LMFDB - Embedded newform 637.2.g.j.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(263,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("637.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.g (of order $3$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 7x^{6} + 38x^{4} - 16x^{3} + 15x^{2} + 3x + 1 $ x^8 - x^7 + 7x^6 + 38x^4 - 16x^3 + 15x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.2
Root			$-0.115680 - 0.200364i$ of defining polynomial
Character	$\chi$	$=$	637.373
Dual form			637.2.g.j.263.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.115680 - 0.200364i) q^{2} +3.32225 q^{3} +(0.973236 - 1.68569i) q^{4} +(-1.11568 + 1.93242i) q^{5} +(-0.384320 - 0.665661i) q^{6} -0.913059 q^{8} +8.03736 q^{9} +O(q^{10})$	\(q+(-0.115680 - 0.200364i) q^{2} +3.32225 q^{3} +(0.973236 - 1.68569i) q^{4} +(-1.11568 + 1.93242i) q^{5} +(-0.384320 - 0.665661i) q^{6} -0.913059 q^{8} +8.03736 q^{9} +0.516249 q^{10} +3.32225 q^{11} +(3.23334 - 5.60030i) q^{12} +(-3.40300 - 1.19146i) q^{13} +(-3.70657 + 6.41997i) q^{15} +(-1.84085 - 3.18844i) q^{16} +(-0.687890 + 1.19146i) q^{17} +(-0.929766 - 1.61040i) q^{18} -3.23531 q^{19} +(2.17164 + 3.76139i) q^{20} +(-0.384320 - 0.665661i) q^{22} +(-0.419251 - 0.726164i) q^{23} -3.03341 q^{24} +(0.0105144 + 0.0182115i) q^{25} +(0.154934 + 0.819669i) q^{26} +16.7354 q^{27} +(0.303571 - 0.525800i) q^{29} +1.71511 q^{30} +(0.857556 + 1.48533i) q^{31} +(-1.33896 + 2.31915i) q^{32} +11.0374 q^{33} +0.318302 q^{34} +(7.82225 - 13.5485i) q^{36} +(-0.776807 - 1.34547i) q^{37} +(0.374262 + 0.648241i) q^{38} +(-11.3056 - 3.95833i) q^{39} +(1.01868 - 1.76441i) q^{40} +(-4.58892 + 7.94824i) q^{41} +(-0.615680 - 1.06639i) q^{43} +(3.23334 - 5.60030i) q^{44} +(-8.96713 + 15.5315i) q^{45} +(-0.0969983 + 0.168006i) q^{46} +(-0.814085 + 1.41004i) q^{47} +(-6.11577 - 10.5928i) q^{48} +(0.00243263 - 0.00421343i) q^{50} +(-2.28535 + 3.95833i) q^{51} +(-5.32036 + 4.57685i) q^{52} +(-4.19803 - 7.27121i) q^{53} +(-1.93596 - 3.35318i) q^{54} +(-3.70657 + 6.41997i) q^{55} -10.7485 q^{57} -0.140469 q^{58} +(4.41117 - 7.64037i) q^{59} +(7.21474 + 12.4963i) q^{60} -5.46667 q^{61} +(0.198405 - 0.343647i) q^{62} -6.74383 q^{64} +(6.09906 - 5.24672i) q^{65} +(-1.27681 - 2.21149i) q^{66} -10.1857 q^{67} +(1.33896 + 2.31915i) q^{68} +(-1.39286 - 2.41250i) q^{69} +(2.60714 + 4.51570i) q^{71} -7.33859 q^{72} +(-1.98177 - 3.43253i) q^{73} +(-0.179723 + 0.311289i) q^{74} +(0.0349316 + 0.0605033i) q^{75} +(-3.14872 + 5.45375i) q^{76} +(0.514731 + 2.72315i) q^{78} +(-3.22525 + 5.58630i) q^{79} +8.21520 q^{80} +31.4871 q^{81} +2.12339 q^{82} +4.64055 q^{83} +(-1.53493 - 2.65858i) q^{85} +(-0.142444 + 0.246721i) q^{86} +(1.00854 - 1.74684i) q^{87} -3.03341 q^{88} +(4.56413 + 7.90530i) q^{89} +4.14929 q^{90} -1.63212 q^{92} +(2.84902 + 4.93464i) q^{93} +0.376695 q^{94} +(3.60957 - 6.25197i) q^{95} +(-4.44836 + 7.70479i) q^{96} +(-7.67944 - 13.3012i) q^{97} +26.7022 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 2 q^{3} - 5 q^{4} - 7 q^{5} - 5 q^{6} - 12 q^{8} + 14 q^{9}+O(q^{10}) $ 8 * q + q^2 - 2 * q^3 - 5 * q^4 - 7 * q^5 - 5 * q^6 - 12 * q^8 + 14 * q^9	$ 8 q + q^{2} - 2 q^{3} - 5 q^{4} - 7 q^{5} - 5 q^{6} - 12 q^{8} + 14 q^{9} + 22 q^{10} - 2 q^{11} + 12 q^{12} - 4 q^{13} - 3 q^{15} - 19 q^{16} - 4 q^{17} + 3 q^{18} - 2 q^{19} - 2 q^{20} - 5 q^{22} + 2 q^{23} + 6 q^{24} - 5 q^{25} - 3 q^{26} + 52 q^{27} - q^{29} - 8 q^{30} - 4 q^{31} + 33 q^{32} + 38 q^{33} - 6 q^{34} + 34 q^{36} + 10 q^{37} - 23 q^{38} - 19 q^{39} - 17 q^{40} - 22 q^{41} - 3 q^{43} + 12 q^{44} - 11 q^{45} - 24 q^{46} + 2 q^{47} + 11 q^{48} - 43 q^{50} - 7 q^{51} + 34 q^{52} - 2 q^{53} + 5 q^{54} - 3 q^{55} - 34 q^{57} - 22 q^{58} - 8 q^{59} + 11 q^{60} - 16 q^{61} - 5 q^{62} + 28 q^{64} + 4 q^{65} + 6 q^{66} - 12 q^{67} - 33 q^{68} - 18 q^{69} + 14 q^{71} + 10 q^{72} - 8 q^{73} - 20 q^{74} - 7 q^{75} + 32 q^{76} - q^{78} + 26 q^{79} - 14 q^{80} + 48 q^{81} + 28 q^{82} - 5 q^{85} - 12 q^{86} + 13 q^{87} + 6 q^{88} - q^{89} - 52 q^{90} + 24 q^{92} + 7 q^{93} - 66 q^{94} - 21 q^{95} - 58 q^{96} + 3 q^{97} + 46 q^{99}+O(q^{100}) $ 8 * q + q^2 - 2 * q^3 - 5 * q^4 - 7 * q^5 - 5 * q^6 - 12 * q^8 + 14 * q^9 + 22 * q^10 - 2 * q^11 + 12 * q^12 - 4 * q^13 - 3 * q^15 - 19 * q^16 - 4 * q^17 + 3 * q^18 - 2 * q^19 - 2 * q^20 - 5 * q^22 + 2 * q^23 + 6 * q^24 - 5 * q^25 - 3 * q^26 + 52 * q^27 - q^29 - 8 * q^30 - 4 * q^31 + 33 * q^32 + 38 * q^33 - 6 * q^34 + 34 * q^36 + 10 * q^37 - 23 * q^38 - 19 * q^39 - 17 * q^40 - 22 * q^41 - 3 * q^43 + 12 * q^44 - 11 * q^45 - 24 * q^46 + 2 * q^47 + 11 * q^48 - 43 * q^50 - 7 * q^51 + 34 * q^52 - 2 * q^53 + 5 * q^54 - 3 * q^55 - 34 * q^57 - 22 * q^58 - 8 * q^59 + 11 * q^60 - 16 * q^61 - 5 * q^62 + 28 * q^64 + 4 * q^65 + 6 * q^66 - 12 * q^67 - 33 * q^68 - 18 * q^69 + 14 * q^71 + 10 * q^72 - 8 * q^73 - 20 * q^74 - 7 * q^75 + 32 * q^76 - q^78 + 26 * q^79 - 14 * q^80 + 48 * q^81 + 28 * q^82 - 5 * q^85 - 12 * q^86 + 13 * q^87 + 6 * q^88 - q^89 - 52 * q^90 + 24 * q^92 + 7 * q^93 - 66 * q^94 - 21 * q^95 - 58 * q^96 + 3 * q^97 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.115680	−	0.200364i	−0.0817984	−	0.141679i	0.822224	−	0.569164i	$-0.192733\pi$
$2$	−0.115680	−	0.200364i	−0.0817984	−	0.141679i	−0.904022	+	0.427485i	$0.859400\pi$
$3$	3.32225			1.91810			0.959052	−	0.283231i	$-0.0914062\pi$
$3$	3.32225			1.91810			0.959052	+	0.283231i	$0.0914062\pi$
$4$	0.973236	−	1.68569i	0.486618	−	0.842847i
$5$	−1.11568	+	1.93242i	−0.498947	+	0.864202i	−0.999999	−	0.00121496i	$-0.999613\pi$
$5$	−1.11568	+	1.93242i	−0.498947	+	0.864202i	0.501052	+	0.865417i	$0.332947\pi$
$6$	−0.384320	−	0.665661i	−0.156898	−	0.271755i
$7$		0			0
$7$		0			0
$8$	−0.913059			−0.322815
$9$	8.03736			2.67912
$10$	0.516249			0.163252
$11$	3.32225			1.00170			0.500848	−	0.865535i	$-0.333021\pi$
$11$	3.32225			1.00170			0.500848	+	0.865535i	$0.333021\pi$
$12$	3.23334	−	5.60030i	0.933384	−	1.61667i
$13$	−3.40300	−	1.19146i	−0.943823	−	0.330452i
$13$	−3.40300	−	1.19146i	−0.943823	−	0.330452i
$14$		0			0
$15$	−3.70657	+	6.41997i	−0.957033	+	1.65763i
$16$	−1.84085	−	3.18844i	−0.460212	−	0.797111i
$17$	−0.687890	+	1.19146i	−0.166838	+	0.288972i	−0.937306	−	0.348506i	$-0.886689\pi$
$17$	−0.687890	+	1.19146i	−0.166838	+	0.288972i	0.770469	+	0.637478i	$0.220022\pi$
$18$	−0.929766	−	1.61040i	−0.219148	−	0.379575i
$19$	−3.23531			−0.742231			−0.371116	−	0.928587i	$-0.621025\pi$
$19$	−3.23531			−0.742231			−0.371116	+	0.928587i	$0.621025\pi$
$20$	2.17164	+	3.76139i	0.485594	+	0.841073i
$21$		0			0
$22$	−0.384320	−	0.665661i	−0.0819372	−	0.141919i
$23$	−0.419251	−	0.726164i	−0.0874199	−	0.151416i	0.819000	−	0.573794i	$-0.194529\pi$
$23$	−0.419251	−	0.726164i	−0.0874199	−	0.151416i	−0.906420	+	0.422378i	$0.861196\pi$
$24$	−3.03341			−0.619193
$25$	0.0105144	+	0.0182115i	0.00210289	+	0.00364231i
$26$	0.154934	+	0.819669i	0.0303851	+	0.160750i
$27$	16.7354			3.22073
$28$		0			0
$29$	0.303571	−	0.525800i	0.0563717	−	0.0976386i	−0.836462	−	0.548024i	$-0.815380\pi$
$29$	0.303571	−	0.525800i	0.0563717	−	0.0976386i	0.892834	+	0.450386i	$0.148713\pi$
$30$	1.71511			0.313135
$31$	0.857556	+	1.48533i	0.154022	+	0.266773i	0.932702	−	0.360647i	$-0.117444\pi$
$31$	0.857556	+	1.48533i	0.154022	+	0.266773i	−0.778681	+	0.627420i	$0.784111\pi$
$32$	−1.33896	+	2.31915i	−0.236697	+	0.409971i
$33$	11.0374			1.92136
$34$	0.318302			0.0545883
$35$		0			0
$36$	7.82225	−	13.5485i	1.30371	−	2.25809i
$37$	−0.776807	−	1.34547i	−0.127706	−	0.221194i	0.795081	−	0.606503i	$-0.207428\pi$
$37$	−0.776807	−	1.34547i	−0.127706	−	0.221194i	−0.922788	+	0.385309i	$0.874095\pi$
$38$	0.374262	+	0.648241i	0.0607133	+	0.105159i
$39$	−11.3056	−	3.95833i	−1.81035	−	0.633841i
$40$	1.01868	−	1.76441i	0.161068	−	0.278978i
$41$	−4.58892	+	7.94824i	−0.716668	+	1.24131i	0.245644	+	0.969360i	$0.421001\pi$
$41$	−4.58892	+	7.94824i	−0.716668	+	1.24131i	−0.962313	+	0.271946i	$0.912333\pi$
$42$		0			0
$43$	−0.615680	−	1.06639i	−0.0938904	−	0.162623i	0.815255	−	0.579103i	$-0.196597\pi$
$43$	−0.615680	−	1.06639i	−0.0938904	−	0.162623i	−0.909145	+	0.416480i	$0.863264\pi$
$44$	3.23334	−	5.60030i	0.487444	−	0.844277i
$45$	−8.96713	+	15.5315i	−1.33674	+	2.31530i
$46$	−0.0969983	+	0.168006i	−0.0143016	+	0.0247711i
$47$	−0.814085	+	1.41004i	−0.118747	+	0.205675i	−0.919271	−	0.393625i	$-0.871221\pi$
$47$	−0.814085	+	1.41004i	−0.118747	+	0.205675i	0.800525	+	0.599300i	$0.204554\pi$
$48$	−6.11577	−	10.5928i	−0.882735	−	1.52894i
$49$		0			0
$50$	0.00243263	−	0.00421343i	0.000344025	−	0.000595870i
$51$	−2.28535	+	3.95833i	−0.320012	+	0.554278i
$52$	−5.32036	+	4.57685i	−0.737802	+	0.634695i
$53$	−4.19803	−	7.27121i	−0.576644	−	0.998777i	−0.995861	−	0.0908909i	$-0.971029\pi$
$53$	−4.19803	−	7.27121i	−0.576644	−	0.998777i	0.419217	−	0.907886i	$-0.362305\pi$
$54$	−1.93596	−	3.35318i	−0.263450	−	0.456310i
$55$	−3.70657	+	6.41997i	−0.499794	+	0.865669i
$56$		0			0
$57$	−10.7485			−1.42368
$58$	−0.140469			−0.0184445
$59$	4.41117	−	7.64037i	0.574285	−	0.994691i	−0.421834	−	0.906673i	$-0.638613\pi$
$59$	4.41117	−	7.64037i	0.574285	−	0.994691i	0.996119	−	0.0880181i	$-0.0280533\pi$
$60$	7.21474	+	12.4963i	0.931419	+	1.61326i
$61$	−5.46667			−0.699936			−0.349968	−	0.936762i	$-0.613807\pi$
$61$	−5.46667			−0.699936			−0.349968	+	0.936762i	$0.613807\pi$
$62$	0.198405	−	0.343647i	0.0251974	−	0.0436432i
$63$		0			0
$64$	−6.74383			−0.842979
$65$	6.09906	−	5.24672i	0.756495	−	0.650776i
$66$	−1.27681	−	2.21149i	−0.157164	−	0.272216i
$67$	−10.1857			−1.24439			−0.622193	−	0.782864i	$-0.713758\pi$
$67$	−10.1857			−1.24439			−0.622193	+	0.782864i	$0.713758\pi$
$68$	1.33896	+	2.31915i	0.162373	+	0.281238i
$69$	−1.39286	−	2.41250i	−0.167680	−	0.290431i
$70$		0			0
$71$	2.60714	+	4.51570i	0.309411	+	0.535915i	0.978234	−	0.207507i	$-0.0665349\pi$
$71$	2.60714	+	4.51570i	0.309411	+	0.535915i	−0.668823	+	0.743422i	$0.733202\pi$
$72$	−7.33859			−0.864861
$73$	−1.98177	−	3.43253i	−0.231949	−	0.401748i	0.726432	−	0.687238i	$-0.241177\pi$
$73$	−1.98177	−	3.43253i	−0.231949	−	0.401748i	−0.958382	+	0.285490i	$0.907844\pi$
$74$	−0.179723	+	0.311289i	−0.0208923	+	0.0361866i
$75$	0.0349316	+	0.0605033i	0.00403355	+	0.00698632i
$76$	−3.14872	+	5.45375i	−0.361183	+	0.625588i
$77$		0			0
$78$	0.514731	+	2.72315i	0.0582818	+	0.308336i
$79$	−3.22525	+	5.58630i	−0.362869	+	0.628508i	−0.988432	−	0.151666i	$-0.951536\pi$
$79$	−3.22525	+	5.58630i	−0.362869	+	0.628508i	0.625562	+	0.780174i	$0.284870\pi$
$80$	8.21520			0.918487
$81$	31.4871			3.49857
$82$	2.12339			0.234489
$83$	4.64055			0.509367			0.254684	−	0.967024i	$-0.418029\pi$
$83$	4.64055			0.509367			0.254684	+	0.967024i	$0.418029\pi$
$84$		0			0
$85$	−1.53493	−	2.65858i	−0.166487	−	0.288363i
$86$	−0.142444	+	0.246721i	−0.0153602	+	0.0266046i
$87$	1.00854	−	1.74684i	0.108127	−	0.187281i
$88$	−3.03341			−0.323363
$89$	4.56413	+	7.90530i	0.483797	+	0.837960i	0.999827	−	0.0186101i	$-0.00592411\pi$
$89$	4.56413	+	7.90530i	0.483797	+	0.837960i	−0.516030	+	0.856570i	$0.672591\pi$
$90$	4.14929			0.437373
$91$		0			0
$92$	−1.63212			−0.170160
$93$	2.84902	+	4.93464i	0.295429	+	0.511699i
$94$	0.376695			0.0388531
$95$	3.60957	−	6.25197i	0.370334	−	0.641438i
$96$	−4.44836	+	7.70479i	−0.454009	+	0.786367i
$97$	−7.67944	−	13.3012i	−0.779729	−	1.35053i	−0.932098	−	0.362206i	$-0.882024\pi$
$97$	−7.67944	−	13.3012i	−0.779729	−	1.35053i	0.152369	−	0.988324i	$-0.451310\pi$
$98$		0			0
$99$	26.7022			2.68367
$100$	0.0409321			0.00409321
$101$	7.95042			0.791097			0.395548	−	0.918445i	$-0.370555\pi$
$101$	7.95042			0.791097			0.395548	+	0.918445i	$0.370555\pi$
$102$	1.05748			0.104706
$103$	0.347412	−	0.601736i	0.0342316	−	0.0592908i	−0.848402	−	0.529352i	$-0.822435\pi$
$103$	0.347412	−	0.601736i	0.0342316	−	0.0592908i	0.882634	+	0.470062i	$0.155768\pi$
$104$	3.10714	+	1.08787i	0.304680	+	0.106675i
$105$		0			0
$106$	−0.971261	+	1.68227i	−0.0943372	+	0.163397i
$107$	−4.47324	−	7.74787i	−0.432444	−	0.749015i	0.564639	−	0.825338i	$-0.309015\pi$
$107$	−4.47324	−	7.74787i	−0.432444	−	0.749015i	−0.997083	+	0.0763228i	$0.975682\pi$
$108$	16.2875	−	28.2108i	1.56726	−	2.71458i
$109$	1.13634	+	1.96820i	0.108841	+	0.188519i	0.915301	−	0.402770i	$-0.131953\pi$
$109$	1.13634	+	1.96820i	0.108841	+	0.188519i	−0.806460	+	0.591289i	$0.798619\pi$
$110$	1.71511			0.163529
$111$	−2.58075	−	4.46999i	−0.244954	−	0.424272i
$112$		0			0
$113$	4.75239	+	8.23138i	0.447067	+	0.774343i	0.998194	−	0.0600786i	$-0.0191351\pi$
$113$	4.75239	+	8.23138i	0.447067	+	0.774343i	−0.551126	+	0.834422i	$0.685802\pi$
$114$	1.24339	+	2.15362i	0.116454	+	0.201705i
$115$	1.87100			0.174472
$116$	−0.590892	−	1.02346i	−0.0548630	−	0.0950254i
$117$	−27.3512	−	9.57621i	−2.52862	−	0.885321i
$118$	−2.04114			−0.187902
$119$		0			0
$120$	3.38432	−	5.86181i	0.308945	−	0.535108i
$121$	0.0373642			0.00339675
$122$	0.632387	+	1.09533i	0.0572536	+	0.0991662i
$123$	−15.2455	+	26.4061i	−1.37464	+	2.38095i
$124$	3.33842			0.299799
$125$	−11.2037			−1.00209
$126$		0			0
$127$	−9.21672	+	15.9638i	−0.817851	+	1.41656i	0.0894111	+	0.995995i	$0.471502\pi$
$127$	−9.21672	+	15.9638i	−0.817851	+	1.41656i	−0.907262	+	0.420565i	$0.861832\pi$
$128$	3.45805	+	5.98951i	0.305651	+	0.529403i
$129$	−2.04545	−	3.54282i	−0.180091	−	0.311928i
$130$	−1.75680	−	0.615091i	−0.154081	−	0.0539471i
$131$	−0.874176	+	1.51412i	−0.0763771	+	0.132289i	−0.901684	−	0.432395i	$-0.857669\pi$
$131$	−0.874176	+	1.51412i	−0.0763771	+	0.132289i	0.825307	+	0.564684i	$0.191002\pi$
$132$	10.7420	−	18.6056i	0.934968	−	1.61941i
$133$		0			0
$134$	1.17829	+	2.04086i	0.101789	+	0.176303i
$135$	−18.6714	+	32.3397i	−1.60697	+	2.78336i
$136$	0.628085	−	1.08787i	0.0538578	−	0.0932845i
$137$	9.00160	−	15.5912i	0.769059	−	1.33205i	−0.169015	−	0.985614i	$-0.554059\pi$
$137$	9.00160	−	15.5912i	0.769059	−	1.33205i	0.938074	−	0.346436i	$-0.112608\pi$
$138$	−0.322253	+	0.558158i	−0.0274320	+	0.0475136i
$139$	6.95896	+	12.0533i	0.590251	+	1.02235i	0.994198	+	0.107563i	$0.0343048\pi$
$139$	6.95896	+	12.0533i	0.590251	+	1.02235i	−0.403947	+	0.914782i	$0.632362\pi$
$140$		0			0
$141$	−2.70460	+	4.68450i	−0.227768	+	0.394506i
$142$	0.603190	−	1.04476i	0.0506186	−	0.0876740i
$143$	−11.3056	−	3.95833i	−0.945424	−	0.331013i
$144$	−14.7956	−	25.6267i	−1.23296	−	2.13556i
$145$	0.677376	+	1.17325i	0.0562530	+	0.0974331i
$146$	−0.458505	+	0.794154i	−0.0379462	+	0.0657247i
$147$		0			0
$148$	−3.02407			−0.248577
$149$	−15.9303			−1.30506			−0.652531	−	0.757762i	$-0.726293\pi$
$149$	−15.9303			−1.30506			−0.652531	+	0.757762i	$0.726293\pi$
$150$	0.00808180	−	0.0139981i	0.000659876	−	0.00114294i
$151$	6.97484	+	12.0808i	0.567604	+	0.983120i	0.996802	+	0.0799092i	$0.0254630\pi$
$151$	6.97484	+	12.0808i	0.567604	+	0.983120i	−0.429198	+	0.903211i	$0.641204\pi$
$152$	2.95403			0.239604
$153$	−5.52883	+	9.57621i	−0.446979	+	0.774190i
$154$		0			0
$155$	−3.82703			−0.307395
$156$	−17.6756	+	15.2054i	−1.41518	+	1.21741i
$157$	−6.48733	−	11.2364i	−0.517745	−	0.896761i	−0.999788	−	0.0206132i	$-0.993438\pi$
$157$	−6.48733	−	11.2364i	−0.517745	−	0.896761i	0.482042	−	0.876148i	$-0.339895\pi$
$158$	1.49240			0.118729
$159$	−13.9469	−	24.1568i	−1.10606	−	1.91576i
$160$	−2.98770	−	5.17485i	−0.236199	−	0.409108i
$161$		0			0
$162$	−3.64244	−	6.30890i	−0.286177	−	0.495674i
$163$	18.4085			1.44186			0.720931	−	0.693007i	$-0.243715\pi$
$163$	18.4085			1.44186			0.720931	+	0.693007i	$0.243715\pi$
$164$	8.93220	+	15.4710i	0.697488	+	1.20808i
$165$	−12.3142	+	21.3288i	−0.958657	+	1.66044i
$166$	−0.536821	−	0.929802i	−0.0416654	−	0.0721666i
$167$	−9.24967	+	16.0209i	−0.715761	+	1.23973i	0.246904	+	0.969040i	$0.420587\pi$
$167$	−9.24967	+	16.0209i	−0.715761	+	1.23973i	−0.962665	+	0.270695i	$0.912747\pi$
$168$		0			0
$169$	10.1608	+	8.10909i	0.781603	+	0.623776i
$170$	−0.355123	+	0.615091i	−0.0272367	+	0.0471753i
$171$	−26.0034			−1.98853
$172$	−2.39681			−0.182755
$173$	17.1981			1.30755			0.653774	−	0.756690i	$-0.273185\pi$
$173$	17.1981			1.30755			0.653774	+	0.756690i	$0.273185\pi$
$174$	−0.466673			−0.0353784
$175$		0			0
$176$	−6.11577	−	10.5928i	−0.460993	−	0.798464i
$177$	14.6550	−	25.3832i	1.10154	−	1.90792i
$178$	1.05596	−	1.82898i	0.0791476	−	0.137088i
$179$	14.4886			1.08293			0.541465	−	0.840723i	$-0.317870\pi$
$179$	14.4886			1.08293			0.541465	+	0.840723i	$0.317870\pi$
$180$	17.4543	+	30.2317i	1.30096	+	2.25334i
$181$	−6.85484			−0.509516			−0.254758	−	0.967005i	$-0.581996\pi$
$181$	−6.85484			−0.509516			−0.254758	+	0.967005i	$0.581996\pi$
$182$		0			0
$183$	−18.1617			−1.34255
$184$	0.382801	+	0.663031i	0.0282205	+	0.0488793i
$185$	3.46667			0.254875
$186$	0.659151	−	1.14168i	0.0483313	−	0.0837122i
$187$	−2.28535	+	3.95833i	−0.167121	+	0.289462i
$188$	1.58459	+	2.74460i	0.115568	+	0.200170i
$189$		0			0
$190$	−1.67023			−0.121171
$191$	−2.85163			−0.206337			−0.103168	−	0.994664i	$-0.532898\pi$
$191$	−2.85163			−0.206337			−0.103168	+	0.994664i	$0.532898\pi$
$192$	−22.4047			−1.61692
$193$	−10.0505			−0.723450			−0.361725	−	0.932285i	$-0.617812\pi$
$193$	−10.0505			−0.723450			−0.361725	+	0.932285i	$0.617812\pi$
$194$	−1.77672	+	3.07737i	−0.127561	+	0.220942i
$195$	20.2626	−	17.4309i	1.45104	−	1.24826i
$196$		0			0
$197$	12.7085	−	22.0119i	0.905447	−	1.56828i	0.0851299	−	0.996370i	$-0.472869\pi$
$197$	12.7085	−	22.0119i	0.905447	−	1.56828i	0.820317	−	0.571910i	$-0.193797\pi$
$198$	−3.08892	−	5.35016i	−0.219520	−	0.380219i
$199$	−6.22328	+	10.7790i	−0.441157	+	0.764106i	−0.997776	−	0.0666623i	$-0.978765\pi$
$199$	−6.22328	+	10.7790i	−0.441157	+	0.764106i	0.556619	+	0.830768i	$0.312098\pi$
$200$	−0.00960030	−	0.0166282i	−0.000678843	−	0.00117579i
$201$	−33.8396			−2.38686
$202$	−0.919708	−	1.59298i	−0.0647104	−	0.112082i
$203$		0			0
$204$	4.44836	+	7.70479i	0.311448	+	0.539443i
$205$	−10.2395	−	17.7354i	−0.715160	−	1.23869i
$206$	−0.160755			−0.0112003
$207$	−3.36967	−	5.83645i	−0.234209	−	0.405661i
$208$	2.46551	+	13.0436i	0.170952	+	0.904410i
$209$	−10.7485			−0.743491
$210$		0			0
$211$	12.1961	−	21.1243i	0.839617	−	1.45426i	−0.0505979	−	0.998719i	$-0.516113\pi$
$211$	12.1961	−	21.1243i	0.839617	−	1.45426i	0.890215	−	0.455540i	$-0.150554\pi$
$212$	−16.3427			−1.12242
$213$	8.66158	+	15.0023i	0.593482	+	1.02794i
$214$	−1.03493	+	1.79255i	−0.0707465	+	0.122536i
$215$	2.74761			0.187385
$216$	−15.2804			−1.03970
$217$		0			0
$218$	0.262904	−	0.455363i	0.0178061	−	0.0308411i
$219$	−6.58396	−	11.4037i	−0.444903	−	0.770594i
$220$	7.21474	+	12.4963i	0.486418	+	0.842500i
$221$	3.76047	−	3.23495i	0.252957	−	0.217606i
$222$	−0.597084	+	1.03418i	−0.0400737	+	0.0694096i
$223$	11.3247	−	19.6149i	0.758357	−	1.31351i	−0.185331	−	0.982676i	$-0.559336\pi$
$223$	11.3247	−	19.6149i	0.758357	−	1.31351i	0.943688	−	0.330837i	$-0.107331\pi$
$224$		0			0
$225$	0.0845083	+	0.146373i	0.00563389	+	0.00975818i
$226$	1.09952	−	1.90442i	0.0731388	−	0.126680i
$227$	0.642530	−	1.11289i	0.0426462	−	0.0738654i	−0.843914	−	0.536478i	$-0.819754\pi$
$227$	0.642530	−	1.11289i	0.0426462	−	0.0738654i	0.886561	+	0.462612i	$0.153088\pi$
$228$	−10.4609	+	18.1187i	−0.692787	+	1.19994i
$229$	−2.32225	+	4.02226i	−0.153459	+	0.265798i	−0.932497	−	0.361178i	$-0.882375\pi$
$229$	−2.32225	+	4.02226i	−0.153459	+	0.265798i	0.779038	+	0.626977i	$0.215708\pi$
$230$	−0.216438	−	0.374882i	−0.0142715	−	0.0247190i
$231$		0			0
$232$	−0.277178	+	0.480086i	−0.0181976	+	0.0315192i
$233$	−5.94386	+	10.2951i	−0.389395	+	0.674452i	−0.992368	−	0.123309i	$-0.960649\pi$
$233$	−5.94386	+	10.2951i	−0.389395	+	0.674452i	0.602973	+	0.797762i	$0.293983\pi$
$234$	1.24526	+	6.58798i	0.0814054	+	0.430670i
$235$	−1.81652	−	3.14630i	−0.118497	−	0.205242i
$236$	−8.58622	−	14.8718i	−0.558915	−	0.968070i
$237$	−10.7151	+	18.5591i	−0.696021	+	1.20554i
$238$		0			0
$239$	−4.17783			−0.270242			−0.135121	−	0.990829i	$-0.543142\pi$
$239$	−4.17783			−0.270242			−0.135121	+	0.990829i	$0.543142\pi$
$240$	27.2930			1.76175
$241$	2.01671	−	3.49304i	0.129907	−	0.225006i	−0.793733	−	0.608266i	$-0.791865\pi$
$241$	2.01671	−	3.49304i	0.129907	−	0.225006i	0.923641	+	0.383260i	$0.125199\pi$
$242$	−0.00432231	−	0.00748646i	−0.000277849	−	0.000481248i
$243$	54.4020			3.48989
$244$	−5.32036	+	9.21514i	−0.340601	+	0.589939i
$245$		0			0
$246$	7.05444			0.449775
$247$	11.0098	+	3.85475i	0.700535	+	0.245272i
$248$	−0.782999	−	1.35619i	−0.0497205	−	0.0861184i
$249$	15.4171			0.977019
$250$	1.29605	+	2.24483i	0.0819695	+	0.141975i
$251$	13.9343	+	24.1348i	0.879523	+	1.52338i	0.851866	+	0.523760i	$0.175471\pi$
$251$	13.9343	+	24.1348i	0.879523	+	1.52338i	0.0276571	+	0.999617i	$0.491195\pi$
$252$		0			0
$253$	−1.39286	−	2.41250i	−0.0875683	−	0.151673i
$254$	4.26477			0.267596
$255$	−5.09943	−	8.83247i	−0.319339	−	0.553111i
$256$	−5.94377	+	10.2949i	−0.371486	+	0.643432i
$257$	−3.57032	−	6.18398i	−0.222710	−	0.385746i	0.732920	−	0.680315i	$-0.238157\pi$
$257$	−3.57032	−	6.18398i	−0.222710	−	0.385746i	−0.955630	+	0.294569i	$0.904824\pi$
$258$	−0.473236	+	0.819669i	−0.0294624	+	0.0510304i
$259$		0			0
$260$	−2.90855	−	15.3874i	−0.180380	−	0.954289i
$261$	2.43991	−	4.22605i	0.151027	−	0.261586i
$262$	0.404500			0.0249901
$263$	21.3192			1.31460			0.657300	−	0.753629i	$-0.271699\pi$
$263$	21.3192			1.31460			0.657300	+	0.753629i	$0.271699\pi$
$264$	−10.0778			−0.620244
$265$	18.7347			1.15086
$266$		0			0
$267$	15.1632	+	26.2634i	0.927972	+	1.60729i
$268$	−9.91313	+	17.1700i	−0.605540	+	1.04883i
$269$	1.39438	−	2.41513i	0.0850167	−	0.147253i	−0.820382	−	0.571816i	$-0.806239\pi$
$269$	1.39438	−	2.41513i	0.0850167	−	0.147253i	0.905398	+	0.424563i	$0.139572\pi$
$270$	8.63964			0.525792
$271$	−7.73737	−	13.4015i	−0.470012	−	0.814085i	0.529400	−	0.848372i	$-0.322417\pi$
$271$	−7.73737	−	13.4015i	−0.470012	−	0.814085i	−0.999412	+	0.0342877i	$0.989084\pi$
$272$	5.06521			0.307123
$273$		0			0
$274$	−4.16524			−0.251631
$275$	0.0349316	+	0.0605033i	0.00210645	+	0.00364849i
$276$	−5.42232			−0.326385
$277$	−2.76477	+	4.78873i	−0.166119	+	0.287727i	−0.937052	−	0.349189i	$-0.886457\pi$
$277$	−2.76477	+	4.78873i	−0.166119	+	0.287727i	0.770933	+	0.636916i	$0.219790\pi$
$278$	1.61003	−	2.78866i	0.0965633	−	0.167252i
$279$	6.89249	+	11.9381i	0.412642	+	0.714718i
$280$		0			0
$281$	−31.4871			−1.87836			−0.939182	−	0.343419i	$-0.888415\pi$
$281$	−31.4871			−1.87836			−0.939182	+	0.343419i	$0.888415\pi$
$282$	1.25148			0.0745243
$283$	7.35118			0.436983			0.218491	−	0.975839i	$-0.429886\pi$
$283$	7.35118			0.436983			0.218491	+	0.975839i	$0.429886\pi$
$284$	10.1495			0.602259
$285$	11.9919	−	20.7706i	0.710340	−	1.23034i
$286$	0.514731	+	2.72315i	0.0304367	+	0.161023i
$287$		0			0
$288$	−10.7617	+	18.6398i	−0.634140	+	1.09836i
$289$	7.55361	+	13.0832i	0.444330	+	0.769603i
$290$	0.156718	−	0.271444i	0.00920281	−	0.0159397i
$291$	−25.5130	−	44.1899i	−1.49560	−	2.59046i
$292$	−7.71494			−0.451483
$293$	−6.76675	−	11.7204i	−0.395318	−	0.684710i	0.597824	−	0.801627i	$-0.296032\pi$
$293$	−6.76675	−	11.7204i	−0.395318	−	0.684710i	−0.993142	+	0.116917i	$0.962699\pi$
$294$		0			0
$295$	9.84291	+	17.0484i	0.573076	+	0.992597i
$296$	0.709271	+	1.22849i	0.0412255	+	0.0714047i
$297$	55.5992			3.22619
$298$	1.84282	+	3.19187i	0.106752	+	0.184900i
$299$	0.561516	+	2.97066i	0.0324733	+	0.171798i
$300$	0.135987			0.00785120
$301$		0			0
$302$	1.61370	−	2.79502i	0.0928583	−	0.160835i
$303$	26.4133			1.51741
$304$	5.95572	+	10.3156i	0.341584	+	0.591641i
$305$	6.09906	−	10.5639i	0.349231	−	0.604886i
$306$	2.55831			0.146249
$307$	3.30609			0.188688			0.0943442	−	0.995540i	$-0.469925\pi$
$307$	3.30609			0.188688			0.0943442	+	0.995540i	$0.469925\pi$
$308$		0			0
$309$	1.15419	−	1.99912i	0.0656597	−	0.113726i
$310$	0.442713	+	0.766801i	0.0251444	+	0.0435514i
$311$	−17.1531	−	29.7101i	−0.972665	−	1.68470i	−0.687435	−	0.726246i	$-0.741264\pi$
$311$	−17.1531	−	29.7101i	−0.972665	−	1.68470i	−0.285229	−	0.958459i	$-0.592070\pi$
$312$	10.3227	+	3.61419i	0.584408	+	0.204613i
$313$	3.60714	−	6.24775i	0.203888	−	0.353144i	−0.745890	−	0.666069i	$-0.767976\pi$
$313$	3.60714	−	6.24775i	0.203888	−	0.353144i	0.949778	+	0.312925i	$0.101309\pi$
$314$	−1.50091	+	2.59966i	−0.0847015	+	0.146707i
$315$		0			0
$316$	6.27787	+	10.8736i	0.353158	+	0.611687i
$317$	4.02020	−	6.96319i	0.225797	−	0.391092i	−0.730761	−	0.682633i	$-0.760835\pi$
$317$	4.02020	−	6.96319i	0.225797	−	0.391092i	0.956558	+	0.291541i	$0.0941681\pi$
$318$	−3.22677	+	5.58893i	−0.180948	+	0.313412i
$319$	1.00854	−	1.74684i	0.0564673	−	0.0978043i
$320$	7.52396	−	13.0319i	0.420602	−	0.728504i
$321$	−14.8612	−	25.7404i	−0.829472	−	1.43669i
$322$		0			0
$323$	2.22554	−	3.85475i	0.123832	−	0.214484i
$324$	30.6444	−	53.0777i	1.70247	−	2.94876i
$325$	−0.0140823	−	0.0745014i	−0.000781145	−	0.00413259i
$326$	−2.12950	−	3.68840i	−0.117942	−	0.204281i
$327$	3.77520	+	6.53884i	0.208769	+	0.361599i
$328$	4.18995	−	7.25721i	0.231351	−	0.400712i
$329$		0			0
$330$	5.69803			0.313666
$331$	0.893687			0.0491215			0.0245607	−	0.999698i	$-0.492181\pi$
$331$	0.893687			0.0491215			0.0245607	+	0.999698i	$0.492181\pi$
$332$	4.51636	−	7.82256i	0.247867	−	0.429319i
$333$	−6.24348	−	10.8140i	−0.342141	−	0.592605i
$334$	4.28002			0.234192
$335$	11.3640	−	19.6831i	0.620883	−	1.07540i
$336$		0			0
$337$	15.0717			0.821007			0.410504	−	0.911859i	$-0.365353\pi$
$337$	15.0717			0.821007			0.410504	+	0.911859i	$0.365353\pi$
$338$	0.449362	−	2.97393i	0.0244421	−	0.161761i
$339$	15.7886	+	27.3467i	0.857521	+	1.48527i
$340$	−5.97540			−0.324062
$341$	2.84902	+	4.93464i	0.154283	+	0.267226i
$342$	3.00808	+	5.21015i	0.162658	+	0.281733i
$343$		0			0
$344$	0.562153	+	0.973677i	0.0303092	+	0.0524971i
$345$	6.21594			0.334655
$346$	−1.98949	−	3.44589i	−0.106955	−	0.185252i
$347$	8.20818	−	14.2170i	0.440638	−	0.763207i	−0.557099	−	0.830446i	$-0.688086\pi$
$347$	8.20818	−	14.2170i	0.440638	−	0.763207i	0.997737	+	0.0672387i	$0.0214189\pi$
$348$	−1.96309	−	3.40018i	−0.105233	−	0.182269i
$349$	17.1861	−	29.7672i	0.919950	−	1.59340i	0.120462	−	0.992718i	$-0.461562\pi$
$349$	17.1861	−	29.7672i	0.919950	−	1.59340i	0.799488	−	0.600682i	$-0.205104\pi$
$350$		0			0
$351$	−56.9506	−	19.9396i	−3.03980	−	1.06430i
$352$	−4.44836	+	7.70479i	−0.237098	+	0.410667i
$353$	23.9163			1.27293			0.636467	−	0.771304i	$-0.280395\pi$
$353$	23.9163			1.27293			0.636467	+	0.771304i	$0.280395\pi$
$354$	−6.78120			−0.360416
$355$	−11.6349			−0.617519
$356$	17.7679			0.941697
$357$		0			0
$358$	−1.67605	−	2.90300i	−0.0885819	−	0.153428i
$359$	3.08937	−	5.35095i	0.163051	−	0.282412i	−0.772911	−	0.634515i	$-0.781200\pi$
$359$	3.08937	−	5.35095i	0.163051	−	0.282412i	0.935961	+	0.352103i	$0.114533\pi$
$360$	8.18752	−	14.1812i	0.431520	−	0.747415i
$361$	−8.53276			−0.449092
$362$	0.792970	+	1.37347i	0.0416776	+	0.0721877i
$363$	0.124133			0.00651531
$364$		0			0
$365$	8.84411			0.462922
$366$	2.10095	+	3.63895i	0.109818	+	0.190211i
$367$	−19.8560			−1.03647			−0.518236	−	0.855237i	$-0.673411\pi$
$367$	−19.8560			−1.03647			−0.518236	+	0.855237i	$0.673411\pi$
$368$	−1.54356	+	2.67352i	−0.0804634	+	0.139367i
$369$	−36.8828	+	63.8829i	−1.92004	+	3.32561i
$370$	−0.401026	−	0.694598i	−0.0208484	−	0.0361104i
$371$		0			0
$372$	11.0911			0.575045
$373$	30.1951			1.56344			0.781721	−	0.623628i	$-0.214342\pi$
$373$	30.1951			1.56344			0.781721	+	0.623628i	$0.214342\pi$
$374$	1.05748			0.0546809
$375$	−37.2216			−1.92212
$376$	0.743308	−	1.28745i	0.0383332	−	0.0663950i
$377$	−1.65952	+	1.42761i	−0.0854697	+	0.0735254i
$378$		0			0
$379$	2.16121	−	3.74333i	0.111014	−	0.192282i	−0.805165	−	0.593050i	$-0.797923\pi$
$379$	2.16121	−	3.74333i	0.111014	−	0.192282i	0.916179	+	0.400768i	$0.131257\pi$
$380$	−7.02594	−	12.1693i	−0.360423	−	0.624271i
$381$	−30.6203	+	53.0358i	−1.56872	+	2.71711i
$382$	0.329878	+	0.571365i	0.0168780	+	0.0292336i
$383$	17.3481			0.886449			0.443224	−	0.896411i	$-0.353834\pi$
$383$	17.3481			0.886449			0.443224	+	0.896411i	$0.353834\pi$
$384$	11.4885	+	19.8987i	0.586271	+	1.01545i
$385$		0			0
$386$	1.16264	+	2.01376i	0.0591771	+	0.102498i
$387$	−4.94845	−	8.57096i	−0.251544	−	0.435687i
$388$	−29.8956			−1.51772
$389$	12.6737	+	21.9515i	0.642582	+	1.11299i	0.984854	+	0.173384i	$0.0554702\pi$
$389$	12.6737	+	21.9515i	0.642582	+	1.11299i	−0.342272	+	0.939601i	$0.611196\pi$
$390$	−5.83653	−	2.04349i	−0.295544	−	0.103476i
$391$	1.15360			0.0583398
$392$		0			0
$393$	−2.90423	+	5.03028i	−0.146499	+	0.253744i
$394$	−5.88052			−0.296256
$395$	−7.19671	−	12.4651i	−0.362106	−	0.627185i
$396$	25.9875	−	45.0117i	1.30592	−	2.26192i
$397$	27.0749			1.35885			0.679425	−	0.733745i	$-0.262229\pi$
$397$	27.0749			1.35885			0.679425	+	0.733745i	$0.262229\pi$
$398$	2.87965			0.144344
$399$		0			0
$400$	0.0387110	−	0.0670494i	0.00193555	−	0.00335247i
$401$	14.6429	+	25.3622i	0.731232	+	1.26653i	0.956357	+	0.292201i	$0.0943875\pi$
$401$	14.6429	+	25.3622i	0.731232	+	1.26653i	−0.225125	+	0.974330i	$0.572279\pi$
$402$	3.91458	+	6.78025i	0.195241	+	0.338168i
$403$	−1.14855	−	6.07632i	−0.0572134	−	0.302683i
$404$	7.73764	−	13.4020i	0.384962	−	0.666774i
$405$	−35.1296	+	60.8462i	−1.74560	+	3.02347i
$406$		0			0
$407$	−2.58075	−	4.46999i	−0.127923	−	0.221569i
$408$	2.08666	−	3.61419i	0.103305	−	0.178929i
$409$	11.6856	−	20.2401i	0.577817	−	1.00081i	−0.417912	−	0.908487i	$-0.637238\pi$
$409$	11.6856	−	20.2401i	0.577817	−	1.00081i	0.995729	−	0.0923213i	$-0.0294287\pi$
$410$	−2.36903	+	4.10327i	−0.116998	+	0.202646i
$411$	29.9056	−	51.7980i	1.47513	−	2.55501i
$412$	−0.676229	−	1.17126i	−0.0333154	−	0.0577040i
$413$		0			0
$414$	−0.779611	+	1.35033i	−0.0383158	+	0.0663649i
$415$	−5.17738	+	8.96748i	−0.254147	+	0.440196i
$416$	7.31965	−	6.29674i	0.358876	−	0.308723i
$417$	23.1194	+	40.0440i	1.13216	+	1.96096i
$418$	1.24339	+	2.15362i	0.0608164	+	0.105337i
$419$	7.30320	−	12.6495i	0.356785	−	0.617969i	−0.630637	−	0.776078i	$-0.717206\pi$
$419$	7.30320	−	12.6495i	0.356785	−	0.617969i	0.987422	+	0.158109i	$0.0505397\pi$
$420$		0			0
$421$	10.2728			0.500668			0.250334	−	0.968160i	$-0.419460\pi$
$421$	10.2728			0.500668			0.250334	+	0.968160i	$0.419460\pi$
$422$	−5.64342			−0.274717
$423$	−6.54310	+	11.3330i	−0.318136	+	0.551028i
$424$	3.83305	+	6.63904i	0.186149	+	0.322420i
$425$	−0.0289311			−0.00140336
$426$	2.00395	−	3.47095i	0.0970917	−	0.168168i
$427$		0			0
$428$	−17.4141			−0.841740
$429$	−37.5602	−	13.1506i	−1.81342	−	0.634916i
$430$	−0.317845	−	0.550523i	−0.0153278	−	0.0265486i
$431$	−12.5017			−0.602188			−0.301094	−	0.953595i	$-0.597352\pi$
$431$	−12.5017			−0.602188			−0.301094	+	0.953595i	$0.597352\pi$
$432$	−30.8073	−	53.3599i	−1.48222	−	2.56728i
$433$	−5.47361	−	9.48057i	−0.263045	−	0.455607i	0.704005	−	0.710195i	$-0.251393\pi$
$433$	−5.47361	−	9.48057i	−0.263045	−	0.455607i	−0.967050	+	0.254588i	$0.918060\pi$
$434$		0			0
$435$	2.25041	+	3.89783i	0.107899	+	0.186887i
$436$	4.42370			0.211857
$437$	1.35641	+	2.34937i	0.0648858	+	0.112386i
$438$	−1.52327	+	2.63838i	−0.0727846	+	0.126067i
$439$	−8.95896	−	15.5174i	−0.427588	−	0.740604i	0.569070	−	0.822289i	$-0.307303\pi$
$439$	−8.95896	−	15.5174i	−0.427588	−	0.740604i	−0.996658	+	0.0816849i	$0.973970\pi$
$440$	3.38432	−	5.86181i	0.161341	−	0.279451i
$441$		0			0
$442$	−1.08318	−	0.379244i	−0.0515217	−	0.0180388i
$443$	−13.8597	+	24.0057i	−0.658494	+	1.14055i	0.322511	+	0.946566i	$0.395473\pi$
$443$	−13.8597	+	24.0057i	−0.658494	+	1.14055i	−0.981005	+	0.193980i	$0.937860\pi$
$444$	−10.0467			−0.476796
$445$	−20.3684			−0.965556
$446$	−5.24018			−0.248130
$447$	−52.9245			−2.50324
$448$		0			0
$449$	0.0829898	+	0.143743i	0.00391653	+	0.00678363i	0.867977	−	0.496604i	$-0.165420\pi$
$449$	0.0829898	+	0.143743i	0.00391653	+	0.00678363i	−0.864060	+	0.503388i	$0.832087\pi$
$450$	0.0195519	−	0.0338649i	0.000921686	−	0.00159641i
$451$	−15.2455	+	26.4061i	−0.717884	+	1.24341i
$452$	18.5008			0.870204
$453$	23.1722	+	40.1354i	1.08872	+	1.88573i
$454$	−0.297313			−0.0139536
$455$		0			0
$456$	9.81404			0.459584
$457$	−15.8677	−	27.4837i	−0.742260	−	1.28563i	−0.951464	−	0.307760i	$-0.900421\pi$
$457$	−15.8677	−	27.4837i	−0.742260	−	1.28563i	0.209205	−	0.977872i	$-0.432913\pi$
$458$	1.07456			0.0502107
$459$	−11.5121	+	19.9396i	−0.537340	+	0.930700i
$460$	1.82093	−	3.15394i	0.0849011	−	0.147053i
$461$	14.5328	+	25.1715i	0.676859	+	1.17235i	0.975922	+	0.218121i	$0.0699926\pi$
$461$	14.5328	+	25.1715i	0.676859	+	1.17235i	−0.299063	+	0.954233i	$0.596674\pi$
$462$		0			0
$463$	6.31904			0.293671			0.146835	−	0.989161i	$-0.453091\pi$
$463$	6.31904			0.293671			0.146835	+	0.989161i	$0.453091\pi$
$464$	−2.23531			−0.103772
$465$	−12.7144			−0.589615
$466$	2.75035			0.127408
$467$	−17.3204	+	29.9999i	−0.801495	+	1.38823i	0.117137	+	0.993116i	$0.462628\pi$
$467$	−17.3204	+	29.9999i	−0.801495	+	1.38823i	−0.918632	+	0.395114i	$0.870705\pi$
$468$	−42.7617	+	36.7858i	−1.97666	+	1.70042i
$469$		0			0
$470$	−0.420271	+	0.727931i	−0.0193857	+	0.0335769i
$471$	−21.5526	−	37.3301i	−0.993089	−	1.72008i
$472$	−4.02766	+	6.97611i	−0.185388	+	0.321101i
$473$	−2.04545	−	3.54282i	−0.0940497	−	0.162899i
$474$	4.95811			0.227734
$475$	−0.0340175	−	0.0589200i	−0.00156083	−	0.00270343i
$476$		0			0
$477$	−33.7411	−	58.4413i	−1.54490	−	2.67585i
$478$	0.483293	+	0.837089i	0.0221053	+	0.0382876i
$479$	7.14230			0.326340			0.163170	−	0.986598i	$-0.447828\pi$
$479$	7.14230			0.326340			0.163170	+	0.986598i	$0.447828\pi$
$480$	−9.92590	−	17.1922i	−0.453053	−	0.784711i
$481$	1.04040	+	5.50417i	0.0474382	+	0.250968i
$482$	−0.933174			−0.0425049
$483$		0			0
$484$	0.0363642	−	0.0629847i	0.00165292	−	0.00286294i
$485$	34.2712			1.55617
$486$	−6.29325	−	10.9002i	−0.285468	−	0.494444i
$487$	9.25013	−	16.0217i	0.419163	−	0.726012i	−0.576692	−	0.816962i	$-0.695657\pi$
$487$	9.25013	−	16.0217i	0.419163	−	0.726012i	0.995856	+	0.0909493i	$0.0289901\pi$
$488$	4.99140			0.225950
$489$	61.1575			2.76564
$490$		0			0
$491$	7.63904	−	13.2312i	0.344745	−	0.597116i	−0.640563	−	0.767906i	$-0.721299\pi$
$491$	7.63904	−	13.2312i	0.344745	−	0.597116i	0.985307	+	0.170790i	$0.0546321\pi$
$492$	29.6750	+	51.3986i	1.33785	+	2.31723i
$493$	0.417647	+	0.723386i	0.0188099	+	0.0325796i
$494$	−0.501261	−	2.65188i	−0.0225528	−	0.119314i
$495$	−29.7911	+	51.5997i	−1.33901	+	2.31923i
$496$	3.15726	−	5.46854i	0.141765	−	0.245545i
$497$		0			0
$498$	−1.78346	−	3.08904i	−0.0799186	−	0.138423i
$499$	−6.23916	+	10.8065i	−0.279303	+	0.483767i	−0.971212	−	0.238218i	$-0.923437\pi$
$499$	−6.23916	+	10.8065i	−0.279303	+	0.483767i	0.691909	+	0.721985i	$0.256770\pi$
$500$	−10.9039	+	18.8861i	−0.487636	+	0.844610i
$501$	−30.7297	+	53.2255i	−1.37290	+	2.37794i
$502$	3.22384	−	5.58386i	0.143887	−	0.249220i
$503$	−1.29004	−	2.23441i	−0.0575200	−	0.0996276i	0.835832	−	0.548986i	$-0.184986\pi$
$503$	−1.29004	−	2.23441i	−0.0575200	−	0.0996276i	−0.893352	+	0.449358i	$0.851653\pi$
$504$		0			0
$505$	−8.87013	+	15.3635i	−0.394716	+	0.683668i
$506$	−0.322253	+	0.558158i	−0.0143259	+	0.0248132i
$507$	33.7569	+	26.9404i	1.49920	+	1.19647i
$508$	17.9401	+	31.0731i	0.795962	+	1.37865i
$509$	17.8404	+	30.9005i	0.790761	+	1.36964i	0.925496	+	0.378757i	$0.123648\pi$
$509$	17.8404	+	30.9005i	0.790761	+	1.36964i	−0.134735	+	0.990882i	$0.543018\pi$
$510$	−1.17981	+	2.04349i	−0.0522428	+	0.0904872i
$511$		0			0
$512$	16.5825			0.732850
$513$	−54.1442			−2.39053
$514$	−0.826032	+	1.43073i	−0.0364347	+	0.0631068i
$515$	0.775202	+	1.34269i	0.0341595	+	0.0591660i
$516$	−7.96281			−0.350543
$517$	−2.70460	+	4.68450i	−0.118948	+	0.206024i
$518$		0			0
$519$	57.1365			2.50801
$520$	−5.56880	+	4.79057i	−0.244208	+	0.210080i
$521$	−10.4819	−	18.1551i	−0.459219	−	0.795390i	0.539701	−	0.841857i	$-0.318537\pi$
$521$	−10.4819	−	18.1551i	−0.459219	−	0.795390i	−0.998920	+	0.0464666i	$0.985204\pi$
$522$	−1.12900			−0.0494149
$523$	−11.4131	−	19.7681i	−0.499062	−	0.864401i	0.500937	−	0.865484i	$-0.332989\pi$
$523$	−11.4131	−	19.7681i	−0.499062	−	0.864401i	−0.999999	+	0.00108279i	$0.999655\pi$
$524$	1.70156	+	2.94719i	0.0743330	+	0.128749i
$525$		0			0
$526$	−2.46622	−	4.27161i	−0.107532	−	0.186251i
$527$	−2.35962			−0.102787
$528$	−20.3181	−	35.1920i	−0.884233	−	1.53154i
$529$	11.1485	−	19.3097i	0.484716	−	0.839552i
$530$	−2.16723	−	3.75376i	−0.0941386	−	0.163053i
$531$	35.4542	−	61.4084i	1.53858	−	2.66490i
$532$		0			0
$533$	25.0861	−	21.5803i	1.08660	−	0.934749i
$534$	3.50817	−	6.07632i	0.151813	−	0.262948i
$535$	19.9628			0.863067
$536$	9.30018			0.401707
$537$	48.1348			2.07717
$538$	−0.645208			−0.0278169
$539$		0			0
$540$	36.3433	+	62.9484i	1.56397	+	2.70887i
$541$	−15.1096	+	26.1706i	−0.649611	+	1.12516i	0.333604	+	0.942713i	$0.391735\pi$
$541$	−15.1096	+	26.1706i	−0.649611	+	1.12516i	−0.983216	+	0.182447i	$0.941598\pi$
$542$	−1.79013	+	3.10059i	−0.0768925	+	0.133182i
$543$	−22.7735			−0.977305
$544$	−1.84211	−	3.19064i	−0.0789800	−	0.136797i
$545$	−5.07116			−0.217225
$546$		0			0
$547$	−16.8223			−0.719271			−0.359636	−	0.933093i	$-0.617099\pi$
$547$	−16.8223			−0.719271			−0.359636	+	0.933093i	$0.617099\pi$
$548$	−17.5214	−	30.3479i	−0.748476	−	1.29640i
$549$	−43.9376			−1.87521
$550$	0.00808180	−	0.0139981i	0.000344609	−	0.000596881i
$551$	−0.982146	+	1.70113i	−0.0418408	+	0.0724704i
$552$	1.27176	+	2.20276i	0.0541298	+	0.0937555i
$553$		0			0
$554$	1.27932			0.0543531
$555$	11.5172			0.488876
$556$	27.0909			1.14891
$557$	−10.4918			−0.444553			−0.222276	−	0.974984i	$-0.571349\pi$
$557$	−10.4918			−0.444553			−0.222276	+	0.974984i	$0.571349\pi$
$558$	1.59465	−	2.76202i	0.0675070	−	0.116926i
$559$	0.824600	+	4.36249i	0.0348768	+	0.184513i
$560$		0			0
$561$	−7.59250	+	13.1506i	−0.320555	+	0.555218i
$562$	3.64244	+	6.30890i	0.153647	+	0.266125i
$563$	15.4737	−	26.8012i	0.652138	−	1.12954i	−0.330465	−	0.943818i	$-0.607205\pi$
$563$	15.4737	−	26.8012i	0.652138	−	1.12954i	0.982603	−	0.185718i	$-0.0594612\pi$
$564$	5.26442	+	9.11825i	0.221672	+	0.383947i
$565$	−21.2086			−0.892252
$566$	−0.850388	−	1.47292i	−0.0357445	−	0.0619112i
$567$		0			0
$568$	−2.38047	−	4.12310i	−0.0998825	−	0.173002i
$569$	18.4545	+	31.9641i	0.773651	+	1.34000i	0.935549	+	0.353196i	$0.114905\pi$
$569$	18.4545	+	31.9641i	0.773651	+	1.34000i	−0.161898	+	0.986807i	$0.551762\pi$
$570$	−5.54892			−0.232419
$571$	0.885467	+	1.53367i	0.0370556	+	0.0641822i	0.883958	−	0.467565i	$-0.154869\pi$
$571$	0.885467	+	1.53367i	0.0370556	+	0.0641822i	−0.846903	+	0.531748i	$0.821535\pi$
$572$	−17.6756	+	15.2054i	−0.739054	+	0.635772i
$573$	−9.47383			−0.395775
$574$		0			0
$575$	0.00881638	−	0.0152704i	0.000367668	−	0.000636820i
$576$	−54.2026			−2.25844
$577$	−4.91999	−	8.52168i	−0.204822	−	0.354762i	0.745254	−	0.666781i	$-0.232328\pi$
$577$	−4.91999	−	8.52168i	−0.204822	−	0.354762i	−0.950076	+	0.312019i	$0.898995\pi$
$578$	1.74761	−	3.02695i	0.0726910	−	0.125905i
$579$	−33.3903			−1.38765
$580$	2.63699			0.109495
$581$		0			0
$582$	−5.90272	+	10.2238i	−0.244675	+	0.423790i
$583$	−13.9469	−	24.1568i	−0.577623	−	1.00047i
$584$	1.80948	+	3.13411i	0.0748767	+	0.129690i
$585$	49.0204	−	42.1698i	2.02674	−	1.74351i
$586$	−1.56556	+	2.71163i	−0.0646727	+	0.112016i
$587$	−7.56917	+	13.1102i	−0.312413	+	0.541116i	−0.978884	−	0.204415i	$-0.934471\pi$
$587$	−7.56917	+	13.1102i	−0.312413	+	0.541116i	0.666471	+	0.745531i	$0.267804\pi$
$588$		0			0
$589$	−2.77446	−	4.80551i	−0.114320	−	0.198007i
$590$	2.27726	−	3.94434i	0.0937535	−	0.162386i
$591$	42.2210	−	73.1289i	1.73674	−	3.00812i
$592$	−2.85997	+	4.95361i	−0.117544	+	0.203592i
$593$	4.58574	−	7.94274i	0.188314	−	0.326169i	−0.756374	−	0.654139i	$-0.773031\pi$
$593$	4.58574	−	7.94274i	0.188314	−	0.326169i	0.944688	+	0.327970i	$0.106364\pi$
$594$	−6.43174	−	11.1401i	−0.263898	−	0.457084i
$595$		0			0
$596$	−15.5040	+	26.8536i	−0.635067	+	1.09997i
$597$	−20.6753	+	35.8107i	−0.846184	+	1.46563i
$598$	0.530258	−	0.456155i	0.0216839	−	0.0186536i
$599$	9.29053	+	16.0917i	0.379601	+	0.657488i	0.991004	−	0.133831i	$-0.0427280\pi$
$599$	9.29053	+	16.0917i	0.379601	+	0.657488i	−0.611403	+	0.791319i	$0.709395\pi$
$600$	−0.0318946	−	0.0552431i	−0.00130209	−	0.00225529i
$601$	−6.70179	+	11.6078i	−0.273372	+	0.473494i	−0.969723	−	0.244207i	$-0.921472\pi$
$601$	−6.70179	+	11.6078i	−0.273372	+	0.473494i	0.696351	+	0.717701i	$0.254806\pi$
$602$		0			0
$603$	−81.8665			−3.33386
$604$	27.1527			1.10483
$605$	−0.0416865	+	0.0722032i	−0.00169480	+	0.00293548i
$606$	−3.05550	−	5.29229i	−0.124121	−	0.214984i
$607$	−12.6362			−0.512889			−0.256445	−	0.966559i	$-0.582551\pi$
$607$	−12.6362			−0.512889			−0.256445	+	0.966559i	$0.582551\pi$
$608$	4.33195	−	7.50316i	0.175684	−	0.304293i
$609$		0			0
$610$	−2.82217			−0.114266
$611$	4.45034	−	3.82841i	0.180041	−	0.154881i
$612$	10.7617	+	18.6398i	0.435016	+	0.753470i
$613$	25.7079			1.03833			0.519167	−	0.854673i	$-0.326242\pi$
$613$	25.7079			1.03833			0.519167	+	0.854673i	$0.326242\pi$
$614$	−0.382450	−	0.662422i	−0.0154344	−	0.0267332i
$615$	−34.0183	−	58.9214i	−1.37175	−	2.37594i
$616$		0			0
$617$	3.29810	+	5.71248i	0.132777	+	0.229976i	0.924746	−	0.380585i	$-0.124277\pi$
$617$	3.29810	+	5.71248i	0.132777	+	0.229976i	−0.791969	+	0.610561i	$0.790944\pi$
$618$	−0.534070			−0.0214834
$619$	−10.5062	−	18.1973i	−0.422280	−	0.731410i	0.573883	−	0.818938i	$-0.305437\pi$
$619$	−10.5062	−	18.1973i	−0.422280	−	0.731410i	−0.996162	+	0.0875280i	$0.972103\pi$
$620$	−3.72461	+	6.45121i	−0.149584	+	0.259087i
$621$	−7.01634	−	12.1526i	−0.281556	−	0.487669i
$622$	−3.96856	+	6.87375i	−0.159125	+	0.275612i
$623$		0			0
$624$	8.19103	+	43.3341i	0.327904	+	1.73475i
$625$	12.4472	−	21.5592i	0.497888	−	0.862368i
$626$	−1.66910			−0.0667108
$627$	−35.7093			−1.42609
$628$	−25.2548			−1.00778
$629$	2.13743			0.0852250
$630$		0			0
$631$	−13.0105	−	22.5349i	−0.517940	−	0.897099i	−0.999783	−	0.0208412i	$-0.993366\pi$
$631$	−13.0105	−	22.5349i	−0.517940	−	0.897099i	0.481842	−	0.876258i	$-0.339968\pi$
$632$	2.94485	−	5.10063i	0.117140	−	0.202892i
$633$	40.5187	−	70.1804i	1.61047	−	2.78942i
$634$	−1.86023			−0.0738793
$635$	−20.5658	−	35.6210i	−0.816130	−	1.41358i
$636$	−54.2946			−2.15292
$637$		0			0
$638$	−0.466673			−0.0184758
$639$	20.9545	+	36.2943i	0.828949	+	1.43578i
$640$	−15.4323			−0.610015
$641$	−9.26694	+	16.0508i	−0.366022	+	0.633969i	−0.988940	−	0.148319i	$-0.952614\pi$
$641$	−9.26694	+	16.0508i	−0.366022	+	0.633969i	0.622917	+	0.782288i	$0.285947\pi$
$642$	−3.43830	+	5.95532i	−0.135699	+	0.235038i
$643$	−7.22328	−	12.5111i	−0.284858	−	0.493389i	0.687716	−	0.725979i	$-0.258613\pi$
$643$	−7.22328	−	12.5111i	−0.284858	−	0.493389i	−0.972575	+	0.232590i	$0.925280\pi$
$644$		0			0
$645$	9.12826			0.359425
$646$	−1.02981			−0.0405172
$647$	−29.2875			−1.15141			−0.575706	−	0.817657i	$-0.695273\pi$
$647$	−29.2875			−1.15141			−0.575706	+	0.817657i	$0.695273\pi$
$648$	−28.7496			−1.12939
$649$	14.6550	−	25.3832i	0.575260	−	0.996379i
$650$	−0.0132984	+	0.0114399i	−0.000521605	+	0.000448711i
$651$		0			0
$652$	17.9158	−	31.0310i	0.701636	−	1.21527i
$653$	15.4807	+	26.8134i	0.605808	+	1.04929i	0.991923	+	0.126840i	$0.0404836\pi$
$653$	15.4807	+	26.8134i	0.605808	+	1.04929i	−0.386115	+	0.922451i	$0.626183\pi$
$654$	0.873434	−	1.51283i	0.0341540	−	0.0591564i
$655$	−1.95060	−	3.37854i	−0.0762164	−	0.132011i
$656$	33.7900			1.31928
$657$	−15.9282	−	27.5885i	−0.621420	−	1.07633i
$658$		0			0
$659$	18.5414	+	32.1146i	0.722270	+	1.25101i	0.960088	+	0.279699i	$0.0902347\pi$
$659$	18.5414	+	32.1146i	0.722270	+	1.25101i	−0.237817	+	0.971310i	$0.576432\pi$
$660$	23.9692	+	41.5159i	0.933000	+	1.61600i
$661$	20.4018			0.793540			0.396770	−	0.917918i	$-0.370131\pi$
$661$	20.4018			0.793540			0.396770	+	0.917918i	$0.370131\pi$
$662$	−0.103382	−	0.179063i	−0.00401806	−	0.00695948i
$663$	12.4932	−	10.7473i	0.485197	−	0.417391i
$664$	−4.23710			−0.164431
$665$		0			0
$666$	−1.44450	+	2.50194i	−0.0559731	+	0.0969483i
$667$	−0.509090			−0.0197120
$668$	18.0042	+	31.1842i	0.696605	+	1.20655i
$669$	37.6235	−	65.1658i	1.45461	−	2.51945i
$670$	−5.25838			−0.203149
$671$	−18.1617			−0.701123
$672$		0			0
$673$	−7.25551	+	12.5669i	−0.279679	+	0.484419i	−0.971305	−	0.237837i	$-0.923562\pi$
$673$	−7.25551	+	12.5669i	−0.279679	+	0.484419i	0.691626	+	0.722256i	$0.256895\pi$
$674$	−1.74350	−	3.01983i	−0.0671571	−	0.116319i
$675$	0.175963	+	0.304777i	0.00677283	+	0.0117309i
$676$	23.5583	−	9.23602i	0.906090	−	0.355231i
$677$	−1.75738	+	3.04388i	−0.0675417	+	0.116986i	−0.897819	−	0.440365i	$-0.854849\pi$
$677$	−1.75738	+	3.04388i	−0.0675417	+	0.116986i	0.830277	+	0.557351i	$0.188182\pi$
$678$	3.65287	−	6.32696i	0.140288	−	0.242985i
$679$		0			0
$680$	1.40148	+	2.42744i	0.0537444	+	0.0930881i
$681$	2.13465	−	3.69732i	0.0817999	−	0.141682i
$682$	0.659151	−	1.14168i	0.0252402	−	0.0437173i
$683$	13.5376	−	23.4479i	0.518003	−	0.897208i	−0.481778	−	0.876293i	$-0.660009\pi$
$683$	13.5376	−	23.4479i	0.518003	−	0.897208i	0.999781	−	0.0209144i	$-0.00665773\pi$
$684$	−25.3074	+	43.8338i	−0.967654	+	1.67603i
$685$	20.0858	+	34.7897i	0.767440	+	1.32925i
$686$		0			0
$687$	−7.71511	+	13.3630i	−0.294350	+	0.509829i
$688$	−2.26675	+	3.92613i	−0.0864190	+	0.149682i
$689$	5.62255	+	29.7457i	0.214202	+	1.13322i
$690$	−0.719062	−	1.24545i	−0.0273742	−	0.0474136i
$691$	14.8702	+	25.7560i	0.565690	+	0.979803i	0.996985	+	0.0775926i	$0.0247233\pi$
$691$	14.8702	+	25.7560i	0.565690	+	0.979803i	−0.431295	+	0.902211i	$0.641943\pi$
$692$	16.7378	−	28.9908i	0.636277	−	1.10206i
$693$		0			0
$694$	−3.79810			−0.144174
$695$	−31.0559			−1.17802
$696$	−0.920856	+	1.59497i	−0.0349049	+	0.0604571i
$697$	−6.31334	−	10.9350i	−0.239135	−	0.414194i
$698$	−7.95237			−0.301002
$699$	−19.7470	+	34.2028i	−0.746900	+	1.29367i
$700$		0			0
$701$	18.2888			0.690760			0.345380	−	0.938463i	$-0.387750\pi$
$701$	18.2888			0.690760			0.345380	+	0.938463i	$0.387750\pi$
$702$	2.59289	+	13.7175i	0.0978622	+	0.517733i
$703$	2.51321	+	4.35301i	0.0947876	+	0.164177i
$704$	−22.4047			−0.844409
$705$	−6.03493	−	10.4528i	−0.227289	−	0.393676i
$706$	−2.76664	−	4.79197i	−0.104124	−	0.180348i
$707$		0			0
$708$	−28.5256	−	49.4078i	−1.07206	−	1.85686i
$709$	−28.6804			−1.07711			−0.538557	−	0.842589i	$-0.681030\pi$
$709$	−28.6804			−1.07711			−0.538557	+	0.842589i	$0.681030\pi$
$710$	1.34594	+	2.33123i	0.0505121	+	0.0874895i
$711$	−25.9225	+	44.8992i	−0.972171	+	1.68385i
$712$	−4.16732	−	7.21801i	−0.156177	−	0.270506i
$713$	0.719062	−	1.24545i	0.0269291	−	0.0466426i
$714$		0			0
$715$	20.2626	−	17.4309i	0.757779	−	0.651880i
$716$	14.1008	−	24.4234i	0.526973	−	0.912744i
$717$	−13.8798			−0.518351
$718$	−1.42952			−0.0533492
$719$	−25.4762			−0.950103			−0.475052	−	0.879958i	$-0.657571\pi$
$719$	−25.4762			−0.950103			−0.475052	+	0.879958i	$0.657571\pi$
$720$	66.0285			2.46074
$721$		0			0
$722$	0.987073	+	1.70966i	0.0367350	+	0.0636270i
$723$	6.70001	−	11.6048i	0.249176	−	0.431586i
$724$	−6.67138	+	11.5552i	−0.247940	+	0.429444i
$725$	0.0127675			0.000474173
$726$	−0.0143598	−	0.0248719i	−0.000532942	−	0.000923083i
$727$	9.02572			0.334746			0.167373	−	0.985894i	$-0.446472\pi$
$727$	9.02572			0.334746			0.167373	+	0.985894i	$0.446472\pi$
$728$		0			0
$729$	86.2759			3.19540
$730$	−1.02309	−	1.77204i	−0.0378663	−	0.0655863i
$731$	1.69408			0.0626579
$732$	−17.6756	+	30.6150i	−0.653309	+	1.13156i
$733$	−3.78535	+	6.55641i	−0.139815	+	0.242167i	−0.927426	−	0.374006i	$-0.877984\pi$
$733$	−3.78535	+	6.55641i	−0.139815	+	0.242167i	0.787612	+	0.616172i	$0.211317\pi$
$734$	2.29695	+	3.97843i	0.0847818	+	0.146846i
$735$		0			0
$736$	2.24544			0.0827681
$737$	−33.8396			−1.24650
$738$	17.0665			0.628225
$739$	−6.37296			−0.234433			−0.117216	−	0.993106i	$-0.537397\pi$
$739$	−6.37296			−0.234433			−0.117216	+	0.993106i	$0.537397\pi$
$740$	3.37389	−	5.84375i	0.124027	−	0.214821i
$741$	36.5772	+	12.8064i	1.34370	+	0.470457i
$742$		0			0
$743$	11.4148	−	19.7711i	0.418770	−	0.725330i	−0.577046	−	0.816711i	$-0.695795\pi$
$743$	11.4148	−	19.7711i	0.418770	−	0.725330i	0.995816	+	0.0913811i	$0.0291281\pi$
$744$	−2.60132	−	4.50562i	−0.0953690	−	0.165184i
$745$	17.7731	−	30.7840i	0.651157	−	1.12784i
$746$	−3.49298	−	6.05002i	−0.127887	−	0.221507i
$747$	37.2978			1.36466
$748$	4.44836	+	7.70479i	0.162648	+	0.281715i
$749$		0			0
$750$	4.30581	+	7.45788i	0.157226	+	0.272323i
$751$	−19.6848	−	34.0950i	−0.718307	−	1.24414i	−0.961670	−	0.274209i	$-0.911584\pi$
$751$	−19.6848	−	34.0950i	−0.718307	−	1.24414i	0.243363	−	0.969935i	$-0.421749\pi$
$752$	5.99443			0.218594
$753$	46.2931	+	80.1821i	1.68702	+	2.92200i
$754$	0.478015	+	0.167363i	0.0174083	+	0.00609500i
$755$	−31.1268			−1.13282
$756$		0			0
$757$	−4.36357	+	7.55792i	−0.158597	+	0.274697i	−0.934363	−	0.356323i	$-0.884030\pi$
$757$	−4.36357	+	7.55792i	−0.158597	+	0.274697i	0.775766	+	0.631020i	$0.217364\pi$
$758$	−1.00004			−0.0363231
$759$	−4.62743	−	8.01494i	−0.167965	−	0.290924i
$760$	−3.29575	+	5.70841i	−0.119550	+	0.207066i
$761$	22.8391			0.827915			0.413958	−	0.910296i	$-0.364146\pi$
$761$	22.8391			0.827915			0.413958	+	0.910296i	$0.364146\pi$
$762$	14.1687			0.513276
$763$		0			0
$764$	−2.77531	+	4.80697i	−0.100407	+	0.173910i
$765$	−12.3368	−	21.3680i	−0.446038	−	0.772561i
$766$	−2.00684	−	3.47595i	−0.0725101	−	0.125591i
$767$	−24.1144	+	20.7445i	−0.870721	+	0.749039i
$768$	−19.7467	+	34.2023i	−0.712548	+	1.23417i
$769$	17.4174	−	30.1679i	0.628089	−	1.08788i	−0.359846	−	0.933012i	$-0.617171\pi$
$769$	17.4174	−	30.1679i	0.628089	−	1.08788i	0.987935	−	0.154871i	$-0.0494960\pi$
$770$		0			0
$771$	−11.8615	−	20.5447i	−0.427182	−	0.739900i
$772$	−9.78150	+	16.9421i	−0.352044	+	0.609758i
$773$	−16.6372	+	28.8164i	−0.598397	+	1.03645i	0.394661	+	0.918827i	$0.370862\pi$
$773$	−16.6372	+	28.8164i	−0.598397	+	1.03645i	−0.993058	+	0.117627i	$0.962471\pi$
$774$	−1.14488	+	1.98299i	−0.0411518	+	0.0712769i
$775$	−0.0180334	+	0.0312348i	−0.000647780	+	0.00112199i
$776$	7.01178	+	12.1448i	0.251708	+	0.435971i
$777$		0			0
$778$	2.93220	−	5.07872i	0.105124	−	0.182081i
$779$	14.8466	−	25.7150i	0.531934	−	0.921336i
$780$	−9.66292	−	51.1210i	−0.345988	−	1.83043i
$781$	8.66158	+	15.0023i	0.309936	+	0.536825i
$782$	−0.133448	−	0.231139i	−0.00477210	−	0.00826553i
$783$	5.08038	−	8.79947i	0.181558	−	0.314467i
$784$		0			0
$785$	28.9512			1.03331
$786$	1.34385			0.0479336
$787$	−13.9079	+	24.0891i	−0.495762	+	0.858685i	−0.999988	−	0.00488682i	$-0.998444\pi$
$787$	−13.9079	+	24.0891i	−0.495762	+	0.858685i	0.504226	+	0.863572i	$0.331778\pi$
$788$	−24.7368	−	42.8455i	−0.881213	−	1.52631i
$789$	70.8278			2.52154
$790$	−1.66504	+	2.88393i	−0.0592393	+	0.102606i
$791$		0			0
$792$	−24.3806			−0.866329
$793$	18.6031	+	6.51333i	0.660615	+	0.231295i
$794$	−3.13204	−	5.42484i	−0.111152	−	0.192521i
$795$	62.2413			2.20747
$796$	12.1134	+	20.9811i	0.429349	+	0.743655i
$797$	17.9343	+	31.0630i	0.635264	+	1.10031i	0.986459	+	0.164007i	$0.0524421\pi$
$797$	17.9343	+	31.0630i	0.635264	+	1.10031i	−0.351195	+	0.936302i	$0.614225\pi$
$798$		0			0
$799$	−1.12000	−	1.93990i	−0.0396228	−	0.0686288i
$800$	−0.0563136			−0.00199099
$801$	36.6836	+	63.5378i	1.29615	+	2.24500i
$802$	3.38779	−	5.86783i	0.119627	−	0.207200i
$803$	−6.58396	−	11.4037i	−0.232343	−	0.402430i
$804$	−32.9339	+	57.0432i	−1.16149	+	2.01176i
$805$		0			0
$806$	−1.08461	+	0.933040i	−0.0382039	+	0.0328649i
$807$	4.63247	−	8.02368i	0.163071	−	0.282447i
$808$	−7.25921			−0.255378
$809$	−17.8245			−0.626675			−0.313337	−	0.949642i	$-0.601447\pi$
$809$	−17.8245			−0.626675			−0.313337	+	0.949642i	$0.601447\pi$
$810$	16.2552			0.571150
$811$	−25.2152			−0.885425			−0.442713	−	0.896664i	$-0.645984\pi$
$811$	−25.2152			−0.885425			−0.442713	+	0.896664i	$0.645984\pi$
$812$		0			0
$813$	−25.7055	−	44.5233i	−0.901532	−	1.56150i
$814$	−0.597084	+	1.03418i	−0.0209278	+	0.0362480i
$815$	−20.5379	+	35.5728i	−0.719413	+	1.24606i
$816$	16.8279			0.589095
$817$	1.99192	+	3.45010i	0.0696884	+	0.120704i
$818$	−5.40719			−0.189058
$819$		0			0
$820$	−39.8619			−1.39204
$821$	5.22797	+	9.05511i	0.182457	+	0.316026i	0.942717	−	0.333594i	$-0.108261\pi$
$821$	5.22797	+	9.05511i	0.182457	+	0.316026i	−0.760259	+	0.649620i	$0.774928\pi$
$822$	−13.8380			−0.482655
$823$	16.6203	−	28.7871i	0.579346	−	1.00346i	−0.416209	−	0.909269i	$-0.636641\pi$
$823$	16.6203	−	28.7871i	0.579346	−	1.00346i	0.995554	−	0.0941873i	$-0.0300253\pi$
$824$	−0.317208	+	0.549420i	−0.0110505	+	0.0191400i
$825$	0.116052	+	0.201007i	0.00404040	+	0.00699817i
$826$		0			0
$827$	−37.9927			−1.32113			−0.660567	−	0.750767i	$-0.729684\pi$
$827$	−37.9927			−1.32113			−0.660567	+	0.750767i	$0.729684\pi$
$828$	−13.1180			−0.455880
$829$	−16.6944			−0.579821			−0.289911	−	0.957054i	$-0.593626\pi$
$829$	−16.6944			−0.579821			−0.289911	+	0.957054i	$0.593626\pi$
$830$	2.39568			0.0831554
$831$	−9.18528	+	15.9094i	−0.318634	+	0.551890i
$832$	22.9493	+	8.03501i	0.795623	+	0.278564i
$833$		0			0
$834$	5.34893	−	9.26462i	0.185218	−	0.320808i
$835$	−20.6394	−	35.7484i	−0.714254	−	1.23712i
$836$	−10.4609	+	18.1187i	−0.361796	+	0.626649i
$837$	14.3515	+	24.8576i	0.496062	+	0.859204i
$838$	−3.37935			−0.116738
$839$	−23.3206	−	40.3924i	−0.805115	−	1.39450i	−0.916213	−	0.400691i	$-0.868770\pi$
$839$	−23.3206	−	40.3924i	−0.805115	−	1.39450i	0.111098	−	0.993809i	$-0.464563\pi$
$840$		0			0
$841$	14.3157	+	24.7955i	0.493644	+	0.855017i
$842$	−1.18837	−	2.05831i	−0.0409538	−	0.0709341i
$843$	−104.608			−3.60290
$844$	−23.7395	−	41.1179i	−0.817146	−	1.41534i
$845$	−27.0064	+	10.5878i	−0.929048	+	0.364232i
$846$	3.02763			0.104092
$847$		0			0
$848$	−15.4559	+	26.7704i	−0.530758	+	0.919299i
$849$	24.4225			0.838178
$850$	0.00334676	+	0.00579676i	0.000114793	+	0.000198827i
$851$	−0.651354	+	1.12818i	−0.0223281	+	0.0386735i
$852$	33.7191			1.15520
$853$	−39.5640			−1.35464			−0.677322	−	0.735686i	$-0.736860\pi$
$853$	−39.5640			−1.35464			−0.677322	+	0.735686i	$0.736860\pi$
$854$		0			0
$855$	29.0115	−	50.2493i	0.992171	−	1.71849i
$856$	4.08433	+	7.07426i	0.139599	+	0.241793i
$857$	−9.78065	−	16.9406i	−0.334101	−	0.578679i	0.649211	−	0.760608i	$-0.275099\pi$
$857$	−9.78065	−	16.9406i	−0.334101	−	0.578679i	−0.983312	+	0.181929i	$0.941766\pi$
$858$	1.71007	+	9.04698i	0.0583807	+	0.308859i
$859$	−5.08158	+	8.80155i	−0.173381	+	0.300305i	−0.939600	−	0.342275i	$-0.888803\pi$
$859$	−5.08158	+	8.80155i	−0.173381	+	0.300305i	0.766219	+	0.642580i	$0.222136\pi$
$860$	2.67407	−	4.63163i	0.0911851	−	0.157937i
$861$		0			0
$862$	1.44621	+	2.50490i	0.0492580	+	0.0853174i
$863$	−13.4451	+	23.2877i	−0.457678	+	0.792722i	−0.998838	−	0.0481982i	$-0.984652\pi$
$863$	−13.4451	+	23.2877i	−0.457678	+	0.792722i	0.541160	+	0.840920i	$0.317985\pi$
$864$	−22.4080	+	38.8118i	−0.762336	+	1.32041i
$865$	−19.1876	+	33.2339i	−0.652398	+	1.12999i
$866$	−1.26638	+	2.19343i	−0.0430333	+	0.0745358i
$867$	25.0950	+	43.4658i	0.852271	+	1.47618i
$868$		0			0
$869$	−10.7151	+	18.5591i	−0.363485	+	0.629575i
$870$	0.520658	−	0.901806i	0.0176519	−	0.0305741i
$871$	34.6621	+	12.1359i	1.17448	+	0.411210i
$872$	−1.03754	−	1.79708i	−0.0351357	−	0.0608568i
$873$	−61.7224	−	106.906i	−2.08899	−	3.61823i
$874$	0.313820	−	0.543552i	0.0106151	−	0.0183859i
$875$		0			0
$876$	−25.6310			−0.865991
$877$	−1.70160			−0.0574590			−0.0287295	−	0.999587i	$-0.509146\pi$
$877$	−1.70160			−0.0574590			−0.0287295	+	0.999587i	$0.509146\pi$
$878$	−2.07275	+	3.59011i	−0.0699520	+	0.121160i
$879$	−22.4809	−	38.9380i	−0.758260	−	1.31335i
$880$	27.2930			0.920046
$881$	−5.65448	+	9.79384i	−0.190504	+	0.329963i	−0.945417	−	0.325862i	$-0.894346\pi$
$881$	−5.65448	+	9.79384i	−0.190504	+	0.329963i	0.754913	+	0.655825i	$0.227679\pi$
$882$		0			0
$883$	−46.9068			−1.57854			−0.789270	−	0.614047i	$-0.789541\pi$
$883$	−46.9068			−1.57854			−0.789270	+	0.614047i	$0.789541\pi$
$884$	−1.79331	−	9.48738i	−0.0603155	−	0.319095i
$885$	32.7006	+	56.6392i	1.09922	+	1.90390i
$886$	6.41318			0.215455
$887$	−1.22346	−	2.11909i	−0.0410797	−	0.0711522i	0.844755	−	0.535154i	$-0.179746\pi$
$887$	−1.22346	−	2.11909i	−0.0410797	−	0.0711522i	−0.885834	+	0.464002i	$0.846413\pi$
$888$	2.35638	+	4.08136i	0.0790748	+	0.136962i
$889$		0			0
$890$	2.35623	+	4.08111i	0.0789810	+	0.136799i
$891$	104.608			3.50451
$892$	−22.0432	−	38.1799i	−0.738060	−	1.27836i
$893$	2.63382	−	4.56191i	0.0881374	−	0.152658i
$894$	6.12233	+	10.6042i	0.204761	+	0.354657i
$895$	−16.1647	+	27.9980i	−0.540325	+	0.935871i
$896$		0			0
$897$	1.86550	+	9.86928i	0.0622872	+	0.329526i
$898$	0.0192006	−	0.0332564i	0.000640732	−	0.00110978i
$899$	1.04132			0.0347298
$900$	0.328986			0.0109662
$901$	11.5511			0.384825
$902$	7.05444			0.234887
$903$		0			0
$904$	−4.33921	−	7.51574i	−0.144320	−	0.249970i
$905$	7.64781	−	13.2464i	0.254222	−	0.440325i
$906$	5.36114	−	9.28576i	0.178112	−	0.308499i
$907$	−41.4165			−1.37521			−0.687607	−	0.726083i	$-0.741339\pi$
$907$	−41.4165			−1.37521			−0.687607	+	0.726083i	$0.741339\pi$
$908$	−1.25067	−	2.16622i	−0.0415048	−	0.0718885i
$909$	63.9004			2.11944
$910$		0			0
$911$	−11.9951			−0.397416			−0.198708	−	0.980059i	$-0.563675\pi$
$911$	−11.9951			−0.397416			−0.198708	+	0.980059i	$0.563675\pi$
$912$	19.7864	+	34.2711i	0.655194	+	1.13483i
$913$	15.4171			0.510231
$914$	−3.67116	+	6.35864i	−0.121431	+	0.210325i
$915$	20.2626	−	35.0959i	0.669862	−	1.16023i
$916$	4.52020	+	7.82922i	0.149352	+	0.258685i
$917$		0			0
$918$	5.32691			0.175814
$919$	44.9416			1.48249			0.741243	−	0.671237i	$-0.234237\pi$
$919$	44.9416			1.48249			0.741243	+	0.671237i	$0.234237\pi$
$920$	−1.70833			−0.0563221
$921$	10.9837			0.361924
$922$	3.36232	−	5.82370i	0.110732	−	0.191793i
$923$	−3.49182	−	18.4732i	−0.114935	−	0.608054i
$924$		0			0
$925$	0.0163354	−	0.0282937i	0.000537103	−	0.000930290i
$926$	−0.730990	−	1.26611i	−0.0240218	−	0.0416070i
$927$	2.79228	−	4.83637i	0.0917105	−	0.158847i
$928$	0.812938	+	1.40805i	0.0266860	+	0.0462215i
$929$	−28.2595			−0.927164			−0.463582	−	0.886054i	$-0.653436\pi$
$929$	−28.2595			−0.927164			−0.463582	+	0.886054i	$0.653436\pi$
$930$	1.47080	+	2.54751i	0.0482295	+	0.0835360i
$931$		0			0
$932$	11.5696	+	20.0391i	0.378973	+	0.656401i
$933$	−56.9870	−	98.7044i	−1.86567	−	3.23144i
$934$	8.01455			0.262244
$935$	−5.09943	−	8.83247i	−0.166769	−	0.288853i
$936$	24.9732	+	8.74364i	0.816276	+	0.285795i
$937$	−32.4601			−1.06042			−0.530212	−	0.847865i	$-0.677888\pi$
$937$	−32.4601			−1.06042			−0.530212	+	0.847865i	$0.677888\pi$
$938$		0			0
$939$	11.9838	−	20.7566i	0.391078	−	0.677366i
$940$	−7.07160			−0.230650
$941$	−6.30253	−	10.9163i	−0.205457	−	0.355861i	0.744822	−	0.667264i	$-0.232535\pi$
$941$	−6.30253	−	10.9163i	−0.205457	−	0.355861i	−0.950278	+	0.311402i	$0.899201\pi$
$942$	−4.98642	+	8.63673i	−0.162466	+	0.281400i
$943$	7.69563			0.250604
$944$	−32.4812			−1.05717
$945$		0			0
$946$	−0.473236	+	0.819669i	−0.0153862	+	0.0266497i
$947$	6.64010	+	11.5010i	0.215774	+	0.373732i	0.953512	−	0.301356i	$-0.0974392\pi$
$947$	6.64010	+	11.5010i	0.215774	+	0.373732i	−0.737738	+	0.675088i	$0.764106\pi$
$948$	20.8567	+	36.1248i	0.677393	+	1.17328i
$949$	2.65425	+	14.0421i	0.0861607	+	0.455827i
$950$	−0.00787031	+	0.0136318i	−0.000255347	+	0.000442273i
$951$	13.3561	−	23.1335i	0.433102	−	0.750155i
$952$		0			0
$953$	29.2159	+	50.6035i	0.946397	+	1.63921i	0.752930	+	0.658101i	$0.228640\pi$
$953$	29.2159	+	50.6035i	0.946397	+	1.63921i	0.193467	+	0.981107i	$0.438027\pi$
$954$	−7.80637	+	13.5210i	−0.252741	+	0.437760i
$955$	3.18151	−	5.51053i	0.102951	−	0.178317i
$956$	−4.06602	+	7.04255i	−0.131504	+	0.227772i
$957$	3.35062	−	5.80345i	0.108310	−	0.187599i
$958$	−0.826224	−	1.43106i	−0.0266941	−	0.0462355i
$959$		0			0
$960$	24.9965	−	43.2952i	0.806759	−	1.39735i
$961$	14.0292	−	24.2993i	0.452555	−	0.783848i
$962$	0.982485	−	0.845184i	0.0316766	−	0.0272498i
$963$	−35.9530	−	62.2725i	−1.15857	−	2.00670i
$964$	−3.92546	−	6.79910i	−0.126431	−	0.218984i
$965$	11.2131	−	19.4217i	0.360964	−	0.625207i
$966$		0			0
$967$	33.2182			1.06823			0.534113	−	0.845413i	$-0.320646\pi$
$967$	33.2182			1.06823			0.534113	+	0.845413i	$0.320646\pi$
$968$	−0.0341157			−0.00109652
$969$	7.39381	−	12.8064i	0.237523	−	0.411402i
$970$	−3.96451	−	6.86673i	−0.127293	−	0.220477i
$971$	−16.7778			−0.538425			−0.269213	−	0.963081i	$-0.586763\pi$
$971$	−16.7778			−0.538425			−0.269213	+	0.963081i	$0.586763\pi$
$972$	52.9460	−	91.7052i	1.69824	−	2.94144i
$973$		0			0
$974$	−4.28023			−0.137148
$975$	−0.0467850	−	0.247512i	−0.00149832	−	0.00792674i
$976$	10.0633	+	17.4302i	0.322119	+	0.557927i
$977$	−50.0422			−1.60099			−0.800496	−	0.599338i	$-0.795431\pi$
$977$	−50.0422			−1.60099			−0.800496	+	0.599338i	$0.795431\pi$
$978$	−7.07473	−	12.2538i	−0.226225	−	0.391833i
$979$	15.1632	+	26.2634i	0.484618	+	0.839382i
$980$		0			0
$981$	9.13316	+	15.8191i	0.291599	+	0.505065i
$982$	−3.53475			−0.112798
$983$	8.33707	+	14.4402i	0.265911	+	0.460572i	0.967802	−	0.251713i	$-0.0809939\pi$
$983$	8.33707	+	14.4402i	0.265911	+	0.460572i	−0.701891	+	0.712285i	$0.747661\pi$
$984$	13.9201	−	24.1103i	0.443756	−	0.768608i
$985$	28.3574	+	49.1164i	0.903540	+	1.56498i
$986$	0.0966271	−	0.167363i	0.00307723	−	0.00532993i
$987$		0			0
$988$	17.2130	−	14.8075i	0.547620	−	0.471090i
$989$	−0.516249	+	0.894170i	−0.0164158	+	0.0284330i
$990$	13.7850			0.438115
$991$	20.3285			0.645756			0.322878	−	0.946441i	$-0.395350\pi$
$991$	20.3285			0.645756			0.322878	+	0.946441i	$0.395350\pi$
$992$	−4.59293			−0.145826
$993$	2.96905			0.0942201
$994$		0			0
$995$	−13.8864	−	24.0519i	−0.440228	−	0.762497i
$996$	15.0045	−	25.9885i	0.475435	−	0.823478i
$997$	3.13823	−	5.43557i	0.0993887	−	0.172146i	−0.812043	−	0.583597i	$-0.801645\pi$
$997$	3.13823	−	5.43557i	0.0993887	−	0.172146i	0.911432	+	0.411451i	$0.134978\pi$
$998$	2.88699			0.0913862
$999$	−13.0002	−	22.5170i	−0.411307	−	0.712405i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.g.j.373.2		8
7.2	even	3		637.2.f.i.295.2		8
7.3	odd	6		637.2.h.h.165.3		8
7.4	even	3		637.2.h.i.165.3		8
7.5	odd	6		91.2.f.c.22.2	✓	8
7.6	odd	2		637.2.g.k.373.2		8
13.3	even	3		637.2.h.i.471.3		8
21.5	even	6		819.2.o.h.568.3		8
28.19	even	6		1456.2.s.q.113.1		8
91.3	odd	6		637.2.g.k.263.2		8
91.9	even	3		8281.2.a.bp.1.3		4
91.16	even	3		637.2.f.i.393.2		8
91.19	even	12		1183.2.c.g.337.4		8
91.30	even	6		8281.2.a.bt.1.2		4
91.33	even	12		1183.2.c.g.337.5		8
91.55	odd	6		637.2.h.h.471.3		8
91.61	odd	6		1183.2.a.k.1.3		4
91.68	odd	6		91.2.f.c.29.2	yes	8
91.81	even	3	inner	637.2.g.j.263.2		8
91.82	odd	6		1183.2.a.l.1.2		4
273.68	even	6		819.2.o.h.757.3		8
364.159	even	6		1456.2.s.q.1121.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.2	✓	8	7.5	odd	6
91.2.f.c.29.2	yes	8	91.68	odd	6
637.2.f.i.295.2		8	7.2	even	3
637.2.f.i.393.2		8	91.16	even	3
637.2.g.j.263.2		8	91.81	even	3	inner
637.2.g.j.373.2		8	1.1	even	1	trivial
637.2.g.k.263.2		8	91.3	odd	6
637.2.g.k.373.2		8	7.6	odd	2
637.2.h.h.165.3		8	7.3	odd	6
637.2.h.h.471.3		8	91.55	odd	6
637.2.h.i.165.3		8	7.4	even	3
637.2.h.i.471.3		8	13.3	even	3
819.2.o.h.568.3		8	21.5	even	6
819.2.o.h.757.3		8	273.68	even	6
1183.2.a.k.1.3		4	91.61	odd	6
1183.2.a.l.1.2		4	91.82	odd	6
1183.2.c.g.337.4		8	91.19	even	12
1183.2.c.g.337.5		8	91.33	even	12
1456.2.s.q.113.1		8	28.19	even	6
1456.2.s.q.1121.1		8	364.159	even	6
8281.2.a.bp.1.3		4	91.9	even	3
8281.2.a.bt.1.2		4	91.30	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.115680 - 0.200364i) q^{2} +3.32225 q^{3} +(0.973236 - 1.68569i) q^{4} +(-1.11568 + 1.93242i) q^{5} +(-0.384320 - 0.665661i) q^{6} -0.913059 q^{8} +8.03736 q^{9} +O(q^{10})\)	\(q+(-0.115680 - 0.200364i) q^{2} +3.32225 q^{3} +(0.973236 - 1.68569i) q^{4} +(-1.11568 + 1.93242i) q^{5} +(-0.384320 - 0.665661i) q^{6} -0.913059 q^{8} +8.03736 q^{9} +0.516249 q^{10} +3.32225 q^{11} +(3.23334 - 5.60030i) q^{12} +(-3.40300 - 1.19146i) q^{13} +(-3.70657 + 6.41997i) q^{15} +(-1.84085 - 3.18844i) q^{16} +(-0.687890 + 1.19146i) q^{17} +(-0.929766 - 1.61040i) q^{18} -3.23531 q^{19} +(2.17164 + 3.76139i) q^{20} +(-0.384320 - 0.665661i) q^{22} +(-0.419251 - 0.726164i) q^{23} -3.03341 q^{24} +(0.0105144 + 0.0182115i) q^{25} +(0.154934 + 0.819669i) q^{26} +16.7354 q^{27} +(0.303571 - 0.525800i) q^{29} +1.71511 q^{30} +(0.857556 + 1.48533i) q^{31} +(-1.33896 + 2.31915i) q^{32} +11.0374 q^{33} +0.318302 q^{34} +(7.82225 - 13.5485i) q^{36} +(-0.776807 - 1.34547i) q^{37} +(0.374262 + 0.648241i) q^{38} +(-11.3056 - 3.95833i) q^{39} +(1.01868 - 1.76441i) q^{40} +(-4.58892 + 7.94824i) q^{41} +(-0.615680 - 1.06639i) q^{43} +(3.23334 - 5.60030i) q^{44} +(-8.96713 + 15.5315i) q^{45} +(-0.0969983 + 0.168006i) q^{46} +(-0.814085 + 1.41004i) q^{47} +(-6.11577 - 10.5928i) q^{48} +(0.00243263 - 0.00421343i) q^{50} +(-2.28535 + 3.95833i) q^{51} +(-5.32036 + 4.57685i) q^{52} +(-4.19803 - 7.27121i) q^{53} +(-1.93596 - 3.35318i) q^{54} +(-3.70657 + 6.41997i) q^{55} -10.7485 q^{57} -0.140469 q^{58} +(4.41117 - 7.64037i) q^{59} +(7.21474 + 12.4963i) q^{60} -5.46667 q^{61} +(0.198405 - 0.343647i) q^{62} -6.74383 q^{64} +(6.09906 - 5.24672i) q^{65} +(-1.27681 - 2.21149i) q^{66} -10.1857 q^{67} +(1.33896 + 2.31915i) q^{68} +(-1.39286 - 2.41250i) q^{69} +(2.60714 + 4.51570i) q^{71} -7.33859 q^{72} +(-1.98177 - 3.43253i) q^{73} +(-0.179723 + 0.311289i) q^{74} +(0.0349316 + 0.0605033i) q^{75} +(-3.14872 + 5.45375i) q^{76} +(0.514731 + 2.72315i) q^{78} +(-3.22525 + 5.58630i) q^{79} +8.21520 q^{80} +31.4871 q^{81} +2.12339 q^{82} +4.64055 q^{83} +(-1.53493 - 2.65858i) q^{85} +(-0.142444 + 0.246721i) q^{86} +(1.00854 - 1.74684i) q^{87} -3.03341 q^{88} +(4.56413 + 7.90530i) q^{89} +4.14929 q^{90} -1.63212 q^{92} +(2.84902 + 4.93464i) q^{93} +0.376695 q^{94} +(3.60957 - 6.25197i) q^{95} +(-4.44836 + 7.70479i) q^{96} +(-7.67944 - 13.3012i) q^{97} +26.7022 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 2 q^{3} - 5 q^{4} - 7 q^{5} - 5 q^{6} - 12 q^{8} + 14 q^{9}+O(q^{10}) \) 8 * q + q^2 - 2 * q^3 - 5 * q^4 - 7 * q^5 - 5 * q^6 - 12 * q^8 + 14 * q^9	\( 8 q + q^{2} - 2 q^{3} - 5 q^{4} - 7 q^{5} - 5 q^{6} - 12 q^{8} + 14 q^{9} + 22 q^{10} - 2 q^{11} + 12 q^{12} - 4 q^{13} - 3 q^{15} - 19 q^{16} - 4 q^{17} + 3 q^{18} - 2 q^{19} - 2 q^{20} - 5 q^{22} + 2 q^{23} + 6 q^{24} - 5 q^{25} - 3 q^{26} + 52 q^{27} - q^{29} - 8 q^{30} - 4 q^{31} + 33 q^{32} + 38 q^{33} - 6 q^{34} + 34 q^{36} + 10 q^{37} - 23 q^{38} - 19 q^{39} - 17 q^{40} - 22 q^{41} - 3 q^{43} + 12 q^{44} - 11 q^{45} - 24 q^{46} + 2 q^{47} + 11 q^{48} - 43 q^{50} - 7 q^{51} + 34 q^{52} - 2 q^{53} + 5 q^{54} - 3 q^{55} - 34 q^{57} - 22 q^{58} - 8 q^{59} + 11 q^{60} - 16 q^{61} - 5 q^{62} + 28 q^{64} + 4 q^{65} + 6 q^{66} - 12 q^{67} - 33 q^{68} - 18 q^{69} + 14 q^{71} + 10 q^{72} - 8 q^{73} - 20 q^{74} - 7 q^{75} + 32 q^{76} - q^{78} + 26 q^{79} - 14 q^{80} + 48 q^{81} + 28 q^{82} - 5 q^{85} - 12 q^{86} + 13 q^{87} + 6 q^{88} - q^{89} - 52 q^{90} + 24 q^{92} + 7 q^{93} - 66 q^{94} - 21 q^{95} - 58 q^{96} + 3 q^{97} + 46 q^{99}+O(q^{100}) \) 8 * q + q^2 - 2 * q^3 - 5 * q^4 - 7 * q^5 - 5 * q^6 - 12 * q^8 + 14 * q^9 + 22 * q^10 - 2 * q^11 + 12 * q^12 - 4 * q^13 - 3 * q^15 - 19 * q^16 - 4 * q^17 + 3 * q^18 - 2 * q^19 - 2 * q^20 - 5 * q^22 + 2 * q^23 + 6 * q^24 - 5 * q^25 - 3 * q^26 + 52 * q^27 - q^29 - 8 * q^30 - 4 * q^31 + 33 * q^32 + 38 * q^33 - 6 * q^34 + 34 * q^36 + 10 * q^37 - 23 * q^38 - 19 * q^39 - 17 * q^40 - 22 * q^41 - 3 * q^43 + 12 * q^44 - 11 * q^45 - 24 * q^46 + 2 * q^47 + 11 * q^48 - 43 * q^50 - 7 * q^51 + 34 * q^52 - 2 * q^53 + 5 * q^54 - 3 * q^55 - 34 * q^57 - 22 * q^58 - 8 * q^59 + 11 * q^60 - 16 * q^61 - 5 * q^62 + 28 * q^64 + 4 * q^65 + 6 * q^66 - 12 * q^67 - 33 * q^68 - 18 * q^69 + 14 * q^71 + 10 * q^72 - 8 * q^73 - 20 * q^74 - 7 * q^75 + 32 * q^76 - q^78 + 26 * q^79 - 14 * q^80 + 48 * q^81 + 28 * q^82 - 5 * q^85 - 12 * q^86 + 13 * q^87 + 6 * q^88 - q^89 - 52 * q^90 + 24 * q^92 + 7 * q^93 - 66 * q^94 - 21 * q^95 - 58 * q^96 + 3 * q^97 + 46 * q^99

Introduction

L-functions

Modular forms

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