LMFDB - Embedded newform 1071.2.i.g.613.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1071,2,Mod(613,1071)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1071, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1071.613");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1071 = 3^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1071.i (of order $3$, 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:	$8.55197805648$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.5743021975227.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} + 2x^{8} + 10x^{7} - 8x^{6} - 12x^{5} - 24x^{4} + 90x^{3} + 54x^{2} - 324x + 243 $ x^10 - 4x^9 + 2x^8 + 10x^7 - 8x^6 - 12x^5 - 24x^4 + 90x^3 + 54x^2 - 324*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 357)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			613.4
Root			$1.13499 - 1.30836i$ of defining polynomial
Character	$\chi$	$=$	1071.613
Dual form			1071.2.i.g.919.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.565575 + 0.979604i) q^{2} +(0.360251 - 0.623973i) q^{4} +(-0.634991 - 1.09984i) q^{5} +(2.62416 + 0.337337i) q^{7} +3.07729 q^{8} +O(q^{10})$	\(q+(0.565575 + 0.979604i) q^{2} +(0.360251 - 0.623973i) q^{4} +(-0.634991 - 1.09984i) q^{5} +(2.62416 + 0.337337i) q^{7} +3.07729 q^{8} +(0.718269 - 1.24408i) q^{10} +(-1.90366 + 3.29723i) q^{11} +2.00447 q^{13} +(1.15370 + 2.76142i) q^{14} +(1.01994 + 1.76658i) q^{16} +(0.500000 - 0.866025i) q^{17} +(-0.436658 - 0.756314i) q^{19} -0.915024 q^{20} -4.30664 q^{22} +(-0.799435 - 1.38466i) q^{23} +(1.69357 - 2.93336i) q^{25} +(1.13367 + 1.96358i) q^{26} +(1.15584 - 1.51588i) q^{28} +10.3441 q^{29} +(-2.88019 + 4.98863i) q^{31} +(1.92359 - 3.33176i) q^{32} +1.13115 q^{34} +(-1.29530 - 3.10035i) q^{35} +(-2.41975 - 4.19113i) q^{37} +(0.493926 - 0.855504i) q^{38} +(-1.95405 - 3.38452i) q^{40} -3.84719 q^{41} +6.29525 q^{43} +(1.37159 + 2.37566i) q^{44} +(0.904280 - 1.56626i) q^{46} +(-0.128916 - 0.223289i) q^{47} +(6.77241 + 1.77045i) q^{49} +3.83137 q^{50} +(0.722111 - 1.25073i) q^{52} +(2.44576 - 4.23618i) q^{53} +4.83521 q^{55} +(8.07530 + 1.03808i) q^{56} +(5.85033 + 10.1331i) q^{58} +(1.17587 - 2.03667i) q^{59} +(-0.510833 - 0.884788i) q^{61} -6.51584 q^{62} +8.43149 q^{64} +(-1.27282 - 2.20458i) q^{65} +(-5.46793 + 9.47074i) q^{67} +(-0.360251 - 0.623973i) q^{68} +(2.30452 - 3.02236i) q^{70} +0.690145 q^{71} +(-2.39758 + 4.15273i) q^{73} +(2.73710 - 4.74079i) q^{74} -0.629226 q^{76} +(-6.10777 + 8.01028i) q^{77} +(4.43978 + 7.68992i) q^{79} +(1.29530 - 2.24353i) q^{80} +(-2.17587 - 3.76872i) q^{82} -15.1651 q^{83} -1.26998 q^{85} +(3.56043 + 6.16685i) q^{86} +(-5.85811 + 10.1465i) q^{88} +(-2.73314 - 4.73393i) q^{89} +(5.26003 + 0.676180i) q^{91} -1.15199 q^{92} +(0.145823 - 0.252574i) q^{94} +(-0.554548 + 0.960505i) q^{95} +16.4991 q^{97} +(2.09596 + 7.63560i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 8 q^{4} + q^{5} - 5 q^{7}+O(q^{10}) $ 10 * q - 2 * q^2 - 8 * q^4 + q^5 - 5 * q^7	$ 10 q - 2 q^{2} - 8 q^{4} + q^{5} - 5 q^{7} - 13 q^{10} - 11 q^{11} + 14 q^{13} - 3 q^{14} + 2 q^{16} + 5 q^{17} - 9 q^{19} - 24 q^{20} + 10 q^{22} - 23 q^{23} - 14 q^{25} + 18 q^{26} + 7 q^{28} + 36 q^{29} - 9 q^{31} + 3 q^{32} - 4 q^{34} + 5 q^{35} - 31 q^{40} - 6 q^{41} + 24 q^{43} - 33 q^{44} - 13 q^{46} + 11 q^{47} + 3 q^{49} - 48 q^{50} - 5 q^{52} - 3 q^{53} - 20 q^{55} + 27 q^{56} + 34 q^{58} - 14 q^{59} - 29 q^{61} + 10 q^{62} - 8 q^{65} - 16 q^{67} + 8 q^{68} + 18 q^{70} + 38 q^{71} - 11 q^{73} + 45 q^{74} + 18 q^{76} - 21 q^{77} - q^{79} - 5 q^{80} + 4 q^{82} - 10 q^{83} + 2 q^{85} - 3 q^{86} - 37 q^{88} + 8 q^{89} - 33 q^{91} + 96 q^{92} + 18 q^{94} - 21 q^{95} + 38 q^{97} + 17 q^{98}+O(q^{100}) $ 10 * q - 2 * q^2 - 8 * q^4 + q^5 - 5 * q^7 - 13 * q^10 - 11 * q^11 + 14 * q^13 - 3 * q^14 + 2 * q^16 + 5 * q^17 - 9 * q^19 - 24 * q^20 + 10 * q^22 - 23 * q^23 - 14 * q^25 + 18 * q^26 + 7 * q^28 + 36 * q^29 - 9 * q^31 + 3 * q^32 - 4 * q^34 + 5 * q^35 - 31 * q^40 - 6 * q^41 + 24 * q^43 - 33 * q^44 - 13 * q^46 + 11 * q^47 + 3 * q^49 - 48 * q^50 - 5 * q^52 - 3 * q^53 - 20 * q^55 + 27 * q^56 + 34 * q^58 - 14 * q^59 - 29 * q^61 + 10 * q^62 - 8 * q^65 - 16 * q^67 + 8 * q^68 + 18 * q^70 + 38 * q^71 - 11 * q^73 + 45 * q^74 + 18 * q^76 - 21 * q^77 - q^79 - 5 * q^80 + 4 * q^82 - 10 * q^83 + 2 * q^85 - 3 * q^86 - 37 * q^88 + 8 * q^89 - 33 * q^91 + 96 * q^92 + 18 * q^94 - 21 * q^95 + 38 * q^97 + 17 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1071\mathbb{Z}\right)^\times$.

$n$	$190$	$596$	$766$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.565575	+	0.979604i	0.399922	+	0.692684i	0.993716	−	0.111932i	$-0.0357040\pi$
$2$	0.565575	+	0.979604i	0.399922	+	0.692684i	−0.593794	+	0.804617i	$0.702371\pi$
$3$		0			0
$3$		0			0
$4$	0.360251	−	0.623973i	0.180125	−	0.311986i
$5$	−0.634991	−	1.09984i	−0.283976	−	0.491862i	0.688384	−	0.725346i	$-0.258320\pi$
$5$	−0.634991	−	1.09984i	−0.283976	−	0.491862i	−0.972360	+	0.233485i	$0.924987\pi$
$6$		0			0
$7$	2.62416	+	0.337337i	0.991838	+	0.127501i
$7$	2.62416	+	0.337337i	0.991838	+	0.127501i
$8$	3.07729			1.08799
$9$		0			0
$10$	0.718269	−	1.24408i	0.227137	−	0.393412i
$11$	−1.90366	+	3.29723i	−0.573974	+	0.994152i	0.422178	+	0.906513i	$0.361266\pi$
$11$	−1.90366	+	3.29723i	−0.573974	+	0.994152i	−0.996152	+	0.0876391i	$0.972068\pi$
$12$		0			0
$13$	2.00447			0.555939			0.277969	−	0.960590i	$-0.410339\pi$
$13$	2.00447			0.555939			0.277969	+	0.960590i	$0.410339\pi$
$14$	1.15370	+	2.76142i	0.308339	+	0.738022i
$15$		0			0
$16$	1.01994	+	1.76658i	0.254984	+	0.441646i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$18$		0			0
$19$	−0.436658	−	0.756314i	−0.100176	−	0.173510i	0.811581	−	0.584240i	$-0.198607\pi$
$19$	−0.436658	−	0.756314i	−0.100176	−	0.173510i	−0.911757	+	0.410730i	$0.865274\pi$
$20$	−0.915024			−0.204606
$21$		0			0
$22$	−4.30664			−0.918178
$23$	−0.799435	−	1.38466i	−0.166694	−	0.288722i	0.770562	−	0.637365i	$-0.219976\pi$
$23$	−0.799435	−	1.38466i	−0.166694	−	0.288722i	−0.937255	+	0.348643i	$0.886642\pi$
$24$		0			0
$25$	1.69357	−	2.93336i	0.338715	−	0.586671i
$26$	1.13367	+	1.96358i	0.222332	+	0.385090i
$27$		0			0
$28$	1.15584	−	1.51588i	0.218434	−	0.286474i
$29$	10.3441			1.92084			0.960422	−	0.278551i	$-0.0898540\pi$
$29$	10.3441			1.92084			0.960422	+	0.278551i	$0.0898540\pi$
$30$		0			0
$31$	−2.88019	+	4.98863i	−0.517297	+	0.895985i	0.482501	+	0.875895i	$0.339728\pi$
$31$	−2.88019	+	4.98863i	−0.517297	+	0.895985i	−0.999798	+	0.0200893i	$0.993605\pi$
$32$	1.92359	−	3.33176i	0.340046	−	0.588978i
$33$		0			0
$34$	1.13115			0.193990
$35$	−1.29530	−	3.10035i	−0.218946	−	0.524055i
$36$		0			0
$37$	−2.41975	−	4.19113i	−0.397805	−	0.689018i	0.595650	−	0.803244i	$-0.296894\pi$
$37$	−2.41975	−	4.19113i	−0.397805	−	0.689018i	−0.993455	+	0.114226i	$0.963561\pi$
$38$	0.493926	−	0.855504i	0.0801253	−	0.138781i
$39$		0			0
$40$	−1.95405	−	3.38452i	−0.308963	−	0.535139i
$41$	−3.84719			−0.600829			−0.300415	−	0.953809i	$-0.597125\pi$
$41$	−3.84719			−0.600829			−0.300415	+	0.953809i	$0.597125\pi$
$42$		0			0
$43$	6.29525			0.960017			0.480008	−	0.877264i	$-0.340634\pi$
$43$	6.29525			0.960017			0.480008	+	0.877264i	$0.340634\pi$
$44$	1.37159	+	2.37566i	0.206775	+	0.358144i
$45$		0			0
$46$	0.904280	−	1.56626i	0.133329	−	0.230932i
$47$	−0.128916	−	0.223289i	−0.0188044	−	0.0325701i	0.856470	−	0.516197i	$-0.172653\pi$
$47$	−0.128916	−	0.223289i	−0.0188044	−	0.0325701i	−0.875274	+	0.483627i	$0.839319\pi$
$48$		0			0
$49$	6.77241	+	1.77045i	0.967487	+	0.252921i
$50$	3.83137			0.541837
$51$		0			0
$52$	0.722111	−	1.25073i	0.100139	−	0.173445i
$53$	2.44576	−	4.23618i	0.335951	−	0.581885i	−0.647716	−	0.761882i	$-0.724276\pi$
$53$	2.44576	−	4.23618i	0.335951	−	0.581885i	0.983667	+	0.179997i	$0.0576089\pi$
$54$		0			0
$55$	4.83521			0.651980
$56$	8.07530	+	1.03808i	1.07911	+	0.138720i
$57$		0			0
$58$	5.85033	+	10.1331i	0.768187	+	1.33054i
$59$	1.17587	−	2.03667i	0.153085	−	0.265151i	−0.779275	−	0.626682i	$-0.784412\pi$
$59$	1.17587	−	2.03667i	0.153085	−	0.265151i	0.932360	+	0.361531i	$0.117746\pi$
$60$		0			0
$61$	−0.510833	−	0.884788i	−0.0654054	−	0.113286i	0.831468	−	0.555572i	$-0.187501\pi$
$61$	−0.510833	−	0.884788i	−0.0654054	−	0.113286i	−0.896874	+	0.442287i	$0.854167\pi$
$62$	−6.51584			−0.827513
$63$		0			0
$64$	8.43149			1.05394
$65$	−1.27282	−	2.20458i	−0.157874	−	0.273445i
$66$		0			0
$67$	−5.46793	+	9.47074i	−0.668014	+	1.15703i	0.310444	+	0.950592i	$0.399522\pi$
$67$	−5.46793	+	9.47074i	−0.668014	+	1.15703i	−0.978459	+	0.206443i	$0.933811\pi$
$68$	−0.360251	−	0.623973i	−0.0436868	−	0.0756678i
$69$		0			0
$70$	2.30452	−	3.02236i	0.275443	−	0.361241i
$71$	0.690145			0.0819052			0.0409526	−	0.999161i	$-0.486961\pi$
$71$	0.690145			0.0819052			0.0409526	+	0.999161i	$0.486961\pi$
$72$		0			0
$73$	−2.39758	+	4.15273i	−0.280616	+	0.486041i	−0.971537	−	0.236890i	$-0.923872\pi$
$73$	−2.39758	+	4.15273i	−0.280616	+	0.486041i	0.690921	+	0.722930i	$0.257205\pi$
$74$	2.73710	−	4.74079i	0.318181	−	0.551106i
$75$		0			0
$76$	−0.629226			−0.0721772
$77$	−6.10777	+	8.01028i	−0.696045	+	0.912856i
$78$		0			0
$79$	4.43978	+	7.68992i	0.499514	+	0.865183i	1.00000		0.000561191i	$-0.000178633\pi$
$79$	4.43978	+	7.68992i	0.499514	+	0.865183i	−0.500486	+	0.865745i	$0.666845\pi$
$80$	1.29530	−	2.24353i	0.144819	−	0.250834i
$81$		0			0
$82$	−2.17587	−	3.76872i	−0.240285	−	0.416185i
$83$	−15.1651			−1.66459			−0.832294	−	0.554335i	$-0.812973\pi$
$83$	−15.1651			−1.66459			−0.832294	+	0.554335i	$0.812973\pi$
$84$		0			0
$85$	−1.26998			−0.137749
$86$	3.56043	+	6.16685i	0.383931	+	0.664989i
$87$		0			0
$88$	−5.85811	+	10.1465i	−0.624476	+	1.08162i
$89$	−2.73314	−	4.73393i	−0.289712	−	0.501796i	0.684029	−	0.729455i	$-0.260226\pi$
$89$	−2.73314	−	4.73393i	−0.289712	−	0.501796i	−0.973741	+	0.227659i	$0.926893\pi$
$90$		0			0
$91$	5.26003	+	0.676180i	0.551401	+	0.0708829i
$92$	−1.15199			−0.120103
$93$		0			0
$94$	0.145823	−	0.252574i	0.0150405	−	0.0260510i
$95$	−0.554548	+	0.960505i	−0.0568954	+	0.0985457i
$96$		0			0
$97$	16.4991			1.67523			0.837614	−	0.546262i	$-0.183950\pi$
$97$	16.4991			1.67523			0.837614	+	0.546262i	$0.183950\pi$
$98$	2.09596	+	7.63560i	0.211724	+	0.771312i
$99$		0			0
$100$	−1.22022	−	2.11349i	−0.122022	−	0.211349i
$101$	1.96861	−	3.40973i	0.195884	−	0.339280i	−0.751306	−	0.659954i	$-0.770576\pi$
$101$	1.96861	−	3.40973i	0.195884	−	0.339280i	0.947190	+	0.320673i	$0.103909\pi$
$102$		0			0
$103$	−6.57215	−	11.3833i	−0.647573	−	1.12163i	−0.983701	−	0.179814i	$-0.942451\pi$
$103$	−6.57215	−	11.3833i	−0.647573	−	1.12163i	0.336127	−	0.941817i	$-0.390883\pi$
$104$	6.16833			0.604854
$105$		0			0
$106$	5.53304			0.537417
$107$	−0.540879	−	0.936831i	−0.0522888	−	0.0905668i	0.838696	−	0.544599i	$-0.183318\pi$
$107$	−0.540879	−	0.936831i	−0.0522888	−	0.0905668i	−0.890985	+	0.454033i	$0.849985\pi$
$108$		0			0
$109$	−8.93279	+	15.4720i	−0.855606	+	1.48195i	0.0204763	+	0.999790i	$0.493482\pi$
$109$	−8.93279	+	15.4720i	−0.855606	+	1.48195i	−0.876082	+	0.482162i	$0.839852\pi$
$110$	2.73467	+	4.73659i	0.260741	+	0.451617i
$111$		0			0
$112$	2.08054	+	4.97985i	0.196593	+	0.470552i
$113$	−7.09492			−0.667433			−0.333717	−	0.942673i	$-0.608303\pi$
$113$	−7.09492			−0.667433			−0.333717	+	0.942673i	$0.608303\pi$
$114$		0			0
$115$	−1.01527	+	1.75849i	−0.0946742	+	0.163980i
$116$	3.72646	−	6.45441i	0.345993	−	0.599277i
$117$		0			0
$118$	2.66017			0.244888
$119$	1.60422	−	2.10392i	0.147059	−	0.192866i
$120$		0			0
$121$	−1.74781	−	3.02730i	−0.158892	−	0.275209i
$122$	0.577828	−	1.00083i	0.0523141	−	0.0906107i
$123$		0			0
$124$	2.07518	+	3.59432i	0.186357	+	0.322779i
$125$	−10.6515			−0.952701
$126$		0			0
$127$	−14.4800			−1.28489			−0.642447	−	0.766330i	$-0.722081\pi$
$127$	−14.4800			−1.28489			−0.642447	+	0.766330i	$0.722081\pi$
$128$	0.921449	+	1.59600i	0.0814453	+	0.141067i
$129$		0			0
$130$	1.43975	−	2.49371i	0.126274	−	0.218713i
$131$	−8.85136	−	15.3310i	−0.773347	−	1.33948i	−0.935719	−	0.352746i	$-0.885248\pi$
$131$	−8.85136	−	15.3310i	−0.773347	−	1.33948i	0.162372	−	0.986730i	$-0.448085\pi$
$132$		0			0
$133$	−0.890728	−	2.13199i	−0.0772359	−	0.184867i
$134$	−12.3701			−1.06861
$135$		0			0
$136$	1.53865	−	2.66501i	0.131938	−	0.228523i
$137$	−6.47518	+	11.2153i	−0.553212	+	0.958192i	0.444828	+	0.895616i	$0.353265\pi$
$137$	−6.47518	+	11.2153i	−0.553212	+	0.958192i	−0.998040	+	0.0625758i	$0.980068\pi$
$138$		0			0
$139$	−22.4136			−1.90110			−0.950549	−	0.310576i	$-0.899478\pi$
$139$	−22.4136			−1.90110			−0.950549	+	0.310576i	$0.899478\pi$
$140$	−2.40117	−	0.308671i	−0.202936	−	0.0260875i
$141$		0			0
$142$	0.390329	+	0.676069i	0.0327557	+	0.0567345i
$143$	−3.81581	+	6.60918i	−0.319094	+	0.552688i
$144$		0			0
$145$	−6.56838	−	11.3768i	−0.545474	−	0.944789i
$146$	−5.42404			−0.448897
$147$		0			0
$148$	−3.48687			−0.286619
$149$	10.8025	+	18.7104i	0.884972	+	1.53282i	0.845746	+	0.533585i	$0.179156\pi$
$149$	10.8025	+	18.7104i	0.884972	+	1.53282i	0.0392253	+	0.999230i	$0.487511\pi$
$150$		0			0
$151$	−3.44130	+	5.96050i	−0.280049	+	0.485059i	−0.971396	−	0.237464i	$-0.923684\pi$
$151$	−3.44130	+	5.96050i	−0.280049	+	0.485059i	0.691348	+	0.722522i	$0.257017\pi$
$152$	−1.34373	−	2.32740i	−0.108991	−	0.188777i
$153$		0			0
$154$	−11.3013	−	1.45279i	−0.910684	−	0.117069i
$155$	7.31557			0.587601
$156$		0			0
$157$	6.76926	−	11.7247i	0.540246	−	0.935733i	−0.458644	−	0.888620i	$-0.651665\pi$
$157$	6.76926	−	11.7247i	0.540246	−	0.935733i	0.998890	−	0.0471127i	$-0.0150020\pi$
$158$	−5.02205	+	8.69844i	−0.399533	+	0.692011i
$159$		0			0
$160$	−4.88585			−0.386261
$161$	−1.63075	−	3.90325i	−0.128521	−	0.307619i
$162$		0			0
$163$	1.64986	+	2.85764i	0.129227	+	0.223828i	0.923377	−	0.383894i	$-0.125417\pi$
$163$	1.64986	+	2.85764i	0.129227	+	0.223828i	−0.794150	+	0.607721i	$0.792084\pi$
$164$	−1.38595	+	2.40054i	−0.108225	+	0.187451i
$165$		0			0
$166$	−8.57700	−	14.8558i	−0.665704	−	1.15303i
$167$	0.327233			0.0253220			0.0126610	−	0.999920i	$-0.495970\pi$
$167$	0.327233			0.0253220			0.0126610	+	0.999920i	$0.495970\pi$
$168$		0			0
$169$	−8.98212			−0.690932
$170$	−0.718269	−	1.24408i	−0.0550887	−	0.0954165i
$171$		0			0
$172$	2.26787	−	3.92807i	0.172923	−	0.299512i
$173$	8.12697	+	14.0763i	0.617882	+	1.07020i	0.989872	+	0.141966i	$0.0453423\pi$
$173$	8.12697	+	14.0763i	0.617882	+	1.07020i	−0.371990	+	0.928237i	$0.621324\pi$
$174$		0			0
$175$	5.43373	−	7.12628i	0.410752	−	0.538696i
$176$	−7.76643			−0.585417
$177$		0			0
$178$	3.09159	−	5.35478i	0.231724	−	0.401358i
$179$	8.28473	−	14.3496i	0.619230	−	1.07254i	−0.370397	−	0.928874i	$-0.620778\pi$
$179$	8.28473	−	14.3496i	0.619230	−	1.07254i	0.989627	−	0.143664i	$-0.0458884\pi$
$180$		0			0
$181$	6.34603			0.471696			0.235848	−	0.971790i	$-0.424213\pi$
$181$	6.34603			0.471696			0.235848	+	0.971790i	$0.424213\pi$
$182$	2.31255	+	5.53518i	0.171418	+	0.410295i
$183$		0			0
$184$	−2.46010	−	4.26101i	−0.181361	−	0.314126i
$185$	−3.07304	+	5.32266i	−0.225934	+	0.391330i
$186$		0			0
$187$	1.90366	+	3.29723i	0.139209	+	0.241117i
$188$	−0.185769			−0.0135486
$189$		0			0
$190$	−1.25455			−0.0910148
$191$	0.901113	+	1.56077i	0.0652023	+	0.112934i	0.896784	−	0.442469i	$-0.145897\pi$
$191$	0.901113	+	1.56077i	0.0652023	+	0.112934i	−0.831581	+	0.555403i	$0.812564\pi$
$192$		0			0
$193$	1.91600	−	3.31861i	0.137917	−	0.238879i	−0.788791	−	0.614661i	$-0.789293\pi$
$193$	1.91600	−	3.31861i	0.137917	−	0.238879i	0.926708	+	0.375783i	$0.122626\pi$
$194$	9.33146	+	16.1626i	0.669960	+	1.16040i
$195$		0			0
$196$	3.54448	−	3.58799i	0.253177	−	0.256285i
$197$	3.10588			0.221285			0.110642	−	0.993860i	$-0.464709\pi$
$197$	3.10588			0.221285			0.110642	+	0.993860i	$0.464709\pi$
$198$		0			0
$199$	−3.67890	+	6.37204i	−0.260790	+	0.451702i	−0.966452	−	0.256847i	$-0.917316\pi$
$199$	−3.67890	+	6.37204i	−0.260790	+	0.451702i	0.705662	+	0.708549i	$0.250650\pi$
$200$	5.21162	−	9.02680i	0.368517	−	0.638291i
$201$		0			0
$202$	4.45357			0.313352
$203$	27.1444	+	3.48943i	1.90517	+	0.244910i
$204$		0			0
$205$	2.44293	+	4.23127i	0.170621	+	0.295525i
$206$	7.43408	−	12.8762i	0.517957	−	0.897128i
$207$		0			0
$208$	2.04443	+	3.54105i	0.141756	+	0.245528i
$209$	3.32499			0.229994
$210$		0			0
$211$	−10.1892			−0.701456			−0.350728	−	0.936477i	$-0.614066\pi$
$211$	−10.1892			−0.701456			−0.350728	+	0.936477i	$0.614066\pi$
$212$	−1.76218	−	3.05218i	−0.121027	−	0.209624i
$213$		0			0
$214$	0.611815	−	1.05969i	0.0418228	−	0.0724393i
$215$	−3.99743	−	6.92374i	−0.272622	−	0.472195i
$216$		0			0
$217$	−9.24092	+	12.1194i	−0.627314	+	0.822716i
$218$	−20.2086			−1.36870
$219$		0			0
$220$	1.74189	−	3.01704i	0.117438	−	0.203409i
$221$	1.00223	−	1.73592i	0.0674175	−	0.116770i
$222$		0			0
$223$	−16.1738			−1.08308			−0.541539	−	0.840676i	$-0.682158\pi$
$223$	−16.1738			−1.08308			−0.541539	+	0.840676i	$0.682158\pi$
$224$	6.17174	−	8.09417i	0.412366	−	0.540814i
$225$		0			0
$226$	−4.01270	−	6.95021i	−0.266921	−	0.462321i
$227$	−8.47458	+	14.6784i	−0.562478	+	0.974240i	0.434802	+	0.900526i	$0.356818\pi$
$227$	−8.47458	+	14.6784i	−0.562478	+	0.974240i	−0.997279	+	0.0737138i	$0.976515\pi$
$228$		0			0
$229$	−14.0231	−	24.2886i	−0.926670	−	1.60504i	−0.788854	−	0.614581i	$-0.789325\pi$
$229$	−14.0231	−	24.2886i	−0.926670	−	1.60504i	−0.137816	−	0.990458i	$-0.544008\pi$
$230$	−2.29684			−0.151449
$231$		0			0
$232$	31.8317			2.08985
$233$	−0.647919	−	1.12223i	−0.0424466	−	0.0735196i	0.844022	−	0.536309i	$-0.180182\pi$
$233$	−0.647919	−	1.12223i	−0.0424466	−	0.0735196i	−0.886468	+	0.462790i	$0.846849\pi$
$234$		0			0
$235$	−0.163721	+	0.283573i	−0.0106800	+	0.0184983i
$236$	−0.847216	−	1.46742i	−0.0551491	−	0.0955210i
$237$		0			0
$238$	2.96831	+	0.381578i	0.192407	+	0.0247340i
$239$	23.2720			1.50534			0.752669	−	0.658399i	$-0.228766\pi$
$239$	23.2720			1.50534			0.752669	+	0.658399i	$0.228766\pi$
$240$		0			0
$241$	−0.0551235	+	0.0954768i	−0.00355082	+	0.00615020i	−0.867795	−	0.496922i	$-0.834464\pi$
$241$	−0.0551235	+	0.0954768i	−0.00355082	+	0.00615020i	0.864245	+	0.503072i	$0.167797\pi$
$242$	1.97704	−	3.42433i	0.127089	−	0.220124i
$243$		0			0
$244$	−0.736112			−0.0471247
$245$	−2.35321	−	8.57276i	−0.150341	−	0.547693i
$246$		0			0
$247$	−0.875267	−	1.51601i	−0.0556919	−	0.0964612i
$248$	−8.86318	+	15.3515i	−0.562813	+	0.974820i
$249$		0			0
$250$	−6.02423	−	10.4343i	−0.381006	−	0.659921i
$251$	−21.4206			−1.35206			−0.676028	−	0.736876i	$-0.736300\pi$
$251$	−21.4206			−1.35206			−0.676028	+	0.736876i	$0.736300\pi$
$252$		0			0
$253$	6.08740			0.382711
$254$	−8.18953	−	14.1847i	−0.513857	−	0.890026i
$255$		0			0
$256$	7.38919	−	12.7985i	0.461824	−	0.799903i
$257$	0.265516	+	0.459886i	0.0165624	+	0.0286869i	0.874188	−	0.485588i	$-0.161394\pi$
$257$	0.265516	+	0.459886i	0.0165624	+	0.0286869i	−0.857625	+	0.514275i	$0.828061\pi$
$258$		0			0
$259$	−4.93599	−	11.8145i	−0.306707	−	0.734115i
$260$	−1.83413			−0.113748
$261$		0			0
$262$	10.0122	−	17.3416i	0.618556	−	1.07137i
$263$	9.47799	−	16.4164i	0.584438	−	1.01228i	−0.410507	−	0.911857i	$-0.634648\pi$
$263$	9.47799	−	16.4164i	0.584438	−	1.01228i	0.994945	−	0.100419i	$-0.0320184\pi$
$264$		0			0
$265$	−6.21214			−0.381609
$266$	1.58473	−	2.07836i	0.0971661	−	0.127432i
$267$		0			0
$268$	3.93965	+	6.82368i	0.240653	+	0.416823i
$269$	1.32018	−	2.28663i	0.0804930	−	0.139418i	−0.822969	−	0.568087i	$-0.807684\pi$
$269$	1.32018	−	2.28663i	0.0804930	−	0.139418i	0.903462	+	0.428669i	$0.141017\pi$
$270$		0			0
$271$	14.2074	+	24.6080i	0.863040	+	1.49483i	0.868981	+	0.494846i	$0.164776\pi$
$271$	14.2074	+	24.6080i	0.863040	+	1.49483i	−0.00594088	+	0.999982i	$0.501891\pi$
$272$	2.03987			0.123685
$273$		0			0
$274$	−14.6488			−0.884966
$275$	6.44796	+	11.1682i	0.388827	+	0.673468i
$276$		0			0
$277$	−8.66916	+	15.0154i	−0.520879	+	0.902190i	0.478826	+	0.877910i	$0.341063\pi$
$277$	−8.66916	+	15.0154i	−0.520879	+	0.902190i	−0.999705	+	0.0242797i	$0.992271\pi$
$278$	−12.6766	−	21.9565i	−0.760290	−	1.31686i
$279$		0			0
$280$	−3.98602	−	9.54068i	−0.238210	−	0.570165i
$281$	−1.20542			−0.0719095			−0.0359547	−	0.999353i	$-0.511447\pi$
$281$	−1.20542			−0.0719095			−0.0359547	+	0.999353i	$0.511447\pi$
$282$		0			0
$283$	−5.00919	+	8.67618i	−0.297766	+	0.515745i	−0.975624	−	0.219447i	$-0.929575\pi$
$283$	−5.00919	+	8.67618i	−0.297766	+	0.515745i	0.677859	+	0.735192i	$0.262908\pi$
$284$	0.248626	−	0.430632i	0.0147532	−	0.0255533i
$285$		0			0
$286$	−8.63251			−0.510451
$287$	−10.0956	−	1.29780i	−0.595926	−	0.0766065i
$288$		0			0
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	7.42982	−	12.8688i	0.436294	−	0.755683i
$291$		0			0
$292$	1.72746	+	2.99205i	0.101092	+	0.175097i
$293$	−24.7556			−1.44624			−0.723120	−	0.690722i	$-0.757293\pi$
$293$	−24.7556			−1.44624			−0.723120	+	0.690722i	$0.757293\pi$
$294$		0			0
$295$	−2.98667			−0.173890
$296$	−7.44628	−	12.8973i	−0.432806	−	0.749643i
$297$		0			0
$298$	−12.2192	+	21.1643i	−0.707838	+	1.22601i
$299$	−1.60244	−	2.77551i	−0.0926715	−	0.160512i
$300$		0			0
$301$	16.5197	+	2.12362i	0.952182	+	0.122403i
$302$	−7.78524			−0.447990
$303$		0			0
$304$	0.890728	−	1.54279i	0.0510867	−	0.0884848i
$305$	−0.648748	+	1.12366i	−0.0371472	+	0.0643409i
$306$		0			0
$307$	2.65875			0.151743			0.0758715	−	0.997118i	$-0.475826\pi$
$307$	2.65875			0.151743			0.0758715	+	0.997118i	$0.475826\pi$
$308$	2.79787	+	6.69679i	0.159423	+	0.381585i
$309$		0			0
$310$	4.13750	+	7.16636i	0.234994	+	0.407022i
$311$	−0.303088	+	0.524965i	−0.0171866	+	0.0297680i	−0.874491	−	0.485042i	$-0.838804\pi$
$311$	−0.303088	+	0.524965i	−0.0171866	+	0.0297680i	0.857304	+	0.514810i	$0.172138\pi$
$312$		0			0
$313$	−1.81238	−	3.13913i	−0.102442	−	0.177434i	0.810248	−	0.586087i	$-0.199332\pi$
$313$	−1.81238	−	3.13913i	−0.102442	−	0.177434i	−0.912690	+	0.408652i	$0.865999\pi$
$314$	15.3141			0.864224
$315$		0			0
$316$	6.39773			0.359901
$317$	−15.4081	−	26.6876i	−0.865405	−	1.49893i	−0.866645	−	0.498926i	$-0.833728\pi$
$317$	−15.4081	−	26.6876i	−0.865405	−	1.49893i	0.00123968	−	0.999999i	$-0.499605\pi$
$318$		0			0
$319$	−19.6915	+	34.1067i	−1.10251	+	1.90961i
$320$	−5.35391	−	9.27325i	−0.299293	−	0.518391i
$321$		0			0
$322$	2.90133	−	3.80506i	0.161685	−	0.212048i
$323$	−0.873317			−0.0485926
$324$		0			0
$325$	3.39471	−	5.87981i	0.188305	−	0.326153i
$326$	−1.86624	+	3.23242i	−0.103361	+	0.179027i
$327$		0			0
$328$	−11.8389			−0.653695
$329$	−0.262973	−	0.629435i	−0.0144982	−	0.0347019i
$330$		0			0
$331$	−17.3401	−	30.0339i	−0.953098	−	1.65081i	−0.738662	−	0.674076i	$-0.764542\pi$
$331$	−17.3401	−	30.0339i	−0.953098	−	1.65081i	−0.214436	−	0.976738i	$-0.568791\pi$
$332$	−5.46325	+	9.46262i	−0.299835	+	0.519329i
$333$		0			0
$334$	0.185075	+	0.320558i	0.0101268	+	0.0175402i
$335$	13.8883			0.758801
$336$		0			0
$337$	14.5859			0.794547			0.397273	−	0.917700i	$-0.369956\pi$
$337$	14.5859			0.794547			0.397273	+	0.917700i	$0.369956\pi$
$338$	−5.08006	−	8.79892i	−0.276319	−	0.478598i
$339$		0			0
$340$	−0.457512	+	0.792434i	−0.0248121	+	0.0429758i
$341$	−10.9658	−	18.9933i	−0.593830	−	1.02854i
$342$		0			0
$343$	17.1746	+	6.93052i	0.927343	+	0.374213i
$344$	19.3723			1.04449
$345$		0			0
$346$	−9.19281	+	15.9224i	−0.494209	+	0.855994i
$347$	−17.1301	+	29.6703i	−0.919594	+	1.59278i	−0.119561	+	0.992827i	$0.538149\pi$
$347$	−17.1301	+	29.6703i	−0.919594	+	1.59278i	−0.800033	+	0.599956i	$0.795185\pi$
$348$		0			0
$349$	−29.7212			−1.59094			−0.795471	−	0.605992i	$-0.792776\pi$
$349$	−29.7212			−1.59094			−0.795471	+	0.605992i	$0.792776\pi$
$350$	10.0541	+	1.29246i	0.537415	+	0.0690850i
$351$		0			0
$352$	7.32372	+	12.6850i	0.390355	+	0.676115i
$353$	−0.396062	+	0.685999i	−0.0210802	+	0.0365121i	−0.876373	−	0.481633i	$-0.840044\pi$
$353$	−0.396062	+	0.685999i	−0.0210802	+	0.0365121i	0.855293	+	0.518145i	$0.173377\pi$
$354$		0			0
$355$	−0.438236	−	0.759047i	−0.0232591	−	0.0402860i
$356$	−3.93846			−0.208738
$357$		0			0
$358$	18.7425			0.990573
$359$	3.98960	+	6.91019i	0.210563	+	0.364706i	0.951891	−	0.306437i	$-0.0991370\pi$
$359$	3.98960	+	6.91019i	0.210563	+	0.364706i	−0.741328	+	0.671143i	$0.765804\pi$
$360$		0			0
$361$	9.11866	−	15.7940i	0.479929	−	0.831262i
$362$	3.58915	+	6.21659i	0.188642	+	0.326737i
$363$		0			0
$364$	2.31685	−	3.03852i	0.121436	−	0.159262i
$365$	6.08977			0.318753
$366$		0			0
$367$	−6.06887	+	10.5116i	−0.316792	+	0.548700i	−0.979817	−	0.199897i	$-0.935939\pi$
$367$	−6.06887	+	10.5116i	−0.316792	+	0.548700i	0.663025	+	0.748598i	$0.269272\pi$
$368$	1.63075	−	2.82453i	0.0850085	−	0.147239i
$369$		0			0
$370$	−6.95213			−0.361424
$371$	7.84709	−	10.2914i	0.407400	−	0.534301i
$372$		0			0
$373$	−13.2629	−	22.9720i	−0.686726	−	1.18945i	−0.972891	−	0.231265i	$-0.925714\pi$
$373$	−13.2629	−	22.9720i	−0.686726	−	1.18945i	0.286164	−	0.958181i	$-0.407620\pi$
$374$	−2.15332	+	3.72966i	−0.111345	+	0.192856i
$375$		0			0
$376$	−0.396713	−	0.687127i	−0.0204589	−	0.0354359i
$377$	20.7343			1.06787
$378$		0			0
$379$	−12.2516			−0.629321			−0.314661	−	0.949204i	$-0.601891\pi$
$379$	−12.2516			−0.629321			−0.314661	+	0.949204i	$0.601891\pi$
$380$	0.399553	+	0.692046i	0.0204966	+	0.0355012i
$381$		0			0
$382$	−1.01929	+	1.76547i	−0.0521516	+	0.0903292i
$383$	9.21860	+	15.9671i	0.471048	+	0.815880i	0.999452	−	0.0331137i	$-0.0105424\pi$
$383$	9.21860	+	15.9671i	0.471048	+	0.815880i	−0.528403	+	0.848994i	$0.677209\pi$
$384$		0			0
$385$	12.6884	+	1.63110i	0.646659	+	0.0831283i
$386$	4.33456			0.220623
$387$		0			0
$388$	5.94381	−	10.2950i	0.301751	−	0.522649i
$389$	−15.4342	+	26.7328i	−0.782544	+	1.35541i	0.147912	+	0.989001i	$0.452745\pi$
$389$	−15.4342	+	26.7328i	−0.782544	+	1.35541i	−0.930455	+	0.366405i	$0.880588\pi$
$390$		0			0
$391$	−1.59887			−0.0808583
$392$	20.8407	+	5.44819i	1.05261	+	0.275175i
$393$		0			0
$394$	1.75661	+	3.04253i	0.0884965	+	0.153280i
$395$	5.63843	−	9.76605i	0.283700	−	0.491383i
$396$		0			0
$397$	−5.57763	−	9.66075i	−0.279933	−	0.484859i	0.691434	−	0.722439i	$-0.256979\pi$
$397$	−5.57763	−	9.66075i	−0.279933	−	0.484859i	−0.971368	+	0.237580i	$0.923646\pi$
$398$	−8.32277			−0.417183
$399$		0			0
$400$	6.90935			0.345468
$401$	9.71026	+	16.8187i	0.484907	+	0.839884i	0.999850	−	0.0173407i	$-0.00551999\pi$
$401$	9.71026	+	16.8187i	0.484907	+	0.839884i	−0.514942	+	0.857225i	$0.672187\pi$
$402$		0			0
$403$	−5.77324	+	9.99954i	−0.287585	+	0.498113i
$404$	−1.41838	−	2.45671i	−0.0705673	−	0.122226i
$405$		0			0
$406$	11.9339	+	28.5643i	0.592272	+	1.41762i
$407$	18.4255			0.913318
$408$		0			0
$409$	−1.37898	+	2.38846i	−0.0681861	+	0.118102i	−0.898103	−	0.439785i	$-0.855054\pi$
$409$	−1.37898	+	2.38846i	−0.0681861	+	0.118102i	0.829917	+	0.557887i	$0.188388\pi$
$410$	−2.76331	+	4.78620i	−0.136470	+	0.236374i
$411$		0			0
$412$	−9.47050			−0.466578
$413$	3.77271	−	4.94787i	0.185643	−	0.243469i
$414$		0			0
$415$	9.62970	+	16.6791i	0.472704	+	0.818747i
$416$	3.85578	−	6.67840i	0.189045	−	0.327435i
$417$		0			0
$418$	1.88053	+	3.25717i	0.0919797	+	0.159313i
$419$	24.2339			1.18390			0.591952	−	0.805974i	$-0.298358\pi$
$419$	24.2339			1.18390			0.591952	+	0.805974i	$0.298358\pi$
$420$		0			0
$421$	19.4173			0.946340			0.473170	−	0.880971i	$-0.343110\pi$
$421$	19.4173			0.946340			0.473170	+	0.880971i	$0.343110\pi$
$422$	−5.76277	−	9.98141i	−0.280527	−	0.485887i
$423$		0			0
$424$	7.52633	−	13.0360i	0.365511	−	0.633083i
$425$	−1.69357	−	2.93336i	−0.0821504	−	0.142289i
$426$		0			0
$427$	−1.04203	−	2.49415i	−0.0504276	−	0.120700i
$428$	−0.779409			−0.0376742
$429$		0			0
$430$	4.52168	−	7.83179i	0.218055	−	0.377682i
$431$	−7.60528	+	13.1727i	−0.366333	+	0.634508i	−0.988989	−	0.147988i	$-0.952720\pi$
$431$	−7.60528	+	13.1727i	−0.366333	+	0.634508i	0.622656	+	0.782496i	$0.286054\pi$
$432$		0			0
$433$	11.2886			0.542494			0.271247	−	0.962510i	$-0.412564\pi$
$433$	11.2886			0.542494			0.271247	+	0.962510i	$0.412564\pi$
$434$	−17.0986	−	2.19803i	−0.820759	−	0.105509i
$435$		0			0
$436$	6.43609	+	11.1476i	0.308233	+	0.533875i
$437$	−0.698160	+	1.20925i	−0.0333975	+	0.0578462i
$438$		0			0
$439$	18.9582	+	32.8366i	0.904827	+	1.56721i	0.821149	+	0.570714i	$0.193333\pi$
$439$	18.9582	+	32.8366i	0.904827	+	1.56721i	0.0836783	+	0.996493i	$0.473333\pi$
$440$	14.8794			0.709346
$441$		0			0
$442$	2.26735			0.107847
$443$	−0.300683	−	0.520798i	−0.0142859	−	0.0247439i	0.858794	−	0.512321i	$-0.171214\pi$
$443$	−0.300683	−	0.520798i	−0.0142859	−	0.0247439i	−0.873080	+	0.487577i	$0.837881\pi$
$444$		0			0
$445$	−3.47103	+	6.01201i	−0.164543	+	0.284996i
$446$	−9.14749	−	15.8439i	−0.433146	−	0.750231i
$447$		0			0
$448$	22.1256	+	2.84425i	1.04533	+	0.134378i
$449$	−25.8212			−1.21858			−0.609290	−	0.792948i	$-0.708545\pi$
$449$	−25.8212			−1.21858			−0.609290	+	0.792948i	$0.708545\pi$
$450$		0			0
$451$	7.32372	−	12.6850i	0.344860	−	0.597316i
$452$	−2.55595	+	4.42703i	−0.120222	+	0.208230i
$453$		0			0
$454$	−19.1720			−0.899788
$455$	−2.59639	−	6.21454i	−0.121720	−	0.291342i
$456$		0			0
$457$	−7.99167	−	13.8420i	−0.373834	−	0.647500i	0.616317	−	0.787498i	$-0.288624\pi$
$457$	−7.99167	−	13.8420i	−0.373834	−	0.647500i	−0.990152	+	0.139998i	$0.955290\pi$
$458$	15.8622	−	27.4741i	0.741190	−	1.28378i
$459$		0			0
$460$	0.731502	+	1.26700i	0.0341065	+	0.0590741i
$461$	−12.9802			−0.604548			−0.302274	−	0.953221i	$-0.597746\pi$
$461$	−12.9802			−0.604548			−0.302274	+	0.953221i	$0.597746\pi$
$462$		0			0
$463$	23.7170			1.10222			0.551111	−	0.834432i	$-0.314204\pi$
$463$	23.7170			1.10222			0.551111	+	0.834432i	$0.314204\pi$
$464$	10.5503	+	18.2736i	0.489785	+	0.848332i
$465$		0			0
$466$	0.732893	−	1.26941i	0.0339506	−	0.0588042i
$467$	1.90731	+	3.30356i	0.0882598	+	0.152870i	0.906776	−	0.421614i	$-0.138536\pi$
$467$	1.90731	+	3.30356i	0.0882598	+	0.152870i	−0.818516	+	0.574484i	$0.805203\pi$
$468$		0			0
$469$	−17.5435	+	23.0082i	−0.810086	+	1.06242i
$470$	−0.370386			−0.0170846
$471$		0			0
$472$	3.61850	−	6.26742i	0.166555	−	0.288481i
$473$	−11.9840	+	20.7569i	−0.551025	+	0.954403i
$474$		0			0
$475$	−2.95805			−0.135725
$476$	−0.734866	−	1.75893i	−0.0336825	−	0.0806204i
$477$		0			0
$478$	13.1620	+	22.7973i	0.602017	+	1.04272i
$479$	−13.2648	+	22.9753i	−0.606084	+	1.04977i	0.385795	+	0.922584i	$0.373927\pi$
$479$	−13.2648	+	22.9753i	−0.606084	+	1.04977i	−0.991879	+	0.127184i	$0.959406\pi$
$480$		0			0
$481$	−4.85031	−	8.40098i	−0.221155	−	0.383052i
$482$	−0.124706			−0.00568020
$483$		0			0
$484$	−2.51860			−0.114482
$485$	−10.4768	−	18.1463i	−0.475725	−	0.823980i
$486$		0			0
$487$	11.3160	−	19.5999i	0.512777	−	0.888156i	−0.487113	−	0.873339i	$-0.661950\pi$
$487$	11.3160	−	19.5999i	0.512777	−	0.888156i	0.999890	−	0.0148172i	$-0.00471664\pi$
$488$	−1.57198	−	2.72275i	−0.0711603	−	0.123253i
$489$		0			0
$490$	7.06699	−	7.15375i	0.319254	−	0.323173i
$491$	1.20460			0.0543630			0.0271815	−	0.999631i	$-0.491347\pi$
$491$	1.20460			0.0543630			0.0271815	+	0.999631i	$0.491347\pi$
$492$		0			0
$493$	5.17203	−	8.95822i	0.232936	−	0.403458i
$494$	0.990057	−	1.71483i	0.0445448	−	0.0771538i
$495$		0			0
$496$	−11.7504			−0.527610
$497$	1.81105	+	0.232811i	0.0812367	+	0.0104430i
$498$		0			0
$499$	−15.4069	−	26.6855i	−0.689706	−	1.19461i	−0.971933	−	0.235258i	$-0.924406\pi$
$499$	−15.4069	−	26.6855i	−0.689706	−	1.19461i	0.282227	−	0.959348i	$-0.408927\pi$
$500$	−3.83722	+	6.64626i	−0.171606	+	0.297230i
$501$		0			0
$502$	−12.1149	−	20.9837i	−0.540716	−	0.936548i
$503$	13.9302			0.621116			0.310558	−	0.950554i	$-0.399484\pi$
$503$	13.9302			0.621116			0.310558	+	0.950554i	$0.399484\pi$
$504$		0			0
$505$	−5.00019			−0.222505
$506$	3.44288	+	5.96324i	0.153055	+	0.265098i
$507$		0			0
$508$	−5.21644	+	9.03514i	−0.231442	+	0.400869i
$509$	19.2235	+	33.2962i	0.852069	+	1.47583i	0.879338	+	0.476198i	$0.157986\pi$
$509$	19.2235	+	33.2962i	0.852069	+	1.47583i	−0.0272691	+	0.999628i	$0.508681\pi$
$510$		0			0
$511$	−7.69250	+	10.0886i	−0.340296	+	0.446295i
$512$	20.4023			0.901665
$513$		0			0
$514$	−0.300338	+	0.520200i	−0.0132473	+	0.0229450i
$515$	−8.34651	+	14.4566i	−0.367791	+	0.637033i
$516$		0			0
$517$	0.981649			0.0431729
$518$	8.78182	−	11.5173i	0.385851	−	0.506040i
$519$		0			0
$520$	−3.91683	−	6.78415i	−0.171764	−	0.297505i
$521$	20.7578	−	35.9536i	0.909417	−	1.57516i	0.0945404	−	0.995521i	$-0.469862\pi$
$521$	20.7578	−	35.9536i	0.909417	−	1.57516i	0.814876	−	0.579635i	$-0.196805\pi$
$522$		0			0
$523$	2.57508	+	4.46016i	0.112600	+	0.195029i	0.916818	−	0.399305i	$-0.130749\pi$
$523$	2.57508	+	4.46016i	0.112600	+	0.195029i	−0.804218	+	0.594335i	$0.797415\pi$
$524$	−12.7548			−0.557198
$525$		0			0
$526$	21.4420			0.934918
$527$	2.88019	+	4.98863i	0.125463	+	0.217308i
$528$		0			0
$529$	10.2218	−	17.7047i	0.444426	−	0.769769i
$530$	−3.51343	−	6.08544i	−0.152614	−	0.264335i
$531$		0			0
$532$	−1.65119	−	0.212261i	−0.0715881	−	0.00920269i
$533$	−7.71155			−0.334024
$534$		0			0
$535$	−0.686907	+	1.18976i	−0.0296976	+	0.0514377i
$536$	−16.8264	+	29.1442i	−0.726791	+	1.25884i
$537$		0			0
$538$	2.98665			0.128764
$539$	−18.7299	+	18.9599i	−0.806754	+	0.816659i
$540$		0			0
$541$	−18.5457	−	32.1222i	−0.797344	−	1.38104i	−0.921340	−	0.388757i	$-0.872904\pi$
$541$	−18.5457	−	32.1222i	−0.797344	−	1.38104i	0.123996	−	0.992283i	$-0.460429\pi$
$542$	−16.0707	+	27.8353i	−0.690296	+	1.19563i
$543$		0			0
$544$	−1.92359	−	3.33176i	−0.0824734	−	0.142848i
$545$	22.6889			0.971887
$546$		0			0
$547$	40.6339			1.73738			0.868689	−	0.495357i	$-0.164963\pi$
$547$	40.6339			1.73738			0.868689	+	0.495357i	$0.164963\pi$
$548$	4.66538	+	8.08068i	0.199295	+	0.345190i
$549$		0			0
$550$	−7.29361	+	12.6329i	−0.311000	+	0.538669i
$551$	−4.51682	−	7.82336i	−0.192423	−	0.333286i
$552$		0			0
$553$	9.05658	+	21.6773i	0.385125	+	0.921811i
$554$	−19.6122			−0.833244
$555$		0			0
$556$	−8.07452	+	13.9855i	−0.342436	+	0.593117i
$557$	−1.71403	+	2.96878i	−0.0726257	+	0.125791i	−0.900051	−	0.435784i	$-0.856471\pi$
$557$	−1.71403	+	2.96878i	−0.0726257	+	0.125791i	0.827426	+	0.561575i	$0.189805\pi$
$558$		0			0
$559$	12.6186			0.533711
$560$	4.15590	−	5.45041i	0.175619	−	0.230322i
$561$		0			0
$562$	−0.681756	−	1.18084i	−0.0287582	−	0.0498106i
$563$	2.01729	−	3.49406i	0.0850188	−	0.147257i	−0.820380	−	0.571818i	$-0.806238\pi$
$563$	2.01729	−	3.49406i	0.0850188	−	0.147257i	0.905399	+	0.424561i	$0.139572\pi$
$564$		0			0
$565$	4.50520	+	7.80324i	0.189535	+	0.328285i
$566$	−11.3323			−0.476332
$567$		0			0
$568$	2.12378			0.0891118
$569$	5.89464	+	10.2098i	0.247116	+	0.428018i	0.962724	−	0.270484i	$-0.0871837\pi$
$569$	5.89464	+	10.2098i	0.247116	+	0.428018i	−0.715608	+	0.698502i	$0.753850\pi$
$570$		0			0
$571$	−9.60544	+	16.6371i	−0.401975	+	0.696241i	−0.993964	−	0.109705i	$-0.965009\pi$
$571$	−9.60544	+	16.6371i	−0.401975	+	0.696241i	0.591989	+	0.805946i	$0.298343\pi$
$572$	2.74930	+	4.76193i	0.114954	+	0.199106i
$573$		0			0
$574$	−4.43850	−	10.6237i	−0.185259	−	0.443425i
$575$	−5.41561			−0.225846
$576$		0			0
$577$	16.2203	−	28.0944i	0.675261	−	1.16959i	−0.301132	−	0.953583i	$-0.597364\pi$
$577$	16.2203	−	28.0944i	0.675261	−	1.16959i	0.976393	−	0.216004i	$-0.0693023\pi$
$578$	0.565575	−	0.979604i	0.0235248	−	0.0407461i
$579$		0			0
$580$	−9.46506			−0.393015
$581$	−39.7956	−	5.11575i	−1.65100	−	0.212237i
$582$		0			0
$583$	9.31178	+	16.1285i	0.385654	+	0.667973i
$584$	−7.37806	+	12.7792i	−0.305306	+	0.528806i
$585$		0			0
$586$	−14.0012	−	24.2507i	−0.578383	−	1.00179i
$587$	19.7468			0.815037			0.407518	−	0.913197i	$-0.366394\pi$
$587$	19.7468			0.815037			0.407518	+	0.913197i	$0.366394\pi$
$588$		0			0
$589$	5.03063			0.207284
$590$	−1.68918	−	2.92575i	−0.0695425	−	0.120451i
$591$		0			0
$592$	4.93599	−	8.54938i	0.202868	−	0.351377i
$593$	−6.89254	−	11.9382i	−0.283043	−	0.490244i	0.689090	−	0.724676i	$-0.258010\pi$
$593$	−6.89254	−	11.9382i	−0.283043	−	0.490244i	−0.972133	+	0.234431i	$0.924677\pi$
$594$		0			0
$595$	−3.33263	−	0.428411i	−0.136625	−	0.0175632i
$596$	15.5664			0.637624
$597$		0			0
$598$	1.81260	−	3.13951i	0.0741227	−	0.128384i
$599$	0.622119	−	1.07754i	0.0254191	−	0.0440271i	−0.853036	−	0.521852i	$-0.825241\pi$
$599$	0.622119	−	1.07754i	0.0254191	−	0.0440271i	0.878455	+	0.477825i	$0.158575\pi$
$600$		0			0
$601$	9.66516			0.394250			0.197125	−	0.980378i	$-0.436840\pi$
$601$	9.66516			0.394250			0.197125	+	0.980378i	$0.436840\pi$
$602$	7.26284	+	17.3839i	0.296011	+	0.708513i
$603$		0			0
$604$	2.47946	+	4.29455i	0.100888	+	0.174743i
$605$	−2.21969	+	3.84461i	−0.0902432	+	0.156306i
$606$		0			0
$607$	21.5518	+	37.3288i	0.874760	+	1.51513i	0.857018	+	0.515286i	$0.172314\pi$
$607$	21.5518	+	37.3288i	0.874760	+	1.51513i	0.0177418	+	0.999843i	$0.494352\pi$
$608$	−3.35981			−0.136258
$609$		0			0
$610$	−1.46766			−0.0594239
$611$	−0.258408	−	0.447576i	−0.0104541	−	0.0181070i
$612$		0			0
$613$	11.4314	−	19.7997i	0.461709	−	0.799704i	−0.537337	−	0.843368i	$-0.680570\pi$
$613$	11.4314	−	19.7997i	0.461709	−	0.799704i	0.999046	+	0.0436636i	$0.0139030\pi$
$614$	1.50372	+	2.60452i	0.0606853	+	0.105110i
$615$		0			0
$616$	−18.7954	+	24.6500i	−0.757288	+	0.993175i
$617$	33.6339			1.35405			0.677024	−	0.735961i	$-0.263269\pi$
$617$	33.6339			1.35405			0.677024	+	0.735961i	$0.263269\pi$
$618$		0			0
$619$	−18.0514	+	31.2659i	−0.725546	+	1.25668i	0.233203	+	0.972428i	$0.425079\pi$
$619$	−18.0514	+	31.2659i	−0.725546	+	1.25668i	−0.958749	+	0.284254i	$0.908254\pi$
$620$	2.63544	−	4.56472i	0.105842	−	0.183323i
$621$		0			0
$622$	−0.685676			−0.0274931
$623$	−5.57525	−	13.3446i	−0.223368	−	0.534639i
$624$		0			0
$625$	−1.70425	−	2.95185i	−0.0681702	−	0.118074i
$626$	2.05007	−	3.55083i	0.0819374	−	0.141920i
$627$		0			0
$628$	−4.87726	−	8.44767i	−0.194624	−	0.337099i
$629$	−4.83950			−0.192964
$630$		0			0
$631$	−14.0386			−0.558866			−0.279433	−	0.960165i	$-0.590147\pi$
$631$	−14.0386			−0.558866			−0.279433	+	0.960165i	$0.590147\pi$
$632$	13.6625	+	23.6641i	0.543465	+	0.941309i
$633$		0			0
$634$	17.4289	−	30.1877i	0.692188	−	1.19891i
$635$	9.19467	+	15.9256i	0.364880	+	0.631990i
$636$		0			0
$637$	13.5751	+	3.54881i	0.537863	+	0.140609i
$638$	−44.5481			−1.76368
$639$		0			0
$640$	1.17022	−	2.02689i	0.0462571	−	0.0801197i
$641$	−11.5711	+	20.0418i	−0.457032	+	0.791603i	−0.998803	−	0.0489233i	$-0.984421\pi$
$641$	−11.5711	+	20.0418i	−0.457032	+	0.791603i	0.541770	+	0.840527i	$0.317754\pi$
$642$		0			0
$643$	42.5561			1.67825			0.839124	−	0.543940i	$-0.183068\pi$
$643$	42.5561			1.67825			0.839124	+	0.543940i	$0.183068\pi$
$644$	−3.02300	−	0.388608i	−0.119123	−	0.0153133i
$645$		0			0
$646$	−0.493926	−	0.855504i	−0.0194332	−	0.0336594i
$647$	22.8574	−	39.5902i	0.898617	−	1.55645i	0.0693527	−	0.997592i	$-0.477907\pi$
$647$	22.8574	−	39.5902i	0.898617	−	1.55645i	0.829264	−	0.558857i	$-0.188760\pi$
$648$		0			0
$649$	4.47690	+	7.75422i	0.175734	+	0.304380i
$650$	7.67985			0.301228
$651$		0			0
$652$	2.37745			0.0931082
$653$	1.09774	+	1.90135i	0.0429580	+	0.0744055i	0.886705	−	0.462336i	$-0.152988\pi$
$653$	1.09774	+	1.90135i	0.0429580	+	0.0744055i	−0.843747	+	0.536741i	$0.819655\pi$
$654$		0			0
$655$	−11.2411	+	19.4701i	−0.439225	+	0.760759i
$656$	−3.92389	−	6.79637i	−0.153202	−	0.265354i
$657$		0			0
$658$	0.467866	−	0.613601i	0.0182393	−	0.0239207i
$659$	16.5488			0.644650			0.322325	−	0.946629i	$-0.395536\pi$
$659$	16.5488			0.644650			0.322325	+	0.946629i	$0.395536\pi$
$660$		0			0
$661$	−9.17616	+	15.8936i	−0.356911	+	0.618189i	−0.987443	−	0.157975i	$-0.949504\pi$
$661$	−9.17616	+	15.8936i	−0.356911	+	0.618189i	0.630532	+	0.776163i	$0.282837\pi$
$662$	19.6142	−	33.9728i	0.762329	−	1.32039i
$663$		0			0
$664$	−46.6675			−1.81105
$665$	−1.77923	+	2.33345i	−0.0689958	+	0.0904872i
$666$		0			0
$667$	−8.26940	−	14.3230i	−0.320192	−	0.554590i
$668$	0.117886	−	0.204184i	0.00456114	−	0.00790013i
$669$		0			0
$670$	7.85489	+	13.6051i	0.303461	+	0.525610i
$671$	3.88980			0.150164
$672$		0			0
$673$	−5.15709			−0.198791			−0.0993957	−	0.995048i	$-0.531691\pi$
$673$	−5.15709			−0.198791			−0.0993957	+	0.995048i	$0.531691\pi$
$674$	8.24943	+	14.2884i	0.317756	+	0.550370i
$675$		0			0
$676$	−3.23582	+	5.60460i	−0.124454	+	0.215561i
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	0.917899	−	0.396813i	$-0.129884\pi$
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	−0.802600	+	0.596518i	$0.796551\pi$
$678$		0			0
$679$	43.2962	+	5.56575i	1.66156	+	0.213594i
$680$	−3.90810			−0.149869
$681$		0			0
$682$	12.4039	−	21.4842i	0.474971	−	0.822673i
$683$	−12.7561	+	22.0941i	−0.488097	+	0.845409i	−0.999906	−	0.0136901i	$-0.995642\pi$
$683$	−12.7561	+	22.0941i	−0.488097	+	0.845409i	0.511809	+	0.859099i	$0.328975\pi$
$684$		0			0
$685$	16.4467			0.628397
$686$	2.92437	+	20.7441i	0.111653	+	0.792012i
$687$		0			0
$688$	6.42076	+	11.1211i	0.244789	+	0.423987i
$689$	4.90245	−	8.49129i	0.186768	−	0.323492i
$690$		0			0
$691$	−17.8153	−	30.8570i	−0.677725	−	1.17385i	−0.975664	−	0.219269i	$-0.929633\pi$
$691$	−17.8153	−	30.8570i	−0.677725	−	1.17385i	0.297940	−	0.954585i	$-0.403701\pi$
$692$	11.7110			0.445185
$693$		0			0
$694$	−38.7535			−1.47106
$695$	14.2324	+	24.6513i	0.539867	+	0.935077i
$696$		0			0
$697$	−1.92359	+	3.33176i	−0.0728613	+	0.126199i
$698$	−16.8096	−	29.1150i	−0.636252	−	1.10202i
$699$		0			0
$700$	−2.48910	−	5.95775i	−0.0940792	−	0.225182i
$701$	37.6000			1.42013			0.710067	−	0.704134i	$-0.248665\pi$
$701$	37.6000			1.42013			0.710067	+	0.704134i	$0.248665\pi$
$702$		0			0
$703$	−2.11321	+	3.66018i	−0.0797012	+	0.138046i
$704$	−16.0506	+	27.8005i	−0.604932	+	1.04777i
$705$		0			0
$706$	−0.896010			−0.0337218
$707$	6.31616	−	8.28358i	0.237544	−	0.311536i
$708$		0			0
$709$	9.85612	+	17.0713i	0.370154	+	0.641126i	0.989589	−	0.143922i	$-0.0459715\pi$
$709$	9.85612	+	17.0713i	0.370154	+	0.641126i	−0.619435	+	0.785048i	$0.712638\pi$
$710$	0.495710	−	0.858595i	0.0186037	−	0.0322225i
$711$		0			0
$712$	−8.41066	−	14.5677i	−0.315203	−	0.545948i
$713$	9.21009			0.344921
$714$		0			0
$715$	9.69202			0.362461
$716$	−5.96916	−	10.3389i	−0.223078	−	0.386383i
$717$		0			0
$718$	−4.51283	+	7.81645i	−0.168417	+	0.291707i
$719$	−22.6696	−	39.2648i	−0.845432	−	1.46433i	−0.885246	−	0.465124i	$-0.846010\pi$
$719$	−22.6696	−	39.2648i	−0.845432	−	1.46433i	0.0398135	−	0.999207i	$-0.487324\pi$
$720$		0			0
$721$	−13.4064	−	32.0886i	−0.499279	−	1.19504i
$722$	20.6291			0.767737
$723$		0			0
$724$	2.28616	−	3.95975i	0.0849645	−	0.147163i
$725$	17.5184	−	30.3428i	0.650618	−	1.12690i
$726$		0			0
$727$	42.1706			1.56402			0.782010	−	0.623266i	$-0.214195\pi$
$727$	42.1706			1.56402			0.782010	+	0.623266i	$0.214195\pi$
$728$	16.1867	+	2.08080i	0.599918	+	0.0771197i
$729$		0			0
$730$	3.44422	+	5.96556i	0.127476	+	0.220795i
$731$	3.14763	−	5.45185i	0.116419	−	0.201644i
$732$		0			0
$733$	−7.86938	−	13.6302i	−0.290662	−	0.503441i	0.683304	−	0.730134i	$-0.260542\pi$
$733$	−7.86938	−	13.6302i	−0.290662	−	0.503441i	−0.973966	+	0.226692i	$0.927209\pi$
$734$	−13.7296			−0.506768
$735$		0			0
$736$	−6.15115			−0.226734
$737$	−20.8181	−	36.0580i	−0.766845	−	1.32822i
$738$		0			0
$739$	−5.95012	+	10.3059i	−0.218879	+	0.379109i	−0.954465	−	0.298321i	$-0.903573\pi$
$739$	−5.95012	+	10.3059i	−0.218879	+	0.379109i	0.735587	+	0.677431i	$0.236907\pi$
$740$	2.21413	+	3.83499i	0.0813930	+	0.140977i
$741$		0			0
$742$	14.5196	+	1.86650i	0.533030	+	0.0685213i
$743$	−4.32945			−0.158832			−0.0794161	−	0.996842i	$-0.525306\pi$
$743$	−4.32945			−0.158832			−0.0794161	+	0.996842i	$0.525306\pi$
$744$		0			0
$745$	13.7189	−	23.7619i	0.502622	−	0.870567i
$746$	15.0023	−	25.9848i	0.549273	−	0.951370i
$747$		0			0
$748$	2.74318			0.100300
$749$	−1.10333	−	2.64085i	−0.0403146	−	0.0964945i
$750$		0			0
$751$	−8.17507	−	14.1596i	−0.298313	−	0.516693i	0.677437	−	0.735580i	$-0.263090\pi$
$751$	−8.17507	−	14.1596i	−0.298313	−	0.516693i	−0.975750	+	0.218888i	$0.929757\pi$
$752$	0.262973	−	0.455482i	0.00958963	−	0.0166097i
$753$		0			0
$754$	11.7268	+	20.3114i	0.427065	+	0.739698i
$755$	8.74076			0.318109
$756$		0			0
$757$	−8.29059			−0.301327			−0.150663	−	0.988585i	$-0.548141\pi$
$757$	−8.29059			−0.301327			−0.150663	+	0.988585i	$0.548141\pi$
$758$	−6.92918	−	12.0017i	−0.251679	−	0.435921i
$759$		0			0
$760$	−1.70651	+	2.95576i	−0.0619015	+	0.107217i
$761$	7.19409	+	12.4605i	0.260786	+	0.451694i	0.966451	−	0.256851i	$-0.0826851\pi$
$761$	7.19409	+	12.4605i	0.260786	+	0.451694i	−0.705665	+	0.708545i	$0.749352\pi$
$762$		0			0
$763$	−28.6603	+	37.5877i	−1.03757	+	1.36077i
$764$	1.29851			0.0469783
$765$		0			0
$766$	−10.4276	+	18.0612i	−0.376765	+	0.652576i
$767$	2.35699	−	4.08243i	0.0851060	−	0.147408i
$768$		0			0
$769$	5.87349			0.211804			0.105902	−	0.994377i	$-0.466227\pi$
$769$	5.87349			0.211804			0.105902	+	0.994377i	$0.466227\pi$
$770$	5.57839	+	13.3521i	0.201031	+	0.481175i
$771$		0			0
$772$	−1.38048	−	2.39106i	−0.0496846	−	0.0860562i
$773$	3.44609	−	5.96881i	0.123947	−	0.214683i	−0.797374	−	0.603486i	$-0.793778\pi$
$773$	3.44609	−	5.96881i	0.123947	−	0.214683i	0.921321	+	0.388803i	$0.127111\pi$
$774$		0			0
$775$	9.75562	+	16.8972i	0.350432	+	0.606966i
$776$	50.7725			1.82263
$777$		0			0
$778$	−34.9167			−1.25182
$779$	1.67991	+	2.90968i	0.0601889	+	0.104250i
$780$		0			0
$781$	−1.31380	+	2.27557i	−0.0470114	+	0.0814262i
$782$	−0.904280	−	1.56626i	−0.0323370	−	0.0560093i
$783$		0			0
$784$	3.77978	+	13.7698i	0.134992	+	0.491777i
$785$	−17.1937			−0.613668
$786$		0			0
$787$	−20.8369	+	36.0905i	−0.742754	+	1.28649i	0.208483	+	0.978026i	$0.433147\pi$
$787$	−20.8369	+	36.0905i	−0.742754	+	1.28649i	−0.951237	+	0.308461i	$0.900186\pi$
$788$	1.11890	−	1.93798i	0.0398590	−	0.0690378i
$789$		0			0
$790$	12.7558			0.453832
$791$	−18.6182	−	2.39338i	−0.661986	−	0.0850986i
$792$		0			0
$793$	−1.02395	−	1.77353i	−0.0363614	−	0.0629798i
$794$	6.30914	−	10.9277i	0.223903	−	0.387811i
$795$		0			0
$796$	2.65065	+	4.59107i	0.0939499	+	0.162726i
$797$	−5.89623			−0.208855			−0.104428	−	0.994532i	$-0.533301\pi$
$797$	−5.89623			−0.208855			−0.104428	+	0.994532i	$0.533301\pi$
$798$		0			0
$799$	−0.257832			−0.00912146
$800$	−6.51549	−	11.2852i	−0.230357	−	0.398991i
$801$		0			0
$802$	−10.9838	+	19.0244i	−0.387850	+	0.671776i
$803$	−9.12834	−	15.8107i	−0.322132	−	0.557949i
$804$		0			0
$805$	−3.25743	+	4.27208i	−0.114809	+	0.150571i
$806$	−13.0608			−0.460046
$807$		0			0
$808$	6.05798	−	10.4927i	0.213119	−	0.369133i
$809$	16.5150	−	28.6048i	0.580636	−	1.00569i	−0.414768	−	0.909927i	$-0.636137\pi$
$809$	16.5150	−	28.6048i	0.580636	−	1.00569i	0.995404	−	0.0957637i	$-0.0305293\pi$
$810$		0			0
$811$	40.9506			1.43797			0.718985	−	0.695025i	$-0.244607\pi$
$811$	40.9506			1.43797			0.718985	+	0.695025i	$0.244607\pi$
$812$	11.9561	−	15.6803i	0.419577	−	0.550271i
$813$		0			0
$814$	10.4210	+	18.0497i	0.365256	+	0.632641i
$815$	2.09529	−	3.62915i	0.0733948	−	0.127124i
$816$		0			0
$817$	−2.74887	−	4.76119i	−0.0961709	−	0.166573i
$818$	−3.11966			−0.109076
$819$		0			0
$820$	3.52027			0.122933
$821$	−26.1415	−	45.2784i	−0.912344	−	1.58023i	−0.810744	−	0.585401i	$-0.800937\pi$
$821$	−26.1415	−	45.2784i	−0.912344	−	1.58023i	−0.101601	−	0.994825i	$-0.532396\pi$
$822$		0			0
$823$	2.39673	−	4.15126i	0.0835448	−	0.144704i	−0.821225	−	0.570604i	$-0.806709\pi$
$823$	2.39673	−	4.15126i	0.0835448	−	0.144704i	0.904770	+	0.425900i	$0.140042\pi$
$824$	−20.2244	−	35.0298i	−0.704552	−	1.22032i
$825$		0			0
$826$	6.98070	+	0.897372i	0.242890	+	0.0312236i
$827$	23.2746			0.809336			0.404668	−	0.914464i	$-0.367387\pi$
$827$	23.2746			0.809336			0.404668	+	0.914464i	$0.367387\pi$
$828$		0			0
$829$	−0.231610	+	0.401161i	−0.00804416	+	0.0139329i	−0.870019	−	0.493017i	$-0.835894\pi$
$829$	−0.231610	+	0.401161i	−0.00804416	+	0.0139329i	0.861975	+	0.506950i	$0.169227\pi$
$830$	−10.8926	+	18.8666i	−0.378089	+	0.654869i
$831$		0			0
$832$	16.9006			0.585924
$833$	4.91946	−	4.97985i	0.170449	−	0.172542i
$834$		0			0
$835$	−0.207790	−	0.359902i	−0.00719086	−	0.0124549i
$836$	1.19783	−	2.07470i	0.0414278	−	0.0717551i
$837$		0			0
$838$	13.7061	+	23.7396i	0.473468	+	0.820071i
$839$	−36.3733			−1.25575			−0.627873	−	0.778316i	$-0.716074\pi$
$839$	−36.3733			−1.25575			−0.627873	+	0.778316i	$0.716074\pi$
$840$		0			0
$841$	77.9995			2.68964
$842$	10.9819	+	19.0212i	0.378462	+	0.655515i
$843$		0			0
$844$	−3.67068	+	6.35780i	−0.126350	+	0.218845i
$845$	5.70356	+	9.87886i	0.196208	+	0.339843i
$846$		0			0
$847$	−3.56531	−	8.53371i	−0.122506	−	0.293222i
$848$	9.97809			0.342649
$849$		0			0
$850$	1.91568	−	3.31806i	0.0657074	−	0.113809i
$851$	−3.86887	+	6.70107i	−0.132623	+	0.229710i
$852$		0			0
$853$	−37.6533			−1.28922			−0.644612	−	0.764510i	$-0.722981\pi$
$853$	−37.6533			−1.28922			−0.644612	+	0.764510i	$0.722981\pi$
$854$	1.85393	−	2.43141i	0.0634401	−	0.0832010i
$855$		0			0
$856$	−1.66444	−	2.88290i	−0.0568895	−	0.0985356i
$857$	26.4986	−	45.8969i	0.905175	−	1.56781i	0.0844936	−	0.996424i	$-0.473073\pi$
$857$	26.4986	−	45.8969i	0.905175	−	1.56781i	0.820682	−	0.571386i	$-0.193594\pi$
$858$		0			0
$859$	−1.54281	−	2.67223i	−0.0526401	−	0.0911753i	0.838505	−	0.544894i	$-0.183430\pi$
$859$	−1.54281	−	2.67223i	−0.0526401	−	0.0911753i	−0.891145	+	0.453719i	$0.850097\pi$
$860$	−5.76031			−0.196425
$861$		0			0
$862$	−17.2054			−0.586019
$863$	8.13128	+	14.0838i	0.276792	+	0.479418i	0.970586	−	0.240756i	$-0.0773954\pi$
$863$	8.13128	+	14.0838i	0.276792	+	0.479418i	−0.693794	+	0.720174i	$0.744062\pi$
$864$		0			0
$865$	10.3211	−	17.8767i	0.350928	−	0.607825i
$866$	6.38453	+	11.0583i	0.216955	+	0.375777i
$867$		0			0
$868$	4.23311	+	10.1321i	0.143681	+	0.343906i
$869$	−33.8072			−1.14683
$870$		0			0
$871$	−10.9603	+	18.9838i	−0.371375	+	0.643240i
$872$	−27.4888	+	47.6120i	−0.930888	+	1.61235i
$873$		0			0
$874$	−1.57945			−0.0534255
$875$	−27.9513	−	3.59315i	−0.944925	−	0.121471i
$876$		0			0
$877$	−25.7774	−	44.6478i	−0.870442	−	1.50765i	−0.861540	−	0.507690i	$-0.830500\pi$
$877$	−25.7774	−	44.6478i	−0.870442	−	1.50765i	−0.00890200	−	0.999960i	$-0.502834\pi$
$878$	−21.4446	+	37.1431i	−0.723720	+	1.25352i
$879$		0			0
$880$	4.93161	+	8.54180i	0.166245	+	0.287944i
$881$	3.58468			0.120771			0.0603855	−	0.998175i	$-0.480767\pi$
$881$	3.58468			0.120771			0.0603855	+	0.998175i	$0.480767\pi$
$882$		0			0
$883$	19.0576			0.641340			0.320670	−	0.947191i	$-0.396092\pi$
$883$	19.0576			0.641340			0.320670	+	0.947191i	$0.396092\pi$
$884$	−0.722111	−	1.25073i	−0.0242872	−	0.0420667i
$885$		0			0
$886$	0.340117	−	0.589100i	0.0114265	−	0.0197912i
$887$	3.29080	+	5.69984i	0.110494	+	0.191382i	0.915970	−	0.401247i	$-0.131423\pi$
$887$	3.29080	+	5.69984i	0.110494	+	0.191382i	−0.805475	+	0.592629i	$0.798090\pi$
$888$		0			0
$889$	−37.9978	−	4.88464i	−1.27441	−	0.163826i
$890$	−7.85251			−0.263217
$891$		0			0
$892$	−5.82663	+	10.0920i	−0.195090	+	0.337906i
$893$	−0.112585	+	0.195002i	−0.00376750	+	0.00652551i
$894$		0			0
$895$	−21.0429			−0.703387
$896$	1.87964	+	4.49898i	0.0627943	+	0.150301i
$897$		0			0
$898$	−14.6038	−	25.2946i	−0.487336	−	0.844091i
$899$	−29.7928	+	51.6027i	−0.993646	+	1.72105i
$900$		0			0
$901$	−2.44576	−	4.23618i	−0.0814802	−	0.141128i
$902$	16.5684			0.551668
$903$		0			0
$904$	−21.8331			−0.726159
$905$	−4.02967	−	6.97959i	−0.133951	−	0.232009i
$906$		0			0
$907$	14.1716	−	24.5460i	0.470561	−	0.815036i	−0.528872	−	0.848702i	$-0.677385\pi$
$907$	14.1716	−	24.5460i	0.470561	−	0.815036i	0.999433	+	0.0336654i	$0.0107181\pi$
$908$	6.10595	+	10.5758i	0.202633	+	0.350971i
$909$		0			0
$910$	4.61934	−	6.05822i	0.153130	−	0.200828i
$911$	−24.3403			−0.806430			−0.403215	−	0.915105i	$-0.632107\pi$
$911$	−24.3403			−0.806430			−0.403215	+	0.915105i	$0.632107\pi$
$912$		0			0
$913$	28.8692	−	50.0028i	0.955430	−	1.65485i
$914$	9.03976	−	15.6573i	0.299009	−	0.517899i
$915$		0			0
$916$	−20.2073			−0.667667
$917$	−18.0556	−	43.2169i	−0.596250	−	1.42715i
$918$		0			0
$919$	1.37495	+	2.38148i	0.0453553	+	0.0785577i	0.887812	−	0.460207i	$-0.152225\pi$
$919$	1.37495	+	2.38148i	0.0453553	+	0.0785577i	−0.842457	+	0.538764i	$0.818891\pi$
$920$	−3.12427	+	5.41140i	−0.103004	+	0.178409i
$921$		0			0
$922$	−7.34127	−	12.7155i	−0.241772	−	0.418761i
$923$	1.38337			0.0455343
$924$		0			0
$925$	−16.3921			−0.538969
$926$	13.4137	+	23.2333i	0.440802	+	0.763492i
$927$		0			0
$928$	19.8978	−	34.4639i	0.653176	−	1.13133i
$929$	11.2906	+	19.5560i	0.370434	+	0.641610i	0.989632	−	0.143624i	$-0.0458757\pi$
$929$	11.2906	+	19.5560i	0.370434	+	0.641610i	−0.619198	+	0.785235i	$0.712542\pi$
$930$		0			0
$931$	−1.61821	−	5.89515i	−0.0530347	−	0.193206i
$932$	−0.933653			−0.0305828
$933$		0			0
$934$	−2.15745	+	3.73682i	−0.0705940	+	0.122272i
$935$	2.41761	−	4.18742i	0.0790642	−	0.136943i
$936$		0			0
$937$	1.72499			0.0563529			0.0281764	−	0.999603i	$-0.491030\pi$
$937$	1.72499			0.0563529			0.0281764	+	0.999603i	$0.491030\pi$
$938$	−32.4611	−	4.17289i	−1.05989	−	0.136250i
$939$		0			0
$940$	0.117961	+	0.204315i	0.00384748	+	0.00666403i
$941$	16.5097	−	28.5956i	0.538201	−	0.932191i	−0.460800	−	0.887504i	$-0.652438\pi$
$941$	16.5097	−	28.5956i	0.538201	−	0.932191i	0.999001	−	0.0446870i	$-0.0142291\pi$
$942$		0			0
$943$	3.07557	+	5.32705i	0.100154	+	0.173473i
$944$	4.79725			0.156137
$945$		0			0
$946$	−27.1114			−0.881467
$947$	0.877744	+	1.52030i	0.0285228	+	0.0494030i	0.879934	−	0.475095i	$-0.157586\pi$
$947$	0.877744	+	1.52030i	0.0285228	+	0.0494030i	−0.851412	+	0.524498i	$0.824253\pi$
$948$		0			0
$949$	−4.80587	+	8.32401i	−0.156005	+	0.270209i
$950$	−1.67300	−	2.89772i	−0.0542793	−	0.0940144i
$951$		0			0
$952$	4.93666	−	6.47438i	0.159998	−	0.209836i
$953$	−12.5307			−0.405908			−0.202954	−	0.979188i	$-0.565054\pi$
$953$	−12.5307			−0.405908			−0.202954	+	0.979188i	$0.565054\pi$
$954$		0			0
$955$	1.14440	−	1.98215i	0.0370318	−	0.0641410i
$956$	8.38375	−	14.5211i	0.271150	−	0.469645i
$957$		0			0
$958$	−30.0089			−0.969544
$959$	−20.7753	+	27.2465i	−0.670868	+	0.879836i
$960$		0			0
$961$	−1.09096	−	1.88960i	−0.0351923	−	0.0609549i
$962$	5.48642	−	9.50276i	0.176889	−	0.306381i
$963$		0			0
$964$	0.0397166	+	0.0687912i	0.00127919	+	0.00221561i
$965$	−4.86656			−0.156660
$966$		0			0
$967$	11.2810			0.362771			0.181386	−	0.983412i	$-0.441942\pi$
$967$	11.2810			0.362771			0.181386	+	0.983412i	$0.441942\pi$
$968$	−5.37853	−	9.31589i	−0.172872	−	0.299424i
$969$		0			0
$970$	11.8508	−	20.5262i	0.380506	−	0.659055i
$971$	11.7128	+	20.2872i	0.375881	+	0.651046i	0.990459	−	0.137811i	$-0.0440067\pi$
$971$	11.7128	+	20.2872i	0.375881	+	0.651046i	−0.614577	+	0.788857i	$0.710673\pi$
$972$		0			0
$973$	−58.8168	−	7.56093i	−1.88558	−	0.242392i
$974$	25.6002			0.820283
$975$		0			0
$976$	1.04203	−	1.80486i	0.0333547	−	0.0577720i
$977$	19.2008	−	33.2567i	0.614287	−	1.06398i	−0.376222	−	0.926530i	$-0.622777\pi$
$977$	19.2008	−	33.2567i	0.614287	−	1.06398i	0.990509	−	0.137447i	$-0.0438897\pi$
$978$		0			0
$979$	20.8118			0.665148
$980$	−6.19691	−	1.62000i	−0.197953	−	0.0517491i
$981$		0			0
$982$	0.681294	+	1.18004i	0.0217410	+	0.0376564i
$983$	−6.57262	+	11.3841i	−0.209634	+	0.363097i	−0.951599	−	0.307341i	$-0.900561\pi$
$983$	−6.57262	+	11.3841i	−0.209634	+	0.363097i	0.741965	+	0.670438i	$0.233894\pi$
$984$		0			0
$985$	−1.97220	−	3.41596i	−0.0628396	−	0.108841i
$986$	11.7007			0.372625
$987$		0			0
$988$	−1.26126			−0.0401261
$989$	−5.03264	−	8.71680i	−0.160029	−	0.277178i
$990$		0			0
$991$	5.98714	−	10.3700i	0.190188	−	0.329415i	−0.755125	−	0.655581i	$-0.772424\pi$
$991$	5.98714	−	10.3700i	0.190188	−	0.329415i	0.945312	+	0.326166i	$0.105757\pi$
$992$	11.0806	+	19.1922i	0.351810	+	0.609353i
$993$		0			0
$994$	0.796221	+	1.90578i	0.0252546	+	0.0604478i
$995$	9.34427			0.296233
$996$		0			0
$997$	−13.9204	+	24.1109i	−0.440865	+	0.763600i	−0.997754	−	0.0669867i	$-0.978661\pi$
$997$	−13.9204	+	24.1109i	−0.440865	+	0.763600i	0.556889	+	0.830587i	$0.311995\pi$
$998$	17.4275	−	30.1852i	0.551657	−	0.955497i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1071.2.i.g.613.4		10
3.2	odd	2		357.2.i.f.256.2	yes	10
7.2	even	3	inner	1071.2.i.g.919.4		10
7.3	odd	6		7497.2.a.bw.1.2		5
7.4	even	3		7497.2.a.bv.1.2		5
21.2	odd	6		357.2.i.f.205.2	✓	10
21.11	odd	6		2499.2.a.ba.1.4		5
21.17	even	6		2499.2.a.bb.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.i.f.205.2	✓	10	21.2	odd	6
357.2.i.f.256.2	yes	10	3.2	odd	2
1071.2.i.g.613.4		10	1.1	even	1	trivial
1071.2.i.g.919.4		10	7.2	even	3	inner
2499.2.a.ba.1.4		5	21.11	odd	6
2499.2.a.bb.1.4		5	21.17	even	6
7497.2.a.bv.1.2		5	7.4	even	3
7497.2.a.bw.1.2		5	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1071 = 3^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1071.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.565575 + 0.979604i) q^{2} +(0.360251 - 0.623973i) q^{4} +(-0.634991 - 1.09984i) q^{5} +(2.62416 + 0.337337i) q^{7} +3.07729 q^{8} +O(q^{10})\)	\(q+(0.565575 + 0.979604i) q^{2} +(0.360251 - 0.623973i) q^{4} +(-0.634991 - 1.09984i) q^{5} +(2.62416 + 0.337337i) q^{7} +3.07729 q^{8} +(0.718269 - 1.24408i) q^{10} +(-1.90366 + 3.29723i) q^{11} +2.00447 q^{13} +(1.15370 + 2.76142i) q^{14} +(1.01994 + 1.76658i) q^{16} +(0.500000 - 0.866025i) q^{17} +(-0.436658 - 0.756314i) q^{19} -0.915024 q^{20} -4.30664 q^{22} +(-0.799435 - 1.38466i) q^{23} +(1.69357 - 2.93336i) q^{25} +(1.13367 + 1.96358i) q^{26} +(1.15584 - 1.51588i) q^{28} +10.3441 q^{29} +(-2.88019 + 4.98863i) q^{31} +(1.92359 - 3.33176i) q^{32} +1.13115 q^{34} +(-1.29530 - 3.10035i) q^{35} +(-2.41975 - 4.19113i) q^{37} +(0.493926 - 0.855504i) q^{38} +(-1.95405 - 3.38452i) q^{40} -3.84719 q^{41} +6.29525 q^{43} +(1.37159 + 2.37566i) q^{44} +(0.904280 - 1.56626i) q^{46} +(-0.128916 - 0.223289i) q^{47} +(6.77241 + 1.77045i) q^{49} +3.83137 q^{50} +(0.722111 - 1.25073i) q^{52} +(2.44576 - 4.23618i) q^{53} +4.83521 q^{55} +(8.07530 + 1.03808i) q^{56} +(5.85033 + 10.1331i) q^{58} +(1.17587 - 2.03667i) q^{59} +(-0.510833 - 0.884788i) q^{61} -6.51584 q^{62} +8.43149 q^{64} +(-1.27282 - 2.20458i) q^{65} +(-5.46793 + 9.47074i) q^{67} +(-0.360251 - 0.623973i) q^{68} +(2.30452 - 3.02236i) q^{70} +0.690145 q^{71} +(-2.39758 + 4.15273i) q^{73} +(2.73710 - 4.74079i) q^{74} -0.629226 q^{76} +(-6.10777 + 8.01028i) q^{77} +(4.43978 + 7.68992i) q^{79} +(1.29530 - 2.24353i) q^{80} +(-2.17587 - 3.76872i) q^{82} -15.1651 q^{83} -1.26998 q^{85} +(3.56043 + 6.16685i) q^{86} +(-5.85811 + 10.1465i) q^{88} +(-2.73314 - 4.73393i) q^{89} +(5.26003 + 0.676180i) q^{91} -1.15199 q^{92} +(0.145823 - 0.252574i) q^{94} +(-0.554548 + 0.960505i) q^{95} +16.4991 q^{97} +(2.09596 + 7.63560i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 8 q^{4} + q^{5} - 5 q^{7}+O(q^{10}) \) 10 * q - 2 * q^2 - 8 * q^4 + q^5 - 5 * q^7	\( 10 q - 2 q^{2} - 8 q^{4} + q^{5} - 5 q^{7} - 13 q^{10} - 11 q^{11} + 14 q^{13} - 3 q^{14} + 2 q^{16} + 5 q^{17} - 9 q^{19} - 24 q^{20} + 10 q^{22} - 23 q^{23} - 14 q^{25} + 18 q^{26} + 7 q^{28} + 36 q^{29} - 9 q^{31} + 3 q^{32} - 4 q^{34} + 5 q^{35} - 31 q^{40} - 6 q^{41} + 24 q^{43} - 33 q^{44} - 13 q^{46} + 11 q^{47} + 3 q^{49} - 48 q^{50} - 5 q^{52} - 3 q^{53} - 20 q^{55} + 27 q^{56} + 34 q^{58} - 14 q^{59} - 29 q^{61} + 10 q^{62} - 8 q^{65} - 16 q^{67} + 8 q^{68} + 18 q^{70} + 38 q^{71} - 11 q^{73} + 45 q^{74} + 18 q^{76} - 21 q^{77} - q^{79} - 5 q^{80} + 4 q^{82} - 10 q^{83} + 2 q^{85} - 3 q^{86} - 37 q^{88} + 8 q^{89} - 33 q^{91} + 96 q^{92} + 18 q^{94} - 21 q^{95} + 38 q^{97} + 17 q^{98}+O(q^{100}) \) 10 * q - 2 * q^2 - 8 * q^4 + q^5 - 5 * q^7 - 13 * q^10 - 11 * q^11 + 14 * q^13 - 3 * q^14 + 2 * q^16 + 5 * q^17 - 9 * q^19 - 24 * q^20 + 10 * q^22 - 23 * q^23 - 14 * q^25 + 18 * q^26 + 7 * q^28 + 36 * q^29 - 9 * q^31 + 3 * q^32 - 4 * q^34 + 5 * q^35 - 31 * q^40 - 6 * q^41 + 24 * q^43 - 33 * q^44 - 13 * q^46 + 11 * q^47 + 3 * q^49 - 48 * q^50 - 5 * q^52 - 3 * q^53 - 20 * q^55 + 27 * q^56 + 34 * q^58 - 14 * q^59 - 29 * q^61 + 10 * q^62 - 8 * q^65 - 16 * q^67 + 8 * q^68 + 18 * q^70 + 38 * q^71 - 11 * q^73 + 45 * q^74 + 18 * q^76 - 21 * q^77 - q^79 - 5 * q^80 + 4 * q^82 - 10 * q^83 + 2 * q^85 - 3 * q^86 - 37 * q^88 + 8 * q^89 - 33 * q^91 + 96 * q^92 + 18 * q^94 - 21 * q^95 + 38 * q^97 + 17 * q^98

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