LMFDB - Embedded newform 637.2.k.g.459.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(459,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("637.459");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.k (of order $6$, degree $2$, not 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			459.2
Root			$1.40744 - 0.138282i$ of defining polynomial
Character	$\chi$	$=$	637.459
Dual form			637.2.k.g.569.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.27656i q^{2} +(-0.583963 - 1.01145i) q^{3} +0.370384 q^{4} +(-1.57173 + 0.907437i) q^{5} +(-1.29118 + 0.745466i) q^{6} -3.02595i q^{8} +(0.817975 - 1.41677i) q^{9} +O(q^{10})$	\(q-1.27656i q^{2} +(-0.583963 - 1.01145i) q^{3} +0.370384 q^{4} +(-1.57173 + 0.907437i) q^{5} +(-1.29118 + 0.745466i) q^{6} -3.02595i q^{8} +(0.817975 - 1.41677i) q^{9} +(1.15840 + 2.00641i) q^{10} +(2.40625 - 1.38925i) q^{11} +(-0.216290 - 0.374626i) q^{12} +(3.58305 - 0.402155i) q^{13} +(1.83566 + 1.05982i) q^{15} -3.12205 q^{16} +2.74396 q^{17} +(-1.80860 - 1.04420i) q^{18} +(-5.08351 - 2.93497i) q^{19} +(-0.582143 + 0.336100i) q^{20} +(-1.77346 - 3.07173i) q^{22} -6.99909 q^{23} +(-3.06060 + 1.76704i) q^{24} +(-0.853117 + 1.47764i) q^{25} +(-0.513376 - 4.57400i) q^{26} -5.41444 q^{27} +(1.75806 - 3.04505i) q^{29} +(1.35293 - 2.34334i) q^{30} +(-1.79004 - 1.03348i) q^{31} -2.06640i q^{32} +(-2.81031 - 1.62254i) q^{33} -3.50284i q^{34} +(0.302965 - 0.524751i) q^{36} -1.74302i q^{37} +(-3.74667 + 6.48942i) q^{38} +(-2.49913 - 3.38925i) q^{39} +(2.74586 + 4.75596i) q^{40} +(-5.51406 - 3.18355i) q^{41} +(4.55195 + 7.88422i) q^{43} +(0.891235 - 0.514555i) q^{44} +2.96904i q^{45} +8.93479i q^{46} +(5.76714 - 3.32966i) q^{47} +(1.82316 + 3.15780i) q^{48} +(1.88631 + 1.08906i) q^{50} +(-1.60237 - 2.77539i) q^{51} +(1.32711 - 0.148952i) q^{52} +(5.24396 - 9.08280i) q^{53} +6.91188i q^{54} +(-2.52131 + 4.36703i) q^{55} +6.85564i q^{57} +(-3.88720 - 2.24427i) q^{58} -3.07396i q^{59} +(0.679899 + 0.392540i) q^{60} +(0.540892 - 0.936853i) q^{61} +(-1.31931 + 2.28511i) q^{62} -8.88199 q^{64} +(-5.26665 + 3.88347i) q^{65} +(-2.07127 + 3.58755i) q^{66} +(-4.34568 + 2.50898i) q^{67} +1.01632 q^{68} +(4.08721 + 7.07925i) q^{69} +(2.35453 - 1.35939i) q^{71} +(-4.28709 - 2.47515i) q^{72} +(6.64426 + 3.83607i) q^{73} -2.22508 q^{74} +1.99275 q^{75} +(-1.88285 - 1.08706i) q^{76} +(-4.32659 + 3.19030i) q^{78} +(7.86993 + 13.6311i) q^{79} +(4.90700 - 2.83306i) q^{80} +(0.707906 + 1.22613i) q^{81} +(-4.06400 + 7.03905i) q^{82} +7.97408i q^{83} +(-4.31275 + 2.48997i) q^{85} +(10.0647 - 5.81086i) q^{86} -4.10656 q^{87} +(-4.20379 - 7.28117i) q^{88} -16.0640i q^{89} +3.79017 q^{90} -2.59235 q^{92} +2.41406i q^{93} +(-4.25052 - 7.36212i) q^{94} +10.6532 q^{95} +(-2.09007 + 1.20670i) q^{96} +(12.3209 - 7.11347i) q^{97} -4.54548i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{4} - 6 q^{5} + 18 q^{6} - 4 q^{9}+O(q^{10}) $ 12 * q - 8 * q^4 - 6 * q^5 + 18 * q^6 - 4 * q^9	$ 12 q - 8 q^{4} - 6 q^{5} + 18 q^{6} - 4 q^{9} - 12 q^{10} - 6 q^{11} - 2 q^{12} - 4 q^{13} + 6 q^{15} + 16 q^{16} - 8 q^{17} + 12 q^{18} + 12 q^{20} + 6 q^{22} + 24 q^{23} + 12 q^{24} + 10 q^{25} - 18 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 18 q^{31} - 30 q^{33} - 10 q^{36} + 2 q^{38} + 14 q^{39} + 46 q^{40} - 30 q^{41} + 2 q^{43} - 24 q^{44} + 42 q^{47} + 2 q^{48} - 18 q^{50} - 26 q^{51} + 28 q^{52} + 22 q^{53} + 6 q^{55} + 12 q^{58} - 66 q^{60} - 14 q^{61} + 4 q^{62} - 52 q^{64} - 18 q^{65} - 26 q^{66} + 24 q^{67} - 16 q^{68} - 4 q^{69} - 24 q^{71} - 60 q^{72} + 30 q^{73} - 12 q^{74} + 92 q^{75} + 18 q^{76} - 10 q^{78} + 28 q^{79} - 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 60 q^{86} - 4 q^{87} - 14 q^{88} - 24 q^{90} + 24 q^{92} - 4 q^{94} + 44 q^{95} + 6 q^{96} - 6 q^{97}+O(q^{100}) $ 12 * q - 8 * q^4 - 6 * q^5 + 18 * q^6 - 4 * q^9 - 12 * q^10 - 6 * q^11 - 2 * q^12 - 4 * q^13 + 6 * q^15 + 16 * q^16 - 8 * q^17 + 12 * q^18 + 12 * q^20 + 6 * q^22 + 24 * q^23 + 12 * q^24 + 10 * q^25 - 18 * q^26 - 12 * q^27 + 8 * q^29 + 8 * q^30 + 18 * q^31 - 30 * q^33 - 10 * q^36 + 2 * q^38 + 14 * q^39 + 46 * q^40 - 30 * q^41 + 2 * q^43 - 24 * q^44 + 42 * q^47 + 2 * q^48 - 18 * q^50 - 26 * q^51 + 28 * q^52 + 22 * q^53 + 6 * q^55 + 12 * q^58 - 66 * q^60 - 14 * q^61 + 4 * q^62 - 52 * q^64 - 18 * q^65 - 26 * q^66 + 24 * q^67 - 16 * q^68 - 4 * q^69 - 24 * q^71 - 60 * q^72 + 30 * q^73 - 12 * q^74 + 92 * q^75 + 18 * q^76 - 10 * q^78 + 28 * q^79 - 72 * q^80 + 2 * q^81 - 14 * q^82 - 48 * q^85 + 60 * q^86 - 4 * q^87 - 14 * q^88 - 24 * q^90 + 24 * q^92 - 4 * q^94 + 44 * q^95 + 6 * q^96 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	1.27656i		−	0.902667i	−0.892355	−	0.451334i	$-0.850948\pi$
$2$		−	1.27656i		−	0.902667i	0.892355	−	0.451334i	$-0.149052\pi$
$3$	−0.583963	−	1.01145i	−0.337151	−	0.583963i	0.646745	−	0.762707i	$-0.276130\pi$
$3$	−0.583963	−	1.01145i	−0.337151	−	0.583963i	−0.983896	+	0.178744i	$0.942797\pi$
$4$	0.370384			0.185192
$5$	−1.57173	+	0.907437i	−0.702897	+	0.405818i	−0.808426	−	0.588598i	$-0.799680\pi$
$5$	−1.57173	+	0.907437i	−0.702897	+	0.405818i	0.105528	+	0.994416i	$0.466347\pi$
$6$	−1.29118	+	0.745466i	−0.527124	+	0.304335i
$7$		0			0
$7$		0			0
$8$		−	3.02595i		−	1.06983i
$9$	0.817975	−	1.41677i	0.272658	−	0.472258i
$10$	1.15840	+	2.00641i	0.366319	+	0.634482i
$11$	2.40625	−	1.38925i	0.725510	−	0.418874i	−0.0912671	−	0.995826i	$-0.529092\pi$
$11$	2.40625	−	1.38925i	0.725510	−	0.418874i	0.816777	+	0.576953i	$0.195758\pi$
$12$	−0.216290	−	0.374626i	−0.0624377	−	0.108145i
$13$	3.58305	−	0.402155i	0.993760	−	0.111538i
$13$	3.58305	−	0.402155i	0.993760	−	0.111538i
$14$		0			0
$15$	1.83566	+	1.05982i	0.473965	+	0.273644i
$16$	−3.12205			−0.780512
$17$	2.74396			0.665508			0.332754	−	0.943014i	$-0.392022\pi$
$17$	2.74396			0.665508			0.332754	+	0.943014i	$0.392022\pi$
$18$	−1.80860	−	1.04420i	−0.426292	−	0.246120i
$19$	−5.08351	−	2.93497i	−1.16624	−	0.673327i	−0.213446	−	0.976955i	$-0.568469\pi$
$19$	−5.08351	−	2.93497i	−1.16624	−	0.673327i	−0.952791	+	0.303628i	$0.901802\pi$
$20$	−0.582143	+	0.336100i	−0.130171	+	0.0751543i
$21$		0			0
$22$	−1.77346	−	3.07173i	−0.378103	−	0.654894i
$23$	−6.99909			−1.45941			−0.729706	−	0.683761i	$-0.760343\pi$
$23$	−6.99909			−1.45941			−0.729706	+	0.683761i	$0.760343\pi$
$24$	−3.06060	+	1.76704i	−0.624743	+	0.360696i
$25$	−0.853117	+	1.47764i	−0.170623	+	0.295528i
$26$	−0.513376	−	4.57400i	−0.100681	−	0.897035i
$27$	−5.41444			−1.04201
$28$		0			0
$29$	1.75806	−	3.04505i	0.326463	−	0.565451i	−0.655344	−	0.755330i	$-0.727476\pi$
$29$	1.75806	−	3.04505i	0.326463	−	0.565451i	0.981807	+	0.189879i	$0.0608097\pi$
$30$	1.35293	−	2.34334i	0.247009	−	0.427833i
$31$	−1.79004	−	1.03348i	−0.321501	−	0.185619i	0.330560	−	0.943785i	$-0.392762\pi$
$31$	−1.79004	−	1.03348i	−0.321501	−	0.185619i	−0.652062	+	0.758166i	$0.726096\pi$
$32$		−	2.06640i		−	0.365292i
$33$	−2.81031	−	1.62254i	−0.489213	−	0.282447i
$34$		−	3.50284i		−	0.600732i
$35$		0			0
$36$	0.302965	−	0.524751i	0.0504942	−	0.0874585i
$37$		−	1.74302i		−	0.286551i	−0.989683	−	0.143276i	$-0.954236\pi$
$37$		−	1.74302i		−	0.286551i	0.989683	−	0.143276i	$-0.0457635\pi$
$38$	−3.74667	+	6.48942i	−0.607790	+	1.05272i
$39$	−2.49913	−	3.38925i	−0.400181	−	0.542714i
$40$	2.74586	+	4.75596i	0.434158	+	0.751984i
$41$	−5.51406	−	3.18355i	−0.861152	−	0.497186i	0.00324599	−	0.999995i	$-0.498967\pi$
$41$	−5.51406	−	3.18355i	−0.861152	−	0.497186i	−0.864398	+	0.502808i	$0.832300\pi$
$42$		0			0
$43$	4.55195	+	7.88422i	0.694167	+	1.20233i	0.970461	+	0.241259i	$0.0775603\pi$
$43$	4.55195	+	7.88422i	0.694167	+	1.20233i	−0.276294	+	0.961073i	$0.589106\pi$
$44$	0.891235	−	0.514555i	0.134359	−	0.0775721i
$45$			2.96904i			0.442599i
$46$			8.93479i			1.31736i
$47$	5.76714	−	3.32966i	0.841224	−	0.485681i	−0.0164563	−	0.999865i	$-0.505238\pi$
$47$	5.76714	−	3.32966i	0.841224	−	0.485681i	0.857680	+	0.514184i	$0.171905\pi$
$48$	1.82316	+	3.15780i	0.263150	+	0.455790i
$49$		0			0
$50$	1.88631	+	1.08906i	0.266764	+	0.154016i
$51$	−1.60237	−	2.77539i	−0.224377	−	0.388632i
$52$	1.32711	−	0.148952i	0.184037	−	0.0206559i
$53$	5.24396	−	9.08280i	0.720313	−	1.24762i	−0.240561	−	0.970634i	$-0.577331\pi$
$53$	5.24396	−	9.08280i	0.720313	−	1.24762i	0.960874	−	0.276985i	$-0.0893352\pi$
$54$			6.91188i			0.940588i
$55$	−2.52131	+	4.36703i	−0.339973	+	0.588850i
$56$		0			0
$57$			6.85564i			0.908052i
$58$	−3.88720	−	2.24427i	−0.510414	−	0.294688i
$59$		−	3.07396i		−	0.400195i	−0.979776	−	0.200097i	$-0.935874\pi$
$59$		−	3.07396i		−	0.400195i	0.979776	−	0.200097i	$-0.0641259\pi$
$60$	0.679899	+	0.392540i	0.0877746	+	0.0506767i
$61$	0.540892	−	0.936853i	0.0692541	−	0.119952i	−0.829319	−	0.558775i	$-0.811271\pi$
$61$	0.540892	−	0.936853i	0.0692541	−	0.119952i	0.898573	+	0.438824i	$0.144605\pi$
$62$	−1.31931	+	2.28511i	−0.167552	+	0.290209i
$63$		0			0
$64$	−8.88199			−1.11025
$65$	−5.26665	+	3.88347i	−0.653248	+	0.481685i
$66$	−2.07127	+	3.58755i	−0.254956	+	0.441596i
$67$	−4.34568	+	2.50898i	−0.530910	+	0.306521i	−0.741387	−	0.671078i	$-0.765832\pi$
$67$	−4.34568	+	2.50898i	−0.530910	+	0.306521i	0.210477	+	0.977599i	$0.432498\pi$
$68$	1.01632			0.123247
$69$	4.08721	+	7.07925i	0.492042	+	0.852242i
$70$		0			0
$71$	2.35453	−	1.35939i	0.279431	−	0.161330i	−0.353735	−	0.935346i	$-0.615088\pi$
$71$	2.35453	−	1.35939i	0.279431	−	0.161330i	0.633166	+	0.774016i	$0.281755\pi$
$72$	−4.28709	−	2.47515i	−0.505238	−	0.291699i
$73$	6.64426	+	3.83607i	0.777652	+	0.448978i	0.835598	−	0.549342i	$-0.185122\pi$
$73$	6.64426	+	3.83607i	0.777652	+	0.448978i	−0.0579454	+	0.998320i	$0.518455\pi$
$74$	−2.22508			−0.258660
$75$	1.99275			0.230103
$76$	−1.88285	−	1.08706i	−0.215978	−	0.124695i
$77$		0			0
$78$	−4.32659	+	3.19030i	−0.489890	+	0.361230i
$79$	7.86993	+	13.6311i	0.885436	+	1.53362i	0.845213	+	0.534430i	$0.179474\pi$
$79$	7.86993	+	13.6311i	0.885436	+	1.53362i	0.0402236	+	0.999191i	$0.487193\pi$
$80$	4.90700	−	2.83306i	0.548620	−	0.316746i
$81$	0.707906	+	1.22613i	0.0786563	+	0.136237i
$82$	−4.06400	+	7.03905i	−0.448794	+	0.777333i
$83$			7.97408i			0.875269i	0.899153	+	0.437635i	$0.144184\pi$
$83$			7.97408i			0.875269i	−0.899153	+	0.437635i	$0.855816\pi$
$84$		0			0
$85$	−4.31275	+	2.48997i	−0.467784	+	0.270075i
$86$	10.0647	−	5.81086i	1.08531	−	0.626601i
$87$	−4.10656			−0.440270
$88$	−4.20379	−	7.28117i	−0.448125	−	0.776176i
$89$		−	16.0640i		−	1.70278i	−0.524537	−	0.851388i	$-0.675761\pi$
$89$		−	16.0640i		−	1.70278i	0.524537	−	0.851388i	$-0.324239\pi$
$90$	3.79017			0.399519
$91$		0			0
$92$	−2.59235			−0.270271
$93$			2.41406i			0.250326i
$94$	−4.25052	−	7.36212i	−0.438408	−	0.759345i
$95$	10.6532			1.09299
$96$	−2.09007	+	1.20670i	−0.213317	+	0.123158i
$97$	12.3209	−	7.11347i	1.25100	−	0.722263i	0.279689	−	0.960091i	$-0.409769\pi$
$97$	12.3209	−	7.11347i	1.25100	−	0.722263i	0.971307	+	0.237827i	$0.0764353\pi$
$98$		0			0
$99$		−	4.54548i		−	0.456838i
$100$	−0.315981	+	0.547295i	−0.0315981	+	0.0547295i
$101$	0.0365612	+	0.0633259i	0.00363798	+	0.00630117i	0.867839	−	0.496846i	$-0.165509\pi$
$101$	0.0365612	+	0.0633259i	0.00363798	+	0.00630117i	−0.864201	+	0.503147i	$0.832175\pi$
$102$	−3.54296	+	2.04553i	−0.350805	+	0.202537i
$103$	6.45980	+	11.1887i	0.636503	+	1.10245i	0.986195	+	0.165590i	$0.0529529\pi$
$103$	6.45980	+	11.1887i	0.636503	+	1.10245i	−0.349692	+	0.936865i	$0.613714\pi$
$104$	−1.21690	−	10.8421i	−0.119327	−	1.06316i
$105$		0			0
$106$	−11.5948	−	6.69425i	−1.12618	−	0.650203i
$107$	4.00855			0.387521			0.193761	−	0.981049i	$-0.437932\pi$
$107$	4.00855			0.387521			0.193761	+	0.981049i	$0.437932\pi$
$108$	−2.00542			−0.192972
$109$	−1.71984	−	0.992947i	−0.164730	−	0.0951071i	0.415368	−	0.909653i	$-0.363653\pi$
$109$	−1.71984	−	0.992947i	−0.164730	−	0.0951071i	−0.580099	+	0.814546i	$0.696986\pi$
$110$	5.57479	+	3.21861i	0.531536	+	0.306882i
$111$	−1.76299	+	1.01786i	−0.167335	+	0.0966110i
$112$		0			0
$113$	5.28711	+	9.15754i	0.497369	+	0.861469i	0.999995	−	0.00303506i	$-0.000966090\pi$
$113$	5.28711	+	9.15754i	0.497369	+	0.861469i	−0.502626	+	0.864504i	$0.667633\pi$
$114$	8.75166			0.819668
$115$	11.0007	−	6.35123i	1.02582	−	0.592256i
$116$	0.651157	−	1.12784i	0.0604584	−	0.104717i
$117$	2.36109	−	5.40533i	0.218283	−	0.499723i
$118$	−3.92410			−0.361243
$119$		0			0
$120$	3.20695	−	5.55461i	0.292753	−	0.507064i
$121$	−1.63999	+	2.84054i	−0.149090	+	0.258231i
$122$	−1.19595	−	0.690483i	−0.108276	−	0.0625134i
$123$			7.43629i			0.670507i
$124$	−0.663004	−	0.382786i	−0.0595395	−	0.0343752i
$125$		−	12.1710i		−	1.08860i
$126$		0			0
$127$	5.63478	−	9.75972i	0.500006	−	0.866035i	−0.499994	−	0.866029i	$-0.666665\pi$
$127$	5.63478	−	9.75972i	0.500006	−	0.866035i	1.00000		6.53271e-6i	$-2.07943e-6\pi$
$128$			7.20562i			0.636893i
$129$	5.31634	−	9.20818i	0.468078	−	0.810735i
$130$	4.95750	+	6.72322i	0.434801	+	0.589665i
$131$	1.53241	+	2.65421i	0.133887	+	0.231899i	0.925172	−	0.379549i	$-0.123921\pi$
$131$	1.53241	+	2.65421i	0.133887	+	0.231899i	−0.791285	+	0.611448i	$0.790587\pi$
$132$	−1.04090	−	0.600962i	−0.0905984	−	0.0523070i
$133$		0			0
$134$	3.20288	+	5.54754i	0.276686	+	0.479235i
$135$	8.51002	−	4.91326i	0.732426	−	0.422867i
$136$		−	8.30308i		−	0.711983i
$137$			21.8830i			1.86959i	0.355185	+	0.934796i	$0.384418\pi$
$137$			21.8830i			1.86959i	−0.355185	+	0.934796i	$0.615582\pi$
$138$	9.03712	−	5.21758i	0.769291	−	0.444150i
$139$	5.53535	+	9.58750i	0.469502	+	0.813201i	0.999392	−	0.0348652i	$-0.0111002\pi$
$139$	5.53535	+	9.58750i	0.469502	+	0.813201i	−0.529890	+	0.848066i	$0.677767\pi$
$140$		0			0
$141$	−6.73559	−	3.88879i	−0.567239	−	0.327495i
$142$	−1.73534	−	3.00570i	−0.145627	−	0.252233i
$143$	8.06301	−	5.94543i	0.674263	−	0.497182i
$144$	−2.55376	+	4.42324i	−0.212813	+	0.368603i
$145$			6.38131i			0.529939i
$146$	4.89699	−	8.48183i	0.405277	−	0.701961i
$147$		0			0
$148$		−	0.645588i		−	0.0530670i
$149$	1.99824	+	1.15369i	0.163702	+	0.0945136i	0.579613	−	0.814892i	$-0.303204\pi$
$149$	1.99824	+	1.15369i	0.163702	+	0.0945136i	−0.415911	+	0.909406i	$0.636537\pi$
$150$		−	2.54388i		−	0.207707i
$151$	−17.8538	−	10.3079i	−1.45292	−	0.838845i	−0.454275	−	0.890861i	$-0.650102\pi$
$151$	−17.8538	−	10.3079i	−1.45292	−	0.838845i	−0.998646	+	0.0520168i	$0.983435\pi$
$152$	−8.88105	+	15.3824i	−0.720348	+	1.24768i
$153$	2.24449	−	3.88757i	0.181456	−	0.314292i
$154$		0			0
$155$	3.75128			0.301310
$156$	−0.925638	−	1.25532i	−0.0741103	−	0.100506i
$157$	1.44824	−	2.50843i	0.115582	−	0.200194i	−0.802430	−	0.596746i	$-0.796460\pi$
$157$	1.44824	−	2.50843i	0.115582	−	0.200194i	0.918012	+	0.396552i	$0.129793\pi$
$158$	17.4010	−	10.0465i	1.38435	−	0.799254i
$159$	−12.2491			−0.971417
$160$	1.87513	+	3.24782i	0.148242	+	0.256763i
$161$		0			0
$162$	1.56523	−	0.903688i	0.122976	−	0.0710004i
$163$	20.2944	+	11.7170i	1.58958	+	0.917743i	0.993376	+	0.114907i	$0.0366571\pi$
$163$	20.2944	+	11.7170i	1.58958	+	0.917743i	0.596201	+	0.802835i	$0.296676\pi$
$164$	−2.04232	−	1.17913i	−0.159478	−	0.0920750i
$165$	5.88939			0.458489
$166$	10.1794			0.790077
$167$	−6.58349	−	3.80098i	−0.509446	−	0.294129i	0.223160	−	0.974782i	$-0.428363\pi$
$167$	−6.58349	−	3.80098i	−0.509446	−	0.294129i	−0.732606	+	0.680653i	$0.761696\pi$
$168$		0			0
$169$	12.6765	−	2.88188i	0.975119	−	0.221683i
$170$	3.17861	+	5.50551i	0.243788	+	0.422253i
$171$	−8.31637	+	4.80146i	−0.635969	+	0.367177i
$172$	1.68597	+	2.92019i	0.128554	+	0.222662i
$173$	−2.69861	+	4.67412i	−0.205171	+	0.355367i	−0.950187	−	0.311679i	$-0.899108\pi$
$173$	−2.69861	+	4.67412i	−0.205171	+	0.355367i	0.745016	+	0.667047i	$0.232442\pi$
$174$			5.24229i			0.397417i
$175$		0			0
$176$	−7.51241	+	4.33729i	−0.566269	+	0.326936i
$177$	−3.10916	+	1.79508i	−0.233699	+	0.134926i
$178$	−20.5067			−1.53704
$179$	−6.14571	−	10.6447i	−0.459352	−	0.795621i	0.539575	−	0.841938i	$-0.318585\pi$
$179$	−6.14571	−	10.6447i	−0.459352	−	0.795621i	−0.998927	+	0.0463168i	$0.985252\pi$
$180$			1.09969i			0.0819658i
$181$	21.8525			1.62428			0.812140	−	0.583463i	$-0.198303\pi$
$181$	21.8525			1.62428			0.812140	+	0.583463i	$0.198303\pi$
$182$		0			0
$183$	−1.26344			−0.0933964
$184$			21.1789i			1.56133i
$185$	1.58168	+	2.73956i	0.116288	+	0.201416i
$186$	3.08170			0.225961
$187$	6.60264	−	3.81204i	0.482833	−	0.278764i
$188$	2.13606	−	1.23325i	0.155788	−	0.0899442i
$189$		0			0
$190$		−	13.5995i		−	0.986609i
$191$	−1.37858	+	2.38777i	−0.0997507	+	0.172773i	−0.911581	−	0.411120i	$-0.865138\pi$
$191$	−1.37858	+	2.38777i	−0.0997507	+	0.172773i	0.811831	+	0.583893i	$0.198471\pi$
$192$	5.18675	+	8.98371i	0.374321	+	0.648344i
$193$	−11.2491	+	6.49467i	−0.809728	+	0.467497i	−0.846861	−	0.531814i	$-0.821511\pi$
$193$	−11.2491	+	6.49467i	−0.809728	+	0.467497i	0.0371334	+	0.999310i	$0.488177\pi$
$194$	−9.08080	−	15.7284i	−0.651963	−	1.12923i
$195$	7.00347	+	3.05917i	0.501529	+	0.219071i
$196$		0			0
$197$	16.4772	+	9.51312i	1.17395	+	0.677781i	0.954608	−	0.297866i	$-0.0962749\pi$
$197$	16.4772	+	9.51312i	1.17395	+	0.677781i	0.219344	+	0.975648i	$0.429608\pi$
$198$	−5.80259			−0.412372
$199$	−20.0317			−1.42001			−0.710006	−	0.704195i	$-0.751308\pi$
$199$	−20.0317			−1.42001			−0.710006	+	0.704195i	$0.751308\pi$
$200$	4.47127	+	2.58149i	0.316166	+	0.182539i
$201$	5.07543	+	2.93030i	0.357993	+	0.206688i
$202$	0.0808396	−	0.0466728i	0.00568785	−	0.00328388i
$203$		0			0
$204$	−0.593492	−	1.02796i	−0.0415528	−	0.0719715i
$205$	11.5555			0.807069
$206$	14.2831	−	8.24634i	0.995150	−	0.574550i
$207$	−5.72509	+	9.91614i	−0.397921	+	0.689219i
$208$	−11.1865	+	1.25555i	−0.775642	+	0.0870564i
$209$	−16.3096			−1.12816
$210$		0			0
$211$	−5.00015	+	8.66052i	−0.344225	+	0.596215i	−0.985213	−	0.171336i	$-0.945192\pi$
$211$	−5.00015	+	8.66052i	−0.344225	+	0.596215i	0.640988	+	0.767551i	$0.278525\pi$
$212$	1.94228	−	3.36413i	0.133396	−	0.231049i
$213$	−2.74991	−	1.58766i	−0.188421	−	0.108785i
$214$		−	5.11717i		−	0.349802i
$215$	−14.3089	−	8.26122i	−0.975856	−	0.563411i
$216$			16.3838i			1.11478i
$217$		0			0
$218$	−1.26756	+	2.19548i	−0.0858501	+	0.148697i
$219$		−	8.96048i		−	0.605493i
$220$	−0.933852	+	1.61748i	−0.0629603	+	0.109050i
$221$	9.83175	−	1.10350i	0.661355	−	0.0742292i
$222$	1.29936	+	2.25056i	0.0872076	+	0.151048i
$223$	−7.25954	−	4.19130i	−0.486135	−	0.280670i	0.236835	−	0.971550i	$-0.423890\pi$
$223$	−7.25954	−	4.19130i	−0.486135	−	0.280670i	−0.722970	+	0.690880i	$0.757223\pi$
$224$		0			0
$225$	1.39566	+	2.41735i	0.0930439	+	0.161157i
$226$	11.6902	−	6.74933i	0.777620	−	0.448959i
$227$			0.919719i			0.0610439i	0.999534	+	0.0305220i	$0.00971695\pi$
$227$			0.919719i			0.0610439i	−0.999534	+	0.0305220i	$0.990283\pi$
$228$			2.53922i			0.168164i
$229$	21.3222	−	12.3104i	1.40901	−	0.813494i	0.413719	−	0.910404i	$-0.364229\pi$
$229$	21.3222	−	12.3104i	1.40901	−	0.813494i	0.995293	+	0.0969108i	$0.0308962\pi$
$230$	−8.10776	−	14.0430i	−0.534610	−	0.925971i
$231$		0			0
$232$	−9.21415	−	5.31979i	−0.604939	−	0.349261i
$233$	−8.63847	−	14.9623i	−0.565925	−	0.980211i	−0.996963	−	0.0778773i	$-0.975186\pi$
$233$	−8.63847	−	14.9623i	−0.565925	−	0.980211i	0.431038	−	0.902334i	$-0.358148\pi$
$234$	−6.90025	−	3.01408i	−0.451084	−	0.197036i
$235$	−6.04291	+	10.4666i	−0.394196	+	0.682767i
$236$		−	1.13854i		−	0.0741129i
$237$	9.19149	−	15.9201i	0.597051	−	1.03412i
$238$		0			0
$239$		−	14.4828i		−	0.936816i	−0.883512	−	0.468408i	$-0.844828\pi$
$239$		−	14.4828i		−	0.936816i	0.883512	−	0.468408i	$-0.155172\pi$
$240$	−5.73101	−	3.30880i	−0.369935	−	0.213582i
$241$			8.43441i			0.543308i	0.962395	+	0.271654i	$0.0875706\pi$
$241$			8.43441i			0.543308i	−0.962395	+	0.271654i	$0.912429\pi$
$242$	3.62614	+	2.09355i	0.233097	+	0.134579i
$243$	−7.29488	+	12.6351i	−0.467967	+	0.810543i
$244$	0.200338	−	0.346995i	0.0128253	−	0.0222141i
$245$		0			0
$246$	9.49290			0.605245
$247$	−19.3948	−	8.47178i	−1.23406	−	0.539046i
$248$	−3.12726	+	5.41658i	−0.198581	+	0.343953i
$249$	8.06541	−	4.65657i	0.511124	−	0.295098i
$250$	−15.5370			−0.982647
$251$	7.33631	+	12.7069i	0.463064	+	0.802050i	0.999112	−	0.0421373i	$-0.0134167\pi$
$251$	7.33631	+	12.7069i	0.463064	+	0.802050i	−0.536048	+	0.844188i	$0.680083\pi$
$252$		0			0
$253$	−16.8415	+	9.72346i	−1.05882	+	0.611309i
$254$	−12.4589	−	7.19315i	−0.781742	−	0.451339i
$255$	5.03697	+	2.90810i	0.315427	+	0.182112i
$256$	−8.56553			−0.535346
$257$	29.3286			1.82947			0.914733	−	0.404059i	$-0.132401\pi$
$257$	29.3286			1.82947			0.914733	+	0.404059i	$0.132401\pi$
$258$	−11.7548	−	6.78665i	−0.731824	−	0.422519i
$259$		0			0
$260$	−1.95068	+	1.43838i	−0.120976	+	0.0892043i
$261$	−2.87610	−	4.98155i	−0.178026	−	0.308350i
$262$	3.38826	−	1.95622i	0.209328	−	0.120855i
$263$	−9.95747	−	17.2468i	−0.614004	−	1.06349i	−0.990558	−	0.137091i	$-0.956225\pi$
$263$	−9.95747	−	17.2468i	−0.614004	−	1.06349i	0.376555	−	0.926394i	$-0.377109\pi$
$264$	−4.90971	+	8.50386i	−0.302172	+	0.523377i
$265$			19.0342i			1.16926i
$266$		0			0
$267$	−16.2479	+	9.38075i	−0.994357	+	0.574092i
$268$	−1.60957	+	0.929287i	−0.0983203	+	0.0567652i
$269$	22.3250			1.36118			0.680589	−	0.732666i	$-0.261724\pi$
$269$	22.3250			1.36118			0.680589	+	0.732666i	$0.261724\pi$
$270$	−6.27210	−	10.8636i	−0.381708	−	0.661137i
$271$		−	9.39988i		−	0.571002i	−0.958378	−	0.285501i	$-0.907840\pi$
$271$		−	9.39988i		−	0.571002i	0.958378	−	0.285501i	$-0.0921600\pi$
$272$	−8.56677			−0.519437
$273$		0			0
$274$	27.9351			1.68762
$275$			4.74076i			0.285879i
$276$	1.51384	+	2.62204i	0.0911223	+	0.157828i
$277$	14.3427			0.861767			0.430883	−	0.902408i	$-0.358202\pi$
$277$	14.3427			0.861767			0.430883	+	0.902408i	$0.358202\pi$
$278$	12.2391	−	7.06622i	0.734050	−	0.423804i
$279$	−2.92842	+	1.69073i	−0.175320	+	0.101221i
$280$		0			0
$281$		−	0.0988416i		−	0.00589640i	−0.999996	−	0.00294820i	$-0.999062\pi$
$281$		−	0.0988416i		−	0.00589640i	0.999996	−	0.00294820i	$-0.000938442\pi$
$282$	−4.96429	+	8.59841i	−0.295619	+	0.512028i
$283$	0.310336	+	0.537518i	0.0184476	+	0.0319521i	0.875102	−	0.483939i	$-0.160794\pi$
$283$	0.310336	+	0.537518i	0.0184476	+	0.0319521i	−0.856654	+	0.515891i	$0.827461\pi$
$284$	0.872079	−	0.503495i	0.0517484	−	0.0298769i
$285$	−6.22106	−	10.7752i	−0.368504	−	0.638267i
$286$	−7.58972	−	10.2930i	−0.448789	−	0.608635i
$287$		0			0
$288$	−2.92763	−	1.69027i	−0.172512	−	0.0995998i
$289$	−9.47069			−0.557099
$290$	8.14615			0.478358
$291$	−14.3899	−	8.30800i	−0.843549	−	0.487023i
$292$	2.46093	+	1.42082i	0.144015	+	0.0831471i
$293$	−21.5586	+	12.4469i	−1.25947	+	0.727153i	−0.972971	−	0.230928i	$-0.925824\pi$
$293$	−21.5586	+	12.4469i	−1.25947	+	0.727153i	−0.286496	+	0.958082i	$0.592490\pi$
$294$		0			0
$295$	2.78942	+	4.83142i	0.162406	+	0.281296i
$296$	−5.27430			−0.306562
$297$	−13.0285	+	7.52200i	−0.755989	+	0.436471i
$298$	1.47275	−	2.55088i	0.0853143	−	0.147769i
$299$	−25.0781	+	2.81472i	−1.45031	+	0.162779i
$300$	0.738085			0.0426133
$301$		0			0
$302$	−13.1587	+	22.7915i	−0.757197	+	1.31150i
$303$	0.0427008	−	0.0739599i	0.00245310	−	0.00424889i
$304$	15.8710	+	9.16310i	0.910262	+	0.525540i
$305$			1.96330i			0.112418i
$306$	−4.96274	−	2.86524i	−0.283701	−	0.163795i
$307$			9.89767i			0.564890i	0.959284	+	0.282445i	$0.0911455\pi$
$307$			9.89767i			0.564890i	−0.959284	+	0.282445i	$0.908855\pi$
$308$		0			0
$309$	7.54456	−	13.0676i	0.429195	−	0.743387i
$310$		−	4.78875i		−	0.271983i
$311$	−3.61895	+	6.26820i	−0.205212	+	0.355437i	−0.950200	−	0.311640i	$-0.899122\pi$
$311$	−3.61895	+	6.26820i	−0.205212	+	0.355437i	0.744988	+	0.667077i	$0.232455\pi$
$312$	−10.2557	+	7.56223i	−0.580614	+	0.428127i
$313$	16.3303	+	28.2849i	0.923043	+	1.59876i	0.794678	+	0.607031i	$0.207640\pi$
$313$	16.3303	+	28.2849i	0.923043	+	1.59876i	0.128365	+	0.991727i	$0.459027\pi$
$314$	−3.20217	−	1.84877i	−0.180709	−	0.104332i
$315$		0			0
$316$	2.91490	+	5.04875i	0.163976	+	0.284014i
$317$	−14.8734	+	8.58718i	−0.835375	+	0.482304i	−0.855690	−	0.517489i	$-0.826867\pi$
$317$	−14.8734	+	8.58718i	−0.835375	+	0.482304i	0.0203143	+	0.999794i	$0.493533\pi$
$318$			15.6368i			0.876866i
$319$		−	9.76951i		−	0.546987i
$320$	13.9601	−	8.05984i	0.780391	−	0.450559i
$321$	−2.34084	−	4.05446i	−0.130653	−	0.226298i
$322$		0			0
$323$	−13.9489	−	8.05342i	−0.776140	−	0.448105i
$324$	0.262197	+	0.454139i	0.0145665	+	0.0252299i
$325$	−2.46252	+	5.63756i	−0.136596	+	0.312715i
$326$	14.9574	−	25.9071i	0.828416	−	1.43486i
$327$			2.31938i			0.128262i
$328$	−9.63324	+	16.6853i	−0.531907	+	0.921289i
$329$		0			0
$330$		−	7.51819i		−	0.413863i
$331$	−17.2633	−	9.96698i	−0.948877	−	0.547835i	−0.0561454	−	0.998423i	$-0.517881\pi$
$331$	−17.2633	−	9.96698i	−0.948877	−	0.547835i	−0.892732	+	0.450588i	$0.851214\pi$
$332$			2.95347i			0.162093i
$333$	−2.46947	−	1.42575i	−0.135326	−	0.0781306i
$334$	−4.85219	+	8.40424i	−0.265500	+	0.459860i
$335$	4.55348	−	7.88687i	0.248783	−	0.430905i
$336$		0			0
$337$	1.27189			0.0692842			0.0346421	−	0.999400i	$-0.488971\pi$
$337$	1.27189			0.0692842			0.0346421	+	0.999400i	$0.488971\pi$
$338$	−3.67891	−	16.1824i	−0.200106	−	0.880208i
$339$	6.17495	−	10.6953i	0.335377	−	0.580890i
$340$	−1.59738	+	0.922245i	−0.0866298	+	0.0500158i
$341$	−5.74305			−0.311004
$342$	6.12937	+	10.6164i	0.331438	+	0.574068i
$343$		0			0
$344$	23.8572	−	13.7740i	1.28630	−	0.742643i
$345$	−12.8479	−	7.41777i	−0.691710	−	0.399359i
$346$	5.96682	+	3.44494i	0.320778	+	0.185201i
$347$	25.8833			1.38949			0.694744	−	0.719257i	$-0.255518\pi$
$347$	25.8833			1.38949			0.694744	+	0.719257i	$0.255518\pi$
$348$	−1.52101			−0.0815344
$349$	14.9967	+	8.65837i	0.802757	+	0.463472i	0.844434	−	0.535659i	$-0.179937\pi$
$349$	14.9967	+	8.65837i	0.802757	+	0.463472i	−0.0416774	+	0.999131i	$0.513270\pi$
$350$		0			0
$351$	−19.4002	+	2.17744i	−1.03551	+	0.116223i
$352$	−2.87074	−	4.97227i	−0.153011	−	0.265023i
$353$	−21.9533	+	12.6747i	−1.16846	+	0.674608i	−0.953316	−	0.301975i	$-0.902354\pi$
$353$	−21.9533	+	12.6747i	−1.16846	+	0.674608i	−0.215140	+	0.976583i	$0.569021\pi$
$354$	2.29153	+	3.96904i	0.121793	+	0.210952i
$355$	−2.46711	+	4.27317i	−0.130941	+	0.226796i
$356$		−	5.94983i		−	0.315341i
$357$		0			0
$358$	−13.5886	+	7.84539i	−0.718181	+	0.414642i
$359$	4.56434	−	2.63522i	0.240897	−	0.139082i	−0.374692	−	0.927149i	$-0.622252\pi$
$359$	4.56434	−	2.63522i	0.240897	−	0.139082i	0.615589	+	0.788068i	$0.288918\pi$
$360$	8.98417			0.473507
$361$	7.72804	+	13.3854i	0.406739	+	0.704493i
$362$		−	27.8961i		−	1.46618i
$363$	3.83077			0.201063
$364$		0			0
$365$	−13.9240			−0.728813
$366$			1.61287i			0.0843058i
$367$	12.6588	+	21.9257i	0.660783	+	1.14451i	0.980410	+	0.196967i	$0.0631092\pi$
$367$	12.6588	+	21.9257i	0.660783	+	1.14451i	−0.319627	+	0.947544i	$0.603557\pi$
$368$	21.8515			1.13909
$369$	−9.02073	+	5.20812i	−0.469601	+	0.271124i
$370$	3.49722	−	2.01912i	0.181812	−	0.104969i
$371$		0			0
$372$			0.894130i			0.0463585i
$373$	3.39391	−	5.87842i	0.175730	−	0.304373i	−0.764684	−	0.644406i	$-0.777105\pi$
$373$	3.39391	−	5.87842i	0.175730	−	0.304373i	0.940414	+	0.340033i	$0.110438\pi$
$374$	−4.86631	−	8.42869i	−0.251631	−	0.435837i
$375$	−12.3104	+	7.10739i	−0.635704	+	0.367024i
$376$	−10.0754	−	17.4511i	−0.519598	−	0.899970i
$377$	5.07464	−	11.6176i	0.261357	−	0.598336i
$378$		0			0
$379$	10.6717	+	6.16130i	0.548168	+	0.316485i	0.748383	−	0.663267i	$-0.230831\pi$
$379$	10.6717	+	6.16130i	0.548168	+	0.316485i	−0.200215	+	0.979752i	$0.564164\pi$
$380$	3.94577			0.202414
$381$	−13.1620			−0.674310
$382$	3.04815	+	1.75985i	0.155957	+	0.0900417i
$383$	−6.28662	−	3.62958i	−0.321232	−	0.185463i	0.330710	−	0.943732i	$-0.392712\pi$
$383$	−6.28662	−	3.62958i	−0.321232	−	0.185463i	−0.651941	+	0.758269i	$0.726045\pi$
$384$	7.28815	−	4.20782i	0.371922	−	0.214729i
$385$		0			0
$386$	8.29086	+	14.3602i	0.421994	+	0.730915i
$387$	14.8935			0.757082
$388$	4.56346	−	2.63472i	0.231675	−	0.133757i
$389$	−3.57406	+	6.19045i	−0.181212	+	0.313868i	−0.942293	−	0.334788i	$-0.891335\pi$
$389$	−3.57406	+	6.19045i	−0.181212	+	0.313868i	0.761082	+	0.648656i	$0.224669\pi$
$390$	3.90522	−	8.94038i	0.197749	−	0.452714i
$391$	−19.2052			−0.971250
$392$		0			0
$393$	1.78974	−	3.09991i	0.0902802	−	0.156370i
$394$	12.1441	−	21.0342i	0.611811	−	1.05969i
$395$	−24.7388	−	14.2829i	−1.24474	−	0.718652i
$396$		−	1.68357i		−	0.0846027i
$397$	−19.4520	−	11.2306i	−0.976266	−	0.563647i	−0.0751252	−	0.997174i	$-0.523936\pi$
$397$	−19.4520	−	11.2306i	−0.976266	−	0.563647i	−0.901141	+	0.433527i	$0.857269\pi$
$398$			25.5718i			1.28180i
$399$		0			0
$400$	2.66347	−	4.61327i	0.133174	−	0.230663i
$401$			3.05473i			0.152546i	0.997087	+	0.0762729i	$0.0243020\pi$
$401$			3.05473i			0.152546i	−0.997087	+	0.0762729i	$0.975698\pi$
$402$	3.74072	−	6.47912i	0.186570	−	0.323149i
$403$	−6.82944	−	2.98315i	−0.340199	−	0.148601i
$404$	0.0135417	+	0.0234549i	0.000673725	+	0.00116693i
$405$	−2.22527	−	1.28476i	−0.110575	−	0.0638403i
$406$		0			0
$407$	−2.42149	−	4.19414i	−0.120029	−	0.207896i
$408$	−8.39817	+	4.84869i	−0.415771	+	0.240046i
$409$		−	5.60586i		−	0.277192i	−0.990349	−	0.138596i	$-0.955741\pi$
$409$		−	5.60586i		−	0.277192i	0.990349	−	0.138596i	$-0.0442590\pi$
$410$		−	14.7513i		−	0.728514i
$411$	22.1336	−	12.7789i	1.09177	−	0.630335i
$412$	2.39261	+	4.14412i	0.117875	+	0.204166i
$413$		0			0
$414$	12.6586	+	7.30844i	0.622136	+	0.359190i
$415$	−7.23597	−	12.5331i	−0.355200	−	0.615224i
$416$	−0.831013	−	7.40403i	−0.0407437	−	0.363012i
$417$	6.46487	−	11.1975i	0.316586	−	0.548343i
$418$			20.8202i			1.01835i
$419$	3.06969	−	5.31687i	0.149964	−	0.259746i	−0.781250	−	0.624219i	$-0.785417\pi$
$419$	3.06969	−	5.31687i	0.149964	−	0.259746i	0.931214	+	0.364473i	$0.118751\pi$
$420$		0			0
$421$			1.92589i			0.0938622i	0.998898	+	0.0469311i	$0.0149441\pi$
$421$			1.92589i			0.0938622i	−0.998898	+	0.0469311i	$0.985056\pi$
$422$	11.0557	+	6.38302i	0.538184	+	0.310720i
$423$		−	10.8943i		−	0.529700i
$424$	−27.4841	−	15.8679i	−1.33475	−	0.770615i
$425$	−2.34092	+	4.05459i	−0.113551	+	0.196677i
$426$	−2.02675	+	3.51044i	−0.0981965	+	0.170081i
$427$		0			0
$428$	1.48470			0.0717658
$429$	−10.7220	−	4.68345i	−0.517664	−	0.226119i
$430$	−10.5460	+	18.2662i	−0.508572	+	0.880873i
$431$	−9.30923	+	5.37469i	−0.448410	+	0.258890i	−0.707158	−	0.707055i	$-0.750023\pi$
$431$	−9.30923	+	5.37469i	−0.448410	+	0.258890i	0.258749	+	0.965945i	$0.416690\pi$
$432$	16.9041			0.813301
$433$	−20.1328	−	34.8710i	−0.967520	−	1.67579i	−0.702685	−	0.711501i	$-0.748016\pi$
$433$	−20.1328	−	34.8710i	−0.967520	−	1.67579i	−0.264835	−	0.964294i	$-0.585318\pi$
$434$		0			0
$435$	6.45439	−	3.72644i	0.309464	−	0.178669i
$436$	−0.637000	−	0.367772i	−0.0305068	−	0.0176131i
$437$	35.5799	+	20.5421i	1.70202	+	0.982662i
$438$	−11.4386			−0.546559
$439$	−21.9508			−1.04765			−0.523826	−	0.851825i	$-0.675496\pi$
$439$	−21.9508			−1.04765			−0.523826	+	0.851825i	$0.675496\pi$
$440$	13.2144	+	7.62934i	0.629972	+	0.363715i
$441$		0			0
$442$	−1.40868	−	12.5509i	−0.0670042	−	0.596984i
$443$	13.9482	+	24.1589i	0.662697	+	1.14783i	0.979904	+	0.199469i	$0.0639217\pi$
$443$	13.9482	+	24.1589i	0.662697	+	1.14783i	−0.317207	+	0.948356i	$0.602745\pi$
$444$	−0.652982	+	0.376999i	−0.0309892	+	0.0178916i
$445$	14.5770	+	25.2481i	0.691017	+	1.19688i
$446$	−5.35046	+	9.26727i	−0.253352	+	0.438818i
$447$		−	2.69484i		−	0.127461i
$448$		0			0
$449$	19.1056	−	11.0306i	0.901648	−	0.520567i	0.0239134	−	0.999714i	$-0.492387\pi$
$449$	19.1056	−	11.0306i	0.901648	−	0.520567i	0.877734	+	0.479147i	$0.159054\pi$
$450$	3.08590	−	1.78165i	0.145471	−	0.0839876i
$451$	−17.6909			−0.833033
$452$	1.95826	+	3.39181i	0.0921088	+	0.159537i
$453$			24.0777i			1.13127i
$454$	1.17408			0.0551023
$455$		0			0
$456$	20.7448			0.971464
$457$		−	5.51628i		−	0.258041i	−0.991642	−	0.129020i	$-0.958817\pi$
$457$		−	5.51628i		−	0.258041i	0.991642	−	0.129020i	$-0.0411833\pi$
$458$	−15.7150	−	27.2192i	−0.734314	−	1.27187i
$459$	−14.8570			−0.693466
$460$	4.07447	−	2.35240i	0.189973	−	0.109681i
$461$	−25.0092	+	14.4391i	−1.16479	+	0.672494i	−0.952448	−	0.304700i	$-0.901444\pi$
$461$	−25.0092	+	14.4391i	−1.16479	+	0.672494i	−0.212346	+	0.977195i	$0.568110\pi$
$462$		0			0
$463$		−	14.2284i		−	0.661251i	−0.943762	−	0.330625i	$-0.892740\pi$
$463$		−	14.2284i		−	0.661251i	0.943762	−	0.330625i	$-0.107260\pi$
$464$	−5.48874	+	9.50678i	−0.254808	+	0.441341i
$465$	−2.19061	−	3.79424i	−0.101587	−	0.175954i
$466$	−19.1003	+	11.0276i	−0.884804	+	0.510842i
$467$	2.27163	+	3.93457i	0.105118	+	0.182070i	0.913787	−	0.406195i	$-0.133145\pi$
$467$	2.27163	+	3.93457i	0.105118	+	0.182070i	−0.808668	+	0.588265i	$0.799811\pi$
$468$	0.874509	−	2.00205i	0.0404242	−	0.0925448i
$469$		0			0
$470$	13.3613	+	7.71416i	0.616312	+	0.355828i
$471$	−3.38288			−0.155875
$472$	−9.30163			−0.428142
$473$	21.9062	+	12.6476i	1.00725	+	0.581536i
$474$	−20.3231	−	11.7335i	−0.933469	−	0.538939i
$475$	8.67366	−	5.00774i	0.397975	−	0.229771i
$476$		0			0
$477$	−8.57886	−	14.8590i	−0.392799	−	0.680348i
$478$	−18.4883			−0.845633
$479$	−1.44239	+	0.832764i	−0.0659044	+	0.0380499i	−0.532590	−	0.846373i	$-0.678781\pi$
$479$	−1.44239	+	0.832764i	−0.0659044	+	0.0380499i	0.466686	+	0.884423i	$0.345448\pi$
$480$	2.19001	−	3.79321i	0.0999598	−	0.173135i
$481$	−0.700965	−	6.24535i	−0.0319612	−	0.284763i
$482$	10.7671			0.490426
$483$		0			0
$484$	−0.607426	+	1.05209i	−0.0276103	+	0.0478224i
$485$	−12.9100	+	22.3608i	−0.586215	+	1.01535i
$486$	16.1295	+	9.31239i	0.731650	+	0.422418i
$487$		−	1.48493i		−	0.0672884i	−0.999434	−	0.0336442i	$-0.989289\pi$
$487$		−	1.48493i		−	0.0672884i	0.999434	−	0.0336442i	$-0.0107113\pi$
$488$	−2.83487	−	1.63671i	−0.128328	−	0.0740904i
$489$		−	27.3691i		−	1.23767i
$490$		0			0
$491$	7.99791	−	13.8528i	0.360941	−	0.625167i	−0.627175	−	0.778878i	$-0.715789\pi$
$491$	7.99791	−	13.8528i	0.360941	−	0.625167i	0.988116	+	0.153711i	$0.0491224\pi$
$492$			2.75428i			0.124173i
$493$	4.82404	−	8.35548i	0.217264	−	0.376312i
$494$	−10.8148	+	24.7587i	−0.486580	+	1.11395i
$495$	4.12473	+	7.14425i	0.185393	+	0.321110i
$496$	5.58860	+	3.22658i	0.250936	+	0.144878i
$497$		0			0
$498$	−5.94440	−	10.2960i	−0.266375	−	0.461375i
$499$	15.3459	−	8.85997i	0.686977	−	0.396627i	−0.115501	−	0.993307i	$-0.536847\pi$
$499$	15.3459	−	8.85997i	0.686977	−	0.396627i	0.802479	+	0.596681i	$0.203514\pi$
$500$		−	4.50793i		−	0.201601i
$501$			8.87852i			0.396663i
$502$	16.2211	−	9.36527i	0.723984	−	0.417993i
$503$	−0.598451	−	1.03655i	−0.0266836	−	0.0462174i	0.852375	−	0.522931i	$-0.175161\pi$
$503$	−0.598451	−	1.03655i	−0.0266836	−	0.0462174i	−0.879059	+	0.476713i	$0.841828\pi$
$504$		0			0
$505$	−0.114929	−	0.0663540i	−0.00511425	−	0.00295272i
$506$	12.4126	+	21.4993i	0.551809	+	0.955760i
$507$	−10.3175	−	11.1388i	−0.458217	−	0.494692i
$508$	2.08703	−	3.61485i	0.0925971	−	0.160383i
$509$			6.28614i			0.278628i	0.990248	+	0.139314i	$0.0444898\pi$
$509$			6.28614i			0.278628i	−0.990248	+	0.139314i	$0.955510\pi$
$510$	3.71237	−	6.43002i	0.164387	−	0.284726i
$511$		0			0
$512$			25.3457i			1.12013i
$513$	27.5244	+	15.8912i	1.21523	+	0.701614i
$514$		−	37.4398i		−	1.65140i
$515$	−20.3061	−	11.7237i	−0.894792	−	0.516608i
$516$	1.96909	−	3.41056i	0.0866843	−	0.150142i
$517$	9.25143	−	16.0240i	0.406878	−	0.704733i
$518$		0			0
$519$	6.30354			0.276695
$520$	11.7512	+	15.9366i	0.515323	+	0.698866i
$521$	−5.42367	+	9.39407i	−0.237615	+	0.411562i	−0.960029	−	0.279899i	$-0.909699\pi$
$521$	−5.42367	+	9.39407i	−0.237615	+	0.411562i	0.722414	+	0.691460i	$0.243032\pi$
$522$	−6.35926	+	3.67152i	−0.278337	+	0.160698i
$523$	−1.34726			−0.0589114			−0.0294557	−	0.999566i	$-0.509377\pi$
$523$	−1.34726			−0.0589114			−0.0294557	+	0.999566i	$0.509377\pi$
$524$	0.567579	+	0.983076i	0.0247948	+	0.0429459i
$525$		0			0
$526$	−22.0167	+	12.7113i	−0.959974	+	0.554241i
$527$	−4.91181	−	2.83583i	−0.213962	−	0.123531i
$528$	8.77394	+	5.06563i	0.381837	+	0.220453i
$529$	25.9873			1.12988
$530$	24.2984			1.05546
$531$	−4.35510	−	2.51442i	−0.188995	−	0.109117i
$532$		0			0
$533$	−21.0375	−	9.18931i	−0.911233	−	0.398033i
$534$	11.9751	+	20.7415i	0.518214	+	0.897574i
$535$	−6.30034	+	3.63750i	−0.272388	+	0.157263i
$536$	7.59205	+	13.1498i	0.327926	+	0.567985i
$537$	−7.17773	+	12.4322i	−0.309742	+	0.536489i
$538$		−	28.4993i		−	1.22869i
$539$		0			0
$540$	3.15198	−	1.81980i	0.135640	−	0.0783115i
$541$	17.4565	−	10.0785i	0.750516	−	0.433310i	−0.0753646	−	0.997156i	$-0.524012\pi$
$541$	17.4565	−	10.0785i	0.750516	−	0.433310i	0.825880	+	0.563846i	$0.190679\pi$
$542$	−11.9996			−0.515425
$543$	−12.7610	−	22.1027i	−0.547628	−	0.948519i
$544$		−	5.67012i		−	0.243104i
$545$	3.60415			0.154385
$546$		0			0
$547$	−3.42286			−0.146351			−0.0731755	−	0.997319i	$-0.523313\pi$
$547$	−3.42286			−0.146351			−0.0731755	+	0.997319i	$0.523313\pi$
$548$			8.10512i			0.346234i
$549$	−0.884873	−	1.53264i	−0.0377654	−	0.0654117i
$550$	6.05188			0.258053
$551$	−17.8742	+	10.3197i	−0.761467	+	0.439633i
$552$	21.4214	−	12.3677i	0.911757	−	0.526403i
$553$		0			0
$554$		−	18.3093i		−	0.777889i
$555$	1.84729	−	3.19960i	0.0784130	−	0.135815i
$556$	2.05020	+	3.55106i	0.0869480	+	0.150598i
$557$	20.4948	−	11.8327i	0.868394	−	0.501367i	0.00157977	−	0.999999i	$-0.499497\pi$
$557$	20.4948	−	11.8327i	0.868394	−	0.501367i	0.866814	+	0.498631i	$0.166164\pi$
$558$	2.15832	+	3.73832i	0.0913690	+	0.158256i
$559$	19.4806	+	26.4190i	0.823940	+	1.11740i
$560$		0			0
$561$	−7.71139	−	4.45217i	−0.325575	−	0.187971i
$562$	−0.126178			−0.00532248
$563$	28.8075			1.21409			0.607045	−	0.794668i	$-0.292355\pi$
$563$	28.8075			1.21409			0.607045	+	0.794668i	$0.292355\pi$
$564$	−2.49475	−	1.44035i	−0.105048	−	0.0606496i
$565$	−16.6198	−	9.59543i	−0.699199	−	0.403683i
$566$	0.686177	−	0.396164i	0.0288422	−	0.0166520i
$567$		0			0
$568$	−4.11343	−	7.12467i	−0.172596	−	0.298945i
$569$	27.6722			1.16008			0.580040	−	0.814588i	$-0.303037\pi$
$569$	27.6722			1.16008			0.580040	+	0.814588i	$0.303037\pi$
$570$	−13.7552	+	7.94158i	−0.576143	+	0.332636i
$571$	6.48273	−	11.2284i	0.271294	−	0.469895i	−0.697899	−	0.716196i	$-0.745882\pi$
$571$	6.48273	−	11.2284i	0.271294	−	0.469895i	0.969193	+	0.246301i	$0.0792151\pi$
$572$	2.98641	−	2.20209i	0.124868	−	0.0920741i
$573$	3.22016			0.134524
$574$		0			0
$575$	5.97105	−	10.3422i	0.249010	−	0.431298i
$576$	−7.26525	+	12.5838i	−0.302719	+	0.524324i
$577$	8.19301	+	4.73023i	0.341079	+	0.196922i	0.660749	−	0.750607i	$-0.270239\pi$
$577$	8.19301	+	4.73023i	0.341079	+	0.196922i	−0.319670	+	0.947529i	$0.603572\pi$
$578$			12.0899i			0.502875i
$579$	13.1381	+	7.58529i	0.546001	+	0.315234i
$580$			2.36354i			0.0981405i
$581$		0			0
$582$	−10.6057	+	18.3696i	−0.439620	+	0.761444i
$583$		−	29.1406i		−	1.20688i
$584$	11.6077	−	20.1052i	0.480332	−	0.831959i
$585$	1.19401	+	10.6382i	0.0493664	+	0.439837i
$586$	15.8892	+	27.5209i	0.656377	+	1.13688i
$587$	18.6673	+	10.7776i	0.770481	+	0.444837i	0.833046	−	0.553204i	$-0.186595\pi$
$587$	18.6673	+	10.7776i	0.770481	+	0.444837i	−0.0625654	+	0.998041i	$0.519928\pi$
$588$		0			0
$589$	6.06647	+	10.5074i	0.249965	+	0.432951i
$590$	6.16761	−	3.56087i	0.253917	−	0.146599i
$591$		−	22.2212i		−	0.914059i
$592$			5.44180i			0.223657i
$593$	−3.44015	+	1.98617i	−0.141270	+	0.0815622i	−0.568969	−	0.822359i	$-0.692658\pi$
$593$	−3.44015	+	1.98617i	−0.141270	+	0.0815622i	0.427699	+	0.903921i	$0.359324\pi$
$594$	9.60231	+	16.6317i	0.393988	+	0.682407i
$595$		0			0
$596$	0.740117	+	0.427307i	0.0303164	+	0.0175032i
$597$	11.6978	+	20.2612i	0.478759	+	0.829234i
$598$	3.59317	+	32.0138i	0.146936	+	1.30914i
$599$	9.75246	−	16.8918i	0.398475	−	0.690179i	−0.595063	−	0.803679i	$-0.702873\pi$
$599$	9.75246	−	16.8918i	0.398475	−	0.690179i	0.993538	+	0.113500i	$0.0362063\pi$
$600$		−	6.02997i		−	0.246172i
$601$	−13.4368	+	23.2733i	−0.548100	+	0.949336i	0.450305	+	0.892875i	$0.351315\pi$
$601$	−13.4368	+	23.2733i	−0.548100	+	0.949336i	−0.998405	+	0.0564616i	$0.982018\pi$
$602$		0			0
$603$			8.20914i			0.334302i
$604$	−6.61276	−	3.81788i	−0.269070	−	0.155347i
$605$		−	5.95274i		−	0.242013i
$606$	−0.0944146	−	0.0545103i	−0.00383533	−	0.00221433i
$607$	12.5102	−	21.6682i	0.507772	−	0.879487i	−0.492187	−	0.870489i	$-0.663803\pi$
$607$	12.5102	−	21.6682i	0.507772	−	0.879487i	0.999960	−	0.00899773i	$-0.00286411\pi$
$608$	−6.06482	+	10.5046i	−0.245961	+	0.426016i
$609$		0			0
$610$	2.50628			0.101476
$611$	19.3249	−	14.2496i	0.781803	−	0.576478i
$612$	0.831324	−	1.43990i	0.0336043	−	0.0582043i
$613$	18.4970	−	10.6793i	0.747088	−	0.431332i	−0.0775527	−	0.996988i	$-0.524711\pi$
$613$	18.4970	−	10.6793i	0.747088	−	0.431332i	0.824641	+	0.565657i	$0.191377\pi$
$614$	12.6350			0.509908
$615$	−6.74796	−	11.6878i	−0.272104	−	0.471298i
$616$		0			0
$617$	−28.5425	+	16.4790i	−1.14908	+	0.663420i	−0.948662	−	0.316291i	$-0.897562\pi$
$617$	−28.5425	+	16.4790i	−1.14908	+	0.663420i	−0.200415	+	0.979711i	$0.564229\pi$
$618$	−16.6816	−	9.63111i	−0.671031	−	0.387420i
$619$	−42.3588	−	24.4559i	−1.70254	−	0.982965i	−0.943170	−	0.332311i	$-0.892172\pi$
$619$	−42.3588	−	24.4559i	−1.70254	−	0.982965i	−0.759375	−	0.650654i	$-0.774495\pi$
$620$	1.38941			0.0558002
$621$	37.8962			1.52072
$622$	8.00176	+	4.61982i	0.320841	+	0.185238i
$623$		0			0
$624$	7.80240	+	10.5814i	0.312346	+	0.423595i
$625$	6.77880	+	11.7412i	0.271152	+	0.469649i
$626$	36.1075	−	20.8467i	1.44315	−	0.833201i
$627$	9.52417	+	16.4964i	0.380359	+	0.658801i
$628$	0.536406	−	0.929083i	0.0214049	−	0.0370744i
$629$		−	4.78278i		−	0.190702i
$630$		0			0
$631$	4.65076	−	2.68512i	0.185144	−	0.106893i	−0.404563	−	0.914510i	$-0.632576\pi$
$631$	4.65076	−	2.68512i	0.185144	−	0.106893i	0.589707	+	0.807617i	$0.299243\pi$
$632$	41.2470	−	23.8140i	1.64072	−	0.947270i
$633$	11.6796			0.464223
$634$	10.9621	+	18.9869i	0.435360	+	0.754066i
$635$			20.4528i			0.811645i
$636$	−4.53687			−0.179899
$637$		0			0
$638$	−12.4714			−0.493747
$639$		−	4.44778i		−	0.175951i
$640$	−6.53865	−	11.3253i	−0.258463	−	0.447671i
$641$	−39.7020			−1.56813			−0.784066	−	0.620677i	$-0.786858\pi$
$641$	−39.7020			−1.56813			−0.784066	+	0.620677i	$0.786858\pi$
$642$	−5.17578	+	2.98824i	−0.204272	+	0.117936i
$643$	−27.8388	+	16.0727i	−1.09785	+	0.633847i	−0.935657	−	0.352911i	$-0.885192\pi$
$643$	−27.8388	+	16.0727i	−1.09785	+	0.633847i	−0.162198	+	0.986758i	$0.551858\pi$
$644$		0			0
$645$			19.2970i			0.759818i
$646$	−10.2807	+	17.8067i	−0.404489	+	0.700596i
$647$	9.92502	+	17.1906i	0.390193	+	0.675833i	0.992475	−	0.122450i	$-0.0390751\pi$
$647$	9.92502	+	17.1906i	0.390193	+	0.675833i	−0.602282	+	0.798283i	$0.705742\pi$
$648$	3.71020	−	2.14209i	0.145751	−	0.0841491i
$649$	−4.27048	−	7.39669i	−0.167631	−	0.290346i
$650$	7.19670	+	3.14357i	0.282278	+	0.123301i
$651$		0			0
$652$	7.51671	+	4.33977i	0.294377	+	0.169959i
$653$	−19.0005			−0.743547			−0.371773	−	0.928324i	$-0.621250\pi$
$653$	−19.0005			−0.743547			−0.371773	+	0.928324i	$0.621250\pi$
$654$	2.96083			0.115778
$655$	−4.81705	−	2.78112i	−0.188218	−	0.108667i
$656$	17.2152	+	9.93918i	0.672139	+	0.388060i
$657$	10.8697	−	6.27562i	0.424067	−	0.244835i
$658$		0			0
$659$	3.60729	+	6.24801i	0.140520	+	0.243388i	0.927693	−	0.373345i	$-0.121789\pi$
$659$	3.60729	+	6.24801i	0.140520	+	0.243388i	−0.787173	+	0.616733i	$0.788456\pi$
$660$	2.18134			0.0849085
$661$	14.5068	−	8.37548i	0.564248	−	0.325769i	−0.190601	−	0.981668i	$-0.561044\pi$
$661$	14.5068	−	8.37548i	0.564248	−	0.325769i	0.754849	+	0.655899i	$0.227710\pi$
$662$	−12.7235	+	22.0377i	−0.494512	+	0.856520i
$663$	−6.85751	−	9.29995i	−0.266324	−	0.361180i
$664$	24.1291			0.936393
$665$		0			0
$666$	−1.82006	+	3.15244i	−0.0705259	+	0.122155i
$667$	−12.3048	+	21.3126i	−0.476444	+	0.825226i
$668$	−2.43842	−	1.40782i	−0.0943453	−	0.0544703i
$669$			9.79025i			0.378513i
$670$	−10.0681	−	5.81281i	−0.388964	−	0.224569i
$671$		−	3.00573i		−	0.116035i
$672$		0			0
$673$	−18.6684	+	32.3346i	−0.719614	+	1.24641i	0.241539	+	0.970391i	$0.422348\pi$
$673$	−18.6684	+	32.3346i	−0.719614	+	1.24641i	−0.961153	+	0.276016i	$0.910986\pi$
$674$		−	1.62365i		−	0.0625406i
$675$	4.61916	−	8.00061i	0.177791	−	0.307944i
$676$	4.69519	−	1.06740i	0.180584	−	0.0410540i
$677$	14.0671	+	24.3649i	0.540641	+	0.936418i	0.998867	+	0.0475826i	$0.0151517\pi$
$677$	14.0671	+	24.3649i	0.540641	+	0.936418i	−0.458226	+	0.888836i	$0.651515\pi$
$678$	−13.6533	−	7.88271i	−0.524350	−	0.302734i
$679$		0			0
$680$	7.53452	+	13.0502i	0.288935	+	0.500451i
$681$	0.930253	−	0.537082i	0.0356474	−	0.0205810i
$682$			7.33137i			0.280733i
$683$		−	2.07032i		−	0.0792186i	−0.999215	−	0.0396093i	$-0.987389\pi$
$683$		−	2.07032i		−	0.0792186i	0.999215	−	0.0396093i	$-0.0126113\pi$
$684$	−3.08025	+	1.77838i	−0.117776	+	0.0679982i
$685$	−19.8574	−	34.3941i	−0.758714	−	1.31413i
$686$		0			0
$687$	−24.9028	−	14.3776i	−0.950100	−	0.548540i
$688$	−14.2114	−	24.6149i	−0.541805	−	0.938434i
$689$	15.1367	−	34.6531i	0.576662	−	1.32018i
$690$	−9.46925	+	16.4012i	−0.360488	+	0.624384i
$691$			35.8583i			1.36411i	0.731299	+	0.682057i	$0.238914\pi$
$691$			35.8583i			1.36411i	−0.731299	+	0.682057i	$0.761086\pi$
$692$	−0.999521	+	1.73122i	−0.0379961	+	0.0658112i
$693$		0			0
$694$		−	33.0417i		−	1.25425i
$695$	−17.4001	−	10.0460i	−0.660023	−	0.381065i
$696$			12.4262i			0.471015i
$697$	−15.1304	−	8.73552i	−0.573103	−	0.330881i
$698$	11.0530	−	19.1443i	0.418361	−	0.724622i
$699$	−10.0891	+	17.4748i	−0.381604	+	0.660958i
$700$		0			0
$701$	−44.8940			−1.69562			−0.847812	−	0.530297i	$-0.822081\pi$
$701$	−44.8940			−1.69562			−0.847812	+	0.530297i	$0.822081\pi$
$702$	2.77965	+	24.7657i	0.104911	+	0.934719i
$703$	−5.11571	+	8.86067i	−0.192943	+	0.334187i
$704$	−21.3722	+	12.3393i	−0.805497	+	0.465054i
$705$	14.1153			0.531614
$706$	16.1801	+	28.0248i	0.608947	+	1.05473i
$707$		0			0
$708$	−1.15158	+	0.664867i	−0.0432792	+	0.0249872i
$709$	14.0864	+	8.13279i	0.529026	+	0.305433i	0.740620	−	0.671924i	$-0.234532\pi$
$709$	14.0864	+	8.13279i	0.529026	+	0.305433i	−0.211594	+	0.977358i	$0.567865\pi$
$710$	5.45497	+	3.14943i	0.204721	+	0.118196i
$711$	25.7496			0.965687
$712$	−48.6087			−1.82169
$713$	12.5287	+	7.23344i	0.469203	+	0.270894i
$714$		0			0
$715$	−7.27775	+	16.6613i	−0.272173	+	0.623096i
$716$	−2.27627	−	3.94262i	−0.0850683	−	0.147343i
$717$	−14.6487	+	8.45743i	−0.547066	+	0.315849i
$718$	−3.36403	−	5.82667i	−0.125544	−	0.217449i
$719$	5.00744	−	8.67314i	0.186746	−	0.323454i	−0.757417	−	0.652931i	$-0.773539\pi$
$719$	5.00744	−	8.67314i	0.186746	−	0.323454i	0.944164	+	0.329477i	$0.106873\pi$
$720$		−	9.26949i		−	0.345454i
$721$		0			0
$722$	17.0873	−	9.86534i	0.635922	−	0.367150i
$723$	8.53100	−	4.92538i	0.317271	−	0.183177i
$724$	8.09380			0.300804
$725$	2.99966	+	5.19556i	0.111405	+	0.192958i
$726$		−	4.89022i		−	0.181493i
$727$	−34.5299			−1.28064			−0.640322	−	0.768106i	$-0.721199\pi$
$727$	−34.5299			−1.28064			−0.640322	+	0.768106i	$0.721199\pi$
$728$		0			0
$729$	21.2872			0.788415
$730$			17.7748i			0.657875i
$731$	12.4904	+	21.6340i	0.461973	+	0.800161i
$732$	−0.467959			−0.0172963
$733$	28.6966	−	16.5680i	1.05993	−	0.611953i	0.134520	−	0.990911i	$-0.457051\pi$
$733$	28.6966	−	16.5680i	1.05993	−	0.611953i	0.925414	+	0.378958i	$0.123717\pi$
$734$	27.9895	−	16.1598i	1.03311	−	0.596468i
$735$		0			0
$736$			14.4629i			0.533111i
$737$	−6.97119	+	12.0745i	−0.256787	+	0.444768i
$738$	6.64850	+	11.5155i	0.244735	+	0.423893i
$739$	3.47767	−	2.00784i	0.127928	−	0.0738594i	−0.434670	−	0.900590i	$-0.643135\pi$
$739$	3.47767	−	2.00784i	0.127928	−	0.0738594i	0.562598	+	0.826730i	$0.309802\pi$
$740$	0.585830	+	1.01469i	0.0215356	+	0.0373007i
$741$	2.75703	+	24.5641i	0.101282	+	0.902386i
$742$		0			0
$743$	10.8361	+	6.25622i	0.397538	+	0.229519i	0.685421	−	0.728147i	$-0.259618\pi$
$743$	10.8361	+	6.25622i	0.397538	+	0.229519i	−0.287883	+	0.957666i	$0.592952\pi$
$744$	7.30482			0.267808
$745$	−4.18759			−0.153421
$746$	−7.50418	−	4.33254i	−0.274748	−	0.158626i
$747$	11.2975	+	6.52260i	0.413353	+	0.238650i
$748$	2.44551	−	1.41192i	0.0894168	−	0.0516248i
$749$		0			0
$750$	9.07304	+	15.7150i	0.331300	+	0.573829i
$751$	−37.5158			−1.36897			−0.684486	−	0.729026i	$-0.739973\pi$
$751$	−37.5158			−1.36897			−0.684486	+	0.729026i	$0.739973\pi$
$752$	−18.0053	+	10.3954i	−0.656585	+	0.379080i
$753$	8.56826	−	14.8407i	0.312245	−	0.540824i
$754$	−14.8306	−	6.47810i	−0.540098	−	0.235919i
$755$	37.4150			1.36167
$756$		0			0
$757$	17.5223	−	30.3496i	0.636860	−	1.10307i	−0.349258	−	0.937027i	$-0.613566\pi$
$757$	17.5223	−	30.3496i	0.636860	−	1.10307i	0.986118	−	0.166047i	$-0.0531004\pi$
$758$	7.86530	−	13.6231i	0.285680	−	0.494813i
$759$	19.6697	+	11.3563i	0.713963	+	0.412207i
$760$		−	32.2360i		−	1.16932i
$761$	−3.72586	−	2.15113i	−0.135062	−	0.0779782i	0.430946	−	0.902378i	$-0.358180\pi$
$761$	−3.72586	−	2.15113i	−0.135062	−	0.0779782i	−0.566009	+	0.824399i	$0.691513\pi$
$762$			16.8021i			0.608677i
$763$		0			0
$764$	−0.510605	+	0.884394i	−0.0184730	+	0.0319962i
$765$			8.14693i			0.294553i
$766$	−4.63340	+	8.02528i	−0.167411	+	0.289965i
$767$	−1.23621	−	11.0141i	−0.0446368	−	0.397698i
$768$	5.00195	+	8.66363i	0.180492	+	0.312622i
$769$	−10.6146	−	6.12834i	−0.382772	−	0.220994i	0.296251	−	0.955110i	$-0.404263\pi$
$769$	−10.6146	−	6.12834i	−0.382772	−	0.220994i	−0.679024	+	0.734116i	$0.737597\pi$
$770$		0			0
$771$	−17.1268	−	29.6645i	−0.616806	−	1.06834i
$772$	−4.16649	+	2.40552i	−0.149955	+	0.0865767i
$773$			3.80327i			0.136794i	0.997658	+	0.0683970i	$0.0217884\pi$
$773$			3.80327i			0.136794i	−0.997658	+	0.0683970i	$0.978212\pi$
$774$		−	19.0126i		−	0.683393i
$775$	3.05424	−	1.76336i	0.109711	−	0.0633419i
$776$	−21.5250	−	37.2824i	−0.772702	−	1.33836i
$777$		0			0
$778$	7.90250	+	4.56251i	0.283318	+	0.163574i
$779$	18.6872	+	32.3672i	0.669538	+	1.15967i
$780$	2.59398	+	1.13307i	0.0928792	+	0.0405703i
$781$	3.77705	−	6.54204i	0.135153	−	0.234092i
$782$			24.5167i			0.876715i
$783$	−9.51891	+	16.4872i	−0.340178	+	0.589206i
$784$		0			0
$785$			5.25675i			0.187622i
$786$	−3.95724	−	2.28471i	−0.141150	−	0.0814930i
$787$		−	17.3337i		−	0.617879i	−0.951082	−	0.308940i	$-0.900026\pi$
$787$		−	17.3337i		−	0.617879i	0.951082	−	0.308940i	$-0.0999741\pi$
$788$	6.10289	+	3.52351i	0.217407	+	0.125520i
$789$	−11.6296	+	20.1430i	−0.414024	+	0.717110i
$790$	−18.2331	+	31.5806i	−0.648704	+	1.12359i
$791$		0			0
$792$	−13.7544			−0.488740
$793$	1.56129	−	3.57431i	0.0554429	−	0.126928i
$794$	−14.3366	+	24.8317i	−0.508786	+	0.881243i
$795$	19.2522	−	11.1153i	0.682807	−	0.394219i
$796$	−7.41944			−0.262975
$797$	−25.1707	−	43.5969i	−0.891592	−	1.54428i	−0.837967	−	0.545721i	$-0.816256\pi$
$797$	−25.1707	−	43.5969i	−0.891592	−	1.54428i	−0.0536245	−	0.998561i	$-0.517077\pi$
$798$		0			0
$799$	15.8248	−	9.13645i	0.559841	−	0.323224i
$800$	3.05340	+	1.76288i	0.107954	+	0.0623273i
$801$	−22.7590	−	13.1399i	−0.804150	−	0.464276i
$802$	3.89955			0.137698
$803$	21.3170			0.752260
$804$	1.87986	+	1.08534i	0.0662975	+	0.0382769i
$805$		0			0
$806$	−3.80818	+	8.71822i	−0.134137	+	0.307086i
$807$	−13.0369	−	22.5807i	−0.458922	−	0.794877i
$808$	0.191621	−	0.110632i	0.00674120	−	0.00389203i
$809$	−8.03694	−	13.9204i	−0.282564	−	0.489415i	0.689452	−	0.724332i	$-0.257852\pi$
$809$	−8.03694	−	13.9204i	−0.282564	−	0.489415i	−0.972015	+	0.234917i	$0.924518\pi$
$810$	−1.64008	+	2.84070i	−0.0576265	+	0.0998120i
$811$		−	36.9875i		−	1.29881i	−0.760443	−	0.649404i	$-0.775018\pi$
$811$		−	36.9875i		−	1.29881i	0.760443	−	0.649404i	$-0.224982\pi$
$812$		0			0
$813$	−9.50754	+	5.48918i	−0.333444	+	0.192514i
$814$	−5.35409	+	3.09119i	−0.187661	+	0.108346i
$815$	−42.5296			−1.48975
$816$	5.00267	+	8.66488i	0.175129	+	0.303332i
$817$		−	53.4393i		−	1.86961i
$818$	−7.15624			−0.250212
$819$		0			0
$820$	4.27996			0.149463
$821$		−	30.1401i		−	1.05190i	−0.850517	−	0.525948i	$-0.823711\pi$
$821$		−	30.1401i		−	1.05190i	0.850517	−	0.525948i	$-0.176289\pi$
$822$	−16.3130	−	28.2550i	−0.568982	−	0.985507i
$823$	−41.6502			−1.45184			−0.725918	−	0.687781i	$-0.758585\pi$
$823$	−41.6502			−1.45184			−0.725918	+	0.687781i	$0.758585\pi$
$824$	33.8564	−	19.5470i	1.17944	−	0.680952i
$825$	4.79506	−	2.76843i	0.166942	−	0.0963842i
$826$		0			0
$827$		−	37.6524i		−	1.30930i	−0.755932	−	0.654651i	$-0.772816\pi$
$827$		−	37.6524i		−	1.30930i	0.755932	−	0.654651i	$-0.227184\pi$
$828$	−2.12048	+	3.67278i	−0.0736918	+	0.127638i
$829$	3.73737	+	6.47332i	0.129804	+	0.224828i	0.923601	−	0.383356i	$-0.125232\pi$
$829$	3.73737	+	6.47332i	0.129804	+	0.224828i	−0.793796	+	0.608184i	$0.791898\pi$
$830$	−15.9993	+	9.23718i	−0.555343	+	0.320627i
$831$	−8.37558	−	14.5069i	−0.290546	−	0.503240i
$832$	−31.8246	+	3.57193i	−1.10332	+	0.123834i
$833$		0			0
$834$	−14.2943	−	8.25282i	−0.494971	−	0.285772i
$835$	13.7966			0.477451
$836$	−6.04080			−0.208926
$837$	9.69209	+	5.59573i	0.335008	+	0.193417i
$838$	−6.78732	−	3.91866i	−0.234464	−	0.135368i
$839$	9.51957	−	5.49613i	0.328652	−	0.189747i	−0.326590	−	0.945166i	$-0.605900\pi$
$839$	9.51957	−	5.49613i	0.328652	−	0.189747i	0.655242	+	0.755419i	$0.272566\pi$
$840$		0			0
$841$	8.31846	+	14.4080i	0.286843	+	0.496827i
$842$	2.45852			0.0847263
$843$	−0.0999736	+	0.0577198i	−0.00344328	+	0.00198798i
$844$	−1.85198	+	3.20772i	−0.0637477	+	0.110414i
$845$	−17.3089	+	16.0327i	−0.595445	+	0.551541i
$846$	−13.9073			−0.478143
$847$		0			0
$848$	−16.3719	+	28.3569i	−0.562213	+	0.973781i
$849$	0.362450	−	0.627781i	0.0124392	−	0.0215454i
$850$	5.17594	+	2.98833i	0.177533	+	0.102499i
$851$			12.1996i			0.418196i
$852$	−1.01852	−	0.588045i	−0.0348940	−	0.0201461i
$853$			35.2031i			1.20533i	0.797994	+	0.602666i	$0.205895\pi$
$853$			35.2031i			1.20533i	−0.797994	+	0.602666i	$0.794105\pi$
$854$		0			0
$855$	8.71404	−	15.0932i	0.298014	−	0.516175i
$856$		−	12.1297i		−	0.414583i
$857$	−15.1841	+	26.2996i	−0.518678	+	0.898377i	0.481086	+	0.876673i	$0.340242\pi$
$857$	−15.1841	+	26.2996i	−0.518678	+	0.898377i	−0.999764	+	0.0217035i	$0.993091\pi$
$858$	−5.97873	+	13.6873i	−0.204110	+	0.467278i
$859$	−17.9153	−	31.0302i	−0.611262	−	1.05874i	−0.991028	−	0.133654i	$-0.957329\pi$
$859$	−17.9153	−	31.0302i	−0.611262	−	1.05874i	0.379767	−	0.925082i	$-0.376004\pi$
$860$	−5.29977	−	3.05983i	−0.180721	−	0.104339i
$861$		0			0
$862$	6.86113	+	11.8838i	0.233691	+	0.404765i
$863$	−28.0075	+	16.1702i	−0.953387	+	0.550438i	−0.894131	−	0.447805i	$-0.852206\pi$
$863$	−28.0075	+	16.1702i	−0.953387	+	0.550438i	−0.0592557	+	0.998243i	$0.518873\pi$
$864$			11.1884i			0.380638i
$865$		−	9.79526i		−	0.333049i
$866$	−44.5151	+	25.7008i	−1.51268	+	0.873349i
$867$	5.53053	+	9.57916i	0.187827	+	0.325325i
$868$		0			0
$869$	37.8740	+	21.8665i	1.28479	+	0.741772i
$870$	−4.75705	−	8.23944i	−0.161279	−	0.279343i
$871$	−14.5618	+	10.7375i	−0.493408	+	0.363825i
$872$	−3.00461	+	5.20413i	−0.101749	+	0.176234i
$873$		−	23.2746i		−	0.787725i
$874$	26.2233	−	45.4201i	0.887016	−	1.53636i
$875$		0			0
$876$		−	3.31882i		−	0.112133i
$877$	−3.82446	−	2.20805i	−0.129143	−	0.0745607i	0.434037	−	0.900895i	$-0.357089\pi$
$877$	−3.82446	−	2.20805i	−0.129143	−	0.0745607i	−0.563180	+	0.826334i	$0.690422\pi$
$878$			28.0216i			0.945682i
$879$	25.1788	+	14.5370i	0.849261	+	0.490321i
$880$	7.87164	−	13.6341i	0.265353	−	0.459605i
$881$	−9.97753	+	17.2816i	−0.336152	+	0.582232i	−0.983705	−	0.179788i	$-0.942459\pi$
$881$	−9.97753	+	17.2816i	−0.336152	+	0.582232i	0.647554	+	0.762020i	$0.275792\pi$
$882$		0			0
$883$	−12.9725			−0.436559			−0.218280	−	0.975886i	$-0.570045\pi$
$883$	−12.9725			−0.436559			−0.218280	+	0.975886i	$0.570045\pi$
$884$	3.64153	−	0.408717i	0.122478	−	0.0137467i
$885$	3.25783	−	5.64273i	0.109511	−	0.189678i
$886$	30.8404	−	17.8057i	1.03610	−	0.598195i
$887$	−54.1725			−1.81893			−0.909467	−	0.415776i	$-0.863510\pi$
$887$	−54.1725			−1.81893			−0.909467	+	0.415776i	$0.863510\pi$
$888$	3.07999	+	5.33470i	0.103358	+	0.179021i
$889$		0			0
$890$	32.2309	−	18.6085i	1.08038	−	0.623758i
$891$	3.40679	+	1.96691i	0.114132	+	0.0658941i
$892$	−2.68882	−	1.55239i	−0.0900283	−	0.0519779i
$893$	−39.0897			−1.30809
$894$	−3.44013			−0.115055
$895$	19.3187	+	11.1537i	0.645755	+	0.372827i
$896$		0			0
$897$	17.4916	+	23.7216i	0.584029	+	0.792043i
$898$	−14.0813	−	24.3895i	−0.469898	−	0.813888i
$899$	−6.29401	+	3.63385i	−0.209917	+	0.121196i
$900$	0.516930	+	0.895348i	0.0172310	+	0.0298449i
$901$	14.3892	−	24.9228i	0.479374	−	0.830300i
$902$			22.5836i			0.751951i
$903$		0			0
$904$	27.7102	−	15.9985i	0.921629	−	0.532103i
$905$	−34.3461	+	19.8297i	−1.14170	+	0.659162i
$906$	30.7367			1.02116
$907$	−1.29570	−	2.24421i	−0.0430229	−	0.0745178i	0.843712	−	0.536796i	$-0.180365\pi$
$907$	−1.29570	−	2.24421i	−0.0430229	−	0.0745178i	−0.886735	+	0.462278i	$0.847032\pi$
$908$			0.340649i			0.0113048i
$909$	0.119625			0.00396770
$910$		0			0
$911$	3.59896			0.119239			0.0596195	−	0.998221i	$-0.481011\pi$
$911$	3.59896			0.119239			0.0596195	+	0.998221i	$0.481011\pi$
$912$		−	21.4036i		−	0.708745i
$913$	11.0780	+	19.1876i	0.366627	+	0.635017i
$914$	−7.04189			−0.232925
$915$	1.98579	−	1.14649i	0.0656481	−	0.0379019i
$916$	7.89741	−	4.55957i	0.260938	−	0.150653i
$917$		0			0
$918$			18.9659i			0.625969i
$919$	13.9624	−	24.1836i	0.460578	−	0.797745i	−0.538412	−	0.842682i	$-0.680975\pi$
$919$	13.9624	−	24.1836i	0.460578	−	0.797745i	0.998990	+	0.0449372i	$0.0143088\pi$
$920$	−19.2185	−	33.2874i	−0.633615	−	1.09745i
$921$	10.0110	−	5.77987i	0.329875	−	0.190453i
$922$	18.4324	+	31.9258i	0.607039	+	1.05142i
$923$	7.88971	−	5.81764i	0.259693	−	0.191490i
$924$		0			0
$925$	2.57557	+	1.48700i	0.0846841	+	0.0488924i
$926$	−18.1635			−0.596889
$927$	21.1358			0.694191
$928$	−6.29229	−	3.63285i	−0.206554	−	0.119254i
$929$	−23.0067	−	13.2830i	−0.754827	−	0.435800i	0.0726084	−	0.997361i	$-0.476868\pi$
$929$	−23.0067	−	13.2830i	−0.754827	−	0.435800i	−0.827435	+	0.561561i	$0.810201\pi$
$930$	−4.84359	+	2.79645i	−0.158828	+	0.0916992i
$931$		0			0
$932$	−3.19955	−	5.54179i	−0.104805	−	0.181527i
$933$	8.45332			0.276749
$934$	5.02274	−	2.89988i	0.164349	−	0.0948869i
$935$	−6.91836	+	11.9830i	−0.226255	+	0.391885i
$936$	−16.3563	−	7.14452i	−0.534621	−	0.233526i
$937$	−3.02509			−0.0988255			−0.0494128	−	0.998778i	$-0.515735\pi$
$937$	−3.02509			−0.0988255			−0.0494128	+	0.998778i	$0.515735\pi$
$938$		0			0
$939$	19.0726	−	33.0347i	0.622410	−	1.07805i
$940$	−2.23820	+	3.87667i	−0.0730020	+	0.126443i
$941$	5.61587	+	3.24232i	0.183072	+	0.105697i	0.588735	−	0.808326i	$-0.299626\pi$
$941$	5.61587	+	3.24232i	0.183072	+	0.105697i	−0.405663	+	0.914023i	$0.632959\pi$
$942$			4.31846i			0.140703i
$943$	38.5934	+	22.2819i	1.25678	+	0.725599i
$944$			9.59704i			0.312357i
$945$		0			0
$946$	16.1454	−	27.9647i	0.524934	−	0.909212i
$947$		−	21.1533i		−	0.687391i	−0.939081	−	0.343695i	$-0.888321\pi$
$947$		−	21.1533i		−	0.687391i	0.939081	−	0.343695i	$-0.111679\pi$
$948$	3.40438	−	5.89656i	0.110569	−	0.191511i
$949$	25.3494	+	11.0728i	0.822878	+	0.359439i
$950$	−6.39270	−	11.0725i	−0.207407	−	0.359239i
$951$	17.3711	+	10.0292i	0.563295	+	0.325219i
$952$		0			0
$953$	−18.1393	−	31.4182i	−0.587590	−	1.01774i	−0.994547	−	0.104289i	$-0.966743\pi$
$953$	−18.1393	−	31.4182i	−0.587590	−	1.01774i	0.406957	−	0.913447i	$-0.366590\pi$
$954$	−18.9685	+	10.9515i	−0.614128	+	0.354567i
$955$		−	5.00390i		−	0.161923i
$956$		−	5.36421i		−	0.173491i
$957$	−9.88140	+	5.70503i	−0.319420	+	0.184417i
$958$	1.06308	+	1.84130i	0.0343464	+	0.0594898i
$959$		0			0
$960$	−16.3043	−	9.41329i	−0.526219	−	0.303813i
$961$	−13.3638	−	23.1468i	−0.431091	−	0.746672i
$962$	−7.97258	+	0.894826i	−0.257046	+	0.0288504i
$963$	3.27889	−	5.67921i	0.105661	−	0.183010i
$964$			3.12397i			0.100616i
$965$	11.7870	−	20.4157i	0.379437	−	0.657204i
$966$		0			0
$967$			16.2828i			0.523621i	0.965119	+	0.261810i	$0.0843195\pi$
$967$			16.2828i			0.523621i	−0.965119	+	0.261810i	$0.915681\pi$
$968$	8.59534	+	4.96252i	0.276265	+	0.159501i
$969$			18.8116i			0.604315i
$970$	28.5451	+	16.4805i	0.916527	+	0.529157i
$971$	−12.2605	+	21.2358i	−0.393458	+	0.681489i	−0.992903	−	0.118927i	$-0.962055\pi$
$971$	−12.2605	+	21.2358i	−0.393458	+	0.681489i	0.599445	+	0.800416i	$0.295388\pi$
$972$	−2.70191	+	4.67984i	−0.0866638	+	0.150106i
$973$		0			0
$974$	−1.89560			−0.0607390
$975$	7.14014	−	0.801395i	0.228668	−	0.0256652i
$976$	−1.68869	+	2.92490i	−0.0540537	+	0.0936237i
$977$	−9.45681	+	5.45989i	−0.302550	+	0.174677i	−0.643588	−	0.765372i	$-0.722555\pi$
$977$	−9.45681	+	5.45989i	−0.302550	+	0.174677i	0.341038	+	0.940050i	$0.389222\pi$
$978$	−34.9384			−1.11721
$979$	−22.3168	−	38.6538i	−0.713248	−	1.23538i
$980$		0			0
$981$	−2.81357	+	1.62441i	−0.0898302	+	0.0518635i
$982$	−17.6840	−	10.2098i	−0.564318	−	0.325809i
$983$	−17.0360	−	9.83574i	−0.543364	−	0.313711i	0.203077	−	0.979163i	$-0.434906\pi$
$983$	−17.0360	−	9.83574i	−0.543364	−	0.313711i	−0.746441	+	0.665451i	$0.768239\pi$
$984$	22.5018			0.717331
$985$	−34.5302			−1.10022
$986$	−10.6663	−	6.15820i	−0.339685	−	0.196117i
$987$		0			0
$988$	−7.18352	−	3.13781i	−0.228538	−	0.0998271i
$989$	−31.8596	−	55.1824i	−1.01307	−	1.75470i
$990$	9.12009	−	5.26549i	0.289855	−	0.167348i
$991$	0.869000	+	1.50515i	0.0276047	+	0.0478127i	0.879498	−	0.475903i	$-0.157879\pi$
$991$	0.869000	+	1.50515i	0.0276047	+	0.0478127i	−0.851893	+	0.523716i	$0.824545\pi$
$992$	−2.13559	+	3.69895i	−0.0678050	+	0.117442i
$993$			23.2814i			0.738812i
$994$		0			0
$995$	31.4844	−	18.1775i	0.998123	−	0.576267i
$996$	2.98730	−	1.72472i	0.0946562	−	0.0546498i
$997$	46.9537			1.48704			0.743519	−	0.668715i	$-0.233155\pi$
$997$	46.9537			1.48704			0.743519	+	0.668715i	$0.233155\pi$
$998$	−11.3103	−	19.5900i	−0.358022	−	0.620112i
$999$			9.43750i			0.298589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.k.g.459.2		12
7.2	even	3		637.2.u.i.30.2		12
7.3	odd	6		91.2.q.a.43.5	yes	12
7.4	even	3		637.2.q.h.589.5		12
7.5	odd	6		637.2.u.h.30.2		12
7.6	odd	2		637.2.k.h.459.2		12
13.10	even	6		637.2.u.i.361.2		12
21.17	even	6		819.2.ct.a.316.2		12
28.3	even	6		1456.2.cc.c.225.2		12
91.10	odd	6		91.2.q.a.36.5	✓	12
91.17	odd	6		1183.2.c.i.337.9		12
91.23	even	6	inner	637.2.k.g.569.5		12
91.32	odd	12		8281.2.a.by.1.3		6
91.45	even	12		1183.2.a.m.1.3		6
91.46	odd	12		8281.2.a.ch.1.4		6
91.59	even	12		1183.2.a.p.1.4		6
91.62	odd	6		637.2.u.h.361.2		12
91.75	odd	6		637.2.k.h.569.5		12
91.87	odd	6		1183.2.c.i.337.4		12
91.88	even	6		637.2.q.h.491.5		12
273.101	even	6		819.2.ct.a.127.2		12
364.283	even	6		1456.2.cc.c.673.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.5	✓	12	91.10	odd	6
91.2.q.a.43.5	yes	12	7.3	odd	6
637.2.k.g.459.2		12	1.1	even	1	trivial
637.2.k.g.569.5		12	91.23	even	6	inner
637.2.k.h.459.2		12	7.6	odd	2
637.2.k.h.569.5		12	91.75	odd	6
637.2.q.h.491.5		12	91.88	even	6
637.2.q.h.589.5		12	7.4	even	3
637.2.u.h.30.2		12	7.5	odd	6
637.2.u.h.361.2		12	91.62	odd	6
637.2.u.i.30.2		12	7.2	even	3
637.2.u.i.361.2		12	13.10	even	6
819.2.ct.a.127.2		12	273.101	even	6
819.2.ct.a.316.2		12	21.17	even	6
1183.2.a.m.1.3		6	91.45	even	12
1183.2.a.p.1.4		6	91.59	even	12
1183.2.c.i.337.4		12	91.87	odd	6
1183.2.c.i.337.9		12	91.17	odd	6
1456.2.cc.c.225.2		12	28.3	even	6
1456.2.cc.c.673.2		12	364.283	even	6
8281.2.a.by.1.3		6	91.32	odd	12
8281.2.a.ch.1.4		6	91.46	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.27656i q^{2} +(-0.583963 - 1.01145i) q^{3} +0.370384 q^{4} +(-1.57173 + 0.907437i) q^{5} +(-1.29118 + 0.745466i) q^{6} -3.02595i q^{8} +(0.817975 - 1.41677i) q^{9} +O(q^{10})\)	\(q-1.27656i q^{2} +(-0.583963 - 1.01145i) q^{3} +0.370384 q^{4} +(-1.57173 + 0.907437i) q^{5} +(-1.29118 + 0.745466i) q^{6} -3.02595i q^{8} +(0.817975 - 1.41677i) q^{9} +(1.15840 + 2.00641i) q^{10} +(2.40625 - 1.38925i) q^{11} +(-0.216290 - 0.374626i) q^{12} +(3.58305 - 0.402155i) q^{13} +(1.83566 + 1.05982i) q^{15} -3.12205 q^{16} +2.74396 q^{17} +(-1.80860 - 1.04420i) q^{18} +(-5.08351 - 2.93497i) q^{19} +(-0.582143 + 0.336100i) q^{20} +(-1.77346 - 3.07173i) q^{22} -6.99909 q^{23} +(-3.06060 + 1.76704i) q^{24} +(-0.853117 + 1.47764i) q^{25} +(-0.513376 - 4.57400i) q^{26} -5.41444 q^{27} +(1.75806 - 3.04505i) q^{29} +(1.35293 - 2.34334i) q^{30} +(-1.79004 - 1.03348i) q^{31} -2.06640i q^{32} +(-2.81031 - 1.62254i) q^{33} -3.50284i q^{34} +(0.302965 - 0.524751i) q^{36} -1.74302i q^{37} +(-3.74667 + 6.48942i) q^{38} +(-2.49913 - 3.38925i) q^{39} +(2.74586 + 4.75596i) q^{40} +(-5.51406 - 3.18355i) q^{41} +(4.55195 + 7.88422i) q^{43} +(0.891235 - 0.514555i) q^{44} +2.96904i q^{45} +8.93479i q^{46} +(5.76714 - 3.32966i) q^{47} +(1.82316 + 3.15780i) q^{48} +(1.88631 + 1.08906i) q^{50} +(-1.60237 - 2.77539i) q^{51} +(1.32711 - 0.148952i) q^{52} +(5.24396 - 9.08280i) q^{53} +6.91188i q^{54} +(-2.52131 + 4.36703i) q^{55} +6.85564i q^{57} +(-3.88720 - 2.24427i) q^{58} -3.07396i q^{59} +(0.679899 + 0.392540i) q^{60} +(0.540892 - 0.936853i) q^{61} +(-1.31931 + 2.28511i) q^{62} -8.88199 q^{64} +(-5.26665 + 3.88347i) q^{65} +(-2.07127 + 3.58755i) q^{66} +(-4.34568 + 2.50898i) q^{67} +1.01632 q^{68} +(4.08721 + 7.07925i) q^{69} +(2.35453 - 1.35939i) q^{71} +(-4.28709 - 2.47515i) q^{72} +(6.64426 + 3.83607i) q^{73} -2.22508 q^{74} +1.99275 q^{75} +(-1.88285 - 1.08706i) q^{76} +(-4.32659 + 3.19030i) q^{78} +(7.86993 + 13.6311i) q^{79} +(4.90700 - 2.83306i) q^{80} +(0.707906 + 1.22613i) q^{81} +(-4.06400 + 7.03905i) q^{82} +7.97408i q^{83} +(-4.31275 + 2.48997i) q^{85} +(10.0647 - 5.81086i) q^{86} -4.10656 q^{87} +(-4.20379 - 7.28117i) q^{88} -16.0640i q^{89} +3.79017 q^{90} -2.59235 q^{92} +2.41406i q^{93} +(-4.25052 - 7.36212i) q^{94} +10.6532 q^{95} +(-2.09007 + 1.20670i) q^{96} +(12.3209 - 7.11347i) q^{97} -4.54548i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} - 6 q^{5} + 18 q^{6} - 4 q^{9}+O(q^{10}) \) 12 * q - 8 * q^4 - 6 * q^5 + 18 * q^6 - 4 * q^9	\( 12 q - 8 q^{4} - 6 q^{5} + 18 q^{6} - 4 q^{9} - 12 q^{10} - 6 q^{11} - 2 q^{12} - 4 q^{13} + 6 q^{15} + 16 q^{16} - 8 q^{17} + 12 q^{18} + 12 q^{20} + 6 q^{22} + 24 q^{23} + 12 q^{24} + 10 q^{25} - 18 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 18 q^{31} - 30 q^{33} - 10 q^{36} + 2 q^{38} + 14 q^{39} + 46 q^{40} - 30 q^{41} + 2 q^{43} - 24 q^{44} + 42 q^{47} + 2 q^{48} - 18 q^{50} - 26 q^{51} + 28 q^{52} + 22 q^{53} + 6 q^{55} + 12 q^{58} - 66 q^{60} - 14 q^{61} + 4 q^{62} - 52 q^{64} - 18 q^{65} - 26 q^{66} + 24 q^{67} - 16 q^{68} - 4 q^{69} - 24 q^{71} - 60 q^{72} + 30 q^{73} - 12 q^{74} + 92 q^{75} + 18 q^{76} - 10 q^{78} + 28 q^{79} - 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 60 q^{86} - 4 q^{87} - 14 q^{88} - 24 q^{90} + 24 q^{92} - 4 q^{94} + 44 q^{95} + 6 q^{96} - 6 q^{97}+O(q^{100}) \) 12 * q - 8 * q^4 - 6 * q^5 + 18 * q^6 - 4 * q^9 - 12 * q^10 - 6 * q^11 - 2 * q^12 - 4 * q^13 + 6 * q^15 + 16 * q^16 - 8 * q^17 + 12 * q^18 + 12 * q^20 + 6 * q^22 + 24 * q^23 + 12 * q^24 + 10 * q^25 - 18 * q^26 - 12 * q^27 + 8 * q^29 + 8 * q^30 + 18 * q^31 - 30 * q^33 - 10 * q^36 + 2 * q^38 + 14 * q^39 + 46 * q^40 - 30 * q^41 + 2 * q^43 - 24 * q^44 + 42 * q^47 + 2 * q^48 - 18 * q^50 - 26 * q^51 + 28 * q^52 + 22 * q^53 + 6 * q^55 + 12 * q^58 - 66 * q^60 - 14 * q^61 + 4 * q^62 - 52 * q^64 - 18 * q^65 - 26 * q^66 + 24 * q^67 - 16 * q^68 - 4 * q^69 - 24 * q^71 - 60 * q^72 + 30 * q^73 - 12 * q^74 + 92 * q^75 + 18 * q^76 - 10 * q^78 + 28 * q^79 - 72 * q^80 + 2 * q^81 - 14 * q^82 - 48 * q^85 + 60 * q^86 - 4 * q^87 - 14 * q^88 - 24 * q^90 + 24 * q^92 - 4 * q^94 + 44 * q^95 + 6 * q^96 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more