LMFDB - Embedded newform 637.2.u.h.30.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(30,637)]

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([2, 1]))

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

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

chi := DirichletCharacter("637.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.u (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:	$\Z[a_1, a_2, a_3]$
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			30.2
Root			$1.40744 + 0.138282i$ of defining polynomial
Character	$\chi$	$=$	637.30
Dual form			637.2.u.h.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10554 + 0.638282i) q^{2} -1.16793 q^{3} +(-0.185192 + 0.320762i) q^{4} +(-1.57173 - 0.907437i) q^{5} +(1.29118 - 0.745466i) q^{6} -3.02595i q^{8} -1.63595 q^{9} +O(q^{10})$	\(q+(-1.10554 + 0.638282i) q^{2} -1.16793 q^{3} +(-0.185192 + 0.320762i) q^{4} +(-1.57173 - 0.907437i) q^{5} +(1.29118 - 0.745466i) q^{6} -3.02595i q^{8} -1.63595 q^{9} +2.31680 q^{10} +2.77849i q^{11} +(0.216290 - 0.374626i) q^{12} +(-3.58305 + 0.402155i) q^{13} +(1.83566 + 1.05982i) q^{15} +(1.56102 + 2.70377i) q^{16} +(1.37198 - 2.37634i) q^{17} +(1.80860 - 1.04420i) q^{18} -5.86993i q^{19} +(0.582143 - 0.336100i) q^{20} +(-1.77346 - 3.07173i) q^{22} +(3.49955 + 6.06139i) q^{23} +3.53408i q^{24} +(-0.853117 - 1.47764i) q^{25} +(3.70451 - 2.73160i) q^{26} +5.41444 q^{27} +(1.75806 - 3.04505i) q^{29} -2.70585 q^{30} +(-1.79004 + 1.03348i) q^{31} +(1.78956 + 1.03320i) q^{32} -3.24507i q^{33} +3.50284i q^{34} +(0.302965 - 0.524751i) q^{36} +(-1.50950 + 0.871512i) q^{37} +(3.74667 + 6.48942i) q^{38} +(4.18474 - 0.469686i) 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} +(2.57127 + 1.48452i) q^{45} +(-7.73776 - 4.46740i) 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} +(0.534557 - 1.22378i) q^{52} +(5.24396 + 9.08280i) q^{53} +(-5.98587 + 3.45594i) q^{54} +(2.52131 - 4.36703i) q^{55} +6.85564i q^{57} +4.48855i q^{58} +(-2.66212 - 1.53698i) q^{59} +(-0.679899 + 0.392540i) q^{60} +1.08178 q^{61} +(1.31931 - 2.28511i) q^{62} -8.88199 q^{64} +(5.99651 + 2.61932i) q^{65} +(2.07127 + 3.58755i) q^{66} -5.01796i q^{67} +(0.508159 + 0.880158i) q^{68} +(-4.08721 - 7.07925i) q^{69} +(2.35453 - 1.35939i) q^{71} +4.95030i q^{72} +(6.64426 - 3.83607i) q^{73} +(1.11254 - 1.92698i) q^{74} +(0.996377 + 1.72578i) q^{75} +(1.88285 + 1.08706i) q^{76} +(-4.32659 + 3.19030i) q^{78} +(7.86993 - 13.6311i) q^{79} -5.66612i q^{80} -1.41581 q^{81} -8.12800 q^{82} -7.97408i q^{83} +(-4.31275 + 2.48997i) q^{85} +(-10.0647 - 5.81086i) q^{86} +(-2.05328 + 3.55639i) q^{87} +8.40757 q^{88} +(13.9118 - 8.03198i) q^{89} -3.79017 q^{90} -2.59235 q^{92} +(2.09064 - 1.20703i) q^{93} -8.50105 q^{94} +(-5.32659 + 9.22592i) 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 + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 - 6 * q^5 - 18 * q^6 + 8 * q^9	$ 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} - 24 q^{10} + 2 q^{12} + 4 q^{13} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{18} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} + 24 q^{26} + 12 q^{27} + 8 q^{29} - 16 q^{30} + 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} - 2 q^{38} - 10 q^{39} - 46 q^{40} + 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} + 42 q^{47} - 2 q^{48} - 18 q^{50} - 26 q^{51} + 26 q^{52} + 22 q^{53} - 12 q^{54} - 6 q^{55} - 18 q^{59} + 66 q^{60} - 28 q^{61} - 4 q^{62} - 52 q^{64} - 42 q^{65} + 26 q^{66} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 30 q^{73} + 6 q^{74} + 46 q^{75} - 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} - 28 q^{82} - 48 q^{85} - 60 q^{86} - 2 q^{87} + 28 q^{88} + 12 q^{89} + 24 q^{90} + 24 q^{92} + 18 q^{93} - 8 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 - 6 * q^5 - 18 * q^6 + 8 * q^9 - 24 * q^10 + 2 * q^12 + 4 * q^13 + 6 * q^15 - 8 * q^16 - 4 * q^17 - 12 * q^18 - 12 * q^20 + 6 * q^22 - 12 * q^23 + 10 * q^25 + 24 * q^26 + 12 * q^27 + 8 * q^29 - 16 * q^30 + 18 * q^31 - 36 * q^32 - 10 * q^36 + 42 * q^37 - 2 * q^38 - 10 * q^39 - 46 * q^40 + 30 * q^41 + 2 * q^43 + 24 * q^44 - 12 * q^46 + 42 * q^47 - 2 * q^48 - 18 * q^50 - 26 * q^51 + 26 * q^52 + 22 * q^53 - 12 * q^54 - 6 * q^55 - 18 * q^59 + 66 * q^60 - 28 * q^61 - 4 * q^62 - 52 * q^64 - 42 * q^65 + 26 * q^66 - 8 * q^68 + 4 * q^69 - 24 * q^71 + 30 * q^73 + 6 * q^74 + 46 * q^75 - 18 * q^76 - 10 * q^78 + 28 * q^79 - 4 * q^81 - 28 * q^82 - 48 * q^85 - 60 * q^86 - 2 * q^87 + 28 * q^88 + 12 * q^89 + 24 * q^90 + 24 * q^92 + 18 * q^93 - 8 * q^94 - 22 * q^95 + 6 * q^96 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.10554	+	0.638282i	−0.781733	+	0.451334i	−0.837044	−	0.547136i	$-0.815718\pi$
$2$	−1.10554	+	0.638282i	−0.781733	+	0.451334i	0.0553113	+	0.998469i	$0.482385\pi$
$3$	−1.16793			−0.674302			−0.337151	−	0.941451i	$-0.609463\pi$
$3$	−1.16793			−0.674302			−0.337151	+	0.941451i	$0.609463\pi$
$4$	−0.185192	+	0.320762i	−0.0925960	+	0.160381i
$5$	−1.57173	−	0.907437i	−0.702897	−	0.405818i	0.105528	−	0.994416i	$-0.466347\pi$
$5$	−1.57173	−	0.907437i	−0.702897	−	0.405818i	−0.808426	+	0.588598i	$0.799680\pi$
$6$	1.29118	−	0.745466i	0.527124	−	0.304335i
$7$		0			0
$7$		0			0
$8$		−	3.02595i		−	1.06983i
$9$	−1.63595			−0.545317
$10$	2.31680			0.732637
$11$			2.77849i			0.837747i	0.908045	+	0.418874i	$0.137575\pi$
$11$			2.77849i			0.837747i	−0.908045	+	0.418874i	$0.862425\pi$
$12$	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
$16$	1.56102	+	2.70377i	0.390256	+	0.675943i
$17$	1.37198	−	2.37634i	0.332754	−	0.576347i	−0.650297	−	0.759680i	$-0.725355\pi$
$17$	1.37198	−	2.37634i	0.332754	−	0.576347i	0.983051	+	0.183334i	$0.0586888\pi$
$18$	1.80860	−	1.04420i	0.426292	−	0.246120i
$19$		−	5.86993i		−	1.34665i	−0.739345	−	0.673327i	$-0.764865\pi$
$19$		−	5.86993i		−	1.34665i	0.739345	−	0.673327i	$-0.235135\pi$
$20$	0.582143	−	0.336100i	0.130171	−	0.0751543i
$21$		0			0
$22$	−1.77346	−	3.07173i	−0.378103	−	0.654894i
$23$	3.49955	+	6.06139i	0.729706	+	1.26389i	0.957007	+	0.290063i	$0.0936763\pi$
$23$	3.49955	+	6.06139i	0.729706	+	1.26389i	−0.227302	+	0.973824i	$0.572990\pi$
$24$			3.53408i			0.721391i
$25$	−0.853117	−	1.47764i	−0.170623	−	0.295528i
$26$	3.70451	−	2.73160i	0.726514	−	0.535710i
$27$	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	$0.0608097\pi$
$30$	−2.70585			−0.494019
$31$	−1.79004	+	1.03348i	−0.321501	+	0.185619i	−0.652062	−	0.758166i	$-0.726096\pi$
$31$	−1.79004	+	1.03348i	−0.321501	+	0.185619i	0.330560	+	0.943785i	$0.392762\pi$
$32$	1.78956	+	1.03320i	0.316352	+	0.182646i
$33$		−	3.24507i		−	0.564894i
$34$			3.50284i			0.600732i
$35$		0			0
$36$	0.302965	−	0.524751i	0.0504942	−	0.0874585i
$37$	−1.50950	+	0.871512i	−0.248161	+	0.143276i	−0.618922	−	0.785453i	$-0.712430\pi$
$37$	−1.50950	+	0.871512i	−0.248161	+	0.143276i	0.370761	+	0.928728i	$0.379097\pi$
$38$	3.74667	+	6.48942i	0.607790	+	1.05272i
$39$	4.18474	−	0.469686i	0.670094	−	0.0752100i
$40$	−2.74586	+	4.75596i	−0.434158	+	0.751984i
$41$	5.51406	+	3.18355i	0.861152	+	0.497186i	0.864398	−	0.502808i	$-0.167700\pi$
$41$	5.51406	+	3.18355i	0.861152	+	0.497186i	−0.00324599	+	0.999995i	$0.501033\pi$
$42$		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
$45$	2.57127	+	1.48452i	0.383302	+	0.221299i
$46$	−7.73776	−	4.46740i	−1.14087	−	0.658681i
$47$	5.76714	+	3.32966i	0.841224	+	0.485681i	0.857680	−	0.514184i	$-0.171905\pi$
$47$	5.76714	+	3.32966i	0.841224	+	0.485681i	−0.0164563	+	0.999865i	$0.505238\pi$
$48$	−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
$52$	0.534557	−	1.22378i	0.0741297	−	0.169708i
$53$	5.24396	+	9.08280i	0.720313	+	1.24762i	0.960874	+	0.276985i	$0.0893352\pi$
$53$	5.24396	+	9.08280i	0.720313	+	1.24762i	−0.240561	+	0.970634i	$0.577331\pi$
$54$	−5.98587	+	3.45594i	−0.814573	+	0.470294i
$55$	2.52131	−	4.36703i	0.339973	−	0.588850i
$56$		0			0
$57$			6.85564i			0.908052i
$58$			4.48855i			0.589375i
$59$	−2.66212	−	1.53698i	−0.346579	−	0.200097i	0.316598	−	0.948560i	$-0.397459\pi$
$59$	−2.66212	−	1.53698i	−0.346579	−	0.200097i	−0.663177	+	0.748462i	$0.730793\pi$
$60$	−0.679899	+	0.392540i	−0.0877746	+	0.0506767i
$61$	1.08178			0.138508			0.0692541	−	0.997599i	$-0.477938\pi$
$61$	1.08178			0.138508			0.0692541	+	0.997599i	$0.477938\pi$
$62$	1.31931	−	2.28511i	0.167552	−	0.290209i
$63$		0			0
$64$	−8.88199			−1.11025
$65$	5.99651	+	2.61932i	0.743775	+	0.324886i
$66$	2.07127	+	3.58755i	0.254956	+	0.441596i
$67$		−	5.01796i		−	0.613042i	−0.951864	−	0.306521i	$-0.900835\pi$
$67$		−	5.01796i		−	0.613042i	0.951864	−	0.306521i	$-0.0991649\pi$
$68$	0.508159	+	0.880158i	0.0616234	+	0.106735i
$69$	−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	$0.281755\pi$
$72$			4.95030i			0.583399i
$73$	6.64426	−	3.83607i	0.777652	−	0.448978i	−0.0579454	−	0.998320i	$-0.518455\pi$
$73$	6.64426	−	3.83607i	0.777652	−	0.448978i	0.835598	+	0.549342i	$0.185122\pi$
$74$	1.11254	−	1.92698i	0.129330	−	0.224006i
$75$	0.996377	+	1.72578i	0.115052	+	0.199275i
$76$	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	0.0402236	−	0.999191i	$-0.487193\pi$
$79$	7.86993	−	13.6311i	0.885436	−	1.53362i	0.845213	−	0.534430i	$-0.179474\pi$
$80$		−	5.66612i		−	0.633492i
$81$	−1.41581			−0.157313
$82$	−8.12800			−0.897587
$83$		−	7.97408i		−	0.875269i	−0.899153	−	0.437635i	$-0.855816\pi$
$83$		−	7.97408i		−	0.875269i	0.899153	−	0.437635i	$-0.144184\pi$
$84$		0			0
$85$	−4.31275	+	2.48997i	−0.467784	+	0.270075i
$86$	−10.0647	−	5.81086i	−1.08531	−	0.626601i
$87$	−2.05328	+	3.55639i	−0.220135	+	0.381285i
$88$	8.40757			0.896250
$89$	13.9118	−	8.03198i	1.47465	−	0.851388i	0.475055	−	0.879956i	$-0.342428\pi$
$89$	13.9118	−	8.03198i	1.47465	−	0.851388i	0.999592	+	0.0285683i	$0.00909482\pi$
$90$	−3.79017			−0.399519
$91$		0			0
$92$	−2.59235			−0.270271
$93$	2.09064	−	1.20703i	0.216789	−	0.125163i
$94$	−8.50105			−0.876816
$95$	−5.32659	+	9.22592i	−0.546497	+	0.946560i
$96$	−2.09007	−	1.20670i	−0.213317	−	0.123158i
$97$	−12.3209	+	7.11347i	−1.25100	+	0.722263i	−0.971307	−	0.237827i	$-0.923565\pi$
$97$	−12.3209	+	7.11347i	−1.25100	+	0.722263i	−0.279689	+	0.960091i	$0.590231\pi$
$98$		0			0
$99$		−	4.54548i		−	0.456838i
$100$	0.631962			0.0631962
$101$	0.0731225			0.00727596			0.00363798	−	0.999993i	$-0.498842\pi$
$101$	0.0731225			0.00727596			0.00363798	+	0.999993i	$0.498842\pi$
$102$		−	4.09105i		−	0.405075i
$103$	−6.45980	+	11.1887i	−0.636503	+	1.10245i	0.349692	+	0.936865i	$0.386286\pi$
$103$	−6.45980	+	11.1887i	−0.636503	+	1.10245i	−0.986195	+	0.165590i	$0.947047\pi$
$104$	1.21690	+	10.8421i	0.119327	+	1.06316i
$105$		0			0
$106$	−11.5948	−	6.69425i	−1.12618	−	0.650203i
$107$	−2.00427	−	3.47150i	−0.193761	−	0.335603i	0.752733	−	0.658326i	$-0.228735\pi$
$107$	−2.00427	−	3.47150i	−0.193761	−	0.335603i	−0.946493	+	0.322723i	$0.895402\pi$
$108$	−1.00271	+	1.73675i	−0.0964860	+	0.167119i
$109$	1.71984	−	0.992947i	0.164730	−	0.0951071i	−0.415368	−	0.909653i	$-0.636347\pi$
$109$	1.71984	−	0.992947i	0.164730	−	0.0951071i	0.580099	+	0.814546i	$0.303014\pi$
$110$			6.43722i			0.613765i
$111$	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	$0.667633\pi$
$114$	−4.37583	−	7.57916i	−0.409834	−	0.709854i
$115$		−	12.7025i		−	1.18451i
$116$	0.651157	+	1.12784i	0.0604584	+	0.104717i
$117$	5.86170	−	0.657905i	0.541914	−	0.0608233i
$118$	3.92410			0.361243
$119$		0			0
$120$	3.20695	−	5.55461i	0.292753	−	0.507064i
$121$	3.27998			0.298180
$122$	−1.19595	+	0.690483i	−0.108276	+	0.0625134i
$123$	−6.44001	−	3.71814i	−0.580676	−	0.335254i
$124$		−	0.765571i		−	0.0687503i
$125$			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	$-2.07943e-6\pi$
$128$	6.24025	−	3.60281i	0.551566	−	0.318447i
$129$	−5.31634	−	9.20818i	−0.468078	−	0.810735i
$130$	−8.30123	+	0.931713i	−0.728066	+	0.0817166i
$131$	−1.53241	+	2.65421i	−0.133887	+	0.231899i	−0.925172	−	0.379549i	$-0.876079\pi$
$131$	−1.53241	+	2.65421i	−0.133887	+	0.231899i	0.791285	+	0.611448i	$0.209413\pi$
$132$	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
$136$	−7.19067	−	4.15154i	−0.616595	−	0.355991i
$137$	−18.9512	−	10.9415i	−1.61911	−	0.934796i	−0.987150	−	0.159799i	$-0.948915\pi$
$137$	−18.9512	−	10.9415i	−1.61911	−	0.934796i	−0.631965	−	0.774997i	$-0.717751\pi$
$138$	9.03712	+	5.21758i	0.769291	+	0.444150i
$139$	−5.53535	−	9.58750i	−0.469502	−	0.813201i	0.529890	−	0.848066i	$-0.322233\pi$
$139$	−5.53535	−	9.58750i	−0.469502	−	0.813201i	−0.999392	+	0.0348652i	$0.988900\pi$
$140$		0			0
$141$	−6.73559	−	3.88879i	−0.567239	−	0.327495i
$142$	−1.73534	+	3.00570i	−0.145627	+	0.252233i
$143$	−1.11738	−	9.95549i	−0.0934403	−	0.832520i
$144$	−2.55376	−	4.42324i	−0.212813	−	0.368603i
$145$	−5.52637	+	3.19065i	−0.458940	+	0.264969i
$146$	−4.89699	+	8.48183i	−0.405277	+	0.701961i
$147$		0			0
$148$		−	0.645588i		−	0.0530670i
$149$		−	2.30737i		−	0.189027i	−0.995524	−	0.0945136i	$-0.969870\pi$
$149$		−	2.30737i		−	0.189027i	0.995524	−	0.0945136i	$-0.0301296\pi$
$150$	−2.20306	−	1.27194i	−0.179879	−	0.103853i
$151$	17.8538	−	10.3079i	1.45292	−	0.838845i	0.454275	−	0.890861i	$-0.349898\pi$
$151$	17.8538	−	10.3079i	1.45292	−	0.838845i	0.998646	+	0.0520168i	$0.0165649\pi$
$152$	−17.7621			−1.44070
$153$	−2.24449	+	3.88757i	−0.181456	+	0.314292i
$154$		0			0
$155$	3.75128			0.301310
$156$	−0.624323	+	1.42929i	−0.0499858	+	0.114435i
$157$	−1.44824	−	2.50843i	−0.115582	−	0.200194i	0.802430	−	0.596746i	$-0.203540\pi$
$157$	−1.44824	−	2.50843i	−0.115582	−	0.200194i	−0.918012	+	0.396552i	$0.870207\pi$
$158$			20.0929i			1.59851i
$159$	−6.12455	−	10.6080i	−0.485709	−	0.841272i
$160$	−1.87513	−	3.24782i	−0.148242	−	0.256763i
$161$		0			0
$162$	1.56523	−	0.903688i	0.122976	−	0.0710004i
$163$		−	23.4339i		−	1.83549i	−0.397175	−	0.917743i	$-0.630010\pi$
$163$		−	23.4339i		−	1.83549i	0.397175	−	0.917743i	$-0.369990\pi$
$164$	−2.04232	+	1.17913i	−0.159478	+	0.0920750i
$165$	−2.94470	+	5.10037i	−0.229244	+	0.397063i
$166$	5.08971	+	8.81564i	0.395038	+	0.684226i
$167$	6.58349	+	3.80098i	0.509446	+	0.294129i	0.732606	−	0.680653i	$-0.238304\pi$
$167$	6.58349	+	3.80098i	0.509446	+	0.294129i	−0.223160	+	0.974782i	$0.571637\pi$
$168$		0			0
$169$	12.6765	−	2.88188i	0.975119	−	0.221683i
$170$	3.17861	−	5.50551i	0.243788	−	0.422253i
$171$			9.60292i			0.734353i
$172$	−3.37194			−0.257108
$173$	−5.39721			−0.410343			−0.205171	−	0.978726i	$-0.565775\pi$
$173$	−5.39721			−0.410343			−0.205171	+	0.978726i	$0.565775\pi$
$174$		−	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
$178$	−10.2533	+	17.7593i	−0.768520	+	1.33112i
$179$	12.2914			0.918704			0.459352	−	0.888254i	$-0.348082\pi$
$179$	12.2914			0.918704			0.459352	+	0.888254i	$0.348082\pi$
$180$	−0.952357	+	0.549843i	−0.0709845	+	0.0409829i
$181$	−21.8525			−1.62428			−0.812140	−	0.583463i	$-0.801697\pi$
$181$	−21.8525			−1.62428			−0.812140	+	0.583463i	$0.801697\pi$
$182$		0			0
$183$	−1.26344			−0.0933964
$184$	18.3415	−	10.5894i	1.35215	−	0.780664i
$185$	3.16337			0.232575
$186$	−1.54085	+	2.66883i	−0.112981	+	0.195688i
$187$	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
$191$	2.75716			0.199501			0.0997507	−	0.995012i	$-0.468195\pi$
$191$	2.75716			0.199501			0.0997507	+	0.995012i	$0.468195\pi$
$192$	10.3735			0.748643
$193$		−	12.9893i		−	0.934993i	−0.883995	−	0.467497i	$-0.845156\pi$
$193$		−	12.9893i		−	0.934993i	0.883995	−	0.467497i	$-0.154844\pi$
$194$	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	$0.429608\pi$
$198$	2.90130	+	5.02519i	0.206186	+	0.357125i
$199$	−10.0159	+	17.3480i	−0.710006	+	1.22977i	0.254848	+	0.966981i	$0.417975\pi$
$199$	−10.0159	+	17.3480i	−0.710006	+	1.22977i	−0.964854	+	0.262786i	$0.915359\pi$
$200$	−4.47127	+	2.58149i	−0.316166	+	0.182539i
$201$			5.86061i			0.413375i
$202$	−0.0808396	+	0.0466728i	−0.00568785	+	0.00328388i
$203$		0			0
$204$	−0.593492	−	1.02796i	−0.0415528	−	0.0719715i
$205$	−5.77773	−	10.0073i	−0.403534	−	0.698942i
$206$		−	16.4927i		−	1.14910i
$207$	−5.72509	−	9.91614i	−0.397921	−	0.689219i
$208$	−6.68057	−	9.05999i	−0.463214	−	0.628197i
$209$	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	$0.278525\pi$
$212$	−3.88456			−0.266793
$213$	−2.74991	+	1.58766i	−0.188421	+	0.108785i
$214$	4.43160	+	2.55858i	0.302938	+	0.174901i
$215$		−	16.5224i		−	1.12682i
$216$		−	16.3838i		−	1.11478i
$217$		0			0
$218$	−1.26756	+	2.19548i	−0.0858501	+	0.148697i
$219$	−7.76000	+	4.48024i	−0.524372	+	0.302747i
$220$	0.933852	+	1.61748i	0.0629603	+	0.109050i
$221$	−3.96022	+	9.06629i	−0.266393	+	0.609865i
$222$	−1.29936	+	2.25056i	−0.0872076	+	0.151048i
$223$	7.25954	+	4.19130i	0.486135	+	0.280670i	0.722970	−	0.690880i	$-0.242777\pi$
$223$	7.25954	+	4.19130i	0.486135	+	0.280670i	−0.236835	+	0.971550i	$0.576110\pi$
$224$		0			0
$225$	1.39566	+	2.41735i	0.0930439	+	0.161157i
$226$	−11.6902	−	6.74933i	−0.777620	−	0.448959i
$227$	0.796500	+	0.459860i	0.0528656	+	0.0305220i	0.526200	−	0.850361i	$-0.323616\pi$
$227$	0.796500	+	0.459860i	0.0528656	+	0.0305220i	−0.473334	+	0.880883i	$0.656950\pi$
$228$	−2.19903	−	1.26961i	−0.145634	−	0.0840820i
$229$	21.3222	+	12.3104i	1.40901	+	0.813494i	0.995293	−	0.0969108i	$-0.0308962\pi$
$229$	21.3222	+	12.3104i	1.40901	+	0.813494i	0.413719	+	0.910404i	$0.364229\pi$
$230$	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	0.431038	+	0.902334i	$0.358148\pi$
$233$	−8.63847	+	14.9623i	−0.565925	+	0.980211i	−0.996963	+	0.0778773i	$0.975186\pi$
$234$	−6.06040	+	4.46876i	−0.396180	+	0.292132i
$235$	−6.04291	−	10.4666i	−0.394196	−	0.682767i
$236$	0.986008	−	0.569272i	0.0641837	−	0.0370565i
$237$	−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	$-0.155172\pi$
$240$			6.61760i			0.427165i
$241$	7.30441	+	4.21720i	0.470518	+	0.271654i	0.716457	−	0.697632i	$-0.245763\pi$
$241$	7.30441	+	4.21720i	0.470518	+	0.271654i	−0.245938	+	0.969285i	$0.579096\pi$
$242$	−3.62614	+	2.09355i	−0.233097	+	0.134579i
$243$	−14.5898			−0.935934
$244$	−0.200338	+	0.346995i	−0.0128253	+	0.0222141i
$245$		0			0
$246$	9.49290			0.605245
$247$	2.36062	+	21.0323i	0.150203	+	1.33825i
$248$	3.12726	+	5.41658i	0.198581	+	0.343953i
$249$			9.31313i			0.590196i
$250$	−7.76851	−	13.4555i	−0.491324	−	0.850998i
$251$	−7.33631	−	12.7069i	−0.463064	−	0.802050i	0.536048	−	0.844188i	$-0.319917\pi$
$251$	−7.33631	−	12.7069i	−0.463064	−	0.802050i	−0.999112	+	0.0421373i	$0.986583\pi$
$252$		0			0
$253$	−16.8415	+	9.72346i	−1.05882	+	0.611309i
$254$			14.3863i			0.902677i
$255$	5.03697	−	2.90810i	0.315427	−	0.182112i
$256$	4.28277	−	7.41797i	0.267673	−	0.463623i
$257$	14.6643	+	25.3993i	0.914733	+	1.58436i	0.807292	+	0.590152i	$0.200932\pi$
$257$	14.6643	+	25.3993i	0.914733	+	1.58436i	0.107441	+	0.994211i	$0.465734\pi$
$258$	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
$262$		−	3.91243i		−	0.241711i
$263$	19.9149			1.22801			0.614004	−	0.789303i	$-0.289558\pi$
$263$	19.9149			1.22801			0.614004	+	0.789303i	$0.289558\pi$
$264$	−9.81942			−0.604343
$265$		−	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
$269$	11.1625	−	19.3340i	0.680589	−	1.17881i	−0.294213	−	0.955740i	$-0.595057\pi$
$269$	11.1625	−	19.3340i	0.680589	−	1.17881i	0.974801	−	0.223074i	$-0.0716093\pi$
$270$	12.5442			0.763415
$271$	8.14054	−	4.69994i	0.494502	−	0.285501i	−0.231938	−	0.972731i	$-0.574507\pi$
$271$	8.14054	−	4.69994i	0.494502	−	0.285501i	0.726440	+	0.687230i	$0.241173\pi$
$272$	8.56677			0.519437
$273$		0			0
$274$	27.9351			1.68762
$275$	4.10562	−	2.37038i	0.247578	−	0.142939i
$276$	3.02767			0.182245
$277$	−7.17133	+	12.4211i	−0.430883	+	0.746312i	−0.996950	−	0.0780478i	$-0.975131\pi$
$277$	−7.17133	+	12.4211i	−0.430883	+	0.746312i	0.566066	+	0.824360i	$0.308465\pi$
$278$	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	$-0.000938442\pi$
$282$	9.92859			0.591239
$283$	0.620673			0.0368952			0.0184476	−	0.999830i	$-0.494128\pi$
$283$	0.620673			0.0368952			0.0184476	+	0.999830i	$0.494128\pi$
$284$			1.00699i			0.0597539i
$285$	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
$289$	4.73534	+	8.20186i	0.278550	+	0.482462i
$290$	4.07307	−	7.05477i	0.239179	−	0.414270i
$291$	14.3899	−	8.30800i	0.843549	−	0.487023i
$292$			2.84164i			0.166294i
$293$	21.5586	−	12.4469i	1.25947	−	0.727153i	0.286496	−	0.958082i	$-0.407510\pi$
$293$	21.5586	−	12.4469i	1.25947	−	0.727153i	0.972971	+	0.230928i	$0.0741762\pi$
$294$		0			0
$295$	2.78942	+	4.83142i	0.162406	+	0.281296i
$296$	2.63715	+	4.56767i	0.153281	+	0.265491i
$297$			15.0440i			0.872941i
$298$	1.47275	+	2.55088i	0.0853143	+	0.147769i
$299$	−14.9767	−	20.3109i	−0.866124	−	1.17461i
$300$	−0.738085			−0.0426133
$301$		0			0
$302$	−13.1587	+	22.7915i	−0.757197	+	1.31150i
$303$	−0.0854016			−0.00490619
$304$	15.8710	−	9.16310i	0.910262	−	0.525540i
$305$	−1.70027	−	0.981651i	−0.0973571	−	0.0562091i
$306$		−	5.73047i		−	0.327589i
$307$		−	9.89767i		−	0.564890i	−0.959284	−	0.282445i	$-0.908855\pi$
$307$		−	9.89767i		−	0.564890i	0.959284	−	0.282445i	$-0.0911455\pi$
$308$		0			0
$309$	7.54456	−	13.0676i	0.429195	−	0.743387i
$310$	−4.14718	+	2.39437i	−0.235544	+	0.135991i
$311$	3.61895	+	6.26820i	0.205212	+	0.355437i	0.950200	−	0.311640i	$-0.100878\pi$
$311$	3.61895	+	6.26820i	0.205212	+	0.355437i	−0.744988	+	0.667077i	$0.767545\pi$
$312$	−1.42125	−	12.6628i	−0.0804622	−	0.716890i
$313$	−16.3303	+	28.2849i	−0.923043	+	1.59876i	−0.128365	+	0.991727i	$0.540973\pi$
$313$	−16.3303	+	28.2849i	−0.923043	+	1.59876i	−0.794678	+	0.607031i	$0.792360\pi$
$314$	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	$-0.173133\pi$
$317$	14.8734	+	8.58718i	0.835375	+	0.482304i	−0.0203143	+	0.999794i	$0.506467\pi$
$318$	13.5418	+	7.81838i	0.759388	+	0.438433i
$319$	8.46064	+	4.88475i	0.473705	+	0.273494i
$320$	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
$325$	3.65101	+	4.95139i	0.202521	+	0.274654i
$326$	14.9574	+	25.9071i	0.828416	+	1.43486i
$327$	−2.00864	+	1.15969i	−0.111078	+	0.0641309i
$328$	9.63324	−	16.6853i	0.531907	−	0.921289i
$329$		0			0
$330$		−	7.51819i		−	0.413863i
$331$			19.9340i			1.09567i	0.836587	+	0.547835i	$0.184548\pi$
$331$			19.9340i			1.09567i	−0.836587	+	0.547835i	$0.815452\pi$
$332$	2.55778	+	1.47674i	0.140377	+	0.0810465i
$333$	2.46947	−	1.42575i	0.135326	−	0.0781306i
$334$	−9.70438			−0.531000
$335$	−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	$0.488971\pi$
$338$	−12.1749	+	11.2772i	−0.662229	+	0.613401i
$339$	−6.17495	−	10.6953i	−0.335377	−	0.580890i
$340$		−	1.84449i		−	0.100032i
$341$	−2.87152	−	4.97363i	−0.155502	−	0.269337i
$342$	−6.12937	−	10.6164i	−0.331438	−	0.574068i
$343$		0			0
$344$	23.8572	−	13.7740i	1.28630	−	0.742643i
$345$			14.8355i			0.798718i
$346$	5.96682	−	3.44494i	0.320778	−	0.185201i
$347$	−12.9417	+	22.4156i	−0.694744	+	1.20333i	0.275522	+	0.961295i	$0.411149\pi$
$347$	−12.9417	+	22.4156i	−0.694744	+	1.20333i	−0.970267	+	0.242038i	$0.922184\pi$
$348$	−0.760503	−	1.31723i	−0.0407672	−	0.0706109i
$349$	−14.9967	−	8.65837i	−0.802757	−	0.463472i	0.0416774	−	0.999131i	$-0.486730\pi$
$349$	−14.9967	−	8.65837i	−0.802757	−	0.463472i	−0.844434	+	0.535659i	$0.820063\pi$
$350$		0			0
$351$	−19.4002	+	2.17744i	−1.03551	+	0.116223i
$352$	−2.87074	+	4.97227i	−0.153011	+	0.265023i
$353$			25.3495i			1.34922i	0.738176	+	0.674608i	$0.235687\pi$
$353$			25.3495i			1.34922i	−0.738176	+	0.674608i	$0.764313\pi$
$354$	−4.58306			−0.243587
$355$	−4.93423			−0.261882
$356$			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	$-0.377748\pi$
$359$	−4.56434	−	2.63522i	−0.240897	−	0.139082i	−0.615589	+	0.788068i	$0.711082\pi$
$360$	4.49208	−	7.78052i	0.236754	−	0.410069i
$361$	−15.4561			−0.813478
$362$	24.1587	−	13.9480i	1.26975	−	0.733092i
$363$	−3.83077			−0.201063
$364$		0			0
$365$	−13.9240			−0.728813
$366$	1.39678	−	0.806433i	0.0730110	−	0.0421529i
$367$	25.3176			1.32157			0.660783	−	0.750577i	$-0.270224\pi$
$367$	25.3176			1.32157			0.660783	+	0.750577i	$0.270224\pi$
$368$	−10.9257	+	18.9240i	−0.569544	+	0.986479i
$369$	−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
$373$	−6.78782			−0.351460			−0.175730	−	0.984438i	$-0.556229\pi$
$373$	−6.78782			−0.351460			−0.175730	+	0.984438i	$0.556229\pi$
$374$	−9.73261			−0.503262
$375$		−	14.2148i		−	0.734048i
$376$	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	$0.564164\pi$
$380$	−1.97288	−	3.41714i	−0.101207	−	0.175295i
$381$	−6.58100	+	11.3986i	−0.337155	+	0.583969i
$382$	−3.04815	+	1.75985i	−0.155957	+	0.0900417i
$383$		−	7.25917i		−	0.370926i	−0.982651	−	0.185463i	$-0.940621\pi$
$383$		−	7.25917i		−	0.370926i	0.982651	−	0.185463i	$-0.0593785\pi$
$384$	−7.28815	+	4.20782i	−0.371922	+	0.214729i
$385$		0			0
$386$	8.29086	+	14.3602i	0.421994	+	0.730915i
$387$	−7.44677	−	12.8982i	−0.378541	−	0.655652i
$388$		−	5.26943i		−	0.267515i
$389$	−3.57406	−	6.19045i	−0.181212	−	0.313868i	0.761082	−	0.648656i	$-0.224669\pi$
$389$	−3.57406	−	6.19045i	−0.181212	−	0.313868i	−0.942293	+	0.334788i	$0.891335\pi$
$390$	9.69521	−	1.08817i	0.490936	−	0.0551017i
$391$	19.2052			0.971250
$392$		0			0
$393$	1.78974	−	3.09991i	0.0902802	−	0.156370i
$394$	−24.2882			−1.22362
$395$	−24.7388	+	14.2829i	−1.24474	+	0.718652i
$396$	1.45802	+	0.841786i	0.0732681	+	0.0423014i
$397$		−	22.4612i		−	1.12729i	−0.826016	−	0.563647i	$-0.809398\pi$
$397$		−	22.4612i		−	1.12729i	0.826016	−	0.563647i	$-0.190602\pi$
$398$		−	25.5718i		−	1.28180i
$399$		0			0
$400$	2.66347	−	4.61327i	0.133174	−	0.230663i
$401$	2.64547	−	1.52736i	0.132108	−	0.0762729i	−0.432489	−	0.901639i	$-0.642365\pi$
$401$	2.64547	−	1.52736i	0.132108	−	0.0762729i	0.564598	+	0.825366i	$0.309031\pi$
$402$	−3.74072	−	6.47912i	−0.186570	−	0.323149i
$403$	5.99820	−	4.42290i	0.298792	−	0.220320i
$404$	−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
$409$	−4.85482	−	2.80293i	−0.240055	−	0.138596i	0.375147	−	0.926965i	$-0.377592\pi$
$409$	−4.85482	−	2.80293i	−0.240055	−	0.138596i	−0.615202	+	0.788369i	$0.710926\pi$
$410$	12.7750	+	7.37564i	0.630912	+	0.364257i
$411$	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
$416$	−6.82758	−	2.98233i	−0.334750	−	0.146221i
$417$	6.46487	+	11.1975i	0.316586	+	0.548343i
$418$	−18.0308	+	10.4101i	−0.881916	+	0.509175i
$419$	−3.06969	+	5.31687i	−0.149964	+	0.259746i	−0.931214	−	0.364473i	$-0.881249\pi$
$419$	−3.06969	+	5.31687i	−0.149964	+	0.259746i	0.781250	+	0.624219i	$0.214583\pi$
$420$		0			0
$421$			1.92589i			0.0938622i	0.998898	+	0.0469311i	$0.0149441\pi$
$421$			1.92589i			0.0938622i	−0.998898	+	0.0469311i	$0.985056\pi$
$422$		−	12.7660i		−	0.621441i
$423$	−9.43475	−	5.44716i	−0.458733	−	0.264850i
$424$	27.4841	−	15.8679i	1.33475	−	0.770615i
$425$	−4.68184			−0.227102
$426$	2.02675	−	3.51044i	0.0981965	−	0.170081i
$427$		0			0
$428$	1.48470			0.0717658
$429$	1.30502	+	11.6273i	0.0630070	+	0.561370i
$430$	10.5460	+	18.2662i	0.508572	+	0.880873i
$431$		−	10.7494i		−	0.517779i	−0.965907	−	0.258890i	$-0.916643\pi$
$431$		−	10.7494i		−	0.517779i	0.965907	−	0.258890i	$-0.0833566\pi$
$432$	8.45207	+	14.6394i	0.406651	+	0.704340i
$433$	20.1328	+	34.8710i	0.967520	+	1.67579i	0.702685	+	0.711501i	$0.251984\pi$
$433$	20.1328	+	34.8710i	0.967520	+	1.67579i	0.264835	+	0.964294i	$0.414682\pi$
$434$		0			0
$435$	6.45439	−	3.72644i	0.309464	−	0.178669i
$436$			0.735544i			0.0352262i
$437$	35.5799	−	20.5421i	1.70202	−	0.982662i
$438$	5.71931	−	9.90614i	0.273279	−	0.473334i
$439$	−10.9754	−	19.0099i	−0.523826	−	0.907294i	−0.999615	−	0.0277345i	$-0.991171\pi$
$439$	−10.9754	−	19.0099i	−0.523826	−	0.907294i	0.475789	−	0.879560i	$-0.342163\pi$
$440$	−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	−0.317207	−	0.948356i	$-0.602745\pi$
$443$	13.9482	−	24.1589i	0.662697	−	1.14783i	0.979904	−	0.199469i	$-0.0639217\pi$
$444$			0.753999i			0.0357832i
$445$	−29.1540			−1.38203
$446$	−10.7009			−0.506703
$447$			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
$451$	−8.84546	+	15.3208i	−0.416516	+	0.721427i
$452$	−3.91652			−0.184218
$453$	−20.8519	+	12.0389i	−0.979708	+	0.565635i
$454$	−1.17408			−0.0551023
$455$		0			0
$456$	20.7448			0.971464
$457$	−4.77724	+	2.75814i	−0.223470	+	0.129020i	−0.607556	−	0.794277i	$-0.707850\pi$
$457$	−4.77724	+	2.75814i	−0.223470	+	0.129020i	0.384086	+	0.923297i	$0.374517\pi$
$458$	−31.4300			−1.46863
$459$	7.42851	−	12.8665i	0.346733	−	0.600559i
$460$	4.07447	+	2.35240i	0.189973	+	0.109681i
$461$	25.0092	−	14.4391i	1.16479	−	0.672494i	0.212346	−	0.977195i	$-0.431890\pi$
$461$	25.0092	−	14.4391i	1.16479	−	0.672494i	0.952448	+	0.304700i	$0.0985562\pi$
$462$		0			0
$463$		−	14.2284i		−	0.661251i	−0.943762	−	0.330625i	$-0.892740\pi$
$463$		−	14.2284i		−	0.661251i	0.943762	−	0.330625i	$-0.107260\pi$
$464$	10.9775			0.509617
$465$	−4.38121			−0.203174
$466$		−	22.0551i		−	1.02168i
$467$	−2.27163	+	3.93457i	−0.105118	+	0.182070i	−0.913787	−	0.406195i	$-0.866855\pi$
$467$	−2.27163	+	3.93457i	−0.105118	+	0.182070i	0.808668	+	0.588265i	$0.200189\pi$
$468$	−0.874509	+	2.00205i	−0.0404242	+	0.0925448i
$469$		0			0
$470$	13.3613	+	7.71416i	0.616312	+	0.355828i
$471$	1.69144	+	2.92966i	0.0779374	+	0.134992i
$472$	−4.65081	+	8.05545i	−0.214071	+	0.370782i
$473$	−21.9062	+	12.6476i	−1.00725	+	0.581536i
$474$		−	23.4671i		−	1.07788i
$475$	−8.67366	+	5.00774i	−0.397975	+	0.229771i
$476$		0			0
$477$	−8.57886	−	14.8590i	−0.392799	−	0.680348i
$478$	9.24413	+	16.0113i	0.422817	+	0.732340i
$479$			1.66553i			0.0760999i	0.999276	+	0.0380499i	$0.0121146\pi$
$479$			1.66553i			0.0760999i	−0.999276	+	0.0380499i	$0.987885\pi$
$480$	2.19001	+	3.79321i	0.0999598	+	0.173135i
$481$	5.05815	−	3.72973i	0.230632	−	0.170061i
$482$	−10.7671			−0.490426
$483$		0			0
$484$	−0.607426	+	1.05209i	−0.0276103	+	0.0478224i
$485$	25.8201			1.17243
$486$	16.1295	−	9.31239i	0.731650	−	0.422418i
$487$	1.28598	+	0.742463i	0.0582735	+	0.0336442i	0.528854	−	0.848713i	$-0.322622\pi$
$487$	1.28598	+	0.742463i	0.0582735	+	0.0336442i	−0.470580	+	0.882357i	$0.655955\pi$
$488$		−	3.27342i		−	0.148181i
$489$			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	$0.0491224\pi$
$492$	2.38528	−	1.37714i	0.107537	−	0.0620863i
$493$	−4.82404	−	8.35548i	−0.217264	−	0.376312i
$494$	−16.0343	−	21.7452i	−0.721416	−	0.978363i
$495$	−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	$-0.463153\pi$
$499$	−15.3459	−	8.85997i	−0.686977	−	0.396627i	−0.802479	+	0.596681i	$0.796486\pi$
$500$	−3.90398	−	2.25397i	−0.174591	−	0.100800i
$501$	−7.68902	−	4.43926i	−0.343520	−	0.198331i
$502$	16.2211	+	9.36527i	0.723984	+	0.417993i
$503$	0.598451	+	1.03655i	0.0266836	+	0.0462174i	0.879059	−	0.476713i	$-0.158172\pi$
$503$	0.598451	+	1.03655i	0.0266836	+	0.0462174i	−0.852375	+	0.522931i	$0.824839\pi$
$504$		0			0
$505$	−0.114929	−	0.0663540i	−0.00511425	−	0.00295272i
$506$	12.4126	−	21.4993i	0.551809	−	0.955760i
$507$	−14.8053	+	3.36582i	−0.657524	+	0.149481i
$508$	2.08703	+	3.61485i	0.0925971	+	0.160383i
$509$	−5.44396	+	3.14307i	−0.241299	+	0.139314i	−0.615774	−	0.787923i	$-0.711156\pi$
$509$	−5.44396	+	3.14307i	−0.241299	+	0.139314i	0.374474	+	0.927237i	$0.377823\pi$
$510$	−3.71237	+	6.43002i	−0.164387	+	0.284726i
$511$		0			0
$512$			25.3457i			1.12013i
$513$		−	31.7824i		−	1.40323i
$514$	−32.4238	−	18.7199i	−1.43015	−	0.825699i
$515$	20.3061	−	11.7237i	0.894792	−	0.516608i
$516$	3.93818			0.173369
$517$	−9.25143	+	16.0240i	−0.406878	+	0.704733i
$518$		0			0
$519$	6.30354			0.276695
$520$	7.92592	−	18.1451i	0.347574	−	0.795716i
$521$	5.42367	+	9.39407i	0.237615	+	0.411562i	0.960029	−	0.279899i	$-0.0903010\pi$
$521$	5.42367	+	9.39407i	0.237615	+	0.411562i	−0.722414	+	0.691460i	$0.756968\pi$
$522$		−	7.34304i		−	0.321396i
$523$	−0.673629	−	1.16676i	−0.0294557	−	0.0510188i	0.850922	−	0.525292i	$-0.176044\pi$
$523$	−0.673629	−	1.16676i	−0.0294557	−	0.0510188i	−0.880377	+	0.474274i	$0.842711\pi$
$524$	−0.567579	−	0.983076i	−0.0247948	−	0.0429459i
$525$		0			0
$526$	−22.0167	+	12.7113i	−0.959974	+	0.554241i
$527$			5.67167i			0.247062i
$528$	8.77394	−	5.06563i	0.381837	−	0.220453i
$529$	−12.9936	+	22.5057i	−0.564941	+	0.978507i
$530$	12.1492	+	21.0431i	0.527728	+	0.914052i
$531$	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
$535$			7.27501i			0.314526i
$536$	−15.1841			−0.655853
$537$	−14.3555			−0.619484
$538$			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	$-0.475988\pi$
$541$	−17.4565	−	10.0785i	−0.750516	−	0.433310i	−0.825880	+	0.563846i	$0.809321\pi$
$542$	−5.99978	+	10.3919i	−0.257712	+	0.446371i
$543$	25.5220			1.09526
$544$	4.91047	−	2.83506i	0.210535	−	0.121552i
$545$	−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	$0.523313\pi$
$548$	7.01924	−	4.05256i	0.299847	−	0.173117i
$549$	−1.76975			−0.0755309
$550$	−3.02594	+	5.24109i	−0.129027	+	0.223481i
$551$	−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
$555$	−3.69458			−0.156826
$556$	4.10041			0.173896
$557$			23.6654i			1.00273i	0.865234	+	0.501367i	$0.167170\pi$
$557$			23.6654i			1.00273i	−0.865234	+	0.501367i	$0.832830\pi$
$558$	−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
$562$	0.0630888	+	0.109273i	0.00266124	+	0.00460941i
$563$	14.4037	−	24.9480i	0.607045	−	1.05143i	−0.384680	−	0.923050i	$-0.625688\pi$
$563$	14.4037	−	24.9480i	0.607045	−	1.05143i	0.991725	−	0.128382i	$-0.0409784\pi$
$564$	2.49475	−	1.44035i	0.105048	−	0.0606496i
$565$		−	19.1909i		−	0.807366i
$566$	−0.686177	+	0.396164i	−0.0288422	+	0.0166520i
$567$		0			0
$568$	−4.11343	−	7.12467i	−0.172596	−	0.298945i
$569$	−13.8361	−	23.9648i	−0.580040	−	1.00466i	−0.995474	−	0.0950353i	$-0.969704\pi$
$569$	−13.8361	−	23.9648i	−0.580040	−	1.00466i	0.415434	−	0.909623i	$-0.363630\pi$
$570$			15.8832i			0.665272i
$571$	6.48273	+	11.2284i	0.271294	+	0.469895i	0.969193	−	0.246301i	$-0.0792151\pi$
$571$	6.48273	+	11.2284i	0.271294	+	0.469895i	−0.697899	+	0.716196i	$0.745882\pi$
$572$	3.40027	+	1.48526i	0.142173	+	0.0621020i
$573$	−3.22016			−0.134524
$574$		0			0
$575$	5.97105	−	10.3422i	0.249010	−	0.431298i
$576$	14.5305			0.605437
$577$	8.19301	−	4.73023i	0.341079	−	0.196922i	−0.319670	−	0.947529i	$-0.603572\pi$
$577$	8.19301	−	4.73023i	0.341079	−	0.196922i	0.660749	+	0.750607i	$0.270239\pi$
$578$	−10.4702	−	6.04497i	−0.435503	−	0.251438i
$579$			15.1706i			0.630468i
$580$		−	2.36354i		−	0.0981405i
$581$		0			0
$582$	−10.6057	+	18.3696i	−0.439620	+	0.761444i
$583$	−25.2365	+	14.5703i	−1.04519	+	0.603440i
$584$	−11.6077	−	20.1052i	−0.480332	−	0.831959i
$585$	−9.80999	−	4.28507i	−0.405593	−	0.177166i
$586$	−15.8892	+	27.5209i	−0.656377	+	1.13688i
$587$	−18.6673	−	10.7776i	−0.770481	−	0.444837i	0.0625654	−	0.998041i	$-0.480072\pi$
$587$	−18.6673	−	10.7776i	−0.770481	−	0.444837i	−0.833046	+	0.553204i	$0.813405\pi$
$588$		0			0
$589$	6.06647	+	10.5074i	0.249965	+	0.432951i
$590$	−6.16761	−	3.56087i	−0.253917	−	0.146599i
$591$	−19.2441	−	11.1106i	−0.791598	−	0.457029i
$592$	−4.71274	−	2.72090i	−0.193692	−	0.111828i
$593$	−3.44015	−	1.98617i	−0.141270	−	0.0815622i	0.427699	−	0.903921i	$-0.359324\pi$
$593$	−3.44015	−	1.98617i	−0.141270	−	0.0815622i	−0.568969	+	0.822359i	$0.692658\pi$
$594$	−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
$598$	29.5214	+	12.8951i	1.20722	+	0.527322i
$599$	9.75246	+	16.8918i	0.398475	+	0.690179i	0.993538	−	0.113500i	$-0.0362063\pi$
$599$	9.75246	+	16.8918i	0.398475	+	0.690179i	−0.595063	+	0.803679i	$0.702873\pi$
$600$	5.22211	−	3.01498i	0.213192	−	0.123086i
$601$	13.4368	−	23.2733i	0.548100	−	0.949336i	−0.450305	−	0.892875i	$-0.648685\pi$
$601$	13.4368	−	23.2733i	0.548100	−	0.949336i	0.998405	−	0.0564616i	$-0.0179818\pi$
$602$		0			0
$603$			8.20914i			0.334302i
$604$			7.63576i			0.310695i
$605$	−5.15523	−	2.97637i	−0.209590	−	0.121007i
$606$	0.0944146	−	0.0545103i	0.00383533	−	0.00221433i
$607$	25.0203			1.01554			0.507772	−	0.861491i	$-0.330469\pi$
$607$	25.0203			1.01554			0.507772	+	0.861491i	$0.330469\pi$
$608$	6.06482	−	10.5046i	0.245961	−	0.426016i
$609$		0			0
$610$	2.50628			0.101476
$611$	−22.0030	−	9.61106i	−0.890146	−	0.388822i
$612$	−0.831324	−	1.43990i	−0.0336043	−	0.0582043i
$613$			21.3585i			0.862663i	0.902194	+	0.431332i	$0.141956\pi$
$613$			21.3585i			0.862663i	−0.902194	+	0.431332i	$0.858044\pi$
$614$	6.31751	+	10.9422i	0.254954	+	0.441593i
$615$	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	$0.564229\pi$
$618$			19.2622i			0.774840i
$619$	−42.3588	+	24.4559i	−1.70254	+	0.982965i	−0.759375	+	0.650654i	$0.774495\pi$
$619$	−42.3588	+	24.4559i	−1.70254	+	0.982965i	−0.943170	+	0.332311i	$0.892172\pi$
$620$	−0.694707	+	1.20327i	−0.0279001	+	0.0483244i
$621$	18.9481	+	32.8191i	0.760361	+	1.31698i
$622$	−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
$626$		−	41.6934i		−	1.66640i
$627$	−19.0483			−0.760718
$628$	1.07281			0.0428099
$629$			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
$633$	5.83981	−	10.1148i	0.232111	−	0.402029i
$634$	−21.9242			−0.870720
$635$	−17.7127	+	10.2264i	−0.702905	+	0.405823i
$636$	4.53687			0.179899
$637$		0			0
$638$	−12.4714			−0.493747
$639$	−3.85189	+	2.22389i	−0.152378	+	0.0879757i
$640$	−13.0773			−0.516926
$641$	19.8510	−	34.3829i	0.784066	−	1.35804i	−0.145489	−	0.989360i	$-0.546475\pi$
$641$	19.8510	−	34.3829i	0.784066	−	1.35804i	0.929555	−	0.368683i	$-0.120191\pi$
$642$	−5.17578	−	2.98824i	−0.204272	−	0.117936i
$643$	27.8388	−	16.0727i	1.09785	−	0.633847i	0.162198	−	0.986758i	$-0.448142\pi$
$643$	27.8388	−	16.0727i	1.09785	−	0.633847i	0.935657	+	0.352911i	$0.114808\pi$
$644$		0			0
$645$			19.2970i			0.759818i
$646$	20.5614			0.808978
$647$	19.8500			0.780385			0.390193	−	0.920733i	$-0.372408\pi$
$647$	19.8500			0.780385			0.390193	+	0.920733i	$0.372408\pi$
$648$			4.28417i			0.168298i
$649$	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
$653$	9.50024	+	16.4549i	0.371773	+	0.643930i	0.989838	−	0.142197i	$-0.0454165\pi$
$653$	9.50024	+	16.4549i	0.371773	+	0.643930i	−0.618065	+	0.786127i	$0.712083\pi$
$654$	1.48042	−	2.56416i	0.0578889	−	0.100266i
$655$	4.81705	−	2.78112i	0.188218	−	0.108667i
$656$			19.8784i			0.776120i
$657$	−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	$0.788456\pi$
$660$	−1.09067	−	1.88909i	−0.0424542	−	0.0735329i
$661$		−	16.7510i		−	0.651537i	−0.945450	−	0.325769i	$-0.894377\pi$
$661$		−	16.7510i		−	0.651537i	0.945450	−	0.325769i	$-0.105623\pi$
$662$	−12.7235	−	22.0377i	−0.494512	−	0.856520i
$663$	4.62524	−	10.5888i	0.179629	−	0.411233i
$664$	−24.1291			−0.936393
$665$		0			0
$666$	−1.82006	+	3.15244i	−0.0705259	+	0.122155i
$667$	24.6096			0.952889
$668$	−2.43842	+	1.40782i	−0.0943453	+	0.0544703i
$669$	−8.47860	−	4.89512i	−0.327802	−	0.189256i
$670$		−	11.6256i		−	0.449137i
$671$			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	$0.910986\pi$
$674$	−1.40612	+	0.811824i	−0.0541618	+	0.0312703i
$675$	−4.61916	−	8.00061i	−0.177791	−	0.307944i
$676$	−1.42320	+	4.59986i	−0.0547383	+	0.176918i
$677$	−14.0671	+	24.3649i	−0.540641	+	0.936418i	0.458226	+	0.888836i	$0.348485\pi$
$677$	−14.0671	+	24.3649i	−0.540641	+	0.936418i	−0.998867	+	0.0475826i	$0.984848\pi$
$678$	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
$682$	6.34915	+	3.66568i	0.243122	+	0.140366i
$683$	1.79295	+	1.03516i	0.0686053	+	0.0396093i	0.533910	−	0.845541i	$-0.320722\pi$
$683$	1.79295	+	1.03516i	0.0686053	+	0.0396093i	−0.465305	+	0.885150i	$0.654055\pi$
$684$	−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
$689$	−22.4421	−	30.4353i	−0.854975	−	1.15949i
$690$	−9.46925	−	16.4012i	−0.360488	−	0.624384i
$691$	−31.0542	+	17.9291i	−1.18136	+	0.682057i	−0.956328	−	0.292295i	$-0.905581\pi$
$691$	−31.0542	+	17.9291i	−1.18136	+	0.682057i	−0.225029	+	0.974352i	$0.572248\pi$
$692$	0.999521	−	1.73122i	0.0379961	−	0.0658112i
$693$		0			0
$694$		−	33.0417i		−	1.25425i
$695$			20.0919i			0.762129i
$696$	10.7614	+	6.21312i	0.407911	+	0.235508i
$697$	15.1304	−	8.73552i	0.573103	−	0.330881i
$698$	22.1059			0.836722
$699$	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	$0.822081\pi$
$702$	20.0579	−	14.7901i	0.757035	−	0.558215i
$703$	5.11571	+	8.86067i	0.192943	+	0.334187i
$704$		−	24.6785i		−	0.930107i
$705$	7.05767	+	12.2242i	0.265807	+	0.460391i
$706$	−16.1801	−	28.0248i	−0.608947	−	1.05473i
$707$		0			0
$708$	−1.15158	+	0.664867i	−0.0432792	+	0.0249872i
$709$		−	16.2656i		−	0.610866i	−0.952213	−	0.305433i	$-0.901199\pi$
$709$		−	16.2656i		−	0.610866i	0.952213	−	0.305433i	$-0.0988013\pi$
$710$	5.45497	−	3.14943i	0.204721	−	0.118196i
$711$	−12.8748	+	22.2998i	−0.482843	+	0.836309i
$712$	−24.3043	−	42.0963i	−0.910843	−	1.57763i
$713$	−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
$717$			16.9149i			0.631697i
$718$	6.72806			0.251089
$719$	10.0149			0.373492			0.186746	−	0.982408i	$-0.440206\pi$
$719$	10.0149			0.373492			0.186746	+	0.982408i	$0.440206\pi$
$720$			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
$724$	4.04690	−	7.00944i	0.150402	−	0.260504i
$725$	−5.99932			−0.222809
$726$	4.23506	−	2.44511i	0.157178	−	0.0907466i
$727$	34.5299			1.28064			0.640322	−	0.768106i	$-0.278801\pi$
$727$	34.5299			1.28064			0.640322	+	0.768106i	$0.278801\pi$
$728$		0			0
$729$	21.2872			0.788415
$730$	15.3934	−	8.88741i	0.569737	−	0.328938i
$731$	24.9808			0.923947
$732$	0.233980	−	0.405265i	0.00864814	−	0.0149790i
$733$	28.6966	+	16.5680i	1.05993	+	0.611953i	0.925414	−	0.378958i	$-0.123717\pi$
$733$	28.6966	+	16.5680i	1.05993	+	0.611953i	0.134520	+	0.990911i	$0.457051\pi$
$734$	−27.9895	+	16.1598i	−1.03311	+	0.596468i
$735$		0			0
$736$			14.4629i			0.533111i
$737$	13.9424			0.513574
$738$	13.2970			0.489470
$739$			4.01567i			0.147719i	0.997269	+	0.0738594i	$0.0235316\pi$
$739$			4.01567i			0.147719i	−0.997269	+	0.0738594i	$0.976468\pi$
$740$	−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	$0.592952\pi$
$744$	−3.65241	−	6.32616i	−0.133904	−	0.231928i
$745$	−2.09379	+	3.62656i	−0.0767107	+	0.132867i
$746$	7.50418	−	4.33254i	0.274748	−	0.158626i
$747$			13.0452i			0.477299i
$748$	−2.44551	+	1.41192i	−0.0894168	+	0.0516248i
$749$		0			0
$750$	9.07304	+	15.7150i	0.331300	+	0.573829i
$751$	18.7579	+	32.4896i	0.684486	+	1.18556i	0.973598	+	0.228269i	$0.0733065\pi$
$751$	18.7579	+	32.4896i	0.684486	+	1.18556i	−0.289112	+	0.957295i	$0.593360\pi$
$752$			20.7907i			0.758159i
$753$	8.56826	+	14.8407i	0.312245	+	0.540824i
$754$	−1.80509	−	16.0827i	−0.0657375	−	0.585698i
$755$	−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	$-0.0531004\pi$
$758$	−15.7306			−0.571361
$759$	19.6697	−	11.3563i	0.713963	−	0.412207i
$760$	27.9172	+	16.1180i	1.01266	+	0.584661i
$761$		−	4.30225i		−	0.155956i	−0.996955	−	0.0779782i	$-0.975154\pi$
$761$		−	4.30225i		−	0.155956i	0.996955	−	0.0779782i	$-0.0248465\pi$
$762$		−	16.8021i		−	0.608677i
$763$		0			0
$764$	−0.510605	+	0.884394i	−0.0184730	+	0.0319962i
$765$	7.05545	−	4.07347i	0.255090	−	0.147277i
$766$	4.63340	+	8.02528i	0.167411	+	0.289965i
$767$	10.1566	+	4.43649i	0.366735	+	0.160192i
$768$	−5.00195	+	8.66363i	−0.180492	+	0.312622i
$769$	10.6146	+	6.12834i	0.382772	+	0.220994i	0.679024	−	0.734116i	$-0.262403\pi$
$769$	10.6146	+	6.12834i	0.382772	+	0.220994i	−0.296251	+	0.955110i	$0.595737\pi$
$770$		0			0
$771$	−17.1268	−	29.6645i	−0.616806	−	1.06834i
$772$	4.16649	+	2.40552i	0.149955	+	0.0865767i
$773$	3.29372	+	1.90163i	0.118467	+	0.0683970i	0.558063	−	0.829799i	$-0.311545\pi$
$773$	3.29372	+	1.90163i	0.118467	+	0.0683970i	−0.439596	+	0.898196i	$0.644878\pi$
$774$	16.4654	+	9.50628i	0.591835	+	0.341696i
$775$	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
$780$	2.27825	−	1.67992i	0.0815745	−	0.0601506i
$781$	3.77705	+	6.54204i	0.135153	+	0.234092i
$782$	−21.2321	+	12.2583i	−0.759258	+	0.438358i
$783$	9.51891	−	16.4872i	0.340178	−	0.589206i
$784$		0			0
$785$			5.25675i			0.187622i
$786$			4.56943i			0.162986i
$787$	−15.0114	−	8.66684i	−0.535099	−	0.308940i	0.207991	−	0.978131i	$-0.433307\pi$
$787$	−15.0114	−	8.66684i	−0.535099	−	0.308940i	−0.743090	+	0.669191i	$0.766641\pi$
$788$	−6.10289	+	3.52351i	−0.217407	+	0.125520i
$789$	−23.2592			−0.828048
$790$	18.2331	−	31.5806i	0.648704	−	1.12359i
$791$		0			0
$792$	−13.7544			−0.488740
$793$	−3.87609	+	0.435044i	−0.137644	+	0.0154489i
$794$	14.3366	+	24.8317i	0.508786	+	0.881243i
$795$			22.2306i			0.788437i
$796$	−3.70972	−	6.42542i	−0.131488	−	0.227743i
$797$	25.1707	+	43.5969i	0.891592	+	1.54428i	0.837967	+	0.545721i	$0.183744\pi$
$797$	25.1707	+	43.5969i	0.891592	+	1.54428i	0.0536245	+	0.998561i	$0.482923\pi$
$798$		0			0
$799$	15.8248	−	9.13645i	0.559841	−	0.323224i
$800$		−	3.52576i		−	0.124655i
$801$	−22.7590	+	13.1399i	−0.804150	+	0.464276i
$802$	−1.94978	+	3.37711i	−0.0688490	+	0.119250i
$803$	10.6585	+	18.4610i	0.376130	+	0.651476i
$804$	−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
$808$		−	0.221265i		−	0.00778407i
$809$	16.0739			0.565128			0.282564	−	0.959249i	$-0.408815\pi$
$809$	16.0739			0.565128			0.282564	+	0.959249i	$0.408815\pi$
$810$	−3.28016			−0.115253
$811$			36.9875i			1.29881i	0.760443	+	0.649404i	$0.224982\pi$
$811$			36.9875i			1.29881i	−0.760443	+	0.649404i	$0.775018\pi$
$812$		0			0
$813$	−9.50754	+	5.48918i	−0.333444	+	0.192514i
$814$	5.35409	+	3.09119i	0.187661	+	0.108346i
$815$	−21.2648	+	36.8317i	−0.744873	+	1.29016i
$816$	−10.0053			−0.350257
$817$	46.2798	−	26.7197i	1.61913	−	0.934803i
$818$	7.15624			0.250212
$819$		0			0
$820$	4.27996			0.149463
$821$	−26.1021	+	15.0700i	−0.910968	+	0.525948i	−0.880743	−	0.473595i	$-0.842956\pi$
$821$	−26.1021	+	15.0700i	−0.910968	+	0.525948i	−0.0302256	+	0.999543i	$0.509623\pi$
$822$	−32.6261			−1.13796
$823$	20.8251	−	36.0702i	0.725918	−	1.25733i	−0.232677	−	0.972554i	$-0.574749\pi$
$823$	20.8251	−	36.0702i	0.725918	−	1.25733i	0.958595	−	0.284773i	$-0.0919181\pi$
$824$	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	$-0.227184\pi$
$828$	4.24096			0.147384
$829$	7.47474			0.259609			0.129804	−	0.991540i	$-0.458565\pi$
$829$	7.47474			0.259609			0.129804	+	0.991540i	$0.458565\pi$
$830$		−	18.4744i		−	0.641255i
$831$	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
$835$	−6.89829	−	11.9482i	−0.238725	−	0.413484i
$836$	−3.02040	+	5.23149i	−0.104463	+	0.180935i
$837$	−9.69209	+	5.59573i	−0.335008	+	0.193417i
$838$		−	7.83732i		−	0.270736i
$839$	−9.51957	+	5.49613i	−0.328652	+	0.189747i	−0.655242	−	0.755419i	$-0.727434\pi$
$839$	−9.51957	+	5.49613i	−0.328652	+	0.189747i	0.326590	+	0.945166i	$0.394100\pi$
$840$		0			0
$841$	8.31846	+	14.4080i	0.286843	+	0.496827i
$842$	−1.22926	−	2.12914i	−0.0423632	−	0.0733752i
$843$			0.115440i			0.00397595i
$844$	−1.85198	−	3.20772i	−0.0637477	−	0.110414i
$845$	−22.5392	−	6.97363i	−0.775372	−	0.239900i
$846$	13.9073			0.478143
$847$		0			0
$848$	−16.3719	+	28.3569i	−0.562213	+	0.973781i
$849$	−0.724899			−0.0248785
$850$	5.17594	−	2.98833i	0.177533	−	0.102499i
$851$	−10.5651	−	6.09979i	−0.362169	−	0.209098i
$852$		−	1.17609i		−	0.0402922i
$853$		−	35.2031i		−	1.20533i	−0.797994	−	0.602666i	$-0.794105\pi$
$853$		−	35.2031i		−	1.20533i	0.797994	−	0.602666i	$-0.205895\pi$
$854$		0			0
$855$	8.71404	−	15.0932i	0.298014	−	0.516175i
$856$	−10.5046	+	6.06483i	−0.359040	+	0.207292i
$857$	15.1841	+	26.2996i	0.518678	+	0.898377i	0.999764	+	0.0217035i	$0.00690898\pi$
$857$	15.1841	+	26.2996i	0.518678	+	0.898377i	−0.481086	+	0.876673i	$0.659758\pi$
$858$	−8.86422	−	12.0214i	−0.302620	−	0.410404i
$859$	17.9153	−	31.0302i	0.611262	−	1.05874i	−0.379767	−	0.925082i	$-0.623996\pi$
$859$	17.9153	−	31.0302i	0.611262	−	1.05874i	0.991028	−	0.133654i	$-0.0426710\pi$
$860$	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	$-0.147794\pi$
$863$	28.0075	+	16.1702i	0.953387	+	0.550438i	0.0592557	+	0.998243i	$0.481127\pi$
$864$	9.68945	+	5.59421i	0.329642	+	0.190319i
$865$	8.48294	+	4.89763i	0.288429	+	0.166524i
$866$	−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
$871$	2.01800	+	17.9796i	0.0683772	+	0.609216i
$872$	−3.00461	−	5.20413i	−0.101749	−	0.176234i
$873$	20.1564	−	11.6373i	0.682190	−	0.393862i
$874$	−26.2233	+	45.4201i	−0.887016	+	1.53636i
$875$		0			0
$876$		−	3.31882i		−	0.112133i
$877$			4.41611i			0.149121i	0.997216	+	0.0745607i	$0.0237555\pi$
$877$			4.41611i			0.149121i	−0.997216	+	0.0745607i	$0.976245\pi$
$878$	24.2674	+	14.0108i	0.818984	+	0.472841i
$879$	−25.1788	+	14.5370i	−0.849261	+	0.490321i
$880$	15.7433			0.530706
$881$	9.97753	−	17.2816i	0.336152	−	0.582232i	−0.647554	−	0.762020i	$-0.724208\pi$
$881$	9.97753	−	17.2816i	0.336152	−	0.582232i	0.983705	+	0.179788i	$0.0575412\pi$
$882$		0			0
$883$	−12.9725			−0.436559			−0.218280	−	0.975886i	$-0.570045\pi$
$883$	−12.9725			−0.436559			−0.218280	+	0.975886i	$0.570045\pi$
$884$	−2.17472	−	2.94929i	−0.0731438	−	0.0991955i
$885$	−3.25783	−	5.64273i	−0.109511	−	0.189678i
$886$			35.6114i			1.19639i
$887$	−27.0862	−	46.9147i	−0.909467	−	1.57524i	−0.814806	−	0.579733i	$-0.803157\pi$
$887$	−27.0862	−	46.9147i	−0.909467	−	1.57524i	−0.0946605	−	0.995510i	$-0.530177\pi$
$888$	−3.07999	−	5.33470i	−0.103358	−	0.179021i
$889$		0			0
$890$	32.2309	−	18.6085i	1.08038	−	0.623758i
$891$		−	3.93383i		−	0.131788i
$892$	−2.68882	+	1.55239i	−0.0900283	+	0.0519779i
$893$	19.5449	−	33.8527i	0.654044	−	1.13284i
$894$	−1.72007	−	2.97924i	−0.0575276	−	0.0996408i
$895$	−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
$899$			7.26769i			0.242391i
$900$	−1.03386			−0.0344620
$901$	28.7784			0.958748
$902$		−	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
$906$	15.3684	−	26.6188i	0.510580	−	0.884350i
$907$	2.59139			0.0860457			0.0430229	−	0.999074i	$-0.486301\pi$
$907$	2.59139			0.0860457			0.0430229	+	0.999074i	$0.486301\pi$
$908$	−0.295011	+	0.170325i	−0.00979029	+	0.00565242i
$909$	−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	$0.481011\pi$
$912$	−18.5361	+	10.7018i	−0.613791	+	0.354373i
$913$	22.1559			0.733254
$914$	3.52094	−	6.09845i	0.116462	−	0.201719i
$915$	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
$919$	−27.9249			−0.921156			−0.460578	−	0.887619i	$-0.652358\pi$
$919$	−27.9249			−0.921156			−0.460578	+	0.887619i	$0.652358\pi$
$920$	−38.4370			−1.26723
$921$			11.5597i			0.380906i
$922$	−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
$926$	9.08174	+	15.7300i	0.298445	+	0.516921i
$927$	10.5679	−	18.3042i	0.347096	−	0.601187i
$928$	6.29229	−	3.63285i	0.206554	−	0.119254i
$929$		−	26.5659i		−	0.871599i	−0.900044	−	0.435800i	$-0.856466\pi$
$929$		−	26.5659i		−	0.871599i	0.900044	−	0.435800i	$-0.143534\pi$
$930$	4.84359	−	2.79645i	0.158828	−	0.0916992i
$931$		0			0
$932$	−3.19955	−	5.54179i	−0.104805	−	0.181527i
$933$	−4.22666	−	7.32079i	−0.138375	−	0.239672i
$934$		−	5.79976i		−	0.189774i
$935$	−6.91836	−	11.9830i	−0.226255	−	0.391885i
$936$	−1.99079	−	17.7372i	−0.0650709	−	0.579758i
$937$	3.02509			0.0988255			0.0494128	−	0.998778i	$-0.484265\pi$
$937$	3.02509			0.0988255			0.0494128	+	0.998778i	$0.484265\pi$
$938$		0			0
$939$	19.0726	−	33.0347i	0.622410	−	1.07805i
$940$	4.47640			0.146004
$941$	5.61587	−	3.24232i	0.183072	−	0.105697i	−0.405663	−	0.914023i	$-0.632959\pi$
$941$	5.61587	−	3.24232i	0.183072	−	0.105697i	0.588735	+	0.808326i	$0.299626\pi$
$942$	−3.73990	−	2.15923i	−0.121852	−	0.0703515i
$943$			44.5639i			1.45120i
$944$		−	9.59704i		−	0.312357i
$945$		0			0
$946$	16.1454	−	27.9647i	0.524934	−	0.909212i
$947$	−18.3193	+	10.5767i	−0.595298	+	0.343695i	−0.767190	−	0.641420i	$-0.778345\pi$
$947$	−18.3193	+	10.5767i	−0.595298	+	0.343695i	0.171892	+	0.985116i	$0.445012\pi$
$948$	−3.40438	−	5.89656i	−0.110569	−	0.191511i
$949$	−22.2641	+	16.4169i	−0.722722	+	0.532914i
$950$	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
$955$	−4.33351	−	2.50195i	−0.140229	−	0.0809613i
$956$	4.64554	+	2.68211i	0.150248	+	0.0867455i
$957$	−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
$962$	−3.21135	+	7.35187i	−0.103538	+	0.237034i
$963$	3.27889	+	5.67921i	0.105661	+	0.183010i
$964$	−2.70544	+	1.56199i	−0.0871363	+	0.0503082i
$965$	−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	$0.915681\pi$
$968$		−	9.92504i		−	0.319003i
$969$	16.2913	+	9.40580i	0.523353	+	0.302158i
$970$	−28.5451	+	16.4805i	−0.916527	+	0.529157i
$971$	−24.5210			−0.786915			−0.393458	−	0.919343i	$-0.628721\pi$
$971$	−24.5210			−0.786915			−0.393458	+	0.919343i	$0.628721\pi$
$972$	2.70191	−	4.67984i	0.0866638	−	0.150106i
$973$		0			0
$974$	−1.89560			−0.0607390
$975$	−4.26410	−	5.78285i	−0.136561	−	0.185199i
$976$	1.68869	+	2.92490i	0.0540537	+	0.0936237i
$977$		−	10.9198i		−	0.349355i	−0.984626	−	0.174677i	$-0.944112\pi$
$977$		−	10.9198i		−	0.349355i	0.984626	−	0.174677i	$-0.0558883\pi$
$978$	−17.4692	−	30.2575i	−0.558603	−	0.967528i
$979$	22.3168	+	38.6538i	0.713248	+	1.23538i
$980$		0			0
$981$	−2.81357	+	1.62441i	−0.0898302	+	0.0518635i
$982$			20.4197i			0.651618i
$983$	−17.0360	+	9.83574i	−0.543364	+	0.313711i	−0.746441	−	0.665451i	$-0.768239\pi$
$983$	−17.0360	+	9.83574i	−0.543364	+	0.313711i	0.203077	+	0.979163i	$0.434906\pi$
$984$	−11.2509	+	19.4871i	−0.358666	+	0.621227i
$985$	−17.2651	−	29.9040i	−0.550112	−	0.952822i
$986$	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
$990$		−	10.5310i		−	0.334696i
$991$	−1.73800			−0.0552094			−0.0276047	−	0.999619i	$-0.508788\pi$
$991$	−1.73800			−0.0552094			−0.0276047	+	0.999619i	$0.508788\pi$
$992$	−4.27118			−0.135610
$993$		−	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
$997$	23.4768	−	40.6631i	0.743519	−	1.28781i	−0.207365	−	0.978264i	$-0.566489\pi$
$997$	23.4768	−	40.6631i	0.743519	−	1.28781i	0.950884	−	0.309549i	$-0.100178\pi$
$998$	22.6206			0.716044
$999$	−8.17312	+	4.71875i	−0.258586	+	0.149295i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.u.h.30.2		12
7.2	even	3		91.2.q.a.43.5	yes	12
7.3	odd	6		637.2.k.g.459.2		12
7.4	even	3		637.2.k.h.459.2		12
7.5	odd	6		637.2.q.h.589.5		12
7.6	odd	2		637.2.u.i.30.2		12
13.10	even	6		637.2.k.h.569.5		12
21.2	odd	6		819.2.ct.a.316.2		12
28.23	odd	6		1456.2.cc.c.225.2		12
91.9	even	3		1183.2.c.i.337.4		12
91.10	odd	6		637.2.u.i.361.2		12
91.19	even	12		8281.2.a.by.1.3		6
91.23	even	6		91.2.q.a.36.5	✓	12
91.30	even	6		1183.2.c.i.337.9		12
91.33	even	12		8281.2.a.ch.1.4		6
91.58	odd	12		1183.2.a.m.1.3		6
91.62	odd	6		637.2.k.g.569.5		12
91.72	odd	12		1183.2.a.p.1.4		6
91.75	odd	6		637.2.q.h.491.5		12
91.88	even	6	inner	637.2.u.h.361.2		12
273.23	odd	6		819.2.ct.a.127.2		12
364.23	odd	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	91.23	even	6
91.2.q.a.43.5	yes	12	7.2	even	3
637.2.k.g.459.2		12	7.3	odd	6
637.2.k.g.569.5		12	91.62	odd	6
637.2.k.h.459.2		12	7.4	even	3
637.2.k.h.569.5		12	13.10	even	6
637.2.q.h.491.5		12	91.75	odd	6
637.2.q.h.589.5		12	7.5	odd	6
637.2.u.h.30.2		12	1.1	even	1	trivial
637.2.u.h.361.2		12	91.88	even	6	inner
637.2.u.i.30.2		12	7.6	odd	2
637.2.u.i.361.2		12	91.10	odd	6
819.2.ct.a.127.2		12	273.23	odd	6
819.2.ct.a.316.2		12	21.2	odd	6
1183.2.a.m.1.3		6	91.58	odd	12
1183.2.a.p.1.4		6	91.72	odd	12
1183.2.c.i.337.4		12	91.9	even	3
1183.2.c.i.337.9		12	91.30	even	6
1456.2.cc.c.225.2		12	28.23	odd	6
1456.2.cc.c.673.2		12	364.23	odd	6
8281.2.a.by.1.3		6	91.19	even	12
8281.2.a.ch.1.4		6	91.33	even	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.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.10554 + 0.638282i) q^{2} -1.16793 q^{3} +(-0.185192 + 0.320762i) q^{4} +(-1.57173 - 0.907437i) q^{5} +(1.29118 - 0.745466i) q^{6} -3.02595i q^{8} -1.63595 q^{9} +O(q^{10})\)	\(q+(-1.10554 + 0.638282i) q^{2} -1.16793 q^{3} +(-0.185192 + 0.320762i) q^{4} +(-1.57173 - 0.907437i) q^{5} +(1.29118 - 0.745466i) q^{6} -3.02595i q^{8} -1.63595 q^{9} +2.31680 q^{10} +2.77849i q^{11} +(0.216290 - 0.374626i) q^{12} +(-3.58305 + 0.402155i) q^{13} +(1.83566 + 1.05982i) q^{15} +(1.56102 + 2.70377i) q^{16} +(1.37198 - 2.37634i) q^{17} +(1.80860 - 1.04420i) q^{18} -5.86993i q^{19} +(0.582143 - 0.336100i) q^{20} +(-1.77346 - 3.07173i) q^{22} +(3.49955 + 6.06139i) q^{23} +3.53408i q^{24} +(-0.853117 - 1.47764i) q^{25} +(3.70451 - 2.73160i) q^{26} +5.41444 q^{27} +(1.75806 - 3.04505i) q^{29} -2.70585 q^{30} +(-1.79004 + 1.03348i) q^{31} +(1.78956 + 1.03320i) q^{32} -3.24507i q^{33} +3.50284i q^{34} +(0.302965 - 0.524751i) q^{36} +(-1.50950 + 0.871512i) q^{37} +(3.74667 + 6.48942i) q^{38} +(4.18474 - 0.469686i) 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} +(2.57127 + 1.48452i) q^{45} +(-7.73776 - 4.46740i) 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} +(0.534557 - 1.22378i) q^{52} +(5.24396 + 9.08280i) q^{53} +(-5.98587 + 3.45594i) q^{54} +(2.52131 - 4.36703i) q^{55} +6.85564i q^{57} +4.48855i q^{58} +(-2.66212 - 1.53698i) q^{59} +(-0.679899 + 0.392540i) q^{60} +1.08178 q^{61} +(1.31931 - 2.28511i) q^{62} -8.88199 q^{64} +(5.99651 + 2.61932i) q^{65} +(2.07127 + 3.58755i) q^{66} -5.01796i q^{67} +(0.508159 + 0.880158i) q^{68} +(-4.08721 - 7.07925i) q^{69} +(2.35453 - 1.35939i) q^{71} +4.95030i q^{72} +(6.64426 - 3.83607i) q^{73} +(1.11254 - 1.92698i) q^{74} +(0.996377 + 1.72578i) q^{75} +(1.88285 + 1.08706i) q^{76} +(-4.32659 + 3.19030i) q^{78} +(7.86993 - 13.6311i) q^{79} -5.66612i q^{80} -1.41581 q^{81} -8.12800 q^{82} -7.97408i q^{83} +(-4.31275 + 2.48997i) q^{85} +(-10.0647 - 5.81086i) q^{86} +(-2.05328 + 3.55639i) q^{87} +8.40757 q^{88} +(13.9118 - 8.03198i) q^{89} -3.79017 q^{90} -2.59235 q^{92} +(2.09064 - 1.20703i) q^{93} -8.50105 q^{94} +(-5.32659 + 9.22592i) q^{95} +(-2.09007 - 1.20670i) q^{96} +(-12.3209 + 7.11347i) q^{97} -4.54548i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 - 6 * q^5 - 18 * q^6 + 8 * q^9	\( 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} - 24 q^{10} + 2 q^{12} + 4 q^{13} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{18} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} + 24 q^{26} + 12 q^{27} + 8 q^{29} - 16 q^{30} + 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} - 2 q^{38} - 10 q^{39} - 46 q^{40} + 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} + 42 q^{47} - 2 q^{48} - 18 q^{50} - 26 q^{51} + 26 q^{52} + 22 q^{53} - 12 q^{54} - 6 q^{55} - 18 q^{59} + 66 q^{60} - 28 q^{61} - 4 q^{62} - 52 q^{64} - 42 q^{65} + 26 q^{66} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 30 q^{73} + 6 q^{74} + 46 q^{75} - 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} - 28 q^{82} - 48 q^{85} - 60 q^{86} - 2 q^{87} + 28 q^{88} + 12 q^{89} + 24 q^{90} + 24 q^{92} + 18 q^{93} - 8 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 - 6 * q^5 - 18 * q^6 + 8 * q^9 - 24 * q^10 + 2 * q^12 + 4 * q^13 + 6 * q^15 - 8 * q^16 - 4 * q^17 - 12 * q^18 - 12 * q^20 + 6 * q^22 - 12 * q^23 + 10 * q^25 + 24 * q^26 + 12 * q^27 + 8 * q^29 - 16 * q^30 + 18 * q^31 - 36 * q^32 - 10 * q^36 + 42 * q^37 - 2 * q^38 - 10 * q^39 - 46 * q^40 + 30 * q^41 + 2 * q^43 + 24 * q^44 - 12 * q^46 + 42 * q^47 - 2 * q^48 - 18 * q^50 - 26 * q^51 + 26 * q^52 + 22 * q^53 - 12 * q^54 - 6 * q^55 - 18 * q^59 + 66 * q^60 - 28 * q^61 - 4 * q^62 - 52 * q^64 - 42 * q^65 + 26 * q^66 - 8 * q^68 + 4 * q^69 - 24 * q^71 + 30 * q^73 + 6 * q^74 + 46 * q^75 - 18 * q^76 - 10 * q^78 + 28 * q^79 - 4 * q^81 - 28 * q^82 - 48 * q^85 - 60 * q^86 - 2 * q^87 + 28 * q^88 + 12 * q^89 + 24 * q^90 + 24 * q^92 + 18 * q^93 - 8 * q^94 - 22 * q^95 + 6 * q^96 + 6 * q^97

Introduction

L-functions

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Database

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