LMFDB - Embedded newform 637.2.h.l.165.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(165,637)]

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, 4]))

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

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

chi := DirichletCharacter("637.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.h (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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + 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			165.1
Root			$-0.181721 + 0.314749i$ of defining polynomial
Character	$\chi$	$=$	637.165
Dual form			637.2.h.l.471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38804 q^{2} +(-1.37574 - 2.38285i) q^{3} +3.70272 q^{4} +(0.491140 + 0.850679i) q^{5} +(3.28532 + 5.69033i) q^{6} -4.06616 q^{8} +(-2.28532 + 3.95828i) q^{9} +O(q^{10})$	\(q-2.38804 q^{2} +(-1.37574 - 2.38285i) q^{3} +3.70272 q^{4} +(0.491140 + 0.850679i) q^{5} +(3.28532 + 5.69033i) q^{6} -4.06616 q^{8} +(-2.28532 + 3.95828i) q^{9} +(-1.17286 - 2.03145i) q^{10} +(0.293901 + 0.509052i) q^{11} +(-5.09398 - 8.82303i) q^{12} +(-2.39227 - 2.69760i) q^{13} +(1.35136 - 2.34063i) q^{15} +2.30470 q^{16} +6.45420 q^{17} +(5.45742 - 9.45253i) q^{18} +(-1.91345 + 3.31419i) q^{19} +(1.81855 + 3.14983i) q^{20} +(-0.701847 - 1.21563i) q^{22} +8.26001 q^{23} +(5.59398 + 9.68906i) q^{24} +(2.01756 - 3.49452i) q^{25} +(5.71283 + 6.44197i) q^{26} +4.32156 q^{27} +(1.98009 - 3.42962i) q^{29} +(-3.22710 + 5.58950i) q^{30} +(-1.49436 + 2.58831i) q^{31} +2.62861 q^{32} +(0.808663 - 1.40065i) q^{33} -15.4129 q^{34} +(-8.46189 + 14.6564i) q^{36} +1.75588 q^{37} +(4.56938 - 7.91440i) q^{38} +(-3.13683 + 9.41161i) q^{39} +(-1.99705 - 3.45900i) q^{40} +(1.83584 - 3.17977i) q^{41} +(-3.19042 - 5.52598i) q^{43} +(1.08823 + 1.88488i) q^{44} -4.48964 q^{45} -19.7252 q^{46} +(-2.17030 - 3.75906i) q^{47} +(-3.17067 - 5.49176i) q^{48} +(-4.81802 + 8.34505i) q^{50} +(-8.87930 - 15.3794i) q^{51} +(-8.85791 - 9.98846i) q^{52} +(-0.212770 + 0.368529i) q^{53} -10.3200 q^{54} +(-0.288693 + 0.500031i) q^{55} +10.5296 q^{57} +(-4.72853 + 8.19006i) q^{58} -6.00863 q^{59} +(5.00371 - 8.66669i) q^{60} +(1.10337 - 1.91109i) q^{61} +(3.56859 - 6.18097i) q^{62} -10.8866 q^{64} +(1.11985 - 3.35995i) q^{65} +(-1.93112 + 3.34479i) q^{66} +(-3.50651 - 6.07346i) q^{67} +23.8981 q^{68} +(-11.3636 - 19.6824i) q^{69} +(-1.80127 - 3.11988i) q^{71} +(9.29247 - 16.0950i) q^{72} +(2.46714 - 4.27321i) q^{73} -4.19311 q^{74} -11.1026 q^{75} +(-7.08496 + 12.2715i) q^{76} +(7.49088 - 22.4753i) q^{78} +(-1.39270 - 2.41223i) q^{79} +(1.13193 + 1.96056i) q^{80} +(0.910609 + 1.57722i) q^{81} +(-4.38406 + 7.59342i) q^{82} +2.86819 q^{83} +(3.16992 + 5.49045i) q^{85} +(7.61885 + 13.1962i) q^{86} -10.8964 q^{87} +(-1.19505 - 2.06989i) q^{88} +2.09311 q^{89} +10.7214 q^{90} +30.5845 q^{92} +8.22340 q^{93} +(5.18275 + 8.97679i) q^{94} -3.75908 q^{95} +(-3.61628 - 6.26357i) q^{96} +(3.84852 + 6.66584i) q^{97} -2.68663 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9	$ 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} - 16 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + q^{20} - 5 q^{22} + 2 q^{23} + 11 q^{24} + 7 q^{25} + 16 q^{26} + 8 q^{27} + 3 q^{29} - 5 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 32 q^{34} - 21 q^{36} + 26 q^{37} + 17 q^{38} - 20 q^{39} + 5 q^{40} + 8 q^{41} - 11 q^{43} + 21 q^{44} - 14 q^{45} - 32 q^{46} + q^{47} - 21 q^{48} + 6 q^{50} - 20 q^{51} - 41 q^{52} - 2 q^{53} - 36 q^{54} - 9 q^{55} + 42 q^{57} - 8 q^{58} + 26 q^{59} + 20 q^{60} + 5 q^{61} - 5 q^{62} - 30 q^{64} - 5 q^{65} - 18 q^{66} - 11 q^{67} + 58 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} + 30 q^{73} + 6 q^{74} - 6 q^{75} + 9 q^{76} + 16 q^{78} + 7 q^{79} + 7 q^{80} - 6 q^{81} - q^{82} + 54 q^{83} - q^{85} - 7 q^{86} + 32 q^{87} + 8 q^{89} + 16 q^{90} + 54 q^{92} + 14 q^{93} - 45 q^{94} + 12 q^{95} - 19 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 - 16 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + q^20 - 5 * q^22 + 2 * q^23 + 11 * q^24 + 7 * q^25 + 16 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 + 26 * q^37 + 17 * q^38 - 20 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 - 14 * q^45 - 32 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 - 41 * q^52 - 2 * q^53 - 36 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 + 26 * q^59 + 20 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 5 * q^65 - 18 * q^66 - 11 * q^67 + 58 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 + 30 * q^73 + 6 * q^74 - 6 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 - 7 * q^86 + 32 * q^87 + 8 * q^89 + 16 * q^90 + 54 * q^92 + 14 * q^93 - 45 * q^94 + 12 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−2.38804			−1.68860			−0.844299	−	0.535873i	$-0.819983\pi$
$2$	−2.38804			−1.68860			−0.844299	+	0.535873i	$0.819983\pi$
$3$	−1.37574	−	2.38285i	−0.794283	−	1.37574i	−0.923293	−	0.384096i	$-0.874513\pi$
$3$	−1.37574	−	2.38285i	−0.794283	−	1.37574i	0.129010	−	0.991643i	$-0.458820\pi$
$4$	3.70272			1.85136
$5$	0.491140	+	0.850679i	0.219644	+	0.380435i	0.954699	−	0.297572i	$-0.0961769\pi$
$5$	0.491140	+	0.850679i	0.219644	+	0.380435i	−0.735055	+	0.678008i	$0.762844\pi$
$6$	3.28532	+	5.69033i	1.34122	+	2.32307i
$7$		0			0
$7$		0			0
$8$	−4.06616			−1.43761
$9$	−2.28532	+	3.95828i	−0.761772	+	1.31943i
$10$	−1.17286	−	2.03145i	−0.370891	−	0.642402i
$11$	0.293901	+	0.509052i	0.0886146	+	0.153485i	0.906926	−	0.421291i	$-0.138423\pi$
$11$	0.293901	+	0.509052i	0.0886146	+	0.153485i	−0.818311	+	0.574775i	$0.805089\pi$
$12$	−5.09398	−	8.82303i	−1.47051	−	2.54699i
$13$	−2.39227	−	2.69760i	−0.663496	−	0.748179i
$13$	−2.39227	−	2.69760i	−0.663496	−	0.748179i
$14$		0			0
$15$	1.35136	−	2.34063i	0.348920	−	0.604347i
$16$	2.30470			0.576176
$17$	6.45420			1.56537			0.782687	−	0.622416i	$-0.213849\pi$
$17$	6.45420			1.56537			0.782687	+	0.622416i	$0.213849\pi$
$18$	5.45742	−	9.45253i	1.28633	−	2.22798i
$19$	−1.91345	+	3.31419i	−0.438975	+	0.760327i	−0.997611	−	0.0690863i	$-0.977992\pi$
$19$	−1.91345	+	3.31419i	−0.438975	+	0.760327i	0.558636	+	0.829413i	$0.311325\pi$
$20$	1.81855	+	3.14983i	0.406641	+	0.704323i
$21$		0			0
$22$	−0.701847	−	1.21563i	−0.149634	−	0.259174i
$23$	8.26001			1.72233			0.861166	−	0.508324i	$-0.169735\pi$
$23$	8.26001			1.72233			0.861166	+	0.508324i	$0.169735\pi$
$24$	5.59398	+	9.68906i	1.14187	+	1.97777i
$25$	2.01756	−	3.49452i	0.403513	−	0.698904i
$26$	5.71283	+	6.44197i	1.12038	+	1.26337i
$27$	4.32156			0.831685
$28$		0			0
$29$	1.98009	−	3.42962i	0.367694	−	0.636864i	−0.621511	−	0.783406i	$-0.713481\pi$
$29$	1.98009	−	3.42962i	0.367694	−	0.636864i	0.989205	+	0.146541i	$0.0468141\pi$
$30$	−3.22710	+	5.58950i	−0.589185	+	1.02050i
$31$	−1.49436	+	2.58831i	−0.268395	+	0.464874i	−0.968448	−	0.249218i	$-0.919827\pi$
$31$	−1.49436	+	2.58831i	−0.268395	+	0.464874i	0.700053	+	0.714091i	$0.253160\pi$
$32$	2.62861			0.464676
$33$	0.808663	−	1.40065i	0.140770	−	0.243821i
$34$	−15.4129			−2.64329
$35$		0			0
$36$	−8.46189	+	14.6564i	−1.41031	+	2.44274i
$37$	1.75588			0.288665			0.144333	−	0.989529i	$-0.453896\pi$
$37$	1.75588			0.288665			0.144333	+	0.989529i	$0.453896\pi$
$38$	4.56938	−	7.91440i	0.741252	−	1.28389i
$39$	−3.13683	+	9.41161i	−0.502295	+	1.50706i
$40$	−1.99705	−	3.45900i	−0.315762	−	0.546916i
$41$	1.83584	−	3.17977i	0.286710	−	0.496597i	−0.686312	−	0.727307i	$-0.740772\pi$
$41$	1.83584	−	3.17977i	0.286710	−	0.496597i	0.973023	+	0.230710i	$0.0741049\pi$
$42$		0			0
$43$	−3.19042	−	5.52598i	−0.486535	−	0.842703i	0.513345	−	0.858182i	$-0.328406\pi$
$43$	−3.19042	−	5.52598i	−0.486535	−	0.842703i	−0.999880	+	0.0154788i	$0.995073\pi$
$44$	1.08823	+	1.88488i	0.164058	+	0.284156i
$45$	−4.48964			−0.669276
$46$	−19.7252			−2.90832
$47$	−2.17030	−	3.75906i	−0.316570	−	0.548316i	0.663200	−	0.748442i	$-0.269198\pi$
$47$	−2.17030	−	3.75906i	−0.316570	−	0.548316i	−0.979770	+	0.200127i	$0.935865\pi$
$48$	−3.17067	−	5.49176i	−0.457647	−	0.792668i
$49$		0			0
$50$	−4.81802	+	8.34505i	−0.681370	+	1.18017i
$51$	−8.87930	−	15.3794i	−1.24335	−	2.15355i
$52$	−8.85791	−	9.98846i	−1.22837	−	1.38515i
$53$	−0.212770	+	0.368529i	−0.0292263	+	0.0506214i	−0.880269	−	0.474476i	$-0.842638\pi$
$53$	−0.212770	+	0.368529i	−0.0292263	+	0.0506214i	0.851042	+	0.525097i	$0.175971\pi$
$54$	−10.3200			−1.40438
$55$	−0.288693	+	0.500031i	−0.0389274	+	0.0674242i
$56$		0			0
$57$	10.5296			1.39468
$58$	−4.72853	+	8.19006i	−0.620887	+	1.07541i
$59$	−6.00863			−0.782256			−0.391128	−	0.920336i	$-0.627915\pi$
$59$	−6.00863			−0.782256			−0.391128	+	0.920336i	$0.627915\pi$
$60$	5.00371	−	8.66669i	0.645977	−	1.11886i
$61$	1.10337	−	1.91109i	0.141272	−	0.244691i	−0.786704	−	0.617331i	$-0.788214\pi$
$61$	1.10337	−	1.91109i	0.141272	−	0.244691i	0.927976	+	0.372640i	$0.121547\pi$
$62$	3.56859	−	6.18097i	0.453211	−	0.784985i
$63$		0			0
$64$	−10.8866			−1.36083
$65$	1.11985	−	3.35995i	0.138901	−	0.416751i
$66$	−1.93112	+	3.34479i	−0.237704	+	0.411716i
$67$	−3.50651	−	6.07346i	−0.428389	−	0.741991i	0.568341	−	0.822793i	$-0.307585\pi$
$67$	−3.50651	−	6.07346i	−0.428389	−	0.741991i	−0.996730	+	0.0808015i	$0.974252\pi$
$68$	23.8981			2.89807
$69$	−11.3636	−	19.6824i	−1.36802	−	2.36948i
$70$		0			0
$71$	−1.80127	−	3.11988i	−0.213771	−	0.370262i	0.739121	−	0.673573i	$-0.235241\pi$
$71$	−1.80127	−	3.11988i	−0.213771	−	0.370262i	−0.952892	+	0.303311i	$0.901908\pi$
$72$	9.29247	−	16.0950i	1.09513	−	1.89682i
$73$	2.46714	−	4.27321i	0.288756	−	0.500141i	−0.684757	−	0.728772i	$-0.740092\pi$
$73$	2.46714	−	4.27321i	0.288756	−	0.500141i	0.973513	+	0.228631i	$0.0734249\pi$
$74$	−4.19311			−0.487439
$75$	−11.1026			−1.28201
$76$	−7.08496	+	12.2715i	−0.812701	+	1.40764i
$77$		0			0
$78$	7.49088	−	22.4753i	0.848175	−	2.54483i
$79$	−1.39270	−	2.41223i	−0.156691	−	0.271397i	0.776982	−	0.629522i	$-0.216749\pi$
$79$	−1.39270	−	2.41223i	−0.156691	−	0.271397i	−0.933674	+	0.358125i	$0.883416\pi$
$80$	1.13193	+	1.96056i	0.126554	+	0.219198i
$81$	0.910609	+	1.57722i	0.101179	+	0.175247i
$82$	−4.38406	+	7.59342i	−0.484138	+	0.838552i
$83$	2.86819			0.314825			0.157412	−	0.987533i	$-0.449685\pi$
$83$	2.86819			0.314825			0.157412	+	0.987533i	$0.449685\pi$
$84$		0			0
$85$	3.16992	+	5.49045i	0.343826	+	0.595523i
$86$	7.61885	+	13.1962i	0.821562	+	1.42299i
$87$	−10.8964			−1.16821
$88$	−1.19505	−	2.06989i	−0.127393	−	0.220651i
$89$	2.09311			0.221870			0.110935	−	0.993828i	$-0.464616\pi$
$89$	2.09311			0.221870			0.110935	+	0.993828i	$0.464616\pi$
$90$	10.7214			1.13014
$91$		0			0
$92$	30.5845			3.18866
$93$	8.22340			0.852727
$94$	5.18275	+	8.97679i	0.534560	+	0.925885i
$95$	−3.75908			−0.385674
$96$	−3.61628	−	6.26357i	−0.369085	−	0.639273i
$97$	3.84852	+	6.66584i	0.390758	+	0.676813i	0.992550	−	0.121840i	$-0.0388795\pi$
$97$	3.84852	+	6.66584i	0.390758	+	0.676813i	−0.601791	+	0.798653i	$0.705546\pi$
$98$		0			0
$99$	−2.68663			−0.270016
$100$	7.47047	−	12.9392i	0.747047	−	1.29392i
$101$	−1.31866	−	2.28399i	−0.131212	−	0.227265i	0.792932	−	0.609310i	$-0.208553\pi$
$101$	−1.31866	−	2.28399i	−0.131212	−	0.227265i	−0.924144	+	0.382045i	$0.875220\pi$
$102$	21.2041	+	36.7266i	2.09952	+	3.63647i
$103$	−5.43095	−	9.40669i	−0.535128	−	0.926868i	−0.999157	−	0.0410486i	$-0.986930\pi$
$103$	−5.43095	−	9.40669i	−0.535128	−	0.926868i	0.464029	−	0.885820i	$-0.346403\pi$
$104$	9.72736	+	10.9689i	0.953846	+	1.07559i
$105$		0			0
$106$	0.508103	−	0.880061i	0.0493514	−	0.0854791i
$107$	−15.9805			−1.54489			−0.772446	−	0.635080i	$-0.780967\pi$
$107$	−15.9805			−1.54489			−0.772446	+	0.635080i	$0.780967\pi$
$108$	16.0015			1.53975
$109$	−4.61738	+	7.99754i	−0.442265	+	0.766026i	−0.997857	−	0.0654294i	$-0.979158\pi$
$109$	−4.61738	+	7.99754i	−0.442265	+	0.766026i	0.555592	+	0.831455i	$0.312492\pi$
$110$	0.689410	−	1.19409i	0.0657327	−	0.113852i
$111$	−2.41564	−	4.18400i	−0.229282	−	0.397128i
$112$		0			0
$113$	−5.09012	−	8.81635i	−0.478838	−	0.829372i	0.520867	−	0.853638i	$-0.325609\pi$
$113$	−5.09012	−	8.81635i	−0.478838	−	0.829372i	−0.999706	+	0.0242655i	$0.992275\pi$
$114$	−25.1451			−2.35506
$115$	4.05682	+	7.02662i	0.378301	+	0.655236i
$116$	7.33173	−	12.6989i	0.680734	−	1.17907i
$117$	16.1450	−	3.30442i	1.49260	−	0.305494i
$118$	14.3488			1.32092
$119$		0			0
$120$	−5.49485	+	9.51736i	−0.501609	+	0.868813i
$121$	5.32724	−	9.22706i	0.484295	−	0.838823i
$122$	−2.63489	+	4.56376i	−0.238552	+	0.413184i
$123$	−10.1026			−0.910917
$124$	−5.53320	+	9.58378i	−0.496896	+	0.860649i
$125$	8.87502			0.793806
$126$		0			0
$127$	−2.12513	+	3.68083i	−0.188575	+	0.326621i	−0.944775	−	0.327719i	$-0.893720\pi$
$127$	−2.12513	+	3.68083i	−0.188575	+	0.326621i	0.756201	+	0.654340i	$0.227053\pi$
$128$	20.7404			1.83321
$129$	−8.77838	+	15.2046i	−0.772893	+	1.33869i
$130$	−2.67425	+	8.02369i	−0.234547	+	0.703725i
$131$	−1.08478	−	1.87890i	−0.0947779	−	0.164160i	0.814738	−	0.579829i	$-0.196881\pi$
$131$	−1.08478	−	1.87890i	−0.0947779	−	0.164160i	−0.909516	+	0.415669i	$0.863547\pi$
$132$	2.99425	−	5.18620i	0.260616	−	0.451401i
$133$		0			0
$134$	8.37369	+	14.5037i	0.723376	+	1.25292i
$135$	2.12249	+	3.67626i	0.182675	+	0.316402i
$136$	−26.2438			−2.25039
$137$	8.36316			0.714513			0.357257	−	0.934006i	$-0.383712\pi$
$137$	8.36316			0.714513			0.357257	+	0.934006i	$0.383712\pi$
$138$	27.1367	+	47.0022i	2.31003	+	4.00110i
$139$	−0.288457	−	0.499622i	−0.0244666	−	0.0423774i	0.853533	−	0.521039i	$-0.174455\pi$
$139$	−0.288457	−	0.499622i	−0.0244666	−	0.0423774i	−0.877999	+	0.478662i	$0.841122\pi$
$140$		0			0
$141$	−5.97152	+	10.3430i	−0.502893	+	0.871036i
$142$	4.30149	+	7.45040i	0.360973	+	0.625224i
$143$	0.670127	−	2.01062i	0.0560388	−	0.168136i
$144$	−5.26698	+	9.12267i	−0.438915	+	0.760223i
$145$	3.89001			0.323048
$146$	−5.89161	+	10.2046i	−0.487593	+	0.844537i
$147$		0			0
$148$	6.50154			0.534423
$149$	−1.40331	+	2.43061i	−0.114964	+	0.199123i	−0.917765	−	0.397123i	$-0.870009\pi$
$149$	−1.40331	+	2.43061i	−0.114964	+	0.199123i	0.802801	+	0.596246i	$0.203342\pi$
$150$	26.5133			2.16480
$151$	11.5054	−	19.9280i	0.936300	−	1.62172i	0.164000	−	0.986460i	$-0.447560\pi$
$151$	11.5054	−	19.9280i	0.936300	−	1.62172i	0.772300	−	0.635258i	$-0.219106\pi$
$152$	7.78039	−	13.4760i	0.631073	−	1.09305i
$153$	−14.7499	+	25.5476i	−1.19246	+	2.06540i
$154$		0			0
$155$	−2.93576			−0.235806
$156$	−11.6148	+	34.8486i	−0.929930	+	2.79012i
$157$	11.2880	−	19.5513i	0.900879	−	1.56037i	0.0745227	−	0.997219i	$-0.476257\pi$
$157$	11.2880	−	19.5513i	0.900879	−	1.56037i	0.826356	−	0.563148i	$-0.190410\pi$
$158$	3.32583	+	5.76050i	0.264588	+	0.458281i
$159$	1.17087			0.0928557
$160$	1.29101	+	2.23610i	0.102064	+	0.176779i
$161$		0			0
$162$	−2.17457	−	3.76646i	−0.170850	−	0.295921i
$163$	−4.08857	+	7.08161i	−0.320242	+	0.554675i	−0.980538	−	0.196331i	$-0.937097\pi$
$163$	−4.08857	+	7.08161i	−0.320242	+	0.554675i	0.660296	+	0.751005i	$0.270431\pi$
$164$	6.79761	−	11.7738i	0.530804	−	0.919380i
$165$	1.58867			0.123678
$166$	−6.84934			−0.531612
$167$	−1.16386	+	2.01586i	−0.0900619	+	0.155992i	−0.907537	−	0.419972i	$-0.862040\pi$
$167$	−1.16386	+	2.01586i	−0.0900619	+	0.155992i	0.817475	+	0.575964i	$0.195373\pi$
$168$		0			0
$169$	−1.55408	+	12.9068i	−0.119545	+	0.992829i
$170$	−7.56988	−	13.1114i	−0.580583	−	1.00560i
$171$	−8.74566	−	15.1479i	−0.668798	−	1.15839i
$172$	−11.8133	−	20.4611i	−0.900752	−	1.56015i
$173$	−4.06686	+	7.04401i	−0.309198	+	0.535546i	−0.978187	−	0.207726i	$-0.933394\pi$
$173$	−4.06686	+	7.04401i	−0.309198	+	0.535546i	0.668989	+	0.743272i	$0.266727\pi$
$174$	26.0209			1.97264
$175$		0			0
$176$	0.677355	+	1.17321i	0.0510576	+	0.0884343i
$177$	8.26630	+	14.3177i	0.621333	+	1.07618i
$178$	−4.99843			−0.374648
$179$	10.4963	+	18.1801i	0.784528	+	1.35884i	0.929281	+	0.369375i	$0.120428\pi$
$179$	10.4963	+	18.1801i	0.784528	+	1.35884i	−0.144752	+	0.989468i	$0.546239\pi$
$180$	−16.6239			−1.23907
$181$	1.60807			0.119527			0.0597635	−	0.998213i	$-0.480965\pi$
$181$	1.60807			0.119527			0.0597635	+	0.998213i	$0.480965\pi$
$182$		0			0
$183$	−6.07180			−0.448841
$184$	−33.5865			−2.47603
$185$	0.862384	+	1.49369i	0.0634037	+	0.109818i
$186$	−19.6378			−1.43991
$187$	1.89690	+	3.28552i	0.138715	+	0.240261i
$188$	−8.03601	−	13.9188i	−0.586086	−	1.01513i
$189$		0			0
$190$	8.97683			0.651247
$191$	5.78111	−	10.0132i	0.418307	−	0.724529i	−0.577463	−	0.816417i	$-0.695957\pi$
$191$	5.78111	−	10.0132i	0.418307	−	0.724529i	0.995769	+	0.0918886i	$0.0292904\pi$
$192$	14.9771	+	25.9412i	1.08088	+	1.87214i
$193$	−11.7894	−	20.4199i	−0.848621	−	1.46985i	−0.882439	−	0.470427i	$-0.844100\pi$
$193$	−11.7894	−	20.4199i	−0.848621	−	1.46985i	0.0338178	−	0.999428i	$-0.489233\pi$
$194$	−9.19041	−	15.9183i	−0.659833	−	1.14286i
$195$	−9.54689	+	1.95398i	−0.683667	+	0.139927i
$196$		0			0
$197$	0.735472	−	1.27387i	0.0524002	−	0.0907598i	−0.838636	−	0.544693i	$-0.816646\pi$
$197$	0.735472	−	1.27387i	0.0524002	−	0.0907598i	0.891036	+	0.453933i	$0.149980\pi$
$198$	6.41577			0.455949
$199$	−9.39399			−0.665922			−0.332961	−	0.942941i	$-0.608048\pi$
$199$	−9.39399			−0.665922			−0.332961	+	0.942941i	$0.608048\pi$
$200$	−8.20374	+	14.2093i	−0.580092	+	1.00475i
$201$	−9.64810	+	16.7110i	−0.680524	+	1.17870i
$202$	3.14901	+	5.45425i	0.221564	+	0.383760i
$203$		0			0
$204$	−32.8776	−	56.9456i	−2.30189	−	3.98699i
$205$	3.60662			0.251897
$206$	12.9693	+	22.4635i	0.903615	+	1.56511i
$207$	−18.8767	+	32.6955i	−1.31202	+	2.27249i
$208$	−5.51348	−	6.21717i	−0.382291	−	0.431083i
$209$	−2.24946			−0.155598
$210$		0			0
$211$	4.47109	−	7.74416i	0.307803	−	0.533130i	−0.670079	−	0.742290i	$-0.733740\pi$
$211$	4.47109	−	7.74416i	0.307803	−	0.533130i	0.977881	+	0.209160i	$0.0670730\pi$
$212$	−0.787829	+	1.36456i	−0.0541083	+	0.0937184i
$213$	−4.95615	+	8.58430i	−0.339589	+	0.588186i
$214$	38.1620			2.60870
$215$	3.13389	−	5.42805i	0.213729	−	0.370190i
$216$	−17.5722			−1.19563
$217$		0			0
$218$	11.0265	−	19.0984i	0.746808	−	1.29351i
$219$	−13.5765			−0.917418
$220$	−1.06895	+	1.85148i	−0.0720686	+	0.124827i
$221$	−15.4402	−	17.4108i	−1.03862	−	1.17118i
$222$	5.76863	+	9.99156i	0.387165	+	0.670589i
$223$	10.9098	−	18.8963i	0.730574	−	1.26539i	−0.226064	−	0.974112i	$-0.572586\pi$
$223$	10.9098	−	18.8963i	0.730574	−	1.26539i	0.956638	−	0.291279i	$-0.0940809\pi$
$224$		0			0
$225$	9.22154	+	15.9722i	0.614769	+	1.06481i
$226$	12.1554	+	21.0538i	0.808565	+	1.40048i
$227$	18.5525			1.23137			0.615687	−	0.787990i	$-0.288878\pi$
$227$	18.5525			1.23137			0.615687	+	0.787990i	$0.288878\pi$
$228$	38.9882			2.58206
$229$	9.67525	+	16.7580i	0.639359	+	1.10740i	0.985574	+	0.169247i	$0.0541334\pi$
$229$	9.67525	+	16.7580i	0.639359	+	1.10740i	−0.346215	+	0.938155i	$0.612533\pi$
$230$	−9.68784	−	16.7798i	−0.638797	−	1.10643i
$231$		0			0
$232$	−8.05137	+	13.9454i	−0.528599	+	0.915560i
$233$	−8.08170	−	13.9979i	−0.529450	−	0.917034i	−0.999410	−	0.0343462i	$-0.989065\pi$
$233$	−8.08170	−	13.9979i	−0.529450	−	0.917034i	0.469960	−	0.882688i	$-0.344268\pi$
$234$	−38.5548	+	7.89108i	−2.52040	+	0.515856i
$235$	2.13184	−	3.69245i	0.139066	−	0.240869i
$236$	−22.2483			−1.44824
$237$	−3.83199	+	6.63720i	−0.248915	+	0.431133i
$238$		0			0
$239$	16.1037			1.04166			0.520831	−	0.853660i	$-0.325622\pi$
$239$	16.1037			1.04166			0.520831	+	0.853660i	$0.325622\pi$
$240$	3.11449	−	5.39445i	0.201039	−	0.348210i
$241$	4.00600			0.258049			0.129025	−	0.991641i	$-0.458815\pi$
$241$	4.00600			0.258049			0.129025	+	0.991641i	$0.458815\pi$
$242$	−12.7217	+	22.0346i	−0.817779	+	1.41643i
$243$	8.98786	−	15.5674i	0.576572	−	0.998651i
$244$	4.08548	−	7.07625i	0.261546	−	0.453011i
$245$		0			0
$246$	24.1253			1.53817
$247$	13.5178	−	2.76672i	0.860119	−	0.176042i
$248$	6.07631	−	10.5245i	0.385846	−	0.668305i
$249$	−3.94588	−	6.83446i	−0.250060	−	0.433116i
$250$	−21.1939			−1.34042
$251$	1.62344	+	2.81188i	0.102471	+	0.177484i	0.912702	−	0.408626i	$-0.133992\pi$
$251$	1.62344	+	2.81188i	0.102471	+	0.177484i	−0.810231	+	0.586110i	$0.800659\pi$
$252$		0			0
$253$	2.42763	+	4.20477i	0.152624	+	0.264352i
$254$	5.07489	−	8.78996i	0.318427	−	0.551531i
$255$	8.72195	−	15.1069i	0.546190	−	0.946029i
$256$	−27.7557			−1.73473
$257$	26.8924			1.67750			0.838751	−	0.544516i	$-0.183287\pi$
$257$	26.8924			1.67750			0.838751	+	0.544516i	$0.183287\pi$
$258$	20.9631	−	36.3092i	1.30511	−	2.26051i
$259$		0			0
$260$	4.14650	−	12.4410i	0.257155	−	0.771556i
$261$	9.05027	+	15.6755i	0.560198	+	0.970291i
$262$	2.59050	+	4.48688i	0.160042	+	0.277200i
$263$	1.90353	+	3.29701i	0.117377	+	0.203302i	0.918727	−	0.394893i	$-0.129218\pi$
$263$	1.90353	+	3.29701i	0.117377	+	0.203302i	−0.801351	+	0.598195i	$0.795885\pi$
$264$	−3.28815	+	5.69525i	−0.202372	+	0.350518i
$265$	−0.418000			−0.0256775
$266$		0			0
$267$	−2.87958	−	4.98757i	−0.176227	−	0.305235i
$268$	−12.9836	−	22.4883i	−0.793102	−	1.37369i
$269$	23.8381			1.45343			0.726716	−	0.686938i	$-0.241046\pi$
$269$	23.8381			1.45343			0.726716	+	0.686938i	$0.241046\pi$
$270$	−5.06859	−	8.77905i	−0.308464	−	0.534276i
$271$	−9.90135			−0.601464			−0.300732	−	0.953709i	$-0.597231\pi$
$271$	−9.90135			−0.601464			−0.300732	+	0.953709i	$0.597231\pi$
$272$	14.8750			0.901931
$273$		0			0
$274$	−19.9715			−1.20653
$275$	2.37186			0.143028
$276$	−42.0763	−	72.8783i	−2.53270	−	4.38676i
$277$	11.7858			0.708139			0.354069	−	0.935219i	$-0.384798\pi$
$277$	11.7858			0.708139			0.354069	+	0.935219i	$0.384798\pi$
$278$	0.688846	+	1.19312i	0.0413142	+	0.0715584i
$279$	−6.83017	−	11.8302i	−0.408912	−	0.708256i
$280$		0			0
$281$	12.9976			0.775372			0.387686	−	0.921791i	$-0.373274\pi$
$281$	12.9976			0.775372			0.387686	+	0.921791i	$0.373274\pi$
$282$	14.2602	−	24.6994i	0.849184	−	1.47083i
$283$	−8.40249	−	14.5535i	−0.499476	−	0.865118i	0.500524	−	0.865723i	$-0.333141\pi$
$283$	−8.40249	−	14.5535i	−0.499476	−	0.865118i	−1.00000		0.000604910i	$0.999807\pi$
$284$	−6.66959	−	11.5521i	−0.395767	−	0.685489i
$285$	5.17151	+	8.95733i	0.306334	+	0.530586i
$286$	−1.60029	+	4.80143i	−0.0946270	+	0.283914i
$287$		0			0
$288$	−6.00719	+	10.4048i	−0.353977	+	0.613107i
$289$	24.6567			1.45039
$290$	−9.28948			−0.545497
$291$	10.5891	−	18.3409i	0.620746	−	1.07516i
$292$	9.13512	−	15.8225i	0.534592	−	0.925941i
$293$	−7.04782	−	12.2072i	−0.411738	−	0.713151i	0.583342	−	0.812227i	$-0.301745\pi$
$293$	−7.04782	−	12.2072i	−0.411738	−	0.713151i	−0.995080	+	0.0990757i	$0.968411\pi$
$294$		0			0
$295$	−2.95108	−	5.11141i	−0.171818	−	0.297598i
$296$	−7.13970			−0.414987
$297$	1.27011	+	2.19990i	0.0736994	+	0.127651i
$298$	3.35116	−	5.80438i	0.194128	−	0.336239i
$299$	−19.7602	−	22.2822i	−1.14276	−	1.28861i
$300$	−41.1097			−2.37347
$301$		0			0
$302$	−27.4754	+	47.5888i	−1.58103	+	2.73843i
$303$	−3.62827	+	6.28434i	−0.208439	+	0.361026i
$304$	−4.40993	+	7.63822i	−0.252927	+	0.438082i
$305$	2.16764			0.124119
$306$	35.2233	−	61.0085i	2.01358	−	3.48762i
$307$	−15.8786			−0.906240			−0.453120	−	0.891450i	$-0.649689\pi$
$307$	−15.8786			−0.906240			−0.453120	+	0.891450i	$0.649689\pi$
$308$		0			0
$309$	−14.9431	+	25.8823i	−0.850086	+	1.47239i
$310$	7.01070			0.398181
$311$	−14.3017	+	24.7713i	−0.810975	+	1.40465i	0.101208	+	0.994865i	$0.467729\pi$
$311$	−14.3017	+	24.7713i	−0.810975	+	1.40465i	−0.912183	+	0.409784i	$0.865604\pi$
$312$	12.7549	−	38.2692i	0.722103	−	2.16656i
$313$	−9.28962	−	16.0901i	−0.525080	−	0.909465i	−0.999573	−	0.0292063i	$-0.990702\pi$
$313$	−9.28962	−	16.0901i	−0.525080	−	0.909465i	0.474493	−	0.880259i	$-0.342631\pi$
$314$	−26.9561	+	46.6893i	−1.52122	+	2.63483i
$315$		0			0
$316$	−5.15679	−	8.93182i	−0.290092	−	0.502454i
$317$	−15.3223	−	26.5389i	−0.860584	−	1.49057i	−0.871366	−	0.490633i	$-0.836766\pi$
$317$	−15.3223	−	26.5389i	−0.860584	−	1.49057i	0.0107826	−	0.999942i	$-0.496568\pi$
$318$	−2.79607			−0.156796
$319$	2.32781			0.130332
$320$	−5.34685	−	9.26102i	−0.298898	−	0.517707i
$321$	21.9850	+	38.0791i	1.22708	+	2.12537i
$322$		0			0
$323$	−12.3498	+	21.3904i	−0.687160	+	1.19020i
$324$	3.37173	+	5.84001i	0.187318	+	0.324445i
$325$	−14.2534	+	2.91727i	−0.790635	+	0.161821i
$326$	9.76366	−	16.9112i	0.540759	−	0.936622i
$327$	25.4093			1.40514
$328$	−7.46483	+	12.9295i	−0.412177	+	0.713911i
$329$		0			0
$330$	−3.79379			−0.208842
$331$	−13.6138	+	23.5799i	−0.748284	+	1.29607i	0.200360	+	0.979722i	$0.435789\pi$
$331$	−13.6138	+	23.5799i	−0.748284	+	1.29607i	−0.948644	+	0.316344i	$0.897545\pi$
$332$	10.6201			0.582854
$333$	−4.01275	+	6.95028i	−0.219897	+	0.380873i
$334$	2.77933	−	4.81395i	0.152078	−	0.263407i
$335$	3.44438	−	5.96584i	0.188187	−	0.325949i
$336$		0			0
$337$	−12.3160			−0.670898			−0.335449	−	0.942058i	$-0.608888\pi$
$337$	−12.3160			−0.670898			−0.335449	+	0.942058i	$0.608888\pi$
$338$	3.71121	−	30.8219i	0.201863	−	1.67649i
$339$	−14.0054	+	24.2580i	−0.760666	+	1.31751i
$340$	11.7373	+	20.3296i	0.636545	+	1.10253i
$341$	−1.75678			−0.0951348
$342$	20.8850	+	36.1738i	1.12933	+	1.95606i
$343$		0			0
$344$	12.9728	+	22.4695i	0.699445	+	1.21148i
$345$	11.1623	−	19.3336i	0.600956	−	1.04089i
$346$	9.71182	−	16.8214i	0.522111	−	0.904322i
$347$	6.14506			0.329884			0.164942	−	0.986303i	$-0.447256\pi$
$347$	6.14506			0.329884			0.164942	+	0.986303i	$0.447256\pi$
$348$	−40.3462			−2.16278
$349$	6.51563	−	11.2854i	0.348774	−	0.604094i	−0.637258	−	0.770650i	$-0.719932\pi$
$349$	6.51563	−	11.2854i	0.348774	−	0.604094i	0.986032	+	0.166557i	$0.0532649\pi$
$350$		0			0
$351$	−10.3383	−	11.6578i	−0.551820	−	0.622249i
$352$	0.772550	+	1.33810i	0.0411771	+	0.0713208i
$353$	15.8332	+	27.4240i	0.842718	+	1.45963i	0.887589	+	0.460637i	$0.152379\pi$
$353$	15.8332	+	27.4240i	0.842718	+	1.45963i	−0.0448710	+	0.998993i	$0.514288\pi$
$354$	−19.7402	−	34.1911i	−1.04918	−	1.81724i
$355$	1.76935	−	3.06460i	0.0939072	−	0.162652i
$356$	7.75021			0.410761
$357$		0			0
$358$	−25.0655	−	43.4147i	−1.32475	−	2.29454i
$359$	−9.96610	−	17.2618i	−0.525991	−	0.911043i	−0.999542	−	0.0302764i	$-0.990361\pi$
$359$	−9.96610	−	17.2618i	−0.525991	−	0.911043i	0.473551	−	0.880767i	$-0.342972\pi$
$360$	18.2556			0.962155
$361$	2.17744	+	3.77144i	0.114602	+	0.198497i
$362$	−3.84014			−0.201833
$363$	−29.3156			−1.53867
$364$		0			0
$365$	4.84684			0.253695
$366$	14.4997			0.757911
$367$	9.85950	+	17.0772i	0.514662	+	0.891420i	0.999855	+	0.0170133i	$0.00541577\pi$
$367$	9.85950	+	17.0772i	0.514662	+	0.891420i	−0.485194	+	0.874407i	$0.661251\pi$
$368$	19.0369			0.992366
$369$	8.39096	+	14.5336i	0.436816	+	0.756588i
$370$	−2.05940	−	3.56699i	−0.107063	−	0.185439i
$371$		0			0
$372$	30.4490			1.57870
$373$	−8.77345	+	15.1961i	−0.454272	+	0.786823i	−0.998646	−	0.0520202i	$-0.983434\pi$
$373$	−8.77345	+	15.1961i	−0.454272	+	0.786823i	0.544374	+	0.838843i	$0.316767\pi$
$374$	−4.52986	−	7.84595i	−0.234234	−	0.405704i
$375$	−12.2097	−	21.1478i	−0.630507	−	1.09207i
$376$	8.82478	+	15.2850i	0.455103	+	0.788262i
$377$	−13.9887	+	2.86308i	−0.720452	+	0.147456i
$378$		0			0
$379$	5.85068	−	10.1337i	0.300529	−	0.520532i	−0.675727	−	0.737152i	$-0.736170\pi$
$379$	5.85068	−	10.1337i	0.300529	−	0.520532i	0.976256	+	0.216620i	$0.0695034\pi$
$380$	−13.9188			−0.714021
$381$	11.6945			0.599127
$382$	−13.8055	+	23.9119i	−0.706352	+	1.22344i
$383$	−10.7644	+	18.6445i	−0.550036	+	0.952690i	0.448235	+	0.893916i	$0.352053\pi$
$383$	−10.7644	+	18.6445i	−0.550036	+	0.952690i	−0.998271	+	0.0587748i	$0.981281\pi$
$384$	−28.5334	−	49.4213i	−1.45609	−	2.52202i
$385$		0			0
$386$	28.1536	+	48.7634i	1.43298	+	2.48199i
$387$	29.1645			1.48252
$388$	14.2500	+	24.6817i	0.723435	+	1.25303i
$389$	−13.2455	+	22.9419i	−0.671574	+	1.16320i	0.305884	+	0.952069i	$0.401048\pi$
$389$	−13.2455	+	22.9419i	−0.671574	+	1.16320i	−0.977458	+	0.211131i	$0.932285\pi$
$390$	22.7983	−	4.66618i	1.15444	−	0.236281i
$391$	53.3118			2.69609
$392$		0			0
$393$	−2.98476	+	5.16975i	−0.150561	+	0.260779i
$394$	−1.75633	+	3.04206i	−0.0884828	+	0.153257i
$395$	1.36802	−	2.36949i	0.0688327	−	0.119222i
$396$	−9.94784			−0.499898
$397$	−16.8995	+	29.2707i	−0.848160	+	1.46906i	0.0346887	+	0.999398i	$0.488956\pi$
$397$	−16.8995	+	29.2707i	−0.848160	+	1.46906i	−0.882849	+	0.469658i	$0.844377\pi$
$398$	22.4332			1.12447
$399$		0			0
$400$	4.64989	−	8.05384i	0.232494	−	0.402692i
$401$	21.6119			1.07925			0.539623	−	0.841907i	$-0.318567\pi$
$401$	21.6119			1.07925			0.539623	+	0.841907i	$0.318567\pi$
$402$	23.0400	−	39.9065i	1.14913	−	1.99035i
$403$	10.5571	−	2.16075i	0.525888	−	0.107635i
$404$	−4.88264	−	8.45697i	−0.242920	−	0.420750i
$405$	−0.894473	+	1.54927i	−0.0444467	+	0.0769839i
$406$		0			0
$407$	0.516056	+	0.893835i	0.0255799	+	0.0443058i
$408$	36.1047	+	62.5351i	1.78745	+	3.09595i
$409$	−7.74217			−0.382826			−0.191413	−	0.981510i	$-0.561307\pi$
$409$	−7.74217			−0.382826			−0.191413	+	0.981510i	$0.561307\pi$
$410$	−8.61275			−0.425353
$411$	−11.5055	−	19.9282i	−0.567526	−	0.982984i
$412$	−20.1093	−	34.8303i	−0.990714	−	1.71597i
$413$		0			0
$414$	45.0783	−	78.0780i	2.21548	−	3.83732i
$415$	1.40868	+	2.43991i	0.0691495	+	0.119770i
$416$	−6.28834	−	7.09092i	−0.308311	−	0.347661i
$417$	−0.793683	+	1.37470i	−0.0388668	+	0.0673193i
$418$	5.37179			0.262743
$419$	−4.05097	+	7.01649i	−0.197903	+	0.342778i	−0.947848	−	0.318722i	$-0.896746\pi$
$419$	−4.05097	+	7.01649i	−0.197903	+	0.342778i	0.749945	+	0.661500i	$0.230080\pi$
$420$		0			0
$421$	−32.1124			−1.56506			−0.782530	−	0.622612i	$-0.786071\pi$
$421$	−32.1124			−1.56506			−0.782530	+	0.622612i	$0.786071\pi$
$422$	−10.6771	+	18.4933i	−0.519755	+	0.900242i
$423$	19.8393			0.964618
$424$	0.865159	−	1.49850i	0.0420158	−	0.0727735i
$425$	13.0218	−	22.5543i	0.631648	−	1.09405i
$426$	11.8355	−	20.4996i	0.573430	−	0.993210i
$427$		0			0
$428$	−59.1713			−2.86015
$429$	−5.71292	+	1.16927i	−0.275822	+	0.0564531i
$430$	−7.48384	+	12.9624i	−0.360903	+	0.625102i
$431$	14.7640	+	25.5721i	0.711159	+	1.23176i	0.964422	+	0.264366i	$0.0851627\pi$
$431$	14.7640	+	25.5721i	0.711159	+	1.23176i	−0.253263	+	0.967397i	$0.581504\pi$
$432$	9.95992			0.479197
$433$	11.0455	+	19.1314i	0.530813	+	0.919395i	0.999353	+	0.0359531i	$0.0114467\pi$
$433$	11.0455	+	19.1314i	0.530813	+	0.919395i	−0.468540	+	0.883442i	$0.655220\pi$
$434$		0			0
$435$	−5.35164	−	9.26931i	−0.256591	−	0.444429i
$436$	−17.0969	+	29.6127i	−0.818792	+	1.41819i
$437$	−15.8051	+	27.3752i	−0.756060	+	1.30953i
$438$	32.4213			1.54915
$439$	6.35580			0.303346			0.151673	−	0.988431i	$-0.451534\pi$
$439$	6.35580			0.303346			0.151673	+	0.988431i	$0.451534\pi$
$440$	1.17387	−	2.03321i	0.0559622	−	0.0969294i
$441$		0			0
$442$	36.8718	+	41.5777i	1.75381	+	1.97765i
$443$	6.78135	+	11.7456i	0.322192	+	0.558052i	0.980940	−	0.194311i	$-0.0622472\pi$
$443$	6.78135	+	11.7456i	0.322192	+	0.558052i	−0.658748	+	0.752363i	$0.728914\pi$
$444$	−8.94443	−	15.4922i	−0.424484	−	0.735227i
$445$	1.02801	+	1.78057i	0.0487324	+	0.0844070i
$446$	−26.0530	+	45.1251i	−1.23365	+	2.13674i
$447$	7.72237			0.365255
$448$		0			0
$449$	−10.9559	−	18.9762i	−0.517041	−	0.895541i	−0.999804	−	0.0197900i	$-0.993700\pi$
$449$	−10.9559	−	18.9762i	−0.517041	−	0.895541i	0.482763	−	0.875751i	$-0.339633\pi$
$450$	−22.0214	−	38.1421i	−1.03810	−	1.79804i
$451$	2.15823			0.101627
$452$	−18.8473	−	32.6445i	−0.886502	−	1.53547i
$453$	−63.3139			−2.97475
$454$	−44.3041			−2.07930
$455$		0			0
$456$	−42.8151			−2.00500
$457$	15.2146			0.711710			0.355855	−	0.934541i	$-0.384190\pi$
$457$	15.2146			0.711710			0.355855	+	0.934541i	$0.384190\pi$
$458$	−23.1049	−	40.0188i	−1.07962	−	1.86996i
$459$	27.8922			1.30190
$460$	15.0213	+	26.0176i	0.700371	+	1.21308i
$461$	−8.10813	−	14.0437i	−0.377633	−	0.654080i	0.613084	−	0.790018i	$-0.289929\pi$
$461$	−8.10813	−	14.0437i	−0.377633	−	0.654080i	−0.990717	+	0.135937i	$0.956595\pi$
$462$		0			0
$463$	−1.44769			−0.0672799			−0.0336400	−	0.999434i	$-0.510710\pi$
$463$	−1.44769			−0.0672799			−0.0336400	+	0.999434i	$0.510710\pi$
$464$	4.56353	−	7.90426i	0.211856	−	0.366946i
$465$	4.03884	+	6.99547i	0.187297	+	0.324407i
$466$	19.2994	+	33.4275i	0.894027	+	1.54850i
$467$	7.00337	+	12.1302i	0.324078	+	0.561319i	0.981325	−	0.192356i	$-0.0616128\pi$
$467$	7.00337	+	12.1302i	0.324078	+	0.561319i	−0.657248	+	0.753675i	$0.728279\pi$
$468$	59.7803	−	12.2353i	2.76334	−	0.565579i
$469$		0			0
$470$	−5.09091	+	8.81772i	−0.234826	+	0.406731i
$471$	−62.1172			−2.86221
$472$	24.4320			1.12458
$473$	1.87534	−	3.24818i	0.0862282	−	0.149352i
$474$	9.15094	−	15.8499i	0.420316	−	0.728009i
$475$	7.72100	+	13.3732i	0.354264	+	0.613603i
$476$		0			0
$477$	−0.972495	−	1.68441i	−0.0445275	−	0.0771239i
$478$	−38.4562			−1.75895
$479$	−15.0122	−	26.0018i	−0.685923	−	1.18805i	−0.973146	−	0.230189i	$-0.926065\pi$
$479$	−15.0122	−	26.0018i	−0.685923	−	1.18805i	0.287223	−	0.957864i	$-0.407268\pi$
$480$	3.55219	−	6.15258i	0.162135	−	0.280826i
$481$	−4.20055	−	4.73667i	−0.191528	−	0.215973i
$482$	−9.56649			−0.435742
$483$		0			0
$484$	19.7253	−	34.1652i	0.896605	−	1.55296i
$485$	−3.78033	+	6.54772i	−0.171656	+	0.297317i
$486$	−21.4633	+	37.1756i	−0.973597	+	1.68632i
$487$	−28.4903			−1.29102			−0.645510	−	0.763752i	$-0.723355\pi$
$487$	−28.4903			−1.29102			−0.645510	+	0.763752i	$0.723355\pi$
$488$	−4.48649	+	7.77082i	−0.203094	+	0.351769i
$489$	22.4992			1.01745
$490$		0			0
$491$	14.2339	−	24.6538i	0.642365	−	1.11261i	−0.342539	−	0.939504i	$-0.611287\pi$
$491$	14.2339	−	24.6538i	0.642365	−	1.11261i	0.984903	−	0.173105i	$-0.0553799\pi$
$492$	−37.4070			−1.68644
$493$	12.7799	−	22.1354i	0.575578	−	0.996930i
$494$	−32.2811	+	6.60703i	−1.45239	+	0.297264i
$495$	−1.31951	−	2.28546i	−0.0593076	−	0.102724i
$496$	−3.44406	+	5.96528i	−0.154643	+	0.267849i
$497$		0			0
$498$	9.42290	+	16.3209i	0.422250	+	0.731359i
$499$	13.1164	+	22.7183i	0.587172	+	1.01701i	0.994601	+	0.103775i	$0.0330921\pi$
$499$	13.1164	+	22.7183i	0.587172	+	1.01701i	−0.407429	+	0.913237i	$0.633575\pi$
$500$	32.8617			1.46962
$501$	6.40465			0.286139
$502$	−3.87684	−	6.71488i	−0.173032	−	0.299700i
$503$	4.26588	+	7.38872i	0.190206	+	0.329447i	0.945318	−	0.326149i	$-0.105751\pi$
$503$	4.26588	+	7.38872i	0.190206	+	0.329447i	−0.755112	+	0.655595i	$0.772418\pi$
$504$		0			0
$505$	1.29529	−	2.24352i	0.0576398	−	0.0998351i
$506$	−5.79726	−	10.0412i	−0.257720	−	0.446384i
$507$	32.8929	−	14.0532i	1.46083	−	0.624125i
$508$	−7.86876	+	13.6291i	−0.349120	+	0.604693i
$509$	13.0260			0.577366			0.288683	−	0.957425i	$-0.406783\pi$
$509$	13.0260			0.577366			0.288683	+	0.957425i	$0.406783\pi$
$510$	−20.8283	+	36.0758i	−0.922295	+	1.59746i
$511$		0			0
$512$	24.8008			1.09605
$513$	−8.26908	+	14.3225i	−0.365089	+	0.632352i
$514$	−64.2200			−2.83262
$515$	5.33472	−	9.24000i	0.235076	−	0.407163i
$516$	−32.5039	+	56.2984i	−1.43090	+	2.47840i
$517$	1.27571	−	2.20959i	0.0561055	−	0.0971775i
$518$		0			0
$519$	22.3798			0.982363
$520$	−4.55350	+	13.6621i	−0.199684	+	0.599124i
$521$	2.23285	−	3.86741i	0.0978230	−	0.169434i	−0.812960	−	0.582319i	$-0.802145\pi$
$521$	2.23285	−	3.86741i	0.0978230	−	0.169434i	0.910783	+	0.412885i	$0.135479\pi$
$522$	−21.6124	−	37.4337i	−0.945948	−	1.63843i
$523$	2.90811			0.127163			0.0635815	−	0.997977i	$-0.479748\pi$
$523$	2.90811			0.127163			0.0635815	+	0.997977i	$0.479748\pi$
$524$	−4.01665	−	6.95704i	−0.175468	−	0.303920i
$525$		0			0
$526$	−4.54570	−	7.87339i	−0.198202	−	0.343296i
$527$	−9.64490	+	16.7055i	−0.420138	+	0.727701i
$528$	1.86373	−	3.22807i	0.0811084	−	0.140484i
$529$	45.2278			1.96643
$530$	0.998200			0.0433590
$531$	13.7316	−	23.7838i	0.595901	−	1.03213i
$532$		0			0
$533$	−12.9696	+	2.65451i	−0.561775	+	0.114980i
$534$	6.87654	+	11.9105i	0.297577	+	0.515418i
$535$	−7.84866	−	13.5943i	−0.339327	−	0.587732i
$536$	14.2581	+	24.6957i	0.615854	+	1.06669i
$537$	28.8803	−	50.0221i	1.24628	−	2.15861i
$538$	−56.9262			−2.45426
$539$		0			0
$540$	7.85899	+	13.6122i	0.338197	+	0.585775i
$541$	9.23193	+	15.9902i	0.396912	+	0.687471i	0.993343	−	0.115193i	$-0.0367486\pi$
$541$	9.23193	+	15.9902i	0.396912	+	0.687471i	−0.596431	+	0.802664i	$0.703415\pi$
$542$	23.6448			1.01563
$543$	−2.21229	−	3.83180i	−0.0949384	−	0.164438i
$544$	16.9655			0.727392
$545$	−9.07112			−0.388564
$546$		0			0
$547$	34.9817			1.49571			0.747856	−	0.663861i	$-0.231083\pi$
$547$	34.9817			1.49571			0.747856	+	0.663861i	$0.231083\pi$
$548$	30.9665			1.32282
$549$	5.04310	+	8.73491i	0.215234	+	0.372797i
$550$	−5.66408			−0.241517
$551$	7.57760	+	13.1248i	0.322817	+	0.559135i
$552$	46.2063	+	80.0317i	1.96667	+	3.40638i
$553$		0			0
$554$	−28.1449			−1.19576
$555$	2.37283	−	4.10986i	0.100721	−	0.174454i
$556$	−1.06808	−	1.84996i	−0.0452965	−	0.0784559i
$557$	−0.0265706	−	0.0460217i	−0.00112583	−	0.00195000i	0.865462	−	0.500975i	$-0.167025\pi$
$557$	−0.0265706	−	0.0460217i	−0.00112583	−	0.00195000i	−0.866588	+	0.499025i	$0.833692\pi$
$558$	16.3107	+	28.2510i	0.690487	+	1.19596i
$559$	−7.27451	+	21.8261i	−0.307679	+	0.923146i
$560$		0			0
$561$	5.21927	−	9.04004i	0.220358	−	0.381671i
$562$	−31.0388			−1.30929
$563$	−7.98506			−0.336530			−0.168265	−	0.985742i	$-0.553816\pi$
$563$	−7.98506			−0.336530			−0.168265	+	0.985742i	$0.553816\pi$
$564$	−22.1109	+	38.2972i	−0.931037	+	1.61260i
$565$	4.99992	−	8.66012i	0.210348	−	0.364334i
$566$	20.0655	+	34.7544i	0.843414	+	1.46084i
$567$		0			0
$568$	7.32424	+	12.6860i	0.307318	+	0.532291i
$569$	−26.7241			−1.12033			−0.560167	−	0.828380i	$-0.689263\pi$
$569$	−26.7241			−1.12033			−0.560167	+	0.828380i	$0.689263\pi$
$570$	−12.3498	−	21.3904i	−0.517275	−	0.895946i
$571$	−6.74647	+	11.6852i	−0.282331	+	0.489012i	−0.971958	−	0.235153i	$-0.924441\pi$
$571$	−6.74647	+	11.6852i	−0.282331	+	0.489012i	0.689627	+	0.724164i	$0.257774\pi$
$572$	2.48129	−	7.44476i	0.103748	−	0.311281i
$573$	−31.8132			−1.32902
$574$		0			0
$575$	16.6651	−	28.8648i	0.694982	−	1.20374i
$576$	24.8794	−	43.0923i	1.03664	−	1.79551i
$577$	6.00662	−	10.4038i	0.250059	−	0.433115i	−0.713483	−	0.700673i	$-0.752883\pi$
$577$	6.00662	−	10.4038i	0.250059	−	0.433115i	0.963542	+	0.267558i	$0.0862167\pi$
$578$	−58.8811			−2.44913
$579$	−32.4383	+	56.1848i	−1.34809	+	2.33496i
$580$	14.4036			0.598078
$581$		0			0
$582$	−25.2872	+	43.7988i	−1.04819	+	1.81552i
$583$	−0.250134			−0.0103595
$584$	−10.0318	+	17.3756i	−0.415118	+	0.719005i
$585$	10.7404	+	12.1112i	0.444062	+	0.500739i
$586$	16.8305	+	29.1512i	0.695260	+	1.20422i
$587$	5.21177	−	9.02705i	0.215113	−	0.372586i	−0.738195	−	0.674588i	$-0.764321\pi$
$587$	5.21177	−	9.02705i	0.215113	−	0.372586i	0.953307	+	0.302002i	$0.0976548\pi$
$588$		0			0
$589$	−5.71876	−	9.90518i	−0.235637	−	0.408136i
$590$	7.04728	+	12.2062i	0.290132	+	0.502523i
$591$	−4.04727			−0.166482
$592$	4.04679			0.166322
$593$	−11.1751	−	19.3558i	−0.458905	−	0.794847i	0.539998	−	0.841666i	$-0.318425\pi$
$593$	−11.1751	−	19.3558i	−0.458905	−	0.794847i	−0.998903	+	0.0468194i	$0.985091\pi$
$594$	−3.03307	−	5.25344i	−0.124449	−	0.215551i
$595$		0			0
$596$	−5.19607	+	8.99986i	−0.212839	+	0.368649i
$597$	12.9237	+	22.3845i	0.528931	+	0.916135i
$598$	47.1880	+	53.2107i	1.92966	+	2.17595i
$599$	−0.579463	+	1.00366i	−0.0236762	+	0.0410084i	−0.877621	−	0.479356i	$-0.840870\pi$
$599$	−0.579463	+	1.00366i	−0.0236762	+	0.0410084i	0.853945	+	0.520364i	$0.174204\pi$
$600$	45.1448			1.84303
$601$	21.0907	−	36.5301i	0.860306	−	1.49009i	−0.0113271	−	0.999936i	$-0.503606\pi$
$601$	21.0907	−	36.5301i	0.860306	−	1.49009i	0.871633	−	0.490158i	$-0.163061\pi$
$602$		0			0
$603$	32.0540			1.30534
$604$	42.6014	−	73.7879i	1.73343	−	3.00239i
$605$	10.4657			0.425491
$606$	8.66444	−	15.0072i	0.351969	−	0.609628i
$607$	−9.07844	+	15.7243i	−0.368482	+	0.638230i	−0.989328	−	0.145702i	$-0.953456\pi$
$607$	−9.07844	+	15.7243i	−0.368482	+	0.638230i	0.620846	+	0.783932i	$0.286789\pi$
$608$	−5.02970	+	8.71169i	−0.203981	+	0.353306i
$609$		0			0
$610$	−5.17640			−0.209586
$611$	−4.94851	+	14.8473i	−0.200195	+	0.600657i
$612$	−54.6147	+	94.5955i	−2.20767	+	3.82380i
$613$	0.451323	+	0.781714i	0.0182288	+	0.0315731i	0.874996	−	0.484130i	$-0.160864\pi$
$613$	0.451323	+	0.781714i	0.0182288	+	0.0315731i	−0.856767	+	0.515703i	$0.827531\pi$
$614$	37.9187			1.53027
$615$	−4.96177	−	8.59404i	−0.200078	−	0.346545i
$616$		0			0
$617$	13.0218	+	22.5544i	0.524238	+	0.908008i	0.999602	+	0.0282180i	$0.00898327\pi$
$617$	13.0218	+	22.5544i	0.524238	+	0.908008i	−0.475363	+	0.879790i	$0.657683\pi$
$618$	35.6848	−	61.8079i	1.43545	−	2.48628i
$619$	13.4171	−	23.2390i	0.539277	−	0.934056i	−0.459666	−	0.888092i	$-0.652031\pi$
$619$	13.4171	−	23.2390i	0.539277	−	0.934056i	0.998943	−	0.0459638i	$-0.0146359\pi$
$620$	−10.8703			−0.436562
$621$	35.6961			1.43244
$622$	34.1530	−	59.1547i	1.36941	−	2.37189i
$623$		0			0
$624$	−7.22948	+	21.6910i	−0.289411	+	0.868335i
$625$	−5.72894	−	9.92281i	−0.229158	−	0.396912i
$626$	22.1839	+	38.4237i	0.886649	+	1.53572i
$627$	3.09467	+	5.36012i	0.123589	+	0.214063i
$628$	41.7962	−	72.3932i	1.66785	−	2.88880i
$629$	11.3328			0.451869
$630$		0			0
$631$	16.8061	+	29.1089i	0.669039	+	1.15881i	0.978173	+	0.207791i	$0.0666273\pi$
$631$	16.8061	+	29.1089i	0.669039	+	1.15881i	−0.309135	+	0.951018i	$0.600039\pi$
$632$	5.66296	+	9.80853i	0.225260	+	0.390162i
$633$	−24.6042			−0.977930
$634$	36.5901	+	63.3760i	1.45318	+	2.51698i
$635$	−4.17494			−0.165678
$636$	4.33539			0.171909
$637$		0			0
$638$	−5.55889			−0.220078
$639$	16.4659			0.651379
$640$	10.1865	+	17.6435i	0.402655	+	0.697419i
$641$	21.1841			0.836722			0.418361	−	0.908281i	$-0.362605\pi$
$641$	21.1841			0.836722			0.418361	+	0.908281i	$0.362605\pi$
$642$	−52.5010	−	90.9343i	−2.07205	−	3.58889i
$643$	0.330770	+	0.572910i	0.0130443	+	0.0225933i	0.872474	−	0.488661i	$-0.162514\pi$
$643$	0.330770	+	0.572910i	0.0130443	+	0.0225933i	−0.859430	+	0.511254i	$0.829181\pi$
$644$		0			0
$645$	−17.2457			−0.679047
$646$	29.4917	−	51.0811i	1.16034	−	2.00976i
$647$	−20.0162	−	34.6690i	−0.786916	−	1.36298i	−0.927848	−	0.372960i	$-0.878343\pi$
$647$	−20.0162	−	34.6690i	−0.786916	−	1.36298i	0.140931	−	0.990019i	$-0.454990\pi$
$648$	−3.70268	−	6.41323i	−0.145455	−	0.251936i
$649$	−1.76594	−	3.05870i	−0.0693193	−	0.120065i
$650$	34.0376	−	6.96654i	1.33506	−	0.273250i
$651$		0			0
$652$	−15.1388	+	26.2212i	−0.592883	+	1.02690i
$653$	12.7120			0.497460			0.248730	−	0.968573i	$-0.419987\pi$
$653$	12.7120			0.497460			0.248730	+	0.968573i	$0.419987\pi$
$654$	−60.6782			−2.37271
$655$	1.06556	−	1.84560i	0.0416349	−	0.0721138i
$656$	4.23107	−	7.32844i	0.165196	−	0.286127i
$657$	11.2764	+	19.5313i	0.439933	+	0.761987i
$658$		0			0
$659$	7.09522	+	12.2893i	0.276391	+	0.478723i	0.970485	−	0.241161i	$-0.0775283\pi$
$659$	7.09522	+	12.2893i	0.276391	+	0.478723i	−0.694094	+	0.719884i	$0.744195\pi$
$660$	5.88239			0.228972
$661$	25.0890	+	43.4554i	0.975848	+	1.69022i	0.677106	+	0.735885i	$0.263234\pi$
$661$	25.0890	+	43.4554i	0.975848	+	1.69022i	0.298742	+	0.954334i	$0.403433\pi$
$662$	32.5104	−	56.3096i	1.26355	−	2.18853i
$663$	−20.2458	+	60.7444i	−0.786280	+	2.35912i
$664$	−11.6625			−0.452594
$665$		0			0
$666$	9.58259	−	16.5975i	0.371318	−	0.643141i
$667$	16.3556	−	28.3287i	0.633290	−	1.09689i
$668$	−4.30944	+	7.46417i	−0.166737	+	0.288797i
$669$	−60.0362			−2.32113
$670$	−8.22530	+	14.2466i	−0.317771	+	0.550396i
$671$	1.29713			0.0500751
$672$		0			0
$673$	0.937137	−	1.62317i	0.0361240	−	0.0625685i	−0.847398	−	0.530958i	$-0.821832\pi$
$673$	0.937137	−	1.62317i	0.0361240	−	0.0625685i	0.883522	+	0.468389i	$0.155166\pi$
$674$	29.4112			1.13288
$675$	8.71902	−	15.1018i	0.335595	−	0.581268i
$676$	−5.75433	+	47.7902i	−0.221321	+	1.83808i
$677$	−1.00439	−	1.73966i	−0.0386020	−	0.0668607i	0.846079	−	0.533058i	$-0.178957\pi$
$677$	−1.00439	−	1.73966i	−0.0386020	−	0.0668607i	−0.884681	+	0.466197i	$0.845624\pi$
$678$	33.4453	−	57.9290i	1.28446	−	2.22475i
$679$		0			0
$680$	−12.8894	−	22.3251i	−0.494286	−	0.856128i
$681$	−25.5234	−	44.2079i	−0.978061	−	1.69405i
$682$	4.19525			0.160644
$683$	−14.1012			−0.539568			−0.269784	−	0.962921i	$-0.586952\pi$
$683$	−14.1012			−0.539568			−0.269784	+	0.962921i	$0.586952\pi$
$684$	−32.3828	−	56.0886i	−1.23819	−	2.14460i
$685$	4.10748	+	7.11437i	0.156939	+	0.271826i
$686$		0			0
$687$	26.6212	−	46.1094i	1.01566	−	1.75918i
$688$	−7.35298	−	12.7357i	−0.280330	−	0.485546i
$689$	1.50315	−	0.307652i	0.0572654	−	0.0117206i
$690$	−26.6559	+	46.1693i	−1.01477	+	1.75764i
$691$	35.6920			1.35779			0.678895	−	0.734236i	$-0.262459\pi$
$691$	35.6920			1.35779			0.678895	+	0.734236i	$0.262459\pi$
$692$	−15.0585	+	26.0820i	−0.572437	+	0.991489i
$693$		0			0
$694$	−14.6746			−0.557041
$695$	0.283346	−	0.490769i	0.0107479	−	0.0186159i
$696$	44.3064			1.67943
$697$	11.8489	−	20.5229i	0.448809	−	0.777360i
$698$	−15.5596	+	26.9500i	−0.588938	+	1.02007i
$699$	−22.2366	+	38.5150i	−0.841066	+	1.45677i
$700$		0			0
$701$	−6.15865			−0.232609			−0.116305	−	0.993214i	$-0.537105\pi$
$701$	−6.15865			−0.232609			−0.116305	+	0.993214i	$0.537105\pi$
$702$	24.6883	+	27.8394i	0.931802	+	1.05073i
$703$	−3.35979	+	5.81932i	−0.126717	+	0.219480i
$704$	−3.19959	−	5.54185i	−0.120589	−	0.208866i
$705$	−11.7314			−0.441831
$706$	−37.8103	−	65.4894i	−1.42301	−	2.46473i
$707$		0			0
$708$	30.6078	+	53.0143i	1.15031	+	1.99240i
$709$	−17.0185	+	29.4770i	−0.639144	+	1.10703i	0.346477	+	0.938059i	$0.387378\pi$
$709$	−17.0185	+	29.4770i	−0.639144	+	1.10703i	−0.985621	+	0.168972i	$0.945955\pi$
$710$	−4.22527	+	7.31838i	−0.158571	+	0.274654i
$711$	12.7311			0.477452
$712$	−8.51094			−0.318961
$713$	−12.3434	+	21.3794i	−0.462265	+	0.800667i
$714$		0			0
$715$	2.03952	−	0.417432i	0.0762736	−	0.0156111i
$716$	38.8648	+	67.3158i	1.45244	+	2.51571i
$717$	−22.1545	−	38.3727i	−0.827375	−	1.43306i
$718$	23.7994	+	41.2218i	0.888187	+	1.53838i
$719$	−11.4824	+	19.8881i	−0.428222	+	0.741702i	−0.996715	−	0.0809859i	$-0.974193\pi$
$719$	−11.4824	+	19.8881i	−0.428222	+	0.741702i	0.568493	+	0.822688i	$0.307526\pi$
$720$	−10.3473			−0.385621
$721$		0			0
$722$	−5.19981	−	9.00633i	−0.193517	−	0.335181i
$723$	−5.51122	−	9.54571i	−0.204964	−	0.355009i
$724$	5.95424			0.221288
$725$	−7.98992	−	13.8389i	−0.296738	−	0.513966i
$726$	70.0067			2.59819
$727$	−1.06558			−0.0395203			−0.0197601	−	0.999805i	$-0.506290\pi$
$727$	−1.06558			−0.0395203			−0.0197601	+	0.999805i	$0.506290\pi$
$728$		0			0
$729$	−43.9962			−1.62949
$730$	−11.5744			−0.428389
$731$	−20.5916	−	35.6658i	−0.761609	−	1.31915i
$732$	−22.4822			−0.830966
$733$	−13.1689	−	22.8092i	−0.486404	−	0.842476i	0.513474	−	0.858105i	$-0.328358\pi$
$733$	−13.1689	−	22.8092i	−0.486404	−	0.842476i	−0.999878	+	0.0156289i	$0.995025\pi$
$734$	−23.5448	−	40.7809i	−0.869056	−	1.50525i
$735$		0			0
$736$	21.7123			0.800326
$737$	2.06114	−	3.57000i	0.0759230	−	0.131502i
$738$	−20.0379	−	34.7067i	−0.737606	−	1.27757i
$739$	−17.1075	−	29.6310i	−0.629308	−	1.08999i	−0.987691	−	0.156419i	$-0.950005\pi$
$739$	−17.1075	−	29.6310i	−0.629308	−	1.08999i	0.358383	−	0.933575i	$-0.383328\pi$
$740$	3.19317	+	5.53073i	0.117383	+	0.203314i
$741$	−25.1897	−	28.4047i	−0.925366	−	1.04347i
$742$		0			0
$743$	−11.2391	+	19.4667i	−0.412322	+	0.714163i	−0.995143	−	0.0984379i	$-0.968615\pi$
$743$	−11.2391	+	19.4667i	−0.412322	+	0.714163i	0.582821	+	0.812600i	$0.301949\pi$
$744$	−33.4377			−1.22588
$745$	−2.75689			−0.101005
$746$	20.9513	−	36.2888i	0.767083	−	1.32863i
$747$	−6.55472	+	11.3531i	−0.239825	+	0.415388i
$748$	7.02368	+	12.1654i	0.256811	+	0.444810i
$749$		0			0
$750$	29.1573	+	50.5018i	1.06467	+	1.84407i
$751$	−42.5424			−1.55239			−0.776197	−	0.630491i	$-0.782854\pi$
$751$	−42.5424			−1.55239			−0.776197	+	0.630491i	$0.782854\pi$
$752$	−5.00189	−	8.66353i	−0.182400	−	0.315927i
$753$	4.46686	−	7.73683i	0.162781	−	0.281946i
$754$	33.4054	−	6.83715i	1.21655	−	0.248994i
$755$	22.6031			0.822612
$756$		0			0
$757$	5.61902	−	9.73243i	0.204227	−	0.353731i	−0.745659	−	0.666327i	$-0.767865\pi$
$757$	5.61902	−	9.73243i	0.204227	−	0.353731i	0.949886	+	0.312596i	$0.101199\pi$
$758$	−13.9716	+	24.1996i	−0.507473	+	0.878969i
$759$	6.67956	−	11.5693i	0.242453	−	0.419941i
$760$	15.2850			0.554447
$761$	6.40422	−	11.0924i	0.232153	−	0.402101i	−0.726289	−	0.687390i	$-0.758756\pi$
$761$	6.40422	−	11.0924i	0.232153	−	0.402101i	0.958441	+	0.285289i	$0.0920897\pi$
$762$	−27.9269			−1.01168
$763$		0			0
$764$	21.4059	−	37.0760i	0.774437	−	1.34136i
$765$	−28.9770			−1.04767
$766$	25.7058	−	44.5238i	0.928789	−	1.60871i
$767$	14.3743	+	16.2089i	0.519024	+	0.585268i
$768$	38.1846	+	66.1377i	1.37787	+	2.38654i
$769$	−25.6759	+	44.4719i	−0.925895	+	1.60370i	−0.135780	+	0.990739i	$0.543354\pi$
$769$	−25.6759	+	44.4719i	−0.925895	+	1.60370i	−0.790115	+	0.612958i	$0.789979\pi$
$770$		0			0
$771$	−36.9969	−	64.0805i	−1.33241	−	2.30780i
$772$	−43.6529	−	75.6091i	−1.57110	−	2.72123i
$773$	−20.0046			−0.719517			−0.359759	−	0.933045i	$-0.617141\pi$
$773$	−20.0046			−0.719517			−0.359759	+	0.933045i	$0.617141\pi$
$774$	−69.6459			−2.50337
$775$	6.02993	+	10.4441i	0.216602	+	0.375165i

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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.38804 q^{2} +(-1.37574 - 2.38285i) q^{3} +3.70272 q^{4} +(0.491140 + 0.850679i) q^{5} +(3.28532 + 5.69033i) q^{6} -4.06616 q^{8} +(-2.28532 + 3.95828i) q^{9} +O(q^{10})\)	\(q-2.38804 q^{2} +(-1.37574 - 2.38285i) q^{3} +3.70272 q^{4} +(0.491140 + 0.850679i) q^{5} +(3.28532 + 5.69033i) q^{6} -4.06616 q^{8} +(-2.28532 + 3.95828i) q^{9} +(-1.17286 - 2.03145i) q^{10} +(0.293901 + 0.509052i) q^{11} +(-5.09398 - 8.82303i) q^{12} +(-2.39227 - 2.69760i) q^{13} +(1.35136 - 2.34063i) q^{15} +2.30470 q^{16} +6.45420 q^{17} +(5.45742 - 9.45253i) q^{18} +(-1.91345 + 3.31419i) q^{19} +(1.81855 + 3.14983i) q^{20} +(-0.701847 - 1.21563i) q^{22} +8.26001 q^{23} +(5.59398 + 9.68906i) q^{24} +(2.01756 - 3.49452i) q^{25} +(5.71283 + 6.44197i) q^{26} +4.32156 q^{27} +(1.98009 - 3.42962i) q^{29} +(-3.22710 + 5.58950i) q^{30} +(-1.49436 + 2.58831i) q^{31} +2.62861 q^{32} +(0.808663 - 1.40065i) q^{33} -15.4129 q^{34} +(-8.46189 + 14.6564i) q^{36} +1.75588 q^{37} +(4.56938 - 7.91440i) q^{38} +(-3.13683 + 9.41161i) q^{39} +(-1.99705 - 3.45900i) q^{40} +(1.83584 - 3.17977i) q^{41} +(-3.19042 - 5.52598i) q^{43} +(1.08823 + 1.88488i) q^{44} -4.48964 q^{45} -19.7252 q^{46} +(-2.17030 - 3.75906i) q^{47} +(-3.17067 - 5.49176i) q^{48} +(-4.81802 + 8.34505i) q^{50} +(-8.87930 - 15.3794i) q^{51} +(-8.85791 - 9.98846i) q^{52} +(-0.212770 + 0.368529i) q^{53} -10.3200 q^{54} +(-0.288693 + 0.500031i) q^{55} +10.5296 q^{57} +(-4.72853 + 8.19006i) q^{58} -6.00863 q^{59} +(5.00371 - 8.66669i) q^{60} +(1.10337 - 1.91109i) q^{61} +(3.56859 - 6.18097i) q^{62} -10.8866 q^{64} +(1.11985 - 3.35995i) q^{65} +(-1.93112 + 3.34479i) q^{66} +(-3.50651 - 6.07346i) q^{67} +23.8981 q^{68} +(-11.3636 - 19.6824i) q^{69} +(-1.80127 - 3.11988i) q^{71} +(9.29247 - 16.0950i) q^{72} +(2.46714 - 4.27321i) q^{73} -4.19311 q^{74} -11.1026 q^{75} +(-7.08496 + 12.2715i) q^{76} +(7.49088 - 22.4753i) q^{78} +(-1.39270 - 2.41223i) q^{79} +(1.13193 + 1.96056i) q^{80} +(0.910609 + 1.57722i) q^{81} +(-4.38406 + 7.59342i) q^{82} +2.86819 q^{83} +(3.16992 + 5.49045i) q^{85} +(7.61885 + 13.1962i) q^{86} -10.8964 q^{87} +(-1.19505 - 2.06989i) q^{88} +2.09311 q^{89} +10.7214 q^{90} +30.5845 q^{92} +8.22340 q^{93} +(5.18275 + 8.97679i) q^{94} -3.75908 q^{95} +(-3.61628 - 6.26357i) q^{96} +(3.84852 + 6.66584i) q^{97} -2.68663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9	\( 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} - 16 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + q^{20} - 5 q^{22} + 2 q^{23} + 11 q^{24} + 7 q^{25} + 16 q^{26} + 8 q^{27} + 3 q^{29} - 5 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 32 q^{34} - 21 q^{36} + 26 q^{37} + 17 q^{38} - 20 q^{39} + 5 q^{40} + 8 q^{41} - 11 q^{43} + 21 q^{44} - 14 q^{45} - 32 q^{46} + q^{47} - 21 q^{48} + 6 q^{50} - 20 q^{51} - 41 q^{52} - 2 q^{53} - 36 q^{54} - 9 q^{55} + 42 q^{57} - 8 q^{58} + 26 q^{59} + 20 q^{60} + 5 q^{61} - 5 q^{62} - 30 q^{64} - 5 q^{65} - 18 q^{66} - 11 q^{67} + 58 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} + 30 q^{73} + 6 q^{74} - 6 q^{75} + 9 q^{76} + 16 q^{78} + 7 q^{79} + 7 q^{80} - 6 q^{81} - q^{82} + 54 q^{83} - q^{85} - 7 q^{86} + 32 q^{87} + 8 q^{89} + 16 q^{90} + 54 q^{92} + 14 q^{93} - 45 q^{94} + 12 q^{95} - 19 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 - 16 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + q^20 - 5 * q^22 + 2 * q^23 + 11 * q^24 + 7 * q^25 + 16 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 + 26 * q^37 + 17 * q^38 - 20 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 - 14 * q^45 - 32 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 - 41 * q^52 - 2 * q^53 - 36 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 + 26 * q^59 + 20 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 5 * q^65 - 18 * q^66 - 11 * q^67 + 58 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 + 30 * q^73 + 6 * q^74 - 6 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 - 7 * q^86 + 32 * q^87 + 8 * q^89 + 16 * q^90 + 54 * q^92 + 14 * q^93 - 45 * q^94 + 12 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Introduction

L-functions

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