LMFDB - Embedded newform 637.2.q.h.589.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(491,637)]

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([0, 5]))

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

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

chi := DirichletCharacter("637.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
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			589.5
Root			$1.40744 - 0.138282i$ of defining polynomial
Character	$\chi$	$=$	637.589
Dual form			637.2.q.h.491.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10554 + 0.638282i) q^{2} +(-0.583963 + 1.01145i) q^{3} +(-0.185192 - 0.320762i) q^{4} -1.81487i q^{5} +(-1.29118 + 0.745466i) q^{6} -3.02595i q^{8} +(0.817975 + 1.41677i) q^{9} +O(q^{10})$	\(q+(1.10554 + 0.638282i) q^{2} +(-0.583963 + 1.01145i) q^{3} +(-0.185192 - 0.320762i) q^{4} -1.81487i 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} +0.432581 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} +2.08840i q^{18} +(5.08351 - 2.93497i) q^{19} +(-0.582143 + 0.336100i) q^{20} +(-1.77346 - 3.07173i) q^{22} +(3.49955 - 6.06139i) q^{23} +(3.06060 + 1.76704i) q^{24} +1.70623 q^{25} +(4.21789 + 1.84240i) q^{26} -5.41444 q^{27} +(1.75806 - 3.04505i) q^{29} +(1.35293 + 2.34334i) q^{30} +2.06697i q^{31} +(-1.78956 + 1.03320i) q^{32} +(2.81031 - 1.62254i) q^{33} -3.50284i q^{34} +(0.302965 - 0.524751i) q^{36} +(1.50950 + 0.871512i) q^{37} +7.49334 q^{38} +(-1.68561 + 3.85893i) q^{39} -5.49171 q^{40} +(-5.51406 - 3.18355i) q^{41} +(4.55195 + 7.88422i) q^{43} +1.02911i q^{44} +(2.57127 - 1.48452i) q^{45} +(7.73776 - 4.46740i) q^{46} +6.65932i q^{47} +(1.82316 + 3.15780i) q^{48} +(1.88631 + 1.08906i) q^{50} +3.20474 q^{51} +(-0.792549 - 1.07483i) q^{52} -10.4879 q^{53} +(-5.98587 - 3.45594i) q^{54} +(-2.52131 + 4.36703i) q^{55} +6.85564i q^{57} +(3.88720 - 2.24427i) q^{58} +(-2.66212 + 1.53698i) q^{59} -0.785080i q^{60} +(0.540892 + 0.936853i) q^{61} +(-1.31931 + 2.28511i) q^{62} -8.88199 q^{64} +(-0.729860 - 6.50279i) q^{65} +4.14254 q^{66} +(4.34568 + 2.50898i) q^{67} +(-0.508159 + 0.880158i) q^{68} +(4.08721 + 7.07925i) q^{69} +(2.35453 - 1.35939i) q^{71} +(4.28709 - 2.47515i) q^{72} -7.67213i 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} -15.7399 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} +11.6217i q^{86} +(2.05328 + 3.55639i) q^{87} +(-4.20379 + 7.28117i) q^{88} +(13.9118 + 8.03198i) q^{89} +3.79017 q^{90} -2.59235 q^{92} +(-2.09064 - 1.20703i) q^{93} +(-4.25052 + 7.36212i) q^{94} +(-5.32659 - 9.22592i) q^{95} -2.41340i q^{96} +(12.3209 - 7.11347i) q^{97} -4.54548i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9	$ 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} + 30 q^{33} - 10 q^{36} - 42 q^{37} - 4 q^{38} - 4 q^{39} - 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 2 q^{48} - 18 q^{50} + 52 q^{51} - 2 q^{52} - 44 q^{53} - 12 q^{54} + 6 q^{55} - 12 q^{58} - 18 q^{59} - 14 q^{61} + 4 q^{62} - 52 q^{64} + 60 q^{65} + 52 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} - 56 q^{79} + 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 2 q^{87} - 14 q^{88} + 12 q^{89} - 24 q^{90} + 24 q^{92} - 18 q^{93} - 4 q^{94} - 22 q^{95} - 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9 - 12 * q^10 + 6 * q^11 + 4 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 + 12 * q^20 + 6 * q^22 - 12 * q^23 - 12 * q^24 - 20 * q^25 + 42 * q^26 - 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 + 30 * q^33 - 10 * q^36 - 42 * q^37 - 4 * q^38 - 4 * q^39 - 92 * q^40 - 30 * q^41 + 2 * q^43 + 12 * q^46 + 2 * q^48 - 18 * q^50 + 52 * q^51 - 2 * q^52 - 44 * q^53 - 12 * q^54 + 6 * q^55 - 12 * q^58 - 18 * q^59 - 14 * q^61 + 4 * q^62 - 52 * q^64 + 60 * q^65 + 52 * q^66 - 24 * q^67 + 8 * q^68 - 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 - 56 * q^79 + 72 * q^80 + 2 * q^81 - 14 * q^82 - 48 * q^85 + 2 * q^87 - 14 * q^88 + 12 * q^89 - 24 * q^90 + 24 * q^92 - 18 * q^93 - 4 * q^94 - 22 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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	$-0.184282\pi$
$2$	1.10554	+	0.638282i	0.781733	+	0.451334i	−0.0553113	+	0.998469i	$0.517615\pi$
$3$	−0.583963	+	1.01145i	−0.337151	+	0.583963i	−0.983896	−	0.178744i	$-0.942797\pi$
$3$	−0.583963	+	1.01145i	−0.337151	+	0.583963i	0.646745	+	0.762707i	$0.276130\pi$
$4$	−0.185192	−	0.320762i	−0.0925960	−	0.160381i
$5$		−	1.81487i		−	0.811636i	−0.913954	−	0.405818i	$-0.866987\pi$
$5$		−	1.81487i		−	0.811636i	0.913954	−	0.405818i	$-0.133013\pi$
$6$	−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	$-0.470908\pi$
$11$	−2.40625	−	1.38925i	−0.725510	−	0.418874i	−0.816777	+	0.576953i	$0.804242\pi$
$12$	0.432581			0.124875
$13$	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	$-0.274645\pi$
$17$	−1.37198	−	2.37634i	−0.332754	−	0.576347i	−0.983051	+	0.183334i	$0.941311\pi$
$18$			2.08840i			0.492240i
$19$	5.08351	−	2.93497i	1.16624	−	0.673327i	0.213446	−	0.976955i	$-0.431531\pi$
$19$	5.08351	−	2.93497i	1.16624	−	0.673327i	0.952791	+	0.303628i	$0.0981979\pi$
$20$	−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	−0.227302	−	0.973824i	$-0.572990\pi$
$23$	3.49955	−	6.06139i	0.729706	−	1.26389i	0.957007	−	0.290063i	$-0.0936763\pi$
$24$	3.06060	+	1.76704i	0.624743	+	0.360696i
$25$	1.70623			0.341247
$26$	4.21789	+	1.84240i	0.827195	+	0.361325i
$27$	−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
$31$			2.06697i			0.371238i	0.982622	+	0.185619i	$0.0594290\pi$
$31$			2.06697i			0.371238i	−0.982622	+	0.185619i	$0.940571\pi$
$32$	−1.78956	+	1.03320i	−0.316352	+	0.182646i
$33$	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
$37$	1.50950	+	0.871512i	0.248161	+	0.143276i	0.618922	−	0.785453i	$-0.287570\pi$
$37$	1.50950	+	0.871512i	0.248161	+	0.143276i	−0.370761	+	0.928728i	$0.620903\pi$
$38$	7.49334			1.21558
$39$	−1.68561	+	3.85893i	−0.269913	+	0.617924i
$40$	−5.49171			−0.868316
$41$	−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	$0.589106\pi$
$44$			1.02911i			0.155144i
$45$	2.57127	−	1.48452i	0.383302	−	0.221299i
$46$	7.73776	−	4.46740i	1.14087	−	0.658681i
$47$			6.65932i			0.971361i	0.874136	+	0.485681i	$0.161428\pi$
$47$			6.65932i			0.971361i	−0.874136	+	0.485681i	$0.838572\pi$
$48$	1.82316	+	3.15780i	0.263150	+	0.455790i
$49$		0			0
$50$	1.88631	+	1.08906i	0.266764	+	0.154016i
$51$	3.20474			0.448753
$52$	−0.792549	−	1.07483i	−0.109907	−	0.149052i
$53$	−10.4879			−1.44063			−0.720313	−	0.693649i	$-0.756002\pi$
$53$	−10.4879			−1.44063			−0.720313	+	0.693649i	$0.756002\pi$
$54$	−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
$58$	3.88720	−	2.24427i	0.510414	−	0.294688i
$59$	−2.66212	+	1.53698i	−0.346579	+	0.200097i	−0.663177	−	0.748462i	$-0.730793\pi$
$59$	−2.66212	+	1.53698i	−0.346579	+	0.200097i	0.316598	+	0.948560i	$0.397459\pi$
$60$		−	0.785080i		−	0.101353i
$61$	0.540892	+	0.936853i	0.0692541	+	0.119952i	0.898573	−	0.438824i	$-0.144605\pi$
$61$	0.540892	+	0.936853i	0.0692541	+	0.119952i	−0.829319	+	0.558775i	$0.811271\pi$
$62$	−1.31931	+	2.28511i	−0.167552	+	0.290209i
$63$		0			0
$64$	−8.88199			−1.11025
$65$	−0.729860	−	6.50279i	−0.0905280	−	0.806572i
$66$	4.14254			0.509912
$67$	4.34568	+	2.50898i	0.530910	+	0.306521i	0.741387	−	0.671078i	$-0.234168\pi$
$67$	4.34568	+	2.50898i	0.530910	+	0.306521i	−0.210477	+	0.977599i	$0.567502\pi$
$68$	−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	$0.281755\pi$
$72$	4.28709	−	2.47515i	0.505238	−	0.291699i
$73$		−	7.67213i		−	0.897955i	−0.893543	−	0.448978i	$-0.851788\pi$
$73$		−	7.67213i		−	0.897955i	0.893543	−	0.448978i	$-0.148212\pi$
$74$	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
$79$	−15.7399			−1.77087			−0.885436	−	0.464761i	$-0.846140\pi$
$79$	−15.7399			−1.77087			−0.885436	+	0.464761i	$0.846140\pi$
$80$	−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
$86$			11.6217i			1.25320i
$87$	2.05328	+	3.55639i	0.220135	+	0.381285i
$88$	−4.20379	+	7.28117i	−0.448125	+	0.776176i
$89$	13.9118	+	8.03198i	1.47465	+	0.851388i	0.999592	−	0.0285683i	$-0.00909482\pi$
$89$	13.9118	+	8.03198i	1.47465	+	0.851388i	0.475055	+	0.879956i	$0.342428\pi$
$90$	3.79017			0.399519
$91$		0			0
$92$	−2.59235			−0.270271
$93$	−2.09064	−	1.20703i	−0.216789	−	0.125163i
$94$	−4.25052	+	7.36212i	−0.438408	+	0.759345i
$95$	−5.32659	−	9.22592i	−0.546497	−	0.946560i
$96$		−	2.41340i		−	0.246317i
$97$	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	−0.864201	−	0.503147i	$-0.832175\pi$
$101$	0.0365612	−	0.0633259i	0.00363798	−	0.00630117i	0.867839	+	0.496846i	$0.165509\pi$
$102$	3.54296	+	2.04553i	0.350805	+	0.202537i
$103$	−12.9196			−1.27301			−0.636503	−	0.771275i	$-0.719620\pi$
$103$	−12.9196			−1.27301			−0.636503	+	0.771275i	$0.719620\pi$
$104$	−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	−0.946493	−	0.322723i	$-0.895402\pi$
$107$	−2.00427	+	3.47150i	−0.193761	+	0.335603i	0.752733	+	0.658326i	$0.228735\pi$
$108$	1.00271	+	1.73675i	0.0964860	+	0.167119i
$109$			1.98589i			0.190214i	0.995467	+	0.0951071i	$0.0303194\pi$
$109$			1.98589i			0.190214i	−0.995467	+	0.0951071i	$0.969681\pi$
$110$	−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	$0.667633\pi$
$114$	−4.37583	+	7.57916i	−0.409834	+	0.709854i
$115$	−11.0007	−	6.35123i	−1.02582	−	0.592256i
$116$	−1.30231			−0.120917
$117$	3.50061	+	4.74743i	0.323632	+	0.438900i
$118$	−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
$122$			1.38097i			0.125027i
$123$	6.44001	−	3.71814i	0.580676	−	0.335254i
$124$	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	$-2.07943e-6\pi$
$128$	−6.24025	−	3.60281i	−0.551566	−	0.318447i
$129$	−10.6327			−0.936156
$130$	3.34373	−	7.65493i	0.293264	−	0.671382i
$131$	−3.06481			−0.267774			−0.133887	−	0.990997i	$-0.542746\pi$
$131$	−3.06481			−0.267774			−0.133887	+	0.990997i	$0.542746\pi$
$132$	−1.04090	−	0.600962i	−0.0905984	−	0.0523070i
$133$		0			0
$134$	3.20288	+	5.54754i	0.276686	+	0.479235i
$135$			9.82653i			0.845733i
$136$	−7.19067	+	4.15154i	−0.616595	+	0.355991i
$137$	18.9512	−	10.9415i	1.61911	−	0.934796i	0.631965	−	0.774997i	$-0.282249\pi$
$137$	18.9512	−	10.9415i	1.61911	−	0.934796i	0.987150	−	0.159799i	$-0.0510845\pi$
$138$			10.4352i			0.888300i
$139$	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
$142$	3.47069			0.291254
$143$	−9.18040	−	4.01006i	−0.767703	−	0.335338i
$144$	5.10752			0.425626
$145$	−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
$149$	−1.99824	+	1.15369i	−0.163702	+	0.0945136i	−0.579613	−	0.814892i	$-0.696796\pi$
$149$	−1.99824	+	1.15369i	−0.163702	+	0.0945136i	0.415911	+	0.909406i	$0.363463\pi$
$150$	−2.20306	+	1.27194i	−0.179879	+	0.103853i
$151$			20.6158i			1.67769i	0.544371	+	0.838845i	$0.316768\pi$
$151$			20.6158i			1.67769i	−0.544371	+	0.838845i	$0.683232\pi$
$152$	−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
$156$	1.54996	−	0.173964i	0.124096	−	0.0139283i
$157$	−2.89649			−0.231165			−0.115582	−	0.993298i	$-0.536873\pi$
$157$	−2.89649			−0.231165			−0.115582	+	0.993298i	$0.536873\pi$
$158$	−17.4010	−	10.0465i	−1.38435	−	0.799254i
$159$	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
$163$	−20.2944	+	11.7170i	−1.58958	+	0.917743i	−0.596201	+	0.802835i	$0.703324\pi$
$163$	−20.2944	+	11.7170i	−1.58958	+	0.917743i	−0.993376	+	0.114907i	$0.963343\pi$
$164$			2.35827i			0.184150i
$165$	−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	0.223160	−	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
$170$	−6.35721			−0.487576
$171$	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	0.745016	−	0.667047i	$-0.232442\pi$
$173$	−2.69861	−	4.67412i	−0.205171	−	0.355367i	−0.950187	+	0.311679i	$0.899108\pi$
$174$			5.24229i			0.397417i
$175$		0			0
$176$	−7.51241	+	4.33729i	−0.566269	+	0.326936i
$177$		−	3.59015i		−	0.269852i
$178$	10.2533	+	17.7593i	0.768520	+	1.33112i
$179$	−6.14571	+	10.6447i	−0.459352	+	0.795621i	−0.998927	−	0.0463168i	$-0.985252\pi$
$179$	−6.14571	+	10.6447i	−0.459352	+	0.795621i	0.539575	+	0.841938i	$0.318585\pi$
$180$	−0.952357	−	0.549843i	−0.0709845	−	0.0409829i
$181$	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
$184$	−18.3415	−	10.5894i	−1.35215	−	0.780664i
$185$	1.58168	−	2.73956i	0.116288	−	0.201416i
$186$	−1.54085	−	2.66883i	−0.112981	−	0.195688i
$187$			7.62407i			0.557527i
$188$	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	0.811831	−	0.583893i	$-0.198471\pi$
$191$	−1.37858	−	2.38777i	−0.0997507	−	0.172773i	−0.911581	+	0.411120i	$0.865138\pi$
$192$	5.18675	−	8.98371i	0.374321	−	0.648344i
$193$	11.2491	+	6.49467i	0.809728	+	0.467497i	0.846861	−	0.531814i	$-0.178489\pi$
$193$	11.2491	+	6.49467i	0.809728	+	0.467497i	−0.0371334	+	0.999310i	$0.511823\pi$
$194$	18.1616			1.30393
$195$	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	0.964854	+	0.262786i	$0.0846412\pi$
$199$	10.0159	+	17.3480i	0.710006	+	1.22977i	−0.254848	+	0.966981i	$0.582025\pi$
$200$		−	5.16298i		−	0.365078i
$201$	−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
$205$	−5.77773	+	10.0073i	−0.403534	+	0.698942i
$206$	−14.2831	−	8.24634i	−0.995150	−	0.574550i
$207$	11.4502			0.795842
$208$	4.50590	−	10.3155i	0.312428	−	0.715254i
$209$	−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
$213$			3.17532i			0.217570i
$214$	−4.43160	+	2.55858i	−0.302938	+	0.174901i
$215$	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
$219$	7.76000	+	4.48024i	0.524372	+	0.302747i
$220$	1.86770			0.125921
$221$	−5.87153	−	7.96280i	−0.394962	−	0.535636i
$222$	−2.59873			−0.174415
$223$	−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
$226$			13.4987i			0.897918i
$227$	0.796500	−	0.459860i	0.0528656	−	0.0305220i	−0.473334	−	0.880883i	$-0.656950\pi$
$227$	0.796500	−	0.459860i	0.0528656	−	0.0305220i	0.526200	+	0.850361i	$0.323616\pi$
$228$	2.19903	−	1.26961i	0.145634	−	0.0840820i
$229$			24.6208i			1.62699i	0.581574	+	0.813494i	$0.302437\pi$
$229$			24.6208i			1.62699i	−0.581574	+	0.813494i	$0.697563\pi$
$230$	−8.10776	−	14.0430i	−0.534610	−	0.925971i
$231$		0			0
$232$	−9.21415	−	5.31979i	−0.604939	−	0.349261i
$233$	17.2769			1.13185			0.565925	−	0.824457i	$-0.308519\pi$
$233$	17.2769			1.13185			0.565925	+	0.824457i	$0.308519\pi$
$234$	0.839858	+	7.48283i	0.0549032	+	0.489168i
$235$	12.0858			0.788392
$236$	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	$-0.155172\pi$
$240$	5.73101	−	3.30880i	0.369935	−	0.213582i
$241$	7.30441	−	4.21720i	0.470518	−	0.271654i	−0.245938	−	0.969285i	$-0.579096\pi$
$241$	7.30441	−	4.21720i	0.470518	−	0.271654i	0.716457	+	0.697632i	$0.245763\pi$
$242$		−	4.18710i		−	0.269157i
$243$	−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
$247$	17.0342	−	12.5605i	1.08386	−	0.799205i
$248$	6.25453			0.397163
$249$	−8.06541	−	4.65657i	−0.511124	−	0.295098i
$250$	7.76851	−	13.4555i	0.491324	−	0.850998i
$251$	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
$255$		−	5.81620i		−	0.364224i
$256$	4.28277	+	7.41797i	0.267673	+	0.463623i
$257$	−14.6643	+	25.3993i	−0.914733	+	1.58436i	−0.107441	+	0.994211i	$0.534266\pi$
$257$	−14.6643	+	25.3993i	−0.914733	+	1.58436i	−0.807292	+	0.590152i	$0.799068\pi$
$258$	−11.7548	−	6.78665i	−0.731824	−	0.422519i
$259$		0			0
$260$	−1.95068	+	1.43838i	−0.120976	+	0.0892043i
$261$	5.75219			0.356052
$262$	−3.38826	−	1.95622i	−0.209328	−	0.120855i
$263$	−9.95747	+	17.2468i	−0.614004	+	1.06349i	0.376555	+	0.926394i	$0.377109\pi$
$263$	−9.95747	+	17.2468i	−0.614004	+	1.06349i	−0.990558	+	0.137091i	$0.956225\pi$
$264$	−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
$268$		−	1.85857i		−	0.113530i
$269$	−11.1625	−	19.3340i	−0.680589	−	1.17881i	−0.974801	−	0.223074i	$-0.928391\pi$
$269$	−11.1625	−	19.3340i	−0.680589	−	1.17881i	0.294213	−	0.955740i	$-0.404943\pi$
$270$	−6.27210	+	10.8636i	−0.381708	+	0.661137i
$271$	8.14054	+	4.69994i	0.494502	+	0.285501i	0.726440	−	0.687230i	$-0.241173\pi$
$271$	8.14054	+	4.69994i	0.494502	+	0.285501i	−0.231938	+	0.972731i	$0.574507\pi$
$272$	−8.56677			−0.519437
$273$		0			0
$274$	27.9351			1.68762
$275$	−4.10562	−	2.37038i	−0.247578	−	0.142939i
$276$	1.51384	−	2.62204i	0.0911223	−	0.157828i
$277$	−7.17133	−	12.4211i	−0.430883	−	0.746312i	0.566066	−	0.824360i	$-0.308465\pi$
$277$	−7.17133	−	12.4211i	−0.430883	−	0.746312i	−0.996950	+	0.0780478i	$0.975131\pi$
$278$			14.1324i			0.847608i
$279$	−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	−0.856654	−	0.515891i	$-0.827461\pi$
$283$	0.310336	−	0.537518i	0.0184476	−	0.0319521i	0.875102	+	0.483939i	$0.160794\pi$
$284$	−0.872079	−	0.503495i	−0.0517484	−	0.0298769i
$285$	12.4421			0.737007
$286$	−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
$291$			16.6160i			0.974047i
$292$	−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
$296$	2.63715	−	4.56767i	0.153281	−	0.265491i
$297$	13.0285	+	7.52200i	0.755989	+	0.436471i
$298$	−2.94551			−0.170629
$299$	10.1014	−	23.1256i	0.584182	−	1.33739i
$300$	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
$304$		−	18.3262i		−	1.05108i
$305$	1.70027	−	0.981651i	0.0973571	−	0.0562091i
$306$	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
$310$	4.14718	+	2.39437i	0.235544	+	0.135991i
$311$	7.23790			0.410423			0.205212	−	0.978718i	$-0.434212\pi$
$311$	7.23790			0.410423			0.205212	+	0.978718i	$0.434212\pi$
$312$	11.6769	+	5.10056i	0.661076	+	0.288763i
$313$	−32.6606			−1.84609			−0.923043	−	0.384696i	$-0.874306\pi$
$313$	−32.6606			−1.84609			−0.923043	+	0.384696i	$0.874306\pi$
$314$	−3.20217	−	1.84877i	−0.180709	−	0.104332i
$315$		0			0
$316$	2.91490	+	5.04875i	0.163976	+	0.284014i
$317$		−	17.1744i		−	0.964608i	−0.876004	−	0.482304i	$-0.839800\pi$
$317$		−	17.1744i		−	0.964608i	0.876004	−	0.482304i	$-0.160200\pi$
$318$	13.5418	−	7.81838i	0.759388	−	0.438433i
$319$	−8.46064	+	4.88475i	−0.473705	+	0.273494i
$320$			16.1197i			0.901118i
$321$	−2.34084	−	4.05446i	−0.130653	−	0.226298i
$322$		0			0
$323$	−13.9489	−	8.05342i	−0.776140	−	0.448105i
$324$	−0.524395			−0.0291330
$325$	6.11353	−	0.686170i	0.339118	−	0.0380619i
$326$	−29.9149			−1.65683
$327$	−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
$331$	17.2633	−	9.96698i	0.948877	−	0.547835i	0.0561454	−	0.998423i	$-0.482119\pi$
$331$	17.2633	−	9.96698i	0.948877	−	0.547835i	0.892732	+	0.450588i	$0.148786\pi$
$332$	2.55778	−	1.47674i	0.140377	−	0.0810465i
$333$			2.85150i			0.156261i
$334$	−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	$0.488971\pi$
$338$	15.8538	+	4.90518i	0.862335	+	0.266807i
$339$	−12.3499			−0.670754
$340$	1.59738	+	0.922245i	0.0866298	+	0.0500158i
$341$	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
$345$	12.8479	−	7.41777i	0.691710	−	0.399359i
$346$		−	6.88989i		−	0.370403i
$347$	−12.9417	−	22.4156i	−0.694744	−	1.20333i	−0.970267	−	0.242038i	$-0.922184\pi$
$347$	−12.9417	−	22.4156i	−0.694744	−	1.20333i	0.275522	−	0.961295i	$-0.411149\pi$
$348$	0.760503	−	1.31723i	0.0407672	−	0.0706109i
$349$	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
$352$	5.74148			0.306022
$353$	21.9533	+	12.6747i	1.16846	+	0.674608i	0.953316	−	0.301975i	$-0.0976459\pi$
$353$	21.9533	+	12.6747i	1.16846	+	0.674608i	0.215140	+	0.976583i	$0.430979\pi$
$354$	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
$359$			5.27044i			0.278163i	0.990281	+	0.139082i	$0.0444151\pi$
$359$			5.27044i			0.278163i	−0.990281	+	0.139082i	$0.955585\pi$
$360$	−4.49208	−	7.78052i	−0.236754	−	0.410069i
$361$	7.72804	−	13.3854i	0.406739	−	0.704493i
$362$	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
$367$	12.6588	−	21.9257i	0.660783	−	1.14451i	−0.319627	−	0.947544i	$-0.603557\pi$
$367$	12.6588	−	21.9257i	0.660783	−	1.14451i	0.980410	−	0.196967i	$-0.0631092\pi$
$368$	−10.9257	−	18.9240i	−0.569544	−	0.986479i
$369$		−	10.4162i		−	0.542248i
$370$	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	0.940414	−	0.340033i	$-0.110438\pi$
$373$	3.39391	+	5.87842i	0.175730	+	0.304373i	−0.764684	+	0.644406i	$0.777105\pi$
$374$	−4.86631	+	8.42869i	−0.251631	+	0.435837i
$375$	12.3104	+	7.10739i	0.635704	+	0.367024i
$376$	20.1507			1.03920
$377$	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
$382$		−	3.51970i		−	0.180083i
$383$	6.28662	−	3.62958i	0.321232	−	0.185463i	−0.330710	−	0.943732i	$-0.607288\pi$
$383$	6.28662	−	3.62958i	0.321232	−	0.185463i	0.651941	+	0.758269i	$0.273955\pi$
$384$	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
$388$	−4.56346	−	2.63472i	−0.231675	−	0.133757i
$389$	7.14811			0.362424			0.181212	−	0.983444i	$-0.441998\pi$
$389$	7.14811			0.362424			0.181212	+	0.983444i	$0.441998\pi$
$390$	5.78999	+	7.85221i	0.293187	+	0.397612i
$391$	−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
$395$			28.5659i			1.43730i
$396$	−1.45802	+	0.841786i	−0.0732681	+	0.0423014i
$397$	19.4520	−	11.2306i	0.976266	−	0.563647i	0.0751252	−	0.997174i	$-0.476064\pi$
$397$	19.4520	−	11.2306i	0.976266	−	0.563647i	0.901141	+	0.433527i	$0.142731\pi$
$398$			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	$-0.357635\pi$
$401$	−2.64547	−	1.52736i	−0.132108	−	0.0762729i	−0.564598	+	0.825366i	$0.690969\pi$
$402$	−7.48144			−0.373140
$403$	0.831240	+	7.40605i	0.0414070	+	0.368921i
$404$	−0.0270834			−0.00134745
$405$	−2.22527	−	1.28476i	−0.110575	−	0.0638403i
$406$		0			0
$407$	−2.42149	−	4.19414i	−0.120029	−	0.207896i
$408$		−	9.69737i		−	0.480091i
$409$	−4.85482	+	2.80293i	−0.240055	+	0.138596i	−0.615202	−	0.788369i	$-0.710926\pi$
$409$	−4.85482	+	2.80293i	−0.240055	+	0.138596i	0.375147	+	0.926965i	$0.377592\pi$
$410$	−12.7750	+	7.37564i	−0.630912	+	0.364257i
$411$			25.5577i			1.26067i
$412$	2.39261	+	4.14412i	0.117875	+	0.204166i
$413$		0			0
$414$	12.6586	+	7.30844i	0.622136	+	0.359190i
$415$	14.4719			0.710400
$416$	−5.99657	+	4.42169i	−0.294006	+	0.216791i
$417$	−12.9297			−0.633172
$418$	−18.0308	−	10.4101i	−0.881916	−	0.509175i
$419$	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
$423$	−9.43475	+	5.44716i	−0.458733	+	0.264850i
$424$			31.7359i			1.54123i
$425$	−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
$429$	9.41700	−	6.94381i	0.454657	−	0.335250i
$430$	21.0920			1.01714
$431$	9.30923	+	5.37469i	0.448410	+	0.258890i	0.707158	−	0.707055i	$-0.249977\pi$
$431$	9.30923	+	5.37469i	0.448410	+	0.258890i	−0.258749	+	0.965945i	$0.583310\pi$
$432$	−8.45207	+	14.6394i	−0.406651	+	0.704340i
$433$	−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
$437$		−	41.0842i		−	1.96532i
$438$	5.71931	+	9.90614i	0.273279	+	0.473334i
$439$	10.9754	−	19.0099i	0.523826	−	0.907294i	−0.475789	−	0.879560i	$-0.657837\pi$
$439$	10.9754	−	19.0099i	0.523826	−	0.907294i	0.999615	−	0.0277345i	$-0.00882930\pi$
$440$	13.2144	+	7.62934i	0.629972	+	0.363715i
$441$		0			0
$442$	−1.40868	−	12.5509i	−0.0670042	−	0.596984i
$443$	−27.8963			−1.32539			−0.662697	−	0.748887i	$-0.730588\pi$
$443$	−27.8963			−1.32539			−0.662697	+	0.748887i	$0.730588\pi$
$444$	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	$0.159054\pi$
$450$			3.56329i			0.167975i
$451$	8.84546	+	15.3208i	0.416516	+	0.721427i
$452$	1.95826	−	3.39181i	0.0921088	−	0.159537i
$453$	−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	$-0.292150\pi$
$457$	4.77724	+	2.75814i	0.223470	+	0.129020i	−0.384086	+	0.923297i	$0.625483\pi$
$458$	−15.7150	+	27.2192i	−0.734314	+	1.27187i
$459$	7.42851	+	12.8665i	0.346733	+	0.600559i
$460$			4.70479i			0.219362i
$461$	−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
$467$	−4.54326			−0.210237			−0.105118	−	0.994460i	$-0.533522\pi$
$467$	−4.54326			−0.210237			−0.105118	+	0.994460i	$0.533522\pi$
$468$	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
$473$		−	25.2951i		−	1.16307i
$474$	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
$478$	9.24413	−	16.0113i	0.422817	−	0.732340i
$479$	1.44239	+	0.832764i	0.0659044	+	0.0380499i	0.532590	−	0.846373i	$-0.321219\pi$
$479$	1.44239	+	0.832764i	0.0659044	+	0.0380499i	−0.466686	+	0.884423i	$0.654552\pi$
$480$	−4.38002			−0.199920
$481$	5.75911	+	2.51562i	0.262593	+	0.114702i
$482$	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
$486$		−	18.6248i		−	0.844837i
$487$	−1.28598	+	0.742463i	−0.0582735	+	0.0336442i	−0.528854	−	0.848713i	$-0.677378\pi$
$487$	−1.28598	+	0.742463i	−0.0582735	+	0.0336442i	0.470580	+	0.882357i	$0.344045\pi$
$488$	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	$0.0491224\pi$
$492$	−2.38528	−	1.37714i	−0.107537	−	0.0620863i
$493$	−9.64808			−0.434528
$494$	26.8490	−	3.01348i	1.20800	−	0.135583i
$495$	−8.24947			−0.370786
$496$	5.58860	+	3.22658i	0.250936	+	0.144878i
$497$		0			0
$498$	−5.94440	−	10.2960i	−0.266375	−	0.461375i
$499$			17.7199i			0.793253i	0.917980	+	0.396627i	$0.129819\pi$
$499$			17.7199i			0.793253i	−0.917980	+	0.396627i	$0.870181\pi$
$500$	−3.90398	+	2.25397i	−0.174591	+	0.100800i
$501$	7.68902	−	4.43926i	0.343520	−	0.198331i
$502$			18.7305i			0.835985i
$503$	−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
$506$	−24.8253			−1.10362
$507$	−4.48774	+	14.5046i	−0.199307	+	0.644174i
$508$	−4.17406			−0.185194
$509$	−5.44396	−	3.14307i	−0.241299	−	0.139314i	0.374474	−	0.927237i	$-0.377823\pi$
$509$	−5.44396	−	3.14307i	−0.241299	−	0.139314i	−0.615774	+	0.787923i	$0.711156\pi$
$510$	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
$514$	−32.4238	+	18.7199i	−1.43015	+	0.825699i
$515$			23.4474i			1.03322i
$516$	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
$520$	−19.6771	+	2.20852i	−0.862898	+	0.0968499i
$521$	10.8473			0.475230			0.237615	−	0.971359i	$-0.423634\pi$
$521$	10.8473			0.475230			0.237615	+	0.971359i	$0.423634\pi$
$522$	6.35926	+	3.67152i	0.278337	+	0.160698i
$523$	0.673629	−	1.16676i	0.0294557	−	0.0510188i	−0.850922	−	0.525292i	$-0.823956\pi$
$523$	0.673629	−	1.16676i	0.0294557	−	0.0510188i	0.880377	+	0.474274i	$0.157289\pi$
$524$	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
$528$		−	10.1313i		−	0.440907i
$529$	−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
$534$	−23.9502			−1.03643
$535$	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
$541$			20.1571i			0.866621i	0.901245	+	0.433310i	$0.142655\pi$
$541$			20.1571i			0.866621i	−0.901245	+	0.433310i	$0.857345\pi$
$542$	5.99978	+	10.3919i	0.257712	+	0.446371i
$543$	−12.7610	+	22.1027i	−0.547628	+	0.948519i
$544$	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
$549$	−0.884873	+	1.53264i	−0.0377654	+	0.0654117i
$550$	−3.02594	−	5.24109i	−0.129027	−	0.223481i
$551$		−	20.6394i		−	0.879266i
$552$	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	$-0.500503\pi$
$557$	−20.4948	−	11.8327i	−0.868394	−	0.501367i	−0.866814	+	0.498631i	$0.833836\pi$
$558$	−4.31664			−0.182738
$559$	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	−0.991725	−	0.128382i	$-0.959022\pi$
$563$	−14.4037	−	24.9480i	−0.607045	−	1.05143i	0.384680	−	0.923050i	$-0.374312\pi$
$564$			2.88069i			0.121299i
$565$	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
$569$	−13.8361	+	23.9648i	−0.580040	+	1.00466i	0.415434	+	0.909623i	$0.363630\pi$
$569$	−13.8361	+	23.9648i	−0.580040	+	1.00466i	−0.995474	+	0.0950353i	$0.969704\pi$
$570$	13.7552	+	7.94158i	0.576143	+	0.332636i
$571$	−12.9655			−0.542588			−0.271294	−	0.962497i	$-0.587452\pi$
$571$	−12.9655			−0.542588			−0.271294	+	0.962497i	$0.587452\pi$
$572$	0.413861	+	3.68736i	0.0173044	+	0.154176i
$573$	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
$577$		−	9.46047i		−	0.393844i	−0.980419	−	0.196922i	$-0.936905\pi$
$577$		−	9.46047i		−	0.393844i	0.980419	−	0.196922i	$-0.0630947\pi$
$578$	10.4702	−	6.04497i	0.435503	−	0.251438i
$579$	−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
$583$	25.2365	+	14.5703i	1.04519	+	0.603440i
$584$	−23.2155			−0.960663
$585$	8.61598	−	6.35317i	0.356227	−	0.262671i
$586$	−31.7784			−1.31275
$587$	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
$590$			7.12175i			0.293198i
$591$	−19.2441	+	11.1106i	−0.791598	+	0.457029i
$592$	4.71274	−	2.72090i	0.193692	−	0.111828i
$593$		−	3.97234i		−	0.163124i	−0.996668	−	0.0815622i	$-0.974009\pi$
$593$		−	3.97234i		−	0.163124i	0.996668	−	0.0815622i	$-0.0259909\pi$
$594$	9.60231	+	16.6317i	0.393988	+	0.682407i
$595$		0			0
$596$	0.740117	+	0.427307i	0.0303164	+	0.0175032i
$597$	−23.3956			−0.957517
$598$	25.9282	−	19.1187i	1.06028	−	0.781821i
$599$	−19.5049			−0.796950			−0.398475	−	0.917179i	$-0.630460\pi$
$599$	−19.5049			−0.796950			−0.398475	+	0.917179i	$0.630460\pi$
$600$	5.22211	+	3.01498i	0.213192	+	0.123086i
$601$	−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
$605$	−5.15523	+	2.97637i	−0.209590	+	0.121007i
$606$			0.109021i			0.00442866i
$607$	12.5102	+	21.6682i	0.507772	+	0.879487i	0.999960	+	0.00899773i	$0.00286411\pi$
$607$	12.5102	+	21.6682i	0.507772	+	0.879487i	−0.492187	+	0.870489i	$0.663803\pi$
$608$	−6.06482	+	10.5046i	−0.245961	+	0.426016i
$609$		0			0
$610$	2.50628			0.101476
$611$	2.67808	+	23.8607i	0.108343	+	0.965300i
$612$	−1.66265			−0.0672086
$613$	−18.4970	−	10.6793i	−0.747088	−	0.431332i	0.0775527	−	0.996988i	$-0.475289\pi$
$613$	−18.4970	−	10.6793i	−0.747088	−	0.431332i	−0.824641	+	0.565657i	$0.808623\pi$
$614$	−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	$0.564229\pi$
$618$	16.6816	−	9.63111i	0.671031	−	0.387420i
$619$			48.9117i			1.96593i	0.183795	+	0.982965i	$0.441162\pi$
$619$			48.9117i			1.96593i	−0.183795	+	0.982965i	$0.558838\pi$
$620$	−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
$625$	−13.5576			−0.542304
$626$	−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	$0.299243\pi$
$632$			47.6280i			1.89454i
$633$	−5.83981	−	10.1148i	−0.232111	−	0.402029i
$634$	10.9621	−	18.9869i	0.435360	−	0.754066i
$635$	−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
$640$	−6.53865	+	11.3253i	−0.258463	+	0.447671i
$641$	19.8510	+	34.3829i	0.784066	+	1.35804i	0.929555	+	0.368683i	$0.120191\pi$
$641$	19.8510	+	34.3829i	0.784066	+	1.35804i	−0.145489	+	0.989360i	$0.546475\pi$
$642$		−	5.97647i		−	0.235872i
$643$	−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	−0.602282	−	0.798283i	$-0.705742\pi$
$647$	9.92502	−	17.1906i	0.390193	−	0.675833i	0.992475	+	0.122450i	$0.0390751\pi$
$648$	−3.71020	−	2.14209i	−0.145751	−	0.0841491i
$649$	8.54096			0.335262
$650$	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	−0.618065	−	0.786127i	$-0.712083\pi$
$653$	9.50024	−	16.4549i	0.371773	−	0.643930i	0.989838	+	0.142197i	$0.0454165\pi$
$654$	−1.48042	−	2.56416i	−0.0578889	−	0.100266i
$655$			5.56225i			0.217335i
$656$	−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	$0.788456\pi$
$660$	−1.09067	+	1.88909i	−0.0424542	+	0.0735329i
$661$	−14.5068	−	8.37548i	−0.564248	−	0.325769i	0.190601	−	0.981668i	$-0.438956\pi$
$661$	−14.5068	−	8.37548i	−0.564248	−	0.325769i	−0.754849	+	0.655899i	$0.772290\pi$
$662$	25.4470			0.989025
$663$	11.4828	−	1.28880i	0.445953	−	0.0500529i
$664$	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
$668$			2.81564i			0.108941i
$669$	8.47860	−	4.89512i	0.327802	−	0.189256i
$670$	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	$0.910986\pi$
$674$	1.40612	+	0.811824i	0.0541618	+	0.0312703i
$675$	−9.23831			−0.355583
$676$	−3.27199	−	3.53245i	−0.125846	−	0.135864i
$677$	−28.1341			−1.08128			−0.540641	−	0.841253i	$-0.681818\pi$
$677$	−28.1341			−1.08128			−0.540641	+	0.841253i	$0.681818\pi$
$678$	−13.6533	−	7.88271i	−0.524350	−	0.302734i
$679$		0			0
$680$	7.53452	+	13.0502i	0.288935	+	0.500451i
$681$			1.07416i			0.0411620i
$682$	6.34915	−	3.66568i	0.243122	−	0.140366i
$683$	−1.79295	+	1.03516i	−0.0686053	+	0.0396093i	−0.533910	−	0.845541i	$-0.679278\pi$
$683$	−1.79295	+	1.03516i	−0.0686053	+	0.0396093i	0.465305	+	0.885150i	$0.345945\pi$
$684$		−	3.55677i		−	0.135996i
$685$	−19.8574	−	34.3941i	−0.758714	−	1.31413i
$686$		0			0
$687$	−24.9028	−	14.3776i	−0.950100	−	0.548540i
$688$	28.4228			1.08361
$689$	−37.5788	+	4.21776i	−1.43164	+	0.160684i
$690$	18.9385			0.720977
$691$	−31.0542	−	17.9291i	−1.18136	−	0.682057i	−0.225029	−	0.974352i	$-0.572248\pi$
$691$	−31.0542	−	17.9291i	−1.18136	−	0.682057i	−0.956328	+	0.292295i	$0.905581\pi$
$692$	−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
$696$	10.7614	−	6.21312i	0.407911	−	0.235508i
$697$			17.4710i			0.661763i
$698$	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	$0.822081\pi$
$702$	−22.8375	−	9.97558i	−0.861946	−	0.376504i
$703$	10.2314			0.385885
$704$	21.3722	+	12.3393i	0.805497	+	0.465054i
$705$	−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
$709$	−14.0864	+	8.13279i	−0.529026	+	0.305433i	−0.740620	−	0.671924i	$-0.765468\pi$
$709$	−14.0864	+	8.13279i	−0.529026	+	0.305433i	0.211594	+	0.977358i	$0.432135\pi$
$710$		−	6.29886i		−	0.236392i
$711$	−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
$716$	4.55255			0.170137
$717$	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	0.944164	−	0.329477i	$-0.106873\pi$
$719$	5.00744	+	8.67314i	0.186746	+	0.323454i	−0.757417	+	0.652931i	$0.773539\pi$
$720$		−	9.26949i		−	0.345454i
$721$		0			0
$722$	17.0873	−	9.86534i	0.635922	−	0.367150i
$723$			9.85076i			0.366354i
$724$	−4.04690	−	7.00944i	−0.150402	−	0.260504i
$725$	2.99966	−	5.19556i	0.111405	−	0.192958i
$726$	4.23506	+	2.44511i	0.157178	+	0.0907466i
$727$	−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
$730$	−15.3934	−	8.88741i	−0.569737	−	0.328938i
$731$	12.4904	−	21.6340i	0.461973	−	0.800161i
$732$	0.233980	+	0.405265i	0.00864814	+	0.0149790i
$733$			33.1360i			1.22391i	0.790894	+	0.611953i	$0.209616\pi$
$733$			33.1360i			1.22391i	−0.790894	+	0.611953i	$0.790384\pi$
$734$	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	$-0.356865\pi$
$739$	−3.47767	−	2.00784i	−0.127928	−	0.0738594i	−0.562598	+	0.826730i	$0.690198\pi$
$740$	−1.17166			−0.0430711
$741$	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
$746$			8.66508i			0.317251i
$747$	−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
$751$	18.7579	−	32.4896i	0.684486	−	1.18556i	−0.289112	−	0.957295i	$-0.593360\pi$
$751$	18.7579	−	32.4896i	0.684486	−	1.18556i	0.973598	−	0.228269i	$-0.0733065\pi$
$752$	18.0053	+	10.3954i	0.656585	+	0.379080i
$753$	−17.1365			−0.624490
$754$	13.0255	−	9.60461i	0.474360	−	0.349779i
$755$	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
$759$		−	22.7126i		−	0.824414i
$760$	−27.9172	+	16.1180i	−1.01266	+	0.584661i
$761$	3.72586	−	2.15113i	0.135062	−	0.0779782i	−0.430946	−	0.902378i	$-0.641820\pi$
$761$	3.72586	−	2.15113i	0.135062	−	0.0779782i	0.566009	+	0.824399i	$0.308487\pi$
$762$			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
$766$	9.26679			0.334823
$767$	−8.92043	+	6.57766i	−0.322098	+	0.237506i
$768$	−10.0039			−0.360985
$769$	−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
$772$		−	4.81105i		−	0.173153i
$773$	3.29372	−	1.90163i	0.118467	−	0.0683970i	−0.439596	−	0.898196i	$-0.644878\pi$
$773$	3.29372	−	1.90163i	0.118467	−	0.0683970i	0.558063	+	0.829799i	$0.311545\pi$
$774$	−16.4654	+	9.50628i	−0.591835	+	0.341696i
$775$			3.52673i			0.126684i
$776$	−21.5250	−	37.2824i	−0.772702	−	1.33836i
$777$		0			0
$778$	7.90250	+	4.56251i	0.283318	+	0.163574i
$779$	−37.3744			−1.33908
$780$	−0.315723	−	2.81298i	−0.0113047	−	0.100721i
$781$	−7.55409			−0.270307
$782$	−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
$786$	3.95724	−	2.28471i	0.141150	−	0.0814930i
$787$	−15.0114	+	8.66684i	−0.535099	+	0.308940i	−0.743090	−	0.669191i	$-0.766641\pi$
$787$	−15.0114	+	8.66684i	−0.535099	+	0.308940i	0.207991	+	0.978131i	$0.433307\pi$
$788$		−	7.04701i		−	0.251039i
$789$	−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
$793$	2.31480	+	3.13927i	0.0822011	+	0.111479i
$794$	28.6731			1.01757
$795$	−19.2522	−	11.1153i	−0.682807	−	0.394219i
$796$	3.70972	−	6.42542i	0.131488	−	0.227743i
$797$	−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
$801$			26.2798i			0.928552i
$802$	−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
$807$	26.0739			0.917845
$808$	−0.191621	−	0.110632i	−0.00674120	−	0.00389203i
$809$	−8.03694	+	13.9204i	−0.282564	+	0.489415i	−0.972015	−	0.234917i	$-0.924518\pi$
$809$	−8.03694	+	13.9204i	−0.282564	+	0.489415i	0.689452	+	0.724332i	$0.257852\pi$
$810$	−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
$814$		−	6.18237i		−	0.216692i
$815$	21.2648	+	36.8317i	0.744873	+	1.29016i
$816$	5.00267	−	8.66488i	0.175129	−	0.303332i
$817$	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	$-0.157044\pi$
$821$	26.1021	+	15.0700i	0.910968	+	0.525948i	0.0302256	+	0.999543i	$0.490377\pi$
$822$	−16.3130	+	28.2550i	−0.568982	+	0.985507i
$823$	20.8251	+	36.0702i	0.725918	+	1.25733i	0.958595	+	0.284773i	$0.0919181\pi$
$823$	20.8251	+	36.0702i	0.725918	+	1.25733i	−0.232677	+	0.972554i	$0.574749\pi$
$824$			39.0940i			1.36190i
$825$	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	−0.793796	−	0.608184i	$-0.791898\pi$
$829$	3.73737	−	6.47332i	0.129804	−	0.224828i	0.923601	+	0.383356i	$0.125232\pi$
$830$	15.9993	+	9.23718i	0.555343	+	0.320627i
$831$	16.7512			0.581091
$832$	−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
$837$		−	11.1915i		−	0.386834i
$838$	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
$842$	−1.22926	+	2.12914i	−0.0423632	+	0.0733752i
$843$	0.0999736	+	0.0577198i	0.00344328	+	0.00198798i
$844$	3.70396			0.127495
$845$	−5.23025	−	23.0063i	−0.179926	−	0.791442i
$846$	−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
$850$		−	5.97667i		−	0.204998i
$851$	10.5651	−	6.09979i	0.362169	−	0.209098i
$852$	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
$856$	10.5046	+	6.06483i	0.359040	+	0.207292i
$857$	30.3681			1.03736			0.518678	−	0.854970i	$-0.326424\pi$
$857$	30.3681			1.03736			0.518678	+	0.854970i	$0.326424\pi$
$858$	14.8429	−	1.66594i	0.506730	−	0.0568743i
$859$	35.8306			1.22252			0.611262	−	0.791429i	$-0.290662\pi$
$859$	35.8306			1.22252			0.611262	+	0.791429i	$0.290662\pi$
$860$	−5.29977	−	3.05983i	−0.180721	−	0.104339i
$861$		0			0
$862$	6.86113	+	11.8838i	0.233691	+	0.404765i
$863$		−	32.3403i		−	1.10088i	−0.834876	−	0.550438i	$-0.814461\pi$
$863$		−	32.3403i		−	1.10088i	0.834876	−	0.550438i	$-0.185539\pi$
$864$	9.68945	−	5.59421i	0.329642	−	0.190319i
$865$	−8.48294	+	4.89763i	−0.288429	+	0.166524i
$866$		−	51.4016i		−	1.74670i
$867$	5.53053	+	9.57916i	0.187827	+	0.325325i
$868$		0			0
$869$	37.8740	+	21.8665i	1.28479	+	0.741772i
$870$	9.51409			0.322558
$871$	16.5798	+	7.24218i	0.561786	+	0.245392i
$872$	6.00921			0.203498
$873$	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
$877$	3.82446	−	2.20805i	0.129143	−	0.0745607i	−0.434037	−	0.900895i	$-0.642911\pi$
$877$	3.82446	−	2.20805i	0.129143	−	0.0745607i	0.563180	+	0.826334i	$0.309578\pi$
$878$	24.2674	−	14.0108i	0.818984	−	0.472841i
$879$		−	29.0740i		−	0.980642i
$880$	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	$0.570045\pi$
$884$	−1.46680	+	3.35801i	−0.0493339	+	0.112942i
$885$	−6.51567			−0.219022
$886$	−30.8404	−	17.8057i	−1.03610	−	0.598195i
$887$	27.0862	−	46.9147i	0.909467	−	1.57524i	0.0946605	−	0.995510i	$-0.469823\pi$
$887$	27.0862	−	46.9147i	0.909467	−	1.57524i	0.814806	−	0.579733i	$-0.196843\pi$
$888$	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
$892$			3.10478i			0.103956i
$893$	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
$898$	28.1626			0.939797
$899$	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
$905$		−	39.6594i		−	1.31832i
$906$	−15.3684	−	26.6188i	−0.510580	−	0.884350i
$907$	−1.29570	+	2.24421i	−0.0430229	+	0.0745178i	−0.886735	−	0.462278i	$-0.847032\pi$
$907$	−1.29570	+	2.24421i	−0.0430229	+	0.0745178i	0.843712	+	0.536796i	$0.180365\pi$
$908$	−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
$913$	11.0780	−	19.1876i	0.366627	−	0.635017i
$914$	3.52094	+	6.09845i	0.116462	+	0.201719i
$915$			2.29299i			0.0758039i
$916$	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	0.998990	−	0.0449372i	$-0.0143088\pi$
$919$	13.9624	+	24.1836i	0.460578	+	0.797745i	−0.538412	+	0.842682i	$0.680975\pi$
$920$	−19.2185	+	33.2874i	−0.633615	+	1.09745i
$921$	−10.0110	−	5.77987i	−0.329875	−	0.190453i
$922$	−36.8648			−1.21408
$923$	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
$928$			7.26571i			0.238509i
$929$	23.0067	−	13.2830i	0.754827	−	0.435800i	−0.0726084	−	0.997361i	$-0.523132\pi$
$929$	23.0067	−	13.2830i	0.754827	−	0.435800i	0.827435	+	0.561561i	$0.189799\pi$
$930$	−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
$934$	−5.02274	−	2.89988i	−0.164349	−	0.0948869i
$935$	13.8367			0.452509
$936$	14.3655	−	10.5927i	0.469550	−	0.346232i
$937$	−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
$941$		−	6.48465i		−	0.211394i	−0.994398	−	0.105697i	$-0.966293\pi$
$941$		−	6.48465i		−	0.211394i	0.994398	−	0.105697i	$-0.0337073\pi$
$942$	3.73990	−	2.15923i	0.121852	−	0.0703515i
$943$	−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
$947$	18.3193	+	10.5767i	0.595298	+	0.343695i	0.767190	−	0.641420i	$-0.221655\pi$
$947$	18.3193	+	10.5767i	0.595298	+	0.343695i	−0.171892	+	0.985116i	$0.554988\pi$
$948$	−6.80876			−0.221138
$949$	−3.08538	−	27.4897i	−0.100156	−	0.892352i
$950$	12.7854			0.414813
$951$	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	$-0.366590\pi$
$954$		−	21.9029i		−	0.709133i
$955$	−4.33351	+	2.50195i	−0.140229	+	0.0809613i
$956$	−4.64554	+	2.68211i	−0.150248	+	0.0867455i
$957$		−	11.4101i		−	0.368835i
$958$	1.06308	+	1.84130i	0.0343464	+	0.0594898i
$959$		0			0
$960$	−16.3043	−	9.41329i	−0.526219	−	0.303813i
$961$	26.7277			0.862182
$962$	4.76123	+	6.45705i	0.153508	+	0.208184i
$963$	−6.55779			−0.211322
$964$	−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	$0.915681\pi$
$968$	−8.59534	+	4.96252i	−0.276265	+	0.159501i
$969$	16.2913	−	9.40580i	0.523353	−	0.302158i
$970$		−	32.9610i		−	1.05831i
$971$	−12.2605	−	21.2358i	−0.393458	−	0.681489i	0.599445	−	0.800416i	$-0.295388\pi$
$971$	−12.2605	−	21.2358i	−0.393458	−	0.681489i	−0.992903	+	0.118927i	$0.962055\pi$
$972$	−2.70191	+	4.67984i	−0.0866638	+	0.150106i
$973$		0			0
$974$	−1.89560			−0.0607390
$975$	−2.87604	+	6.58424i	−0.0921071	+	0.210865i
$976$	3.37738			0.108107
$977$	9.45681	+	5.45989i	0.302550	+	0.174677i	0.643588	−	0.765372i	$-0.277445\pi$
$977$	9.45681	+	5.45989i	0.302550	+	0.174677i	−0.341038	+	0.940050i	$0.610778\pi$
$978$	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
$982$	17.6840	−	10.2098i	0.564318	−	0.325809i
$983$			19.6715i			0.627423i	0.949518	+	0.313711i	$0.101572\pi$
$983$			19.6715i			0.627423i	−0.949518	+	0.313711i	$0.898428\pi$
$984$	−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
$989$	63.7191			2.02615
$990$	−9.12009	−	5.26549i	−0.289855	−	0.167348i
$991$	0.869000	−	1.50515i	0.0276047	−	0.0478127i	−0.851893	−	0.523716i	$-0.824545\pi$
$991$	0.869000	−	1.50515i	0.0276047	−	0.0478127i	0.879498	+	0.475903i	$0.157879\pi$
$992$	−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
$996$			3.44944i			0.109300i
$997$	−23.4768	−	40.6631i	−0.743519	−	1.28781i	−0.950884	−	0.309549i	$-0.899822\pi$
$997$	−23.4768	−	40.6631i	−0.743519	−	1.28781i	0.207365	−	0.978264i	$-0.433511\pi$
$998$	−11.3103	+	19.5900i	−0.358022	+	0.620112i
$999$	−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.q.h.589.5		12
7.2	even	3		637.2.k.g.459.2		12
7.3	odd	6		637.2.u.h.30.2		12
7.4	even	3		637.2.u.i.30.2		12
7.5	odd	6		637.2.k.h.459.2		12
7.6	odd	2		91.2.q.a.43.5	yes	12
13.6	odd	12		8281.2.a.by.1.3		6
13.7	odd	12		8281.2.a.ch.1.4		6
13.10	even	6	inner	637.2.q.h.491.5		12
21.20	even	2		819.2.ct.a.316.2		12
28.27	even	2		1456.2.cc.c.225.2		12
91.6	even	12		1183.2.a.m.1.3		6
91.10	odd	6		637.2.k.h.569.5		12
91.20	even	12		1183.2.a.p.1.4		6
91.23	even	6		637.2.u.i.361.2		12
91.48	odd	6		1183.2.c.i.337.4		12
91.62	odd	6		91.2.q.a.36.5	✓	12
91.69	odd	6		1183.2.c.i.337.9		12
91.75	odd	6		637.2.u.h.361.2		12
91.88	even	6		637.2.k.g.569.5		12
273.62	even	6		819.2.ct.a.127.2		12
364.335	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	91.62	odd	6
91.2.q.a.43.5	yes	12	7.6	odd	2
637.2.k.g.459.2		12	7.2	even	3
637.2.k.g.569.5		12	91.88	even	6
637.2.k.h.459.2		12	7.5	odd	6
637.2.k.h.569.5		12	91.10	odd	6
637.2.q.h.491.5		12	13.10	even	6	inner
637.2.q.h.589.5		12	1.1	even	1	trivial
637.2.u.h.30.2		12	7.3	odd	6
637.2.u.h.361.2		12	91.75	odd	6
637.2.u.i.30.2		12	7.4	even	3
637.2.u.i.361.2		12	91.23	even	6
819.2.ct.a.127.2		12	273.62	even	6
819.2.ct.a.316.2		12	21.20	even	2
1183.2.a.m.1.3		6	91.6	even	12
1183.2.a.p.1.4		6	91.20	even	12
1183.2.c.i.337.4		12	91.48	odd	6
1183.2.c.i.337.9		12	91.69	odd	6
1456.2.cc.c.225.2		12	28.27	even	2
1456.2.cc.c.673.2		12	364.335	even	6
8281.2.a.by.1.3		6	13.6	odd	12
8281.2.a.ch.1.4		6	13.7	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.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10554 + 0.638282i) q^{2} +(-0.583963 + 1.01145i) q^{3} +(-0.185192 - 0.320762i) q^{4} -1.81487i q^{5} +(-1.29118 + 0.745466i) q^{6} -3.02595i q^{8} +(0.817975 + 1.41677i) q^{9} +O(q^{10})\)	\(q+(1.10554 + 0.638282i) q^{2} +(-0.583963 + 1.01145i) q^{3} +(-0.185192 - 0.320762i) q^{4} -1.81487i 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} +0.432581 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} +2.08840i q^{18} +(5.08351 - 2.93497i) q^{19} +(-0.582143 + 0.336100i) q^{20} +(-1.77346 - 3.07173i) q^{22} +(3.49955 - 6.06139i) q^{23} +(3.06060 + 1.76704i) q^{24} +1.70623 q^{25} +(4.21789 + 1.84240i) q^{26} -5.41444 q^{27} +(1.75806 - 3.04505i) q^{29} +(1.35293 + 2.34334i) q^{30} +2.06697i q^{31} +(-1.78956 + 1.03320i) q^{32} +(2.81031 - 1.62254i) q^{33} -3.50284i q^{34} +(0.302965 - 0.524751i) q^{36} +(1.50950 + 0.871512i) q^{37} +7.49334 q^{38} +(-1.68561 + 3.85893i) q^{39} -5.49171 q^{40} +(-5.51406 - 3.18355i) q^{41} +(4.55195 + 7.88422i) q^{43} +1.02911i q^{44} +(2.57127 - 1.48452i) q^{45} +(7.73776 - 4.46740i) q^{46} +6.65932i q^{47} +(1.82316 + 3.15780i) q^{48} +(1.88631 + 1.08906i) q^{50} +3.20474 q^{51} +(-0.792549 - 1.07483i) q^{52} -10.4879 q^{53} +(-5.98587 - 3.45594i) q^{54} +(-2.52131 + 4.36703i) q^{55} +6.85564i q^{57} +(3.88720 - 2.24427i) q^{58} +(-2.66212 + 1.53698i) q^{59} -0.785080i q^{60} +(0.540892 + 0.936853i) q^{61} +(-1.31931 + 2.28511i) q^{62} -8.88199 q^{64} +(-0.729860 - 6.50279i) q^{65} +4.14254 q^{66} +(4.34568 + 2.50898i) q^{67} +(-0.508159 + 0.880158i) q^{68} +(4.08721 + 7.07925i) q^{69} +(2.35453 - 1.35939i) q^{71} +(4.28709 - 2.47515i) q^{72} -7.67213i 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} -15.7399 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} +11.6217i q^{86} +(2.05328 + 3.55639i) q^{87} +(-4.20379 + 7.28117i) q^{88} +(13.9118 + 8.03198i) q^{89} +3.79017 q^{90} -2.59235 q^{92} +(-2.09064 - 1.20703i) q^{93} +(-4.25052 + 7.36212i) q^{94} +(-5.32659 - 9.22592i) q^{95} -2.41340i q^{96} +(12.3209 - 7.11347i) q^{97} -4.54548i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9	\( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} + 30 q^{33} - 10 q^{36} - 42 q^{37} - 4 q^{38} - 4 q^{39} - 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 2 q^{48} - 18 q^{50} + 52 q^{51} - 2 q^{52} - 44 q^{53} - 12 q^{54} + 6 q^{55} - 12 q^{58} - 18 q^{59} - 14 q^{61} + 4 q^{62} - 52 q^{64} + 60 q^{65} + 52 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} - 56 q^{79} + 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 2 q^{87} - 14 q^{88} + 12 q^{89} - 24 q^{90} + 24 q^{92} - 18 q^{93} - 4 q^{94} - 22 q^{95} - 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9 - 12 * q^10 + 6 * q^11 + 4 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 + 12 * q^20 + 6 * q^22 - 12 * q^23 - 12 * q^24 - 20 * q^25 + 42 * q^26 - 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 + 30 * q^33 - 10 * q^36 - 42 * q^37 - 4 * q^38 - 4 * q^39 - 92 * q^40 - 30 * q^41 + 2 * q^43 + 12 * q^46 + 2 * q^48 - 18 * q^50 + 52 * q^51 - 2 * q^52 - 44 * q^53 - 12 * q^54 + 6 * q^55 - 12 * q^58 - 18 * q^59 - 14 * q^61 + 4 * q^62 - 52 * q^64 + 60 * q^65 + 52 * q^66 - 24 * q^67 + 8 * q^68 - 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 - 56 * q^79 + 72 * q^80 + 2 * q^81 - 14 * q^82 - 48 * q^85 + 2 * q^87 - 14 * q^88 + 12 * q^89 - 24 * q^90 + 24 * q^92 - 18 * q^93 - 4 * q^94 - 22 * q^95 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more