LMFDB - Embedded newform 1274.2.o.e.569.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1274,2,Mod(459,1274)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1274, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1274.459");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			569.6
Root			$0.500000 + 3.15681i$ of defining polynomial
Character	$\chi$	$=$	1274.569
Dual form			1274.2.o.e.459.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.14539 - 1.98388i) q^{3} -1.00000 q^{4} +(-0.781015 - 0.450919i) q^{5} +(1.98388 + 1.14539i) q^{6} -1.00000i q^{8} +(-1.12385 - 1.94657i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.14539 - 1.98388i) q^{3} -1.00000 q^{4} +(-0.781015 - 0.450919i) q^{5} +(1.98388 + 1.14539i) q^{6} -1.00000i q^{8} +(-1.12385 - 1.94657i) q^{9} +(0.450919 - 0.781015i) q^{10} +(3.75609 + 2.16858i) q^{11} +(-1.14539 + 1.98388i) q^{12} +(0.426876 + 3.58019i) q^{13} +(-1.78914 + 1.03296i) q^{15} +1.00000 q^{16} +5.06592 q^{17} +(1.94657 - 1.12385i) q^{18} +(5.34544 - 3.08619i) q^{19} +(0.781015 + 0.450919i) q^{20} +(-2.16858 + 3.75609i) q^{22} -8.45117 q^{23} +(-1.98388 - 1.14539i) q^{24} +(-2.09334 - 3.62578i) q^{25} +(-3.58019 + 0.426876i) q^{26} +1.72335 q^{27} +(1.09643 + 1.89907i) q^{29} +(-1.03296 - 1.78914i) q^{30} +(0.756094 - 0.436531i) q^{31} +1.00000i q^{32} +(8.60441 - 4.96776i) q^{33} +5.06592i q^{34} +(1.12385 + 1.94657i) q^{36} +0.144306i q^{37} +(3.08619 + 5.34544i) q^{38} +(7.59161 + 3.25386i) q^{39} +(-0.450919 + 0.781015i) q^{40} +(3.46110 - 1.99827i) q^{41} +(3.85426 - 6.67577i) q^{43} +(-3.75609 - 2.16858i) q^{44} +2.02707i q^{45} -8.45117i q^{46} +(2.52979 + 1.46057i) q^{47} +(1.14539 - 1.98388i) q^{48} +(3.62578 - 2.09334i) q^{50} +(5.80247 - 10.0502i) q^{51} +(-0.426876 - 3.58019i) q^{52} +(-0.848493 - 1.46963i) q^{53} +1.72335i q^{54} +(-1.95571 - 3.38739i) q^{55} -14.1396i q^{57} +(-1.89907 + 1.09643i) q^{58} -8.54933i q^{59} +(1.78914 - 1.03296i) q^{60} +(4.16720 + 7.21780i) q^{61} +(0.436531 + 0.756094i) q^{62} -1.00000 q^{64} +(1.28098 - 2.98867i) q^{65} +(4.96776 + 8.60441i) q^{66} +(8.99180 + 5.19142i) q^{67} -5.06592 q^{68} +(-9.67992 + 16.7661i) q^{69} +(-2.83932 - 1.63928i) q^{71} +(-1.94657 + 1.12385i) q^{72} +(0.466808 - 0.269511i) q^{73} -0.144306 q^{74} -9.59081 q^{75} +(-5.34544 + 3.08619i) q^{76} +(-3.25386 + 7.59161i) q^{78} +(-3.26674 + 5.65817i) q^{79} +(-0.781015 - 0.450919i) q^{80} +(5.34547 - 9.25862i) q^{81} +(1.99827 + 3.46110i) q^{82} -13.2348i q^{83} +(-3.95656 - 2.28432i) q^{85} +(6.67577 + 3.85426i) q^{86} +5.02337 q^{87} +(2.16858 - 3.75609i) q^{88} +7.79180i q^{89} -2.02707 q^{90} +8.45117 q^{92} -2.00000i q^{93} +(-1.46057 + 2.52979i) q^{94} -5.56649 q^{95} +(1.98388 + 1.14539i) q^{96} +(-10.1378 - 5.85305i) q^{97} -9.74866i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} - 12 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q + 2 * q^3 - 12 * q^4 - 6 * q^6 - 6 * q^9	$ 12 q + 2 q^{3} - 12 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} + 18 q^{11} - 2 q^{12} + 8 q^{13} - 6 q^{15} + 12 q^{16} + 8 q^{17} + 12 q^{19} - 2 q^{22} + 12 q^{23} + 6 q^{24} + 12 q^{25} + 2 q^{26} - 40 q^{27} - 10 q^{29} + 14 q^{30} - 18 q^{31} + 12 q^{33} + 6 q^{36} + 4 q^{38} + 24 q^{39} - 2 q^{40} + 24 q^{41} + 26 q^{43} - 18 q^{44} - 48 q^{47} + 2 q^{48} - 12 q^{50} + 18 q^{51} - 8 q^{52} - 18 q^{53} + 6 q^{55} - 24 q^{58} + 6 q^{60} + 28 q^{61} + 2 q^{62} - 12 q^{64} - 4 q^{65} + 42 q^{67} - 8 q^{68} - 32 q^{69} + 48 q^{71} + 48 q^{73} - 96 q^{75} - 12 q^{76} - 8 q^{78} - 22 q^{79} - 34 q^{81} - 6 q^{82} + 54 q^{85} + 6 q^{86} + 4 q^{87} + 2 q^{88} - 12 q^{90} - 12 q^{92} - 8 q^{94} - 64 q^{95} - 6 q^{96} - 60 q^{97}+O(q^{100}) $ 12 * q + 2 * q^3 - 12 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 + 18 * q^11 - 2 * q^12 + 8 * q^13 - 6 * q^15 + 12 * q^16 + 8 * q^17 + 12 * q^19 - 2 * q^22 + 12 * q^23 + 6 * q^24 + 12 * q^25 + 2 * q^26 - 40 * q^27 - 10 * q^29 + 14 * q^30 - 18 * q^31 + 12 * q^33 + 6 * q^36 + 4 * q^38 + 24 * q^39 - 2 * q^40 + 24 * q^41 + 26 * q^43 - 18 * q^44 - 48 * q^47 + 2 * q^48 - 12 * q^50 + 18 * q^51 - 8 * q^52 - 18 * q^53 + 6 * q^55 - 24 * q^58 + 6 * q^60 + 28 * q^61 + 2 * q^62 - 12 * q^64 - 4 * q^65 + 42 * q^67 - 8 * q^68 - 32 * q^69 + 48 * q^71 + 48 * q^73 - 96 * q^75 - 12 * q^76 - 8 * q^78 - 22 * q^79 - 34 * q^81 - 6 * q^82 + 54 * q^85 + 6 * q^86 + 4 * q^87 + 2 * q^88 - 12 * q^90 - 12 * q^92 - 8 * q^94 - 64 * q^95 - 6 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.14539	−	1.98388i	0.661293	−	1.14539i	−0.318983	−	0.947760i	$-0.603341\pi$
$3$	1.14539	−	1.98388i	0.661293	−	1.14539i	0.980276	−	0.197633i	$-0.0633254\pi$
$4$	−1.00000			−0.500000
$5$	−0.781015	−	0.450919i	−0.349281	−	0.201657i	0.315088	−	0.949063i	$-0.397966\pi$
$5$	−0.781015	−	0.450919i	−0.349281	−	0.201657i	−0.664368	+	0.747405i	$0.731299\pi$
$6$	1.98388	+	1.14539i	0.809915	+	0.467605i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−1.12385	−	1.94657i	−0.374617	−	0.648856i
$10$	0.450919	−	0.781015i	0.142593	−	0.246979i
$11$	3.75609	+	2.16858i	1.13251	+	0.653852i	0.944564	−	0.328328i	$-0.106485\pi$
$11$	3.75609	+	2.16858i	1.13251	+	0.653852i	0.187941	+	0.982180i	$0.439819\pi$
$12$	−1.14539	+	1.98388i	−0.330647	+	0.572697i
$13$	0.426876	+	3.58019i	0.118394	+	0.992967i
$13$	0.426876	+	3.58019i	0.118394	+	0.992967i
$14$		0			0
$15$	−1.78914	+	1.03296i	−0.461954	+	0.266709i
$16$	1.00000			0.250000
$17$	5.06592			1.22867			0.614333	−	0.789047i	$-0.289425\pi$
$17$	5.06592			1.22867			0.614333	+	0.789047i	$0.289425\pi$
$18$	1.94657	−	1.12385i	0.458811	−	0.264894i
$19$	5.34544	−	3.08619i	1.22633	−	0.708021i	0.260068	−	0.965590i	$-0.416255\pi$
$19$	5.34544	−	3.08619i	1.22633	−	0.708021i	0.966260	+	0.257570i	$0.0829217\pi$
$20$	0.781015	+	0.450919i	0.174640	+	0.100829i
$21$		0			0
$22$	−2.16858	+	3.75609i	−0.462343	+	0.800802i
$23$	−8.45117			−1.76219			−0.881096	−	0.472938i	$-0.843193\pi$
$23$	−8.45117			−1.76219			−0.881096	+	0.472938i	$0.843193\pi$
$24$	−1.98388	−	1.14539i	−0.404958	−	0.233802i
$25$	−2.09334	−	3.62578i	−0.418669	−	0.725155i
$26$	−3.58019	+	0.426876i	−0.702133	+	0.0837173i
$27$	1.72335			0.331659
$28$		0			0
$29$	1.09643	+	1.89907i	0.203602	+	0.352649i	0.949686	−	0.313203i	$-0.101402\pi$
$29$	1.09643	+	1.89907i	0.203602	+	0.352649i	−0.746085	+	0.665851i	$0.768069\pi$
$30$	−1.03296	−	1.78914i	−0.188592	−	0.326651i
$31$	0.756094	−	0.436531i	0.135799	−	0.0784033i	−0.430562	−	0.902561i	$-0.641684\pi$
$31$	0.756094	−	0.436531i	0.135799	−	0.0784033i	0.566360	+	0.824158i	$0.308351\pi$
$32$			1.00000i			0.176777i
$33$	8.60441	−	4.96776i	1.49784	−	0.864776i
$34$			5.06592i			0.868798i
$35$		0			0
$36$	1.12385	+	1.94657i	0.187309	+	0.324428i
$37$			0.144306i			0.0237238i	0.999930	+	0.0118619i	$0.00377585\pi$
$37$			0.144306i			0.0237238i	−0.999930	+	0.0118619i	$0.996224\pi$
$38$	3.08619	+	5.34544i	0.500646	+	0.867145i
$39$	7.59161	+	3.25386i	1.21563	+	0.521034i
$40$	−0.450919	+	0.781015i	−0.0712966	+	0.123489i
$41$	3.46110	−	1.99827i	0.540533	−	0.312077i	−0.204762	−	0.978812i	$-0.565642\pi$
$41$	3.46110	−	1.99827i	0.540533	−	0.312077i	0.745295	+	0.666735i	$0.232309\pi$
$42$		0			0
$43$	3.85426	−	6.67577i	0.587768	−	1.01804i	−0.406756	−	0.913537i	$-0.633340\pi$
$43$	3.85426	−	6.67577i	0.587768	−	1.01804i	0.994524	−	0.104508i	$-0.0333267\pi$
$44$	−3.75609	−	2.16858i	−0.566253	−	0.326926i
$45$			2.02707i			0.302177i
$46$		−	8.45117i		−	1.24606i
$47$	2.52979	+	1.46057i	0.369008	+	0.213047i	0.673025	−	0.739620i	$-0.264995\pi$
$47$	2.52979	+	1.46057i	0.369008	+	0.213047i	−0.304017	+	0.952667i	$0.598328\pi$
$48$	1.14539	−	1.98388i	0.165323	−	0.286348i
$49$		0			0
$50$	3.62578	−	2.09334i	0.512762	−	0.296043i
$51$	5.80247	−	10.0502i	0.812509	−	1.40731i
$52$	−0.426876	−	3.58019i	−0.0591970	−	0.496483i
$53$	−0.848493	−	1.46963i	−0.116549	−	0.201870i	0.801849	−	0.597527i	$-0.203850\pi$
$53$	−0.848493	−	1.46963i	−0.116549	−	0.201870i	−0.918398	+	0.395658i	$0.870517\pi$
$54$			1.72335i			0.234518i
$55$	−1.95571	−	3.38739i	−0.263708	−	0.456756i
$56$		0			0
$57$		−	14.1396i		−	1.87284i
$58$	−1.89907	+	1.09643i	−0.249360	+	0.143968i
$59$		−	8.54933i		−	1.11303i	−0.830838	−	0.556514i	$-0.812139\pi$
$59$		−	8.54933i		−	1.11303i	0.830838	−	0.556514i	$-0.187861\pi$
$60$	1.78914	−	1.03296i	0.230977	−	0.133355i
$61$	4.16720	+	7.21780i	0.533555	+	0.924145i	0.999232	+	0.0391900i	$0.0124777\pi$
$61$	4.16720	+	7.21780i	0.533555	+	0.924145i	−0.465676	+	0.884955i	$0.654189\pi$
$62$	0.436531	+	0.756094i	0.0554395	+	0.0960241i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.28098	−	2.98867i	0.158886	−	0.370699i
$66$	4.96776	+	8.60441i	0.611489	+	1.05913i
$67$	8.99180	+	5.19142i	1.09852	+	0.634233i	0.935833	−	0.352444i	$-0.114649\pi$
$67$	8.99180	+	5.19142i	1.09852	+	0.634233i	0.162691	+	0.986677i	$0.447983\pi$
$68$	−5.06592			−0.614333
$69$	−9.67992	+	16.7661i	−1.16532	+	2.01840i
$70$		0			0
$71$	−2.83932	−	1.63928i	−0.336965	−	0.194547i	0.321964	−	0.946752i	$-0.395657\pi$
$71$	−2.83932	−	1.63928i	−0.336965	−	0.194547i	−0.658929	+	0.752205i	$0.728990\pi$
$72$	−1.94657	+	1.12385i	−0.229405	+	0.132447i
$73$	0.466808	−	0.269511i	0.0546357	−	0.0315439i	−0.472433	−	0.881366i	$-0.656624\pi$
$73$	0.466808	−	0.269511i	0.0546357	−	0.0315439i	0.527069	+	0.849822i	$0.323291\pi$
$74$	−0.144306			−0.0167753
$75$	−9.59081			−1.10745
$76$	−5.34544	+	3.08619i	−0.613164	+	0.354010i
$77$		0			0
$78$	−3.25386	+	7.59161i	−0.368427	+	0.859581i
$79$	−3.26674	+	5.65817i	−0.367537	+	0.636593i	−0.989180	−	0.146708i	$-0.953132\pi$
$79$	−3.26674	+	5.65817i	−0.367537	+	0.636593i	0.621643	+	0.783301i	$0.286466\pi$
$80$	−0.781015	−	0.450919i	−0.0873202	−	0.0504143i
$81$	5.34547	−	9.25862i	0.593941	−	1.02874i
$82$	1.99827	+	3.46110i	0.220672	+	0.382215i
$83$		−	13.2348i		−	1.45271i	−0.687319	−	0.726356i	$-0.741212\pi$
$83$		−	13.2348i		−	1.45271i	0.687319	−	0.726356i	$-0.258788\pi$
$84$		0			0
$85$	−3.95656	−	2.28432i	−0.429149	−	0.247769i
$86$	6.67577	+	3.85426i	0.719866	+	0.415615i
$87$	5.02337			0.538562
$88$	2.16858	−	3.75609i	0.231172	−	0.400401i
$89$			7.79180i			0.825929i	0.910747	+	0.412965i	$0.135507\pi$
$89$			7.79180i			0.825929i	−0.910747	+	0.412965i	$0.864493\pi$
$90$	−2.02707			−0.213672
$91$		0			0
$92$	8.45117			0.881096
$93$		−	2.00000i		−	0.207390i
$94$	−1.46057	+	2.52979i	−0.150647	+	0.260928i
$95$	−5.56649			−0.571110
$96$	1.98388	+	1.14539i	0.202479	+	0.116901i
$97$	−10.1378	−	5.85305i	−1.02934	−	0.594287i	−0.112541	−	0.993647i	$-0.535899\pi$
$97$	−10.1378	−	5.85305i	−1.02934	−	0.594287i	−0.916794	+	0.399360i	$0.869232\pi$
$98$		0			0
$99$		−	9.74866i		−	0.979777i
$100$	2.09334	+	3.62578i	0.209334	+	0.362578i
$101$	5.37145	−	9.30362i	0.534479	−	0.925745i	−0.464709	−	0.885463i	$-0.653841\pi$
$101$	5.37145	−	9.30362i	0.534479	−	0.925745i	0.999188	−	0.0402814i	$-0.0128254\pi$
$102$	10.0502	+	5.80247i	0.995116	+	0.574530i
$103$	2.40550	−	4.16644i	0.237021	−	0.410532i	−0.722837	−	0.691018i	$-0.757162\pi$
$103$	2.40550	−	4.16644i	0.237021	−	0.410532i	0.959858	+	0.280486i	$0.0904958\pi$
$104$	3.58019	−	0.426876i	0.351067	−	0.0418586i
$105$		0			0
$106$	1.46963	−	0.848493i	0.142743	−	0.0824129i
$107$	13.6530			1.31989			0.659944	−	0.751315i	$-0.270580\pi$
$107$	13.6530			1.31989			0.659944	+	0.751315i	$0.270580\pi$
$108$	−1.72335			−0.165829
$109$	−4.43186	+	2.55874i	−0.424495	+	0.245082i	−0.696999	−	0.717072i	$-0.745482\pi$
$109$	−4.43186	+	2.55874i	−0.424495	+	0.245082i	0.272503	+	0.962155i	$0.412148\pi$
$110$	3.38739	−	1.95571i	0.322975	−	0.186470i
$111$	0.286286	+	0.165287i	0.0271731	+	0.0156884i
$112$		0			0
$113$	−8.96603	+	15.5296i	−0.843453	+	1.46090i	0.0435052	+	0.999053i	$0.486147\pi$
$113$	−8.96603	+	15.5296i	−0.843453	+	1.46090i	−0.886958	+	0.461850i	$0.847186\pi$
$114$	14.1396			1.32430
$115$	6.60049	+	3.81080i	0.615499	+	0.355359i
$116$	−1.09643	−	1.89907i	−0.101801	−	0.176324i
$117$	6.48935	−	4.85455i	0.599940	−	0.448803i
$118$	8.54933			0.787030
$119$		0			0
$120$	1.03296	+	1.78914i	0.0942959	+	0.163325i
$121$	3.90550	+	6.76452i	0.355045	+	0.614956i
$122$	−7.21780	+	4.16720i	−0.653469	+	0.377281i
$123$		−	9.15521i		−	0.825498i
$124$	−0.756094	+	0.436531i	−0.0678993	+	0.0392017i
$125$			8.28491i			0.741025i
$126$		0			0
$127$	−9.75681	−	16.8993i	−0.865777	−	1.49957i	−0.866273	−	0.499570i	$-0.833491\pi$
$127$	−9.75681	−	16.8993i	−0.865777	−	1.49957i	0.000496195	−	1.00000i	$-0.499842\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−8.82928	−	15.2928i	−0.777375	−	1.34645i
$130$	2.98867	+	1.28098i	0.262124	+	0.112350i
$131$	−10.3248	+	17.8831i	−0.902083	+	1.56245i	−0.0772984	+	0.997008i	$0.524629\pi$
$131$	−10.3248	+	17.8831i	−0.902083	+	1.56245i	−0.824785	+	0.565446i	$0.808704\pi$
$132$	−8.60441	+	4.96776i	−0.748918	+	0.432388i
$133$		0			0
$134$	−5.19142	+	8.99180i	−0.448470	+	0.776773i
$135$	−1.34596	−	0.777092i	−0.115842	−	0.0668814i
$136$		−	5.06592i		−	0.434399i
$137$		−	3.18956i		−	0.272503i	−0.990674	−	0.136251i	$-0.956495\pi$
$137$		−	3.18956i		−	0.272503i	0.990674	−	0.136251i	$-0.0435055\pi$
$138$	−16.7661	−	9.67992i	−1.42723	−	0.824009i
$139$	−0.297855	+	0.515900i	−0.0252637	+	0.0437581i	−0.878381	−	0.477961i	$-0.841376\pi$
$139$	−0.297855	+	0.515900i	−0.0252637	+	0.0437581i	0.853117	+	0.521719i	$0.174709\pi$
$140$		0			0
$141$	5.79521	−	3.34587i	0.488045	−	0.281773i
$142$	1.63928	−	2.83932i	0.137565	−	0.238270i
$143$	−6.16055	+	14.3733i	−0.515171	+	1.20195i
$144$	−1.12385	−	1.94657i	−0.0936543	−	0.162214i
$145$		−	1.97760i		−	0.164231i
$146$	0.269511	+	0.466808i	0.0223049	+	0.0386333i
$147$		0			0
$148$		−	0.144306i		−	0.0118619i
$149$	−9.70783	+	5.60482i	−0.795297	+	0.459165i	−0.841824	−	0.539752i	$-0.818518\pi$
$149$	−9.70783	+	5.60482i	−0.795297	+	0.459165i	0.0465273	+	0.998917i	$0.485185\pi$
$150$		−	9.59081i		−	0.783086i
$151$	11.3216	−	6.53653i	0.921339	−	0.531935i	0.0372772	−	0.999305i	$-0.488132\pi$
$151$	11.3216	−	6.53653i	0.921339	−	0.531935i	0.884062	+	0.467369i	$0.154798\pi$
$152$	−3.08619	−	5.34544i	−0.250323	−	0.433572i
$153$	−5.69334	−	9.86116i	−0.460280	−	0.797228i
$154$		0			0
$155$	−0.787362			−0.0632424
$156$	−7.59161	−	3.25386i	−0.607815	−	0.260517i
$157$	8.96225	+	15.5231i	0.715266	+	1.23888i	0.962857	+	0.270012i	$0.0870276\pi$
$157$	8.96225	+	15.5231i	0.715266	+	1.23888i	−0.247591	+	0.968865i	$0.579639\pi$
$158$	−5.65817	−	3.26674i	−0.450139	−	0.259888i
$159$	−3.88743			−0.308293
$160$	0.450919	−	0.781015i	0.0356483	−	0.0617447i
$161$		0			0
$162$	9.25862	+	5.34547i	0.727426	+	0.419980i
$163$	−17.5958	+	10.1589i	−1.37821	+	0.795710i	−0.991944	−	0.126677i	$-0.959569\pi$
$163$	−17.5958	+	10.1589i	−1.37821	+	0.795710i	−0.386266	+	0.922387i	$0.626235\pi$
$164$	−3.46110	+	1.99827i	−0.270267	+	0.156038i
$165$	−8.96024			−0.697553
$166$	13.2348			1.02722
$167$	2.79770	−	1.61525i	0.216493	−	0.124992i	−0.387833	−	0.921730i	$-0.626776\pi$
$167$	2.79770	−	1.61525i	0.216493	−	0.124992i	0.604325	+	0.796738i	$0.293443\pi$
$168$		0			0
$169$	−12.6356	+	3.05660i	−0.971966	+	0.235123i
$170$	2.28432	−	3.95656i	0.175199	−	0.303454i
$171$	−12.0150	−	6.93684i	−0.918807	−	0.530474i
$172$	−3.85426	+	6.67577i	−0.293884	+	0.509022i
$173$	4.58522	+	7.94183i	0.348608	+	0.603806i	0.986002	−	0.166731i	$-0.0533212\pi$
$173$	4.58522	+	7.94183i	0.348608	+	0.603806i	−0.637395	+	0.770538i	$0.719988\pi$
$174$			5.02337i			0.380821i
$175$		0			0
$176$	3.75609	+	2.16858i	0.283126	+	0.163463i
$177$	−16.9608	−	9.79235i	−1.27486	−	0.736038i
$178$	−7.79180			−0.584020
$179$	−8.47747	+	14.6834i	−0.633636	+	1.09749i	0.353166	+	0.935561i	$0.385105\pi$
$179$	−8.47747	+	14.6834i	−0.633636	+	1.09749i	−0.986802	+	0.161929i	$0.948228\pi$
$180$		−	2.02707i		−	0.151089i
$181$	2.65743			0.197525			0.0987626	−	0.995111i	$-0.468512\pi$
$181$	2.65743			0.197525			0.0987626	+	0.995111i	$0.468512\pi$
$182$		0			0
$183$	19.0923			1.41135
$184$			8.45117i			0.623029i
$185$	0.0650705	−	0.112705i	0.00478408	−	0.00828627i
$186$	2.00000			0.146647
$187$	19.0281	+	10.9859i	1.39147	+	0.803366i
$188$	−2.52979	−	1.46057i	−0.184504	−	0.106523i
$189$		0			0
$190$		−	5.56649i		−	0.403836i
$191$	12.2430	+	21.2056i	0.885875	+	1.53438i	0.844708	+	0.535228i	$0.179774\pi$
$191$	12.2430	+	21.2056i	0.885875	+	1.53438i	0.0411671	+	0.999152i	$0.486892\pi$
$192$	−1.14539	+	1.98388i	−0.0826616	+	0.143174i
$193$	−10.6009	−	6.12046i	−0.763072	−	0.440560i	0.0673254	−	0.997731i	$-0.478553\pi$
$193$	−10.6009	−	6.12046i	−0.763072	−	0.440560i	−0.830398	+	0.557171i	$0.811887\pi$
$194$	5.85305	−	10.1378i	0.420224	−	0.727850i
$195$	−4.46194	−	5.96452i	−0.319526	−	0.427128i
$196$		0			0
$197$	4.72634	−	2.72876i	0.336738	−	0.194416i	−0.322091	−	0.946709i	$-0.604386\pi$
$197$	4.72634	−	2.72876i	0.336738	−	0.194416i	0.658829	+	0.752293i	$0.271052\pi$
$198$	9.74866			0.692807
$199$	−12.8166			−0.908548			−0.454274	−	0.890862i	$-0.650101\pi$
$199$	−12.8166			−0.908548			−0.454274	+	0.890862i	$0.650101\pi$
$200$	−3.62578	+	2.09334i	−0.256381	+	0.148022i
$201$	20.5983	−	11.8924i	1.45289	−	0.838828i
$202$	9.30362	+	5.37145i	0.654600	+	0.377934i
$203$		0			0
$204$	−5.80247	+	10.0502i	−0.406254	+	0.703653i
$205$	−3.60423			−0.251730
$206$	4.16644	+	2.40550i	0.290290	+	0.167599i
$207$	9.49787	+	16.4508i	0.660147	+	1.14341i
$208$	0.426876	+	3.58019i	0.0295985	+	0.248242i
$209$	26.7706			1.85176
$210$		0			0
$211$	9.65552	+	16.7239i	0.664713	+	1.15132i	0.979363	+	0.202110i	$0.0647797\pi$
$211$	9.65552	+	16.7239i	0.664713	+	1.15132i	−0.314649	+	0.949208i	$0.601887\pi$
$212$	0.848493	+	1.46963i	0.0582747	+	0.100935i
$213$	−6.50427	+	3.75524i	−0.445665	+	0.257305i
$214$			13.6530i			0.933302i
$215$	−6.02046	+	3.47592i	−0.410592	+	0.237056i
$216$		−	1.72335i		−	0.117259i
$217$		0			0
$218$	−2.55874	−	4.43186i	−0.173299	−	0.300163i
$219$		−	1.23479i		−	0.0834391i
$220$	1.95571	+	3.38739i	0.131854	+	0.228378i
$221$	2.16252	+	18.1370i	0.145467	+	1.22002i
$222$	−0.165287	+	0.286286i	−0.0110934	+	0.0192143i
$223$	9.21079	−	5.31785i	0.616800	−	0.356110i	−0.158822	−	0.987307i	$-0.550770\pi$
$223$	9.21079	−	5.31785i	0.616800	−	0.356110i	0.775622	+	0.631197i	$0.217436\pi$
$224$		0			0
$225$	−4.70522	+	8.14967i	−0.313681	+	0.543312i
$226$	−15.5296	−	8.96603i	−1.03301	−	0.596411i
$227$			22.7217i			1.50809i	0.656821	+	0.754047i	$0.271901\pi$
$227$			22.7217i			1.50809i	−0.656821	+	0.754047i	$0.728099\pi$
$228$			14.1396i			0.936418i
$229$	−17.5885	−	10.1547i	−1.16228	−	0.671042i	−0.210429	−	0.977609i	$-0.567486\pi$
$229$	−17.5885	−	10.1547i	−1.16228	−	0.671042i	−0.951849	+	0.306567i	$0.900820\pi$
$230$	−3.81080	+	6.60049i	−0.251277	+	0.435224i
$231$		0			0
$232$	1.89907	−	1.09643i	0.124680	−	0.0719841i
$233$	−5.32231	+	9.21851i	−0.348676	+	0.603925i	−0.986015	−	0.166659i	$-0.946702\pi$
$233$	−5.32231	+	9.21851i	−0.348676	+	0.603925i	0.637338	+	0.770584i	$0.280035\pi$
$234$	4.85455	+	6.48935i	0.317352	+	0.424222i
$235$	−1.31720	−	2.28146i	−0.0859248	−	0.148826i
$236$			8.54933i			0.556514i
$237$	7.48341	+	12.9617i	0.486100	+	0.841950i
$238$		0			0
$239$			0.311564i			0.0201534i	0.999949	+	0.0100767i	$0.00320757\pi$
$239$			0.311564i			0.0201534i	−0.999949	+	0.0100767i	$0.996792\pi$
$240$	−1.78914	+	1.03296i	−0.115488	+	0.0666773i
$241$		−	25.2995i		−	1.62969i	−0.579682	−	0.814843i	$-0.696823\pi$
$241$		−	25.2995i		−	1.62969i	0.579682	−	0.814843i	$-0.303177\pi$
$242$	−6.76452	+	3.90550i	−0.434840	+	0.251055i
$243$	−9.66031	−	16.7321i	−0.619709	−	1.07337i
$244$	−4.16720	−	7.21780i	−0.266778	−	0.462073i
$245$		0			0
$246$	9.15521			0.583715
$247$	13.3310	+	17.8203i	0.848231	+	1.13388i
$248$	−0.436531	−	0.756094i	−0.0277198	−	0.0480120i
$249$	−26.2563	−	15.1591i	−1.66393	−	0.960669i
$250$	−8.28491			−0.523984
$251$	−4.02015	+	6.96311i	−0.253750	+	0.439507i	−0.964555	−	0.263881i	$-0.914997\pi$
$251$	−4.02015	+	6.96311i	−0.253750	+	0.439507i	0.710805	+	0.703389i	$0.248331\pi$
$252$		0			0
$253$	−31.7434	−	18.3271i	−1.99569	−	1.15221i
$254$	16.8993	−	9.75681i	1.06036	−	0.612197i
$255$	−9.06364	+	5.23289i	−0.567587	+	0.327697i
$256$	1.00000			0.0625000
$257$	−16.9327			−1.05623			−0.528116	−	0.849172i	$-0.677101\pi$
$257$	−16.9327			−1.05623			−0.528116	+	0.849172i	$0.677101\pi$
$258$	15.2928	−	8.82928i	0.952085	−	0.549687i
$259$		0			0
$260$	−1.28098	+	2.98867i	−0.0794431	+	0.185350i
$261$	2.46445	−	4.26855i	0.152545	−	0.264217i
$262$	−17.8831	−	10.3248i	−1.10482	−	0.637869i
$263$	−5.16045	+	8.93817i	−0.318207	+	0.551151i	−0.980114	−	0.198435i	$-0.936414\pi$
$263$	−5.16045	+	8.93817i	−0.318207	+	0.551151i	0.661907	+	0.749586i	$0.269747\pi$
$264$	−4.96776	−	8.60441i	−0.305744	−	0.529565i
$265$			1.53041i			0.0940122i
$266$		0			0
$267$	15.4580	+	8.92468i	0.946014	+	0.546181i
$268$	−8.99180	−	5.19142i	−0.549262	−	0.317116i
$269$	6.13999			0.374362			0.187181	−	0.982325i	$-0.440065\pi$
$269$	6.13999			0.374362			0.187181	+	0.982325i	$0.440065\pi$
$270$	0.777092	−	1.34596i	0.0472923	−	0.0819127i
$271$		−	10.6772i		−	0.648594i	−0.945955	−	0.324297i	$-0.894872\pi$
$271$		−	10.6772i		−	0.648594i	0.945955	−	0.324297i	$-0.105128\pi$
$272$	5.06592			0.307167
$273$		0			0
$274$	3.18956			0.192689
$275$		−	18.1583i		−	1.09499i
$276$	9.67992	−	16.7661i	0.582662	−	1.00920i
$277$	−21.9090			−1.31638			−0.658191	−	0.752851i	$-0.728678\pi$
$277$	−21.9090			−1.31638			−0.658191	+	0.752851i	$0.728678\pi$
$278$	−0.515900	−	0.297855i	−0.0309416	−	0.0178642i
$279$	−1.69948	−	0.981193i	−0.101745	−	0.0587425i
$280$		0			0
$281$			25.7719i			1.53743i	0.639594	+	0.768713i	$0.279102\pi$
$281$			25.7719i			1.53743i	−0.639594	+	0.768713i	$0.720898\pi$
$282$	3.34587	+	5.79521i	0.199243	+	0.345100i
$283$	5.66344	−	9.80937i	0.336657	−	0.583107i	−0.647145	−	0.762367i	$-0.724037\pi$
$283$	5.66344	−	9.80937i	0.336657	−	0.583107i	0.983802	+	0.179260i	$0.0573704\pi$
$284$	2.83932	+	1.63928i	0.168482	+	0.0972733i
$285$	−6.37582	+	11.0432i	−0.377671	+	0.654146i
$286$	−14.3733	−	6.16055i	−0.849908	−	0.364281i
$287$		0			0
$288$	1.94657	−	1.12385i	0.114703	−	0.0662236i
$289$	8.66355			0.509621
$290$	1.97760			0.116129
$291$	−23.2235	+	13.4081i	−1.36139	+	0.785996i
$292$	−0.466808	+	0.269511i	−0.0273178	+	0.0157720i
$293$	−20.5646	−	11.8730i	−1.20140	−	0.693626i	−0.240530	−	0.970642i	$-0.577321\pi$
$293$	−20.5646	−	11.8730i	−1.20140	−	0.693626i	−0.960865	+	0.277016i	$0.910655\pi$
$294$		0			0
$295$	−3.85506	+	6.67716i	−0.224450	+	0.388759i
$296$	0.144306			0.00838763
$297$	6.47306	+	3.73723i	0.375605	+	0.216856i
$298$	−5.60482	−	9.70783i	−0.324678	−	0.562360i
$299$	−3.60760	−	30.2568i	−0.208633	−	1.74980i
$300$	9.59081			0.553725
$301$		0			0
$302$	6.53653	+	11.3216i	0.376135	+	0.651485i
$303$	−12.3048	−	21.3126i	−0.706894	−	1.22438i
$304$	5.34544	−	3.08619i	0.306582	−	0.177005i
$305$		−	7.51629i		−	0.430381i
$306$	9.86116	−	5.69334i	0.563725	−	0.325467i
$307$		−	6.68810i		−	0.381710i	−0.981618	−	0.190855i	$-0.938874\pi$
$307$		−	6.68810i		−	0.381710i	0.981618	−	0.190855i	$-0.0611261\pi$
$308$		0			0
$309$	−5.51048	−	9.54443i	−0.313480	−	0.542964i
$310$		−	0.787362i		−	0.0447191i
$311$	4.59362	+	7.95639i	0.260480	+	0.451165i	0.966370	−	0.257157i	$-0.0827857\pi$
$311$	4.59362	+	7.95639i	0.260480	+	0.451165i	−0.705889	+	0.708322i	$0.749452\pi$
$312$	3.25386	−	7.59161i	0.184213	−	0.429790i
$313$	−8.58157	+	14.8637i	−0.485059	+	0.840147i	−0.999853	−	0.0171671i	$-0.994535\pi$
$313$	−8.58157	+	14.8637i	−0.485059	+	0.840147i	0.514793	+	0.857314i	$0.327869\pi$
$314$	−15.5231	+	8.96225i	−0.876018	+	0.505769i
$315$		0			0
$316$	3.26674	−	5.65817i	0.183769	−	0.318297i
$317$	−3.25840	−	1.88124i	−0.183010	−	0.105661i	0.405696	−	0.914008i	$-0.367029\pi$
$317$	−3.25840	−	1.88124i	−0.183010	−	0.105661i	−0.588706	+	0.808347i	$0.700362\pi$
$318$		−	3.88743i		−	0.217996i
$319$			9.51078i			0.532502i
$320$	0.781015	+	0.450919i	0.0436601	+	0.0252072i
$321$	15.6381	−	27.0860i	0.872833	−	1.51179i
$322$		0			0
$323$	27.0796	−	15.6344i	1.50675	−	0.869921i
$324$	−5.34547	+	9.25862i	−0.296971	+	0.514368i
$325$	12.0874	−	9.04233i	0.670487	−	0.501578i
$326$	−10.1589	−	17.5958i	−0.562652	−	0.974542i
$327$			11.7230i			0.648285i
$328$	−1.99827	−	3.46110i	−0.110336	−	0.191107i
$329$		0			0
$330$		−	8.96024i		−	0.493245i
$331$	27.9083	−	16.1129i	1.53398	−	0.885643i	0.534806	−	0.844975i	$-0.320385\pi$
$331$	27.9083	−	16.1129i	1.53398	−	0.885643i	0.999173	−	0.0406683i	$-0.0129487\pi$
$332$			13.2348i			0.726356i
$333$	0.280902	−	0.162179i	0.0153933	−	0.00888735i
$334$	1.61525	+	2.79770i	0.0883827	+	0.153083i
$335$	−4.68182	−	8.10916i	−0.255795	−	0.443051i
$336$		0			0
$337$	−3.01703			−0.164348			−0.0821740	−	0.996618i	$-0.526186\pi$
$337$	−3.01703			−0.164348			−0.0821740	+	0.996618i	$0.526186\pi$
$338$	−3.05660	−	12.6356i	−0.166257	−	0.687284i
$339$	20.5393	+	35.5750i	1.11554	+	1.93217i
$340$	3.95656	+	2.28432i	0.214575	+	0.123885i
$341$	3.78662			0.205057
$342$	6.93684	−	12.0150i	0.375101	−	0.649695i
$343$		0			0
$344$	−6.67577	−	3.85426i	−0.359933	−	0.207808i
$345$	15.1203	−	8.72972i	0.814051	−	0.469993i
$346$	−7.94183	+	4.58522i	−0.426956	+	0.246503i
$347$	0.468540			0.0251526			0.0125763	−	0.999921i	$-0.495997\pi$
$347$	0.468540			0.0251526			0.0125763	+	0.999921i	$0.495997\pi$
$348$	−5.02337			−0.269281
$349$	27.9044	−	16.1106i	1.49369	−	0.862380i	0.493712	−	0.869625i	$-0.335640\pi$
$349$	27.9044	−	16.1106i	1.49369	−	0.862380i	0.999974	+	0.00724565i	$0.00230638\pi$
$350$		0			0
$351$	0.735656	+	6.16992i	0.0392664	+	0.329326i
$352$	−2.16858	+	3.75609i	−0.115586	+	0.200200i
$353$	−11.3583	−	6.55771i	−0.604540	−	0.349031i	0.166285	−	0.986078i	$-0.446823\pi$
$353$	−11.3583	−	6.55771i	−0.604540	−	0.349031i	−0.770826	+	0.637046i	$0.780156\pi$
$354$	9.79235	−	16.9608i	0.520457	−	0.901459i
$355$	1.47837	+	2.56060i	0.0784635	+	0.135903i
$356$		−	7.79180i		−	0.412965i
$357$		0			0
$358$	−14.6834	−	8.47747i	−0.776043	−	0.448048i
$359$	3.79302	+	2.18990i	0.200188	+	0.115579i	0.596743	−	0.802432i	$-0.296461\pi$
$359$	3.79302	+	2.18990i	0.200188	+	0.115579i	−0.396555	+	0.918011i	$0.629794\pi$
$360$	2.02707			0.106836
$361$	9.54914	−	16.5396i	0.502586	−	0.870505i
$362$			2.65743i			0.139671i
$363$	17.8933			0.939156
$364$		0			0
$365$	−0.486112			−0.0254443
$366$			19.0923i			0.997972i
$367$	12.9094	−	22.3597i	0.673865	−	1.16717i	−0.302934	−	0.953011i	$-0.597966\pi$
$367$	12.9094	−	22.3597i	0.673865	−	1.16717i	0.976799	−	0.214157i	$-0.0687004\pi$
$368$	−8.45117			−0.440548
$369$	−7.77953	−	4.49151i	−0.404986	−	0.233819i
$370$	0.112705	+	0.0650705i	0.00585928	+	0.00338285i
$371$		0			0
$372$			2.00000i			0.103695i
$373$	−15.3143	−	26.5251i	−0.792942	−	1.37342i	−0.924138	−	0.382059i	$-0.875215\pi$
$373$	−15.3143	−	26.5251i	−0.792942	−	1.37342i	0.131196	−	0.991356i	$-0.458118\pi$
$374$	−10.9859	+	19.0281i	−0.568065	+	0.983918i
$375$	16.4363	+	9.48948i	0.848765	+	0.490035i
$376$	1.46057	−	2.52979i	0.0753234	−	0.130464i
$377$	−6.33100	+	4.73609i	−0.326063	+	0.243921i
$378$		0			0
$379$	−33.0409	+	19.0762i	−1.69720	+	0.979877i	−0.748796	+	0.662801i	$0.769368\pi$
$379$	−33.0409	+	19.0762i	−1.69720	+	0.979877i	−0.948400	+	0.317076i	$0.897299\pi$
$380$	5.56649			0.285555
$381$	−44.7016			−2.29013
$382$	−21.2056	+	12.2430i	−1.08497	+	0.626408i
$383$	−27.6783	+	15.9801i	−1.41430	+	0.816544i	−0.995790	−	0.0916693i	$-0.970780\pi$
$383$	−27.6783	+	15.9801i	−1.41430	+	0.816544i	−0.418507	+	0.908214i	$0.637446\pi$
$384$	−1.98388	−	1.14539i	−0.101239	−	0.0584506i
$385$		0			0
$386$	6.12046	−	10.6009i	0.311523	−	0.539574i
$387$	−17.3265			−0.880753
$388$	10.1378	+	5.85305i	0.514668	+	0.297144i
$389$	−2.62292	−	4.54304i	−0.132988	−	0.230341i	0.791839	−	0.610729i	$-0.209124\pi$
$389$	−2.62292	−	4.54304i	−0.132988	−	0.230341i	−0.924827	+	0.380388i	$0.875790\pi$
$390$	5.96452	−	4.46194i	0.302025	−	0.225939i
$391$	−42.8130			−2.16514
$392$		0			0
$393$	23.6520	+	40.9664i	1.19308	+	2.06648i
$394$	2.72876	+	4.72634i	0.137473	+	0.238110i
$395$	5.10275	−	2.94608i	0.256747	−	0.148233i
$396$			9.74866i			0.489889i
$397$	21.2432	−	12.2648i	1.06617	−	0.615552i	0.139035	−	0.990287i	$-0.455600\pi$
$397$	21.2432	−	12.2648i	1.06617	−	0.615552i	0.927132	+	0.374736i	$0.122266\pi$
$398$		−	12.8166i		−	0.642440i
$399$		0			0
$400$	−2.09334	−	3.62578i	−0.104667	−	0.181289i
$401$			4.27143i			0.213305i	0.994296	+	0.106652i	$0.0340132\pi$
$401$			4.27143i			0.213305i	−0.994296	+	0.106652i	$0.965987\pi$
$402$	11.8924	+	20.5983i	0.593141	+	1.02735i
$403$	1.88562	+	2.52062i	0.0939296	+	0.125561i
$404$	−5.37145	+	9.30362i	−0.267239	+	0.462872i
$405$	−8.34979	+	4.82075i	−0.414904	+	0.239545i
$406$		0			0
$407$	−0.312940	+	0.542028i	−0.0155119	+	0.0268673i
$408$	−10.0502	−	5.80247i	−0.497558	−	0.287265i
$409$		−	1.61647i		−	0.0799293i	−0.999201	−	0.0399646i	$-0.987275\pi$
$409$		−	1.61647i		−	0.0799293i	0.999201	−	0.0399646i	$-0.0127245\pi$
$410$		−	3.60423i		−	0.178000i
$411$	−6.32771	−	3.65330i	−0.312123	−	0.180204i
$412$	−2.40550	+	4.16644i	−0.118510	+	0.205266i
$413$		0			0
$414$	−16.4508	+	9.49787i	−0.808512	+	0.466795i
$415$	−5.96784	+	10.3366i	−0.292950	+	0.507404i
$416$	−3.58019	+	0.426876i	−0.175533	+	0.0209293i
$417$	0.682322	+	1.18182i	0.0334135	+	0.0578738i
$418$			26.7706i			1.30939i
$419$	−13.0156	−	22.5437i	−0.635854	−	1.10133i	−0.986334	−	0.164761i	$-0.947315\pi$
$419$	−13.0156	−	22.5437i	−0.635854	−	1.10133i	0.350480	−	0.936570i	$-0.386018\pi$
$420$		0			0
$421$		−	37.5391i		−	1.82954i	−0.403971	−	0.914772i	$-0.632370\pi$
$421$		−	37.5391i		−	1.82954i	0.403971	−	0.914772i	$-0.367630\pi$
$422$	−16.7239	+	9.65552i	−0.814104	+	0.470023i
$423$		−	6.56588i		−	0.319244i
$424$	−1.46963	+	0.848493i	−0.0713717	+	0.0412064i
$425$	−10.6047	−	18.3679i	−0.514404	−	0.890974i
$426$	−3.75524	−	6.50427i	−0.181942	−	0.315133i
$427$		0			0
$428$	−13.6530			−0.659944
$429$	21.4585	+	28.6848i	1.03603	+	1.38492i
$430$	−3.47592	−	6.02046i	−0.167624	−	0.290333i
$431$	−18.6662	−	10.7769i	−0.899118	−	0.519106i	−0.0222041	−	0.999753i	$-0.507068\pi$
$431$	−18.6662	−	10.7769i	−0.899118	−	0.519106i	−0.876914	+	0.480647i	$0.840402\pi$
$432$	1.72335			0.0829147
$433$	−1.59958	+	2.77056i	−0.0768710	+	0.133145i	−0.901898	−	0.431948i	$-0.857826\pi$
$433$	−1.59958	+	2.77056i	−0.0768710	+	0.133145i	0.825027	+	0.565093i	$0.191160\pi$
$434$		0			0
$435$	−3.92333	−	2.26513i	−0.188109	−	0.108605i
$436$	4.43186	−	2.55874i	0.212248	−	0.122541i
$437$	−45.1752	+	26.0819i	−2.16102	+	1.24767i
$438$	1.23479			0.0590004
$439$	26.6227			1.27063			0.635317	−	0.772252i	$-0.280870\pi$
$439$	26.6227			1.27063			0.635317	+	0.772252i	$0.280870\pi$
$440$	−3.38739	+	1.95571i	−0.161488	+	0.0932349i
$441$		0			0
$442$	−18.1370	+	2.16252i	−0.862688	+	0.102861i
$443$	−4.54933	+	7.87968i	−0.216145	+	0.374375i	−0.953626	−	0.300993i	$-0.902682\pi$
$443$	−4.54933	+	7.87968i	−0.216145	+	0.374375i	0.737481	+	0.675368i	$0.236015\pi$
$444$	−0.286286	−	0.165287i	−0.0135865	−	0.00784420i
$445$	3.51347	−	6.08551i	0.166555	−	0.288481i
$446$	5.31785	+	9.21079i	0.251808	+	0.436144i
$447$			25.6789i			1.21457i
$448$		0			0
$449$	6.08550	+	3.51346i	0.287192	+	0.165811i	0.636675	−	0.771132i	$-0.280309\pi$
$449$	6.08550	+	3.51346i	0.287192	+	0.165811i	−0.349483	+	0.936943i	$0.613643\pi$
$450$	−8.14967	−	4.70522i	−0.384179	−	0.221806i
$451$	17.3336			0.816209
$452$	8.96603	−	15.5296i	0.421726	−	0.730452i
$453$		−	29.9476i		−	1.40706i
$454$	−22.7217			−1.06638
$455$		0			0
$456$	−14.1396			−0.662148
$457$		−	19.1511i		−	0.895851i	−0.894071	−	0.447926i	$-0.852163\pi$
$457$		−	19.1511i		−	0.895851i	0.894071	−	0.447926i	$-0.147837\pi$
$458$	10.1547	−	17.5885i	0.474498	−	0.821855i
$459$	8.73035			0.407498
$460$	−6.60049	−	3.81080i	−0.307750	−	0.177679i
$461$	2.82026	+	1.62828i	0.131353	+	0.0758365i	0.564236	−	0.825613i	$-0.309171\pi$
$461$	2.82026	+	1.62828i	0.131353	+	0.0758365i	−0.432884	+	0.901450i	$0.642504\pi$
$462$		0			0
$463$		−	21.2761i		−	0.988786i	−0.869238	−	0.494393i	$-0.835390\pi$
$463$		−	21.2761i		−	0.988786i	0.869238	−	0.494393i	$-0.164610\pi$
$464$	1.09643	+	1.89907i	0.0509004	+	0.0881621i
$465$	−0.901839	+	1.56203i	−0.0418218	+	0.0724374i
$466$	−9.21851	−	5.32231i	−0.427039	−	0.246551i
$467$	−1.66586	+	2.88535i	−0.0770866	+	0.133518i	−0.901992	−	0.431753i	$-0.857895\pi$
$467$	−1.66586	+	2.88535i	−0.0770866	+	0.133518i	0.824905	+	0.565271i	$0.191228\pi$
$468$	−6.48935	+	4.85455i	−0.299970	+	0.224402i
$469$		0			0
$470$	2.28146	−	1.31720i	0.105236	−	0.0607580i
$471$	41.0612			1.89200
$472$	−8.54933			−0.393515
$473$	28.9539	−	16.7165i	1.33130	−	0.768627i
$474$	−12.9617	+	7.48341i	−0.595348	+	0.343725i
$475$	−22.3797	−	12.9209i	−1.02685	−	0.592852i
$476$		0			0
$477$	−1.90716	+	3.30330i	−0.0873229	+	0.151248i
$478$	−0.311564			−0.0142506
$479$	−0.160402	−	0.0926079i	−0.00732894	−	0.00423136i	0.496331	−	0.868133i	$-0.334680\pi$
$479$	−0.160402	−	0.0926079i	−0.00732894	−	0.00423136i	−0.503660	+	0.863902i	$0.668014\pi$
$480$	−1.03296	−	1.78914i	−0.0471480	−	0.0816627i
$481$	−0.516644	+	0.0616009i	−0.0235569	+	0.00280876i
$482$	25.2995			1.15236
$483$		0			0
$484$	−3.90550	−	6.76452i	−0.177523	−	0.307478i
$485$	5.27851	+	9.14264i	0.239685	+	0.415146i
$486$	16.7321	−	9.66031i	0.758985	−	0.438200i
$487$			31.2308i			1.41520i	0.706613	+	0.707601i	$0.250222\pi$
$487$			31.2308i			1.41520i	−0.706613	+	0.707601i	$0.749778\pi$
$488$	7.21780	−	4.16720i	0.326735	−	0.188640i
$489$			46.5440i			2.10479i
$490$		0			0
$491$	13.4236	+	23.2504i	0.605799	+	1.04927i	0.991925	+	0.126829i	$0.0404798\pi$
$491$	13.4236	+	23.2504i	0.605799	+	1.04927i	−0.386126	+	0.922446i	$0.626187\pi$
$492$			9.15521i			0.412749i
$493$	5.55442	+	9.62054i	0.250159	+	0.433287i
$494$	−17.8203	+	13.3310i	−0.801772	+	0.599790i
$495$	−4.39586	+	7.61385i	−0.197579	+	0.342217i
$496$	0.756094	−	0.436531i	0.0339496	−	0.0196008i
$497$		0			0
$498$	15.1591	−	26.2563i	0.679295	−	1.17657i
$499$	−13.2389	−	7.64346i	−0.592653	−	0.342168i	0.173493	−	0.984835i	$-0.444495\pi$
$499$	−13.2389	−	7.64346i	−0.592653	−	0.342168i	−0.766146	+	0.642667i	$0.777828\pi$
$500$		−	8.28491i		−	0.370512i
$501$		−	7.40040i		−	0.330625i
$502$	−6.96311	−	4.02015i	−0.310779	−	0.179428i
$503$	−13.0551	+	22.6121i	−0.582097	+	1.00822i	0.413133	+	0.910671i	$0.364434\pi$
$503$	−13.0551	+	22.6121i	−0.582097	+	1.00822i	−0.995230	+	0.0975513i	$0.968899\pi$
$504$		0			0
$505$	−8.39036	+	4.84418i	−0.373366	+	0.215563i
$506$	18.3271	−	31.7434i	0.814737	−	1.41117i
$507$	−8.40876	+	28.5684i	−0.373446	+	1.26877i
$508$	9.75681	+	16.8993i	0.432889	+	0.749785i
$509$		−	17.0271i		−	0.754715i	−0.926068	−	0.377357i	$-0.876833\pi$
$509$		−	17.0271i		−	0.754715i	0.926068	−	0.377357i	$-0.123167\pi$
$510$	−5.23289	−	9.06364i	−0.231716	−	0.401345i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	9.21206	−	5.31858i	0.406722	−	0.234821i
$514$		−	16.9327i		−	0.746868i
$515$	−3.75746	+	2.16937i	−0.165573	+	0.0955939i
$516$	8.82928	+	15.2928i	0.388687	+	0.673226i
$517$	6.33475	+	10.9721i	0.278602	+	0.482553i
$518$		0			0
$519$	21.0075			0.922128
$520$	−2.98867	−	1.28098i	−0.131062	−	0.0561748i
$521$	−9.38802	−	16.2605i	−0.411297	−	0.712387i	0.583735	−	0.811944i	$-0.301591\pi$
$521$	−9.38802	−	16.2605i	−0.411297	−	0.712387i	−0.995032	+	0.0995575i	$0.968257\pi$
$522$	4.26855	+	2.46445i	0.186829	+	0.107866i
$523$	3.03247			0.132601			0.0663004	−	0.997800i	$-0.478880\pi$
$523$	3.03247			0.132601			0.0663004	+	0.997800i	$0.478880\pi$
$524$	10.3248	−	17.8831i	0.451042	−	0.781227i
$525$		0			0
$526$	−8.93817	−	5.16045i	−0.389723	−	0.225006i
$527$	3.83031	−	2.21143i	0.166851	−	0.0963315i
$528$	8.60441	−	4.96776i	0.374459	−	0.216194i
$529$	48.4223			2.10532
$530$	−1.53041			−0.0664766
$531$	−16.6419	+	9.60818i	−0.722195	+	0.416960i
$532$		0			0
$533$	8.63164	+	11.5384i	0.373878	+	0.499783i
$534$	−8.92468	+	15.4580i	−0.386209	+	0.668933i
$535$	−10.6632	−	6.15642i	−0.461011	−	0.266165i
$536$	5.19142	−	8.99180i	0.224235	−	0.388387i
$537$	19.4201	+	33.6366i	0.838038	+	1.45153i
$538$			6.13999i			0.264714i
$539$		0			0
$540$	1.34596	+	0.777092i	0.0579210	+	0.0334407i
$541$	5.29873	+	3.05922i	0.227810	+	0.131526i	0.609561	−	0.792739i	$-0.291346\pi$
$541$	5.29873	+	3.05922i	0.227810	+	0.131526i	−0.381751	+	0.924265i	$0.624679\pi$
$542$	10.6772			0.458625
$543$	3.04380	−	5.27202i	0.130622	−	0.226244i
$544$			5.06592i			0.217200i
$545$	4.61513			0.197691
$546$		0			0
$547$	−37.4754			−1.60233			−0.801166	−	0.598442i	$-0.795786\pi$
$547$	−37.4754			−1.60233			−0.801166	+	0.598442i	$0.795786\pi$
$548$			3.18956i			0.136251i
$549$	9.36663	−	16.2235i	0.399758	−	0.692402i
$550$	18.1583			0.774275
$551$	11.7218	+	6.76758i	0.499365	+	0.288308i
$552$	16.7661	+	9.67992i	0.713613	+	0.412005i
$553$		0			0
$554$		−	21.9090i		−	0.930823i
$555$	−0.149063	−	0.258184i	−0.00632736	−	0.0109593i
$556$	0.297855	−	0.515900i	0.0126319	−	0.0218790i
$557$	7.69941	+	4.44526i	0.326234	+	0.188352i	0.654168	−	0.756349i	$-0.273019\pi$
$557$	7.69941	+	4.44526i	0.326234	+	0.188352i	−0.327934	+	0.944701i	$0.606352\pi$
$558$	0.981193	−	1.69948i	0.0415372	−	0.0719446i
$559$	25.5458	+	10.9493i	1.08047	+	0.463104i
$560$		0			0
$561$	43.5893	−	25.1663i	1.84034	−	1.06252i
$562$	−25.7719			−1.08712
$563$	17.7920			0.749841			0.374921	−	0.927057i	$-0.377670\pi$
$563$	17.7920			0.749841			0.374921	+	0.927057i	$0.377670\pi$
$564$	−5.79521	+	3.34587i	−0.244022	+	0.140886i
$565$	14.0052	−	8.08591i	0.589204	−	0.340177i
$566$	9.80937	+	5.66344i	0.412319	+	0.238052i
$567$		0			0
$568$	−1.63928	+	2.83932i	−0.0687826	+	0.119135i
$569$	−11.1737			−0.468425			−0.234212	−	0.972185i	$-0.575251\pi$
$569$	−11.1737			−0.468425			−0.234212	+	0.972185i	$0.575251\pi$
$570$	−11.0432	−	6.37582i	−0.462551	−	0.267054i
$571$	8.36194	+	14.4833i	0.349936	+	0.606108i	0.986238	−	0.165333i	$-0.0528698\pi$
$571$	8.36194	+	14.4833i	0.349936	+	0.606108i	−0.636301	+	0.771441i	$0.719537\pi$
$572$	6.16055	−	14.3733i	0.257586	−	0.600976i
$573$	56.0924			2.34329
$574$		0			0
$575$	17.6912	+	30.6421i	0.737774	+	1.27786i
$576$	1.12385	+	1.94657i	0.0468272	+	0.0811070i
$577$	0.691857	−	0.399444i	0.0288024	−	0.0166291i	−0.485530	−	0.874220i	$-0.661373\pi$
$577$	0.691857	−	0.399444i	0.0288024	−	0.0166291i	0.514332	+	0.857591i	$0.328040\pi$
$578$			8.66355i			0.360356i
$579$	−24.2845	+	14.0207i	−1.00923	+	0.582679i
$580$			1.97760i			0.0821155i
$581$		0			0
$582$	−13.4081	−	23.2235i	−0.555783	−	0.962645i
$583$		−	7.36010i		−	0.304824i
$584$	−0.269511	−	0.466808i	−0.0111525	−	0.0193166i
$585$	−7.25729	+	0.865306i	−0.300052	+	0.0357760i
$586$	11.8730	−	20.5646i	0.490468	−	0.849515i
$587$	−6.94921	+	4.01213i	−0.286825	+	0.165598i	−0.636509	−	0.771269i	$-0.719622\pi$
$587$	−6.94921	+	4.01213i	−0.286825	+	0.165598i	0.349684	+	0.936868i	$0.386289\pi$
$588$		0			0
$589$	2.69444	−	4.66690i	0.111022	−	0.192296i
$590$	−6.67716	−	3.85506i	−0.274894	−	0.158710i
$591$		−	12.5020i		−	0.514263i
$592$			0.144306i			0.00593095i
$593$	4.27055	+	2.46560i	0.175370	+	0.101250i	0.585116	−	0.810950i	$-0.301049\pi$
$593$	4.27055	+	2.46560i	0.175370	+	0.101250i	−0.409745	+	0.912200i	$0.634382\pi$
$594$	−3.73723	+	6.47306i	−0.153340	+	0.265593i
$595$		0			0
$596$	9.70783	−	5.60482i	0.397648	−	0.229582i
$597$	−14.6801	+	25.4267i	−0.600816	+	1.04064i
$598$	30.2568	−	3.60760i	1.23729	−	0.147526i
$599$	8.91246	+	15.4368i	0.364153	+	0.630732i	0.988640	−	0.150304i	$-0.0480251\pi$
$599$	8.91246	+	15.4368i	0.364153	+	0.630732i	−0.624487	+	0.781035i	$0.714692\pi$
$600$			9.59081i			0.391543i
$601$	−0.0809165	−	0.140152i	−0.00330065	−	0.00571690i	0.864370	−	0.502856i	$-0.167717\pi$
$601$	−0.0809165	−	0.140152i	−0.00330065	−	0.00571690i	−0.867671	+	0.497139i	$0.834384\pi$
$602$		0			0
$603$		−	23.3375i		−	0.950378i
$604$	−11.3216	+	6.53653i	−0.460670	+	0.265968i
$605$		−	7.04426i		−	0.286390i
$606$	21.3126	−	12.3048i	0.865765	−	0.499850i
$607$	3.09423	+	5.35937i	0.125591	+	0.217530i	0.921964	−	0.387276i	$-0.126584\pi$
$607$	3.09423	+	5.35937i	0.125591	+	0.217530i	−0.796373	+	0.604806i	$0.793251\pi$
$608$	3.08619	+	5.34544i	0.125162	+	0.216786i
$609$		0			0
$610$	7.51629			0.304326
$611$	−4.14923	+	9.68062i	−0.167860	+	0.391636i
$612$	5.69334	+	9.86116i	0.230140	+	0.398614i
$613$	−32.2269	−	18.6062i	−1.30163	−	0.751497i	−0.320947	−	0.947097i	$-0.604001\pi$
$613$	−32.2269	−	18.6062i	−1.30163	−	0.751497i	−0.980684	+	0.195600i	$0.937335\pi$
$614$	6.68810			0.269910
$615$	−4.12826	+	7.15036i	−0.166468	+	0.288330i
$616$		0			0
$617$	−5.78536	−	3.34018i	−0.232910	−	0.134471i	0.379004	−	0.925395i	$-0.376267\pi$
$617$	−5.78536	−	3.34018i	−0.232910	−	0.134471i	−0.611914	+	0.790924i	$0.709600\pi$
$618$	9.54443	−	5.51048i	0.383933	−	0.221664i
$619$	−20.5546	+	11.8672i	−0.826158	+	0.476982i	−0.852535	−	0.522670i	$-0.824936\pi$
$619$	−20.5546	+	11.8672i	−0.826158	+	0.476982i	0.0263776	+	0.999652i	$0.491603\pi$
$620$	0.787362			0.0316212
$621$	−14.5643			−0.584446
$622$	−7.95639	+	4.59362i	−0.319022	+	0.184187i
$623$		0			0
$624$	7.59161	+	3.25386i	0.303908	+	0.130259i
$625$	−6.73089	+	11.6582i	−0.269236	+	0.466330i
$626$	−14.8637	−	8.58157i	−0.594074	−	0.342989i
$627$	30.6629	−	53.1097i	1.22456	−	2.12100i
$628$	−8.96225	−	15.5231i	−0.357633	−	0.619438i
$629$			0.731044i			0.0291486i
$630$		0			0
$631$	19.9348	+	11.5093i	0.793590	+	0.458180i	0.841225	−	0.540685i	$-0.181835\pi$
$631$	19.9348	+	11.5093i	0.793590	+	0.458180i	−0.0476346	+	0.998865i	$0.515168\pi$
$632$	5.65817	+	3.26674i	0.225070	+	0.129944i
$633$	44.2375			1.75828
$634$	1.88124	−	3.25840i	0.0747135	−	0.129408i
$635$			17.5981i			0.698361i
$636$	3.88743			0.154147
$637$		0			0
$638$	−9.51078			−0.376536
$639$			7.36923i			0.291522i
$640$	−0.450919	+	0.781015i	−0.0178242	+	0.0308723i
$641$	−12.6508			−0.499676			−0.249838	−	0.968288i	$-0.580377\pi$
$641$	−12.6508			−0.499676			−0.249838	+	0.968288i	$0.580377\pi$
$642$	27.0860	+	15.6381i	1.06900	+	0.617186i
$643$	13.1971	+	7.61938i	0.520445	+	0.300479i	0.737117	−	0.675766i	$-0.236187\pi$
$643$	13.1971	+	7.61938i	0.520445	+	0.300479i	−0.216672	+	0.976244i	$0.569520\pi$
$644$		0			0
$645$			15.9252i			0.627053i
$646$	15.6344	+	27.0796i	0.615127	+	1.06543i
$647$	14.6821	−	25.4301i	0.577213	−	0.999762i	−0.418585	−	0.908178i	$-0.637474\pi$
$647$	14.6821	−	25.4301i	0.577213	−	0.999762i	0.995797	−	0.0915840i	$-0.0291930\pi$
$648$	−9.25862	−	5.34547i	−0.363713	−	0.209990i
$649$	18.5399	−	32.1121i	0.727756	−	1.26051i
$650$	9.04233	+	12.0874i	0.354669	+	0.474106i
$651$		0			0
$652$	17.5958	−	10.1589i	0.689105	−	0.397855i
$653$	−29.0211			−1.13568			−0.567842	−	0.823137i	$-0.692222\pi$
$653$	−29.0211			−1.13568			−0.567842	+	0.823137i	$0.692222\pi$
$654$	−11.7230			−0.458407
$655$	16.1277	−	9.31132i	0.630161	−	0.363823i
$656$	3.46110	−	1.99827i	0.135133	−	0.0780192i
$657$	−1.04925	−	0.605782i	−0.0409350	−	0.0236338i
$658$		0			0
$659$	−3.98651	+	6.90484i	−0.155293	+	0.268975i	−0.933166	−	0.359447i	$-0.882965\pi$
$659$	−3.98651	+	6.90484i	−0.155293	+	0.268975i	0.777873	+	0.628422i	$0.216299\pi$
$660$	8.96024			0.348777
$661$	3.40668	+	1.96685i	0.132505	+	0.0765015i	0.564787	−	0.825237i	$-0.308958\pi$
$661$	3.40668	+	1.96685i	0.132505	+	0.0765015i	−0.432282	+	0.901738i	$0.642292\pi$
$662$	16.1129	+	27.9083i	0.626244	+	1.08469i
$663$	38.4585	+	16.4838i	1.49360	+	0.640177i
$664$	−13.2348			−0.513611
$665$		0			0
$666$	0.162179	+	0.280902i	0.00628430	+	0.0108847i
$667$	−9.26611	−	16.0494i	−0.358785	−	0.621434i
$668$	−2.79770	+	1.61525i	−0.108246	+	0.0624960i
$669$		−	24.3641i		−	0.941972i
$670$	8.10916	−	4.68182i	0.313284	−	0.180875i
$671$			36.1477i			1.39547i
$672$		0			0
$673$	18.1599	+	31.4539i	0.700014	+	1.21246i	0.968461	+	0.249166i	$0.0801563\pi$
$673$	18.1599	+	31.4539i	0.700014	+	1.21246i	−0.268447	+	0.963295i	$0.586510\pi$
$674$		−	3.01703i		−	0.116212i
$675$	−3.60756	−	6.24848i	−0.138855	−	0.240504i
$676$	12.6356	−	3.05660i	0.485983	−	0.117561i
$677$	−10.5534	+	18.2790i	−0.405600	+	0.702520i	−0.994391	−	0.105765i	$-0.966271\pi$
$677$	−10.5534	+	18.2790i	−0.405600	+	0.702520i	0.588791	+	0.808285i	$0.299604\pi$
$678$	−35.5750	+	20.5393i	−1.36625	+	0.788805i
$679$		0			0
$680$	−2.28432	+	3.95656i	−0.0875997	+	0.151727i
$681$	45.0771	+	26.0253i	1.72736	+	0.997292i
$682$			3.78662i			0.144997i
$683$			26.4258i			1.01115i	0.862782	+	0.505577i	$0.168720\pi$
$683$			26.4258i			1.01115i	−0.862782	+	0.505577i	$0.831280\pi$
$684$	12.0150	+	6.93684i	0.459404	+	0.265237i
$685$	−1.43824	+	2.49110i	−0.0549522	+	0.0951799i
$686$		0			0
$687$	−40.2914	+	23.2623i	−1.53721	+	0.887511i
$688$	3.85426	−	6.67577i	0.146942	−	0.254511i
$689$	4.89937	−	3.66512i	0.186651	−	0.139630i
$690$	8.72972	+	15.1203i	0.332335	+	0.575621i
$691$		−	0.779759i		−	0.0296634i	−0.999890	−	0.0148317i	$-0.995279\pi$
$691$		−	0.779759i		−	0.0296634i	0.999890	−	0.0148317i	$-0.00472125\pi$
$692$	−4.58522	−	7.94183i	−0.174304	−	0.301903i
$693$		0			0
$694$			0.468540i			0.0177855i
$695$	0.465259	−	0.268617i	0.0176483	−	0.0101892i
$696$		−	5.02337i		−	0.190410i
$697$	17.5337	−	10.1231i	0.664135	−	0.383438i
$698$	16.1106	+	27.9044i	0.609795	+	1.05620i
$699$	12.1923	+	21.1176i	0.461154	+	0.798742i
$700$		0			0
$701$	21.5491			0.813899			0.406950	−	0.913451i	$-0.366592\pi$
$701$	21.5491			0.813899			0.406950	+	0.913451i	$0.366592\pi$
$702$	−6.16992	+	0.735656i	−0.232869	+	0.0277656i
$703$	0.445357	+	0.771380i	0.0167969	+	0.0290932i
$704$	−3.75609	−	2.16858i	−0.141563	−	0.0817315i
$705$	−6.03486			−0.227286
$706$	6.55771	−	11.3583i	0.246803	−	0.427474i
$707$		0			0
$708$	16.9608	+	9.79235i	0.637428	+	0.368019i
$709$	3.92952	−	2.26871i	0.147576	−	0.0852031i	−0.424394	−	0.905478i	$-0.639513\pi$
$709$	3.92952	−	2.26871i	0.147576	−	0.0852031i	0.571970	+	0.820275i	$0.306179\pi$
$710$	−2.56060	+	1.47837i	−0.0960978	+	0.0554821i
$711$	14.6853			0.550743
$712$	7.79180			0.292010
$713$	−6.38988	+	3.68920i	−0.239303	+	0.138162i
$714$		0			0
$715$	11.2927	−	8.44782i	0.422322	−	0.315931i
$716$	8.47747	−	14.6834i	0.316818	−	0.548745i
$717$	0.618106	+	0.356863i	0.0230836	+	0.0133273i
$718$	−2.18990	+	3.79302i	−0.0817265	+	0.141554i
$719$	7.30036	+	12.6446i	0.272258	+	0.471564i	0.969440	−	0.245330i	$-0.0788964\pi$
$719$	7.30036	+	12.6446i	0.272258	+	0.471564i	−0.697182	+	0.716894i	$0.745563\pi$
$720$			2.02707i			0.0755443i
$721$		0			0
$722$	16.5396	+	9.54914i	0.615540	+	0.355382i
$723$	−50.1912	−	28.9779i	−1.86663	−	1.07770i
$724$	−2.65743			−0.0987626
$725$	4.59040	−	7.95081i	0.170483	−	0.295286i
$726$			17.8933i			0.664083i
$727$	−30.6315			−1.13606			−0.568030	−	0.823008i	$-0.692294\pi$
$727$	−30.6315			−1.13606			−0.568030	+	0.823008i	$0.692294\pi$
$728$		0			0
$729$	−12.1866			−0.451355
$730$		−	0.486112i		−	0.0179918i
$731$	19.5254	−	33.8189i	0.722171	−	1.25084i
$732$	−19.0923			−0.705673
$733$	−15.3455	−	8.85973i	−0.566799	−	0.327242i	0.189071	−	0.981963i	$-0.439452\pi$
$733$	−15.3455	−	8.85973i	−0.566799	−	0.327242i	−0.755870	+	0.654722i	$0.772786\pi$
$734$	22.3597	+	12.9094i	0.825313	+	0.476495i
$735$		0			0
$736$		−	8.45117i		−	0.311514i
$737$	22.5160	+	38.9989i	0.829389	+	1.43654i
$738$	4.49151	−	7.77953i	0.165335	−	0.286368i
$739$	9.05014	+	5.22510i	0.332915	+	0.192208i	0.657134	−	0.753773i	$-0.271768\pi$
$739$	9.05014	+	5.22510i	0.332915	+	0.192208i	−0.324220	+	0.945982i	$0.605102\pi$
$740$	−0.0650705	+	0.112705i	−0.00239204	+	0.00414313i
$741$	50.6225	−	6.03586i	1.85966	−	0.221733i
$742$		0			0
$743$	42.0103	−	24.2547i	1.54121	−	0.889818i	0.542447	−	0.840090i	$-0.317498\pi$
$743$	42.0103	−	24.2547i	1.54121	−	0.889818i	0.998763	−	0.0497278i	$-0.0158354\pi$
$744$	−2.00000			−0.0733236
$745$	10.1093			0.370376
$746$	26.5251	−	15.3143i	0.971152	−	0.560695i
$747$	−25.7625	+	14.8740i	−0.942601	+	0.544211i
$748$	−19.0281	−	10.9859i	−0.695735	−	0.401683i
$749$		0			0
$750$	−9.48948	+	16.4363i	−0.346507	+	0.600168i
$751$	−31.4555			−1.14783			−0.573914	−	0.818915i	$-0.694576\pi$
$751$	−31.4555			−1.14783			−0.573914	+	0.818915i	$0.694576\pi$
$752$	2.52979	+	1.46057i	0.0922519	+	0.0532617i
$753$	9.20931	+	15.9510i	0.335606	+	0.581286i
$754$	−4.73609	−	6.33100i	−0.172478	−	0.230561i
$755$	−11.7898			−0.429075
$756$		0			0
$757$	−24.3442	−	42.1654i	−0.884805	−	1.53253i	−0.845937	−	0.533283i	$-0.820958\pi$
$757$	−24.3442	−	42.1654i	−0.884805	−	1.53253i	−0.0388676	−	0.999244i	$-0.512375\pi$
$758$	−19.0762	−	33.0409i	−0.692877	−	1.20010i
$759$	−72.7174	+	41.9834i	−2.63947	+	1.52390i
$760$			5.56649i			0.201918i
$761$	−40.3350	+	23.2874i	−1.46214	+	0.844169i	−0.999110	−	0.0421718i	$-0.986572\pi$
$761$	−40.3350	+	23.2874i	−1.46214	+	0.844169i	−0.463033	+	0.886341i	$0.653239\pi$
$762$		−	44.7016i		−	1.61937i
$763$		0			0
$764$	−12.2430	−	21.2056i	−0.442937	−	0.767190i
$765$			10.2690i			0.371275i
$766$	−15.9801	−	27.6783i	−0.577384	−	1.00006i
$767$	30.6083	−	3.64950i	1.10520	−	0.131776i
$768$	1.14539	−	1.98388i	0.0413308	−	0.0715871i
$769$	24.1069	−	13.9181i	0.869315	−	0.501899i	0.00219468	−	0.999998i	$-0.499301\pi$
$769$	24.1069	−	13.9181i	0.869315	−	0.501899i	0.867121	+	0.498098i	$0.165968\pi$
$770$		0			0
$771$	−19.3946	+	33.5924i	−0.698479	+	1.20980i
$772$	10.6009	+	6.12046i	0.381536	+	0.220280i
$773$			28.4724i			1.02408i	0.858961	+	0.512040i	$0.171110\pi$
$773$			28.4724i			1.02408i	−0.858961	+	0.512040i	$0.828890\pi$
$774$		−	17.3265i		−	0.622786i
$775$	−3.16553	−	1.82762i	−0.113709	−	0.0656500i
$776$	−5.85305	+	10.1378i	−0.210112	+	0.363925i
$777$		0			0
$778$	4.54304	−	2.62292i	0.162876	−	0.0940364i
$779$	12.3341	−	21.3632i	0.441914	−	0.765417i
$780$	4.46194	+	5.96452i	0.159763	+	0.213564i
$781$	−7.10982	−	12.3146i	−0.254409	−	0.440650i
$782$		−	42.8130i		−	1.53099i
$783$	1.88953	+	3.27276i	0.0675263	+	0.116959i
$784$		0			0
$785$		−	16.1650i		−	0.576954i
$786$	−40.9664	+	23.6520i	−1.46122	+	0.843637i
$787$			15.1319i			0.539393i	0.962945	+	0.269697i	$0.0869234\pi$
$787$			15.1319i			0.539393i	−0.962945	+	0.269697i	$0.913077\pi$
$788$	−4.72634	+	2.72876i	−0.168369	+	0.0972079i
$789$	11.8215	+	20.4754i	0.420856	+	0.728945i
$790$	2.94608	+	5.10275i	0.104817	+	0.181548i
$791$		0			0
$792$	−9.74866			−0.346404
$793$	−24.0622	+	18.0005i	−0.854475	+	0.639216i
$794$	12.2648	+	21.2432i	0.435261	+	0.753894i
$795$	3.03614	+	1.75292i	0.107681	+	0.0621696i
$796$	12.8166			0.454274
$797$	−6.97234	+	12.0764i	−0.246973	+	0.427770i	−0.962684	−	0.270626i	$-0.912769\pi$
$797$	−6.97234	+	12.0764i	−0.246973	+	0.427770i	0.715712	+	0.698396i	$0.246103\pi$
$798$		0			0
$799$	12.8157	+	7.39916i	0.453387	+	0.261763i
$800$	3.62578	−	2.09334i	0.128191	−	0.0740109i
$801$	15.1673	−	8.75683i	0.535909	−	0.309407i
$802$	−4.27143			−0.150829
$803$	2.33783			0.0825003
$804$	−20.5983	+	11.8924i	−0.726446	+	0.419414i
$805$		0			0
$806$	−2.52062	+	1.88562i	−0.0887850	+	0.0664183i
$807$	7.03270	−	12.1810i	0.247563	−	0.428791i
$808$	−9.30362	−	5.37145i	−0.327300	−	0.188967i
$809$	10.8714	−	18.8299i	0.382220	−	0.662024i	−0.609159	−	0.793048i	$-0.708493\pi$
$809$	10.8714	−	18.8299i	0.382220	−	0.662024i	0.991379	+	0.131024i	$0.0418264\pi$
$810$	−4.82075	−	8.34979i	−0.169384	−	0.293382i
$811$			21.1256i			0.741819i	0.928669	+	0.370910i	$0.120954\pi$
$811$			21.1256i			0.741819i	−0.928669	+	0.370910i	$0.879046\pi$
$812$		0			0
$813$	−21.1823	−	12.2296i	−0.742895	−	0.428911i
$814$	−0.542028	−	0.312940i	−0.0189981	−	0.0109685i
$815$	18.3235			0.641843
$816$	5.80247	−	10.0502i	0.203127	−	0.351827i
$817$		−	47.5799i		−	1.66461i
$818$	1.61647			0.0565185
$819$		0			0
$820$	3.60423			0.125865
$821$		−	16.2736i		−	0.567951i	−0.958831	−	0.283976i	$-0.908347\pi$
$821$		−	16.2736i		−	0.567951i	0.958831	−	0.283976i	$-0.0916535\pi$
$822$	3.65330	−	6.32771i	0.127424	−	0.220704i
$823$	−18.6543			−0.650246			−0.325123	−	0.945672i	$-0.605406\pi$
$823$	−18.6543			−0.650246			−0.325123	+	0.945672i	$0.605406\pi$
$824$	−4.16644	−	2.40550i	−0.145145	−	0.0837994i
$825$	−36.0240	−	20.7985i	−1.25419	−	0.724109i
$826$		0			0
$827$		−	47.3361i		−	1.64604i	−0.568015	−	0.823018i	$-0.692288\pi$
$827$		−	47.3361i		−	1.64604i	0.568015	−	0.823018i	$-0.307712\pi$
$828$	−9.49787	−	16.4508i	−0.330074	−	0.571704i
$829$	−0.460988	+	0.798454i	−0.0160108	+	0.0277315i	−0.873920	−	0.486070i	$-0.838430\pi$
$829$	−0.460988	+	0.798454i	−0.0160108	+	0.0277315i	0.857909	+	0.513802i	$0.171763\pi$
$830$	−10.3366	−	5.96784i	−0.358789	−	0.207147i
$831$	−25.0944	+	43.4647i	−0.870515	+	1.50778i
$832$	−0.426876	−	3.58019i	−0.0147993	−	0.124121i
$833$		0			0
$834$	−1.18182	+	0.682322i	−0.0409230	+	0.0236269i
$835$	−2.91339			−0.100822
$836$	−26.7706			−0.925881
$837$	1.30301	−	0.752296i	0.0450388	−	0.0260032i
$838$	22.5437	−	13.0156i	0.778758	−	0.449616i
$839$	14.3894	+	8.30775i	0.496779	+	0.286815i	0.727382	−	0.686232i	$-0.240737\pi$
$839$	14.3894	+	8.30775i	0.496779	+	0.286815i	−0.230604	+	0.973048i	$0.574070\pi$
$840$		0			0
$841$	12.0957	−	20.9503i	0.417093	−	0.722426i
$842$	37.5391			1.29368
$843$	51.1284	+	29.5190i	1.76096	+	1.01669i
$844$	−9.65552	−	16.7239i	−0.332357	−	0.575659i
$845$	11.2468	+	3.31037i	0.386903	+	0.113880i
$846$	6.56588			0.225740
$847$		0			0
$848$	−0.848493	−	1.46963i	−0.0291374	−	0.0504674i
$849$	−12.9737	−	22.4712i	−0.445258	−	0.771209i
$850$	18.3679	−	10.6047i	0.630014	−	0.363739i
$851$		−	1.21956i		−	0.0418059i
$852$	6.50427	−	3.75524i	0.222832	−	0.128652i
$853$		−	26.3277i		−	0.901445i	−0.892664	−	0.450722i	$-0.851166\pi$
$853$		−	26.3277i		−	0.901445i	0.892664	−	0.450722i	$-0.148834\pi$
$854$		0			0
$855$	6.25591	+	10.8356i	0.213948	+	0.370568i
$856$		−	13.6530i		−	0.466651i
$857$	7.05290	+	12.2160i	0.240923	+	0.417290i	0.960977	−	0.276627i	$-0.0892167\pi$
$857$	7.05290	+	12.2160i	0.240923	+	0.417290i	−0.720055	+	0.693917i	$0.755883\pi$
$858$	−28.6848	+	21.4585i	−0.979284	+	0.732583i
$859$	11.7359	−	20.3272i	0.400425	−	0.693557i	−0.593352	−	0.804943i	$-0.702196\pi$
$859$	11.7359	−	20.3272i	0.400425	−	0.693557i	0.993777	+	0.111386i	$0.0355291\pi$
$860$	6.02046	−	3.47592i	0.205296	−	0.118528i
$861$		0			0
$862$	10.7769	−	18.6662i	0.367063	−	0.635772i
$863$	10.3476	+	5.97418i	0.352236	+	0.203364i	0.665670	−	0.746247i	$-0.268146\pi$
$863$	10.3476	+	5.97418i	0.352236	+	0.203364i	−0.313434	+	0.949610i	$0.601479\pi$
$864$			1.72335i			0.0586295i
$865$		−	8.27026i		−	0.281197i
$866$	−2.77056	−	1.59958i	−0.0941474	−	0.0543560i
$867$	9.92317	−	17.1874i	0.337009	−	0.583716i
$868$		0			0
$869$	−24.5404	+	14.1684i	−0.832476	+	0.480630i
$870$	2.26513	−	3.92333i	0.0767953	−	0.133013i
$871$	−14.7479	+	34.4085i	−0.499713	+	1.16589i
$872$	2.55874	+	4.43186i	0.0866497	+	0.150082i
$873$			26.3118i			0.890521i
$874$	−26.0819	−	45.1752i	−0.882234	−	1.52807i
$875$		0			0
$876$			1.23479i			0.0417196i
$877$	28.3486	−	16.3671i	0.957264	−	0.552677i	0.0619342	−	0.998080i	$-0.480273\pi$
$877$	28.3486	−	16.3671i	0.957264	−	0.552677i	0.895330	+	0.445403i	$0.146940\pi$
$878$			26.6227i			0.898474i
$879$	−47.1091	+	27.1984i	−1.58895	+	0.917380i
$880$	−1.95571	−	3.38739i	−0.0659270	−	0.114189i
$881$	5.29540	+	9.17190i	0.178407	+	0.309009i	0.941335	−	0.337474i	$-0.109572\pi$
$881$	5.29540	+	9.17190i	0.178407	+	0.309009i	−0.762928	+	0.646483i	$0.776239\pi$
$882$		0			0
$883$	−38.6713			−1.30139			−0.650696	−	0.759338i	$-0.725523\pi$
$883$	−38.6713			−1.30139			−0.650696	+	0.759338i	$0.725523\pi$
$884$	−2.16252	−	18.1370i	−0.0727334	−	0.610012i
$885$	8.83112	+	15.2959i	0.296855	+	0.514168i
$886$	−7.87968	−	4.54933i	−0.264723	−	0.152838i
$887$	−4.72164			−0.158537			−0.0792685	−	0.996853i	$-0.525258\pi$
$887$	−4.72164			−0.158537			−0.0792685	+	0.996853i	$0.525258\pi$
$888$	0.165287	−	0.286286i	0.00554668	−	0.00960714i
$889$		0			0
$890$	6.08551	+	3.51347i	0.203987	+	0.117772i
$891$	40.1562	−	23.1842i	1.34528	−	0.776699i
$892$	−9.21079	+	5.31785i	−0.308400	+	0.178055i
$893$	18.0304			0.603366
$894$	−25.6789			−0.858831
$895$	13.2421	−	7.64531i	0.442634	−	0.255555i
$896$		0			0
$897$	−64.1580	−	27.4989i	−2.14217	−	0.918162i
$898$	−3.51346	+	6.08550i	−0.117246	+	0.203076i
$899$	1.65801	+	0.957251i	0.0552976	+	0.0319261i
$900$	4.70522	−	8.14967i	0.156841	−	0.271656i
$901$	−4.29840	−	7.44504i	−0.143200	−	0.248030i
$902$			17.3336i			0.577147i
$903$		0			0
$904$	15.5296	+	8.96603i	0.516507	+	0.298206i
$905$	−2.07549	−	1.19829i	−0.0689917	−	0.0398324i
$906$	29.9476			0.994943
$907$	−20.9654	+	36.3132i	−0.696146	+	1.20576i	0.273646	+	0.961830i	$0.411770\pi$
$907$	−20.9654	+	36.3132i	−0.696146	+	1.20576i	−0.969793	+	0.243930i	$0.921563\pi$
$908$		−	22.7217i		−	0.754047i
$909$	−24.1468			−0.800900
$910$		0			0
$911$	−54.1425			−1.79382			−0.896910	−	0.442213i	$-0.854194\pi$
$911$	−54.1425			−1.79382			−0.896910	+	0.442213i	$0.854194\pi$
$912$		−	14.1396i		−	0.468209i
$913$	28.7008	−	49.7113i	0.949859	−	1.64520i
$914$	19.1511			0.633462
$915$	−14.9114	−	8.60910i	−0.492956	−	0.284608i
$916$	17.5885	+	10.1547i	0.581139	+	0.335521i
$917$		0			0
$918$			8.73035i			0.288145i
$919$	12.9117	+	22.3636i	0.425916	+	0.737708i	0.996506	−	0.0835271i	$-0.0266185\pi$
$919$	12.9117	+	22.3636i	0.425916	+	0.737708i	−0.570589	+	0.821236i	$0.693285\pi$
$920$	3.81080	−	6.60049i	0.125638	−	0.217612i
$921$	−13.2684	−	7.66051i	−0.437208	−	0.252422i
$922$	−1.62828	+	2.82026i	−0.0536245	+	0.0928804i
$923$	4.65690	−	10.8651i	0.153284	−	0.357628i
$924$		0			0
$925$	0.523222	−	0.302083i	0.0172034	−	0.00993241i
$926$	21.2761			0.699178
$927$	−10.8137			−0.355168
$928$	−1.89907	+	1.09643i	−0.0623400	+	0.0359920i
$929$	13.8843	−	8.01610i	0.455529	−	0.263000i	−0.254633	−	0.967038i	$-0.581955\pi$
$929$	13.8843	−	8.01610i	0.455529	−	0.263000i	0.710162	+	0.704038i	$0.248621\pi$
$930$	−1.56203	−	0.901839i	−0.0512210	−	0.0295725i
$931$		0			0
$932$	5.32231	−	9.21851i	0.174338	−	0.301962i
$933$	21.0460			0.689016
$934$	−2.88535	−	1.66586i	−0.0944115	−	0.0545085i
$935$	−9.90748	−	17.1603i	−0.324009	−	0.561200i
$936$	−4.85455	−	6.48935i	−0.158676	−	0.212111i
$937$	−47.0232			−1.53618			−0.768091	−	0.640340i	$-0.778793\pi$
$937$	−47.0232			−1.53618			−0.768091	+	0.640340i	$0.778793\pi$
$938$		0			0
$939$	19.6586	+	34.0496i	0.641533	+	1.11117i
$940$	1.31720	+	2.28146i	0.0429624	+	0.0744131i
$941$	−45.7754	+	26.4284i	−1.49224	+	0.861542i	−0.999960	−	0.00889731i	$-0.997168\pi$
$941$	−45.7754	+	26.4284i	−1.49224	+	0.861542i	−0.492275	+	0.870440i	$0.663835\pi$
$942$			41.0612i			1.33785i
$943$	−29.2504	+	16.8877i	−0.952523	+	0.549939i
$944$		−	8.54933i		−	0.278257i
$945$		0			0
$946$	16.7165	+	28.9539i	0.543502	+	0.941372i
$947$		−	38.5704i		−	1.25337i	−0.779273	−	0.626684i	$-0.784412\pi$
$947$		−	38.5704i		−	1.25337i	0.779273	−	0.626684i	$-0.215588\pi$
$948$	−7.48341	−	12.9617i	−0.243050	−	0.420975i
$949$	1.16417	+	1.55621i	0.0377906	+	0.0505168i
$950$	12.9209	−	22.3797i	0.419210	−	0.726093i
$951$	−7.46430	+	4.30951i	−0.242046	+	0.139746i
$952$		0			0
$953$	13.6505	−	23.6433i	0.442182	−	0.765882i	−0.555669	−	0.831404i	$-0.687538\pi$
$953$	13.6505	−	23.6433i	0.442182	−	0.765882i	0.997851	+	0.0655217i	$0.0208711\pi$
$954$	−3.30330	−	1.90716i	−0.106948	−	0.0617466i
$955$		−	22.0825i		−	0.714572i
$956$		−	0.311564i		−	0.0100767i
$957$	18.8683	+	10.8936i	0.609924	+	0.352140i
$958$	0.0926079	−	0.160402i	0.00299203	−	0.00518234i
$959$		0			0
$960$	1.78914	−	1.03296i	0.0577442	−	0.0333386i
$961$	−15.1189	+	26.1867i	−0.487706	+	0.844731i
$962$	−0.0616009	−	0.516644i	−0.00198609	−	0.0166573i
$963$	−15.3440	−	26.5766i	−0.494453	−	0.856418i
$964$			25.2995i			0.814843i
$965$	5.51966	+	9.56034i	0.177684	+	0.307758i
$966$		0			0
$967$			25.2494i			0.811966i	0.913881	+	0.405983i	$0.133071\pi$
$967$			25.2494i			0.811966i	−0.913881	+	0.405983i	$0.866929\pi$
$968$	6.76452	−	3.90550i	0.217420	−	0.125527i
$969$		−	71.6301i		−	2.30109i
$970$	−9.14264	+	5.27851i	−0.293553	+	0.169483i
$971$	−3.28682	−	5.69294i	−0.105479	−	0.182695i	0.808455	−	0.588558i	$-0.200304\pi$
$971$	−3.28682	−	5.69294i	−0.105479	−	0.182695i	−0.913934	+	0.405863i	$0.866971\pi$
$972$	9.66031	+	16.7321i	0.309854	+	0.536684i
$973$		0			0
$974$	−31.2308			−1.00070
$975$	−4.09408	−	34.3369i	−0.131116	−	1.09966i
$976$	4.16720	+	7.21780i	0.133389	+	0.231036i
$977$	−12.0773	−	6.97285i	−0.386388	−	0.223081i	0.294206	−	0.955742i	$-0.404945\pi$
$977$	−12.0773	−	6.97285i	−0.386388	−	0.223081i	−0.680594	+	0.732661i	$0.738278\pi$
$978$	−46.5440			−1.48831
$979$	−16.8972	+	29.2667i	−0.540036	+	0.935369i
$980$		0			0
$981$	9.96151	+	5.75128i	0.318047	+	0.183624i
$982$	−23.2504	+	13.4236i	−0.741949	+	0.428365i
$983$	40.8235	−	23.5695i	1.30207	−	0.751750i	0.321310	−	0.946974i	$-0.395877\pi$
$983$	40.8235	−	23.5695i	1.30207	−	0.751750i	0.980759	+	0.195224i	$0.0625435\pi$
$984$	−9.15521			−0.291857
$985$	−4.92180			−0.156821
$986$	−9.62054	+	5.55442i	−0.306380	+	0.176889i
$987$		0			0
$988$	−13.3310	−	17.8203i	−0.424115	−	0.566939i
$989$	−32.5730	+	56.4180i	−1.03576	+	1.79399i
$990$	−7.61385	−	4.39586i	−0.241984	−	0.139710i
$991$	−4.70805	+	8.15458i	−0.149556	+	0.259039i	−0.931063	−	0.364857i	$-0.881118\pi$
$991$	−4.70805	+	8.15458i	−0.149556	+	0.259039i	0.781507	+	0.623896i	$0.214451\pi$
$992$	0.436531	+	0.756094i	0.0138599	+	0.0240060i
$993$		−	73.8223i		−	2.34268i
$994$		0			0
$995$	10.0100	+	5.77927i	0.317338	+	0.183215i
$996$	26.2563	+	15.1591i	0.831963	+	0.480334i
$997$	−40.5215			−1.28333			−0.641664	−	0.766986i	$-0.721755\pi$
$997$	−40.5215			−1.28333			−0.641664	+	0.766986i	$0.721755\pi$
$998$	7.64346	−	13.2389i	0.241950	−	0.419069i
$999$			0.248690i			0.00786821i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.o.e.569.6		12
7.2	even	3		1274.2.m.c.491.6		12
7.3	odd	6		1274.2.v.e.361.3		12
7.4	even	3		1274.2.v.d.361.1		12
7.5	odd	6		182.2.m.b.127.4	yes	12
7.6	odd	2		1274.2.o.d.569.4		12
13.4	even	6		1274.2.v.d.667.1		12
21.5	even	6		1638.2.bj.g.127.2		12
28.19	even	6		1456.2.cc.d.673.5		12
91.4	even	6	inner	1274.2.o.e.459.3		12
91.17	odd	6		1274.2.o.d.459.1		12
91.30	even	6		1274.2.m.c.589.6		12
91.54	even	12		2366.2.a.bh.1.5		6
91.68	odd	6		2366.2.d.r.337.11		12
91.69	odd	6		1274.2.v.e.667.3		12
91.75	odd	6		2366.2.d.r.337.5		12
91.82	odd	6		182.2.m.b.43.4	✓	12
91.89	even	12		2366.2.a.bf.1.5		6
273.173	even	6		1638.2.bj.g.1135.2		12
364.355	even	6		1456.2.cc.d.225.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.4	✓	12	91.82	odd	6
182.2.m.b.127.4	yes	12	7.5	odd	6
1274.2.m.c.491.6		12	7.2	even	3
1274.2.m.c.589.6		12	91.30	even	6
1274.2.o.d.459.1		12	91.17	odd	6
1274.2.o.d.569.4		12	7.6	odd	2
1274.2.o.e.459.3		12	91.4	even	6	inner
1274.2.o.e.569.6		12	1.1	even	1	trivial
1274.2.v.d.361.1		12	7.4	even	3
1274.2.v.d.667.1		12	13.4	even	6
1274.2.v.e.361.3		12	7.3	odd	6
1274.2.v.e.667.3		12	91.69	odd	6
1456.2.cc.d.225.5		12	364.355	even	6
1456.2.cc.d.673.5		12	28.19	even	6
1638.2.bj.g.127.2		12	21.5	even	6
1638.2.bj.g.1135.2		12	273.173	even	6
2366.2.a.bf.1.5		6	91.89	even	12
2366.2.a.bh.1.5		6	91.54	even	12
2366.2.d.r.337.5		12	91.75	odd	6
2366.2.d.r.337.11		12	91.68	odd	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:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.14539 - 1.98388i) q^{3} -1.00000 q^{4} +(-0.781015 - 0.450919i) q^{5} +(1.98388 + 1.14539i) q^{6} -1.00000i q^{8} +(-1.12385 - 1.94657i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.14539 - 1.98388i) q^{3} -1.00000 q^{4} +(-0.781015 - 0.450919i) q^{5} +(1.98388 + 1.14539i) q^{6} -1.00000i q^{8} +(-1.12385 - 1.94657i) q^{9} +(0.450919 - 0.781015i) q^{10} +(3.75609 + 2.16858i) q^{11} +(-1.14539 + 1.98388i) q^{12} +(0.426876 + 3.58019i) q^{13} +(-1.78914 + 1.03296i) q^{15} +1.00000 q^{16} +5.06592 q^{17} +(1.94657 - 1.12385i) q^{18} +(5.34544 - 3.08619i) q^{19} +(0.781015 + 0.450919i) q^{20} +(-2.16858 + 3.75609i) q^{22} -8.45117 q^{23} +(-1.98388 - 1.14539i) q^{24} +(-2.09334 - 3.62578i) q^{25} +(-3.58019 + 0.426876i) q^{26} +1.72335 q^{27} +(1.09643 + 1.89907i) q^{29} +(-1.03296 - 1.78914i) q^{30} +(0.756094 - 0.436531i) q^{31} +1.00000i q^{32} +(8.60441 - 4.96776i) q^{33} +5.06592i q^{34} +(1.12385 + 1.94657i) q^{36} +0.144306i q^{37} +(3.08619 + 5.34544i) q^{38} +(7.59161 + 3.25386i) q^{39} +(-0.450919 + 0.781015i) q^{40} +(3.46110 - 1.99827i) q^{41} +(3.85426 - 6.67577i) q^{43} +(-3.75609 - 2.16858i) q^{44} +2.02707i q^{45} -8.45117i q^{46} +(2.52979 + 1.46057i) q^{47} +(1.14539 - 1.98388i) q^{48} +(3.62578 - 2.09334i) q^{50} +(5.80247 - 10.0502i) q^{51} +(-0.426876 - 3.58019i) q^{52} +(-0.848493 - 1.46963i) q^{53} +1.72335i q^{54} +(-1.95571 - 3.38739i) q^{55} -14.1396i q^{57} +(-1.89907 + 1.09643i) q^{58} -8.54933i q^{59} +(1.78914 - 1.03296i) q^{60} +(4.16720 + 7.21780i) q^{61} +(0.436531 + 0.756094i) q^{62} -1.00000 q^{64} +(1.28098 - 2.98867i) q^{65} +(4.96776 + 8.60441i) q^{66} +(8.99180 + 5.19142i) q^{67} -5.06592 q^{68} +(-9.67992 + 16.7661i) q^{69} +(-2.83932 - 1.63928i) q^{71} +(-1.94657 + 1.12385i) q^{72} +(0.466808 - 0.269511i) q^{73} -0.144306 q^{74} -9.59081 q^{75} +(-5.34544 + 3.08619i) q^{76} +(-3.25386 + 7.59161i) q^{78} +(-3.26674 + 5.65817i) q^{79} +(-0.781015 - 0.450919i) q^{80} +(5.34547 - 9.25862i) q^{81} +(1.99827 + 3.46110i) q^{82} -13.2348i q^{83} +(-3.95656 - 2.28432i) q^{85} +(6.67577 + 3.85426i) q^{86} +5.02337 q^{87} +(2.16858 - 3.75609i) q^{88} +7.79180i q^{89} -2.02707 q^{90} +8.45117 q^{92} -2.00000i q^{93} +(-1.46057 + 2.52979i) q^{94} -5.56649 q^{95} +(1.98388 + 1.14539i) q^{96} +(-10.1378 - 5.85305i) q^{97} -9.74866i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} - 12 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q + 2 * q^3 - 12 * q^4 - 6 * q^6 - 6 * q^9	\( 12 q + 2 q^{3} - 12 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} + 18 q^{11} - 2 q^{12} + 8 q^{13} - 6 q^{15} + 12 q^{16} + 8 q^{17} + 12 q^{19} - 2 q^{22} + 12 q^{23} + 6 q^{24} + 12 q^{25} + 2 q^{26} - 40 q^{27} - 10 q^{29} + 14 q^{30} - 18 q^{31} + 12 q^{33} + 6 q^{36} + 4 q^{38} + 24 q^{39} - 2 q^{40} + 24 q^{41} + 26 q^{43} - 18 q^{44} - 48 q^{47} + 2 q^{48} - 12 q^{50} + 18 q^{51} - 8 q^{52} - 18 q^{53} + 6 q^{55} - 24 q^{58} + 6 q^{60} + 28 q^{61} + 2 q^{62} - 12 q^{64} - 4 q^{65} + 42 q^{67} - 8 q^{68} - 32 q^{69} + 48 q^{71} + 48 q^{73} - 96 q^{75} - 12 q^{76} - 8 q^{78} - 22 q^{79} - 34 q^{81} - 6 q^{82} + 54 q^{85} + 6 q^{86} + 4 q^{87} + 2 q^{88} - 12 q^{90} - 12 q^{92} - 8 q^{94} - 64 q^{95} - 6 q^{96} - 60 q^{97}+O(q^{100}) \) 12 * q + 2 * q^3 - 12 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 + 18 * q^11 - 2 * q^12 + 8 * q^13 - 6 * q^15 + 12 * q^16 + 8 * q^17 + 12 * q^19 - 2 * q^22 + 12 * q^23 + 6 * q^24 + 12 * q^25 + 2 * q^26 - 40 * q^27 - 10 * q^29 + 14 * q^30 - 18 * q^31 + 12 * q^33 + 6 * q^36 + 4 * q^38 + 24 * q^39 - 2 * q^40 + 24 * q^41 + 26 * q^43 - 18 * q^44 - 48 * q^47 + 2 * q^48 - 12 * q^50 + 18 * q^51 - 8 * q^52 - 18 * q^53 + 6 * q^55 - 24 * q^58 + 6 * q^60 + 28 * q^61 + 2 * q^62 - 12 * q^64 - 4 * q^65 + 42 * q^67 - 8 * q^68 - 32 * q^69 + 48 * q^71 + 48 * q^73 - 96 * q^75 - 12 * q^76 - 8 * q^78 - 22 * q^79 - 34 * q^81 - 6 * q^82 + 54 * q^85 + 6 * q^86 + 4 * q^87 + 2 * q^88 - 12 * q^90 - 12 * q^92 - 8 * q^94 - 64 * q^95 - 6 * q^96 - 60 * q^97

Introduction

L-functions

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