2.91881i) 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} +(-1.17225 + 1.27508i) q^{42} +(-7.18740 + 7.18740i) q^{43} +2.48992 q^{44} +(4.92633 - 4.55316i) q^{45} -5.42542 q^{46} +(9.47825 - 9.47825i) q^{47} +(-1.17225 + 1.27508i) 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} +(-1.60912 - 1.47935i) q^{57} +(-1.90141 + 1.90141i) q^{58} +1.66786 q^{59} +(0.314678 - 3.86018i) q^{60} -1.70551 q^{61} +(7.14250 - 7.14250i) q^{62} +(-1.93589 + 2.29180i) 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} +(-1.93589 + 2.29180i) q^{72} +(8.49621 - 8.49621i) q^{73} +5.27645 q^{74} +(4.75129 + 7.24053i) q^{75} -1.26198 q^{76} +(1.76064 - 1.76064i) q^{77} +(2.36473 + 2.17402i) 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} +(-3.15217 + 3.42869i) q^{87} +(1.76064 - 1.76064i) q^{88} -11.6683 q^{89} +(0.263871 - 6.70301i) q^{90} +1.85457 q^{91} +(-3.83635 + 3.83635i) q^{92} +(11.8409 - 12.8796i) 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} + 20 q^{15} - 12 q^{16} + 28 q^{17} - 4 q^{21} + 4 q^{22} - 24 q^{23} - 4 q^{24} + 20 q^{25} - 20 q^{27} + 8 q^{29} + 16 q^{30} - 8 q^{31} + 4 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} + 8 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} - 12 q^{57} - 8 q^{58} + 32 q^{59} - 4 q^{60} + 28 q^{62} + 8 q^{63} - 8 q^{66} - 28 q^{68} - 32 q^{69} + 4 q^{70} + 8 q^{72} - 24 q^{73} + 8 q^{74} + 36 q^{75} + 4 q^{77} + 4 q^{80} - 36 q^{81} + 32 q^{82} - 24 q^{83} - 36 q^{85} - 64 q^{87} + 4 q^{88} + 48 q^{89} + 48 q^{90} + 24 q^{91} - 24 q^{92} + 76 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 + 20 * q^15 - 12 * q^16 + 28 * q^17 - 4 * q^21 + 4 * q^22 - 24 * q^23 - 4 * q^24 + 20 * q^25 - 20 * q^27 + 8 * q^29 + 16 * q^30 - 8 * q^31 + 4 * 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 + 8 * 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 - 12 * q^57 - 8 * q^58 + 32 * q^59 - 4 * q^60 + 28 * q^62 + 8 * q^63 - 8 * q^66 - 28 * q^68 - 32 * q^69 + 4 * q^70 + 8 * q^72 - 24 * q^73 + 8 * q^74 + 36 * q^75 + 4 * q^77 + 4 * q^80 - 36 * q^81 + 32 * q^82 - 24 * q^83 - 36 * q^85 - 64 * q^87 + 4 * q^88 + 48 * q^89 + 48 * q^90 + 24 * q^91 - 24 * q^92 + 76 * q^93 + 8 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.17225	−	1.27508i	0.676798	−	0.736168i
$3$	1.17225	−	1.27508i	0.676798	−	0.736168i
$4$		−	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	$0.877516\pi$
$12$	−1.27508	−	1.17225i	−0.368084	−	0.338399i
$13$	−1.31138	+	1.31138i	−0.363712	+	0.363712i	−0.865178	−	0.501466i	$-0.832794\pi$
$13$	−1.31138	+	1.31138i	−0.363712	+	0.363712i	0.501466	+	0.865178i	$0.332794\pi$
$14$	−1.00000			−0.267261
$15$	3.86018	+	0.314678i	0.996694	+	0.0812494i
$16$	−1.00000			−0.250000
$17$	−2.15197	+	2.15197i	−0.521931	+	0.521931i	−0.918154	−	0.396223i	$-0.870321\pi$
$17$	−2.15197	+	2.15197i	−0.521931	+	0.521931i	0.396223	+	0.918154i	$0.370321\pi$
$18$	−2.29180	−	1.93589i	−0.540182	−	0.456294i
$19$		−	1.26198i		−	0.289517i	−0.989467	−	0.144759i	$-0.953759\pi$
$19$		−	1.26198i		−	0.289517i	0.989467	−	0.144759i	$-0.0462406\pi$
$20$	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	$-0.441371\pi$
$23$	−3.83635	−	3.83635i	−0.799935	−	0.799935i	−0.983085	+	0.183150i	$0.941371\pi$
$24$	−1.73052	+	0.0727133i	−0.353242	+	0.0148425i
$25$	−1.22086	+	4.84866i	−0.244171	+	0.969732i
$26$			1.85457i			0.363712i
$27$	−4.10677	−	3.18346i	−0.790349	−	0.612657i
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$	−2.68900			−0.499334			−0.249667	−	0.968332i	$-0.580321\pi$
$29$	−2.68900			−0.499334			−0.249667	+	0.968332i	$0.580321\pi$
$30$	2.95207	−	2.50705i	0.538972	−	0.457722i
$31$	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
$33$	3.17486	+	2.91881i	0.552672	+	0.508100i
$34$			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	0.943824	−	0.330449i	$-0.107200\pi$
$37$	3.73101	+	3.73101i	0.613375	+	0.613375i	−0.330449	+	0.943824i	$0.607200\pi$
$38$	−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	$0.717596\pi$
$42$	−1.17225	+	1.27508i	−0.180882	+	0.196749i
$43$	−7.18740	+	7.18740i	−1.09607	+	1.09607i	−0.101202	+	0.994866i	$0.532269\pi$
$43$	−7.18740	+	7.18740i	−1.09607	+	1.09607i	−0.994866	+	0.101202i	$0.967731\pi$
$44$	2.48992			0.375370
$45$	4.92633	−	4.55316i	0.734374	−	0.678745i
$46$	−5.42542			−0.799935
$47$	9.47825	−	9.47825i	1.38255	−	1.38255i	0.542471	−	0.840075i	$-0.317489\pi$
$47$	9.47825	−	9.47825i	1.38255	−	1.38255i	0.840075	−	0.542471i	$-0.182511\pi$
$48$	−1.17225	+	1.27508i	−0.169200	+	0.184042i
$49$			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	$-0.471114\pi$
$53$	−6.59040	−	6.59040i	−0.905262	−	0.905262i	−0.995885	+	0.0906236i	$0.971114\pi$
$54$	−5.15497	+	0.652882i	−0.701503	+	0.0888460i
$55$	−4.39133	+	3.42269i	−0.592127	+	0.461516i
$56$			1.00000i			0.133631i
$57$	−1.60912	−	1.47935i	−0.213133	−	0.195945i
$58$	−1.90141	+	1.90141i	−0.249667	+	0.249667i
$59$	1.66786			0.217137			0.108569	−	0.994089i	$-0.465373\pi$
$59$	1.66786			0.217137			0.108569	+	0.994089i	$0.465373\pi$
$60$	0.314678	−	3.86018i	0.0406247	−	0.498347i
$61$	−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
$63$	−1.93589	+	2.29180i	−0.243899	+	0.288739i
$64$			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	0.369325	−	0.929300i	$-0.379589\pi$
$67$	−4.58359	−	4.58359i	−0.559975	−	0.559975i	−0.929300	+	0.369325i	$0.879589\pi$
$68$	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	$-0.0496474\pi$
$72$	−1.93589	+	2.29180i	−0.228147	+	0.270091i
$73$	8.49621	−	8.49621i	0.994406	−	0.994406i	−0.00557820	−	0.999984i	$-0.501776\pi$
$73$	8.49621	−	8.49621i	0.994406	−	0.994406i	0.999984	+	0.00557820i	$0.00177561\pi$
$74$	5.27645			0.613375
$75$	4.75129	+	7.24053i	0.548632	+	0.836064i
$76$	−1.26198			−0.144759
$77$	1.76064	−	1.76064i	0.200644	−	0.200644i
$78$	2.36473	+	2.17402i	0.267753	+	0.246160i
$79$			3.26305i			0.367122i	0.983008	+	0.183561i	$0.0587624\pi$
$79$			3.26305i			0.367122i	−0.983008	+	0.183561i	$0.941238\pi$
$80$	−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	$-0.214736\pi$
$83$	1.42445	+	1.42445i	0.156354	+	0.156354i	−0.624595	+	0.780949i	$0.714736\pi$
$84$	0.0727133	+	1.73052i	0.00793367	+	0.188816i
$85$	−6.75345	−	0.837169i	−0.732515	−	0.0908037i
$86$			10.1645i			1.09607i
$87$	−3.15217	+	3.42869i	−0.337948	+	0.367594i
$88$	1.76064	−	1.76064i	0.187685	−	0.187685i
$89$	−11.6683			−1.23684			−0.618420	−	0.785848i	$-0.712227\pi$
$89$	−11.6683			−1.23684			−0.618420	+	0.785848i	$0.712227\pi$
$90$	0.263871	−	6.70301i	0.0278145	−	0.706560i
$91$	1.85457			0.194412
$92$	−3.83635	+	3.83635i	−0.399968	+	0.399968i
$93$	11.8409	−	12.8796i	1.22784	−	1.33555i
$94$		−	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	0.655389	−	0.755292i	$-0.272505\pi$
$97$	−0.983930	−	0.983930i	−0.0999029	−	0.0999029i	−0.755292	+	0.655389i	$0.772505\pi$
$98$	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	$0.959222\pi$
$102$	3.88052	+	3.56757i	0.384229	+	0.353242i
$103$	10.5580	−	10.5580i	1.04032	−	1.04032i	0.0411626	−	0.999152i	$-0.486894\pi$
$103$	10.5580	−	10.5580i	1.04032	−	1.04032i	0.999152	−	0.0411626i	$-0.0131062\pi$
$104$	1.85457			0.181856
$105$	−2.50705	−	2.95207i	−0.244663	−	0.288092i
$106$	−9.32024			−0.905262
$107$	6.91089	−	6.91089i	0.668100	−	0.668100i	−0.289176	−	0.957276i	$-0.593381\pi$
$107$	6.91089	−	6.91089i	0.668100	−	0.668100i	0.957276	+	0.289176i	$0.0933811\pi$
$108$	−3.18346	+	4.10677i	−0.306329	+	0.395174i
$109$		−	9.17118i		−	0.878439i	−0.898380	−	0.439220i	$-0.855255\pi$
$109$		−	9.17118i		−	0.878439i	0.898380	−	0.439220i	$-0.144745\pi$
$110$	−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	−0.979617	−	0.200873i	$-0.935622\pi$
$113$	−12.5488	−	12.5488i	−1.18049	−	1.18049i	−0.200873	−	0.979617i	$-0.564378\pi$
$114$	−2.18388	+	0.0917624i	−0.204539	+	0.00859434i
$115$	1.49243	−	12.0395i	0.139170	−	1.12269i
$116$			2.68900i			0.249667i
$117$	4.25030	+	3.59025i	0.392941	+	0.331919i
$118$	1.17936	−	1.17936i	0.108569	−	0.108569i
$119$	3.04335			0.278984
$120$	−2.50705	−	2.95207i	−0.228861	−	0.269486i
$121$	4.80027			0.436389
$122$	−1.20598	+	1.20598i	−0.109184	+	0.109184i
$123$	12.6600	+	11.6390i	1.14151	+	1.04945i
$124$		−	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	0.246879	−	0.969046i	$-0.420595\pi$
$127$	−8.13842	−	8.13842i	−0.722168	−	0.722168i	−0.969046	+	0.246879i	$0.920595\pi$
$128$	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	$-0.131363\pi$
$132$	2.91881	−	3.17486i	0.254050	−	0.276336i
$133$	−0.892352	+	0.892352i	−0.0773767	+	0.0773767i
$134$	−6.48218			−0.559975
$135$	−0.0307628	−	11.6189i	−0.00264764	−	0.999996i
$136$	3.04335			0.260965
$137$	−10.3214	+	10.3214i	−0.881813	+	0.881813i	−0.993719	−	0.111906i	$-0.964304\pi$
$137$	−10.3214	+	10.3214i	−0.881813	+	0.881813i	0.111906	+	0.993719i	$0.464304\pi$
$138$	−6.35995	+	6.91786i	−0.541395	+	0.588887i
$139$			6.42231i			0.544733i	0.962194	+	0.272367i	$0.0878064\pi$
$139$			6.42231i			0.544733i	−0.962194	+	0.272367i	$0.912194\pi$
$140$	−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
$147$	1.27508	+	1.17225i	0.105167	+	0.0966855i
$148$	3.73101	−	3.73101i	0.306687	−	0.306687i
$149$	17.9577			1.47115			0.735576	−	0.677442i	$-0.236912\pi$
$149$	17.9577			1.47115			0.735576	+	0.677442i	$0.236912\pi$
$150$	8.47950	+	1.76016i	0.692348	+	0.143716i
$151$	−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
$153$	6.97474	+	5.89159i	0.563875	+	0.476307i
$154$		−	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	0.621910	−	0.783089i	$-0.286357\pi$
$157$	−2.01956	−	2.01956i	−0.161178	−	0.161178i	−0.783089	+	0.621910i	$0.786357\pi$
$158$	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
$162$	−5.21044	+	7.33835i	−0.409370	+	0.576555i
$163$	−10.4716	+	10.4716i	−0.820199	+	0.820199i	−0.986136	−	0.165937i	$-0.946935\pi$
$163$	−10.4716	+	10.4716i	−0.820199	+	0.820199i	0.165937	+	0.986136i	$0.446935\pi$
$164$	9.92875			0.775305
$165$	−0.783524	+	9.61155i	−0.0609973	+	0.748258i
$166$	2.01448			0.156354
$167$	4.80821	−	4.80821i	0.372071	−	0.372071i	−0.496160	−	0.868231i	$-0.665257\pi$
$167$	4.80821	−	4.80821i	0.372071	−	0.372071i	0.868231	+	0.496160i	$0.165257\pi$
$168$	1.27508	+	1.17225i	0.0983747	+	0.0904410i
$169$			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	$-0.0857172\pi$
$173$	9.17963	+	9.17963i	0.697915	+	0.697915i	−0.266046	+	0.963960i	$0.585717\pi$
$174$	0.195526	+	4.65337i	0.0148228	+	0.352771i
$175$	4.29180	−	2.56525i	0.324429	−	0.193914i
$176$		−	2.48992i		−	0.187685i
$177$	1.95515	−	2.12666i	0.146958	−	0.159850i
$178$	−8.25075	+	8.25075i	−0.618420	+	0.618420i
$179$	10.4187			0.778728			0.389364	−	0.921084i	$-0.372695\pi$
$179$	10.4187			0.778728			0.389364	+	0.921084i	$0.372695\pi$
$180$	−4.55316	−	4.92633i	−0.339373	−	0.367187i
$181$	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
$183$	−1.99928	+	2.17466i	−0.147791	+	0.160756i
$184$			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	$-0.105926\pi$
$192$	1.27508	+	1.17225i	0.0920211	+	0.0845998i
$193$	4.88918	−	4.88918i	0.351931	−	0.351931i	−0.508897	−	0.860828i	$-0.669946\pi$
$193$	4.88918	−	4.88918i	0.351931	−	0.351931i	0.860828	+	0.508897i	$0.169946\pi$
$194$	−1.39149			−0.0999029
$195$	−5.47483	+	4.64950i	−0.392061	+	0.332958i
$196$	1.00000			0.0714286
$197$	−9.74560	+	9.74560i	−0.694345	+	0.694345i	−0.963185	−	0.268840i	$-0.913360\pi$
$197$	−9.74560	+	9.74560i	−0.694345	+	0.694345i	0.268840	+	0.963185i	$0.413360\pi$
$198$	4.82022	−	5.70640i	0.342558	−	0.405536i
$199$			6.73634i			0.477526i	0.971078	+	0.238763i	$0.0767419\pi$
$199$			6.73634i			0.477526i	−0.971078	+	0.238763i	$0.923258\pi$
$200$	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
$207$	−10.5030	+	12.4340i	−0.730010	+	0.864220i
$208$	1.31138	−	1.31138i	0.0909279	−	0.0909279i
$209$	3.14223			0.217352
$210$	−3.86018	−	0.314678i	−0.266378	−	0.0217148i
$211$	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
$213$	−3.33796	−	3.06876i	−0.228713	−	0.210268i
$214$		−	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
$222$	6.18532	−	6.72790i	0.415131	−	0.451547i
$223$	−15.0658	+	15.0658i	−1.00888	+	1.00888i	−0.00891851	+	0.999960i	$0.502839\pi$
$223$	−15.0658	+	15.0658i	−1.00888	+	1.00888i	−0.999960	+	0.00891851i	$0.997161\pi$
$224$	1.00000			0.0668153
$225$	14.8020	+	2.42942i	0.986797	+	0.161962i
$226$	−17.7467			−1.18049
$227$	−18.5051	+	18.5051i	−1.22822	+	1.22822i	−0.263589	+	0.964635i	$0.584906\pi$
$227$	−18.5051	+	18.5051i	−1.22822	+	1.22822i	−0.964635	+	0.263589i	$0.915094\pi$
$228$	−1.47935	+	1.60912i	−0.0979724	+	0.106567i
$229$			8.01695i			0.529775i	0.964279	+	0.264887i	$0.0853348\pi$
$229$			8.01695i			0.529775i	−0.964279	+	0.264887i	$0.914665\pi$
$230$	−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	$-0.00577580\pi$
$233$	14.9849	+	14.9849i	0.981691	+	0.981691i	−0.0181442	+	0.999835i	$0.505776\pi$
$234$	5.54411	−	0.466730i	0.362430	−	0.0305111i
$235$	29.7452	+	3.68726i	1.94036	+	0.240531i
$236$		−	1.66786i		−	0.108569i
$237$	4.16065	+	3.82510i	0.270263	+	0.248467i
$238$	2.15197	−	2.15197i	0.139492	−	0.139492i
$239$	16.0367			1.03733			0.518664	−	0.854978i	$-0.326430\pi$
$239$	16.0367			1.03733			0.518664	+	0.854978i	$0.326430\pi$
$240$	−3.86018	−	0.314678i	−0.249173	−	0.0203124i
$241$	−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
$243$	−8.48319	+	13.0781i	−0.544197	+	0.838958i
$244$			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	$0.734093\pi$
$252$	2.29180	+	1.93589i	0.144370	+	0.121950i
$253$	9.55223	−	9.55223i	0.600544	−	0.600544i
$254$	−11.5095			−0.722168
$255$	−8.98419	+	7.62983i	−0.562612	+	0.477798i
$256$	1.00000			0.0625000
$257$	14.3897	−	14.3897i	0.897604	−	0.897604i	−0.0976195	−	0.995224i	$-0.531123\pi$
$257$	14.3897	−	14.3897i	0.897604	−	0.897604i	0.995224	+	0.0976195i	$0.0311228\pi$
$258$	12.9606	+	11.9153i	0.806891	+	0.741817i
$259$		−	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	$-0.395524\pi$
$263$	−10.1237	−	10.1237i	−0.624257	−	0.624257i	−0.946617	+	0.322360i	$0.895524\pi$
$264$	−0.181051	−	4.30887i	−0.0111429	−	0.265193i
$265$	2.56382	−	20.6824i	0.157494	−	1.27051i
$266$			1.26198i			0.0773767i
$267$	−13.6782	+	14.8781i	−0.837091	+	0.910522i
$268$	−4.58359	+	4.58359i	−0.279988	+	0.279988i
$269$	26.0829			1.59030			0.795151	−	0.606412i	$-0.207392\pi$
$269$	26.0829			1.59030			0.795151	+	0.606412i	$0.207392\pi$
$270$	−8.23756	−	8.19406i	−0.501322	−	0.498674i
$271$	−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
$273$	2.17402	−	2.36473i	0.131578	−	0.143120i
$274$			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	0.829705	−	0.558203i	$-0.188509\pi$
$277$	4.51869	+	4.51869i	0.271502	+	0.271502i	−0.558203	+	0.829705i	$0.688509\pi$
$278$	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	$-0.192681\pi$
$282$	−17.0915	−	15.7131i	−1.01779	−	0.935704i
$283$	−10.8604	+	10.8604i	−0.645583	+	0.645583i	−0.951922	−	0.306340i	$-0.900896\pi$
$283$	−10.8604	+	10.8604i	−0.645583	+	0.645583i	0.306340	+	0.951922i	$0.400896\pi$
$284$	−2.61784			−0.155340
$285$	0.397116	−	4.87145i	0.0235231	−	0.288560i
$286$	−4.61775			−0.273053
$287$	7.02069	−	7.02069i	0.414418	−	0.414418i
$288$	2.29180	+	1.93589i	0.135045	+	0.114073i
$289$			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	$-0.157799\pi$
$293$	6.91427	+	6.91427i	0.403936	+	0.403936i	−0.475682	+	0.879617i	$0.657799\pi$
$294$	1.73052	−	0.0727133i	0.100926	−	0.00424072i
$295$	2.29268	+	2.94151i	0.133485	+	0.171262i
$296$		−	5.27645i		−	0.306687i
$297$	7.92657	−	10.2256i	0.459946	−	0.593347i
$298$	12.6980	−	12.6980i	0.735576	−	0.735576i
$299$	10.0618			0.581892
$300$	7.24053	−	4.75129i	0.418032	−	0.274316i
$301$	10.1645			0.585873
$302$	−4.41877	+	4.41877i	−0.254271	+	0.254271i
$303$	3.27428	+	3.01022i	0.188103	+	0.172933i
$304$			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	0.869419	−	0.494076i	$-0.164494\pi$
$307$	6.57653	+	6.57653i	0.375343	+	0.375343i	−0.494076	+	0.869419i	$0.664494\pi$
$308$	−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	$-0.356042\pi$
$312$	2.17402	−	2.36473i	0.123080	−	0.133877i
$313$	7.97460	−	7.97460i	0.450751	−	0.450751i	−0.444853	−	0.895604i	$-0.646744\pi$
$313$	7.97460	−	7.97460i	0.450751	−	0.450751i	0.895604	+	0.444853i	$0.146744\pi$
$314$	−2.85609			−0.161178
$315$	−6.70301	−	0.263871i	−0.377672	−	0.0148675i
$316$	3.26305			0.183561
$317$	7.61016	−	7.61016i	0.427429	−	0.427429i	−0.460323	−	0.887752i	$-0.652266\pi$
$317$	7.61016	−	7.61016i	0.427429	−	0.427429i	0.887752	+	0.460323i	$0.152266\pi$
$318$	−10.9256	+	11.8841i	−0.612680	+	0.666425i
$319$		−	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
$327$	−11.6940	−	10.7509i	−0.646679	−	0.594526i
$328$	7.02069	−	7.02069i	0.387653	−	0.387653i
$329$	−13.4043			−0.739002
$330$	6.24236	+	7.35043i	0.343631	+	0.404628i
$331$	−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
$333$	10.2146	−	12.0926i	0.559758	−	0.662668i
$334$		−	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	0.996369	−	0.0851350i	$-0.0271321\pi$
$337$	16.7280	+	16.7280i	0.911234	+	0.911234i	−0.0851350	+	0.996369i	$0.527132\pi$
$338$	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
$342$	−2.44305	+	2.89219i	−0.132105	+	0.156392i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	10.1645			0.548034
$345$	−13.6018	−	16.0162i	−0.732296	−	0.862285i
$346$	12.9820			0.697915
$347$	12.6747	−	12.6747i	0.680411	−	0.680411i	−0.279682	−	0.960093i	$-0.590229\pi$
$347$	12.6747	−	12.6747i	0.680411	−	0.680411i	0.960093	+	0.279682i	$0.0902289\pi$
$348$	3.42869	+	3.15217i	0.183797	+	0.168974i
$349$		−	3.51880i		−	0.188357i	−0.995555	−	0.0941786i	$-0.969978\pi$
$349$		−	3.51880i		−	0.188357i	0.995555	−	0.0941786i	$-0.0300225\pi$
$350$	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	$-0.0443353\pi$
$353$	15.9979	+	15.9979i	0.851482	+	0.851482i	−0.138834	+	0.990316i	$0.544335\pi$
$354$	−0.121276	−	2.88628i	−0.00644574	−	0.153404i
$355$	4.61693	−	3.59853i	0.245041	−	0.190990i
$356$			11.6683i			0.618420i
$357$	3.56757	−	3.88052i	0.188816	−	0.205379i
$358$	7.36712	−	7.36712i	0.389364	−	0.389364i
$359$	−32.9263			−1.73778			−0.868891	−	0.495004i	$-0.835167\pi$
$359$	−32.9263			−1.73778			−0.868891	+	0.495004i	$0.835167\pi$
$360$	−6.70301	−	0.263871i	−0.353280	−	0.0139072i
$361$	17.4074			0.916180
$362$	2.45674	−	2.45674i	0.129124	−	0.129124i
$363$	5.62712	−	6.12074i	0.295347	−	0.321256i
$364$		−	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	0.342467	−	0.939530i	$-0.388737\pi$
$367$	−11.4381	−	11.4381i	−0.597062	−	0.597062i	−0.939530	+	0.342467i	$0.888737\pi$
$368$	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
$372$	−12.8796	−	11.8409i	−0.667777	−	0.613922i
$373$	−19.1458	+	19.1458i	−0.991330	+	0.991330i	−0.999963	−	0.00863259i	$-0.997252\pi$
$373$	−19.1458	+	19.1458i	−0.991330	+	0.991330i	0.00863259	+	0.999963i	$0.497252\pi$
$374$	−7.57772			−0.391834
$375$	−6.23849	+	18.3325i	−0.322154	+	0.946687i
$376$	−13.4043			−0.691273
$377$	3.52630	−	3.52630i	0.181614	−	0.181614i
$378$	4.10677	+	3.18346i	0.211230	+	0.163739i
$379$		−	9.89995i		−	0.508526i	−0.967135	−	0.254263i	$-0.918167\pi$
$379$		−	9.89995i		−	0.508526i	0.967135	−	0.254263i	$-0.0818329\pi$
$380$	−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	$-0.295134\pi$
$383$	−3.91121	−	3.91121i	−0.199853	−	0.199853i	−0.799937	+	0.600084i	$0.795134\pi$
$384$	1.73052	−	0.0727133i	0.0883104	−	0.00371063i
$385$	5.52535	+	0.684931i	0.281598	+	0.0349073i
$386$		−	6.91435i		−	0.351931i
$387$	23.2950	+	19.6774i	1.18415	+	1.00026i
$388$	−0.983930	+	0.983930i	−0.0499515	+	0.0499515i
$389$	−18.4682			−0.936373			−0.468186	−	0.883630i	$-0.655092\pi$
$389$	−18.4682			−0.936373			−0.468186	+	0.883630i	$0.655092\pi$
$390$	−0.583593	+	7.15898i	−0.0295514	+	0.362509i
$391$	16.5115			0.835021
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$	−11.7066	−	10.7625i	−0.590518	−	0.542894i
$394$			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	0.981105	−	0.193477i	$-0.0619765\pi$
$397$	15.6934	+	15.6934i	0.787628	+	0.787628i	−0.193477	+	0.981105i	$0.561977\pi$
$398$	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	$-0.0265994\pi$
$402$	−7.59873	+	8.26531i	−0.378990	+	0.412236i
$403$	−13.2463	+	13.2463i	−0.659844	+	0.659844i
$404$	2.56790			0.127758
$405$	−14.8511	−	13.5810i	−0.737958	−	0.674847i
$406$	2.68900			0.133453
$407$	−9.28995	+	9.28995i	−0.460485	+	0.460485i
$408$	3.56757	−	3.88052i	0.176621	−	0.192114i
$409$			15.4069i			0.761824i	0.924611	+	0.380912i	$0.124390\pi$
$409$			15.4069i			0.761824i	−0.924611	+	0.380912i	$0.875610\pi$
$410$	−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
$417$	8.18897	+	7.52855i	0.401016	+	0.368675i
$418$	2.22189	−	2.22189i	0.108676	−	0.108676i
$419$	−12.4526			−0.608350			−0.304175	−	0.952616i	$-0.598381\pi$
$419$	−12.4526			−0.608350			−0.304175	+	0.952616i	$0.598381\pi$
$420$	−2.95207	+	2.50705i	−0.144046	+	0.122331i
$421$	−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
$423$	−30.7199	−	25.9492i	−1.49365	−	1.26169i
$424$			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	$-0.0305149\pi$
$432$	4.10677	+	3.18346i	0.197587	+	0.153164i
$433$	−4.89906	+	4.89906i	−0.235434	+	0.235434i	−0.814956	−	0.579522i	$-0.803239\pi$
$433$	−4.89906	+	4.89906i	−0.235434	+	0.235434i	0.579522	+	0.814956i	$0.303239\pi$
$434$	−10.1010			−0.484864
$435$	−10.3800	−	0.846167i	−0.497683	−	0.0405706i
$436$	−9.17118			−0.439220
$437$	−4.84139	+	4.84139i	−0.231595	+	0.231595i
$438$	−15.3207	−	14.0851i	−0.732051	−	0.673012i
$439$			31.2830i			1.49306i	0.665353	+	0.746528i	$0.268281\pi$
$439$			31.2830i			1.49306i	−0.665353	+	0.746528i	$0.731719\pi$
$440$	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	$-0.377141\pi$
$443$	−11.5755	−	11.5755i	−0.549971	−	0.549971i	−0.926432	+	0.376462i	$0.877141\pi$
$444$	−0.383668	−	9.13102i	−0.0182081	−	0.433339i
$445$	−16.0395	−	20.5787i	−0.760344	−	0.975525i
$446$			21.3062i			1.00888i
$447$	21.0509	−	22.8975i	0.995673	−	1.08302i
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$	0.439882			0.0207593			0.0103796	−	0.999946i	$-0.496696\pi$
$449$	0.439882			0.0207593			0.0103796	+	0.999946i	$0.496696\pi$
$450$	12.1844	−	8.74870i	0.574379	−	0.412418i
$451$	−24.7218			−1.16411
$452$	−12.5488	+	12.5488i	−0.590245	+	0.590245i
$453$	−7.32548	+	7.96808i	−0.344181	+	0.374373i
$454$			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	0.643839	−	0.765161i	$-0.277341\pi$
$457$	−2.59356	−	2.59356i	−0.121322	−	0.121322i	−0.765161	+	0.643839i	$0.777341\pi$
$458$	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	$0.915934\pi$
$462$	−3.17486	−	2.91881i	−0.147708	−	0.135795i
$463$	−1.38982	+	1.38982i	−0.0645903	+	0.0645903i	−0.738664	−	0.674074i	$-0.764543\pi$
$463$	−1.38982	+	1.38982i	−0.0645903	+	0.0645903i	0.674074	+	0.738664i	$0.264543\pi$
$464$	2.68900			0.124834
$465$	38.9917	+	3.17857i	1.80820	+	0.147402i
$466$	21.1918			0.981691
$467$	−3.70297	+	3.70297i	−0.171353	+	0.171353i	−0.787574	−	0.616221i	$-0.788663\pi$
$467$	−3.70297	+	3.70297i	−0.171353	+	0.171353i	0.616221	+	0.787574i	$0.288663\pi$
$468$	3.59025	−	4.25030i	0.165959	−	0.196470i
$469$			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
$477$	−18.0430	+	21.3601i	−0.826130	+	0.978011i
$478$	11.3397	−	11.3397i	0.518664	−	0.518664i
$479$	6.21338			0.283897			0.141948	−	0.989874i	$-0.454663\pi$
$479$	6.21338			0.283897			0.141948	+	0.989874i	$0.454663\pi$
$480$	−2.95207	+	2.50705i	−0.134743	+	0.114431i
$481$	−9.78557			−0.446183
$482$	−11.3312	+	11.3312i	−0.516121	+	0.516121i
$483$	6.91786	+	6.35995i	0.314773	+	0.289388i
$484$		−	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	0.480187	−	0.877166i	$-0.340569\pi$
$487$	−8.76055	−	8.76055i	−0.396979	−	0.396979i	−0.877166	+	0.480187i	$0.840569\pi$
$488$	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	$0.886356\pi$
$492$	11.6390	−	12.6600i	0.524725	−	0.570755i
$493$	5.78665	−	5.78665i	0.260618	−	0.260618i
$494$	2.34043			0.105301
$495$	11.3370	+	12.2662i	0.509561	+	0.551324i
$496$	−10.1010			−0.453549
$497$	−1.85109	+	1.85109i	−0.0830328	+	0.0830328i
$498$	2.36147	−	2.56862i	0.105820	−	0.115103i
$499$		−	33.2574i		−	1.48880i	−0.667732	−	0.744402i	$-0.732735\pi$
$499$		−	33.2574i		−	1.48880i	0.667732	−	0.744402i	$-0.267265\pi$
$500$	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	$-0.0961650\pi$
$503$	14.7389	+	14.7389i	0.657174	+	0.657174i	−0.297536	+	0.954710i	$0.596165\pi$
$504$	2.98943	−	0.251664i	0.133160	−	0.0112100i
$505$	−4.52886	+	3.52988i	−0.201532	+	0.157078i
$506$		−	13.5089i		−	0.600544i
$507$	12.1905	+	11.2074i	0.541399	+	0.497736i
$508$	−8.13842	+	8.13842i	−0.361084	+	0.361084i
$509$	−2.69010			−0.119236			−0.0596182	−	0.998221i	$-0.518988\pi$
$509$	−2.69010			−0.119236			−0.0596182	+	0.998221i	$0.518988\pi$
$510$	−0.957675	+	11.7479i	−0.0424066	+	0.520205i
$511$	−12.0155			−0.531532
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−4.01745	+	5.18265i	−0.177375	+	0.228820i
$514$		−	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	$-0.0519939\pi$
$522$	6.16263	+	5.20560i	0.269731	+	0.227843i
$523$	12.4973	−	12.4973i	0.546470	−	0.546470i	−0.378948	−	0.925418i	$-0.623714\pi$
$523$	12.4973	−	12.4973i	0.546470	−	0.546470i	0.925418	+	0.378948i	$0.123714\pi$
$524$	−9.18103			−0.401075
$525$	1.76016	−	8.47950i	0.0768196	−	0.370076i
$526$	−14.3171			−0.624257
$527$	−21.7371	+	21.7371i	−0.946884	+	0.946884i
$528$	−3.17486	−	2.91881i	−0.138168	−	0.127025i
$529$			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
$537$	12.2133	−	13.2847i	0.527042	−	0.573275i
$538$	18.4434	−	18.4434i	0.795151	−	0.795151i
$539$	−2.48992			−0.107249
$540$	−11.6189	+	0.0307628i	−0.499998	+	0.00132382i
$541$	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
$543$	4.07282	−	4.43009i	0.174781	−	0.190113i
$544$		−	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	0.487184	−	0.873299i	$-0.338024\pi$
$547$	−9.03049	−	9.03049i	−0.386116	−	0.386116i	−0.873299	+	0.487184i	$0.838024\pi$
$548$	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
$552$	6.91786	+	6.35995i	0.294443	+	0.270697i
$553$	2.30732	−	2.30732i	0.0981174	−	0.0981174i
$554$	6.39040			0.271502
$555$	13.2283	+	15.5764i	0.561511	+	0.661183i
$556$	6.42231			0.272367
$557$	22.4290	−	22.4290i	0.950345	−	0.950345i	−0.0484790	−	0.998824i	$-0.515437\pi$
$557$	22.4290	−	22.4290i	0.950345	−	0.950345i	0.998824	+	0.0484790i	$0.0154374\pi$
$558$	−23.1495	−	19.5545i	−0.979995	−	0.827806i
$559$		−	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	$-0.289320\pi$
$563$	−4.13454	−	4.13454i	−0.174250	−	0.174250i	−0.788844	+	0.614594i	$0.789320\pi$
$564$	−23.1964	+	0.974669i	−0.976745	+	0.0410410i
$565$	4.88177	−	39.3813i	0.205378	−	1.65678i
$566$			15.3589i			0.645583i
$567$	7.33835	+	5.21044i	0.308182	+	0.218818i
$568$	−1.85109	+	1.85109i	−0.0776701	+	0.0776701i
$569$	−18.9758			−0.795507			−0.397754	−	0.917492i	$-0.630210\pi$
$569$	−18.9758			−0.795507			−0.397754	+	0.917492i	$0.630210\pi$
$570$	−3.16383	−	3.72544i	−0.132518	−	0.156042i
$571$	−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
$573$	−11.5131	−	10.5846i	−0.480966	−	0.442177i
$574$		−	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	0.743482	−	0.668756i	$-0.233173\pi$
$577$	1.79499	+	1.79499i	0.0747263	+	0.0747263i	−0.668756	+	0.743482i	$0.733173\pi$
$578$	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
$582$	−1.63117	+	1.77426i	−0.0676141	+	0.0735454i
$583$	16.4096	−	16.4096i	0.679617	−	0.679617i
$584$	−12.0155			−0.497203
$585$	−0.489368	+	12.4312i	−0.0202329	+	0.513968i
$586$	9.77825			0.403936
$587$	−4.68454	+	4.68454i	−0.193352	+	0.193352i	−0.797143	−	0.603791i	$-0.793656\pi$
$587$	−4.68454	+	4.68454i	−0.193352	+	0.193352i	0.603791	+	0.797143i	$0.293656\pi$
$588$	1.17225	−	1.27508i	0.0483427	−	0.0525835i
$589$		−	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	$-0.328394\pi$
$593$	−8.39604	−	8.39604i	−0.344784	−	0.344784i	−0.858162	+	0.513378i	$0.828394\pi$
$594$	−1.62563	−	12.8355i	−0.0667003	−	0.526647i
$595$	4.18344	+	5.36738i	0.171504	+	0.220041i
$596$		−	17.9577i		−	0.735576i
$597$	8.58938	+	7.89666i	0.351540	+	0.323189i
$598$	7.11480	−	7.11480i	0.290946	−	0.290946i
$599$	−16.7879			−0.685935			−0.342968	−	0.939347i	$-0.611432\pi$
$599$	−16.7879			−0.685935			−0.342968	+	0.939347i	$0.611432\pi$
$600$	1.76016	−	8.47950i	0.0718582	−	0.346174i
$601$	−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
$603$	−12.5488	+	14.8558i	−0.511026	+	0.604976i
$604$			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	0.0922293	−	0.995738i	$-0.470601\pi$
$607$	−22.2601	−	22.2601i	−0.903509	−	0.903509i	−0.995738	+	0.0922293i	$0.970601\pi$
$608$	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
$612$	5.89159	−	6.97474i	0.238154	−	0.281937i
$613$	−4.97308	+	4.97308i	−0.200861	+	0.200861i	−0.800369	−	0.599508i	$-0.795363\pi$
$613$	−4.97308	+	4.97308i	−0.200861	+	0.200861i	0.599508	+	0.800369i	$0.295363\pi$
$614$	9.30062			0.375343
$615$	−3.12436	+	38.3268i	−0.125986	+	1.54548i
$616$	−2.48992			−0.100322
$617$	−17.9613	+	17.9613i	−0.723094	+	0.723094i	−0.969234	−	0.246140i	$-0.920838\pi$
$617$	−17.9613	+	17.9613i	−0.723094	+	0.723094i	0.246140	+	0.969234i	$0.420838\pi$
$618$	−19.0387	−	17.5032i	−0.765847	−	0.704084i
$619$		−	2.56903i		−	0.103258i	−0.998666	−	0.0516291i	$-0.983559\pi$
$619$		−	2.56903i		−	0.103258i	0.998666	−	0.0516291i	$-0.0164414\pi$
$620$	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
$627$	3.68347	−	4.00659i	0.147104	−	0.160008i
$628$	−2.01956	+	2.01956i	−0.0805892	+	0.0805892i
$629$	−16.0581			−0.640278
$630$	−4.92633	+	4.55316i	−0.196270	+	0.181402i
$631$	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
$633$	28.1929	−	30.6661i	1.12057	−	1.21887i
$634$		−	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	$-0.0376904\pi$
$642$	−12.4620	−	11.4569i	−0.491835	−	0.452169i
$643$	10.3036	−	10.3036i	0.406335	−	0.406335i	−0.474123	−	0.880458i	$-0.657235\pi$
$643$	10.3036	−	10.3036i	0.406335	−	0.406335i	0.880458	+	0.474123i	$0.157235\pi$
$644$	5.42542			0.213792
$645$	−30.0064	+	25.4829i	−1.18150	+	1.00339i
$646$	3.84064			0.151108
$647$	14.4071	−	14.4071i	0.566401	−	0.566401i	−0.364717	−	0.931118i	$-0.618834\pi$
$647$	14.4071	−	14.4071i	0.566401	−	0.566401i	0.931118	+	0.364717i	$0.118834\pi$
$648$	7.33835	+	5.21044i	0.288278	+	0.204685i
$649$			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	0.986800	+	0.161945i	$0.0517767\pi$
$653$	29.3549	+	29.3549i	1.14874	+	1.14874i	0.161945	+	0.986800i	$0.448223\pi$
$654$	−15.8709	+	0.666866i	−0.620603	+	0.0260765i
$655$	16.1920	−	12.6204i	0.632675	−	0.493120i
$656$		−	9.92875i		−	0.387653i
$657$	−27.5370	−	23.2606i	−1.07432	−	0.907482i
$658$	−9.47825	+	9.47825i	−0.369501	+	0.369501i
$659$	−14.4888			−0.564403			−0.282202	−	0.959355i	$-0.591065\pi$
$659$	−14.4888			−0.564403			−0.282202	+	0.959355i	$0.591065\pi$
$660$	9.61155	+	0.783524i	0.374129	+	0.0304986i
$661$	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
$663$	−7.19671	−	6.61631i	−0.279497	−	0.256956i
$664$		−	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
$672$	1.17225	−	1.27508i	0.0452205	−	0.0491873i
$673$	2.40134	−	2.40134i	0.0925647	−	0.0925647i	−0.659308	−	0.751873i	$-0.729151\pi$
$673$	2.40134	−	2.40134i	0.0925647	−	0.0925647i	0.751873	+	0.659308i	$0.229151\pi$
$674$	23.6570			0.911234
$675$	20.4493	−	16.0258i	0.787094	−	0.616834i
$676$	9.56056			0.367714
$677$	−32.4655	+	32.4655i	−1.24775	+	1.24775i	−0.291038	+	0.956711i	$0.594001\pi$
$677$	−32.4655	+	32.4655i	−1.24775	+	1.24775i	−0.956711	+	0.291038i	$0.905999\pi$
$678$	−20.8035	+	22.6284i	−0.798954	+	0.869040i
$679$			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	$-0.0649442\pi$
$683$	20.2970	+	20.2970i	0.776643	+	0.776643i	−0.202616	+	0.979258i	$0.564944\pi$
$684$	0.317594	+	3.77258i	0.0121435	+	0.144248i
$685$	−32.3911	−	4.01525i	−1.23760	−	0.153415i
$686$		−	1.00000i		−	0.0381802i
$687$	10.2223	+	9.39786i	0.390004	+	0.358551i
$688$	7.18740	−	7.18740i	0.274017	−	0.274017i
$689$	17.2851			0.658509
$690$	−20.9431	−	1.70726i	−0.797290	−	0.0649943i
$691$	−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
$693$	−5.70640	−	4.82022i	−0.216768	−	0.183105i
$694$		−	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	$0.719880\pi$
$702$	5.90396	−	7.61631i	0.222831	−	0.287459i
$703$	4.70845	−	4.70845i	0.177583	−	0.177583i
$704$	−2.48992			−0.0938426
$705$	39.5703	−	33.6052i	1.49031	−	1.26564i
$706$	22.6244			0.851482
$707$	1.81578	−	1.81578i	0.0682895	−	0.0682895i
$708$	−2.12666	−	1.95515i	−0.0799249	−	0.0734791i
$709$		−	39.7104i		−	1.49136i	−0.666307	−	0.745678i	$-0.732126\pi$
$709$		−	39.7104i		−	1.49136i	0.666307	−	0.745678i	$-0.267874\pi$
$710$	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
$717$	18.7990	−	20.4481i	0.702062	−	0.763648i
$718$	−23.2824	+	23.2824i	−0.868891	+	0.868891i
$719$	−11.2595			−0.419907			−0.209954	−	0.977711i	$-0.567331\pi$
$719$	−11.2595			−0.419907			−0.209954	+	0.977711i	$0.567331\pi$
$720$	−4.92633	+	4.55316i	−0.183593	+	0.169686i
$721$	−14.9313			−0.556072
$722$	12.3089	−	12.3089i	0.458090	−	0.458090i
$723$	−18.7849	+	20.4328i	−0.698619	+	0.759903i
$724$		−	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	0.580345	−	0.814371i	$-0.302918\pi$
$727$	−6.31002	−	6.31002i	−0.234026	−	0.234026i	−0.814371	+	0.580345i	$0.802918\pi$
$728$	−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
$732$	2.17466	+	1.99928i	0.0803779	+	0.0738956i
$733$	−26.3661	+	26.3661i	−0.973855	+	0.973855i	−0.999667	−	0.0258120i	$-0.991783\pi$
$733$	−26.3661	+	26.3661i	−0.973855	+	0.973855i	0.0258120	+	0.999667i	$0.491783\pi$
$734$	−16.1759			−0.597062
$735$	−0.314678	+	3.86018i	−0.0116071	+	0.142385i
$736$	5.42542			0.199984
$737$	11.4128	−	11.4128i	0.420396	−	0.420396i
$738$	19.2210	−	22.7547i	0.707534	−	0.837611i
$739$			29.8538i			1.09819i	0.835761	+	0.549094i	$0.185027\pi$
$739$			29.8538i			1.09819i	−0.835761	+	0.549094i	$0.814973\pi$
$740$	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	$-0.367936\pi$
$743$	−13.9580	−	13.9580i	−0.512068	−	0.512068i	−0.915160	+	0.403092i	$0.867936\pi$
$744$	−17.4800	+	0.734478i	−0.640850	+	0.0269273i
$745$	24.6850	+	31.6709i	0.904387	+	1.16033i
$746$			27.0762i			0.991330i
$747$	3.89980	−	4.61677i	0.142686	−	0.168919i
$748$	−5.35826	+	5.35826i	−0.195917	+	0.195917i
$749$	−9.77347			−0.357115
$750$	8.55177	+	17.3743i	0.312267	+	0.634421i
$751$	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
$753$	29.9600	+	27.5438i	1.09180	+	1.00375i
$754$		−	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	0.877166	−	0.480187i	$-0.159431\pi$
$757$	10.9223	+	10.9223i	0.396979	+	0.396979i	−0.480187	+	0.877166i	$0.659431\pi$
$758$	−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	$-0.162383\pi$
$762$	−13.4920	+	14.6755i	−0.488762	+	0.531637i
$763$	−6.48500	+	6.48500i	−0.234773	+	0.234773i
$764$	−9.02930			−0.326668
$765$	−0.803053	+	20.3996i	−0.0290344	+	0.737550i
$766$	−5.53128			−0.199853
$767$	−2.18721	+	2.18721i	−0.0789755	+	0.0789755i
$768$	1.17225	−	1.27508i	0.0422999	−	0.0460105i
$769$		−	19.3890i		−	0.699185i	−0.936902	−	0.349592i	$-0.886320\pi$
$769$		−	19.3890i		−	0.699185i	0.936902	−	0.349592i	$-0.113680\pi$
$770$	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	0.970885	+	0.239546i	$0.0769985\pi$
$773$	33.6535	+	33.6535i	1.21043	+	1.21043i	0.239546	+	0.970885i	$0.423002\pi$
$774$	30.3861	−	2.55804i	1.09220	−	0.0919470i
$775$	−12.3319	+	48.9764i	−0.442974	+	1.75928i
$776$			1.39149i			0.0499515i
$777$	−6.72790	−	6.18532i	−0.241362	−	0.221897i
$778$	−13.0590	+	13.0590i	−0.468186	+	0.468186i
$779$	12.5298			0.448928
$780$	4.64950	+	5.47483i	0.166479	+	0.196030i
$781$	6.51822			0.233240
$782$	11.6754	−	11.6754i	0.417511	−	0.417511i
$783$	11.0431	+	8.56031i	0.394648	+	0.305921i
$784$		−	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	0.853269	−	0.521472i	$-0.174617\pi$
$787$	9.30807	+	9.30807i	0.331797	+	0.331797i	−0.521472	+	0.853269i	$0.674617\pi$
$788$	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
$792$	−5.70640	−	4.82022i	−0.202768	−	0.171279i
$793$	2.23657	−	2.23657i	0.0794231	−	0.0794231i
$794$	22.1938			0.787628
$795$	−23.3663	−	27.5140i	−0.828717	−	0.975821i
$796$	6.73634			0.238763
$797$	30.9837	−	30.9837i	1.09750	−	1.09750i	0.102795	−	0.994703i	$-0.467221\pi$
$797$	30.9837	−	30.9837i	1.09750	−	1.09750i	0.994703	−	0.102795i	$-0.0327786\pi$
$798$	1.60912	+	1.47935i	0.0569623	+	0.0523684i
$799$			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
$807$	30.5756	−	33.2578i	1.07631	−	1.17073i
$808$	1.81578	−	1.81578i	0.0638790	−	0.0638790i
$809$	−37.5965			−1.32182			−0.660911	−	0.750464i	$-0.729830\pi$
$809$	−37.5965			−1.32182			−0.660911	+	0.750464i	$0.729830\pi$
$810$	−20.1046	+	0.898085i	−0.706402	+	0.0315555i
$811$	−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
$813$	−4.03350	+	4.38733i	−0.141461	+	0.153870i
$814$			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	$-0.338246\pi$
$822$	18.6118	+	17.1109i	0.649163	+	0.596809i
$823$	−33.3463	+	33.3463i	−1.16238	+	1.16238i	−0.178425	+	0.983953i	$0.557100\pi$
$823$	−33.3463	+	33.3463i	−1.16238	+	1.16238i	−0.983953	+	0.178425i	$0.942900\pi$
$824$	−14.9313			−0.520158
$825$	−18.0284	+	11.8304i	−0.627667	+	0.411880i
$826$	−1.66786			−0.0580324
$827$	11.0886	−	11.0886i	0.385588	−	0.385588i	−0.487522	−	0.873110i	$-0.662099\pi$
$827$	11.0886	−	11.0886i	0.385588	−	0.385588i	0.873110	+	0.487522i	$0.162099\pi$
$828$	12.4340	+	10.5030i	0.432110	+	0.365005i
$829$		−	22.1675i		−	0.769909i	−0.922936	−	0.384954i	$-0.874217\pi$
$829$		−	22.1675i		−	0.769909i	0.922936	−	0.384954i	$-0.125783\pi$
$830$	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
$837$	−41.4826	−	32.1562i	−1.43385	−	1.11148i
$838$	−8.80532	+	8.80532i	−0.304175	+	0.304175i
$839$	32.9972			1.13919			0.569595	−	0.821925i	$-0.307100\pi$
$839$	32.9972			1.13919			0.569595	+	0.821925i	$0.307100\pi$
$840$	−0.314678	+	3.86018i	−0.0108574	+	0.133189i
$841$	−21.7693			−0.750665
$842$	−17.5114	+	17.5114i	−0.603482	+	0.603482i
$843$	−24.3252	−	22.3634i	−0.837805	−	0.770238i
$844$		−	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
$852$	−3.06876	+	3.33796i	−0.105134	+	0.114357i
$853$	3.03563	−	3.03563i	0.103938	−	0.103938i	−0.653225	−	0.757163i	$-0.726585\pi$
$853$	3.03563	−	3.03563i	0.103938	−	0.103938i	0.757163	+	0.653225i	$0.226585\pi$
$854$	1.70551			0.0583614
$855$	−5.74598	−	6.21691i	−0.196508	−	0.212614i
$856$	−9.77347			−0.334050
$857$	−33.3587	+	33.3587i	−1.13951	+	1.13951i	−0.150972	+	0.988538i	$0.548240\pi$
$857$	−33.3587	+	33.3587i	−1.13951	+	1.13951i	−0.988538	+	0.150972i	$0.951760\pi$
$858$	−5.41315	+	5.88800i	−0.184802	+	0.201013i
$859$			10.1819i			0.347402i	0.984798	+	0.173701i	$0.0555726\pi$
$859$			10.1819i			0.347402i	−0.984798	+	0.173701i	$0.944427\pi$
$860$	−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	$-0.205881\pi$
$863$	5.73988	+	5.73988i	0.195388	+	0.195388i	−0.602632	+	0.798019i	$0.705881\pi$
$864$	5.15497	−	0.652882i	0.175376	−	0.0222115i
$865$	−3.57109	+	28.8081i	−0.121421	+	0.979503i
$866$			6.92832i			0.235434i
$867$	9.86659	+	9.07087i	0.335087	+	0.308063i
$868$	−7.14250	+	7.14250i	−0.242432	+	0.242432i
$869$	−8.12474			−0.275613
$870$	−7.93810	+	6.74144i	−0.269127	+	0.228556i
$871$	12.0217			0.407339
$872$	−6.48500	+	6.48500i	−0.219610	+	0.219610i
$873$	−2.69376	+	3.18900i	−0.0911701	+	0.107931i
$874$			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	0.692359	−	0.721553i	$-0.256571\pi$
$877$	−0.864549	−	0.864549i	−0.0291937	−	0.0291937i	−0.721553	+	0.692359i	$0.756571\pi$
$878$	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	$-0.128425\pi$
$882$	1.93589	−	2.29180i	0.0651848	−	0.0771688i
$883$	−2.59691	+	2.59691i	−0.0873928	+	0.0873928i	−0.749452	−	0.662059i	$-0.769683\pi$
$883$	−2.59691	+	2.59691i	−0.0873928	+	0.0873928i	0.662059	+	0.749452i	$0.269683\pi$
$884$	−5.64412			−0.189832
$885$	6.43826	+	0.524840i	0.216420	+	0.0176423i
$886$	−16.3703			−0.549971
$887$	−11.5313	+	11.5313i	−0.387183	+	0.387183i	−0.873681	−	0.486499i	$-0.838274\pi$
$887$	−11.5313	+	11.5313i	−0.387183	+	0.387183i	0.486499	+	0.873681i	$0.338274\pi$
$888$	−6.72790	−	6.18532i	−0.225774	−	0.207566i
$889$			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
$897$	11.7950	−	12.8297i	0.393823	−	0.428370i
$898$	0.311043	−	0.311043i	0.0103796	−	0.0103796i
$899$	−27.1616			−0.905890
$900$	2.42942	−	14.8020i	0.0809808	−	0.493399i
$901$	28.3648			0.944967
$902$	−17.4810	+	17.4810i	−0.582053	+	0.582053i
$903$	11.9153	−	12.9606i	0.396518	−	0.431301i
$904$			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	0.997152	+	0.0754116i	$0.0240271\pi$
$907$	32.3018	+	32.3018i	1.07256	+	1.07256i	0.0754116	+	0.997152i	$0.475973\pi$
$908$	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	$0.977368\pi$
$912$	1.60912	+	1.47935i	0.0532834	+	0.0489862i
$913$	−3.54677	+	3.54677i	−0.117381	+	0.117381i
$914$	−3.66785			−0.121322
$915$	−6.58358	−	0.536686i	−0.217646	−	0.0177423i
$916$	8.01695			0.264887
$917$	−6.49197	+	6.49197i	−0.214384	+	0.214384i
$918$	9.68839	−	12.4984i	0.319764	−	0.412507i
$919$		−	32.7595i		−	1.08064i	−0.841461	−	0.540319i	$-0.818304\pi$
$919$		−	32.7595i		−	1.08064i	0.841461	−	0.540319i	$-0.181696\pi$
$920$	−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
$927$	−34.2196	−	28.9054i	−1.12392	−	0.949378i
$928$	1.90141	−	1.90141i	0.0624168	−	0.0624168i
$929$	14.4962			0.475605			0.237802	−	0.971314i	$-0.423573\pi$
$929$	14.4962			0.475605			0.237802	+	0.971314i	$0.423573\pi$
$930$	29.8189	−	25.3237i	0.977800	−	0.830398i
$931$	1.26198			0.0413596
$932$	14.9849	−	14.9849i	0.490846	−	0.490846i
$933$	−40.4512	−	37.1889i	−1.32431	−	1.21751i
$934$			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	0.942862	−	0.333183i	$-0.108123\pi$
$937$	18.6626	+	18.6626i	0.609680	+	0.609680i	−0.333183	+	0.942862i	$0.608123\pi$
$938$	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	$-0.147321\pi$
$942$	−3.34805	+	3.64174i	−0.109085	+	0.118654i
$943$	38.0902	−	38.0902i	1.24039	−	1.24039i
$944$	−1.66786			−0.0542844
$945$	−8.19406	+	8.23756i	−0.266553	+	0.267968i
$946$	−25.3089			−0.822863
$947$	−18.4757	+	18.4757i	−0.600380	+	0.600380i	−0.940413	−	0.340033i	$-0.889562\pi$
$947$	−18.4757	+	18.4757i	−0.600380	+	0.600380i	0.340033	+	0.940413i	$0.389562\pi$
$948$	3.82510	−	4.16065i	0.124234	−	0.135132i
$949$			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	$-0.0896588\pi$
$953$	21.0733	+	21.0733i	0.682631	+	0.682631i	−0.277961	+	0.960592i	$0.589659\pi$
$954$	2.34557	+	27.8622i	0.0759406	+	0.902071i
$955$	15.9244	−	12.4118i	0.515302	−	0.401637i
$956$		−	16.0367i		−	0.518664i
$957$	−8.53718	−	7.84867i	−0.275968	−	0.253712i
$958$	4.39353	−	4.39353i	0.141948	−	0.141948i
$959$	14.5966			0.471349
$960$	−0.314678	+	3.86018i	−0.0101562	+	0.124587i
$961$	71.0305			2.29131
$962$	−6.91944	+	6.91944i	−0.223092	+	0.223092i
$963$	−22.3988	−	18.9204i	−0.721791	−	0.609700i
$964$			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	−0.999860	−	0.0167296i	$-0.994675\pi$
$967$	−31.6125	−	31.6125i	−1.01659	−	1.01659i	−0.0167296	−	0.999860i	$-0.505325\pi$
$968$	−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	$-0.0846470\pi$
$972$	13.0781	+	8.48319i	0.419479	+	0.272098i
$973$	4.54126	−	4.54126i	0.145586	−	0.145586i
$974$	−12.3893			−0.396979
$975$	−15.7258	−	3.26434i	−0.503630	−	0.104543i
$976$	1.70551			0.0545921
$977$	−28.0270	+	28.0270i	−0.896663	+	0.896663i	−0.995139	−	0.0984762i	$-0.968603\pi$
$977$	−28.0270	+	28.0270i	−0.896663	+	0.896663i	0.0984762	+	0.995139i	$0.468603\pi$
$978$	18.8828	+	17.3599i	0.603804	+	0.555109i
$979$		−	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	$-0.0958372\pi$
$983$	20.6447	+	20.6447i	0.658463	+	0.658463i	−0.296553	+	0.955016i	$0.595837\pi$
$984$	−0.721952	−	17.1819i	−0.0230150	−	0.547740i
$985$	−30.5842	−	3.79127i	−0.974494	−	0.120800i
$986$		−	8.18356i		−	0.260618i
$987$	−15.7131	+	17.0915i	−0.500155	+	0.544030i
$988$	1.65493	−	1.65493i	0.0526504	−	0.0526504i
$989$	55.1468			1.75357
$990$	16.6900	+	0.657019i	0.530443	+	0.0208814i
$991$	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
$993$	−5.67911	+	6.17729i	−0.180221	+	0.196030i
$994$			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	0.305692	−	0.952130i	$-0.401112\pi$
$997$	−20.4115	−	20.4115i	−0.646438	−	0.646438i	−0.952130	+	0.305692i	$0.901112\pi$
$998$	−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.a.197.5	yes	12
3.2	odd	2		210.2.j.b.197.2	yes	12
5.2	odd	4		1050.2.j.d.743.5		12
5.3	odd	4		210.2.j.b.113.2	yes	12
5.4	even	2		1050.2.j.c.407.2		12
15.2	even	4		1050.2.j.c.743.2		12
15.8	even	4	inner	210.2.j.a.113.5	✓	12
15.14	odd	2		1050.2.j.d.407.5		12

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

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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.17225 - 1.27508i) q^{3} -1.00000i q^{4} +(1.37462 + 1.76364i) q^{5} +(-0.0727133 - 1.73052i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.251664 - 2.98943i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.17225 - 1.27508i) 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} +(-1.27508 - 1.17225i) q^{12} +(-1.31138 + 1.31138i) q^{13} -1.00000 q^{14} +(3.86018 + 0.314678i) q^{15} -1.00000 q^{16} +(-2.15197 + 2.15197i) q^{17} +(-2.29180 - 1.93589i) 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} +(-4.10677 - 3.18346i) q^{27} +(-0.707107 + 0.707107i) q^{28} -2.68900 q^{29} +(2.95207 - 2.50705i) q^{30} +10.1010 q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.17486 + 2.91881i) 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} +(-1.17225 + 1.27508i) q^{42} +(-7.18740 + 7.18740i) q^{43} +2.48992 q^{44} +(4.92633 - 4.55316i) q^{45} -5.42542 q^{46} +(9.47825 - 9.47825i) q^{47} +(-1.17225 + 1.27508i) 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} +(-1.60912 - 1.47935i) q^{57} +(-1.90141 + 1.90141i) q^{58} +1.66786 q^{59} +(0.314678 - 3.86018i) q^{60} -1.70551 q^{61} +(7.14250 - 7.14250i) q^{62} +(-1.93589 + 2.29180i) 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} +(-1.93589 + 2.29180i) q^{72} +(8.49621 - 8.49621i) q^{73} +5.27645 q^{74} +(4.75129 + 7.24053i) q^{75} -1.26198 q^{76} +(1.76064 - 1.76064i) q^{77} +(2.36473 + 2.17402i) 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} +(-3.15217 + 3.42869i) q^{87} +(1.76064 - 1.76064i) q^{88} -11.6683 q^{89} +(0.263871 - 6.70301i) q^{90} +1.85457 q^{91} +(-3.83635 + 3.83635i) q^{92} +(11.8409 - 12.8796i) 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	\( 12 q + 4 q^{3} - 4 q^{5} - 4 q^{12} - 12 q^{14} + 20 q^{15} - 12 q^{16} + 28 q^{17} - 4 q^{21} + 4 q^{22} - 24 q^{23} - 4 q^{24} + 20 q^{25} - 20 q^{27} + 8 q^{29} + 16 q^{30} - 8 q^{31} + 4 q^{33} - 8 q^{35} + 4 q^{36} - 20 q^{37} - 4 q^{38} - 40 q^{39} - 8 q^{40} - 4 q^{42} + 8 q^{43} + 8 q^{44} + 8 q^{45} + 8 q^{46} + 16 q^{47} - 4 q^{48} - 16 q^{50} + 8 q^{51} - 24 q^{53} - 4 q^{54} - 16 q^{55} - 12 q^{57} - 8 q^{58} + 32 q^{59} - 4 q^{60} + 28 q^{62} + 8 q^{63} - 8 q^{66} - 28 q^{68} - 32 q^{69} + 4 q^{70} + 8 q^{72} - 24 q^{73} + 8 q^{74} + 36 q^{75} + 4 q^{77} + 4 q^{80} - 36 q^{81} + 32 q^{82} - 24 q^{83} - 36 q^{85} - 64 q^{87} + 4 q^{88} + 48 q^{89} + 48 q^{90} + 24 q^{91} - 24 q^{92} + 76 q^{93} + 8 q^{97} - 40 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 - 4 * q^5 - 4 * q^12 - 12 * q^14 + 20 * q^15 - 12 * q^16 + 28 * q^17 - 4 * q^21 + 4 * q^22 - 24 * q^23 - 4 * q^24 + 20 * q^25 - 20 * q^27 + 8 * q^29 + 16 * q^30 - 8 * q^31 + 4 * 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 + 8 * 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 - 12 * q^57 - 8 * q^58 + 32 * q^59 - 4 * q^60 + 28 * q^62 + 8 * q^63 - 8 * q^66 - 28 * q^68 - 32 * q^69 + 4 * q^70 + 8 * q^72 - 24 * q^73 + 8 * q^74 + 36 * q^75 + 4 * q^77 + 4 * q^80 - 36 * q^81 + 32 * q^82 - 24 * q^83 - 36 * q^85 - 64 * q^87 + 4 * q^88 + 48 * q^89 + 48 * q^90 + 24 * q^91 - 24 * q^92 + 76 * q^93 + 8 * q^97 - 40 * q^99

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